LMFDB - Embedded newform 90.2.l.b.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(23,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("90.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	90.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.4
Root			$0.500000 + 1.00333i$ of defining polynomial
Character	$\chi$	$=$	90.23
Dual form			90.2.l.b.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.45865 + 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.29554 - 1.82252i) q^{5} +(1.27970 - 1.16721i) q^{6} +(1.94786 + 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.45865 + 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.29554 - 1.82252i) q^{5} +(1.27970 - 1.16721i) q^{6} +(1.94786 + 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +(-2.09573 + 0.779698i) q^{10} +(-1.70563 + 0.984748i) q^{11} +(-0.796225 - 1.53819i) q^{12} +(-3.92790 + 1.05248i) q^{13} +(1.00829 - 1.74641i) q^{14} +(-0.187514 - 3.86844i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.35877 - 2.35877i) q^{17} +(2.95680 - 0.507306i) q^{18} +3.70753i q^{19} +(0.210717 + 2.22612i) q^{20} +(2.35376 + 2.58061i) q^{21} +(0.509743 + 1.90239i) q^{22} +(-1.62200 - 6.05338i) q^{23} +(-1.69185 + 0.370982i) q^{24} +(-1.64313 + 4.72230i) q^{25} +4.06647i q^{26} +(-0.713876 + 5.14688i) q^{27} +(-1.42594 - 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(-3.78516 - 0.820101i) q^{30} +(3.48837 - 6.04204i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.40767 - 0.156660i) q^{33} +(-2.88889 + 1.66790i) q^{34} +(-1.57232 - 4.22619i) q^{35} +(0.275255 - 2.98735i) q^{36} +(4.26692 - 4.26692i) q^{37} +(3.58120 + 0.959578i) q^{38} +(-6.71243 - 2.13346i) q^{39} +(2.20480 + 0.372625i) q^{40} +(6.13601 + 3.54263i) q^{41} +(3.10188 - 1.60565i) q^{42} +(2.43757 - 9.09714i) q^{43} +1.96950 q^{44} +(3.33960 - 5.81782i) q^{45} -6.26692 q^{46} +(2.00837 - 7.49533i) q^{47} +(-0.0795432 + 1.73022i) q^{48} +(-2.54041 - 1.46671i) q^{49} +(4.13612 + 2.80936i) q^{50} +(-1.23752 - 5.64369i) q^{51} +(3.92790 + 1.05248i) q^{52} +(-7.03027 + 7.03027i) q^{53} +(4.78674 + 2.02166i) q^{54} +(4.00444 + 1.83276i) q^{55} +(-1.74641 + 1.00829i) q^{56} +(-3.46282 + 5.40797i) q^{57} +(7.24179 - 1.94043i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-1.77183 + 3.44393i) q^{60} +(-4.37353 - 7.57518i) q^{61} +(-4.93330 - 4.93330i) q^{62} +(1.02302 + 5.96261i) q^{63} -1.00000i q^{64} +(7.00693 + 5.79513i) q^{65} +(-1.03329 + 3.25101i) q^{66} +(2.19259 + 8.18285i) q^{67} +(0.863368 + 3.22213i) q^{68} +(3.28793 - 10.3447i) q^{69} +(-4.48914 + 0.424926i) q^{70} +5.68481i q^{71} +(-2.81431 - 1.03906i) q^{72} +(1.14928 + 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(-6.80736 + 5.35349i) q^{75} +(1.85376 - 3.21081i) q^{76} +(-3.83631 + 1.02794i) q^{77} +(-3.79807 + 5.93153i) q^{78} +(10.0535 - 5.80440i) q^{79} +(0.930573 - 2.03323i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(5.01003 - 5.01003i) q^{82} +(-1.64569 - 0.440961i) q^{83} +(-0.748114 - 3.41176i) q^{84} +(-1.24300 + 7.35477i) q^{85} +(-8.15627 - 4.70902i) q^{86} +(-0.596356 + 12.9719i) q^{87} +(0.509743 - 1.90239i) q^{88} +2.04989 q^{89} +(-4.75523 - 4.73157i) q^{90} -8.20034 q^{91} +(-1.62200 + 6.05338i) q^{92} +(10.7315 - 5.55506i) q^{93} +(-6.72013 - 3.87987i) q^{94} +(6.75702 - 4.80327i) q^{95} +(1.65068 + 0.524648i) q^{96} +(-9.71905 - 2.60421i) q^{97} +(-2.07424 + 2.07424i) q^{98} +(-4.82426 - 3.41127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 + 8 * q^7	$ 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q - 12 * q^5 + 8 * q^7 - 8 * q^10 - 24 * q^15 + 8 * q^16 - 12 * q^20 + 24 * q^21 + 8 * q^22 - 24 * q^23 - 16 * q^25 - 16 * q^28 - 12 * q^30 - 8 * q^31 + 24 * q^36 + 24 * q^38 - 4 * q^40 + 24 * q^41 + 24 * q^42 + 36 * q^45 - 32 * q^46 + 48 * q^47 + 24 * q^50 - 48 * q^51 + 24 * q^55 + 24 * q^56 + 24 * q^57 + 16 * q^58 + 12 * q^60 - 24 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 24 * q^68 + 16 * q^70 - 24 * q^72 + 16 * q^73 + 16 * q^76 - 72 * q^77 + 24 * q^81 - 16 * q^82 + 48 * q^83 - 4 * q^85 - 48 * q^86 - 48 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^92 + 72 * q^93 + 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.45865	+	0.933998i	0.842150	+	0.539244i
$3$	1.45865	+	0.933998i	0.842150	+	0.539244i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.29554	−	1.82252i	−0.579385	−	0.815054i
$5$	−1.29554	−	1.82252i	−0.579385	−	0.815054i
$6$	1.27970	−	1.16721i	0.522435	−	0.476510i
$7$	1.94786	+	0.521929i	0.736223	+	0.197270i	0.607399	−	0.794397i	$-0.292213\pi$
$7$	1.94786	+	0.521929i	0.736223	+	0.197270i	0.128824	+	0.991667i	$0.458880\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.25529	+	2.72474i	0.418432	+	0.908248i
$10$	−2.09573	+	0.779698i	−0.662727	+	0.246562i
$11$	−1.70563	+	0.984748i	−0.514268	+	0.296913i	−0.734586	−	0.678515i	$-0.762624\pi$
$11$	−1.70563	+	0.984748i	−0.514268	+	0.296913i	0.220318	+	0.975428i	$0.429290\pi$
$12$	−0.796225	−	1.53819i	−0.229850	−	0.444037i
$13$	−3.92790	+	1.05248i	−1.08940	+	0.291905i	−0.758443	−	0.651739i	$-0.774040\pi$
$13$	−3.92790	+	1.05248i	−1.08940	+	0.291905i	−0.330961	+	0.943644i	$0.607373\pi$
$14$	1.00829	−	1.74641i	0.269476	−	0.466747i
$15$	−0.187514	−	3.86844i	−0.0484160	−	0.998827i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.35877	−	2.35877i	−0.572085	−	0.572085i	0.360626	−	0.932711i	$-0.382563\pi$
$17$	−2.35877	−	2.35877i	−0.572085	−	0.572085i	−0.932711	+	0.360626i	$0.882563\pi$
$18$	2.95680	−	0.507306i	0.696923	−	0.119573i
$19$			3.70753i			0.850565i	0.905061	+	0.425282i	$0.139825\pi$
$19$			3.70753i			0.850565i	−0.905061	+	0.425282i	$0.860175\pi$
$20$	0.210717	+	2.22612i	0.0471177	+	0.497775i
$21$	2.35376	+	2.58061i	0.513633	+	0.563135i
$22$	0.509743	+	1.90239i	0.108678	+	0.405590i
$23$	−1.62200	−	6.05338i	−0.338210	−	1.26222i	−0.900347	−	0.435173i	$-0.856687\pi$
$23$	−1.62200	−	6.05338i	−0.338210	−	1.26222i	0.562137	−	0.827044i	$-0.309979\pi$
$24$	−1.69185	+	0.370982i	−0.345348	+	0.0757264i
$25$	−1.64313	+	4.72230i	−0.328626	+	0.944460i
$26$			4.06647i			0.797499i
$27$	−0.713876	+	5.14688i	−0.137386	+	0.990518i
$28$	−1.42594	−	1.42594i	−0.269476	−	0.269476i
$29$	3.74863	+	6.49281i	0.696103	+	1.20569i	0.969808	+	0.243872i	$0.0784175\pi$
$29$	3.74863	+	6.49281i	0.696103	+	1.20569i	−0.273705	+	0.961814i	$0.588249\pi$
$30$	−3.78516	−	0.820101i	−0.691072	−	0.149729i
$31$	3.48837	−	6.04204i	0.626530	−	1.08518i	−0.361713	−	0.932289i	$-0.617808\pi$
$31$	3.48837	−	6.04204i	0.626530	−	1.08518i	0.988243	−	0.152892i	$-0.0488587\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−3.40767	−	0.156660i	−0.593199	−	0.0272710i
$34$	−2.88889	+	1.66790i	−0.495440	+	0.286042i
$35$	−1.57232	−	4.22619i	−0.265771	−	0.714357i
$36$	0.275255	−	2.98735i	0.0458759	−	0.497891i
$37$	4.26692	−	4.26692i	0.701478	−	0.701478i	−0.263250	−	0.964728i	$-0.584794\pi$
$37$	4.26692	−	4.26692i	0.701478	−	0.701478i	0.964728	+	0.263250i	$0.0847944\pi$
$38$	3.58120	+	0.959578i	0.580947	+	0.155664i
$39$	−6.71243	−	2.13346i	−1.07485	−	0.341627i
$40$	2.20480	+	0.372625i	0.348610	+	0.0589172i
$41$	6.13601	+	3.54263i	0.958284	+	0.553266i	0.895644	−	0.444771i	$-0.146715\pi$
$41$	6.13601	+	3.54263i	0.958284	+	0.553266i	0.0626396	+	0.998036i	$0.480048\pi$
$42$	3.10188	−	1.60565i	0.478630	−	0.247757i
$43$	2.43757	−	9.09714i	0.371726	−	1.38730i	−0.486344	−	0.873767i	$-0.661670\pi$
$43$	2.43757	−	9.09714i	0.371726	−	1.38730i	0.858070	−	0.513533i	$-0.171664\pi$
$44$	1.96950			0.296913
$45$	3.33960	−	5.81782i	0.497838	−	0.867270i
$46$	−6.26692			−0.924007
$47$	2.00837	−	7.49533i	0.292951	−	1.09331i	−0.649881	−	0.760036i	$-0.725181\pi$
$47$	2.00837	−	7.49533i	0.292951	−	1.09331i	0.942831	−	0.333270i	$-0.108152\pi$
$48$	−0.0795432	+	1.73022i	−0.0114811	+	0.249736i
$49$	−2.54041	−	1.46671i	−0.362916	−	0.209530i
$50$	4.13612	+	2.80936i	0.584936	+	0.397304i
$51$	−1.23752	−	5.64369i	−0.173288	−	0.790274i
$52$	3.92790	+	1.05248i	0.544702	+	0.145953i
$53$	−7.03027	+	7.03027i	−0.965682	+	0.965682i	−0.999430	−	0.0337485i	$-0.989255\pi$
$53$	−7.03027	+	7.03027i	−0.965682	+	0.965682i	0.0337485	+	0.999430i	$0.489255\pi$
$54$	4.78674	+	2.02166i	0.651393	+	0.275113i
$55$	4.00444	+	1.83276i	0.539959	+	0.247129i
$56$	−1.74641	+	1.00829i	−0.233373	+	0.134738i
$57$	−3.46282	+	5.40797i	−0.458662	+	0.716303i
$58$	7.24179	−	1.94043i	0.950894	−	0.254791i
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	−0.940407	−	0.340050i	$-0.889556\pi$
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	0.764696	+	0.644392i	$0.222889\pi$
$60$	−1.77183	+	3.44393i	−0.228742	+	0.444609i
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	−0.997498	−	0.0706960i	$-0.977478\pi$
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	0.437524	−	0.899207i	$-0.355855\pi$
$62$	−4.93330	−	4.93330i	−0.626530	−	0.626530i
$63$	1.02302	+	5.96261i	0.128889	+	0.751218i
$64$		−	1.00000i		−	0.125000i
$65$	7.00693	+	5.79513i	0.869103	+	0.718798i
$66$	−1.03329	+	3.25101i	−0.127189	+	0.400171i
$67$	2.19259	+	8.18285i	0.267867	+	0.999694i	0.960472	+	0.278377i	$0.0897964\pi$
$67$	2.19259	+	8.18285i	0.267867	+	0.999694i	−0.692605	+	0.721317i	$0.743537\pi$
$68$	0.863368	+	3.22213i	0.104699	+	0.390741i
$69$	3.28793	−	10.3447i	0.395820	−	1.24535i
$70$	−4.48914	+	0.424926i	−0.536554	+	0.0507884i
$71$			5.68481i			0.674663i	0.941386	+	0.337332i	$0.109524\pi$
