LMFDB - Embedded newform 192.2.r.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	192.13
Dual form			192.2.r.a.133.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.744400 + 1.20244i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-0.891737 - 1.79020i) q^{4} +(-4.01045 + 0.797728i) q^{5} +(0.0490954 + 1.41336i) q^{6} +(-1.73589 - 4.19080i) q^{7} +(2.81642 + 0.260360i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(-0.744400 + 1.20244i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-0.891737 - 1.79020i) q^{4} +(-4.01045 + 0.797728i) q^{5} +(0.0490954 + 1.41336i) q^{6} +(-1.73589 - 4.19080i) q^{7} +(2.81642 + 0.260360i) q^{8} +(0.382683 - 0.923880i) q^{9} +(2.02616 - 5.41616i) q^{10} +(0.722828 - 1.08179i) q^{11} +(-1.73603 - 0.993072i) q^{12} +(-1.73842 - 0.345793i) q^{13} +(6.33139 + 1.03233i) q^{14} +(-2.89137 + 2.89137i) q^{15} +(-2.40961 + 3.19277i) q^{16} +(-3.23483 - 3.23483i) q^{17} +(0.826043 + 1.14789i) q^{18} +(-0.619852 + 3.11621i) q^{19} +(5.00435 + 6.46813i) q^{20} +(-3.77162 - 2.52012i) q^{21} +(0.762715 + 1.67444i) q^{22} +(-0.548801 - 0.227321i) q^{23} +(2.48641 - 1.34824i) q^{24} +(10.8279 - 4.48507i) q^{25} +(1.70988 - 1.83294i) q^{26} +(-0.195090 - 0.980785i) q^{27} +(-5.95441 + 6.84467i) q^{28} +(1.91901 + 2.87200i) q^{29} +(-1.32437 - 5.62905i) q^{30} -1.17436i q^{31} +(-2.04541 - 5.27412i) q^{32} -1.30106i q^{33} +(6.29770 - 1.48169i) q^{34} +(10.3048 + 15.4222i) q^{35} +(-1.99518 + 0.138779i) q^{36} +(-1.01965 - 5.12614i) q^{37} +(-3.28564 - 3.06504i) q^{38} +(-1.63756 + 0.678298i) q^{39} +(-11.5028 + 1.20257i) q^{40} +(-10.6821 - 4.42467i) q^{41} +(5.83789 - 2.65918i) q^{42} +(4.61506 + 3.08368i) q^{43} +(-2.58119 - 0.329333i) q^{44} +(-0.797728 + 4.01045i) q^{45} +(0.681867 - 0.490684i) q^{46} +(5.57066 + 5.57066i) q^{47} +(-0.229710 + 3.99340i) q^{48} +(-9.59977 + 9.59977i) q^{49} +(-2.66726 + 16.3586i) q^{50} +(-4.48683 - 0.892487i) q^{51} +(0.931176 + 3.42047i) q^{52} +(3.33168 - 4.98621i) q^{53} +(1.32456 + 0.495512i) q^{54} +(-2.03589 + 4.91507i) q^{55} +(-3.79787 - 12.2550i) q^{56} +(1.21588 + 2.93540i) q^{57} +(-4.88192 + 0.169581i) q^{58} +(-2.77551 + 0.552083i) q^{59} +(7.75447 + 2.59778i) q^{60} +(-0.177964 + 0.118912i) q^{61} +(1.41210 + 0.874196i) q^{62} -4.53609 q^{63} +(7.86443 + 1.46657i) q^{64} +7.24769 q^{65} +(1.56444 + 0.968506i) q^{66} +(1.88157 - 1.25723i) q^{67} +(-2.90636 + 8.67559i) q^{68} +(-0.582604 + 0.115887i) q^{69} +(-26.2152 + 0.910628i) q^{70} +(-2.23974 - 5.40720i) q^{71} +(1.31834 - 2.50240i) q^{72} +(2.86687 - 6.92124i) q^{73} +(6.92291 + 2.58982i) q^{74} +(6.51132 - 9.74487i) q^{75} +(6.13137 - 1.66918i) q^{76} +(-5.78831 - 1.15137i) q^{77} +(0.403382 - 2.47399i) q^{78} +(9.06639 - 9.06639i) q^{79} +(7.11665 - 14.7266i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(13.2722 - 9.55089i) q^{82} +(0.276166 - 1.38838i) q^{83} +(-1.14821 + 8.99923i) q^{84} +(15.5536 + 10.3926i) q^{85} +(-7.14340 + 3.25385i) q^{86} +(3.19119 + 1.32183i) q^{87} +(2.31744 - 2.85857i) q^{88} +(5.14596 - 2.13153i) q^{89} +(-4.22850 - 3.94460i) q^{90} +(1.56855 + 7.88563i) q^{91} +(0.0824371 + 1.18517i) q^{92} +(-0.652441 - 0.976447i) q^{93} +(-10.8452 + 2.55160i) q^{94} -12.9919i q^{95} +(-4.63084 - 3.24890i) q^{96} -10.5410i q^{97} +(-4.39710 - 18.6892i) q^{98} +(-0.722828 - 1.08179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.744400	+	1.20244i	−0.526370	+	0.850255i
$2$	−0.744400	+	1.20244i	−0.526370	+	0.850255i
$3$	0.831470	−	0.555570i	0.480049	−	0.320759i
$3$	0.831470	−	0.555570i	0.480049	−	0.320759i
$4$	−0.891737	−	1.79020i	−0.445869	−	0.895098i
$5$	−4.01045	+	0.797728i	−1.79353	+	0.356755i	−0.975768	−	0.218807i	$-0.929784\pi$
$5$	−4.01045	+	0.797728i	−1.79353	+	0.356755i	−0.817758	+	0.575562i	$0.804784\pi$
$6$	0.0490954	+	1.41336i	0.0200431	+	0.577002i
$7$	−1.73589	−	4.19080i	−0.656104	−	1.58397i	−0.803772	−	0.594937i	$-0.797177\pi$
$7$	−1.73589	−	4.19080i	−0.656104	−	1.58397i	0.147668	−	0.989037i	$-0.452823\pi$
$8$	2.81642	+	0.260360i	0.995754	+	0.0920511i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	2.02616	−	5.41616i	0.640727	−	1.71274i
$11$	0.722828	−	1.08179i	0.217941	−	0.326171i	−0.706348	−	0.707864i	$-0.749659\pi$
$11$	0.722828	−	1.08179i	0.217941	−	0.326171i	0.924289	+	0.381693i	$0.124659\pi$
$12$	−1.73603	−	0.993072i	−0.501149	−	0.286675i
$13$	−1.73842	−	0.345793i	−0.482151	−	0.0959058i	−0.0519703	−	0.998649i	$-0.516550\pi$
$13$	−1.73842	−	0.345793i	−0.482151	−	0.0959058i	−0.430181	+	0.902743i	$0.641550\pi$
$14$	6.33139	+	1.03233i	1.69214	+	0.275901i
$15$	−2.89137	+	2.89137i	−0.746549	+	0.746549i
$16$	−2.40961	+	3.19277i	−0.602402	+	0.798192i
$17$	−3.23483	−	3.23483i	−0.784561	−	0.784561i	0.196036	−	0.980597i	$-0.437193\pi$
$17$	−3.23483	−	3.23483i	−0.784561	−	0.784561i	−0.980597	+	0.196036i	$0.937193\pi$
$18$	0.826043	+	1.14789i	0.194700	+	0.270560i
$19$	−0.619852	+	3.11621i	−0.142204	+	0.714907i	0.842225	+	0.539126i	$0.181245\pi$
$19$	−0.619852	+	3.11621i	−0.142204	+	0.714907i	−0.984429	+	0.175781i	$0.943755\pi$
$20$	5.00435	+	6.46813i	1.11901	+	1.44632i
$21$	−3.77162	−	2.52012i	−0.823035	−	0.549935i
$22$	0.762715	+	1.67444i	0.162611	+	0.356992i
$23$	−0.548801	−	0.227321i	−0.114433	−	0.0473996i	0.324732	−	0.945806i	$-0.394726\pi$
$23$	−0.548801	−	0.227321i	−0.114433	−	0.0473996i	−0.439165	+	0.898406i	$0.644726\pi$
$24$	2.48641	−	1.34824i	0.507537	−	0.275208i
$25$	10.8279	−	4.48507i	2.16558	−	0.897014i
$26$	1.70988	−	1.83294i	0.335334	−	0.359470i
$27$	−0.195090	−	0.980785i	−0.0375451	−	0.188752i
$28$	−5.95441	+	6.84467i	−1.12528	+	1.29352i
$29$	1.91901	+	2.87200i	0.356351	+	0.533316i	0.965725	−	0.259566i	$-0.0835795\pi$
$29$	1.91901	+	2.87200i	0.356351	+	0.533316i	−0.609375	+	0.792882i	$0.708579\pi$
$30$	−1.32437	−	5.62905i	−0.241796	−	1.02772i
$31$		−	1.17436i		−	0.210922i	−0.994423	−	0.105461i	$-0.966368\pi$
$31$		−	1.17436i		−	0.210922i	0.994423	−	0.105461i	$-0.0336318\pi$
$32$	−2.04541	−	5.27412i	−0.361581	−	0.932341i
$33$		−	1.30106i		−	0.226485i
$34$	6.29770	−	1.48169i	1.08005	−	0.254108i
$35$	10.3048	+	15.4222i	1.74183	+	2.60683i
$36$	−1.99518	+	0.138779i	−0.332530	+	0.0231298i
$37$	−1.01965	−	5.12614i	−0.167630	−	0.842732i	−0.969473	−	0.245197i	$-0.921147\pi$
$37$	−1.01965	−	5.12614i	−0.167630	−	0.842732i	0.801843	−	0.597534i	$-0.203853\pi$
$38$	−3.28564	−	3.06504i	−0.533002	−	0.497215i
$39$	−1.63756	+	0.678298i	−0.262219	+	0.108615i
$40$	−11.5028	+	1.20257i	−1.81875	+	0.190144i
$41$	−10.6821	−	4.42467i	−1.66826	−	0.691017i	−0.669601	−	0.742721i	$-0.733535\pi$
$41$	−10.6821	−	4.42467i	−1.66826	−	0.691017i	−0.998662	+	0.0517037i	$0.983535\pi$
$42$	5.83789	−	2.65918i	0.900806	−	0.410321i
$43$	4.61506	+	3.08368i	0.703789	+	0.470257i	0.855256	−	0.518205i	$-0.173400\pi$
$43$	4.61506	+	3.08368i	0.703789	+	0.470257i	−0.151467	+	0.988462i	$0.548400\pi$
$44$	−2.58119	−	0.329333i	−0.389128	−	0.0496489i
$45$	−0.797728	+	4.01045i	−0.118918	+	0.597842i
$46$	0.681867	−	0.490684i	0.100536	−	0.0723474i
$47$	5.57066	+	5.57066i	0.812565	+	0.812565i	0.985018	−	0.172453i	$-0.0551692\pi$
$47$	5.57066	+	5.57066i	0.812565	+	0.812565i	−0.172453	+	0.985018i	$0.555169\pi$
$48$	−0.229710	+	3.99340i	−0.0331557	+	0.576397i
$49$	−9.59977	+	9.59977i	−1.37140	+	1.37140i
$50$	−2.66726	+	16.3586i	−0.377208	+	2.31346i
$51$	−4.48683	−	0.892487i	−0.628282	−	0.124973i
$52$	0.931176	+	3.42047i	0.129131	+	0.474334i
$53$	3.33168	−	4.98621i	0.457641	−	0.684908i	−0.528851	−	0.848714i	$-0.677377\pi$
$53$	3.33168	−	4.98621i	0.457641	−	0.684908i	0.986493	+	0.163806i	$0.0523771\pi$
$54$	1.32456	+	0.495512i	0.180250	+	0.0674306i
$55$	−2.03589	+	4.91507i	−0.274519	+	0.662748i
$56$	−3.79787	−	12.2550i	−0.507511	−	1.63764i
$57$	1.21588	+	2.93540i	0.161048	+	0.388804i
$58$	−4.88192	+	0.169581i	−0.641028	+	0.0222671i
$59$	−2.77551	+	0.552083i	−0.361341	+	0.0718751i	−0.372422	−	0.928063i	$-0.621473\pi$
$59$	−2.77551	+	0.552083i	−0.361341	+	0.0718751i	0.0110814	+	0.999939i	$0.496473\pi$
$60$	7.75447	+	2.59778i	1.00110	+	0.335372i
$61$	−0.177964	+	0.118912i	−0.0227860	+	0.0152251i	−0.566911	−	0.823779i	$-0.691862\pi$
$61$	−0.177964	+	0.118912i	−0.0227860	+	0.0152251i	0.544125	+	0.839004i	$0.316862\pi$
$62$	1.41210	+	0.874196i	0.179337	+	0.111023i
$63$	−4.53609			−0.571494
$64$	7.86443	+	1.46657i	0.983053	+	0.183321i
$65$	7.24769			0.898965
$66$	1.56444	+	0.968506i	0.192570	+	0.119215i
$67$	1.88157	−	1.25723i	0.229871	−	0.153595i	−0.435301	−	0.900285i	$-0.643358\pi$
$67$	1.88157	−	1.25723i	0.229871	−	0.153595i	0.665172	+	0.746690i	$0.268358\pi$
$68$	−2.90636	+	8.67559i	−0.352448	+	1.05207i
$69$	−0.582604	+	0.115887i	−0.0701373	+	0.0139512i
$70$	−26.2152	+	0.910628i	−3.13332	+	0.108841i
$71$	−2.23974	−	5.40720i	−0.265808	−	0.641716i	0.733470	−	0.679722i	$-0.237900\pi$
$71$	−2.23974	−	5.40720i	−0.265808	−	0.641716i	−0.999278	+	0.0380055i	$0.987900\pi$
$72$	1.31834	−	2.50240i	0.155368	−	0.294910i
$73$	2.86687	−	6.92124i	0.335542	−	0.810070i	−0.662591	−	0.748982i	$-0.730543\pi$
$73$	2.86687	−	6.92124i	0.335542	−	0.810070i	0.998132	−	0.0610878i	$-0.0194570\pi$
$74$	6.92291	+	2.58982i	0.804773	+	0.301061i
$75$	6.51132	−	9.74487i	0.751862	−	1.12524i
$76$	6.13137	−	1.66918i	0.703316	−	0.191468i
