LMFDB - Embedded newform 338.3.f.b.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,3,Mod(19,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(12))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("338.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.f (of order $12$, degree $4$, 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:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.89
Dual form			338.3.f.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-3.00000 - 3.00000i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-3.00000 - 3.00000i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.50000 - 7.79423i) q^{9} +(-5.19615 + 3.00000i) q^{10} +(-8.19615 - 2.19615i) q^{11} +4.00000 q^{14} +(2.00000 + 3.46410i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(-9.00000 - 9.00000i) q^{18} +(-35.5167 + 9.51666i) q^{19} +(2.19615 + 8.19615i) q^{20} +(-6.00000 + 10.3923i) q^{22} +(-20.7846 + 12.0000i) q^{23} -7.00000i q^{25} +(1.46410 - 5.46410i) q^{28} +(24.0000 + 41.5692i) q^{29} +(-14.0000 - 14.0000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-6.00000 + 6.00000i) q^{34} +(6.00000 - 10.3923i) q^{35} +(-15.5885 + 9.00000i) q^{36} +(-50.5429 - 13.5429i) q^{37} +52.0000i q^{38} +12.0000 q^{40} +(-3.29423 + 12.2942i) q^{41} +(-31.1769 - 18.0000i) q^{43} +(12.0000 + 12.0000i) q^{44} +(-36.8827 + 9.88269i) q^{45} +(8.78461 + 32.7846i) q^{46} +(42.0000 - 42.0000i) q^{47} +(35.5070 - 20.5000i) q^{49} +(-9.56218 - 2.56218i) q^{50} +30.0000 q^{53} +(18.0000 + 31.1769i) q^{55} +(-6.92820 - 4.00000i) q^{56} +(65.5692 - 17.5692i) q^{58} +(-19.7654 - 73.7654i) q^{59} +(9.00000 - 15.5885i) q^{61} +(-24.2487 + 14.0000i) q^{62} +(24.5885 + 6.58846i) q^{63} -8.00000i q^{64} +(-8.05256 + 30.0526i) q^{67} +(6.00000 + 10.3923i) q^{68} +(-12.0000 - 12.0000i) q^{70} +(-8.19615 + 2.19615i) q^{71} +(6.58846 + 24.5885i) q^{72} +(17.0000 - 17.0000i) q^{73} +(-37.0000 + 64.0859i) q^{74} +(71.0333 + 19.0333i) q^{76} -24.0000i q^{77} -108.000 q^{79} +(4.39230 - 16.3923i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(15.5885 + 9.00000i) q^{82} +(78.0000 + 78.0000i) q^{83} +(6.58846 + 24.5885i) q^{85} +(-36.0000 + 36.0000i) q^{86} +(20.7846 - 12.0000i) q^{88} +(12.2942 + 3.29423i) q^{89} +54.0000i q^{90} +48.0000 q^{92} +(-42.0000 - 72.7461i) q^{94} +(135.100 + 78.0000i) q^{95} +(64.2032 - 17.2032i) q^{97} +(-15.0070 - 56.0070i) q^{98} +(-54.0000 + 54.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 12 q^{5} - 4 q^{7} - 8 q^{8} + 18 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 12 * q^5 - 4 * q^7 - 8 * q^8 + 18 * q^9	$ 4 q - 2 q^{2} - 12 q^{5} - 4 q^{7} - 8 q^{8} + 18 q^{9} - 12 q^{11} + 16 q^{14} + 8 q^{16} - 36 q^{18} - 52 q^{19} - 12 q^{20} - 24 q^{22} - 8 q^{28} + 96 q^{29} - 56 q^{31} + 8 q^{32} - 24 q^{34} + 24 q^{35} - 74 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{44} - 54 q^{45} - 48 q^{46} + 168 q^{47} - 14 q^{50} + 120 q^{53} + 72 q^{55} + 96 q^{58} + 108 q^{59} + 36 q^{61} + 36 q^{63} + 44 q^{67} + 24 q^{68} - 48 q^{70} - 12 q^{71} - 36 q^{72} + 68 q^{73} - 148 q^{74} + 104 q^{76} - 432 q^{79} - 24 q^{80} - 162 q^{81} + 312 q^{83} - 36 q^{85} - 144 q^{86} + 18 q^{89} + 192 q^{92} - 168 q^{94} + 94 q^{97} + 82 q^{98} - 216 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 12 * q^5 - 4 * q^7 - 8 * q^8 + 18 * q^9 - 12 * q^11 + 16 * q^14 + 8 * q^16 - 36 * q^18 - 52 * q^19 - 12 * q^20 - 24 * q^22 - 8 * q^28 + 96 * q^29 - 56 * q^31 + 8 * q^32 - 24 * q^34 + 24 * q^35 - 74 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^44 - 54 * q^45 - 48 * q^46 + 168 * q^47 - 14 * q^50 + 120 * q^53 + 72 * q^55 + 96 * q^58 + 108 * q^59 + 36 * q^61 + 36 * q^63 + 44 * q^67 + 24 * q^68 - 48 * q^70 - 12 * q^71 - 36 * q^72 + 68 * q^73 - 148 * q^74 + 104 * q^76 - 432 * q^79 - 24 * q^80 - 162 * q^81 + 312 * q^83 - 36 * q^85 - 144 * q^86 + 18 * q^89 + 192 * q^92 - 168 * q^94 + 94 * q^97 + 82 * q^98 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	−3.00000	−	3.00000i	−0.600000	−	0.600000i	0.340312	−	0.940312i	$-0.389467\pi$
$5$	−3.00000	−	3.00000i	−0.600000	−	0.600000i	−0.940312	+	0.340312i	$0.889467\pi$
$6$		0			0
$7$	0.732051	+	2.73205i	0.104579	+	0.390293i	0.998297	−	0.0583355i	$-0.0185793\pi$
$7$	0.732051	+	2.73205i	0.104579	+	0.390293i	−0.893718	+	0.448628i	$0.851913\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	4.50000	−	7.79423i	0.500000	−	0.866025i
$10$	−5.19615	+	3.00000i	−0.519615	+	0.300000i
$11$	−8.19615	−	2.19615i	−0.745105	−	0.199650i	−0.133759	−	0.991014i	$-0.542705\pi$
$11$	−8.19615	−	2.19615i	−0.745105	−	0.199650i	−0.611346	+	0.791364i	$0.709371\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$	4.00000			0.285714
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−5.19615	−	3.00000i	−0.305656	−	0.176471i	0.339325	−	0.940669i	$-0.389801\pi$
$17$	−5.19615	−	3.00000i	−0.305656	−	0.176471i	−0.644981	+	0.764199i	$0.723135\pi$
$18$	−9.00000	−	9.00000i	−0.500000	−	0.500000i
$19$	−35.5167	+	9.51666i	−1.86930	+	0.500877i	−0.869320	+	0.494250i	$0.835443\pi$
$19$	−35.5167	+	9.51666i	−1.86930	+	0.500877i	−0.999978	+	0.00662699i	$0.997891\pi$
$20$	2.19615	+	8.19615i	0.109808	+	0.409808i
$21$		0			0
$22$	−6.00000	+	10.3923i	−0.272727	+	0.472377i
$23$	−20.7846	+	12.0000i	−0.903679	+	0.521739i	−0.878392	−	0.477941i	$-0.841383\pi$
$23$	−20.7846	+	12.0000i	−0.903679	+	0.521739i	−0.0252868	+	0.999680i	$0.508050\pi$
$24$		0			0
$25$		−	7.00000i		−	0.280000i
$26$		0			0
$27$		0			0
$28$	1.46410	−	5.46410i	0.0522893	−	0.195146i
$29$	24.0000	+	41.5692i	0.827586	+	1.43342i	0.899927	+	0.436041i	$0.143620\pi$
$29$	24.0000	+	41.5692i	0.827586	+	1.43342i	−0.0723404	+	0.997380i	$0.523047\pi$
$30$		0			0
$31$	−14.0000	−	14.0000i	−0.451613	−	0.451613i	0.444277	−	0.895890i	$-0.353461\pi$
$31$	−14.0000	−	14.0000i	−0.451613	−	0.451613i	−0.895890	+	0.444277i	$0.853461\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$		0			0
$34$	−6.00000	+	6.00000i	−0.176471	+	0.176471i
$35$	6.00000	−	10.3923i	0.171429	−	0.296923i
$36$	−15.5885	+	9.00000i	−0.433013	+	0.250000i
$37$	−50.5429	−	13.5429i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	−50.5429	−	13.5429i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$38$			52.0000i			1.36842i
$39$		0			0
$40$	12.0000			0.300000
$41$	−3.29423	+	12.2942i	−0.0803470	+	0.299859i	−0.994392	−	0.105753i	$-0.966275\pi$
$41$	−3.29423	+	12.2942i	−0.0803470	+	0.299859i	0.914045	+	0.405612i	$0.132942\pi$
$42$		0			0
$43$	−31.1769	−	18.0000i	−0.725045	−	0.418605i	0.0915620	−	0.995799i	$-0.470814\pi$
$43$	−31.1769	−	18.0000i	−0.725045	−	0.418605i	−0.816607	+	0.577195i	$0.804147\pi$
$44$	12.0000	+	12.0000i	0.272727	+	0.272727i
$45$	−36.8827	+	9.88269i	−0.819615	+	0.219615i
$46$	8.78461	+	32.7846i	0.190970	+	0.712709i
$47$	42.0000	−	42.0000i	0.893617	−	0.893617i	−0.101245	−	0.994862i	$-0.532282\pi$
$47$	42.0000	−	42.0000i	0.893617	−	0.893617i	0.994862	+	0.101245i	$0.0322825\pi$
$48$		0			0
$49$	35.5070	−	20.5000i	0.724634	−	0.418367i
$50$	−9.56218	−	2.56218i	−0.191244	−	0.0512436i
$51$		0			0
$52$		0			0
$53$	30.0000			0.566038			0.283019	−	0.959114i	$-0.408664\pi$
$53$	30.0000			0.566038			0.283019	+	0.959114i	$0.408664\pi$
$54$		0			0
$55$	18.0000	+	31.1769i	0.327273	+	0.566853i
$56$	−6.92820	−	4.00000i	−0.123718	−	0.0714286i
$57$		0			0
$58$	65.5692	−	17.5692i	1.13050	−	0.302918i
$59$	−19.7654	−	73.7654i	−0.335006	−	1.25026i	−0.903862	−	0.427823i	$-0.859281\pi$
$59$	−19.7654	−	73.7654i	−0.335006	−	1.25026i	0.568856	−	0.822437i	$-0.307386\pi$
$60$		0			0
$61$	9.00000	−	15.5885i	0.147541	−	0.255548i	−0.782777	−	0.622302i	$-0.786198\pi$
$61$	9.00000	−	15.5885i	0.147541	−	0.255548i	0.930318	+	0.366754i	$0.119531\pi$
$62$	−24.2487	+	14.0000i	−0.391108	+	0.225806i
$63$	24.5885	+	6.58846i	0.390293	+	0.104579i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−8.05256	+	30.0526i	−0.120187	+	0.448546i	−0.999623	−	0.0274732i	$-0.991254\pi$
