LMFDB - Embedded newform 882.2.e.o.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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			373.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	882.373
Dual form			882.2.e.o.655.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.933463 - 1.45899i) q^{3} +1.00000 q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.933463 - 1.45899i) q^{3} +1.00000 q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +(-0.296790 - 0.514055i) q^{10} +(0.296790 - 0.514055i) q^{11} +(-0.933463 - 1.45899i) q^{12} +(1.25729 - 2.17770i) q^{13} +(0.472958 - 0.912864i) q^{15} +1.00000 q^{16} +(-1.46050 - 2.52967i) q^{17} +(1.25729 - 2.72382i) q^{18} +(-2.69076 + 4.66053i) q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(-2.23025 - 3.86291i) q^{23} +(0.933463 + 1.45899i) q^{24} +(2.32383 - 4.02499i) q^{25} +(-1.25729 + 2.17770i) q^{26} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +(-0.472958 + 0.912864i) q^{30} +7.86693 q^{31} -1.00000 q^{32} +(-1.02704 + 0.0468383i) q^{33} +(1.46050 + 2.52967i) q^{34} +(-1.25729 + 2.72382i) q^{36} +(0.500000 - 0.866025i) q^{37} +(2.69076 - 4.66053i) q^{38} +(-4.35087 + 0.198422i) q^{39} +(-0.296790 - 0.514055i) q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(0.296790 - 0.514055i) q^{44} +(-1.77335 + 0.162084i) q^{45} +(2.23025 + 3.86291i) q^{46} -12.1623 q^{47} +(-0.933463 - 1.45899i) q^{48} +(-2.32383 + 4.02499i) q^{50} +(-2.32743 + 4.49221i) q^{51} +(1.25729 - 2.17770i) q^{52} +(4.02704 + 6.97504i) q^{53} +(-5.14766 + 0.708209i) q^{54} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} +(3.09718 + 5.36447i) q^{58} -8.64766 q^{59} +(0.472958 - 0.912864i) q^{60} +6.64766 q^{61} -7.86693 q^{62} +1.00000 q^{64} +1.49261 q^{65} +(1.02704 - 0.0468383i) q^{66} -1.91381 q^{67} +(-1.46050 - 2.52967i) q^{68} +(-3.55408 + 6.85980i) q^{69} -14.4107 q^{71} +(1.25729 - 2.72382i) q^{72} +(-3.95691 - 6.85356i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-8.04163 + 0.366739i) q^{75} +(-2.69076 + 4.66053i) q^{76} +(4.35087 - 0.198422i) q^{78} -9.24844 q^{79} +(0.296790 + 0.514055i) q^{80} +(-5.83842 - 6.84929i) q^{81} +(-0.136673 + 0.236725i) q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(5.58113 + 9.66679i) q^{86} +(-4.93560 + 9.52628i) q^{87} +(-0.296790 + 0.514055i) q^{88} +(6.21780 - 10.7695i) q^{89} +(1.77335 - 0.162084i) q^{90} +(-2.23025 - 3.86291i) q^{92} +(-7.34348 - 11.4778i) q^{93} +12.1623 q^{94} -3.19436 q^{95} +(0.933463 + 1.45899i) q^{96} +(-5.86693 - 10.1618i) q^{97} +(1.02704 + 1.45472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} + q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} + 6 q^{16} + 4 q^{17} - 8 q^{18} + 3 q^{19} - q^{20} + q^{22} - 7 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} - 12 q^{30} + 40 q^{31} - 6 q^{32} + 3 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} - 3 q^{38} - 5 q^{39} + q^{40} - 6 q^{43} - q^{44} - 9 q^{45} + 7 q^{46} - 18 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{51} - 8 q^{52} + 15 q^{53} - 7 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} - 28 q^{59} + 12 q^{60} + 16 q^{61} - 40 q^{62} + 6 q^{64} + 24 q^{65} - 3 q^{66} - 2 q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} - 8 q^{72} - 19 q^{73} - 3 q^{74} - 8 q^{75} + 3 q^{76} + 5 q^{78} - 10 q^{79} - q^{80} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} + 27 q^{87} + q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} - 38 q^{93} + 18 q^{94} + 8 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 + q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 + 6 * q^16 + 4 * q^17 - 8 * q^18 + 3 * q^19 - q^20 + q^22 - 7 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 - 12 * q^30 + 40 * q^31 - 6 * q^32 + 3 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 - 3 * q^38 - 5 * q^39 + q^40 - 6 * q^43 - q^44 - 9 * q^45 + 7 * q^46 - 18 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^51 - 8 * q^52 + 15 * q^53 - 7 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 - 28 * q^59 + 12 * q^60 + 16 * q^61 - 40 * q^62 + 6 * q^64 + 24 * q^65 - 3 * q^66 - 2 * q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 - 8 * q^72 - 19 * q^73 - 3 * q^74 - 8 * q^75 + 3 * q^76 + 5 * q^78 - 10 * q^79 - q^80 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 + 27 * q^87 + q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 - 38 * q^93 + 18 * q^94 + 8 * 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.933463	−	1.45899i	−0.538935	−	0.842347i
$3$	−0.933463	−	1.45899i	−0.538935	−	0.842347i
$4$	1.00000			0.500000
$5$	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
$9$	−1.25729	+	2.72382i	−0.419098	+	0.907941i
$10$	−0.296790	−	0.514055i	−0.0938531	−	0.162558i
$11$	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	$0.138144\pi$
$12$	−0.933463	−	1.45899i	−0.269467	−	0.421174i
$13$	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
$16$	1.00000			0.250000
$17$	−1.46050	−	2.52967i	−0.354224	−	0.613535i	0.632760	−	0.774348i	$-0.281922\pi$
$17$	−1.46050	−	2.52967i	−0.354224	−	0.613535i	−0.986985	+	0.160813i	$0.948588\pi$
$18$	1.25729	−	2.72382i	0.296347	−	0.642011i
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	0.372674	+	0.927962i	$0.378441\pi$
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	−0.989976	+	0.141236i	$0.954892\pi$
$20$	0.296790	+	0.514055i	0.0663642	+	0.114946i
$21$		0			0
$22$	−0.296790	+	0.514055i	−0.0632758	+	0.109597i
$23$	−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	$0.987293\pi$
$24$	0.933463	+	1.45899i	0.190542	+	0.297815i
$25$	2.32383	−	4.02499i	0.464766	−	0.804999i
$26$	−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	$-0.361716\pi$
$30$	−0.472958	+	0.912864i	−0.0863499	+	0.166665i
$31$	7.86693			1.41294			0.706471	−	0.707742i	$-0.250286\pi$
$31$	7.86693			1.41294			0.706471	+	0.707742i	$0.250286\pi$
$32$	−1.00000			−0.176777
$33$	−1.02704	+	0.0468383i	−0.178785	+	0.00815350i
$34$	1.46050	+	2.52967i	0.250475	+	0.433835i
$35$		0			0
$36$	−1.25729	+	2.72382i	−0.209549	+	0.453970i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	2.69076	−	4.66053i	0.436498	−	0.756038i
$39$	−4.35087	+	0.198422i	−0.696697	+	0.0317729i
$40$	−0.296790	−	0.514055i	−0.0469266	−	0.0812792i
$41$	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
