LMFDB - Embedded newform 430.2.j.a.49.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(49,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("430.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.j (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.12
Character	$\chi$	$=$	430.49
Dual form			430.2.j.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-2.36034 - 1.36274i) q^{3} -1.00000 q^{4} +(-1.55068 - 1.61102i) q^{5} +(1.36274 - 2.36034i) q^{6} +(2.77719 - 1.60341i) q^{7} -1.00000i q^{8} +(2.21413 + 3.83499i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-2.36034 - 1.36274i) q^{3} -1.00000 q^{4} +(-1.55068 - 1.61102i) q^{5} +(1.36274 - 2.36034i) q^{6} +(2.77719 - 1.60341i) q^{7} -1.00000i q^{8} +(2.21413 + 3.83499i) q^{9} +(1.61102 - 1.55068i) q^{10} -0.912389 q^{11} +(2.36034 + 1.36274i) q^{12} +(-4.63472 + 2.67585i) q^{13} +(1.60341 + 2.77719i) q^{14} +(1.46472 + 5.91573i) q^{15} +1.00000 q^{16} +(-1.04642 + 0.604151i) q^{17} +(-3.83499 + 2.21413i) q^{18} +(-1.17935 + 2.04270i) q^{19} +(1.55068 + 1.61102i) q^{20} -8.74013 q^{21} -0.912389i q^{22} +(0.0863270 + 0.0498409i) q^{23} +(-1.36274 + 2.36034i) q^{24} +(-0.190781 + 4.99636i) q^{25} +(-2.67585 - 4.63472i) q^{26} -3.89271i q^{27} +(-2.77719 + 1.60341i) q^{28} +(-4.05319 - 7.02033i) q^{29} +(-5.91573 + 1.46472i) q^{30} +(-4.12477 + 7.14430i) q^{31} +1.00000i q^{32} +(2.15355 + 1.24335i) q^{33} +(-0.604151 - 1.04642i) q^{34} +(-6.88965 - 1.98773i) q^{35} +(-2.21413 - 3.83499i) q^{36} +(0.0240969 + 0.0139123i) q^{37} +(-2.04270 - 1.17935i) q^{38} +14.5860 q^{39} +(-1.61102 + 1.55068i) q^{40} -0.174537 q^{41} -8.74013i q^{42} +(0.613453 + 6.52868i) q^{43} +0.912389 q^{44} +(2.74484 - 9.51386i) q^{45} +(-0.0498409 + 0.0863270i) q^{46} +7.23055i q^{47} +(-2.36034 - 1.36274i) q^{48} +(1.64184 - 2.84375i) q^{49} +(-4.99636 - 0.190781i) q^{50} +3.29321 q^{51} +(4.63472 - 2.67585i) q^{52} +(-1.00900 - 0.582544i) q^{53} +3.89271 q^{54} +(1.41482 + 1.46988i) q^{55} +(-1.60341 - 2.77719i) q^{56} +(5.56735 - 3.21431i) q^{57} +(7.02033 - 4.05319i) q^{58} +1.44431 q^{59} +(-1.46472 - 5.91573i) q^{60} +(-3.43693 - 5.95294i) q^{61} +(-7.14430 - 4.12477i) q^{62} +(12.2981 + 7.10032i) q^{63} -1.00000 q^{64} +(11.4978 + 3.31723i) q^{65} +(-1.24335 + 2.15355i) q^{66} +(14.0178 + 8.09318i) q^{67} +(1.04642 - 0.604151i) q^{68} +(-0.135841 - 0.235283i) q^{69} +(1.98773 - 6.88965i) q^{70} +(-0.176907 - 0.306412i) q^{71} +(3.83499 - 2.21413i) q^{72} +(-10.0014 + 5.77430i) q^{73} +(-0.0139123 + 0.0240969i) q^{74} +(7.25906 - 11.5331i) q^{75} +(1.17935 - 2.04270i) q^{76} +(-2.53387 + 1.46293i) q^{77} +14.5860i q^{78} +(-7.17235 - 12.4229i) q^{79} +(-1.55068 - 1.61102i) q^{80} +(1.33763 - 2.31685i) q^{81} -0.174537i q^{82} +(-9.42282 - 5.44026i) q^{83} +8.74013 q^{84} +(2.59596 + 0.748961i) q^{85} +(-6.52868 + 0.613453i) q^{86} +22.0938i q^{87} +0.912389i q^{88} +(-2.18480 + 3.78418i) q^{89} +(9.51386 + 2.74484i) q^{90} +(-8.58098 + 14.8627i) q^{91} +(-0.0863270 - 0.0498409i) q^{92} +(19.4717 - 11.2420i) q^{93} -7.23055 q^{94} +(5.11964 - 1.26761i) q^{95} +(1.36274 - 2.36034i) q^{96} -17.1148i q^{97} +(2.84375 + 1.64184i) q^{98} +(-2.02015 - 3.49900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−2.36034	−	1.36274i	−1.36274	−	0.786780i	−0.372754	−	0.927930i	$-0.621586\pi$
$3$	−2.36034	−	1.36274i	−1.36274	−	0.786780i	−0.989988	+	0.141151i	$0.954920\pi$
$4$	−1.00000			−0.500000
$5$	−1.55068	−	1.61102i	−0.693485	−	0.720471i
$5$	−1.55068	−	1.61102i	−0.693485	−	0.720471i
$6$	1.36274	−	2.36034i	0.556337	−	0.963604i
$7$	2.77719	−	1.60341i	1.04968	−	0.606032i	0.127119	−	0.991888i	$-0.459427\pi$
$7$	2.77719	−	1.60341i	1.04968	−	0.606032i	0.922559	+	0.385856i	$0.126094\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.21413	+	3.83499i	0.738044	+	1.27833i
$10$	1.61102	−	1.55068i	0.509450	−	0.490368i
$11$	−0.912389			−0.275096			−0.137548	−	0.990495i	$-0.543922\pi$
$11$	−0.912389			−0.275096			−0.137548	+	0.990495i	$0.543922\pi$
$12$	2.36034	+	1.36274i	0.681371	+	0.393390i
$13$	−4.63472	+	2.67585i	−1.28544	+	0.742149i	−0.977837	−	0.209367i	$-0.932860\pi$
$13$	−4.63472	+	2.67585i	−1.28544	+	0.742149i	−0.307602	+	0.951515i	$0.599526\pi$
$14$	1.60341	+	2.77719i	0.428529	+	0.742234i
$15$	1.46472	+	5.91573i	0.378190	+	1.52744i
$16$	1.00000			0.250000
$17$	−1.04642	+	0.604151i	−0.253794	+	0.146528i	−0.621500	−	0.783414i	$-0.713477\pi$
$17$	−1.04642	+	0.604151i	−0.253794	+	0.146528i	0.367706	+	0.929942i	$0.380143\pi$
$18$	−3.83499	+	2.21413i	−0.903916	+	0.521876i
$19$	−1.17935	+	2.04270i	−0.270563	+	0.468628i	−0.969006	−	0.247037i	$-0.920543\pi$
$19$	−1.17935	+	2.04270i	−0.270563	+	0.468628i	0.698443	+	0.715665i	$0.253876\pi$
$20$	1.55068	+	1.61102i	0.346743	+	0.360235i
$21$	−8.74013			−1.90725
$22$		−	0.912389i		−	0.194522i
$23$	0.0863270	+	0.0498409i	0.0180004	+	0.0103925i	0.508973	−	0.860782i	$-0.330025\pi$
$23$	0.0863270	+	0.0498409i	0.0180004	+	0.0103925i	−0.490973	+	0.871175i	$0.663359\pi$
$24$	−1.36274	+	2.36034i	−0.278169	+	0.481802i
$25$	−0.190781	+	4.99636i	−0.0381561	+	0.999272i
$26$	−2.67585	−	4.63472i	−0.524778	−	0.908943i
$27$		−	3.89271i		−	0.749153i
$28$	−2.77719	+	1.60341i	−0.524839	+	0.303016i
$29$	−4.05319	−	7.02033i	−0.752659	−	1.30364i	−0.946530	−	0.322616i	$-0.895438\pi$
$29$	−4.05319	−	7.02033i	−0.752659	−	1.30364i	0.193871	−	0.981027i	$-0.437896\pi$
$30$	−5.91573	+	1.46472i	−1.08006	+	0.267421i
$31$	−4.12477	+	7.14430i	−0.740830	+	1.28315i	0.211288	+	0.977424i	$0.432234\pi$
$31$	−4.12477	+	7.14430i	−0.740830	+	1.28315i	−0.952118	+	0.305731i	$0.901099\pi$
$32$			1.00000i			0.176777i
$33$	2.15355	+	1.24335i	0.374884	+	0.216440i
$34$	−0.604151	−	1.04642i	−0.103611	−	0.179460i
$35$	−6.88965	−	1.98773i	−1.16456	−	0.335988i
$36$	−2.21413	−	3.83499i	−0.369022	−	0.639165i
$37$	0.0240969	+	0.0139123i	0.00396150	+	0.00228718i	0.501979	−	0.864880i	$-0.332605\pi$
$37$	0.0240969	+	0.0139123i	0.00396150	+	0.00228718i	−0.498018	+	0.867167i	$0.665939\pi$
$38$	−2.04270	−	1.17935i	−0.331370	−	0.191317i
$39$	14.5860			2.33563
$40$	−1.61102	+	1.55068i	−0.254725	+	0.245184i
$41$	−0.174537			−0.0272580			−0.0136290	−	0.999907i	$-0.504338\pi$
$41$	−0.174537			−0.0272580			−0.0136290	+	0.999907i	$0.504338\pi$
$42$		−	8.74013i		−	1.34863i
$43$	0.613453	+	6.52868i	0.0935507	+	0.995615i
$43$	0.613453	+	6.52868i	0.0935507	+	0.995615i
$44$	0.912389			0.137548
$45$	2.74484	−	9.51386i	0.409176	−	1.41824i
$46$	−0.0498409	+	0.0863270i	−0.00734864	+	0.0127282i
$47$			7.23055i			1.05468i	0.849653	+	0.527342i	$0.176811\pi$
$47$			7.23055i			1.05468i	−0.849653	+	0.527342i	$0.823189\pi$
$48$	−2.36034	−	1.36274i	−0.340686	−	0.196695i
$49$	1.64184	−	2.84375i	0.234549	−	0.406250i
$50$	−4.99636	−	0.190781i	−0.706592	−	0.0269805i
$51$	3.29321			0.461142
$52$	4.63472	−	2.67585i	0.642719	−	0.371074i
$53$	−1.00900	−	0.582544i	−0.138596	−	0.0800185i	0.429099	−	0.903258i	$-0.358831\pi$
$53$	−1.00900	−	0.582544i	−0.138596	−	0.0800185i	−0.567695	+	0.823239i	$0.692165\pi$
$54$	3.89271			0.529731
$55$	1.41482	+	1.46988i	0.190775	+	0.198198i
$56$	−1.60341	−	2.77719i	−0.214265	−	0.371117i
$57$	5.56735	−	3.21431i	0.737414	−	0.425746i
$58$	7.02033	−	4.05319i	0.921815	−	0.532210i
$59$	1.44431			0.188034			0.0940168	−	0.995571i	$-0.470029\pi$
$59$	1.44431			0.188034			0.0940168	+	0.995571i	$0.470029\pi$
$60$	−1.46472	−	5.91573i	−0.189095	−	0.763718i
$61$	−3.43693	−	5.95294i	−0.440054	−	0.762196i	0.557639	−	0.830084i	$-0.311707\pi$
$61$	−3.43693	−	5.95294i	−0.440054	−	0.762196i	−0.997693	+	0.0678875i	$0.978374\pi$
$62$	−7.14430	−	4.12477i	−0.907328	−	0.523846i
$63$	12.2981	+	7.10032i	1.54942	+	0.894556i
$64$	−1.00000			−0.125000
$65$	11.4978	+	3.31723i	1.42613	+	0.411452i
$66$	−1.24335	+	2.15355i	−0.153046	+	0.265083i
$67$	14.0178	+	8.09318i	1.71255	+	0.988739i	0.931099	+	0.364768i	$0.118852\pi$
$67$	14.0178	+	8.09318i	1.71255	+	0.988739i	0.781447	+	0.623971i	$0.214482\pi$
$68$	1.04642	−	0.604151i	0.126897	−	0.0732641i
$69$	−0.135841	−	0.235283i	−0.0163533	−	0.0283247i
$70$	1.98773	−	6.88965i	0.237579	−	0.823471i
$71$	−0.176907	−	0.306412i	−0.0209950	−	0.0363644i	0.855337	−	0.518072i	$-0.173350\pi$
$71$	−0.176907	−	0.306412i	−0.0209950	−	0.0363644i	−0.876332	+	0.481708i	$0.840017\pi$
$72$	3.83499	−	2.21413i	0.451958	−	0.260938i
$73$	−10.0014	+	5.77430i	−1.17057	+	0.675831i	−0.953815	−	0.300394i	$-0.902882\pi$
$73$	−10.0014	+	5.77430i	−1.17057	+	0.675831i	−0.216759	+	0.976225i	$0.569549\pi$
$74$	−0.0139123	+	0.0240969i	−0.00161728	+	0.00280121i
$75$	7.25906	−	11.5331i	0.838204	−	1.33173i
$76$	1.17935	−	2.04270i	0.135281	−	0.234314i
