LMFDB - Embedded newform 450.2.j.e.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(49,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("450.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
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 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	450.349
Dual form			450.2.j.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.73205 q^{12} +(-1.73205 + 1.00000i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000i q^{17} +3.00000i q^{18} +1.00000 q^{19} +(3.00000 - 1.73205i) q^{21} +(-2.59808 + 1.50000i) q^{22} +(5.19615 - 3.00000i) q^{23} +(1.50000 + 0.866025i) q^{24} +2.00000 q^{26} +5.19615 q^{27} -2.00000i q^{28} +(3.00000 - 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.59808 + 4.50000i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} -4.00000i q^{37} +(-0.866025 - 0.500000i) q^{38} -3.46410i q^{39} +(-4.50000 - 7.79423i) q^{41} -3.46410 q^{42} +(-0.866025 - 0.500000i) q^{43} +3.00000 q^{44} -6.00000 q^{46} +(5.19615 + 3.00000i) q^{47} +(-0.866025 - 1.50000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(4.50000 + 2.59808i) q^{51} +(-1.73205 - 1.00000i) q^{52} -12.0000i q^{53} +(-4.50000 - 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +(-0.866025 + 1.50000i) q^{57} +(-5.19615 + 3.00000i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.00000i q^{62} +6.00000i q^{63} -1.00000 q^{64} -5.19615i q^{66} +(4.33013 - 2.50000i) q^{67} +(2.59808 - 1.50000i) q^{68} +10.3923i q^{69} -12.0000 q^{71} +(-2.59808 + 1.50000i) q^{72} -11.0000i q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(-1.73205 + 3.00000i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +9.00000i q^{82} +(10.3923 + 6.00000i) q^{83} +(3.00000 + 1.73205i) q^{84} +(0.500000 + 0.866025i) q^{86} +(5.19615 + 9.00000i) q^{87} +(-2.59808 - 1.50000i) q^{88} -6.00000 q^{89} +4.00000 q^{91} +(5.19615 + 3.00000i) q^{92} -6.92820 q^{93} +(-3.00000 - 5.19615i) q^{94} +1.73205i q^{96} +(-4.33013 - 2.50000i) q^{97} +3.00000i q^{98} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 6 q^{6} - 6 q^{9} + 6 q^{11} + 4 q^{14} - 2 q^{16} + 4 q^{19} + 12 q^{21} + 6 q^{24} + 8 q^{26} + 12 q^{29} + 8 q^{31} - 6 q^{34} + 6 q^{36} - 18 q^{41} + 12 q^{44} - 24 q^{46} - 6 q^{49}+ \cdots - 36 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^6 - 6 * q^9 + 6 * q^11 + 4 * q^14 - 2 * q^16 + 4 * q^19 + 12 * q^21 + 6 * q^24 + 8 * q^26 + 12 * q^29 + 8 * q^31 - 6 * q^34 + 6 * q^36 - 18 * q^41 + 12 * q^44 - 24 * q^46 - 6 * q^49 + 18 * q^51 - 18 * q^54 - 4 * q^56 + 6 * q^59 - 16 * q^61 - 4 * q^64 - 48 * q^71 - 8 * q^74 + 2 * q^76 - 8 * q^79 - 18 * q^81 + 12 * q^84 + 2 * q^86 - 24 * q^89 + 16 * q^91 - 12 * q^94 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−1.73205			−0.500000
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	0.240192	+	0.970725i	$0.422790\pi$
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$			3.00000i			0.707107i
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	3.00000	−	1.73205i	0.654654	−	0.377964i
$22$	−2.59808	+	1.50000i	−0.553912	+	0.319801i
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$		0			0
$26$	2.00000			0.392232
$27$	5.19615			1.00000
$28$		−	2.00000i		−	0.377964i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.59808	+	4.50000i	0.452267	+	0.783349i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	−0.866025	−	0.500000i	−0.140488	−	0.0811107i
$39$		−	3.46410i		−	0.554700i
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−3.46410			−0.534522
$43$	−0.866025	−	0.500000i	−0.132068	−	0.0762493i	0.432511	−	0.901629i	$-0.357628\pi$
$43$	−0.866025	−	0.500000i	−0.132068	−	0.0762493i	−0.564578	+	0.825380i	$0.690961\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	0.828554	−	0.559908i	$-0.189164\pi$
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	−0.0706177	+	0.997503i	$0.522497\pi$
$48$	−0.866025	−	1.50000i	−0.125000	−	0.216506i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$	4.50000	+	2.59808i	0.630126	+	0.363803i
$52$	−1.73205	−	1.00000i	−0.240192	−	0.138675i
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	−0.866025	+	1.50000i	−0.114708	+	0.198680i
$58$	−5.19615	+	3.00000i	−0.682288	+	0.393919i
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		−	4.00000i		−	0.508001i
$63$			6.00000i			0.755929i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	5.19615i		−	0.639602i
$67$	4.33013	−	2.50000i	0.529009	−	0.305424i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$	4.33013	−	2.50000i	0.529009	−	0.305424i	0.740613	+	0.671932i	$0.234535\pi$
$68$	2.59808	−	1.50000i	0.315063	−	0.181902i
$69$			10.3923i			1.25109i
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$		−	11.0000i		−	1.28745i	−0.765256	−	0.643726i	$-0.777388\pi$
$73$		−	11.0000i		−	1.28745i	0.765256	−	0.643726i	$-0.222612\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$	−5.19615	+	3.00000i	−0.592157	+	0.341882i
$78$	−1.73205	+	3.00000i	−0.196116	+	0.339683i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$			9.00000i			0.993884i
$83$	10.3923	+	6.00000i	1.14070	+	0.658586i	0.946605	−	0.322396i	$-0.104488\pi$
$83$	10.3923	+	6.00000i	1.14070	+	0.658586i	0.194099	+	0.980982i	$0.437822\pi$
$84$	3.00000	+	1.73205i	0.327327	+	0.188982i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	5.19615	+	9.00000i	0.557086	+	0.964901i
$88$	−2.59808	−	1.50000i	−0.276956	−	0.159901i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$	−6.92820			−0.718421
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$			1.73205i			0.176777i
$97$	−4.33013	−	2.50000i	−0.439658	−	0.253837i	0.263795	−	0.964579i	$-0.415026\pi$
$97$	−4.33013	−	2.50000i	−0.439658	−	0.253837i	−0.703452	+	0.710742i	$0.748359\pi$
$98$			3.00000i			0.303046i
$99$	−9.00000			−0.904534
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−2.59808	−	4.50000i	−0.257248	−	0.445566i
$103$	−12.1244	+	7.00000i	−1.19465	+	0.689730i	−0.959357	−	0.282194i	$-0.908938\pi$
$103$	−12.1244	+	7.00000i	−1.19465	+	0.689730i	−0.235291	+	0.971925i	$0.575604\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$			3.00000i			0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$			3.00000i			0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$	2.59808	+	4.50000i	0.250000	+	0.433013i
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$		0			0
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	1.73205	−	1.00000i	0.163663	−	0.0944911i
