LMFDB - Embedded newform 336.2.bo.a.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15775 - 0.812169i) q^{2} +(-1.44132 + 0.960512i) q^{3} +(0.680764 + 1.88057i) q^{4} +(-0.0464448 + 0.0124448i) q^{5} +(2.44879 + 0.0585683i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(0.739191 - 2.73013i) q^{8} +(1.15484 - 2.76882i) q^{9} +O(q^{10})$	\(q+(-1.15775 - 0.812169i) q^{2} +(-1.44132 + 0.960512i) q^{3} +(0.680764 + 1.88057i) q^{4} +(-0.0464448 + 0.0124448i) q^{5} +(2.44879 + 0.0585683i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(0.739191 - 2.73013i) q^{8} +(1.15484 - 2.76882i) q^{9} +(0.0638787 + 0.0233130i) q^{10} +(-0.714547 - 0.191462i) q^{11} +(-2.78752 - 2.05664i) q^{12} +(3.92820 + 3.92820i) q^{13} +(0.355654 + 3.72472i) q^{14} +(0.0549886 - 0.0625478i) q^{15} +(-3.07312 + 2.56045i) q^{16} +(2.15674 + 3.73558i) q^{17} +(-3.58576 + 2.26767i) q^{18} +(4.52089 - 1.21137i) q^{19} +(-0.0550214 - 0.0788709i) q^{20} +(4.40909 + 1.24897i) q^{21} +(0.671766 + 0.801998i) q^{22} +(-3.18448 + 5.51567i) q^{23} +(1.55690 + 4.64500i) q^{24} +(-4.32812 + 2.49884i) q^{25} +(-1.35751 - 7.73823i) q^{26} +(0.994989 + 5.10000i) q^{27} +(2.61334 - 4.60114i) q^{28} +(5.72866 + 5.72866i) q^{29} +(-0.114462 + 0.0277546i) q^{30} +(7.88207 - 4.55072i) q^{31} +(5.63742 - 0.468468i) q^{32} +(1.21380 - 0.410371i) q^{33} +(0.536961 - 6.07650i) q^{34} +(0.104848 + 0.0720482i) q^{35} +(5.99314 + 0.286843i) q^{36} +(4.91744 - 1.31762i) q^{37} +(-6.21789 - 2.26926i) q^{38} +(-9.43489 - 1.88873i) q^{39} +(-0.000355551 + 0.135999i) q^{40} -9.05930i q^{41} +(-4.09025 - 5.02692i) q^{42} +(0.936949 + 0.936949i) q^{43} +(-0.126379 - 1.47410i) q^{44} +(-0.0191786 + 0.142969i) q^{45} +(8.16648 - 3.79943i) q^{46} +(-3.32126 + 5.75259i) q^{47} +(1.97002 - 6.64221i) q^{48} +(-1.09401 + 6.91398i) q^{49} +(7.04036 + 0.622135i) q^{50} +(-6.69663 - 3.31261i) q^{51} +(-4.71310 + 10.0614i) q^{52} +(0.831041 + 0.222677i) q^{53} +(2.99011 - 6.71262i) q^{54} +0.0355697 q^{55} +(-6.76249 + 3.20449i) q^{56} +(-5.35254 + 6.08834i) q^{57} +(-1.97971 - 11.2850i) q^{58} +(-0.850708 + 3.17489i) q^{59} +(0.155060 + 0.0608299i) q^{60} +(4.88233 - 1.30822i) q^{61} +(-12.8214 - 1.13299i) q^{62} +(-7.55458 + 2.43481i) q^{63} +(-6.90719 - 4.03617i) q^{64} +(-0.231330 - 0.133559i) q^{65} +(-1.73856 - 0.510701i) q^{66} +(-7.17601 - 1.92281i) q^{67} +(-5.55681 + 6.59895i) q^{68} +(-0.708004 - 11.0086i) q^{69} +(-0.0628718 - 0.168568i) q^{70} +9.82008 q^{71} +(-6.70558 - 5.19953i) q^{72} +(0.701314 + 1.21471i) q^{73} +(-6.76329 - 2.46831i) q^{74} +(3.83807 - 7.75886i) q^{75} +(5.35572 + 7.67721i) q^{76} +(0.842730 + 1.76648i) q^{77} +(9.38926 + 9.84940i) q^{78} +(-4.88205 + 8.45596i) q^{79} +(0.110866 - 0.157164i) q^{80} +(-6.33271 - 6.39506i) q^{81} +(-7.35768 + 10.4884i) q^{82} +(4.54243 - 4.54243i) q^{83} +(0.652772 + 9.14188i) q^{84} +(-0.146658 - 0.146658i) q^{85} +(-0.323791 - 1.84571i) q^{86} +(-13.7593 - 2.75442i) q^{87} +(-1.05090 + 1.80928i) q^{88} +(4.11344 + 2.37490i) q^{89} +(0.138319 - 0.149946i) q^{90} +(1.15210 - 14.6528i) q^{91} +(-12.5405 - 2.23377i) q^{92} +(-6.98961 + 14.1299i) q^{93} +(8.51726 - 3.96263i) q^{94} +(-0.194896 + 0.112524i) q^{95} +(-7.67539 + 6.09002i) q^{96} -3.21854i q^{97} +(6.88191 - 7.11613i) q^{98} +(-1.35531 + 1.75734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.15775	−	0.812169i	−0.818652	−	0.574290i
$2$	−1.15775	−	0.812169i	−0.818652	−	0.574290i
$3$	−1.44132	+	0.960512i	−0.832149	+	0.554552i
$3$	−1.44132	+	0.960512i	−0.832149	+	0.554552i
$4$	0.680764	+	1.88057i	0.340382	+	0.940287i
$5$	−0.0464448	+	0.0124448i	−0.0207707	+	0.00556551i	−0.269189	−	0.963087i	$-0.586756\pi$
$5$	−0.0464448	+	0.0124448i	−0.0207707	+	0.00556551i	0.248419	+	0.968653i	$0.420089\pi$
$6$	2.44879	+	0.0585683i	0.999714	+	0.0239104i
$7$	−1.71843	−	2.01172i	−0.649505	−	0.760357i
$7$	−1.71843	−	2.01172i	−0.649505	−	0.760357i
$8$	0.739191	−	2.73013i	0.261343	−	0.965246i
$9$	1.15484	−	2.76882i	0.384945	−	0.922939i
$10$	0.0638787	+	0.0233130i	0.0202002	+	0.00737222i
$11$	−0.714547	−	0.191462i	−0.215444	−	0.0577281i	0.149483	−	0.988764i	$-0.452239\pi$
$11$	−0.714547	−	0.191462i	−0.215444	−	0.0577281i	−0.364927	+	0.931036i	$0.618906\pi$
$12$	−2.78752	−	2.05664i	−0.804686	−	0.593700i
$13$	3.92820	+	3.92820i	1.08949	+	1.08949i	0.995581	+	0.0939052i	$0.0299351\pi$
$13$	3.92820	+	3.92820i	1.08949	+	1.08949i	0.0939052	+	0.995581i	$0.470065\pi$
$14$	0.355654	+	3.72472i	0.0950526	+	0.995472i
$15$	0.0549886	−	0.0625478i	0.0141980	−	0.0161498i
$16$	−3.07312	+	2.56045i	−0.768280	+	0.640113i
$17$	2.15674	+	3.73558i	0.523086	+	0.906011i	0.999639	+	0.0268654i	$0.00855255\pi$
$17$	2.15674	+	3.73558i	0.523086	+	0.906011i	−0.476553	+	0.879146i	$0.658114\pi$
$18$	−3.58576	+	2.26767i	−0.845171	+	0.534496i
$19$	4.52089	−	1.21137i	1.03716	−	0.277907i	0.300226	−	0.953868i	$-0.402938\pi$
$19$	4.52089	−	1.21137i	1.03716	−	0.277907i	0.736937	+	0.675961i	$0.236271\pi$
$20$	−0.0550214	−	0.0788709i	−0.0123032	−	0.0176361i
$21$	4.40909	+	1.24897i	0.962142	+	0.272547i
$22$	0.671766	+	0.801998i	0.143221	+	0.170987i
$23$	−3.18448	+	5.51567i	−0.664009	+	1.15010i	0.315544	+	0.948911i	$0.397813\pi$
$23$	−3.18448	+	5.51567i	−0.664009	+	1.15010i	−0.979553	+	0.201187i	$0.935520\pi$
$24$	1.55690	+	4.64500i	0.317802	+	0.948157i
$25$	−4.32812	+	2.49884i	−0.865625	+	0.499769i
$26$	−1.35751	−	7.73823i	−0.266229	−	1.51759i
$27$	0.994989	+	5.10000i	0.191486	+	0.981495i
$28$	2.61334	−	4.60114i	0.493875	−	0.869533i
$29$	5.72866	+	5.72866i	1.06379	+	1.06379i	0.997822	+	0.0659633i	$0.0210120\pi$
$29$	5.72866	+	5.72866i	1.06379	+	1.06379i	0.0659633	+	0.997822i	$0.478988\pi$
$30$	−0.114462	+	0.0277546i	−0.0208979	+	0.00506728i
$31$	7.88207	−	4.55072i	1.41566	−	0.817333i	0.419748	−	0.907641i	$-0.362118\pi$
$31$	7.88207	−	4.55072i	1.41566	−	0.817333i	0.995914	+	0.0903078i	$0.0287851\pi$
$32$	5.63742	−	0.468468i	0.996565	−	0.0828143i
$33$	1.21380	−	0.410371i	0.211295	−	0.0714365i
$34$	0.536961	−	6.07650i	0.0920880	−	1.04211i
$35$	0.104848	+	0.0720482i	0.0177225	+	0.0121784i
$36$	5.99314	+	0.286843i	0.998857	+	0.0478071i
$37$	4.91744	−	1.31762i	0.808422	−	0.216616i	0.169144	−	0.985591i	$-0.445900\pi$
$37$	4.91744	−	1.31762i	0.808422	−	0.216616i	0.639278	+	0.768975i	$0.279233\pi$
$38$	−6.21789	−	2.26926i	−1.00867	−	0.368123i
$39$	−9.43489	−	1.88873i	−1.51079	−	0.302439i
$40$	−0.000355551		0.135999i	−5.62175e−5		0.0215034i
$41$		−	9.05930i		−	1.41483i	−0.706801	−	0.707413i	$-0.749862\pi$
$41$		−	9.05930i		−	1.41483i	0.706801	−	0.707413i	$-0.250138\pi$
$42$	−4.09025	−	5.02692i	−0.631139	−	0.775670i
$43$	0.936949	+	0.936949i	0.142883	+	0.142883i	0.774930	−	0.632047i	$-0.217785\pi$
$43$	0.936949	+	0.936949i	0.142883	+	0.142883i	−0.632047	+	0.774930i	$0.717785\pi$
$44$	−0.126379	−	1.47410i	−0.0190523	−	0.222229i
$45$	−0.0191786	+	0.142969i	−0.00285897	+	0.0213126i
$46$	8.16648	−	3.79943i	1.20408	−	0.560196i
$47$	−3.32126	+	5.75259i	−0.484456	+	0.839102i	−0.999841	−	0.0178568i	$-0.994316\pi$
$47$	−3.32126	+	5.75259i	−0.484456	+	0.839102i	0.515385	+	0.856959i	$0.327649\pi$
$48$	1.97002	−	6.64221i	0.284348	−	0.958721i
$49$	−1.09401	+	6.91398i	−0.156287	+	0.987712i
$50$	7.04036	+	0.622135i	0.995658	+	0.0879831i
$51$	−6.69663	−	3.31261i	−0.937715	−	0.463858i
$52$	−4.71310	+	10.0614i	−0.653589	+	1.39527i
$53$	0.831041	+	0.222677i	0.114152	+	0.0305870i	0.315443	−	0.948945i	$-0.397847\pi$
$53$	0.831041	+	0.222677i	0.114152	+	0.0305870i	−0.201291	+	0.979532i	$0.564514\pi$
$54$	2.99011	−	6.71262i	0.406903	−	0.913471i
$55$	0.0355697			0.00479622
$56$	−6.76249	+	3.20449i	−0.903676	+	0.428217i
$57$	−5.35254	+	6.08834i	−0.708961	+	0.806420i
$58$	−1.97971	−	11.2850i	−0.259949	−	1.48179i
$59$	−0.850708	+	3.17489i	−0.110753	+	0.413335i	−0.998934	−	0.0461580i	$-0.985302\pi$
$59$	−0.850708	+	3.17489i	−0.110753	+	0.413335i	0.888181	+	0.459493i	$0.151969\pi$
$60$	0.155060	+	0.0608299i	0.0200182	+	0.00785311i
$61$	4.88233	−	1.30822i	0.625119	−	0.167500i	0.0676651	−	0.997708i	$-0.478445\pi$
$61$	4.88233	−	1.30822i	0.625119	−	0.167500i	0.557454	+	0.830208i	$0.311778\pi$
$62$	−12.8214	−	1.13299i	−1.62832	−	0.143890i
$63$	−7.55458	+	2.43481i	−0.951788	+	0.306758i
$64$	−6.90719	−	4.03617i	−0.863399	−	0.504521i
$65$	−0.231330	−	0.133559i	−0.0286930	−	0.0165659i
$66$	−1.73856	−	0.510701i	−0.214002	−	0.0628629i
$67$	−7.17601	−	1.92281i	−0.876689	−	0.234908i	−0.207711	−	0.978190i	$-0.566601\pi$
$67$	−7.17601	−	1.92281i	−0.876689	−	0.234908i	−0.668978	+	0.743282i	$0.733268\pi$
$68$	−5.55681	+	6.59895i	−0.673862	+	0.800240i
$69$	−0.708004	−	11.0086i	−0.0852337	−	1.32528i
$70$	−0.0628718	−	0.168568i	−0.00751462	−	0.0201477i
$71$	9.82008			1.16543			0.582714	−	0.812677i	$-0.301991\pi$
$71$	9.82008			1.16543			0.582714	+	0.812677i	$0.301991\pi$
$72$	−6.70558	−	5.19953i	−0.790261	−	0.612771i
$73$	0.701314	+	1.21471i	0.0820826	+	0.142171i	0.904144	−	0.427227i	$-0.140510\pi$
$73$	0.701314	+	1.21471i	0.0820826	+	0.142171i	−0.822062	+	0.569398i	$0.807176\pi$
$74$	−6.76329	−	2.46831i	−0.786217	−	0.286936i
$75$	3.83807	−	7.75886i	0.443182	−	0.895916i
$76$	5.35572	+	7.67721i	0.614344	+	0.880637i
$77$	0.842730	+	1.76648i	0.0960380	+	0.201309i
$78$	9.38926	+	9.84940i	1.06312	+	1.11522i
$79$	−4.88205	+	8.45596i	−0.549274	+	0.951370i	0.449051	+	0.893506i	$0.351762\pi$
