LMFDB - Embedded newform 184.2.j.a.107.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [184,2,Mod(11,184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(184, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 9]))

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

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

chi := DirichletCharacter("184.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	184.j (of order $22$, degree $10$, 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:	$1.46924739719$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			107.15
Character	$\chi$	$=$	184.107
Dual form			184.2.j.a.43.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.692401 - 1.23312i) q^{2} +(-1.18656 - 2.59820i) q^{3} +(-1.04116 - 1.70763i) q^{4} +(-1.01624 - 1.17280i) q^{5} +(-4.02545 - 0.335830i) q^{6} +(4.25438 + 2.73413i) q^{7} +(-2.82660 + 0.101512i) q^{8} +(-3.37812 + 3.89856i) q^{9} +O(q^{10})$	\(q+(0.692401 - 1.23312i) q^{2} +(-1.18656 - 2.59820i) q^{3} +(-1.04116 - 1.70763i) q^{4} +(-1.01624 - 1.17280i) q^{5} +(-4.02545 - 0.335830i) q^{6} +(4.25438 + 2.73413i) q^{7} +(-2.82660 + 0.101512i) q^{8} +(-3.37812 + 3.89856i) q^{9} +(-2.14985 + 0.441093i) q^{10} +(1.77318 - 0.254945i) q^{11} +(-3.20135 + 4.73133i) q^{12} +(-0.511843 - 0.796443i) q^{13} +(6.31724 - 3.35305i) q^{14} +(-1.84135 + 4.03199i) q^{15} +(-1.83197 + 3.55582i) q^{16} +(-1.67446 - 5.70268i) q^{17} +(2.46837 + 6.86499i) q^{18} +(-0.812847 + 2.76830i) q^{19} +(-0.944640 + 2.95643i) q^{20} +(2.05573 - 14.2979i) q^{21} +(0.913375 - 2.36306i) q^{22} +(3.08571 - 3.67130i) q^{23} +(3.61767 + 7.22362i) q^{24} +(0.368850 - 2.56541i) q^{25} +(-1.33651 + 0.0797045i) q^{26} +(5.91571 + 1.73701i) q^{27} +(0.239366 - 10.1116i) q^{28} +(1.87742 + 6.39390i) q^{29} +(3.69696 + 5.06235i) q^{30} +(2.15218 + 0.982870i) q^{31} +(3.11629 + 4.72109i) q^{32} +(-2.76637 - 4.30456i) q^{33} +(-8.19148 - 1.88374i) q^{34} +(-1.11688 - 7.76808i) q^{35} +(10.1744 + 1.70954i) q^{36} +(-3.98474 + 4.59863i) q^{37} +(2.85083 + 2.91911i) q^{38} +(-1.46198 + 2.27489i) q^{39} +(2.99156 + 3.21189i) q^{40} +(-3.66827 - 4.23341i) q^{41} +(-16.2076 - 12.4349i) q^{42} +(5.98202 - 2.73190i) q^{43} +(-2.28152 - 2.76249i) q^{44} +8.00523 q^{45} +(-2.39059 - 6.34705i) q^{46} +4.26175i q^{47} +(11.4125 + 0.540627i) q^{48} +(7.71643 + 16.8966i) q^{49} +(-2.90806 - 2.23113i) q^{50} +(-12.8298 + 11.1171i) q^{51} +(-0.827116 + 1.70326i) q^{52} +(3.03402 + 1.94985i) q^{53} +(6.23798 - 6.09206i) q^{54} +(-2.10098 - 1.82051i) q^{55} +(-12.3030 - 7.29642i) q^{56} +(8.15708 - 1.17281i) q^{57} +(9.18436 + 2.11207i) q^{58} +(2.53954 - 1.63207i) q^{59} +(8.80226 - 1.05362i) q^{60} +(2.27952 - 4.99144i) q^{61} +(2.70217 - 1.97336i) q^{62} +(-25.0310 + 7.34976i) q^{63} +(7.97939 - 0.573869i) q^{64} +(-0.413916 + 1.40967i) q^{65} +(-7.22347 + 0.430781i) q^{66} +(10.4452 + 1.50179i) q^{67} +(-7.99466 + 8.79676i) q^{68} +(-13.2001 - 3.66107i) q^{69} +(-10.3523 - 4.00139i) q^{70} +(-2.06420 - 0.296788i) q^{71} +(9.15286 - 11.3626i) q^{72} +(-2.05582 - 0.603644i) q^{73} +(2.91162 + 8.09775i) q^{74} +(-7.10309 + 2.08566i) q^{75} +(5.57353 - 1.49421i) q^{76} +(8.24084 + 3.76346i) q^{77} +(1.79293 + 3.37794i) q^{78} +(-6.55104 + 4.21010i) q^{79} +(6.03200 - 1.46503i) q^{80} +(-0.303823 - 2.11314i) q^{81} +(-7.76022 + 1.59219i) q^{82} +(6.06755 + 5.25756i) q^{83} +(-26.5558 + 11.3760i) q^{84} +(-4.98647 + 7.75910i) q^{85} +(0.773208 - 9.26811i) q^{86} +(14.3849 - 12.4646i) q^{87} +(-4.98620 + 0.900627i) q^{88} +(2.48788 - 1.13618i) q^{89} +(5.54283 - 9.87139i) q^{90} -4.78782i q^{91} +(-9.48191 - 1.44682i) q^{92} -6.75803i q^{93} +(5.25524 + 2.95084i) q^{94} +(4.07272 - 1.85995i) q^{95} +(8.56866 - 13.6986i) q^{96} +(0.549986 - 0.476566i) q^{97} +(26.1784 + 2.18398i) q^{98} +(-4.99610 + 7.77408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 11 q^{2} - 18 q^{3} - 3 q^{4} - 12 q^{6} - 8 q^{8} - 36 q^{9}+O(q^{10}) $ 220 * q - 11 * q^2 - 18 * q^3 - 3 * q^4 - 12 * q^6 - 8 * q^8 - 36 * q^9	$ 220 q - 11 q^{2} - 18 q^{3} - 3 q^{4} - 12 q^{6} - 8 q^{8} - 36 q^{9} - 11 q^{10} - 22 q^{11} - 6 q^{12} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 6 q^{18} - 22 q^{19} - 11 q^{20} - 18 q^{24} - 32 q^{25} - 10 q^{26} - 18 q^{27} - 11 q^{28} - 11 q^{30} - 11 q^{32} - 22 q^{33} + 11 q^{34} + 2 q^{35} - 41 q^{36} + 44 q^{38} - 99 q^{40} - 18 q^{41} + 99 q^{42} - 22 q^{43} - 88 q^{44} + 45 q^{46} - 100 q^{48} - 28 q^{49} + 14 q^{50} - 22 q^{51} - 118 q^{52} + 102 q^{54} - 66 q^{56} - 22 q^{57} + 43 q^{58} - 6 q^{59} - 33 q^{60} - 56 q^{62} + 18 q^{64} - 22 q^{65} + 22 q^{66} - 22 q^{67} - 10 q^{70} - 23 q^{72} - 18 q^{73} + 14 q^{75} + 44 q^{76} + 98 q^{78} + 88 q^{80} + 4 q^{81} + 14 q^{82} - 22 q^{83} + 143 q^{84} + 99 q^{86} + 77 q^{88} - 22 q^{89} + 176 q^{90} + 36 q^{92} + 111 q^{94} + 101 q^{96} - 22 q^{97} + 121 q^{98} - 22 q^{99}+O(q^{100}) $ 220 * q - 11 * q^2 - 18 * q^3 - 3 * q^4 - 12 * q^6 - 8 * q^8 - 36 * q^9 - 11 * q^10 - 22 * q^11 - 6 * q^12 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 6 * q^18 - 22 * q^19 - 11 * q^20 - 18 * q^24 - 32 * q^25 - 10 * q^26 - 18 * q^27 - 11 * q^28 - 11 * q^30 - 11 * q^32 - 22 * q^33 + 11 * q^34 + 2 * q^35 - 41 * q^36 + 44 * q^38 - 99 * q^40 - 18 * q^41 + 99 * q^42 - 22 * q^43 - 88 * q^44 + 45 * q^46 - 100 * q^48 - 28 * q^49 + 14 * q^50 - 22 * q^51 - 118 * q^52 + 102 * q^54 - 66 * q^56 - 22 * q^57 + 43 * q^58 - 6 * q^59 - 33 * q^60 - 56 * q^62 + 18 * q^64 - 22 * q^65 + 22 * q^66 - 22 * q^67 - 10 * q^70 - 23 * q^72 - 18 * q^73 + 14 * q^75 + 44 * q^76 + 98 * q^78 + 88 * q^80 + 4 * q^81 + 14 * q^82 - 22 * q^83 + 143 * q^84 + 99 * q^86 + 77 * q^88 - 22 * q^89 + 176 * q^90 + 36 * q^92 + 111 * q^94 + 101 * q^96 - 22 * q^97 + 121 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	0.692401	−	1.23312i	0.489602	−	0.871946i
$2$	0.692401	−	1.23312i	0.489602	−	0.871946i
$3$	−1.18656	−	2.59820i	−0.685058	−	1.50007i	−0.857193	−	0.514995i	$-0.827794\pi$
$3$	−1.18656	−	2.59820i	−0.685058	−	1.50007i	0.172135	−	0.985073i	$-0.444934\pi$
$4$	−1.04116	−	1.70763i	−0.520580	−	0.853813i
$5$	−1.01624	−	1.17280i	−0.454476	−	0.524494i	0.481552	−	0.876417i	$-0.340073\pi$
$5$	−1.01624	−	1.17280i	−0.454476	−	0.524494i	−0.936029	+	0.351924i	$0.885528\pi$
$6$	−4.02545	−	0.335830i	−1.64338	−	0.137102i
$7$	4.25438	+	2.73413i	1.60801	+	1.03340i	0.963101	+	0.269140i	$0.0867394\pi$
$7$	4.25438	+	2.73413i	1.60801	+	1.03340i	0.644905	+	0.764263i	$0.276897\pi$
$8$	−2.82660	+	0.101512i	−0.999356	+	0.0358899i
$9$	−3.37812	+	3.89856i	−1.12604	+	1.29952i
$10$	−2.14985	+	0.441093i	−0.679843	+	0.139486i
$11$	1.77318	−	0.254945i	0.534634	−	0.0768687i	0.130290	−	0.991476i	$-0.458409\pi$
$11$	1.77318	−	0.254945i	0.534634	−	0.0768687i	0.404344	+	0.914607i	$0.367500\pi$
$12$	−3.20135	+	4.73133i	−0.924150	+	1.36582i
$13$	−0.511843	−	0.796443i	−0.141960	−	0.220894i	0.762992	−	0.646408i	$-0.223730\pi$
$13$	−0.511843	−	0.796443i	−0.141960	−	0.220894i	−0.904952	+	0.425514i	$0.860093\pi$
$14$	6.31724	−	3.35305i	1.68835	−	0.896139i
$15$	−1.84135	+	4.03199i	−0.475434	+	1.04105i
$16$	−1.83197	+	3.55582i	−0.457992	+	0.888956i
$17$	−1.67446	−	5.70268i	−0.406116	−	1.38310i	−0.868177	−	0.496255i	$-0.834708\pi$
$17$	−1.67446	−	5.70268i	−0.406116	−	1.38310i	0.462061	−	0.886848i	$-0.347110\pi$
$18$	2.46837	+	6.86499i	0.581800	+	1.61809i
$19$	−0.812847	+	2.76830i	−0.186480	+	0.635093i	0.812183	+	0.583403i	$0.198279\pi$
$19$	−0.812847	+	2.76830i	−0.186480	+	0.635093i	−0.998663	+	0.0516900i	$0.983539\pi$
$20$	−0.944640	+	2.95643i	−0.211228	+	0.661079i
$21$	2.05573	−	14.2979i	0.448597	−	3.12006i
$22$	0.913375	−	2.36306i	0.194732	−	0.503807i
$23$	3.08571	−	3.67130i	0.643414	−	0.765518i
$23$	3.08571	−	3.67130i	0.643414	−	0.765518i
$24$	3.61767	+	7.22362i	0.738454	+	1.47452i
$25$	0.368850	−	2.56541i	0.0737700	−	0.513082i
$26$	−1.33651	+	0.0797045i	−0.262111	+	0.0156313i
$27$	5.91571	+	1.73701i	1.13848	+	0.334287i
$28$	0.239366	−	10.1116i	0.0452360	−	1.91091i
$29$	1.87742	+	6.39390i	0.348628	+	1.18732i	0.928102	+	0.372326i	$0.121440\pi$
$29$	1.87742	+	6.39390i	0.348628	+	1.18732i	−0.579474	+	0.814991i	$0.696742\pi$
$30$	3.69696	+	5.06235i	0.674970	+	0.924255i
$31$	2.15218	+	0.982870i	0.386544	+	0.176529i	0.599202	−	0.800598i	$-0.295485\pi$
$31$	2.15218	+	0.982870i	0.386544	+	0.176529i	−0.212658	+	0.977127i	$0.568212\pi$
$32$	3.11629	+	4.72109i	0.550888	+	0.834579i
$33$	−2.76637	−	4.30456i	−0.481564	−	0.749328i
$34$	−8.19148	−	1.88374i	−1.40483	−	0.323059i
$35$	−1.11688	−	7.76808i	−0.188788	−	1.31305i
$36$	10.1744	+	1.70954i	1.69574	+	0.284923i
$37$	−3.98474	+	4.59863i	−0.655087	+	0.756010i	−0.981966	−	0.189056i	$-0.939457\pi$
$37$	−3.98474	+	4.59863i	−0.655087	+	0.756010i	0.326880	+	0.945066i	$0.394003\pi$
$38$	2.85083	+	2.91911i	0.462466	+	0.473543i
$39$	−1.46198	+	2.27489i	−0.234105	+	0.364274i
$40$	2.99156	+	3.21189i	0.473008	+	0.507845i
$41$	−3.66827	−	4.23341i	−0.572888	−	0.661148i	0.393172	−	0.919465i	$-0.371378\pi$
$41$	−3.66827	−	4.23341i	−0.572888	−	0.661148i	−0.966060	+	0.258317i	$0.916832\pi$
$42$	−16.2076	−	12.4349i	−2.50089	−	1.91874i
$43$	5.98202	−	2.73190i	0.912250	−	0.416611i	0.0967109	−	0.995313i	$-0.469168\pi$
$43$	5.98202	−	2.73190i	0.912250	−	0.416611i	0.815539	+	0.578702i	$0.196441\pi$
$44$	−2.28152	−	2.76249i	−0.343951	−	0.416461i
$45$	8.00523			1.19335
$46$	−2.39059	−	6.34705i	−0.352474	−	0.935822i
$47$			4.26175i			0.621641i	0.950469	+	0.310820i	$0.100604\pi$
$47$			4.26175i			0.621641i	−0.950469	+	0.310820i	$0.899396\pi$
$48$	11.4125	+	0.540627i	1.64725	+	0.0780328i
$49$	7.71643	+	16.8966i	1.10235	+	2.41380i
$50$	−2.90806	−	2.23113i	−0.411262	−	0.315529i
$51$	−12.8298	+	11.1171i	−1.79654	+	1.55671i
$52$	−0.827116	+	1.70326i	−0.114700	+	0.236200i
