LMFDB - Embedded newform 390.2.be.b.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(17,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("390.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.be (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	390.17
Dual form			390.2.be.b.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.793519 - 1.53959i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16310 + 0.566581i) q^{5} +(1.16496 + 1.28175i) q^{6} +(4.16232 + 1.11529i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.74065 + 2.44338i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.793519 - 1.53959i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16310 + 0.566581i) q^{5} +(1.16496 + 1.28175i) q^{6} +(4.16232 + 1.11529i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.74065 + 2.44338i) q^{9} +(1.94275 - 1.10713i) q^{10} +(1.69009 - 2.92732i) q^{11} +(-1.45700 - 0.936562i) q^{12} +(-0.196065 + 3.60022i) q^{13} -4.30915 q^{14} +(2.58876 + 2.88068i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.12553 + 0.569533i) q^{17} +(1.04895 - 2.81064i) q^{18} +(-2.88749 - 5.00129i) q^{19} +(-1.59001 + 1.57222i) q^{20} +(-1.58579 - 7.29325i) q^{21} +(-0.874856 + 3.26501i) q^{22} +(8.91110 - 2.38772i) q^{23} +(1.64976 + 0.527549i) q^{24} +(4.35797 - 2.45114i) q^{25} +(-0.742420 - 3.52829i) q^{26} +(5.14304 + 0.741018i) q^{27} +(4.16232 - 1.11529i) q^{28} +(0.535774 - 0.927987i) q^{29} +(-3.24612 - 2.11250i) q^{30} -1.90588i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-5.84799 - 0.279155i) q^{33} -2.20051 q^{34} +(-9.63539 - 0.0541891i) q^{35} +(-0.285760 + 2.98636i) q^{36} +(-1.70514 - 6.36367i) q^{37} +(4.08353 + 4.08353i) q^{38} +(5.69843 - 2.55498i) q^{39} +(1.12891 - 1.93017i) q^{40} +(3.09985 - 5.36910i) q^{41} +(3.41939 + 6.63431i) q^{42} +(-1.32563 - 0.355202i) q^{43} -3.38018i q^{44} +(2.38083 - 6.27150i) q^{45} +(-7.98947 + 4.61272i) q^{46} +(4.37366 + 4.37366i) q^{47} +(-1.73008 - 0.0825856i) q^{48} +(10.0188 + 5.78437i) q^{49} +(-3.57508 + 3.49554i) q^{50} +(-0.809801 - 3.72437i) q^{51} +(1.63031 + 3.21591i) q^{52} +(1.30264 + 1.30264i) q^{53} +(-5.15959 + 0.615349i) q^{54} +(-1.99726 + 7.28966i) q^{55} +(-3.73183 + 2.15457i) q^{56} +(-5.40863 + 8.41417i) q^{57} +(-0.277337 + 1.03504i) q^{58} +(-1.13299 + 0.654133i) q^{59} +(3.68227 + 1.20036i) q^{60} +(5.42353 + 9.39383i) q^{61} +(0.493278 + 1.84094i) q^{62} +(-9.97023 + 8.22880i) q^{63} -1.00000i q^{64} +(-1.61571 - 7.89870i) q^{65} +(5.72098 - 1.24393i) q^{66} +(1.54886 + 5.78042i) q^{67} +(2.12553 - 0.569533i) q^{68} +(-10.7472 - 11.8247i) q^{69} +(9.32110 - 2.44148i) q^{70} +(3.45805 + 5.98951i) q^{71} +(-0.496904 - 2.95856i) q^{72} +(2.13050 + 2.13050i) q^{73} +(3.29408 + 5.70551i) q^{74} +(-7.23187 - 4.76445i) q^{75} +(-5.00129 - 2.88749i) q^{76} +(10.2995 - 10.2995i) q^{77} +(-4.84298 + 3.94278i) q^{78} -9.17586i q^{79} +(-0.590875 + 2.15659i) q^{80} +(-2.94024 - 8.50617i) q^{81} +(-1.60460 + 5.98845i) q^{82} +(-10.5216 + 10.5216i) q^{83} +(-5.01996 - 5.52324i) q^{84} +(-4.92041 - 0.0276722i) q^{85} +1.37240 q^{86} +(-1.85386 - 0.0884944i) q^{87} +(0.874856 + 3.26501i) q^{88} +(-15.9723 - 9.22160i) q^{89} +(-0.676522 + 6.67400i) q^{90} +(-4.83137 + 14.7666i) q^{91} +(6.52338 - 6.52338i) q^{92} +(-2.93427 + 1.51235i) q^{93} +(-5.35661 - 3.09264i) q^{94} +(9.07956 + 9.18227i) q^{95} +(1.69250 - 0.368006i) q^{96} +(-2.35371 - 0.630674i) q^{97} +(-11.1746 - 2.99421i) q^{98} +(4.21071 + 9.22500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{3} + 24 q^{7}+O(q^{10}) $ 96 * q + 4 * q^3 + 24 * q^7	$ 96 q + 4 q^{3} + 24 q^{7} + 16 q^{10} - 8 q^{12} + 40 q^{13} + 48 q^{16} - 8 q^{22} + 64 q^{25} - 32 q^{27} + 24 q^{28} - 8 q^{30} - 96 q^{33} - 24 q^{36} + 72 q^{37} - 8 q^{42} + 16 q^{43} - 60 q^{45} + 24 q^{46} - 4 q^{48} - 128 q^{51} - 8 q^{52} + 32 q^{61} - 120 q^{63} - 16 q^{66} - 96 q^{67} - 24 q^{72} - 4 q^{75} - 24 q^{76} - 16 q^{78} - 48 q^{81} + 32 q^{82} + 32 q^{87} + 8 q^{88} - 56 q^{90} - 56 q^{91} - 12 q^{93} + 24 q^{97}+O(q^{100}) $ 96 * q + 4 * q^3 + 24 * q^7 + 16 * q^10 - 8 * q^12 + 40 * q^13 + 48 * q^16 - 8 * q^22 + 64 * q^25 - 32 * q^27 + 24 * q^28 - 8 * q^30 - 96 * q^33 - 24 * q^36 + 72 * q^37 - 8 * q^42 + 16 * q^43 - 60 * q^45 + 24 * q^46 - 4 * q^48 - 128 * q^51 - 8 * q^52 + 32 * q^61 - 120 * q^63 - 16 * q^66 - 96 * q^67 - 24 * q^72 - 4 * q^75 - 24 * q^76 - 16 * q^78 - 48 * q^81 + 32 * q^82 + 32 * q^87 + 8 * q^88 - 56 * q^90 - 56 * q^91 - 12 * q^93 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.793519	−	1.53959i	−0.458138	−	0.888881i
$3$	−0.793519	−	1.53959i	−0.458138	−	0.888881i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.16310	+	0.566581i	−0.967366	+	0.253383i
$5$	−2.16310	+	0.566581i	−0.967366	+	0.253383i
$6$	1.16496	+	1.28175i	0.475591	+	0.523272i
$7$	4.16232	+	1.11529i	1.57321	+	0.421540i	0.936815	−	0.349825i	$-0.113759\pi$
$7$	4.16232	+	1.11529i	1.57321	+	0.421540i	0.636393	+	0.771365i	$0.280426\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.74065	+	2.44338i	−0.580218	+	0.814461i
$10$	1.94275	−	1.10713i	0.614351	−	0.350104i
$11$	1.69009	−	2.92732i	0.509582	−	0.882622i	−0.490357	−	0.871522i	$-0.663133\pi$
$11$	1.69009	−	2.92732i	0.509582	−	0.882622i	0.999938	−	0.0110997i	$-0.00353321\pi$
$12$	−1.45700	−	0.936562i	−0.420600	−	0.270362i
$13$	−0.196065	+	3.60022i	−0.0543787	+	0.998520i
$13$	−0.196065	+	3.60022i	−0.0543787	+	0.998520i
$14$	−4.30915			−1.15167
$15$	2.58876	+	2.88068i	0.668415	+	0.743789i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.12553	+	0.569533i	0.515516	+	0.138132i	0.507192	−	0.861833i	$-0.330684\pi$
$17$	2.12553	+	0.569533i	0.515516	+	0.138132i	0.00832436	+	0.999965i	$0.497350\pi$
$18$	1.04895	−	2.81064i	0.247240	−	0.662475i
$19$	−2.88749	−	5.00129i	−0.662437	−	1.14737i	−0.979973	−	0.199128i	$-0.936189\pi$
$19$	−2.88749	−	5.00129i	−0.662437	−	1.14737i	0.317537	−	0.948246i	$-0.397144\pi$
$20$	−1.59001	+	1.57222i	−0.355536	+	0.351559i
$21$	−1.58579	−	7.29325i	−0.346048	−	1.59152i
$22$	−0.874856	+	3.26501i	−0.186520	+	0.696102i
$23$	8.91110	−	2.38772i	1.85809	−	0.497874i	0.858212	−	0.513296i	$-0.171576\pi$
$23$	8.91110	−	2.38772i	1.85809	−	0.497874i	0.999881	+	0.0154215i	$0.00490900\pi$
$24$	1.64976	+	0.527549i	0.336755	+	0.107686i
$25$	4.35797	−	2.45114i	0.871594	−	0.490228i
$26$	−0.742420	−	3.52829i	−0.145601	−	0.691954i
$27$	5.14304	+	0.741018i	0.989779	+	0.142609i
$28$	4.16232	−	1.11529i	0.786604	−	0.210770i
$29$	0.535774	−	0.927987i	0.0994907	−	0.172323i	−0.811983	−	0.583681i	$-0.801612\pi$
$29$	0.535774	−	0.927987i	0.0994907	−	0.172323i	0.911474	+	0.411358i	$0.134945\pi$
$30$	−3.24612	−	2.11250i	−0.592659	−	0.385689i
$31$		−	1.90588i		−	0.342306i	−0.985244	−	0.171153i	$-0.945251\pi$
$31$		−	1.90588i		−	0.342306i	0.985244	−	0.171153i	$-0.0547492\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−5.84799	−	0.279155i	−1.01800	−	0.0485946i
$34$	−2.20051			−0.377384
$35$	−9.63539	−	0.0541891i	−1.62868	−	0.00915964i
$36$	−0.285760	+	2.98636i	−0.0476266	+	0.497727i
$37$	−1.70514	−	6.36367i	−0.280323	−	1.04618i	−0.952189	−	0.305508i	$-0.901174\pi$
$37$	−1.70514	−	6.36367i	−0.280323	−	1.04618i	0.671866	−	0.740673i	$-0.265493\pi$
$38$	4.08353	+	4.08353i	0.662437	+	0.662437i
$39$	5.69843	−	2.55498i	0.912479	−	0.409124i
$40$	1.12891	−	1.93017i	0.178496	−	0.305187i
$41$	3.09985	−	5.36910i	0.484115	−	0.838512i	−0.515718	−	0.856758i	$-0.672475\pi$
$41$	3.09985	−	5.36910i	0.484115	−	0.838512i	0.999834	+	0.0182462i	$0.00580826\pi$
$42$	3.41939	+	6.63431i	0.527623	+	1.02370i
$43$	−1.32563	−	0.355202i	−0.202157	−	0.0541678i	0.156320	−	0.987707i	$-0.450037\pi$
$43$	−1.32563	−	0.355202i	−0.202157	−	0.0541678i	−0.358477	+	0.933539i	$0.616704\pi$
$44$		−	3.38018i		−	0.509582i
$45$	2.38083	−	6.27150i	0.354913	−	0.934899i
$46$	−7.98947	+	4.61272i	−1.17798	+	0.680109i
$47$	4.37366	+	4.37366i	0.637963	+	0.637963i	0.950053	−	0.312089i	$-0.101029\pi$
$47$	4.37366	+	4.37366i	0.637963	+	0.637963i	−0.312089	+	0.950053i	$0.601029\pi$
$48$	−1.73008	−	0.0825856i	−0.249716	−	0.0119202i
$49$	10.0188	+	5.78437i	1.43126	+	0.826339i
$50$	−3.57508	+	3.49554i	−0.505592	+	0.494345i
$51$	−0.809801	−	3.72437i	−0.113395	−	0.521516i
$52$	1.63031	+	3.21591i	0.226083	+	0.445967i
$53$	1.30264	+	1.30264i	0.178932	+	0.178932i	0.790890	−	0.611958i	$-0.209618\pi$
$53$	1.30264	+	1.30264i	0.178932	+	0.178932i	−0.611958	+	0.790890i	$0.709618\pi$
$54$	−5.15959	+	0.615349i	−0.702131	+	0.0837385i
$55$	−1.99726	+	7.28966i	−0.269311	+	0.982937i
$56$	−3.73183	+	2.15457i	−0.498687	+	0.287917i
$57$	−5.40863	+	8.41417i	−0.716391	+	1.11448i
$58$	−0.277337	+	1.03504i	−0.0364161	+	0.135907i
$59$	−1.13299	+	0.654133i	−0.147503	+	0.0851609i	−0.571935	−	0.820299i	$-0.693807\pi$
$59$	−1.13299	+	0.654133i	−0.147503	+	0.0851609i	0.424432	+	0.905460i	$0.360474\pi$
$60$	3.68227	+	1.20036i	0.475379	+	0.154966i
$61$	5.42353	+	9.39383i	0.694412	+	1.20276i	0.970378	+	0.241590i	$0.0776688\pi$
$61$	5.42353	+	9.39383i	0.694412	+	1.20276i	−0.275966	+	0.961167i	$0.588998\pi$
$62$	0.493278	+	1.84094i	0.0626463	+	0.233799i
$63$	−9.97023	+	8.22880i	−1.25613	+	1.03673i
$64$		−	1.00000i		−	0.125000i
$65$	−1.61571	−	7.89870i	−0.200404	−	0.979713i
$66$	5.72098	−	1.24393i	0.704203	−	0.153117i
$67$	1.54886	+	5.78042i	0.189223	+	0.706191i	0.993687	+	0.112189i	$0.0357862\pi$
$67$	1.54886	+	5.78042i	0.189223	+	0.706191i	−0.804464	+	0.594002i	$0.797547\pi$
