LMFDB - Embedded newform 126.2.t.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(47,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("126.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.t (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.2
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	126.59
Dual form			126.2.t.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.128499 - 1.72728i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.61932 q^{5} +(-0.752355 + 1.56012i) q^{6} +(0.266972 - 2.63225i) q^{7} -1.00000i q^{8} +(-2.96698 + 0.443907i) q^{9} +(3.13442 + 1.80966i) q^{10} +2.00379i q^{11} +(1.43162 - 0.974922i) q^{12} +(-2.95206 - 1.70437i) q^{13} +(-1.54733 + 2.14611i) q^{14} +(0.465079 + 6.25156i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.08709 - 5.34700i) q^{17} +(2.79143 + 1.09905i) q^{18} +(0.877353 - 0.506540i) q^{19} +(-1.80966 - 3.13442i) q^{20} +(-4.58093 - 0.122894i) q^{21} +(1.00190 - 1.73534i) q^{22} -3.02799i q^{23} +(-1.72728 + 0.128499i) q^{24} +8.09945 q^{25} +(1.70437 + 2.95206i) q^{26} +(1.14800 + 5.06775i) q^{27} +(2.41308 - 1.08492i) q^{28} +(5.04560 - 2.91308i) q^{29} +(2.72301 - 5.64655i) q^{30} +(0.787812 - 0.454844i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.46111 - 0.257486i) q^{33} +(-5.34700 + 3.08709i) q^{34} +(-0.966257 + 9.52693i) q^{35} +(-1.86792 - 2.34752i) q^{36} +(3.66825 + 6.35359i) q^{37} -1.01308 q^{38} +(-2.56459 + 5.31804i) q^{39} +3.61932i q^{40} +(2.85045 - 4.93712i) q^{41} +(3.90575 + 2.39689i) q^{42} +(-2.39949 - 4.15605i) q^{43} +(-1.73534 + 1.00190i) q^{44} +(10.7384 - 1.60664i) q^{45} +(-1.51400 + 2.62232i) q^{46} +(-1.11511 + 1.93143i) q^{47} +(1.56012 + 0.752355i) q^{48} +(-6.85745 - 1.40547i) q^{49} +(-7.01433 - 4.04972i) q^{50} +(-9.63244 - 4.64518i) q^{51} -3.40874i q^{52} +(-7.58088 - 4.37683i) q^{53} +(1.53967 - 4.96280i) q^{54} -7.25237i q^{55} +(-2.63225 - 0.266972i) q^{56} +(-0.987674 - 1.45034i) q^{57} -5.82616 q^{58} +(4.49313 + 7.78233i) q^{59} +(-5.18147 + 3.52855i) q^{60} +(-12.7410 - 7.35603i) q^{61} -0.909687 q^{62} +(0.376373 + 7.92833i) q^{63} -1.00000 q^{64} +(10.6844 + 6.16866i) q^{65} +(-3.12615 - 1.50757i) q^{66} +(4.15821 + 7.20222i) q^{67} +6.17418 q^{68} +(-5.23019 + 0.389094i) q^{69} +(5.60027 - 7.76744i) q^{70} +0.466287i q^{71} +(0.443907 + 2.96698i) q^{72} +(-3.65022 - 2.10746i) q^{73} -7.33650i q^{74} +(-1.04077 - 13.9900i) q^{75} +(0.877353 + 0.506540i) q^{76} +(5.27448 + 0.534957i) q^{77} +(4.88001 - 3.32326i) q^{78} +(-1.91267 + 3.31284i) q^{79} +(1.80966 - 3.13442i) q^{80} +(8.60589 - 2.63412i) q^{81} +(-4.93712 + 2.85045i) q^{82} +(4.00481 + 6.93654i) q^{83} +(-2.18403 - 4.02865i) q^{84} +(-11.1732 + 19.3525i) q^{85} +4.79899i q^{86} +(-5.68005 - 8.34083i) q^{87} +2.00379 q^{88} +(2.39324 + 4.14521i) q^{89} +(-10.1031 - 3.97782i) q^{90} +(-5.27445 + 7.31553i) q^{91} +(2.62232 - 1.51400i) q^{92} +(-0.886874 - 1.30232i) q^{93} +(1.93143 - 1.11511i) q^{94} +(-3.17542 + 1.83333i) q^{95} +(-0.974922 - 1.43162i) q^{96} +(10.1835 - 5.87944i) q^{97} +(5.23599 + 4.64590i) q^{98} +(-0.889499 - 5.94521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.128499	−	1.72728i	−0.0741890	−	0.997244i
$3$	−0.128499	−	1.72728i	−0.0741890	−	0.997244i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−3.61932			−1.61861			−0.809304	−	0.587391i	$-0.800155\pi$
$5$	−3.61932			−1.61861			−0.809304	+	0.587391i	$0.800155\pi$
$6$	−0.752355	+	1.56012i	−0.307148	+	0.636915i
$7$	0.266972	−	2.63225i	0.100906	−	0.994896i
$7$	0.266972	−	2.63225i	0.100906	−	0.994896i
$8$		−	1.00000i		−	0.353553i
$9$	−2.96698	+	0.443907i	−0.988992	+	0.147969i
$10$	3.13442	+	1.80966i	0.991190	+	0.572264i
$11$			2.00379i			0.604167i	0.953281	+	0.302083i	$0.0976821\pi$
$11$			2.00379i			0.604167i	−0.953281	+	0.302083i	$0.902318\pi$
$12$	1.43162	−	0.974922i	0.413272	−	0.281436i
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	0.0312328	−	0.999512i	$-0.490057\pi$
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	−0.849987	+	0.526804i	$0.823390\pi$
$14$	−1.54733	+	2.14611i	−0.413541	+	0.573571i
$15$	0.465079	+	6.25156i	0.120083	+	1.61415i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.08709	−	5.34700i	0.748730	−	1.29684i	−0.199702	−	0.979857i	$-0.563998\pi$
$17$	3.08709	−	5.34700i	0.748730	−	1.29684i	0.948432	−	0.316981i	$-0.102669\pi$
$18$	2.79143	+	1.09905i	0.657946	+	0.259049i
$19$	0.877353	−	0.506540i	0.201279	−	0.116208i	−0.395973	−	0.918262i	$-0.629593\pi$
$19$	0.877353	−	0.506540i	0.201279	−	0.116208i	0.597252	+	0.802054i	$0.296259\pi$
$20$	−1.80966	−	3.13442i	−0.404652	−	0.700877i
$21$	−4.58093	−	0.122894i	−0.999640	−	0.0268176i
$22$	1.00190	−	1.73534i	0.213605	−	0.369975i
$23$		−	3.02799i		−	0.631380i	−0.948862	−	0.315690i	$-0.897764\pi$
$23$		−	3.02799i		−	0.631380i	0.948862	−	0.315690i	$-0.102236\pi$
$24$	−1.72728	+	0.128499i	−0.352579	+	0.0262298i
$25$	8.09945			1.61989
$26$	1.70437	+	2.95206i	0.334255	+	0.578946i
$27$	1.14800	+	5.06775i	0.220934	+	0.975289i
$28$	2.41308	−	1.08492i	0.456029	−	0.205030i
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.0479434	−	0.998850i	$-0.484733\pi$
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.889001	+	0.457905i	$0.151400\pi$
$30$	2.72301	−	5.64655i	0.497152	−	1.03091i
$31$	0.787812	−	0.454844i	0.141495	−	0.0816923i	−0.427581	−	0.903977i	$-0.640634\pi$
$31$	0.787812	−	0.454844i	0.141495	−	0.0816923i	0.569076	+	0.822285i	$0.307301\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.46111	−	0.257486i	0.602502	−	0.0448225i
$34$	−5.34700	+	3.08709i	−0.917003	+	0.529432i
$35$	−0.966257	+	9.52693i	−0.163327	+	1.61035i
$36$	−1.86792	−	2.34752i	−0.311320	−	0.391254i
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	0.992355	+	0.123413i	$0.0393839\pi$
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	−0.389299	+	0.921111i	$0.627283\pi$
$38$	−1.01308			−0.164343
$39$	−2.56459	+	5.31804i	−0.410663	+	0.851567i
$40$			3.61932i			0.572264i
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	0.998064	+	0.0622002i	$0.0198117\pi$
$42$	3.90575	+	2.39689i	0.602671	+	0.369849i
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	0.623004	−	0.782219i	$-0.285912\pi$
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	−0.988923	+	0.148428i	$0.952579\pi$
$44$	−1.73534	+	1.00190i	−0.261612	+	0.151042i
$45$	10.7384	−	1.60664i	1.60079	−	0.239504i
$46$	−1.51400	+	2.62232i	−0.223227	+	0.386640i
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	−0.935820	−	0.352478i	$-0.885339\pi$
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	0.773165	+	0.634205i	$0.218673\pi$
$48$	1.56012	+	0.752355i	0.225183	+	0.108593i
$49$	−6.85745	−	1.40547i	−0.979636	−	0.200782i
$50$	−7.01433	−	4.04972i	−0.991975	−	0.572717i
$51$	−9.63244	−	4.64518i	−1.34881	−	0.650455i
$52$		−	3.40874i		−	0.472708i
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.121109	−	0.992639i	$-0.538645\pi$
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.920205	+	0.391436i	$0.871978\pi$
$54$	1.53967	−	4.96280i	0.209523	−	0.675352i
$55$		−	7.25237i		−	0.977909i
$56$	−2.63225	−	0.266972i	−0.351749	−	0.0356757i
$57$	−0.987674	−	1.45034i	−0.130821	−	0.192103i
$58$	−5.82616			−0.765012
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	0.994881	+	0.101054i	$0.0322216\pi$
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	−0.409925	+	0.912119i	$0.634445\pi$
$60$	−5.18147	+	3.52855i	−0.668925	+	0.455534i
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.983686	−	0.179892i	$-0.942425\pi$
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.647634	−	0.761952i	$-0.724241\pi$
$62$	−0.909687			−0.115530
$63$	0.376373	+	7.92833i	0.0474185	+	0.998875i
$64$	−1.00000			−0.125000
$65$	10.6844	+	6.16866i	1.32524	+	0.765128i
$66$	−3.12615	−	1.50757i	−0.384803	−	0.185569i
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	0.999957	+	0.00926908i	$0.00295048\pi$
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	−0.491951	+	0.870623i	$0.663716\pi$
$68$	6.17418			0.748730
$69$	−5.23019	+	0.389094i	−0.629640	+	0.0468415i
$70$	5.60027	−	7.76744i	0.669360	−	0.928386i
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$	0.443907	+	2.96698i	0.0523149	+	0.349661i
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	0.270938	−	0.962597i	$-0.412666\pi$
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	−0.698164	+	0.715938i	$0.746000\pi$
$74$		−	7.33650i		−	0.852850i
$75$	−1.04077	−	13.9900i	−0.120178	−	1.61543i
$76$	0.877353	+	0.506540i	0.100639	+	0.0581041i
$77$	5.27448	+	0.534957i	0.601083	+	0.0609641i
$78$	4.88001	−	3.32326i	0.552553	−	0.376285i
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	−0.953332	−	0.301924i	$-0.902371\pi$
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	0.738140	+	0.674648i	$0.235704\pi$
$80$	1.80966	−	3.13442i	0.202326	−	0.350439i
