LMFDB - Embedded newform 189.2.ba.a.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575801 + 0.686212i) q^{2} +(1.25894 + 1.18957i) q^{3} +(0.207955 + 1.17937i) q^{4} +(0.100696 - 0.0844942i) q^{5} +(-1.54119 + 0.178947i) q^{6} +(-1.70219 + 2.02548i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(0.169862 + 2.99519i) q^{9} +O(q^{10})$	\(q+(-0.575801 + 0.686212i) q^{2} +(1.25894 + 1.18957i) q^{3} +(0.207955 + 1.17937i) q^{4} +(0.100696 - 0.0844942i) q^{5} +(-1.54119 + 0.178947i) q^{6} +(-1.70219 + 2.02548i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(0.169862 + 2.99519i) q^{9} +0.117751i q^{10} +(2.57587 - 3.06980i) q^{11} +(-1.14114 + 1.73214i) q^{12} +(1.02604 - 2.81901i) q^{13} +(-0.409789 - 2.33433i) q^{14} +(0.227282 + 0.0134118i) q^{15} +(0.160408 - 0.0583836i) q^{16} -0.344621 q^{17} +(-2.15314 - 1.60807i) q^{18} +4.89841i q^{19} +(0.120590 + 0.101187i) q^{20} +(-4.55239 + 0.525094i) q^{21} +(0.623349 + 3.53519i) q^{22} +(2.18009 - 5.98976i) q^{23} +(-1.41925 - 4.75384i) q^{24} +(-0.865240 + 4.90702i) q^{25} +(1.34365 + 2.32726i) q^{26} +(-3.34913 + 3.97282i) q^{27} +(-2.74277 - 1.58630i) q^{28} +(2.29851 + 6.31510i) q^{29} +(-0.140072 + 0.148241i) q^{30} +(8.59607 - 1.51572i) q^{31} +(1.90702 - 5.23950i) q^{32} +(6.89460 - 0.800529i) q^{33} +(0.198433 - 0.236483i) q^{34} +(-0.000262488 + 0.347783i) q^{35} +(-3.49712 + 0.823195i) q^{36} +(3.64300 - 6.30985i) q^{37} +(-3.36135 - 2.82051i) q^{38} +(4.64512 - 2.32843i) q^{39} +(-0.370796 + 0.0653813i) q^{40} +(-9.04416 - 3.29180i) q^{41} +(2.26094 - 3.42626i) q^{42} +(0.350643 - 1.98860i) q^{43} +(4.15611 + 2.39953i) q^{44} +(0.270180 + 0.287252i) q^{45} +(2.85495 + 4.94491i) q^{46} +(0.771769 - 4.37692i) q^{47} +(0.271395 + 0.117314i) q^{48} +(-1.20513 - 6.89548i) q^{49} +(-2.86905 - 3.41920i) q^{50} +(-0.433857 - 0.409950i) q^{51} +(3.53803 + 0.623850i) q^{52} +(5.49931 + 3.17503i) q^{53} +(-0.797771 - 4.58577i) q^{54} -0.526764i q^{55} +(7.12325 - 2.58656i) q^{56} +(-5.82699 + 6.16681i) q^{57} +(-5.65698 - 2.05897i) q^{58} +(0.167214 + 0.0608610i) q^{59} +(0.0314470 + 0.270839i) q^{60} +(-4.60007 - 0.811116i) q^{61} +(-3.90952 + 6.77148i) q^{62} +(-6.35583 - 4.75431i) q^{63} +(2.66805 + 4.62120i) q^{64} +(-0.134872 - 0.370558i) q^{65} +(-3.42058 + 5.19210i) q^{66} +(8.83064 - 7.40979i) q^{67} +(-0.0716657 - 0.406437i) q^{68} +(9.86983 - 4.94738i) q^{69} +(-0.238502 - 0.200434i) q^{70} +(0.373587 - 0.215690i) q^{71} +(3.86826 - 7.67310i) q^{72} +(1.31951 - 0.761822i) q^{73} +(2.23226 + 6.13309i) q^{74} +(-6.92652 + 5.14839i) q^{75} +(-5.77706 + 1.01865i) q^{76} +(1.83321 + 10.4427i) q^{77} +(-1.07687 + 4.52825i) q^{78} +(1.81204 + 1.52049i) q^{79} +(0.0112194 - 0.0194325i) q^{80} +(-8.94229 + 1.01754i) q^{81} +(7.46651 - 4.31079i) q^{82} +(-6.81615 + 2.48087i) q^{83} +(-1.56598 - 5.25977i) q^{84} +(-0.0347021 + 0.0291185i) q^{85} +(1.16270 + 1.38565i) q^{86} +(-4.61855 + 10.6846i) q^{87} +(-10.7861 + 3.92584i) q^{88} -15.4181 q^{89} +(-0.352686 + 0.0200014i) q^{90} +(3.96334 + 6.87669i) q^{91} +(7.51752 + 1.32554i) q^{92} +(12.6250 + 8.31740i) q^{93} +(2.55911 + 3.04983i) q^{94} +(0.413888 + 0.493252i) q^{95} +(8.63357 - 4.32769i) q^{96} +(-12.2061 - 2.15226i) q^{97} +(5.42568 + 3.14345i) q^{98} +(9.63217 + 7.19377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.575801	+	0.686212i	−0.407152	+	0.485225i	−0.930187	−	0.367086i	$-0.880355\pi$
$2$	−0.575801	+	0.686212i	−0.407152	+	0.485225i	0.523034	+	0.852312i	$0.324800\pi$
$3$	1.25894	+	1.18957i	0.726850	+	0.686797i
$3$	1.25894	+	1.18957i	0.726850	+	0.686797i
$4$	0.207955	+	1.17937i	0.103978	+	0.589686i
$5$	0.100696	−	0.0844942i	0.0450327	−	0.0377870i	−0.619994	−	0.784607i	$-0.712865\pi$
$5$	0.100696	−	0.0844942i	0.0450327	−	0.0377870i	0.665026	+	0.746820i	$0.268420\pi$
$6$	−1.54119	+	0.178947i	−0.629190	+	0.0730549i
$7$	−1.70219	+	2.02548i	−0.643366	+	0.765559i
$7$	−1.70219	+	2.02548i	−0.643366	+	0.765559i
$8$	−2.48059	−	1.43217i	−0.877021	−	0.506348i
$9$	0.169862	+	2.99519i	0.0566207	+	0.998396i
$10$			0.117751i			0.0372361i
$11$	2.57587	−	3.06980i	0.776654	−	0.925580i	−0.222123	−	0.975019i	$-0.571299\pi$
$11$	2.57587	−	3.06980i	0.776654	−	0.925580i	0.998777	+	0.0494386i	$0.0157432\pi$
$12$	−1.14114	+	1.73214i	−0.329419	+	0.500025i
$13$	1.02604	−	2.81901i	0.284571	−	0.781852i	−0.712231	−	0.701945i	$-0.752315\pi$
$13$	1.02604	−	2.81901i	0.284571	−	0.781852i	0.996802	−	0.0799075i	$-0.0254625\pi$
$14$	−0.409789	−	2.33433i	−0.109521	−	0.623877i
$15$	0.227282	+	0.0134118i	0.0586840	+	0.00346290i
$16$	0.160408	−	0.0583836i	0.0401019	−	0.0145959i
$17$	−0.344621			−0.0835829			−0.0417914	−	0.999126i	$-0.513307\pi$
$17$	−0.344621			−0.0835829			−0.0417914	+	0.999126i	$0.513307\pi$
