LMFDB - Embedded newform 1950.2.bc.c.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.c.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(4.09808 + 2.36603i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(4.09808 + 2.36603i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.09808 - 2.36603i) q^{11} -1.00000 q^{12} +(3.59808 + 0.232051i) q^{13} -4.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.59808 - 4.50000i) q^{17} -1.00000i q^{18} +(1.09808 + 0.633975i) q^{19} -4.73205i q^{21} +(-2.36603 + 4.09808i) q^{22} +(-1.09808 - 1.90192i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-3.23205 + 1.59808i) q^{26} +1.00000 q^{27} +(4.09808 - 2.36603i) q^{28} +(1.50000 + 2.59808i) q^{29} -2.53590i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.09808 - 2.36603i) q^{33} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(-2.59808 + 1.50000i) q^{37} -1.26795 q^{38} +(-1.59808 - 3.23205i) q^{39} +(0.401924 - 0.232051i) q^{41} +(2.36603 + 4.09808i) q^{42} +(-3.09808 + 5.36603i) q^{43} -4.73205i q^{44} +(1.90192 + 1.09808i) q^{46} +1.26795i q^{47} +(-0.500000 + 0.866025i) q^{48} +(7.69615 + 13.3301i) q^{49} -5.19615 q^{51} +(2.00000 - 3.00000i) q^{52} -3.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{56} -1.26795i q^{57} +(-2.59808 - 1.50000i) q^{58} +(-12.0000 - 6.92820i) q^{59} +(-2.40192 + 4.16025i) q^{61} +(1.26795 + 2.19615i) q^{62} +(-4.09808 + 2.36603i) q^{63} -1.00000 q^{64} +4.73205 q^{66} +(9.29423 - 5.36603i) q^{67} +(-2.59808 - 4.50000i) q^{68} +(-1.09808 + 1.90192i) q^{69} +(7.09808 + 4.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 - 2.59808i) q^{74} +(1.09808 - 0.633975i) q^{76} +22.3923 q^{77} +(3.00000 + 2.00000i) q^{78} -12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.232051 + 0.401924i) q^{82} -11.6603i q^{83} +(-4.09808 - 2.36603i) q^{84} -6.19615i q^{86} +(1.50000 - 2.59808i) q^{87} +(2.36603 + 4.09808i) q^{88} +(2.19615 - 1.26795i) q^{89} +(14.1962 + 9.46410i) q^{91} -2.19615 q^{92} +(-2.19615 + 1.26795i) q^{93} +(-0.633975 - 1.09808i) q^{94} -1.00000i q^{96} +(-5.19615 - 3.00000i) q^{97} +(-13.3301 - 7.69615i) q^{98} +4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 12 q^{14} - 2 q^{16} - 6 q^{19} - 6 q^{22} + 6 q^{23} - 6 q^{26} + 4 q^{27} + 6 q^{28} + 6 q^{29} - 6 q^{33} + 2 q^{36} - 12 q^{38} + 4 q^{39} + 12 q^{41} + 6 q^{42} - 2 q^{43} + 18 q^{46} - 2 q^{48} + 10 q^{49} + 8 q^{52} - 12 q^{53} - 6 q^{56} - 48 q^{59} - 20 q^{61} + 12 q^{62} - 6 q^{63} - 4 q^{64} + 12 q^{66} + 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} - 6 q^{76} + 48 q^{77} + 12 q^{78} - 8 q^{79} - 2 q^{81} + 6 q^{82} - 6 q^{84} + 6 q^{87} + 6 q^{88} - 12 q^{89} + 36 q^{91} + 12 q^{92} + 12 q^{93} - 6 q^{94} - 36 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 12 * q^14 - 2 * q^16 - 6 * q^19 - 6 * q^22 + 6 * q^23 - 6 * q^26 + 4 * q^27 + 6 * q^28 + 6 * q^29 - 6 * q^33 + 2 * q^36 - 12 * q^38 + 4 * q^39 + 12 * q^41 + 6 * q^42 - 2 * q^43 + 18 * q^46 - 2 * q^48 + 10 * q^49 + 8 * q^52 - 12 * q^53 - 6 * q^56 - 48 * q^59 - 20 * q^61 + 12 * q^62 - 6 * q^63 - 4 * q^64 + 12 * q^66 + 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 - 6 * q^76 + 48 * q^77 + 12 * q^78 - 8 * q^79 - 2 * q^81 + 6 * q^82 - 6 * q^84 + 6 * q^87 + 6 * q^88 - 12 * q^89 + 36 * q^91 + 12 * q^92 + 12 * q^93 - 6 * q^94 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	4.09808	+	2.36603i	1.54893	+	0.894274i	0.998224	+	0.0595724i	$0.0189737\pi$
$7$	4.09808	+	2.36603i	1.54893	+	0.894274i	0.550703	+	0.834701i	$0.314360\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.267421	−	0.963580i	$-0.413828\pi$
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.968195	+	0.250196i	$0.0804951\pi$
$12$	−1.00000			−0.288675
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$14$	−4.73205			−1.26469
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	−0.357400	−	0.933952i	$-0.616337\pi$
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	0.987526	−	0.157459i	$-0.0503301\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$		0			0
$21$		−	4.73205i		−	1.03262i
$22$	−2.36603	+	4.09808i	−0.504438	+	0.873713i
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	0.728537	−	0.685007i	$-0.240201\pi$
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	−0.957502	+	0.288428i	$0.906867\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	−3.23205	+	1.59808i	−0.633857	+	0.313409i
$27$	1.00000			0.192450
$28$	4.09808	−	2.36603i	0.774464	−	0.447137i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$		−	2.53590i		−	0.455461i	−0.973724	−	0.227730i	$-0.926870\pi$
$31$		−	2.53590i		−	0.455461i	0.973724	−	0.227730i	$-0.0731305\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.09808	−	2.36603i	−0.713384	−	0.411872i
$34$			5.19615i			0.891133i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	−0.698119	−	0.715981i	$-0.745980\pi$
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	0.270998	+	0.962580i	$0.412646\pi$
$38$	−1.26795			−0.205689
$39$	−1.59808	−	3.23205i	−0.255897	−	0.517542i
$40$		0			0
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	−0.468287	−	0.883577i	$-0.655129\pi$
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	0.531057	+	0.847336i	$0.321795\pi$
$42$	2.36603	+	4.09808i	0.365086	+	0.632347i
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	−0.999503	−	0.0315225i	$-0.989964\pi$
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	0.527051	+	0.849834i	$0.323298\pi$
$44$		−	4.73205i		−	0.713384i
$45$		0			0
$46$	1.90192	+	1.09808i	0.280423	+	0.161903i
$47$			1.26795i			0.184949i	0.995715	+	0.0924747i	$0.0294777\pi$
$47$			1.26795i			0.184949i	−0.995715	+	0.0924747i	$0.970522\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	7.69615	+	13.3301i	1.09945	+	1.90430i
$50$		0			0
$51$	−5.19615			−0.727607
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−2.36603	+	4.09808i	−0.316173	+	0.547628i
$57$		−	1.26795i		−	0.167944i
$58$	−2.59808	−	1.50000i	−0.341144	−	0.196960i
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.997027	−	0.0770484i	$-0.975450\pi$
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.565240	−	0.824927i	$-0.691216\pi$
$60$		0			0
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$	1.26795	+	2.19615i	0.161030	+	0.278912i
$63$	−4.09808	+	2.36603i	−0.516309	+	0.298091i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.73205			0.582475
$67$	9.29423	−	5.36603i	1.13547	−	0.655564i	0.190166	−	0.981752i	$-0.439097\pi$
$67$	9.29423	−	5.36603i	1.13547	−	0.655564i	0.945305	+	0.326188i	$0.105764\pi$
$68$	−2.59808	−	4.50000i	−0.315063	−	0.545705i
$69$	−1.09808	+	1.90192i	−0.132193	+	0.228965i
$70$		0			0
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	0.858075	−	0.513525i	$-0.171661\pi$
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	−0.0156881	+	0.999877i	$0.504994\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			12.1244i			1.41905i	0.704681	+	0.709524i	$0.251090\pi$
$73$			12.1244i			1.41905i	−0.704681	+	0.709524i	$0.748910\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$		0			0
$76$	1.09808	−	0.633975i	0.125958	−	0.0727219i
$77$	22.3923			2.55184
$78$	3.00000	+	2.00000i	0.339683	+	0.226455i
$79$	−12.3923			−1.39424			−0.697122	−	0.716953i	$-0.745536\pi$
$79$	−12.3923			−1.39424			−0.697122	+	0.716953i	$0.745536\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.232051	+	0.401924i	−0.0256257	+	0.0443851i
$83$		−	11.6603i		−	1.27988i	−0.768425	−	0.639940i	$-0.778959\pi$
$83$		−	11.6603i		−	1.27988i	0.768425	−	0.639940i	$-0.221041\pi$
$84$	−4.09808	−	2.36603i	−0.447137	−	0.258155i
$85$		0			0
