LMFDB - Embedded newform 882.2.f.h.589.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$882 = 2 \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	882.f (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:	$7.04280545828$
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:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.h.295.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.00000 q^{8} -3.00000 q^{9} -3.00000 q^{10} +(3.00000 + 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +7.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(-3.00000 + 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} -1.73205i q^{24} +(-2.00000 - 3.46410i) q^{25} +2.00000 q^{26} -5.19615i q^{27} +(-3.00000 - 5.19615i) q^{29} -5.19615i q^{30} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.00000 + 5.19615i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(1.50000 - 2.59808i) q^{36} +2.00000 q^{37} +(3.50000 + 6.06218i) q^{38} +(3.00000 + 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-1.00000 - 1.73205i) q^{43} -6.00000 q^{44} +(4.50000 - 7.79423i) q^{45} -3.00000 q^{46} +(1.50000 - 0.866025i) q^{48} +(2.00000 - 3.46410i) q^{50} -10.3923i q^{51} +(1.00000 + 1.73205i) q^{52} +6.00000 q^{53} +(4.50000 - 2.59808i) q^{54} -18.0000 q^{55} +12.1244i q^{57} +(3.00000 - 5.19615i) q^{58} +(4.50000 - 2.59808i) q^{60} +(2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-9.00000 - 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-4.50000 - 2.59808i) q^{69} +3.00000 q^{71} +3.00000 q^{72} -2.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(6.00000 - 3.46410i) q^{75} +(-3.50000 + 6.06218i) q^{76} +3.46410i q^{78} +(-2.50000 - 4.33013i) q^{79} +3.00000 q^{80} +9.00000 q^{81} +(6.00000 + 10.3923i) q^{83} +(9.00000 - 15.5885i) q^{85} +(1.00000 - 1.73205i) q^{86} +(9.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{88} +9.00000 q^{90} +(-1.50000 - 2.59808i) q^{92} +(3.00000 + 1.73205i) q^{93} +(-10.5000 + 18.1865i) q^{95} +(1.50000 + 0.866025i) q^{96} +(1.00000 + 1.73205i) q^{97} +(-9.00000 - 15.5885i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{2} - q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{8} - 6 q^{9} - 6 q^{10} + 6 q^{11} - 3 q^{12} + 2 q^{13} - 9 q^{15} - q^{16} - 12 q^{17} - 3 q^{18} + 14 q^{19} - 3 q^{20} - 6 q^{22} - 3 q^{23} - 4 q^{25}+ \cdots - 18 q^{99}+O(q^{100})$ 2 * q + q^2 - q^4 - 3 * q^5 - 3 * q^6 - 2 * q^8 - 6 * q^9 - 6 * q^10 + 6 * q^11 - 3 * q^12 + 2 * q^13 - 9 * q^15 - q^16 - 12 * q^17 - 3 * q^18 + 14 * q^19 - 3 * q^20 - 6 * q^22 - 3 * q^23 - 4 * q^25 + 4 * q^26 - 6 * q^29 + 2 * q^31 + q^32 - 18 * q^33 - 6 * q^34 + 3 * q^36 + 4 * q^37 + 7 * q^38 + 6 * q^39 + 3 * q^40 - 2 * q^43 - 12 * q^44 + 9 * q^45 - 6 * q^46 + 3 * q^48 + 4 * q^50 + 2 * q^52 + 12 * q^53 + 9 * q^54 - 36 * q^55 + 6 * q^58 + 9 * q^60 + 5 * q^61 + 4 * q^62 + 2 * q^64 + 6 * q^65 - 18 * q^66 - 8 * q^67 + 6 * q^68 - 9 * q^69 + 6 * q^71 + 6 * q^72 - 4 * q^73 + 2 * q^74 + 12 * q^75 - 7 * q^76 - 5 * q^79 + 6 * q^80 + 18 * q^81 + 12 * q^83 + 18 * q^85 + 2 * q^86 + 18 * q^87 - 6 * q^88 + 18 * q^90 - 3 * q^92 + 6 * q^93 - 21 * q^95 + 3 * q^96 + 2 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$ .

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−3.00000			−1.00000
$10$	−3.00000			−0.948683
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$	−4.50000	−	2.59808i	−1.16190	−	0.670820i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	2.00000			0.392232
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		−	5.19615i		−	0.948683i
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−9.00000	+	5.19615i	−1.56670	+	0.904534i
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$	3.00000	+	1.73205i	0.480384	+	0.277350i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	−6.00000			−0.904534
$45$	4.50000	−	7.79423i	0.670820	−	1.16190i
$46$	−3.00000			−0.442326
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$		0			0
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		−	10.3923i		−	1.45521i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	−18.0000			−2.42712
$56$		0			0
$57$			12.1244i			1.60591i
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	4.50000	−	2.59808i	0.580948	−	0.335410i
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$		0			0
$71$	3.00000			0.356034			0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000			0.356034			0.178017	+	0.984027i	$0.443032\pi$
$72$	3.00000			0.353553
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$		0			0
$78$			3.46410i			0.392232i
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$	3.00000			0.335410
$81$	9.00000			1.00000
$82$		0			0
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	9.00000	−	15.5885i	0.976187	−	1.69081i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	9.00000	−	5.19615i	0.964901	−	0.557086i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	9.00000			0.948683
$91$		0			0
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$		0			0
$95$	−10.5000	+	18.1865i	−1.07728	+	1.86590i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$		0			0
$99$	−9.00000	−	15.5885i	−0.904534	−	1.56670i
$100$	4.00000			0.400000
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	9.00000	−	5.19615i	0.891133	−	0.514496i
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	−0.999964	−	0.00844953i	$-0.997310\pi$
