LMFDB - Embedded newform 450.2.e.a.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(151,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.151"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$450 = 2 \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	450.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,-3,-1,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$1$
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			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	450.151
Dual form			450.2.e.a.301.1

$q$ -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} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +(1.50000 + 2.59808i) q^{18} -4.00000 q^{19} -6.92820i q^{21} +(-1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-1.50000 + 0.866025i) q^{24} +4.00000 q^{26} +5.19615i q^{27} +4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -5.19615i q^{33} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{36} -8.00000 q^{37} +(2.00000 - 3.46410i) q^{38} +(6.00000 + 3.46410i) q^{39} +(3.00000 + 5.19615i) q^{41} +(6.00000 + 3.46410i) q^{42} +(-0.500000 + 0.866025i) q^{43} +3.00000 q^{44} +6.00000 q^{46} +(6.00000 - 10.3923i) q^{47} -1.73205i q^{48} +(-4.50000 - 7.79423i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-4.50000 - 2.59808i) q^{54} +(-2.00000 + 3.46410i) q^{56} +(6.00000 - 3.46410i) q^{57} +(3.00000 + 5.19615i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +(6.00000 + 10.3923i) q^{63} +1.00000 q^{64} +(4.50000 + 2.59808i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(9.00000 + 5.19615i) q^{69} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{72} -14.0000 q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(-6.00000 + 3.46410i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-4.50000 - 7.79423i) q^{81} -6.00000 q^{82} +(-4.50000 + 7.79423i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(-0.500000 - 0.866025i) q^{86} +10.3923i q^{87} +(-1.50000 + 2.59808i) q^{88} -9.00000 q^{89} +16.0000 q^{91} +(-3.00000 + 5.19615i) q^{92} +(12.0000 + 6.92820i) q^{93} +(6.00000 + 10.3923i) q^{94} +(1.50000 + 0.866025i) q^{96} +(-3.50000 + 6.06218i) q^{97} +9.00000 q^{98} +(4.50000 + 7.79423i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - q^{2} - 3 q^{3} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{11} + 3 q^{12} - 4 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 3 q^{18} - 8 q^{19} - 3 q^{22} - 6 q^{23} - 3 q^{24} + 8 q^{26} + 8 q^{28}+ \cdots + 9 q^{99}+O(q^{100})$ 2 * q - q^2 - 3 * q^3 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^11 + 3 * q^12 - 4 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 3 * q^18 - 8 * q^19 - 3 * q^22 - 6 * q^23 - 3 * q^24 + 8 * q^26 + 8 * q^28 + 6 * q^29 - 8 * q^31 - q^32 - 3 * q^34 - 6 * q^36 - 16 * q^37 + 4 * q^38 + 12 * q^39 + 6 * q^41 + 12 * q^42 - q^43 + 6 * q^44 + 12 * q^46 + 12 * q^47 - 9 * q^49 - 9 * q^51 - 4 * q^52 - 9 * q^54 - 4 * q^56 + 12 * q^57 + 6 * q^58 + 9 * q^59 - 8 * q^61 + 16 * q^62 + 12 * q^63 + 2 * q^64 + 9 * q^66 - 4 * q^67 - 3 * q^68 + 18 * q^69 - 12 * q^71 + 3 * q^72 - 28 * q^73 + 8 * q^74 + 4 * q^76 - 12 * q^77 - 12 * q^78 - 8 * q^79 - 9 * q^81 - 12 * q^82 - 9 * q^83 - 12 * q^84 - q^86 - 3 * q^88 - 18 * q^89 + 32 * q^91 - 6 * q^92 + 24 * q^93 + 12 * q^94 + 3 * q^96 - 7 * q^97 + 18 * q^98 + 9 * 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

)

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

$2$	−0.500000	+	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
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	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	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		−	6.92820i		−	1.51186i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$		0			0
$26$	4.00000			0.784465
$27$			5.19615i			1.00000i
$28$	4.00000			0.755929
$29$	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
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		−	5.19615i		−	0.904534i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	6.00000	+	3.46410i	0.960769	+	0.554700i
$40$		0			0
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$	6.00000	+	3.46410i	0.925820	+	0.534522i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	6.00000			0.884652
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.0186297	−	0.999826i	$-0.494070\pi$
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.856560	−	0.516047i	$-0.172597\pi$
$48$		−	1.73205i		−	0.250000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$		0			0
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$		0			0
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$	6.00000	−	3.46410i	0.794719	−	0.458831i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		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	$0.995517\pi$
$62$	8.00000			1.01600
$63$	6.00000	+	10.3923i	0.755929	+	1.30931i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.50000	+	2.59808i	0.553912	+	0.319801i
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	9.00000	+	5.19615i	1.08347	+	0.625543i
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−6.00000	−	10.3923i	−0.683763	−	1.18431i
$78$	−6.00000	+	3.46410i	−0.679366	+	0.392232i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−6.00000			−0.662589