$18$	−2.15314	−	1.60807i	−0.507500	−	0.379026i
$19$			4.89841i			1.12377i	0.827214	+	0.561887i	$0.189924\pi$
$19$			4.89841i			1.12377i	−0.827214	+	0.561887i	$0.810076\pi$
$20$	0.120590	+	0.101187i	0.0269649	+	0.0226262i
$21$	−4.55239	+	0.525094i	−0.993413	+	0.114585i
$22$	0.623349	+	3.53519i	0.132898	+	0.753704i
$23$	2.18009	−	5.98976i	0.454581	−	1.24895i	−0.474887	−	0.880047i	$-0.657511\pi$
$23$	2.18009	−	5.98976i	0.454581	−	1.24895i	0.929468	−	0.368904i	$-0.120267\pi$
$24$	−1.41925	−	4.75384i	−0.289704	−	0.970374i
$25$	−0.865240	+	4.90702i	−0.173048	+	0.981404i
$26$	1.34365	+	2.32726i	0.263511	+	0.456414i
$27$	−3.34913	+	3.97282i	−0.644540	+	0.764570i
$28$	−2.74277	−	1.58630i	−0.518335	−	0.299783i
$29$	2.29851	+	6.31510i	0.426822	+	1.17268i	0.947731	+	0.319072i	$0.103371\pi$
$29$	2.29851	+	6.31510i	0.426822	+	1.17268i	−0.520908	+	0.853613i	$0.674407\pi$
$30$	−0.140072	+	0.148241i	−0.0255736	+	0.0270650i
$31$	8.59607	−	1.51572i	1.54390	−	0.272231i	0.664125	−	0.747622i	$-0.268804\pi$
$31$	8.59607	−	1.51572i	1.54390	−	0.272231i	0.879775	+	0.475391i	$0.157693\pi$
$32$	1.90702	−	5.23950i	0.337117	−	0.926222i
$33$	6.89460	−	0.800529i	1.20020	−	0.139354i
$34$	0.198433	−	0.236483i	0.0340310	−	0.0405565i
$35$	−0.000262488		0.347783i	−4.43686e−5		0.0587861i
$36$	−3.49712	+	0.823195i	−0.582853	+	0.137199i
$37$	3.64300	−	6.30985i	0.598905	−	1.03733i	−0.394078	−	0.919077i	$-0.628936\pi$
$37$	3.64300	−	6.30985i	0.598905	−	1.03733i	0.992983	−	0.118257i	$-0.0377305\pi$
$38$	−3.36135	−	2.82051i	−0.545283	−	0.457547i
$39$	4.64512	−	2.32843i	0.743814	−	0.372847i
$40$	−0.370796	+	0.0653813i	−0.0586280	+	0.0103377i
$41$	−9.04416	−	3.29180i	−1.41246	−	0.514094i	−0.480609	−	0.876935i	$-0.659585\pi$
$41$	−9.04416	−	3.29180i	−1.41246	−	0.514094i	−0.931851	+	0.362841i	$0.881807\pi$
$42$	2.26094	−	3.42626i	0.348871	−	0.528683i
$43$	0.350643	−	1.98860i	0.0534726	−	0.303258i	−0.946328	−	0.323207i	$-0.895239\pi$
$43$	0.350643	−	1.98860i	0.0534726	−	0.303258i	0.999801	+	0.0199486i	$0.00635026\pi$
$44$	4.15611	+	2.39953i	0.626556	+	0.361743i
$45$	0.270180	+	0.287252i	0.0402761	+	0.0428210i
$46$	2.85495	+	4.94491i	0.420939	+	0.729088i
$47$	0.771769	−	4.37692i	0.112574	−	0.638439i	−0.875349	−	0.483492i	$-0.839368\pi$
$47$	0.771769	−	4.37692i	0.112574	−	0.638439i	0.987923	−	0.154947i	$-0.0495207\pi$
$48$	0.271395	+	0.117314i	0.0391725	+	0.0169328i
$49$	−1.20513	−	6.89548i	−0.172161	−	0.985069i
$50$	−2.86905	−	3.41920i	−0.405745	−	0.483549i
$51$	−0.433857	−	0.409950i	−0.0607522	−	0.0574044i
$52$	3.53803	+	0.623850i	0.490637	+	0.0865125i
$53$	5.49931	+	3.17503i	0.755388	+	0.436123i	0.827637	−	0.561263i	$-0.189684\pi$
$53$	5.49931	+	3.17503i	0.755388	+	0.436123i	−0.0722494	+	0.997387i	$0.523018\pi$
$54$	−0.797771	−	4.58577i	−0.108563	−	0.624044i
$55$		−	0.526764i		−	0.0710288i
$56$	7.12325	−	2.58656i	0.951884	−	0.345644i
$57$	−5.82699	+	6.16681i	−0.771804	+	0.816814i
$58$	−5.65698	−	2.05897i	−0.742798	−	0.270356i
$59$	0.167214	+	0.0608610i	0.0217694	+	0.00792343i	0.352882	−	0.935668i	$-0.385202\pi$
$59$	0.167214	+	0.0608610i	0.0217694	+	0.00792343i	−0.331112	+	0.943591i	$0.607424\pi$
$60$	0.0314470	+	0.270839i	0.00405979	+	0.0349652i
$61$	−4.60007	−	0.811116i	−0.588978	−	0.103853i	−0.128787	−	0.991672i	$-0.541108\pi$
$61$	−4.60007	−	0.811116i	−0.588978	−	0.103853i	−0.460192	+	0.887820i	$0.652219\pi$
$62$	−3.90952	+	6.77148i	−0.496509	+	0.859979i
$63$	−6.35583	−	4.75431i	−0.800759	−	0.598987i
$64$	2.66805	+	4.62120i	0.333506	+	0.577649i
$65$	−0.134872	−	0.370558i	−0.0167288	−	0.0459620i
$66$	−3.42058	+	5.19210i	−0.421044	+	0.639104i
$67$	8.83064	−	7.40979i	1.07883	−	0.905249i	0.0830108	−	0.996549i	$-0.473546\pi$
$67$	8.83064	−	7.40979i	1.07883	−	0.905249i	0.995824	+	0.0912992i	$0.0291020\pi$
$68$	−0.0716657	−	0.406437i	−0.00869075	−	0.0492877i
$69$	9.86983	−	4.94738i	1.18819	−	0.595595i
$70$	−0.238502	−	0.200434i	−0.0285064	−	0.0239564i
$71$	0.373587	−	0.215690i	0.0443366	−	0.0255977i	−0.477668	−	0.878540i	$-0.658518\pi$
$71$	0.373587	−	0.215690i	0.0443366	−	0.0255977i	0.522004	+	0.852943i	$0.325184\pi$
$72$	3.86826	−	7.67310i	0.455878	−	0.904283i
$73$	1.31951	−	0.761822i	0.154437	−	0.0891645i	−0.420790	−	0.907158i	$-0.638247\pi$
$73$	1.31951	−	0.761822i	0.154437	−	0.0891645i	0.575227	+	0.817994i	$0.304914\pi$
$74$	2.23226	+	6.13309i	0.259495	+	0.712957i
$75$	−6.92652	+	5.14839i	−0.799805	+	0.594485i
$76$	−5.77706	+	1.01865i	−0.662674	+	0.116847i
$77$	1.83321	+	10.4427i	0.208914	+	1.19006i
$78$	−1.07687	+	4.52825i	−0.121931	+	0.512723i
$79$	1.81204	+	1.52049i	0.203871	+	0.171068i	0.739007	−	0.673698i	$-0.235295\pi$
$79$	1.81204	+	1.52049i	0.203871	+	0.171068i	−0.535136	+	0.844766i	$0.679740\pi$
