LMFDB - Embedded newform 18.2.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,2,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, 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:	$0.143730723638$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	18.7
Dual form			18.2.c.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(-1.00000 - 1.73205i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} -3.00000 q^{18} -1.00000 q^{19} +(3.00000 - 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +2.00000 q^{26} -5.19615i q^{27} +2.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} -4.00000 q^{37} +(0.500000 - 0.866025i) q^{38} +3.46410i q^{39} +(-4.50000 - 7.79423i) q^{41} +3.46410i q^{42} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.50000 + 4.33013i) q^{50} +(4.50000 + 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +(1.50000 + 0.866025i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -5.19615i q^{66} +(-2.50000 - 4.33013i) q^{67} +(1.50000 + 2.59808i) q^{68} -10.3923i q^{69} -12.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +11.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(-7.50000 + 4.33013i) q^{75} +(0.500000 + 0.866025i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-3.00000 - 1.73205i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +9.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-3.00000 - 1.73205i) q^{84} +(0.500000 + 0.866025i) q^{86} +(9.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +4.00000 q^{91} +(3.00000 - 5.19615i) q^{92} -6.92820i q^{93} +(3.00000 + 5.19615i) q^{94} +1.73205i q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{98} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} + 3 q^{11} - 2 q^{13} - 2 q^{14} - q^{16} - 6 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} + 5 q^{25}+ \cdots + 18 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 + 3 * q^11 - 2 * q^13 - 2 * q^14 - q^16 - 6 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 + 5 * q^25 + 4 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 - 9 * q^33 + 3 * q^34 + 3 * q^36 - 8 * q^37 + q^38 - 9 * q^41 + q^43 - 6 * q^44 - 12 * q^46 + 6 * q^47 + 3 * q^48 + 3 * q^49 + 5 * q^50 + 9 * q^51 - 2 * q^52 + 24 * q^53 + 9 * q^54 - 2 * q^56 + 3 * q^57 - 6 * q^58 - 3 * q^59 - 8 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 5 * q^67 + 3 * q^68 - 24 * q^71 + 3 * q^72 + 22 * q^73 + 4 * q^74 - 15 * q^75 + q^76 + 6 * q^77 - 6 * q^78 + 4 * q^79 - 9 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 + q^86 + 18 * q^87 + 3 * q^88 + 12 * q^89 + 8 * q^91 + 6 * q^92 + 6 * q^94 - 5 * q^97 - 6 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	1.00000			0.353553
$9$	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	$0.0172821\pi$
$12$			1.73205i			0.500000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−1.00000	−	1.73205i	−0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	−3.00000			−0.707107
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$		0			0
$21$	3.00000	−	1.73205i	0.654654	−	0.377964i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	2.00000			0.392232
$27$		−	5.19615i		−	1.00000i
$28$	2.00000			0.377964
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		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	$0.716379\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$			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	$-0.414726\pi$
$42$			3.46410i			0.534522i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	4.50000	+	2.59808i	0.630126	+	0.363803i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		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	$0.995517\pi$
$62$	−4.00000			−0.508001
$63$	−6.00000			−0.755929
$64$	1.00000			0.125000
$65$		0			0
$66$		−	5.19615i		−	0.639602i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		−	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	$0.752242\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	−7.50000	+	4.33013i	−0.866025	+	0.500000i
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$	3.00000	+	5.19615i	0.341882	+	0.592157i
$78$	−3.00000	−	1.73205i	−0.339683	−	0.196116i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	9.00000			0.993884
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$	−3.00000	−	1.73205i	−0.327327	−	0.188982i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	9.00000	−	5.19615i	0.964901	−	0.557086i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$		−	6.92820i		−	0.718421i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$			1.73205i			0.176777i
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$	−3.00000			−0.303046
$99$	9.00000			0.904534
$100$	−5.00000			−0.500000
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$		0			0
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	−1.00000	−	1.73205i	−0.0944911	−	0.163663i
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	−1.50000	+	0.866025i	−0.140488	+	0.0811107i
$115$		0			0
$116$	6.00000			0.557086
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$	3.00000			0.276172
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$			15.5885i			1.40556i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−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	$0.833333\pi$
$132$	4.50000	+	2.59808i	0.391675	+	0.226134i