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$	−6.00000	+	3.46410i	−0.654654	+	0.377964i
$85$		0			0
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$			10.3923i			1.11417i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$	12.0000	+	6.92820i	1.24434	+	0.718421i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$		0			0
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$	9.00000			0.909137
$99$	4.50000	+	7.79423i	0.452267	+	0.783349i
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		−	5.19615i		−	0.514496i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	12.0000	−	6.92820i	1.13899	−	0.657596i
$112$	−2.00000	−	3.46410i	−0.188982	−	0.327327i
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	0.927914	−	0.372794i	$-0.121600\pi$
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	−0.786806	+	0.617200i	$0.788267\pi$
$114$			6.92820i			0.648886i
$115$		0			0
$116$	−6.00000			−0.557086
$117$	−12.0000			−1.10940
$118$	−9.00000			−0.828517
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	−9.00000	−	5.19615i	−0.811503	−	0.468521i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$		0			0
$126$	−12.0000			−1.06904
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		−	1.73205i		−	0.152499i
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	−4.50000	+	2.59808i	−0.391675	+	0.226134i
$133$	8.00000	−	13.8564i	0.693688	−	1.20150i
$134$	4.00000			0.345547
$135$		0			0
$136$	3.00000			0.257248
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$	−9.00000	+	5.19615i	−0.766131	+	0.442326i
$139$	−5.50000	−	9.52628i	−0.466504	−	0.808008i	0.532764	−	0.846264i	$-0.321153\pi$
$139$	−5.50000	−	9.52628i	−0.466504	−	0.808008i	−0.999268	+	0.0382553i	$0.987820\pi$
$140$		0			0
$141$			20.7846i			1.75038i
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	12.0000			1.00349
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$		0			0
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	13.5000	+	7.79423i	1.11346	+	0.642857i
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	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	$0.754293\pi$
$150$		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	$0.0332784\pi$
$152$	−4.00000			−0.324443
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$	12.0000			0.966988
$155$		0			0
$156$		−	6.92820i		−	0.554700i
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$		0			0
$160$		0			0
$161$	24.0000			1.89146
$162$	9.00000			0.707107
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$		−	6.92820i		−	0.534522i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$	−6.00000	+	10.3923i	−0.458831	+	0.794719i
$172$	1.00000			0.0762493
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−9.00000	−	5.19615i	−0.682288	−	0.393919i
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−13.5000	−	7.79423i	−1.01472	−	0.585850i
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−8.00000	+	13.8564i	−0.592999	+	1.02711i
$183$		−	13.8564i		−	1.02430i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	−12.0000	+	6.92820i	−0.879883	+	0.508001i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$	−12.0000			−0.875190
$189$	−18.0000	−	10.3923i	−1.30931	−	0.755929i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$	−3.50000	−	6.06218i	−0.251285	−	0.435239i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−9.00000			−0.639602
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$		0			0
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$	−6.00000	−	10.3923i	−0.422159	−	0.731200i
$203$	12.0000	+	20.7846i	0.842235	+	1.45879i
$204$	4.50000	+	2.59808i	0.315063	+	0.181902i
$205$		0			0
$206$	−8.00000			−0.557386
$207$	−18.0000			−1.25109
$208$	4.00000			0.277350
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$		0			0
$213$	9.00000	−	5.19615i	0.616670	−	0.356034i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$			5.19615i			0.353553i
$217$	32.0000			2.17230
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$	21.0000	−	12.1244i	1.41905	−	0.819288i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$			13.8564i			0.929981i
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	−0.830599	−	0.556871i	$-0.812002\pi$
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	0.897564	+	0.440884i	$0.145335\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	−3.00000			−0.199557
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.0634974	+	0.997982i	$0.520225\pi$
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.832529	+	0.553981i	$0.813108\pi$
$228$	−6.00000	−	3.46410i	−0.397360	−	0.229416i
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	0.703060	−	0.711131i	$-0.251817\pi$
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	−0.967387	+	0.253302i	$0.918483\pi$
$230$		0			0
$231$	18.0000	+	10.3923i	1.18431	+	0.683763i
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−15.0000			−0.982683			−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000			−0.982683			−0.491341	+	0.870967i	$0.663493\pi$
$234$	6.00000	−	10.3923i	0.392232	−	0.679366i
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$		−	13.8564i		−	0.900070i
