LMFDB - Embedded newform 650.2.n.b.49.1

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:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.49
Dual form			650.2.n.b.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.633975 - 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.633975 + 0.366025i) q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(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	−0.305695	−	0.952129i	$-0.598889\pi$
$3$	0.633975	−	0.366025i	0.366025	−	0.211325i	0.671721	+	0.740805i	$0.265556\pi$
$4$	−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	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$	−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	$0.131575\pi$
$17$	7.09808	+	4.09808i	1.72154	+	0.993929i	0.805759	+	0.592244i	$0.201758\pi$
$18$	−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	$-0.218638\pi$
$23$	8.19615	−	4.73205i	1.70902	−	0.986701i	0.935781	−	0.352581i	$-0.114696\pi$
$24$	−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	0.897171	−	0.441684i	$-0.145619\pi$
$37$	0.401924	+	0.696152i	0.0660759	+	0.114447i	−0.831095	+	0.556131i	$0.812285\pi$
$38$			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	0.362084	−	0.932145i	$-0.382065\pi$
$43$	−1.73205	−	1.00000i	−0.264135	−	0.152499i	−0.626219	+	0.779647i	$0.715399\pi$
$44$			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	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−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	$0.0101477\pi$
$53$			0.464102i			0.0637493i	−0.999492	+	0.0318746i	$0.989852\pi$
$54$	−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	$-0.260952\pi$
$73$	11.6603			1.36473			0.682365	+	0.731012i	$0.260952\pi$
$74$	−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	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$	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	−0.535900	−	0.844281i	$-0.680028\pi$
$97$	4.56218	−	7.90192i	0.463219	−	0.802319i	0.999119	+	0.0419625i	$0.0133610\pi$
$98$	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	$-0.850332\pi$
$103$		−	9.19615i		−	0.906124i	0.891479	−	0.453062i	$-0.149668\pi$
$104$	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	−0.999706	−	0.0242598i	$-0.992277\pi$
$107$	−15.2942	+	8.83013i	−1.47855	+	0.853641i	−0.478843	+	0.877900i	$0.658944\pi$
$108$	−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	0.190490	−	0.981689i	$-0.438992\pi$
$113$	−6.00000	−	3.46410i	−0.564433	−	0.325875i	−0.754923	+	0.655814i	$0.772326\pi$
$114$	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	−0.853937	−	0.520376i	$-0.825792\pi$
$127$	−9.35641	+	5.40192i	−0.830247	+	0.479343i	0.0236904	+	0.999719i	$0.492458\pi$
$128$	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	−0.815298	−	0.579041i	$-0.803427\pi$
$137$	1.09808	−	1.90192i	0.0938150	−	0.162492i	0.909113	+	0.416549i	$0.136760\pi$
$138$	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	$0.173605\pi$
$157$			13.0000i			1.03751i	−0.854922	+	0.518756i	$0.826395\pi$
$158$	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	−0.575669	−	0.817683i	$-0.695258\pi$
$163$	5.36603	−	9.29423i	0.420300	−	0.727980i	0.995969	+	0.0897026i	$0.0285917\pi$
$164$		−	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	0.802135	−	0.597143i	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$			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	0.904568	−	0.426329i	$-0.140193\pi$
$173$	12.9904	+	7.50000i	0.987640	+	0.570214i	0.0830722	+	0.996544i	$0.473527\pi$
$174$		−	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	$-0.965805\pi$
$193$	−8.19615	−	14.1962i	−0.589972	−	1.02186i	0.404263	−	0.914643i	$-0.367528\pi$
$194$	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	$-0.887393\pi$
$197$	−10.7942	−	18.6962i	−0.769057	−	1.33205i	0.169018	−	0.985613i	$-0.445940\pi$
$198$	−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	0.737281	−	0.675586i	$-0.236109\pi$
$223$	−3.23205	−	5.59808i	−0.216434	−	0.374875i	−0.953715	+	0.300711i	$0.902776\pi$