$68$	2.12553	−	0.569533i	0.257758	−	0.0690661i
$69$	−10.7472	−	11.8247i	−1.29381	−	1.42353i
$70$	9.32110	−	2.44148i	1.11408	−	0.291813i
$71$	3.45805	+	5.98951i	0.410395	+	0.710824i	0.994933	−	0.100542i	$-0.0320576\pi$
$71$	3.45805	+	5.98951i	0.410395	+	0.710824i	−0.584538	+	0.811366i	$0.698724\pi$
$72$	−0.496904	−	2.95856i	−0.0585607	−	0.348670i
$73$	2.13050	+	2.13050i	0.249356	+	0.249356i	0.820706	−	0.571350i	$-0.193580\pi$
$73$	2.13050	+	2.13050i	0.249356	+	0.249356i	−0.571350	+	0.820706i	$0.693580\pi$
$74$	3.29408	+	5.70551i	0.382929	+	0.663252i
$75$	−7.23187	−	4.76445i	−0.835065	−	0.550151i
$76$	−5.00129	−	2.88749i	−0.573687	−	0.331218i
$77$	10.2995	−	10.2995i	1.17374	−	1.17374i
$78$	−4.84298	+	3.94278i	−0.548360	+	0.446432i
$79$		−	9.17586i		−	1.03236i	−0.856479	−	0.516182i	$-0.827353\pi$
$79$		−	9.17586i		−	1.03236i	0.856479	−	0.516182i	$-0.172647\pi$
$80$	−0.590875	+	2.15659i	−0.0660618	+	0.241114i
$81$	−2.94024	−	8.50617i	−0.326694	−	0.945130i
$82$	−1.60460	+	5.98845i	−0.177198	+	0.661314i
$83$	−10.5216	+	10.5216i	−1.15490	+	1.15490i	−0.169338	+	0.985558i	$0.554163\pi$
$83$	−10.5216	+	10.5216i	−1.15490	+	1.15490i	−0.985558	+	0.169338i	$0.945837\pi$
$84$	−5.01996	−	5.52324i	−0.547723	−	0.602635i
$85$	−4.92041	−	0.0276722i	−0.533693	−	0.00300147i
$86$	1.37240			0.147989
$87$	−1.85386	−	0.0884944i	−0.198755	−	0.00948760i
$88$	0.874856	+	3.26501i	0.0932599	+	0.348051i
$89$	−15.9723	−	9.22160i	−1.69306	−	0.977488i	−0.952026	−	0.306019i	$-0.901003\pi$
$89$	−15.9723	−	9.22160i	−1.69306	−	0.977488i	−0.741033	−	0.671469i	$-0.765664\pi$
$90$	−0.676522	+	6.67400i	−0.0713117	+	0.703502i
$91$	−4.83137	+	14.7666i	−0.506465	+	1.54796i
$92$	6.52338	−	6.52338i	0.680109	−	0.680109i
$93$	−2.93427	+	1.51235i	−0.304269	+	0.156824i
$94$	−5.35661	−	3.09264i	−0.552492	−	0.318982i
$95$	9.07956	+	9.18227i	0.931544	+	0.942081i
$96$	1.69250	−	0.368006i	0.172741	−	0.0375595i
$97$	−2.35371	−	0.630674i	−0.238983	−	0.0640352i	0.137340	−	0.990524i	$-0.456145\pi$
$97$	−2.35371	−	0.630674i	−0.238983	−	0.0640352i	−0.376322	+	0.926489i	$0.622811\pi$
$98$	−11.1746	−	2.99421i	−1.12880	−	0.302461i
$99$	4.21071	+	9.22500i	0.423192	+	0.927148i
$100$	2.54855	−	4.30173i	0.254855	−	0.430173i
$101$	−0.381858	−	0.220466i	−0.0379962	−	0.0219371i	0.480882	−	0.876786i	$-0.340317\pi$
$101$	−0.381858	−	0.220466i	−0.0379962	−	0.0219371i	−0.518878	+	0.854848i	$0.673650\pi$
$102$	1.74615	+	3.38787i	0.172894	+	0.335449i
$103$	−0.625737	+	0.625737i	−0.0616557	+	0.0616557i	−0.737262	−	0.675607i	$-0.763882\pi$
$103$	−0.625737	+	0.625737i	−0.0616557	+	0.0616557i	0.675607	+	0.737262i	$0.263882\pi$
$104$	−2.40710	−	2.68438i	−0.236035	−	0.263225i
$105$	7.56244	+	14.8775i	0.738019	+	1.45190i
$106$	−1.59541	−	0.921108i	−0.154959	−	0.0894659i
$107$	−0.139737	−	0.521504i	−0.0135089	−	0.0504157i	0.958842	−	0.283939i	$-0.0916412\pi$
$107$	−0.139737	−	0.521504i	−0.0135089	−	0.0504157i	−0.972351	+	0.233523i	$0.924975\pi$
$108$	4.82451	−	1.92978i	0.464239	−	0.185693i
$109$	10.2607			0.982798			0.491399	−	0.870935i	$-0.336486\pi$
$109$	10.2607			0.982798			0.491399	+	0.870935i	$0.336486\pi$
$110$	0.0425071	−	7.55820i	0.00405289	−	0.720646i
$111$	−8.44436	+	7.67491i	−0.801503	+	0.728470i
$112$	3.04703	−	3.04703i	0.287917	−	0.287917i
$113$	0.779697	−	2.90987i	0.0733477	−	0.273737i	−0.919506	−	0.393076i	$-0.871411\pi$
$113$	0.779697	−	2.90987i	0.0733477	−	0.273737i	0.992854	+	0.119339i	$0.0380775\pi$
$114$	3.04659	−	9.52732i	0.285340	−	0.892315i
$115$	−17.9227	+	10.2137i	−1.67130	+	0.952435i
$116$		−	1.07155i		−	0.0994907i
$117$	−8.45543	−	6.74580i	−0.781704	−	0.623649i
$118$	0.925084	−	0.925084i	0.0851609	−	0.0851609i
$119$	8.21192	+	4.74116i	0.752786	+	0.434621i
$120$	−3.86748	−	0.206421i	−0.353051	−	0.0188435i
$121$	−0.212819	−	0.368614i	−0.0193472	−	0.0335104i
$122$	−7.67003	−	7.67003i	−0.694412	−	0.694412i
$123$	−10.7260	−	0.512006i	−0.967129	−	0.0461660i
$124$	−0.952939	−	1.65054i	−0.0855765	−	0.148223i
$125$	−8.03795	+	7.77119i	−0.718936	+	0.695077i
$126$	7.50074	−	10.5289i	0.668219	−	0.937989i
$127$	0.328046	−	0.0878996i	0.0291094	−	0.00779983i	−0.244235	−	0.969716i	$-0.578537\pi$
$127$	0.328046	−	0.0878996i	0.0291094	−	0.00779983i	0.273344	+	0.961916i	$0.411870\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	0.505050	+	2.32278i	0.0444672	+	0.204510i
$130$	3.60499	+	7.21138i	0.316178	+	0.632480i
$131$			13.7039i			1.19732i	0.801004	+	0.598659i	$0.204300\pi$
$131$			13.7039i			1.19732i	−0.801004	+	0.598659i	$0.795700\pi$
$132$	−5.20409	+	2.68224i	−0.452957	+	0.233459i
$133$	−6.44078	−	24.0373i	−0.558487	−	2.08430i
$134$	−2.99217	−	5.18258i	−0.258484	−	0.447707i
$135$	−11.5447	+	1.31106i	−0.993613	+	0.112838i
$136$	−1.90570	+	1.10025i	−0.163412	+	0.0943460i
$137$	0.526934	−	1.96654i	0.0450190	−	0.168013i	−0.939756	−	0.341845i	$-0.888948\pi$
$137$	0.526934	−	1.96654i	0.0450190	−	0.168013i	0.984775	+	0.173832i	$0.0556149\pi$
$138$	13.4415	+	8.64020i	1.14422	+	0.735503i
$139$	12.8453	−	7.41626i	1.08953	−	0.629039i	0.156077	−	0.987745i	$-0.450115\pi$
$139$	12.8453	−	7.41626i	1.08953	−	0.629039i	0.933451	+	0.358706i	$0.116782\pi$
$140$	−8.37159	+	4.77077i	−0.707528	+	0.403203i
$141$	3.26304	−	10.2042i	0.274798	−	0.859349i
$142$	−4.89042	−	4.89042i	−0.410395	−	0.410395i
$143$	10.2076	+	6.65864i	0.853605	+	0.556824i
$144$	1.24570	+	2.72914i	0.103809	+	0.227429i
$145$	−0.633150	+	2.31088i	−0.0525803	+	0.191909i
$146$	−2.60932	−	1.50649i	−0.215949	−	0.124678i
$147$	0.955412	−	20.0149i	0.0788011	−	1.65080i
$148$	−4.65853	−	4.65853i	−0.382929	−	0.382929i
$149$	−14.2668	+	8.23697i	−1.16879	+	0.674799i	−0.953394	−	0.301729i	$-0.902436\pi$
$149$	−14.2668	+	8.23697i	−1.16879	+	0.674799i	−0.215392	+	0.976528i	$0.569103\pi$
$150$	8.21858	+	2.73036i	0.671045	+	0.222933i
$151$			1.13106i			0.0920441i	0.998940	+	0.0460221i	$0.0146545\pi$
$151$			1.13106i			0.0920441i	−0.998940	+	0.0460221i	$0.985346\pi$
$152$	5.57821	+	1.49468i	0.452453	+	0.121234i
$153$	−5.09140	+	4.20212i	−0.411615	+	0.339721i
$154$	−7.28285	+	12.6143i	−0.586869	+	1.01649i
$155$	1.07983	+	4.12260i	0.0867344	+	0.331135i
$156$	3.65749	−	5.06189i	0.292834	−	0.405276i
$157$	0.659053	+	0.659053i	0.0525982	+	0.0525982i	0.732917	−	0.680318i	$-0.238159\pi$
$157$	0.659053	+	0.659053i	0.0525982	+	0.0525982i	−0.680318	+	0.732917i	$0.738159\pi$
$158$	2.37489	+	8.86320i	0.188936	+	0.705118i
$159$	0.971860	−	3.03920i	0.0770735	−	0.241025i
$160$	0.0125754	−	2.23603i	0.000994171	−	0.176774i
$161$	39.7538			3.13304
$162$	5.04162	+	7.45534i	0.396107	+	0.585747i
$163$	1.12837	−	4.21113i	0.0883806	−	0.329841i	−0.907552	−	0.419939i	$-0.862051\pi$
$163$	1.12837	−	4.21113i	0.0883806	−	0.329841i	0.995933	+	0.0900982i	$0.0287181\pi$
$164$		−	6.19970i		−	0.484115i
$165$	12.8079	−	2.70952i	0.997096	−	0.210936i
$166$	7.43990	−	12.8863i	0.577448	−	1.00017i
$167$	11.8891	−	3.18568i	0.920009	−	0.246516i	0.232420	−	0.972616i	$-0.425336\pi$
$167$	11.8891	−	3.18568i	0.920009	−	0.246516i	0.687589	+	0.726100i	$0.258669\pi$
$168$	6.27843	+	4.03578i	0.484392	+	0.311367i
$169$	−12.9231	−	1.41175i	−0.994086	−	0.108597i
$170$	4.75991	−	1.24677i	0.365069	−	0.0956226i
$171$	17.2462	+	1.65026i	1.31885	+	0.126198i
$172$	−1.32563	+	0.355202i	−0.101078	+	0.0270839i
$173$	3.11765	−	11.6352i	0.237030	−	0.884609i	−0.740193	−	0.672395i	$-0.765266\pi$
$173$	3.11765	−	11.6352i	0.237030	−	0.884609i	0.977223	−	0.212215i	$-0.0680676\pi$
$174$	1.81360	−	0.394336i	0.137489	−	0.0298945i
$175$	20.8730	−	5.34201i	1.57785	−	0.403818i
$176$	−1.69009	−	2.92732i	−0.127395	−	0.220655i
$177$	1.90615	+	1.22527i	0.143275	+	0.0920971i
$178$	17.8148	+	4.77345i	1.33527	+	0.357785i
$179$	4.87645	−	8.44626i	0.364483	−	0.631303i	−0.624210	−	0.781257i	$-0.714579\pi$
$179$	4.87645	−	8.44626i	0.364483	−	0.631303i	0.988693	+	0.149953i	$0.0479123\pi$
$180$	−1.07389	−	6.62169i	−0.0800429	−	0.493552i
$181$	7.59744			0.564714			0.282357	−	0.959309i	$-0.408884\pi$
$181$	7.59744			0.564714			0.282357	+	0.959309i	$0.408884\pi$
$182$	0.844874	−	15.5139i	0.0626262	−	1.14996i
$183$	10.1589	−	15.8042i	0.750971	−	1.16828i
$184$	−4.61272	+	7.98947i	−0.340055	+	0.588992i
$185$	7.29392	+	12.7991i	0.536259	+	0.941011i
$186$	2.44286	−	2.22026i	0.179119	−	0.162798i
$187$	5.25955	−	5.25955i	0.384616	−	0.384616i
$188$	5.97452	+	1.60087i	0.435737	+	0.116755i
$189$	20.5805	+	8.82033i	1.49701	+	0.641585i
$190$	−11.1467	−	6.51942i	−0.808669	−	0.472969i
$191$	−19.5144	+	11.2667i	−1.41201	+	0.815226i	−0.995578	−	0.0939392i	$-0.970054\pi$
$191$	−19.5144	+	11.2667i	−1.41201	+	0.815226i	−0.416435	+	0.909165i	$0.636721\pi$
$192$	−1.53959	+	0.793519i	−0.111110	+	0.0572673i
$193$	−7.71984	+	2.06853i	−0.555686	+	0.148896i	−0.525724	−	0.850655i	$-0.676205\pi$
$193$	−7.71984	+	2.06853i	−0.555686	+	0.148896i	−0.0299625	+	0.999551i	$0.509539\pi$
$194$	2.43674			0.174947
$195$	−10.8786	+	8.75529i	−0.779036	+	0.626979i
$196$	11.5687			0.826339
$197$	−6.04194	+	1.61893i	−0.430470	+	0.115344i	−0.467547	−	0.883968i	$-0.654862\pi$
$197$	−6.04194	+	1.61893i	−0.430470	+	0.115344i	0.0370767	+	0.999312i	$0.488195\pi$
$198$	−6.45484	−	7.82086i	−0.458725	−	0.555804i
$199$	−21.9713	+	12.6852i	−1.55751	+	0.899227i	−0.560013	+	0.828484i	$0.689204\pi$
$199$	−21.9713	+	12.6852i	−1.55751	+	0.899227i	−0.997495	+	0.0707433i	$0.977463\pi$
$200$	−1.34834	+	4.81477i	−0.0953417	+	0.340456i
$201$	7.67041	−	6.97148i	0.541029	−	0.491730i
$202$	0.425907	+	0.114121i	0.0299667	+	0.00802955i
