LMFDB - Embedded newform 882.2.f.o.295.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
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			295.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.o.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +0.593579 q^{10} +(0.296790 - 0.514055i) q^{11} +(-0.796790 - 1.53790i) q^{12} +(1.25729 + 2.17770i) q^{13} +(0.472958 + 0.912864i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.92101 q^{17} +(1.73025 - 2.45076i) q^{18} +5.38151 q^{19} +(0.296790 - 0.514055i) q^{20} +(-0.296790 - 0.514055i) q^{22} +(-2.23025 - 3.86291i) q^{23} +(-1.73025 - 0.0789082i) q^{24} +(2.32383 - 4.02499i) q^{25} +2.51459 q^{26} +(5.14766 + 0.708209i) q^{27} +(-3.09718 + 5.36447i) q^{29} +(1.02704 + 0.0468383i) q^{30} +(-3.93346 - 6.81296i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.554084 - 0.866025i) q^{33} +(1.46050 - 2.52967i) q^{34} +(-1.25729 - 2.72382i) q^{36} -1.00000 q^{37} +(2.69076 - 4.66053i) q^{38} +(2.00360 + 3.86718i) q^{39} +(-0.296790 - 0.514055i) q^{40} +(0.136673 + 0.236725i) q^{41} +(-5.58113 + 9.66679i) q^{43} -0.593579 q^{44} +(0.746304 + 1.61680i) q^{45} -4.46050 q^{46} +(6.08113 - 10.5328i) q^{47} +(-0.933463 + 1.45899i) q^{48} +(-2.32383 - 4.02499i) q^{50} +(5.05408 + 0.230492i) q^{51} +(1.25729 - 2.17770i) q^{52} -8.05408 q^{53} +(3.18716 - 4.10390i) q^{54} +0.352336 q^{55} +(9.31138 + 0.424646i) q^{57} +(3.09718 + 5.36447i) q^{58} +(4.32383 + 7.48910i) q^{59} +(0.554084 - 0.866025i) q^{60} +(-3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 + 1.29264i) q^{65} +(-0.472958 - 0.912864i) q^{66} +(0.956906 + 1.65741i) q^{67} +(-1.46050 - 2.52967i) q^{68} +(-3.55408 - 6.85980i) q^{69} -14.4107 q^{71} +(-2.98755 - 0.273062i) q^{72} +7.91381 q^{73} +(-0.500000 + 0.866025i) q^{74} +(4.33842 - 6.78089i) q^{75} +(-2.69076 - 4.66053i) q^{76} +(4.35087 + 0.198422i) q^{78} +(4.62422 - 8.00938i) q^{79} -0.593579 q^{80} +(8.85087 + 1.63157i) q^{81} +0.273346 q^{82} +(-3.85087 + 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} +(5.58113 + 9.66679i) q^{86} +(-5.78220 + 9.03749i) q^{87} +(-0.296790 + 0.514055i) q^{88} -12.4356 q^{89} +(1.77335 + 0.162084i) q^{90} +(-2.23025 + 3.86291i) q^{92} +(-6.26829 - 12.0985i) q^{93} +(-6.08113 - 10.5328i) q^{94} +(1.59718 + 2.76639i) q^{95} +(0.796790 + 1.53790i) 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} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 6 q + 3 q^{2} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - q^{20} + q^{22} - 7 q^{23} - 4 q^{24} + 2 q^{25} - 16 q^{26} + 7 q^{27} - 5 q^{29} - 3 q^{30} - 20 q^{31} + 3 q^{32} - 15 q^{33} - 4 q^{34} + 8 q^{36} - 6 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} - 6 q^{43} + 2 q^{44} + 12 q^{45} - 14 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} + 12 q^{51} - 8 q^{52} - 30 q^{53} + 8 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} + 14 q^{59} - 15 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} - 12 q^{66} + q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} + 38 q^{73} - 3 q^{74} - 17 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} + 2 q^{80} + 32 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} - 63 q^{87} + q^{88} - 18 q^{89} + 9 q^{90} - 7 q^{92} + q^{93} - 9 q^{94} - 4 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 - 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 - q^20 + q^22 - 7 * q^23 - 4 * q^24 + 2 * q^25 - 16 * q^26 + 7 * q^27 - 5 * q^29 - 3 * q^30 - 20 * q^31 + 3 * q^32 - 15 * q^33 - 4 * q^34 + 8 * q^36 - 6 * q^37 - 3 * q^38 + 4 * q^39 + q^40 - 6 * q^43 + 2 * q^44 + 12 * q^45 - 14 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 + 12 * q^51 - 8 * q^52 - 30 * q^53 + 8 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 + 14 * q^59 - 15 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 - 12 * q^66 + q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 + 38 * q^73 - 3 * q^74 - 17 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 + 2 * q^80 + 32 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 - 63 * q^87 + q^88 - 18 * q^89 + 9 * q^90 - 7 * q^92 + q^93 - 9 * q^94 - 4 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.73025	+	0.0789082i	0.998962	+	0.0455577i
$3$	1.73025	+	0.0789082i	0.998962	+	0.0455577i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.296790	+	0.514055i	0.132728	+	0.229892i	0.924727	−	0.380630i	$-0.124293\pi$
$5$	0.296790	+	0.514055i	0.132728	+	0.229892i	−0.791999	+	0.610522i	$0.790960\pi$
$6$	0.933463	−	1.45899i	0.381085	−	0.595630i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.98755	+	0.273062i	0.995849	+	0.0910208i
$10$	0.593579			0.187706
$11$	0.296790	−	0.514055i	0.0894855	−	0.154993i	−0.817808	−	0.575491i	$-0.804811\pi$
$11$	0.296790	−	0.514055i	0.0894855	−	0.154993i	0.907294	+	0.420497i	$0.138144\pi$
$12$	−0.796790	−	1.53790i	−0.230013	−	0.443953i
$13$	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
$17$	2.92101			0.708449			0.354224	−	0.935160i	$-0.384745\pi$
$17$	2.92101			0.708449			0.354224	+	0.935160i	$0.384745\pi$
$18$	1.73025	−	2.45076i	0.407824	−	0.577650i
$19$	5.38151			1.23460			0.617302	−	0.786726i	$-0.288226\pi$
$19$	5.38151			1.23460			0.617302	+	0.786726i	$0.288226\pi$
$20$	0.296790	−	0.514055i	0.0663642	−	0.114946i
$21$		0			0
$22$	−0.296790	−	0.514055i	−0.0632758	−	0.109597i
$23$	−2.23025	−	3.86291i	−0.465040	−	0.805473i	0.534164	−	0.845381i	$-0.320627\pi$
$23$	−2.23025	−	3.86291i	−0.465040	−	0.805473i	−0.999203	+	0.0399086i	$0.987293\pi$
$24$	−1.73025	−	0.0789082i	−0.353186	−	0.0161071i
$25$	2.32383	−	4.02499i	0.464766	−	0.804999i
$26$	2.51459			0.493151
$27$	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	$0.971618\pi$
$30$	1.02704	+	0.0468383i	0.187511	+	0.00855147i
$31$	−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
$33$	0.554084	−	0.866025i	0.0964537	−	0.150756i
$34$	1.46050	−	2.52967i	0.250475	−	0.433835i
$35$		0			0
$36$	−1.25729	−	2.72382i	−0.209549	−	0.453970i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	2.69076	−	4.66053i	0.436498	−	0.756038i
$39$	2.00360	+	3.86718i	0.320833	+	0.619244i
$40$	−0.296790	−	0.514055i	−0.0469266	−	0.0812792i
$41$	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	$0.842594\pi$
$44$	−0.593579			−0.0894855
$45$	0.746304	+	1.61680i	0.111252	+	0.241019i
$46$	−4.46050			−0.657666
$47$	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