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$114$	1.50000	−	0.866025i	0.140488	−	0.0811107i
$115$		0			0
$116$	6.00000			0.557086
$117$	5.19615	+	3.00000i	0.480384	+	0.277350i
$118$		−	3.00000i		−	0.276172i
$119$	−3.00000	+	5.19615i	−0.275010	+	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	6.92820	−	4.00000i	0.627250	−	0.362143i
$123$	15.5885			1.40556
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−2.59808	+	4.50000i	−0.226134	+	0.391675i
$133$	−1.73205	−	1.00000i	−0.150188	−	0.0867110i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	−3.00000			−0.257248
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	0.606861	−	0.794808i	$-0.292428\pi$
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	−0.384893	+	0.922961i	$0.625762\pi$
$138$	5.19615	−	9.00000i	0.442326	−	0.766131i
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	−0.915764	−	0.401718i	$-0.868413\pi$
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	0.109984	−	0.993933i	$-0.464920\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$	10.3923	+	6.00000i	0.872103	+	0.503509i
$143$			6.00000i			0.501745i
$144$	3.00000			0.250000
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	5.19615			0.428571
$148$	3.46410	−	2.00000i	0.284747	−	0.164399i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$		−	1.00000i		−	0.0811107i
$153$	−7.79423	+	4.50000i	−0.630126	+	0.363803i
$154$	6.00000			0.483494
$155$		0			0
$156$	3.00000	−	1.73205i	0.240192	−	0.138675i
$157$	−3.46410	+	2.00000i	−0.276465	+	0.159617i	−0.631822	−	0.775113i	$-0.717693\pi$
$157$	−3.46410	+	2.00000i	−0.276465	+	0.159617i	0.355357	+	0.934731i	$0.384359\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$	18.0000	+	10.3923i	1.42749	+	0.824163i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	7.79423	−	4.50000i	0.612372	−	0.353553i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	−0.844931	−	0.534875i	$-0.820359\pi$
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	0.0407502	+	0.999169i	$0.487025\pi$
$168$	−1.73205	−	3.00000i	−0.133631	−	0.231455i
$169$	−4.50000	+	7.79423i	−0.346154	+	0.599556i
$170$		0			0
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$		−	1.00000i		−	0.0762493i
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$		−	10.3923i		−	0.787839i
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−5.19615			−0.390567
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	−3.46410	−	2.00000i	−0.256776	−	0.148250i
$183$	−6.92820	−	12.0000i	−0.512148	−	0.887066i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	6.00000	+	3.46410i	0.439941	+	0.254000i
$187$	−7.79423	−	4.50000i	−0.569970	−	0.329073i
$188$			6.00000i			0.437595i
$189$	−9.00000	−	5.19615i	−0.654654	−	0.377964i
$190$		0			0
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	−4.33013	+	2.50000i	−0.311689	+	0.179954i	−0.647682	−	0.761911i	$-0.724262\pi$
$193$	−4.33013	+	2.50000i	−0.311689	+	0.179954i	0.335993	+	0.941865i	$0.390928\pi$
$194$	2.50000	+	4.33013i	0.179490	+	0.310885i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	7.79423	+	4.50000i	0.553912	+	0.319801i
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$			8.66025i			0.610847i
$202$		0			0
$203$	−10.3923	+	6.00000i	−0.729397	+	0.421117i
$204$			5.19615i			0.363803i
$205$		0			0
$206$	14.0000			0.975426
$207$	−15.5885	−	9.00000i	−1.08347	−	0.625543i
$208$		−	2.00000i		−	0.138675i
$209$	1.50000	−	2.59808i	0.103757	−	0.179713i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	10.3923	−	6.00000i	0.713746	−	0.412082i
$213$	10.3923	−	18.0000i	0.712069	−	1.23334i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$		−	8.00000i		−	0.543075i
$218$	−13.8564	−	8.00000i	−0.938474	−	0.541828i
$219$	16.5000	+	9.52628i	1.11497	+	0.643726i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$	−3.46410	−	6.00000i	−0.232495	−	0.402694i
$223$	22.5167	+	13.0000i	1.50783	+	0.870544i	0.999959	+	0.00910984i	$0.00289979\pi$
$223$	22.5167	+	13.0000i	1.50783	+	0.870544i	0.507869	+	0.861435i	$0.330434\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	6.00000			0.399114
$227$	−18.1865	−	10.5000i	−1.20708	−	0.696909i	−0.244962	−	0.969533i	$-0.578775\pi$
$227$	−18.1865	−	10.5000i	−1.20708	−	0.696909i	−0.962121	+	0.272623i	$0.912109\pi$
$228$	−1.73205			−0.114708
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$		−	10.3923i		−	0.683763i
$232$	−5.19615	−	3.00000i	−0.341144	−	0.196960i
$233$		−	3.00000i		−	0.196537i	−0.995160	−	0.0982683i	$-0.968670\pi$
$233$		−	3.00000i		−	0.196537i	0.995160	−	0.0982683i	$-0.0313303\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$		0			0
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	−3.46410	−	6.00000i	−0.225018	−	0.389742i
$238$	5.19615	−	3.00000i	0.336817	−	0.194461i
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	0.946590	−	0.322440i	$-0.104503\pi$
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	−0.752536	+	0.658551i	$0.771170\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$		−	2.00000i		−	0.128565i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	−1.73205	+	1.00000i	−0.110208	+	0.0636285i
$248$	3.46410	−	2.00000i	0.219971	−	0.127000i
$249$	−18.0000	+	10.3923i	−1.14070	+	0.658586i
$250$		0			0
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$	−5.19615	+	3.00000i	−0.327327	+	0.188982i
$253$		−	18.0000i		−	1.13165i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−18.1865	+	10.5000i	−1.13444	+	0.654972i	−0.945049	−	0.326929i	$-0.893986\pi$
$257$	−18.1865	+	10.5000i	−1.13444	+	0.654972i	−0.189396	+	0.981901i	$0.560653\pi$
$258$	−1.73205			−0.107833
$259$	−4.00000	+	6.92820i	−0.248548	+	0.430498i
$260$		0			0
$261$	−18.0000			−1.11417
$262$		0			0
$263$	15.5885	+	9.00000i	0.961225	+	0.554964i	0.896550	−	0.442943i	$-0.146065\pi$
$263$	15.5885	+	9.00000i	0.961225	+	0.554964i	0.0646755	+	0.997906i	$0.479399\pi$
$264$	4.50000	−	2.59808i	0.276956	−	0.159901i
$265$		0			0
$266$	1.00000	+	1.73205i	0.0613139	+	0.106199i
$267$	5.19615	−	9.00000i	0.317999	−	0.550791i
$268$	4.33013	+	2.50000i	0.264505	+	0.152712i
$269$	24.0000			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	2.59808	+	1.50000i	0.157532	+	0.0909509i
$273$	−3.46410	+	6.00000i	−0.209657	+	0.363137i
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$		0			0
$276$	−9.00000	+	5.19615i	−0.541736	+	0.312772i
$277$	8.66025	+	5.00000i	0.520344	+	0.300421i	0.737075	−	0.675810i	$-0.236206\pi$
$277$	8.66025	+	5.00000i	0.520344	+	0.300421i	−0.216731	+	0.976231i	$0.569540\pi$
