LMFDB - Embedded newform 336.2.bo.a.5.50

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			5.50
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15775 + 0.812169i) q^{2} +(0.767968 + 1.55249i) q^{3} +(0.680764 + 1.88057i) q^{4} +(0.0464448 - 0.0124448i) q^{5} +(-0.371770 + 2.42111i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(-0.739191 + 2.73013i) q^{8} +(-1.82045 + 2.38453i) q^{9} +O(q^{10})$	\(q+(1.15775 + 0.812169i) q^{2} +(0.767968 + 1.55249i) q^{3} +(0.680764 + 1.88057i) q^{4} +(0.0464448 - 0.0124448i) q^{5} +(-0.371770 + 2.42111i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(-0.739191 + 2.73013i) q^{8} +(-1.82045 + 2.38453i) q^{9} +(0.0638787 + 0.0233130i) q^{10} +(0.714547 + 0.191462i) q^{11} +(-2.39677 + 2.50110i) 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} +(-4.04426 + 1.28217i) q^{18} +(4.52089 - 1.21137i) q^{19} +(0.0550214 + 0.0788709i) q^{20} +(1.80347 - 4.21278i) q^{21} +(0.671766 + 0.801998i) q^{22} +(3.18448 - 5.51567i) q^{23} +(-4.80617 + 0.949065i) q^{24} +(-4.32812 + 2.49884i) q^{25} +(1.35751 + 7.73823i) q^{26} +(-5.10000 - 0.994989i) q^{27} +(2.61334 - 4.60114i) q^{28} +(-5.72866 - 5.72866i) q^{29} +(0.0128636 + 0.117075i) q^{30} +(7.88207 - 4.55072i) q^{31} +(-5.63742 + 0.468468i) q^{32} +(0.251506 + 1.25636i) q^{33} +(0.536961 - 6.07650i) q^{34} +(-0.104848 - 0.0720482i) q^{35} +(-5.72357 - 1.80019i) q^{36} +(4.91744 - 1.31762i) q^{37} +(6.21789 + 2.26926i) q^{38} +(-3.08176 + 9.11522i) q^{39} +(-0.000355551 + 0.135999i) q^{40} +9.05930i q^{41} +(5.50945 - 3.41261i) q^{42} +(0.936949 + 0.936949i) q^{43} +(0.126379 + 1.47410i) q^{44} +(-0.0548754 + 0.133404i) q^{45} +(8.16648 - 3.79943i) q^{46} +(3.32126 - 5.75259i) q^{47} +(-6.33514 - 2.80464i) q^{48} +(-1.09401 + 6.91398i) q^{49} +(-7.04036 - 0.622135i) q^{50} +(4.14314 - 6.21712i) q^{51} +(-4.71310 + 10.0614i) q^{52} +(-0.831041 - 0.222677i) q^{53} +(-5.09642 - 5.29401i) 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} +(-0.0801916 + 0.145991i) q^{60} +(4.88233 - 1.30822i) q^{61} +(12.8214 + 1.13299i) q^{62} +(7.92530 - 0.435407i) q^{63} +(-6.90719 - 4.03617i) q^{64} +(0.231330 + 0.133559i) q^{65} +(-0.729199 + 1.65882i) q^{66} +(-7.17601 - 1.92281i) q^{67} +(5.55681 - 6.59895i) q^{68} +(11.0086 + 0.708004i) q^{69} +(-0.0628718 - 0.168568i) q^{70} -9.82008 q^{71} +(-5.16440 - 6.73268i) q^{72} +(0.701314 + 1.21471i) q^{73} +(6.76329 + 2.46831i) q^{74} +(-7.20329 - 4.80034i) q^{75} +(5.35572 + 7.67721i) q^{76} +(-0.842730 - 1.76648i) q^{77} +(-10.9710 + 8.05023i) q^{78} +(-4.88205 + 8.45596i) q^{79} +(-0.110866 + 0.157164i) q^{80} +(-2.37193 - 8.68182i) q^{81} +(-7.35768 + 10.4884i) q^{82} +(-4.54243 + 4.54243i) q^{83} +(9.15018 + 0.523658i) q^{84} +(-0.146658 - 0.146658i) q^{85} +(0.323791 + 1.84571i) q^{86} +(4.49426 - 13.2931i) q^{87} +(-1.05090 + 1.80928i) q^{88} +(-4.11344 - 2.37490i) q^{89} +(-0.171878 + 0.109880i) q^{90} +(1.15210 - 14.6528i) q^{91} +(12.5405 + 2.23377i) q^{92} +(13.1181 + 8.74203i) q^{93} +(8.51726 - 3.96263i) q^{94} +(0.194896 - 0.112524i) q^{95} +(-5.05665 - 8.39227i) q^{96} -3.21854i q^{97} +(-6.88191 + 7.11613i) q^{98} +(-1.75734 + 1.35531i) 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
$3$	0.767968	+	1.55249i	0.443387	+	0.896330i
$3$	0.767968	+	1.55249i	0.443387	+	0.896330i
$4$	0.680764	+	1.88057i	0.340382	+	0.940287i
$5$	0.0464448	−	0.0124448i	0.0207707	−	0.00556551i	−0.248419	−	0.968653i	$-0.579911\pi$
$5$	0.0464448	−	0.0124448i	0.0207707	−	0.00556551i	0.269189	+	0.963087i	$0.413244\pi$
$6$	−0.371770	+	2.42111i	−0.151774	+	0.988415i
$7$	−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
$9$	−1.82045	+	2.38453i	−0.606817	+	0.794842i
$10$	0.0638787	+	0.0233130i	0.0202002	+	0.00737222i
$11$	0.714547	+	0.191462i	0.215444	+	0.0577281i	0.364927	−	0.931036i	$-0.381094\pi$
$11$	0.714547	+	0.191462i	0.215444	+	0.0577281i	−0.149483	+	0.988764i	$0.547761\pi$
$12$	−2.39677	+	2.50110i	−0.691887	+	0.722005i
$13$	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	$-0.991447\pi$
$17$	−2.15674	−	3.73558i	−0.523086	−	0.906011i	0.476553	−	0.879146i	$-0.341886\pi$
$18$	−4.04426	+	1.28217i	−0.953241	+	0.302210i
$19$	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
$21$	1.80347	−	4.21278i	0.393550	−	0.919303i
$22$	0.671766	+	0.801998i	0.143221	+	0.170987i
$23$	3.18448	−	5.51567i	0.664009	−	1.15010i	−0.315544	−	0.948911i	$-0.602187\pi$
$23$	3.18448	−	5.51567i	0.664009	−	1.15010i	0.979553	−	0.201187i	$-0.0644798\pi$
$24$	−4.80617	+	0.949065i	−0.981055	+	0.193727i
$25$	−4.32812	+	2.49884i	−0.865625	+	0.499769i
$26$	1.35751	+	7.73823i	0.266229	+	1.51759i
$27$	−5.10000	−	0.994989i	−0.981495	−	0.191486i
$28$	2.61334	−	4.60114i	0.493875	−	0.869533i
$29$	−5.72866	−	5.72866i	−1.06379	−	1.06379i	−0.997822	−	0.0659633i	$-0.978988\pi$
$29$	−5.72866	−	5.72866i	−1.06379	−	1.06379i	−0.0659633	−	0.997822i	$-0.521012\pi$
$30$	0.0128636	+	0.117075i	0.00234856	+	0.0213748i
$31$	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
$33$	0.251506	+	1.25636i	0.0437816	+	0.218705i
$34$	0.536961	−	6.07650i	0.0920880	−	1.04211i
$35$	−0.104848	−	0.0720482i	−0.0177225	−	0.0121784i
$36$	−5.72357	−	1.80019i	−0.953929	−	0.300032i
$37$	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
$39$	−3.08176	+	9.11522i	−0.493476	+	1.45960i
$40$	−0.000355551		0.135999i	−5.62175e−5		0.0215034i
$41$			9.05930i			1.41483i	0.706801	+	0.707413i	$0.250138\pi$
$41$			9.05930i			1.41483i	−0.706801	+	0.707413i	$0.749862\pi$
$42$	5.50945	−	3.41261i	0.850127	−	0.526578i
$43$	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
$45$	−0.0548754	+	0.133404i	−0.00818034	+	0.0198867i
$46$	8.16648	−	3.79943i	1.20408	−	0.560196i
$47$	3.32126	−	5.75259i	0.484456	−	0.839102i	−0.515385	−	0.856959i	$-0.672351\pi$
$47$	3.32126	−	5.75259i	0.484456	−	0.839102i	0.999841	+	0.0178568i	$0.00568431\pi$
$48$	−6.33514	−	2.80464i	−0.914398	−	0.404815i
$49$	−1.09401	+	6.91398i	−0.156287	+	0.987712i
$50$	−7.04036	−	0.622135i	−0.995658	−	0.0879831i
$51$	4.14314	−	6.21712i	0.580156	−	0.870571i
$52$	−4.71310	+	10.0614i	−0.653589	+	1.39527i
$53$	−0.831041	−	0.222677i	−0.114152	−	0.0305870i	0.201291	−	0.979532i	$-0.435486\pi$
$53$	−0.831041	−	0.222677i	−0.114152	−	0.0305870i	−0.315443	+	0.948945i	$0.602153\pi$
$54$	−5.09642	−	5.29401i	−0.693535	−	0.720423i
$55$	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	−0.888181	−	0.459493i	$-0.848031\pi$
$59$	0.850708	−	3.17489i	0.110753	−	0.413335i	0.998934	+	0.0461580i	$0.0146978\pi$
$60$	−0.0801916	+	0.145991i	−0.0103527	+	0.0188473i
$61$	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
$63$	7.92530	−	0.435407i	0.998494	−	0.0548562i
$64$	−6.90719	−	4.03617i	−0.863399	−	0.504521i
$65$	0.231330	+	0.133559i	0.0286930	+	0.0165659i
$66$	−0.729199	+	1.65882i	−0.0897582	+	0.204187i
$67$	−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
$69$	11.0086	+	0.708004i	1.32528	+	0.0852337i
$70$	−0.0628718	−	0.168568i	−0.00751462	−	0.0201477i
$71$	−9.82008			−1.16543			−0.582714	−	0.812677i	$-0.698009\pi$
$71$	−9.82008			−1.16543			−0.582714	+	0.812677i	$0.698009\pi$
$72$	−5.16440	−	6.73268i	−0.608630	−	0.793454i
$73$	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