$51$	5.05408	+	0.230492i	0.707713	+	0.0322753i
$52$	1.25729	−	2.17770i	0.174355	−	0.301992i
$53$	−8.05408			−1.10631			−0.553157	−	0.833077i	$-0.686577\pi$
$53$	−8.05408			−1.10631			−0.553157	+	0.833077i	$0.686577\pi$
$54$	3.18716	−	4.10390i	0.433717	−	0.558470i
$55$	0.352336			0.0475090
$56$		0			0
$57$	9.31138	+	0.424646i	1.23332	+	0.0562457i
$58$	3.09718	+	5.36447i	0.406679	+	0.704389i
$59$	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	$0.643013\pi$
$60$	0.554084	−	0.866025i	0.0715320	−	0.111803i
$61$	−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
$66$	−0.472958	−	0.912864i	−0.0582171	−	0.112366i
$67$	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	$0.796036\pi$
$68$	−1.46050	−	2.52967i	−0.177112	−	0.306767i
$69$	−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	$0.826515\pi$
$72$	−2.98755	−	0.273062i	−0.352086	−	0.0321807i
$73$	7.91381			0.926242			0.463121	−	0.886295i	$-0.346730\pi$
$73$	7.91381			0.926242			0.463121	+	0.886295i	$0.346730\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	4.33842	−	6.78089i	0.500958	−	0.782989i
$76$	−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	$-0.00750031\pi$
$80$	−0.593579			−0.0663642
$81$	8.85087	+	1.63157i	0.983430	+	0.181286i
$82$	0.273346			0.0301860
$83$	−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
$86$	5.58113	+	9.66679i	0.601828	+	1.04240i
$87$	−5.78220	+	9.03749i	−0.619917	+	0.968921i
$88$	−0.296790	+	0.514055i	−0.0316379	+	0.0547984i
$89$	−12.4356			−1.31817			−0.659085	−	0.752068i	$-0.729056\pi$
$89$	−12.4356			−1.31817			−0.659085	+	0.752068i	$0.729056\pi$
$90$	1.77335	+	0.162084i	0.186927	+	0.0170852i
$91$		0			0
$92$	−2.23025	+	3.86291i	−0.232520	+	0.402736i
$93$	−6.26829	−	12.0985i	−0.649991	−	1.25456i
$94$	−6.08113	−	10.5328i	−0.627220	−	1.08638i
$95$	1.59718	+	2.76639i	0.163867	+	0.283826i
$96$	0.796790	+	1.53790i	0.0813220	+	0.156961i
$97$	−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
$100$	−4.64766			−0.464766
$101$	−0.811379	+	1.40535i	−0.0807352	+	0.139837i	−0.903566	−	0.428449i	$-0.859060\pi$
$101$	−0.811379	+	1.40535i	−0.0807352	+	0.139837i	0.822831	+	0.568287i	$0.192393\pi$
$102$	2.72665	−	4.26172i	0.269979	−	0.421973i
$103$	3.19076	+	5.52655i	0.314395	+	0.544548i	0.979309	−	0.202372i	$-0.0648651\pi$
$103$	3.19076	+	5.52655i	0.314395	+	0.544548i	−0.664914	+	0.746920i	$0.731532\pi$
$104$	−1.25729	−	2.17770i	−0.123288	−	0.213541i
$105$		0			0
$106$	−4.02704	+	6.97504i	−0.391141	+	0.677476i
$107$	−18.7089			−1.80866			−0.904331	−	0.426832i	$-0.859630\pi$
$107$	−18.7089			−1.80866			−0.904331	+	0.426832i	$0.859630\pi$
$108$	−1.96050	−	4.81211i	−0.188650	−	0.463046i
$109$	2.86693			0.274602			0.137301	−	0.990529i	$-0.456157\pi$
$109$	2.86693			0.274602			0.137301	+	0.990529i	$0.456157\pi$
$110$	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	$-0.363417\pi$
$114$	5.02344	−	7.85157i	0.470489	−	0.735367i
$115$	1.32383	−	2.29294i	0.123448	−	0.213818i
$116$	6.19436			0.575132
$117$	3.16158	+	6.84929i	0.292288	+	0.633218i
$118$	8.64766			0.796082
$119$		0			0
$120$	−0.472958	−	0.912864i	−0.0431750	−	0.0833327i
$121$	5.32383	+	9.22115i	0.483985	+	0.838286i
$122$	3.32383	+	5.75705i	0.300926	+	0.521218i
$123$	0.217799	+	0.420378i	0.0196383	+	0.0379042i
$124$	−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
$129$	−10.4195	+	16.2856i	−0.917390	+	1.43387i
$130$	0.746304	+	1.29264i	0.0654552	+	0.113372i
$131$	−0.593579	−	1.02811i	−0.0518613	−	0.0898264i	0.838929	−	0.544240i	$-0.183182\pi$
$131$	−0.593579	−	1.02811i	−0.0518613	−	0.0898264i	−0.890791	+	0.454414i	$0.849849\pi$
$132$	−1.02704	−	0.0468383i	−0.0893925	−	0.00407675i
$133$		0			0
$134$	1.91381			0.165328
$135$	1.16372	+	2.85637i	0.100157	+	0.245837i
$136$	−2.92101			−0.250475
$137$	−1.26089	+	2.18393i	−0.107725	+	0.186586i	−0.914848	−	0.403797i	$-0.867690\pi$
$137$	−1.26089	+	2.18393i	−0.107725	+	0.186586i	0.807123	+	0.590383i	$0.201023\pi$
$138$	−7.71780	−	0.351971i	−0.656983	−	0.0299617i
$139$	−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
$143$	1.49261			0.124818
$144$	−1.73025	+	2.45076i	−0.144188	+	0.204230i
$145$	−3.67684			−0.305345
$146$	3.95691	−	6.85356i	0.327476	−	0.567205i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−9.02558	−	15.6328i	−0.739404	−	1.28069i	−0.952764	−	0.303712i	$-0.901774\pi$
$149$	−9.02558	−	15.6328i	−0.739404	−	1.28069i	0.213360	−	0.976974i	$-0.431559\pi$
$150$	−3.70321	−	7.14763i	−0.302366	−	0.583601i
$151$	−0.823832	+	1.42692i	−0.0670425	+	0.116121i	−0.897598	−	0.440815i	$-0.854690\pi$
$151$	−0.823832	+	1.42692i	−0.0670425	+	0.116121i	0.830556	+	0.556936i	$0.188023\pi$
$152$	−5.38151			−0.436498
$153$	8.72665	+	0.797618i	0.705508	+	0.0644836i
$154$		0			0
$155$	2.33482	−	4.04403i	0.187537	−	0.324824i
$156$	2.34728	−	3.66876i	0.187932	−	0.293736i
$157$	−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
$159$	−13.9356	−	0.635534i	−1.10516	−	0.0504011i
$160$	−0.296790	+	0.514055i	−0.0234633	+	0.0406396i
$161$		0			0
$162$	5.83842	−	6.84929i	0.458710	−	0.538131i
$163$	5.98229			0.468569			0.234285	−	0.972168i	$-0.424725\pi$
$163$	5.98229			0.468569			0.234285	+	0.972168i	$0.424725\pi$
$164$	0.136673	−	0.236725i	0.0106724	−	0.0184851i
$165$	0.609631	+	0.0278023i	0.0474597	+	0.00216440i
$166$	3.85087	+	6.66991i	0.298886	+	0.517685i
$167$	−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
$170$	1.73385			0.132980
$171$	16.0775	+	1.46949i	1.22948	+	0.112375i
$172$	11.1623			0.851114
$173$	−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
$177$	6.89037	+	13.2992i	0.517912	+	0.999630i
$178$	−6.21780	+	10.7695i	−0.466044	+	0.807211i
$179$	−15.0364			−1.12387			−0.561936	−	0.827181i	$-0.689943\pi$
$179$	−15.0364			−1.12387			−0.561936	+	0.827181i	$0.689943\pi$
$180$	1.02704	−	1.45472i	0.0765512	−	0.108428i
$181$	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
$184$	2.23025	+	3.86291i	0.164416	+	0.284778i
$185$	−0.296790	−	0.514055i	−0.0218204	−	0.0377941i
$186$	−13.6118	−	0.620765i	−0.998063	−	0.0455167i
$187$	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	$0.212687\pi$
$192$	1.73025	+	0.0789082i	0.124870	+	0.00569471i
$193$	−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	$0.911808\pi$
$194$	5.86693	+	10.1618i	0.421221	+	0.729576i
$195$	−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	$0.371113\pi$
$198$	−0.746304	−	1.61680i	−0.0530375	−	0.114901i
$199$	5.61849			0.398284			0.199142	−	0.979971i	$-0.436185\pi$