$278$			19.0000i			1.13954i
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$		0			0
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$	10.3923			0.618853
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$			18.0000i			1.06251i
$288$	−2.59808	−	1.50000i	−0.153093	−	0.0883883i
$289$	8.00000			0.470588
$290$		0			0
$291$	7.50000	−	4.33013i	0.439658	−	0.253837i
$292$	9.52628	−	5.50000i	0.557483	−	0.321863i
$293$	−25.9808	+	15.0000i	−1.51781	+	0.876309i	−0.518032	+	0.855361i	$0.673335\pi$
$293$	−25.9808	+	15.0000i	−1.51781	+	0.876309i	−0.999781	+	0.0209480i	$0.993332\pi$
$294$	−4.50000	−	2.59808i	−0.262445	−	0.151523i
$295$		0			0
$296$	−4.00000			−0.232495
$297$	7.79423	−	13.5000i	0.452267	−	0.783349i
$298$			6.00000i			0.347571i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	−8.66025	+	5.00000i	−0.498342	+	0.287718i
$303$		0			0
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$		0			0
$306$	9.00000			0.514496
$307$		−	7.00000i		−	0.399511i	−0.979846	−	0.199756i	$-0.935985\pi$
$307$		−	7.00000i		−	0.399511i	0.979846	−	0.199756i	$-0.0640148\pi$
$308$	−5.19615	−	3.00000i	−0.296078	−	0.170941i
$309$		−	24.2487i		−	1.37946i
$310$		0			0
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	−3.46410			−0.196116
$313$	25.1147	+	14.5000i	1.41957	+	0.819588i	0.996261	−	0.0863973i	$-0.0275355\pi$
$313$	25.1147	+	14.5000i	1.41957	+	0.819588i	0.423308	+	0.905986i	$0.360869\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−4.00000			−0.225018
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	−10.3923	−	18.0000i	−0.582772	−	1.00939i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	10.3923	+	6.00000i	0.579141	+	0.334367i
$323$		−	3.00000i		−	0.166924i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−13.8564	+	24.0000i	−0.766261	+	1.32720i
$328$	−7.79423	+	4.50000i	−0.430364	+	0.248471i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$			12.0000i			0.658586i
$333$	−10.3923	+	6.00000i	−0.569495	+	0.328798i
$334$	12.0000			0.656611
$335$		0			0
$336$			3.46410i			0.188982i
$337$	−0.866025	+	0.500000i	−0.0471754	+	0.0272367i	−0.523402	−	0.852086i	$-0.675337\pi$
$337$	−0.866025	+	0.500000i	−0.0471754	+	0.0272367i	0.476227	+	0.879322i	$0.342004\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$		−	10.3923i		−	0.564433i
$340$		0			0
$341$	12.0000			0.649836
$342$			3.00000i			0.162221i
$343$			20.0000i			1.07990i
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	28.5788	−	16.5000i	1.53419	−	0.885766i	0.535031	−	0.844833i	$-0.320300\pi$
$347$	28.5788	−	16.5000i	1.53419	−	0.885766i	0.999162	−	0.0409337i	$-0.0130332\pi$
$348$	−5.19615	+	9.00000i	−0.278543	+	0.482451i
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	−0.996716	−	0.0809766i	$-0.974196\pi$
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	0.568486	+	0.822693i	$0.307529\pi$
$350$		0			0
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$		−	3.00000i		−	0.159901i
$353$	−18.1865	−	10.5000i	−0.967972	−	0.558859i	−0.0693543	−	0.997592i	$-0.522094\pi$
$353$	−18.1865	−	10.5000i	−0.967972	−	0.558859i	−0.898617	+	0.438733i	$0.855427\pi$
$354$	4.50000	+	2.59808i	0.239172	+	0.138086i
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−5.19615	−	9.00000i	−0.275010	−	0.476331i
$358$	10.3923	+	6.00000i	0.549250	+	0.317110i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	−12.1244	−	7.00000i	−0.637242	−	0.367912i
$363$	−3.46410			−0.181818
$364$	2.00000	+	3.46410i	0.104828	+	0.181568i
$365$		0			0
$366$			13.8564i			0.724286i
$367$	24.2487	+	14.0000i	1.26577	+	0.730794i	0.974185	−	0.225750i	$-0.0724833\pi$
$367$	24.2487	+	14.0000i	1.26577	+	0.730794i	0.291587	+	0.956544i	$0.405817\pi$
$368$			6.00000i			0.312772i
$369$	−13.5000	+	23.3827i	−0.702782	+	1.21725i
$370$		0			0
$371$	−12.0000	+	20.7846i	−0.623009	+	1.07908i
$372$	−3.46410	−	6.00000i	−0.179605	−	0.311086i
$373$	29.4449	−	17.0000i	1.52460	−	0.880227i	0.525022	−	0.851089i	$-0.324057\pi$
$373$	29.4449	−	17.0000i	1.52460	−	0.880227i	0.999575	−	0.0291379i	$-0.00927619\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$			12.0000i			0.618031i
$378$	5.19615	+	9.00000i	0.267261	+	0.462910i
$379$	−23.0000			−1.18143			−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000			−1.18143			−0.590715	+	0.806880i	$0.701154\pi$
$380$		0			0
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$	−15.5885	+	9.00000i	−0.797575	+	0.460480i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$		0			0
$386$	5.00000			0.254493
$387$			3.00000i			0.152499i
$388$		−	5.00000i		−	0.253837i
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	−2.59808	+	1.50000i	−0.131223	+	0.0757614i
$393$		0			0
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$		0			0
$396$	−4.50000	−	7.79423i	−0.226134	−	0.391675i
$397$			20.0000i			1.00377i	0.864934	+	0.501886i	$0.167360\pi$
$397$			20.0000i			1.00377i	−0.864934	+	0.501886i	$0.832640\pi$
$398$	−8.66025	−	5.00000i	−0.434099	−	0.250627i
$399$	3.00000	−	1.73205i	0.150188	−	0.0867110i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	4.33013	−	7.50000i	0.215967	−	0.374066i
$403$	−6.92820	−	4.00000i	−0.345118	−	0.199254i
$404$		0			0
$405$		0			0
$406$	12.0000			0.595550
$407$	−10.3923	−	6.00000i	−0.515127	−	0.297409i
$408$	2.59808	−	4.50000i	0.128624	−	0.222783i
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	0.995968	−	0.0897044i	$-0.0285922\pi$
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	−0.575670	+	0.817682i	$0.695259\pi$
$410$		0			0
$411$	−4.50000	+	2.59808i	−0.221969	+	0.128154i
$412$	−12.1244	−	7.00000i	−0.597324	−	0.344865i
$413$		−	6.00000i		−	0.295241i
$414$	9.00000	+	15.5885i	0.442326	+	0.766131i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$	32.9090			1.61156
$418$	−2.59808	+	1.50000i	−0.127076	+	0.0733674i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	−0.999895	−	0.0145228i	$-0.995377\pi$
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	0.512524	+	0.858673i	$0.328710\pi$
$422$			20.0000i			0.973585i
$423$		−	18.0000i		−	0.875190i
$424$	−12.0000			−0.582772
$425$		0			0
$426$	−18.0000	+	10.3923i	−0.872103	+	0.503509i
$427$	13.8564	−	8.00000i	0.670559	−	0.387147i
$428$	−2.59808	+	1.50000i	−0.125583	+	0.0725052i
$429$	−9.00000	−	5.19615i	−0.434524	−	0.250873i
$430$		0			0
$431$	−30.0000			−1.44505			−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000			−1.44505			−0.722525	+	0.691345i	$0.757018\pi$
$432$	−2.59808	+	4.50000i	−0.125000	+	0.216506i
