LMFDB - Embedded newform 930.2.bg.i.691.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.1
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.i.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-4.59456 + 2.04563i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-4.59456 + 2.04563i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(0.443073 - 4.21556i) q^{11} +(0.669131 + 0.743145i) q^{12} +(4.36582 - 4.84873i) q^{13} +(-0.525712 - 5.00182i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.108009 - 1.02764i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(2.38554 + 2.64941i) q^{19} +(0.104528 - 0.994522i) q^{20} +(4.91947 - 1.04567i) q^{21} +(3.87232 + 1.72407i) q^{22} +(-2.20629 + 1.60296i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.26231 + 5.65048i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.91947 + 1.04567i) q^{28} +(-1.89133 + 5.82093i) q^{29} +1.00000 q^{30} +(4.41175 - 3.39654i) q^{31} -1.00000 q^{32} +(-1.30986 + 4.03132i) q^{33} +(1.01072 + 0.214835i) q^{34} +(-4.06885 - 2.95619i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.78114 + 6.54913i) q^{37} +(-3.25691 + 1.45007i) q^{38} +(-5.27852 + 3.83507i) q^{39} +(0.913545 + 0.406737i) q^{40} +(10.7693 - 2.28909i) q^{41} +(-0.525712 + 5.00182i) q^{42} +(1.47980 + 1.64348i) q^{43} +(-2.83630 + 3.15003i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.842727 - 2.59365i) q^{46} +(1.97598 + 6.08144i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(12.2415 - 13.5955i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(-0.108009 + 1.02764i) q^{51} +(-6.38204 + 1.35654i) q^{52} +(10.7663 + 4.79346i) q^{53} +(0.809017 - 0.587785i) q^{54} +(3.87232 - 1.72407i) q^{55} +(-2.51469 + 4.35556i) q^{56} +(-1.78257 - 3.08749i) q^{57} +(-4.95158 - 3.59753i) q^{58} +(7.24092 + 1.53910i) q^{59} +(-0.309017 + 0.951057i) q^{60} +11.1699 q^{61} +(1.86700 + 5.24541i) q^{62} -5.02937 q^{63} +(0.309017 - 0.951057i) q^{64} +(6.38204 + 1.35654i) q^{65} +(-3.42925 - 2.49149i) q^{66} +(-4.94775 - 8.56975i) q^{67} +(-0.516649 + 0.894863i) q^{68} +(2.49135 - 1.10922i) q^{69} +(4.06885 - 2.95619i) q^{70} +(-5.54478 - 2.46870i) q^{71} +(0.978148 - 0.207912i) q^{72} +(0.872359 - 8.29995i) q^{73} +(-5.06016 - 5.61988i) q^{74} +(0.669131 - 0.743145i) q^{75} +(-0.372658 - 3.54560i) q^{76} +(6.58775 + 20.2750i) q^{77} +(-2.01622 - 6.20528i) q^{78} +(-0.869869 - 8.27625i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-1.15085 + 10.9496i) q^{82} +(5.43029 - 1.15424i) q^{83} +(-4.59456 - 2.04563i) q^{84} +(0.835956 - 0.607357i) q^{85} +(-2.02032 + 0.899506i) q^{86} +(3.06024 - 5.30050i) q^{87} +(-2.11939 - 3.67089i) q^{88} +(2.70495 + 1.96526i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(-10.1403 + 31.2086i) q^{91} +2.72712 q^{92} +(-5.02152 + 2.40506i) q^{93} -6.39440 q^{94} +(-1.10169 + 3.39064i) q^{95} +(0.978148 + 0.207912i) q^{96} +(-6.87317 - 4.99365i) q^{97} +(9.14729 + 15.8436i) q^{98} +(2.11939 - 3.67089i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{15}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−4.59456	+	2.04563i	−1.73658	+	0.773175i	−0.741860	+	0.670555i	$0.766056\pi$
$7$	−4.59456	+	2.04563i	−1.73658	+	0.773175i	−0.994721	+	0.102620i	$0.967277\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−0.978148	+	0.207912i	−0.309317	+	0.0657474i
$11$	0.443073	−	4.21556i	0.133592	−	1.27104i	−0.698180	−	0.715922i	$-0.746007\pi$
$11$	0.443073	−	4.21556i	0.133592	−	1.27104i	0.831772	−	0.555117i	$-0.187327\pi$
$12$	0.669131	+	0.743145i	0.193161	+	0.214527i
$13$	4.36582	−	4.84873i	1.21086	−	1.34480i	0.288974	−	0.957337i	$-0.406686\pi$
$13$	4.36582	−	4.84873i	1.21086	−	1.34480i	0.921887	−	0.387459i	$-0.126647\pi$
$14$	−0.525712	−	5.00182i	−0.140503	−	1.33679i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.108009	−	1.02764i	−0.0261961	−	0.249239i	−0.999781	−	0.0209148i	$-0.993342\pi$
$17$	−0.108009	−	1.02764i	−0.0261961	−	0.249239i	0.973585	−	0.228324i	$-0.0733245\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	2.38554	+	2.64941i	0.547280	+	0.607816i	0.951802	−	0.306712i	$-0.0992289\pi$
$19$	2.38554	+	2.64941i	0.547280	+	0.607816i	−0.404522	+	0.914528i	$0.632562\pi$
$20$	0.104528	−	0.994522i	0.0233733	−	0.222382i
$21$	4.91947	−	1.04567i	1.07352	−	0.228183i
$22$	3.87232	+	1.72407i	0.825581	+	0.367572i
$23$	−2.20629	+	1.60296i	−0.460043	+	0.334241i	−0.793548	−	0.608508i	$-0.791768\pi$
$23$	−2.20629	+	1.60296i	−0.460043	+	0.334241i	0.333505	+	0.942748i	$0.391768\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.26231	+	5.65048i	0.639791	+	1.10815i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	4.91947	+	1.04567i	0.929692	+	0.197612i
$29$	−1.89133	+	5.82093i	−0.351212	+	1.08092i	0.606961	+	0.794731i	$0.292388\pi$
$29$	−1.89133	+	5.82093i	−0.351212	+	1.08092i	−0.958173	+	0.286188i	$0.907612\pi$
$30$	1.00000			0.182574
$31$	4.41175	−	3.39654i	0.792373	−	0.610037i
$31$	4.41175	−	3.39654i	0.792373	−	0.610037i
$32$	−1.00000			−0.176777
$33$	−1.30986	+	4.03132i	−0.228017	+	0.701763i
$34$	1.01072	+	0.214835i	0.173337	+	0.0368439i
$35$	−4.06885	−	2.95619i	−0.687761	−	0.499687i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.78114	+	6.54913i	−0.621616	+	1.07667i	0.367568	+	0.929996i	$0.380190\pi$
$37$	−3.78114	+	6.54913i	−0.621616	+	1.07667i	−0.989185	+	0.146675i	$0.953143\pi$
$38$	−3.25691	+	1.45007i	−0.528340	+	0.235232i
$39$	−5.27852	+	3.83507i	−0.845240	+	0.614103i
$40$	0.913545	+	0.406737i	0.144444	+	0.0643107i
$41$	10.7693	−	2.28909i	1.68189	−	0.357496i	0.734752	−	0.678335i	$-0.237298\pi$
$41$	10.7693	−	2.28909i	1.68189	−	0.357496i	0.947134	+	0.320840i	$0.103965\pi$
$42$	−0.525712	+	5.00182i	−0.0811192	+	0.771798i
$43$	1.47980	+	1.64348i	0.225667	+	0.250628i	0.845336	−	0.534234i	$-0.179400\pi$
$43$	1.47980	+	1.64348i	0.225667	+	0.250628i	−0.619670	+	0.784863i	$0.712733\pi$
$44$	−2.83630	+	3.15003i	−0.427588	+	0.474885i
$45$	0.104528	+	0.994522i	0.0155822	+	0.148255i
$46$	−0.842727	−	2.59365i	−0.124253	−	0.382412i
$47$	1.97598	+	6.08144i	0.288226	+	0.887069i	0.985413	+	0.170179i	$0.0544347\pi$
$47$	1.97598	+	6.08144i	0.288226	+	0.887069i	−0.697187	+	0.716889i	$0.745565\pi$
$48$	−0.104528	−	0.994522i	−0.0150874	−	0.143547i
$49$	12.2415	−	13.5955i	1.74878	−	1.94222i
$50$	−0.669131	−	0.743145i	−0.0946294	−	0.105097i
$51$	−0.108009	+	1.02764i	−0.0151243	+	0.143898i
$52$	−6.38204	+	1.35654i	−0.885029	+	0.188119i
$53$	10.7663	+	4.79346i	1.47886	+	0.658432i	0.978286	−	0.207260i	$-0.0664547\pi$
$53$	10.7663	+	4.79346i	1.47886	+	0.658432i	0.500576	+	0.865692i	$0.333121\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	3.87232	−	1.72407i	0.522143	−	0.232473i
$56$	−2.51469	+	4.35556i	−0.336039	+	0.582037i
$57$	−1.78257	−	3.08749i	−0.236107	−	0.408949i
$58$	−4.95158	−	3.59753i	−0.650174	−	0.472379i
$59$	7.24092	+	1.53910i	0.942687	+	0.200374i	0.653524	−	0.756906i	$-0.273290\pi$
$59$	7.24092	+	1.53910i	0.942687	+	0.200374i	0.289163	+	0.957280i	$0.406623\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	11.1699			1.43016			0.715080	−	0.699043i	$-0.246390\pi$
$61$	11.1699			1.43016			0.715080	+	0.699043i	$0.246390\pi$
$62$	1.86700	+	5.24541i	0.237109	+	0.666168i
$63$	−5.02937			−0.633641
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	6.38204	+	1.35654i	0.791594	+	0.168259i
$66$	−3.42925	−	2.49149i	−0.422111	−	0.306682i
$67$	−4.94775	−	8.56975i	−0.604464	−	1.04696i	−0.992136	−	0.125164i	$-0.960054\pi$
$67$	−4.94775	−	8.56975i	−0.604464	−	1.04696i	0.387672	−	0.921797i	$-0.373279\pi$
$68$	−0.516649	+	0.894863i	−0.0626529	+	0.108518i
$69$	2.49135	−	1.10922i	0.299923	−	0.133534i
$70$	4.06885	−	2.95619i	0.486320	−	0.353332i
$71$	−5.54478	−	2.46870i	−0.658044	−	0.292980i	0.0504186	−	0.998728i	$-0.483944\pi$
$71$	−5.54478	−	2.46870i	−0.658044	−	0.292980i	−0.708463	+	0.705748i	$0.750611\pi$
$72$	0.978148	−	0.207912i	0.115276	−	0.0245026i
$73$	0.872359	−	8.29995i	0.102102	−	0.971435i	−0.816792	−	0.576932i	$-0.804250\pi$
$73$	0.872359	−	8.29995i	0.102102	−	0.971435i	0.918894	−	0.394504i	$-0.129083\pi$
$74$	−5.06016	−	5.61988i	−0.588232	−	0.653297i
$75$	0.669131	−	0.743145i	0.0772645	−	0.0858110i
$76$	−0.372658	−	3.54560i	−0.0427468	−	0.406708i
$77$	6.58775	+	20.2750i	0.750744	+	2.31055i
$78$	−2.01622	−	6.20528i	−0.228292	−	0.702609i
$79$	−0.869869	−	8.27625i	−0.0978679	−	0.931150i	−0.927748	−	0.373208i	$-0.878258\pi$
$79$	−0.869869	−	8.27625i	−0.0978679	−	0.931150i	0.829880	−	0.557942i	$-0.188409\pi$
$80$	−0.669131	+	0.743145i	−0.0748111	+	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−1.15085	+	10.9496i	−0.127090	+	1.20918i
$83$	5.43029	−	1.15424i	0.596052	−	0.126695i	0.0999997	−	0.994987i	$-0.468116\pi$
$83$	5.43029	−	1.15424i	0.596052	−	0.126695i	0.496052	+	0.868293i	$0.334782\pi$
$84$	−4.59456	−	2.04563i	−0.501308	−	0.223197i
$85$	0.835956	−	0.607357i	0.0906721	−	0.0658772i
$86$	−2.02032	+	0.899506i	−0.217857	+	0.0969963i
$87$	3.06024	−	5.30050i	0.328093	−	0.568273i
$88$	−2.11939	−	3.67089i	−0.225928	−	0.391318i