$199$	5.61849			0.398284			0.199142	+	0.979971i	$0.436185\pi$
$200$	−2.32383	+	4.02499i	−0.164320	+	0.284610i
$201$	1.52491	+	2.94325i	0.107559	+	0.207601i
$202$	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
$206$	6.38151			0.444621
$207$	−5.60817	−	12.1496i	−0.389795	−	0.844457i
$208$	−2.51459			−0.174355
$209$	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	$0.601689\pi$
$212$	4.02704	+	6.97504i	0.276578	+	0.479048i
$213$	−24.9341	−	1.13712i	−1.70846	−	0.0779143i
$214$	−9.35447	+	16.2024i	−0.639459	+	1.10757i
$215$	−6.62568			−0.451868
$216$	−5.14766	−	0.708209i	−0.350254	−	0.0481875i
$217$		0			0
$218$	1.43346	−	2.48283i	0.0970863	−	0.168158i
$219$	13.6929	+	0.624465i	0.925280	+	0.0421974i
$220$	−0.176168	−	0.305132i	−0.0118773	−	0.0205720i
$221$	3.67257	+	6.36108i	0.247044	+	0.427892i
$222$	−0.933463	+	1.45899i	−0.0626499	+	0.0979209i
$223$	−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
$226$	−12.3202			−0.819530
$227$	2.40856	−	4.17174i	0.159862	−	0.276888i	−0.774957	−	0.632014i	$-0.782229\pi$
$227$	2.40856	−	4.17174i	0.159862	−	0.276888i	0.934819	+	0.355126i	$0.115562\pi$
$228$	−4.28794	−	8.27621i	−0.283975	−	0.548106i
$229$	−4.64766	−	8.04999i	−0.307126	−	0.531958i	0.670606	−	0.741814i	$-0.266034\pi$
$229$	−4.64766	−	8.04999i	−0.307126	−	0.531958i	−0.977732	+	0.209855i	$0.932701\pi$
$230$	−1.32383	−	2.29294i	−0.0872909	−	0.151192i
$231$		0			0
$232$	3.09718	−	5.36447i	0.203340	−	0.352195i
$233$	−0.194356			−0.0127327			−0.00636634	−	0.999980i	$-0.502026\pi$
$233$	−0.194356			−0.0127327			−0.00636634	+	0.999980i	$0.502026\pi$
$234$	7.51245	+	0.686640i	0.491104	+	0.0448870i
$235$	7.21926			0.470933
$236$	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	$0.978933\pi$
$240$	−1.02704	−	0.0468383i	−0.0662953	−	0.00302340i
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	−0.995809	−	0.0914555i	$-0.970848\pi$
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	0.577107	+	0.816668i	$0.304181\pi$
$242$	10.6477			0.684458
$243$	15.1855	+	3.52144i	0.974150	+	0.225901i
$244$	6.64766			0.425573
$245$		0			0
$246$	0.472958	+	0.0215693i	0.0301547	+	0.00137521i
$247$	6.76615	+	11.7193i	0.430520	+	0.745682i
$248$	3.93346	+	6.81296i	0.249775	+	0.432623i
$249$	−7.18929	+	11.2368i	−0.455603	+	0.712101i
$250$	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
$255$	1.38151	+	2.66648i	0.0865138	+	0.166982i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.16372	+	7.21177i	0.259725	+	0.449858i	0.966168	−	0.257912i	$-0.0830346\pi$
$257$	4.16372	+	7.21177i	0.259725	+	0.449858i	−0.706443	+	0.707770i	$0.749701\pi$
$258$	8.89397	+	17.1664i	0.553714	+	1.06873i
$259$		0			0
$260$	1.49261			0.0925676
$261$	−10.7178	+	15.1809i	−0.663415	+	0.939673i
$262$	−1.18716			−0.0733429
$263$	8.54523	−	14.8008i	0.526921	−	0.912655i	−0.472586	−	0.881284i	$-0.656680\pi$
$263$	8.54523	−	14.8008i	0.526921	−	0.912655i	0.999508	−	0.0313704i	$-0.00998713\pi$
$264$	−0.554084	+	0.866025i	−0.0341015	+	0.0533002i
$265$	−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
$269$	−10.0144			−0.610588			−0.305294	−	0.952258i	$-0.598755\pi$
$269$	−10.0144			−0.610588			−0.305294	+	0.952258i	$0.598755\pi$
$270$	3.05555	+	0.420378i	0.185955	+	0.0255834i
$271$	10.2091			0.620161			0.310081	−	0.950710i	$-0.399644\pi$
$271$	10.2091			0.620161			0.310081	+	0.950710i	$0.399644\pi$
$272$	−1.46050	+	2.52967i	−0.0885561	+	0.153384i
$273$		0			0
$274$	1.26089	+	2.18393i	0.0761733	+	0.131936i
$275$	−1.37938	−	2.38915i	−0.0831797	−	0.144071i
$276$	−4.16372	+	6.50783i	−0.250626	+	0.391725i
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	0.414271	+	0.910154i	$0.364037\pi$
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	−0.995352	+	0.0963074i	$0.969297\pi$
$278$	−4.91381			−0.294711
$279$	−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	$0.291388\pi$
$282$	−9.69076	−	18.7043i	−0.577076	−	1.11382i
$283$	−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
$285$	2.54523	+	4.91259i	0.150766	+	0.290997i
$286$	0.746304	−	1.29264i	0.0441299	−	0.0764352i
$287$		0			0
$288$	1.25729	+	2.72382i	0.0740868	+	0.160503i
$289$	−8.46770			−0.498100
$290$	−1.83842	+	3.18424i	−0.107956	+	0.186985i
$291$	−10.9531	+	17.1196i	−0.642083	+	1.00357i
$292$	−3.95691	−	6.85356i	−0.231560	−	0.401074i
$293$	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
$296$	1.00000			0.0581238
$297$	1.89183	−	2.43599i	0.109775	−	0.141351i
$298$	−18.0512			−1.04568
$299$	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
$303$	−1.51478	+	2.36758i	−0.0870221	+	0.136014i
$304$	−2.69076	+	4.66053i	−0.154326	+	0.267300i
$305$	−3.94592			−0.225942
$306$	5.05408	−	7.15869i	0.288923	−	0.409235i
$307$	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
$310$	−2.33482	−	4.04403i	−0.132609	−	0.229686i
$311$	−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	$0.892466\pi$
$312$	−2.00360	−	3.86718i	−0.113431	−	0.218936i
$313$	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	$0.312244\pi$
$318$	−7.51819	+	11.7508i	−0.421599	+	0.658953i
$319$	1.83842	+	3.18424i	0.102932	+	0.178283i
$320$	0.296790	+	0.514055i	0.0165910	+	0.0287365i
$321$	−32.3712	−	1.47629i	−1.80678	−	0.0823985i
$322$		0			0
$323$	15.7195			0.874654
$324$	−3.01245	−	8.48087i	−0.167359	−	0.471159i
$325$	11.6870			0.648276
$326$	2.99115	−	5.18082i	0.165664	−	0.286939i
$327$	4.96050	+	0.226224i	0.274317	+	0.0125102i
$328$	−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	$-0.0763925\pi$
$332$	7.70175			0.422688
$333$	−2.98755	−	0.273062i	−0.163717	−	0.0149637i
$334$	−7.46050			−0.408221
$335$	−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	$-0.337113\pi$
$338$	−3.33842	−	5.78231i	−0.181586	−	0.314516i
$339$	−9.81663	−	18.9472i	−0.533166	−	1.02907i
$340$	0.866926	−	1.50156i	0.0470156	−	0.0814335i
$341$	−4.66964			−0.252875
$342$	9.31138	−	13.1888i	0.503502	−	0.713169i
$343$		0			0
$344$	5.58113	−	9.66679i	0.300914	−	0.521199i
$345$	2.47150	−	3.86291i	0.133061	−	0.207972i
$346$	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	$-0.373536\pi$
$348$	10.7178	+	0.488786i	0.574534	+	0.0262017i
$349$	−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
$352$	0.593579			0.0316379
$353$	3.41741	−	5.91913i	0.181890	−	0.315043i	−0.760634	−	0.649181i	$-0.775112\pi$
$353$	3.41741	−	5.91913i	0.181890	−	0.315043i	0.942524	+	0.334138i	$0.108445\pi$
$354$	14.9626	+	0.682372i	0.795255	+	0.0362677i