$67$	−8.05256	+	30.0526i	−0.120187	+	0.448546i	0.879435	+	0.476019i	$0.157921\pi$
$68$	6.00000	+	10.3923i	0.0882353	+	0.152828i
$69$		0			0
$70$	−12.0000	−	12.0000i	−0.171429	−	0.171429i
$71$	−8.19615	+	2.19615i	−0.115439	+	0.0309317i	−0.316076	−	0.948734i	$-0.602365\pi$
$71$	−8.19615	+	2.19615i	−0.115439	+	0.0309317i	0.200637	+	0.979666i	$0.435699\pi$
$72$	6.58846	+	24.5885i	0.0915064	+	0.341506i
$73$	17.0000	−	17.0000i	0.232877	−	0.232877i	−0.581016	−	0.813892i	$-0.697345\pi$
$73$	17.0000	−	17.0000i	0.232877	−	0.232877i	0.813892	+	0.581016i	$0.197345\pi$
$74$	−37.0000	+	64.0859i	−0.500000	+	0.866025i
$75$		0			0
$76$	71.0333	+	19.0333i	0.934649	+	0.250438i
$77$		−	24.0000i		−	0.311688i
$78$		0			0
$79$	−108.000			−1.36709			−0.683544	−	0.729909i	$-0.739562\pi$
$79$	−108.000			−1.36709			−0.683544	+	0.729909i	$0.739562\pi$
$80$	4.39230	−	16.3923i	0.0549038	−	0.204904i
$81$	−40.5000	−	70.1481i	−0.500000	−	0.866025i
$82$	15.5885	+	9.00000i	0.190103	+	0.109756i
$83$	78.0000	+	78.0000i	0.939759	+	0.939759i	0.998286	−	0.0585268i	$-0.0186403\pi$
$83$	78.0000	+	78.0000i	0.939759	+	0.939759i	−0.0585268	+	0.998286i	$0.518640\pi$
$84$		0			0
$85$	6.58846	+	24.5885i	0.0775113	+	0.289276i
$86$	−36.0000	+	36.0000i	−0.418605	+	0.418605i
$87$		0			0
$88$	20.7846	−	12.0000i	0.236189	−	0.136364i
$89$	12.2942	+	3.29423i	0.138137	+	0.0370138i	0.327225	−	0.944946i	$-0.393886\pi$
$89$	12.2942	+	3.29423i	0.138137	+	0.0370138i	−0.189088	+	0.981960i	$0.560553\pi$
$90$			54.0000i			0.600000i
$91$		0			0
$92$	48.0000			0.521739
$93$		0			0
$94$	−42.0000	−	72.7461i	−0.446809	−	0.773895i
$95$	135.100	+	78.0000i	1.42210	+	0.821053i
$96$		0			0
$97$	64.2032	−	17.2032i	0.661889	−	0.177353i	0.0877904	−	0.996139i	$-0.472019\pi$
$97$	64.2032	−	17.2032i	0.661889	−	0.177353i	0.574098	+	0.818786i	$0.305353\pi$
$98$	−15.0070	−	56.0070i	−0.153133	−	0.571500i
$99$	−54.0000	+	54.0000i	−0.545455	+	0.545455i
$100$	−7.00000	+	12.1244i	−0.0700000	+	0.121244i
$101$	103.923	−	60.0000i	1.02894	−	0.594059i	0.112260	−	0.993679i	$-0.464191\pi$
$101$	103.923	−	60.0000i	1.02894	−	0.594059i	0.916681	+	0.399619i	$0.130858\pi$
$102$		0			0
$103$		−	144.000i		−	1.39806i	−0.715093	−	0.699029i	$-0.753616\pi$
$103$		−	144.000i		−	1.39806i	0.715093	−	0.699029i	$-0.246384\pi$
$104$		0			0
$105$		0			0
$106$	10.9808	−	40.9808i	0.103592	−	0.386611i
$107$	−60.0000	−	103.923i	−0.560748	−	0.971243i	−0.997431	−	0.0716283i	$-0.977180\pi$
$107$	−60.0000	−	103.923i	−0.560748	−	0.971243i	0.436684	−	0.899615i	$-0.356153\pi$
$108$		0			0
$109$	−19.0000	−	19.0000i	−0.174312	−	0.174312i	0.614559	−	0.788871i	$-0.289334\pi$
$109$	−19.0000	−	19.0000i	−0.174312	−	0.174312i	−0.788871	+	0.614559i	$0.789334\pi$
$110$	49.1769	−	13.1769i	0.447063	−	0.119790i
$111$		0			0
$112$	−8.00000	+	8.00000i	−0.0714286	+	0.0714286i
$113$	60.0000	−	103.923i	0.530973	−	0.919673i	−0.468373	−	0.883531i	$-0.655160\pi$
$113$	60.0000	−	103.923i	0.530973	−	0.919673i	0.999347	−	0.0361423i	$-0.0115069\pi$
$114$		0			0
$115$	98.3538	+	26.3538i	0.855251	+	0.229164i
$116$		−	96.0000i		−	0.827586i
$117$		0			0
$118$	−108.000			−0.915254
$119$	4.39230	−	16.3923i	0.0369101	−	0.137750i
$120$		0			0
$121$	−42.4352	−	24.5000i	−0.350705	−	0.202479i
$122$	−18.0000	−	18.0000i	−0.147541	−	0.147541i
$123$		0			0
$124$	10.2487	+	38.2487i	0.0826509	+	0.308457i
$125$	−96.0000	+	96.0000i	−0.768000	+	0.768000i
$126$	18.0000	−	31.1769i	0.142857	−	0.247436i
$127$	48.4974	−	28.0000i	0.381869	−	0.220472i	−0.296762	−	0.954952i	$-0.595907\pi$
$127$	48.4974	−	28.0000i	0.381869	−	0.220472i	0.678631	+	0.734479i	$0.262573\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$		0			0
$130$		0			0
$131$	72.0000			0.549618			0.274809	−	0.961499i	$-0.411385\pi$
$131$	72.0000			0.549618			0.274809	+	0.961499i	$0.411385\pi$
$132$		0			0
$133$	−52.0000	−	90.0666i	−0.390977	−	0.677193i
$134$	38.1051	+	22.0000i	0.284367	+	0.164179i
$135$		0			0
$136$	16.3923	−	4.39230i	0.120532	−	0.0322964i
$137$	−23.0596	−	86.0596i	−0.168318	−	0.628172i	−0.997594	−	0.0693321i	$-0.977913\pi$
$137$	−23.0596	−	86.0596i	−0.168318	−	0.628172i	0.829275	−	0.558840i	$-0.188753\pi$
$138$		0			0
$139$	−76.0000	+	131.636i	−0.546763	+	0.947021i	0.451731	+	0.892154i	$0.350807\pi$
$139$	−76.0000	+	131.636i	−0.546763	+	0.947021i	−0.998494	+	0.0548664i	$0.982527\pi$
$140$	−20.7846	+	12.0000i	−0.148461	+	0.0857143i
$141$		0			0
$142$			12.0000i			0.0845070i
$143$		0			0
$144$	36.0000			0.250000
$145$	52.7077	−	196.708i	0.363501	−	1.35660i
$146$	−17.0000	−	29.4449i	−0.116438	−	0.201677i
$147$		0			0
$148$	74.0000	+	74.0000i	0.500000	+	0.500000i
$149$	135.237	−	36.2365i	0.907628	−	0.243198i	0.225338	−	0.974281i	$-0.427651\pi$
$149$	135.237	−	36.2365i	0.907628	−	0.243198i	0.682289	+	0.731082i	$0.260985\pi$
$150$		0			0
$151$	106.000	−	106.000i	0.701987	−	0.701987i	−0.262850	−	0.964837i	$-0.584662\pi$
$151$	106.000	−	106.000i	0.701987	−	0.701987i	0.964837	+	0.262850i	$0.0846624\pi$
$152$	52.0000	−	90.0666i	0.342105	−	0.592544i
$153$	−46.7654	+	27.0000i	−0.305656	+	0.176471i
$154$	−32.7846	−	8.78461i	−0.212887	−	0.0570429i
$155$			84.0000i			0.541935i
$156$		0			0
$157$	−80.0000			−0.509554			−0.254777	−	0.967000i	$-0.582002\pi$
$157$	−80.0000			−0.509554			−0.254777	+	0.967000i	$0.582002\pi$
$158$	−39.5307	+	147.531i	−0.250195	+	0.933739i
$159$		0			0
$160$	−20.7846	−	12.0000i	−0.129904	−	0.0750000i
$161$	−48.0000	−	48.0000i	−0.298137	−	0.298137i
$162$	−110.648	+	29.6481i	−0.683013	+	0.183013i
$163$	30.0141	+	112.014i	0.184135	+	0.687203i	0.994814	+	0.101711i	$0.0324318\pi$
$163$	30.0141	+	112.014i	0.184135	+	0.687203i	−0.810678	+	0.585492i	$0.800902\pi$
$164$	18.0000	−	18.0000i	0.109756	−	0.109756i
$165$		0			0
$166$	135.100	−	78.0000i	0.813855	−	0.469880i
$167$	188.512	+	50.5115i	1.12881	+	0.302464i	0.774444	−	0.632642i	$-0.218030\pi$
$167$	188.512	+	50.5115i	1.12881	+	0.302464i	0.354367	+	0.935106i	$0.384696\pi$
$168$		0			0
$169$		0			0
$170$	36.0000			0.211765
$171$	−85.6499	+	319.650i	−0.500877	+	1.86930i
$172$	36.0000	+	62.3538i	0.209302	+	0.362522i
$173$	20.7846	+	12.0000i	0.120142	+	0.0693642i	0.558867	−	0.829257i	$-0.311236\pi$
$173$	20.7846	+	12.0000i	0.120142	+	0.0693642i	−0.438725	+	0.898622i	$0.644570\pi$
$174$		0			0
$175$	19.1244	−	5.12436i	0.109282	−	0.0292820i
$176$	−8.78461	−	32.7846i	−0.0499126	−	0.186276i
$177$		0			0
$178$	9.00000	−	15.5885i	0.0505618	−	0.0875756i
$179$	−259.808	+	150.000i	−1.45144	+	0.837989i	−0.998563	−	0.0535847i	$-0.982935\pi$
$179$	−259.808	+	150.000i	−1.45144	+	0.837989i	−0.452876	+	0.891574i	$0.649602\pi$
$180$	73.7654	+	19.7654i	0.409808	+	0.109808i
$181$			90.0000i			0.497238i	0.968601	+	0.248619i	$0.0799766\pi$
$181$			90.0000i			0.497238i	−0.968601	+	0.248619i	$0.920023\pi$
$182$		0			0
$183$		0			0
$184$	17.5692	−	65.5692i	0.0954849	−	0.356354i
$185$	111.000	+	192.258i	0.600000	+	1.03923i
$186$		0			0
$187$	36.0000	+	36.0000i	0.192513	+	0.192513i
$188$	−114.746	+	30.7461i	−0.610352	+	0.163543i
$189$		0			0
$190$	156.000	−	156.000i	0.821053	−	0.821053i
$191$	−126.000	+	218.238i	−0.659686	+	1.14261i	0.321011	+	0.947075i	$0.395977\pi$
$191$	−126.000	+	218.238i	−0.659686	+	1.14261i	−0.980697	+	0.195534i	$0.937356\pi$
$192$		0			0
$193$	−351.069	−	94.0685i	−1.81901	−	0.487402i	−0.822342	−	0.568993i	$-0.807333\pi$
$193$	−351.069	−	94.0685i	−1.81901	−	0.487402i	−0.996666	+	0.0815917i	$0.974000\pi$
$194$		−	94.0000i		−	0.484536i
$195$		0			0
$196$	−82.0000			−0.418367
$197$	45.0211	−	168.021i	0.228534	−	0.852899i	−0.752424	−	0.658679i	$-0.771116\pi$
$197$	45.0211	−	168.021i	0.228534	−	0.852899i	0.980958	−	0.194220i	$-0.0622177\pi$
$198$	54.0000	+	93.5307i	0.272727	+	0.472377i
$199$	−173.205	−	100.000i	−0.870377	−	0.502513i	−0.00290369	−	0.999996i	$-0.500924\pi$