$86$		−	6.19615i		−	0.668148i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	2.36603	+	4.09808i	0.252219	+	0.436856i
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	−0.379068	−	0.925369i	$-0.623755\pi$
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	0.611859	+	0.790967i	$0.290422\pi$
$90$		0			0
$91$	14.1962	+	9.46410i	1.48816	+	0.992107i
$92$	−2.19615			−0.228965
$93$	−2.19615	+	1.26795i	−0.227730	+	0.131480i
$94$	−0.633975	−	1.09808i	−0.0653895	−	0.113258i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	0.212445	−	0.977173i	$-0.431857\pi$
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	−0.740034	+	0.672569i	$0.765191\pi$
$98$	−13.3301	−	7.69615i	−1.34655	−	0.777429i
$99$			4.73205i			0.475589i
$100$		0			0
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	0.829310	−	0.558788i	$-0.188734\pi$
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	−0.898580	+	0.438810i	$0.855400\pi$
$102$	4.50000	−	2.59808i	0.445566	−	0.257248i
$103$	−4.19615			−0.413459			−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615			−0.413459			−0.206730	+	0.978398i	$0.566282\pi$
$104$	−0.232051	+	3.59808i	−0.0227545	+	0.352820i
$105$		0			0
$106$	2.59808	−	1.50000i	0.252347	−	0.145693i
$107$	4.09808	+	7.09808i	0.396176	+	0.686197i	0.993251	−	0.115989i	$-0.0370037\pi$
$107$	4.09808	+	7.09808i	0.396176	+	0.686197i	−0.597075	+	0.802186i	$0.703670\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	16.3923i		−	1.57010i	−0.619434	−	0.785049i	$-0.712638\pi$
$109$		−	16.3923i		−	1.57010i	0.619434	−	0.785049i	$-0.287362\pi$
$110$		0			0
$111$	2.59808	+	1.50000i	0.246598	+	0.142374i
$112$		−	4.73205i		−	0.447137i
$113$	5.59808	−	9.69615i	0.526623	−	0.912137i	−0.472896	−	0.881118i	$-0.656791\pi$
$113$	5.59808	−	9.69615i	0.526623	−	0.912137i	0.999519	−	0.0310191i	$-0.00987527\pi$
$114$	0.633975	+	1.09808i	0.0593772	+	0.102844i
$115$		0			0
$116$	3.00000			0.278543
$117$	−2.00000	+	3.00000i	−0.184900	+	0.277350i
$118$	13.8564			1.27559
$119$	21.2942	−	12.2942i	1.95204	−	1.12701i
$120$		0			0
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$		−	4.80385i		−	0.434920i
$123$	−0.401924	−	0.232051i	−0.0362402	−	0.0209233i
$124$	−2.19615	−	1.26795i	−0.197220	−	0.113865i
$125$		0			0
$126$	2.36603	−	4.09808i	0.210782	−	0.365086i
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	6.19615			0.545541
$130$		0			0
$131$	16.3923			1.43220			0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923			1.43220			0.716101	+	0.697997i	$0.245925\pi$
$132$	−4.09808	+	2.36603i	−0.356692	+	0.205936i
$133$	3.00000	+	5.19615i	0.260133	+	0.450564i
$134$	−5.36603	+	9.29423i	−0.463554	+	0.802899i
$135$		0			0
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$138$		−	2.19615i		−	0.186949i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	1.09808	−	0.633975i	0.0924747	−	0.0533903i
$142$	−8.19615			−0.687806
$143$	15.2942	−	7.56218i	1.27897	−	0.632381i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−6.06218	−	10.5000i	−0.501709	−	0.868986i
$147$	7.69615	−	13.3301i	0.634768	−	1.09945i
$148$			3.00000i			0.246598i
$149$	−15.6962	−	9.06218i	−1.28588	−	0.742403i	−0.307962	−	0.951399i	$-0.599647\pi$
$149$	−15.6962	−	9.06218i	−1.28588	−	0.742403i	−0.977916	+	0.208996i	$0.932980\pi$
$150$		0			0
$151$			7.26795i			0.591457i	0.955272	+	0.295729i	$0.0955624\pi$
$151$			7.26795i			0.591457i	−0.955272	+	0.295729i	$0.904438\pi$
$152$	−0.633975	+	1.09808i	−0.0514221	+	0.0890657i
$153$	2.59808	+	4.50000i	0.210042	+	0.363803i
$154$	−19.3923	+	11.1962i	−1.56268	+	0.902212i
$155$		0			0
$156$	−3.59808	−	0.232051i	−0.288077	−	0.0185789i
$157$	3.19615			0.255081			0.127540	−	0.991833i	$-0.459292\pi$
$157$	3.19615			0.255081			0.127540	+	0.991833i	$0.459292\pi$
$158$	10.7321	−	6.19615i	0.853796	−	0.492939i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	8.19615	+	4.73205i	0.641972	+	0.370643i	0.785374	−	0.619022i	$-0.212471\pi$
$163$	8.19615	+	4.73205i	0.641972	+	0.370643i	−0.143402	+	0.989665i	$0.545804\pi$
$164$		−	0.464102i		−	0.0362402i
$165$		0			0
$166$	5.83013	+	10.0981i	0.452506	+	0.783763i
$167$	2.19615	−	1.26795i	0.169943	−	0.0981169i	−0.412616	−	0.910905i	$-0.635385\pi$
$167$	2.19615	−	1.26795i	0.169943	−	0.0981169i	0.582559	+	0.812788i	$0.302051\pi$
$168$	4.73205			0.365086
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$		0			0
$171$	−1.09808	+	0.633975i	−0.0839720	+	0.0484812i
$172$	3.09808	+	5.36603i	0.236226	+	0.409156i
$173$	−8.19615	+	14.1962i	−0.623142	+	1.07931i	0.365755	+	0.930711i	$0.380811\pi$
$173$	−8.19615	+	14.1962i	−0.623142	+	1.07931i	−0.988897	+	0.148602i	$0.952523\pi$
$174$			3.00000i			0.227429i
$175$		0			0
$176$	−4.09808	−	2.36603i	−0.308904	−	0.178346i
$177$			13.8564i			1.04151i
$178$	−1.26795	+	2.19615i	−0.0950368	+	0.164609i
$179$	−4.09808	−	7.09808i	−0.306305	−	0.530535i	0.671246	−	0.741234i	$-0.265759\pi$
$179$	−4.09808	−	7.09808i	−0.306305	−	0.530535i	−0.977551	+	0.210699i	$0.932426\pi$
$180$		0			0
$181$	11.5885			0.861363			0.430682	−	0.902504i	$-0.358273\pi$
$181$	11.5885			0.861363			0.430682	+	0.902504i	$0.358273\pi$
$182$	−17.0263	−	1.09808i	−1.26207	−	0.0813948i
$183$	4.80385			0.355111
$184$	1.90192	−	1.09808i	0.140212	−	0.0809513i
$185$		0			0
$186$	1.26795	−	2.19615i	0.0929705	−	0.161030i
$187$		−	24.5885i		−	1.79809i
$188$	1.09808	+	0.633975i	0.0800854	+	0.0462373i
$189$	4.09808	+	2.36603i	0.298091	+	0.172103i
$190$		0			0
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	0.194910	+	0.980821i	$0.437558\pi$
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	−0.946871	+	0.321613i	$0.895775\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.0885	−	6.40192i	0.798165	−	0.460821i	−0.0446644	−	0.999002i	$-0.514222\pi$
$193$	11.0885	−	6.40192i	0.798165	−	0.460821i	0.842829	+	0.538181i	$0.180889\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	15.3923			1.09945
$197$	6.00000	−	3.46410i	0.427482	−	0.246807i	−0.270791	−	0.962638i	$-0.587285\pi$
$197$	6.00000	−	3.46410i	0.427482	−	0.246807i	0.698273	+	0.715831i	$0.253952\pi$
$198$	−2.36603	−	4.09808i	−0.168146	−	0.291238i
$199$	4.29423	−	7.43782i	0.304410	−	0.527253i	−0.672720	−	0.739897i	$-0.734874\pi$
$199$	4.29423	−	7.43782i	0.304410	−	0.527253i	0.977130	+	0.212644i	$0.0682074\pi$
$200$		0			0
$201$	−9.29423	−	5.36603i	−0.655564	−	0.378490i
$202$	1.20577	+	0.696152i	0.0848378	+	0.0489811i
$203$			14.1962i			0.996375i
$204$	−2.59808	+	4.50000i	−0.181902	+	0.315063i
$205$		0			0
$206$	3.63397	−	2.09808i	0.253191	−	0.146180i
$207$	2.19615			0.152643
$208$	−1.59808	−	3.23205i	−0.110807	−	0.224102i
$209$	6.00000			0.415029
$210$		0			0
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	0.921413	−	0.388585i	$-0.127036\pi$
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	−0.797231	+	0.603674i	$0.793703\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		−	8.19615i		−	0.561591i
$214$	−7.09808	−	4.09808i	−0.485215	−	0.280139i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	6.00000	−	10.3923i	0.407307	−	0.705476i
$218$	8.19615	+	14.1962i	0.555113	+	0.961485i
$219$	10.5000	−	6.06218i	0.709524	−	0.409644i
$220$		0			0
$221$	10.3923	−	15.5885i	0.699062	−	1.04859i
$222$	−3.00000			−0.201347
$223$	−16.3923	+	9.46410i	−1.09771	+	0.633763i	−0.935619	−	0.353013i	$-0.885157\pi$
$223$	−16.3923	+	9.46410i	−1.09771	+	0.633763i	−0.162091	+	0.986776i	$0.551824\pi$
$224$	2.36603	+	4.09808i	0.158087	+	0.273814i
$225$		0			0
$226$			11.1962i			0.744757i
$227$	8.49038	+	4.90192i	0.563526	+	0.325352i	0.754560	−	0.656231i	$-0.227851\pi$
$227$	8.49038	+	4.90192i	0.563526	+	0.325352i	−0.191033	+	0.981584i	$0.561184\pi$