$77$	−2.53387	+	1.46293i	−0.288762	+	0.166717i
$78$			14.5860i			1.65154i
$79$	−7.17235	−	12.4229i	−0.806953	−	1.39768i	−0.914965	−	0.403534i	$-0.867782\pi$
$79$	−7.17235	−	12.4229i	−0.806953	−	1.39768i	0.108012	−	0.994150i	$-0.465552\pi$
$80$	−1.55068	−	1.61102i	−0.173371	−	0.180118i
$81$	1.33763	−	2.31685i	0.148626	−	0.257428i
$82$		−	0.174537i		−	0.0192743i
$83$	−9.42282	−	5.44026i	−1.03429	−	0.597147i	−0.116078	−	0.993240i	$-0.537032\pi$
$83$	−9.42282	−	5.44026i	−1.03429	−	0.597147i	−0.918210	+	0.396093i	$0.870366\pi$
$84$	8.74013			0.953627
$85$	2.59596	+	0.748961i	0.281572	+	0.0812362i
$86$	−6.52868	+	0.613453i	−0.704006	+	0.0661503i
$87$			22.0938i			2.36871i
$88$			0.912389i			0.0972610i
$89$	−2.18480	+	3.78418i	−0.231588	+	0.401122i	−0.958276	−	0.285846i	$-0.907725\pi$
$89$	−2.18480	+	3.78418i	−0.231588	+	0.401122i	0.726688	+	0.686968i	$0.241059\pi$
$90$	9.51386	+	2.74484i	1.00285	+	0.289331i
$91$	−8.58098	+	14.8627i	−0.899531	+	1.55803i
$92$	−0.0863270	−	0.0498409i	−0.00900021	−	0.00519627i
$93$	19.4717	−	11.2420i	2.01912	−	1.16574i
$94$	−7.23055			−0.745774
$95$	5.11964	−	1.26761i	0.525264	−	0.130054i
$96$	1.36274	−	2.36034i	0.139084	−	0.240901i
$97$		−	17.1148i		−	1.73774i	−0.495038	−	0.868872i	$-0.664846\pi$
$97$		−	17.1148i		−	1.73774i	0.495038	−	0.868872i	$-0.335154\pi$
$98$	2.84375	+	1.64184i	0.287262	+	0.165851i
$99$	−2.02015	−	3.49900i	−0.203033	−	0.351663i
$100$	0.190781	−	4.99636i	0.0190781	−	0.499636i
$101$	−5.64277	−	9.77357i	−0.561477	−	0.972506i	−0.997368	−	0.0725069i	$-0.976900\pi$
$101$	−5.64277	−	9.77357i	−0.561477	−	0.972506i	0.435891	−	0.899999i	$-0.356433\pi$
$102$			3.29321i			0.326076i
$103$	−0.728016	+	0.420320i	−0.0717335	+	0.0414154i	−0.535438	−	0.844575i	$-0.679853\pi$
$103$	−0.728016	+	0.420320i	−0.0717335	+	0.0414154i	0.463704	+	0.885990i	$0.346520\pi$
$104$	2.67585	+	4.63472i	0.262389	+	0.454471i
$105$	13.5532	+	14.0805i	1.32265	+	1.37412i
$106$	0.582544	−	1.00900i	0.0565816	−	0.0980023i
$107$		−	12.9755i		−	1.25439i	−0.778863	−	0.627194i	$-0.784203\pi$
$107$		−	12.9755i		−	1.25439i	0.778863	−	0.627194i	$-0.215797\pi$
$108$			3.89271i			0.374577i
$109$	−6.92931	+	12.0019i	−0.663708	+	1.14958i	0.315926	+	0.948784i	$0.397685\pi$
$109$	−6.92931	+	12.0019i	−0.663708	+	1.14958i	−0.979634	+	0.200792i	$0.935649\pi$
$110$	−1.46988	+	1.41482i	−0.140147	+	0.134898i
$111$	−0.0379179	−	0.0656757i	−0.00359901	−	0.00623366i
$112$	2.77719	−	1.60341i	0.262419	−	0.151508i
$113$		−	19.8182i		−	1.86434i	−0.362026	−	0.932168i	$-0.617915\pi$
$113$		−	19.8182i		−	1.86434i	0.362026	−	0.932168i	$-0.382085\pi$
$114$	3.21431	+	5.56735i	0.301048	+	0.521430i
$115$	−0.0535708	−	0.216362i	−0.00499550	−	0.0201759i
$116$	4.05319	+	7.02033i	0.376329	+	0.651822i
$117$	−20.5238	−	11.8494i	−1.89742	−	1.09548i
$118$			1.44431i			0.132960i
$119$	−1.93740	+	3.35568i	−0.177601	+	0.307615i
$120$	5.91573	−	1.46472i	0.540030	−	0.133710i
$121$	−10.1675			−0.924322
$122$	5.95294	−	3.43693i	0.538954	−	0.311165i
$123$	0.411965	+	0.237848i	0.0371457	+	0.0214461i
$124$	4.12477	−	7.14430i	0.370415	−	0.641577i
$125$	8.34508	−	7.44040i	0.746407	−	0.665490i
$126$	−7.10032	+	12.2981i	−0.632547	+	1.09560i
$127$			10.0188i			0.889025i	0.895773	+	0.444513i	$0.146623\pi$
$127$			10.0188i			0.889025i	−0.895773	+	0.444513i	$0.853377\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	7.44895	−	16.2459i	0.655844	−	1.43037i
$130$	−3.31723	+	11.4978i	−0.290941	+	1.00843i
$131$	3.61614			0.315943			0.157972	−	0.987444i	$-0.449505\pi$
$131$	3.61614			0.315943			0.157972	+	0.987444i	$0.449505\pi$
$132$	−2.15355	−	1.24335i	−0.187442	−	0.108220i
$133$			7.56395i			0.655878i
$134$	−8.09318	+	14.0178i	−0.699144	+	1.21095i
$135$	−6.27124	+	6.03635i	−0.539743	+	0.519527i
$136$	0.604151	+	1.04642i	0.0518055	+	0.0897298i
$137$			19.3504i			1.65322i	0.562776	+	0.826610i	$0.309733\pi$
$137$			19.3504i			1.65322i	−0.562776	+	0.826610i	$0.690267\pi$
$138$	0.235283	−	0.135841i	0.0200286	−	0.0115635i
$139$	−3.23013	+	5.59475i	−0.273976	+	0.474540i	−0.969876	−	0.243598i	$-0.921672\pi$
$139$	−3.23013	+	5.59475i	−0.273976	+	0.474540i	0.695900	+	0.718138i	$0.255006\pi$
$140$	6.88965	+	1.98773i	0.582282	+	0.167994i
$141$	9.85337	−	17.0665i	0.829804	−	1.43726i
$142$	0.306412	−	0.176907i	0.0257135	−	0.0148457i
$143$	4.22866	−	2.44142i	0.353619	−	0.204162i
$144$	2.21413	+	3.83499i	0.184511	+	0.319582i
$145$	−5.02470	+	17.4161i	−0.417279	+	1.44633i
$146$	−5.77430	−	10.0014i	−0.477885	−	0.827721i
$147$	−7.75060	+	4.47481i	−0.639259	+	0.369076i
$148$	−0.0240969	−	0.0139123i	−0.00198075	−	0.00114359i
$149$	−8.83430	+	15.3015i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$149$	−8.83430	+	15.3015i	−0.723734	+	1.25354i	−0.959493	+	0.281732i	$0.909091\pi$
$150$	11.5331	+	7.25906i	0.941675	+	0.592699i
$151$	14.8850			1.21133			0.605663	−	0.795721i	$-0.292908\pi$
$151$	14.8850			1.21133			0.605663	+	0.795721i	$0.292908\pi$
$152$	2.04270	+	1.17935i	0.165685	+	0.0956583i
$153$	−4.63383	−	2.67534i	−0.374623	−	0.216289i
$154$	−1.46293	−	2.53387i	−0.117886	−	0.204185i
$155$	17.9058	−	4.43345i	1.43823	−	0.356103i
$156$	−14.5860			−1.16781
$157$	−14.1940	+	8.19492i	−1.13281	+	0.654026i	−0.944639	−	0.328111i	$-0.893588\pi$
$157$	−14.1940	+	8.19492i	−1.13281	+	0.654026i	−0.188167	+	0.982137i	$0.560255\pi$
$158$	12.4229	−	7.17235i	0.988311	−	0.570602i
$159$	1.58771	+	2.75000i	0.125914	+	0.218089i
$160$	1.61102	−	1.55068i	0.127362	−	0.122592i
$161$	0.319661			0.0251928
$162$	2.31685	+	1.33763i	0.182029	+	0.105094i
$163$	12.8133	−	7.39776i	1.00362	−	0.579438i	0.0942993	−	0.995544i	$-0.469939\pi$
$163$	12.8133	−	7.39776i	1.00362	−	0.579438i	0.909316	+	0.416106i	$0.136606\pi$
$164$	0.174537			0.0136290
$165$	−1.33640	−	5.39745i	−0.104038	−	0.420191i
$166$	5.44026	−	9.42282i	0.422246	−	0.731352i
$167$	−11.6885	−	6.74836i	−0.904483	−	0.522204i	−0.0258313	−	0.999666i	$-0.508223\pi$
$167$	−11.6885	−	6.74836i	−0.904483	−	0.522204i	−0.878652	+	0.477463i	$0.841557\pi$
$168$			8.74013i			0.674316i
$169$	7.82040	−	13.5453i	0.601569	−	1.04195i
$170$	−0.748961	+	2.59596i	−0.0574427	+	0.199101i
$171$	−10.4450			−0.798748
$172$	−0.613453	−	6.52868i	−0.0467753	−	0.497807i
$173$		−	8.02239i		−	0.609931i	−0.952363	−	0.304965i	$-0.901355\pi$
$173$		−	8.02239i		−	0.609931i	0.952363	−	0.304965i	$-0.0986449\pi$
$174$	−22.0938			−1.67493
$175$	7.48137	+	14.1817i	0.565539	+	1.07204i
$176$	−0.912389			−0.0687739
$177$	−3.40907	−	1.96823i	−0.256241	−	0.147941i
$178$	−3.78418	−	2.18480i	−0.283636	−	0.163757i
$179$	0.332592	+	0.576066i	0.0248591	+	0.0430572i	0.878187	−	0.478317i	$-0.158753\pi$
$179$	0.332592	+	0.576066i	0.0248591	+	0.0430572i	−0.853328	+	0.521374i	$0.825420\pi$
$180$	−2.74484	+	9.51386i	−0.204588	+	0.709121i
$181$	−6.04735	−	10.4743i	−0.449496	−	0.778550i	0.548857	−	0.835916i	$-0.315063\pi$
$181$	−6.04735	−	10.4743i	−0.449496	−	0.778550i	−0.998353	+	0.0573661i	$0.981730\pi$
$182$	−14.8627	−	8.58098i	−1.10170	−	0.636064i
$183$			18.7346i			1.38490i
$184$	0.0498409	−	0.0863270i	0.00367432	−	0.00636411i
$185$	−0.0149535	−	0.0603942i	−0.00109940	−	0.00444027i
$186$	11.2420	+	19.4717i	0.824302	+	1.42773i
$187$	0.954743	−	0.551221i	0.0698177	−	0.0403093i
$188$		−	7.23055i		−	0.527342i
$189$	−6.24161	−	10.8108i	−0.454010	−	0.786369i
$190$	1.26761	+	5.11964i	0.0919623	+	0.371418i
$191$	−3.47593	+	6.02048i	−0.251509	+	0.435627i	−0.963942	−	0.266114i	$-0.914260\pi$
$191$	−3.47593	+	6.02048i	−0.251509	+	0.435627i	0.712432	+	0.701741i	$0.247594\pi$
$192$	2.36034	+	1.36274i	0.170343	+	0.0983474i
$193$		−	9.13122i		−	0.657280i	−0.944455	−	0.328640i	$-0.893410\pi$
$193$		−	9.13122i		−	0.657280i	0.944455	−	0.328640i	$-0.106590\pi$
$194$	17.1148			1.22877
$195$	−22.6182	−	23.4984i	−1.61972	−	1.68275i
$196$	−1.64184	+	2.84375i	−0.117274	+	0.203125i
$197$	−17.8426	+	10.3014i	−1.27123	+	0.733947i	−0.975220	−	0.221236i	$-0.928991\pi$
$197$	−17.8426	+	10.3014i	−1.27123	+	0.733947i	−0.296014	+	0.955184i	$0.595657\pi$
$198$	3.49900	−	2.02015i	0.248663	−	0.143566i
$199$	12.8760			0.912753			0.456377	−	0.889787i	$-0.349147\pi$
$199$	12.8760			0.912753			0.456377	+	0.889787i	$0.349147\pi$
$200$	4.99636	+	0.190781i	0.353296	+	0.0134902i
$201$	−22.0578	−	38.2053i	−1.55584	−	2.69479i
$202$	9.77357	−	5.64277i	0.687666	−	0.397024i
$203$	−22.5129	−	12.9978i	−1.58010	−	0.912270i
$204$	−3.29321			−0.230571
$205$	0.270650	+	0.281182i	0.0189031	+	0.0196386i
$206$	−0.420320	−	0.728016i	−0.0292851	−	0.0507232i
$207$			0.441417i			0.0306806i
$208$	−4.63472	+	2.67585i	−0.321360	+	0.185537i