$53$	3.03402	+	1.94985i	0.416755	+	0.267832i	0.732170	−	0.681122i	$-0.238508\pi$
$53$	3.03402	+	1.94985i	0.416755	+	0.267832i	−0.315416	+	0.948954i	$0.602144\pi$
$54$	6.23798	−	6.09206i	0.848882	−	0.829024i
$55$	−2.10098	−	1.82051i	−0.283296	−	0.245477i
$56$	−12.3030	−	7.29642i	−1.64406	−	0.975026i
$57$	8.15708	−	1.17281i	1.08043	−	0.155343i
$58$	9.18436	+	2.11207i	1.20597	+	0.277328i
$59$	2.53954	−	1.63207i	0.330620	−	0.212477i	−0.364790	−	0.931090i	$-0.618859\pi$
$59$	2.53954	−	1.63207i	0.330620	−	0.212477i	0.695410	+	0.718613i	$0.255223\pi$
$60$	8.80226	−	1.05362i	1.13637	−	0.136021i
$61$	2.27952	−	4.99144i	0.291862	−	0.639089i	−0.705727	−	0.708484i	$-0.749380\pi$
$61$	2.27952	−	4.99144i	0.291862	−	0.639089i	0.997589	+	0.0693948i	$0.0221068\pi$
$62$	2.70217	−	1.97336i	0.343176	−	0.250617i
$63$	−25.0310	+	7.34976i	−3.15361	+	0.925983i
$64$	7.97939	−	0.573869i	0.997424	−	0.0717336i
$65$	−0.413916	+	1.40967i	−0.0513399	+	0.174848i
$66$	−7.22347	+	0.430781i	−0.889148	+	0.0530255i
$67$	10.4452	+	1.50179i	1.27608	+	0.183472i	0.746842	−	0.665002i	$-0.231569\pi$
$67$	10.4452	+	1.50179i	1.27608	+	0.183472i	0.529237	+	0.848474i	$0.322478\pi$
$68$	−7.99466	+	8.79676i	−0.969496	+	1.06676i
$69$	−13.2001	−	3.66107i	−1.58911	−	0.440741i
$70$	−10.3523	−	4.00139i	−1.23734	−	0.478257i
$71$	−2.06420	−	0.296788i	−0.244976	−	0.0352222i	0.0187330	−	0.999825i	$-0.494037\pi$
$71$	−2.06420	−	0.296788i	−0.244976	−	0.0352222i	−0.263709	+	0.964602i	$0.584946\pi$
$72$	9.15286	−	11.3626i	1.07868	−	1.33910i
$73$	−2.05582	−	0.603644i	−0.240616	−	0.0706512i	0.159201	−	0.987246i	$-0.449108\pi$
$73$	−2.05582	−	0.603644i	−0.240616	−	0.0706512i	−0.399817	+	0.916595i	$0.630926\pi$
$74$	2.91162	+	8.09775i	0.338469	+	0.941344i
$75$	−7.10309	+	2.08566i	−0.820194	+	0.240831i
$76$	5.57353	−	1.49421i	0.639328	−	0.171398i
$77$	8.24084	+	3.76346i	0.939131	+	0.428887i
$78$	1.79293	+	3.37794i	0.203009	+	0.382476i
$79$	−6.55104	+	4.21010i	−0.737050	+	0.473673i	−0.854530	−	0.519402i	$-0.826155\pi$
$79$	−6.55104	+	4.21010i	−0.737050	+	0.473673i	0.117480	+	0.993075i	$0.462518\pi$
$80$	6.03200	−	1.46503i	0.674398	−	0.163796i
$81$	−0.303823	−	2.11314i	−0.0337582	−	0.234793i
$82$	−7.76022	+	1.59219i	−0.856972	+	0.175828i
$83$	6.06755	+	5.25756i	0.666000	+	0.577092i	0.920864	−	0.389885i	$-0.127485\pi$
$83$	6.06755	+	5.25756i	0.666000	+	0.577092i	−0.254864	+	0.966977i	$0.582031\pi$
$84$	−26.5558	+	11.3760i	−2.89748	+	1.24122i
$85$	−4.98647	+	7.75910i	−0.540859	+	0.841593i
$86$	0.773208	−	9.26811i	0.0833771	−	0.999406i
$87$	14.3849	−	12.4646i	1.54223	−	1.33635i
$88$	−4.98620	+	0.900627i	−0.531531	+	0.0960072i
$89$	2.48788	−	1.13618i	0.263715	−	0.120435i	−0.279170	−	0.960242i	$-0.590059\pi$
$89$	2.48788	−	1.13618i	0.263715	−	0.120435i	0.542885	+	0.839807i	$0.317332\pi$
$90$	5.54283	−	9.87139i	0.584265	−	1.04054i
$91$		−	4.78782i		−	0.501900i
$92$	−9.48191	−	1.44682i	−0.988558	−	0.150842i
$93$		−	6.75803i		−	0.700775i
$94$	5.25524	+	2.95084i	0.542037	+	0.304356i
$95$	4.07272	−	1.85995i	0.417853	−	0.190827i
$96$	8.56866	−	13.6986i	0.874535	−	1.39811i
$97$	0.549986	−	0.476566i	0.0558426	−	0.0483879i	−0.626492	−	0.779428i	$-0.715510\pi$
$97$	0.549986	−	0.476566i	0.0558426	−	0.0483879i	0.682335	+	0.731040i	$0.260965\pi$
$98$	26.1784	+	2.18398i	2.64442	+	0.220615i
$99$	−4.99610	+	7.77408i	−0.502127	+	0.781325i
$100$	−4.76479	+	2.04114i	−0.476479	+	0.204114i
$101$	−4.97284	−	4.30899i	−0.494816	−	0.428760i	0.371368	−	0.928486i	$-0.378889\pi$
$101$	−4.97284	−	4.30899i	−0.494816	−	0.428760i	−0.866184	+	0.499725i	$0.833434\pi$
$102$	4.82532	+	23.5182i	0.477778	+	2.32865i
$103$	0.433456	+	3.01475i	0.0427097	+	0.297052i	0.999969	+	0.00782265i	$0.00249005\pi$
$103$	0.433456	+	3.01475i	0.0427097	+	0.297052i	−0.957260	+	0.289230i	$0.906601\pi$
$104$	1.52763	+	2.19927i	0.149796	+	0.215656i
$105$	−18.8578	+	12.1191i	−1.84033	+	1.18271i
$106$	4.50515	−	2.39123i	0.437579	−	0.232257i
$107$	−4.86924	−	2.22371i	−0.470727	−	0.214974i	0.165905	−	0.986142i	$-0.446946\pi$
$107$	−4.86924	−	2.22371i	−0.470727	−	0.214974i	−0.636632	+	0.771168i	$0.719673\pi$
$108$	−3.19304	−	11.9103i	−0.307251	−	1.14607i
$109$	−11.1429	+	3.27186i	−1.06730	+	0.313388i	−0.767787	−	0.640705i	$-0.778642\pi$
$109$	−11.1429	+	3.27186i	−1.06730	+	0.313388i	−0.299513	+	0.954092i	$0.596824\pi$
$110$	−3.69962	+	1.33023i	−0.352745	+	0.126833i
$111$	16.6763	+	4.89659i	1.58284	+	0.464764i
$112$	−17.5160	+	10.1190i	−1.65510	+	0.956157i
$113$	5.70500	+	0.820255i	0.536681	+	0.0771631i	0.405326	−	0.914172i	$-0.367158\pi$
$113$	5.70500	+	0.820255i	0.536681	+	0.0771631i	0.131355	+	0.991335i	$0.458067\pi$
$114$	4.20176	−	10.8707i	0.393531	−	1.01813i
$115$	−7.44153	+	0.111989i	−0.693926	+	0.0104430i
$116$	8.96369	−	9.86300i	0.832258	−	0.915757i
$117$	4.83405	+	0.695031i	0.446908	+	0.0642556i
$118$	−0.254146	−	4.26160i	−0.0233961	−	0.392312i
$119$	8.46807	−	28.8396i	0.776266	−	2.64372i
$120$	4.79546	−	11.5838i	0.437764	−	1.05745i
$121$	−7.47525	+	2.19493i	−0.679568	+	0.199539i
$122$	−4.57670	−	6.26700i	−0.414355	−	0.567387i
$123$	−6.64662	+	14.5541i	−0.599306	+	1.31230i
$124$	−0.562397	−	4.69845i	−0.0505047	−	0.421933i
$125$	−9.91102	+	6.36943i	−0.886468	+	0.569699i
$126$	−8.26836	+	35.9551i	−0.736604	+	3.20314i
$127$	−7.31678	+	1.05199i	−0.649259	+	0.0933494i	−0.459073	−	0.888399i	$-0.651818\pi$
$127$	−7.31678	+	1.05199i	−0.649259	+	0.0933494i	−0.190186	+	0.981748i	$0.560909\pi$
$128$	4.81729	−	10.2369i	0.425793	−	0.904821i
$129$	−14.1960	−	12.3009i	−1.24989	−	1.08304i
$130$	1.45169	+	1.48646i	0.127322	+	0.130371i
$131$	−10.2101	−	6.56165i	−0.892062	−	0.573294i	0.0123639	−	0.999924i	$-0.496064\pi$
$131$	−10.2101	−	6.56165i	−0.892062	−	0.573294i	−0.904426	+	0.426630i	$0.859701\pi$
$132$	−4.47034	+	9.20567i	−0.389093	+	0.801251i
$133$	−11.0271	+	9.55500i	−0.956167	+	0.828524i
$134$	9.08412	−	11.8403i	0.784749	−	1.02284i
$135$	−3.97461	−	8.70318i	−0.342080	−	0.749050i
$136$	5.31192	+	15.9493i	0.455494	+	1.36764i
$137$			7.56507i			0.646328i	0.946343	+	0.323164i	$0.104746\pi$
$137$			7.56507i			0.646328i	−0.946343	+	0.323164i	$0.895254\pi$
$138$	−13.6543	+	13.7424i	−1.16233	+	1.16983i
$139$	−0.118762			−0.0100732			−0.00503662	−	0.999987i	$-0.501603\pi$
$139$	−0.118762			−0.0100732			−0.00503662	+	0.999987i	$0.501603\pi$
$140$	−12.1021	+	9.99504i	−1.02282	+	0.844735i
$141$	11.0729	−	5.05681i	0.932504	−	0.425860i
$142$	−1.79523	+	2.33991i	−0.150653	+	0.196361i
$143$	−1.11064	−	1.28174i	−0.0928762	−	0.107185i
$144$	−7.67398	−	19.1540i	−0.639499	−	1.59617i
$145$	5.59088	−	8.69958i	0.464297	−	0.722460i
$146$	−2.16782	+	2.11711i	−0.179410	+	0.175213i
$147$	34.7448	−	40.0976i	2.86570	−	3.30719i
$148$	12.0015	+	2.01652i	0.986517	+	0.165757i
$149$	0.0580693	+	0.403881i	0.00475722	+	0.0330872i	0.992062	−	0.125751i	$-0.0401342\pi$
$149$	0.0580693	+	0.403881i	0.00475722	+	0.0330872i	−0.987305	+	0.158839i	$0.949225\pi$
$150$	−2.34633	+	10.2031i	−0.191577	+	0.833077i
$151$	10.8362	+	16.8615i	0.881841	+	1.37217i	0.927741	+	0.373225i	$0.121748\pi$
$151$	10.8362	+	16.8615i	0.881841	+	1.37217i	−0.0459004	+	0.998946i	$0.514616\pi$
$152$	2.01658	−	7.90742i	0.163566	−	0.641376i
$153$	27.8888	+	12.7364i	2.25467	+	1.02967i
$154$	10.3468	−	7.55610i	0.833766	−	0.608888i
$155$	−1.03442	−	3.52292i	−0.0830869	−	0.282968i
$156$	5.40682	+	0.127993i	0.432892	+	0.0102477i
$157$	−4.95710	−	1.45554i	−0.395620	−	0.116164i	0.0778705	−	0.996963i	$-0.475188\pi$
$157$	−4.95710	−	1.45554i	−0.395620	−	0.116164i	−0.473490	+	0.880799i	$0.657006\pi$
$158$	0.655599	+	10.9933i	0.0521566	+	0.874579i
$159$	1.46605	−	10.1966i	0.116265	−	0.808641i
$160$	2.37001	−	8.45256i	0.187366	−	0.668234i
$161$	23.1656	−	7.18239i	1.82570	−	0.566051i
$162$	−2.81612	−	1.08849i	−0.221255	−	0.0855198i
$163$	−2.18799	+	15.2178i	−0.171377	+	1.19195i	0.704602	+	0.709602i	$0.251125\pi$
$163$	−2.18799	+	15.2178i	−0.171377	+	1.19195i	−0.875979	+	0.482349i	$0.839784\pi$
$164$	−3.40982	+	10.6717i	−0.266262	+	0.833320i
$165$	−2.23710	+	7.61888i	−0.174158	+	0.593129i
$166$	10.6844	−	3.84166i	0.829268	−	0.298171i
$167$	6.78687	+	23.1139i	0.525183	+	1.78861i	0.610219	+	0.792233i	$0.291081\pi$
$167$	6.78687	+	23.1139i	0.525183	+	1.78861i	−0.0850357	+	0.996378i	$0.527100\pi$
$168$	−4.35933	+	40.6232i	−0.336329	+	3.13415i
$169$	5.02806	−	11.0099i	0.386774	−	0.846916i
$170$	6.11525	+	11.5213i	0.469018	+	0.883645i
$171$	−8.04650	−	12.5206i	−0.615331	−	0.957474i
$172$	−10.8933	−	7.37071i	−0.830607	−	0.562011i
$173$	23.6841	−	3.40525i	1.80067	−	0.258897i	0.841200	−	0.540724i	$-0.181850\pi$
$173$	23.6841	−	3.40525i	1.80067	−	0.258897i	0.959465	+	0.281827i	$0.0909405\pi$
$174$	−5.41020	−	26.3688i	−0.410146	−	1.99902i
$175$	8.58338	−	9.90575i	0.648843	−	0.748804i
$176$	−2.34187	+	6.77217i	−0.176525	+	0.510471i
$177$	−7.25374	−	4.66169i	−0.545224	−	0.350394i
$178$	0.321572	−	3.85454i	0.0241028	−	0.288910i
$179$	−0.730648	−	0.843213i	−0.0546112	−	0.0630247i	0.727787	−	0.685804i	$-0.240549\pi$
$179$	−0.730648	−	0.843213i	−0.0546112	−	0.0630247i	−0.782398	+	0.622779i	$0.786004\pi$
$180$	−8.33473	−	13.6699i	−0.621234	−	1.01890i
$181$	−2.00254	−	4.38495i	−0.148847	−	0.325931i	0.820491	−	0.571659i	$-0.193700\pi$
$181$	−2.00254	−	4.38495i	−0.148847	−	0.325931i	−0.969339	+	0.245729i	$0.920973\pi$
$182$	−5.90394	−	3.31509i	−0.437629	−	0.245731i
$183$	−15.6735			−1.15862
$184$	−8.34940	+	10.6905i	−0.615526	+	0.788117i
$185$	9.44274			0.694244
$186$	−8.33344	−	4.67927i	−0.611038	−	0.343100i
$187$	−4.42299	−	9.68499i	−0.323441	−	0.708236i
$188$	7.27748	−	4.43717i	0.530765	−	0.323614i
$189$	20.4185	+	23.5642i	1.48523	+	1.71404i
$190$	0.526421	−	6.30998i	0.0381906	−	0.457774i
$191$	−16.9573	−	10.8978i	−1.22699	−	0.788538i	−0.243570	−	0.969883i	$-0.578319\pi$
$191$	−16.9573	−	10.8978i	−1.22699	−	0.788538i	−0.983420	+	0.181345i	$0.941955\pi$
