LMFDB - Embedded newform 360.2.bm.b.11.16

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			11.16
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.884203 - 1.10371i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-0.436372 - 1.95181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.44183 + 0.193576i) q^{6} +(-2.20775 - 1.27465i) q^{7} +(-2.54009 - 1.24417i) q^{8} +(-0.185091 + 2.99428i) q^{9} +O(q^{10})$	\(q+(0.884203 - 1.10371i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-0.436372 - 1.95181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.44183 + 0.193576i) 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} +(-1.94542 + 2.86624i) q^{12} +(3.23898 - 1.87003i) q^{13} +(-3.35895 + 1.30968i) q^{14} +(0.499709 - 1.65840i) q^{15} +(-3.61916 + 1.70343i) q^{16} -3.38689i q^{17} +(3.14118 + 2.85184i) q^{18} -5.12923 q^{19} +(1.47213 - 1.35382i) q^{20} +(1.01064 + 4.29829i) q^{21} +(-6.12765 + 2.38923i) q^{22} +(4.16526 + 7.21444i) q^{23} +(1.44337 + 4.68153i) 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} +(-1.38856 - 2.01790i) q^{30} +(4.88169 - 2.81845i) q^{31} +(-1.31996 + 5.50070i) q^{32} +(1.84369 + 7.84127i) q^{33} +(-3.73816 - 2.99470i) q^{34} -2.54929i q^{35} +(5.92506 - 0.945359i) q^{36} -7.40207i q^{37} +(-4.53528 + 5.66121i) q^{38} +(-6.20251 - 1.86894i) q^{39} +(-0.192561 - 2.82186i) q^{40} +(-5.23156 + 3.02044i) q^{41} +(5.63769 + 2.68510i) 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} +(6.44330 + 2.54635i) q^{48} +(-0.250553 - 0.433970i) q^{49} +(0.513744 + 1.31760i) q^{50} +(-4.27412 + 4.01808i) q^{51} +(-5.06335 - 5.50587i) q^{52} +2.05427 q^{53} +(-0.127662 - 7.34736i) q^{54} -4.65062i q^{55} +(4.02201 + 5.98453i) q^{56} +(6.08512 + 6.47289i) q^{57} +(-2.07539 - 5.32277i) q^{58} +(-0.351174 + 0.202750i) q^{59} +(-3.45495 - 0.251661i) 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} +(10.2847 + 4.89837i) q^{66} +(-6.17580 - 10.6968i) q^{67} +(-6.61058 + 1.47794i) q^{68} +(4.16284 - 13.8153i) q^{69} +(-2.81369 - 2.25409i) q^{70} +5.43205 q^{71} +(4.19554 - 7.37546i) q^{72} +13.3990 q^{73} +(-8.16977 - 6.54493i) q^{74} +(1.68607 - 0.396439i) q^{75} +(2.23825 + 10.0113i) q^{76} +(5.92789 + 10.2674i) q^{77} +(-7.54705 + 5.19328i) 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} +(7.94845 - 3.84823i) q^{84} +(2.93313 - 1.69345i) q^{85} +(-5.40738 - 13.8683i) q^{86} +(-6.81130 + 1.60151i) q^{87} +(7.33726 + 10.9174i) q^{88} -2.72618i q^{89} +(-0.899178 + 4.14626i) q^{90} -9.53450 q^{91} +(12.2637 - 11.2780i) q^{92} +(-9.34823 - 2.81681i) q^{93} +(-0.638080 - 1.63649i) q^{94} +(-2.56462 - 4.44204i) q^{95} +(8.50762 - 4.86008i) 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} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * 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 $

$2$	0.884203	−	1.10371i	0.625226	−	0.780444i
$2$	0.884203	−	1.10371i	0.625226	−	0.780444i
$3$	−1.18636	−	1.26196i	−0.684946	−	0.728593i
$3$	−1.18636	−	1.26196i	−0.684946	−	0.728593i
$4$	−0.436372	−	1.95181i	−0.218186	−	0.975907i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.44183	+	0.193576i	−0.996872	+	0.0790271i
$7$	−2.20775	−	1.27465i	−0.834452	−	0.481771i	0.0209226	−	0.999781i	$-0.493340\pi$
$7$	−2.20775	−	1.27465i	−0.834452	−	0.481771i	−0.855375	+	0.518010i	$0.826673\pi$
$8$	−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	$0.913977\pi$
$12$	−1.94542	+	2.86624i	−0.561594	+	0.827413i
$13$	3.23898	−	1.87003i	0.898332	−	0.518653i	0.0216737	−	0.999765i	$-0.493101\pi$
$13$	3.23898	−	1.87003i	0.898332	−	0.518653i	0.876659	+	0.481113i	$0.159767\pi$
$14$	−3.35895	+	1.30968i	−0.897716	+	0.350028i
$15$	0.499709	−	1.65840i	0.129024	−	0.428197i
$16$	−3.61916	+	1.70343i	−0.904790	+	0.425858i
$17$		−	3.38689i		−	0.821442i	−0.911761	−	0.410721i	$-0.865277\pi$
$17$		−	3.38689i		−	0.821442i	0.911761	−	0.410721i	$-0.134723\pi$
$18$	3.14118	+	2.85184i	0.740383	+	0.672185i
$19$	−5.12923			−1.17673			−0.588363	−	0.808597i	$-0.700227\pi$
$19$	−5.12923			−1.17673			−0.588363	+	0.808597i	$0.700227\pi$
$20$	1.47213	−	1.35382i	0.329179	−	0.302723i
$21$	1.01064	+	4.29829i	0.220540	+	0.937964i
$22$	−6.12765	+	2.38923i	−1.30642	+	0.509385i
$23$	4.16526	+	7.21444i	0.868517	+	1.50432i	0.863512	+	0.504328i	$0.168260\pi$
$23$	4.16526	+	7.21444i	0.868517	+	1.50432i	0.00500444	+	0.999987i	$0.498407\pi$
$24$	1.44337	+	4.68153i	0.294627	+	0.955612i
$25$	−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	−0.615258	−	0.788326i	$-0.710948\pi$
$29$	2.01987	−	3.49852i	0.375081	−	0.649659i	0.990339	+	0.138666i	$0.0442816\pi$
$30$	−1.38856	−	2.01790i	−0.253515	−	0.368416i
$31$	4.88169	−	2.81845i	0.876778	−	0.506208i	0.00718342	−	0.999974i	$-0.497713\pi$
$31$	4.88169	−	2.81845i	0.876778	−	0.506208i	0.869595	+	0.493766i	$0.164380\pi$
$32$	−1.31996	+	5.50070i	−0.233339	+	0.972395i
$33$	1.84369	+	7.84127i	0.320945	+	1.36499i
$34$	−3.73816	−	2.99470i	−0.641089	−	0.513586i
$35$		−	2.54929i		−	0.430909i
$36$	5.92506	−	0.945359i	0.987509	−	0.157560i
$37$		−	7.40207i		−	1.21689i	−0.793595	−	0.608446i	$-0.791793\pi$
$37$		−	7.40207i		−	1.21689i	0.793595	−	0.608446i	$-0.208207\pi$
$38$	−4.53528	+	5.66121i	−0.735719	+	0.918369i
$39$	−6.20251	−	1.86894i	−0.993196	−	0.299270i
$40$	−0.192561	−	2.82186i	−0.0304466	−	0.446176i
$41$	−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	$0.489698\pi$
$42$	5.63769	+	2.68510i	0.869915	+	0.414320i
$43$	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	−0.817173	−	0.576392i	$-0.804460\pi$
$47$	0.621010	−	1.07562i	0.0905837	−	0.156896i	0.907757	+	0.419497i	$0.137793\pi$
$48$	6.44330	+	2.54635i	0.930010	+	0.367534i
$49$	−0.250553	−	0.433970i	−0.0357933	−	0.0619958i
$50$	0.513744	+	1.31760i	0.0726543	+	0.186337i
$51$	−4.27412	+	4.01808i	−0.598497	+	0.562643i
$52$	−5.06335	−	5.50587i	−0.702160	−	0.763526i
$53$	2.05427			0.282176			0.141088	−	0.989997i	$-0.454940\pi$
$53$	2.05427			0.282176			0.141088	+	0.989997i	$0.454940\pi$
$54$	−0.127662	−	7.34736i	−0.0173726	−	0.999849i
$55$		−	4.65062i		−	0.627089i
$56$	4.02201	+	5.98453i	0.537463	+	0.799717i
$57$	6.08512	+	6.47289i	0.805994	+	0.857355i
$58$	−2.07539	−	5.32277i	−0.272513	−	0.698913i
$59$	−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	$0.341736\pi$
$60$	−3.45495	−	0.251661i	−0.446032	−	0.0324892i
$61$	−4.57621	−	2.64207i	−0.585923	−	0.338283i	0.177561	−	0.984110i	$-0.443179\pi$
$61$	−4.57621	−	2.64207i	−0.585923	−	0.338283i	−0.763484	+	0.645827i	$0.776513\pi$
$62$	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
$66$	10.2847	+	4.89837i	1.26596	+	0.602948i
$67$	−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	$-0.438784\pi$
$68$	−6.61058	+	1.47794i	−0.801651	+	0.179227i
$69$	4.16284	−	13.8153i	0.501147	−	1.66317i
$70$	−2.81369	−	2.25409i	−0.336300	−	0.269415i
$71$	5.43205			0.644666			0.322333	−	0.946626i	$-0.395533\pi$
$71$	5.43205			0.644666			0.322333	+	0.946626i	$0.395533\pi$
$72$	4.19554	−	7.37546i	0.494450	−	0.869206i