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	0.507300	+	0.861770i	$0.330644\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	−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
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−9.00000	−	15.5885i	−0.858116	−	1.48630i
$111$			3.46410i			0.328798i
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−10.5000	+	6.06218i	−0.983415	+	0.567775i
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	6.00000			0.557086
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$		0			0
$119$		0			0
$120$	4.50000	+	2.59808i	0.410792	+	0.237171i
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−2.50000	+	4.33013i	−0.226339	+	0.392031i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	3.00000	−	1.73205i	0.264135	−	0.152499i
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		−	10.3923i		−	0.904534i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	13.5000	+	7.79423i	1.16190	+	0.670820i
$136$	6.00000			0.514496
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		−	5.19615i		−	0.442326i
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	−0.740308	−	0.672268i	$-0.765320\pi$
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	0.952355	+	0.304991i	$0.0986536\pi$
$140$		0			0
$141$		0			0
$142$	1.50000	+	2.59808i	0.125877	+	0.218026i
$143$	12.0000			1.00349
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	18.0000			1.49482
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	6.00000	+	3.46410i	0.489898	+	0.282843i
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.162758	−	0.986666i	$-0.552039\pi$
$152$	−7.00000			−0.567775
$153$	18.0000			1.45521
$154$		0			0
$155$	3.00000	+	5.19615i	0.240966	+	0.417365i
$156$	−3.00000	+	1.73205i	−0.240192	+	0.138675i
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	0.481006	+	0.876717i	$0.340272\pi$
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	−0.999762	+	0.0217953i	$0.993062\pi$
$158$	2.50000	−	4.33013i	0.198889	−	0.344486i
$159$			10.3923i			0.824163i
$160$	1.50000	+	2.59808i	0.118585	+	0.205396i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$		0			0
$165$		−	31.1769i		−	2.42712i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	18.0000			1.38054
$171$	−21.0000			−1.60591
$172$	2.00000			0.152499
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	9.00000	+	5.19615i	0.682288	+	0.393919i
$175$		0			0
$176$	3.00000	−	5.19615i	0.226134	−	0.391675i
$177$		0			0
$178$		0			0
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$	4.50000	+	7.79423i	0.335410	+	0.580948i
$181$	25.0000			1.85824			0.929118	−	0.369784i	$-0.120568\pi$
$181$	25.0000			1.85824			0.929118	+	0.369784i	$0.120568\pi$
$182$		0			0
$183$	−7.50000	+	4.33013i	−0.554416	+	0.320092i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$			3.46410i			0.254000i
$187$	−18.0000	−	31.1769i	−1.31629	−	2.27988i
$188$		0			0
$189$		0			0
$190$	−21.0000			−1.52350
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	0.981635	−	0.190767i	$-0.0610975\pi$
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	−0.656027	+	0.754738i	$0.727764\pi$
$192$			1.73205i			0.125000i
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	0.379086	+	0.925361i	$0.376238\pi$
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	−0.990930	+	0.134382i	$0.957095\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	−9.00000	+	5.19615i	−0.644503	+	0.372104i
$196$		0			0
$197$	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	−	15.5885i	0.639602	−	1.10782i
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	−12.0000	−	6.92820i	−0.846415	−	0.488678i
$202$	−4.50000	+	7.79423i	−0.316619	+	0.548400i
$203$		0			0
$204$	9.00000	+	5.19615i	0.630126	+	0.363803i
$205$		0			0
$206$	−10.0000			−0.696733
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$	−2.00000			−0.138675
$209$	21.0000	+	36.3731i	1.45260	+	2.51598i
$210$		0			0
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$			5.19615i			0.356034i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	6.00000			0.409197
$216$			5.19615i			0.353553i
$217$		0			0
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$		−	3.46410i		−	0.234082i
$220$	9.00000	−	15.5885i	0.606780	−	1.05097i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	−3.00000	+	1.73205i	−0.201347	+	0.116248i
$223$	−14.0000	−	24.2487i	−0.937509	−	1.62381i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−14.0000	−	24.2487i	−0.937509	−	1.62381i	−0.167412	−	0.985887i	$-0.553541\pi$
$224$		0			0
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$	−15.0000			−0.997785
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	0.502204	−	0.864749i	$-0.332523\pi$
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	−0.999997	+	0.00254715i	$0.999189\pi$
$228$	−10.5000	−	6.06218i	−0.695379	−	0.401478i
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$	4.50000	−	7.79423i	0.296721	−	0.513936i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$	−6.00000			−0.392232
$235$		0			0
$236$		0			0
$237$	7.50000	−	4.33013i	0.487177	−	0.281272i
$238$		0			0
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	−0.514719	−	0.857359i	$-0.672104\pi$
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	0.999854	+	0.0170808i	$0.00543724\pi$
$240$			5.19615i			0.335410i
$241$	4.00000	+	6.92820i	0.257663	+	0.446285i	0.965615	−	0.259975i	$-0.0837143\pi$
$241$	4.00000	+	6.92820i	0.257663	+	0.446285i	−0.707953	+	0.706260i	$0.750381\pi$
$242$	−25.0000			−1.60706