$199$	−173.205	−	100.000i	−0.870377	−	0.502513i	−0.867474	+	0.497483i	$0.834258\pi$
$200$	14.0000	+	14.0000i	0.0700000	+	0.0700000i
$201$		0			0
$202$	−43.9230	−	163.923i	−0.217441	−	0.811500i
$203$	−96.0000	+	96.0000i	−0.472906	+	0.472906i
$204$		0			0
$205$	46.7654	−	27.0000i	0.228124	−	0.131707i
$206$	−196.708	−	52.7077i	−0.954892	−	0.255862i
$207$			216.000i			1.04348i
$208$		0			0
$209$	312.000			1.49282
$210$		0			0
$211$	144.000	+	249.415i	0.682464	+	1.18206i	0.974226	+	0.225572i	$0.0724251\pi$
$211$	144.000	+	249.415i	0.682464	+	1.18206i	−0.291762	+	0.956491i	$0.594242\pi$
$212$	−51.9615	−	30.0000i	−0.245102	−	0.141509i
$213$		0			0
$214$	−163.923	+	43.9230i	−0.765996	+	0.205248i
$215$	39.5307	+	147.531i	0.183864	+	0.686190i
$216$		0			0
$217$	28.0000	−	48.4974i	0.129032	−	0.223490i
$218$	−32.9090	+	19.0000i	−0.150959	+	0.0871560i
$219$		0			0
$220$		−	72.0000i		−	0.327273i
$221$		0			0
$222$		0			0
$223$	13.9090	−	51.9090i	0.0623720	−	0.232776i	−0.927702	−	0.373321i	$-0.878219\pi$
$223$	13.9090	−	51.9090i	0.0623720	−	0.232776i	0.990074	+	0.140546i	$0.0448856\pi$
$224$	8.00000	+	13.8564i	0.0357143	+	0.0618590i
$225$	−54.5596	−	31.5000i	−0.242487	−	0.140000i
$226$	−120.000	−	120.000i	−0.530973	−	0.530973i
$227$	−188.512	+	50.5115i	−0.830447	+	0.222518i	−0.648909	−	0.760866i	$-0.724774\pi$
$227$	−188.512	+	50.5115i	−0.830447	+	0.222518i	−0.181538	+	0.983384i	$0.558108\pi$
$228$		0			0
$229$	131.000	−	131.000i	0.572052	−	0.572052i	−0.360649	−	0.932702i	$-0.617445\pi$
$229$	131.000	−	131.000i	0.572052	−	0.572052i	0.932702	+	0.360649i	$0.117445\pi$
$230$	72.0000	−	124.708i	0.313043	−	0.542207i
$231$		0			0
$232$	−131.138	−	35.1384i	−0.565252	−	0.151459i
$233$			336.000i			1.44206i	0.692904	+	0.721030i	$0.256331\pi$
$233$			336.000i			1.44206i	−0.692904	+	0.721030i	$0.743669\pi$
$234$		0			0
$235$	−252.000			−1.07234
$236$	−39.5307	+	147.531i	−0.167503	+	0.625130i
$237$		0			0
$238$	−20.7846	−	12.0000i	−0.0873303	−	0.0504202i
$239$	−114.000	−	114.000i	−0.476987	−	0.476987i	0.427179	−	0.904167i	$-0.359507\pi$
$239$	−114.000	−	114.000i	−0.476987	−	0.476987i	−0.904167	+	0.427179i	$0.859507\pi$
$240$		0			0
$241$	55.2698	+	206.270i	0.229335	+	0.855891i	0.980621	+	0.195914i	$0.0627674\pi$
$241$	55.2698	+	206.270i	0.229335	+	0.855891i	−0.751286	+	0.659977i	$0.770566\pi$
$242$	−49.0000	+	49.0000i	−0.202479	+	0.202479i
$243$		0			0
$244$	−31.1769	+	18.0000i	−0.127774	+	0.0737705i
$245$	−168.021	−	45.0211i	−0.685801	−	0.183760i
$246$		0			0
$247$		0			0
$248$	56.0000			0.225806
$249$		0			0
$250$	96.0000	+	166.277i	0.384000	+	0.665108i
$251$	155.885	+	90.0000i	0.621054	+	0.358566i	0.777279	−	0.629156i	$-0.216599\pi$
$251$	155.885	+	90.0000i	0.621054	+	0.358566i	−0.156225	+	0.987721i	$0.549933\pi$
$252$	−36.0000	−	36.0000i	−0.142857	−	0.142857i
$253$	196.708	−	52.7077i	0.777501	−	0.208331i
$254$	−20.4974	−	76.4974i	−0.0806985	−	0.301171i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−124.708	+	72.0000i	−0.485244	+	0.280156i	−0.722599	−	0.691267i	$-0.757053\pi$
$257$	−124.708	+	72.0000i	−0.485244	+	0.280156i	0.237355	+	0.971423i	$0.423719\pi$
$258$		0			0
$259$		−	148.000i		−	0.571429i
$260$		0			0
$261$	432.000			1.65517
$262$	26.3538	−	98.3538i	0.100587	−	0.375396i
$263$	30.0000	+	51.9615i	0.114068	+	0.197572i	0.917407	−	0.397950i	$-0.130278\pi$
$263$	30.0000	+	51.9615i	0.114068	+	0.197572i	−0.803339	+	0.595523i	$0.796945\pi$
$264$		0			0
$265$	−90.0000	−	90.0000i	−0.339623	−	0.339623i
$266$	−142.067	+	38.0666i	−0.534085	+	0.143108i
$267$		0			0
$268$	44.0000	−	44.0000i	0.164179	−	0.164179i
$269$	144.000	−	249.415i	0.535316	−	0.927194i	−0.463832	−	0.885923i	$-0.653526\pi$
$269$	144.000	−	249.415i	0.535316	−	0.927194i	0.999148	−	0.0412713i	$-0.0131408\pi$
$270$		0			0
$271$	183.047	+	49.0474i	0.675452	+	0.180987i	0.580209	−	0.814467i	$-0.302971\pi$
$271$	183.047	+	49.0474i	0.675452	+	0.180987i	0.0952423	+	0.995454i	$0.469637\pi$
$272$		−	24.0000i		−	0.0882353i
$273$		0			0
$274$	−126.000			−0.459854
$275$	−15.3731	+	57.3731i	−0.0559021	+	0.208629i
$276$		0			0
$277$	−187.061	−	108.000i	−0.675312	−	0.389892i	0.122774	−	0.992435i	$-0.460821\pi$
$277$	−187.061	−	108.000i	−0.675312	−	0.389892i	−0.798086	+	0.602543i	$0.794154\pi$
$278$	152.000	+	152.000i	0.546763	+	0.546763i
$279$	−172.119	+	46.1192i	−0.616915	+	0.165302i
$280$	8.78461	+	32.7846i	0.0313736	+	0.117088i
$281$	−159.000	+	159.000i	−0.565836	+	0.565836i	−0.930959	−	0.365123i	$-0.881027\pi$
$281$	−159.000	+	159.000i	−0.565836	+	0.565836i	0.365123	+	0.930959i	$0.381027\pi$
$282$		0			0
$283$	−349.874	+	202.000i	−1.23630	+	0.713781i	−0.968337	−	0.249647i	$-0.919685\pi$
$283$	−349.874	+	202.000i	−1.23630	+	0.713781i	−0.267968	+	0.963428i	$0.586352\pi$
$284$	16.3923	+	4.39230i	0.0577194	+	0.0154659i
$285$		0			0
$286$		0			0
$287$	−36.0000			−0.125436
$288$	13.1769	−	49.1769i	0.0457532	−	0.170753i
$289$	−126.500	−	219.104i	−0.437716	−	0.758147i
$290$	−249.415	−	144.000i	−0.860053	−	0.496552i
$291$		0			0
$292$	−46.4449	+	12.4449i	−0.159058	+	0.0426194i
$293$	53.8057	+	200.806i	0.183637	+	0.685344i	0.994918	+	0.100687i	$0.0321041\pi$
$293$	53.8057	+	200.806i	0.183637	+	0.685344i	−0.811281	+	0.584657i	$0.801229\pi$
$294$		0			0
$295$	−162.000	+	280.592i	−0.549153	+	0.951160i
$296$	128.172	−	74.0000i	0.433013	−	0.250000i
$297$		0			0
$298$		−	198.000i		−	0.664430i
$299$		0			0
$300$		0			0
$301$	26.3538	−	98.3538i	0.0875542	−	0.326757i
$302$	−106.000	−	183.597i	−0.350993	−	0.607938i
$303$		0			0
$304$	−104.000	−	104.000i	−0.342105	−	0.342105i
$305$	−73.7654	+	19.7654i	−0.241854	+	0.0648045i
$306$	19.7654	+	73.7654i	0.0645927	+	0.241063i
$307$	82.0000	−	82.0000i	0.267101	−	0.267101i	−0.560830	−	0.827931i	$-0.689518\pi$
$307$	82.0000	−	82.0000i	0.267101	−	0.267101i	0.827931	+	0.560830i	$0.189518\pi$
$308$	−24.0000	+	41.5692i	−0.0779221	+	0.134965i
$309$		0			0
$310$	114.746	+	30.7461i	0.370149	+	0.0991811i
$311$		−	120.000i		−	0.385852i	−0.981213	−	0.192926i	$-0.938202\pi$
$311$		−	120.000i		−	0.385852i	0.981213	−	0.192926i	$-0.0617977\pi$
$312$		0			0
$313$	−360.000			−1.15016			−0.575080	−	0.818097i	$-0.695029\pi$
$313$	−360.000			−1.15016			−0.575080	+	0.818097i	$0.695029\pi$
$314$	−29.2820	+	109.282i	−0.0932549	+	0.348032i
$315$	−54.0000	−	93.5307i	−0.171429	−	0.296923i
$316$	187.061	+	108.000i	0.591967	+	0.341772i
$317$	−147.000	−	147.000i	−0.463722	−	0.463722i	0.436151	−	0.899873i	$-0.356341\pi$
$317$	−147.000	−	147.000i	−0.463722	−	0.463722i	−0.899873	+	0.436151i	$0.856341\pi$
$318$		0			0
$319$	−105.415	−	393.415i	−0.330456	−	1.23328i
$320$	−24.0000	+	24.0000i	−0.0750000	+	0.0750000i
$321$		0			0
$322$	−83.1384	+	48.0000i	−0.258194	+	0.149068i
$323$	213.100	+	57.1000i	0.659752	+	0.176780i
$324$			162.000i			0.500000i
$325$		0			0
$326$	164.000			0.503067
$327$		0			0
$328$	−18.0000	−	31.1769i	−0.0548780	−	0.0950516i
$329$	145.492	+	84.0000i	0.442226	+	0.255319i
$330$		0			0
$331$	292.329	−	78.3294i	0.883171	−	0.236645i	0.211396	−	0.977401i	$-0.432199\pi$
$331$	292.329	−	78.3294i	0.883171	−	0.236645i	0.671775	+	0.740756i	$0.265532\pi$
$332$	−57.1000	−	213.100i	−0.171988	−	0.641867i
$333$	−333.000	+	333.000i	−1.00000	+	1.00000i
$334$	138.000	−	239.023i	0.413174	−	0.715638i
$335$	114.315	−	66.0000i	0.341240	−	0.197015i
$336$		0			0
$337$		−	314.000i		−	0.931751i	−0.884850	−	0.465875i	$-0.845740\pi$
$337$		−	314.000i		−	0.931751i	0.884850	−	0.465875i	$-0.154260\pi$
$338$		0			0
$339$		0			0
$340$	13.1769	−	49.1769i	0.0387556	−	0.144638i
$341$	84.0000	+	145.492i	0.246334	+	0.426664i
$342$	405.300	+	234.000i	1.18509	+	0.684211i
$343$	180.000	+	180.000i	0.524781	+	0.524781i
$344$	98.3538	−	26.3538i	0.285912	−	0.0766100i
$345$		0			0
$346$	24.0000	−	24.0000i	0.0693642	−	0.0693642i
$347$	60.0000	−	103.923i	0.172911	−	0.299490i	−0.766526	−	0.642214i	$-0.778016\pi$
$347$	60.0000	−	103.923i	0.172911	−	0.299490i	0.939436	+	0.342724i	$0.111349\pi$