$77$	−5.78831	−	1.15137i	−0.659639	−	0.131210i
$78$	0.403382	−	2.47399i	0.0456741	−	0.280124i
$79$	9.06639	−	9.06639i	1.02005	−	1.02005i	0.0202541	−	0.999795i	$-0.493552\pi$
$79$	9.06639	−	9.06639i	1.02005	−	1.02005i	0.999795	−	0.0202541i	$-0.00644751\pi$
$80$	7.11665	−	14.7266i	0.795666	−	1.64649i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	13.2722	−	9.55089i	1.46567	−	1.05472i
$83$	0.276166	−	1.38838i	0.0303131	−	0.152394i	−0.962664	−	0.270698i	$-0.912746\pi$
$83$	0.276166	−	1.38838i	0.0303131	−	0.152394i	0.992977	+	0.118303i	$0.0377456\pi$
$84$	−1.14821	+	8.99923i	−0.125280	+	0.981896i
$85$	15.5536	+	10.3926i	1.68703	+	1.12723i
$86$	−7.14340	+	3.25385i	−0.770292	+	0.350871i
$87$	3.19119	+	1.32183i	0.342132	+	0.141716i
$88$	2.31744	−	2.85857i	0.247040	−	0.304725i
$89$	5.14596	−	2.13153i	0.545470	−	0.225941i	−0.0928934	−	0.995676i	$-0.529612\pi$
$89$	5.14596	−	2.13153i	0.545470	−	0.225941i	0.638364	+	0.769735i	$0.279612\pi$
$90$	−4.22850	−	3.94460i	−0.445724	−	0.415797i
$91$	1.56855	+	7.88563i	0.164429	+	0.826639i
$92$	0.0824371	+	1.18517i	0.00859467	+	0.123563i
$93$	−0.652441	−	0.976447i	−0.0676550	−	0.101253i
$94$	−10.8452	+	2.55160i	−1.11860	+	0.263178i
$95$		−	12.9919i		−	1.33294i
$96$	−4.63084	−	3.24890i	−0.472633	−	0.331589i
$97$		−	10.5410i		−	1.07028i	−0.844765	−	0.535138i	$-0.820260\pi$
$97$		−	10.5410i		−	1.07028i	0.844765	−	0.535138i	$-0.179740\pi$
$98$	−4.39710	−	18.6892i	−0.444175	−	1.88790i
$99$	−0.722828	−	1.08179i	−0.0726469	−	0.108724i
$100$	−17.6848	−	15.3846i	−1.76848	−	1.53846i
$101$	−0.127670	−	0.641842i	−0.0127037	−	0.0638657i	0.973913	−	0.226920i	$-0.0728655\pi$
$101$	−0.127670	−	0.641842i	−0.0127037	−	0.0638657i	−0.986617	+	0.163054i	$0.947866\pi$
$102$	4.41316	−	4.73079i	0.436968	−	0.468418i
$103$	−4.35764	+	1.80499i	−0.429371	+	0.177851i	−0.586894	−	0.809664i	$-0.699649\pi$
$103$	−4.35764	+	1.80499i	−0.429371	+	0.177851i	0.157523	+	0.987515i	$0.449649\pi$
$104$	−4.80609	−	1.42651i	−0.471276	−	0.139881i
$105$	17.1363	+	7.09807i	1.67233	+	0.692701i
$106$	3.51553	+	7.71788i	0.341458	+	0.749627i
$107$	−13.3967	−	8.95140i	−1.29511	−	0.865365i	−0.299067	−	0.954232i	$-0.596675\pi$
$107$	−13.3967	−	8.95140i	−1.29511	−	0.865365i	−0.996043	+	0.0888674i	$0.971675\pi$
$108$	−1.58183	+	1.22385i	−0.152212	+	0.117765i
$109$	−3.44120	+	17.3001i	−0.329607	+	1.65705i	0.360066	+	0.932927i	$0.382754\pi$
$109$	−3.44120	+	17.3001i	−0.329607	+	1.65705i	−0.689673	+	0.724121i	$0.742246\pi$
$110$	−4.39458	−	6.10682i	−0.419007	−	0.582263i
$111$	−3.69574	−	3.69574i	−0.350784	−	0.350784i
$112$	17.5631	+	4.55591i	1.65955	+	0.430493i
$113$	4.68379	−	4.68379i	0.440614	−	0.440614i	−0.451605	−	0.892218i	$-0.649148\pi$
$113$	4.68379	−	4.68379i	0.440614	−	0.440614i	0.892218	+	0.451605i	$0.149148\pi$
$114$	−4.43476	−	0.723083i	−0.415353	−	0.0677230i
$115$	2.38228	+	0.473864i	0.222148	+	0.0441881i
$116$	3.43019	−	5.99647i	0.318485	−	0.556758i
$117$	−0.984736	+	1.47376i	−0.0910389	+	0.136249i
$118$	1.40224	−	3.74836i	0.129087	−	0.345065i
$119$	−7.94123	+	19.1718i	−0.727971	+	1.75748i
$120$	−8.89611	+	7.39051i	−0.812100	+	0.674659i
$121$	3.56173	+	8.59878i	0.323794	+	0.781707i
$122$	−0.0105082	−	0.302510i	−0.000951366	−	0.0273880i
$123$	−11.3401	+	2.25568i	−1.02250	+	0.203388i
$124$	−2.10234	+	1.04722i	−0.188796	+	0.0940434i
$125$	−22.8475	+	15.2662i	−2.04354	+	1.36545i
$126$	3.37667	−	5.45439i	0.300817	−	0.485916i
$127$	20.6460			1.83203			0.916016	−	0.401141i	$-0.131386\pi$
$127$	20.6460			1.83203			0.916016	+	0.401141i	$0.131386\pi$
$128$	−7.61774	+	8.36481i	−0.673319	+	0.739352i
$129$	5.55048			0.488693
$130$	−5.39518	+	8.71493i	−0.473189	+	0.764350i
$131$	15.0484	−	10.0550i	1.31479	−	0.878513i	0.317229	−	0.948349i	$-0.397248\pi$
$131$	15.0484	−	10.0550i	1.31479	−	0.878513i	0.997558	+	0.0698363i	$0.0222477\pi$
$132$	−2.32915	+	1.16020i	−0.202726	+	0.100982i
$133$	14.1354	−	2.81171i	1.22569	−	0.243806i
$134$	0.111100	+	3.19836i	0.00959759	+	0.276296i
$135$	1.56480	+	3.77776i	0.134676	+	0.325138i
$136$	−8.26841	−	9.95285i	−0.709010	−	0.853449i
$137$	0.919638	−	2.22020i	0.0785700	−	0.189685i	−0.879714	−	0.475504i	$-0.842266\pi$
$137$	0.919638	−	2.22020i	0.0785700	−	0.189685i	0.958284	+	0.285819i	$0.0922657\pi$
$138$	0.294343	−	0.786814i	0.0250561	−	0.0669781i
$139$	−1.99082	+	2.97948i	−0.168859	+	0.252716i	−0.906242	−	0.422759i	$-0.861062\pi$
$139$	−1.99082	+	2.97948i	−0.168859	+	0.252716i	0.737383	+	0.675475i	$0.236062\pi$
$140$	18.4196	−	32.2002i	1.55674	−	2.72141i
$141$	7.72673	+	1.53694i	0.650708	+	0.129434i
$142$	8.16911	+	1.33197i	0.685536	+	0.111776i
$143$	−1.63065	+	1.63065i	−0.136362	+	0.136362i
$144$	2.02762	+	3.44801i	0.168968	+	0.287334i
$145$	−9.98715	−	9.98715i	−0.829387	−	0.829387i
$146$	6.18829	+	8.59942i	0.512147	+	0.711693i
$147$	−2.64857	+	13.3153i	−0.218450	+	1.09822i
$148$	−8.26753	+	6.39654i	−0.679587	+	0.525793i
$149$	−13.4778	−	9.00558i	−1.10415	−	0.737766i	−0.136641	−	0.990621i	$-0.543631\pi$
$149$	−13.4778	−	9.00558i	−1.10415	−	0.737766i	−0.967504	+	0.252854i	$0.918631\pi$
$150$	6.87063	+	15.0836i	0.560984	+	1.23157i
$151$	−15.8119	−	6.54951i	−1.28676	−	0.532991i	−0.368738	−	0.929533i	$-0.620210\pi$
$151$	−15.8119	−	6.54951i	−1.28676	−	0.532991i	−0.918017	+	0.396542i	$0.870210\pi$
$152$	−2.55710	+	8.61516i	−0.207408	+	0.698781i
$153$	−4.22650	+	1.75068i	−0.341693	+	0.141534i
$154$	5.69327	−	6.10303i	0.458777	−	0.491796i
$155$	0.936822	+	4.70972i	0.0752473	+	0.378294i
$156$	2.67456	+	2.32668i	0.214136	+	0.186284i
$157$	−7.65178	−	11.4517i	−0.610678	−	0.913945i	0.389296	−	0.921113i	$-0.372718\pi$
$157$	−7.65178	−	11.4517i	−0.610678	−	0.913945i	−0.999974	+	0.00716789i	$0.997718\pi$
$158$	4.15279	+	17.6508i	0.330379	+	1.40423i
$159$		−	5.99686i		−	0.475582i
$160$	12.4103	+	19.5199i	0.981121	+	1.54318i
$161$			2.69452i			0.212358i
$162$	1.37663	−	0.323885i	0.108158	−	0.0254468i
$163$	−1.58440	−	2.37122i	−0.124100	−	0.185728i	0.764218	−	0.644958i	$-0.223125\pi$
$163$	−1.58440	−	2.37122i	−0.124100	−	0.185728i	−0.888317	+	0.459230i	$0.848125\pi$
$164$	1.60459	+	23.0687i	0.125298	+	1.80136i
$165$	1.03789	+	5.21782i	0.0807995	+	0.406206i
$166$	1.46387	+	1.36558i	0.113618	+	0.105990i
$167$	15.1608	−	6.27981i	1.17318	−	0.485946i	0.290936	−	0.956742i	$-0.406033\pi$
$167$	15.1608	−	6.27981i	1.17318	−	0.485946i	0.882242	+	0.470796i	$0.156033\pi$
$168$	−9.96633	−	8.07968i	−0.768919	−	0.623361i
$169$	−9.10790	−	3.77262i	−0.700608	−	0.290201i
$170$	−24.0746	+	10.9661i	−1.84644	+	0.841060i
$171$	2.64179	+	1.76519i	0.202023	+	0.134987i
$172$	1.40498	−	11.0117i	0.107129	−	0.839634i
$173$	0.135046	−	0.678922i	0.0102674	−	0.0516175i	−0.975312	−	0.220832i	$-0.929123\pi$
$173$	0.135046	−	0.678922i	0.0102674	−	0.0516175i	0.985579	+	0.169214i	$0.0541229\pi$
$174$	−3.96495	+	2.85325i	−0.300582	+	0.216304i
$175$	−37.5921	−	37.5921i	−2.84170	−	2.84170i
$176$	1.71217	+	4.91451i	0.129060	+	0.370445i
$177$	−2.00103	+	2.00103i	−0.150407	+	0.150407i
$178$	−1.26761	+	7.77443i	−0.0950117	+	0.582718i
$179$	5.87963	+	1.16953i	0.439464	+	0.0874149i	0.409863	−	0.912147i	$-0.365576\pi$
$179$	5.87963	+	1.16953i	0.439464	+	0.0874149i	0.0296010	+	0.999562i	$0.490576\pi$
$180$	7.89085	−	2.14818i	0.588150	−	0.160116i
$181$	−4.37239	+	6.54374i	−0.324997	+	0.486393i	−0.957607	−	0.288078i	$-0.906984\pi$
$181$	−4.37239	+	6.54374i	−0.324997	+	0.486393i	0.632610	+	0.774471i	$0.281984\pi$
$182$	−10.6496	−	3.98397i	−0.789405	−	0.295312i
$183$	−0.0819081	+	0.197744i	−0.00605482	+	0.0146176i
$184$	−1.48647	−	0.783116i	−0.109584	−	0.0577321i
$185$	8.17852	+	19.7447i	0.601297	+	1.45166i
$186$	1.65980	−	0.0576558i	0.121702	−	0.00422752i
$187$	−5.83762	+	1.16117i	−0.426889	+	0.0849135i
$188$	5.00502	−	14.9402i	0.365028	−	1.08962i
$189$	−3.77162	+	2.52012i	−0.274345	+	0.183312i
$190$	15.6220	+	9.67114i	1.13334	+	0.701618i
$191$	2.85671			0.206704			0.103352	−	0.994645i	$-0.467043\pi$
$191$	2.85671			0.206704			0.103352	+	0.994645i	$0.467043\pi$
$192$	7.35381	−	3.14984i	0.530716	−	0.227320i
$193$	−7.82449			−0.563219			−0.281610	−	0.959529i	$-0.590868\pi$
$193$	−7.82449			−0.563219			−0.281610	+	0.959529i	$0.590868\pi$
$194$	12.6749	+	7.84672i	0.910008	+	0.563362i
$195$	6.02623	−	4.02660i	0.431548	−	0.288351i
$196$	25.7460	+	8.62501i	1.83900	+	0.616072i
$197$	−19.5243	+	3.88363i	−1.39105	+	0.276697i	−0.833075	−	0.553161i	$-0.813422\pi$
$197$	−19.5243	+	3.88363i	−1.39105	+	0.276697i	−0.557975	+	0.829858i	$0.688422\pi$
$198$	1.83886	−	0.0638758i	0.130682	−	0.00453945i
$199$	2.11015	+	5.09435i	0.149585	+	0.361129i	0.980855	−	0.194739i	$-0.0623860\pi$
$199$	2.11015	+	5.09435i	0.149585	+	0.361129i	−0.831271	+	0.555868i	$0.812386\pi$
$200$	31.6637	−	9.81268i	2.23896	−	0.693861i
$201$	0.865992	−	2.09069i	0.0610824	−	0.147466i
$202$	0.866816	+	0.324271i	0.0609890	+	0.0228156i
$203$	8.70479	−	13.0276i	0.610957	−	0.914361i
$204$	2.40335	+	8.82818i	0.168268	+	0.618096i
$205$	46.3697	+	9.22350i	3.23860	+	0.644197i
$206$	1.07343	−	6.58345i	0.0747891	−	0.458691i
$207$	−0.420034	+	0.420034i	−0.0291944	+	0.0291944i
$208$	5.29295	−	4.71715i	0.367000	−	0.327075i
$209$	2.92303	+	2.92303i	0.202190	+	0.202190i
$210$	−21.2913	+	15.3216i	−1.46924	+	1.05729i