$73$	13.3990			1.56823			0.784115	−	0.620616i	$-0.213117\pi$
$73$	13.3990			1.56823			0.784115	+	0.620616i	$0.213117\pi$
$74$	−8.16977	−	6.54493i	−0.949717	−	0.760833i
$75$	1.68607	−	0.396439i	0.194691	−	0.0457768i
$76$	2.23825	+	10.0113i	0.256745	+	1.14838i
$77$	5.92789	+	10.2674i	0.675546	+	1.17008i
$78$	−7.54705	+	5.19328i	−0.854535	+	0.588023i
$79$	5.40268	+	3.11924i	0.607849	+	0.350942i	0.772123	−	0.635473i	$-0.219195\pi$
$79$	5.40268	+	3.11924i	0.607849	+	0.350942i	−0.164274	+	0.986415i	$0.552528\pi$
$80$	−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	$0.389221\pi$
$84$	7.94845	−	3.84823i	0.867247	−	0.419877i
$85$	2.93313	−	1.69345i	0.318143	−	0.183680i
$86$	−5.40738	−	13.8683i	−0.583093	−	1.49546i
$87$	−6.81130	+	1.60151i	−0.730248	+	0.171700i
$88$	7.33726	+	10.9174i	0.782154	+	1.16380i
$89$		−	2.72618i		−	0.288975i	−0.989507	−	0.144487i	$-0.953847\pi$
$89$		−	2.72618i		−	0.288975i	0.989507	−	0.144487i	$-0.0461533\pi$
$90$	−0.899178	+	4.14626i	−0.0947817	+	0.437054i
$91$	−9.53450			−0.999487
$92$	12.2637	−	11.2780i	1.27857	−	1.17581i
$93$	−9.34823	−	2.81681i	−0.969366	−	0.292089i
$94$	−0.638080	−	1.63649i	−0.0658130	−	0.168791i
$95$	−2.56462	−	4.44204i	−0.263124	−	0.455744i
$96$	8.50762	−	4.86008i	0.868306	−	0.496029i
$97$	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	$0.453068\pi$
$101$	−7.87081	+	13.6326i	−0.783175	+	1.35650i	−0.930083	+	0.367348i	$0.880266\pi$
$102$	0.655621	+	8.27021i	0.0649161	+	0.818872i
$103$	−8.19174	+	4.72950i	−0.807156	+	0.466012i	−0.845967	−	0.533235i	$-0.820976\pi$
$103$	−8.19174	+	4.72950i	−0.807156	+	0.466012i	0.0388112	+	0.999247i	$0.487643\pi$
$104$	−10.5539	+	0.720191i	−1.03490	+	0.0706205i
$105$	−3.21711	+	3.02438i	−0.313958	+	0.295150i
$106$	1.81639	−	2.26733i	0.176424	−	0.220223i
$107$			9.14609i			0.884186i	0.896969	+	0.442093i	$0.145764\pi$
$107$			9.14609i			0.884186i	−0.896969	+	0.442093i	$0.854236\pi$
$108$	−8.22227	−	6.35565i	−0.791188	−	0.611573i
$109$		−	2.24057i		−	0.214608i	−0.994226	−	0.107304i	$-0.965778\pi$
$109$		−	2.24057i		−	0.214608i	0.994226	−	0.107304i	$-0.0342218\pi$
$110$	−5.13296	−	4.11209i	−0.489408	−	0.392072i
$111$	−9.34112	+	8.78154i	−0.886620	+	0.833506i
$112$	10.1615	+	0.852388i	0.960170	+	0.0805431i
$113$	−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	$0.427633\pi$
$114$	12.5247	−	0.992896i	1.17305	−	0.0929932i
$115$	−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
$120$	−3.33264	+	3.59076i	−0.304227	+	0.327790i
$121$	5.31412	+	9.20433i	0.483102	+	0.836758i
$122$	−6.96239	+	2.71470i	−0.630345	+	0.245777i
$123$	10.0182	+	3.01869i	0.903311	+	0.272186i
$124$	−7.63132	−	8.29827i	−0.685313	−	0.745207i
$125$	−1.00000			−0.0894427
$126$	−3.29985	−	10.3001i	−0.293974	−	0.917602i
$127$		−	12.8277i		−	1.13827i	−0.822243	−	0.569137i	$-0.807277\pi$
$127$		−	12.8277i		−	1.13827i	0.822243	−	0.569137i	$-0.192723\pi$
$128$	11.3123	+	0.175976i	0.999879	+	0.0155543i
$129$	−17.7467	+	4.17270i	−1.56251	+	0.367386i
$130$	4.92790	−	1.92143i	0.432205	−	0.168521i
$131$	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	$0.195294\pi$
$132$	14.5002	−	7.02025i	1.26208	−	0.611034i
$133$	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	$0.803983\pi$
$138$	−11.5674	−	16.8101i	−0.984682	−	1.43097i
$139$	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	$0.747651\pi$
$140$	−4.97575	+	1.11244i	−0.420527	+	0.0940183i
$141$	−2.09414	+	0.492386i	−0.176358	+	0.0414664i
$142$	4.80304	−	5.99544i	0.403062	−	0.503126i
$143$	−17.3936			−1.45452
$144$	−4.43069	−	11.1521i	−0.369224	−	0.929340i
$145$	4.03975			0.335483
$146$	11.8474	−	14.7886i	0.980498	−	1.22392i
$147$	−0.250407	+	0.831034i	−0.0206532	+	0.0685425i
$148$	−14.4475	+	3.23006i	−1.18757	+	0.265509i
$149$	−2.41284	−	4.17916i	−0.197667	−	0.342370i	0.750104	−	0.661319i	$-0.230003\pi$
$149$	−2.41284	−	4.17916i	−0.197667	−	0.342370i	−0.947772	+	0.318950i	$0.896670\pi$
$150$	1.05327	−	2.21147i	0.0859994	−	0.180566i
$151$	10.6615	+	6.15545i	0.867624	+	0.500923i	0.866558	−	0.499076i	$-0.166327\pi$
$151$	10.6615	+	6.15545i	0.867624	+	0.500923i	0.00106627	+	0.999999i	$0.499661\pi$
$152$	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
$156$	−0.941225	+	12.9217i	−0.0753583	+	1.03456i
$157$	−6.14993	+	3.55066i	−0.490818	+	0.283374i	−0.724914	−	0.688840i	$-0.758120\pi$
$157$	−6.14993	+	3.55066i	−0.490818	+	0.283374i	0.234096	+	0.972213i	$0.424787\pi$
$158$	8.21981	−	3.20498i	0.653933	−	0.254974i
$159$	−2.43711	−	2.59241i	−0.193276	−	0.205592i
$160$	−5.42373	+	1.60723i	−0.428783	+	0.127062i
$161$		−	21.2369i		−	1.67371i
$162$	−9.12063	+	8.87773i	−0.716584	+	0.697501i
$163$	−4.88666			−0.382753			−0.191377	−	0.981517i	$-0.561295\pi$
$163$	−4.88666			−0.382753			−0.191377	+	0.981517i	$0.561295\pi$
$164$	8.17825	+	8.89300i	0.638614	+	0.694426i
$165$	−5.86890	+	5.51732i	−0.456893	+	0.429522i
$166$	18.3749	−	7.16455i	1.42617	−	0.556077i
$167$	7.41709	+	12.8468i	0.573951	+	0.994113i	0.996155	+	0.0876117i	$0.0279235\pi$
$167$	7.41709	+	12.8468i	0.573951	+	0.994113i	−0.422203	+	0.906501i	$0.638743\pi$
$168$	2.78069	−	12.1754i	0.214535	−	0.939355i
$169$	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	−0.962091	−	0.272729i	$-0.912074\pi$
$173$	−3.22057	+	5.57819i	−0.244855	+	0.424102i	0.717236	+	0.696831i	$0.245407\pi$
$174$	−4.25495	+	8.93379i	−0.322567	+	0.677269i
$175$	2.20775	−	1.27465i	0.166890	−	0.0963542i
$176$	18.5374	+	1.55499i	1.39731	+	0.117212i
$177$	0.672483	+	0.202632i	0.0505469	+	0.0152308i
$178$	−3.00893	−	2.41050i	−0.225529	−	0.180674i
$179$			8.76690i			0.655269i	0.944805	+	0.327634i	$0.106251\pi$
$179$			8.76690i			0.655269i	−0.944805	+	0.327634i	$0.893749\pi$
$180$	3.78123	+	4.65857i	0.281836	+	0.347229i
$181$			15.3572i			1.14149i	0.821126	+	0.570747i	$0.193346\pi$
$181$			15.3572i			1.14149i	−0.821126	+	0.570747i	$0.806654\pi$
$182$	−8.43043	+	10.5234i	−0.624905	+	0.780044i
$183$	2.09484	+	8.90945i	0.154855	+	0.658605i
$184$	−1.60414	−	23.5076i	−0.118259	−	1.73300i
$185$	6.41038	−	3.70104i	0.471301	−	0.272106i
$186$	−11.3747	+	7.82715i	−0.834032	+	0.573914i
$187$	−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	−0.806811	−	0.590810i	$-0.798808\pi$
$191$	1.49605	−	2.59124i	0.108251	−	0.187496i	0.915062	+	0.403314i	$0.132142\pi$
$192$	2.15833	−	13.6873i	0.155764	−	0.987794i
$193$	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	$0.804053\pi$
$194$	−1.35218	−	3.46794i	−0.0970810	−	0.248984i
$195$	−1.48270	−	6.30600i	−0.106179	−	0.451582i
$196$	−0.737695	+	0.678405i	−0.0526925	+	0.0484575i
$197$	10.5167			0.749283			0.374642	−	0.927170i	$-0.377766\pi$
$197$	10.5167			0.749283			0.374642	+	0.927170i	$0.377766\pi$
$198$	−6.01985	−	18.7902i	−0.427812	−	1.33536i
$199$			12.4162i			0.880162i	0.897958	+	0.440081i	$0.145050\pi$
$199$			12.4162i			0.880162i	−0.897958	+	0.440081i	$0.854950\pi$
$200$	2.34753	−	1.57770i	0.165995	−	0.111560i
$201$	−6.17221	+	20.4839i	−0.435354	+	1.44482i
$202$	8.08716	+	20.7411i	0.569010	+	1.45934i
$203$	−8.91876	+	5.14925i	−0.625974	+	0.361406i