$80$	0.0112194	−	0.0194325i	0.00125436	−	0.00217262i
$81$	−8.94229	+	1.01754i	−0.993588	+	0.113060i
$82$	7.46651	−	4.31079i	0.824538	−	0.476047i
$83$	−6.81615	+	2.48087i	−0.748169	+	0.272311i	−0.687835	−	0.725867i	$-0.741439\pi$
$83$	−6.81615	+	2.48087i	−0.748169	+	0.272311i	−0.0603341	+	0.998178i	$0.519217\pi$
$84$	−1.56598	−	5.25977i	−0.170862	−	0.573888i
$85$	−0.0347021	+	0.0291185i	−0.00376397	+	0.00315834i
$86$	1.16270	+	1.38565i	0.125377	+	0.149418i
$87$	−4.61855	+	10.6846i	−0.495160	+	1.14551i
$88$	−10.7861	+	3.92584i	−1.14981	+	0.418496i
$89$	−15.4181			−1.63431			−0.817156	−	0.576417i	$-0.804450\pi$
$89$	−15.4181			−1.63431			−0.817156	+	0.576417i	$0.804450\pi$
$90$	−0.352686	+	0.0200014i	−0.0371764	+	0.00210833i
$91$	3.96334	+	6.87669i	0.415471	+	0.720873i
$92$	7.51752	+	1.32554i	0.783756	+	0.138197i
$93$	12.6250	+	8.31740i	1.30915	+	0.862474i
$94$	2.55911	+	3.04983i	0.263952	+	0.314566i
$95$	0.413888	+	0.493252i	0.0424640	+	0.0506066i
$96$	8.63357	−	4.32769i	0.881160	−	0.441693i
$97$	−12.2061	−	2.15226i	−1.23934	−	0.218529i	−0.484708	−	0.874676i	$-0.661074\pi$
$97$	−12.2061	−	2.15226i	−1.23934	−	0.218529i	−0.754634	+	0.656147i	$0.772185\pi$
$98$	5.42568	+	3.14345i	0.548076	+	0.317536i
$99$	9.63217	+	7.19377i	0.968070	+	0.723001i
$100$	−5.96714			−0.596714
$101$	−3.54678	+	1.29092i	−0.352917	+	0.128451i	−0.512394	−	0.858750i	$-0.671241\pi$
$101$	−3.54678	+	1.29092i	−0.352917	+	0.128451i	0.159477	+	0.987202i	$0.449019\pi$
$102$	0.531128	−	0.0616690i	0.0525895	−	0.00610614i
$103$	−6.43432	−	7.66812i	−0.633992	−	0.755563i	0.349416	−	0.936968i	$-0.386380\pi$
$103$	−6.43432	−	7.66812i	−0.633992	−	0.755563i	−0.983408	+	0.181405i	$0.941935\pi$
$104$	−6.58247	+	5.52335i	−0.645464	+	0.541609i
$105$	−0.414042	+	0.437526i	−0.0404063	+	0.0426982i
$106$	−5.34525	+	1.94551i	−0.519176	+	0.188965i
$107$	−4.00378	+	2.31158i	−0.387060	+	0.223469i	−0.680885	−	0.732390i	$-0.738405\pi$
$107$	−4.00378	+	2.31158i	−0.387060	+	0.223469i	0.293826	+	0.955859i	$0.405072\pi$
$108$	−5.38191	−	3.12370i	−0.517874	−	0.300578i
$109$	−5.95833	+	10.3201i	−0.570704	+	0.988489i	0.425789	+	0.904822i	$0.359996\pi$
$109$	−5.95833	+	10.3201i	−0.570704	+	0.988489i	−0.996494	+	0.0836667i	$0.973337\pi$
$110$	0.361472	+	0.303311i	0.0344650	+	0.0289196i
$111$	12.0923	−	3.61014i	1.14775	−	0.342660i
$112$	−0.154789	+	0.424282i	−0.0146262	+	0.0400909i
$113$	−3.00669	+	0.530160i	−0.282846	+	0.0498733i	−0.313271	−	0.949664i	$-0.601425\pi$
$113$	−3.00669	+	0.530160i	−0.282846	+	0.0498733i	0.0304256	+	0.999537i	$0.490314\pi$
$114$	−0.876558	−	7.54941i	−0.0820972	−	0.707067i
$115$	−0.286573	−	0.787352i	−0.0267230	−	0.0734209i
$116$	−6.96987	+	4.02405i	−0.647136	+	0.373624i
$117$	8.61774	+	2.59433i	0.796711	+	0.239845i
$118$	−0.138046	+	0.0797007i	−0.0127081	+	0.00733704i
$119$	0.586609	−	0.698023i	0.0537744	−	0.0639876i
$120$	−0.544586	−	0.358775i	−0.0497136	−	0.0327516i
$121$	−0.878449	−	4.98193i	−0.0798590	−	0.452903i
$122$	3.20532	−	2.68958i	0.290196	−	0.243503i
$123$	−7.47024	−	14.9028i	−0.673569	−	1.34374i
$124$	3.57519	+	9.82277i	0.321062	+	0.882110i
$125$	0.656113	+	1.13642i	0.0586845	+	0.101645i
$126$	6.92216	−	1.62391i	0.616675	−	0.144669i
$127$	4.57273	−	7.92020i	0.405764	−	0.702804i	−0.588646	−	0.808391i	$-0.700339\pi$
$127$	4.57273	−	7.92020i	0.405764	−	0.702804i	0.994410	+	0.105587i	$0.0336720\pi$
$128$	6.27472	+	1.10640i	0.554612	+	0.0977931i
$129$	2.80701	−	2.08641i	0.247143	−	0.183698i
$130$	0.331941	+	0.120817i	0.0291131	+	0.0105963i
$131$	−5.23893	−	1.90681i	−0.457727	−	0.166599i	0.102858	−	0.994696i	$-0.467201\pi$
$131$	−5.23893	−	1.90681i	−0.457727	−	0.166599i	−0.560585	+	0.828097i	$0.689424\pi$
$132$	2.37789	+	7.96483i	0.206969	+	0.693249i
$133$	−9.92164	−	8.33801i	−0.860315	−	0.722997i
$134$			10.3263i			0.892052i
$135$	−0.00156415	+	0.683031i	−0.000134621	+	0.0587859i
$136$	0.854863	+	0.493555i	0.0733039	+	0.0423220i
$137$	14.2458	+	2.51192i	1.21710	+	0.214608i	0.745077	−	0.666979i	$-0.232413\pi$
$137$	14.2458	+	2.51192i	1.21710	+	0.214608i	0.472023	+	0.881586i	$0.343524\pi$
$138$	−2.28810	+	9.62150i	−0.194776	+	0.819037i
$139$	−8.80185	−	10.4896i	−0.746563	−	0.889720i	0.250356	−	0.968154i	$-0.419452\pi$
$139$	−8.80185	−	10.4896i	−0.746563	−	0.889720i	−0.996919	+	0.0784343i	$0.975008\pi$
$140$	−0.410220	+	0.0720137i	−0.0346699	+	0.00608627i
$141$	6.17825	−	4.59221i	0.520302	−	0.386734i
$142$	−0.0671020	+	0.380554i	−0.00563107	+	0.0319354i
$143$	−6.01086	−	10.4111i	−0.502654	−	0.870622i
$144$	0.202117	+	0.470534i	0.0168431	+	0.0392112i
$145$	0.765040	+	0.441696i	0.0635331	+	0.0366809i
$146$	−0.237005	+	1.34412i	−0.0196147	+	0.111241i
$147$	6.68545	−	10.1146i	0.551406	−	0.834237i