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	−0.995223	−	0.0976302i	$-0.968874\pi$
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	0.413061	−	0.910703i	$-0.364460\pi$
$240$		0			0
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$	−2.00000			−0.128565
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	8.00000			0.512148
$245$		0			0
$246$	9.00000	−	5.19615i	0.573819	−	0.331295i
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		−	15.5885i		−	0.987878i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	6.00000	−	10.3923i	0.377964	−	0.654654i
$253$	18.0000			1.13165
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	1.50000	+	0.866025i	0.0933859	+	0.0539164i
$259$	16.0000	−	27.7128i	0.994192	−	1.72199i
$260$		0			0
$261$	−9.00000	−	15.5885i	−0.557086	−	0.964901i
$262$	12.0000			0.741362
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		−	5.19615i		−	0.319801i
$265$		0			0
$266$	8.00000	+	13.8564i	0.490511	+	0.849591i
$267$	13.5000	−	7.79423i	0.826187	−	0.476999i
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−12.0000			−0.731653			−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000			−0.731653			−0.365826	+	0.930683i	$0.619214\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	−24.0000	+	13.8564i	−1.45255	+	0.838628i
$274$	9.00000	+	15.5885i	0.543710	+	0.941733i
$275$		0			0
$276$		−	10.3923i		−	0.625543i
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	11.0000			0.659736
$279$	−24.0000			−1.43684
$280$		0			0
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$	−18.0000	−	10.3923i	−1.07188	−	0.618853i
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$	−24.0000			−1.41668
$288$	−3.00000			−0.176777
$289$	−8.00000			−0.470588
$290$		0			0
$291$		−	12.1244i		−	0.710742i
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$	−13.5000	+	7.79423i	−0.787336	+	0.454569i
$295$		0			0
$296$	−8.00000			−0.464991
$297$	−13.5000	−	7.79423i	−0.783349	−	0.452267i
$298$	−6.00000			−0.347571
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		−	20.7846i		−	1.19404i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$	4.50000	+	7.79423i	0.257248	+	0.445566i
$307$	1.00000			0.0570730			0.0285365	−	0.999593i	$-0.490915\pi$
$307$	1.00000			0.0570730			0.0285365	+	0.999593i	$0.490915\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$	−12.0000	−	6.92820i	−0.682656	−	0.394132i
$310$		0			0
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$	6.00000	+	3.46410i	0.339683	+	0.196116i
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	8.00000			0.450035
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	18.0000	−	10.3923i	1.00466	−	0.580042i
$322$	−12.0000	+	20.7846i	−0.668734	+	1.15828i
$323$	−12.0000			−0.667698
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$		0			0
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$	−3.00000	+	1.73205i	−0.165900	+	0.0957826i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	24.0000	+	41.5692i	1.32316	+	2.29179i
$330$		0			0
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	−0.999298	−	0.0374662i	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$	9.00000			0.493939
$333$	−12.0000	+	20.7846i	−0.657596	+	1.13899i
$334$	−18.0000			−0.984916
$335$		0			0
$336$	6.00000	+	3.46410i	0.327327	+	0.188982i
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−4.50000	−	2.59808i	−0.244406	−	0.141108i
$340$		0			0
$341$	24.0000			1.29967
$342$	−6.00000	−	10.3923i	−0.324443	−	0.561951i
$343$	8.00000			0.431959
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	13.5000	+	23.3827i	0.724718	+	1.25525i	0.959090	+	0.283101i	$0.0913633\pi$
$347$	13.5000	+	23.3827i	0.724718	+	1.25525i	−0.234372	+	0.972147i	$0.575303\pi$
$348$	9.00000	−	5.19615i	0.482451	−	0.278543i
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$	3.00000			0.159901
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$	13.5000	−	7.79423i	0.717517	−	0.414259i
$355$		0			0
$356$	4.50000	+	7.79423i	0.238500	+	0.413093i
$357$		−	20.7846i		−	1.10004i
$358$	1.50000	−	2.59808i	0.0792775	−	0.137313i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	−3.00000	−	1.73205i	−0.157459	−	0.0909091i
$364$	−8.00000	−	13.8564i	−0.419314	−	0.726273i
$365$		0			0
$366$	12.0000	+	6.92820i	0.627250	+	0.362143i
$367$	13.0000	−	22.5167i	0.678594	−	1.17536i	−0.296810	−	0.954937i	$-0.595923\pi$
$367$	13.0000	−	22.5167i	0.678594	−	1.17536i	0.975404	−	0.220423i	$-0.0707439\pi$
$368$	6.00000			0.312772
$369$	18.0000			0.937043
$370$		0			0
$371$		0			0
$372$		−	13.8564i		−	0.718421i
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	0.950804	−	0.309794i	$-0.100260\pi$
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	−0.743691	+	0.668523i	$0.766927\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$		0			0
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	−24.0000			−1.23606
$378$	18.0000	−	10.3923i	0.925820	−	0.534522i
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$		0			0
$381$	−24.0000	+	13.8564i	−1.22956	+	0.709885i
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		−	1.73205i		−	0.0883883i
$385$		0			0
$386$	−5.00000			−0.254493
$387$	1.50000	+	2.59808i	0.0762493	+	0.132068i
$388$	7.00000			0.355371
