LMFDB - Embedded newform 114.2.i.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	114.43
Dual form			114.2.i.b.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.97178 - 2.49362i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.613341 - 1.06234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.97178 - 2.49362i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.613341 - 1.06234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(3.64543 + 1.32683i) q^{10} +(1.06031 - 1.83651i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.0851223 + 0.482753i) q^{13} +(0.939693 + 0.788496i) q^{14} +(-2.97178 + 2.49362i) q^{15} +(0.173648 - 0.984808i) q^{16} +(5.19846 - 1.89209i) q^{17} +1.00000 q^{18} +(2.77719 - 3.35965i) q^{19} -3.87939 q^{20} +(-1.15270 + 0.419550i) q^{21} +(-0.368241 + 2.08840i) q^{22} +(-6.85117 + 5.74881i) q^{23} +(0.766044 + 0.642788i) q^{24} +(1.74510 + 9.89695i) q^{25} +(-0.245100 - 0.424525i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-1.15270 - 0.419550i) q^{28} +(7.96451 + 2.89884i) q^{29} +(1.93969 - 3.35965i) q^{30} +(-1.20574 - 2.08840i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.62449 - 1.36310i) q^{33} +(-4.23783 + 3.55596i) q^{34} +(-0.826352 + 4.68647i) q^{35} +(-0.939693 + 0.342020i) q^{36} +1.69459 q^{37} +(-1.46064 + 4.10689i) q^{38} +0.490200 q^{39} +(3.64543 - 1.32683i) q^{40} +(0.277189 - 1.57202i) q^{41} +(0.939693 - 0.788496i) q^{42} +(-5.08512 - 4.26692i) q^{43} +(-0.368241 - 2.08840i) q^{44} +(1.93969 + 3.35965i) q^{45} +(4.47178 - 7.74535i) q^{46} +(-2.03936 - 0.742267i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(2.74763 - 4.75903i) q^{49} +(-5.02481 - 8.70323i) q^{50} +(-0.960637 - 5.44804i) q^{51} +(0.375515 + 0.315094i) q^{52} +(6.80793 - 5.71253i) q^{53} +(0.173648 - 0.984808i) q^{54} +(-7.73055 + 2.81369i) q^{55} +1.22668 q^{56} +(-2.82635 - 3.31839i) q^{57} -8.47565 q^{58} +(10.7306 - 3.90560i) q^{59} +(-0.673648 + 3.82045i) q^{60} +(0.0320889 - 0.0269258i) q^{61} +(1.84730 + 1.55007i) q^{62} +(0.213011 + 1.20805i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.950837 - 1.64690i) q^{65} +(1.99273 + 0.725293i) q^{66} +(-4.20574 - 1.53076i) q^{67} +(2.76604 - 4.79093i) q^{68} +(4.47178 + 7.74535i) q^{69} +(-0.826352 - 4.68647i) q^{70} +(2.02094 + 1.69577i) q^{71} +(0.766044 - 0.642788i) q^{72} +(-2.66772 + 15.1294i) q^{73} +(-1.59240 + 0.579585i) q^{74} +10.0496 q^{75} +(-0.0320889 - 4.35878i) q^{76} -2.60132 q^{77} +(-0.460637 + 0.167658i) q^{78} +(-0.809278 + 4.58964i) q^{79} +(-2.97178 + 2.49362i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.277189 + 1.57202i) q^{82} +(-6.24035 - 10.8086i) q^{83} +(-0.613341 + 1.06234i) q^{84} +(-20.1668 - 7.34013i) q^{85} +(6.23783 + 2.27038i) q^{86} +(4.23783 - 7.34013i) q^{87} +(1.06031 + 1.83651i) q^{88} +(1.46838 + 8.32759i) q^{89} +(-2.97178 - 2.49362i) q^{90} +(0.460637 - 0.386520i) q^{91} +(-1.55303 + 8.80769i) q^{92} +(-2.26604 + 0.824773i) q^{93} +2.17024 q^{94} +(-16.6309 + 3.05888i) q^{95} +1.00000 q^{96} +(13.5103 - 4.91734i) q^{97} +(-0.954241 + 5.41177i) q^{98} +(-1.62449 + 1.36310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8	$ 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8} + 6 q^{10} + 12 q^{11} - 3 q^{12} - 21 q^{13} - 3 q^{15} + 3 q^{17} + 6 q^{18} + 6 q^{19} - 12 q^{20} - 9 q^{21} + 3 q^{22} - 15 q^{23} + 9 q^{25} - 3 q^{27} - 9 q^{28} + 15 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{33} - 6 q^{34} - 6 q^{35} + 6 q^{37} + 6 q^{40} - 9 q^{41} - 9 q^{43} + 3 q^{44} + 6 q^{45} + 12 q^{46} - 21 q^{47} - 3 q^{50} + 3 q^{51} + 15 q^{52} + 30 q^{53} - 9 q^{55} - 6 q^{56} - 18 q^{57} - 12 q^{58} + 27 q^{59} - 3 q^{60} - 9 q^{61} + 9 q^{62} + 9 q^{63} - 3 q^{64} - 6 q^{65} - 6 q^{66} - 15 q^{67} + 12 q^{68} + 12 q^{69} - 6 q^{70} + 9 q^{71} + 12 q^{73} - 6 q^{74} + 6 q^{75} + 9 q^{76} + 42 q^{77} + 6 q^{78} + 15 q^{79} - 3 q^{80} - 9 q^{82} - 3 q^{83} + 3 q^{84} - 36 q^{85} + 18 q^{86} + 6 q^{87} + 12 q^{88} - 48 q^{89} - 3 q^{90} - 6 q^{91} + 3 q^{92} - 9 q^{93} - 30 q^{94} - 48 q^{95} + 6 q^{96} + 18 q^{97} - 36 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8 + 6 * q^10 + 12 * q^11 - 3 * q^12 - 21 * q^13 - 3 * q^15 + 3 * q^17 + 6 * q^18 + 6 * q^19 - 12 * q^20 - 9 * q^21 + 3 * q^22 - 15 * q^23 + 9 * q^25 - 3 * q^27 - 9 * q^28 + 15 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^33 - 6 * q^34 - 6 * q^35 + 6 * q^37 + 6 * q^40 - 9 * q^41 - 9 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 - 21 * q^47 - 3 * q^50 + 3 * q^51 + 15 * q^52 + 30 * q^53 - 9 * q^55 - 6 * q^56 - 18 * q^57 - 12 * q^58 + 27 * q^59 - 3 * q^60 - 9 * q^61 + 9 * q^62 + 9 * q^63 - 3 * q^64 - 6 * q^65 - 6 * q^66 - 15 * q^67 + 12 * q^68 + 12 * q^69 - 6 * q^70 + 9 * q^71 + 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 42 * q^77 + 6 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^82 - 3 * q^83 + 3 * q^84 - 36 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 48 * q^89 - 3 * q^90 - 6 * q^91 + 3 * q^92 - 9 * q^93 - 30 * q^94 - 48 * q^95 + 6 * q^96 + 18 * q^97 - 36 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−2.97178	−	2.49362i	−1.32902	−	1.11518i	−0.984305	−	0.176474i	$-0.943531\pi$
$5$	−2.97178	−	2.49362i	−1.32902	−	1.11518i	−0.344716	−	0.938707i	$-0.612025\pi$
$6$	0.173648	+	0.984808i	0.0708916	+	0.402046i
$7$	−0.613341	−	1.06234i	−0.231821	−	0.401526i	0.726523	−	0.687142i	$-0.241135\pi$
$7$	−0.613341	−	1.06234i	−0.231821	−	0.401526i	−0.958344	+	0.285616i	$0.907802\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	3.64543	+	1.32683i	1.15279	+	0.419580i
$11$	1.06031	−	1.83651i	0.319695	−	0.553727i	−0.660730	−	0.750624i	$-0.729753\pi$
$11$	1.06031	−	1.83651i	0.319695	−	0.553727i	0.980424	+	0.196897i	$0.0630863\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.0851223	+	0.482753i	0.0236087	+	0.133891i	0.994334	−	0.106301i	$-0.0339006\pi$
$13$	0.0851223	+	0.482753i	0.0236087	+	0.133891i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.939693	+	0.788496i	0.251143	+	0.210734i
$15$	−2.97178	+	2.49362i	−0.767311	+	0.643850i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	5.19846	−	1.89209i	1.26081	−	0.458898i	0.376771	−	0.926306i	$-0.377034\pi$
$17$	5.19846	−	1.89209i	1.26081	−	0.458898i	0.884042	+	0.467408i	$0.154812\pi$
$18$	1.00000			0.235702
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$20$	−3.87939			−0.867457
$21$	−1.15270	+	0.419550i	−0.251541	+	0.0915533i
$22$	−0.368241	+	2.08840i	−0.0785092	+	0.445248i
$23$	−6.85117	+	5.74881i	−1.42857	+	1.19871i	−0.482013	+	0.876164i	$0.660094\pi$
$23$	−6.85117	+	5.74881i	−1.42857	+	1.19871i	−0.946554	+	0.322546i	$0.895461\pi$
$24$	0.766044	+	0.642788i	0.156368	+	0.131208i
$25$	1.74510	+	9.89695i	0.349020	+	1.97939i
$26$	−0.245100	−	0.424525i	−0.0480680	−	0.0832563i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−1.15270	−	0.419550i	−0.217841	−	0.0792875i
$29$	7.96451	+	2.89884i	1.47897	+	0.538302i	0.950521	−	0.310662i	$-0.100551\pi$
$29$	7.96451	+	2.89884i	1.47897	+	0.538302i	0.528451	+	0.848964i	$0.322773\pi$
$30$	1.93969	−	3.35965i	0.354138	−	0.613385i
$31$	−1.20574	−	2.08840i	−0.216557	−	0.375087i	0.737196	−	0.675679i	$-0.236149\pi$
$31$	−1.20574	−	2.08840i	−0.216557	−	0.375087i	−0.953753	+	0.300591i	$0.902816\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−1.62449	−	1.36310i	−0.282787	−	0.237286i
$34$	−4.23783	+	3.55596i	−0.726781	+	0.609842i
$35$	−0.826352	+	4.68647i	−0.139679	+	0.792159i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	1.69459			0.278589			0.139295	−	0.990251i	$-0.455516\pi$
$37$	1.69459			0.278589			0.139295	+	0.990251i	$0.455516\pi$
$38$	−1.46064	+	4.10689i	−0.236947	+	0.666225i
$39$	0.490200			0.0784948
$40$	3.64543	−	1.32683i	0.576393	−	0.209790i
$41$	0.277189	−	1.57202i	0.0432896	−	0.245508i	−0.955483	−	0.295048i	$-0.904664\pi$
$41$	0.277189	−	1.57202i	0.0432896	−	0.245508i	0.998772	+	0.0495401i	$0.0157756\pi$
$42$	0.939693	−	0.788496i	0.144998	−	0.121668i
$43$	−5.08512	−	4.26692i	−0.775474	−	0.650700i	0.166631	−	0.986019i	$-0.446711\pi$
$43$	−5.08512	−	4.26692i	−0.775474	−	0.650700i	−0.942104	+	0.335320i	$0.891156\pi$
$44$	−0.368241	−	2.08840i	−0.0555144	−	0.314838i
$45$	1.93969	+	3.35965i	0.289152	+	0.500826i
$46$	4.47178	−	7.74535i	0.659328	−	1.14199i
$47$	−2.03936	−	0.742267i	−0.297472	−	0.108271i	0.188973	−	0.981982i	$-0.439484\pi$
$47$	−2.03936	−	0.742267i	−0.297472	−	0.108271i	−0.486444	+	0.873711i	$0.661706\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	2.74763	−	4.75903i	0.392518	−	0.679861i
$50$	−5.02481	−	8.70323i	−0.710616	−	1.23082i
$51$	−0.960637	−	5.44804i	−0.134516	−	0.762879i
$52$	0.375515	+	0.315094i	0.0520745	+	0.0436957i
$53$	6.80793	−	5.71253i	0.935142	−	0.784677i	−0.0415917	−	0.999135i	$-0.513243\pi$
$53$	6.80793	−	5.71253i	0.935142	−	0.784677i	0.976733	+	0.214458i	$0.0687984\pi$
$54$	0.173648	−	0.984808i	0.0236305	−	0.134015i
$55$	−7.73055	+	2.81369i	−1.04239	+	0.379398i
$56$	1.22668			0.163922
$57$	−2.82635	−	3.31839i	−0.374359	−	0.439532i
$58$	−8.47565			−1.11291
$59$	10.7306	−	3.90560i	1.39700	−	0.508466i	0.469713	−	0.882819i	$-0.344357\pi$
$59$	10.7306	−	3.90560i	1.39700	−	0.508466i	0.927286	+	0.374353i	$0.122135\pi$
$60$	−0.673648	+	3.82045i	−0.0869676	+	0.493218i
$61$	0.0320889	−	0.0269258i	0.00410856	−	0.00344749i	−0.640731	−	0.767765i	$-0.721369\pi$
$61$	0.0320889	−	0.0269258i	0.00410856	−	0.00344749i	0.644840	+	0.764318i	$0.276924\pi$
$62$	1.84730	+	1.55007i	0.234607	+	0.196859i
$63$	0.213011	+	1.20805i	0.0268369	+	0.152199i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.950837	−	1.64690i	0.117937	−	0.204273i