$71$			5.68481i			0.674663i	−0.941386	+	0.337332i	$0.890476\pi$
$72$	−2.81431	−	1.03906i	−0.331670	−	0.122454i
$73$	1.14928	+	1.14928i	0.134513	+	0.134513i	0.771157	−	0.636645i	$-0.219678\pi$
$73$	1.14928	+	1.14928i	0.134513	+	0.134513i	−0.636645	+	0.771157i	$0.719678\pi$
$74$	−3.01717	−	5.22589i	−0.350739	−	0.607498i
$75$	−6.80736	+	5.35349i	−0.786047	+	0.618167i
$76$	1.85376	−	3.21081i	0.212641	−	0.368305i
$77$	−3.83631	+	1.02794i	−0.437188	+	0.117144i
$78$	−3.79807	+	5.93153i	−0.430047	+	0.671614i
$79$	10.0535	−	5.80440i	1.13111	−	0.653046i	0.186895	−	0.982380i	$-0.440158\pi$
$79$	10.0535	−	5.80440i	1.13111	−	0.653046i	0.944214	+	0.329334i	$0.106824\pi$
$80$	0.930573	−	2.03323i	0.104041	−	0.227322i
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$	5.01003	−	5.01003i	0.553266	−	0.553266i
$83$	−1.64569	−	0.440961i	−0.180638	−	0.0484017i	0.167366	−	0.985895i	$-0.446474\pi$
$83$	−1.64569	−	0.440961i	−0.180638	−	0.0484017i	−0.348004	+	0.937493i	$0.613140\pi$
$84$	−0.748114	−	3.41176i	−0.0816259	−	0.372253i
$85$	−1.24300	+	7.35477i	−0.134822	+	0.797737i
$86$	−8.15627	−	4.70902i	−0.879513	−	0.507787i
$87$	−0.596356	+	12.9719i	−0.0639361	+	1.39074i
$88$	0.509743	−	1.90239i	0.0543388	−	0.202795i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$	−4.75523	−	4.73157i	−0.501246	−	0.498751i
$91$	−8.20034			−0.859629
$92$	−1.62200	+	6.05338i	−0.169105	+	0.631109i
$93$	10.7315	−	5.55506i	1.11281	−	0.576033i
$94$	−6.72013	−	3.87987i	−0.693128	−	0.400178i
$95$	6.75702	−	4.80327i	0.693256	−	0.492805i
$96$	1.65068	+	0.524648i	0.168472	+	0.0535466i
$97$	−9.71905	−	2.60421i	−0.986820	−	0.264418i	−0.270906	−	0.962606i	$-0.587323\pi$
$97$	−9.71905	−	2.60421i	−0.986820	−	0.264418i	−0.715914	+	0.698188i	$0.753990\pi$
$98$	−2.07424	+	2.07424i	−0.209530	+	0.209530i
$99$	−4.82426	−	3.41127i	−0.484856	−	0.342845i
$100$	3.78414	−	3.26807i	0.378414	−	0.326807i
$101$	−4.09014	+	2.36144i	−0.406984	+	0.234972i	−0.689493	−	0.724292i	$-0.742167\pi$
$101$	−4.09014	+	2.36144i	−0.406984	+	0.234972i	0.282509	+	0.959265i	$0.408833\pi$
$102$	−5.77168	−	0.265340i	−0.571481	−	0.0262726i
$103$	−3.86872	+	1.03662i	−0.381196	+	0.102141i	−0.444329	−	0.895864i	$-0.646558\pi$
$103$	−3.86872	+	1.03662i	−0.381196	+	0.102141i	0.0631321	+	0.998005i	$0.479891\pi$
$104$	2.03323	−	3.52166i	0.199375	−	0.345327i
$105$	1.65380	−	7.63307i	0.161394	−	0.744911i
$106$	4.97115	+	8.61029i	0.482841	+	0.836305i
$107$	5.40296	+	5.40296i	0.522324	+	0.522324i	0.918273	−	0.395949i	$-0.129584\pi$
$107$	5.40296	+	5.40296i	0.522324	+	0.522324i	−0.395949	+	0.918273i	$0.629584\pi$
$108$	3.19168	−	4.10039i	0.307119	−	0.394560i
$109$			4.35357i			0.416996i	0.978023	+	0.208498i	$0.0668575\pi$
$109$			4.35357i			0.416996i	−0.978023	+	0.208498i	$0.933142\pi$
$110$	2.80674	−	3.39364i	0.267612	−	0.323571i
$111$	10.2092	−	2.23863i	0.969017	−	0.212481i
$112$	0.521929	+	1.94786i	0.0493176	+	0.184056i
$113$	0.767544	+	2.86451i	0.0722045	+	0.269471i	0.992585	−	0.121553i	$-0.0387876\pi$
$113$	0.767544	+	2.86451i	0.0722045	+	0.269471i	−0.920380	+	0.391024i	$0.872121\pi$
$114$	4.32745	+	4.74451i	0.405303	+	0.444364i
$115$	−8.93101	+	10.7985i	−0.832821	+	1.00697i
$116$		−	7.49726i		−	0.696103i
$117$	−7.79841	−	9.38136i	−0.720964	−	0.867307i
$118$	1.90872	+	1.90872i	0.175712	+	0.175712i
$119$	−3.36345	−	5.82566i	−0.308327	−	0.534037i
$120$	2.86799	+	2.60281i	0.261811	+	0.237603i
$121$	−3.56054	+	6.16704i	−0.323686	+	0.560640i
$122$	−8.44902	+	2.26391i	−0.764938	+	0.204965i
$123$	5.64146	+	10.8985i	0.508673	+	0.982681i
$124$	−6.04204	+	3.48837i	−0.542591	+	0.313265i
$125$	10.7352	−	3.12333i	0.960187	−	0.279359i
$126$	6.02421	+	0.555073i	0.536680	+	0.0494498i
$127$	−3.41734	+	3.41734i	−0.303240	+	0.303240i	−0.842280	−	0.539040i	$-0.818787\pi$
$127$	−3.41734	+	3.41734i	−0.303240	+	0.303240i	0.539040	+	0.842280i	$0.318787\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	12.0523	−	10.9928i	1.06114	−	0.967863i
$130$	7.41120	−	5.26829i	0.650005	−	0.462059i
$131$	−0.411267	−	0.237445i	−0.0359326	−	0.0207457i	0.481926	−	0.876212i	$-0.339937\pi$
$131$	−0.411267	−	0.237445i	−0.0359326	−	0.0207457i	−0.517859	+	0.855466i	$0.673271\pi$
$132$	2.87280	+	1.83951i	0.250045	+	0.160108i
$133$	−1.93506	+	7.22176i	−0.167791	+	0.626206i
$134$	8.47151			0.731827
$135$	10.3051	−	5.36696i	0.886924	−	0.461915i
$136$	3.33580			0.286042
$137$	2.54985	−	9.51618i	0.217849	−	0.813022i	−0.767296	−	0.641293i	$-0.778398\pi$
$137$	2.54985	−	9.51618i	0.217849	−	0.813022i	0.985144	−	0.171728i	$-0.0549352\pi$
$138$	−9.14122	−	5.85329i	−0.778152	−	0.498265i
$139$	−0.608318	−	0.351212i	−0.0515968	−	0.0297894i	0.473980	−	0.880536i	$-0.342817\pi$
$139$	−0.608318	−	0.351212i	−0.0515968	−	0.0297894i	−0.525577	+	0.850746i	$0.676150\pi$
$140$	−0.751427	+	4.44615i	−0.0635072	+	0.375768i
$141$	9.93012	−	9.05722i	0.836267	−	0.762755i
$142$	5.49111	+	1.47134i	0.460803	+	0.123472i
$143$	5.66314	−	5.66314i	0.473575	−	0.473575i
$144$	−1.73205	+	2.44949i	−0.144338	+	0.204124i
$145$	6.97674	−	15.2437i	0.579387	−	1.26592i
$146$	1.40757	−	0.812661i	0.116491	−	0.0672563i
$147$	−2.33566	−	4.51215i	−0.192642	−	0.372156i
$148$	−5.82872	+	1.56180i	−0.479118	+	0.128379i
$149$	−4.05609	+	7.02536i	−0.332288	+	0.575540i	−0.982960	−	0.183819i	$-0.941154\pi$
$149$	−4.05609	+	7.02536i	−0.332288	+	0.575540i	0.650672	+	0.759359i	$0.274487\pi$
$150$	3.40920	+	7.96099i	0.278360	+	0.650012i
$151$	4.61739	+	7.99755i	0.375758	+	0.650832i	0.990440	−	0.137943i	$-0.0440491\pi$
$151$	4.61739	+	7.99755i	0.375758	+	0.650832i	−0.614682	+	0.788775i	$0.710716\pi$
$152$	−2.62162	−	2.62162i	−0.212641	−	0.212641i
$153$	3.46609	−	9.38798i	0.280217	−	0.758973i
$154$			3.97164i			0.320044i
$155$	−15.5310	+	1.47012i	−1.24748	+	0.118083i
$156$	4.74641	+	5.20385i	0.380017	+	0.416641i
$157$	−2.80938	−	10.4848i	−0.224213	−	0.836775i	−0.982718	−	0.185108i	$-0.940736\pi$
$157$	−2.80938	−	10.4848i	−0.224213	−	0.836775i	0.758505	−	0.651667i	$-0.225930\pi$
$158$	−3.00458	−	11.2132i	−0.239031	−	0.892077i
$159$	−16.8209	+	3.68841i	−1.33399	+	0.292510i
$160$	−1.72310	−	1.42510i	−0.136223	−	0.112664i
$161$		−	12.6377i		−	0.995993i
$162$	5.09393	+	7.41970i	0.400217	+	0.582946i
$163$	9.68197	+	9.68197i	0.758351	+	0.758351i	0.976022	−	0.217671i	$-0.0698461\pi$
$163$	9.68197	+	9.68197i	0.758351	+	0.758351i	−0.217671	+	0.976022i	$0.569846\pi$
$164$	−3.54263	−	6.13601i	−0.276633	−	0.479142i
$165$	4.12927	+	6.41349i	0.321463	+	0.499289i
$166$	−0.851871	+	1.47548i	−0.0661180	+	0.114520i
$167$	4.93579	−	1.32254i	0.381943	−	0.102341i	−0.0627387	−	0.998030i	$-0.519983\pi$
$167$	4.93579	−	1.32254i	0.381943	−	0.102341i	0.444682	+	0.895689i	$0.353317\pi$
$168$	−3.48913	−	0.160405i	−0.269192	−	0.0123755i
$169$	3.06239	−	1.76807i	0.235568	−	0.136005i
$170$	6.78245	+	3.10420i	0.520190	+	0.238081i
$171$	−10.1021	+	4.65404i	−0.772524	+	0.355903i
$172$	−6.65957	+	6.65957i	−0.507787	+	0.507787i
$173$	−7.16239	−	1.91916i	−0.544546	−	0.145911i	−0.0239492	−	0.999713i	$-0.507624\pi$
$173$	−7.16239	−	1.91916i	−0.544546	−	0.145911i	−0.520597	+	0.853802i	$0.674291\pi$
$174$	12.3756	+	3.93342i	0.938190	+	0.298192i
$175$	−5.66529	+	8.34080i	−0.428256	+	0.630506i
$176$	−1.70563	−	0.984748i	−0.128567	−	0.0742282i
$177$	−4.15208	+	2.14928i	−0.312090	+	0.161550i
$178$	0.530550	−	1.98004i	0.0397664	−	0.148410i
$179$	−2.73426			−0.204369			−0.102184	−	0.994765i	$-0.532583\pi$
$179$	−2.73426			−0.204369			−0.102184	+	0.994765i	$0.532583\pi$
$180$	−5.80109	+	3.36858i	−0.432388	+	0.251079i
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	−2.12240	+	7.92092i	−0.157323	+	0.587138i
$183$	0.695770	−	15.1344i	0.0514328	−	1.11877i
$184$	5.42731	+	3.13346i	0.400107	+	0.231002i
$185$	−13.3045	−	2.24855i	−0.978168	−	0.165316i
$186$	−2.58824	−	11.8036i	−0.189779	−	0.865484i
$187$	6.34598	+	1.70040i	0.464064	+	0.124346i
$188$	−5.48696	+	5.48696i	−0.400178	+	0.400178i
$189$	−4.07684	+	9.65283i	−0.296546	+	0.702140i
$190$	−2.89075	−	7.76996i	−0.209717	−	0.563692i
$191$	−1.11154	+	0.641749i	−0.0804283	+	0.0464353i	−0.539675	−	0.841874i	$-0.681453\pi$
$191$	−1.11154	+	0.641749i	−0.0804283	+	0.0464353i	0.459246	+	0.888309i	$0.348119\pi$
$192$	0.933998	−	1.45865i	0.0674055	−	0.105269i
$193$	−5.28063	+	1.41494i	−0.380108	+	0.101850i	−0.443814	−	0.896119i	$-0.646375\pi$
$193$	−5.28063	+	1.41494i	−0.380108	+	0.101850i	0.0637057	+	0.997969i	$0.479708\pi$
$194$	−5.03095	+	8.71386i	−0.361201	+	0.625619i
$195$	4.80799	+	14.9975i	0.344307	+	1.07399i
$196$	1.46671	+	2.54041i	0.104765	+	0.181458i
$197$	12.0386	+	12.0386i	0.857716	+	0.857716i	0.991069	−	0.133353i	$-0.0425744\pi$
$197$	12.0386	+	12.0386i	0.857716	+	0.857716i	−0.133353	+	0.991069i	$0.542574\pi$
$198$	−4.54364	+	3.77698i	−0.322903	+	0.268418i
$199$			4.43831i			0.314623i	0.987549	+	0.157312i	$0.0502827\pi$
$199$			4.43831i			0.314623i	−0.987549	+	0.157312i	$0.949717\pi$
$200$	−2.17730	−	4.50104i	−0.153959	−	0.318271i
$201$	−4.44456	+	13.9838i	−0.313495	+	0.986338i
$202$	1.22237	+	4.56196i	0.0860058	+	0.320978i
$203$	3.91303	+	14.6036i	0.274641	+	1.02497i
$204$	−1.75012	+	5.50634i	−0.122533	+	0.385521i
$205$	−1.49298	−	15.7726i	−0.104274	−	1.10161i
$206$			4.00520i			0.279055i
$207$	14.4578	−	12.0183i	1.00489	−	0.835331i
$208$	−2.87542	−	2.87542i	−0.199375	−	0.199375i
$209$	−3.65098	−	6.32368i	−0.252543	−	0.437418i
$210$	−6.94494	−	3.57303i	−0.479246	−	0.246562i
$211$	12.0425	−	20.8582i	0.829038	−	1.43594i	−0.0697556	−	0.997564i	$-0.522222\pi$
