LMFDB - Embedded newform 882.2.h.p.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.p.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.796790 - 1.53790i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.796790 - 1.53790i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +(-0.296790 - 0.514055i) q^{10} -0.593579 q^{11} +(1.73025 + 0.0789082i) q^{12} +(1.25729 + 2.17770i) q^{13} +(0.472958 + 0.912864i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.46050 - 2.52967i) q^{17} +(-2.98755 - 0.273062i) q^{18} +(-2.69076 + 4.66053i) q^{19} +(0.296790 - 0.514055i) q^{20} +(-0.296790 - 0.514055i) q^{22} +4.46050 q^{23} +(0.796790 + 1.53790i) q^{24} -4.64766 q^{25} +(-1.25729 + 2.17770i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-3.09718 + 5.36447i) q^{29} +(-0.554084 + 0.866025i) q^{30} +(-3.93346 + 6.81296i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.472958 + 0.912864i) q^{33} +(1.46050 - 2.52967i) q^{34} +(-1.25729 - 2.72382i) q^{36} +(0.500000 - 0.866025i) q^{37} -5.38151 q^{38} +(2.34728 - 3.66876i) q^{39} +0.593579 q^{40} +(0.136673 + 0.236725i) q^{41} +(-5.58113 + 9.66679i) q^{43} +(0.296790 - 0.514055i) q^{44} +(1.02704 - 1.45472i) q^{45} +(2.23025 + 3.86291i) q^{46} +(6.08113 + 10.5328i) q^{47} +(-0.933463 + 1.45899i) q^{48} +(-2.32383 - 4.02499i) q^{50} +(-2.72665 + 4.26172i) q^{51} -2.51459 q^{52} +(4.02704 + 6.97504i) q^{53} +(1.96050 + 4.81211i) q^{54} +0.352336 q^{55} +(9.31138 + 0.424646i) q^{57} -6.19436 q^{58} +(4.32383 - 7.48910i) q^{59} +(-1.02704 - 0.0468383i) q^{60} +(-3.32383 - 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 - 1.29264i) q^{65} +(-0.554084 + 0.866025i) q^{66} +(0.956906 - 1.65741i) q^{67} +2.92101 q^{68} +(-3.55408 - 6.85980i) q^{69} -14.4107 q^{71} +(1.73025 - 2.45076i) q^{72} +(-3.95691 - 6.85356i) q^{73} +1.00000 q^{74} +(3.70321 + 7.14763i) q^{75} +(-2.69076 - 4.66053i) q^{76} +(4.35087 + 0.198422i) q^{78} +(4.62422 + 8.00938i) q^{79} +(0.296790 + 0.514055i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(-0.136673 + 0.236725i) q^{82} +(-3.85087 + 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} -11.1623 q^{86} +(10.7178 + 0.488786i) q^{87} +0.593579 q^{88} +(6.21780 - 10.7695i) q^{89} +(1.77335 + 0.162084i) q^{90} +(-2.23025 + 3.86291i) q^{92} +(13.6118 + 0.620765i) q^{93} +(-6.08113 + 10.5328i) q^{94} +(1.59718 - 2.76639i) q^{95} +(-1.73025 - 0.0789082i) q^{96} +(-5.86693 + 10.1618i) q^{97} +(1.02704 - 1.45472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.796790	−	1.53790i	−0.460027	−	0.887905i
$3$	−0.796790	−	1.53790i	−0.460027	−	0.887905i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.593579			−0.265457			−0.132728	−	0.991152i	$-0.542374\pi$
$5$	−0.593579			−0.265457			−0.132728	+	0.991152i	$0.542374\pi$
$6$	0.933463	−	1.45899i	0.381085	−	0.595630i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−1.73025	+	2.45076i	−0.576751	+	0.816920i
$10$	−0.296790	−	0.514055i	−0.0938531	−	0.162558i
$11$	−0.593579			−0.178971			−0.0894855	−	0.995988i	$-0.528522\pi$
$11$	−0.593579			−0.178971			−0.0894855	+	0.995988i	$0.528522\pi$
$12$	1.73025	+	0.0789082i	0.499481	+	0.0227788i
$13$	1.25729	+	2.17770i	0.348711	+	0.603985i	0.986021	−	0.166623i	$-0.0532862\pi$
$13$	1.25729	+	2.17770i	0.348711	+	0.603985i	−0.637310	+	0.770608i	$0.719953\pi$
$14$		0			0
$15$	0.472958	+	0.912864i	0.122117	+	0.235700i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.46050	−	2.52967i	−0.354224	−	0.613535i	0.632760	−	0.774348i	$-0.281922\pi$
$17$	−1.46050	−	2.52967i	−0.354224	−	0.613535i	−0.986985	+	0.160813i	$0.948588\pi$
$18$	−2.98755	−	0.273062i	−0.704172	−	0.0643614i
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	0.372674	+	0.927962i	$0.378441\pi$
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	−0.989976	+	0.141236i	$0.954892\pi$
$20$	0.296790	−	0.514055i	0.0663642	−	0.114946i
$21$		0			0
$22$	−0.296790	−	0.514055i	−0.0632758	−	0.109597i
$23$	4.46050			0.930080			0.465040	−	0.885290i	$-0.346040\pi$
$23$	4.46050			0.930080			0.465040	+	0.885290i	$0.346040\pi$
$24$	0.796790	+	1.53790i	0.162644	+	0.313922i
$25$	−4.64766			−0.929533
$26$	−1.25729	+	2.17770i	−0.246576	+	0.427082i
$27$	5.14766	+	0.708209i	0.990668	+	0.136295i
$28$		0			0
$29$	−3.09718	+	5.36447i	−0.575132	+	0.996157i	0.420896	+	0.907109i	$0.361716\pi$
$29$	−3.09718	+	5.36447i	−0.575132	+	0.996157i	−0.996027	+	0.0890480i	$0.971618\pi$
$30$	−0.554084	+	0.866025i	−0.101161	+	0.158114i
$31$	−3.93346	+	6.81296i	−0.706471	+	1.22364i	0.259687	+	0.965693i	$0.416380\pi$
$31$	−3.93346	+	6.81296i	−0.706471	+	1.22364i	−0.966158	+	0.257951i	$0.916953\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.472958	+	0.912864i	0.0823314	+	0.158909i
$34$	1.46050	−	2.52967i	0.250475	−	0.433835i
$35$		0			0
$36$	−1.25729	−	2.72382i	−0.209549	−	0.453970i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−5.38151			−0.872997
$39$	2.34728	−	3.66876i	0.375865	−	0.587471i
$40$	0.593579			0.0938531
$41$	0.136673	+	0.236725i	0.0213448	+	0.0369702i	0.876500	−	0.481401i	$-0.159872\pi$
$41$	0.136673	+	0.236725i	0.0213448	+	0.0369702i	−0.855156	+	0.518371i	$0.826539\pi$
$42$		0			0
$43$	−5.58113	+	9.66679i	−0.851114	+	1.47417i	0.0290902	+	0.999577i	$0.490739\pi$
$43$	−5.58113	+	9.66679i	−0.851114	+	1.47417i	−0.880204	+	0.474596i	$0.842594\pi$
$44$	0.296790	−	0.514055i	0.0447427	−	0.0774967i
$45$	1.02704	−	1.45472i	0.153102	−	0.216857i
$46$	2.23025	+	3.86291i	0.328833	+	0.569555i
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.843377	+	0.537323i	$0.180564\pi$
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.0436467	+	0.999047i	$0.486102\pi$
$48$	−0.933463	+	1.45899i	−0.134734	+	0.210587i
$49$		0			0
$50$	−2.32383	−	4.02499i	−0.328639	−	0.569220i
$51$	−2.72665	+	4.26172i	−0.381808	+	0.596760i
$52$	−2.51459			−0.348711
$53$	4.02704	+	6.97504i	0.553157	+	0.958096i	0.998044	+	0.0625092i	$0.0199103\pi$
$53$	4.02704	+	6.97504i	0.553157	+	0.958096i	−0.444888	+	0.895586i	$0.646756\pi$
$54$	1.96050	+	4.81211i	0.266791	+	0.654845i
$55$	0.352336			0.0475090
$56$		0			0
$57$	9.31138	+	0.424646i	1.23332	+	0.0562457i
$58$	−6.19436			−0.813359
$59$	4.32383	−	7.48910i	0.562915	−	0.974997i	−0.434325	−	0.900756i	$-0.643013\pi$
$59$	4.32383	−	7.48910i	0.562915	−	0.974997i	0.997240	−	0.0742412i	$-0.0236535\pi$
$60$	−1.02704	−	0.0468383i	−0.132591	−	0.00604680i
$61$	−3.32383	−	5.75705i	−0.425573	−	0.737114i	0.570901	−	0.821019i	$-0.306594\pi$
$61$	−3.32383	−	5.75705i	−0.425573	−	0.737114i	−0.996474	+	0.0839050i	$0.973261\pi$
$62$	−7.86693			−0.999101
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.746304	−	1.29264i	−0.0925676	−	0.160332i
$66$	−0.554084	+	0.866025i	−0.0682031	+	0.106600i
$67$	0.956906	−	1.65741i	0.116905	−	0.202485i	−0.801635	−	0.597814i	$-0.796036\pi$
$67$	0.956906	−	1.65741i	0.116905	−	0.202485i	0.918540	+	0.395329i	$0.129369\pi$
$68$	2.92101			0.354224
$69$	−3.55408	−	6.85980i	−0.427861	−	0.825822i
$70$		0			0
$71$	−14.4107			−1.71023			−0.855117	−	0.518435i	$-0.826515\pi$
$71$	−14.4107			−1.71023			−0.855117	+	0.518435i	$0.826515\pi$
$72$	1.73025	−	2.45076i	0.203912	−	0.288825i
$73$	−3.95691	−	6.85356i	−0.463121	−	0.802149i	0.535994	−	0.844222i	$-0.319937\pi$
$73$	−3.95691	−	6.85356i	−0.463121	−	0.802149i	−0.999115	+	0.0420732i	$0.986604\pi$
$74$	1.00000			0.116248
$75$	3.70321	+	7.14763i	0.427610	+	0.825337i
$76$	−2.69076	−	4.66053i	−0.308651	−	0.534599i
$77$		0			0
$78$	4.35087	+	0.198422i	0.492639	+	0.0224668i
$79$	4.62422	+	8.00938i	0.520265	+	0.901126i	0.999722	+	0.0235607i	$0.00750031\pi$
$79$	4.62422	+	8.00938i	0.520265	+	0.901126i	−0.479457	+	0.877565i	$0.659166\pi$
$80$	0.296790	+	0.514055i	0.0331821	+	0.0574731i
$81$	−3.01245	−	8.48087i	−0.334717	−	0.942319i
$82$	−0.136673	+	0.236725i	−0.0150930	+	0.0261419i
$83$	−3.85087	+	6.66991i	−0.422688	+	0.732118i	−0.996201	−	0.0870787i	$-0.972247\pi$
$83$	−3.85087	+	6.66991i	−0.422688	+	0.732118i	0.573513	+	0.819196i	$0.305580\pi$
$84$		0			0
$85$	0.866926	+	1.50156i	0.0940313	+	0.162867i
$86$	−11.1623			−1.20366
$87$	10.7178	+	0.488786i	1.14907	+	0.0524033i
$88$	0.593579			0.0632758
$89$	6.21780	−	10.7695i	0.659085	−	1.14157i	−0.321767	−	0.946819i	$-0.604277\pi$