$81$	8.60589	−	2.63412i	0.956210	−	0.292680i
$82$	−4.93712	+	2.85045i	−0.545213	+	0.314779i
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	0.997657	−	0.0684084i	$-0.0217921\pi$
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	−0.558072	+	0.829792i	$0.688459\pi$
$84$	−2.18403	−	4.02865i	−0.238298	−	0.439561i
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$			4.79899i			0.517488i
$87$	−5.68005	−	8.34083i	−0.608965	−	0.894230i
$88$	2.00379			0.213605
$89$	2.39324	+	4.14521i	0.253683	+	0.439391i	0.964537	−	0.263948i	$-0.0850248\pi$
$89$	2.39324	+	4.14521i	0.253683	+	0.439391i	−0.710854	+	0.703339i	$0.751691\pi$
$90$	−10.1031	−	3.97782i	−1.06496	−	0.419299i
$91$	−5.27445	+	7.31553i	−0.552912	+	0.766876i
$92$	2.62232	−	1.51400i	0.273396	−	0.157845i
$93$	−0.886874	−	1.30232i	−0.0919646	−	0.135045i
$94$	1.93143	−	1.11511i	0.199211	−	0.115015i
$95$	−3.17542	+	1.83333i	−0.325791	+	0.188096i
$96$	−0.974922	−	1.43162i	−0.0995026	−	0.146114i
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.115856	−	0.993266i	$-0.463039\pi$
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.918121	+	0.396299i	$0.129706\pi$
$98$	5.23599	+	4.64590i	0.528915	+	0.469307i
$99$	−0.889499	−	5.94521i	−0.0893980	−	0.597516i
$100$	4.04972	+	7.01433i	0.404972	+	0.701433i
$101$	−12.8922			−1.28282			−0.641411	−	0.767197i	$-0.721651\pi$
$101$	−12.8922			−1.28282			−0.641411	+	0.767197i	$0.721651\pi$
$102$	6.01935	+	8.83906i	0.596004	+	0.875198i
$103$		−	10.7588i		−	1.06010i	−0.847968	−	0.530048i	$-0.822174\pi$
$103$		−	10.7588i		−	1.06010i	0.847968	−	0.530048i	$-0.177826\pi$
$104$	−1.70437	+	2.95206i	−0.167127	+	0.289473i
$105$	16.5798	+	0.444792i	1.61803	+	0.0434072i
$106$	4.37683	+	7.58088i	0.425115	+	0.736321i
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	−0.385414	−	0.922744i	$-0.625942\pi$
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$108$	−3.81480	+	3.52808i	−0.367079	+	0.339489i
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	−0.564391	−	0.825507i	$-0.690889\pi$
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	0.997106	+	0.0760233i	$0.0242224\pi$
$110$	−3.62618	+	6.28073i	−0.345743	+	0.598844i
$111$	10.5031	−	7.15251i	0.996905	−	0.678886i
$112$	2.14611	+	1.54733i	0.202788	+	0.146209i
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	0.429551	−	0.903043i	$-0.358672\pi$
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	−0.567283	+	0.823523i	$0.692005\pi$
$114$	0.130180	+	1.74987i	0.0121925	+	0.163890i
$115$			10.9593i			1.02196i
$116$	5.04560	+	2.91308i	0.468472	+	0.270473i
$117$	9.51527	+	3.74639i	0.879687	+	0.346354i
$118$		−	8.98627i		−	0.827253i
$119$	−13.2505	−	9.55349i	−1.21467	−	0.875767i
$120$	6.25156	−	0.465079i	0.570687	−	0.0424557i
$121$	6.98481			0.634982
$122$	7.35603	+	12.7410i	0.665984	+	1.15352i
$123$	−8.89405	−	4.28910i	−0.801950	−	0.386735i
$124$	0.787812	+	0.454844i	0.0707476	+	0.0408462i
$125$	−11.2179			−1.00336
$126$	3.63821	−	7.05432i	0.324118	−	0.628449i
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.87031	+	4.67864i	−0.604897	+	0.411931i
$130$	−6.16866	−	10.6844i	−0.541027	−	0.937087i
$131$	17.3313			1.51425			0.757123	−	0.653272i	$-0.226604\pi$
$131$	17.3313			1.51425			0.757123	+	0.653272i	$0.226604\pi$
$132$	1.95354	+	2.86867i	0.170034	+	0.249685i
$133$	−1.09911	−	2.44464i	−0.0953049	−	0.211977i
$134$		−	8.31641i		−	0.718429i
$135$	−4.15499	−	18.3418i	−0.357605	−	1.57861i
$136$	−5.34700	−	3.08709i	−0.458501	−	0.264716i
$137$		0	0.000645123i		0	5.51166e-5i	−1.00000		2.75583e-5i	$-0.999991\pi$
$137$		0	0.000645123i		0	5.51166e-5i	1.00000		2.75583e-5i	$-8.77208e-6\pi$
$138$	4.72402	+	2.27813i	0.402135	+	0.193927i
$139$	8.73273	+	5.04185i	0.740701	+	0.427644i	0.822324	−	0.569019i	$-0.192677\pi$
$139$	8.73273	+	5.04185i	0.740701	+	0.427644i	−0.0816233	+	0.996663i	$0.526010\pi$
$140$	−8.73370	+	3.92666i	−0.738132	+	0.331864i
$141$	3.47940	+	1.67792i	0.293018	+	0.141306i
$142$	0.233144	−	0.403817i	0.0195650	−	0.0338875i
$143$	3.41521	−	5.91532i	0.285594	−	0.494664i
$144$	1.09905	−	2.79143i	0.0915878	−	0.232619i
$145$	−18.2616	+	10.5434i	−1.51655	+	0.875578i
$146$	2.10746	+	3.65022i	0.174414	+	0.302095i
$147$	−1.54647	+	12.0253i	−0.127550	+	0.991832i
$148$	−3.66825	+	6.35359i	−0.301528	+	0.522262i
$149$		−	11.2475i		−	0.921433i	−0.887547	−	0.460716i	$-0.847593\pi$
$149$		−	11.2475i		−	0.921433i	0.887547	−	0.460716i	$-0.152407\pi$
$150$	−6.09366	+	12.6361i	−0.497545	+	1.03173i
$151$	−4.72379			−0.384417			−0.192208	−	0.981354i	$-0.561565\pi$
$151$	−4.72379			−0.384417			−0.192208	+	0.981354i	$0.561565\pi$
$152$	−0.506540	−	0.877353i	−0.0410858	−	0.0711627i
$153$	−6.78575	+	17.2348i	−0.548596	+	1.39335i
$154$	−4.30036	−	3.10053i	−0.346533	−	0.249848i
$155$	−2.85134	+	1.64622i	−0.229025	+	0.132228i
$156$	−5.88785	+	0.438020i	−0.471405	+	0.0350697i
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	−0.390151	−	0.920751i	$-0.627577\pi$
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	0.602318	+	0.798256i	$0.294244\pi$
$158$	3.31284	−	1.91267i	0.263555	−	0.152164i
$159$	−6.58586	+	13.6567i	−0.522292	+	1.08305i
$160$	−3.13442	+	1.80966i	−0.247798	+	0.143066i
$161$	−7.97043	−	0.808390i	−0.628158	−	0.0637101i
$162$	−8.76998	−	2.02173i	−0.689035	−	0.158842i
$163$	−1.43687	−	2.48873i	−0.112544	−	0.194932i	0.804251	−	0.594289i	$-0.202567\pi$
$163$	−1.43687	−	2.48873i	−0.112544	−	0.194932i	−0.916795	+	0.399357i	$0.869233\pi$
$164$	5.70089			0.445165
$165$	−12.5268	+	0.931922i	−0.975214	+	0.0725500i
$166$		−	8.00963i		−	0.621668i
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	−0.892905	−	0.450245i	$-0.851337\pi$
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	0.836376	+	0.548156i	$0.184670\pi$
$168$	−0.122894	+	4.58093i	−0.00948147	+	0.353426i
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$	19.3525	−	11.1732i	1.48427	−	0.856942i
$171$	−2.37823	+	1.89236i	−0.181868	+	0.144712i
$172$	2.39949	−	4.15605i	0.182960	−	0.316896i
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	−0.918472	−	0.395486i	$-0.870576\pi$
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	0.801737	+	0.597677i	$0.203909\pi$
$174$	0.748656	+	10.0634i	0.0567554	+	0.762904i
$175$	2.16233	−	21.3197i	0.163457	−	1.61162i
$176$	−1.73534	−	1.00190i	−0.130806	−	0.0755209i
$177$	12.8649	−	8.76091i	0.966984	−	0.658510i
$178$		−	4.78647i		−	0.358761i
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.279320	−	0.960198i	$-0.590109\pi$
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.971216	+	0.238201i	$0.923442\pi$
$180$	6.76060	+	8.49643i	0.503906	+	0.633286i
$181$			7.89318i			0.586695i	0.956006	+	0.293348i	$0.0947693\pi$
$181$			7.89318i			0.586695i	−0.956006	+	0.293348i	$0.905231\pi$
$182$	8.22557	−	3.69821i	0.609720	−	0.274130i
$183$	−11.0687	+	22.9525i	−0.818222	+	1.69670i
$184$	−3.02799			−0.223227
$185$	−13.2765	−	22.9957i	−0.976111	−	1.69067i
$186$	0.116894	+	1.57128i	0.00857108	+	0.115212i
$187$	10.7143	+	6.18590i	0.783506	+	0.452358i
$188$	−2.23022			−0.162655
$189$	13.6461	−	1.66888i	0.992604	−	0.121393i
$190$	3.66666			0.266007
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	0.855114	−	0.518441i	$-0.173487\pi$
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	−0.0214259	+	0.999770i	$0.506821\pi$
$192$	0.128499	+	1.72728i	0.00927362	+	0.124656i
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$	−11.7589			−0.844239
$195$	9.28205	−	19.2476i	0.664701	−	1.37835i
$196$	−2.21155	−	6.64146i	−0.157968	−	0.474390i
$197$		−	4.44250i		−	0.316515i	−0.987398	−	0.158258i	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$	−2.20228	+	5.59345i	−0.156509	+	0.397509i
$199$	9.96868	+	5.75542i	0.706661	+	0.407991i	0.809823	−	0.586674i	$-0.199563\pi$
$199$	9.96868	+	5.75542i	0.706661	+	0.407991i	−0.103163	+	0.994665i	$0.532896\pi$
$200$		−	8.09945i		−	0.572717i
$201$	11.9059	−	8.10786i	0.839779	−	0.571884i
$202$	11.1650	+	6.44610i	0.785565	+	0.453546i
$203$	−6.32091	−	14.0590i	−0.443641	−	0.986747i
$204$	−0.793376	−	10.6645i	−0.0555475	−	0.746666i
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$	−5.37940	+	9.31740i	−0.374801	+	0.649174i
$207$	1.34415	+	8.98399i	0.0934247	+	0.624430i
$208$	2.95206	−	1.70437i	0.204688	−	0.118177i
$209$	1.01500	+	1.75804i	0.0702092	+	0.121606i
$210$	−14.1362	−	8.67511i	−0.975487	−	0.598640i
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	−0.155155	−	0.987890i	$-0.549588\pi$
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	0.933115	−	0.359577i	$-0.117079\pi$
$212$		−	8.75365i		−	0.601203i
$213$	0.805408	−	0.0599175i	0.0551856	−	0.00410548i
$214$	−2.63967			−0.180444
$215$	8.68453	+	15.0420i	0.592280	+	1.02586i
$216$	5.06775	−	1.14800i	0.344817	−	0.0781118i
$217$	−0.986937	−	2.19515i	−0.0669976	−	0.149016i
$218$	−7.82484	+	4.51768i	−0.529965	+	0.305976i
$219$	−3.17111	+	6.57576i	−0.214284	+	0.444348i
$220$	6.28073	−	3.62618i	0.423447	−	0.244477i