$192$	−10.9590	−	20.0511i	−0.790899	−	1.44706i
$193$	−15.5292	+	17.9216i	−1.11781	+	1.29002i	−0.165058	+	0.986284i	$0.552781\pi$
$193$	−15.5292	+	17.9216i	−1.11781	+	1.29002i	−0.952755	+	0.303741i	$0.901764\pi$
$194$	−0.206851	−	1.00817i	−0.0148510	−	0.0723826i
$195$	4.15373	−	0.597216i	0.297455	−	0.0427675i
$196$	20.8191	−	30.7689i	1.48708	−	2.19778i
$197$	7.43508	+	11.5692i	0.529727	+	0.824272i	0.998247	−	0.0591811i	$-0.0188489\pi$
$197$	7.43508	+	11.5692i	0.529727	+	0.824272i	−0.468520	+	0.883453i	$0.655213\pi$
$198$	6.12705	+	11.5436i	0.435431	+	0.820365i
$199$	4.70110	−	10.2940i	0.333252	−	0.729721i	−0.666625	−	0.745394i	$-0.732262\pi$
$199$	4.70110	−	10.2940i	0.333252	−	0.729721i	0.999877	+	0.0156724i	$0.00498888\pi$
$200$	−0.782173	+	7.28884i	−0.0553080	+	0.515399i
$201$	−8.49183	−	28.9205i	−0.598967	−	2.03990i
$202$	−8.75669	+	3.14855i	−0.616119	+	0.221531i
$203$	−9.49447	+	32.3352i	−0.666381	+	2.26949i
$204$	32.3418	+	10.3339i	2.26438	+	0.723515i
$205$	−1.23712	+	8.60433i	−0.0864039	+	0.600952i
$206$	4.01767	+	1.55292i	0.279924	+	0.108197i
$207$	3.88887	+	24.4319i	0.270295	+	1.69813i
$208$	3.76969	−	0.360965i	0.261381	−	0.0250284i
$209$	−0.735560	+	5.11593i	−0.0508797	+	0.353876i
$210$	1.88720	+	31.6452i	0.130229	+	2.18372i
$211$	19.8313	+	5.82299i	1.36524	+	0.400871i	0.880608	−	0.473846i	$-0.157134\pi$
$211$	19.8313	+	5.82299i	1.36524	+	0.400871i	0.484634	+	0.874717i	$0.338953\pi$
$212$	0.170705	−	7.21107i	0.0117240	−	0.495259i
$213$	1.67818	+	5.71536i	0.114987	+	0.391610i
$214$	−6.11356	+	4.46465i	−0.417915	+	0.305197i
$215$	−9.28315	−	4.23947i	−0.633106	−	0.289130i
$216$	−16.8977	−	4.30932i	−1.14974	−	0.293212i
$217$	6.46893	+	10.0659i	0.439140	+	0.683315i
$218$	−3.68079	+	16.0060i	−0.249295	+	1.08406i
$219$	0.870964	+	6.05769i	0.0588543	+	0.409340i
$220$	−0.921289	+	5.48312i	−0.0621133	+	0.369672i
$221$	−3.68480	+	4.25249i	−0.247867	+	0.286053i
$222$	17.5847	−	17.1734i	1.18021	−	1.15260i
$223$	9.09188	−	14.1472i	0.608838	−	0.947370i	−0.390801	−	0.920475i	$-0.627802\pi$
$223$	9.09188	−	14.1472i	0.608838	−	0.947370i	0.999638	−	0.0268945i	$-0.00856182\pi$
$224$	0.349850	+	28.6057i	0.0233753	+	1.91130i
$225$	8.75538	+	10.1042i	0.583692	+	0.673616i
$226$	4.96162	−	6.46699i	0.330042	−	0.430178i
$227$	−8.26371	+	3.77391i	−0.548482	+	0.250483i	−0.670327	−	0.742066i	$-0.733846\pi$
$227$	−8.26371	+	3.77391i	−0.548482	+	0.250483i	0.121845	+	0.992549i	$0.461119\pi$
$228$	−10.4956	−	12.7082i	−0.695085	−	0.841618i
$229$	−5.97598			−0.394904			−0.197452	−	0.980313i	$-0.563267\pi$
$229$	−5.97598			−0.394904			−0.197452	+	0.980313i	$0.563267\pi$
$230$	−5.01443	+	9.25382i	−0.330642	+	0.610179i
$231$		−	25.8769i		−	1.70257i
$232$	−5.95578	−	17.8824i	−0.391016	−	1.17404i
$233$	−5.31970	−	11.6485i	−0.348505	−	0.763120i	−0.999990	−	0.00445810i	$-0.998581\pi$
$233$	−5.31970	−	11.6485i	−0.348505	−	0.763120i	0.651485	−	0.758662i	$-0.274146\pi$
$234$	4.20416	−	5.47971i	0.274834	−	0.358220i
$235$	4.99820	−	4.33096i	0.326047	−	0.282521i
$236$	−5.43103	−	2.63735i	−0.353530	−	0.171677i
$237$	18.7118	+	12.0254i	1.21546	+	0.781131i
$238$	−29.6993	−	30.4107i	−1.92512	−	1.97123i
$239$	−11.2879	−	9.78101i	−0.730153	−	0.632681i	0.208309	−	0.978063i	$-0.433204\pi$
$239$	−11.2879	−	9.78101i	−0.730153	−	0.632681i	−0.938462	+	0.345382i	$0.887749\pi$
$240$	−10.9637	−	13.9340i	−0.707707	−	0.899434i
$241$	5.50463	−	0.791446i	0.354584	−	0.0509815i	0.0372789	−	0.999305i	$-0.488131\pi$
$241$	5.50463	−	0.791446i	0.354584	−	0.0509815i	0.317306	+	0.948323i	$0.397222\pi$
$242$	−2.46926	+	10.7376i	−0.158730	+	0.690242i
$243$	10.4303	−	6.70313i	0.669103	−	0.430006i
$244$	−10.8969	+	1.30434i	−0.697600	+	0.0835016i
$245$	11.9747	−	26.2209i	0.765034	−	1.67519i
$246$	13.3448	+	18.2733i	0.850831	+	1.16506i
$247$	2.62085	−	0.769550i	0.166760	−	0.0489653i
$248$	−6.18315	−	2.55971i	−0.392630	−	0.162542i
$249$	6.46069	−	22.0031i	0.409429	−	1.39439i
$250$	0.991851	+	16.6317i	0.0627301	+	1.05188i
$251$	−29.2090	−	4.19961i	−1.84365	−	0.265077i	−0.869990	−	0.493069i	$-0.835875\pi$
$251$	−29.2090	−	4.19961i	−1.84365	−	0.265077i	−0.973663	+	0.227992i	$0.926784\pi$
$252$	38.6119	+	35.0913i	2.43232	+	2.21054i
$253$	4.53554	−	7.29655i	0.285147	−	0.458730i
$254$	−3.76892	+	9.75086i	−0.236483	+	0.611823i
$255$	26.0764	+	3.74922i	1.63297	+	0.234785i
$256$	−9.28778	−	13.0283i	−0.580486	−	0.814270i
$257$	−17.9623	−	5.27421i	−1.12046	−	0.328996i	−0.331507	−	0.943453i	$-0.607557\pi$
$257$	−17.9623	−	5.27421i	−1.12046	−	0.328996i	−0.788951	+	0.614457i	$0.789375\pi$
$258$	−24.9978	+	8.98819i	−1.55630	+	0.559580i
$259$	−29.5258	+	8.66957i	−1.83465	+	0.538701i
$260$	2.83814	−	0.760878i	0.176014	−	0.0471876i
$261$	−31.2691	−	14.2801i	−1.93551	−	0.883918i
$262$	−15.1608	+	8.04699i	−0.936636	+	0.497145i
$263$	−5.04812	+	3.24423i	−0.311280	+	0.200048i	−0.686948	−	0.726707i	$-0.741050\pi$
$263$	−5.04812	+	3.24423i	−0.311280	+	0.200048i	0.375667	+	0.926755i	$0.377414\pi$
$264$	8.25641	+	11.8865i	0.508147	+	0.731562i
$265$	−0.796506	−	5.53982i	−0.0489290	−	0.340308i
$266$	4.14729	+	20.2136i	0.254287	+	1.23937i
$267$	−5.90402	−	5.11587i	−0.361320	−	0.313086i
$268$	−8.31060	−	19.4000i	−0.507651	−	1.18504i
$269$	−7.79282	+	12.1259i	−0.475137	+	0.739327i	−0.993251	−	0.115984i	$-0.962998\pi$
$269$	−7.79282	+	12.1259i	−0.475137	+	0.739327i	0.518114	+	0.855311i	$0.326634\pi$
$270$	−13.4841	−	1.12493i	−0.820614	−	0.0684611i
$271$	−14.9068	+	12.9168i	−0.905521	+	0.784638i	−0.977096	−	0.212797i	$-0.931743\pi$
$271$	−14.9068	+	12.9168i	−0.905521	+	0.784638i	0.0715755	+	0.997435i	$0.477197\pi$
$272$	23.3453	+	4.49305i	1.41552	+	0.272431i
$273$	−12.4397	+	5.68101i	−0.752884	+	0.343831i
$274$	9.32863	+	5.23806i	0.563563	+	0.316443i
$275$		−	4.64297i		−	0.279981i
$276$	7.49169	+	26.3526i	0.450947	+	1.58624i
$277$		−	25.9987i		−	1.56211i	−0.624462	−	0.781055i	$-0.714682\pi$
$277$		−	25.9987i		−	1.56211i	0.624462	−	0.781055i	$-0.285318\pi$
$278$	−0.0822307	+	0.146447i	−0.00493187	+	0.00878332i
$279$	−11.1021	+	5.07017i	−0.664666	+	0.303543i
$280$	3.94554	+	21.8439i	0.235791	+	1.30542i
$281$	−7.23906	+	6.27268i	−0.431846	+	0.374197i	−0.843487	−	0.537149i	$-0.819501\pi$
$281$	−7.23906	+	6.27268i	−0.431846	+	0.374197i	0.411641	+	0.911346i	$0.364956\pi$
$282$	1.43123	−	17.1555i	0.0852282	−	1.02159i
$283$	12.4318	−	19.3442i	0.738992	−	1.14989i	−0.244624	−	0.969618i	$-0.578664\pi$
$283$	12.4318	−	19.3442i	0.738992	−	1.14989i	0.983616	−	0.180276i	$-0.0576992\pi$
$284$	1.64237	+	3.83389i	0.0974565	+	0.227500i
$285$	−9.66503	−	8.37480i	−0.572507	−	0.496080i
$286$	−2.34955	+	0.482066i	−0.138932	+	0.0285052i
$287$	−4.03156	−	28.0401i	−0.237975	−	1.65515i
$288$	−28.9327	−	3.79936i	−1.70487	−	0.223879i
$289$	−15.4155	+	9.90692i	−0.906792	+	0.582760i
$290$	−6.85647	−	12.9178i	−0.402626	−	0.758560i
$291$	−1.89080	−	0.863499i	−0.110841	−	0.0506192i
$292$	1.10964	+	4.13906i	0.0649370	+	0.242220i
$293$	−4.91323	+	1.44266i	−0.287034	+	0.0842808i	−0.422080	−	0.906559i	$-0.638700\pi$
$293$	−4.91323	+	1.44266i	−0.287034	+	0.0842808i	0.135046	+	0.990839i	$0.456882\pi$
$294$	−25.3877	−	70.6080i	−1.48064	−	4.11794i
$295$	−4.49488	−	1.31982i	−0.261702	−	0.0768426i
$296$	10.7965	−	13.4030i	0.627532	−	0.779034i
$297$	10.9325	+	1.57185i	0.634365	+	0.0912080i
$298$	0.538240	+	0.208041i	0.0311794	+	0.0120515i
$299$	−4.50337	−	0.578464i	−0.260437	−	0.0334534i
$300$	10.9570	+	9.95792i	0.632602	+	0.574921i
$301$	32.9192	+	4.73306i	1.89743	+	0.272809i
$302$	28.2953	−	1.68743i	1.62821	−	0.0971004i
$303$	−5.29504	+	18.0333i	−0.304192	+	1.03598i
$304$	−8.35449	−	7.96179i	−0.479163	−	0.456640i
$305$	−8.17052	+	2.39908i	−0.467843	+	0.137371i
$306$	35.0157	−	25.5715i	2.00171	−	1.46182i
$307$	−5.47087	+	11.9795i	−0.312239	+	0.683708i	−0.999070	−	0.0431085i	$-0.986274\pi$
$307$	−5.47087	+	11.9795i	−0.312239	+	0.683708i	0.686831	+	0.726817i	$0.259001\pi$
$308$	−2.15345	−	17.9906i	−0.122704	−	1.02511i
$309$	7.31860	−	4.70338i	0.416340	−	0.267566i
$310$	−5.06041	−	1.16371i	−0.287412	−	0.0660943i
$311$	−11.6388	+	1.67340i	−0.659974	+	0.0948900i	−0.464160	−	0.885751i	$-0.653644\pi$
$311$	−11.6388	+	1.67340i	−0.659974	+	0.0948900i	−0.195814	+	0.980641i	$0.562735\pi$
$312$	3.90152	−	6.57863i	0.220880	−	0.372442i
$313$	−4.12965	−	3.57836i	−0.233422	−	0.202261i	0.530294	−	0.847814i	$-0.322082\pi$
$313$	−4.12965	−	3.57836i	−0.233422	−	0.202261i	−0.763716	+	0.645553i	$0.776627\pi$
$314$	−5.22715	+	5.10488i	−0.294985	+	0.288085i
$315$	34.0573	+	21.8873i	1.91891	+	1.23321i
$316$	14.0100	+	6.80333i	0.788121	+	0.382717i
$317$	0.757874	−	0.656701i	0.0425664	−	0.0368840i	−0.633318	−	0.773892i	$-0.718307\pi$
$317$	0.757874	−	0.656701i	0.0425664	−	0.0368840i	0.675884	+	0.737008i	$0.263762\pi$
$318$	−11.5585	−	8.86793i	−0.648168	−	0.497289i
$319$	4.95909	+	10.8589i	0.277656	+	0.607981i
$320$	−8.78201	−	8.77507i	−0.490929	−	0.490541i
$321$			15.2898i			0.853393i
$322$	7.18314	−	33.5390i	0.400301	−	1.86905i
$323$	17.1478			0.954131
$324$	−3.29212	+	2.71893i	−0.182896	+	0.151052i
$325$	−2.23199	+	1.01932i	−0.123809	+	0.0565416i
$326$	17.2504	+	13.2349i	0.955411	+	0.733013i
$327$	21.7227	+	25.0693i	1.20127	+	1.38633i
$328$	10.7985	+	11.5938i	0.596248	+	0.640161i
$329$	−11.6522	+	18.1311i	−0.642405	+	0.999602i
$330$	7.84600	+	8.03394i	0.431908	+	0.442254i
$331$	−0.0677879	+	0.0782314i	−0.00372596	+	0.00429998i	−0.757609	−	0.652708i	$-0.773633\pi$
$331$	−0.0677879	+	0.0782314i	−0.00372596	+	0.00429998i	0.753884	+	0.657008i	$0.228178\pi$
$332$	2.66065	−	15.8351i	0.146022	−	0.869062i
$333$	−4.46712	−	31.0695i	−0.244796	−	1.70260i
$334$	33.2015	+	7.63512i	1.81670	+	0.417775i
$335$	−8.85349	−	13.7763i	−0.483718	−	0.752679i
$336$	47.0748	+	33.5031i	2.56814	+	1.82775i
$337$	3.26885	+	1.49283i	0.178066	+	0.0813199i	0.502453	−	0.864604i	$-0.332431\pi$