$89$	6.21780	−	10.7695i	0.659085	−	1.14157i	0.980853	−	0.194751i	$-0.0623898\pi$
$90$	1.77335	+	0.162084i	0.186927	+	0.0170852i
$91$		0			0
$92$	−2.23025	+	3.86291i	−0.232520	+	0.402736i
$93$	13.6118	+	0.620765i	1.41147	+	0.0643704i
$94$	−6.08113	+	10.5328i	−0.627220	+	1.08638i
$95$	1.59718	−	2.76639i	0.163867	−	0.283826i
$96$	−1.73025	−	0.0789082i	−0.176593	−	0.00805354i
$97$	−5.86693	+	10.1618i	−0.595696	+	1.03178i	0.397752	+	0.917493i	$0.369790\pi$
$97$	−5.86693	+	10.1618i	−0.595696	+	1.03178i	−0.993448	+	0.114283i	$0.963543\pi$
$98$		0			0
$99$	1.02704	−	1.45472i	0.103222	−	0.146205i
$100$	2.32383	−	4.02499i	0.232383	−	0.402499i
$101$	1.62276			0.161470			0.0807352	−	0.996736i	$-0.474273\pi$
$101$	1.62276			0.161470			0.0807352	+	0.996736i	$0.474273\pi$
$102$	−5.05408	−	0.230492i	−0.500429	−	0.0228221i
$103$	−6.38151			−0.628789			−0.314395	−	0.949292i	$-0.601802\pi$
$103$	−6.38151			−0.628789			−0.314395	+	0.949292i	$0.601802\pi$
$104$	−1.25729	−	2.17770i	−0.123288	−	0.213541i
$105$		0			0
$106$	−4.02704	+	6.97504i	−0.391141	+	0.677476i
$107$	9.35447	−	16.2024i	0.904331	−	1.56635i	0.0825182	−	0.996590i	$-0.473704\pi$
$107$	9.35447	−	16.2024i	0.904331	−	1.56635i	0.821813	−	0.569758i	$-0.192963\pi$
$108$	−3.18716	+	4.10390i	−0.306684	+	0.394898i
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	0.789173	−	0.614171i	$-0.210509\pi$
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	−0.926474	+	0.376359i	$0.877176\pi$
$110$	0.176168	+	0.305132i	0.0167970	+	0.0290932i
$111$	−1.73025	−	0.0789082i	−0.164228	−	0.00748964i
$112$		0			0
$113$	−6.16012	−	10.6696i	−0.579495	−	1.00371i	−0.995537	−	0.0943695i	$-0.969916\pi$
$113$	−6.16012	−	10.6696i	−0.579495	−	1.00371i	0.416042	−	0.909345i	$-0.363417\pi$
$114$	4.28794	+	8.27621i	0.401602	+	0.775138i
$115$	−2.64766			−0.246896
$116$	−3.09718	−	5.36447i	−0.287566	−	0.498078i
$117$	−7.51245	−	0.686640i	−0.694527	−	0.0634799i
$118$	8.64766			0.796082
$119$		0			0
$120$	−0.472958	−	0.912864i	−0.0431750	−	0.0833327i
$121$	−10.6477			−0.967969
$122$	3.32383	−	5.75705i	0.300926	−	0.521218i
$123$	0.255158	−	0.398809i	0.0230069	−	0.0359594i
$124$	−3.93346	−	6.81296i	−0.353235	−	0.611822i
$125$	5.72665			0.512207
$126$		0			0
$127$	12.3346			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$127$	12.3346			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	19.3135	+	0.880794i	1.70046	+	0.0775496i
$130$	0.746304	−	1.29264i	0.0654552	−	0.113372i
$131$	1.18716			0.103723			0.0518613	−	0.998654i	$-0.483485\pi$
$131$	1.18716			0.103723			0.0518613	+	0.998654i	$0.483485\pi$
$132$	−1.02704	−	0.0468383i	−0.0893925	−	0.00407675i
$133$		0			0
$134$	1.91381			0.165328
$135$	−3.05555	−	0.420378i	−0.262980	−	0.0361804i
$136$	1.46050	+	2.52967i	0.125237	+	0.216917i
$137$	2.52179			0.215451			0.107725	−	0.994181i	$-0.465643\pi$
$137$	2.52179			0.215451			0.107725	+	0.994181i	$0.465643\pi$
$138$	4.16372	−	6.50783i	0.354439	−	0.553983i
$139$	−2.45691	−	4.25549i	−0.208392	−	0.360946i	0.742816	−	0.669496i	$-0.233490\pi$
$139$	−2.45691	−	4.25549i	−0.208392	−	0.360946i	−0.951208	+	0.308550i	$0.900156\pi$
$140$		0			0
$141$	11.3530	−	17.7446i	0.956096	−	1.49436i
$142$	−7.20535	−	12.4800i	−0.604659	−	1.04730i
$143$	−0.746304	−	1.29264i	−0.0624091	−	0.108096i
$144$	2.98755	+	0.273062i	0.248962	+	0.0227552i
$145$	1.83842	−	3.18424i	0.152673	−	0.264437i
$146$	3.95691	−	6.85356i	0.327476	−	0.567205i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	18.0512			1.47881			0.739404	−	0.673262i	$-0.235107\pi$
$149$	18.0512			1.47881			0.739404	+	0.673262i	$0.235107\pi$
$150$	−4.33842	+	6.78089i	−0.354231	+	0.553657i
$151$	1.64766			0.134085			0.0670425	−	0.997750i	$-0.478644\pi$
$151$	1.64766			0.134085			0.0670425	+	0.997750i	$0.478644\pi$
$152$	2.69076	−	4.66053i	0.218249	−	0.378019i
$153$	8.72665	+	0.797618i	0.705508	+	0.0644836i
$154$		0			0
$155$	2.33482	−	4.04403i	0.187537	−	0.324824i
$156$	2.00360	+	3.86718i	0.160416	+	0.309622i
$157$	−3.30039	+	5.71644i	−0.263400	+	0.456222i	−0.967143	−	0.254233i	$-0.918177\pi$
$157$	−3.30039	+	5.71644i	−0.263400	+	0.456222i	0.703743	+	0.710454i	$0.251510\pi$
$158$	−4.62422	+	8.00938i	−0.367883	+	0.637192i
$159$	7.51819	−	11.7508i	0.596231	−	0.931900i
$160$	−0.296790	+	0.514055i	−0.0234633	+	0.0406396i
$161$		0			0
$162$	5.83842	−	6.84929i	0.458710	−	0.538131i
$163$	−2.99115	+	5.18082i	−0.234285	+	0.405793i	−0.959065	−	0.283188i	$-0.908608\pi$
$163$	−2.99115	+	5.18082i	−0.234285	+	0.405793i	0.724780	+	0.688980i	$0.241941\pi$
$164$	−0.273346			−0.0213448
$165$	−0.280738	−	0.541857i	−0.0218554	−	0.0421835i
$166$	−7.70175			−0.597772
$167$	−3.73025	−	6.46099i	−0.288656	−	0.499966i	0.684833	−	0.728700i	$-0.259875\pi$
$167$	−3.73025	−	6.46099i	−0.288656	−	0.499966i	−0.973489	+	0.228733i	$0.926542\pi$
$168$		0			0
$169$	3.33842	−	5.78231i	0.256802	−	0.444793i
$170$	−0.866926	+	1.50156i	−0.0664902	+	0.115164i
$171$	−6.76615	−	14.6583i	−0.517420	−	1.12095i
$172$	−5.58113	−	9.66679i	−0.425557	−	0.737086i
$173$	−12.8296	−	22.2215i	−0.975414	−	1.68947i	−0.678562	−	0.734543i	$-0.737397\pi$
$173$	−12.8296	−	22.2215i	−0.975414	−	1.68947i	−0.296851	−	0.954924i	$-0.595937\pi$
$174$	4.93560	+	9.52628i	0.374167	+	0.722185i
$175$		0			0
$176$	0.296790	+	0.514055i	0.0223714	+	0.0387483i
$177$	−14.9626	−	0.682372i	−1.12466	−	0.0512902i
$178$	12.4356			0.932088
$179$	7.51819	+	13.0219i	0.561936	+	0.973301i	0.997328	+	0.0730602i	$0.0232765\pi$
$179$	7.51819	+	13.0219i	0.561936	+	0.973301i	−0.435392	+	0.900241i	$0.643390\pi$
$180$	0.746304	+	1.61680i	0.0556262	+	0.120510i
$181$	0.0861875			0.00640627			0.00320313	−	0.999995i	$-0.498980\pi$
$181$	0.0861875			0.00640627			0.00320313	+	0.999995i	$0.498980\pi$
$182$		0			0
$183$	−6.20535	+	9.69886i	−0.458712	+	0.716961i
$184$	−4.46050			−0.328833
$185$	−0.296790	+	0.514055i	−0.0218204	+	0.0377941i
$186$	6.26829	+	12.0985i	0.459613	+	0.887106i
$187$	0.866926	+	1.50156i	0.0633959	+	0.109805i
$188$	−12.1623			−0.887023
$189$		0			0
$190$	3.19436			0.231743
$191$	−1.99115	−	3.44877i	−0.144074	−	0.249544i	0.784953	−	0.619555i	$-0.212687\pi$
$191$	−1.99115	−	3.44877i	−0.144074	−	0.249544i	−0.929027	+	0.370011i	$0.879354\pi$
$192$	−0.796790	−	1.53790i	−0.0575033	−	0.110988i
$193$	−3.39037	+	5.87229i	−0.244044	+	0.422697i	−0.961862	−	0.273534i	$-0.911808\pi$
$193$	−3.39037	+	5.87229i	−0.244044	+	0.422697i	0.717818	+	0.696230i	$0.245141\pi$
$194$	−11.7339			−0.842441
$195$	−1.39329	+	2.17770i	−0.0997759	+	0.155948i
$196$		0			0
$197$	11.0584			0.787875			0.393938	−	0.919137i	$-0.371113\pi$
$197$	11.0584			0.787875			0.393938	+	0.919137i	$0.371113\pi$
$198$	1.77335	+	0.162084i	0.126026	+	0.0115188i
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	0.749109	−	0.662447i	$-0.230482\pi$
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	−0.948250	+	0.317523i	$0.897149\pi$
$200$	4.64766			0.328639
$201$	−3.31138	−	0.151016i	−0.233567	−	0.0106518i
$202$	0.811379	+	1.40535i	0.0570884	+	0.0988800i
$203$		0			0
$204$	−2.32743	−	4.49221i	−0.162953	−	0.314518i
$205$	−0.0811263	−	0.140515i	−0.00566611	−	0.00981399i
$206$	−3.19076	−	5.52655i	−0.222311	−	0.385053i
$207$	−7.71780	+	10.9316i	−0.536424	+	0.759801i
$208$	1.25729	−	2.17770i	0.0871777	−	0.150996i
$209$	1.59718	−	2.76639i	0.110479	−	0.191355i
$210$		0			0
$211$	9.66225	+	16.7355i	0.665177	+	1.15212i	0.979237	+	0.202717i	$0.0649772\pi$
$211$	9.66225	+	16.7355i	0.665177	+	1.15212i	−0.314060	+	0.949403i	$0.601689\pi$
$212$	−8.05408			−0.553157
$213$	11.4823	+	22.1622i	0.786754	+	1.51853i
$214$	18.7089			1.27892
$215$	3.31284	−	5.73801i	0.225934	−	0.391329i
$216$	−5.14766	−	0.708209i	−0.350254	−	0.0481875i
$217$		0			0
$218$	1.43346	−	2.48283i	0.0970863	−	0.168158i
$219$	−7.38725	+	11.5462i	−0.499184	+	0.780217i
$220$	−0.176168	+	0.305132i	−0.0118773	+	0.0205720i
$221$	3.67257	−	6.36108i	0.247044	−	0.427892i
$222$	−0.796790	−	1.53790i	−0.0534770	−	0.103217i
$223$	−12.6623	+	21.9317i	−0.847927	+	1.46865i	0.0351275	+	0.999383i	$0.488816\pi$
$223$	−12.6623	+	21.9317i	−0.847927	+	1.46865i	−0.883055	+	0.469270i	$0.844517\pi$
$224$		0			0
$225$	8.04163	−	11.3903i	0.536109	−	0.759354i
$226$	6.16012	−	10.6696i	0.409765	−	0.709734i