$209$	1.07603	−	1.86374i	0.0744306	−	0.128917i
$210$	−14.0805	+	13.5532i	−0.971650	+	0.935256i
$211$	−21.5897			−1.48629			−0.743147	−	0.669128i	$-0.766668\pi$
$211$	−21.5897			−1.48629			−0.743147	+	0.669128i	$0.766668\pi$
$212$	1.00900	+	0.582544i	0.0692981	+	0.0400093i
$213$			0.964314i			0.0660737i
$214$	12.9755			0.886986
$215$	9.56658	−	11.1122i	0.652435	−	0.757845i
$216$	−3.89271			−0.264866
$217$			26.4547i			1.79587i
$218$	−12.0019	−	6.92931i	−0.812872	−	0.469312i
$219$	31.4756			2.12692
$220$	−1.41482	−	1.46988i	−0.0953874	−	0.0990991i
$221$	3.23324	−	5.60014i	0.217491	−	0.376706i
$222$	0.0656757	−	0.0379179i	0.00440786	−	0.00254488i
$223$		−	12.3882i		−	0.829572i	−0.909919	−	0.414786i	$-0.863856\pi$
$223$		−	12.3882i		−	0.829572i	0.909919	−	0.414786i	$-0.136144\pi$
$224$	1.60341	+	2.77719i	0.107132	+	0.185559i
$225$	−19.5834	+	10.3310i	−1.30556	+	0.688731i
$226$	19.8182			1.31828
$227$	−24.2324	−	13.9906i	−1.60836	−	0.928589i	−0.989737	−	0.142904i	$-0.954356\pi$
$227$	−24.2324	−	13.9906i	−1.60836	−	0.928589i	−0.618626	−	0.785685i	$-0.712311\pi$
$228$	−5.56735	+	3.21431i	−0.368707	+	0.212873i
$229$	−3.26880	−	5.66173i	−0.216009	−	0.374138i	0.737576	−	0.675265i	$-0.235971\pi$
$229$	−3.26880	−	5.66173i	−0.216009	−	0.374138i	−0.953584	+	0.301127i	$0.902637\pi$
$230$	0.216362	−	0.0535708i	0.0142665	−	0.00353235i
$231$	7.97440			0.524677
$232$	−7.02033	+	4.05319i	−0.460908	+	0.266105i
$233$	−1.63608	+	0.944594i	−0.107183	+	0.0618824i	−0.552633	−	0.833424i	$-0.686377\pi$
$233$	−1.63608	+	0.944594i	−0.107183	+	0.0618824i	0.445450	+	0.895307i	$0.353044\pi$
$234$	11.8494	−	20.5238i	0.774619	−	1.34168i
$235$	11.6486	−	11.2123i	0.759869	−	0.731408i
$236$	−1.44431			−0.0940168
$237$			39.0963i			2.53958i
$238$	−3.35568	−	1.93740i	−0.217516	−	0.125583i
$239$	2.76789	−	4.79413i	0.179040	−	0.310106i	−0.762512	−	0.646974i	$-0.776034\pi$
$239$	2.76789	−	4.79413i	0.179040	−	0.310106i	0.941552	+	0.336868i	$0.109368\pi$
$240$	1.46472	+	5.91573i	0.0945475	+	0.381859i
$241$	10.5903	+	18.3430i	0.682183	+	1.18157i	0.974313	+	0.225197i	$0.0723024\pi$
$241$	10.5903	+	18.3430i	0.682183	+	1.18157i	−0.292131	+	0.956378i	$0.594364\pi$
$242$		−	10.1675i		−	0.653595i
$243$	−16.4281	+	9.48477i	−1.05386	+	0.608448i
$244$	3.43693	+	5.95294i	0.220027	+	0.381098i
$245$	−7.12732	+	1.76471i	−0.455347	+	0.112743i
$246$	−0.237848	+	0.411965i	−0.0151647	+	0.0262660i
$247$		−	12.6231i		−	0.803190i
$248$	7.14430	+	4.12477i	0.453664	+	0.261923i
$249$	14.8274	+	25.6817i	0.939646	+	1.62751i
$250$	7.44040	+	8.34508i	0.470572	+	0.527789i
$251$	15.5214	+	26.8838i	0.979700	+	1.69689i	0.663463	+	0.748210i	$0.269086\pi$
$251$	15.5214	+	26.8838i	0.979700	+	1.69689i	0.316237	+	0.948680i	$0.397580\pi$
$252$	−12.2981	−	7.10032i	−0.774708	−	0.447278i
$253$	−0.0787638	−	0.0454743i	−0.00495184	−	0.00285894i
$254$	−10.0188			−0.628636
$255$	−5.10672	−	5.30543i	−0.319795	−	0.332239i
$256$	1.00000			0.0625000
$257$		−	10.6950i		−	0.667136i	−0.942726	−	0.333568i	$-0.891747\pi$
$257$		−	10.6950i		−	0.667136i	0.942726	−	0.333568i	$-0.108253\pi$
$258$	16.2459	+	7.44895i	1.01142	+	0.463752i
$259$	0.0892287			0.00554440
$260$	−11.4978	−	3.31723i	−0.713065	−	0.205726i
$261$	17.9486	−	31.0879i	1.11099	−	1.92429i
$262$			3.61614i			0.223406i
$263$	−1.49118	−	0.860934i	−0.0919502	−	0.0530875i	0.453320	−	0.891348i	$-0.350240\pi$
$263$	−1.49118	−	0.860934i	−0.0919502	−	0.0530875i	−0.545270	+	0.838260i	$0.683573\pi$
$264$	1.24335	−	2.15355i	0.0765229	−	0.132542i
$265$	0.626139	+	2.52885i	0.0384634	+	0.155346i
$266$	−7.56395			−0.463776
$267$	10.3137	−	5.95463i	0.631189	−	0.364417i
$268$	−14.0178	−	8.09318i	−0.856273	−	0.494369i
$269$	−4.96027			−0.302433			−0.151217	−	0.988501i	$-0.548319\pi$
$269$	−4.96027			−0.302433			−0.151217	+	0.988501i	$0.548319\pi$
$270$	−6.03635	−	6.27124i	−0.367361	−	0.381656i
$271$	−3.96571	−	6.86881i	−0.240900	−	0.417251i	0.720071	−	0.693900i	$-0.244109\pi$
$271$	−3.96571	−	6.86881i	−0.240900	−	0.417251i	−0.960971	+	0.276650i	$0.910776\pi$
$272$	−1.04642	+	0.604151i	−0.0634486	+	0.0366321i
$273$	40.5080	−	23.3873i	2.45166	−	1.41547i
$274$	−19.3504			−1.16900
$275$	0.174066	−	4.55862i	0.0104966	−	0.274895i
$276$	0.135841	+	0.235283i	0.00817664	+	0.0141624i
$277$	17.7469	+	10.2462i	1.06631	+	0.615633i	0.927170	−	0.374641i	$-0.122234\pi$
$277$	17.7469	+	10.2462i	1.06631	+	0.615633i	0.139137	+	0.990273i	$0.455567\pi$
$278$	−5.59475	−	3.23013i	−0.335551	−	0.193730i
$279$	−36.5311			−2.18706
$280$	−1.98773	+	6.88965i	−0.118790	+	0.411736i
$281$	14.5733	−	25.2417i	0.869371	−	1.50579i	0.00673064	−	0.999977i	$-0.497858\pi$
$281$	14.5733	−	25.2417i	0.869371	−	1.50579i	0.862640	−	0.505818i	$-0.168809\pi$
$282$	17.0665	+	9.85337i	1.01630	+	0.586760i
$283$	2.13417	−	1.23216i	0.126863	−	0.0732446i	−0.435225	−	0.900322i	$-0.643331\pi$
$283$	2.13417	−	1.23216i	0.126863	−	0.0732446i	0.562089	+	0.827077i	$0.309998\pi$
$284$	0.176907	+	0.306412i	0.0104975	+	0.0181822i
$285$	−13.8115	−	3.98475i	−0.818123	−	0.236036i
$286$	2.44142	+	4.22866i	0.144364	+	0.250046i
$287$	−0.484721	+	0.279854i	−0.0286122	+	0.0165192i
$288$	−3.83499	+	2.21413i	−0.225979	+	0.130469i
$289$	−7.77000	+	13.4580i	−0.457059	+	0.791649i
$290$	−17.4161	−	5.02470i	−1.02271	−	0.295061i
$291$	−23.3230	+	40.3967i	−1.36722	+	2.36810i
$292$	10.0014	−	5.77430i	0.585287	−	0.337916i
$293$			21.4582i			1.25360i	0.779179	+	0.626801i	$0.215636\pi$
$293$			21.4582i			1.25360i	−0.779179	+	0.626801i	$0.784364\pi$
$294$	−4.47481	−	7.75060i	−0.260976	−	0.452024i
$295$	−2.23967	−	2.32682i	−0.130399	−	0.135473i
$296$	0.0139123	−	0.0240969i	0.000808639	−	0.00140060i
$297$			3.55167i			0.206089i
$298$	−15.3015	−	8.83430i	−0.886389	−	0.511757i
$299$	−0.533468			−0.0308513
$300$	−7.25906	+	11.5331i	−0.419102	+	0.665865i
$301$	12.1718	+	17.1477i	0.701572	+	0.988380i
$302$			14.8850i			0.856537i
$303$			30.7586i			1.76703i
$304$	−1.17935	+	2.04270i	−0.0676406	+	0.117157i
$305$	−4.26073	+	14.7681i	−0.243969	+	0.845618i
$306$	2.67534	−	4.63383i	0.152939	−	0.264898i
$307$	4.29205	+	2.47802i	0.244960	+	0.141428i	0.617454	−	0.786607i	$-0.288164\pi$
$307$	4.29205	+	2.47802i	0.244960	+	0.141428i	−0.372494	+	0.928035i	$0.621497\pi$
$308$	2.53387	−	1.46293i	0.144381	−	0.0833583i
$309$	2.29115			0.130339
$310$	4.43345	+	17.9058i	0.251803	+	1.01698i
$311$	−4.29007	+	7.43061i	−0.243267	+	0.421351i	−0.961643	−	0.274304i	$-0.911553\pi$
$311$	−4.29007	+	7.43061i	−0.243267	+	0.421351i	0.718376	+	0.695655i	$0.244886\pi$
$312$		−	14.5860i		−	0.825770i
$313$	11.6207	+	6.70919i	0.656839	+	0.379226i	0.791071	−	0.611724i	$-0.209524\pi$
$313$	11.6207	+	6.70919i	0.656839	+	0.379226i	−0.134233	+	0.990950i	$0.542857\pi$
$314$	−8.19492	−	14.1940i	−0.462466	−	0.801015i
$315$	−7.63168	−	30.8229i	−0.429996	−	1.73667i
$316$	7.17235	+	12.4229i	0.403476	+	0.698842i
$317$		−	7.46372i		−	0.419204i	−0.977787	−	0.209602i	$-0.932783\pi$
$317$		−	7.46372i		−	0.419204i	0.977787	−	0.209602i	$-0.0672168\pi$
$318$	−2.75000	+	1.58771i	−0.154212	+	0.0890346i
$319$	3.69809	+	6.40527i	0.207053	+	0.358626i
$320$	1.55068	+	1.61102i	0.0866857	+	0.0900588i
$321$	−17.6822	+	30.6265i	−0.986927	+	1.70941i
$322$			0.319661i			0.0178140i
$323$		−	2.85003i		−	0.158580i
$324$	−1.33763	+	2.31685i	−0.0743129	+	0.128714i
$325$	−12.4853	−	23.6672i	−0.692561	−	1.31282i
$326$	7.39776	+	12.8133i	0.409724	+	0.709663i
$327$	32.7110	−	18.8857i	1.80892	−	1.04438i
$328$			0.174537i			0.00963717i
$329$	11.5935	+	20.0806i	0.639172	+	1.10708i
$330$	5.39745	−	1.33640i	0.297120	−	0.0735663i
$331$	6.58699	+	11.4090i	0.362054	+	0.627095i	0.988299	−	0.152531i	$-0.0487424\pi$
$331$	6.58699	+	11.4090i	0.362054	+	0.627095i	−0.626245	+	0.779626i	$0.715409\pi$
$332$	9.42282	+	5.44026i	0.517144	+	0.298573i
$333$			0.123215i			0.00675215i
$334$	6.74836	−	11.6885i	0.369254	−	0.639566i
$335$	−8.69883	−	35.1329i	−0.475268	−	1.91952i
$336$	−8.74013			−0.476813
$337$	11.0640	−	6.38780i	0.602694	−	0.347966i	−0.167407	−	0.985888i	$-0.553539\pi$
$337$	11.0640	−	6.38780i	0.602694	−	0.347966i	0.770101	+	0.637922i	$0.220206\pi$
$338$	13.5453	+	7.82040i	0.736768	+	0.425373i
$339$	−27.0070	+	46.7776i	−1.46682	+	2.54061i
$340$	−2.59596	−	0.748961i	−0.140786	−	0.0406181i
$341$	3.76339	−	6.51838i	0.203799	−	0.352990i
$342$		−	10.4450i		−	0.564800i
$343$			11.9176i			0.643488i
$344$	6.52868	−	0.613453i	0.352003	−	0.0330752i
$345$	−0.168400	+	0.583691i	−0.00906637	+	0.0314248i
$346$	8.02239			0.431286
$347$	−16.3252	−	9.42536i	−0.876382	−	0.505980i	−0.00691849	−	0.999976i	$-0.502202\pi$
$347$	−16.3252	−	9.42536i	−0.876382	−	0.505980i	−0.869464	+	0.493996i	$0.835536\pi$