$337$	3.26885	+	1.49283i	0.178066	+	0.0813199i	−0.324388	+	0.945924i	$0.605158\pi$
$338$	−10.0951	−	13.8235i	−0.549100	−	0.751897i
$339$	−4.63812	−	15.7960i	−0.251908	−	0.857920i
$340$	18.4414	+	0.436554i	1.00012	+	0.0236755i
$341$	4.06679	+	1.19412i	0.220229	+	0.0646650i
$342$	−21.0108	+	1.25301i	−1.13613	+	0.0677548i
$343$	−8.33086	+	57.9424i	−0.449824	+	3.12859i
$344$	−16.6315	+	8.32925i	−0.896710	+	0.449083i
$345$	9.12076	+	19.2017i	0.491045	+	1.03378i
$346$	12.1998	−	31.5630i	0.655865	−	1.69684i
$347$	1.43435	−	9.97614i	0.0770000	−	0.535547i	−0.914413	−	0.404782i	$-0.867347\pi$
$347$	1.43435	−	9.97614i	0.0770000	−	0.535547i	0.991413	−	0.130765i	$-0.0417434\pi$
$348$	−36.2619	−	11.5864i	−1.94384	−	0.621097i
$349$	−3.47686	+	11.8411i	−0.186112	+	0.633839i	0.812587	+	0.582840i	$0.198059\pi$
$349$	−3.47686	+	11.8411i	−0.186112	+	0.633839i	−0.998699	+	0.0509990i	$0.983759\pi$
$350$	−6.27181	−	17.4431i	−0.335243	−	0.932372i
$351$	−1.64448	−	5.60060i	−0.0877761	−	0.298938i
$352$	6.72937	+	7.57686i	0.358676	+	0.403848i
$353$	5.28114	−	11.5641i	0.281087	−	0.615494i	−0.715448	−	0.698666i	$-0.753778\pi$
$353$	5.28114	−	11.5641i	0.281087	−	0.615494i	0.996535	+	0.0831712i	$0.0265048\pi$
$354$	−10.7709	+	5.71695i	−0.572468	+	0.303853i
$355$	1.74965	+	2.72251i	0.0928619	+	0.144496i
$356$	−4.53045	−	3.06543i	−0.240113	−	0.162467i
$357$	−84.9787	+	12.2181i	−4.49755	+	0.646650i
$358$	−1.54568	+	0.317134i	−0.0816919	+	0.0167610i
$359$	−12.0759	+	13.9363i	−0.637342	+	0.735532i	−0.978902	−	0.204328i	$-0.934499\pi$
$359$	−12.0759	+	13.9363i	−0.637342	+	0.735532i	0.341561	+	0.939860i	$0.389044\pi$
$360$	−22.6276	+	0.812626i	−1.19258	+	0.0428292i
$361$	8.98103	+	5.77176i	0.472686	+	0.303777i
$362$	−6.79372	−	0.566777i	−0.357070	−	0.0297891i
$363$	14.5727	+	16.8178i	0.764867	+	0.882703i
$364$	−8.17580	+	4.98489i	−0.428528	+	0.261279i
$365$	1.38125	+	3.02452i	0.0722981	+	0.158311i
$366$	−10.8524	+	19.3273i	−0.567262	+	1.01025i
$367$	32.2136			1.68154			0.840768	−	0.541396i	$-0.182104\pi$
$367$	32.2136			1.68154			0.840768	+	0.541396i	$0.182104\pi$
$368$	7.40156	+	17.6979i	0.385833	+	0.922569i
$369$	28.8961			1.50427
$370$	6.53817	−	11.6440i	0.339903	−	0.605344i
$371$	7.57676	+	16.5908i	0.393366	+	0.861351i
$372$	−11.5402	+	7.03619i	−0.598330	+	0.364810i
$373$	−19.2000	−	22.1580i	−0.994137	−	1.14730i	−0.989091	−	0.147308i	$-0.952939\pi$
$373$	−19.2000	−	22.1580i	−0.994137	−	1.14730i	−0.00504651	−	0.999987i	$-0.501606\pi$
$374$	−15.0052	−	1.25183i	−0.775901	−	0.0647308i
$375$	28.3090	+	18.1931i	1.46187	+	0.939487i
$376$	−0.432619	−	12.0463i	−0.0223106	−	0.621240i
$377$	4.13143	−	4.76793i	0.212780	−	0.245561i
$378$	43.1952	−	8.86253i	2.22172	−	0.455839i
$379$	6.85191	−	0.985157i	0.351959	−	0.0506041i	0.0359320	−	0.999354i	$-0.488560\pi$
$379$	6.85191	−	0.985157i	0.351959	−	0.0506041i	0.316027	+	0.948750i	$0.397651\pi$
$380$	−7.41646	−	5.01818i	−0.380456	−	0.257427i
$381$	11.4151	+	17.7622i	0.584811	+	0.909984i
$382$	−25.1796	+	13.3647i	−1.28830	+	0.683799i
$383$	−2.51646	+	5.51028i	−0.128585	+	0.281562i	−0.962964	−	0.269629i	$-0.913099\pi$
$383$	−2.51646	+	5.51028i	−0.128585	+	0.281562i	0.834379	+	0.551191i	$0.185826\pi$
$384$	−32.3134	−	0.369638i	−1.64899	−	0.0188630i
$385$	−3.96086	−	13.4895i	−0.201864	−	0.687487i
$386$	11.3470	+	31.5582i	0.577549	+	1.60627i
$387$	−9.55753	+	32.5500i	−0.485837	+	1.65461i
$388$	−1.38642	−	0.442989i	−0.0703848	−	0.0224893i
$389$	1.30274	−	9.06078i	0.0660517	−	0.459400i	−0.929774	−	0.368130i	$-0.879998\pi$
$389$	1.30274	−	9.06078i	0.0660517	−	0.459400i	0.995826	−	0.0912700i	$-0.0290926\pi$
$390$	2.13961	−	5.53555i	0.108343	−	0.280303i
$391$	−26.1031	−	11.4494i	−1.32009	−	0.579020i
$392$	−23.5265	−	46.9768i	−1.18827	−	2.37269i
$393$	−4.93356	+	34.3136i	−0.248865	+	1.73089i
$394$	19.4143	−	1.15779i	0.978076	−	0.0583289i
$395$	11.5950	+	3.40461i	0.583410	+	0.171305i
$396$	18.4770	+	0.437397i	0.928502	+	0.0219800i
$397$	−5.55659	−	18.9240i	−0.278877	−	0.949769i	−0.973172	−	0.230078i	$-0.926102\pi$
$397$	−5.55659	−	18.9240i	−0.278877	−	0.949769i	0.694295	−	0.719691i	$-0.255716\pi$
$398$	−9.43865	−	12.9246i	−0.473117	−	0.647851i
$399$	37.9100	+	17.3129i	1.89787	+	0.866730i
$400$	8.44642	+	6.01131i	0.422321	+	0.300566i
$401$	0.0268091	+	0.0417158i	0.00133878	+	0.00208319i	0.841922	−	0.539599i	$-0.181424\pi$
$401$	0.0268091	+	0.0417158i	0.00133878	+	0.00208319i	−0.840583	+	0.541682i	$0.817788\pi$
$402$	−41.5422	−	9.55317i	−2.07193	−	0.476469i
$403$	−0.318781	−	2.21717i	−0.0158796	−	0.110445i
$404$	−2.18061	+	12.9781i	−0.108490	+	0.645684i
$405$	−2.16954	+	2.50378i	−0.107805	+	0.124414i
$406$	33.2991	+	34.0967i	1.65261	+	1.69219i
$407$	−5.89326	+	9.17009i	−0.292118	+	0.454544i
$408$	35.1364	−	32.7261i	1.73951	−	1.62018i
$409$	9.98127	+	11.5190i	0.493542	+	0.569578i	0.946809	−	0.321797i	$-0.104287\pi$
$409$	9.98127	+	11.5190i	0.493542	+	0.569578i	−0.453267	+	0.891375i	$0.649741\pi$
$410$	9.75357	+	7.48316i	0.481695	+	0.369567i
$411$	19.6555	−	8.97638i	0.969536	−	0.442772i
$412$	4.69677	−	3.87902i	0.231393	−	0.191106i
$413$	15.2665			0.751214
$414$	32.8201	+	12.1212i	1.61302	+	0.595726i
$415$		−	12.4590i		−	0.611588i
$416$	2.16503	−	4.89841i	0.106149	−	0.240164i
$417$	0.140917	+	0.308566i	0.00690075	+	0.0151105i
$418$	5.79925	+	4.44931i	0.283650	+	0.217623i
$419$	21.4069	−	18.5492i	1.04579	−	0.906186i	0.0500876	−	0.998745i	$-0.484050\pi$
$419$	21.4069	−	18.5492i	1.04579	−	0.906186i	0.995707	+	0.0925585i	$0.0295045\pi$
$420$	40.3289	+	19.5840i	1.96785	+	0.955602i
$421$	−29.3409	−	18.8562i	−1.42999	−	0.918996i	−0.999868	−	0.0162229i	$-0.994836\pi$
$421$	−29.3409	−	18.8562i	−1.42999	−	0.918996i	−0.430117	−	0.902773i	$-0.641528\pi$
$422$	20.9117	−	20.4225i	1.01796	−	0.994151i
$423$	−16.6147	−	14.3967i	−0.807834	−	0.699992i
$424$	−8.77391	−	5.20346i	−0.426099	−	0.252702i
$425$	−15.2473	+	2.19224i	−0.739604	+	0.106339i
$426$	8.20969	+	1.88793i	0.397761	+	0.0914704i
$427$	23.3452	−	15.0030i	1.12975	−	0.726048i
$428$	1.27240	+	10.6301i	0.0615039	+	0.513824i
$429$	−2.01239	+	4.40652i	−0.0971590	+	0.212749i
$430$	−11.6554	+	8.51181i	−0.562075	+	0.410476i
$431$	8.68040	−	2.54879i	0.418120	−	0.122771i	−0.0659037	−	0.997826i	$-0.520993\pi$
$431$	8.68040	−	2.54879i	0.418120	−	0.122771i	0.484024	+	0.875055i	$0.339175\pi$
$432$	−17.0139	+	17.8531i	−0.818581	+	0.858956i
$433$	8.64141	−	29.4300i	0.415280	−	1.41431i	−0.440863	−	0.897574i	$-0.645328\pi$
$433$	8.64141	−	29.4300i	0.415280	−	1.41431i	0.856143	−	0.516739i	$-0.172854\pi$
$434$	16.8915	−	1.00735i	0.810817	−	0.0483541i
$435$	−29.2371	−	4.20366i	−1.40181	−	0.201550i
$436$	17.1887	+	15.6214i	0.823190	+	0.748131i
$437$	7.65505	+	11.5264i	0.366191	+	0.551382i
$438$	8.07290	+	3.12035i	0.385738	+	0.149096i
$439$	−15.5033	−	2.22904i	−0.739934	−	0.106386i	−0.237967	−	0.971273i	$-0.576481\pi$
$439$	−15.5033	−	2.22904i	−0.739934	−	0.106386i	−0.501967	+	0.864887i	$0.667390\pi$
$440$	6.12343	+	4.93258i	0.291923	+	0.235151i
$441$	−91.9395	−	26.9959i	−4.37807	−	1.28552i
$442$	2.69246	+	7.48822i	0.128067	+	0.356179i
$443$	1.84283	−	0.541103i	0.0875553	−	0.0257086i	−0.237662	−	0.971348i	$-0.576381\pi$
$443$	1.84283	−	0.541103i	0.0875553	−	0.0257086i	0.325217	+	0.945639i	$0.394563\pi$
$444$	−9.00112	−	33.5749i	−0.427174	−	1.59340i
$445$	−3.86080	−	1.76317i	−0.183019	−	0.0835822i
$446$	−11.1500	−	21.0069i	−0.527968	−	0.994708i
$447$	0.980458	−	0.630102i	0.0463741	−	0.0298028i
$448$	35.5164	+	19.3752i	1.67799	+	0.915392i
$449$	−0.675575	−	4.69872i	−0.0318823	−	0.221747i	0.967651	−	0.252292i	$-0.0811845\pi$
$449$	−0.675575	−	4.69872i	−0.0318823	−	0.221747i	−0.999533	+	0.0305459i	$0.990275\pi$
$450$	18.5220	−	3.80022i	0.873134	−	0.179144i
$451$	−7.58379	−	6.57139i	−0.357107	−	0.309435i
$452$	−4.53913	−	10.5960i	−0.213503	−	0.498395i
$453$	30.9517	−	48.1618i	1.45424	−	2.26284i
$454$	−1.06813	+	12.8032i	−0.0501297	+	0.600884i
$455$	−5.61517	+	4.86557i	−0.263243	+	0.228101i
$456$	−22.9378	+	4.14312i	−1.07416	+	0.194019i
$457$	34.4422	−	15.7292i	1.61114	−	0.735783i	0.612630	−	0.790370i	$-0.290112\pi$
$457$	34.4422	−	15.7292i	1.61114	−	0.735783i	0.998509	+	0.0545870i	$0.0173842\pi$
$458$	−4.13778	+	7.36909i	−0.193346	+	0.344335i
$459$		−	36.6439i		−	1.71039i
$460$	7.93906	+	12.5907i	0.370161	+	0.587046i
$461$			26.0410i			1.21285i	0.795140	+	0.606426i	$0.207397\pi$
$461$			26.0410i			1.21285i	−0.795140	+	0.606426i	$0.792603\pi$
$462$	−31.9092	−	17.9172i	−1.48455	−	0.833583i
$463$	18.5165	−	8.45622i	0.860536	−	0.392994i	0.0642646	−	0.997933i	$-0.479530\pi$
$463$	18.5165	−	8.45622i	0.860536	−	0.392994i	0.796272	+	0.604939i	$0.206803\pi$
$464$	−26.1749	−	5.03765i	−1.21514	−	0.233867i
$465$	−7.92584	+	6.86778i	−0.367552	+	0.318485i
$466$	−18.0474	−	1.50563i	−0.836028	−	0.0697470i
$467$	−19.9073	+	30.9763i	−0.921199	+	1.43341i	−0.0201018	+	0.999798i	$0.506399\pi$
$467$	−19.9073	+	30.9763i	−0.921199	+	1.43341i	−0.901098	+	0.433616i	$0.857237\pi$
$468$	−3.84617	−	8.97838i	−0.177789	−	0.415026i
$469$	40.3316	+	34.9476i	1.86234	+	1.61373i
$470$	−1.87983	−	9.16213i	−0.0867101	−	0.422618i
$471$	2.10011	+	14.6066i	0.0967680	+	0.673036i
$472$	−7.01261	+	4.87100i	−0.322782	+	0.224206i
$473$	9.91072	−	6.36923i	0.455695	−	0.292858i
$474$	27.7848	−	14.7475i	1.27620	−	0.677376i
$475$	6.80201	+	3.10637i	0.312098	+	0.142530i
$476$	−58.0638	+	15.5664i	−2.66135	+	0.713483i
$477$	−17.8509	+	5.24149i	−0.817336	+	0.239991i
$478$	−19.8769	+	7.14692i	−0.909148	+	0.326892i
$479$	−8.41142	−	2.46982i	−0.384328	−	0.112849i	0.0838606	−	0.996477i	$-0.473275\pi$
$479$	−8.41142	−	2.46982i	−0.384328	−	0.112849i	−0.468188	+	0.883629i	$0.655093\pi$
$480$	−24.7736	+	3.87169i	−1.13075	+	0.176718i
$481$	5.70211	+	0.819839i	0.259994	+	0.0373815i
$482$	2.83547	−	7.33586i	0.129152	−	0.334139i