$211$	12.0425	−	20.8582i	0.829038	−	1.43594i	0.898794	−	0.438372i	$-0.144445\pi$
$212$	9.60353	−	2.57326i	0.659573	−	0.176732i
$213$	−5.30960	+	8.29213i	−0.363808	+	0.568167i
$214$	6.61725	−	3.82047i	0.452346	−	0.261162i
$215$	−19.7377	+	7.34324i	−1.34610	+	0.500805i
$216$	−3.13461	−	4.14418i	−0.213283	−	0.281976i
$217$	9.94838	−	9.94838i	0.675340	−	0.675340i
$218$	4.20523	+	1.12679i	0.284814	+	0.0763156i
$219$	0.602965	+	2.74981i	0.0407446	+	0.185815i
$220$	−2.55157	−	3.58944i	−0.172027	−	0.242000i
$221$	11.7476	+	6.78245i	0.790226	+	0.456237i
$222$	0.479991	−	10.4408i	0.0322149	−	0.700738i
$223$	4.34272	−	16.2073i	0.290810	−	1.08532i	−0.653678	−	0.756773i	$-0.726775\pi$
$223$	4.34272	−	16.2073i	0.290810	−	1.08532i	0.944488	−	0.328546i	$-0.106559\pi$
$224$	2.01658			0.134738
$225$	−14.9297	+	1.45078i	−0.995312	+	0.0967184i
$226$	2.96556			0.197266
$227$	1.92533	−	7.18543i	0.127789	−	0.476914i	−0.872135	−	0.489265i	$-0.837265\pi$
$227$	1.92533	−	7.18543i	0.127789	−	0.476914i	0.999924	+	0.0123515i	$0.00393171\pi$
$228$	5.70288	−	2.95203i	0.377682	−	0.195503i
$229$	7.74183	+	4.46975i	0.511595	+	0.295369i	0.733489	−	0.679701i	$-0.237891\pi$
$229$	7.74183	+	4.46975i	0.511595	+	0.295369i	−0.221894	+	0.975071i	$0.571224\pi$
$230$	8.11908	+	11.4216i	0.535356	+	0.753116i
$231$	−6.55591	−	2.08371i	−0.431347	−	0.137098i
$232$	−7.24179	−	1.94043i	−0.475447	−	0.127396i
$233$	15.0591	−	15.0591i	0.986558	−	0.986558i	−0.0133533	−	0.999911i	$-0.504251\pi$
$233$	15.0591	−	15.0591i	0.986558	−	0.986558i	0.999911	+	0.0133533i	$0.00425061\pi$
$234$	−11.0801	+	5.10461i	−0.724327	+	0.333699i
$235$	−16.2623	+	6.05025i	−1.06083	+	0.394675i
$236$	2.33769	−	1.34967i	0.152171	−	0.0878558i
$237$	20.0858	+	0.923401i	1.30471	+	0.0599814i
$238$	−6.49768	+	1.74105i	−0.421182	+	0.112855i
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	−0.986436	−	0.164146i	$-0.947513\pi$
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	0.635372	+	0.772206i	$0.280847\pi$
$240$	3.25641	−	2.09661i	0.210200	−	0.135336i
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	0.947112	+	0.320904i	$0.103987\pi$
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	−0.195645	+	0.980675i	$0.562680\pi$
$242$	5.03537	+	5.03537i	0.323686	+	0.323686i
$243$	−14.9201	+	4.51572i	−0.957122	+	0.289684i
$244$			8.74707i			0.559973i
$245$	0.618120	+	6.53013i	0.0394902	+	0.417195i
$246$	11.9872	−	2.62850i	0.764277	−	0.167587i
$247$	−3.90209	−	14.5628i	−0.248284	−	0.926609i
$248$	1.80571	+	6.73901i	0.114663	+	0.427928i
$249$	−1.98862	−	2.18027i	−0.126024	−	0.138169i
$250$	−0.238423	−	11.1778i	−0.0150792	−	0.706946i
$251$		−	13.3860i		−	0.844914i	−0.906383	−	0.422457i	$-0.861168\pi$
$251$		−	13.3860i		−	0.844914i	0.906383	−	0.422457i	$-0.138832\pi$
$252$	2.09534	−	5.67528i	0.131994	−	0.357509i
$253$	8.72759	+	8.72759i	0.548699	+	0.548699i
$254$	2.41643	+	4.18538i	0.151620	+	0.262614i
$255$	−8.68244	+	9.56705i	−0.543716	+	0.599112i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.29595	+	1.95494i	−0.455109	+	0.121946i	−0.479089	−	0.877766i	$-0.659033\pi$
$257$	−7.29595	+	1.95494i	−0.455109	+	0.121946i	0.0239802	+	0.999712i	$0.492366\pi$
$258$	−7.49889	−	14.4867i	−0.466860	−	0.901905i
$259$	10.5384	−	6.08436i	0.654825	−	0.378063i
$260$	−3.17062	−	8.52220i	−0.196633	−	0.528524i
$261$	−12.9856	+	18.3645i	−0.803790	+	1.13673i
$262$	−0.335798	+	0.335798i	−0.0207457	+	0.0207457i
$263$	10.7695	+	2.88569i	0.664078	+	0.177939i	0.575086	−	0.818093i	$-0.304969\pi$
$263$	10.7695	+	2.88569i	0.664078	+	0.177939i	0.0889923	+	0.996032i	$0.471635\pi$
$264$	2.52036	−	2.29881i	0.155117	−	0.141482i
$265$	21.9208	+	3.70475i	1.34658	+	0.227581i
$266$	6.47485	+	3.73826i	0.396998	+	0.229207i
$267$	2.99006	+	1.91459i	0.182989	+	0.117171i
$268$	2.19259	−	8.18285i	0.133934	−	0.499847i
$269$	−13.4707			−0.821326			−0.410663	−	0.911787i	$-0.634703\pi$
$269$	−13.4707			−0.821326			−0.410663	+	0.911787i	$0.634703\pi$
$270$	−2.51692	−	11.3431i	−0.153175	−	0.690317i
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	0.863368	−	3.22213i	0.0523494	−	0.195371i
$273$	−11.9614	−	7.65910i	−0.723936	−	0.463550i
$274$	−8.53197	−	4.92594i	−0.515435	−	0.297587i
$275$	−1.84770	−	9.67258i	−0.111421	−	0.583279i
$276$	−8.01977	+	7.31480i	−0.482733	+	0.440299i
$277$	−23.4121	−	6.27326i	−1.40670	−	0.376924i	−0.525953	−	0.850514i	$-0.676291\pi$
$277$	−23.4121	−	6.27326i	−1.40670	−	0.376924i	−0.880745	+	0.473590i	$0.842958\pi$
$278$	−0.496689	+	0.496689i	−0.0297894	+	0.0297894i
$279$	20.8419	+	1.92038i	1.24777	+	0.114970i
$280$	4.10017	+	1.87657i	0.245032	+	0.112147i
$281$	19.5424	−	11.2828i	1.16580	−	0.673076i	0.213114	−	0.977027i	$-0.431640\pi$
$281$	19.5424	−	11.2828i	1.16580	−	0.673076i	0.952687	+	0.303952i	$0.0983062\pi$
$282$	−6.17850	−	11.9359i	−0.367924	−	0.710775i
$283$	−2.05136	+	0.549660i	−0.121941	+	0.0326739i	−0.319273	−	0.947663i	$-0.603439\pi$
$283$	−2.05136	+	0.549660i	−0.121941	+	0.0326739i	0.197333	+	0.980337i	$0.436772\pi$
$284$	2.84241	−	4.92319i	0.168666	−	0.292138i
$285$	14.3423	−	0.695214i	0.849567	−	0.0411809i
$286$	−4.00444	−	6.93590i	−0.236788	−	0.410128i
$287$	10.1031	+	10.1031i	0.596368	+	0.596368i
$288$	1.91774	+	2.30701i	0.113004	+	0.135942i
$289$		−	5.87245i		−	0.345438i
$290$	−12.9185	−	10.6844i	−0.758602	−	0.627408i
$291$	−11.7443	−	12.8762i	−0.688464	−	0.754816i
$292$	−0.420664	−	1.56994i	−0.0246175	−	0.0918738i
$293$	−0.946406	−	3.53204i	−0.0552896	−	0.206344i	0.932755	−	0.360510i	$-0.117397\pi$
$293$	−0.946406	−	3.53204i	−0.0552896	−	0.206344i	−0.988045	+	0.154167i	$0.950731\pi$
$294$	−4.96292	+	1.08824i	−0.289443	+	0.0634677i
$295$	6.00903	−	0.568794i	0.349859	−	0.0331165i
$296$			6.03434i			0.350739i
$297$	−3.85077	−	9.48168i	−0.223444	−	0.550183i
$298$	5.73618	+	5.73618i	0.332288	+	0.332288i
$299$	12.7421	+	22.0700i	0.736895	+	1.27634i
$300$	8.57209	−	1.23257i	0.494910	−	0.0711627i
$301$	9.49611	−	16.4477i	0.547347	−	0.948032i
$302$	8.92011	−	2.39014i	0.513295	−	0.137537i
$303$	−8.17164	−	0.375673i	−0.469449	−	0.0215819i
$304$	−3.21081	+	1.85376i	−0.184153	+	0.106321i
$305$	−8.13978	+	17.7848i	−0.466082	+	1.01836i
$306$	−8.17100	−	5.77777i	−0.467105	−	0.330293i
$307$	−10.5436	+	10.5436i	−0.601754	+	0.601754i	−0.940778	−	0.339024i	$-0.889903\pi$
$307$	−10.5436	+	10.5436i	−0.601754	+	0.601754i	0.339024	+	0.940778i	$0.389903\pi$
$308$	3.83631	+	1.02794i	0.218594	+	0.0585721i
$309$	−6.61130	−	2.10132i	−0.376104	−	0.119540i
$310$	−2.59971	+	15.3823i	−0.147653	+	0.873658i
$311$	−9.08436	−	5.24485i	−0.515127	−	0.297408i	0.219812	−	0.975542i	$-0.429456\pi$
$311$	−9.08436	−	5.24485i	−0.515127	−	0.297408i	−0.734938	+	0.678134i	$0.762789\pi$
$312$	6.25499	−	3.23782i	0.354119	−	0.183306i
$313$	−4.56901	+	17.0518i	−0.258256	+	0.963824i	0.707994	+	0.706218i	$0.249600\pi$
$313$	−4.56901	+	17.0518i	−0.258256	+	0.963824i	−0.966250	+	0.257606i	$0.917066\pi$
$314$	−10.8546			−0.612562
$315$	9.54157	−	9.58930i	0.537607	−	0.540296i
$316$	−11.6088			−0.653046
$317$	−6.00131	+	22.3972i	−0.337067	+	1.25795i	0.564543	+	0.825403i	$0.309052\pi$
$317$	−6.00131	+	22.3972i	−0.337067	+	1.25795i	−0.901611	+	0.432549i	$0.857614\pi$
$318$	−0.790843	+	17.2024i	−0.0443483	+	0.964663i
$319$	−12.7876	−	7.38291i	−0.715966	−	0.413363i
$320$	−1.82252	+	1.29554i	−0.101882	+	0.0724231i
$321$	2.83465	+	12.9274i	0.158215	+	0.721535i
$322$	−12.2071	−	3.27089i	−0.680276	−	0.182279i
$323$	8.74518	−	8.74518i	0.486595	−	0.486595i
$324$	8.48528	−	3.00000i	0.471405	−	0.166667i
$325$	1.48393	−	20.2781i	0.0823135	−	1.12483i
$326$	11.8579	−	6.84619i	0.656751	−	0.379175i
$327$	−4.06623	+	6.35032i	−0.224863	+	0.351173i
$328$	−6.84383	+	1.83380i	−0.377887	+	0.101255i
$329$	7.82405	−	13.5517i	0.431354	−	0.747127i
$330$	7.26369	−	2.32864i	0.399853	−	0.128187i
$331$	12.9130	+	22.3659i	0.709761	+	1.22934i	0.964946	+	0.262450i	$0.0845303\pi$
$331$	12.9130	+	22.3659i	0.709761	+	1.22934i	−0.255185	+	0.966892i	$0.582136\pi$
$332$	1.20473	+	1.20473i	0.0661180	+	0.0661180i
$333$	16.9825	+	6.27003i	0.930636	+	0.343595i
$334$		−	5.10991i		−	0.279602i
$335$	12.0728	−	14.5973i	0.659606	−	0.797534i
$336$	−1.05799	+	3.32872i	−0.0577182	+	0.181597i
$337$	8.30344	+	30.9889i	0.452317	+	1.68807i	0.695858	+	0.718180i	$0.255024\pi$
$337$	8.30344	+	30.9889i	0.452317	+	1.68807i	−0.243541	+	0.969891i	$0.578309\pi$
$338$	−0.915220	−	3.41565i	−0.0497814	−	0.185787i
$339$	−1.55588	+	4.89519i	−0.0845035	+	0.265870i
$340$	4.75386	−	5.74792i	0.257814	−	0.311725i
$341$			13.7407i			0.744099i
$342$	1.88085	+	10.9624i	0.101705	+	0.592779i
$343$	−14.1644	−	14.1644i	−0.764806	−	0.764806i
$344$	4.70902	+	8.15627i	0.253894	+	0.439757i
$345$	−23.1130	+	7.40970i	−1.24436	+	0.398925i
$346$	−3.70753	+	6.42162i	−0.199318	+	0.345229i
$347$	−14.3001	+	3.83170i	−0.767670	+	0.205696i	−0.621342	−	0.783540i	$-0.713412\pi$
$347$	−14.3001	+	3.83170i	−0.767670	+	0.205696i	−0.146328	+	0.989236i	$0.546745\pi$
$348$	7.00242	−	10.9358i	0.375369	−	0.586223i
$349$	−13.3741	+	7.72151i	−0.715897	+	0.413323i	−0.813241	−	0.581928i	$-0.802299\pi$
$349$	−13.3741	+	7.72151i	−0.715897	+	0.413323i	0.0973439	+	0.995251i	$0.468965\pi$
$350$	6.59031	+	7.63101i	0.352267	+	0.407895i
$351$	−2.61295	−	20.9678i	−0.139469	−	1.11918i
$352$	−1.39264	+	1.39264i	−0.0742282	+	0.0742282i
$353$	−20.1446	−	5.39774i	−1.07219	−	0.287293i	−0.320798	−	0.947148i	$-0.603951\pi$