$133$	1.00000	−	1.73205i	0.0867110	−	0.150188i
$134$	5.00000			0.431934
$135$		0			0
$136$	−3.00000			−0.257248
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$	9.00000	+	5.19615i	0.766131	+	0.442326i
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−6.00000			−0.501745
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		−	5.19615i		−	0.428571i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		−	8.66025i		−	0.707107i
$151$	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	$0.0332784\pi$
$152$	−1.00000			−0.0811107
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$	−6.00000			−0.483494
$155$		0			0
$156$	3.00000	−	1.73205i	0.240192	−	0.138675i
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$	−18.0000	−	10.3923i	−1.42749	−	0.824163i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$	3.00000	−	1.73205i	0.231455	−	0.133631i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$	−1.00000			−0.0762493
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$			10.3923i			0.787839i
$175$	5.00000	+	8.66025i	0.377964	+	0.654654i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$			5.19615i			0.390567i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	−2.00000	+	3.46410i	−0.148250	+	0.256776i
$183$	12.0000	−	6.92820i	0.887066	−	0.512148i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$	6.00000	+	3.46410i	0.439941	+	0.254000i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$	−6.00000			−0.437595
$189$	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	$-0.0590746\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−4.50000	+	7.79423i	−0.319801	+	0.553912i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	2.50000	−	4.33013i	0.176777	−	0.306186i
$201$			8.66025i			0.610847i
$202$		0			0
$203$	−6.00000	−	10.3923i	−0.421117	−	0.729397i
$204$		−	5.19615i		−	0.363803i
$205$		0			0
$206$	14.0000			0.975426
$207$	−9.00000	+	15.5885i	−0.625543	+	1.08347i
$208$	2.00000			0.138675
$209$	−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	$-0.408366\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$	18.0000	+	10.3923i	1.23334	+	0.712069i
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$	−8.00000			−0.543075
$218$	8.00000	−	13.8564i	0.541828	−	0.938474i
$219$	−16.5000	−	9.52628i	−1.11497	−	0.643726i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$	−6.00000	+	3.46410i	−0.402694	+	0.232495i
$223$	−13.0000	+	22.5167i	−0.870544	+	1.50783i	−0.00910984	+	0.999959i	$0.502900\pi$
$223$	−13.0000	+	22.5167i	−0.870544	+	1.50783i	−0.861435	+	0.507869i	$0.830434\pi$
$224$	2.00000			0.133631
$225$	15.0000			1.00000
$226$	6.00000			0.399114
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	0.272623	+	0.962121i	$0.412109\pi$
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	−0.969533	+	0.244962i	$0.921225\pi$
$228$		−	1.73205i		−	0.114708i
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$		−	10.3923i		−	0.683763i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$		0			0
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	−6.00000	+	3.46410i	−0.389742	+	0.225018i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$		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	$0.0942799\pi$
$242$	−2.00000			−0.128565
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	8.00000			0.512148
$245$		0			0
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	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	$0.269387\pi$
$252$	3.00000	+	5.19615i	0.188982	+	0.327327i
$253$	18.0000			1.13165
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	0.981901	+	0.189396i	$0.0606529\pi$
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	−0.326929	+	0.945049i	$0.606014\pi$
$258$		−	1.73205i		−	0.107833i
$259$	4.00000	−	6.92820i	0.248548	−	0.430498i
$260$		0			0
$261$	−18.0000			−1.11417
$262$		0			0
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	−4.50000	+	2.59808i	−0.276956	+	0.159901i
$265$		0			0
$266$	1.00000	+	1.73205i	0.0613139	+	0.106199i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$	−6.00000	−	3.46410i	−0.363137	−	0.209657i
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	−7.50000	−	12.9904i	−0.452267	−	0.783349i
$276$	−9.00000	+	5.19615i	−0.541736	+	0.312772i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	−19.0000			−1.13954
$279$	−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	$0.223942\pi$
$282$		−	10.3923i		−	0.618853i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$	18.0000			1.06251
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	−8.00000			−0.470588
$290$		0			0
$291$	7.50000	−	4.33013i	0.439658	−	0.253837i
$292$	−5.50000	−	9.52628i	−0.321863	−	0.557483i
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.855361	−	0.518032i	$-0.826665\pi$
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.0209480	−	0.999781i	$-0.506668\pi$
$294$	4.50000	+	2.59808i	0.262445	+	0.151523i
$295$		0			0
$296$	−4.00000			−0.232495
$297$	−13.5000	−	7.79423i	−0.783349	−	0.452267i
$298$	−6.00000			−0.347571
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	7.50000	+	4.33013i	0.433013	+	0.250000i
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		0			0
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$		0			0
$306$	9.00000			0.514496