$228$	−1.09808	−	0.633975i	−0.0727219	−	0.0419860i
$229$			19.8564i			1.31215i	0.754696	+	0.656074i	$0.227784\pi$
$229$			19.8564i			1.31215i	−0.754696	+	0.656074i	$0.772216\pi$
$230$		0			0
$231$	−11.1962	−	19.3923i	−0.736653	−	1.27592i
$232$	−2.59808	+	1.50000i	−0.170572	+	0.0984798i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	0.232051	−	3.59808i	0.0151696	−	0.235214i
$235$		0			0
$236$	−12.0000	+	6.92820i	−0.781133	+	0.450988i
$237$	6.19615	+	10.7321i	0.402483	+	0.697122i
$238$	−12.2942	+	21.2942i	−0.796916	+	1.38030i
$239$			24.5885i			1.59050i	0.606285	+	0.795248i	$0.292659\pi$
$239$			24.5885i			1.59050i	−0.606285	+	0.795248i	$0.707341\pi$
$240$		0			0
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	0.477411	−	0.878680i	$-0.341575\pi$
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	−0.522254	+	0.852790i	$0.674909\pi$
$242$			11.3923i			0.732325i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.40192	+	4.16025i	0.153767	+	0.266333i
$245$		0			0
$246$	0.464102			0.0295900
$247$	3.80385	+	2.53590i	0.242033	+	0.161355i
$248$	2.53590			0.161030
$249$	−10.0981	+	5.83013i	−0.639940	+	0.369469i
$250$		0			0
$251$	−2.19615	+	3.80385i	−0.138620	+	0.240097i	−0.926974	−	0.375124i	$-0.877600\pi$
$251$	−2.19615	+	3.80385i	−0.138620	+	0.240097i	0.788355	+	0.615221i	$0.210933\pi$
$252$			4.73205i			0.298091i
$253$	−9.00000	−	5.19615i	−0.565825	−	0.326679i
$254$	−3.46410	−	2.00000i	−0.217357	−	0.125491i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.40192	−	11.0885i	−0.399341	−	0.691679i	0.594304	−	0.804241i	$-0.297428\pi$
$257$	−6.40192	−	11.0885i	−0.399341	−	0.691679i	−0.993645	+	0.112562i	$0.964094\pi$
$258$	−5.36603	+	3.09808i	−0.334074	+	0.192878i
$259$	−14.1962			−0.882106
$260$		0			0
$261$	−3.00000			−0.185695
$262$	−14.1962	+	8.19615i	−0.877041	+	0.506360i
$263$	−1.09808	−	1.90192i	−0.0677103	−	0.117278i	0.830183	−	0.557491i	$-0.188236\pi$
$263$	−1.09808	−	1.90192i	−0.0677103	−	0.117278i	−0.897893	+	0.440214i	$0.854903\pi$
$264$	2.36603	−	4.09808i	0.145619	−	0.252219i
$265$		0			0
$266$	−5.19615	−	3.00000i	−0.318597	−	0.183942i
$267$	−2.19615	−	1.26795i	−0.134402	−	0.0775972i
$268$		−	10.7321i		−	0.655564i
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	−0.000940662	−	1.00000i	$-0.500299\pi$
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	0.866495	−	0.499185i	$-0.166367\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	−5.19615			−0.315063
$273$	1.09808	−	17.0263i	0.0664586	−	1.03048i
$274$	9.00000			0.543710
$275$		0			0
$276$	1.09808	+	1.90192i	0.0660964	+	0.114482i
$277$	−7.59808	+	13.1603i	−0.456524	+	0.790723i	−0.998774	−	0.0494940i	$-0.984239\pi$
$277$	−7.59808	+	13.1603i	−0.456524	+	0.790723i	0.542250	+	0.840217i	$0.317572\pi$
$278$			4.00000i			0.239904i
$279$	2.19615	+	1.26795i	0.131480	+	0.0759101i
$280$		0			0
$281$			24.4641i			1.45941i	0.683764	+	0.729703i	$0.260342\pi$
$281$			24.4641i			1.45941i	−0.683764	+	0.729703i	$0.739658\pi$
$282$	−0.633975	+	1.09808i	−0.0377526	+	0.0653895i
$283$	15.0981	+	26.1506i	0.897487	+	1.55449i	0.830696	+	0.556727i	$0.187943\pi$
$283$	15.0981	+	26.1506i	0.897487	+	1.55449i	0.0667919	+	0.997767i	$0.478724\pi$
$284$	7.09808	−	4.09808i	0.421193	−	0.243176i
$285$		0			0
$286$	−9.46410	+	14.1962i	−0.559624	+	0.839436i
$287$	2.19615			0.129635
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$		0			0
$291$			6.00000i			0.351726i
$292$	10.5000	+	6.06218i	0.614466	+	0.354762i
$293$	−12.6962	−	7.33013i	−0.741717	−	0.428231i	0.0809762	−	0.996716i	$-0.474196\pi$
$293$	−12.6962	−	7.33013i	−0.741717	−	0.428231i	−0.822693	+	0.568485i	$0.807530\pi$
$294$			15.3923i			0.897697i
$295$		0			0
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	4.09808	−	2.36603i	0.237795	−	0.137291i
$298$	18.1244			1.04992
$299$	−3.50962	−	7.09808i	−0.202967	−	0.410492i
$300$		0			0
$301$	−25.3923	+	14.6603i	−1.46359	+	0.845003i
$302$	−3.63397	−	6.29423i	−0.209112	−	0.362192i
$303$	−0.696152	+	1.20577i	−0.0399929	+	0.0692698i
$304$		−	1.26795i		−	0.0727219i
$305$		0			0
$306$	−4.50000	−	2.59808i	−0.257248	−	0.148522i
$307$		−	10.7321i		−	0.612510i	−0.951949	−	0.306255i	$-0.900924\pi$
$307$		−	10.7321i		−	0.612510i	0.951949	−	0.306255i	$-0.0990761\pi$
$308$	11.1962	−	19.3923i	0.637960	−	1.10498i
$309$	2.09808	+	3.63397i	0.119355	+	0.206730i
$310$		0			0
$311$	−2.19615			−0.124532			−0.0622662	−	0.998060i	$-0.519833\pi$
$311$	−2.19615			−0.124532			−0.0622662	+	0.998060i	$0.519833\pi$
$312$	3.23205	−	1.59808i	0.182979	−	0.0904732i
$313$	24.3923			1.37873			0.689367	−	0.724412i	$-0.257889\pi$
$313$	24.3923			1.37873			0.689367	+	0.724412i	$0.257889\pi$
$314$	−2.76795	+	1.59808i	−0.156204	+	0.0901847i
$315$		0			0
$316$	−6.19615	+	10.7321i	−0.348561	+	0.603725i
$317$			6.12436i			0.343978i	0.985099	+	0.171989i	$0.0550194\pi$
$317$			6.12436i			0.343978i	−0.985099	+	0.171989i	$0.944981\pi$
$318$	−2.59808	−	1.50000i	−0.145693	−	0.0841158i
$319$	12.2942	+	7.09808i	0.688345	+	0.397416i
$320$		0			0
$321$	4.09808	−	7.09808i	0.228732	−	0.396176i
$322$	5.19615	+	9.00000i	0.289570	+	0.501550i
$323$	5.70577	−	3.29423i	0.317478	−	0.183296i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−9.46410			−0.524168
$327$	−14.1962	+	8.19615i	−0.785049	+	0.453248i
$328$	0.232051	+	0.401924i	0.0128129	+	0.0221925i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$	−10.0981	−	5.83013i	−0.554204	−	0.319970i
$333$		−	3.00000i		−	0.164399i
$334$	−1.26795	+	2.19615i	−0.0693791	+	0.120168i
$335$		0			0
$336$	−4.09808	+	2.36603i	−0.223568	+	0.129077i
$337$	−31.0000			−1.68868			−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000			−1.68868			−0.844339	+	0.535810i	$0.820006\pi$
$338$	−12.0000	+	5.00000i	−0.652714	+	0.271964i
$339$	−11.1962			−0.608092
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	0.633975	−	1.09808i	0.0342814	−	0.0593772i
$343$			39.7128i			2.14429i
$344$	−5.36603	−	3.09808i	−0.289317	−	0.167037i
$345$		0			0
$346$		−	16.3923i		−	0.881256i
$347$	−6.29423	+	10.9019i	−0.337892	+	0.585246i	−0.984036	−	0.177969i	$-0.943047\pi$
$347$	−6.29423	+	10.9019i	−0.337892	+	0.585246i	0.646144	+	0.763215i	$0.276380\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	2.19615	−	1.26795i	0.117557	−	0.0678718i	−0.440068	−	0.897964i	$-0.645046\pi$
$349$	2.19615	−	1.26795i	0.117557	−	0.0678718i	0.557626	+	0.830093i	$0.311712\pi$
$350$		0			0
$351$	3.59808	+	0.232051i	0.192051	+	0.0123860i
$352$	4.73205			0.252219
$353$	5.00962	−	2.89230i	0.266635	−	0.153942i	−0.360722	−	0.932673i	$-0.617470\pi$
$353$	5.00962	−	2.89230i	0.266635	−	0.153942i	0.627358	+	0.778731i	$0.284136\pi$
$354$	−6.92820	−	12.0000i	−0.368230	−	0.637793i
$355$		0			0
$356$		−	2.53590i		−	0.134402i
$357$	−21.2942	−	12.2942i	−1.12701	−	0.650680i
$358$	7.09808	+	4.09808i	0.375145	+	0.216590i
$359$			22.0526i			1.16389i	0.813228	+	0.581945i	$0.197708\pi$
$359$			22.0526i			1.16389i	−0.813228	+	0.581945i	$0.802292\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	−10.0359	+	5.79423i	−0.527475	+	0.304538i
$363$	−11.3923			−0.597941
$364$	15.2942	−	7.56218i	0.801635	−	0.396366i
$365$		0			0
$366$	−4.16025	+	2.40192i	−0.217460	+	0.125551i
$367$	−12.0981	−	20.9545i	−0.631514	−	1.09382i	−0.987242	−	0.159225i	$-0.949100\pi$
$367$	−12.0981	−	20.9545i	−0.631514	−	1.09382i	0.355728	−	0.934590i	$-0.384233\pi$
$368$	−1.09808	+	1.90192i	−0.0572412	+	0.0991446i
$369$			0.464102i			0.0241602i
$370$		0			0
$371$	−12.2942	−	7.09808i	−0.638285	−	0.368514i
$372$			2.53590i			0.131480i
$373$	11.9904	−	20.7679i	0.620838	−	1.07532i	−0.368492	−	0.929631i	$-0.620126\pi$
$373$	11.9904	−	20.7679i	0.620838	−	1.07532i	0.989330	−	0.145693i	$-0.0465410\pi$