$348$		0			0
$349$	−137.969	−	36.9686i	−0.395325	−	0.105927i	0.0556793	−	0.998449i	$-0.482268\pi$
$349$	−137.969	−	36.9686i	−0.395325	−	0.105927i	−0.451005	+	0.892522i	$0.648934\pi$
$350$		−	28.0000i		−	0.0800000i
$351$		0			0
$352$	−48.0000			−0.136364
$353$	12.0788	−	45.0788i	0.0342177	−	0.127702i	−0.946704	−	0.322104i	$-0.895610\pi$
$353$	12.0788	−	45.0788i	0.0342177	−	0.127702i	0.980922	+	0.194402i	$0.0622766\pi$
$354$		0			0
$355$	31.1769	+	18.0000i	0.0878223	+	0.0507042i
$356$	−18.0000	−	18.0000i	−0.0505618	−	0.0505618i
$357$		0			0
$358$	109.808	+	409.808i	0.306725	+	1.14471i
$359$	186.000	−	186.000i	0.518106	−	0.518106i	−0.398892	−	0.916998i	$-0.630605\pi$
$359$	186.000	−	186.000i	0.518106	−	0.518106i	0.916998	+	0.398892i	$0.130605\pi$
$360$	54.0000	−	93.5307i	0.150000	−	0.259808i
$361$	858.231	−	495.500i	2.37737	−	1.37258i
$362$	122.942	+	32.9423i	0.339620	+	0.0910008i
$363$		0			0
$364$		0			0
$365$	−102.000			−0.279452
$366$		0			0
$367$	−290.000	−	502.295i	−0.790191	−	1.36865i	−0.925849	−	0.377895i	$-0.876648\pi$
$367$	−290.000	−	502.295i	−0.790191	−	1.36865i	0.135658	−	0.990756i	$-0.456685\pi$
$368$	−83.1384	−	48.0000i	−0.225920	−	0.130435i
$369$	81.0000	+	81.0000i	0.219512	+	0.219512i
$370$	303.258	−	81.2576i	0.819615	−	0.219615i
$371$	21.9615	+	81.9615i	0.0591955	+	0.220921i
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$	62.3538	−	36.0000i	0.166721	−	0.0962567i
$375$		0			0
$376$			168.000i			0.446809i
$377$		0			0
$378$		0			0
$379$	82.7217	−	308.722i	0.218263	−	0.814569i	−0.766729	−	0.641971i	$-0.778117\pi$
$379$	82.7217	−	308.722i	0.218263	−	0.814569i	0.984992	−	0.172598i	$-0.0552163\pi$
$380$	−156.000	−	270.200i	−0.410526	−	0.711052i
$381$		0			0
$382$	252.000	+	252.000i	0.659686	+	0.659686i
$383$	−106.550	+	28.5500i	−0.278198	+	0.0745430i	−0.395221	−	0.918586i	$-0.629332\pi$
$383$	−106.550	+	28.5500i	−0.278198	+	0.0745430i	0.117022	+	0.993129i	$0.462665\pi$
$384$		0			0
$385$	−72.0000	+	72.0000i	−0.187013	+	0.187013i
$386$	−257.000	+	445.137i	−0.665803	+	1.15320i
$387$	−280.592	+	162.000i	−0.725045	+	0.418605i
$388$	−128.406	−	34.4064i	−0.330944	−	0.0886763i
$389$			150.000i			0.385604i	0.981238	+	0.192802i	$0.0617575\pi$
$389$			150.000i			0.385604i	−0.981238	+	0.192802i	$0.938242\pi$
$390$		0			0
$391$	144.000			0.368286
$392$	−30.0141	+	112.014i	−0.0765665	+	0.285750i
$393$		0			0
$394$	−213.042	−	123.000i	−0.540716	−	0.312183i
$395$	324.000	+	324.000i	0.820253	+	0.820253i
$396$	147.531	−	39.5307i	0.372552	−	0.0998251i
$397$	−92.6044	−	345.604i	−0.233261	−	0.870540i	−0.978925	−	0.204219i	$-0.934535\pi$
$397$	−92.6044	−	345.604i	−0.233261	−	0.870540i	0.745665	−	0.666321i	$-0.232132\pi$
$398$	−200.000	+	200.000i	−0.502513	+	0.502513i
$399$		0			0
$400$	24.2487	−	14.0000i	0.0606218	−	0.0350000i
$401$	340.140	+	91.1403i	0.848230	+	0.227283i	0.656651	−	0.754195i	$-0.271972\pi$
$401$	340.140	+	91.1403i	0.848230	+	0.227283i	0.191579	+	0.981477i	$0.438639\pi$
$402$		0			0
$403$		0			0
$404$	−240.000			−0.594059
$405$	−88.9442	+	331.944i	−0.219615	+	0.819615i
$406$	96.0000	+	166.277i	0.236453	+	0.409549i
$407$	384.515	+	222.000i	0.944755	+	0.545455i
$408$		0			0
$409$	435.762	−	116.762i	1.06543	−	0.285482i	0.316818	−	0.948486i	$-0.397386\pi$
$409$	435.762	−	116.762i	1.06543	−	0.285482i	0.748615	+	0.663005i	$0.230719\pi$
$410$	−19.7654	−	73.7654i	−0.0482082	−	0.179916i
$411$		0			0
$412$	−144.000	+	249.415i	−0.349515	+	0.605377i
$413$	187.061	−	108.000i	0.452933	−	0.261501i
$414$	295.061	+	79.0615i	0.712709	+	0.190970i
$415$		−	468.000i		−	1.12771i
$416$		0			0
$417$		0			0
$418$	114.200	−	426.200i	0.273206	−	1.01962i
$419$	24.0000	+	41.5692i	0.0572792	+	0.0992105i	0.893243	−	0.449574i	$-0.148424\pi$
$419$	24.0000	+	41.5692i	0.0572792	+	0.0992105i	−0.835964	+	0.548784i	$0.815091\pi$
$420$		0			0
$421$	11.0000	+	11.0000i	0.0261283	+	0.0261283i	0.720050	−	0.693922i	$-0.244119\pi$
$421$	11.0000	+	11.0000i	0.0261283	+	0.0261283i	−0.693922	+	0.720050i	$0.744119\pi$
$422$	393.415	−	105.415i	0.932264	−	0.249799i
$423$	−138.358	−	516.358i	−0.327087	−	1.22070i
$424$	−60.0000	+	60.0000i	−0.141509	+	0.141509i
$425$	−21.0000	+	36.3731i	−0.0494118	+	0.0855837i
$426$		0			0
$427$	49.1769	+	13.1769i	0.115168	+	0.0308593i
$428$			240.000i			0.560748i
$429$		0			0
$430$	216.000			0.502326
$431$	−151.535	+	565.535i	−0.351588	+	1.31215i	0.533136	+	0.846030i	$0.321013\pi$
$431$	−151.535	+	565.535i	−0.351588	+	1.31215i	−0.884724	+	0.466115i	$0.845653\pi$
$432$		0			0
$433$	−13.8564	−	8.00000i	−0.0320009	−	0.0184758i	0.483914	−	0.875115i	$-0.339215\pi$
$433$	−13.8564	−	8.00000i	−0.0320009	−	0.0184758i	−0.515915	+	0.856640i	$0.672548\pi$
$434$	−56.0000	−	56.0000i	−0.129032	−	0.129032i
$435$		0			0
$436$	13.9090	+	51.9090i	0.0319013	+	0.119057i
$437$	624.000	−	624.000i	1.42792	−	1.42792i
$438$		0			0
$439$	311.769	−	180.000i	0.710180	−	0.410023i	−0.100947	−	0.994892i	$-0.532187\pi$
$439$	311.769	−	180.000i	0.710180	−	0.410023i	0.811128	+	0.584869i	$0.198854\pi$
$440$	−98.3538	−	26.3538i	−0.223531	−	0.0598951i
$441$		−	369.000i		−	0.836735i
$442$		0			0
$443$	−600.000			−1.35440			−0.677201	−	0.735798i	$-0.736807\pi$
$443$	−600.000			−1.35440			−0.677201	+	0.735798i	$0.736807\pi$
$444$		0			0
$445$	−27.0000	−	46.7654i	−0.0606742	−	0.105091i
$446$	−65.8179	−	38.0000i	−0.147574	−	0.0852018i
$447$		0			0
$448$	21.8564	−	5.85641i	0.0487866	−	0.0130723i
$449$	−3.29423	−	12.2942i	−0.00733681	−	0.0273814i	0.962160	−	0.272484i	$-0.0878451\pi$
$449$	−3.29423	−	12.2942i	−0.00733681	−	0.0273814i	−0.969497	+	0.245102i	$0.921178\pi$
$450$	−63.0000	+	63.0000i	−0.140000	+	0.140000i
$451$	54.0000	−	93.5307i	0.119734	−	0.207385i
$452$	−207.846	+	120.000i	−0.459836	+	0.265487i
$453$		0			0
$454$			276.000i			0.607930i
$455$		0			0
$456$		0			0
$457$	−17.2032	+	64.2032i	−0.0376438	+	0.140488i	−0.982190	−	0.187890i	$-0.939835\pi$
$457$	−17.2032	+	64.2032i	−0.0376438	+	0.140488i	0.944546	+	0.328378i	$0.106502\pi$
$458$	−131.000	−	226.899i	−0.286026	−	0.495412i
$459$		0			0
$460$	−144.000	−	144.000i	−0.313043	−	0.313043i
$461$	−233.590	+	62.5903i	−0.506704	+	0.135771i	−0.503109	−	0.864223i	$-0.667811\pi$
$461$	−233.590	+	62.5903i	−0.506704	+	0.135771i	−0.00359416	+	0.999994i	$0.501144\pi$
$462$		0			0
$463$	202.000	−	202.000i	0.436285	−	0.436285i	−0.454475	−	0.890760i	$-0.650173\pi$
$463$	202.000	−	202.000i	0.436285	−	0.436285i	0.890760	+	0.454475i	$0.150173\pi$
$464$	−96.0000	+	166.277i	−0.206897	+	0.358355i
$465$		0			0
$466$	458.985	+	122.985i	0.984945	+	0.263915i
$467$			516.000i			1.10493i	0.833538	+	0.552463i	$0.186312\pi$
$467$			516.000i			1.10493i	−0.833538	+	0.552463i	$0.813688\pi$
$468$		0			0
$469$	−88.0000			−0.187633
$470$	−92.2384	+	344.238i	−0.196252	+	0.732422i
$471$		0			0
$472$	187.061	+	108.000i	0.396317	+	0.228814i
$473$	216.000	+	216.000i	0.456660	+	0.456660i
$474$		0			0
$475$	66.6166	+	248.617i	0.140246	+	0.523403i
$476$	−24.0000	+	24.0000i	−0.0504202	+	0.0504202i
$477$	135.000	−	233.827i	0.283019	−	0.490203i
$478$	−197.454	+	114.000i	−0.413083	+	0.238494i
$479$	319.650	+	85.6499i	0.667328	+	0.178810i	0.576551	−	0.817061i	$-0.304398\pi$
$479$	319.650	+	85.6499i	0.667328	+	0.178810i	0.0907769	+	0.995871i	$0.471065\pi$
$480$		0			0
$481$		0			0
$482$	302.000			0.626556
$483$		0			0
$484$	49.0000	+	84.8705i	0.101240	+	0.175352i
$485$	−244.219	−	141.000i	−0.503545	−	0.290722i
$486$		0			0
$487$	−407.076	+	109.076i	−0.835884	+	0.223974i	−0.651279	−	0.758838i	$-0.725767\pi$
$487$	−407.076	+	109.076i	−0.835884	+	0.223974i	−0.184605	+	0.982813i	$0.559101\pi$
$488$	13.1769	+	49.1769i	0.0270019	+	0.100772i
$489$		0			0
$490$	−123.000	+	213.042i	−0.251020	+	0.434780i
$491$	363.731	−	210.000i	0.740796	−	0.427699i	−0.0815629	−	0.996668i	$-0.525991\pi$
$491$	363.731	−	210.000i	0.740796	−	0.427699i	0.822359	+	0.568970i	$0.192658\pi$