$45$	−1.77335	+	0.162084i	−0.264355	+	0.0241621i
$46$	2.23025	+	3.86291i	0.328833	+	0.569555i
$47$	−12.1623			−1.77405			−0.887023	−	0.461724i	$-0.847231\pi$
$47$	−12.1623			−1.77405			−0.887023	+	0.461724i	$0.847231\pi$
$48$	−0.933463	−	1.45899i	−0.134734	−	0.210587i
$49$		0			0
$50$	−2.32383	+	4.02499i	−0.328639	+	0.569220i
$51$	−2.32743	+	4.49221i	−0.325905	+	0.629035i
$52$	1.25729	−	2.17770i	0.174355	−	0.301992i
$53$	4.02704	+	6.97504i	0.553157	+	0.958096i	0.998044	+	0.0625092i	$0.0199103\pi$
$53$	4.02704	+	6.97504i	0.553157	+	0.958096i	−0.444888	+	0.895586i	$0.646756\pi$
$54$	−5.14766	+	0.708209i	−0.700508	+	0.0963750i
$55$	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
$59$	−8.64766			−1.12583			−0.562915	−	0.826515i	$-0.690320\pi$
$59$	−8.64766			−1.12583			−0.562915	+	0.826515i	$0.690320\pi$
$60$	0.472958	−	0.912864i	0.0610586	−	0.117850i
$61$	6.64766			0.851146			0.425573	−	0.904924i	$-0.360073\pi$
$61$	6.64766			0.851146			0.425573	+	0.904924i	$0.360073\pi$
$62$	−7.86693			−0.999101
$63$		0			0
$64$	1.00000			0.125000
$65$	1.49261			0.185135
$66$	1.02704	−	0.0468383i	0.126420	−	0.00576540i
$67$	−1.91381			−0.233809			−0.116905	−	0.993143i	$-0.537297\pi$
$67$	−1.91381			−0.233809			−0.116905	+	0.993143i	$0.537297\pi$
$68$	−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	$0.826515\pi$
$72$	1.25729	−	2.72382i	0.148174	−	0.321006i
$73$	−3.95691	−	6.85356i	−0.463121	−	0.802149i	0.535994	−	0.844222i	$-0.319937\pi$
$73$	−3.95691	−	6.85356i	−0.463121	−	0.802149i	−0.999115	+	0.0420732i	$0.986604\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	−8.04163	+	0.366739i	−0.928568	+	0.0423474i
$76$	−2.69076	+	4.66053i	−0.308651	+	0.534599i
$77$		0			0
$78$	4.35087	−	0.198422i	0.492639	−	0.0224668i
$79$	−9.24844			−1.04053			−0.520265	−	0.854005i	$-0.674167\pi$
$79$	−9.24844			−1.04053			−0.520265	+	0.854005i	$0.674167\pi$
$80$	0.296790	+	0.514055i	0.0331821	+	0.0574731i
$81$	−5.83842	−	6.84929i	−0.648713	−	0.761033i
$82$	−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
$86$	5.58113	+	9.66679i	0.601828	+	1.04240i
$87$	−4.93560	+	9.52628i	−0.529152	+	1.02132i
$88$	−0.296790	+	0.514055i	−0.0316379	+	0.0547984i
$89$	6.21780	−	10.7695i	0.659085	−	1.14157i	−0.321767	−	0.946819i	$-0.604277\pi$
$89$	6.21780	−	10.7695i	0.659085	−	1.14157i	0.980853	−	0.194751i	$-0.0623898\pi$
$90$	1.77335	−	0.162084i	0.186927	−	0.0170852i
$91$		0			0
$92$	−2.23025	−	3.86291i	−0.232520	−	0.402736i
$93$	−7.34348	−	11.4778i	−0.761484	−	1.19019i
$94$	12.1623			1.25444
$95$	−3.19436			−0.327734
$96$	0.933463	+	1.45899i	0.0952711	+	0.148907i
$97$	−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
$101$	−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	$0.192393\pi$
$102$	2.32743	−	4.49221i	0.230450	−	0.444795i
$103$	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
$107$	9.35447	−	16.2024i	0.904331	−	1.56635i	0.0825182	−	0.996590i	$-0.473704\pi$
$107$	9.35447	−	16.2024i	0.904331	−	1.56635i	0.821813	−	0.569758i	$-0.192963\pi$
$108$	5.14766	−	0.708209i	0.495334	−	0.0681474i
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	0.789173	−	0.614171i	$-0.210509\pi$
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	−0.926474	+	0.376359i	$0.877176\pi$
$110$	−0.352336			−0.0335940
$111$	−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	$0.969916\pi$
$114$	−9.31138	+	0.424646i	−0.872091	+	0.0397717i
$115$	1.32383	−	2.29294i	0.123448	−	0.213818i
$116$	−3.09718	−	5.36447i	−0.287566	−	0.498078i
$117$	4.35087	+	6.16266i	0.402238	+	0.569738i
$118$	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
$122$	−6.64766			−0.601851
$123$	−0.472958	+	0.0215693i	−0.0426452	+	0.00194484i
$124$	7.86693			0.706471
$125$	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	$0.315671\pi$
$128$	−1.00000			−0.0883883
$129$	−8.89397	+	17.1664i	−0.783070	+	1.51142i
$130$	−1.49261			−0.130910
$131$	−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
$135$	1.89183	+	2.43599i	0.162823	+	0.209657i
$136$	1.46050	+	2.52967i	0.125237	+	0.216917i
$137$	−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	$0.201023\pi$
$138$	3.55408	−	6.85980i	0.302544	−	0.583945i
$139$	−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
$142$	14.4107			1.20932
$143$	−0.746304	−	1.29264i	−0.0624091	−	0.108096i
$144$	−1.25729	+	2.72382i	−0.104775	+	0.226985i
$145$	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
$149$	−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	$-0.431559\pi$
$150$	8.04163	−	0.366739i	0.656596	−	0.0299441i
$151$	−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	$0.188023\pi$
$152$	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
$156$	−4.35087	+	0.198422i	−0.348349	+	0.0158865i
$157$	6.60078			0.526799			0.263400	−	0.964687i	$-0.415156\pi$
$157$	6.60078			0.526799			0.263400	+	0.964687i	$0.415156\pi$
$158$	9.24844			0.735766
$159$	6.41741	−	12.3863i	0.508934	−	0.982301i
$160$	−0.296790	−	0.514055i	−0.0234633	−	0.0406396i
$161$		0			0
$162$	5.83842	+	6.84929i	0.458710	+	0.538131i
$163$	−2.99115	+	5.18082i	−0.234285	+	0.405793i	−0.959065	−	0.283188i	$-0.908608\pi$
$163$	−2.99115	+	5.18082i	−0.234285	+	0.405793i	0.724780	+	0.688980i	$0.241941\pi$
$164$	0.136673	−	0.236725i	0.0106724	−	0.0184851i
$165$	−0.328893	−	0.514055i	−0.0256043	−	0.0400191i
$166$	3.85087	+	6.66991i	0.298886	+	0.517685i
$167$	−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
$171$	−9.31138	−	13.1888i	−0.712059	−	1.00857i
$172$	−5.58113	−	9.66679i	−0.425557	−	0.737086i
$173$	25.6591			1.95083			0.975414	−	0.220381i	$-0.0707301\pi$
$173$	25.6591			1.95083			0.975414	+	0.220381i	$0.0707301\pi$
$174$	4.93560	−	9.52628i	0.374167	−	0.722185i
$175$		0			0
$176$	0.296790	−	0.514055i	0.0223714	−	0.0387483i
$177$	8.07227	+	12.6168i	0.606749	+	0.948340i
$178$	−6.21780	+	10.7695i	−0.466044	+	0.807211i
$179$	7.51819	+	13.0219i	0.561936	+	0.973301i	0.997328	+	0.0730602i	$0.0232765\pi$
$179$	7.51819	+	13.0219i	0.561936	+	0.973301i	−0.435392	+	0.900241i	$0.643390\pi$
$180$	−1.77335	+	0.162084i	−0.132177	+	0.0120810i
$181$	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
$185$	0.593579			0.0436408
$186$	7.34348	+	11.4778i	0.538450	+	0.841590i
$187$	−1.73385			−0.126792
$188$	−12.1623			−0.887023
$189$		0			0
$190$	3.19436			0.231743
$191$	3.98229			0.288148			0.144074	−	0.989567i	$-0.453980\pi$