$79$	−4.88205	+	8.45596i	−0.549274	+	0.951370i	−0.998324	+	0.0578636i	$0.981571\pi$
$80$	0.110866	−	0.157164i	0.0123952	−	0.0175715i
$81$	−6.33271	−	6.39506i	−0.703635	−	0.710562i
$82$	−7.35768	+	10.4884i	−0.812520	+	1.15825i
$83$	4.54243	−	4.54243i	0.498596	−	0.498596i	−0.412405	−	0.911001i	$-0.635311\pi$
$83$	4.54243	−	4.54243i	0.498596	−	0.498596i	0.911001	+	0.412405i	$0.135311\pi$
$84$	0.652772	+	9.14188i	0.0712233	+	0.997460i
$85$	−0.146658	−	0.146658i	−0.0159073	−	0.0159073i
$86$	−0.323791	−	1.84571i	−0.0349153	−	0.199028i
$87$	−13.7593	−	2.75442i	−1.47515	−	0.295304i
$88$	−1.05090	+	1.80928i	−0.112027	+	0.192870i
$89$	4.11344	+	2.37490i	0.436024	+	0.251738i	0.701910	−	0.712266i	$-0.252331\pi$
$89$	4.11344	+	2.37490i	0.436024	+	0.251738i	−0.265886	+	0.964005i	$0.585664\pi$
$90$	0.138319	−	0.149946i	0.0145801	−	0.0158057i
$91$	1.15210	−	14.6528i	0.120772	−	1.53603i
$92$	−12.5405	−	2.23377i	−1.30744	−	0.232887i
$93$	−6.98961	+	14.1299i	−0.724789	+	1.46520i
$94$	8.51726	−	3.96263i	0.878489	−	0.408714i
$95$	−0.194896	+	0.112524i	−0.0199960	+	0.0115447i
$96$	−7.67539	+	6.09002i	−0.783366	+	0.621561i
$97$		−	3.21854i		−	0.326793i	−0.986560	−	0.163397i	$-0.947755\pi$
$97$		−	3.21854i		−	0.326793i	0.986560	−	0.163397i	$-0.0522450\pi$
$98$	6.88191	−	7.11613i	0.695178	−	0.718838i
$99$	−1.35531	+	1.75734i	−0.136214	+	0.176620i
$100$	−7.64569	−	6.43824i	−0.764569	−	0.643824i
$101$	1.14917	−	4.28876i	0.114347	−	0.426747i	−0.884891	−	0.465799i	$-0.845767\pi$
$101$	1.14917	−	4.28876i	0.114347	−	0.426747i	0.999237	+	0.0390516i	$0.0124337\pi$
$102$	5.06261	+	9.27396i	0.501273	+	0.918259i
$103$	−0.654096	+	1.13293i	−0.0644500	+	0.111631i	−0.896450	−	0.443145i	$-0.853863\pi$
$103$	−0.654096	+	1.13293i	−0.0644500	+	0.111631i	0.832000	+	0.554776i	$0.187196\pi$
$104$	13.6282	−	7.82080i	1.33635	−	0.766892i
$105$	−0.220323	−	0.00313759i	−0.0215013	−	0.000306198i
$106$	−0.781285	−	0.932749i	−0.0758852	−	0.0905966i
$107$	2.74629	+	10.2493i	0.265494	+	0.990837i	0.961947	+	0.273235i	$0.0880936\pi$
$107$	2.74629	+	10.2493i	0.265494	+	0.990837i	−0.696453	+	0.717602i	$0.745240\pi$
$108$	−8.91358	+	5.34305i	−0.857709	+	0.514135i
$109$	−2.63141	−	0.705083i	−0.252043	−	0.0675347i	0.130585	−	0.991437i	$-0.458314\pi$
$109$	−2.63141	−	0.705083i	−0.252043	−	0.0675347i	−0.382628	+	0.923902i	$0.624981\pi$
$110$	−0.0411808	−	0.0288886i	−0.00392643	−	0.00275442i
$111$	−5.82203	+	6.62238i	−0.552603	+	0.628569i
$112$	10.4318	+	1.78229i	0.985717	+	0.168411i
$113$		−	12.6871i		−	1.19350i	−0.802428	−	0.596749i	$-0.796459\pi$
$113$		−	12.6871i		−	1.19350i	0.802428	−	0.596749i	$-0.203541\pi$
$114$	11.1416	−	2.70161i	1.04351	−	0.253029i
$115$	0.0792606	−	0.295805i	0.00739109	−	0.0275839i
$116$	−6.87331	+	14.6730i	−0.638171	+	1.36236i
$117$	15.4129	−	6.34005i	1.42492	−	0.586138i
$118$	3.56345	−	2.98480i	0.328042	−	0.274773i
$119$	3.80873	−	10.7581i	0.349146	−	0.986191i
$120$	−0.130116	−	0.196361i	−0.0118780	−	0.0179252i
$121$	−9.05236	−	5.22638i	−0.822942	−	0.475126i
$122$	−6.71501	−	2.45069i	−0.607948	−	0.221875i
$123$	8.70157	+	13.0574i	0.784594	+	1.17735i
$124$	13.9238	+	11.7249i	1.25039	+	1.05292i
$125$	0.339921	−	0.339921i	0.0304035	−	0.0304035i
$126$	10.7238	+	3.31669i	0.955351	+	0.295474i
$127$	−6.04307			−0.536235			−0.268118	−	0.963386i	$-0.586402\pi$
$127$	−6.04307			−0.536235			−0.268118	+	0.963386i	$0.586402\pi$
$128$	4.71874	+	10.2827i	0.417082	+	0.908869i
$129$	−2.25040	−	0.450498i	−0.198137	−	0.0396641i
$130$	0.159350	+	0.342506i	0.0139759	+	0.0300398i
$131$	0.892258	+	3.32995i	0.0779569	+	0.290939i	0.993888	−	0.110398i	$-0.0352124\pi$
$131$	0.892258	+	3.32995i	0.0779569	+	0.290939i	−0.915931	+	0.401337i	$0.868546\pi$
$132$	1.59804	+	2.00327i	0.139092	+	0.174362i
$133$	−10.2058	−	7.01310i	−0.884951	−	0.608113i
$134$	6.74637	+	8.05425i	0.582798	+	0.695782i
$135$	−0.109681	−	0.224486i	−0.00943982	−	0.0193207i
$136$	11.7928	−	3.12686i	1.01123	−	0.268126i
$137$	−10.5524	−	18.2773i	−0.901554	−	1.56154i	−0.825478	−	0.564435i	$-0.809094\pi$
$137$	−10.5524	−	18.2773i	−0.901554	−	1.56154i	−0.0760758	−	0.997102i	$-0.524239\pi$
$138$	−8.12116	+	13.3202i	−0.691319	+	1.13389i
$139$	9.09341	−	9.09341i	0.771293	−	0.771293i	−0.207039	−	0.978333i	$-0.566383\pi$
$139$	9.09341	−	9.09341i	0.771293	−	0.771293i	0.978333	+	0.207039i	$0.0663828\pi$
$140$	−0.0641156	+	0.246221i	−0.00541876	+	0.0208095i
$141$	−0.738416	−	11.4815i	−0.0621858	−	0.966914i
$142$	−11.3692	−	7.97556i	−0.954080	−	0.669294i
$143$	−2.05478	−	3.55898i	−0.171829	−	0.297617i
$144$	3.54048	+	11.4658i	0.295040	+	0.955485i
$145$	−0.337359	−	0.194774i	−0.0280161	−	0.0161751i
$146$	0.174605	−	1.97592i	0.0144504	−	0.163528i
$147$	−5.06414	−	11.0161i	−0.417683	−	0.908593i
$148$	5.82550	+	8.35062i	0.478853	+	0.686417i
$149$	3.13969	+	11.7175i	0.257213	+	0.959934i	0.966846	+	0.255361i	$0.0821945\pi$
$149$	3.13969	+	11.7175i	0.257213	+	0.959934i	−0.709632	+	0.704572i	$0.751139\pi$
$150$	−10.7450	+	5.86565i	−0.877327	+	0.478928i
$151$	3.91707	−	2.26152i	0.318767	−	0.184040i	−0.332076	−	0.943253i	$-0.607749\pi$
$151$	3.91707	−	2.26152i	0.318767	−	0.184040i	0.650843	+	0.759213i	$0.274416\pi$
$152$	0.0346089	−	13.2380i	0.00280715	−	1.07375i
$153$	12.8338	−	1.65764i	1.03755	−	0.134012i
$154$	0.459011	−	2.72958i	0.0369882	−	0.219956i
$155$	−0.309448	+	0.309448i	−0.0248555	+	0.0248555i
$156$	−2.87103	−	19.0288i	−0.229867	−	1.52352i
$157$	−0.990580	+	3.69690i	−0.0790569	+	0.295044i	−0.994123	−	0.108261i	$-0.965472\pi$
$157$	−0.990580	+	3.69690i	−0.0790569	+	0.295044i	0.915066	+	0.403305i	$0.132139\pi$
$158$	12.5199	−	5.82483i	0.996026	−	0.463398i
$159$	−1.41168	+	0.477275i	−0.111954	+	0.0378504i
$160$	−0.255999	+	0.0919148i	−0.0202385	+	0.00726650i
$161$	16.5683	−	3.07203i	1.30576	−	0.242110i
$162$	2.13782	+	12.5471i	0.167963	+	0.985793i
$163$	0.208274	+	0.777290i	0.0163133	+	0.0608820i	0.973603	−	0.228249i	$-0.0733002\pi$
$163$	0.208274	+	0.777290i	0.0163133	+	0.0608820i	−0.957289	+	0.289132i	$0.906634\pi$
$164$	17.0367	−	6.16724i	1.33034	−	0.481581i
$165$	−0.0512675	+	0.0341651i	−0.00399117	+	0.00265975i
$166$	−8.94820	+	1.56977i	−0.694515	+	0.121838i
$167$			6.74143i			0.521667i	0.965384	+	0.260834i	$0.0839974\pi$
$167$			6.74143i			0.521667i	−0.965384	+	0.260834i	$0.916003\pi$
$168$	6.66900	−	11.1142i	0.514525	−	0.857476i
$169$			17.8615i			1.37396i
$170$	0.0506820	+	0.288904i	0.00388713	+	0.0221579i
$171$	1.86682	−	13.9164i	0.142759	−	1.06422i
$172$	−1.12416	+	2.39984i	−0.0857166	+	0.182986i
$173$	4.96927	+	18.5456i	0.377807	+	1.40999i	0.849200	+	0.528071i	$0.177084\pi$
$173$	4.96927	+	18.5456i	0.377807	+	1.40999i	−0.471394	+	0.881923i	$0.656249\pi$
$174$	13.6928	+	14.3638i	1.03805	+	1.08892i
$175$	12.4645	+	4.41288i	0.942231	+	0.333582i
$176$	2.68612	−	1.24118i	0.202474	−	0.0935573i
$177$	−1.82337	−	5.39316i	−0.137053	−	0.405375i
$178$	−2.83351	−	6.09034i	−0.212381	−	0.456490i
$179$	3.62655	−	13.5345i	0.271061	−	1.01161i	−0.687375	−	0.726303i	$-0.741237\pi$
$179$	3.62655	−	13.5345i	0.271061	−	1.01161i	0.958435	−	0.285310i	$-0.0920964\pi$
$180$	−0.281920	+	0.0612614i	−0.0210131	+	0.00456615i
$181$	−14.6604	+	14.6604i	−1.08970	+	1.08970i	−0.0941372	+	0.995559i	$0.530009\pi$
$181$	−14.6604	+	14.6604i	−1.08970	+	1.08970i	−0.995559	+	0.0941372i	$0.969991\pi$
$182$	−13.2343	+	16.0285i	−0.980995	+	1.18811i
$183$	−5.78047	+	6.57510i	−0.427305	+	0.486046i
$184$	12.7046	+	12.7712i	0.936593	+	0.941503i
$185$	−0.211992	+	0.122394i	−0.0155860	+	0.00899855i
$186$	19.5681	−	10.6821i	1.43480	−	0.783250i
$187$	−0.825868	−	3.08218i	−0.0603934	−	0.225391i
$188$	−13.0792	−	2.32972i	−0.953897	−	0.169913i
$189$	8.54994	−	10.7656i	0.621916	−	0.783084i
$190$	0.317029	+	0.0280149i	0.0229997	+	0.00203241i
$191$	3.45767	+	1.99628i	0.250188	+	0.144446i	0.619850	−	0.784720i	$-0.287193\pi$
$191$	3.45767	+	1.99628i	0.250188	+	0.144446i	−0.369662	+	0.929166i	$0.620527\pi$
$192$	13.8323	−	0.817006i	0.998260	−	0.0589623i
$193$	−5.60398	−	9.70638i	−0.403383	−	0.698681i	0.590748	−	0.806856i	$-0.298833\pi$
$193$	−5.60398	−	9.70638i	−0.403383	−	0.698681i	−0.994132	+	0.108175i	$0.965499\pi$
$194$	−2.61400	+	3.72626i	−0.187674	+	0.267530i
$195$	0.461707	−	0.0296941i	0.0330635	−	0.00212644i
$196$	−13.7470	+	2.64942i	−0.981930	+	0.189244i
$197$	0.749065	−	0.749065i	0.0533687	−	0.0533687i	−0.679919	−	0.733287i	$-0.737985\pi$
$197$	0.749065	−	0.749065i	0.0533687	−	0.0533687i	0.733287	+	0.679919i	$0.237985\pi$
$198$	2.99637	−	0.933823i	0.212942	−	0.0663639i
$199$	3.47383	+	6.01685i	0.246253	+	0.426523i	0.962483	−	0.271341i	$-0.0874672\pi$
$199$	3.47383	+	6.01685i	0.246253	+	0.426523i	−0.716230	+	0.697864i	$0.754134\pi$
$200$	3.62285	+	13.6635i	0.256174	+	0.966152i
$201$	12.1898	−	4.12125i	0.859805	−	0.290691i
$202$	−4.81364	+	4.03198i	−0.338687	+	0.283689i
$203$	1.68015	−	21.3687i	0.117923	−	1.49979i
$204$	1.67079	−	14.8486i	0.116979	−	1.03961i
$205$	0.112742	+	0.420758i	0.00787422	+	0.0293870i
$206$	1.67741	−	0.780409i	0.116870	−	0.0543737i
$207$	11.5944	+	15.1869i	0.805864	+	1.05556i
$208$	−22.1298	−	2.01386i	−1.53443	−	0.139636i
$209$	−3.46232			−0.239494
$210$	0.252530	+	0.182572i	0.0174262	+	0.0125986i
$211$	−8.20028	+	8.20028i	−0.564531	+	0.564531i	−0.930591	−	0.366060i	$-0.880706\pi$
$211$	−8.20028	+	8.20028i	−0.564531	+	0.564531i	0.366060	+	0.930591i	$0.380706\pi$