$243$			15.5885i			1.00000i
$244$	−5.00000			−0.320092
$245$		0			0
$246$		0			0
$247$	7.00000	−	12.1244i	0.445399	−	0.771454i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$	−18.0000	+	10.3923i	−1.14070	+	0.658586i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$	8.50000	+	14.7224i	0.533337	+	0.923768i
$255$	27.0000	+	15.5885i	1.69081	+	0.976187i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	3.00000	+	1.73205i	0.186772	+	0.107833i
$259$		0			0
$260$	−6.00000			−0.372104
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	−9.00000			−0.556022
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$	9.00000	−	5.19615i	0.553912	−	0.319801i
$265$	−9.00000	+	15.5885i	−0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	9.00000			0.548740			0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000			0.548740			0.274370	+	0.961624i	$0.411531\pi$
$270$			15.5885i			0.948683i
$271$	28.0000			1.70088			0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000			1.70088			0.850439	+	0.526073i	$0.176336\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$		0			0
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$	12.0000	−	20.7846i	0.723627	−	1.25336i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	5.00000			0.299880
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$		0			0
$281$	13.5000	+	23.3827i	0.805342	+	1.39489i	0.916060	+	0.401042i	$0.131352\pi$
$281$	13.5000	+	23.3827i	0.805342	+	1.39489i	−0.110717	+	0.993852i	$0.535315\pi$
$282$		0			0
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	0.432360	+	0.901701i	$0.357681\pi$
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	−0.997076	+	0.0764162i	$0.975652\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$	−31.5000	−	18.1865i	−1.86590	−	1.07728i
$286$	6.00000	+	10.3923i	0.354787	+	0.614510i
$287$		0			0
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	19.0000			1.11765
$290$	9.00000	+	15.5885i	0.528498	+	0.915386i
$291$	−3.00000	+	1.73205i	−0.175863	+	0.101535i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	−0.906509	−	0.422186i	$-0.861263\pi$
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	0.818878	+	0.573967i	$0.194596\pi$
$294$		0			0
$295$		0			0
$296$	−2.00000			−0.116248
$297$	27.0000	−	15.5885i	1.56670	−	0.904534i
$298$	6.00000			0.347571
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$			6.92820i			0.400000i
$301$		0			0
$302$	11.5000	−	19.9186i	0.661751	−	1.14619i
$303$	−13.5000	+	7.79423i	−0.775555	+	0.447767i
$304$	−3.50000	−	6.06218i	−0.200739	−	0.347690i
$305$	−15.0000			−0.858898
$306$	9.00000	+	15.5885i	0.514496	+	0.891133i
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$		0			0
$309$	−15.0000	−	8.66025i	−0.853320	−	0.492665i
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$	−3.00000	−	1.73205i	−0.169842	−	0.0980581i
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	5.00000			0.281272
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	−9.00000	+	5.19615i	−0.504695	+	0.291386i
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		−	20.7846i		−	1.16008i
$322$		0			0
$323$	−42.0000			−2.33694
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−8.00000			−0.443760
$326$	1.00000	+	1.73205i	0.0553849	+	0.0959294i
$327$		−	17.3205i		−	0.957826i
$328$		0			0
$329$		0			0
$330$	27.0000	−	15.5885i	1.48630	−	0.858116i
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	−0.963135	−	0.269019i	$-0.913301\pi$
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	0.248590	−	0.968609i	$-0.420033\pi$
$332$	−12.0000			−0.658586
$333$	−6.00000			−0.328798
$334$		0			0
$335$	−12.0000	−	20.7846i	−0.655630	−	1.13558i
$336$		0			0
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−22.5000	−	12.9904i	−1.22203	−	0.705541i
$340$	9.00000	+	15.5885i	0.488094	+	0.845403i
$341$	12.0000			0.649836
$342$	−10.5000	−	18.1865i	−0.567775	−	0.983415i
$343$		0			0
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$	13.5000	−	7.79423i	0.726816	−	0.419627i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$			10.3923i			0.557086i
$349$	13.0000	+	22.5167i	0.695874	+	1.20529i	0.969885	+	0.243563i	$0.0783162\pi$
$349$	13.0000	+	22.5167i	0.695874	+	1.20529i	−0.274011	+	0.961727i	$0.588351\pi$
$350$		0			0
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$	6.00000			0.319801
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$		0			0
$357$		0			0
$358$	9.00000	+	15.5885i	0.475665	+	0.823876i
$359$	−3.00000			−0.158334			−0.0791670	−	0.996861i	$-0.525226\pi$
$359$	−3.00000			−0.158334			−0.0791670	+	0.996861i	$0.525226\pi$
$360$	−4.50000	+	7.79423i	−0.237171	+	0.410792i
$361$	30.0000			1.57895
$362$	12.5000	+	21.6506i	0.656985	+	1.13793i
$363$	−37.5000	−	21.6506i	−1.96824	−	1.13636i
$364$		0			0
$365$	3.00000	−	5.19615i	0.157027	−	0.271979i
$366$	−7.50000	−	4.33013i	−0.392031	−	0.226339i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$	−6.00000			−0.311925
$371$		0			0
$372$	−3.00000	+	1.73205i	−0.155543	+	0.0898027i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$		−	5.19615i		−	0.268328i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	−10.5000	−	18.1865i	−0.538639	−	0.932949i
$381$			29.4449i			1.50851i
$382$	−4.50000	+	7.79423i	−0.230240	+	0.398787i
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$		0			0
$386$	−17.0000			−0.865277
$387$	3.00000	+	5.19615i	0.152499	+	0.264135i
$388$	−2.00000			−0.101535