$75$	−7.20329	−	4.80034i	−0.831765	−	0.554295i
$76$	5.35572	+	7.67721i	0.614344	+	0.880637i
$77$	−0.842730	−	1.76648i	−0.0960380	−	0.201309i
$78$	−10.9710	+	8.05023i	−1.24222	+	0.911509i
$79$	−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
$81$	−2.37193	−	8.68182i	−0.263547	−	0.964646i
$82$	−7.35768	+	10.4884i	−0.812520	+	1.15825i
$83$	−4.54243	+	4.54243i	−0.498596	+	0.498596i	−0.911001	−	0.412405i	$-0.864689\pi$
$83$	−4.54243	+	4.54243i	−0.498596	+	0.498596i	0.412405	+	0.911001i	$0.364689\pi$
$84$	9.15018	+	0.523658i	0.998366	+	0.0571357i
$85$	−0.146658	−	0.146658i	−0.0159073	−	0.0159073i
$86$	0.323791	+	1.84571i	0.0349153	+	0.199028i
$87$	4.49426	−	13.2931i	0.481835	−	1.42517i
$88$	−1.05090	+	1.80928i	−0.112027	+	0.192870i
$89$	−4.11344	−	2.37490i	−0.436024	−	0.251738i	0.265886	−	0.964005i	$-0.414336\pi$
$89$	−4.11344	−	2.37490i	−0.436024	−	0.251738i	−0.701910	+	0.712266i	$0.747669\pi$
$90$	−0.171878	+	0.109880i	−0.0181176	+	0.0115824i
$91$	1.15210	−	14.6528i	0.120772	−	1.53603i
$92$	12.5405	+	2.23377i	1.30744	+	0.232887i
$93$	13.1181	+	8.74203i	1.36029	+	0.906506i
$94$	8.51726	−	3.96263i	0.878489	−	0.408714i
$95$	0.194896	−	0.112524i	0.0199960	−	0.0115447i
$96$	−5.05665	−	8.39227i	−0.516093	−	0.856533i
$97$		−	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
$99$	−1.75734	+	1.35531i	−0.176620	+	0.136214i
$100$	−7.64569	−	6.43824i	−0.764569	−	0.643824i
$101$	−1.14917	+	4.28876i	−0.114347	+	0.426747i	−0.999237	−	0.0390516i	$-0.987566\pi$
$101$	−1.14917	+	4.28876i	−0.114347	+	0.426747i	0.884891	+	0.465799i	$0.154233\pi$
$102$	9.84607	−	3.83293i	0.974906	−	0.379517i
$103$	−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
$105$	0.0313345	−	0.218106i	0.00305794	−	0.0212849i
$106$	−0.781285	−	0.932749i	−0.0758852	−	0.0905966i
$107$	−2.74629	−	10.2493i	−0.265494	−	0.990837i	−0.961947	−	0.273235i	$-0.911906\pi$
$107$	−2.74629	−	10.2493i	−0.265494	−	0.990837i	0.696453	−	0.717602i	$-0.254760\pi$
$108$	−1.60074	−	10.2683i	−0.154032	−	0.988066i
$109$	−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	$0.203541\pi$
$113$			12.6871i			1.19350i	−0.802428	+	0.596749i	$0.796459\pi$
$114$	1.25213	+	11.3959i	0.117273	+	1.06733i
$115$	0.0792606	−	0.295805i	0.00739109	−	0.0275839i
$116$	6.87331	−	14.6730i	0.638171	−	1.36236i
$117$	−16.5180	+	2.21580i	−1.52709	+	0.204851i
$118$	3.56345	−	2.98480i	0.328042	−	0.274773i
$119$	−3.80873	+	10.7581i	−0.349146	+	0.986191i
$120$	−0.211411	+	0.103891i	−0.0192991	+	0.00948393i
$121$	−9.05236	−	5.22638i	−0.822942	−	0.475126i
$122$	6.71501	+	2.45069i	0.607948	+	0.221875i
$123$	−14.0645	+	6.95726i	−1.26815	+	0.627315i
$124$	13.9238	+	11.7249i	1.25039	+	1.05292i
$125$	−0.339921	+	0.339921i	−0.0304035	+	0.0304035i
$126$	9.52913	+	5.93259i	0.848923	+	0.528517i
$127$	−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
$129$	−0.735057	+	2.17415i	−0.0647182	+	0.191423i
$130$	0.159350	+	0.342506i	0.0139759	+	0.0300398i
$131$	−0.892258	−	3.32995i	−0.0779569	−	0.290939i	0.915931	−	0.401337i	$-0.131454\pi$
$131$	−0.892258	−	3.32995i	−0.0779569	−	0.290939i	−0.993888	+	0.110398i	$0.964788\pi$
$132$	−2.19147	+	1.32826i	−0.190743	+	0.115610i
$133$	−10.2058	−	7.01310i	−0.884951	−	0.608113i
$134$	−6.74637	−	8.05425i	−0.582798	−	0.695782i
$135$	−0.249251	+	0.0172566i	−0.0214521	+	0.00148521i
$136$	11.7928	−	3.12686i	1.01123	−	0.268126i
$137$	10.5524	+	18.2773i	0.901554	+	1.56154i	0.825478	+	0.564435i	$0.190906\pi$
$137$	10.5524	+	18.2773i	0.901554	+	1.56154i	0.0760758	+	0.997102i	$0.475761\pi$
$138$	12.1702	+	9.76054i	1.03599	+	0.830872i
$139$	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
$141$	11.4815	+	0.738416i	0.966914	+	0.0621858i
$142$	−11.3692	−	7.97556i	−0.954080	−	0.669294i
$143$	2.05478	+	3.55898i	0.171829	+	0.297617i
$144$	−0.511005	−	11.9891i	−0.0425838	−	0.999093i
$145$	−0.337359	−	0.194774i	−0.0280161	−	0.0161751i
$146$	−0.174605	+	1.97592i	−0.0144504	+	0.163528i
$147$	−11.5741	+	3.61128i	−0.954612	+	0.297853i
$148$	5.82550	+	8.35062i	0.478853	+	0.686417i
$149$	−3.13969	−	11.7175i	−0.257213	−	0.959934i	−0.966846	−	0.255361i	$-0.917806\pi$
$149$	−3.13969	−	11.7175i	−0.257213	−	0.959934i	0.709632	−	0.704572i	$-0.248861\pi$
$150$	−4.44092	−	11.4079i	−0.362599	−	0.931449i
$151$	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
$156$	−19.2398	+	0.409837i	−1.54042	+	0.0328133i
$157$	−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
$159$	−0.292510	−	1.46119i	−0.0231975	−	0.115880i
$160$	−0.255999	+	0.0919148i	−0.0202385	+	0.00726650i
$161$	−16.5683	+	3.07203i	−1.30576	+	0.242110i
$162$	4.30501	−	11.9778i	0.338233	−	0.941062i
$163$	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
$165$	0.0273164	+	0.0552216i	0.00212658	+	0.00429900i
$166$	−8.94820	+	1.56977i	−0.694515	+	0.121838i
$167$		−	6.74143i		−	0.521667i	−0.965384	−	0.260834i	$-0.916003\pi$
$167$		−	6.74143i		−	0.521667i	0.965384	−	0.260834i	$-0.0839974\pi$
$168$	10.1683	+	8.03775i	0.784502	+	0.620126i
$169$			17.8615i			1.37396i
$170$	−0.0506820	−	0.288904i	−0.00388713	−	0.0221579i
$171$	−5.34151	+	12.9854i	−0.408475	+	0.993019i
$172$	−1.12416	+	2.39984i	−0.0857166	+	0.182986i
$173$	−4.96927	−	18.5456i	−0.377807	−	1.40999i	−0.849200	−	0.528071i	$-0.822916\pi$
$173$	−4.96927	−	18.5456i	−0.377807	−	1.40999i	0.471394	−	0.881923i	$-0.343751\pi$
$174$	15.9995	−	11.7400i	1.21292	−	0.890006i
$175$	12.4645	+	4.41288i	0.942231	+	0.333582i
$176$	−2.68612	+	1.24118i	−0.202474	+	0.0935573i
$177$	5.58230	−	1.11750i	0.419591	−	0.0839962i
$178$	−2.83351	−	6.09034i	−0.212381	−	0.456490i
$179$	−3.62655	+	13.5345i	−0.271061	+	1.01161i	0.687375	+	0.726303i	$0.258763\pi$
$179$	−3.62655	+	13.5345i	−0.271061	+	1.01161i	−0.958435	+	0.285310i	$0.907904\pi$
$180$	−0.288233	−	0.0123806i	−0.0214837	−	0.000922794i
$181$	−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
$186$	8.08748	+	20.7752i	0.593003	+	1.52331i
$187$	−0.825868	−	3.08218i	−0.0603934	−	0.225391i
$188$	13.0792	+	2.32972i	0.953897	+	0.169913i
$189$	6.76235	+	11.9696i	0.491888	+	0.870658i
$190$	0.317029	+	0.0280149i	0.0229997	+	0.00203241i
$191$	−3.45767	−	1.99628i	−0.250188	−	0.144446i	0.369662	−	0.929166i	$-0.379473\pi$
$191$	−3.45767	−	1.99628i	−0.250188	−	0.144446i	−0.619850	+	0.784720i	$0.712807\pi$
$192$	0.961608	−	13.8230i	0.0693981	−	0.997589i
$193$	−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
$195$	−0.0296941	+	0.461707i	−0.00212644	+	0.0330635i
$196$	−13.7470	+	2.64942i	−0.981930	+	0.189244i
$197$	−0.749065	+	0.749065i	−0.0533687	+	0.0533687i	−0.733287	−	0.679919i	$-0.762015\pi$
$197$	−0.749065	+	0.749065i	−0.0533687	+	0.0533687i	0.679919	+	0.733287i	$0.262015\pi$
$198$	−3.13530	+	0.141847i	−0.222816	+	0.0100806i
$199$	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
$201$	−2.52581	−	12.6173i	−0.178157	−	0.889958i
$202$	−4.81364	+	4.03198i	−0.338687	+	0.283689i
$203$	−1.68015	+	21.3687i	−0.117923	+	1.49979i
$204$	14.5123	+	3.55910i	1.01606	+	0.249187i
$205$	0.112742	+	0.420758i	0.00787422	+	0.0293870i
$206$	−1.67741	+	0.780409i	−0.116870	+	0.0543737i
$207$	7.35509	+	17.6345i	0.511214	+	1.22568i
$208$	−22.1298	−	2.01386i	−1.53443	−	0.139636i
$209$	3.46232			0.239494
$210$	0.213416	−	0.227062i	0.0147271	−	0.0156688i