$66$	1.99273	+	0.725293i	0.245288	+	0.0892774i
$67$	−4.20574	−	1.53076i	−0.513813	−	0.187012i	0.0720836	−	0.997399i	$-0.477035\pi$
$67$	−4.20574	−	1.53076i	−0.513813	−	0.187012i	−0.585896	+	0.810386i	$0.699257\pi$
$68$	2.76604	−	4.79093i	0.335432	−	0.580986i
$69$	4.47178	+	7.74535i	0.538339	+	0.932431i
$70$	−0.826352	−	4.68647i	−0.0987679	−	0.560141i
$71$	2.02094	+	1.69577i	0.239842	+	0.201251i	0.754783	−	0.655974i	$-0.227742\pi$
$71$	2.02094	+	1.69577i	0.239842	+	0.201251i	−0.514941	+	0.857225i	$0.672186\pi$
$72$	0.766044	−	0.642788i	0.0902792	−	0.0757532i
$73$	−2.66772	+	15.1294i	−0.312233	+	1.77076i	0.275101	+	0.961415i	$0.411289\pi$
$73$	−2.66772	+	15.1294i	−0.312233	+	1.77076i	−0.587334	+	0.809345i	$0.699822\pi$
$74$	−1.59240	+	0.579585i	−0.185112	+	0.0673754i
$75$	10.0496			1.16043
$76$	−0.0320889	−	4.35878i	−0.00368085	−	0.499986i
$77$	−2.60132			−0.296448
$78$	−0.460637	+	0.167658i	−0.0521569	+	0.0189836i
$79$	−0.809278	+	4.58964i	−0.0910509	+	0.516375i	0.904835	+	0.425762i	$0.139994\pi$
$79$	−0.809278	+	4.58964i	−0.0910509	+	0.516375i	−0.995886	+	0.0906133i	$0.971117\pi$
$80$	−2.97178	+	2.49362i	−0.332255	+	0.278795i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	0.277189	+	1.57202i	0.0306104	+	0.173600i
$83$	−6.24035	−	10.8086i	−0.684968	−	1.18640i	−0.973447	−	0.228913i	$-0.926483\pi$
$83$	−6.24035	−	10.8086i	−0.684968	−	1.18640i	0.288479	−	0.957486i	$-0.406850\pi$
$84$	−0.613341	+	1.06234i	−0.0669210	+	0.115911i
$85$	−20.1668	−	7.34013i	−2.18740	−	0.796149i
$86$	6.23783	+	2.27038i	0.672642	+	0.244822i
$87$	4.23783	−	7.34013i	0.454343	−	0.786945i
$88$	1.06031	+	1.83651i	0.113029	+	0.195772i
$89$	1.46838	+	8.32759i	0.155648	+	0.882722i	0.958191	+	0.286129i	$0.0923685\pi$
$89$	1.46838	+	8.32759i	0.155648	+	0.882722i	−0.802543	+	0.596594i	$0.796520\pi$
$90$	−2.97178	−	2.49362i	−0.313253	−	0.262851i
$91$	0.460637	−	0.386520i	0.0482879	−	0.0405184i
$92$	−1.55303	+	8.80769i	−0.161915	+	0.918265i
$93$	−2.26604	+	0.824773i	−0.234978	+	0.0855249i
$94$	2.17024			0.223844
$95$	−16.6309	+	3.05888i	−1.70629	+	0.313834i
$96$	1.00000			0.102062
$97$	13.5103	−	4.91734i	1.37176	−	0.499280i	0.452090	−	0.891972i	$-0.350679\pi$
$97$	13.5103	−	4.91734i	1.37176	−	0.499280i	0.919670	+	0.392693i	$0.128456\pi$
$98$	−0.954241	+	5.41177i	−0.0963929	+	0.546671i
$99$	−1.62449	+	1.36310i	−0.163267	+	0.136997i
$100$	7.69846	+	6.45978i	0.769846	+	0.645978i
$101$	0.988856	+	5.60808i	0.0983948	+	0.558025i	0.993654	+	0.112479i	$0.0358792\pi$
$101$	0.988856	+	5.60808i	0.0983948	+	0.558025i	−0.895259	+	0.445546i	$0.853010\pi$
$102$	2.76604	+	4.79093i	0.273879	+	0.474373i
$103$	0.156574	−	0.271194i	0.0154277	−	0.0267216i	−0.858208	−	0.513301i	$-0.828422\pi$
$103$	0.156574	−	0.271194i	0.0154277	−	0.0267216i	0.873636	+	0.486580i	$0.161756\pi$
$104$	−0.460637	−	0.167658i	−0.0451692	−	0.0164402i
$105$	4.47178	+	1.62760i	0.436401	+	0.158837i
$106$	−4.44356	+	7.69648i	−0.431597	+	0.747548i
$107$	8.41400	+	14.5735i	0.813412	+	1.40887i	0.910462	+	0.413592i	$0.135726\pi$
$107$	8.41400	+	14.5735i	0.813412	+	1.40887i	−0.0970504	+	0.995279i	$0.530941\pi$
$108$	0.173648	+	0.984808i	0.0167093	+	0.0947632i
$109$	−7.97565	−	6.69237i	−0.763929	−	0.641012i	0.175217	−	0.984530i	$-0.443937\pi$
$109$	−7.97565	−	6.69237i	−0.763929	−	0.641012i	−0.939146	+	0.343517i	$0.888382\pi$
$110$	6.30200	−	5.28801i	0.600872	−	0.504192i
$111$	0.294263	−	1.66885i	0.0279302	−	0.158400i
$112$	−1.15270	+	0.419550i	−0.108920	+	0.0396437i
$113$	−17.3824			−1.63520			−0.817598	−	0.575789i	$-0.804695\pi$
$113$	−17.3824			−1.63520			−0.817598	+	0.575789i	$0.804695\pi$
$114$	3.79086	+	2.15160i	0.355047	+	0.201516i
$115$	34.6955			3.23537
$116$	7.96451	−	2.89884i	0.739486	−	0.269151i
$117$	0.0851223	−	0.482753i	0.00786956	−	0.0446305i
$118$	−8.74763	+	7.34013i	−0.805284	+	0.675714i
$119$	−5.19846	−	4.36203i	−0.476542	−	0.399866i
$120$	−0.673648	−	3.82045i	−0.0614954	−	0.348758i
$121$	3.25150	+	5.63176i	0.295591	+	0.511978i
$122$	−0.0209445	+	0.0362770i	−0.00189623	+	0.00328436i
$123$	−1.50000	−	0.545955i	−0.135250	−	0.0492271i
$124$	−2.26604	−	0.824773i	−0.203497	−	0.0740668i
$125$	9.79473	−	16.9650i	0.876067	−	1.51739i
$126$	−0.613341	−	1.06234i	−0.0546407	−	0.0946405i
$127$	−0.283119	−	1.60565i	−0.0251227	−	0.142478i	0.969666	−	0.244432i	$-0.0786016\pi$
$127$	−0.283119	−	1.60565i	−0.0251227	−	0.142478i	−0.994789	+	0.101954i	$0.967490\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−5.08512	+	4.26692i	−0.447720	+	0.375682i
$130$	−0.330222	+	1.87278i	−0.0289624	+	0.164254i
$131$	−5.60354	+	2.03952i	−0.489584	+	0.178194i	−0.575003	−	0.818151i	$-0.694999\pi$
$131$	−5.60354	+	2.03952i	−0.489584	+	0.178194i	0.0854195	+	0.996345i	$0.472777\pi$
$132$	−2.12061			−0.184576
$133$	−5.27244	−	0.889704i	−0.457179	−	0.0771471i
$134$	4.47565			0.386637
$135$	3.64543	−	1.32683i	0.313749	−	0.114195i
$136$	−0.960637	+	5.44804i	−0.0823740	+	0.467166i
$137$	−0.0150147	+	0.0125989i	−0.00128280	+	0.00107639i	−0.643429	−	0.765506i	$-0.722489\pi$
$137$	−0.0150147	+	0.0125989i	−0.00128280	+	0.00107639i	0.642146	+	0.766582i	$0.278044\pi$
$138$	−6.85117	−	5.74881i	−0.583210	−	0.489371i
$139$	0.780592	+	4.42696i	0.0662090	+	0.375490i	0.999851	+	0.0172815i	$0.00550113\pi$
$139$	0.780592	+	4.42696i	0.0662090	+	0.375490i	−0.933642	+	0.358208i	$0.883388\pi$
$140$	2.37939	+	4.12122i	0.201095	+	0.348306i
$141$	−1.08512	+	1.87949i	−0.0913838	+	0.158281i
$142$	−2.47906	−	0.902302i	−0.208038	−	0.0757195i
$143$	0.976834	+	0.355538i	0.0816870	+	0.0297316i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−16.4402	−	28.4752i	−1.36528	−	2.36474i
$146$	−2.66772	−	15.1294i	−0.220782	−	1.25212i
$147$	−4.20961	−	3.53228i	−0.347203	−	0.291338i
$148$	1.29813	−	1.08926i	0.106706	−	0.0895369i
$149$	2.08899	−	11.8473i	0.171137	−	0.970566i	−0.771372	−	0.636385i	$-0.780429\pi$
$149$	2.08899	−	11.8473i	0.171137	−	0.970566i	0.942509	−	0.334181i	$-0.108460\pi$
$150$	−9.44356	+	3.43718i	−0.771064	+	0.280644i
$151$	0.0591253			0.00481155			0.00240578	−	0.999997i	$-0.499234\pi$
$151$	0.0591253			0.00481155			0.00240578	+	0.999997i	$0.499234\pi$
$152$	1.52094	+	4.08494i	0.123365	+	0.331332i
$153$	−5.53209			−0.447243
$154$	2.44444	−	0.889704i	0.196979	−	0.0716944i
$155$	−1.62449	+	9.21291i	−0.130482	+	0.739999i
$156$	0.375515	−	0.315094i	0.0300652	−	0.0252277i
$157$	9.92649	+	8.32931i	0.792220	+	0.664752i	0.946294	−	0.323308i	$-0.104795\pi$
$157$	9.92649	+	8.32931i	0.792220	+	0.664752i	−0.154074	+	0.988059i	$0.549239\pi$
$158$	−0.809278	−	4.58964i	−0.0643827	−	0.365132i
$159$	−4.44356	−	7.69648i	−0.352397	−	0.610370i
$160$	1.93969	−	3.35965i	0.153346	−	0.265603i
$161$	10.3093	+	3.75227i	0.812485	+	0.295720i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	−7.53596	+	13.0527i	−0.590262	+	1.02236i	0.403935	+	0.914788i	$0.367642\pi$
$163$	−7.53596	+	13.0527i	−0.590262	+	1.02236i	−0.994197	+	0.107576i	$0.965691\pi$
$164$	−0.798133	−	1.38241i	−0.0623237	−	0.107948i
$165$	1.42855	+	8.10170i	0.111212	+	0.630716i
$166$	9.56077	+	8.02244i	0.742060	+	0.622662i
$167$	−1.48680	+	1.24757i	−0.115052	+	0.0965399i	−0.698499	−	0.715612i	$-0.746148\pi$
$167$	−1.48680	+	1.24757i	−0.115052	+	0.0965399i	0.583447	+	0.812151i	$0.301704\pi$
$168$	0.213011	−	1.20805i	0.0164342	−	0.0932027i
$169$	11.9902	−	4.36408i	0.922323	−	0.335698i
$170$	21.4611			1.64599
$171$	−3.75877	+	2.20718i	−0.287440	+	0.168787i
$172$	−6.63816			−0.506155
$173$	−15.1027	+	5.49692i	−1.14823	+	0.417923i	−0.844881	−	0.534955i	$-0.820329\pi$
$173$	−15.1027	+	5.49692i	−1.14823	+	0.417923i	−0.303354	+	0.952878i	$0.598106\pi$
$174$	−1.47178	+	8.34689i	−0.111575	+	0.632776i
$175$	9.44356	−	7.92409i	0.713866	−	0.599005i
$176$	−1.62449	−	1.36310i	−0.122450	−	0.102748i
$177$	−1.98293	−	11.2457i	−0.149046	−	0.845281i
$178$	−4.22803	−	7.32316i	−0.316904	−	0.548894i
$179$	−7.38713	+	12.7949i	−0.552140	+	0.956334i	0.445980	+	0.895043i	$0.352855\pi$
$179$	−7.38713	+	12.7949i	−0.552140	+	0.956334i	−0.998120	+	0.0612912i	$0.980478\pi$
$180$	3.64543	+	1.32683i	0.271714	+	0.0988959i
$181$	17.1275	+	6.23389i	1.27308	+	0.463362i	0.888136	−	0.459580i	$-0.152000\pi$
$181$	17.1275	+	6.23389i	1.27308	+	0.463362i	0.384939	+	0.922942i	$0.374222\pi$
$182$	−0.300660	+	0.520758i	−0.0222864	+	0.0386011i
$183$	−0.0209445	−	0.0362770i	−0.00154826	−	0.00268167i
$184$	−1.55303	−	8.80769i	−0.114491	−	0.649312i
$185$	−5.03596	−	4.22567i	−0.370251	−	0.310678i
$186$	1.84730	−	1.55007i	0.135450	−	0.113656i
$187$	2.03714	−	11.5532i	0.148971	−	0.844854i
$188$	−2.03936	+	0.742267i	−0.148736	+	0.0541354i
$189$	1.22668			0.0892280
$190$	14.5817	−	8.56250i	1.05787	−	0.621189i
$191$	1.29086			0.0934033			0.0467017	−	0.998909i	$-0.485129\pi$
$191$	1.29086			0.0934033			0.0467017	+	0.998909i	$0.485129\pi$
$192$	−0.939693	+	0.342020i	−0.0678165	+	0.0246832i
$193$	−1.58378	+	8.98205i	−0.114003	+	0.646542i	0.873236	+	0.487297i	$0.162017\pi$
$193$	−1.58378	+	8.98205i	−0.114003	+	0.646542i	−0.987239	+	0.159245i	$0.949094\pi$
$194$	−11.0137	+	9.24157i	−0.790735	+	0.663506i
$195$	−1.45677	−	1.22237i	−0.104321	−	0.0875359i
$196$	−0.954241	−	5.41177i	−0.0681600	−	0.386555i
$197$	−9.31180	−	16.1285i	−0.663439	−	1.14911i	−0.979706	−	0.200439i	$-0.935763\pi$
$197$	−9.31180	−	16.1285i	−0.663439	−	1.14911i	0.316268	−	0.948670i	$-0.397570\pi$
$198$	1.06031	−	1.83651i	0.0753528	−	0.130515i
$199$	−7.92262	−	2.88360i	−0.561620	−	0.204413i	0.0455821	−	0.998961i	$-0.485486\pi$
$199$	−7.92262	−	2.88360i	−0.561620	−	0.204413i	−0.607202	+	0.794548i	$0.707708\pi$