$203$	3.26503	−	3.26503i	0.229160	−	0.229160i
$204$	−2.56349	−	2.82050i	−0.179480	−	0.197474i
$205$	−3.66324	+	13.3702i	−0.255852	+	0.933814i
$206$	0.442463	−	0.766369i	0.0308279	−	0.0533954i
$207$	−9.67703	+	25.9294i	−0.672600	+	1.80222i
$208$	3.01985	+	1.96991i	0.209389	+	0.136588i
$209$	−19.5205			−1.35026
$210$	−11.1553	−	12.4133i	−0.769792	−	0.856598i
$211$	10.1146	−	17.5190i	0.696317	−	1.20606i	−0.273418	−	0.961895i	$-0.588154\pi$
$211$	10.1146	−	17.5190i	0.696317	−	1.20606i	0.969735	−	0.244161i	$-0.0785125\pi$
$212$	1.77944	+	0.476800i	0.122213	+	0.0327468i
$213$	6.47735	−	10.0768i	0.443821	−	0.690448i
$214$	0.269951	+	0.467568i	0.0184534	+	0.0319623i
$215$	3.06872	+	0.0172584i	0.209285	+	0.00117701i
$216$	−4.16066	+	3.11270i	−0.283097	+	0.211793i
$217$	2.12561	−	7.93287i	0.144296	−	0.538518i
$218$	−9.91109	+	2.65567i	−0.671264	+	0.179865i
$219$	1.58950	−	4.97068i	0.107408	−	0.335887i
$220$	1.91515	+	7.31166i	0.129119	+	0.492952i
$221$	−2.46719	+	7.54069i	−0.165961	+	0.507242i
$222$	6.17021	−	9.59895i	0.414118	−	0.644239i
$223$	−26.7395	+	7.16483i	−1.79061	+	0.479792i	−0.992450	−	0.122653i	$-0.960860\pi$
$223$	−26.7395	+	7.16483i	−1.79061	+	0.479792i	−0.798160	+	0.602446i	$0.794193\pi$
$224$	−2.15457	+	3.73183i	−0.143958	+	0.249343i
$225$	−1.59665	+	14.9148i	−0.106444	+	0.994319i
$226$			3.01252i			0.200390i
$227$	2.62893	−	9.81129i	0.174488	−	0.651198i	−0.822150	−	0.569271i	$-0.807226\pi$
$227$	2.62893	−	9.81129i	0.174488	−	0.651198i	0.996638	−	0.0819278i	$-0.0261077\pi$
$228$	−0.476931	+	9.99120i	−0.0315855	+	0.661683i
$229$	12.0742			0.797883			0.398942	−	0.916976i	$-0.369378\pi$
$229$	12.0742			0.797883			0.398942	+	0.916976i	$0.369378\pi$
$230$	14.6685	−	14.5045i	0.967214	−	0.956395i
$231$	−24.0298	−	7.68413i	−1.58105	−	0.505579i
$232$	0.277337	+	1.03504i	0.0182081	+	0.0679534i
$233$	13.2383	+	13.2383i	0.867267	+	0.867267i	0.992169	−	0.124902i	$-0.0398616\pi$
$233$	13.2383	+	13.2383i	0.867267	+	0.867267i	−0.124902	+	0.992169i	$0.539862\pi$
$234$	9.91326	+	4.32751i	0.648050	+	0.282898i
$235$	−11.9387	−	6.98261i	−0.778793	−	0.455495i
$236$	−0.654133	+	1.13299i	−0.0425805	+	0.0737515i
$237$	−14.1270	+	7.28122i	−0.917649	+	0.472966i
$238$	−9.15921	−	2.45420i	−0.593703	−	0.159082i
$239$		−	20.9409i		−	1.35456i	−0.735727	−	0.677278i	$-0.763159\pi$
$239$		−	20.9409i		−	1.35456i	0.735727	−	0.677278i	$-0.236841\pi$
$240$	3.78912	−	0.801590i	0.244587	−	0.0517424i
$241$	−7.60364	+	4.38996i	−0.489793	+	0.282782i	−0.724489	−	0.689287i	$-0.757924\pi$
$241$	−7.60364	+	4.38996i	−0.489793	+	0.282782i	0.234695	+	0.972069i	$0.424591\pi$
$242$	0.300972	+	0.300972i	0.0193472	+	0.0193472i
$243$	−10.7629	+	11.2766i	−0.690437	+	0.723392i
$244$	9.39383	+	5.42353i	0.601379	+	0.347206i
$245$	−24.9490	−	6.83568i	−1.59393	−	0.436716i
$246$	10.4930	−	2.28153i	0.669010	−	0.145465i
$247$	18.5719	−	9.41503i	1.18170	−	0.599064i
$248$	1.34766	+	1.34766i	0.0855765	+	0.0855765i
$249$	24.5480	+	7.84983i	1.55567	+	0.497463i
$250$	5.75273	−	9.58677i	0.363834	−	0.606321i
$251$	−11.5184	+	6.65018i	−0.727038	+	0.419756i	−0.817338	−	0.576159i	$-0.804551\pi$
$251$	−11.5184	+	6.65018i	−0.727038	+	0.419756i	0.0902996	+	0.995915i	$0.471218\pi$
$252$	−4.52008	+	12.1115i	−0.284738	+	0.762951i
$253$	8.07094	−	30.1212i	0.507416	−	1.89370i
$254$	−0.294118	+	0.169809i	−0.0184546	+	0.0106548i
$255$	3.86183	+	7.59735i	0.241837	+	0.475765i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.85617	+	21.8555i	0.365298	+	1.36331i	0.867017	+	0.498279i	$0.166035\pi$
$257$	5.85617	+	21.8555i	0.365298	+	1.36331i	−0.501719	+	0.865031i	$0.667299\pi$
$258$	−1.08902	−	2.11292i	−0.0677995	−	0.131545i
$259$		−	28.3893i		−	1.76403i
$260$	−5.34859	−	6.03262i	−0.331706	−	0.374127i
$261$	1.33483	+	2.92441i	0.0826240	+	0.181016i
$262$	−3.54684	−	13.2370i	−0.219125	−	0.817784i
$263$	−1.04669	+	0.280459i	−0.0645415	+	0.0172938i	−0.290945	−	0.956740i	$-0.593970\pi$
$263$	−1.04669	+	0.280459i	−0.0645415	+	0.0172938i	0.226404	+	0.974034i	$0.427303\pi$
$264$	4.33255	−	3.93776i	0.266650	−	0.242352i
$265$	−3.55580	−	2.07969i	−0.218431	−	0.127754i
$266$	12.4426	+	21.5513i	0.762907	+	1.32139i
$267$	−1.52314	+	31.9082i	−0.0932149	+	1.95275i
$268$	4.23156	+	4.23156i	0.258484	+	0.258484i
$269$	−0.0522065	−	0.0904244i	−0.00318309	−	0.00551327i	0.864429	−	0.502754i	$-0.167680\pi$
$269$	−0.0522065	−	0.0904244i	−0.00318309	−	0.00551327i	−0.867613	+	0.497241i	$0.834347\pi$
$270$	10.8120	−	4.25438i	0.658000	−	0.258914i
$271$	−6.16959	−	3.56201i	−0.374776	−	0.216377i	0.300767	−	0.953698i	$-0.402757\pi$
$271$	−6.16959	−	3.56201i	−0.374776	−	0.216377i	−0.675543	+	0.737321i	$0.736091\pi$
$272$	1.55599	−	1.55599i	0.0943460	−	0.0943460i
$273$	26.5682	−	4.27925i	1.60798	−	0.258992i
$274$			2.03592i			0.122994i
$275$	0.190094	−	16.8998i	0.0114631	−	1.01910i
$276$	−15.2197	−	4.86688i	−0.916120	−	0.292952i
$277$	1.26232	−	4.71103i	0.0758453	−	0.283058i	−0.917578	−	0.397555i	$-0.869859\pi$
$277$	1.26232	−	4.71103i	0.0758453	−	0.283058i	0.993424	+	0.114497i	$0.0365255\pi$
$278$	−10.4882	+	10.4882i	−0.629039	+	0.629039i
$279$	4.65679	+	3.31748i	0.278795	+	0.198612i
$280$	6.85157	−	6.77493i	0.409460	−	0.404880i
$281$	−18.1741			−1.08418			−0.542088	−	0.840321i	$-0.682366\pi$
$281$	−18.1741			−1.08418			−0.542088	+	0.840321i	$0.682366\pi$
$282$	−0.510816	+	10.7010i	−0.0304186	+	0.637238i
$283$	1.87627	+	7.00234i	0.111533	+	0.416246i	0.999004	−	0.0446168i	$-0.0142067\pi$
$283$	1.87627	+	7.00234i	0.111533	+	0.416246i	−0.887471	+	0.460863i	$0.847540\pi$
$284$	5.98951	+	3.45805i	0.355412	+	0.205197i
$285$	6.93209	−	21.2651i	0.410622	−	1.25963i
$286$	−11.5832	−	3.78982i	−0.684929	−	0.224097i
$287$	18.8906	−	18.8906i	1.11508	−	1.11508i
$288$	−1.90961	−	2.31374i	−0.112525	−	0.136338i
$289$	−10.5289	−	6.07888i	−0.619349	−	0.357581i
$290$	0.0134751	−	2.39601i	0.000791286	−	0.140699i
$291$	0.896734	+	4.12419i	0.0525675	+	0.241764i
$292$	2.91032	+	0.779817i	0.170313	+	0.0456353i
$293$	−4.88878	−	1.30994i	−0.285605	−	0.0765277i	0.113172	−	0.993575i	$-0.463899\pi$
$293$	−4.88878	−	1.30994i	−0.285605	−	0.0765277i	−0.398778	+	0.917048i	$0.630565\pi$
$294$	4.25737	+	19.5802i	0.248295	+	1.14194i
$295$	2.08015	−	2.05689i	0.121111	−	0.119756i
$296$	5.70551	+	3.29408i	0.331626	+	0.191464i
$297$	10.8614	−	13.8030i	0.630243	−	0.800929i
$298$	11.6488	−	11.6488i	0.674799	−	0.674799i
$299$	6.84916	+	32.5500i	0.396097	+	1.88242i
$300$	−8.64521	−	0.510198i	−0.499132	−	0.0294563i
$301$	−5.12155	−	2.95693i	−0.295201	−	0.170434i
$302$	−0.292739	−	1.09252i	−0.0168452	−	0.0628673i
$303$	−0.0364146	+	0.762846i	−0.00209196	+	0.0438244i
$304$	−5.77499			−0.331218
$305$	−17.0540	−	17.2469i	−0.976509	−	0.987554i
$306$	3.83032	−	5.37668i	0.218965	−	0.307365i
$307$	−18.5415	+	18.5415i	−1.05822	+	1.05822i	−0.0600209	+	0.998197i	$0.519117\pi$
$307$	−18.5415	+	18.5415i	−1.05822	+	1.05822i	−0.998197	+	0.0600209i	$0.980883\pi$
$308$	3.76988	−	14.0694i	0.214809	−	0.801678i
$309$	1.45991	+	0.466842i	0.0830515	+	0.0265577i
$310$	−2.11005	−	3.70264i	−0.119843	−	0.210296i
$311$		−	22.3363i		−	1.26658i	−0.773916	−	0.633288i	$-0.781705\pi$
$311$		−	22.3363i		−	1.26658i	0.773916	−	0.633288i	$-0.218295\pi$
$312$	−2.22275	+	5.83604i	−0.125839	+	0.330401i
$313$	−15.4772	+	15.4772i	−0.874822	+	0.874822i	−0.992993	−	0.118171i	$-0.962297\pi$
$313$	−15.4772	+	15.4772i	−0.874822	+	0.874822i	0.118171	+	0.992993i	$0.462297\pi$
$314$	−0.807172	−	0.466021i	−0.0455514	−	0.0262991i
$315$	16.9043	−	23.4486i	0.952449	−	1.32118i
$316$	−4.58793	−	7.94653i	−0.258091	−	0.447027i
$317$	−16.4099	−	16.4099i	−0.921674	−	0.921674i	0.0754737	−	0.997148i	$-0.475953\pi$
$317$	−16.4099	−	16.4099i	−0.921674	−	0.921674i	−0.997148	+	0.0754737i	$0.975953\pi$
$318$	−0.152141	+	3.18718i	−0.00853162	+	0.178728i
$319$	−1.81101	−	3.13677i	−0.101397	−	0.175625i
$320$	0.566581	+	2.16310i	0.0316728	+	0.120921i
$321$	−0.692017	+	0.628960i	−0.0386246	+	0.0351051i
$322$	−38.3992	+	10.2890i	−2.13991	+	0.573386i
$323$	−3.28905	−	12.2749i	−0.183008	−	0.682994i
$324$	−6.79941	−	5.89644i	−0.377745	−	0.327580i
$325$	7.97018	+	16.1702i	0.442106	+	0.896963i
$326$			4.35968i			0.241460i
$327$	−8.14207	−	15.7973i	−0.450258	−	0.873590i
$328$	1.60460	+	5.98845i	0.0885992	+	0.330657i
$329$	13.3266	+	23.0824i	0.734722	+	1.27258i
$330$	−11.6702	+	5.93213i	−0.642425	+	0.326553i
$331$	−11.5104	+	6.64555i	−0.632671	+	0.365273i	−0.781786	−	0.623547i	$-0.785691\pi$
$331$	−11.5104	+	6.64555i	−0.632671	+	0.365273i	0.149115	+	0.988820i	$0.452358\pi$
$332$	−3.85117	+	14.3728i	−0.211361	+	0.788809i
$333$	18.5169	+	6.91064i	1.01472	+	0.378701i
$334$	−10.6595	+	6.15427i	−0.583262	+	0.336746i
$335$	−6.62541	−	11.6261i	−0.361985	−	0.635199i
$336$	−7.10904	−	2.27329i	−0.387830	−	0.124018i
$337$	9.89913	+	9.89913i	0.539240	+	0.539240i	0.923306	−	0.384066i	$-0.125476\pi$
$337$	9.89913	+	9.89913i	0.539240	+	0.539240i	−0.384066	+	0.923306i	$0.625476\pi$
$338$	12.8482	−	1.98110i	0.698848	−	0.107758i
$339$	−5.09870	+	1.10862i	−0.276923	+	0.0602122i
$340$	−4.27503	+	2.43624i	−0.231846	+	0.132124i
$341$	−5.57913	−	3.22111i	−0.302127	−	0.174433i
$342$	−17.0857	+	2.86962i	−0.923887	+	0.155171i
$343$	13.9211	+	13.9211i	0.751668	+	0.751668i
$344$	1.18853	−	0.686198i	0.0640812	−	0.0369973i
$345$	29.9470	+	19.4888i	1.61229	+	1.04924i
$346$			12.0457i			0.647579i
$347$	−12.2788	−	3.29008i	−0.659158	−	0.176621i	−0.0862920	−	0.996270i	$-0.527502\pi$