$374$	12.2942	+	21.2942i	0.635719	+	1.10110i
$375$		0			0
$376$	−1.26795			−0.0653895
$377$	4.79423	+	9.69615i	0.246915	+	0.499377i
$378$	−4.73205			−0.243390
$379$	15.8038	−	9.12436i	0.811789	−	0.468687i	−0.0357877	−	0.999359i	$-0.511394\pi$
$379$	15.8038	−	9.12436i	0.811789	−	0.468687i	0.847577	+	0.530673i	$0.178061\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$		−	20.7846i		−	1.06343i
$383$	−9.80385	−	5.66025i	−0.500953	−	0.289225i	0.228154	−	0.973625i	$-0.426731\pi$
$383$	−9.80385	−	5.66025i	−0.500953	−	0.289225i	−0.729107	+	0.684400i	$0.760064\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	−6.40192	+	11.0885i	−0.325849	+	0.564388i
$387$	−3.09808	−	5.36603i	−0.157484	−	0.272770i
$388$	−5.19615	+	3.00000i	−0.263795	+	0.152302i
$389$	13.3923			0.679017			0.339508	−	0.940603i	$-0.389739\pi$
$389$	13.3923			0.679017			0.339508	+	0.940603i	$0.389739\pi$
$390$		0			0
$391$	−11.4115			−0.577107
$392$	−13.3301	+	7.69615i	−0.673273	+	0.388714i
$393$	−8.19615	−	14.1962i	−0.413441	−	0.716101i
$394$	−3.46410	+	6.00000i	−0.174519	+	0.302276i
$395$		0			0
$396$	4.09808	+	2.36603i	0.205936	+	0.118897i
$397$	−14.1962	−	8.19615i	−0.712484	−	0.411353i	0.0994958	−	0.995038i	$-0.468277\pi$
$397$	−14.1962	−	8.19615i	−0.712484	−	0.411353i	−0.811980	+	0.583685i	$0.801610\pi$
$398$			8.58846i			0.430500i
$399$	3.00000	−	5.19615i	0.150188	−	0.260133i
$400$		0			0
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.0283431	−	0.999598i	$-0.490977\pi$
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.879849	+	0.475253i	$0.157644\pi$
$402$	10.7321			0.535266
$403$	0.588457	−	9.12436i	0.0293131	−	0.454517i
$404$	−1.39230			−0.0692698
$405$		0			0
$406$	−7.09808	−	12.2942i	−0.352272	−	0.610152i
$407$	−7.09808	+	12.2942i	−0.351839	+	0.609402i
$408$		−	5.19615i		−	0.257248i
$409$	−2.89230	−	1.66987i	−0.143015	−	0.0825699i	0.426785	−	0.904353i	$-0.359646\pi$
$409$	−2.89230	−	1.66987i	−0.143015	−	0.0825699i	−0.569800	+	0.821783i	$0.692979\pi$
$410$		0			0
$411$			9.00000i			0.443937i
$412$	−2.09808	+	3.63397i	−0.103365	+	0.179033i
$413$	−32.7846	−	56.7846i	−1.61323	−	2.79419i
$414$	−1.90192	+	1.09808i	−0.0934745	+	0.0539675i
$415$		0			0
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$	−4.00000			−0.195881
$418$	−5.19615	+	3.00000i	−0.254152	+	0.146735i
$419$	−8.19615	−	14.1962i	−0.400408	−	0.693527i	0.593367	−	0.804932i	$-0.297798\pi$
$419$	−8.19615	−	14.1962i	−0.400408	−	0.693527i	−0.993775	+	0.111405i	$0.964465\pi$
$420$		0			0
$421$		−	0.464102i		−	0.0226189i	−0.999936	−	0.0113095i	$-0.996400\pi$
$421$		−	0.464102i		−	0.0226189i	0.999936	−	0.0113095i	$-0.00359999\pi$
$422$	−3.12436	−	1.80385i	−0.152091	−	0.0878099i
$423$	−1.09808	−	0.633975i	−0.0533903	−	0.0308249i
$424$		−	3.00000i		−	0.145693i
$425$		0			0
$426$	4.09808	+	7.09808i	0.198552	+	0.343903i
$427$	−19.6865	+	11.3660i	−0.952698	+	0.550041i
$428$	8.19615			0.396176
$429$	−14.1962	−	9.46410i	−0.685397	−	0.456931i
$430$		0			0
$431$	−24.0788	+	13.9019i	−1.15984	+	0.669632i	−0.951265	−	0.308375i	$-0.900215\pi$
$431$	−24.0788	+	13.9019i	−1.15984	+	0.669632i	−0.208572	+	0.978007i	$0.566882\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	16.8923	−	29.2583i	0.811792	−	1.40607i	−0.0998161	−	0.995006i	$-0.531825\pi$
$433$	16.8923	−	29.2583i	0.811792	−	1.40607i	0.911608	−	0.411060i	$-0.134841\pi$
$434$			12.0000i			0.576018i
$435$		0			0
$436$	−14.1962	−	8.19615i	−0.679872	−	0.392525i
$437$		−	2.78461i		−	0.133206i
$438$	−6.06218	+	10.5000i	−0.289662	+	0.501709i
$439$	8.29423	+	14.3660i	0.395862	+	0.685653i	0.993211	−	0.116329i	$-0.0371125\pi$
$439$	8.29423	+	14.3660i	0.395862	+	0.685653i	−0.597349	+	0.801982i	$0.703779\pi$
$440$		0			0
$441$	−15.3923			−0.732967
$442$	−1.20577	+	18.6962i	−0.0573527	+	0.889285i
$443$	4.39230			0.208685			0.104342	−	0.994541i	$-0.466726\pi$
$443$	4.39230			0.208685			0.104342	+	0.994541i	$0.466726\pi$
$444$	2.59808	−	1.50000i	0.123299	−	0.0711868i
$445$		0			0
$446$	9.46410	−	16.3923i	0.448138	−	0.776198i
$447$			18.1244i			0.857253i
$448$	−4.09808	−	2.36603i	−0.193616	−	0.111784i
$449$	−28.9808	−	16.7321i	−1.36769	−	0.789634i	−0.377054	−	0.926191i	$-0.623063\pi$
$449$	−28.9808	−	16.7321i	−1.36769	−	0.789634i	−0.990632	+	0.136557i	$0.956396\pi$
$450$		0			0
$451$	1.09808	−	1.90192i	0.0517064	−	0.0895581i
$452$	−5.59808	−	9.69615i	−0.263311	−	0.456069i
$453$	6.29423	−	3.63397i	0.295729	−	0.170739i
$454$	−9.80385			−0.460117
$455$		0			0
$456$	1.26795			0.0593772
$457$	17.3038	−	9.99038i	0.809440	−	0.467330i	−0.0373215	−	0.999303i	$-0.511883\pi$
$457$	17.3038	−	9.99038i	0.809440	−	0.467330i	0.846761	+	0.531973i	$0.178549\pi$
$458$	−9.92820	−	17.1962i	−0.463914	−	0.803523i
$459$	2.59808	−	4.50000i	0.121268	−	0.210042i
$460$		0			0
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	0.0396167	−	0.999215i	$-0.487386\pi$
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	−0.845537	+	0.533917i	$0.820720\pi$
$462$	19.3923	+	11.1962i	0.902212	+	0.520892i
$463$			26.1962i			1.21744i	0.793386	+	0.608719i	$0.208316\pi$
$463$			26.1962i			1.21744i	−0.793386	+	0.608719i	$0.791684\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	15.5885	−	9.00000i	0.722121	−	0.416917i
$467$	36.5885			1.69311			0.846556	−	0.532300i	$-0.178672\pi$
$467$	36.5885			1.69311			0.846556	+	0.532300i	$0.178672\pi$
$468$	1.59808	+	3.23205i	0.0738711	+	0.149402i
$469$	50.7846			2.34502
$470$		0			0
$471$	−1.59808	−	2.76795i	−0.0736355	−	0.127540i
$472$	6.92820	−	12.0000i	0.318896	−	0.552345i
$473$			29.3205i			1.34816i
$474$	−10.7321	−	6.19615i	−0.492939	−	0.284599i
$475$		0			0
$476$		−	24.5885i		−	1.12701i
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	−12.2942	−	21.2942i	−0.562325	−	0.973975i
$479$	−30.5885	+	17.6603i	−1.39762	+	0.806918i	−0.994143	−	0.108071i	$-0.965533\pi$
$479$	−30.5885	+	17.6603i	−1.39762	+	0.806918i	−0.403479	+	0.914989i	$0.632199\pi$
$480$		0			0
$481$	−9.69615	+	4.79423i	−0.442106	+	0.218598i
$482$	0.803848			0.0366143
$483$	−9.00000	+	5.19615i	−0.409514	+	0.236433i
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−7.90192	−	4.56218i	−0.358070	−	0.206732i	0.310164	−	0.950683i	$-0.399616\pi$
$487$	−7.90192	−	4.56218i	−0.358070	−	0.206732i	−0.668234	+	0.743951i	$0.732949\pi$
$488$	−4.16025	−	2.40192i	−0.188326	−	0.108730i
$489$		−	9.46410i		−	0.427981i
$490$		0			0
$491$	0.294229	+	0.509619i	0.0132784	+	0.0229988i	0.872588	−	0.488457i	$-0.162440\pi$
$491$	0.294229	+	0.509619i	0.0132784	+	0.0229988i	−0.859310	+	0.511455i	$0.829107\pi$
$492$	−0.401924	+	0.232051i	−0.0181201	+	0.0104617i
$493$	15.5885			0.702069
$494$	−4.56218	−	0.294229i	−0.205262	−	0.0132380i
$495$		0			0
$496$	−2.19615	+	1.26795i	−0.0986102	+	0.0569326i
$497$	19.3923	+	33.5885i	0.869864	+	1.50665i
$498$	5.83013	−	10.0981i	0.261254	−	0.452506i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	−2.19615	−	1.26795i	−0.0981169	−	0.0566478i
$502$		−	4.39230i		−	0.196038i
$503$	−9.29423	+	16.0981i	−0.414409	+	0.717778i	−0.995366	−	0.0961565i	$-0.969345\pi$
$503$	−9.29423	+	16.0981i	−0.414409	+	0.717778i	0.580957	+	0.813934i	$0.302678\pi$
$504$	−2.36603	−	4.09808i	−0.105391	−	0.182543i
$505$		0			0
$506$	10.3923			0.461994
$507$	−5.00000	−	12.0000i	−0.222058	−	0.532939i
$508$	4.00000			0.177471
$509$	−8.08846	+	4.66987i	−0.358515	+	0.206988i	−0.668429	−	0.743776i	$-0.733033\pi$
$509$	−8.08846	+	4.66987i	−0.358515	+	0.206988i	0.309914	+	0.950764i	$0.399700\pi$
$510$		0			0
$511$	−28.6865	+	49.6865i	−1.26902	+	2.19800i
$512$		−	1.00000i		−	0.0441942i
$513$	1.09808	+	0.633975i	0.0484812	+	0.0279907i
$514$	11.0885	+	6.40192i	0.489091	+	0.282377i