$200$	−9.44356	−	3.43718i	−0.667761	−	0.243045i
$201$	−2.23783	+	3.87603i	−0.157844	+	0.273394i
$202$	−2.84730	−	4.93166i	−0.200335	−	0.346991i
$203$	−1.80541	−	10.2390i	−0.126715	−	0.718635i
$204$	−4.23783	−	3.55596i	−0.296707	−	0.248967i
$205$	−4.74376	+	3.98048i	−0.331318	+	0.278009i
$206$	−0.0543776	+	0.308391i	−0.00378867	+	0.0214866i
$207$	8.40420	−	3.05888i	0.584132	−	0.212607i
$208$	0.490200			0.0339892
$209$	−3.22534	−	8.66258i	−0.223101	−	0.599203i
$210$	−4.75877			−0.328386
$211$	1.37939	−	0.502055i	0.0949608	−	0.0345629i	−0.294103	−	0.955774i	$-0.595021\pi$
$211$	1.37939	−	0.502055i	0.0949608	−	0.0345629i	0.389064	+	0.921211i	$0.372799\pi$
$212$	1.54323	−	8.75211i	0.105990	−	0.601097i
$213$	2.02094	−	1.69577i	0.138473	−	0.116193i
$214$	−12.8910	−	10.8168i	−0.881210	−	0.739423i
$215$	4.47178	+	25.3607i	0.304973	+	1.72959i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−1.47906	+	2.56180i	−0.100405	+	0.173906i
$218$	9.78359	+	3.56093i	0.662628	+	0.241177i
$219$	14.4363	+	5.25438i	0.975514	+	0.355058i
$220$	−4.11334	+	7.12452i	−0.277321	+	0.480335i
$221$	1.35591	+	2.34851i	0.0912087	+	0.157978i
$222$	0.294263	+	1.66885i	0.0197496	+	0.112006i
$223$	20.1229	+	16.8851i	1.34753	+	1.13071i	0.979622	+	0.200848i	$0.0643697\pi$
$223$	20.1229	+	16.8851i	1.34753	+	1.13071i	0.367906	+	0.929863i	$0.380075\pi$
$224$	0.939693	−	0.788496i	0.0627859	−	0.0526836i
$225$	1.74510	−	9.89695i	0.116340	−	0.659797i
$226$	16.3341	−	5.94512i	1.08653	−	0.395464i
$227$	18.3678			1.21912			0.609558	−	0.792742i	$-0.291347\pi$
$227$	18.3678			1.21912			0.609558	+	0.792742i	$0.291347\pi$
$228$	−4.29813	−	0.725293i	−0.284651	−	0.0480337i
$229$	3.87164			0.255845			0.127923	−	0.991784i	$-0.459169\pi$
$229$	3.87164			0.255845			0.127923	+	0.991784i	$0.459169\pi$
$230$	−32.6031	+	11.8666i	−2.14979	+	0.782458i
$231$	−0.451714	+	2.56180i	−0.0297206	+	0.168554i
$232$	−6.49273	+	5.44804i	−0.426268	+	0.357682i
$233$	12.5988	+	10.5716i	0.825374	+	0.692571i	0.954224	−	0.299093i	$-0.0966840\pi$
$233$	12.5988	+	10.5716i	0.825374	+	0.692571i	−0.128850	+	0.991664i	$0.541128\pi$
$234$	0.0851223	+	0.482753i	0.00556462	+	0.0315585i
$235$	4.20961	+	7.29125i	0.274605	+	0.475629i
$236$	5.70961	−	9.88933i	0.371664	−	0.643741i
$237$	4.37939	+	1.59397i	0.284472	+	0.103539i
$238$	6.37686	+	2.32099i	0.413350	+	0.150447i
$239$	−1.65270	+	2.86257i	−0.106905	+	0.185164i	−0.914515	−	0.404553i	$-0.867427\pi$
$239$	−1.65270	+	2.86257i	−0.106905	+	0.185164i	0.807610	+	0.589717i	$0.200761\pi$
$240$	1.93969	+	3.35965i	0.125207	+	0.216864i
$241$	0.523633	+	2.96967i	0.0337302	+	0.191293i	0.997017	−	0.0771806i	$-0.0245918\pi$
$241$	0.523633	+	2.96967i	0.0337302	+	0.191293i	−0.963287	+	0.268474i	$0.913481\pi$
$242$	−4.98158	−	4.18004i	−0.320228	−	0.268703i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	0.00727396	−	0.0412527i	0.000465668	−	0.00264093i
$245$	−20.0326	+	7.29125i	−1.27983	+	0.465821i
$246$	1.59627			0.101774
$247$	1.85828	+	1.05471i	0.118239	+	0.0671099i
$248$	2.41147			0.153129
$249$	−11.7280	+	4.26865i	−0.743233	+	0.270515i
$250$	−3.40167	+	19.2919i	−0.215141	+	1.22012i
$251$	−2.70780	+	2.27211i	−0.170915	+	0.143414i	−0.724233	−	0.689556i	$-0.757806\pi$
$251$	−2.70780	+	2.27211i	−0.170915	+	0.143414i	0.553318	+	0.832970i	$0.313361\pi$
$252$	0.939693	+	0.788496i	0.0591951	+	0.0496706i
$253$	3.29339	+	18.6777i	0.207053	+	1.17426i
$254$	0.815207	+	1.41198i	0.0511507	+	0.0885956i
$255$	−10.7306	+	18.5859i	−0.671973	+	1.16389i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	4.41875	+	1.60829i	0.275634	+	0.100323i	0.476139	−	0.879370i	$-0.342036\pi$
$257$	4.41875	+	1.60829i	0.275634	+	0.100323i	−0.200505	+	0.979693i	$0.564258\pi$
$258$	3.31908	−	5.74881i	0.206637	−	0.357905i
$259$	−1.03936	−	1.80023i	−0.0645829	−	0.111861i
$260$	−0.330222	−	1.87278i	−0.0204795	−	0.116145i
$261$	−6.49273	−	5.44804i	−0.401890	−	0.337225i
$262$	4.56805	−	3.83305i	0.282215	−	0.236806i
$263$	3.65745	−	20.7424i	0.225528	−	1.27903i	−0.636145	−	0.771570i	$-0.719472\pi$
$263$	3.65745	−	20.7424i	0.225528	−	1.27903i	0.861673	−	0.507464i	$-0.169417\pi$
$264$	1.99273	−	0.725293i	0.122644	−	0.0446387i
$265$	−34.4766			−2.11788
$266$	5.25877	−	0.967233i	0.322436	−	0.0593049i
$267$	8.45605			0.517502
$268$	−4.20574	+	1.53076i	−0.256906	+	0.0935062i
$269$	1.75015	−	9.92561i	0.106709	−	0.605175i	−0.883815	−	0.467836i	$-0.845034\pi$
$269$	1.75015	−	9.92561i	0.106709	−	0.605175i	0.990524	−	0.137339i	$-0.0438550\pi$
$270$	−2.97178	+	2.49362i	−0.180857	+	0.151757i
$271$	−7.47952	−	6.27606i	−0.454349	−	0.381244i	0.386698	−	0.922206i	$-0.373616\pi$
$271$	−7.47952	−	6.27606i	−0.454349	−	0.381244i	−0.841047	+	0.540963i	$0.818060\pi$
$272$	−0.960637	−	5.44804i	−0.0582472	−	0.330336i
$273$	−0.300660	−	0.520758i	−0.0181967	−	0.0315177i
$274$	0.00980018	−	0.0169744i	0.000592051	−	0.00102546i
$275$	20.0262	+	7.28893i	1.20762	+	0.439539i
$276$	8.40420	+	3.05888i	0.505873	+	0.184123i
$277$	−8.42855	+	14.5987i	−0.506422	+	0.877149i	0.493550	+	0.869717i	$0.335699\pi$
$277$	−8.42855	+	14.5987i	−0.506422	+	0.877149i	−0.999972	+	0.00743188i	$0.997634\pi$
$278$	−2.24763	−	3.89300i	−0.134804	−	0.233487i
$279$	0.418748	+	2.37484i	0.0250698	+	0.142178i
$280$	−3.64543	−	3.05888i	−0.217856	−	0.182803i
$281$	−8.98158	+	7.53644i	−0.535796	+	0.449586i	−0.870097	−	0.492880i	$-0.835944\pi$
$281$	−8.98158	+	7.53644i	−0.535796	+	0.449586i	0.334301	+	0.942466i	$0.391500\pi$
$282$	0.376859	−	2.13727i	0.0224416	−	0.127273i
$283$	20.2456	−	7.36878i	1.20347	−	0.438029i	0.339039	−	0.940772i	$-0.389898\pi$
$283$	20.2456	−	7.36878i	1.20347	−	0.438029i	0.864435	+	0.502744i	$0.167676\pi$
$284$	2.63816			0.156546
$285$	0.124485	+	16.9094i	0.00737386	+	1.00163i
$286$	−1.03952			−0.0614684
$287$	−1.84002	+	0.669713i	−0.108613	+	0.0395319i
$288$	0.173648	−	0.984808i	0.0102323	−	0.0580304i
$289$	10.4213	−	8.74449i	0.613016	−	0.514382i
$290$	25.1878	+	21.1351i	1.47908	+	1.24109i
$291$	−2.49660	−	14.1589i	−0.146353	−	0.830010i
$292$	7.68139	+	13.3046i	0.449519	+	0.778590i
$293$	5.56031	−	9.63073i	0.324837	−	0.562634i	−0.656643	−	0.754202i	$-0.728024\pi$
$293$	5.56031	−	9.63073i	0.324837	−	0.562634i	0.981479	+	0.191568i	$0.0613573\pi$
$294$	5.16385	+	1.87949i	0.301162	+	0.109614i
$295$	−41.6279	−	15.1513i	−2.42367	−	0.882145i
$296$	−0.847296	+	1.46756i	−0.0492481	+	0.0853002i
$297$	1.06031	+	1.83651i	0.0615253	+	0.106565i
$298$	2.08899	+	11.8473i	0.121012	+	0.686294i
$299$	−3.35844	−	2.81807i	−0.194224	−	0.162973i
$300$	7.69846	−	6.45978i	0.444471	−	0.372955i
$301$	−1.41400	+	8.01919i	−0.0815016	+	0.462219i
$302$	−0.0555596	+	0.0202221i	−0.00319710	+	0.00116365i
$303$	5.69459			0.327146
$304$	−2.82635	−	3.31839i	−0.162102	−	0.190323i
$305$	−0.162504			−0.00930494
$306$	5.19846	−	1.89209i	0.297176	−	0.108163i
$307$	4.34817	−	24.6597i	0.248163	−	1.40740i	−0.564866	−	0.825182i	$-0.691072\pi$
$307$	4.34817	−	24.6597i	0.248163	−	1.40740i	0.813030	−	0.582222i	$-0.197817\pi$
$308$	−1.99273	+	1.67210i	−0.113546	+	0.0952765i
$309$	−0.239885	−	0.201288i	−0.0136466	−	0.0114509i
$310$	−1.62449	−	9.21291i	−0.0922646	−	0.523258i
$311$	−0.0282185	−	0.0488759i	−0.00160012	−	0.00277150i	0.865224	−	0.501385i	$-0.167176\pi$
$311$	−0.0282185	−	0.0488759i	−0.00160012	−	0.00277150i	−0.866824	+	0.498614i	$0.833843\pi$
$312$	−0.245100	+	0.424525i	−0.0138760	+	0.0240340i
$313$	−12.9338	−	4.70750i	−0.731059	−	0.266084i	−0.0504462	−	0.998727i	$-0.516064\pi$
$313$	−12.9338	−	4.70750i	−0.731059	−	0.266084i	−0.680613	+	0.732643i	$0.738287\pi$
$314$	−12.1766	−	4.43193i	−0.687168	−	0.250109i
$315$	2.37939	−	4.12122i	0.134063	−	0.232204i
$316$	2.33022	+	4.03606i	0.131085	+	0.227046i
$317$	1.89347	+	10.7384i	0.106348	+	0.603128i	0.990673	+	0.136257i	$0.0435074\pi$
$317$	1.89347	+	10.7384i	0.106348	+	0.603128i	−0.884326	+	0.466870i	$0.845381\pi$
$318$	6.80793	+	5.71253i	0.381770	+	0.320343i
$319$	13.7686	−	11.5532i	0.770892	−	0.646855i
$320$	−0.673648	+	3.82045i	−0.0376581	+	0.213570i
$321$	15.8131	−	5.75552i	0.882604	−	0.321242i
$322$	−10.9709			−0.611385
$323$	8.08037	−	22.7197i	0.449604	−	1.26416i
$324$	1.00000			0.0555556
$325$	−4.62923	+	1.68490i	−0.256784	+	0.0934616i
$326$	2.61721	−	14.8429i	0.144954	−	0.822075i
$327$	−7.97565	+	6.69237i	−0.441055	+	0.370089i
$328$	1.22281	+	1.02606i	0.0675185	+	0.0566547i
$329$	0.462286	+	2.62175i	0.0254867	+	0.144542i
$330$	−4.11334	−	7.12452i	−0.226432	−	0.392192i
$331$	−4.29561	+	7.44021i	−0.236108	+	0.408951i	−0.959594	−	0.281388i	$-0.909205\pi$
$331$	−4.29561	+	7.44021i	−0.236108	+	0.408951i	0.723486	+	0.690339i	$0.242539\pi$
$332$	−11.7280	−	4.26865i	−0.643659	−	0.234273i
$333$	−1.59240	−	0.579585i	−0.0872628	−	0.0317611i
$334$	0.970437	−	1.68085i	0.0531000	−	0.0919718i
$335$	8.68139	+	15.0366i	0.474315	+	0.821538i
$336$	0.213011	+	1.20805i	0.0116207	+	0.0659043i
$337$	−1.76991	−	1.48513i	−0.0964134	−	0.0809005i	0.593307	−	0.804976i	$-0.297822\pi$
$337$	−1.76991	−	1.48513i	−0.0964134	−	0.0809005i	−0.689720	+	0.724076i	$0.742267\pi$
$338$	−9.77450	+	8.20178i	−0.531663	+	0.446118i
$339$	−3.01842	+	17.1183i	−0.163938	+	0.929738i
$340$	−20.1668	+	7.34013i	−1.09370	+	0.398074i
$341$	−5.11381			−0.276928
$342$	2.77719	−	3.35965i	0.150173	−	0.181669i
$343$	−15.3277			−0.827618
$344$	6.23783	−	2.27038i	0.336321	−	0.122411i
$345$	6.02481	−	34.1684i	0.324365	−	1.83957i
$346$	12.3118	−	10.3308i	0.661887	−	0.555389i
$347$	−2.51707	−	2.11208i	−0.135124	−	0.113382i	0.572721	−	0.819750i	$-0.305888\pi$
$347$	−2.51707	−	2.11208i	−0.135124	−	0.113382i	−0.707845	+	0.706368i	$0.750332\pi$
