LMFDB - Embedded newform 135.2.q.a.122.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.7
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.807333 - 0.565301i) q^{2} +(-0.756415 - 1.55815i) q^{3} +(-0.351818 - 0.966613i) q^{4} +(-2.04189 + 0.911409i) q^{5} +(-0.270145 + 1.68555i) q^{6} +(-0.275357 - 0.590505i) q^{7} +(-0.772562 + 2.88324i) q^{8} +(-1.85567 + 2.35722i) q^{9} +O(q^{10})$	\(q+(-0.807333 - 0.565301i) q^{2} +(-0.756415 - 1.55815i) q^{3} +(-0.351818 - 0.966613i) q^{4} +(-2.04189 + 0.911409i) q^{5} +(-0.270145 + 1.68555i) q^{6} +(-0.275357 - 0.590505i) q^{7} +(-0.772562 + 2.88324i) q^{8} +(-1.85567 + 2.35722i) q^{9} +(2.16371 + 0.418474i) q^{10} +(0.890417 + 1.06116i) q^{11} +(-1.24001 + 1.27935i) q^{12} +(-2.93770 - 4.19546i) q^{13} +(-0.111508 + 0.632393i) q^{14} +(2.96463 + 2.49218i) q^{15} +(0.677632 - 0.568601i) q^{16} +(-1.18168 - 4.41009i) q^{17} +(2.83068 - 0.854048i) q^{18} +(0.00652973 - 0.00376994i) q^{19} +(1.59936 + 1.65307i) q^{20} +(-0.711812 + 0.875714i) q^{21} +(-0.118990 - 1.36006i) q^{22} +(-6.70560 - 3.12687i) q^{23} +(5.07690 - 0.977159i) q^{24} +(3.33867 - 3.72200i) q^{25} +5.04782i q^{26} +(5.07656 + 1.10838i) q^{27} +(-0.473914 + 0.473914i) q^{28} +(-0.586508 - 3.32625i) q^{29} +(-0.984617 - 3.68793i) q^{30} +(3.73277 - 1.35862i) q^{31} +(5.07868 - 0.444327i) q^{32} +(0.979919 - 2.19008i) q^{33} +(-1.53902 + 4.22842i) q^{34} +(1.10044 + 0.954786i) q^{35} +(2.93138 + 0.964404i) q^{36} +(1.60572 - 0.430252i) q^{37} +(-0.00740282 - 0.000647662i) q^{38} +(-4.31505 + 7.75089i) q^{39} +(-1.05032 - 6.59139i) q^{40} +(-1.90299 - 0.335548i) q^{41} +(1.06971 - 0.304606i) q^{42} +(-0.929732 + 10.6269i) q^{43} +(0.712464 - 1.23402i) q^{44} +(1.64070 - 6.50447i) q^{45} +(3.64603 + 6.31511i) q^{46} +(6.61847 - 3.08624i) q^{47} +(-1.39854 - 0.625755i) q^{48} +(4.22664 - 5.03711i) q^{49} +(-4.79947 + 1.11755i) q^{50} +(-5.97775 + 5.17710i) q^{51} +(-3.02186 + 4.31566i) q^{52} +(-1.18766 - 1.18766i) q^{53} +(-3.47191 - 3.76462i) q^{54} +(-2.78529 - 1.35524i) q^{55} +(1.91530 - 0.337719i) q^{56} +(-0.0108133 - 0.00732266i) q^{57} +(-1.40682 + 3.01694i) q^{58} +(-7.77643 - 6.52520i) q^{59} +(1.36596 - 3.74245i) q^{60} +(-9.02437 - 3.28460i) q^{61} +(-3.78162 - 1.01328i) q^{62} +(1.90292 + 0.446706i) q^{63} +(-5.88351 - 3.39685i) q^{64} +(9.82225 + 5.88925i) q^{65} +(-2.02918 + 1.21418i) q^{66} +(-12.3176 + 8.62489i) q^{67} +(-3.84712 + 2.69378i) q^{68} +(0.200077 + 12.8136i) q^{69} +(-0.348682 - 1.39291i) q^{70} +(5.41550 + 3.12664i) q^{71} +(-5.36281 - 7.17145i) q^{72} +(12.1662 + 3.25991i) q^{73} +(-1.53958 - 0.560360i) q^{74} +(-8.32486 - 2.38677i) q^{75} +(-0.00594135 - 0.00498539i) q^{76} +(0.381436 - 0.817993i) q^{77} +(7.86527 - 3.81825i) q^{78} +(-0.782046 + 0.137896i) q^{79} +(-0.865425 + 1.77862i) q^{80} +(-2.11296 - 8.74845i) q^{81} +(1.34666 + 1.34666i) q^{82} +(5.32053 - 7.59850i) q^{83} +(1.09691 + 0.379954i) q^{84} +(6.43227 + 7.92795i) q^{85} +(6.75799 - 8.05386i) q^{86} +(-4.73916 + 3.42989i) q^{87} +(-3.74748 + 1.74748i) q^{88} +(5.89645 + 10.2130i) q^{89} +(-5.00157 + 4.32379i) q^{90} +(-1.66853 + 2.88997i) q^{91} +(-0.663323 + 7.58182i) q^{92} +(-4.94046 - 4.78855i) q^{93} +(-7.08796 - 1.24980i) q^{94} +(-0.00989706 + 0.0136491i) q^{95} +(-4.53392 - 7.57725i) q^{96} +(-2.18091 - 0.190805i) q^{97} +(-6.25979 + 1.67731i) q^{98} +(-4.15370 + 0.129748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.807333	−	0.565301i	−0.570871	−	0.399728i	0.252193	−	0.967677i	$-0.418848\pi$
$2$	−0.807333	−	0.565301i	−0.570871	−	0.399728i	−0.823064	+	0.567949i	$0.807737\pi$
$3$	−0.756415	−	1.55815i	−0.436717	−	0.899599i
$3$	−0.756415	−	1.55815i	−0.436717	−	0.899599i
$4$	−0.351818	−	0.966613i	−0.175909	−	0.483307i
$5$	−2.04189	+	0.911409i	−0.913163	+	0.407595i
$5$	−2.04189	+	0.911409i	−0.913163	+	0.407595i
$6$	−0.270145	+	1.68555i	−0.110286	+	0.688123i
$7$	−0.275357	−	0.590505i	−0.104075	−	0.223190i	0.847374	−	0.530997i	$-0.178183\pi$
$7$	−0.275357	−	0.590505i	−0.104075	−	0.223190i	−0.951449	+	0.307807i	$0.900405\pi$
$8$	−0.772562	+	2.88324i	−0.273142	+	1.01938i
$9$	−1.85567	+	2.35722i	−0.618557	+	0.785740i
$10$	2.16371	+	0.418474i	0.684225	+	0.132333i
$11$	0.890417	+	1.06116i	0.268471	+	0.319951i	0.883390	−	0.468639i	$-0.155256\pi$
$11$	0.890417	+	1.06116i	0.268471	+	0.319951i	−0.614919	+	0.788591i	$0.710811\pi$
$12$	−1.24001	+	1.27935i	−0.357960	+	0.369316i
$13$	−2.93770	−	4.19546i	−0.814770	−	1.16361i	−0.984023	−	0.178040i	$-0.943024\pi$
$13$	−2.93770	−	4.19546i	−0.814770	−	1.16361i	0.169253	−	0.985573i	$-0.445864\pi$
$14$	−0.111508	+	0.632393i	−0.0298018	+	0.169014i
$15$	2.96463	+	2.49218i	0.765465	+	0.643477i
$16$	0.677632	−	0.568601i	0.169408	−	0.142150i
$17$	−1.18168	−	4.41009i	−0.286600	−	1.06961i	−0.947662	−	0.319274i	$-0.896561\pi$
$17$	−1.18168	−	4.41009i	−0.286600	−	1.06961i	0.661063	−	0.750331i	$-0.270106\pi$
$18$	2.83068	−	0.854048i	0.667198	−	0.201301i
$19$	0.00652973	−	0.00376994i	0.00149802	−	0.000864884i	−0.499251	−	0.866458i	$-0.666391\pi$
$19$	0.00652973	−	0.00376994i	0.00149802	−	0.000864884i	0.500749	+	0.865593i	$0.333058\pi$
$20$	1.59936	+	1.65307i	0.357627	+	0.369638i
$21$	−0.711812	+	0.875714i	−0.155330	+	0.191097i
$22$	−0.118990	−	1.36006i	−0.0253687	−	0.289966i
$23$	−6.70560	−	3.12687i	−1.39822	−	0.651998i	−0.430164	−	0.902751i	$-0.641544\pi$
$23$	−6.70560	−	3.12687i	−1.39822	−	0.651998i	−0.968051	+	0.250752i	$0.919322\pi$
$24$	5.07690	−	0.977159i	1.03632	−	0.199462i
$25$	3.33867	−	3.72200i	0.667733	−	0.744401i
$26$			5.04782i			0.989959i
$27$	5.07656	+	1.10838i	0.976985	+	0.213308i
$28$	−0.473914	+	0.473914i	−0.0895613	+	0.0895613i
$29$	−0.586508	−	3.32625i	−0.108912	−	0.617669i	−0.989586	−	0.143946i	$-0.954021\pi$
$29$	−0.586508	−	3.32625i	−0.108912	−	0.617669i	0.880674	−	0.473723i	$-0.157090\pi$
$30$	−0.984617	−	3.68793i	−0.179766	−	0.673320i
$31$	3.73277	−	1.35862i	0.670426	−	0.244015i	0.0156946	−	0.999877i	$-0.495004\pi$
$31$	3.73277	−	1.35862i	0.670426	−	0.244015i	0.654731	+	0.755862i	$0.272782\pi$
$32$	5.07868	−	0.444327i	0.897792	−	0.0785466i
$33$	0.979919	−	2.19008i	0.170582	−	0.381244i
$34$	−1.53902	+	4.22842i	−0.263940	+	0.725168i
$35$	1.10044	+	0.954786i	0.186008	+	0.161388i
$36$	2.93138	+	0.964404i	0.488563	+	0.160734i
$37$	1.60572	−	0.430252i	0.263979	−	0.0707331i	−0.124402	−	0.992232i	$-0.539701\pi$
$37$	1.60572	−	0.430252i	0.263979	−	0.0707331i	0.388381	+	0.921499i	$0.373034\pi$
$38$	−0.00740282		0.000647662i	−0.00120090		0.000105065i
$39$	−4.31505	+	7.75089i	−0.690961	+	1.24114i
$40$	−1.05032	−	6.59139i	−0.166070	−	1.04219i
$41$	−1.90299	−	0.335548i	−0.297197	−	0.0524038i	0.0230615	−	0.999734i	$-0.492659\pi$
$41$	−1.90299	−	0.335548i	−0.297197	−	0.0524038i	−0.320258	+	0.947330i	$0.603770\pi$
$42$	1.06971	−	0.304606i	0.165060	−	0.0470017i
$43$	−0.929732	+	10.6269i	−0.141783	+	1.62058i	0.508617	+	0.860993i	$0.330157\pi$
$43$	−0.929732	+	10.6269i	−0.141783	+	1.62058i	−0.650400	+	0.759592i	$0.725399\pi$
$44$	0.712464	−	1.23402i	0.107408	−	0.186036i
$45$	1.64070	−	6.50447i	0.244580	−	0.969629i
$46$	3.64603	+	6.31511i	0.537578	+	0.931113i
$47$	6.61847	−	3.08624i	0.965403	−	0.450175i	0.125012	−	0.992155i	$-0.460103\pi$
$47$	6.61847	−	3.08624i	0.965403	−	0.450175i	0.840391	+	0.541980i	$0.182325\pi$
$48$	−1.39854	−	0.625755i	−0.201862	−	0.0903200i
$49$	4.22664	−	5.03711i	0.603806	−	0.719587i
$50$	−4.79947	+	1.11755i	−0.678747	+	0.158045i
$51$	−5.97775	+	5.17710i	−0.837053	+	0.724939i
$52$	−3.02186	+	4.31566i	−0.419056	+	0.598474i
$53$	−1.18766	−	1.18766i	−0.163138	−	0.163138i	0.620817	−	0.783955i	$-0.286801\pi$
$53$	−1.18766	−	1.18766i	−0.163138	−	0.163138i	−0.783955	+	0.620817i	$0.786801\pi$
$54$	−3.47191	−	3.76462i	−0.472467	−	0.512300i
$55$	−2.78529	−	1.35524i	−0.375568	−	0.182740i
$56$	1.91530	−	0.337719i	0.255942	−	0.0451295i
$57$	−0.0108133	−	0.00732266i	−0.00143226	−	0.000969911i
$58$	−1.40682	+	3.01694i	−0.184725	+	0.396144i
$59$	−7.77643	−	6.52520i	−1.01240	−	0.849508i	−0.0237505	−	0.999718i	$-0.507561\pi$
$59$	−7.77643	−	6.52520i	−1.01240	−	0.849508i	−0.988654	+	0.150210i	$0.952005\pi$
$60$	1.36596	−	3.74245i	0.176345	−	0.483148i
$61$	−9.02437	−	3.28460i	−1.15545	−	0.420550i	−0.307981	−	0.951392i	$-0.599653\pi$
$61$	−9.02437	−	3.28460i	−1.15545	−	0.420550i	−0.847471	+	0.530842i	$0.821876\pi$
$62$	−3.78162	−	1.01328i	−0.480266	−	0.128687i
$63$	1.90292	+	0.446706i	0.239746	+	0.0562797i
$64$	−5.88351	−	3.39685i	−0.735439	−	0.424606i
$65$	9.82225	+	5.88925i	1.21830	+	0.730472i
$66$	−2.02918	+	1.21418i	−0.249774	+	0.149455i
$67$	−12.3176	+	8.62489i	−1.50484	+	1.05370i	−0.525658	+	0.850696i	$0.676181\pi$
$67$	−12.3176	+	8.62489i	−1.50484	+	1.05370i	−0.979178	+	0.203002i	$0.934930\pi$
$68$	−3.84712	+	2.69378i	−0.466532	+	0.326669i
$69$	0.200077	+	12.8136i	0.0240865	+	1.54257i
$70$	−0.348682	−	1.39291i	−0.0416754	−	0.166485i
$71$	5.41550	+	3.12664i	0.642702	+	0.371064i	0.785654	−	0.618666i	$-0.212326\pi$
$71$	5.41550	+	3.12664i	0.642702	+	0.371064i	−0.142953	+	0.989730i	$0.545660\pi$
$72$	−5.36281	−	7.17145i	−0.632013	−	0.845163i
$73$	12.1662	+	3.25991i	1.42394	+	0.381544i	0.886880	−	0.461999i	$-0.152868\pi$
$73$	12.1662	+	3.25991i	1.42394	+	0.381544i	0.537061	+	0.843543i	$0.319534\pi$
$74$	−1.53958	−	0.560360i	−0.178972	−	0.0651405i
$75$	−8.32486	−	2.38677i	−0.961272	−	0.275600i
$76$	−0.00594135	−	0.00498539i	−0.000681520	−	0.000571863i
$77$	0.381436	−	0.817993i	0.0434687	−	0.0932189i