$353$	−20.1446	−	5.39774i	−1.07219	−	0.287293i	−0.751393	+	0.659855i	$0.770618\pi$
$354$	1.00140	+	4.56688i	0.0532240	+	0.242727i
$355$	10.3607	−	7.36493i	0.549887	−	0.390890i
$356$	−1.77526	−	1.02494i	−0.0940883	−	0.0543219i
$357$	0.535079	−	11.6390i	0.0283194	−	0.616003i
$358$	−0.707680	+	2.64110i	−0.0374020	+	0.139586i
$359$	3.39466			0.179163			0.0895815	−	0.995979i	$-0.471447\pi$
$359$	3.39466			0.179163			0.0895815	+	0.995979i	$0.471447\pi$
$360$	1.75237	+	6.47528i	0.0923579	+	0.341277i
$361$	5.25425			0.276540
$362$	−5.87729	+	21.9344i	−0.308904	+	1.15284i
$363$	−10.9536	+	5.66999i	−0.574914	+	0.297597i
$364$	7.10170	+	4.10017i	0.372230	+	0.214907i
$365$	0.605635	−	3.58351i	0.0317004	−	0.187570i
$366$	−14.4386	−	4.58913i	−0.754718	−	0.239878i
$367$	−21.2279	−	5.68801i	−1.10809	−	0.296912i	−0.342035	−	0.939687i	$-0.611116\pi$
$367$	−21.2279	−	5.68801i	−1.10809	−	0.296912i	−0.766054	+	0.642776i	$0.777783\pi$
$368$	4.43138	−	4.43138i	0.231002	−	0.231002i
$369$	−1.95025	+	21.1661i	−0.101526	+	1.10186i
$370$	−5.61539	+	12.2692i	−0.291930	+	0.637846i
$371$	−17.3633	+	10.0247i	−0.901458	+	0.520457i
$372$	−12.0713	−	0.554953i	−0.625869	−	0.0287730i
$373$	1.42207	−	0.381044i	0.0736322	−	0.0197297i	−0.221815	−	0.975089i	$-0.571198\pi$
$373$	1.42207	−	0.381044i	0.0736322	−	0.0197297i	0.295447	+	0.955359i	$0.404531\pi$
$374$	3.28492	−	5.68965i	0.169859	−	0.294205i
$375$	18.5761	+	5.47085i	0.959263	+	0.282513i
$376$	3.87987	+	6.72013i	0.200089	+	0.346564i
$377$	−21.5578	−	21.5578i	−1.11028	−	1.11028i
$378$	8.26875	+	6.43626i	0.425299	+	0.331045i
$379$		−	30.1323i		−	1.54779i	−0.633314	−	0.773895i	$-0.718306\pi$
$379$		−	30.1323i		−	1.54779i	0.633314	−	0.773895i	$-0.281694\pi$
$380$	−8.25339	+	0.781237i	−0.423390	+	0.0400766i
$381$	−8.17649	+	1.79290i	−0.418894	+	0.0918531i
$382$	0.332194	+	1.23976i	0.0169965	+	0.0634318i
$383$	−4.43826	−	16.5638i	−0.226785	−	0.846372i	−0.981682	−	0.190528i	$-0.938980\pi$
$383$	−4.43826	−	16.5638i	−0.226785	−	0.846372i	0.754897	−	0.655843i	$-0.227687\pi$
$384$	−1.16721	−	1.27970i	−0.0595638	−	0.0653043i
$385$	6.84354	+	5.66000i	0.348779	+	0.288460i
$386$			5.46691i			0.278258i
$387$	27.8472	−	4.77783i	1.41556	−	0.242871i
$388$	7.11484	+	7.11484i	0.361201	+	0.361201i
$389$	−15.1070	−	26.1660i	−0.765953	−	1.32667i	−0.939741	−	0.341886i	$-0.888934\pi$
$389$	−15.1070	−	26.1660i	−0.765953	−	1.32667i	0.173789	−	0.984783i	$-0.444399\pi$
$390$	15.7309	−	0.762520i	0.796564	−	0.0386117i
$391$	−10.4526	+	18.1044i	−0.528610	+	0.915580i
$392$	2.83346	−	0.759224i	0.143112	−	0.0383466i
$393$	−0.378120	−	0.730471i	−0.0190736	−	0.0368474i
$394$	14.7442	−	8.51258i	0.742803	−	0.428858i
$395$	−23.6034	−	10.8028i	−1.18762	−	0.543549i
$396$	2.47230	+	5.36637i	0.124238	+	0.269670i
$397$	−2.16969	+	2.16969i	−0.108893	+	0.108893i	−0.759454	−	0.650561i	$-0.774534\pi$
$397$	−2.16969	+	2.16969i	−0.108893	+	0.108893i	0.650561	+	0.759454i	$0.274534\pi$
$398$	4.28708	+	1.14872i	0.214892	+	0.0575801i
$399$	−9.56768	+	8.72664i	−0.478983	+	0.436878i
$400$	−4.91120	+	0.938160i	−0.245560	+	0.0469080i
$401$	−12.3209	−	7.11346i	−0.615275	−	0.355229i	0.159752	−	0.987157i	$-0.448931\pi$
$401$	−12.3209	−	7.11346i	−0.615275	−	0.355229i	−0.775027	+	0.631928i	$0.782264\pi$
$402$	12.3569	+	7.91238i	0.616308	+	0.394633i
$403$	−7.34287	+	27.4040i	−0.365774	+	1.36509i
$404$	4.72288			0.234972
$405$	20.0443	+	1.79647i	0.996008	+	0.0892675i
$406$	15.1188			0.750333
$407$	−3.07596	+	11.4796i	−0.152470	+	0.569025i
$408$	4.86575	+	3.11563i	0.240890	+	0.154247i
$409$	10.2963	+	5.94456i	0.509118	+	0.293939i	0.732471	−	0.680798i	$-0.238367\pi$
$409$	10.2963	+	5.94456i	0.509118	+	0.293939i	−0.223353	+	0.974738i	$0.571700\pi$
$410$	−15.6216	−	2.64014i	−0.771495	−	0.130387i
$411$	12.6074	−	11.4992i	0.621878	−	0.567212i
$412$	3.86872	+	1.03662i	0.190598	+	0.0510706i
$413$	−3.84907	+	3.84907i	−0.189401	+	0.189401i
$414$	−7.86684	−	17.0758i	−0.386634	−	0.839228i
$415$	1.32840	+	3.57058i	0.0652088	+	0.175273i
$416$	−3.52166	+	2.03323i	−0.172664	+	0.0996874i
$417$	−0.559288	−	1.08046i	−0.0273885	−	0.0529104i
$418$	−7.05315	+	1.88989i	−0.344981	+	0.0924373i
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.234926	−	0.972013i	$-0.424515\pi$
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.724325	−	0.689458i	$-0.242151\pi$
$420$	−5.24876	+	5.78353i	−0.256113	+	0.282207i
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	−0.993262	−	0.115887i	$-0.963029\pi$
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	0.396270	−	0.918134i	$-0.370304\pi$
$422$	−17.0306	−	17.0306i	−0.829038	−	0.829038i
$423$	22.9440	−	3.93656i	1.11557	−	0.191402i
$424$		−	9.94230i		−	0.482841i
$425$	15.0146	−	7.26305i	0.728313	−	0.352310i
$426$	6.63535	+	7.27484i	0.321484	+	0.352467i
$427$	−4.56534	−	17.0381i	−0.220932	−	0.824531i
$428$	−1.97762	−	7.38058i	−0.0955920	−	0.356754i
$429$	13.5499	−	2.97115i	0.654194	−	0.143449i
$430$	1.98454	+	20.9657i	0.0957030	+	1.01105i
$431$		−	6.10703i		−	0.294165i	−0.989124	−	0.147083i	$-0.953012\pi$
$431$		−	6.10703i		−	0.294165i	0.989124	−	0.147083i	$-0.0469883\pi$
$432$	−4.81427	+	1.95521i	−0.231627	+	0.0940699i
$433$	10.2605	+	10.2605i	0.493088	+	0.493088i	0.909278	−	0.416190i	$-0.136635\pi$
$433$	10.2605	+	10.2605i	0.493088	+	0.493088i	−0.416190	+	0.909278i	$0.636635\pi$
$434$	−7.03457	−	12.1842i	−0.337670	−	0.584862i
$435$	24.4141	−	15.7188i	1.17057	−	0.753661i
$436$	2.17679	−	3.77030i	0.104249	−	0.180565i
$437$	22.4431	−	6.01360i	1.07360	−	0.287670i
$438$	2.81217	+	0.129283i	0.134371	+	0.00617740i
$439$	−1.96604	+	1.13510i	−0.0938342	+	0.0541752i	−0.546183	−	0.837666i	$-0.683920\pi$
$439$	−1.96604	+	1.13510i	−0.0938342	+	0.0541752i	0.452349	+	0.891841i	$0.350586\pi$
$440$	−4.12753	+	1.53561i	−0.196772	+	0.0732075i
$441$	0.807438	−	8.76313i	0.0384494	−	0.417292i
$442$	9.59184	−	9.59184i	0.456237	−	0.456237i
$443$	26.8719	+	7.20031i	1.27672	+	0.342097i	0.832603	−	0.553870i	$-0.186850\pi$
$443$	26.8719	+	7.20031i	1.27672	+	0.342097i	0.444120	+	0.895967i	$0.353516\pi$
$444$	−9.96076	−	3.16590i	−0.472717	−	0.150247i
$445$	−2.65572	−	3.73595i	−0.125893	−	0.177101i
$446$	−14.5310	−	8.38950i	−0.688065	−	0.397254i
$447$	−12.4781	+	6.45913i	−0.590193	+	0.305506i
$448$	0.521929	−	1.94786i	0.0246588	−	0.0920279i
$449$	−11.7712			−0.555516			−0.277758	−	0.960651i	$-0.589591\pi$
$449$	−11.7712			−0.555516			−0.277758	+	0.960651i	$0.589591\pi$
$450$	−2.46274	+	14.7964i	−0.116095	+	0.697511i
$451$	−13.9544			−0.657086
$452$	0.767544	−	2.86451i	0.0361022	−	0.134735i
$453$	−0.734564	+	15.9782i	−0.0345128	+	0.750723i
$454$	−6.44228	−	3.71945i	−0.302351	−	0.174562i
$455$	10.6239	+	14.9452i	0.498056	+	0.700644i
$456$	−1.37542	−	6.27260i	−0.0644102	−	0.293741i
$457$	37.5970	+	10.0741i	1.75871	+	0.471246i	0.986451	−	0.164058i	$-0.0524583\pi$
$457$	37.5970	+	10.0741i	1.75871	+	0.471246i	0.772263	+	0.635303i	$0.219125\pi$
$458$	6.32118	−	6.32118i	0.295369	−	0.295369i
$459$	13.8242	−	10.4564i	0.645256	−	0.488064i
$460$	13.1338	−	4.88631i	0.612365	−	0.227825i
$461$	−2.62200	+	1.51381i	−0.122119	+	0.0705053i	−0.559815	−	0.828618i	$-0.689128\pi$
$461$	−2.62200	+	1.51381i	−0.122119	+	0.0705053i	0.437696	+	0.899123i	$0.355795\pi$
$462$	−3.70950	+	5.79322i	−0.172582	+	0.269525i
$463$	−6.60350	+	1.76940i	−0.306891	+	0.0822311i	−0.408978	−	0.912544i	$-0.634115\pi$
$463$	−6.60350	+	1.76940i	−0.306891	+	0.0822311i	0.102087	+	0.994775i	$0.467448\pi$
$464$	−3.74863	+	6.49281i	−0.174026	+	0.301421i
$465$	−24.0274	−	12.3616i	−1.11424	−	0.573255i
$466$	−10.6484	−	18.4436i	−0.493279	−	0.854384i
$467$	8.05359	+	8.05359i	0.372676	+	0.372676i	0.868451	−	0.495775i	$-0.165116\pi$
$467$	8.05359	+	8.05359i	0.372676	+	0.372676i	−0.495775	+	0.868451i	$0.665116\pi$
$468$	2.06294	+	12.0237i	0.0953595	+	0.555796i
$469$			17.0835i			0.788841i
$470$	1.63511	+	17.2741i	0.0754218	+	0.796794i
$471$	5.69485	−	17.9175i	0.262405	−	0.825596i
$472$	−0.698639	−	2.60736i	−0.0321575	−	0.120013i
$473$	4.80079	+	17.9168i	0.220740	+	0.823814i
$474$	6.09053	−	19.1624i	0.279747	−	0.880159i
$475$	−17.5081	−	6.09194i	−0.803325	−	0.279517i
$476$			6.72689i			0.308327i
$477$	−27.9808	−	10.3306i	−1.28115	−	0.473007i
$478$	7.67538	+	7.67538i	0.351064	+	0.351064i
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	0.944296	+	0.329097i	$0.106744\pi$
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	−0.187142	+	0.982333i	$0.559922\pi$
$480$	−1.18235	−	3.68810i	−0.0539667	−	0.168338i
$481$	−12.2692	+	21.2509i	−0.559428	+	0.968958i
$482$	22.5368	−	6.03872i	1.02652	−	0.275056i
$483$	11.8036	−	18.4340i	0.537083	−	0.838775i
$484$	6.16704	−	3.56054i	0.280320	−	0.161843i
$485$	7.84525	+	21.0870i	0.356234	+	0.957511i
$486$	0.500258	+	15.5804i	0.0226921	+	0.706743i
$487$	−14.8248	+	14.8248i	−0.671777	+	0.671777i	−0.958126	−	0.286349i	$-0.907558\pi$
$487$	−14.8248	+	14.8248i	−0.671777	+	0.671777i	0.286349	+	0.958126i	$0.407558\pi$
$488$	8.44902	+	2.26391i	0.382469	+	0.102482i
$489$	5.07962	+	23.1655i	0.229709	+	1.04758i
$490$	6.46760	+	1.09306i	0.292177	+	0.0493796i
$491$	16.1505	+	9.32449i	0.728861	+	0.420808i	0.818005	−	0.575210i	$-0.195080\pi$
$491$	16.1505	+	9.32449i	0.728861	+	0.420808i	−0.0891441	+	0.996019i	$0.528413\pi$
$492$	0.563584	−	12.2591i	0.0254083	−	0.552682i
$493$	6.47289	−	24.1572i	0.291524	−	1.08798i
$494$	−15.0765			−0.678325
$495$	0.0329562	+	13.2117i	0.00148127	+	0.593824i
$496$	6.97674			0.313265