$348$	−1.47178	−	8.34689i	−0.0788958	−	0.447440i
$349$	−14.6741	−	25.4163i	−0.785487	−	1.36050i	−0.928707	−	0.370813i	$-0.879079\pi$
$349$	−14.6741	−	25.4163i	−0.785487	−	1.36050i	0.143220	−	0.989691i	$-0.454254\pi$
$350$	−6.16385	+	10.6761i	−0.329472	+	0.570661i
$351$	−0.460637	−	0.167658i	−0.0245870	−	0.00894893i
$352$	1.99273	+	0.725293i	0.106213	+	0.0386582i
$353$	3.86959	−	6.70232i	0.205957	−	0.356728i	−0.744480	−	0.667645i	$-0.767303\pi$
$353$	3.86959	−	6.70232i	0.205957	−	0.356728i	0.950437	+	0.310916i	$0.100636\pi$
$354$	5.70961	+	9.88933i	0.303462	+	0.525612i
$355$	−1.77719	−	10.0789i	−0.0943234	−	0.534935i
$356$	6.47771	+	5.43545i	0.343318	+	0.288078i
$357$	−5.19846	+	4.36203i	−0.275132	+	0.230863i
$358$	2.56552	−	14.5498i	0.135592	−	0.768981i
$359$	−2.69459	+	0.980752i	−0.142215	+	0.0517621i	−0.412147	−	0.911117i	$-0.635221\pi$
$359$	−2.69459	+	0.980752i	−0.142215	+	0.0517621i	0.269932	+	0.962879i	$0.412999\pi$
$360$	−3.87939			−0.204462
$361$	−3.57444	−	18.6607i	−0.188129	−	0.982144i
$362$	−18.2267			−0.957973
$363$	6.11081	−	2.22415i	0.320735	−	0.116738i
$364$	0.104418	−	0.592184i	0.00547299	−	0.0310389i
$365$	45.6548	−	38.3089i	2.38968	−	2.00518i
$366$	0.0320889	+	0.0269258i	0.00167731	+	0.00140743i
$367$	−3.98798	−	22.6169i	−0.208171	−	1.18060i	−0.892372	−	0.451301i	$-0.850960\pi$
$367$	−3.98798	−	22.6169i	−0.208171	−	1.18060i	0.684201	−	0.729294i	$-0.260151\pi$
$368$	4.47178	+	7.74535i	0.233108	+	0.403754i
$369$	−0.798133	+	1.38241i	−0.0415492	+	0.0719653i
$370$	6.17752	+	2.24843i	0.321154	+	0.116890i
$371$	−10.2442	−	3.72859i	−0.531854	−	0.193579i
$372$	−1.20574	+	2.08840i	−0.0625146	+	0.108278i
$373$	11.5954	+	20.0838i	0.600387	+	1.03990i	0.992762	+	0.120095i	$0.0383199\pi$
$373$	11.5954	+	20.0838i	0.600387	+	1.03990i	−0.392376	+	0.919805i	$0.628347\pi$
$374$	2.03714	+	11.5532i	0.105338	+	0.597402i
$375$	−15.0064	−	12.5919i	−0.774927	−	0.650241i
$376$	1.66250	−	1.39501i	0.0857371	−	0.0719420i
$377$	−0.721467	+	4.09164i	−0.0371574	+	0.210730i
$378$	−1.15270	+	0.419550i	−0.0592887	+	0.0215793i
$379$	−33.5185			−1.72173			−0.860864	−	0.508835i	$-0.830076\pi$
$379$	−33.5185			−1.72173			−0.860864	+	0.508835i	$0.830076\pi$
$380$	−10.7738	+	13.0334i	−0.552684	+	0.668597i
$381$	−1.63041			−0.0835287
$382$	−1.21301	+	0.441500i	−0.0620630	+	0.0225891i
$383$	1.16860	−	6.62744i	0.0597125	−	0.338646i	−0.940286	−	0.340385i	$-0.889442\pi$
$383$	1.16860	−	6.62744i	0.0597125	−	0.338646i	0.999998	+	0.00173918i	$0.000553599\pi$
$384$	0.766044	−	0.642788i	0.0390920	−	0.0328021i
$385$	7.73055	+	6.48670i	0.393985	+	0.330593i
$386$	−1.58378	−	8.98205i	−0.0806122	−	0.457174i
$387$	3.31908	+	5.74881i	0.168718	+	0.292229i
$388$	7.18866	−	12.4511i	0.364949	−	0.632110i
$389$	17.8751	+	6.50601i	0.906304	+	0.329868i	0.752776	−	0.658277i	$-0.228714\pi$
$389$	17.8751	+	6.50601i	0.906304	+	0.329868i	0.153528	+	0.988144i	$0.450937\pi$
$390$	1.78699	+	0.650411i	0.0904877	+	0.0329348i
$391$	−24.7383	+	42.8480i	−1.25107	+	2.16692i
$392$	2.74763	+	4.75903i	0.138776	+	0.240367i
$393$	1.03549	+	5.87257i	0.0522337	+	0.296232i
$394$	14.2665	+	11.9710i	0.718736	+	0.603091i
$395$	13.8498	−	11.6214i	0.696860	−	0.584735i
$396$	−0.368241	+	2.08840i	−0.0185048	+	0.104946i
$397$	25.2913	−	9.20529i	1.26934	−	0.462000i	0.382444	−	0.923979i	$-0.375082\pi$
$397$	25.2913	−	9.20529i	1.26934	−	0.462000i	0.886891	+	0.461978i	$0.152860\pi$
$398$	8.43107			0.422612
$399$	−1.79174	+	5.03785i	−0.0896990	+	0.252208i
$400$	10.0496			0.502481
$401$	5.35756	−	1.94999i	0.267544	−	0.0973780i	−0.204765	−	0.978811i	$-0.565643\pi$
$401$	5.35756	−	1.94999i	0.267544	−	0.0973780i	0.472309	+	0.881433i	$0.343421\pi$
$402$	0.777189	−	4.40766i	0.0387627	−	0.219834i
$403$	0.905544	−	0.759842i	0.0451084	−	0.0378504i
$404$	4.36231	+	3.66041i	0.217033	+	0.182112i
$405$	−0.673648	−	3.82045i	−0.0334738	−	0.189840i
$406$	5.19846	+	9.00400i	0.257995	+	0.446861i
$407$	1.79679	−	3.11213i	0.0890635	−	0.154263i
$408$	5.19846	+	1.89209i	0.257362	+	0.0936722i
$409$	0.758770	+	0.276170i	0.0375188	+	0.0136557i	0.360711	−	0.932677i	$-0.382534\pi$
$409$	0.758770	+	0.276170i	0.0375188	+	0.0136557i	−0.323193	+	0.946333i	$0.604756\pi$
$410$	3.09627	−	5.36289i	0.152914	−	0.264854i
$411$	0.00980018	+	0.0169744i	0.000483407	+	0.000837286i
$412$	−0.0543776	−	0.308391i	−0.00267899	−	0.0151933i
$413$	−10.7306	−	9.00400i	−0.528016	−	0.443058i
$414$	−6.85117	+	5.74881i	−0.336716	+	0.282539i
$415$	−8.40760	+	47.6819i	−0.412713	+	2.34061i
$416$	−0.460637	+	0.167658i	−0.0225846	+	0.00822012i
$417$	4.49525			0.220133
$418$	5.99360	+	7.03703i	0.293157	+	0.344193i
$419$	−19.1215			−0.934149			−0.467074	−	0.884218i	$-0.654692\pi$
$419$	−19.1215			−0.934149			−0.467074	+	0.884218i	$0.654692\pi$
$420$	4.47178	−	1.62760i	0.218201	−	0.0794185i
$421$	−4.86618	+	27.5975i	−0.237163	+	1.34502i	0.600847	+	0.799364i	$0.294830\pi$
$421$	−4.86618	+	27.5975i	−0.237163	+	1.34502i	−0.838010	+	0.545655i	$0.816281\pi$
$422$	−1.12449	+	0.943555i	−0.0547391	+	0.0459315i
$423$	1.66250	+	1.39501i	0.0808337	+	0.0678275i
$424$	1.54323	+	8.75211i	0.0749460	+	0.425040i
$425$	27.7977	+	48.1471i	1.34839	+	2.33548i
$426$	−1.31908	+	2.28471i	−0.0639095	+	0.110695i
$427$	−0.0482857	−	0.0175745i	−0.00233671	−	0.000850492i
$428$	15.8131	+	5.75552i	0.764357	+	0.278203i
$429$	0.519762	−	0.900255i	0.0250944	−	0.0434647i
$430$	−12.8760	−	22.3019i	−0.620935	−	1.07549i
$431$	−1.56923	−	8.89955i	−0.0755872	−	0.428676i	−0.998994	−	0.0448525i	$-0.985718\pi$
$431$	−1.56923	−	8.89955i	−0.0755872	−	0.428676i	0.923406	−	0.383824i	$-0.125393\pi$
$432$	0.766044	+	0.642788i	0.0368563	+	0.0309261i
$433$	1.12061	−	0.940307i	0.0538533	−	0.0451883i	−0.615464	−	0.788165i	$-0.711031\pi$
$433$	1.12061	−	0.940307i	0.0538533	−	0.0451883i	0.669317	+	0.742977i	$0.266587\pi$
$434$	0.513671	−	2.91317i	0.0246570	−	0.139837i
$435$	−30.8974	+	11.2457i	−1.48142	+	0.539192i
$436$	−10.4115			−0.498619
$437$	0.286989	+	38.9830i	0.0137285	+	1.86481i
$438$	−15.3628			−0.734062
$439$	5.08987	−	1.85256i	0.242926	−	0.0884179i	−0.217688	−	0.976018i	$-0.569851\pi$
$439$	5.08987	−	1.85256i	0.242926	−	0.0884179i	0.460614	+	0.887601i	$0.347629\pi$
$440$	1.42855	−	8.10170i	0.0681034	−	0.386233i
$441$	−4.20961	+	3.53228i	−0.200457	+	0.168204i
$442$	−2.07738	−	1.74313i	−0.0988110	−	0.0829122i
$443$	−4.94310	−	28.0337i	−0.234854	−	1.33192i	−0.842922	−	0.538036i	$-0.819166\pi$
$443$	−4.94310	−	28.0337i	−0.234854	−	1.33192i	0.608068	−	0.793885i	$-0.291945\pi$
$444$	−0.847296	−	1.46756i	−0.0402109	−	0.0696473i
$445$	16.4021	−	28.4093i	0.777536	−	1.34673i
$446$	−24.6844	−	8.98438i	−1.16884	−	0.425423i
$447$	−11.3045	−	4.11451i	−0.534686	−	0.194610i
$448$	−0.613341	+	1.06234i	−0.0289776	+	0.0501907i
$449$	11.3824	+	19.7149i	0.537168	+	0.930402i	0.999055	+	0.0434631i	$0.0138391\pi$
$449$	11.3824	+	19.7149i	0.537168	+	0.930402i	−0.461887	+	0.886939i	$0.652828\pi$
$450$	1.74510	+	9.89695i	0.0822648	+	0.466547i
$451$	−2.59311	−	2.17588i	−0.122105	−	0.102458i
$452$	−13.3157	+	11.1732i	−0.626317	+	0.525542i
$453$	0.0102670	−	0.0582271i	0.000482386	−	0.00273575i
$454$	−17.2601	+	6.28217i	−0.810057	+	0.294837i
$455$	−2.33275			−0.109361
$456$	4.28699	−	0.788496i	0.200757	−	0.0369247i
$457$	−1.13011			−0.0528643			−0.0264322	−	0.999651i	$-0.508415\pi$
$457$	−1.13011			−0.0528643			−0.0264322	+	0.999651i	$0.508415\pi$
$458$	−3.63816	+	1.32418i	−0.170000	+	0.0618749i
$459$	−0.960637	+	5.44804i	−0.0448387	+	0.254293i
$460$	26.5783	−	22.3019i	1.23922	−	1.03983i
$461$	−9.94562	−	8.34537i	−0.463214	−	0.388683i	0.381098	−	0.924535i	$-0.375546\pi$
$461$	−9.94562	−	8.34537i	−0.463214	−	0.388683i	−0.844312	+	0.535852i	$0.819990\pi$
$462$	−0.451714	−	2.56180i	−0.0210157	−	0.119186i
$463$	15.3123	+	26.5216i	0.711622	+	1.23256i	0.964248	+	0.265001i	$0.0853722\pi$
$463$	15.3123	+	26.5216i	0.711622	+	1.23256i	−0.252627	+	0.967564i	$0.581294\pi$
$464$	4.23783	−	7.34013i	0.196736	−	0.340757i
$465$	8.79086	+	3.19961i	0.407666	+	0.148378i
$466$	−15.4547	−	5.62505i	−0.715925	−	0.260576i
$467$	−5.52869	+	9.57596i	−0.255837	+	0.443123i	−0.965123	−	0.261799i	$-0.915684\pi$
$467$	−5.52869	+	9.57596i	−0.255837	+	0.443123i	0.709285	+	0.704921i	$0.249018\pi$
$468$	−0.245100	−	0.424525i	−0.0113297	−	0.0196237i
$469$	0.953363	+	5.40679i	0.0440222	+	0.249662i
$470$	−6.44949	−	5.41177i	−0.297493	−	0.249626i
$471$	9.92649	−	8.32931i	0.457388	−	0.383794i
$472$	−1.98293	+	11.2457i	−0.0912716	+	0.517627i
$473$	−13.2280	+	4.81461i	−0.608225	+	0.221376i
$474$	−4.66044			−0.214061
$475$	38.0967	+	21.6228i	1.74800	+	0.992122i
$476$	−6.78611			−0.311041
$477$	−8.35117	+	3.03958i	−0.382374	+	0.139173i
$478$	0.573978	−	3.25519i	0.0262531	−	0.148889i
$479$	−13.5116	+	11.3376i	−0.617361	+	0.518028i	−0.896973	−	0.442086i	$-0.854239\pi$
$479$	−13.5116	+	11.3376i	−0.617361	+	0.518028i	0.279612	+	0.960113i	$0.409794\pi$
$480$	−2.97178	−	2.49362i	−0.135643	−	0.113818i
$481$	0.144248	+	0.818069i	0.00657713	+	0.0373007i
$482$	−1.50774	−	2.61148i	−0.0686757	−	0.118950i
$483$	5.48545	−	9.50108i	0.249597	−	0.432314i
$484$	6.11081	+	2.22415i	0.277764	+	0.101098i
$485$	−52.4115	−	19.0762i	−2.37989	−	0.866207i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	7.64677	+	13.2446i	0.346508	+	0.600170i	0.985627	−	0.168938i	$-0.0540339\pi$
$487$	7.64677	+	13.2446i	0.346508	+	0.600170i	−0.639118	+	0.769109i	$0.720701\pi$
$488$	0.00727396	+	0.0412527i	0.000329277	+	0.00186742i
$489$	11.5458	+	9.68804i	0.522117	+	0.438108i
$490$	16.3307	−	13.7031i	0.737745	−	0.619042i