$211$	−3.56457	+	17.9203i	−0.245395	+	1.23368i	0.639828	+	0.768518i	$0.279006\pi$
$211$	−3.56457	+	17.9203i	−0.245395	+	1.23368i	−0.885223	+	0.465167i	$0.845994\pi$
$212$	−11.8973	−	1.51797i	−0.817108	−	0.104255i
$213$	−4.86635	−	3.25159i	−0.333437	−	0.222795i
$214$	20.7361	−	9.44537i	1.41749	−	0.645672i
$215$	−20.9684	−	8.68539i	−1.43003	−	0.592338i
$216$	−0.294099	−	2.81310i	−0.0200109	−	0.191407i
$217$	−4.92152	+	2.03856i	−0.334095	+	0.138387i
$218$	−18.2407	−	17.0160i	−1.23542	−	1.15247i
$219$	−1.46152	−	7.34755i	−0.0987602	−	0.496501i
$220$	10.6144	−	0.738309i	0.715625	−	0.0497768i
$221$	4.50491	+	6.74207i	0.303033	+	0.453521i
$222$	7.19502	−	1.69281i	0.482898	−	0.113614i
$223$			15.8006i			1.05809i	0.848594	+	0.529044i	$0.177450\pi$
$223$			15.8006i			1.05809i	−0.848594	+	0.529044i	$0.822550\pi$
$224$	−18.5522	+	17.7272i	−1.23957	+	1.18445i
$225$		−	11.7201i		−	0.781337i
$226$	2.14537	+	9.11860i	0.142708	+	0.606560i
$227$	−7.59929	−	11.3731i	−0.504383	−	0.754862i	0.488678	−	0.872464i	$-0.337479\pi$
$227$	−7.59929	−	11.3731i	−0.504383	−	0.754862i	−0.993061	+	0.117602i	$0.962479\pi$
$228$	4.17070	−	4.79428i	0.276211	−	0.317509i
$229$	1.96821	+	9.89484i	0.130063	+	0.653869i	0.989722	+	0.143002i	$0.0456756\pi$
$229$	1.96821	+	9.89484i	0.130063	+	0.653869i	−0.859660	+	0.510867i	$0.829324\pi$
$230$	−2.34316	+	2.51181i	−0.154503	+	0.165624i
$231$	−5.45247	+	2.25849i	−0.358746	+	0.148597i
$232$	4.65697	+	8.58838i	0.305745	+	0.563855i
$233$	14.8819	+	6.16428i	0.974944	+	0.403835i	0.812551	−	0.582891i	$-0.198078\pi$
$233$	14.8819	+	6.16428i	0.974944	+	0.403835i	0.162394	+	0.986726i	$0.448078\pi$
$234$	−1.03908	−	2.28116i	−0.0679265	−	0.149124i
$235$	−26.7847	−	17.8970i	−1.74724	−	1.16747i
$236$	3.46336	+	4.47640i	0.225446	+	0.291389i
$237$	2.50141	−	12.5754i	0.162484	−	0.816863i
$238$	−17.1416	−	23.8204i	−1.11112	−	1.54405i
$239$	18.6334	+	18.6334i	1.20530	+	1.20530i	0.972534	+	0.232762i	$0.0747764\pi$
$239$	18.6334	+	18.6334i	1.20530	+	1.20530i	0.232762	+	0.972534i	$0.425224\pi$
$240$	−2.26441	−	16.1986i	−0.146167	−	1.04561i
$241$	−16.3162	+	16.3162i	−1.05102	+	1.05102i	−0.0523927	+	0.998627i	$0.516685\pi$
$241$	−16.3162	+	16.3162i	−1.05102	+	1.05102i	−0.998627	+	0.0523927i	$0.983315\pi$
$242$	−12.9909	−	2.11815i	−0.835086	−	0.136160i
$243$	−0.980785	−	0.195090i	−0.0629174	−	0.0125150i
$244$	0.371574	+	0.212553i	0.0237876	+	0.0136073i
$245$	30.8414	−	46.1574i	1.97038	−	2.94889i
$246$	5.72922	−	15.3149i	0.365281	−	0.976442i
$247$	2.15513	−	5.20294i	0.137127	−	0.331055i
$248$	0.305757	−	3.30750i	0.0194156	−	0.210026i
$249$	−0.541719	−	1.30782i	−0.0343300	−	0.0828800i
$250$	−1.34906	−	38.8369i	−0.0853223	−	2.45626i
$251$	0.0582707	−	0.0115908i	0.00367802	−	0.000731603i	−0.193251	−	0.981149i	$-0.561903\pi$
$251$	0.0582707	−	0.0115908i	0.00367802	−	0.000731603i	0.196929	+	0.980418i	$0.436903\pi$
$252$	4.04500	+	8.12050i	0.254811	+	0.511543i
$253$	−0.642601	+	0.429372i	−0.0404000	+	0.0269944i
$254$	−15.3689	+	24.8256i	−0.964327	+	1.55770i
$255$	18.7062			1.17143
$256$	−4.38756	−	15.3867i	−0.274222	−	0.961666i
$257$	−8.12008			−0.506517			−0.253258	−	0.967399i	$-0.581502\pi$
$257$	−8.12008			−0.506517			−0.253258	+	0.967399i	$0.581502\pi$
$258$	−4.13178	+	6.67413i	−0.257233	+	0.415513i
$259$	−19.7126	+	13.1716i	−1.22488	+	0.818441i
$260$	−6.46303	−	12.9748i	−0.400820	−	0.804663i
$261$	3.38775	−	0.673866i	0.209697	−	0.0417112i
$262$	0.888557	+	25.5798i	0.0548952	+	1.58033i
$263$	−1.25763	−	3.03618i	−0.0775486	−	0.187219i	0.880351	−	0.474323i	$-0.157307\pi$
$263$	−1.25763	−	3.03618i	−0.0775486	−	0.187219i	−0.957899	+	0.287105i	$0.907307\pi$
$264$	0.338743	−	3.66432i	0.0208482	−	0.225523i
$265$	−9.38388	+	22.6547i	−0.576447	+	1.39167i
$266$	−7.14148	+	19.0900i	−0.437872	+	1.17049i
$267$	3.09450	−	4.63124i	0.189380	−	0.283427i
$268$	−3.92855	−	2.24727i	−0.239974	−	0.137274i
$269$	11.3344	+	2.25455i	0.691070	+	0.137462i	0.528117	−	0.849171i	$-0.322898\pi$
$269$	11.3344	+	2.25455i	0.691070	+	0.137462i	0.162953	+	0.986634i	$0.447898\pi$
$270$	−5.70738	−	0.930583i	−0.347340	−	0.0566335i
$271$	8.66595	−	8.66595i	0.526419	−	0.526419i	−0.393084	−	0.919503i	$-0.628592\pi$
$271$	8.66595	−	8.66595i	0.526419	−	0.526419i	0.919503	+	0.393084i	$0.128592\pi$
$272$	18.1227	−	2.53339i	1.09885	−	0.153609i
$273$	5.68522	+	5.68522i	0.344085	+	0.344085i
$274$	1.98509	+	2.75853i	0.119924	+	0.166649i
$275$	2.97482	−	14.9555i	0.179389	−	0.901848i
$276$	0.726990	+	0.939635i	0.0437597	+	0.0565594i
$277$	−17.1148	−	11.4357i	−1.02833	−	0.687106i	−0.0775515	−	0.996988i	$-0.524710\pi$
$277$	−17.1148	−	11.4357i	−1.02833	−	0.687106i	−0.950775	+	0.309883i	$0.899710\pi$
$278$	−2.10068	−	4.61177i	−0.125990	−	0.276596i
$279$	−1.08497	−	0.449409i	−0.0649554	−	0.0269054i
$280$	25.0073	+	46.1184i	1.49447	+	2.75610i
$281$	−12.9964	+	5.38328i	−0.775299	+	0.321139i	−0.735017	−	0.678049i	$-0.762826\pi$
$281$	−12.9964	+	5.38328i	−0.775299	+	0.321139i	−0.0402822	+	0.999188i	$0.512826\pi$
$282$	−7.59987	+	8.14685i	−0.452565	+	0.485138i
$283$	0.252988	+	1.27186i	0.0150386	+	0.0756040i	0.987576	−	0.157143i	$-0.0502285\pi$
$283$	0.252988	+	1.27186i	0.0150386	+	0.0756040i	−0.972537	+	0.232747i	$0.925228\pi$
$284$	−7.68270	+	8.83137i	−0.455884	+	0.524045i
$285$	−7.21789	−	10.8023i	−0.427551	−	0.639875i
$286$	−0.746909	−	3.17463i	−0.0441656	−	0.187720i
$287$			52.4473i			3.09587i
$288$	−5.65539	−	0.128605i	−0.333247	−	0.00757813i
$289$			3.92821i			0.231071i
$290$	19.4434	−	4.57454i	1.14176	−	0.268626i
$291$	−5.85627	−	8.76452i	−0.343300	−	0.513785i
$292$	−14.9469	+	1.03966i	−0.874700	+	0.0608416i
$293$	−0.672220	−	3.37948i	−0.0392715	−	0.197431i	0.956169	−	0.292815i	$-0.0945921\pi$
$293$	−0.672220	−	3.37948i	−0.0392715	−	0.197431i	−0.995441	+	0.0953840i	$0.969592\pi$
$294$	−14.0392	−	13.0966i	−0.818786	−	0.763811i
$295$	10.6906	−	4.42820i	0.622432	−	0.257820i
$296$	−1.53713	−	14.7028i	−0.0893436	−	0.854584i
$297$	−1.20202	−	0.497892i	−0.0697482	−	0.0288906i
$298$	20.8616	−	9.50254i	1.20848	−	0.550467i
$299$	0.875440	+	0.584950i	0.0506280	+	0.0338286i
$300$	−23.2516	−	2.96667i	−1.34243	−	0.171281i
$301$	4.91188	−	24.6937i	0.283116	−	1.42332i
$302$	19.6458	−	14.1375i	1.13049	−	0.813520i
$303$	−0.462742	−	0.462742i	−0.0265839	−	0.0265839i
$304$	−8.45573	−	9.48789i	−0.484969	−	0.544168i
$305$	0.618858	−	0.618858i	0.0354357	−	0.0354357i
$306$	1.04112	−	6.38533i	0.0595171	−	0.365025i
$307$	−12.9128	−	2.56851i	−0.736972	−	0.146593i	−0.187688	−	0.982229i	$-0.560099\pi$
$307$	−12.9128	−	2.56851i	−0.736972	−	0.146593i	−0.549284	+	0.835636i	$0.685099\pi$
$308$	3.10048	+	11.3889i	0.176666	+	0.648944i
$309$	−2.62044	+	3.92177i	−0.149072	+	0.223102i
$310$	−6.36054	−	2.37944i	−0.361254	−	0.135143i
$311$	−3.93278	+	9.49457i	−0.223008	+	0.538388i	−0.995296	−	0.0968846i	$-0.969112\pi$
$311$	−3.93278	+	9.49457i	−0.223008	+	0.538388i	0.772288	+	0.635272i	$0.219112\pi$
$312$	−4.78864	+	1.48402i	−0.271104	+	0.0840159i
$313$	−2.69849	−	6.51473i	−0.152528	−	0.368234i	0.829084	−	0.559124i	$-0.188863\pi$
$313$	−2.69849	−	6.51473i	−0.152528	−	0.368234i	−0.981611	+	0.190890i	$0.938863\pi$
$314$	19.4660	−	0.676182i	1.09853	−	0.0381592i
$315$	18.1918	−	3.61857i	1.02499	−	0.203883i
$316$	−24.3155	−	8.14579i	−1.36785	−	0.458237i
$317$	6.07716	−	4.06063i	0.341327	−	0.228068i	−0.373078	−	0.927800i	$-0.621697\pi$
$317$	6.07716	−	4.06063i	0.341327	−	0.228068i	0.714405	+	0.699732i	$0.246697\pi$
$318$	7.21088	+	4.46406i	0.404366	+	0.250332i
$319$	4.49400			0.251616
$320$	−32.7098	+	0.392087i	−1.82853	+	0.0219183i
$321$	−16.1121			−0.899290
$322$	−3.24000	−	2.00580i	−0.180558	−	0.111779i
$323$	12.0855	−	8.07527i	0.672455	−	0.449320i
$324$	−0.635307	+	1.89641i	−0.0352948	+	0.105356i
$325$	−20.3744	+	4.05272i	−1.13017	+	0.224804i
$326$	4.03068	−	0.140012i	0.223239	−	0.00775456i
$327$	6.75016	+	16.2963i	0.373285	+	0.901189i
$328$	−28.9333	−	15.2429i	−1.59757	−	0.841649i
$329$	13.6755	−	33.0156i	0.753955	−	1.82021i
$330$	−7.04673	−	2.63614i	−0.387910	−	0.145115i
$331$	8.91742	−	13.3459i	0.490146	−	0.733555i	−0.501128	−	0.865373i	$-0.667081\pi$
$331$	8.91742	−	13.3459i	0.490146	−	0.733555i	0.991274	+	0.131818i	$0.0420815\pi$
$332$	−2.73174	+	0.743678i	−0.149924	+	0.0408146i
$333$	−5.12614	−	1.01965i	−0.280911	−	0.0558766i
$334$	−3.73459	+	22.9047i	−0.204348	+	1.25329i
$335$	−6.54302	+	6.54302i	−0.357483	+	0.357483i
$336$	17.1343	−	5.96942i	0.934752	−	0.325659i
$337$	−19.9228	−	19.9228i	−1.08526	−	1.08526i	−0.996009	−	0.0892528i	$-0.971552\pi$
$337$	−19.9228	−	19.9228i	−1.08526	−	1.08526i	−0.0892528	−	0.996009i	$-0.528448\pi$
$338$	11.3163	−	8.14340i	0.615524	−	0.442942i
$339$	1.29225	−	6.49660i	0.0701856	−	0.352847i
$340$	4.73505	−	37.1115i	0.256794	−	2.01265i
$341$	−1.27041	−	0.848862i	−0.0687966	−	0.0459685i
$342$	−4.08909	+	1.86260i	−0.221113	+	0.100718i
$343$	27.5592	+	11.4154i	1.48806	+	0.616374i
$344$	12.1951	+	9.88651i	0.657514	+	0.533045i
$345$	2.24406	−	0.929518i	0.120816	−	0.0500436i
$346$	0.715837	+	0.667775i	0.0384836	+	0.0358998i
$347$	−0.00965266	−	0.0485272i	−0.000518182	−	0.00260508i	0.980525	−	0.196393i	$-0.0629227\pi$
$347$	−0.00965266	−	0.0485272i	−0.000518182	−	0.00260508i	−0.981044	+	0.193788i	$0.937923\pi$
