LMFDB - Embedded newform 650.2.m.a.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(101,650)]

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([0, 5]))

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

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

chi := DirichletCharacter("650.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (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:	$5.19027613138$
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:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.251
Dual form			650.2.m.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	−0.740805	−	0.671721i	$-0.765556\pi$
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	0.952129	+	0.305695i	$0.0988889\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.633975	−	0.366025i	0.258819	−	0.149429i
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.902867	−	0.429919i	$-0.858542\pi$
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.0791130	+	0.996866i	$0.525209\pi$
$8$			1.00000i			0.353553i
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$		0			0
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$	0.732051			0.211325
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.09808	+	7.09808i	0.993929	+	1.72154i	0.592244	+	0.805759i	$0.298242\pi$
$17$	4.09808	+	7.09808i	0.993929	+	1.72154i	0.401685	+	0.915778i	$0.368425\pi$
$18$			2.46410i			0.580794i
$19$	−0.401924	+	0.232051i	−0.0922076	+	0.0532361i	−0.545395	−	0.838179i	$-0.683620\pi$
$19$	−0.401924	+	0.232051i	−0.0922076	+	0.0532361i	0.453187	+	0.891415i	$0.350287\pi$
$20$		0			0
$21$			2.19615i			0.479240i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	4.73205	−	8.19615i	0.986701	−	1.70902i	0.352581	−	0.935781i	$-0.385304\pi$
$23$	4.73205	−	8.19615i	0.986701	−	1.70902i	0.634120	−	0.773234i	$-0.281362\pi$
$24$	0.633975	+	0.366025i	0.129410	+	0.0747146i
$25$		0			0
$26$	−3.46410	−	1.00000i	−0.679366	−	0.196116i
$27$	4.00000			0.769800
$28$	−2.59808	−	1.50000i	−0.490990	−	0.283473i
$29$	1.26795	−	2.19615i	0.235452	−	0.407815i	−0.723952	−	0.689851i	$-0.757676\pi$
$29$	1.26795	−	2.19615i	0.235452	−	0.407815i	0.959404	+	0.282035i	$0.0910095\pi$
$30$		0			0
$31$			4.73205i			0.849901i	0.905216	+	0.424951i	$0.139709\pi$
$31$			4.73205i			0.849901i	−0.905216	+	0.424951i	$0.860291\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.90192	−	1.09808i	0.331082	−	0.191151i
$34$			8.19615i			1.40563i
$35$		0			0
$36$	−1.23205	+	2.13397i	−0.205342	+	0.355662i
$37$	0.696152	+	0.401924i	0.114447	+	0.0660759i	0.556131	−	0.831095i	$-0.312285\pi$
$37$	0.696152	+	0.401924i	0.114447	+	0.0660759i	−0.441684	+	0.897171i	$0.645619\pi$
$38$	−0.464102			−0.0752872
$39$	−0.732051	+	2.53590i	−0.117222	+	0.406069i
$40$		0			0
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.410608	−	0.911812i	$-0.634683\pi$
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.994956	+	0.100309i	$0.968017\pi$
$42$	−1.09808	+	1.90192i	−0.169437	+	0.293473i
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	8.19615	−	4.73205i	1.20846	−	0.697703i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	0.366025	+	0.633975i	0.0528312	+	0.0915064i
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$		0			0
$51$	6.00000			0.840168
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	−0.464102			−0.0637493			−0.0318746	−	0.999492i	$-0.510148\pi$
$53$	−0.464102			−0.0637493			−0.0318746	+	0.999492i	$0.510148\pi$
$54$	3.46410	+	2.00000i	0.471405	+	0.272166i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$			0.339746i			0.0450005i
$58$	2.19615	−	1.26795i	0.288369	−	0.166490i
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.217620	−	0.976034i	$-0.430171\pi$
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.954080	+	0.299552i	$0.0968372\pi$
$60$		0			0
$61$	−3.09808	−	5.36603i	−0.396668	−	0.687049i	0.596645	−	0.802506i	$-0.296500\pi$
$61$	−3.09808	−	5.36603i	−0.396668	−	0.687049i	−0.993313	+	0.115456i	$0.963167\pi$
$62$	−2.36603	+	4.09808i	−0.300486	+	0.520456i
$63$	−6.40192	−	3.69615i	−0.806567	−	0.465671i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.19615			0.270328
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−4.09808	+	7.09808i	−0.496965	+	0.860768i
$69$	−3.46410	−	6.00000i	−0.417029	−	0.722315i
$70$		0			0
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	−0.775571	−	0.631260i	$-0.782538\pi$
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	0.158901	+	0.987294i	$0.449205\pi$
$72$	−2.13397	+	1.23205i	−0.251491	+	0.145199i
$73$		−	11.6603i		−	1.36473i	−0.731012	−	0.682365i	$-0.760952\pi$
$73$		−	11.6603i		−	1.36473i	0.731012	−	0.682365i	$-0.239048\pi$
$74$	0.401924	+	0.696152i	0.0467227	+	0.0809261i
$75$		0			0
$76$	−0.401924	−	0.232051i	−0.0461038	−	0.0266181i
$77$	−9.00000			−1.02565
$78$	−1.90192	+	1.83013i	−0.215350	+	0.207221i
$79$	−4.19615			−0.472104			−0.236052	−	0.971740i	$-0.575854\pi$
$79$	−4.19615			−0.472104			−0.236052	+	0.971740i	$0.575854\pi$
$80$		0			0
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	−5.19615	−	9.00000i	−0.573819	−	0.993884i
$83$			8.19615i			0.899645i	0.893118	+	0.449822i	$0.148513\pi$
$83$			8.19615i			0.899645i	−0.893118	+	0.449822i	$0.851487\pi$
$84$	−1.90192	+	1.09808i	−0.207517	+	0.119810i
$85$		0			0
$86$			2.00000i			0.215666i
$87$	−0.928203	−	1.60770i	−0.0995138	−	0.172363i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	5.89230	+	3.40192i	0.624583	+	0.360603i	0.778651	−	0.627457i	$-0.215904\pi$
$89$	5.89230	+	3.40192i	0.624583	+	0.360603i	−0.154068	+	0.988060i	$0.549238\pi$
$90$		0			0
$91$	7.79423	−	7.50000i	0.817057	−	0.786214i
$92$	9.46410			0.986701
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$		0			0
$96$			0.732051i			0.0747146i
$97$	−7.90192	+	4.56218i	−0.802319	+	0.463219i	−0.844281	−	0.535900i	$-0.819972\pi$
$97$	−7.90192	+	4.56218i	−0.802319	+	0.463219i	0.0419625	+	0.999119i	$0.486639\pi$
$98$	1.73205	−	1.00000i	0.174964	−	0.101015i
$99$			7.39230i			0.742955i
$100$		0			0
$101$	−5.36603	+	9.29423i	−0.533939	+	0.924810i	0.465274	+	0.885167i	$0.345956\pi$
$101$	−5.36603	+	9.29423i	−0.533939	+	0.924810i	−0.999214	+	0.0396438i	$0.987378\pi$
$102$	5.19615	+	3.00000i	0.514496	+	0.297044i
$103$	9.19615			0.906124			0.453062	−	0.891479i	$-0.350332\pi$
$103$	9.19615			0.906124			0.453062	+	0.891479i	$0.350332\pi$
$104$	−0.866025	−	3.50000i	−0.0849208	−	0.343203i
$105$		0			0
$106$	−0.401924	−	0.232051i	−0.0390383	−	0.0225388i
$107$	8.83013	−	15.2942i	0.853641	−	1.47855i	−0.0242598	−	0.999706i	$-0.507723\pi$
$107$	8.83013	−	15.2942i	0.853641	−	1.47855i	0.877900	−	0.478843i	$-0.158944\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$		−	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
$112$		−	3.00000i		−	0.283473i