$211$	−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
$213$	−7.54151	−	15.2456i	−0.516736	−	1.04461i
$214$	5.14464	−	14.0966i	0.351681	−	0.963621i
$215$	0.0551766	+	0.0318562i	0.00376301	+	0.00217258i
$216$	6.48632	−	13.1882i	0.441338	−	0.897341i
$217$	−22.6995	−	8.03642i	−1.54094	−	0.545548i
$218$	−2.47386	−	2.95346i	−0.167551	−	0.200033i
$219$	−1.34724	+	2.02164i	−0.0910381	+	0.136610i
$220$	0.0242146	+	0.0668915i	0.00163255	+	0.00450982i
$221$	6.20200	−	23.1462i	0.417192	−	1.55698i
$222$	1.36196	+	12.3955i	0.0914088	+	0.831933i
$223$			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	0.744354	−	0.667785i	$-0.232758\pi$
$227$	15.8965	+	4.25947i	1.05509	+	0.282711i	0.310737	+	0.950496i	$0.399424\pi$
$228$	−7.80577	+	14.2106i	−0.516949	+	0.941117i
$229$	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
$231$	2.09525	−	2.66493i	0.137858	−	0.175340i
$232$	19.8745	−	11.4054i	1.30483	−	0.748801i
$233$	2.64143	−	4.57509i	0.173046	−	0.299724i	−0.766437	−	0.642319i	$-0.777972\pi$
$233$	2.64143	−	4.57509i	0.173046	−	0.299724i	0.939483	+	0.342595i	$0.111306\pi$
$234$	−20.9233	−	10.8500i	−1.36780	−	0.709290i
$235$	0.0826652	−	0.308511i	0.00539248	−	0.0201250i
$236$	6.54974	−	0.561527i	0.426352	−	0.0365523i
$237$	−16.8771	−	1.08543i	−1.09628	−	0.0705060i
$238$	−13.1469	+	9.36181i	−0.852188	+	0.606836i
$239$			14.5366i			0.940297i	0.882587	+	0.470148i	$0.155800\pi$
$239$			14.5366i			0.940297i	−0.882587	+	0.470148i	$0.844200\pi$
$240$	−0.329138	−	0.0514213i	−0.0212457	−	0.00331923i
$241$	−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
$243$	11.6569	−	10.3498i	0.747789	−	0.663937i
$244$	5.78392	+	8.29101i	0.370277	+	0.530777i
$245$	0.0352324	+	0.334733i	0.00225092	+	0.0213853i
$246$	−21.9336	−	3.36797i	−1.39843	−	0.214734i
$247$	22.5174	+	13.0005i	1.43275	+	0.827199i
$248$	6.59768	+	24.8829i	0.418953	+	1.58007i
$249$	−10.5405	−	3.56363i	−0.667978	−	0.225836i
$250$	−0.669616	+	0.117470i	−0.0423502	+	0.00742944i
$251$	−14.4125	−	14.4125i	−0.909712	−	0.909712i	0.0865367	−	0.996249i	$-0.472420\pi$
$251$	−14.4125	−	14.4125i	−0.909712	−	0.909712i	−0.996249	+	0.0865367i	$0.972420\pi$
$252$	6.21407	+	14.6077i	0.391450	+	0.920199i
$253$	3.33150	−	3.33150i	0.209450	−	0.209450i
$254$	−6.99635	−	4.90799i	−0.438990	−	0.307955i
$255$	0.115056	−	0.340314i	0.00720511	−	0.0213113i
$256$	2.88815	−	15.7372i	0.180510	−	0.983573i
$257$	−8.02522	+	13.9001i	−0.500599	+	0.867064i	0.499400	+	0.866371i	$0.333554\pi$
$257$	−8.02522	+	13.9001i	−0.500599	+	0.867064i	−1.00000		0.000692363i	$0.999780\pi$
$258$	−2.61679	+	1.92013i	−0.162914	+	0.119542i
$259$	−11.1010	−	7.62825i	−0.689780	−	0.473997i
$260$	−0.0936857	+	0.525956i	−0.00581014	+	0.0326184i
$261$	24.0889	−	3.23140i	1.49106	−	0.200019i
$262$	1.67147	−	4.57991i	0.103264	−	0.282948i
$263$	−3.12924	−	5.42001i	−0.192957	−	0.334212i	0.753272	−	0.657710i	$-0.228475\pi$
$263$	−3.12924	−	5.42001i	−0.192957	−	0.334212i	−0.946229	+	0.323497i	$0.895141\pi$
$264$	−3.61594	−	0.242049i	−0.222546	−	0.0148971i
$265$	−0.0413687			−0.00254126
$266$	−6.11988	−	16.4082i	−0.375234	−	1.00605i
$267$	0.528010	−	8.20992i	0.0323137	−	0.502439i
$268$	−1.26919	−	14.8040i	−0.0775279	−	0.904298i
$269$	2.42162	+	0.648871i	0.147649	+	0.0395623i	0.331886	−	0.943319i	$-0.392315\pi$
$269$	2.42162	+	0.648871i	0.147649	+	0.0395623i	−0.184238	+	0.982882i	$0.558982\pi$
$270$	−0.302585	−	0.182455i	−0.0184148	−	0.0111039i
$271$	−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
$273$	23.6330	−	9.46423i	1.43034	−	0.572801i
$274$	−2.62722	+	29.7309i	−0.158716	+	1.79611i
$275$	−3.57108	+	0.956869i	−0.215344	+	0.0577014i
$276$	6.16280	+	21.1845i	0.370957	+	1.27516i
$277$	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	$-0.217080\pi$
$281$	26.0273			1.55266			0.776328	+	0.630329i	$0.217080\pi$
$282$	12.6929	+	10.1798i	0.755853	+	0.606198i
$283$	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
$285$	0.324366	+	0.216160i	0.0192138	+	0.0128042i
$286$	−0.511577	+	5.78924i	−0.0302502	+	0.342325i
$287$	18.2248	−	15.5678i	1.07577	−	0.918936i
$288$	9.14557	−	14.2954i	0.538908	−	0.842365i
$289$	−0.803033	+	1.39089i	−0.0472372	+	0.0818172i
$290$	−0.232387	−	0.499492i	−0.0136462	−	0.0293312i
$291$	4.99675	−	2.47174i	0.292915	−	0.144896i
$292$	−1.80693	+	2.14580i	−0.105742	+	0.125574i
$293$	7.21013	+	7.21013i	0.421220	+	0.421220i	0.885624	−	0.464404i	$-0.153731\pi$
$293$	7.21013	+	7.21013i	0.421220	+	0.421220i	−0.464404	+	0.885624i	$0.653731\pi$
$294$	−16.3328	−	5.21913i	−0.952549	−	0.304386i
$295$		−	0.158044i		−	0.00920167i
$296$	−0.0376446	+	14.3992i	−0.00218805	+	0.836937i
$297$	−3.45369	−	1.68742i	−0.200403	−	0.0979143i
$298$	5.88160	−	16.1159i	0.340712	−	0.933567i
$299$	34.1759	−	9.15741i	1.97644	−	0.529587i
$300$	4.12365	−	16.8142i	0.238079	−	0.970770i
$301$	0.274797	−	3.49496i	0.0158390	−	0.201446i
$302$	6.37173	+	0.563049i	0.366652	+	0.0323998i
$303$	−7.54078	+	1.50956i	−0.433206	+	0.0867217i
$304$	−10.7916	+	15.2982i	−0.618940	+	0.877412i
$305$	0.210478	−	0.121520i	0.0120520	−	0.00695820i
$306$	13.5121	+	12.3424i	0.772433	+	0.705565i
$307$	−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
$309$	−2.26118	−	0.145425i	−0.128634	−	0.00827294i
$310$	0.609588	−	0.106939i	0.0346223	−	0.00607373i
$311$	−22.2452	+	12.8433i	−1.26141	+	0.728275i	−0.973347	−	0.229337i	$-0.926344\pi$
$311$	−22.2452	+	12.8433i	−1.26141	+	0.728275i	−0.288062	+	0.957612i	$0.593011\pi$
$312$	−22.6077	−	15.1515i	−1.27991	−	0.857783i
$313$	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
$315$	0.362671	−	0.118852i	0.0204342	−	0.00669653i
$316$	−19.2256	−	3.42455i	−1.08152	−	0.192646i
$317$	27.0536	−	7.24899i	1.51948	−	0.407144i	0.599910	−	0.800067i	$-0.295203\pi$
$317$	27.0536	−	7.24899i	1.51948	−	0.407144i	0.919571	+	0.392923i	$0.128536\pi$
$318$	0.848081	−	1.92926i	0.0475580	−	0.108188i
$319$	−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
$324$	14.7121	−	10.3709i	0.817338	−	0.576158i
$325$	−26.8177	−	7.18578i	−1.48758	−	0.398595i
$326$	−0.390161	+	1.06906i	−0.0216090	+	0.0592098i
$327$	−0.926202	−	4.62671i	−0.0512191	−	0.255858i
$328$	−24.7331	−	6.69655i	−1.36565	−	0.369755i
$329$	−17.2799	+	3.20398i	−0.952674	+	0.176641i
$330$	−0.0132237	+	0.0861183i	−0.000727943	+	0.00474066i
$331$	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
$333$	−5.81004	+	14.1244i	−0.318388	+	0.774014i
$334$	5.47518	−	7.80488i	0.299588	−	0.427064i
$335$	−0.357217			−0.0195169
$336$	5.24433	+	17.5641i	0.286102	+	0.958199i
$337$	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
$339$	−19.6965	+	9.74326i	−1.06977	+	0.529181i
$340$	0.175962	−	0.375641i	0.00954287	−	0.0203720i
$341$	6.50340	−	1.74258i	0.352179	−	0.0943661i
$342$	−16.7305	+	10.6956i	−0.904680	+	0.578353i
$343$	15.7889	−	9.68034i	0.852523	−	0.522689i
$344$	−3.25058	+	1.86541i	−0.175259	+	0.100576i
$345$	0.520104	−	0.104117i	0.0280014	−	0.00560549i
$346$	9.30897	−	25.5070i	0.500453	−	1.37126i
$347$	17.3129	+	4.63898i	0.929405	+	0.249033i	0.691601	−	0.722280i	$-0.256906\pi$
$347$	17.3129	+	4.63898i	0.929405	+	0.249033i	0.237804	+	0.971313i	$0.423572\pi$
$348$	28.0582	−	0.597683i	1.50408	−	0.0320392i
$349$	−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	$-0.985815\pi$