$227$	−4.81711			−0.319723			−0.159862	−	0.987139i	$-0.551105\pi$
$227$	−4.81711			−0.319723			−0.159862	+	0.987139i	$0.551105\pi$
$228$	−5.02344	+	7.85157i	−0.332686	+	0.519983i
$229$	9.29533			0.614253			0.307126	−	0.951669i	$-0.400633\pi$
$229$	9.29533			0.614253			0.307126	+	0.951669i	$0.400633\pi$
$230$	−1.32383	−	2.29294i	−0.0872909	−	0.151192i
$231$		0			0
$232$	3.09718	−	5.36447i	0.203340	−	0.352195i
$233$	0.0971780	−	0.168317i	0.00636634	−	0.0110268i	−0.862825	−	0.505503i	$-0.831307\pi$
$233$	0.0971780	−	0.168317i	0.00636634	−	0.0110268i	0.869191	+	0.494476i	$0.164640\pi$
$234$	−3.16158	−	6.84929i	−0.206679	−	0.447752i
$235$	−3.60963	−	6.25206i	−0.235466	−	0.407840i
$236$	4.32383	+	7.48910i	0.281457	+	0.487499i
$237$	8.63307	−	13.4934i	0.560778	−	0.876488i
$238$		0			0
$239$	−6.82743	−	11.8255i	−0.441630	−	0.764925i	0.556181	−	0.831061i	$-0.312266\pi$
$239$	−6.82743	−	11.8255i	−0.441630	−	0.764925i	−0.997811	+	0.0661361i	$0.978933\pi$
$240$	0.554084	−	0.866025i	0.0357660	−	0.0559017i
$241$	13.0000			0.837404			0.418702	−	0.908124i	$-0.362485\pi$
$241$	13.0000			0.837404			0.418702	+	0.908124i	$0.362485\pi$
$242$	−5.32383	−	9.22115i	−0.342229	−	0.592758i
$243$	−10.6424	+	11.3903i	−0.682711	+	0.730689i
$244$	6.64766			0.425573
$245$		0			0
$246$	0.472958	+	0.0215693i	0.0301547	+	0.00137521i
$247$	−13.5323			−0.861039
$248$	3.93346	−	6.81296i	0.249775	−	0.432623i
$249$	13.3260	+	0.607731i	0.844499	+	0.0385134i
$250$	2.86333	+	4.95943i	0.181093	+	0.313662i
$251$	19.5438			1.23359			0.616796	−	0.787123i	$-0.288430\pi$
$251$	19.5438			1.23359			0.616796	+	0.787123i	$0.288430\pi$
$252$		0			0
$253$	−2.64766			−0.166457
$254$	6.16731	+	10.6821i	0.386972	+	0.670255i
$255$	1.61849	−	2.52967i	0.101353	−	0.158414i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.32743			−0.519451			−0.259725	−	0.965683i	$-0.583632\pi$
$257$	−8.32743			−0.519451			−0.259725	+	0.965683i	$0.583632\pi$
$258$	8.89397	+	17.1664i	0.553714	+	1.06873i
$259$		0			0
$260$	1.49261			0.0925676
$261$	−7.78813	−	16.8723i	−0.482073	−	1.04437i
$262$	0.593579	+	1.02811i	0.0366715	+	0.0635168i
$263$	−17.0905			−1.05384			−0.526921	−	0.849914i	$-0.676654\pi$
$263$	−17.0905			−1.05384			−0.526921	+	0.849914i	$0.676654\pi$
$264$	−0.472958	−	0.912864i	−0.0291085	−	0.0561829i
$265$	−2.39037	−	4.14024i	−0.146839	−	0.254333i
$266$		0			0
$267$	−21.5167	−	0.981271i	−1.31680	−	0.0600528i
$268$	0.956906	+	1.65741i	0.0584524	+	0.101242i
$269$	5.00720	+	8.67272i	0.305294	+	0.528785i	0.977327	−	0.211737i	$-0.0679119\pi$
$269$	5.00720	+	8.67272i	0.305294	+	0.528785i	−0.672033	+	0.740522i	$0.734579\pi$
$270$	−1.16372	−	2.85637i	−0.0708215	−	0.173833i
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	−0.978380	−	0.206818i	$-0.933689\pi$
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	0.668299	+	0.743893i	$0.267023\pi$
$272$	−1.46050	+	2.52967i	−0.0885561	+	0.153384i
$273$		0			0
$274$	1.26089	+	2.18393i	0.0761733	+	0.131936i
$275$	2.75876			0.166359
$276$	7.71780	+	0.351971i	0.464557	+	0.0211861i
$277$	19.3422			1.16216			0.581081	−	0.813846i	$-0.302630\pi$
$277$	19.3422			1.16216			0.581081	+	0.813846i	$0.302630\pi$
$278$	2.45691	−	4.25549i	0.147355	−	0.255227i
$279$	−9.89104	−	21.4281i	−0.592161	−	1.28287i
$280$		0			0
$281$	−6.40136	+	11.0875i	−0.381873	+	0.661424i	−0.991330	−	0.131396i	$-0.958054\pi$
$281$	−6.40136	+	11.0875i	−0.381873	+	0.661424i	0.609457	+	0.792819i	$0.291388\pi$
$282$	21.0438	+	0.959702i	1.25314	+	0.0571494i
$283$	−8.17617	+	14.1615i	−0.486023	+	0.841816i	−0.999871	−	0.0160650i	$-0.994886\pi$
$283$	−8.17617	+	14.1615i	−0.486023	+	0.841816i	0.513848	+	0.857881i	$0.328219\pi$
$284$	7.20535	−	12.4800i	0.427559	−	0.740553i
$285$	−5.52704	−	0.252061i	−0.327394	−	0.0149308i
$286$	0.746304	−	1.29264i	0.0441299	−	0.0764352i
$287$		0			0
$288$	1.25729	+	2.72382i	0.0740868	+	0.160503i
$289$	4.23385	−	7.33325i	0.249050	−	0.431367i
$290$	3.67684			0.215912
$291$	20.3025	+	0.925898i	1.19016	+	0.0542771i
$292$	7.91381			0.463121
$293$	10.3889	+	17.9941i	0.606926	+	1.05123i	0.991744	+	0.128235i	$0.0409311\pi$
$293$	10.3889	+	17.9941i	0.606926	+	1.05123i	−0.384817	+	0.922993i	$0.625736\pi$
$294$		0			0
$295$	−2.56654	+	4.44537i	−0.149430	+	0.258820i
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	−3.05555	−	0.420378i	−0.177301	−	0.0243928i
$298$	9.02558	+	15.6328i	0.522838	+	0.905582i
$299$	5.60817	+	9.71363i	0.324329	+	0.561754i
$300$	−8.04163	−	0.366739i	−0.464284	−	0.0211737i
$301$		0			0
$302$	0.823832	+	1.42692i	0.0474062	+	0.0821099i
$303$	−1.29300	−	2.49563i	−0.0742807	−	0.143370i
$304$	5.38151			0.308651
$305$	1.97296	+	3.41726i	0.112971	+	0.195672i
$306$	3.67257	+	7.95631i	0.209947	+	0.454832i
$307$	22.6768			1.29424			0.647118	−	0.762390i	$-0.275974\pi$
$307$	22.6768			1.29424			0.647118	+	0.762390i	$0.275974\pi$
$308$		0			0
$309$	5.08472	+	9.81411i	0.289260	+	0.558305i
$310$	4.66964			0.265218
$311$	−3.25729	+	5.64180i	−0.184704	+	0.319917i	−0.943477	−	0.331439i	$-0.892466\pi$
$311$	−3.25729	+	5.64180i	−0.184704	+	0.319917i	0.758773	+	0.651356i	$0.225799\pi$
$312$	−2.34728	+	3.66876i	−0.132888	+	0.207702i
$313$	0.133074	+	0.230492i	0.00752181	+	0.0130282i	0.869762	−	0.493472i	$-0.164272\pi$
$313$	0.133074	+	0.230492i	0.00752181	+	0.0130282i	−0.862240	+	0.506500i	$0.830939\pi$
$314$	−6.60078			−0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	−7.86186	−	13.6171i	−0.441566	−	0.764815i	0.556240	−	0.831022i	$-0.312244\pi$
$317$	−7.86186	−	13.6171i	−0.441566	−	0.764815i	−0.997806	+	0.0662067i	$0.978910\pi$
$318$	13.9356	+	0.635534i	0.781470	+	0.0356390i
$319$	1.83842	−	3.18424i	0.102932	−	0.178283i
$320$	−0.593579			−0.0331821
$321$	−32.3712	−	1.47629i	−1.80678	−	0.0823985i
$322$		0			0
$323$	15.7195			0.874654
$324$	8.85087	+	1.63157i	0.491715	+	0.0906430i
$325$	−5.84348	−	10.1212i	−0.324138	−	0.561424i
$326$	−5.98229			−0.331328
$327$	−2.67617	+	4.18281i	−0.147992	+	0.231310i
$328$	−0.136673	−	0.236725i	−0.00754651	−	0.0130709i
$329$		0			0
$330$	0.328893	−	0.514055i	0.0181050	−	0.0282978i
$331$	12.5811	+	21.7912i	0.691521	+	1.19775i	0.971339	+	0.237697i	$0.0763925\pi$
$331$	12.5811	+	21.7912i	0.691521	+	1.19775i	−0.279818	+	0.960053i	$0.590274\pi$
$332$	−3.85087	−	6.66991i	−0.211344	−	0.366059i
$333$	1.25729	+	2.72382i	0.0688993	+	0.149265i
$334$	3.73025	−	6.46099i	0.204110	−	0.353529i
$335$	−0.568000	+	0.983804i	−0.0310331	+	0.0537510i
$336$		0			0
$337$	−9.36693	−	16.2240i	−0.510249	−	0.883777i	−0.999929	−	0.0118752i	$-0.996220\pi$
$337$	−9.36693	−	16.2240i	−0.510249	−	0.883777i	0.489681	−	0.871902i	$-0.337113\pi$
$338$	6.67684			0.363172
$339$	−11.5005	+	17.9751i	−0.624620	+	0.976272i
$340$	−1.73385			−0.0940313
$341$	2.33482	−	4.04403i	0.126438	−	0.218997i
$342$	9.31138	−	13.1888i	0.503502	−	0.713169i
$343$		0			0
$344$	5.58113	−	9.66679i	0.300914	−	0.521199i
$345$	2.10963	+	4.07183i	0.113579	+	0.219220i
$346$	12.8296	−	22.2215i	0.689722	−	1.19463i
$347$	−11.2719	+	19.5235i	−0.605106	+	1.04808i	0.386928	+	0.922110i	$0.373536\pi$
$347$	−11.2719	+	19.5235i	−0.605106	+	1.04808i	−0.992035	+	0.125965i	$0.959797\pi$
$348$	−5.78220	+	9.03749i	−0.309958	+	0.484461i
$349$	−1.89543	+	3.28298i	−0.101460	+	0.175734i	−0.912286	−	0.409553i	$-0.865685\pi$
$349$	−1.89543	+	3.28298i	−0.101460	+	0.175734i	0.810826	+	0.585287i	$0.199018\pi$
$350$		0			0
$351$	4.92986	+	12.1005i	0.263137	+	0.645876i
$352$	−0.296790	+	0.514055i	−0.0158189	+	0.0273992i
$353$	−6.83482			−0.363781			−0.181890	−	0.983319i	$-0.558222\pi$
$353$	−6.83482			−0.363781			−0.181890	+	0.983319i	$0.558222\pi$
$354$	−6.89037	−	13.2992i	−0.366219	−	0.706845i
$355$	8.55389			0.453993
$356$	6.21780	+	10.7695i	0.329543	+	0.570785i
$357$		0			0
$358$	−7.51819	+	13.0219i	−0.397349	+	0.688228i
$359$	−6.32237	+	10.9507i	−0.333682	+	0.577954i	−0.983231	−	0.182366i	$-0.941624\pi$
$359$	−6.32237	+	10.9507i	−0.333682	+	0.577954i	0.649549	+	0.760320i	$0.274958\pi$
$360$	−1.02704	+	1.45472i	−0.0541299	+	0.0766705i
$361$	−4.98035	−	8.62622i	−0.262124	−	0.454012i
$362$	0.0430937	+	0.0746406i	0.00226496	+	0.00392302i
$363$	8.48395	+	16.3750i	0.445292	+	0.859465i
$364$		0			0
$365$	2.34874	+	4.06813i	0.122939	+	0.212936i
$366$	−11.5021	−	0.524555i	−0.601226	−	0.0274190i