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$			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	$0.662852\pi$
$312$			3.46410i			0.196116i
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	0.0863973	+	0.996261i	$0.472465\pi$
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	−0.905986	+	0.423308i	$0.860869\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−4.00000			−0.225018
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	18.0000	−	10.3923i	1.00939	−	0.582772i
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	3.00000			0.166924
$324$	9.00000			0.500000
$325$	−10.0000			−0.554700
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	24.0000	+	13.8564i	1.32720	+	0.766261i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	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	$0.131604\pi$
$332$	12.0000			0.658586
$333$	−6.00000	−	10.3923i	−0.328798	−	0.569495i
$334$	−12.0000			−0.656611
$335$		0			0
$336$			3.46410i			0.188982i
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$			10.3923i			0.564433i
$340$		0			0
$341$	12.0000			0.649836
$342$	3.00000			0.162221
$343$	−20.0000			−1.07990
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$	−9.00000	−	5.19615i	−0.482451	−	0.278543i
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	−0.568486	−	0.822693i	$-0.692471\pi$
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	0.996716	+	0.0809766i	$0.0258039\pi$
$350$	−10.0000			−0.534522
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	−3.00000			−0.159901
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$	−4.50000	−	2.59808i	−0.239172	−	0.138086i
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−9.00000	+	5.19615i	−0.476331	+	0.275010i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$		−	3.46410i		−	0.181818i
$364$	−2.00000	−	3.46410i	−0.104828	−	0.181568i
$365$		0			0
$366$			13.8564i			0.724286i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	−6.00000			−0.312772
$369$	13.5000	−	23.3827i	0.702782	−	1.21725i
$370$		0			0
$371$	−12.0000	+	20.7846i	−0.623009	+	1.07908i
$372$	−6.00000	+	3.46410i	−0.311086	+	0.179605i
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.851089	+	0.525022i	$0.175943\pi$
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.0291379	+	0.999575i	$0.490724\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	12.0000			0.618031
$378$	−9.00000	+	5.19615i	−0.462910	+	0.267261i
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$		0			0
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$	5.00000			0.254493
$387$	3.00000			0.152499
$388$	5.00000			0.253837
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$		0			0
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$		0			0
$396$	−4.50000	−	7.79423i	−0.226134	−	0.391675i
$397$	20.0000			1.00377			0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000			1.00377			0.501886	+	0.864934i	$0.332640\pi$
$398$	5.00000	−	8.66025i	0.250627	−	0.434099i
$399$	−3.00000	+	1.73205i	−0.150188	+	0.0867110i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	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	$0.597840\pi$
$402$	−7.50000	−	4.33013i	−0.374066	−	0.215967i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$		0			0
$406$	12.0000			0.595550
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$	4.50000	+	2.59808i	0.222783	+	0.128624i
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	0.575670	−	0.817682i	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$		0			0
$411$	−4.50000	+	2.59808i	−0.221969	+	0.128154i
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$	6.00000			0.295241
$414$	−9.00000	−	15.5885i	−0.442326	−	0.766131i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		−	32.9090i		−	1.61156i
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		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	$0.328710\pi$
$422$	20.0000			0.973585
$423$	18.0000			0.875190
$424$	12.0000			0.582772
$425$	−7.50000	+	12.9904i	−0.363803	+	0.630126i
$426$	−18.0000	+	10.3923i	−0.872103	+	0.503509i
$427$	−8.00000	−	13.8564i	−0.387147	−	0.670559i
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$	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	$0.757018\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	4.00000	−	6.92820i	0.192006	−	0.332564i
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$	16.5000	−	9.52628i	0.788400	−	0.455183i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$	−4.50000	+	7.79423i	−0.214286	+	0.371154i
$442$	−6.00000			−0.285391
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$		−	6.92820i		−	0.328798i
$445$		0			0
$446$	−13.0000	−	22.5167i	−0.615568	−	1.06619i
$447$		−	10.3923i		−	0.491539i
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−7.50000	+	12.9904i	−0.353553	+	0.612372i
$451$	−27.0000			−1.27138
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−15.0000	+	8.66025i	−0.704761	+	0.406894i
$454$	−10.5000	−	18.1865i	−0.492789	−	0.853536i
$455$		0			0
$456$	1.50000	+	0.866025i	0.0702439	+	0.0405554i
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	−0.993431	−	0.114433i	$-0.963495\pi$
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	0.595818	+	0.803120i	$0.296828\pi$
$458$	14.0000			0.654177
$459$			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	$-0.0795353\pi$
$462$	9.00000	+	5.19615i	0.418718	+	0.241747i
