LMFDB - Embedded newform 360.2.bm.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.513744 + 1.31760i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-1.47213 - 1.35382i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.27224 - 0.914825i) q^{6} +(2.20775 + 1.27465i) q^{7} +(2.54009 - 1.24417i) q^{8} +(-0.185091 + 2.99428i) q^{9} +O(q^{10})$	\(q+(-0.513744 + 1.31760i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-1.47213 - 1.35382i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.27224 - 0.914825i) q^{6} +(2.20775 + 1.27465i) q^{7} +(2.54009 - 1.24417i) q^{8} +(-0.185091 + 2.99428i) q^{9} +(1.39795 - 0.213885i) q^{10} +(-4.02755 - 2.32531i) q^{11} +(0.0380216 + 3.46389i) q^{12} +(-3.23898 + 1.87003i) q^{13} +(-2.81369 + 2.25409i) q^{14} +(-0.499709 + 1.65840i) q^{15} +(0.334363 + 3.98600i) q^{16} -3.38689i q^{17} +(-3.85018 - 1.78217i) q^{18} -5.12923 q^{19} +(-0.436372 + 1.95181i) q^{20} +(-1.01064 - 4.29829i) q^{21} +(5.13296 - 4.11209i) q^{22} +(-4.16526 - 7.21444i) q^{23} +(-4.58356 - 1.72946i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.799940 - 5.22840i) q^{26} +(3.99825 - 3.31873i) q^{27} +(-1.52447 - 4.86534i) q^{28} +(-2.01987 + 3.49852i) q^{29} +(-1.92838 - 1.51041i) q^{30} +(-4.88169 + 2.81845i) q^{31} +(-5.42373 - 1.60723i) q^{32} +(1.84369 + 7.84127i) q^{33} +(4.46256 + 1.73999i) q^{34} -2.54929i q^{35} +(4.32619 - 4.15741i) q^{36} +7.40207i q^{37} +(2.63511 - 6.75827i) q^{38} +(6.20251 + 1.86894i) q^{39} +(-2.34753 - 1.57770i) q^{40} +(-5.23156 + 3.02044i) q^{41} +(6.18263 + 0.876601i) q^{42} +(5.26273 - 9.11531i) q^{43} +(2.78106 + 8.87574i) q^{44} +(2.68567 - 1.33685i) q^{45} +(11.6456 - 1.78177i) q^{46} +(-0.621010 + 1.07562i) q^{47} +(4.63350 - 5.15079i) q^{48} +(-0.250553 - 0.433970i) q^{49} +(-0.884203 - 1.10371i) q^{50} +(-4.27412 + 4.01808i) q^{51} +(7.29990 + 1.63206i) q^{52} -2.05427 q^{53} +(2.31868 + 6.97307i) q^{54} +4.65062i q^{55} +(7.19376 + 0.490895i) q^{56} +(6.08512 + 6.47289i) q^{57} +(-3.57195 - 4.45873i) q^{58} +(-0.351174 + 0.202750i) q^{59} +(2.98081 - 1.76487i) q^{60} +(4.57621 + 2.64207i) q^{61} +(-1.20564 - 7.88008i) q^{62} +(-4.22529 + 6.37471i) q^{63} +(4.90409 - 6.32060i) q^{64} +(3.23898 + 1.87003i) q^{65} +(-11.2788 - 1.59916i) q^{66} +(-6.17580 - 10.6968i) q^{67} +(-4.58523 + 4.98596i) q^{68} +(-4.16284 + 13.8153i) q^{69} +(3.35895 + 1.30968i) q^{70} -5.43205 q^{71} +(3.25525 + 7.83603i) q^{72} +13.3990 q^{73} +(-9.75296 - 3.80277i) q^{74} +(1.68607 - 0.396439i) q^{75} +(7.55092 + 6.94404i) q^{76} +(-5.92789 - 10.2674i) q^{77} +(-5.64901 + 7.21226i) q^{78} +(-5.40268 - 3.11924i) q^{79} +(3.28480 - 2.28257i) q^{80} +(-8.93148 - 1.10843i) q^{81} +(-1.29205 - 8.44483i) q^{82} +(12.0774 + 6.97289i) q^{83} +(-4.33130 + 7.69588i) q^{84} +(-2.93313 + 1.69345i) q^{85} +(9.30663 + 11.6171i) q^{86} +(6.81130 - 1.60151i) q^{87} +(-13.1234 - 0.895530i) q^{88} -2.72618i q^{89} +(0.381684 + 4.22544i) q^{90} -9.53450 q^{91} +(-3.63520 + 16.2596i) q^{92} +(9.34823 + 2.81681i) q^{93} +(-1.09820 - 1.37084i) q^{94} +(2.56462 + 4.44204i) q^{95} +(4.40625 + 8.75128i) q^{96} +(1.31601 - 2.27939i) q^{97} +(0.700519 - 0.107179i) q^{98} +(7.70810 - 11.6292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.513744	+	1.31760i	−0.363272	+	0.931683i
$2$	−0.513744	+	1.31760i	−0.363272	+	0.931683i
$3$	−1.18636	−	1.26196i	−0.684946	−	0.728593i
$3$	−1.18636	−	1.26196i	−0.684946	−	0.728593i
$4$	−1.47213	−	1.35382i	−0.736067	−	0.676908i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.27224	−	0.914825i	0.927640	−	0.373476i
$7$	2.20775	+	1.27465i	0.834452	+	0.481771i	0.855375	−	0.518010i	$-0.173327\pi$
$7$	2.20775	+	1.27465i	0.834452	+	0.481771i	−0.0209226	+	0.999781i	$0.506660\pi$
$8$	2.54009	−	1.24417i	0.898056	−	0.439880i
$9$	−0.185091	+	2.99428i	−0.0616969	+	0.998095i
$10$	1.39795	−	0.213885i	0.442069	−	0.0676362i
$11$	−4.02755	−	2.32531i	−1.21435	−	0.701107i	−0.250649	−	0.968078i	$-0.580644\pi$
$11$	−4.02755	−	2.32531i	−1.21435	−	0.701107i	−0.963705	+	0.266971i	$0.913977\pi$
$12$	0.0380216	+	3.46389i	0.0109759	+	0.999940i
$13$	−3.23898	+	1.87003i	−0.898332	+	0.518653i	−0.876659	−	0.481113i	$-0.840233\pi$
$13$	−3.23898	+	1.87003i	−0.898332	+	0.518653i	−0.0216737	+	0.999765i	$0.506899\pi$
$14$	−2.81369	+	2.25409i	−0.751991	+	0.602431i
$15$	−0.499709	+	1.65840i	−0.129024	+	0.428197i
$16$	0.334363	+	3.98600i	0.0835907	+	0.996500i
$17$		−	3.38689i		−	0.821442i	−0.911761	−	0.410721i	$-0.865277\pi$
$17$		−	3.38689i		−	0.821442i	0.911761	−	0.410721i	$-0.134723\pi$
$18$	−3.85018	−	1.78217i	−0.907496	−	0.420062i
$19$	−5.12923			−1.17673			−0.588363	−	0.808597i	$-0.700227\pi$
$19$	−5.12923			−1.17673			−0.588363	+	0.808597i	$0.700227\pi$
$20$	−0.436372	+	1.95181i	−0.0975757	+	0.436439i
$21$	−1.01064	−	4.29829i	−0.220540	−	0.937964i
$22$	5.13296	−	4.11209i	1.09435	−	0.876700i
$23$	−4.16526	−	7.21444i	−0.868517	−	1.50432i	−0.863512	−	0.504328i	$-0.831740\pi$
$23$	−4.16526	−	7.21444i	−0.868517	−	1.50432i	−0.00500444	−	0.999987i	$-0.501593\pi$
$24$	−4.58356	−	1.72946i	−0.935614	−	0.353024i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.799940	−	5.22840i	−0.156881	−	1.02537i
$27$	3.99825	−	3.31873i	0.769465	−	0.638690i
$28$	−1.52447	−	4.86534i	−0.288098	−	0.919463i
$29$	−2.01987	+	3.49852i	−0.375081	+	0.649659i	−0.990339	−	0.138666i	$-0.955718\pi$
$29$	−2.01987	+	3.49852i	−0.375081	+	0.649659i	0.615258	+	0.788326i	$0.289052\pi$
$30$	−1.92838	−	1.51041i	−0.352073	−	0.275762i
$31$	−4.88169	+	2.81845i	−0.876778	+	0.506208i	−0.869595	−	0.493766i	$-0.835620\pi$
$31$	−4.88169	+	2.81845i	−0.876778	+	0.506208i	−0.00718342	+	0.999974i	$0.502287\pi$
$32$	−5.42373	−	1.60723i	−0.958789	−	0.284120i
$33$	1.84369	+	7.84127i	0.320945	+	1.36499i
$34$	4.46256	+	1.73999i	0.765323	+	0.298406i
$35$		−	2.54929i		−	0.430909i
$36$	4.32619	−	4.15741i	0.721032	−	0.692902i
$37$			7.40207i			1.21689i	0.793595	+	0.608446i	$0.208207\pi$
$37$			7.40207i			1.21689i	−0.793595	+	0.608446i	$0.791793\pi$
$38$	2.63511	−	6.75827i	0.427471	−	1.09634i
$39$	6.20251	+	1.86894i	0.993196	+	0.299270i
$40$	−2.34753	−	1.57770i	−0.371176	−	0.249456i
$41$	−5.23156	+	3.02044i	−0.817032	+	0.471714i	−0.849392	−	0.527762i	$-0.823031\pi$
$41$	−5.23156	+	3.02044i	−0.817032	+	0.471714i	0.0323597	+	0.999476i	$0.489698\pi$
$42$	6.18263	+	0.876601i	0.954001	+	0.135262i
$43$	5.26273	−	9.11531i	0.802558	−	1.39007i	−0.115369	−	0.993323i	$-0.536805\pi$
$43$	5.26273	−	9.11531i	0.802558	−	1.39007i	0.917927	−	0.396749i	$-0.129862\pi$
$44$	2.78106	+	8.87574i	0.419261	+	1.33807i
$45$	2.68567	−	1.33685i	0.400356	−	0.199286i
$46$	11.6456	−	1.78177i	1.71705	−	0.262708i
$47$	−0.621010	+	1.07562i	−0.0905837	+	0.156896i	−0.907757	−	0.419497i	$-0.862207\pi$
$47$	−0.621010	+	1.07562i	−0.0905837	+	0.156896i	0.817173	+	0.576392i	$0.195540\pi$
$48$	4.63350	−	5.15079i	0.668788	−	0.743453i
$49$	−0.250553	−	0.433970i	−0.0357933	−	0.0619958i
$50$	−0.884203	−	1.10371i	−0.125045	−	0.156089i
$51$	−4.27412	+	4.01808i	−0.598497	+	0.562643i
$52$	7.29990	+	1.63206i	1.01231	+	0.226325i
$53$	−2.05427			−0.282176			−0.141088	−	0.989997i	$-0.545060\pi$
$53$	−2.05427			−0.282176			−0.141088	+	0.989997i	$0.545060\pi$
$54$	2.31868	+	6.97307i	0.315532	+	0.948915i
$55$			4.65062i			0.627089i
$56$	7.19376	+	0.490895i	0.961307	+	0.0655987i
$57$	6.08512	+	6.47289i	0.805994	+	0.857355i
$58$	−3.57195	−	4.45873i	−0.469020	−	0.585459i
$59$	−0.351174	+	0.202750i	−0.0457190	+	0.0263959i	−0.522685	−	0.852526i	$-0.675070\pi$
$59$	−0.351174	+	0.202750i	−0.0457190	+	0.0263959i	0.476966	+	0.878922i	$0.341736\pi$
$60$	2.98081	−	1.76487i	0.384821	−	0.227844i
$61$	4.57621	+	2.64207i	0.585923	+	0.338283i	0.763484	−	0.645827i	$-0.223487\pi$
$61$	4.57621	+	2.64207i	0.585923	+	0.338283i	−0.177561	+	0.984110i	$0.556821\pi$
$62$	−1.20564	−	7.88008i	−0.153117	−	1.00077i
$63$	−4.22529	+	6.37471i	−0.532336	+	0.803139i
$64$	4.90409	−	6.32060i	0.613011	−	0.790075i
$65$	3.23898	+	1.87003i	0.401746	+	0.231948i
$66$	−11.2788	−	1.59916i	−1.38833	−	0.196843i
$67$	−6.17580	−	10.6968i	−0.754494	−	1.30682i	−0.945625	−	0.325258i	$-0.894549\pi$
$67$	−6.17580	−	10.6968i	−0.754494	−	1.30682i	0.191131	−	0.981565i	$-0.438784\pi$
$68$	−4.58523	+	4.98596i	−0.556040	+	0.604636i
$69$	−4.16284	+	13.8153i	−0.501147	+	1.66317i
$70$	3.35895	+	1.30968i	0.401471	+	0.156537i
$71$	−5.43205			−0.644666			−0.322333	−	0.946626i	$-0.604467\pi$
$71$	−5.43205			−0.644666			−0.322333	+	0.946626i	$0.604467\pi$
$72$	3.25525	+	7.83603i	0.383635	+	0.923485i
$73$	13.3990			1.56823			0.784115	−	0.620616i	$-0.213117\pi$
$73$	13.3990			1.56823			0.784115	+	0.620616i	$0.213117\pi$
$74$	−9.75296	−	3.80277i	−1.13376	−	0.442063i
$75$	1.68607	−	0.396439i	0.194691	−	0.0457768i
$76$	7.55092	+	6.94404i	0.866150	+	0.796536i
$77$	−5.92789	−	10.2674i	−0.675546	−	1.17008i
$78$	−5.64901	+	7.21226i	−0.639625	+	0.816628i
$79$	−5.40268	−	3.11924i	−0.607849	−	0.350942i	0.164274	−	0.986415i	$-0.447472\pi$
$79$	−5.40268	−	3.11924i	−0.607849	−	0.350942i	−0.772123	+	0.635473i	$0.780805\pi$