$515$		0			0
$516$	3.09808	−	5.36603i	0.136385	−	0.236226i
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	12.2942	−	7.09808i	0.540177	−	0.311872i
$519$	16.3923			0.719542
$520$		0			0
$521$	−18.8038			−0.823812			−0.411906	−	0.911226i	$-0.635137\pi$
$521$	−18.8038			−0.823812			−0.411906	+	0.911226i	$0.635137\pi$
$522$	2.59808	−	1.50000i	0.113715	−	0.0656532i
$523$	0.705771	+	1.22243i	0.0308612	+	0.0534532i	0.881044	−	0.473035i	$-0.156842\pi$
$523$	0.705771	+	1.22243i	0.0308612	+	0.0534532i	−0.850182	+	0.526488i	$0.823508\pi$
$524$	8.19615	−	14.1962i	0.358051	−	0.620162i
$525$		0			0
$526$	1.90192	+	1.09808i	0.0829278	+	0.0478784i
$527$	−11.4115	−	6.58846i	−0.497095	−	0.286998i
$528$			4.73205i			0.205936i
$529$	9.08846	−	15.7417i	0.395150	−	0.684420i
$530$		0			0
$531$	12.0000	−	6.92820i	0.520756	−	0.300658i
$532$	6.00000			0.260133
$533$	1.50000	−	0.741670i	0.0649722	−	0.0321253i
$534$	2.53590			0.109739
$535$		0			0
$536$	5.36603	+	9.29423i	0.231777	+	0.401450i
$537$	−4.09808	+	7.09808i	−0.176845	+	0.306305i
$538$			28.3923i			1.22408i
$539$	63.0788	+	36.4186i	2.71700	+	1.56866i
$540$		0			0
$541$			16.8564i			0.724714i	0.932039	+	0.362357i	$0.118028\pi$
$541$			16.8564i			0.724714i	−0.932039	+	0.362357i	$0.881972\pi$
$542$		0			0
$543$	−5.79423	−	10.0359i	−0.248654	−	0.430682i
$544$	4.50000	−	2.59808i	0.192936	−	0.111392i
$545$		0			0
$546$	7.56218	+	15.2942i	0.323631	+	0.654533i
$547$	6.19615			0.264928			0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615			0.264928			0.132464	+	0.991188i	$0.457711\pi$
$548$	−7.79423	+	4.50000i	−0.332953	+	0.192230i
$549$	−2.40192	−	4.16025i	−0.102512	−	0.177555i
$550$		0			0
$551$			3.80385i			0.162049i
$552$	−1.90192	−	1.09808i	−0.0809513	−	0.0467372i
$553$	−50.7846	−	29.3205i	−2.15958	−	1.24683i
$554$		−	15.1962i		−	0.645623i
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	−19.2846	+	11.1340i	−0.817115	+	0.471762i	−0.849421	−	0.527716i	$-0.823048\pi$
$557$	−19.2846	+	11.1340i	−0.817115	+	0.471762i	0.0323055	+	0.999478i	$0.489715\pi$
$558$	−2.53590			−0.107353
$559$	−12.3923	+	18.5885i	−0.524139	+	0.786208i
$560$		0			0
$561$	−21.2942	+	12.2942i	−0.899043	+	0.519063i
$562$	−12.2321	−	21.1865i	−0.515978	−	0.893700i
$563$	−4.39230	+	7.60770i	−0.185114	+	0.320626i	−0.943615	−	0.331046i	$-0.892599\pi$
$563$	−4.39230	+	7.60770i	−0.185114	+	0.320626i	0.758501	+	0.651672i	$0.225932\pi$
$564$		−	1.26795i		−	0.0533903i
$565$		0			0
$566$	−26.1506	−	15.0981i	−1.09919	−	0.634619i
$567$		−	4.73205i		−	0.198727i
$568$	−4.09808	+	7.09808i	−0.171951	+	0.297829i
$569$	−16.3923	−	28.3923i	−0.687201	−	1.19027i	−0.972740	−	0.231900i	$-0.925506\pi$
$569$	−16.3923	−	28.3923i	−0.687201	−	1.19027i	0.285538	−	0.958367i	$-0.407828\pi$
$570$		0			0
$571$	13.8038			0.577673			0.288837	−	0.957378i	$-0.406732\pi$
$571$	13.8038			0.577673			0.288837	+	0.957378i	$0.406732\pi$
$572$	1.09808	−	17.0263i	0.0459129	−	0.711905i
$573$	20.7846			0.868290
$574$	−1.90192	+	1.09808i	−0.0793848	+	0.0458328i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	16.2679i		−	0.677244i	−0.940923	−	0.338622i	$-0.890039\pi$
$577$		−	16.2679i		−	0.677244i	0.940923	−	0.338622i	$-0.109961\pi$
$578$	8.66025	+	5.00000i	0.360219	+	0.207973i
$579$	−11.0885	−	6.40192i	−0.460821	−	0.266055i
$580$		0			0
$581$	27.5885	−	47.7846i	1.14456	−	1.98244i
$582$	−3.00000	−	5.19615i	−0.124354	−	0.215387i
$583$	−12.2942	+	7.09808i	−0.509175	+	0.293972i
$584$	−12.1244			−0.501709
$585$		0			0
$586$	14.6603			0.605610
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$	−7.69615	−	13.3301i	−0.317384	−	0.549725i
$589$	1.60770	−	2.78461i	0.0662439	−	0.114738i
$590$		0			0
$591$	−6.00000	−	3.46410i	−0.246807	−	0.142494i
$592$	2.59808	+	1.50000i	0.106780	+	0.0616496i
$593$			46.8564i			1.92416i	0.272764	+	0.962081i	$0.412062\pi$
$593$			46.8564i			1.92416i	−0.272764	+	0.962081i	$0.587938\pi$
$594$	−2.36603	+	4.09808i	−0.0970792	+	0.168146i
$595$		0			0
$596$	−15.6962	+	9.06218i	−0.642939	+	0.371201i
$597$	−8.58846			−0.351502
$598$	6.58846	+	4.39230i	0.269422	+	0.179615i
$599$	−4.39230			−0.179465			−0.0897324	−	0.995966i	$-0.528601\pi$
$599$	−4.39230			−0.179465			−0.0897324	+	0.995966i	$0.528601\pi$
$600$		0			0
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$	14.6603	−	25.3923i	0.597507	−	1.03491i
$603$			10.7321i			0.437043i
$604$	6.29423	+	3.63397i	0.256109	+	0.147864i
$605$		0			0
$606$		−	1.39230i		−	0.0565585i
$607$	−24.3923	+	42.2487i	−0.990053	+	1.71482i	−0.373182	+	0.927758i	$0.621733\pi$
$607$	−24.3923	+	42.2487i	−0.990053	+	1.71482i	−0.616871	+	0.787064i	$0.711600\pi$
$608$	0.633975	+	1.09808i	0.0257111	+	0.0445329i
$609$	12.2942	−	7.09808i	0.498187	−	0.287629i
$610$		0			0
$611$	−0.294229	+	4.56218i	−0.0119032	+	0.184566i
$612$	5.19615			0.210042
$613$	−35.3827	+	20.4282i	−1.42909	+	0.825087i	−0.997049	−	0.0767652i	$-0.975541\pi$
$613$	−35.3827	+	20.4282i	−1.42909	+	0.825087i	−0.432044	+	0.901853i	$0.642207\pi$
$614$	5.36603	+	9.29423i	0.216555	+	0.375085i
$615$		0			0
$616$			22.3923i			0.902212i
$617$	−9.18653	−	5.30385i	−0.369836	−	0.213525i	0.303551	−	0.952815i	$-0.401828\pi$
$617$	−9.18653	−	5.30385i	−0.369836	−	0.213525i	−0.673387	+	0.739290i	$0.735161\pi$
$618$	−3.63397	−	2.09808i	−0.146180	−	0.0843970i
$619$		−	7.60770i		−	0.305779i	−0.988243	−	0.152890i	$-0.951142\pi$
$619$		−	7.60770i		−	0.305779i	0.988243	−	0.152890i	$-0.0488579\pi$
$620$		0			0
$621$	−1.09808	−	1.90192i	−0.0440643	−	0.0763216i
$622$	1.90192	−	1.09808i	0.0762602	−	0.0440288i
$623$	12.0000			0.480770
$624$	−2.00000	+	3.00000i	−0.0800641	+	0.120096i
$625$		0			0
$626$	−21.1244	+	12.1962i	−0.844299	+	0.487456i
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$	1.59808	−	2.76795i	0.0637702	−	0.110453i
$629$			15.5885i			0.621552i
$630$		0			0
$631$	−22.3923	−	12.9282i	−0.891424	−	0.514664i	−0.0170157	−	0.999855i	$-0.505417\pi$
$631$	−22.3923	−	12.9282i	−0.891424	−	0.514664i	−0.874408	+	0.485192i	$0.838750\pi$
$632$		−	12.3923i		−	0.492939i
$633$	1.80385	−	3.12436i	0.0716965	−	0.124182i
$634$	−3.06218	−	5.30385i	−0.121615	−	0.210643i
$635$		0			0
$636$	3.00000			0.118958
$637$	24.5981	+	49.7487i	0.974611	+	1.97112i
$638$	−14.1962			−0.562031
$639$	−7.09808	+	4.09808i	−0.280796	+	0.162117i
$640$		0			0
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	0.383175	+	0.923676i	$0.374831\pi$
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	−0.991514	+	0.129999i	$0.958503\pi$
$642$			8.19615i			0.323476i
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.891982	−	0.452071i	$-0.149315\pi$
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.0544858	+	0.998515i	$0.482648\pi$
$644$	−9.00000	−	5.19615i	−0.354650	−	0.204757i
$645$		0			0
$646$	−3.29423	+	5.70577i	−0.129610	+	0.224491i
$647$	−6.58846	−	11.4115i	−0.259019	−	0.448634i	0.706960	−	0.707253i	$-0.250066\pi$
$647$	−6.58846	−	11.4115i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916733\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−65.5692			−2.57382
$650$		0			0
$651$	−12.0000			−0.470317
$652$	8.19615	−	4.73205i	0.320986	−	0.185321i
$653$	−24.5885	−	42.5885i	−0.962221	−	1.66662i	−0.716904	−	0.697172i	$-0.754441\pi$
$653$	−24.5885	−	42.5885i	−0.962221	−	1.66662i	−0.245317	−	0.969443i	$-0.578892\pi$
$654$	8.19615	−	14.1962i	0.320495	−	0.555113i
$655$		0			0
$656$	−0.401924	−	0.232051i	−0.0156925	−	0.00906006i
$657$	−10.5000	−	6.06218i	−0.409644	−	0.236508i
$658$		−	6.00000i		−	0.233904i
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	−0.999939	−	0.0110766i	$-0.996474\pi$
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	0.509562	+	0.860434i	$0.329807\pi$