$148$	8.19925	+	2.98428i	0.673974	+	0.245306i
$149$	16.0341	−	2.82725i	1.31357	−	0.231617i	0.527393	−	0.849622i	$-0.323170\pi$
$149$	16.0341	−	2.82725i	1.31357	−	0.231617i	0.786175	+	0.618004i	$0.212059\pi$
$150$	0.455405	−	7.71751i	0.0371836	−	0.630132i
$151$	−3.24977	−	2.72688i	−0.264462	−	0.221910i	0.500908	−	0.865501i	$-0.333000\pi$
$151$	−3.24977	−	2.72688i	−0.264462	−	0.221910i	−0.765370	+	0.643590i	$0.777444\pi$
$152$	7.01536	−	12.1510i	0.569020	−	0.985572i
$153$	−0.0585380	−	1.03220i	−0.00473252	−	0.0834488i
$154$	−8.22150	−	4.75496i	−0.662508	−	0.383166i
$155$	0.737523	−	0.878945i	0.0592393	−	0.0705986i
$156$	3.71206	+	4.99411i	0.297203	+	0.399849i
$157$	−1.56492	+	4.29960i	−0.124895	+	0.343145i	−0.986344	−	0.164698i	$-0.947335\pi$
$157$	−1.56492	+	4.29960i	−0.124895	+	0.343145i	0.861449	+	0.507843i	$0.169557\pi$
$158$	−2.08675	+	0.367951i	−0.166013	+	0.0292726i
$159$	3.14639	+	10.5390i	0.249525	+	0.835794i
$160$	−0.250677	−	0.688731i	−0.0198178	−	0.0544489i
$161$	8.42121	+	14.6114i	0.663684	+	1.15154i
$162$	4.45073	−	6.72221i	0.349682	−	0.528147i
$163$	−4.14531	−	7.17988i	−0.324686	−	0.562372i	0.656763	−	0.754097i	$-0.271925\pi$
$163$	−4.14531	−	7.17988i	−0.324686	−	0.562372i	−0.981449	+	0.191725i	$0.938592\pi$
$164$	2.00148	−	11.3510i	0.156290	−	0.886363i
$165$	0.626621	−	0.663164i	0.0487823	−	0.0516273i
$166$	2.22233	−	6.10581i	0.172487	−	0.473903i
$167$	0.761050	+	4.31613i	0.0588919	+	0.333992i	0.999991	−	0.00413722i	$-0.00131692\pi$
$167$	0.761050	+	4.31613i	0.0588919	+	0.333992i	−0.941100	+	0.338130i	$0.890206\pi$
$168$	12.0446	+	5.21725i	0.929264	+	0.402520i
$169$	3.06452	+	2.57143i	0.235732	+	0.197803i
$170$		−	0.0405794i		−	0.00311230i
$171$	−14.6717	+	0.832054i	−1.12197	+	0.0636288i
$172$	2.41821			0.184387
$173$	−15.5919	+	5.67499i	−1.18543	+	0.431462i	−0.858117	−	0.513454i	$-0.828366\pi$
$173$	−15.5919	+	5.67499i	−1.18543	+	0.431462i	−0.327314	+	0.944916i	$0.606144\pi$
$174$	−4.67252	−	9.32148i	−0.354223	−	0.706659i
$175$	−8.46627	−	10.1052i	−0.639990	−	0.763880i
$176$	0.233963	−	0.642808i	0.0176356	−	0.0484535i
$177$	0.138115	+	0.275533i	0.0103813	+	0.0207103i
$178$	8.87773	−	10.5801i	0.665414	−	0.793010i
$179$		−	10.4083i		−	0.777951i	−0.921248	−	0.388976i	$-0.872829\pi$
$179$		−	10.4083i		−	0.777951i	0.921248	−	0.388976i	$-0.127171\pi$
$180$	−0.282592	+	0.378379i	−0.0210631	+	0.0282027i
$181$	14.3465	+	8.28296i	1.06637	+	0.615668i	0.927187	−	0.374599i	$-0.122220\pi$
$181$	14.3465	+	8.28296i	1.06637	+	0.615668i	0.139181	+	0.990267i	$0.455553\pi$
$182$	−7.00096	−	1.23991i	−0.518946	−	0.0919081i
$183$	−4.82633	−	6.49323i	−0.356773	−	0.479994i
$184$	−13.9863	+	11.7359i	−1.03108	+	0.865179i
$185$	−0.166310	−	0.943191i	−0.0122274	−	0.0693448i
$186$	−12.9770	+	3.87426i	−0.951518	+	0.284075i
$187$	−0.887699	+	1.05792i	−0.0649150	+	0.0773626i
$188$	5.32251			0.388184
$189$	−2.34603	−	13.5461i	−0.170649	−	0.985332i
$190$	−0.576792			−0.0418449
$191$	−6.66865	+	7.94739i	−0.482527	+	0.575053i	−0.951300	−	0.308265i	$-0.900252\pi$
$191$	−6.66865	+	7.94739i	−0.482527	+	0.575053i	0.468774	+	0.883318i	$0.344696\pi$
$192$	−2.13831	+	8.99163i	−0.154319	+	0.648915i
$193$	3.16593	+	17.9549i	0.227888	+	1.29242i	0.857086	+	0.515174i	$0.172273\pi$
$193$	3.16593	+	17.9549i	0.227888	+	1.29242i	−0.629197	+	0.777246i	$0.716616\pi$
$194$	8.50519	−	7.13670i	0.610637	−	0.512385i
$195$	0.271007	−	0.626949i	0.0194072	−	0.0448968i
$196$	7.88173	−	2.85525i	0.562981	−	0.203946i
$197$	−18.9850	−	10.9610i	−1.35263	−	0.780941i	−0.364012	−	0.931394i	$-0.618593\pi$
$197$	−18.9850	−	10.9610i	−1.35263	−	0.780941i	−0.988617	+	0.150454i	$0.951927\pi$
$198$	−10.4827	+	2.46754i	−0.744970	+	0.175360i
$199$			7.25537i			0.514320i	0.966369	+	0.257160i	$0.0827867\pi$
$199$			7.25537i			0.514320i	−0.966369	+	0.257160i	$0.917213\pi$
$200$	9.17399	−	10.9331i	0.648699	−	0.773089i
$201$	19.9317	+	1.17616i	1.40587	+	0.0829596i
$202$	1.15639	−	3.17715i	0.0813633	−	0.223544i
$203$	−16.7036	−	6.09389i	−1.17236	−	0.427707i
$204$	0.393261	−	0.596931i	0.0275337	−	0.0417935i
$205$	−1.18885	+	0.432707i	−0.0830330	+	0.0302215i
$206$	8.96685			0.624750
$207$	18.3108	+	5.51236i	1.27269	+	0.383135i
$208$		−	0.512094i		−	0.0355074i
$209$	15.0372	+	12.6177i	1.04014	+	0.872783i
$210$	−0.0618303	−	0.536048i	−0.00426670	−	0.0369908i
$211$	0.796078	+	4.51478i	0.0548043	+	0.310810i	0.999871	−	0.0160673i	$-0.00511459\pi$
$211$	0.796078	+	4.51478i	0.0548043	+	0.310810i	−0.945067	+	0.326878i	$0.894003\pi$
$212$	−2.60093	+	7.14600i	−0.178633	+	0.490789i
$213$	0.726901	+	0.172865i	0.0498064	+	0.0118445i
$214$	0.719141	−	4.07845i	0.0491595	−	0.278797i
$215$	−0.132716	−	0.229871i	−0.00905118	−	0.0156771i
$216$	13.9976	−	5.05843i	0.952414	−	0.344182i