$367$	−6.54377			−0.341582			−0.170791	−	0.985307i	$-0.554632\pi$
$367$	−6.54377			−0.341582			−0.170791	+	0.985307i	$0.554632\pi$
$368$	−2.23025	−	3.86291i	−0.116260	−	0.201368i
$369$	−0.816635	−	0.0746406i	−0.0425123	−	0.00388563i
$370$	−0.593579			−0.0308587
$371$		0			0
$372$	−7.34348	+	11.4778i	−0.380742	+	0.595094i
$373$	9.42840			0.488184			0.244092	−	0.969752i	$-0.421510\pi$
$373$	9.42840			0.488184			0.244092	+	0.969752i	$0.421510\pi$
$374$	−0.866926	+	1.50156i	−0.0448277	+	0.0776438i
$375$	−4.56294	−	8.80700i	−0.235629	−	0.454792i
$376$	−6.08113	−	10.5328i	−0.313610	−	0.543189i
$377$	−15.5763			−0.802218
$378$		0			0
$379$	−7.27762			−0.373826			−0.186913	−	0.982376i	$-0.559848\pi$
$379$	−7.27762			−0.373826			−0.186913	+	0.982376i	$0.559848\pi$
$380$	1.59718	+	2.76639i	0.0819335	+	0.141913i
$381$	−9.82810	−	18.9694i	−0.503509	−	0.971831i
$382$	1.99115	−	3.44877i	0.101876	−	0.176454i
$383$	24.0833			1.23060			0.615299	−	0.788294i	$-0.289035\pi$
$383$	24.0833			1.23060			0.615299	+	0.788294i	$0.289035\pi$
$384$	0.933463	−	1.45899i	0.0476356	−	0.0744537i
$385$		0			0
$386$	−6.78074			−0.345130
$387$	−14.0342	−	30.4040i	−0.713400	−	1.54552i
$388$	−5.86693	−	10.1618i	−0.297848	−	0.515888i
$389$	−16.2983			−0.826354			−0.413177	−	0.910651i	$-0.635581\pi$
$389$	−16.2983			−0.826354			−0.413177	+	0.910651i	$0.635581\pi$
$390$	−2.58259	−	0.117779i	−0.130774	−	0.00596398i
$391$	−6.51459	−	11.2836i	−0.329457	−	0.570636i
$392$		0			0
$393$	−0.945916	−	1.82573i	−0.0477151	−	0.0920958i
$394$	5.52918	+	9.57682i	0.278556	+	0.482473i
$395$	−2.74484	−	4.75420i	−0.138108	−	0.239210i
$396$	0.746304	+	1.61680i	0.0375032	+	0.0812475i
$397$	6.08619	−	10.5416i	0.305457	−	0.529067i	−0.671906	−	0.740636i	$-0.734524\pi$
$397$	6.08619	−	10.5416i	0.305457	−	0.529067i	0.977363	+	0.211569i	$0.0678574\pi$
$398$	2.80924	−	4.86575i	0.140815	−	0.243898i
$399$		0			0
$400$	2.32383	+	4.02499i	0.116192	+	0.201250i
$401$	−33.3609			−1.66596			−0.832981	−	0.553301i	$-0.813368\pi$
$401$	−33.3609			−1.66596			−0.832981	+	0.553301i	$0.813368\pi$
$402$	−1.52491	−	2.94325i	−0.0760554	−	0.146796i
$403$	−19.7821			−0.985416
$404$	−0.811379	+	1.40535i	−0.0403676	+	0.0699187i
$405$	1.78813	+	5.03407i	0.0888529	+	0.250145i
$406$		0			0
$407$	−0.296790	+	0.514055i	−0.0147113	+	0.0254808i
$408$	2.72665	−	4.26172i	0.134989	−	0.210987i
$409$	−2.89037	+	5.00627i	−0.142920	+	0.247544i	−0.928595	−	0.371095i	$-0.878982\pi$
$409$	−2.89037	+	5.00627i	−0.142920	+	0.247544i	0.785675	+	0.618639i	$0.212316\pi$
$410$	0.0811263	−	0.140515i	0.00400654	−	0.00693954i
$411$	−2.00933	−	3.87825i	−0.0991131	−	0.191300i
$412$	3.19076	−	5.52655i	0.157197	−	0.272274i
$413$		0			0
$414$	−13.3260	−	1.21800i	−0.654936	−	0.0598612i
$415$	2.28580	−	3.95912i	0.112205	−	0.194346i
$416$	2.51459			0.123288
$417$	−4.58686	+	7.16920i	−0.224620	+	0.351077i
$418$	3.19436			0.156241
$419$	−15.4356	−	26.7352i	−0.754078	−	1.30610i	−0.945831	−	0.324659i	$-0.894751\pi$
$419$	−15.4356	−	26.7352i	−0.754078	−	1.30610i	0.191753	−	0.981443i	$-0.438583\pi$
$420$		0			0
$421$	−1.86693	+	3.23361i	−0.0909884	+	0.157597i	−0.907927	−	0.419128i	$-0.862336\pi$
$421$	−1.86693	+	3.23361i	−0.0909884	+	0.157597i	0.816939	+	0.576724i	$0.195669\pi$
$422$	−9.66225	+	16.7355i	−0.470351	+	0.814672i
$423$	−36.3353	−	3.32105i	−1.76668	−	0.161475i
$424$	−4.02704	−	6.97504i	−0.195570	−	0.338738i
$425$	6.78794	+	11.7570i	0.329263	+	0.570301i
$426$	−13.4518	+	21.0250i	−0.651744	+	1.01867i
$427$		0			0
$428$	9.35447	+	16.2024i	0.452165	+	0.783174i
$429$	−1.39329	+	2.17770i	−0.0672689	+	0.105140i
$430$	6.62568			0.319519
$431$	−14.0979	−	24.4182i	−0.679070	−	1.17618i	−0.975261	−	0.221055i	$-0.929050\pi$
$431$	−14.0979	−	24.4182i	−0.679070	−	1.17618i	0.296192	−	0.955128i	$-0.404283\pi$
$432$	−1.96050	−	4.81211i	−0.0943248	−	0.231523i
$433$	−12.5438			−0.602815			−0.301407	−	0.953495i	$-0.597456\pi$
$433$	−12.5438			−0.602815			−0.301407	+	0.953495i	$0.597456\pi$
$434$		0			0
$435$	−6.36186	−	0.290133i	−0.305028	−	0.0139108i
$436$	2.86693			0.137301
$437$	−12.0021	+	20.7883i	−0.574140	+	0.994440i
$438$	−13.6929	−	0.624465i	−0.654272	−	0.0298381i
$439$	13.0203	+	22.5519i	0.621426	+	1.07634i	0.989220	+	0.146434i	$0.0467797\pi$
$439$	13.0203	+	22.5519i	0.621426	+	1.07634i	−0.367794	+	0.929907i	$0.619887\pi$
$440$	−0.352336			−0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	11.7865	+	20.4148i	0.559992	+	0.969935i	0.997496	+	0.0707186i	$0.0225292\pi$
$443$	11.7865	+	20.4148i	0.559992	+	0.969935i	−0.437504	+	0.899216i	$0.644137\pi$
$444$	0.933463	−	1.45899i	0.0443002	−	0.0692405i
$445$	−3.69076	+	6.39258i	−0.174959	+	0.303037i
$446$	−25.3245			−1.19915
$447$	−14.3830	−	27.7608i	−0.680291	−	1.31304i
$448$		0			0
$449$	13.6870			0.645928			0.322964	−	0.946411i	$-0.395321\pi$
$449$	13.6870			0.645928			0.322964	+	0.946411i	$0.395321\pi$
$450$	13.8851	+	1.26910i	0.654551	+	0.0598260i
$451$	−0.0811263	−	0.140515i	−0.00382009	−	0.00661659i
$452$	12.3202			0.579495
$453$	−1.31284	−	2.53394i	−0.0616827	−	0.119055i
$454$	−2.40856	−	4.17174i	−0.113039	−	0.195790i
$455$		0			0
$456$	−9.31138	−	0.424646i	−0.436045	−	0.0198859i
$457$	11.1762	+	19.3577i	0.522799	+	0.905515i	0.999648	+	0.0265293i	$0.00844554\pi$
$457$	11.1762	+	19.3577i	0.522799	+	0.905515i	−0.476849	+	0.878985i	$0.658221\pi$
$458$	4.64766	+	8.04999i	0.217171	+	0.376151i
$459$	−5.72665	−	14.0562i	−0.267297	−	0.656088i
$460$	1.32383	−	2.29294i	0.0617240	−	0.106909i
$461$	3.98755	−	6.90663i	0.185719	−	0.321674i	−0.758100	−	0.652138i	$-0.773872\pi$
$461$	3.98755	−	6.90663i	0.185719	−	0.321674i	0.943818	+	0.330464i	$0.107205\pi$
$462$		0			0
$463$	−14.3676	−	24.8854i	−0.667719	−	1.15652i	−0.978540	−	0.206055i	$-0.933937\pi$
$463$	−14.3676	−	24.8854i	−0.667719	−	1.15652i	0.310821	−	0.950468i	$-0.399396\pi$
$464$	6.19436			0.287566
$465$	−8.07966	−	0.368473i	−0.374685	−	0.0170875i
$466$	0.194356			0.00900336
$467$	−16.7829	+	29.0688i	−0.776619	+	1.34514i	0.157261	+	0.987557i	$0.449733\pi$
$467$	−16.7829	+	29.0688i	−0.776619	+	1.34514i	−0.933880	+	0.357586i	$0.883600\pi$
$468$	4.35087	−	6.16266i	0.201119	−	0.284869i
$469$		0			0
$470$	3.60963	−	6.25206i	0.166500	−	0.288386i
$471$	11.4210	+	0.520856i	0.526252	+	0.0239998i
$472$	−4.32383	+	7.48910i	−0.199020	+	0.344714i
$473$	3.31284	−	5.73801i	0.152325	−	0.263834i
$474$	16.0021	+	0.729778i	0.735002	+	0.0335198i
$475$	12.5057	−	21.6606i	0.573802	−	0.993855i
$476$		0			0
$477$	−24.0620	−	2.19927i	−1.10172	−	0.100698i
$478$	6.82743	−	11.8255i	0.312279	−	0.540884i
$479$	−0.367120			−0.0167741			−0.00838707	−	0.999965i	$-0.502670\pi$
$479$	−0.367120			−0.0167741			−0.00838707	+	0.999965i	$0.502670\pi$
$480$	1.02704	+	0.0468383i	0.0468778	+	0.00213787i
$481$	2.51459			0.114655
$482$	6.50000	+	11.2583i	0.296067	+	0.512803i
$483$		0			0
$484$	5.32383	−	9.22115i	0.241992	−	0.419143i
$485$	3.48249	−	6.03184i	0.158132	−	0.273892i
$486$	−15.1855	−	3.52144i	−0.688828	−	0.159736i
$487$	−14.9538	−	25.9007i	−0.677621	−	1.17367i	−0.975695	−	0.219131i	$-0.929678\pi$
$487$	−14.9538	−	25.9007i	−0.677621	−	1.17367i	0.298075	−	0.954543i	$-0.403656\pi$
$488$	3.32383	+	5.75705i	0.150463	+	0.260609i
$489$	10.3509	+	0.472052i	0.468083	+	0.0213469i
$490$		0			0
$491$	−0.255158	−	0.441947i	−0.0115151	−	0.0199448i	0.860210	−	0.509939i	$-0.170332\pi$
$491$	−0.255158	−	0.441947i	−0.0115151	−	0.0199448i	−0.871726	+	0.489994i	$0.836999\pi$
$492$	0.217799	+	0.420378i	0.00981916	+	0.0189521i
$493$	18.0938			0.814903
$494$	−6.76615	−	11.7193i	−0.304423	−	0.527277i
$495$	−0.609631	+	0.863492i	−0.0274009	+	0.0388111i
$496$	7.86693			0.353235
$497$		0			0
$498$	6.13667	+	11.8445i	0.274991	+	0.530764i
$499$	−19.0191			−0.851410			−0.425705	−	0.904862i	$-0.639974\pi$
$499$	−19.0191			−0.851410			−0.425705	+	0.904862i	$0.639974\pi$
$500$	−2.86333	+	4.95943i	−0.128052	+	0.221792i
$501$	−6.96410	+	10.8848i	−0.311133	+	0.486297i
$502$	9.77188	+	16.9254i	0.436141	+	0.755418i
$503$	37.7807			1.68456			0.842280	−	0.539040i	$-0.181213\pi$
$503$	37.7807			1.68456			0.842280	+	0.539040i	$0.181213\pi$
$504$		0			0
$505$	−0.963235			−0.0428634
$506$	−1.32383	−	2.29294i	−0.0588515	−	0.101934i