$204$	9.70765	+	6.58892i	0.679671	+	0.461317i
$205$	−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
$210$	0.493482	+	6.22494i	0.0340535	+	0.429561i
$211$	−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	$-0.347071\pi$
$212$	−0.896427	−	4.00956i	−0.0615669	−	0.275378i
$213$	−6.44438	−	6.85504i	−0.441562	−	0.469700i
$214$	10.0947	+	8.08699i	0.690057	+	0.552816i
$215$	10.5255			0.717830
$216$	−14.2850	+	3.45535i	−0.971969	+	0.235107i
$217$	−14.3701			−0.975506
$218$	−2.47295	−	1.98112i	−0.167490	−	0.134178i
$219$	−15.8960	−	16.9090i	−1.07415	−	1.14260i
$220$	−9.07714	+	2.02940i	−0.611981	+	0.136822i
$221$	−6.33358	−	10.9701i	−0.426043	−	0.737928i
$222$	1.43286	+	18.0746i	0.0961675	+	1.21309i
$223$	1.43709	+	0.829706i	0.0962348	+	0.0555612i	0.547345	−	0.836907i	$-0.315639\pi$
$223$	1.43709	+	0.829706i	0.0962348	+	0.0555612i	−0.451110	+	0.892468i	$0.648972\pi$
$224$	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	$0.772452\pi$
$228$	9.97850	−	14.7016i	0.660842	−	0.973639i
$229$	9.39914	−	5.42659i	0.621112	−	0.358599i	−0.156190	−	0.987727i	$-0.549921\pi$
$229$	9.39914	−	5.42659i	0.621112	−	0.358599i	0.777302	+	0.629128i	$0.216588\pi$
$230$	4.27975	+	10.9763i	0.282198	+	0.723755i
$231$	5.92445	−	19.6616i	0.389800	−	1.29364i
$232$	−9.48341	+	6.37349i	−0.622616	+	0.418440i
$233$		−	26.3031i		−	1.72318i	−0.507609	−	0.861588i	$-0.669470\pi$
$233$		−	26.3031i		−	1.72318i	0.507609	−	0.861588i	$-0.330530\pi$
$234$	15.5072	+	3.36298i	1.01374	+	0.219845i
$235$	1.24202			0.0810205
$236$	0.548974	+	0.596952i	0.0357351	+	0.0388583i
$237$	−2.47317	−	10.5185i	−0.160650	−	0.683251i
$238$	4.43575	+	11.3764i	0.287527	+	0.737421i
$239$	−3.17976	−	5.50750i	−0.205681	−	0.356251i	0.744668	−	0.667435i	$-0.232608\pi$
$239$	−3.17976	−	5.50750i	−0.205681	−	0.356251i	−0.950350	+	0.311184i	$0.899274\pi$
$240$	1.01645	+	6.85324i	0.0656114	+	0.442374i
$241$	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
$246$	12.1899	−	8.38811i	0.777199	−	0.534806i
$247$	−16.6135	+	9.59181i	−1.05709	+	0.610312i
$248$	−15.9066	+	1.08545i	−1.01007	+	0.0689261i
$249$	−5.52865	−	23.5136i	−0.350364	−	1.49011i
$250$	−0.884203	+	1.10371i	−0.0559219	+	0.0698050i
$251$			17.3175i			1.09307i	0.837436	+	0.546535i	$0.184054\pi$
$251$			17.3175i			1.09307i	−0.837436	+	0.546535i	$0.815946\pi$
$252$	−14.2861	−	5.46523i	−0.899937	−	0.344277i
$253$		−	38.7421i		−	2.43569i
$254$	−14.1581	−	11.3423i	−0.888359	−	0.711678i
$255$	−5.61682	−	1.69246i	−0.351739	−	0.105986i
$256$	10.1966	−	12.3300i	0.637289	−	0.770625i
$257$	−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	$0.400020\pi$
$258$	−11.0862	+	23.2768i	−0.690195	+	1.44915i
$259$	−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	$-0.542393\pi$
$263$	12.8435	−	22.2455i	0.791962	−	1.37172i	0.924750	−	0.380575i	$-0.124274\pi$
$264$	5.07275	−	22.2114i	0.312206	−	1.36702i
$265$	1.02714	+	1.77905i	0.0630965	+	0.109286i
$266$	17.2288	−	6.71767i	1.05637	−	0.411887i
$267$	−3.44033	+	3.23424i	−0.210545	+	0.197932i
$268$	−18.1832	+	16.7218i	−1.11072	+	1.02145i
$269$	−17.0236			−1.03794			−0.518972	−	0.854791i	$-0.673685\pi$
$269$	−17.0236			−1.03794			−0.518972	+	0.854791i	$0.673685\pi$
$270$	6.29917	−	3.78424i	0.383355	−	0.230301i
$271$		−	31.1779i		−	1.89392i	−0.321350	−	0.946960i	$-0.604137\pi$
$271$		−	31.1779i		−	1.89392i	0.321350	−	0.946960i	$-0.395863\pi$
$272$	5.76934	+	12.2577i	0.349818	+	0.743232i
$273$	11.3114	+	12.0322i	0.684595	+	0.728220i
$274$	−12.8970	+	5.02867i	−0.779139	+	0.303793i
$275$	4.02755	−	2.32531i	0.242871	−	0.140221i
$276$	−28.7815	−	2.09646i	−1.73244	−	0.126192i
$277$	9.16573	+	5.29183i	0.550715	+	0.317956i	0.749410	−	0.662106i	$-0.230337\pi$
$277$	9.16573	+	5.29183i	0.550715	+	0.317956i	−0.198695	+	0.980061i	$0.563670\pi$
$278$	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	$0.770916\pi$
$282$	−1.30819	+	2.74670i	−0.0779014	+	0.163563i
$283$	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	$0.706732\pi$
$284$	−2.37040	−	10.6024i	−0.140657	−	0.629134i
$285$	−2.56312	+	8.50632i	−0.151826	+	0.503871i
$286$	−15.3794	+	19.1975i	−0.909405	+	1.13517i
$287$	15.4000			0.909032
$288$	−16.2263	−	4.97048i	−0.956147	−	0.292888i
$289$	5.52898			0.325234
$290$	3.57195	−	4.45873i	0.209752	−	0.261825i
$291$	−4.43777	+	1.04343i	−0.260146	+	0.0611672i
$292$	−5.84693	−	26.1523i	−0.342166	−	1.53045i
$293$	8.77812	+	15.2041i	0.512823	+	0.888236i	0.999889	+	0.0148707i	$0.00473368\pi$
$293$	8.77812	+	15.2041i	0.512823	+	0.888236i	−0.487066	+	0.873365i	$0.661933\pi$
$294$	0.695814	+	1.01118i	0.0405807	+	0.0589732i
$295$	−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
$300$	−1.50953	−	3.11790i	−0.0871527	−	0.180012i
$301$	−23.2376	+	13.4162i	−1.33939	+	0.773299i
$302$	16.2208	−	6.32464i	0.933403	−	0.363942i
$303$	26.5415	−	6.24059i	1.52477	−	0.358513i
$304$	18.5635	−	8.73730i	1.06469	−	0.501119i
$305$		−	5.28415i		−	0.302569i
$306$	9.65887	−	10.6388i	0.552161	−	0.608181i
$307$	−14.8826			−0.849397			−0.424699	−	0.905335i	$-0.639620\pi$
$307$	−14.8826			−0.849397			−0.424699	+	0.905335i	$0.639620\pi$
$308$	17.4533	−	16.0506i	0.994495	−	0.914565i
$309$	15.6868	+	4.72675i	0.892392	+	0.268896i
$310$	7.42717	−	2.89592i	0.421835	−	0.164477i
$311$	3.87344	+	6.70899i	0.219642	+	0.380432i	0.954699	−	0.297574i	$-0.0961776\pi$
$311$	3.87344	+	6.70899i	0.219642	+	0.380432i	−0.735056	+	0.678006i	$0.762844\pi$
$312$	13.4296	+	12.4642i	0.760303	+	0.705649i
$313$	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	$-0.369666\pi$
$317$	17.6886	−	30.6376i	0.993493	−	1.72078i	0.595383	−	0.803442i	$-0.297000\pi$
$318$	−5.01618	+	0.397658i	−0.281294	+	0.0222996i
$319$	−16.2703	+	9.39366i	−0.910962	+	0.525944i
$320$	−3.02175	+	7.40736i	−0.168921	+	0.414084i
$321$	11.5420	−	10.8506i	0.644212	−	0.605620i
$322$	−23.4395	−	18.7778i	−1.30623	−	1.04644i
$323$			17.3721i			0.966612i
$324$	1.73400	+	17.9163i	0.0963334	+	0.995349i
$325$			3.74006i			0.207461i
$326$	−4.32080	+	5.39348i	−0.239307	+	0.298717i
$327$	−2.82752	+	2.65813i	−0.156362	+	0.146995i
$328$	17.0466	−	1.16324i	0.941239	−	0.0642293i
$329$	−2.74207	+	1.58314i	−0.151175	+	0.0872812i
$330$	0.900248	+	11.3560i	0.0495570	+	0.625128i
$331$	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
$336$	−10.9795	−	13.8346i	−0.598982	−	0.754741i
$337$	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	$0.662488\pi$
$338$	−0.507590	−	1.30182i	−0.0276092	−	0.0708095i
$339$	10.2931	+	3.10153i	0.559047	+	0.168452i
$340$	−4.58523	−	4.98596i	−0.248669	−	0.270402i
$341$	−26.2150			−1.41962
$342$	−16.1118	−	14.6278i	−0.871228	−	0.790978i
$343$			19.1225i			1.03252i
$344$	−24.7088	+	16.6060i	−1.33221	+	0.895333i
$345$	14.0459	−	3.30254i	0.756203	−	0.177803i
$346$	3.30909	+	8.48683i	0.177898	+	0.456255i
$347$	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	$0.104793\pi$
$348$	6.09812	+	12.5955i	0.326893	+	0.675192i
$349$	20.5838	+	11.8841i	1.10183	+	0.636140i	0.936700	−	0.350133i	$-0.113863\pi$