$89$	2.70495	+	1.96526i	0.286724	+	0.208317i	0.721845	−	0.692055i	$-0.243294\pi$
$89$	2.70495	+	1.96526i	0.286724	+	0.208317i	−0.435121	+	0.900372i	$0.643294\pi$
$90$	−0.978148	−	0.207912i	−0.103106	−	0.0219158i
$91$	−10.1403	+	31.2086i	−1.06299	+	3.27155i
$92$	2.72712			0.284322
$93$	−5.02152	+	2.40506i	−0.520707	+	0.249393i
$94$	−6.39440			−0.659532
$95$	−1.10169	+	3.39064i	−0.113031	+	0.347872i
$96$	0.978148	+	0.207912i	0.0998318	+	0.0212199i
$97$	−6.87317	−	4.99365i	−0.697865	−	0.507029i	0.181371	−	0.983415i	$-0.441946\pi$
$97$	−6.87317	−	4.99365i	−0.697865	−	0.507029i	−0.879236	+	0.476386i	$0.841946\pi$
$98$	9.14729	+	15.8436i	0.924016	+	1.60044i
$99$	2.11939	−	3.67089i	0.213007	−	0.368939i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	2.18072	−	1.58439i	0.216990	−	0.157652i	−0.473981	−	0.880535i	$-0.657183\pi$
$101$	2.18072	−	1.58439i	0.216990	−	0.157652i	0.690971	+	0.722883i	$0.257183\pi$
$102$	−0.943965	−	0.420280i	−0.0934665	−	0.0416139i
$103$	1.69618	−	0.360533i	0.167129	−	0.0355244i	−0.123587	−	0.992334i	$-0.539440\pi$
$103$	1.69618	−	0.360533i	0.167129	−	0.0355244i	0.290716	+	0.956809i	$0.406106\pi$
$104$	0.682008	−	6.48887i	0.0668764	−	0.636286i
$105$	3.36531	+	3.73755i	0.328420	+	0.364748i
$106$	−7.88581	+	8.75808i	−0.765938	+	0.850660i
$107$	0.759041	+	7.22179i	0.0733792	+	0.698157i	0.967935	+	0.251201i	$0.0808254\pi$
$107$	0.759041	+	7.22179i	0.0733792	+	0.698157i	−0.894556	+	0.446956i	$0.852508\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−4.23990	−	13.0491i	−0.406109	−	1.24988i	−0.919966	−	0.391999i	$-0.871784\pi$
$109$	−4.23990	−	13.0491i	−0.406109	−	1.24988i	0.513856	−	0.857876i	$-0.328216\pi$
$110$	0.443073	+	4.21556i	0.0422454	+	0.401938i
$111$	5.06016	−	5.61988i	0.480289	−	0.533415i
$112$	−3.36531	−	3.73755i	−0.317992	−	0.353165i
$113$	−0.973807	+	9.26516i	−0.0916081	+	0.871593i	0.848151	+	0.529755i	$0.177716\pi$
$113$	−0.973807	+	9.26516i	−0.0916081	+	0.871593i	−0.939759	+	0.341838i	$0.888951\pi$
$114$	3.48722	−	0.741232i	0.326608	−	0.0694228i
$115$	−2.49135	−	1.10922i	−0.232319	−	0.103435i
$116$	4.95158	−	3.59753i	0.459743	−	0.334023i
$117$	5.96053	−	2.65380i	0.551051	−	0.245344i
$118$	−3.70134	+	6.41091i	−0.340736	+	0.590172i
$119$	2.59842	+	4.50060i	0.238197	+	0.412569i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−6.81501	−	1.44858i	−0.619546	−	0.131689i
$122$	−3.45169	+	10.6232i	−0.312501	+	0.961780i
$123$	−11.0099			−0.992731
$124$	−5.56561	+	0.154698i	−0.499807	+	0.0138923i
$125$	−1.00000			−0.0894427
$126$	1.55416	−	4.78322i	0.138456	−	0.426123i
$127$	18.0399	+	3.83449i	1.60078	+	0.340256i	0.919904	−	0.392144i	$-0.128266\pi$
$127$	18.0399	+	3.83449i	1.60078	+	0.340256i	0.680875	+	0.732400i	$0.261600\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.10576	−	1.91523i	−0.0973568	−	0.168627i
$130$	−3.26231	+	5.65048i	−0.286123	+	0.495580i
$131$	−16.7261	+	7.44694i	−1.46137	+	0.650642i	−0.974816	−	0.223011i	$-0.928411\pi$
$131$	−16.7261	+	7.44694i	−1.46137	+	0.650642i	−0.486550	+	0.873653i	$0.661745\pi$
$132$	3.42925	−	2.49149i	0.298478	−	0.216857i
$133$	−16.3802	−	7.29294i	−1.42034	−	0.632378i
$134$	9.67926	−	2.05739i	0.836160	−	0.177731i
$135$	0.104528	−	0.994522i	0.00899638	−	0.0855948i
$136$	−0.691412	−	0.767890i	−0.0592880	−	0.0658460i
$137$	1.84399	−	2.04796i	0.157543	−	0.174969i	−0.659206	−	0.751962i	$-0.729107\pi$
$137$	1.84399	−	2.04796i	0.157543	−	0.174969i	0.816749	+	0.576993i	$0.195774\pi$
$138$	0.285062	+	2.71218i	0.0242661	+	0.230876i
$139$	1.51904	+	4.67512i	0.128843	+	0.396538i	0.994582	−	0.103958i	$-0.0331508\pi$
$139$	1.51904	+	4.67512i	0.128843	+	0.396538i	−0.865739	+	0.500496i	$0.833151\pi$
$140$	1.55416	+	4.78322i	0.131351	+	0.404256i
$141$	−0.668397	−	6.35937i	−0.0562892	−	0.535556i
$142$	4.06130	−	4.51053i	0.340817	−	0.378515i
$143$	−18.5057	−	20.5527i	−1.54753	−	1.71870i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	−5.98674	+	1.27252i	−0.497172	+	0.105677i
$146$	7.62414	+	3.39449i	0.630979	+	0.280930i
$147$	−14.8006	+	10.7533i	−1.22074	+	0.886916i
$148$	6.90849	−	3.07586i	0.567875	−	0.252834i
$149$	1.17340	−	2.03240i	0.0961290	−	0.166500i	−0.813950	−	0.580935i	$-0.802687\pi$
$149$	1.17340	−	2.03240i	0.0961290	−	0.166500i	0.910079	+	0.414434i	$0.136021\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	10.8352	+	7.87220i	0.881753	+	0.640631i	0.933715	−	0.358018i	$-0.116547\pi$
$151$	10.8352	+	7.87220i	0.881753	+	0.640631i	−0.0519620	+	0.998649i	$0.516547\pi$
$152$	3.48722	+	0.741232i	0.282851	+	0.0601219i
$153$	0.319307	−	0.982725i	0.0258144	−	0.0794486i
$154$	−21.3184			−1.71789
$155$	5.14736	+	2.12242i	0.413446	+	0.170477i
$156$	6.52461			0.522387
$157$	3.12520	−	9.61838i	0.249418	−	0.767631i	−0.745460	−	0.666550i	$-0.767770\pi$
$157$	3.12520	−	9.61838i	0.249418	−	0.767631i	0.994878	−	0.101080i	$-0.0322299\pi$
$158$	8.13998	+	1.73021i	0.647582	+	0.137648i
$159$	−9.53440	−	6.92714i	−0.756127	−	0.549358i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	6.85785	−	11.8781i	0.540474	−	0.936129i
$162$	−0.913545	+	0.406737i	−0.0717749	+	0.0319562i
$163$	16.7617	−	12.1781i	1.31288	−	0.953860i	0.312883	−	0.949792i	$-0.398705\pi$
$163$	16.7617	−	12.1781i	1.31288	−	0.953860i	0.999992	−	0.00406796i	$-0.00129488\pi$
$164$	−10.0581	−	4.47814i	−0.785403	−	0.349684i
$165$	−4.14615	+	0.881292i	−0.322778	+	0.0686085i
$166$	−0.580301	+	5.52119i	−0.0450401	+	0.428528i
$167$	−11.9929	−	13.3195i	−0.928041	−	1.03069i	−0.999447	−	0.0332465i	$-0.989415\pi$
$167$	−11.9929	−	13.3195i	−0.928041	−	1.03069i	0.0714063	−	0.997447i	$-0.477251\pi$
$168$	3.36531	−	3.73755i	0.259639	−	0.288358i
$169$	−3.09097	−	29.4086i	−0.237767	−	2.26220i
$170$	0.319307	+	0.982725i	0.0244897	+	0.0753716i
$171$	1.10169	+	3.39064i	0.0842480	+	0.259289i
$172$	−0.231167	−	2.19941i	−0.0176263	−	0.167703i
$173$	−4.63046	+	5.14264i	−0.352047	+	0.390988i	−0.892994	−	0.450069i	$-0.851399\pi$
$173$	−4.63046	+	5.14264i	−0.352047	+	0.390988i	0.540947	+	0.841057i	$0.318066\pi$
$174$	4.09541	+	4.54841i	0.310472	+	0.344814i
$175$	0.525712	−	5.00182i	0.0397401	−	0.378102i
$176$	4.14615	−	0.881292i	0.312528	−	0.0664299i
$177$	−6.76269	−	3.01094i	−0.508315	−	0.226316i
$178$	−2.70495	+	1.96526i	−0.202744	+	0.147302i
$179$	2.32895	−	1.03692i	0.174074	−	0.0775027i	−0.317849	−	0.948141i	$-0.602961\pi$
$179$	2.32895	−	1.03692i	0.174074	−	0.0775027i	0.491923	+	0.870638i	$0.336294\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−0.354952	−	0.614794i	−0.0263833	−	0.0456973i	0.852532	−	0.522675i	$-0.175066\pi$
$181$	−0.354952	−	0.614794i	−0.0263833	−	0.0456973i	−0.878916	+	0.476977i	$0.841732\pi$
$182$	−26.5477	−	19.2880i	−1.96784	−	1.42972i
$183$	−10.9258	−	2.32235i	−0.807659	−	0.171673i
$184$	−0.842727	+	2.59365i	−0.0621266	+	0.191206i
$185$	−7.56229			−0.555991
$186$	−0.735616	−	5.51896i	−0.0539380	−	0.404669i
$187$	−4.37992			−0.320292
$188$	1.97598	−	6.08144i	0.144113	−	0.443534i
$189$	4.91947	+	1.04567i	0.357839	+	0.0760609i
$190$	−2.88425	−	2.09553i	−0.209246	−	0.152026i
$191$	−2.81492	−	4.87559i	−0.203681	−	0.352785i	0.746031	−	0.665911i	$-0.231957\pi$
$191$	−2.81492	−	4.87559i	−0.203681	−	0.352785i	−0.949712	+	0.313126i	$0.898624\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−3.86472	+	1.72068i	−0.278189	+	0.123858i	−0.541089	−	0.840966i	$-0.681988\pi$
$193$	−3.86472	+	1.72068i	−0.278189	+	0.123858i	0.262900	+	0.964823i	$0.415321\pi$
$194$	6.87317	−	4.99365i	0.493465	−	0.358523i
$195$	−5.96053	−	2.65380i	−0.426843	−	0.190043i
$196$	−17.8948	+	3.80366i	−1.27820	+	0.271690i
$197$	−2.35986	+	22.4526i	−0.168133	+	1.59968i	0.506974	+	0.861961i	$0.330764\pi$
$197$	−2.35986	+	22.4526i	−0.168133	+	1.59968i	−0.675108	+	0.737719i	$0.735903\pi$
$198$	2.83630	+	3.15003i	0.201567	+	0.223863i
$199$	−8.87158	+	9.85288i	−0.628889	+	0.698452i	−0.970421	−	0.241418i	$-0.922388\pi$
$199$	−8.87158	+	9.85288i	−0.628889	+	0.698452i	0.341532	+	0.939870i	$0.389054\pi$
$200$	0.104528	+	0.994522i	0.00739128	+	0.0703233i
$201$	3.05788	+	9.41118i	0.215686	+	0.663813i
$202$	0.832961	+	2.56359i	0.0586070	+	0.180374i
$203$	−3.21762	−	30.6136i	−0.225832	−	2.14865i
$204$	0.691412	−	0.767890i	0.0484085	−	0.0537631i
$205$	7.36707	+	8.18196i	0.514539	+	0.571453i
$206$	−0.181260	+	1.72457i	−0.0126290	+	0.120156i
$207$	−2.66753	+	0.567000i	−0.185406	+	0.0394092i
$208$	5.96053	+	2.65380i	0.413288	+	0.184008i
$209$	12.2257	−	8.88250i	0.845670	−	0.614415i
$210$	−4.59456	+	2.04563i	−0.317055	+	0.141162i
$211$	8.29609	−	14.3692i	0.571126	−	0.989220i	−0.425324	−	0.905041i	$-0.639840\pi$
$211$	8.29609	−	14.3692i	0.571126	−	0.989220i	0.996451	−	0.0841788i	$-0.0268267\pi$
$212$	−5.89258	−	10.2062i	−0.404704	−	0.700968i
$213$	4.91034	+	3.56757i	0.336451	+	0.244446i
$214$	−7.10289	−	1.50977i	−0.485543	−	0.103205i
$215$	−0.683397	+	2.10328i	−0.0466073	+	0.143443i
$216$	−1.00000			−0.0680414
$217$	−13.3220	+	24.6304i	−0.904355	+	1.67202i
$218$	13.7206			0.929277
$219$	−2.57895	+	7.93720i	−0.174269	+	0.536346i