$507$	−11.5526	−	0.526858i	−0.513070	−	0.0233986i
$508$	−6.16731	+	10.6821i	−0.273630	+	0.473942i
$509$	11.2163			0.497155			0.248578	−	0.968612i	$-0.420037\pi$
$509$	11.2163			0.497155			0.248578	+	0.968612i	$0.420037\pi$
$510$	3.00000	+	0.136815i	0.132842	+	0.00605828i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−17.1517	+	22.0852i	−0.757268	+	0.975086i
$514$	−4.16372	−	7.21177i	−0.183654	−	0.318097i
$515$	3.78794			0.166916
$516$	−10.4195	+	16.2856i	−0.458695	+	0.716933i
$517$	−3.60963	−	6.25206i	−0.158751	−	0.274965i
$518$		0			0
$519$	−23.9518	+	37.4364i	−1.05137	+	1.64327i
$520$	0.746304	+	1.29264i	0.0327276	+	0.0566859i
$521$	13.7360	+	23.7914i	0.601785	+	1.04232i	0.992551	+	0.121831i	$0.0388767\pi$
$521$	13.7360	+	23.7914i	0.601785	+	1.04232i	−0.390766	+	0.920490i	$0.627790\pi$
$522$	10.7178	−	15.1809i	0.469105	−	0.664449i
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	−0.999852	−	0.0172166i	$-0.994520\pi$
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	0.514836	+	0.857289i	$0.327853\pi$
$524$	−0.593579	+	1.02811i	−0.0259306	+	0.0449132i
$525$		0			0
$526$	−8.54523	−	14.8008i	−0.372590	−	0.645344i
$527$	22.9794			1.00100
$528$	0.554084	−	0.866025i	0.0241134	−	0.0376889i
$529$	−3.10390			−0.134952
$530$	2.39037	−	4.14024i	0.103831	−	0.179841i
$531$	10.8727	+	23.5547i	0.471833	+	1.02219i
$532$		0			0
$533$	−0.343677	+	0.595265i	−0.0148863	+	0.0257838i
$534$	−9.90856	−	19.1247i	−0.428785	−	0.827605i
$535$	−5.55262	+	9.61742i	−0.240061	+	0.415797i
$536$	−0.956906	+	1.65741i	−0.0413321	+	0.0715892i
$537$	14.0359	−	21.9379i	0.605694	−	0.946690i
$538$	−5.00720	+	8.67272i	−0.215876	+	0.373908i
$539$		0			0
$540$	1.89183	−	2.43599i	0.0814115	−	0.104828i
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	−0.343403	−	0.939188i	$-0.611580\pi$
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	0.985062	−	0.172198i	$-0.0550869\pi$
$542$	−10.2091			−0.438520
$543$	−0.0686733	−	0.132547i	−0.00294705	−	0.00568816i
$544$	−2.92101			−0.125237
$545$	0.850874	+	1.47376i	0.0364474	+	0.0631288i
$546$		0			0
$547$	8.84348	−	15.3174i	0.378120	−	0.654923i	−0.612669	−	0.790340i	$-0.709904\pi$
$547$	8.84348	−	15.3174i	0.378120	−	0.654923i	0.990789	+	0.135417i	$0.0432373\pi$
$548$	−1.26089	+	2.18393i	−0.0538627	+	0.0932929i
$549$	19.8602	+	1.81523i	0.847613	+	0.0774720i
$550$	1.37938	+	2.38915i	0.0588169	+	0.101874i
$551$	−16.6675	−	28.8690i	−0.710060	−	1.22986i
$552$	3.55408	+	6.85980i	0.151272	+	0.291972i
$553$		0			0
$554$	9.67111	+	16.7508i	0.410886	+	0.711675i
$555$	1.02704	+	0.0468383i	0.0435955	+	0.00198818i
$556$	4.91381			0.208392
$557$	15.0651	+	26.0935i	0.638328	+	1.10562i	0.985800	+	0.167926i	$0.0537069\pi$
$557$	15.0651	+	26.0935i	0.638328	+	1.10562i	−0.347472	+	0.937690i	$0.612960\pi$
$558$	13.6118	−	19.2799i	0.576232	−	0.816185i
$559$	−28.0685			−1.18717
$560$		0			0
$561$	1.61849	−	2.52967i	0.0683325	−	0.106803i
$562$	−12.8027			−0.540050
$563$	2.04883	−	3.54867i	0.0863478	−	0.149559i	−0.819617	−	0.572912i	$-0.805814\pi$
$563$	2.04883	−	3.54867i	0.0863478	−	0.149559i	0.905965	+	0.423353i	$0.139147\pi$
$564$	9.69076	+	18.7043i	0.408054	+	0.787593i
$565$	3.65652	+	6.33327i	0.153831	+	0.266443i
$566$	−16.3523			−0.687340
$567$		0			0
$568$	14.4107			0.604659
$569$	−3.11849	−	5.40138i	−0.130734	−	0.226437i	0.793226	−	0.608927i	$-0.208400\pi$
$569$	−3.11849	−	5.40138i	−0.130734	−	0.226437i	−0.923960	+	0.382490i	$0.875067\pi$
$570$	−2.54523	−	4.91259i	−0.106608	−	0.205766i
$571$	−17.8011	+	30.8323i	−0.744951	+	1.29029i	0.205266	+	0.978706i	$0.434194\pi$
$571$	−17.8011	+	30.8323i	−0.744951	+	1.29029i	−0.950218	+	0.311587i	$0.899139\pi$
$572$	1.49261			0.0624091
$573$	−3.71732	+	5.81012i	−0.155293	+	0.242721i
$574$		0			0
$575$	−20.7309			−0.864539
$576$	−1.73025	+	2.45076i	−0.0720939	+	0.102115i
$577$	−23.1388	−	40.0776i	−0.963281	−	1.66845i	−0.714164	−	0.699979i	$-0.753193\pi$
$577$	−23.1388	−	40.0776i	−0.963281	−	1.66845i	−0.249118	−	0.968473i	$-0.580141\pi$
$578$	8.46770			0.352210
$579$	11.7324	+	0.535056i	0.487581	+	0.0222362i
$580$	1.83842	+	3.18424i	0.0763363	+	0.132218i
$581$		0			0
$582$	9.34941	+	18.0455i	0.387546	+	0.748008i
$583$	−2.39037	−	4.14024i	−0.0989990	−	0.171471i
$584$	3.95691	+	6.85356i	0.163738	+	0.283602i
$585$	4.45924	+	0.407575i	0.184367	+	0.0168512i
$586$	−10.3889	+	17.9941i	−0.429162	+	0.743330i
$587$	−1.13161	+	1.96001i	−0.0467066	+	0.0808982i	−0.888434	−	0.459005i	$-0.848206\pi$
$587$	−1.13161	+	1.96001i	−0.0467066	+	0.0808982i	0.841727	+	0.539903i	$0.181539\pi$
$588$		0			0
$589$	−21.1680	−	36.6640i	−0.872212	−	1.51072i
$590$	−5.13307			−0.211325
$591$	−8.81118	−	17.0066i	−0.362444	−	0.699558i
$592$	−1.00000			−0.0410997
$593$	−23.0979	+	40.0067i	−0.948515	+	1.64288i	−0.199960	+	0.979804i	$0.564081\pi$
$593$	−23.0979	+	40.0067i	−0.948515	+	1.64288i	−0.748555	+	0.663072i	$0.769252\pi$
$594$	−1.16372	−	2.85637i	−0.0477478	−	0.117198i
$595$		0			0
$596$	−9.02558	+	15.6328i	−0.369702	+	0.640343i
$597$	−5.24465	+	8.19731i	−0.214649	+	0.335493i
$598$	−5.60817	+	9.71363i	−0.229335	+	0.397220i
$599$	8.39037	−	14.5325i	0.342821	−	0.593784i	−0.642134	−	0.766592i	$-0.721951\pi$
$599$	8.39037	−	14.5325i	0.342821	−	0.593784i	0.984955	+	0.172808i	$0.0552842\pi$
$600$	−3.70321	−	7.14763i	−0.151183	−	0.291801i
$601$	5.69961	−	9.87202i	0.232492	−	0.402688i	−0.726049	−	0.687643i	$-0.758645\pi$
$601$	5.69961	−	9.87202i	0.232492	−	0.402688i	0.958541	+	0.284955i	$0.0919787\pi$
$602$		0			0
$603$	2.40623	+	5.21289i	0.0979891	+	0.212285i
$604$	−0.823832	+	1.42692i	−0.0335212	+	0.0580605i
$605$	6.32023			0.256954
$606$	1.51478	−	2.36758i	0.0615339	−	0.0961765i
$607$	14.4284			0.585631			0.292815	−	0.956169i	$-0.405408\pi$
$607$	14.4284			0.585631			0.292815	+	0.956169i	$0.405408\pi$
$608$	2.69076	+	4.66053i	0.109125	+	0.189009i
$609$		0			0
$610$	−1.97296	+	3.41726i	−0.0798827	+	0.138361i
$611$	−15.2915	+	26.4857i	−0.618629	+	1.07150i
$612$	−5.05408	+	7.15869i	−0.204299	+	0.289373i
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	0.999967	−	0.00809942i	$-0.00257815\pi$
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	−0.506998	+	0.861947i	$0.669245\pi$
$614$	11.3384	+	19.6387i	0.457581	+	0.792554i
$615$	−0.151457	+	0.236725i	−0.00610733	+	0.00954566i
$616$		0			0
$617$	24.4698	+	42.3830i	0.985119	+	1.70628i	0.641408	+	0.767200i	$0.278350\pi$
$617$	24.4698	+	42.3830i	0.985119	+	1.70628i	0.343710	+	0.939076i	$0.388316\pi$
$618$	−5.95691	+	9.31056i	−0.239622	+	0.374525i
$619$	44.6591			1.79500			0.897501	−	0.441012i	$-0.145380\pi$
$619$	44.6591			1.79500			0.897501	+	0.441012i	$0.145380\pi$
$620$	2.33482	+	4.04403i	0.0937687	+	0.162412i
$621$	22.9612	+	3.15897i	0.921400	+	0.126765i
$622$	−6.51459			−0.261211
$623$		0			0
$624$	−4.35087	−	0.198422i	−0.174174	−	0.00794323i
$625$	19.8391			0.793564
$626$	−0.133074	+	0.230492i	−0.00531873	+	0.00921230i
$627$	−5.52704	−	0.252061i	−0.220729	−	0.0100663i
$628$	−3.30039	−	5.71644i	−0.131700	−	0.228111i
$629$	−2.92101			−0.116468
$630$		0			0
$631$	33.2852			1.32506			0.662532	−	0.749034i	$-0.269482\pi$
$631$	33.2852			1.32506			0.662532	+	0.749034i	$0.269482\pi$
$632$	−4.62422	−	8.00938i	−0.183942	−	0.318596i
$633$	18.0387	−	28.1942i	0.716974	−	1.12062i
$634$	7.86186	−	13.6171i	0.312235	−	0.540806i
$635$	−7.32158			−0.290548
$636$	6.41741	+	12.3863i	0.254467	+	0.491151i
$637$		0			0
$638$	3.67684			0.145568
$639$	24.9341	−	35.3172i	0.986379	−	1.39713i
$640$	−0.296790	−	0.514055i	−0.0117316	−	0.0203198i
$641$	30.7879			1.21605			0.608025	−	0.793918i	$-0.291962\pi$
$641$	30.7879			1.21605			0.608025	+	0.793918i	$0.291962\pi$
$642$	−14.9071	−	28.7724i	−0.588336	−	1.13556i
$643$	13.7345	+	23.7889i	0.541637	+	0.938142i	0.998810	+	0.0487649i	$0.0155285\pi$
$643$	13.7345	+	23.7889i	0.541637	+	0.938142i	−0.457174	+	0.889378i	$0.651138\pi$
$644$		0			0
$645$	−11.4641	−	0.522821i	−0.451399	−	0.0205861i
$646$	7.85973	+	13.6134i	0.309237	+	0.535614i
$647$	6.63521	+	11.4925i	0.260857	+	0.451818i	0.966470	−	0.256780i	$-0.0826615\pi$
$647$	6.63521	+	11.4925i	0.260857	+	0.451818i	−0.705613	+	0.708598i	$0.749328\pi$
$648$	3.01245	+	8.48087i	0.118340	+	0.333160i
$649$	−2.56654	+	4.44537i	−0.100745	+	0.174496i