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$	−0.169873	+	0.294229i	−0.0159101	+	0.0275570i
$115$		0			0
$116$	2.53590			0.235452
$117$	−6.16025	−	6.40192i	−0.569516	−	0.591858i
$118$	10.3923			0.956689
$119$	−21.2942	−	12.2942i	−1.95204	−	1.12701i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		−	6.19615i		−	0.560973i
$123$	−6.58846	+	3.80385i	−0.594061	+	0.342981i
$124$	−4.09808	+	2.36603i	−0.368018	+	0.212475i
$125$		0			0
$126$	−3.69615	−	6.40192i	−0.329279	−	0.570329i
$127$	5.40192	−	9.35641i	0.479343	−	0.830247i	−0.520376	−	0.853937i	$-0.674208\pi$
$127$	5.40192	−	9.35641i	0.479343	−	0.830247i	0.999719	+	0.0236904i	$0.00754158\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	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	$0.413788\pi$
$132$	1.90192	+	1.09808i	0.165541	+	0.0955753i
$133$	0.696152	−	1.20577i	0.0603641	−	0.104554i
$134$		0			0
$135$		0			0
$136$	−7.09808	+	4.09808i	−0.608655	+	0.351407i
$137$	−1.90192	+	1.09808i	−0.162492	+	0.0938150i	−0.579041	−	0.815298i	$-0.696573\pi$
$137$	−1.90192	+	1.09808i	−0.162492	+	0.0938150i	0.416549	+	0.909113i	$0.363240\pi$
$138$		−	6.92820i		−	0.589768i
$139$	−0.598076	−	1.03590i	−0.0507282	−	0.0878638i	0.839546	−	0.543288i	$-0.182821\pi$
$139$	−0.598076	−	1.03590i	−0.0507282	−	0.0878638i	−0.890274	+	0.455424i	$0.849488\pi$
$140$		0			0
$141$	−1.90192	−	1.09808i	−0.160171	−	0.0924747i
$142$	−6.00000			−0.503509
$143$	−10.3923	−	3.00000i	−0.869048	−	0.250873i
$144$	−2.46410			−0.205342
$145$		0			0
$146$	5.83013	−	10.0981i	0.482505	−	0.835723i
$147$	−0.732051	−	1.26795i	−0.0603785	−	0.104579i
$148$			0.803848i			0.0660759i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$		0			0
$151$		−	23.6603i		−	1.92544i	−0.270492	−	0.962722i	$-0.587187\pi$
$151$		−	23.6603i		−	1.92544i	0.270492	−	0.962722i	$-0.412813\pi$
$152$	−0.232051	−	0.401924i	−0.0188218	−	0.0326003i
$153$	−10.0981	+	17.4904i	−0.816381	+	1.41401i
$154$	−7.79423	−	4.50000i	−0.628077	−	0.362620i
$155$		0			0
$156$	−2.56218	+	0.633975i	−0.205138	+	0.0507586i
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$	−3.63397	−	2.09808i	−0.289103	−	0.166914i
$159$	−0.169873	+	0.294229i	−0.0134718	+	0.0233338i
$160$		0			0
$161$			28.3923i			2.23763i
$162$	−3.86603	+	2.23205i	−0.303744	+	0.175366i
$163$	9.29423	−	5.36603i	0.727980	−	0.420300i	−0.0897026	−	0.995969i	$-0.528592\pi$
$163$	9.29423	−	5.36603i	0.727980	−	0.420300i	0.817683	+	0.575669i	$0.195258\pi$
$164$		−	10.3923i		−	0.811503i
$165$		0			0
$166$	−4.09808	+	7.09808i	−0.318072	+	0.550918i
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$	−2.19615			−0.169437
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	−0.990381	−	0.571797i	−0.0757363	−	0.0437264i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		−	1.85641i		−	0.140734i
$175$		0			0
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$		−	7.60770i		−	0.571829i
$178$	3.40192	+	5.89230i	0.254985	+	0.441647i
$179$	4.73205	−	8.19615i	0.353690	−	0.612609i	−0.633203	−	0.773986i	$-0.718260\pi$
$179$	4.73205	−	8.19615i	0.353690	−	0.612609i	0.986893	+	0.161377i	$0.0515934\pi$
$180$		0			0
$181$	14.5885			1.08435			0.542176	−	0.840265i	$-0.317601\pi$
$181$	14.5885			1.08435			0.542176	+	0.840265i	$0.317601\pi$
$182$	10.5000	−	2.59808i	0.778312	−	0.192582i
$183$	−4.53590			−0.335303
$184$	8.19615	+	4.73205i	0.604228	+	0.348851i
$185$		0			0
$186$	1.73205	+	3.00000i	0.127000	+	0.219971i
$187$			24.5885i			1.79809i
$188$	2.59808	−	1.50000i	0.189484	−	0.109399i
$189$	−10.3923	+	6.00000i	−0.755929	+	0.436436i
$190$		0			0
$191$	11.3660	+	19.6865i	0.822417	+	1.42447i	0.903878	+	0.427791i	$0.140708\pi$
$191$	11.3660	+	19.6865i	0.822417	+	1.42447i	−0.0814609	+	0.996677i	$0.525959\pi$
$192$	−0.366025	+	0.633975i	−0.0264156	+	0.0457532i
$193$	14.1962	+	8.19615i	1.02186	+	0.589972i	0.914643	−	0.404263i	$-0.132472\pi$
$193$	14.1962	+	8.19615i	1.02186	+	0.589972i	0.107219	+	0.994235i	$0.465805\pi$
$194$	−9.12436			−0.655091
$195$		0			0
$196$	2.00000			0.142857
$197$	−18.6962	−	10.7942i	−1.33205	−	0.769057i	−0.346433	−	0.938075i	$-0.612607\pi$
$197$	−18.6962	−	10.7942i	−1.33205	−	0.769057i	−0.985613	+	0.169018i	$0.945940\pi$
$198$	−3.69615	+	6.40192i	−0.262674	+	0.454965i
$199$	3.19615	+	5.53590i	0.226569	+	0.392429i	0.956789	−	0.290783i	$-0.0939157\pi$
$199$	3.19615	+	5.53590i	0.226569	+	0.392429i	−0.730220	+	0.683212i	$0.760582\pi$
$200$		0			0
$201$		0			0
$202$	−9.29423	+	5.36603i	−0.653940	+	0.377552i
$203$			7.60770i			0.533956i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	7.96410	+	4.59808i	0.554885	+	0.320363i
$207$	23.3205			1.62089
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	−1.39230			−0.0963077
$210$		0			0
$211$	8.79423	−	15.2321i	0.605420	−	1.04862i	−0.386565	−	0.922262i	$-0.626339\pi$
$211$	8.79423	−	15.2321i	0.605420	−	1.04862i	0.991985	−	0.126356i	$-0.0403280\pi$
$212$	−0.232051	−	0.401924i	−0.0159373	−	0.0276042i
$213$			4.39230i			0.300956i
$214$	15.2942	−	8.83013i	1.04549	−	0.603615i
$215$		0			0
$216$			4.00000i			0.272166i
$217$	−7.09808	−	12.2942i	−0.481849	−	0.834587i
$218$	4.26795	−	7.39230i	0.289062	−	0.500670i
$219$	−7.39230	−	4.26795i	−0.499526	−	0.288401i
$220$		0			0
$221$	−20.4904	−	21.2942i	−1.37833	−	1.43240i
$222$	0.588457			0.0394947
$223$	5.59808	+	3.23205i	0.374875	+	0.216434i	0.675586	−	0.737281i	$-0.263891\pi$
$223$	5.59808	+	3.23205i	0.374875	+	0.216434i	−0.300711	+	0.953715i	$0.597224\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$			6.92820i			0.460857i
$227$	−14.1962	+	8.19615i	−0.942232	+	0.543998i	−0.890659	−	0.454672i	$-0.849757\pi$
$227$	−14.1962	+	8.19615i	−0.942232	+	0.543998i	−0.0515725	+	0.998669i	$0.516423\pi$
$228$	−0.294229	+	0.169873i	−0.0194858	+	0.0112501i
$229$		−	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
$232$	2.19615	+	1.26795i	0.144184	+	0.0832449i
$233$	−4.73205			−0.310007			−0.155003	−	0.987914i	$-0.549539\pi$
$233$	−4.73205			−0.310007			−0.155003	+	0.987914i	$0.549539\pi$
$234$	−2.13397	−	8.62436i	−0.139502	−	0.563792i
$235$		0			0
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$	−1.53590	+	2.66025i	−0.0997673	+	0.172802i
$238$	−12.2942	−	21.2942i	−0.796916	−	1.38030i
$239$			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	−0.721715	−	0.692191i	$-0.756646\pi$
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	0.238597	+	0.971119i	$0.423312\pi$
$242$		−	2.00000i		−	0.128565i
$243$	7.63397	+	13.2224i	0.489720	+	0.848219i
$244$	3.09808	−	5.36603i	0.198334	−	0.343525i
$245$		0			0
$246$	−7.60770			−0.485049
$247$	1.20577	−	1.16025i	0.0767214	−	0.0738252i
$248$	−4.73205			−0.300486
$249$	5.19615	+	3.00000i	0.329293	+	0.190117i
$250$		0			0
$251$	−8.59808	−	14.8923i	−0.542706	−	0.939994i	−0.998747	−	0.0500355i	$-0.984067\pi$