$497$	−2.96707	+	11.0732i	−0.133091	+	0.496703i
$498$	−2.62068	+	1.35656i	−0.117435	+	0.0607890i
$499$	−19.6189	−	11.3270i	−0.878263	−	0.507065i	−0.00817742	−	0.999967i	$-0.502603\pi$
$499$	−19.6189	−	11.3270i	−0.878263	−	0.507065i	−0.870085	+	0.492901i	$0.835936\pi$
$500$	−10.8586	−	2.66273i	−0.485613	−	0.119081i
$501$	8.43482	+	2.68090i	0.376840	+	0.119774i
$502$	−12.9298	−	3.46454i	−0.577087	−	0.154630i
$503$	−9.64801	+	9.64801i	−0.430183	+	0.430183i	−0.888691	−	0.458507i	$-0.848384\pi$
$503$	−9.64801	+	9.64801i	−0.430183	+	0.430183i	0.458507	+	0.888691i	$0.348384\pi$
$504$	−4.93958	−	3.49281i	−0.220027	−	0.155582i
$505$	9.60272	+	4.39499i	0.427315	+	0.195574i
$506$	10.6891	−	6.17134i	0.475187	−	0.274349i
$507$	6.11831	+	0.281276i	0.271724	+	0.0124919i
$508$	4.66818	−	1.25084i	0.207117	−	0.0554968i
$509$	13.5882	−	23.5355i	0.602286	−	1.04319i	−0.390188	−	0.920735i	$-0.627590\pi$
$509$	13.5882	−	23.5355i	0.602286	−	1.04319i	0.992474	−	0.122455i	$-0.0390768\pi$
$510$	6.99388	+	10.8627i	0.309694	+	0.481010i
$511$	1.63879	+	2.83847i	0.0724959	+	0.125567i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−19.0822	−	2.64671i	−0.842499	−	0.116855i
$514$			7.55332i			0.333163i
$515$	6.90136	+	5.70782i	0.304110	+	0.251517i
$516$	−15.9340	+	3.49393i	−0.701454	+	0.153812i
$517$	3.95547	+	14.7620i	0.173961	+	0.649233i
$518$	−3.14949	−	11.7541i	−0.138381	−	0.516444i
$519$	−8.65490	−	9.48903i	−0.379908	−	0.416522i
$520$	−9.05243	+	0.856872i	−0.396975	+	0.0375763i
$521$		−	18.3542i		−	0.804114i	−0.915615	−	0.402057i	$-0.868295\pi$
$521$		−	18.3542i		−	0.804114i	0.915615	−	0.402057i	$-0.131705\pi$
$522$	14.3778	+	17.2962i	0.629298	+	0.757035i
$523$	−25.8576	−	25.8576i	−1.13067	−	1.13067i	−0.990066	−	0.140607i	$-0.955095\pi$
$523$	−25.8576	−	25.8576i	−1.13067	−	1.13067i	−0.140607	−	0.990066i	$-0.544905\pi$
$524$	0.237445	+	0.411267i	0.0103728	+	0.0179663i
$525$	−16.0540	+	6.87491i	−0.700652	+	0.300045i
$526$	5.57472	−	9.65570i	0.243069	−	0.421009i
$527$	−22.4800	+	6.02350i	−0.979244	+	0.262388i
$528$	−1.56816	−	3.02946i	−0.0682455	−	0.131840i
$529$	−14.0940	+	8.13716i	−0.612781	+	0.353789i
$530$	9.25204	−	20.2150i	0.401883	−	0.878084i
$531$	−8.06384	−	0.743005i	−0.349941	−	0.0322437i
$532$	5.28669	−	5.28669i	0.229207	−	0.229207i
$533$	−27.8302	−	7.45708i	−1.20546	−	0.323002i
$534$	2.62324	−	2.39264i	0.113519	−	0.103540i
$535$	2.84721	−	16.8468i	0.123095	−	0.728349i
$536$	−7.33654	−	4.23576i	−0.316890	−	0.182957i
$537$	−3.98832	−	2.55380i	−0.172109	−	0.110205i
$538$	−3.48649	+	13.0117i	−0.150313	+	0.560976i
$539$	5.77735			0.248848
$540$	−11.6080	−	0.504638i	−0.499528	−	0.0217162i
$541$	−4.54804			−0.195536			−0.0977678	−	0.995209i	$-0.531170\pi$
$541$	−4.54804			−0.195536			−0.0977678	+	0.995209i	$0.531170\pi$
$542$	5.29032	−	19.7437i	0.227239	−	0.848066i
$543$	−33.1231	−	21.2093i	−1.42145	−	0.910180i
$544$	−2.88889	−	1.66790i	−0.123860	−	0.0715106i
$545$	7.93445	−	5.64024i	0.339875	−	0.241602i
$546$	−10.4940	+	9.57149i	−0.449100	+	0.409622i
$547$	21.6180	+	5.79252i	0.924319	+	0.247670i	0.689430	−	0.724352i	$-0.257861\pi$
$547$	21.6180	+	5.79252i	0.924319	+	0.247670i	0.234888	+	0.972022i	$0.424528\pi$
$548$	−6.96632	+	6.96632i	−0.297587	+	0.297587i
$549$	15.1504	−	21.4258i	0.646602	−	0.914433i
$550$	−9.82122	−	0.718705i	−0.418778	−	0.0306457i
$551$	−24.0723	+	13.8981i	−1.02551	+	0.592080i
$552$	4.98988	+	9.63971i	0.212383	+	0.410293i
$553$	22.6124	−	6.05896i	0.961575	−	0.257653i
$554$	−12.1190	+	20.9907i	−0.514887	+	0.891811i
$555$	−17.3064	−	15.7062i	−0.734618	−	0.666692i
$556$	0.351212	+	0.608318i	0.0148947	+	0.0257984i
$557$	20.5740	+	20.5740i	0.871749	+	0.871749i	0.992663	−	0.120914i	$-0.0385825\pi$
$557$	20.5740	+	20.5740i	0.871749	+	0.871749i	−0.120914	+	0.992663i	$0.538583\pi$
$558$	7.24924	−	19.6347i	0.306885	−	0.831205i
$559$			38.2982i			1.61984i
$560$	2.87383	−	3.47477i	0.121442	−	0.146836i
$561$	7.66836	+	8.40741i	0.323759	+	0.354961i
$562$	−5.84041	−	21.7967i	−0.246363	−	0.919438i
$563$	9.17805	+	34.2529i	0.386809	+	1.44359i	0.835296	+	0.549800i	$0.185296\pi$
$563$	9.17805	+	34.2529i	0.386809	+	1.44359i	−0.448487	+	0.893789i	$0.648037\pi$
$564$	−13.1283	+	2.87872i	−0.552803	+	0.121216i
$565$	4.22623	−	5.10997i	0.177799	−	0.214978i
$566$			2.12372i			0.0892668i
$567$	−14.9624	+	10.2723i	−0.628361	+	0.431396i
$568$	−4.01977	−	4.01977i	−0.168666	−	0.168666i
$569$	12.0592	+	20.8872i	0.505549	+	0.875637i	0.999979	+	0.00641982i	$0.00204351\pi$
$569$	12.0592	+	20.8872i	0.505549	+	0.875637i	−0.494430	+	0.869217i	$0.664623\pi$
$570$	3.04055	−	14.0336i	0.127355	−	0.587802i
$571$	2.24726	−	3.89236i	0.0940448	−	0.162890i	−0.815165	−	0.579229i	$-0.803354\pi$
$571$	2.24726	−	3.89236i	0.0940448	−	0.162890i	0.909210	+	0.416339i	$0.136687\pi$
$572$	−7.73599	+	2.07285i	−0.323458	+	0.0866703i
$573$	−2.22074	−	0.102094i	−0.0927726	−	0.00426502i
$574$	12.3737	−	7.14398i	0.516470	−	0.298184i
$575$	31.2510	+	2.28691i	1.30326	+	0.0953709i
$576$	2.72474	−	1.25529i	0.113531	−	0.0523040i
$577$	0.186522	−	0.186522i	0.00776502	−	0.00776502i	−0.703214	−	0.710979i	$-0.748252\pi$
$577$	0.186522	−	0.186522i	0.00776502	−	0.00776502i	0.710979	+	0.703214i	$0.248252\pi$
$578$	−5.67235	−	1.51990i	−0.235939	−	0.0632196i
$579$	−9.02412	−	2.86820i	−0.375030	−	0.119198i
$580$	−13.6639	+	9.71303i	−0.567361	+	0.403312i
$581$	−2.97543	−	1.71786i	−0.123441	−	0.0712689i
$582$	−15.4771	+	8.01154i	−0.641547	+	0.332089i
$583$	5.06802	−	18.9141i	0.209896	−	0.783342i
$584$	−1.62532			−0.0672563
$585$	−6.99449	+	26.3667i	−0.289187	+	1.09013i
$586$	−3.65663			−0.151054
$587$	11.6992	−	43.6620i	0.482878	−	1.80212i	−0.106555	−	0.994307i	$-0.533982\pi$
$587$	11.6992	−	43.6620i	0.482878	−	1.80212i	0.589433	−	0.807818i	$-0.299351\pi$
$588$	−0.233334	+	5.07547i	−0.00962251	+	0.209309i
$589$	22.4010	+	12.9332i	0.923017	+	0.532904i
$590$	1.00584	−	5.95149i	0.0414097	−	0.245019i
$591$	6.31603	+	28.8041i	0.259807	+	1.18484i
$592$	5.82872	+	1.56180i	0.239559	+	0.0641897i
$593$	−3.60323	+	3.60323i	−0.147967	+	0.147967i	−0.777209	−	0.629242i	$-0.783365\pi$
$593$	−3.60323	+	3.60323i	−0.147967	+	0.147967i	0.629242	+	0.777209i	$0.283365\pi$
$594$	−10.1553	+	1.26552i	−0.416675	+	0.0519248i
$595$	−6.25986	+	13.6773i	−0.256629	+	0.560716i
$596$	7.02536	−	4.05609i	0.287770	−	0.166144i
$597$	−4.14537	+	6.47392i	−0.169659	+	0.264960i
$598$	24.6159	−	6.59580i	1.00662	−	0.269722i
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.232260	+	0.972654i	$0.574612\pi$
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.726213	+	0.687470i	$0.758721\pi$
$600$	1.02805	−	8.59902i	0.0419698	−	0.351053i
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	−0.890715	−	0.454563i	$-0.849795\pi$
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	0.0516943	−	0.998663i	$-0.483538\pi$
$602$	−13.4295	−	13.4295i	−0.547347	−	0.547347i
$603$	−19.5438	+	16.2461i	−0.795887	+	0.661594i
$604$		−	9.23478i		−	0.375758i
$605$	15.8524	−	1.50053i	0.644491	−	0.0610053i
$606$	−2.47785	+	7.79597i	−0.100656	+	0.316690i
$607$	4.28061	+	15.9755i	0.173745	+	0.648424i	0.996762	+	0.0804079i	$0.0256223\pi$
$607$	4.28061	+	15.9755i	0.173745	+	0.648424i	−0.823017	+	0.568016i	$0.807711\pi$
$608$	0.959578	+	3.58120i	0.0389160	+	0.145237i
$609$	−7.93204	+	24.9563i	−0.321422	+	1.01128i
$610$	15.0721	+	12.4655i	0.610251	+	0.504712i
$611$			31.5547i			1.27657i
$612$	−7.69571	+	6.39719i	−0.311081	+	0.258591i
$613$	−21.1512	−	21.1512i	−0.854290	−	0.854290i	0.136368	−	0.990658i	$-0.456457\pi$
$613$	−21.1512	−	21.1512i	−0.854290	−	0.854290i	−0.990658	+	0.136368i	$0.956457\pi$
$614$	7.45544	+	12.9132i	0.300877	+	0.521134i
$615$	12.5539	−	24.4011i	0.506220	−	0.983947i
$616$	1.98582	−	3.43954i	0.0800110	−	0.138583i
$617$	−10.1671	+	2.72427i	−0.409312	+	0.109675i	−0.457599	−	0.889159i	$-0.651290\pi$
$617$	−10.1671	+	2.72427i	−0.409312	+	0.109675i	0.0482869	+	0.998834i	$0.484624\pi$
$618$	−3.74085	+	5.84216i	−0.150479	+	0.235006i
$619$	2.77044	−	1.59951i	0.111353	−	0.0642898i	−0.443289	−	0.896379i	$-0.646188\pi$
$619$	2.77044	−	1.59951i	0.111353	−	0.0642898i	0.554642	+	0.832089i	$0.312855\pi$
$620$	14.1853	+	6.49237i	0.569697	+	0.260740i
$621$	32.3139	−	4.02687i	1.29671	−	0.161593i
$622$	−7.41734	+	7.41734i	−0.297408	+	0.297408i
$623$	3.99290	+	1.06990i	0.159972	+	0.0428644i
$624$	−1.50858	−	6.87987i	−0.0603917	−	0.275415i
$625$	−19.6003	−	15.5187i	−0.784010	−	0.620748i
$626$	15.2882	+	8.82666i	0.611040	+	0.352784i
$627$	0.580821	−	12.6340i	0.0231958	−	0.504554i
$628$	−2.80938	+	10.4848i	−0.112107	+	0.418388i
$629$	−20.1293			−0.802609
$630$	−6.79301	−	11.6983i	−0.270640	−	0.466073i
$631$	21.2335			0.845291			0.422645	−	0.906295i	$-0.361102\pi$
$631$	21.2335			0.845291			0.422645	+	0.906295i	$0.361102\pi$
$632$	−3.00458	+	11.2132i	−0.119516	+	0.446039i
$633$	37.0472	−	19.1770i	1.47249	−	0.762219i
$634$	20.0808	+	11.5936i	0.797510	+	0.460442i
$635$	10.6555	+	1.80084i	0.422850	+	0.0714642i
$636$	16.4116	+	5.21621i	0.650761	+	0.206836i
$637$	11.5222	+	3.08736i	0.456525	+	0.122326i
$638$	−10.4410	+	10.4410i	−0.413363	+	0.413363i
$639$	−15.4897	+	7.13612i	−0.612762	+	0.282300i
$640$	0.779698	+	2.09573i	0.0308203	+	0.0828409i
$641$	42.6583	−	24.6288i	1.68490	−	0.972778i	0.726582	−	0.687080i	$-0.241108\pi$
$641$	42.6583	−	24.6288i	1.68490	−	0.972778i	0.958320	−	0.285698i	$-0.0922254\pi$
$642$	13.2205	+	0.607785i	0.521773	+	0.0239874i