$191$	3.98229			0.288148			0.144074	+	0.989567i	$0.453980\pi$
$192$	−0.933463	−	1.45899i	−0.0673669	−	0.105293i
$193$	6.78074			0.488088			0.244044	−	0.969764i	$-0.421526\pi$
$193$	6.78074			0.488088			0.244044	+	0.969764i	$0.421526\pi$
$194$	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	$0.371113\pi$
$198$	−1.02704	−	1.45472i	−0.0729887	−	0.103383i
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	0.749109	−	0.662447i	$-0.230482\pi$
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	−0.948250	+	0.317523i	$0.897149\pi$
$200$	−2.32383	+	4.02499i	−0.164320	+	0.284610i
$201$	1.78647	+	2.79223i	0.126008	+	0.196949i
$202$	0.811379	−	1.40535i	0.0570884	−	0.0988800i
$203$		0			0
$204$	−2.32743	+	4.49221i	−0.162953	+	0.314518i
$205$	0.162253			0.0113322
$206$	−3.19076	−	5.52655i	−0.222311	−	0.385053i
$207$	13.3260	−	1.21800i	0.926219	−	0.0846566i
$208$	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	$-0.0649772\pi$
$212$	4.02704	+	6.97504i	0.276578	+	0.479048i
$213$	13.4518	+	21.0250i	0.921705	+	1.44061i
$214$	−9.35447	+	16.2024i	−0.639459	+	1.10757i
$215$	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
$219$	−6.30564	+	12.1706i	−0.426096	+	0.822415i
$220$	0.352336			0.0237545
$221$	−7.34514			−0.494088
$222$	1.73025	−	0.0789082i	0.116127	−	0.00529597i
$223$	−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
$227$	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	$0.115562\pi$
$228$	9.31138	−	0.424646i	0.616661	−	0.0281229i
$229$	−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
$233$	0.0971780	−	0.168317i	0.00636634	−	0.0110268i	−0.862825	−	0.505503i	$-0.831307\pi$
$233$	0.0971780	−	0.168317i	0.00636634	−	0.0110268i	0.869191	+	0.494476i	$0.164640\pi$
$234$	−4.35087	−	6.16266i	−0.284426	−	0.402865i
$235$	−3.60963	−	6.25206i	−0.235466	−	0.407840i
$236$	−8.64766			−0.562915
$237$	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	$0.312266\pi$
$240$	0.472958	−	0.912864i	0.0305293	−	0.0589251i
$241$	−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	$0.304181\pi$
$242$	−5.32383	−	9.22115i	−0.342229	−	0.592758i
$243$	−4.54309	+	14.9118i	−0.291440	+	0.956589i
$244$	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
$248$	−7.86693			−0.499550
$249$	−6.13667	+	11.8445i	−0.388896	+	0.750614i
$250$	−5.72665			−0.362185
$251$	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
$254$	−12.3346			−0.773943
$255$	−3.00000	+	0.136815i	−0.187867	+	0.00856770i
$256$	1.00000			0.0625000
$257$	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
$261$	18.5059	−	1.69145i	1.14549	−	0.104698i
$262$	0.593579	+	1.02811i	0.0366715	+	0.0635168i
$263$	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	$-0.00998713\pi$
$264$	1.02704	−	0.0468383i	0.0632101	−	0.00288270i
$265$	−2.39037	+	4.14024i	−0.146839	+	0.254333i
$266$		0			0
$267$	−21.5167	+	0.981271i	−1.31680	+	0.0600528i
$268$	−1.91381			−0.116905
$269$	5.00720	+	8.67272i	0.305294	+	0.528785i	0.977327	−	0.211737i	$-0.0679119\pi$
$269$	5.00720	+	8.67272i	0.305294	+	0.528785i	−0.672033	+	0.740522i	$0.734579\pi$
$270$	−1.89183	−	2.43599i	−0.115133	−	0.148250i
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	−0.978380	−	0.206818i	$-0.933689\pi$
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	0.668299	+	0.743893i	$0.267023\pi$
$272$	−1.46050	−	2.52967i	−0.0885561	−	0.153384i
$273$		0			0
$274$	1.26089	−	2.18393i	0.0761733	−	0.131936i
$275$	−1.37938	−	2.38915i	−0.0831797	−	0.144071i
$276$	−3.55408	+	6.85980i	−0.213931	+	0.412911i
$277$	−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	$0.969297\pi$
$278$	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	$0.958054\pi$
$282$	−11.3530	−	17.7446i	−0.676062	−	1.05667i
$283$	16.3523			0.972046			0.486023	−	0.873946i	$-0.338447\pi$
$283$	16.3523			0.972046			0.486023	+	0.873946i	$0.338447\pi$
$284$	−14.4107			−0.855117
$285$	2.98181	+	4.66053i	0.176627	+	0.276066i
$286$	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
$290$	−1.83842	+	3.18424i	−0.107956	+	0.186985i
$291$	−9.34941	+	18.0455i	−0.548072	+	1.05784i
$292$	−3.95691	−	6.85356i	−0.231560	−	0.401074i
$293$	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
$297$	1.16372	−	2.85637i	0.0675256	−	0.165743i
$298$	9.02558	+	15.6328i	0.522838	+	0.905582i
$299$	−11.2163			−0.648658
$300$	−8.04163	+	0.366739i	−0.464284	+	0.0211737i
$301$		0			0
$302$	0.823832	−	1.42692i	0.0474062	−	0.0821099i
$303$	2.80778	−	0.128049i	0.161303	−	0.00735622i
$304$	−2.69076	+	4.66053i	−0.154326	+	0.267300i
$305$	1.97296	+	3.41726i	0.112971	+	0.195672i
$306$	−8.72665	+	0.797618i	−0.498870	+	0.0455968i
$307$	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
$311$	6.51459			0.369408			0.184704	−	0.982794i	$-0.440867\pi$
$311$	6.51459			0.369408			0.184704	+	0.982794i	$0.440867\pi$
$312$	4.35087	−	0.198422i	0.246320	−	0.0112334i
$313$	−0.266149			−0.0150436			−0.00752181	−	0.999972i	$-0.502394\pi$
$313$	−0.266149			−0.0150436			−0.00752181	+	0.999972i	$0.502394\pi$
$314$	−6.60078			−0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	15.7237			0.883133			0.441566	−	0.897229i	$-0.354423\pi$
$317$	15.7237			0.883133			0.441566	+	0.897229i	$0.354423\pi$
$318$	−6.41741	+	12.3863i	−0.359871	+	0.694592i
$319$	−3.67684			−0.205864
$320$	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
$324$	−5.83842	−	6.84929i	−0.324357	−	0.380516i
$325$	−5.84348	−	10.1212i	−0.324138	−	0.561424i
$326$	2.99115	−	5.18082i	0.165664	−	0.286939i
$327$	−2.28434	+	4.40904i	−0.126324	+	0.243820i
$328$	−0.136673	+	0.236725i	−0.00754651	+	0.0130709i
$329$		0			0
$330$	0.328893	+	0.514055i	0.0181050	+	0.0282978i
$331$	−25.1623			−1.38304			−0.691521	−	0.722356i	$-0.743059\pi$
$331$	−25.1623			−1.38304			−0.691521	+	0.722356i	$0.743059\pi$
$332$	−3.85087	−	6.66991i	−0.211344	−	0.366059i
$333$	1.73025	+	2.45076i	0.0948172	+	0.134301i
$334$	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	$0.996220\pi$
$338$	−3.33842	−	5.78231i	−0.181586	−	0.314516i
$339$	21.3171	−	0.972168i	1.15779	−	0.0528009i
$340$	0.866926	−	1.50156i	0.0470156	−	0.0814335i
$341$	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
$345$	−4.58113	+	0.208922i	−0.246640	+	0.0112480i
$346$	−25.6591			−1.37944
$347$	22.5438			1.21021			0.605106	−	0.796145i	$-0.293131\pi$
$347$	22.5438			1.21021			0.605106	+	0.796145i	$0.293131\pi$