$347$	−12.2788	−	3.29008i	−0.659158	−	0.176621i	−0.572866	+	0.819649i	$0.694168\pi$
$348$	−1.64974	+	0.850293i	−0.0884353	+	0.0455805i
$349$	−9.15077	+	15.8496i	−0.489829	+	0.848409i	−0.999931	−	0.0117046i	$-0.996274\pi$
$349$	−9.15077	+	15.8496i	−0.489829	+	0.848409i	0.510102	+	0.860114i	$0.329608\pi$
$350$	−18.7791	+	10.5623i	−1.00379	+	0.564579i
$351$	−3.67620	+	18.3708i	−0.196221	+	0.980560i
$352$	2.39015	+	2.39015i	0.127395	+	0.127395i
$353$	−5.46118	−	20.3814i	−0.290669	−	1.08479i	−0.944596	−	0.328235i	$-0.893546\pi$
$353$	−5.46118	−	20.3814i	−0.290669	−	1.08479i	0.653927	−	0.756558i	$-0.273121\pi$
$354$	−2.15832	−	0.690175i	−0.114713	−	0.0366824i
$355$	−10.8736	−	10.9966i	−0.577113	−	0.583641i
$356$	−18.4432			−0.977488
$357$	0.783103	−	16.4052i	0.0414462	−	0.868253i
$358$	−2.52424	+	9.42058i	−0.133410	+	0.497893i
$359$			3.00211i			0.158445i	0.996857	+	0.0792226i	$0.0252438\pi$
$359$			3.00211i			0.158445i	−0.996857	+	0.0792226i	$0.974756\pi$
$360$	2.75112	+	6.11812i	0.144997	+	0.322453i
$361$	−7.17525	+	12.4279i	−0.377645	+	0.654100i
$362$	−7.33857	+	1.96636i	−0.385707	+	0.103350i
$363$	−0.398637	+	0.620156i	−0.0209230	+	0.0325498i
$364$	3.19920	+	15.2039i	0.167683	+	0.796901i
$365$	−5.81557	−	3.40137i	−0.304401	−	0.178036i
$366$	−5.72236	+	17.8950i	−0.299113	+	0.935387i
$367$	8.41526	−	2.25486i	0.439273	−	0.117703i	−0.0324027	−	0.999475i	$-0.510316\pi$
$367$	8.41526	−	2.25486i	0.439273	−	0.117703i	0.471676	+	0.881772i	$0.343649\pi$
$368$	2.38772	−	8.91110i	0.124469	−	0.464523i
$369$	7.72299	+	16.9199i	0.402043	+	0.880813i
$370$	−10.3580	−	10.4752i	−0.538489	−	0.544580i
$371$	3.96919	+	6.87484i	0.206070	+	0.356924i
$372$	−1.78497	+	2.77687i	−0.0925465	+	0.143974i
$373$	−15.3857	−	4.12260i	−0.796644	−	0.213460i	−0.162534	−	0.986703i	$-0.551967\pi$
$373$	−15.3857	−	4.12260i	−0.796644	−	0.213460i	−0.634110	+	0.773243i	$0.718633\pi$
$374$	−3.71906	+	6.44160i	−0.192308	+	0.333087i
$375$	18.3427	+	6.20852i	0.947212	+	0.320607i
$376$	−6.18528			−0.318982
$377$	3.23591	+	2.11085i	0.166658	+	0.108714i
$378$	−22.1621	−	3.19315i	−1.13990	−	0.164238i
$379$	2.43890	−	4.22429i	0.125278	−	0.216987i	−0.796564	−	0.604555i	$-0.793351\pi$
$379$	2.43890	−	4.22429i	0.125278	−	0.216987i	0.921841	+	0.387567i	$0.126684\pi$
$380$	12.4543	+	3.41229i	0.638890	+	0.175047i
$381$	−0.395640	−	0.435305i	−0.0202692	−	0.0223014i
$382$	15.9334	−	15.9334i	0.815226	−	0.815226i
$383$	18.8947	+	5.06283i	0.965475	+	0.258698i	0.706916	−	0.707297i	$-0.250086\pi$
$383$	18.8947	+	5.06283i	0.965475	+	0.258698i	0.258559	+	0.965995i	$0.416752\pi$
$384$	1.28175	−	1.16496i	0.0654090	−	0.0594489i
$385$	−16.4433	+	28.1143i	−0.838029	+	1.43284i
$386$	6.92142	−	3.99608i	0.352291	−	0.203395i
$387$	3.17536	−	2.62074i	0.161413	−	0.133220i
$388$	−2.35371	+	0.630674i	−0.119491	+	0.0320176i
$389$	9.26171			0.469587			0.234794	−	0.972045i	$-0.424559\pi$
$389$	9.26171			0.469587			0.234794	+	0.972045i	$0.424559\pi$
$390$	8.24193	−	11.2726i	0.417346	−	0.570808i
$391$	20.3007			1.02665
$392$	−11.1746	+	2.99421i	−0.564400	+	0.151231i
$393$	21.0984	−	10.8743i	1.06427	−	0.548538i
$394$	5.41705	−	3.12754i	0.272907	−	0.157563i
$395$	5.19887	+	19.8483i	0.261583	+	0.998675i
$396$	8.25908	+	5.88373i	0.415035	+	0.295669i
$397$	−18.7534	−	5.02496i	−0.941207	−	0.252196i	−0.244580	−	0.969629i	$-0.578650\pi$
$397$	−18.7534	−	5.02496i	−0.941207	−	0.252196i	−0.696627	+	0.717433i	$0.745317\pi$
$398$	17.9395	−	17.9395i	0.899227	−	0.899227i
$399$	−31.8967	+	28.9902i	−1.59683	+	1.45133i
$400$	0.0562379	−	4.99968i	0.00281189	−	0.249984i
$401$	−12.8194	+	22.2038i	−0.640170	+	1.10881i	0.345224	+	0.938520i	$0.387803\pi$
$401$	−12.8194	+	22.2038i	−0.640170	+	1.10881i	−0.985395	+	0.170287i	$0.945531\pi$
$402$	−5.60470	+	8.71918i	−0.279537	+	0.434873i
$403$	6.86158	+	0.373677i	0.341799	+	0.0186142i
$404$	−0.440931			−0.0219371
$405$	11.1795	+	16.7338i	0.555512	+	0.831509i
$406$	−2.30873	+	3.99883i	−0.114580	+	0.198459i
$407$	−21.5104	−	5.76369i	−1.06623	−	0.285695i
$408$	3.20614	+	2.06091i	0.158728	+	0.102030i
$409$	−6.47241	−	11.2105i	−0.320040	−	0.554326i	0.660456	−	0.750865i	$-0.270363\pi$
$409$	−6.47241	−	11.2105i	−0.320040	−	0.554326i	−0.980496	+	0.196539i	$0.937030\pi$
$410$	0.0779635	−	13.8627i	0.00385034	−	0.684631i
$411$	−3.44580	+	0.749230i	−0.169969	+	0.0369568i
$412$	−0.229036	+	0.854773i	−0.0112838	+	0.0421117i
$413$	−5.44542	+	1.45910i	−0.267952	+	0.0717974i
$414$	2.63626	−	27.5505i	0.129565	−	1.35403i
$415$	16.7979	−	28.7206i	0.824577	−	1.40984i
$416$	−3.42680	−	1.12119i	−0.168013	−	0.0549708i
$417$	−21.6110	−	13.8916i	−1.05830	−	0.680273i
$418$	18.8554	−	5.05228i	0.922247	−	0.247115i
$419$	5.25335	−	9.09907i	0.256643	−	0.444519i	−0.708697	−	0.705512i	$-0.750717\pi$
$419$	5.25335	−	9.09907i	0.256643	−	0.444519i	0.965340	+	0.260994i	$0.0840502\pi$
$420$	13.9880	+	9.10309i	0.682546	+	0.444185i
$421$			11.9637i			0.583076i	0.956559	+	0.291538i	$0.0941669\pi$
$421$			11.9637i			0.583076i	−0.956559	+	0.291538i	$0.905833\pi$
$422$	−5.23570	+	19.5399i	−0.254870	+	0.951187i
$423$	−18.2995	+	3.07349i	−0.889754	+	0.149438i
$424$	−1.84222			−0.0894659
$425$	10.6590	−	2.72795i	0.517037	−	0.132325i
$426$	−3.64858	+	11.4099i	−0.176774	+	0.552810i
$427$	12.0976	+	45.1489i	0.585445	+	2.18491i
$428$	−0.381768	−	0.381768i	−0.0184534	−	0.0184534i
$429$	2.15160	−	20.9993i	0.103880	−	1.01386i
$430$	−2.96862	+	0.777573i	−0.143160	+	0.0374979i
$431$	7.82146	−	13.5472i	0.376746	−	0.652544i	−0.613840	−	0.789430i	$-0.710376\pi$
$431$	7.82146	−	13.5472i	0.376746	−	0.652544i	0.990587	+	0.136886i	$0.0437095\pi$
$432$	3.21326	−	4.08350i	0.154598	−	0.196467i
$433$	−23.5253	−	6.30358i	−1.13055	−	0.302931i	−0.355406	−	0.934712i	$-0.615657\pi$
$433$	−23.5253	−	6.30358i	−1.13055	−	0.302931i	−0.775146	+	0.631782i	$0.782324\pi$
$434$			8.21271i			0.394223i
$435$	4.06022	−	0.858942i	0.194673	−	0.0411831i
$436$	8.88604	−	5.13036i	0.425564	−	0.245700i
$437$	−37.6724	−	37.6724i	−1.80212	−	1.80212i
$438$	−0.248829	+	5.21270i	−0.0118895	+	0.249072i
$439$	4.78870	+	2.76476i	0.228552	+	0.131955i	0.609904	−	0.792475i	$-0.291208\pi$
$439$	4.78870	+	2.76476i	0.228552	+	0.131955i	−0.381352	+	0.924430i	$0.624541\pi$
$440$	−3.74229	−	6.56685i	−0.178407	−	0.313062i
$441$	−31.5728	+	14.4112i	−1.50346	+	0.686249i
$442$	0.431443	−	7.92231i	0.0205217	−	0.376826i
$443$	13.4799	+	13.4799i	0.640450	+	0.640450i	0.950666	−	0.310216i	$-0.100402\pi$
$443$	13.4799	+	13.4799i	0.640450	+	0.640450i	−0.310216	+	0.950666i	$0.600402\pi$
$444$	−3.47558	+	10.8688i	−0.164944	+	0.515813i
$445$	39.7744	+	10.8976i	1.88549	+	0.516597i
$446$	23.9740	−	13.8414i	1.13520	−	0.655409i
$447$	24.0025	+	15.4289i	1.13528	+	0.729760i
$448$	1.11529	−	4.16232i	0.0526925	−	0.196651i
$449$	16.2033	−	9.35496i	0.764679	−	0.441488i	−0.0662939	−	0.997800i	$-0.521117\pi$
$449$	16.2033	−	9.35496i	0.764679	−	0.441488i	0.830973	+	0.556312i	$0.187784\pi$
$450$	−2.31798	−	14.8198i	−0.109271	−	0.698613i
$451$	−10.4781	−	18.1485i	−0.493392	−	0.854581i
$452$	−0.779697	−	2.90987i	−0.0366738	−	0.136869i
$453$	1.74136	−	0.897516i	0.0818163	−	0.0421690i
$454$			10.1574i			0.476710i
$455$	2.08426	−	34.6789i	0.0977115	−	1.62577i
$456$	−2.12523	−	9.77419i	−0.0995231	−	0.457719i
$457$	−4.07178	−	15.1961i	−0.190470	−	0.710843i	−0.993393	−	0.114761i	$-0.963390\pi$
$457$	−4.07178	−	15.1961i	−0.190470	−	0.710843i	0.802923	−	0.596082i	$-0.203277\pi$
$458$	−11.6627	+	3.12502i	−0.544964	+	0.146023i
$459$	10.5096	+	4.50419i	0.490548	+	0.210237i
$460$	−10.4147	+	17.8067i	−0.485587	+	0.830242i
$461$	−5.65705	−	9.79830i	−0.263475	−	0.456352i	0.703688	−	0.710509i	$-0.251535\pi$
$461$	−5.65705	−	9.79830i	−0.263475	−	0.456352i	−0.967163	+	0.254157i	$0.918202\pi$
$462$	25.1998	+	1.20292i	1.17240	+	0.0559648i
$463$	14.9083	+	14.9083i	0.692848	+	0.692848i	0.962858	−	0.270009i	$-0.0870268\pi$
$463$	14.9083	+	14.9083i	0.692848	+	0.692848i	−0.270009	+	0.962858i	$0.587027\pi$
$464$	−0.535774	−	0.927987i	−0.0248727	−	0.0430807i
$465$	5.49023	−	4.93386i	0.254603	−	0.228802i
$466$	−16.2135	−	9.36086i	−0.751076	−	0.433634i
$467$	6.70377	−	6.70377i	0.310213	−	0.310213i	−0.534779	−	0.844992i	$-0.679605\pi$
$467$	6.70377	−	6.70377i	0.310213	−	0.310213i	0.844992	+	0.534779i	$0.179605\pi$
$468$	−10.6955	−	1.61432i	−0.494400	−	0.0746219i
$469$			25.7874i			1.19075i
$470$	13.3391	+	3.65473i	0.615287	+	0.168580i
$471$	0.491698	−	1.53764i	0.0226563	−	0.0708508i
$472$	0.338604	−	1.26369i	0.0155855	−	0.0581660i
$473$	−3.28023	+	3.28023i	−0.150825	+	0.150825i
$474$	11.7611	−	10.6895i	0.540207	−	0.490983i
$475$	−24.8425	−	14.7178i	−1.13985	−	0.675300i
$476$	9.48231			0.434621
$477$	−5.45031	+	0.915404i	−0.249552	+	0.0419135i
$478$	5.41991	+	20.2274i	0.247901	+	0.925179i
$479$	24.6721	+	14.2444i	1.12730	+	0.650845i	0.943254	−	0.332073i	$-0.107748\pi$
$479$	24.6721	+	14.2444i	1.12730	+	0.650845i	0.184043	+	0.982918i	$0.441081\pi$
$480$	−3.45254	+	1.75497i	−0.157586	+	0.0801032i
$481$	23.2449	−	4.89118i	1.05988	−	0.223019i
$482$	6.20834	−	6.20834i	0.282782	−	0.282782i
$483$	−31.5454	−	61.2044i	−1.43537	−	2.78490i
$484$	−0.368614	−	0.212819i	−0.0167552	−	0.00967361i
$485$	5.44862	+	0.0306429i	0.247409	+	0.00139142i
$486$	7.47753	−	13.6780i	0.339187	−	0.620445i
$487$	−8.84769	−	2.37073i	−0.400927	−	0.107428i	0.0527203	−	0.998609i	$-0.483211\pi$
$487$	−8.84769	−	2.37073i	−0.400927	−	0.107428i	−0.453648	+	0.891181i	$0.649877\pi$