$221$	−18.2265	+	10.5231i	−1.22605	+	0.707860i
$222$	−12.6722	+	0.942733i	−0.850500	+	0.0632721i
$223$	−16.2994	+	9.41045i	−1.09149	+	0.630170i	−0.933972	−	0.357346i	$-0.883682\pi$
$223$	−16.2994	+	9.41045i	−1.09149	+	0.630170i	−0.157515	+	0.987517i	$0.550348\pi$
$224$	−1.08492	−	2.41308i	−0.0724892	−	0.161231i
$225$	−24.0309	+	3.59540i	−1.60206	+	0.239693i
$226$	0.845306	+	1.46411i	0.0562289	+	0.0973914i
$227$	−14.6133			−0.969919			−0.484960	−	0.874537i	$-0.661166\pi$
$227$	−14.6133			−0.969919			−0.484960	+	0.874537i	$0.661166\pi$
$228$	0.762196	−	1.58052i	0.0504777	−	0.104673i
$229$		−	2.37919i		−	0.157221i	−0.996905	−	0.0786106i	$-0.974952\pi$
$229$		−	2.37919i		−	0.157221i	0.996905	−	0.0786106i	$-0.0250484\pi$
$230$	5.47963	−	9.49100i	0.361316	−	0.625818i
$231$	0.246254	−	9.17924i	0.0162023	−	0.603950i
$232$	−2.91308	−	5.04560i	−0.191253	−	0.331260i
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	−0.765842	−	0.643029i	$-0.777677\pi$
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	0.173959	+	0.984753i	$0.444344\pi$
$234$	−6.36727	−	8.00210i	−0.416241	−	0.523114i
$235$	4.03593	−	6.99044i	0.263275	−	0.456006i
$236$	−4.49313	+	7.78233i	−0.292478	+	0.506587i
$237$	5.96796	+	2.87801i	0.387661	+	0.186947i
$238$	6.69849	+	14.8988i	0.434198	+	0.965745i
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.985654	−	0.168777i	$-0.0539818\pi$
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.346662	+	0.937990i	$0.387315\pi$
$240$	−5.64655	−	2.72301i	−0.364483	−	0.175770i
$241$			28.6487i			1.84542i	0.385489	+	0.922712i	$0.374033\pi$
$241$			28.6487i			1.84542i	−0.385489	+	0.922712i	$0.625967\pi$
$242$	−6.04902	−	3.49240i	−0.388846	−	0.224500i
$243$	−5.65571	−	14.5263i	−0.362814	−	0.931862i
$244$		−	14.7121i		−	0.941843i
$245$	24.8193	+	5.08685i	1.58565	+	0.324987i
$246$	5.55793	+	8.16149i	0.354360	+	0.520358i
$247$	−3.45333			−0.219730
$248$	−0.454844	−	0.787812i	−0.0288826	−	0.0500261i
$249$	11.4667	−	7.80876i	0.726673	−	0.494860i
$250$	9.71496	+	5.60894i	0.614428	+	0.354740i
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$	−6.67794	+	4.29011i	−0.420671	+	0.270252i
$253$	6.06748			0.381459
$254$	−15.5271	−	8.96458i	−0.974257	−	0.562488i
$255$	34.8628	+	16.8124i	2.18320	+	1.05283i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.0978			−0.941775			−0.470888	−	0.882193i	$-0.656066\pi$
$257$	−15.0978			−0.941775			−0.470888	+	0.882193i	$0.656066\pi$
$258$	8.28919	−	0.616665i	0.516062	−	0.0383919i
$259$	17.7035	−	7.95950i	1.10004	−	0.494579i
$260$			12.3373i			0.765128i
$261$	−13.6770	+	10.8828i	−0.846588	+	0.673629i
$262$	−15.0094	−	8.66567i	−0.927283	−	0.535367i
$263$		−	19.6385i		−	1.21096i	−0.795859	−	0.605482i	$-0.792980\pi$
$263$		−	19.6385i		−	1.21096i	0.795859	−	0.605482i	$-0.207020\pi$
$264$	−0.257486	−	3.46111i	−0.0158472	−	0.213017i
$265$	27.4376	+	15.8411i	1.68548	+	0.973112i
$266$	−0.270464	+	2.66668i	−0.0165832	+	0.163504i
$267$	6.85240	−	4.66644i	0.419360	−	0.285581i
$268$	−4.15821	+	7.20222i	−0.254003	+	0.439946i
$269$	−0.245503	+	0.425223i	−0.0149686	+	0.0259263i	−0.873413	−	0.486981i	$-0.838098\pi$
$269$	−0.245503	+	0.425223i	−0.0149686	+	0.0259263i	0.858444	+	0.512907i	$0.171431\pi$
$270$	−5.57257	+	17.9619i	−0.339136	+	1.09313i
$271$	−12.1927	+	7.03945i	−0.740653	+	0.427616i	−0.822307	−	0.569045i	$-0.807313\pi$
$271$	−12.1927	+	7.03945i	−0.740653	+	0.427616i	0.0816537	+	0.996661i	$0.473980\pi$
$272$	3.08709	+	5.34700i	0.187182	+	0.324209i
$273$	13.3137	+	8.17039i	0.805782	+	0.494495i
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$			16.2296i			0.978683i
$276$	−2.95206	−	4.33493i	−0.177693	−	0.260932i
$277$	30.7200			1.84579			0.922894	−	0.385054i	$-0.125817\pi$
$277$	30.7200			1.84579			0.922894	+	0.385054i	$0.125817\pi$
$278$	−5.04185	−	8.73273i	−0.302390	−	0.523755i
$279$	−2.13551	+	1.69923i	−0.127850	+	0.101730i
$280$	9.52693	+	0.966257i	0.569343	+	0.0577449i
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	−0.281130	−	0.959670i	$-0.590709\pi$
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	0.690534	+	0.723300i	$0.257376\pi$
$282$	−2.17429	−	3.19282i	−0.129477	−	0.190130i
$283$	−9.97303	+	5.75793i	−0.592835	+	0.342273i	−0.766218	−	0.642581i	$-0.777864\pi$
$283$	−9.97303	+	5.75793i	−0.592835	+	0.342273i	0.173383	+	0.984855i	$0.444530\pi$
$284$	−0.403817	+	0.233144i	−0.0239621	+	0.0138345i
$285$	3.57471	+	5.24925i	0.211747	+	0.310939i
$286$	−5.91532	+	3.41521i	−0.349780	+	0.201946i
$287$	−12.2347	−	8.82115i	−0.722193	−	0.520696i
$288$	−2.34752	+	1.86792i	−0.138329	+	0.110068i
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$	21.0867			1.23825
$291$	−11.4640	−	16.8342i	−0.672031	−	0.986839i
$292$		−	4.21492i		−	0.246659i
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	−0.783369	−	0.621557i	$-0.786501\pi$
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	0.929968	+	0.367639i	$0.119834\pi$
$294$	7.35194	−	9.64100i	0.428774	−	0.562275i
$295$	−16.2621	−	28.1667i	−0.946814	−	1.63993i
$296$	6.35359	−	3.66825i	0.369295	−	0.213213i
$297$	−10.1547	+	2.30037i	−0.589237	+	0.133481i
$298$	−5.62376	+	9.74064i	−0.325776	+	0.564260i
$299$	−5.16083	+	8.93882i	−0.298458	+	0.516945i
$300$	11.5953	−	7.89633i	0.669455	−	0.455895i
$301$	−11.5803	+	5.20651i	−0.667480	+	0.300098i
$302$	4.09092	+	2.36189i	0.235406	+	0.135912i
$303$	1.65664	+	22.2684i	0.0951712	+	1.27929i
$304$			1.01308i			0.0581041i
$305$	46.1138	+	26.6238i	2.64047	+	1.52447i
$306$	14.4940	−	11.5329i	0.828569	−	0.659292i
$307$		−	17.5309i		−	1.00054i	−0.865869	−	0.500271i	$-0.833234\pi$
$307$		−	17.5309i		−	1.00054i	0.865869	−	0.500271i	$-0.166766\pi$
$308$	2.17395	+	4.83532i	0.123873	+	0.275518i
$309$	−18.5834	+	1.38250i	−1.05717	+	0.0786474i
$310$	3.29245			0.186998
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	0.999938	−	0.0110959i	$-0.00353200\pi$
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	−0.509579	+	0.860424i	$0.670199\pi$
$312$	5.31804	+	2.56459i	0.301074	+	0.145191i
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	0.703729	−	0.710468i	$-0.251517\pi$
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	−0.263419	+	0.964681i	$0.584850\pi$
$314$	−3.06972			−0.173234
$315$	−1.36221	−	28.6951i	−0.0767520	−	1.61679i
$316$	−3.82533			−0.215192
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	0.327572	−	0.944826i	$-0.393770\pi$
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	−0.654457	+	0.756099i	$0.727103\pi$
$318$	12.5319	−	8.53413i	0.702753	−	0.478570i
$319$	5.83721	+	10.1103i	0.326821	+	0.566071i
$320$	3.61932			0.202326
$321$	−2.57347	−	3.77899i	−0.143637	−	0.210923i
$322$	6.49840	+	4.68530i	0.362142	+	0.261102i
$323$		−	6.25494i		−	0.348034i
$324$	6.58416	+	6.13586i	0.365787	+	0.340881i
$325$	−23.9100	−	13.8045i	−1.32629	−	0.765734i
$326$			2.87373i			0.159161i
$327$	−14.0962	−	6.79780i	−0.779521	−	0.375919i
$328$	−4.93712	−	2.85045i	−0.272607	−	0.157390i
$329$	4.78629	+	3.45088i	0.263876	+	0.190253i
$330$	11.3145	+	5.45636i	0.622844	+	0.300363i
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	−0.483858	−	0.875146i	$-0.660765\pi$
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	0.999828	−	0.0185396i	$-0.00590167\pi$
$332$	−4.00481	+	6.93654i	−0.219793	+	0.380692i
$333$	−13.7040	−	17.2226i	−0.750975	−	0.943792i
$334$	1.26529	−	0.730517i	0.0692338	−	0.0399721i
$335$	−15.0499	−	26.0671i	−0.822262	−	1.42420i
$336$	2.39689	−	3.90575i	0.130761	−	0.213076i
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$			1.38047i			0.0750874i
$339$	−1.27194	+	2.63755i	−0.0690824	+	0.143252i
$340$	−22.3463			−1.21190
$341$	0.911413	+	1.57861i	0.0493558	+	0.0854868i
$342$	3.00578	−	0.449713i	0.162534	−	0.0243177i
$343$	−5.53030	+	17.6753i	−0.298608	+	0.954376i
$344$	−4.15605	+	2.39949i	−0.224079	+	0.129372i
$345$	18.9297	−	1.40826i	1.01914	−	0.0758179i
$346$	2.65940	−	1.53541i	0.142970	−	0.0825440i
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	−0.847736	−	0.530419i	$-0.822035\pi$
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	0.0354887	+	0.999370i	$0.488701\pi$
$348$	4.38334	−	9.08948i	0.234972	−	0.487247i
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.937399	−	0.348257i	$-0.886774\pi$
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.167101	+	0.985940i	$0.553440\pi$
$350$	−12.5325	+	17.3823i	−0.669890	+	0.929122i
$351$	5.24835	−	16.9169i	0.280136	−	0.902958i
$352$	1.00190	+	1.73534i	0.0534013	+	0.0924938i
$353$	10.0412			0.534441			0.267220	−	0.963635i	$-0.413895\pi$
$353$	10.0412			0.534441			0.267220	+	0.963635i	$0.413895\pi$
$354$	−15.5218	+	1.15473i	−0.824973	+	0.0613730i
$355$		−	1.68764i		−	0.0895707i
$356$	−2.39324	+	4.14521i	−0.126841	+	0.219696i
$357$	−14.7989	+	24.1148i	−0.783238	+	1.27629i
$358$	9.65966	+	16.7310i	0.510529	+	0.884262i
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	−0.195521	−	0.980700i	$-0.562640\pi$