$348$	−4.93560	+	9.52628i	−0.264576	+	0.510662i
$349$	−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
$353$	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	$0.108445\pi$
$354$	−8.07227	−	12.6168i	−0.429036	−	0.670578i
$355$	−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
$359$	−6.32237	+	10.9507i	−0.333682	+	0.577954i	−0.983231	−	0.182366i	$-0.941624\pi$
$359$	−6.32237	+	10.9507i	−0.333682	+	0.577954i	0.649549	+	0.760320i	$0.274958\pi$
$360$	1.77335	−	0.162084i	0.0934636	−	0.00854259i
$361$	−4.98035	−	8.62622i	−0.262124	−	0.454012i
$362$	−0.0861875			−0.00452991
$363$	8.48395	−	16.3750i	0.445292	−	0.859465i
$364$		0			0
$365$	2.34874	−	4.06813i	0.122939	−	0.212936i
$366$	6.20535	+	9.69886i	0.324359	+	0.506968i
$367$	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	$0.112034\pi$
$368$	−2.23025	−	3.86291i	−0.116260	−	0.201368i
$369$	0.472958	+	0.669906i	0.0246212	+	0.0348739i
$370$	−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	$0.911823\pi$
$374$	1.73385			0.0896553
$375$	−5.34562	−	8.35512i	−0.276047	−	0.431457i
$376$	12.1623			0.627220
$377$	−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	$0.559848\pi$
$380$	−3.19436			−0.163867
$381$	−11.5139	−	17.9961i	−0.589876	−	0.921967i
$382$	−3.98229			−0.203752
$383$	−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
$387$	33.3478	−	3.04799i	1.69516	−	0.154938i
$388$	−5.86693	−	10.1618i	−0.297848	−	0.515888i
$389$	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	$0.0310857\pi$
$390$	1.39329	+	2.17770i	0.0705522	+	0.110272i
$391$	−6.51459	+	11.2836i	−0.329457	+	0.570636i
$392$		0			0
$393$	−0.945916	+	1.82573i	−0.0477151	+	0.0920958i
$394$	−11.0584			−0.557112
$395$	−2.74484	−	4.75420i	−0.138108	−	0.239210i
$396$	1.02704	+	1.45472i	0.0516108	+	0.0731025i
$397$	6.08619	−	10.5416i	0.305457	−	0.529067i	−0.671906	−	0.740636i	$-0.734524\pi$
$397$	6.08619	−	10.5416i	0.305457	−	0.529067i	0.977363	+	0.211569i	$0.0678574\pi$
$398$	2.80924	+	4.86575i	0.140815	+	0.243898i
$399$		0			0
$400$	2.32383	−	4.02499i	0.116192	−	0.201250i
$401$	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	$0.519965\pi$
$402$	−1.78647	−	2.79223i	−0.0891012	−	0.139264i
$403$	9.89104	−	17.1318i	0.492708	−	0.853395i
$404$	−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
$408$	2.32743	−	4.49221i	0.115225	−	0.222398i
$409$	5.78074			0.285839			0.142920	−	0.989734i	$-0.454351\pi$
$409$	5.78074			0.285839			0.142920	+	0.989734i	$0.454351\pi$
$410$	−0.162253			−0.00801309
$411$	4.36333	−	0.198990i	0.215227	−	0.00981544i
$412$	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
$416$	−1.25729	+	2.17770i	−0.0616439	+	0.106770i
$417$	8.50214	−	0.387740i	0.416351	−	0.0189877i
$418$	−1.59718	−	2.76639i	−0.0781205	−	0.135309i
$419$	−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
$423$	15.2915	−	33.1278i	0.743500	−	1.61073i
$424$	−4.02704	−	6.97504i	−0.195570	−	0.338738i
$425$	−13.5759			−0.658526
$426$	−13.4518	−	21.0250i	−0.651744	−	1.01867i
$427$		0			0
$428$	9.35447	−	16.2024i	0.452165	−	0.783174i
$429$	−1.18929	+	2.29548i	−0.0574197	+	0.110827i
$430$	−3.31284	+	5.73801i	−0.159759	+	0.276711i
$431$	−14.0979	−	24.4182i	−0.679070	−	1.17618i	−0.975261	−	0.221055i	$-0.929050\pi$
$431$	−14.0979	−	24.4182i	−0.679070	−	1.17618i	0.296192	−	0.955128i	$-0.404283\pi$
$432$	5.14766	−	0.708209i	0.247667	−	0.0340737i
$433$	−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
$437$	24.0043			1.14828
$438$	6.30564	−	12.1706i	0.301295	−	0.581535i
$439$	−26.0406			−1.24285			−0.621426	−	0.783473i	$-0.713446\pi$
$439$	−26.0406			−1.24285			−0.621426	+	0.783473i	$0.713446\pi$
$440$	−0.352336			−0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	−23.5729			−1.11998			−0.559992	−	0.828498i	$-0.689196\pi$
$443$	−23.5729			−1.11998			−0.559992	+	0.828498i	$0.689196\pi$
$444$	−1.73025	+	0.0789082i	−0.0821141	+	0.00374482i
$445$	7.38151			0.349917
$446$	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	$0.395321\pi$
$450$	−8.04163	−	11.3903i	−0.379086	−	0.536944i
$451$	−0.0811263	−	0.140515i	−0.00382009	−	0.00661659i
$452$	−6.16012	+	10.6696i	−0.289748	+	0.501857i
$453$	2.85087	−	0.130014i	0.133946	−	0.00610860i
$454$	−2.40856	+	4.17174i	−0.113039	+	0.195790i
$455$		0			0
$456$	−9.31138	+	0.424646i	−0.436045	+	0.0198859i
$457$	−22.3523			−1.04560			−0.522799	−	0.852456i	$-0.675112\pi$
$457$	−22.3523			−1.04560			−0.522799	+	0.852456i	$0.675112\pi$
$458$	4.64766	+	8.04999i	0.217171	+	0.376151i
$459$	−9.30972	−	11.9875i	−0.434541	−	0.559530i
$460$	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	$0.933937\pi$
$464$	−3.09718	−	5.36447i	−0.143783	−	0.249039i
$465$	3.72072	−	7.18143i	0.172544	−	0.333031i
$466$	−0.0971780	+	0.168317i	−0.00450168	+	0.00779714i
$467$	−16.7829	+	29.0688i	−0.776619	+	1.34514i	0.157261	+	0.987557i	$0.449733\pi$
$467$	−16.7829	+	29.0688i	−0.776619	+	1.34514i	−0.933880	+	0.357586i	$0.883600\pi$
$468$	4.35087	+	6.16266i	0.201119	+	0.284869i
$469$		0			0
$470$	3.60963	+	6.25206i	0.166500	+	0.288386i
$471$	−6.16158	−	9.63046i	−0.283911	−	0.443748i
$472$	8.64766			0.398041
$473$	−6.62568			−0.304649
$474$	−8.63307	−	13.4934i	−0.396530	−	0.619771i
$475$	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
$479$	0.183560	−	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	$0.163997\pi$
$480$	−0.472958	+	0.912864i	−0.0215875	+	0.0416663i
$481$	−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
$485$	3.48249	−	6.03184i	0.158132	−	0.273892i
$486$	4.54309	−	14.9118i	0.206079	−	0.676411i
$487$	−14.9538	−	25.9007i	−0.677621	−	1.17367i	−0.975695	−	0.219131i	$-0.929678\pi$
$487$	−14.9538	−	25.9007i	−0.677621	−	1.17367i	0.298075	−	0.954543i	$-0.403656\pi$
$488$	−6.64766			−0.300926
$489$	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	$0.170332\pi$
$492$	−0.472958	+	0.0215693i	−0.0213226	+	0.000972418i
$493$	−9.04689	+	15.6697i	−0.407451	+	0.705726i
$494$	−6.76615	−	11.7193i	−0.304423	−	0.527277i
$495$	−0.442991	+	0.959702i	−0.0199110	+	0.0431354i
$496$	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	$0.693359\pi$
$500$	5.72665			0.256104
$501$	12.9086	−	0.588695i	0.576712	−	0.0263010i
$502$	−19.5438			−0.872281
$503$	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
$506$	2.64766			0.117703
$507$	5.32004	−	10.2683i	0.236271	−	0.456031i
$508$	12.3346			0.547261