$212$	0.146982	+	1.71442i	0.0100948	+	0.117747i
$213$	−14.1539	+	9.43230i	−0.969811	+	0.646290i
$214$	5.14464	−	14.0966i	0.351681	−	0.963621i
$215$	−0.0551766	−	0.0318562i	−0.00376301	−	0.00217258i
$216$	14.6591	+	1.05342i	0.997428	+	0.0716765i
$217$	−22.6995	−	8.03642i	−1.54094	−	0.545548i
$218$	2.47386	+	2.95346i	0.167551	+	0.200033i
$219$	−2.17757	−	1.07717i	−0.147146	−	0.0727886i
$220$	0.0242146	+	0.0668915i	0.00163255	+	0.00450982i
$221$	−6.20200	+	23.1462i	−0.417192	+	1.55698i
$222$	12.1189	−	2.93858i	0.813370	−	0.197224i
$223$			9.36889i			0.627387i	0.949524	+	0.313694i	$0.101566\pi$
$223$			9.36889i			0.627387i	−0.949524	+	0.313694i	$0.898434\pi$
$224$	−10.6299	−	10.5359i	−0.710242	−	0.703957i
$225$	1.92057	+	14.8695i	0.128038	+	0.991303i
$226$	−10.3040	+	14.6884i	−0.685414	+	0.977060i
$227$	−15.8965	−	4.25947i	−1.05509	−	0.282711i	−0.310737	−	0.950496i	$-0.600576\pi$
$227$	−15.8965	−	4.25947i	−1.05509	−	0.282711i	−0.744354	+	0.667785i	$0.767242\pi$
$228$	−15.0934	−	5.92112i	−0.999584	−	0.392136i
$229$	4.65917	+	17.3883i	0.307887	+	1.14905i	0.930432	+	0.366465i	$0.119432\pi$
$229$	4.65917	+	17.3883i	0.307887	+	1.14905i	−0.622545	+	0.782584i	$0.713901\pi$
$230$	−0.332007	+	0.278095i	−0.0218919	+	0.0183370i
$231$	−2.91137	−	1.73662i	−0.191554	−	0.114261i
$232$	19.8745	−	11.4054i	1.30483	−	0.748801i
$233$	−2.64143	+	4.57509i	−0.173046	+	0.299724i	−0.939483	−	0.342595i	$-0.888694\pi$
$233$	−2.64143	+	4.57509i	−0.173046	+	0.299724i	0.766437	+	0.642319i	$0.222028\pi$
$234$	−22.9934	−	5.17769i	−1.50313	−	0.338476i
$235$	0.0826652	−	0.308511i	0.00539248	−	0.0201250i
$236$	−6.54974	+	0.561527i	−0.426352	+	0.0365523i
$237$	−1.08543	−	16.8771i	−0.0705060	−	1.09628i
$238$	−13.1469	+	9.36181i	−0.852188	+	0.606836i
$239$		−	14.5366i		−	0.940297i	−0.882587	−	0.470148i	$-0.844200\pi$
$239$		−	14.5366i		−	0.940297i	0.882587	−	0.470148i	$-0.155800\pi$
$240$	−0.00883591	+	0.333013i	−0.000570356	+	0.0214959i
$241$	−8.35260	+	4.82238i	−0.538038	+	0.310636i	−0.744283	−	0.667864i	$-0.767209\pi$
$241$	−8.35260	+	4.82238i	−0.538038	+	0.310636i	0.206245	+	0.978500i	$0.433876\pi$
$242$	6.23565	+	13.4029i	0.400843	+	0.861570i
$243$	15.2700	+	3.13471i	0.979572	+	0.201092i
$244$	5.78392	+	8.29101i	0.370277	+	0.530777i
$245$	−0.0352324	−	0.334733i	−0.00225092	−	0.0213853i
$246$	0.530588	−	22.1843i	0.0338290	−	1.41442i
$247$	22.5174	+	13.0005i	1.43275	+	0.827199i
$248$	−6.59768	−	24.8829i	−0.418953	−	1.58007i
$249$	−2.18406	+	10.9102i	−0.138409	+	0.691404i
$250$	−0.669616	+	0.117470i	−0.0423502	+	0.00742944i
$251$	14.4125	+	14.4125i	0.909712	+	0.909712i	0.996249	−	0.0865367i	$-0.0275800\pi$
$251$	14.4125	+	14.4125i	0.909712	+	0.909712i	−0.0865367	+	0.996249i	$0.527580\pi$
$252$	−9.72173	−	12.5494i	−0.612412	−	0.790539i
$253$	3.33150	−	3.33150i	0.209450	−	0.209450i
$254$	6.99635	+	4.90799i	0.438990	+	0.307955i
$255$	0.352248	+	0.0705151i	0.0220587	+	0.00441583i
$256$	2.88815	−	15.7372i	0.180510	−	0.983573i
$257$	8.02522	−	13.9001i	0.500599	−	0.867064i	−0.499400	−	0.866371i	$-0.666446\pi$
$257$	8.02522	−	13.9001i	0.500599	−	0.867064i	1.00000		0.000692363i	$-0.000220386\pi$
$258$	2.23952	+	2.34927i	0.139426	+	0.146259i
$259$	−11.1010	−	7.62825i	−0.689780	−	0.473997i
$260$	0.0936857	−	0.525956i	0.00581014	−	0.0326184i
$261$	22.4773	−	9.24596i	1.39131	−	0.572311i
$262$	1.67147	−	4.57991i	0.103264	−	0.282948i
$263$	3.12924	+	5.42001i	0.192957	+	0.334212i	0.946229	−	0.323497i	$-0.104859\pi$
$263$	3.12924	+	5.42001i	0.192957	+	0.334212i	−0.753272	+	0.657710i	$0.771525\pi$
$264$	−0.223139	−	3.61716i	−0.0137333	−	0.222621i
$265$	−0.0413687			−0.00254126
$266$	6.11988	+	16.4082i	0.375234	+	1.00605i
$267$	−8.20992	+	0.528010i	−0.502439	+	0.0323137i
$268$	−1.26919	−	14.8040i	−0.0775279	−	0.904298i
$269$	−2.42162	−	0.648871i	−0.147649	−	0.0395623i	0.184238	−	0.982882i	$-0.441018\pi$
$269$	−2.42162	−	0.648871i	−0.147649	−	0.0395623i	−0.331886	+	0.943319i	$0.607685\pi$
$270$	−0.0553377	+	0.348978i	−0.00336775	+	0.0212381i
$271$	−19.1704	−	11.0680i	−1.16452	−	0.672335i	−0.212136	−	0.977240i	$-0.568042\pi$
$271$	−19.1704	−	11.0680i	−1.16452	−	0.672335i	−0.952383	+	0.304905i	$0.901375\pi$
$272$	−16.1927	−	5.95766i	−0.981826	−	0.361236i
$273$	12.4136	+	22.2260i	0.751305	+	1.34518i
$274$	−2.62722	+	29.7309i	−0.158716	+	1.79611i
$275$	3.57108	−	0.956869i	0.215344	−	0.0577014i
$276$	20.2205	−	8.82571i	1.21713	−	0.531246i
$277$	1.97131	−	7.35704i	0.118445	−	0.442042i	−0.881077	−	0.472973i	$-0.843181\pi$
$277$	1.97131	−	7.35704i	0.118445	−	0.442042i	0.999522	+	0.0309315i	$0.00984738\pi$
$278$	−17.9133	+	3.14250i	−1.07437	+	0.188475i
$279$	−3.49761	−	27.0794i	−0.209397	−	1.62120i
$280$	0.274203	−	0.232990i	0.0163868	−	0.0139238i
$281$	−26.0273			−1.55266			−0.776328	−	0.630329i	$-0.782920\pi$
$281$	−26.0273			−1.55266			−0.776328	+	0.630329i	$0.782920\pi$
$282$	−8.46999	+	13.8924i	−0.504381	+	0.827279i
$283$	20.2855	+	5.43548i	1.20585	+	0.323106i	0.805132	−	0.593096i	$-0.202095\pi$
$283$	20.2855	+	5.43548i	1.20585	+	0.323106i	0.400716	+	0.916202i	$0.368761\pi$
$284$	6.68515	+	18.4674i	0.396691	+	1.09584i
$285$	0.172829	−	0.349383i	0.0102375	−	0.0206957i
$286$	−0.511577	+	5.78924i	−0.0302502	+	0.342325i
$287$	−18.2248	+	15.5678i	−1.07577	+	0.918936i
$288$	5.21319	−	16.1500i	0.307190	−	0.951648i
$289$	−0.803033	+	1.39089i	−0.0472372	+	0.0818172i
$290$	0.232387	+	0.499492i	0.0136462	+	0.0293312i
$291$	3.09144	+	4.63896i	0.181224	+	0.271941i
$292$	−1.80693	+	2.14580i	−0.105742	+	0.125574i
$293$	−7.21013	−	7.21013i	−0.421220	−	0.421220i	0.464404	−	0.885624i	$-0.346269\pi$
$293$	−7.21013	−	7.21013i	−0.421220	−	0.421220i	−0.885624	+	0.464404i	$0.846269\pi$
$294$	−3.08394	+	16.8668i	−0.179859	+	0.983692i
$295$		−	0.158044i		−	0.00920167i
$296$	0.0376446	−	14.3992i	0.00218805	−	0.836937i
$297$	0.265491	−	3.83469i	0.0154053	−	0.222511i
$298$	5.88160	−	16.1159i	0.340712	−	0.933567i
$299$	−34.1759	+	9.15741i	−1.97644	+	0.529587i
$300$	17.2039	+	1.93582i	0.993269	+	0.111765i
$301$	0.274797	−	3.49496i	0.0158390	−	0.201446i
$302$	−6.37173	−	0.563049i	−0.366652	−	0.0323998i
$303$	2.46307	+	7.28528i	0.141500	+	0.418529i
$304$	−10.7916	+	15.2982i	−0.618940	+	0.877412i
$305$	−0.210478	+	0.121520i	−0.0120520	+	0.00695820i
$306$	−16.2046	−	8.50410i	−0.926356	−	0.486147i
$307$	−0.520044	−	0.520044i	−0.0296805	−	0.0296805i	0.692111	−	0.721791i	$-0.256681\pi$
$307$	−0.520044	−	0.520044i	−0.0296805	−	0.0296805i	−0.721791	+	0.692111i	$0.756681\pi$
$308$	−2.74830	+	2.78737i	−0.156599	+	0.158825i
$309$	−0.145425	−	2.26118i	−0.00827294	−	0.128634i
$310$	0.609588	−	0.106939i	0.0346223	−	0.00607373i
$311$	22.2452	−	12.8433i	1.26141	−	0.728275i	0.288062	−	0.957612i	$-0.406989\pi$
$311$	22.2452	−	12.8433i	1.26141	−	0.728275i	0.973347	+	0.229337i	$0.0736557\pi$
$312$	−12.1307	+	24.3623i	−0.686763	+	1.37925i
$313$	9.05901	−	15.6907i	0.512045	−	0.886889i	−0.487857	−	0.872924i	$-0.662221\pi$
$313$	9.05901	−	15.6907i	0.512045	−	0.886889i	0.999902	−	0.0139652i	$-0.00444542\pi$
$314$	4.14935	−	3.47556i	0.234161	−	0.196137i
$315$	0.320570	−	0.207100i	0.0180621	−	0.0116688i
$316$	−19.2256	−	3.42455i	−1.08152	−	0.192646i
$317$	−27.0536	+	7.24899i	−1.51948	+	0.407144i	−0.919571	−	0.392923i	$-0.871464\pi$
$317$	−27.0536	+	7.24899i	−1.51948	+	0.407144i	−0.599910	+	0.800067i	$0.704797\pi$
$318$	2.02200	+	0.593961i	0.113388	+	0.0333077i
$319$	−2.99657	−	5.19022i	−0.167776	−	0.290596i
$320$	0.371033	+	0.101500i	0.0207414	+	0.00567403i
$321$	−13.8029	−	12.1347i	−0.770401	−	0.677294i
$322$	−21.6769	−	9.89960i	−1.20801	−	0.551683i
$323$	14.2755	+	14.2755i	0.794312	+	0.794312i
$324$	7.71530	−	16.2627i	0.428628	−	0.903481i
$325$	−26.8177	−	7.18578i	−1.48758	−	0.398595i
$326$	0.390161	−	1.06906i	0.0216090	−	0.0592098i
$327$	4.46995	−	1.51124i	0.247189	−	0.0835719i
$328$	−24.7331	−	6.69655i	−1.36565	−	0.369755i
$329$	17.2799	−	3.20398i	0.952674	−	0.176641i
$330$	0.0871027	+	0.00208326i	0.00479485	+	0.000114679i
$331$	0.759927	−	0.203622i	0.0417693	−	0.0111921i	−0.237874	−	0.971296i	$-0.576450\pi$
$331$	0.759927	−	0.203622i	0.0417693	−	0.0111921i	0.279643	+	0.960104i	$0.409784\pi$
$332$	11.6347	+	5.45005i	0.638536	+	0.299110i
$333$	2.03057	−	15.1371i	0.111275	−	0.829510i
$334$	5.47518	−	7.80488i	0.299588	−	0.427064i
$335$	0.357217			0.0195169
$336$	−16.7476	+	7.45104i	−0.913656	+	0.406488i
$337$	18.0736			0.984532			0.492266	−	0.870445i	$-0.336169\pi$
$337$	18.0736			0.984532			0.492266	+	0.870445i	$0.336169\pi$
$338$	14.5065	−	20.6791i	0.789052	−	1.12480i
$339$	12.1861	+	18.2862i	0.661857	+	0.993169i
$340$	0.175962	−	0.375641i	0.00954287	−	0.0203720i
$341$	−6.50340	+	1.74258i	−0.352179	+	0.0943661i
$342$	−13.4638	+	14.5956i	−0.728040	+	0.789238i
$343$	15.7889	−	9.68034i	0.852523	−	0.522689i
$344$	3.25058	−	1.86541i	0.175259	−	0.100576i
$345$	0.169884	+	0.502482i	0.00914622	+	0.0270527i
$346$	9.30897	−	25.5070i	0.500453	−	1.37126i
$347$	−17.3129	−	4.63898i	−0.929405	−	0.249033i	−0.237804	−	0.971313i	$-0.576428\pi$
$347$	−17.3129	−	4.63898i	−0.929405	−	0.249033i	−0.691601	+	0.722280i	$0.743094\pi$
$348$	−4.18695	−	27.7505i	−0.224444	−	1.48758i
$349$	−24.9093	−	24.9093i	−1.33337	−	1.33337i	−0.902339	−	0.431028i	$-0.858151\pi$
$349$	−24.9093	−	24.9093i	−1.33337	−	1.33337i	−0.431028	−	0.902339i	$-0.641849\pi$
$350$	−10.8468	−	15.2323i	−0.579786	−	0.814201i
