LMFDB - Embedded newform 882.2.h.p.67.2

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			67.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.p.79.2

$q$-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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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
$3$	−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	−0.637310	−	0.770608i	$-0.719953\pi$
$13$	1.25729	−	2.17770i	0.348711	−	0.603985i	0.986021	+	0.166623i	$0.0532862\pi$
$14$		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	−0.986985	−	0.160813i	$-0.948588\pi$
$17$	−1.46050	+	2.52967i	−0.354224	+	0.613535i	0.632760	+	0.774348i	$0.281922\pi$
$18$	−2.98755	+	0.273062i	−0.704172	+	0.0643614i
$19$	−2.69076	−	4.66053i	−0.617302	−	1.06920i	−0.989976	−	0.141236i	$-0.954892\pi$
$19$	−2.69076	−	4.66053i	−0.617302	−	1.06920i	0.372674	−	0.927962i	$-0.378441\pi$
$20$	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	−0.996027	−	0.0890480i	$-0.971618\pi$
$29$	−3.09718	−	5.36447i	−0.575132	−	0.996157i	0.420896	−	0.907109i	$-0.361716\pi$
$30$	−0.554084	−	0.866025i	−0.101161	−	0.158114i
$31$	−3.93346	−	6.81296i	−0.706471	−	1.22364i	−0.966158	−	0.257951i	$-0.916953\pi$
$31$	−3.93346	−	6.81296i	−0.706471	−	1.22364i	0.259687	−	0.965693i	$-0.416380\pi$
$32$	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	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−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	−0.855156	−	0.518371i	$-0.826539\pi$
$41$	0.136673	−	0.236725i	0.0213448	−	0.0369702i	0.876500	+	0.481401i	$0.159872\pi$
$42$		0			0
$43$	−5.58113	−	9.66679i	−0.851114	−	1.47417i	−0.880204	−	0.474596i	$-0.842594\pi$
$43$	−5.58113	−	9.66679i	−0.851114	−	1.47417i	0.0290902	−	0.999577i	$-0.490739\pi$
$44$	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	0.0436467	−	0.999047i	$-0.486102\pi$
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.843377	−	0.537323i	$-0.180564\pi$
$48$	−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	−0.444888	−	0.895586i	$-0.646756\pi$
$53$	4.02704	−	6.97504i	0.553157	−	0.958096i	0.998044	−	0.0625092i	$-0.0199103\pi$
$54$	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	0.997240	+	0.0742412i	$0.0236535\pi$
$59$	4.32383	+	7.48910i	0.562915	+	0.974997i	−0.434325	+	0.900756i	$0.643013\pi$
$60$	−1.02704	+	0.0468383i	−0.132591	+	0.00604680i
$61$	−3.32383	+	5.75705i	−0.425573	+	0.737114i	−0.996474	−	0.0839050i	$-0.973261\pi$
$61$	−3.32383	+	5.75705i	−0.425573	+	0.737114i	0.570901	+	0.821019i	$0.306594\pi$
$62$	−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	0.918540	−	0.395329i	$-0.129369\pi$
$67$	0.956906	+	1.65741i	0.116905	+	0.202485i	−0.801635	+	0.597814i	$0.796036\pi$
$68$	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	−0.999115	−	0.0420732i	$-0.986604\pi$
$73$	−3.95691	+	6.85356i	−0.463121	+	0.802149i	0.535994	+	0.844222i	$0.319937\pi$
$74$	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	−0.479457	−	0.877565i	$-0.659166\pi$
$79$	4.62422	−	8.00938i	0.520265	−	0.901126i	0.999722	−	0.0235607i	$-0.00750031\pi$
$80$	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	0.573513	−	0.819196i	$-0.305580\pi$
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	−0.996201	+	0.0870787i	$0.972247\pi$
$84$		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	0.980853	+	0.194751i	$0.0623898\pi$