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	−0.991500	−	0.130105i	$-0.958469\pi$
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	0.383076	−	0.923717i	$-0.374865\pi$
$390$	−9.00000	−	5.19615i	−0.455733	−	0.263117i
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$		0			0
$393$	−13.5000	−	7.79423i	−0.680985	−	0.393167i
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	15.0000			0.754732
$396$	18.0000			0.904534
$397$	−26.0000			−1.30490			−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000			−1.30490			−0.652451	+	0.757831i	$0.726259\pi$
$398$	−7.00000	−	12.1244i	−0.350878	−	0.607739i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		−	13.8564i		−	0.691095i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	−9.00000			−0.447767
$405$	−13.5000	+	23.3827i	−0.670820	+	1.16190i
$406$		0			0
$407$	6.00000	+	10.3923i	0.297409	+	0.515127i
$408$			10.3923i			0.514496i
$409$	16.0000	−	27.7128i	0.791149	−	1.37031i	−0.134107	−	0.990967i	$-0.542817\pi$
$409$	16.0000	−	27.7128i	0.791149	−	1.37031i	0.925256	−	0.379344i	$-0.123850\pi$
$410$		0			0
$411$	9.00000	−	5.19615i	0.443937	−	0.256307i
$412$	−5.00000	−	8.66025i	−0.246332	−	0.426660i
$413$		0			0
$414$	9.00000			0.442326
$415$	−36.0000			−1.76717
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	7.50000	+	4.33013i	0.367277	+	0.212047i
$418$	−21.0000	+	36.3731i	−1.02714	+	1.77906i
$419$	7.50000	−	12.9904i	0.366399	−	0.634622i	−0.622601	−	0.782540i	$-0.713924\pi$
$419$	7.50000	−	12.9904i	0.366399	−	0.634622i	0.989000	+	0.147918i	$0.0472572\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	−8.00000			−0.389434
$423$		0			0
$424$	−6.00000			−0.291386
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$	−4.50000	+	2.59808i	−0.218026	+	0.125877i
$427$		0			0
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$			20.7846i			1.00349i
$430$	3.00000	+	5.19615i	0.144673	+	0.250581i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	−4.50000	+	2.59808i	−0.216506	+	0.125000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$			31.1769i			1.49482i
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−10.5000	+	18.1865i	−0.502283	+	0.869980i
$438$	3.00000	−	1.73205i	0.143346	−	0.0827606i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	18.0000			0.858116
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$		0			0
$446$	14.0000	−	24.2487i	0.662919	−	1.14821i
$447$	9.00000	+	5.19615i	0.425685	+	0.245770i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$	−6.00000	+	10.3923i	−0.282843	+	0.489898i
$451$		0			0
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	34.5000	−	19.9186i	1.62095	−	0.935857i
$454$	7.50000	−	12.9904i	0.351992	−	0.609669i
$455$		0			0
$456$		−	12.1244i		−	0.567775i
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	−0.975498	−	0.220008i	$-0.929392\pi$
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	0.297217	−	0.954810i	$-0.403942\pi$
$458$	−1.00000			−0.0467269
$459$			31.1769i			1.45521i
$460$	9.00000			0.419627
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	−0.938386	−	0.345589i	$-0.887679\pi$
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	0.169904	−	0.985461i	$-0.445654\pi$
$462$		0			0
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	−0.674526	−	0.738251i	$-0.735652\pi$
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	0.976607	+	0.215032i	$0.0689855\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−9.00000	+	5.19615i	−0.417365	+	0.240966i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	−3.00000	−	5.19615i	−0.138675	−	0.240192i
$469$		0			0
$470$		0			0
$471$	−19.5000	−	11.2583i	−0.898513	−	0.518756i
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$	7.50000	+	4.33013i	0.344486	+	0.198889i
$475$	−14.0000	−	24.2487i	−0.642364	−	1.11261i
$476$		0			0
$477$	−18.0000			−0.824163
$478$	15.0000			0.686084
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	0.789314	−	0.613990i	$-0.210436\pi$
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	−0.926388	+	0.376571i	$0.877103\pi$
$480$	−4.50000	+	2.59808i	−0.205396	+	0.118585i
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	−4.00000	+	6.92820i	−0.182195	+	0.315571i
$483$		0			0
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$	−6.00000			−0.272446
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	29.0000			1.31412			0.657058	−	0.753840i	$-0.271801\pi$
$487$	29.0000			1.31412			0.657058	+	0.753840i	$0.271801\pi$
$488$	−2.50000	−	4.33013i	−0.113170	−	0.196016i
$489$			3.46410i			0.156652i
$490$		0			0
$491$	−9.00000	+	15.5885i	−0.406164	+	0.703497i	−0.994456	−	0.105151i	$-0.966467\pi$
$491$	−9.00000	+	15.5885i	−0.406164	+	0.703497i	0.588292	+	0.808649i	$0.299801\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$	14.0000			0.629890
$495$	54.0000			2.42712
$496$	−2.00000			−0.0898027
$497$		0			0
$498$	−18.0000	−	10.3923i	−0.806599	−	0.465690i
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	−1.50000	−	2.59808i	−0.0669483	−	0.115958i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−27.0000			−1.20148
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	−8.50000	+	14.7224i	−0.377127	+	0.653202i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$			31.1769i			1.38054i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		−	36.3731i		−	1.60591i
$514$	18.0000			0.793946
$515$	−15.0000	−	25.9808i	−0.660979	−	1.14485i
$516$			3.46410i			0.152499i
$517$		0			0
$518$		0			0