$348$	−0.479359	−	6.89159i	−0.0256964	−	0.369428i
$349$	−8.48723	−	12.7020i	−0.454311	−	0.679924i	0.531638	−	0.846972i	$-0.321577\pi$
$349$	−8.48723	−	12.7020i	−0.454311	−	0.679924i	−0.985949	+	0.167047i	$0.946577\pi$
$350$	73.1859	−	17.2188i	3.91195	−	0.920383i
$351$			1.77248i			0.0946079i
$352$	−7.18396	−	1.59958i	−0.382906	−	0.0852578i
$353$			32.8510i			1.74848i	0.485494	+	0.874240i	$0.338640\pi$
$353$			32.8510i			1.74848i	−0.485494	+	0.874240i	$0.661360\pi$
$354$	−0.916558	−	3.89569i	−0.0487145	−	0.207054i
$355$	13.2958	+	19.8986i	0.705668	+	1.05611i
$356$	−8.40469	−	7.31152i	−0.445448	−	0.387510i
$357$	4.04840	+	20.3527i	0.214264	+	1.07718i
$358$	−5.78310	+	6.19932i	−0.305646	+	0.327644i
$359$	18.0832	−	7.49032i	0.954396	−	0.395324i	0.149515	−	0.988759i	$-0.452229\pi$
$359$	18.0832	−	7.49032i	0.954396	−	0.395324i	0.804881	+	0.593436i	$0.202229\pi$
$360$	−3.29089	+	11.0874i	−0.173445	+	0.584357i
$361$	8.22718	+	3.40781i	0.433010	+	0.179359i
$362$	−4.61367	−	10.1287i	−0.242489	−	0.532353i
$363$	7.73870	+	5.17083i	0.406176	+	0.271398i
$364$	12.7181	−	9.83992i	0.666610	−	0.515752i
$365$	−5.97617	+	30.0442i	−0.312807	+	1.57259i
$366$	−0.176803	−	0.245690i	−0.00924164	−	0.0128424i
$367$	13.1965	+	13.1965i	0.688851	+	0.688851i	0.961978	−	0.273127i	$-0.0880579\pi$
$367$	13.1965	+	13.1965i	0.688851	+	0.688851i	−0.273127	+	0.961978i	$0.588058\pi$
$368$	2.04818	−	1.20444i	0.106769	−	0.0627858i
$369$	−8.17572	+	8.17572i	−0.425611	+	0.425611i
$370$	−29.8300	−	4.86375i	−1.55079	−	0.252854i
$371$	−26.6796	−	5.30691i	−1.38514	−	0.275521i
$372$	−1.16623	+	2.03873i	−0.0604660	+	0.105703i
$373$	9.99202	−	14.9541i	0.517367	−	0.774295i	−0.477155	−	0.878819i	$-0.658332\pi$
$373$	9.99202	−	14.9541i	0.517367	−	0.774295i	0.994522	+	0.104524i	$0.0333321\pi$
$374$	2.94928	−	7.88378i	0.152504	−	0.407661i
$375$	−10.5155	+	25.3868i	−0.543020	+	1.31097i
$376$	14.2389	+	17.1397i	0.734317	+	0.883913i
$377$	−2.34292	−	5.65632i	−0.120667	−	0.291315i
$378$	−0.222701	−	6.41114i	−0.0114545	−	0.329753i
$379$	34.1988	−	6.80256i	1.75667	−	0.349424i	0.791527	−	0.611134i	$-0.209286\pi$
$379$	34.1988	−	6.80256i	1.75667	−	0.349424i	0.965147	+	0.261710i	$0.0842863\pi$
$380$	−23.2580	+	11.5853i	−1.19311	+	0.594314i
$381$	17.1665	−	11.4703i	0.879466	−	0.587640i
$382$	−2.12654	+	3.43503i	−0.108803	+	0.175751i
$383$	18.3695			0.938636			0.469318	−	0.883029i	$-0.344500\pi$
$383$	18.3695			0.938636			0.469318	+	0.883029i	$0.344500\pi$
$384$	−1.68668	+	11.1873i	−0.0860730	+	0.570898i
$385$	24.1322			1.22989
$386$	5.82455	−	9.40850i	0.296462	−	0.478880i
$387$	4.61506	−	3.08368i	0.234596	−	0.156752i
$388$	−18.8705	+	9.39980i	−0.958003	+	0.477203i
$389$	31.2255	−	6.21114i	1.58320	−	0.314917i	0.676416	−	0.736520i	$-0.263532\pi$
$389$	31.2255	−	6.21114i	1.58320	−	0.314917i	0.906781	+	0.421603i	$0.138532\pi$
$390$	0.355828	+	10.2436i	0.0180180	+	0.518705i
$391$	1.03993	+	2.51062i	0.0525916	+	0.126967i
$392$	−29.5364	+	24.5376i	−1.49181	+	1.23933i
$393$	6.92603	−	16.7209i	0.349372	−	0.843459i
$394$	9.86406	−	26.3678i	0.496944	−	1.32839i
$395$	−29.1278	+	43.5928i	−1.46558	+	2.19339i
$396$	−1.29204	+	2.25867i	−0.0649275	+	0.113503i
$397$	5.94005	+	1.18155i	0.298123	+	0.0593003i	0.341885	−	0.939742i	$-0.388935\pi$
$397$	5.94005	+	1.18155i	0.298123	+	0.0593003i	−0.0437627	+	0.999042i	$0.513935\pi$
$398$	−7.69646	−	1.25490i	−0.385789	−	0.0629026i
$399$	10.1911	−	10.1911i	0.510191	−	0.510191i
$400$	−11.7713	+	45.3783i	−0.588563	+	2.26892i
$401$	16.5957	+	16.5957i	0.828751	+	0.828751i	0.987344	−	0.158593i	$-0.0506957\pi$
$401$	16.5957	+	16.5957i	0.828751	+	0.828751i	−0.158593	+	0.987344i	$0.550696\pi$
$402$	1.86929	+	2.59762i	0.0932317	+	0.129557i
$403$	−0.406087	+	2.04154i	−0.0202286	+	0.101696i
$404$	−1.03518	+	0.800909i	−0.0515019	+	0.0398467i
$405$	3.39989	+	2.27174i	0.168942	+	0.112883i
$406$	9.18514	+	20.1648i	0.455851	+	1.00076i
$407$	−6.28243	−	2.60227i	−0.311408	−	0.128990i
$408$	−12.4044	−	3.68181i	−0.614111	−	0.182277i
$409$	−11.7077	+	4.84948i	−0.578908	+	0.239792i	−0.652871	−	0.757469i	$-0.726435\pi$
$409$	−11.7077	+	4.84948i	−0.578908	+	0.239792i	0.0739626	+	0.997261i	$0.476435\pi$
$410$	−45.6083	+	48.8909i	−2.25243	+	2.41455i
$411$	−0.468827	−	2.35695i	−0.0231255	−	0.116260i
$412$	7.11716	+	6.19145i	0.350637	+	0.305031i
$413$	7.13165	+	10.6733i	0.350925	+	0.525197i
$414$	−0.192393	−	0.817740i	−0.00945562	−	0.0401897i
$415$			5.78833i			0.284138i
$416$	1.73203	+	9.87592i	0.0849196	+	0.484207i
$417$			3.58339i			0.175479i
$418$	−5.69068	+	1.33887i	−0.278340	+	0.0654864i
$419$	−0.676823	−	1.01294i	−0.0330649	−	0.0494852i	0.814569	−	0.580067i	$-0.196974\pi$
$419$	−0.676823	−	1.01294i	−0.0330649	−	0.0494852i	−0.847634	+	0.530582i	$0.821974\pi$
$420$	−2.57409	−	37.0069i	−0.125603	−	1.80575i
$421$	−1.62892	−	8.18913i	−0.0793887	−	0.399114i	−0.999963	−	0.00854753i	$-0.997279\pi$
$421$	−1.62892	−	8.18913i	−0.0793887	−	0.399114i	0.920575	−	0.390566i	$-0.127721\pi$
$422$	−18.8947	−	17.6261i	−0.919778	−	0.858024i
$423$	7.27842	−	3.01482i	0.353889	−	0.146586i
$424$	10.6816	−	13.1758i	0.518745	−	0.639874i
$425$	−49.5349	−	20.5180i	−2.40279	−	0.995270i
$426$	7.53236	−	3.43102i	0.364944	−	0.166234i
$427$	0.807263	+	0.539396i	0.0390662	+	0.0261032i
$428$	−4.07842	+	31.9651i	−0.197138	+	1.54509i
$429$	−0.449896	+	2.26178i	−0.0217212	+	0.109200i
$430$	26.0525	−	18.7479i	1.25636	−	0.904103i
$431$	−14.9255	−	14.9255i	−0.718937	−	0.718937i	0.249450	−	0.968388i	$-0.419750\pi$
$431$	−14.9255	−	14.9255i	−0.718937	−	0.718937i	−0.968388	+	0.249450i	$0.919750\pi$
$432$	3.60151	+	1.74043i	0.173278	+	0.0837365i
$433$	12.1572	−	12.1572i	0.584240	−	0.584240i	−0.351826	−	0.936066i	$-0.614439\pi$
$433$	12.1572	−	12.1572i	0.584240	−	0.584240i	0.936066	+	0.351826i	$0.114439\pi$
$434$	1.21233	−	7.43535i	0.0581936	−	0.356908i
$435$	−13.8526	−	2.75545i	−0.664180	−	0.132114i
$436$	34.0392	−	9.26670i	1.63018	−	0.443794i
$437$	1.04855	−	1.56927i	0.0501591	−	0.0750684i
$438$	9.92296	+	3.71212i	0.474137	+	0.177372i
$439$	−2.18755	+	5.28122i	−0.104406	+	0.252059i	−0.967446	−	0.253077i	$-0.918558\pi$
$439$	−2.18755	+	5.28122i	−0.104406	+	0.252059i	0.863040	+	0.505136i	$0.168558\pi$
$440$	−7.01361	+	13.3128i	−0.334361	+	0.634665i
$441$	5.19536	+	12.5427i	0.247398	+	0.597272i
$442$	−11.4604	+	0.398095i	−0.545116	+	0.0189355i
$443$	2.85674	−	0.568240i	0.135728	−	0.0269979i	−0.126759	−	0.991934i	$-0.540457\pi$
$443$	2.85674	−	0.568240i	0.135728	−	0.0269979i	0.262487	+	0.964936i	$0.415457\pi$
$444$	−3.32047	+	9.91173i	−0.157583	+	0.470390i
$445$	−18.9372	+	12.6534i	−0.897710	+	0.599831i
$446$	−18.9994	−	11.7620i	−0.899646	−	0.556947i
$447$	−16.2096			−0.766689
$448$	−7.50567	−	35.5040i	−0.354610	−	1.67741i
$449$	23.0117			1.08599			0.542995	−	0.839736i	$-0.317290\pi$
$449$	23.0117			1.08599			0.542995	+	0.839736i	$0.317290\pi$
$450$	14.0927	+	8.72441i	0.664336	+	0.411273i
$451$	−12.5079	+	8.35749i	−0.588973	+	0.393539i
$452$	−12.5616	−	4.20820i	−0.590848	−	0.197937i
$453$	−16.7858	+	3.33891i	−0.788667	+	0.156876i
$454$	19.3325	−	0.671544i	0.907318	−	0.0315171i
$455$	−12.5812	−	30.3736i	−0.589814	−	1.42394i
$456$	2.66018	+	8.58389i	0.124574	+	0.401977i
$457$	−1.42735	+	3.44592i	−0.0667685	+	0.161193i	−0.953742	−	0.300628i	$-0.902804\pi$
$457$	−1.42735	+	3.44592i	−0.0667685	+	0.161193i	0.886973	+	0.461821i	$0.152804\pi$
$458$	−13.3631	−	4.99906i	−0.624417	−	0.233591i
$459$	−2.54159	+	3.80375i	−0.118631	+	0.177544i
$460$	−1.27605	−	4.68731i	−0.0594963	−	0.218547i
$461$	−15.1262	−	3.00880i	−0.704499	−	0.140134i	−0.170176	−	0.985414i	$-0.554434\pi$
$461$	−15.1262	−	3.00880i	−0.704499	−	0.140134i	−0.534324	+	0.845280i	$0.679434\pi$
$462$	1.34312	−	8.23750i	0.0624875	−	0.383243i
$463$	4.32369	−	4.32369i	0.200939	−	0.200939i	−0.599463	−	0.800402i	$-0.704619\pi$
$463$	4.32369	−	4.32369i	0.200939	−	0.200939i	0.800402	+	0.599463i	$0.204619\pi$
$464$	−13.7937	−	0.793445i	−0.640356	−	0.0368347i
$465$	3.39552	+	3.39552i	0.157463	+	0.157463i
$466$	−18.4903	+	13.3059i	−0.856545	+	0.616385i
$467$	−0.254035	+	1.27712i	−0.0117553	+	0.0590980i	−0.986218	−	0.165453i	$-0.947091\pi$
$467$	−0.254035	+	1.27712i	−0.0117553	+	0.0590980i	0.974462	+	0.224551i	$0.0720915\pi$
$468$	3.51645	+	0.448663i	0.162548	+	0.0207395i
$469$	−8.53498	−	5.70289i	−0.394109	−	0.263335i
$470$	41.4587	−	18.8846i	1.91235	−	0.871081i
$471$	−12.7244	−	5.27064i	−0.586311	−	0.242858i
$472$	−7.96074	+	0.832266i	−0.366423	+	0.0383082i
$473$	6.67178	−	2.76354i	0.306769	−	0.127068i
$474$	13.2592	+	12.3690i	0.609015	+	0.568126i
$475$	7.26470	+	36.5221i	0.333327	+	1.67575i
$476$	41.4028	−	2.87986i	1.89769	−	0.131998i
$477$	−3.33168	−	4.98621i	−0.152547	−	0.228303i
$478$	−36.2763	+	8.53490i	−1.65924	+	0.390377i
$479$		−	27.3923i		−	1.25159i	−0.779989	−	0.625794i	$-0.784775\pi$
$479$		−	27.3923i		−	1.25159i	0.779989	−	0.625794i	$-0.215225\pi$
$480$	21.1635	+	9.33539i	0.965976	+	0.426100i
$481$			9.26397i			0.422401i
$482$	−7.47352	−	31.7651i	−0.340409	−	1.44686i
$483$	1.49699	+	2.24041i	0.0681156	+	0.101942i
$484$	12.2174	−	14.0441i	0.555336	−	0.638366i
$485$	8.40885	+	42.2741i	0.381826	+	1.91957i
$486$	0.964682	−	1.03411i	0.0437588	−	0.0469083i
$487$	−2.55988	+	1.06034i	−0.115999	+	0.0480485i	−0.439928	−	0.898033i	$-0.644996\pi$