$353$	−10.1097	−	17.5105i	−0.538084	−	0.931989i	0.460923	−	0.887440i	$-0.347518\pi$
$354$	7.37049	+	3.23999i	0.391737	+	0.172203i
$355$	−0.456092	+	0.122209i	−0.0242068	+	0.00648620i
$356$	1.66589	−	9.35237i	0.0882919	−	0.495675i
$357$	−19.6268	+	2.34884i	−1.03876	+	0.124314i
$358$	−15.1909	+	12.7241i	−0.802864	+	0.672491i
$359$	7.64827	−	13.2472i	0.403660	−	0.699160i	−0.590504	−	0.807035i	$-0.701071\pi$
$359$	7.64827	−	13.2472i	0.403660	−	0.699160i	0.994165	+	0.107874i	$0.0344044\pi$
$360$	−0.323647	−	0.248428i	−0.0170577	−	0.0130933i
$361$	2.51653	−	1.45292i	0.132449	−	0.0764694i
$362$	−28.8797	+	5.06633i	−1.51788	+	0.266280i
$363$	1.16198	−	18.0674i	0.0609882	−	0.948292i
$364$	28.3399	−	7.80846i	1.48541	−	0.409274i
$365$	0.0476893	+	0.0476893i	0.00249617	+	0.00249617i
$366$	1.35224	+	12.3070i	0.0706826	+	0.643299i
$367$	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
$369$	−21.6021	−	16.4920i	−1.12456	−	0.858539i
$370$	0.344837	+	0.0304722i	0.0179272	+	0.00158417i
$371$	0.980122	+	2.05447i	0.0508854	+	0.106663i
$372$	−7.50970	+	30.6209i	−0.389360	+	1.58762i
$373$	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
$375$	−0.788772	−	0.266675i	−0.0407320	−	0.0137711i
$376$	13.2503	+	13.3197i	0.683330	+	0.686913i
$377$		−	45.0066i		−	2.31796i
$378$	−1.89222	+	19.3499i	−0.0973251	+	0.995253i
$379$	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
$381$	−4.64088	−	9.38180i	−0.237760	−	0.480644i
$382$	−2.38179	−	5.11940i	−0.121863	−	0.261931i
$383$	−6.58458	+	11.4048i	−0.336457	+	0.582760i	−0.983764	−	0.179470i	$-0.942562\pi$
$383$	−6.58458	+	11.4048i	−0.336457	+	0.582760i	0.647307	+	0.762229i	$0.275895\pi$
$384$	12.3399	−	15.2226i	0.629718	−	0.776824i
$385$	−0.0611240	−	0.0715562i	−0.00311517	−	0.00364684i
$386$	1.39522	−	15.7889i	0.0710147	−	0.803635i
$387$	−3.93985	+	0.528511i	−0.200274	+	0.0268657i
$388$	6.05270	−	2.19106i	0.307279	−	0.111234i
$389$	18.4065	+	4.93201i	0.933248	+	0.250063i	0.693239	−	0.720708i	$-0.256183\pi$
$389$	18.4065	+	4.93201i	0.933248	+	0.250063i	0.240009	+	0.970771i	$0.422850\pi$
$390$	−0.409362	+	0.510424i	−0.0207289	+	0.0258463i
$391$	−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
$396$	−3.74509	−	2.38217i	−0.188198	−	0.119709i
$397$	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
$399$	3.05007	−	21.2302i	0.152694	−	1.06284i
$400$	6.90268	−	18.7612i	0.345134	−	0.938061i
$401$	9.55498	+	5.51657i	0.477153	+	0.275484i	0.719229	−	0.694773i	$-0.244495\pi$
$401$	9.55498	+	5.51657i	0.477153	+	0.275484i	−0.242076	+	0.970257i	$0.577828\pi$
$402$	7.32315	−	16.6591i	0.365246	−	0.830879i
$403$	48.8385	+	13.0862i	2.43282	+	0.651871i
$404$	−8.84764	+	0.758532i	−0.440187	+	0.0377384i
$405$	−0.218208	−	0.373707i	−0.0108428	−	0.0185697i
$406$	−19.3002	+	23.3751i	−0.957853	+	1.16008i
$407$	3.76602			0.186674
$408$	13.9110	+	15.9069i	0.688695	+	0.787511i
$409$	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
$411$	−20.2714	+	30.4189i	−0.999916	+	1.50045i
$412$	−2.57584	−	0.458820i	−0.126902	−	0.0226045i
$413$	−7.84886	+	3.74443i	−0.386217	+	0.184251i
$414$	−5.80682	+	26.3899i	−0.285390	+	1.29699i
$415$	−0.154442	+	0.267502i	−0.00758127	+	0.0131311i
$416$	−23.9852	−	20.3047i	−1.17597	−	0.995519i
$417$	21.1009	+	7.13398i	1.03331	+	0.349352i
$418$	4.00849	+	2.81199i	0.196062	+	0.137539i
$419$	−5.90253	+	5.90253i	−0.288357	+	0.288357i	−0.836430	−	0.548073i	$-0.815362\pi$
$419$	−5.90253	+	5.90253i	−0.288357	+	0.288357i	0.548073	+	0.836430i	$0.315362\pi$
$420$	0.431495	−	0.0895514i	0.0210548	−	0.00436966i
$421$	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
$423$	7.67102	+	18.3919i	0.372978	+	0.894247i
$424$	1.22223	−	2.10425i	0.0593569	−	0.102191i
$425$	18.6693	+	10.7787i	0.905592	+	0.522844i
$426$	3.65081	−	23.7755i	0.176882	−	1.15193i
$427$	−11.0217	−	7.57380i	−0.533378	−	0.366522i
$428$	17.4050	−	12.1420i	0.841302	−	0.586903i
$429$	−3.94728	+	5.92321i	−0.190577	+	0.285975i
$430$	0.0380080	+	0.0816942i	0.00183291	+	0.00393965i
$431$	−34.0209	+	19.6420i	−1.63873	+	0.946122i	−0.657461	+	0.753489i	$0.728369\pi$
$431$	−34.0209	+	19.6420i	−1.63873	+	0.946122i	−0.981271	+	0.192633i	$0.938297\pi$
$432$	18.2205	−	10.0006i	0.876636	−	0.481154i
$433$			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
$435$	0.0433041	−	0.673326i	0.00207627	−	0.0322835i
$436$	−0.465404	−	5.42855i	−0.0222888	−	0.259981i
$437$	7.71515	−	28.7933i	0.369066	−	1.37737i
$438$	−3.20168	+	1.24637i	−0.152982	+	0.0595537i
$439$	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
$441$	−14.4950	−	15.1952i	−0.690237	−	0.723583i
$442$	25.9790	−	21.7604i	1.23569	−	1.03504i
$443$	6.43837	+	24.0283i	0.305896	+	1.14162i	0.932171	+	0.362018i	$0.117912\pi$
$443$	6.43837	+	24.0283i	0.305896	+	1.14162i	−0.626275	+	0.779602i	$0.715421\pi$
$444$	−8.49045	+	15.4570i	−0.402939	+	0.733559i
$445$	−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	$0.288736\pi$
$449$			33.3828i			1.57543i	−0.616040	+	0.787715i	$0.711264\pi$
$450$	14.3001	−	15.6554i	0.674114	−	0.738001i
$451$	−1.73451	+	6.47330i	−0.0816751	+	0.304816i
$452$	−23.8590	+	8.63689i	−1.12223	+	0.406245i
$453$	6.51918	+	4.34444i	0.306298	+	0.204120i
$454$	14.9448	+	17.8421i	0.701394	+	0.837370i
$455$	−0.128842	−	0.694882i	−0.00604022	−	0.0325766i
$456$	−20.5785	+	10.1127i	−0.963676	+	0.473569i
$457$	−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
$459$	7.28250	+	21.1974i	0.339918	+	0.989409i
$460$	0.610241	−	0.0523176i	0.0284526	−	0.00243932i
$461$	−17.9478	+	17.9478i	−0.835913	+	0.835913i	−0.988318	−	0.152405i	$-0.951298\pi$
$461$	−17.9478	+	17.9478i	−0.835913	+	0.835913i	0.152405	+	0.988318i	$0.451298\pi$
$462$	4.59015	−	1.38362i	0.213553	−	0.0643718i
$463$	−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
$465$	0.718062	+	0.242769i	0.0332993	+	0.0112581i
$466$	6.77386	−	3.15152i	0.313793	−	0.145991i
$467$	−0.336830	−	1.25707i	−0.0155866	−	0.0581700i	0.957695	−	0.287787i	$-0.0929194\pi$
$467$	−0.336830	−	1.25707i	−0.0155866	−	0.0581700i	−0.973281	+	0.229617i	$0.926253\pi$
$468$	−15.4118	−	29.5549i	−0.712412	−	1.36617i
$469$	8.46331	+	17.7403i	0.390799	+	0.819171i
$470$	0.346268	−	0.290040i	0.0159722	−	0.0133785i
$471$	−6.50013	+	1.30123i	−0.299510	+	0.0599576i
$472$	8.03901	+	4.66939i	0.370025	+	0.214926i
$473$	0.490104	+	0.848885i	0.0225350	+	0.0390318i
$474$	−18.6578	−	14.9637i	−0.856983	−	0.687304i
$475$	−16.5399	+	16.5399i	−0.758905	+	0.758905i
$476$	−22.8242	+	0.161105i	−1.04615	+	0.00738422i
$477$	2.04385	−	1.57627i	0.0935813	−	0.0721723i
$478$	−11.8062	+	16.8298i	−0.540003	+	0.769776i
$479$	5.69448	+	9.86313i	0.260187	+	0.450658i	0.966292	−	0.257450i	$-0.0828823\pi$
$479$	5.69448	+	9.86313i	0.260187	+	0.450658i	−0.706104	+	0.708108i	$0.749549\pi$
$480$	−0.339296	−	0.326848i	−0.0154867	−	0.0149185i
$481$	24.4926	+	14.1408i	1.11676	+	0.644764i
$482$	−13.5868	−	1.20062i	−0.618861	−	0.0546868i
$483$	−17.4932	−	23.3629i	−0.795968	−	1.06305i
$484$	3.66608	−	20.5816i	0.166640	−	0.935526i
$485$	−0.0400542	−	0.149484i	−0.00181877	−	0.00678774i
$486$	21.9015	−	2.51507i	0.993471	−	0.114086i
$487$	−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	$-0.305415\pi$
$491$	30.8632	−	30.8632i	1.39284	−	1.39284i	0.818898	−	0.573939i	$-0.194585\pi$