$80$	3.28480	−	2.28257i	0.367251	−	0.255199i
$81$	−8.93148	−	1.10843i	−0.992387	−	0.123159i
$82$	−1.29205	−	8.44483i	−0.142683	−	0.932576i
$83$	12.0774	+	6.97289i	1.32567	+	0.765374i	0.984626	−	0.174675i	$-0.0558875\pi$
$83$	12.0774	+	6.97289i	1.32567	+	0.765374i	0.341040	+	0.940049i	$0.389221\pi$
$84$	−4.33130	+	7.69588i	−0.472583	+	0.839690i
$85$	−2.93313	+	1.69345i	−0.318143	+	0.183680i
$86$	9.30663	+	11.6171i	1.00356	+	1.25270i
$87$	6.81130	−	1.60151i	0.730248	−	0.171700i
$88$	−13.1234	−	0.895530i	−1.39896	−	0.0954638i
$89$		−	2.72618i		−	0.288975i	−0.989507	−	0.144487i	$-0.953847\pi$
$89$		−	2.72618i		−	0.288975i	0.989507	−	0.144487i	$-0.0461533\pi$
$90$	0.381684	+	4.22544i	0.0402331	+	0.445400i
$91$	−9.53450			−0.999487
$92$	−3.63520	+	16.2596i	−0.378996	+	1.69518i
$93$	9.34823	+	2.81681i	0.969366	+	0.292089i
$94$	−1.09820	−	1.37084i	−0.113270	−	0.141391i
$95$	2.56462	+	4.44204i	0.263124	+	0.455744i
$96$	4.40625	+	8.75128i	0.449711	+	0.893174i
$97$	1.31601	−	2.27939i	0.133620	−	0.231437i	−0.791449	−	0.611235i	$-0.790673\pi$
$97$	1.31601	−	2.27939i	0.133620	−	0.231437i	0.925070	+	0.379798i	$0.124006\pi$
$98$	0.700519	−	0.107179i	0.0707631	−	0.0108267i
$99$	7.70810	−	11.6292i	0.774693	−	1.16878i
$100$	1.90851	−	0.597998i	0.190851	−	0.0597998i
$101$	7.87081	−	13.6326i	0.783175	−	1.35650i	−0.146909	−	0.989150i	$-0.546932\pi$
$101$	7.87081	−	13.6326i	0.783175	−	1.35650i	0.930083	−	0.367348i	$-0.119734\pi$
$102$	−3.09841	−	7.69584i	−0.306789	−	0.762002i
$103$	8.19174	−	4.72950i	0.807156	−	0.466012i	−0.0388112	−	0.999247i	$-0.512357\pi$
$103$	8.19174	−	4.72950i	0.807156	−	0.466012i	0.845967	+	0.533235i	$0.179024\pi$
$104$	−5.90067	+	8.77988i	−0.578608	+	0.860938i
$105$	−3.21711	+	3.02438i	−0.313958	+	0.295150i
$106$	1.05537	−	2.70671i	0.102507	−	0.262899i
$107$			9.14609i			0.884186i	0.896969	+	0.442093i	$0.145764\pi$
$107$			9.14609i			0.884186i	−0.896969	+	0.442093i	$0.854236\pi$
$108$	−10.3789	−	0.527287i	−0.998712	−	0.0507382i
$109$			2.24057i			0.214608i	0.994226	+	0.107304i	$0.0342218\pi$
$109$			2.24057i			0.214608i	−0.994226	+	0.107304i	$0.965778\pi$
$110$	−6.12765	−	2.38923i	−0.584249	−	0.227804i
$111$	9.34112	−	8.78154i	0.886620	−	0.833506i
$112$	−4.34255	+	9.22630i	−0.410333	+	0.871803i
$113$	−5.37513	+	3.10333i	−0.505650	+	0.291937i	−0.731044	−	0.682331i	$-0.760966\pi$
$113$	−5.37513	+	3.10333i	−0.505650	+	0.291937i	0.225394	+	0.974268i	$0.427633\pi$
$114$	−11.6549	+	4.69235i	−1.09158	+	0.439479i
$115$	−4.16526	+	7.21444i	−0.388413	+	0.672750i
$116$	7.70988	−	2.41576i	0.715845	−	0.224298i
$117$	−4.99989	−	10.0446i	−0.462240	−	0.928620i
$118$	−0.0867303	−	0.566868i	−0.00798418	−	0.0521845i
$119$	4.31709	−	7.47741i	0.395747	−	0.685453i
$120$	0.794025	+	4.83420i	0.0724843	+	0.441300i
$121$	5.31412	+	9.20433i	0.483102	+	0.836758i
$122$	−5.83219	+	4.67226i	−0.528022	+	0.423006i
$123$	10.0182	+	3.01869i	0.903311	+	0.272186i
$124$	11.0022	+	2.45978i	0.988024	+	0.220895i
$125$	1.00000			0.0894427
$126$	−6.22860	−	8.84221i	−0.554888	−	0.787726i
$127$			12.8277i			1.13827i	0.822243	+	0.569137i	$0.192723\pi$
$127$			12.8277i			1.13827i	−0.822243	+	0.569137i	$0.807277\pi$
$128$	5.80857	+	9.70879i	0.513410	+	0.858144i
$129$	−17.7467	+	4.17270i	−1.56251	+	0.367386i
$130$	−4.12795	+	3.30697i	−0.362046	+	0.290040i
$131$	8.33011	−	4.80939i	0.727805	−	0.420199i	−0.0898134	−	0.995959i	$-0.528627\pi$
$131$	8.33011	−	4.80939i	0.727805	−	0.420199i	0.817619	+	0.575760i	$0.195294\pi$
$132$	7.90149	−	14.0394i	0.687736	−	1.22198i
$133$	−11.3241	−	6.53796i	−0.981922	−	0.566913i
$134$	17.2669	−	2.64182i	1.49163	−	0.228218i
$135$	−4.87323	−	1.80323i	−0.419421	−	0.155197i
$136$	−4.21386	−	8.60300i	−0.361336	−	0.737701i
$137$	−8.47690	−	4.89414i	−0.724231	−	0.418135i	0.0920770	−	0.995752i	$-0.470649\pi$
$137$	−8.47690	−	4.89414i	−0.724231	−	0.418135i	−0.816308	+	0.577617i	$0.803983\pi$
$138$	−16.0644	−	12.5825i	−1.36750	−	1.07109i
$139$	3.13540	+	5.43067i	0.265941	+	0.460624i	0.967810	−	0.251683i	$-0.0809840\pi$
$139$	3.13540	+	5.43067i	0.265941	+	0.460624i	−0.701869	+	0.712306i	$0.747651\pi$
$140$	−3.45127	+	3.75290i	−0.291686	+	0.317178i
$141$	2.09414	−	0.492386i	0.176358	−	0.0414664i
$142$	2.79068	−	7.15727i	0.234189	−	0.600625i
$143$	17.3936			1.45452
$144$	−11.9971	+	0.263406i	−0.999759	+	0.0219505i
$145$	4.03975			0.335483
$146$	−6.88363	+	17.6545i	−0.569693	+	1.46109i
$147$	−0.250407	+	0.831034i	−0.0206532	+	0.0685425i
$148$	10.0210	−	10.8968i	0.823725	−	0.895715i
$149$	2.41284	+	4.17916i	0.197667	+	0.342370i	0.947772	−	0.318950i	$-0.103330\pi$
$149$	2.41284	+	4.17916i	0.197667	+	0.342370i	−0.750104	+	0.661319i	$0.769997\pi$
$150$	−0.343860	+	2.42523i	−0.0280761	+	0.198020i
$151$	−10.6615	−	6.15545i	−0.867624	−	0.500923i	−0.00106627	−	0.999999i	$-0.500339\pi$
$151$	−10.6615	−	6.15545i	−0.867624	−	0.500923i	−0.866558	+	0.499076i	$0.833673\pi$
$152$	−13.0287	+	6.38163i	−1.05677	+	0.517619i
$153$	10.1413	+	0.626882i	0.819877	+	0.0506804i
$154$	16.5738	−	2.53577i	1.33555	−	0.204338i
$155$	4.88169	+	2.81845i	0.392107	+	0.226383i
$156$	−6.60073	−	11.1484i	−0.528481	−	0.892586i
$157$	6.14993	−	3.55066i	0.490818	−	0.283374i	−0.234096	−	0.972213i	$-0.575213\pi$
$157$	6.14993	−	3.55066i	0.490818	−	0.283374i	0.724914	+	0.688840i	$0.241880\pi$
$158$	6.88549	−	5.51607i	0.547780	−	0.438835i
$159$	2.43711	+	2.59241i	0.193276	+	0.205592i
$160$	1.31996	+	5.50070i	0.104352	+	0.434868i
$161$		−	21.2369i		−	1.67371i
$162$	6.04896	−	11.1987i	0.475251	−	0.879850i
$163$	−4.88666			−0.382753			−0.191377	−	0.981517i	$-0.561295\pi$
$163$	−4.88666			−0.382753			−0.191377	+	0.981517i	$0.561295\pi$
$164$	11.7907	+	2.63607i	0.920698	+	0.205843i
$165$	5.86890	−	5.51732i	0.456893	−	0.429522i
$166$	−15.3922	+	12.3309i	−1.19466	+	0.957062i
$167$	−7.41709	−	12.8468i	−0.573951	−	0.994113i	−0.996155	−	0.0876117i	$-0.972077\pi$
$167$	−7.41709	−	12.8468i	−0.573951	−	0.994113i	0.422203	−	0.906501i	$-0.361257\pi$
$168$	−7.91491	−	9.66062i	−0.610649	−	0.745333i
$169$	0.494011	−	0.855652i	0.0380008	−	0.0658194i
$170$	−0.724403	−	4.73469i	−0.0555592	−	0.363134i
$171$	0.949373	−	15.3584i	0.0726004	−	1.17448i
$172$	−20.0879	+	6.29420i	−1.53169	+	0.479928i
$173$	3.22057	−	5.57819i	0.244855	−	0.424102i	−0.717236	−	0.696831i	$-0.754593\pi$
$173$	3.22057	−	5.57819i	0.244855	−	0.424102i	0.962091	+	0.272729i	$0.0879262\pi$
$174$	−1.38911	+	9.79733i	−0.105308	+	0.742734i
$175$	−2.20775	+	1.27465i	−0.166890	+	0.0963542i
$176$	7.92202	−	16.8313i	0.597145	−	1.26871i
$177$	0.672483	+	0.202632i	0.0505469	+	0.0152308i
$178$	3.59201	+	1.40056i	0.269233	+	0.104976i
$179$			8.76690i			0.655269i	0.944805	+	0.327634i	$0.106251\pi$
$179$			8.76690i			0.655269i	−0.944805	+	0.327634i	$0.893749\pi$
$180$	−5.76352	−	1.66788i	−0.429587	−	0.124317i
$181$		−	15.3572i		−	1.14149i	−0.821126	−	0.570747i	$-0.806654\pi$
$181$		−	15.3572i		−	1.14149i	0.821126	−	0.570747i	$-0.193346\pi$
$182$	4.89829	−	12.5626i	0.363085	−	0.931205i
$183$	−2.09484	−	8.90945i	−0.154855	−	0.658605i
$184$	−19.5561	−	13.1430i	−1.44170	−	0.968917i
$185$	6.41038	−	3.70104i	0.471301	−	0.272106i
$186$	−8.51402	+	10.8701i	−0.624278	+	0.797034i
$187$	−7.87557	+	13.6409i	−0.575918	+	0.997520i
$188$	2.37041	−	0.742726i	0.172880	−	0.0541689i
$189$	13.0574	−	2.23057i	0.949783	−	0.162250i
$190$	−7.17039	+	1.09706i	−0.520195	+	0.0795893i
$191$	−1.49605	+	2.59124i	−0.108251	+	0.187496i	−0.915062	−	0.403314i	$-0.867858\pi$
$191$	−1.49605	+	2.59124i	−0.108251	+	0.187496i	0.806811	+	0.590810i	$0.201192\pi$
$192$	−13.7944	+	1.30975i	−0.995523	+	0.0945231i
$193$	1.27611	+	2.21028i	0.0918562	+	0.159100i	0.908292	−	0.418336i	$-0.137387\pi$
$193$	1.27611	+	2.21028i	0.0918562	+	0.159100i	−0.816436	+	0.577436i	$0.804053\pi$
$194$	2.32724	+	2.90499i	0.167086	+	0.208566i
$195$	−1.48270	−	6.30600i	−0.106179	−	0.451582i
$196$	−0.218668	+	0.978065i	−0.0156192	+	0.0698618i
$197$	−10.5167			−0.749283			−0.374642	−	0.927170i	$-0.622234\pi$
$197$	−10.5167			−0.749283			−0.374642	+	0.927170i	$0.622234\pi$
$198$	11.3627	+	16.1306i	0.807512	+	1.14635i
$199$		−	12.4162i		−	0.880162i	−0.897958	−	0.440081i	$-0.854950\pi$
$199$		−	12.4162i		−	0.880162i	0.897958	−	0.440081i	$-0.145050\pi$
$200$	−0.192561	+	2.82186i	−0.0136161	+	0.199536i
$201$	−6.17221	+	20.4839i	−0.435354	+	1.44482i
$202$	13.9188	+	17.3743i	0.979322	+	1.22245i
$203$	−8.91876	+	5.14925i	−0.625974	+	0.361406i
$204$	11.7318	−	0.128775i	0.821392	−	0.00901605i
$205$	5.23156	+	3.02044i	0.365388	+	0.210957i
$206$	2.02314	+	13.2232i	0.140959	+	0.921303i
$207$	22.3730	−	11.1366i	1.55503	−	0.774051i
$208$	−8.53693	−	12.2853i	−0.591930	−	0.851834i
$209$	20.6583	+	11.9270i	1.42896	+	0.825011i
$210$	−2.33216	−	5.79262i	−0.160934	−	0.399729i
$211$	−7.79890	−	13.5081i	−0.536899	−	0.929936i	−0.999069	−	0.0431444i	$-0.986262\pi$
$211$	−7.79890	−	13.5081i	−0.536899	−	0.929936i	0.462170	−	0.886791i	$-0.347071\pi$
$212$	3.02417	+	2.78111i	0.207701	+	0.191007i
$213$	6.44438	+	6.85504i	0.441562	+	0.469700i
$214$	−12.0509	−	4.69874i	−0.823781	−	0.321200i