$660$		0			0
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	−0.340701	−	0.940172i	$-0.610665\pi$
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	0.643862	+	0.765142i	$0.277331\pi$
$662$	−12.0000			−0.466393
$663$	−18.6962	−	1.20577i	−0.726098	−	0.0468283i
$664$	11.6603			0.452506
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	3.29423	−	5.70577i	0.127553	−	0.220928i
$668$		−	2.53590i		−	0.0981169i
$669$	16.3923	+	9.46410i	0.633763	+	0.365903i
$670$		0			0
$671$			22.7321i			0.877561i
$672$	2.36603	−	4.09808i	0.0912714	−	0.158087i
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	0.856228	−	0.516599i	$-0.172802\pi$
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	−0.875501	+	0.483216i	$0.839469\pi$
$674$	26.8468	−	15.5000i	1.03410	−	0.597038i
$675$		0			0
$676$	7.89230	−	10.3301i	0.303550	−	0.397313i
$677$	−4.39230			−0.168810			−0.0844050	−	0.996432i	$-0.526899\pi$
$677$	−4.39230			−0.168810			−0.0844050	+	0.996432i	$0.526899\pi$
$678$	9.69615	−	5.59808i	0.372378	−	0.214993i
$679$	−14.1962	−	24.5885i	−0.544798	−	0.943618i
$680$		0			0
$681$		−	9.80385i		−	0.375684i
$682$	10.3923	+	6.00000i	0.397942	+	0.229752i
$683$	24.0000	+	13.8564i	0.918334	+	0.530201i	0.883103	−	0.469179i	$-0.155450\pi$
$683$	24.0000	+	13.8564i	0.918334	+	0.530201i	0.0352311	+	0.999379i	$0.488783\pi$
$684$			1.26795i			0.0484812i
$685$		0			0
$686$	−19.8564	−	34.3923i	−0.758121	−	1.31310i
$687$	17.1962	−	9.92820i	0.656074	−	0.378785i
$688$	6.19615			0.236226
$689$	−10.7942	−	0.696152i	−0.411227	−	0.0265213i
$690$		0			0
$691$	16.9019	−	9.75833i	0.642979	−	0.371224i	−0.142782	−	0.989754i	$-0.545605\pi$
$691$	16.9019	−	9.75833i	0.642979	−	0.371224i	0.785761	+	0.618530i	$0.212271\pi$
$692$	8.19615	+	14.1962i	0.311571	+	0.539657i
$693$	−11.1962	+	19.3923i	−0.425307	+	0.736653i
$694$		−	12.5885i		−	0.477851i
$695$		0			0
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$		−	2.41154i		−	0.0913437i
$698$	−1.26795	+	2.19615i	−0.0479926	+	0.0831256i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$		0			0
$701$	−4.39230			−0.165895			−0.0829475	−	0.996554i	$-0.526433\pi$
$701$	−4.39230			−0.165895			−0.0829475	+	0.996554i	$0.526433\pi$
$702$	−3.23205	+	1.59808i	−0.121986	+	0.0603155i
$703$	−3.80385			−0.143465
$704$	−4.09808	+	2.36603i	−0.154452	+	0.0891729i
$705$		0			0
$706$	−2.89230	+	5.00962i	−0.108853	+	0.188539i
$707$		−	6.58846i		−	0.247784i
$708$	12.0000	+	6.92820i	0.450988	+	0.260378i
$709$	−2.81347	−	1.62436i	−0.105662	−	0.0610040i	0.446238	−	0.894914i	$-0.352764\pi$
$709$	−2.81347	−	1.62436i	−0.105662	−	0.0610040i	−0.551900	+	0.833910i	$0.686097\pi$
$710$		0			0
$711$	6.19615	−	10.7321i	0.232374	−	0.402483i
$712$	1.26795	+	2.19615i	0.0475184	+	0.0823043i
$713$	−4.82309	+	2.78461i	−0.180626	+	0.104284i
$714$	24.5885			0.920200
$715$		0			0
$716$	−8.19615			−0.306305
$717$	21.2942	−	12.2942i	0.795248	−	0.459136i
$718$	−11.0263	−	19.0981i	−0.411497	−	0.712734i
$719$	26.1962	−	45.3731i	0.976952	−	1.69213i	0.303613	−	0.952795i	$-0.401807\pi$
$719$	26.1962	−	45.3731i	0.976952	−	1.69213i	0.673338	−	0.739335i	$-0.264860\pi$
$720$		0			0
$721$	−17.1962	−	9.92820i	−0.640418	−	0.369746i
$722$	15.0622	+	8.69615i	0.560556	+	0.323637i
$723$			0.803848i			0.0298954i
$724$	5.79423	−	10.0359i	0.215341	−	0.372981i
$725$		0			0
$726$	9.86603	−	5.69615i	0.366163	−	0.211404i
$727$	−24.1962			−0.897386			−0.448693	−	0.893686i	$-0.648110\pi$
$727$	−24.1962			−0.897386			−0.448693	+	0.893686i	$0.648110\pi$
$728$	−9.46410	+	14.1962i	−0.350763	+	0.526144i
$729$	1.00000			0.0370370
$730$		0			0
$731$	16.0981	+	27.8827i	0.595409	+	1.03128i
$732$	2.40192	−	4.16025i	0.0887777	−	0.153767i
$733$		−	14.3205i		−	0.528940i	−0.964394	−	0.264470i	$-0.914803\pi$
$733$		−	14.3205i		−	0.528940i	0.964394	−	0.264470i	$-0.0851970\pi$
$734$	20.9545	+	12.0981i	0.773444	+	0.446548i
$735$		0			0
$736$		−	2.19615i		−	0.0809513i
$737$	25.3923	−	43.9808i	0.935338	−	1.62005i
$738$	−0.232051	−	0.401924i	−0.00854191	−	0.0147950i
$739$	−16.3923	+	9.46410i	−0.603001	+	0.348143i	−0.770221	−	0.637777i	$-0.779854\pi$
$739$	−16.3923	+	9.46410i	−0.603001	+	0.348143i	0.167220	+	0.985920i	$0.446521\pi$
$740$		0			0
$741$	0.294229	−	4.56218i	0.0108088	−	0.167596i
$742$	14.1962			0.521157
$743$	3.80385	−	2.19615i	0.139550	−	0.0805690i	−0.428600	−	0.903494i	$-0.640993\pi$
$743$	3.80385	−	2.19615i	0.139550	−	0.0805690i	0.568149	+	0.822925i	$0.307660\pi$
$744$	−1.26795	−	2.19615i	−0.0464853	−	0.0805149i
$745$		0			0
$746$			23.9808i			0.877998i
$747$	10.0981	+	5.83013i	0.369469	+	0.213313i
$748$	−21.2942	−	12.2942i	−0.778594	−	0.449522i
$749$			38.7846i			1.41716i
$750$		0			0
$751$	−12.4904	−	21.6340i	−0.455780	−	0.789435i	0.542952	−	0.839764i	$-0.317306\pi$
$751$	−12.4904	−	21.6340i	−0.455780	−	0.789435i	−0.998733	+	0.0503286i	$0.983973\pi$
$752$	1.09808	−	0.633975i	0.0400427	−	0.0231187i
$753$	4.39230			0.160064
$754$	−9.00000	−	6.00000i	−0.327761	−	0.218507i
$755$		0			0
$756$	4.09808	−	2.36603i	0.149046	−	0.0860515i
$757$	9.39230	+	16.2679i	0.341369	+	0.591269i	0.984687	−	0.174330i	$-0.0557761\pi$
$757$	9.39230	+	16.2679i	0.341369	+	0.591269i	−0.643318	+	0.765599i	$0.722443\pi$
$758$	−9.12436	+	15.8038i	−0.331412	+	0.574022i
$759$			10.3923i			0.377217i
$760$		0			0
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	0.567358	−	0.823471i	$-0.307966\pi$
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	−0.429468	+	0.903082i	$0.641299\pi$
$762$			4.00000i			0.144905i
$763$	38.7846	−	67.1769i	1.40410	−	2.43197i
$764$	10.3923	+	18.0000i	0.375980	+	0.651217i
$765$		0			0
$766$	11.3205			0.409027
$767$	−41.5692	−	27.7128i	−1.50098	−	1.00065i
$768$	1.00000			0.0360844
$769$	−29.1962	+	16.8564i	−1.05284	+	0.607858i	−0.923443	−	0.383735i	$-0.874638\pi$
$769$	−29.1962	+	16.8564i	−1.05284	+	0.607858i	−0.129397	+	0.991593i	$0.541304\pi$
$770$		0			0
$771$	−6.40192	+	11.0885i	−0.230560	+	0.399341i
$772$		−	12.8038i		−	0.460821i
$773$	43.9808	+	25.3923i	1.58188	+	0.913298i	0.994585	+	0.103923i	$0.0331396\pi$
$773$	43.9808	+	25.3923i	1.58188	+	0.913298i	0.587293	+	0.809375i	$0.300194\pi$
$774$	5.36603	+	3.09808i	0.192878	+	0.111358i
$775$		0			0
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	7.09808	+	12.2942i	0.254642	+	0.441053i
$778$	−11.5981	+	6.69615i	−0.415811	+	0.240069i
$779$	0.588457			0.0210837
$780$		0			0
$781$	38.7846			1.38782
$782$	9.88269	−	5.70577i	0.353404	−	0.204038i
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$	7.69615	−	13.3301i	0.274863	−	0.476076i
$785$		0			0
$786$	14.1962	+	8.19615i	0.506360	+	0.292347i
$787$	−12.5885	−	7.26795i	−0.448730	−	0.259074i	0.258564	−	0.965994i	$-0.416751\pi$
$787$	−12.5885	−	7.26795i	−0.448730	−	0.259074i	−0.707294	+	0.706920i	$0.750084\pi$
$788$		−	6.92820i		−	0.246807i
$789$	−1.09808	+	1.90192i	−0.0390925	+	0.0677103i
$790$		0			0
$791$	45.8827	−	26.4904i	1.63140	−	0.941890i
$792$	−4.73205			−0.168146
$793$	−9.60770	+	14.4115i	−0.341179	+	0.511769i
$794$	16.3923			0.581741
$795$		0			0
$796$	−4.29423	−	7.43782i	−0.152205	−	0.263627i
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	−0.914255	−	0.405140i	$-0.867223\pi$
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	0.807989	+	0.589197i	$0.200556\pi$
$798$			6.00000i			0.212398i
$799$	5.70577	+	3.29423i	0.201856	+	0.116541i
$800$		0			0
$801$			2.53590i			0.0896016i
$802$	−10.5000	+	18.1865i	−0.370768	+	0.642189i
$803$	28.6865	+	49.6865i	1.01233	+	1.75340i
$804$	−9.29423	+	5.36603i	−0.327782	+	0.189245i
$805$		0			0
$806$	4.05256	+	8.19615i	0.142745	+	0.288697i
$807$	−28.3923			−0.999456