$251$	−8.59808	−	14.8923i	−0.542706	−	0.939994i	0.456042	−	0.889958i	$-0.349267\pi$
$252$		−	7.39230i		−	0.465671i
$253$	24.5885	−	14.1962i	1.54586	−	0.892504i
$254$	9.35641	−	5.40192i	0.587073	−	0.338947i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.92820	+	12.0000i	−0.432169	+	0.748539i	−0.997060	−	0.0766265i	$-0.975585\pi$
$257$	−6.92820	+	12.0000i	−0.432169	+	0.748539i	0.564890	+	0.825166i	$0.308918\pi$
$258$	1.26795	+	0.732051i	0.0789391	+	0.0455755i
$259$	−2.41154			−0.149846
$260$		0			0
$261$	6.24871			0.386786
$262$	5.30385	+	3.06218i	0.327673	+	0.189182i
$263$	1.79423	−	3.10770i	0.110637	−	0.191629i	−0.805390	−	0.592745i	$-0.798044\pi$
$263$	1.79423	−	3.10770i	0.110637	−	0.191629i	0.916027	+	0.401116i	$0.131378\pi$
$264$	1.09808	+	1.90192i	0.0675819	+	0.117055i
$265$		0			0
$266$	1.20577	−	0.696152i	0.0739306	−	0.0426838i
$267$	4.31347	−	2.49038i	0.263980	−	0.152409i
$268$		0			0
$269$	13.5622	+	23.4904i	0.826901	+	1.43223i	0.900458	+	0.434943i	$0.143231\pi$
$269$	13.5622	+	23.4904i	0.826901	+	1.43223i	−0.0735575	+	0.997291i	$0.523435\pi$
$270$		0			0
$271$	8.19615	+	4.73205i	0.497881	+	0.287452i	0.727838	−	0.685749i	$-0.240525\pi$
$271$	8.19615	+	4.73205i	0.497881	+	0.287452i	−0.229957	+	0.973201i	$0.573859\pi$
$272$	−8.19615			−0.496965
$273$	−1.90192	−	7.68653i	−0.115110	−	0.465210i
$274$	−2.19615			−0.132674
$275$		0			0
$276$	3.46410	−	6.00000i	0.208514	−	0.361158i
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$		−	1.19615i		−	0.0717405i
$279$	−10.0981	+	5.83013i	−0.604556	+	0.349041i
$280$		0			0
$281$		−	10.3923i		−	0.619953i	−0.950744	−	0.309976i	$-0.899679\pi$
$281$		−	10.3923i		−	0.619953i	0.950744	−	0.309976i	$-0.100321\pi$
$282$	−1.09808	−	1.90192i	−0.0653895	−	0.113258i
$283$	−4.80385	+	8.32051i	−0.285559	+	0.494603i	−0.972745	−	0.231879i	$-0.925513\pi$
$283$	−4.80385	+	8.32051i	−0.285559	+	0.494603i	0.687186	+	0.726482i	$0.258846\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$	−7.50000	−	7.79423i	−0.443484	−	0.460882i
$287$	31.1769			1.84032
$288$	−2.13397	−	1.23205i	−0.125746	−	0.0725993i
$289$	−25.0885	+	43.4545i	−1.47579	+	2.55615i
$290$		0			0
$291$			6.67949i			0.391559i
$292$	10.0981	−	5.83013i	0.590945	−	0.341182i
$293$	−9.69615	+	5.59808i	−0.566455	+	0.327043i	−0.755732	−	0.654881i	$-0.772719\pi$
$293$	−9.69615	+	5.59808i	−0.566455	+	0.327043i	0.189277	+	0.981924i	$0.439386\pi$
$294$		−	1.46410i		−	0.0853881i
$295$		0			0
$296$	−0.401924	+	0.696152i	−0.0233613	+	0.0404630i
$297$	10.3923	+	6.00000i	0.603023	+	0.348155i
$298$	6.00000			0.347571
$299$	−9.46410	+	32.7846i	−0.547323	+	1.89598i
$300$		0			0
$301$	−5.19615	−	3.00000i	−0.299501	−	0.172917i
$302$	11.8301	−	20.4904i	0.680747	−	1.17909i
$303$	3.92820	+	6.80385i	0.225669	+	0.390871i
$304$		−	0.464102i		−	0.0266181i
$305$		0			0
$306$	−17.4904	+	10.0981i	−0.999859	+	0.577269i
$307$			27.4641i			1.56746i	0.621102	+	0.783730i	$0.286685\pi$
$307$			27.4641i			1.56746i	−0.621102	+	0.783730i	$0.713315\pi$
$308$	−4.50000	−	7.79423i	−0.256411	−	0.444117i
$309$	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	$0.583293\pi$
$312$	−2.53590	−	0.732051i	−0.143567	−	0.0414442i
$313$	−26.3923			−1.49178			−0.745891	−	0.666068i	$-0.767976\pi$
$313$	−26.3923			−1.49178			−0.745891	+	0.666068i	$0.767976\pi$
$314$	11.2583	+	6.50000i	0.635344	+	0.366816i
$315$		0			0
$316$	−2.09808	−	3.63397i	−0.118026	−	0.204427i
$317$			23.1962i			1.30283i	0.758723	+	0.651413i	$0.225823\pi$
$317$			23.1962i			1.30283i	−0.758723	+	0.651413i	$0.774177\pi$
$318$	−0.294229	+	0.169873i	−0.0164995	+	0.00952600i
$319$	6.58846	−	3.80385i	0.368883	−	0.212975i
$320$		0			0
$321$	−6.46410	−	11.1962i	−0.360791	−	0.624908i
$322$	−14.1962	+	24.5885i	−0.791121	+	1.37026i
$323$	−3.29423	−	1.90192i	−0.183296	−	0.105826i
$324$	−4.46410			−0.248006
$325$		0			0
$326$	10.7321			0.594393
$327$	−5.41154	−	3.12436i	−0.299259	−	0.172777i
$328$	5.19615	−	9.00000i	0.286910	−	0.496942i
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$		0			0
$331$	11.1962	−	6.46410i	0.615396	−	0.355299i	−0.159678	−	0.987169i	$-0.551046\pi$
$331$	11.1962	−	6.46410i	0.615396	−	0.355299i	0.775074	+	0.631870i	$0.217712\pi$
$332$	−7.09808	+	4.09808i	−0.389558	+	0.224911i
$333$			1.98076i			0.108545i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	−1.90192	−	1.09808i	−0.103758	−	0.0599050i
$337$	−6.19615			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$337$	−6.19615			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$338$	12.9904	+	0.500000i	0.706584	+	0.0271964i
$339$	5.07180			0.275462
$340$		0			0
$341$	−7.09808	+	12.2942i	−0.384382	+	0.665770i
$342$	−0.571797	−	0.990381i	−0.0309192	−	0.0535537i
$343$		−	15.0000i		−	0.809924i
$344$	−1.73205	+	1.00000i	−0.0933859	+	0.0539164i
$345$		0			0
$346$		−	15.0000i		−	0.806405i
$347$	−14.3660	−	24.8827i	−0.771209	−	1.33577i	−0.936901	−	0.349595i	$-0.886319\pi$
$347$	−14.3660	−	24.8827i	−0.771209	−	1.33577i	0.165692	−	0.986178i	$-0.447014\pi$
$348$	0.928203	−	1.60770i	0.0497569	−	0.0861815i
$349$	−3.50962	−	2.02628i	−0.187866	−	0.108464i	0.403117	−	0.915148i	$-0.367927\pi$
$349$	−3.50962	−	2.02628i	−0.187866	−	0.108464i	−0.590983	+	0.806684i	$0.701260\pi$
$350$		0			0
$351$	−14.0000	+	3.46410i	−0.747265	+	0.184900i
$352$	−3.00000			−0.159901
$353$	−8.49038	−	4.90192i	−0.451897	−	0.260903i	0.256734	−	0.966482i	$-0.417354\pi$
$353$	−8.49038	−	4.90192i	−0.451897	−	0.260903i	−0.708631	+	0.705579i	$0.750687\pi$
$354$	3.80385	−	6.58846i	0.202172	−	0.350173i
$355$		0			0
$356$			6.80385i			0.360603i
$357$	−15.5885	+	9.00000i	−0.825029	+	0.476331i
$358$	8.19615	−	4.73205i	0.433180	−	0.250097i
$359$			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
$362$	12.6340	+	7.29423i	0.664027	+	0.383376i
$363$	−1.46410			−0.0768454
$364$	10.3923	+	3.00000i	0.544705	+	0.157243i
$365$		0			0
$366$	−3.92820	−	2.26795i	−0.205330	−	0.118548i
$367$	−2.80385	+	4.85641i	−0.146360	+	0.253502i	−0.929879	−	0.367865i	$-0.880089\pi$
$367$	−2.80385	+	4.85641i	−0.146360	+	0.253502i	0.783520	+	0.621367i	$0.213422\pi$
$368$	4.73205	+	8.19615i	0.246675	+	0.427254i
$369$		−	25.6077i		−	1.33308i
$370$		0			0
$371$	1.20577	−	0.696152i	0.0626005	−	0.0361424i
$372$			3.46410i			0.179605i
$373$	−0.196152	−	0.339746i	−0.0101564	−	0.0175914i	0.860903	−	0.508770i	$-0.169900\pi$
$373$	−0.196152	−	0.339746i	−0.0101564	−	0.0175914i	−0.871059	+	0.491179i	$0.836566\pi$
$374$	−12.2942	+	21.2942i	−0.635719	+	1.10110i
$375$		0			0
$376$	3.00000			0.154713
$377$	−2.53590	+	8.78461i	−0.130605	+	0.452430i
$378$	−12.0000			−0.617213
$379$	25.7942	+	14.8923i	1.32496	+	0.764966i	0.984515	−	0.175298i	$-0.0560889\pi$
$379$	25.7942	+	14.8923i	1.32496	+	0.764966i	0.340445	+	0.940264i	$0.389422\pi$