$215$	−10.5255			−0.717830
$216$	6.02686	−	13.4044i	0.410076	−	0.912052i
$217$	−14.3701			−0.975506
$218$	−2.95218	−	1.15108i	−0.199947	−	0.0779610i
$219$	−15.8960	−	16.9090i	−1.07415	−	1.14260i
$220$	6.29608	−	6.84634i	0.424482	−	0.461580i
$221$	6.33358	+	10.9701i	0.426043	+	0.737928i
$222$	6.77160	+	16.8193i	0.454480	+	1.12884i
$223$	−1.43709	−	0.829706i	−0.0962348	−	0.0555612i	0.451110	−	0.892468i	$-0.351028\pi$
$223$	−1.43709	−	0.829706i	−0.0962348	−	0.0555612i	−0.547345	+	0.836907i	$0.684361\pi$
$224$	−9.92560	−	10.4617i	−0.663182	−	0.699001i
$225$	−2.50058	−	1.65744i	−0.166705	−	0.110496i
$226$	−1.32751	−	8.67659i	−0.0883047	−	0.577158i
$227$	−8.51386	−	4.91548i	−0.565085	−	0.326252i	0.190099	−	0.981765i	$-0.439119\pi$
$227$	−8.51386	−	4.91548i	−0.565085	−	0.326252i	−0.755184	+	0.655513i	$0.772452\pi$
$228$	−0.195022	−	17.7671i	−0.0129156	−	1.17666i
$229$	−9.39914	+	5.42659i	−0.621112	+	0.358599i	−0.777302	−	0.629128i	$-0.783412\pi$
$229$	−9.39914	+	5.42659i	−0.621112	+	0.358599i	0.156190	+	0.987727i	$0.450079\pi$
$230$	−7.36587	−	9.19452i	−0.485691	−	0.606268i
$231$	−5.92445	+	19.6616i	−0.389800	+	1.29364i
$232$	−0.777899	+	11.3996i	−0.0510716	+	0.748421i
$233$		−	26.3031i		−	1.72318i	−0.507609	−	0.861588i	$-0.669470\pi$
$233$		−	26.3031i		−	1.72318i	0.507609	−	0.861588i	$-0.330530\pi$
$234$	15.8034	−	1.42752i	1.03310	−	0.0933200i
$235$	1.24202			0.0810205
$236$	0.791462	+	0.176949i	0.0515198	+	0.0115184i
$237$	2.47317	+	10.5185i	0.160650	+	0.683251i
$238$	7.63436	+	9.52967i	0.494862	+	0.617716i
$239$	3.17976	+	5.50750i	0.205681	+	0.356251i	0.950350	−	0.311184i	$-0.100726\pi$
$239$	3.17976	+	5.50750i	0.205681	+	0.356251i	−0.744668	+	0.667435i	$0.767392\pi$
$240$	−6.77747	−	1.43733i	−0.437484	−	0.0927795i
$241$	5.71542	−	9.89940i	0.368163	−	0.637677i	−0.621116	−	0.783719i	$-0.713320\pi$
$241$	5.71542	−	9.89940i	0.368163	−	0.637677i	0.989278	+	0.146042i	$0.0466536\pi$
$242$	−14.8577	+	2.27322i	−0.955090	+	0.146128i
$243$	9.19718	+	12.5862i	0.589999	+	0.807404i
$244$	−3.15991	−	10.0848i	−0.202293	−	0.645615i
$245$	−0.250553	+	0.433970i	−0.0160072	+	0.0277253i
$246$	−9.12421	+	11.6491i	−0.581738	+	0.742722i
$247$	16.6135	−	9.59181i	1.05709	−	0.610312i
$248$	−8.89330	+	13.2328i	−0.564725	+	0.840281i
$249$	−5.52865	−	23.5136i	−0.350364	−	1.49011i
$250$	−0.513744	+	1.31760i	−0.0324920	+	0.0833323i
$251$			17.3175i			1.09307i	0.837436	+	0.546535i	$0.184054\pi$
$251$			17.3175i			1.09307i	−0.837436	+	0.546535i	$0.815946\pi$
$252$	14.8504	−	3.66417i	0.935486	−	0.230821i
$253$			38.7421i			2.43569i
$254$	−16.9018	−	6.59015i	−1.06051	−	0.413503i
$255$	5.61682	+	1.69246i	0.351739	+	0.105986i
$256$	−15.7764	+	2.66554i	−0.986025	+	0.166596i
$257$	−5.77481	+	3.33409i	−0.360223	+	0.207975i	−0.669178	−	0.743102i	$-0.733354\pi$
$257$	−5.77481	+	3.33409i	−0.360223	+	0.207975i	0.308956	+	0.951076i	$0.400020\pi$
$258$	3.61929	−	25.5267i	0.225327	−	1.58922i
$259$	−9.43502	+	16.3419i	−0.586264	+	1.01544i
$260$	−2.23655	−	7.13792i	−0.138705	−	0.442675i
$261$	−10.1017	−	6.69562i	−0.625280	−	0.414448i
$262$	2.05731	+	13.4465i	0.127101	+	0.830730i
$263$	−12.8435	+	22.2455i	−0.791962	+	1.37172i	0.132788	+	0.991144i	$0.457607\pi$
$263$	−12.8435	+	22.2455i	−0.791962	+	1.37172i	−0.924750	+	0.380575i	$0.875726\pi$
$264$	14.4390	+	17.6237i	0.888659	+	1.08466i
$265$	1.02714	+	1.77905i	0.0630965	+	0.109286i
$266$	14.4321	−	11.5618i	0.884887	−	0.708897i
$267$	−3.44033	+	3.23424i	−0.210545	+	0.197932i
$268$	−5.38989	+	24.1080i	−0.329240	+	1.47263i
$269$	17.0236			1.03794			0.518972	−	0.854791i	$-0.326315\pi$
$269$	17.0236			1.03794			0.518972	+	0.854791i	$0.326315\pi$
$270$	4.87952	−	5.49457i	0.296958	−	0.334389i
$271$			31.1779i			1.89392i	0.321350	+	0.946960i	$0.395863\pi$
$271$			31.1779i			1.89392i	−0.321350	+	0.946960i	$0.604137\pi$
$272$	13.5001	−	1.13245i	0.818567	−	0.0686649i
$273$	11.3114	+	12.0322i	0.684595	+	0.728220i
$274$	10.8035	−	8.65483i	0.652662	−	0.522857i
$275$	4.02755	−	2.32531i	0.242871	−	0.140221i
$276$	24.8317	−	14.7023i	1.49469	−	0.884976i
$277$	−9.16573	−	5.29183i	−0.550715	−	0.317956i	0.198695	−	0.980061i	$-0.436330\pi$
$277$	−9.16573	−	5.29183i	−0.550715	−	0.317956i	−0.749410	+	0.662106i	$0.769663\pi$
$278$	−8.76624	+	1.34123i	−0.525764	+	0.0804414i
$279$	−7.53568	−	15.1389i	−0.451149	−	0.906339i
$280$	−3.17175	−	6.47543i	−0.189548	−	0.386981i
$281$	−9.33995	−	5.39242i	−0.557175	−	0.321685i	0.194836	−	0.980836i	$-0.437582\pi$
$281$	−9.33995	−	5.39242i	−0.557175	−	0.321685i	−0.752011	+	0.659151i	$0.770916\pi$
$282$	−0.427082	+	3.01219i	−0.0254324	+	0.179373i
$283$	6.51583	+	11.2858i	0.387326	+	0.670868i	0.992089	−	0.125537i	$-0.0400655\pi$
$283$	6.51583	+	11.2858i	0.387326	+	0.670868i	−0.604763	+	0.796406i	$0.706732\pi$
$284$	7.99672	+	7.35400i	0.474518	+	0.436380i
$285$	2.56312	−	8.50632i	0.151826	−	0.503871i
$286$	−8.93584	+	22.9178i	−0.528387	+	1.35516i
$287$	−15.4000			−0.909032
$288$	5.81638	−	15.9427i	0.342733	−	0.939433i
$289$	5.52898			0.325234
$290$	−2.07539	+	5.32277i	−0.121871	+	0.312564i
$291$	−4.43777	+	1.04343i	−0.260146	+	0.0611672i
$292$	−19.7251	−	18.1397i	−1.15432	−	1.06155i
$293$	−8.77812	−	15.2041i	−0.512823	−	0.888236i	−0.999889	−	0.0148707i	$-0.995266\pi$
$293$	−8.77812	−	15.2041i	−0.512823	−	0.888236i	0.487066	−	0.873365i	$-0.338067\pi$
$294$	−0.966324	−	0.756875i	−0.0563572	−	0.0441418i
$295$	0.351174	+	0.202750i	0.0204461	+	0.0118046i
$296$	9.20943	+	18.8019i	0.535287	+	1.09284i
$297$	−23.8203	+	4.06918i	−1.38219	+	0.236118i
$298$	−6.74603	+	1.03214i	−0.390787	+	0.0597901i
$299$	26.9824	+	15.5783i	1.56043	+	0.900917i
$300$	−3.01883	−	1.69902i	−0.174292	−	0.0980929i
$301$	23.2376	−	13.4162i	1.33939	−	0.773299i
$302$	13.5877	−	10.8853i	0.781885	−	0.626380i
$303$	−26.5415	+	6.24059i	−1.52477	+	0.358513i
$304$	−1.71502	−	20.4451i	−0.0983633	−	1.17261i
$305$		−	5.28415i		−	0.302569i
$306$	−6.03601	+	13.0401i	−0.345056	+	0.745455i
$307$	−14.8826			−0.849397			−0.424699	−	0.905335i	$-0.639620\pi$
$307$	−14.8826			−0.849397			−0.424699	+	0.905335i	$0.639620\pi$
$308$	−5.17353	+	23.1403i	−0.294789	+	1.31854i
$309$	−15.6868	−	4.72675i	−0.892392	−	0.268896i
$310$	−6.22152	+	4.98416i	−0.353359	+	0.283081i
$311$	−3.87344	−	6.70899i	−0.219642	−	0.380432i	0.735056	−	0.678006i	$-0.237156\pi$
$311$	−3.87344	−	6.70899i	−0.219642	−	0.380432i	−0.954699	+	0.297574i	$0.903822\pi$
$312$	18.0802	−	2.96970i	1.02359	−	0.168126i
$313$	9.95594	−	17.2442i	0.562743	−	0.974700i	−0.434513	−	0.900666i	$-0.643079\pi$
$313$	9.95594	−	17.2442i	0.562743	−	0.974700i	0.997256	−	0.0740338i	$-0.0235873\pi$
$314$	1.51886	+	9.92727i	0.0857144	+	0.560228i
$315$	7.63331	+	0.471850i	0.430088	+	0.0265858i
$316$	3.73059	+	11.9062i	0.209862	+	0.669774i
$317$	−17.6886	+	30.6376i	−0.993493	+	1.72078i	−0.398109	+	0.917338i	$0.630334\pi$
$317$	−17.6886	+	30.6376i	−0.993493	+	1.72078i	−0.595383	+	0.803442i	$0.703000\pi$
$318$	−4.66781	+	1.87930i	−0.261758	+	0.105386i
$319$	16.2703	−	9.39366i	0.910962	−	0.525944i
$320$	−7.92584	−	1.08676i	−0.443068	−	0.0607520i
$321$	11.5420	−	10.8506i	0.644212	−	0.605620i
$322$	27.9818	+	10.9103i	1.55936	+	0.608010i
$323$			17.3721i			0.966612i
$324$	11.6477	+	13.7233i	0.647097	+	0.762408i
$325$		−	3.74006i		−	0.207461i
$326$	2.51049	−	6.43867i	0.139043	−	0.356605i
$327$	2.82752	−	2.65813i	0.156362	−	0.146995i
$328$	−9.53068	+	14.1811i	−0.526244	+	0.783022i
$329$	−2.74207	+	1.58314i	−0.151175	+	0.0872812i
$330$	4.25450	+	10.5673i	0.234203	+	0.581713i
$331$	0.0768415	−	0.133093i	0.00422359	−	0.00731547i	−0.863906	−	0.503653i	$-0.831989\pi$
$331$	0.0768415	−	0.133093i	0.00422359	−	0.00731547i	0.868129	+	0.496338i	$0.165322\pi$
$332$	−8.33955	−	26.6156i	−0.457692	−	1.46072i
$333$	−22.1639	−	1.37005i	−1.21457	−	0.0750785i
$334$	20.7374	−	3.17280i	1.13470	−	0.173608i
$335$	−6.17580	+	10.6968i	−0.337420	+	0.584429i
$336$	16.7951	−	5.46560i	0.916246	−	0.298173i
$337$	9.38668	+	16.2582i	0.511325	+	0.885641i	0.999914	+	0.0131265i	$0.00417842\pi$
$337$	9.38668	+	16.2582i	0.511325	+	0.885641i	−0.488589	+	0.872514i	$0.662488\pi$
$338$	0.873611	+	1.09049i	0.0475182	+	0.0593151i
$339$	10.2931	+	3.10153i	0.559047	+	0.168452i
$340$	6.61058	+	1.47794i	0.358509	+	0.0801527i
$341$	26.2150			1.41962
$342$	19.7485	+	9.14116i	1.06787	+	0.494297i
$343$		−	19.1225i		−	1.03252i
$344$	2.02680	−	29.7014i	0.109278	−	1.60139i
$345$	14.0459	−	3.30254i	0.756203	−	0.177803i
$346$	5.69527	+	7.10917i	0.306179	+	0.382192i
$347$	21.2257	−	12.2547i	1.13945	−	0.657864i	0.193159	−	0.981168i	$-0.438127\pi$
$347$	21.2257	−	12.2547i	1.13945	−	0.657864i	0.946295	+	0.323303i	$0.104793\pi$
$348$	−12.1953	−	6.86360i	−0.653737	−	0.367928i
$349$	−20.5838	−	11.8841i	−1.10183	−	0.636140i	−0.165126	−	0.986272i	$-0.552803\pi$
$349$	−20.5838	−	11.8841i	−1.10183	−	0.636140i	−0.936700	+	0.350133i	$0.886137\pi$
$350$	−0.545254	−	3.56377i	−0.0291451	−	0.190492i
$351$	−6.74417	+	18.2262i	−0.359977	+	0.972840i
$352$	18.1071	+	19.0850i	0.965109	+	1.01724i