$349$	20.5838	+	11.8841i	1.10183	+	0.636140i	0.165126	+	0.986272i	$0.447197\pi$
$350$	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	$0.673287\pi$
$354$	0.818259	−	0.563061i	0.0434900	−	0.0299263i
$355$	2.71603	+	4.70430i	0.144152	+	0.249678i
$356$	−5.32100	+	1.18963i	−0.282012	+	0.0630502i
$357$	14.5578	−	3.42292i	0.770482	−	0.181160i
$358$	9.67615	+	7.75171i	0.511401	+	0.409691i
$359$	−10.9728			−0.579123			−0.289561	−	0.957159i	$-0.593509\pi$
$359$	−10.9728			−0.579123			−0.289561	+	0.957159i	$0.593509\pi$
$360$	8.48511	−	0.0542829i	0.447204	−	0.00286096i
$361$	7.30901			0.384685
$362$	16.9500	+	13.5789i	0.890872	+	0.713691i
$363$	5.31103	−	17.6259i	0.278757	−	0.925119i
$364$	4.16059	+	18.6096i	0.218074	+	0.975407i
$365$	6.69948	+	11.6038i	0.350667	+	0.607373i
$366$	11.6858	+	5.56565i	0.610824	+	0.290921i
$367$	7.62051	+	4.39970i	0.397787	+	0.229663i	0.685529	−	0.728045i	$-0.259571\pi$
$367$	7.62051	+	4.39970i	0.397787	+	0.229663i	−0.287741	+	0.957708i	$0.592904\pi$
$368$	−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
$372$	−1.41858	+	19.4752i	−0.0735502	+	1.00974i
$373$	−15.1314	+	8.73611i	−0.783473	+	0.452338i	−0.837660	−	0.546192i	$-0.816077\pi$
$373$	−15.1314	+	8.73611i	−0.783473	+	0.452338i	0.0541866	+	0.998531i	$0.482743\pi$
$374$	8.09204	+	20.7537i	0.418430	+	1.07315i
$375$	1.18636	+	1.26196i	0.0612635	+	0.0651674i
$376$	−2.91568	+	1.95953i	−0.150365	+	0.101055i
$377$		−	15.1089i		−	0.778147i
$378$	−9.08344	+	16.3839i	−0.467202	+	0.842696i
$379$	−25.7713			−1.32378			−0.661892	−	0.749600i	$-0.730246\pi$
$379$	−25.7713			−1.32378			−0.661892	+	0.749600i	$0.730246\pi$
$380$	−7.55092	+	6.94404i	−0.387354	+	0.356222i
$381$	−16.1881	+	15.2183i	−0.829339	+	0.779657i
$382$	−1.53718	−	3.94240i	−0.0786488	−	0.201711i
$383$	−18.0206	−	31.2126i	−0.920809	−	1.59489i	−0.798166	−	0.602437i	$-0.794196\pi$
$383$	−18.0206	−	31.2126i	−0.920809	−	1.59489i	−0.122643	−	0.992451i	$-0.539137\pi$
$384$	−13.1985	−	14.4845i	−0.673531	−	0.739159i
$385$	−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	−0.527084	−	0.849813i	$-0.676715\pi$
$389$	9.31753	−	16.1384i	0.472418	−	0.818251i	0.999502	+	0.0315617i	$0.0100481\pi$
$390$	−8.27104	−	3.93930i	−0.418820	−	0.199474i
$391$	24.4345	−	14.1073i	1.23571	−	0.713436i
$392$	0.0964936	+	1.41405i	0.00487366	+	0.0714204i
$393$	−15.9518	−	4.80660i	−0.804662	−	0.242461i
$394$	9.29889	−	11.6074i	0.468471	−	0.584774i
$395$			6.23847i			0.313892i
$396$	−26.0617	−	9.97010i	−1.30965	−	0.501017i
$397$		−	27.9154i		−	1.40103i	−0.713635	−	0.700517i	$-0.752953\pi$
$397$		−	27.9154i		−	1.40103i	0.713635	−	0.700517i	$-0.247047\pi$
$398$	13.7040	+	10.9784i	0.686917	+	0.550300i
$399$	−5.18380	−	22.0469i	−0.259515	−	1.10373i
$400$	0.334363	−	3.98600i	0.0167181	−	0.199300i
$401$	−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	$0.449283\pi$
$402$	17.1509	+	24.9243i	0.855409	+	1.24311i
$403$	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
$408$	15.8558	−	4.88854i	0.784980	−	0.242019i
$409$	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	$0.798562\pi$
$410$	−7.95946	+	3.10347i	−0.393090	+	0.153269i
$411$	3.88046	+	16.5037i	0.191409	+	0.814070i
$412$	12.8058	+	13.9249i	0.630894	+	0.686032i
$413$	1.03374			0.0508670
$414$	−7.49062	+	34.5405i	−0.368144	+	1.69757i
$415$			13.9458i			0.684571i
$416$	6.01112	+	20.2850i	0.294719	+	0.994556i
$417$	3.13358	−	10.3995i	0.153452	−	0.509265i
$418$	31.4301	−	12.2549i	1.53730	−	0.599406i
$419$	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	$0.165232\pi$
$420$	7.30689	+	4.95944i	0.356540	+	0.241996i
$421$	3.57346	+	2.06314i	0.174160	+	0.100551i	0.584546	−	0.811361i	$-0.301273\pi$
$421$	3.57346	+	2.06314i	0.174160	+	0.100551i	−0.410386	+	0.911912i	$0.634606\pi$
$422$	−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
$426$	−13.2641	+	1.05152i	−0.642650	+	0.0509461i
$427$	6.73542	+	11.6661i	0.325950	+	0.564562i
$428$	17.8515	−	3.99110i	0.862883	−	0.192917i
$429$	20.6351	+	21.9500i	0.996271	+	1.05976i
$430$	9.30663	−	11.6171i	0.448806	−	0.560226i
$431$	26.0944			1.25692			0.628462	−	0.777841i	$-0.283685\pi$
$431$	26.0944			1.25692			0.628462	+	0.777841i	$0.283685\pi$
$432$	−8.81709	+	18.8218i	−0.424212	+	0.905563i
$433$	0.448125			0.0215355			0.0107677	−	0.999942i	$-0.496572\pi$
$433$	0.448125			0.0215355			0.0107677	+	0.999942i	$0.496572\pi$
$434$	−12.7061	+	15.8605i	−0.609911	+	0.761328i
$435$	−4.79260	−	5.09800i	−0.229788	−	0.244430i
$436$	−4.37319	+	0.977724i	−0.209438	+	0.0468245i
$437$	−21.3646	−	37.0045i	−1.02201	−	1.77017i
$438$	−32.7180	+	2.59372i	−1.56333	+	0.123933i
$439$	29.0457	+	16.7695i	1.38627	+	0.800366i	0.992893	−	0.119010i	$-0.0379720\pi$
$439$	29.0457	+	16.7695i	1.38627	+	0.800366i	0.393381	+	0.919376i	$0.371305\pi$
$440$	−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	$-0.677991\pi$
$444$	21.2161	+	14.4001i	1.00687	+	0.683400i
$445$	2.36094	−	1.36309i	0.111919	−	0.0646167i
$446$	2.18644	−	0.852512i	0.103531	−	0.0403676i
$447$	−2.41143	+	8.00290i	−0.114057	+	0.378524i
$448$	−2.77048	−	20.2053i	−0.130893	−	0.954610i
$449$		−	26.7099i		−	1.26052i	−0.776384	−	0.630260i	$-0.782948\pi$
$449$		−	26.7099i		−	1.26052i	0.776384	−	0.630260i	$-0.217052\pi$
$450$	−4.04036	+	1.29442i	−0.190464	+	0.0610195i
$451$	28.0938			1.32289
$452$	8.40269	+	9.13705i	0.395229	+	0.429771i
$453$	−4.88052	−	20.7570i	−0.229307	−	0.975251i
$454$	−12.9533	+	5.05059i	−0.607927	+	0.237036i
$455$	−4.76725	−	8.25712i	−0.223492	−	0.387100i
$456$	−7.40338	−	24.0126i	−0.346695	−	1.12449i
$457$	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	−0.708096	−	0.706116i	$-0.750446\pi$
$461$	5.52803	−	9.57483i	0.257466	−	0.445944i	0.965562	+	0.260171i	$0.0837791\pi$
$462$	−16.4624	−	23.9238i	−0.765901	−	1.11303i
$463$	−19.4701	+	11.2411i	−0.904851	+	0.522416i	−0.878771	−	0.477244i	$-0.841636\pi$
$463$	−19.4701	+	11.2411i	−0.904851	+	0.522416i	−0.0260804	+	0.999660i	$0.508303\pi$
$464$	−1.35074	+	16.1024i	−0.0627065	+	0.747537i
$465$	−2.23469	−	9.50421i	−0.103631	−	0.440747i
$466$	−29.0311	−	23.2573i	−1.34484	−	1.07737i
$467$			20.5034i			0.948784i	0.880314	+	0.474392i	$0.157332\pi$
$467$			20.5034i			0.948784i	−0.880314	+	0.474392i	$0.842668\pi$
$468$	17.4233	−	14.1420i	0.805393	−	0.653715i
$469$			31.4879i			1.45397i
$470$	1.09820	−	1.37084i	0.0506561	−	0.0632320i
$471$	11.7768	+	3.54860i	0.542648	+	0.163511i
$472$	1.14427	−	0.0780838i	0.0526692	−	0.00359410i
$473$	−42.3918	+	24.4749i	−1.94918	+	1.12536i
$474$	−13.7962	−	6.57081i	−0.633681	−	0.301807i
$475$	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	−0.885232	−	0.465149i	$-0.846001\pi$
$479$	−0.870737	+	1.50816i	−0.0397850	+	0.0689096i	0.845447	+	0.534059i	$0.179334\pi$
$480$	8.46276	+	4.93778i	0.386270	+	0.225378i
$481$	−13.8421	−	23.9752i	−0.631145	−	1.09317i
$482$	−5.87253	−	15.0613i	−0.267486	−	0.686022i
$483$	−26.8002	+	25.1947i	−1.21945	+	1.14640i
$484$	15.6462	−	14.3887i	0.711192	−	0.654032i
$485$	2.63202			0.119514
$486$	22.0237	+	0.977672i	0.999016	+	0.0443481i