$650$	5.84348	−	10.1212i	0.229200	−	0.396986i
$651$		0			0
$652$	−2.99115	−	5.18082i	−0.117142	−	0.202896i
$653$	−17.1416			−0.670803			−0.335402	−	0.942075i	$-0.608872\pi$
$653$	−17.1416			−0.670803			−0.335402	+	0.942075i	$0.608872\pi$
$654$	−4.96050	−	0.226224i	−0.193971	−	0.00884606i
$655$	−0.704673			−0.0275338
$656$	0.136673	−	0.236725i	0.00533619	−	0.00924255i
$657$	23.6429	+	2.16096i	0.922397	+	0.0843072i
$658$		0			0
$659$	4.26089	−	7.38008i	0.165981	−	0.287487i	−0.771022	−	0.636808i	$-0.780254\pi$
$659$	4.26089	−	7.38008i	0.165981	−	0.287487i	0.937003	+	0.349321i	$0.113588\pi$
$660$	0.609631	+	0.0278023i	0.0237299	+	0.00108220i
$661$	17.1680	−	29.7358i	0.667757	−	1.15659i	−0.310773	−	0.950484i	$-0.600588\pi$
$661$	17.1680	−	29.7358i	0.667757	−	1.15659i	0.978530	−	0.206105i	$-0.0660789\pi$
$662$	−12.5811	+	21.7912i	−0.488979	+	0.846937i
$663$	−12.7089	−	0.579592i	−0.493575	−	0.0225095i
$664$	3.85087	−	6.66991i	0.149443	−	0.258843i
$665$		0			0
$666$	−1.73025	+	2.45076i	−0.0670459	+	0.0949650i
$667$	−13.8150	+	23.9282i	−0.534918	+	0.926505i
$668$	7.46050			0.288656
$669$	43.8178	+	1.99831i	1.69409	+	0.0772592i
$670$	−1.13600			−0.0438875
$671$	1.97296	+	3.41726i	0.0761652	+	0.131922i
$672$		0			0
$673$	−7.70155	+	13.3395i	−0.296873	+	0.514199i	−0.975419	−	0.220359i	$-0.929277\pi$
$673$	−7.70155	+	13.3395i	−0.296873	+	0.514199i	0.678546	+	0.734558i	$0.262610\pi$
$674$	9.36693	−	16.2240i	0.360800	−	0.624925i
$675$	−23.9246	−	3.29152i	−0.920859	−	0.126691i
$676$	3.33842	+	5.78231i	0.128401	+	0.222397i
$677$	−3.69076	−	6.39258i	−0.141847	−	0.245687i	0.786345	−	0.617788i	$-0.211971\pi$
$677$	−3.69076	−	6.39258i	−0.141847	−	0.245687i	−0.928192	+	0.372101i	$0.878638\pi$
$678$	−21.3171	−	0.972168i	−0.818679	−	0.0373359i
$679$		0			0
$680$	−0.866926	−	1.50156i	−0.0332451	−	0.0575822i
$681$	3.83823	+	7.40822i	0.147081	+	0.283884i
$682$	4.66964			0.178810
$683$	4.79893	+	8.31198i	0.183626	+	0.318049i	0.943113	−	0.332474i	$-0.107883\pi$
$683$	4.79893	+	8.31198i	0.183626	+	0.318049i	−0.759487	+	0.650523i	$0.774550\pi$
$684$	16.0775	+	1.46949i	0.614740	+	0.0561873i
$685$	−1.49688			−0.0571929
$686$		0			0
$687$	−7.40642	−	14.2953i	−0.282573	−	0.545398i
$688$	11.1623			0.425557
$689$	−10.1264	+	17.5394i	−0.385783	+	0.668197i
$690$	−2.47150	+	3.86291i	−0.0940882	+	0.147058i
$691$	−7.07227	−	12.2495i	−0.269042	−	0.465994i	0.699573	−	0.714561i	$-0.253374\pi$
$691$	−7.07227	−	12.2495i	−0.269042	−	0.465994i	−0.968615	+	0.248567i	$0.920040\pi$
$692$	25.6591			0.975414
$693$		0			0
$694$	−22.5438			−0.855750
$695$	1.45837	+	2.52597i	0.0553191	+	0.0958155i
$696$	−10.7178	−	0.488786i	−0.406257	−	0.0185274i
$697$	0.399223	−	0.691475i	0.0151217	−	0.0261915i
$698$	−3.79086			−0.143486
$699$	−0.336285	−	0.0153363i	−0.0127195	−	0.000580072i
$700$		0			0
$701$	37.3753			1.41164			0.705822	−	0.708389i	$-0.250578\pi$
$701$	37.3753			1.41164			0.705822	+	0.708389i	$0.250578\pi$
$702$	−8.01439	+	10.3196i	−0.302484	+	0.389489i
$703$	2.69076	+	4.66053i	0.101484	+	0.175775i
$704$	−0.593579			−0.0223714
$705$	−6.73891	+	10.5328i	−0.253802	+	0.396689i
$706$	−3.41741	−	5.91913i	−0.128616	−	0.222769i
$707$		0			0
$708$	8.07227	−	12.6168i	0.303375	−	0.474170i
$709$	5.24338	+	9.08180i	0.196919	+	0.341074i	0.947528	−	0.319673i	$-0.103573\pi$
$709$	5.24338	+	9.08180i	0.196919	+	0.341074i	−0.750609	+	0.660747i	$0.770240\pi$
$710$	4.27694	+	7.40789i	0.160511	+	0.278013i
$711$	−27.6301	−	2.52540i	−1.03621	−	0.0947099i
$712$	−6.21780	+	10.7695i	−0.233022	+	0.403606i
$713$	−17.5452	+	30.3892i	−0.657074	+	1.13809i
$714$		0			0
$715$	0.442991	+	0.767282i	0.0165669	+	0.0286947i
$716$	−15.0364			−0.561936
$717$	−12.7463	+	19.9223i	−0.476019	+	0.744011i
$718$	−12.6447			−0.471897
$719$	−1.11995	+	1.93981i	−0.0417670	+	0.0723426i	−0.886153	−	0.463392i	$-0.846632\pi$
$719$	−1.11995	+	1.93981i	−0.0417670	+	0.0723426i	0.844386	+	0.535735i	$0.179965\pi$
$720$	−1.77335	−	0.162084i	−0.0660887	−	0.00604052i
$721$		0			0
$722$	4.98035	−	8.62622i	0.185349	−	0.321035i
$723$	−10.3583	−	19.9927i	−0.385228	−	0.743535i
$724$	−0.0430937	+	0.0746406i	−0.00160157	+	0.00277399i
$725$	14.3946	−	24.9322i	0.534604	−	0.925961i
$726$	−9.93920	+	15.5348i	−0.368878	+	0.576551i
$727$	−0.185023	+	0.320469i	−0.00686211	+	0.0118855i	−0.869436	−	0.494045i	$-0.835518\pi$
$727$	−0.185023	+	0.320469i	−0.00686211	+	0.0118855i	0.862574	+	0.505931i	$0.168851\pi$
$728$		0			0
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$	−2.34874	+	4.06813i	−0.0869307	+	0.150568i
$731$	32.6050			1.20594
$732$	−5.29679	−	10.2234i	−0.195775	−	0.377868i
$733$	−14.0191			−0.517806			−0.258903	−	0.965903i	$-0.583361\pi$
$733$	−14.0191			−0.517806			−0.258903	+	0.965903i	$0.583361\pi$
$734$	−3.27188	−	5.66707i	−0.120767	−	0.209175i
$735$		0			0
$736$	2.23025	−	3.86291i	0.0822082	−	0.142389i
$737$	−0.568000	+	0.983804i	−0.0209225	+	0.0362389i
$738$	−0.343677	−	0.744547i	−0.0126509	−	0.0274071i
$739$	13.3872	+	23.1874i	0.492458	+	0.852962i	0.999962	−	0.00868705i	$-0.00276521\pi$
$739$	13.3872	+	23.1874i	0.492458	+	0.852962i	−0.507504	+	0.861649i	$0.669432\pi$
$740$	−0.296790	−	0.514055i	−0.0109102	−	0.0188970i
$741$	10.7824	+	20.8113i	0.396101	+	0.764521i
$742$		0			0
$743$	−5.04669	−	8.74113i	−0.185145	−	0.320681i	0.758480	−	0.651696i	$-0.225942\pi$
$743$	−5.04669	−	8.74113i	−0.185145	−	0.320681i	−0.943625	+	0.331015i	$0.892609\pi$
$744$	−13.6118	−	0.620765i	−0.499032	−	0.0227584i
$745$	−10.7148			−0.392560
$746$	4.71420	+	8.16524i	0.172599	+	0.298951i
$747$	−9.68337	−	20.9782i	−0.354296	−	0.767552i
$748$	−1.73385			−0.0633959
$749$		0			0
$750$	5.34562	−	8.35512i	0.195194	−	0.305086i
$751$	11.5146			0.420173			0.210087	−	0.977683i	$-0.432625\pi$
$751$	11.5146			0.420173			0.210087	+	0.977683i	$0.432625\pi$
$752$	6.08113	−	10.5328i	0.221756	−	0.384092i
$753$	−15.5723	−	30.0563i	−0.567485	−	1.09531i
$754$	−7.78813	−	13.4894i	−0.283627	−	0.491256i
$755$	−0.978019			−0.0355938
$756$		0			0
$757$	−15.2484			−0.554214			−0.277107	−	0.960839i	$-0.589376\pi$
$757$	−15.2484			−0.554214			−0.277107	+	0.960839i	$0.589376\pi$
$758$	−3.63881	−	6.30260i	−0.132168	−	0.228921i
$759$	2.10963	+	4.07183i	0.0765748	+	0.147798i
$760$	−1.59718	+	2.76639i	−0.0579357	+	0.100348i
$761$	1.70175			0.0616883			0.0308442	−	0.999524i	$-0.490180\pi$
$761$	1.70175			0.0616883			0.0308442	+	0.999524i	$0.490180\pi$
$762$	11.5139	−	17.9961i	0.417105	−	0.651929i
$763$		0			0
$764$	3.98229			0.144074
$765$	−5.17996	−	0.473449i	−0.187282	−	0.0171176i
$766$	12.0416	+	20.8567i	0.435082	+	0.753584i
$767$	21.7453			0.785178
$768$	1.73025	+	0.0789082i	0.0624351	+	0.00284736i
$769$	−24.1211	−	41.7790i	−0.869829	−	1.50659i	−0.862171	−	0.506618i	$-0.830896\pi$
$769$	−24.1211	−	41.7790i	−0.869829	−	1.50659i	−0.00765823	−	0.999971i	$-0.502438\pi$
$770$		0			0
$771$	6.63521	+	12.8067i	0.238961	+	0.461223i
$772$	−3.39037	−	5.87229i	−0.122022	−	0.211348i
$773$	−3.10243	−	5.37357i	−0.111587	−	0.193274i	0.804823	−	0.593514i	$-0.202260\pi$
$773$	−3.10243	−	5.37357i	−0.111587	−	0.193274i	−0.916410	+	0.400240i	$0.868927\pi$
$774$	19.3135	−	27.3560i	0.694210	−	0.983291i
$775$	18.2814	−	31.6643i	0.656688	−	1.13742i
$776$	5.86693	−	10.1618i	0.210610	−	0.364788i
$777$		0			0
$778$	−8.14913	−	14.1147i	−0.292160	−	0.506037i
$779$	−1.47102			−0.0527046
$780$	−1.18929	−	2.29548i	−0.0425836	−	0.0821913i
$781$	8.55389			0.306082
$782$	6.51459	−	11.2836i	0.232961	−	0.403501i
$783$	−19.7424	+	25.4210i	−0.705536	+	0.908474i
$784$		0			0
$785$	1.95904	−	3.39316i	0.0699212	−	0.121107i
$786$	1.10817	−	1.73205i	0.0395271	−	0.0617802i
$787$	3.04883	−	5.28073i	0.108679	−	0.188238i	−0.806556	−	0.591157i	$-0.798671\pi$
$787$	3.04883	−	5.28073i	0.108679	−	0.188238i	0.915235	+	0.402920i	$0.132005\pi$
$788$	−5.52918	+	9.57682i	−0.196969	+	0.341160i
$789$	13.6175	+	26.2834i	0.484796	+	0.935712i
$790$	2.74484	−	4.75420i	0.0976571	−	0.169147i
$791$		0			0
$792$	−1.02704	+	1.45472i	−0.0364944	+	0.0516913i
$793$	8.35807	−	14.4766i	0.296804	−	0.514079i
$794$	12.1724			0.431981
$795$	−4.46264	+	6.97504i	−0.158274	+	0.247379i
$796$	5.61849			0.199142
$797$	6.22860	+	10.7882i	0.220628	+	0.382139i	0.954999	−	0.296609i	$-0.0958559\pi$