$519$	9.00000	−	5.19615i	0.395056	−	0.228086i
$520$	−3.00000	−	5.19615i	−0.131559	−	0.227866i
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	13.0000			0.568450			0.284225	−	0.958758i	$-0.408264\pi$
$523$	13.0000			0.568450			0.284225	+	0.958758i	$0.408264\pi$
$524$	−4.50000	−	7.79423i	−0.196583	−	0.340492i
$525$		0			0
$526$	−10.5000	+	18.1865i	−0.457822	+	0.792971i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	9.00000	+	5.19615i	0.391675	+	0.226134i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−18.0000			−0.781870
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	18.0000	−	31.1769i	0.778208	−	1.34790i
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$			31.1769i			1.34538i
$538$	4.50000	+	7.79423i	0.194009	+	0.336033i
$539$		0			0
$540$	−13.5000	+	7.79423i	−0.580948	+	0.335410i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	14.0000	+	24.2487i	0.601351	+	1.04157i
$543$			43.3013i			1.85824i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	15.0000	−	25.9808i	0.642529	−	1.11289i
$546$		0			0
$547$	−16.0000	−	27.7128i	−0.684111	−	1.18491i	−0.973715	−	0.227768i	$-0.926857\pi$
$547$	−16.0000	−	27.7128i	−0.684111	−	1.18491i	0.289605	−	0.957146i	$-0.406476\pi$
$548$	6.00000			0.256307
$549$	−7.50000	−	12.9904i	−0.320092	−	0.554416i
$550$	24.0000			1.02336
$551$	−21.0000	−	36.3731i	−0.894630	−	1.54954i
$552$	4.50000	+	2.59808i	0.191533	+	0.110581i
$553$		0			0
$554$	−8.00000	+	13.8564i	−0.339887	+	0.588702i
$555$	−9.00000	−	5.19615i	−0.382029	−	0.220564i
$556$	2.50000	+	4.33013i	0.106024	+	0.183638i
$557$	−24.0000			−1.01691			−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$	−6.00000			−0.254000
$559$	−4.00000			−0.169182
$560$		0			0
$561$	54.0000	−	31.1769i	2.27988	−	1.31629i
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	−16.5000	+	28.5788i	−0.695392	+	1.20445i	0.274656	+	0.961542i	$0.411436\pi$
$563$	−16.5000	+	28.5788i	−0.695392	+	1.20445i	−0.970048	+	0.242912i	$0.921897\pi$
$564$		0			0
$565$	−22.5000	−	38.9711i	−0.946582	−	1.63953i
$566$	−19.0000			−0.798630
$567$		0			0
$568$	−3.00000			−0.125877
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		−	36.3731i		−	1.52350i
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$	−13.5000	+	7.79423i	−0.563971	+	0.325609i
$574$		0			0
$575$	12.0000			0.500435
$576$	−3.00000			−0.125000
$577$	4.00000			0.166522			0.0832611	−	0.996528i	$-0.473466\pi$
$577$	4.00000			0.166522			0.0832611	+	0.996528i	$0.473466\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	−25.5000	−	14.7224i	−1.05974	−	0.611843i
$580$	−9.00000	+	15.5885i	−0.373705	+	0.647275i
$581$		0			0
$582$	−3.00000	−	1.73205i	−0.124354	−	0.0717958i
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$	2.00000			0.0827606
$585$	−9.00000	−	15.5885i	−0.372104	−	0.644503i
$586$	−3.00000			−0.123929
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	7.00000	−	12.1244i	0.288430	−	0.499575i
$590$		0			0
$591$			31.1769i			1.28245i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	27.0000	+	15.5885i	1.10782	+	0.639602i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$		−	24.2487i		−	0.992434i
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	−6.00000	+	3.46410i	−0.244949	+	0.141421i
$601$	7.00000	+	12.1244i	0.285536	+	0.494563i	0.972739	−	0.231903i	$-0.0744951\pi$
$601$	7.00000	+	12.1244i	0.285536	+	0.494563i	−0.687203	+	0.726465i	$0.741162\pi$
$602$		0			0
$603$	12.0000	−	20.7846i	0.488678	−	0.846415i
$604$	23.0000			0.935857
$605$	−37.5000	−	64.9519i	−1.52459	−	2.64067i
$606$	−13.5000	−	7.79423i	−0.548400	−	0.316619i
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	−0.998154	−	0.0607380i	$-0.980655\pi$
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	0.551678	+	0.834058i	$0.313988\pi$
$608$	3.50000	−	6.06218i	0.141944	−	0.245854i
$609$		0			0
$610$	−7.50000	−	12.9904i	−0.303666	−	0.525965i
$611$		0			0
$612$	−9.00000	+	15.5885i	−0.363803	+	0.630126i
$613$	8.00000			0.323117			0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000			0.323117			0.161558	+	0.986863i	$0.448348\pi$
$614$	12.5000	+	21.6506i	0.504459	+	0.873749i
$615$		0			0
$616$		0			0
$617$	−21.0000	+	36.3731i	−0.845428	+	1.46432i	0.0398207	+	0.999207i	$0.487321\pi$
$617$	−21.0000	+	36.3731i	−0.845428	+	1.46432i	−0.885249	+	0.465118i	$0.846012\pi$
$618$		−	17.3205i		−	0.696733i
$619$	−3.50000	−	6.06218i	−0.140677	−	0.243659i	0.787075	−	0.616858i	$-0.211595\pi$
$619$	−3.50000	−	6.06218i	−0.140677	−	0.243659i	−0.927752	+	0.373198i	$0.878261\pi$
$620$	−6.00000			−0.240966
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$	12.0000			0.481156
$623$		0			0
$624$		−	3.46410i		−	0.138675i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$	−63.0000	+	36.3731i	−2.51598	+	1.45260i
$628$	−6.50000	−	11.2583i	−0.259378	−	0.449256i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	2.50000	+	4.33013i	0.0994447	+	0.172243i
$633$	−12.0000	−	6.92820i	−0.476957	−	0.275371i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	−25.5000	+	44.1673i	−1.01194	+	1.75273i
$636$	−9.00000	−	5.19615i	−0.356873	−	0.206041i
$637$		0			0
$638$	36.0000			1.42525
$639$	−9.00000			−0.356034
$640$	−3.00000			−0.118585
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$	18.0000	−	10.3923i	0.710403	−	0.410152i
$643$	−2.00000	+	3.46410i	−0.0788723	+	0.136611i	−0.902764	−	0.430137i	$-0.858465\pi$
$643$	−2.00000	+	3.46410i	−0.0788723	+	0.136611i	0.823891	+	0.566748i	$0.191799\pi$