$487$	−2.55988	+	1.06034i	−0.115999	+	0.0480485i	0.323929	+	0.946081i	$0.394996\pi$
$488$	−0.532182	+	0.288571i	−0.0240908	+	0.0130630i
$489$	−2.63476	−	1.09135i	−0.119148	−	0.0493527i
$490$	32.5433	+	71.4445i	1.47016	+	3.22754i
$491$	−11.4129	−	7.62588i	−0.515059	−	0.344151i	0.270721	−	0.962658i	$-0.412738\pi$
$491$	−11.4129	−	7.62588i	−0.515059	−	0.344151i	−0.785780	+	0.618507i	$0.787738\pi$
$492$	14.1505	+	18.2895i	0.637952	+	0.824553i
$493$	3.08276	−	15.4981i	0.138840	−	0.697998i
$494$	4.65196	+	6.46448i	0.209301	+	0.290851i
$495$	3.76184	+	3.76184i	0.169082	+	0.169082i
$496$	3.74947	+	2.82976i	0.168356	+	0.127060i
$497$	−18.7726	+	18.7726i	−0.842065	+	0.842065i
$498$	1.97584	+	0.322159i	0.0885395	+	0.0144363i
$499$	3.76971	+	0.749842i	0.168755	+	0.0335675i	0.278745	−	0.960365i	$-0.410082\pi$
$499$	3.76971	+	0.749842i	0.168755	+	0.0335675i	−0.109989	+	0.993933i	$0.535082\pi$
$500$	47.7034	+	27.2881i	2.13336	+	1.22036i
$501$	9.11687	−	13.6444i	0.407312	−	0.609585i
$502$	−0.0294395	+	0.0786954i	−0.00131395	+	0.00351235i
$503$	9.19296	−	22.1938i	0.409894	−	0.989571i	−0.575271	−	0.817963i	$-0.695104\pi$
$503$	9.19296	−	22.1938i	0.409894	−	0.989571i	0.985165	−	0.171609i	$-0.0548965\pi$
$504$	−12.7755	−	1.18102i	−0.569067	−	0.0526067i
$505$	1.02403	+	2.47223i	0.0455687	+	0.110013i
$506$	−0.0379433	−	1.09232i	−0.00168679	−	0.0485594i
$507$	−9.66890	+	1.92326i	−0.429411	+	0.0854151i
$508$	−18.4108	−	36.9603i	−0.816846	−	1.63985i
$509$	11.6476	−	7.78269i	0.516272	−	0.344962i	−0.269982	−	0.962865i	$-0.587018\pi$
$509$	11.6476	−	7.78269i	0.516272	−	0.344962i	0.786254	+	0.617904i	$0.212018\pi$
$510$	−13.9249	+	22.4931i	−0.616604	+	0.996011i
$511$	−33.9821			−1.50328
$512$	21.7677	+	6.17804i	0.962005	+	0.273033i
$513$	3.17726			0.140279
$514$	6.04459	−	9.76393i	0.266615	−	0.430669i
$515$	16.0362	−	10.7150i	0.706639	−	0.472161i
$516$	−4.94957	−	9.93645i	−0.217893	−	0.437428i
$517$	10.0529	−	1.99965i	0.442126	−	0.0879444i
$518$	−1.16396	−	33.5082i	−0.0511415	−	1.47227i
$519$	−0.264902	−	0.639531i	−0.0116279	−	0.0280723i
$520$	20.4125	+	1.88701i	0.895149	+	0.0827508i
$521$	−9.40851	+	22.7141i	−0.412194	+	0.995125i	0.572353	+	0.820007i	$0.306031\pi$
$521$	−9.40851	+	22.7141i	−0.412194	+	0.995125i	−0.984548	+	0.175118i	$0.943969\pi$
$522$	−1.71156	+	4.57520i	−0.0749128	+	0.200251i
$523$	13.7124	−	20.5221i	0.599602	−	0.897368i	−0.400217	−	0.916421i	$-0.631065\pi$
$523$	13.7124	−	20.5221i	0.599602	−	0.897368i	0.999818	+	0.0190529i	$0.00606508\pi$
$524$	−31.4197	−	17.9732i	−1.37258	−	0.785163i
$525$	−52.1417	−	10.3716i	−2.27565	−	0.452655i
$526$	4.58701	+	0.747908i	0.200003	+	0.0326104i
$527$	−3.79886	+	3.79886i	−0.165481	+	0.165481i
$528$	4.15397	+	3.13504i	0.180778	+	0.136435i
$529$	−16.0139	−	16.0139i	−0.696259	−	0.696259i
$530$	−20.2556	−	28.1477i	−0.879847	−	1.22266i
$531$	−0.552083	+	2.77551i	−0.0239584	+	0.120447i
$532$	−17.6386	−	22.7978i	−0.764729	−	0.988412i
$533$	17.0400	+	11.3857i	0.738082	+	0.493171i
$534$	3.26526	+	7.16845i	0.141302	+	0.310209i
$535$	60.8676	+	25.2122i	2.63154	+	1.09002i
$536$	5.62662	−	3.05099i	0.243033	−	0.131783i
$537$	5.53849	−	2.29412i	0.239004	−	0.0989986i
$538$	−11.1483	+	11.9507i	−0.480637	+	0.515230i
$539$	3.44594	+	17.3239i	0.148427	+	0.746193i
$540$	5.36754	−	6.17007i	0.230982	−	0.265517i
$541$	2.06815	+	3.09521i	0.0889167	+	0.133073i	0.873261	−	0.487252i	$-0.162001\pi$
$541$	2.06815	+	3.09521i	0.0889167	+	0.133073i	−0.784345	+	0.620325i	$0.787001\pi$
$542$	3.96937	+	16.8712i	0.170499	+	0.724682i
$543$			7.87009i			0.337738i
$544$	−10.4443	+	23.6774i	−0.447796	+	1.01516i
$545$		−	72.1262i		−	3.08955i
$546$	−11.0682	+	2.60408i	−0.473677	+	0.111444i
$547$	22.6187	+	33.8513i	0.967105	+	1.44737i	0.892964	+	0.450127i	$0.148621\pi$
$547$	22.6187	+	33.8513i	0.967105	+	1.44737i	0.0741406	+	0.997248i	$0.476379\pi$
$548$	−4.79468	+	0.333504i	−0.204818	+	0.0142466i
$549$	0.0417564	+	0.209923i	0.00178212	+	0.00895931i
$550$	15.7686	+	14.7099i	0.672376	+	0.627232i
$551$	−10.1392	+	4.19981i	−0.431946	+	0.178918i
$552$	−1.67103	+	0.174700i	−0.0711237	+	0.00743572i
$553$	−53.7337	−	22.2572i	−2.28499	−	0.946473i
$554$	26.4910	−	12.0668i	1.12550	−	0.512668i
$555$	17.7698	+	11.8734i	0.754284	+	0.503997i
$556$	7.10914	+	0.907055i	0.301495	+	0.0384677i
$557$	5.84576	−	29.3886i	0.247693	−	1.24524i	−0.633971	−	0.773357i	$-0.718576\pi$
$557$	5.84576	−	29.3886i	0.247693	−	1.24524i	0.881664	−	0.471879i	$-0.156424\pi$
$558$	1.34804	−	0.970074i	0.0570671	−	0.0410665i
$559$	−6.95659	−	6.95659i	−0.294232	−	0.294232i
$560$	−74.0702	−	4.26069i	−3.13004	−	0.180047i
$561$	−4.20869	+	4.20869i	−0.177691	+	0.177691i
$562$	3.20142	−	19.6347i	0.135044	−	0.828240i
$563$	−10.2185	−	2.03258i	−0.430657	−	0.0856630i	−0.0249979	−	0.999688i	$-0.507958\pi$
$563$	−10.2185	−	2.03258i	−0.430657	−	0.0856630i	−0.405659	+	0.914025i	$0.632958\pi$
$564$	−4.13878	−	15.2029i	−0.174274	−	0.640159i
$565$	−15.0477	+	22.5205i	−0.633061	+	0.947443i
$566$	−1.71766	−	0.642567i	−0.0721986	−	0.0270091i
$567$	−1.73589	+	4.19080i	−0.0729004	+	0.175997i
$568$	−4.90021	−	15.8121i	−0.205608	−	0.663460i
$569$	−3.71456	−	8.96774i	−0.155722	−	0.375947i	0.826694	−	0.562652i	$-0.190219\pi$
$569$	−3.71456	−	8.96774i	−0.155722	−	0.375947i	−0.982416	+	0.186705i	$0.940219\pi$
$570$	18.3622	−	0.637840i	0.769107	−	0.0267162i
$571$	−21.1491	+	4.20682i	−0.885063	+	0.176050i	−0.616634	−	0.787250i	$-0.711504\pi$
$571$	−21.1491	+	4.20682i	−0.885063	+	0.176050i	−0.268428	+	0.963300i	$0.586504\pi$
$572$	4.37330	+	1.46508i	0.182857	+	0.0612579i
$573$	2.37527	−	1.58710i	0.0992283	−	0.0663022i
$574$	−63.0649	−	39.0418i	−2.63228	−	1.62957i
$575$	−6.96192			−0.290332
$576$	4.36451	−	6.70455i	0.181855	−	0.279356i
$577$	6.63674			0.276291			0.138146	−	0.990412i	$-0.455886\pi$
$577$	6.63674			0.276291			0.138146	+	0.990412i	$0.455886\pi$
$578$	−4.72345	−	2.92416i	−0.196469	−	0.121629i
$579$	−6.50583	+	4.34706i	−0.270373	+	0.180657i
$580$	−8.97305	+	26.7849i	−0.372586	+	1.11218i
$581$	−6.29782	+	1.25271i	−0.261277	+	0.0519713i
$582$	14.8982	−	0.517514i	0.617552	−	0.0214517i
$583$	−2.98579	−	7.20834i	−0.123659	−	0.298539i
$584$	9.87632	−	18.7467i	0.408685	−	0.775743i
$585$	2.77357	−	6.69599i	0.114673	−	0.276845i
$586$	4.56403	+	1.70738i	0.188538	+	0.0705312i
$587$	6.44617	−	9.64737i	0.266062	−	0.398189i	−0.674250	−	0.738503i	$-0.735533\pi$
$587$	6.44617	−	9.64737i	0.266062	−	0.398189i	0.940312	+	0.340313i	$0.110533\pi$
$588$	26.1988	−	7.13225i	1.08042	−	0.294129i
$589$	3.65956	+	0.727931i	0.150789	+	0.0299939i
$590$	−2.63344	+	16.1512i	−0.108417	+	0.664935i
$591$	−14.0762	+	14.0762i	−0.579019	+	0.579019i
$592$	18.8235	+	9.09648i	0.773643	+	0.373863i
$593$	19.5921	+	19.5921i	0.804551	+	0.804551i	0.983803	−	0.179252i	$-0.0573679\pi$
$593$	19.5921	+	19.5921i	0.804551	+	0.804551i	−0.179252	+	0.983803i	$0.557368\pi$
$594$	1.49347	−	1.07473i	0.0612778	−	0.0440966i
$595$	16.5540	−	83.2225i	0.678647	−	3.41179i
$596$	−4.10311	+	32.1585i	−0.168070	+	1.31727i
$597$	4.58480	+	3.06346i	0.187643	+	0.125379i
$598$	−1.35505	+	0.617230i	−0.0554120	+	0.0252404i
$599$	0.452107	+	0.187269i	0.0184726	+	0.00765160i	0.391901	−	0.920008i	$-0.371818\pi$
$599$	0.452107	+	0.187269i	0.0184726	+	0.00765160i	−0.373428	+	0.927659i	$0.621818\pi$
$600$	20.8758	−	25.7504i	0.852249	−	1.05125i
$601$	39.3817	−	16.3124i	1.60641	−	0.665399i	0.614110	−	0.789221i	$-0.289515\pi$
$601$	39.3817	−	16.3124i	1.60641	−	0.665399i	0.992304	+	0.123822i	$0.0395152\pi$
$602$	26.0364	+	24.2883i	1.06116	+	0.989915i
$603$	−0.441479	−	2.21947i	−0.0179784	−	0.0903836i
$604$	2.37516	+	34.1469i	0.0966438	+	1.38942i
$605$	−21.1436	−	31.6437i	−0.859611	−	1.28650i
$606$	0.900887	−	0.211956i	0.0365960	−	0.00861011i
$607$			13.7428i			0.557804i	0.960320	+	0.278902i	$0.0899704\pi$
$607$			13.7428i			0.557804i	−0.960320	+	0.278902i	$0.910030\pi$
$608$	17.7031	−	3.10475i	0.717955	−	0.125914i
$609$		−	15.6682i		−	0.634908i
$610$	0.283463	+	1.20482i	0.0114771	+	0.0487817i
$611$	−7.75786	−	11.6105i	−0.313849	−	0.469709i
$612$	6.90299	+	6.00513i	0.279037	+	0.242743i
$613$	3.99415	+	20.0799i	0.161322	+	0.811020i	0.973690	+	0.227876i	$0.0731780\pi$
$613$	3.99415	+	20.0799i	0.161322	+	0.811020i	−0.812368	+	0.583145i	$0.801822\pi$
$614$	12.7008	−	13.6149i	0.512562	−	0.549452i
$615$	43.6793	−	18.0925i	1.76132	−	0.729562i
$616$	−16.0025	−	4.74977i	−0.644760	−	0.191374i
$617$	2.61341	+	1.08251i	0.105212	+	0.0435802i	0.434669	−	0.900590i	$-0.356866\pi$
$617$	2.61341	+	1.08251i	0.105212	+	0.0435802i	−0.329457	+	0.944171i	$0.606866\pi$
$618$	−2.76505	−	6.07030i	−0.111227	−	0.244183i
$619$	−21.4460	−	14.3297i	−0.861987	−	0.575961i	0.0441125	−	0.999027i	$-0.485954\pi$
$619$	−21.4460	−	14.3297i	−0.861987	−	0.575961i	−0.906099	+	0.423066i	$0.860954\pi$
$620$	7.59593	−	5.87693i	0.305060	−	0.236023i
$621$	−0.115887	+	0.582604i	−0.00465039	+	0.0233791i
$622$	−8.48912	−	11.7967i	−0.340383	−	0.473005i
$623$	−17.8656	−	17.8656i	−0.715770	−	0.715770i
$624$	1.78022	−	6.86277i	0.0712659	−	0.274731i
$625$	38.0137	−	38.0137i	1.52055	−	1.52055i
$626$	9.84234	+	1.60479i	0.393379	+	0.0641401i
$627$	4.05436	+	0.806462i	0.161915	+	0.0322070i