$492$	−22.6582	−	21.7130i	−1.02151	−	0.978900i
$493$	−9.04464	+	33.7551i	−0.407350	+	1.52025i
$494$	15.5110	+	33.3392i	0.697872	+	1.50000i
$495$	−0.0647529	+	0.0848169i	−0.00291043	+	0.00381224i
$496$	−12.5707	+	34.1666i	−0.564440	+	1.53413i
$497$	16.8751	+	19.7552i	0.756952	+	0.886142i
$498$	−9.30899	−	12.6865i	−0.417146	−	0.568494i
$499$	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
$501$	10.4660	−	5.17720i	0.467586	−	0.231300i
$502$	−4.98069	−	28.3915i	−0.222299	−	1.26718i
$503$		−	18.3232i		−	0.816989i	−0.912761	−	0.408495i	$-0.866054\pi$
$503$		−	18.3232i		−	0.816989i	0.912761	−	0.408495i	$-0.133946\pi$
$504$	−4.66959	+	21.9589i	−0.208000	+	0.978129i
$505$			0.213492i			0.00950026i
$506$	6.56278	−	1.15130i	0.291751	−	0.0511815i
$507$	−27.7298	+	13.7171i	−1.23152	+	0.609196i
$508$	−4.11390	−	11.3644i	−0.182525	−	0.504215i
$509$	5.84711	+	21.8217i	0.259169	+	0.967231i	0.965724	+	0.259573i	$0.0835817\pi$
$509$	5.84711	+	21.8217i	0.259169	+	0.967231i	−0.706555	+	0.707658i	$0.749752\pi$
$510$	0.409598	−	0.300552i	0.0181373	−	0.0133087i
$511$	1.23850	−	3.49824i	0.0547879	−	0.154753i
$512$	16.1250	−	15.8740i	0.712631	−	0.701539i
$513$	−24.2618	+	1.67974i	−1.07119	+	0.0741624i
$514$	−20.5804	+	9.57498i	−0.907763	+	0.422334i
$515$	−0.0162802	+	0.0607587i	−0.000717393	+	0.00267735i
$516$	−4.58905	+	0.0977539i	−0.202022	+	0.00430338i
$517$	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	−0.215170	−	0.976577i	$-0.569030\pi$
$521$	11.9374	−	6.89205i	0.522986	−	0.301946i	0.738155	+	0.674631i	$0.235697\pi$
$522$	30.5133	+	15.8231i	1.33553	+	0.692557i
$523$	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
$525$	2.72142	+	22.7400i	0.118773	+	0.992456i
$526$	0.779085	−	8.81648i	0.0339697	−	0.384417i
$527$	−33.9991	−	19.6294i	−1.48102	−	0.855070i
$528$	−3.98977	−	3.21699i	−0.173632	−	0.140001i
$529$	−8.78178	−	15.2105i	−0.381816	−	0.661326i
$530$	−0.0478946	−	0.0335984i	−0.00208041	−	0.00145942i
$531$	6.02193	+	7.80826i	0.261329	+	0.338850i
$532$	6.24095	−	23.9669i	0.270579	−	1.03910i
$533$	−35.5867	+	35.5867i	−1.54143	+	1.54143i
$534$	7.27914	−	9.07619i	0.314999	−	0.392765i
$535$	−0.255102	−	0.441849i	−0.0110290	−	0.0191028i
$536$	10.5539	−	18.1701i	0.455861	−	0.784829i
$537$	−23.7972	+	4.76386i	−1.02692	+	0.205576i
$538$	2.27663	+	2.71799i	0.0981526	+	0.117181i
$539$	−2.10549	+	4.73090i	−0.0906898	+	0.203774i
$540$	−0.202133	−	0.456987i	−0.00869844	−	0.0196656i
$541$	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
$543$	−34.0188	−	11.5014i	−1.45988	−	0.493571i
$544$	13.9084	+	20.0487i	0.596319	+	0.859580i
$545$	−0.130990			−0.00561099
$546$	35.0476	+	8.23680i	1.49990	+	0.352503i
$547$	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
$549$	−5.76856	+	14.0236i	−0.246196	+	0.598512i
$550$	−4.91156	−	1.79251i	−0.209429	−	0.0764328i
$551$	−32.8381	−	18.9591i	−1.39895	−	0.807685i
$552$	−10.0704	+	29.5315i	−0.428625	+	1.25695i
$553$	25.4005	−	4.70966i	1.08014	−	0.200275i
$554$	8.25744	−	6.91657i	0.350825	−	0.293857i
$555$	0.352818	+	0.235121i	0.0149763	+	0.00998032i
$556$	23.2913	+	10.9104i	0.987771	+	0.462703i
$557$	1.27312	−	4.75136i	0.0539439	−	0.201322i	−0.933695	−	0.358071i	$-0.883435\pi$
$557$	1.27312	−	4.75136i	0.0539439	−	0.201322i	0.987638	+	0.156749i	$0.0501014\pi$
$558$	−26.0424	+	28.5104i	−1.10246	+	1.20694i
$559$			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	0.902092	−	0.431544i	$-0.142031\pi$
$563$	34.8216	+	9.33041i	1.46755	+	0.393230i	0.565462	+	0.824774i	$0.308698\pi$
$564$	6.42752	+	22.0944i	0.270647	+	0.930344i
$565$	0.157889	+	0.589248i	0.00664242	+	0.0247899i
$566$	19.0710	+	22.7682i	0.801613	+	0.957018i
$567$	−13.3894	+	19.6907i	−0.562301	+	0.826933i
$568$	7.25891	−	26.8101i	0.304577	−	1.12493i
$569$	−19.4334	+	33.6597i	−0.814692	+	1.41109i	0.0948571	+	0.995491i	$0.469761\pi$
$569$	−19.4334	+	33.6597i	−0.814692	+	1.41109i	−0.909549	+	0.415597i	$0.863573\pi$
$570$	0.199976	+	0.513699i	0.00837605	+	0.0215165i
$571$	−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
$573$	0.443834	−	6.90107i	0.0185414	−	0.288296i
$574$	33.7433	−	3.22198i	1.40842	−	0.134483i
$575$			31.8300i			1.32740i
$576$	22.1986	−	9.12274i	0.924940	−	0.380114i
$577$	−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
$579$	10.7654	−	16.1543i	0.447394	−	0.671350i
$580$	0.136626	−	0.767024i	0.00567308	−	0.0318489i
$581$	16.9439	+	1.33224i	0.702952	+	0.0552707i
$582$	7.79244	+	1.19655i	0.323007	+	0.0495988i
$583$	−0.551184	−	0.318226i	−0.0228277	−	0.0131796i
$584$	−3.83472	+	1.01677i	−0.158682	+	0.0420744i
$585$	−0.739599	+	0.308476i	−0.0305787	+	0.0127539i
$586$	2.49167	+	14.2034i	0.102930	+	0.586735i
$587$	19.4368	+	19.4368i	0.802244	+	0.802244i	0.983446	−	0.181202i	$-0.0579987\pi$
$587$	19.4368	+	19.4368i	0.802244	+	0.802244i	−0.181202	+	0.983446i	$0.557999\pi$
$588$	−14.6705	−	19.3074i	−0.605000	−	0.796225i
$589$	30.1214	−	30.1214i	1.24113	−	1.24113i
$590$	0.128358	−	0.182975i	0.00528443	−	0.00753297i
$591$	−1.73817	−	0.587658i	−0.0714989	−	0.0241730i
$592$	−11.7382	+	16.6401i	−0.482436	+	0.683904i
$593$	8.91827	−	15.4469i	0.366229	−	0.634328i	−0.622743	−	0.782426i	$-0.713982\pi$
$593$	8.91827	−	15.4469i	0.366229	−	0.634328i	0.988973	+	0.148098i	$0.0473152\pi$
$594$	−2.62803	−	4.75859i	−0.107829	−	0.195247i
$595$	−0.0430131	+	0.547055i	−0.00176337	+	0.0224271i
$596$	19.8982	−	13.8813i	0.815063	−	0.568599i
$597$	−6.67330	+	10.0138i	−0.273120	+	0.409839i
$598$	47.0045	+	17.1546i	1.92216	+	0.701505i
$599$	2.95431	+	5.11701i	0.120710	+	0.209075i	0.920048	−	0.391806i	$-0.128150\pi$
$599$	2.95431	+	5.11701i	0.120710	+	0.209075i	−0.799338	+	0.600882i	$0.794816\pi$
$600$	18.4301	−	16.1175i	0.752407	−	0.657996i
$601$	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
$603$	17.6485	−	13.6110i	0.718704	−	0.554283i
$604$	6.91956	+	5.82679i	0.281553	+	0.237089i
$605$	−0.485477	−	0.130083i	−0.0197374	−	0.00528863i
$606$	−9.95634	−	4.37670i	−0.404449	−	0.177791i
$607$	−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
$609$	−34.4650	+	13.8021i	−1.39659	+	0.559289i
$610$	0.342376	+	0.0302547i	0.0138624	+	0.00122498i
$611$	35.6439	−	9.55076i	1.44200	−	0.386382i
$612$	5.61949	+	25.2634i	0.227154	+	1.02121i
$613$	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	$-0.760530\pi$
$617$	−36.2709			−1.46021			−0.730106	+	0.683333i	$0.760530\pi$
$618$	−2.49977	−	2.00483i	−0.100556	−	0.0806460i
$619$	−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
$621$	−21.7289	+	24.9614i	−0.871949	+	1.00167i
$622$	−36.1852	−	3.19758i	−1.45090	−	0.128211i
$623$	2.29103	+	12.3562i	0.0917883	+	0.495039i
$624$	−13.8685	−	35.9029i	−0.555184	−	1.43727i
$625$	12.4827	−	21.6206i	0.499307	−	0.864824i
$626$	23.2315	−	10.8084i	0.928518	−	0.431991i
$627$	2.65895	+	5.37521i	0.106188	+	0.214665i
$628$	−7.62664	+	0.653852i	−0.304336	+	0.0260915i
$629$	−15.5277	−	15.5277i	−0.619130	−	0.619130i
$630$	0.516409	+	0.156949i	0.0205742	+	0.00625302i
$631$		−	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
$633$	−19.0284	−	6.43330i	−0.756311	−	0.255701i
$634$	37.2087	+	13.5796i	1.47775	+	0.539314i
$635$	−0.280669	+	0.0752050i	−0.0111380	+	0.00298442i
$636$	2.54875	−	1.54481i	0.101064	−	0.0612558i