$217$	−11.5620	+	19.9912i	−0.784883	+	1.35709i
$218$	−3.65099	−	10.0310i	−0.247276	−	0.679386i
$219$	2.56743	+	0.610562i	0.173491	+	0.0412580i
$220$	0.621251	−	0.109543i	0.0418847	−	0.00738540i
$221$	−0.353593	+	0.971490i	−0.0237853	+	0.0653495i
$222$	−4.48543	+	10.3766i	−0.301042	+	0.696433i
$223$	15.1586	−	18.0653i	1.01510	−	1.20974i	0.0374904	−	0.999297i	$-0.488064\pi$
$223$	15.1586	−	18.0653i	1.01510	−	1.20974i	0.977605	−	0.210447i	$-0.0674919\pi$
$224$	7.36639	+	12.7812i	0.492188	+	0.853982i
$225$	−14.8444	−	1.75804i	−0.989628	−	0.117203i
$226$	1.36745	−	2.36849i	0.0909615	−	0.157550i
$227$	−1.87601	−	1.57416i	−0.124515	−	0.104480i	0.578404	−	0.815751i	$-0.303676\pi$
$227$	−1.87601	−	1.57416i	−0.124515	−	0.104480i	−0.702919	+	0.711270i	$0.748120\pi$
$228$	−8.48472	−	5.58977i	−0.561914	−	0.370192i
$229$	0.258016	−	0.0454952i	0.0170502	−	0.00300640i	−0.165117	−	0.986274i	$-0.552800\pi$
$229$	0.258016	−	0.0454952i	0.0170502	−	0.00300640i	0.182167	+	0.983268i	$0.441689\pi$
$230$	0.705299	+	0.256708i	0.0465060	+	0.0169268i
$231$	−10.1144	+	15.3275i	−0.665481	+	1.00848i
$232$	3.34263	−	18.9570i	0.219455	−	1.24459i
$233$	−25.1425	−	14.5160i	−1.64714	−	0.950977i	−0.978201	−	0.207662i	$-0.933415\pi$
$233$	−25.1425	−	14.5160i	−1.64714	−	0.950977i	−0.668941	−	0.743316i	$-0.733252\pi$
$234$	−6.74236	+	4.41979i	−0.440762	+	0.288931i
$235$	−0.292110	−	0.505950i	−0.0190552	−	0.0330045i
$236$	−0.0370047	+	0.209864i	−0.00240880	+	0.0136610i
$237$	0.472537	+	4.06975i	0.0306945	+	0.264359i
$238$	0.141222	+	0.804460i	0.00915407	+	0.0521454i
$239$	1.21344	+	1.44612i	0.0784911	+	0.0935420i	0.803861	−	0.594817i	$-0.202776\pi$
$239$	1.21344	+	1.44612i	0.0784911	+	0.0935420i	−0.725370	+	0.688359i	$0.758331\pi$
$240$	0.0372408	−	0.0111182i	0.00240389	−	0.000717677i
$241$	18.0533	+	3.18328i	1.16291	+	0.205053i	0.721607	−	0.692303i	$-0.243404\pi$
$241$	18.0533	+	3.18328i	1.16291	+	0.205053i	0.441307	+	0.897356i	$0.354515\pi$
$242$	3.92447	+	2.26580i	0.252275	+	0.145651i
$243$	−12.4682	−	9.35644i	−0.799838	−	0.600216i
$244$		−	5.59387i		−	0.358111i
$245$	−0.703980	−	0.592523i	−0.0449757	−	0.0378549i
$246$	14.5279	+	3.45488i	0.926263	+	0.220275i
$247$	13.8087	+	5.02595i	0.878625	+	0.319793i
$248$	−23.4941	−	8.55114i	−1.49188	−	0.542998i
$249$	−11.5323	−	4.98499i	−0.730829	−	0.315911i
$250$	−1.15762	−	0.204119i	−0.0732141	−	0.0129096i
$251$	3.29266	−	5.70305i	0.207831	−	0.359973i	−0.743200	−	0.669069i	$-0.766693\pi$
$251$	3.29266	−	5.70305i	0.207831	−	0.359973i	0.951031	+	0.309096i	$0.100026\pi$
$252$	4.28538	−	8.48457i	0.269953	−	0.534478i
$253$	−12.7717	−	22.1213i	−0.802952	−	1.39075i
$254$	2.80196	+	7.69832i	0.175811	+	0.483036i
$255$	−0.0783262	−	0.00462198i	−0.00490498	−	0.000289439i
$256$	−12.5476	+	10.5287i	−0.784224	+	0.658042i
$257$	5.02735	+	28.5115i	0.313598	+	1.77850i	0.579978	+	0.814632i	$0.303061\pi$
$257$	5.02735	+	28.5115i	0.313598	+	1.77850i	−0.266381	+	0.963868i	$0.585828\pi$
$258$	−0.184555	+	3.12756i	−0.0114899	+	0.194713i
$259$	6.57942	+	18.1193i	0.408825	+	1.12588i
$260$	0.408978	−	0.236124i	0.0253638	−	0.0146438i
$261$	−18.5245	+	7.95716i	−1.14664	+	0.492536i
$262$	4.32506	−	2.49707i	0.267203	−	0.154270i
$263$	−7.94138	−	21.8188i	−0.489686	−	1.34540i	−0.900965	−	0.433892i	$-0.857140\pi$
$263$	−7.94138	−	21.8188i	−0.489686	−	1.34540i	0.411278	−	0.911510i	$-0.365082\pi$
$264$	−18.2492	−	7.88845i	−1.12316	−	0.485500i
$265$	0.822031	−	0.144946i	0.0504970	−	0.00890398i
$266$	11.4345	−	2.00732i	0.701096	−	0.123077i
$267$	−19.4104	−	18.3408i	−1.18790	−	1.12244i
$268$	10.5753	+	8.87371i	0.645988	+	0.542048i
$269$	−4.60903	+	7.98308i	−0.281018	+	0.486737i	−0.971636	−	0.236483i	$-0.924005\pi$
$269$	−4.60903	+	7.98308i	−0.281018	+	0.486737i	0.690618	+	0.723220i	$0.257339\pi$
$270$	−0.467803	−	0.394363i	−0.0284696	−	0.0240002i
$271$	25.5138	−	14.7304i	1.54985	−	0.894807i	0.551700	−	0.834043i	$-0.313980\pi$
$271$	25.5138	−	14.7304i	1.54985	−	0.894807i	0.998152	−	0.0607643i	$-0.0193538\pi$
$272$	−0.0552799	+	0.0201202i	−0.00335183	+	0.00121997i
$273$	−3.19067	+	13.3720i	−0.193108	+	0.809310i
$274$	−9.92644	+	8.32927i	−0.599678	+	0.503190i
$275$	12.8348	+	15.2960i	0.773970	+	0.922381i
$276$	7.88729	+	10.6114i	0.474759	+	0.638729i
$277$	−2.86248	+	1.04186i	−0.171990	+	0.0625991i	−0.426580	−	0.904450i	$-0.640282\pi$
$277$	−2.86248	+	1.04186i	−0.171990	+	0.0625991i	0.254590	+	0.967049i	$0.418059\pi$
$278$	12.2662			0.735680
$279$	6.00001	+	25.4894i	0.359211	+	1.52601i
$280$	0.498735	−	0.862331i	0.0298051	−	0.0515341i
$281$	24.6845	+	4.35255i	1.47256	+	0.259651i	0.851599	−	0.524194i	$-0.175633\pi$
$281$	24.6845	+	4.35255i	1.47256	+	0.259651i	0.620956	+	0.783845i	$0.286744\pi$