$644$		0			0
$645$			10.3923i			0.409197i
$646$	−21.0000	−	36.3731i	−0.826234	−	1.43108i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$	−4.00000	−	6.92820i	−0.156893	−	0.271746i
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	15.0000	−	8.66025i	0.586546	−	0.338643i
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$		0			0
$657$	6.00000			0.234082
$658$		0			0
$659$	−21.0000	−	36.3731i	−0.818044	−	1.41689i	−0.907122	−	0.420869i	$-0.861725\pi$
$659$	−21.0000	−	36.3731i	−0.818044	−	1.41689i	0.0890776	−	0.996025i	$-0.471608\pi$
$660$	27.0000	+	15.5885i	1.05097	+	0.606780i
$661$	2.50000	−	4.33013i	0.0972387	−	0.168422i	−0.813302	−	0.581842i	$-0.802332\pi$
$661$	2.50000	−	4.33013i	0.0972387	−	0.168422i	0.910541	+	0.413419i	$0.135666\pi$
$662$	13.0000	−	22.5167i	0.505259	−	0.875135i
$663$	−18.0000	−	10.3923i	−0.699062	−	0.403604i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$		0			0
$666$	−3.00000	−	5.19615i	−0.116248	−	0.201347i
$667$	18.0000			0.696963
$668$		0			0
$669$	42.0000	−	24.2487i	1.62381	−	0.937509i
$670$	12.0000	−	20.7846i	0.463600	−	0.802980i
$671$	−15.0000	+	25.9808i	−0.579069	+	1.00298i
$672$		0			0
$673$	18.5000	+	32.0429i	0.713123	+	1.23516i	0.963679	+	0.267063i	$0.0860531\pi$
$673$	18.5000	+	32.0429i	0.713123	+	1.23516i	−0.250557	+	0.968102i	$0.580614\pi$
$674$	22.0000			0.847408
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$	−9.00000			−0.346154
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$		−	25.9808i		−	0.997785i
$679$		0			0
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$	22.5000	−	12.9904i	0.862202	−	0.497792i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$	10.5000	−	18.1865i	0.401478	−	0.695379i
$685$	18.0000			0.687745
$686$		0			0
$687$	−1.50000	−	0.866025i	−0.0572286	−	0.0330409i
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$	13.5000	+	7.79423i	0.513936	+	0.296721i
$691$	23.5000	+	40.7032i	0.893982	+	1.54842i	0.835059	+	0.550160i	$0.185433\pi$
$691$	23.5000	+	40.7032i	0.893982	+	1.54842i	0.0589228	+	0.998263i	$0.481233\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	24.0000			0.911028
$695$	7.50000	+	12.9904i	0.284491	+	0.492753i
$696$	−9.00000	+	5.19615i	−0.341144	+	0.196960i
$697$		0			0
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$			15.5885i			0.589610i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		−	10.3923i		−	0.392232i
$703$	14.0000			0.528020
$704$	3.00000	+	5.19615i	0.113067	+	0.195837i
$705$		0			0
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$		0			0
$708$		0			0
$709$	26.0000	+	45.0333i	0.976450	+	1.69126i	0.675063	+	0.737760i	$0.264116\pi$
$709$	26.0000	+	45.0333i	0.976450	+	1.69126i	0.301388	+	0.953502i	$0.402550\pi$
$710$	−9.00000			−0.337764
$711$	7.50000	+	12.9904i	0.281272	+	0.487177i
$712$		0			0
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$		0			0
$715$	−18.0000	+	31.1769i	−0.673162	+	1.16595i
$716$	−9.00000	+	15.5885i	−0.336346	+	0.582568i
$717$	22.5000	+	12.9904i	0.840278	+	0.485135i
$718$	−1.50000	−	2.59808i	−0.0559795	−	0.0969593i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$	−9.00000			−0.335410
$721$		0			0
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$	−12.0000	+	6.92820i	−0.446285	+	0.257663i
$724$	−12.5000	+	21.6506i	−0.464559	+	0.804640i
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$		−	43.3013i		−	1.60706i
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	6.00000			0.222070
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		−	8.66025i		−	0.320092i
$733$	14.5000	−	25.1147i	0.535570	−	0.927634i	−0.463566	−	0.886062i	$-0.653430\pi$
$733$	14.5000	−	25.1147i	0.535570	−	0.927634i	0.999136	−	0.0415715i	$-0.0132364\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	−48.0000			−1.76810
$738$		0			0
$739$	26.0000			0.956425			0.478213	−	0.878244i	$-0.341285\pi$
$739$	26.0000			0.956425			0.478213	+	0.878244i	$0.341285\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	21.0000	+	12.1244i	0.771454	+	0.445399i
$742$		0			0
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$	−3.00000	−	1.73205i	−0.109985	−	0.0635001i
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	−14.0000			−0.512576
$747$	−18.0000	−	31.1769i	−0.658586	−	1.14070i
$748$	36.0000			1.31629
$749$		0			0
$750$	4.50000	−	2.59808i	0.164317	−	0.0948683i
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$		−	5.19615i		−	0.189358i
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	69.0000			2.51117
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	1.00000	+	1.73205i	0.0363216	+	0.0629109i
$759$		−	31.1769i		−	1.13165i
$760$	10.5000	−	18.1865i	0.380875	−	0.659695i
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$	−25.5000	+	14.7224i	−0.923768	+	0.533337i
$763$		0			0
$764$	−9.00000			−0.325609
$765$	−27.0000	+	46.7654i	−0.976187	+	1.69081i
$766$	−18.0000			−0.650366
$767$		0			0
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$770$		0			0
$771$	27.0000	+	15.5885i	0.972381	+	0.561405i
$772$	−8.50000	−	14.7224i	−0.305922	−	0.529872i
$773$	51.0000			1.83434			0.917171	−	0.398493i	$-0.130467\pi$
$773$	51.0000			1.83434			0.917171	+	0.398493i	$0.130467\pi$
$774$	−3.00000	+	5.19615i	−0.107833	+	0.186772i
$775$	−8.00000			−0.287368
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$		0			0
$778$	12.0000	−	20.7846i	0.430221	−	0.745164i
$779$		0			0
$780$		−	10.3923i		−	0.372104i