$224$	−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	$-0.650243\pi$
$227$	8.19615	−	14.1962i	0.543998	−	0.942232i	0.998669	−	0.0515725i	$-0.0164233\pi$
$228$	−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	$0.0495389\pi$
$233$			4.73205i			0.310007i	−0.987914	+	0.155003i	$0.950461\pi$
$234$	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	−0.0766265	−	0.997060i	$-0.524415\pi$
$257$	12.0000	−	6.92820i	0.748539	−	0.432169i	0.825166	+	0.564890i	$0.191082\pi$
$258$	−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	−0.401116	−	0.916027i	$-0.631378\pi$
$263$	3.10770	−	1.79423i	0.191629	−	0.110637i	0.592745	+	0.805390i	$0.298044\pi$
$264$	−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	0.473757	−	0.880656i	$-0.342897\pi$
$277$	−0.866025	−	0.500000i	−0.0520344	−	0.0300421i	−0.525792	+	0.850613i	$0.676231\pi$
$278$	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	−0.726482	−	0.687186i	$-0.758846\pi$
$283$	−8.32051	+	4.80385i	−0.494603	+	0.285559i	0.231879	+	0.972745i	$0.425513\pi$
$284$	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	−0.981924	−	0.189277i	$-0.939386\pi$
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	0.654881	+	0.755732i	$0.272719\pi$
$294$		−	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	$-0.213315\pi$
$307$	27.4641			1.56746			0.783730	+	0.621102i	$0.213315\pi$
$308$	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	$0.267976\pi$
$313$			26.3923i			1.49178i	−0.666068	+	0.745891i	$0.732024\pi$
$314$	−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	$-0.274177\pi$
$317$	23.1962			1.30283			0.651413	+	0.758723i	$0.274177\pi$
$318$	−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	$-0.946023\pi$
$337$		−	6.19615i		−	0.337526i	0.985657	−	0.168763i	$-0.0539772\pi$
$338$	−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	−0.349595	−	0.936901i	$-0.613681\pi$
$347$	−24.8827	−	14.3660i	−1.33577	−	0.771209i	−0.986178	+	0.165692i	$0.947014\pi$
$348$	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	0.966482	−	0.256734i	$-0.0826464\pi$
$353$	4.90192	+	8.49038i	0.260903	+	0.451897i	−0.705579	+	0.708631i	$0.749313\pi$
$354$	−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	−0.367865	−	0.929879i	$-0.619911\pi$
$367$	4.85641	−	2.80385i	0.253502	−	0.146360i	0.621367	+	0.783520i	$0.286578\pi$
$368$	−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	0.508770	−	0.860903i	$-0.330100\pi$
$373$	0.339746	+	0.196152i	0.0175914	+	0.0101564i	−0.491179	+	0.871059i	$0.663434\pi$
$374$	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	$0.360536\pi$
$383$	−11.1962	+	19.3923i	−0.572097	+	0.990900i	−0.996350	+	0.0853571i	$0.972797\pi$
$384$	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	−0.971621	−	0.236542i	$-0.923986\pi$
$397$	−5.59808	+	9.69615i	−0.280959	+	0.486636i	0.690662	+	0.723178i	$0.257319\pi$
$398$	−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	0.315091	−	0.949062i	$-0.397965\pi$
$433$	−7.26795	−	4.19615i	−0.349275	−	0.201654i	−0.664366	+	0.747407i	$0.731298\pi$
$434$		−	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	$-0.821461\pi$
$443$		−	22.3923i		−	1.06389i	0.846779	−	0.531945i	$-0.178539\pi$
$444$	−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	0.567832	−	0.823145i	$-0.307783\pi$
$457$	−9.16987	−	15.8827i	−0.428949	−	0.742961i	−0.996780	+	0.0801841i	$0.974449\pi$
$458$	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	$-0.402876\pi$
$463$	12.9282			0.600825			0.300412	+	0.953809i	$0.402876\pi$
$464$	−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	$0.339727\pi$
$467$			37.8564i			1.75179i	−0.482506	+	0.875893i	$0.660273\pi$
$468$	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	−0.985443	−	0.170005i	$-0.945621\pi$
$487$	−7.62436	+	13.2058i	−0.345493	+	0.598411i	0.639951	+	0.768416i	$0.278955\pi$
$488$	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	0.916831	−	0.399276i	$-0.130738\pi$
$503$	23.0885	+	13.3301i	1.02946	+	0.594361i	0.112633	+	0.993637i	$0.464072\pi$
$504$	−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	−0.544612	−	0.838688i	$-0.683323\pi$