$643$	19.6155	−	5.25595i	0.773559	−	0.207274i	0.149616	−	0.988744i	$-0.452196\pi$
$643$	19.6155	−	5.25595i	0.773559	−	0.207274i	0.623943	+	0.781470i	$0.285530\pi$
$644$	−6.31887	+	10.9446i	−0.248998	+	0.431278i
$645$	−35.6488	−	7.72376i	−1.40367	−	0.304123i
$646$	−6.18378	−	10.7106i	−0.243298	−	0.421404i
$647$	−29.0632	−	29.0632i	−1.14259	−	1.14259i	−0.987974	−	0.154619i	$-0.950585\pi$
$647$	−29.0632	−	29.0632i	−1.14259	−	1.14259i	−0.154619	−	0.987974i	$-0.549415\pi$
$648$	−0.701625	−	8.97261i	−0.0275624	−	0.352477i
$649$		−	5.31632i		−	0.208684i
$650$	−19.2031	−	6.68172i	−0.753207	−	0.262079i
$651$	23.8029	−	5.21939i	0.932911	−	0.204564i
$652$	−3.54385	−	13.2258i	−0.138788	−	0.517963i
$653$	0.736931	+	2.75027i	0.0288384	+	0.107626i	0.978845	−	0.204604i	$-0.0655906\pi$
$653$	0.736931	+	2.75027i	0.0288384	+	0.107626i	−0.950006	+	0.312230i	$0.898924\pi$
$654$	5.08152	+	5.57126i	0.198703	+	0.217853i
$655$	0.100067	+	1.05716i	0.00390995	+	0.0413067i
$656$			7.08526i			0.276633i
$657$	−1.68880	+	4.57416i	−0.0658865	+	0.178455i
$658$	−11.0649	−	11.0649i	−0.431354	−	0.431354i
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	−0.955058	−	0.296420i	$-0.904207\pi$
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	0.220822	−	0.975314i	$-0.429126\pi$
$660$	−0.369309	−	7.61888i	−0.0143753	−	0.296564i
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	−0.785320	−	0.619091i	$-0.787501\pi$
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	0.928808	+	0.370561i	$0.120835\pi$
$662$	24.9459	−	6.68424i	0.969551	−	0.259791i
$663$	10.8007	+	20.8654i	0.419465	+	0.810345i
$664$	1.47548	−	0.851871i	0.0572598	−	0.0330590i
$665$	15.6687	−	5.82942i	0.607607	−	0.226055i
$666$	10.4518	−	14.7811i	0.404998	−	0.572754i
$667$	33.2232	−	33.2232i	1.28641	−	1.28641i
$668$	−4.93579	−	1.32254i	−0.190971	−	0.0511707i
$669$	21.4721	−	19.5846i	0.830157	−	0.757183i
$670$	−10.9752	−	15.4395i	−0.424010	−	0.596479i
$671$	14.9193	+	8.61365i	0.575953	+	0.332526i
$672$	2.94147	+	1.88348i	0.113470	+	0.0726568i
$673$	1.84460	−	6.88414i	0.0711041	−	0.265364i	−0.921218	−	0.389048i	$-0.872804\pi$
$673$	1.84460	−	6.88414i	0.0711041	−	0.265364i	0.992322	+	0.123684i	$0.0394708\pi$
$674$	32.0820			1.23575
$675$	−23.1321	−	11.8281i	−0.890356	−	0.455265i
$676$	−3.53614			−0.136005
$677$	2.16966	−	8.09727i	0.0833867	−	0.311203i	−0.911617	−	0.411040i	$-0.865166\pi$
$677$	2.16966	−	8.09727i	0.0833867	−	0.311203i	0.995004	+	0.0998372i	$0.0318322\pi$
$678$	4.32570	+	2.76983i	0.166128	+	0.106375i
$679$	−17.5722	−	10.1453i	−0.674358	−	0.389341i
$680$	−4.32168	−	6.07954i	−0.165729	−	0.233140i
$681$	9.51955	−	8.68274i	0.364790	−	0.332723i
$682$	13.2725	+	3.55635i	0.508229	+	0.136180i
$683$	−15.8873	+	15.8873i	−0.607911	+	0.607911i	−0.942400	−	0.334488i	$-0.891436\pi$
$683$	−15.8873	+	15.8873i	−0.607911	+	0.607911i	0.334488	+	0.942400i	$0.391436\pi$
$684$	11.0757	+	1.02052i	0.423489	+	0.0390204i
$685$	−20.6468	+	7.68149i	−0.788875	+	0.293494i
$686$	−17.3478	+	10.0158i	−0.662342	+	0.382403i
$687$	7.11785	+	13.7506i	0.271563	+	0.524619i
$688$	9.09714	−	2.43757i	0.346825	−	0.0929315i
$689$	20.2150	−	35.0134i	0.770131	−	1.33391i
$690$	1.17514	+	24.2432i	0.0447367	+	0.922924i
$691$	9.16297	+	15.8707i	0.348576	+	0.603751i	0.985997	−	0.166765i	$-0.0533321\pi$
$691$	9.16297	+	15.8707i	0.348576	+	0.603751i	−0.637421	+	0.770516i	$0.719999\pi$
$692$	5.24323	+	5.24323i	0.199318	+	0.199318i
$693$	−7.61656	−	9.16260i	−0.289329	−	0.348058i
$694$			14.8046i			0.561973i
$695$	0.148013	+	1.56368i	0.00561444	+	0.0593138i
$696$	−8.75085	−	9.59422i	−0.331700	−	0.363668i
$697$	−6.11718	−	22.8296i	−0.231705	−	0.864734i
$698$	3.99695	+	14.9168i	0.151287	+	0.564610i
$699$	36.0312	−	7.90075i	1.36282	−	0.298834i
$700$	9.07669	−	4.39070i	0.343067	−	0.165953i
$701$		−	21.1738i		−	0.799724i	−0.916575	−	0.399862i	$-0.869058\pi$
$701$		−	21.1738i		−	0.799724i	0.916575	−	0.399862i	$-0.130942\pi$
$702$	−20.9296	−	2.90295i	−0.789937	−	0.109565i
$703$	15.8197	+	15.8197i	0.596652	+	0.596652i
$704$	0.984748	+	1.70563i	0.0371141	+	0.0642835i
$705$	−29.3718	−	6.36377i	−1.10621	−	0.239673i
$706$	−10.4276	+	18.0612i	−0.392449	+	0.679742i
$707$	−9.19953	+	2.46501i	−0.345984	+	0.0927062i
$708$	4.67045	+	0.214714i	0.175526	+	0.00806943i
$709$	−20.4846	+	11.8268i	−0.769316	+	0.444165i	−0.832631	−	0.553829i	$-0.813166\pi$
$709$	−20.4846	+	11.8268i	−0.769316	+	0.444165i	0.0633143	+	0.997994i	$0.479833\pi$
$710$	−4.43244	−	11.9138i	−0.166346	−	0.447117i
$711$	28.4356	+	20.1070i	1.06642	+	0.754072i
$712$	−1.44949	+	1.44949i	−0.0543219	+	0.0543219i
$713$	−42.2329	−	11.3163i	−1.58163	−	0.423798i
$714$	−11.1039	−	3.52925i	−0.415555	−	0.132079i
$715$	−17.6580	−	2.98431i	−0.660372	−	0.111607i
$716$	2.36794	+	1.36713i	0.0884942	+	0.0510921i
$717$	−16.6965	+	8.64273i	−0.623541	+	0.322769i
$718$	0.878601	−	3.27899i	0.0327891	−	0.122371i
$719$	21.3695			0.796947			0.398473	−	0.917180i	$-0.369540\pi$
$719$	21.3695			0.796947			0.398473	+	0.917180i	$0.369540\pi$
$720$	6.70818	−	0.0167333i	0.249999	−	0.000623613i
$721$	−8.07679			−0.300795
$722$	1.35990	−	5.07522i	0.0506102	−	0.188880i
$723$	−1.85589	+	40.3692i	−0.0690212	+	1.50135i
$724$	19.6658	+	11.3541i	0.730874	+	0.421970i
$725$	−36.8205	+	7.03363i	−1.36748	+	0.261222i
$726$	2.64179	+	12.0478i	0.0980462	+	0.447137i
$727$	2.97151	+	0.796213i	0.110207	+	0.0295299i	0.313501	−	0.949588i	$-0.398498\pi$
$727$	2.97151	+	0.796213i	0.110207	+	0.0295299i	−0.203294	+	0.979118i	$0.565165\pi$
$728$	5.79852	−	5.79852i	0.214907	−	0.214907i
$729$	−25.9808	−	7.34847i	−0.962250	−	0.272166i
$730$	−3.30466	−	1.51248i	−0.122311	−	0.0559794i
$731$	−27.2077	+	15.7084i	−1.00631	+	0.580994i
$732$	−8.16974	+	12.7589i	−0.301962	+	0.471581i
$733$	23.5366	−	6.30661i	0.869343	−	0.232940i	0.203540	−	0.979067i	$-0.434755\pi$
$733$	23.5366	−	6.30661i	0.869343	−	0.232940i	0.665804	+	0.746127i	$0.268089\pi$
$734$	−10.9884	+	19.0324i	−0.405589	+	0.702500i
$735$	−5.19751	+	10.1025i	−0.191713	+	0.372635i
$736$	−3.13346	−	5.42731i	−0.115501	−	0.200053i
$737$	−11.7978	−	11.7978i	−0.434578	−	0.434578i
$738$	19.9401	+	7.36199i	0.734006	+	0.270999i
$739$		−	5.68805i		−	0.209238i	−0.994512	−	0.104619i	$-0.966638\pi$
$739$		−	5.68805i		−	0.209238i	0.994512	−	0.104619i	$-0.0333624\pi$
$740$	10.3978	+	8.59956i	0.382230	+	0.316126i
$741$	7.90986	−	24.8865i	0.290576	−	0.914229i
$742$	5.18917	+	19.3663i	0.190500	+	0.710958i
$743$	−4.04871	−	15.1100i	−0.148533	−	0.554332i	−0.999573	−	0.0292311i	$-0.990694\pi$
$743$	−4.04871	−	15.1100i	−0.148533	−	0.554332i	0.851040	−	0.525101i	$-0.175973\pi$
$744$	−3.66033	+	11.5164i	−0.134194	+	0.422211i
$745$	18.0587	−	1.70937i	0.661619	−	0.0626266i
$746$		−	1.47224i		−	0.0539025i
$747$	−0.864318	−	5.03761i	−0.0316237	−	0.184317i
$748$	−4.64558	−	4.64558i	−0.169859	−	0.169859i
$749$	7.70428	+	13.3442i	0.281508	+	0.487586i
$750$	10.0923	−	16.5271i	0.368518	−	0.603486i
$751$	−21.6240	+	37.4538i	−0.789070	+	1.36671i	0.137467	+	0.990506i	$0.456104\pi$
$751$	−21.6240	+	37.4538i	−0.789070	+	1.36671i	−0.926537	+	0.376203i	$0.877229\pi$
$752$	7.49533	−	2.00837i	0.273327	−	0.0732376i
$753$	12.5025	−	19.5254i	0.455615	−	0.711544i
$754$	−26.4028	+	15.2437i	−0.961533	+	0.555141i
$755$	8.59363	−	18.7764i	0.312754	−	0.683345i
$756$	8.35706	−	6.32118i	0.303943	−	0.229899i
$757$	22.7266	−	22.7266i	0.826013	−	0.826013i	−0.160950	−	0.986963i	$-0.551456\pi$
$757$	22.7266	−	22.7266i	0.826013	−	0.826013i	0.986963	+	0.160950i	$0.0514557\pi$
$758$	−29.1055	−	7.79880i	−1.05716	−	0.283265i
$759$	4.57891	+	20.8820i	0.166204	+	0.757969i
$760$	−1.38152	+	8.17436i	−0.0501129	+	0.296515i
$761$	−24.8744	−	14.3612i	−0.901696	−	0.520595i	−0.0239461	−	0.999713i	$-0.507623\pi$
$761$	−24.8744	−	14.3612i	−0.901696	−	0.520595i	−0.877750	+	0.479119i	$0.840956\pi$
$762$	−0.384421	+	8.36192i	−0.0139261	+	0.302920i
$763$	−2.27225	+	8.48016i	−0.0822611	+	0.307002i
$764$	1.28350			0.0464353
$765$	−21.6002	+	5.84555i	−0.780957	+	0.211346i
$766$	−17.1481			−0.619587
$767$	2.84099	−	10.6027i	0.102582	−	0.382842i
$768$	−1.53819	+	0.796225i	−0.0555046	+	0.0287313i
$769$	−29.3558	−	16.9486i	−1.05860	−	0.611180i	−0.133552	−	0.991042i	$-0.542638\pi$
$769$	−29.3558	−	16.9486i	−1.05860	−	0.611180i	−0.925043	+	0.379861i	$0.875972\pi$
$770$	7.23838	−	5.14544i	0.260853	−	0.185429i
$771$	−12.4681	−	3.96283i	−0.449028	−	0.142718i
$772$	5.28063	+	1.41494i	0.190054	+	0.0509248i
$773$	30.1093	−	30.1093i	1.08296	−	1.08296i	0.0867231	−	0.996232i	$-0.472360\pi$
$773$	30.1093	−	30.1093i	1.08296	−	1.08296i	0.996232	−	0.0867231i	$-0.0276395\pi$
$774$	2.59237	−	28.1350i	0.0931807	−	1.01129i
$775$	22.8005	+	26.4010i	0.819017	+	0.948351i
$776$	8.71386	−	5.03095i	0.312809	−	0.180601i
$777$	21.0546	+	0.967939i	0.755329	+	0.0347246i
$778$	−29.1844	+	7.81993i	−1.04631	+	0.280358i
$779$	−13.1344	+	22.7494i	−0.470588	+	0.815083i
$780$	3.33491	−	15.3922i	0.119409	−	0.551130i
$781$	−5.59811	−	9.69621i	−0.200316	−	0.346958i
$782$	14.7822	+	14.7822i	0.528610	+	0.528610i
$783$	−36.0938	+	14.6587i	−1.28989	+	0.523858i
$784$		−	2.93342i		−	0.104765i
$785$	−15.4690	+	18.7036i	−0.552111	+	0.667561i
$786$	−0.803445	+	0.176176i	−0.0286579	+	0.00628398i
$787$	2.73876	+	10.2212i	0.0976263	+	0.364346i	0.997405	−	0.0720011i	$-0.0229385\pi$
$787$	2.73876	+	10.2212i	0.0976263	+	0.364346i	−0.899778	+	0.436347i	$0.856272\pi$
$788$	−4.40644	−	16.4450i	−0.156973	−	0.585831i
$789$	13.0137	+	14.2679i	0.463300	+	0.507952i