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	0.751550	+	0.659676i	$0.229306\pi$
$360$	−1.60664	−	10.7384i	−0.0846774	−	0.565965i
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$	3.94659	−	6.83569i	0.207428	−	0.359276i
$363$	−0.897541	−	12.0647i	−0.0471087	−	0.633233i
$364$	−8.97266	−	0.910040i	−0.470295	−	0.0476990i
$365$	13.2113	+	7.62756i	0.691512	+	0.399245i
$366$	21.0620	−	14.3431i	1.10093	−	0.749727i
$367$			3.63061i			0.189516i	0.995500	+	0.0947582i	$0.0302078\pi$
$367$			3.63061i			0.189516i	−0.995500	+	0.0947582i	$0.969792\pi$
$368$	2.62232	+	1.51400i	0.136698	+	0.0789225i
$369$	−6.26558	+	15.9136i	−0.326173	+	0.828431i
$370$			26.5531i			1.38043i
$371$	−13.5448	+	18.7863i	−0.703210	+	0.975335i
$372$	0.684408	−	1.41922i	0.0354849	−	0.0735830i
$373$	5.49231			0.284381			0.142191	−	0.989839i	$-0.454585\pi$
$373$	5.49231			0.284381			0.142191	+	0.989839i	$0.454585\pi$
$374$	−6.18590	−	10.7143i	−0.319865	−	0.554023i
$375$	1.44149	+	19.3764i	0.0744380	+	1.00059i
$376$	1.93143	+	1.11511i	0.0996057	+	0.0575074i
$377$	−19.8599			−1.02284
$378$	−12.6523	−	5.37773i	−0.650763	−	0.276601i
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$	−3.17542	−	1.83333i	−0.162896	−	0.0940478i
$381$	−2.30388	−	30.9686i	−0.118031	−	1.58657i
$382$	−6.65211	−	11.5218i	−0.340352	−	0.589506i
$383$	9.43067			0.481885			0.240942	−	0.970539i	$-0.422544\pi$
$383$	9.43067			0.481885			0.240942	+	0.970539i	$0.422544\pi$
$384$	0.752355	−	1.56012i	0.0383935	−	0.0796143i
$385$	−19.0900	−	1.93618i	−0.972918	−	0.0986769i
$386$			6.53573i			0.332660i
$387$	8.96414	+	11.2657i	0.455673	+	0.572670i
$388$	10.1835	+	5.87944i	0.516989	+	0.298483i
$389$		−	6.42177i		−	0.325597i	−0.986659	−	0.162798i	$-0.947948\pi$
$389$		−	6.42177i		−	0.325597i	0.986659	−	0.162798i	$-0.0520520\pi$
$390$	−17.6623	+	12.0279i	−0.894366	+	0.609058i
$391$	−16.1907	−	9.34769i	−0.818798	−	0.472733i
$392$	−1.40547	+	6.85745i	−0.0709871	+	0.346354i
$393$	−2.22706	−	29.9360i	−0.112340	−	1.51007i
$394$	−2.22125	+	3.84732i	−0.111905	+	0.193825i
$395$	6.92255	−	11.9902i	0.348311	−	0.603293i
$396$	4.70395	−	3.74293i	0.236383	−	0.188090i
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	−0.341889	−	0.939740i	$-0.611067\pi$
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	0.642895	+	0.765955i	$0.277733\pi$
$398$	−5.75542	−	9.96868i	−0.288493	−	0.499685i
$399$	−4.08134	+	2.21260i	−0.204323	+	0.110769i
$400$	−4.04972	+	7.01433i	−0.202486	+	0.350716i
$401$		−	10.5869i		−	0.528682i	−0.964429	−	0.264341i	$-0.914846\pi$
$401$		−	10.5869i		−	0.528682i	0.964429	−	0.264341i	$-0.0851545\pi$
$402$	−14.3648	+	1.06865i	−0.716449	+	0.0532995i
$403$	−3.10089			−0.154466
$404$	−6.44610	−	11.1650i	−0.320705	−	0.555478i
$405$	−31.1474	+	9.53372i	−1.54773	+	0.473735i
$406$	−1.55542	+	15.3359i	−0.0771943	+	0.761107i
$407$	−12.7313	+	7.35042i	−0.631067	+	0.364347i
$408$	−4.64518	+	9.63244i	−0.229971	+	0.476877i
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	−0.296620	−	0.954996i	$-0.595859\pi$
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	0.678741	+	0.734378i	$0.262526\pi$
$410$	17.8690	−	10.3167i	0.882486	−	0.509504i
$411$	−0.00111431		8.28977e-5i	−5.49647e−5		4.08904e-6i
$412$	9.31740	−	5.37940i	0.459035	−	0.265024i
$413$	21.6846	−	9.74937i	1.06703	−	0.479735i
$414$	3.32793	−	8.45243i	0.163559	−	0.415414i
$415$	−14.4947	−	25.1055i	−0.711516	−	1.23238i
$416$	−3.40874			−0.167127
$417$	7.58652	−	15.7317i	0.371513	−	0.770386i
$418$		−	2.03000i		−	0.0992908i
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	0.0500724	+	0.998746i	$0.484055\pi$
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	−0.889975	+	0.456009i	$0.849279\pi$
$420$	7.90471	+	14.5809i	0.385710	+	0.711477i
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$	−19.5731	+	11.3005i	−0.952803	+	0.550101i
$423$	2.45113	−	6.22550i	0.119178	−	0.302694i
$424$	−4.37683	+	7.58088i	−0.212557	+	0.368160i
$425$	25.0037	−	43.3077i	1.21286	−	2.10073i
$426$	−0.727462	−	0.350814i	−0.0352457	−	0.0169970i
$427$	−22.7644	+	31.5737i	−1.10165	+	1.52796i
$428$	2.28602	+	1.31983i	0.110499	+	0.0637965i
$429$	−10.6563	−	5.13891i	−0.514489	−	0.248109i
$430$		−	17.3691i		−	0.837610i
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.978247	−	0.207442i	$-0.0665138\pi$
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.309474	+	0.950908i	$0.399847\pi$
$432$	−4.96280	−	1.53967i	−0.238773	−	0.0740776i
$433$		−	23.2463i		−	1.11715i	−0.829455	−	0.558574i	$-0.811349\pi$
$433$		−	23.2463i		−	1.11715i	0.829455	−	0.558574i	$-0.188651\pi$
$434$	−0.242861	+	2.39452i	−0.0116577	+	0.114941i
$435$	20.5579	+	30.1881i	0.985676	+	1.44741i
$436$	9.03535			0.432715
$437$	−1.53380	−	2.65662i	−0.0733716	−	0.127083i
$438$	6.03414	−	4.10922i	0.288323	−	0.196346i
$439$	19.2887	+	11.1364i	0.920601	+	0.531509i	0.883827	−	0.467814i	$-0.154958\pi$
$439$	19.2887	+	11.1364i	0.920601	+	0.531509i	0.0367744	+	0.999324i	$0.488292\pi$
$440$	−7.25237			−0.345743
$441$	20.9698	+	1.12594i	0.998562	+	0.0536160i
$442$	21.0462			1.00107
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	0.822077	−	0.569377i	$-0.192815\pi$
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	−0.0820566	+	0.996628i	$0.526149\pi$
$444$	11.4458	+	5.51965i	0.543193	+	0.261951i
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$	18.8209			0.891195
$447$	−19.4276	+	1.44530i	−0.918894	+	0.0683601i
$448$	−0.266972	+	2.63225i	−0.0126133	+	0.124362i
$449$			9.44363i			0.445673i	0.974856	+	0.222836i	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$	22.6090	+	8.90172i	1.06580	+	0.419631i
$451$	9.89297	+	5.71171i	0.465842	+	0.268954i
$452$		−	1.69061i		−	0.0795197i
$453$	0.607002	+	8.15930i	0.0285195	+	0.383357i
$454$	12.6555	+	7.30665i	0.593952	+	0.342918i
$455$	19.0899	−	26.4772i	0.894948	−	1.24127i
$456$	−1.45034	+	0.987674i	−0.0679185	+	0.0462521i
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$	−1.18959	+	2.06044i	−0.0555861	+	0.0962779i
$459$	30.6412	+	9.50623i	1.43021	+	0.443713i
$460$	−9.49100	+	5.47963i	−0.442520	+	0.255489i
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	0.883829	+	0.467810i	$0.154957\pi$
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	−0.0367790	+	0.999323i	$0.511710\pi$
$462$	−4.80288	+	7.82633i	−0.223450	+	0.364114i
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	0.208425	+	0.978038i	$0.433166\pi$
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	−0.951219	+	0.308518i	$0.900167\pi$
$464$			5.82616i			0.270473i
$465$	3.20988	+	4.71352i	0.148855	+	0.218584i
$466$	10.4324			0.483271
$467$	−12.2206	−	21.1666i	−0.565500	−	0.979475i	−0.997003	−	0.0773632i	$-0.975350\pi$
$467$	−12.2206	−	21.1666i	−0.565500	−	0.979475i	0.431503	−	0.902112i	$-0.357983\pi$
$468$	1.51317	+	10.1137i	0.0699461	+	0.467504i
$469$	20.0682	−	9.02263i	0.926662	−	0.416627i
$470$	−6.99044	+	4.03593i	−0.322445	+	0.186164i
$471$	−2.99273	−	4.39466i	−0.137898	−	0.202495i
$472$	7.78233	−	4.49313i	0.358211	−	0.206813i
$473$	8.32786	−	4.80809i	0.382916	−	0.221076i
$474$	−3.72940	−	5.47641i	−0.171297	−	0.251540i
$475$	7.10607	−	4.10269i	0.326049	−	0.188245i
$476$	1.64833	−	16.2520i	0.0755513	−	0.744908i
$477$	24.4352	+	9.62073i	1.11881	+	0.440503i
$478$	−11.8917	−	20.5971i	−0.543916	−	0.942090i
$479$	10.9606			0.500805			0.250402	−	0.968142i	$-0.419437\pi$
$479$	10.9606			0.500805			0.250402	+	0.968142i	$0.419437\pi$
$480$	3.52855	+	5.18147i	0.161056	+	0.236501i
$481$		−	25.0082i		−	1.14028i
$482$	14.3243	−	24.8105i	0.652456	−	1.13009i
$483$	−0.372122	+	13.8710i	−0.0169321	+	0.631153i
$484$	3.49240	+	6.04902i	0.158746	+	0.274955i
$485$	−36.8573	+	21.2796i	−1.67360	+	0.966255i
$486$	−2.36515	+	15.4080i	−0.107286	+	0.698920i
$487$	−16.8087	+	29.1136i	−0.761677	+	1.31926i	0.180309	+	0.983610i	$0.442290\pi$
$487$	−16.8087	+	29.1136i	−0.761677	+	1.31926i	−0.941986	+	0.335653i	$0.891043\pi$
$488$	−7.35603	+	12.7410i	−0.332992	+	0.576759i
$489$	−4.11408	+	2.80167i	−0.186045	+	0.126696i
$490$	−18.9507	−	16.8150i	−0.856105	−	0.759624i
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.0150939	−	0.999886i	$-0.504805\pi$
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.873474	+	0.486871i	$0.838138\pi$
$492$	−0.732559	−	9.84702i	−0.0330263	−	0.443938i
$493$		−	35.9718i		−	1.62009i
$494$	2.99067	+	1.72667i	0.134557	+	0.0776863i
$495$	3.21938	+	21.5176i	0.144700	+	0.967144i
$496$			0.909687i			0.0408462i
$497$	1.22738	+	0.124486i	0.0550557	+	0.00558395i
$498$	−13.8348	+	1.02923i	−0.619954	+	0.0461209i
$499$	19.5235			0.873992			0.436996	−	0.899463i	$-0.356042\pi$
$499$	19.5235			0.873992			0.436996	+	0.899463i	$0.356042\pi$
$500$	−5.60894	−	9.71496i	−0.250839	−	0.434466i
$501$	2.27938	+	1.09922i	0.101835	+	0.0491094i
$502$	−9.55238	−	5.51507i	−0.426343	−	0.246149i