$78$	7.86527	−	3.81825i	0.890566	−	0.432331i
$79$	−0.782046	+	0.137896i	−0.0879871	+	0.0155145i	−0.217468	−	0.976067i	$-0.569780\pi$
$79$	−0.782046	+	0.137896i	−0.0879871	+	0.0155145i	0.129481	+	0.991582i	$0.458669\pi$
$80$	−0.865425	+	1.77862i	−0.0967575	+	0.198856i
$81$	−2.11296	−	8.74845i	−0.234774	−	0.972050i
$82$	1.34666	+	1.34666i	0.148714	+	0.148714i
$83$	5.32053	−	7.59850i	0.584004	−	0.834044i	−0.413053	−	0.910707i	$-0.635538\pi$
$83$	5.32053	−	7.59850i	0.584004	−	0.834044i	0.997057	+	0.0766627i	$0.0244265\pi$
$84$	1.09691	+	0.379954i	0.119682	+	0.0414564i
$85$	6.43227	+	7.92795i	0.697678	+	0.859907i
$86$	6.75799	−	8.05386i	0.728733	−	0.868470i
$87$	−4.73916	+	3.42989i	−0.508091	+	0.367723i
$88$	−3.74748	+	1.74748i	−0.399482	+	0.186282i
$89$	5.89645	+	10.2130i	0.625023	+	1.08257i	0.988537	+	0.150982i	$0.0482435\pi$
$89$	5.89645	+	10.2130i	0.625023	+	1.08257i	−0.363514	+	0.931589i	$0.618423\pi$
$90$	−5.00157	+	4.32379i	−0.527212	+	0.455767i
$91$	−1.66853	+	2.88997i	−0.174909	+	0.302951i
$92$	−0.663323	+	7.58182i	−0.0691562	+	0.790459i
$93$	−4.94046	−	4.78855i	−0.512302	−	0.496549i
$94$	−7.08796	−	1.24980i	−0.731068	−	0.128907i
$95$	−0.00989706	+	0.0136491i	−0.00101542	+	0.00140037i
$96$	−4.53392	−	7.57725i	−0.462741	−	0.773350i
$97$	−2.18091	−	0.190805i	−0.221438	−	0.0193733i	−0.0241031	−	0.999709i	$-0.507673\pi$
$97$	−2.18091	−	0.190805i	−0.221438	−	0.0193733i	−0.197335	+	0.980336i	$0.563229\pi$
$98$	−6.25979	+	1.67731i	−0.632334	+	0.169433i
$99$	−4.15370	+	0.129748i	−0.417463	+	0.0130401i
$100$	−4.77234	−	1.91773i	−0.477234	−	0.191773i
$101$	2.19882	−	6.04120i	0.218790	−	0.601122i	−0.780934	−	0.624614i	$-0.785256\pi$
$101$	2.19882	−	6.04120i	0.218790	−	0.601122i	0.999724	+	0.0234923i	$0.00747853\pi$
$102$	7.75266	−	0.800417i	0.767627	−	0.0792531i
$103$	9.32840	−	0.816129i	0.919154	−	0.0804156i	0.382250	−	0.924059i	$-0.375149\pi$
$103$	9.32840	−	0.816129i	0.919154	−	0.0804156i	0.536904	+	0.843643i	$0.319594\pi$
$104$	14.3661	−	5.22883i	1.40871	−	0.512729i
$105$	0.655310	−	2.43687i	0.0639517	−	0.237814i
$106$	0.287452	+	1.63022i	0.0279198	+	0.158341i
$107$	2.45371	−	2.45371i	0.237210	−	0.237210i	−0.578484	−	0.815694i	$-0.696356\pi$
$107$	2.45371	−	2.45371i	0.237210	−	0.237210i	0.815694	+	0.578484i	$0.196356\pi$
$108$	−0.714653	−	5.29702i	−0.0687675	−	0.509706i
$109$		−	11.1343i		−	1.06647i	−0.845967	−	0.533235i	$-0.820976\pi$
$109$		−	11.1343i		−	1.06647i	0.845967	−	0.533235i	$-0.179024\pi$
$110$	1.48254	+	2.66865i	0.141354	+	0.254446i
$111$	−1.88499	−	2.17651i	−0.178916	−	0.206585i
$112$	−0.522352	−	0.243577i	−0.0493576	−	0.0230158i
$113$	0.776537	+	8.87586i	0.0730505	+	0.834971i	0.941019	+	0.338353i	$0.109870\pi$
$113$	0.776537	+	8.87586i	0.0730505	+	0.834971i	−0.867969	+	0.496619i	$0.834575\pi$
$114$	0.00459045	+	0.0120246i	0.000429935	+	0.00112621i
$115$	16.5420	+	0.273199i	1.54255	+	0.0254760i
$116$	−3.00885	+	1.73716i	−0.279365	+	0.161291i
$117$	15.3410	+	0.860612i	1.41828	+	0.0795636i
$118$	2.58947	+	9.66403i	0.238380	+	0.889646i
$119$	−2.27880	+	1.91214i	−0.208897	+	0.175285i
$120$	−9.47591	+	6.62239i	−0.865028	+	0.604539i
$121$	1.57692	−	8.94314i	0.143356	−	0.813013i
$122$	5.42888	+	7.75325i	0.491508	+	0.701946i
$123$	0.916615	+	3.21896i	0.0826484	+	0.290244i
$124$	−2.62652	−	3.13016i	−0.235868	−	0.281097i
$125$	−3.42494	+	10.6428i	−0.306336	+	0.951924i
$126$	−1.28377	−	1.43636i	−0.114367	−	0.127961i
$127$	0.737710	−	2.75317i	0.0654611	−	0.244304i	−0.925440	−	0.378893i	$-0.876305\pi$
$127$	0.737710	−	2.75317i	0.0654611	−	0.244304i	0.990902	+	0.134589i	$0.0429714\pi$
$128$	−1.47937	−	3.17252i	−0.130759	−	0.280413i
$129$	17.2616	−	6.58968i	1.51980	−	0.580189i
$130$	−4.60063	−	10.3071i	−0.403502	−	0.903994i
$131$	2.22104	+	6.10227i	0.194053	+	0.533158i	0.998114	−	0.0613901i	$-0.0195534\pi$
$131$	2.22104	+	6.10227i	0.194053	+	0.533158i	−0.804060	+	0.594548i	$0.797331\pi$
$132$	−2.46171	−	0.176692i	−0.214265	−	0.0153791i
$133$	−0.00402417	−	0.00281776i	−0.000348940	−	0.000244330i
$134$	14.8201			1.28026
$135$	−11.3760	+	2.36363i	−0.979090	+	0.203429i
$136$	13.6283			1.16862
$137$	−15.1709	−	10.6228i	−1.29614	−	0.907567i	−0.297256	−	0.954798i	$-0.596071\pi$
$137$	−15.1709	−	10.6228i	−1.29614	−	0.907567i	−0.998884	+	0.0472310i	$0.984960\pi$
$138$	7.08199	−	10.4579i	0.602859	−	0.890237i
$139$	6.75787	+	18.5671i	0.573195	+	1.57484i	0.799424	+	0.600767i	$0.205138\pi$
$139$	6.75787	+	18.5671i	0.573195	+	1.57484i	−0.226229	+	0.974074i	$0.572640\pi$
$140$	0.535753	−	1.39961i	0.0452794	−	0.118289i
$141$	−9.81515	−	7.97810i	−0.826584	−	0.671877i
$142$	−2.60462	−	5.58563i	−0.218575	−	0.468735i
$143$	1.83628	−	6.85307i	0.153557	−	0.573083i
$144$	0.0828540	+	2.65246i	0.00690450	+	0.221039i
$145$	4.22916	+	6.25730i	0.351213	+	0.519641i
$146$	−7.97931	−	9.50937i	−0.660373	−	0.787001i
$147$	−11.0457	−	2.77559i	−0.911032	−	0.228927i
$148$	−0.980811	−	1.40074i	−0.0806222	−	0.115140i
$149$	2.60422	−	14.7692i	0.213346	−	1.20994i	−0.670408	−	0.741992i	$-0.733881\pi$
$149$	2.60422	−	14.7692i	0.213346	−	1.20994i	0.883754	−	0.467952i	$-0.155008\pi$
$150$	5.37169	+	6.63297i	0.438597	+	0.541580i
$151$	0.694966	−	0.583146i	0.0565555	−	0.0474557i	−0.614072	−	0.789250i	$-0.710469\pi$
$151$	0.694966	−	0.583146i	0.0565555	−	0.0474557i	0.670627	+	0.741794i	$0.266025\pi$
$152$	0.00582502	+	0.0217393i	0.000472472	+	0.00176329i
$153$	12.5884	+	5.39821i	1.01771	+	0.436419i
$154$	−0.770358	+	0.444766i	−0.0620772	+	0.0358403i
$155$	−6.38367	+	6.17624i	−0.512749	+	0.496087i
$156$	9.01023	+	1.44408i	0.721395	+	0.115619i
$157$	0.403811	+	4.61558i	0.0322276	+	0.368363i	0.995134	+	0.0985286i	$0.0314136\pi$
$157$	0.403811	+	4.61558i	0.0322276	+	0.368363i	−0.962907	+	0.269835i	$0.913031\pi$
$158$	0.709324	+	0.330763i	0.0564308	+	0.0263141i
$159$	−0.952190	+	2.74892i	−0.0755136	+	0.218003i
$160$	−9.96516	+	5.53602i	−0.787815	+	0.437661i
$161$			4.82070i			0.379924i
$162$	−3.23964	+	8.25737i	−0.254530	+	0.648761i
$163$	−7.94001	+	7.94001i	−0.621909	+	0.621909i	−0.946019	−	0.324110i	$-0.894935\pi$
$163$	−7.94001	+	7.94001i	−0.621909	+	0.621909i	0.324110	+	0.946019i	$0.394935\pi$
$164$	0.345161	+	1.95751i	0.0269526	+	0.152856i
$165$	−0.00483266	+	5.36502i	−0.000376222	+	0.417666i
$166$	−8.59088	+	3.12682i	−0.666782	+	0.242689i
$167$	0.896457	−	0.0784299i	0.0693700	−	0.00606908i	−0.0524179	−	0.998625i	$-0.516693\pi$
$167$	0.896457	−	0.0784299i	0.0693700	−	0.00606908i	0.121788	+	0.992556i	$0.461137\pi$
$168$	−1.97498	−	2.72887i	−0.152373	−	0.210537i
$169$	−4.52560	+	12.4340i	−0.348123	+	0.956461i
$170$	−0.711306	−	10.0367i	−0.0545547	−	0.769777i
$171$	−0.00323046	+	0.0223878i	−0.000247039	+	0.00171204i
$172$	10.5992	−	2.84004i	0.808180	−	0.216551i
$173$	−13.3057	−	1.16409i	−1.01161	−	0.0885045i	−0.430720	−	0.902486i	$-0.641740\pi$
$173$	−13.3057	−	1.16409i	−1.01161	−	0.0885045i	−0.580891	+	0.813981i	$0.697296\pi$
$174$	5.76500	−	0.0900176i	0.437044	−	0.00682422i
$175$	−3.11718	−	0.946619i	−0.235637	−	0.0715577i
$176$	1.20675	+	0.212783i	0.0909622	+	0.0160391i
$177$	−4.28504	+	17.0526i	−0.322083	+	1.28175i
$178$	1.01299	−	11.5785i	0.0759268	−	0.867847i
$179$	−3.72605	+	6.45370i	−0.278498	+	0.482372i	−0.971012	−	0.239032i	$-0.923170\pi$
$179$	−3.72605	+	6.45370i	−0.278498	+	0.482372i	0.692514	+	0.721405i	$0.256503\pi$
$180$	−6.86453	+	0.702475i	−0.511652	+	0.0523594i
$181$	−13.1147	−	22.7153i	−0.974806	−	1.68841i	−0.680574	−	0.732679i	$-0.738270\pi$
$181$	−13.1147	−	22.7153i	−0.974806	−	1.68841i	−0.294232	−	0.955734i	$-0.595064\pi$
$182$	2.98076	−	1.38995i	0.220949	−	0.103030i
$183$	1.70826	+	16.5459i	0.126278	+	1.22310i
$184$	14.1960	−	16.9182i	1.04655	−	1.24722i
$185$	−2.88658	+	2.34200i	−0.212226	+	0.172187i
$186$	1.28163	+	6.65880i	0.0939735	+	0.488247i
$187$	3.62762	−	5.18077i	0.265278	−	0.378856i
$188$	−5.31170	−	5.31170i	−0.387396	−	0.387396i
$189$	−0.743362	−	3.30293i	−0.0540716	−	0.240253i
$190$	0.0157061	−	0.00542454i	0.00113944	−	0.000393537i
$191$	−1.57094	+	0.276999i	−0.113669	+	0.0200430i	−0.230193	−	0.973145i	$-0.573936\pi$
$191$	−1.57094	+	0.276999i	−0.113669	+	0.0200430i	0.116524	+	0.993188i	$0.462825\pi$
$192$	−0.842424	+	11.7368i	−0.0607967	+	0.847033i
$193$	−3.55560	+	7.62500i	−0.255937	+	0.548860i	−0.991729	−	0.128348i	$-0.959032\pi$
$193$	−3.55560	+	7.62500i	−0.255937	+	0.548860i	0.735792	+	0.677208i	$0.236810\pi$
$194$	1.65286	+	1.38691i	0.118668	+	0.0995745i
$195$	1.74665	−	19.7593i	0.125080	−	1.41499i
$196$	−6.35595	−	2.31338i	−0.453996	−	0.165241i
$197$	−10.9609	−	2.93696i	−0.780931	−	0.209250i	−0.153736	−	0.988112i	$-0.549131\pi$
$197$	−10.9609	−	2.93696i	−0.780931	−	0.209250i	−0.627195	+	0.778862i	$0.715797\pi$
$198$	3.42677	+	2.24334i	0.243530	+	0.159427i
$199$	−21.0022	−	12.1256i	−1.48881	−	0.859563i	−0.488889	−	0.872346i	$-0.662598\pi$
$199$	−21.0022	−	12.1256i	−1.48881	−	0.859563i	−0.999918	+	0.0127826i	$0.995931\pi$
$200$	8.15210	+	12.5017i	0.576441	+	0.884001i
$201$	22.7561	+	12.6687i	1.60509	+	0.893582i
$202$	−5.19027	+	3.63427i	−0.365186	+	0.255706i
$203$	−1.80267	+	1.26224i	−0.126522	+	0.0885920i
$204$	7.10734	+	3.95678i	0.497613	+	0.277030i
$205$	4.19153	−	1.04925i	0.292749	−	0.0732826i
$206$	−7.99248	−	4.61446i	−0.556863	−	0.321505i
$207$	19.8141	−	10.0041i	1.37718	−	0.695335i
$208$	−4.37622	−	1.17261i	−0.303436	−	0.0813055i
$209$	0.00981468	+	0.00357225i	0.000678896	+	0.000247098i
$210$	−1.90662	+	1.59692i	−0.131569	+	0.110198i
$211$	6.98736	+	5.86309i	0.481029	+	0.403632i	0.850799	−	0.525492i	$-0.176119\pi$