$353$	−0.676798	−	0.390750i	−0.0360223	−	0.0207975i	0.481881	−	0.876237i	$-0.339954\pi$
$353$	−0.676798	−	0.390750i	−0.0360223	−	0.0207975i	−0.517903	+	0.855439i	$0.673287\pi$
$354$	−0.612472	+	0.781961i	−0.0325525	+	0.0415608i
$355$	2.71603	+	4.70430i	0.144152	+	0.249678i
$356$	−3.69075	+	4.01331i	−0.195609	+	0.212705i
$357$	−14.5578	+	3.42292i	−0.770482	+	0.181160i
$358$	−11.5513	−	4.50394i	−0.610503	−	0.238041i
$359$	10.9728			0.579123			0.289561	−	0.957159i	$-0.406491\pi$
$359$	10.9728			0.579123			0.289561	+	0.957159i	$0.406491\pi$
$360$	5.15857	−	6.73714i	0.271881	−	0.355079i
$361$	7.30901			0.384685
$362$	20.2347	+	7.88968i	1.06351	+	0.414672i
$363$	5.31103	−	17.6259i	0.278757	−	0.925119i
$364$	14.0361	+	12.9080i	0.735690	+	0.676561i
$365$	−6.69948	−	11.6038i	−0.350667	−	0.607373i
$366$	12.8153	+	1.81701i	0.669866	+	0.0949766i
$367$	−7.62051	−	4.39970i	−0.397787	−	0.229663i	0.287741	−	0.957708i	$-0.407096\pi$
$367$	−7.62051	−	4.39970i	−0.397787	−	0.229663i	−0.685529	+	0.728045i	$0.740429\pi$
$368$	27.3641	−	19.0150i	1.42645	−	0.991224i
$369$	−8.07575	−	16.2238i	−0.420407	−	0.844579i
$370$	1.58319	+	10.3477i	0.0823060	+	0.537951i
$371$	−4.53533	−	2.61847i	−0.235462	−	0.135944i
$372$	−9.94841	−	16.8025i	−0.515801	−	0.871169i
$373$	15.1314	−	8.73611i	0.783473	−	0.452338i	−0.0541866	−	0.998531i	$-0.517257\pi$
$373$	15.1314	−	8.73611i	0.783473	−	0.452338i	0.837660	+	0.546192i	$0.183923\pi$
$374$	−13.9272	−	17.3848i	−0.720158	−	0.898944i
$375$	−1.18636	−	1.26196i	−0.0612635	−	0.0651674i
$376$	−0.239165	+	3.50482i	−0.0123340	+	0.180747i
$377$		−	15.1089i		−	0.778147i
$378$	−3.76914	+	18.3503i	−0.193864	+	0.943838i
$379$	−25.7713			−1.32378			−0.661892	−	0.749600i	$-0.730246\pi$
$379$	−25.7713			−1.32378			−0.661892	+	0.749600i	$0.730246\pi$
$380$	2.23825	−	10.0113i	0.114820	−	0.513569i
$381$	16.1881	−	15.2183i	0.829339	−	0.779657i
$382$	−2.64563	−	3.30243i	−0.135362	−	0.168967i
$383$	18.0206	+	31.2126i	0.920809	+	1.59489i	0.798166	+	0.602437i	$0.205804\pi$
$383$	18.0206	+	31.2126i	0.920809	+	1.59489i	0.122643	+	0.992451i	$0.460863\pi$
$384$	5.36104	−	18.8483i	0.273580	−	0.961849i
$385$	−5.92789	+	10.2674i	−0.302113	+	0.523276i
$386$	−3.56786	+	0.545879i	−0.181599	+	0.0277845i
$387$	26.3198	+	17.4453i	1.33791	+	0.886792i
$388$	−5.02322	+	1.57394i	−0.255015	+	0.0799047i
$389$	−9.31753	+	16.1384i	−0.472418	+	0.818251i	−0.999502	−	0.0315617i	$-0.989952\pi$
$389$	−9.31753	+	16.1384i	−0.472418	+	0.818251i	0.527084	+	0.849813i	$0.323285\pi$
$390$	9.07051	+	1.28606i	0.459303	+	0.0651221i
$391$	−24.4345	+	14.1073i	−1.23571	+	0.713436i
$392$	−1.17636	−	0.790592i	−0.0594151	−	0.0399309i
$393$	−15.9518	−	4.80660i	−0.804662	−	0.242461i
$394$	5.40288	−	13.8568i	0.272193	−	0.698095i
$395$			6.23847i			0.313892i
$396$	−27.0912	+	6.68447i	−1.36139	+	0.335907i
$397$			27.9154i			1.40103i	0.713635	+	0.700517i	$0.247047\pi$
$397$			27.9154i			1.40103i	−0.713635	+	0.700517i	$0.752953\pi$
$398$	16.3596	+	6.37875i	0.820032	+	0.319738i
$399$	5.18380	+	22.0469i	0.259515	+	1.10373i
$400$	−3.61916	−	1.70343i	−0.180958	−	0.0851717i
$401$	−12.3568	+	7.13421i	−0.617070	+	0.356265i	−0.775727	−	0.631068i	$-0.782617\pi$
$401$	−12.3568	+	7.13421i	−0.617070	+	0.356265i	0.158657	+	0.987334i	$0.449283\pi$
$402$	−23.8186	−	18.6560i	−1.18797	−	0.930475i
$403$	10.5412	−	18.2578i	0.525092	−	0.909486i
$404$	−30.0430	+	9.41346i	−1.49469	+	0.468337i
$405$	3.50581	+	8.28911i	0.174205	+	0.411889i
$406$	−2.20269	−	14.3967i	−0.109318	−	0.714498i
$407$	17.2121	−	29.8122i	0.853172	−	1.47774i
$408$	−5.85748	+	15.5240i	−0.289988	+	0.768553i
$409$	2.20480	+	3.81883i	0.109020	+	0.188829i	0.915374	−	0.402605i	$-0.131895\pi$
$409$	2.20480	+	3.81883i	0.109020	+	0.188829i	−0.806353	+	0.591434i	$0.798562\pi$
$410$	−6.66741	+	5.34137i	−0.329280	+	0.263791i
$411$	3.88046	+	16.5037i	0.191409	+	0.814070i
$412$	−18.4622	−	4.12764i	−0.909569	−	0.203354i
$413$	−1.03374			−0.0508670
$414$	3.17963	+	35.2001i	0.156270	+	1.72999i
$415$		−	13.9458i		−	0.684571i
$416$	20.5729	−	4.93674i	1.00867	−	0.242044i
$417$	3.13358	−	10.3995i	0.153452	−	0.509265i
$418$	−26.3281	+	21.0918i	−1.28775	+	1.03164i
$419$	17.8653	−	10.3145i	0.872777	−	0.503898i	0.00450661	−	0.999990i	$-0.498565\pi$
$419$	17.8653	−	10.3145i	0.872777	−	0.503898i	0.868270	+	0.496092i	$0.165232\pi$
$420$	8.83048	−	0.0969282i	0.430883	−	0.00472961i
$421$	−3.57346	−	2.06314i	−0.174160	−	0.100551i	0.410386	−	0.911912i	$-0.365394\pi$
$421$	−3.57346	−	2.06314i	−0.174160	−	0.100551i	−0.584546	+	0.811361i	$0.698727\pi$
$422$	21.8049	−	3.33613i	1.06145	−	0.162400i
$423$	−3.10577	−	2.05857i	−0.151008	−	0.100091i
$424$	−5.21803	+	2.55586i	−0.253410	+	0.124124i
$425$	2.93313	+	1.69345i	0.142278	+	0.0821442i
$426$	−12.3430	+	4.96938i	−0.598018	+	0.240767i
$427$	6.73542	+	11.6661i	0.325950	+	0.564562i
$428$	12.3821	−	13.4643i	0.598513	−	0.650820i
$429$	−20.6351	−	21.9500i	−0.996271	−	1.05976i
$430$	5.40738	−	13.8683i	0.260767	−	0.668790i
$431$	−26.0944			−1.25692			−0.628462	−	0.777841i	$-0.716315\pi$
$431$	−26.0944			−1.25692			−0.628462	+	0.777841i	$0.716315\pi$
$432$	14.5653	+	14.8274i	0.700774	+	0.713383i
$433$	0.448125			0.0215355			0.0107677	−	0.999942i	$-0.496572\pi$
$433$	0.448125			0.0215355			0.0107677	+	0.999942i	$0.496572\pi$
$434$	7.38255	−	18.9340i	0.354374	−	0.908862i
$435$	−4.79260	−	5.09800i	−0.229788	−	0.244430i
$436$	3.03333	−	3.29843i	0.145270	−	0.157966i
$437$	21.3646	+	37.0045i	1.02201	+	1.77017i
$438$	30.4457	−	12.2577i	1.45475	−	0.585696i
$439$	−29.0457	−	16.7695i	−1.38627	−	0.800366i	−0.393381	−	0.919376i	$-0.628695\pi$
$439$	−29.0457	−	16.7695i	−1.38627	−	0.800366i	−0.992893	+	0.119010i	$0.962028\pi$
$440$	5.78616	+	11.8130i	0.275844	+	0.563162i
$441$	1.34581	−	0.669903i	0.0640860	−	0.0319001i
$442$	−17.7080	+	2.70931i	−0.842284	+	0.128869i
$443$	−32.1997	−	18.5905i	−1.52986	−	0.883262i	−0.999367	−	0.0355701i	$-0.988675\pi$
$443$	−32.1997	−	18.5905i	−1.52986	−	0.883262i	−0.530488	−	0.847692i	$-0.677991\pi$
$444$	−25.6400	+	0.281439i	−1.21682	+	0.0133565i
$445$	−2.36094	+	1.36309i	−0.111919	+	0.0646167i
$446$	1.83152	−	1.46726i	0.0867248	−	0.0694766i
$447$	2.41143	−	8.00290i	0.114057	−	0.378524i
$448$	18.8835	−	7.70334i	0.892163	−	0.363948i
$449$		−	26.7099i		−	1.26052i	−0.776384	−	0.630260i	$-0.782948\pi$
$449$		−	26.7099i		−	1.26052i	0.776384	−	0.630260i	$-0.217052\pi$
$450$	3.46849	−	2.44327i	0.163506	−	0.115177i
$451$	28.0938			1.32289
$452$	12.1143	+	2.70842i	0.569807	+	0.127393i
$453$	4.88052	+	20.7570i	0.229307	+	0.975251i
$454$	10.8506	−	8.69256i	0.509243	−	0.407962i
$455$	4.76725	+	8.25712i	0.223492	+	0.387100i
$456$	23.5101	+	8.87078i	1.10096	+	0.415412i
$457$	20.4459	−	35.4134i	0.956421	−	1.65657i	0.225338	−	0.974281i	$-0.427651\pi$
$457$	20.4459	−	35.4134i	0.956421	−	1.65657i	0.731083	−	0.682289i	$-0.239015\pi$
$458$	−2.32133	−	15.1722i	−0.108469	−	0.708949i
$459$	−11.2402	−	13.5417i	−0.524646	−	0.632070i
$460$	15.8989	−	4.98164i	0.741288	−	0.232270i
$461$	−5.52803	+	9.57483i	−0.257466	+	0.445944i	−0.965562	−	0.260171i	$-0.916221\pi$
$461$	−5.52803	+	9.57483i	−0.257466	+	0.445944i	0.708096	+	0.706116i	$0.249554\pi$
$462$	−22.8625	−	17.9071i	−1.06366	−	0.833113i
$463$	19.4701	−	11.2411i	0.904851	−	0.522416i	0.0260804	−	0.999660i	$-0.491697\pi$
$463$	19.4701	−	11.2411i	0.904851	−	0.522416i	0.878771	+	0.477244i	$0.158364\pi$
$464$	−14.6205	−	6.88144i	−0.678739	−	0.319463i
$465$	−2.23469	−	9.50421i	−0.103631	−	0.440747i
$466$	34.6570	+	13.5131i	1.60545	+	0.625981i
$467$			20.5034i			0.948784i	0.880314	+	0.474392i	$0.157332\pi$
$467$			20.5034i			0.948784i	−0.880314	+	0.474392i	$0.842668\pi$
$468$	−6.23798	+	21.5559i	−0.288351	+	0.996421i
$469$		−	31.4879i		−	1.45397i
$470$	−0.638080	+	1.63649i	−0.0294325	+	0.0754855i
$471$	−11.7768	−	3.54860i	−0.542648	−	0.163511i
$472$	−0.639757	+	0.951924i	−0.0294472	+	0.0438158i
$473$	−42.3918	+	24.4749i	−1.94918	+	1.12536i
$474$	−15.1298	−	2.14516i	−0.694933	−	0.0985307i
$475$	2.56462	−	4.44204i	0.117673	−	0.203815i
$476$	−16.4784	+	5.16322i	−0.755285	+	0.236656i
$477$	0.380227	−	6.15108i	0.0174094	−	0.281639i
$478$	−8.89026	+	1.36020i	−0.406631	+	0.0622142i
$479$	0.870737	−	1.50816i	0.0397850	−	0.0689096i	−0.845447	−	0.534059i	$-0.820666\pi$
$479$	0.870737	−	1.50816i	0.0397850	−	0.0689096i	0.885232	+	0.465149i	$0.153999\pi$
$480$	5.37571	−	8.19156i	0.245367	−	0.373892i
$481$	−13.8421	−	23.9752i	−0.631145	−	1.09317i
$482$	10.1072	+	12.6164i	0.460370	+	0.574661i
$483$	−26.8002	+	25.1947i	−1.21945	+	1.14640i
$484$	4.63787	−	20.7444i	0.210812	−	0.942926i
$485$	−2.63202			−0.119514
$486$	−21.3085	+	5.65212i	−0.966575	+	0.256386i
$487$		−	0.442827i		−	0.0200664i	−0.999950	−	0.0100332i	$-0.996806\pi$
$487$		−	0.442827i		−	0.0200664i	0.999950	−	0.0100332i	$-0.00319372\pi$
$488$	14.9112	+	1.01752i	0.674996	+	0.0460611i
$489$	5.79735	+	6.16678i	0.262165	+	0.278871i
$490$	−0.443079	−	0.553078i	−0.0200163	−	0.0249855i
$491$	−25.3759	+	14.6508i	−1.14520	+	0.661181i	−0.947713	−	0.319124i	$-0.896611\pi$