$488$	−10.4775	−	2.80743i	−0.474292	−	0.127086i
$489$	−7.37878	+	1.60439i	−0.333680	+	0.0725530i
$490$	25.8681	+	0.145481i	1.16860	+	0.00657218i
$491$	25.8849	+	14.9447i	1.16817	+	0.674443i	0.953248	−	0.302188i	$-0.0977171\pi$
$491$	25.8849	+	14.9447i	1.16817	+	0.674443i	0.214921	+	0.976631i	$0.431050\pi$
$492$	−9.54497	+	4.91958i	−0.430321	+	0.221792i
$493$	1.66732	−	1.66732i	0.0750924	−	0.0750924i
$494$	−15.5022	+	13.9010i	−0.697479	+	0.625434i
$495$	−14.3349	−	17.5689i	−0.644305	−	0.789662i
$496$	−1.65054	−	0.952939i	−0.0741114	−	0.0427882i
$497$	7.71345	+	28.7870i	0.345995	+	1.29127i
$498$	−25.7433	−	1.22886i	−1.15358	−	0.0550664i
$499$	20.4195			0.914102			0.457051	−	0.889440i	$-0.348906\pi$
$499$	20.4195			0.914102			0.457051	+	0.889440i	$0.348906\pi$
$500$	−3.07547	+	10.7490i	−0.137539	+	0.480711i
$501$	−14.3389	−	15.7764i	−0.640614	−	0.704840i
$502$	9.40477	−	9.40477i	0.419756	−	0.419756i
$503$	−6.15483	+	22.9701i	−0.274430	+	1.02419i	0.681792	+	0.731546i	$0.261201\pi$
$503$	−6.15483	+	22.9701i	−0.274430	+	1.02419i	−0.956222	+	0.292641i	$0.905466\pi$
$504$	1.23138	−	12.8687i	0.0548500	−	0.573216i
$505$	0.950906	+	0.260535i	0.0423148	+	0.0115937i
$506$			31.1837i			1.38628i
$507$	8.08122	+	21.0165i	0.358900	+	0.933376i
$508$	0.240146	−	0.240146i	0.0106548	−	0.0106548i
$509$	11.0516	+	6.38062i	0.489852	+	0.282816i	0.724513	−	0.689261i	$-0.242065\pi$
$509$	11.0516	+	6.38062i	0.489852	+	0.282816i	−0.234661	+	0.972077i	$0.575398\pi$
$510$	−5.69658	−	6.33896i	−0.252249	−	0.280694i
$511$	6.49169	+	11.2439i	0.287175	+	0.497402i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−11.1445	−	27.8615i	−0.492040	−	1.23012i
$514$	−11.3133	−	19.5951i	−0.499006	−	0.864304i
$515$	0.999000	−	1.70806i	0.0440212	−	0.0752662i
$516$	1.59878	+	1.75907i	0.0703823	+	0.0774385i
$517$	20.1950	−	5.41123i	0.888175	−	0.237986i
$518$	7.34770	+	27.4220i	0.322839	+	1.20485i
$519$	−20.3873	+	4.43288i	−0.894905	+	0.194582i
$520$	6.72770	+	4.44275i	0.295029	+	0.194827i
$521$		−	13.2838i		−	0.581975i	−0.956727	−	0.290988i	$-0.906016\pi$
$521$		−	13.2838i		−	0.581975i	0.956727	−	0.290988i	$-0.0939838\pi$
$522$	−2.04624	−	2.47928i	−0.0895615	−	0.108515i
$523$	8.85892	+	33.0619i	0.387374	+	1.44570i	0.834391	+	0.551173i	$0.185819\pi$
$523$	8.85892	+	33.0619i	0.387374	+	1.44570i	−0.447018	+	0.894525i	$0.647514\pi$
$524$	6.85197	+	11.8680i	0.299330	+	0.518454i
$525$	−24.7876	−	27.8968i	−1.08182	−	1.21752i
$526$	0.938434	−	0.541805i	0.0409177	−	0.0236238i
$527$	1.08546	−	4.05100i	0.0472834	−	0.176464i
$528$	−3.16575	+	4.92493i	−0.137772	+	0.214330i
$529$	53.7879	−	31.0545i	2.33860	−	1.35019i
$530$	3.97290	+	1.08852i	0.172572	+	0.0472822i
$531$	0.373850	−	3.90695i	0.0162237	−	0.169547i
$532$	−17.5965	−	17.5965i	−0.762907	−	0.762907i
$533$	18.7221	+	12.2128i	0.810946	+	0.528996i
$534$	−6.78721	−	31.2152i	−0.293711	−	1.35081i
$535$	0.597738	+	1.04889i	0.0258425	+	0.0453476i
$536$	−5.18258	−	2.99217i	−0.223854	−	0.129242i
$537$	−16.8733	−	0.805450i	−0.728137	−	0.0347577i
$538$	0.0738312	+	0.0738312i	0.00318309	+	0.00318309i
$539$	33.8655	−	19.5522i	1.45869	−	0.842175i
$540$	−9.34251	+	6.90778i	−0.402038	+	0.297264i
$541$		−	42.2101i		−	1.81476i	−0.420316	−	0.907378i	$-0.638081\pi$
$541$		−	42.2101i		−	1.81476i	0.420316	−	0.907378i	$-0.361919\pi$
$542$	6.88128	+	1.84383i	0.295576	+	0.0791994i
$543$	−6.02872	−	11.6969i	−0.258717	−	0.501963i
$544$	−1.10025	+	1.90570i	−0.0471730	+	0.0817060i
$545$	−22.1949	+	5.81353i	−0.950726	+	0.249024i
$546$	−24.5554	+	11.0098i	−1.05087	+	0.471175i
$547$	17.5451	+	17.5451i	0.750173	+	0.750173i	0.974511	−	0.224338i	$-0.0720220\pi$
$547$	17.5451	+	17.5451i	0.750173	+	0.750173i	−0.224338	+	0.974511i	$0.572022\pi$
$548$	−0.526934	−	1.96654i	−0.0225095	−	0.0840066i
$549$	−32.3932	−	3.09965i	−1.38251	−	0.132290i
$550$	4.19039	+	16.3732i	0.178679	+	0.698156i
$551$	−6.18817			−0.263625
$552$	15.9608	+	0.761890i	0.679336	+	0.0324282i
$553$	10.2337	−	38.1928i	0.435183	−	1.62412i
$554$			4.87722i			0.207213i
$555$	13.9175	−	21.3860i	0.590765	−	0.907784i
$556$	7.41626	−	12.8453i	0.314520	−	0.544764i
$557$	24.8201	−	6.65053i	1.05166	−	0.281792i	0.308723	−	0.951152i	$-0.400098\pi$
$557$	24.8201	−	6.65053i	1.05166	−	0.281792i	0.742938	+	0.669360i	$0.233432\pi$
$558$	−5.35674	−	1.99917i	−0.226769	−	0.0846316i
$559$	1.53871	−	4.70292i	0.0650807	−	0.198912i
$560$	−4.86463	+	8.31740i	−0.205568	+	0.351474i
$561$	−12.2711	−	3.92398i	−0.518085	−	0.165670i
$562$	17.5548	−	4.70381i	0.740507	−	0.198418i
$563$	2.23973	−	8.35880i	0.0943935	−	0.352281i	−0.902533	−	0.430620i	$-0.858295\pi$
$563$	2.23973	−	8.35880i	0.0943935	−	0.352281i	0.996927	+	0.0783387i	$0.0249616\pi$
$564$	−2.27622	−	10.4686i	−0.0958463	−	0.440808i
$565$	−0.0378835	+	6.73608i	−0.00159377	+	0.283389i
$566$	−3.62468	−	6.27813i	−0.152357	−	0.263889i
$567$	−2.75138	−	38.6846i	−0.115547	−	1.62460i
$568$	−6.68043	−	1.79002i	−0.280305	−	0.0751074i
$569$	−17.5904	+	30.4675i	−0.737428	+	1.27726i	0.216222	+	0.976344i	$0.430626\pi$
$569$	−17.5904	+	30.4675i	−0.737428	+	1.27726i	−0.953650	+	0.300918i	$0.902707\pi$
$570$	−1.19208	+	22.3346i	−0.0499306	+	0.935495i
$571$	1.84208			0.0770886			0.0385443	−	0.999257i	$-0.487728\pi$
$571$	1.84208			0.0770886			0.0385443	+	0.999257i	$0.487728\pi$
$572$	12.1694	+	0.662737i	0.508828	+	0.0277104i
$573$	32.8310	+	21.1038i	1.37154	+	0.881625i
$574$	−13.3577	+	23.1362i	−0.557540	+	0.965687i
$575$	32.9817	−	32.2480i	1.37543	−	1.34483i
$576$	2.44338	+	1.74065i	0.101808	+	0.0725273i
$577$	−20.6516	+	20.6516i	−0.859737	+	0.859737i	−0.991307	−	0.131570i	$-0.957998\pi$
$577$	−20.6516	+	20.6516i	−0.859737	+	0.859737i	0.131570	+	0.991307i	$0.457998\pi$
$578$	11.7435	+	3.14666i	0.488465	+	0.130884i
$579$	9.31052	+	10.2440i	0.386932	+	0.425724i
$580$	0.607118	+	2.31786i	0.0252092	+	0.0962439i
$581$	−55.5289	+	32.0596i	−2.30373	+	1.33006i
$582$	−1.93360	−	3.75157i	−0.0801502	−	0.155507i
$583$	6.01485	−	1.61167i	0.249109	−	0.0667487i
$584$	−3.01298			−0.124678
$585$	22.1119	+	9.80112i	0.914216	+	0.405227i
$586$	5.06123			0.209078
$587$	−30.5412	+	8.18350i	−1.26057	+	0.337769i	−0.826412	−	0.563066i	$-0.809622\pi$
$587$	−30.5412	+	8.18350i	−1.26057	+	0.337769i	−0.434160	+	0.900836i	$0.642955\pi$
$588$	−9.18002	−	17.8111i	−0.378578	−	0.734517i
$589$	−9.53185	+	5.50321i	−0.392753	+	0.226756i
$590$	−1.47691	+	2.52518i	−0.0608035	+	0.103960i
$591$	7.28688	+	8.01743i	0.299742	+	0.329793i
$592$	−6.36367	−	1.70514i	−0.261545	−	0.0700808i
$593$	−23.6436	+	23.6436i	−0.970925	+	0.970925i	−0.999589	−	0.0286637i	$-0.990875\pi$
$593$	−23.6436	+	23.6436i	−0.970925	+	0.970925i	0.0286637	+	0.999589i	$0.490875\pi$
$594$	−6.91885	+	16.1438i	−0.283884	+	0.662388i
$595$	−20.4494	−	5.60286i	−0.838345	−	0.229695i
$596$	−8.23697	+	14.2668i	−0.337399	+	0.584393i
$597$	36.9646	+	23.7609i	1.51286	+	0.972468i
$598$	−15.0403	−	29.6682i	−0.615046	−	1.21322i
$599$	−43.3969			−1.77315			−0.886575	−	0.462584i	$-0.846922\pi$
$599$	−43.3969			−1.77315			−0.886575	+	0.462584i	$0.846922\pi$
$600$	8.48268	−	1.74473i	0.346304	−	0.0712284i
$601$	7.30029	−	12.6445i	0.297785	−	0.515779i	−0.677844	−	0.735206i	$-0.737085\pi$
$601$	7.30029	−	12.6445i	0.297785	−	0.515779i	0.975629	+	0.219427i	$0.0704188\pi$
$602$	5.71234	+	1.53062i	0.232818	+	0.0623833i
$603$	−16.8198	−	6.27726i	−0.684956	−	0.255630i
$604$	0.565529	+	0.979524i	0.0230110	+	0.0398563i
$605$	0.669199	+	0.676768i	0.0272068	+	0.0275146i
$606$	−0.162265	−	0.746278i	−0.00659158	−	0.0303155i
$607$	5.69823	−	21.2661i	0.231284	−	0.863164i	−0.748505	−	0.663130i	$-0.769228\pi$
$607$	5.69823	−	21.2661i	0.231284	−	0.863164i	0.979789	−	0.200035i	$-0.0641055\pi$
$608$	5.57821	−	1.49468i	0.226226	−	0.0606172i
$609$	−7.61767	−	2.43594i	−0.308683	−	0.0987091i
$610$	20.9367	+	12.2453i	0.847703	+	0.495799i
$611$	−16.6036	+	14.8886i	−0.671711	+	0.602328i
$612$	−2.30822	+	6.18484i	−0.0933043	+	0.250007i
$613$	26.6408	−	7.13839i	1.07601	−	0.288317i	0.323052	−	0.946381i	$-0.395291\pi$
$613$	26.6408	−	7.13839i	1.07601	−	0.288317i	0.752962	+	0.658064i	$0.228625\pi$
$614$	13.1108	−	22.7086i	0.529109	−	0.916444i
$615$	23.4914	−	4.96962i	0.947265	−	0.200394i
$616$			14.5657i			0.586869i
$617$	−4.33801	+	16.1897i	−0.174642	+	0.651772i	0.821971	+	0.569530i	$0.192875\pi$
$617$	−4.33801	+	16.1897i	−0.174642	+	0.651772i	−0.996612	+	0.0822418i	$0.973792\pi$
$618$	−1.53099	−	0.0730822i	−0.0615856	−	0.00293980i
$619$	4.76038			0.191336			0.0956679	−	0.995413i	$-0.469501\pi$
$619$	4.76038			0.191336			0.0956679	+	0.995413i	$0.469501\pi$
$620$	2.99646	+	3.03036i	0.120341	+	0.121702i
$621$	47.5995	−	5.67688i	1.91010	−	0.227805i
$622$	5.78106	+	21.5752i	0.231799	+	0.865087i
$623$	−56.1969	−	56.1969i	−2.25148	−	2.25148i
$624$	0.636535	−	6.21247i	0.0254818	−	0.248698i
$625$	12.9838	−	21.3640i	0.519354	−	0.854559i
$626$	10.9440	−	18.9556i	0.437411	−	0.757618i
$627$	15.4899	+	30.0535i	0.618607	+	1.20022i
$628$	0.900284	+	0.241230i	0.0359252	+	0.00962614i
$629$		−	14.4973i		−	0.578045i
$630$	−10.2593	+	27.0248i	−0.408742	+	1.07669i
$631$	−5.57619	+	3.21941i	−0.221985	+	0.128163i	−0.606869	−	0.794802i	$-0.707575\pi$
$631$	−5.57619	+	3.21941i	−0.221985	+	0.128163i	0.384884	+	0.922965i	$0.374241\pi$
$632$	6.48831	+	6.48831i	0.258091	+	0.258091i
$633$	−34.9981	−	1.67064i	−1.39105	−	0.0664019i
$634$	20.0980	+	11.6036i	0.798193	+	0.460837i
$635$	−0.659793	+	0.376000i	−0.0261831	+	0.0149211i