$348$		−	22.0938i		−	1.18435i
$349$	8.20018	−	14.2031i	0.438946	−	0.760276i	−0.558663	−	0.829395i	$-0.688685\pi$
$349$	8.20018	−	14.2031i	0.438946	−	0.760276i	0.997608	+	0.0691187i	$0.0220187\pi$
$350$	−14.1817	+	7.48137i	−0.758045	+	0.399896i
$351$	10.4163	+	18.0416i	0.555983	+	0.962990i
$352$		−	0.912389i		−	0.0486305i
$353$	−27.1426	+	15.6708i	−1.44465	+	0.834071i	−0.998155	−	0.0607133i	$-0.980662\pi$
$353$	−27.1426	+	15.6708i	−1.44465	+	0.834071i	−0.446498	+	0.894784i	$0.647329\pi$
$354$	1.96823	−	3.40907i	0.104610	−	0.181190i
$355$	−0.219310	+	0.760147i	−0.0116398	+	0.0403444i
$356$	2.18480	−	3.78418i	0.115794	−	0.200561i
$357$	9.14586	−	5.28036i	0.484050	−	0.279466i
$358$	−0.576066	+	0.332592i	−0.0304460	+	0.0175780i
$359$	−6.21388	−	10.7628i	−0.327956	−	0.568036i	0.654150	−	0.756365i	$-0.273026\pi$
$359$	−6.21388	−	10.7628i	−0.327956	−	0.568036i	−0.982106	+	0.188328i	$0.939693\pi$
$360$	−9.51386	−	2.74484i	−0.501424	−	0.144666i
$361$	6.71824	+	11.6363i	0.353592	+	0.612439i
$362$	10.4743	−	6.04735i	0.550518	−	0.317842i
$363$	23.9989	+	13.8557i	1.25961	+	0.727238i
$364$	8.58098	−	14.8627i	0.449765	−	0.779017i
$365$	24.8115	+	7.15835i	1.29869	+	0.374685i
$366$	−18.7346			−0.979274
$367$	4.77541	+	2.75709i	0.249274	+	0.143919i	0.619432	−	0.785050i	$-0.287363\pi$
$367$	4.77541	+	2.75709i	0.249274	+	0.143919i	−0.370158	+	0.928969i	$0.620696\pi$
$368$	0.0863270	+	0.0498409i	0.00450010	+	0.00259814i
$369$	−0.386447	−	0.669346i	−0.0201176	−	0.0348448i
$370$	0.0603942	−	0.0149535i	0.00313975	−	0.000777395i
$371$	−3.73622			−0.193975
$372$	−19.4717	+	11.2420i	−1.00956	+	0.582870i
$373$	29.2250	−	16.8731i	1.51321	−	0.873654i	0.513332	−	0.858190i	$-0.328411\pi$
$373$	29.2250	−	16.8731i	1.51321	−	0.873654i	0.999880	−	0.0154638i	$-0.00492247\pi$
$374$	0.551221	+	0.954743i	0.0285030	+	0.0493686i
$375$	−29.8366	+	6.18968i	−1.54075	+	0.319634i
$376$	7.23055			0.372887
$377$	37.5708	+	21.6915i	1.93499	+	1.11717i
$378$	10.8108	−	6.24161i	0.556047	−	0.321034i
$379$	−7.44448			−0.382397			−0.191199	−	0.981551i	$-0.561237\pi$
$379$	−7.44448			−0.382397			−0.191199	+	0.981551i	$0.561237\pi$
$380$	−5.11964	+	1.26761i	−0.262632	+	0.0650272i
$381$	13.6530	−	23.6478i	0.699467	−	1.21151i
$382$	−6.02048	−	3.47593i	−0.308035	−	0.177844i
$383$		−	32.9101i		−	1.68163i	−0.541325	−	0.840813i	$-0.682077\pi$
$383$		−	32.9101i		−	1.68163i	0.541325	−	0.840813i	$-0.317923\pi$
$384$	−1.36274	+	2.36034i	−0.0695421	+	0.120451i
$385$	6.28604	+	1.81358i	0.320366	+	0.0924288i
$386$	9.13122			0.464767
$387$	−23.6792	+	16.8079i	−1.20368	+	0.854396i
$388$			17.1148i			0.868872i
$389$	−2.61573			−0.132623			−0.0663114	−	0.997799i	$-0.521123\pi$
$389$	−2.61573			−0.132623			−0.0663114	+	0.997799i	$0.521123\pi$
$390$	23.4984	−	22.6182i	1.18989	−	1.14532i
$391$	−0.120446			−0.00609121
$392$	−2.84375	−	1.64184i	−0.143631	−	0.0829255i
$393$	−8.53531	−	4.92786i	−0.430549	−	0.248578i
$394$	−10.3014	−	17.8426i	−0.518979	−	0.898898i
$395$	−8.89150	+	30.8187i	−0.447380	+	1.55066i
$396$	2.02015	+	3.49900i	0.101516	+	0.175831i
$397$	18.7829	+	10.8443i	0.942684	+	0.544259i	0.890801	−	0.454394i	$-0.150144\pi$
$397$	18.7829	+	10.8443i	0.942684	+	0.544259i	0.0518836	+	0.998653i	$0.483478\pi$
$398$			12.8760i			0.645414i
$399$	10.3077	−	17.8535i	0.516031	−	0.893792i
$400$	−0.190781	+	4.99636i	−0.00953903	+	0.249818i
$401$	9.19724	+	15.9301i	0.459288	+	0.795510i	0.998923	−	0.0463885i	$-0.0147712\pi$
$401$	9.19724	+	15.9301i	0.459288	+	0.795510i	−0.539635	+	0.841899i	$0.681438\pi$
$402$	38.2053	−	22.0578i	1.90551	−	1.10014i
$403$		−	44.1491i		−	2.19922i
$404$	5.64277	+	9.77357i	0.280738	+	0.486253i
$405$	−5.80673	+	1.43774i	−0.288539	+	0.0714416i
$406$	12.9978	−	22.5129i	0.645072	−	1.11730i
$407$	−0.0219857	−	0.0126935i	−0.00108979	−	0.000629192i
$408$		−	3.29321i		−	0.163038i
$409$	−9.15657			−0.452763			−0.226382	−	0.974039i	$-0.572690\pi$
$409$	−9.15657			−0.452763			−0.226382	+	0.974039i	$0.572690\pi$
$410$	−0.281182	+	0.270650i	−0.0138866	+	0.0133665i
$411$	26.3697	−	45.6736i	1.30072	−	2.25291i
$412$	0.728016	−	0.420320i	0.0358667	−	0.0207077i
$413$	4.01113	−	2.31583i	0.197375	−	0.113954i
$414$	−0.441417			−0.0216945
$415$	5.84739	+	23.6165i	0.287037	+	1.15929i
$416$	−2.67585	−	4.63472i	−0.131195	−	0.227236i
$417$	15.2484	−	8.80367i	0.746717	−	0.431118i
$418$	1.86374	+	1.07603i	0.0911584	+	0.0526303i
$419$	21.7483			1.06247			0.531236	−	0.847224i	$-0.321728\pi$
$419$	21.7483			1.06247			0.531236	+	0.847224i	$0.321728\pi$
$420$	−13.5532	−	14.0805i	−0.661326	−	0.687060i
$421$	−7.82838	−	13.5591i	−0.381532	−	0.660833i	0.609750	−	0.792594i	$-0.291270\pi$
$421$	−7.82838	−	13.5591i	−0.381532	−	0.660833i	−0.991281	+	0.131762i	$0.957937\pi$
$422$		−	21.5897i		−	1.05097i
$423$	−27.7291	+	16.0094i	−1.34823	+	0.778403i
$424$	−0.582544	+	1.00900i	−0.0282908	+	0.0490011i
$425$	−2.81892	−	5.34355i	−0.136738	−	0.259200i
$426$	−0.964314			−0.0467212
$427$	−19.0900	−	11.0216i	−0.923830	−	0.533373i
$428$			12.9755i			0.627194i
$429$	−13.3081			−0.642521
$430$	11.1122	+	9.56658i	0.535877	+	0.461341i
$431$	3.94678			0.190110			0.0950548	−	0.995472i	$-0.469697\pi$
$431$	3.94678			0.190110			0.0950548	+	0.995472i	$0.469697\pi$
$432$		−	3.89271i		−	0.187288i
$433$	−27.1548	−	15.6778i	−1.30498	−	0.753429i	−0.323724	−	0.946152i	$-0.604935\pi$
$433$	−27.1548	−	15.6778i	−1.30498	−	0.753429i	−0.981253	+	0.192723i	$0.938268\pi$
$434$	−26.4547			−1.26987
$435$	35.5936	−	34.2605i	1.70658	−	1.64266i
$436$	6.92931	−	12.0019i	0.331854	−	0.574788i
$437$	−0.203620	+	0.117560i	−0.00974048	+	0.00562367i
$438$			31.4756i			1.50396i
$439$	−15.3016	−	26.5032i	−0.730306	−	1.26493i	−0.956752	−	0.290903i	$-0.906044\pi$
$439$	−15.3016	−	26.5032i	−0.730306	−	1.26493i	0.226446	−	0.974024i	$-0.427289\pi$
$440$	1.46988	−	1.41482i	0.0700737	−	0.0674491i
$441$	14.5410			0.692429
$442$	5.60014	+	3.23324i	0.266371	+	0.153790i
$443$	−0.906515	+	0.523376i	−0.0430698	+	0.0248664i	−0.521380	−	0.853324i	$-0.674583\pi$
$443$	−0.906515	+	0.523376i	−0.0430698	+	0.0248664i	0.478310	+	0.878191i	$0.341249\pi$
$444$	0.0379179	+	0.0656757i	0.00179950	+	0.00311683i
$445$	9.48431	−	2.34830i	0.449600	−	0.111320i
$446$	12.3882			0.586596
$447$	41.7039	−	24.0777i	1.97253	−	1.13884i
$448$	−2.77719	+	1.60341i	−0.131210	+	0.0757540i
$449$	−6.48865	+	11.2387i	−0.306218	+	0.530386i	−0.977532	−	0.210788i	$-0.932397\pi$
$449$	−6.48865	+	11.2387i	−0.306218	+	0.530386i	0.671314	+	0.741174i	$0.265730\pi$
$450$	−10.3310	−	19.5834i	−0.487006	−	0.923170i
$451$	0.159245			0.00749857
$452$			19.8182i			0.932168i
$453$	−35.1337	−	20.2844i	−1.65072	−	0.953046i
$454$	13.9906	−	24.2324i	0.656611	−	1.13728i
$455$	37.2505	−	9.22314i	1.74633	−	0.432388i
$456$	−3.21431	−	5.56735i	−0.150524	−	0.260715i
$457$		−	25.9490i		−	1.21384i	−0.794762	−	0.606922i	$-0.792404\pi$
$457$		−	25.9490i		−	1.21384i	0.794762	−	0.606922i	$-0.207596\pi$
$458$	5.66173	−	3.26880i	0.264555	−	0.152741i
$459$	2.35179	+	4.07342i	0.109772	+	0.190131i
$460$	0.0535708	+	0.216362i	0.00249775	+	0.0100879i
$461$	−9.76304	+	16.9101i	−0.454710	+	0.787581i	−0.998671	−	0.0515294i	$-0.983590\pi$
$461$	−9.76304	+	16.9101i	−0.454710	+	0.787581i	0.543962	+	0.839110i	$0.316924\pi$
$462$			7.97440i			0.371003i
$463$	13.2055	+	7.62419i	0.613711	+	0.354326i	0.774416	−	0.632676i	$-0.218044\pi$
$463$	13.2055	+	7.62419i	0.613711	+	0.354326i	−0.160705	+	0.987002i	$0.551377\pi$
$464$	−4.05319	−	7.02033i	−0.188165	−	0.325911i
$465$	−48.3054	−	13.9366i	−2.24011	−	0.646294i
$466$	−0.944594	−	1.63608i	−0.0437575	−	0.0757902i
$467$	34.0174	+	19.6400i	1.57414	+	0.908830i	0.995653	+	0.0931375i	$0.0296896\pi$
$467$	34.0174	+	19.6400i	1.57414	+	0.908830i	0.578486	+	0.815692i	$0.303644\pi$
$468$	20.5238	+	11.8494i	0.948711	+	0.547738i
$469$	51.9067			2.39683
$470$	11.2123	+	11.6486i	0.517184	+	0.537308i
$471$	44.6703			2.05830
$472$		−	1.44431i		−	0.0664799i
$473$	−0.559707	−	5.95670i	−0.0257354	−	0.273889i
$474$	−39.0963			−1.79575
$475$	−9.98108	−	6.28219i	−0.457963	−	0.288247i
$476$	1.93740	−	3.35568i	0.0888007	−	0.153807i
$477$		−	5.15932i		−	0.236229i
$478$	4.79413	+	2.76789i	0.219278	+	0.126600i
$479$	−0.576054	+	0.997754i	−0.0263206	+	0.0455886i	−0.878886	−	0.477032i	$-0.841712\pi$
$479$	−0.576054	+	0.997754i	−0.0263206	+	0.0455886i	0.852565	+	0.522621i	$0.175046\pi$
$480$	−5.91573	+	1.46472i	−0.270015	+	0.0668552i
$481$	−0.148910			−0.00678970
$482$	−18.3430	+	10.5903i	−0.835500	+	0.482376i
$483$	−0.754509	−	0.435616i	−0.0343314	−	0.0198212i
$484$	10.1675			0.462161
$485$	−27.5723	+	26.5396i	−1.25199	+	1.20510i