$211$	6.98736	+	5.86309i	0.481029	+	0.403632i	−0.369769	+	0.929124i	$0.620563\pi$
$212$	−0.730167	+	1.56585i	−0.0501481	+	0.107543i
$213$	0.775412	−	10.8032i	0.0531304	−	0.740224i
$214$	−3.36805	+	0.593878i	−0.230235	+	0.0405967i
$215$	−7.78703	−	22.5463i	−0.531071	−	1.53765i
$216$	−7.11769	+	13.7807i	−0.484297	+	0.937655i
$217$	−1.83011	−	1.83011i	−0.124236	−	0.124236i
$218$	−6.29421	+	8.98907i	−0.426298	+	0.608817i
$219$	−4.12323	−	21.4226i	−0.278622	−	1.44760i
$220$	−0.330076	+	3.16909i	−0.0222537	+	0.213660i
$221$	−15.0310	+	17.9132i	−1.01109	+	1.20497i
$222$	0.291433	+	2.82276i	0.0195597	+	0.189451i
$223$	14.8136	−	6.90768i	0.991990	−	0.462572i	0.142282	−	0.989826i	$-0.454556\pi$
$223$	14.8136	−	6.90768i	0.991990	−	0.462572i	0.849708	+	0.527254i	$0.176778\pi$
$224$	−1.66083	−	2.87663i	−0.110969	−	0.192203i
$225$	2.57811	+	14.7768i	0.171874	+	0.985119i
$226$	4.39061	−	7.60476i	0.292059	−	0.505861i
$227$	1.10129	−	12.5878i	0.0730949	−	0.835479i	−0.867830	−	0.496862i	$-0.834485\pi$
$227$	1.10129	−	12.5878i	0.0730949	−	0.835479i	0.940924	−	0.338617i	$-0.109959\pi$
$228$	−0.00327386	+	0.0130286i	−0.000216817	+	0.000862837i
$229$	8.89322	+	1.56812i	0.587681	+	0.103624i	0.459579	−	0.888137i	$-0.348000\pi$
$229$	8.89322	+	1.56812i	0.587681	+	0.103624i	0.128102	+	0.991761i	$0.459112\pi$
$230$	−13.2005	−	9.57177i	−0.870413	−	0.631144i
$231$	−1.56308	+	0.0244067i	−0.102843	+	0.00160584i
$232$	10.0435	+	0.878692i	0.659388	+	0.0576889i
$233$	20.6198	−	5.52507i	1.35085	−	0.361959i	0.490402	−	0.871496i	$-0.336850\pi$
$233$	20.6198	−	5.52507i	1.35085	−	0.361959i	0.860449	+	0.509537i	$0.170183\pi$
$234$	−11.8988	−	9.36710i	−0.777850	−	0.612346i
$235$	−10.7014	+	12.3339i	−0.698081	+	0.804576i
$236$	−3.57145	+	9.81248i	−0.232482	+	0.638738i
$237$	0.806414	+	1.11424i	0.0523822	+	0.0723776i
$238$	2.92068	−	0.255527i	0.189320	−	0.0165633i
$239$	−5.43398	+	1.97781i	−0.351495	+	0.127934i	−0.511733	−	0.859145i	$-0.670996\pi$
$239$	−5.43398	+	1.97781i	−0.351495	+	0.127934i	0.160238	+	0.987078i	$0.448774\pi$
$240$	3.42599	+	0.00308603i	0.221146	+	0.000199203i
$241$	−4.00297	−	22.7020i	−0.257854	−	1.46236i	−0.788639	−	0.614857i	$-0.789214\pi$
$241$	−4.00297	−	22.7020i	−0.257854	−	1.46236i	0.530784	−	0.847507i	$-0.321897\pi$
$242$	−6.32866	+	6.32866i	−0.406822	+	0.406822i
$243$	−12.0331	+	9.90978i	−0.771926	+	0.635713i
$244$			9.87866i			0.632416i
$245$	−4.03948	+	14.1374i	−0.258073	+	0.903208i
$246$	1.07967	−	3.11694i	0.0688370	−	0.198729i
$247$	−0.0349990	−	0.0163203i	−0.00222693	−	0.00103844i
$248$	1.03342	+	11.8121i	0.0656225	+	0.750069i
$249$	−15.8642	−	2.54257i	−1.00535	−	0.161129i
$250$	8.78146	−	6.65619i	0.555389	−	0.420974i
$251$	−2.17404	+	1.25518i	−0.137224	+	0.0792266i	−0.567041	−	0.823690i	$-0.691912\pi$
$251$	−2.17404	+	1.25518i	−0.137224	+	0.0792266i	0.429816	+	0.902916i	$0.358578\pi$
$252$	−0.237690	−	1.99655i	−0.0149731	−	0.125771i
$253$	−2.65268	−	9.89993i	−0.166772	−	0.622403i
$254$	−2.15195	+	1.80570i	−0.135025	+	0.113300i
$255$	7.48749	−	16.0193i	0.468885	−	1.00317i
$256$	−2.95851	+	16.7785i	−0.184907	+	1.04866i
$257$	7.24292	+	10.3440i	0.451801	+	0.645238i	0.978846	−	0.204599i	$-0.0655890\pi$
$257$	7.24292	+	10.3440i	0.451801	+	0.645238i	−0.527045	+	0.849837i	$0.676700\pi$
$258$	−17.6610	−	4.43791i	−1.09952	−	0.276292i
$259$	−0.696213	−	0.829715i	−0.0432606	−	0.0515560i
$260$	2.23698	−	11.5663i	0.138732	−	0.717309i
$261$	8.92907	+	4.78990i	0.552695	+	0.296487i
$262$	1.65649	−	6.18212i	0.102339	−	0.381933i
$263$	7.09675	+	15.2190i	0.437604	+	0.938445i	0.994188	+	0.107654i	$0.0343339\pi$
$263$	7.09675	+	15.2190i	0.437604	+	0.938445i	−0.556584	+	0.830791i	$0.687888\pi$
$264$	5.55748	+	4.51732i	0.342039	+	0.278022i
$265$	3.50752	+	1.34263i	0.215465	+	0.0824772i
$266$	0.00165597	+	0.00454974i	0.000101534	+	0.000278962i
$267$	11.4532	−	16.9128i	0.700922	−	1.03505i
$268$	12.6705	+	8.87198i	0.773974	+	0.541942i
$269$	−3.27377			−0.199605			−0.0998027	−	0.995007i	$-0.531821\pi$
$269$	−3.27377			−0.199605			−0.0998027	+	0.995007i	$0.531821\pi$
$270$	10.5204	+	4.52262i	0.640250	+	0.275238i
$271$	8.46872			0.514438			0.257219	−	0.966353i	$-0.417194\pi$
$271$	8.46872			0.514438			0.257219	+	0.966353i	$0.417194\pi$
$272$	−3.30833	−	2.31652i	−0.200597	−	0.140459i
$273$	5.76511	+	0.413798i	0.348921	+	0.0250442i
$274$	6.24292	+	17.1523i	0.377148	+	1.03621i
$275$	6.92244	+	0.228717i	0.417439	+	0.0137922i
$276$	12.3154	−	4.70145i	0.741298	−	0.282994i
$277$	−1.04261	−	2.23589i	−0.0626445	−	0.134342i	0.872493	−	0.488627i	$-0.162502\pi$
$277$	−1.04261	−	2.23589i	−0.0626445	−	0.134342i	−0.935137	+	0.354285i	$0.884724\pi$
$278$	5.04014	−	18.8101i	0.302288	−	1.12815i
$279$	−3.72424	+	11.3201i	−0.222964	+	0.677717i
$280$	−3.60304	+	2.43521i	−0.215323	+	0.145531i
$281$	−12.4917	−	14.8870i	−0.745190	−	0.888082i	0.251626	−	0.967825i	$-0.419035\pi$
$281$	−12.4917	−	14.8870i	−0.745190	−	0.888082i	−0.996816	+	0.0797423i	$0.974590\pi$
$282$	3.41407	+	11.9895i	0.203305	+	0.713964i
$283$	−10.8099	−	15.4382i	−0.642583	−	0.917703i	0.357285	−	0.933996i	$-0.383703\pi$
$283$	−10.8099	−	15.4382i	−0.642583	−	0.917703i	−0.999867	+	0.0162923i	$0.994814\pi$
$284$	1.11698	−	6.33470i	0.0662805	−	0.375896i
$285$	0.0287536	+	0.00509675i	0.00170322	+	0.000301905i
$286$	−5.35653	+	4.49466i	−0.316738	+	0.265775i
$287$	0.325858	+	1.21612i	0.0192348	+	0.0717853i
$288$	−8.37698	+	12.7961i	−0.493619	+	0.754016i
$289$	−3.33013	+	1.92265i	−0.195890	+	0.113097i
$290$	0.122916	−	7.44248i	0.00721789	−	0.437037i
$291$	1.35237	+	3.54252i	0.0792774	+	0.207666i
$292$	−1.12920	−	12.9069i	−0.0660817	−	0.755317i
$293$	3.65580	+	1.70473i	0.213574	+	0.0995913i	0.526461	−	0.850199i	$-0.323518\pi$
$293$	3.65580	+	1.70473i	0.213574	+	0.0995913i	−0.312887	+	0.949790i	$0.601296\pi$
$294$	7.34850	+	8.48496i	0.428573	+	0.494853i
$295$	21.8258	+	6.23626i	1.27075	+	0.363089i
$296$			4.96208i			0.288415i
$297$	3.34409	+	6.37396i	0.194044	+	0.369854i
$298$	−10.4515	+	10.4515i	−0.605441	+	0.605441i
$299$	6.58033	+	37.3189i	0.380551	+	2.15821i
$300$	0.621758	+	8.88663i	0.0358972	+	0.513070i
$301$	6.53123	−	2.37717i	0.376454	−	0.137018i
$302$	−0.890722	+	0.0779280i	−0.0512553	+	0.00448426i
$303$	−11.0763	+	1.14357i	−0.636318	+	0.0656961i
$304$	0.00228116	−	0.00626744i	0.000130834	−	0.000359462i
$305$	21.4204	−	1.51808i	1.22653	−	0.0869251i
$306$	−7.11140	−	11.4744i	−0.406532	−	0.655946i
$307$	8.60536	−	2.30580i	0.491134	−	0.131599i	−0.00474824	−	0.999989i	$-0.501511\pi$
$307$	8.60536	−	2.30580i	0.491134	−	0.131599i	0.495882	+	0.868390i	$0.334845\pi$
$308$	−0.924879	−	0.0809164i	−0.0526999	−	0.00461064i
$309$	−8.32780	−	13.9177i	−0.473752	−	0.791752i
$310$	8.64518	−	1.37759i	0.491013	−	0.0782417i
$311$	26.8272	+	4.73035i	1.52123	+	0.268234i	0.870916	−	0.491433i	$-0.163527\pi$
$311$	26.8272	+	4.73035i	1.52123	+	0.268234i	0.650313	+	0.759666i	$0.274638\pi$
$312$	−19.0140	−	18.4294i	−1.07646	−	1.04336i
$313$	1.36924	−	15.6505i	0.0773941	−	0.884618i	−0.853921	−	0.520403i	$-0.825782\pi$
$313$	1.36924	−	15.6505i	0.0773941	−	0.884618i	0.931315	−	0.364215i	$-0.118663\pi$
$314$	2.28318	−	3.95459i	0.128847	−	0.223170i
$315$	−4.29270	+	0.822212i	−0.241866	+	0.0463264i
$316$	0.408430	+	0.707422i	0.0229760	+	0.0397956i
$317$	12.8207	−	5.97838i	0.720081	−	0.335779i	−0.0277988	−	0.999614i	$-0.508850\pi$
$317$	12.8207	−	5.97838i	0.720081	−	0.335779i	0.747880	+	0.663834i	$0.231072\pi$
$318$	2.32270	−	1.68102i	0.130251	−	0.0942669i
$319$	3.00744	−	3.58413i	0.168384	−	0.200673i
$320$	15.1094	+	1.57372i	0.844643	+	0.0879735i
$321$	−5.67929	−	1.96723i	−0.316987	−	0.109800i
$322$	2.72514	−	3.89191i	0.151866	−	0.216888i
$323$	−0.0243419	−	0.0243419i	−0.00135442	−	0.00135442i
$324$	−7.71299	+	5.12029i	−0.428499	+	0.284460i
$325$	−25.4235	−	3.07315i	−1.41024	−	0.170467i
$326$	10.8987	−	1.92174i	0.603624	−	0.106435i
$327$	−17.3489	+	8.42214i	−0.959396	+	0.465745i
$328$	2.43764	−	5.22754i	0.134596	−	0.288643i
$329$	−3.64488	−	3.05842i	−0.200949	−	0.168616i
$330$	3.03675	−	4.32863i	0.167168	−	0.238283i
$331$	15.8479	+	5.76816i	0.871078	+	0.317047i	0.738604	−	0.674140i	$-0.235485\pi$
$331$	15.8479	+	5.76816i	0.871078	+	0.317047i	0.132475	+	0.991186i	$0.457708\pi$
$332$	−9.21668	−	2.46960i	−0.505831	−	0.135537i
$333$	−1.96550	+	4.58345i	−0.107709	+	0.251172i
$334$	−0.768076	−	0.443449i	−0.0420273	−	0.0242645i
$335$	17.2905	−	28.8375i	0.944680	−	1.57556i
$336$	0.0155856	+	0.998149i	0.000850264	+	0.0544535i
$337$	−16.0410	+	11.2321i	−0.873811	+	0.611849i	−0.922086	−	0.386985i	$-0.873516\pi$
$337$	−16.0410	+	11.2321i	−0.873811	+	0.611849i	0.0482752	+	0.998834i	$0.484628\pi$
$338$	10.6826	−	7.48005i	0.581058	−	0.406861i
$339$	13.2426	−	7.92380i	0.719237	−	0.430362i
$340$	5.40027	−	9.00672i	0.292871	−	0.488458i
$341$	4.76543	+	2.75132i	0.258063	+	0.148993i
$342$	0.0152639	−	0.0162482i	0.000825376	−	0.000878603i
$343$	−8.54371	−	2.28928i	−0.461317	−	0.123610i
$344$	−29.9216	−	10.8906i	−1.61326	−	0.587180i
$345$	−12.0869	−	25.9816i	−0.650739	−	1.39880i
$346$	10.0840	+	8.46151i	0.542121	+	0.454894i
$347$	4.69183	−	10.0617i	0.251871	−	0.540138i	−0.739199	−	0.673488i	$-0.764795\pi$
$347$	4.69183	−	10.0617i	0.251871	−	0.540138i	0.991069	+	0.133349i	$0.0425733\pi$
$348$	4.98270	+	3.37423i	0.267101	+	0.180878i
$349$	−5.91569	+	1.04309i	−0.316659	+	0.0558356i	−0.329719	−	0.944079i	$-0.606954\pi$
$349$	−5.91569	+	1.04309i	−0.316659	+	0.0558356i	0.0130596	+	0.999915i	$0.495843\pi$