$380$		0			0
$381$	−3.95448	−	6.84936i	−0.202594	−	0.350904i
$382$			22.7321i			1.16307i
$383$	−19.3923	+	11.1962i	−0.990900	+	0.572097i	−0.905543	−	0.424254i	$-0.860536\pi$
$383$	−19.3923	+	11.1962i	−0.990900	+	0.572097i	−0.0853571	+	0.996350i	$0.527203\pi$
$384$	−0.633975	+	0.366025i	−0.0323524	+	0.0186787i
$385$		0			0
$386$	8.19615	+	14.1962i	0.417173	+	0.722565i
$387$	−2.46410	+	4.26795i	−0.125257	+	0.216952i
$388$	−7.90192	−	4.56218i	−0.401159	−	0.231609i
$389$	22.7321			1.15256			0.576280	−	0.817252i	$-0.304504\pi$
$389$	22.7321			1.15256			0.576280	+	0.817252i	$0.304504\pi$
$390$		0			0
$391$	77.5692			3.92284
$392$	1.73205	+	1.00000i	0.0874818	+	0.0505076i
$393$	2.24167	−	3.88269i	0.113077	−	0.195856i
$394$	−10.7942	−	18.6962i	−0.543805	−	0.941899i
$395$		0			0
$396$	−6.40192	+	3.69615i	−0.321709	+	0.185739i
$397$	9.69615	−	5.59808i	0.486636	−	0.280959i	−0.236542	−	0.971621i	$-0.576014\pi$
$397$	9.69615	−	5.59808i	0.486636	−	0.280959i	0.723178	+	0.690662i	$0.242681\pi$
$398$			6.39230i			0.320417i
$399$	−0.509619	−	0.882686i	−0.0255129	−	0.0441896i
$400$		0			0
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	0.383414	−	0.923576i	$-0.374748\pi$
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	−0.608134	+	0.793835i	$0.708081\pi$
$402$		0			0
$403$	−4.09808	−	16.5622i	−0.204140	−	0.825021i
$404$	−10.7321			−0.533939
$405$		0			0
$406$	−3.80385	+	6.58846i	−0.188782	+	0.326980i
$407$	1.20577	+	2.08846i	0.0597679	+	0.103521i
$408$			6.00000i			0.297044i
$409$	−14.0885	+	8.13397i	−0.696629	+	0.402199i	−0.806091	−	0.591792i	$-0.798421\pi$
$409$	−14.0885	+	8.13397i	−0.696629	+	0.402199i	0.109461	+	0.993991i	$0.465087\pi$
$410$		0			0
$411$			1.60770i			0.0793018i
$412$	4.59808	+	7.96410i	0.226531	+	0.392363i
$413$	−15.5885	+	27.0000i	−0.767058	+	1.32858i
$414$	20.1962	+	11.6603i	0.992587	+	0.573070i
$415$		0			0
$416$	2.59808	−	2.50000i	0.127381	−	0.122573i
$417$	−0.875644			−0.0428805
$418$	−1.20577	−	0.696152i	−0.0589762	−	0.0340499i
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$		0			0
$421$			2.87564i			0.140150i	0.997542	+	0.0700752i	$0.0223239\pi$
$421$			2.87564i			0.140150i	−0.997542	+	0.0700752i	$0.977676\pi$
$422$	15.2321	−	8.79423i	0.741485	−	0.428096i
$423$	6.40192	−	3.69615i	0.311272	−	0.179713i
$424$		−	0.464102i		−	0.0225388i
$425$		0			0
$426$	−2.19615	+	3.80385i	−0.106404	+	0.184297i
$427$	16.0981	+	9.29423i	0.779041	+	0.449779i
$428$	17.6603			0.853641
$429$	−5.70577	+	5.49038i	−0.275477	+	0.265078i
$430$		0			0
$431$	−7.09808	−	4.09808i	−0.341902	−	0.197397i	0.319211	−	0.947684i	$-0.396582\pi$
$431$	−7.09808	−	4.09808i	−0.341902	−	0.197397i	−0.661113	+	0.750286i	$0.729916\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	4.19615	+	7.26795i	0.201654	+	0.349275i	0.949062	−	0.315091i	$-0.102035\pi$
$433$	4.19615	+	7.26795i	0.201654	+	0.349275i	−0.747407	+	0.664366i	$0.768702\pi$
$434$		−	14.1962i		−	0.681437i
$435$		0			0
$436$	7.39230	−	4.26795i	0.354027	−	0.204398i
$437$			4.39230i			0.210112i
$438$	−4.26795	−	7.39230i	−0.203931	−	0.353218i
$439$	1.70577	−	2.95448i	0.0814120	−	0.141010i	−0.822445	−	0.568845i	$-0.807390\pi$
$439$	1.70577	−	2.95448i	0.0814120	−	0.141010i	0.903857	+	0.427835i	$0.140724\pi$
$440$		0			0
$441$	4.92820			0.234676
$442$	−7.09808	−	28.6865i	−0.337621	−	1.36448i
$443$	22.3923			1.06389			0.531945	−	0.846779i	$-0.321461\pi$
$443$	22.3923			1.06389			0.531945	+	0.846779i	$0.321461\pi$
$444$	0.509619	+	0.294229i	0.0241854	+	0.0139635i
$445$		0			0
$446$	3.23205	+	5.59808i	0.153042	+	0.265077i
$447$		−	4.39230i		−	0.207749i
$448$	2.59808	−	1.50000i	0.122748	−	0.0708683i
$449$	13.5000	−	7.79423i	0.637104	−	0.367832i	−0.146394	−	0.989226i	$-0.546767\pi$
$449$	13.5000	−	7.79423i	0.637104	−	0.367832i	0.783498	+	0.621394i	$0.213433\pi$
$450$		0			0
$451$	−15.5885	−	27.0000i	−0.734032	−	1.27138i
$452$	−3.46410	+	6.00000i	−0.162938	+	0.282216i
$453$	−15.0000	−	8.66025i	−0.704761	−	0.406894i
$454$	−16.3923			−0.769329
$455$		0			0
$456$	−0.339746			−0.0159101
$457$	−15.8827	−	9.16987i	−0.742961	−	0.428949i	0.0801841	−	0.996780i	$-0.474449\pi$
$457$	−15.8827	−	9.16987i	−0.742961	−	0.428949i	−0.823145	+	0.567832i	$0.807783\pi$
$458$	0.633975	−	1.09808i	0.0296237	−	0.0513097i
$459$	16.3923	+	28.3923i	0.765127	+	1.32524i
$460$		0			0
$461$	−26.4904	+	15.2942i	−1.23378	+	0.712323i	−0.967816	−	0.251660i	$-0.919024\pi$
$461$	−26.4904	+	15.2942i	−1.23378	+	0.712323i	−0.265964	+	0.963983i	$0.585690\pi$
$462$	−5.70577	+	3.29423i	−0.265457	+	0.153261i
$463$		−	12.9282i		−	0.600825i	−0.953809	−	0.300412i	$-0.902876\pi$
$463$		−	12.9282i		−	0.600825i	0.953809	−	0.300412i	$-0.0971243\pi$
$464$	1.26795	+	2.19615i	0.0588631	+	0.101954i
$465$		0			0
$466$	−4.09808	−	2.36603i	−0.189840	−	0.109604i
$467$	37.8564			1.75179			0.875893	−	0.482506i	$-0.160273\pi$
$467$	37.8564			1.75179			0.875893	+	0.482506i	$0.160273\pi$
$468$	2.46410	−	8.53590i	0.113903	−	0.394572i
$469$		0			0
$470$		0			0
$471$	4.75833	−	8.24167i	0.219252	−	0.379756i
$472$	5.19615	+	9.00000i	0.239172	+	0.414259i
$473$			6.00000i			0.275880i
$474$	−2.66025	+	1.53590i	−0.122190	+	0.0705461i
$475$		0			0
$476$		−	24.5885i		−	1.12701i
$477$	−0.571797	−	0.990381i	−0.0261808	−	0.0453464i
$478$	−1.09808	+	1.90192i	−0.0502248	+	0.0869920i
$479$	−35.4904	−	20.4904i	−1.62160	−	0.936229i	−0.986493	−	0.163803i	$-0.947624\pi$
$479$	−35.4904	−	20.4904i	−1.62160	−	0.936229i	−0.635104	−	0.772427i	$-0.719043\pi$
$480$		0			0
$481$	−2.78461	−	0.803848i	−0.126967	−	0.0366523i
$482$	−8.66025			−0.394464
$483$	18.0000	+	10.3923i	0.819028	+	0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$			15.2679i			0.692568i
$487$	13.2058	−	7.62436i	0.598411	−	0.345493i	−0.170005	−	0.985443i	$-0.554379\pi$
$487$	13.2058	−	7.62436i	0.598411	−	0.345493i	0.768416	+	0.639951i	$0.221045\pi$
$488$	5.36603	−	3.09808i	0.242909	−	0.140243i
$489$		−	7.85641i		−	0.355279i
$490$		0			0
$491$	−10.3301	+	17.8923i	−0.466192	+	0.807468i	−0.999254	−	0.0386076i	$-0.987708\pi$
$491$	−10.3301	+	17.8923i	−0.466192	+	0.807468i	0.533062	+	0.846076i	$0.321041\pi$
$492$	−6.58846	−	3.80385i	−0.297031	−	0.171491i
$493$	20.7846			0.936092
$494$	1.62436	−	0.401924i	0.0730832	−	0.0180834i
$495$		0			0
$496$	−4.09808	−	2.36603i	−0.184009	−	0.106238i
$497$	9.00000	−	15.5885i	0.403705	−	0.699238i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$			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
$502$		−	17.1962i		−	0.767502i
$503$	−13.3301	−	23.0885i	−0.594361	−	1.02946i	−0.993637	−	0.112633i	$-0.964072\pi$
$503$	−13.3301	−	23.0885i	−0.594361	−	1.02946i	0.399276	−	0.916831i	$-0.369262\pi$
$504$	3.69615	−	6.40192i	0.164640	−	0.285164i
$505$		0			0
$506$	28.3923			1.26219
$507$	0.366025	−	9.50962i	0.0162558	−	0.422337i