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$	18.0000	+	10.3923i	0.907980	+	0.524222i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$		0			0
$396$	4.50000	−	7.79423i	0.226134	−	0.391675i
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	−1.00000	+	1.73205i	−0.0501255	+	0.0868199i
$399$			27.7128i			1.38738i
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$	−6.00000	+	3.46410i	−0.299253	+	0.172774i
$403$	−16.0000	+	27.7128i	−0.797017	+	1.38047i
$404$	12.0000			0.597022
$405$		0			0
$406$	−24.0000			−1.19110
$407$	12.0000	−	20.7846i	0.594818	−	1.03025i
$408$	−4.50000	+	2.59808i	−0.222783	+	0.128624i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$		0			0
$411$			31.1769i			1.53784i
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$	−36.0000			−1.77144
$414$	9.00000	−	15.5885i	0.442326	−	0.766131i
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	16.5000	+	9.52628i	0.808008	+	0.466504i
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	−16.0000	+	27.7128i	−0.779792	+	1.35064i	0.152269	+	0.988339i	$0.451342\pi$
$421$	−16.0000	+	27.7128i	−0.779792	+	1.35064i	−0.932061	+	0.362301i	$0.881991\pi$
$422$	23.0000			1.11962
$423$	−18.0000	−	31.1769i	−0.875190	−	1.51587i
$424$		0			0
$425$		0			0
$426$			10.3923i			0.503509i
$427$	−16.0000	−	27.7128i	−0.774294	−	1.34112i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	−18.0000	+	10.3923i	−0.869048	+	0.501745i
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	7.00000			0.336399			0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000			0.336399			0.168199	+	0.985753i	$0.446205\pi$
$434$	−16.0000	+	27.7128i	−0.768025	+	1.33026i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$			24.2487i			1.15865i
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$	−27.0000			−1.28571
$442$	12.0000			0.570782
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$	−12.0000	−	6.92820i	−0.569495	−	0.328798i
$445$		0			0
$446$	1.00000	+	1.73205i	0.0473514	+	0.0820150i
$447$	−9.00000	−	5.19615i	−0.425685	−	0.245770i
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$	1.50000	−	2.59808i	0.0705541	−	0.122203i
$453$			17.3205i			0.813788i
$454$	−13.5000	−	23.3827i	−0.633586	−	1.09740i
$455$		0			0
$456$	6.00000	−	3.46410i	0.280976	−	0.162221i
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	8.00000			0.373815
$459$			15.5885i			0.727607i
$460$		0			0
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	−0.787668	−	0.616100i	$-0.788712\pi$
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	0.927392	+	0.374091i	$0.122045\pi$
$462$	−18.0000	+	10.3923i	−0.837436	+	0.483494i
$463$	7.00000	+	12.1244i	0.325318	+	0.563467i	0.981577	−	0.191069i	$-0.0611955\pi$
$463$	7.00000	+	12.1244i	0.325318	+	0.563467i	−0.656259	+	0.754536i	$0.727862\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	7.50000	−	12.9904i	0.347431	−	0.601768i
$467$	−9.00000			−0.416470			−0.208235	−	0.978079i	$-0.566772\pi$
$467$	−9.00000			−0.416470			−0.208235	+	0.978079i	$0.566772\pi$
$468$	6.00000	+	10.3923i	0.277350	+	0.480384i
$469$	16.0000			0.738811
$470$		0			0
$471$	6.00000	+	3.46410i	0.276465	+	0.159617i
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$	12.0000	+	6.92820i	0.551178	+	0.318223i
$475$		0			0
$476$	12.0000			0.550019
$477$		0			0
$478$	18.0000			0.823301
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	−13.0000	−	22.5167i	−0.592134	−	1.02561i
$483$	−36.0000	+	20.7846i	−1.63806	+	0.945732i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	16.5000	−	9.52628i	0.746156	−	0.430793i
$490$		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	$0.723424\pi$
$492$			10.3923i			0.468521i
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	8.00000			0.359211
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$	13.5000	+	7.79423i	0.604949	+	0.349268i
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$		0			0
$501$	−27.0000	−	15.5885i	−1.20627	−	0.696441i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$	6.00000	+	10.3923i	0.267261	+	0.462910i
$505$		0			0
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$		−	5.19615i		−	0.230769i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	28.0000	−	48.4974i	1.23865	−	2.14540i
$512$	1.00000			0.0441942
$513$		−	20.7846i		−	0.917663i
$514$	−3.00000			−0.132324
$515$		0			0
$516$	−1.50000	+	0.866025i	−0.0660338	+	0.0381246i
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	16.0000	+	27.7128i	0.703000	+	1.21763i
$519$		−	10.3923i		−	0.456172i
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$	18.0000			0.787839
$523$	−29.0000			−1.26808			−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000			−1.26808			−0.634041	+	0.773300i	$0.718605\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$	4.50000	+	2.59808i	0.195837	+	0.113067i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	27.0000			1.17170
$532$	−16.0000			−0.693688
$533$	12.0000	−	20.7846i	0.519778	−	0.900281i
$534$			15.5885i			0.674579i
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	4.50000	−	2.59808i	0.194189	−	0.112115i
$538$	6.00000	−	10.3923i	0.258678	−	0.448044i
$539$	27.0000			1.16297
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	2.00000	−	3.46410i	0.0859074	−	0.148796i