$355$	−4.27694	−	7.40789i	−0.226997	−	0.393170i
$356$	6.21780	+	10.7695i	0.329543	+	0.570785i
$357$		0			0
$358$	−7.51819	+	13.0219i	−0.397349	+	0.688228i
$359$	12.6447			0.667364			0.333682	−	0.942686i	$-0.391709\pi$
$359$	12.6447			0.667364			0.333682	+	0.942686i	$0.391709\pi$
$360$	−0.746304	−	1.61680i	−0.0393337	−	0.0852131i
$361$	9.96070			0.524247
$362$	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
$366$	5.29679	+	10.2234i	0.276868	+	0.534387i
$367$	3.27188	−	5.66707i	0.170791	−	0.295819i	−0.767906	−	0.640563i	$-0.778701\pi$
$367$	3.27188	−	5.66707i	0.170791	−	0.295819i	0.938697	+	0.344744i	$0.112034\pi$
$368$	4.46050			0.232520
$369$	0.343677	+	0.744547i	0.0178911	+	0.0387595i
$370$	−0.593579			−0.0308587
$371$		0			0
$372$	−7.34348	+	11.4778i	−0.380742	+	0.595094i
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	0.717784	−	0.696266i	$-0.245157\pi$
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	−0.961876	+	0.273486i	$0.911823\pi$
$374$	−0.866926	−	1.50156i	−0.0448277	−	0.0776438i
$375$	9.90856	+	0.451880i	0.511676	+	0.0233350i
$376$	−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
$381$	21.3420	+	0.973304i	1.09338	+	0.0498639i
$382$	1.99115	+	3.44877i	0.101876	+	0.176454i
$383$	−12.0416	−	20.8567i	−0.615299	−	1.06573i	−0.990332	−	0.138717i	$-0.955702\pi$
$383$	−12.0416	−	20.8567i	−0.615299	−	1.06573i	0.375033	−	0.927011i	$-0.377631\pi$
$384$	0.933463	−	1.45899i	0.0476356	−	0.0744537i
$385$		0			0
$386$	−6.78074			−0.345130
$387$	−19.3135	+	27.3560i	−0.981761	+	1.39058i
$388$	11.7339			0.595696
$389$	8.14913	−	14.1147i	0.413177	−	0.715644i	−0.582058	−	0.813147i	$-0.697752\pi$
$389$	8.14913	−	14.1147i	0.413177	−	0.715644i	0.995235	+	0.0975035i	$0.0310857\pi$
$390$	1.18929	+	2.29548i	0.0602223	+	0.116236i
$391$	−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
$395$	5.48968			0.276216
$396$	−1.77335	−	0.162084i	−0.0891140	−	0.00814504i
$397$	−12.1724			−0.610914			−0.305457	−	0.952206i	$-0.598809\pi$
$397$	−12.1724			−0.610914			−0.305457	+	0.952206i	$0.598809\pi$
$398$	2.80924	−	4.86575i	0.140815	−	0.243898i
$399$		0			0
$400$	2.32383	+	4.02499i	0.116192	+	0.201250i
$401$	16.6804	+	28.8914i	0.832981	+	1.44277i	0.895663	+	0.444733i	$0.146701\pi$
$401$	16.6804	+	28.8914i	0.832981	+	1.44277i	−0.0626819	+	0.998034i	$0.519965\pi$
$402$	3.31138	+	0.151016i	0.165157	+	0.00753197i
$403$	9.89104	−	17.1318i	0.492708	−	0.853395i
$404$	1.62276			0.0807352
$405$	1.78813	+	5.03407i	0.0888529	+	0.250145i
$406$		0			0
$407$	−0.296790	+	0.514055i	−0.0147113	+	0.0254808i
$408$	−5.05408	−	0.230492i	−0.250214	−	0.0114110i
$409$	−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
$411$	−2.35399	+	3.67926i	−0.116114	+	0.181484i
$412$	3.19076	−	5.52655i	0.157197	−	0.272274i
$413$		0			0
$414$	−13.3260	−	1.21800i	−0.654936	−	0.0598612i
$415$	−4.57160			−0.224411
$416$	−1.25729	+	2.17770i	−0.0616439	+	0.106770i
$417$	−3.91528	−	7.55694i	−0.191732	−	0.370065i
$418$	−1.59718	−	2.76639i	−0.0781205	−	0.135309i
$419$	−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	$0.195669\pi$
$422$	19.3245			0.940702
$423$	21.0438	−	29.8068i	1.02318	−	1.44925i
$424$	8.05408			0.391141
$425$	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
$429$	2.58259	+	0.117779i	0.124689	+	0.00568643i
$430$	−3.31284	+	5.73801i	−0.159759	+	0.276711i
$431$	28.1957			1.35814			0.679070	−	0.734074i	$-0.262383\pi$
$431$	28.1957			1.35814			0.679070	+	0.734074i	$0.262383\pi$
$432$	−3.18716	+	4.10390i	−0.153342	+	0.197449i
$433$	−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
$436$	−1.43346	−	2.48283i	−0.0686504	−	0.118906i
$437$	−12.0021	−	20.7883i	−0.574140	−	0.994440i
$438$	7.38725	−	11.5462i	0.352976	−	0.551697i
$439$	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	$-0.0225292\pi$
$444$	0.796790	+	1.53790i	0.0378140	+	0.0729853i
$445$	−3.69076	−	6.39258i	−0.174959	−	0.303037i
$446$	12.6623	+	21.9317i	0.599575	+	1.03849i
$447$	−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	$0.395321\pi$
$450$	−5.84348	−	12.6594i	−0.275464	−	0.596770i
$451$	0.162253			0.00764018
$452$	−6.16012	+	10.6696i	−0.289748	+	0.501857i
$453$	−1.53803	+	2.40392i	−0.0722631	+	0.112946i
$454$	−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	$-0.00844554\pi$
$458$	−9.29533			−0.434342
$459$	15.0364	+	2.06869i	0.701838	+	0.0965580i
$460$	−2.64766			−0.123448
$461$	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	$-0.399396\pi$
$464$	−3.09718	−	5.36447i	−0.143783	−	0.249039i
$465$	4.35894	−	6.81296i	0.202141	−	0.315943i
$466$	−0.0971780	+	0.168317i	−0.00450168	+	0.00779714i
$467$	33.5657			1.55324			0.776619	−	0.629971i	$-0.216933\pi$
$467$	33.5657			1.55324			0.776619	+	0.629971i	$0.216933\pi$
$468$	4.35087	−	6.16266i	0.201119	−	0.284869i
$469$		0			0
$470$	3.60963	−	6.25206i	0.166500	−	0.288386i
$471$	−5.25943	−	10.1513i	−0.242342	−	0.467748i
$472$	−4.32383	−	7.48910i	−0.199020	−	0.344714i
$473$	3.31284	+	5.73801i	0.152325	+	0.263834i
$474$	−7.36906	−	14.2231i	−0.338472	−	0.653291i
$475$	12.5057	−	21.6606i	0.573802	−	0.993855i
$476$		0			0
$477$	−24.0620	−	2.19927i	−1.10172	−	0.100698i
$478$	−13.6549			−0.624559
$479$	0.183560	−	0.317935i	0.00838707	−	0.0145268i	−0.861801	−	0.507246i	$-0.830664\pi$
$479$	0.183560	−	0.317935i	0.00838707	−	0.0145268i	0.870188	+	0.492719i	$0.163997\pi$
$480$	−0.554084	+	0.866025i	−0.0252904	+	0.0395285i
$481$	−1.25729	−	2.17770i	−0.0573277	−	0.0992945i
$482$	6.50000	+	11.2583i	0.296067	+	0.512803i
$483$		0			0
$484$	5.32383	−	9.22115i	0.241992	−	0.419143i
$485$	−6.96497			−0.316263
$486$	10.6424	−	11.3903i	0.482749	−	0.516675i
$487$	29.9076			1.35524			0.677621	−	0.735412i	$-0.263011\pi$
$487$	29.9076			1.35524			0.677621	+	0.735412i	$0.263011\pi$
$488$	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	$0.836999\pi$
$492$	0.255158	−	0.398809i	0.0115034	−	0.0179797i
$493$	−9.04689	+	15.6697i	−0.407451	+	0.705726i
$494$	13.5323			0.608847
$495$	1.05262	+	0.0962098i	0.0473118	+	0.00432431i
$496$	7.86693			0.353235
$497$		0			0
$498$	6.13667	+	11.8445i	0.274991	+	0.530764i
$499$	9.50953	+	16.4710i	0.425705	+	0.737343i	0.996486	−	0.0837597i	$-0.0266928\pi$
$499$	9.50953	+	16.4710i	0.425705	+	0.737343i	−0.570781	+	0.821102i	$0.693359\pi$
$500$	−2.86333	−	4.95943i	−0.128052	−	0.221792i
$501$	−5.94445	−	11.4735i	−0.265579	−	0.512598i
$502$	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
$507$	6.23258	−	9.74143i	0.276799	−	0.432632i