$89$	6.21780	+	10.7695i	0.659085	+	1.14157i	−0.321767	+	0.946819i	$0.604277\pi$
$90$	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	−0.993448	−	0.114283i	$-0.963543\pi$
$97$	−5.86693	−	10.1618i	−0.595696	−	1.03178i	0.397752	−	0.917493i	$-0.369790\pi$
$98$		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	0.821813	+	0.569758i	$0.192963\pi$
$107$	9.35447	+	16.2024i	0.904331	+	1.56635i	0.0825182	+	0.996590i	$0.473704\pi$
$108$	−3.18716	−	4.10390i	−0.306684	−	0.394898i
$109$	−1.43346	+	2.48283i	−0.137301	+	0.237812i	−0.926474	−	0.376359i	$-0.877176\pi$
$109$	−1.43346	+	2.48283i	−0.137301	+	0.237812i	0.789173	+	0.614171i	$0.210509\pi$
$110$	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	0.416042	+	0.909345i	$0.363417\pi$
$113$	−6.16012	+	10.6696i	−0.579495	+	1.00371i	−0.995537	+	0.0943695i	$0.969916\pi$
$114$	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	−0.951208	−	0.308550i	$-0.900156\pi$
$139$	−2.45691	+	4.25549i	−0.208392	+	0.360946i	0.742816	+	0.669496i	$0.233490\pi$
$140$		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	0.703743	−	0.710454i	$-0.251510\pi$
$157$	−3.30039	−	5.71644i	−0.263400	−	0.456222i	−0.967143	+	0.254233i	$0.918177\pi$
$158$	−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	0.724780	−	0.688980i	$-0.241941\pi$
$163$	−2.99115	−	5.18082i	−0.234285	−	0.405793i	−0.959065	+	0.283188i	$0.908608\pi$
$164$	−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	−0.973489	−	0.228733i	$-0.926542\pi$
$167$	−3.73025	+	6.46099i	−0.288656	+	0.499966i	0.684833	+	0.728700i	$0.259875\pi$
$168$		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	−0.296851	+	0.954924i	$0.595937\pi$
$173$	−12.8296	+	22.2215i	−0.975414	+	1.68947i	−0.678562	+	0.734543i	$0.737397\pi$
$174$	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	−0.435392	−	0.900241i	$-0.643390\pi$
$179$	7.51819	−	13.0219i	0.561936	−	0.973301i	0.997328	−	0.0730602i	$-0.0232765\pi$
$180$	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	−0.929027	−	0.370011i	$-0.879354\pi$
$191$	−1.99115	+	3.44877i	−0.144074	+	0.249544i	0.784953	+	0.619555i	$0.212687\pi$
$192$	−0.796790	+	1.53790i	−0.0575033	+	0.110988i
$193$	−3.39037	−	5.87229i	−0.244044	−	0.422697i	0.717818	−	0.696230i	$-0.245141\pi$
$193$	−3.39037	−	5.87229i	−0.244044	−	0.422697i	−0.961862	+	0.273534i	$0.911808\pi$
$194$	−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	−0.948250	−	0.317523i	$-0.897149\pi$
$199$	−2.80924	+	4.86575i	−0.199142	+	0.344924i	0.749109	+	0.662447i	$0.230482\pi$
$200$	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	−0.314060	−	0.949403i	$-0.601689\pi$
$211$	9.66225	−	16.7355i	0.665177	−	1.15212i	0.979237	−	0.202717i	$-0.0649772\pi$
$212$	−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	−0.883055	−	0.469270i	$-0.844517\pi$
$223$	−12.6623	−	21.9317i	−0.847927	−	1.46865i	0.0351275	−	0.999383i	$-0.488816\pi$
$224$		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	0.869191	−	0.494476i	$-0.164640\pi$
$233$	0.0971780	+	0.168317i	0.00636634	+	0.0110268i	−0.862825	+	0.505503i	$0.831307\pi$
$234$	−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	−0.997811	−	0.0661361i	$-0.978933\pi$
$239$	−6.82743	+	11.8255i	−0.441630	+	0.764925i	0.556181	+	0.831061i	$0.312266\pi$