$486$	−9.48477	−	16.4281i	−0.430238	−	0.745194i
$487$	−23.9046	+	13.8013i	−1.08322	+	0.625397i	−0.931763	−	0.363067i	$-0.881729\pi$
$487$	−23.9046	+	13.8013i	−1.08322	+	0.625397i	−0.151456	+	0.988464i	$0.548396\pi$
$488$	−5.95294	+	3.43693i	−0.269477	+	0.155583i
$489$	−40.3250			−1.82356
$490$	−1.76471	−	7.12732i	−0.0797214	−	0.321979i
$491$	−10.9263	−	18.9248i	−0.493095	−	0.854066i	0.506873	−	0.862021i	$-0.330801\pi$
$491$	−10.9263	−	18.9248i	−0.493095	−	0.854066i	−0.999968	+	0.00795472i	$0.997468\pi$
$492$	−0.411965	−	0.237848i	−0.0185728	−	0.0107230i
$493$	8.48269	+	4.89748i	0.382041	+	0.220572i
$494$	12.6231			0.567941
$495$	−2.50436	+	8.68034i	−0.112563	+	0.390152i
$496$	−4.12477	+	7.14430i	−0.185207	+	0.320789i
$497$	−0.982607	−	0.567308i	−0.0440759	−	0.0254472i
$498$	−25.6817	+	14.8274i	−1.15083	+	0.664430i
$499$	2.87661	+	4.98244i	0.128775	+	0.223045i	0.923202	−	0.384315i	$-0.125562\pi$
$499$	2.87661	+	4.98244i	0.128775	+	0.223045i	−0.794427	+	0.607359i	$0.792229\pi$
$500$	−8.34508	+	7.44040i	−0.373203	+	0.332745i
$501$	18.3925	+	31.8568i	0.821718	+	1.42326i
$502$	−26.8838	+	15.5214i	−1.19988	+	0.692752i
$503$	6.79187	−	3.92129i	0.302834	−	0.174842i	−0.340881	−	0.940106i	$-0.610725\pi$
$503$	6.79187	−	3.92129i	0.302834	−	0.174842i	0.643715	+	0.765265i	$0.277392\pi$
$504$	7.10032	−	12.2981i	0.316273	−	0.547802i
$505$	−6.99529	+	24.2463i	−0.311286	+	1.07895i
$506$	0.0454743	−	0.0787638i	0.00202158	−	0.00350148i
$507$	−36.9176	+	21.3144i	−1.63957	+	0.946604i
$508$		−	10.0188i		−	0.444513i
$509$	1.13150	+	1.95981i	0.0501528	+	0.0868672i	0.890012	−	0.455937i	$-0.150696\pi$
$509$	1.13150	+	1.95981i	0.0501528	+	0.0868672i	−0.839859	+	0.542804i	$0.817363\pi$
$510$	5.30543	−	5.10672i	0.234928	−	0.226129i
$511$	−18.5171	+	32.0726i	−0.819150	+	1.41881i
$512$			1.00000i			0.0441942i
$513$	7.95165	+	4.59089i	0.351074	+	0.202693i
$514$	10.6950			0.471736
$515$	1.80606	+	0.521067i	0.0795847	+	0.0229609i
$516$	−7.44895	+	16.2459i	−0.327922	+	0.715185i
$517$		−	6.59707i		−	0.290139i
$518$			0.0892287i			0.00392048i
$519$	−10.9324	+	18.9355i	−0.479881	+	0.831178i
$520$	3.31723	−	11.4978i	0.145470	−	0.504213i
$521$	−7.41799	+	12.8483i	−0.324988	+	0.562896i	−0.981510	−	0.191411i	$-0.938694\pi$
$521$	−7.41799	+	12.8483i	−0.324988	+	0.562896i	0.656522	+	0.754307i	$0.272027\pi$
$522$	31.0879	+	17.9486i	1.36068	+	0.785589i
$523$	−17.3823	+	10.0357i	−0.760074	+	0.438829i	−0.829322	−	0.558770i	$-0.811273\pi$
$523$	−17.3823	+	10.0357i	−0.760074	+	0.438829i	0.0692481	+	0.997599i	$0.477940\pi$
$524$	−3.61614			−0.157972
$525$	1.66745	−	43.6688i	0.0727734	−	1.90586i
$526$	0.860934	−	1.49118i	0.0375385	−	0.0650186i
$527$		−	9.96793i		−	0.434210i
$528$	2.15355	+	1.24335i	0.0937211	+	0.0541099i
$529$	−11.4950	−	19.9100i	−0.499784	−	0.865651i
$530$	−2.52885	+	0.626139i	−0.109846	+	0.0271977i
$531$	3.19790	+	5.53893i	0.138777	+	0.240369i
$532$		−	7.56395i		−	0.327939i
$533$	0.808928	−	0.467035i	0.0350385	−	0.0202295i
$534$	5.95463	+	10.3137i	0.257682	+	0.446318i
$535$	−20.9038	+	20.1208i	−0.903750	+	0.869899i
$536$	8.09318	−	14.0178i	0.349572	−	0.605476i
$537$		−	1.81295i		−	0.0782344i
$538$		−	4.96027i		−	0.213853i
$539$	−1.49800	+	2.59461i	−0.0645233	+	0.111758i
$540$	6.27124	−	6.03635i	0.269871	−	0.259763i
$541$	−7.63794	−	13.2293i	−0.328381	−	0.568772i	0.653810	−	0.756659i	$-0.273170\pi$
$541$	−7.63794	−	13.2293i	−0.328381	−	0.568772i	−0.982191	+	0.187887i	$0.939836\pi$
$542$	6.86881	−	3.96571i	0.295041	−	0.170342i
$543$			32.9639i			1.41462i
$544$	−0.604151	−	1.04642i	−0.0259028	−	0.0448649i
$545$	30.0805	−	7.44787i	1.28851	−	0.319032i
$546$	23.3873	+	40.5080i	1.00089	+	1.73358i
$547$	31.4499	+	18.1576i	1.34470	+	0.776362i	0.987493	−	0.157663i	$-0.0503960\pi$
$547$	31.4499	+	18.1576i	1.34470	+	0.776362i	0.357206	+	0.934026i	$0.383729\pi$
$548$		−	19.3504i		−	0.826610i
$549$	15.2196	−	26.3612i	0.649559	−	1.12507i
$550$	4.55862	+	0.174066i	0.194380	+	0.00742220i
$551$	19.1206			0.814565
$552$	−0.235283	+	0.135841i	−0.0100143	+	0.00578176i
$553$	−39.8379	−	23.0004i	−1.69408	−	0.978078i
$554$	−10.2462	+	17.7469i	−0.435318	+	0.753993i
$555$	−0.0470064	+	0.162929i	−0.00199531	+	0.00691593i
$556$	3.23013	−	5.59475i	0.136988	−	0.237270i
$557$		−	12.1344i		−	0.514150i	−0.966391	−	0.257075i	$-0.917241\pi$
$557$		−	12.1344i		−	0.514150i	0.966391	−	0.257075i	$-0.0827588\pi$
$558$		−	36.5311i		−	1.54649i
$559$	−20.3130	−	28.6171i	−0.859148	−	1.21037i
$560$	−6.88965	−	1.98773i	−0.291141	−	0.0839970i
$561$	−3.00469			−0.126858
$562$	25.2417	+	14.5733i	1.06476	+	0.614738i
$563$			32.3317i			1.36262i	0.731996	+	0.681309i	$0.238589\pi$
$563$			32.3317i			1.36262i	−0.731996	+	0.681309i	$0.761411\pi$
$564$	−9.85337	+	17.0665i	−0.414902	+	0.718631i
$565$	−31.9275	+	30.7316i	−1.34320	+	1.29289i
$566$	1.23216	+	2.13417i	0.0517917	+	0.0897059i
$567$		−	8.57909i		−	0.360288i
$568$	−0.306412	+	0.176907i	−0.0128567	+	0.00742285i
$569$	1.11654	−	1.93390i	0.0468078	−	0.0810735i	−0.841672	−	0.539989i	$-0.818428\pi$
$569$	1.11654	−	1.93390i	0.0468078	−	0.0810735i	0.888480	+	0.458915i	$0.151762\pi$
$570$	3.98475	−	13.8115i	0.166903	−	0.578501i
$571$	−7.21965	+	12.5048i	−0.302133	+	0.523310i	−0.976619	−	0.214978i	$-0.931032\pi$
$571$	−7.21965	+	12.5048i	−0.302133	+	0.523310i	0.674486	+	0.738288i	$0.264365\pi$
$572$	−4.22866	+	2.44142i	−0.176809	+	0.102081i
$573$	16.4087	−	9.47358i	0.685484	−	0.395765i
$574$	−0.279854	−	0.484721i	−0.0116809	−	0.0202318i
$575$	−0.265493	+	0.421812i	−0.0110718	+	0.0175908i
$576$	−2.21413	−	3.83499i	−0.0922555	−	0.159791i
$577$	−12.5067	+	7.22073i	−0.520660	+	0.300603i	−0.737205	−	0.675670i	$-0.763855\pi$
$577$	−12.5067	+	7.22073i	−0.520660	+	0.300603i	0.216545	+	0.976273i	$0.430521\pi$
$578$	−13.4580	−	7.77000i	−0.559781	−	0.323189i
$579$	−12.4435	+	21.5528i	−0.517134	+	0.895703i
$580$	5.02470	−	17.4161i	0.208639	−	0.723163i
$581$	−34.8919			−1.44756
$582$	−40.3967	−	23.3230i	−1.67450	−	0.966771i
$583$	0.920596	+	0.531506i	0.0381272	+	0.0220127i
$584$	5.77430	+	10.0014i	0.238942	+	0.413860i
$585$	12.7362	+	51.4388i	0.526575	+	2.12673i
$586$	−21.4582			−0.886431
$587$	10.3908	−	5.99912i	0.428873	−	0.247610i	−0.269993	−	0.962862i	$-0.587022\pi$
$587$	10.3908	−	5.99912i	0.428873	−	0.247610i	0.698866	+	0.715252i	$0.253688\pi$
$588$	7.75060	−	4.47481i	0.319629	−	0.184538i
$589$	−9.72912	−	16.8513i	−0.400882	−	0.694347i
$590$	2.32682	−	2.23967i	0.0957937	−	0.0922057i
$591$	56.1528			2.30982
$592$	0.0240969	+	0.0139123i	0.000990376	+	0.000571794i
$593$	4.21630	−	2.43428i	0.173143	−	0.0999640i	−0.410924	−	0.911670i	$-0.634794\pi$
$593$	4.21630	−	2.43428i	0.173143	−	0.0999640i	0.584067	+	0.811706i	$0.301461\pi$
$594$	−3.55167			−0.145727
$595$	8.41037	−	2.08239i	0.344791	−	0.0853697i
$596$	8.83430	−	15.3015i	0.361867	−	0.626772i
$597$	−30.3917	−	17.5466i	−1.24385	−	0.718136i
$598$		−	0.533468i		−	0.0218151i
$599$	8.22004	−	14.2375i	0.335862	−	0.581729i	−0.647788	−	0.761820i	$-0.724306\pi$
$599$	8.22004	−	14.2375i	0.335862	−	0.581729i	0.983650	+	0.180091i	$0.0576392\pi$
$600$	−11.5331	−	7.25906i	−0.470837	−	0.296350i
$601$	13.0894			0.533927			0.266964	−	0.963707i	$-0.413980\pi$
$601$	13.0894			0.533927			0.266964	+	0.963707i	$0.413980\pi$
$602$	−17.1477	+	12.1718i	−0.698890	+	0.496086i
$603$			71.6775i			2.91893i
$604$	−14.8850			−0.605663
$605$	15.7666	+	16.3801i	0.641004	+	0.665947i
$606$	−30.7586			−1.24948
$607$	−21.8144	−	12.5945i	−0.885418	−	0.511196i	−0.0129771	−	0.999916i	$-0.504131\pi$
$607$	−21.8144	−	12.5945i	−0.885418	−	0.511196i	−0.872441	+	0.488719i	$0.837464\pi$
$608$	−2.04270	−	1.17935i	−0.0828425	−	0.0478292i
$609$	35.4254	+	61.3586i	1.43551	+	2.48638i
$610$	−14.7681	−	4.26073i	−0.597942	−	0.172512i
$611$	−19.3479	−	33.5115i	−0.782732	−	1.35573i
$612$	4.63383	+	2.67534i	0.187311	+	0.108144i
$613$		−	14.8625i		−	0.600292i	−0.953893	−	0.300146i	$-0.902965\pi$
$613$		−	14.8625i		−	0.600292i	0.953893	−	0.300146i	$-0.0970354\pi$
$614$	−2.47802	+	4.29205i	−0.100005	+	0.173213i
$615$	−0.255648	−	1.03251i	−0.0103087	−	0.0416349i
$616$	1.46293	+	2.53387i	0.0589432	+	0.102093i
$617$	−30.9795	+	17.8860i	−1.24719	+	0.720065i	−0.970548	−	0.240908i	$-0.922555\pi$
$617$	−30.9795	+	17.8860i	−1.24719	+	0.720065i	−0.276642	+	0.960973i	$0.589221\pi$
$618$			2.29115i			0.0921636i
$619$	−5.23901	−	9.07424i	−0.210574	−	0.364724i	0.741321	−	0.671151i	$-0.234200\pi$
$619$	−5.23901	−	9.07424i	−0.210574	−	0.364724i	−0.951894	+	0.306427i	$0.900867\pi$
$620$	−17.9058	+	4.43345i	−0.719115	+	0.178051i
$621$	0.194016	−	0.336046i	0.00778561	−	0.0134851i