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$	7.92833	−	0.376373i	0.353156	−	0.0167650i
$505$	46.6609			2.07638
$506$	−5.25459	−	3.03374i	−0.233595	−	0.134866i
$507$	−1.97630	+	1.34585i	−0.0877705	+	0.0597712i
$508$	8.96458	+	15.5271i	0.397739	+	0.688904i
$509$	−2.29166			−0.101576			−0.0507881	−	0.998709i	$-0.516173\pi$
$509$	−2.29166			−0.101576			−0.0507881	+	0.998709i	$0.516173\pi$
$510$	−21.7859	−	31.9914i	−0.964697	−	1.41660i
$511$	−6.52186	+	9.04566i	−0.288510	+	0.400156i
$512$			1.00000i			0.0441942i
$513$	3.57422	+	3.86470i	0.157806	+	0.170630i
$514$	13.0751	+	7.54890i	0.576717	+	0.332968i
$515$			38.9395i			1.71588i
$516$	−7.48698	−	3.61054i	−0.329596	−	0.158945i
$517$	−3.87018	−	2.23445i	−0.170210	−	0.0982710i
$518$	−19.3115	−	1.95864i	−0.848497	−	0.0860577i
$519$	4.79082	+	2.31034i	0.210294	+	0.101413i
$520$	6.16866	−	10.6844i	0.270514	−	0.468543i
$521$	−8.54102	+	14.7935i	−0.374189	+	0.648114i	−0.990205	−	0.139619i	$-0.955412\pi$
$521$	−8.54102	+	14.7935i	−0.374189	+	0.648114i	0.616017	+	0.787733i	$0.288745\pi$
$522$	17.2861	−	2.58627i	0.756591	−	0.113198i
$523$	35.7462	−	20.6381i	1.56307	−	0.902440i	0.566128	−	0.824317i	$-0.308441\pi$
$523$	35.7462	−	20.6381i	1.56307	−	0.902440i	0.996944	−	0.0781229i	$-0.0248927\pi$
$524$	8.66567	+	15.0094i	0.378562	+	0.655688i
$525$	−37.1030	−	0.995372i	−1.61931	−	0.0434416i
$526$	−9.81926	+	17.0075i	−0.428140	+	0.741561i
$527$		−	5.61657i		−	0.244662i
$528$	−1.50757	+	3.12615i	−0.0656084	+	0.136048i
$529$	13.8313			0.601359
$530$	−15.8411	−	27.4376i	−0.688094	−	1.19181i
$531$	−16.7857	−	21.0955i	−0.728435	−	0.915465i
$532$	1.56757	−	2.17418i	0.0679627	−	0.0942626i
$533$	−16.8294	+	9.71644i	−0.728961	+	0.420866i
$534$	−8.26757	+	0.615057i	−0.357773	+	0.0266161i
$535$	−8.27382	+	4.77689i	−0.357708	+	0.206523i
$536$	7.20222	−	4.15821i	0.311089	−	0.179607i
$537$	−14.5350	+	30.1404i	−0.627231	+	1.30065i
$538$	0.425223	−	0.245503i	0.0183327	−	0.0105844i
$539$	2.81628	−	13.7409i	0.121306	−	0.591864i
$540$	13.8070	−	12.7692i	0.594157	−	0.549500i
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.673880	+	0.738841i	$0.264627\pi$
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.302915	+	0.953018i	$0.402040\pi$
$542$	14.0789			0.604741
$543$	13.6337	−	1.01427i	0.585078	−	0.0435263i
$544$		−	6.17418i		−	0.264716i
$545$	−16.3509	+	28.3206i	−0.700395	+	1.21312i
$546$	−7.44481	−	13.7326i	−0.318609	−	0.587702i
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	0.984061	+	0.177832i	$0.0569082\pi$
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	−0.338024	+	0.941138i	$0.609758\pi$
$548$	0.000558693	0	0.000322562i	2.38662e−5	0	1.37791e-5i
$549$	41.0677	+	16.1693i	1.75273	+	0.690091i
$550$	8.11481	−	14.0553i	0.346017	−	0.599319i
$551$	2.95118	−	5.11160i	0.125725	−	0.217761i
$552$	0.389094	+	5.23019i	0.0165610	+	0.222612i
$553$	8.20958	+	5.91905i	0.349107	+	0.251704i
$554$	−26.6043	−	15.3600i	−1.13031	−	0.652585i
$555$	−38.0139	+	25.8872i	−1.61360	+	1.09885i
$556$			10.0837i			0.427644i
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.0451189	−	0.998982i	$-0.514367\pi$
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.887703	+	0.460417i	$0.847700\pi$
$558$	2.69902	−	0.403817i	0.114259	−	0.0170949i
$559$			16.3585i			0.691892i
$560$	−7.76744	−	5.60027i	−0.328234	−	0.236655i
$561$	9.30799	−	19.3014i	0.392983	−	0.814907i
$562$	−7.92455			−0.334277
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	0.894839	−	0.446390i	$-0.147290\pi$
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	−0.834004	+	0.551758i	$0.813957\pi$
$564$	0.286581	+	3.85221i	0.0120672	+	0.162207i
$565$	5.29909	+	3.05943i	0.222934	+	0.128711i
$566$	11.5159			0.484048
$567$	−4.63613	−	23.3561i	−0.194699	−	0.980863i
$568$	0.466287			0.0195650
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.987445	−	0.157963i	$-0.949507\pi$
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.630523	−	0.776171i	$-0.717159\pi$
$570$	−0.471162	−	6.33333i	−0.0197348	−	0.265274i
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	0.926216	−	0.376992i	$-0.123042\pi$
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	−0.789593	+	0.613631i	$0.789708\pi$
$572$	6.83042			0.285594
$573$	10.0095	−	20.7561i	0.418153	−	0.867100i
$574$	6.18501	+	13.7567i	0.258157	+	0.574194i
$575$		−	24.5251i		−	1.02277i
$576$	2.96698	−	0.443907i	0.123624	−	0.0184961i
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	0.524304	−	0.851531i	$-0.324326\pi$
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	−0.475296	+	0.879826i	$0.657659\pi$
$578$			21.1205i			0.878498i
$579$	−9.35666	+	6.37183i	−0.388850	+	0.264804i
$580$	−18.2616	−	10.5434i	−0.758273	−	0.437789i
$581$	19.3279	−	8.68979i	0.801855	−	0.360513i
$582$	1.51101	+	20.3109i	0.0626332	+	0.841912i
$583$	8.77026	−	15.1905i	0.363227	−	0.629128i
$584$	−2.10746	+	3.65022i	−0.0872072	+	0.151047i
$585$	−34.4388	−	13.5594i	−1.42387	−	0.560611i
$586$	−4.34636	+	2.50937i	−0.179547	+	0.103661i
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.804843	−	0.593488i	$-0.797750\pi$
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.111555	−	0.993758i	$-0.535583\pi$
$588$	−11.1875	+	4.67338i	−0.461364	+	0.192727i
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$			32.5241i			1.33900i
$591$	−7.67343	+	0.570857i	−0.315643	+	0.0234819i
$592$	−7.33650			−0.301528
$593$	−7.17564	−	12.4286i	−0.294668	−	0.510380i	0.680240	−	0.732990i	$-0.261876\pi$
$593$	−7.17564	−	12.4286i	−0.294668	−	0.510380i	−0.974908	+	0.222610i	$0.928542\pi$
$594$	9.94444	+	3.08519i	0.408025	+	0.126587i
$595$	47.9576	+	34.5771i	1.96607	+	1.41752i
$596$	9.74064	−	5.62376i	0.398992	−	0.230358i
$597$	8.66024	−	17.9582i	0.354440	−	0.734982i
$598$	8.93882	−	5.16083i	0.365535	−	0.211042i
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	−0.560691	−	0.828025i	$-0.689464\pi$
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	0.436746	+	0.899585i	$0.356131\pi$
$600$	−13.9900	+	1.04077i	−0.571139	+	0.0424893i
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	−0.776633	−	0.629953i	$-0.783074\pi$
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	0.157239	+	0.987561i	$0.449741\pi$
$602$	12.6321	+	1.28120i	0.514847	+	0.0522177i
$603$	−15.5344	−	19.5230i	−0.632610	−	0.795037i
$604$	−2.36189	−	4.09092i	−0.0961041	−	0.166457i
$605$	−25.2802			−1.02779
$606$	9.69952	−	20.1133i	0.394016	−	0.817048i
$607$		−	0.0872864i		−	0.00354285i	−0.999998	−	0.00177142i	$-0.999436\pi$
$607$		−	0.0872864i		−	0.00354285i	0.999998	−	0.00177142i	$-0.000563862\pi$
$608$	0.506540	−	0.877353i	0.0205429	−	0.0355814i
$609$	−23.4715	+	12.7245i	−0.951114	+	0.515624i
$610$	−26.6238	−	46.1138i	−1.07797	−	1.86709i
$611$	6.58373	−	3.80112i	0.266349	−	0.153777i
$612$	−18.3186	+	2.74076i	−0.740488	+	0.110789i
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	−0.493681	−	0.869643i	$-0.664349\pi$
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	0.999973	−	0.00728071i	$-0.00231754\pi$
$614$	−8.76545	+	15.1822i	−0.353745	+	0.612704i
$615$	32.1904	+	15.5236i	1.29804	+	0.625972i
$616$	0.534957	−	5.27448i	0.0215541	−	0.212515i
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	0.270373	−	0.962756i	$-0.412853\pi$
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	−0.698584	+	0.715528i	$0.746186\pi$
$618$	16.7850	+	8.09444i	0.675191	+	0.325606i
$619$		−	20.3076i		−	0.816229i	−0.912931	−	0.408115i	$-0.866186\pi$
$619$		−	20.3076i		−	0.816229i	0.912931	−	0.408115i	$-0.133814\pi$
$620$	−2.85134	−	1.64622i	−0.114513	−	0.0661139i
$621$	15.3451	−	3.47615i	0.615778	−	0.139493i
$622$		−	17.2952i		−	0.693474i
$623$	11.5501	−	5.19294i	0.462747	−	0.208051i
$624$	−3.32326	−	4.88001i	−0.133037	−	0.195357i
$625$	0.103794			0.00415176
$626$	−4.49749	−	7.78988i	−0.179756	−	0.311346i
$627$	2.90619	−	1.97910i	0.116062	−	0.0790375i
$628$	2.65845	+	1.53486i	0.106084	+	0.0612475i
$629$	45.2969			1.80610
$630$	−13.1678	+	25.5318i	−0.524620	+	1.01721i
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$	3.31284	+	1.91267i	0.131778	+	0.0760818i
$633$	−35.2603	−	17.0040i	−1.40147	−	0.675850i
$634$	3.36019	+	5.82002i	0.133450	+	0.231143i
$635$	−64.8913			−2.57513
$636$	−15.1200	+	1.12484i	−0.599546	+	0.0446026i
$637$	17.8482	+	15.8367i	0.707169	+	0.627472i
$638$		−	11.6744i		−	0.462195i
$639$	−0.206988	−	1.38346i	−0.00818833	−	0.0547290i
$640$	−3.13442	−	1.80966i	−0.123899	−	0.0715330i
$641$			31.6509i			1.25013i	0.780571	+	0.625067i	$0.214928\pi$
$641$			31.6509i			1.25013i	−0.780571	+	0.625067i	$0.785072\pi$
$642$	0.339195	+	4.55944i	0.0133869	+	0.179947i
$643$	10.0106	+	5.77960i	0.394778	+	0.227925i	0.684228	−	0.729268i	$-0.260139\pi$
$643$	10.0106	+	5.77960i	0.394778	+	0.227925i	−0.289450	+	0.957193i	$0.593472\pi$
$644$	−3.28513	−	7.30679i	−0.129452	−	0.287928i
$645$	24.8658	−	16.9335i	0.979091	−	0.666755i
$646$	−3.12747	+	5.41694i	−0.123049	+	0.213127i