$240$	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	−0.672033	−	0.740522i	$-0.734579\pi$
$269$	5.00720	−	8.67272i	0.305294	−	0.528785i	0.977327	+	0.211737i	$0.0679119\pi$
$270$	−1.16372	+	2.85637i	−0.0708215	+	0.173833i
$271$	−5.10457	−	8.84137i	−0.310081	−	0.537075i	0.668299	−	0.743893i	$-0.267023\pi$
$271$	−5.10457	−	8.84137i	−0.310081	−	0.537075i	−0.978380	+	0.206818i	$0.933689\pi$
$272$	−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	0.609457	−	0.792819i	$-0.291388\pi$
$281$	−6.40136	−	11.0875i	−0.381873	−	0.661424i	−0.991330	+	0.131396i	$0.958054\pi$
$282$	21.0438	−	0.959702i	1.25314	−	0.0571494i
$283$	−8.17617	−	14.1615i	−0.486023	−	0.841816i	0.513848	−	0.857881i	$-0.328219\pi$
$283$	−8.17617	−	14.1615i	−0.486023	−	0.841816i	−0.999871	+	0.0160650i	$0.994886\pi$
$284$	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	−0.384817	−	0.922993i	$-0.625736\pi$
$293$	10.3889	−	17.9941i	0.606926	−	1.05123i	0.991744	−	0.128235i	$-0.0409311\pi$
$294$		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	0.758773	−	0.651356i	$-0.225799\pi$
$311$	−3.25729	−	5.64180i	−0.184704	−	0.319917i	−0.943477	+	0.331439i	$0.892466\pi$
$312$	−2.34728	−	3.66876i	−0.132888	−	0.207702i
$313$	0.133074	−	0.230492i	0.00752181	−	0.0130282i	−0.862240	−	0.506500i	$-0.830939\pi$
$313$	0.133074	−	0.230492i	0.00752181	−	0.0130282i	0.869762	+	0.493472i	$0.164272\pi$
$314$	−6.60078			−0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	−7.86186	+	13.6171i	−0.441566	+	0.764815i	−0.997806	−	0.0662067i	$-0.978910\pi$
$317$	−7.86186	+	13.6171i	−0.441566	+	0.764815i	0.556240	+	0.831022i	$0.312244\pi$
$318$	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	−0.279818	−	0.960053i	$-0.590274\pi$
$331$	12.5811	−	21.7912i	0.691521	−	1.19775i	0.971339	−	0.237697i	$-0.0763925\pi$
$332$	−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	0.489681	+	0.871902i	$0.337113\pi$
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	−0.999929	+	0.0118752i	$0.996220\pi$
$338$	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	−0.992035	−	0.125965i	$-0.959797\pi$
$347$	−11.2719	−	19.5235i	−0.605106	−	1.04808i	0.386928	−	0.922110i	$-0.373536\pi$
$348$	−5.78220	−	9.03749i	−0.309958	−	0.484461i
$349$	−1.89543	−	3.28298i	−0.101460	−	0.175734i	0.810826	−	0.585287i	$-0.199018\pi$
$349$	−1.89543	−	3.28298i	−0.101460	−	0.175734i	−0.912286	+	0.409553i	$0.865685\pi$
$350$		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	0.649549	−	0.760320i	$-0.274958\pi$
$359$	−6.32237	−	10.9507i	−0.333682	−	0.577954i	−0.983231	+	0.182366i	$0.941624\pi$
$360$	−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	0.977363	−	0.211569i	$-0.0678574\pi$
$397$	6.08619	+	10.5416i	0.305457	+	0.529067i	−0.671906	+	0.740636i	$0.734524\pi$
$398$	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	0.785675	−	0.618639i	$-0.212316\pi$
$409$	−2.89037	−	5.00627i	−0.142920	−	0.247544i	−0.928595	+	0.371095i	$0.878982\pi$
$410$	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	0.191753	+	0.981443i	$0.438583\pi$
$419$	−15.4356	+	26.7352i	−0.754078	+	1.30610i	−0.945831	+	0.324659i	$0.894751\pi$
$420$		0			0
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	0.816939	−	0.576724i	$-0.195669\pi$
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	−0.907927	+	0.419128i	$0.862336\pi$