$523$	−2.07180	+	1.19615i	−0.0905933	+	0.0523041i	0.454019	+	0.890992i	$0.349990\pi$
$524$	−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	$0.0463325\pi$
$547$			6.78461i			0.290089i	−0.989425	+	0.145044i	$0.953667\pi$
$548$	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	0.929053	−	0.369946i	$-0.120624\pi$
$557$	3.40192	+	5.89230i	0.144144	+	0.249665i	−0.784909	+	0.619611i	$0.787290\pi$
$558$			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	0.210696	−	0.977552i	$-0.432427\pi$
$563$	−12.5885	−	7.26795i	−0.530540	−	0.306308i	−0.741236	+	0.671244i	$0.765760\pi$
$564$		−	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	$-0.314453\pi$
$577$	26.4449			1.10091			0.550457	+	0.834863i	$0.314453\pi$
$578$	−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	$-0.954158\pi$
$587$	−15.0000	−	25.9808i	−0.619116	−	1.07234i	0.370531	−	0.928820i	$-0.379176\pi$
$588$	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	$-0.640345\pi$
$593$	−20.7846			−0.853522			−0.426761	+	0.904365i	$0.640345\pi$
$594$	−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	−0.337337	−	0.941384i	$-0.609526\pi$
$607$	−32.5526	−	18.7942i	−1.32127	−	0.762834i	−0.983931	+	0.178550i	$0.942859\pi$
$608$	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	$0.121061\pi$
$613$	19.4545	+	33.6962i	0.785759	+	1.36097i	−0.142785	+	0.989754i	$0.545606\pi$
$614$	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	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$	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	−0.740605	−	0.671941i	$-0.765461\pi$
$643$	5.36603	−	9.29423i	0.211615	−	0.366529i	0.952220	+	0.305412i	$0.0987943\pi$
$644$	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	−0.486253	−	0.873818i	$-0.661637\pi$
$647$	0.696152	−	0.401924i	0.0273686	−	0.0158013i	0.513622	+	0.858017i	$0.328303\pi$
$648$	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	−0.476222	−	0.879325i	$-0.657994\pi$
$653$	1.20577	−	0.696152i	0.0471855	−	0.0272425i	0.523407	+	0.852083i	$0.324661\pi$
$654$	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	−0.0341573	−	0.999416i	$-0.510875\pi$
$673$	21.1244	−	12.1962i	0.814284	−	0.470127i	0.848441	+	0.529289i	$0.177541\pi$
$674$	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	$0.165518\pi$
$677$			25.8564i			0.993742i	−0.867824	+	0.496871i	$0.834482\pi$
$678$	−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	$0.370099\pi$
$683$	−15.5885	+	27.0000i	−0.596476	+	1.03313i	−0.993337	+	0.115248i	$0.963234\pi$
$684$		−	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	$-0.780004\pi$
$727$		−	34.3731i		−	1.27483i	0.770522	−	0.637413i	$-0.219996\pi$
$728$	−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	$-0.411210\pi$
$733$	14.9090			0.550675			0.275338	+	0.961348i	$0.411210\pi$
$734$	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	0.713808	−	0.700341i	$-0.246969\pi$
$743$	−6.80385	−	11.7846i	−0.249609	−	0.432335i	−0.963417	+	0.268006i	$0.913635\pi$
$744$	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	0.231166	−	0.972914i	$-0.425746\pi$
$757$	32.7224	−	18.8923i	1.18932	−	0.686652i	0.958151	+	0.286262i	$0.0924127\pi$
$758$	−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	−0.886895	−	0.461971i	$-0.847142\pi$
$773$	−1.20577	+	2.08846i	−0.0433686	+	0.0751166i	0.843526	+	0.537088i	$0.180476\pi$
$774$	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	$0.443182\pi$
$787$	−21.4186	+	37.0981i	−0.763490	+	1.32240i	−0.941041	+	0.338292i	$0.890151\pi$
$788$	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	0.288423	−	0.957503i	$-0.406869\pi$
$797$	−11.1962	−	6.46410i	−0.396588	−	0.228970i	−0.685011	+	0.728533i	$0.740203\pi$
$798$	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	0.850758	−	0.525558i	$-0.176143\pi$
$823$	23.5526	+	13.5981i	0.820991	+	0.473999i	−0.0297674	+	0.999557i	$0.509477\pi$
$824$			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	$-0.234602\pi$
$827$	42.5885			1.48095			0.740473	+	0.672086i	$0.234602\pi$