$483$	−46.1485	−	51.6664i	−2.09983	−	2.35090i
$484$	11.5311	+	10.4797i	0.524139	+	0.476348i
$485$	−1.11784	−	0.160720i	−0.0507583	−	0.00729794i
$486$	−1.04382	−	17.5030i	−0.0473485	−	0.793953i
$487$	−4.41486	+	15.0356i	−0.200056	+	0.681330i	0.796952	+	0.604042i	$0.206444\pi$
$487$	−4.41486	+	15.0356i	−0.200056	+	0.681330i	−0.997009	+	0.0772876i	$0.975374\pi$
$488$	−5.93660	+	14.3402i	−0.268737	+	0.649152i
$489$	42.1350	−	12.3720i	1.90541	−	0.559480i
$490$	−24.0422	−	32.9216i	−1.08611	−	1.48724i
$491$	−10.6783	+	23.3822i	−0.481905	+	1.05522i	0.500031	+	0.866008i	$0.333322\pi$
$491$	−10.6783	+	23.3822i	−0.481905	+	1.05522i	−0.981935	+	0.189217i	$0.939405\pi$
$492$	31.7731	−	3.80319i	1.43244	−	0.171461i
$493$	33.3187	−	21.4126i	1.50060	−	0.964377i
$494$	0.865732	−	3.76465i	0.0389511	−	0.169380i
$495$	14.1947	−	2.04089i	0.638004	−	0.0917312i
$496$	−7.43765	+	5.85221i	−0.333960	+	0.262772i
$497$	−7.97046	−	6.90645i	−0.357524	−	0.309796i
$498$	−22.6590	−	23.2017i	−1.01537	−	1.03970i
$499$	−5.08585	−	3.26848i	−0.227674	−	0.146317i	0.421831	−	0.906674i	$-0.361388\pi$
$499$	−5.08585	−	3.26848i	−0.227674	−	0.146317i	−0.649505	+	0.760357i	$0.725024\pi$
$500$	21.1956	+	10.2927i	0.947894	+	0.460304i
$501$	52.0015	−	45.0596i	2.32326	−	2.01311i
$502$	−25.4029	+	33.1103i	−1.13379	+	1.47778i
$503$	2.18735	+	4.78963i	0.0975291	+	0.213559i	0.952108	−	0.305763i	$-0.0989117\pi$
$503$	2.18735	+	4.78963i	0.0975291	+	0.213559i	−0.854578	+	0.519322i	$0.826184\pi$
$504$	70.0066	−	23.3158i	3.11834	−	1.03857i
$505$			10.2111i			0.454389i
$506$	−5.85710	−	10.6450i	−0.260380	−	0.473228i
$507$	−34.5720			−1.53539
$508$	9.41436	+	11.3990i	0.417695	+	0.505750i
$509$	16.0937	−	7.34974i	0.713340	−	0.325771i	−0.0254791	−	0.999675i	$-0.508111\pi$
$509$	16.0937	−	7.34974i	0.713340	−	0.325771i	0.738819	+	0.673904i	$0.235384\pi$
$510$	22.6786	−	29.5593i	1.00422	−	1.30891i
$511$	−7.09582	−	8.18901i	−0.313901	−	0.362261i
$512$	−22.4963	+	2.43210i	−0.994207	+	0.107485i
$513$	−9.61714	+	14.9646i	−0.424607	+	0.660701i
$514$	−18.9408	+	18.4978i	−0.835445	+	0.815902i
$515$	3.09522	−	3.57207i	0.136392	−	0.157404i
$516$	−6.22502	+	37.0487i	−0.274041	+	1.63098i
$517$	1.08651	+	7.55685i	0.0477847	+	0.332350i
$518$	−9.75313	+	42.4117i	−0.428528	+	1.86346i
$519$	−36.9500	−	57.4953i	−1.62192	−	2.52376i
$520$	1.02688	−	4.02659i	0.0450316	−	0.176578i
$521$	4.77483	+	2.18059i	0.209189	+	0.0955335i	0.517254	−	0.855832i	$-0.326954\pi$
$521$	4.77483	+	2.18059i	0.209189	+	0.0955335i	−0.308065	+	0.951365i	$0.599681\pi$
$522$	−39.2599	+	28.6710i	−1.71836	+	1.25489i
$523$	4.60996	+	15.7001i	0.201580	+	0.686517i	0.996781	+	0.0801719i	$0.0255469\pi$
$523$	4.60996	+	15.7001i	0.201580	+	0.686517i	−0.795201	+	0.606345i	$0.792635\pi$
$524$	−0.574457	+	24.2668i	−0.0250953	+	1.06010i
$525$	−35.9217	−	10.5476i	−1.56775	−	0.460334i
$526$	0.505193	+	8.47124i	0.0220275	+	0.369363i
$527$	2.00125	−	13.9190i	0.0871758	−	0.606321i
$528$	20.3742	−	1.95092i	0.886672	−	0.0849028i
$529$	−3.95682	−	22.6571i	−0.172036	−	0.985091i
$530$	−7.38276	−	2.85359i	−0.320686	−	0.123952i
$531$	−2.21618	+	15.4139i	−0.0961741	+	0.668905i
$532$	27.7973	+	8.88179i	1.20517	+	0.385075i
$533$	−1.49409	+	5.08841i	−0.0647163	+	0.220404i
$534$	−10.3964	+	3.73813i	−0.449897	+	0.161765i
$535$	2.34034	+	7.97048i	0.101182	+	0.344594i
$536$	−29.6768	−	3.18465i	−1.28184	−	0.137556i
$537$	−1.32388	+	2.89889i	−0.0571295	+	0.125096i
$538$	9.55687	+	18.0054i	0.412026	+	0.776270i
$539$	17.9903	+	27.9935i	0.774898	+	1.20576i
$540$	−10.7236	+	15.8485i	−0.461469	+	0.682013i
$541$	23.8290	−	3.42610i	1.02449	−	0.147299i	0.390470	−	0.920616i	$-0.372313\pi$
$541$	23.8290	−	3.42610i	1.02449	−	0.147299i	0.634021	+	0.773316i	$0.281403\pi$
$542$	5.60646	+	27.3254i	0.240818	+	1.17373i
$543$	−9.01683	+	10.4060i	−0.386949	+	0.446563i
$544$	21.7048	−	25.6765i	0.930585	−	1.10087i
$545$	15.1612	+	9.74348i	0.649433	+	0.417365i
$546$	−1.60789	+	19.2731i	−0.0688115	+	0.824814i
$547$	4.35607	+	5.02717i	0.186252	+	0.214946i	0.841195	−	0.540732i	$-0.181853\pi$
$547$	4.35607	+	5.02717i	0.186252	+	0.214946i	−0.654943	+	0.755678i	$0.727307\pi$
$548$	12.9183	−	7.87645i	0.551843	−	0.336465i
$549$	11.7590	+	25.7485i	0.501860	+	1.09892i
$550$	−5.72533	−	3.21480i	−0.244129	−	0.137079i
$551$	−19.2263			−0.819068
$552$	37.6831	+	9.00844i	1.60390	+	0.383425i
$553$	−39.3816			−1.67468
$554$	−32.0595	−	18.0015i	−1.36208	−	0.764812i
$555$	−11.2043	−	24.5341i	−0.475598	−	1.04141i
$556$	0.123650	+	0.202800i	0.00524393	+	0.00860065i
$557$	−10.3521	−	11.9470i	−0.438635	−	0.506211i	0.492789	−	0.870149i	$-0.335978\pi$
$557$	−10.3521	−	11.9470i	−0.438635	−	0.506211i	−0.931423	+	0.363938i	$0.881432\pi$
$558$	−1.43501	+	17.2008i	−0.0607487	+	0.728168i
$559$	−5.23766	−	3.36604i	−0.221529	−	0.142368i
$560$	29.6680	+	10.2595i	1.25370	+	0.433541i
$561$	−19.9154	+	22.9836i	−0.840827	+	0.970367i
$562$	2.72262	+	13.2698i	0.114847	+	0.559754i
$563$	16.8778	−	2.42666i	0.711313	−	0.102271i	0.222846	−	0.974854i	$-0.428465\pi$
$563$	16.8778	−	2.42666i	0.711313	−	0.102271i	0.488467	+	0.872582i	$0.337556\pi$
$564$	−20.1638	−	13.6434i	−0.849048	−	0.574489i
$565$	−4.83565	−	7.52442i	−0.203437	−	0.316555i
$566$	−15.2459	−	28.7238i	−0.640834	−	1.20735i
$567$	4.48501	−	9.82079i	0.188353	−	0.412435i
$568$	5.86482	+	0.629360i	0.246082	+	0.0264074i
$569$	6.28352	+	21.3997i	0.263419	+	0.897122i	0.979896	+	0.199511i	$0.0639354\pi$
$569$	6.28352	+	21.3997i	0.263419	+	0.897122i	−0.716477	+	0.697611i	$0.754246\pi$
$570$	−17.0192	+	6.11940i	−0.712856	+	0.256314i
$571$	9.12923	−	31.0913i	0.382046	−	1.30113i	−0.514237	−	0.857648i	$-0.671925\pi$
$571$	9.12923	−	31.0913i	0.382046	−	1.30113i	0.896283	−	0.443482i	$-0.146257\pi$
$572$	−1.03239	+	3.23106i	−0.0431663	+	0.135097i
$573$	−8.19383	+	56.9893i	−0.342302	+	2.38076i
$574$	−37.3682	−	14.4436i	−1.55972	−	0.602865i
$575$	−8.28021	−	9.27026i	−0.345309	−	0.386596i
$576$	−24.7181	+	33.0467i	−1.02992	+	1.37695i
$577$	−2.92744	+	20.3608i	−0.121871	+	0.847632i	0.833562	+	0.552425i	$0.186298\pi$
$577$	−2.92744	+	20.3608i	−0.121871	+	0.847632i	−0.955433	+	0.295206i	$0.904612\pi$
$578$	1.54271	+	25.8687i	0.0641683	+	1.07599i
$579$	64.9900	+	19.0828i	2.70089	+	0.793054i
$580$	−20.6766	−	0.489468i	−0.858550	−	0.0203241i
$581$	11.4388	+	38.9571i	0.474563	+	1.61621i
$582$	−2.37399	+	1.73369i	−0.0984050	+	0.0718638i
$583$	5.87697	+	2.68392i	0.243399	+	0.111157i
$584$	5.87227	+	1.49757i	0.242996	+	0.0619700i
$585$	−4.09742	−	6.37571i	−0.169407	−	0.263603i
$586$	−1.62296	+	7.05749i	−0.0670440	+	0.291542i
$587$	−0.369212	−	2.56793i	−0.0152390	−	0.105990i	0.980782	−	0.195106i	$-0.0625049\pi$
$587$	−0.369212	−	2.56793i	−0.0152390	−	0.105990i	−0.996021	+	0.0891159i	$0.971596\pi$
$588$	−104.647	−	17.5830i	−4.31555	−	0.725111i
$589$	−4.47028	+	5.15898i	−0.184195	+	0.212572i
$590$	−4.73975	+	4.62887i	−0.195132	+	0.190568i
$591$	21.2369	−	33.0453i	0.873570	−	1.35930i
$592$	−9.05202	−	22.5936i	−0.372036	−	0.928590i
$593$	−23.6073	−	27.2443i	−0.969437	−	1.11879i	−0.992886	−	0.119065i	$-0.962010\pi$
$593$	−23.6073	−	27.2443i	−0.969437	−	1.11879i	0.0234490	−	0.999725i	$-0.492535\pi$
$594$	9.50792	−	12.3927i	0.390115	−	0.508477i
$595$	−42.4287	+	19.3766i	−1.73941	+	0.794362i
$596$	0.629217	−	0.519665i	0.0257738	−	0.0212863i
$597$	−32.3239			−1.32293
$598$	−3.83146	+	5.15266i	−0.156680	+	0.210708i
$599$			26.2291i			1.07169i	0.844316	+	0.535846i	$0.180007\pi$
$599$			26.2291i			1.07169i	−0.844316	+	0.535846i	$0.819993\pi$
$600$	19.8659	−	6.61637i	0.811023	−	0.270112i
$601$	−6.19230	−	13.5592i	−0.252589	−	0.553093i	0.740280	−	0.672298i	$-0.234693\pi$
$601$	−6.19230	−	13.5592i	−0.252589	−	0.553093i	−0.992870	+	0.119205i	$0.961965\pi$
$602$	28.6297	−	37.3161i	1.16686	−	1.52089i
$603$	−41.1398	+	35.6479i	−1.67534	+	1.45169i
$604$	17.5109	−	36.0598i	0.712508	−	1.46725i
$605$	10.1709	+	6.53642i	0.413505	+	0.265743i
$606$	18.5708	+	19.0157i	0.754389	+	0.772459i
$607$	−10.7092	−	9.27954i	−0.434671	−	0.376645i	0.409862	−	0.912147i	$-0.365577\pi$
$607$	−10.7092	−	9.27954i	−0.434671	−	0.376645i	−0.844534	+	0.535502i	$0.820122\pi$
$608$	−15.6025	+	4.78932i	−0.632765	+	0.194233i
$609$	95.2789	−	13.6990i	3.86089	−	0.555113i
$610$	−2.69893	+	11.7363i	−0.109276	+	0.475191i
$611$	3.39424	−	2.18135i	0.137316	−	0.0882479i
$612$	−7.28774	−	60.8842i	−0.294589	−	2.46110i
$613$	−15.0550	+	32.9658i	−0.608065	+	1.33148i	0.315825	+	0.948818i	$0.397719\pi$
$613$	−15.0550	+	32.9658i	−0.608065	+	1.33148i	−0.923890	+	0.382659i	$0.875008\pi$
$614$	10.9841	+	15.0409i	0.443284	+	0.607001i
$615$	23.8236	−	6.99525i	0.960661	−	0.282076i
$616$	−23.6756	−	9.80128i	−0.953918	−	0.394905i
$617$	2.83232	−	9.64601i	0.114025	−	0.388334i	−0.882629	−	0.470070i	$-0.844228\pi$
$617$	2.83232	−	9.64601i	0.114025	−	0.388334i	0.996654	+	0.0817367i	$0.0260467\pi$
$618$	−0.732412	−	12.2813i	−0.0294619	−	0.494027i
$619$	−33.9420	−	4.88013i	−1.36425	−	0.196149i	−0.578997	−	0.815330i	$-0.696556\pi$
$619$	−33.9420	−	4.88013i	−1.36425	−	0.196149i	−0.785248	+	0.619181i	$0.787465\pi$
$620$	−4.93883	+	5.43433i	−0.198348	+	0.218248i
$621$	24.6312	−	16.3584i	0.988417	−	0.656440i
$622$	−5.99520	+	15.5106i	−0.240386	+	0.621920i
$623$	13.6909	+	1.96845i	0.548513	+	0.0788642i
$624$	−5.41081	−	9.36609i	−0.216606	−	0.374944i
$625$	5.10804	+	1.49986i	0.204322	+	0.0599942i
$626$	−7.27192	+	2.61469i	−0.290645	+	0.104504i
$627$	14.1650	−	4.15921i	0.565695	−	0.166103i
$628$	2.67563	+	9.98032i	0.106769	+	0.398258i
$629$	32.8968	+	15.0235i	1.31168	+	0.599025i
$630$	50.5709	−	26.8419i	2.01479	−	1.06941i
$631$	22.0076	−	14.1434i	0.876109	−	0.563041i	−0.0235068	−	0.999724i	$-0.507483\pi$
$631$	22.0076	−	14.1434i	0.876109	−	0.563041i	0.899616	+	0.436683i	$0.143847\pi$
$632$	18.0898	−	12.5653i	0.719575	−	0.499820i