$808$	1.20577	−	0.696152i	0.0424189	−	0.0244906i
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	0.898302	+	0.439379i	$0.144801\pi$
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	−0.0686377	+	0.997642i	$0.521865\pi$
$810$		0			0
$811$		−	4.39230i		−	0.154235i	−0.997022	−	0.0771173i	$-0.975428\pi$
$811$		−	4.39230i		−	0.154235i	0.997022	−	0.0771173i	$-0.0245716\pi$
$812$	12.2942	+	7.09808i	0.431443	+	0.249094i
$813$		0			0
$814$		−	14.1962i		−	0.497575i
$815$		0			0
$816$	2.59808	+	4.50000i	0.0909509	+	0.157532i
$817$	−6.80385	+	3.92820i	−0.238036	+	0.137430i
$818$	3.33975			0.116771
$819$	−15.2942	+	7.56218i	−0.534424	+	0.264244i
$820$		0			0
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.261669	−	0.965158i	$-0.415727\pi$
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.966685	+	0.255967i	$0.0823939\pi$
$822$	−4.50000	−	7.79423i	−0.156956	−	0.271855i
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$		−	4.19615i		−	0.146180i
$825$		0			0
$826$	56.7846	+	32.7846i	1.97579	+	1.14072i
$827$			32.1051i			1.11640i	0.829705	+	0.558202i	$0.188509\pi$
$827$			32.1051i			1.11640i	−0.829705	+	0.558202i	$0.811491\pi$
$828$	1.09808	−	1.90192i	0.0381608	−	0.0660964i
$829$	−5.99038	−	10.3756i	−0.208055	−	0.360361i	0.743047	−	0.669239i	$-0.233380\pi$
$829$	−5.99038	−	10.3756i	−0.208055	−	0.360361i	−0.951102	+	0.308878i	$0.900046\pi$
$830$		0			0
$831$	15.1962			0.527149
$832$	−3.59808	−	0.232051i	−0.124741	−	0.00804491i
$833$	79.9808			2.77117
$834$	3.46410	−	2.00000i	0.119952	−	0.0692543i
$835$		0			0
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$		−	2.53590i		−	0.0876535i
$838$	14.1962	+	8.19615i	0.490398	+	0.283131i
$839$	10.3923	+	6.00000i	0.358782	+	0.207143i	0.668546	−	0.743670i	$-0.266917\pi$
$839$	10.3923	+	6.00000i	0.358782	+	0.207143i	−0.309764	+	0.950813i	$0.600250\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	0.232051	+	0.401924i	0.00799700	+	0.0138512i
$843$	21.1865	−	12.2321i	0.729703	−	0.421294i
$844$	3.60770			0.124182
$845$		0			0
$846$	1.26795			0.0435930
$847$	46.6865	−	26.9545i	1.60417	−	0.926167i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	15.0981	−	26.1506i	0.518165	−	0.897487i
$850$		0			0
$851$	5.70577	+	3.29423i	0.195591	+	0.112925i
$852$	−7.09808	−	4.09808i	−0.243176	−	0.140398i
$853$		−	9.00000i		−	0.308154i	−0.988059	−	0.154077i	$-0.950760\pi$
$853$		−	9.00000i		−	0.308154i	0.988059	−	0.154077i	$-0.0492404\pi$
$854$	11.3660	−	19.6865i	0.388937	−	0.673659i
$855$		0			0
$856$	−7.09808	+	4.09808i	−0.242607	+	0.140069i
$857$	−54.3731			−1.85735			−0.928674	−	0.370896i	$-0.879051\pi$
$857$	−54.3731			−1.85735			−0.928674	+	0.370896i	$0.879051\pi$
$858$	17.0263	+	1.09808i	0.581268	+	0.0374877i
$859$	10.5885			0.361273			0.180637	−	0.983550i	$-0.442184\pi$
$859$	10.5885			0.361273			0.180637	+	0.983550i	$0.442184\pi$
$860$		0			0
$861$	−1.09808	−	1.90192i	−0.0374223	−	0.0648174i
$862$	13.9019	−	24.0788i	0.473501	−	0.820128i
$863$			4.48334i			0.152615i	0.997084	+	0.0763073i	$0.0243130\pi$
$863$			4.48334i			0.152615i	−0.997084	+	0.0763073i	$0.975687\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$			33.7846i			1.14805i
$867$	−5.00000	+	8.66025i	−0.169809	+	0.294118i
$868$	−6.00000	−	10.3923i	−0.203653	−	0.352738i
$869$	−50.7846	+	29.3205i	−1.72275	+	0.994630i
$870$		0			0
$871$	34.6865	−	17.1506i	1.17531	−	0.581127i
$872$	16.3923			0.555113
$873$	5.19615	−	3.00000i	0.175863	−	0.101535i
$874$	1.39230	+	2.41154i	0.0470954	+	0.0815716i
$875$		0			0
$876$		−	12.1244i		−	0.409644i
$877$	−37.5788	−	21.6962i	−1.26895	−	0.732627i	−0.294158	−	0.955757i	$-0.595039\pi$
$877$	−37.5788	−	21.6962i	−1.26895	−	0.732627i	−0.974789	+	0.223130i	$0.928373\pi$
$878$	−14.3660	−	8.29423i	−0.484830	−	0.279917i
$879$			14.6603i			0.494478i
$880$		0			0
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	0.985476	+	0.169815i	$0.0543171\pi$
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	−0.345674	+	0.938355i	$0.612350\pi$
$882$	13.3301	−	7.69615i	0.448849	−	0.259143i
$883$	−24.7846			−0.834069			−0.417034	−	0.908891i	$-0.636930\pi$
$883$	−24.7846			−0.834069			−0.417034	+	0.908891i	$0.636930\pi$
$884$	−8.30385	−	16.7942i	−0.279289	−	0.564851i
$885$		0			0
$886$	−3.80385	+	2.19615i	−0.127793	+	0.0737812i
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$	−1.50000	+	2.59808i	−0.0503367	+	0.0871857i
$889$			18.9282i			0.634832i
$890$		0			0
$891$	−4.09808	−	2.36603i	−0.137291	−	0.0792648i
$892$			18.9282i			0.633763i
$893$	−0.803848	+	1.39230i	−0.0268997	+	0.0465917i
$894$	−9.06218	−	15.6962i	−0.303085	−	0.524958i
$895$		0			0
$896$	4.73205			0.158087
$897$	−4.39230	+	6.58846i	−0.146655	+	0.219982i
$898$	33.4641			1.11671
$899$	6.58846	−	3.80385i	0.219737	−	0.126865i
$900$		0			0
$901$	−7.79423	+	13.5000i	−0.259663	+	0.449750i
$902$			2.19615i			0.0731239i
$903$	25.3923	+	14.6603i	0.845003	+	0.487863i
$904$	9.69615	+	5.59808i	0.322489	+	0.186189i
$905$		0			0
$906$	−3.63397	+	6.29423i	−0.120731	+	0.209112i
$907$	20.5885	+	35.6603i	0.683629	+	1.18408i	0.973866	+	0.227125i	$0.0729325\pi$
$907$	20.5885	+	35.6603i	0.683629	+	1.18408i	−0.290237	+	0.956955i	$0.593734\pi$
$908$	8.49038	−	4.90192i	0.281763	−	0.162676i
$909$	1.39230			0.0461798
$910$		0			0
$911$	37.1769			1.23173			0.615863	−	0.787853i	$-0.288807\pi$
$911$	37.1769			1.23173			0.615863	+	0.787853i	$0.288807\pi$
$912$	−1.09808	+	0.633975i	−0.0363609	+	0.0209930i
$913$	−27.5885	−	47.7846i	−0.913045	−	1.58144i
$914$	−9.99038	+	17.3038i	−0.330452	+	0.572360i
$915$		0			0
$916$	17.1962	+	9.92820i	0.568177	+	0.328037i
$917$	67.1769	+	38.7846i	2.21838	+	1.28078i
$918$			5.19615i			0.171499i
$919$	−16.1962	+	28.0526i	−0.534262	+	0.925369i	0.464937	+	0.885344i	$0.346077\pi$
$919$	−16.1962	+	28.0526i	−0.534262	+	0.925369i	−0.999199	+	0.0400247i	$0.987256\pi$
$920$		0			0
$921$	−9.29423	+	5.36603i	−0.306255	+	0.176817i
$922$	19.9808			0.658031
$923$	24.5885	+	16.3923i	0.809339	+	0.539559i
$924$	−22.3923			−0.736653
$925$		0			0
$926$	−13.0981	−	22.6865i	−0.430429	−	0.745526i
$927$	2.09808	−	3.63397i	0.0689099	−	0.119355i
$928$			3.00000i			0.0984798i
$929$	−29.9711	−	17.3038i	−0.983321	−	0.567721i	−0.0800501	−	0.996791i	$-0.525508\pi$
$929$	−29.9711	−	17.3038i	−0.983321	−	0.567721i	−0.903271	+	0.429070i	$0.858841\pi$
$930$		0			0
$931$			19.5167i			0.639633i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$	1.09808	+	1.90192i	0.0359494	+	0.0622662i
$934$	−31.6865	+	18.2942i	−1.03682	+	0.598605i
$935$		0			0
$936$	−3.00000	−	2.00000i	−0.0980581	−	0.0653720i
$937$	−5.39230			−0.176159			−0.0880795	−	0.996113i	$-0.528073\pi$
$937$	−5.39230			−0.176159			−0.0880795	+	0.996113i	$0.528073\pi$
$938$	−43.9808	+	25.3923i	−1.43602	+	0.829088i
$939$	−12.1962	−	21.1244i	−0.398006	−	0.689367i
$940$		0			0
$941$		−	2.78461i		−	0.0907757i	−0.998969	−	0.0453878i	$-0.985548\pi$
$941$		−	2.78461i		−	0.0907757i	0.998969	−	0.0453878i	$-0.0144524\pi$
$942$	2.76795	+	1.59808i	0.0901847	+	0.0520681i
$943$	−0.882686	−	0.509619i	−0.0287442	−	0.0165955i
$944$			13.8564i			0.450988i
$945$		0			0
$946$	−14.6603	−	25.3923i	−0.476646	−	0.825575i
$947$	37.1769	−	21.4641i	1.20809	−	0.697490i	0.245746	−	0.969334i	$-0.420967\pi$
$947$	37.1769	−	21.4641i	1.20809	−	0.697490i	0.962341	+	0.271845i	$0.0876337\pi$
$948$	12.3923			0.402483
$949$	−2.81347	+	43.6244i	−0.0913290	+	1.41611i
$950$		0			0
$951$	5.30385	−	3.06218i	0.171989	−	0.0992979i
$952$	12.2942	+	21.2942i	0.398458	+	0.690150i
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	−0.603559	−	0.797318i	$-0.706251\pi$
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	0.992277	+	0.124039i	$0.0395847\pi$