$637$	−31.4570	+	22.8620i	−1.24637	+	0.905826i
$638$	0.746054	−	8.44269i	0.0295366	−	0.334249i
$639$	17.8770	−	23.4162i	0.707201	−	0.926332i
$640$	−0.347127	−	0.418853i	−0.0137214	−	0.0165566i
$641$	−8.09505	+	4.67368i	−0.319735	+	0.184599i	−0.651275	−	0.758842i	$-0.725765\pi$
$641$	−8.09505	+	4.67368i	−0.319735	+	0.184599i	0.331539	+	0.943441i	$0.392432\pi$
$642$	25.8357	−	2.83870i	1.01965	−	0.112035i
$643$	−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
$645$	−0.00708259	+	0.110126i	−0.000278877	+	0.00433620i
$646$	−4.93333	−	28.1216i	−0.194099	−	1.10643i
$647$	20.9785	−	12.1119i	0.824749	−	0.476169i	−0.0273021	−	0.999627i	$-0.508692\pi$
$647$	20.9785	−	12.1119i	0.824749	−	0.476169i	0.852052	+	0.523458i	$0.175358\pi$
$648$	25.4558	−	0.0581428i	0.999997	−	0.00228406i
$649$	1.21574	−	2.10573i	0.0477221	−	0.0826570i
$650$	−25.2121	−	30.0998i	−0.988899	−	1.18061i
$651$	−4.95606	−	41.4125i	−0.194243	−	1.62308i
$652$	−1.31997	+	0.920826i	−0.0516939	+	0.0360623i
$653$	−17.7192	+	4.74784i	−0.693405	+	0.185797i	−0.588275	−	0.808661i	$-0.700193\pi$
$653$	−17.7192	+	4.74784i	−0.693405	+	0.185797i	−0.105130	+	0.994458i	$0.533526\pi$
$654$	2.68536	−	6.10881i	0.105006	−	0.238873i
$655$	−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	0.833242	−	0.552908i	$-0.186482\pi$
$659$	7.19647	+	7.19647i	0.280335	+	0.280335i	−0.552908	+	0.833242i	$0.686482\pi$
$660$	−0.0852524	+	0.0889634i	−0.00331844	+	0.00346290i
$661$	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
$663$	40.6972	−	8.14699i	1.58055	−	0.316403i
$664$	−9.04368	−	15.7591i	−0.350963	−	0.611572i
$665$	−0.561281	−	0.198713i	−0.0217655	−	0.00770576i
$666$	−18.1980	+	11.6338i	−0.705158	+	0.450801i
$667$	−49.8402	+	13.3546i	−1.92982	+	0.517094i
$668$	12.6778	−	4.58932i	0.490517	−	0.177566i
$669$	−14.5451	+	7.19501i	−0.562346	+	0.278175i
$670$	−0.413568	−	0.290121i	−0.0159775	−	0.0112083i
$671$	3.73913			0.144348
$672$	−8.19338	+	24.5941i	−0.316067	+	0.948737i
$673$	−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
$675$	24.5598	−	8.43767i	0.945306	−	0.324766i
$676$	−33.5899	+	12.1595i	−1.29192	+	0.467671i
$677$	1.57854	−	0.422967i	0.0606680	−	0.0162560i	−0.228357	−	0.973577i	$-0.573335\pi$
$677$	1.57854	−	0.422967i	0.0606680	−	0.0162560i	0.289025	+	0.957321i	$0.406669\pi$
$678$	−30.7168	−	4.71667i	−1.17967	−	0.181142i
$679$	−6.47479	+	5.53083i	−0.248480	+	0.212254i
$680$	0.508803	−	0.291987i	0.0195117	−	0.0111972i
$681$	5.59526	+	27.9504i	0.214411	+	1.07106i
$682$	8.94457	+	3.26439i	0.342505	+	0.125000i
$683$	−16.7743	−	4.49467i	−0.641852	−	0.171984i	−0.0768100	−	0.997046i	$-0.524473\pi$
$683$	−16.7743	−	4.49467i	−0.641852	−	0.171984i	−0.565042	+	0.825062i	$0.691140\pi$
$684$	−28.0563	−	1.20511i	−1.07276	−	0.0460786i
$685$	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
$690$	0.686710	+	0.301870i	0.0261426	+	0.0114920i
$691$	−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
$693$	5.74637	+	1.20628i	0.218286	+	0.0458227i
$694$	16.2764	+	19.4318i	0.617842	+	0.737620i
$695$	0.309176	−	0.535508i	0.0117277	−	0.0203130i
$696$	32.9698	+	22.0960i	1.24972	+	0.837548i
$697$	33.8417	−	19.5385i	1.28185	−	0.740075i
$698$	−8.60816	−	49.0693i	−0.325824	−	1.85730i
$699$	9.13132	+	0.587269i	0.345378	+	0.0222125i
$700$	0.186659	+	26.4446i	0.00705506	+	0.999513i
$701$	−18.0951	−	18.0951i	−0.683442	−	0.683442i	0.277332	−	0.960774i	$-0.410550\pi$
$701$	−18.0951	−	18.0951i	−0.683442	−	0.683442i	−0.960774	+	0.277332i	$0.910550\pi$
$702$	0.776173	−	40.8157i	0.0292948	−	1.54049i
$703$	20.6351	−	11.9137i	0.778266	−	0.449332i
$704$	−4.16274	−	4.20650i	−0.156889	−	0.158538i
$705$	0.542444	−	0.108590i	0.0204296	−	0.00408972i
$706$	2.51700	−	28.4835i	0.0947284	−	1.07199i
$707$	10.6025	−	5.05812i	0.398749	−	0.190230i
$708$	5.90176	+	9.73718i	0.221802	+	0.365945i
$709$	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
$711$	−11.2759	−	27.0350i	−0.422880	−	1.01389i
$712$	9.52439	−	9.47472i	0.356941	−	0.355080i
$713$		−	57.9666i		−	2.17087i
$714$	−24.6305	−	13.2209i	−0.921774	−	0.494779i
$715$	0.139725	+	0.139725i	0.00522542	+	0.00522542i
$716$	−27.9214	+	2.39377i	−1.04347	+	0.0894596i
$717$	−22.5680	+	11.1637i	−0.842817	+	0.416915i
$718$	19.6137	−	9.12523i	0.731978	−	0.340551i
$719$	−9.67059	+	16.7500i	−0.360652	+	0.624668i	−0.988068	−	0.154016i	$-0.950779\pi$
$719$	−9.67059	+	16.7500i	−0.360652	+	0.624668i	0.627416	+	0.778684i	$0.284113\pi$
$720$	−0.172936	−	0.550473i	−0.00644495	−	0.0205149i
$721$	3.40315	−	0.630999i	0.126740	−	0.0234996i
$722$	4.09353	+	0.361732i	0.152345	+	0.0134623i
$723$	−13.9012	−	9.26389i	−0.516992	−	0.344528i
$724$	−37.5502	−	17.5897i	−1.39554	−	0.653715i
$725$	39.1094	+	10.4793i	1.45249	+	0.389192i
$726$	16.0191	−	19.9738i	0.594523	−	0.741296i
$727$	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
$732$	−8.42984	+	15.3467i	−0.311576	+	0.567230i
$733$	−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
$735$	−0.492613	+	0.311763i	−0.0181703	+	0.0114995i
$736$	−15.3683	+	32.5860i	−0.566484	+	1.20114i
$737$	−4.75945	−	2.74787i	−0.175317	−	0.101219i
$738$	−11.6156	−	36.6382i	−0.427575	−	1.34867i
$739$	−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
$741$	−2.89039	+	44.9420i	−0.106181	+	1.65099i
$742$	−0.533845	+	3.17459i	−0.0195980	+	0.116543i
$743$	−32.0924			−1.17736			−0.588678	−	0.808368i	$-0.700351\pi$
$743$	−32.0924			−1.17736			−0.588678	+	0.808368i	$0.700351\pi$
$744$	−33.5637	+	29.3521i	−1.23050	+	1.07610i
$745$	−0.291645	−	0.505143i	−0.0106850	−	0.0185070i
$746$	30.0568	+	10.9695i	1.10046	+	0.401621i
$747$	−2.56227	−	19.1008i	−0.0937487	−	0.698861i
$748$	5.23405	−	3.65134i	0.191376	−	0.133506i
$749$	−15.8994	+	23.1374i	−0.580951	+	0.845423i
$750$	−0.696615	−	0.949359i	−0.0254368	−	0.0346657i
$751$	−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
$753$	11.3070	−	33.4437i	0.412048	−	1.21876i
$754$	36.5530	−	52.1064i	1.33118	−	1.89760i
$755$	0.153783	−	0.153783i	0.00559675	−	0.00559675i
$756$	−17.9061	+	20.8655i	−0.651239	+	0.758873i
$757$	−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
$759$	7.73061	+	2.61364i	0.280603	+	0.0948689i
$760$	0.163138	+	0.615269i	0.00591763	+	0.0223181i
$761$	6.47138	+	3.73625i	0.234587	+	0.135439i	0.612686	−	0.790326i	$-0.290089\pi$
$761$	6.47138	+	3.73625i	0.234587	+	0.135439i	−0.378099	+	0.925765i	$0.623422\pi$
$762$	2.24663	−	14.6309i	0.0813868	−	0.530023i
$763$	3.10346	+	6.50528i	0.112353	+	0.235507i
$764$	1.40031	−	7.86139i	0.0506614	−	0.284415i
$765$	0.616693	−	0.0827263i	0.0222966	−	0.00299097i
$766$	−16.8859	+	7.85614i	−0.610114	+	0.283854i
$767$	15.8133	−	9.12984i	0.570987	−	0.329659i
$768$	26.6498	−	7.60182i	0.961642	−	0.274307i
$769$			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
$771$	−27.7429	−	1.78425i	−0.999135	−	0.0642580i
$772$	14.4386	−	17.1465i	0.519656	−	0.617114i
$773$	2.90234	−	10.8317i	0.104390	−	0.389589i	−0.893885	−	0.448296i	$-0.852031\pi$
$773$	2.90234	−	10.8317i	0.104390	−	0.389589i	0.998275	+	0.0587071i	$0.0186978\pi$
$774$	−4.99059	−	2.58794i	−0.179383	−	0.0930216i
$775$	−22.7431	+	39.3921i	−0.816955	+	1.41501i
$776$	8.78702	+	2.37911i	0.315436	+	0.0854052i
$777$	3.31761	−	23.0924i	0.119018	−	0.828434i
$778$	17.3045	+	20.6592i	0.620397	+	0.740670i