$636$	−0.677947	−	3.11796i	−0.0268823	−	0.123635i
$637$	−22.7893	+	34.9358i	−0.902946	+	1.38421i
$638$	2.56116	+	2.56116i	0.101397	+	0.101397i
$639$	−20.6539	−	1.97634i	−0.817057	−	0.0781828i
$640$	−1.10713	−	1.94275i	−0.0437630	−	0.0767939i
$641$	25.0624	−	14.4698i	0.989904	−	0.571522i	0.0846586	−	0.996410i	$-0.473020\pi$
$641$	25.0624	−	14.4698i	0.989904	−	0.571522i	0.905246	+	0.424888i	$0.139687\pi$
$642$	0.505651	−	0.786636i	0.0199564	−	0.0310461i
$643$	−10.3484	+	38.6207i	−0.408101	+	1.52305i	0.390163	+	0.920746i	$0.372418\pi$
$643$	−10.3484	+	38.6207i	−0.408101	+	1.52305i	−0.798264	+	0.602307i	$0.794248\pi$
$644$	34.4278	−	19.8769i	1.35665	−	0.783260i
$645$	−2.40852	−	4.73826i	−0.0948353	−	0.186569i
$646$	6.35395	+	11.0054i	0.249993	+	0.433001i
$647$	3.58467	+	13.3782i	0.140928	+	0.525951i	0.999903	+	0.0139329i	$0.00443512\pi$
$647$	3.58467	+	13.3782i	0.140928	+	0.525951i	−0.858975	+	0.512018i	$0.828898\pi$
$648$	8.09384	+	3.93571i	0.317956	+	0.154609i
$649$			4.42218i			0.173586i
$650$	−11.8838	−	13.5564i	−0.466120	−	0.531726i
$651$	−13.9000	+	3.02233i	−0.544786	+	0.118454i
$652$	−1.12837	−	4.21113i	−0.0441903	−	0.164920i
$653$	−45.0982	+	12.0840i	−1.76483	+	0.472884i	−0.987687	−	0.156442i	$-0.949997\pi$
$653$	−45.0982	+	12.0840i	−1.76483	+	0.472884i	−0.777141	+	0.629327i	$0.783331\pi$
$654$	11.9533	+	13.1517i	0.467410	+	0.514271i
$655$	−7.76439	−	29.6429i	−0.303380	−	1.15825i
$656$	−3.09985	−	5.36910i	−0.121029	−	0.209628i
$657$	−8.91409	+	1.49716i	−0.347772	+	0.0584099i
$658$	−18.8467	−	18.8467i	−0.734722	−	0.734722i
$659$	−2.76620	−	4.79120i	−0.107756	−	0.186639i	0.807105	−	0.590408i	$-0.201033\pi$
$659$	−2.76620	−	4.79120i	−0.107756	−	0.186639i	−0.914861	+	0.403769i	$0.867700\pi$
$660$	9.73723	−	8.75048i	0.379021	−	0.340612i
$661$	−5.48701	−	3.16793i	−0.213420	−	0.123218i	0.389480	−	0.921035i	$-0.372655\pi$
$661$	−5.48701	−	3.16793i	−0.213420	−	0.123218i	−0.602900	+	0.797817i	$0.705988\pi$
$662$	9.39823	−	9.39823i	0.365273	−	0.365273i
$663$	13.5673	−	2.18524i	0.526911	−	0.0848676i
$664$		−	14.8798i		−	0.577448i
$665$	27.5511	+	48.3458i	1.06839	+	1.87477i
$666$	−19.6746	−	1.88263i	−0.762375	−	0.0729504i
$667$	2.55856	−	9.54866i	0.0990677	−	0.369726i
$668$	8.70345	−	8.70345i	0.336746	−	0.336746i
$669$	32.2492	+	35.4824i	1.24683	+	1.37183i
$670$	9.40870	+	9.51512i	0.363490	+	0.367601i
$671$	36.6651			1.41544
$672$	7.45517	+	0.355874i	0.287590	+	0.0137281i
$673$	1.76732	+	6.59574i	0.0681254	+	0.254247i	0.991587	−	0.129444i	$-0.0413193\pi$
$673$	1.76732	+	6.59574i	0.0681254	+	0.254247i	−0.923461	+	0.383691i	$0.874653\pi$
$674$	−12.1239	−	6.99974i	−0.466995	−	0.269620i
$675$	24.2296	−	9.37698i	0.932597	−	0.360920i
$676$	−11.8976	+	5.23894i	−0.457601	+	0.201498i
$677$	12.6853	−	12.6853i	0.487537	−	0.487537i	−0.419991	−	0.907528i	$-0.637967\pi$
$677$	12.6853	−	12.6853i	0.487537	−	0.487537i	0.907528	+	0.419991i	$0.137967\pi$
$678$	4.63803	−	2.39049i	0.178122	−	0.0918062i
$679$	−9.09349	−	5.25013i	−0.348976	−	0.201481i
$680$	3.49882	−	3.45969i	0.134174	−	0.132673i
$681$	−17.1914	+	3.73799i	−0.658778	+	0.143240i
$682$	6.22271	+	1.66737i	0.238280	+	0.0638469i
$683$	30.7026	+	8.22675i	1.17480	+	0.314788i	0.792864	−	0.609399i	$-0.208589\pi$
$683$	30.7026	+	8.22675i	1.17480	+	0.314788i	0.381940	+	0.924187i	$0.375256\pi$
$684$	15.7608	−	7.19393i	0.602628	−	0.275067i
$685$	−0.0256024	+	4.55237i	−0.000978217	+	0.173937i
$686$	−17.0498	−	9.84370i	−0.650964	−	0.375834i
$687$	−9.58108	−	18.5892i	−0.365541	−	0.709223i
$688$	−0.970430	+	0.970430i	−0.0369973	+	0.0369973i
$689$	−4.94520	+	4.43439i	−0.188397	+	0.168937i
$690$	−33.9706	−	11.0739i	−1.29324	−	0.421576i
$691$	31.3707	+	18.1119i	1.19340	+	0.689009i	0.959076	−	0.283150i	$-0.0913793\pi$
$691$	31.3707	+	18.1119i	1.19340	+	0.689009i	0.234323	+	0.972159i	$0.424713\pi$
$692$	−3.11765	−	11.6352i	−0.118515	−	0.442305i
$693$	7.23776	+	43.0935i	0.274940	+	1.63699i
$694$	12.7119			0.482537
$695$	−23.5838	+	23.3200i	−0.894585	+	0.884579i
$696$	1.37345	−	1.24830i	0.0520606	−	0.0473169i
$697$	9.64669	−	9.64669i	0.365395	−	0.365395i
$698$	4.73679	−	17.6779i	0.179290	−	0.669119i
$699$	9.87664	−	30.8863i	0.373569	−	1.16823i
$700$	15.4055	−	15.0628i	0.582274	−	0.569321i
$701$		−	2.21073i		−	0.0834982i	−0.999128	−	0.0417491i	$-0.986707\pi$
$701$		−	2.21073i		−	0.0834982i	0.999128	−	0.0417491i	$-0.0132930\pi$
$702$	−1.20378	−	18.6963i	−0.0454336	−	0.705646i
$703$	−26.9030	+	26.9030i	−1.01466	+	1.01466i
$704$	−2.92732	−	1.69009i	−0.110328	−	0.0636977i
$705$	−1.27677	+	23.9214i	−0.0480859	+	0.900934i
$706$	10.5502	+	18.2735i	0.397062	+	0.687731i
$707$	−1.34353	−	1.34353i	−0.0505286	−	0.0505286i
$708$	2.26341	+	0.108044i	0.0850640	+	0.00406054i
$709$	−6.71530	−	11.6312i	−0.252198	−	0.436820i	0.711933	−	0.702248i	$-0.247820\pi$
$709$	−6.71530	−	11.6312i	−0.252198	−	0.436820i	−0.964131	+	0.265428i	$0.914487\pi$
$710$	13.3493	+	7.80763i	0.500989	+	0.293015i
$711$	22.4201	+	15.9720i	0.840821	+	0.598997i
$712$	17.8148	−	4.77345i	0.667636	−	0.178893i
$713$	−4.55071	−	16.9835i	−0.170425	−	0.636036i
$714$	3.48955	+	16.0489i	0.130593	+	0.600613i
$715$	−25.8528	−	8.61983i	−0.966838	−	0.322364i
$716$		−	9.75290i		−	0.364483i
$717$	−32.2404	+	16.6170i	−1.20404	+	0.620575i
$718$	−0.777003	−	2.89981i	−0.0289975	−	0.108220i
$719$	−6.36901	−	11.0314i	−0.237524	−	0.411403i	0.722479	−	0.691393i	$-0.243002\pi$
$719$	−6.36901	−	11.0314i	−0.237524	−	0.411403i	−0.960003	+	0.279989i	$0.909669\pi$
$720$	−4.24086	−	5.19761i	−0.158047	−	0.193703i
$721$	−3.30240	+	1.90664i	−0.122988	+	0.0710069i
$722$	3.71418	−	13.8615i	0.138228	−	0.515872i
$723$	12.7924	+	8.22294i	0.475753	+	0.305814i
$724$	6.57958	−	3.79872i	0.244528	−	0.141178i
$725$	0.0602616	−	5.35740i	0.00223806	−	0.198969i
$726$	0.224546	−	0.702200i	0.00833367	−	0.0260611i
$727$	−5.29473	−	5.29473i	−0.196371	−	0.196371i	0.602072	−	0.798442i	$-0.294342\pi$
$727$	−5.29473	−	5.29473i	−0.196371	−	0.196371i	−0.798442	+	0.602072i	$0.794342\pi$
$728$	−7.02525	−	13.8578i	−0.260373	−	0.513606i
$729$	25.9018	+	7.62217i	0.959325	+	0.282303i
$730$	6.49775	+	1.78029i	0.240493	+	0.0658916i
$731$	−2.61537	−	1.50998i	−0.0967329	−	0.0558487i
$732$	0.895812	−	18.7663i	0.0331102	−	0.693622i
$733$	18.6037	+	18.6037i	0.687144	+	0.687144i	0.961600	−	0.274456i	$-0.0884978\pi$
$733$	18.6037	+	18.6037i	0.687144	+	0.687144i	−0.274456	+	0.961600i	$0.588498\pi$
$734$	−7.54492	+	4.35606i	−0.278488	+	0.160785i
$735$	9.27339	+	43.8354i	0.342054	+	1.61689i
$736$			9.22545i			0.340055i
$737$	19.5389	+	5.23543i	0.719724	+	0.192849i
$738$	−11.8390	−	14.3445i	−0.435800	−	0.528027i
$739$	17.5009	−	30.3124i	0.643781	−	1.11506i	−0.340801	−	0.940135i	$-0.610698\pi$
$739$	17.5009	−	30.3124i	0.643781	−	1.11506i	0.984582	−	0.174925i	$-0.0559684\pi$
$740$	12.7163	+	7.43742i	0.467460	+	0.273405i
$741$	−29.2324	−	21.1220i	−1.07388	−	0.775935i
$742$	−5.61328	−	5.61328i	−0.206070	−	0.206070i
$743$	3.69143	+	13.7766i	0.135426	+	0.505415i	0.999996	+	0.00290301i	$0.000924057\pi$
$743$	3.69143	+	13.7766i	0.135426	+	0.505415i	−0.864570	+	0.502512i	$0.832409\pi$
$744$	1.00545	−	3.14423i	0.0368614	−	0.115273i
$745$	26.1937	−	25.9007i	0.959661	−	0.948927i
$746$	15.9285			0.583184
$747$	−7.39383	−	44.0228i	−0.270526	−	1.61071i
$748$	1.92513	−	7.18467i	0.0703896	−	0.262698i
$749$		−	2.32651i		−	0.0850089i
$750$	−19.3246	−	1.24954i	−0.705633	−	0.0456266i
$751$	0.683895	−	1.18454i	0.0249557	−	0.0432245i	−0.853278	−	0.521457i	$-0.825389\pi$
$751$	0.683895	−	1.18454i	0.0249557	−	0.0432245i	0.878234	+	0.478232i	$0.158722\pi$
$752$	5.97452	−	1.60087i	0.217868	−	0.0583777i
$753$	19.3786	+	12.4566i	0.706197	+	0.453944i
$754$	−3.67197	−	1.20141i	−0.133725	−	0.0437527i
$755$	−0.640835	−	2.44659i	−0.0233224	−	0.0890404i
$756$	22.2334	−	2.65163i	0.808622	−	0.0964389i
$757$	−27.2218	+	7.29405i	−0.989392	+	0.265107i	−0.716995	−	0.697078i	$-0.754483\pi$
$757$	−27.2218	+	7.29405i	−0.989392	+	0.265107i	−0.272397	+	0.962185i	$0.587816\pi$
$758$	−1.26247	+	4.71159i	−0.0458548	+	0.171133i
$759$	−52.7786	+	11.4758i	−1.91574	+	0.416545i
$760$	−12.9131	−	0.0726227i	−0.468406	−	0.00263430i
$761$	10.5572	+	18.2857i	0.382700	+	0.662855i	0.991447	−	0.130509i	$-0.0416611\pi$
$761$	10.5572	+	18.2857i	0.382700	+	0.662855i	−0.608747	+	0.793364i	$0.708328\pi$
$762$	0.494824	+	0.318073i	0.0179256	+	0.0115226i
$763$	42.7083	+	11.4437i	1.54615	+	0.414288i
$764$	−11.2667	+	19.5144i	−0.407613	+	0.706007i
$765$	8.63234	−	11.9743i	0.312103	−	0.432931i
$766$	−19.5613			−0.706777
$767$	−2.13288	−	4.20727i	−0.0770139	−	0.151916i
$768$	−0.936562	+	1.45700i	−0.0337953	+	0.0525750i
$769$	−12.3724	+	21.4296i	−0.446160	+	0.772773i	−0.998132	−	0.0610902i	$-0.980542\pi$
$769$	−12.3724	+	21.4296i	−0.446160	+	0.772773i	0.551972	+	0.833863i	$0.313876\pi$
$770$	8.60651	−	31.4122i	0.310157	−	1.13202i
$771$	29.0015	−	26.3589i	1.04446	−	0.949291i
$772$	−5.65132	+	5.65132i	−0.203395	+	0.203395i
$773$	9.77510	+	2.61923i	0.351586	+	0.0942071i	0.430290	−	0.902691i	$-0.358411\pi$
$773$	9.77510	+	2.61923i	0.351586	+	0.0942071i	−0.0787037	+	0.996898i	$0.525078\pi$
$774$	−2.38887	+	3.35329i	−0.0858660	+	0.120531i
$775$	−4.67157	−	8.30577i	−0.167808	−	0.298352i
$776$	2.11028	−	1.21837i	0.0757545	−	0.0437369i
$777$	−43.7078	+	22.5275i	−1.56801	+	0.808169i
$778$	−8.94613	+	2.39711i	−0.320734	+	0.0859405i
$779$	−35.8032			−1.28278
$780$	−5.04354	+	13.0216i	−0.180588	+	0.466249i
$781$	23.3777			0.836519