$543$	−3.00000	+	1.73205i	−0.128742	+	0.0743294i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$		−	27.7128i		−	1.18600i
$547$	10.0000	−	17.3205i	0.427569	−	0.740571i	−0.569087	−	0.822277i	$-0.692703\pi$
$547$	10.0000	−	17.3205i	0.427569	−	0.740571i	0.996657	+	0.0817056i	$0.0260367\pi$
$548$	−18.0000			−0.768922
$549$	12.0000	+	20.7846i	0.512148	+	0.887066i
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$	9.00000	+	5.19615i	0.383065	+	0.221163i
$553$	−16.0000	−	27.7128i	−0.680389	−	1.17847i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		0			0
$556$	−5.50000	+	9.52628i	−0.233252	+	0.404004i
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$	12.0000	−	20.7846i	0.508001	−	0.879883i
$559$	4.00000			0.169182
$560$		0			0
$561$		−	15.5885i		−	0.658145i
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	0.832684	−	0.553748i	$-0.186803\pi$
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	−0.895902	+	0.444252i	$0.853470\pi$
$564$	18.0000	−	10.3923i	0.757937	−	0.437595i
$565$		0			0
$566$	1.00000			0.0420331
$567$	36.0000			1.51186
$568$	−6.00000			−0.251754
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	−0.431011	−	0.902347i	$-0.641843\pi$
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	0.996961	−	0.0779066i	$-0.0248236\pi$
$570$		0			0
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	0.999638	+	0.0268925i	$0.00856117\pi$
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	−0.476530	+	0.879158i	$0.658105\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$		−	10.3923i		−	0.434145i
$574$	12.0000	−	20.7846i	0.500870	−	0.867533i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−7.50000	−	4.33013i	−0.311689	−	0.179954i
$580$		0			0
$581$	−18.0000	−	31.1769i	−0.746766	−	1.29344i
$582$	10.5000	+	6.06218i	0.435239	+	0.251285i
$583$		0			0
$584$	−14.0000			−0.579324
$585$		0			0
$586$	12.0000			0.495715
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$		−	15.5885i		−	0.642857i
$589$	16.0000	+	27.7128i	0.659269	+	1.14189i
$590$		0			0
$591$	−27.0000	+	15.5885i	−1.11063	+	0.641223i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	45.0000			1.84793			0.923964	−	0.382479i	$-0.124930\pi$
$593$	45.0000			1.84793			0.923964	+	0.382479i	$0.124930\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−3.00000	+	1.73205i	−0.122782	+	0.0708881i
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$		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	$-0.105517\pi$
$602$	4.00000			0.163028
$603$	−12.0000			−0.488678
$604$	−10.0000			−0.406894
$605$		0			0
$606$	18.0000	+	10.3923i	0.731200	+	0.422159i
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$	−36.0000	−	20.7846i	−1.45879	−	0.842235i
$610$		0			0
$611$	−48.0000			−1.94187
$612$	−9.00000			−0.363803
$613$	−14.0000			−0.565455			−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000			−0.565455			−0.282727	+	0.959200i	$0.591239\pi$
$614$	−0.500000	+	0.866025i	−0.0201784	+	0.0349499i
$615$		0			0
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	0.998700	+	0.0509678i	$0.0162306\pi$
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$618$	12.0000	−	6.92820i	0.482711	−	0.278693i
$619$	−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
$622$	6.00000			0.240578
$623$	18.0000	−	31.1769i	0.721155	−	1.24908i
$624$	−6.00000	+	3.46410i	−0.240192	+	0.138675i
$625$		0			0
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$			20.7846i			0.830057i
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	34.5000	+	19.9186i	1.37125	+	0.791693i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$		0			0
$637$	−18.0000	+	31.1769i	−0.713186	+	1.23527i
$638$	−18.0000			−0.712627
$639$	−9.00000	+	15.5885i	−0.356034	+	0.616670i
$640$		0			0
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$			20.7846i			0.820303i
$643$	11.5000	+	19.9186i	0.453516	+	0.785512i	0.998602	−	0.0528680i	$-0.0168363\pi$
$643$	11.5000	+	19.9186i	0.453516	+	0.785512i	−0.545086	+	0.838380i	$0.683503\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$		0			0
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−27.0000			−1.05984
$650$		0			0
$651$	−48.0000	+	27.7128i	−1.88127	+	1.08615i
$652$	5.50000	+	9.52628i	0.215397	+	0.373078i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$		−	3.46410i		−	0.135457i
$655$		0			0
$656$	−6.00000			−0.234261
$657$	−21.0000	+	36.3731i	−0.819288	+	1.41905i
$658$	−48.0000			−1.87123
$659$	22.5000	−	38.9711i	0.876476	−	1.51810i	0.0212930	−	0.999773i	$-0.493222\pi$
$659$	22.5000	−	38.9711i	0.876476	−	1.51810i	0.855183	−	0.518327i	$-0.173445\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−8.50000	−	14.7224i	−0.330362	−	0.572204i
$663$	18.0000	+	10.3923i	0.699062	+	0.403604i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$		0			0
$666$	−12.0000	−	20.7846i	−0.464991	−	0.805387i
$667$	−36.0000			−1.39393
$668$	9.00000	−	15.5885i	0.348220	−	0.603136i
$669$			3.46410i			0.133930i
$670$		0			0
$671$	−12.0000	−	20.7846i	−0.463255	−	0.802381i
$672$	−6.00000	+	3.46410i	−0.231455	+	0.133631i
$673$	−23.0000	+	39.8372i	−0.886585	+	1.53561i	−0.0426985	+	0.999088i	$0.513595\pi$
$673$	−23.0000	+	39.8372i	−0.886585	+	1.53561i	−0.843886	+	0.536522i	$0.819738\pi$
$674$	13.0000			0.500741
$675$		0			0