$954$			3.00000i			0.0971286i
$955$		0			0
$956$	21.2942	+	12.2942i	0.688705	+	0.397624i
$957$		−	14.1962i		−	0.458896i
$958$	17.6603	−	30.5885i	0.570577	−	0.988268i
$959$	−21.2942	−	36.8827i	−0.687627	−	1.19100i
$960$		0			0
$961$	24.5692			0.792555
$962$	6.00000	−	9.00000i	0.193448	−	0.290172i
$963$	−8.19615			−0.264117
$964$	−0.696152	+	0.401924i	−0.0224216	+	0.0129451i
$965$		0			0
$966$	5.19615	−	9.00000i	0.167183	−	0.289570i
$967$		−	14.8756i		−	0.478368i	−0.970974	−	0.239184i	$-0.923120\pi$
$967$		−	14.8756i		−	0.478368i	0.970974	−	0.239184i	$-0.0768800\pi$
$968$	9.86603	+	5.69615i	0.317106	+	0.183081i
$969$	−5.70577	−	3.29423i	−0.183296	−	0.105826i
$970$		0			0
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	−0.740730	−	0.671803i	$-0.765520\pi$
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	0.952163	+	0.305589i	$0.0988534\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	16.3923	−	9.46410i	0.525513	−	0.303405i
$974$	9.12436			0.292363
$975$		0			0
$976$	4.80385			0.153767
$977$	−14.5981	+	8.42820i	−0.467034	+	0.269642i	−0.714997	−	0.699127i	$-0.753572\pi$
$977$	−14.5981	+	8.42820i	−0.467034	+	0.269642i	0.247963	+	0.968769i	$0.420239\pi$
$978$	4.73205	+	8.19615i	0.151314	+	0.262084i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	14.1962	+	8.19615i	0.453248	+	0.261683i
$982$	−0.509619	−	0.294229i	−0.0162626	−	0.00938921i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$	0.232051	−	0.401924i	0.00739751	−	0.0128129i
$985$		0			0
$986$	−13.5000	+	7.79423i	−0.429928	+	0.248219i
$987$	6.00000			0.190982
$988$	4.09808	−	2.02628i	0.130377	−	0.0644645i
$989$	13.6077			0.432700
$990$		0			0
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	0.532736	−	0.846281i	$-0.321164\pi$
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	−0.999269	+	0.0382223i	$0.987830\pi$
$992$	1.26795	−	2.19615i	0.0402574	−	0.0697279i
$993$		−	12.0000i		−	0.380808i
$994$	−33.5885	−	19.3923i	−1.06536	−	0.615087i
$995$		0			0
$996$			11.6603i			0.369469i
$997$	6.59808	−	11.4282i	0.208963	−	0.361935i	−0.742425	−	0.669929i	$-0.766324\pi$
$997$	6.59808	−	11.4282i	0.208963	−	0.361935i	0.951388	+	0.307994i	$0.0996578\pi$
$998$		0			0
$999$	−2.59808	+	1.50000i	−0.0821995	+	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.c.751.1		4
5.2	odd	4		1950.2.y.a.49.1		4
5.3	odd	4		1950.2.y.h.49.2		4
5.4	even	2		78.2.i.b.49.2	yes	4
13.4	even	6	inner	1950.2.bc.c.901.1		4
15.14	odd	2		234.2.l.a.127.1		4
20.19	odd	2		624.2.bv.d.49.2		4
60.59	even	2		1872.2.by.k.1297.2		4
65.4	even	6		78.2.i.b.43.2	✓	4
65.9	even	6		1014.2.i.f.823.1		4
65.17	odd	12		1950.2.y.h.199.2		4
65.19	odd	12		1014.2.e.h.529.2		4
65.24	odd	12		1014.2.a.h.1.1		2
65.29	even	6		1014.2.b.d.337.4		4
65.34	odd	4		1014.2.e.j.991.1		4
65.43	odd	12		1950.2.y.a.199.1		4
65.44	odd	4		1014.2.e.h.991.2		4
65.49	even	6		1014.2.b.d.337.1		4
65.54	odd	12		1014.2.a.j.1.2		2
65.59	odd	12		1014.2.e.j.529.1		4
65.64	even	2		1014.2.i.f.361.1		4
195.29	odd	6		3042.2.b.l.1351.1		4
195.89	even	12		3042.2.a.v.1.2		2
195.119	even	12		3042.2.a.s.1.1		2
195.134	odd	6		234.2.l.a.199.1		4
195.179	odd	6		3042.2.b.l.1351.4		4
260.119	even	12		8112.2.a.bx.1.2		2
260.199	odd	6		624.2.bv.d.433.2		4
260.219	even	12		8112.2.a.bq.1.1		2
780.719	even	6		1872.2.by.k.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.2	✓	4	65.4	even	6
78.2.i.b.49.2	yes	4	5.4	even	2
234.2.l.a.127.1		4	15.14	odd	2
234.2.l.a.199.1		4	195.134	odd	6
624.2.bv.d.49.2		4	20.19	odd	2
624.2.bv.d.433.2		4	260.199	odd	6
1014.2.a.h.1.1		2	65.24	odd	12
1014.2.a.j.1.2		2	65.54	odd	12
1014.2.b.d.337.1		4	65.49	even	6
1014.2.b.d.337.4		4	65.29	even	6
1014.2.e.h.529.2		4	65.19	odd	12
1014.2.e.h.991.2		4	65.44	odd	4
1014.2.e.j.529.1		4	65.59	odd	12
1014.2.e.j.991.1		4	65.34	odd	4
1014.2.i.f.361.1		4	65.64	even	2
1014.2.i.f.823.1		4	65.9	even	6
1872.2.by.k.433.2		4	780.719	even	6
1872.2.by.k.1297.2		4	60.59	even	2
1950.2.y.a.49.1		4	5.2	odd	4
1950.2.y.a.199.1		4	65.43	odd	12
1950.2.y.h.49.2		4	5.3	odd	4
1950.2.y.h.199.2		4	65.17	odd	12
1950.2.bc.c.751.1		4	1.1	even	1	trivial
1950.2.bc.c.901.1		4	13.4	even	6	inner
3042.2.a.s.1.1		2	195.119	even	12
3042.2.a.v.1.2		2	195.89	even	12
3042.2.b.l.1351.1		4	195.29	odd	6
3042.2.b.l.1351.4		4	195.179	odd	6
8112.2.a.bq.1.1		2	260.219	even	12
8112.2.a.bx.1.2		2	260.119	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(4.09808 + 2.36603i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(4.09808 + 2.36603i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.09808 - 2.36603i) q^{11} -1.00000 q^{12} +(3.59808 + 0.232051i) q^{13} -4.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.59808 - 4.50000i) q^{17} -1.00000i q^{18} +(1.09808 + 0.633975i) q^{19} -4.73205i q^{21} +(-2.36603 + 4.09808i) q^{22} +(-1.09808 - 1.90192i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-3.23205 + 1.59808i) q^{26} +1.00000 q^{27} +(4.09808 - 2.36603i) q^{28} +(1.50000 + 2.59808i) q^{29} -2.53590i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.09808 - 2.36603i) q^{33} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(-2.59808 + 1.50000i) q^{37} -1.26795 q^{38} +(-1.59808 - 3.23205i) q^{39} +(0.401924 - 0.232051i) q^{41} +(2.36603 + 4.09808i) q^{42} +(-3.09808 + 5.36603i) q^{43} -4.73205i q^{44} +(1.90192 + 1.09808i) q^{46} +1.26795i q^{47} +(-0.500000 + 0.866025i) q^{48} +(7.69615 + 13.3301i) q^{49} -5.19615 q^{51} +(2.00000 - 3.00000i) q^{52} -3.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{56} -1.26795i q^{57} +(-2.59808 - 1.50000i) q^{58} +(-12.0000 - 6.92820i) q^{59} +(-2.40192 + 4.16025i) q^{61} +(1.26795 + 2.19615i) q^{62} +(-4.09808 + 2.36603i) q^{63} -1.00000 q^{64} +4.73205 q^{66} +(9.29423 - 5.36603i) q^{67} +(-2.59808 - 4.50000i) q^{68} +(-1.09808 + 1.90192i) q^{69} +(7.09808 + 4.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 - 2.59808i) q^{74} +(1.09808 - 0.633975i) q^{76} +22.3923 q^{77} +(3.00000 + 2.00000i) q^{78} -12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.232051 + 0.401924i) q^{82} -11.6603i q^{83} +(-4.09808 - 2.36603i) q^{84} -6.19615i q^{86} +(1.50000 - 2.59808i) q^{87} +(2.36603 + 4.09808i) q^{88} +(2.19615 - 1.26795i) q^{89} +(14.1962 + 9.46410i) q^{91} -2.19615 q^{92} +(-2.19615 + 1.26795i) q^{93} +(-0.633975 - 1.09808i) q^{94} -1.00000i q^{96} +(-5.19615 - 3.00000i) q^{97} +(-13.3301 - 7.69615i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 12 q^{14} - 2 q^{16} - 6 q^{19} - 6 q^{22} + 6 q^{23} - 6 q^{26} + 4 q^{27} + 6 q^{28} + 6 q^{29} - 6 q^{33} + 2 q^{36} - 12 q^{38} + 4 q^{39} + 12 q^{41} + 6 q^{42} - 2 q^{43} + 18 q^{46} - 2 q^{48} + 10 q^{49} + 8 q^{52} - 12 q^{53} - 6 q^{56} - 48 q^{59} - 20 q^{61} + 12 q^{62} - 6 q^{63} - 4 q^{64} + 12 q^{66} + 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} - 6 q^{76} + 48 q^{77} + 12 q^{78} - 8 q^{79} - 2 q^{81} + 6 q^{82} - 6 q^{84} + 6 q^{87} + 6 q^{88} - 12 q^{89} + 36 q^{91} + 12 q^{92} + 12 q^{93} - 6 q^{94} - 36 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 12 * q^14 - 2 * q^16 - 6 * q^19 - 6 * q^22 + 6 * q^23 - 6 * q^26 + 4 * q^27 + 6 * q^28 + 6 * q^29 - 6 * q^33 + 2 * q^36 - 12 * q^38 + 4 * q^39 + 12 * q^41 + 6 * q^42 - 2 * q^43 + 18 * q^46 - 2 * q^48 + 10 * q^49 + 8 * q^52 - 12 * q^53 - 6 * q^56 - 48 * q^59 - 20 * q^61 + 12 * q^62 - 6 * q^63 - 4 * q^64 + 12 * q^66 + 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 - 6 * q^76 + 48 * q^77 + 12 * q^78 - 8 * q^79 - 2 * q^81 + 6 * q^82 - 6 * q^84 + 6 * q^87 + 6 * q^88 - 12 * q^89 + 36 * q^91 + 12 * q^92 + 12 * q^93 - 6 * q^94 - 36 * q^98

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