$633$	−8.40167	−	58.4349i	−0.333936	−	2.32258i
$634$	−0.285038	−	1.38925i	−0.0113203	−	0.0551741i
$635$	8.66939	+	7.51207i	0.344034	+	0.298107i
$636$	−18.9383	+	8.11282i	−0.750954	+	0.321694i
$637$	9.50760	−	14.7941i	0.376705	−	0.586164i
$638$	16.8240	+	1.40357i	0.666068	+	0.0555678i
$639$	8.13018	−	7.04484i	0.321625	−	0.278690i
$640$	−16.9014	+	4.75339i	−0.668085	+	0.187894i
$641$	−13.6583	+	6.23754i	−0.539471	+	0.246368i	−0.666466	−	0.745535i	$-0.732194\pi$
$641$	−13.6583	+	6.23754i	−0.539471	+	0.246368i	0.126995	+	0.991903i	$0.459467\pi$
$642$	18.8541	+	10.5867i	0.744113	+	0.417823i
$643$		−	35.7644i		−	1.41041i	−0.709003	−	0.705205i	$-0.750855\pi$
$643$		−	35.7644i		−	1.41041i	0.709003	−	0.705205i	$-0.249145\pi$
$644$	−36.3839	−	32.0801i	−1.43373	−	1.26413i
$645$			29.1498i			1.14777i
$646$	11.8732	−	21.1453i	0.467144	−	0.831951i
$647$	−1.09000	+	0.497786i	−0.0428523	+	0.0195700i	−0.436726	−	0.899595i	$-0.643862\pi$
$647$	−1.09000	+	0.497786i	−0.0428523	+	0.0195700i	0.393874	+	0.919165i	$0.371135\pi$
$648$	1.07330	+	5.94217i	0.0421631	+	0.233430i
$649$	4.08698	−	3.54139i	0.160428	−	0.139012i
$650$	−0.288497	+	3.45809i	−0.0113158	+	0.135637i
$651$	18.4773	−	28.7512i	0.724182	−	1.12685i
$652$	28.2644	−	12.1079i	1.10692	−	0.474183i
$653$	−10.6665	−	9.24256i	−0.417412	−	0.361689i	0.420689	−	0.907205i	$-0.361788\pi$
$653$	−10.6665	−	9.24256i	−0.417412	−	0.361689i	−0.838101	+	0.545516i	$0.816334\pi$
$654$	45.9542	−	9.42860i	1.79695	−	0.368687i
$655$	2.68041	+	18.6427i	0.104732	+	0.728429i
$656$	21.7734	−	5.28826i	0.850110	−	0.206472i
$657$	9.29816	−	5.97556i	0.362756	−	0.233129i
$658$	14.2899	+	26.9225i	0.557076	+	1.04955i
$659$	−11.2336	−	5.13020i	−0.437598	−	0.199844i	0.184420	−	0.982848i	$-0.440959\pi$
$659$	−11.2336	−	5.13020i	−0.437598	−	0.199844i	−0.622017	+	0.783003i	$0.713687\pi$
$660$	15.3394	−	4.11234i	0.597084	−	0.160073i
$661$	−19.0983	+	5.60776i	−0.742836	+	0.218116i	−0.631186	−	0.775631i	$-0.717432\pi$
$661$	−19.0983	+	5.60776i	−0.742836	+	0.218116i	−0.111650	+	0.993748i	$0.535614\pi$
$662$	0.0495321	+	0.137758i	0.00192512	+	0.00535411i
$663$	15.4210	+	4.52802i	0.598903	+	0.175854i
$664$	−17.6843	−	14.2451i	−0.686283	−	0.552818i
$665$	22.4123	+	3.22240i	0.869111	+	0.124959i
$666$	−41.4054	−	16.0041i	−1.60443	−	0.620145i
$667$	29.2670	+	12.8371i	1.13322	+	0.497056i
$668$	32.4037	−	35.6548i	1.25374	−	1.37952i
$669$	−47.5453	−	6.83599i	−1.83821	−	0.264295i
$670$	−23.1180	+	1.37867i	−0.893125	+	0.0532627i
$671$	2.76945	−	9.43188i	0.106913	−	0.364114i
$672$	73.9080	−	34.8512i	2.85106	−	1.34442i
$673$	−12.3190	+	3.61717i	−0.474861	+	0.139432i	−0.510401	−	0.859937i	$-0.670503\pi$
$673$	−12.3190	+	3.61717i	−0.474861	+	0.139432i	0.0355402	+	0.999368i	$0.488685\pi$
$674$	4.10420	−	2.99724i	0.158088	−	0.115449i
$675$	6.63814	−	14.5355i	0.255502	−	0.559472i
$676$	−24.0358	+	2.87705i	−0.924454	+	0.110656i
$677$	−10.7903	+	6.93450i	−0.414704	+	0.266514i	−0.731313	−	0.682042i	$-0.761092\pi$
$677$	−10.7903	+	6.93450i	−0.414704	+	0.266514i	0.316609	+	0.948556i	$0.397456\pi$
$678$	−22.6898	−	5.21781i	−0.871395	−	0.200389i
$679$	3.64284	−	0.523762i	0.139799	−	0.0201001i
$680$	13.3071	−	22.4381i	0.510306	−	0.860462i
$681$	19.6107	+	16.9928i	0.751484	+	0.651165i
$682$	4.28834	−	4.18802i	0.164209	−	0.160368i
$683$	40.3338	+	25.9210i	1.54333	+	0.991838i	0.986971	+	0.160897i	$0.0514386\pi$
$683$	40.3338	+	25.9210i	1.54333	+	0.991838i	0.556359	+	0.830942i	$0.312198\pi$
$684$	−13.0028	+	26.7764i	−0.497174	+	1.02382i
$685$	8.87234	−	7.68793i	0.338995	−	0.293741i
$686$	65.6815	+	50.3923i	2.50773	+	1.92399i
$687$	7.09084	+	15.5268i	0.270532	+	0.592383i
$688$	−1.24473	+	26.2758i	−0.0474548	+	1.00175i
$689$		−	3.41444i		−	0.130080i
$690$	29.9931	+	2.04828i	1.14182	+	0.0779768i
$691$	16.9423			0.644515			0.322258	−	0.946652i	$-0.395558\pi$
$691$	16.9423			0.644515			0.322258	+	0.946652i	$0.395558\pi$
$692$	−30.4738	−	36.8981i	−1.15844	−	1.40265i
$693$	−42.5106	+	19.4140i	−1.61485	+	0.737475i
$694$	−11.3086	−	8.67622i	−0.429269	−	0.329345i
$695$	0.120690	+	0.139284i	0.00457804	+	0.00528335i
$696$	−39.3952	+	36.6928i	−1.49327	+	1.39084i
$697$	−17.9994	+	28.0077i	−0.681777	+	1.06087i
$698$	12.1941	+	12.4862i	0.461553	+	0.472608i
$699$	−23.9530	+	27.6432i	−0.905986	+	1.04556i
$700$	−25.8520	−	4.34372i	−0.977113	−	0.164177i
$701$	−6.72785	−	46.7932i	−0.254107	−	1.76735i	−0.572992	−	0.819561i	$-0.694217\pi$
$701$	−6.72785	−	46.7932i	−0.254107	−	1.76735i	0.318885	−	0.947793i	$-0.396692\pi$
$702$	−8.04484	−	1.85002i	−0.303633	−	0.0698245i
$703$	−9.49143	−	14.7690i	−0.357976	−	0.557022i
$704$	14.0026	−	3.05188i	0.527742	−	0.115022i
$705$	−17.1833	−	7.84736i	−0.647162	−	0.295549i
$706$	−10.6032	−	14.5193i	−0.399057	−	0.546440i
$707$	−9.37504	−	31.9285i	−0.352585	−	1.20079i
$708$	−0.408121	+	17.2402i	−0.0153381	+	0.647928i
$709$	21.7974	+	6.40031i	0.818620	+	0.240369i	0.664122	−	0.747625i	$-0.268806\pi$
$709$	21.7974	+	6.40031i	0.818620	+	0.240369i	0.154498	+	0.987993i	$0.450624\pi$
$710$	4.56864	−	0.272457i	0.171458	−	0.0102251i
$711$	5.71689	−	39.7618i	0.214400	−	1.49119i
$712$	−6.91693	+	3.46408i	−0.259223	+	0.129822i
$713$	10.2494	−	4.86846i	0.383844	−	0.182325i
$714$	−43.7730	+	113.249i	−1.63816	+	4.23822i
$715$	−0.374560	+	2.60512i	−0.0140077	+	0.0974260i
$716$	−0.679170	+	2.12559i	−0.0253818	+	0.0794372i
$717$	−12.0193	+	40.9339i	−0.448868	+	1.52870i
$718$	8.82377	+	24.5405i	0.329300	+	0.915845i
$719$	11.8548	+	40.3738i	0.442110	+	1.50569i	0.815910	+	0.578179i	$0.196236\pi$
$719$	11.8548	+	40.3738i	0.442110	+	1.50569i	−0.373800	+	0.927509i	$0.621945\pi$
$720$	−14.6653	+	28.4652i	−0.546544	+	1.06083i
$721$	−6.39863	+	14.0110i	−0.238297	+	0.521798i
$722$	13.3357	−	7.07830i	0.496305	−	0.263427i
$723$	−8.58788	−	13.3630i	−0.319387	−	0.496976i
$724$	−5.40288	+	7.98502i	−0.200797	+	0.296761i
$725$	17.0954	−	2.45795i	0.634909	−	0.0912861i
$726$	30.8284	−	6.32519i	1.14415	−	0.234750i
$727$	5.67584	−	6.55027i	0.210505	−	0.242936i	−0.640672	−	0.767815i	$-0.721344\pi$
$727$	5.67584	−	6.55027i	0.210505	−	0.242936i	0.851177	+	0.524879i	$0.175889\pi$
$728$	0.486021	+	13.5333i	0.0180131	+	0.501576i
$729$	−35.1801	−	22.6089i	−1.30297	−	0.837365i
$730$	4.68598	+	0.390935i	0.173436	+	0.0144692i
$731$	−25.5958	−	29.5391i	−0.946695	−	1.09254i
$732$	16.3187	+	26.7645i	0.603155	+	0.989244i
$733$	5.47637	+	11.9916i	0.202274	+	0.442919i	0.983399	−	0.181456i	$-0.0580810\pi$
$733$	5.47637	+	11.9916i	0.202274	+	0.442919i	−0.781125	+	0.624375i	$0.785354\pi$
$734$	22.3047	−	39.7232i	0.823283	−	1.46621i
$735$	−82.3356			−3.03699
$736$	26.9485	+	3.12707i	0.993335	+	0.115265i
$737$	18.9040			0.696338
$738$	20.0077	−	35.6323i	0.736493	−	1.31164i
$739$	12.4623	+	27.2886i	0.458432	+	1.00383i	0.987842	+	0.155461i	$0.0496862\pi$
$739$	12.4623	+	27.2886i	0.458432	+	1.00383i	−0.529410	+	0.848366i	$0.677587\pi$
$740$	−9.83141	−	16.1247i	−0.361410	−	0.592754i
$741$	−5.10922	−	5.89636i	−0.187692	−	0.216608i
$742$	25.7046	+	2.14445i	0.943644	+	0.0787251i
$743$	−13.1475	−	8.44939i	−0.482335	−	0.309978i	0.276781	−	0.960933i	$-0.410732\pi$
$743$	−13.1475	−	8.44939i	−0.482335	−	0.309978i	−0.759116	+	0.650955i	$0.774369\pi$
$744$	0.686021	+	19.1023i	0.0251507	+	0.700323i
$745$	0.414660	−	0.478544i	0.0151920	−	0.0175325i
$746$	−40.6175	+	8.33364i	−1.48711	+	0.305116i
$747$	−40.9938	+	5.89402i	−1.49989	+	0.215651i
$748$	−11.9333	+	17.6364i	−0.436324	+	0.644852i
$749$	−14.6357	−	22.7736i	−0.534778	−	0.832130i
$750$	42.0354	−	22.3114i	1.53492	−	0.814698i
$751$	16.9947	−	37.2132i	0.620145	−	1.35793i	−0.295270	−	0.955414i	$-0.595409\pi$
$751$	16.9947	−	37.2132i	0.620145	−	1.35793i	0.915414	−	0.402513i	$-0.131863\pi$
$752$	−15.1540	−	7.80740i	−0.552611	−	0.284707i
$753$	23.7467	+	80.8737i	0.865376	+	2.94720i
$754$	−3.01881	−	8.39586i	−0.109938	−	0.305759i
$755$	8.76303	−	29.8441i	0.318919	−	1.08614i
$756$	18.9799	−	59.4012i	0.690292	−	2.16040i
$757$	2.54318	−	17.6882i	0.0924336	−	0.642890i	−0.889956	−	0.456046i	$-0.849265\pi$
$757$	2.54318	−	17.6882i	0.0924336	−	0.642890i	0.982390	−	0.186844i	$-0.0598257\pi$
$758$	3.52946	−	9.13134i	0.128196	−	0.331665i
$759$	−24.3395	−	3.12644i	−0.883469	−	0.113483i
$760$	−11.3232	+	5.67078i	−0.410735	+	0.205701i
$761$	−3.72667	+	25.9195i	−0.135092	+	0.939583i	0.803685	+	0.595055i	$0.202870\pi$
$761$	−3.72667	+	25.9195i	−0.135092	+	0.939583i	−0.938776	+	0.344527i	$0.888039\pi$
$762$	29.8067	−	1.77756i	1.07978	−	0.0643942i
$763$	−56.3520	−	16.5465i	−2.04008	−	0.599022i
$764$	−0.954079	+	40.3032i	−0.0345174	+	1.45812i
$765$	−13.4044	−	45.6513i	−0.484638	−	1.65052i
$766$	5.05242	+	6.91842i	0.182552	+	0.249973i
$767$	−2.59969	−	1.18724i	−0.0938695	−	0.0428688i
$768$	−22.8296	+	39.5903i	−0.823794	+	1.42859i
$769$	−25.1988	−	39.2101i	−0.908692	−	1.41395i	−0.910298	−	0.413953i	$-0.864148\pi$
$769$	−25.1988	−	39.2101i	−0.908692	−	1.41395i	0.00160673	−	0.999999i	$-0.499489\pi$
$770$	−19.3766	−	4.45591i	−0.698285	−	0.160580i
$771$	7.60986	+	52.9277i	0.274062	+	1.90615i
$772$	46.7717	+	7.85871i	1.68335	+	0.282841i
$773$	8.58697	−	9.90989i	0.308852	−	0.356434i	−0.580010	−	0.814609i	$-0.696951\pi$
$773$	8.58697	−	9.90989i	0.308852	−	0.356434i	0.888862	+	0.458175i	$0.151497\pi$
$774$	33.5203	+	34.3232i	1.20486	+	1.23372i
$775$	3.31530	−	5.15870i	0.119089	−	0.185306i
$776$	−1.50622	+	1.40289i	−0.0540700	+	0.0503609i
$777$	57.5593	+	66.4270i	2.06493	+	2.38305i
$778$	−10.2710	−	7.88013i	−0.368233	−	0.282516i
$779$	14.7011	−	6.71378i	0.526722	−	0.240546i
$780$	−5.34452	−	6.47121i	−0.191364	−	0.231707i
$781$	−3.73587			−0.133680
$782$	−32.1923	+	24.2607i	−1.15119	+	0.867560i
$783$			41.0855i			1.46828i
$784$	−74.2177	−	3.51582i	−2.65063	−	0.125565i
$785$	3.33055	+	7.29288i	0.118872	+	0.260294i
$786$	38.8968	+	29.8425i	1.38740	+	1.06445i