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	0.534450	−	0.845200i	$-0.320519\pi$
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	−1.50000	+	2.59808i	−0.0694862	+	0.120354i
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$	−6.00000			−0.277350
$469$	10.0000			0.461757
$470$		0			0
$471$		−	6.92820i		−	0.319235i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$		−	6.92820i		−	0.318223i
$475$	−2.50000	+	4.33013i	−0.114708	+	0.198680i
$476$	−6.00000			−0.275010
$477$	18.0000	+	31.1769i	0.824163	+	1.42749i
$478$	6.00000			0.274434
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.235833	−	0.971794i	$-0.424218\pi$
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.723681	−	0.690134i	$-0.242449\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	3.50000	+	6.06218i	0.159421	+	0.276125i
$483$	18.0000	+	10.3923i	0.819028	+	0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$			15.5885i			0.707107i
$487$	26.0000			1.17817			0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000			1.17817			0.589086	+	0.808070i	$0.299488\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	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	$0.723424\pi$
$492$	13.5000	−	7.79423i	0.608627	−	0.351391i
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	−2.00000			−0.0899843
$495$		0			0
$496$	−4.00000			−0.179605
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$			20.7846i			0.931381i
$499$	6.50000	+	11.2583i	0.290980	+	0.503992i	0.974042	−	0.226369i	$-0.0726854\pi$
$499$	6.50000	+	11.2583i	0.290980	+	0.503992i	−0.683062	+	0.730361i	$0.739352\pi$
$500$		0			0
$501$		−	20.7846i		−	0.928588i
$502$	−10.5000	+	18.1865i	−0.468638	+	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−6.00000			−0.267261
$505$		0			0
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$		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
$512$	1.00000			0.0441942
$513$			5.19615i			0.229416i
$514$	−21.0000			−0.926270
$515$		0			0
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$	4.00000	+	6.92820i	0.175750	+	0.304408i
$519$	−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	$0.520933\pi$
$522$	9.00000	−	15.5885i	0.393919	−	0.682288i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$		0			0
$525$		−	17.3205i		−	0.755929i
$526$	−9.00000	−	15.5885i	−0.392419	−	0.679689i
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		−	5.19615i		−	0.226134i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$	−2.00000			−0.0867110
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$	9.00000	−	5.19615i	0.389468	−	0.224860i
$535$		0			0
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$	−18.0000	−	10.3923i	−0.776757	−	0.448461i
$538$	12.0000	−	20.7846i	0.517357	−	0.896088i
$539$	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	$0.527404\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$	−21.0000	−	12.1244i	−0.901196	−	0.520306i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$		0			0
$546$	6.00000	−	3.46410i	0.256776	−	0.148250i
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	0.876517	+	0.481371i	$0.159861\pi$
$548$	−3.00000			−0.128154
$549$	−24.0000			−1.02430
$550$	15.0000			0.639602
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$		−	10.3923i		−	0.442326i
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	5.00000	+	8.66025i	0.212430	+	0.367939i
$555$		0			0
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$	−6.00000	−	10.3923i	−0.254000	−	0.439941i
$559$	−2.00000			−0.0845910
$560$		0			0
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	0.904320	+	0.426855i	$0.140378\pi$
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	−0.0824933	+	0.996592i	$0.526288\pi$
$564$	9.00000	+	5.19615i	0.378968	+	0.218797i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	−9.00000	−	15.5885i	−0.377964	−	0.654654i
$568$	−12.0000			−0.503509
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.184030	+	0.982921i	$0.558914\pi$
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.759220	+	0.650835i	$0.774419\pi$
$570$		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	$0.551485\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	−27.0000	+	15.5885i	−1.12794	+	0.651217i
$574$	−9.00000	+	15.5885i	−0.375653	+	0.650650i
$575$	30.0000			1.25109
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$			8.66025i			0.359908i
$580$		0			0
$581$	−12.0000	−	20.7846i	−0.497844	−	0.862291i
$582$			8.66025i			0.358979i
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	11.0000			0.455183
$585$		0			0
$586$	30.0000			1.23929
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	−0.758089	−	0.652151i	$-0.773867\pi$
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	0.943824	+	0.330449i	$0.107200\pi$
$588$	−4.50000	+	2.59808i	−0.185577	+	0.107143i
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	15.0000	+	8.66025i	0.613909	+	0.354441i
$598$	6.00000	+	10.3923i	0.245358	+	0.424973i
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$	−7.50000	+	4.33013i	−0.306186	+	0.176777i
$601$	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	$-0.105517\pi$
$602$	−2.00000			−0.0815139
$603$	7.50000	−	12.9904i	0.305424	−	0.529009i
$604$	−10.0000			−0.406894
$605$		0			0
$606$		0			0
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	0.996740	+	0.0806818i	$0.0257098\pi$