$351$	−16.1253	+	23.9423i	−0.860705	+	1.27795i
$352$	−4.11790	−	0.744611i	−0.219485	−	0.0396879i
$353$	10.1097	+	17.5105i	0.538084	+	0.931989i	0.999007	+	0.0445488i	$0.0141850\pi$
$353$	10.1097	+	17.5105i	0.538084	+	0.931989i	−0.460923	+	0.887440i	$0.652482\pi$
$354$	−2.26915	+	7.72481i	−0.120604	+	0.410569i
$355$	−0.456092	+	0.122209i	−0.0242068	+	0.00648620i
$356$	−1.66589	+	9.35237i	−0.0882919	+	0.495675i
$357$	4.84363	+	19.1642i	0.256352	+	1.01428i
$358$	−15.1909	+	12.7241i	−0.802864	+	0.672491i
$359$	−7.64827	+	13.2472i	−0.403660	+	0.699160i	−0.994165	−	0.107874i	$-0.965596\pi$
$359$	−7.64827	+	13.2472i	−0.403660	+	0.699160i	0.590504	+	0.807035i	$0.298929\pi$
$360$	0.376147	+	0.158041i	0.0198247	+	0.00832951i
$361$	2.51653	−	1.45292i	0.132449	−	0.0764694i
$362$	28.8797	−	5.06633i	1.51788	−	0.266280i
$363$	18.0674	−	1.16198i	0.948292	−	0.0609882i
$364$	28.3399	−	7.80846i	1.48541	−	0.409274i
$365$	−0.0476893	−	0.0476893i	−0.00249617	−	0.00249617i
$366$	12.0324	−	2.91760i	0.628945	−	0.152505i
$367$	30.8584	−	17.8161i	1.61079	−	0.929992i	0.621608	−	0.783329i	$-0.286480\pi$
$367$	30.8584	−	17.8161i	1.61079	−	0.929992i	0.989186	−	0.146664i	$-0.0468536\pi$
$368$	−4.33635	−	25.1040i	−0.226048	−	1.30864i
$369$	−25.0836	−	10.4620i	−1.30580	−	0.544630i
$370$	0.344837	+	0.0304722i	0.0179272	+	0.00158417i
$371$	−0.980122	−	2.05447i	−0.0508854	−	0.106663i
$372$	−31.3306	−	3.52538i	−1.62441	−	0.182782i
$373$	21.8537	−	5.85567i	1.13154	−	0.303195i	0.355995	−	0.934488i	$-0.384142\pi$
$373$	21.8537	−	5.85567i	1.13154	−	0.303195i	0.775545	+	0.631293i	$0.217475\pi$
$374$	−1.54710	+	4.23913i	−0.0799988	+	0.219200i
$375$	−0.163439	+	0.816435i	−0.00843993	+	0.0421605i
$376$	13.2503	+	13.3197i	0.683330	+	0.686913i
$377$			45.0066i			2.31796i
$378$	−18.6422	+	5.51989i	−0.958850	+	0.283912i
$379$	6.55573	+	6.55573i	0.336745	+	0.336745i	0.855141	−	0.518396i	$-0.173471\pi$
$379$	6.55573	+	6.55573i	0.336745	+	0.336745i	−0.518396	+	0.855141i	$0.673471\pi$
$380$	−0.344287	−	0.289915i	−0.0176616	−	0.0148723i
$381$	8.71002	−	5.80443i	0.446228	−	0.297370i
$382$	−2.38179	−	5.11940i	−0.121863	−	0.261931i
$383$	6.58458	−	11.4048i	0.336457	−	0.582760i	−0.647307	−	0.762229i	$-0.724105\pi$
$383$	6.58458	−	11.4048i	0.336457	−	0.582760i	0.983764	+	0.179470i	$0.0574382\pi$
$384$	−16.6779	−	10.2883i	−0.851089	−	0.525021i
$385$	−0.0611240	−	0.0715562i	−0.00311517	−	0.00364684i
$386$	−1.39522	+	15.7889i	−0.0710147	+	0.803635i
$387$	3.67626	−	1.51222i	0.186875	−	0.0768705i
$388$	6.05270	−	2.19106i	0.307279	−	0.111234i
$389$	−18.4065	−	4.93201i	−0.933248	−	0.250063i	−0.240009	−	0.970771i	$-0.577150\pi$
$389$	−18.4065	−	4.93201i	−0.933248	−	0.250063i	−0.693239	+	0.720708i	$0.743817\pi$
$390$	−0.558657	−	0.340605i	−0.0282887	−	0.0172472i
$391$	−27.4723			−1.38933
$392$	18.0674	+	8.09754i	0.912540	+	0.408987i
$393$	−4.48449	−	3.94252i	−0.226213	−	0.198874i
$394$	−1.47560	+	0.258862i	−0.0743395	+	0.0130413i
$395$	0.121513	−	0.453492i	0.00611397	−	0.0228176i
$396$	−4.22746	−	1.35242i	−0.212438	−	0.0679618i
$397$	12.3001	−	3.29580i	0.617323	−	0.165411i	0.0634125	−	0.997987i	$-0.479802\pi$
$397$	12.3001	−	3.29580i	0.617323	−	0.165411i	0.553911	+	0.832576i	$0.313135\pi$
$398$	0.864876	−	9.78733i	0.0433523	−	0.490595i
$399$	21.4460	+	0.305410i	1.07364	+	0.0152896i
$400$	6.90268	−	18.7612i	0.345134	−	0.938061i
$401$	−9.55498	−	5.51657i	−0.477153	−	0.275484i	0.242076	−	0.970257i	$-0.422172\pi$
$401$	−9.55498	−	5.51657i	−0.477153	−	0.275484i	−0.719229	+	0.694773i	$0.755505\pi$
$402$	−17.4599	−	5.12883i	−0.870821	−	0.255803i
$403$	48.8385	+	13.0862i	2.43282	+	0.651871i
$404$	8.84764	−	0.758532i	0.440187	−	0.0377384i
$405$	0.373707	+	0.218208i	0.0185697	+	0.0108428i
$406$	−19.3002	+	23.3751i	−0.957853	+	1.16008i
$407$	−3.76602			−0.186674
$408$	−13.9939	+	15.8340i	−0.692803	+	0.783899i
$409$	9.28820	+	16.0876i	0.459272	+	0.795482i	0.998923	−	0.0464069i	$-0.0147771\pi$
$409$	9.28820	+	16.0876i	0.459272	+	0.795482i	−0.539651	+	0.841889i	$0.681444\pi$
$410$	0.211200	−	0.578697i	0.0104304	−	0.0285798i
$411$	32.7650	+	16.2078i	1.61618	+	0.799474i
$412$	−2.57584	−	0.458820i	−0.126902	−	0.0226045i
$413$	7.84886	−	3.74443i	0.386217	−	0.184251i
$414$	−1.08900	−	26.9992i	−0.0535213	−	1.32694i
$415$	−0.154442	+	0.267502i	−0.00758127	+	0.0131311i
$416$	23.9852	+	20.3047i	1.17597	+	0.995519i
$417$	−4.37223	+	21.8409i	−0.214109	+	1.06955i
$418$	4.00849	+	2.81199i	0.196062	+	0.137539i
$419$	5.90253	−	5.90253i	0.288357	−	0.288357i	−0.548073	−	0.836430i	$-0.684638\pi$
$419$	5.90253	−	5.90253i	0.288357	−	0.288357i	0.836430	+	0.548073i	$0.184638\pi$
$420$	−0.144087	−	0.416469i	−0.00703073	−	0.0203216i
$421$	2.60313	+	2.60313i	0.126869	+	0.126869i	0.767690	−	0.640821i	$-0.221406\pi$
$421$	2.60313	+	2.60313i	0.126869	+	0.126869i	−0.640821	+	0.767690i	$0.721406\pi$
$422$	16.1539	−	2.83385i	0.786358	−	0.137950i
$423$	12.0924	+	15.8393i	0.587952	+	0.770132i
$424$	1.22223	−	2.10425i	0.0593569	−	0.102191i
$425$	−18.6693	−	10.7787i	−0.905592	−	0.522844i
$426$	24.0473	+	0.575145i	1.16510	+	0.0278659i
$427$	−11.0217	−	7.57380i	−0.533378	−	0.366522i
$428$	−17.4050	+	12.1420i	−0.841302	+	0.586903i
$429$	6.38005	+	3.15601i	0.308032	+	0.152374i
$430$	0.0380080	+	0.0816942i	0.00183291	+	0.00393965i
$431$	34.0209	−	19.6420i	1.63873	−	0.946122i	0.657461	−	0.753489i	$-0.271631\pi$
$431$	34.0209	−	19.6420i	1.63873	−	0.946122i	0.981271	−	0.192633i	$-0.0617027\pi$
$432$	−16.1160	−	13.1253i	−0.775383	−	0.631491i
$433$			22.2155i			1.06761i	0.845607	+	0.533805i	$0.179239\pi$
$433$			22.2155i			1.06761i	−0.845607	+	0.533805i	$0.820761\pi$
$434$	19.7534	+	27.7400i	0.948195	+	1.33156i
$435$	0.673326	−	0.0433041i	0.0322835	−	0.00207627i
$436$	−0.465404	−	5.42855i	−0.0222888	−	0.259981i
$437$	−7.71515	+	28.7933i	−0.369066	+	1.37737i
$438$	1.64623	+	3.01565i	0.0786598	+	0.144093i
$439$	2.41920	−	4.19017i	0.115462	−	0.199986i	−0.802502	−	0.596649i	$-0.796499\pi$
$439$	2.41920	−	4.19017i	0.115462	−	0.199986i	0.917964	+	0.396663i	$0.129832\pi$
$440$	0.0262928	−	0.0971099i	0.00125346	−	0.00462953i
$441$	17.8802	+	11.0136i	0.851436	+	0.524458i
$442$	25.9790	−	21.7604i	1.23569	−	1.03504i
$443$	−6.43837	−	24.0283i	−0.305896	−	1.14162i	−0.932171	−	0.362018i	$-0.882088\pi$
$443$	−6.43837	−	24.0283i	−0.305896	−	1.14162i	0.626275	−	0.779602i	$-0.284579\pi$
$444$	−16.4173	−	6.44049i	−0.779131	−	0.305652i
$445$	−0.220603	−	0.0591104i	−0.0104576	−	0.00280210i
$446$	7.60912	−	10.8468i	0.360302	−	0.513612i
$447$	−15.7801	−	13.8730i	−0.746373	−	0.656170i
$448$	3.74988	+	20.8312i	0.177165	+	0.984181i
$449$		−	33.3828i		−	1.57543i	−0.616040	−	0.787715i	$-0.711264\pi$
$449$		−	33.3828i		−	1.57543i	0.616040	−	0.787715i	$-0.288736\pi$
$450$	9.85304	−	18.7750i	0.464477	−	0.885063i
$451$	−1.73451	+	6.47330i	−0.0816751	+	0.304816i
$452$	23.8590	−	8.63689i	1.12223	−	0.406245i
$453$	−3.47356	+	7.02198i	−0.163202	+	0.329922i
$454$	14.9448	+	17.8421i	0.701394	+	0.837370i
$455$	0.128842	+	0.694882i	0.00604022	+	0.0325766i
$456$	12.6654	+	19.1135i	0.593112	+	0.895074i
$457$	−28.9169	−	16.6952i	−1.35268	−	0.780969i	−0.364054	−	0.931378i	$-0.618608\pi$
$457$	−28.9169	−	16.6952i	−1.35268	−	0.780969i	−0.988624	+	0.150409i	$0.951941\pi$
$458$	8.72805	−	23.9153i	0.407835	−	1.11749i
$459$	−16.9055	+	14.7162i	−0.789082	+	0.686894i
$460$	0.610241	−	0.0523176i	0.0284526	−	0.00243932i
$461$	17.9478	−	17.9478i	0.835913	−	0.835913i	−0.152405	−	0.988318i	$-0.548702\pi$
$461$	17.9478	−	17.9478i	0.835913	−	0.835913i	0.988318	+	0.152405i	$0.0487020\pi$
$462$	1.96021	+	4.37510i	0.0911971	+	0.203548i
$463$	−13.0149			−0.604852			−0.302426	−	0.953173i	$-0.597797\pi$
$463$	−13.0149			−0.604852			−0.302426	+	0.953173i	$0.597797\pi$
$464$	−32.2728	−	2.93690i	−1.49823	−	0.136342i
$465$	0.148787	−	0.743244i	0.00689983	−	0.0344671i
$466$	6.77386	−	3.15152i	0.313793	−	0.145991i
$467$	0.336830	+	1.25707i	0.0155866	+	0.0581700i	0.973281	−	0.229617i	$-0.0737472\pi$
$467$	0.336830	+	1.25707i	0.0155866	+	0.0581700i	−0.957695	+	0.287787i	$0.907081\pi$
$468$	22.4155	+	24.6690i	1.03616	+	1.14033i
$469$	8.46331	+	17.7403i	0.390799	+	0.819171i
$470$	−0.346268	+	0.290040i	−0.0159722	+	0.0133785i
$471$	−2.12316	−	6.27989i	−0.0978302	−	0.289362i
$472$	8.03901	+	4.66939i	0.370025	+	0.214926i
$473$	−0.490104	−	0.848885i	−0.0225350	−	0.0390318i
$474$	−12.4504	+	20.4209i	−0.571864	+	0.937964i
$475$	−16.5399	+	16.5399i	−0.758905	+	0.758905i
$476$	22.8242	−	0.161105i	1.04615	−	0.00738422i
$477$	1.57627	−	2.04385i	0.0721723	−	0.0935813i
$478$	−11.8062	+	16.8298i	−0.540003	+	0.769776i
$479$	−5.69448	−	9.86313i	−0.260187	−	0.450658i	0.706104	−	0.708108i	$-0.250451\pi$
$479$	−5.69448	−	9.86313i	−0.260187	−	0.450658i	−0.966292	+	0.257450i	$0.917118\pi$
$480$	0.280693	−	0.378369i	0.0128118	−	0.0172701i
$481$	24.4926	+	14.1408i	1.11676	+	0.644764i
$482$	13.5868	+	1.20062i	0.618861	+	0.0546868i
$483$	−20.9295	+	20.3418i	−0.952327	+	0.925584i
$484$	3.66608	−	20.5816i	0.166640	−	0.935526i
$485$	0.0400542	+	0.149484i	0.00181877	+	0.00678774i
$486$	−15.1329	−	16.0310i	−0.686444	−	0.727183i
$487$	−11.9437	+	6.89572i	−0.541223	+	0.312475i	−0.745574	−	0.666423i	$-0.767825\pi$
$487$	−11.9437	+	6.89572i	−0.541223	+	0.312475i	0.204352	+	0.978898i	$0.434491\pi$
$488$	0.0373759	−	14.2964i	0.00169193	−	0.647168i