$508$	10.8038			0.479343
$509$	−19.3923	−	11.1962i	−0.859549	−	0.496261i	0.00431237	−	0.999991i	$-0.498627\pi$
$509$	−19.3923	−	11.1962i	−0.859549	−	0.496261i	−0.863861	+	0.503730i	$0.831961\pi$
$510$		0			0
$511$	17.4904	+	30.2942i	0.773729	+	1.34014i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.60770	+	0.928203i	−0.0709815	+	0.0409812i
$514$	−12.0000	+	6.92820i	−0.529297	+	0.305590i
$515$		0			0
$516$	0.732051	+	1.26795i	0.0322267	+	0.0558184i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	−2.08846	−	1.20577i	−0.0917615	−	0.0529786i
$519$	−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	$0.454776\pi$
$522$	5.41154	+	3.12436i	0.236857	+	0.136749i
$523$	−1.19615	+	2.07180i	−0.0523041	+	0.0905933i	−0.890992	−	0.454019i	$-0.849990\pi$
$523$	−1.19615	+	2.07180i	−0.0523041	+	0.0905933i	0.838688	+	0.544612i	$0.183323\pi$
$524$	3.06218	+	5.30385i	0.133772	+	0.231700i
$525$		0			0
$526$	3.10770	−	1.79423i	0.135502	−	0.0782321i
$527$	−33.5885	+	19.3923i	−1.46314	+	0.844742i
$528$			2.19615i			0.0955753i
$529$	−33.2846	−	57.6506i	−1.44716	−	2.50655i
$530$		0			0
$531$	22.1769	+	12.8038i	0.962396	+	0.555640i
$532$	1.39230			0.0603641
$533$	36.0000	+	10.3923i	1.55933	+	0.450141i
$534$	4.98076			0.215539
$535$		0			0
$536$		0			0
$537$	−3.46410	−	6.00000i	−0.149487	−	0.258919i
$538$			27.1244i			1.16941i
$539$	5.19615	−	3.00000i	0.223814	−	0.129219i
$540$		0			0
$541$			22.0526i			0.948114i	0.880494	+	0.474057i	$0.157211\pi$
$541$			22.0526i			0.948114i	−0.880494	+	0.474057i	$0.842789\pi$
$542$	4.73205	+	8.19615i	0.203259	+	0.352055i
$543$	5.33975	−	9.24871i	0.229150	−	0.396900i
$544$	−7.09808	−	4.09808i	−0.304328	−	0.175704i
$545$		0			0
$546$	2.19615	−	7.60770i	0.0939866	−	0.325579i
$547$	6.78461			0.290089			0.145044	−	0.989425i	$-0.453667\pi$
$547$	6.78461			0.290089			0.145044	+	0.989425i	$0.453667\pi$
$548$	−1.90192	−	1.09808i	−0.0812462	−	0.0469075i
$549$	7.63397	−	13.2224i	0.325810	−	0.564320i
$550$		0			0
$551$			1.17691i			0.0501382i
$552$	6.00000	−	3.46410i	0.255377	−	0.147442i
$553$	10.9019	−	6.29423i	0.463597	−	0.267658i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	0.598076	−	1.03590i	0.0253641	−	0.0439319i
$557$	5.89230	+	3.40192i	0.249665	+	0.144144i	0.619611	−	0.784909i	$-0.287290\pi$
$557$	5.89230	+	3.40192i	0.249665	+	0.144144i	−0.369946	+	0.929053i	$0.620624\pi$
$558$	−11.6603			−0.493618
$559$	−5.00000	−	5.19615i	−0.211477	−	0.219774i
$560$		0			0
$561$	15.5885	+	9.00000i	0.658145	+	0.379980i
$562$	5.19615	−	9.00000i	0.219186	−	0.379642i
$563$	7.26795	+	12.5885i	0.306308	+	0.530540i	0.977552	−	0.210696i	$-0.0675731\pi$
$563$	7.26795	+	12.5885i	0.306308	+	0.530540i	−0.671244	+	0.741236i	$0.734240\pi$
$564$		−	2.19615i		−	0.0924747i
$565$		0			0
$566$	−8.32051	+	4.80385i	−0.349737	+	0.201921i
$567$		−	13.3923i		−	0.562424i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	13.6244	−	23.5981i	0.571163	−	0.989283i	−0.425284	−	0.905060i	$-0.639826\pi$
$569$	13.6244	−	23.5981i	0.571163	−	0.989283i	0.996447	−	0.0842230i	$-0.0268408\pi$
$570$		0			0
$571$	−38.3731			−1.60586			−0.802931	−	0.596071i	$-0.796728\pi$
$571$	−38.3731			−1.60586			−0.802931	+	0.596071i	$0.796728\pi$
$572$	−2.59808	−	10.5000i	−0.108631	−	0.439027i
$573$	16.6410			0.695188
$574$	27.0000	+	15.5885i	1.12696	+	0.650650i
$575$		0			0
$576$	−1.23205	−	2.13397i	−0.0513355	−	0.0889156i
$577$			26.4449i			1.10091i	0.834863	+	0.550457i	$0.185547\pi$
$577$			26.4449i			1.10091i	−0.834863	+	0.550457i	$0.814453\pi$
$578$	−43.4545	+	25.0885i	−1.80747	+	1.04354i
$579$	10.3923	−	6.00000i	0.431889	−	0.249351i
$580$		0			0
$581$	−12.2942	−	21.2942i	−0.510051	−	0.883433i
$582$	−3.33975	+	5.78461i	−0.138437	+	0.239780i
$583$	−1.20577	−	0.696152i	−0.0499379	−	0.0288317i
$584$	11.6603			0.482505
$585$		0			0
$586$	−11.1962			−0.462509
$587$	−25.9808	−	15.0000i	−1.07234	−	0.619116i	−0.143521	−	0.989647i	$-0.545842\pi$
$587$	−25.9808	−	15.0000i	−1.07234	−	0.619116i	−0.928820	+	0.370531i	$0.879176\pi$
$588$	0.732051	−	1.26795i	0.0301893	−	0.0522893i
$589$	−1.09808	−	1.90192i	−0.0452454	−	0.0783674i
$590$		0			0
$591$	−13.6865	+	7.90192i	−0.562989	+	0.325042i
$592$	−0.696152	+	0.401924i	−0.0286117	+	0.0165190i
$593$			20.7846i			0.853522i	0.904365	+	0.426761i	$0.140345\pi$
$593$			20.7846i			0.853522i	−0.904365	+	0.426761i	$0.859655\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$		0			0
$596$	5.19615	+	3.00000i	0.212843	+	0.122885i
$597$	4.67949			0.191519
$598$	−24.5885	+	23.6603i	−1.00550	+	0.967540i
$599$	−19.8564			−0.811311			−0.405655	−	0.914026i	$-0.632957\pi$
$599$	−19.8564			−0.811311			−0.405655	+	0.914026i	$0.632957\pi$
$600$		0			0
$601$	18.8923	−	32.7224i	0.770633	−	1.33478i	−0.166583	−	0.986027i	$-0.553273\pi$
$601$	18.8923	−	32.7224i	0.770633	−	1.33478i	0.937216	−	0.348748i	$-0.113393\pi$
$602$	−3.00000	−	5.19615i	−0.122271	−	0.211779i
$603$		0			0
$604$	20.4904	−	11.8301i	0.833742	−	0.481361i
$605$		0			0
$606$			7.85641i			0.319145i
$607$	−18.7942	−	32.5526i	−0.762834	−	1.32127i	−0.941384	−	0.337337i	$-0.890474\pi$
$607$	−18.7942	−	32.5526i	−0.762834	−	1.32127i	0.178550	−	0.983931i	$-0.442859\pi$
$608$	0.232051	−	0.401924i	0.00941090	−	0.0163002i
$609$	4.82309	+	2.78461i	0.195441	+	0.112838i
$610$		0			0
$611$	2.59808	+	10.5000i	0.105107	+	0.424785i
$612$	−20.1962			−0.816381
$613$	−33.6962	−	19.4545i	−1.36097	−	0.785759i	−0.371221	−	0.928545i	$-0.621061\pi$
$613$	−33.6962	−	19.4545i	−1.36097	−	0.785759i	−0.989754	+	0.142785i	$0.954394\pi$
$614$	−13.7321	+	23.7846i	−0.554180	+	0.959869i
$615$		0			0
$616$		−	9.00000i		−	0.362620i
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	−0.779809	−	0.626017i	$-0.784684\pi$
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	0.152242	+	0.988343i	$0.451351\pi$
$618$	5.83013	−	3.36603i	0.234522	−	0.135401i
$619$		−	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
$622$	−7.90192	−	4.56218i	−0.316838	−	0.182927i
$623$	−20.4115			−0.817771
$624$	−1.83013	−	1.90192i	−0.0732637	−	0.0761379i
$625$		0			0
$626$	−22.8564	−	13.1962i	−0.913526	−	0.527424i
$627$	−0.509619	+	0.882686i	−0.0203522	+	0.0352511i
$628$	6.50000	+	11.2583i	0.259378	+	0.449256i
$629$			6.58846i			0.262699i
$630$		0			0
$631$	−18.0000	+	10.3923i	−0.716569	+	0.413711i	−0.813488	−	0.581581i	$-0.802434\pi$
$631$	−18.0000	+	10.3923i	−0.716569	+	0.413711i	0.0969198	+	0.995292i	$0.469101\pi$
$632$		−	4.19615i		−	0.166914i
$633$	−6.43782	−	11.1506i	−0.255880	−	0.443198i
$634$	−11.5981	+	20.0885i	−0.460618	+	0.797815i
$635$		0			0
$636$	−0.339746			−0.0134718
$637$	−2.00000	+	6.92820i	−0.0792429	+	0.274505i
$638$	7.60770			0.301192
$639$	−12.8038	−	7.39230i	−0.506512	−	0.292435i
$640$		0			0
$641$	−16.0359	−	27.7750i	−0.633380	−	1.09705i	−0.986856	−	0.161603i	$-0.948334\pi$