$492$		0			0
$493$		−	288.000i		−	0.584178i
$494$		0			0
$495$	324.000			0.654545
$496$	20.4974	−	76.4974i	0.0413254	−	0.154229i
$497$	−12.0000	−	20.7846i	−0.0241449	−	0.0418201i
$498$		0			0
$499$	346.000	+	346.000i	0.693387	+	0.693387i	0.962976	−	0.269589i	$-0.0868878\pi$
$499$	346.000	+	346.000i	0.693387	+	0.693387i	−0.269589	+	0.962976i	$0.586888\pi$
$500$	262.277	−	70.2769i	0.524554	−	0.140554i
$501$		0			0
$502$	180.000	−	180.000i	0.358566	−	0.358566i
$503$	210.000	−	363.731i	0.417495	−	0.723123i	−0.578192	−	0.815901i	$-0.696241\pi$
$503$	210.000	−	363.731i	0.417495	−	0.723123i	0.995687	+	0.0927783i	$0.0295748\pi$
$504$	−62.3538	+	36.0000i	−0.123718	+	0.0714286i
$505$	−491.769	−	131.769i	−0.973800	−	0.260929i
$506$		−	288.000i		−	0.569170i
$507$		0			0
$508$	−112.000			−0.220472
$509$	139.456	−	520.456i	0.273980	−	1.02251i	−0.682542	−	0.730846i	$-0.739126\pi$
$509$	139.456	−	520.456i	0.273980	−	1.02251i	0.956522	−	0.291660i	$-0.0942076\pi$
$510$		0			0
$511$	58.8897	+	34.0000i	0.115244	+	0.0665362i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		0			0
$514$	52.7077	+	196.708i	0.102544	+	0.382700i
$515$	−432.000	+	432.000i	−0.838835	+	0.838835i
$516$		0			0
$517$	−436.477	+	252.000i	−0.844249	+	0.487427i
$518$	−202.172	−	54.1718i	−0.390293	−	0.104579i
$519$		0			0
$520$		0			0
$521$	312.000			0.598848			0.299424	−	0.954120i	$-0.403205\pi$
$521$	312.000			0.598848			0.299424	+	0.954120i	$0.403205\pi$
$522$	158.123	−	590.123i	0.302918	−	1.13050i
$523$	280.000	+	484.974i	0.535373	+	0.927293i	0.999145	+	0.0413386i	$0.0131622\pi$
$523$	280.000	+	484.974i	0.535373	+	0.927293i	−0.463772	+	0.885954i	$0.653504\pi$
$524$	−124.708	−	72.0000i	−0.237992	−	0.137405i
$525$		0			0
$526$	81.9615	−	21.9615i	0.155820	−	0.0417519i
$527$	30.7461	+	114.746i	0.0583418	+	0.217735i
$528$		0			0
$529$	23.5000	−	40.7032i	0.0444234	−	0.0769437i
$530$	−155.885	+	90.0000i	−0.294122	+	0.169811i
$531$	−663.888	−	177.888i	−1.25026	−	0.335006i
$532$			208.000i			0.390977i
$533$		0			0
$534$		0			0
$535$	−131.769	+	491.769i	−0.246297	+	0.919195i
$536$	−44.0000	−	76.2102i	−0.0820896	−	0.142183i
$537$		0			0
$538$	−288.000	−	288.000i	−0.535316	−	0.535316i
$539$	−336.042	+	90.0422i	−0.623455	+	0.167054i
$540$		0			0
$541$	−379.000	+	379.000i	−0.700555	+	0.700555i	−0.964530	−	0.263975i	$-0.914966\pi$
$541$	−379.000	+	379.000i	−0.700555	+	0.700555i	0.263975	+	0.964530i	$0.414966\pi$
$542$	134.000	−	232.095i	0.247232	−	0.428219i
$543$		0			0
$544$	−32.7846	−	8.78461i	−0.0602658	−	0.0161482i
$545$			114.000i			0.209174i
$546$		0			0
$547$	−400.000			−0.731261			−0.365631	−	0.930760i	$-0.619147\pi$
$547$	−400.000			−0.731261			−0.365631	+	0.930760i	$0.619147\pi$
$548$	−46.1192	+	172.119i	−0.0841591	+	0.314086i
$549$	−81.0000	−	140.296i	−0.147541	−	0.255548i
$550$	72.7461	+	42.0000i	0.132266	+	0.0763636i
$551$	−1248.00	−	1248.00i	−2.26497	−	2.26497i
$552$		0			0
$553$	−79.0615	−	295.061i	−0.142968	−	0.533565i
$554$	−216.000	+	216.000i	−0.389892	+	0.389892i
$555$		0			0
$556$	263.272	−	152.000i	0.473510	−	0.273381i
$557$	−159.825	−	42.8250i	−0.286939	−	0.0768850i	0.112479	−	0.993654i	$-0.464121\pi$
$557$	−159.825	−	42.8250i	−0.286939	−	0.0768850i	−0.399418	+	0.916769i	$0.630788\pi$
$558$			252.000i			0.451613i
$559$		0			0
$560$	48.0000			0.0857143
$561$		0			0
$562$	159.000	+	275.396i	0.282918	+	0.490029i
$563$	−758.638	−	438.000i	−1.34749	−	0.777975i	−0.359599	−	0.933107i	$-0.617086\pi$
$563$	−758.638	−	438.000i	−1.34749	−	0.777975i	−0.987894	+	0.155132i	$0.950420\pi$
$564$		0			0
$565$	−491.769	+	131.769i	−0.870388	+	0.233220i
$566$	147.874	+	551.874i	0.261262	+	0.975043i
$567$	162.000	−	162.000i	0.285714	−	0.285714i
$568$	12.0000	−	20.7846i	0.0211268	−	0.0365926i
$569$	−623.538	+	360.000i	−1.09585	+	0.632689i	−0.935128	−	0.354311i	$-0.884715\pi$
$569$	−623.538	+	360.000i	−1.09585	+	0.632689i	−0.160722	+	0.987000i	$0.551382\pi$
$570$		0			0
$571$		−	460.000i		−	0.805604i	−0.915287	−	0.402802i	$-0.868036\pi$
$571$		−	460.000i		−	0.805604i	0.915287	−	0.402802i	$-0.131964\pi$
$572$		0			0
$573$		0			0
$574$	−13.1769	+	49.1769i	−0.0229563	+	0.0856741i
$575$	84.0000	+	145.492i	0.146087	+	0.253030i
$576$	−62.3538	−	36.0000i	−0.108253	−	0.0625000i
$577$	−377.000	−	377.000i	−0.653380	−	0.653380i	0.300426	−	0.953805i	$-0.402871\pi$
$577$	−377.000	−	377.000i	−0.653380	−	0.653380i	−0.953805	+	0.300426i	$0.902871\pi$
$578$	−345.604	+	92.6044i	−0.597932	+	0.160215i
$579$		0			0
$580$	−288.000	+	288.000i	−0.496552	+	0.496552i
$581$	−156.000	+	270.200i	−0.268503	+	0.465060i
$582$		0			0
$583$	−245.885	−	65.8846i	−0.421757	−	0.113010i
$584$			68.0000i			0.116438i
$585$		0			0
$586$	294.000			0.501706
$587$	270.127	−	1008.13i	0.460182	−	1.71742i	−0.212208	−	0.977225i	$-0.568065\pi$
$587$	270.127	−	1008.13i	0.460182	−	1.71742i	0.672390	−	0.740197i	$-0.265268\pi$
$588$		0			0
$589$	630.466	+	364.000i	1.07040	+	0.617997i
$590$	324.000	+	324.000i	0.549153	+	0.549153i
$591$		0			0
$592$	−54.1718	−	202.172i	−0.0915064	−	0.341506i
$593$	327.000	−	327.000i	0.551433	−	0.551433i	−0.375421	−	0.926854i	$-0.622502\pi$
$593$	327.000	−	327.000i	0.551433	−	0.551433i	0.926854	+	0.375421i	$0.122502\pi$
$594$		0			0
$595$	−62.3538	+	36.0000i	−0.104796	+	0.0605042i
$596$	−270.473	−	72.4730i	−0.453814	−	0.121599i
$597$		0			0
$598$		0			0
$599$	372.000			0.621035			0.310518	−	0.950568i	$-0.399498\pi$
$599$	372.000			0.621035			0.310518	+	0.950568i	$0.399498\pi$
$600$		0			0
$601$	324.000	+	561.184i	0.539101	+	0.933751i	0.998953	+	0.0457552i	$0.0145694\pi$
$601$	324.000	+	561.184i	0.539101	+	0.933751i	−0.459851	+	0.887996i	$0.652097\pi$
$602$	−124.708	−	72.0000i	−0.207156	−	0.119601i
$603$	198.000	+	198.000i	0.328358	+	0.328358i
$604$	−289.597	+	77.5974i	−0.479466	+	0.128472i
$605$	53.8057	+	200.806i	0.0889351	+	0.331910i
$606$		0			0
$607$	130.000	−	225.167i	0.214168	−	0.370950i	−0.738847	−	0.673873i	$-0.764629\pi$
$607$	130.000	−	225.167i	0.214168	−	0.370950i	0.953015	+	0.302923i	$0.0979627\pi$
$608$	−180.133	+	104.000i	−0.296272	+	0.171053i
$609$		0			0
$610$			108.000i			0.177049i
$611$		0			0
$612$	108.000			0.176471
$613$	−72.1070	+	269.107i	−0.117630	+	0.439000i	−0.999470	−	0.0325478i	$-0.989638\pi$
$613$	−72.1070	+	269.107i	−0.117630	+	0.439000i	0.881840	+	0.471548i	$0.156305\pi$
$614$	−82.0000	−	142.028i	−0.133550	−	0.231316i
$615$		0			0
$616$	48.0000	+	48.0000i	0.0779221	+	0.0779221i
$617$	−1028.62	+	275.617i	−1.66713	+	0.446705i	−0.964334	−	0.264689i	$-0.914731\pi$
$617$	−1028.62	+	275.617i	−1.66713	+	0.446705i	−0.702793	+	0.711395i	$0.748064\pi$
$618$		0			0
$619$	−34.0000	+	34.0000i	−0.0549273	+	0.0549273i	−0.734037	−	0.679110i	$-0.762366\pi$
$619$	−34.0000	+	34.0000i	−0.0549273	+	0.0549273i	0.679110	+	0.734037i	$0.262366\pi$
$620$	84.0000	−	145.492i	0.135484	−	0.234665i
$621$		0			0
$622$	−163.923	−	43.9230i	−0.263542	−	0.0706158i
$623$			36.0000i			0.0577849i
$624$		0			0
$625$	401.000			0.641600
$626$	−131.769	+	491.769i	−0.210494	+	0.785574i
$627$		0			0
$628$	138.564	+	80.0000i	0.220643	+	0.127389i
$629$	222.000	+	222.000i	0.352941	+	0.352941i
$630$	−147.531	+	39.5307i	−0.234176	+	0.0627472i
$631$	141.286	+	527.286i	0.223908	+	0.835635i	0.982839	+	0.184465i	$0.0590551\pi$
$631$	141.286	+	527.286i	0.223908	+	0.835635i	−0.758931	+	0.651171i	$0.774278\pi$
$632$	216.000	−	216.000i	0.341772	−	0.341772i
$633$		0			0
$634$	−254.611	+	147.000i	−0.401595	+	0.231861i
$635$	−229.492	−	61.4923i	−0.361405	−	0.0968382i
$636$		0			0
$637$		0			0
$638$	−576.000			−0.902821
$639$	−19.7654	+	73.7654i	−0.0309317	+	0.115439i
$640$	24.0000	+	41.5692i	0.0375000	+	0.0649519i
$641$	−77.9423	−	45.0000i	−0.121595	−	0.0702028i	0.437969	−	0.898990i	$-0.355698\pi$
$641$	−77.9423	−	45.0000i	−0.121595	−	0.0702028i	−0.559564	+	0.828787i	$0.689031\pi$
$642$		0			0