$489$	−1.04679	−	0.920278i	−0.0473373	−	0.0416164i
$490$	−0.231070	+	0.416152i	−0.0104387	+	0.0187998i
$491$	−30.8632	+	30.8632i	−1.39284	+	1.39284i	−0.573939	+	0.818898i	$0.694585\pi$
$491$	−30.8632	+	30.8632i	−1.39284	+	1.39284i	−0.818898	+	0.573939i	$0.805415\pi$
$492$	−18.6317	+	25.2529i	−0.839982	+	1.13849i
$493$	−9.04464	+	33.7551i	−0.407350	+	1.52025i
$494$	−15.5110	−	33.3392i	−0.697872	−	1.50000i
$495$	0.0410772	−	0.0984861i	0.00184628	−	0.00442662i
$496$	−12.5707	+	34.1666i	−0.564440	+	1.53413i
$497$	−16.8751	−	19.7552i	−0.756952	−	0.886142i
$498$	11.3895	−	10.8574i	0.510375	−	0.486532i
$499$	6.30877	+	23.5446i	0.282419	+	1.05400i	0.950705	+	0.310098i	$0.100362\pi$
$499$	6.30877	+	23.5446i	0.282419	+	1.05400i	−0.668285	+	0.743905i	$0.732971\pi$
$500$	0.870653	+	0.407841i	0.0389368	+	0.0182392i
$501$	−6.47522	−	9.71659i	−0.289291	−	0.434105i
$502$	−4.98069	−	28.3915i	−0.222299	−	1.26718i
$503$			18.3232i			0.816989i	0.912761	+	0.408495i	$0.133946\pi$
$503$			18.3232i			0.816989i	−0.912761	+	0.408495i	$0.866054\pi$
$504$	1.06308	+	22.4248i	0.0473532	+	0.998878i
$505$			0.213492i			0.00950026i
$506$	−6.56278	+	1.15130i	−0.291751	+	0.0511815i
$507$	−17.1562	−	25.7442i	−0.761932	−	1.14334i
$508$	−4.11390	−	11.3644i	−0.182525	−	0.504215i
$509$	−5.84711	−	21.8217i	−0.259169	−	0.967231i	−0.965724	−	0.259573i	$-0.916418\pi$
$509$	−5.84711	−	21.8217i	−0.259169	−	0.967231i	0.706555	−	0.707658i	$-0.250248\pi$
$510$	−0.350545	−	0.367724i	−0.0155224	−	0.0162831i
$511$	1.23850	−	3.49824i	0.0547879	−	0.154753i
$512$	−16.1250	+	15.8740i	−0.712631	+	0.701539i
$513$	10.6762	+	21.8512i	0.471366	+	0.964755i
$514$	−20.5804	+	9.57498i	−0.907763	+	0.422334i
$515$	0.0162802	−	0.0607587i	0.000717393	−	0.00267735i
$516$	−0.684795	−	4.53873i	−0.0301464	−	0.199806i
$517$	3.47460	−	3.47460i	0.152813	−	0.152813i
$518$	6.65668	+	17.8474i	0.292478	+	0.784172i
$519$	−24.9756	−	21.9572i	−1.09631	−	0.963812i
$520$	−0.535629	+	0.532836i	−0.0234889	+	0.0233664i
$521$	−11.9374	+	6.89205i	−0.522986	+	0.301946i	−0.738155	−	0.674631i	$-0.764303\pi$
$521$	−11.9374	+	6.89205i	−0.522986	+	0.301946i	0.215170	+	0.976577i	$0.430970\pi$
$522$	−33.5323	−	7.55084i	−1.46767	−	0.330491i
$523$	0.247255	+	0.922767i	0.0108117	+	0.0403498i	0.971121	−	0.238588i	$-0.0766844\pi$
$523$	0.247255	+	0.922767i	0.0108117	+	0.0403498i	−0.960309	+	0.278937i	$0.910018\pi$
$524$	−5.65480	+	3.94487i	−0.247031	+	0.172332i
$525$	−22.2041	+	5.61194i	−0.969065	+	0.244925i
$526$	0.779085	−	8.81648i	0.0339697	−	0.384417i
$527$	33.9991	+	19.6294i	1.48102	+	0.855070i
$528$	−2.67941	+	4.36899i	−0.116606	+	0.190136i
$529$	−8.78178	−	15.2105i	−0.381816	−	0.661326i
$530$	0.0478946	+	0.0335984i	0.00208041	+	0.00145942i
$531$	7.80826	+	6.02193i	0.338850	+	0.261329i
$532$	6.24095	−	23.9669i	0.270579	−	1.03910i
$533$	35.5867	−	35.5867i	1.54143	−	1.54143i
$534$	9.93386	+	6.05654i	0.429880	+	0.262092i
$535$	−0.255102	−	0.441849i	−0.0110290	−	0.0191028i
$536$	−10.5539	+	18.1701i	−0.455861	+	0.784829i
$537$	7.77297	+	22.9909i	0.335428	+	0.992130i
$538$	2.27663	+	2.71799i	0.0981526	+	0.117181i
$539$	2.10549	−	4.73090i	0.0906898	−	0.203774i
$540$	0.347496	−	0.359085i	0.0149538	−	0.0154526i
$541$	1.90589	+	7.11290i	0.0819408	+	0.305807i	0.994717	−	0.102652i	$-0.0327328\pi$
$541$	1.90589	+	7.11290i	0.0819408	+	0.305807i	−0.912777	+	0.408459i	$0.866066\pi$
$542$	13.2054	+	28.3836i	0.567220	+	1.21918i
$543$	7.04890	−	35.2118i	0.302497	−	1.51108i
$544$	13.9084	+	20.0487i	0.596319	+	0.859580i
$545$	0.130990			0.00561099
$546$	3.67943	−	35.8140i	0.157465	−	1.53270i
$547$	12.8901	−	12.8901i	0.551141	−	0.551141i	−0.375629	−	0.926770i	$-0.622573\pi$
$547$	12.8901	−	12.8901i	0.551141	−	0.551141i	0.926770	+	0.375629i	$0.122573\pi$
$548$	27.1882	−	32.2871i	1.16142	−	1.37924i
$549$	2.01607	−	15.0291i	0.0860440	−	0.641425i
$550$	−4.91156	−	1.79251i	−0.209429	−	0.0764328i
$551$	32.8381	+	18.9591i	1.39895	+	0.807685i
$552$	−30.5782	−	6.20452i	−1.30150	−	0.264082i
$553$	25.4005	−	4.70966i	1.08014	−	0.200275i
$554$	−8.25744	+	6.91657i	−0.350825	+	0.293857i
$555$	0.187989	−	0.380029i	0.00797968	−	0.0161314i
$556$	23.2913	+	10.9104i	0.987771	+	0.462703i
$557$	−1.27312	+	4.75136i	−0.0539439	+	0.201322i	−0.987638	−	0.156749i	$-0.949899\pi$
$557$	−1.27312	+	4.75136i	−0.0539439	+	0.201322i	0.933695	+	0.358071i	$0.116565\pi$
$558$	−17.9437	+	34.1917i	−0.759615	+	1.44745i
$559$			7.36105i			0.311339i
$560$	−0.506685	+	0.0470444i	−0.0214114	+	0.00198799i
$561$	4.15081	+	3.64917i	0.175247	+	0.154068i
$562$	30.1330	+	21.1385i	1.27108	+	0.891675i
$563$	−34.8216	−	9.33041i	−1.46755	−	0.393230i	−0.565462	−	0.824774i	$-0.691302\pi$
$563$	−34.8216	−	9.33041i	−1.46755	−	0.393230i	−0.902092	+	0.431544i	$0.857969\pi$
$564$	21.0891	−	9.20481i	0.888010	−	0.387592i
$565$	0.157889	+	0.589248i	0.00664242	+	0.0247899i
$566$	−19.0710	−	22.7682i	−0.801613	−	0.957018i
$567$	−1.98274	+	23.7291i	−0.0832671	+	0.996527i
$568$	7.25891	−	26.8101i	0.304577	−	1.12493i
$569$	19.4334	−	33.6597i	0.814692	−	1.41109i	−0.0948571	−	0.995491i	$-0.530239\pi$
$569$	19.4334	−	33.6597i	0.814692	−	1.41109i	0.909549	−	0.415597i	$-0.136427\pi$
$570$	−0.483851	+	0.264132i	−0.0202663	+	0.0110633i
$571$	−7.85472	+	29.3142i	−0.328710	+	1.22676i	0.581820	+	0.813318i	$0.302341\pi$
$571$	−7.85472	+	29.3142i	−0.328710	+	1.22676i	−0.910530	+	0.413444i	$0.864326\pi$
$572$	5.29412	−	6.28700i	0.221358	−	0.262873i
$573$	−6.90107	+	0.443834i	−0.288296	+	0.0185414i
$574$	33.7433	−	3.22198i	1.40842	−	0.134483i
$575$		−	31.8300i		−	1.32740i
$576$	−19.1521	+	14.4637i	−0.798004	+	0.602652i
$577$	−4.92288	+	2.84223i	−0.204942	+	0.118323i	−0.598959	−	0.800780i	$-0.704419\pi$
$577$	−4.92288	+	2.84223i	−0.204942	+	0.118323i	0.394016	+	0.919103i	$0.371085\pi$
$578$	2.05935	−	0.958107i	0.0856577	−	0.0398520i
$579$	17.4002	+	8.60736i	0.723130	+	0.357710i
$580$	0.136626	−	0.767024i	0.00567308	−	0.0318489i
$581$	−16.9439	−	1.33224i	−0.702952	−	0.0552707i
$582$	0.188504	−	7.88152i	0.00781375	−	0.326700i
$583$	−0.551184	−	0.318226i	−0.0228277	−	0.0131796i
$584$	3.83472	−	1.01677i	0.158682	−	0.0420744i
$585$	−0.636948	+	0.486273i	−0.0263346	+	0.0201049i
$586$	2.49167	+	14.2034i	0.102930	+	0.586735i
$587$	−19.4368	−	19.4368i	−0.802244	−	0.802244i	0.181202	−	0.983446i	$-0.442001\pi$
$587$	−19.4368	−	19.4368i	−0.802244	−	0.802244i	−0.983446	+	0.181202i	$0.942001\pi$
$588$	17.2691	−	17.0228i	0.712167	−	0.702010i
$589$	30.1214	−	30.1214i	1.24113	−	1.24113i
$590$	−0.128358	+	0.182975i	−0.00528443	+	0.00753297i
$591$	−0.360161	+	1.79913i	−0.0148150	+	0.0740064i
$592$	−11.7382	+	16.6401i	−0.482436	+	0.683904i
$593$	−8.91827	+	15.4469i	−0.366229	+	0.634328i	−0.988973	−	0.148098i	$-0.952685\pi$
$593$	−8.91827	+	15.4469i	−0.366229	+	0.634328i	0.622743	+	0.782426i	$0.286018\pi$
$594$	−3.42179	+	4.22399i	−0.140398	+	0.173312i
$595$	−0.0430131	+	0.547055i	−0.00176337	+	0.0224271i
$596$	−19.8982	+	13.8813i	−0.815063	+	0.568599i
$597$	−10.7862	−	5.33558i	−0.441448	−	0.218371i
$598$	47.0045	+	17.1546i	1.92216	+	0.701505i
$599$	−2.95431	−	5.11701i	−0.120710	−	0.209075i	0.799338	−	0.600882i	$-0.205184\pi$
$599$	−2.95431	−	5.11701i	−0.120710	−	0.209075i	−0.920048	+	0.391806i	$0.871850\pi$
$600$	−18.3456	−	16.2137i	−0.748957	−	0.661921i
$601$	35.3462			1.44180			0.720900	−	0.693039i	$-0.243729\pi$
$601$	35.3462			1.44180			0.720900	+	0.693039i	$0.243729\pi$
$602$	−3.15664	+	3.82310i	−0.128655	+	0.155818i
$603$	−13.6110	+	17.6485i	−0.554283	+	0.718704i
$604$	6.91956	+	5.82679i	0.281553	+	0.237089i
$605$	0.485477	+	0.130083i	0.0197374	+	0.00528863i
$606$	3.06526	−	10.4350i	0.124518	−	0.423891i
$607$	−34.3771	−	19.8476i	−1.39532	−	0.805589i	−0.401424	−	0.915892i	$-0.631484\pi$
$607$	−34.3771	−	19.8476i	−1.39532	−	0.805589i	−0.993898	+	0.110303i	$0.964818\pi$
$608$	24.9187	−	8.94689i	1.01059	−	0.362844i
$609$	18.1033	+	32.4131i	0.733581	+	1.31344i
$610$	0.342376	+	0.0302547i	0.0138624	+	0.00122498i
$611$	−35.6439	+	9.55076i	−1.44200	+	0.386382i
$612$	11.8541	+	23.0065i	0.479174	+	0.929982i
$613$	8.55124	−	31.9137i	0.345381	−	1.28898i	−0.546785	−	0.837273i	$-0.684148\pi$
$613$	8.55124	−	31.9137i	0.345381	−	1.28898i	0.892166	−	0.451708i	$-0.149185\pi$
$614$	0.179717	+	1.02444i	0.00725277	+	0.0413432i
$615$	−0.566640	−	0.498159i	−0.0228491	−	0.0200877i
$616$	5.44566	−	0.994994i	0.219412	−	0.0400894i
$617$	36.2709			1.46021			0.730106	−	0.683333i	$-0.239470\pi$
$617$	36.2709			1.46021			0.730106	+	0.683333i	$0.239470\pi$
$618$	−1.66810	+	2.73599i	−0.0671007	+	0.110058i
$619$	−3.28219	−	0.879460i	−0.131922	−	0.0353485i	0.192254	−	0.981345i	$-0.438420\pi$
$619$	−3.28219	−	0.879460i	−0.131922	−	0.0353485i	−0.324176	+	0.945997i	$0.605087\pi$
$620$	−0.792602	−	0.371280i	−0.0318317	−	0.0149109i
$621$	−31.2985	−	10.7528i	−1.25596	−	0.431495i
$622$	−36.1852	−	3.19758i	−1.45090	−	0.128211i
$623$	−2.29103	−	12.3562i	−0.0917883	−	0.495039i
$624$	33.8306	−	18.3533i	1.35431	−	0.734720i
$625$	12.4827	−	21.6206i	0.499307	−	0.864824i
$626$	−23.2315	+	10.8084i	−0.928518	+	0.431991i
$627$	4.99033	−	3.32560i	0.199294	−	0.132812i
$628$	−7.62664	+	0.653852i	−0.304336	+	0.0260915i
$629$	15.5277	+	15.5277i	0.619130	+	0.619130i
$630$	−0.539340	−	0.0205872i	−0.0214878	−	0.000820214i
$631$		−	45.7384i		−	1.82081i	−0.413713	−	0.910407i	$-0.635768\pi$
$631$		−	45.7384i		−	1.82081i	0.413713	−	0.910407i	$-0.364232\pi$