$282$	−0.406208	+	6.88379i	−0.0241893	+	0.409924i
$283$	7.17877	+	8.55533i	0.426734	+	0.508562i	0.935977	−	0.352061i	$-0.114519\pi$
$283$	7.17877	+	8.55533i	0.426734	+	0.508562i	−0.509243	+	0.860623i	$0.670075\pi$
$284$	0.332068	+	0.395744i	0.0197046	+	0.0234831i
$285$	−0.0656964	+	1.11332i	−0.00389152	+	0.0659475i
$286$	10.6053	+	1.87000i	0.627105	+	0.110575i
$287$	22.0623	−	12.7155i	1.30230	−	0.750572i
$288$	16.0172	+	4.82190i	0.943824	+	0.284133i
$289$	−16.8812			−0.993014
$290$	−0.743608	+	0.270651i	−0.0436662	+	0.0158932i
$291$	−12.8065	−	17.2295i	−0.750730	−	1.01001i
$292$	1.17287	+	1.39777i	0.0686371	+	0.0817986i
$293$	3.69754	−	3.10260i	0.216012	−	0.181256i	−0.528360	−	0.849020i	$-0.677193\pi$
$293$	3.69754	−	3.10260i	0.216012	−	0.181256i	0.744373	+	0.667764i	$0.232749\pi$
$294$	3.09127	+	10.4116i	0.180286	+	0.607218i
$295$	0.0219803	−	0.00800016i	0.00127974	−	0.000465787i
$296$	−18.0735	+	10.4348i	−1.05050	+	0.606508i
$297$	3.56886	+	20.5146i	0.207087	+	1.19038i
$298$	−7.29237	+	12.6308i	−0.422436	+	0.731680i
$299$	−14.6483	−	12.2914i	−0.847135	−	0.710830i
$300$	−7.51227	−	7.09831i	−0.433721	−	0.409821i
$301$	3.43100	+	4.09518i	0.197759	+	0.236042i
$302$	3.74243	−	0.659892i	0.215353	−	0.0379725i
$303$	−6.00082	−	2.59393i	−0.344738	−	0.149018i
$304$	0.285987	+	0.785743i	0.0164025	+	0.0450655i
$305$	−0.531744	+	0.307003i	−0.0304476	+	0.0175789i
$306$	0.742018	+	0.554174i	0.0424183	+	0.0316800i
$307$	−17.7257	+	10.2339i	−1.01166	+	0.584082i	−0.911677	−	0.410907i	$-0.865212\pi$
$307$	−17.7257	+	10.2339i	−1.01166	+	0.584082i	−0.0999825	+	0.994989i	$0.531879\pi$
$308$	−11.9347	+	4.33366i	−0.680040	+	0.246933i
$309$	1.02132	−	17.3078i	0.0581008	−	0.984604i
$310$	0.178477	+	1.01219i	0.0101368	+	0.0574888i
$311$	11.3004	−	9.48217i	0.640787	−	0.537684i	−0.263473	−	0.964667i	$-0.584868\pi$
$311$	11.3004	−	9.48217i	0.640787	−	0.537684i	0.904260	+	0.426982i	$0.140423\pi$
$312$	−14.8573	−	0.876721i	−0.841130	−	0.0496345i
$313$	4.05965	+	11.1538i	0.229465	+	0.630450i	0.999976	−	0.00697724i	$-0.00222094\pi$
$313$	4.05965	+	11.1538i	0.229465	+	0.630450i	−0.770511	+	0.637427i	$0.779999\pi$
$314$	−2.04935	−	3.54958i	−0.115652	−	0.200314i
$315$	−1.04172	+	0.0582889i	−0.0586943	+	0.00328421i
$316$	−1.41639	+	2.45327i	−0.0796784	+	0.138007i
$317$	−20.1601	−	3.55477i	−1.13230	−	0.199656i	−0.424067	−	0.905631i	$-0.639398\pi$
$317$	−20.1601	−	3.55477i	−1.13230	−	0.199656i	−0.708237	+	0.705975i	$0.750509\pi$
$318$	−9.04366	−	3.90925i	−0.507143	−	0.219220i
$319$	25.3068	+	9.21090i	1.41691	+	0.515712i
$320$	0.659127	+	0.239903i	0.0368463	+	0.0134110i
$321$	−7.79030	−	1.85262i	−0.434812	−	0.103403i
$322$	−14.8755	−	2.63452i	−0.828977	−	0.146816i
$323$		−	1.68810i		−	0.0939282i
$324$	−3.05965	−	10.3347i	−0.169981	−	0.574150i
$325$	12.9452	+	7.47390i	0.718069	+	0.414577i
$326$	7.31379	+	1.28962i	0.405074	+	0.0714254i
$327$	−19.7777	+	5.90460i	−1.09371	+	0.326525i
$328$	17.7204	+	21.1184i	0.978447	+	1.16607i
$329$	7.55166	+	9.01353i	0.416337	+	0.496932i
$330$	0.0942630	+	0.811845i	0.00518900	+	0.0446906i
$331$	−2.39022	+	13.5556i	−0.131378	+	0.745083i	0.845935	+	0.533285i	$0.179043\pi$
$331$	−2.39022	+	13.5556i	−0.131378	+	0.745083i	−0.977314	+	0.211798i	$0.932068\pi$
$332$	−4.34333	−	7.52287i	−0.238371	−	0.412871i
$333$	19.5180	+	9.83965i	1.06958	+	0.539209i
$334$	−3.40000	−	1.96299i	−0.186040	−	0.107410i
$335$	0.263129	−	1.49228i	0.0143762	−	0.0815317i
$336$	−0.699582	+	0.350014i	−0.0381653	+	0.0190948i
$337$	−11.8712	−	4.32077i	−0.646667	−	0.235367i	−0.00219742	−	0.999998i	$-0.500699\pi$
$337$	−11.8712	−	4.32077i	−0.646667	−	0.235367i	−0.644469	+	0.764630i	$0.722922\pi$
$338$	−3.52910	+	0.622276i	−0.191958	+	0.0338473i
$339$	−4.41590	−	2.90922i	−0.239839	−	0.158007i
$340$	−0.0415580	−	0.0348713i	−0.00225380	−	0.00189116i
$341$	17.4894	−	30.2925i	0.947104	−	1.64043i
$342$	7.87699	−	10.5470i	0.425939	−	0.570315i
$343$	16.0180	+	9.29642i	0.864891	+	0.501960i
$344$	−3.71780	+	4.43071i	−0.200451	+	0.238888i
$345$	0.575830	−	1.33213i	0.0310016	−	0.0717193i
$346$	5.08358	−	13.9670i	0.273295	−	0.750872i
$347$	17.8481	−	3.14709i	0.958134	−	0.168945i	0.327350	−	0.944903i	$-0.393845\pi$
$347$	17.8481	−	3.14709i	0.958134	−	0.168945i	0.630784	+	0.775958i	$0.282733\pi$
$348$	−13.5615	−	3.22508i	−0.726974	−	0.172882i
$349$	−6.17471	−	16.9649i	−0.330525	−	0.908109i	−0.987975	−	0.154612i	$-0.950587\pi$
$349$	−6.17471	−	16.9649i	−0.330525	−	0.908109i	0.657450	−	0.753498i	$-0.271635\pi$
$350$	11.8092	+	0.00891295i	0.631228	+	0.000476417i
$351$	7.76310	+	13.5175i	0.414364	+	0.721510i
$352$	−11.1720	−	19.3505i	−0.595469	−	1.03138i
$353$	−2.71457	+	15.3951i	−0.144482	+	0.819398i	0.823300	+	0.567607i	$0.192131\pi$