$491$	−25.3759	+	14.6508i	−1.14520	+	0.661181i	−0.197487	+	0.980306i	$0.563278\pi$
$492$	−10.6614	−	18.0067i	−0.480653	−	0.811806i
$493$	11.8491	+	6.84109i	0.533657	+	0.308107i
$494$	4.10308	+	26.8177i	0.184606	+	1.20658i
$495$	−13.9253	−	0.860786i	−0.625895	−	0.0386895i
$496$	−12.8666	−	18.5161i	−0.577727	−	0.831395i
$497$	−11.9926	−	6.92395i	−0.537943	−	0.310582i
$498$	33.8218	+	4.79540i	1.51559	+	0.214887i
$499$	14.0808	+	24.3886i	0.630341	+	1.09178i	0.987482	+	0.157733i	$0.0504184\pi$
$499$	14.0808	+	24.3886i	0.630341	+	1.09178i	−0.357141	+	0.934051i	$0.616248\pi$
$500$	−1.47213	−	1.35382i	−0.0658359	−	0.0605445i
$501$	−7.41277	+	24.6010i	−0.331178	+	1.09909i
$502$	−22.8175	−	8.89675i	−1.01840	−	0.397081i
$503$	15.0167			0.669560			0.334780	−	0.942296i	$-0.391338\pi$
$503$	15.0167			0.669560			0.334780	+	0.942296i	$0.391338\pi$
$504$	−2.80138	+	21.4493i	−0.124783	+	0.955428i
$505$	−15.7416			−0.700493
$506$	−51.0465	−	19.9035i	−2.26929	−	0.884818i
$507$	−1.66587	+	0.391690i	−0.0739841	+	0.0173956i
$508$	17.3663	−	18.8841i	0.770507	−	0.837847i
$509$	−9.57636	−	16.5867i	−0.424465	−	0.735194i	0.571906	−	0.820319i	$-0.306204\pi$
$509$	−9.57636	−	16.5867i	−0.424465	−	0.735194i	−0.996370	+	0.0851250i	$0.972871\pi$
$510$	−5.11559	+	6.53122i	−0.226522	+	0.289207i
$511$	29.5816	+	17.0789i	1.30861	+	0.755528i
$512$	4.59291	−	22.1564i	0.202980	−	0.979183i
$513$	−20.5080	+	17.0225i	−0.905449	+	0.751563i
$514$	−1.42622	−	9.32175i	−0.0629078	−	0.411165i
$515$	−8.19174	−	4.72950i	−0.360971	−	0.208407i
$516$	31.7746	+	17.8829i	1.39880	+	0.787253i
$517$	5.00231	−	2.88808i	0.220001	−	0.127018i
$518$	−16.6849	−	20.8271i	−0.733094	−	0.915092i
$519$	−10.8602	+	2.55352i	−0.476710	+	0.112087i
$520$	10.5539	+	0.720191i	0.462821	+	0.0315824i
$521$			36.1713i			1.58469i	0.610072	+	0.792346i	$0.291141\pi$
$521$			36.1713i			1.58469i	−0.610072	+	0.792346i	$0.708859\pi$
$522$	14.0118	−	9.87018i	0.613281	−	0.432006i
$523$	12.2116			0.533975			0.266988	−	0.963700i	$-0.413972\pi$
$523$	12.2116			0.533975			0.266988	+	0.963700i	$0.413972\pi$
$524$	−18.7741	−	4.19737i	−0.820150	−	0.183363i
$525$	4.22775	+	1.27391i	0.184514	+	0.0555978i
$526$	−22.7125	−	28.3511i	−0.990310	−	1.23616i
$527$	9.54577	+	16.5338i	0.415820	+	0.720222i
$528$	−30.6389	+	9.97077i	−1.33339	+	0.433922i
$529$	−23.1988	+	40.1815i	−1.00864	+	1.74702i
$530$	−2.87176	+	0.439377i	−0.124741	+	0.0190853i
$531$	−0.542093	−	1.08904i	−0.0235248	−	0.0472604i
$532$	7.81937	+	24.9555i	0.339013	+	1.08196i
$533$	11.2966	−	19.5663i	0.489311	−	0.847512i
$534$	−2.49398	−	6.19455i	−0.107925	−	0.268064i
$535$	7.92074	−	4.57304i	0.342444	−	0.197710i
$536$	−28.9957	−	19.4871i	−1.25242	−	0.841713i
$537$	11.0635	−	10.4007i	0.477425	−	0.448824i
$538$	−8.74575	+	22.4302i	−0.377056	+	0.967036i
$539$			2.33045i			0.100380i
$540$	4.73282	+	9.25205i	0.203668	+	0.398145i
$541$		−	34.9053i		−	1.50070i	−0.661042	−	0.750349i	$-0.729886\pi$
$541$		−	34.9053i		−	1.50070i	0.661042	−	0.750349i	$-0.270114\pi$
$542$	−41.0799	−	16.0174i	−1.76453	−	0.688008i
$543$	−19.3802	+	18.2192i	−0.831685	+	0.781862i
$544$	−5.44350	+	18.3696i	−0.233388	+	0.787589i
$545$	1.94039	−	1.12029i	0.0831174	−	0.0479878i
$546$	−21.6647	+	8.72240i	−0.927164	+	0.373284i
$547$	11.0482	−	19.1361i	0.472388	−	0.818200i	−0.527113	−	0.849795i	$-0.676725\pi$
$547$	11.0482	−	19.1361i	0.472388	−	0.818200i	0.999501	+	0.0315955i	$0.0100588\pi$
$548$	5.85338	+	18.6810i	0.250044	+	0.798013i
$549$	−8.75814	+	13.2134i	−0.373788	+	0.563936i
$550$	0.994695	+	6.50131i	0.0424139	+	0.277217i
$551$	10.3604	−	17.9447i	0.441368	−	0.764471i
$552$	6.61464	+	40.2714i	0.281538	+	1.71407i
$553$	−7.95185	−	13.7730i	−0.338147	−	0.585688i
$554$	11.6813	−	9.35811i	0.496293	−	0.397588i
$555$	−12.2756	−	3.69888i	−0.521070	−	0.157009i
$556$	2.73640	−	12.2394i	0.116049	−	0.519068i
$557$	−11.3188			−0.479591			−0.239796	−	0.970823i	$-0.577080\pi$
$557$	−11.3188			−0.479591			−0.239796	+	0.970823i	$0.577080\pi$
$558$	23.8183	−	2.15151i	1.00831	−	0.0910809i
$559$			39.3658i			1.66500i
$560$	10.1615	−	0.852388i	0.429401	−	0.0360200i
$561$	26.5575	−	6.24437i	1.12126	−	0.263637i
$562$	11.9034	−	9.53598i	0.502114	−	0.402251i
$563$	−21.3524	+	12.3278i	−0.899896	+	0.519555i	−0.877167	−	0.480186i	$-0.840569\pi$
$563$	−21.3524	+	12.3278i	−0.899896	+	0.519555i	−0.0227299	+	0.999742i	$0.507236\pi$
$564$	−3.74945	−	2.11022i	−0.157880	−	0.0888562i
$565$	5.37513	+	3.10333i	0.226134	+	0.130558i
$566$	−18.2176	+	2.78727i	−0.765741	+	0.117158i
$567$	−18.3056	−	13.8316i	−0.768765	−	0.580873i
$568$	−13.7979	+	6.75839i	−0.578947	+	0.283576i
$569$	10.4402	+	6.02768i	0.437678	+	0.252693i	0.702612	−	0.711573i	$-0.252017\pi$
$569$	10.4402	+	6.02768i	0.437678	+	0.252693i	−0.264934	+	0.964266i	$0.585350\pi$
$570$	9.89113	+	7.74724i	0.414294	+	0.324496i
$571$	−4.73898	−	8.20815i	−0.198320	−	0.343501i	0.749664	−	0.661819i	$-0.230215\pi$
$571$	−4.73898	−	8.20815i	−0.198320	−	0.343501i	−0.947984	+	0.318318i	$0.896882\pi$
$572$	−25.6057	−	23.5477i	−1.07063	−	0.984579i
$573$	5.04491	−	1.18619i	0.210754	−	0.0495538i
$574$	7.91164	−	20.2910i	0.330226	−	0.846930i
$575$	8.33052			0.347407
$576$	18.0180	+	15.8541i	0.750749	+	0.660588i
$577$	7.47489			0.311184			0.155592	−	0.987821i	$-0.450272\pi$
$577$	7.47489			0.311184			0.155592	+	0.987821i	$0.450272\pi$
$578$	−2.84048	+	7.28497i	−0.118148	+	0.303015i
$579$	1.27536	−	4.23259i	0.0530023	−	0.175900i
$580$	−5.94705	−	5.46907i	−0.246938	−	0.227091i
$581$	17.7759	+	30.7888i	0.737470	+	1.27734i
$582$	0.905046	−	6.38326i	0.0375154	−	0.264594i
$583$	8.27369	+	4.77682i	0.342661	+	0.197836i
$584$	34.0345	−	16.6706i	1.40836	−	0.689833i
$585$	−6.19890	+	9.35232i	−0.256293	+	0.386671i
$586$	24.5427	−	3.75501i	1.01385	−	0.155118i
$587$	−29.4957	−	17.0293i	−1.21742	−	0.702876i	−0.253052	−	0.967453i	$-0.581434\pi$
$587$	−29.4957	−	17.0293i	−1.21742	−	0.702876i	−0.964365	+	0.264577i	$0.914768\pi$
$588$	1.49370	−	0.884389i	0.0615992	−	0.0364716i
$589$	25.0393	−	14.4565i	1.03173	−	0.595668i
$590$	−0.447557	+	0.358545i	−0.0184256	+	0.0147611i
$591$	12.4766	+	13.2717i	0.513219	+	0.545923i
$592$	−29.5047	+	2.47498i	−1.21263	+	0.101721i
$593$			5.46511i			0.224425i	0.993684	+	0.112213i	$0.0357937\pi$
$593$			5.46511i			0.224425i	−0.993684	+	0.112213i	$0.964206\pi$
$594$	6.87596	−	33.4761i	0.282124	−	1.37354i
$595$	−8.63417			−0.353967
$596$	2.10579	−	9.41882i	0.0862565	−	0.385810i
$597$	−15.6688	+	14.7301i	−0.641280	+	0.602864i
$598$	−34.3880	+	27.5488i	−1.40623	+	1.12655i
$599$	8.10483	+	14.0380i	0.331154	+	0.573576i	0.982738	−	0.185000i	$-0.0592286\pi$
$599$	8.10483	+	14.0380i	0.331154	+	0.573576i	−0.651584	+	0.758576i	$0.725895\pi$
$600$	3.78953	−	3.10475i	0.154707	−	0.126751i
$601$	−4.73112	+	8.19455i	−0.192987	+	0.334263i	−0.946239	−	0.323469i	$-0.895151\pi$
$601$	−4.73112	+	8.19455i	−0.192987	+	0.334263i	0.753252	+	0.657732i	$0.228484\pi$
$602$	5.73905	+	37.5103i	0.233906	+	1.52881i
$603$	33.1724	−	16.5122i	1.35088	−	0.672430i
$604$	7.36189	+	23.4954i	0.299551	+	0.956015i
$605$	5.31412	−	9.20433i	0.216050	−	0.374209i
$606$	5.41292	−	38.1771i	0.219885	−	1.55084i
$607$	13.9365	−	8.04627i	0.565667	−	0.326588i	−0.189750	−	0.981832i	$-0.560768\pi$
$607$	13.9365	−	8.04627i	0.565667	−	0.326588i	0.755417	+	0.655244i	$0.227434\pi$
$608$	27.8196	+	8.24384i	1.12823	+	0.334332i
$609$	17.0790	+	5.14625i	0.692077	+	0.208537i
$610$	6.96239	+	2.71470i	0.281899	+	0.109915i
$611$		−	4.64523i		−	0.187926i
$612$	−14.0807	−	14.6523i	−0.569179	−	0.592285i
$613$			9.72482i			0.392782i	0.980526	+	0.196391i	$0.0629221\pi$
$613$			9.72482i			0.392782i	−0.980526	+	0.196391i	$0.937078\pi$
$614$	7.64586	−	19.6094i	0.308562	−	0.791369i
$615$	−2.39484	−	10.1854i	−0.0965694	−	0.410713i
$616$	−27.8318	−	18.7048i	−1.12137	−	0.753639i
$617$	26.6764	−	15.4016i	1.07395	−	0.620046i	0.144692	−	0.989477i	$-0.453781\pi$
$617$	26.6764	−	15.4016i	1.07395	−	0.620046i	0.929258	+	0.369431i	$0.120447\pi$
$618$	14.2870	−	18.2406i	0.574706	−	0.733744i
$619$	15.0957	−	26.1466i	0.606749	−	1.05092i	−0.385024	−	0.922907i	$-0.625807\pi$
$619$	15.0957	−	26.1466i	0.606749	−	1.05092i	0.991772	−	0.128013i	$-0.0408600\pi$
$620$	−3.37085	−	10.7581i	−0.135377	−	0.432054i
$621$	−40.5965	−	15.0218i	−1.62908	−	0.602805i
$622$	10.8297	−	1.65694i	0.434232	−	0.0664371i
$623$	3.47492	−	6.01873i	0.139220	−	0.241135i
$624$	−5.37571	+	25.3481i	−0.215201	+	1.01474i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	17.6061	+	21.9770i	0.703683	+	0.878379i
$627$	−9.45670	−	40.2197i	−0.377664	−	1.60622i
$628$	−13.8605	−	3.09882i	−0.553093	−	0.123656i
$629$	25.0700			0.999606
$630$	−4.54327	+	9.81523i	−0.181008	+	0.391048i
$631$		−	28.3960i		−	1.13043i	−0.824944	−	0.565214i	$-0.808794\pi$
$631$		−	28.3960i		−	1.13043i	0.824944	−	0.565214i	$-0.191206\pi$
$632$	−17.6041	−	1.20129i	−0.700255	−	0.0477847i
$633$	−7.79437	+	25.8674i	−0.309798	+	1.02814i
$634$	−31.2807	−	39.0464i	−1.24231	−	1.55073i
$635$	11.1091	−	6.41385i	0.440852	−	0.254526i
$636$	−0.0781068	−	7.11578i	−0.00309713	−	0.282159i