$782$	−19.6089	+	5.25420i	−0.701215	+	0.187890i
$783$	3.44316	−	4.37566i	0.123049	−	0.156373i
$784$	10.0188	−	5.78437i	0.357815	−	0.206585i
$785$	−1.79900	−	1.05219i	−0.0642092	−	0.0375542i
$786$	−17.5650	+	15.9645i	−0.626523	+	0.569434i
$787$	−17.4690	−	4.68081i	−0.622703	−	0.166853i	−0.0663469	−	0.997797i	$-0.521134\pi$
$787$	−17.4690	−	4.68081i	−0.622703	−	0.166853i	−0.556356	+	0.830944i	$0.687801\pi$
$788$	−4.42300	+	4.42300i	−0.157563	+	0.157563i
$789$	1.26236	+	1.38892i	0.0449411	+	0.0494467i
$790$	−10.1588	−	17.8264i	−0.361435	−	0.634235i
$791$	6.49069	−	11.2422i	0.230782	−	0.399727i
$792$	−9.50048	−	3.54564i	−0.337585	−	0.125989i
$793$	−34.8832	+	17.6841i	−1.23874	+	0.627980i
$794$	19.4150			0.689011
$795$	−0.380271	+	7.12473i	−0.0134868	+	0.252688i
$796$	−12.6852	+	21.9713i	−0.449614	+	0.778754i
$797$	−26.8184	−	7.18596i	−0.949955	−	0.254540i	−0.249612	−	0.968346i	$-0.580303\pi$
$797$	−26.8184	−	7.18596i	−0.949955	−	0.254540i	−0.700343	+	0.713806i	$0.746970\pi$
$798$	23.3066	−	36.2579i	0.825045	−	1.28351i
$799$	6.80538	+	11.7873i	0.240757	+	0.417004i
$800$	1.23969	+	4.84388i	0.0438297	+	0.171257i
$801$	50.3341	−	22.9748i	1.77847	−	0.811774i
$802$	6.63581	−	24.7652i	0.234319	−	0.874489i
$803$	9.83740	−	2.63592i	0.347154	−	0.0930197i
$804$	3.15703	−	9.87268i	0.111340	−	0.348183i
$805$	−85.9913	+	22.5238i	−3.03080	+	0.793858i
$806$	−6.72449	+	1.41496i	−0.236860	+	0.0498399i
$807$	−0.0977893	+	0.152130i	−0.00344235	+	0.00535523i
$808$	0.425907	−	0.114121i	0.0149833	−	0.00401478i
$809$	0.0323193	−	0.0559786i	0.00113628	−	0.00196810i	−0.865457	−	0.500984i	$-0.832972\pi$
$809$	0.0323193	−	0.0559786i	0.00113628	−	0.00196810i	0.866593	+	0.499016i	$0.166305\pi$
$810$	−15.1296	−	13.2701i	−0.531598	−	0.466265i
$811$			6.77587i			0.237933i	0.992898	+	0.118966i	$0.0379581\pi$
$811$			6.77587i			0.237933i	−0.992898	+	0.118966i	$0.962042\pi$
$812$	1.19509	−	4.46012i	0.0419393	−	0.156519i
$813$	−0.588342	+	12.3251i	−0.0206341	+	0.432262i
$814$	22.2692			0.780534
$815$	−0.0548246	+	9.74838i	−0.00192042	+	0.341471i
$816$	−3.63030	−	1.16088i	−0.127086	−	0.0406388i
$817$	2.05129	+	7.65551i	0.0717655	+	0.267832i
$818$	9.15337	+	9.15337i	0.320040	+	0.320040i
$819$	−27.6706	−	37.5084i	−0.966891	−	1.31065i
$820$	3.51263	+	13.4105i	0.122666	+	0.468317i
$821$	1.36442	−	2.36325i	0.0476187	−	0.0824780i	−0.841234	−	0.540672i	$-0.818170\pi$
$821$	1.36442	−	2.36325i	0.0476187	−	0.0824780i	0.888852	+	0.458194i	$0.151503\pi$
$822$	3.13447	−	1.61554i	0.109327	−	0.0563484i
$823$	46.6210	+	12.4921i	1.62511	+	0.435446i	0.952496	−	0.304552i	$-0.0985068\pi$
$823$	46.6210	+	12.4921i	1.62511	+	0.435446i	0.672609	+	0.739998i	$0.265173\pi$
$824$		−	0.884926i		−	0.0308279i
$825$	−26.1696	+	13.1177i	−0.911109	+	0.456699i
$826$	4.88223	−	2.81876i	0.169874	−	0.0980771i
$827$	−7.99581	−	7.99581i	−0.278041	−	0.278041i	0.554285	−	0.832327i	$-0.312992\pi$
$827$	−7.99581	−	7.99581i	−0.278041	−	0.278041i	−0.832327	+	0.554285i	$0.812992\pi$
$828$	4.58416	+	27.2941i	0.159311	+	0.948534i
$829$	−13.0465	−	7.53239i	−0.453123	−	0.261611i	0.256025	−	0.966670i	$-0.417587\pi$
$829$	−13.0465	−	7.53239i	−0.453123	−	0.261611i	−0.709148	+	0.705059i	$0.750920\pi$
$830$	−8.79210	+	32.0896i	−0.305178	+	1.11385i
$831$	−8.25471	+	1.79485i	−0.286353	+	0.0622625i
$832$	3.60022	+	0.196065i	0.124815	+	0.00679734i
$833$	18.0009	+	18.0009i	0.623694	+	0.623694i
$834$	24.4700	+	7.82489i	0.847328	+	0.270954i
$835$	−23.9124	+	13.6271i	−0.827522	+	0.471585i
$836$	−16.9053	+	9.76026i	−0.584681	+	0.337566i
$837$	1.41229	−	9.80202i	0.0488159	−	0.338807i
$838$	−2.71933	+	10.1487i	−0.0939379	+	0.350581i
$839$	1.67110	−	0.964808i	0.0576927	−	0.0333089i	−0.470876	−	0.882199i	$-0.656062\pi$
$839$	1.67110	−	0.964808i	0.0576927	−	0.0333089i	0.528569	+	0.848890i	$0.322729\pi$
$840$	−15.8674	−	5.17255i	−0.547479	−	0.178470i
$841$	13.9259	+	24.1204i	0.480203	+	0.831736i
$842$	−3.09644	−	11.5561i	−0.106710	−	0.398248i
$843$	14.4215	+	27.9806i	0.496703	+	0.963704i
$844$		−	20.2292i		−	0.696317i
$845$	28.7538	−	4.26823i	0.989162	−	0.146832i
$846$	16.8805	−	7.70504i	0.580364	−	0.264905i
$847$	−0.474711	−	1.77164i	−0.0163112	−	0.0608744i
$848$	1.77944	−	0.476800i	0.0611063	−	0.0163734i
$849$	9.29185	−	8.44518i	0.318896	−	0.289838i
$850$	−9.58975	+	5.39375i	−0.328926	+	0.185004i
$851$	−30.3894	−	52.6359i	−1.04173	−	1.80434i
$852$	0.571170	−	11.9654i	0.0195680	−	0.409928i
$853$	−23.5872	−	23.5872i	−0.807612	−	0.807612i	0.176660	−	0.984272i	$-0.443471\pi$
$853$	−23.5872	−	23.5872i	−0.807612	−	0.807612i	−0.984272	+	0.176660i	$0.943471\pi$
$854$	−23.3708	−	40.4794i	−0.799732	−	1.38518i
$855$	−38.2402	+	6.20169i	−1.30779	+	0.212093i
$856$	0.467568	+	0.269951i	0.0159811	+	0.00922672i
$857$	4.65914	−	4.65914i	0.159153	−	0.159153i	−0.623038	−	0.782191i	$-0.714102\pi$
$857$	4.65914	−	4.65914i	0.159153	−	0.159153i	0.782191	+	0.623038i	$0.214102\pi$
$858$	3.35673	+	20.8406i	0.114597	+	0.711488i
$859$			12.2319i			0.417347i	0.977985	+	0.208674i	$0.0669146\pi$
$859$			12.2319i			0.417347i	−0.977985	+	0.208674i	$0.933085\pi$
$860$	2.66622	−	1.51941i	0.0909173	−	0.0518116i
$861$	−44.0739	−	14.0937i	−1.50203	−	0.480312i
$862$	−4.04868	+	15.1099i	−0.137899	+	0.514645i
$863$	31.9524	−	31.9524i	1.08767	−	1.08767i	0.0919057	−	0.995768i	$-0.470704\pi$
$863$	31.9524	−	31.9524i	1.08767	−	1.08767i	0.995768	−	0.0919057i	$-0.0292958\pi$
$864$	−2.04689	+	4.77601i	−0.0696365	+	0.162483i
$865$	−0.151479	+	26.9345i	−0.00515043	+	0.915801i
$866$	24.3552			0.827622
$867$	−1.00406	+	21.0339i	−0.0340996	+	0.714349i
$868$	−2.12561	−	7.93287i	−0.0721478	−	0.269259i
$869$	−26.8607	−	15.5080i	−0.911188	−	0.526074i
$870$	−3.69956	+	1.88054i	−0.125427	+	0.0637562i
$871$	−21.1144	+	4.44289i	−0.715436	+	0.150542i
$872$	−7.25542	+	7.25542i	−0.245700	+	0.245700i
$873$	5.63797	−	4.65322i	0.190816	−	0.157488i
$874$	46.1391	+	26.6384i	1.56068	+	0.901058i
$875$	−42.1236	+	23.3815i	−1.42404	+	0.790440i
$876$	−1.10880	−	5.09948i	−0.0374627	−	0.172296i
$877$	−16.8051	−	4.50292i	−0.567468	−	0.152053i	−0.0363332	−	0.999340i	$-0.511568\pi$
$877$	−16.8051	−	4.50292i	−0.567468	−	0.152053i	−0.531135	+	0.847287i	$0.678234\pi$
$878$	−5.34111	−	1.43114i	−0.180254	−	0.0482988i
$879$	1.86257	+	8.56616i	0.0628228	+	0.288929i
$880$	5.31440	+	5.37451i	0.179148	+	0.181175i
$881$	−19.2459	−	11.1116i	−0.648412	−	0.374361i	0.139436	−	0.990231i	$-0.455471\pi$
$881$	−19.2459	−	11.1116i	−0.648412	−	0.374361i	−0.787847	+	0.615870i	$0.788804\pi$
$882$	26.7670	−	22.0918i	0.901293	−	0.743870i
$883$	4.33367	−	4.33367i	0.145839	−	0.145839i	−0.630417	−	0.776257i	$-0.717116\pi$
$883$	4.33367	−	4.33367i	0.145839	−	0.145839i	0.776257	+	0.630417i	$0.217116\pi$
$884$	1.63370	+	7.76402i	0.0549473	+	0.261132i
$885$	−4.81739	−	1.57040i	−0.161935	−	0.0527883i
$886$	−16.5094	−	9.53173i	−0.554646	−	0.320225i
$887$	13.5857	+	50.7027i	0.456164	+	1.70243i	0.684642	+	0.728880i	$0.259959\pi$
$887$	13.5857	+	50.7027i	0.456164	+	1.70243i	−0.228477	+	0.973549i	$0.573375\pi$
$888$	0.544087	−	11.3980i	0.0182584	−	0.382493i
$889$	1.46346			0.0490830
$890$	−41.2396	−	0.231930i	−1.38235	−	0.00777432i
$891$	−29.8696	−	5.76917i	−1.00067	−	0.193274i
$892$	−19.5747	+	19.5747i	−0.655409	+	0.655409i
$893$	9.24500	−	34.5028i	0.309372	−	1.15459i
$894$	−27.1780	−	8.69082i	−0.908967	−	0.290664i
$895$	−5.76274	+	21.0330i	−0.192627	+	0.703055i
$896$			4.30915i			0.143958i
$897$	44.6787	−	36.3740i	1.49178	−	1.21449i
$898$	−13.2299	+	13.2299i	−0.441488	+	0.441488i
$899$	−1.76863	−	1.02112i	−0.0589871	−	0.0340562i
$900$	6.07465	+	13.7149i	0.202488	+	0.457164i
$901$	2.02691	+	3.51070i	0.0675260	+	0.116958i
$902$	14.8182	+	14.8182i	0.493392	+	0.493392i
$903$	−0.488399	+	10.2314i	−0.0162529	+	0.340481i
$904$	1.50626	+	2.60892i	0.0500974	+	0.0867712i
$905$	−16.4340	+	4.30457i	−0.546285	+	0.143089i
$906$	−1.44973	+	1.31763i	−0.0481641	+	0.0437753i
$907$	49.8577	−	13.3593i	1.65550	−	0.443589i	0.694353	−	0.719635i	$-0.255691\pi$
$907$	49.8577	−	13.3593i	1.65550	−	0.443589i	0.961145	+	0.276045i	$0.0890240\pi$
$908$	−2.62893	−	9.81129i	−0.0872441	−	0.325599i
$909$	1.20336	−	0.549270i	0.0399131	−	0.0182181i
$910$	6.96231	+	34.0367i	0.230798	+	1.12830i
$911$			13.4451i			0.445454i	0.974881	+	0.222727i	$0.0714959\pi$
$911$			13.4451i			0.445454i	−0.974881	+	0.222727i	$0.928504\pi$
$912$	4.58256	+	8.89110i	0.151744	+	0.294414i
$913$	13.0177	+	48.5826i	0.430822	+	1.60785i
$914$	7.86608	+	13.6244i	0.260187	+	0.450657i
$915$	−13.0204	+	39.9418i	−0.430442	+	1.32044i
$916$	10.4565	−	6.03708i	0.345494	−	0.199471i
$917$	−15.2839	+	57.0401i	−0.504717	+	1.88363i
$918$	−11.3173	−	1.63062i	−0.373527	−	0.0538183i
$919$	−46.4888	+	26.8403i	−1.53353	+	0.885381i	−0.534330	+	0.845276i	$0.679436\pi$
$919$	−46.4888	+	26.8403i	−1.53353	+	0.885381i	−0.999195	+	0.0401052i	$0.987231\pi$
$920$	5.45108	−	19.8955i	0.179717	−	0.655935i
$921$	43.2592	+	13.8332i	1.42544	+	0.455819i
$922$	8.00028	+	8.00028i	0.263475	+	0.263475i
$923$	−22.2415	+	11.2754i	−0.732089	+	0.371134i
$924$	−24.6525	+	5.36027i	−0.811008	+	0.176340i
$925$	−23.0292	−	23.5532i	−0.757195	−	0.774423i
$926$	−18.2589	−	10.5418i	−0.600024	−	0.346424i
$927$	−0.439723	−	2.61811i	−0.0144424	−	0.0859900i
$928$	0.757698	+	0.757698i	0.0248727	+	0.0248727i
$929$	4.69690	−	2.71176i	0.154100	−	0.0889699i	−0.420967	−	0.907076i	$-0.638309\pi$
$929$	4.69690	−	2.71176i	0.154100	−	0.0889699i	0.575067	+	0.818106i	$0.304976\pi$