$676$	3.00000			0.115385
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$	4.50000	−	2.59808i	0.172821	−	0.0997785i
$679$	−14.0000	−	24.2487i	−0.537271	−	0.930580i
$680$		0			0
$681$		−	46.7654i		−	1.79205i
$682$	−12.0000	+	20.7846i	−0.459504	+	0.795884i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	12.0000			0.458831
$685$		0			0
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$	12.0000	+	6.92820i	0.457829	+	0.264327i
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$		0			0
$690$		0			0
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	−0.626794	−	0.779185i	$-0.715633\pi$
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	0.988191	+	0.153227i	$0.0489666\pi$
$692$	6.00000			0.228086
$693$	−36.0000			−1.36753
$694$	−27.0000			−1.02491
$695$		0			0
$696$			10.3923i			0.393919i
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$	22.5000	−	12.9904i	0.851028	−	0.491341i
$700$		0			0
$701$	48.0000			1.81293			0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000			1.81293			0.906467	+	0.422276i	$0.138769\pi$
$702$			20.7846i			0.784465i
$703$	32.0000			1.20690
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	−4.50000	−	7.79423i	−0.169360	−	0.293340i
$707$	−24.0000	−	41.5692i	−0.902613	−	1.56337i
$708$			15.5885i			0.585850i
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.301388	−	0.953502i	$-0.402550\pi$
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.675063	−	0.737760i	$-0.264116\pi$
$710$		0			0
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$	−9.00000			−0.337289
$713$	−24.0000	+	41.5692i	−0.898807	+	1.55678i
$714$	18.0000	+	10.3923i	0.673633	+	0.388922i
$715$		0			0
$716$	1.50000	+	2.59808i	0.0560576	+	0.0970947i
$717$	27.0000	+	15.5885i	1.00833	+	0.582162i
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	−32.0000			−1.19174
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$		−	45.0333i		−	1.67481i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$		0			0
$726$	3.00000	−	1.73205i	0.111340	−	0.0642824i
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	−0.706523	−	0.707690i	$-0.749737\pi$
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	0.966139	+	0.258022i	$0.0830708\pi$
$728$	16.0000			0.592999
$729$	−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
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	0.826723	−	0.562609i	$-0.190202\pi$
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	−0.900595	+	0.434659i	$0.856869\pi$
$734$	13.0000	+	22.5167i	0.479839	+	0.831105i
$735$		0			0
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	12.0000			0.442026
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	−25.0000			−0.919640			−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000			−0.919640			−0.459820	+	0.888012i	$0.652086\pi$
$740$		0			0
$741$	−24.0000	−	13.8564i	−0.881662	−	0.509028i
$742$		0			0
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$	12.0000	+	6.92820i	0.439941	+	0.254000i
$745$		0			0
$746$	−8.00000			−0.292901
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$	9.00000			0.329073
$749$	24.0000	−	41.5692i	0.876941	−	1.51891i
$750$		0			0
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	0.989423	+	0.145062i	$0.0463382\pi$
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	−0.369084	+	0.929396i	$0.620328\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	18.0000	−	10.3923i	0.655956	−	0.378717i
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$		0			0
$756$			20.7846i			0.755929i
$757$	−20.0000			−0.726912			−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000			−0.726912			−0.363456	+	0.931611i	$0.618403\pi$
$758$	−14.5000	+	25.1147i	−0.526664	+	0.912208i
$759$	−27.0000	+	15.5885i	−0.980038	+	0.565825i
$760$		0			0
$761$	19.5000	+	33.7750i	0.706874	+	1.22434i	0.966011	+	0.258502i	$0.0832288\pi$
$761$	19.5000	+	33.7750i	0.706874	+	1.22434i	−0.259136	+	0.965841i	$0.583438\pi$
$762$		−	27.7128i		−	1.00393i
$763$	−4.00000	+	6.92820i	−0.144810	+	0.250818i
$764$	6.00000			0.217072
$765$		0			0
$766$	−18.0000			−0.650366
$767$	18.0000	−	31.1769i	0.649942	−	1.12573i
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$		0			0
$771$	−4.50000	−	2.59808i	−0.162064	−	0.0935674i
$772$	2.50000	−	4.33013i	0.0899770	−	0.155845i
$773$	42.0000			1.51064			0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000			1.51064			0.755318	+	0.655359i	$0.227483\pi$
$774$	−3.00000			−0.107833
$775$		0			0
$776$	−3.50000	+	6.06218i	−0.125643	+	0.217620i
$777$			55.4256i			1.98838i
$778$	3.00000	+	5.19615i	0.107555	+	0.186291i
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$	18.0000			0.643679
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	9.00000			0.321429
$785$		0			0
$786$	−18.0000	+	10.3923i	−0.642039	+	0.370681i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$			41.5692i			1.47990i
$790$		0			0
$791$	−12.0000			−0.426671
$792$	4.50000	+	7.79423i	0.159901	+	0.276956i
$793$	32.0000			1.13635
$794$	7.00000	−	12.1244i	0.248421	−	0.430277i
$795$		0			0
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	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	$0.765163\pi$
$798$	−24.0000	−	13.8564i	−0.849591	−	0.490511i