$637$	1.62307	+	0.937082i	0.0643085	+	0.0371285i
$638$	4.01832	+	26.2637i	0.159087	+	1.03979i
$639$	1.00542	−	16.2651i	0.0397739	−	0.643438i
$640$	5.50377	−	9.88476i	0.217556	−	0.390730i
$641$	3.53067	+	2.03844i	0.139453	+	0.0805134i	0.568103	−	0.822957i	$-0.307677\pi$
$641$	3.53067	+	2.03844i	0.139453	+	0.0805134i	−0.428650	+	0.903471i	$0.641011\pi$
$642$	8.36707	+	20.7821i	0.330222	+	0.820206i
$643$	−11.1471	−	19.3074i	−0.439600	−	0.761410i	0.558058	−	0.829802i	$-0.311547\pi$
$643$	−11.1471	−	19.3074i	−0.439600	−	0.761410i	−0.997659	+	0.0683917i	$0.978213\pi$
$644$	−28.7509	+	31.2636i	−1.13294	+	1.23196i
$645$	12.4870	+	13.2827i	0.491675	+	0.523006i
$646$	−22.8895	−	8.92483i	−0.900576	−	0.351143i
$647$	11.9935			0.471513			0.235757	−	0.971812i	$-0.424243\pi$
$647$	11.9935			0.471513			0.235757	+	0.971812i	$0.424243\pi$
$648$	−24.0658	+	8.29677i	−0.945395	+	0.325928i
$649$	1.88583			0.0740253
$650$	4.92790	+	1.92143i	0.193288	+	0.0753647i
$651$	17.0481	+	18.1345i	0.668169	+	0.710747i
$652$	7.19383	+	6.61565i	0.281732	+	0.259089i
$653$	−22.7175	−	39.3478i	−0.889004	−	1.53980i	−0.841055	−	0.540950i	$-0.818065\pi$
$653$	−22.7175	−	39.3478i	−0.889004	−	1.53980i	−0.0479492	−	0.998850i	$-0.515269\pi$
$654$	2.04973	+	5.09113i	0.0801509	+	0.199079i
$655$	−8.33011	−	4.80939i	−0.325484	−	0.187919i
$656$	−13.7887	−	19.8431i	−0.538359	−	0.774742i
$657$	−2.48002	+	40.1203i	−0.0967549	+	1.56524i
$658$	−0.677217	−	4.42628i	−0.0264007	−	0.172554i
$659$	−11.4821	−	6.62918i	−0.447278	−	0.258236i	0.259402	−	0.965769i	$-0.416475\pi$
$659$	−11.4821	−	6.62918i	−0.447278	−	0.258236i	−0.706680	+	0.707533i	$0.749808\pi$
$660$	−16.1092	+	0.176824i	−0.627051	+	0.00688286i
$661$	38.9627	−	22.4951i	1.51547	−	0.874959i	0.515638	−	0.856807i	$-0.327555\pi$
$661$	38.9627	−	22.4951i	1.51547	−	0.874959i	0.999835	−	0.0181521i	$-0.00577830\pi$
$662$	0.135887	+	0.169622i	0.00528139	+	0.00659255i
$663$	6.32990	−	21.0072i	0.245833	−	0.815853i
$664$	39.3531	+	2.68542i	1.52720	+	0.104214i
$665$			13.0759i			0.507062i
$666$	13.1917	−	28.4993i	0.511170	−	1.10433i
$667$	33.6532			1.30306
$668$	−6.47321	+	28.9536i	−0.250456	+	1.12025i
$669$	0.657856	+	2.79789i	0.0254342	+	0.108173i
$670$	−10.9213	−	13.6326i	−0.421927	−	0.526675i
$671$	−12.2873	−	21.2822i	−0.474345	−	0.821590i
$672$	−1.42689	+	24.9371i	−0.0550435	+	0.961969i
$673$	8.61513	−	14.9218i	0.332089	−	0.575195i	−0.650832	−	0.759221i	$-0.725580\pi$
$673$	8.61513	−	14.9218i	0.332089	−	0.575195i	0.982921	+	0.184027i	$0.0589133\pi$
$674$	−26.2441	+	4.01533i	−1.01089	+	0.154665i
$675$	0.874976	+	5.12195i	0.0336778	+	0.197144i
$676$	−1.88565	+	0.590835i	−0.0725248	+	0.0227244i
$677$	14.7680	−	25.5790i	0.567581	−	0.983079i	−0.429223	−	0.903198i	$-0.641213\pi$
$677$	14.7680	−	25.5790i	0.567581	−	0.983079i	0.996804	−	0.0798808i	$-0.0254540\pi$
$678$	−9.37461	+	11.9688i	−0.360030	+	0.459661i
$679$	5.81084	−	3.35489i	0.223000	−	0.128749i
$680$	−5.34348	+	7.95081i	−0.204913	+	0.304900i
$681$	3.89738	+	16.5757i	0.149348	+	0.635182i
$682$	−13.4678	+	34.5409i	−0.515709	+	1.32264i
$683$		−	31.4320i		−	1.20271i	−0.798982	−	0.601355i	$-0.794628\pi$
$683$		−	31.4320i		−	1.20271i	0.798982	−	0.601355i	$-0.205372\pi$
$684$	−22.1900	+	21.3243i	−0.848457	+	0.815356i
$685$			9.78829i			0.373991i
$686$	25.1958	+	9.82407i	0.961980	+	0.375085i
$687$	17.9989	+	5.42344i	0.686702	+	0.206917i
$688$	38.0933	+	17.9294i	1.45229	+	0.683552i
$689$	6.65376	−	3.84155i	0.253488	−	0.146351i
$690$	−2.86454	+	20.2035i	−0.109051	+	0.769133i
$691$	0.540149	−	0.935565i	0.0205482	−	0.0355906i	−0.855568	−	0.517690i	$-0.826792\pi$
$691$	0.540149	−	0.935565i	0.0205482	−	0.0355906i	0.876117	+	0.482099i	$0.160126\pi$
$692$	−12.2929	+	3.85179i	−0.467308	+	0.146423i
$693$	31.8408	−	15.8494i	1.20953	−	0.602069i
$694$	5.24216	+	34.2627i	0.198990	+	1.30059i
$695$	3.13540	−	5.43067i	0.118932	−	0.205997i
$696$	15.3087	−	12.5424i	0.580276	−	0.475418i
$697$	10.2299	+	17.7187i	0.387485	+	0.671144i
$698$	26.2333	−	21.0159i	0.992943	−	0.795462i
$699$	−33.1935	+	31.2050i	−1.25549	+	1.18028i
$700$	4.97575	+	1.11244i	0.188066	+	0.0420463i
$701$	−31.7591			−1.19952			−0.599762	−	0.800179i	$-0.704738\pi$
$701$	−31.7591			−1.19952			−0.599762	+	0.800179i	$0.704738\pi$
$702$	−20.5500	−	18.2497i	−0.775610	−	0.688790i
$703$		−	37.9669i		−	1.43195i
$704$	−34.4488	+	14.0530i	−1.29834	+	0.529643i
$705$	−1.47349	−	1.56738i	−0.0554947	−	0.0590310i
$706$	0.862552	−	0.691004i	0.0324626	−	0.0260063i
$707$	34.7536	−	20.0650i	1.30704	−	0.754622i
$708$	−0.715658	−	1.20872i	−0.0268961	−	0.0454265i
$709$	5.26182	+	3.03791i	0.197612	+	0.114091i	0.595541	−	0.803325i	$-0.296938\pi$
$709$	5.26182	+	3.03791i	0.197612	+	0.114091i	−0.397929	+	0.917416i	$0.630271\pi$
$710$	−7.59372	+	1.16183i	−0.284987	+	0.0436028i
$711$	10.3399	−	15.5998i	0.387775	−	0.585039i
$712$	−3.39183	−	6.92474i	−0.127114	−	0.259516i
$713$	40.6671	+	23.4791i	1.52299	+	0.879301i
$714$	2.96895	−	20.9399i	0.111110	−	0.783656i
$715$	−8.69679	−	15.0633i	−0.325241	−	0.563335i
$716$	11.8688	−	12.9061i	0.443557	−	0.482322i
$717$	3.17791	−	10.5466i	0.118681	−	0.393871i
$718$	−5.63721	+	14.4578i	−0.210379	+	0.539559i
$719$	−3.28970			−0.122685			−0.0613425	−	0.998117i	$-0.519538\pi$
$719$	−3.28970			−0.122685			−0.0613425	+	0.998117i	$0.519538\pi$
$720$	6.22667	+	10.2581i	0.232054	+	0.382297i
$721$	24.1138			0.898044
$722$	−3.75496	+	9.63034i	−0.139745	+	0.358404i
$723$	−19.2732	+	4.53164i	−0.716779	+	0.168533i
$724$	−20.7909	+	22.6079i	−0.772686	+	0.840216i
$725$	−2.01987	−	3.49852i	−0.0750162	−	0.129932i
$726$	20.4953	+	16.0530i	0.760654	+	0.595783i
$727$	0.500514	+	0.288972i	0.0185630	+	0.0107174i	0.509253	−	0.860617i	$-0.329922\pi$
$727$	0.500514	+	0.288972i	0.0185630	+	0.0107174i	−0.490690	+	0.871334i	$0.663255\pi$
$728$	−24.2185	+	11.8625i	−0.897596	+	0.439655i
$729$	4.97208	−	26.5382i	0.184151	−	0.982898i
$730$	18.7310	−	2.86583i	0.693266	−	0.106069i
$731$	−30.8726	−	17.8243i	−1.14186	−	0.659255i
$732$	−8.97787	+	15.9519i	−0.331832	+	0.589601i
$733$	−42.8431	+	24.7354i	−1.58244	+	0.913625i	−0.587943	+	0.808903i	$0.700062\pi$
$733$	−42.8431	+	24.7354i	−1.58244	+	0.913625i	−0.994502	+	0.104722i	$0.966605\pi$
$734$	9.71203	−	7.78046i	0.358478	−	0.287182i
$735$	0.844900	−	0.198658i	0.0311646	−	0.00732761i
$736$	10.9960	+	45.8237i	0.405318	+	1.68908i
$737$			57.4426i			2.11593i
$738$	25.5254	−	2.30571i	0.939602	−	0.0848744i
$739$	5.51433			0.202848			0.101424	−	0.994843i	$-0.467660\pi$
$739$	5.51433			0.202848			0.101424	+	0.994843i	$0.467660\pi$
$740$	−14.4475	−	3.23006i	−0.531100	−	0.118739i
$741$	−31.8141	−	9.58623i	−1.16872	−	0.352159i
$742$	5.78009	−	4.63052i	0.212194	−	0.169992i
$743$	7.32352	+	12.6847i	0.268674	+	0.465357i	0.968520	−	0.248937i	$-0.0800812\pi$
$743$	7.32352	+	12.6847i	0.268674	+	0.465357i	−0.699846	+	0.714294i	$0.746748\pi$
$744$	27.2499	−	4.47584i	0.999030	−	0.164092i
$745$	2.41284	−	4.17916i	0.0883995	−	0.153112i
$746$	3.73704	+	24.4252i	0.136823	+	0.894271i
$747$	−23.1142	+	34.8725i	−0.845705	+	1.27592i
$748$	30.0611	−	9.41915i	1.09914	−	0.344398i
$749$	−11.6580	+	20.1923i	−0.425975	+	0.737810i
$750$	2.27224	−	0.914825i	0.0829706	−	0.0334047i
$751$	−37.8937	+	21.8780i	−1.38276	+	0.798338i	−0.992486	−	0.122360i	$-0.960954\pi$
$751$	−37.8937	+	21.8780i	−1.38276	+	0.798338i	−0.390276	+	0.920698i	$0.627620\pi$
$752$	−4.49507	−	2.11570i	−0.163918	−	0.0771517i
$753$	21.8540	−	20.5448i	0.796404	−	0.748695i
$754$	19.9074	+	7.76209i	0.724986	+	0.282679i
$755$			12.3109i			0.448039i
$756$	−22.2420	−	14.3936i	−0.808933	−	0.523489i
$757$		−	16.8688i		−	0.613108i	−0.951853	−	0.306554i	$-0.900824\pi$
$757$		−	16.8688i		−	0.613108i	0.951853	−	0.306554i	$-0.0991759\pi$
$758$	13.2398	−	33.9563i	0.480893	−	1.23335i
$759$	48.8910	−	45.9621i	1.77463	−	1.66832i
$760$	12.0410	+	8.09236i	0.436773	+	0.293541i
$761$	0.899605	−	0.519387i	0.0326107	−	0.0188278i	−0.483606	−	0.875286i	$-0.660673\pi$
$761$	0.899605	−	0.519387i	0.0326107	−	0.0188278i	0.516217	+	0.856458i	$0.327340\pi$
$762$	11.7351	+	29.1477i	0.425118	+	1.05591i
$763$	−2.85594	+	4.94663i	−0.103392	+	0.179080i
$764$	5.71046	−	1.78928i	0.206597	−	0.0647337i
$765$	−4.52776	−	9.09608i	−0.163702	−	0.328869i
$766$	−50.3836	+	7.70865i	−1.82043	+	0.278525i
$767$	0.758298	−	1.31341i	0.0273806	−	0.0474245i
$768$	22.0803	+	16.7469i	0.796755	+	0.604302i
$769$	13.8495	+	23.9881i	0.499427	+	0.865032i	1.00000		0.000662003i	$-0.000210722\pi$
$769$	13.8495	+	23.9881i	0.499427	+	0.865032i	−0.500573	+	0.865694i	$0.666877\pi$
$770$	−10.4829	−	13.0854i	−0.377778	−	0.471565i
$771$	11.0585	+	3.33215i	0.398262	+	0.120004i
$772$	1.11371	−	4.98145i	0.0400834	−	0.179286i
$773$	−8.84895			−0.318275			−0.159137	−	0.987256i	$-0.550871\pi$
$773$	−8.84895			−0.318275			−0.159137	+	0.987256i	$0.550871\pi$
$774$	−36.5075	+	25.7165i	−1.31223	+	0.924360i
$775$		−	5.63690i		−	0.202483i
$776$	0.506825	−	7.42719i	0.0181940	−	0.266621i
$777$	31.8162	−	7.48082i	1.14140	−	0.268373i
$778$	−16.4772	−	20.5678i	−0.590735	−	0.737391i
$779$	26.8339	−	15.4925i	0.961423	−	0.555078i