$643$	275.937	−	73.9371i	0.429140	−	0.114988i	−0.0377823	−	0.999286i	$-0.512029\pi$
$643$	275.937	−	73.9371i	0.429140	−	0.114988i	0.466923	+	0.884298i	$0.345363\pi$
$644$	35.1384	+	131.138i	0.0545628	+	0.203631i
$645$		0			0
$646$	156.000	−	270.200i	0.241486	−	0.418266i
$647$	−124.708	+	72.0000i	−0.192748	+	0.111283i	−0.593268	−	0.805005i	$-0.702163\pi$
$647$	−124.708	+	72.0000i	−0.192748	+	0.111283i	0.400521	+	0.916288i	$0.368829\pi$
$648$	221.296	+	59.2961i	0.341506	+	0.0915064i
$649$			648.000i			0.998459i
$650$		0			0
$651$		0			0
$652$	60.0282	−	224.028i	0.0920677	−	0.343601i
$653$	120.000	+	207.846i	0.183767	+	0.318294i	0.943160	−	0.332338i	$-0.107837\pi$
$653$	120.000	+	207.846i	0.183767	+	0.318294i	−0.759393	+	0.650632i	$0.774504\pi$
$654$		0			0
$655$	−216.000	−	216.000i	−0.329771	−	0.329771i
$656$	−49.1769	+	13.1769i	−0.0749648	+	0.0200868i
$657$	−56.0019	−	209.002i	−0.0852388	−	0.318116i
$658$	168.000	−	168.000i	0.255319	−	0.255319i
$659$	84.0000	−	145.492i	0.127466	−	0.220777i	−0.795228	−	0.606310i	$-0.792649\pi$
$659$	84.0000	−	145.492i	0.127466	−	0.220777i	0.922694	+	0.385533i	$0.125982\pi$
$660$		0			0
$661$	695.307	+	186.307i	1.05190	+	0.281856i	0.743037	−	0.669250i	$-0.233384\pi$
$661$	695.307	+	186.307i	1.05190	+	0.281856i	0.308864	+	0.951106i	$0.400051\pi$
$662$		−	428.000i		−	0.646526i
$663$		0			0
$664$	−312.000			−0.469880
$665$	−114.200	+	426.200i	−0.171729	+	0.640902i
$666$	333.000	+	576.773i	0.500000	+	0.866025i
$667$	−997.661	−	576.000i	−1.49574	−	0.863568i
$668$	−276.000	−	276.000i	−0.413174	−	0.413174i
$669$		0			0
$670$	−48.3154	−	180.315i	−0.0721125	−	0.269127i
$671$	−108.000	+	108.000i	−0.160954	+	0.160954i
$672$		0			0
$673$	−826.188	+	477.000i	−1.22762	+	0.708767i	−0.966531	−	0.256548i	$-0.917415\pi$
$673$	−826.188	+	477.000i	−1.22762	+	0.708767i	−0.261089	+	0.965315i	$0.584081\pi$
$674$	−428.932	−	114.932i	−0.636398	−	0.170522i
$675$		0			0
$676$		0			0
$677$	−930.000			−1.37371			−0.686854	−	0.726796i	$-0.741009\pi$
$677$	−930.000			−1.37371			−0.686854	+	0.726796i	$0.741009\pi$
$678$		0			0
$679$	94.0000	+	162.813i	0.138439	+	0.239783i
$680$	−62.3538	−	36.0000i	−0.0916968	−	0.0529412i
$681$		0			0
$682$	229.492	−	61.4923i	0.336499	−	0.0901646i
$683$	125.181	+	467.181i	0.183281	+	0.684013i	0.994992	+	0.0999540i	$0.0318696\pi$
$683$	125.181	+	467.181i	0.183281	+	0.684013i	−0.811711	+	0.584059i	$0.801464\pi$
$684$	468.000	−	468.000i	0.684211	−	0.684211i
$685$	−189.000	+	327.358i	−0.275912	+	0.477894i
$686$	311.769	−	180.000i	0.454474	−	0.262391i
$687$		0			0
$688$		−	144.000i		−	0.209302i
$689$		0			0
$690$		0			0
$691$	−92.9705	+	346.970i	−0.134545	+	0.502128i	0.865455	+	0.500987i	$0.167030\pi$
$691$	−92.9705	+	346.970i	−0.134545	+	0.502128i	−0.999999	+	0.00114057i	$0.999637\pi$
$692$	−24.0000	−	41.5692i	−0.0346821	−	0.0600711i
$693$	−187.061	−	108.000i	−0.269930	−	0.155844i
$694$	−120.000	−	120.000i	−0.172911	−	0.172911i
$695$	622.908	−	166.908i	0.896270	−	0.240155i
$696$		0			0
$697$	54.0000	−	54.0000i	0.0774749	−	0.0774749i
$698$	−101.000	+	174.937i	−0.144699	+	0.250626i
$699$		0			0
$700$	−38.2487	−	10.2487i	−0.0546410	−	0.0146410i
$701$			150.000i			0.213980i	0.994260	+	0.106990i	$0.0341213\pi$
$701$			150.000i			0.213980i	−0.994260	+	0.106990i	$0.965879\pi$
$702$		0			0
$703$	1924.00			2.73684
$704$	−17.5692	+	65.5692i	−0.0249563	+	0.0931381i
$705$		0			0
$706$	−57.1577	−	33.0000i	−0.0809599	−	0.0467422i
$707$	240.000	+	240.000i	0.339463	+	0.339463i
$708$		0			0
$709$	−109.442	−	408.442i	−0.154361	−	0.576081i	−0.999159	−	0.0409971i	$-0.986947\pi$
$709$	−109.442	−	408.442i	−0.154361	−	0.576081i	0.844799	−	0.535084i	$-0.179720\pi$
$710$	36.0000	−	36.0000i	0.0507042	−	0.0507042i
$711$	−486.000	+	841.777i	−0.683544	+	1.18393i
$712$	−31.1769	+	18.0000i	−0.0437878	+	0.0252809i
$713$	458.985	+	122.985i	0.643737	+	0.172489i
$714$		0			0
$715$		0			0
$716$	600.000			0.837989
$717$		0			0
$718$	−186.000	−	322.161i	−0.259053	−	0.448693i
$719$	1039.23	+	600.000i	1.44538	+	0.834492i	0.998201	−	0.0599507i	$-0.0190944\pi$
$719$	1039.23	+	600.000i	1.44538	+	0.834492i	0.447182	+	0.894443i	$0.352428\pi$
$720$	−108.000	−	108.000i	−0.150000	−	0.150000i
$721$	393.415	−	105.415i	0.545652	−	0.146207i
$722$	−362.731	−	1353.73i	−0.502398	−	1.87497i
$723$		0			0
$724$	90.0000	−	155.885i	0.124309	−	0.215310i
$725$	290.985	−	168.000i	0.401358	−	0.231724i
$726$		0			0
$727$			1336.00i			1.83769i	0.394620	+	0.918845i	$0.370876\pi$
$727$			1336.00i			1.83769i	−0.394620	+	0.918845i	$0.629124\pi$
$728$		0			0
$729$	−729.000			−1.00000
$730$	−37.3346	+	139.335i	−0.0511433	+	0.190869i
$731$	108.000	+	187.061i	0.147743	+	0.255898i
$732$		0			0
$733$	283.000	+	283.000i	0.386085	+	0.386085i	0.873288	−	0.487204i	$-0.161983\pi$
$733$	283.000	+	283.000i	0.386085	+	0.386085i	−0.487204	+	0.873288i	$0.661983\pi$
$734$	−792.295	+	212.295i	−1.07942	+	0.289230i
$735$		0			0
$736$	−96.0000	+	96.0000i	−0.130435	+	0.130435i
$737$	132.000	−	228.631i	0.179104	−	0.310218i
$738$	140.296	−	81.0000i	0.190103	−	0.109756i
$739$	−1264.94	−	338.940i	−1.71169	−	0.458646i	−0.735853	−	0.677141i	$-0.763218\pi$
$739$	−1264.94	−	338.940i	−1.71169	−	0.458646i	−0.975838	+	0.218495i	$0.929885\pi$
$740$		−	444.000i		−	0.600000i
$741$		0			0
$742$	120.000			0.161725
$743$	292.088	−	1090.09i	0.393120	−	1.46714i	−0.431838	−	0.901951i	$-0.642135\pi$
$743$	292.088	−	1090.09i	0.393120	−	1.46714i	0.824958	−	0.565193i	$-0.191198\pi$
$744$		0			0
$745$	−514.419	−	297.000i	−0.690495	−	0.398658i
$746$		0			0
$747$	958.950	−	256.950i	1.28373	−	0.343976i
$748$	−26.3538	−	98.3538i	−0.0352324	−	0.131489i
$749$	240.000	−	240.000i	0.320427	−	0.320427i
$750$		0			0
$751$	935.307	−	540.000i	1.24542	−	0.719041i	0.275224	−	0.961380i	$-0.411248\pi$
$751$	935.307	−	540.000i	1.24542	−	0.719041i	0.970192	+	0.242339i	$0.0779145\pi$
$752$	229.492	+	61.4923i	0.305176	+	0.0817716i
$753$		0			0
$754$		0			0
$755$	−636.000			−0.842384
$756$		0			0
$757$	−495.000	−	857.365i	−0.653897	−	1.13258i	−0.982169	−	0.188000i	$-0.939800\pi$
$757$	−495.000	−	857.365i	−0.653897	−	1.13258i	0.328272	−	0.944583i	$-0.393534\pi$
$758$	−391.443	−	226.000i	−0.516416	−	0.298153i
$759$		0			0
$760$	−426.200	+	114.200i	−0.560789	+	0.150263i
$761$	293.186	+	1094.19i	0.385265	+	1.43783i	0.837749	+	0.546055i	$0.183871\pi$
$761$	293.186	+	1094.19i	0.385265	+	1.43783i	−0.452485	+	0.891772i	$0.649462\pi$
$762$		0			0
$763$	38.0000	−	65.8179i	0.0498034	−	0.0862620i
$764$	436.477	−	252.000i	0.571305	−	0.329843i
$765$	221.296	+	59.2961i	0.289276	+	0.0775113i
$766$			156.000i			0.203655i
$767$		0			0
$768$		0			0
$769$	−120.422	+	449.422i	−0.156596	+	0.584424i	0.842367	+	0.538904i	$0.181161\pi$
$769$	−120.422	+	449.422i	−0.156596	+	0.584424i	−0.998963	+	0.0455207i	$0.985505\pi$
$770$	72.0000	+	124.708i	0.0935065	+	0.161958i
$771$		0			0
$772$	514.000	+	514.000i	0.665803	+	0.665803i
$773$	1184.34	−	317.344i	1.53214	−	0.410536i	0.608423	−	0.793613i	$-0.291802\pi$
$773$	1184.34	−	317.344i	1.53214	−	0.410536i	0.923716	+	0.383077i	$0.125136\pi$
$774$	118.592	+	442.592i	0.153220	+	0.571825i
$775$	−98.0000	+	98.0000i	−0.126452	+	0.126452i
$776$	−94.0000	+	162.813i	−0.121134	+	0.209810i
$777$		0			0
$778$	204.904	+	54.9038i	0.263373	+	0.0705705i
$779$		−	468.000i		−	0.600770i
$780$		0			0
$781$	72.0000			0.0921895
$782$	52.7077	−	196.708i	0.0674011	−	0.251544i
$783$		0			0
$784$	142.028	+	82.0000i	0.181158	+	0.104592i
$785$	240.000	+	240.000i	0.305732	+	0.305732i
$786$		0			0
$787$	−57.8320	−	215.832i	−0.0734841	−	0.274247i	0.919401	−	0.393321i	$-0.128674\pi$
$787$	−57.8320	−	215.832i	−0.0734841	−	0.274247i	−0.992885	+	0.119075i	$0.962007\pi$
$788$	−246.000	+	246.000i	−0.312183	+	0.312183i
$789$		0			0
$790$	561.184	−	324.000i	0.710360	−	0.410127i
$791$	327.846	+	87.8461i	0.414470	+	0.111057i
$792$		−	216.000i		−	0.272727i
$793$		0			0
$794$	−506.000			−0.637280