$422$	−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	0.296192	+	0.955128i	$0.404283\pi$
$431$	−14.0979	+	24.4182i	−0.679070	+	1.17618i	−0.975261	+	0.221055i	$0.929050\pi$
$432$	−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	−0.367794	−	0.929907i	$-0.619887\pi$
$439$	13.0203	−	22.5519i	0.621426	−	1.07634i	0.989220	−	0.146434i	$-0.0467797\pi$
$440$	−0.352336			−0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	11.7865	−	20.4148i	0.559992	−	0.969935i	−0.437504	−	0.899216i	$-0.644137\pi$
$443$	11.7865	−	20.4148i	0.559992	−	0.969935i	0.997496	−	0.0707186i	$-0.0225292\pi$
$444$	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	−0.476849	−	0.878985i	$-0.658221\pi$
$457$	11.1762	−	19.3577i	0.522799	−	0.905515i	0.999648	−	0.0265293i	$-0.00844554\pi$
$458$	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	0.943818	−	0.330464i	$-0.107205\pi$
$461$	3.98755	+	6.90663i	0.185719	+	0.321674i	−0.758100	+	0.652138i	$0.773872\pi$
$462$		0			0
$463$	−14.3676	+	24.8854i	−0.667719	+	1.15652i	0.310821	+	0.950468i	$0.399396\pi$
$463$	−14.3676	+	24.8854i	−0.667719	+	1.15652i	−0.978540	+	0.206055i	$0.933937\pi$
$464$	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	−0.933880	−	0.357586i	$-0.883600\pi$
$467$	−16.7829	−	29.0688i	−0.776619	−	1.34514i	0.157261	−	0.987557i	$-0.449733\pi$
$468$	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	0.298075	+	0.954543i	$0.403656\pi$
$487$	−14.9538	+	25.9007i	−0.677621	+	1.17367i	−0.975695	+	0.219131i	$0.929678\pi$
$488$	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	−0.871726	−	0.489994i	$-0.836999\pi$
$491$	−0.255158	+	0.441947i	−0.0115151	+	0.0199448i	0.860210	+	0.509939i	$0.170332\pi$
$492$	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	−0.390766	−	0.920490i	$-0.627790\pi$
$521$	13.7360	−	23.7914i	0.601785	−	1.04232i	0.992551	−	0.121831i	$-0.0388767\pi$
$522$	10.7178	+	15.1809i	0.469105	+	0.664449i
$523$	−11.0919	−	19.2118i	−0.485016	−	0.840072i	0.514836	−	0.857289i	$-0.327853\pi$
$523$	−11.0919	−	19.2118i	−0.485016	−	0.840072i	−0.999852	+	0.0172166i	$0.994520\pi$
$524$	−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	0.985062	+	0.172198i	$0.0550869\pi$
$541$	14.9246	+	25.8502i	0.641659	+	1.11139i	−0.343403	+	0.939188i	$0.611580\pi$
$542$	−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	0.990789	−	0.135417i	$-0.0432373\pi$
$547$	8.84348	+	15.3174i	0.378120	+	0.654923i	−0.612669	+	0.790340i	$0.709904\pi$
$548$	−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	−0.347472	−	0.937690i	$-0.612960\pi$
$557$	15.0651	−	26.0935i	0.638328	−	1.10562i	0.985800	−	0.167926i	$-0.0537069\pi$
$558$	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	0.905965	−	0.423353i	$-0.139147\pi$
$563$	2.04883	+	3.54867i	0.0863478	+	0.149559i	−0.819617	+	0.572912i	$0.805814\pi$
$564$	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	−0.923960	−	0.382490i	$-0.875067\pi$
$569$	−3.11849	+	5.40138i	−0.130734	+	0.226437i	0.793226	+	0.608927i	$0.208400\pi$
$570$	−2.54523	+	4.91259i	−0.106608	+	0.205766i
$571$	−17.8011	−	30.8323i	−0.744951	−	1.29029i	−0.950218	−	0.311587i	$-0.899139\pi$
$571$	−17.8011	−	30.8323i	−0.744951	−	1.29029i	0.205266	−	0.978706i	$-0.434194\pi$
$572$	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	−0.249118	+	0.968473i	$0.580141\pi$
$577$	−23.1388	+	40.0776i	−0.963281	+	1.66845i	−0.714164	+	0.699979i	$0.753193\pi$