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	18.0000			0.643679
$783$	−27.0000	+	15.5885i	−0.964901	+	0.557086i
$784$		0			0
$785$	−19.5000	−	33.7750i	−0.695985	−	1.20548i
$786$		−	15.5885i		−	0.556022i
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	−31.5000	+	18.1865i	−1.12143	+	0.647458i
$790$	7.50000	+	12.9904i	0.266838	+	0.462177i
$791$		0			0
$792$	9.00000	+	15.5885i	0.319801	+	0.553912i
$793$	10.0000			0.355110
$794$	−13.0000	−	22.5167i	−0.461353	−	0.799086i
$795$	−27.0000	−	15.5885i	−0.957591	−	0.552866i
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	−0.838236	−	0.545308i	$-0.816413\pi$
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	0.891368	+	0.453279i	$0.149746\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000			−0.141421
$801$		0			0
$802$	−3.00000			−0.105934
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$	12.0000	−	6.92820i	0.423207	−	0.244339i
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$			15.5885i			0.548740i
$808$	−4.50000	−	7.79423i	−0.158309	−	0.274200i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$	−27.0000			−0.948683
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$			48.4974i			1.70088i
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	−3.00000	+	5.19615i	−0.105085	+	0.182013i
$816$	−9.00000	+	5.19615i	−0.315063	+	0.181902i
$817$	−7.00000	−	12.1244i	−0.244899	−	0.424178i
$818$	32.0000			1.11885
$819$		0			0
$820$		0			0
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	0.995819	−	0.0913446i	$-0.0291165\pi$
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	−0.577016	+	0.816733i	$0.695783\pi$
$822$	9.00000	+	5.19615i	0.313911	+	0.181237i
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$	5.00000	−	8.66025i	0.174183	−	0.301694i
$825$	36.0000	+	20.7846i	1.25336	+	0.723627i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	4.50000	+	7.79423i	0.156386	+	0.270868i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−18.0000	−	31.1769i	−0.624789	−	1.08217i
$831$	−24.0000	+	13.8564i	−0.832551	+	0.480673i
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$			8.66025i			0.299880i
$835$		0			0
$836$	−42.0000			−1.45260
$837$	−9.00000	−	5.19615i	−0.311086	−	0.179605i
$838$	15.0000			0.518166
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$	−40.5000	+	23.3827i	−1.39489	+	0.805342i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−27.0000			−0.928828
$846$		0			0
$847$		0			0
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$	−28.5000	−	16.4545i	−0.978117	−	0.564716i
$850$	−12.0000	+	20.7846i	−0.411597	+	0.712906i
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$	−4.50000	−	2.59808i	−0.154167	−	0.0890086i
$853$	17.5000	+	30.3109i	0.599189	+	1.03783i	0.992941	+	0.118609i	$0.0378434\pi$
$853$	17.5000	+	30.3109i	0.599189	+	1.03783i	−0.393753	+	0.919216i	$0.628823\pi$
$854$		0			0
$855$	31.5000	−	54.5596i	1.07728	−	1.86590i
$856$	12.0000			0.410152
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$	−18.0000	+	10.3923i	−0.614510	+	0.354787i
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$	−3.00000	+	5.19615i	−0.102299	+	0.177187i
$861$		0			0
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	9.00000			0.306364			0.153182	−	0.988198i	$-0.451048\pi$
$863$	9.00000			0.306364			0.153182	+	0.988198i	$0.451048\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	18.0000			0.612018
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$			32.9090i			1.11765i
$868$		0			0
$869$	15.0000	−	25.9808i	0.508840	−	0.881337i
$870$	−27.0000	+	15.5885i	−0.915386	+	0.528498i
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$	10.0000			0.338643
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$	−21.0000			−0.710336
$875$		0			0
$876$	3.00000	+	1.73205i	0.101361	+	0.0585206i
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$	−4.50000	−	2.59808i	−0.151781	−	0.0876309i
$880$	9.00000	+	15.5885i	0.303390	+	0.525487i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$		−	3.46410i		−	0.116248i
$889$		0			0
$890$		0			0
$891$	27.0000	+	46.7654i	0.904534	+	1.56670i
$892$	28.0000			0.937509
$893$		0			0
$894$			10.3923i			0.347571i
$895$	−27.0000	+	46.7654i	−0.902510	+	1.56319i
$896$		0			0
$897$	−9.00000	+	5.19615i	−0.300501	+	0.173494i
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$	−12.0000			−0.400222
$900$	−12.0000			−0.400000
$901$	−36.0000			−1.19933
$902$		0			0
$903$		0			0
$904$	7.50000	−	12.9904i	0.249446	−	0.432054i
$905$	−37.5000	+	64.9519i	−1.24654	+	2.15907i
$906$	34.5000	+	19.9186i	1.14619	+	0.661751i
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	−0.999334	−	0.0364935i	$-0.988381\pi$
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	0.468063	−	0.883695i	$-0.344952\pi$
$908$	15.0000			0.497792
$909$	−13.5000	−	23.3827i	−0.447767	−	0.775555i
$910$		0			0
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	0.714620	−	0.699513i	$-0.246600\pi$
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	−0.963106	+	0.269122i	$0.913266\pi$
$912$	10.5000	−	6.06218i	0.347690	−	0.200739i
$913$	−36.0000	+	62.3538i	−1.19143	+	2.06361i
$914$	14.5000	−	25.1147i	0.479617	−	0.830722i
$915$		−	25.9808i		−	0.858898i
$916$	−0.500000	−	0.866025i	−0.0165205	−	0.0286143i
$917$		0			0
$918$	−27.0000	+	15.5885i	−0.891133	+	0.514496i
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$			43.3013i			1.42683i
$922$	16.5000	−	28.5788i	0.543399	−	0.941194i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	13.0000			0.427207