$220$	−4.14615	−	0.881292i	−0.279534	−	0.0594167i
$221$	−5.45429	−	3.96277i	−0.366895	−	0.266565i
$222$	3.78114	+	6.54913i	0.253774	+	0.439549i
$223$	0.910585	−	1.57718i	0.0609773	−	0.105616i	−0.833925	−	0.551877i	$-0.813912\pi$
$223$	0.910585	−	1.57718i	0.0609773	−	0.105616i	0.894902	+	0.446262i	$0.147245\pi$
$224$	4.59456	−	2.04563i	0.306987	−	0.136679i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−8.51077	−	3.78924i	−0.566128	−	0.252056i
$227$	22.3857	−	4.75823i	1.48579	−	0.315815i	0.607646	−	0.794208i	$-0.292114\pi$
$227$	22.3857	−	4.75823i	1.48579	−	0.315815i	0.878146	+	0.478393i	$0.158781\pi$
$228$	−0.372658	+	3.54560i	−0.0246799	+	0.234813i
$229$	12.0094	+	13.3378i	0.793601	+	0.881384i	0.995178	−	0.0980893i	$-0.0312731\pi$
$229$	12.0094	+	13.3378i	0.793601	+	0.881384i	−0.201576	+	0.979473i	$0.564606\pi$
$230$	1.82480	−	2.02665i	0.120324	−	0.133633i
$231$	−2.22838	−	21.2016i	−0.146617	−	1.39496i
$232$	1.89133	+	5.82093i	0.124172	+	0.382163i
$233$	−3.90115	−	12.0065i	−0.255573	−	0.786572i	−0.993716	−	0.111928i	$-0.964297\pi$
$233$	−3.90115	−	12.0065i	−0.255573	−	0.786572i	0.738144	−	0.674644i	$-0.235703\pi$
$234$	0.682008	+	6.48887i	0.0445842	+	0.424191i
$235$	−4.27869	+	4.75197i	−0.279111	+	0.309984i
$236$	−4.95336	−	5.50126i	−0.322436	−	0.358102i
$237$	−0.869869	+	8.27625i	−0.0565040	+	0.537600i
$238$	−5.08328	+	1.08048i	−0.329500	+	0.0700374i
$239$	0.495680	+	0.220691i	0.0320629	+	0.0142753i	0.422705	−	0.906267i	$-0.361080\pi$
$239$	0.495680	+	0.220691i	0.0320629	+	0.0142753i	−0.390643	+	0.920542i	$0.627747\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	6.41858	−	2.85774i	0.413457	−	0.184083i	−0.189457	−	0.981889i	$-0.560673\pi$
$241$	6.41858	−	2.85774i	0.413457	−	0.184083i	0.602914	+	0.797806i	$0.294006\pi$
$242$	3.48363	−	6.03383i	0.223936	−	0.387869i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−9.03664	−	6.56550i	−0.578512	−	0.420313i
$245$	17.8948	+	3.80366i	1.14326	+	0.243007i
$246$	3.40225	−	10.4711i	0.216920	−	0.667610i
$247$	23.2611			1.48007
$248$	1.57274	−	5.34102i	0.0998693	−	0.339155i
$249$	−5.55161			−0.351819
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−12.0858	−	2.56892i	−0.762849	−	0.162149i	−0.189971	−	0.981790i	$-0.560840\pi$
$251$	−12.0858	−	2.56892i	−0.762849	−	0.162149i	−0.572877	+	0.819641i	$0.694173\pi$
$252$	4.06885	+	2.95619i	0.256313	+	0.186222i
$253$	5.77983	+	10.0110i	0.363375	+	0.629384i
$254$	−9.22144	+	15.9720i	−0.578605	+	1.00217i
$255$	−0.943965	+	0.420280i	−0.0591134	+	0.0263190i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−5.73470	−	2.55325i	−0.357721	−	0.159267i	0.220005	−	0.975499i	$-0.429393\pi$
$257$	−5.73470	−	2.55325i	−0.357721	−	0.159267i	−0.577725	+	0.816231i	$0.696059\pi$
$258$	2.16319	−	0.459801i	0.134675	−	0.0286260i
$259$	3.97559	−	37.8252i	0.247031	−	2.35034i
$260$	−4.36582	−	4.84873i	−0.270757	−	0.300706i
$261$	−4.09541	+	4.54841i	−0.253499	+	0.281539i
$262$	−1.91381	−	18.2087i	−0.118236	−	1.12494i
$263$	6.70739	+	20.6432i	0.413595	+	1.27292i	0.913501	+	0.406835i	$0.133368\pi$
$263$	6.70739	+	20.6432i	0.413595	+	1.27292i	−0.499906	+	0.866080i	$0.666632\pi$
$264$	1.30986	+	4.03132i	0.0806160	+	0.248111i
$265$	1.23188	+	11.7206i	0.0756741	+	0.719991i
$266$	11.9978	−	13.3249i	0.735630	−	0.817000i
$267$	−2.23724	−	2.48470i	−0.136917	−	0.152061i
$268$	−1.03436	+	9.84129i	−0.0631837	+	0.601152i
$269$	−7.96953	+	1.69398i	−0.485911	+	0.103283i	−0.444351	−	0.895853i	$-0.646566\pi$
$269$	−7.96953	+	1.69398i	−0.485911	+	0.103283i	−0.0415592	+	0.999136i	$0.513233\pi$
$270$	0.913545	+	0.406737i	0.0555966	+	0.0247532i
$271$	−10.7955	+	7.84338i	−0.655779	+	0.476452i	−0.865235	−	0.501367i	$-0.832831\pi$
$271$	−10.7955	+	7.84338i	−0.655779	+	0.476452i	0.209456	+	0.977818i	$0.432831\pi$
$272$	0.943965	−	0.420280i	0.0572363	−	0.0254832i
$273$	16.4074	−	28.4184i	0.993018	−	1.71996i
$274$	1.37790	+	2.38660i	0.0832421	+	0.144180i
$275$	3.42925	+	2.49149i	0.206791	+	0.150243i
$276$	−2.66753	−	0.567000i	−0.160566	−	0.0341294i
$277$	8.34164	−	25.6729i	0.501201	−	1.54254i	−0.305865	−	0.952075i	$-0.598946\pi$
$277$	8.34164	−	25.6729i	0.501201	−	1.54254i	0.807065	−	0.590462i	$-0.201054\pi$
$278$	−4.91571			−0.294825
$279$	5.41183	−	1.30847i	0.323998	−	0.0783363i
$280$	−5.02937			−0.300562
$281$	4.62864	−	14.2455i	0.276122	−	0.849815i	−0.712799	−	0.701369i	$-0.752573\pi$
$281$	4.62864	−	14.2455i	0.276122	−	0.849815i	0.988920	−	0.148447i	$-0.0474273\pi$
$282$	6.25467	+	1.32947i	0.372460	+	0.0791688i
$283$	−22.1794	−	16.1143i	−1.31843	−	0.957895i	−0.999950	−	0.00996526i	$-0.996828\pi$
$283$	−22.1794	−	16.1143i	−1.31843	−	0.957895i	−0.318479	−	0.947930i	$-0.603172\pi$
$284$	3.03476	+	5.25636i	0.180080	+	0.311907i
$285$	1.78257	−	3.08749i	0.105590	−	0.182887i
$286$	25.2654	−	11.2489i	1.49397	−	0.665160i
$287$	−44.7977	+	32.5474i	−2.64432	+	1.92121i
$288$	−0.913545	−	0.406737i	−0.0538312	−	0.0239672i
$289$	15.5841	−	3.31251i	0.916714	−	0.194854i
$290$	0.639765	−	6.08696i	0.0375683	−	0.357439i
$291$	5.68474	+	6.31354i	0.333245	+	0.370106i
$292$	−5.58434	+	6.20204i	−0.326799	+	0.362947i
$293$	1.56180	+	14.8595i	0.0912411	+	0.868101i	0.940424	+	0.340003i	$0.110428\pi$
$293$	1.56180	+	14.8595i	0.0912411	+	0.868101i	−0.849183	+	0.528098i	$0.822905\pi$
$294$	−5.65334	−	17.3992i	−0.329709	−	1.01474i
$295$	2.28755	+	7.04037i	0.133187	+	0.409906i
$296$	0.790474	+	7.52086i	0.0459454	+	0.437141i
$297$	−2.83630	+	3.15003i	−0.164579	+	0.182783i
$298$	1.57032	+	1.74402i	0.0909663	+	0.101028i
$299$	−1.85992	+	17.6959i	−0.107562	+	1.02338i
$300$	−0.978148	+	0.207912i	−0.0564734	+	0.0120038i
$301$	−10.1610	−	4.52395i	−0.585668	−	0.260756i
$302$	−10.8352	+	7.87220i	−0.623493	+	0.452994i
$303$	−2.46248	+	1.09637i	−0.141466	+	0.0629846i
$304$	−1.78257	+	3.08749i	−0.102237	+	0.177080i
$305$	5.58495	+	9.67342i	0.319793	+	0.553898i
$306$	0.835956	+	0.607357i	0.0477884	+	0.0347203i
$307$	15.1389	+	3.21788i	0.864024	+	0.183654i	0.618547	−	0.785748i	$-0.287722\pi$
$307$	15.1389	+	3.21788i	0.864024	+	0.183654i	0.245478	+	0.969402i	$0.421055\pi$
$308$	6.58775	−	20.2750i	0.375372	−	1.15528i
$309$	−1.73407			−0.0986478
$310$	−3.60916	+	4.23957i	−0.204987	+	0.240791i
$311$	34.0955			1.93338			0.966689	−	0.255955i	$-0.0823900\pi$
$311$	34.0955			1.93338			0.966689	+	0.255955i	$0.0823900\pi$
$312$	−2.01622	+	6.20528i	−0.114146	+	0.351305i
$313$	−2.22039	−	0.471958i	−0.125504	−	0.0266767i	0.144731	−	0.989471i	$-0.453768\pi$
$313$	−2.22039	−	0.471958i	−0.125504	−	0.0266767i	−0.270235	+	0.962794i	$0.587101\pi$
$314$	8.18189	+	5.94449i	0.461731	+	0.335467i
$315$	−2.51469	−	4.35556i	−0.141686	−	0.245408i
$316$	−4.16092	+	7.20692i	−0.234070	+	0.405421i
$317$	−9.74904	+	4.34055i	−0.547560	+	0.243790i	−0.661822	−	0.749661i	$-0.730217\pi$
$317$	−9.74904	+	4.34055i	−0.547560	+	0.243790i	0.114261	+	0.993451i	$0.463550\pi$
$318$	9.53440	−	6.92714i	0.534662	−	0.388455i
$319$	23.7005	+	10.5521i	1.32697	+	0.590806i
$320$	0.978148	−	0.207912i	0.0546801	−	0.0116226i
$321$	0.759041	−	7.22179i	0.0423655	−	0.403081i
$322$	9.17760	+	10.1928i	0.511447	+	0.568020i
$323$	2.46497	−	2.73763i	0.137155	−	0.152326i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	2.01622	+	6.20528i	0.111840	+	0.344207i
$326$	6.40239	+	19.7045i	0.354595	+	1.09133i
$327$	1.43419	+	13.6455i	0.0793112	+	0.754595i
$328$	7.36707	−	8.18196i	0.406779	−	0.451773i
$329$	−21.5191	−	23.8994i	−1.18639	−	1.31762i
$330$	0.443073	−	4.21556i	0.0243904	−	0.232059i
$331$	−23.0835	+	4.90655i	−1.26878	+	0.269688i	−0.792646	−	0.609683i	$-0.791297\pi$
$331$	−23.0835	+	4.90655i	−1.26878	+	0.269688i	−0.476137	+	0.879371i	$0.657964\pi$
$332$	−5.07165	−	2.25804i	−0.278343	−	0.123926i
$333$	−6.11802	+	4.44500i	−0.335265	+	0.243585i
$334$	16.3736	−	7.29000i	0.895924	−	0.398891i
$335$	4.94775	−	8.56975i	0.270324	−	0.468216i
$336$	2.51469	+	4.35556i	0.137187	+	0.237615i
$337$	7.34351	+	5.33537i	0.400027	+	0.290636i	0.769552	−	0.638584i	$-0.220480\pi$
$337$	7.34351	+	5.33537i	0.400027	+	0.290636i	−0.369525	+	0.929221i	$0.620480\pi$
$338$	28.9244	+	6.14807i	1.57328	+	0.334411i
$339$	2.87886	−	8.86023i	0.156358	−	0.481221i
$340$	−1.03330			−0.0560385
$341$	−12.3636	−	20.1029i	−0.669526	−	1.08863i
$342$	−3.56513			−0.192780
$343$	−17.5536	+	54.0244i	−0.947805	+	2.91704i
$344$	2.16319	+	0.459801i	0.116632	+	0.0247908i
$345$	2.20629	+	1.60296i	0.118782	+	0.0863005i
$346$	−3.46005	−	5.99299i	−0.186014	−	0.322185i
$347$	−13.1037	+	22.6964i	−0.703446	+	1.21840i	0.263803	+	0.964577i	$0.415023\pi$
$347$	−13.1037	+	22.6964i	−0.703446	+	1.21840i	−0.967249	+	0.253828i	$0.918310\pi$
$348$	−5.59134	+	2.48943i	−0.299728	+	0.133447i
$349$	−12.5452	+	9.11459i	−0.671527	+	0.487893i	−0.870536	−	0.492105i	$-0.836228\pi$
$349$	−12.5452	+	9.11459i	−0.671527	+	0.487893i	0.199009	+	0.979998i	$0.436228\pi$
$350$	4.59456	+	2.04563i	0.245590	+	0.109344i
$351$	−6.38204	+	1.35654i	−0.340648	+	0.0724069i
$352$	−0.443073	+	4.21556i	−0.0236159	+	0.224690i
$353$	11.3943	+	12.6547i	0.606459	+	0.673541i	0.965687	−	0.259709i	$-0.0836266\pi$