$628$	−13.6774	+	23.9101i	−0.545788	+	0.954117i
$629$	−13.2838	+	19.8806i	−0.529658	+	0.792690i
$630$	−9.19083	+	24.5682i	−0.366171	+	0.978821i
$631$	14.5168	−	35.0467i	0.577905	−	1.39519i	−0.316784	−	0.948498i	$-0.602603\pi$
$631$	14.5168	−	35.0467i	0.577905	−	1.39519i	0.894690	−	0.446689i	$-0.147397\pi$
$632$	27.8953	−	23.1742i	1.10961	−	0.921821i
$633$	6.99216	+	16.8806i	0.277913	+	0.670942i
$634$	0.358835	+	10.3302i	0.0142512	+	0.410264i
$635$	−82.7995	+	16.4698i	−3.28580	+	0.653586i
$636$	−10.7356	+	5.34762i	−0.425693	+	0.212047i
$637$	20.0080	−	13.3689i	0.792745	−	0.529695i
$638$	−3.34534	+	5.40378i	−0.132443	+	0.213938i
$639$	−5.85271			−0.231530
$640$	23.8777	−	39.6235i	0.943849	−	1.56626i
$641$	32.5219			1.28454			0.642268	−	0.766480i	$-0.277994\pi$
$641$	32.5219			1.28454			0.642268	+	0.766480i	$0.277994\pi$
$642$	11.9938	−	19.3739i	0.473359	−	0.764626i
$643$	36.7784	−	24.5746i	1.45040	−	0.969126i	0.453433	−	0.891290i	$-0.350199\pi$
$643$	36.7784	−	24.5746i	1.45040	−	0.969126i	0.996966	−	0.0778357i	$-0.0248009\pi$
$644$	4.82372	−	2.40280i	0.190081	−	0.0946837i
$645$	−22.2599	+	4.42777i	−0.876483	+	0.174343i
$646$	0.713606	+	20.5434i	0.0280765	+	0.808268i
$647$	1.44320	+	3.48420i	0.0567381	+	0.136978i	0.949706	−	0.313141i	$-0.101381\pi$
$647$	1.44320	+	3.48420i	0.0567381	+	0.136978i	−0.892968	+	0.450119i	$0.851381\pi$
$648$	−1.80741	−	2.17561i	−0.0710016	−	0.0854661i
$649$	−1.40898	+	3.40158i	−0.0553073	+	0.133524i
$650$	10.2935	−	27.5159i	0.403746	−	1.07926i
$651$	−2.95953	+	4.42925i	−0.115993	+	0.173596i
$652$	−2.83208	+	4.95089i	−0.110913	+	0.193892i
$653$	−27.7630	−	5.52240i	−1.08645	−	0.216108i	−0.380791	−	0.924661i	$-0.624348\pi$
$653$	−27.7630	−	5.52240i	−1.08645	−	0.216108i	−0.705658	+	0.708553i	$0.749348\pi$
$654$	−24.6202	−	4.01430i	−0.962726	−	0.156972i
$655$	−52.3297	+	52.3297i	−2.04469	+	2.04469i
$656$	39.8666	−	23.4438i	1.55653	−	0.915325i
$657$	−5.29729	−	5.29729i	−0.206667	−	0.206667i
$658$	29.5193	+	41.0208i	1.15078	+	1.59916i
$659$	−4.66561	+	23.4556i	−0.181746	+	0.913701i	0.777014	+	0.629484i	$0.216734\pi$
$659$	−4.66561	+	23.4556i	−0.181746	+	0.913701i	−0.958760	+	0.284217i	$0.908266\pi$
$660$	8.41539	−	6.51094i	0.327569	−	0.253438i
$661$	17.4595	+	11.6661i	0.679096	+	0.453757i	0.846681	−	0.532100i	$-0.178597\pi$
$661$	17.4595	+	11.6661i	0.679096	+	0.453757i	−0.167586	+	0.985858i	$0.553597\pi$
$662$	9.40951	+	20.6573i	0.365711	+	0.802871i
$663$	7.49139	+	3.10303i	0.290941	+	0.120512i
$664$	1.13928	−	3.83835i	0.0442125	−	0.148957i
$665$	−54.4463	+	22.5524i	−2.11134	+	0.874544i
$666$	5.04197	−	5.40486i	0.195372	−	0.209434i
$667$	−0.400288	−	2.01238i	−0.0154992	−	0.0779198i
$668$	−24.7616	−	21.5409i	−0.958053	−	0.833442i
$669$	8.77836	+	13.1378i	0.339391	+	0.507935i
$670$	−2.99698	−	12.7382i	−0.115784	−	0.492121i
$671$			0.278473i			0.0107503i
$672$	−5.57688	+	25.0466i	−0.215133	+	0.966195i
$673$			36.9872i			1.42575i	0.701289	+	0.712877i	$0.252608\pi$
$673$			36.9872i			1.42575i	−0.701289	+	0.712877i	$0.747392\pi$
$674$	38.7865	−	9.12547i	1.49400	−	0.351500i
$675$	−6.51132	−	9.74487i	−0.250621	−	0.375080i
$676$	1.36813	+	19.6691i	0.0526203	+	0.756505i
$677$	−7.11236	−	35.7562i	−0.273350	−	1.37422i	−0.836544	−	0.547899i	$-0.815428\pi$
$677$	−7.11236	−	35.7562i	−0.273350	−	1.37422i	0.563194	−	0.826325i	$-0.309572\pi$
$678$	6.84984	+	6.38993i	0.263066	+	0.245404i
$679$	−44.1752	+	18.2980i	−1.69529	+	0.702212i
$680$	41.0997	+	33.3194i	1.57610	+	1.27774i
$681$	−12.6372	−	5.23448i	−0.484257	−	0.200586i
$682$	1.96640	−	0.895704i	0.0752974	−	0.0342983i
$683$	1.95101	+	1.30362i	0.0746533	+	0.0498818i	0.592337	−	0.805690i	$-0.298206\pi$
$683$	1.95101	+	1.30362i	0.0746533	+	0.0498818i	−0.517683	+	0.855572i	$0.673206\pi$
$684$	0.804252	−	6.30341i	0.0307513	−	0.241017i
$685$	−1.91704	+	9.63763i	−0.0732465	+	0.368235i
$686$	−34.2415	+	24.6408i	−1.30735	+	0.940789i
$687$	7.13378	+	7.13378i	0.272171	+	0.272171i
$688$	−20.9660	+	7.30434i	−0.799320	+	0.278475i
$689$	−7.51605	+	7.51605i	−0.286339	+	0.286339i
$690$	−0.552783	+	3.39028i	−0.0210441	+	0.129066i
$691$	−44.0175	−	8.75562i	−1.67450	−	0.333079i	−0.735641	−	0.677372i	$-0.763119\pi$
$691$	−44.0175	−	8.75562i	−1.67450	−	0.333079i	−0.938863	+	0.344292i	$0.888119\pi$
$692$	−1.33583	+	0.363661i	−0.0507806	+	0.0138243i
$693$	−3.27881	+	4.90709i	−0.124552	+	0.186405i
$694$	0.0655366	+	0.0245169i	0.00248774	+	0.000930648i
$695$	5.60728	−	13.5372i	0.212696	−	0.513494i
$696$	8.64358	+	4.55370i	0.327634	+	0.172607i
$697$	20.2417	+	48.8678i	0.766709	+	1.85100i
$698$	21.5914	−	0.750010i	0.817245	−	0.0283883i
$699$	15.7985	−	3.14252i	0.597555	−	0.118861i
$700$	−33.7750	+	100.820i	−1.27657	+	3.81062i
$701$	27.5233	−	18.3905i	1.03954	−	0.694598i	0.0861323	−	0.996284i	$-0.472549\pi$
$701$	27.5233	−	18.3905i	1.03954	−	0.694598i	0.953408	+	0.301685i	$0.0975492\pi$
$702$	−2.13130	−	1.31943i	−0.0804408	−	0.0497988i
$703$	16.6061			0.626312
$704$	7.27114	−	7.44757i	0.274041	−	0.280691i
$705$	−32.2137			−1.21324
$706$	−39.5014	−	24.4543i	−1.48665	−	0.920348i
$707$	−2.46821	+	1.64921i	−0.0928267	+	0.0620248i
$708$	5.36664	+	1.79785i	0.201691	+	0.0675672i
$709$	3.98658	−	0.792980i	0.149719	−	0.0297810i	−0.119662	−	0.992815i	$-0.538181\pi$
$709$	3.98658	−	0.792980i	0.149719	−	0.0297810i	0.269381	+	0.963034i	$0.413181\pi$
$710$	−33.8243	+	1.17494i	−1.26940	+	0.0440948i
$711$	−4.90670	−	11.8458i	−0.184016	−	0.444253i
$712$	15.0481	−	4.66347i	0.563953	−	0.174771i
$713$	−0.266957	+	0.644491i	−0.00999762	+	0.0241364i
$714$	−27.4866	−	10.2826i	−1.02866	−	0.384816i
$715$	5.23883	−	7.84047i	0.195921	−	0.293217i
$716$	−3.14940	−	11.5686i	−0.117698	−	0.432340i
$717$	25.8453	+	5.14095i	0.965210	+	0.191992i
$718$	−4.45448	+	27.3198i	−0.166240	+	1.01957i
$719$	−15.9557	+	15.9557i	−0.595047	+	0.595047i	−0.938990	−	0.343944i	$-0.888237\pi$
$719$	−15.9557	+	15.9557i	−0.595047	+	0.595047i	0.343944	+	0.938990i	$0.388237\pi$
$720$	−10.8822	−	12.2106i	−0.405557	−	0.455061i
$721$	15.1287	+	15.1287i	0.563424	+	0.563424i
$722$	−10.2220	+	7.35594i	−0.380424	+	0.273760i
$723$	−4.50163	+	22.6312i	−0.167417	+	0.841664i
$724$	15.6136	+	1.99214i	0.580275	+	0.0740373i
$725$	33.6600	+	22.4909i	1.25010	+	0.835290i
$726$	−11.9783	+	5.45617i	−0.444557	+	0.202498i
$727$	6.51432	+	2.69832i	0.241603	+	0.100075i	0.500199	−	0.865910i	$-0.333260\pi$
$727$	6.51432	+	2.69832i	0.241603	+	0.100075i	−0.258597	+	0.965985i	$0.583260\pi$
$728$	2.36459	+	22.6176i	0.0876375	+	0.838265i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	−31.6778	−	29.5509i	−1.17245	−	1.09373i
$731$	−4.95373	−	24.9041i	−0.183220	−	0.921111i
$732$	0.427040	−	0.0297037i	0.0157839	−	0.00109788i
$733$	−0.0619423	−	0.0927032i	−0.00228789	−	0.00342407i	0.830324	−	0.557281i	$-0.188155\pi$
$733$	−0.0619423	−	0.0927032i	−0.00228789	−	0.00342407i	−0.832612	+	0.553857i	$0.813155\pi$
$734$	−25.6915	+	6.04455i	−0.948290	+	0.223109i
$735$		−	55.5130i		−	2.04763i
$736$	−0.0763938	+	3.35940i	−0.00281591	+	0.123829i
$737$		−	2.94422i		−	0.108452i
$738$	−3.74483	−	15.9168i	−0.137849	−	0.585907i
$739$	−6.27439	−	9.39029i	−0.230807	−	0.345427i	0.697930	−	0.716166i	$-0.254105\pi$
$739$	−6.27439	−	9.39029i	−0.230807	−	0.345427i	−0.928737	+	0.370738i	$0.879105\pi$
$740$	28.0538	−	32.2482i	1.03128	−	1.18547i
$741$	−1.09867	−	5.52341i	−0.0403608	−	0.202907i
$742$	26.2416	−	28.1303i	0.963358	−	1.03269i
$743$	−25.6395	+	10.6202i	−0.940622	+	0.389619i	−0.799698	−	0.600402i	$-0.795007\pi$
$743$	−25.6395	+	10.6202i	−0.940622	+	0.389619i	−0.140924	+	0.990020i	$0.545007\pi$
$744$	−1.58332	−	2.91995i	−0.0580473	−	0.107051i
$745$	61.2360	+	25.3648i	2.24352	+	0.929294i
$746$	10.5434	+	23.1467i	0.386021	+	0.847460i
$747$	−1.17701	−	0.786454i	−0.0430646	−	0.0287748i
$748$	7.28435	+	9.41503i	0.266342	+	0.344247i
$749$	−14.2584	+	71.6816i	−0.520989	+	2.61919i
$750$	−22.6984	−	31.5422i	−0.828827	−	1.15176i
$751$	−7.86802	−	7.86802i	−0.287108	−	0.287108i	0.548828	−	0.835936i	$-0.315074\pi$
$751$	−7.86802	−	7.86802i	−0.287108	−	0.287108i	−0.835936	+	0.548828i	$0.815074\pi$
$752$	−31.2090	+	4.36272i	−1.13807	+	0.159092i
$753$	0.0420109	−	0.0420109i	0.00153096	−	0.00153096i
$754$	8.54547	+	1.39333i	0.311208	+	0.0507421i
$755$	68.6376	+	13.6529i	2.49798	+	0.496878i
$756$	7.87480	+	4.50466i	0.286404	+	0.163833i
$757$	−29.1014	+	43.5534i	−1.05771	+	1.58297i	−0.274120	+	0.961696i	$0.588386\pi$
$757$	−29.1014	+	43.5534i	−1.05771	+	1.58297i	−0.783590	+	0.621279i	$0.786614\pi$
$758$	−17.2779	+	46.1859i	−0.627561	+	1.67755i
$759$	−0.295757	+	0.714020i	−0.0107353	+	0.0259173i
$760$	3.38256	−	36.5905i	0.122698	−	1.32728i
$761$	−10.0467	−	24.2548i	−0.364191	−	0.879235i	−0.994678	−	0.103035i	$-0.967145\pi$
$761$	−10.0467	−	24.2548i	−0.364191	−	0.879235i	0.630487	−	0.776200i	$-0.282855\pi$
$762$	1.01362	+	29.1802i	0.0367196	+	1.05709i
$763$	78.4748	−	15.6096i	2.84098	−	0.565105i
$764$	−2.54743	−	5.11407i	−0.0921630	−	0.185021i
$765$	15.5536	−	10.3926i	0.562342	−	0.375745i
$766$	−13.6742	+	22.0882i	−0.494070	+	0.798081i
$767$	5.01591			0.181114
$768$	−12.1965	−	10.3559i	−0.440103	−	0.373688i
$769$	−6.87137			−0.247788			−0.123894	−	0.992295i	$-0.539538\pi$
$769$	−6.87137			−0.247788			−0.123894	+	0.992295i	$0.539538\pi$