$930$	−4.02618	+	6.18672i	−0.132024	+	0.202871i
$931$		−	66.8094i		−	2.18959i
$932$	18.0838	+	4.84554i	0.592355	+	0.158721i
$933$	−34.3887	+	17.7243i	−1.12583	+	0.580267i
$934$	−4.74028	+	8.21041i	−0.155107	+	0.268653i
$935$	−8.39695	+	14.3569i	−0.274609	+	0.469520i
$936$	10.7489	−	1.20889i	0.351338	−	0.0395138i
$937$	−21.5597	−	21.5597i	−0.704325	−	0.704325i	0.261011	−	0.965336i	$-0.415944\pi$
$937$	−21.5597	−	21.5597i	−0.704325	−	0.704325i	−0.965336	+	0.261011i	$0.915944\pi$
$938$	−6.67426	−	24.9087i	−0.217922	−	0.813297i
$939$	36.1099	+	11.5470i	1.17840	+	0.376823i
$940$	−13.8305	−	0.0777823i	−0.451101	−	0.00253698i
$941$	30.5205			0.994940			0.497470	−	0.867481i	$-0.334263\pi$
$941$	30.5205			0.994940			0.497470	+	0.867481i	$0.334263\pi$
$942$	−0.0769733	+	1.61251i	−0.00250793	+	0.0525384i
$943$	14.8032	−	55.2461i	0.482057	−	1.79906i
$944$			1.30827i			0.0425805i
$945$	−49.5151	−	7.41869i	−1.61073	−	0.241330i
$946$	2.31947	−	4.01745i	0.0754126	−	0.130618i
$947$	30.1907	−	8.08957i	0.981066	−	0.262876i	0.267573	−	0.963538i	$-0.413779\pi$
$947$	30.1907	−	8.08957i	0.981066	−	0.262876i	0.713493	+	0.700662i	$0.247112\pi$
$948$	−8.59376	+	13.3692i	−0.279112	+	0.434213i
$949$	−8.08797	+	7.25254i	−0.262547	+	0.235427i
$950$	27.8052	+	7.78662i	0.902121	+	0.252631i
$951$	−12.2429	+	38.2861i	−0.397004	+	1.24151i
$952$	−9.15921	+	2.45420i	−0.296852	+	0.0795412i
$953$	0.875639	−	3.26793i	0.0283647	−	0.105859i	−0.950292	−	0.311359i	$-0.899216\pi$
$953$	0.875639	−	3.26793i	0.0283647	−	0.105859i	0.978657	+	0.205501i	$0.0658823\pi$
$954$	5.02767	−	2.29486i	0.162777	−	0.0742987i
$955$	35.8281	−	35.4273i	1.15937	−	1.14640i
$956$	−10.4705	−	18.1354i	−0.338639	−	0.586540i
$957$	−3.39225	+	5.27730i	−0.109656	+	0.170591i
$958$	−27.5181	−	7.37346i	−0.889071	−	0.238226i
$959$	4.38653	−	7.59769i	0.141648	−	0.245342i
$960$	2.88068	−	2.58876i	0.0929736	−	0.0835518i
$961$	27.3676			0.882827
$962$	−21.1869	+	10.7407i	−0.683094	+	0.346295i
$963$	1.51747	+	0.566329i	0.0488997	+	0.0182497i
$964$	−4.38996	+	7.60364i	−0.141391	+	0.244897i
$965$	15.5268	−	8.84834i	0.499825	−	0.284838i
$966$	46.3114	+	50.9544i	1.49005	+	1.63943i
$967$	6.92958	−	6.92958i	0.222840	−	0.222840i	−0.586853	−	0.809693i	$-0.699633\pi$
$967$	6.92958	−	6.92958i	0.222840	−	0.222840i	0.809693	+	0.586853i	$0.199633\pi$
$968$	0.411136	+	0.110163i	0.0132144	+	0.00354079i
$969$	−16.2883	+	14.8041i	−0.523257	+	0.475578i
$970$	−5.27090	+	1.38061i	−0.169238	+	0.0443287i
$971$	−11.8952	+	6.86770i	−0.381735	+	0.220395i	−0.678573	−	0.734533i	$-0.737401\pi$
$971$	−11.8952	+	6.86770i	−0.381735	+	0.220395i	0.296838	+	0.954928i	$0.404068\pi$
$972$	−3.68262	+	15.1472i	−0.118120	+	0.485847i
$973$	61.7377	−	16.5426i	1.97922	−	0.530330i
$974$	9.15980			0.293499
$975$	18.5710	−	25.1022i	0.594747	−	0.803913i
$976$	10.8471			0.347206
$977$	21.4900	−	5.75823i	0.687527	−	0.184222i	0.101890	−	0.994796i	$-0.467511\pi$
$977$	21.4900	−	5.75823i	0.687527	−	0.184222i	0.585637	+	0.810573i	$0.300844\pi$
$978$	6.71210	−	3.45949i	0.214629	−	0.110622i
$979$	−53.9892	+	31.1707i	−1.72550	+	0.996220i
$980$	−25.0243	+	6.55463i	−0.799372	+	0.209380i
$981$	−17.8604	+	25.0709i	−0.570237	+	0.800451i
$982$	−28.8709	−	7.73593i	−0.921306	−	0.246863i
$983$	13.9010	−	13.9010i	0.443372	−	0.443372i	−0.449772	−	0.893144i	$-0.648495\pi$
$983$	13.9010	−	13.9010i	0.443372	−	0.443372i	0.893144	+	0.449772i	$0.148495\pi$
$984$	7.94646	−	7.22237i	0.253324	−	0.230241i
$985$	12.1520	−	6.92515i	0.387196	−	0.220654i
$986$	−1.17897	+	2.04204i	−0.0375462	+	0.0650319i
$987$	24.9625	−	38.8339i	0.794564	−	1.23610i
$988$	11.3762	−	17.4396i	0.361925	−	0.554827i
$989$	−12.6610			−0.402595
$990$	18.3936	+	13.2601i	0.584587	+	0.421433i
$991$	−26.3296	+	45.6042i	−0.836387	+	1.44866i	0.0565095	+	0.998402i	$0.482003\pi$
$991$	−26.3296	+	45.6042i	−0.836387	+	1.44866i	−0.892896	+	0.450262i	$0.851330\pi$
$992$	1.84094	+	0.493278i	0.0584498	+	0.0156616i
$993$	19.3652	+	12.4479i	0.614535	+	0.395024i
$994$	−14.9012	−	25.8097i	−0.472638	−	0.818634i
$995$	40.3390	−	39.8878i	1.27883	−	1.26453i
$996$	25.1841	−	5.47586i	0.797989	−	0.173509i
$997$	−1.96558	+	7.33563i	−0.0622504	+	0.232322i	−0.990041	−	0.140780i	$-0.955039\pi$
$997$	−1.96558	+	7.33563i	−0.0622504	+	0.232322i	0.927790	+	0.373102i	$0.121706\pi$
$998$	−19.7237	+	5.28496i	−0.624344	+	0.167292i
$999$	−4.05402	−	33.9922i	−0.128263	−	1.07546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.be.b.17.4	✓	96
3.2	odd	2	inner	390.2.be.b.17.18	yes	96
5.3	odd	4	inner	390.2.be.b.173.23	yes	96
13.10	even	6	inner	390.2.be.b.257.12	yes	96
15.8	even	4	inner	390.2.be.b.173.12	yes	96
39.23	odd	6	inner	390.2.be.b.257.23	yes	96
65.23	odd	12	inner	390.2.be.b.23.18	yes	96
195.23	even	12	inner	390.2.be.b.23.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.be.b.17.4	✓	96	1.1	even	1	trivial
390.2.be.b.17.18	yes	96	3.2	odd	2	inner
390.2.be.b.23.4	yes	96	195.23	even	12	inner
390.2.be.b.23.18	yes	96	65.23	odd	12	inner
390.2.be.b.173.12	yes	96	15.8	even	4	inner
390.2.be.b.173.23	yes	96	5.3	odd	4	inner
390.2.be.b.257.12	yes	96	13.10	even	6	inner
390.2.be.b.257.23	yes	96	39.23	odd	6	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.793519 - 1.53959i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16310 + 0.566581i) q^{5} +(1.16496 + 1.28175i) q^{6} +(4.16232 + 1.11529i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.74065 + 2.44338i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.793519 - 1.53959i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16310 + 0.566581i) q^{5} +(1.16496 + 1.28175i) q^{6} +(4.16232 + 1.11529i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.74065 + 2.44338i) q^{9} +(1.94275 - 1.10713i) q^{10} +(1.69009 - 2.92732i) q^{11} +(-1.45700 - 0.936562i) q^{12} +(-0.196065 + 3.60022i) q^{13} -4.30915 q^{14} +(2.58876 + 2.88068i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.12553 + 0.569533i) q^{17} +(1.04895 - 2.81064i) q^{18} +(-2.88749 - 5.00129i) q^{19} +(-1.59001 + 1.57222i) q^{20} +(-1.58579 - 7.29325i) q^{21} +(-0.874856 + 3.26501i) q^{22} +(8.91110 - 2.38772i) q^{23} +(1.64976 + 0.527549i) q^{24} +(4.35797 - 2.45114i) q^{25} +(-0.742420 - 3.52829i) q^{26} +(5.14304 + 0.741018i) q^{27} +(4.16232 - 1.11529i) q^{28} +(0.535774 - 0.927987i) q^{29} +(-3.24612 - 2.11250i) q^{30} -1.90588i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-5.84799 - 0.279155i) q^{33} -2.20051 q^{34} +(-9.63539 - 0.0541891i) q^{35} +(-0.285760 + 2.98636i) q^{36} +(-1.70514 - 6.36367i) q^{37} +(4.08353 + 4.08353i) q^{38} +(5.69843 - 2.55498i) q^{39} +(1.12891 - 1.93017i) q^{40} +(3.09985 - 5.36910i) q^{41} +(3.41939 + 6.63431i) q^{42} +(-1.32563 - 0.355202i) q^{43} -3.38018i q^{44} +(2.38083 - 6.27150i) q^{45} +(-7.98947 + 4.61272i) q^{46} +(4.37366 + 4.37366i) q^{47} +(-1.73008 - 0.0825856i) q^{48} +(10.0188 + 5.78437i) q^{49} +(-3.57508 + 3.49554i) q^{50} +(-0.809801 - 3.72437i) q^{51} +(1.63031 + 3.21591i) q^{52} +(1.30264 + 1.30264i) q^{53} +(-5.15959 + 0.615349i) q^{54} +(-1.99726 + 7.28966i) q^{55} +(-3.73183 + 2.15457i) q^{56} +(-5.40863 + 8.41417i) q^{57} +(-0.277337 + 1.03504i) q^{58} +(-1.13299 + 0.654133i) q^{59} +(3.68227 + 1.20036i) q^{60} +(5.42353 + 9.39383i) q^{61} +(0.493278 + 1.84094i) q^{62} +(-9.97023 + 8.22880i) q^{63} -1.00000i q^{64} +(-1.61571 - 7.89870i) q^{65} +(5.72098 - 1.24393i) q^{66} +(1.54886 + 5.78042i) q^{67} +(2.12553 - 0.569533i) q^{68} +(-10.7472 - 11.8247i) q^{69} +(9.32110 - 2.44148i) q^{70} +(3.45805 + 5.98951i) q^{71} +(-0.496904 - 2.95856i) q^{72} +(2.13050 + 2.13050i) q^{73} +(3.29408 + 5.70551i) q^{74} +(-7.23187 - 4.76445i) q^{75} +(-5.00129 - 2.88749i) q^{76} +(10.2995 - 10.2995i) q^{77} +(-4.84298 + 3.94278i) q^{78} -9.17586i q^{79} +(-0.590875 + 2.15659i) q^{80} +(-2.94024 - 8.50617i) q^{81} +(-1.60460 + 5.98845i) q^{82} +(-10.5216 + 10.5216i) q^{83} +(-5.01996 - 5.52324i) q^{84} +(-4.92041 - 0.0276722i) q^{85} +1.37240 q^{86} +(-1.85386 - 0.0884944i) q^{87} +(0.874856 + 3.26501i) q^{88} +(-15.9723 - 9.22160i) q^{89} +(-0.676522 + 6.67400i) q^{90} +(-4.83137 + 14.7666i) q^{91} +(6.52338 - 6.52338i) q^{92} +(-2.93427 + 1.51235i) q^{93} +(-5.35661 - 3.09264i) q^{94} +(9.07956 + 9.18227i) q^{95} +(1.69250 - 0.368006i) q^{96} +(-2.35371 - 0.630674i) q^{97} +(-11.1746 - 2.99421i) q^{98} +(4.21071 + 9.22500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{3} + 24 q^{7}+O(q^{10}) \) 96 * q + 4 * q^3 + 24 * q^7	\( 96 q + 4 q^{3} + 24 q^{7} + 16 q^{10} - 8 q^{12} + 40 q^{13} + 48 q^{16} - 8 q^{22} + 64 q^{25} - 32 q^{27} + 24 q^{28} - 8 q^{30} - 96 q^{33} - 24 q^{36} + 72 q^{37} - 8 q^{42} + 16 q^{43} - 60 q^{45} + 24 q^{46} - 4 q^{48} - 128 q^{51} - 8 q^{52} + 32 q^{61} - 120 q^{63} - 16 q^{66} - 96 q^{67} - 24 q^{72} - 4 q^{75} - 24 q^{76} - 16 q^{78} - 48 q^{81} + 32 q^{82} + 32 q^{87} + 8 q^{88} - 56 q^{90} - 56 q^{91} - 12 q^{93} + 24 q^{97}+O(q^{100}) \) 96 * q + 4 * q^3 + 24 * q^7 + 16 * q^10 - 8 * q^12 + 40 * q^13 + 48 * q^16 - 8 * q^22 + 64 * q^25 - 32 * q^27 + 24 * q^28 - 8 * q^30 - 96 * q^33 - 24 * q^36 + 72 * q^37 - 8 * q^42 + 16 * q^43 - 60 * q^45 + 24 * q^46 - 4 * q^48 - 128 * q^51 - 8 * q^52 + 32 * q^61 - 120 * q^63 - 16 * q^66 - 96 * q^67 - 24 * q^72 - 4 * q^75 - 24 * q^76 - 16 * q^78 - 48 * q^81 + 32 * q^82 + 32 * q^87 + 8 * q^88 - 56 * q^90 - 56 * q^91 - 12 * q^93 + 24 * q^97

Introduction

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