$578$	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	0.841727	−	0.539903i	$-0.181539\pi$
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	−0.888434	+	0.459005i	$0.848206\pi$
$588$		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	−0.748555	−	0.663072i	$-0.769252\pi$
$593$	−23.0979	−	40.0067i	−0.948515	−	1.64288i	−0.199960	−	0.979804i	$-0.564081\pi$
$594$	−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	0.984955	−	0.172808i	$-0.0552842\pi$
$599$	8.39037	+	14.5325i	0.342821	+	0.593784i	−0.642134	+	0.766592i	$0.721951\pi$
$600$	−3.70321	+	7.14763i	−0.151183	+	0.291801i
$601$	5.69961	+	9.87202i	0.232492	+	0.402688i	0.958541	−	0.284955i	$-0.0919787\pi$
$601$	5.69961	+	9.87202i	0.232492	+	0.402688i	−0.726049	+	0.687643i	$0.758645\pi$
$602$		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	−0.506998	−	0.861947i	$-0.669245\pi$
$613$	12.2053	−	21.1403i	0.492969	−	0.853848i	0.999967	+	0.00809942i	$0.00257815\pi$
$614$	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	0.343710	−	0.939076i	$-0.388316\pi$
$617$	24.4698	−	42.3830i	0.985119	−	1.70628i	0.641408	−	0.767200i	$-0.278350\pi$
$618$	−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	−0.457174	−	0.889378i	$-0.651138\pi$
$643$	13.7345	−	23.7889i	0.541637	−	0.938142i	0.998810	−	0.0487649i	$-0.0155285\pi$
$644$		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	−0.705613	−	0.708598i	$-0.749328\pi$
$647$	6.63521	−	11.4925i	0.260857	−	0.451818i	0.966470	+	0.256780i	$0.0826615\pi$
$648$	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	0.937003	−	0.349321i	$-0.113588\pi$
$659$	4.26089	+	7.38008i	0.165981	+	0.287487i	−0.771022	+	0.636808i	$0.780254\pi$
$660$	0.609631	−	0.0278023i	0.0237299	−	0.00108220i
$661$	17.1680	+	29.7358i	0.667757	+	1.15659i	0.978530	+	0.206105i	$0.0660789\pi$
$661$	17.1680	+	29.7358i	0.667757	+	1.15659i	−0.310773	+	0.950484i	$0.600588\pi$
$662$	−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	0.678546	−	0.734558i	$-0.262610\pi$
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	−0.975419	+	0.220359i	$0.929277\pi$
$674$	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	−0.928192	−	0.372101i	$-0.878638\pi$
$677$	−3.69076	+	6.39258i	−0.141847	+	0.245687i	0.786345	+	0.617788i	$0.211971\pi$
$678$	−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	−0.759487	−	0.650523i	$-0.774550\pi$
$683$	4.79893	−	8.31198i	0.183626	−	0.318049i	0.943113	+	0.332474i	$0.107883\pi$
$684$	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	−0.968615	−	0.248567i	$-0.920040\pi$
$691$	−7.07227	+	12.2495i	−0.269042	+	0.465994i	0.699573	+	0.714561i	$0.253374\pi$
$692$	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	−0.750609	−	0.660747i	$-0.770240\pi$
$709$	5.24338	−	9.08180i	0.196919	−	0.341074i	0.947528	+	0.319673i	$0.103573\pi$
$710$	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	0.844386	−	0.535735i	$-0.179965\pi$
$719$	−1.11995	−	1.93981i	−0.0417670	−	0.0723426i	−0.886153	+	0.463392i	$0.846632\pi$
$720$	−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	0.862574	−	0.505931i	$-0.168851\pi$
$727$	−0.185023	−	0.320469i	−0.00686211	−	0.0118855i	−0.869436	+	0.494045i	$0.835518\pi$
$728$		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	−0.507504	−	0.861649i	$-0.669432\pi$