$632$	19.4771	+	19.5792i	0.774757	+	0.778818i
$633$	3.94281	−	19.6957i	0.156712	−	0.782835i
$634$	37.2087	+	13.5796i	1.47775	+	0.539314i
$635$	0.280669	−	0.0752050i	0.0111380	−	0.00298442i
$636$	−1.85857	−	2.32987i	−0.0736973	−	0.0923852i
$637$	−31.4570	+	22.8620i	−1.24637	+	0.905826i
$638$	−0.746054	+	8.44269i	−0.0295366	+	0.334249i
$639$	11.3406	−	27.1900i	0.448626	−	1.07562i
$640$	−0.347127	−	0.418853i	−0.0137214	−	0.0165566i
$641$	8.09505	−	4.67368i	0.319735	−	0.184599i	−0.331539	−	0.943441i	$-0.607568\pi$
$641$	8.09505	−	4.67368i	0.319735	−	0.184599i	0.651275	+	0.758842i	$0.274235\pi$
$642$	6.12480	+	25.2592i	0.241727	+	0.996902i
$643$	−18.6520	−	18.6520i	−0.735562	−	0.735562i	0.236153	−	0.971716i	$-0.424113\pi$
$643$	−18.6520	−	18.6520i	−0.735562	−	0.735562i	−0.971716	+	0.236153i	$0.924113\pi$
$644$	17.0563	+	29.0665i	0.672110	+	1.14538i
$645$	0.110126	−	0.00708259i	0.00433620	−	0.000278877i
$646$	−4.93333	−	28.1216i	−0.194099	−	1.10643i
$647$	−20.9785	+	12.1119i	−0.824749	+	0.476169i	−0.852052	−	0.523458i	$-0.824642\pi$
$647$	−20.9785	+	12.1119i	−0.824749	+	0.476169i	0.0273021	+	0.999627i	$0.491308\pi$
$648$	−22.1404	+	12.5619i	−0.869757	+	0.493480i
$649$	1.21574	−	2.10573i	0.0477221	−	0.0826570i
$650$	25.2121	+	30.0998i	0.988899	+	1.18061i
$651$	40.4365	−	10.2201i	1.58483	−	0.400556i
$652$	−1.31997	+	0.920826i	−0.0516939	+	0.0360623i
$653$	17.7192	−	4.74784i	0.693405	−	0.185797i	0.105130	−	0.994458i	$-0.466474\pi$
$653$	17.7192	−	4.74784i	0.693405	−	0.185797i	0.588275	+	0.808661i	$0.299807\pi$
$654$	−6.40247	−	1.88072i	−0.250356	−	0.0735419i
$655$	−0.0828815	−	0.143555i	−0.00323845	−	0.00560915i
$656$	23.1959	+	27.8403i	0.905649	+	1.08698i
$657$	4.17322	−	0.539020i	0.162813	−	0.0210292i
$658$	−22.6080	−	10.3248i	−0.881352	−	0.402504i
$659$	−7.19647	−	7.19647i	−0.280335	−	0.280335i	0.552908	−	0.833242i	$-0.313518\pi$
$659$	−7.19647	−	7.19647i	−0.280335	−	0.280335i	−0.833242	+	0.552908i	$0.813518\pi$
$660$	−0.0991511	−	0.0731540i	−0.00385945	−	0.00284752i
$661$	11.0098	+	2.95007i	0.428233	+	0.114745i	0.466496	−	0.884523i	$-0.345516\pi$
$661$	11.0098	+	2.95007i	0.428233	+	0.114745i	−0.0382638	+	0.999268i	$0.512183\pi$
$662$	−1.04518	−	0.381446i	−0.0406220	−	0.0148253i
$663$	−13.2931	−	39.3183i	−0.516260	−	1.52700i
$664$	−9.04368	−	15.7591i	−0.350963	−	0.611572i
$665$	0.561281	+	0.198713i	0.0217655	+	0.00770576i
$666$	−14.6448	+	15.8758i	−0.567474	+	0.615176i
$667$	−49.8402	+	13.3546i	−1.92982	+	0.517094i
$668$	−12.6778	+	4.58932i	−0.490517	+	0.177566i
$669$	−8.99893	−	13.5036i	−0.347919	−	0.522080i
$670$	−0.413568	−	0.290121i	−0.0159775	−	0.0112083i
$671$	−3.73913			−0.144348
$672$	25.4410	+	4.97544i	0.981408	+	0.191932i
$673$	−47.7001			−1.83870			−0.919352	−	0.393436i	$-0.871286\pi$
$673$	−47.7001			−1.83870			−0.919352	+	0.393436i	$0.871286\pi$
$674$	−20.9247	−	14.6788i	−0.805989	−	0.565407i
$675$	−17.0505	−	19.5871i	−0.656276	−	0.753908i
$676$	−33.5899	+	12.1595i	−1.29192	+	0.467671i
$677$	−1.57854	+	0.422967i	−0.0606680	+	0.0162560i	−0.289025	−	0.957321i	$-0.593331\pi$
$677$	−1.57854	+	0.422967i	−0.0606680	+	0.0162560i	0.228357	+	0.973577i	$0.426665\pi$
$678$	0.743059	−	31.0679i	0.0285370	−	1.19316i
$679$	−6.47479	+	5.53083i	−0.248480	+	0.212254i
$680$	−0.508803	+	0.291987i	−0.0195117	+	0.0111972i
$681$	27.0033	−	9.12954i	1.03477	−	0.349845i
$682$	8.94457	+	3.26439i	0.342505	+	0.125000i
$683$	16.7743	+	4.49467i	0.641852	+	0.171984i	0.565042	−	0.825062i	$-0.308860\pi$
$683$	16.7743	+	4.49467i	0.641852	+	0.171984i	0.0768100	+	0.997046i	$0.475527\pi$
$684$	27.4418	−	5.96312i	1.04926	−	0.228005i
$685$	0.717563	+	0.717563i	0.0274167	+	0.0274167i
$686$	−26.1417	−	1.61589i	−0.998095	−	0.0616949i
$687$	−23.4170	−	20.5869i	−0.893414	−	0.785441i
$688$	−5.27837	−	0.480344i	−0.201236	−	0.0183129i
$689$	2.38978	+	4.13921i	0.0910432	+	0.157691i
$690$	0.211417	−	0.719721i	0.00804852	−	0.0273993i
$691$	−4.67095	+	1.25158i	−0.177691	+	0.0476122i	−0.346568	−	0.938025i	$-0.612653\pi$
$691$	−4.67095	+	1.25158i	−0.177691	+	0.0476122i	0.168876	+	0.985637i	$0.445986\pi$
$692$	−31.4934	+	21.9702i	−1.19720	+	0.835183i
$693$	5.86428	−	0.293372i	0.222765	−	0.0111443i
$694$	16.2764	+	19.4318i	0.617842	+	0.737620i
$695$	−0.309176	+	0.535508i	−0.0117277	+	0.0203130i
$696$	−17.6907	+	35.5286i	−0.670563	+	1.34671i
$697$	33.8417	−	19.5385i	1.28185	−	0.740075i
$698$	8.60816	+	49.0693i	0.325824	+	1.85730i
$699$	−0.587269	−	9.13132i	−0.0222125	−	0.345378i
$700$	0.186659	+	26.4446i	0.00705506	+	0.999513i
$701$	18.0951	+	18.0951i	0.683442	+	0.683442i	0.960774	−	0.277332i	$-0.0894502\pi$
$701$	18.0951	+	18.0951i	0.683442	+	0.683442i	−0.277332	+	0.960774i	$0.589450\pi$
$702$	38.1143	−	14.6227i	1.43853	−	0.551900i
$703$	20.6351	−	11.9137i	0.778266	−	0.449332i
$704$	4.16274	+	4.20650i	0.156889	+	0.158538i
$705$	0.177181	+	0.524065i	0.00667301	+	0.0197374i
$706$	2.51700	−	28.4835i	0.0947284	−	1.07199i
$707$	−10.6025	+	5.05812i	−0.398749	+	0.190230i
$708$	8.90096	−	7.10045i	0.334518	−	0.266851i
$709$	3.45754	−	0.926445i	0.129851	−	0.0347934i	−0.193308	−	0.981138i	$-0.561922\pi$
$709$	3.45754	−	0.926445i	0.129851	−	0.0347934i	0.323159	+	0.946345i	$0.395255\pi$
$710$	0.627294	+	0.228936i	0.0235419	+	0.00859180i
$711$	17.7751	+	23.2828i	0.666617	+	0.873171i
$712$	9.52439	−	9.47472i	0.356941	−	0.355080i
$713$			57.9666i			2.17087i
$714$	9.95686	−	26.1212i	0.372626	−	0.977560i
$715$	0.139725	+	0.139725i	0.00522542	+	0.00522542i
$716$	27.9214	−	2.39377i	1.04347	−	0.0894596i
$717$	13.9626	+	20.9520i	0.521443	+	0.782467i
$718$	19.6137	−	9.12523i	0.731978	−	0.340551i
$719$	9.67059	−	16.7500i	0.360652	−	0.624668i	−0.627416	−	0.778684i	$-0.715887\pi$
$719$	9.67059	−	16.7500i	0.360652	−	0.624668i	0.988068	+	0.154016i	$0.0492208\pi$
$720$	−0.307127	−	0.488467i	−0.0114460	−	0.0182041i
$721$	3.40315	−	0.630999i	0.126740	−	0.0234996i
$722$	−4.09353	−	0.361732i	−0.152345	−	0.0134623i
$723$	7.40686	−	14.9734i	0.275464	−	0.556866i
$724$	−37.5502	−	17.5897i	−1.39554	−	0.653715i
$725$	−39.1094	−	10.4793i	−1.45249	−	0.389192i
$726$	−21.8612	−	13.3285i	−0.811346	−	0.494667i
$727$	15.1864			0.563234			0.281617	−	0.959527i	$-0.409129\pi$
$727$	15.1864			0.563234			0.281617	+	0.959527i	$0.409129\pi$
$728$	−39.1523	−	13.9765i	−1.45108	−	0.518005i
$729$	−25.0200	+	10.1489i	−0.926666	+	0.375885i
$730$	0.0164805	+	0.0939440i	0.000609969	+	0.00347702i
$731$	−1.47929	+	5.52080i	−0.0547137	+	0.204194i
$732$	−16.3001	−	6.39452i	−0.602469	−	0.236348i
$733$	−6.75082	+	1.80888i	−0.249347	+	0.0668124i	−0.381328	−	0.924440i	$-0.624533\pi$
$733$	−6.75082	+	1.80888i	−0.249347	+	0.0668124i	0.131981	+	0.991252i	$0.457866\pi$
$734$	−50.1959	−	4.43566i	−1.85277	−	0.163723i
$735$	0.372297	+	0.448618i	0.0137324	+	0.0165475i
$736$	−15.3683	+	32.5860i	−0.566484	+	1.20114i
$737$	4.75945	+	2.74787i	0.175317	+	0.101219i
$738$	20.5436	+	32.4845i	0.756219	+	1.19577i
$739$	−45.6723	−	12.2378i	−1.68008	−	0.450177i	−0.712281	−	0.701894i	$-0.752338\pi$
$739$	−45.6723	−	12.2378i	−1.68008	−	0.450177i	−0.967801	+	0.251718i	$0.919005\pi$
$740$	−0.374487	−	0.315345i	−0.0137664	−	0.0115923i
$741$	−44.9420	+	2.89039i	−1.65099	+	0.106181i
$742$	−0.533845	+	3.17459i	−0.0195980	+	0.116543i
$743$	32.0924			1.17736			0.588678	−	0.808368i	$-0.299649\pi$
$743$	32.0924			1.17736			0.588678	+	0.808368i	$0.299649\pi$
$744$	33.4097	+	29.5272i	1.22486	+	1.08252i
$745$	−0.291645	−	0.505143i	−0.0106850	−	0.0185070i
$746$	−30.0568	−	10.9695i	−1.10046	−	0.401621i
$747$	−7.33140	−	17.8229i	−0.268242	−	0.652106i
$748$	5.23405	−	3.65134i	0.191376	−	0.133506i
$749$	15.8994	−	23.1374i	0.580951	−	0.845423i
$750$	0.852303	−	0.812486i	0.0311217	−	0.0296678i
$751$	−2.69098	+	4.66092i	−0.0981954	+	0.170079i	−0.910938	−	0.412544i	$-0.864640\pi$
$751$	−2.69098	+	4.66092i	−0.0981954	+	0.170079i	0.812742	+	0.582623i	$0.197974\pi$
$752$	−4.52261	−	26.1824i	−0.164923	−	0.954772i
$753$	−34.6166	−	6.92975i	−1.26150	−	0.252534i
$754$	36.5530	−	52.1064i	1.33118	−	1.89760i
$755$	−0.153783	+	0.153783i	−0.00559675	+	0.00559675i
$756$	26.0660	+	8.74995i	0.948013	+	0.318233i
$757$	−0.835396	−	0.835396i	−0.0303630	−	0.0303630i	0.691762	−	0.722125i	$-0.256835\pi$
$757$	−0.835396	−	0.835396i	−0.0303630	−	0.0303630i	−0.722125	+	0.691762i	$0.756835\pi$
$758$	−2.26553	−	12.9143i	−0.0822877	−	0.469067i
$759$	−1.60183	+	8.00172i	−0.0581428	+	0.290444i
$760$	0.163138	+	0.615269i	0.00591763	+	0.0223181i
$761$	−6.47138	−	3.73625i	−0.234587	−	0.135439i	0.378099	−	0.925765i	$-0.376578\pi$
$761$	−6.47138	−	3.73625i	−0.234587	−	0.135439i	−0.612686	+	0.790326i	$0.709911\pi$
$762$	−14.7982	−	0.353932i	−0.536082	−	0.0128216i
$763$	3.10346	+	6.50528i	0.112353	+	0.235507i
$764$	−1.40031	+	7.86139i	−0.0506614	+	0.284415i
$765$	−0.575435	+	0.236703i	−0.0208049	+	0.00855803i
$766$	−16.8859	+	7.85614i	−0.610114	+	0.283854i
$767$	−15.8133	+	9.12984i	−0.570987	+	0.329659i
$768$	10.9530	+	25.4565i	0.395231	+	0.918582i
$769$			3.05207i			0.110060i	0.998485	+	0.0550302i	$0.0175255\pi$
$769$			3.05207i			0.110060i	−0.998485	+	0.0550302i	$0.982474\pi$
$770$	0.0126505	+	0.132487i	0.000455893	+	0.00477450i
$771$	1.78425	+	27.7429i	0.0642580	+	0.999135i
$772$	14.4386	−	17.1465i	0.519656	−	0.617114i
$773$	−2.90234	+	10.8317i	−0.104390	+	0.389589i	−0.998275	−	0.0587071i	$-0.981302\pi$