$509$	−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
$513$	−10.5505	+	25.8965i	−0.465815	+	1.14336i
$514$	−4.16372	−	7.21177i	−0.183654	−	0.318097i
$515$	−1.89397	+	3.28045i	−0.0834582	+	0.144554i
$516$	−8.89397	+	17.1664i	−0.391535	+	0.755708i
$517$	−3.60963	+	6.25206i	−0.158751	+	0.274965i
$518$		0			0
$519$	−23.9518	−	37.4364i	−1.05137	−	1.64327i
$520$	−1.49261			−0.0654552
$521$	13.7360	+	23.7914i	0.601785	+	1.04232i	0.992551	+	0.121831i	$0.0388767\pi$
$521$	13.7360	+	23.7914i	0.601785	+	1.04232i	−0.390766	+	0.920490i	$0.627790\pi$
$522$	−18.5059	+	1.69145i	−0.809983	+	0.0740326i
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	−0.999852	−	0.0172166i	$-0.994520\pi$
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	0.514836	+	0.857289i	$0.327853\pi$
$524$	−0.593579	−	1.02811i	−0.0259306	−	0.0449132i
$525$		0			0
$526$	−8.54523	+	14.8008i	−0.372590	+	0.645344i
$527$	−11.4897	−	19.9007i	−0.500498	−	0.866889i
$528$	−1.02704	+	0.0468383i	−0.0446963	+	0.00203838i
$529$	1.55195	−	2.68805i	0.0674760	−	0.116872i
$530$	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
$534$	21.5167	−	0.981271i	0.931120	−	0.0424638i
$535$	11.1052			0.480122
$536$	1.91381			0.0826641
$537$	11.9808	−	23.1244i	0.517011	−	0.997891i
$538$	−5.00720	−	8.67272i	−0.215876	−	0.373908i
$539$		0			0
$540$	1.89183	+	2.43599i	0.0814115	+	0.104828i
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	−0.343403	−	0.939188i	$-0.611580\pi$
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	0.985062	−	0.172198i	$-0.0550869\pi$
$542$	5.10457	−	8.84137i	0.219260	−	0.379770i
$543$	−0.0804528	−	0.125747i	−0.00345256	−	0.00539630i
$544$	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	0.990789	−	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
$549$	−8.35807	+	18.1071i	−0.356714	+	0.772790i
$550$	1.37938	+	2.38915i	0.0588169	+	0.101874i
$551$	33.3350			1.42012
$552$	3.55408	−	6.85980i	0.151272	−	0.291972i
$553$		0			0
$554$	9.67111	−	16.7508i	0.410886	−	0.711675i
$555$	−0.554084	−	0.866025i	−0.0235196	−	0.0367607i
$556$	−2.45691	+	4.25549i	−0.104196	+	0.180473i
$557$	15.0651	+	26.0935i	0.638328	+	1.10562i	0.985800	+	0.167926i	$0.0537069\pi$
$557$	15.0651	+	26.0935i	0.638328	+	1.10562i	−0.347472	+	0.937690i	$0.612960\pi$
$558$	9.89104	−	21.4281i	0.418721	−	0.907124i
$559$	−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
$563$	−4.09766			−0.172696			−0.0863478	−	0.996265i	$-0.527520\pi$
$563$	−4.09766			−0.172696			−0.0863478	+	0.996265i	$0.527520\pi$
$564$	11.3530	+	17.7446i	0.478048	+	0.747182i
$565$	−7.31304			−0.307662
$566$	−16.3523			−0.687340
$567$		0			0
$568$	14.4107			0.604659
$569$	6.23697			0.261467			0.130734	−	0.991418i	$-0.458267\pi$
$569$	6.23697			0.261467			0.130734	+	0.991418i	$0.458267\pi$
$570$	−2.98181	−	4.66053i	−0.124894	−	0.195208i
$571$	35.6021			1.48990			0.744951	−	0.667119i	$-0.232473\pi$
$571$	35.6021			1.48990			0.744951	+	0.667119i	$0.232473\pi$
$572$	−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
$576$	−1.25729	+	2.72382i	−0.0523873	+	0.113493i
$577$	−23.1388	−	40.0776i	−0.963281	−	1.66845i	−0.714164	−	0.699979i	$-0.753193\pi$
$577$	−23.1388	−	40.0776i	−0.963281	−	1.66845i	−0.249118	−	0.968473i	$-0.580141\pi$
$578$	−4.23385	+	7.33325i	−0.176105	+	0.305023i
$579$	−6.32957	−	9.89302i	−0.263048	−	0.411140i
$580$	1.83842	−	3.18424i	0.0763363	−	0.132218i
$581$		0			0
$582$	9.34941	−	18.0455i	0.387546	−	0.748008i
$583$	4.78074			0.197998
$584$	3.95691	+	6.85356i	0.163738	+	0.283602i
$585$	−1.87665	+	4.06560i	−0.0775898	+	0.168092i
$586$	−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
$590$	2.56654	+	4.44537i	0.105663	+	0.183013i
$591$	−10.3226	−	16.1340i	−0.424614	−	0.663665i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−23.0979	+	40.0067i	−0.948515	+	1.64288i	−0.199960	+	0.979804i	$0.564081\pi$
$593$	−23.0979	+	40.0067i	−0.948515	+	1.64288i	−0.748555	+	0.663072i	$0.769252\pi$
$594$	−1.16372	+	2.85637i	−0.0477478	+	0.117198i
$595$		0			0
$596$	−9.02558	−	15.6328i	−0.369702	−	0.640343i
$597$	−4.47675	+	8.64065i	−0.183221	+	0.353638i
$598$	11.2163			0.458670
$599$	−16.7807			−0.685642			−0.342821	−	0.939401i	$-0.611382\pi$
$599$	−16.7807			−0.685642			−0.342821	+	0.939401i	$0.611382\pi$
$600$	8.04163	−	0.366739i	0.328298	−	0.0149721i
$601$	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
$605$	−3.16012	+	5.47348i	−0.128477	+	0.222529i
$606$	−2.80778	+	0.128049i	−0.114058	+	0.00520163i
$607$	−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
$611$	−15.2915	+	26.4857i	−0.618629	+	1.07150i
$612$	8.72665	−	0.797618i	0.352754	−	0.0322418i
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	0.999967	−	0.00809942i	$-0.00257815\pi$
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	−0.506998	+	0.861947i	$0.669245\pi$
$614$	−22.6768			−0.915163
$615$	−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	$-0.278350\pi$
$618$	−5.08472	+	9.81411i	−0.204538	+	0.394781i
$619$	−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	$0.812047\pi$
$620$	2.33482	+	4.04403i	0.0937687	+	0.162412i
$621$	−14.2163	−	18.3055i	−0.570482	−	0.734574i
$622$	−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
$626$	0.266149			0.0106375
$627$	2.54523	−	4.91259i	0.101647	−	0.196190i
$628$	6.60078			0.263400
$629$	−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	$0.269482\pi$
$632$	9.24844			0.367883
$633$	−33.4363	+	1.52486i	−1.32897	+	0.0606079i
$634$	−15.7237			−0.624469
$635$	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
$639$	18.1185	−	39.2522i	0.716756	−	1.55279i
$640$	−0.296790	−	0.514055i	−0.0117316	−	0.0203198i
$641$	−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	$0.958629\pi$
$642$	32.3712	−	1.47629i	1.27759	−	0.0582645i
$643$	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
$646$	−15.7195			−0.618474
$647$	6.63521	+	11.4925i	0.260857	+	0.451818i	0.966470	−	0.256780i	$-0.0826615\pi$
$647$	6.63521	+	11.4925i	0.260857	+	0.451818i	−0.705613	+	0.708598i	$0.749328\pi$
$648$	5.83842	+	6.84929i	0.229355	+	0.269066i
$649$	−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
$653$	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	$0.724461\pi$
$654$	2.28434	−	4.40904i	0.0893246	−	0.172407i
$655$	0.352336	−	0.610265i	0.0137669	−	0.0238450i
$656$	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	$0.780254\pi$