$828$	−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	$-0.423765\pi$
$853$	13.8564			0.474434			0.237217	+	0.971457i	$0.423765\pi$
$854$	−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	$0.0922520\pi$
$857$			16.7321i			0.571556i	−0.958296	+	0.285778i	$0.907748\pi$
$858$	−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	$-0.237239\pi$
$863$	43.1769			1.46976			0.734880	+	0.678198i	$0.237239\pi$
$864$	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	−0.999142	−	0.0414220i	$-0.986811\pi$
$877$	−13.7321	+	23.7846i	−0.463698	+	0.803149i	0.535443	+	0.844571i	$0.320145\pi$
$878$	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	$0.0246002\pi$
$883$			4.58846i			0.154414i	−0.997015	+	0.0772069i	$0.975400\pi$
$884$	−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	0.228133	−	0.973630i	$-0.426738\pi$
$887$	35.3038	−	20.3827i	1.18539	−	0.684384i	0.957255	+	0.289246i	$0.0934047\pi$
$888$	−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	−0.564520	−	0.825420i	$-0.690939\pi$
$907$	−3.97372	+	2.29423i	−0.131945	+	0.0761786i	0.432574	+	0.901598i	$0.357605\pi$
$908$	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	$0.0501613\pi$
$937$			9.60770i			0.313870i	−0.987609	+	0.156935i	$0.949839\pi$
$938$		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	0.713686	−	0.700466i	$-0.247025\pi$
$947$	−7.68653	−	13.3135i	−0.249779	−	0.432630i	−0.963464	+	0.267837i	$0.913691\pi$
$948$			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	0.589559	−	0.807725i	$-0.299302\pi$
$953$	5.70577	+	3.29423i	0.184828	+	0.106711i	−0.404731	+	0.914436i	$0.632635\pi$
$954$		−	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	$-0.245686\pi$
$967$	44.5692			1.43325			0.716625	+	0.697459i	$0.245686\pi$
$968$	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	0.704613	−	0.709592i	$-0.251121\pi$
$977$	−8.19615	−	14.1962i	−0.262218	−	0.454175i	−0.966831	+	0.255417i	$0.917787\pi$
$978$	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	$-0.248347\pi$
$983$	44.5692			1.42154			0.710769	+	0.703426i	$0.248347\pi$
$984$	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	0.939528	−	0.342471i	$-0.111264\pi$
$997$	35.1340	+	20.2846i	1.11270	+	0.642420i	0.173176	+	0.984891i	$0.444597\pi$
$998$	−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.b.49.1		4
5.2	odd	4		130.2.l.a.101.1	✓	4
5.3	odd	4		650.2.m.a.101.2		4
5.4	even	2		650.2.n.a.49.2		4
13.4	even	6		650.2.n.a.199.2		4
15.2	even	4		1170.2.bs.c.361.2		4
20.7	even	4		1040.2.da.a.881.2		4
65.2	even	12		1690.2.a.j.1.2		2
65.4	even	6	inner	650.2.n.b.199.1		4
65.7	even	12		1690.2.e.l.191.1		4
65.12	odd	4		1690.2.l.g.361.2		4
65.17	odd	12		130.2.l.a.121.1	yes	4
65.22	odd	12		1690.2.l.g.1161.2		4
65.28	even	12		8450.2.a.bm.1.1		2
65.32	even	12		1690.2.e.n.191.1		4
65.37	even	12		1690.2.a.m.1.2		2
65.42	odd	12		1690.2.d.f.1351.2		4
65.43	odd	12		650.2.m.a.251.2		4
65.47	even	4		1690.2.e.l.991.1		4
65.57	even	4		1690.2.e.n.991.1		4
65.62	odd	12		1690.2.d.f.1351.4		4
65.63	even	12		8450.2.a.bf.1.1		2
195.17	even	12		1170.2.bs.c.901.2		4
260.147	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	5.2	odd	4
130.2.l.a.121.1	yes	4	65.17	odd	12
650.2.m.a.101.2		4	5.3	odd	4
650.2.m.a.251.2		4	65.43	odd	12
650.2.n.a.49.2		4	5.4	even	2
650.2.n.a.199.2		4	13.4	even	6
650.2.n.b.49.1		4	1.1	even	1	trivial
650.2.n.b.199.1		4	65.4	even	6	inner
1040.2.da.a.641.2		4	260.147	even	12
1040.2.da.a.881.2		4	20.7	even	4
1170.2.bs.c.361.2		4	15.2	even	4
1170.2.bs.c.901.2		4	195.17	even	12
1690.2.a.j.1.2		2	65.2	even	12
1690.2.a.m.1.2		2	65.37	even	12
1690.2.d.f.1351.2		4	65.42	odd	12
1690.2.d.f.1351.4		4	65.62	odd	12
1690.2.e.l.191.1		4	65.7	even	12
1690.2.e.l.991.1		4	65.47	even	4
1690.2.e.n.191.1		4	65.32	even	12
1690.2.e.n.991.1		4	65.57	even	4
1690.2.l.g.361.2		4	65.12	odd	4
1690.2.l.g.1161.2		4	65.22	odd	12
8450.2.a.bf.1.1		2	65.63	even	12
8450.2.a.bm.1.1		2	65.28	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

Introduction

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