$487$			0.442827i			0.0200664i	0.999950	+	0.0100332i	$0.00319372\pi$
$487$			0.442827i			0.0200664i	−0.999950	+	0.0100332i	$0.996806\pi$
$488$	8.33678	+	12.4047i	0.377388	+	0.561533i
$489$	5.79735	+	6.16678i	0.262165	+	0.278871i
$490$	−0.257440	−	0.660257i	−0.0116299	−	0.0298273i
$491$	−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	$0.563278\pi$
$492$	1.52025	−	20.8709i	0.0685383	−	0.940935i
$493$	−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
$498$	−30.8407	−	14.6887i	−1.38201	−	0.658216i
$499$	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	$0.616248\pi$
$500$	0.436372	+	1.95181i	0.0195151	+	0.0872878i
$501$	7.41277	−	24.6010i	0.331178	−	1.09909i
$502$	19.1136	+	15.3122i	0.853080	+	0.683416i
$503$	−15.0167			−0.669560			−0.334780	−	0.942296i	$-0.608662\pi$
$503$	−15.0167			−0.669560			−0.334780	+	0.942296i	$0.608662\pi$
$504$	−18.6638	+	10.9354i	−0.831353	+	0.487099i
$505$	−15.7416			−0.700493
$506$	−42.7602	−	34.2558i	−1.90092	−	1.52286i
$507$	−1.66587	+	0.391690i	−0.0739841	+	0.0173956i
$508$	−25.0373	+	5.59765i	−1.11085	+	0.248355i
$509$	9.57636	+	16.5867i	0.424465	+	0.735194i	0.996370	−	0.0851250i	$-0.0271290\pi$
$509$	9.57636	+	16.5867i	0.424465	+	0.735194i	−0.571906	+	0.820319i	$0.693796\pi$
$510$	−6.83440	+	4.70289i	−0.302632	+	0.208247i
$511$	−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
$516$	15.8885	+	32.8173i	0.699451	+	1.44470i
$517$	−5.00231	+	2.88808i	−0.220001	+	0.127018i
$518$	9.69437	+	24.8632i	0.425946	+	1.09242i
$519$	10.8602	−	2.55352i	0.476710	−	0.112087i
$520$	−5.90067	−	8.77988i	−0.258761	−	0.385023i
$521$			36.1713i			1.58469i	0.610072	+	0.792346i	$0.291141\pi$
$521$			36.1713i			1.58469i	−0.610072	+	0.792346i	$0.708859\pi$
$522$	16.3220	−	5.22913i	0.714395	−	0.228873i
$523$	12.2116			0.533975			0.266988	−	0.963700i	$-0.413972\pi$
$523$	12.2116			0.533975			0.266988	+	0.963700i	$0.413972\pi$
$524$	−13.0221	−	14.1602i	−0.568872	−	0.618589i
$525$	−4.22775	−	1.27391i	−0.184514	−	0.0555978i
$526$	−13.1965	−	33.8451i	−0.575395	−	1.47572i
$527$	−9.54577	−	16.5338i	−0.415820	−	0.720222i
$528$	−20.0297	−	25.2382i	−0.871680	−	1.09835i
$529$	−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
$534$	0.527723	+	6.65687i	0.0228368	+	0.288071i
$535$	−7.92074	+	4.57304i	−0.342444	+	0.197710i
$536$	2.37844	+	34.8546i	0.102733	+	1.50549i
$537$	11.0635	−	10.4007i	0.477425	−	0.448824i
$538$	−15.0523	+	18.7892i	−0.648950	+	0.810058i
$539$			2.33045i			0.100380i
$540$	1.39302	−	10.2985i	0.0599461	−	0.443178i
$541$			34.9053i			1.50070i	0.661042	+	0.750349i	$0.270114\pi$
$541$			34.9053i			1.50070i	−0.661042	+	0.750349i	$0.729886\pi$
$542$	−34.4115	−	27.5676i	−1.47810	−	1.18413i
$543$	19.3802	−	18.2192i	0.831685	−	0.781862i
$544$	18.6303	+	4.47058i	0.798766	+	0.191674i
$545$	1.94039	−	1.12029i	0.0831174	−	0.0479878i
$546$	23.2816	−	1.84565i	0.996361	−	0.0789865i
$547$	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
$552$	−27.7626	+	29.9129i	−1.18165	+	1.27318i
$553$	−7.95185	−	13.7730i	−0.338147	−	0.585688i
$554$	13.9450	−	5.43729i	0.592468	−	0.231008i
$555$	−12.2756	−	3.69888i	−0.521070	−	0.157009i
$556$	9.23146	−	8.48951i	0.391501	−	0.360035i
$557$	11.3188			0.479591			0.239796	−	0.970823i	$-0.422920\pi$
$557$	11.3188			0.479591			0.239796	+	0.970823i	$0.422920\pi$
$558$	23.3720	+	5.06857i	0.989417	+	0.214570i
$559$		−	39.3658i		−	1.66500i
$560$	4.34255	+	9.22630i	0.183506	+	0.389882i
$561$	26.5575	−	6.24437i	1.12126	−	0.263637i
$562$	−14.2101	+	5.54064i	−0.599417	+	0.233718i
$563$	−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	$0.507236\pi$
$564$	1.87487	+	3.87250i	0.0789462	+	0.163062i
$565$	−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	$0.585350\pi$
$570$	7.12223	+	10.3503i	0.298317	+	0.433525i
$571$	−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	$0.896882\pi$
$572$	7.59007	+	33.9490i	0.317357	+	1.41948i
$573$	−5.04491	+	1.18619i	−0.210754	+	0.0495538i
$574$	13.6167	−	16.9972i	0.568350	−	0.709449i
$575$	−8.33052			−0.347407
$576$	−19.8334	+	13.5143i	−0.826390	+	0.563098i
$577$	7.47489			0.311184			0.155592	−	0.987821i	$-0.450272\pi$
$577$	7.47489			0.311184			0.155592	+	0.987821i	$0.450272\pi$
$578$	4.88873	−	6.10241i	0.203345	−	0.253827i
$579$	1.27536	−	4.23259i	0.0530023	−	0.175900i
$580$	−1.76283	−	7.88483i	−0.0731976	−	0.327400i
$581$	−17.7759	−	30.7888i	−0.737470	−	1.27734i
$582$	−2.77223	+	5.82064i	−0.114913	+	0.241273i
$583$	−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	$0.914768\pi$
$588$	1.73129	+	0.126109i	0.0713974	+	0.00520063i
$589$	−25.0393	+	14.4565i	−1.03173	+	0.595668i
$590$	−0.534287	+	0.208323i	−0.0219963	+	0.00857654i
$591$	−12.4766	−	13.2717i	−0.513219	−	0.545923i
$592$	12.6089	+	26.7893i	0.518224	+	1.10103i
$593$			5.46511i			0.224425i	0.993684	+	0.112213i	$0.0357937\pi$
$593$			5.46511i			0.224425i	−0.993684	+	0.112213i	$0.964206\pi$
$594$	−16.5707	+	29.8887i	−0.679905	+	1.22635i
$595$	−8.63417			−0.353967
$596$	−7.10404	+	6.53308i	−0.290993	+	0.267605i
$597$	15.6688	−	14.7301i	0.641280	−	0.602864i
$598$	41.0519	−	16.0065i	1.67874	−	0.654555i
$599$	−8.10483	−	14.0380i	−0.331154	−	0.573576i	0.651584	−	0.758576i	$-0.274105\pi$
$599$	−8.10483	−	14.0380i	−0.331154	−	0.573576i	−0.982738	+	0.185000i	$0.940771\pi$
$600$	−4.77601	−	1.09077i	−0.194980	−	0.0445304i
$601$	−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
$606$	16.5802	−	34.8122i	0.673525	−	1.41415i
$607$	−13.9365	+	8.04627i	−0.565667	+	0.326588i	−0.755417	−	0.655244i	$-0.772566\pi$
$607$	−13.9365	+	8.04627i	−0.565667	+	0.326588i	0.189750	+	0.981832i	$0.439232\pi$
$608$	6.77040	−	28.2144i	0.274576	−	1.14424i
$609$	17.0790	+	5.14625i	0.692077	+	0.208537i
$610$	−5.83219	−	4.67226i	−0.236139	−	0.189174i
$611$		−	4.64523i		−	0.187926i
$612$	−3.20183	−	20.0675i	−0.129426	−	0.811181i
$613$		−	9.72482i		−	0.392782i	−0.980526	−	0.196391i	$-0.937078\pi$
$613$		−	9.72482i		−	0.392782i	0.980526	−	0.196391i	$-0.0629221\pi$
$614$	−13.1593	+	16.4262i	−0.531065	+	0.662907i
$615$	2.39484	+	10.1854i	0.0965694	+	0.410713i
$616$	−2.28297	−	33.4554i	−0.0919834	−	1.34796i
$617$	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	$0.120447\pi$
$618$	19.0873	−	13.1344i	0.767804	−	0.528342i
$619$	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
$624$	25.6315	−	3.80157i	1.02608	−	0.152185i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.2296	−	26.2359i	−0.408857	−	1.04860i
$627$	−9.45670	−	40.2197i	−0.377664	−	1.60622i
$628$	9.61389	+	10.4541i	0.383636	+	0.417164i
$629$	−25.0700			−0.999606
$630$	7.27018	−	8.00778i	0.289651	−	0.319038i
$631$			28.3960i			1.13043i	0.824944	+	0.565214i	$0.191206\pi$
$631$			28.3960i			1.13043i	−0.824944	+	0.565214i	$0.808794\pi$
$632$	−9.84241	−	14.6450i	−0.391510	−	0.582546i
$633$	−7.79437	+	25.8674i	−0.309798	+	1.02814i
$634$	−18.1748	−	46.6131i	−0.721815	−	1.85124i
$635$	11.1091	−	6.41385i	0.440852	−	0.254526i
$636$	−3.99642	+	5.88805i	−0.158468	+	0.233476i