$491$	−0.308811	+	1.75135i	−0.0139364	+	0.0790375i	−0.990983	−	0.133990i	$-0.957221\pi$
$491$	−0.308811	+	1.75135i	−0.0139364	+	0.0790375i	0.977046	+	0.213027i	$0.0683322\pi$
$492$	−1.50000	+	0.545955i	−0.0676252	+	0.0246136i
$493$	46.8881			2.11173
$494$	−2.10694	−	0.355538i	−0.0947959	−	0.0159964i
$495$	8.22668			0.369762
$496$	−2.26604	+	0.824773i	−0.101748	+	0.0370334i
$497$	0.561956	−	3.18701i	0.0252072	−	0.142957i
$498$	9.56077	−	8.02244i	0.428429	−	0.359494i
$499$	−0.0825961	−	0.0693063i	−0.00369751	−	0.00310258i	0.640937	−	0.767594i	$-0.278546\pi$
$499$	−0.0825961	−	0.0693063i	−0.00369751	−	0.00310258i	−0.644634	+	0.764491i	$0.722990\pi$
$500$	−3.40167	−	19.2919i	−0.152127	−	0.862758i
$501$	0.970437	+	1.68085i	0.0433559	+	0.0750947i
$502$	1.76739	−	3.06121i	0.0788824	−	0.136628i
$503$	22.2615	+	8.10251i	0.992589	+	0.361273i	0.786722	−	0.617307i	$-0.211776\pi$
$503$	22.2615	+	8.10251i	0.992589	+	0.361273i	0.205867	+	0.978580i	$0.433999\pi$
$504$	−1.15270	−	0.419550i	−0.0513455	−	0.0186882i
$505$	11.0458	−	19.1318i	0.491530	−	0.851355i
$506$	−9.48293	−	16.4249i	−0.421567	−	0.730176i
$507$	−2.21570	−	12.5659i	−0.0984027	−	0.558069i
$508$	−1.24897	−	1.04801i	−0.0554141	−	0.0464979i
$509$	−2.73783	+	2.29731i	−0.121352	+	0.101826i	−0.701444	−	0.712724i	$-0.747461\pi$
$509$	−2.73783	+	2.29731i	−0.121352	+	0.101826i	0.580092	+	0.814551i	$0.303017\pi$
$510$	3.72668	−	21.1351i	0.165020	−	0.935876i
$511$	17.7087	−	6.44545i	0.783388	−	0.285130i
$512$	1.00000			0.0441942
$513$	1.52094	+	4.08494i	0.0671513	+	0.180354i
$514$	−4.70233			−0.207411
$515$	−1.14156	+	0.415494i	−0.0503031	+	0.0183088i
$516$	−1.15270	+	6.53731i	−0.0507449	+	0.287789i
$517$	−3.52553	+	2.95827i	−0.155053	+	0.130105i
$518$	1.59240	+	1.33618i	0.0699659	+	0.0587083i
$519$	2.79086	+	15.8278i	0.122505	+	0.694761i
$520$	0.950837	+	1.64690i	0.0416970	+	0.0722213i
$521$	−17.0608	+	29.5501i	−0.747446	+	1.29461i	0.201597	+	0.979469i	$0.435387\pi$
$521$	−17.0608	+	29.5501i	−0.747446	+	1.29461i	−0.949043	+	0.315146i	$0.897946\pi$
$522$	7.96451	+	2.89884i	0.348597	+	0.126879i
$523$	−16.0376	−	5.83721i	−0.701276	−	0.255243i	−0.0333202	−	0.999445i	$-0.510608\pi$
$523$	−16.0376	−	5.83721i	−0.701276	−	0.255243i	−0.667955	+	0.744201i	$0.732830\pi$
$524$	−2.98158	+	5.16425i	−0.130251	+	0.225601i
$525$	−6.16385	−	10.6761i	−0.269012	−	0.465943i
$526$	3.65745	+	20.7424i	0.159472	+	0.904413i
$527$	−10.2194	−	8.57510i	−0.445164	−	0.373537i
$528$	−1.62449	+	1.36310i	−0.0706966	+	0.0593215i
$529$	9.89574	−	56.1216i	0.430250	−	2.44007i
$530$	32.3974	−	11.7917i	1.40725	−	0.512198i
$531$	−11.4192			−0.495552
$532$	−4.61081	+	2.70751i	−0.199904	+	0.117385i
$533$	0.782490			0.0338934
$534$	−7.94609	+	2.89214i	−0.343861	+	0.125155i
$535$	11.3362	−	64.2905i	0.490105	−	2.77952i
$536$	3.42855	−	2.87689i	0.148091	−	0.124263i
$537$	11.3177	+	9.49671i	0.488396	+	0.409813i
$538$	1.75015	+	9.92561i	0.0754544	+	0.427923i
$539$	−5.82666	−	10.0921i	−0.250972	−	0.434696i
$540$	1.93969	−	3.35965i	0.0834711	−	0.144576i
$541$	−24.7841	−	9.02066i	−1.06555	−	0.387828i	−0.251039	−	0.967977i	$-0.580772\pi$
$541$	−24.7841	−	9.02066i	−1.06555	−	0.387828i	−0.814511	+	0.580149i	$0.802994\pi$
$542$	9.17499	+	3.33942i	0.394100	+	0.143441i
$543$	9.11334	−	15.7848i	0.391091	−	0.677389i
$544$	2.76604	+	4.79093i	0.118593	+	0.205409i
$545$	7.01367	+	39.7765i	0.300433	+	1.70384i
$546$	0.460637	+	0.386520i	0.0197135	+	0.0165415i
$547$	−26.7317	+	22.4306i	−1.14297	+	0.959063i	−0.999532	−	0.0305971i	$-0.990259\pi$
$547$	−26.7317	+	22.4306i	−1.14297	+	0.959063i	−0.143435	+	0.989660i	$0.545815\pi$
$548$	−0.00340357	+	0.0193026i	−0.000145393	+	0.000824566i
$549$	−0.0393628	+	0.0143269i	−0.00167997	+	0.000611457i
$550$	−21.3114			−0.908721
$551$	31.8580	−	18.7073i	1.35720	−	0.796957i
$552$	−8.94356			−0.380663
$553$	5.37211	−	1.95529i	0.228445	−	0.0831473i
$554$	2.92720	−	16.6010i	0.124365	−	0.705309i
$555$	−5.03596	+	4.22567i	−0.213765	+	0.179370i
$556$	3.44356	+	2.88949i	0.146040	+	0.122542i
$557$	−5.65957	−	32.0970i	−0.239804	−	1.35999i	−0.832258	−	0.554389i	$-0.812952\pi$
$557$	−5.65957	−	32.0970i	−0.239804	−	1.35999i	0.592454	−	0.805604i	$-0.298159\pi$
$558$	−1.20574	−	2.08840i	−0.0510429	−	0.0884089i
$559$	1.62701	−	2.81807i	0.0688152	−	0.119192i
$560$	4.47178	+	1.62760i	0.188967	+	0.0687785i
$561$	−11.0239	−	4.01239i	−0.465431	−	0.169403i
$562$	5.86231	−	10.1538i	0.247287	−	0.428313i
$563$	2.39780	+	4.15312i	0.101055	+	0.175033i	0.912120	−	0.409924i	$-0.134445\pi$
$563$	2.39780	+	4.15312i	0.101055	+	0.175033i	−0.811064	+	0.584957i	$0.801111\pi$
$564$	0.376859	+	2.13727i	0.0158686	+	0.0899955i
$565$	51.6566	+	43.3451i	2.17321	+	1.82354i
$566$	−16.5043	+	13.8488i	−0.693729	+	0.582108i
$567$	0.213011	−	1.20805i	0.00894562	−	0.0507331i
$568$	−2.47906	+	0.902302i	−0.104019	+	0.0378598i
$569$	−32.7006			−1.37088			−0.685440	−	0.728129i	$-0.740390\pi$
$569$	−32.7006			−1.37088			−0.685440	+	0.728129i	$0.740390\pi$
$570$	−5.90033	−	15.8471i	−0.247138	−	0.663760i
$571$	−10.9531			−0.458371			−0.229186	−	0.973383i	$-0.573606\pi$
$571$	−10.9531			−0.458371			−0.229186	+	0.973383i	$0.573606\pi$
$572$	0.976834	−	0.355538i	0.0408435	−	0.0148658i
$573$	0.224155	−	1.27125i	0.00936423	−	0.0531072i
$574$	1.50000	−	1.25865i	0.0626088	−	0.0525350i
$575$	−68.8517	−	57.7734i	−2.87131	−	2.40932i
$576$	0.173648	+	0.984808i	0.00723534	+	0.0410337i
$577$	9.15136	+	15.8506i	0.380976	+	0.659870i	0.991202	−	0.132357i	$-0.0422547\pi$
$577$	9.15136	+	15.8506i	0.380976	+	0.659870i	−0.610226	+	0.792227i	$0.708921\pi$
$578$	−6.80200	+	11.7814i	−0.282926	+	0.490042i
$579$	8.57057	+	3.11943i	0.356181	+	0.129639i
$580$	−30.8974	−	11.2457i	−1.28294	−	0.466954i
$581$	−7.65493	+	13.2587i	−0.317580	+	0.550064i
$582$	7.18866	+	12.4511i	0.297980	+	0.516116i
$583$	−3.27260	−	18.5599i	−0.135537	−	0.768671i
$584$	−11.7686	−	9.87500i	−0.486987	−	0.408631i
$585$	−1.45677	+	1.22237i	−0.0602299	+	0.0505389i
$586$	−1.93107	+	10.9517i	−0.0797720	+	0.452409i
$587$	5.34137	−	1.94410i	0.220462	−	0.0802415i	−0.229428	−	0.973326i	$-0.573686\pi$
$587$	5.34137	−	1.94410i	0.220462	−	0.0802415i	0.449890	+	0.893084i	$0.351463\pi$
$588$	−5.49525			−0.226620
$589$	−10.3648	−	1.74903i	−0.427076	−	0.0720673i
$590$	44.2995			1.82378
$591$	−17.5005	+	6.36965i	−0.719873	+	0.262012i
$592$	0.294263	−	1.66885i	0.0120941	−	0.0685892i
$593$	−8.05097	+	6.75557i	−0.330614	+	0.277418i	−0.792950	−	0.609287i	$-0.791456\pi$
$593$	−8.05097	+	6.75557i	−0.330614	+	0.277418i	0.462336	+	0.886705i	$0.347011\pi$
$594$	−1.62449	−	1.36310i	−0.0666534	−	0.0559289i
$595$	4.57145	+	25.9260i	0.187411	+	1.06286i
$596$	−6.01501	−	10.4183i	−0.246385	−	0.426751i
$597$	−4.21554	+	7.30152i	−0.172530	+	0.298832i
$598$	4.11974	+	1.49946i	0.168469	+	0.0613176i
$599$	42.0146	+	15.2921i	1.71667	+	0.624817i	0.997543	−	0.0700613i	$-0.0223195\pi$
$599$	42.0146	+	15.2921i	1.71667	+	0.624817i	0.719128	+	0.694878i	$0.244542\pi$
$600$	−5.02481	+	8.70323i	−0.205137	+	0.355308i
$601$	−16.4363	−	28.4685i	−0.670450	−	1.16125i	−0.977777	−	0.209650i	$-0.932768\pi$
$601$	−16.4363	−	28.4685i	−0.670450	−	1.16125i	0.307326	−	0.951604i	$-0.400566\pi$
$602$	−1.41400	−	8.01919i	−0.0576304	−	0.326838i
$603$	3.42855	+	2.87689i	0.139621	+	0.117156i
$604$	0.0452926	−	0.0380050i	0.00184293	−	0.00154640i
$605$	4.38073	−	24.8444i	0.178102	−	1.01007i
$606$	−5.35117	+	1.94767i	−0.217376	+	0.0791185i
$607$	29.9486			1.21558			0.607788	−	0.794099i	$-0.292057\pi$
$607$	29.9486			1.21558			0.607788	+	0.794099i	$0.292057\pi$
$608$	3.79086	+	2.15160i	0.153740	+	0.0872589i
$609$	−10.3969			−0.421305
$610$	0.152704	−	0.0555796i	0.00618279	−	0.00225035i
$611$	0.184736	−	1.04769i	0.00747363	−	0.0423850i
$612$	−4.23783	+	3.55596i	−0.171304	+	0.143741i
$613$	4.47384	+	3.75400i	0.180697	+	0.151623i	0.728650	−	0.684887i	$-0.240148\pi$
$613$	4.47384	+	3.75400i	0.180697	+	0.151623i	−0.547953	+	0.836509i	$0.684593\pi$
$614$	4.34817	+	24.6597i	0.175478	+	0.995185i
$615$	3.09627	+	5.36289i	0.124854	+	0.216253i
$616$	1.30066	−	2.25281i	0.0524051	−	0.0907682i
$617$	11.8135	+	4.29975i	0.475592	+	0.173101i	0.568684	−	0.822556i	$-0.307453\pi$
$617$	11.8135	+	4.29975i	0.475592	+	0.173101i	−0.0930920	+	0.995658i	$0.529675\pi$
$618$	0.294263	+	0.107103i	0.0118370	+	0.00430831i
$619$	−4.14290	+	7.17572i	−0.166517	+	0.288417i	−0.937193	−	0.348811i	$-0.886586\pi$
$619$	−4.14290	+	7.17572i	−0.166517	+	0.288417i	0.770676	+	0.637228i	$0.219919\pi$
$620$	4.67752	+	8.10170i	0.187854	+	0.325372i
$621$	−1.55303	−	8.80769i	−0.0623211	−	0.353440i
$622$	0.0432332	+	0.0362770i	0.00173349	+	0.00145457i
$623$	7.94609	−	6.66756i	0.318353	−	0.267130i
$624$	0.0851223	−	0.482753i	0.00340762	−	0.0193256i
$625$	−24.1942	+	8.80596i	−0.967767	+	0.352238i
$626$	13.7638			0.550113
$627$	−9.09105	+	1.67210i	−0.363062	+	0.0667771i
$628$	12.9581			0.517085
$629$	8.80928	−	3.20631i	0.351249	−	0.127844i
$630$	−0.826352	+	4.68647i	−0.0329226	+	0.186714i
$631$	5.23055	−	4.38895i	0.208225	−	0.174722i	−0.532711	−	0.846297i	$-0.678827\pi$
$631$	5.23055	−	4.38895i	0.208225	−	0.174722i	0.740936	+	0.671576i	$0.234382\pi$
$632$	−3.57011	−	2.99568i	−0.142011	−	0.119162i
$633$	−0.254900	−	1.44561i	−0.0101314	−	0.0574578i
$634$	−5.45202	−	9.44317i	−0.216527	−	0.375036i
$635$	−3.16250	+	5.47762i	−0.125500	+	0.217373i
$636$	−8.35117	−	3.03958i	−0.331145	−	0.120527i
$637$	2.53132	+	0.921324i	0.100294	+	0.0365042i
$638$	−8.98680	+	15.5656i	−0.355791	+	0.616248i
$639$	−1.31908	−	2.28471i	−0.0521819	−	0.0903817i
$640$	−0.673648	−	3.82045i	−0.0266283	−	0.151016i