$350$	1.98148	+	2.52638i	0.105915	+	0.135041i
$351$	−10.2632	−	24.5546i	−0.547810	−	1.31063i
$352$	4.99364	+	4.99364i	0.266162	+	0.266162i
$353$	6.60297	−	9.43001i	0.351440	−	0.501909i	−0.604044	−	0.796951i	$-0.706445\pi$
$353$	6.60297	−	9.43001i	0.351440	−	0.501909i	0.955484	+	0.295042i	$0.0953337\pi$
$354$	13.0993	−	11.3448i	0.696220	−	0.602969i
$355$	−13.9075	−	1.44853i	−0.738135	−	0.0768802i
$356$	7.79749	−	9.29269i	0.413266	−	0.492512i
$357$	4.70312	+	2.10434i	0.248915	+	0.111374i
$358$	6.65644	−	3.10395i	0.351804	−	0.164049i
$359$	7.64807	+	13.2468i	0.403649	+	0.699141i	0.994163	−	0.107886i	$-0.0344082\pi$
$359$	7.64807	+	13.2468i	0.403649	+	0.699141i	−0.590514	+	0.807028i	$0.701075\pi$
$360$	17.4864	+	9.75562i	0.921615	+	0.514167i
$361$	−9.49997	+	16.4544i	−0.499999	+	0.866023i
$362$	−2.25305	+	25.7525i	−0.118418	+	1.35352i
$363$	−15.1276	+	4.30765i	−0.793991	+	0.226093i
$364$	3.38050	+	0.596074i	0.177187	+	0.0312428i
$365$	−27.8131	+	4.43195i	−1.45581	+	0.231979i
$366$	7.97424	−	14.3237i	0.416820	−	0.748712i
$367$	−12.8423	−	1.12355i	−0.670361	−	0.0586490i	−0.253106	−	0.967439i	$-0.581452\pi$
$367$	−12.8423	−	1.12355i	−0.670361	−	0.0586490i	−0.417255	+	0.908790i	$0.637008\pi$
$368$	−6.32188	+	1.69394i	−0.329551	+	0.0883028i
$369$	4.32228	−	3.86309i	0.225009	−	0.201105i
$370$	3.65437	−	0.258988i	0.189982	−	0.0134641i
$371$	−0.374288	+	1.02835i	−0.0194321	+	0.0533892i
$372$	−2.89053	+	6.46021i	−0.149867	+	0.334946i
$373$	−16.1018	+	1.40873i	−0.833720	+	0.0729411i	−0.496018	−	0.868312i	$-0.665205\pi$
$373$	−16.1018	+	1.40873i	−0.833720	+	0.0729411i	−0.337702	+	0.941253i	$0.609650\pi$
$374$	−5.85739	+	2.13192i	−0.302878	+	0.110239i
$375$	19.1738	−	2.71383i	0.990132	−	0.140141i
$376$	3.78520	+	21.4670i	0.195207	+	1.10707i
$377$	−12.2322	+	12.2322i	−0.629989	+	0.629989i
$378$	−1.26701	+	3.08679i	−0.0651680	+	0.158767i
$379$			9.64380i			0.495369i	0.968841	+	0.247684i	$0.0796696\pi$
$379$			9.64380i			0.495369i	−0.968841	+	0.247684i	$0.920330\pi$
$380$	0.0166753	+	0.00476463i	0.000855427	+	0.000244420i
$381$	−4.84787	+	0.933076i	−0.248364	+	0.0478029i
$382$	1.42486	+	0.664424i	0.0729023	+	0.0339949i
$383$	−1.26741	−	14.4866i	−0.0647619	−	0.740232i	−0.957269	−	0.289199i	$-0.906611\pi$
$383$	−1.26741	−	14.4866i	−0.0647619	−	0.740232i	0.892507	−	0.451033i	$-0.148944\pi$
$384$	−3.82424	+	4.70482i	−0.195155	+	0.240092i
$385$	−0.0333266	+	2.01790i	−0.00169848	+	0.102842i
$386$	7.18097	−	4.14594i	0.365502	−	0.211023i
$387$	−23.3246	−	21.9116i	−1.18566	−	1.11383i
$388$	0.582850	+	2.17522i	0.0295897	+	0.110430i
$389$	−12.6045	+	10.5764i	−0.639073	+	0.536246i	−0.903733	−	0.428096i	$-0.859185\pi$
$389$	−12.6045	+	10.5764i	−0.639073	+	0.536246i	0.264660	+	0.964342i	$0.414740\pi$
$390$	−12.5801	+	14.9649i	−0.637016	+	0.757779i
$391$	−5.86593	+	33.2673i	−0.296653	+	1.68240i
$392$	11.2579	+	16.0779i	0.568608	+	0.812056i
$393$	7.82823	−	8.07657i	0.394882	−	0.407409i
$394$	7.18883	+	8.56731i	0.362168	+	0.431615i
$395$	1.47118	−	0.994333i	0.0740229	−	0.0500303i
$396$	1.58677	+	3.96938i	0.0797380	+	0.199469i
$397$	−5.64123	+	21.0533i	−0.283125	+	1.05664i	0.667073	+	0.744992i	$0.267547\pi$
$397$	−5.64123	+	21.0533i	−0.283125	+	1.05664i	−0.950199	+	0.311645i	$0.899120\pi$
$398$	10.1012	+	21.6620i	0.506325	+	1.08582i
$399$	−0.00134655	+	0.00840166i	−6.74116e−5	+	0.000420609i
$400$	0.146054	−	4.42052i	0.00730270	−	0.221026i
$401$	9.14946	+	25.1379i	0.456902	+	1.25533i	0.927779	+	0.373130i	$0.121715\pi$
$401$	9.14946	+	25.1379i	0.456902	+	1.25533i	−0.470877	+	0.882199i	$0.656062\pi$
$402$	−11.2101	−	23.0919i	−0.559111	−	1.15172i
$403$	−16.6658	−	11.6695i	−0.830182	−	0.581300i
$404$	−6.61309			−0.329013
$405$	12.2879	+	15.9376i	0.610589	+	0.791948i
$406$	2.16890			0.107641
$407$	1.88633	+	1.32082i	0.0935019	+	0.0654707i
$408$	−10.3086	−	21.2349i	−0.510354	−	1.05129i
$409$	−6.85481	−	18.8334i	−0.338949	−	0.931253i	−0.985694	−	0.168547i	$-0.946092\pi$
$409$	−6.85481	−	18.8334i	−0.338949	−	0.931253i	0.646745	−	0.762706i	$-0.276130\pi$
$410$	−3.97710	−	1.52238i	−0.196415	−	0.0751850i
$411$	−5.07641	+	31.6738i	−0.250401	+	1.56236i
$412$	−4.07078	−	8.72982i	−0.200553	−	0.430088i
$413$	−1.71187	+	6.38878i	−0.0842355	+	0.314371i
$414$	−21.6519	−	3.12428i	−1.06414	−	0.153550i
$415$	−3.93862	+	20.3645i	−0.193339	+	0.999655i
$416$	−16.7838	−	20.0021i	−0.822892	−	0.980684i
$417$	23.8186	−	24.5742i	1.16640	−	1.20341i
$418$	−0.00590432	−	0.00843224i	−0.000288790	−	0.000412435i
$419$	0.389697	−	2.21008i	0.0190379	−	0.107969i	−0.973808	−	0.227372i	$-0.926987\pi$
$419$	0.389697	−	2.21008i	0.0190379	−	0.107969i	0.992846	+	0.119402i	$0.0380978\pi$
$420$	−2.58606	+	0.223904i	−0.126187	+	0.0109254i
$421$	−17.9696	+	15.0783i	−0.875786	+	0.734872i	−0.965308	−	0.261113i	$-0.915911\pi$
$421$	−17.9696	+	15.0783i	−0.875786	+	0.734872i	0.0895219	+	0.995985i	$0.471466\pi$
$422$	−2.32672	−	8.68342i	−0.113263	−	0.422702i
$423$	−5.00676	+	21.3282i	−0.243437	+	1.03701i
$424$	4.34185	−	2.50677i	0.210859	−	0.121739i
$425$	−20.3596	−	10.3256i	−0.987587	−	0.500866i
$426$	−6.73308	+	8.28345i	−0.326219	+	0.401334i
$427$	0.545349	+	6.23337i	0.0263913	+	0.301654i
$428$	−3.23505	−	1.50853i	−0.156372	−	0.0729176i
$429$	−12.0671	+	2.32257i	−0.582606	+	0.112135i
$430$	−6.45874	+	22.6044i	−0.311468	+	1.09008i
$431$		−	15.7591i		−	0.759089i	−0.925173	−	0.379545i	$-0.876081\pi$
$431$		−	15.7591i		−	0.759089i	0.925173	−	0.379545i	$-0.123919\pi$
$432$	4.07027	−	2.13546i	0.195831	−	0.102743i
$433$	14.0286	−	14.0286i	0.674170	−	0.674170i	−0.284505	−	0.958675i	$-0.591829\pi$
$433$	14.0286	−	14.0286i	0.674170	−	0.674170i	0.958675	+	0.284505i	$0.0918291\pi$
$434$	0.442947	+	2.51208i	0.0212621	+	0.120584i
$435$	6.55082	−	11.3228i	0.314088	−	0.542886i
$436$	−10.7625	+	3.91724i	−0.515432	+	0.187602i
$437$	−0.0555739	+	0.00486209i	−0.00265846	+	0.000232585i
$438$	−8.78137	+	19.6260i	−0.419590	+	0.937767i
$439$	1.43394	−	3.93972i	0.0684382	−	0.188033i	−0.900759	−	0.434320i	$-0.856989\pi$
$439$	1.43394	−	3.93972i	0.0684382	−	0.188033i	0.969197	+	0.246288i	$0.0792108\pi$
$440$	6.05928	−	6.98365i	0.288865	−	0.332932i
$441$	4.03032	+	19.3103i	0.191920	+	0.919540i
$442$	22.2614	−	5.96491i	1.05886	−	0.283722i
$443$	21.2489	+	1.85904i	1.00957	+	0.0883257i	0.579922	−	0.814672i	$-0.303083\pi$
$443$	21.2489	+	1.85904i	1.00957	+	0.0883257i	0.429646	+	0.902998i	$0.358639\pi$
$444$	−1.44067	+	2.58780i	−0.0683712	+	0.122811i
$445$	−21.3481	−	15.4797i	−1.01200	−	0.733808i
$446$	−15.8644	−	2.79732i	−0.751201	−	0.132457i
$447$	−24.9826	+	7.11392i	−1.18164	+	0.336477i
$448$	−0.385789	+	4.40959i	−0.0182268	+	0.208333i
$449$	9.32000	−	16.1427i	0.439838	−	0.761822i	−0.557839	−	0.829949i	$-0.688369\pi$
$449$	9.32000	−	16.1427i	0.439838	−	0.761822i	0.997677	+	0.0681276i	$0.0217025\pi$
$450$	6.27194	−	13.3872i	0.295662	−	0.631078i
$451$	−1.33838	−	2.31815i	−0.0630221	−	0.109157i
$452$	8.30633	−	3.87330i	0.390697	−	0.182185i
$453$	−1.43431	−	0.641762i	−0.0673899	−	0.0301526i
$454$	−8.00497	+	9.53996i	−0.375692	+	0.447732i
$455$	0.773008	−	7.42173i	0.0362392	−	0.347936i
$456$	0.0294670	−	0.0255202i	0.00137992	−	0.00119509i
$457$	8.19900	−	11.7094i	0.383533	−	0.547742i	−0.580247	−	0.814441i	$-0.697044\pi$
$457$	8.19900	−	11.7094i	0.383533	−	0.547742i	0.963780	+	0.266699i	$0.0859328\pi$
$458$	−6.29334	−	6.29334i	−0.294068	−	0.294068i
$459$	−1.11081	−	23.6979i	−0.0518483	−	1.10612i
$460$	−5.55570	−	16.0858i	−0.259036	−	0.750006i
$461$	24.9949	−	4.40727i	1.16413	−	0.205267i	0.441992	−	0.897019i	$-0.354272\pi$
$461$	24.9949	−	4.40727i	1.16413	−	0.205267i	0.722135	+	0.691752i	$0.243161\pi$
$462$	1.27572	+	0.863906i	0.0593520	+	0.0401926i
$463$	−5.43841	+	11.6627i	−0.252744	+	0.542012i	−0.991213	−	0.132276i	$-0.957772\pi$
$463$	−5.43841	+	11.6627i	−0.252744	+	0.542012i	0.738469	+	0.674288i	$0.235549\pi$
$464$	−2.28875	−	1.92049i	−0.106252	−	0.0891563i
$465$	14.4522	+	5.27493i	0.670206	+	0.244619i
$466$	−19.7704	−	7.19584i	−0.915846	−	0.333341i
$467$	26.2781	+	7.04119i	1.21600	+	0.325828i	0.809115	−	0.587650i	$-0.199947\pi$
$467$	26.2781	+	7.04119i	1.21600	+	0.325828i	0.406890	+	0.913477i	$0.366613\pi$
$468$	−4.56538	−	15.1316i	−0.211035	−	0.699459i
$469$	8.48478	+	4.89869i	0.391791	+	0.226200i
$470$	15.6120	−	3.90808i	0.720126	−	0.180266i
$471$	6.88633	−	4.12050i	0.317305	−	0.189862i
$472$	24.8215	−	17.3802i	1.14250	−	0.799988i
$473$	−12.1047	+	8.47577i	−0.556572	+	0.389716i
$474$	−0.0211643	−	1.35543i	−0.000972111	−	0.0622569i
$475$	0.00776886	−	0.0368902i	0.000356460	−	0.00169264i
$476$	2.65002	+	1.52999i	0.121464	+	0.0701270i
$477$	5.00348	−	0.595668i	0.229094	−	0.0272737i
$478$	5.50508	+	1.47508i	0.251797	+	0.0674687i
$479$	−17.2415	−	6.27539i	−0.787784	−	0.286730i	−0.0833693	−	0.996519i	$-0.526568\pi$
$479$	−17.2415	−	6.27539i	−0.787784	−	0.286730i	−0.704415	+	0.709789i	$0.748790\pi$
$480$	16.1638	+	11.3397i	0.737771	+	0.517584i
$481$	−6.52224	−	5.47281i	−0.297388	−	0.249538i
$482$	−9.60172	+	20.5910i	−0.437346	+	0.937892i
$483$	7.51138	−	3.64645i	0.341779	−	0.165919i
$484$	−9.19935	+	1.62209i	−0.418152	+	0.0737315i
$485$	4.62709	−	1.59810i	0.210105	−	0.0725659i
$486$	15.3168	−	1.19815i	0.694782	−	0.0543494i
$487$	4.34114	+	4.34114i	0.196716	+	0.196716i	0.798591	−	0.601875i	$-0.205579\pi$
$487$	4.34114	+	4.34114i	0.196716	+	0.196716i	−0.601875	+	0.798591i	$0.705579\pi$
$488$	16.4422	−	23.4819i	0.744302	−	1.06297i
$489$	18.3777	+	6.36579i	0.831067	+	0.287871i