$647$	13.0365	−	22.5799i	0.512519	−	0.887708i	−0.487376	−	0.873192i	$-0.662046\pi$
$647$	13.0365	−	22.5799i	0.512519	−	0.887708i	0.999895	−	0.0145160i	$-0.00462076\pi$
$648$	−2.63412	−	8.60589i	−0.103478	−	0.338071i
$649$	−15.5942	+	9.00332i	−0.612126	+	0.353411i
$650$	13.8045	+	23.9100i	0.541456	+	0.937829i
$651$	−3.66481	+	1.98679i	−0.143635	+	0.0778684i
$652$	1.43687	−	2.48873i	0.0562720	−	0.0974660i
$653$			18.9315i			0.740847i	0.928863	+	0.370424i	$0.120788\pi$
$653$			18.9315i			0.740847i	−0.928863	+	0.370424i	$0.879212\pi$
$654$	8.80877	+	12.9352i	0.344450	+	0.505805i
$655$	−62.7276			−2.45097
$656$	2.85045	+	4.93712i	0.111291	+	0.192762i
$657$	11.7656	+	4.63242i	0.459021	+	0.180728i
$658$	−2.41961	−	5.38169i	−0.0943260	−	0.209800i
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.0293098	−	0.999570i	$-0.490669\pi$
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.880308	+	0.474402i	$0.157336\pi$
$660$	−7.07049	−	10.3826i	−0.275219	−	0.404142i
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.00141768	−	0.999999i	$-0.499549\pi$
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.866733	+	0.498772i	$0.166215\pi$
$662$	−16.2592	+	9.38725i	−0.631931	+	0.364846i
$663$	20.5184	+	30.1301i	0.796869	+	1.17016i
$664$	6.93654	−	4.00481i	0.269190	−	0.155417i
$665$	3.97803	+	8.84793i	0.154261	+	0.343108i
$666$	3.25672	+	21.7672i	0.126195	+	0.843462i
$667$	−8.82079	−	15.2780i	−0.341542	−	0.591568i
$668$	−1.46103			−0.0565291
$669$	18.3489	+	26.9443i	0.709410	+	1.04173i
$670$			30.0997i			1.16285i
$671$	14.7400	−	25.5304i	0.569030	−	0.985590i
$672$	−4.02865	+	2.18403i	−0.155408	+	0.0842510i
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$	−4.19654	+	2.42287i	−0.161645	+	0.0933256i
$675$	9.29820	+	41.0460i	0.357888	+	1.57986i
$676$	0.690233	−	1.19552i	0.0265474	−	0.0459815i
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	−0.712161	−	0.702016i	$-0.752283\pi$
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	0.964044	+	0.265741i	$0.0856166\pi$
$678$	2.42031	−	1.64822i	0.0929514	−	0.0632993i
$679$	−12.7574	−	28.3751i	−0.489585	−	1.08894i
$680$	19.3525	+	11.1732i	0.742134	+	0.428471i
$681$	1.87780	+	25.2412i	0.0719573	+	0.967246i
$682$		−	1.82283i		−	0.0697996i
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.0798523	−	0.996807i	$-0.525445\pi$
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.903186	+	0.429249i	$0.858778\pi$
$684$	−2.82794	−	1.11343i	−0.108129	−	0.0425730i
$685$			0.00233490i			8.92121e-5i
$686$	13.6270	−	12.5421i	0.520282	−	0.478859i
$687$	−4.10952	+	0.305723i	−0.156788	+	0.0116641i
$688$	4.79899			0.182960
$689$	14.9195	+	25.8413i	0.568387	+	0.984475i
$690$	−17.0977	−	8.24526i	−0.650899	−	0.313892i
$691$	40.9767	+	23.6579i	1.55883	+	0.899990i	0.997369	+	0.0724857i	$0.0230932\pi$
$691$	40.9767	+	23.6579i	1.55883	+	0.899990i	0.561459	+	0.827504i	$0.310240\pi$
$692$	−3.07081			−0.116735
$693$	−15.8867	+	0.754174i	−0.603487	+	0.0286487i
$694$	17.4712			0.663197
$695$	−31.6065	−	18.2480i	−1.19890	−	0.692187i
$696$	−8.34083	+	5.68005i	−0.316158	+	0.215302i
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$	23.8258			0.901820
$699$	10.1708	+	14.9352i	0.384693	+	0.564900i
$700$	19.5446	−	8.78724i	0.738717	−	0.332127i
$701$			13.7742i			0.520244i	0.965576	+	0.260122i	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$	−13.0037	+	12.0263i	−0.490792	+	0.453904i
$703$	6.43670	+	3.71623i	0.242765	+	0.140160i
$704$		−	2.00379i		−	0.0755209i
$705$	−12.5930	−	6.07291i	−0.474281	−	0.228719i
$706$	−8.69596	−	5.02061i	−0.327277	−	0.188953i
$707$	−3.44186	+	33.9355i	−0.129444	+	1.27627i
$708$	14.0196	+	6.76087i	0.526889	+	0.254089i
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$	−0.843820	+	1.46154i	−0.0316680	+	0.0548506i
$711$	4.20425	−	10.6782i	0.157672	−	0.400462i
$712$	4.14521	−	2.39324i	0.155348	−	0.0896903i
$713$	−1.37726	−	2.38549i	−0.0515789	−	0.0893373i
$714$	24.8736	−	13.4846i	0.930871	−	0.504649i
$715$	−12.3607	+	21.4094i	−0.462265	+	0.800667i
$716$		−	19.3193i		−	0.721997i
$717$	17.8936	−	37.1050i	0.668250	−	1.38571i
$718$	−12.1651			−0.453997
$719$	14.7930	+	25.6223i	0.551687	+	0.955549i	0.998153	+	0.0607489i	$0.0193489\pi$
$719$	14.7930	+	25.6223i	0.551687	+	0.955549i	−0.446466	+	0.894800i	$0.647318\pi$
$720$	−3.97782	+	10.1031i	−0.148245	+	0.376519i
$721$	−28.3198	−	2.87230i	−1.05469	−	0.106970i
$722$	15.5657	−	8.98683i	0.579294	−	0.334455i
$723$	49.4843	−	3.68133i	1.84034	−	0.136910i
$724$	−6.83569	+	3.94659i	−0.254046	+	0.146674i
$725$	40.8666	−	23.5943i	1.51775	−	0.876271i
$726$	−5.25506	+	10.8971i	−0.195033	+	0.404430i
$727$	−10.1244	+	5.84534i	−0.375494	+	0.216792i	−0.675856	−	0.737034i	$-0.736226\pi$
$727$	−10.1244	+	5.84534i	−0.375494	+	0.216792i	0.300362	+	0.953825i	$0.402893\pi$
$728$	7.31553	+	5.27445i	0.271132	+	0.195484i
$729$	−24.3642	+	11.6356i	−0.902377	+	0.430948i
$730$	−7.62756	−	13.2113i	−0.282308	−	0.488973i
$731$	−29.6298			−1.09590
$732$	−25.4118	+	1.89049i	−0.939248	+	0.0698744i
$733$			33.0733i			1.22159i	0.791789	+	0.610795i	$0.209150\pi$
$733$			33.0733i			1.22159i	−0.791789	+	0.610795i	$0.790850\pi$
$734$	1.81531	−	3.14420i	0.0670042	−	0.116055i
$735$	5.59715	−	43.5234i	0.206454	−	1.60539i
$736$	−1.51400	−	2.62232i	−0.0558067	−	0.0966600i
$737$	−14.4318	+	8.33219i	−0.531601	+	0.306920i
$738$	13.3830	−	10.6488i	0.492634	−	0.391989i
$739$	−21.7528	+	37.6770i	−0.800190	+	1.38597i	0.119301	+	0.992858i	$0.461935\pi$
$739$	−21.7528	+	37.6770i	−0.800190	+	1.38597i	−0.919491	+	0.393111i	$0.871399\pi$
$740$	13.2765	−	22.9957i	0.488056	−	0.845337i
$741$	0.443750	+	5.96486i	0.0163016	+	0.219125i
$742$	21.1233	−	9.49700i	0.775459	−	0.348646i
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	0.792701	−	0.609611i	$-0.208674\pi$
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	−0.131589	+	0.991304i	$0.542008\pi$
$744$	−1.30232	+	0.886874i	−0.0477455	+	0.0325144i
$745$			40.7083i			1.49144i
$746$	−4.75648	−	2.74616i	−0.174147	−	0.100544i
$747$	−14.9614	−	18.8028i	−0.547408	−	0.687958i
$748$			12.3718i			0.452358i
$749$	−2.86382	−	6.36972i	−0.104642	−	0.232745i
$750$	8.43983	−	17.5012i	0.308179	−	0.639053i
$751$	−39.8984			−1.45591			−0.727957	−	0.685623i	$-0.759530\pi$
$751$	−39.8984			−1.45591			−0.727957	+	0.685623i	$0.759530\pi$
$752$	−1.11511	−	1.93143i	−0.0406638	−	0.0704318i
$753$	−1.41736	−	19.0521i	−0.0516515	−	0.694297i
$754$	17.1992	+	9.92994i	0.626357	+	0.361627i
$755$	17.0969			0.622219
$756$	8.26832	+	10.9834i	0.300716	+	0.399462i
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$	13.5065	+	7.79800i	0.490579	+	0.283236i
$759$	−0.779665	−	10.4802i	−0.0283001	−	0.380408i
$760$	1.83333	+	3.17542i	0.0665018	+	0.115185i
$761$	−8.64924			−0.313535			−0.156767	−	0.987636i	$-0.550107\pi$
$761$	−8.64924			−0.313535			−0.156767	+	0.987636i	$0.550107\pi$
$762$	−13.4891	+	27.9716i	−0.488658	+	1.01330i
$763$	−19.3908	−	13.9807i	−0.701995	−	0.506134i
$764$			13.3042i			0.481330i
$765$	24.5598	−	62.3782i	0.887961	−	2.25529i
$766$	−8.16720	−	4.71534i	−0.295093	−	0.170372i
$767$		−	30.6319i		−	1.10605i
$768$	−1.43162	+	0.974922i	−0.0516590	+	0.0351795i
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	0.0829652	−	0.996552i	$-0.473561\pi$
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	−0.821557	+	0.570126i	$0.806894\pi$
$770$	15.5644	+	11.2218i	0.560900	+	0.404405i
$771$	1.94005	+	26.0781i	0.0698693	+	0.939180i
$772$	3.26786	−	5.66011i	0.117613	−	0.203712i
$773$	−23.2849	+	40.3307i	−0.837501	+	1.45059i	0.0544774	+	0.998515i	$0.482651\pi$
$773$	−23.2849	+	40.3307i	−0.837501	+	1.45059i	−0.891978	+	0.452079i	$0.850683\pi$
$774$	−2.13030	−	14.2385i	−0.0765722	−	0.511792i
$775$	6.38084	−	3.68398i	0.229207	−	0.132333i
$776$	−5.87944	−	10.1835i	−0.211060	−	0.365566i
$777$	−16.0232	−	29.5561i	−0.574828	−	1.06032i
$778$	−3.21089	+	5.56142i	−0.115116	+	0.199387i
$779$		−	5.77546i		−	0.206927i
$780$	21.3100	−	1.58533i	0.763020	−	0.0567641i
$781$	−0.934344			−0.0334335
$782$	9.34769	+	16.1907i	0.334273	+	0.578977i
$783$	20.5551	+	22.2256i	0.734580	+	0.794279i
$784$	4.64590	−	5.23599i	0.165925	−	0.187000i
$785$	−9.62178	+	5.55513i	−0.343416	+	0.198271i
$786$	−13.0393	+	27.0389i	−0.465098	+	0.964446i
$787$	−21.1657	+	12.2200i	−0.754474	+	0.435596i	−0.827308	−	0.561748i	$-0.810129\pi$
$787$	−21.1657	+	12.2200i	−0.754474	+	0.435596i	0.0728341	+	0.997344i	$0.476796\pi$
$788$	3.84732	−	2.22125i	0.137055	−	0.0791288i
$789$	−33.9212	+	2.52353i	−1.20763	+	0.0898401i
$790$	−11.9902	+	6.92255i	−0.426592	+	0.246293i
$791$	−2.61593	+	3.62823i	−0.0930118	+	0.129005i
$792$	−5.94521	+	0.889499i	−0.211254	+	0.0316070i
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$	−6.92531			−0.245770
$795$	23.8363	−	49.4279i	0.845386	−	1.75303i
$796$			11.5108i			0.407991i
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.0344128	−	0.999408i	$-0.489044\pi$