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	−0.428497	+	0.903543i	$0.640957\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$			20.7846i			0.842235i
$610$		0			0
$611$	−12.0000			−0.485468
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$		0			0
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$	−21.0000	−	12.1244i	−0.844744	−	0.487713i
$619$	−17.5000	+	30.3109i	−0.703384	+	1.21830i	0.263887	+	0.964554i	$0.414995\pi$
$619$	−17.5000	+	30.3109i	−0.703384	+	1.21830i	−0.967271	+	0.253744i	$0.918338\pi$
$620$		0			0
$621$	27.0000	−	15.5885i	1.08347	−	0.625543i
$622$	−18.0000			−0.721734
$623$	−6.00000	+	10.3923i	−0.240385	+	0.416359i
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−14.5000	−	25.1147i	−0.579537	−	1.00379i
$627$	4.50000	−	2.59808i	0.179713	−	0.103757i
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	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	$0.793153\pi$
$632$	2.00000	−	3.46410i	0.0795557	−	0.137795i
$633$			34.6410i			1.37686i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$			20.7846i			0.824163i
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$	−18.0000			−0.712627
$639$	−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	$0.147797\pi$
$642$	4.50000	−	2.59808i	0.177601	−	0.102538i
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	−9.00000			−0.353281
$650$	5.00000	−	8.66025i	0.196116	−	0.339683i
$651$	12.0000	+	6.92820i	0.470317	+	0.271538i
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	−24.0000	+	13.8564i	−0.938474	+	0.541828i
$655$		0			0
$656$	9.00000			0.351391
$657$	16.5000	+	28.5788i	0.643726	+	1.11497i
$658$	−12.0000			−0.467809
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		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	$0.808547\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		−	10.3923i		−	0.403604i
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$	12.0000			0.464991
$667$	−36.0000			−1.39393
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	39.0000	−	22.5167i	1.50783	−	0.870544i
$670$		0			0
$671$	12.0000	+	20.7846i	0.463255	+	0.802381i
$672$	−3.00000	−	1.73205i	−0.115728	−	0.0668153i
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	−0.572309	−	0.820038i	$-0.693952\pi$
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	0.996328	+	0.0856156i	$0.0272857\pi$
$674$	−1.00000			−0.0385186
$675$	−22.5000	−	12.9904i	−0.866025	−	0.500000i
$676$	−9.00000			−0.346154
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	0.279453	+	0.960159i	$0.409847\pi$
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	−0.971249	+	0.238067i	$0.923486\pi$
$678$	−9.00000	−	5.19615i	−0.345643	−	0.199557i
$679$	−5.00000	−	8.66025i	−0.191882	−	0.332350i
$680$		0			0
$681$	31.5000	−	18.1865i	1.20708	−	0.696909i
$682$	−6.00000	+	10.3923i	−0.229752	+	0.397942i
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$		0			0
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$			24.2487i			0.925146i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−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	$0.215292\pi$
$692$	−6.00000			−0.228086
$693$	−9.00000	+	15.5885i	−0.341882	+	0.592157i
$694$	33.0000			1.25266
$695$		0			0
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$	13.5000	+	23.3827i	0.511349	+	0.885682i
$698$	8.00000	+	13.8564i	0.302804	+	0.524473i
$699$	−4.50000	−	2.59808i	−0.170206	−	0.0982683i
$700$	5.00000	−	8.66025i	0.188982	−	0.327327i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		−	10.3923i		−	0.392232i
$703$	4.00000			0.150863
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	10.5000	+	18.1865i	0.395173	+	0.684459i
$707$		0			0
$708$	4.50000	−	2.59808i	0.169120	−	0.0976417i
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	−0.826023	−	0.563636i	$-0.809402\pi$
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	0.901135	+	0.433539i	$0.142735\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$	6.00000			0.224860
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		−	10.3923i		−	0.388922i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$			10.3923i			0.388108i
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$	28.0000			1.04277
$722$	9.00000	−	15.5885i	0.334945	−	0.580142i
$723$	−10.5000	+	6.06218i	−0.390499	+	0.225455i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	15.0000	+	25.9808i	0.557086	+	0.964901i
$726$	3.00000	+	1.73205i	0.111340	+	0.0642824i
$727$	−13.0000	+	22.5167i	−0.482143	+	0.835097i	−0.999790	−	0.0204978i	$-0.993475\pi$
$727$	−13.0000	+	22.5167i	−0.482143	+	0.835097i	0.517647	+	0.855595i	$0.326808\pi$
$728$	4.00000			0.148250
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	−12.0000	−	6.92820i	−0.443533	−	0.256074i
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	14.0000	+	24.2487i	0.516749	+	0.895036i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−15.0000			−0.552532
$738$	13.5000	+	23.3827i	0.496942	+	0.860729i
$739$	47.0000			1.72892			0.864461	−	0.502699i	$-0.167660\pi$
$739$	47.0000			1.72892			0.864461	+	0.502699i	$0.167660\pi$
$740$		0			0
$741$		−	3.46410i		−	0.127257i
$742$	−12.0000	−	20.7846i	−0.440534	−	0.763027i
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$		−	6.92820i		−	0.254000i
$745$		0			0
$746$	−34.0000			−1.24483