$508$	−6.16731	−	10.6821i	−0.273630	−	0.473942i
$509$	−5.60817	−	9.71363i	−0.248578	−	0.430549i	0.714554	−	0.699581i	$-0.246630\pi$
$509$	−5.60817	−	9.71363i	−0.248578	−	0.430549i	−0.963131	+	0.269031i	$0.913296\pi$
$510$	3.00000	+	0.136815i	0.132842	+	0.00605828i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	27.7022	+	3.81124i	1.22308	+	0.168270i
$514$	8.32743			0.367307
$515$	−1.89397	+	3.28045i	−0.0834582	+	0.144554i
$516$	19.3135	+	0.880794i	0.850230	+	0.0387748i
$517$	−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
$521$	−27.4720			−1.20357			−0.601785	−	0.798658i	$-0.705543\pi$
$521$	−27.4720			−1.20357			−0.601785	+	0.798658i	$0.705543\pi$
$522$	7.78813	+	16.8723i	0.340877	+	0.738482i
$523$	22.1838			0.970032			0.485016	−	0.874505i	$-0.338814\pi$
$523$	22.1838			0.970032			0.485016	+	0.874505i	$0.338814\pi$
$524$	−0.593579	+	1.02811i	−0.0259306	+	0.0449132i
$525$		0			0
$526$	−8.54523	−	14.8008i	−0.372590	−	0.645344i
$527$	−11.4897	−	19.9007i	−0.500498	−	0.866889i
$528$	0.472958	+	0.912864i	0.0205829	+	0.0397273i
$529$	1.55195	−	2.68805i	0.0674760	−	0.116872i
$530$	−4.78074			−0.207662
$531$	10.8727	+	23.5547i	0.471833	+	1.02219i
$532$		0			0
$533$	−0.343677	+	0.595265i	−0.0148863	+	0.0257838i
$534$	−11.6082	+	18.1434i	−0.502335	+	0.785141i
$535$	−5.55262	−	9.61742i	−0.240061	−	0.415797i
$536$	−0.956906	−	1.65741i	−0.0413321	−	0.0715892i
$537$	−26.0167	−	1.18649i	−1.12270	−	0.0512010i
$538$	−5.00720	+	8.67272i	−0.215876	+	0.373908i
$539$		0			0
$540$	1.89183	−	2.43599i	0.0814115	−	0.104828i
$541$	−29.8492			−1.28332			−0.641659	−	0.766990i	$-0.721754\pi$
$541$	−29.8492			−1.28332			−0.641659	+	0.766990i	$0.721754\pi$
$542$	5.10457	−	8.84137i	0.219260	−	0.379770i
$543$	0.149126	+	0.00680090i	0.00639961	+	0.000291855i
$544$	1.46050	+	2.52967i	0.0626186	+	0.108459i
$545$	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	$0.0432373\pi$
$548$	2.52179			0.107725
$549$	−11.5021	+	16.2918i	−0.490899	+	0.695318i
$550$	−2.75876			−0.117634
$551$	−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
$555$	−0.472958	−	0.912864i	−0.0200759	−	0.0387489i
$556$	−2.45691	+	4.25549i	−0.104196	+	0.180473i
$557$	−30.1301			−1.27666			−0.638328	−	0.769765i	$-0.720374\pi$
$557$	−30.1301			−1.27666			−0.638328	+	0.769765i	$0.720374\pi$
$558$	−23.5028	−	2.14816i	−0.994953	−	0.0909389i
$559$	−28.0685			−1.18717
$560$		0			0
$561$	1.61849	−	2.52967i	0.0683325	−	0.106803i
$562$	6.40136	+	11.0875i	0.270025	+	0.467697i
$563$	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	$0.805814\pi$
$564$	−21.0438	−	0.959702i	−0.886102	−	0.0404107i
$565$	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	$0.208400\pi$
$570$	5.52704	+	0.252061i	0.231502	+	0.0105577i
$571$	−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	$-0.434194\pi$
$572$	−0.746304	−	1.29264i	−0.0312045	−	0.0540479i
$573$	−3.71732	+	5.81012i	−0.155293	+	0.242721i
$574$		0			0
$575$	−20.7309			−0.864539
$576$	2.98755	+	0.273062i	0.124481	+	0.0113776i
$577$	46.2776			1.92656			0.963281	−	0.268494i	$-0.0865261\pi$
$577$	46.2776			1.92656			0.963281	+	0.268494i	$0.0865261\pi$
$578$	−4.23385	+	7.33325i	−0.176105	+	0.305023i
$579$	−5.40282	−	10.4281i	−0.224534	−	0.433376i
$580$	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
$584$	−7.91381			−0.327476
$585$	−2.58259	+	3.65802i	−0.106777	+	0.151241i
$586$	20.7778			0.858324
$587$	−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
$590$	2.56654	+	4.44537i	0.105663	+	0.183013i
$591$	19.1337	+	0.872595i	0.787057	+	0.0358938i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	46.1957			1.89703			0.948515	−	0.316732i	$-0.102586\pi$
$593$	46.1957			1.89703			0.948515	+	0.316732i	$0.102586\pi$
$594$	−1.16372	−	2.85637i	−0.0477478	−	0.117198i
$595$		0			0
$596$	−9.02558	+	15.6328i	−0.369702	+	0.640343i
$597$	9.72140	+	0.443345i	0.397870	+	0.0181449i
$598$	−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	$0.721951\pi$
$600$	−4.33842	+	6.78089i	−0.177115	+	0.276829i
$601$	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
$604$	1.64766			0.0670425
$605$	−3.16012	+	5.47348i	−0.128477	+	0.222529i
$606$	1.29300	+	2.49563i	0.0525244	+	0.101378i
$607$	−7.21420	−	12.4954i	−0.292815	−	0.507171i	0.681659	−	0.731670i	$-0.261259\pi$
$607$	−7.21420	−	12.4954i	−0.292815	−	0.507171i	−0.974474	+	0.224499i	$0.927925\pi$
$608$	2.69076	+	4.66053i	0.109125	+	0.189009i
$609$		0			0
$610$	−1.97296	+	3.41726i	−0.0798827	+	0.138361i
$611$	30.5831			1.23726
$612$	−3.67257	−	7.95631i	−0.148455	−	0.321615i
$613$	−24.4107			−0.985939			−0.492969	−	0.870047i	$-0.664089\pi$
$613$	−24.4107			−0.985939			−0.492969	+	0.870047i	$0.664089\pi$
$614$	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	$0.388316\pi$
$618$	11.0416	+	0.503554i	0.444160	+	0.0202559i
$619$	−22.3296	+	38.6759i	−0.897501	+	1.55452i	−0.0668227	+	0.997765i	$0.521286\pi$
$619$	−22.3296	+	38.6759i	−0.897501	+	1.55452i	−0.830678	+	0.556753i	$0.812047\pi$
$620$	−4.66964			−0.187537
$621$	−8.74484	−	21.4644i	−0.350918	−	0.861339i
$622$	−6.51459			−0.261211
$623$		0			0
$624$	−4.35087	−	0.198422i	−0.174174	−	0.00794323i
$625$	−9.91955	−	17.1812i	−0.396782	−	0.687246i
$626$	−0.133074	−	0.230492i	−0.00531873	−	0.00921230i
$627$	2.98181	−	4.66053i	0.119082	−	0.186124i
$628$	−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
$633$	15.3976	+	29.7191i	0.611998	+	1.18123i
$634$	7.86186	+	13.6171i	0.312235	+	0.540806i
$635$	3.66079	+	6.34067i	0.145274	+	0.251622i
$636$	6.41741	+	12.3863i	0.254467	+	0.491151i
$637$		0			0
$638$	3.67684			0.145568
$639$	−43.0526	−	3.93502i	−1.70314	−	0.155667i
$640$	0.593579			0.0234633
$641$	−15.3940	+	26.6631i	−0.608025	+	1.05313i	0.383540	+	0.923524i	$0.374705\pi$
$641$	−15.3940	+	26.6631i	−0.608025	+	1.05313i	−0.991566	+	0.129606i	$0.958629\pi$
$642$	−17.4641	+	27.2961i	−0.689253	+	1.07729i
$643$	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
$647$	−13.2704			−0.521714			−0.260857	−	0.965377i	$-0.584005\pi$
$647$	−13.2704			−0.521714			−0.260857	+	0.965377i	$0.584005\pi$
$648$	−8.85087	−	1.63157i	−0.347695	−	0.0640943i
$649$	5.13307			0.201491
$650$	5.84348	−	10.1212i	0.229200	−	0.396986i
$651$		0			0
$652$	−2.99115	−	5.18082i	−0.117142	−	0.202896i
$653$	8.57081	+	14.8451i	0.335402	+	0.580933i	0.983562	−	0.180571i	$-0.0577946\pi$
$653$	8.57081	+	14.8451i	0.335402	+	0.580933i	−0.648160	+	0.761504i	$0.724461\pi$
$654$	2.67617	−	4.18281i	0.104646	−	0.163561i