$787$	−14.4910	+	12.5565i	−0.516547	+	0.447591i	−0.873707	−	0.486453i	$-0.838291\pi$
$787$	−14.4910	+	12.5565i	−0.516547	+	0.447591i	0.357160	+	0.934043i	$0.383745\pi$
$788$	12.0148	−	24.7417i	0.428008	−	0.881388i
$789$	14.4190	+	9.26654i	0.513331	+	0.329898i
$790$	12.2267	−	11.9407i	0.435007	−	0.424831i
$791$	22.0286	+	19.0879i	0.783246	+	0.678687i
$792$	13.3328	−	22.4814i	0.473762	−	0.798842i
$793$	−5.14215	+	0.739330i	−0.182603	+	0.0262544i
$794$	−27.1829	−	6.25108i	−0.964686	−	0.221843i
$795$	−13.4484	+	8.64279i	−0.476967	+	0.306528i
$796$	−22.4729	+	2.68997i	−0.796530	+	0.0953433i
$797$	−17.1629	+	37.5815i	−0.607941	+	1.33120i	0.316033	+	0.948748i	$0.397649\pi$
$797$	−17.1629	+	37.5815i	−0.607941	+	1.33120i	−0.923974	+	0.382456i	$0.875078\pi$
$798$	47.5978	−	34.7600i	1.68494	−	1.23049i
$799$	24.3034	−	7.13613i	0.859793	−	0.252458i
$800$	13.2610	−	6.25319i	0.468846	−	0.221084i
$801$	−3.97491	+	13.5373i	−0.140447	+	0.478317i
$802$	0.0700032	−	0.00417473i	0.00247190	−	0.000147415i
$803$	−3.79924	−	0.546248i	−0.134072	−	0.0192767i
$804$	−40.5440	+	44.6118i	−1.42988	+	1.57334i
$805$	−31.9653	−	19.8696i	−1.12663	−	0.700313i
$806$	−2.95475	−	1.14208i	−0.104077	−	0.0402279i
$807$	40.7520	+	5.85925i	1.43454	+	0.206255i
$808$	14.4937	+	11.6750i	0.509885	+	0.410725i
$809$	33.4662	+	9.82656i	1.17661	+	0.345483i	0.810866	−	0.585233i	$-0.198997\pi$
$809$	33.4662	+	9.82656i	1.17661	+	0.345483i	0.365743	+	0.930716i	$0.380815\pi$
$810$	1.58527	+	4.40892i	0.0557006	+	0.154914i
$811$	14.0562	−	4.12727i	0.493579	−	0.144928i	−0.0254643	−	0.999676i	$-0.508106\pi$
$811$	14.0562	−	4.12727i	0.493579	−	0.144928i	0.519044	+	0.854748i	$0.326288\pi$
$812$	65.1017	−	17.4531i	2.28462	−	0.612485i
$813$	51.2480	+	23.4042i	1.79735	+	0.820821i
$814$	7.22730	+	13.6165i	0.253317	+	0.477257i
$815$	20.0710	−	12.8989i	0.703058	−	0.451828i
$816$	−16.0267	−	65.9869i	−0.561046	−	2.31000i
$817$	2.70025	+	18.7807i	0.0944699	+	0.657053i
$818$	21.1153	−	4.33231i	0.738280	−	0.151476i
$819$	18.6656	+	16.1738i	0.652229	+	0.565159i
$820$	15.9810	−	6.84596i	0.558081	−	0.239071i
$821$	−19.8827	+	30.9380i	−0.693910	+	1.07975i	0.298216	+	0.954499i	$0.403609\pi$
$821$	−19.8827	+	30.9380i	−0.693910	+	1.07975i	−0.992126	+	0.125247i	$0.960028\pi$
$822$	2.54058	−	30.4528i	0.0886129	−	1.06217i
$823$	20.5637	−	17.8186i	0.716806	−	0.621116i	−0.218135	−	0.975919i	$-0.569997\pi$
$823$	20.5637	−	17.8186i	0.716806	−	0.621116i	0.934941	+	0.354802i	$0.115452\pi$
$824$	−1.53124	−	8.47751i	−0.0533434	−	0.295328i
$825$	−12.0633	+	5.50914i	−0.419991	+	0.191804i
$826$	10.5705	−	18.8254i	0.367796	−	0.655018i
$827$		−	51.2196i		−	1.78108i	−0.454903	−	0.890541i	$-0.650326\pi$
$827$		−	51.2196i		−	1.78108i	0.454903	−	0.890541i	$-0.349674\pi$
$828$	37.6716	−	32.0783i	1.30918	−	1.11480i
$829$		−	28.0969i		−	0.975846i	−0.872887	−	0.487923i	$-0.837755\pi$
$829$		−	28.0969i		−	0.975846i	0.872887	−	0.487923i	$-0.162245\pi$
$830$	−15.3634	−	8.62662i	−0.533272	−	0.299434i
$831$	−67.5497	+	30.8489i	−2.34327	+	1.07014i
$832$	−4.54125	−	6.06140i	−0.157439	−	0.210141i
$833$	83.4353	−	72.2971i	2.89086	−	2.50494i
$834$	0.478070	+	0.0398837i	0.0165542	+	0.00138106i
$835$	20.2110	−	31.4490i	0.699431	−	1.08834i
$836$	9.50193	−	4.07045i	0.328631	−	0.140779i
$837$	11.0244	+	9.55273i	0.381060	+	0.330191i
$838$	−8.05116	−	39.2407i	−0.278123	−	1.35555i
$839$	−1.77813	−	12.3672i	−0.0613878	−	0.426962i	−0.997220	−	0.0745153i	$-0.976259\pi$
$839$	−1.77813	−	12.3672i	−0.0613878	−	0.426962i	0.935832	−	0.352446i	$-0.114650\pi$
$840$	52.0732	−	36.1703i	1.79670	−	1.24799i
$841$	−12.9609	+	8.32945i	−0.446927	+	0.287222i
$842$	−43.5676	+	23.1247i	−1.50144	+	0.796929i
$843$	24.8872	+	11.3656i	0.857161	+	0.391452i
$844$	−10.7041	−	39.9271i	−0.368449	−	1.37435i
$845$	−18.0222	+	5.29179i	−0.619981	+	0.182043i
$846$	−29.2569	+	10.5196i	−1.00587	+	0.361671i
$847$	−37.8038	−	11.1002i	−1.29895	−	0.381408i
$848$	−12.4915	+	7.21639i	−0.428961	+	0.247812i
$849$	−65.0110	−	9.34718i	−2.23117	−	0.320794i
$850$	−7.85399	+	20.3197i	−0.269390	+	0.696959i
$851$	4.58720	+	28.8192i	0.157247	+	0.987909i
$852$	8.01244	−	8.81632i	0.274502	−	0.302042i
$853$	44.0942	+	6.33980i	1.50976	+	0.217070i	0.846931	−	0.531702i	$-0.178447\pi$
$853$	44.0942	+	6.33980i	1.50976	+	0.217070i	0.662827	+	0.748773i	$0.269357\pi$
$854$	−2.33628	−	39.1755i	−0.0799459	−	1.34056i
$855$	−6.50703	+	22.1609i	−0.222536	+	0.757887i
$856$	13.9892	+	5.79126i	0.478139	+	0.197941i
$857$	−27.7333	+	8.14322i	−0.947350	+	0.278167i	−0.718683	−	0.695338i	$-0.755255\pi$
$857$	−27.7333	+	8.14322i	−0.947350	+	0.278167i	−0.228667	+	0.973505i	$0.573437\pi$
$858$	4.04038	+	5.53259i	0.137936	+	0.188880i
$859$	−10.7736	+	23.5909i	−0.367591	+	0.804911i	0.631962	+	0.775000i	$0.282250\pi$
$859$	−10.7736	+	23.5909i	−0.367591	+	0.804911i	−0.999553	+	0.0299119i	$0.990477\pi$
$860$	2.42582	+	20.2661i	0.0827198	+	0.691069i
$861$	−68.0700	+	43.7459i	−2.31982	+	1.49086i
$862$	2.86735	−	12.4687i	0.0976625	−	0.424687i
$863$	18.7725	−	2.69908i	0.639023	−	0.0918776i	0.184815	−	0.982773i	$-0.440831\pi$
$863$	18.7725	−	2.69908i	0.639023	−	0.0918776i	0.454208	+	0.890896i	$0.349922\pi$
$864$	10.2345	+	33.3416i	0.348185	+	1.13431i
$865$	−28.0624	−	24.3162i	−0.954149	−	0.826775i
$866$	−30.3073	−	31.0332i	−1.02988	−	1.05455i
$867$	44.0314	+	28.2973i	1.49539	+	0.961026i
$868$	10.4535	−	21.5267i	0.354815	−	0.730663i
$869$	−10.5428	+	9.13541i	−0.357641	+	0.309898i
$870$	−25.4274	+	33.1422i	−0.862070	+	1.12362i
$871$	−4.15019	−	9.08765i	−0.140624	−	0.307923i
$872$	31.1646	−	10.3794i	1.05537	−	0.351491i
$873$			3.75405i			0.127055i
$874$	19.5138	−	1.45870i	0.660063	−	0.0493414i
$875$	−59.5801			−2.01417
$876$	9.43744	−	7.79430i	0.318862	−	0.263345i
$877$	−13.4336	+	6.13494i	−0.453622	+	0.207162i	−0.629105	−	0.777320i	$-0.716578\pi$
$877$	−13.4336	+	6.13494i	−0.453622	+	0.207162i	0.175483	+	0.984482i	$0.443851\pi$
$878$	−13.4832	+	17.5740i	−0.455036	+	0.593095i
$879$	9.57812	+	11.0537i	0.323062	+	0.372834i
$880$	10.3223	−	4.13559i	0.347965	−	0.139411i
$881$	5.64865	−	8.78948i	0.190308	−	0.296125i	−0.732967	−	0.680264i	$-0.761865\pi$
$881$	5.64865	−	8.78948i	0.190308	−	0.296125i	0.923275	+	0.384139i	$0.125502\pi$
$882$	−96.9482	+	94.6803i	−3.26442	+	3.18805i
$883$	19.5356	−	22.5453i	0.657427	−	0.758711i	−0.324928	−	0.945739i	$-0.605340\pi$
$883$	19.5356	−	22.5453i	0.657427	−	0.758711i	0.982355	+	0.187028i	$0.0598854\pi$
$884$	11.0981	+	1.86474i	0.373270	+	0.0627179i
$885$	1.90429	+	13.2446i	0.0640119	+	0.445213i
$886$	0.608732	−	2.64708i	0.0204507	−	0.0889305i
$887$	2.24655	+	3.49570i	0.0754317	+	0.117374i	0.876920	−	0.480637i	$-0.159594\pi$
$887$	2.24655	+	3.49570i	0.0754317	+	0.117374i	−0.801488	+	0.598011i	$0.795958\pi$
$888$	−47.6343	−	12.1479i	−1.59850	−	0.407656i
$889$	−34.0047	−	15.5294i	−1.14048	−	0.520840i
$890$	−4.84742	+	3.54000i	−0.162486	+	0.118661i
$891$	−1.07747	−	3.66952i	−0.0360965	−	0.122933i
$892$	−33.6243	−	0.795974i	−1.12583	−	0.0266512i
$893$	−11.7978	−	3.46416i	−0.394799	−	0.115924i
$894$	−0.0981199	−	1.64530i	−0.00328162	−	0.0550272i
$895$	−0.246409	+	1.71381i	−0.00823655	+	0.0572865i
$896$	48.4835	−	30.3805i	1.61972	−	1.01494i
$897$	3.84054	+	12.3870i	0.128232	+	0.413591i
$898$	−6.26185	−	2.42034i	−0.208961	−	0.0807678i
$899$	−2.24382	+	15.6061i	−0.0748356	+	0.520493i
$900$	8.13851	−	25.4710i	0.271284	−	0.849035i
$901$	6.03901	−	20.5670i	0.201189	−	0.685186i
$902$	−13.3543	+	4.80167i	−0.444651	+	0.159878i
$903$	−26.7630	−	91.1465i	−0.890618	−	3.03317i
$904$	−16.2090	−	1.73941i	−0.539105	−	0.0578520i
$905$	−3.10762	+	6.80474i	−0.103301	+	0.226197i
$906$	−37.9582	−	71.5144i	−1.26108	−	2.37591i
$907$	18.8527	+	29.3354i	0.625994	+	0.974066i	0.998932	+	0.0462092i	$0.0147141\pi$
$907$	18.8527	+	29.3354i	0.625994	+	0.974066i	−0.372938	+	0.927856i	$0.621650\pi$
$908$	15.0483	+	10.1821i	0.499395	+	0.337904i
$909$	33.5977	−	4.83062i	1.11437	−	0.160222i
$910$	2.11187	+	10.2931i	0.0700079	+	0.341213i
$911$	−3.03578	+	3.50347i	−0.100580	+	0.116075i	−0.803808	−	0.594889i	$-0.797196\pi$
$911$	−3.03578	+	3.50347i	−0.100580	+	0.116075i	0.703228	+	0.710964i	$0.251741\pi$
$912$	−10.7732	+	31.1537i	−0.356737	+	1.03160i
$913$	12.0992	+	7.77571i	0.400427	+	0.257339i
$914$	4.45184	−	53.3623i	0.147254	−	1.76507i
$915$	15.9281	+	18.3820i	0.526565	+	0.607689i
$916$	6.22196	+	10.2047i	0.205579	+	0.337174i
$917$	−25.4974	−	55.8315i	−0.841998	−	1.84372i
$918$	−45.1863	−	25.3723i	−1.49137	−	0.837411i
$919$	9.64342			0.318107			0.159054	−	0.987270i	$-0.449156\pi$
$919$	9.64342			0.318107			0.159054	+	0.987270i	$0.449156\pi$
$920$	21.0229	−	1.07195i	0.693104	−	0.0353412i
$921$	37.6167			1.23951
$922$	32.1117	+	18.0309i	1.05754	+	0.593815i
$923$	0.820174	+	1.79593i	0.0269963	+	0.0591137i
$924$	−44.1880	+	26.9420i	−1.45368	+	0.886326i
$925$	10.3276	+	11.9187i	0.339569	+	0.391884i
$926$	2.39336	−	28.6882i	0.0786506	−	0.942752i
$927$	−13.2175	−	8.49434i	−0.434118	−	0.278991i
$928$	−24.3356	+	28.7887i	−0.798855	+	0.945036i
$929$	−20.5715	+	23.7408i	−0.674930	+	0.778910i	−0.985139	−	0.171758i	$-0.945055\pi$
$929$	−20.5715	+	23.7408i	−0.674930	+	0.778910i	0.310210	+	0.950668i	$0.399601\pi$
$930$	2.98092	+	14.5287i	0.0977482	+	0.476416i
$931$	−53.0473	+	7.62705i	−1.73855	+	0.249966i
$932$	−14.3526	+	21.2120i	−0.470136	+	0.694823i
$933$	18.1579	+	28.2542i	0.594462	+	0.925001i
$934$	24.4137	+	45.9961i	0.798839	+	1.50504i
$935$	−6.86377	+	15.0296i	−0.224469	+	0.491519i
$936$	−13.7345	−	1.47386i	−0.448926	−	0.0481748i
$937$	−3.56682	−	12.1475i	−0.116523	−	0.396840i	0.880491	−	0.474063i	$-0.157213\pi$
$937$	−3.56682	−	12.1475i	−0.116523	−	0.396840i	−0.997014	+	0.0772224i	$0.975395\pi$
$938$	71.0202	−	25.5359i	2.31889	−	0.833778i
$939$	−4.39723	+	14.9756i	−0.143498	+	0.488709i
$940$	−12.5996	−	4.02582i	−0.410953	−	0.131308i