$660$	−0.328893	−	0.514055i	−0.0128021	−	0.0200096i
$661$	−34.3360			−1.33551			−0.667757	−	0.744379i	$-0.732746\pi$
$661$	−34.3360			−1.33551			−0.667757	+	0.744379i	$0.732746\pi$
$662$	25.1623			0.977959
$663$	6.85641	+	10.7165i	0.266281	+	0.416193i
$664$	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
$668$	−3.73025	+	6.46099i	−0.144328	+	0.249983i
$669$	−20.1783	+	38.9465i	−0.780138	+	1.50576i
$670$	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	0.678546	−	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
$675$	9.11177	−	22.3651i	0.350712	−	0.860832i
$676$	3.33842	+	5.78231i	0.128401	+	0.222397i
$677$	7.38151			0.283695			0.141847	−	0.989889i	$-0.454696\pi$
$677$	7.38151			0.283695			0.141847	+	0.989889i	$0.454696\pi$
$678$	−21.3171	+	0.972168i	−0.818679	+	0.0373359i
$679$		0			0
$680$	−0.866926	+	1.50156i	−0.0332451	+	0.0575822i
$681$	−8.33482	+	0.380110i	−0.319391	+	0.0145658i
$682$	−2.33482	+	4.04403i	−0.0894050	+	0.154854i
$683$	4.79893	+	8.31198i	0.183626	+	0.318049i	0.943113	−	0.332474i	$-0.107883\pi$
$683$	4.79893	+	8.31198i	0.183626	+	0.318049i	−0.759487	+	0.650523i	$0.774550\pi$
$684$	−9.31138	−	13.1888i	−0.356029	−	0.504286i
$685$	−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
$689$	20.2527			0.771567
$690$	4.58113	−	0.208922i	0.174400	−	0.00795354i
$691$	14.1445			0.538084			0.269042	−	0.963128i	$-0.413293\pi$
$691$	14.1445			0.538084			0.269042	+	0.963128i	$0.413293\pi$
$692$	25.6591			0.975414
$693$		0			0
$694$	−22.5438			−0.855750
$695$	−2.91674			−0.110638
$696$	4.93560	−	9.52628i	0.187083	−	0.361093i
$697$	−0.798447			−0.0302433
$698$	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	$0.250578\pi$
$702$	−4.92986	+	12.1005i	−0.186066	+	0.456703i
$703$	2.69076	+	4.66053i	0.101484	+	0.175775i
$704$	0.296790	−	0.514055i	0.0111857	−	0.0193742i
$705$	−5.75223	+	11.1025i	−0.216642	+	0.418144i
$706$	−3.41741	+	5.91913i	−0.128616	+	0.222769i
$707$		0			0
$708$	8.07227	+	12.6168i	0.303375	+	0.474170i
$709$	−10.4868			−0.393838			−0.196919	−	0.980420i	$-0.563094\pi$
$709$	−10.4868			−0.393838			−0.196919	+	0.980420i	$0.563094\pi$
$710$	4.27694	+	7.40789i	0.160511	+	0.278013i
$711$	11.6280	−	25.1911i	0.436085	−	0.944741i
$712$	−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
$716$	7.51819	+	13.0219i	0.280968	+	0.486651i
$717$	23.6264	−	1.07748i	0.882342	−	0.0402393i
$718$	6.32237	−	10.9507i	0.235949	−	0.408675i
$719$	−1.11995	+	1.93981i	−0.0417670	+	0.0723426i	−0.886153	−	0.463392i	$-0.846632\pi$
$719$	−1.11995	+	1.93981i	−0.0417670	+	0.0723426i	0.844386	+	0.535735i	$0.179965\pi$
$720$	−1.77335	+	0.162084i	−0.0660887	+	0.00604052i
$721$		0			0
$722$	4.98035	+	8.62622i	0.185349	+	0.321035i
$723$	22.4933	−	1.02581i	0.836534	−	0.0381502i
$724$	0.0861875			0.00320313
$725$	−28.7893			−1.06921
$726$	−8.48395	+	16.3750i	−0.314869	+	0.607733i
$727$	−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
$731$	−16.3025	+	28.2368i	−0.602971	+	1.04438i
$732$	−6.20535	−	9.69886i	−0.229356	−	0.358480i
$733$	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
$737$	−0.568000	+	0.983804i	−0.0209225	+	0.0362389i
$738$	−0.472958	−	0.669906i	−0.0174098	−	0.0246596i
$739$	13.3872	+	23.1874i	0.492458	+	0.852962i	0.999962	−	0.00868705i	$-0.00276521\pi$
$739$	13.3872	+	23.1874i	0.492458	+	0.852962i	−0.507504	+	0.861649i	$0.669432\pi$
$740$	0.593579			0.0218204
$741$	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	$0.225942\pi$
$744$	7.34348	+	11.4778i	0.269225	+	0.420795i
$745$	5.35740	−	9.27928i	0.196280	−	0.339967i
$746$	4.71420	+	8.16524i	0.172599	+	0.298951i
$747$	23.0093	−	2.10306i	0.841867	−	0.0769468i
$748$	−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	$0.900708\pi$
$752$	−12.1623			−0.443512
$753$	−18.2434	−	28.5141i	−0.664826	−	1.03911i
$754$	15.5763			0.567254
$755$	−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	$0.589376\pi$
$758$	7.27762			0.264335
$759$	2.47150	+	3.86291i	0.0897096	+	0.140215i
$760$	3.19436			0.115871
$761$	−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
$765$	3.00000	+	4.24925i	0.108465	+	0.153632i
$766$	12.0416	+	20.8567i	0.435082	+	0.753584i
$767$	−10.8727	+	18.8320i	−0.392589	+	0.679984i
$768$	−0.933463	−	1.45899i	−0.0336834	−	0.0526467i
$769$	−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
$772$	6.78074			0.244044
$773$	−3.10243	−	5.37357i	−0.111587	−	0.193274i	0.804823	−	0.593514i	$-0.202260\pi$
$773$	−3.10243	−	5.37357i	−0.111587	−	0.193274i	−0.916410	+	0.400240i	$0.868927\pi$
$774$	−33.3478	+	3.04799i	−1.19866	+	0.109558i
$775$	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
$779$	0.735508	+	1.27394i	0.0263523	+	0.0456436i
$780$	−1.39329	−	2.17770i	−0.0498879	−	0.0779741i
$781$	−4.27694	+	7.40789i	−0.153041	+	0.265075i
$782$	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
$786$	0.945916	−	1.82573i	0.0337397	−	0.0651215i
$787$	−6.09766			−0.217358			−0.108679	−	0.994077i	$-0.534662\pi$
$787$	−6.09766			−0.217358			−0.108679	+	0.994077i	$0.534662\pi$
$788$	11.0584			0.393938
$789$	−29.5708	+	1.34858i	−1.05275	+	0.0480107i
$790$	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
$794$	−6.08619	+	10.5416i	−0.215991	+	0.374107i
$795$	8.27188	−	0.377240i	0.293373	−	0.0133793i
$796$	−2.80924	−	4.86575i	−0.0995710	−	0.172462i
$797$	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
$801$	21.5167	+	30.4767i	0.760256	+	1.07684i
$802$	−16.6804	−	28.8914i	−0.589007	−	1.02019i
$803$	−4.69748			−0.165770
$804$	1.78647	+	2.79223i	0.0630040	+	0.0984744i
$805$		0			0
$806$	−9.89104	+	17.1318i	−0.348397	+	0.603442i
$807$	7.97937	−	15.4011i	0.280887	−	0.542145i
$808$	0.811379	−	1.40535i	0.0285442	−	0.0494400i
$809$	−2.81644	−	4.87822i	−0.0990208	−	0.171509i	0.812259	−	0.583297i	$-0.198238\pi$
$809$	−2.81644	−	4.87822i	−0.0990208	−	0.171509i	−0.911280	+	0.411788i	$0.864904\pi$
$810$	−1.78813	+	5.03407i	−0.0628285	+	0.176879i
$811$	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
$815$	−3.55096			−0.124385
$816$	−2.32743	+	4.49221i	−0.0814764	+	0.157259i
$817$	60.0698			2.10158
$818$	−5.78074			−0.202119
$819$		0			0
$820$	0.162253			0.00566611
$821$	32.6946			1.14105			0.570524	−	0.821281i	$-0.306740\pi$
$821$	32.6946			1.14105			0.570524	+	0.821281i	$0.306740\pi$
$822$	−4.36333	+	0.198990i	−0.152189	+	0.00694056i