$353$	11.3943	+	12.6547i	0.606459	+	0.673541i	−0.359228	+	0.933250i	$0.616960\pi$
$354$	4.95336	−	5.50126i	0.263268	−	0.292389i
$355$	−0.634437	−	6.03627i	−0.0336724	−	0.320372i
$356$	−1.03320	−	3.17986i	−0.0547594	−	0.168532i
$357$	−1.60591	−	4.94249i	−0.0849939	−	0.261584i
$358$	0.266480	+	2.53539i	0.0140839	+	0.133999i
$359$	−2.07063	+	2.29966i	−0.109284	+	0.121372i	−0.795305	−	0.606210i	$-0.792689\pi$
$359$	−2.07063	+	2.29966i	−0.109284	+	0.121372i	0.686021	+	0.727582i	$0.259356\pi$
$360$	0.669131	+	0.743145i	0.0352663	+	0.0391672i
$361$	0.657468	−	6.25539i	0.0346036	−	0.329231i
$362$	0.694390	−	0.147597i	0.0364963	−	0.00775753i
$363$	6.36491	+	2.83384i	0.334071	+	0.148738i
$364$	26.5477	−	19.2880i	1.39148	−	1.01097i
$365$	7.62414	−	3.39449i	0.399066	−	0.177676i
$366$	5.58495	−	9.67342i	0.291930	−	0.505638i
$367$	−6.40559	−	11.0948i	−0.334369	−	0.579144i	0.648995	−	0.760793i	$-0.275190\pi$
$367$	−6.40559	−	11.0948i	−0.334369	−	0.579144i	−0.983363	+	0.181649i	$0.941856\pi$
$368$	−2.20629	−	1.60296i	−0.115011	−	0.0835601i
$369$	10.7693	+	2.28909i	0.560629	+	0.119165i
$370$	2.33688	−	7.19216i	0.121488	−	0.373903i
$371$	−59.2720			−3.07725
$372$	5.47616	+	1.00584i	0.283925	+	0.0521503i
$373$	−28.4471			−1.47293			−0.736467	−	0.676474i	$-0.763507\pi$
$373$	−28.4471			−1.47293			−0.736467	+	0.676474i	$0.763507\pi$
$374$	1.35347	−	4.16556i	0.0699863	−	0.215396i
$375$	0.978148	+	0.207912i	0.0505113	+	0.0107365i
$376$	5.17318	+	3.75853i	0.266786	+	0.193832i
$377$	19.9669	+	34.5837i	1.02835	+	1.78115i
$378$	−2.51469	+	4.35556i	−0.129341	+	0.224026i
$379$	−15.9333	+	7.09395i	−0.818437	+	0.364392i	−0.772866	−	0.634570i	$-0.781177\pi$
$379$	−15.9333	+	7.09395i	−0.818437	+	0.364392i	−0.0455710	+	0.998961i	$0.514511\pi$
$380$	2.88425	−	2.09553i	0.147959	−	0.107498i
$381$	−16.8484	−	7.50140i	−0.863170	−	0.384308i
$382$	5.50682	−	1.17051i	0.281753	−	0.0598885i
$383$	1.83291	−	17.4389i	0.0936572	−	0.891088i	−0.842308	−	0.538996i	$-0.818804\pi$
$383$	1.83291	−	17.4389i	0.0936572	−	0.891088i	0.935965	−	0.352092i	$-0.114530\pi$
$384$	−0.669131	−	0.743145i	−0.0341464	−	0.0379235i
$385$	−14.2648	+	15.8427i	−0.727001	+	0.807417i
$386$	−0.442204	−	4.20729i	−0.0225076	−	0.214145i
$387$	0.683397	+	2.10328i	0.0347390	+	0.106916i
$388$	2.62532	+	8.07990i	0.133280	+	0.410195i
$389$	−1.23203	−	11.7220i	−0.0624664	−	0.594328i	−0.980321	−	0.197411i	$-0.936747\pi$
$389$	−1.23203	−	11.7220i	−0.0624664	−	0.594328i	0.917855	−	0.396917i	$-0.129920\pi$
$390$	4.36582	−	4.84873i	0.221072	−	0.245525i
$391$	1.88556	+	2.09413i	0.0953570	+	0.105905i
$392$	1.91230	−	18.1944i	0.0965860	−	0.918954i
$393$	17.9089	−	3.80665i	0.903384	−	0.192020i
$394$	−20.6244	−	9.18259i	−1.03904	−	0.462612i
$395$	6.73251	−	4.89145i	0.338749	−	0.246116i
$396$	−3.87232	+	1.72407i	−0.194591	+	0.0866376i
$397$	9.20792	−	15.9486i	0.462132	−	0.800437i	−0.536935	−	0.843624i	$-0.680418\pi$
$397$	9.20792	−	15.9486i	0.462132	−	0.800437i	0.999067	+	0.0431871i	$0.0137512\pi$
$398$	−6.62918	−	11.4821i	−0.332291	−	0.575545i
$399$	14.5060	+	10.5392i	0.726207	+	0.527620i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	2.90919	−	8.95356i	0.145278	−	0.447119i	−0.851769	−	0.523918i	$-0.824470\pi$
$401$	2.90919	−	8.95356i	0.145278	−	0.447119i	0.997047	+	0.0767987i	$0.0244699\pi$
$402$	−9.89550			−0.493542
$403$	2.79198	−	36.2201i	0.139078	−	1.80425i
$404$	−2.69552			−0.134107
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	30.1095	+	6.39998i	1.49431	+	0.317626i
$407$	25.9329	+	18.8414i	1.28545	+	0.933933i
$408$	0.516649	+	0.894863i	0.0255779	+	0.0443023i
$409$	−19.2802	+	33.3943i	−0.953346	+	1.65124i	−0.215238	+	0.976562i	$0.569053\pi$
$409$	−19.2802	+	33.3943i	−0.953346	+	1.65124i	−0.738108	+	0.674683i	$0.764280\pi$
$410$	−10.0581	+	4.47814i	−0.496732	+	0.221159i
$411$	−2.22949	+	1.61982i	−0.109973	+	0.0798999i
$412$	−1.58415	−	0.705310i	−0.0780455	−	0.0347481i
$413$	−36.4173	+	7.74073i	−1.79198	+	0.380896i
$414$	0.285062	−	2.71218i	0.0140100	−	0.133296i
$415$	3.71475	+	4.12565i	0.182350	+	0.202520i
$416$	−4.36582	+	4.84873i	−0.214052	+	0.237729i
$417$	−0.513831	−	4.88878i	−0.0251624	−	0.239405i
$418$	4.66981	+	14.3722i	0.228408	+	0.702966i
$419$	3.45330	+	10.6282i	0.168705	+	0.519219i	0.999290	−	0.0376717i	$-0.0119941\pi$
$419$	3.45330	+	10.6282i	0.168705	+	0.519219i	−0.830586	+	0.556891i	$0.811994\pi$
$420$	−0.525712	−	5.00182i	−0.0256521	−	0.244064i
$421$	6.92772	−	7.69401i	0.337636	−	0.374983i	−0.550286	−	0.834976i	$-0.685481\pi$
$421$	6.92772	−	7.69401i	0.337636	−	0.374983i	0.887923	+	0.459993i	$0.152148\pi$
$422$	11.1023	+	12.3304i	0.540453	+	0.600234i
$423$	−0.668397	+	6.35937i	−0.0324986	+	0.309203i
$424$	11.5276	−	2.45027i	0.559831	−	0.118996i
$425$	0.943965	+	0.420280i	0.0457890	+	0.0203866i
$426$	−4.91034	+	3.56757i	−0.237907	+	0.172849i
$427$	−51.3208	+	22.8495i	−2.48359	+	1.10576i
$428$	3.63078	−	6.28870i	0.175501	−	0.303976i
$429$	13.8282	+	23.9512i	0.667632	+	1.15637i
$430$	−1.78916	−	1.29990i	−0.0862808	−	0.0626867i
$431$	5.79693	+	1.23218i	0.279228	+	0.0593518i	0.345397	−	0.938457i	$-0.387744\pi$
$431$	5.79693	+	1.23218i	0.279228	+	0.0593518i	−0.0661687	+	0.997808i	$0.521078\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−12.8710			−0.618542			−0.309271	−	0.950974i	$-0.600085\pi$
$433$	−12.8710			−0.618542			−0.309271	+	0.950974i	$0.600085\pi$
$434$	−19.3082	−	20.2812i	−0.926823	−	0.973527i
$435$	6.12049			0.293455
$436$	−4.23990	+	13.0491i	−0.203055	+	0.624938i
$437$	−9.51008	−	2.02143i	−0.454929	−	0.0966981i
$438$	−6.75178	−	4.90546i	−0.322613	−	0.234392i
$439$	−7.16867	−	12.4165i	−0.342142	−	0.592607i	0.642688	−	0.766128i	$-0.277819\pi$
$439$	−7.16867	−	12.4165i	−0.342142	−	0.592607i	−0.984830	+	0.173521i	$0.944486\pi$
$440$	2.11939	−	3.67089i	0.101038	−	0.175003i
$441$	16.7129	−	7.44108i	0.795854	−	0.354337i
$442$	5.45429	−	3.96277i	0.259434	−	0.188490i
$443$	25.0501	+	11.1530i	1.19017	+	0.529896i	0.903689	−	0.428190i	$-0.140849\pi$
$443$	25.0501	+	11.1530i	1.19017	+	0.529896i	0.286478	+	0.958087i	$0.407515\pi$
$444$	−7.39703	+	1.57229i	−0.351048	+	0.0746175i
$445$	−0.349491	+	3.32518i	−0.0165674	+	0.157629i
$446$	1.21860	+	1.35339i	0.0577024	+	0.0640850i
$447$	−1.57032	+	1.74402i	−0.0742737	+	0.0824892i
$448$	0.525712	+	5.00182i	0.0248376	+	0.236314i
$449$	2.14223	+	6.59311i	0.101098	+	0.311148i	0.988795	−	0.149281i	$-0.0476958\pi$
$449$	2.14223	+	6.59311i	0.101098	+	0.311148i	−0.887697	+	0.460429i	$0.847696\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−4.87820	−	46.4130i	−0.229705	−	2.18550i
$452$	6.23375	−	6.92328i	0.293211	−	0.325644i
$453$	−8.96166	−	9.95293i	−0.421056	−	0.467630i
$454$	−2.39222	+	22.7604i	−0.112272	+	1.06820i
$455$	−32.0976	+	6.82256i	−1.50476	+	0.319847i
$456$	−3.25691	−	1.45007i	−0.152519	−	0.0679057i
$457$	11.8158	−	8.58466i	0.552719	−	0.401574i	−0.276068	−	0.961138i	$-0.589032\pi$
$457$	11.8158	−	8.58466i	0.552719	−	0.401574i	0.828787	+	0.559564i	$0.189032\pi$
$458$	−16.3961	+	7.29999i	−0.766137	+	0.341106i
$459$	−0.516649	+	0.894863i	−0.0241151	+	0.0417686i
$460$	1.36356	+	2.36176i	0.0635763	+	0.110117i
$461$	10.9811	+	7.97823i	0.511441	+	0.371583i	0.813370	−	0.581747i	$-0.197631\pi$
$461$	10.9811	+	7.97823i	0.511441	+	0.371583i	−0.301929	+	0.953330i	$0.597631\pi$
$462$	20.8525	+	4.43235i	0.970148	+	0.206211i
$463$	2.16274	−	6.65622i	0.100511	−	0.309341i	−0.888140	−	0.459573i	$-0.848002\pi$
$463$	2.16274	−	6.65622i	0.100511	−	0.309341i	0.988651	+	0.150233i	$0.0480023\pi$
$464$	−6.12049			−0.284137
$465$	−4.59361	−	3.14623i	−0.213023	−	0.145903i
$466$	12.6244			0.584813
$467$	11.5677	−	35.6017i	0.535289	−	1.64745i	−0.207733	−	0.978185i	$-0.566609\pi$
$467$	11.5677	−	35.6017i	0.535289	−	1.64745i	0.743023	−	0.669266i	$-0.233391\pi$
$468$	−6.38204	−	1.35654i	−0.295010	−	0.0627062i
$469$	40.2633	+	29.2530i	1.85918	+	1.35078i
$470$	−3.19720	−	5.53771i	−0.147476	−	0.255436i
$471$	−5.05668	+	8.75843i	−0.233000	+	0.403567i
$472$	6.76269	−	3.01094i	0.311278	−	0.138590i
$473$	7.58385	−	5.50999i	0.348706	−	0.253349i
$474$	−7.60237	−	3.38480i	−0.349189	−	0.155469i
$475$	−3.48722	+	0.741232i	−0.160005	+	0.0340101i
$476$	0.543218	−	5.16837i	0.0248983	−	0.236892i
$477$	7.88581	+	8.75808i	0.361067	+	0.401005i
$478$	−0.363063	+	0.403222i	−0.0166061	+	0.0184430i
$479$	3.02749	+	28.8046i	0.138329	+	1.31612i	0.814841	+	0.579685i	$0.196824\pi$
$479$	3.02749	+	28.8046i	0.138329	+	1.31612i	−0.676511	+	0.736432i	$0.736509\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	15.2472	+	46.9261i	0.695213	+	2.13965i
$482$	0.734418	+	6.98752i	0.0334518	+	0.318273i
$483$	−9.17760	+	10.1928i	−0.417595	+	0.463786i
$484$	4.66201	+	5.17768i	0.211909	+	0.235349i
$485$	0.888043	−	8.44917i	0.0403240	−	0.383657i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	14.3637	+	6.39512i	0.650880	+	0.289790i	0.705493	−	0.708717i	$-0.250726\pi$
$487$	14.3637	+	6.39512i	0.650880	+	0.289790i	−0.0546128	+	0.998508i	$0.517392\pi$