$641$	−16.0359	−	27.7750i	−0.633380	−	1.09705i	0.353476	−	0.935444i	$-0.385000\pi$
$642$		−	12.9282i		−	0.510235i
$643$	9.29423	−	5.36603i	0.366529	−	0.211615i	−0.305412	−	0.952220i	$-0.598794\pi$
$643$	9.29423	−	5.36603i	0.366529	−	0.211615i	0.671941	+	0.740605i	$0.265461\pi$
$644$	−24.5885	+	14.1962i	−0.968921	+	0.559407i
$645$		0			0
$646$	−1.90192	−	3.29423i	−0.0748302	−	0.129610i
$647$	−0.401924	+	0.696152i	−0.0158013	+	0.0273686i	−0.873818	−	0.486253i	$-0.838363\pi$
$647$	−0.401924	+	0.696152i	−0.0158013	+	0.0273686i	0.858017	+	0.513622i	$0.171697\pi$
$648$	−3.86603	−	2.23205i	−0.151872	−	0.0876832i
$649$	31.1769			1.22380
$650$		0			0
$651$	−10.3923			−0.407307
$652$	9.29423	+	5.36603i	0.363990	+	0.210150i
$653$	0.696152	−	1.20577i	0.0272425	−	0.0471855i	−0.852083	−	0.523407i	$-0.824661\pi$
$653$	0.696152	−	1.20577i	0.0272425	−	0.0471855i	0.879325	+	0.476222i	$0.157994\pi$
$654$	−3.12436	−	5.41154i	−0.122172	−	0.211608i
$655$		0			0
$656$	9.00000	−	5.19615i	0.351391	−	0.202876i
$657$	24.8827	−	14.3660i	0.970766	−	0.560472i
$658$			9.00000i			0.350857i
$659$	2.66025	+	4.60770i	0.103629	+	0.179490i	0.913177	−	0.407563i	$-0.133621\pi$
$659$	2.66025	+	4.60770i	0.103629	+	0.179490i	−0.809548	+	0.587053i	$0.800288\pi$
$660$		0			0
$661$	31.0981	+	17.9545i	1.20957	+	0.698348i	0.962666	−	0.270690i	$-0.0872520\pi$
$661$	31.0981	+	17.9545i	1.20957	+	0.698348i	0.246909	+	0.969039i	$0.420585\pi$
$662$	12.9282			0.502469
$663$	−21.0000	+	5.19615i	−0.815572	+	0.201802i
$664$	−8.19615			−0.318072
$665$		0			0
$666$	−0.990381	+	1.71539i	−0.0383765	+	0.0664700i
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$		−	3.00000i		−	0.116073i
$669$	4.09808	−	2.36603i	0.158441	−	0.0914758i
$670$		0			0
$671$		−	18.5885i		−	0.717599i
$672$	−1.09808	−	1.90192i	−0.0423592	−	0.0733683i
$673$	12.1962	−	21.1244i	0.470127	−	0.814284i	−0.529289	−	0.848441i	$-0.677541\pi$
$673$	12.1962	−	21.1244i	0.470127	−	0.814284i	0.999416	+	0.0341573i	$0.0108747\pi$
$674$	−5.36603	−	3.09808i	−0.206692	−	0.119333i
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	25.8564			0.993742			0.496871	−	0.867824i	$-0.334482\pi$
$677$	25.8564			0.993742			0.496871	+	0.867824i	$0.334482\pi$
$678$	4.39230	+	2.53590i	0.168685	+	0.0973906i
$679$	13.6865	−	23.7058i	0.525241	−	0.909744i
$680$		0			0
$681$			12.0000i			0.459841i
$682$	−12.2942	+	7.09808i	−0.470770	+	0.271799i
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.917879	−	0.396861i	$-0.870099\pi$
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.115248	+	0.993337i	$0.536766\pi$
$684$		−	1.14359i		−	0.0437264i
$685$		0			0
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	−0.803848	−	0.464102i	−0.0306687	−	0.0177066i
$688$	−2.00000			−0.0762493
$689$	1.62436	−	0.401924i	0.0618830	−	0.0153121i
$690$		0			0
$691$	−31.7942	−	18.3564i	−1.20951	−	0.698311i	−0.246857	−	0.969052i	$-0.579398\pi$
$691$	−31.7942	−	18.3564i	−1.20951	−	0.698311i	−0.962652	+	0.270741i	$0.912731\pi$
$692$	7.50000	−	12.9904i	0.285107	−	0.493820i
$693$	−11.0885	−	19.2058i	−0.421216	−	0.729567i
$694$		−	28.7321i		−	1.09065i
$695$		0			0
$696$	1.60770	−	0.928203i	0.0609395	−	0.0351835i
$697$		−	85.1769i		−	3.22631i
$698$	−2.02628	−	3.50962i	−0.0766958	−	0.132841i
$699$	−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	$0.262790\pi$
$702$	−13.8564	−	4.00000i	−0.522976	−	0.150970i
$703$	−0.373067			−0.0140705
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	−4.90192	−	8.49038i	−0.184486	−	0.319540i
$707$		−	32.1962i		−	1.21086i
$708$	6.58846	−	3.80385i	0.247609	−	0.142957i
$709$	9.50962	−	5.49038i	0.357141	−	0.206196i	−0.310685	−	0.950513i	$-0.600558\pi$
$709$	9.50962	−	5.49038i	0.357141	−	0.206196i	0.667826	+	0.744317i	$0.267225\pi$
$710$		0			0
$711$	−5.16987	−	8.95448i	−0.193885	−	0.335819i
$712$	−3.40192	+	5.89230i	−0.127492	+	0.220823i
$713$	38.7846	+	22.3923i	1.45250	+	0.838598i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	9.46410			0.353690
$717$	1.39230	+	0.803848i	0.0519966	+	0.0300202i
$718$	−0.803848	+	1.39230i	−0.0299993	+	0.0519604i
$719$	−12.9282	−	22.3923i	−0.482141	−	0.835092i	0.517649	−	0.855593i	$-0.326807\pi$
$719$	−12.9282	−	22.3923i	−0.482141	−	0.835092i	−0.999790	+	0.0205009i	$0.993474\pi$
$720$		0			0
$721$	−23.8923	+	13.7942i	−0.889796	+	0.513724i
$722$	−16.2679	+	9.39230i	−0.605430	+	0.349545i
$723$			6.33975i			0.235778i
$724$	7.29423	+	12.6340i	0.271088	+	0.469538i
$725$		0			0
$726$	−1.26795	−	0.732051i	−0.0470580	−	0.0271690i
$727$	−34.3731			−1.27483			−0.637413	−	0.770522i	$-0.719996\pi$
$727$	−34.3731			−1.27483			−0.637413	+	0.770522i	$0.719996\pi$
$728$	7.50000	+	7.79423i	0.277968	+	0.288873i
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	−8.19615	+	14.1962i	−0.303146	+	0.525064i
$732$	−2.26795	−	3.92820i	−0.0838258	−	0.145191i
$733$		−	14.9090i		−	0.550675i	−0.961348	−	0.275338i	$-0.911210\pi$
$733$		−	14.9090i		−	0.550675i	0.961348	−	0.275338i	$-0.0887896\pi$
$734$	−4.85641	+	2.80385i	−0.179253	+	0.103492i
$735$		0			0
$736$			9.46410i			0.348851i
$737$		0			0
$738$	12.8038	−	22.1769i	0.471316	−	0.816344i
$739$	28.2058	+	16.2846i	1.03757	+	0.599039i	0.919143	−	0.393924i	$-0.128883\pi$
$739$	28.2058	+	16.2846i	1.03757	+	0.599039i	0.118423	+	0.992963i	$0.462216\pi$
$740$		0			0
$741$	−0.294229	−	1.18911i	−0.0108088	−	0.0436831i
$742$	1.39230			0.0511131
$743$	11.7846	+	6.80385i	0.432335	+	0.249609i	0.700341	−	0.713808i	$-0.253031\pi$
$743$	11.7846	+	6.80385i	0.432335	+	0.249609i	−0.268006	+	0.963417i	$0.586365\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$		0			0
$746$		−	0.392305i		−	0.0143633i
$747$	−17.4904	+	10.0981i	−0.639940	+	0.369469i
$748$	−21.2942	+	12.2942i	−0.778594	+	0.449522i
$749$			52.9808i			1.93587i
$750$		0			0
$751$	10.1962	−	17.6603i	0.372063	−	0.644432i	−0.617820	−	0.786320i	$-0.711984\pi$
$751$	10.1962	−	17.6603i	0.372063	−	0.644432i	0.989883	+	0.141888i	$0.0453172\pi$
$752$	2.59808	+	1.50000i	0.0947421	+	0.0546994i
$753$	−12.5885			−0.458749
$754$	−6.58846	+	6.33975i	−0.239937	+	0.230880i
$755$		0			0
$756$	−10.3923	−	6.00000i	−0.377964	−	0.218218i
$757$	−18.8923	+	32.7224i	−0.686652	+	1.18932i	0.286262	+	0.958151i	$0.407587\pi$
$757$	−18.8923	+	32.7224i	−0.686652	+	1.18932i	−0.972914	+	0.231166i	$0.925746\pi$
$758$	14.8923	+	25.7942i	0.540913	+	0.936889i
$759$		−	20.7846i		−	0.754434i
$760$		0			0
$761$	16.2846	−	9.40192i	0.590317	−	0.340819i	−0.174906	−	0.984585i	$-0.555962\pi$
$761$	16.2846	−	9.40192i	0.590317	−	0.340819i	0.765223	+	0.643766i	$0.222629\pi$
$762$		−	7.90897i		−	0.286512i
$763$	12.8038	+	22.1769i	0.463530	+	0.802858i
$764$	−11.3660	+	19.6865i	−0.411208	+	0.712234i
$765$		0			0
$766$	−22.3923			−0.809067
$767$	−27.0000	+	25.9808i	−0.974913	+	0.938111i