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.848306	−	0.529506i	$-0.177623\pi$
$798$	4.64085	+	0.124501i	0.164284	+	0.00440730i
$799$	6.88489	+	11.9250i	0.243570	+	0.421875i
$800$	7.01433	−	4.04972i	0.247994	−	0.143179i
$801$	−8.94076	−	11.2364i	−0.315906	−	0.397017i
$802$	−5.29343	+	9.16848i	−0.186917	+	0.323750i
$803$	4.22291	−	7.31430i	0.149023	−	0.258116i
$804$	12.9746	+	6.25690i	0.457578	+	0.220664i
$805$	28.8475	+	2.92582i	1.01674	+	0.103122i
$806$	2.68545	+	1.55045i	0.0945910	+	0.0546121i
$807$	0.766025	+	0.369410i	0.0269654	+	0.0130039i
$808$			12.8922i			0.453546i
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	0.675755	−	0.737127i	$-0.263818\pi$
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	−0.300493	+	0.953784i	$0.597151\pi$
$810$	31.7413	+	7.31728i	1.11528	+	0.257103i
$811$		−	24.8017i		−	0.870906i	−0.900212	−	0.435453i	$-0.856588\pi$
$811$		−	24.8017i		−	0.870906i	0.900212	−	0.435453i	$-0.143412\pi$
$812$	9.01498	−	12.5036i	0.316364	−	0.438789i
$813$	13.7258	+	20.1556i	0.481386	+	0.706888i
$814$	14.7008			0.515264
$815$	5.20047	+	9.00748i	0.182165	+	0.315518i
$816$	8.83906	−	6.01935i	0.309429	−	0.210719i
$817$	−4.21041	−	2.43088i	−0.147304	−	0.0850457i
$818$	−8.92343			−0.312000
$819$	12.4017	−	24.0464i	0.433352	−	0.840248i
$820$	−20.6333			−0.720547
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.934738	−	0.355336i	$-0.115634\pi$
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.159639	+	0.987175i	$0.448967\pi$
$822$	0.00100647		0.000485362i	3.51046e−5		1.69289e-5i
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	0.983016	−	0.183519i	$-0.0587489\pi$
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	−0.650440	+	0.759557i	$0.725416\pi$
$824$	−10.7588			−0.374801
$825$	28.0331	−	2.08549i	0.975986	−	0.0726075i
$826$	−23.6541	−	2.39908i	−0.823030	−	0.0834748i
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$	−7.10829	+	5.65606i	−0.247030	+	0.196562i
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	0.709412	−	0.704794i	$-0.248961\pi$
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	−0.255664	+	0.966766i	$0.582294\pi$
$830$			28.9894i			1.00624i
$831$	−3.94750	−	53.0620i	−0.136937	−	1.84070i
$832$	2.95206	+	1.70437i	0.102344	+	0.0590885i
$833$	−28.6846	+	32.3280i	−0.993864	+	1.12010i
$834$	−14.4360	+	9.83082i	−0.499877	+	0.340413i
$835$	2.64397	−	4.57950i	0.0914985	−	0.158480i
$836$	−1.01500	+	1.75804i	−0.0351046	+	0.0608029i
$837$	3.20945	+	3.47027i	0.110935	+	0.119950i
$838$	29.7781	−	17.1924i	1.02867	−	0.593901i
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	0.972134	−	0.234427i	$-0.0753214\pi$
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	−0.689087	+	0.724679i	$0.741988\pi$
$840$	0.444792	−	16.5798i	0.0153468	−	0.572058i
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$			35.5680i			1.22575i
$843$	−7.72582	−	11.3449i	−0.266091	−	0.390740i
$844$	22.6011			0.777961
$845$	2.49817	+	4.32696i	0.0859397	+	0.148852i
$846$	−5.23549	+	4.16587i	−0.180000	+	0.143226i
$847$	1.86475	−	18.3857i	0.0640735	−	0.631741i
$848$	7.58088	−	4.37683i	0.260329	−	0.150301i
$849$	11.2271	+	16.4863i	0.385312	+	0.565808i
$850$	−43.3077	+	25.0037i	−1.48544	+	0.857621i
$851$	19.2386	−	11.1074i	0.659492	−	0.380758i
$852$	0.454594	+	0.667545i	0.0155741	+	0.0228697i
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	−0.756411	−	0.654096i	$-0.773049\pi$
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	0.188258	+	0.982120i	$0.439716\pi$
$854$	35.5014	−	15.9614i	1.21483	−	0.546188i
$855$	8.60756	−	6.84903i	0.294372	−	0.234232i
$856$	−1.31983	−	2.28602i	−0.0451110	−	0.0781345i
$857$	16.1145			0.550460			0.275230	−	0.961378i	$-0.411246\pi$
$857$	16.1145			0.550460			0.275230	+	0.961378i	$0.411246\pi$
$858$	6.65913	+	9.77855i	0.227339	+	0.333834i
$859$		−	12.1048i		−	0.413009i	−0.978446	−	0.206505i	$-0.933791\pi$
$859$		−	12.1048i		−	0.413009i	0.978446	−	0.206505i	$-0.0662089\pi$
$860$	−8.68453	+	15.0420i	−0.296140	+	0.512929i
$861$	−13.6644	+	22.2663i	−0.465682	+	0.758833i
$862$	−15.4348	−	26.7338i	−0.525710	−	0.910556i
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.935848	−	0.352405i	$-0.885364\pi$
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.162732	+	0.986670i	$0.552031\pi$
$864$	3.52808	+	3.81480i	0.120028	+	0.129782i
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$	−11.6232	+	20.1319i	−0.394971	+	0.684110i
$867$	−30.2365	+	20.5909i	−1.02689	+	0.699303i
$868$	1.40758	−	1.95229i	0.0477765	−	0.0662649i
$869$	−6.63824	−	3.83259i	−0.225187	−	0.130012i
$870$	−2.70962	−	36.4226i	−0.0918648	−	1.23484i
$871$		−	28.3485i		−	0.960553i
$872$	−7.82484	−	4.51768i	−0.264983	−	0.152988i
$873$	−27.6043	+	21.9647i	−0.934262	+	0.743392i
$874$			3.06760i			0.103763i
$875$	−2.99486	+	29.5282i	−0.101245	+	0.998236i
$876$	−7.28033	+	0.541613i	−0.245980	+	0.0182994i
$877$	−9.70948			−0.327866			−0.163933	−	0.986471i	$-0.552418\pi$
$877$	−9.70948			−0.327866			−0.163933	+	0.986471i	$0.552418\pi$
$878$	−11.1364	−	19.2887i	−0.375834	−	0.650963i
$879$	−7.82983	−	3.77588i	−0.264094	−	0.127357i
$880$	6.28073	+	3.62618i	0.211723	+	0.122239i
$881$	2.63241			0.0886881			0.0443440	−	0.999016i	$-0.485880\pi$
$881$	2.63241			0.0886881			0.0443440	+	0.999016i	$0.485880\pi$
$882$	−17.5974	−	11.4600i	−0.592536	−	0.385878i
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$	−18.2265	−	10.5231i	−0.613025	−	0.353930i
$885$	−46.5621	+	31.7085i	−1.56517	+	1.06587i
$886$	−8.99259	−	15.5756i	−0.302112	−	0.523273i
$887$	−16.3642			−0.549455			−0.274728	−	0.961522i	$-0.588588\pi$
$887$	−16.3642			−0.549455			−0.274728	+	0.961522i	$0.588588\pi$
$888$	−7.15251	−	10.5031i	−0.240023	−	0.352459i
$889$	4.78659	−	47.1940i	0.160537	−	1.58284i
$890$			17.3238i			0.580694i
$891$	5.27824	+	17.2444i	0.176828	+	0.577711i
$892$	−16.2994	−	9.41045i	−0.545744	−	0.315085i
$893$			2.25939i			0.0756076i
$894$	17.5474	+	8.46213i	0.586874	+	0.283016i
$895$	60.5549	+	34.9614i	2.02413	+	1.16863i
$896$	1.54733	−	2.14611i	0.0516926	−	0.0716964i
$897$	16.1030	+	7.76555i	0.537663	+	0.259284i
$898$	4.72182	−	8.17843i	0.157569	−	0.272918i
$899$	2.64999	−	4.58992i	0.0883822	−	0.153082i
$900$	−15.1291	−	19.0136i	−0.504305	−	0.633788i
$901$	−46.8058	+	27.0233i	−1.55933	+	0.900277i
$902$	−5.71171	−	9.89297i	−0.190179	−	0.329400i
$903$	10.4812	+	19.3334i	0.348791	+	0.643376i
$904$	−0.845306	+	1.46411i	−0.0281145	+	0.0486957i
$905$		−	28.5679i		−	0.949629i
$906$	3.55397	−	7.36966i	0.118073	−	0.244840i
$907$	10.8333			0.359714			0.179857	−	0.983693i	$-0.442436\pi$
$907$	10.8333			0.359714			0.179857	+	0.983693i	$0.442436\pi$
$908$	−7.30665	−	12.6555i	−0.242480	−	0.419987i
$909$	38.2509	−	5.72294i	1.26870	−	0.189818i
$910$	−29.7709	+	13.3850i	−0.986897	+	0.443708i
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.255817	−	0.966725i	$-0.417655\pi$
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.965117	+	0.261818i	$0.0843221\pi$
$912$	1.74987	−	0.130180i	0.0579440	−	0.00431069i
$913$	−13.8994	+	8.02482i	−0.460003	+	0.265583i
$914$	−1.59739	+	0.922251i	−0.0528368	+	0.0305053i
$915$	40.0611	−	83.0724i	1.32438	−	2.74629i
$916$	2.06044	−	1.18959i	0.0680788	−	0.0393053i
$917$	4.62699	−	45.6204i	0.152797	−	1.50652i
$918$	−21.7830	−	23.5533i	−0.718946	−	0.777373i
$919$	−12.9697	−	22.4641i	−0.427829	−	0.741022i	0.568851	−	0.822441i	$-0.307388\pi$
$919$	−12.9697	−	22.4641i	−0.427829	−	0.741022i	−0.996680	+	0.0814187i	$0.974055\pi$
$920$	10.9593			0.361316
$921$	−30.2807	+	2.25271i	−0.997785	+	0.0742292i
$922$		−	36.3739i		−	1.19791i
$923$	0.794727	−	1.37651i	0.0261588	−	0.0453083i
$924$	8.07258	−	4.37636i	0.265568	−	0.143972i
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$	27.6834	−	15.9830i	0.909733	−	0.525234i
$927$	4.77591	+	31.9211i	0.156861	+	1.04843i
$928$	2.91308	−	5.04560i	0.0956265	−	0.165630i
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	−0.168760	−	0.985657i	$-0.553976\pi$
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	0.937984	−	0.346678i	$-0.112690\pi$
$930$	−0.423076	−	5.68697i	−0.0138732	−	0.186483i
$931$	−6.72834	+	2.24048i	−0.220512	+	0.0734287i
$932$	−9.03470	−	5.21619i	−0.295942	−	0.170862i
$933$	24.7601	−	16.8615i	0.810608	−	0.552019i
$934$			24.4411i			0.799738i
$935$	−38.7784	−	22.3887i	−1.26819	−	0.732189i
$936$	3.74639	−	9.51527i	0.122455	−	0.311016i
$937$		−	0.209357i		−	0.00683939i	−0.999994	−	0.00341969i	$-0.998911\pi$
$937$		−	0.209357i		−	0.00683939i	0.999994	−	0.00341969i	$-0.00108852\pi$
$938$	−21.8909	−	2.22025i	−0.714762	−	0.0724938i
$939$	6.76742	−	14.0332i	0.220846	−	0.457956i
$940$	8.07186			0.263275
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	0.859622	−	0.510930i	$-0.170699\pi$
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	−0.872289	+	0.488990i	$0.837365\pi$
$942$	0.394456	+	5.30225i	0.0128521	+	0.172757i