$488$	9.03664	−	6.56550i	0.409070	−	0.297206i
$489$	−18.9273	+	8.42700i	−0.855924	+	0.381082i
$490$	−9.14729	+	15.8436i	−0.413232	+	0.715740i
$491$	−11.1232	−	19.2660i	−0.501984	−	0.869462i	−0.999997	−	0.00229284i	$-0.999270\pi$
$491$	−11.1232	−	19.2660i	−0.501984	−	0.869462i	0.498013	−	0.867170i	$-0.334063\pi$
$492$	8.90721	+	6.47147i	0.401568	+	0.291756i
$493$	6.18609	+	1.31489i	0.278607	+	0.0592198i
$494$	−7.18808	+	22.1226i	−0.323407	+	0.995344i
$495$	4.23878			0.190519
$496$	4.59361	+	3.14623i	0.206259	+	0.141270i
$497$	30.5259			1.36927
$498$	1.71554	−	5.27989i	0.0768752	−	0.236598i
$499$	27.1801	+	5.77732i	1.21675	+	0.258628i	0.771179	−	0.636618i	$-0.219667\pi$
$499$	27.1801	+	5.77732i	1.21675	+	0.258628i	0.445571	+	0.895247i	$0.353001\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	8.96158	+	15.5219i	0.400374	+	0.693468i
$502$	6.17790	−	10.7004i	0.275733	−	0.477584i
$503$	−16.8581	+	7.50570i	−0.751664	+	0.334663i	−0.746554	−	0.665324i	$-0.768293\pi$
$503$	−16.8581	+	7.50570i	−0.751664	+	0.334663i	−0.00511001	+	0.999987i	$0.501627\pi$
$504$	−4.06885	+	2.95619i	−0.181241	+	0.131679i
$505$	2.46248	+	1.09637i	0.109579	+	0.0487877i
$506$	−11.3071	+	2.40339i	−0.502660	+	0.106844i
$507$	−3.09097	+	29.4086i	−0.137275	+	1.30608i
$508$	−12.3407	−	13.7057i	−0.547530	−	0.608094i
$509$	0.927534	−	1.03013i	0.0411122	−	0.0456598i	−0.722238	−	0.691645i	$-0.756886\pi$
$509$	0.927534	−	1.03013i	0.0411122	−	0.0456598i	0.763350	+	0.645985i	$0.223553\pi$
$510$	−0.108009	−	1.02764i	−0.00478272	−	0.0455046i
$511$	12.9705	+	39.9191i	0.573781	+	1.76592i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−0.372658	−	3.54560i	−0.0164532	−	0.156542i
$514$	4.20041	−	4.66502i	0.185272	−	0.205765i
$515$	1.16032	+	1.28866i	0.0511298	+	0.0567853i
$516$	−0.231167	+	2.19941i	−0.0101766	+	0.0968234i
$517$	26.5122	−	5.63533i	1.16600	−	0.247842i
$518$	34.7454	+	15.4696i	1.52662	+	0.679697i
$519$	5.59848	−	4.06754i	0.245746	−	0.178545i
$520$	5.96053	−	2.65380i	0.261387	−	0.116377i
$521$	−18.2578	+	31.6235i	−0.799891	+	1.38545i	0.119796	+	0.992798i	$0.461776\pi$
$521$	−18.2578	+	31.6235i	−0.799891	+	1.38545i	−0.919687	+	0.392653i	$0.871557\pi$
$522$	−3.06024	−	5.30050i	−0.133943	−	0.231997i
$523$	4.96836	+	3.60973i	0.217251	+	0.157842i	0.691088	−	0.722770i	$-0.257131\pi$
$523$	4.96836	+	3.60973i	0.217251	+	0.157842i	−0.473837	+	0.880612i	$0.657131\pi$
$524$	17.9089	+	3.80665i	0.782354	+	0.166294i
$525$	−1.55416	+	4.78322i	−0.0678292	+	0.208757i
$526$	−21.7056			−0.946407
$527$	−3.96692	−	4.16682i	−0.172802	−	0.181510i
$528$	−4.23878			−0.184469
$529$	−4.80917	+	14.8011i	−0.209095	+	0.643527i
$530$	−11.5276	−	2.45027i	−0.500728	−	0.106433i
$531$	5.98890	+	4.35119i	0.259896	+	0.188825i
$532$	8.96518	+	15.5282i	0.388690	+	0.673231i
$533$	35.9177	−	62.2113i	1.55577	−	2.69467i
$534$	3.05444	−	1.35992i	0.132178	−	0.0588496i
$535$	−5.87473	+	4.26824i	−0.253987	+	0.184532i
$536$	−9.03999	−	4.02486i	−0.390468	−	0.173848i
$537$	−2.49364	+	0.530041i	−0.107609	+	0.0228729i
$538$	0.851653	−	8.10294i	0.0367174	−	0.349342i
$539$	−51.8889	−	57.6284i	−2.23501	−	2.48223i
$540$	−0.669131	+	0.743145i	−0.0287948	+	0.0319799i
$541$	1.50911	+	14.3583i	0.0648819	+	0.617310i	0.977854	+	0.209288i	$0.0671146\pi$
$541$	1.50911	+	14.3583i	0.0648819	+	0.617310i	−0.912972	+	0.408022i	$0.866219\pi$
$542$	−4.12351	−	12.6909i	−0.177120	−	0.545119i
$543$	0.219372	+	0.675158i	0.00941416	+	0.0289738i
$544$	0.108009	+	1.02764i	0.00463085	+	0.0440596i
$545$	9.18088	−	10.1964i	0.393266	−	0.436766i
$546$	21.9573	+	24.3861i	0.939687	+	1.04363i
$547$	1.05882	−	10.0740i	0.0452719	−	0.430733i	−0.948287	−	0.317415i	$-0.897185\pi$
$547$	1.05882	−	10.0740i	0.0452719	−	0.430733i	0.993559	−	0.113318i	$-0.0361480\pi$
$548$	−2.69558	+	0.572964i	−0.115150	+	0.0244758i
$549$	10.2042	+	4.54321i	0.435505	+	0.193899i
$550$	−3.42925	+	2.49149i	−0.146224	+	0.106238i
$551$	−19.9339	+	8.87513i	−0.849212	+	0.378093i
$552$	1.36356	−	2.36176i	0.0580370	−	0.100523i
$553$	20.9268	+	36.2463i	0.889898	+	1.54135i
$554$	21.8387	+	15.8667i	0.927837	+	0.674113i
$555$	7.39703	+	1.57229i	0.313987	+	0.0667399i
$556$	1.51904	−	4.67512i	0.0644215	−	0.198269i
$557$	6.03624			0.255764			0.127882	−	0.991789i	$-0.459182\pi$
$557$	6.03624			0.255764			0.127882	+	0.991789i	$0.459182\pi$
$558$	−0.427914	+	5.55130i	−0.0181151	+	0.235005i
$559$	14.4293			0.610295
$560$	1.55416	−	4.78322i	0.0656753	−	0.202128i
$561$	4.28421	+	0.910638i	0.180880	+	0.0384471i
$562$	12.1179	+	8.80420i	0.511165	+	0.371383i
$563$	−1.03378	−	1.79057i	−0.0435688	−	0.0754634i	0.843419	−	0.537257i	$-0.180539\pi$
$563$	−1.03378	−	1.79057i	−0.0435688	−	0.0754634i	−0.886987	+	0.461793i	$0.847206\pi$
$564$	−3.19720	+	5.53771i	−0.134626	+	0.233180i
$565$	−8.51077	+	3.78924i	−0.358051	+	0.159414i
$566$	22.1794	−	16.1143i	0.932270	−	0.677334i
$567$	−4.59456	−	2.04563i	−0.192953	−	0.0859084i
$568$	−5.93688	+	1.26192i	−0.249106	+	0.0529491i
$569$	2.54339	−	24.1988i	0.106625	−	1.01447i	−0.802134	−	0.597144i	$-0.796302\pi$
$569$	2.54339	−	24.1988i	0.106625	−	1.01447i	0.908759	−	0.417322i	$-0.137031\pi$
$570$	2.38554	+	2.64941i	0.0999192	+	0.110972i
$571$	−5.82752	+	6.47212i	−0.243874	+	0.270850i	−0.852638	−	0.522502i	$-0.824999\pi$
$571$	−5.82752	+	6.47212i	−0.243874	+	0.270850i	0.608764	+	0.793351i	$0.291666\pi$
$572$	2.89088	+	27.5049i	0.120874	+	1.15004i
$573$	1.73972	+	5.35430i	0.0726777	+	0.223679i
$574$	−17.1112	−	52.6628i	−0.714207	−	2.19810i
$575$	−0.285062	−	2.71218i	−0.0118879	−	0.113106i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−7.75823	−	8.61639i	−0.322979	−	0.358705i	0.559688	−	0.828704i	$-0.310921\pi$
$577$	−7.75823	−	8.61639i	−0.322979	−	0.358705i	−0.882667	+	0.469999i	$0.844254\pi$
$578$	−1.66538	+	15.8450i	−0.0692706	+	0.659066i
$579$	4.13802	−	0.879562i	0.171970	−	0.0365534i
$580$	5.59134	+	2.48943i	0.232168	+	0.103368i
$581$	−22.5886	+	16.4116i	−0.937135	+	0.680868i
$582$	−7.76122	+	3.45552i	−0.321713	+	0.143236i
$583$	24.9774	−	43.2620i	1.03446	−	1.79173i
$584$	−4.17283	−	7.22756i	−0.172673	−	0.299078i
$585$	5.27852	+	3.83507i	0.218240	+	0.158561i
$586$	−14.6148	−	3.10648i	−0.603734	−	0.128328i
$587$	10.0956	−	31.0709i	0.416688	−	1.28243i	−0.494044	−	0.869437i	$-0.664482\pi$
$587$	10.0956	−	31.0709i	0.416688	−	1.28243i	0.910732	−	0.412997i	$-0.135518\pi$
$588$	18.2946			0.754456
$589$	19.5232	+	3.58595i	0.804440	+	0.147756i
$590$	−7.40268			−0.304764
$591$	6.97645	−	21.4713i	0.286973	−	0.883211i
$592$	−7.39703	−	1.57229i	−0.304016	−	0.0646206i
$593$	7.54985	+	5.48528i	0.310035	+	0.225254i	0.731912	−	0.681400i	$-0.238628\pi$
$593$	7.54985	+	5.48528i	0.310035	+	0.225254i	−0.421876	+	0.906653i	$0.638628\pi$
$594$	−2.11939	−	3.67089i	−0.0869596	−	0.150619i
$595$	−2.59842	+	4.50060i	−0.106525	+	0.184506i
$596$	−2.14392	+	0.954533i	−0.0878182	+	0.0390992i
$597$	10.7262	−	7.79307i	0.438996	−	0.318949i
$598$	−16.2551	−	7.23723i	−0.664720	−	0.295952i
$599$	10.8138	−	2.29854i	0.441839	−	0.0939158i	0.0183800	−	0.999831i	$-0.494149\pi$
$599$	10.8138	−	2.29854i	0.441839	−	0.0939158i	0.423459	+	0.905915i	$0.360816\pi$
$600$	0.104528	−	0.994522i	0.00426736	−	0.0406012i
$601$	22.8797	+	25.4105i	0.933284	+	1.03652i	0.999251	+	0.0386956i	$0.0123203\pi$
$601$	22.8797	+	25.4105i	0.933284	+	1.03652i	−0.0659666	+	0.997822i	$0.521013\pi$
$602$	7.44244	−	8.26567i	0.303331	−	0.336884i
$603$	−1.03436	−	9.84129i	−0.0421224	−	0.400768i
$604$	−4.13866	−	12.7375i	−0.168400	−	0.518281i
$605$	−2.15300	−	6.62626i	−0.0875320	−	0.269396i
$606$	−0.281759	−	2.68075i	−0.0114457	−	0.108898i
$607$	−1.57860	+	1.75322i	−0.0640736	+	0.0711609i	−0.774329	−	0.632783i	$-0.781913\pi$
$607$	−1.57860	+	1.75322i	−0.0640736	+	0.0711609i	0.710256	+	0.703944i	$0.248579\pi$
$608$	−2.38554	−	2.64941i	−0.0967463	−	0.107448i
$609$	−3.21762	+	30.6136i	−0.130384	+	1.24052i
$610$	−10.9258	+	2.32235i	−0.442373	+	0.0940294i
$611$	38.1140	+	16.9695i	1.54193	+	0.686511i
$612$	−0.835956	+	0.607357i	−0.0337915	+	0.0245510i
$613$	−9.42676	+	4.19707i	−0.380743	+	0.169518i	−0.588179	−	0.808731i	$-0.700155\pi$
$613$	−9.42676	+	4.19707i	−0.380743	+	0.169518i	0.207436	+	0.978249i	$0.433488\pi$
$614$	−7.73857	+	13.4036i	−0.312303	+	0.540925i
$615$	−5.50496	−	9.53487i	−0.221981	−	0.384483i
$616$	17.2470	+	12.5306i	0.694899	+	0.504874i
$617$	2.87456	+	0.611006i	0.115725	+	0.0245982i	0.265410	−	0.964136i	$-0.414493\pi$
$617$	2.87456	+	0.611006i	0.115725	+	0.0245982i	−0.149685	+	0.988734i	$0.547826\pi$
$618$	0.535857	−	1.64920i	0.0215553	−	0.0663405i
$619$	31.7776			1.27725			0.638625	−	0.769518i	$-0.279503\pi$
$619$	31.7776			1.27725			0.638625	+	0.769518i	$0.279503\pi$
$620$	−2.91678	−	4.74261i	−0.117141	−	0.190468i
$621$	2.72712			0.109436
$622$	−10.5361	+	32.4267i	−0.422458	+	1.30019i
$623$	−16.4482	−	3.49618i	−0.658984	−	0.140071i
$624$	−5.27852	−	3.83507i	−0.211310	−	0.153526i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.13500	−	1.96587i	0.0453636	−	0.0785721i
$627$	−13.8053	+	6.14653i	−0.551331	+	0.245469i