$790$	−16.5437	+	20.0031i	−0.588600	+	0.711680i
$791$			5.98028i			0.212634i
$792$	5.82340	−	0.999137i	0.206925	−	0.0355028i
$793$	25.1515	+	25.1515i	0.893157	+	0.893157i
$794$	1.53420	+	2.65731i	0.0544467	+	0.0943045i
$795$	28.5145	+	25.8779i	1.01130	+	0.917795i
$796$	2.21916	−	3.84369i	0.0786559	−	0.136236i
$797$	−13.1409	+	3.52110i	−0.465476	+	0.124724i	−0.483932	−	0.875106i	$-0.660792\pi$
$797$	−13.1409	+	3.52110i	−0.465476	+	0.124724i	0.0184558	+	0.999830i	$0.494125\pi$
$798$	5.95299	+	11.5003i	0.210733	+	0.407106i
$799$	−22.4170	+	12.9425i	−0.793056	+	0.457871i
$800$	−0.364918	+	4.98667i	−0.0129018	+	0.176305i
$801$	2.57321	+	5.58542i	0.0909200	+	0.197351i
$802$	−10.0599	+	10.0599i	−0.355229	+	0.355229i
$803$	−3.09199	−	0.828496i	−0.109114	−	0.0292370i
$804$	10.8410	−	9.88801i	0.382332	−	0.348723i
$805$	−23.0325	+	16.3727i	−0.811788	+	0.577063i
$806$	24.5697	+	14.1853i	0.865432	+	0.499657i
$807$	−19.6490	−	12.5816i	−0.691679	−	0.442895i
$808$	1.22237	−	4.56196i	0.0430029	−	0.160489i
$809$	33.4429			1.17579			0.587895	−	0.808937i	$-0.299957\pi$
$809$	33.4429			1.17579			0.587895	+	0.808937i	$0.299957\pi$
$810$	6.92310	−	18.8963i	0.243253	−	0.663949i
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	3.91303	−	14.6036i	0.137320	−	0.512487i
$813$	29.8150	+	19.0911i	1.04566	+	0.669555i
$814$	10.2924	+	5.94230i	0.360747	+	0.208278i
$815$	5.10212	−	30.1890i	0.178720	−	1.05747i
$816$	4.26881	−	3.89357i	0.149438	−	0.136302i
$817$	33.7279	+	9.03736i	1.17999	+	0.316177i
$818$	8.40687	−	8.40687i	0.293939	−	0.293939i
$819$	−10.2938	−	22.3438i	−0.359696	−	0.780757i
$820$	−6.59335	+	14.4060i	−0.230250	+	0.503078i
$821$	−38.4941	+	22.2246i	−1.34345	+	0.775643i	−0.987313	−	0.158789i	$-0.949241\pi$
$821$	−38.4941	+	22.2246i	−1.34345	+	0.775643i	−0.356141	+	0.934432i	$0.615908\pi$
$822$	−7.84431	−	15.1540i	−0.273602	−	0.528558i
$823$	−24.6311	+	6.59989i	−0.858588	+	0.230058i	−0.661146	−	0.750257i	$-0.729930\pi$
$823$	−24.6311	+	6.59989i	−0.858588	+	0.230058i	−0.197441	+	0.980315i	$0.563263\pi$
$824$	2.00260	−	3.46860i	0.0697638	−	0.120834i
$825$	6.33903	−	15.8346i	0.220697	−	0.551291i
$826$	2.72171	+	4.71413i	0.0947003	+	0.164026i
$827$	10.7808	+	10.7808i	0.374885	+	0.374885i	0.869253	−	0.494368i	$-0.164600\pi$
$827$	10.7808	+	10.7808i	0.374885	+	0.374885i	−0.494368	+	0.869253i	$0.664600\pi$
$828$	−18.5300	+	3.17925i	−0.643962	+	0.110486i
$829$			4.02079i			0.139648i	0.997559	+	0.0698239i	$0.0222437\pi$
$829$			4.02079i			0.139648i	−0.997559	+	0.0698239i	$0.977756\pi$
$830$	3.79273	−	0.359007i	0.131647	−	0.0124613i
$831$	−28.2908	−	31.0173i	−0.981396	−	1.07598i
$832$	1.05248	+	3.92790i	0.0364881	+	0.136176i
$833$	2.53262	+	9.45186i	0.0877500	+	0.327488i
$834$	−1.18840	+	0.260587i	−0.0411509	+	0.00902338i
$835$	−8.80489	−	7.28215i	−0.304706	−	0.252009i
$836$			7.30196i			0.252543i
$837$	28.6074	+	22.2675i	0.988815	+	0.769677i
$838$	−27.7686	−	27.7686i	−0.959251	−	0.959251i
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	−0.995527	−	0.0944825i	$-0.969880\pi$
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	0.415939	−	0.909393i	$-0.363453\pi$
$840$	4.22798	+	6.56680i	0.145879	+	0.226576i
$841$	−13.6044	+	23.5635i	−0.469118	+	0.812536i
$842$	−23.6637	+	6.34068i	−0.815506	+	0.218514i
$843$	39.0435	+	1.79494i	1.34473	+	0.0618211i
$844$	−20.8582	+	12.0425i	−0.717968	+	0.414519i
$845$	−7.18979	−	3.29063i	−0.247336	−	0.113201i
$846$	2.13591	−	23.1810i	0.0734340	−	0.796980i
$847$	−10.1542	+	10.1542i	−0.348903	+	0.348903i
$848$	−9.60353	−	2.57326i	−0.329786	−	0.0883660i
$849$	−3.50559	−	1.11421i	−0.120312	−	0.0382395i
$850$	−3.12951	−	16.3828i	−0.107341	−	0.561924i
$851$	−32.7503	−	18.9084i	−1.12266	−	0.648171i
$852$	8.74432	−	4.52639i	0.299575	−	0.155072i
$853$	−6.15572	+	22.9734i	−0.210768	+	0.786596i	0.776846	+	0.629691i	$0.216818\pi$
$853$	−6.15572	+	22.9734i	−0.210768	+	0.786596i	−0.987614	+	0.156905i	$0.949848\pi$
$854$	−17.6391			−0.603599
$855$	21.5697	+	12.3817i	0.737669	+	0.423444i
$856$	−7.64094			−0.261162
$857$	3.06736	−	11.4475i	0.104779	−	0.391040i	−0.893541	−	0.448981i	$-0.851787\pi$
$857$	3.06736	−	11.4475i	0.104779	−	0.391040i	0.998320	+	0.0579412i	$0.0184536\pi$
$858$	0.637053	−	13.8572i	0.0217486	−	0.473076i
$859$	34.6670	+	20.0150i	1.18282	+	0.682904i	0.956666	−	0.291187i	$-0.0940501\pi$
$859$	34.6670	+	20.0150i	1.18282	+	0.682904i	0.226158	+	0.974091i	$0.427383\pi$
$860$	20.7649	+	3.50940i	0.708078	+	0.119670i
$861$	5.30058	+	24.1732i	0.180643	+	0.823819i
$862$	−5.89894	−	1.58062i	−0.200919	−	0.0538360i
$863$	−1.78680	+	1.78680i	−0.0608233	+	0.0608233i	−0.736864	−	0.676041i	$-0.763694\pi$
$863$	−1.78680	+	1.78680i	−0.0608233	+	0.0608233i	0.676041	+	0.736864i	$0.263694\pi$
$864$	0.642559	+	5.15627i	0.0218603	+	0.175420i
$865$	5.78150	+	15.5399i	0.196577	+	0.528373i
$866$	12.5665	−	7.25527i	0.427027	−	0.246544i
$867$	5.48486	−	8.56583i	0.186276	−	0.290911i
$868$	−13.5897	+	3.64136i	−0.461266	+	0.123596i
$869$	−11.4317	+	19.8004i	−0.387795	+	0.671681i
$870$	−8.86439	−	27.6506i	−0.300531	−	0.937443i
$871$	−17.2246	−	29.8338i	−0.583632	−	1.01088i
$872$	−3.07844	−	3.07844i	−0.104249	−	0.104249i
$873$	−5.10446	−	29.7510i	−0.172760	−	1.00692i
$874$		−	23.2348i		−	0.785928i
$875$	22.5409	−	0.480797i	0.762021	−	0.0162539i
$876$	0.852721	−	2.68289i	0.0288108	−	0.0906463i
$877$	−1.78537	−	6.66309i	−0.0602876	−	0.224996i	0.929208	−	0.369556i	$-0.120490\pi$
$877$	−1.78537	−	6.66309i	−0.0602876	−	0.224996i	−0.989496	+	0.144559i	$0.953824\pi$
$878$	0.587569	+	2.19284i	0.0198295	+	0.0740047i
$879$	1.91844	−	6.03593i	0.0647075	−	0.203587i
$880$	0.415006	+	4.38433i	0.0139898	+	0.147796i
$881$		−	3.01999i		−	0.101746i	−0.998705	−	0.0508731i	$-0.983800\pi$
$881$		−	3.01999i		−	0.101746i	0.998705	−	0.0508731i	$-0.0162004\pi$
$882$	−8.25555	−	3.04799i	−0.277979	−	0.102631i
$883$	−8.50404	−	8.50404i	−0.286184	−	0.286184i	0.549385	−	0.835569i	$-0.314862\pi$
$883$	−8.50404	−	8.50404i	−0.286184	−	0.286184i	−0.835569	+	0.549385i	$0.814862\pi$
$884$	−6.78245	−	11.7476i	−0.228119	−	0.395113i
$885$	9.29630	+	4.78275i	0.312492	+	0.160771i
$886$	13.9099	−	24.0927i	0.467313	−	0.809410i
$887$	−17.2055	+	4.61020i	−0.577705	+	0.154796i	−0.535828	−	0.844327i	$-0.680000\pi$
$887$	−17.2055	+	4.61020i	−0.577705	+	0.154796i	−0.0418769	+	0.999123i	$0.513334\pi$
$888$	−5.63606	+	8.80196i	−0.189134	+	0.295375i
$889$	−8.44013	+	4.87291i	−0.283073	+	0.163432i
$890$	−4.29601	+	1.59829i	−0.144002	+	0.0535749i
$891$	3.23896	−	17.4270i	0.108509	−	0.583827i
$892$	−11.8645	+	11.8645i	−0.397254	+	0.397254i
$893$	27.7891	+	7.44607i	0.929928	+	0.249173i
$894$	3.00947	+	13.7246i	0.100652	+	0.459021i
$895$	3.54236	+	4.98324i	0.118408	+	0.166571i
$896$	−1.74641	−	1.00829i	−0.0583434	−	0.0336846i
$897$	−2.02710	+	44.0934i	−0.0676828	+	1.47224i
$898$	−3.04660	+	11.3701i	−0.101666	+	0.379424i
$899$	52.3064			1.74452
$900$	13.6549	+	6.20843i	0.455162	+	0.206948i
$901$	33.1655			1.10490
$902$	−3.61166	+	13.4789i	−0.120255	+	0.448798i
$903$	29.2136	−	15.1221i	0.972169	−	0.503231i
$904$	−2.56825	−	1.48278i	−0.0854188	−	0.0493166i
$905$	29.4194	+	41.3859i	0.977933	+	1.37571i
$906$	15.2437	+	4.84500i	0.506437	+	0.160964i
$907$	−1.21188	−	0.324723i	−0.0402399	−	0.0107822i	0.238643	−	0.971107i	$-0.423297\pi$
$907$	−1.21188	−	0.324723i	−0.0402399	−	0.0107822i	−0.278883	+	0.960325i	$0.589964\pi$
$908$	−5.26010	+	5.26010i	−0.174562	+	0.174562i
$909$	−11.5687	−	8.18027i	−0.383708	−	0.271323i
$910$	17.1857	−	6.39379i	0.569699	−	0.211952i
$911$	−23.3987	+	13.5092i	−0.775232	+	0.447581i	−0.834738	−	0.550647i	$-0.814381\pi$
$911$	−23.3987	+	13.5092i	−0.775232	+	0.447581i	0.0595057	+	0.998228i	$0.481048\pi$
$912$	−6.41485	−	0.294909i	−0.212417	−	0.00976540i
$913$	3.24117	−	0.868470i	0.107267	−	0.0287422i
$914$	19.4616	−	33.7085i	0.643734	−	1.11498i
$915$	−28.4840	+	18.3392i	−0.941653	+	0.606276i
$916$	−4.46975	−	7.74183i	−0.147685	−	0.255797i
$917$	−0.677163	−	0.677163i	−0.0223619	−	0.0223619i
$918$	−6.52217	−	16.0594i	−0.215264	−	0.530040i
$919$		−	54.3202i		−	1.79186i	−0.444196	−	0.895930i	$-0.646511\pi$
$919$		−	54.3202i		−	1.79186i	0.444196	−	0.895930i	$-0.353489\pi$
$920$	−1.32054	−	13.9509i	−0.0435371	−	0.459948i
$921$	−25.2270	+	5.53167i	−0.831259	+	0.182275i
$922$	0.783607	+	2.92446i	0.0258067	+	0.0963121i
$923$	−5.98314	−	22.3294i	−0.196938	−	0.734981i
$924$	4.63573	+	5.08250i	0.152504	+	0.167202i
$925$	13.1386	+	27.1608i	0.431994	+	0.893041i
$926$			6.83645i			0.224660i
$927$	−7.68091	−	9.24002i	−0.252274	−	0.303482i
$928$	5.30136	+	5.30136i	0.174026	+	0.174026i
$929$	−13.9274	−	24.1230i	−0.456944	−	0.791450i	0.541854	−	0.840473i	$-0.317723\pi$
$929$	−13.9274	−	24.1230i	−0.456944	−	0.791450i	−0.998798	+	0.0490228i	$0.984389\pi$
$930$	−18.1591	+	20.0093i	−0.595461	+	0.656129i
$931$	5.43786	−	9.41865i	0.178219	−	0.308684i
$932$	−20.5712	+	5.51203i	−0.673831	+	0.180553i
$933$	−8.35217	−	16.1352i	−0.273438	−	0.528241i
$934$	9.86360	−	5.69475i	0.322747	−	0.186338i
$935$	−5.12249	−	13.7686i	−0.167523	−	0.450281i
$936$	12.1479	+	1.11932i	0.397068	+	0.0365860i
$937$	−16.8770	+	16.8770i	−0.551349	+	0.551349i	−0.926830	−	0.375481i	$-0.877477\pi$
$937$	−16.8770	+	16.8770i	−0.551349	+	0.551349i	0.375481	+	0.926830i	$0.377477\pi$
$938$	16.5014	+	4.42152i	0.538788	+	0.144368i
$939$	−22.5909	+	20.6051i	−0.737227	+	0.672421i
$940$	17.1087	+	2.89147i	0.558024	+	0.0943094i