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$		0			0
$801$	−13.5000	+	23.3827i	−0.476999	+	0.826187i
$802$	−15.0000			−0.529668
$803$	21.0000	−	36.3731i	0.741074	−	1.28358i
$804$		−	6.92820i		−	0.244339i
$805$		0			0
$806$	−16.0000	−	27.7128i	−0.563576	−	0.976142i
$807$	18.0000	−	10.3923i	0.633630	−	0.365826i
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$	12.0000	−	20.7846i	0.421117	−	0.729397i
$813$	6.00000	−	3.46410i	0.210429	−	0.121491i
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$		0			0
$816$		−	5.19615i		−	0.181902i
$817$	2.00000	−	3.46410i	0.0699711	−	0.121194i
$818$	−22.0000			−0.769212
$819$	24.0000	−	41.5692i	0.838628	−	1.45255i
$820$		0			0
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	−0.995819	−	0.0913446i	$-0.970884\pi$
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	0.577016	+	0.816733i	$0.304217\pi$
$822$	−27.0000	−	15.5885i	−0.941733	−	0.543710i
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$	9.00000	+	15.5885i	0.312772	+	0.541736i
$829$	20.0000			0.694629			0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000			0.694629			0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$			3.46410i			0.120168i
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	−13.5000	−	23.3827i	−0.467747	−	0.810162i
$834$	−16.5000	+	9.52628i	−0.571348	+	0.329868i
$835$		0			0
$836$	−12.0000			−0.415029
$837$	36.0000	−	20.7846i	1.24434	−	0.718421i
$838$	9.00000			0.310900
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	0.0705865	+	0.997506i	$0.477513\pi$
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	−0.899158	+	0.437623i	$0.855820\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−16.0000	−	27.7128i	−0.551396	−	0.955047i
$843$			31.1769i			1.07379i
$844$	−11.5000	+	19.9186i	−0.395846	+	0.685626i
$845$		0			0
$846$	36.0000			1.23771
$847$	−8.00000			−0.274883
$848$		0			0
$849$	1.50000	+	0.866025i	0.0514799	+	0.0297219i
$850$		0			0
$851$	24.0000	+	41.5692i	0.822709	+	1.42497i
$852$	−9.00000	−	5.19615i	−0.308335	−	0.178017i
$853$	−23.0000	+	39.8372i	−0.787505	+	1.36400i	0.139986	+	0.990153i	$0.455294\pi$
$853$	−23.0000	+	39.8372i	−0.787505	+	1.36400i	−0.927491	+	0.373845i	$0.878039\pi$
$854$	32.0000			1.09502
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−13.5000	+	23.3827i	−0.461151	+	0.798737i	−0.999019	−	0.0442921i	$-0.985897\pi$
$857$	−13.5000	+	23.3827i	−0.461151	+	0.798737i	0.537867	+	0.843029i	$0.319230\pi$
$858$		−	20.7846i		−	0.709575i
$859$	8.00000	+	13.8564i	0.272956	+	0.472774i	0.969618	−	0.244626i	$-0.0786652\pi$
$859$	8.00000	+	13.8564i	0.272956	+	0.472774i	−0.696661	+	0.717400i	$0.745332\pi$
$860$		0			0
$861$	36.0000	−	20.7846i	1.22688	−	0.708338i
$862$	−3.00000	+	5.19615i	−0.102180	+	0.176982i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	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
$868$	−16.0000	−	27.7128i	−0.543075	−	0.940634i
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$	2.00000			0.0677285
$873$	10.5000	+	18.1865i	0.355371	+	0.615521i
$874$	−24.0000			−0.811812
$875$		0			0
$876$	−21.0000	−	12.1244i	−0.709524	−	0.409644i
$877$	−8.00000	−	13.8564i	−0.270141	−	0.467898i	0.698757	−	0.715359i	$-0.253737\pi$
$877$	−8.00000	−	13.8564i	−0.270141	−	0.467898i	−0.968898	+	0.247462i	$0.920404\pi$
$878$	−7.00000	−	12.1244i	−0.236239	−	0.409177i
$879$	18.0000	+	10.3923i	0.607125	+	0.350524i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	13.5000	−	23.3827i	0.454569	−	0.787336i
$883$	13.0000			0.437485			0.218742	−	0.975783i	$-0.429805\pi$
$883$	13.0000			0.437485			0.218742	+	0.975783i	$0.429805\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	4.50000	+	7.79423i	0.151180	+	0.261852i
$887$	15.0000	+	25.9808i	0.503651	+	0.872349i	0.999991	+	0.00422062i	$0.00134347\pi$
$887$	15.0000	+	25.9808i	0.503651	+	0.872349i	−0.496340	+	0.868128i	$0.665323\pi$
$888$	12.0000	−	6.92820i	0.402694	−	0.232495i
$889$	−32.0000	+	55.4256i	−1.07325	+	1.85892i
$890$		0			0
$891$	27.0000			0.904534
$892$	−2.00000			−0.0669650
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$	9.00000	−	5.19615i	0.301005	−	0.173785i
$895$		0			0
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$		−	41.5692i		−	1.38796i
$898$	−9.00000	+	15.5885i	−0.300334	+	0.520194i
$899$	−48.0000			−1.60089
$900$		0			0
$901$		0			0
$902$	9.00000	−	15.5885i	0.299667	−	0.519039i
$903$	6.00000	+	3.46410i	0.199667	+	0.115278i
$904$	1.50000	+	2.59808i	0.0498893	+	0.0864107i
$905$		0			0
$906$	−15.0000	−	8.66025i	−0.498342	−	0.287718i
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$	27.0000			0.896026
$909$	18.0000	+	31.1769i	0.597022	+	1.03407i
$910$		0			0
$911$	9.00000	−	15.5885i	0.298183	−	0.516469i	−0.677537	−	0.735489i	$-0.736953\pi$
$911$	9.00000	−	15.5885i	0.298183	−	0.516469i	0.975720	+	0.219020i	$0.0702860\pi$
$912$			6.92820i			0.229416i
$913$	−13.5000	−	23.3827i	−0.446785	−	0.773854i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	−4.00000	+	6.92820i	−0.132164	+	0.228914i
$917$	48.0000			1.58510
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	−46.0000			−1.51740			−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000			−1.51740			−0.758700	+	0.651440i	$0.774165\pi$
$920$		0			0
$921$	−1.50000	+	0.866025i	−0.0494267	+	0.0285365i