$637$	−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	$0.641011\pi$
$642$	−1.77046	−	22.3332i	−0.0698746	−	0.881420i
$643$	−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	$0.978213\pi$
$644$	−41.4506	+	9.26720i	−1.63338	+	0.365179i
$645$	−12.4870	−	13.2827i	−0.491675	−	0.523006i
$646$	19.1739	+	15.3605i	0.754386	+	0.604350i
$647$	−11.9935			−0.471513			−0.235757	−	0.971812i	$-0.575757\pi$
$647$	−11.9935			−0.471513			−0.235757	+	0.971812i	$0.575757\pi$
$648$	21.3077	+	13.9278i	0.837044	+	0.547135i
$649$	1.88583			0.0740253
$650$	4.12795	+	3.30697i	0.161912	+	0.129710i
$651$	17.0481	+	18.1345i	0.668169	+	0.710747i
$652$	2.13240	+	9.53786i	0.0835113	+	0.373532i
$653$	22.7175	+	39.3478i	0.889004	+	1.53980i	0.841055	+	0.540950i	$0.181935\pi$
$653$	22.7175	+	39.3478i	0.889004	+	1.53980i	0.0479492	+	0.998850i	$0.484731\pi$
$654$	0.433721	+	5.47110i	0.0169599	+	0.213937i
$655$	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	$0.749808\pi$
$660$	13.3298	+	9.04740i	0.518862	+	0.352170i
$661$	−38.9627	+	22.4951i	−1.51547	+	0.874959i	−0.515638	+	0.856807i	$0.672445\pi$
$661$	−38.9627	+	22.4951i	−1.51547	+	0.874959i	−0.999835	+	0.0181521i	$0.994222\pi$
$662$	−0.0789537	−	0.202493i	−0.00306862	−	0.00787010i
$663$	−6.32990	+	21.0072i	−0.245833	+	0.815853i
$664$	−22.0022	−	32.7381i	−0.853850	−	1.27048i
$665$			13.0759i			0.507062i
$666$	21.1095	−	23.2512i	0.817978	−	0.900967i
$667$	33.6532			1.30306
$668$	21.8379	−	20.0827i	0.844934	−	0.777025i
$669$	−0.657856	−	2.79789i	−0.0254342	−	0.108173i
$670$	−6.34556	−	16.2745i	−0.245150	−	0.628737i
$671$	12.2873	+	21.2822i	0.474345	+	0.821590i
$672$	−24.9776	−	0.114367i	−0.963532	−	0.00441182i
$673$	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	$0.358787\pi$
$677$	−14.7680	+	25.5790i	−0.567581	+	0.983079i	−0.996804	+	0.0798808i	$0.974546\pi$
$678$	12.5244	−	8.61831i	0.480998	−	0.330984i
$679$	−5.81084	+	3.35489i	−0.223000	+	0.128749i
$680$	−9.55735	+	0.652184i	−0.366507	+	0.0250101i
$681$	3.89738	+	16.5757i	0.149348	+	0.635182i
$682$	−23.1794	+	28.9339i	−0.887585	+	1.10794i
$683$		−	31.4320i		−	1.20271i	−0.798982	−	0.601355i	$-0.794628\pi$
$683$		−	31.4320i		−	1.20271i	0.798982	−	0.601355i	$-0.205372\pi$
$684$	−30.3910	+	4.84896i	−1.16203	+	0.185405i
$685$		−	9.78829i		−	0.373991i
$686$	21.1058	+	16.9082i	0.805823	+	0.645557i
$687$	−17.9989	−	5.42344i	−0.686702	−	0.206917i
$688$	−3.51932	+	41.9545i	−0.134173	+	1.59950i
$689$	6.65376	−	3.84155i	0.253488	−	0.146351i
$690$	8.77431	−	18.4227i	0.334032	−	0.701341i
$691$	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
$696$	19.2938	+	4.40643i	0.731331	+	0.167025i
$697$	10.2299	+	17.7187i	0.387485	+	0.671144i
$698$	31.3169	−	12.2107i	1.18536	−	0.462183i
$699$	−33.1935	+	31.2050i	−1.25549	+	1.18028i
$700$	−3.45127	−	3.75290i	−0.130446	−	0.141846i
$701$	31.7591			1.19952			0.599762	−	0.800179i	$-0.295262\pi$
$701$	31.7591			1.19952			0.599762	+	0.800179i	$0.295262\pi$
$702$	−14.1533	−	23.5592i	−0.534181	−	0.889187i
$703$			37.9669i			1.43195i
$704$	−5.05413	−	36.8601i	−0.190485	−	1.38922i
$705$	−1.47349	−	1.56738i	−0.0554947	−	0.0590310i
$706$	−1.02970	+	0.401490i	−0.0387534	+	0.0151103i
$707$	34.7536	−	20.0650i	1.30704	−	0.754622i
$708$	0.102049	−	1.40098i	0.00383522	−	0.0526522i
$709$	−5.26182	−	3.03791i	−0.197612	−	0.114091i	0.397929	−	0.917416i	$-0.369729\pi$
$709$	−5.26182	−	3.03791i	−0.197612	−	0.114091i	−0.595541	+	0.803325i	$0.703062\pi$
$710$	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
$714$	9.09414	−	19.0943i	0.340340	−	0.714584i
$715$	−8.69679	−	15.0633i	−0.325241	−	0.563335i
$716$	17.1114	−	3.82563i	0.639482	−	0.142970i
$717$	−3.17791	+	10.5466i	−0.118681	+	0.393871i
$718$	−9.70219	+	12.1109i	−0.362082	+	0.451973i
$719$	3.28970			0.122685			0.0613425	−	0.998117i	$-0.480462\pi$
$719$	3.28970			0.122685			0.0613425	+	0.998117i	$0.480462\pi$
$720$	7.44264	−	9.41313i	0.277371	−	0.350807i
$721$	24.1138			0.898044
$722$	6.46264	−	8.06706i	0.240515	−	0.300225i
$723$	−19.2732	+	4.53164i	−0.716779	+	0.168533i
$724$	29.9745	−	6.70146i	1.11399	−	0.249058i
$725$	2.01987	+	3.49852i	0.0750162	+	0.129932i
$726$	−14.7579	−	21.4467i	−0.547718	−	0.795962i
$727$	−0.500514	−	0.288972i	−0.0185630	−	0.0107174i	0.490690	−	0.871334i	$-0.336745\pi$
$727$	−0.500514	−	0.288972i	−0.0185630	−	0.0107174i	−0.509253	+	0.860617i	$0.670078\pi$
$728$	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
$732$	16.4755	−	7.97658i	0.608951	−	0.294823i
$733$	42.8431	−	24.7354i	1.58244	−	0.913625i	0.587943	−	0.808903i	$-0.299938\pi$
$733$	42.8431	−	24.7354i	1.58244	−	0.913625i	0.994502	−	0.104722i	$-0.0333953\pi$
$734$	11.5941	−	4.52064i	0.427946	−	0.166860i
$735$	−0.844900	+	0.198658i	−0.0311646	+	0.00732761i
$736$	−45.1825	+	13.3890i	−1.66545	+	0.493526i
$737$			57.4426i			2.11593i
$738$	−25.0471	−	5.43183i	−0.921996	−	0.199948i
$739$	5.51433			0.202848			0.101424	−	0.994843i	$-0.467660\pi$
$739$	5.51433			0.202848			0.101424	+	0.994843i	$0.467660\pi$
$740$	−10.0210	−	10.8968i	−0.368381	−	0.400576i
$741$	31.8141	+	9.58623i	1.16872	+	0.352159i
$742$	−6.90019	+	2.69045i	−0.253314	+	0.0987694i
$743$	−7.32352	−	12.6847i	−0.268674	−	0.465357i	0.699846	−	0.714294i	$-0.253252\pi$
$743$	−7.32352	−	12.6847i	−0.268674	−	0.465357i	−0.968520	+	0.248937i	$0.919919\pi$
$744$	20.2407	+	18.7857i	0.742061	+	0.688718i
$745$	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
$750$	2.44183	−	0.193576i	0.0891630	−	0.00706840i
$751$	37.8937	−	21.8780i	1.38276	−	0.798338i	0.390276	−	0.920698i	$-0.372380\pi$
$751$	37.8937	−	21.8780i	1.38276	−	0.798338i	0.992486	+	0.122360i	$0.0390462\pi$
$752$	−0.415285	+	4.95070i	−0.0151439	+	0.180533i
$753$	21.8540	−	20.5448i	0.796404	−	0.748695i
$754$	−16.6759	−	13.3593i	−0.607300	−	0.486517i
$755$			12.3109i			0.448039i
$756$	10.0515	+	24.5122i	0.365570	+	0.891500i
$757$			16.8688i			0.613108i	0.951853	+	0.306554i	$0.0991759\pi$
$757$			16.8688i			0.613108i	−0.951853	+	0.306554i	$0.900824\pi$
$758$	−22.7871	+	28.4442i	−0.827663	+	1.03314i
$759$	−48.8910	+	45.9621i	−1.77463	+	1.66832i
$760$	0.987692	+	14.4740i	0.0358274	+	0.525027i
$761$	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	$0.327340\pi$
$762$	2.48313	+	31.3230i	0.0899545	+	1.13471i
$763$	−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
$768$	−27.6569	+	1.76009i	−0.997981	+	0.0635119i
$769$	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	$0.666877\pi$
$770$	6.09084	+	15.6212i	0.219498	+	0.562948i
$771$	11.0585	+	3.33215i	0.398262	+	0.120004i
$772$	3.75720	−	3.45523i	0.135225	−	0.124356i
$773$	8.84895			0.318275			0.159137	−	0.987256i	$-0.449129\pi$
$773$	8.84895			0.318275			0.159137	+	0.987256i	$0.449129\pi$
$774$	42.5266	−	13.6244i	1.52859	−	0.489717i
$775$			5.63690i			0.202483i
$776$	−6.17873	+	4.15252i	−0.221803	+	0.149067i
$777$	31.8162	−	7.48082i	1.14140	−	0.268373i
$778$	−9.57365	−	24.5535i	−0.343232	−	0.880287i
$779$	26.8339	−	15.4925i	0.961423	−	0.555078i
$780$	−11.6611	+	5.64573i	−0.417536	+	0.202149i