$770$	−17.9640	+	29.0176i	−0.647377	+	1.04572i
$771$	−6.75160	+	4.51128i	−0.243153	+	0.162470i
$772$	6.97739	+	14.0074i	0.251122	+	0.504137i
$773$	1.23618	−	0.245892i	0.0444623	−	0.00884411i	−0.172809	−	0.984955i	$-0.555284\pi$
$773$	1.23618	−	0.245892i	0.0444623	−	0.00884411i	0.217271	+	0.976111i	$0.430284\pi$
$774$	0.272503	+	7.84483i	0.00979491	+	0.281977i
$775$	−5.26710	−	12.7159i	−0.189200	−	0.456769i
$776$	2.74445	−	29.6879i	0.0985202	−	1.06573i
$777$	−9.07272	+	21.9035i	−0.325482	+	0.785783i
$778$	−15.7757	+	42.1705i	−0.565587	+	1.51188i
$779$	20.4095	−	30.5450i	0.731246	−	1.09439i
$780$	−12.5822	−	7.19748i	−0.450516	−	0.257711i
$781$	−7.46839	−	1.48555i	−0.267240	−	0.0531573i
$782$	−3.79300	−	0.618446i	−0.135637	−	0.0221156i
$783$	2.44243	−	2.44243i	0.0872854	−	0.0872854i
$784$	−7.51816	−	53.7816i	−0.268506	−	1.92077i
$785$	39.8224	+	39.8224i	1.42132	+	1.42132i
$786$	14.9502	+	20.7752i	0.533256	+	0.741027i
$787$	1.88041	−	9.45348i	0.0670295	−	0.336980i	−0.932690	−	0.360680i	$-0.882545\pi$
$787$	1.88041	−	9.45348i	0.0670295	−	0.336980i	0.999719	+	0.0236999i	$0.00754460\pi$
$788$	24.3630	+	31.4892i	0.867896	+	1.12176i
$789$	−2.73249	−	1.82579i	−0.0972792	−	0.0649999i
$790$	−30.7351	−	67.4750i	−1.09351	−	2.40065i
$791$	−27.7594	−	11.4983i	−0.987009	−	0.408833i
$792$	−1.75413	−	3.23496i	−0.0623303	−	0.114949i
$793$	0.350496	−	0.145180i	0.0124465	−	0.00515550i
$794$	−5.84252	+	6.26302i	−0.207343	+	0.222266i
$795$	4.78386	+	24.0501i	0.169666	+	0.852969i
$796$	7.23820	−	8.32041i	0.256551	−	0.294909i
$797$	8.56674	+	12.8210i	0.303450	+	0.454144i	0.951587	−	0.307379i	$-0.0994518\pi$
$797$	8.56674	+	12.8210i	0.303450	+	0.454144i	−0.648138	+	0.761523i	$0.724452\pi$
$798$	4.66794	+	19.8404i	0.165243	+	0.702342i
$799$		−	36.0403i		−	1.27501i
$800$	−45.8023	−	47.9339i	−1.61936	−	1.69472i
$801$		−	5.56994i		−	0.196804i
$802$	−32.3093	+	7.60155i	−1.14088	+	0.268420i
$803$	−5.41506	−	8.10421i	−0.191093	−	0.285991i
$804$	−4.51498	+	0.314049i	−0.159231	+	0.0110757i
$805$	−2.14949	−	10.8062i	−0.0757596	−	0.380869i
$806$	−2.15254	−	2.00802i	−0.0758199	−	0.0707293i
$807$	10.6768	−	4.42246i	0.375840	−	0.155678i
$808$	−0.192463	−	1.84094i	−0.00677083	−	0.0647639i
$809$	39.6299	+	16.4153i	1.39331	+	0.577130i	0.948008	−	0.318248i	$-0.103094\pi$
$809$	39.6299	+	16.4153i	1.39331	+	0.577130i	0.445307	+	0.895378i	$0.353094\pi$
$810$	−5.26251	+	2.39710i	−0.184906	+	0.0842254i
$811$	31.1873	+	20.8387i	1.09513	+	0.731745i	0.965652	−	0.259837i	$-0.0836688\pi$
$811$	31.1873	+	20.8387i	1.09513	+	0.731745i	0.129481	+	0.991582i	$0.458669\pi$
$812$	−31.0844	−	3.96606i	−1.09085	−	0.139181i
$813$	2.39093	−	12.0200i	0.0838536	−	0.421560i
$814$	7.80572	−	5.61713i	0.273590	−	0.196880i
$815$	8.24574	+	8.24574i	0.288836	+	0.288836i
$816$	13.6610	−	12.1749i	0.478231	−	0.426206i
$817$	−12.4700	+	12.4700i	−0.436271	+	0.436271i
$818$	2.88398	−	17.6878i	0.100836	−	0.618439i
$819$	7.88563	+	1.56855i	0.275546	+	0.0548096i
$820$	−24.8377	−	91.2358i	−0.867369	−	3.18609i
$821$	−29.0696	+	43.5058i	−1.01454	+	1.51836i	−0.168172	+	0.985758i	$0.553786\pi$
$821$	−29.0696	+	43.5058i	−1.01454	+	1.51836i	−0.846365	+	0.532604i	$0.821214\pi$
$822$	3.18310	+	1.19078i	0.111023	+	0.0415332i
$823$	10.7811	−	26.0279i	0.375806	−	0.907277i	−0.616936	−	0.787013i	$-0.711626\pi$
$823$	10.7811	−	26.0279i	0.375806	−	0.907277i	0.992742	−	0.120263i	$-0.0383738\pi$
$824$	−12.7429	+	3.94906i	−0.443919	+	0.137572i
$825$	−5.83533	−	14.0877i	−0.203160	−	0.490472i
$826$	−18.1428	+	0.630219i	−0.631268	+	0.0219281i
$827$	−4.90741	+	0.976144i	−0.170647	+	0.0339439i	−0.279674	−	0.960095i	$-0.590226\pi$
$827$	−4.90741	+	0.976144i	−0.170647	+	0.0339439i	0.109027	+	0.994039i	$0.465226\pi$
$828$	1.12650	+	0.377384i	0.0391487	+	0.0131150i
$829$	−38.1693	+	25.5039i	−1.32567	+	0.885788i	−0.998253	−	0.0590906i	$-0.981180\pi$
$829$	−38.1693	+	25.5039i	−1.32567	+	0.885788i	−0.327422	+	0.944878i	$0.606180\pi$
$830$	−6.96013	−	4.30883i	−0.241590	−	0.149562i
$831$	−20.5837			−0.714042
$832$	−13.1645	−	5.26897i	−0.456399	−	0.182669i
$833$	62.1072			2.15189
$834$	−4.30882	−	2.66747i	−0.149202	−	0.0923670i
$835$	−55.7920	+	37.2791i	−1.93076	+	1.29009i
$836$	2.62622	−	7.83937i	0.0908299	−	0.271130i
$837$	−1.15180	+	0.229107i	−0.0398120	+	0.00791909i
$838$	1.72182	−	0.0598103i	0.0594795	−	0.00206611i
$839$	3.00847	+	7.26309i	0.103864	+	0.250750i	0.967265	−	0.253768i	$-0.0816701\pi$
$839$	3.00847	+	7.26309i	0.103864	+	0.250750i	−0.863401	+	0.504518i	$0.831670\pi$
$840$	46.4148	+	24.4527i	1.60146	+	0.843699i
$841$	6.53204	−	15.7697i	0.225243	−	0.543784i
$842$	11.0595	+	4.13731i	0.381137	+	0.142581i
$843$	−7.81530	+	11.6964i	−0.269173	+	0.402846i
$844$	35.2595	−	9.59892i	1.21368	−	0.330408i
$845$	39.5363	+	7.86426i	1.36009	+	0.270539i
$846$	−1.79291	+	10.9961i	−0.0616415	+	0.378054i
$847$	29.8530	−	29.8530i	1.02576	−	1.02576i
$848$	7.89177	+	22.6521i	0.271005	+	0.777876i
$849$	0.916958	+	0.916958i	0.0314699	+	0.0314699i
$850$	61.5455	−	44.2892i	2.11099	−	1.51911i
$851$	−0.605691	+	3.04502i	−0.0207628	+	0.104382i
$852$	−1.48148	+	11.6113i	−0.0507548	+	0.397796i
$853$	25.3177	+	16.9167i	0.866862	+	0.579218i	0.907546	−	0.419954i	$-0.137954\pi$
$853$	25.3177	+	16.9167i	0.866862	+	0.579218i	−0.0406839	+	0.999172i	$0.512954\pi$
$854$	−1.24952	+	0.569161i	−0.0427577	+	0.0194763i
$855$	−12.0029	−	4.97177i	−0.410491	−	0.170031i
$856$	−35.4002	−	28.6989i	−1.20995	−	0.980907i
$857$	−20.2196	+	8.37525i	−0.690690	+	0.286093i	−0.700287	−	0.713861i	$-0.746945\pi$
$857$	−20.2196	+	8.37525i	−0.690690	+	0.286093i	0.00959790	+	0.999954i	$0.496945\pi$
$858$	−2.38476	−	2.22464i	−0.0814143	−	0.0759481i
$859$	9.99305	+	50.2385i	0.340958	+	1.71411i	0.647337	+	0.762204i	$0.275883\pi$
$859$	9.99305	+	50.2385i	0.340958	+	1.71411i	−0.306378	+	0.951910i	$0.599117\pi$
$860$	3.14973	+	45.2826i	0.107405	+	1.54412i
$861$	29.1382	+	43.6083i	0.993026	+	1.48617i
$862$	29.0576	−	6.83653i	0.989707	−	0.232853i
$863$			36.8120i			1.25310i	0.779383	+	0.626548i	$0.215533\pi$
$863$			36.8120i			1.25310i	−0.779383	+	0.626548i	$0.784467\pi$
$864$	−4.77374	+	3.03504i	−0.162406	+	0.103254i
$865$			2.83051i			0.0962403i
$866$	5.56854	+	23.6683i	0.189227	+	0.804280i
$867$	2.18240	+	3.26619i	0.0741181	+	0.110926i
$868$	8.03813	+	6.99263i	0.272832	+	0.237345i
$869$	−3.25448	−	16.3614i	−0.110401	−	0.555021i
$870$	13.6251	−	14.6058i	0.461935	−	0.495182i
$871$	−3.70570	+	1.53495i	−0.125563	+	0.0520099i
$872$	−14.1961	+	47.8283i	−0.480741	+	1.61967i
$873$	−9.73861	−	4.03387i	−0.329602	−	0.136526i
$874$	1.10642	+	2.42899i	0.0374251	+	0.0821619i
$875$	103.638	+	69.2489i	3.50361	+	2.34104i
$876$	−11.8503	+	9.16848i	−0.400383	+	0.309774i
$877$	9.52963	−	47.9087i	0.321793	−	1.61776i	−0.393768	−	0.919210i	$-0.628829\pi$
$877$	9.52963	−	47.9087i	0.321793	−	1.61776i	0.715560	−	0.698551i	$-0.246171\pi$
$878$	−4.72195	−	6.56175i	−0.159358	−	0.221448i
$879$	−2.43647	−	2.43647i	−0.0821801	−	0.0821801i
$880$	−10.7870	−	18.3435i	−0.363630	−	0.618361i
$881$	17.4351	−	17.4351i	0.587403	−	0.587403i	−0.349524	−	0.936927i	$-0.613657\pi$
$881$	17.4351	−	17.4351i	0.587403	−	0.587403i	0.936927	+	0.349524i	$0.113657\pi$
$882$	−18.9493	−	3.08967i	−0.638056	−	0.104035i
$883$	3.81598	+	0.759045i	0.128418	+	0.0255439i	0.258881	−	0.965909i	$-0.416646\pi$
$883$	3.81598	+	0.759045i	0.128418	+	0.0255439i	−0.130463	+	0.991453i	$0.541646\pi$
$884$	8.05244	−	14.0768i	0.270833	−	0.473455i
$885$	6.42875	−	9.62131i	0.216100	−	0.323417i
$886$	−1.44328	+	3.85806i	−0.0484879	+	0.129614i
$887$	16.9403	−	40.8976i	0.568801	−	1.37321i	−0.333765	−	0.942656i	$-0.608319\pi$
$887$	16.9403	−	40.8976i	0.568801	−	1.37321i	0.902566	−	0.430551i	$-0.141681\pi$
$888$	−9.44652	−	11.3710i	−0.317005	−	0.381585i
$889$	−35.8390	−	86.5231i	−1.20200	−	2.90189i
$890$	−1.11818	−	32.1901i	−0.0374813	−	1.07902i
$891$	−1.27606	+	0.253823i	−0.0427495	+	0.00850340i
$892$	28.2863	−	14.0900i	0.947094	−	0.471769i
$893$	−20.8123	+	13.9064i	−0.696458	+	0.465358i
$894$	12.0664	−	19.4911i	0.403562	−	0.651881i
$895$	−24.5129			−0.819377
$896$	48.2788	+	17.4041i	1.61288	+	0.581429i
$897$	1.05288			0.0351547
$898$	−17.1299	+	27.6702i	−0.571632	+	0.923368i
$899$	3.37277	−	2.25361i	0.112488	−	0.0751621i
$900$	−20.9812	+	10.4512i	−0.699374	+	0.348374i
$901$	−26.9069	+	5.35212i	−0.896399	+	0.178305i
$902$	−0.738546	−	21.2613i	−0.0245909	−	0.707924i
$903$	−9.63501	−	23.2610i	−0.320633	−	0.774076i
$904$	14.4110	−	11.9720i	0.479302	−	0.398184i
$905$	12.3151	−	29.7313i	0.409368	−	0.988302i
$906$	8.48053	−	22.6695i	0.281747	−	0.753143i
$907$	−16.0996	+	24.0948i	−0.534579	+	0.800053i	−0.996207	−	0.0870202i	$-0.972266\pi$
$907$	−16.0996	+	24.0948i	−0.534579	+	0.800053i	0.461628	+	0.887074i	$0.347266\pi$
$908$	−13.5836	+	23.7461i	−0.450788	+	0.788042i
$909$	−0.641842	−	0.127670i	−0.0212886	−	0.00423456i
$910$	45.8880	+	7.48200i	1.52117	+	0.248026i
$911$	13.6975	−	13.6975i	0.453819	−	0.453819i	−0.442801	−	0.896620i	$-0.646015\pi$
$911$	13.6975	−	13.6975i	0.453819	−	0.453819i	0.896620	+	0.442801i	$0.146015\pi$
$912$	−12.3019	−	3.19114i	−0.407356	−	0.105669i
$913$	−1.30231	−	1.30231i	−0.0431002	−	0.0431002i
$914$	−3.08101	−	4.28145i	−0.101911	−	0.141618i