$628$	−8.18189	+	5.94449i	−0.326493	+	0.237211i
$629$	7.13854	+	3.17828i	0.284632	+	0.126726i
$630$	4.91947	−	1.04567i	0.195996	−	0.0416603i
$631$	−2.82504	+	26.8784i	−0.112463	+	1.07001i	0.782125	+	0.623122i	$0.214136\pi$
$631$	−2.82504	+	26.8784i	−0.112463	+	1.07001i	−0.894588	+	0.446892i	$0.852531\pi$
$632$	−5.56839	−	6.18433i	−0.221499	−	0.245999i
$633$	−11.1023	+	12.3304i	−0.441278	+	0.490089i
$634$	−1.11549	−	10.6132i	−0.0443018	−	0.421504i
$635$	5.69916	+	17.5402i	0.226164	+	0.696062i
$636$	3.64181	+	11.2084i	0.144407	+	0.444440i
$637$	−12.4770	−	118.711i	−0.494359	−	4.70351i
$638$	−17.3595	+	19.2797i	−0.687270	+	0.763291i
$639$	−4.06130	−	4.51053i	−0.160663	−	0.178434i
$640$	−0.104528	+	0.994522i	−0.00413185	+	0.0393119i
$641$	−33.6045	+	7.14286i	−1.32730	+	0.282126i	−0.816386	−	0.577506i	$-0.804026\pi$
$641$	−33.6045	+	7.14286i	−1.32730	+	0.282126i	−0.510913	+	0.859632i	$0.670693\pi$
$642$	6.63377	+	2.95355i	0.261814	+	0.116567i
$643$	4.37472	−	3.17842i	0.172522	−	0.125345i	−0.498173	−	0.867077i	$-0.665996\pi$
$643$	4.37472	−	3.17842i	0.172522	−	0.125345i	0.670696	+	0.741733i	$0.265996\pi$
$644$	−12.5299	+	5.57868i	−0.493748	+	0.219831i
$645$	1.10576	−	1.91523i	0.0435393	−	0.0754122i
$646$	1.84192	+	3.19030i	0.0724694	+	0.125521i
$647$	−2.15450	−	1.56533i	−0.0847021	−	0.0615397i	0.544628	−	0.838678i	$-0.316671\pi$
$647$	−2.15450	−	1.56533i	−0.0847021	−	0.0615397i	−0.629330	+	0.777138i	$0.716671\pi$
$648$	0.978148	+	0.207912i	0.0384253	+	0.00816754i
$649$	9.69644	−	29.8426i	0.380619	−	1.17142i
$650$	−6.52461			−0.255916
$651$	18.1518	−	21.3224i	0.711425	−	0.835690i
$652$	−20.7186			−0.811401
$653$	5.08069	−	15.6368i	0.198823	−	0.611914i	−0.801088	−	0.598547i	$-0.795745\pi$
$653$	5.08069	−	15.6368i	0.198823	−	0.611914i	0.999911	−	0.0133669i	$-0.00425496\pi$
$654$	−13.4208	−	2.85268i	−0.524794	−	0.111548i
$655$	−14.8123	−	10.7618i	−0.578764	−	0.420496i
$656$	5.50496	+	9.53487i	0.214933	+	0.372274i
$657$	4.17283	−	7.22756i	0.162798	−	0.281974i
$658$	29.3795	−	13.0806i	1.14533	−	0.509934i
$659$	−35.1966	+	25.5718i	−1.37107	+	0.996137i	−0.373412	+	0.927666i	$0.621812\pi$
$659$	−35.1966	+	25.5718i	−1.37107	+	0.996137i	−0.997653	+	0.0684718i	$0.978188\pi$
$660$	3.87232	+	1.72407i	0.150730	+	0.0671092i
$661$	−37.9789	+	8.07266i	−1.47721	+	0.313990i	−0.874911	−	0.484283i	$-0.839080\pi$
$661$	−37.9789	+	8.07266i	−1.47721	+	0.313990i	−0.602296	+	0.798273i	$0.705747\pi$
$662$	2.46679	−	23.4699i	0.0958744	−	0.912184i
$663$	4.51119	+	5.01019i	0.175200	+	0.194580i
$664$	3.71475	−	4.12565i	0.144160	−	0.160106i
$665$	−1.87423	−	17.8321i	−0.0726797	−	0.691501i
$666$	−2.33688	−	7.19216i	−0.0905521	−	0.278691i
$667$	−5.15790	−	15.8744i	−0.199715	−	0.614658i
$668$	1.87348	+	17.8250i	0.0724871	+	0.689669i
$669$	−1.21860	+	1.35339i	−0.0471138	+	0.0523252i
$670$	6.62138	+	7.35379i	0.255806	+	0.284102i
$671$	4.94909	−	47.0874i	0.191057	−	1.81779i
$672$	−4.91947	+	1.04567i	−0.189773	+	0.0403374i
$673$	−31.2247	−	13.9021i	−1.20363	−	0.535888i	−0.295805	−	0.955248i	$-0.595588\pi$
$673$	−31.2247	−	13.9021i	−1.20363	−	0.535888i	−0.907820	+	0.419360i	$0.862255\pi$
$674$	−7.34351	+	5.33537i	−0.282862	+	0.205511i
$675$	0.913545	−	0.406737i	0.0351624	−	0.0156553i
$676$	−14.7853	+	25.6089i	−0.568665	+	0.984957i
$677$	−14.2887	−	24.7488i	−0.549161	−	0.951175i	−0.998332	−	0.0577290i	$-0.981614\pi$
$677$	−14.2887	−	24.7488i	−0.549161	−	0.951175i	0.449171	−	0.893446i	$-0.351719\pi$
$678$	7.53696	+	5.47592i	0.289455	+	0.210301i
$679$	41.7944	+	8.88367i	1.60392	+	0.340924i
$680$	0.319307	−	0.982725i	0.0122449	−	0.0376858i
$681$	−22.8858			−0.876986
$682$	22.9396	−	5.54634i	0.878401	−	0.212380i
$683$	−9.16050			−0.350517			−0.175258	−	0.984522i	$-0.556076\pi$
$683$	−9.16050			−0.350517			−0.175258	+	0.984522i	$0.556076\pi$
$684$	1.10169	−	3.39064i	0.0421240	−	0.129644i
$685$	2.69558	+	0.572964i	0.102993	+	0.0218918i
$686$	−45.9559	−	33.3889i	−1.75461	−	1.27480i
$687$	−8.97386	−	15.5432i	−0.342374	−	0.593009i
$688$	−1.10576	+	1.91523i	−0.0421567	+	0.0730176i
$689$	70.2458	−	31.2755i	2.67615	−	1.19150i
$690$	−2.20629	+	1.60296i	−0.0839919	+	0.0610237i
$691$	−11.9247	−	5.30920i	−0.453636	−	0.201972i	0.167183	−	0.985926i	$-0.446533\pi$
$691$	−11.9247	−	5.30920i	−0.453636	−	0.201972i	−0.620818	+	0.783954i	$0.713200\pi$
$692$	6.76889	−	1.43877i	0.257314	−	0.0546939i
$693$	−2.22838	+	21.2016i	−0.0846492	+	0.805383i
$694$	−17.5362	−	19.4760i	−0.665667	−	0.739298i
$695$	−3.28925	+	3.65308i	−0.124768	+	0.138569i
$696$	−0.639765	−	6.08696i	−0.0242502	−	0.230726i
$697$	−3.51554	−	10.8197i	−0.133161	−	0.409826i
$698$	−4.79182	−	14.7477i	−0.181373	−	0.558209i
$699$	1.31961	+	12.5552i	0.0499121	+	0.474882i
$700$	−3.36531	+	3.73755i	−0.127197	+	0.141266i
$701$	−2.74398	−	3.04750i	−0.103639	−	0.115103i	0.689094	−	0.724672i	$-0.258009\pi$
$701$	−2.74398	−	3.04750i	−0.103639	−	0.115103i	−0.792732	+	0.609570i	$0.791342\pi$
$702$	0.682008	−	6.48887i	0.0257407	−	0.244907i
$703$	−26.3714	+	5.60541i	−0.994616	+	0.211412i
$704$	−3.87232	−	1.72407i	−0.145944	−	0.0649782i
$705$	5.17318	−	3.75853i	0.194833	−	0.141555i
$706$	−15.5564	+	6.92614i	−0.585472	+	0.260669i
$707$	−6.77838	+	11.7405i	−0.254927	+	0.441547i
$708$	3.70134	+	6.41091i	0.139105	+	0.240937i
$709$	7.80568	+	5.67116i	0.293148	+	0.212985i	0.724632	−	0.689136i	$-0.242010\pi$
$709$	7.80568	+	5.67116i	0.293148	+	0.212985i	−0.431484	+	0.902121i	$0.642010\pi$
$710$	5.93688	+	1.26192i	0.222807	+	0.0473592i
$711$	2.57159	−	7.91453i	0.0964421	−	0.296818i
$712$	3.34350			0.125303
$713$	−4.28906	+	14.5656i	−0.160627	+	0.545486i
$714$	5.19684			0.194487
$715$	8.54630	−	26.3028i	0.319613	−	0.983669i
$716$	−2.49364	−	0.530041i	−0.0931919	−	0.0198085i
$717$	−0.438964	−	0.318926i	−0.0163934	−	0.0119105i
$718$	−1.54725	−	2.67992i	−0.0577429	−	0.100014i
$719$	−8.11269	+	14.0516i	−0.302552	+	0.524036i	−0.976713	−	0.214548i	$-0.931172\pi$
$719$	−8.11269	+	14.0516i	−0.302552	+	0.524036i	0.674161	+	0.738584i	$0.264505\pi$
$720$	−0.913545	+	0.406737i	−0.0340458	+	0.0151582i
$721$	−7.05566	+	5.12624i	−0.262767	+	0.190911i
$722$	5.74606	+	2.55831i	0.213846	+	0.0952104i
$723$	−6.87248	+	1.46079i	−0.255590	+	0.0543274i
$724$	−0.0742051	+	0.706014i	−0.00275781	+	0.0262388i
$725$	−4.09541	−	4.54841i	−0.152100	−	0.168924i
$726$	−4.66201	+	5.17768i	−0.173023	+	0.192162i
$727$	3.57072	+	33.9731i	0.132431	+	1.25999i	0.835746	+	0.549116i	$0.185035\pi$
$727$	3.57072	+	33.9731i	0.132431	+	1.25999i	−0.703316	+	0.710878i	$0.748298\pi$
$728$	10.1403	+	31.2086i	0.375825	+	1.15667i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.872359	+	8.29995i	0.0322875	+	0.307195i
$731$	1.52907	−	1.69821i	0.0565547	−	0.0628104i
$732$	7.47412	+	8.30086i	0.276252	+	0.306808i
$733$	−3.48749	+	33.1813i	−0.128813	+	1.22558i	0.718896	+	0.695118i	$0.244648\pi$
$733$	−3.48749	+	33.1813i	−0.128813	+	1.22558i	−0.847710	+	0.530461i	$0.822019\pi$
$734$	12.5312	−	2.66359i	0.462536	−	0.0983150i
$735$	−16.7129	−	7.44108i	−0.616466	−	0.274468i
$736$	2.20629	−	1.60296i	0.0813248	−	0.0590859i
$737$	−38.3185	+	17.0605i	−1.41148	+	0.628432i
$738$	−5.50496	+	9.53487i	−0.202640	+	0.350983i
$739$	2.71512	+	4.70273i	0.0998774	+	0.172993i	0.911634	−	0.411003i	$-0.134822\pi$
$739$	2.71512	+	4.70273i	0.0998774	+	0.172993i	−0.811756	+	0.583996i	$0.801488\pi$
$740$	6.11802	+	4.44500i	0.224903	+	0.163402i
$741$	−22.7528	−	4.83625i	−0.835845	−	0.177664i
$742$	18.3160	−	56.3710i	0.672403	−	2.06944i
$743$	1.12167			0.0411501			0.0205751	−	0.999788i	$-0.493450\pi$
$743$	1.12167			0.0411501			0.0205751	+	0.999788i	$0.493450\pi$
$744$	−2.64883	+	4.89731i	−0.0971110	+	0.179544i
$745$	2.34681			0.0859804
$746$	8.79063	−	27.0548i	0.321848	−	0.990546i
$747$	5.43029	+	1.15424i	0.198684	+	0.0422316i
$748$	3.54343	+	2.57446i	0.129561	+	0.0941314i
$749$	−18.2606	−	31.6282i	−0.667227	−	1.15567i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−0.622906	+	0.277336i	−0.0227302	+	0.0101201i	−0.418070	−	0.908415i	$-0.637293\pi$
$751$	−0.622906	+	0.277336i	−0.0227302	+	0.0101201i	0.395340	+	0.918535i	$0.370627\pi$
$752$	−5.17318	+	3.75853i	−0.188646	+	0.137060i
$753$	11.2876	+	5.02556i	0.411343	+	0.183141i
$754$	−39.0612	+	8.30271i	−1.42252	+	0.302367i
$755$	−1.39995	+	13.3196i	−0.0509494	+	0.484751i
$756$	−3.36531	−	3.73755i	−0.122395	−	0.135933i
$757$	15.8183	−	17.5680i	0.574926	−	0.638520i	−0.383609	−	0.923496i	$-0.625319\pi$
$757$	15.8183	−	17.5680i	0.574926	−	0.638520i	0.958535	+	0.284976i	$0.0919856\pi$
$758$	−1.82309	−	17.3456i	−0.0662178	−	0.630020i
$759$	−3.57213	−	10.9939i	−0.129660	−	0.399053i
$760$	1.10169	+	3.39064i	0.0399624	+	0.122991i
$761$	4.44404	+	42.2822i	0.161096	+	1.53273i	0.714393	+	0.699744i	$0.246703\pi$
$761$	4.44404	+	42.2822i	0.161096	+	1.53273i	−0.553297	+	0.832984i	$0.686631\pi$
$762$	12.3407	−	13.7057i	0.447056	−	0.496506i
$763$	46.1741	+	51.2815i	1.67161	+	1.85652i
$764$	−0.588479	+	5.59900i	−0.0212904	+	0.202565i
$765$	1.01072	−	0.214835i	0.0365426	−	0.00776737i