$768$	−0.732051			−0.0264156
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.231701	−	0.972787i	$-0.574429\pi$
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.958309	+	0.285734i	$0.907763\pi$
$770$		0			0
$771$	5.07180	+	8.78461i	0.182656	+	0.316370i
$772$			16.3923i			0.589972i
$773$	−2.08846	+	1.20577i	−0.0751166	+	0.0433686i	−0.537088	−	0.843526i	$-0.680476\pi$
$773$	−2.08846	+	1.20577i	−0.0751166	+	0.0433686i	0.461971	+	0.886895i	$0.347142\pi$
$774$	−4.26795	+	2.46410i	−0.153408	+	0.0885703i
$775$		0			0
$776$	−4.56218	−	7.90192i	−0.163773	−	0.283663i
$777$	−0.882686	+	1.52886i	−0.0316662	+	0.0548474i
$778$	19.6865	+	11.3660i	0.705796	+	0.407492i
$779$	4.82309			0.172805
$780$		0			0
$781$	−18.0000			−0.644091
$782$	67.1769	+	38.7846i	2.40224	+	1.38693i
$783$	5.07180	−	8.78461i	0.181251	−	0.313936i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$		0			0
$786$	3.88269	−	2.24167i	0.138491	−	0.0799577i
$787$	37.0981	−	21.4186i	1.32240	−	0.763490i	0.338292	−	0.941041i	$-0.390151\pi$
$787$	37.0981	−	21.4186i	1.32240	−	0.763490i	0.984112	+	0.177551i	$0.0568175\pi$
$788$		−	21.5885i		−	0.769057i
$789$	−1.31347	−	2.27499i	−0.0467606	−	0.0809918i
$790$		0			0
$791$	−18.0000	−	10.3923i	−0.640006	−	0.369508i
$792$	−7.39230			−0.262674
$793$	15.4904	+	16.0981i	0.550080	+	0.571659i
$794$	11.1962			0.397337
$795$		0			0
$796$	−3.19615	+	5.53590i	−0.113285	+	0.196215i
$797$	−6.46410	−	11.1962i	−0.228970	−	0.396588i	0.728533	−	0.685011i	$-0.240203\pi$
$797$	−6.46410	−	11.1962i	−0.228970	−	0.396588i	−0.957503	+	0.288423i	$0.906869\pi$
$798$		−	1.01924i		−	0.0360806i
$799$	21.2942	−	12.2942i	0.753336	−	0.434939i
$800$		0			0
$801$			16.7654i			0.592375i
$802$	−2.59808	−	4.50000i	−0.0917413	−	0.158901i
$803$	17.4904	−	30.2942i	0.617222	−	1.06906i
$804$		0			0
$805$		0			0
$806$	4.73205	−	16.3923i	0.166679	−	0.577394i
$807$	19.8564			0.698979
$808$	−9.29423	−	5.36603i	−0.326970	−	0.188776i
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$		0			0
$811$			43.3923i			1.52371i	0.647748	+	0.761855i	$0.275711\pi$
$811$			43.3923i			1.52371i	−0.647748	+	0.761855i	$0.724289\pi$
$812$	−6.58846	+	3.80385i	−0.231210	+	0.133489i
$813$	6.00000	−	3.46410i	0.210429	−	0.121491i
$814$			2.41154i			0.0845245i
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−0.803848	−	0.464102i	−0.0281231	−	0.0162369i
$818$	−16.2679			−0.568796
$819$	25.6077	+	7.39230i	0.894805	+	0.258308i
$820$		0			0
$821$	17.4904	+	10.0981i	0.610419	+	0.352425i	0.773129	−	0.634249i	$-0.218690\pi$
$821$	17.4904	+	10.0981i	0.610419	+	0.352425i	−0.162711	+	0.986674i	$0.552024\pi$
$822$	−0.803848	+	1.39230i	−0.0280374	+	0.0485622i
$823$	−13.5981	−	23.5526i	−0.473999	−	0.820991i	0.525558	−	0.850758i	$-0.323857\pi$
$823$	−13.5981	−	23.5526i	−0.473999	−	0.820991i	−0.999557	+	0.0297674i	$0.990523\pi$
$824$			9.19615i			0.320363i
$825$		0			0
$826$	−27.0000	+	15.5885i	−0.939450	+	0.542392i
$827$			42.5885i			1.48095i	0.672086	+	0.740473i	$0.265398\pi$
$827$			42.5885i			1.48095i	−0.672086	+	0.740473i	$0.734602\pi$
$828$	11.6603	+	20.1962i	0.405222	+	0.701865i
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$		0			0
$831$	−0.732051			−0.0253946
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	16.3923			0.567960
$834$	−0.758330	−	0.437822i	−0.0262588	−	0.0151605i
$835$		0			0
$836$	−0.696152	−	1.20577i	−0.0240769	−	0.0417025i
$837$			18.9282i			0.654254i
$838$	15.0000	−	8.66025i	0.518166	−	0.299164i
$839$	18.8827	−	10.9019i	0.651903	−	0.376376i	−0.137282	−	0.990532i	$-0.543837\pi$
$839$	18.8827	−	10.9019i	0.651903	−	0.376376i	0.789185	+	0.614156i	$0.210503\pi$
$840$		0			0
$841$	11.2846	+	19.5455i	0.389124	+	0.673983i
$842$	−1.43782	+	2.49038i	−0.0495506	+	0.0858242i
$843$	−6.58846	−	3.80385i	−0.226919	−	0.131011i
$844$	17.5885			0.605420
$845$		0			0
$846$	7.39230			0.254153
$847$	5.19615	+	3.00000i	0.178542	+	0.103081i
$848$	0.232051	−	0.401924i	0.00796866	−	0.0138021i
$849$	3.51666	+	6.09103i	0.120691	+	0.209044i
$850$		0			0
$851$	6.58846	−	3.80385i	0.225849	−	0.130394i
$852$	−3.80385	+	2.19615i	−0.130318	+	0.0752389i
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	9.29423	+	16.0981i	0.318042	+	0.550865i
$855$		0			0
$856$	15.2942	+	8.83013i	0.522746	+	0.301808i
$857$	16.7321			0.571556			0.285778	−	0.958296i	$-0.407748\pi$
$857$	16.7321			0.571556			0.285778	+	0.958296i	$0.407748\pi$
$858$	−7.68653	+	1.90192i	−0.262414	+	0.0649306i
$859$	−20.3731			−0.695120			−0.347560	−	0.937658i	$-0.612990\pi$
$859$	−20.3731			−0.695120			−0.347560	+	0.937658i	$0.612990\pi$
$860$		0			0
$861$	11.4115	−	19.7654i	0.388904	−	0.673602i
$862$	−4.09808	−	7.09808i	−0.139581	−	0.241761i
$863$		−	43.1769i		−	1.46976i	−0.678198	−	0.734880i	$-0.737239\pi$
$863$		−	43.1769i		−	1.46976i	0.678198	−	0.734880i	$-0.262761\pi$
$864$	−3.46410	+	2.00000i	−0.117851	+	0.0680414i
$865$		0			0
$866$			8.39230i			0.285182i
$867$	18.3660	+	31.8109i	0.623743	+	1.08035i
$868$	7.09808	−	12.2942i	0.240924	−	0.417293i
$869$	−10.9019	−	6.29423i	−0.369822	−	0.213517i
$870$		0			0
$871$		0			0
$872$	8.53590			0.289062
$873$	−19.4711	−	11.2417i	−0.658998	−	0.380473i
$874$	−2.19615	+	3.80385i	−0.0742860	+	0.128667i
$875$		0			0
$876$		−	8.53590i		−	0.288401i
$877$	23.7846	−	13.7321i	0.803149	−	0.463698i	−0.0414220	−	0.999142i	$-0.513189\pi$
$877$	23.7846	−	13.7321i	0.803149	−	0.463698i	0.844571	+	0.535443i	$0.179855\pi$
$878$	2.95448	−	1.70577i	0.0997090	−	0.0575670i
$879$			8.19615i			0.276449i
$880$		0			0
$881$	−13.1603	+	22.7942i	−0.443380	+	0.767957i	−0.997938	−	0.0641883i	$-0.979554\pi$
$881$	−13.1603	+	22.7942i	−0.443380	+	0.767957i	0.554558	+	0.832145i	$0.312888\pi$
$882$	4.26795	+	2.46410i	0.143709	+	0.0829706i
$883$	−4.58846			−0.154414			−0.0772069	−	0.997015i	$-0.524600\pi$
$883$	−4.58846			−0.154414			−0.0772069	+	0.997015i	$0.524600\pi$
$884$	8.19615	−	28.3923i	0.275666	−	0.954937i
$885$		0			0
$886$	19.3923	+	11.1962i	0.651497	+	0.376142i
$887$	−20.3827	+	35.3038i	−0.684384	+	1.18539i	0.289246	+	0.957255i	$0.406595\pi$
$887$	−20.3827	+	35.3038i	−0.684384	+	1.18539i	−0.973630	+	0.228133i	$0.926738\pi$
$888$	0.294229	+	0.509619i	0.00987367	+	0.0171017i
$889$			32.4115i			1.08705i
$890$		0			0
$891$	−11.5981	+	6.69615i	−0.388550	+	0.224330i
$892$			6.46410i			0.216434i
$893$	0.696152	+	1.20577i	0.0232959	+	0.0403496i
$894$	2.19615	−	3.80385i	0.0734503	−	0.127220i
$895$		0			0
$896$	3.00000			0.100223
$897$	17.3205	+	18.0000i	0.578315	+	0.601003i
$898$	15.5885			0.520194
$899$	10.3923	+	6.00000i	0.346603	+	0.200111i
$900$		0			0
$901$	−1.90192	−	3.29423i	−0.0633623	−	0.109747i
$902$		−	31.1769i		−	1.03808i
$903$	−3.80385	+	2.19615i	−0.126584	+	0.0730834i
$904$	−6.00000	+	3.46410i	−0.199557	+	0.115214i