$353$	−2.71457	+	15.3951i	−0.144482	+	0.819398i	−0.967782	+	0.251791i	$0.918981\pi$
$354$	−0.268601	−	0.0638761i	−0.0142760	−	0.00339498i
$355$	0.0193942	−	0.0532851i	0.00102934	−	0.00282808i
$356$	−3.20627	−	18.1836i	−0.169932	−	0.963731i
$357$	1.56885	−	0.180959i	0.0830324	−	0.00957734i
$358$	7.14229	+	5.99309i	0.377482	+	0.316745i
$359$		−	10.1138i		−	0.533785i	−0.963726	−	0.266892i	$-0.914003\pi$
$359$		−	10.1138i		−	0.533785i	0.963726	−	0.266892i	$-0.0859968\pi$
$360$	−0.258814	−	1.09950i	−0.0136407	−	0.0579486i
$361$	−4.99446			−0.262866
$362$	−13.9446	+	5.07542i	−0.732912	+	0.266758i
$363$	4.82042	−	7.31693i	0.253007	−	0.384039i
$364$	−7.28598	+	6.10430i	−0.381889	+	0.319952i
$365$	0.0685006	−	0.188204i	0.00358549	−	0.00985105i
$366$	7.23474	+	0.426917i	0.378166	+	0.0223153i
$367$	−17.9093	+	21.3435i	−0.934859	+	1.11412i	0.0584104	+	0.998293i	$0.481397\pi$
$367$	−17.9093	+	21.3435i	−0.934859	+	1.11412i	−0.993269	+	0.115829i	$0.963048\pi$
$368$		−	1.08809i		−	0.0567204i
$369$	8.32331	−	27.6481i	0.433294	−	1.43930i
$370$	0.742991	+	0.428966i	0.0386262	+	0.0223009i
$371$	−15.7918	+	5.73425i	−0.819869	+	0.297707i
$372$	−7.18388	+	16.6192i	−0.372467	+	0.861666i
$373$	15.1151	−	12.6831i	0.782632	−	0.656706i	−0.161278	−	0.986909i	$-0.551562\pi$
$373$	15.1151	−	12.6831i	0.782632	−	0.656706i	0.943910	+	0.330203i	$0.107117\pi$
$374$	−0.214819	−	1.21830i	−0.0111080	−	0.0629968i
$375$	−0.525841	+	2.21118i	−0.0271543	+	0.114185i
$376$	−8.18293	+	9.75203i	−0.422002	+	0.502923i
$377$	20.1607			1.03833
$378$	10.6463	+	6.18996i	0.547588	+	0.318377i
$379$	3.29633			0.169321			0.0846605	−	0.996410i	$-0.473019\pi$
$379$	3.29633			0.169321			0.0846605	+	0.996410i	$0.473019\pi$
$380$	−0.495658	+	0.590702i	−0.0254267	+	0.0303024i
$381$	15.1784	−	4.53150i	0.777613	−	0.232156i
$382$	−1.61378	−	9.15222i	−0.0825684	−	0.468269i
$383$	−23.6377	+	19.8344i	−1.20783	+	1.01349i	−0.208459	+	0.978031i	$0.566845\pi$
$383$	−23.6377	+	19.8344i	−1.20783	+	1.01349i	−0.999371	+	0.0354584i	$0.988711\pi$
$384$	6.58336	+	8.85709i	0.335956	+	0.451987i
$385$	1.06695	+	0.896649i	0.0543767	+	0.0456975i
$386$	−14.1438	−	8.16592i	−0.719900	−	0.415635i
$387$	6.01578	+	0.712455i	0.305799	+	0.0362161i
$388$		−	14.8431i		−	0.753545i
$389$	−8.64017	+	10.2969i	−0.438074	+	0.522076i	−0.939234	−	0.343279i	$-0.888462\pi$
$389$	−8.64017	+	10.2969i	−0.438074	+	0.522076i	0.501160	+	0.865355i	$0.332907\pi$
$390$	0.274174	+	0.546966i	0.0138834	+	0.0276967i
$391$	−0.751306	+	2.06420i	−0.0379952	+	0.104391i
$392$	−6.88606	+	18.8308i	−0.347799	+	0.951099i
$393$	−4.32721	−	8.63262i	−0.218279	−	0.435458i
$394$	18.4532	−	6.71641i	0.929658	−	0.338368i
$395$	0.310938			0.0156450
$396$	−6.48107	+	12.8559i	−0.325686	+	0.646033i
$397$		−	32.3533i		−	1.62376i	−0.583821	−	0.811882i	$-0.698443\pi$
$397$		−	32.3533i		−	1.62376i	0.583821	−	0.811882i	$-0.301557\pi$
$398$	−4.97873	−	4.17765i	−0.249561	−	0.209407i
$399$	−2.57213	−	22.2995i	−0.128768	−	1.11637i
$400$	0.147699	+	0.837640i	0.00738493	+	0.0418820i
$401$	13.0462	−	35.8442i	0.651498	−	1.78998i	0.0393585	−	0.999225i	$-0.487469\pi$
$401$	13.0462	−	35.8442i	0.651498	−	1.78998i	0.612139	−	0.790750i	$-0.290309\pi$
$402$	−12.2838	+	13.0001i	−0.612659	+	0.648388i
$403$	4.54704	−	25.7876i	0.226504	−	1.28457i
$404$	−2.26005	−	3.91452i	−0.112442	−	0.194754i
$405$	−0.814480	+	0.858034i	−0.0404718	+	0.0426361i
$406$	13.7996	−	7.95334i	0.684864	−	0.394718i
$407$	−9.98612	−	27.4366i	−0.494993	−	1.35998i
$408$	0.489105	+	1.63827i	0.0242143	+	0.0811066i
$409$	−22.3158	+	3.93488i	−1.10345	+	0.194567i	−0.695562	−	0.718466i	$-0.744845\pi$
$409$	−22.3158	+	3.93488i	−1.10345	+	0.194567i	−0.407885	+	0.913033i	$0.633734\pi$
$410$	0.387613	−	1.06496i	0.0191428	−	0.0525945i
$411$	14.9465	+	20.1087i	0.737257	+	0.991888i
$412$	7.70552	−	9.18309i	0.379624	−	0.452418i
$413$	−0.407902	+	0.235092i	−0.0200716	+	0.0115681i
$414$	−14.3260	+	9.39105i	−0.704084	+	0.461545i
$415$	−0.476741	+	0.825740i	−0.0234023	+	0.0405340i
$416$	−12.8135	−	10.7518i	−0.628235	−	0.527152i
$417$	1.39712	−	23.6762i	0.0684172	−	1.15943i
$418$	−17.3168	+	3.05342i	−0.846993	+	0.149348i
$419$	1.24840	+	0.454379i	0.0609881	+	0.0221979i	0.372334	−	0.928099i	$-0.378558\pi$
$419$	1.24840	+	0.454379i	0.0609881	+	0.0221979i	−0.311346	+	0.950297i	$0.600780\pi$
$420$	−0.602108	−	0.397323i	−0.0293799	−	0.0193874i
$421$	−0.798906	+	4.53082i	−0.0389363	+	0.220819i	−0.998067	−	0.0621441i	$-0.980206\pi$
$421$	−0.798906	+	4.53082i	−0.0389363	+	0.220819i	0.959131	+	0.282963i	$0.0913173\pi$
$422$	−3.55648	−	2.05334i	−0.173127	−	0.0999548i
$423$	13.2408	+	1.56812i	0.643789	+	0.0762446i
$424$	−9.09435	−	15.7519i	−0.441661	−	0.764979i
$425$	0.298180	−	1.69106i	0.0144639	−	0.0820286i