$780$	−6.35443	+	11.2906i	−0.227525	+	0.404268i
$781$	21.8779	+	12.6312i	0.782852	+	0.451980i
$782$	−6.03466	−	39.4424i	−0.215799	−	1.41046i
$783$	3.53468	+	20.6914i	0.126319	+	0.739450i
$784$	1.64603	−	1.14381i	0.0587868	−	0.0408503i
$785$	−6.14993	−	3.55066i	−0.219500	−	0.126729i
$786$	14.5283	−	18.5487i	0.518207	−	0.661611i
$787$	10.0300	+	17.3725i	0.357531	+	0.619263i	0.987548	−	0.157319i	$-0.0502852\pi$
$787$	10.0300	+	17.3725i	0.357531	+	0.619263i	−0.630016	+	0.776582i	$0.716952\pi$
$788$	15.4820	+	14.2377i	0.551523	+	0.507196i
$789$	43.3100	−	10.1833i	1.54188	−	0.362535i
$790$	−8.21981	−	3.20498i	−0.292448	−	0.114028i
$791$	−15.8226			−0.562588
$792$	5.11049	−	39.1295i	0.181593	−	1.39041i
$793$	−19.7630			−0.701805
$794$	−36.7813	−	14.3414i	−1.30532	−	0.508956i
$795$	1.02654	−	3.40681i	0.0364076	−	0.120827i
$796$	−16.8093	+	18.2783i	−0.595789	+	0.647859i
$797$	8.24761	+	14.2853i	0.292145	+	0.506011i	0.974317	−	0.225182i	$-0.0722975\pi$
$797$	8.24761	+	14.2853i	0.292145	+	0.506011i	−0.682171	+	0.731192i	$0.738964\pi$
$798$	−31.7121	−	4.49629i	−1.12260	−	0.159167i
$799$	3.64301	+	2.10329i	0.128881	+	0.0744092i
$800$	4.10376	−	3.89347i	0.145090	−	0.137655i
$801$	8.16296	+	0.504591i	0.288424	+	0.0178288i
$802$	−3.05179	−	19.9465i	−0.107763	−	0.704335i
$803$	−53.9650	−	31.1567i	−1.90438	−	1.09950i
$804$	36.8178	−	21.7990i	1.29846	−	0.768792i
$805$	−18.3917	+	10.6185i	−0.648223	+	0.374252i
$806$	18.6410	+	23.2688i	0.656602	+	0.819610i
$807$	−20.1961	−	21.4831i	−0.710937	−	0.756240i
$808$	3.03123	−	44.4207i	0.106638	−	1.56272i
$809$			15.2109i			0.534787i	0.963587	+	0.267394i	$0.0861624\pi$
$809$			15.2109i			0.534787i	−0.963587	+	0.267394i	$0.913838\pi$
$810$	−12.7228	+	0.360783i	−0.447034	+	0.0126766i
$811$	−9.18448			−0.322511			−0.161255	−	0.986913i	$-0.551554\pi$
$811$	−9.18448			−0.322511			−0.161255	+	0.986913i	$0.551554\pi$
$812$	20.1008	+	4.49397i	0.705398	+	0.157708i
$813$	39.3453	−	36.9882i	1.37990	−	1.29723i
$814$	30.4380	+	37.9945i	1.06685	+	1.33171i
$815$	2.44333	+	4.23198i	0.0855862	+	0.148240i
$816$	−17.4452	−	15.6932i	−0.610703	−	0.549371i
$817$	−26.9937	+	46.7545i	−0.944391	+	1.63573i
$818$	−6.16439	+	0.943146i	−0.215533	+	0.0329763i
$819$	1.76475	−	28.5490i	0.0616652	−	0.997583i
$820$	−3.61244	−	11.5291i	−0.126152	−	0.402613i
$821$	−1.37455	+	2.38079i	−0.0479720	+	0.0830900i	−0.889014	−	0.457879i	$-0.848609\pi$
$821$	−1.37455	+	2.38079i	−0.0479720	+	0.0830900i	0.841042	+	0.540969i	$0.181943\pi$
$822$	−23.7389	−	3.36580i	−0.827989	−	0.117396i
$823$	1.97316	−	1.13920i	0.0687799	−	0.0397101i	−0.465216	−	0.885197i	$-0.654023\pi$
$823$	1.97316	−	1.13920i	0.0687799	−	0.0397101i	0.533996	+	0.845487i	$0.320690\pi$
$824$	14.9234	−	22.2053i	0.519882	−	0.773557i
$825$	−7.71259	−	2.32396i	−0.268518	−	0.0809098i
$826$	0.531077	−	1.36206i	0.0184785	−	0.0473920i
$827$			8.53141i			0.296666i	0.988937	+	0.148333i	$0.0473908\pi$
$827$			8.53141i			0.296666i	−0.988937	+	0.148333i	$0.952609\pi$
$828$	−48.0131	−	13.8943i	−1.66857	−	0.482862i
$829$			28.8554i			1.00219i	0.865393	+	0.501094i	$0.167069\pi$
$829$			28.8554i			1.00219i	−0.865393	+	0.501094i	$0.832931\pi$
$830$	18.3749	+	7.16455i	0.637803	+	0.248685i
$831$	4.19578	+	17.8448i	0.145550	+	0.619030i
$832$	−4.06456	+	29.6431i	−0.140913	+	1.02769i
$833$	−1.46981	+	0.848595i	−0.0509259	+	0.0294021i
$834$	12.0925	+	9.47147i	0.418729	+	0.327970i
$835$	−7.41709	+	12.8468i	−0.256679	+	0.444581i
$836$	−14.2647	−	45.5257i	−0.493355	−	1.57454i
$837$	−10.1646	+	27.4699i	−0.351340	+	0.949498i
$838$	4.41224	+	28.8383i	0.152418	+	0.996203i
$839$	−16.6368	+	28.8158i	−0.574367	+	0.994833i	0.421743	+	0.906716i	$0.361419\pi$
$839$	−16.6368	+	28.8158i	−0.574367	+	0.994833i	−0.996110	+	0.0881178i	$0.971915\pi$
$840$	−4.40889	+	11.6848i	−0.152121	+	0.403165i
$841$	6.34023	+	10.9816i	0.218628	+	0.378676i
$842$	4.55423	−	3.64846i	0.156949	−	0.125734i
$843$	4.27553	+	18.1840i	0.147257	+	0.626291i
$844$	−6.80644	+	30.4440i	−0.234287	+	1.04793i
$845$	−0.988022			−0.0339890
$846$	4.30794	−	3.03459i	0.148110	−	0.104331i
$847$			27.0945i			0.930979i
$848$	−0.686872	−	8.18833i	−0.0235873	−	0.281189i
$849$	6.51204	−	21.6117i	0.223493	−	0.741712i
$850$	−3.73816	+	2.99470i	−0.128218	+	0.102717i
$851$	53.4018	−	30.8316i	1.83059	−	1.05689i
$852$	−0.206535	−	18.8161i	−0.00707579	−	0.644627i
$853$	−42.4777	−	24.5245i	−1.45441	−	0.839704i	−0.455683	−	0.890142i	$-0.650605\pi$
$853$	−42.4777	−	24.5245i	−1.45441	−	0.839704i	−0.998727	+	0.0504383i	$0.983938\pi$
$854$	−18.8315	+	2.88120i	−0.644401	+	0.0985928i
$855$	−13.7754	+	6.85701i	−0.471110	+	0.234505i
$856$	11.3793	+	23.2319i	0.388936	+	0.794049i
$857$	11.4294	+	6.59876i	0.390420	+	0.225409i	0.682342	−	0.731033i	$-0.260961\pi$
$857$	11.4294	+	6.59876i	0.390420	+	0.225409i	−0.291922	+	0.956442i	$0.594295\pi$
$858$	39.5225	−	15.9121i	1.34927	−	0.543229i
$859$	−6.61059	−	11.4499i	−0.225550	−	0.390665i	0.730934	−	0.682448i	$-0.239085\pi$
$859$	−6.61059	−	11.4499i	−0.225550	−	0.390665i	−0.956484	+	0.291783i	$0.905751\pi$
$860$	15.4949	+	14.2495i	0.528371	+	0.485905i
$861$	18.2700	+	19.4342i	0.622638	+	0.662315i
$862$	13.4058	−	34.3820i	0.456605	−	1.17105i
$863$	−8.26851			−0.281463			−0.140732	−	0.990048i	$-0.544945\pi$
$863$	−8.26851			−0.281463			−0.140732	+	0.990048i	$0.544945\pi$
$864$	−27.0194	+	11.5738i	−0.919218	+	0.393748i
$865$	−6.44113			−0.219005
$866$	−0.230221	+	0.590449i	−0.00782323	+	0.0200643i
$867$	−6.55937	−	6.97735i	−0.222768	−	0.236963i
$868$	21.1547	+	19.4545i	0.718038	+	0.660328i
$869$	14.5064	+	25.1258i	0.492095	+	0.852334i
$870$	9.17929	−	3.69566i	0.311207	−	0.125295i
$871$	40.0066	+	23.0978i	1.35557	+	0.782641i
$872$	2.78765	+	5.69125i	0.0944019	+	0.192730i
$873$	6.58157	+	4.36240i	0.222752	+	0.147645i
$874$	−59.7331	+	9.13911i	−2.02050	+	0.309135i
$875$	2.20775	+	1.27465i	0.0746357	+	0.0430909i
$876$	0.509450	+	46.4126i	0.0172127	+	1.56814i
$877$	−4.51357	+	2.60591i	−0.152412	+	0.0879953i	−0.574267	−	0.818668i	$-0.694713\pi$
$877$	−4.51357	+	2.60591i	−0.152412	+	0.0879953i	0.421854	+	0.906664i	$0.361379\pi$
$878$	37.0175	−	29.6553i	1.24928	−	1.00082i
$879$	−8.77301	+	29.1153i	−0.295906	+	0.982033i
$880$	−18.5374	+	1.55499i	−0.624895	+	0.0524188i
$881$			17.9255i			0.603925i	0.953320	+	0.301963i	$0.0976418\pi$
$881$			17.9255i			0.603925i	−0.953320	+	0.301963i	$0.902358\pi$
$882$	0.191264	+	2.11739i	0.00644020	+	0.0712963i
$883$	20.5203			0.690564			0.345282	−	0.938499i	$-0.387783\pi$
$883$	20.5203			0.690564			0.345282	+	0.938499i	$0.387783\pi$
$884$	5.52759	−	24.7239i	0.185913	−	0.831556i
$885$	−0.160756	−	0.683703i	−0.00540377	−	0.0229824i
$886$	41.0373	−	32.8756i	1.37867	−	1.10448i
$887$	−19.1974	−	33.2509i	−0.644587	−	1.11646i	−0.984397	−	0.175963i	$-0.943696\pi$
$887$	−19.1974	−	33.2509i	−0.644587	−	1.11646i	0.339810	−	0.940494i	$-0.389637\pi$
$888$	12.8016	−	33.9278i	0.429592	−	1.13854i
$889$	−16.3508	+	28.3204i	−0.548388	+	0.949835i
$890$	−0.583088	−	3.81105i	−0.0195452	−	0.127747i
$891$	33.3946	+	25.2327i	1.11876	+	0.845328i
$892$	0.992325	+	3.16700i	0.0332255	+	0.106039i
$893$	3.18531	−	5.51711i	0.106592	−	0.184623i
$894$	9.30575	+	7.28874i	0.311231	+	0.243772i
$895$	7.59236	−	4.38345i	0.253784	−	0.146523i
$896$	0.448615	+	28.8385i	0.0149872	+	0.963426i
$897$	−12.3517	−	52.5323i	−0.412411	−	1.75400i
$898$	35.1930	+	13.7221i	1.17440	+	0.457911i
$899$		−	22.7716i		−	0.759476i
$900$	1.43733	+	5.82530i	0.0479110	+	0.194177i
$901$			6.95760i			0.231791i
$902$	−14.4330	+	37.0164i	−0.480567	+	1.23251i
$903$	−44.4990	−	13.4084i	−1.48083	−	0.446205i
$904$	−9.79223	+	14.5703i	−0.325685	+	0.484601i
$905$	−13.2997	+	7.67861i	−0.442099	+	0.255246i
$906$	−29.8568	−	4.23323i	−0.991926	−	0.140640i
$907$	−1.90633	+	3.30185i	−0.0632985	+	0.109636i	−0.895938	−	0.444179i	$-0.853495\pi$
$907$	−1.90633	+	3.30185i	−0.0632985	+	0.109636i	0.832639	+	0.553815i	$0.186829\pi$
$908$	5.87890	+	18.7625i	0.195098	+	0.622654i
$909$	39.3632	+	26.0907i	1.30559	+	0.865375i
$910$	−13.3287	+	2.03928i	−0.441843	+	0.0676015i
$911$	−4.06826	+	7.04644i	−0.134788	+	0.233459i	−0.925516	−	0.378708i	$-0.876369\pi$
$911$	−4.06826	+	7.04644i	−0.134788	+	0.233459i	0.790729	+	0.612167i	$0.209702\pi$
$912$	−23.7663	+	26.4196i	−0.786981	+	0.874840i
$913$	−32.4282	−	56.1673i	−1.07322	−	1.85887i
$914$	36.1567	+	45.1330i	1.19596	+	1.49287i
$915$	−6.66839	+	6.26891i	−0.220450	+	0.207244i
$916$	21.1834	+	4.73603i	0.699919	+	0.156483i
$917$	24.5211			0.809758
$918$	23.6170	−	7.85310i	0.779478	−	0.259191i
$919$			25.3748i			0.837038i	0.908208	+	0.418519i	$0.137451\pi$
$919$			25.3748i			0.837038i	−0.908208	+	0.418519i	$0.862549\pi$
$920$	−1.60414	+	23.5076i	−0.0528868	+	0.775023i
$921$	17.6562	+	18.7813i	0.581792	+	0.618865i
$922$	−9.77580	−	12.2027i	−0.321949	−	0.401876i
$923$	17.5943	−	10.1581i	0.579125	−	0.334358i
$924$	35.3398	−	20.9240i	1.16260	−	0.688348i
$925$	−6.41038	−	3.70104i	−0.210772	−	0.121689i
$926$	4.80858	+	31.4288i	0.158020	+	1.03281i
$927$	12.6453	+	25.4038i	0.415325	+	0.834370i