$641$	29.6544	+	24.8830i	1.17128	+	0.982818i	0.999997	−	0.00240481i	$-0.000765477\pi$
$641$	29.6544	+	24.8830i	1.17128	+	0.982818i	0.171279	+	0.985222i	$0.445210\pi$
$642$	−12.8910	+	10.8168i	−0.508767	+	0.426906i
$643$	−2.18820	+	12.4099i	−0.0862940	+	0.489398i	0.910776	+	0.412901i	$0.135485\pi$
$643$	−2.18820	+	12.4099i	−0.0862940	+	0.489398i	−0.997070	+	0.0764965i	$0.975627\pi$
$644$	10.3093	−	3.75227i	0.406242	−	0.147860i
$645$	25.7520			1.01398
$646$	0.177519	+	24.1132i	0.00698437	+	0.948720i
$647$	8.41241			0.330726			0.165363	−	0.986233i	$-0.447120\pi$
$647$	8.41241			0.330726			0.165363	+	0.986233i	$0.447120\pi$
$648$	−0.939693	+	0.342020i	−0.0369146	+	0.0134358i
$649$	4.20502	−	23.8479i	0.165062	−	0.936111i
$650$	3.77379	−	3.16658i	0.148020	−	0.124204i
$651$	2.26604	+	1.90144i	0.0888133	+	0.0745232i
$652$	2.61721	+	14.8429i	0.102498	+	0.581294i
$653$	−13.1900	−	22.8458i	−0.516165	−	0.894024i	−0.999824	−	0.0187673i	$-0.994026\pi$
$653$	−13.1900	−	22.8458i	−0.516165	−	0.894024i	0.483659	−	0.875257i	$-0.339307\pi$
$654$	5.20574	−	9.01660i	0.203560	−	0.352577i
$655$	21.7383	+	7.91209i	0.849385	+	0.309151i
$656$	−1.50000	−	0.545955i	−0.0585652	−	0.0213160i
$657$	7.68139	−	13.3046i	0.299680	−	0.519060i
$658$	−1.33110	−	2.30553i	−0.0518917	−	0.0898790i
$659$	5.55794	+	31.5207i	0.216507	+	1.22787i	0.878273	+	0.478160i	$0.158696\pi$
$659$	5.55794	+	31.5207i	0.216507	+	1.22787i	−0.661766	+	0.749711i	$0.730193\pi$
$660$	6.30200	+	5.28801i	0.245305	+	0.205835i
$661$	−31.0462	+	26.0509i	−1.20756	+	1.01326i	−0.208177	+	0.978091i	$0.566753\pi$
$661$	−31.0462	+	26.0509i	−1.20756	+	1.01326i	−0.999381	+	0.0351705i	$0.988803\pi$
$662$	1.49185	−	8.46069i	0.0579823	−	0.328834i
$663$	2.54829	−	0.927500i	0.0989672	−	0.0360211i
$664$	12.4807			0.484345
$665$	13.4500	+	15.7915i	0.521567	+	0.612367i
$666$	1.69459			0.0656641
$667$	−71.2311	+	25.9260i	−2.75808	+	1.00386i
$668$	−0.337029	+	1.91139i	−0.0130401	+	0.0739538i
$669$	20.1229	−	16.8851i	0.777996	−	0.652816i
$670$	−13.3007	−	11.1606i	−0.513849	−	0.431171i
$671$	−0.0154253	−	0.0874810i	−0.000595486	−	0.00337717i
$672$	−0.613341	−	1.06234i	−0.0236601	−	0.0409806i
$673$	2.28059	−	3.95010i	0.0879104	−	0.152265i	−0.818717	−	0.574197i	$-0.805314\pi$
$673$	2.28059	−	3.95010i	0.0879104	−	0.152265i	0.906628	+	0.421932i	$0.138648\pi$
$674$	2.17112	+	0.790224i	0.0836285	+	0.0304383i
$675$	−9.44356	−	3.43718i	−0.363483	−	0.132297i
$676$	6.37985	−	11.0502i	0.245379	−	0.425009i
$677$	−16.7208	−	28.9612i	−0.642631	−	1.11307i	−0.984843	−	0.173446i	$-0.944510\pi$
$677$	−16.7208	−	28.9612i	−0.642631	−	1.11307i	0.342213	−	0.939623i	$-0.388824\pi$
$678$	−3.01842	−	17.1183i	−0.115922	−	0.657424i
$679$	−13.5103	−	11.3365i	−0.518476	−	0.435053i
$680$	16.4402	−	13.7949i	0.630451	−	0.529011i
$681$	3.18954	−	18.0888i	0.122223	−	0.693164i
$682$	4.80541	−	1.74903i	0.184009	−	0.0669736i
$683$	−26.4825			−1.01332			−0.506662	−	0.862145i	$-0.669121\pi$
$683$	−26.4825			−1.01332			−0.506662	+	0.862145i	$0.669121\pi$
$684$	−1.46064	+	4.10689i	−0.0558489	+	0.157031i
$685$	0.0760373			0.00290524
$686$	14.4033	−	5.24238i	0.549921	−	0.200155i
$687$	0.672304	−	3.81283i	0.0256500	−	0.145468i
$688$	−5.08512	+	4.26692i	−0.193868	+	0.162675i
$689$	3.33725	+	2.80028i	0.127139	+	0.106682i
$690$	6.02481	+	34.1684i	0.229361	+	1.30077i
$691$	−16.7003	−	28.9257i	−0.635308	−	1.10039i	−0.986450	−	0.164064i	$-0.947540\pi$
$691$	−16.7003	−	28.9257i	−0.635308	−	1.10039i	0.351141	−	0.936322i	$-0.385794\pi$
$692$	−8.03596	+	13.9187i	−0.305481	+	0.529109i
$693$	2.44444	+	0.889704i	0.0928566	+	0.0337970i
$694$	3.08765	+	1.12381i	0.117206	+	0.0426593i
$695$	8.71941	−	15.1025i	0.330746	−	0.572869i
$696$	4.23783	+	7.34013i	0.160634	+	0.278227i
$697$	−1.53343	−	8.69653i	−0.0580829	−	0.329405i
$698$	22.4820	+	18.8647i	0.850958	+	0.714039i
$699$	12.5988	−	10.5716i	0.476530	−	0.399856i
$700$	2.14068	−	12.1404i	0.0809102	−	0.458864i
$701$	−17.7408	+	6.45713i	−0.670061	+	0.243882i	−0.654574	−	0.755998i	$-0.727152\pi$
$701$	−17.7408	+	6.45713i	−0.670061	+	0.243882i	−0.0154871	+	0.999880i	$0.504930\pi$
$702$	0.490200			0.0185014
$703$	4.70620	−	5.69323i	0.177498	−	0.214724i
$704$	−2.12061			−0.0799237
$705$	7.91147	−	2.87954i	0.297963	−	0.108450i
$706$	−1.34389	+	7.62159i	−0.0505781	+	0.286843i
$707$	5.35117	−	4.49016i	0.201251	−	0.168870i
$708$	−8.74763	−	7.34013i	−0.328756	−	0.275859i
$709$	−0.0369988	−	0.209830i	−0.00138952	−	0.00788034i	0.984105	−	0.177587i	$-0.0568291\pi$
$709$	−0.0369988	−	0.209830i	−0.00138952	−	0.00788034i	−0.985495	+	0.169707i	$0.945718\pi$
$710$	5.11721	+	8.86327i	0.192046	+	0.332633i
$711$	2.33022	−	4.03606i	0.0873902	−	0.151364i
$712$	−7.94609	−	2.89214i	−0.297792	−	0.108388i
$713$	20.2665	+	7.37641i	0.758987	+	0.276249i
$714$	3.39306	−	5.87695i	0.126982	−	0.219939i
$715$	−2.01636	−	3.49244i	−0.0754075	−	0.130610i
$716$	2.56552	+	14.5498i	0.0958781	+	0.543751i
$717$	2.53209	+	2.12467i	0.0945626	+	0.0793474i
$718$	2.19665	−	1.84321i	0.0819783	−	0.0687880i
$719$	−2.25150	+	12.7689i	−0.0839667	+	0.476199i	0.913608	+	0.406596i	$0.133284\pi$
$719$	−2.25150	+	12.7689i	−0.0839667	+	0.476199i	−0.997575	+	0.0696027i	$0.977827\pi$
$720$	3.64543	−	1.32683i	0.135857	−	0.0494480i
$721$	−0.384133			−0.0143059
$722$	9.74123	+	16.3128i	0.362531	+	0.607101i
$723$	3.01548			0.112147
$724$	17.1275	−	6.23389i	0.636538	−	0.231681i
$725$	−14.7909	+	83.8831i	−0.549319	+	3.11534i
$726$	−4.98158	+	4.18004i	−0.184884	+	0.155136i
$727$	19.7062	+	16.5355i	0.730863	+	0.613267i	0.930367	−	0.366630i	$-0.119489\pi$
$727$	19.7062	+	16.5355i	0.730863	+	0.613267i	−0.199504	+	0.979897i	$0.563933\pi$
$728$	0.104418	+	0.592184i	0.00386999	+	0.0219478i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−29.7991	+	51.6135i	−1.10291	+	1.91030i
$731$	−34.5082	−	12.5600i	−1.27633	−	0.464547i
$732$	−0.0393628	−	0.0143269i	−0.00145489	−	0.000529538i
$733$	−4.25995	+	7.37845i	−0.157345	+	0.272529i	−0.933910	−	0.357507i	$-0.883627\pi$
$733$	−4.25995	+	7.37845i	−0.157345	+	0.272529i	0.776565	+	0.630037i	$0.216960\pi$
$734$	11.4829	+	19.8890i	0.423843	+	0.734117i
$735$	3.70187	+	20.9943i	0.136545	+	0.774387i
$736$	−6.85117	−	5.74881i	−0.252537	−	0.211904i
$737$	−7.27063	+	6.10078i	−0.267817	+	0.224725i
$738$	0.277189	−	1.57202i	0.0102035	−	0.0578667i
$739$	12.5030	−	4.55072i	0.459930	−	0.167401i	−0.101655	−	0.994820i	$-0.532414\pi$
$739$	12.5030	−	4.55072i	0.459930	−	0.167401i	0.561585	+	0.827419i	$0.310192\pi$
$740$	−6.57398			−0.241664
$741$	1.36138	−	1.64690i	0.0500115	−	0.0605003i
$742$	10.9017			0.400213
$743$	25.3307	−	9.21962i	0.929293	−	0.338235i	0.167364	−	0.985895i	$-0.446475\pi$
$743$	25.3307	−	9.21962i	0.929293	−	0.338235i	0.761929	+	0.647660i	$0.224252\pi$
$744$	0.418748	−	2.37484i	0.0153520	−	0.0870658i
$745$	−35.7506	+	29.9983i	−1.30980	+	1.09905i
$746$	−17.7652	−	14.9067i	−0.650429	−	0.545775i
$747$	2.16725	+	12.2911i	0.0792956	+	0.449708i
$748$	−5.86571	−	10.1597i	−0.214472	−	0.371476i
$749$	10.3213	−	17.8770i	0.377132	−	0.653212i
$750$	18.4081	+	6.69999i	0.672168	+	0.244649i
$751$	−17.3277	−	6.30677i	−0.632297	−	0.230137i	0.00593399	−	0.999982i	$-0.498111\pi$
$751$	−17.3277	−	6.30677i	−0.632297	−	0.230137i	−0.638231	+	0.769845i	$0.720333\pi$
$752$	−1.08512	+	1.87949i	−0.0395703	+	0.0685378i
$753$	1.76739	+	3.06121i	0.0644072	+	0.111557i
$754$	−0.721467	−	4.09164i	−0.0262743	−	0.149009i
$755$	−0.175708	−	0.147436i	−0.00639465	−	0.00536575i
$756$	0.939693	−	0.788496i	0.0341763	−	0.0286773i
$757$	5.19490	−	29.4617i	0.188812	−	1.07080i	−0.732148	−	0.681146i	$-0.761482\pi$
$757$	5.19490	−	29.4617i	0.188812	−	1.07080i	0.920959	−	0.389659i	$-0.127407\pi$
$758$	31.4971	−	11.4640i	1.14402	−	0.416391i
$759$	18.9659			0.688417
$760$	5.66637	−	15.9322i	0.205541	−	0.577922i
$761$	−28.6691			−1.03925			−0.519627	−	0.854393i	$-0.673929\pi$
$761$	−28.6691			−1.03925			−0.519627	+	0.854393i	$0.673929\pi$
$762$	1.53209	−	0.557635i	0.0555017	−	0.0202010i
$763$	−2.21776	+	12.5775i	−0.0802883	+	0.455337i
$764$	0.988856	−	0.829748i	0.0357755	−	0.0300192i
$765$	16.4402	+	13.7949i	0.594395	+	0.498757i
$766$	1.16860	+	6.62744i	0.0422231	+	0.239459i
$767$	2.79885	+	4.84775i	0.101061	+	0.175042i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	9.17277	+	3.33862i	0.330779	+	0.120394i	0.502070	−	0.864827i	$-0.332572\pi$
$769$	9.17277	+	3.33862i	0.330779	+	0.120394i	−0.171292	+	0.985220i	$0.554794\pi$
$770$	−9.48293	−	3.45150i	−0.341741	−	0.124384i
$771$	2.35117	−	4.07234i	0.0846752	−	0.146662i
$772$	4.56031	+	7.89868i	0.164129	+	0.284280i
$773$	−0.676641	−	3.83742i	−0.0243371	−	0.138023i	0.970218	−	0.242233i	$-0.0778797\pi$
$773$	−0.676641	−	3.83742i	−0.0243371	−	0.138023i	−0.994555	+	0.104210i	$0.966769\pi$
$774$	−5.08512	−	4.26692i	−0.182781	−	0.153371i
$775$	18.5646	−	15.5776i	0.666862	−	0.559563i
$776$	−2.49660	+	14.1589i	−0.0896226	+	0.508275i
$777$	−1.95336	+	0.710966i	−0.0700765	+	0.0255058i
$778$	−19.0223			−0.681982
$779$	−4.51161	−	5.29704i	−0.161645	−	0.189786i
$780$	−1.90167			−0.0680908
$781$	5.25712	−	1.91344i	0.188115	−	0.0684681i
$782$	8.59152	−	48.7249i	0.307232	−	1.74240i
$783$	−6.49273	+	5.44804i	−0.232031	+	0.194697i
$784$	−4.20961	−	3.53228i	−0.150343	−	0.126153i
$785$	−8.72921	−	49.5058i	−0.311559	−	1.76694i
$786$	−2.98158	−	5.16425i	−0.106349	−	0.184203i
$787$	1.47044	−	2.54687i	0.0524154	−	0.0907862i	−0.838627	−	0.544706i	$-0.816641\pi$
$787$	1.47044	−	2.54687i	0.0524154	−	0.0907862i	0.891043	+	0.453920i	$0.149975\pi$
$788$	−17.5005	−	6.36965i	−0.623428	−	0.226909i
$789$	−19.7922	−	7.20377i	−0.704621	−	0.256461i