$622$	−7.43061	−	4.29007i	−0.297940	−	0.172016i
$623$			14.0125i			0.561398i
$624$	14.5860			0.583907
$625$	−24.9272	−	1.90642i	−0.997088	−	0.0762567i
$626$	−6.70919	+	11.6207i	−0.268153	+	0.464455i
$627$	−5.07959	+	2.93270i	−0.202859	+	0.117121i
$628$	14.1940	−	8.19492i	0.566403	−	0.327013i
$629$	−0.0336206			−0.00134054
$630$	30.8229	−	7.63168i	1.22801	−	0.304053i
$631$	11.2387	+	19.4660i	0.447405	+	0.774928i	0.998216	−	0.0597015i	$-0.0190149\pi$
$631$	11.2387	+	19.4660i	0.447405	+	0.774928i	−0.550811	+	0.834630i	$0.685682\pi$
$632$	−12.4229	+	7.17235i	−0.494156	+	0.285301i
$633$	50.9589	+	29.4211i	2.02544	+	1.16939i
$634$	7.46372			0.296422
$635$	16.1405	−	15.5360i	0.640516	−	0.616526i
$636$	−1.58771	−	2.75000i	−0.0629569	−	0.109045i
$637$			17.5733i			0.696280i
$638$	−6.40527	+	3.69809i	−0.253587	+	0.146409i
$639$	0.783391	−	1.35687i	0.0309905	−	0.0536770i
$640$	−1.61102	+	1.55068i	−0.0636812	+	0.0612960i
$641$	−23.8099			−0.940435			−0.470217	−	0.882551i	$-0.655824\pi$
$641$	−23.8099			−0.940435			−0.470217	+	0.882551i	$0.655824\pi$
$642$	−30.6265	−	17.6822i	−1.20873	−	0.697862i
$643$			28.4416i			1.12163i	0.827941	+	0.560815i	$0.189512\pi$
$643$			28.4416i			1.12163i	−0.827941	+	0.560815i	$0.810488\pi$
$644$	−0.319661			−0.0125964
$645$	−37.7234	+	13.1917i	−1.48536	+	0.519424i
$646$	2.85003			0.112133
$647$		−	7.60287i		−	0.298900i	−0.988769	−	0.149450i	$-0.952250\pi$
$647$		−	7.60287i		−	0.298900i	0.988769	−	0.149450i	$-0.0477502\pi$
$648$	−2.31685	−	1.33763i	−0.0910144	−	0.0525472i
$649$	−1.31778			−0.0517272
$650$	23.6672	−	12.4853i	0.928304	−	0.489714i
$651$	36.0510	−	62.4422i	1.41295	−	2.44730i
$652$	−12.8133	+	7.39776i	−0.501808	+	0.289719i
$653$			14.6137i			0.571877i	0.958248	+	0.285938i	$0.0923053\pi$
$653$			14.6137i			0.571877i	−0.958248	+	0.285938i	$0.907695\pi$
$654$	18.8857	+	32.7110i	0.738490	+	1.27910i
$655$	−5.60747	−	5.82568i	−0.219102	−	0.227628i
$656$	−0.174537			−0.00681451
$657$	−44.2888	−	25.5702i	−1.72787	−	0.997587i
$658$	−20.0806	+	11.5935i	−0.782822	+	0.451963i
$659$	1.33927	+	2.31968i	0.0521706	+	0.0903621i	0.890931	−	0.454138i	$-0.150053\pi$
$659$	1.33927	+	2.31968i	0.0521706	+	0.0903621i	−0.838761	+	0.544500i	$0.816719\pi$
$660$	1.33640	+	5.39745i	0.0520192	+	0.210095i
$661$	19.4506			0.756540			0.378270	−	0.925695i	$-0.376519\pi$
$661$	19.4506			0.756540			0.378270	+	0.925695i	$0.376519\pi$
$662$	−11.4090	+	6.58699i	−0.443423	+	0.256011i
$663$	−15.2631	+	8.81215i	−0.592769	+	0.342236i
$664$	−5.44026	+	9.42282i	−0.211123	+	0.365676i
$665$	12.1857	−	11.7293i	0.472541	−	0.454842i
$666$	−0.123215			−0.00477449
$667$		−	0.808059i		−	0.0312882i
$668$	11.6885	+	6.74836i	0.452242	+	0.261102i
$669$	−16.8819	+	29.2402i	−0.652690	+	1.13049i
$670$	35.1329	−	8.69883i	1.35730	−	0.336065i
$671$	3.13582	+	5.43140i	0.121057	+	0.209677i
$672$		−	8.74013i		−	0.337158i
$673$	−1.82001	+	1.05078i	−0.0701562	+	0.0405047i	−0.534668	−	0.845062i	$-0.679563\pi$
$673$	−1.82001	+	1.05078i	−0.0701562	+	0.0405047i	0.464512	+	0.885567i	$0.346230\pi$
$674$	6.38780	+	11.0640i	0.246049	+	0.426169i
$675$	19.4494	+	0.742654i	0.748607	+	0.0285848i
$676$	−7.82040	+	13.5453i	−0.300784	+	0.520974i
$677$		−	16.6199i		−	0.638754i	−0.947628	−	0.319377i	$-0.896526\pi$
$677$		−	16.6199i		−	0.638754i	0.947628	−	0.319377i	$-0.103474\pi$
$678$	−46.7776	−	27.0070i	−1.79648	−	1.03720i
$679$	−27.4420	−	47.5309i	−1.05313	−	1.82407i
$680$	0.748961	−	2.59596i	0.0287213	−	0.0995507i
$681$	38.1312	+	66.0451i	1.46119	+	2.53085i
$682$	6.51838	+	3.76339i	0.249602	+	0.144108i
$683$	42.6497	+	24.6238i	1.63195	+	0.942204i	0.983492	+	0.180950i	$0.0579174\pi$
$683$	42.6497	+	24.6238i	1.63195	+	0.942204i	0.648454	+	0.761254i	$0.275416\pi$
$684$	10.4450			0.399374
$685$	31.1740	−	30.0063i	1.19110	−	1.14648i
$686$	−11.9176			−0.455014
$687$			17.8181i			0.679804i
$688$	0.613453	+	6.52868i	0.0233877	+	0.248904i
$689$	6.23521			0.237543
$690$	−0.583691	−	0.168400i	−0.0222207	−	0.00641089i
$691$	−13.3902	+	23.1925i	−0.509387	+	0.882284i	0.490554	+	0.871411i	$0.336794\pi$
$691$	−13.3902	+	23.1925i	−0.509387	+	0.882284i	−0.999941	+	0.0108732i	$0.996539\pi$
$692$			8.02239i			0.304965i
$693$	−11.2207	−	6.47825i	−0.426238	−	0.246088i
$694$	9.42536	−	16.3252i	0.357782	−	0.619696i
$695$	14.0222	−	3.47186i	0.531891	−	0.131695i
$696$	22.0938			0.837464
$697$	0.182639	−	0.105447i	0.00691794	−	0.00399407i
$698$	14.2031	+	8.20018i	0.537596	+	0.310381i
$699$	5.14895			0.194751
$700$	−7.48137	−	14.1817i	−0.282769	−	0.536019i
$701$	−2.43057	−	4.20987i	−0.0918013	−	0.159005i	0.816468	−	0.577391i	$-0.195929\pi$
$701$	−2.43057	−	4.20987i	−0.0918013	−	0.159005i	−0.908269	+	0.418386i	$0.862596\pi$
$702$	−18.0416	+	10.4163i	−0.680937	+	0.393139i
$703$	−0.0568376	+	0.0328152i	−0.00214367	+	0.00123765i
$704$	0.912389			0.0343869
$705$	−42.7740	+	10.5908i	−1.61096	+	0.398871i
$706$	−15.6708	−	27.1426i	−0.589777	−	1.02152i
$707$	−31.3421	−	18.0953i	−1.17874	−	0.680545i
$708$	3.40907	+	1.96823i	0.128121	+	0.0739705i
$709$	−45.4251			−1.70597			−0.852987	−	0.521931i	$-0.825212\pi$
$709$	−45.4251			−1.70597			−0.852987	+	0.521931i	$0.825212\pi$
$710$	−0.760147	−	0.219310i	−0.0285278	−	0.00823055i
$711$	31.7611	−	55.0118i	1.19113	−	2.06310i
$712$	3.78418	+	2.18480i	0.141818	+	0.0818787i
$713$	−0.712157	+	0.411164i	−0.0266705	+	0.0153982i
$714$	5.28036	+	9.14586i	0.197613	+	0.342275i
$715$	−10.4905	−	3.02661i	−0.392322	−	0.113189i
$716$	−0.332592	−	0.576066i	−0.0124295	−	0.0215286i
$717$	−13.0663	+	7.54384i	−0.487971	+	0.281730i
$718$	10.7628	−	6.21388i	0.401662	−	0.231900i
$719$	5.21970	−	9.04078i	0.194662	−	0.337164i	−0.752128	−	0.659017i	$-0.770972\pi$
$719$	5.21970	−	9.04078i	0.194662	−	0.337164i	0.946790	+	0.321853i	$0.104306\pi$
$720$	2.74484	−	9.51386i	0.102294	−	0.354561i
$721$	−1.34789	+	2.33461i	−0.0501980	+	0.0869455i
$722$	−11.6363	+	6.71824i	−0.433060	+	0.250027i
$723$		−	57.7275i		−	2.14691i
$724$	6.04735	+	10.4743i	0.224748	+	0.389275i
$725$	35.8494	−	18.9119i	1.33141	−	0.702369i
$726$	−13.8557	+	23.9989i	−0.514235	+	0.890681i
$727$		−	32.0096i		−	1.18717i	−0.804771	−	0.593586i	$-0.797712\pi$
$727$		−	32.0096i		−	1.18717i	0.804771	−	0.593586i	$-0.202288\pi$
$728$	14.8627	+	8.58098i	0.550848	+	0.318032i
$729$	43.6754			1.61761
$730$	−7.15835	+	24.8115i	−0.264942	+	0.918314i
$731$	−4.58624	−	6.46113i	−0.169628	−	0.238973i
$732$		−	18.7346i		−	0.692451i
$733$		−	5.89677i		−	0.217802i	−0.994053	−	0.108901i	$-0.965267\pi$
$733$		−	5.89677i		−	0.217802i	0.994053	−	0.108901i	$-0.0347332\pi$
$734$	−2.75709	+	4.77541i	−0.101766	+	0.176264i
$735$	19.2277	+	5.54738i	0.709225	+	0.204618i
$736$	−0.0498409	+	0.0863270i	−0.00183716	+	0.00318205i
$737$	−12.7897	−	7.38412i	−0.471114	−	0.271998i
$738$	0.669346	−	0.386447i	0.0246390	−	0.0142253i
$739$	32.5962			1.19907			0.599536	−	0.800348i	$-0.295352\pi$
$739$	32.5962			1.19907			0.599536	+	0.800348i	$0.295352\pi$
$740$	0.0149535	+	0.0603942i	0.000549701	+	0.00222014i
$741$	−17.2021	+	29.7949i	−0.631934	+	1.09454i
$742$		−	3.73622i		−	0.137161i
$743$	5.23180	+	3.02058i	0.191936	+	0.110814i	0.592889	−	0.805285i	$-0.297987\pi$
$743$	5.23180	+	3.02058i	0.191936	+	0.110814i	−0.400953	+	0.916099i	$0.631321\pi$
$744$	−11.2420	−	19.4717i	−0.412151	−	0.713867i
$745$	38.3501	−	9.49542i	1.40504	−	0.347885i
$746$	16.8731	+	29.2250i	0.617766	+	1.07000i
$747$		−	48.1819i		−	1.76288i
$748$	−0.954743	+	0.551221i	−0.0349088	+	0.0201546i
$749$	−20.8050	−	36.0353i	−0.760199	−	1.31670i
$750$	−6.18968	−	29.8366i	−0.226015	−	1.08948i
$751$	−7.25044	+	12.5581i	−0.264572	+	0.458253i	−0.967451	−	0.253057i	$-0.918564\pi$
$751$	−7.25044	+	12.5581i	−0.264572	+	0.458253i	0.702879	+	0.711309i	$0.251897\pi$
$752$			7.23055i			0.263671i
$753$		−	84.6065i		−	3.08323i
$754$	−21.6915	+	37.5708i	−0.789958	+	1.36825i
$755$	−23.0819	−	23.9801i	−0.840037	−	0.872725i
$756$	6.24161	+	10.8108i	0.227005	+	0.393185i
$757$	−28.4969	+	16.4527i	−1.03574	+	0.597982i	−0.918623	−	0.395136i	$-0.870697\pi$
$757$	−28.4969	+	16.4527i	−1.03574	+	0.597982i	−0.117113	+	0.993119i	$0.537364\pi$
$758$		−	7.44448i		−	0.270396i
$759$	0.123939	+	0.214669i	0.00449872	+	0.00779201i
$760$	−1.26761	−	5.11964i	−0.0459811	−	0.185709i
$761$	15.1880	+	26.3064i	0.550565	+	0.953606i	0.998234	+	0.0594069i	$0.0189210\pi$
$761$	15.1880	+	26.3064i	0.550565	+	0.953606i	−0.447669	+	0.894199i	$0.647746\pi$
$762$	23.6478	+	13.6530i	0.856668	+	0.494598i
$763$			44.4421i			1.60891i
$764$	3.47593	−	6.02048i	0.125755	−	0.217813i
$765$	2.87555	+	11.6138i	0.103966	+	0.419898i
$766$	32.9101			1.18909
$767$	−6.69398	+	3.86477i	−0.241706	+	0.139549i