$433$			7.00000i			0.336399i	0.985753	+	0.168199i	$0.0537952\pi$
$433$			7.00000i			0.336399i	−0.985753	+	0.168199i	$0.946205\pi$
$434$	−4.00000	+	6.92820i	−0.192006	+	0.332564i
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	5.19615	−	3.00000i	0.248566	−	0.143509i
$438$	−9.52628	−	16.5000i	−0.455183	−	0.788400i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$	−4.50000	+	7.79423i	−0.214286	+	0.371154i
$442$		−	6.00000i		−	0.285391i
$443$	2.59808	+	1.50000i	0.123438	+	0.0712672i	0.560448	−	0.828190i	$-0.310629\pi$
$443$	2.59808	+	1.50000i	0.123438	+	0.0712672i	−0.437009	+	0.899457i	$0.643962\pi$
$444$			6.92820i			0.328798i
$445$		0			0
$446$	−13.0000	−	22.5167i	−0.615568	−	1.06619i
$447$	10.3923			0.491539
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−27.0000			−1.27138
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$	8.66025	+	15.0000i	0.406894	+	0.704761i
$454$	10.5000	+	18.1865i	0.492789	+	0.853536i
$455$		0			0
$456$	1.50000	+	0.866025i	0.0702439	+	0.0405554i
$457$	−14.7224	−	8.50000i	−0.688686	−	0.397613i	0.114433	−	0.993431i	$-0.463495\pi$
$457$	−14.7224	−	8.50000i	−0.688686	−	0.397613i	−0.803120	+	0.595818i	$0.796828\pi$
$458$		−	14.0000i		−	0.654177i
$459$		−	15.5885i		−	0.727607i
$460$		0			0
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	−0.270326	−	0.962769i	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$	−5.19615	+	9.00000i	−0.241747	+	0.418718i
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	−0.845200	−	0.534450i	$-0.820519\pi$
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	0.0402476	+	0.999190i	$0.487185\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−1.50000	+	2.59808i	−0.0694862	+	0.120354i
$467$		−	15.0000i		−	0.694117i	−0.937843	−	0.347059i	$-0.887180\pi$
$467$		−	15.0000i		−	0.694117i	0.937843	−	0.347059i	$-0.112820\pi$
$468$			6.00000i			0.277350i
$469$	−10.0000			−0.461757
$470$		0			0
$471$		−	6.92820i		−	0.319235i
$472$	2.59808	−	1.50000i	0.119586	−	0.0690431i
$473$	−2.59808	+	1.50000i	−0.119460	+	0.0689701i
$474$			6.92820i			0.318223i
$475$		0			0
$476$	−6.00000			−0.275010
$477$	−31.1769	+	18.0000i	−1.42749	+	0.824163i
$478$		−	6.00000i		−	0.274434i
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.235833	+	0.971794i	$0.575782\pi$
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.723681	+	0.690134i	$0.757551\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	−6.06218	+	3.50000i	−0.276125	+	0.159421i
$483$	10.3923	−	18.0000i	0.472866	−	0.819028i
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$			15.5885i			0.707107i
$487$			26.0000i			1.17817i	0.808070	+	0.589086i	$0.200512\pi$
$487$			26.0000i			1.17817i	−0.808070	+	0.589086i	$0.799488\pi$
$488$	6.92820	+	4.00000i	0.313625	+	0.181071i
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$		0			0
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$	7.79423	+	13.5000i	0.351391	+	0.608627i
$493$	−15.5885	−	9.00000i	−0.702069	−	0.405340i
$494$	2.00000			0.0899843
$495$		0			0
$496$	−4.00000			−0.179605
$497$	20.7846	+	12.0000i	0.932317	+	0.538274i
$498$	20.7846			0.931381
$499$	−6.50000	−	11.2583i	−0.290980	−	0.503992i	0.683062	−	0.730361i	$-0.260648\pi$
$499$	−6.50000	−	11.2583i	−0.290980	−	0.503992i	−0.974042	+	0.226369i	$0.927315\pi$
$500$		0			0
$501$		−	20.7846i		−	0.928588i
$502$	−18.1865	−	10.5000i	−0.811705	−	0.468638i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	6.00000			0.267261
$505$		0			0
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$	−7.79423	−	13.5000i	−0.346154	−	0.599556i
$508$	−1.73205	+	1.00000i	−0.0768473	+	0.0443678i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	−11.0000	+	19.0526i	−0.486611	+	0.842836i
$512$			1.00000i			0.0441942i
$513$	5.19615			0.229416
$514$	21.0000			0.926270
$515$		0			0
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$	15.5885	−	9.00000i	0.685580	−	0.395820i
$518$	6.92820	−	4.00000i	0.304408	−	0.175750i
$519$	9.00000	−	5.19615i	0.395056	−	0.228086i
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	15.5885	+	9.00000i	0.682288	+	0.393919i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$		0			0
$525$		0			0
$526$	−9.00000	−	15.5885i	−0.392419	−	0.679689i
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$	−5.19615			−0.226134
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$		−	2.00000i		−	0.0867110i
$533$	15.5885	+	9.00000i	0.675211	+	0.389833i
$534$	−9.00000	+	5.19615i	−0.389468	+	0.224860i
$535$		0			0
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$	10.3923	−	18.0000i	0.448461	−	0.776757i
$538$	−20.7846	−	12.0000i	−0.896088	−	0.517357i
$539$	−9.00000			−0.387657
$540$		0			0
$541$	−4.00000			−0.171973			−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000			−0.171973			−0.0859867	+	0.996296i	$0.527404\pi$
$542$	−17.3205	−	10.0000i	−0.743980	−	0.429537i
$543$	−12.1244	+	21.0000i	−0.520306	+	0.901196i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	6.00000	−	3.46410i	0.256776	−	0.148250i
$547$	0.866025	+	0.500000i	0.0370286	+	0.0213785i	0.518400	−	0.855138i	$-0.326528\pi$
$547$	0.866025	+	0.500000i	0.0370286	+	0.0213785i	−0.481371	+	0.876517i	$0.659861\pi$
$548$			3.00000i			0.128154i
$549$	24.0000			1.02430
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$	10.3923			0.442326
$553$	6.92820	−	4.00000i	0.294617	−	0.170097i
$554$	−5.00000	−	8.66025i	−0.212430	−	0.367939i
$555$		0			0
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$		−	30.0000i		−	1.27114i	−0.772043	−	0.635570i	$-0.780765\pi$
$557$		−	30.0000i		−	1.27114i	0.772043	−	0.635570i	$-0.219235\pi$
$558$	−10.3923	+	6.00000i	−0.439941	+	0.254000i
$559$	2.00000			0.0845910
$560$		0			0
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	5.19615	−	3.00000i	0.219186	−	0.126547i
$563$	33.7750	−	19.5000i	1.42345	−	0.821827i	0.426855	−	0.904320i	$-0.359622\pi$
$563$	33.7750	−	19.5000i	1.42345	−	0.821827i	0.996592	+	0.0824933i	$0.0262883\pi$
$564$	−9.00000	−	5.19615i	−0.378968	−	0.218797i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	15.5885	−	9.00000i	0.654654	−	0.377964i
$568$			12.0000i			0.503509i
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.184030	−	0.982921i	$-0.441086\pi$
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.759220	−	0.650835i	$-0.225581\pi$
$570$		0			0
$571$	18.5000	+	32.0429i	0.774201	+	1.34096i	0.935243	+	0.354008i	$0.115181\pi$
$571$	18.5000	+	32.0429i	0.774201	+	1.34096i	−0.161042	+	0.986948i	$0.551485\pi$