$797$	6.22860	+	10.7882i	0.220628	+	0.382139i	−0.734371	+	0.678749i	$0.762523\pi$
$798$		0			0
$799$	17.7630	−	30.7665i	0.628411	−	1.08844i
$800$	−2.32383	+	4.02499i	−0.0821599	+	0.142305i
$801$	15.6352	+	33.8724i	0.552443	+	1.19682i
$802$	−16.6804	−	28.8914i	−0.589007	−	1.02019i
$803$	2.34874	+	4.06813i	0.0828852	+	0.143561i
$804$	1.78647	−	2.79223i	0.0630040	−	0.0984744i
$805$		0			0
$806$	−9.89104	−	17.1318i	−0.348397	−	0.603442i
$807$	9.34806	−	14.6109i	0.329067	−	0.514328i
$808$	−1.62276			−0.0570884
$809$	−2.81644	−	4.87822i	−0.0990208	−	0.171509i	0.812259	−	0.583297i	$-0.198238\pi$
$809$	−2.81644	−	4.87822i	−0.0990208	−	0.171509i	−0.911280	+	0.411788i	$0.864904\pi$
$810$	−3.46557	+	4.06560i	−0.121768	+	0.142851i
$811$	45.6414			1.60269			0.801344	−	0.598204i	$-0.204119\pi$
$811$	45.6414			1.60269			0.801344	+	0.598204i	$0.204119\pi$
$812$		0			0
$813$	17.6644	+	0.805585i	0.619517	+	0.0282531i
$814$	−0.593579			−0.0208049
$815$	1.77548	−	3.07523i	0.0621924	−	0.107720i
$816$	5.05408	+	0.230492i	0.176928	+	0.00806883i
$817$	−30.0349	−	52.0220i	−1.05079	−	1.82002i
$818$	−5.78074			−0.202119
$819$		0			0
$820$	0.162253			0.00566611
$821$	−16.3473	−	28.3143i	−0.570524	−	0.988176i	−0.996512	−	0.0834476i	$-0.973407\pi$
$821$	−16.3473	−	28.3143i	−0.570524	−	0.988176i	0.425988	−	0.904729i	$-0.359926\pi$
$822$	2.35399	−	3.67926i	0.0821050	−	0.128329i
$823$	5.21994	−	9.04119i	0.181956	−	0.315156i	−0.760591	−	0.649231i	$-0.775091\pi$
$823$	5.21994	−	9.04119i	0.181956	−	0.315156i	0.942546	+	0.334075i	$0.108424\pi$
$824$	6.38151			0.222311
$825$	−2.19815	−	4.24268i	−0.0765297	−	0.147711i
$826$		0			0
$827$	16.7060			0.580925			0.290463	−	0.956886i	$-0.406191\pi$
$827$	16.7060			0.580925			0.290463	+	0.956886i	$0.406191\pi$
$828$	−5.60817	−	12.1496i	−0.194897	−	0.422229i
$829$	13.1046	+	22.6978i	0.455141	+	0.788327i	0.998696	−	0.0510466i	$-0.0162557\pi$
$829$	13.1046	+	22.6978i	0.455141	+	0.788327i	−0.543556	+	0.839373i	$0.682922\pi$
$830$	4.57160			0.158682
$831$	−15.4117	−	29.7463i	−0.534625	−	1.03189i
$832$	1.25729	+	2.17770i	0.0435888	+	0.0754981i
$833$		0			0
$834$	−8.50214	−	0.387740i	−0.294405	−	0.0134263i
$835$	2.21420	+	3.83511i	0.0766256	+	0.132719i
$836$	1.59718	+	2.76639i	0.0552396	+	0.0956777i
$837$	−25.0731	+	32.2851i	−0.866655	+	1.11594i
$838$	15.4356	−	26.7352i	0.533214	−	0.923554i
$839$	−11.1886	+	19.3793i	−0.386274	+	0.669046i	−0.991945	−	0.126669i	$-0.959571\pi$
$839$	−11.1886	+	19.3793i	−0.386274	+	0.669046i	0.605671	+	0.795715i	$0.292905\pi$
$840$		0			0
$841$	−4.68502	−	8.11470i	−0.161553	−	0.279817i
$842$	−3.73385			−0.128677
$843$	22.1519	+	1.01024i	0.762953	+	0.0347945i
$844$	−19.3245			−0.665177
$845$	−1.98162	+	3.43226i	−0.0681697	+	0.118073i
$846$	−15.2915	−	33.1278i	−0.525734	−	1.13896i
$847$		0			0
$848$	4.02704	−	6.97504i	0.138289	−	0.239524i
$849$	28.2937	+	1.29033i	0.971036	+	0.0442842i
$850$	−6.78794	+	11.7570i	−0.232824	+	0.403263i
$851$	2.23025	−	3.86291i	0.0764521	−	0.132419i
$852$	−24.9341	−	1.13712i	−0.854229	−	0.0389572i
$853$	−4.96264	+	8.59555i	−0.169918	+	0.294306i	−0.938391	−	0.345576i	$-0.887683\pi$
$853$	−4.96264	+	8.59555i	−0.169918	+	0.294306i	0.768473	+	0.639882i	$0.221017\pi$
$854$		0			0
$855$	4.01625	+	8.70086i	0.137353	+	0.297563i
$856$	−9.35447	+	16.2024i	−0.319729	+	0.553787i
$857$	−7.79552			−0.266290			−0.133145	−	0.991097i	$-0.542508\pi$
$857$	−7.79552			−0.266290			−0.133145	+	0.991097i	$0.542508\pi$
$858$	−2.58259	−	0.117779i	−0.0881681	−	0.00402091i
$859$	−16.3422			−0.557589			−0.278795	−	0.960351i	$-0.589935\pi$
$859$	−16.3422			−0.557589			−0.278795	+	0.960351i	$0.589935\pi$
$860$	3.31284	+	5.73801i	0.112967	+	0.195664i
$861$		0			0
$862$	14.0979	−	24.4182i	0.480175	−	0.831687i
$863$	0.730252	−	1.26483i	0.0248581	−	0.0430555i	−0.853329	−	0.521373i	$-0.825420\pi$
$863$	0.730252	−	1.26483i	0.0248581	−	0.0430555i	0.878187	+	0.478318i	$0.158753\pi$
$864$	3.18716	−	4.10390i	0.108429	−	0.139618i
$865$	7.61537	+	13.1902i	0.258930	+	0.448480i
$866$	−6.27188	−	10.8632i	−0.213127	−	0.369147i
$867$	−14.6513	−	0.668172i	−0.497583	−	0.0226923i
$868$		0			0
$869$	−2.74484	−	4.75420i	−0.0931124	−	0.161275i
$870$	−2.92967	−	5.65460i	−0.0993251	−	0.191709i
$871$	4.81245			0.163064
$872$	1.43346	+	2.48283i	0.0485432	+	0.0840792i
$873$	−14.7529	−	31.9609i	−0.499310	−	1.08171i
$874$	−24.0043			−0.811957
$875$		0			0
$876$	−6.30564	−	12.1706i	−0.213048	−	0.411207i
$877$	−2.40935			−0.0813578			−0.0406789	−	0.999172i	$-0.512952\pi$
$877$	−2.40935			−0.0813578			−0.0406789	+	0.999172i	$0.512952\pi$
$878$	−13.0203	+	22.5519i	−0.439415	+	0.761088i
$879$	19.3953	−	30.3146i	0.654188	−	1.02249i
$880$	−0.176168	−	0.305132i	−0.00593863	−	0.0102860i
$881$	18.9607			0.638802			0.319401	−	0.947620i	$-0.396518\pi$
$881$	18.9607			0.638802			0.319401	+	0.947620i	$0.396518\pi$
$882$		0			0
$883$	3.64008			0.122498			0.0612492	−	0.998123i	$-0.480492\pi$
$883$	3.64008			0.122498			0.0612492	+	0.998123i	$0.480492\pi$
$884$	3.67257	+	6.36108i	0.123522	+	0.213946i
$885$	8.88151	+	0.405042i	0.298549	+	0.0136153i
$886$	−11.7865	+	20.4148i	−0.395974	+	0.685848i
$887$	24.4572			0.821192			0.410596	−	0.911817i	$-0.365321\pi$
$887$	24.4572			0.821192			0.410596	+	0.911817i	$0.365321\pi$
$888$	1.73025	+	0.0789082i	0.0580635	+	0.00264799i
$889$		0			0
$890$	−7.38151			−0.247429
$891$	1.78813	+	5.03407i	0.0599046	+	0.168648i
$892$	−12.6623	−	21.9317i	−0.423964	−	0.734326i
$893$	−65.4513			−2.19025
$894$	16.8501	−	26.3364i	0.563551	−	0.880822i
$895$	−4.46264	−	7.72952i	−0.149170	−	0.258369i
$896$		0			0
$897$	10.4700	−	16.3645i	0.349584	−	0.546395i
$898$	6.84348	+	11.8533i	0.228370	+	0.395548i
$899$	−24.3653	−	42.2019i	−0.812627	−	1.40751i
$900$	5.84348	+	12.6594i	0.194783	+	0.421980i
$901$	11.7630	−	20.3742i	0.391883	−	0.678762i
$902$	0.0811263	−	0.140515i	0.00270121	−	0.00467863i
$903$		0			0
$904$	6.16012	+	10.6696i	0.204882	+	0.354867i
$905$	−0.0511591			−0.00170059
$906$	1.53803	−	2.40392i	0.0510977	−	0.0798650i
$907$	10.0368			0.333265			0.166633	−	0.986019i	$-0.446711\pi$
$907$	10.0368			0.333265			0.166633	+	0.986019i	$0.446711\pi$
$908$	2.40856	−	4.17174i	0.0799308	−	0.138444i
$909$	−2.80778	+	3.97699i	−0.0931282	+	0.131908i
$910$		0			0
$911$	11.4459	−	19.8249i	0.379220	−	0.656828i	−0.611729	−	0.791067i	$-0.709526\pi$
$911$	11.4459	−	19.8249i	0.379220	−	0.656828i	0.990949	+	0.134239i	$0.0428590\pi$
$912$	−4.28794	−	8.27621i	−0.141988	−	0.274053i
$913$	2.28580	−	3.95912i	0.0756489	−	0.131028i
$914$	−11.1762	+	19.3577i	−0.369675	+	0.640296i
$915$	3.68337	−	5.75705i	0.121768	−	0.190322i
$916$	−4.64766	+	8.04999i	−0.153563	+	0.265979i
$917$		0			0
$918$	9.30972	−	11.9875i	0.307267	−	0.395648i
$919$	10.8910	−	18.8638i	0.359262	−	0.622261i	−0.628575	−	0.777749i	$-0.716362\pi$
$919$	10.8910	−	18.8638i	0.359262	−	0.622261i	0.987838	+	0.155488i	$0.0496950\pi$
$920$	2.64766			0.0872909
$921$	−18.0687	−	34.8746i	−0.595383	−	1.14916i
$922$	7.97509			0.262646
$923$	−18.1185	−	31.3821i	−0.596377	−	1.03296i
$924$		0			0
$925$	−2.32383	+	4.02499i	−0.0764071	+	0.132341i
$926$	14.3676	−	24.8854i	0.472149	−	0.817785i
$927$	11.0416	−	15.6396i	0.362655	−	0.513671i
$928$	3.09718	+	5.36447i	0.101670	+	0.176097i
$929$	−16.4189	−	28.4383i	−0.538686	−	0.933031i	−0.998975	−	0.0452622i	$-0.985588\pi$
$929$	−16.4189	−	28.4383i	−0.538686	−	0.933031i	0.460289	−	0.887769i	$-0.347746\pi$
$930$	−3.72072	−	7.18143i	−0.122007	−	0.235488i
$931$		0			0
$932$	0.0971780	+	0.168317i	0.00318317	+	0.00551341i
$933$	11.2719	+	0.514055i	0.369025	+	0.0168294i
$934$	−33.5657			−1.09830
$935$	−0.514589	−	0.891294i	−0.0168289	−	0.0291484i
$936$	7.51245	+	0.686640i	0.245552	+	0.0224435i
$937$	8.78074			0.286854			0.143427	−	0.989661i	$-0.454188\pi$
$937$	8.78074			0.286854			0.143427	+	0.989661i	$0.454188\pi$
$938$		0			0
$939$	0.248440	−	0.388308i	0.00810754	−	0.0126720i
$940$	7.21926			0.235466
$941$	2.13307	−	3.69459i	0.0695362	−	0.120440i	−0.829161	−	0.559010i	$-0.811181\pi$
$941$	2.13307	−	3.69459i	0.0695362	−	0.120440i	0.898697	+	0.438570i	$0.144515\pi$
$942$	5.25943	+	10.1513i	0.171362	+	0.330748i
$943$	0.609631	+	1.05591i	0.0198523	+	0.0343852i
$944$	−8.64766			−0.281457
$945$		0			0
$946$	6.62568			0.215420