$905$		0			0
$906$	−8.66025	−	15.0000i	−0.287718	−	0.498342i
$907$	2.29423	−	3.97372i	0.0761786	−	0.131945i	−0.825420	−	0.564520i	$-0.809061\pi$
$907$	2.29423	−	3.97372i	0.0761786	−	0.131945i	0.901598	+	0.432574i	$0.142395\pi$
$908$	−14.1962	−	8.19615i	−0.471116	−	0.271999i
$909$	−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	$0.615713\pi$
$912$	−0.294229	−	0.169873i	−0.00974288	−	0.00562506i
$913$	−12.2942	+	21.2942i	−0.406880	+	0.704736i
$914$	−9.16987	−	15.8827i	−0.303312	−	0.525353i
$915$		0			0
$916$	1.09808	−	0.633975i	0.0362815	−	0.0209471i
$917$	−15.9115	+	9.18653i	−0.525445	+	0.303366i
$918$			32.7846i			1.08205i
$919$	−15.3923	−	26.6603i	−0.507745	−	0.879441i	−0.999960	−	0.00896670i	$-0.997146\pi$
$919$	−15.3923	−	26.6603i	−0.507745	−	0.879441i	0.492215	−	0.870474i	$-0.336188\pi$
$920$		0			0
$921$	17.4115	+	10.0526i	0.573730	+	0.331243i
$922$	−30.5885			−1.00738
$923$	15.5885	−	15.0000i	0.513100	−	0.493731i
$924$	−6.58846			−0.216744
$925$		0			0
$926$	6.46410	−	11.1962i	0.212424	−	0.367928i
$927$	11.3301	+	19.6244i	0.372130	+	0.644548i
$928$			2.53590i			0.0832449i
$929$	−2.78461	+	1.60770i	−0.0913601	+	0.0527468i	−0.544984	−	0.838446i	$-0.683464\pi$
$929$	−2.78461	+	1.60770i	−0.0913601	+	0.0527468i	0.453624	+	0.891193i	$0.350131\pi$
$930$		0			0
$931$			0.928203i			0.0304206i
$932$	−2.36603	−	4.09808i	−0.0775017	−	0.134237i
$933$	−3.33975	+	5.78461i	−0.109338	+	0.189380i
$934$	32.7846	+	18.9282i	1.07275	+	0.619350i
$935$		0			0
$936$	6.40192	−	6.16025i	0.209253	−	0.201354i
$937$	9.60770			0.313870			0.156935	−	0.987609i	$-0.449839\pi$
$937$	9.60770			0.313870			0.156935	+	0.987609i	$0.449839\pi$
$938$		0			0
$939$	−9.66025	+	16.7321i	−0.315250	+	0.546030i
$940$		0			0
$941$			3.21539i			0.104819i	0.998626	+	0.0524094i	$0.0166901\pi$
$941$			3.21539i			0.104819i	−0.998626	+	0.0524094i	$0.983310\pi$
$942$	8.24167	−	4.75833i	0.268528	−	0.155035i
$943$	−85.1769	+	49.1769i	−2.77374	+	1.60142i
$944$			10.3923i			0.338241i
$945$		0			0
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	−13.3135	−	7.68653i	−0.432630	−	0.249779i	0.267837	−	0.963464i	$-0.413691\pi$
$947$	−13.3135	−	7.68653i	−0.432630	−	0.249779i	−0.700466	+	0.713686i	$0.747025\pi$
$948$	−3.07180			−0.0997673
$949$	10.0981	+	40.8109i	0.327797	+	1.32478i
$950$		0			0
$951$	14.7058	+	8.49038i	0.476867	+	0.275319i
$952$	12.2942	−	21.2942i	0.398458	−	0.690150i
$953$	−3.29423	−	5.70577i	−0.106711	−	0.184828i	0.807725	−	0.589559i	$-0.200698\pi$
$953$	−3.29423	−	5.70577i	−0.106711	−	0.184828i	−0.914436	+	0.404731i	$0.867365\pi$
$954$		−	1.14359i		−	0.0370252i
$955$		0			0
$956$	−1.90192	+	1.09808i	−0.0615126	+	0.0355143i
$957$		−	5.56922i		−	0.180027i
$958$	−20.4904	−	35.4904i	−0.662014	−	1.14664i
$959$	3.29423	−	5.70577i	0.106376	−	0.184249i
$960$		0			0
$961$	8.60770			0.277668
$962$	−2.00962	−	2.08846i	−0.0647927	−	0.0673346i
$963$	43.5167			1.40230
$964$	−7.50000	−	4.33013i	−0.241559	−	0.139464i
$965$		0			0
$966$	10.3923	+	18.0000i	0.334367	+	0.579141i
$967$			44.5692i			1.43325i	0.697459	+	0.716625i	$0.254314\pi$
$967$			44.5692i			1.43325i	−0.697459	+	0.716625i	$0.745686\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	−2.41154	+	1.39230i	−0.0774699	+	0.0447273i
$970$		0			0
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	−0.947636	−	0.319354i	$-0.896534\pi$
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	0.197250	−	0.980353i	$-0.436799\pi$
$972$	−7.63397	+	13.2224i	−0.244860	+	0.424110i
$973$	3.10770	+	1.79423i	0.0996281	+	0.0575203i
$974$	15.2487			0.488600
$975$		0			0
$976$	6.19615			0.198334
$977$	−14.1962	−	8.19615i	−0.454175	−	0.262218i	0.255417	−	0.966831i	$-0.417787\pi$
$977$	−14.1962	−	8.19615i	−0.454175	−	0.262218i	−0.709592	+	0.704613i	$0.751121\pi$
$978$	3.92820	−	6.80385i	0.125610	−	0.217563i
$979$	10.2058	+	17.6769i	0.326178	+	0.564957i
$980$		0			0
$981$	18.2154	−	10.5167i	0.581573	−	0.335771i
$982$	−17.8923	+	10.3301i	−0.570966	+	0.329648i
$983$		−	44.5692i		−	1.42154i	−0.703426	−	0.710769i	$-0.748347\pi$
$983$		−	44.5692i		−	1.42154i	0.703426	−	0.710769i	$-0.251653\pi$
$984$	−3.80385	−	6.58846i	−0.121262	−	0.210032i
$985$		0			0
$986$	18.0000	+	10.3923i	0.573237	+	0.330958i
$987$	6.58846			0.209713
$988$	1.60770	+	0.464102i	0.0511476	+	0.0147650i
$989$	18.9282			0.601882
$990$		0			0
$991$	5.58846	−	9.67949i	0.177523	−	0.307479i	−0.763508	−	0.645798i	$-0.776525\pi$
$991$	5.58846	−	9.67949i	0.177523	−	0.307479i	0.941032	+	0.338319i	$0.109858\pi$
$992$	−2.36603	−	4.09808i	−0.0751214	−	0.130114i
$993$		−	9.46410i		−	0.300334i
$994$	15.5885	−	9.00000i	0.494436	−	0.285463i
$995$		0			0
$996$			6.00000i			0.190117i
$997$	20.2846	+	35.1340i	0.642420	+	1.11270i	0.984891	+	0.173176i	$0.0554028\pi$
$997$	20.2846	+	35.1340i	0.642420	+	1.11270i	−0.342471	+	0.939528i	$0.611264\pi$
$998$	−12.9282	+	22.3923i	−0.409235	+	0.708816i
$999$	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.m.a.251.2		4
5.2	odd	4		650.2.n.a.199.2		4
5.3	odd	4		650.2.n.b.199.1		4
5.4	even	2		130.2.l.a.121.1	yes	4
13.6	odd	12		8450.2.a.bf.1.1		2
13.7	odd	12		8450.2.a.bm.1.1		2
13.10	even	6	inner	650.2.m.a.101.2		4
15.14	odd	2		1170.2.bs.c.901.2		4
20.19	odd	2		1040.2.da.a.641.2		4
65.4	even	6		1690.2.d.f.1351.2		4
65.9	even	6		1690.2.d.f.1351.4		4
65.19	odd	12		1690.2.a.m.1.2		2
65.23	odd	12		650.2.n.a.49.2		4
65.24	odd	12		1690.2.e.n.991.1		4
65.29	even	6		1690.2.l.g.361.2		4
65.34	odd	4		1690.2.e.n.191.1		4
65.44	odd	4		1690.2.e.l.191.1		4
65.49	even	6		130.2.l.a.101.1	✓	4
65.54	odd	12		1690.2.e.l.991.1		4
65.59	odd	12		1690.2.a.j.1.2		2
65.62	odd	12		650.2.n.b.49.1		4
65.64	even	2		1690.2.l.g.1161.2		4
195.179	odd	6		1170.2.bs.c.361.2		4
260.179	odd	6		1040.2.da.a.881.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.1	✓	4	65.49	even	6
130.2.l.a.121.1	yes	4	5.4	even	2
650.2.m.a.101.2		4	13.10	even	6	inner
650.2.m.a.251.2		4	1.1	even	1	trivial
650.2.n.a.49.2		4	65.23	odd	12
650.2.n.a.199.2		4	5.2	odd	4
650.2.n.b.49.1		4	65.62	odd	12
650.2.n.b.199.1		4	5.3	odd	4
1040.2.da.a.641.2		4	20.19	odd	2
1040.2.da.a.881.2		4	260.179	odd	6
1170.2.bs.c.361.2		4	195.179	odd	6
1170.2.bs.c.901.2		4	15.14	odd	2
1690.2.a.j.1.2		2	65.59	odd	12
1690.2.a.m.1.2		2	65.19	odd	12
1690.2.d.f.1351.2		4	65.4	even	6
1690.2.d.f.1351.4		4	65.9	even	6
1690.2.e.l.191.1		4	65.44	odd	4
1690.2.e.l.991.1		4	65.54	odd	12
1690.2.e.n.191.1		4	65.34	odd	4
1690.2.e.n.991.1		4	65.24	odd	12
1690.2.l.g.361.2		4	65.29	even	6
1690.2.l.g.1161.2		4	65.64	even	2
8450.2.a.bf.1.1		2	13.6	odd	12
8450.2.a.bm.1.1		2	13.7	odd	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.m (of order \(6\), degree \(2\), minimal)

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

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