$572$	−5.19615	+	3.00000i	−0.217262	+	0.125436i
$573$	15.5885	+	27.0000i	0.651217	+	1.12794i
$574$	9.00000	−	15.5885i	0.375653	−	0.650650i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$			11.0000i			0.457936i	0.973434	+	0.228968i	$0.0735351\pi$
$577$			11.0000i			0.457936i	−0.973434	+	0.228968i	$0.926465\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$		−	8.66025i		−	0.359908i
$580$		0			0
$581$	−12.0000	−	20.7846i	−0.497844	−	0.862291i
$582$	−8.66025			−0.358979
$583$	−31.1769	−	18.0000i	−1.29122	−	0.745484i
$584$	−11.0000			−0.455183
$585$		0			0
$586$	30.0000			1.23929
$587$	7.79423	+	4.50000i	0.321702	+	0.185735i	0.652151	−	0.758089i	$-0.273867\pi$
$587$	7.79423	+	4.50000i	0.321702	+	0.185735i	−0.330449	+	0.943824i	$0.607200\pi$
$588$	2.59808	+	4.50000i	0.107143	+	0.185577i
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$		0			0
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	3.46410	+	2.00000i	0.142374	+	0.0821995i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$	−13.5000	+	7.79423i	−0.553912	+	0.319801i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−8.66025	+	15.0000i	−0.354441	+	0.613909i
$598$	10.3923	−	6.00000i	0.424973	−	0.245358i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	−0.190927	−	0.981604i	$-0.561149\pi$
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	0.945558	−	0.325455i	$-0.105517\pi$
$602$		−	2.00000i		−	0.0815139i
$603$	−12.9904	−	7.50000i	−0.529009	−	0.305424i
$604$	10.0000			0.406894
$605$		0			0
$606$		0			0
$607$	−24.2487	+	14.0000i	−0.984225	+	0.568242i	−0.903543	−	0.428497i	$-0.859043\pi$
$607$	−24.2487	+	14.0000i	−0.984225	+	0.568242i	−0.0806818	+	0.996740i	$0.525710\pi$
$608$	0.866025	−	0.500000i	0.0351220	−	0.0202777i
$609$		−	20.7846i		−	0.842235i
$610$		0			0
$611$	−12.0000			−0.485468
$612$	−7.79423	−	4.50000i	−0.315063	−	0.181902i
$613$			16.0000i			0.646234i	0.946359	+	0.323117i	$0.104731\pi$
$613$			16.0000i			0.646234i	−0.946359	+	0.323117i	$0.895269\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$		0			0
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	23.3827	−	13.5000i	0.941351	−	0.543490i	0.0509678	−	0.998700i	$-0.483769\pi$
$617$	23.3827	−	13.5000i	0.941351	−	0.543490i	0.890384	+	0.455211i	$0.150436\pi$
$618$	−12.1244	+	21.0000i	−0.487713	+	0.844744i
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	−0.263887	−	0.964554i	$-0.585005\pi$
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	0.967271	−	0.253744i	$-0.0816620\pi$
$620$		0			0
$621$	27.0000	−	15.5885i	1.08347	−	0.625543i
$622$		−	18.0000i		−	0.721734i
$623$	10.3923	+	6.00000i	0.416359	+	0.240385i
$624$	3.00000	+	1.73205i	0.120096	+	0.0693375i
$625$		0			0
$626$	−14.5000	−	25.1147i	−0.579537	−	1.00379i
$627$	2.59808	+	4.50000i	0.103757	+	0.179713i
$628$	−3.46410	−	2.00000i	−0.138233	−	0.0798087i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	3.46410	+	2.00000i	0.137795	+	0.0795557i
$633$	34.6410			1.37686
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$			20.7846i			0.824163i
$637$	5.19615	+	3.00000i	0.205879	+	0.118864i
$638$			18.0000i			0.712627i
$639$	18.0000	+	31.1769i	0.712069	+	1.23334i
$640$		0			0
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$	2.59808	+	4.50000i	0.102538	+	0.177601i
$643$	−19.9186	+	11.5000i	−0.785512	+	0.453516i	−0.838380	−	0.545086i	$-0.816497\pi$
$643$	−19.9186	+	11.5000i	−0.785512	+	0.453516i	0.0528680	+	0.998602i	$0.483164\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$		0			0
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$			18.0000i			0.707653i	0.935311	+	0.353827i	$0.115120\pi$
$647$			18.0000i			0.707653i	−0.935311	+	0.353827i	$0.884880\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	9.00000			0.353281
$650$		0			0
$651$	12.0000	+	6.92820i	0.470317	+	0.271538i
$652$	−3.46410	+	2.00000i	−0.135665	+	0.0783260i
$653$	5.19615	−	3.00000i	0.203341	−	0.117399i	−0.394872	−	0.918736i	$-0.629211\pi$
$653$	5.19615	−	3.00000i	0.203341	−	0.117399i	0.598213	+	0.801337i	$0.295878\pi$
$654$	24.0000	−	13.8564i	0.938474	−	0.541828i
$655$		0			0
$656$	9.00000			0.351391
$657$	−28.5788	+	16.5000i	−1.11497	+	0.643726i
$658$			12.0000i			0.467809i
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$	−3.46410	+	2.00000i	−0.134636	+	0.0777322i
$663$	−10.3923			−0.403604
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$	12.0000			0.464991
$667$		−	36.0000i		−	1.39393i
$668$	−10.3923	−	6.00000i	−0.402090	−	0.232147i
$669$	−39.0000	+	22.5167i	−1.50783	+	0.870544i
$670$		0			0
$671$	12.0000	+	20.7846i	0.463255	+	0.802381i
$672$	1.73205	−	3.00000i	0.0668153	−	0.115728i
$673$	−19.0526	−	11.0000i	−0.734422	−	0.424019i	0.0856156	−	0.996328i	$-0.472714\pi$
$673$	−19.0526	−	11.0000i	−0.734422	−	0.424019i	−0.820038	+	0.572309i	$0.806048\pi$
$674$	1.00000			0.0385186
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−31.1769	−	18.0000i	−1.19823	−	0.691796i	−0.238067	−	0.971249i	$-0.576514\pi$
$677$	−31.1769	−	18.0000i	−1.19823	−	0.691796i	−0.960159	+	0.279453i	$0.909847\pi$
$678$	−5.19615	+	9.00000i	−0.199557	+	0.345643i
$679$	5.00000	+	8.66025i	0.191882	+	0.332350i
$680$		0			0
$681$	31.5000	−	18.1865i	1.20708	−	0.696909i
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$			9.00000i			0.344375i	0.985064	+	0.172188i	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$	1.50000	−	2.59808i	0.0573539	−	0.0993399i
$685$		0			0
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	−24.2487			−0.925146
$688$	0.866025	−	0.500000i	0.0330169	−	0.0190623i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$		−	6.00000i		−	0.228086i
$693$	15.5885	+	9.00000i	0.592157	+	0.341882i
$694$	−33.0000			−1.25266
$695$		0			0
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$	−23.3827	+	13.5000i	−0.885682	+	0.511349i
$698$	13.8564	−	8.00000i	0.524473	−	0.302804i
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	10.3923			0.392232
$703$		−	4.00000i		−	0.150863i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	10.5000	+	18.1865i	0.395173	+	0.684459i
$707$		0			0
$708$	−2.59808	−	4.50000i	−0.0976417	−	0.169120i
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	−0.901135	−	0.433539i	$-0.857265\pi$
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	0.826023	+	0.563636i	$0.190598\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$			6.00000i			0.224860i
$713$	20.7846	+	12.0000i	0.778390	+	0.449404i