$766$	16.0190	+	7.13213i	0.578791	+	0.257694i
$767$	39.0752	−	28.3898i	1.41092	−	1.02510i
$768$	0.913545	−	0.406737i	0.0329647	−	0.0146768i
$769$	11.8830	−	20.5820i	0.428513	−	0.742206i	−0.568229	−	0.822871i	$-0.692371\pi$
$769$	11.8830	−	20.5820i	0.428513	−	0.742206i	0.996741	+	0.0806651i	$0.0257044\pi$
$770$	−10.6592	−	18.4623i	−0.384131	−	0.665334i
$771$	5.07853	+	3.68977i	0.182899	+	0.132884i
$772$	4.13802	+	0.879562i	0.148930	+	0.0316561i
$773$	−9.77192	+	30.0749i	−0.351472	+	1.08172i	0.606555	+	0.795041i	$0.292551\pi$
$773$	−9.77192	+	30.0749i	−0.351472	+	1.08172i	−0.958027	+	0.286677i	$0.907449\pi$
$774$	−2.21152			−0.0794915
$775$	0.735616	+	5.51896i	0.0264241	+	0.198247i
$776$	−8.49571			−0.304978
$777$	−11.7530	+	36.1721i	−0.421637	+	1.29767i
$778$	11.5290	+	2.45056i	0.413334	+	0.0878568i
$779$	31.7554	+	23.0716i	1.13775	+	0.826627i
$780$	3.26231	+	5.65048i	0.116809	+	0.202320i
$781$	−12.8637	+	22.2805i	−0.460299	+	0.797261i
$782$	−2.57431	+	1.14616i	−0.0920570	+	0.0409864i
$783$	4.95158	−	3.59753i	0.176955	−	0.128565i
$784$	16.7129	+	7.44108i	0.596890	+	0.265753i
$785$	9.89237	−	2.10269i	0.353074	−	0.0750481i
$786$	−1.91381	+	18.2087i	−0.0682634	+	0.649482i
$787$	−18.2142	−	20.2289i	−0.649267	−	0.721084i	0.325193	−	0.945648i	$-0.394571\pi$
$787$	−18.2142	−	20.2289i	−0.649267	−	0.721084i	−0.974459	+	0.224564i	$0.927904\pi$
$788$	15.1065	−	16.7774i	0.538146	−	0.597671i
$789$	−2.26885	−	21.5867i	−0.0807731	−	0.768505i
$790$	2.57159	+	7.91453i	0.0914930	+	0.281587i
$791$	−14.4789	−	44.5614i	−0.514809	−	1.58442i
$792$	−0.443073	−	4.21556i	−0.0157439	−	0.149793i
$793$	48.7658	−	54.1599i	1.73172	−	1.92327i
$794$	12.3226	+	13.6856i	0.437313	+	0.485685i
$795$	1.23188	−	11.7206i	0.0436904	−	0.415687i
$796$	12.9686	−	2.75657i	0.459661	−	0.0977040i
$797$	−32.1583	−	14.3178i	−1.13910	−	0.507162i	−0.251540	−	0.967847i	$-0.580937\pi$
$797$	−32.1583	−	14.3178i	−1.13910	−	0.507162i	−0.887564	+	0.460685i	$0.847604\pi$
$798$	−14.5060	+	10.5392i	−0.513506	+	0.373084i
$799$	6.03609	−	2.68744i	0.213542	−	0.0950748i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	1.67175	+	2.89555i	0.0590683	+	0.102309i
$802$	7.61635	+	5.53360i	0.268943	+	0.195398i
$803$	−34.6024	−	7.35497i	−1.22109	−	0.259551i
$804$	3.05788	−	9.41118i	0.107843	−	0.331907i
$805$	13.7157			0.483415
$806$	33.5846	+	13.8479i	1.18297	+	0.487773i
$807$	8.14757			0.286808
$808$	0.832961	−	2.56359i	0.0293035	−	0.0901868i
$809$	2.05555	+	0.436920i	0.0722692	+	0.0153613i	0.243904	−	0.969799i	$-0.421572\pi$
$809$	2.05555	+	0.436920i	0.0722692	+	0.0153613i	−0.171635	+	0.985161i	$0.554905\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−10.5300	−	18.2385i	−0.369759	−	0.640441i	0.619769	−	0.784784i	$-0.287226\pi$
$811$	−10.5300	−	18.2385i	−0.369759	−	0.640441i	−0.989528	+	0.144343i	$0.953893\pi$
$812$	−15.3911	+	26.6582i	−0.540122	+	0.935519i
$813$	12.1903	−	5.42748i	0.427533	−	0.190350i
$814$	−25.9329	+	18.8414i	−0.908949	+	0.660390i
$815$	18.9273	+	8.42700i	0.662996	+	0.295185i
$816$	−1.01072	+	0.214835i	−0.0353822	+	0.00752072i
$817$	−0.824140	+	7.84117i	−0.0288330	+	0.274328i
$818$	−25.8020	−	28.6560i	−0.902146	−	1.00193i
$819$	−21.9573	+	24.3861i	−0.767251	+	0.852119i
$820$	−1.15085	−	10.9496i	−0.0401894	−	0.382377i
$821$	10.4030	+	32.0171i	0.363066	+	1.11740i	0.951183	+	0.308627i	$0.0998694\pi$
$821$	10.4030	+	32.0171i	0.363066	+	1.11740i	−0.588117	+	0.808776i	$0.700131\pi$
$822$	−0.851590	−	2.62093i	−0.0297026	−	0.0914153i
$823$	−0.781254	−	7.43313i	−0.0272328	−	0.259103i	−0.999664	−	0.0259136i	$-0.991751\pi$
$823$	−0.781254	−	7.43313i	−0.0272328	−	0.259103i	0.972431	−	0.233189i	$-0.0749161\pi$
$824$	1.16032	−	1.28866i	0.0404216	−	0.0448928i
$825$	−2.83630	−	3.15003i	−0.0987472	−	0.109670i
$826$	3.89168	−	37.0269i	0.135409	−	1.28833i
$827$	−17.5868	+	3.73819i	−0.611553	+	0.129990i	−0.503268	−	0.864130i	$-0.667869\pi$
$827$	−17.5868	+	3.73819i	−0.611553	+	0.129990i	−0.108285	+	0.994120i	$0.534536\pi$
$828$	2.49135	+	1.10922i	0.0865804	+	0.0385481i
$829$	−29.6160	+	21.5173i	−1.02861	+	0.747327i	−0.968029	−	0.250837i	$-0.919294\pi$
$829$	−29.6160	+	21.5173i	−1.02861	+	0.747327i	−0.0605777	+	0.998163i	$0.519294\pi$
$830$	−5.07165	+	2.25804i	−0.176039	+	0.0783778i
$831$	−13.4971	+	23.3776i	−0.468208	+	0.810960i
$832$	−3.26231	−	5.65048i	−0.113100	−	0.195895i
$833$	−15.2935	−	11.1113i	−0.529887	−	0.384985i
$834$	4.80829	+	1.02203i	0.166497	+	0.0353901i
$835$	5.53856	−	17.0459i	0.191670	−	0.589899i
$836$	−15.1118			−0.522653
$837$	−5.56561	+	0.154698i	−0.192376	+	0.00534716i
$838$	−11.1751			−0.386037
$839$	−1.91683	+	5.89939i	−0.0661763	+	0.203670i	−0.978677	−	0.205406i	$-0.934149\pi$
$839$	−1.91683	+	5.89939i	−0.0661763	+	0.203670i	0.912501	+	0.409075i	$0.134149\pi$
$840$	4.91947	+	1.04567i	0.169738	+	0.0360789i
$841$	−6.84459	−	4.97288i	−0.236020	−	0.171479i
$842$	5.17666	+	8.96623i	0.178399	+	0.308997i
$843$	−7.48930	+	12.9719i	−0.257945	+	0.446774i
$844$	−15.1577	+	6.74865i	−0.521750	+	0.232298i
$845$	23.9231	−	17.3812i	0.822980	−	0.597930i
$846$	−5.84158	−	2.60084i	−0.200838	−	0.0894186i
$847$	34.2752	−	7.28542i	1.17771	−	0.250330i
$848$	−1.23188	+	11.7206i	−0.0423031	+	0.402487i
$849$	18.3444	+	20.3735i	0.629578	+	0.699217i
$850$	−0.691412	+	0.767890i	−0.0237152	+	0.0263384i
$851$	−2.15572	−	20.5103i	−0.0738971	−	0.703084i
$852$	−1.87558	−	5.77245i	−0.0642565	−	0.197761i
$853$	8.51762	+	26.2145i	0.291638	+	0.897568i	0.984330	+	0.176335i	$0.0564243\pi$
$853$	8.51762	+	26.2145i	0.291638	+	0.897568i	−0.692693	+	0.721233i	$0.743576\pi$
$854$	−5.87216	−	55.8699i	−0.200941	−	1.91183i
$855$	−2.38554	+	2.64941i	−0.0815837	+	0.0906079i
$856$	4.85894	+	5.39640i	0.166075	+	0.184445i
$857$	−5.62585	+	53.5264i	−0.192175	+	1.82843i	0.295431	+	0.955364i	$0.404537\pi$
$857$	−5.62585	+	53.5264i	−0.192175	+	1.82843i	−0.487607	+	0.873064i	$0.662130\pi$
$858$	−27.0520	+	5.75009i	−0.923542	+	0.196305i
$859$	−25.2404	−	11.2377i	−0.861191	−	0.383427i	−0.0718747	−	0.997414i	$-0.522898\pi$
$859$	−25.2404	−	11.2377i	−0.861191	−	0.383427i	−0.789316	+	0.613987i	$0.789565\pi$
$860$	1.78916	−	1.29990i	0.0610098	−	0.0443262i
$861$	50.5857	−	22.5222i	1.72396	−	0.767555i
$862$	−2.96322	+	5.13245i	−0.100928	+	0.174812i
$863$	18.1912	+	31.5080i	0.619235	+	1.07255i	0.989626	+	0.143670i	$0.0458905\pi$
$863$	18.1912	+	31.5080i	0.619235	+	1.07255i	−0.370391	+	0.928876i	$0.620776\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−6.76889	−	1.43877i	−0.230149	−	0.0489197i
$866$	3.97737	−	12.2411i	0.135156	−	0.415969i
$867$	−15.9323			−0.541089
$868$	25.2551	−	12.0960i	0.857214	−	0.410564i
$869$	−35.2744			−1.19660
$870$	−1.89133	+	5.82093i	−0.0641223	+	0.197348i
$871$	−63.1534	−	13.4237i	−2.13987	−	0.454844i
$872$	−11.1002	−	8.06478i	−0.375901	−	0.273108i
$873$	−4.24785	−	7.35750i	−0.143768	−	0.249014i
$874$	4.86127	−	8.41997i	0.164435	−	0.284810i
$875$	4.59456	−	2.04563i	0.155324	−	0.0691549i
$876$	6.75178	−	4.90546i	0.228122	−	0.165740i
$877$	22.6736	+	10.0949i	0.765633	+	0.340882i	0.752120	−	0.659027i	$-0.229032\pi$
$877$	22.6736	+	10.0949i	0.765633	+	0.340882i	0.0135139	+	0.999909i	$0.495698\pi$
$878$	14.0240	−	2.98090i	0.473288	−	0.100601i
$879$	1.56180	−	14.8595i	0.0526781	−	0.501199i
$880$	2.83630	+	3.15003i	0.0956116	+	0.106187i
$881$	−4.72944	+	5.25258i	−0.159339	+	0.176964i	−0.817528	−	0.575889i	$-0.804656\pi$
$881$	−4.72944	+	5.25258i	−0.159339	+	0.176964i	0.658189	+	0.752853i	$0.271323\pi$
$882$	1.91230	+	18.1944i	0.0643906	+	0.612636i
$883$	−7.90861	−	24.3402i	−0.266146	−	0.819113i	−0.991427	−	0.130660i	$-0.958290\pi$
$883$	−7.90861	−	24.3402i	−0.266146	−	0.819113i	0.725281	−	0.688453i	$-0.241710\pi$
$884$	2.08335	+	6.41190i	0.0700707	+	0.215656i
$885$	−0.773791	−	7.36213i	−0.0260107	−	0.247475i
$886$	−18.3481	+	20.3776i	−0.616416	+	0.684599i
$887$	−13.6921	−	15.2066i	−0.459736	−	0.510588i	0.468050	−	0.883702i	$-0.344957\pi$
$887$	−13.6921	−	15.2066i	−0.459736	−	0.510588i	−0.927786	+	0.373114i	$0.878290\pi$
$888$	0.790474	−	7.52086i	0.0265266	−	0.252384i
$889$	−90.7292	+	19.2851i	−3.04296	+	0.646801i
$890$	−3.05444	−	1.35992i	−0.102385	−	0.0455847i
$891$	3.42925	−	2.49149i	0.114884	−	0.0834681i
$892$	−1.66372	+	0.740736i	−0.0557055	+	0.0248017i
$893$	−11.3984	+	19.7427i	−0.381434	+	0.660663i
$894$	−1.17340	−	2.03240i	−0.0392445	−	0.0679735i
$895$	2.06247	+	1.49847i	0.0689408	+	0.0500884i
$896$	−4.91947	−	1.04567i	−0.164348	−	0.0349332i
$897$	5.49847	−	16.9225i	0.183588	−	0.565027i
$898$	−6.93240			−0.231337
$899$	11.4269	+	32.1045i	0.381109	+	1.07074i
$900$	1.00000			0.0333333
$901$	3.76308	−	11.5816i	0.125366	−	0.385838i
$902$	45.6488	+	9.70295i	1.51994	+	0.323073i
$903$	8.99834	+	6.53768i	0.299446	+	0.217560i
$904$	4.65810	+	8.06806i	0.154926	+	0.268340i
$905$	0.354952	−	0.614794i	0.0117990	−	0.0204364i
$906$	12.2351	−	5.44742i	0.406484	−	0.180978i
$907$	9.40505	−	6.83317i	0.312289	−	0.226892i	−0.420589	−	0.907251i	$-0.638176\pi$