$490$	11.2531	−	9.13011i	0.508364	−	0.412456i
$491$	17.5435	−	20.9075i	0.791728	−	0.943544i	−0.207672	−	0.978199i	$-0.566589\pi$
$491$	17.5435	−	20.9075i	0.791728	−	0.943544i	0.999399	+	0.0346544i	$0.0110331\pi$
$492$	2.78901	−	2.01850i	0.125738	−	0.0910011i
$493$	−13.9760	+	6.51712i	−0.629448	+	0.293516i
$494$	0.0190300	+	0.0329609i	0.000856199	+	0.00148298i
$495$	8.36317	−	4.05065i	0.375897	−	0.182063i
$496$	1.75694	−	3.04310i	0.0788887	−	0.136639i
$497$	0.355101	−	4.05882i	0.0159284	−	0.182063i
$498$	11.3703	+	11.0207i	0.509517	+	0.493850i
$499$	43.3225	+	7.63893i	1.93938	+	0.341965i	1.00000		0.000905893i	$-0.000288355\pi$
$499$	43.3225	+	7.63893i	1.93938	+	0.341965i	0.939382	+	0.342871i	$0.111399\pi$
$500$	11.4925	−	0.433752i	0.513958	−	0.0193980i
$501$	−0.800300	−	1.33749i	−0.0357548	−	0.0597547i
$502$	2.46473	+	0.215636i	0.110006	+	0.00962432i
$503$	−4.03331	+	1.08072i	−0.179836	+	0.0481870i	−0.347613	−	0.937638i	$-0.613008\pi$
$503$	−4.03331	+	1.08072i	−0.179836	+	0.0481870i	0.167777	+	0.985825i	$0.446341\pi$
$504$	−2.75809	+	5.14147i	−0.122855	+	0.229019i
$505$	1.01625	+	14.3395i	0.0452226	+	0.638100i
$506$	−3.45484	+	9.49210i	−0.153586	+	0.421975i
$507$	22.7973	−	2.35369i	1.01246	−	0.104531i
$508$	−2.92079	+	0.255536i	−0.129589	+	0.0113376i
$509$	−1.50937	+	0.549366i	−0.0669017	+	0.0243502i	−0.375254	−	0.926922i	$-0.622445\pi$
$509$	−1.50937	+	0.549366i	−0.0669017	+	0.0243502i	0.308353	+	0.951272i	$0.400222\pi$
$510$	−15.1006	+	8.70021i	−0.668666	+	0.385252i
$511$	−1.42504	−	8.08181i	−0.0630401	−	0.357518i
$512$	6.92298	−	6.92298i	0.305956	−	0.305956i
$513$	0.0373271	−	0.0119009i	0.00164803	−	0.000525438i
$514$		−	12.4454i		−	0.548945i
$515$	−18.3038	+	10.1684i	−0.806561	+	0.448075i
$516$	−12.4426	−	14.3669i	−0.547755	−	0.632467i
$517$	9.16819	+	4.27520i	0.403216	+	0.188023i
$518$	0.0930377	+	1.06343i	0.00408784	+	0.0467242i
$519$	8.25077	+	21.6128i	0.362169	+	0.948695i
$520$	−24.5684	+	23.7701i	−1.07740	+	1.04239i
$521$	−28.3338	+	16.3586i	−1.24133	+	0.716681i	−0.969365	−	0.245626i	$-0.921006\pi$
$521$	−28.3338	+	16.3586i	−1.24133	+	0.716681i	−0.271964	+	0.962308i	$0.587673\pi$
$522$	−4.50100	−	8.91465i	−0.197003	−	0.390184i
$523$	−10.7572	−	40.1466i	−0.470381	−	1.75549i	−0.638402	−	0.769703i	$-0.720404\pi$
$523$	−10.7572	−	40.1466i	−0.470381	−	1.75549i	0.168021	−	0.985783i	$-0.446262\pi$
$524$	5.11713	−	4.29378i	0.223543	−	0.187575i
$525$	0.882910	+	5.57308i	0.0385333	+	0.243229i
$526$	2.87389	−	16.2986i	0.125307	−	0.710654i
$527$	−10.4026	−	14.8564i	−0.453144	−	0.647156i
$528$	−0.581257	−	2.04125i	−0.0252960	−	0.0888341i
$529$	20.4037	+	24.3162i	0.887116	+	1.05722i
$530$	−2.07275	−	3.06676i	−0.0900344	−	0.133211i
$531$	29.8118	−	6.22212i	1.29372	−	0.270017i
$532$	−0.00130790	+	0.00488116i	−5.67048e−5	+	0.000211625i
$533$	4.18262	+	8.96966i	0.181169	+	0.388519i
$534$	−18.8073	+	7.17978i	−0.813873	+	0.310699i
$535$	−2.77389	+	7.24656i	−0.119926	+	0.313296i
$536$	−15.3515	−	42.1779i	−0.663084	−	1.82181i
$537$	12.8743	+	0.924066i	0.555566	+	0.0398764i
$538$	2.64303	+	1.85067i	0.113949	+	0.0797879i
$539$	9.10864			0.392337
$540$	6.28700	+	10.1646i	0.270549	+	0.437416i
$541$	14.5826			0.626954			0.313477	−	0.949596i	$-0.398506\pi$
$541$	14.5826			0.626954			0.313477	+	0.949596i	$0.398506\pi$
$542$	−6.83708	−	4.78737i	−0.293678	−	0.205635i
$543$	−25.4737	+	37.6168i	−1.09318	+	1.61429i
$544$	−7.96090	−	21.8724i	−0.341321	−	0.937771i
$545$	10.1479	+	22.7350i	0.434687	+	0.973861i
$546$	−4.42045	−	3.59310i	−0.189178	−	0.153770i
$547$	5.97161	+	12.8062i	0.255327	+	0.547551i	0.991632	−	0.129099i	$-0.0412085\pi$
$547$	5.97161	+	12.8062i	0.255327	+	0.547551i	−0.736304	+	0.676651i	$0.763431\pi$
$548$	−4.93072	+	18.4017i	−0.210630	+	0.786082i
$549$	24.4888	−	15.1773i	1.04516	−	0.647750i
$550$	−5.45942	−	4.09791i	−0.232790	−	0.174735i
$551$	−0.0163695	−	0.0195084i	−0.000697364	−	0.000831086i
$552$	−37.0992	−	9.32240i	−1.57905	−	0.396788i
$553$	0.296770	+	0.423831i	0.0126199	+	0.0180231i
$554$	−0.422214	+	2.39450i	−0.0179382	+	0.101732i
$555$	5.83265	+	2.72621i	0.247582	+	0.115721i
$556$	15.5697	−	13.0645i	0.660301	−	0.554058i
$557$	6.98848	+	26.0814i	0.296111	+	1.10510i	0.940331	+	0.340262i	$0.110516\pi$
$557$	6.98848	+	26.0814i	0.296111	+	1.10510i	−0.644220	+	0.764841i	$0.722818\pi$
$558$	9.40597	−	7.03379i	0.398186	−	0.297764i
$559$	47.3160	−	27.3179i	2.00125	−	1.15542i
$560$	1.28859	+	0.0212816i	0.0544527	+	0.000899314i
$561$	−10.8164	−	1.73356i	−0.456669	−	0.0731910i
$562$	1.66931	+	19.0803i	0.0704155	+	0.804853i
$563$	4.52364	+	2.10941i	0.190649	+	0.0889009i	0.515598	−	0.856830i	$-0.327570\pi$
$563$	4.52364	+	2.10941i	0.190649	+	0.0889009i	−0.324950	+	0.945731i	$0.605347\pi$
$564$	−4.25858	+	12.2943i	−0.179319	+	0.517683i
$565$	−9.67515	−	17.4158i	−0.407037	−	0.732690i
$566$			18.5746i			0.780748i
$567$	−4.58418	+	3.65666i	−0.192518	+	0.153565i
$568$	−13.1987	+	13.1987i	−0.553804	+	0.553804i
$569$	−2.39518	−	13.5837i	−0.100411	−	0.569459i	−0.992954	−	0.118497i	$-0.962192\pi$
$569$	−2.39518	−	13.5837i	−0.100411	−	0.569459i	0.892543	−	0.450962i	$-0.148919\pi$
$570$	−0.0203325	−	0.0203692i	−0.000851637	−	0.000853172i
$571$	4.72552	−	1.71995i	0.197757	−	0.0719776i	−0.241243	−	0.970465i	$-0.577555\pi$
$571$	4.72552	−	1.71995i	0.197757	−	0.0719776i	0.439000	+	0.898487i	$0.355333\pi$
$572$	−7.27031	+	0.636069i	−0.303987	+	0.0265954i
$573$	1.61989	+	2.23824i	0.0676719	+	0.0935038i
$574$	0.424397	−	1.16602i	0.0177140	−	0.0486688i
$575$	−34.0260	+	14.5187i	−1.41898	+	0.605471i
$576$	18.9250	−	7.56529i	0.788541	−	0.315220i
$577$	−2.65137	+	0.710433i	−0.110378	+	0.0295757i	−0.313585	−	0.949560i	$-0.601530\pi$
$577$	−2.65137	+	0.710433i	−0.110378	+	0.0295757i	0.203207	+	0.979136i	$0.434863\pi$
$578$	3.77540	+	0.330305i	0.157036	+	0.0137389i
$579$	14.5704	−	0.227510i	0.605526	−	0.00945498i
$580$	4.56050	−	6.28940i	0.189364	−	0.261153i
$581$	−5.95200	−	1.04950i	−0.246930	−	0.0435405i
$582$	0.910773	−	3.62449i	0.0377528	−	0.150240i
$583$	0.202782	−	2.31781i	0.00839837	−	0.0959938i
$584$	−18.7982	+	32.5595i	−0.777876	+	1.34732i
$585$	−32.1091	+	12.2247i	−1.32755	+	0.505428i
$586$	−1.98777	−	3.44291i	−0.0821138	−	0.142225i
$587$	18.7722	−	8.75362i	0.774811	−	0.361300i	0.00534328	−	0.999986i	$-0.498299\pi$
$587$	18.7722	−	8.75362i	0.774811	−	0.361300i	0.769468	+	0.638685i	$0.220521\pi$
$588$	1.20315	+	11.6534i	0.0496169	+	0.480578i
$589$	0.0192521	−	0.0229437i	0.000793268	−	0.000945380i
$590$	−14.0953	−	17.3729i	−0.580295	−	0.715229i
$591$	3.71476	+	19.3003i	0.152805	+	0.793908i
$592$	0.843448	−	1.20457i	0.0346655	−	0.0495075i
$593$	33.2020	+	33.2020i	1.36344	+	1.36344i	0.869487	+	0.493956i	$0.164450\pi$
$593$	33.2020	+	33.2020i	1.36344	+	1.36344i	0.493956	+	0.869487i	$0.335550\pi$
$594$	0.903406	−	7.03632i	0.0370672	−	0.288704i
$595$	2.91032	−	5.98130i	0.119312	−	0.245209i
$596$	−15.1924	+	2.67882i	−0.622303	+	0.109729i
$597$	−3.00718	+	41.8966i	−0.123076	+	1.71472i
$598$	15.7839	−	33.8487i	0.645452	−	1.38418i
$599$	−9.01503	−	7.56451i	−0.368344	−	0.309078i	0.439762	−	0.898114i	$-0.355063\pi$
$599$	−9.01503	−	7.56451i	−0.368344	−	0.309078i	−0.808106	+	0.589037i	$0.799507\pi$
$600$	13.3131	−	22.1587i	0.543505	−	0.904623i
$601$	13.4574	+	4.89809i	0.548938	+	0.199797i	0.601575	−	0.798817i	$-0.294540\pi$
$601$	13.4574	+	4.89809i	0.548938	+	0.199797i	−0.0526366	+	0.998614i	$0.516763\pi$
$602$	−6.61670	−	1.77294i	−0.269677	−	0.0722596i
$603$	2.52670	−	45.0403i	0.102895	−	1.83418i
$604$	−0.808178	−	0.466602i	−0.0328843	−	0.0189858i
$605$	4.93096	+	19.6982i	0.200472	+	0.800844i
$606$	9.58874	+	5.33821i	0.389516	+	0.216850i
$607$	16.7167	−	11.7051i	0.678509	−	0.475097i	−0.182819	−	0.983147i	$-0.558522\pi$
$607$	16.7167	−	11.7051i	0.678509	−	0.475097i	0.861328	+	0.508049i	$0.169633\pi$
$608$	0.0314873	−	0.0220476i	0.00127698	−	0.000894150i
$609$	3.33033	+	1.85405i	0.134952	+	0.0751299i
$610$	−18.1516	−	10.8834i	−0.734936	−	0.440655i
$611$	−32.3913	−	18.7011i	−1.31041	−	0.756566i
$612$	0.789156	−	14.0673i	0.0318998	−	0.568636i
$613$	32.1941	+	8.62637i	1.30031	+	0.348416i	0.841566	−	0.540155i	$-0.181634\pi$
$613$	32.1941	+	8.62637i	1.30031	+	0.348416i	0.458740	+	0.888571i	$0.348301\pi$
$614$	−8.25087	−	3.00307i	−0.332978	−	0.121194i
$615$	−4.80542	−	5.73736i	−0.193773	−	0.231353i
$616$	2.06379	+	1.73172i	0.0831523	+	0.0697731i
$617$	−0.373483	+	0.800937i	−0.0150359	+	0.0322445i	−0.913682	−	0.406429i	$-0.866774\pi$
$617$	−0.373483	+	0.800937i	−0.0150359	+	0.0322445i	0.898646	+	0.438674i	$0.144552\pi$
$618$	−1.14439	+	15.9439i	−0.0460343	+	0.641360i
$619$	−11.2863	+	1.99007i	−0.453633	+	0.0799877i	−0.395796	−	0.918338i	$-0.629531\pi$
$619$	−11.2863	+	1.99007i	−0.453633	+	0.0799877i	−0.0578365	+	0.998326i	$0.518420\pi$
$620$	8.21593	+	3.99763i	0.329960	+	0.160549i
$621$	−30.5757	−	23.3061i	−1.22696	−	0.935243i
$622$	−18.9844	−	18.9844i	−0.761204	−	0.761204i
$623$	4.40717	−	6.29409i	0.176569	−	0.252167i
$624$	1.48314	+	7.70579i	0.0593733	+	0.308479i
$625$	−2.70661	−	24.8531i	−0.108264	−	0.994122i
$626$	−9.95267	+	11.8611i	−0.397789	+	0.474066i
$627$	−0.00185787	−	0.0179949i	−7.41960e−5	−	0.000718646i
$628$	4.31941	−	2.01418i	0.172363	−	0.0803744i
$629$	−3.79491	−	6.57297i	−0.151313	−	0.262082i
$630$	3.93043	+	1.76287i	0.156592	+	0.0702342i
$631$	0.493720	−	0.855149i	0.0196547	−	0.0340429i	−0.856031	−	0.516925i	$-0.827077\pi$
$631$	0.493720	−	0.855149i	0.0196547	−	0.0340429i	0.875685	+	0.482882i	$0.160410\pi$