$915$	0.170742	−	0.858380i	0.00564457	−	0.0283772i
$916$	15.9586	−	12.3471i	0.527286	−	0.407959i
$917$	−68.2610	−	45.6106i	−2.25418	−	1.50619i
$918$	−2.68184	−	5.88763i	−0.0885139	−	0.194321i
$919$	−47.8387	−	19.8154i	−1.57805	−	0.653651i	−0.589950	−	0.807440i	$-0.700853\pi$
$919$	−47.8387	−	19.8154i	−1.57805	−	0.653651i	−0.988104	+	0.153788i	$0.950853\pi$
$920$	6.58611	+	1.95485i	0.217138	+	0.0644495i
$921$	−12.1636	+	5.03832i	−0.400804	+	0.166018i
$922$	14.8779	−	15.9487i	0.489977	−	0.525242i
$923$	2.02383	+	10.1745i	0.0666151	+	0.334897i
$924$	8.90530	+	7.74701i	0.292963	+	0.254858i
$925$	−34.0318	−	50.9322i	−1.11896	−	1.67464i
$926$	1.98044	+	8.41755i	0.0650812	+	0.276618i
$927$			4.71668i			0.154916i
$928$	11.2221	−	15.9955i	0.368383	−	0.525077i
$929$		−	15.1334i		−	0.496509i	−0.968695	−	0.248255i	$-0.920143\pi$
$929$		−	15.1334i		−	0.496509i	0.968695	−	0.248255i	$-0.0798570\pi$
$930$	−6.61054	+	1.55529i	−0.216768	+	0.0510000i
$931$	−23.9644	−	35.8653i	−0.785402	−	1.17544i
$932$	−2.23546	−	32.1384i	−0.0732248	−	1.05273i
$933$	2.00491	+	10.0794i	0.0656379	+	0.329984i
$934$	−1.34656	−	1.25615i	−0.0440607	−	0.0411024i
$935$	22.4852	−	9.31366i	0.735344	−	0.304589i
$936$	−3.15714	+	3.89434i	−0.103194	+	0.127291i
$937$	−28.0099	−	11.6021i	−0.915044	−	0.379024i	−0.125059	−	0.992149i	$-0.539912\pi$
$937$	−28.0099	−	11.6021i	−0.915044	−	0.379024i	−0.789985	+	0.613126i	$0.789912\pi$
$938$	13.2108	−	6.01759i	0.431349	−	0.196481i
$939$	−5.86310	−	3.91760i	−0.191335	−	0.127846i
$940$	−8.15419	+	63.9093i	−0.265960	+	2.08449i
$941$	7.04623	−	35.4238i	0.229701	−	1.15478i	−0.677967	−	0.735092i	$-0.737139\pi$
$941$	7.04623	−	35.4238i	0.229701	−	1.15478i	0.907667	−	0.419690i	$-0.137861\pi$
$942$	15.8097	−	11.3770i	0.515108	−	0.370681i
$943$	4.85652	+	4.85652i	0.158150	+	0.158150i
$944$	4.92522	−	10.1919i	0.160302	−	0.331717i
$945$	13.1155	−	13.1155i	0.426648	−	0.426648i
$946$	−1.64347	+	10.0796i	−0.0534339	+	0.327717i
$947$	−8.47605	−	1.68599i	−0.275435	−	0.0547873i	0.0554402	−	0.998462i	$-0.482344\pi$
$947$	−8.47605	−	1.68599i	−0.275435	−	0.0547873i	−0.330875	+	0.943675i	$0.607344\pi$
$948$	−24.7431	+	6.73597i	−0.803620	+	0.218774i
$949$	−7.37714	+	11.0407i	−0.239472	+	0.358395i
$950$	−49.3236	−	18.4517i	−1.60027	−	0.598652i
$951$	2.79701	−	6.75258i	0.0906993	−	0.218967i
$952$	−27.3574	+	51.9283i	−0.886658	+	1.68300i
$953$	0.427252	+	1.03148i	0.0138401	+	0.0334129i	0.930648	−	0.365914i	$-0.119244\pi$
$953$	0.427252	+	1.03148i	0.0138401	+	0.0334129i	−0.916808	+	0.399327i	$0.869244\pi$
$954$	8.47573	−	0.294418i	0.274412	−	0.00953214i
$955$	−11.4567	+	2.27888i	−0.370730	+	0.0737427i
$956$	16.7414	−	49.9736i	0.541455	−	1.61626i
$957$	3.73663	−	2.49673i	0.120788	−	0.0807080i
$958$	32.9377	+	20.3909i	1.06417	+	0.658799i
$959$	−10.9008			−0.352006
$960$	−26.9794	+	18.4986i	−0.870755	+	0.597039i
$961$	29.6209			0.955512
$962$	−11.1394	−	6.89610i	−0.359148	−	0.222339i
$963$	−13.3967	+	8.95140i	−0.431703	+	0.288455i
$964$	43.7590	+	14.6595i	1.40938	+	0.472149i
$965$	31.3797	−	6.24181i	1.01015	−	0.200931i
$966$	−3.80833	+	0.132288i	−0.122531	+	0.00425631i
$967$	6.83289	+	16.4961i	0.219731	+	0.530478i	0.994852	−	0.101335i	$-0.0323113\pi$
$967$	6.83289	+	16.4961i	0.219731	+	0.530478i	−0.775121	+	0.631812i	$0.782311\pi$
$968$	7.79255	+	25.1451i	0.250462	+	0.808194i
$969$	5.56235	−	13.4287i	0.178688	−	0.431392i
$970$	−57.0918	−	21.3577i	−1.83311	−	0.685755i
$971$	0.619959	−	0.927835i	0.0198954	−	0.0297756i	−0.821389	−	0.570369i	$-0.806800\pi$
$971$	0.619959	−	0.927835i	0.0198954	−	0.0297756i	0.841284	+	0.540593i	$0.181800\pi$
$972$	0.525353	+	1.92977i	0.0168507	+	0.0618973i
$973$	15.9422	+	3.17111i	0.511085	+	0.101661i
$974$	0.630580	−	3.86742i	0.0202051	−	0.123920i
$975$	−14.6891	+	14.6891i	−0.470428	+	0.470428i
$976$	0.0491661	−	0.854731i	0.00157377	−	0.0273593i
$977$	0.558256	+	0.558256i	0.0178602	+	0.0178602i	0.715980	−	0.698120i	$-0.245980\pi$
$977$	0.558256	+	0.558256i	0.0178602	+	0.0178602i	−0.698120	+	0.715980i	$0.745980\pi$
$978$	3.27360	−	2.35574i	0.104678	−	0.0753284i
$979$	1.41378	−	7.10756i	0.0451847	−	0.227159i
$980$	−110.133	−	14.0519i	−3.51808	−	0.448871i
$981$	14.6663	+	9.79971i	0.468259	+	0.312881i
$982$	17.6655	−	8.04670i	0.563728	−	0.256781i
$983$	−10.1212	−	4.19232i	−0.322815	−	0.133714i	0.215391	−	0.976528i	$-0.430898\pi$
$983$	−10.1212	−	4.19232i	−0.322815	−	0.133714i	−0.538205	+	0.842814i	$0.680898\pi$
$984$	−32.5256	+	3.40043i	−1.03688	+	0.108402i
$985$	75.2032	−	31.1502i	2.39617	−	0.992527i
$986$	16.3407	+	15.2436i	0.520395	+	0.485455i
$987$	−6.97171	−	35.0492i	−0.221912	−	1.11563i
$988$	−11.2361	+	0.781550i	−0.357467	+	0.0248644i
$989$	−1.83176	−	2.74142i	−0.0582466	−	0.0871722i
$990$	−7.32370	+	1.72308i	−0.232763	+	0.0547631i
$991$			42.9712i			1.36502i	0.730874	+	0.682512i	$0.239113\pi$
$991$			42.9712i			1.36502i	−0.730874	+	0.682512i	$0.760887\pi$
$992$	−6.19373	+	2.40205i	−0.196651	+	0.0762652i
$993$		−	16.0509i		−	0.509361i
$994$	−8.59864	−	36.5472i	−0.272732	−	1.15921i
$995$	−12.5266	−	18.7473i	−0.397118	−	0.594330i
$996$	−1.85819	+	2.13602i	−0.0588791	+	0.0676823i
$997$	−10.7127	−	53.8566i	−0.339276	−	1.70566i	−0.654019	−	0.756478i	$-0.726918\pi$
$997$	−10.7127	−	53.8566i	−0.339276	−	1.70566i	0.314743	−	0.949177i	$-0.398082\pi$
$998$	−3.70781	+	3.97468i	−0.117369	+	0.125816i
$999$	−4.82872	+	2.00012i	−0.152774	+	0.0632810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.13.6	✓	128
3.2	odd	2		576.2.bd.b.397.11		128
4.3	odd	2		768.2.r.a.145.1		128
64.5	even	16	inner	192.2.r.a.133.6	yes	128
64.59	odd	16		768.2.r.a.625.1		128
192.5	odd	16		576.2.bd.b.325.11		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.13.6	✓	128	1.1	even	1	trivial
192.2.r.a.133.6	yes	128	64.5	even	16	inner
576.2.bd.b.325.11		128	192.5	odd	16
576.2.bd.b.397.11		128	3.2	odd	2
768.2.r.a.145.1		128	4.3	odd	2
768.2.r.a.625.1		128	64.59	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.744400 + 1.20244i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-0.891737 - 1.79020i) q^{4} +(-4.01045 + 0.797728i) q^{5} +(0.0490954 + 1.41336i) q^{6} +(-1.73589 - 4.19080i) q^{7} +(2.81642 + 0.260360i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(-0.744400 + 1.20244i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-0.891737 - 1.79020i) q^{4} +(-4.01045 + 0.797728i) q^{5} +(0.0490954 + 1.41336i) q^{6} +(-1.73589 - 4.19080i) q^{7} +(2.81642 + 0.260360i) q^{8} +(0.382683 - 0.923880i) q^{9} +(2.02616 - 5.41616i) q^{10} +(0.722828 - 1.08179i) q^{11} +(-1.73603 - 0.993072i) q^{12} +(-1.73842 - 0.345793i) q^{13} +(6.33139 + 1.03233i) q^{14} +(-2.89137 + 2.89137i) q^{15} +(-2.40961 + 3.19277i) q^{16} +(-3.23483 - 3.23483i) q^{17} +(0.826043 + 1.14789i) q^{18} +(-0.619852 + 3.11621i) q^{19} +(5.00435 + 6.46813i) q^{20} +(-3.77162 - 2.52012i) q^{21} +(0.762715 + 1.67444i) q^{22} +(-0.548801 - 0.227321i) q^{23} +(2.48641 - 1.34824i) q^{24} +(10.8279 - 4.48507i) q^{25} +(1.70988 - 1.83294i) q^{26} +(-0.195090 - 0.980785i) q^{27} +(-5.95441 + 6.84467i) q^{28} +(1.91901 + 2.87200i) q^{29} +(-1.32437 - 5.62905i) q^{30} -1.17436i q^{31} +(-2.04541 - 5.27412i) q^{32} -1.30106i q^{33} +(6.29770 - 1.48169i) q^{34} +(10.3048 + 15.4222i) q^{35} +(-1.99518 + 0.138779i) q^{36} +(-1.01965 - 5.12614i) q^{37} +(-3.28564 - 3.06504i) q^{38} +(-1.63756 + 0.678298i) q^{39} +(-11.5028 + 1.20257i) q^{40} +(-10.6821 - 4.42467i) q^{41} +(5.83789 - 2.65918i) q^{42} +(4.61506 + 3.08368i) q^{43} +(-2.58119 - 0.329333i) q^{44} +(-0.797728 + 4.01045i) q^{45} +(0.681867 - 0.490684i) q^{46} +(5.57066 + 5.57066i) q^{47} +(-0.229710 + 3.99340i) q^{48} +(-9.59977 + 9.59977i) q^{49} +(-2.66726 + 16.3586i) q^{50} +(-4.48683 - 0.892487i) q^{51} +(0.931176 + 3.42047i) q^{52} +(3.33168 - 4.98621i) q^{53} +(1.32456 + 0.495512i) q^{54} +(-2.03589 + 4.91507i) q^{55} +(-3.79787 - 12.2550i) q^{56} +(1.21588 + 2.93540i) q^{57} +(-4.88192 + 0.169581i) q^{58} +(-2.77551 + 0.552083i) q^{59} +(7.75447 + 2.59778i) q^{60} +(-0.177964 + 0.118912i) q^{61} +(1.41210 + 0.874196i) q^{62} -4.53609 q^{63} +(7.86443 + 1.46657i) q^{64} +7.24769 q^{65} +(1.56444 + 0.968506i) q^{66} +(1.88157 - 1.25723i) q^{67} +(-2.90636 + 8.67559i) q^{68} +(-0.582604 + 0.115887i) q^{69} +(-26.2152 + 0.910628i) q^{70} +(-2.23974 - 5.40720i) q^{71} +(1.31834 - 2.50240i) q^{72} +(2.86687 - 6.92124i) q^{73} +(6.92291 + 2.58982i) q^{74} +(6.51132 - 9.74487i) q^{75} +(6.13137 - 1.66918i) q^{76} +(-5.78831 - 1.15137i) q^{77} +(0.403382 - 2.47399i) q^{78} +(9.06639 - 9.06639i) q^{79} +(7.11665 - 14.7266i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(13.2722 - 9.55089i) q^{82} +(0.276166 - 1.38838i) q^{83} +(-1.14821 + 8.99923i) q^{84} +(15.5536 + 10.3926i) q^{85} +(-7.14340 + 3.25385i) q^{86} +(3.19119 + 1.32183i) q^{87} +(2.31744 - 2.85857i) q^{88} +(5.14596 - 2.13153i) q^{89} +(-4.22850 - 3.94460i) q^{90} +(1.56855 + 7.88563i) q^{91} +(0.0824371 + 1.18517i) q^{92} +(-0.652441 - 0.976447i) q^{93} +(-10.8452 + 2.55160i) q^{94} -12.9919i q^{95} +(-4.63084 - 3.24890i) q^{96} -10.5410i q^{97} +(-4.39710 - 18.6892i) q^{98} +(-0.722828 - 1.08179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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