$714$			10.3923i			0.388922i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−10.3923			−0.388108
$718$	−15.5885	−	9.00000i	−0.581756	−	0.335877i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	28.0000			1.04277
$722$	15.5885	+	9.00000i	0.580142	+	0.334945i
$723$	6.06218	+	10.5000i	0.225455	+	0.390499i
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$		0			0
$726$	3.00000	+	1.73205i	0.111340	+	0.0642824i
$727$	−22.5167	−	13.0000i	−0.835097	−	0.482143i	0.0204978	−	0.999790i	$-0.493475\pi$
$727$	−22.5167	−	13.0000i	−0.835097	−	0.482143i	−0.855595	+	0.517647i	$0.826808\pi$
$728$		−	4.00000i		−	0.148250i
$729$	27.0000			1.00000
$730$		0			0
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	6.92820	−	12.0000i	0.256074	−	0.443533i
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	−0.706910	−	0.707303i	$-0.749912\pi$
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	0.259087	+	0.965854i	$0.416578\pi$
$734$	−14.0000	−	24.2487i	−0.516749	−	0.895036i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$		−	15.0000i		−	0.552532i
$738$	23.3827	−	13.5000i	0.860729	−	0.496942i
$739$	−47.0000			−1.72892			−0.864461	−	0.502699i	$-0.832340\pi$
$739$	−47.0000			−1.72892			−0.864461	+	0.502699i	$0.832340\pi$
$740$		0			0
$741$		−	3.46410i		−	0.127257i
$742$	20.7846	−	12.0000i	0.763027	−	0.440534i
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	−0.592277	−	0.805735i	$-0.701771\pi$
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	0.401648	+	0.915794i	$0.368437\pi$
$744$			6.92820i			0.254000i
$745$		0			0
$746$	−34.0000			−1.24483
$747$		−	36.0000i		−	1.31717i
$748$		−	9.00000i		−	0.329073i
$749$	3.00000	−	5.19615i	0.109618	−	0.189863i
$750$		0			0
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	−5.19615	+	3.00000i	−0.189484	+	0.109399i
$753$	−18.1865	+	31.5000i	−0.662754	+	1.14792i
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$		0			0
$756$		−	10.3923i		−	0.377964i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	19.9186	+	11.5000i	0.723476	+	0.417699i
$759$	27.0000	+	15.5885i	0.980038	+	0.565825i
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$	1.73205	+	3.00000i	0.0627456	+	0.108679i
$763$	−27.7128	−	16.0000i	−1.00327	−	0.579239i
$764$	18.0000			0.651217
$765$		0			0
$766$		0			0
$767$	−5.19615	−	3.00000i	−0.187622	−	0.108324i
$768$	1.73205			0.0625000
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	0.883493	−	0.468445i	$-0.155186\pi$
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	−0.847432	+	0.530904i	$0.821852\pi$
$770$		0			0
$771$		−	36.3731i		−	1.30994i
$772$	−4.33013	−	2.50000i	−0.155845	−	0.0899770i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$		0			0
$776$	−2.50000	+	4.33013i	−0.0897448	+	0.155443i
$777$	−6.92820	−	12.0000i	−0.248548	−	0.430498i
$778$	−15.5885	+	9.00000i	−0.558873	+	0.322666i
$779$	−4.50000	−	7.79423i	−0.161229	−	0.279257i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$			18.0000i			0.643679i
$783$	15.5885	−	27.0000i	0.557086	−	0.964901i
$784$	3.00000			0.107143
$785$		0			0
$786$		0			0
$787$	−3.46410	+	2.00000i	−0.123482	+	0.0712923i	−0.560469	−	0.828176i	$-0.689379\pi$
$787$	−3.46410	+	2.00000i	−0.123482	+	0.0712923i	0.436987	+	0.899468i	$0.356046\pi$
$788$	10.3923	−	6.00000i	0.370211	−	0.213741i
$789$	−27.0000	+	15.5885i	−0.961225	+	0.554964i
$790$		0			0
$791$	12.0000			0.426671
$792$			9.00000i			0.319801i
$793$		−	16.0000i		−	0.568177i
$794$	10.0000	−	17.3205i	0.354887	−	0.614682i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−10.3923	+	6.00000i	−0.368114	+	0.212531i	−0.672634	−	0.739975i	$-0.734837\pi$
$797$	−10.3923	+	6.00000i	−0.368114	+	0.212531i	0.304520	+	0.952506i	$0.401504\pi$
$798$	−3.46410			−0.122628
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$		0			0
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$		−	27.0000i		−	0.953403i
$803$	−28.5788	−	16.5000i	−1.00853	−	0.582272i
$804$	−7.50000	+	4.33013i	−0.264505	+	0.152712i
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$	−20.7846	+	36.0000i	−0.731653	+	1.26726i
$808$		0			0
$809$	−33.0000			−1.16022			−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000			−1.16022			−0.580109	+	0.814539i	$0.696990\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$	−10.3923	−	6.00000i	−0.364698	−	0.210559i
$813$	−17.3205	+	30.0000i	−0.607457	+	1.05215i
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$		0			0
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	−0.866025	−	0.500000i	−0.0302984	−	0.0174928i
$818$		−	17.0000i		−	0.594391i
$819$	−6.00000	−	10.3923i	−0.209657	−	0.363137i
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	5.19615			0.181237
$823$	13.8564	−	8.00000i	0.483004	−	0.278862i	−0.238664	−	0.971102i	$-0.576709\pi$
$823$	13.8564	−	8.00000i	0.483004	−	0.278862i	0.721668	+	0.692240i	$0.243376\pi$
$824$	7.00000	+	12.1244i	0.243857	+	0.422372i
$825$		0			0
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$		−	18.0000i		−	0.625543i
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$		0			0
$831$	−15.0000	+	8.66025i	−0.520344	+	0.300421i
$832$	1.73205	−	1.00000i	0.0600481	−	0.0346688i
$833$	−7.79423	+	4.50000i	−0.270054	+	0.155916i
$834$	−28.5000	−	16.4545i	−0.986874	−	0.569772i
$835$		0			0
$836$	3.00000			0.103757
$837$	10.3923	+	18.0000i	0.359211	+	0.622171i
$838$			12.0000i			0.414533i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	17.3205	−	10.0000i	0.596904	−	0.344623i
$843$	−5.19615	−	9.00000i	−0.178965	−	0.309976i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$		0			0
$846$	−9.00000	+	15.5885i	−0.309426	+	0.535942i
$847$		−	4.00000i		−	0.137442i
$848$	10.3923	+	6.00000i	0.356873	+	0.206041i
$849$			6.92820i			0.237775i
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	20.7846			0.712069
$853$	22.5167	+	13.0000i	0.770956	+	0.445112i	0.833215	−	0.552948i	$-0.186497\pi$
$853$	22.5167	+	13.0000i	0.770956	+	0.445112i	−0.0622597	+	0.998060i	$0.519831\pi$
$854$	−16.0000			−0.547509
$855$		0			0
$856$	3.00000			0.102538
$857$	36.3731	+	21.0000i	1.24248	+	0.717346i	0.969599	−	0.244701i	$-0.0786899\pi$
$857$	36.3731	+	21.0000i	1.24248	+	0.717346i	0.272882	+	0.962048i	$0.412023\pi$
$858$	5.19615	+	9.00000i	0.177394	+	0.307255i
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	0.993248	+	0.116011i	$0.0370107\pi$
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	−0.396156	+	0.918183i	$0.629656\pi$
$860$		0			0
$861$	−27.0000	−	15.5885i	−0.920158	−	0.531253i