$790$	−9.03983	+	15.6574i	−0.321623	+	0.557067i
$791$	10.6613	+	18.4660i	0.379073	+	0.656574i
$792$	−0.368241	−	2.08840i	−0.0130849	−	0.0742080i
$793$	0.0157300	+	0.0131990i	0.000558587	+	0.000468711i
$794$	−20.6177	+	17.3003i	−0.731694	+	0.613964i
$795$	−5.98680	+	33.9528i	−0.212330	+	1.20418i
$796$	−7.92262	+	2.88360i	−0.280810	+	0.102206i
$797$	8.26950			0.292921			0.146460	−	0.989217i	$-0.453212\pi$
$797$	8.26950			0.292921			0.146460	+	0.989217i	$0.453212\pi$
$798$	−0.0393628	−	5.34684i	−0.00139343	−	0.189276i
$799$	−12.0060			−0.424741
$800$	−9.44356	+	3.43718i	−0.333880	+	0.121523i
$801$	1.46838	−	8.32759i	0.0518826	−	0.294241i
$802$	−4.36753	+	3.66479i	−0.154223	+	0.129408i
$803$	24.9566	+	20.9411i	0.880699	+	0.738995i
$804$	0.777189	+	4.40766i	0.0274093	+	0.155446i
$805$	−21.2802	−	36.8584i	−0.750028	−	1.29909i
$806$	−0.591052	+	1.02373i	−0.0208189	+	0.0360594i
$807$	−9.47090	−	3.44713i	−0.333392	−	0.121345i
$808$	−5.35117	−	1.94767i	−0.188253	−	0.0685186i
$809$	1.04529	−	1.81050i	0.0367505	−	0.0636538i	−0.847065	−	0.531489i	$-0.821633\pi$
$809$	1.04529	−	1.81050i	0.0367505	−	0.0636538i	0.883816	+	0.467835i	$0.154966\pi$
$810$	1.93969	+	3.35965i	0.0681539	+	0.118046i
$811$	0.150177	+	0.851698i	0.00527344	+	0.0299072i	0.987331	−	0.158675i	$-0.0507221\pi$
$811$	0.150177	+	0.851698i	0.00527344	+	0.0299072i	−0.982057	+	0.188582i	$0.939611\pi$
$812$	−7.96451	−	6.68302i	−0.279499	−	0.234528i
$813$	−7.47952	+	6.27606i	−0.262318	+	0.220111i
$814$	−0.624018	+	3.53898i	−0.0218718	+	0.124041i
$815$	54.9436	−	19.9978i	1.92459	−	0.700494i
$816$	−5.53209			−0.193662
$817$	−28.4577	+	5.23416i	−0.995609	+	0.183120i
$818$	−0.807467			−0.0282324
$819$	−0.565055	+	0.205663i	−0.0197446	+	0.00718646i
$820$	−1.07532	+	6.09845i	−0.0375519	+	0.212967i
$821$	17.4394	−	14.6334i	0.608641	−	0.510710i	−0.285569	−	0.958358i	$-0.592183\pi$
$821$	17.4394	−	14.6334i	0.608641	−	0.510710i	0.894210	+	0.447648i	$0.147738\pi$
$822$	−0.0150147	−	0.0125989i	−0.000523699	−	0.000439436i
$823$	−5.75056	−	32.6131i	−0.200452	−	1.13682i	−0.904438	−	0.426606i	$-0.859709\pi$
$823$	−5.75056	−	32.6131i	−0.200452	−	1.13682i	0.703986	−	0.710214i	$-0.251402\pi$
$824$	0.156574	+	0.271194i	0.00545452	+	0.00944750i
$825$	10.6557	−	18.4562i	0.370984	−	0.642563i
$826$	13.1630	+	4.79093i	0.457998	+	0.166698i
$827$	24.9158	+	9.06861i	0.866408	+	0.315347i	0.736712	−	0.676207i	$-0.236378\pi$
$827$	24.9158	+	9.06861i	0.866408	+	0.315347i	0.129696	+	0.991554i	$0.458600\pi$
$828$	4.47178	−	7.74535i	0.155405	−	0.269170i
$829$	1.57873	+	2.73443i	0.0548314	+	0.0949708i	0.892138	−	0.451762i	$-0.149205\pi$
$829$	1.57873	+	2.73443i	0.0548314	+	0.0949708i	−0.837307	+	0.546733i	$0.815871\pi$
$830$	−8.40760	−	47.6819i	−0.291832	−	1.65506i
$831$	12.9133	+	10.8355i	0.447957	+	0.375880i
$832$	0.375515	−	0.315094i	0.0130186	−	0.0109239i
$833$	5.27894	−	29.9384i	0.182905	−	1.03730i
$834$	−4.22416	+	1.53747i	−0.146271	+	0.0532381i
$835$	7.52940			0.260566
$836$	−8.03895	−	4.56272i	−0.278033	−	0.157805i
$837$	2.41147			0.0833527
$838$	17.9684	−	6.53995i	0.620707	−	0.225919i
$839$	−7.31386	+	41.4790i	−0.252503	+	1.43201i	0.549900	+	0.835230i	$0.314666\pi$
$839$	−7.31386	+	41.4790i	−0.252503	+	1.43201i	−0.802403	+	0.596783i	$0.796445\pi$
$840$	−3.64543	+	3.05888i	−0.125779	+	0.105541i
$841$	32.8148	+	27.5349i	1.13154	+	0.949479i
$842$	−4.86618	−	27.5975i	−0.167700	−	0.951072i
$843$	5.86231	+	10.1538i	0.201909	+	0.349716i
$844$	0.733956	−	1.27125i	0.0252638	−	0.0437582i
$845$	−46.5146	−	16.9299i	−1.60015	−	0.582407i
$846$	−2.03936	−	0.742267i	−0.0701147	−	0.0255197i
$847$	3.98855	−	6.90837i	0.137048	−	0.237375i
$848$	−4.44356	−	7.69648i	−0.152593	−	0.264298i
$849$	−3.74123	−	21.2176i	−0.128399	−	0.728185i
$850$	−42.5886	−	35.7361i	−1.46078	−	1.22574i
$851$	−11.6099	+	9.74189i	−0.397984	+	0.333948i
$852$	0.458111	−	2.59808i	0.0156946	−	0.0890086i
$853$	−53.1147	+	19.3322i	−1.81861	+	0.661921i	−0.823035	+	0.567990i	$0.807721\pi$
$853$	−53.1147	+	19.3322i	−1.81861	+	0.661921i	−0.995579	+	0.0939314i	$0.970057\pi$
$854$	0.0513845			0.00175834
$855$	16.6741	+	2.81369i	0.570243	+	0.0962262i
$856$	−16.8280			−0.575169
$857$	−12.3960	+	4.51179i	−0.423441	+	0.154120i	−0.544946	−	0.838471i	$-0.683450\pi$
$857$	−12.3960	+	4.51179i	−0.423441	+	0.154120i	0.121505	+	0.992591i	$0.461228\pi$
$858$	−0.180512	+	1.02373i	−0.00616257	+	0.0349496i
$859$	−16.6623	+	13.9813i	−0.568509	+	0.477036i	−0.881151	−	0.472836i	$-0.843230\pi$
$859$	−16.6623	+	13.9813i	−0.568509	+	0.477036i	0.312642	+	0.949871i	$0.398786\pi$
$860$	19.7271	+	16.5530i	0.672690	+	0.564454i
$861$	0.340022	+	1.92836i	0.0115879	+	0.0657184i
$862$	4.51842	+	7.82613i	0.153898	+	0.266559i
$863$	23.4550	−	40.6253i	0.798418	−	1.38290i	−0.122228	−	0.992502i	$-0.539004\pi$
$863$	23.4550	−	40.6253i	0.798418	−	1.38290i	0.920646	−	0.390398i	$-0.127663\pi$
$864$	−0.939693	−	0.342020i	−0.0319690	−	0.0116358i
$865$	58.5890	+	21.3247i	1.99209	+	0.725061i
$866$	−0.731429	+	1.26687i	−0.0248550	+	0.0430501i
$867$	−6.80200	−	11.7814i	−0.231008	−	0.400118i
$868$	0.513671	+	2.91317i	0.0174351	+	0.0988795i
$869$	7.57082	+	6.35267i	0.256823	+	0.215500i
$870$	25.1878	−	21.1351i	0.853946	−	0.716546i
$871$	0.380978	−	2.16063i	0.0129089	−	0.0732102i
$872$	9.78359	−	3.56093i	0.331314	−	0.120588i
$873$	−14.3773			−0.486599
$874$	−13.6027	−	36.5339i	−0.460117	−	1.23578i
$875$	−24.0300			−0.812363
$876$	14.4363	−	5.25438i	0.487757	−	0.177529i
$877$	−0.464451	+	2.63403i	−0.0156834	+	0.0889450i	−0.991645	−	0.128999i	$-0.958824\pi$
$877$	−0.464451	+	2.63403i	−0.0156834	+	0.0889450i	0.975961	+	0.217944i	$0.0699349\pi$
$878$	−4.14930	+	3.48168i	−0.140032	+	0.117501i
$879$	−8.51889	−	7.14819i	−0.287335	−	0.241103i
$880$	1.42855	+	8.10170i	0.0481564	+	0.273108i
$881$	13.5548	+	23.4777i	0.456674	+	0.790983i	0.998783	−	0.0493254i	$-0.0157071\pi$
$881$	13.5548	+	23.4777i	0.456674	+	0.790983i	−0.542108	+	0.840309i	$0.682374\pi$
$882$	2.74763	−	4.75903i	0.0925174	−	0.160245i
$883$	40.8055	+	14.8520i	1.37321	+	0.499809i	0.920114	−	0.391651i	$-0.128096\pi$
$883$	40.8055	+	14.8520i	1.37321	+	0.499809i	0.453099	+	0.891460i	$0.350318\pi$
$884$	2.54829	+	0.927500i	0.0857081	+	0.0311952i
$885$	−22.1498	+	38.3645i	−0.744556	+	1.28961i
$886$	14.2331	+	24.6524i	0.478170	+	0.828214i
$887$	−3.72251	−	21.1114i	−0.124990	−	0.708851i	−0.981314	−	0.192413i	$-0.938369\pi$
$887$	−3.72251	−	21.1114i	−0.124990	−	0.708851i	0.856325	−	0.516438i	$-0.172742\pi$
$888$	1.29813	+	1.08926i	0.0435625	+	0.0365533i
$889$	−1.53209	+	1.28558i	−0.0513846	+	0.0431168i
$890$	−5.69640	+	32.3059i	−0.190944	+	1.08290i
$891$	1.99273	−	0.725293i	0.0667588	−	0.0242982i
$892$	26.2686			0.879537
$893$	−8.15745	+	4.79012i	−0.272979	+	0.160295i
$894$	12.0300			0.402344
$895$	53.8585	−	19.6029i	1.80029	−	0.655252i
$896$	0.213011	−	1.20805i	0.00711620	−	0.0403580i
$897$	−3.35844	+	2.81807i	−0.112135	+	0.0940925i
$898$	−17.4388	−	14.6329i	−0.581941	−	0.488306i
$899$	−3.54916	−	20.1283i	−0.118371	−	0.671317i
$900$	−5.02481	−	8.70323i	−0.167494	−	0.290108i
$901$	24.5822	−	42.5776i	0.818951	−	1.41847i
$902$	3.18092	+	1.15776i	0.105913	+	0.0385492i
$903$	7.65183	+	2.78504i	0.254637	+	0.0926802i
$904$	8.69119	−	15.0536i	0.289065	−	0.500675i
$905$	−35.3542	−	61.2352i	−1.17521	−	2.03553i
$906$	0.0102670	+	0.0582271i	0.000341098	+	0.00193447i
$907$	−12.5471	−	10.5283i	−0.416620	−	0.349585i	0.410256	−	0.911971i	$-0.365439\pi$
$907$	−12.5471	−	10.5283i	−0.416620	−	0.349585i	−0.826875	+	0.562385i	$0.809884\pi$
$908$	14.0706	−	11.8066i	0.466948	−	0.391816i
$909$	0.988856	−	5.60808i	0.0327983	−	0.186008i
$910$	2.19207	−	0.797847i	0.0726663	−	0.0264484i
$911$	28.4502			0.942596			0.471298	−	0.881974i	$-0.343786\pi$
$911$	28.4502			0.942596			0.471298	+	0.881974i	$0.343786\pi$
$912$	−3.75877	+	2.20718i	−0.124465	+	0.0730870i
$913$	−26.4668			−0.875922
$914$	1.06196	−	0.386520i	0.0351264	−	0.0127850i
$915$	−0.0282185	+	0.160035i	−0.000932875	+	0.00529059i
$916$	2.96585	−	2.48865i	0.0979945	−	0.0822271i
$917$	5.60354	+	4.70193i	0.185045	+	0.155271i
$918$	−0.960637	−	5.44804i	−0.0317058	−	0.179812i
$919$	25.6268	+	44.3869i	0.845349	+	1.46419i	0.885318	+	0.464986i	$0.153941\pi$
$919$	25.6268	+	44.3869i	0.845349	+	1.46419i	−0.0399689	+	0.999201i	$0.512726\pi$
$920$	−17.3478	+	30.0472i	−0.571939	+	0.990627i
$921$	−23.5300	−	8.56423i	−0.775341	−	0.282201i
$922$	12.2001	+	4.44048i	0.401789	+	0.146239i
$923$	−0.646612	+	1.11996i	−0.0212835	+	0.0368641i
$924$	1.30066	+	2.25281i	0.0427886	+	0.0741120i
$925$	2.95723	+	16.7713i	0.0972332	+	0.551437i
$926$	−23.4598	−	19.6851i	−0.770936	−	0.646892i
$927$	−0.239885	+	0.201288i	−0.00787887	+	0.00661116i
$928$	−1.47178	+	8.34689i	−0.0483136	+	0.274000i
$929$	−48.4445	+	17.6324i	−1.58941	+	0.578499i	−0.977223	−	0.212213i	$-0.931933\pi$
$929$	−48.4445	+	17.6324i	−1.58941	+	0.578499i	−0.612189	+	0.790712i	$0.709711\pi$
$930$	−9.35504			−0.306764
$931$	−8.35797	−	22.4478i	−0.273922	−	0.735696i
$932$	16.4466			0.538725
$933$	−0.0530334	+	0.0193026i	−0.00173624	+	0.000631938i
$934$	1.92009	−	10.8894i	0.0628273	−	0.356312i
$935$	−34.8632	+	29.2537i	−1.14015	+	0.956699i
$936$	0.375515	+	0.315094i	0.0122741	+	0.0102992i
$937$	−2.51161	−	14.2441i	−0.0820508	−	0.465333i	−0.997954	−	0.0639341i	$-0.979635\pi$
$937$	−2.51161	−	14.2441i	−0.0820508	−	0.465333i	0.915903	−	0.401399i	$-0.131476\pi$
$938$	−2.74510	−	4.75465i	−0.0896307	−	0.155245i
$939$	−6.88191	+	11.9198i	−0.224583	+	0.388989i
$940$	7.91147	+	2.87954i	0.258044	+	0.0939203i
$941$	12.3855	+	4.50795i	0.403755	+	0.146955i	0.535912	−	0.844274i	$-0.319968\pi$