$781$	−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
$786$	−19.4097	+	13.3562i	−0.692322	+	0.476401i
$787$	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	$0.716952\pi$
$788$	−4.58919	−	20.5266i	−0.163483	−	0.731231i
$789$	−43.3100	+	10.1833i	−1.54188	+	0.362535i
$790$	6.88549	+	5.51607i	0.244975	+	0.196253i
$791$	15.8226			0.562588
$792$	−34.0480	+	19.9491i	−1.20984	+	0.708861i
$793$	−19.7630			−0.701805
$794$	−30.8107	−	24.6829i	−1.09343	−	0.875963i
$795$	1.02654	−	3.40681i	0.0364076	−	0.120827i
$796$	24.2341	−	5.41809i	0.858956	−	0.192039i
$797$	−8.24761	−	14.2853i	−0.292145	−	0.506011i	0.682171	−	0.731192i	$-0.261036\pi$
$797$	−8.24761	−	14.2853i	−0.292145	−	0.506011i	−0.974317	+	0.225182i	$0.927702\pi$
$798$	−28.9170	−	13.7725i	−1.02365	−	0.487541i
$799$	−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
$804$	42.6742	+	3.10841i	1.50500	+	0.109625i
$805$	18.3917	−	10.6185i	0.648223	−	0.374252i
$806$	−10.8309	−	27.7780i	−0.381502	−	0.978439i
$807$	20.1961	+	21.4831i	0.710937	+	0.756240i
$808$	36.9539	−	24.8355i	1.30003	−	0.873709i
$809$			15.2109i			0.534787i	0.963587	+	0.267394i	$0.0861624\pi$
$809$			15.2109i			0.534787i	−0.963587	+	0.267394i	$0.913838\pi$
$810$	−12.2487	−	3.45983i	−0.430374	−	0.121566i
$811$	−9.18448			−0.322511			−0.161255	−	0.986913i	$-0.551554\pi$
$811$	−9.18448			−0.322511			−0.161255	+	0.986913i	$0.551554\pi$
$812$	13.9423	+	15.1608i	0.489278	+	0.532039i
$813$	−39.3453	+	36.9882i	−1.37990	+	1.29723i
$814$	17.6852	+	45.3573i	0.619867	+	1.58977i
$815$	−2.44333	−	4.23198i	−0.0855862	−	0.148240i
$816$	8.62420	−	21.8227i	0.301907	−	0.763949i
$817$	−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	−0.841042	−	0.540969i	$-0.818057\pi$
$821$	1.37455	−	2.38079i	0.0479720	−	0.0830900i	0.889014	+	0.457879i	$0.151391\pi$
$822$	21.6465	+	10.3097i	0.755010	+	0.359593i
$823$	−1.97316	+	1.13920i	−0.0687799	+	0.0397101i	−0.533996	−	0.845487i	$-0.679310\pi$
$823$	−1.97316	+	1.13920i	−0.0687799	+	0.0397101i	0.465216	+	0.885197i	$0.345977\pi$
$824$	26.6920	−	1.82144i	0.929861	−	0.0634529i
$825$	−7.71259	−	2.32396i	−0.268518	−	0.0809098i
$826$	0.914036	−	1.14095i	0.0318034	−	0.0396989i
$827$			8.53141i			0.296666i	0.988937	+	0.148333i	$0.0473908\pi$
$827$			8.53141i			0.296666i	−0.988937	+	0.148333i	$0.952609\pi$
$828$	31.4996	+	38.8083i	1.09469	+	1.34868i
$829$		−	28.8554i		−	1.00219i	−0.865393	−	0.501094i	$-0.832931\pi$
$829$		−	28.8554i		−	1.00219i	0.865393	−	0.501094i	$-0.167069\pi$
$830$	15.3922	+	12.3309i	0.534269	+	0.428011i
$831$	−4.19578	−	17.8448i	−0.145550	−	0.619030i
$832$	27.7039	+	11.3015i	0.960462	+	0.391810i
$833$	−1.46981	+	0.848595i	−0.0509259	+	0.0294021i
$834$	−8.70736	−	12.6538i	−0.301511	−	0.438166i
$835$	−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	$-0.638581\pi$
$839$	16.6368	−	28.8158i	0.574367	−	0.994833i	0.996110	−	0.0881178i	$-0.0280852\pi$
$840$	11.9346	−	3.67957i	0.411782	−	0.126957i
$841$	6.34023	+	10.9816i	0.218628	+	0.378676i
$842$	5.43678	−	2.11985i	0.187364	−	0.0730548i
$843$	4.27553	+	18.1840i	0.147257	+	0.626291i
$844$	−22.9621	+	21.1166i	−0.790387	+	0.726862i
$845$	0.988022			0.0339890
$846$	5.01821	−	1.60770i	0.172530	−	0.0552737i
$847$		−	27.0945i		−	0.930979i
$848$	−7.43474	+	3.49932i	−0.255310	+	0.120167i
$849$	6.51204	−	21.6117i	0.223493	−	0.741712i
$850$	4.46256	−	1.73999i	0.153065	−	0.0596813i
$851$	53.4018	−	30.8316i	1.83059	−	1.05689i
$852$	−10.5676	+	15.5696i	−0.362041	+	0.533405i
$853$	42.4777	+	24.5245i	1.45441	+	0.839704i	0.998727	−	0.0504383i	$-0.0160618\pi$
$853$	42.4777	+	24.5245i	1.45441	+	0.839704i	0.455683	+	0.890142i	$0.349395\pi$
$854$	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	$0.594295\pi$
$858$	42.4721	−	3.36698i	1.44997	−	0.114947i
$859$	−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	$0.905751\pi$
$860$	−4.59301	−	20.5437i	−0.156620	−	0.700535i
$861$	−18.2700	−	19.4342i	−0.622638	−	0.662315i
$862$	23.0727	−	28.8008i	0.785861	−	0.980958i
$863$	8.26851			0.281463			0.140732	−	0.990048i	$-0.455055\pi$
$863$	8.26851			0.281463			0.140732	+	0.990048i	$0.455055\pi$
$864$	12.9778	+	26.3738i	0.441513	+	0.897255i
$865$	−6.44113			−0.219005
$866$	0.396233	−	0.494602i	0.0134645	−	0.0168073i
$867$	−6.55937	−	6.97735i	−0.222768	−	0.236963i
$868$	6.27071	+	28.0478i	0.212842	+	0.952003i
$869$	−14.5064	−	25.1258i	−0.492095	−	0.852334i
$870$	−9.86437	+	0.781998i	−0.334433	+	0.0265122i
$871$	−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
$876$	−26.0666	+	38.4047i	−0.880708	+	1.29757i
$877$	4.51357	−	2.60591i	0.152412	−	0.0879953i	−0.421854	−	0.906664i	$-0.638621\pi$
$877$	4.51357	−	2.60591i	0.152412	−	0.0879953i	0.574267	+	0.818668i	$0.305287\pi$
$878$	44.1910	−	17.2305i	1.49137	−	0.581500i
$879$	8.77301	−	29.1153i	0.295906	−	0.982033i
$880$	7.92202	+	16.8313i	0.267051	+	0.567384i
$881$			17.9255i			0.603925i	0.953320	+	0.301963i	$0.0976418\pi$
$881$			17.9255i			0.603925i	−0.953320	+	0.301963i	$0.902358\pi$
$882$	0.450583	−	2.07772i	0.0151719	−	0.0699603i
$883$	20.5203			0.690564			0.345282	−	0.938499i	$-0.387783\pi$
$883$	20.5203			0.690564			0.345282	+	0.938499i	$0.387783\pi$
$884$	−18.6478	+	17.1490i	−0.627192	+	0.576784i
$885$	0.160756	+	0.683703i	0.00540377	+	0.0229824i
$886$	−48.9897	+	19.1015i	−1.64584	+	0.641728i
$887$	19.1974	+	33.2509i	0.644587	+	1.11646i	0.984397	+	0.175963i	$0.0563039\pi$
$887$	19.1974	+	33.2509i	0.644587	+	1.11646i	−0.339810	+	0.940494i	$0.610363\pi$
$888$	34.6530	−	10.6839i	1.16288	−	0.358529i
$889$	−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
$894$	6.70072	+	9.73772i	0.224106	+	0.325678i
$895$	−7.59236	+	4.38345i	−0.253784	+	0.146523i
$896$	−24.7505	−	14.8077i	−0.826857	−	0.494692i
$897$	−12.3517	−	52.5323i	−0.412411	−	1.75400i
$898$	−29.4801	−	23.6170i	−0.983765	−	0.788109i
$899$		−	22.7716i		−	0.759476i
$900$	−2.14382	+	5.60393i	−0.0714608	+	0.186798i
$901$		−	6.95760i		−	0.231791i
$902$	24.8406	−	31.0076i	0.827103	−	1.03244i
$903$	44.4990	+	13.4084i	1.48083	+	0.446205i
$904$	17.5144	−	1.19517i	0.582520	−	0.0397506i
$905$	−13.2997	+	7.67861i	−0.442099	+	0.255246i
$906$	−27.2252	−	12.9667i	−0.904497	−	0.430791i
$907$	−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	−0.790729	−	0.612167i	$-0.790298\pi$
$911$	4.06826	−	7.04644i	0.134788	−	0.233459i	0.925516	+	0.378708i	$0.123631\pi$
$912$	−33.0492	−	13.0608i	−1.09437	−	0.432487i
$913$	−32.4282	−	56.1673i	−1.07322	−	1.85887i
$914$	−21.0079	−	53.8791i	−0.694881	−	1.78216i
$915$	−6.66839	+	6.26891i	−0.220450	+	0.207244i
$916$	−14.6932	−	15.9774i	−0.485478	−	0.527907i
$917$	−24.5211			−0.809758
$918$	−24.8847	+	0.432377i	−0.821318	+	0.0142706i
$919$		−	25.3748i		−	0.837038i	−0.908208	−	0.418519i	$-0.862549\pi$
$919$		−	25.3748i		−	0.837038i	0.908208	−	0.418519i	$-0.137451\pi$
$920$	19.5561	−	13.1430i	0.644746	−	0.433313i
$921$	17.6562	+	18.7813i	0.581792	+	0.618865i
$922$	−5.67998	−	14.5675i	−0.187060	−	0.479754i
$923$	17.5943	−	10.1581i	0.579125	−	0.334358i
$924$	−40.9611	−	2.98363i	−1.34752	−	0.0981544i