$768$	−2.36034	−	1.36274i	−0.0851714	−	0.0491737i
$769$	12.7673	−	22.1137i	0.460402	−	0.797439i	−0.538579	−	0.842575i	$-0.681039\pi$
$769$	12.7673	−	22.1137i	0.460402	−	0.797439i	0.998981	+	0.0451359i	$0.0143721\pi$
$770$	−1.81358	+	6.28604i	−0.0653570	+	0.226533i
$771$	−14.5745	+	25.2438i	−0.524889	+	0.909134i
$772$			9.13122i			0.328640i
$773$		−	17.7481i		−	0.638355i	−0.947695	−	0.319177i	$-0.896593\pi$
$773$		−	17.7481i		−	0.638355i	0.947695	−	0.319177i	$-0.103407\pi$
$774$	−16.8079	−	23.6792i	−0.604149	−	0.851130i
$775$	−34.9086	−	21.9718i	−1.25395	−	0.789251i
$776$	−17.1148			−0.614385
$777$	−0.210610	−	0.121596i	−0.00755559	−	0.00436222i
$778$		−	2.61573i		−	0.0937785i
$779$	0.205841	−	0.356526i	0.00737500	−	0.0127739i
$780$	22.6182	+	23.4984i	0.809862	+	0.841376i
$781$	0.161408	+	0.279567i	0.00577563	+	0.0100037i
$782$		−	0.120446i		−	0.00430713i
$783$	−27.3281	+	15.7779i	−0.976628	+	0.563857i
$784$	1.64184	−	2.84375i	0.0586372	−	0.101563i
$785$	35.2126	+	10.1592i	1.25679	+	0.362596i
$786$	4.92786	−	8.53531i	0.175771	−	0.304444i
$787$	23.5536	−	13.5987i	0.839595	−	0.484740i	−0.0175317	−	0.999846i	$-0.505581\pi$
$787$	23.5536	−	13.5987i	0.839595	−	0.484740i	0.857126	+	0.515106i	$0.172247\pi$
$788$	17.8426	−	10.3014i	0.635617	−	0.366974i
$789$	2.34646	+	4.06419i	0.0835363	+	0.144689i
$790$	−30.8187	−	8.89150i	−1.09648	−	0.316345i
$791$	−31.7766	−	55.0387i	−1.12985	−	1.95695i
$792$	−3.49900	+	2.02015i	−0.124332	+	0.0717829i
$793$	31.8584	+	18.3935i	1.13133	+	0.653171i
$794$	−10.8443	+	18.7829i	−0.384849	+	0.666579i
$795$	1.96827	−	6.82221i	0.0698075	−	0.241959i
$796$	−12.8760			−0.456377
$797$	28.8639	+	16.6646i	1.02241	+	0.590289i	0.914801	−	0.403904i	$-0.132347\pi$
$797$	28.8639	+	16.6646i	1.02241	+	0.590289i	0.107609	+	0.994193i	$0.465680\pi$
$798$	17.8535	+	10.3077i	0.632007	+	0.364889i
$799$	−4.36835	−	7.56620i	−0.154541	−	0.267673i
$800$	−4.99636	−	0.190781i	−0.176648	−	0.00674511i
$801$	−19.3497			−0.683688
$802$	−15.9301	+	9.19724i	−0.562511	+	0.324766i
$803$	9.12515	−	5.26841i	0.322020	−	0.185918i
$804$	22.0578	+	38.2053i	0.777919	+	1.34740i
$805$	−0.495693	−	0.514981i	−0.0174709	−	0.0181507i
$806$	44.1491			1.55509
$807$	11.7079	+	6.75957i	0.412138	+	0.237948i
$808$	−9.77357	+	5.64277i	−0.343833	+	0.198512i
$809$	−15.0835			−0.530307			−0.265153	−	0.964206i	$-0.585423\pi$
$809$	−15.0835			−0.530307			−0.265153	+	0.964206i	$0.585423\pi$
$810$	−1.43774	−	5.80673i	−0.0505169	−	0.204028i
$811$	13.9562	−	24.1729i	0.490069	−	0.848824i	−0.509866	−	0.860254i	$-0.670305\pi$
$811$	13.9562	−	24.1729i	0.490069	−	0.848824i	0.999935	+	0.0114297i	$0.00363826\pi$
$812$	22.5129	+	12.9978i	0.790049	+	0.456135i
$813$			21.6170i			0.758140i
$814$	0.0126935	−	0.0219857i	0.000444906	−	0.000770599i
$815$	−31.7873	−	9.17094i	−1.11346	−	0.321244i
$816$	3.29321			0.115285
$817$	−14.0596	−	6.44653i	−0.491884	−	0.225536i
$818$		−	9.15657i		−	0.320152i
$819$	−75.9977			−2.65557
$820$	−0.270650	−	0.281182i	−0.00945153	−	0.00981931i
$821$	−9.32940			−0.325598			−0.162799	−	0.986659i	$-0.552052\pi$
$821$	−9.32940			−0.325598			−0.162799	+	0.986659i	$0.552052\pi$
$822$	45.6736	+	26.3697i	1.59305	+	0.919747i
$823$	−19.1493	−	11.0559i	−0.667504	−	0.385384i	0.127626	−	0.991822i	$-0.459264\pi$
$823$	−19.1493	−	11.0559i	−0.667504	−	0.385384i	−0.795130	+	0.606439i	$0.792598\pi$
$824$	0.420320	+	0.728016i	0.0146425	+	0.0253616i
$825$	−6.62308	+	10.5227i	−0.230586	+	0.366353i
$826$	2.31583	+	4.01113i	0.0805779	+	0.139565i
$827$	40.8486	+	23.5840i	1.42045	+	0.820095i	0.996337	−	0.0855165i	$-0.0272540\pi$
$827$	40.8486	+	23.5840i	1.42045	+	0.820095i	0.424109	+	0.905611i	$0.360587\pi$
$828$		−	0.441417i		−	0.0153403i
$829$	13.3018	−	23.0394i	0.461991	−	0.800192i	−0.537069	−	0.843538i	$-0.680469\pi$
$829$	13.3018	−	23.0394i	0.461991	−	0.800192i	0.999060	+	0.0433463i	$0.0138019\pi$
$830$	−23.6165	+	5.84739i	−0.819740	+	0.202966i
$831$	−27.9258	−	48.3689i	−0.968734	−	1.67790i
$832$	4.63472	−	2.67585i	0.160680	−	0.0927686i
$833$			3.96768i			0.137472i
$834$	8.80367	+	15.2484i	0.304846	+	0.528009i
$835$	7.25338	+	29.2950i	0.251013	+	1.01379i
$836$	−1.07603	+	1.86374i	−0.0372153	+	0.0644587i
$837$	27.8107	+	16.0565i	0.961279	+	0.554995i
$838$			21.7483i			0.751281i
$839$	1.35126			0.0466506			0.0233253	−	0.999728i	$-0.492575\pi$
$839$	1.35126			0.0466506			0.0233253	+	0.999728i	$0.492575\pi$
$840$	14.0805	−	13.5532i	0.485825	−	0.467628i
$841$	−18.3567	+	31.7948i	−0.632991	+	1.09637i
$842$	13.5591	−	7.82838i	0.467279	−	0.269784i
$843$	−68.7959	+	39.7193i	−2.36946	+	1.36801i
$844$	21.5897			0.743147
$845$	−33.9487	+	8.40564i	−1.16787	+	0.289163i
$846$	−16.0094	−	27.7291i	−0.550414	−	0.953346i
$847$	−28.2372	+	16.3027i	−0.970241	+	0.560169i
$848$	−1.00900	−	0.582544i	−0.0346490	−	0.0200046i
$849$	−6.71649			−0.230509
$850$	5.34355	−	2.81892i	0.183282	−	0.0966882i
$851$	0.00138681	+	0.00240202i	4.75392e−5	+	8.23402e-5i
$852$		−	0.964314i		−	0.0330368i
$853$	3.69576	−	2.13375i	0.126541	−	0.0730582i	−0.435394	−	0.900240i	$-0.643391\pi$
$853$	3.69576	−	2.13375i	0.126541	−	0.0730582i	0.561934	+	0.827182i	$0.310057\pi$
$854$	11.0216	−	19.0900i	0.377152	−	0.653246i
$855$	16.1968	+	16.8271i	0.553920	+	0.575475i
$856$	−12.9755			−0.443493
$857$	8.46933	+	4.88977i	0.289307	+	0.167031i	0.637629	−	0.770343i	$-0.279915\pi$
$857$	8.46933	+	4.88977i	0.289307	+	0.167031i	−0.348322	+	0.937375i	$0.613249\pi$
$858$		−	13.3081i		−	0.454331i
$859$	−4.17417			−0.142421			−0.0712105	−	0.997461i	$-0.522686\pi$
$859$	−4.17417			−0.142421			−0.0712105	+	0.997461i	$0.522686\pi$
$860$	−9.56658	+	11.1122i	−0.326218	+	0.378922i
$861$	1.52547			0.0519880
$862$			3.94678i			0.134428i
$863$	−28.3525	−	16.3693i	−0.965130	−	0.557218i	−0.0673820	−	0.997727i	$-0.521465\pi$
$863$	−28.3525	−	16.3693i	−0.965130	−	0.557218i	−0.897748	+	0.440509i	$0.854798\pi$
$864$	3.89271			0.132433
$865$	−12.9242	+	12.4402i	−0.439437	+	0.422978i
$866$	15.6778	−	27.1548i	0.532755	−	0.922758i
$867$	36.6797	−	21.1770i	1.24571	−	0.719209i
$868$		−	26.4547i		−	0.897933i
$869$	6.54398	+	11.3345i	0.221989	+	0.384496i
$870$	34.2605	+	35.5936i	1.16154	+	1.20674i
$871$	−86.6247			−2.93516
$872$	12.0019	+	6.92931i	0.406436	+	0.234656i
$873$	65.6350	−	37.8944i	2.22141	−	1.28253i
$874$	−0.117560	−	0.203620i	−0.00397653	−	0.00688756i
$875$	11.2458	−	34.0440i	0.380178	−	1.15090i
$876$	−31.4756			−1.06346
$877$	−23.9229	+	13.8119i	−0.807819	+	0.466395i	−0.846198	−	0.532869i	$-0.821114\pi$
$877$	−23.9229	+	13.8119i	−0.807819	+	0.466395i	0.0383788	+	0.999263i	$0.487781\pi$
$878$	26.5032	−	15.3016i	0.894439	−	0.516404i
$879$	29.2420	−	50.6487i	0.986309	−	1.70834i
$880$	1.41482	+	1.46988i	0.0476937	+	0.0495496i
$881$	3.01383			0.101539			0.0507693	−	0.998710i	$-0.483833\pi$
$881$	3.01383			0.101539			0.0507693	+	0.998710i	$0.483833\pi$
$882$			14.5410i			0.489621i
$883$	−14.5574	−	8.40469i	−0.489894	−	0.282840i	0.234636	−	0.972083i	$-0.424610\pi$
$883$	−14.5574	−	8.40469i	−0.489894	−	0.282840i	−0.724530	+	0.689243i	$0.757943\pi$
$884$	−3.23324	+	5.60014i	−0.108746	+	0.188353i
$885$	2.11552	+	8.54418i	0.0711125	+	0.287209i
$886$	−0.523376	−	0.906515i	−0.0175832	−	0.0304550i
$887$			9.39992i			0.315619i	0.987470	+	0.157809i	$0.0504431\pi$
$887$			9.39992i			0.315619i	−0.987470	+	0.157809i	$0.949557\pi$
$888$	−0.0656757	+	0.0379179i	−0.00220393	+	0.00127244i
$889$	16.0642	+	27.8241i	0.538777	+	0.933190i
$890$	2.34830	+	9.48431i	0.0787151	+	0.317915i
$891$	−1.22044	+	2.11387i	−0.0408863	+	0.0708172i
$892$			12.3882i			0.414786i
$893$	−14.7699	−	8.52738i	−0.494255	−	0.285358i
$894$	24.0777	+	41.7039i	0.805280	+	1.39479i
$895$	0.412311	−	1.42911i	0.0137820	−	0.0477697i
$896$	−1.60341	−	2.77719i	−0.0535661	−	0.0927793i
$897$	1.25917	+	0.726979i	0.0420423	+	0.0242731i
$898$	−11.2387	−	6.48865i	−0.375039	−	0.216529i
$899$	66.8739			2.23037
$900$	19.5834	−	10.3310i	0.652780	−	0.344365i
$901$	1.40778			0.0468999
$902$			0.159245i			0.00530229i
$903$	−5.36166	−	57.0615i	−0.178425	−	1.89889i
$904$	−19.8182			−0.659142
$905$	−7.49685	+	25.9847i	−0.249204	+	0.863762i
$906$	20.2844	−	35.1337i	0.673905	−	1.16724i
$907$		−	0.937129i		−	0.0311169i	−0.999879	−	0.0155584i	$-0.995047\pi$
$907$		−	0.937129i		−	0.0311169i	0.999879	−	0.0155584i	$-0.00495260\pi$
$908$	24.2324	+	13.9906i	0.804182	+	0.464294i
$909$	24.9877	−	43.2799i	0.828789	−	1.43551i
$910$	9.22314	+	37.2505i	0.305744	+	1.23484i
$911$	−6.45171			−0.213755			−0.106877	−	0.994272i	$-0.534085\pi$
$911$	−6.45171			−0.213755			−0.106877	+	0.994272i	$0.534085\pi$