$941$	−4.53269	+	31.5255i	−0.147761	+	1.02770i	0.772112	+	0.635487i	$0.219201\pi$
$941$	−4.53269	+	31.5255i	−0.147761	+	1.02770i	−0.919873	+	0.392216i	$0.871708\pi$
$942$	19.4658	+	7.52394i	0.634229	+	0.245143i
$943$	−26.8613	+	0.404241i	−0.874725	+	0.0131639i
$944$	1.15097	+	12.0201i	0.0374610	+	0.391220i
$945$	6.88608	−	47.8937i	0.224004	−	1.55798i
$946$	−0.991821	−	16.6312i	−0.0322469	−	0.540725i
$947$	−14.9139	−	4.37912i	−0.484637	−	0.142302i	0.0302813	−	0.999541i	$-0.490360\pi$
$947$	−14.9139	−	4.37912i	−0.484637	−	0.142302i	−0.514919	+	0.857239i	$0.672178\pi$
$948$	1.05279	−	44.4731i	0.0341931	−	1.44442i
$949$	0.571490	+	1.94632i	0.0185513	+	0.0631801i
$950$	8.54025	−	6.23683i	0.277082	−	0.202349i
$951$	−2.60550	−	1.18989i	−0.0844891	−	0.0385849i
$952$	−21.0083	+	82.3777i	−0.680883	+	2.66988i
$953$	−10.5180	−	16.3663i	−0.340712	−	0.530158i	0.628043	−	0.778179i	$-0.283856\pi$
$953$	−10.5180	−	16.3663i	−0.340712	−	0.530158i	−0.968755	+	0.248021i	$0.920220\pi$
$954$	−5.89660	+	25.6415i	−0.190909	+	0.830173i
$955$	4.45172	+	30.9624i	0.144054	+	1.00192i
$956$	−4.94980	+	29.4591i	−0.160088	+	0.952775i
$957$	22.3293	−	25.7694i	0.721803	−	0.833005i
$958$	−8.86966	+	8.66217i	−0.286566	+	0.279862i
$959$	−20.6839	+	32.1847i	−0.667917	+	1.03930i
$960$	−12.3790	+	33.2295i	−0.399530	+	1.07248i
$961$	−16.6348	−	19.1976i	−0.536607	−	0.619277i
$962$	4.95911	−	6.46371i	0.159888	−	0.208399i
$963$	25.1181	−	11.4711i	0.809421	−	0.369650i
$964$	−7.08270	−	8.57582i	−0.228118	−	0.276209i
$965$	36.7999			1.18463
$966$	−95.6640	+	21.1327i	−3.07794	+	0.679933i
$967$			52.0426i			1.67358i	0.547527	+	0.836788i	$0.315569\pi$
$967$			52.0426i			1.67358i	−0.547527	+	0.836788i	$0.684431\pi$
$968$	20.9068	−	6.96303i	0.671969	−	0.223800i
$969$	−20.3469	−	44.5534i	−0.653636	−	1.43126i
$970$	−0.972178	+	1.26714i	−0.0312148	+	0.0406854i
$971$	−14.6900	+	12.7290i	−0.471426	+	0.408493i	−0.857907	−	0.513804i	$-0.828236\pi$
$971$	−14.6900	+	12.7290i	−0.471426	+	0.408493i	0.386482	+	0.922297i	$0.373690\pi$
$972$	−22.3060	−	10.8320i	−0.715467	−	0.347436i
$973$	−0.505258	−	0.324709i	−0.0161978	−	0.0104097i
$974$	15.4839	+	15.8547i	0.496135	+	0.508019i
$975$	5.29677	+	4.58968i	0.169632	+	0.146987i
$976$	13.5727	+	17.2497i	0.434452	+	0.552150i
$977$	14.2751	−	2.05245i	0.456700	−	0.0656636i	0.0898742	−	0.995953i	$-0.471354\pi$
$977$	14.2751	−	2.05245i	0.456700	−	0.0656636i	0.366826	+	0.930290i	$0.380444\pi$
$978$	13.9183	−	60.5239i	0.445057	−	1.93534i
$979$	4.12180	−	2.64892i	0.131733	−	0.0846599i
$980$	−57.2430	+	6.85189i	−1.82856	+	0.218876i
$981$	24.8867	−	54.4942i	0.794570	−	1.73987i
$982$	21.4394	+	29.3575i	0.684157	+	0.936835i
$983$	−13.5418	+	3.97623i	−0.431916	+	0.126822i	−0.490462	−	0.871463i	$-0.663172\pi$
$983$	−13.5418	+	3.97623i	−0.431916	+	0.126822i	0.0585456	+	0.998285i	$0.481354\pi$
$984$	17.3100	−	41.8133i	0.551821	−	1.33296i
$985$	6.01258	−	20.4770i	0.191577	−	0.652451i
$986$	−3.33439	−	55.9120i	−0.106189	−	1.78060i
$987$	60.9342	+	8.76101i	1.93956	+	0.278866i
$988$	−4.04283	−	3.67420i	−0.128619	−	0.116892i
$989$	8.42917	−	30.3916i	0.268032	−	0.966397i
$990$	7.31177	−	18.9169i	0.232383	−	0.601217i
$991$	−48.2699	−	6.94017i	−1.53334	−	0.220462i	−0.676657	−	0.736298i	$-0.736572\pi$
$991$	−48.2699	−	6.94017i	−1.53334	−	0.220462i	−0.856687	+	0.515836i	$0.827481\pi$
$992$	2.06662	+	13.2236i	0.0656153	+	0.419849i
$993$	0.283694	+	0.0833002i	0.00900277	+	0.00264345i
$994$	−14.0352	+	5.04649i	−0.445170	+	0.160065i
$995$	−16.8503	+	4.94769i	−0.534189	+	0.156852i
$996$	−44.2996	+	11.8763i	−1.40369	+	0.376315i
$997$	−43.6622	−	19.9399i	−1.38280	−	0.631502i	−0.421452	−	0.906851i	$-0.638479\pi$
$997$	−43.6622	−	19.9399i	−1.38280	−	0.631502i	−0.961344	+	0.275349i	$0.911207\pi$
$998$	−7.55187	+	4.00836i	−0.239050	+	0.126882i
$999$	−31.5604	+	20.2826i	−0.998527	+	0.641714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.2.j.a.107.15	yes	220
4.3	odd	2		736.2.r.a.15.21		220
8.3	odd	2	inner	184.2.j.a.107.10	yes	220
8.5	even	2		736.2.r.a.15.22		220
23.20	odd	22	inner	184.2.j.a.43.10	✓	220
92.43	even	22		736.2.r.a.687.22		220
184.43	even	22	inner	184.2.j.a.43.15	yes	220
184.181	odd	22		736.2.r.a.687.21		220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.j.a.43.10	✓	220	23.20	odd	22	inner
184.2.j.a.43.15	yes	220	184.43	even	22	inner
184.2.j.a.107.10	yes	220	8.3	odd	2	inner
184.2.j.a.107.15	yes	220	1.1	even	1	trivial
736.2.r.a.15.21		220	4.3	odd	2
736.2.r.a.15.22		220	8.5	even	2
736.2.r.a.687.21		220	184.181	odd	22
736.2.r.a.687.22		220	92.43	even	22

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:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.692401 - 1.23312i) q^{2} +(-1.18656 - 2.59820i) q^{3} +(-1.04116 - 1.70763i) q^{4} +(-1.01624 - 1.17280i) q^{5} +(-4.02545 - 0.335830i) q^{6} +(4.25438 + 2.73413i) q^{7} +(-2.82660 + 0.101512i) q^{8} +(-3.37812 + 3.89856i) q^{9} +O(q^{10})\)	\(q+(0.692401 - 1.23312i) q^{2} +(-1.18656 - 2.59820i) q^{3} +(-1.04116 - 1.70763i) q^{4} +(-1.01624 - 1.17280i) q^{5} +(-4.02545 - 0.335830i) q^{6} +(4.25438 + 2.73413i) q^{7} +(-2.82660 + 0.101512i) q^{8} +(-3.37812 + 3.89856i) q^{9} +(-2.14985 + 0.441093i) q^{10} +(1.77318 - 0.254945i) q^{11} +(-3.20135 + 4.73133i) q^{12} +(-0.511843 - 0.796443i) q^{13} +(6.31724 - 3.35305i) q^{14} +(-1.84135 + 4.03199i) q^{15} +(-1.83197 + 3.55582i) q^{16} +(-1.67446 - 5.70268i) q^{17} +(2.46837 + 6.86499i) q^{18} +(-0.812847 + 2.76830i) q^{19} +(-0.944640 + 2.95643i) q^{20} +(2.05573 - 14.2979i) q^{21} +(0.913375 - 2.36306i) q^{22} +(3.08571 - 3.67130i) q^{23} +(3.61767 + 7.22362i) q^{24} +(0.368850 - 2.56541i) q^{25} +(-1.33651 + 0.0797045i) q^{26} +(5.91571 + 1.73701i) q^{27} +(0.239366 - 10.1116i) q^{28} +(1.87742 + 6.39390i) q^{29} +(3.69696 + 5.06235i) q^{30} +(2.15218 + 0.982870i) q^{31} +(3.11629 + 4.72109i) q^{32} +(-2.76637 - 4.30456i) q^{33} +(-8.19148 - 1.88374i) q^{34} +(-1.11688 - 7.76808i) q^{35} +(10.1744 + 1.70954i) q^{36} +(-3.98474 + 4.59863i) q^{37} +(2.85083 + 2.91911i) q^{38} +(-1.46198 + 2.27489i) q^{39} +(2.99156 + 3.21189i) q^{40} +(-3.66827 - 4.23341i) q^{41} +(-16.2076 - 12.4349i) q^{42} +(5.98202 - 2.73190i) q^{43} +(-2.28152 - 2.76249i) q^{44} +8.00523 q^{45} +(-2.39059 - 6.34705i) q^{46} +4.26175i q^{47} +(11.4125 + 0.540627i) q^{48} +(7.71643 + 16.8966i) q^{49} +(-2.90806 - 2.23113i) q^{50} +(-12.8298 + 11.1171i) q^{51} +(-0.827116 + 1.70326i) q^{52} +(3.03402 + 1.94985i) q^{53} +(6.23798 - 6.09206i) q^{54} +(-2.10098 - 1.82051i) q^{55} +(-12.3030 - 7.29642i) q^{56} +(8.15708 - 1.17281i) q^{57} +(9.18436 + 2.11207i) q^{58} +(2.53954 - 1.63207i) q^{59} +(8.80226 - 1.05362i) q^{60} +(2.27952 - 4.99144i) q^{61} +(2.70217 - 1.97336i) q^{62} +(-25.0310 + 7.34976i) q^{63} +(7.97939 - 0.573869i) q^{64} +(-0.413916 + 1.40967i) q^{65} +(-7.22347 + 0.430781i) q^{66} +(10.4452 + 1.50179i) q^{67} +(-7.99466 + 8.79676i) q^{68} +(-13.2001 - 3.66107i) q^{69} +(-10.3523 - 4.00139i) q^{70} +(-2.06420 - 0.296788i) q^{71} +(9.15286 - 11.3626i) q^{72} +(-2.05582 - 0.603644i) q^{73} +(2.91162 + 8.09775i) q^{74} +(-7.10309 + 2.08566i) q^{75} +(5.57353 - 1.49421i) q^{76} +(8.24084 + 3.76346i) q^{77} +(1.79293 + 3.37794i) q^{78} +(-6.55104 + 4.21010i) q^{79} +(6.03200 - 1.46503i) q^{80} +(-0.303823 - 2.11314i) q^{81} +(-7.76022 + 1.59219i) q^{82} +(6.06755 + 5.25756i) q^{83} +(-26.5558 + 11.3760i) q^{84} +(-4.98647 + 7.75910i) q^{85} +(0.773208 - 9.26811i) q^{86} +(14.3849 - 12.4646i) q^{87} +(-4.98620 + 0.900627i) q^{88} +(2.48788 - 1.13618i) q^{89} +(5.54283 - 9.87139i) q^{90} -4.78782i q^{91} +(-9.48191 - 1.44682i) q^{92} -6.75803i q^{93} +(5.25524 + 2.95084i) q^{94} +(4.07272 - 1.85995i) q^{95} +(8.56866 - 13.6986i) q^{96} +(0.549986 - 0.476566i) q^{97} +(26.1784 + 2.18398i) q^{98} +(-4.99610 + 7.77408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 11 q^{2} - 18 q^{3} - 3 q^{4} - 12 q^{6} - 8 q^{8} - 36 q^{9}+O(q^{10}) \) 220 * q - 11 * q^2 - 18 * q^3 - 3 * q^4 - 12 * q^6 - 8 * q^8 - 36 * q^9	\( 220 q - 11 q^{2} - 18 q^{3} - 3 q^{4} - 12 q^{6} - 8 q^{8} - 36 q^{9} - 11 q^{10} - 22 q^{11} - 6 q^{12} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 6 q^{18} - 22 q^{19} - 11 q^{20} - 18 q^{24} - 32 q^{25} - 10 q^{26} - 18 q^{27} - 11 q^{28} - 11 q^{30} - 11 q^{32} - 22 q^{33} + 11 q^{34} + 2 q^{35} - 41 q^{36} + 44 q^{38} - 99 q^{40} - 18 q^{41} + 99 q^{42} - 22 q^{43} - 88 q^{44} + 45 q^{46} - 100 q^{48} - 28 q^{49} + 14 q^{50} - 22 q^{51} - 118 q^{52} + 102 q^{54} - 66 q^{56} - 22 q^{57} + 43 q^{58} - 6 q^{59} - 33 q^{60} - 56 q^{62} + 18 q^{64} - 22 q^{65} + 22 q^{66} - 22 q^{67} - 10 q^{70} - 23 q^{72} - 18 q^{73} + 14 q^{75} + 44 q^{76} + 98 q^{78} + 88 q^{80} + 4 q^{81} + 14 q^{82} - 22 q^{83} + 143 q^{84} + 99 q^{86} + 77 q^{88} - 22 q^{89} + 176 q^{90} + 36 q^{92} + 111 q^{94} + 101 q^{96} - 22 q^{97} + 121 q^{98} - 22 q^{99}+O(q^{100}) \) 220 * q - 11 * q^2 - 18 * q^3 - 3 * q^4 - 12 * q^6 - 8 * q^8 - 36 * q^9 - 11 * q^10 - 22 * q^11 - 6 * q^12 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 6 * q^18 - 22 * q^19 - 11 * q^20 - 18 * q^24 - 32 * q^25 - 10 * q^26 - 18 * q^27 - 11 * q^28 - 11 * q^30 - 11 * q^32 - 22 * q^33 + 11 * q^34 + 2 * q^35 - 41 * q^36 + 44 * q^38 - 99 * q^40 - 18 * q^41 + 99 * q^42 - 22 * q^43 - 88 * q^44 + 45 * q^46 - 100 * q^48 - 28 * q^49 + 14 * q^50 - 22 * q^51 - 118 * q^52 + 102 * q^54 - 66 * q^56 - 22 * q^57 + 43 * q^58 - 6 * q^59 - 33 * q^60 - 56 * q^62 + 18 * q^64 - 22 * q^65 + 22 * q^66 - 22 * q^67 - 10 * q^70 - 23 * q^72 - 18 * q^73 + 14 * q^75 + 44 * q^76 + 98 * q^78 + 88 * q^80 + 4 * q^81 + 14 * q^82 - 22 * q^83 + 143 * q^84 + 99 * q^86 + 77 * q^88 - 22 * q^89 + 176 * q^90 + 36 * q^92 + 111 * q^94 + 101 * q^96 - 22 * q^97 + 121 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more