$655$	0.352336	−	0.610265i	0.0137669	−	0.0238450i
$656$	−0.273346			−0.0106724
$657$	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	$0.113588\pi$
$660$	−0.280738	−	0.541857i	−0.0109277	−	0.0210918i
$661$	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
$663$	5.85253	+	11.2961i	0.227293	+	0.438703i
$664$	3.85087	−	6.66991i	0.149443	−	0.258843i
$665$		0			0
$666$	−1.73025	+	2.45076i	−0.0670459	+	0.0949650i
$667$	27.6300			1.06984
$668$	−3.73025	+	6.46099i	−0.144328	+	0.249983i
$669$	−23.6395	+	36.9482i	−0.913955	+	1.42850i
$670$	0.568000	+	0.983804i	0.0219437	+	0.0380077i
$671$	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	$0.262610\pi$
$674$	−18.7339			−0.721601
$675$	14.8128	−	19.0736i	0.570147	−	0.734142i
$676$	−6.67684			−0.256802
$677$	−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
$681$	4.49660	−	7.02811i	0.172310	−	0.269318i
$682$	−2.33482	+	4.04403i	−0.0894050	+	0.154854i
$683$	−9.59785			−0.367252			−0.183626	−	0.982996i	$-0.558783\pi$
$683$	−9.59785			−0.367252			−0.183626	+	0.982996i	$0.558783\pi$
$684$	−6.76615	−	14.6583i	−0.258710	−	0.560474i
$685$	−1.49688			−0.0571929
$686$		0			0
$687$	−7.40642	−	14.2953i	−0.282573	−	0.545398i
$688$	−5.58113	−	9.66679i	−0.212778	−	0.368543i
$689$	−10.1264	−	17.5394i	−0.385783	−	0.668197i
$690$	−2.10963	−	4.07183i	−0.0803123	−	0.155012i
$691$	−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
$696$	5.78220	−	9.03749i	0.219174	−	0.342565i
$697$	0.399223	+	0.691475i	0.0151217	+	0.0261915i
$698$	1.89543	+	3.28298i	0.0717431	+	0.124263i
$699$	−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	$0.250578\pi$
$702$	12.9443	+	1.78085i	0.488550	+	0.0672140i
$703$	−5.38151			−0.202968
$704$	0.296790	−	0.514055i	0.0111857	−	0.0193742i
$705$	12.4911	+	0.569659i	0.470444	+	0.0214546i
$706$	−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	$0.103573\pi$
$710$	−8.55389			−0.321022
$711$	16.0021	−	22.6657i	0.600127	−	0.850031i
$712$	12.4356			0.466044
$713$	−17.5452	+	30.3892i	−0.657074	+	1.13809i
$714$		0			0
$715$	0.442991	+	0.767282i	0.0165669	+	0.0286947i
$716$	7.51819	+	13.0219i	0.280968	+	0.486651i
$717$	−10.8801	−	20.9998i	−0.406323	−	0.784251i
$718$	6.32237	−	10.9507i	0.235949	−	0.408675i
$719$	2.23990			0.0835340			0.0417670	−	0.999127i	$-0.486701\pi$
$719$	2.23990			0.0835340			0.0417670	+	0.999127i	$0.486701\pi$
$720$	−1.77335	−	0.162084i	−0.0660887	−	0.00604052i
$721$		0			0
$722$	4.98035	−	8.62622i	0.185349	−	0.321035i
$723$	−12.1350	+	18.9668i	−0.451306	+	0.705385i
$724$	−0.0430937	−	0.0746406i	−0.00160157	−	0.00277399i
$725$	14.3946	+	24.9322i	0.534604	+	0.925961i
$726$	18.4231	+	0.840188i	0.683747	+	0.0311823i
$727$	−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
$730$	4.69748			0.173861
$731$	−16.3025	+	28.2368i	−0.602971	+	1.04438i
$732$	11.5021	+	0.524555i	0.425131	+	0.0193881i
$733$	7.00953	+	12.1409i	0.258903	+	0.448433i	0.965948	−	0.258735i	$-0.0833057\pi$
$733$	7.00953	+	12.1409i	0.258903	+	0.448433i	−0.707045	+	0.707168i	$0.749972\pi$
$734$	−3.27188	−	5.66707i	−0.120767	−	0.209175i
$735$		0			0
$736$	2.23025	−	3.86291i	0.0822082	−	0.142389i
$737$	1.13600			0.0418451
$738$	0.816635	+	0.0746406i	0.0300607	+	0.00274756i
$739$	−26.7745			−0.984916			−0.492458	−	0.870336i	$-0.663901\pi$
$739$	−26.7745			−0.984916			−0.492458	+	0.870336i	$0.663901\pi$
$740$	−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	$0.892609\pi$
$744$	6.26829	+	12.0985i	0.229806	+	0.443553i
$745$	5.35740	−	9.27928i	0.196280	−	0.339967i
$746$	−9.42840			−0.345198
$747$	−13.3260	+	18.8751i	−0.487572	+	0.690605i
$748$	−1.73385			−0.0633959
$749$		0			0
$750$	5.34562	−	8.35512i	0.195194	−	0.305086i
$751$	−5.75729	−	9.97193i	−0.210087	−	0.363881i	0.741655	−	0.670782i	$-0.234041\pi$
$751$	−5.75729	−	9.97193i	−0.210087	−	0.363881i	−0.951741	+	0.306901i	$0.900708\pi$
$752$	6.08113	+	10.5328i	0.221756	+	0.384092i
$753$	33.8157	+	1.54216i	1.23231	+	0.0561996i
$754$	−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
$759$	−4.58113	−	0.208922i	−0.166284	−	0.00758341i
$760$	−1.59718	−	2.76639i	−0.0579357	−	0.100348i
$761$	−0.850874	−	1.47376i	−0.0308442	−	0.0534236i	0.850191	−	0.526474i	$-0.176486\pi$
$761$	−0.850874	−	1.47376i	−0.0308442	−	0.0534236i	−0.881035	+	0.473050i	$0.843153\pi$
$762$	11.5139	−	17.9961i	0.417105	−	0.651929i
$763$		0			0
$764$	3.98229			0.144074
$765$	2.17996	+	4.72270i	0.0788167	+	0.170750i
$766$	−24.0833			−0.870164
$767$	−10.8727	+	18.8320i	−0.392589	+	0.679984i
$768$	−0.796790	−	1.53790i	−0.0287517	−	0.0554941i
$769$	−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
$773$	6.20487			0.223174			0.111587	−	0.993755i	$-0.464407\pi$
$773$	6.20487			0.223174			0.111587	+	0.993755i	$0.464407\pi$
$774$	14.0342	+	30.4040i	0.504450	+	1.09285i
$775$	−36.5628			−1.31338
$776$	5.86693	−	10.1618i	0.210610	−	0.364788i
$777$		0			0
$778$	−8.14913	−	14.1147i	−0.292160	−	0.506037i
$779$	0.735508	+	1.27394i	0.0263523	+	0.0456436i
$780$	2.58259	+	0.117779i	0.0924715	+	0.00421717i
$781$	−4.27694	+	7.40789i	−0.153041	+	0.265075i
$782$	−13.0292			−0.465922
$783$	−19.7424	+	25.4210i	−0.705536	+	0.908474i
$784$		0			0
$785$	1.95904	−	3.39316i	0.0699212	−	0.121107i
$786$	−2.05408	−	0.0936766i	−0.0732668	−	0.00334133i
$787$	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
$789$	15.9533	−	24.9348i	0.567953	−	0.887702i
$790$	2.74484	−	4.75420i	0.0976571	−	0.169147i
$791$		0			0
$792$	−1.02704	+	1.45472i	−0.0364944	+	0.0516913i
$793$	−16.7161			−0.593608
$794$	−6.08619	+	10.5416i	−0.215991	+	0.374107i
$795$	−3.80924	−	7.35228i	−0.135100	−	0.260759i
$796$	−2.80924	−	4.86575i	−0.0995710	−	0.172462i
$797$	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
$800$	4.64766			0.164320
$801$	−37.1519	−	3.39569i	−1.31270	−	0.119981i
$802$	33.3609			1.17801
$803$	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
$807$	−17.3274	−	0.790218i	−0.609954	−	0.0278170i
$808$	0.811379	−	1.40535i	0.0285442	−	0.0494400i
$809$	5.63288			0.198042			0.0990208	−	0.995085i	$-0.468429\pi$
$809$	5.63288			0.198042			0.0990208	+	0.995085i	$0.468429\pi$
$810$	5.25370	+	0.968468i	0.184596	+	0.0340285i
$811$	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
$814$	0.296790	+	0.514055i	0.0104025	+	0.0180176i
$815$	1.77548	+	3.07523i	0.0621924	+	0.107720i
$816$	−2.72665	+	4.26172i	−0.0954520	+	0.149190i
$817$	−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	$0.973407\pi$