$747$	−36.0000			−1.31717
$748$	9.00000			0.329073
$749$	−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	$0.879961\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	−31.5000	−	18.1865i	−1.14792	−	0.662754i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$		0			0
$756$		−	10.3923i		−	0.377964i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−11.5000	+	19.9186i	−0.417699	+	0.723476i
$759$	−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	$-0.442080\pi$
$762$	3.00000	−	1.73205i	0.108679	−	0.0627456i
$763$	16.0000	−	27.7128i	0.579239	−	1.00327i
$764$	−18.0000			−0.651217
$765$		0			0
$766$		0			0
$767$	−3.00000	+	5.19615i	−0.108324	+	0.187622i
$768$			1.73205i			0.0625000i
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$		−	36.3731i		−	1.30994i
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	−1.50000	+	2.59808i	−0.0539164	+	0.0933859i
$775$	20.0000			0.718421
$776$	−2.50000	+	4.33013i	−0.0897448	+	0.155443i
$777$	−12.0000	+	6.92820i	−0.430498	+	0.248548i
$778$	−9.00000	−	15.5885i	−0.322666	−	0.558873i
$779$	4.50000	+	7.79423i	0.161229	+	0.279257i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$	18.0000			0.643679
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	−3.00000			−0.107143
$785$		0			0
$786$		0			0
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	27.0000	−	15.5885i	0.961225	−	0.554964i
$790$		0			0
$791$	12.0000			0.426671
$792$	9.00000			0.319801
$793$	16.0000			0.568177
$794$	−10.0000	+	17.3205i	−0.354887	+	0.614682i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	0.952506	−	0.304520i	$-0.0984960\pi$
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	−0.739975	+	0.672634i	$0.765163\pi$
$798$		−	3.46410i		−	0.122628i
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	−5.00000			−0.176777
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	−27.0000			−0.953403
$803$	16.5000	−	28.5788i	0.582272	−	1.00853i
$804$	7.50000	−	4.33013i	0.264505	−	0.152712i
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$	36.0000	+	20.7846i	1.26726	+	0.731653i
$808$		0			0
$809$	33.0000			1.16022			0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000			1.16022			0.580109	+	0.814539i	$0.303010\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$	−6.00000	+	10.3923i	−0.210559	+	0.364698i
$813$	−30.0000	−	17.3205i	−1.05215	−	0.607457i
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$		0			0
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	−0.500000	+	0.866025i	−0.0174928	+	0.0302984i
$818$	17.0000			0.594391
$819$	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	$0.0649632\pi$
$822$		−	5.19615i		−	0.181237i
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	−7.00000	−	12.1244i	−0.243857	−	0.422372i
$825$			25.9808i			0.904534i
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	18.0000			0.625543
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$		0			0
$831$	−15.0000	+	8.66025i	−0.520344	+	0.300421i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−4.50000	−	7.79423i	−0.155916	−	0.270054i
$834$	28.5000	+	16.4545i	0.986874	+	0.569772i
$835$		0			0
$836$	3.00000			0.103757
$837$	18.0000	−	10.3923i	0.622171	−	0.359211i
$838$	−12.0000			−0.414533
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−10.0000	−	17.3205i	−0.344623	−	0.596904i
$843$	9.00000	−	5.19615i	0.309976	−	0.178965i
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$		0			0
$846$	−9.00000	+	15.5885i	−0.309426	+	0.535942i
$847$	−4.00000			−0.137442
$848$	−6.00000	+	10.3923i	−0.206041	+	0.356873i
$849$		−	6.92820i		−	0.237775i
$850$	−7.50000	−	12.9904i	−0.257248	−	0.445566i
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$		−	20.7846i		−	0.712069i
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$	3.00000			0.102538
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$	−9.00000	+	5.19615i	−0.307255	+	0.177394i
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	−0.993248	−	0.116011i	$-0.962989\pi$
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	0.396156	−	0.918183i	$-0.370344\pi$
$860$		0			0
$861$	−27.0000	−	15.5885i	−0.920158	−	0.531253i
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		0			0
$866$	3.50000	−	6.06218i	0.118935	−	0.206001i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$	4.00000	+	6.92820i	0.135769	+	0.235159i
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	−16.0000			−0.541828
$873$	−15.0000			−0.507673
$874$	6.00000			0.202953
$875$		0			0
$876$			19.0526i			0.643726i
$877$	−4.00000	−	6.92820i	−0.135070	−	0.233949i	0.790554	−	0.612392i	$-0.209793\pi$
$877$	−4.00000	−	6.92820i	−0.135070	−	0.233949i	−0.925624	+	0.378444i	$0.876459\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$			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	$0.750181\pi$
$882$	−4.50000	−	7.79423i	−0.151523	−	0.262445i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$		0			0
$886$	−1.50000	−	2.59808i	−0.0503935	−	0.0872841i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	6.00000	+	3.46410i	0.201347	+	0.116248i
$889$	−2.00000	+	3.46410i	−0.0670778	+	0.116182i
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	26.0000			0.870544
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$	9.00000	+	5.19615i	0.301005	+	0.173785i
$895$		0			0
$896$	−1.00000	−	1.73205i	−0.0334077	−	0.0578638i