$632$	0.206592	−	2.36136i	0.00821780	−	0.0939299i
$633$	3.85024	−	15.3223i	0.153033	−	0.609006i
$634$	−13.7301	−	2.42099i	−0.545293	−	0.0961500i
$635$	1.00294	+	6.29404i	0.0398004	+	0.249771i
$636$	2.99214	−	0.0467207i	0.118646	−	0.00185260i
$637$	−33.5496	−	2.93521i	−1.32928	−	0.116297i
$638$	−4.45412	+	1.19348i	−0.176340	+	0.0472502i
$639$	−17.4196	+	6.96350i	−0.689108	+	0.275472i
$640$	5.91217	+	5.12963i	0.233699	+	0.202766i
$641$	−9.55555	+	26.2536i	−0.377421	+	1.03696i	0.595000	+	0.803726i	$0.297152\pi$
$641$	−9.55555	+	26.2536i	−0.377421	+	1.03696i	−0.972421	+	0.233231i	$0.925070\pi$
$642$	3.47300	+	4.79872i	0.137068	+	0.189390i
$643$	−29.9171	+	2.61741i	−1.17982	+	0.103221i	−0.660140	−	0.751142i	$-0.729503\pi$
$643$	−29.9171	+	2.61741i	−1.17982	+	0.103221i	−0.519677	+	0.854363i	$0.673948\pi$
$644$	4.65975	−	1.69601i	0.183620	−	0.0668322i
$645$	−29.2404	+	29.1878i	−1.15134	+	1.14927i
$646$	0.00589152	+	0.0334124i	0.000231799	+	0.00131460i
$647$	−22.0995	+	22.0995i	−0.868820	+	0.868820i	−0.992342	−	0.123522i	$-0.960581\pi$
$647$	−22.0995	+	22.0995i	−0.868820	+	0.868820i	0.123522	+	0.992342i	$0.460581\pi$
$648$	26.8563	+	0.666536i	1.05501	+	0.0261840i
$649$		−	14.0622i		−	0.551988i
$650$	18.7880	+	16.8530i	0.736926	+	0.661028i
$651$	−1.46727	+	4.23592i	−0.0575068	+	0.166019i
$652$	10.4684	+	4.88147i	0.409972	+	0.191173i
$653$	−0.292733	−	3.34596i	−0.0114555	−	0.130937i	0.988313	−	0.152436i	$-0.0487118\pi$
$653$	−0.292733	−	3.34596i	−0.0114555	−	0.130937i	−0.999769	+	0.0214986i	$0.993156\pi$
$654$	18.7674	+	3.00787i	0.733862	+	0.117617i
$655$	−10.0968	−	10.4359i	−0.394515	−	0.407765i
$656$	−1.48032	+	0.854663i	−0.0577968	+	0.0333690i
$657$	−30.2607	+	22.6290i	−1.18058	+	0.882840i
$658$	1.21371	+	4.52962i	0.0473152	+	0.176583i
$659$	19.8580	−	16.6629i	0.773560	−	0.649094i	−0.168058	−	0.985777i	$-0.553750\pi$
$659$	19.8580	−	16.6629i	0.773560	−	0.649094i	0.941618	+	0.336683i	$0.109305\pi$
$660$	5.18760	−	1.88284i	0.201927	−	0.0732895i
$661$	6.41723	−	36.3939i	0.249601	−	1.41556i	−0.559958	−	0.828521i	$-0.689183\pi$
$661$	6.41723	−	36.3939i	0.249601	−	1.41556i	0.809559	−	0.587038i	$-0.199706\pi$
$662$	−9.53378	−	13.6156i	−0.370541	−	0.529187i
$663$	39.2812	+	9.87070i	1.52555	+	0.383346i
$664$	17.7979	+	21.2107i	0.690692	+	0.823134i
$665$	0.0107851	+	0.00208589i	0.000418227	+	8.08875e-5i
$666$	4.17784	−	2.58927i	0.161888	−	0.100332i
$667$	−6.46788	+	24.1385i	−0.250437	+	0.934645i
$668$	−0.391202	−	0.838935i	−0.0151360	−	0.0324594i
$669$	−21.9684	−	17.8567i	−0.849348	−	0.690380i
$670$	−30.2610	+	13.5072i	−1.16909	+	0.521827i
$671$	−4.54997	−	12.5009i	−0.175650	−	0.482593i
$672$	−3.22596	+	4.76375i	−0.124444	+	0.183766i
$673$	−4.90829	−	3.43682i	−0.189201	−	0.132480i	0.475138	−	0.879911i	$-0.342398\pi$
$673$	−4.90829	−	3.43682i	−0.189201	−	0.132480i	−0.664339	+	0.747431i	$0.731287\pi$
$674$	19.2999			0.743406
$675$	21.0743	−	15.1945i	0.811152	−	0.584835i
$676$	13.6111			0.523502
$677$	−28.2910	−	19.8096i	−1.08731	−	0.761345i	−0.114613	−	0.993410i	$-0.536563\pi$
$677$	−28.2910	−	19.8096i	−1.08731	−	0.761345i	−0.972700	+	0.232066i	$0.925452\pi$
$678$	−15.1705	−	1.08888i	−0.582619	−	0.0418181i
$679$	0.487857	+	1.34038i	0.0187222	+	0.0514389i
$680$	−27.8275	+	12.4209i	−1.06714	+	0.476321i
$681$	−20.4467	+	7.80560i	−0.783518	+	0.299111i
$682$	−2.29197	−	4.91514i	−0.0877639	−	0.188210i
$683$	−0.984841	+	3.67548i	−0.0376839	+	0.140638i	−0.982205	−	0.187813i	$-0.939860\pi$
$683$	−0.984841	+	3.67548i	−0.0376839	+	0.140638i	0.944521	+	0.328451i	$0.106527\pi$
$684$	0.0227769	−	0.00475383i	0.000870895	−	0.000181767i
$685$	40.6591	+	7.86371i	1.55351	+	0.300457i
$686$	5.60349	+	6.67798i	0.213942	+	0.254966i
$687$	−4.28361	−	15.0431i	−0.163430	−	0.573931i
$688$	5.41244	+	7.72977i	0.206347	+	0.294695i
$689$	−1.49380	+	8.47177i	−0.0569093	+	0.322749i
$690$	−4.92923	+	27.8086i	−0.187653	+	1.05865i
$691$	0.658559	−	0.552596i	0.0250528	−	0.0210218i	−0.630175	−	0.776453i	$-0.717017\pi$
$691$	0.658559	−	0.552596i	0.0250528	−	0.0210218i	0.655228	+	0.755431i	$0.272573\pi$
$692$	3.55595	+	13.2710i	0.135177	+	0.504487i
$693$	1.22037	+	2.41705i	0.0463579	+	0.0918163i
$694$	−9.47573	+	5.47082i	−0.359694	+	0.207669i
$695$	−30.7211	−	31.7529i	−1.16532	−	1.20446i
$696$	−6.22792	−	16.3139i	−0.236069	−	0.618378i
$697$	0.768927	+	8.78887i	0.0291252	+	0.332902i
$698$	5.36559	+	2.50202i	0.203091	+	0.0947027i
$699$	−24.2061	−	27.9496i	−0.915557	−	1.05715i
$700$	0.181668	+	3.34615i	0.00686641	+	0.126473i
$701$		−	28.2369i		−	1.06649i	−0.845960	−	0.533246i	$-0.820972\pi$
$701$		−	28.2369i		−	1.06649i	0.845960	−	0.533246i	$-0.179028\pi$
$702$	−5.59491	+	25.6256i	−0.211166	+	0.967175i
$703$	0.00886291	−	0.00886291i	0.000334271	−	0.000334271i
$704$	−1.63419	−	9.26794i	−0.0615908	−	0.349299i
$705$	27.3128	+	7.34482i	1.02866	+	0.276622i
$706$	−10.6616	+	3.88050i	−0.401254	+	0.146045i
$707$	−4.17282	+	0.365074i	−0.156935	+	0.0137300i
$708$	17.9908	−	1.85745i	0.676137	−	0.0698072i
$709$	−2.66301	+	7.31657i	−0.100012	+	0.274780i	−0.979600	−	0.200955i	$-0.935596\pi$
$709$	−2.66301	+	7.31657i	−0.100012	+	0.274780i	0.879589	+	0.475735i	$0.157818\pi$
$710$	10.4092	+	9.03139i	0.390649	+	0.338942i
$711$	1.12617	−	2.09934i	0.0422347	−	0.0787315i
$712$	−34.0018	+	9.11075i	−1.27427	+	0.341440i
$713$	−29.2787	−	2.56156i	−1.09650	−	0.0959310i
$714$	−2.60740	−	4.35758i	−0.0975794	−	0.163078i
$715$	2.49647	+	15.6668i	0.0933628	+	0.585907i
$716$	7.54913	+	1.33111i	0.282124	+	0.0497461i
$717$	7.19206	+	6.97092i	0.268593	+	0.260334i
$718$	1.31391	−	15.0181i	0.0490347	−	0.560469i
$719$	−5.23184	+	9.06182i	−0.195115	+	0.337949i	−0.946938	−	0.321416i	$-0.895841\pi$
$719$	−5.23184	+	9.06182i	−0.195115	+	0.337949i	0.751823	+	0.659365i	$0.229175\pi$
$720$	−2.58666	−	5.34054i	−0.0963991	−	0.199030i
$721$	−3.05057	−	5.28374i	−0.113609	−	0.196777i
$722$	16.9713	−	7.91387i	0.631608	−	0.294524i
$723$	−32.3452	+	23.4094i	−1.20293	+	0.870604i
$724$	−17.3429	+	20.6685i	−0.644544	+	0.768138i
$725$	−14.3385	−	8.92226i	−0.532517	−	0.331364i
$726$	14.6481	+	5.07392i	0.543642	+	0.188311i
$727$	10.3885	−	14.8363i	0.385289	−	0.550250i	−0.578923	−	0.815382i	$-0.696527\pi$
$727$	10.3885	−	14.8363i	0.385289	−	0.550250i	0.964212	+	0.265133i	$0.0854157\pi$
$728$	−7.04345	−	7.04345i	−0.261048	−	0.261048i
$729$	24.5430	+	11.2535i	0.908999	+	0.416798i
$730$	24.9598	+	12.1447i	0.923805	+	0.449496i
$731$	47.9642	−	8.45739i	1.77402	−	0.312808i
$732$	15.3924	−	7.47237i	0.568921	−	0.276187i
$733$	12.7723	−	27.3902i	0.471755	−	1.01168i	−0.516133	−	0.856509i	$-0.672629\pi$
$733$	12.7723	−	27.3902i	0.471755	−	1.01168i	0.987887	−	0.155173i	$-0.0495934\pi$
$734$	9.73284	+	8.16683i	0.359246	+	0.301443i
$735$	25.0838	−	4.39966i	0.925230	−	0.162284i
$736$	−35.4450	−	12.9009i	−1.30652	−	0.475534i
$737$	−20.1202	−	5.39119i	−0.741137	−	0.198587i
$738$	−5.67333	+	0.675414i	−0.208838	+	0.0248623i
$739$	−3.17194	−	1.83132i	−0.116682	−	0.0673663i	0.440523	−	0.897741i	$-0.354793\pi$
$739$	−3.17194	−	1.83132i	−0.116682	−	0.0673663i	−0.557205	+	0.830375i	$0.688126\pi$
$740$	3.27936	+	1.96625i	0.120552	+	0.0722808i
$741$	0.00104428	+	0.0668787i	3.83625e−5	+	0.00245685i
$742$	0.883502	−	0.618635i	0.0324344	−	0.0227108i
$743$	26.5204	−	18.5698i	0.972939	−	0.681259i	0.0249919	−	0.999688i	$-0.492044\pi$
$743$	26.5204	−	18.5698i	0.972939	−	0.681259i	0.947947	+	0.318429i	$0.103155\pi$
$744$	17.6233	−	10.5451i	0.646103	−	0.386601i
$745$	8.14329	+	32.5308i	0.298347	+	1.19183i
$746$	13.7959	+	7.96506i	0.505103	+	0.291621i
$747$	8.03818	+	26.6420i	0.294102	+	0.974779i
$748$	−6.28407	−	1.68381i	−0.229768	−	0.0615662i
$749$	−2.12458	−	0.773283i	−0.0776303	−	0.0282551i
$750$	−17.0138	−	8.64801i	−0.621255	−	0.315781i
$751$	−16.4509	−	13.8040i	−0.600303	−	0.503714i	0.291240	−	0.956650i	$-0.405932\pi$
$751$	−16.4509	−	13.8040i	−0.600303	−	0.503714i	−0.891543	+	0.452936i	$0.850377\pi$
$752$	2.73005	−	5.85460i	0.0995546	−	0.213495i
$753$	3.60025	+	2.43805i	0.131200	+	0.0888474i
$754$	16.7903	−	2.96058i	0.611467	−	0.107818i
$755$	−0.887563	+	1.82412i	−0.0323017	+	0.0663865i
$756$	−2.93113	+	1.88058i	−0.106604	+	0.0683959i
$757$	20.3709	+	20.3709i	0.740395	+	0.740395i	0.972654	−	0.232259i	$-0.0746118\pi$
$757$	20.3709	+	20.3709i	0.740395	+	0.740395i	−0.232259	+	0.972654i	$0.574612\pi$
$758$	5.45165	−	7.78576i	0.198013	−	0.282792i
$759$	−13.4191	+	11.6217i	−0.487081	+	0.421842i
$760$	−0.0317075	−	0.0390804i	−0.00115015	−	0.00141759i
$761$	20.6946	−	24.6629i	0.750179	−	0.894028i	−0.247006	−	0.969014i	$-0.579447\pi$
$761$	20.6946	−	24.6629i	0.750179	−	0.894028i	0.997185	+	0.0749859i	$0.0238912\pi$
$762$	4.44131	+	1.98720i	0.160892	+	0.0719887i
$763$	−6.57484	+	3.06590i	−0.238025	+	0.110993i
$764$	0.820438	+	1.42104i	0.0296824	+	0.0514114i
$765$	−30.6241	+	0.450588i	−1.10722	+	0.0162911i
$766$	−7.16607	+	12.4120i	−0.258921	+	0.448464i
$767$	−4.53146	+	51.7948i	−0.163621	+	1.87020i
$768$	28.3813	−	8.08173i	1.02412	−	0.291624i
$769$	−3.27352	−	0.577210i	−0.118046	−	0.0208147i	0.114313	−	0.993445i	$-0.463533\pi$
$769$	−3.27352	−	0.577210i	−0.118046	−	0.0208147i	−0.232359	+	0.972630i	$0.574644\pi$
$770$	1.16763	−	1.61028i	0.0420783	−	0.0580304i
$771$	10.6388	−	19.1099i	0.383147	−	0.688226i
$772$	8.62135	+	0.754271i	0.310289	+	0.0271468i
$773$	−3.47814	+	0.931964i	−0.125100	+	0.0335204i	−0.320826	−	0.947138i	$-0.603960\pi$
$773$	−3.47814	+	0.931964i	−0.125100	+	0.0335204i	0.195726	+	0.980659i	$0.437294\pi$