$862$	25.9808	+	15.0000i	0.884908	+	0.510902i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$		0			0
$866$	3.50000	−	6.06218i	0.118935	−	0.206001i
$867$	−6.92820	+	12.0000i	−0.235294	+	0.407541i
$868$	6.92820	−	4.00000i	0.235159	−	0.135769i
$869$	6.00000	+	10.3923i	0.203536	+	0.352535i
$870$		0			0
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$		−	16.0000i		−	0.541828i
$873$			15.0000i			0.507673i
$874$	−6.00000			−0.202953
$875$		0			0
$876$			19.0526i			0.643726i
$877$	6.92820	−	4.00000i	0.233949	−	0.135070i	−0.378444	−	0.925624i	$-0.623541\pi$
$877$	6.92820	−	4.00000i	0.233949	−	0.135070i	0.612392	+	0.790554i	$0.290207\pi$
$878$	−6.92820	+	4.00000i	−0.233816	+	0.134993i
$879$		−	51.9615i		−	1.75262i
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	7.79423	−	4.50000i	0.262445	−	0.151523i
$883$			19.0000i			0.639401i	0.947519	+	0.319700i	$0.103582\pi$
$883$			19.0000i			0.639401i	−0.947519	+	0.319700i	$0.896418\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$		0			0
$886$	−1.50000	−	2.59808i	−0.0503935	−	0.0872841i
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$	3.46410	−	6.00000i	0.116248	−	0.201347i
$889$	2.00000	−	3.46410i	0.0670778	−	0.116182i
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$			26.0000i			0.870544i
$893$	5.19615	+	3.00000i	0.173883	+	0.100391i
$894$	−9.00000	−	5.19615i	−0.301005	−	0.173785i
$895$		0			0
$896$	−1.00000	−	1.73205i	−0.0334077	−	0.0578638i
$897$	−10.3923	−	18.0000i	−0.346989	−	0.601003i
$898$	7.79423	+	4.50000i	0.260097	+	0.150167i
$899$	24.0000			0.800445
$900$		0			0
$901$	−36.0000			−1.19933
$902$	23.3827	+	13.5000i	0.778558	+	0.449501i
$903$	−3.46410			−0.115278
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$		0			0
$906$		−	17.3205i		−	0.575435i
$907$	26.8468	+	15.5000i	0.891433	+	0.514669i	0.874411	−	0.485186i	$-0.161248\pi$
$907$	26.8468	+	15.5000i	0.891433	+	0.514669i	0.0170220	+	0.999855i	$0.494581\pi$
$908$		−	21.0000i		−	0.696909i
$909$		0			0
$910$		0			0
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	0.127585	+	0.991828i	$0.459277\pi$
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	−0.922740	+	0.385422i	$0.874056\pi$
$912$	−0.866025	−	1.50000i	−0.0286770	−	0.0496700i
$913$	31.1769	−	18.0000i	1.03181	−	0.595713i
$914$	8.50000	+	14.7224i	0.281155	+	0.486975i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$		0			0
$918$	−7.79423	+	13.5000i	−0.257248	+	0.445566i
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$		0			0
$921$	10.5000	+	6.06218i	0.345987	+	0.199756i
$922$	−25.9808	+	15.0000i	−0.855631	+	0.493999i
$923$	20.7846	−	12.0000i	0.684134	−	0.394985i
$924$	9.00000	−	5.19615i	0.296078	−	0.170941i
$925$		0			0
$926$	20.0000			0.657241
$927$	36.3731	+	21.0000i	1.19465	+	0.689730i
$928$		−	6.00000i		−	0.196960i
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$		0			0
$931$	−1.50000	−	2.59808i	−0.0491605	−	0.0851485i
$932$	2.59808	−	1.50000i	0.0851028	−	0.0491341i
$933$	−31.1769			−1.02069
$934$	−7.50000	+	12.9904i	−0.245407	+	0.425058i
$935$		0			0
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$			14.0000i			0.457360i	0.973502	+	0.228680i	$0.0734410\pi$
$937$			14.0000i			0.457360i	−0.973502	+	0.228680i	$0.926559\pi$
$938$	8.66025	+	5.00000i	0.282767	+	0.163256i
$939$	−43.5000	+	25.1147i	−1.41957	+	0.819588i
$940$		0			0
$941$	30.0000	+	51.9615i	0.977972	+	1.69390i	0.669757	+	0.742581i	$0.266398\pi$
$941$	30.0000	+	51.9615i	0.977972	+	1.69390i	0.308215	+	0.951317i	$0.400268\pi$
$942$	−3.46410	+	6.00000i	−0.112867	+	0.195491i
$943$	−46.7654	−	27.0000i	−1.52289	−	0.879241i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	3.00000			0.0975384
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	0.457193	−	0.889368i	$-0.348855\pi$
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	−0.541619	+	0.840624i	$0.682188\pi$
$948$	3.46410	−	6.00000i	0.112509	−	0.194871i
$949$	11.0000	+	19.0526i	0.357075	+	0.618472i
$950$		0			0
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$	5.19615	+	3.00000i	0.168408	+	0.0972306i
$953$		−	9.00000i		−	0.291539i	−0.989319	−	0.145769i	$-0.953434\pi$
$953$		−	9.00000i		−	0.291539i	0.989319	−	0.145769i	$-0.0465657\pi$
$954$	36.0000			1.16554
$955$		0			0
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	31.1769			1.00781
$958$	36.3731	−	21.0000i	1.17516	−	0.678479i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		−	8.00000i		−	0.257930i
$963$	7.79423	−	4.50000i	0.251166	−	0.145010i
$964$	7.00000			0.225455
$965$		0			0
$966$	−18.0000	+	10.3923i	−0.579141	+	0.334367i
$967$	−19.0526	+	11.0000i	−0.612689	+	0.353736i	−0.774017	−	0.633165i	$-0.781756\pi$
$967$	−19.0526	+	11.0000i	−0.612689	+	0.353736i	0.161328	+	0.986901i	$0.448422\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	4.50000	+	2.59808i	0.144561	+	0.0834622i
$970$		0			0
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$	7.79423	−	13.5000i	0.250000	−	0.433013i
$973$			38.0000i			1.21822i
$974$	13.0000	−	22.5167i	0.416547	−	0.721480i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−44.1673	+	25.5000i	−1.41304	+	0.815817i	−0.995673	−	0.0929223i	$-0.970379\pi$
$977$	−44.1673	+	25.5000i	−1.41304	+	0.815817i	−0.417364	+	0.908740i	$0.637046\pi$
$978$	3.46410	+	6.00000i	0.110770	+	0.191859i
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$		0			0
$981$	−24.0000	−	41.5692i	−0.766261	−	1.32720i
$982$		−	15.0000i		−	0.478669i
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$		−	15.5885i		−	0.496942i
$985$		0			0
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$	20.7846			0.661581
$988$	−1.73205	−	1.00000i	−0.0551039	−	0.0318142i
$989$	−6.00000			−0.190789
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	3.46410	+	2.00000i	0.109985	+	0.0635001i
$993$	3.46410	+	6.00000i	0.109930	+	0.190404i
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$		0			0
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	24.2487	+	14.0000i	0.767964	+	0.443384i	0.832148	−	0.554554i	$-0.187111\pi$
$997$	24.2487	+	14.0000i	0.767964	+	0.443384i	−0.0641836	+	0.997938i	$0.520444\pi$
$998$			13.0000i			0.411508i
$999$		−	20.7846i		−	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.j.e.349.1		4
3.2	odd	2		1350.2.j.a.1099.2		4
5.2	odd	4		450.2.e.i.151.1		2
5.3	odd	4		18.2.c.a.7.1	✓	2
5.4	even	2	inner	450.2.j.e.349.2		4
9.2	odd	6		4050.2.c.r.649.1		2
9.4	even	3	inner	450.2.j.e.49.2		4
9.5	odd	6		1350.2.j.a.199.1		4
9.7	even	3		4050.2.c.c.649.2		2
15.2	even	4		1350.2.e.c.451.1		2