$795$		0			0
$796$	200.000	+	346.410i	0.251256	+	0.435189i
$797$	826.188	+	477.000i	1.03662	+	0.598494i	0.918875	−	0.394549i	$-0.129099\pi$
$797$	826.188	+	477.000i	1.03662	+	0.598494i	0.117748	+	0.993044i	$0.462433\pi$
$798$		0			0
$799$	−344.238	+	92.2384i	−0.430837	+	0.115442i
$800$	−10.2487	−	38.2487i	−0.0128109	−	0.0478109i
$801$	81.0000	−	81.0000i	0.101124	−	0.101124i
$802$	249.000	−	431.281i	0.310474	−	0.537756i
$803$	−176.669	+	102.000i	−0.220011	+	0.127024i
$804$		0			0
$805$			288.000i			0.357764i
$806$		0			0
$807$		0			0
$808$	−87.8461	+	327.846i	−0.108720	+	0.405750i
$809$	−156.000	−	270.200i	−0.192831	−	0.333992i	0.753357	−	0.657612i	$-0.228433\pi$
$809$	−156.000	−	270.200i	−0.192831	−	0.333992i	−0.946187	+	0.323620i	$0.895100\pi$
$810$	420.888	+	243.000i	0.519615	+	0.300000i
$811$	566.000	+	566.000i	0.697904	+	0.697904i	0.963958	−	0.266054i	$-0.0857200\pi$
$811$	566.000	+	566.000i	0.697904	+	0.697904i	−0.266054	+	0.963958i	$0.585720\pi$
$812$	262.277	−	70.2769i	0.323001	−	0.0865479i
$813$		0			0
$814$	444.000	−	444.000i	0.545455	−	0.545455i
$815$	246.000	−	426.084i	0.301840	−	0.522803i
$816$		0			0
$817$	1278.60	+	342.600i	1.56499	+	0.419339i
$818$		−	638.000i		−	0.779951i
$819$		0			0
$820$	−108.000			−0.131707
$821$	−124.083	+	463.083i	−0.151136	+	0.564047i	0.848269	+	0.529565i	$0.177645\pi$
$821$	−124.083	+	463.083i	−0.151136	+	0.564047i	−0.999405	+	0.0344820i	$0.989022\pi$
$822$		0			0
$823$	1060.02	+	612.000i	1.28799	+	0.743621i	0.978295	−	0.207215i	$-0.0664401\pi$
$823$	1060.02	+	612.000i	1.28799	+	0.743621i	0.309694	+	0.950836i	$0.399773\pi$
$824$	288.000	+	288.000i	0.349515	+	0.349515i
$825$		0			0
$826$	−79.0615	−	295.061i	−0.0957161	−	0.357217i
$827$	−678.000	+	678.000i	−0.819831	+	0.819831i	−0.986083	−	0.166253i	$-0.946833\pi$
$827$	−678.000	+	678.000i	−0.819831	+	0.819831i	0.166253	+	0.986083i	$0.446833\pi$
$828$	216.000	−	374.123i	0.260870	−	0.451839i
$829$	−796.743	+	460.000i	−0.961090	+	0.554885i	−0.896508	−	0.443027i	$-0.853905\pi$
$829$	−796.743	+	460.000i	−0.961090	+	0.554885i	−0.0645815	+	0.997912i	$0.520571\pi$
$830$	−639.300	−	171.300i	−0.770241	−	0.206385i
$831$		0			0
$832$		0			0
$833$	−246.000			−0.295318
$834$		0			0
$835$	−414.000	−	717.069i	−0.495808	−	0.858765i
$836$	−540.400	−	312.000i	−0.646411	−	0.373206i
$837$		0			0
$838$	65.5692	−	17.5692i	0.0782449	−	0.0209657i
$839$	−283.304	−	1057.30i	−0.337668	−	1.26020i	−0.900947	−	0.433928i	$-0.857127\pi$
$839$	−283.304	−	1057.30i	−0.337668	−	1.26020i	0.563279	−	0.826267i	$-0.309540\pi$
$840$		0			0
$841$	−731.500	+	1267.00i	−0.869798	+	1.50653i
$842$	19.0526	−	11.0000i	0.0226277	−	0.0130641i
$843$		0			0
$844$		−	576.000i		−	0.682464i
$845$		0			0
$846$	−756.000			−0.893617
$847$	35.8705	−	133.870i	0.0423500	−	0.158053i
$848$	60.0000	+	103.923i	0.0707547	+	0.122551i
$849$		0			0
$850$	42.0000	+	42.0000i	0.0494118	+	0.0494118i
$851$	1213.03	−	325.031i	1.42542	−	0.381940i
$852$		0			0
$853$	−443.000	+	443.000i	−0.519343	+	0.519343i	−0.917373	−	0.398029i	$-0.869694\pi$
$853$	−443.000	+	443.000i	−0.519343	+	0.519343i	0.398029	+	0.917373i	$0.369694\pi$
$854$	36.0000	−	62.3538i	0.0421546	−	0.0730139i
$855$	1215.90	−	702.000i	1.42210	−	0.821053i
$856$	327.846	+	87.8461i	0.382998	+	0.102624i
$857$		−	384.000i		−	0.448075i	−0.974581	−	0.224037i	$-0.928076\pi$
$857$		−	384.000i		−	0.448075i	0.974581	−	0.224037i	$-0.0719238\pi$
$858$		0			0
$859$	72.0000			0.0838184			0.0419092	−	0.999121i	$-0.486656\pi$
$859$	72.0000			0.0838184			0.0419092	+	0.999121i	$0.486656\pi$
$860$	79.0615	−	295.061i	0.0919320	−	0.343095i
$861$		0			0
$862$	717.069	+	414.000i	0.831867	+	0.480278i
$863$	−702.000	−	702.000i	−0.813441	−	0.813441i	0.171707	−	0.985148i	$-0.445072\pi$
$863$	−702.000	−	702.000i	−0.813441	−	0.813441i	−0.985148	+	0.171707i	$0.945072\pi$
$864$		0			0
$865$	−26.3538	−	98.3538i	−0.0304669	−	0.113704i
$866$	−16.0000	+	16.0000i	−0.0184758	+	0.0184758i
$867$		0			0
$868$	−96.9948	+	56.0000i	−0.111745	+	0.0645161i
$869$	885.184	+	237.184i	1.01862	+	0.272940i
$870$		0			0
$871$		0			0
$872$	76.0000			0.0871560
$873$	154.829	−	577.829i	0.177353	−	0.661889i
$874$	−624.000	−	1080.80i	−0.713959	−	1.23661i
$875$	−332.554	−	192.000i	−0.380061	−	0.219429i
$876$		0			0
$877$	−1001.30	+	268.297i	−1.14173	+	0.305925i	−0.779646	−	0.626220i	$-0.784601\pi$
$877$	−1001.30	+	268.297i	−1.14173	+	0.305925i	−0.362083	+	0.932146i	$0.617934\pi$
$878$	−131.769	−	491.769i	−0.150079	−	0.560102i
$879$		0			0
$880$	−72.0000	+	124.708i	−0.0818182	+	0.141713i
$881$	831.384	−	480.000i	0.943683	−	0.544835i	0.0525698	−	0.998617i	$-0.483259\pi$
$881$	831.384	−	480.000i	0.943683	−	0.544835i	0.891113	+	0.453782i	$0.149925\pi$
$882$	−504.063	−	135.063i	−0.571500	−	0.153133i
$883$			236.000i			0.267271i	0.991031	+	0.133635i	$0.0426651\pi$
$883$			236.000i			0.267271i	−0.991031	+	0.133635i	$0.957335\pi$
$884$		0			0
$885$		0			0
$886$	−219.615	+	819.615i	−0.247873	+	0.925074i
$887$	−690.000	−	1195.12i	−0.777903	−	1.34737i	−0.933148	−	0.359492i	$-0.882950\pi$
$887$	−690.000	−	1195.12i	−0.777903	−	1.34737i	0.155245	−	0.987876i	$-0.450383\pi$
$888$		0			0
$889$	112.000	+	112.000i	0.125984	+	0.125984i
$890$	−73.7654	+	19.7654i	−0.0828824	+	0.0222083i
$891$	177.888	+	663.888i	0.199650	+	0.745105i
$892$	−76.0000	+	76.0000i	−0.0852018	+	0.0852018i
$893$	−1092.00	+	1891.40i	−1.22284	+	2.11803i
$894$		0			0
$895$	1229.42	+	329.423i	1.37366	+	0.368070i
$896$		−	32.0000i		−	0.0357143i
$897$		0			0
$898$	−18.0000			−0.0200445
$899$	245.969	−	917.969i	0.273603	−	1.02110i
$900$	63.0000	+	109.119i	0.0700000	+	0.121244i
$901$	−155.885	−	90.0000i	−0.173013	−	0.0998890i
$902$	−108.000	−	108.000i	−0.119734	−	0.119734i
$903$		0			0
$904$	87.8461	+	327.846i	0.0971749	+	0.362662i
$905$	270.000	−	270.000i	0.298343	−	0.298343i
$906$		0			0
$907$	−1250.54	+	722.000i	−1.37877	+	0.796031i	−0.992011	−	0.126152i	$-0.959737\pi$
$907$	−1250.54	+	722.000i	−1.37877	+	0.796031i	−0.386755	+	0.922183i	$0.626404\pi$
$908$	377.023	+	101.023i	0.415224	+	0.111259i
$909$		−	1080.00i		−	1.18812i
$910$		0			0
$911$	612.000			0.671789			0.335895	−	0.941900i	$-0.390961\pi$
$911$	612.000			0.671789			0.335895	+	0.941900i	$0.390961\pi$
$912$		0			0
$913$	−468.000	−	810.600i	−0.512596	−	0.887842i
$914$	81.4064	+	47.0000i	0.0890661	+	0.0514223i
$915$		0			0
$916$	−357.899	+	95.8987i	−0.390719	+	0.104693i
$917$	52.7077	+	196.708i	0.0574784	+	0.214512i
$918$		0			0
$919$	774.000	−	1340.61i	0.842220	−	1.45877i	−0.0457941	−	0.998951i	$-0.514582\pi$
$919$	774.000	−	1340.61i	0.842220	−	1.45877i	0.888014	−	0.459817i	$-0.152085\pi$
$920$	−249.415	+	144.000i	−0.271104	+	0.156522i
$921$		0			0
$922$			342.000i			0.370933i
$923$		0			0
$924$		0			0
$925$	−94.8006	+	353.801i	−0.102487	+	0.382487i
$926$	−202.000	−	349.874i	−0.218143	−	0.377834i
$927$	−1122.37	−	648.000i	−1.21075	−	0.699029i
$928$	192.000	+	192.000i	0.206897	+	0.206897i
$929$	1323.68	−	354.679i	1.42484	−	0.381785i	0.537643	−	0.843172i	$-0.319315\pi$
$929$	1323.68	−	354.679i	1.42484	−	0.381785i	0.887199	+	0.461387i	$0.152648\pi$
$930$		0			0
$931$	−1066.00	+	1066.00i	−1.14501	+	1.14501i
$932$	336.000	−	581.969i	0.360515	−	0.624430i
$933$		0			0
$934$	704.869	+	188.869i	0.754678	+	0.202215i
$935$		−	216.000i		−	0.231016i
$936$		0			0
$937$	−450.000			−0.480256			−0.240128	−	0.970741i	$-0.577189\pi$
$937$	−450.000			−0.480256			−0.240128	+	0.970741i	$0.577189\pi$
$938$	−32.2102	+	120.210i	−0.0343393	+	0.128156i
$939$		0			0
$940$	436.477	+	252.000i	0.464337	+	0.268085i
$941$	411.000	+	411.000i	0.436769	+	0.436769i	0.890923	−	0.454154i	$-0.150058\pi$
$941$	411.000	+	411.000i	0.436769	+	0.436769i	−0.454154	+	0.890923i	$0.650058\pi$
$942$		0			0
$943$	−79.0615	−	295.061i	−0.0838404	−	0.312897i
$944$	216.000	−	216.000i	0.228814	−	0.228814i
$945$		0			0
$946$	374.123	−	216.000i	0.395479	−	0.228330i