$912$	5.56735	−	3.21431i	0.184353	−	0.106437i
$913$	8.59727	+	4.96364i	0.284528	+	0.164272i
$914$	25.9490			0.858317
$915$	30.1819	−	29.0514i	0.997782	−	0.960410i
$916$	3.26880	+	5.66173i	0.108004	+	0.187069i
$917$	10.0427	−	5.79815i	0.331639	−	0.191472i
$918$	−4.07342	+	2.35179i	−0.134443	+	0.0776206i
$919$	−34.5285			−1.13899			−0.569494	−	0.821995i	$-0.692861\pi$
$919$	−34.5285			−1.13899			−0.569494	+	0.821995i	$0.692861\pi$
$920$	−0.216362	+	0.0535708i	−0.00713324	+	0.00176618i
$921$	−6.75380	−	11.6979i	−0.222545	−	0.385460i
$922$	−16.9101	−	9.76304i	−0.556904	−	0.321529i
$923$	1.63983	+	0.946754i	0.0539755	+	0.0311628i
$924$	−7.97440			−0.262338
$925$	−0.0741083	+	0.117743i	−0.00243667	+	0.00387135i
$926$	−7.62419	+	13.2055i	−0.250546	+	0.433959i
$927$	−3.22385	−	1.86129i	−0.105885	−	0.0611327i
$928$	7.02033	−	4.05319i	0.230454	−	0.133053i
$929$	11.6576	+	20.1915i	0.382473	+	0.662462i	0.991415	−	0.130752i	$-0.0417393\pi$
$929$	11.6576	+	20.1915i	0.382473	+	0.662462i	−0.608942	+	0.793214i	$0.708406\pi$
$930$	13.9366	−	48.3054i	0.456999	−	1.58400i
$931$	3.87263	+	6.70758i	0.126920	+	0.219832i
$932$	1.63608	−	0.944594i	0.0535917	−	0.0309412i
$933$	20.2520	−	11.6925i	0.663021	−	0.382796i
$934$	−19.6400	+	34.0174i	−0.642640	+	1.11308i
$935$	−2.36853	−	0.683343i	−0.0774592	−	0.0223477i
$936$	−11.8494	+	20.5238i	−0.387310	+	0.670840i
$937$	39.0395	−	22.5395i	1.27536	−	0.736332i	0.299372	−	0.954137i	$-0.403223\pi$
$937$	39.0395	−	22.5395i	1.27536	−	0.736332i	0.975992	+	0.217805i	$0.0698896\pi$
$938$			51.9067i			1.69481i
$939$	−18.2858	−	31.6719i	−0.596734	−	1.03357i
$940$	−11.6486	+	11.2123i	−0.379934	+	0.365704i
$941$	−9.36443	+	16.2197i	−0.305272	+	0.528746i	−0.977322	−	0.211760i	$-0.932081\pi$
$941$	−9.36443	+	16.2197i	−0.305272	+	0.528746i	0.672050	+	0.740506i	$0.265414\pi$
$942$			44.6703i			1.45544i
$943$	−0.0150672	−	0.00869906i	−0.000490656	−	0.000283280i
$944$	1.44431			0.0470084
$945$	−7.73767	+	26.8194i	−0.251706	+	0.872437i
$946$	5.95670	−	0.559707i	0.193669	−	0.0181977i
$947$			15.3714i			0.499503i	0.968310	+	0.249752i	$0.0803489\pi$
$947$			15.3714i			0.499503i	−0.968310	+	0.249752i	$0.919651\pi$
$948$		−	39.0963i		−	1.26979i
$949$	30.9024	−	53.5245i	1.00313	−	1.73748i
$950$	6.28219	−	9.98108i	0.203821	−	0.323829i
$951$	−10.1711	+	17.6169i	−0.329821	+	0.571267i
$952$	3.35568	+	1.93740i	0.108758	+	0.0627916i
$953$	−29.9149	+	17.2714i	−0.969039	+	0.559475i	−0.898943	−	0.438065i	$-0.855664\pi$
$953$	−29.9149	+	17.2714i	−0.969039	+	0.559475i	−0.0700958	+	0.997540i	$0.522331\pi$
$954$	5.15932			0.167039
$955$	15.0892	−	3.73605i	0.488274	−	0.120896i
$956$	−2.76789	+	4.79413i	−0.0895200	+	0.155053i
$957$		−	20.1582i		−	0.651621i
$958$	−0.997754	−	0.576054i	−0.0322360	−	0.0186115i
$959$	31.0267	+	53.7397i	1.00190	+	1.73535i
$960$	−1.46472	−	5.91573i	−0.0472738	−	0.190929i
$961$	−18.5274	−	32.0904i	−0.597658	−	1.03517i
$962$		−	0.148910i		−	0.00480104i
$963$	49.7609	−	28.7294i	1.60352	−	0.925793i
$964$	−10.5903	−	18.3430i	−0.341091	−	0.590787i
$965$	−14.7106	+	14.1596i	−0.473551	+	0.455814i
$966$	0.435616	−	0.754509i	0.0140157	−	0.0242759i
$967$		−	35.9741i		−	1.15685i	−0.815736	−	0.578424i	$-0.803668\pi$
$967$		−	35.9741i		−	1.15685i	0.815736	−	0.578424i	$-0.196332\pi$
$968$			10.1675i			0.326797i
$969$	−3.88386	+	6.72705i	−0.124768	+	0.216104i
$970$	−26.5396	−	27.5723i	−0.852134	−	0.885293i
$971$	9.03590	+	15.6506i	0.289976	+	0.502253i	0.973804	−	0.227391i	$-0.0730194\pi$
$971$	9.03590	+	15.6506i	0.289976	+	0.502253i	−0.683828	+	0.729643i	$0.739686\pi$
$972$	16.4281	−	9.48477i	0.526931	−	0.304224i
$973$			20.7169i			0.664153i
$974$	−13.8013	−	23.9046i	−0.442222	−	0.765951i
$975$	−2.78273	+	72.8769i	−0.0891186	+	2.33393i
$976$	−3.43693	−	5.95294i	−0.110014	−	0.190549i
$977$	19.3487	+	11.1710i	0.619021	+	0.357392i	0.776488	−	0.630133i	$-0.216999\pi$
$977$	19.3487	+	11.1710i	0.619021	+	0.357392i	−0.157467	+	0.987524i	$0.550333\pi$
$978$		−	40.3250i		−	1.28945i
$979$	1.99338	−	3.45264i	0.0637088	−	0.110347i
$980$	7.12732	−	1.76471i	0.227674	−	0.0563716i
$981$	−61.3696			−1.95938
$982$	18.9248	−	10.9263i	0.603916	−	0.348671i
$983$	−44.1940	−	25.5154i	−1.40957	−	0.813815i	−0.414223	−	0.910175i	$-0.635947\pi$
$983$	−44.1940	−	25.5154i	−1.40957	−	0.813815i	−0.995347	+	0.0963602i	$0.969280\pi$
$984$	0.237848	−	0.411965i	0.00758233	−	0.0131330i
$985$	44.2640	+	12.7706i	1.41037	+	0.406905i
$986$	−4.89748	+	8.48269i	−0.155968	+	0.270144i
$987$		−	63.1960i		−	2.01155i
$988$			12.6231i			0.401595i
$989$	−0.272438	+	0.594176i	−0.00866302	+	0.0188937i
$990$	−8.68034	−	2.50436i	−0.275879	−	0.0795938i
$991$	−17.1564			−0.544990			−0.272495	−	0.962157i	$-0.587849\pi$
$991$	−17.1564			−0.544990			−0.272495	+	0.962157i	$0.587849\pi$
$992$	−7.14430	−	4.12477i	−0.226832	−	0.130961i
$993$		−	35.9055i		−	1.13943i
$994$	0.567308	−	0.982607i	0.0179939	−	0.0311664i
$995$	−19.9665	−	20.7435i	−0.632981	−	0.657612i
$996$	−14.8274	−	25.6817i	−0.469823	−	0.813757i
$997$		−	21.1303i		−	0.669203i	−0.942360	−	0.334602i	$-0.891398\pi$
$997$		−	21.1303i		−	0.669203i	0.942360	−	0.334602i	$-0.108602\pi$
$998$	−4.98244	+	2.87661i	−0.157716	+	0.0910576i
$999$	0.0541568	−	0.0938023i	0.00171344	−	0.00296777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.j.a.49.12	yes	44
5.4	even	2	inner	430.2.j.a.49.11	✓	44
43.36	even	3	inner	430.2.j.a.79.22	yes	44
215.79	even	6	inner	430.2.j.a.79.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.j.a.49.11	✓	44	5.4	even	2	inner
430.2.j.a.49.12	yes	44	1.1	even	1	trivial
430.2.j.a.79.1	yes	44	215.79	even	6	inner
430.2.j.a.79.22	yes	44	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-2.36034 - 1.36274i) q^{3} -1.00000 q^{4} +(-1.55068 - 1.61102i) q^{5} +(1.36274 - 2.36034i) q^{6} +(2.77719 - 1.60341i) q^{7} -1.00000i q^{8} +(2.21413 + 3.83499i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-2.36034 - 1.36274i) q^{3} -1.00000 q^{4} +(-1.55068 - 1.61102i) q^{5} +(1.36274 - 2.36034i) q^{6} +(2.77719 - 1.60341i) q^{7} -1.00000i q^{8} +(2.21413 + 3.83499i) q^{9} +(1.61102 - 1.55068i) q^{10} -0.912389 q^{11} +(2.36034 + 1.36274i) q^{12} +(-4.63472 + 2.67585i) q^{13} +(1.60341 + 2.77719i) q^{14} +(1.46472 + 5.91573i) q^{15} +1.00000 q^{16} +(-1.04642 + 0.604151i) q^{17} +(-3.83499 + 2.21413i) q^{18} +(-1.17935 + 2.04270i) q^{19} +(1.55068 + 1.61102i) q^{20} -8.74013 q^{21} -0.912389i q^{22} +(0.0863270 + 0.0498409i) q^{23} +(-1.36274 + 2.36034i) q^{24} +(-0.190781 + 4.99636i) q^{25} +(-2.67585 - 4.63472i) q^{26} -3.89271i q^{27} +(-2.77719 + 1.60341i) q^{28} +(-4.05319 - 7.02033i) q^{29} +(-5.91573 + 1.46472i) q^{30} +(-4.12477 + 7.14430i) q^{31} +1.00000i q^{32} +(2.15355 + 1.24335i) q^{33} +(-0.604151 - 1.04642i) q^{34} +(-6.88965 - 1.98773i) q^{35} +(-2.21413 - 3.83499i) q^{36} +(0.0240969 + 0.0139123i) q^{37} +(-2.04270 - 1.17935i) q^{38} +14.5860 q^{39} +(-1.61102 + 1.55068i) q^{40} -0.174537 q^{41} -8.74013i q^{42} +(0.613453 + 6.52868i) q^{43} +0.912389 q^{44} +(2.74484 - 9.51386i) q^{45} +(-0.0498409 + 0.0863270i) q^{46} +7.23055i q^{47} +(-2.36034 - 1.36274i) q^{48} +(1.64184 - 2.84375i) q^{49} +(-4.99636 - 0.190781i) q^{50} +3.29321 q^{51} +(4.63472 - 2.67585i) q^{52} +(-1.00900 - 0.582544i) q^{53} +3.89271 q^{54} +(1.41482 + 1.46988i) q^{55} +(-1.60341 - 2.77719i) q^{56} +(5.56735 - 3.21431i) q^{57} +(7.02033 - 4.05319i) q^{58} +1.44431 q^{59} +(-1.46472 - 5.91573i) q^{60} +(-3.43693 - 5.95294i) q^{61} +(-7.14430 - 4.12477i) q^{62} +(12.2981 + 7.10032i) q^{63} -1.00000 q^{64} +(11.4978 + 3.31723i) q^{65} +(-1.24335 + 2.15355i) q^{66} +(14.0178 + 8.09318i) q^{67} +(1.04642 - 0.604151i) q^{68} +(-0.135841 - 0.235283i) q^{69} +(1.98773 - 6.88965i) q^{70} +(-0.176907 - 0.306412i) q^{71} +(3.83499 - 2.21413i) q^{72} +(-10.0014 + 5.77430i) q^{73} +(-0.0139123 + 0.0240969i) q^{74} +(7.25906 - 11.5331i) q^{75} +(1.17935 - 2.04270i) q^{76} +(-2.53387 + 1.46293i) q^{77} +14.5860i q^{78} +(-7.17235 - 12.4229i) q^{79} +(-1.55068 - 1.61102i) q^{80} +(1.33763 - 2.31685i) q^{81} -0.174537i q^{82} +(-9.42282 - 5.44026i) q^{83} +8.74013 q^{84} +(2.59596 + 0.748961i) q^{85} +(-6.52868 + 0.613453i) q^{86} +22.0938i q^{87} +0.912389i q^{88} +(-2.18480 + 3.78418i) q^{89} +(9.51386 + 2.74484i) q^{90} +(-8.58098 + 14.8627i) q^{91} +(-0.0863270 - 0.0498409i) q^{92} +(19.4717 - 11.2420i) q^{93} -7.23055 q^{94} +(5.11964 - 1.26761i) q^{95} +(1.36274 - 2.36034i) q^{96} -17.1148i q^{97} +(2.84375 + 1.64184i) q^{98} +(-2.02015 - 3.49900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

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