$941$	28.5039	+	16.4567i	0.929201	+	0.536474i	0.886559	−	0.462616i	$-0.153089\pi$
$941$	28.5039	+	16.4567i	0.929201	+	0.536474i	0.0426420	+	0.999090i	$0.486423\pi$
$942$	−15.8331	−	10.1382i	−0.515869	−	0.330320i
$943$	11.4923	−	42.8898i	0.374240	−	1.39668i
$944$	−2.69933			−0.0878558
$945$	22.8742	−	5.07557i	0.744097	−	0.165108i
$946$	18.5488			0.603074
$947$	3.08335	−	11.5072i	0.100195	−	0.373934i	−0.897560	−	0.440891i	$-0.854662\pi$
$947$	3.08335	−	11.5072i	0.100195	−	0.373934i	0.997756	+	0.0669572i	$0.0213291\pi$
$948$	−16.9331	−	10.8426i	−0.549962	−	0.352151i
$949$	−5.72383	−	3.30466i	−0.185804	−	0.107274i
$950$	−10.4158	+	15.3348i	−0.337933	+	0.497526i
$951$	−29.6727	+	27.0644i	−0.962204	+	0.877622i
$952$	6.49768	+	1.74105i	0.210591	+	0.0564277i
$953$	−13.4723	+	13.4723i	−0.436411	+	0.436411i	−0.890802	−	0.454391i	$-0.849857\pi$
$953$	−13.4723	+	13.4723i	−0.436411	+	0.436411i	0.454391	+	0.890802i	$0.349857\pi$
$954$	−17.2206	+	24.3536i	−0.557537	+	0.788476i
$955$	2.60965	+	1.19439i	0.0844463	+	0.0386495i
$956$	9.40038	−	5.42731i	0.304030	−	0.175532i
$957$	−11.7569	−	22.7126i	−0.380047	−	0.734195i
$958$	32.0130	−	8.57785i	1.03429	−	0.277138i
$959$	9.93353	−	17.2054i	0.320770	−	0.555591i
$960$	−3.86844	+	0.187514i	−0.124853	+	0.00605200i
$961$	−8.83746	−	15.3069i	−0.285079	−	0.493772i
$962$	17.3513	+	17.3513i	0.559428	+	0.559428i
$963$	−7.93938	+	21.5040i	−0.255843	+	0.692957i
$964$		−	23.3318i		−	0.751467i
$965$	9.42004	+	7.79091i	0.303242	+	0.250798i
$966$	−14.7508	−	16.1725i	−0.474601	−	0.520341i
$967$	−2.40036	−	8.95826i	−0.0771904	−	0.288078i	0.916531	−	0.399964i	$-0.130978\pi$
$967$	−2.40036	−	8.95826i	−0.0771904	−	0.288078i	−0.993721	+	0.111886i	$0.964311\pi$
$968$	−1.84307	−	6.87844i	−0.0592386	−	0.221081i
$969$	20.9241	−	4.58814i	0.672179	−	0.147392i
$970$	22.3990	−	2.12021i	0.719188	−	0.0680758i
$971$		−	24.7290i		−	0.793590i	−0.917907	−	0.396795i	$-0.870122\pi$
$971$		−	24.7290i		−	0.793590i	0.917907	−	0.396795i	$-0.129878\pi$
$972$	15.1790	+	3.54930i	0.486867	+	0.113844i
$973$	−1.00161	−	1.00161i	−0.0321102	−	0.0321102i
$974$	10.4827	+	18.1566i	0.335889	+	0.581776i
$975$	21.1042	−	28.1926i	0.675876	−	0.902885i
$976$	4.37353	−	7.57518i	0.139993	−	0.242476i
$977$	23.7190	−	6.35548i	0.758837	−	0.203330i	0.141403	−	0.989952i	$-0.454839\pi$
$977$	23.7190	−	6.35548i	0.758837	−	0.203330i	0.617434	+	0.786622i	$0.288172\pi$
$978$	23.6909	+	1.08914i	0.757551	+	0.0348267i
$979$	−3.49636	+	2.01862i	−0.111744	+	0.0645155i
$980$	2.72976	−	5.96432i	0.0871989	−	0.190523i
$981$	−11.8624	+	5.46502i	−0.378736	+	0.174485i
$982$	13.1868	−	13.1868i	0.420808	−	0.420808i
$983$	40.0954	+	10.7435i	1.27885	+	0.342666i	0.833414	−	0.552650i	$-0.186383\pi$
$983$	40.0954	+	10.7435i	1.27885	+	0.342666i	0.445433	+	0.895316i	$0.353050\pi$
$984$	−11.6955	−	3.71726i	−0.372839	−	0.118502i
$985$	6.34400	−	37.5371i	0.202137	−	1.19603i
$986$	−21.6587	−	12.5047i	−0.689754	−	0.398230i
$987$	24.0697	−	12.4594i	0.766148	−	0.396588i
$988$	−3.90209	+	14.5628i	−0.124142	+	0.463305i
$989$	−59.0222			−1.87680
$990$	12.7701	+	3.38762i	0.405860	+	0.107666i
$991$	36.6089			1.16292			0.581460	−	0.813575i	$-0.302481\pi$
$991$	36.6089			1.16292			0.581460	+	0.813575i	$0.302481\pi$
$992$	1.80571	−	6.73901i	0.0573315	−	0.213964i
$993$	−2.05428	+	44.6846i	−0.0651906	+	1.41802i
$994$	9.92800	+	5.73193i	0.314897	+	0.181806i
$995$	8.08889	−	5.75003i	0.256435	−	0.182288i
$996$	0.632057	+	2.88248i	0.0200275	+	0.0913349i
$997$	−11.5550	−	3.09617i	−0.365952	−	0.0980565i	0.0711569	−	0.997465i	$-0.477331\pi$
$997$	−11.5550	−	3.09617i	−0.365952	−	0.0980565i	−0.437109	+	0.899409i	$0.643998\pi$
$998$	−16.0188	+	16.0188i	−0.507065	+	0.507065i
$999$	18.9153	+	25.0074i	0.598453	+	0.791199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.l.b.23.4	✓	16
3.2	odd	2		270.2.m.b.233.2		16
4.3	odd	2		720.2.cu.b.113.1		16
5.2	odd	4	inner	90.2.l.b.77.4	yes	16
5.3	odd	4		450.2.p.h.257.1		16
5.4	even	2		450.2.p.h.293.1		16
9.2	odd	6	inner	90.2.l.b.83.4	yes	16
9.4	even	3		810.2.f.c.323.7		16
9.5	odd	6		810.2.f.c.323.2		16
9.7	even	3		270.2.m.b.143.2		16
15.2	even	4		270.2.m.b.17.2		16
15.8	even	4		1350.2.q.h.557.4		16
15.14	odd	2		1350.2.q.h.1043.3		16
20.7	even	4		720.2.cu.b.257.2		16
36.11	even	6		720.2.cu.b.353.2		16
45.2	even	12	inner	90.2.l.b.47.4	yes	16
45.7	odd	12		270.2.m.b.197.2		16
45.22	odd	12		810.2.f.c.647.2		16
45.29	odd	6		450.2.p.h.443.1		16
45.32	even	12		810.2.f.c.647.7		16
45.34	even	6		1350.2.q.h.143.4		16
45.38	even	12		450.2.p.h.407.1		16
45.43	odd	12		1350.2.q.h.1007.3		16
180.47	odd	12		720.2.cu.b.497.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	1.1	even	1	trivial
90.2.l.b.47.4	yes	16	45.2	even	12	inner
90.2.l.b.77.4	yes	16	5.2	odd	4	inner
90.2.l.b.83.4	yes	16	9.2	odd	6	inner
270.2.m.b.17.2		16	15.2	even	4
270.2.m.b.143.2		16	9.7	even	3
270.2.m.b.197.2		16	45.7	odd	12
270.2.m.b.233.2		16	3.2	odd	2
450.2.p.h.257.1		16	5.3	odd	4
450.2.p.h.293.1		16	5.4	even	2
450.2.p.h.407.1		16	45.38	even	12
450.2.p.h.443.1		16	45.29	odd	6
720.2.cu.b.113.1		16	4.3	odd	2
720.2.cu.b.257.2		16	20.7	even	4
720.2.cu.b.353.2		16	36.11	even	6
720.2.cu.b.497.1		16	180.47	odd	12
810.2.f.c.323.2		16	9.5	odd	6
810.2.f.c.323.7		16	9.4	even	3
810.2.f.c.647.2		16	45.22	odd	12
810.2.f.c.647.7		16	45.32	even	12
1350.2.q.h.143.4		16	45.34	even	6
1350.2.q.h.557.4		16	15.8	even	4
1350.2.q.h.1007.3		16	45.43	odd	12
1350.2.q.h.1043.3		16	15.14	odd	2

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	90.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.45865 + 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.29554 - 1.82252i) q^{5} +(1.27970 - 1.16721i) q^{6} +(1.94786 + 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.45865 + 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.29554 - 1.82252i) q^{5} +(1.27970 - 1.16721i) q^{6} +(1.94786 + 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +(-2.09573 + 0.779698i) q^{10} +(-1.70563 + 0.984748i) q^{11} +(-0.796225 - 1.53819i) q^{12} +(-3.92790 + 1.05248i) q^{13} +(1.00829 - 1.74641i) q^{14} +(-0.187514 - 3.86844i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.35877 - 2.35877i) q^{17} +(2.95680 - 0.507306i) q^{18} +3.70753i q^{19} +(0.210717 + 2.22612i) q^{20} +(2.35376 + 2.58061i) q^{21} +(0.509743 + 1.90239i) q^{22} +(-1.62200 - 6.05338i) q^{23} +(-1.69185 + 0.370982i) q^{24} +(-1.64313 + 4.72230i) q^{25} +4.06647i q^{26} +(-0.713876 + 5.14688i) q^{27} +(-1.42594 - 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(-3.78516 - 0.820101i) q^{30} +(3.48837 - 6.04204i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.40767 - 0.156660i) q^{33} +(-2.88889 + 1.66790i) q^{34} +(-1.57232 - 4.22619i) q^{35} +(0.275255 - 2.98735i) q^{36} +(4.26692 - 4.26692i) q^{37} +(3.58120 + 0.959578i) q^{38} +(-6.71243 - 2.13346i) q^{39} +(2.20480 + 0.372625i) q^{40} +(6.13601 + 3.54263i) q^{41} +(3.10188 - 1.60565i) q^{42} +(2.43757 - 9.09714i) q^{43} +1.96950 q^{44} +(3.33960 - 5.81782i) q^{45} -6.26692 q^{46} +(2.00837 - 7.49533i) q^{47} +(-0.0795432 + 1.73022i) q^{48} +(-2.54041 - 1.46671i) q^{49} +(4.13612 + 2.80936i) q^{50} +(-1.23752 - 5.64369i) q^{51} +(3.92790 + 1.05248i) q^{52} +(-7.03027 + 7.03027i) q^{53} +(4.78674 + 2.02166i) q^{54} +(4.00444 + 1.83276i) q^{55} +(-1.74641 + 1.00829i) q^{56} +(-3.46282 + 5.40797i) q^{57} +(7.24179 - 1.94043i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-1.77183 + 3.44393i) q^{60} +(-4.37353 - 7.57518i) q^{61} +(-4.93330 - 4.93330i) q^{62} +(1.02302 + 5.96261i) q^{63} -1.00000i q^{64} +(7.00693 + 5.79513i) q^{65} +(-1.03329 + 3.25101i) q^{66} +(2.19259 + 8.18285i) q^{67} +(0.863368 + 3.22213i) q^{68} +(3.28793 - 10.3447i) q^{69} +(-4.48914 + 0.424926i) q^{70} +5.68481i q^{71} +(-2.81431 - 1.03906i) q^{72} +(1.14928 + 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(-6.80736 + 5.35349i) q^{75} +(1.85376 - 3.21081i) q^{76} +(-3.83631 + 1.02794i) q^{77} +(-3.79807 + 5.93153i) q^{78} +(10.0535 - 5.80440i) q^{79} +(0.930573 - 2.03323i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(5.01003 - 5.01003i) q^{82} +(-1.64569 - 0.440961i) q^{83} +(-0.748114 - 3.41176i) q^{84} +(-1.24300 + 7.35477i) q^{85} +(-8.15627 - 4.70902i) q^{86} +(-0.596356 + 12.9719i) q^{87} +(0.509743 - 1.90239i) q^{88} +2.04989 q^{89} +(-4.75523 - 4.73157i) q^{90} -8.20034 q^{91} +(-1.62200 + 6.05338i) q^{92} +(10.7315 - 5.55506i) q^{93} +(-6.72013 - 3.87987i) q^{94} +(6.75702 - 4.80327i) q^{95} +(1.65068 + 0.524648i) q^{96} +(-9.71905 - 2.60421i) q^{97} +(-2.07424 + 2.07424i) q^{98} +(-4.82426 - 3.41127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 + 8 * q^7	\( 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q - 12 * q^5 + 8 * q^7 - 8 * q^10 - 24 * q^15 + 8 * q^16 - 12 * q^20 + 24 * q^21 + 8 * q^22 - 24 * q^23 - 16 * q^25 - 16 * q^28 - 12 * q^30 - 8 * q^31 + 24 * q^36 + 24 * q^38 - 4 * q^40 + 24 * q^41 + 24 * q^42 + 36 * q^45 - 32 * q^46 + 48 * q^47 + 24 * q^50 - 48 * q^51 + 24 * q^55 + 24 * q^56 + 24 * q^57 + 16 * q^58 + 12 * q^60 - 24 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 24 * q^68 + 16 * q^70 - 24 * q^72 + 16 * q^73 + 16 * q^76 - 72 * q^77 + 24 * q^81 - 16 * q^82 + 48 * q^83 - 4 * q^85 - 48 * q^86 - 48 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^92 + 72 * q^93 + 84 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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