$823$	−10.4399			−0.363911			−0.181956	−	0.983307i	$-0.558243\pi$
$823$	−10.4399			−0.363911			−0.181956	+	0.983307i	$0.558243\pi$
$824$	−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	$0.406191\pi$
$828$	13.3260	−	1.21800i	0.463109	−	0.0423283i
$829$	13.1046	+	22.6978i	0.455141	+	0.788327i	0.998696	−	0.0510466i	$-0.0162557\pi$
$829$	13.1046	+	22.6978i	0.455141	+	0.788327i	−0.543556	+	0.839373i	$0.682922\pi$
$830$	−2.28580	+	3.95912i	−0.0793412	+	0.137423i
$831$	33.4669	−	1.52626i	1.16095	−	0.0529454i
$832$	1.25729	−	2.17770i	0.0435888	−	0.0754981i
$833$		0			0
$834$	−8.50214	+	0.387740i	−0.294405	+	0.0134263i
$835$	−4.42840			−0.153251
$836$	1.59718	+	2.76639i	0.0552396	+	0.0956777i
$837$	40.4963	−	5.57143i	1.39976	−	0.192577i
$838$	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
$842$	1.86693	+	3.23361i	0.0643385	+	0.111438i
$843$	−10.2011	+	19.6893i	−0.351344	+	0.678134i
$844$	9.66225	−	16.7355i	0.332588	−	0.576060i
$845$	−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
$849$	−15.2643	−	23.8579i	−0.523869	−	0.818800i
$850$	13.5759			0.465649
$851$	−4.46050			−0.152904
$852$	13.4518	+	21.0250i	0.460853	+	0.720306i
$853$	−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
$857$	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	$0.124159\pi$
$858$	1.18929	−	2.29548i	0.0406019	−	0.0783663i
$859$	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
$863$	0.730252	−	1.26483i	0.0248581	−	0.0430555i	−0.853329	−	0.521373i	$-0.825420\pi$
$863$	0.730252	−	1.26483i	0.0248581	−	0.0430555i	0.878187	+	0.478318i	$0.158753\pi$
$864$	−5.14766	+	0.708209i	−0.175127	+	0.0240938i
$865$	7.61537	+	13.1902i	0.258930	+	0.448480i
$866$	12.5438			0.426255
$867$	−14.6513	+	0.668172i	−0.497583	+	0.0226923i
$868$		0			0
$869$	−2.74484	+	4.75420i	−0.0931124	+	0.161275i
$870$	6.36186	−	0.290133i	0.215687	−	0.00983643i
$871$	−2.40623	+	4.16771i	−0.0815319	+	0.141217i
$872$	1.43346	+	2.48283i	0.0485432	+	0.0840792i
$873$	35.0554	−	3.20407i	1.18645	−	0.108441i
$874$	−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	$0.820381\pi$
$878$	26.0406			0.878829
$879$	−35.9509	+	1.63954i	−1.21259	+	0.0553003i
$880$	0.352336			0.0118773
$881$	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	$0.480492\pi$
$884$	−7.34514			−0.247044
$885$	−4.08998	+	7.89414i	−0.137483	+	0.265359i
$886$	23.5729			0.791949
$887$	−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
$891$	−5.25370	+	0.968468i	−0.176005	+	0.0324449i
$892$	−12.6623	−	21.9317i	−0.423964	−	0.734326i
$893$	32.7257	−	56.6825i	1.09512	−	1.89681i
$894$	14.3830	−	27.7608i	0.481039	−	0.928461i
$895$	−4.46264	+	7.72952i	−0.149170	+	0.258369i
$896$		0			0
$897$	10.4700	+	16.3645i	0.349584	+	0.546395i
$898$	−13.6870			−0.456740
$899$	−24.3653	−	42.2019i	−0.812627	−	1.40751i
$900$	8.04163	+	11.3903i	0.268054	+	0.379677i
$901$	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
$905$	0.0255796	+	0.0443051i	0.000850293	+	0.00147275i
$906$	−2.85087	+	0.130014i	−0.0947139	+	0.00431943i
$907$	−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	$0.219956\pi$
$908$	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	$0.709526\pi$
$912$	9.31138	−	0.424646i	0.308331	−	0.0140614i
$913$	−4.57160			−0.151298
$914$	22.3523			0.739350
$915$	3.14406	−	6.06841i	0.103940	−	0.200615i
$916$	−4.64766	−	8.04999i	−0.153563	−	0.265979i
$917$		0			0
$918$	9.30972	+	11.9875i	0.307267	+	0.395648i
$919$	10.8910	−	18.8638i	0.359262	−	0.622261i	−0.628575	−	0.777749i	$-0.716362\pi$
$919$	10.8910	−	18.8638i	0.359262	−	0.622261i	0.987838	+	0.155488i	$0.0496950\pi$
$920$	−1.32383	+	2.29294i	−0.0436454	+	0.0755961i
$921$	−21.1680	−	33.0852i	−0.697509	−	1.09020i
$922$	−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
$926$	14.3676	−	24.8854i	0.472149	−	0.817785i
$927$	−19.0651	+	1.74255i	−0.626179	+	0.0572329i
$928$	3.09718	+	5.36447i	0.101670	+	0.176097i
$929$	32.8377			1.07737			0.538686	−	0.842507i	$-0.318921\pi$
$929$	32.8377			1.07737			0.538686	+	0.842507i	$0.318921\pi$
$930$	−3.72072	+	7.18143i	−0.122007	+	0.235488i
$931$		0			0
$932$	0.0971780	−	0.168317i	0.00318317	−	0.00551341i
$933$	−6.08113	−	9.50471i	−0.199087	−	0.311170i
$934$	16.7829	−	29.0688i	0.549152	−	0.951160i
$935$	−0.514589	−	0.891294i	−0.0168289	−	0.0291484i
$936$	−4.35087	−	6.16266i	−0.142213	−	0.201433i
$937$	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
$941$	−4.26615			−0.139072			−0.0695362	−	0.997579i	$-0.522152\pi$
$941$	−4.26615			−0.139072			−0.0695362	+	0.997579i	$0.522152\pi$
$942$	6.16158	+	9.63046i	0.200755	+	0.313777i
$943$	−1.21926			−0.0397046
$944$	−8.64766			−0.281457
$945$		0			0
$946$	6.62568			0.215420
$947$	−23.0584			−0.749296			−0.374648	−	0.927167i	$-0.622236\pi$
$947$	−23.0584			−0.749296			−0.374648	+	0.927167i	$0.622236\pi$
$948$	8.63307	+	13.4934i	0.280389	+	0.438244i
$949$	−19.9000			−0.645981
$950$	−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	$0.701689\pi$
$954$	24.0620	−	2.19927i	0.779035	−	0.0712039i
$955$	1.18190	+	2.04712i	0.0382455	+	0.0662431i
$956$	−6.82743	+	11.8255i	−0.220815	+	0.382463i
$957$	3.43219	+	5.36447i	0.110947	+	0.173409i
$958$	−0.183560	+	0.317935i	−0.00593056	+	0.0102720i
$959$		0			0
$960$	0.472958	−	0.912864i	0.0152647	−	0.0294625i
$961$	30.8885			0.996404
$962$	1.25729	+	2.17770i	0.0405368	+	0.0702118i
$963$	32.3712	+	45.8511i	1.04315	+	1.47753i
$964$	−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	$-0.163448\pi$
$968$	−5.32383	−	9.22115i	−0.171114	−	0.296379i
$969$	−14.6735	−	22.9345i	−0.471382	−	0.736762i
$970$	−3.48249	+	6.03184i	−0.111816	+	0.193671i
$971$	15.9897	−	27.6949i	0.513133	−	0.888773i	−0.486751	−	0.873541i	$-0.661818\pi$
$971$	15.9897	−	27.6949i	0.513133	−	0.888773i	0.999884	−	0.0152321i	$-0.00484870\pi$
$972$	−4.54309	+	14.9118i	−0.145720	+	0.478295i
$973$		0			0
$974$	14.9538	+	25.9007i	0.479150	+	0.829913i
$975$	−9.31205	+	17.9733i	−0.298224	+	0.575608i
$976$	6.64766			0.212787
$977$	−27.4208			−0.877270			−0.438635	−	0.898665i	$-0.644538\pi$
$977$	−27.4208			−0.877270			−0.438635	+	0.898665i	$0.644538\pi$
$978$	−10.3509	+	0.472052i	−0.330984	+	0.0150946i
$979$	−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
$983$	−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	$0.774276\pi$
$984$	0.472958	−	0.0215693i	0.0150773	−	0.000687603i