$925$	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	$0.429496\pi$
$930$	−12.4658	−	5.93719i	−0.408771	−	0.194688i
$931$	1.28514	+	2.22593i	0.0421189	+	0.0729520i
$932$	−51.3388	+	11.4779i	−1.68166	+	0.375973i
$933$	3.87118	−	12.8474i	0.126737	−	0.420605i
$934$	22.6299	+	18.1291i	0.740473	+	0.593204i
$935$	−15.7511			−0.515117
$936$	−0.203021	−	31.7348i	−0.00663595	−	1.03728i
$937$	−48.8089			−1.59452			−0.797258	−	0.603639i	$-0.793717\pi$
$937$	−48.8089			−1.59452			−0.797258	+	0.603639i	$0.793717\pi$
$938$	34.7536	+	27.8416i	1.13475	+	0.909062i
$939$	−33.5729	+	7.89385i	−1.09561	+	0.257606i
$940$	−0.541983	−	2.42419i	−0.0176775	−	0.0790685i
$941$	7.53979	+	13.0593i	0.245790	+	0.425721i	0.962353	−	0.271801i	$-0.0876193\pi$
$941$	7.53979	+	13.0593i	0.245790	+	0.425721i	−0.716563	+	0.697522i	$0.754286\pi$
$942$	14.3297	−	9.86059i	0.466888	−	0.321275i
$943$	−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	$0.791542\pi$
$948$	−19.4510	+	9.41716i	−0.631738	+	0.305855i
$949$	43.3990	−	25.0564i	1.40879	−	0.813366i
$950$	−2.63511	−	6.75827i	−0.0854942	−	0.219267i
$951$	−59.6486	+	14.0249i	−1.93424	+	0.454790i
$952$	20.2689	−	13.6221i	0.656920	−	0.441495i
$953$		−	45.3356i		−	1.46856i	−0.678845	−	0.734282i	$-0.737519\pi$
$953$		−	45.3356i		−	1.46856i	0.678845	−	0.734282i	$-0.262481\pi$
$954$	6.45284	+	5.85846i	0.208918	+	0.189675i
$955$	2.99211			0.0968224
$956$	−9.36207	+	8.60962i	−0.302791	+	0.278455i
$957$	31.1569	+	9.38820i	1.00716	+	0.303477i
$958$	0.894671	+	2.29456i	0.0289055	+	0.0741340i
$959$	12.4766	+	21.6101i	0.402891	+	0.697827i
$960$	12.9327	−	4.97448i	0.417401	−	0.160551i
$961$	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
$966$	4.11096	+	51.8570i	0.132268	+	1.66847i
$967$	50.3479	−	29.0684i	1.61908	−	0.934776i	0.631921	−	0.775032i	$-0.282267\pi$
$967$	50.3479	−	29.0684i	1.61908	−	0.934776i	0.987159	−	0.159744i	$-0.0510668\pi$
$968$	−2.04659	−	29.9915i	−0.0657799	−	0.963963i
$969$	21.9230	−	20.6096i	0.704267	−	0.662077i
$970$	2.32724	−	2.90499i	0.0747230	−	0.0932738i
$971$		−	15.8715i		−	0.509340i	−0.967028	−	0.254670i	$-0.918033\pi$
$971$		−	15.8715i		−	0.509340i	0.967028	−	0.254670i	$-0.0819669\pi$
$972$	20.5525	−	23.4434i	0.659222	−	0.751949i
$973$		−	15.9861i		−	0.512491i
$974$	0.488755	+	0.391549i	0.0156607	+	0.0125460i
$975$	4.71980	−	4.43706i	0.151155	−	0.142100i
$976$	21.0626	+	1.76682i	0.674198	+	0.0565546i
$977$	−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	$0.367119\pi$
$978$	11.9324	−	0.945941i	0.381556	−	0.0302479i
$979$	−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	−0.962592	−	0.270956i	$-0.912660\pi$
$983$	−7.73291	+	13.3938i	−0.246642	+	0.427196i	0.715950	+	0.698151i	$0.245994\pi$
$984$	−21.6914	−	20.1321i	−0.691495	−	0.641787i
$985$	5.25835	+	9.10772i	0.167545	+	0.290196i
$986$	−18.0276	+	7.02913i	−0.574116	+	0.223853i
$987$	5.25095	+	1.58222i	0.167140	+	0.0503625i
$988$	25.9711	+	28.2409i	0.826250	+	0.898462i
$989$	87.6825			2.78814
$990$	13.2628	−	14.6084i	0.421520	−	0.464286i
$991$			7.14184i			0.226868i	0.993546	+	0.113434i	$0.0361850\pi$
$991$			7.14184i			0.226868i	−0.993546	+	0.113434i	$0.963815\pi$
$992$	9.05977	+	30.5730i	0.287648	+	0.970693i
$993$	−0.259121	+	0.0609260i	−0.00822294	+	0.00193343i
$994$	−18.2460	+	7.11427i	−0.578727	+	0.225651i
$995$	−10.7528	+	6.20811i	−0.340885	+	0.196810i
$996$	−43.4816	+	21.0516i	−1.37777	+	0.667044i
$997$	14.6617	+	8.46495i	0.464341	+	0.268088i	0.713868	−	0.700280i	$-0.246942\pi$
$997$	14.6617	+	8.46495i	0.464341	+	0.268088i	−0.249527	+	0.968368i	$0.580275\pi$
$998$	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.b.11.16	yes	48
3.2	odd	2		1080.2.bm.a.251.9		48
4.3	odd	2		1440.2.cc.b.911.18		48
8.3	odd	2		360.2.bm.a.11.9	✓	48
8.5	even	2		1440.2.cc.a.911.18		48
9.4	even	3		1080.2.bm.b.611.16		48
9.5	odd	6		360.2.bm.a.131.9	yes	48
12.11	even	2		4320.2.cc.a.1871.18		48
24.5	odd	2		4320.2.cc.b.1871.7		48
24.11	even	2		1080.2.bm.b.251.16		48
36.23	even	6		1440.2.cc.a.1391.18		48
36.31	odd	6		4320.2.cc.b.3311.7		48
72.5	odd	6		1440.2.cc.b.1391.18		48
72.13	even	6		4320.2.cc.a.3311.18		48
72.59	even	6	inner	360.2.bm.b.131.16	yes	48
72.67	odd	6		1080.2.bm.a.611.9		48

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

\(f(q)\)	\(=\)	\(q+(0.884203 - 1.10371i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-0.436372 - 1.95181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.44183 + 0.193576i) q^{6} +(-2.20775 - 1.27465i) q^{7} +(-2.54009 - 1.24417i) q^{8} +(-0.185091 + 2.99428i) q^{9} +O(q^{10})\)	\(q+(0.884203 - 1.10371i) q^{2} +(-1.18636 - 1.26196i) q^{3} +(-0.436372 - 1.95181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.44183 + 0.193576i) 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} +(-1.94542 + 2.86624i) q^{12} +(3.23898 - 1.87003i) q^{13} +(-3.35895 + 1.30968i) q^{14} +(0.499709 - 1.65840i) q^{15} +(-3.61916 + 1.70343i) q^{16} -3.38689i q^{17} +(3.14118 + 2.85184i) q^{18} -5.12923 q^{19} +(1.47213 - 1.35382i) q^{20} +(1.01064 + 4.29829i) q^{21} +(-6.12765 + 2.38923i) q^{22} +(4.16526 + 7.21444i) q^{23} +(1.44337 + 4.68153i) 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} +(-1.38856 - 2.01790i) q^{30} +(4.88169 - 2.81845i) q^{31} +(-1.31996 + 5.50070i) q^{32} +(1.84369 + 7.84127i) q^{33} +(-3.73816 - 2.99470i) q^{34} -2.54929i q^{35} +(5.92506 - 0.945359i) q^{36} -7.40207i q^{37} +(-4.53528 + 5.66121i) q^{38} +(-6.20251 - 1.86894i) q^{39} +(-0.192561 - 2.82186i) q^{40} +(-5.23156 + 3.02044i) q^{41} +(5.63769 + 2.68510i) 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} +(6.44330 + 2.54635i) q^{48} +(-0.250553 - 0.433970i) q^{49} +(0.513744 + 1.31760i) q^{50} +(-4.27412 + 4.01808i) q^{51} +(-5.06335 - 5.50587i) q^{52} +2.05427 q^{53} +(-0.127662 - 7.34736i) q^{54} -4.65062i q^{55} +(4.02201 + 5.98453i) q^{56} +(6.08512 + 6.47289i) q^{57} +(-2.07539 - 5.32277i) q^{58} +(-0.351174 + 0.202750i) q^{59} +(-3.45495 - 0.251661i) 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} +(10.2847 + 4.89837i) q^{66} +(-6.17580 - 10.6968i) q^{67} +(-6.61058 + 1.47794i) q^{68} +(4.16284 - 13.8153i) q^{69} +(-2.81369 - 2.25409i) q^{70} +5.43205 q^{71} +(4.19554 - 7.37546i) q^{72} +13.3990 q^{73} +(-8.16977 - 6.54493i) q^{74} +(1.68607 - 0.396439i) q^{75} +(2.23825 + 10.0113i) q^{76} +(5.92789 + 10.2674i) q^{77} +(-7.54705 + 5.19328i) 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} +(7.94845 - 3.84823i) q^{84} +(2.93313 - 1.69345i) q^{85} +(-5.40738 - 13.8683i) q^{86} +(-6.81130 + 1.60151i) q^{87} +(7.33726 + 10.9174i) q^{88} -2.72618i q^{89} +(-0.899178 + 4.14626i) q^{90} -9.53450 q^{91} +(12.2637 - 11.2780i) q^{92} +(-9.34823 - 2.81681i) q^{93} +(-0.638080 - 1.63649i) q^{94} +(-2.56462 - 4.44204i) q^{95} +(8.50762 - 4.86008i) q^{96} +(1.31601 - 2.27939i) q^{97} +(-0.700519 - 0.107179i) q^{98} +(7.70810 - 11.6292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

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