$774$	6.44410	+	30.8754i	0.231628	+	1.10979i
$775$	7.40570	−	18.4294i	0.266021	−	0.662002i
$776$	2.23502	−	6.14068i	0.0802327	−	0.220437i
$777$	−0.766195	+	1.71241i	−0.0274871	+	0.0614325i
$778$	16.1549	−	1.41337i	0.579181	−	0.0506718i
$779$	−0.0136910	+	0.00498312i	−0.000490531	+	0.000178539i
$780$	−19.7141	+	5.26334i	−0.705877	+	0.188458i
$781$	1.50420	+	8.53071i	0.0538243	+	0.305253i
$782$	23.5418	−	23.5418i	0.841853	−	0.841853i
$783$	0.709310	−	17.5360i	0.0253487	−	0.626685i
$784$		−	5.81658i		−	0.207735i
$785$	−5.03122	−	9.05649i	−0.179572	−	0.323240i
$786$	−10.8857	+	2.09518i	−0.388279	+	0.0747327i
$787$	−33.8637	−	15.7909i	−1.20711	−	0.562886i	−0.288285	−	0.957545i	$-0.593085\pi$
$787$	−33.8637	−	15.7909i	−1.20711	−	0.562886i	−0.918828	+	0.394659i	$0.870863\pi$
$788$	1.01734	+	11.6282i	0.0362412	+	0.414238i
$789$	18.3455	−	22.5697i	0.653116	−	0.803503i
$790$	−1.74983	−	0.0288993i	−0.0622560	−	0.00102819i
$791$	5.02741	−	2.90258i	0.178754	−	0.103204i
$792$	2.83490	−	12.0764i	0.100734	−	0.429115i
$793$	12.7304	+	47.5106i	0.452070	+	1.68715i
$794$	16.4558	−	13.8081i	0.583995	−	0.490030i
$795$	−0.561118	−	6.48084i	−0.0199008	−	0.229852i
$796$	−4.33183	+	24.5670i	−0.153538	+	0.870756i
$797$	−11.3609	−	16.2250i	−0.402423	−	0.574719i	0.565884	−	0.824485i	$-0.308535\pi$
$797$	−11.3609	−	16.2250i	−0.402423	−	0.574719i	−0.968306	+	0.249766i	$0.919646\pi$
$798$	0.00583658	−	0.00602174i	0.000206613	−	0.000213167i
$799$	−21.4315	−	25.5411i	−0.758194	−	0.903580i
$800$	15.3022	−	20.3863i	0.541015	−	0.720765i
$801$	−35.0160	−	5.05266i	−1.23723	−	0.178527i
$802$	6.82383	−	25.4669i	0.240958	−	0.899267i
$803$	7.37368	+	15.8129i	0.260211	+	0.558025i
$804$	4.23973	−	26.4535i	0.149524	−	0.932941i
$805$	−4.39363	−	9.84336i	−0.154855	−	0.346933i
$806$	6.85806	+	18.8424i	0.241565	+	0.663694i
$807$	2.47633	+	5.10103i	0.0871710	+	0.179565i
$808$	15.7195	+	11.0069i	0.553010	+	0.387222i
$809$	0.320020			0.0112513			0.00562564	−	0.999984i	$-0.498209\pi$
$809$	0.320020			0.0112513			0.00562564	+	0.999984i	$0.498209\pi$
$810$	−0.910843	−	19.8133i	−0.0320038	−	0.696169i
$811$	−25.9979			−0.912910			−0.456455	−	0.889747i	$-0.650881\pi$
$811$	−25.9979			−0.912910			−0.456455	+	0.889747i	$0.650881\pi$
$812$	1.85431	+	1.29840i	0.0650736	+	0.0455650i
$813$	−6.40587	−	13.1955i	−0.224664	−	0.462788i
$814$	−0.776235	−	2.13269i	−0.0272070	−	0.0747506i
$815$	8.97606	−	23.4493i	0.314418	−	0.821391i
$816$	−1.10701	+	6.90713i	−0.0387532	+	0.241798i
$817$	0.0339918	+	0.0728957i	0.00118922	+	0.00255030i
$818$	−5.11244	+	19.0799i	−0.178752	+	0.667112i
$819$	−3.71606	−	9.29592i	−0.129850	−	0.324826i
$820$	−2.48887	−	3.68244i	−0.0869152	−	0.128596i
$821$	3.59136	+	4.28001i	0.125339	+	0.149373i	0.825064	−	0.565039i	$-0.191139\pi$
$821$	3.59136	+	4.28001i	0.125339	+	0.149373i	−0.699725	+	0.714412i	$0.746694\pi$
$822$	22.0036	−	22.7017i	0.767464	−	0.791811i
$823$	21.2514	+	30.3501i	0.740776	+	1.05794i	0.995849	+	0.0910165i	$0.0290116\pi$
$823$	21.2514	+	30.3501i	0.740776	+	1.05794i	−0.255073	+	0.966922i	$0.582100\pi$
$824$	−4.85367	+	27.5265i	−0.169086	+	0.958932i
$825$	−4.87986	−	10.9592i	−0.169895	−	0.381551i
$826$	4.99363	−	4.19015i	0.173750	−	0.145794i
$827$	−3.37514	−	12.5962i	−0.117365	−	0.438013i	0.882088	−	0.471085i	$-0.156137\pi$
$827$	−3.37514	−	12.5962i	−0.117365	−	0.438013i	−0.999453	+	0.0330724i	$0.989471\pi$
$828$	−16.6411	−	15.6330i	−0.578318	−	0.543283i
$829$	−22.2366	+	12.8383i	−0.772309	+	0.445893i	−0.833698	−	0.552221i	$-0.813780\pi$
$829$	−22.2366	+	12.8383i	−0.772309	+	0.445893i	0.0613890	+	0.998114i	$0.480447\pi$
$830$	14.6919	−	14.2145i	0.509962	−	0.493391i
$831$	−2.69521	+	3.31581i	−0.0934957	+	0.115024i
$832$	3.03262	+	34.6630i	0.105137	+	1.20172i
$833$	−27.2087	−	12.6876i	−0.942725	−	0.439600i
$834$	−33.1214	+	6.37492i	−1.14690	+	0.220745i
$835$	−1.75899	+	0.977185i	−0.0608724	+	0.0338169i
$836$		−	0.0107438i		−	0.000371582i
$837$	20.4555	−	2.75978i	0.707046	−	0.0953918i
$838$	−1.56397	+	1.56397i	−0.0540266	+	0.0540266i
$839$	1.09940	+	6.23500i	0.0379555	+	0.215256i	0.997887	−	0.0649800i	$-0.0206983\pi$
$839$	1.09940	+	6.23500i	0.0379555	+	0.215256i	−0.959931	+	0.280236i	$0.909587\pi$
$840$	6.51981	+	3.77205i	0.224955	+	0.130148i
$841$	16.5311	−	6.01684i	0.570039	−	0.207477i
$842$	23.0313	−	2.01497i	0.793710	−	0.0694406i
$843$	−13.7473	+	30.7246i	−0.473481	+	1.05821i
$844$	3.20906	−	8.81681i	0.110460	−	0.303487i
$845$	−2.09165	−	29.5136i	−0.0719549	−	1.01530i
$846$	16.0990	−	14.3887i	0.553495	−	0.494693i
$847$	−5.71518	+	1.53138i	−0.196376	+	0.0526188i
$848$	−1.48010	−	0.129492i	−0.0508269	−	0.00444678i
$849$	−15.8782	+	28.5211i	−0.544939	+	0.978843i
$850$	10.5999	+	19.8455i	0.363574	+	0.680696i
$851$	−12.1127	−	2.13579i	−0.415218	−	0.0732141i
$852$	−10.7153	+	3.05124i	−0.367101	+	0.104534i
$853$	−4.29982	+	49.1472i	−0.147223	+	1.68277i	0.459752	+	0.888047i	$0.347938\pi$
$853$	−4.29982	+	49.1472i	−0.147223	+	1.68277i	−0.606975	+	0.794721i	$0.707617\pi$
$854$	3.08345	−	5.34069i	0.105513	−	0.182755i
$855$	−0.0138082	−	0.0486577i	−0.000472229	−	0.00166406i
$856$	5.17900	+	8.97029i	0.177015	+	0.306598i
$857$	50.2090	−	23.4128i	1.71511	−	0.799768i	0.720809	−	0.693134i	$-0.243771\pi$
$857$	50.2090	−	23.4128i	1.71511	−	0.799768i	0.994298	−	0.106634i	$-0.0340073\pi$
$858$	11.0551	+	4.94646i	0.377416	+	0.168869i
$859$	−10.5665	+	12.5926i	−0.360523	+	0.429655i	−0.915566	−	0.402167i	$-0.868257\pi$
$859$	−10.5665	+	12.5926i	−0.360523	+	0.429655i	0.555043	+	0.831821i	$0.312702\pi$
$860$	−19.0540	+	15.4593i	−0.649735	+	0.527156i
$861$	1.64841	−	1.42763i	0.0561778	−	0.0486534i
$862$	−8.90863	+	12.7228i	−0.303429	+	0.433342i
$863$	−13.7094	−	13.7094i	−0.466672	−	0.466672i	0.434162	−	0.900835i	$-0.357044\pi$
$863$	−13.7094	−	13.7094i	−0.466672	−	0.466672i	−0.900835	+	0.434162i	$0.857044\pi$
$864$	26.2747	+	3.37346i	0.893884	+	0.114767i
$865$	28.2297	−	9.74994i	0.959839	−	0.331508i
$866$	−19.2561	+	3.39537i	−0.654348	+	0.115379i
$867$	5.51475	+	3.73453i	0.187291	+	0.126831i
$868$	−1.12515	+	2.41288i	−0.0381899	+	0.0818985i
$869$	−0.842676	−	0.707089i	−0.0285858	−	0.0239864i
$870$	−11.6895	+	5.43808i	−0.396311	+	0.184368i
$871$	72.3708	+	26.3408i	2.45219	+	0.892525i
$872$	32.1028	+	8.60192i	1.08714	+	0.291298i
$873$	4.49682	−	4.78681i	0.152194	−	0.162009i
$874$	0.0476152	+	0.0274906i	0.00161061	+	0.000929885i
$875$	7.22772	−	0.908134i	0.244342	−	0.0307005i
$876$	−19.2567	+	11.5224i	−0.650624	+	0.389307i
$877$	24.0198	−	16.8189i	0.811093	−	0.567933i	−0.0928040	−	0.995684i	$-0.529583\pi$
$877$	24.0198	−	16.8189i	0.811093	−	0.567933i	0.903896	+	0.427751i	$0.140694\pi$
$878$	−3.38479	+	2.37006i	−0.114231	+	0.0799856i
$879$	−0.109079	−	6.98578i	−0.00367916	−	0.235624i
$880$	−2.65799	+	0.665364i	−0.0896008	+	0.0224294i
$881$	24.7559	+	14.2928i	0.834048	+	0.481538i	0.855237	−	0.518237i	$-0.173412\pi$
$881$	24.7559	+	14.2928i	0.834048	+	0.481538i	−0.0211883	+	0.999776i	$0.506745\pi$
$882$	7.66234	−	17.8682i	0.258004	−	0.601654i
$883$	−31.2423	−	8.37134i	−1.05139	−	0.281718i	−0.308562	−	0.951204i	$-0.599848\pi$
$883$	−31.2423	−	8.37134i	−1.05139	−	0.281718i	−0.742825	+	0.669486i	$0.766514\pi$
$884$	22.6033	+	8.22694i	0.760232	+	0.276702i
$885$	−6.79231	−	38.7251i	−0.228321	−	1.30173i
$886$	−16.1041	−	13.5129i	−0.541026	−	0.453975i
$887$	−9.85973	+	21.1443i	−0.331057	+	0.709955i	−0.999426	−	0.0338753i	$-0.989215\pi$
$887$	−9.85973	+	21.1443i	−0.331057	+	0.709955i	0.668369	+	0.743830i	$0.266993\pi$
$888$	7.73168	−	3.75340i	0.259458	−	0.125956i
$889$	−1.82889	+	0.322483i	−0.0613391	+	0.0108157i
$890$	8.48435	+	24.5654i	0.284396	+	0.823433i
$891$	7.40207	−	10.0320i	0.247979	−	0.336083i
$892$	−11.8887	−	11.8887i	−0.398064	−	0.398064i
$893$	0.0315819	−	0.0451036i	0.00105685	−	0.00150933i
$894$	24.1908	+	8.37938i	0.809061	+	0.280248i
$895$	1.72623	−	16.5737i	0.0577016	−	0.553999i
$896$	−1.46603	+	1.74715i	−0.0489767	+	0.0583681i
$897$	53.1711	−	38.4818i	1.77533	−	1.28487i
$898$	−16.6498	+	7.76395i	−0.555612	+	0.259086i
$899$	−6.70840	−	11.6193i	−0.223738	−	0.387525i
$900$	13.3764	−	7.69078i	0.445880	−	0.256359i
$901$	−3.83426	+	6.64113i	−0.127738	+	0.221248i
$902$	−0.229930	+	2.62811i	−0.00765582	+	0.0875064i
$903$	−8.64432	−	8.37852i	−0.287665	−	0.278820i
$904$	−26.1912	−	4.61821i	−0.871105	−	0.153599i
$905$	47.4817	+	34.4294i	1.57834	+	1.14447i
$906$	0.795179	+	1.32893i	0.0264181	+	0.0441509i
$907$	8.44305	+	0.738671i	0.280347	+	0.0245272i	0.226462	−	0.974020i	$-0.427284\pi$
$907$	8.44305	+	0.738671i	0.280347	+	0.0245272i	0.0538847	+	0.998547i	$0.482840\pi$
$908$	−12.5549	+	3.36409i	−0.416650	+	0.111641i
$909$	10.1601	+	16.3936i	0.336991	+	0.543741i
$910$	−4.81958	+	5.55483i	−0.159768	+	0.184141i
$911$	−14.3752	+	39.4954i	−0.476270	+	1.30854i	0.436366	+	0.899769i	$0.356265\pi$
$911$	−14.3752	+	39.4954i	−0.476270	+	1.30854i	−0.912636	+	0.408773i	$0.865957\pi$
$912$	−0.0114911	+	0.00118639i	−0.000380509	+	3.92854e-5i
$913$	12.8007	−	1.11992i	0.423641	−	0.0370638i
$914$	−13.2386	+	4.81847i	−0.437896	+	0.159381i
$915$	−18.5681	−	32.2280i	−0.613844	−	1.06542i
$916$	−1.61304	−	9.14800i	−0.0532963	−	0.302258i
$917$	2.99184	−	2.99184i	0.0987992	−	0.0987992i
$918$	−12.4996	+	19.7600i	−0.412549	+	0.652178i
$919$			49.1112i			1.62003i	0.586409	+	0.810015i	$0.300541\pi$
$919$			49.1112i			1.62003i	−0.586409	+	0.810015i	$0.699459\pi$
$920$	−13.5674	+	47.4835i	−0.447305	+	1.56548i
$921$	−10.1020	−	11.6643i	−0.332873	−	0.384352i