$739$	13.3872	−	23.1874i	0.492458	−	0.852962i	0.999962	+	0.00868705i	$0.00276521\pi$
$740$	−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	−0.943625	−	0.331015i	$-0.892609\pi$
$743$	−5.04669	+	8.74113i	−0.185145	+	0.320681i	0.758480	+	0.651696i	$0.225942\pi$
$744$	−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	−0.00765823	+	0.999971i	$0.502438\pi$
$769$	−24.1211	+	41.7790i	−0.869829	+	1.50659i	−0.862171	+	0.506618i	$0.830896\pi$
$770$		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	−0.916410	−	0.400240i	$-0.868927\pi$
$773$	−3.10243	+	5.37357i	−0.111587	+	0.193274i	0.804823	+	0.593514i	$0.202260\pi$
$774$	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	0.915235	−	0.402920i	$-0.132005\pi$
$787$	3.04883	+	5.28073i	0.108679	+	0.188238i	−0.806556	+	0.591157i	$0.798671\pi$
$788$	−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	−0.734371	−	0.678749i	$-0.762523\pi$
$797$	6.22860	−	10.7882i	0.220628	−	0.382139i	0.954999	+	0.296609i	$0.0958559\pi$
$798$		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	−0.911280	−	0.411788i	$-0.864904\pi$
$809$	−2.81644	+	4.87822i	−0.0990208	+	0.171509i	0.812259	+	0.583297i	$0.198238\pi$
$810$	−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	0.425988	+	0.904729i	$0.359926\pi$
$821$	−16.3473	+	28.3143i	−0.570524	+	0.988176i	−0.996512	+	0.0834476i	$0.973407\pi$
$822$	2.35399	+	3.67926i	0.0821050	+	0.128329i
$823$	5.21994	+	9.04119i	0.181956	+	0.315156i	0.942546	−	0.334075i	$-0.108424\pi$
$823$	5.21994	+	9.04119i	0.181956	+	0.315156i	−0.760591	+	0.649231i	$0.775091\pi$
$824$	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	−0.543556	−	0.839373i	$-0.682922\pi$
$829$	13.1046	−	22.6978i	0.455141	−	0.788327i	0.998696	+	0.0510466i	$0.0162557\pi$
$830$	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	0.605671	−	0.795715i	$-0.292905\pi$
$839$	−11.1886	−	19.3793i	−0.386274	−	0.669046i	−0.991945	+	0.126669i	$0.959571\pi$
$840$		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	0.768473	−	0.639882i	$-0.221017\pi$
$853$	−4.96264	−	8.59555i	−0.169918	−	0.294306i	−0.938391	+	0.345576i	$0.887683\pi$
$854$		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	0.878187	−	0.478318i	$-0.158753\pi$
$863$	0.730252	+	1.26483i	0.0248581	+	0.0430555i	−0.853329	+	0.521373i	$0.825420\pi$
$864$	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	0.990949	−	0.134239i	$-0.0428590\pi$
$911$	11.4459	+	19.8249i	0.379220	+	0.656828i	−0.611729	+	0.791067i	$0.709526\pi$
$912$	−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	0.987838	−	0.155488i	$-0.0496950\pi$
$919$	10.8910	+	18.8638i	0.359262	+	0.622261i	−0.628575	+	0.777749i	$0.716362\pi$
$920$	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	0.460289	+	0.887769i	$0.347746\pi$
$929$	−16.4189	+	28.4383i	−0.538686	+	0.933031i	−0.998975	+	0.0452622i	$0.985588\pi$
$930$	−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	0.898697	−	0.438570i	$-0.144515\pi$
$941$	2.13307	+	3.69459i	0.0695362	+	0.120440i	−0.829161	+	0.559010i	$0.811181\pi$
$942$	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	−0.615626	−	0.788038i	$-0.711097\pi$
$947$	11.5292	−	19.9691i	0.374648	−	0.648909i	0.990274	+	0.139129i	$0.0444302\pi$
$948$	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	−0.0101108	−	0.999949i	$-0.503218\pi$
$967$	26.7719	−	46.3703i	0.860926	−	1.49117i	0.871037	−	0.491218i	$-0.163448\pi$