$985$	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
$989$	−24.8946	+	43.1188i	−0.791604	+	1.37110i
$990$	0.442991	−	0.959702i	0.0140792	−	0.0305013i
$991$	6.41887	+	11.1178i	0.203902	+	0.353169i	0.949782	−	0.312911i	$-0.101304\pi$
$991$	6.41887	+	11.1178i	0.203902	+	0.353169i	−0.745880	+	0.666080i	$0.767971\pi$
$992$	−7.86693			−0.249775
$993$	23.4880	+	36.7114i	0.745370	+	1.16500i
$994$		0			0
$995$	1.66751	−	2.88821i	0.0528636	−	0.0915624i
$996$	−6.13667	+	11.8445i	−0.194448	+	0.375307i
$997$	−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	$0.195845\pi$
$998$	−9.50953	−	16.4710i	−0.301019	−	0.521380i
$999$	1.96050	−	4.81211i	0.0620276	−	0.152248i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	63.52	odd	6
126.2.e.c.121.2	yes	6	7.6	odd	2
126.2.h.d.67.2	yes	6	7.3	odd	6
126.2.h.d.79.2	yes	6	63.34	odd	6
378.2.e.d.37.2		6	21.20	even	2
378.2.e.d.235.2		6	63.38	even	6
378.2.h.c.289.2		6	63.20	even	6
378.2.h.c.361.2		6	21.17	even	6
882.2.e.o.373.2		6	1.1	even	1	trivial
882.2.e.o.655.2		6	63.25	even	3	inner
882.2.f.n.295.1		6	63.61	odd	6
882.2.f.n.589.1		6	7.5	odd	6
882.2.f.o.295.3		6	63.16	even	3
882.2.f.o.589.3		6	7.2	even	3
882.2.h.p.67.2		6	7.4	even	3
882.2.h.p.79.2		6	9.7	even	3
1008.2.q.g.529.2		6	252.115	even	6
1008.2.q.g.625.2		6	28.27	even	2
1008.2.t.h.193.2		6	28.3	even	6
1008.2.t.h.961.2		6	252.223	even	6
1134.2.g.l.163.2		6	63.41	even	6
1134.2.g.l.487.2		6	63.59	even	6
1134.2.g.m.163.2		6	63.13	odd	6
1134.2.g.m.487.2		6	63.31	odd	6
2646.2.e.p.1549.2		6	3.2	odd	2
2646.2.e.p.2125.2		6	63.11	odd	6
2646.2.f.l.883.2		6	63.47	even	6
2646.2.f.l.1765.2		6	21.5	even	6
2646.2.f.m.883.2		6	63.2	odd	6
2646.2.f.m.1765.2		6	21.2	odd	6
2646.2.h.o.361.2		6	21.11	odd	6
2646.2.h.o.667.2		6	9.2	odd	6
3024.2.q.g.2305.2		6	84.83	odd	2
3024.2.q.g.2881.2		6	252.227	odd	6
3024.2.t.h.289.2		6	252.83	odd	6
3024.2.t.h.1873.2		6	84.59	odd	6
7938.2.a.bv.1.2		3	63.40	odd	6
7938.2.a.bw.1.2		3	63.58	even	3
7938.2.a.bz.1.2		3	63.23	odd	6
7938.2.a.ca.1.2		3	63.5	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.933463 - 1.45899i) q^{3} +1.00000 q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.933463 - 1.45899i) q^{3} +1.00000 q^{4} +(0.296790 + 0.514055i) q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +(-0.296790 - 0.514055i) q^{10} +(0.296790 - 0.514055i) q^{11} +(-0.933463 - 1.45899i) q^{12} +(1.25729 - 2.17770i) q^{13} +(0.472958 - 0.912864i) q^{15} +1.00000 q^{16} +(-1.46050 - 2.52967i) q^{17} +(1.25729 - 2.72382i) q^{18} +(-2.69076 + 4.66053i) q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(-2.23025 - 3.86291i) q^{23} +(0.933463 + 1.45899i) q^{24} +(2.32383 - 4.02499i) q^{25} +(-1.25729 + 2.17770i) q^{26} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +(-0.472958 + 0.912864i) q^{30} +7.86693 q^{31} -1.00000 q^{32} +(-1.02704 + 0.0468383i) q^{33} +(1.46050 + 2.52967i) q^{34} +(-1.25729 + 2.72382i) q^{36} +(0.500000 - 0.866025i) q^{37} +(2.69076 - 4.66053i) q^{38} +(-4.35087 + 0.198422i) q^{39} +(-0.296790 - 0.514055i) q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(0.296790 - 0.514055i) q^{44} +(-1.77335 + 0.162084i) q^{45} +(2.23025 + 3.86291i) q^{46} -12.1623 q^{47} +(-0.933463 - 1.45899i) q^{48} +(-2.32383 + 4.02499i) q^{50} +(-2.32743 + 4.49221i) q^{51} +(1.25729 - 2.17770i) q^{52} +(4.02704 + 6.97504i) q^{53} +(-5.14766 + 0.708209i) q^{54} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} +(3.09718 + 5.36447i) q^{58} -8.64766 q^{59} +(0.472958 - 0.912864i) q^{60} +6.64766 q^{61} -7.86693 q^{62} +1.00000 q^{64} +1.49261 q^{65} +(1.02704 - 0.0468383i) q^{66} -1.91381 q^{67} +(-1.46050 - 2.52967i) q^{68} +(-3.55408 + 6.85980i) q^{69} -14.4107 q^{71} +(1.25729 - 2.72382i) q^{72} +(-3.95691 - 6.85356i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-8.04163 + 0.366739i) q^{75} +(-2.69076 + 4.66053i) q^{76} +(4.35087 - 0.198422i) q^{78} -9.24844 q^{79} +(0.296790 + 0.514055i) q^{80} +(-5.83842 - 6.84929i) q^{81} +(-0.136673 + 0.236725i) q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(5.58113 + 9.66679i) q^{86} +(-4.93560 + 9.52628i) q^{87} +(-0.296790 + 0.514055i) q^{88} +(6.21780 - 10.7695i) q^{89} +(1.77335 - 0.162084i) q^{90} +(-2.23025 - 3.86291i) q^{92} +(-7.34348 - 11.4778i) q^{93} +12.1623 q^{94} -3.19436 q^{95} +(0.933463 + 1.45899i) q^{96} +(-5.86693 - 10.1618i) q^{97} +(1.02704 + 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} + q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} + 6 q^{16} + 4 q^{17} - 8 q^{18} + 3 q^{19} - q^{20} + q^{22} - 7 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} - 12 q^{30} + 40 q^{31} - 6 q^{32} + 3 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} - 3 q^{38} - 5 q^{39} + q^{40} - 6 q^{43} - q^{44} - 9 q^{45} + 7 q^{46} - 18 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{51} - 8 q^{52} + 15 q^{53} - 7 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} - 28 q^{59} + 12 q^{60} + 16 q^{61} - 40 q^{62} + 6 q^{64} + 24 q^{65} - 3 q^{66} - 2 q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} - 8 q^{72} - 19 q^{73} - 3 q^{74} - 8 q^{75} + 3 q^{76} + 5 q^{78} - 10 q^{79} - q^{80} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} + 27 q^{87} + q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} - 38 q^{93} + 18 q^{94} + 8 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 + q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 + 6 * q^16 + 4 * q^17 - 8 * q^18 + 3 * q^19 - q^20 + q^22 - 7 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 - 12 * q^30 + 40 * q^31 - 6 * q^32 + 3 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 - 3 * q^38 - 5 * q^39 + q^40 - 6 * q^43 - q^44 - 9 * q^45 + 7 * q^46 - 18 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^51 - 8 * q^52 + 15 * q^53 - 7 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 - 28 * q^59 + 12 * q^60 + 16 * q^61 - 40 * q^62 + 6 * q^64 + 24 * q^65 - 3 * q^66 - 2 * q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 - 8 * q^72 - 19 * q^73 - 3 * q^74 - 8 * q^75 + 3 * q^76 + 5 * q^78 - 10 * q^79 - q^80 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 + 27 * q^87 + q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 - 38 * q^93 + 18 * q^94 + 8 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

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