$773$	−2.90234	+	10.8317i	−0.104390	+	0.389589i	0.893885	+	0.448296i	$0.147969\pi$
$774$	−5.48437	−	1.23498i	−0.197132	−	0.0443903i
$775$	−22.7431	+	39.3921i	−0.816955	+	1.41501i
$776$	−8.78702	−	2.37911i	−0.315436	−	0.0854052i
$777$	23.3271	+	0.332199i	0.836855	+	0.0119176i
$778$	17.3045	+	20.6592i	0.620397	+	0.740670i
$779$	−10.9742	−	40.9561i	−0.393190	−	1.46740i
$780$	0.370155	+	0.848059i	0.0132537	+	0.0303654i
$781$	−7.01691	−	1.88017i	−0.251085	−	0.0672779i
$782$	31.8060	+	22.3122i	1.13738	+	0.797881i
$783$	−23.5162	+	34.9161i	−0.840401	+	1.24780i
$784$	−14.3409	−	24.0487i	−0.512175	−	0.858881i
$785$		−	0.184029i		−	0.00656828i
$786$	1.98992	+	8.20661i	0.0709782	+	0.292720i
$787$	11.9465	−	44.5848i	0.425846	−	1.58928i	−0.336224	−	0.941782i	$-0.609150\pi$
$787$	11.9465	−	44.5848i	0.425846	−	1.58928i	0.762069	−	0.647495i	$-0.224183\pi$
$788$	1.91861	+	0.898737i	0.0683476	+	0.0320162i
$789$	−9.71624	−	4.80632i	−0.345907	−	0.171110i
$790$	−0.508993	+	0.426341i	−0.0181092	+	0.0151685i
$791$	−25.5228	+	21.8018i	−0.907486	+	0.775183i
$792$	3.79594	+	4.99918i	0.134883	+	0.177638i
$793$	24.3177	+	14.0398i	0.863547	+	0.498569i
$794$	−16.9171	−	6.17404i	−0.600367	−	0.219108i
$795$	0.0596258	−	0.0397351i	0.00211471	−	0.00140926i
$796$	−8.95027	+	10.6288i	−0.317234	+	0.376729i
$797$	15.1048	−	15.1048i	0.535040	−	0.535040i	−0.387028	−	0.922068i	$-0.626498\pi$
$797$	15.1048	−	15.1048i	0.535040	−	0.535040i	0.922068	+	0.387028i	$0.126498\pi$
$798$	−24.5810	−	17.7713i	−0.870158	−	0.629098i
$799$	−28.6524			−1.01365
$800$	−23.2288	+	16.1146i	−0.821264	+	0.569738i
$801$	11.3260	−	8.64676i	0.400185	−	0.305518i
$802$	6.58188	+	14.1471i	0.232414	+	0.499550i
$803$	−0.268550	−	1.00224i	−0.00947694	−	0.0353684i
$804$	16.0487	+	20.1183i	0.565995	+	0.709518i
$805$	−0.731279	+	0.348869i	−0.0257742	+	0.0122960i
$806$	−45.9144	−	54.8156i	−1.61727	−	1.93080i
$807$	4.11359	−	1.39076i	0.144805	−	0.0489570i
$808$	−10.8594	−	6.30759i	−0.382032	−	0.221900i
$809$	−7.22744	−	12.5183i	−0.254103	−	0.440120i	0.710548	−	0.703648i	$-0.248447\pi$
$809$	−7.22744	−	12.5183i	−0.254103	−	0.440120i	−0.964652	+	0.263529i	$0.915114\pi$
$810$	−0.255437	−	0.556143i	−0.00897516	−	0.0195409i
$811$	9.88503	−	9.88503i	0.347110	−	0.347110i	−0.511922	−	0.859032i	$-0.671066\pi$
$811$	9.88503	−	9.88503i	0.347110	−	0.347110i	0.859032	+	0.511922i	$0.171066\pi$
$812$	41.3293	−	11.3874i	1.45037	−	0.399620i
$813$	38.2617	−	2.46075i	1.34190	−	0.0863024i
$814$	4.36010	+	3.05864i	0.152821	+	0.107205i
$815$	−0.0193465	−	0.0335091i	−0.000677679	−	0.00117377i
$816$	29.0613	−	6.96634i	1.01735	−	0.243871i
$817$	5.37083	+	3.10085i	0.187902	+	0.108485i
$818$	2.31247	−	26.1690i	0.0808537	−	0.914978i
$819$	−39.2403	−	20.1115i	−1.37117	−	0.702751i
$820$	−0.714516	+	0.498456i	−0.0249520	+	0.0174068i
$821$	−6.43091	−	24.0005i	−0.224440	−	0.837623i	−0.982628	−	0.185586i	$-0.940582\pi$
$821$	−6.43091	−	24.0005i	−0.224440	−	0.837623i	0.758188	−	0.652036i	$-0.226085\pi$
$822$	−24.7702	−	45.3753i	−0.863959	−	1.58265i
$823$	3.05486	−	1.76373i	0.106486	−	0.0614797i	−0.445811	−	0.895127i	$-0.647085\pi$
$823$	3.05486	−	1.76373i	0.106486	−	0.0614797i	0.552297	+	0.833647i	$0.313751\pi$
$824$	2.60953	+	2.62321i	0.0909074	+	0.0913840i
$825$	−4.22801	+	4.80923i	−0.147200	+	0.167436i
$826$	−12.1281	−	2.03949i	−0.421991	−	0.0709628i
$827$	−27.0327	+	27.0327i	−0.940018	+	0.940018i	−0.998300	−	0.0582820i	$-0.981438\pi$
$827$	−27.0327	+	27.0327i	−0.940018	+	0.940018i	0.0582820	+	0.998300i	$0.481438\pi$
$828$	−20.6671	+	32.1428i	−0.718233	+	1.11704i
$829$	0.707194	−	2.63928i	0.0245619	−	0.0916661i	−0.952557	−	0.304361i	$-0.901557\pi$
$829$	0.707194	−	2.63928i	0.0245619	−	0.0916661i	0.977119	+	0.212694i	$0.0682239\pi$
$830$	0.396062	−	0.184267i	0.0137475	−	0.00639599i
$831$	4.22522	+	12.4974i	0.146571	+	0.433528i
$832$	−11.2779	−	42.9877i	−0.390993	−	1.49033i
$833$	−28.1872	+	10.8249i	−0.976629	+	0.375060i
$834$	22.8004	−	21.7353i	0.789515	−	0.752631i
$835$	−0.0838960	−	0.313104i	−0.00290334	−	0.0108354i
$836$	−2.35702	−	6.51115i	−0.0815193	−	0.225193i
$837$	31.0512	+	35.6707i	1.07329	+	1.23296i
$838$	−11.6275	+	2.03979i	−0.401665	+	0.0704635i
$839$			18.6575i			0.644128i	0.946718	+	0.322064i	$0.104377\pi$
$839$			18.6575i			0.644128i	−0.946718	+	0.322064i	$0.895623\pi$
$840$	−0.171426	+	0.599189i	−0.00591477	+	0.0206740i
$841$			36.6351i			1.26328i
$842$	−0.899590	−	5.12796i	−0.0310019	−	0.176721i
$843$	37.5137	−	24.9995i	1.29204	−	0.861028i
$844$	−21.0037	−	9.83879i	−0.722977	−	0.338665i
$845$	−0.222284	−	0.829574i	−0.00764679	−	0.0285382i
$846$	−1.13577	−	28.1589i	−0.0390487	−	0.968124i
$847$	5.04183	+	27.1919i	0.173239	+	0.934326i
$848$	−3.12404	+	1.44353i	−0.107280	+	0.0495710i
$849$	−34.4588	+	11.6502i	−1.18262	+	0.399832i
$850$	12.8602	+	27.6416i	0.441101	+	0.948100i
$851$	−8.39188	+	31.3189i	−0.287670	+	1.07360i
$852$	−27.3736	−	20.1963i	−0.937805	−	0.691915i
$853$	−15.5760	+	15.5760i	−0.533311	+	0.533311i	−0.921556	−	0.388245i	$-0.873081\pi$
$853$	−15.5760	+	15.5760i	−0.533311	+	0.533311i	0.388245	+	0.921556i	$0.373081\pi$
$854$	6.60916	+	17.7200i	0.226161	+	0.606367i
$855$	0.0864839	+	0.669579i	0.00295769	+	0.0228991i
$856$	30.0119	+	0.0784618i	1.02579	+	0.00268177i
$857$	23.2156	−	13.4035i	0.793030	−	0.457856i	−0.0479983	−	0.998847i	$-0.515284\pi$
$857$	23.2156	−	13.4035i	0.793030	−	0.457856i	0.841028	+	0.540991i	$0.181951\pi$
$858$	−4.82328	−	8.83555i	−0.164664	−	0.301641i
$859$	3.47988	+	12.9871i	0.118732	+	0.443114i	0.999539	−	0.0303615i	$-0.00966585\pi$
$859$	3.47988	+	12.9871i	0.118732	+	0.443114i	−0.880807	+	0.473476i	$0.842999\pi$
$860$	0.0223458	−	0.125450i	0.000761985	−	0.00427782i
$861$	11.3148	−	39.9433i	0.385607	−	1.36126i
$862$	−55.3403	−	4.89025i	−1.88490	−	0.166563i
$863$	4.24756	+	2.45233i	0.144589	+	0.0834782i	0.570549	−	0.821264i	$-0.306730\pi$
$863$	4.24756	+	2.45233i	0.144589	+	0.0834782i	−0.425961	+	0.904742i	$0.640064\pi$
$864$	7.99836	+	28.2847i	0.272110	+	0.962266i
$865$	−0.461594	−	0.799504i	−0.0156947	−	0.0271839i
$866$	18.0428	−	25.7200i	0.613118	−	0.874002i
$867$	−0.178538	−	2.77605i	−0.00606347	−	0.0942796i
$868$	−0.339931	−	48.1591i	−0.0115380	−	1.63462i
$869$	5.10745	−	5.10745i	0.173258	−	0.173258i
$870$	−0.814713	−	0.496719i	−0.0276214	−	0.0168404i
$871$	−20.6356	−	35.7419i	−0.699211	−	1.21107i
$872$	−3.87008	+	6.66289i	−0.131057	+	0.225634i
$873$	−8.91155	−	3.71688i	−0.301610	−	0.125797i
$874$	32.3172	−	27.0694i	1.09315	−	0.915637i
$875$	−1.26795	−	0.0996950i	−0.0428647	−	0.00337030i
$876$	0.543298	−	4.82838i	0.0183563	−	0.163136i
$877$	−0.349006	−	1.30251i	−0.0117851	−	0.0439826i	0.959783	−	0.280743i	$-0.0905809\pi$
$877$	−0.349006	−	1.30251i	−0.0117851	−	0.0439826i	−0.971568	+	0.236761i	$0.923914\pi$
$878$	−6.20395	+	2.88637i	−0.209373	+	0.0974102i
$879$	17.3175	+	3.46673i	0.584106	+	0.116930i
$880$	−0.109310	+	0.0910746i	−0.00368484	+	0.00307012i
$881$	15.4458			0.520383			0.260192	−	0.965557i	$-0.416214\pi$
$881$	15.4458			0.520383			0.260192	+	0.965557i	$0.416214\pi$
$882$	−11.7558	−	27.2727i	−0.395839	−	0.918320i
$883$	24.6662	−	24.6662i	0.830085	−	0.830085i	−0.157443	−	0.987528i	$-0.550325\pi$
$883$	24.6662	−	24.6662i	0.830085	−	0.830085i	0.987528	+	0.157443i	$0.0503251\pi$
$884$	−47.7502	+	4.09376i	−1.60601	+	0.137688i
$885$	0.151803	+	0.227793i	0.00510280	+	0.00765717i
$886$	−12.0610	+	33.0478i	−0.405199	+	1.11026i
$887$	−35.8239	−	20.6829i	−1.20285	−	0.694465i	−0.241661	−	0.970361i	$-0.577692\pi$
$887$	−35.8239	−	20.6829i	−1.20285	−	0.694465i	−0.961188	+	0.275896i	$0.911026\pi$
$888$	13.7763	+	20.7901i	0.462304	+	0.697670i
$889$	10.3846	+	12.1569i	0.348287	+	0.407731i
$890$	0.207395	+	0.247602i	0.00695191	+	0.00829964i
$891$	3.30061	+	5.78204i	0.110575	+	0.193706i
$892$	−17.6189	+	6.37800i	−0.589924	+	0.213551i
$893$	−8.04654	+	30.0301i	−0.269267	+	1.00492i
$894$	7.00217	+	28.8775i	0.234188	+	0.965809i
$895$			0.673737i			0.0225205i
$896$	12.5770	−	27.1628i	0.420169	−	0.907446i
$897$	40.4628	−	46.0252i	1.35101	−	1.53674i
$898$	−27.1124	+	38.6488i	−0.904754	+	1.28973i
$899$	71.2232	+	19.0842i	2.37543	+	0.636494i
$900$	−26.6558	+	13.7344i	−0.888528	+	0.457814i
$901$	0.960511	+	3.58467i	0.0319992	+	0.119423i
$902$	7.26554	−	6.08573i	0.241916	−	0.202633i
$903$	2.96088	+	5.30131i	0.0985318	+	0.176417i
$904$	−34.6373	−	9.37816i	−1.15202	−	0.311913i
$905$	0.498452	−	0.863344i	0.0165691	−	0.0286985i
$906$	9.72454	−	5.30858i	0.323076	−	0.176366i
$907$	−0.0678351	+	0.253164i	−0.00225243	+	0.00840617i	−0.967043	−	0.254614i	$-0.918052\pi$
$907$	−0.0678351	+	0.253164i	−0.00225243	+	0.00840617i	0.964790	+	0.263020i	$0.0847184\pi$
$908$	−2.81155	−	32.7943i	−0.0933044	−	1.08832i
$909$	−10.5477	−	8.13465i	−0.349845	−	0.269809i
$910$	0.415194	−	0.909140i	0.0137636	−	0.0301377i
$911$			13.1688i			0.436300i	0.975915	+	0.218150i	$0.0700023\pi$
$911$			13.1688i			0.436300i	−0.975915	+	0.218150i	$0.929998\pi$
$912$	0.860078	−	32.4151i	0.0284800	−	1.07337i
$913$	−4.11548	+	2.37607i	−0.136203	+	0.0786366i
$914$	19.9192	+	42.8143i	0.658870	+	1.41617i
$915$	0.186647	−	0.377317i	0.00617035	−	0.0124737i
$916$	−29.5281	+	20.5992i	−0.975637	+	0.680617i
$917$	5.16564	−	7.51725i	0.170584	−	0.248242i
$918$	31.5244	−	3.30755i	1.04046	−	0.109165i
$919$	−26.2798	−	15.1727i	−0.866892	−	0.500500i	−0.000577856	−	1.00000i	$-0.500184\pi$