$968$	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	0.999884	+	0.0152321i	$0.00484870\pi$
$971$	15.9897	+	27.6949i	0.513133	+	0.888773i	−0.486751	+	0.873541i	$0.661818\pi$
$972$	−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	0.997584	−	0.0694638i	$-0.0221288\pi$
$977$	13.7104	+	23.7471i	0.438635	+	0.759738i	−0.558950	+	0.829202i	$0.688796\pi$
$978$	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	−0.745880	−	0.666080i	$-0.767971\pi$
$991$	6.41887	−	11.1178i	0.203902	−	0.353169i	0.949782	+	0.312911i	$0.101304\pi$
$992$	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.67.2		6
3.2	odd	2		2646.2.h.o.361.2		6
7.2	even	3		882.2.e.o.373.2		6
7.3	odd	6		882.2.f.n.589.1		6
7.4	even	3		882.2.f.o.589.3		6
7.5	odd	6		126.2.e.c.121.2	yes	6
7.6	odd	2		126.2.h.d.67.2	yes	6
9.2	odd	6		2646.2.e.p.2125.2		6
9.7	even	3		882.2.e.o.655.2		6
21.2	odd	6		2646.2.e.p.1549.2		6
21.5	even	6		378.2.e.d.37.2		6
21.11	odd	6		2646.2.f.m.1765.2		6
21.17	even	6		2646.2.f.l.1765.2		6
21.20	even	2		378.2.h.c.361.2		6
28.19	even	6		1008.2.q.g.625.2		6
28.27	even	2		1008.2.t.h.193.2		6
63.2	odd	6		2646.2.h.o.667.2		6
63.4	even	3		7938.2.a.bw.1.2		3
63.5	even	6		1134.2.g.l.163.2		6
63.11	odd	6		2646.2.f.m.883.2		6
63.13	odd	6		1134.2.g.m.487.2		6
63.16	even	3	inner	882.2.h.p.79.2		6
63.20	even	6		378.2.e.d.235.2		6
63.25	even	3		882.2.f.o.295.3		6
63.31	odd	6		7938.2.a.bv.1.2		3
63.32	odd	6		7938.2.a.bz.1.2		3
63.34	odd	6		126.2.e.c.25.2	✓	6
63.38	even	6		2646.2.f.l.883.2		6
63.40	odd	6		1134.2.g.m.163.2		6
63.41	even	6		1134.2.g.l.487.2		6
63.47	even	6		378.2.h.c.289.2		6
63.52	odd	6		882.2.f.n.295.1		6
63.59	even	6		7938.2.a.ca.1.2		3
63.61	odd	6		126.2.h.d.79.2	yes	6
84.47	odd	6		3024.2.q.g.2305.2		6
84.83	odd	2		3024.2.t.h.1873.2		6
252.47	odd	6		3024.2.t.h.289.2		6
252.83	odd	6		3024.2.q.g.2881.2		6
252.187	even	6		1008.2.t.h.961.2		6
252.223	even	6		1008.2.q.g.529.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	63.34	odd	6
126.2.e.c.121.2	yes	6	7.5	odd	6
126.2.h.d.67.2	yes	6	7.6	odd	2
126.2.h.d.79.2	yes	6	63.61	odd	6
378.2.e.d.37.2		6	21.5	even	6
378.2.e.d.235.2		6	63.20	even	6
378.2.h.c.289.2		6	63.47	even	6
378.2.h.c.361.2		6	21.20	even	2
882.2.e.o.373.2		6	7.2	even	3
882.2.e.o.655.2		6	9.7	even	3
882.2.f.n.295.1		6	63.52	odd	6
882.2.f.n.589.1		6	7.3	odd	6
882.2.f.o.295.3		6	63.25	even	3
882.2.f.o.589.3		6	7.4	even	3
882.2.h.p.67.2		6	1.1	even	1	trivial
882.2.h.p.79.2		6	63.16	even	3	inner
1008.2.q.g.529.2		6	252.223	even	6
1008.2.q.g.625.2		6	28.19	even	6
1008.2.t.h.193.2		6	28.27	even	2
1008.2.t.h.961.2		6	252.187	even	6
1134.2.g.l.163.2		6	63.5	even	6
1134.2.g.l.487.2		6	63.41	even	6
1134.2.g.m.163.2		6	63.40	odd	6
1134.2.g.m.487.2		6	63.13	odd	6
2646.2.e.p.1549.2		6	21.2	odd	6
2646.2.e.p.2125.2		6	9.2	odd	6
2646.2.f.l.883.2		6	63.38	even	6
2646.2.f.l.1765.2		6	21.17	even	6
2646.2.f.m.883.2		6	63.11	odd	6
2646.2.f.m.1765.2		6	21.11	odd	6
2646.2.h.o.361.2		6	3.2	odd	2
2646.2.h.o.667.2		6	63.2	odd	6
3024.2.q.g.2305.2		6	84.47	odd	6
3024.2.q.g.2881.2		6	252.83	odd	6
3024.2.t.h.289.2		6	252.47	odd	6
3024.2.t.h.1873.2		6	84.83	odd	2
7938.2.a.bv.1.2		3	63.31	odd	6
7938.2.a.bw.1.2		3	63.4	even	3
7938.2.a.bz.1.2		3	63.32	odd	6
7938.2.a.ca.1.2		3	63.59	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more