$897$	−18.0000	+	10.3923i	−0.601003	+	0.346989i
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	−24.0000			−0.800445
$900$	−7.50000	−	12.9904i	−0.250000	−	0.433013i
$901$	−36.0000			−1.19933
$902$	13.5000	−	23.3827i	0.449501	−	0.778558i
$903$		−	3.46410i		−	0.115278i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$		0			0
$906$		−	17.3205i		−	0.575435i
$907$	15.5000	−	26.8468i	0.514669	−	0.891433i	−0.485186	−	0.874411i	$-0.661248\pi$
$907$	15.5000	−	26.8468i	0.514669	−	0.891433i	0.999855	−	0.0170220i	$-0.00541854\pi$
$908$	21.0000			0.696909
$909$		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	$0.874056\pi$
$912$	−1.50000	+	0.866025i	−0.0496700	+	0.0286770i
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−8.50000	−	14.7224i	−0.281155	−	0.486975i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$		0			0
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	38.0000			1.25350			0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000			1.25350			0.626752	+	0.779219i	$0.284384\pi$
$920$		0			0
$921$	10.5000	+	6.06218i	0.345987	+	0.199756i
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$	−9.00000	+	5.19615i	−0.296078	+	0.170941i
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	20.0000			0.657241
$927$	21.0000	−	36.3731i	0.689730	−	1.19465i
$928$	6.00000			0.196960
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	−1.50000	−	2.59808i	−0.0491605	−	0.0851485i
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$		−	31.1769i		−	1.02069i
$934$	7.50000	−	12.9904i	0.245407	−	0.425058i
$935$		0			0
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$	−5.00000	+	8.66025i	−0.163256	+	0.282767i
$939$	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	$0.400268\pi$
$942$	6.00000	+	3.46410i	0.195491	+	0.112867i
$943$	27.0000	−	46.7654i	0.879241	−	1.52289i
$944$	3.00000			0.0976417
$945$		0			0
$946$	3.00000			0.0975384
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	−0.889368	−	0.457193i	$-0.848855\pi$
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	0.840624	+	0.541619i	$0.182188\pi$
$948$	6.00000	+	3.46410i	0.194871	+	0.112509i
$949$	−11.0000	−	19.0526i	−0.357075	−	0.618472i
$950$	−2.50000	−	4.33013i	−0.0811107	−	0.140488i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$	3.00000	−	5.19615i	0.0972306	−	0.168408i
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$	−36.0000			−1.16554
$955$		0			0
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$		−	31.1769i		−	1.00781i
$958$	21.0000	+	36.3731i	0.678479	+	1.17516i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−8.00000			−0.257930
$963$	4.50000	+	7.79423i	0.145010	+	0.251166i
$964$	−7.00000			−0.225455
$965$		0			0
$966$	−18.0000	+	10.3923i	−0.579141	+	0.334367i
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−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	$0.696029\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	−38.0000			−1.21822
$974$	−13.0000	+	22.5167i	−0.416547	+	0.721480i
$975$	15.0000	+	8.66025i	0.480384	+	0.277350i
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	25.5000	+	44.1673i	0.815817	+	1.41304i	0.908740	+	0.417364i	$0.137046\pi$
$977$	25.5000	+	44.1673i	0.815817	+	1.41304i	−0.0929223	+	0.995673i	$0.529621\pi$
$978$	−6.00000	+	3.46410i	−0.191859	+	0.110770i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	−24.0000	−	41.5692i	−0.766261	−	1.32720i
$982$	−15.0000			−0.478669
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$			15.5885i			0.496942i
$985$		0			0
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$		−	20.7846i		−	0.661581i
$988$	1.00000	−	1.73205i	0.0318142	−	0.0551039i
$989$	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	$0.581789\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−6.00000	+	3.46410i	−0.190404	+	0.109930i
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$		0			0
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	−0.554554	−	0.832148i	$-0.687111\pi$
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	0.997938	+	0.0641836i	$0.0204443\pi$
$998$	−13.0000			−0.411508
$999$			20.7846i			0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.2.c.a.7.1	✓	2
3.2	odd	2		54.2.c.a.19.1		2
4.3	odd	2		144.2.i.c.97.1		2
5.2	odd	4		450.2.j.e.349.1		4
5.3	odd	4		450.2.j.e.349.2		4
5.4	even	2		450.2.e.i.151.1		2
7.2	even	3		882.2.e.i.655.1		2
7.3	odd	6		882.2.h.b.79.1		2
7.4	even	3		882.2.h.c.79.1		2
7.5	odd	6		882.2.e.g.655.1		2
7.6	odd	2		882.2.f.d.295.1		2
8.3	odd	2		576.2.i.a.385.1		2
8.5	even	2		576.2.i.g.385.1		2
9.2	odd	6		162.2.a.b.1.1		1
9.4	even	3	inner	18.2.c.a.13.1	yes	2
9.5	odd	6		54.2.c.a.37.1		2
9.7	even	3		162.2.a.c.1.1		1
12.11	even	2		432.2.i.b.289.1		2
15.2	even	4		1350.2.j.a.1099.2		4
15.8	even	4		1350.2.j.a.1099.1		4
15.14	odd	2		1350.2.e.c.451.1		2
21.2	odd	6		2646.2.e.b.2125.1		2
21.5	even	6		2646.2.e.c.2125.1		2
21.11	odd	6		2646.2.h.h.667.1		2
21.17	even	6		2646.2.h.i.667.1		2
21.20	even	2		2646.2.f.g.883.1		2
24.5	odd	2		1728.2.i.e.1153.1		2
24.11	even	2		1728.2.i.f.1153.1		2
36.7	odd	6		1296.2.a.g.1.1		1
36.11	even	6		1296.2.a.f.1.1		1
36.23	even	6		432.2.i.b.145.1		2
36.31	odd	6		144.2.i.c.49.1		2
45.2	even	12		4050.2.c.r.649.1		2
45.4	even	6		450.2.e.i.301.1		2
45.7	odd	12		4050.2.c.c.649.2		2
45.13	odd	12		450.2.j.e.49.1		4
45.14	odd	6		1350.2.e.c.901.1		2