$943$	−14.9496	−	8.63113i	−0.486825	−	0.281068i
$944$	−8.98627			−0.292478
$945$	−49.3894	+	6.04021i	−1.60664	+	0.196488i
$946$	−9.61619			−0.312649
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.994528	−	0.104470i	$-0.0333145\pi$
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.406791	+	0.913521i	$0.366648\pi$
$948$	0.491552	+	6.60741i	0.0159649	+	0.214599i
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$	−8.20539			−0.266218
$951$	−5.05612	+	10.4846i	−0.163956	+	0.339986i
$952$	−9.55349	+	13.2505i	−0.309630	+	0.429450i
$953$			41.4104i			1.34141i	0.741722	+	0.670707i	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$	−16.3511	−	20.5494i	−0.529388	−	0.665311i
$955$	−41.7010	−	24.0761i	−1.34941	−	0.779084i
$956$			23.7835i			0.769213i
$957$	16.7133	−	11.3817i	0.540264	−	0.367917i
$958$	−9.49220	−	5.48032i	−0.306679	−	0.177061i
$959$	−0.00169812		0.000172230i	−5.48353e−5		5.56160e-6i
$960$	−0.465079	−	6.25156i	−0.0150103	−	0.201768i
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$	−12.5041	+	21.6578i	−0.403149	+	0.698274i
$963$	−6.19668	+	4.93069i	−0.199685	+	0.158889i
$964$	−24.8105	+	14.3243i	−0.799092	+	0.461356i
$965$	11.8274	+	20.4857i	0.380739	+	0.659459i
$966$	7.25778	−	11.8266i	0.233515	−	0.380514i
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	−0.222181	−	0.975005i	$-0.571318\pi$
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	0.955470	−	0.295088i	$-0.0953491\pi$
$968$		−	6.98481i		−	0.224500i
$969$	−10.8040	+	0.803754i	−0.347075	+	0.0258203i
$970$	42.5591			1.36649
$971$	4.36733	+	7.56444i	0.140154	+	0.242754i	0.927555	−	0.373688i	$-0.121907\pi$
$971$	4.36733	+	7.56444i	0.140154	+	0.242754i	−0.787400	+	0.616442i	$0.788573\pi$
$972$	9.75228	−	12.1611i	0.312804	−	0.390068i
$973$	15.6028	−	21.6407i	0.500202	−	0.693768i
$974$	29.1136	−	16.8087i	0.932860	−	0.538587i
$975$	−20.7717	+	43.0731i	−0.665228	+	1.37944i
$976$	12.7410	−	7.35603i	0.407830	−	0.235461i
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	−0.692031	−	0.721867i	$-0.743284\pi$
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	0.279140	+	0.960250i	$0.409951\pi$
$978$	4.96373	−	0.369272i	0.158723	−	0.0118080i
$979$	−8.30615	+	4.79556i	−0.265466	+	0.153267i
$980$	8.00430	+	24.0376i	0.255688	+	0.767852i
$981$	−9.93033	+	25.2216i	−0.317051	+	0.805262i
$982$	11.3676	+	19.6893i	0.362756	+	0.628312i
$983$	−3.06917			−0.0978912			−0.0489456	−	0.998801i	$-0.515586\pi$
$983$	−3.06917			−0.0978912			−0.0489456	+	0.998801i	$0.515586\pi$
$984$	−4.28910	+	8.89405i	−0.136731	+	0.283532i
$985$			16.0788i			0.512314i
$986$	−17.9859	+	31.1525i	−0.572787	+	0.992096i
$987$	5.34559	−	8.71068i	0.170152	−	0.277264i
$988$	−1.72667	−	2.99067i	−0.0549325	−	0.0951460i
$989$	−12.5845	+	7.26565i	−0.400163	+	0.231034i
$990$	7.97074	−	20.2445i	0.253327	−	0.643412i
$991$	27.9075	−	48.3372i	0.886510	−	1.53548i	0.0425375	−	0.999095i	$-0.486456\pi$
$991$	27.9075	−	48.3372i	0.886510	−	1.53548i	0.843973	−	0.536386i	$-0.180211\pi$
$992$	0.454844	−	0.787812i	0.0144413	−	0.0250131i
$993$	−29.2904	−	14.1251i	−0.929502	−	0.448246i
$994$	−1.00070	−	0.721500i	−0.0317404	−	0.0228846i
$995$	−36.0798	−	20.8307i	−1.14381	−	0.660377i
$996$	12.4959	+	6.02608i	0.395949	+	0.190944i
$997$			6.12692i			0.194042i	0.995282	+	0.0970208i	$0.0309313\pi$
$997$			6.12692i			0.194042i	−0.995282	+	0.0970208i	$0.969069\pi$
$998$	−16.9079	−	9.76175i	−0.535209	−	0.309003i
$999$	−27.9872	+	25.8837i	−0.885477	+	0.818924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.t.a.59.2	yes	16
3.2	odd	2		378.2.t.a.17.8		16
4.3	odd	2		1008.2.df.c.689.5		16
7.2	even	3		882.2.l.b.509.8		16
7.3	odd	6		882.2.m.b.293.7		16
7.4	even	3		882.2.m.a.293.6		16
7.5	odd	6		126.2.l.a.5.5	✓	16
7.6	odd	2		882.2.t.a.815.3		16
9.2	odd	6		126.2.l.a.101.1	yes	16
9.4	even	3		1134.2.k.b.647.8		16
9.5	odd	6		1134.2.k.a.647.1		16
9.7	even	3		378.2.l.a.143.8		16
12.11	even	2		3024.2.df.c.17.7		16
21.2	odd	6		2646.2.l.a.1097.1		16
21.5	even	6		378.2.l.a.341.4		16
21.11	odd	6		2646.2.m.a.881.1		16
21.17	even	6		2646.2.m.b.881.4		16
21.20	even	2		2646.2.t.b.2285.5		16
28.19	even	6		1008.2.ca.c.257.8		16
36.7	odd	6		3024.2.ca.c.2033.7		16
36.11	even	6		1008.2.ca.c.353.8		16
63.2	odd	6		882.2.t.a.803.3		16
63.5	even	6		1134.2.k.b.971.8		16
63.11	odd	6		882.2.m.b.587.7		16
63.16	even	3		2646.2.t.b.1979.5		16
63.20	even	6		882.2.l.b.227.4		16
63.25	even	3		2646.2.m.b.1763.4		16
63.34	odd	6		2646.2.l.a.521.5		16
63.38	even	6		882.2.m.a.587.6		16
63.40	odd	6		1134.2.k.a.971.1		16
63.47	even	6	inner	126.2.t.a.47.2	yes	16
63.52	odd	6		2646.2.m.a.1763.1		16
63.61	odd	6		378.2.t.a.89.8		16
84.47	odd	6		3024.2.ca.c.2609.7		16
252.47	odd	6		1008.2.df.c.929.5		16
252.187	even	6		3024.2.df.c.1601.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	7.5	odd	6
126.2.l.a.101.1	yes	16	9.2	odd	6
126.2.t.a.47.2	yes	16	63.47	even	6	inner
126.2.t.a.59.2	yes	16	1.1	even	1	trivial
378.2.l.a.143.8		16	9.7	even	3
378.2.l.a.341.4		16	21.5	even	6
378.2.t.a.17.8		16	3.2	odd	2
378.2.t.a.89.8		16	63.61	odd	6
882.2.l.b.227.4		16	63.20	even	6
882.2.l.b.509.8		16	7.2	even	3
882.2.m.a.293.6		16	7.4	even	3
882.2.m.a.587.6		16	63.38	even	6
882.2.m.b.293.7		16	7.3	odd	6
882.2.m.b.587.7		16	63.11	odd	6
882.2.t.a.803.3		16	63.2	odd	6
882.2.t.a.815.3		16	7.6	odd	2
1008.2.ca.c.257.8		16	28.19	even	6
1008.2.ca.c.353.8		16	36.11	even	6
1008.2.df.c.689.5		16	4.3	odd	2
1008.2.df.c.929.5		16	252.47	odd	6
1134.2.k.a.647.1		16	9.5	odd	6
1134.2.k.a.971.1		16	63.40	odd	6
1134.2.k.b.647.8		16	9.4	even	3
1134.2.k.b.971.8		16	63.5	even	6
2646.2.l.a.521.5		16	63.34	odd	6
2646.2.l.a.1097.1		16	21.2	odd	6
2646.2.m.a.881.1		16	21.11	odd	6
2646.2.m.a.1763.1		16	63.52	odd	6
2646.2.m.b.881.4		16	21.17	even	6
2646.2.m.b.1763.4		16	63.25	even	3
2646.2.t.b.1979.5		16	63.16	even	3
2646.2.t.b.2285.5		16	21.20	even	2
3024.2.ca.c.2033.7		16	36.7	odd	6
3024.2.ca.c.2609.7		16	84.47	odd	6
3024.2.df.c.17.7		16	12.11	even	2
3024.2.df.c.1601.7		16	252.187	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.128499 - 1.72728i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.61932 q^{5} +(-0.752355 + 1.56012i) q^{6} +(0.266972 - 2.63225i) q^{7} -1.00000i q^{8} +(-2.96698 + 0.443907i) q^{9} +(3.13442 + 1.80966i) q^{10} +2.00379i q^{11} +(1.43162 - 0.974922i) q^{12} +(-2.95206 - 1.70437i) q^{13} +(-1.54733 + 2.14611i) q^{14} +(0.465079 + 6.25156i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.08709 - 5.34700i) q^{17} +(2.79143 + 1.09905i) q^{18} +(0.877353 - 0.506540i) q^{19} +(-1.80966 - 3.13442i) q^{20} +(-4.58093 - 0.122894i) q^{21} +(1.00190 - 1.73534i) q^{22} -3.02799i q^{23} +(-1.72728 + 0.128499i) q^{24} +8.09945 q^{25} +(1.70437 + 2.95206i) q^{26} +(1.14800 + 5.06775i) q^{27} +(2.41308 - 1.08492i) q^{28} +(5.04560 - 2.91308i) q^{29} +(2.72301 - 5.64655i) q^{30} +(0.787812 - 0.454844i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.46111 - 0.257486i) q^{33} +(-5.34700 + 3.08709i) q^{34} +(-0.966257 + 9.52693i) q^{35} +(-1.86792 - 2.34752i) q^{36} +(3.66825 + 6.35359i) q^{37} -1.01308 q^{38} +(-2.56459 + 5.31804i) q^{39} +3.61932i q^{40} +(2.85045 - 4.93712i) q^{41} +(3.90575 + 2.39689i) q^{42} +(-2.39949 - 4.15605i) q^{43} +(-1.73534 + 1.00190i) q^{44} +(10.7384 - 1.60664i) q^{45} +(-1.51400 + 2.62232i) q^{46} +(-1.11511 + 1.93143i) q^{47} +(1.56012 + 0.752355i) q^{48} +(-6.85745 - 1.40547i) q^{49} +(-7.01433 - 4.04972i) q^{50} +(-9.63244 - 4.64518i) q^{51} -3.40874i q^{52} +(-7.58088 - 4.37683i) q^{53} +(1.53967 - 4.96280i) q^{54} -7.25237i q^{55} +(-2.63225 - 0.266972i) q^{56} +(-0.987674 - 1.45034i) q^{57} -5.82616 q^{58} +(4.49313 + 7.78233i) q^{59} +(-5.18147 + 3.52855i) q^{60} +(-12.7410 - 7.35603i) q^{61} -0.909687 q^{62} +(0.376373 + 7.92833i) q^{63} -1.00000 q^{64} +(10.6844 + 6.16866i) q^{65} +(-3.12615 - 1.50757i) q^{66} +(4.15821 + 7.20222i) q^{67} +6.17418 q^{68} +(-5.23019 + 0.389094i) q^{69} +(5.60027 - 7.76744i) q^{70} +0.466287i q^{71} +(0.443907 + 2.96698i) q^{72} +(-3.65022 - 2.10746i) q^{73} -7.33650i q^{74} +(-1.04077 - 13.9900i) q^{75} +(0.877353 + 0.506540i) q^{76} +(5.27448 + 0.534957i) q^{77} +(4.88001 - 3.32326i) q^{78} +(-1.91267 + 3.31284i) q^{79} +(1.80966 - 3.13442i) q^{80} +(8.60589 - 2.63412i) q^{81} +(-4.93712 + 2.85045i) q^{82} +(4.00481 + 6.93654i) q^{83} +(-2.18403 - 4.02865i) q^{84} +(-11.1732 + 19.3525i) q^{85} +4.79899i q^{86} +(-5.68005 - 8.34083i) q^{87} +2.00379 q^{88} +(2.39324 + 4.14521i) q^{89} +(-10.1031 - 3.97782i) q^{90} +(-5.27445 + 7.31553i) q^{91} +(2.62232 - 1.51400i) q^{92} +(-0.886874 - 1.30232i) q^{93} +(1.93143 - 1.11511i) q^{94} +(-3.17542 + 1.83333i) q^{95} +(-0.974922 - 1.43162i) q^{96} +(10.1835 - 5.87944i) q^{97} +(5.23599 + 4.64590i) q^{98} +(-0.889499 - 5.94521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

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