$779$	10.9742	+	40.9561i	0.393190	+	1.46740i
$780$	−0.888488	+	0.258471i	−0.0318130	+	0.00925475i
$781$	−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
$786$	8.39390	−	0.922282i	0.299401	−	0.0328967i
$787$	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
$789$	6.01135	−	9.02052i	0.214010	−	0.321139i
$790$	−0.508993	+	0.426341i	−0.0181092	+	0.0151685i
$791$	25.5228	−	21.8018i	0.907486	−	0.775183i
$792$	−2.40115	−	5.79960i	−0.0853212	−	0.206080i
$793$	24.3177	+	14.0398i	0.863547	+	0.498569i
$794$	16.9171	+	6.17404i	0.600367	+	0.219108i
$795$	−0.0317699	−	0.0642245i	−0.00112676	−	0.00227781i
$796$	−8.95027	+	10.6288i	−0.317234	+	0.376729i
$797$	−15.1048	+	15.1048i	−0.535040	+	0.535040i	−0.922068	−	0.387028i	$-0.873502\pi$
$797$	−15.1048	+	15.1048i	−0.535040	+	0.535040i	0.387028	+	0.922068i	$0.373502\pi$
$798$	20.7737	−	22.1020i	0.735381	−	0.782403i
$799$	−28.6524			−1.01365
$800$	23.2288	−	16.1146i	0.821264	−	0.569738i
$801$	13.1513	−	5.48523i	0.464679	−	0.193811i
$802$	6.58188	+	14.1471i	0.232414	+	0.499550i
$803$	0.268550	+	1.00224i	0.00947694	+	0.0353684i
$804$	22.0084	−	13.3394i	0.776175	−	0.470444i
$805$	−0.731279	+	0.348869i	−0.0257742	+	0.0122960i
$806$	45.9144	+	54.8156i	1.61727	+	1.93080i
$807$	0.852361	+	4.25785i	0.0300045	+	0.149883i
$808$	−10.8594	−	6.30759i	−0.382032	−	0.221900i
$809$	7.22744	+	12.5183i	0.254103	+	0.440120i	0.964652	−	0.263529i	$-0.0848864\pi$
$809$	7.22744	+	12.5183i	0.254103	+	0.440120i	−0.710548	+	0.703648i	$0.751553\pi$
$810$	0.0508837	−	0.609880i	0.00178787	−	0.0214290i
$811$	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
$813$	2.46075	−	38.2617i	0.0863024	−	1.34190i
$814$	4.36010	+	3.05864i	0.152821	+	0.107205i
$815$	0.0193465	+	0.0335091i	0.000677679	+	0.00117377i
$816$	3.18626	+	29.7143i	0.111542	+	1.04021i
$817$	5.37083	+	3.10085i	0.187902	+	0.108485i
$818$	−2.31247	+	26.1690i	−0.0808537	+	0.914978i
$819$	32.8425	+	29.4218i	1.14761	+	1.02808i
$820$	−0.714516	+	0.498456i	−0.0249520	+	0.0174068i
$821$	6.43091	+	24.0005i	0.224440	+	0.837623i	0.982628	+	0.185586i	$0.0594184\pi$
$821$	6.43091	+	24.0005i	0.224440	+	0.837623i	−0.758188	+	0.652036i	$0.773915\pi$
$822$	−48.1745	+	18.7536i	−1.68028	+	0.654108i
$823$	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	−0.0582820	−	0.998300i	$-0.518562\pi$
$827$	27.0327	−	27.0327i	0.940018	−	0.940018i	0.998300	+	0.0582820i	$0.0185623\pi$
$828$	−28.1559	+	25.8367i	−0.978484	+	0.897888i
$829$	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
$831$	12.9356	−	2.58953i	0.448732	−	0.0898298i
$832$	−11.2779	−	42.9877i	−0.390993	−	1.49033i
$833$	28.1872	−	10.8249i	0.976629	−	0.375060i
$834$	18.6355	+	25.3968i	0.645295	+	0.879420i
$835$	−0.0838960	−	0.313104i	−0.00290334	−	0.0108354i
$836$	2.35702	+	6.51115i	0.0815193	+	0.225193i
$837$	−44.7265	+	15.3661i	−1.54597	+	0.531129i
$838$	−11.6275	+	2.03979i	−0.401665	+	0.0704635i
$839$		−	18.6575i		−	0.644128i	−0.946718	−	0.322064i	$-0.895623\pi$
$839$		−	18.6575i		−	0.644128i	0.946718	−	0.322064i	$-0.104377\pi$
$840$	0.572294	+	0.246769i	0.0197460	+	0.00851433i
$841$			36.6351i			1.26328i
$842$	0.899590	+	5.12796i	0.0310019	+	0.176721i
$843$	19.9881	+	40.4070i	0.688427	+	1.39169i
$844$	−21.0037	−	9.83879i	−0.722977	−	0.338665i
$845$	0.222284	+	0.829574i	0.00764679	+	0.0285382i
$846$	−6.05625	+	27.5234i	−0.208218	+	0.946274i
$847$	5.04183	+	27.1919i	0.173239	+	0.934326i
$848$	3.12404	−	1.44353i	0.107280	−	0.0495710i
$849$	7.14009	+	35.6673i	0.245047	+	1.22410i
$850$	12.8602	+	27.6416i	0.441101	+	0.948100i
$851$	8.39188	−	31.3189i	0.287670	−	1.07360i
$852$	23.5364	−	24.5610i	0.806345	−	0.841446i
$853$	−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	−0.841028	−	0.540991i	$-0.818049\pi$
$857$	−23.2156	+	13.4035i	−0.793030	+	0.457856i	0.0479983	+	0.998847i	$0.484716\pi$
$858$	−9.38061	+	3.65173i	−0.320249	+	0.124668i
$859$	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
$861$	38.1648	+	16.3382i	1.30065	+	0.556804i
$862$	−55.3403	−	4.89025i	−1.88490	−	0.166563i
$863$	−4.24756	−	2.45233i	−0.144589	−	0.0834782i	0.425961	−	0.904742i	$-0.359936\pi$
$863$	−4.24756	−	2.45233i	−0.144589	−	0.0834782i	−0.570549	+	0.821264i	$0.693270\pi$
$864$	29.2170	+	3.21999i	0.993982	+	0.109546i
$865$	−0.461594	−	0.799504i	−0.0156947	−	0.0271839i
$866$	−18.0428	+	25.7200i	−0.613118	+	0.874002i
$867$	−2.77605	−	0.178538i	−0.0942796	−	0.00606347i
$868$	−0.339931	−	48.1591i	−0.0115380	−	1.63462i
$869$	−5.10745	+	5.10745i	−0.173258	+	0.173258i
$870$	0.596990	−	0.744373i	0.0202399	−	0.0252366i
$871$	−20.6356	−	35.7419i	−0.699211	−	1.21107i
$872$	3.87008	−	6.66289i	0.131057	−	0.225634i
$873$	7.67469	+	5.85919i	0.259749	+	0.198303i
$874$	32.3172	−	27.0694i	1.09315	−	0.915637i
$875$	1.26795	+	0.0996950i	0.0428647	+	0.00337030i
$876$	−4.71900	−	1.15732i	−0.159440	−	0.0391024i
$877$	−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
$879$	−5.65650	+	16.7308i	−0.190789	+	0.564316i
$880$	−0.109310	+	0.0910746i	−0.00368484	+	0.00307012i
$881$	−15.4458			−0.520383			−0.260192	−	0.965557i	$-0.583786\pi$
$881$	−15.4458			−0.520383			−0.260192	+	0.965557i	$0.583786\pi$
$882$	−4.44044	−	29.3646i	−0.149517	−	0.988759i
$883$	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
$885$	0.245362	−	0.121373i	0.00824774	−	0.00407990i
$886$	−12.0610	+	33.0478i	−0.405199	+	1.11026i
$887$	35.8239	+	20.6829i	1.20285	+	0.694465i	0.961188	−	0.275896i	$-0.0889744\pi$
$887$	35.8239	+	20.6829i	1.20285	+	0.694465i	0.241661	+	0.970361i	$0.422308\pi$
$888$	−22.3835	+	10.9997i	−0.751142	+	0.369126i
$889$	10.3846	+	12.1569i	0.348287	+	0.407731i
$890$	−0.207395	−	0.247602i	−0.00695191	−	0.00829964i
$891$	−0.0326124	−	6.65770i	−0.00109256	−	0.223041i
$892$	−17.6189	+	6.37800i	−0.589924	+	0.213551i
$893$	8.04654	−	30.0301i	0.269267	−	1.00492i
$894$	29.5366	−	3.24534i	0.987851	−	0.108540i
$895$			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
$900$	29.2707	−	6.51086i	0.975692	−	0.217029i
$901$	0.960511	+	3.58467i	0.0319992	+	0.119423i
$902$	−7.26554	+	6.08573i	−0.241916	+	0.202633i
$903$	5.63692	−	2.25740i	0.187585	−	0.0751215i
$904$	−34.6373	−	9.37816i	−1.15202	−	0.311913i
$905$	−0.498452	+	0.863344i	−0.0165691	+	0.0286985i
$906$	4.01915	+	10.3244i	0.133527	+	0.343007i
$907$	−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
$909$	−8.13465	−	10.5477i	−0.269809	−	0.349845i
$910$	0.415194	−	0.909140i	0.0137636	−	0.0301377i
$911$		−	13.1688i		−	0.436300i	−0.975915	−	0.218150i	$-0.929998\pi$
$911$		−	13.1688i		−	0.436300i	0.975915	−	0.218150i	$-0.0700023\pi$
$912$	−32.0379	−	5.00529i	−1.06088	−	0.165742i
$913$	−4.11548	+	2.37607i	−0.136203	+	0.0786366i
$914$	−19.9192	−	42.8143i	−0.658870	−	1.41617i
$915$	0.350299	+	0.233442i	0.0115805	+	0.00771737i
$916$	−29.5281	+	20.5992i	−0.975637	+	0.680617i
$917$	−5.16564	+	7.51725i	−0.170584	+	0.248242i
$918$	−8.78455	+	30.4559i	−0.289933	+	1.00519i
$919$	−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
$921$	0.407986	−	1.20674i	0.0134436	−	0.0397634i
$922$	−35.3557	+	6.20240i	−1.16438	+	0.204265i
$923$	−38.5752	−	38.5752i	−1.26972	−	1.26972i
$924$	6.43797	+	2.12609i	0.211794	+	0.0699433i
$925$	−17.9908	+	17.9908i	−0.591532	+	0.591532i
$926$	−15.0679	−	10.5703i	−0.495163	−	0.347361i