$907$	9.40505	−	6.83317i	0.312289	−	0.226892i	0.732878	+	0.680360i	$0.238176\pi$
$908$	−20.9072	−	9.30850i	−0.693831	−	0.308913i
$909$	2.63662	−	0.560430i	0.0874510	−	0.0185883i
$910$	3.43007	−	32.6349i	0.113706	−	1.08184i
$911$	−21.6948	−	24.0946i	−0.718782	−	0.798288i	0.267465	−	0.963568i	$-0.413814\pi$
$911$	−21.6948	−	24.0946i	−0.718782	−	0.798288i	−0.986247	+	0.165279i	$0.947147\pi$
$912$	2.38554	−	2.64941i	0.0789931	−	0.0877307i
$913$	−2.45977	−	23.4031i	−0.0814064	−	0.774531i
$914$	4.51322	+	13.8903i	0.149284	+	0.459450i
$915$	−3.45169	−	10.6232i	−0.114109	−	0.351192i
$916$	−1.87605	−	17.8494i	−0.0619863	−	0.589761i
$917$	61.6154	−	68.4308i	2.03472	−	2.25978i
$918$	−0.691412	−	0.767890i	−0.0228200	−	0.0253442i
$919$	−4.76124	+	45.3002i	−0.157059	+	1.49432i	0.577846	+	0.816146i	$0.303893\pi$
$919$	−4.76124	+	45.3002i	−0.157059	+	1.49432i	−0.734905	+	0.678170i	$0.762773\pi$
$920$	−2.66753	+	0.567000i	−0.0879457	+	0.0186934i
$921$	−14.1391	−	6.29512i	−0.465898	−	0.207431i
$922$	−10.9811	+	7.97823i	−0.361643	+	0.262749i
$923$	−36.1776	+	16.1073i	−1.19080	+	0.530178i
$924$	−10.6592	+	18.4623i	−0.350662	+	0.607364i
$925$	−3.78114	−	6.54913i	−0.124323	−	0.215334i
$926$	5.66212	+	4.11377i	0.186069	+	0.135187i
$927$	1.69618	+	0.360533i	0.0557097	+	0.0118415i
$928$	1.89133	−	5.82093i	0.0620861	−	0.191081i
$929$	−41.4338			−1.35940			−0.679700	−	0.733490i	$-0.737890\pi$
$929$	−41.4338			−1.35940			−0.679700	+	0.733490i	$0.737890\pi$
$930$	4.41175	−	3.39654i	0.144667	−	0.111377i
$931$	65.2226			2.13758
$932$	−3.90115	+	12.0065i	−0.127786	+	0.393286i
$933$	−33.3504	−	7.08885i	−1.09184	−	0.232078i
$934$	30.2846	+	22.0031i	0.990944	+	0.719963i
$935$	−2.18996	−	3.79313i	−0.0716194	−	0.124048i
$936$	3.26231	−	5.65048i	0.106632	−	0.184692i
$937$	21.3472	−	9.50439i	0.697383	−	0.310495i	−0.0272512	−	0.999629i	$-0.508675\pi$
$937$	21.3472	−	9.50439i	0.697383	−	0.310495i	0.724634	+	0.689134i	$0.242009\pi$
$938$	−40.2633	+	29.2530i	−1.31464	+	0.955143i
$939$	2.07374	+	0.923290i	0.0676740	+	0.0301304i
$940$	6.25467	−	1.32947i	0.204005	−	0.0433626i
$941$	2.29179	−	21.8049i	0.0747101	−	0.710819i	−0.891493	−	0.453035i	$-0.850341\pi$
$941$	2.29179	−	21.8049i	0.0747101	−	0.710819i	0.966203	−	0.257784i	$-0.0829922\pi$
$942$	−6.76716	−	7.51570i	−0.220486	−	0.244875i
$943$	−20.0909	+	22.3132i	−0.654250	+	0.726618i
$944$	0.773791	+	7.36213i	0.0251848	+	0.239617i
$945$	1.55416	+	4.78322i	0.0505569	+	0.155598i
$946$	2.89677	+	8.91535i	0.0941822	+	0.289863i
$947$	−5.89822	−	56.1179i	−0.191667	−	1.82359i	−0.492958	−	0.870053i	$-0.664084\pi$
$947$	−5.89822	−	56.1179i	−0.191667	−	1.82359i	0.301291	−	0.953532i	$-0.402582\pi$
$948$	5.56839	−	6.18433i	0.180853	−	0.200858i
$949$	−36.4357	−	40.4659i	−1.18275	−	1.31358i
$950$	0.372658	−	3.54560i	0.0120906	−	0.115034i
$951$	10.4384	−	2.21876i	0.338490	−	0.0719482i
$952$	4.74755	+	2.11375i	0.153869	+	0.0685069i
$953$	−16.8071	+	12.2111i	−0.544436	+	0.395556i	−0.825730	−	0.564066i	$-0.809236\pi$
$953$	−16.8071	+	12.2111i	−0.544436	+	0.395556i	0.281294	+	0.959622i	$0.409236\pi$
$954$	−10.7663	+	4.79346i	−0.348571	+	0.155194i
$955$	2.81492	−	4.87559i	0.0910887	−	0.157770i
$956$	−0.271295	−	0.469896i	−0.00877429	−	0.0151975i
$957$	−20.9887	−	15.2492i	−0.678467	−	0.492935i
$958$	−28.3304	−	6.02181i	−0.915313	−	0.194556i
$959$	−4.28296	+	13.1816i	−0.138304	+	0.425656i
$960$	−1.00000			−0.0322749
$961$	7.92703	−	29.9694i	0.255711	−	0.966753i
$962$	−49.3410			−1.59082
$963$	−2.24395	+	6.90616i	−0.0723102	+	0.222548i
$964$	−6.87248	−	1.46079i	−0.221348	−	0.0470489i
$965$	−3.42251	−	2.48660i	−0.110175	−	0.0800466i
$966$	−6.85785	−	11.8781i	−0.220648	−	0.382173i
$967$	−7.19444	+	12.4611i	−0.231358	+	0.400723i	−0.958208	−	0.286073i	$-0.907650\pi$
$967$	−7.19444	+	12.4611i	−0.231358	+	0.400723i	0.726850	+	0.686796i	$0.240983\pi$
$968$	−6.36491	+	2.83384i	−0.204576	+	0.0910831i
$969$	−2.98029	+	2.16531i	−0.0957408	+	0.0695597i
$970$	7.76122	+	3.45552i	0.249198	+	0.110950i
$971$	−30.5952	+	6.50322i	−0.981847	+	0.208698i	−0.670753	−	0.741681i	$-0.734029\pi$
$971$	−30.5952	+	6.50322i	−0.981847	+	0.208698i	−0.311095	+	0.950379i	$0.600696\pi$
$972$	−0.104528	+	0.994522i	−0.00335275	+	0.0318993i
$973$	−16.5429	−	18.3727i	−0.530340	−	0.589002i
$974$	−10.5207	+	11.6845i	−0.337106	+	0.374394i
$975$	−0.682008	−	6.48887i	−0.0218417	−	0.207810i
$976$	3.45169	+	10.6232i	0.110486	+	0.340041i
$977$	−8.22956	−	25.3280i	−0.263287	−	0.810314i	−0.992083	−	0.125583i	$-0.959920\pi$
$977$	−8.22956	−	25.3280i	−0.263287	−	0.810314i	0.728796	−	0.684731i	$-0.240080\pi$
$978$	−2.16568	−	20.6051i	−0.0692508	−	0.658877i
$979$	9.48316	−	10.5321i	0.303083	−	0.336608i
$980$	−12.2415	−	13.5955i	−0.391039	−	0.434293i
$981$	1.43419	−	13.6455i	0.0457903	−	0.435666i
$982$	21.7603	−	4.62530i	0.694400	−	0.147599i
$983$	42.2136	+	18.7947i	1.34640	+	0.599457i	0.948152	−	0.317819i	$-0.102950\pi$
$983$	42.2136	+	18.7947i	1.34640	+	0.599457i	0.398252	+	0.917276i	$0.369617\pi$
$984$	−8.90721	+	6.47147i	−0.283951	+	0.206303i
$985$	−20.6244	+	9.18259i	−0.657149	+	0.292582i
$986$	−3.16214	+	5.47700i	−0.100703	+	0.174423i
$987$	16.0799	+	27.8512i	0.511829	+	0.886514i
$988$	−18.8186	−	13.6725i	−0.598700	−	0.434981i
$989$	−5.89929	−	1.25393i	−0.187586	−	0.0398727i
$990$	−1.30986	+	4.03132i	−0.0416299	+	0.128124i
$991$	23.0800			0.733161			0.366581	−	0.930386i	$-0.380528\pi$
$991$	23.0800			0.733161			0.366581	+	0.930386i	$0.380528\pi$
$992$	−4.41175	+	3.39654i	−0.140073	+	0.107840i
$993$	23.5992			0.748897
$994$	−9.43301	+	29.0318i	−0.299197	+	0.920833i
$995$	−12.9686	−	2.75657i	−0.411133	−	0.0873891i
$996$	4.49134	+	3.26315i	0.142314	+	0.103397i
$997$	17.0861	+	29.5941i	0.541124	+	0.937254i	0.998840	+	0.0481553i	$0.0153342\pi$
$997$	17.0861	+	29.5941i	0.541124	+	0.937254i	−0.457716	+	0.889098i	$0.651332\pi$
$998$	−13.8937	+	24.0646i	−0.439797	+	0.761750i
$999$	6.90849	−	3.07586i	0.218575	−	0.0973159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.691.1	✓	24
31.7	even	15	inner	930.2.bg.i.751.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.691.1	✓	24	1.1	even	1	trivial
930.2.bg.i.751.1	yes	24	31.7	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-4.59456 + 2.04563i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-4.59456 + 2.04563i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(0.443073 - 4.21556i) q^{11} +(0.669131 + 0.743145i) q^{12} +(4.36582 - 4.84873i) q^{13} +(-0.525712 - 5.00182i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.108009 - 1.02764i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(2.38554 + 2.64941i) q^{19} +(0.104528 - 0.994522i) q^{20} +(4.91947 - 1.04567i) q^{21} +(3.87232 + 1.72407i) q^{22} +(-2.20629 + 1.60296i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.26231 + 5.65048i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.91947 + 1.04567i) q^{28} +(-1.89133 + 5.82093i) q^{29} +1.00000 q^{30} +(4.41175 - 3.39654i) q^{31} -1.00000 q^{32} +(-1.30986 + 4.03132i) q^{33} +(1.01072 + 0.214835i) q^{34} +(-4.06885 - 2.95619i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.78114 + 6.54913i) q^{37} +(-3.25691 + 1.45007i) q^{38} +(-5.27852 + 3.83507i) q^{39} +(0.913545 + 0.406737i) q^{40} +(10.7693 - 2.28909i) q^{41} +(-0.525712 + 5.00182i) q^{42} +(1.47980 + 1.64348i) q^{43} +(-2.83630 + 3.15003i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.842727 - 2.59365i) q^{46} +(1.97598 + 6.08144i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(12.2415 - 13.5955i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(-0.108009 + 1.02764i) q^{51} +(-6.38204 + 1.35654i) q^{52} +(10.7663 + 4.79346i) q^{53} +(0.809017 - 0.587785i) q^{54} +(3.87232 - 1.72407i) q^{55} +(-2.51469 + 4.35556i) q^{56} +(-1.78257 - 3.08749i) q^{57} +(-4.95158 - 3.59753i) q^{58} +(7.24092 + 1.53910i) q^{59} +(-0.309017 + 0.951057i) q^{60} +11.1699 q^{61} +(1.86700 + 5.24541i) q^{62} -5.02937 q^{63} +(0.309017 - 0.951057i) q^{64} +(6.38204 + 1.35654i) q^{65} +(-3.42925 - 2.49149i) q^{66} +(-4.94775 - 8.56975i) q^{67} +(-0.516649 + 0.894863i) q^{68} +(2.49135 - 1.10922i) q^{69} +(4.06885 - 2.95619i) q^{70} +(-5.54478 - 2.46870i) q^{71} +(0.978148 - 0.207912i) q^{72} +(0.872359 - 8.29995i) q^{73} +(-5.06016 - 5.61988i) q^{74} +(0.669131 - 0.743145i) q^{75} +(-0.372658 - 3.54560i) q^{76} +(6.58775 + 20.2750i) q^{77} +(-2.01622 - 6.20528i) q^{78} +(-0.869869 - 8.27625i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-1.15085 + 10.9496i) q^{82} +(5.43029 - 1.15424i) q^{83} +(-4.59456 - 2.04563i) q^{84} +(0.835956 - 0.607357i) q^{85} +(-2.02032 + 0.899506i) q^{86} +(3.06024 - 5.30050i) q^{87} +(-2.11939 - 3.67089i) q^{88} +(2.70495 + 1.96526i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(-10.1403 + 31.2086i) q^{91} +2.72712 q^{92} +(-5.02152 + 2.40506i) q^{93} -6.39440 q^{94} +(-1.10169 + 3.39064i) q^{95} +(0.978148 + 0.207912i) q^{96} +(-6.87317 - 4.99365i) q^{97} +(9.14729 + 15.8436i) q^{98} +(2.11939 - 3.67089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more