$928$	16.5782	−	15.7286i	0.544205	−	0.516318i
$929$	35.7951	+	20.6663i	1.17440	+	0.678040i	0.954713	−	0.297530i	$-0.0961628\pi$
$929$	35.7951	+	20.6663i	1.17440	+	0.678040i	0.219688	+	0.975570i	$0.429496\pi$
$930$	13.6708	+	1.93831i	0.448283	+	0.0635595i
$931$	1.28514	+	2.22593i	0.0421189	+	0.0729520i
$932$	−35.6096	+	38.7218i	−1.16643	+	1.26837i
$933$	−3.87118	+	12.8474i	−0.126737	+	0.420605i
$934$	−27.0152	−	10.5335i	−0.883966	−	0.344666i
$935$	15.7511			0.515117
$936$	−25.1973	−	19.2934i	−0.823599	−	0.630623i
$937$	−48.8089			−1.59452			−0.797258	−	0.603639i	$-0.793717\pi$
$937$	−48.8089			−1.59452			−0.797258	+	0.603639i	$0.793717\pi$
$938$	41.4884	+	16.1767i	1.35464	+	0.528188i
$939$	−33.5729	+	7.89385i	−1.09561	+	0.257606i
$940$	−1.82842	−	1.68147i	−0.0596366	−	0.0548434i
$941$	−7.53979	−	13.0593i	−0.245790	−	0.425721i	0.716563	−	0.697522i	$-0.245714\pi$
$941$	−7.53979	−	13.0593i	−0.245790	−	0.425721i	−0.962353	+	0.271801i	$0.912381\pi$
$942$	10.7259	−	13.6941i	0.349469	−	0.446177i
$943$	43.5816	+	25.1619i	1.41921	+	0.819383i
$944$	−0.925583	−	1.33199i	−0.0301252	−	0.0433525i
$945$	−8.46041	−	10.1927i	−0.275217	−	0.331569i
$946$	−10.4696	−	68.4293i	−0.340397	−	2.22483i
$947$	−20.3781	−	11.7653i	−0.662198	−	0.382320i	0.130916	−	0.991394i	$-0.458208\pi$
$947$	−20.3781	−	11.7653i	−0.662198	−	0.382320i	−0.793114	+	0.609073i	$0.791542\pi$
$948$	10.5993	−	18.8329i	0.344249	−	0.611664i
$949$	−43.3990	+	25.0564i	−1.40879	+	0.813366i
$950$	4.53528	+	5.66121i	0.147144	+	0.183674i
$951$	59.6486	−	14.0249i	1.93424	−	0.454790i
$952$	1.66261	−	24.3645i	0.0538855	−	0.789657i
$953$		−	45.3356i		−	1.46856i	−0.678845	−	0.734282i	$-0.737519\pi$
$953$		−	45.3356i		−	1.46856i	0.678845	−	0.734282i	$-0.262481\pi$
$954$	7.90932	+	3.66106i	0.256074	+	0.118531i
$955$	2.99211			0.0968224
$956$	2.77511	−	12.4126i	0.0897536	−	0.401452i
$957$	−31.1569	−	9.38820i	−1.00716	−	0.303477i
$958$	1.53981	+	1.92209i	0.0497492	+	0.0620999i
$959$	−12.4766	−	21.6101i	−0.402891	−	0.697827i
$960$	8.03146	+	11.2914i	0.259214	+	0.364428i
$961$	0.387293	−	0.670812i	0.0124933	−	0.0216391i
$962$	38.7010	−	5.92121i	1.24777	−	0.190908i
$963$	−27.3860	−	1.69286i	−0.882501	−	0.0545515i
$964$	−21.8159	+	6.83563i	−0.702641	+	0.220161i
$965$	1.27611	−	2.21028i	0.0410793	−	0.0711515i
$966$	−19.4281	−	48.2555i	−0.625088	−	1.55260i
$967$	−50.3479	+	29.0684i	−1.61908	+	0.934776i	−0.631921	+	0.775032i	$0.717733\pi$
$967$	−50.3479	+	29.0684i	−1.61908	+	0.934776i	−0.987159	+	0.159744i	$0.948933\pi$
$968$	24.9501	+	16.7681i	0.801926	+	0.538948i
$969$	21.9230	−	20.6096i	0.704267	−	0.662077i
$970$	1.35218	−	3.46794i	0.0434159	−	0.111349i
$971$		−	15.8715i		−	0.509340i	−0.967028	−	0.254670i	$-0.918033\pi$
$971$		−	15.8715i		−	0.509340i	0.967028	−	0.254670i	$-0.0819669\pi$
$972$	3.49989	−	30.9798i	0.112259	−	0.993679i
$973$			15.9861i			0.512491i
$974$	0.583469	+	0.227500i	0.0186955	+	0.00728956i
$975$	−4.71980	+	4.43706i	−0.151155	+	0.142100i
$976$	−9.00120	+	19.1242i	−0.288121	+	0.612150i
$977$	−5.73553	+	3.31141i	−0.183496	+	0.105941i	−0.588934	−	0.808181i	$-0.700452\pi$
$977$	−5.73553	+	3.31141i	−0.183496	+	0.105941i	0.405438	+	0.914122i	$0.367119\pi$
$978$	−11.1037	+	4.47044i	−0.355057	+	0.142949i
$979$	−6.33921	+	10.9798i	−0.202602	+	0.350917i
$980$	0.956364	−	0.299660i	0.0305499	−	0.00957230i
$981$	−6.70892	−	0.414709i	−0.214199	−	0.0132407i
$982$	−6.26716	−	40.9620i	−0.199993	−	1.30715i
$983$	7.73291	−	13.3938i	0.246642	−	0.427196i	−0.715950	−	0.698151i	$-0.754006\pi$
$983$	7.73291	−	13.3938i	0.246642	−	0.427196i	0.962592	+	0.270956i	$0.0873396\pi$
$984$	29.2029	−	4.79662i	0.930953	−	0.152911i
$985$	5.25835	+	9.10772i	0.167545	+	0.290196i
$986$	−15.1012	+	12.0978i	−0.480921	+	0.385273i
$987$	5.25095	+	1.58222i	0.167140	+	0.0503625i
$988$	−37.4429	−	8.37119i	−1.19122	−	0.266323i
$989$	−87.6825			−2.78814
$990$	8.28819	−	17.9057i	0.263416	−	0.569081i
$991$		−	7.14184i		−	0.226868i	−0.993546	−	0.113434i	$-0.963815\pi$
$991$		−	7.14184i		−	0.226868i	0.993546	−	0.113434i	$-0.0361850\pi$
$992$	31.0069	−	7.44050i	0.984469	−	0.236236i
$993$	−0.259121	+	0.0609260i	−0.00822294	+	0.00193343i
$994$	15.2841	−	12.2443i	0.484783	−	0.388367i
$995$	−10.7528	+	6.20811i	−0.340885	+	0.196810i
$996$	−23.6941	+	42.0999i	−0.750777	+	1.33399i
$997$	−14.6617	−	8.46495i	−0.464341	−	0.268088i	0.249527	−	0.968368i	$-0.419725\pi$
$997$	−14.6617	−	8.46495i	−0.464341	−	0.268088i	−0.713868	+	0.700280i	$0.753058\pi$
$998$	−39.3683	+	6.02331i	−1.24618	+	0.190665i
$999$	24.5655	+	29.5954i	0.777217	+	0.936356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.9	✓	48
3.2	odd	2		1080.2.bm.b.251.16		48
4.3	odd	2		1440.2.cc.a.911.18		48
8.3	odd	2		360.2.bm.b.11.16	yes	48
8.5	even	2		1440.2.cc.b.911.18		48
9.4	even	3		1080.2.bm.a.611.9		48
9.5	odd	6		360.2.bm.b.131.16	yes	48
12.11	even	2		4320.2.cc.b.1871.7		48
24.5	odd	2		4320.2.cc.a.1871.18		48
24.11	even	2		1080.2.bm.a.251.9		48
36.23	even	6		1440.2.cc.b.1391.18		48
36.31	odd	6		4320.2.cc.a.3311.18		48
72.5	odd	6		1440.2.cc.a.1391.18		48
72.13	even	6		4320.2.cc.b.3311.7		48
72.59	even	6	inner	360.2.bm.a.131.9	yes	48
72.67	odd	6		1080.2.bm.b.611.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.9	✓	48	1.1	even	1	trivial
360.2.bm.a.131.9	yes	48	72.59	even	6	inner
360.2.bm.b.11.16	yes	48	8.3	odd	2
360.2.bm.b.131.16	yes	48	9.5	odd	6
1080.2.bm.a.251.9		48	24.11	even	2
1080.2.bm.a.611.9		48	9.4	even	3
1080.2.bm.b.251.16		48	3.2	odd	2
1080.2.bm.b.611.16		48	72.67	odd	6
1440.2.cc.a.911.18		48	4.3	odd	2
1440.2.cc.a.1391.18		48	72.5	odd	6
1440.2.cc.b.911.18		48	8.5	even	2
1440.2.cc.b.1391.18		48	36.23	even	6
4320.2.cc.a.1871.18		48	24.5	odd	2
4320.2.cc.a.3311.18		48	36.31	odd	6
4320.2.cc.b.1871.7		48	12.11	even	2
4320.2.cc.b.3311.7		48	72.13	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.513744 + 1.31760i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-1.47213 - 1.35382i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.27224 - 0.914825i) q^{6} +(2.20775 + 1.27465i) q^{7} +(2.54009 - 1.24417i) q^{8} +(-0.185091 + 2.99428i) q^{9} +O(q^{10})\)	\(q+(-0.513744 + 1.31760i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-1.47213 - 1.35382i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.27224 - 0.914825i) q^{6} +(2.20775 + 1.27465i) q^{7} +(2.54009 - 1.24417i) q^{8} +(-0.185091 + 2.99428i) q^{9} +(1.39795 - 0.213885i) q^{10} +(-4.02755 - 2.32531i) q^{11} +(0.0380216 + 3.46389i) q^{12} +(-3.23898 + 1.87003i) q^{13} +(-2.81369 + 2.25409i) q^{14} +(-0.499709 + 1.65840i) q^{15} +(0.334363 + 3.98600i) q^{16} -3.38689i q^{17} +(-3.85018 - 1.78217i) q^{18} -5.12923 q^{19} +(-0.436372 + 1.95181i) q^{20} +(-1.01064 - 4.29829i) q^{21} +(5.13296 - 4.11209i) q^{22} +(-4.16526 - 7.21444i) q^{23} +(-4.58356 - 1.72946i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.799940 - 5.22840i) q^{26} +(3.99825 - 3.31873i) q^{27} +(-1.52447 - 4.86534i) q^{28} +(-2.01987 + 3.49852i) q^{29} +(-1.92838 - 1.51041i) q^{30} +(-4.88169 + 2.81845i) q^{31} +(-5.42373 - 1.60723i) q^{32} +(1.84369 + 7.84127i) q^{33} +(4.46256 + 1.73999i) q^{34} -2.54929i q^{35} +(4.32619 - 4.15741i) q^{36} +7.40207i q^{37} +(2.63511 - 6.75827i) q^{38} +(6.20251 + 1.86894i) q^{39} +(-2.34753 - 1.57770i) q^{40} +(-5.23156 + 3.02044i) q^{41} +(6.18263 + 0.876601i) q^{42} +(5.26273 - 9.11531i) q^{43} +(2.78106 + 8.87574i) q^{44} +(2.68567 - 1.33685i) q^{45} +(11.6456 - 1.78177i) q^{46} +(-0.621010 + 1.07562i) q^{47} +(4.63350 - 5.15079i) q^{48} +(-0.250553 - 0.433970i) q^{49} +(-0.884203 - 1.10371i) q^{50} +(-4.27412 + 4.01808i) q^{51} +(7.29990 + 1.63206i) q^{52} -2.05427 q^{53} +(2.31868 + 6.97307i) q^{54} +4.65062i q^{55} +(7.19376 + 0.490895i) q^{56} +(6.08512 + 6.47289i) q^{57} +(-3.57195 - 4.45873i) q^{58} +(-0.351174 + 0.202750i) q^{59} +(2.98081 - 1.76487i) q^{60} +(4.57621 + 2.64207i) q^{61} +(-1.20564 - 7.88008i) q^{62} +(-4.22529 + 6.37471i) q^{63} +(4.90409 - 6.32060i) q^{64} +(3.23898 + 1.87003i) q^{65} +(-11.2788 - 1.59916i) q^{66} +(-6.17580 - 10.6968i) q^{67} +(-4.58523 + 4.98596i) q^{68} +(-4.16284 + 13.8153i) q^{69} +(3.35895 + 1.30968i) q^{70} -5.43205 q^{71} +(3.25525 + 7.83603i) q^{72} +13.3990 q^{73} +(-9.75296 - 3.80277i) q^{74} +(1.68607 - 0.396439i) q^{75} +(7.55092 + 6.94404i) q^{76} +(-5.92789 - 10.2674i) q^{77} +(-5.64901 + 7.21226i) q^{78} +(-5.40268 - 3.11924i) q^{79} +(3.28480 - 2.28257i) q^{80} +(-8.93148 - 1.10843i) q^{81} +(-1.29205 - 8.44483i) q^{82} +(12.0774 + 6.97289i) q^{83} +(-4.33130 + 7.69588i) q^{84} +(-2.93313 + 1.69345i) q^{85} +(9.30663 + 11.6171i) q^{86} +(6.81130 - 1.60151i) q^{87} +(-13.1234 - 0.895530i) q^{88} -2.72618i q^{89} +(0.381684 + 4.22544i) q^{90} -9.53450 q^{91} +(-3.63520 + 16.2596i) q^{92} +(9.34823 + 2.81681i) q^{93} +(-1.09820 - 1.37084i) q^{94} +(2.56462 + 4.44204i) q^{95} +(4.40625 + 8.75128i) q^{96} +(1.31601 - 2.27939i) q^{97} +(0.700519 - 0.107179i) q^{98} +(7.70810 - 11.6292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more