15.8	even	4		54.2.c.a.19.1		2
15.14	odd	2		1350.2.j.a.1099.1		4
20.3	even	4		144.2.i.c.97.1		2
35.3	even	12		882.2.h.b.79.1		2
35.13	even	4		882.2.f.d.295.1		2
35.18	odd	12		882.2.h.c.79.1		2
35.23	odd	12		882.2.e.i.655.1		2
35.33	even	12		882.2.e.g.655.1		2
40.3	even	4		576.2.i.a.385.1		2
40.13	odd	4		576.2.i.g.385.1		2
45.2	even	12		4050.2.a.v.1.1		1
45.4	even	6	inner	450.2.j.e.49.1		4
45.7	odd	12		4050.2.a.c.1.1		1
45.13	odd	12		18.2.c.a.13.1	yes	2
45.14	odd	6		1350.2.j.a.199.2		4
45.22	odd	12		450.2.e.i.301.1		2
45.23	even	12		54.2.c.a.37.1		2
45.29	odd	6		4050.2.c.r.649.2		2
45.32	even	12		1350.2.e.c.901.1		2
45.34	even	6		4050.2.c.c.649.1		2
45.38	even	12		162.2.a.b.1.1		1
45.43	odd	12		162.2.a.c.1.1		1
60.23	odd	4		432.2.i.b.289.1		2
105.23	even	12		2646.2.e.b.2125.1		2
105.38	odd	12		2646.2.h.i.667.1		2
105.53	even	12		2646.2.h.h.667.1		2
105.68	odd	12		2646.2.e.c.2125.1		2
105.83	odd	4		2646.2.f.g.883.1		2
120.53	even	4		1728.2.i.e.1153.1		2
120.83	odd	4		1728.2.i.f.1153.1		2
180.23	odd	12		432.2.i.b.145.1		2
180.43	even	12		1296.2.a.g.1.1		1
180.83	odd	12		1296.2.a.f.1.1		1
180.103	even	12		144.2.i.c.49.1		2
315.13	even	12		882.2.f.d.589.1		2
315.23	even	12		2646.2.h.h.361.1		2
315.58	odd	12		882.2.h.c.67.1		2
315.68	odd	12		2646.2.h.i.361.1		2
315.83	odd	12		7938.2.a.i.1.1		1
315.103	even	12		882.2.h.b.67.1		2
315.158	even	12		2646.2.e.b.1549.1		2
315.193	odd	12		882.2.e.i.373.1		2
315.223	even	12		7938.2.a.x.1.1		1
315.248	odd	12		2646.2.e.c.1549.1		2
315.283	even	12		882.2.e.g.373.1		2
315.293	odd	12		2646.2.f.g.1765.1		2
360.13	odd	12		576.2.i.g.193.1		2
360.43	even	12		5184.2.a.o.1.1		1
360.83	odd	12		5184.2.a.p.1.1		1
360.133	odd	12		5184.2.a.r.1.1		1
360.173	even	12		5184.2.a.q.1.1		1
360.203	odd	12		1728.2.i.f.577.1		2
360.283	even	12		576.2.i.a.193.1		2
360.293	even	12		1728.2.i.e.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.2.c.a.7.1	✓	2	5.3	odd	4
18.2.c.a.13.1	yes	2	45.13	odd	12
54.2.c.a.19.1		2	15.8	even	4
54.2.c.a.37.1		2	45.23	even	12
144.2.i.c.49.1		2	180.103	even	12
144.2.i.c.97.1		2	20.3	even	4
162.2.a.b.1.1		1	45.38	even	12
162.2.a.c.1.1		1	45.43	odd	12
432.2.i.b.145.1		2	180.23	odd	12
432.2.i.b.289.1		2	60.23	odd	4
450.2.e.i.151.1		2	5.2	odd	4
450.2.e.i.301.1		2	45.22	odd	12
450.2.j.e.49.1		4	45.4	even	6	inner
450.2.j.e.49.2		4	9.4	even	3	inner
450.2.j.e.349.1		4	1.1	even	1	trivial
450.2.j.e.349.2		4	5.4	even	2	inner
576.2.i.a.193.1		2	360.283	even	12
576.2.i.a.385.1		2	40.3	even	4
576.2.i.g.193.1		2	360.13	odd	12
576.2.i.g.385.1		2	40.13	odd	4
882.2.e.g.373.1		2	315.283	even	12
882.2.e.g.655.1		2	35.33	even	12
882.2.e.i.373.1		2	315.193	odd	12
882.2.e.i.655.1		2	35.23	odd	12
882.2.f.d.295.1		2	35.13	even	4
882.2.f.d.589.1		2	315.13	even	12
882.2.h.b.67.1		2	315.103	even	12
882.2.h.b.79.1		2	35.3	even	12
882.2.h.c.67.1		2	315.58	odd	12
882.2.h.c.79.1		2	35.18	odd	12
1296.2.a.f.1.1		1	180.83	odd	12
1296.2.a.g.1.1		1	180.43	even	12
1350.2.e.c.451.1		2	15.2	even	4
1350.2.e.c.901.1		2	45.32	even	12
1350.2.j.a.199.1		4	9.5	odd	6
1350.2.j.a.199.2		4	45.14	odd	6
1350.2.j.a.1099.1		4	15.14	odd	2
1350.2.j.a.1099.2		4	3.2	odd	2
1728.2.i.e.577.1		2	360.293	even	12
1728.2.i.e.1153.1		2	120.53	even	4
1728.2.i.f.577.1		2	360.203	odd	12
1728.2.i.f.1153.1		2	120.83	odd	4
2646.2.e.b.1549.1		2	315.158	even	12
2646.2.e.b.2125.1		2	105.23	even	12
2646.2.e.c.1549.1		2	315.248	odd	12
2646.2.e.c.2125.1		2	105.68	odd	12
2646.2.f.g.883.1		2	105.83	odd	4
2646.2.f.g.1765.1		2	315.293	odd	12
2646.2.h.h.361.1		2	315.23	even	12
2646.2.h.h.667.1		2	105.53	even	12
2646.2.h.i.361.1		2	315.68	odd	12
2646.2.h.i.667.1		2	105.38	odd	12
4050.2.a.c.1.1		1	45.7	odd	12
4050.2.a.v.1.1		1	45.2	even	12
4050.2.c.c.649.1		2	45.34	even	6
4050.2.c.c.649.2		2	9.7	even	3
4050.2.c.r.649.1		2	9.2	odd	6
4050.2.c.r.649.2		2	45.29	odd	6
5184.2.a.o.1.1		1	360.43	even	12
5184.2.a.p.1.1		1	360.83	odd	12
5184.2.a.q.1.1		1	360.173	even	12
5184.2.a.r.1.1		1	360.133	odd	12
7938.2.a.i.1.1		1	315.83	odd	12
7938.2.a.x.1.1		1	315.223	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.73205 q^{12} +(-1.73205 + 1.00000i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000i q^{17} +3.00000i q^{18} +1.00000 q^{19} +(3.00000 - 1.73205i) q^{21} +(-2.59808 + 1.50000i) q^{22} +(5.19615 - 3.00000i) q^{23} +(1.50000 + 0.866025i) q^{24} +2.00000 q^{26} +5.19615 q^{27} -2.00000i q^{28} +(3.00000 - 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.59808 + 4.50000i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} -4.00000i q^{37} +(-0.866025 - 0.500000i) q^{38} -3.46410i q^{39} +(-4.50000 - 7.79423i) q^{41} -3.46410 q^{42} +(-0.866025 - 0.500000i) q^{43} +3.00000 q^{44} -6.00000 q^{46} +(5.19615 + 3.00000i) q^{47} +(-0.866025 - 1.50000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(4.50000 + 2.59808i) q^{51} +(-1.73205 - 1.00000i) q^{52} -12.0000i q^{53} +(-4.50000 - 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +(-0.866025 + 1.50000i) q^{57} +(-5.19615 + 3.00000i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.00000i q^{62} +6.00000i q^{63} -1.00000 q^{64} -5.19615i q^{66} +(4.33013 - 2.50000i) q^{67} +(2.59808 - 1.50000i) q^{68} +10.3923i q^{69} -12.0000 q^{71} +(-2.59808 + 1.50000i) q^{72} -11.0000i q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(-1.73205 + 3.00000i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +9.00000i q^{82} +(10.3923 + 6.00000i) q^{83} +(3.00000 + 1.73205i) q^{84} +(0.500000 + 0.866025i) q^{86} +(5.19615 + 9.00000i) q^{87} +(-2.59808 - 1.50000i) q^{88} -6.00000 q^{89} +4.00000 q^{91} +(5.19615 + 3.00000i) q^{92} -6.92820 q^{93} +(-3.00000 - 5.19615i) q^{94} +1.73205i q^{96} +(-4.33013 - 2.50000i) q^{97} +3.00000i q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 6 q^{6} - 6 q^{9} + 6 q^{11} + 4 q^{14} - 2 q^{16} + 4 q^{19} + 12 q^{21} + 6 q^{24} + 8 q^{26} + 12 q^{29} + 8 q^{31} - 6 q^{34} + 6 q^{36} - 18 q^{41} + 12 q^{44} - 24 q^{46} - 6 q^{49}+ \cdots - 36 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^6 - 6 * q^9 + 6 * q^11 + 4 * q^14 - 2 * q^16 + 4 * q^19 + 12 * q^21 + 6 * q^24 + 8 * q^26 + 12 * q^29 + 8 * q^31 - 6 * q^34 + 6 * q^36 - 18 * q^41 + 12 * q^44 - 24 * q^46 - 6 * q^49 + 18 * q^51 - 18 * q^54 - 4 * q^56 + 6 * q^59 - 16 * q^61 - 4 * q^64 - 48 * q^71 - 8 * q^74 + 2 * q^76 - 8 * q^79 - 18 * q^81 + 12 * q^84 + 2 * q^86 - 24 * q^89 + 16 * q^91 - 12 * q^94 - 36 * q^99

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