$822$	2.00933	+	3.87825i	0.0700835	+	0.135269i
$823$	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	$0.775091\pi$
$824$	−3.19076	−	5.52655i	−0.111155	−	0.192527i
$825$	−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	$0.406191\pi$
$828$	−7.71780	+	10.9316i	−0.268212	+	0.379900i
$829$	−26.2091			−0.910281			−0.455141	−	0.890420i	$-0.650411\pi$
$829$	−26.2091			−0.910281			−0.455141	+	0.890420i	$0.650411\pi$
$830$	−2.28580	+	3.95912i	−0.0793412	+	0.137423i
$831$	−18.0552	+	28.2201i	−0.626329	+	0.978943i
$832$	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
$836$	−3.19436			−0.110479
$837$	−15.4231	−	37.8565i	−0.533102	−	1.30851i
$838$	−30.8712			−1.06643
$839$	−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
$842$	1.86693	+	3.23361i	0.0643385	+	0.111438i
$843$	−11.9509	+	18.6790i	−0.411610	+	0.643340i
$844$	9.66225	−	16.7355i	0.332588	−	0.576060i
$845$	3.96324			0.136339
$846$	−15.2915	−	33.1278i	−0.525734	−	1.13896i
$847$		0			0
$848$	4.02704	−	6.97504i	0.138289	−	0.239524i
$849$	−13.0294	−	25.1482i	−0.447167	−	0.863084i
$850$	−6.78794	−	11.7570i	−0.232824	−	0.403263i
$851$	2.23025	+	3.86291i	0.0764521	+	0.132419i
$852$	11.4823	+	22.1622i	0.393377	+	0.759263i
$853$	−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
$856$	18.7089			0.639459
$857$	3.89776	−	6.75112i	0.133145	−	0.230614i	−0.791742	−	0.610855i	$-0.790826\pi$
$857$	3.89776	−	6.75112i	0.133145	−	0.230614i	0.924887	+	0.380241i	$0.124159\pi$
$858$	1.39329	−	2.17770i	0.0475663	−	0.0743454i
$859$	8.17111	+	14.1528i	0.278795	+	0.482886i	0.971085	−	0.238732i	$-0.0767318\pi$
$859$	8.17111	+	14.1528i	0.278795	+	0.482886i	−0.692291	+	0.721619i	$0.743398\pi$
$860$	3.31284	+	5.73801i	0.112967	+	0.195664i
$861$		0			0
$862$	14.0979	−	24.4182i	0.480175	−	0.831687i
$863$	−1.46050			−0.0497162			−0.0248581	−	0.999691i	$-0.507913\pi$
$863$	−1.46050			−0.0497162			−0.0248581	+	0.999691i	$0.507913\pi$
$864$	1.96050	+	4.81211i	0.0666977	+	0.163711i
$865$	−15.2307			−0.517860
$866$	−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
$870$	−3.43219	+	5.36447i	−0.116362	+	0.181873i
$871$	−2.40623	+	4.16771i	−0.0815319	+	0.141217i
$872$	−2.86693			−0.0970863
$873$	−20.3025	+	28.7569i	−0.687136	+	0.973272i
$874$	−24.0043			−0.811957
$875$		0			0
$876$	−6.30564	−	12.1706i	−0.213048	−	0.411207i
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	0.885648	−	0.464357i	$-0.153715\pi$
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	−0.844969	+	0.534815i	$0.820381\pi$
$878$	−13.0203	−	22.5519i	−0.439415	−	0.761088i
$879$	16.5555	+	31.9541i	0.558405	+	1.07779i
$880$	−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
$885$	−4.79153	+	7.48910i	−0.161066	+	0.251743i
$886$	−11.7865	−	20.4148i	−0.395974	−	0.685848i
$887$	−12.2286	−	21.1805i	−0.410596	−	0.711173i	0.584359	−	0.811495i	$-0.301346\pi$
$887$	−12.2286	−	21.1805i	−0.410596	−	0.711173i	−0.994955	+	0.100322i	$0.968013\pi$
$888$	1.73025	+	0.0789082i	0.0580635	+	0.00264799i
$889$		0			0
$890$	−7.38151			−0.247429
$891$	3.46557	−	4.06560i	0.116101	−	0.136203i
$892$	25.3245			0.847927
$893$	32.7257	−	56.6825i	1.09512	−	1.89681i
$894$	−31.2331	−	1.42439i	−1.04459	−	0.0476386i
$895$	−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
$899$	48.7305			1.62525
$900$	−13.8851	−	1.26910i	−0.462837	−	0.0423034i
$901$	−23.5261			−0.783767
$902$	0.0811263	−	0.140515i	0.00270121	−	0.00467863i
$903$		0			0
$904$	6.16012	+	10.6696i	0.204882	+	0.354867i
$905$	0.0255796	+	0.0443051i	0.000850293	+	0.00147275i
$906$	1.31284	+	2.53394i	0.0436162	+	0.0841844i
$907$	−5.01838	+	8.69209i	−0.166633	+	0.288616i	−0.937234	−	0.348701i	$-0.886623\pi$
$907$	−5.01838	+	8.69209i	−0.166633	+	0.288616i	0.770601	+	0.637318i	$0.219956\pi$
$908$	−4.81711			−0.159862
$909$	−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	$0.0428590\pi$
$912$	−5.02344	+	7.85157i	−0.166343	+	0.259991i
$913$	2.28580	+	3.95912i	0.0756489	+	0.131028i
$914$	−11.1762	−	19.3577i	−0.369675	−	0.640296i
$915$	−6.82743	−	0.311365i	−0.225708	−	0.0102934i
$916$	−4.64766	+	8.04999i	−0.153563	+	0.265979i
$917$		0			0
$918$	9.30972	−	11.9875i	0.307267	−	0.395648i
$919$	−21.7821			−0.718525			−0.359262	−	0.933237i	$-0.616972\pi$
$919$	−21.7821			−0.718525			−0.359262	+	0.933237i	$0.616972\pi$
$920$	−1.32383	+	2.29294i	−0.0436454	+	0.0755961i
$921$	39.2367	+	1.78939i	1.29289	+	0.0589624i
$922$	−3.98755	−	6.90663i	−0.131323	−	0.227458i
$923$	−18.1185	−	31.3821i	−0.596377	−	1.03296i
$924$		0			0
$925$	−2.32383	+	4.02499i	−0.0764071	+	0.132341i
$926$	−28.7352			−0.944297
$927$	8.02344	+	17.3821i	0.263524	+	0.570904i
$928$	−6.19436			−0.203340
$929$	−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
$933$	−5.19076	−	10.0188i	−0.169938	−	0.328000i
$934$	16.7829	−	29.0688i	0.549152	−	0.951160i
$935$	1.02918			0.0336577
$936$	−3.16158	−	6.84929i	−0.103339	−	0.223876i
$937$	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
$940$	−3.60963	−	6.25206i	−0.117733	−	0.203920i
$941$	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	$0.811181\pi$
$942$	−11.4210	−	0.520856i	−0.372117	−	0.0169704i
$943$	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	$0.0444302\pi$
$948$	−16.0021	−	0.729778i	−0.519725	−	0.0237021i
$949$	9.94999	+	17.2339i	0.322990	+	0.559436i
$950$	−12.5057	−	21.6606i	−0.405740	−	0.702762i
$951$	−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	$0.701689\pi$
$954$	−13.9356	+	19.7386i	−0.451182	+	0.639062i
$955$	−2.36381			−0.0764910
$956$	−6.82743	+	11.8255i	−0.220815	+	0.382463i
$957$	2.92967	+	5.65460i	0.0947028	+	0.182787i
$958$	−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
$962$	−2.51459			−0.0810736
$963$	−55.8939	−	5.10871i	−1.80115	−	0.164626i
$964$	13.0000			0.418702
$965$	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	$0.503218\pi$
$968$	−5.32383	−	9.22115i	−0.171114	−	0.296379i
$969$	27.1986	+	1.24039i	0.873746	+	0.0398472i
$970$	−3.48249	+	6.03184i	−0.111816	+	0.193671i
$971$	−31.9794			−1.02627			−0.513133	−	0.858309i	$-0.671515\pi$
$971$	−31.9794			−1.02627			−0.513133	+	0.858309i	$0.671515\pi$
$972$	−4.54309	−	14.9118i	−0.145720	−	0.478295i
$973$		0			0
$974$	14.9538	−	25.9007i	0.479150	−	0.829913i
$975$	20.2214	+	0.922198i	0.647603	+	0.0295340i
$976$	−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	$0.688796\pi$
$978$	5.58425	−	8.72809i	0.178564	−	0.279094i
$979$	−3.69076	+	6.39258i	−0.117957	+	0.204308i