$947$	11.5292	+	19.9691i	0.374648	+	0.648909i	0.990274	−	0.139129i	$-0.0444302\pi$
$947$	11.5292	+	19.9691i	0.374648	+	0.648909i	−0.615626	+	0.788038i	$0.711097\pi$
$948$	7.36906	+	14.2231i	0.239336	+	0.461946i
$949$	9.94999	−	17.2339i	0.322990	−	0.559436i
$950$	25.0115			0.811479
$951$	−14.6775	+	22.9407i	−0.475951	+	0.743904i
$952$		0			0
$953$	−36.5552			−1.18414			−0.592070	−	0.805886i	$-0.701689\pi$
$953$	−36.5552			−1.18414			−0.592070	+	0.805886i	$0.701689\pi$
$954$	−10.1264	−	21.9379i	−0.327853	−	0.710266i
$955$	1.18190	+	2.04712i	0.0382455	+	0.0662431i
$956$	13.6549			0.441630
$957$	−6.36186	−	0.290133i	−0.205650	−	0.00937867i
$958$	−0.183560	−	0.317935i	−0.00593056	−	0.0102720i
$959$		0			0
$960$	0.472958	+	0.912864i	0.0152647	+	0.0294625i
$961$	−15.4443	−	26.7502i	−0.498202	−	0.862911i
$962$	1.25729	+	2.17770i	0.0405368	+	0.0702118i
$963$	23.5227	+	50.9599i	0.758007	+	1.64216i
$964$	−6.50000	+	11.2583i	−0.209351	+	0.362606i
$965$	2.01245	−	3.48567i	0.0647832	−	0.112208i
$966$		0			0
$967$	26.7719	+	46.3703i	0.860926	+	1.49117i	0.871037	+	0.491218i	$0.163448\pi$
$967$	26.7719	+	46.3703i	0.860926	+	1.49117i	−0.0101108	+	0.999949i	$0.503218\pi$
$968$	10.6477			0.342229
$969$	−12.5251	−	24.1749i	−0.402364	−	0.776610i
$970$	6.96497			0.223632
$971$	15.9897	−	27.6949i	0.513133	−	0.888773i	−0.486751	−	0.873541i	$-0.661818\pi$
$971$	15.9897	−	27.6949i	0.513133	−	0.888773i	0.999884	−	0.0152321i	$-0.00484870\pi$
$972$	−4.54309	−	14.9118i	−0.145720	−	0.478295i
$973$		0			0
$974$	14.9538	−	25.9007i	0.479150	−	0.829913i
$975$	−10.9093	+	17.0511i	−0.349379	+	0.546074i
$976$	−3.32383	+	5.75705i	−0.106393	+	0.184279i
$977$	13.7104	−	23.7471i	0.438635	−	0.759738i	−0.558950	−	0.829202i	$-0.688796\pi$
$977$	13.7104	−	23.7471i	0.438635	−	0.759738i	0.997584	+	0.0694638i	$0.0221288\pi$
$978$	4.76663	+	9.20015i	0.152420	+	0.294188i
$979$	−3.69076	+	6.39258i	−0.117957	+	0.204308i
$980$		0			0
$981$	8.56507	+	0.782849i	0.273462	+	0.0249945i
$982$	0.255158	−	0.441947i	0.00814243	−	0.0141031i
$983$	59.1564			1.88680			0.943398	−	0.331662i	$-0.107610\pi$
$983$	59.1564			1.88680			0.943398	+	0.331662i	$0.107610\pi$
$984$	−0.255158	+	0.398809i	−0.00813416	+	0.0127136i
$985$	−6.56401			−0.209147
$986$	9.04689	+	15.6697i	0.288112	+	0.499024i
$987$		0			0
$988$	6.76615	−	11.7193i	0.215260	−	0.372841i
$989$	−24.8946	+	43.1188i	−0.791604	+	1.37110i
$990$	−1.05262	−	0.0962098i	−0.0334545	−	0.00305775i
$991$	6.41887	+	11.1178i	0.203902	+	0.353169i	0.949782	−	0.312911i	$-0.101304\pi$
$991$	6.41887	+	11.1178i	0.203902	+	0.353169i	−0.745880	+	0.666080i	$0.767971\pi$
$992$	3.93346	+	6.81296i	0.124888	+	0.216312i
$993$	23.4880	−	36.7114i	0.745370	−	1.16500i
$994$		0			0
$995$	1.66751	+	2.88821i	0.0528636	+	0.0915624i
$996$	−7.18929	+	11.2368i	−0.227802	+	0.356050i
$997$	5.78074			0.183078			0.0915389	−	0.995802i	$-0.470821\pi$
$997$	5.78074			0.183078			0.0915389	+	0.995802i	$0.470821\pi$
$998$	−9.50953	−	16.4710i	−0.301019	−	0.521380i
$999$	3.18716	−	4.10390i	0.100837	−	0.129842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.p.79.2		6
3.2	odd	2		2646.2.h.o.667.2		6
7.2	even	3		882.2.f.o.295.3		6
7.3	odd	6		126.2.e.c.25.2	✓	6
7.4	even	3		882.2.e.o.655.2		6
7.5	odd	6		882.2.f.n.295.1		6
7.6	odd	2		126.2.h.d.79.2	yes	6
9.4	even	3		882.2.e.o.373.2		6
9.5	odd	6		2646.2.e.p.1549.2		6
21.2	odd	6		2646.2.f.m.883.2		6
21.5	even	6		2646.2.f.l.883.2		6
21.11	odd	6		2646.2.e.p.2125.2		6
21.17	even	6		378.2.e.d.235.2		6
21.20	even	2		378.2.h.c.289.2		6
28.3	even	6		1008.2.q.g.529.2		6
28.27	even	2		1008.2.t.h.961.2		6
63.2	odd	6		7938.2.a.bz.1.2		3
63.4	even	3	inner	882.2.h.p.67.2		6
63.5	even	6		2646.2.f.l.1765.2		6
63.13	odd	6		126.2.e.c.121.2	yes	6
63.16	even	3		7938.2.a.bw.1.2		3
63.20	even	6		1134.2.g.l.163.2		6
63.23	odd	6		2646.2.f.m.1765.2		6
63.31	odd	6		126.2.h.d.67.2	yes	6
63.32	odd	6		2646.2.h.o.361.2		6
63.34	odd	6		1134.2.g.m.163.2		6
63.38	even	6		1134.2.g.l.487.2		6
63.40	odd	6		882.2.f.n.589.1		6
63.41	even	6		378.2.e.d.37.2		6
63.47	even	6		7938.2.a.ca.1.2		3
63.52	odd	6		1134.2.g.m.487.2		6
63.58	even	3		882.2.f.o.589.3		6
63.59	even	6		378.2.h.c.361.2		6
63.61	odd	6		7938.2.a.bv.1.2		3
84.59	odd	6		3024.2.q.g.2881.2		6
84.83	odd	2		3024.2.t.h.289.2		6
252.31	even	6		1008.2.t.h.193.2		6
252.59	odd	6		3024.2.t.h.1873.2		6
252.139	even	6		1008.2.q.g.625.2		6
252.167	odd	6		3024.2.q.g.2305.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	7.3	odd	6
126.2.e.c.121.2	yes	6	63.13	odd	6
126.2.h.d.67.2	yes	6	63.31	odd	6
126.2.h.d.79.2	yes	6	7.6	odd	2
378.2.e.d.37.2		6	63.41	even	6
378.2.e.d.235.2		6	21.17	even	6
378.2.h.c.289.2		6	21.20	even	2
378.2.h.c.361.2		6	63.59	even	6
882.2.e.o.373.2		6	9.4	even	3
882.2.e.o.655.2		6	7.4	even	3
882.2.f.n.295.1		6	7.5	odd	6
882.2.f.n.589.1		6	63.40	odd	6
882.2.f.o.295.3		6	7.2	even	3
882.2.f.o.589.3		6	63.58	even	3
882.2.h.p.67.2		6	63.4	even	3	inner
882.2.h.p.79.2		6	1.1	even	1	trivial
1008.2.q.g.529.2		6	28.3	even	6
1008.2.q.g.625.2		6	252.139	even	6
1008.2.t.h.193.2		6	252.31	even	6
1008.2.t.h.961.2		6	28.27	even	2
1134.2.g.l.163.2		6	63.20	even	6
1134.2.g.l.487.2		6	63.38	even	6
1134.2.g.m.163.2		6	63.34	odd	6
1134.2.g.m.487.2		6	63.52	odd	6
2646.2.e.p.1549.2		6	9.5	odd	6
2646.2.e.p.2125.2		6	21.11	odd	6
2646.2.f.l.883.2		6	21.5	even	6
2646.2.f.l.1765.2		6	63.5	even	6
2646.2.f.m.883.2		6	21.2	odd	6
2646.2.f.m.1765.2		6	63.23	odd	6
2646.2.h.o.361.2		6	63.32	odd	6
2646.2.h.o.667.2		6	3.2	odd	2
3024.2.q.g.2305.2		6	252.167	odd	6
3024.2.q.g.2881.2		6	84.59	odd	6
3024.2.t.h.289.2		6	84.83	odd	2
3024.2.t.h.1873.2		6	252.59	odd	6
7938.2.a.bv.1.2		3	63.61	odd	6
7938.2.a.bw.1.2		3	63.16	even	3
7938.2.a.bz.1.2		3	63.2	odd	6
7938.2.a.ca.1.2		3	63.47	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.796790 - 1.53790i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.796790 - 1.53790i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +(-0.296790 - 0.514055i) q^{10} -0.593579 q^{11} +(1.73025 + 0.0789082i) q^{12} +(1.25729 + 2.17770i) q^{13} +(0.472958 + 0.912864i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.46050 - 2.52967i) q^{17} +(-2.98755 - 0.273062i) q^{18} +(-2.69076 + 4.66053i) q^{19} +(0.296790 - 0.514055i) q^{20} +(-0.296790 - 0.514055i) q^{22} +4.46050 q^{23} +(0.796790 + 1.53790i) q^{24} -4.64766 q^{25} +(-1.25729 + 2.17770i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-3.09718 + 5.36447i) q^{29} +(-0.554084 + 0.866025i) q^{30} +(-3.93346 + 6.81296i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.472958 + 0.912864i) q^{33} +(1.46050 - 2.52967i) q^{34} +(-1.25729 - 2.72382i) q^{36} +(0.500000 - 0.866025i) q^{37} -5.38151 q^{38} +(2.34728 - 3.66876i) q^{39} +0.593579 q^{40} +(0.136673 + 0.236725i) q^{41} +(-5.58113 + 9.66679i) q^{43} +(0.296790 - 0.514055i) q^{44} +(1.02704 - 1.45472i) q^{45} +(2.23025 + 3.86291i) q^{46} +(6.08113 + 10.5328i) q^{47} +(-0.933463 + 1.45899i) q^{48} +(-2.32383 - 4.02499i) q^{50} +(-2.72665 + 4.26172i) q^{51} -2.51459 q^{52} +(4.02704 + 6.97504i) q^{53} +(1.96050 + 4.81211i) q^{54} +0.352336 q^{55} +(9.31138 + 0.424646i) q^{57} -6.19436 q^{58} +(4.32383 - 7.48910i) q^{59} +(-1.02704 - 0.0468383i) q^{60} +(-3.32383 - 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 - 1.29264i) q^{65} +(-0.554084 + 0.866025i) q^{66} +(0.956906 - 1.65741i) q^{67} +2.92101 q^{68} +(-3.55408 - 6.85980i) q^{69} -14.4107 q^{71} +(1.73025 - 2.45076i) q^{72} +(-3.95691 - 6.85356i) q^{73} +1.00000 q^{74} +(3.70321 + 7.14763i) q^{75} +(-2.69076 - 4.66053i) q^{76} +(4.35087 + 0.198422i) q^{78} +(4.62422 + 8.00938i) q^{79} +(0.296790 + 0.514055i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(-0.136673 + 0.236725i) q^{82} +(-3.85087 + 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} -11.1623 q^{86} +(10.7178 + 0.488786i) q^{87} +0.593579 q^{88} +(6.21780 - 10.7695i) q^{89} +(1.77335 + 0.162084i) q^{90} +(-2.23025 + 3.86291i) q^{92} +(13.6118 + 0.620765i) q^{93} +(-6.08113 + 10.5328i) q^{94} +(1.59718 - 2.76639i) q^{95} +(-1.73025 - 0.0789082i) q^{96} +(-5.86693 + 10.1618i) q^{97} +(1.02704 - 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

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