$927$	15.0000	−	25.9808i	0.492665	−	0.853320i
$928$	−6.00000			−0.196960
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$	−9.00000	−	5.19615i	−0.295122	−	0.170389i
$931$		0			0
$932$	−4.50000	+	7.79423i	−0.147402	+	0.255308i
$933$	18.0000	+	10.3923i	0.589294	+	0.340229i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	108.000			3.53198
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$	15.0000	−	8.66025i	0.489506	−	0.282617i
$940$		0			0
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$		−	22.5167i		−	0.733632i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	12.0000			0.390154
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$			8.66025i			0.281272i
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$	14.0000	−	24.2487i	0.454220	−	0.786732i
$951$	27.0000	−	15.5885i	0.875535	−	0.505490i
$952$		0			0
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$	−9.00000	−	15.5885i	−0.291386	−	0.504695i
$955$	−27.0000			−0.873699
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$	54.0000	+	31.1769i	1.74557	+	1.00781i
$958$	3.00000	−	5.19615i	0.0969256	−	0.167880i
$959$		0			0
$960$	−4.50000	−	2.59808i	−0.145237	−	0.0838525i
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	4.00000			0.128965
$963$	36.0000			1.16008
$964$	−8.00000			−0.257663
$965$	−25.5000	−	44.1673i	−0.820874	−	1.42180i
$966$		0			0
$967$	−8.50000	+	14.7224i	−0.273342	+	0.473441i	−0.969715	−	0.244238i	$-0.921462\pi$
$967$	−8.50000	+	14.7224i	−0.273342	+	0.473441i	0.696374	+	0.717679i	$0.254796\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$		−	72.7461i		−	2.33694i
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	15.0000			0.481373			0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000			0.481373			0.240686	+	0.970603i	$0.422627\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$		0			0
$974$	14.5000	+	25.1147i	0.464610	+	0.804728i
$975$		−	13.8564i		−	0.443760i
$976$	2.50000	−	4.33013i	0.0800230	−	0.138604i
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$978$	−3.00000	+	1.73205i	−0.0959294	+	0.0553849i
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$	−18.0000			−0.574403
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$		0			0
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$	−18.0000	+	31.1769i	−0.573237	+	0.992875i
$987$		0			0
$988$	7.00000	+	12.1244i	0.222700	+	0.385727i
$989$	6.00000			0.190789
$990$	27.0000	+	46.7654i	0.858116	+	1.48630i
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$	39.0000	−	22.5167i	1.23763	−	0.714545i
$994$		0			0
$995$	21.0000	−	36.3731i	0.665745	−	1.15310i
$996$		−	20.7846i		−	0.658586i
$997$	−27.5000	−	47.6314i	−0.870934	−	1.50850i	−0.861032	−	0.508551i	$-0.830182\pi$
$997$	−27.5000	−	47.6314i	−0.870934	−	1.50850i	−0.00990158	−	0.999951i	$-0.503152\pi$
$998$	−32.0000			−1.01294
$999$		−	10.3923i		−	0.328798i

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	882.2.f.h.589.1		2
3.2	odd	2		2646.2.f.c.1765.1		2
7.2	even	3		882.2.h.f.67.1		2
7.3	odd	6		882.2.e.b.373.1		2
7.4	even	3		882.2.e.d.373.1		2
7.5	odd	6		882.2.h.j.67.1		2
7.6	odd	2		126.2.f.a.85.1	yes	2
9.2	odd	6		2646.2.f.c.883.1		2
9.4	even	3		7938.2.a.l.1.1		1
9.5	odd	6		7938.2.a.u.1.1		1
9.7	even	3	inner	882.2.f.h.295.1		2
21.2	odd	6		2646.2.h.a.361.1		2
21.5	even	6		2646.2.h.e.361.1		2
21.11	odd	6		2646.2.e.j.1549.1		2
21.17	even	6		2646.2.e.f.1549.1		2
21.20	even	2		378.2.f.a.253.1		2
28.27	even	2		1008.2.r.d.337.1		2
63.2	odd	6		2646.2.e.j.2125.1		2
63.11	odd	6		2646.2.h.a.667.1		2
63.13	odd	6		1134.2.a.a.1.1		1
63.16	even	3		882.2.e.d.655.1		2
63.20	even	6		378.2.f.a.127.1		2
63.25	even	3		882.2.h.f.79.1		2
63.34	odd	6		126.2.f.a.43.1	✓	2
63.38	even	6		2646.2.h.e.667.1		2
63.41	even	6		1134.2.a.h.1.1		1
63.47	even	6		2646.2.e.f.2125.1		2
63.52	odd	6		882.2.h.j.79.1		2
63.61	odd	6		882.2.e.b.655.1		2
84.83	odd	2		3024.2.r.a.1009.1		2
252.83	odd	6		3024.2.r.a.2017.1		2
252.139	even	6		9072.2.a.c.1.1		1
252.167	odd	6		9072.2.a.w.1.1		1
252.223	even	6		1008.2.r.d.673.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	63.34	odd	6
126.2.f.a.85.1	yes	2	7.6	odd	2
378.2.f.a.127.1		2	63.20	even	6
378.2.f.a.253.1		2	21.20	even	2
882.2.e.b.373.1		2	7.3	odd	6
882.2.e.b.655.1		2	63.61	odd	6
882.2.e.d.373.1		2	7.4	even	3
882.2.e.d.655.1		2	63.16	even	3
882.2.f.h.295.1		2	9.7	even	3	inner
882.2.f.h.589.1		2	1.1	even	1	trivial
882.2.h.f.67.1		2	7.2	even	3
882.2.h.f.79.1		2	63.25	even	3
882.2.h.j.67.1		2	7.5	odd	6
882.2.h.j.79.1		2	63.52	odd	6
1008.2.r.d.337.1		2	28.27	even	2
1008.2.r.d.673.1		2	252.223	even	6
1134.2.a.a.1.1		1	63.13	odd	6
1134.2.a.h.1.1		1	63.41	even	6
2646.2.e.f.1549.1		2	21.17	even	6
2646.2.e.f.2125.1		2	63.47	even	6
2646.2.e.j.1549.1		2	21.11	odd	6
2646.2.e.j.2125.1		2	63.2	odd	6
2646.2.f.c.883.1		2	9.2	odd	6
2646.2.f.c.1765.1		2	3.2	odd	2
2646.2.h.a.361.1		2	21.2	odd	6
2646.2.h.a.667.1		2	63.11	odd	6
2646.2.h.e.361.1		2	21.5	even	6
2646.2.h.e.667.1		2	63.38	even	6
3024.2.r.a.1009.1		2	84.83	odd	2
3024.2.r.a.2017.1		2	252.83	odd	6
7938.2.a.l.1.1		1	9.4	even	3
7938.2.a.u.1.1		1	9.5	odd	6
9072.2.a.c.1.1		1	252.139	even	6
9072.2.a.w.1.1		1	252.167	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

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	882.2.f.h.589.1

Level	$882$
Weight	$2$
Character	882.589
Analytic conductor	$7.043$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$