$927$	−1.51075	−	3.62215i	−0.0496194	−	0.118967i
$928$	34.9786	+	29.6112i	1.14823	+	0.972035i
$929$	6.86282	−	11.8868i	0.225162	−	0.389992i	−0.731206	−	0.682157i	$-0.761042\pi$
$929$	6.86282	−	11.8868i	0.225162	−	0.389992i	0.956368	+	0.292165i	$0.0943756\pi$
$930$	0.634166	+	0.864253i	0.0207951	+	0.0283400i
$931$	3.42949	+	32.5826i	0.112397	+	1.06785i
$932$	10.4020	+	1.85285i	0.340729	+	0.0606921i
$933$	−37.0226	−	24.6722i	−1.21207	−	0.807732i
$934$	0.630985	−	1.72893i	0.0206465	−	0.0565723i
$935$	−0.0767145	−	0.132873i	−0.00250883	−	0.00434543i
$936$	6.16051	−	46.7341i	0.201363	−	1.52755i
$937$	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
$939$	31.3166	+	2.01409i	1.02198	+	0.0657273i
$940$	0.636453	−	0.0545648i	0.0207588	−	0.00177971i
$941$	39.2748	+	10.5237i	1.28032	+	0.343061i	0.833977	−	0.551800i	$-0.186059\pi$
$941$	39.2748	+	10.5237i	1.28032	+	0.343061i	0.446345	+	0.894861i	$0.352725\pi$
$942$	−8.58233	−	3.77270i	−0.279628	−	0.122921i
$943$	49.9682	+	28.8491i	1.62719	+	0.939457i
$944$	5.51482	+	11.9350i	0.179492	+	0.388452i
$945$	0.463035	+	0.471768i	0.0150625	+	0.0153466i
$946$	−0.122021	+	1.38084i	−0.00396723	+	0.0448951i
$947$	−58.1936	+	15.5929i	−1.89104	+	0.506702i	−0.892597	+	0.450855i	$0.851119\pi$
$947$	−58.1936	+	15.5929i	−1.89104	+	0.506702i	−0.998439	+	0.0558468i	$0.982214\pi$
$948$	−9.44806	−	32.4775i	−0.306859	−	1.05482i
$949$	−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	$-0.431275\pi$
$953$	13.2269			0.428462			0.214231	+	0.976783i	$0.431275\pi$
$954$	3.64646	−	0.164972i	0.118058	−	0.00534117i
$955$	−0.185434	−	0.0496869i	−0.00600050	−	0.00160783i
$956$	−27.3372	+	9.89601i	−0.884149	+	0.320060i
$957$	5.75649	−	8.63807i	0.186081	−	0.279229i
$958$	−1.41775	+	16.0439i	−0.0458054	+	0.518355i
$959$	18.6352	−	52.6367i	0.601763	−	1.69973i
$960$	−0.127363	−	0.653974i	−0.00411064	−	0.0211069i
$961$	25.9180	−	44.8914i	0.836066	−	1.44811i
$962$	16.8715	+	36.2636i	0.543960	+	1.16918i
$963$	29.4392	+	12.1097i	0.948665	+	0.390230i
$964$	−14.7550	−	12.4248i	−0.475226	−	0.400175i
$965$	−0.381070	−	0.381070i	−0.0122671	−	0.0122671i
$966$	−1.27814	−	41.2557i	−0.0411236	−	1.32738i
$967$			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
$969$	11.1995	−	33.1258i	0.359779	−	1.06415i
$970$	0.0750338	−	0.205596i	0.00240919	−	0.00660129i
$971$	33.8371	−	9.06663i	1.08589	−	0.290962i	0.328881	−	0.944371i	$-0.393329\pi$
$971$	33.8371	−	9.06663i	1.08589	−	0.290962i	0.757005	+	0.653409i	$0.226662\pi$
$972$	27.3991	+	14.8759i	0.878825	+	0.477144i
$973$	−33.9197	−	2.66699i	−1.08742	−	0.0854999i
$974$	−19.4283	−	1.71682i	−0.622524	−	0.0550105i
$975$	−9.43929	−	47.1526i	−0.302299	−	1.51009i
$976$	−11.6544	+	16.5213i	−0.373047	+	0.528834i
$977$	−24.1166	+	13.9237i	−0.771557	+	0.445459i	−0.833430	−	0.552625i	$-0.813626\pi$
$977$	−24.1166	+	13.9237i	−0.771557	+	0.445459i	0.0618725	+	0.998084i	$0.480293\pi$
$978$	−1.95934	+	0.215283i	−0.0626527	+	0.00688398i
$979$	−2.48454	−	2.48454i	−0.0794064	−	0.0794064i
$980$	−0.605506	+	0.294131i	−0.0193422	+	0.00939568i
$981$	6.47163	−	4.99109i	0.206623	−	0.159353i
$982$	60.7980	−	10.6657i	1.94014	−	0.340356i
$983$	−19.7098	+	11.3794i	−0.628644	+	0.362948i	−0.780227	−	0.625497i	$-0.784896\pi$
$983$	−19.7098	+	11.3794i	−0.628644	+	0.362948i	0.151583	+	0.988445i	$0.451563\pi$
$984$	−8.59787	−	43.5406i	−0.274090	−	1.38802i
$985$	−0.0254682	+	0.0441122i	−0.000811484	+	0.00140553i
$986$	−37.8862	+	31.7341i	−1.20654	+	1.01062i
$987$	−18.2446	−	24.3664i	−0.580732	−	0.775590i
$988$	−9.11926	+	51.1960i	−0.290122	+	1.62876i
$989$	8.15160	−	2.18421i	0.259206	−	0.0694540i
$990$	−0.143853	+	0.0456064i	−0.00457195	+	0.00144947i
$991$	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
$996$	−0.473921	−	22.2482i	−0.0150168	−	0.704961i
$997$	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
$999$	−26.3900	+	1.82708i	−0.834941	+	0.0578063i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.15775 + 0.812169i) q^{2} +(0.767968 + 1.55249i) q^{3} +(0.680764 + 1.88057i) q^{4} +(0.0464448 - 0.0124448i) q^{5} +(-0.371770 + 2.42111i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(-0.739191 + 2.73013i) q^{8} +(-1.82045 + 2.38453i) q^{9} +O(q^{10})\)	\(q+(1.15775 + 0.812169i) q^{2} +(0.767968 + 1.55249i) q^{3} +(0.680764 + 1.88057i) q^{4} +(0.0464448 - 0.0124448i) q^{5} +(-0.371770 + 2.42111i) q^{6} +(-1.71843 - 2.01172i) q^{7} +(-0.739191 + 2.73013i) q^{8} +(-1.82045 + 2.38453i) q^{9} +(0.0638787 + 0.0233130i) q^{10} +(0.714547 + 0.191462i) q^{11} +(-2.39677 + 2.50110i) 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} +(-4.04426 + 1.28217i) q^{18} +(4.52089 - 1.21137i) q^{19} +(0.0550214 + 0.0788709i) q^{20} +(1.80347 - 4.21278i) q^{21} +(0.671766 + 0.801998i) q^{22} +(3.18448 - 5.51567i) q^{23} +(-4.80617 + 0.949065i) q^{24} +(-4.32812 + 2.49884i) q^{25} +(1.35751 + 7.73823i) q^{26} +(-5.10000 - 0.994989i) q^{27} +(2.61334 - 4.60114i) q^{28} +(-5.72866 - 5.72866i) q^{29} +(0.0128636 + 0.117075i) q^{30} +(7.88207 - 4.55072i) q^{31} +(-5.63742 + 0.468468i) q^{32} +(0.251506 + 1.25636i) q^{33} +(0.536961 - 6.07650i) q^{34} +(-0.104848 - 0.0720482i) q^{35} +(-5.72357 - 1.80019i) q^{36} +(4.91744 - 1.31762i) q^{37} +(6.21789 + 2.26926i) q^{38} +(-3.08176 + 9.11522i) q^{39} +(-0.000355551 + 0.135999i) q^{40} +9.05930i q^{41} +(5.50945 - 3.41261i) q^{42} +(0.936949 + 0.936949i) q^{43} +(0.126379 + 1.47410i) q^{44} +(-0.0548754 + 0.133404i) q^{45} +(8.16648 - 3.79943i) q^{46} +(3.32126 - 5.75259i) q^{47} +(-6.33514 - 2.80464i) q^{48} +(-1.09401 + 6.91398i) q^{49} +(-7.04036 - 0.622135i) q^{50} +(4.14314 - 6.21712i) q^{51} +(-4.71310 + 10.0614i) q^{52} +(-0.831041 - 0.222677i) q^{53} +(-5.09642 - 5.29401i) 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} +(-0.0801916 + 0.145991i) q^{60} +(4.88233 - 1.30822i) q^{61} +(12.8214 + 1.13299i) q^{62} +(7.92530 - 0.435407i) q^{63} +(-6.90719 - 4.03617i) q^{64} +(0.231330 + 0.133559i) q^{65} +(-0.729199 + 1.65882i) q^{66} +(-7.17601 - 1.92281i) q^{67} +(5.55681 - 6.59895i) q^{68} +(11.0086 + 0.708004i) q^{69} +(-0.0628718 - 0.168568i) q^{70} -9.82008 q^{71} +(-5.16440 - 6.73268i) q^{72} +(0.701314 + 1.21471i) q^{73} +(6.76329 + 2.46831i) q^{74} +(-7.20329 - 4.80034i) q^{75} +(5.35572 + 7.67721i) q^{76} +(-0.842730 - 1.76648i) q^{77} +(-10.9710 + 8.05023i) q^{78} +(-4.88205 + 8.45596i) q^{79} +(-0.110866 + 0.157164i) q^{80} +(-2.37193 - 8.68182i) q^{81} +(-7.35768 + 10.4884i) q^{82} +(-4.54243 + 4.54243i) q^{83} +(9.15018 + 0.523658i) q^{84} +(-0.146658 - 0.146658i) q^{85} +(0.323791 + 1.84571i) q^{86} +(4.49426 - 13.2931i) q^{87} +(-1.05090 + 1.80928i) q^{88} +(-4.11344 - 2.37490i) q^{89} +(-0.171878 + 0.109880i) q^{90} +(1.15210 - 14.6528i) q^{91} +(12.5405 + 2.23377i) q^{92} +(13.1181 + 8.74203i) q^{93} +(8.51726 - 3.96263i) q^{94} +(0.194896 - 0.112524i) q^{95} +(-5.05665 - 8.39227i) q^{96} -3.21854i q^{97} +(-6.88191 + 7.11613i) q^{98} +(-1.75734 + 1.35531i) 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

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Representations

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Database

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