$947$	−795.027	−	213.027i	−0.839521	−	0.224949i	−0.186658	−	0.982425i	$-0.559766\pi$
$947$	−795.027	−	213.027i	−0.839521	−	0.224949i	−0.652863	+	0.757476i	$0.726432\pi$
$948$		0			0
$949$		0			0
$950$	364.000			0.383158
$951$		0			0
$952$	24.0000	+	41.5692i	0.0252101	+	0.0436651i
$953$	1163.94	+	672.000i	1.22134	+	0.705142i	0.965204	−	0.261499i	$-0.0842167\pi$
$953$	1163.94	+	672.000i	1.22134	+	0.705142i	0.256137	+	0.966640i	$0.417550\pi$
$954$	−270.000	−	270.000i	−0.283019	−	0.283019i
$955$	1032.72	−	276.715i	1.08138	−	0.289754i
$956$	83.4538	+	311.454i	0.0872948	+	0.325788i
$957$		0			0
$958$	234.000	−	405.300i	0.244259	−	0.423069i
$959$	218.238	−	126.000i	0.227569	−	0.131387i
$960$		0			0
$961$		−	569.000i		−	0.592092i
$962$		0			0
$963$	−1080.00			−1.12150
$964$	110.540	−	412.540i	0.114668	−	0.427946i
$965$	771.000	+	1335.41i	0.798964	+	1.38385i
$966$		0			0
$967$	−562.000	−	562.000i	−0.581179	−	0.581179i	0.354048	−	0.935227i	$-0.384805\pi$
$967$	−562.000	−	562.000i	−0.581179	−	0.581179i	−0.935227	+	0.354048i	$0.884805\pi$
$968$	133.870	−	35.8705i	0.138296	−	0.0370563i
$969$		0			0
$970$	−282.000	+	282.000i	−0.290722	+	0.290722i
$971$	624.000	−	1080.80i	0.642636	−	1.11308i	−0.342206	−	0.939625i	$-0.611174\pi$
$971$	624.000	−	1080.80i	0.642636	−	1.11308i	0.984842	−	0.173454i	$-0.0554928\pi$
$972$		0			0
$973$	−415.272	−	111.272i	−0.426795	−	0.114359i
$974$			596.000i			0.611910i
$975$		0			0
$976$	72.0000			0.0737705
$977$	12.0788	−	45.0788i	0.0123632	−	0.0461401i	−0.959469	−	0.281815i	$-0.909063\pi$
$977$	12.0788	−	45.0788i	0.0123632	−	0.0461401i	0.971832	+	0.235675i	$0.0757301\pi$
$978$		0			0
$979$	−93.5307	−	54.0000i	−0.0955370	−	0.0551583i
$980$	246.000	+	246.000i	0.251020	+	0.251020i
$981$	−233.590	+	62.5903i	−0.238115	+	0.0638026i
$982$	−153.731	−	573.731i	−0.156549	−	0.584247i
$983$	702.000	−	702.000i	0.714140	−	0.714140i	−0.253258	−	0.967399i	$-0.581502\pi$
$983$	702.000	−	702.000i	0.714140	−	0.714140i	0.967399	+	0.253258i	$0.0815023\pi$
$984$		0			0
$985$	−639.127	+	369.000i	−0.648860	+	0.374619i
$986$	−393.415	−	105.415i	−0.399001	−	0.106912i
$987$		0			0
$988$		0			0
$989$	864.000			0.873610
$990$	118.592	−	442.592i	0.119790	−	0.447063i
$991$	134.000	+	232.095i	0.135217	+	0.234203i	0.925680	−	0.378307i	$-0.123494\pi$
$991$	134.000	+	232.095i	0.135217	+	0.234203i	−0.790463	+	0.612509i	$0.790160\pi$
$992$	−96.9948	−	56.0000i	−0.0977771	−	0.0564516i
$993$		0			0
$994$	−32.7846	+	8.78461i	−0.0329825	+	0.00883764i
$995$	219.615	+	819.615i	0.220719	+	0.823734i
$996$		0			0
$997$	655.000	−	1134.49i	0.656971	−	1.13791i	−0.324425	−	0.945911i	$-0.605171\pi$
$997$	655.000	−	1134.49i	0.656971	−	1.13791i	0.981396	−	0.191996i	$-0.0614959\pi$
$998$	599.290	−	346.000i	0.600491	−	0.346693i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.f.b.89.1		4
13.2	odd	12		26.3.d.a.5.1	✓	2
13.3	even	3		26.3.d.a.21.1	yes	2
13.4	even	6		338.3.f.g.319.1		4
13.5	odd	4	inner	338.3.f.b.249.1		4
13.6	odd	12	inner	338.3.f.b.19.1		4
13.7	odd	12		338.3.f.g.19.1		4
13.8	odd	4		338.3.f.g.249.1		4
13.9	even	3	inner	338.3.f.b.319.1		4
13.10	even	6		338.3.d.a.99.1		2
13.11	odd	12		338.3.d.a.239.1		2
13.12	even	2		338.3.f.g.89.1		4
39.2	even	12		234.3.i.a.109.1		2
39.29	odd	6		234.3.i.a.73.1		2
52.3	odd	6		208.3.t.b.177.1		2
52.15	even	12		208.3.t.b.161.1		2
65.2	even	12		650.3.f.e.499.1		2
65.3	odd	12		650.3.f.e.99.1		2
65.28	even	12		650.3.f.b.499.1		2
65.29	even	6		650.3.k.b.151.1		2
65.42	odd	12		650.3.f.b.99.1		2
65.54	odd	12		650.3.k.b.551.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.d.a.5.1	✓	2	13.2	odd	12
26.3.d.a.21.1	yes	2	13.3	even	3
208.3.t.b.161.1		2	52.15	even	12
208.3.t.b.177.1		2	52.3	odd	6
234.3.i.a.73.1		2	39.29	odd	6
234.3.i.a.109.1		2	39.2	even	12
338.3.d.a.99.1		2	13.10	even	6
338.3.d.a.239.1		2	13.11	odd	12
338.3.f.b.19.1		4	13.6	odd	12	inner
338.3.f.b.89.1		4	1.1	even	1	trivial
338.3.f.b.249.1		4	13.5	odd	4	inner
338.3.f.b.319.1		4	13.9	even	3	inner
338.3.f.g.19.1		4	13.7	odd	12
338.3.f.g.89.1		4	13.12	even	2
338.3.f.g.249.1		4	13.8	odd	4
338.3.f.g.319.1		4	13.4	even	6
650.3.f.b.99.1		2	65.42	odd	12
650.3.f.b.499.1		2	65.28	even	12
650.3.f.e.99.1		2	65.3	odd	12
650.3.f.e.499.1		2	65.2	even	12
650.3.k.b.151.1		2	65.29	even	6
650.3.k.b.551.1		2	65.54	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-3.00000 - 3.00000i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-3.00000 - 3.00000i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.50000 - 7.79423i) q^{9} +(-5.19615 + 3.00000i) q^{10} +(-8.19615 - 2.19615i) q^{11} +4.00000 q^{14} +(2.00000 + 3.46410i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(-9.00000 - 9.00000i) q^{18} +(-35.5167 + 9.51666i) q^{19} +(2.19615 + 8.19615i) q^{20} +(-6.00000 + 10.3923i) q^{22} +(-20.7846 + 12.0000i) q^{23} -7.00000i q^{25} +(1.46410 - 5.46410i) q^{28} +(24.0000 + 41.5692i) q^{29} +(-14.0000 - 14.0000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-6.00000 + 6.00000i) q^{34} +(6.00000 - 10.3923i) q^{35} +(-15.5885 + 9.00000i) q^{36} +(-50.5429 - 13.5429i) q^{37} +52.0000i q^{38} +12.0000 q^{40} +(-3.29423 + 12.2942i) q^{41} +(-31.1769 - 18.0000i) q^{43} +(12.0000 + 12.0000i) q^{44} +(-36.8827 + 9.88269i) q^{45} +(8.78461 + 32.7846i) q^{46} +(42.0000 - 42.0000i) q^{47} +(35.5070 - 20.5000i) q^{49} +(-9.56218 - 2.56218i) q^{50} +30.0000 q^{53} +(18.0000 + 31.1769i) q^{55} +(-6.92820 - 4.00000i) q^{56} +(65.5692 - 17.5692i) q^{58} +(-19.7654 - 73.7654i) q^{59} +(9.00000 - 15.5885i) q^{61} +(-24.2487 + 14.0000i) q^{62} +(24.5885 + 6.58846i) q^{63} -8.00000i q^{64} +(-8.05256 + 30.0526i) q^{67} +(6.00000 + 10.3923i) q^{68} +(-12.0000 - 12.0000i) q^{70} +(-8.19615 + 2.19615i) q^{71} +(6.58846 + 24.5885i) q^{72} +(17.0000 - 17.0000i) q^{73} +(-37.0000 + 64.0859i) q^{74} +(71.0333 + 19.0333i) q^{76} -24.0000i q^{77} -108.000 q^{79} +(4.39230 - 16.3923i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(15.5885 + 9.00000i) q^{82} +(78.0000 + 78.0000i) q^{83} +(6.58846 + 24.5885i) q^{85} +(-36.0000 + 36.0000i) q^{86} +(20.7846 - 12.0000i) q^{88} +(12.2942 + 3.29423i) q^{89} +54.0000i q^{90} +48.0000 q^{92} +(-42.0000 - 72.7461i) q^{94} +(135.100 + 78.0000i) q^{95} +(64.2032 - 17.2032i) q^{97} +(-15.0070 - 56.0070i) q^{98} +(-54.0000 + 54.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 12 q^{5} - 4 q^{7} - 8 q^{8} + 18 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 12 * q^5 - 4 * q^7 - 8 * q^8 + 18 * q^9	\( 4 q - 2 q^{2} - 12 q^{5} - 4 q^{7} - 8 q^{8} + 18 q^{9} - 12 q^{11} + 16 q^{14} + 8 q^{16} - 36 q^{18} - 52 q^{19} - 12 q^{20} - 24 q^{22} - 8 q^{28} + 96 q^{29} - 56 q^{31} + 8 q^{32} - 24 q^{34} + 24 q^{35} - 74 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{44} - 54 q^{45} - 48 q^{46} + 168 q^{47} - 14 q^{50} + 120 q^{53} + 72 q^{55} + 96 q^{58} + 108 q^{59} + 36 q^{61} + 36 q^{63} + 44 q^{67} + 24 q^{68} - 48 q^{70} - 12 q^{71} - 36 q^{72} + 68 q^{73} - 148 q^{74} + 104 q^{76} - 432 q^{79} - 24 q^{80} - 162 q^{81} + 312 q^{83} - 36 q^{85} - 144 q^{86} + 18 q^{89} + 192 q^{92} - 168 q^{94} + 94 q^{97} + 82 q^{98} - 216 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 12 * q^5 - 4 * q^7 - 8 * q^8 + 18 * q^9 - 12 * q^11 + 16 * q^14 + 8 * q^16 - 36 * q^18 - 52 * q^19 - 12 * q^20 - 24 * q^22 - 8 * q^28 + 96 * q^29 - 56 * q^31 + 8 * q^32 - 24 * q^34 + 24 * q^35 - 74 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^44 - 54 * q^45 - 48 * q^46 + 168 * q^47 - 14 * q^50 + 120 * q^53 + 72 * q^55 + 96 * q^58 + 108 * q^59 + 36 * q^61 + 36 * q^63 + 44 * q^67 + 24 * q^68 - 48 * q^70 - 12 * q^71 - 36 * q^72 + 68 * q^73 - 148 * q^74 + 104 * q^76 - 432 * q^79 - 24 * q^80 - 162 * q^81 + 312 * q^83 - 36 * q^85 - 144 * q^86 + 18 * q^89 + 192 * q^92 - 168 * q^94 + 94 * q^97 + 82 * q^98 - 216 * q^99

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