$919$	−26.2798	−	15.1727i	−0.866892	−	0.500500i	−0.866314	+	0.499499i	$0.833517\pi$
$920$	−0.748996	−	0.435048i	−0.0246937	−	0.0143431i
$921$	1.24906	+	0.250044i	0.0411579	+	0.00823923i
$922$	−35.3557	+	6.20240i	−1.16438	+	0.204265i
$923$	38.5752	+	38.5752i	1.26972	+	1.26972i
$924$	1.28389	−	6.65728i	0.0422368	−	0.219008i
$925$	−17.9908	+	17.9908i	−0.591532	+	0.591532i
$926$	15.0679	+	10.5703i	0.495163	+	0.347361i
$927$	2.38150	+	3.11942i	0.0782186	+	0.102455i
$928$	34.9786	+	29.6112i	1.14823	+	0.972035i
$929$	−6.86282	+	11.8868i	−0.225162	+	0.389992i	−0.956368	−	0.292165i	$-0.905624\pi$
$929$	−6.86282	+	11.8868i	−0.225162	+	0.389992i	0.731206	+	0.682157i	$0.238958\pi$
$930$	−0.775898	+	0.739650i	−0.0254427	+	0.0242541i
$931$	3.42949	+	32.5826i	0.112397	+	1.06785i
$932$	−10.4020	−	1.85285i	−0.340729	−	0.0606921i
$933$	−19.7264	+	39.8781i	−0.645815	+	1.30555i
$934$	0.630985	−	1.72893i	0.0206465	−	0.0565723i
$935$	0.0767145	+	0.132873i	0.00250883	+	0.00434543i
$936$	−5.91607	−	46.7657i	−0.193373	−	1.52858i
$937$	57.4133			1.87561			0.937806	−	0.347160i	$-0.112854\pi$
$937$	57.4133			1.87561			0.937806	+	0.347160i	$0.112854\pi$
$938$	4.60973	−	27.4124i	0.150513	−	0.895048i
$939$	2.01409	+	31.3166i	0.0657273	+	1.02198i
$940$	0.636453	−	0.0545648i	0.0207588	−	0.00177971i
$941$	−39.2748	−	10.5237i	−1.28032	−	0.343061i	−0.446345	−	0.894861i	$-0.647275\pi$
$941$	−39.2748	−	10.5237i	−1.28032	−	0.343061i	−0.833977	+	0.551800i	$0.813941\pi$
$942$	−2.64224	+	8.99490i	−0.0860889	+	0.293070i
$943$	49.9682	+	28.8491i	1.62719	+	0.939457i
$944$	−5.51482	−	11.9350i	−0.179492	−	0.388452i
$945$	−0.263124	+	0.606410i	−0.00855941	+	0.0197265i
$946$	−0.122021	+	1.38084i	−0.00396723	+	0.0448951i
$947$	58.1936	−	15.5929i	1.89104	−	0.506702i	0.892597	−	0.450855i	$-0.148881\pi$
$947$	58.1936	−	15.5929i	1.89104	−	0.506702i	0.998439	−	0.0558468i	$-0.0177858\pi$
$948$	30.9996	−	13.5305i	1.00682	−	0.439450i
$949$	−2.01673	+	7.52653i	−0.0654657	+	0.244321i
$950$	32.5823	−	5.71587i	1.05711	−	0.185447i
$951$	32.0303	−	36.4334i	1.03865	−	1.18144i
$952$	−26.5555	−	18.3506i	−0.860669	−	0.594746i
$953$	−13.2269			−0.428462			−0.214231	−	0.976783i	$-0.568725\pi$
$953$	−13.2269			−0.428462			−0.214231	+	0.976783i	$0.568725\pi$
$954$	−3.48487	+	1.08607i	−0.112827	+	0.0351627i
$955$	−0.185434	−	0.0496869i	−0.00600050	−	0.00160783i
$956$	27.3372	−	9.89601i	0.884149	−	0.320060i
$957$	9.30430	+	4.60255i	0.300765	+	0.148779i
$958$	−1.41775	+	16.0439i	−0.0458054	+	0.518355i
$959$	−18.6352	+	52.6367i	−0.601763	+	1.69973i
$960$	−0.632271	+	0.210087i	−0.0204065	+	0.00678051i
$961$	25.9180	−	44.8914i	0.836066	−	1.44811i
$962$	−16.8715	−	36.2636i	−0.543960	−	1.16918i
$963$	31.5499	+	4.23227i	1.01668	+	0.136383i
$964$	−14.7550	−	12.4248i	−0.475226	−	0.400175i
$965$	0.381070	+	0.381070i	0.0122671	+	0.0122671i
$966$	40.7521	−	6.55237i	1.31118	−	0.210819i
$967$			39.8634i			1.28192i	0.767574	+	0.640961i	$0.221464\pi$
$967$			39.8634i			1.28192i	−0.767574	+	0.640961i	$0.778536\pi$
$968$	−20.9601	+	20.8508i	−0.673684	+	0.670170i
$969$	−34.2875	−	6.86387i	−1.10147	−	0.220499i
$970$	0.0750338	−	0.205596i	0.00240919	−	0.00660129i
$971$	−33.8371	+	9.06663i	−1.08589	+	0.290962i	−0.757005	−	0.653409i	$-0.773338\pi$
$971$	−33.8371	+	9.06663i	−1.08589	+	0.290962i	−0.328881	+	0.944371i	$0.606671\pi$
$972$	4.50021	+	30.8504i	0.144344	+	0.989528i
$973$	−33.9197	−	2.66699i	−1.08742	−	0.0854999i
$974$	19.4283	+	1.71682i	0.622524	+	0.0550105i
$975$	45.5550	−	15.4017i	1.45893	−	0.493248i
$976$	−11.6544	+	16.5213i	−0.373047	+	0.528834i
$977$	24.1166	−	13.9237i	0.771557	−	0.445459i	−0.0618725	−	0.998084i	$-0.519707\pi$
$977$	24.1166	−	13.9237i	0.771557	−	0.445459i	0.833430	+	0.552625i	$0.186374\pi$
$978$	0.464495	+	1.91562i	0.0148529	+	0.0612547i
$979$	−2.48454	−	2.48454i	−0.0794064	−	0.0794064i
$980$	0.605506	−	0.294131i	0.0193422	−	0.00939568i
$981$	−4.99109	+	6.47163i	−0.159353	+	0.206623i
$982$	60.7980	−	10.6657i	1.94014	−	0.340356i
$983$	19.7098	−	11.3794i	0.628644	−	0.362948i	−0.151583	−	0.988445i	$-0.548437\pi$
$983$	19.7098	−	11.3794i	0.628644	−	0.362948i	0.780227	+	0.625497i	$0.215104\pi$
$984$	42.0805	−	14.1045i	1.34148	−	0.449634i
$985$	−0.0254682	+	0.0441122i	−0.000811484	+	0.00140553i
$986$	37.8862	−	31.7341i	1.20654	−	1.01062i
$987$	−21.8285	+	21.2156i	−0.694810	+	0.675299i
$988$	−9.11926	+	51.1960i	−0.290122	+	1.62876i
$989$	−8.15160	+	2.18421i	−0.259206	+	0.0694540i
$990$	−0.127544	+	0.0806605i	−0.00405363	+	0.00256356i
$991$	4.31482	+	7.47348i	0.137065	+	0.237403i	0.926384	−	0.376580i	$-0.122900\pi$
$991$	4.31482	+	7.47348i	0.137065	+	0.237403i	−0.789320	+	0.613983i	$0.789567\pi$
$992$	42.3027	−	29.3468i	1.34311	−	0.931762i
$993$	−0.899720	+	1.02340i	−0.0285518	+	0.0324767i
$994$	3.49255	+	36.5770i	0.110777	+	1.16015i
$995$	−0.236220	−	0.236220i	−0.00748868	−	0.00748868i
$996$	−22.0042	+	3.31996i	−0.697230	+	0.105197i
$997$	25.3589	+	6.79490i	0.803124	+	0.215197i	0.636955	−	0.770901i	$-0.280194\pi$
$997$	25.3589	+	6.79490i	0.803124	+	0.215197i	0.166169	+	0.986097i	$0.446860\pi$
$998$	11.8183	−	32.3826i	0.374100	−	1.02505i
$999$	11.6127	+	23.7679i	0.367409	+	0.751984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.11	✓	240
3.2	odd	2	inner	336.2.bo.a.5.50	yes	240
7.3	odd	6	inner	336.2.bo.a.101.52	yes	240
16.13	even	4	inner	336.2.bo.a.173.9	yes	240
21.17	even	6	inner	336.2.bo.a.101.9	yes	240
48.29	odd	4	inner	336.2.bo.a.173.52	yes	240
112.45	odd	12	inner	336.2.bo.a.269.50	yes	240
336.269	even	12	inner	336.2.bo.a.269.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.11	✓	240	1.1	even	1	trivial
336.2.bo.a.5.50	yes	240	3.2	odd	2	inner
336.2.bo.a.101.9	yes	240	21.17	even	6	inner
336.2.bo.a.101.52	yes	240	7.3	odd	6	inner
336.2.bo.a.173.9	yes	240	16.13	even	4	inner
336.2.bo.a.173.52	yes	240	48.29	odd	4	inner
336.2.bo.a.269.11	yes	240	336.269	even	12	inner
336.2.bo.a.269.50	yes	240	112.45	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15775 - 0.812169i) q^{2} +(-1.44132 + 0.960512i) q^{3} +(0.680764 + 1.88057i) q^{4} +(-0.0464448 + 0.0124448i) q^{5} +(2.44879 + 0.0585683i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(0.739191 - 2.73013i) q^{8} +(1.15484 - 2.76882i) q^{9} +O(q^{10})\)	\(q+(-1.15775 - 0.812169i) q^{2} +(-1.44132 + 0.960512i) q^{3} +(0.680764 + 1.88057i) q^{4} +(-0.0464448 + 0.0124448i) q^{5} +(2.44879 + 0.0585683i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(0.739191 - 2.73013i) q^{8} +(1.15484 - 2.76882i) q^{9} +(0.0638787 + 0.0233130i) q^{10} +(-0.714547 - 0.191462i) q^{11} +(-2.78752 - 2.05664i) q^{12} +(3.92820 + 3.92820i) q^{13} +(0.355654 + 3.72472i) q^{14} +(0.0549886 - 0.0625478i) q^{15} +(-3.07312 + 2.56045i) q^{16} +(2.15674 + 3.73558i) q^{17} +(-3.58576 + 2.26767i) q^{18} +(4.52089 - 1.21137i) q^{19} +(-0.0550214 - 0.0788709i) q^{20} +(4.40909 + 1.24897i) q^{21} +(0.671766 + 0.801998i) q^{22} +(-3.18448 + 5.51567i) q^{23} +(1.55690 + 4.64500i) q^{24} +(-4.32812 + 2.49884i) q^{25} +(-1.35751 - 7.73823i) q^{26} +(0.994989 + 5.10000i) q^{27} +(2.61334 - 4.60114i) q^{28} +(5.72866 + 5.72866i) q^{29} +(-0.114462 + 0.0277546i) q^{30} +(7.88207 - 4.55072i) q^{31} +(5.63742 - 0.468468i) q^{32} +(1.21380 - 0.410371i) q^{33} +(0.536961 - 6.07650i) q^{34} +(0.104848 + 0.0720482i) q^{35} +(5.99314 + 0.286843i) q^{36} +(4.91744 - 1.31762i) q^{37} +(-6.21789 - 2.26926i) q^{38} +(-9.43489 - 1.88873i) q^{39} +(-0.000355551 + 0.135999i) q^{40} -9.05930i q^{41} +(-4.09025 - 5.02692i) q^{42} +(0.936949 + 0.936949i) q^{43} +(-0.126379 - 1.47410i) q^{44} +(-0.0191786 + 0.142969i) q^{45} +(8.16648 - 3.79943i) q^{46} +(-3.32126 + 5.75259i) q^{47} +(1.97002 - 6.64221i) q^{48} +(-1.09401 + 6.91398i) q^{49} +(7.04036 + 0.622135i) q^{50} +(-6.69663 - 3.31261i) q^{51} +(-4.71310 + 10.0614i) q^{52} +(0.831041 + 0.222677i) q^{53} +(2.99011 - 6.71262i) q^{54} +0.0355697 q^{55} +(-6.76249 + 3.20449i) q^{56} +(-5.35254 + 6.08834i) q^{57} +(-1.97971 - 11.2850i) q^{58} +(-0.850708 + 3.17489i) q^{59} +(0.155060 + 0.0608299i) q^{60} +(4.88233 - 1.30822i) q^{61} +(-12.8214 - 1.13299i) q^{62} +(-7.55458 + 2.43481i) q^{63} +(-6.90719 - 4.03617i) q^{64} +(-0.231330 - 0.133559i) q^{65} +(-1.73856 - 0.510701i) q^{66} +(-7.17601 - 1.92281i) q^{67} +(-5.55681 + 6.59895i) q^{68} +(-0.708004 - 11.0086i) q^{69} +(-0.0628718 - 0.168568i) q^{70} +9.82008 q^{71} +(-6.70558 - 5.19953i) q^{72} +(0.701314 + 1.21471i) q^{73} +(-6.76329 - 2.46831i) q^{74} +(3.83807 - 7.75886i) q^{75} +(5.35572 + 7.67721i) q^{76} +(0.842730 + 1.76648i) q^{77} +(9.38926 + 9.84940i) q^{78} +(-4.88205 + 8.45596i) q^{79} +(0.110866 - 0.157164i) q^{80} +(-6.33271 - 6.39506i) q^{81} +(-7.35768 + 10.4884i) q^{82} +(4.54243 - 4.54243i) q^{83} +(0.652772 + 9.14188i) q^{84} +(-0.146658 - 0.146658i) q^{85} +(-0.323791 - 1.84571i) q^{86} +(-13.7593 - 2.75442i) q^{87} +(-1.05090 + 1.80928i) q^{88} +(4.11344 + 2.37490i) q^{89} +(0.138319 - 0.149946i) q^{90} +(1.15210 - 14.6528i) q^{91} +(-12.5405 - 2.23377i) q^{92} +(-6.98961 + 14.1299i) q^{93} +(8.51726 - 3.96263i) q^{94} +(-0.194896 + 0.112524i) q^{95} +(-7.67539 + 6.09002i) q^{96} -3.21854i q^{97} +(6.88191 - 7.11613i) q^{98} +(-1.35531 + 1.75734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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