$941$	12.3855	+	4.50795i	0.403755	+	0.146955i	−0.132157	+	0.991229i	$0.542190\pi$
$942$	−6.47906	+	11.2221i	−0.211099	+	0.365634i
$943$	7.13816	+	12.3636i	0.232450	+	0.402616i
$944$	−1.98293	−	11.2457i	−0.0645387	−	0.366017i
$945$	−3.64543	−	3.05888i	−0.118586	−	0.0995053i
$946$	10.7836	−	9.04850i	0.350605	−	0.294192i
$947$	−7.43676	+	42.1759i	−0.241662	+	1.37053i	0.586456	+	0.809981i	$0.300523\pi$
$947$	−7.43676	+	42.1759i	−0.241662	+	1.37053i	−0.828119	+	0.560553i	$0.810589\pi$
$948$	4.37939	−	1.59397i	0.142236	−	0.0517696i
$949$	−7.53083			−0.244461
$950$	−43.1946	−	7.28893i	−1.40142	−	0.236484i
$951$	10.9040			0.353588
$952$	6.37686	−	2.32099i	0.206675	−	0.0752236i
$953$	−5.59451	+	31.7281i	−0.181224	+	1.02777i	0.749488	+	0.662018i	$0.230300\pi$
$953$	−5.59451	+	31.7281i	−0.181224	+	1.02777i	−0.930712	+	0.365754i	$0.880811\pi$
$954$	6.80793	−	5.71253i	0.220415	−	0.184950i
$955$	−3.83615	−	3.21891i	−0.124135	−	0.104162i
$956$	0.573978	+	3.25519i	0.0185638	+	0.105280i
$957$	−8.98680	−	15.5656i	−0.290502	−	0.503164i
$958$	8.81908	−	15.2751i	0.284931	−	0.493516i
$959$	0.0225934	+	0.00822333i	0.000729579	+	0.000265545i
$960$	3.64543	+	1.32683i	0.117656	+	0.0428232i
$961$	12.5924	−	21.8107i	0.406206	−	0.703570i
$962$	−0.415345	−	0.719398i	−0.0133912	−	0.0231943i
$963$	−2.92215	−	16.5723i	−0.0941650	−	0.534036i
$964$	2.30999	+	1.93831i	0.0743999	+	0.0624289i
$965$	27.1045	−	22.7434i	0.872524	−	0.732134i
$966$	−1.90508	+	10.8042i	−0.0612949	+	0.347620i
$967$	−32.4650	+	11.8163i	−1.04400	+	0.379986i	−0.806396	−	0.591375i	$-0.798585\pi$
$967$	−32.4650	+	11.8163i	−1.04400	+	0.379986i	−0.237607	+	0.971361i	$0.576363\pi$
$968$	−6.50299			−0.209014
$969$	−20.9714	−	11.9028i	−0.673697	−	0.382375i
$970$	55.7752			1.79083
$971$	1.11556	−	0.406031i	0.0358001	−	0.0130302i	−0.324058	−	0.946037i	$-0.605047\pi$
$971$	1.11556	−	0.406031i	0.0358001	−	0.0130302i	0.359858	+	0.933007i	$0.382825\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	4.22416	−	3.54449i	0.135420	−	0.113631i
$974$	−11.7155	−	9.83050i	−0.375390	−	0.314990i
$975$	0.855448	+	4.85148i	0.0273963	+	0.155372i
$976$	−0.0209445	−	0.0362770i	−0.000670418	−	0.00116120i
$977$	−10.4413	+	18.0849i	−0.334048	+	0.578588i	−0.983302	−	0.181984i	$-0.941748\pi$
$977$	−10.4413	+	18.0849i	−0.334048	+	0.578588i	0.649253	+	0.760572i	$0.275081\pi$
$978$	−14.1630	−	5.15490i	−0.452882	−	0.164836i
$979$	16.8506	+	6.13311i	0.538547	+	0.196015i
$980$	−10.6591	+	18.4621i	−0.340492	+	0.589750i
$981$	5.20574	+	9.01660i	0.166206	+	0.287878i
$982$	−0.308811	−	1.75135i	−0.00985455	−	0.0558879i
$983$	−26.8855	−	22.5596i	−0.857515	−	0.719541i	0.103916	−	0.994586i	$-0.466863\pi$
$983$	−26.8855	−	22.5596i	−0.857515	−	0.719541i	−0.961431	+	0.275045i	$0.911307\pi$
$984$	1.22281	−	1.02606i	0.0389818	−	0.0327096i
$985$	−12.5458	+	71.1505i	−0.399741	+	2.26704i
$986$	−44.0604	+	16.0367i	−1.40317	+	0.510711i
$987$	2.66220			0.0847387
$988$	2.10148	−	0.386520i	0.0668570	−	0.0122969i
$989$	59.3688			1.88782
$990$	−7.73055	+	2.81369i	−0.245693	+	0.0894250i
$991$	−8.63651	+	48.9801i	−0.274348	+	1.55590i	0.466679	+	0.884427i	$0.345450\pi$
$991$	−8.63651	+	48.9801i	−0.274348	+	1.55590i	−0.741026	+	0.671476i	$0.765661\pi$
$992$	1.84730	−	1.55007i	0.0586517	−	0.0492146i
$993$	6.58125	+	5.52233i	0.208850	+	0.175246i
$994$	0.561956	+	3.18701i	0.0178242	+	0.101086i
$995$	16.3537	+	28.3254i	0.518447	+	0.897976i
$996$	−6.24035	+	10.8086i	−0.197733	+	0.342484i
$997$	−39.3105	−	14.3079i	−1.24498	−	0.453134i	−0.366275	−	0.930507i	$-0.619367\pi$
$997$	−39.3105	−	14.3079i	−1.24498	−	0.453134i	−0.878701	+	0.477372i	$0.841589\pi$
$998$	0.101319	+	0.0368771i	0.00320720	+	0.00116733i
$999$	−0.847296	+	1.46756i	−0.0268073	+	0.0464316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.b.43.1	✓	6
3.2	odd	2		342.2.u.d.271.1		6
4.3	odd	2		912.2.bo.c.385.1		6
19.2	odd	18		2166.2.a.n.1.1		3
19.4	even	9	inner	114.2.i.b.61.1	yes	6
19.17	even	9		2166.2.a.t.1.1		3
57.2	even	18		6498.2.a.bt.1.3		3
57.17	odd	18		6498.2.a.bo.1.3		3
57.23	odd	18		342.2.u.d.289.1		6
76.23	odd	18		912.2.bo.c.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.43.1	✓	6	1.1	even	1	trivial
114.2.i.b.61.1	yes	6	19.4	even	9	inner
342.2.u.d.271.1		6	3.2	odd	2
342.2.u.d.289.1		6	57.23	odd	18
912.2.bo.c.289.1		6	76.23	odd	18
912.2.bo.c.385.1		6	4.3	odd	2
2166.2.a.n.1.1		3	19.2	odd	18
2166.2.a.t.1.1		3	19.17	even	9
6498.2.a.bo.1.3		3	57.17	odd	18
6498.2.a.bt.1.3		3	57.2	even	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.97178 - 2.49362i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.613341 - 1.06234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.97178 - 2.49362i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-0.613341 - 1.06234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(3.64543 + 1.32683i) q^{10} +(1.06031 - 1.83651i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.0851223 + 0.482753i) q^{13} +(0.939693 + 0.788496i) q^{14} +(-2.97178 + 2.49362i) q^{15} +(0.173648 - 0.984808i) q^{16} +(5.19846 - 1.89209i) q^{17} +1.00000 q^{18} +(2.77719 - 3.35965i) q^{19} -3.87939 q^{20} +(-1.15270 + 0.419550i) q^{21} +(-0.368241 + 2.08840i) q^{22} +(-6.85117 + 5.74881i) q^{23} +(0.766044 + 0.642788i) q^{24} +(1.74510 + 9.89695i) q^{25} +(-0.245100 - 0.424525i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-1.15270 - 0.419550i) q^{28} +(7.96451 + 2.89884i) q^{29} +(1.93969 - 3.35965i) q^{30} +(-1.20574 - 2.08840i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.62449 - 1.36310i) q^{33} +(-4.23783 + 3.55596i) q^{34} +(-0.826352 + 4.68647i) q^{35} +(-0.939693 + 0.342020i) q^{36} +1.69459 q^{37} +(-1.46064 + 4.10689i) q^{38} +0.490200 q^{39} +(3.64543 - 1.32683i) q^{40} +(0.277189 - 1.57202i) q^{41} +(0.939693 - 0.788496i) q^{42} +(-5.08512 - 4.26692i) q^{43} +(-0.368241 - 2.08840i) q^{44} +(1.93969 + 3.35965i) q^{45} +(4.47178 - 7.74535i) q^{46} +(-2.03936 - 0.742267i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(2.74763 - 4.75903i) q^{49} +(-5.02481 - 8.70323i) q^{50} +(-0.960637 - 5.44804i) q^{51} +(0.375515 + 0.315094i) q^{52} +(6.80793 - 5.71253i) q^{53} +(0.173648 - 0.984808i) q^{54} +(-7.73055 + 2.81369i) q^{55} +1.22668 q^{56} +(-2.82635 - 3.31839i) q^{57} -8.47565 q^{58} +(10.7306 - 3.90560i) q^{59} +(-0.673648 + 3.82045i) q^{60} +(0.0320889 - 0.0269258i) q^{61} +(1.84730 + 1.55007i) q^{62} +(0.213011 + 1.20805i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.950837 - 1.64690i) q^{65} +(1.99273 + 0.725293i) q^{66} +(-4.20574 - 1.53076i) q^{67} +(2.76604 - 4.79093i) q^{68} +(4.47178 + 7.74535i) q^{69} +(-0.826352 - 4.68647i) q^{70} +(2.02094 + 1.69577i) q^{71} +(0.766044 - 0.642788i) q^{72} +(-2.66772 + 15.1294i) q^{73} +(-1.59240 + 0.579585i) q^{74} +10.0496 q^{75} +(-0.0320889 - 4.35878i) q^{76} -2.60132 q^{77} +(-0.460637 + 0.167658i) q^{78} +(-0.809278 + 4.58964i) q^{79} +(-2.97178 + 2.49362i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.277189 + 1.57202i) q^{82} +(-6.24035 - 10.8086i) q^{83} +(-0.613341 + 1.06234i) q^{84} +(-20.1668 - 7.34013i) q^{85} +(6.23783 + 2.27038i) q^{86} +(4.23783 - 7.34013i) q^{87} +(1.06031 + 1.83651i) q^{88} +(1.46838 + 8.32759i) q^{89} +(-2.97178 - 2.49362i) q^{90} +(0.460637 - 0.386520i) q^{91} +(-1.55303 + 8.80769i) q^{92} +(-2.26604 + 0.824773i) q^{93} +2.17024 q^{94} +(-16.6309 + 3.05888i) q^{95} +1.00000 q^{96} +(13.5103 - 4.91734i) q^{97} +(-0.954241 + 5.41177i) q^{98} +(-1.62449 + 1.36310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8	\( 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8} + 6 q^{10} + 12 q^{11} - 3 q^{12} - 21 q^{13} - 3 q^{15} + 3 q^{17} + 6 q^{18} + 6 q^{19} - 12 q^{20} - 9 q^{21} + 3 q^{22} - 15 q^{23} + 9 q^{25} - 3 q^{27} - 9 q^{28} + 15 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{33} - 6 q^{34} - 6 q^{35} + 6 q^{37} + 6 q^{40} - 9 q^{41} - 9 q^{43} + 3 q^{44} + 6 q^{45} + 12 q^{46} - 21 q^{47} - 3 q^{50} + 3 q^{51} + 15 q^{52} + 30 q^{53} - 9 q^{55} - 6 q^{56} - 18 q^{57} - 12 q^{58} + 27 q^{59} - 3 q^{60} - 9 q^{61} + 9 q^{62} + 9 q^{63} - 3 q^{64} - 6 q^{65} - 6 q^{66} - 15 q^{67} + 12 q^{68} + 12 q^{69} - 6 q^{70} + 9 q^{71} + 12 q^{73} - 6 q^{74} + 6 q^{75} + 9 q^{76} + 42 q^{77} + 6 q^{78} + 15 q^{79} - 3 q^{80} - 9 q^{82} - 3 q^{83} + 3 q^{84} - 36 q^{85} + 18 q^{86} + 6 q^{87} + 12 q^{88} - 48 q^{89} - 3 q^{90} - 6 q^{91} + 3 q^{92} - 9 q^{93} - 30 q^{94} - 48 q^{95} + 6 q^{96} + 18 q^{97} - 36 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8 + 6 * q^10 + 12 * q^11 - 3 * q^12 - 21 * q^13 - 3 * q^15 + 3 * q^17 + 6 * q^18 + 6 * q^19 - 12 * q^20 - 9 * q^21 + 3 * q^22 - 15 * q^23 + 9 * q^25 - 3 * q^27 - 9 * q^28 + 15 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^33 - 6 * q^34 - 6 * q^35 + 6 * q^37 + 6 * q^40 - 9 * q^41 - 9 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 - 21 * q^47 - 3 * q^50 + 3 * q^51 + 15 * q^52 + 30 * q^53 - 9 * q^55 - 6 * q^56 - 18 * q^57 - 12 * q^58 + 27 * q^59 - 3 * q^60 - 9 * q^61 + 9 * q^62 + 9 * q^63 - 3 * q^64 - 6 * q^65 - 6 * q^66 - 15 * q^67 + 12 * q^68 + 12 * q^69 - 6 * q^70 + 9 * q^71 + 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 42 * q^77 + 6 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^82 - 3 * q^83 + 3 * q^84 - 36 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 48 * q^89 - 3 * q^90 - 6 * q^91 + 3 * q^92 - 9 * q^93 - 30 * q^94 - 48 * q^95 + 6 * q^96 + 18 * q^97 - 36 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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