$922$	−22.6706	−	10.5715i	−0.746617	−	0.348153i
$923$	−2.79138	−	31.9057i	−0.0918795	−	1.05019i
$924$	0.573512	+	1.50231i	0.0188672	+	0.0494223i
$925$	3.75958	−	7.41298i	0.123614	−	0.243737i
$926$	10.9835	−	6.34135i	0.360942	−	0.208390i
$927$	−15.3867	+	23.5035i	−0.505364	+	0.771958i
$928$	−4.45662	−	16.6324i	−0.146296	−	0.545984i
$929$	0.315673	−	0.264881i	0.0103569	−	0.00869047i	−0.637594	−	0.770372i	$-0.720070\pi$
$929$	0.315673	−	0.264881i	0.0103569	−	0.00869047i	0.647951	+	0.761682i	$0.275626\pi$
$930$	−8.68584	−	12.4285i	−0.284820	−	0.407546i
$931$	0.00860919	−	0.0488251i	0.000282155	−	0.00160018i
$932$	−12.5950	−	17.9876i	−0.412564	−	0.589203i
$933$	−12.9219	−	45.3789i	−0.423043	−	1.48564i
$934$	−17.2348	−	20.5396i	−0.563939	−	0.672077i
$935$	−2.68541	+	13.8848i	−0.0878222	+	0.454083i
$936$	−14.3332	+	43.5670i	−0.468497	+	1.42403i
$937$	−0.474207	+	1.76977i	−0.0154917	+	0.0578157i	−0.973239	−	0.229795i	$-0.926194\pi$
$937$	−0.474207	+	1.76977i	−0.0154917	+	0.0578157i	0.957747	+	0.287611i	$0.0928610\pi$
$938$	−4.08081	−	8.75132i	−0.133243	−	0.285741i
$939$	−25.4216	+	9.70479i	−0.829601	+	0.316704i
$940$	15.6871	+	6.00480i	0.511656	+	0.195855i
$941$	2.52471	+	6.93657i	0.0823031	+	0.226126i	0.974018	−	0.226473i	$-0.0727194\pi$
$941$	2.52471	+	6.93657i	0.0823031	+	0.226126i	−0.891714	+	0.452598i	$0.850497\pi$
$942$	−7.88888	−	0.566233i	−0.257034	−	0.0184489i
$943$	11.7115	+	8.20046i	0.381378	+	0.267044i
$944$	−8.97979			−0.292267
$945$	4.52819	+	6.06674i	0.147302	+	0.197351i
$946$	14.5638			0.473511
$947$	−37.0964	−	25.9752i	−1.20547	−	0.844080i	−0.214313	−	0.976765i	$-0.568751\pi$
$947$	−37.0964	−	25.9752i	−1.20547	−	0.844080i	−0.991158	+	0.132685i	$0.957640\pi$
$948$	0.793327	−	1.17150i	0.0257661	−	0.0380486i
$949$	−22.0636	−	60.6193i	−0.716216	−	1.96779i
$950$	−0.0271261	+	0.0253910i	−0.000880088	+	0.000823792i
$951$	−19.0130	−	15.4544i	−0.616538	−	0.501144i
$952$	−3.75264	−	8.04757i	−0.121624	−	0.260823i
$953$	15.2575	−	56.9417i	0.494238	−	1.84452i	−0.0400176	−	0.999199i	$-0.512741\pi$
$953$	15.2575	−	56.9417i	0.494238	−	1.84452i	0.534256	−	0.845323i	$-0.320592\pi$
$954$	−4.37621	−	2.34757i	−0.141685	−	0.0760054i
$955$	2.95524	−	1.99737i	0.0956293	−	0.0646335i
$956$	3.82355	+	4.55672i	0.123662	+	0.147375i
$957$	−7.85949	−	1.97496i	−0.254061	−	0.0638413i
$958$	10.3721	+	14.8130i	0.335109	+	0.478585i
$959$	−2.09539	+	11.8836i	−0.0676638	+	0.383740i
$960$	−8.97691	−	24.7332i	−0.289729	−	0.798259i
$961$	−11.6596	+	9.78359i	−0.376117	+	0.315600i
$962$	2.17184	+	8.10540i	0.0700228	+	0.261329i
$963$	1.23065	+	10.3372i	0.0396573	+	0.333113i
$964$	−20.5357	+	11.8563i	−0.661411	+	0.381866i
$965$	0.310658	−	18.8101i	0.0100004	−	0.605517i
$966$	−8.12552	−	1.30229i	−0.261434	−	0.0419004i
$967$	−3.13774	−	35.8645i	−0.100903	−	1.15332i	−0.862772	−	0.505593i	$-0.831274\pi$
$967$	−3.13774	−	35.8645i	−0.100903	−	1.15332i	0.761869	−	0.647731i	$-0.224282\pi$
$968$	24.5670	+	11.4558i	0.789612	+	0.368202i
$969$	−0.0195157	+	0.0563408i	−0.000626936	+	0.00180993i
$970$	−4.63901	−	1.32550i	−0.148950	−	0.0425592i
$971$			28.3419i			0.909536i	0.890610	+	0.454768i	$0.150278\pi$
$971$			28.3419i			0.909536i	−0.890610	+	0.454768i	$0.849722\pi$
$972$	13.8124	+	8.14494i	0.443033	+	0.261249i
$973$	9.10313	−	9.10313i	0.291833	−	0.291833i
$974$	−1.05070	−	5.95880i	−0.0336665	−	0.190932i
$975$	14.4423	+	41.9383i	0.462524	+	1.34310i
$976$	−7.98283	+	2.90551i	−0.255524	+	0.0930032i
$977$	0.127935	−	0.0111928i	0.00409300	−	0.000358091i	−0.0851091	−	0.996372i	$-0.527124\pi$
$977$	0.127935	−	0.0111928i	0.00409300	−	0.000358091i	0.0892021	+	0.996014i	$0.471568\pi$
$978$	−11.2383	−	15.5282i	−0.359362	−	0.496538i
$979$	−5.58725	+	15.3509i	−0.178569	+	0.490615i
$980$	15.0866	−	1.06920i	0.481924	−	0.0341543i
$981$	26.2459	+	20.6616i	0.837968	+	0.659673i
$982$	−25.9825	+	6.96199i	−0.829135	+	0.222166i
$983$	−42.4506	−	3.71395i	−1.35396	−	0.118457i	−0.613044	−	0.790049i	$-0.710055\pi$
$983$	−42.4506	−	3.71395i	−1.35396	−	0.118457i	−0.740921	+	0.671592i	$0.765611\pi$
$984$	−9.98918	+	0.155976i	−0.318443	+	0.00497233i
$985$	25.0578	−	3.99289i	0.798407	−	0.127224i
$986$	14.9674	+	2.63916i	0.476660	+	0.0840480i
$987$	−2.00844	+	7.99271i	−0.0639292	+	0.254411i
$988$	−0.00346213	+	0.0395723i	−0.000110145	+	0.00125896i
$989$	39.4634	−	68.3525i	1.25486	−	2.17348i
$990$	−9.04170	−	1.45748i	−0.287364	−	0.0463217i
$991$	−9.60146	−	16.6302i	−0.305001	−	0.528276i	0.672261	−	0.740314i	$-0.265323\pi$
$991$	−9.60146	−	16.6302i	−0.305001	−	0.528276i	−0.977261	+	0.212038i	$0.931990\pi$
$992$	18.3539	−	8.55855i	0.582736	−	0.271734i
$993$	−2.99992	−	29.0565i	−0.0951995	−	0.922081i
$994$	−2.58114	+	3.07608i	−0.0818688	+	0.0975674i
$995$	53.9357	+	5.61766i	1.70988	+	0.178092i
$996$	3.12362	+	16.2290i	0.0989758	+	0.514236i
$997$	−17.0633	+	24.3689i	−0.540400	+	0.771771i	−0.992766	−	0.120061i	$-0.961691\pi$
$997$	−17.0633	+	24.3689i	−0.540400	+	0.771771i	0.452367	+	0.891832i	$0.350580\pi$
$998$	−30.6574	−	30.6574i	−0.970443	−	0.970443i
$999$	8.62844	−	0.404449i	0.272992	−	0.0127962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.7	yes	192
3.2	odd	2		405.2.r.a.152.10		192
5.2	odd	4		675.2.ba.b.68.10		192
5.3	odd	4	inner	135.2.q.a.68.7	yes	192
5.4	even	2		675.2.ba.b.257.10		192
15.8	even	4		405.2.r.a.233.10		192
27.2	odd	18	inner	135.2.q.a.2.7	✓	192
27.25	even	9		405.2.r.a.332.10		192
135.2	even	36		675.2.ba.b.218.10		192
135.29	odd	18		675.2.ba.b.407.10		192
135.83	even	36	inner	135.2.q.a.83.7	yes	192
135.133	odd	36		405.2.r.a.8.10		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.7	✓	192	27.2	odd	18	inner
135.2.q.a.68.7	yes	192	5.3	odd	4	inner
135.2.q.a.83.7	yes	192	135.83	even	36	inner
135.2.q.a.122.7	yes	192	1.1	even	1	trivial
405.2.r.a.8.10		192	135.133	odd	36
405.2.r.a.152.10		192	3.2	odd	2
405.2.r.a.233.10		192	15.8	even	4
405.2.r.a.332.10		192	27.25	even	9
675.2.ba.b.68.10		192	5.2	odd	4
675.2.ba.b.218.10		192	135.2	even	36
675.2.ba.b.257.10		192	5.4	even	2
675.2.ba.b.407.10		192	135.29	odd	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.807333 - 0.565301i) q^{2} +(-0.756415 - 1.55815i) q^{3} +(-0.351818 - 0.966613i) q^{4} +(-2.04189 + 0.911409i) q^{5} +(-0.270145 + 1.68555i) q^{6} +(-0.275357 - 0.590505i) q^{7} +(-0.772562 + 2.88324i) q^{8} +(-1.85567 + 2.35722i) q^{9} +O(q^{10})\)	\(q+(-0.807333 - 0.565301i) q^{2} +(-0.756415 - 1.55815i) q^{3} +(-0.351818 - 0.966613i) q^{4} +(-2.04189 + 0.911409i) q^{5} +(-0.270145 + 1.68555i) q^{6} +(-0.275357 - 0.590505i) q^{7} +(-0.772562 + 2.88324i) q^{8} +(-1.85567 + 2.35722i) q^{9} +(2.16371 + 0.418474i) q^{10} +(0.890417 + 1.06116i) q^{11} +(-1.24001 + 1.27935i) q^{12} +(-2.93770 - 4.19546i) q^{13} +(-0.111508 + 0.632393i) q^{14} +(2.96463 + 2.49218i) q^{15} +(0.677632 - 0.568601i) q^{16} +(-1.18168 - 4.41009i) q^{17} +(2.83068 - 0.854048i) q^{18} +(0.00652973 - 0.00376994i) q^{19} +(1.59936 + 1.65307i) q^{20} +(-0.711812 + 0.875714i) q^{21} +(-0.118990 - 1.36006i) q^{22} +(-6.70560 - 3.12687i) q^{23} +(5.07690 - 0.977159i) q^{24} +(3.33867 - 3.72200i) q^{25} +5.04782i q^{26} +(5.07656 + 1.10838i) q^{27} +(-0.473914 + 0.473914i) q^{28} +(-0.586508 - 3.32625i) q^{29} +(-0.984617 - 3.68793i) q^{30} +(3.73277 - 1.35862i) q^{31} +(5.07868 - 0.444327i) q^{32} +(0.979919 - 2.19008i) q^{33} +(-1.53902 + 4.22842i) q^{34} +(1.10044 + 0.954786i) q^{35} +(2.93138 + 0.964404i) q^{36} +(1.60572 - 0.430252i) q^{37} +(-0.00740282 - 0.000647662i) q^{38} +(-4.31505 + 7.75089i) q^{39} +(-1.05032 - 6.59139i) q^{40} +(-1.90299 - 0.335548i) q^{41} +(1.06971 - 0.304606i) q^{42} +(-0.929732 + 10.6269i) q^{43} +(0.712464 - 1.23402i) q^{44} +(1.64070 - 6.50447i) q^{45} +(3.64603 + 6.31511i) q^{46} +(6.61847 - 3.08624i) q^{47} +(-1.39854 - 0.625755i) q^{48} +(4.22664 - 5.03711i) q^{49} +(-4.79947 + 1.11755i) q^{50} +(-5.97775 + 5.17710i) q^{51} +(-3.02186 + 4.31566i) q^{52} +(-1.18766 - 1.18766i) q^{53} +(-3.47191 - 3.76462i) q^{54} +(-2.78529 - 1.35524i) q^{55} +(1.91530 - 0.337719i) q^{56} +(-0.0108133 - 0.00732266i) q^{57} +(-1.40682 + 3.01694i) q^{58} +(-7.77643 - 6.52520i) q^{59} +(1.36596 - 3.74245i) q^{60} +(-9.02437 - 3.28460i) q^{61} +(-3.78162 - 1.01328i) q^{62} +(1.90292 + 0.446706i) q^{63} +(-5.88351 - 3.39685i) q^{64} +(9.82225 + 5.88925i) q^{65} +(-2.02918 + 1.21418i) q^{66} +(-12.3176 + 8.62489i) q^{67} +(-3.84712 + 2.69378i) q^{68} +(0.200077 + 12.8136i) q^{69} +(-0.348682 - 1.39291i) q^{70} +(5.41550 + 3.12664i) q^{71} +(-5.36281 - 7.17145i) q^{72} +(12.1662 + 3.25991i) q^{73} +(-1.53958 - 0.560360i) q^{74} +(-8.32486 - 2.38677i) q^{75} +(-0.00594135 - 0.00498539i) q^{76} +(0.381436 - 0.817993i) q^{77} +(7.86527 - 3.81825i) q^{78} +(-0.782046 + 0.137896i) q^{79} +(-0.865425 + 1.77862i) q^{80} +(-2.11296 - 8.74845i) q^{81} +(1.34666 + 1.34666i) q^{82} +(5.32053 - 7.59850i) q^{83} +(1.09691 + 0.379954i) q^{84} +(6.43227 + 7.92795i) q^{85} +(6.75799 - 8.05386i) q^{86} +(-4.73916 + 3.42989i) q^{87} +(-3.74748 + 1.74748i) q^{88} +(5.89645 + 10.2130i) q^{89} +(-5.00157 + 4.32379i) q^{90} +(-1.66853 + 2.88997i) q^{91} +(-0.663323 + 7.58182i) q^{92} +(-4.94046 - 4.78855i) q^{93} +(-7.08796 - 1.24980i) q^{94} +(-0.00989706 + 0.0136491i) q^{95} +(-4.53392 - 7.57725i) q^{96} +(-2.18091 - 0.190805i) q^{97} +(-6.25979 + 1.67731i) q^{98} +(-4.15370 + 0.129748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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