45.22	odd	12		450.2.j.e.49.2		4
45.23	even	12		1350.2.j.a.199.2		4
45.29	odd	6		4050.2.a.v.1.1		1
45.32	even	12		1350.2.j.a.199.1		4
45.34	even	6		4050.2.a.c.1.1		1
45.38	even	12		4050.2.c.r.649.2		2
45.43	odd	12		4050.2.c.c.649.1		2
63.4	even	3		882.2.e.i.373.1		2
63.5	even	6		2646.2.h.i.361.1		2
63.13	odd	6		882.2.f.d.589.1		2
63.20	even	6		7938.2.a.i.1.1		1
63.23	odd	6		2646.2.h.h.361.1		2
63.31	odd	6		882.2.e.g.373.1		2
63.32	odd	6		2646.2.e.b.1549.1		2
63.34	odd	6		7938.2.a.x.1.1		1
63.40	odd	6		882.2.h.b.67.1		2
63.41	even	6		2646.2.f.g.1765.1		2
63.58	even	3		882.2.h.c.67.1		2
63.59	even	6		2646.2.e.c.1549.1		2
72.5	odd	6		1728.2.i.e.577.1		2
72.11	even	6		5184.2.a.p.1.1		1
72.13	even	6		576.2.i.g.193.1		2
72.29	odd	6		5184.2.a.q.1.1		1
72.43	odd	6		5184.2.a.o.1.1		1
72.59	even	6		1728.2.i.f.577.1		2
72.61	even	6		5184.2.a.r.1.1		1
72.67	odd	6		576.2.i.a.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.2.c.a.7.1	✓	2	1.1	even	1	trivial
18.2.c.a.13.1	yes	2	9.4	even	3	inner
54.2.c.a.19.1		2	3.2	odd	2
54.2.c.a.37.1		2	9.5	odd	6
144.2.i.c.49.1		2	36.31	odd	6
144.2.i.c.97.1		2	4.3	odd	2
162.2.a.b.1.1		1	9.2	odd	6
162.2.a.c.1.1		1	9.7	even	3
432.2.i.b.145.1		2	36.23	even	6
432.2.i.b.289.1		2	12.11	even	2
450.2.e.i.151.1		2	5.4	even	2
450.2.e.i.301.1		2	45.4	even	6
450.2.j.e.49.1		4	45.13	odd	12
450.2.j.e.49.2		4	45.22	odd	12
450.2.j.e.349.1		4	5.2	odd	4
450.2.j.e.349.2		4	5.3	odd	4
576.2.i.a.193.1		2	72.67	odd	6
576.2.i.a.385.1		2	8.3	odd	2
576.2.i.g.193.1		2	72.13	even	6
576.2.i.g.385.1		2	8.5	even	2
882.2.e.g.373.1		2	63.31	odd	6
882.2.e.g.655.1		2	7.5	odd	6
882.2.e.i.373.1		2	63.4	even	3
882.2.e.i.655.1		2	7.2	even	3
882.2.f.d.295.1		2	7.6	odd	2
882.2.f.d.589.1		2	63.13	odd	6
882.2.h.b.67.1		2	63.40	odd	6
882.2.h.b.79.1		2	7.3	odd	6
882.2.h.c.67.1		2	63.58	even	3
882.2.h.c.79.1		2	7.4	even	3
1296.2.a.f.1.1		1	36.11	even	6
1296.2.a.g.1.1		1	36.7	odd	6
1350.2.e.c.451.1		2	15.14	odd	2
1350.2.e.c.901.1		2	45.14	odd	6
1350.2.j.a.199.1		4	45.32	even	12
1350.2.j.a.199.2		4	45.23	even	12
1350.2.j.a.1099.1		4	15.8	even	4
1350.2.j.a.1099.2		4	15.2	even	4
1728.2.i.e.577.1		2	72.5	odd	6
1728.2.i.e.1153.1		2	24.5	odd	2
1728.2.i.f.577.1		2	72.59	even	6
1728.2.i.f.1153.1		2	24.11	even	2
2646.2.e.b.1549.1		2	63.32	odd	6
2646.2.e.b.2125.1		2	21.2	odd	6
2646.2.e.c.1549.1		2	63.59	even	6
2646.2.e.c.2125.1		2	21.5	even	6
2646.2.f.g.883.1		2	21.20	even	2
2646.2.f.g.1765.1		2	63.41	even	6
2646.2.h.h.361.1		2	63.23	odd	6
2646.2.h.h.667.1		2	21.11	odd	6
2646.2.h.i.361.1		2	63.5	even	6
2646.2.h.i.667.1		2	21.17	even	6
4050.2.a.c.1.1		1	45.34	even	6
4050.2.a.v.1.1		1	45.29	odd	6
4050.2.c.c.649.1		2	45.43	odd	12
4050.2.c.c.649.2		2	45.7	odd	12
4050.2.c.r.649.1		2	45.2	even	12
4050.2.c.r.649.2		2	45.38	even	12
5184.2.a.o.1.1		1	72.43	odd	6
5184.2.a.p.1.1		1	72.11	even	6
5184.2.a.q.1.1		1	72.29	odd	6
5184.2.a.r.1.1		1	72.61	even	6
7938.2.a.i.1.1		1	63.20	even	6
7938.2.a.x.1.1		1	63.34	odd	6

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(-1.00000 - 1.73205i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} -3.00000 q^{18} -1.00000 q^{19} +(3.00000 - 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +2.00000 q^{26} -5.19615i q^{27} +2.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} -4.00000 q^{37} +(0.500000 - 0.866025i) q^{38} +3.46410i q^{39} +(-4.50000 - 7.79423i) q^{41} +3.46410i q^{42} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.50000 + 4.33013i) q^{50} +(4.50000 + 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +(1.50000 + 0.866025i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -5.19615i q^{66} +(-2.50000 - 4.33013i) q^{67} +(1.50000 + 2.59808i) q^{68} -10.3923i q^{69} -12.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +11.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(-7.50000 + 4.33013i) q^{75} +(0.500000 + 0.866025i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-3.00000 - 1.73205i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +9.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-3.00000 - 1.73205i) q^{84} +(0.500000 + 0.866025i) q^{86} +(9.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +4.00000 q^{91} +(3.00000 - 5.19615i) q^{92} -6.92820i q^{93} +(3.00000 + 5.19615i) q^{94} +1.73205i q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} + 3 q^{11} - 2 q^{13} - 2 q^{14} - q^{16} - 6 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} + 5 q^{25}+ \cdots + 18 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 + 3 * q^11 - 2 * q^13 - 2 * q^14 - q^16 - 6 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 + 5 * q^25 + 4 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 - 9 * q^33 + 3 * q^34 + 3 * q^36 - 8 * q^37 + q^38 - 9 * q^41 + q^43 - 6 * q^44 - 12 * q^46 + 6 * q^47 + 3 * q^48 + 3 * q^49 + 5 * q^50 + 9 * q^51 - 2 * q^52 + 24 * q^53 + 9 * q^54 - 2 * q^56 + 3 * q^57 - 6 * q^58 - 3 * q^59 - 8 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 5 * q^67 + 3 * q^68 - 24 * q^71 + 3 * q^72 + 22 * q^73 + 4 * q^74 - 15 * q^75 + q^76 + 6 * q^77 - 6 * q^78 + 4 * q^79 - 9 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 + q^86 + 18 * q^87 + 3 * q^88 + 12 * q^89 + 8 * q^91 + 6 * q^92 + 6 * q^94 - 5 * q^97 - 6 * q^98 + 18 * q^99

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