$980$		0			0
$981$	8.56507	+	0.782849i	0.273462	+	0.0249945i
$982$	−0.510317			−0.0162849
$983$	−29.5782	+	51.2309i	−0.943398	+	1.63401i	−0.184471	+	0.982838i	$0.559057\pi$
$983$	−29.5782	+	51.2309i	−0.943398	+	1.63401i	−0.758927	+	0.651175i	$0.774276\pi$
$984$	−0.217799	−	0.420378i	−0.00694319	−	0.0134012i
$985$	3.28201	+	5.68460i	0.104573	+	0.181126i
$986$	9.04689	+	15.6697i	0.288112	+	0.499024i
$987$		0			0
$988$	6.76615	−	11.7193i	0.215260	−	0.372841i
$989$	49.7893			1.58321
$990$	0.609631	−	0.863492i	0.0193753	−	0.0274436i
$991$	−12.8377			−0.407804			−0.203902	−	0.978991i	$-0.565362\pi$
$991$	−12.8377			−0.407804			−0.203902	+	0.978991i	$0.565362\pi$
$992$	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
$996$	13.3260	+	0.607731i	0.422249	+	0.0192567i
$997$	−2.89037	+	5.00627i	−0.0915389	+	0.158550i	−0.908159	−	0.418626i	$-0.862512\pi$
$997$	−2.89037	+	5.00627i	−0.0915389	+	0.158550i	0.816620	+	0.577176i	$0.195845\pi$
$998$	19.0191			0.602038
$999$	−5.14766	−	0.708209i	−0.162865	−	0.0224067i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	7.5	odd	6
126.2.e.c.121.2	yes	6	63.31	odd	6
126.2.h.d.67.2	yes	6	63.40	odd	6
126.2.h.d.79.2	yes	6	7.3	odd	6
378.2.e.d.37.2		6	63.59	even	6
378.2.e.d.235.2		6	21.5	even	6
378.2.h.c.289.2		6	21.17	even	6
378.2.h.c.361.2		6	63.5	even	6
882.2.e.o.373.2		6	63.4	even	3
882.2.e.o.655.2		6	7.2	even	3
882.2.f.n.295.1		6	7.6	odd	2
882.2.f.n.589.1		6	63.13	odd	6
882.2.f.o.295.3		6	1.1	even	1	trivial
882.2.f.o.589.3		6	9.4	even	3	inner
882.2.h.p.67.2		6	63.58	even	3
882.2.h.p.79.2		6	7.4	even	3
1008.2.q.g.529.2		6	28.19	even	6
1008.2.q.g.625.2		6	252.31	even	6
1008.2.t.h.193.2		6	252.103	even	6
1008.2.t.h.961.2		6	28.3	even	6
1134.2.g.l.163.2		6	63.38	even	6
1134.2.g.l.487.2		6	63.47	even	6
1134.2.g.m.163.2		6	63.52	odd	6
1134.2.g.m.487.2		6	63.61	odd	6
2646.2.e.p.1549.2		6	63.32	odd	6
2646.2.e.p.2125.2		6	21.2	odd	6
2646.2.f.l.883.2		6	21.20	even	2
2646.2.f.l.1765.2		6	63.41	even	6
2646.2.f.m.883.2		6	3.2	odd	2
2646.2.f.m.1765.2		6	9.5	odd	6
2646.2.h.o.361.2		6	63.23	odd	6
2646.2.h.o.667.2		6	21.11	odd	6
3024.2.q.g.2305.2		6	252.59	odd	6
3024.2.q.g.2881.2		6	84.47	odd	6
3024.2.t.h.289.2		6	84.59	odd	6
3024.2.t.h.1873.2		6	252.131	odd	6
7938.2.a.bv.1.2		3	63.34	odd	6
7938.2.a.bw.1.2		3	9.7	even	3
7938.2.a.bz.1.2		3	9.2	odd	6
7938.2.a.ca.1.2		3	63.20	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(2.98755 + 0.273062i) q^{9} +0.593579 q^{10} +(0.296790 - 0.514055i) q^{11} +(-0.796790 - 1.53790i) q^{12} +(1.25729 + 2.17770i) q^{13} +(0.472958 + 0.912864i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.92101 q^{17} +(1.73025 - 2.45076i) q^{18} +5.38151 q^{19} +(0.296790 - 0.514055i) q^{20} +(-0.296790 - 0.514055i) q^{22} +(-2.23025 - 3.86291i) q^{23} +(-1.73025 - 0.0789082i) q^{24} +(2.32383 - 4.02499i) q^{25} +2.51459 q^{26} +(5.14766 + 0.708209i) q^{27} +(-3.09718 + 5.36447i) q^{29} +(1.02704 + 0.0468383i) q^{30} +(-3.93346 - 6.81296i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.554084 - 0.866025i) q^{33} +(1.46050 - 2.52967i) q^{34} +(-1.25729 - 2.72382i) q^{36} -1.00000 q^{37} +(2.69076 - 4.66053i) q^{38} +(2.00360 + 3.86718i) q^{39} +(-0.296790 - 0.514055i) q^{40} +(0.136673 + 0.236725i) q^{41} +(-5.58113 + 9.66679i) q^{43} -0.593579 q^{44} +(0.746304 + 1.61680i) q^{45} -4.46050 q^{46} +(6.08113 - 10.5328i) q^{47} +(-0.933463 + 1.45899i) q^{48} +(-2.32383 - 4.02499i) q^{50} +(5.05408 + 0.230492i) q^{51} +(1.25729 - 2.17770i) q^{52} -8.05408 q^{53} +(3.18716 - 4.10390i) q^{54} +0.352336 q^{55} +(9.31138 + 0.424646i) q^{57} +(3.09718 + 5.36447i) q^{58} +(4.32383 + 7.48910i) q^{59} +(0.554084 - 0.866025i) q^{60} +(-3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 + 1.29264i) q^{65} +(-0.472958 - 0.912864i) q^{66} +(0.956906 + 1.65741i) q^{67} +(-1.46050 - 2.52967i) q^{68} +(-3.55408 - 6.85980i) q^{69} -14.4107 q^{71} +(-2.98755 - 0.273062i) q^{72} +7.91381 q^{73} +(-0.500000 + 0.866025i) q^{74} +(4.33842 - 6.78089i) q^{75} +(-2.69076 - 4.66053i) q^{76} +(4.35087 + 0.198422i) q^{78} +(4.62422 - 8.00938i) q^{79} -0.593579 q^{80} +(8.85087 + 1.63157i) q^{81} +0.273346 q^{82} +(-3.85087 + 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} +(5.58113 + 9.66679i) q^{86} +(-5.78220 + 9.03749i) q^{87} +(-0.296790 + 0.514055i) q^{88} -12.4356 q^{89} +(1.77335 + 0.162084i) q^{90} +(-2.23025 + 3.86291i) q^{92} +(-6.26829 - 12.0985i) q^{93} +(-6.08113 - 10.5328i) q^{94} +(1.59718 + 2.76639i) q^{95} +(0.796790 + 1.53790i) q^{96} +(-5.86693 + 10.1618i) q^{97} +(1.02704 - 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 6 q + 3 q^{2} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - q^{20} + q^{22} - 7 q^{23} - 4 q^{24} + 2 q^{25} - 16 q^{26} + 7 q^{27} - 5 q^{29} - 3 q^{30} - 20 q^{31} + 3 q^{32} - 15 q^{33} - 4 q^{34} + 8 q^{36} - 6 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} - 6 q^{43} + 2 q^{44} + 12 q^{45} - 14 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} + 12 q^{51} - 8 q^{52} - 30 q^{53} + 8 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} + 14 q^{59} - 15 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} - 12 q^{66} + q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} + 38 q^{73} - 3 q^{74} - 17 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} + 2 q^{80} + 32 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} - 63 q^{87} + q^{88} - 18 q^{89} + 9 q^{90} - 7 q^{92} + q^{93} - 9 q^{94} - 4 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 - 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 - q^20 + q^22 - 7 * q^23 - 4 * q^24 + 2 * q^25 - 16 * q^26 + 7 * q^27 - 5 * q^29 - 3 * q^30 - 20 * q^31 + 3 * q^32 - 15 * q^33 - 4 * q^34 + 8 * q^36 - 6 * q^37 - 3 * q^38 + 4 * q^39 + q^40 - 6 * q^43 + 2 * q^44 + 12 * q^45 - 14 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 + 12 * q^51 - 8 * q^52 - 30 * q^53 + 8 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 + 14 * q^59 - 15 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 - 12 * q^66 + q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 + 38 * q^73 - 3 * q^74 - 17 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 + 2 * q^80 + 32 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 - 63 * q^87 + q^88 - 18 * q^89 + 9 * q^90 - 7 * q^92 + q^93 - 9 * q^94 - 4 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

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