$922$	3.00000	+	5.19615i	0.0987997	+	0.171126i
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$		−	20.7846i		−	0.683763i
$925$		0			0
$926$	−14.0000			−0.460069
$927$	24.0000			0.788263
$928$	−6.00000			−0.196960
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	0.283178	+	0.959067i	$0.408611\pi$
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$930$		0			0
$931$	18.0000	+	31.1769i	0.589926	+	1.02178i
$932$	7.50000	+	12.9904i	0.245671	+	0.425514i
$933$	9.00000	+	5.19615i	0.294647	+	0.170114i
$934$	4.50000	−	7.79423i	0.147244	−	0.255035i
$935$		0			0
$936$	−12.0000			−0.392232
$937$	37.0000			1.20874			0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000			1.20874			0.604369	+	0.796705i	$0.293425\pi$
$938$	−8.00000	+	13.8564i	−0.261209	+	0.452428i
$939$			29.4449i			0.960897i
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$	−6.00000	+	3.46410i	−0.195491	+	0.112867i
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	−9.00000			−0.292925
$945$		0			0
$946$	3.00000			0.0975384
$947$	−4.50000	+	7.79423i	−0.146230	+	0.253278i	−0.929831	−	0.367986i	$-0.880047\pi$
$947$	−4.50000	+	7.79423i	−0.146230	+	0.253278i	0.783601	+	0.621264i	$0.213381\pi$
$948$	−12.0000	+	6.92820i	−0.389742	+	0.225018i
$949$	28.0000	+	48.4974i	0.908918	+	1.57429i
$950$		0			0
$951$		−	31.1769i		−	1.01098i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	27.0000			0.874616			0.437308	−	0.899312i	$-0.355932\pi$
$953$	27.0000			0.874616			0.437308	+	0.899312i	$0.355932\pi$
$954$		0			0
$955$		0			0
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$	−27.0000	−	15.5885i	−0.872786	−	0.503903i
$958$	6.00000	+	10.3923i	0.193851	+	0.335760i
$959$	36.0000	+	62.3538i	1.16250	+	2.01351i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−32.0000			−1.03172
$963$	−18.0000	+	31.1769i	−0.580042	+	1.00466i
$964$	26.0000			0.837404
$965$		0			0
$966$		−	41.5692i		−	1.33747i
$967$	−14.0000	−	24.2487i	−0.450210	−	0.779786i	0.548189	−	0.836354i	$-0.315317\pi$
$967$	−14.0000	−	24.2487i	−0.450210	−	0.779786i	−0.998399	+	0.0565684i	$0.981984\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	18.0000	−	10.3923i	0.578243	−	0.333849i
$970$		0			0
$971$	−27.0000			−0.866471			−0.433236	−	0.901281i	$-0.642628\pi$
$971$	−27.0000			−0.866471			−0.433236	+	0.901281i	$0.642628\pi$
$972$		−	15.5885i		−	0.500000i
$973$	44.0000			1.41058
$974$	1.00000	−	1.73205i	0.0320421	−	0.0554985i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$			19.0526i			0.609234i
$979$	13.5000	−	23.3827i	0.431462	−	0.747314i
$980$		0			0
$981$	3.00000	−	5.19615i	0.0957826	−	0.165900i
$982$	−15.0000			−0.478669
$983$	27.0000	−	46.7654i	0.861166	−	1.49158i	−0.00963785	−	0.999954i	$-0.503068\pi$
$983$	27.0000	−	46.7654i	0.861166	−	1.49158i	0.870804	−	0.491630i	$-0.163599\pi$
$984$	−9.00000	−	5.19615i	−0.286910	−	0.165647i
$985$		0			0
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$	−72.0000	−	41.5692i	−2.29179	−	1.32316i
$988$	8.00000	−	13.8564i	0.254514	−	0.440831i
$989$	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	$0.581789\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$		−	29.4449i		−	0.934405i
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$		0			0
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	0.775923	+	0.630828i	$0.217285\pi$
$998$	11.0000			0.348199
$999$		−	41.5692i		−	1.31519i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.e.a.151.1	✓	2
3.2	odd	2		1350.2.e.f.451.1		2
5.2	odd	4		450.2.j.d.349.1		4
5.3	odd	4		450.2.j.d.349.2		4
5.4	even	2		450.2.e.h.151.1	yes	2
9.2	odd	6		4050.2.a.p.1.1		1
9.4	even	3	inner	450.2.e.a.301.1	yes	2
9.5	odd	6		1350.2.e.f.901.1		2
9.7	even	3		4050.2.a.bj.1.1		1
15.2	even	4		1350.2.j.d.1099.2		4
15.8	even	4		1350.2.j.d.1099.1		4
15.14	odd	2		1350.2.e.e.451.1		2
45.2	even	12		4050.2.c.e.649.1		2
45.4	even	6		450.2.e.h.301.1	yes	2
45.7	odd	12		4050.2.c.q.649.2		2
45.13	odd	12		450.2.j.d.49.1		4
45.14	odd	6		1350.2.e.e.901.1		2
45.22	odd	12		450.2.j.d.49.2		4
45.23	even	12		1350.2.j.d.199.2		4
45.29	odd	6		4050.2.a.t.1.1		1
45.32	even	12		1350.2.j.d.199.1		4
45.34	even	6		4050.2.a.b.1.1		1
45.38	even	12		4050.2.c.e.649.2		2
45.43	odd	12		4050.2.c.q.649.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.a.151.1	✓	2	1.1	even	1	trivial
450.2.e.a.301.1	yes	2	9.4	even	3	inner
450.2.e.h.151.1	yes	2	5.4	even	2
450.2.e.h.301.1	yes	2	45.4	even	6
450.2.j.d.49.1		4	45.13	odd	12
450.2.j.d.49.2		4	45.22	odd	12
450.2.j.d.349.1		4	5.2	odd	4
450.2.j.d.349.2		4	5.3	odd	4
1350.2.e.e.451.1		2	15.14	odd	2
1350.2.e.e.901.1		2	45.14	odd	6
1350.2.e.f.451.1		2	3.2	odd	2
1350.2.e.f.901.1		2	9.5	odd	6
1350.2.j.d.199.1		4	45.32	even	12
1350.2.j.d.199.2		4	45.23	even	12
1350.2.j.d.1099.1		4	15.8	even	4
1350.2.j.d.1099.2		4	15.2	even	4
4050.2.a.b.1.1		1	45.34	even	6
4050.2.a.p.1.1		1	9.2	odd	6
4050.2.a.t.1.1		1	45.29	odd	6
4050.2.a.bj.1.1		1	9.7	even	3
4050.2.c.e.649.1		2	45.2	even	12
4050.2.c.e.649.2		2	45.38	even	12
4050.2.c.q.649.1		2	45.43	odd	12
4050.2.c.q.649.2		2	45.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	450.2.e.a.151.1

Level	$450$
Weight	$2$
Character	450.151
Analytic conductor	$3.593$
Analytic rank	$1$
Dimension	$2$
Inner twists	$2$