$426$	−0.537172	+	0.399273i	−0.0260261	+	0.0193448i
$427$	9.47306	−	7.93667i	0.458434	−	0.384082i
$428$	−3.55882	−	4.24124i	−0.172022	−	0.205008i
$429$	4.81740	−	20.2573i	0.232586	−	0.978032i
$430$	0.234159	+	0.0412885i	0.0112921	+	0.00199111i
$431$	15.3689	+	8.87327i	0.740296	+	0.427410i	0.822177	−	0.569232i	$-0.192759\pi$
$431$	15.3689	+	8.87327i	0.740296	+	0.427410i	−0.0818808	+	0.996642i	$0.526093\pi$
$432$	−0.305278	+	0.832806i	−0.0146877	+	0.0400684i
$433$		−	1.22234i		−	0.0587418i	−0.999569	−	0.0293709i	$-0.990650\pi$
$433$		−	1.22234i		−	0.0587418i	0.999569	−	0.0293709i	$-0.00935038\pi$
$434$	−7.06077	−	19.4450i	−0.338928	−	0.933388i
$435$	0.437713	+	1.46614i	0.0209867	+	0.0702958i
$436$	−13.4103	−	4.88096i	−0.642239	−	0.233756i
$437$	29.3403	+	10.6790i	1.40354	+	0.510846i
$438$	−1.89730	+	1.41024i	−0.0906566	+	0.0673838i
$439$	4.79703	+	0.845847i	0.228950	+	0.0403701i	0.286946	−	0.957947i	$-0.407360\pi$
$439$	4.79703	+	0.845847i	0.228950	+	0.0403701i	−0.0579961	+	0.998317i	$0.518471\pi$
$440$	−0.754414	+	1.30668i	−0.0359653	+	0.0622937i
$441$	20.4486	−	4.78087i	0.973741	−	0.227660i
$442$	−0.463049	−	0.802024i	−0.0220250	−	0.0381484i
$443$	7.95536	+	21.8572i	0.377971	+	1.03847i	0.972196	+	0.234168i	$0.0752364\pi$
$443$	7.95536	+	21.8572i	0.377971	+	1.03847i	−0.594226	+	0.804298i	$0.702541\pi$
$444$	6.77236	+	13.5106i	0.321402	+	0.641184i
$445$	−1.55254	+	1.30274i	−0.0735975	+	0.0617557i
$446$	3.66832	+	20.8041i	0.173700	+	0.985100i
$447$	23.5492	+	15.5143i	1.11384	+	0.733803i
$448$	−13.9016	−	2.46206i	−0.656791	−	0.116321i
$449$	19.9333	−	11.5085i	0.940710	−	0.543119i	0.0505273	−	0.998723i	$-0.483910\pi$
$449$	19.9333	−	11.5085i	0.940710	−	0.543119i	0.890183	+	0.455603i	$0.150576\pi$
$450$	9.75382	−	9.17415i	0.459799	−	0.432473i
$451$	−33.4018	+	19.2845i	−1.57283	+	0.908072i
$452$	−1.25051	−	3.43576i	−0.0588192	−	0.161604i
$453$	−0.847459	−	7.29879i	−0.0398171	−	0.342927i
$454$	2.16041	−	0.380939i	0.101393	−	0.0178783i
$455$	0.980134	+	0.357578i	0.0459494	+	0.0167635i
$456$	23.2863	−	6.95209i	1.09048	−	0.325561i
$457$	20.3778	+	17.0990i	0.953231	+	0.799856i	0.979839	−	0.199790i	$-0.0640260\pi$
$457$	20.3778	+	17.0990i	0.953231	+	0.799856i	−0.0266074	+	0.999646i	$0.508470\pi$
$458$	−0.117346	+	0.203250i	−0.00548323	+	0.00949724i
$459$	1.15418	−	1.36912i	0.0538725	−	0.0639050i
$460$	0.868987	−	0.501710i	0.0405167	−	0.0233923i
$461$	−25.7975	+	9.38952i	−1.20151	+	0.437314i	−0.863751	−	0.503919i	$-0.831891\pi$
$461$	−25.7975	+	9.38952i	−1.20151	+	0.437314i	−0.337758	+	0.941233i	$0.609669\pi$
$462$	−4.69403	−	15.7662i	−0.218386	−	0.733512i
$463$	2.44473	−	2.05137i	0.113616	−	0.0953355i	−0.584210	−	0.811603i	$-0.698595\pi$
$463$	2.44473	−	2.05137i	0.113616	−	0.0953355i	0.697826	+	0.716267i	$0.254151\pi$
$464$	0.737397	+	0.878795i	0.0342328	+	0.0407970i
$465$	1.97406	−	0.229207i	0.0915449	−	0.0106292i
$466$	24.4382	−	8.89476i	1.13208	−	0.412042i
$467$	16.9027			0.782162			0.391081	−	0.920356i	$-0.372101\pi$
$467$	16.9027			0.782162			0.391081	+	0.920356i	$0.372101\pi$
$468$	−1.26757	+	10.7030i	−0.0585935	+	0.494748i
$469$	−0.0230191	+	30.4991i	−0.00106292	+	1.40832i
$470$	0.515386	+	0.0908765i	0.0237730	+	0.00419182i
$471$	−7.08480	+	3.55135i	−0.326450	+	0.163638i
$472$	−0.327627	−	0.390450i	−0.0150802	−	0.0179719i
$473$	−5.20138	−	6.19877i	−0.239160	−	0.285020i
$474$	−3.06480	−	2.01910i	−0.140771	−	0.0927405i
$475$	−24.0366	−	4.23831i	−1.10288	−	0.194467i
$476$	0.945217	+	0.546673i	0.0433240	+	0.0250567i
$477$	−8.57568	+	17.0108i	−0.392653	+	0.778870i
$478$	−1.69105			−0.0773468
$479$	35.4520	−	12.9035i	1.61984	−	0.589574i	0.636490	−	0.771285i	$-0.280386\pi$
$479$	35.4520	−	12.9035i	1.61984	−	0.589574i	0.983352	+	0.181710i	$0.0581633\pi$
$480$	0.503703	−	1.16527i	0.0229908	−	0.0531870i
$481$	−14.0497	−	16.7438i	−0.640611	−	0.763450i
$482$	−12.5795	+	10.5554i	−0.572980	+	0.480787i
$483$	−6.77945	+	28.4125i	−0.308476	+	1.29281i
$484$	5.69287	−	2.07204i	0.258767	−	0.0941835i
$485$	−1.41096	+	0.814620i	−0.0640685	+	0.0369900i
$486$	13.5997	−	3.16842i	0.616896	−	0.143723i
$487$	−9.18231	+	15.9042i	−0.416090	+	0.720689i	−0.995542	−	0.0943172i	$-0.969933\pi$
$487$	−9.18231	+	15.9042i	−0.416090	+	0.720689i	0.579452	+	0.815006i	$0.303267\pi$
$488$	10.2492	+	8.60012i	0.463960	+	0.389309i
$489$	3.32225	−	13.9702i	0.150238	−	0.631753i
$490$	0.811949	−	0.141905i	0.0366801	−	0.00641062i
$491$	−17.9717	+	3.16890i	−0.811053	+	0.143011i	−0.563769	−	0.825933i	$-0.690649\pi$
$491$	−17.9717	+	3.16890i	−0.811053	+	0.143011i	−0.247284	+	0.968943i	$0.579538\pi$
$492$	16.0225	−	11.9093i	0.722350	−	0.536913i
$493$	−0.792114	−	2.17632i	−0.0356750	−	0.0980163i
$494$	−11.3999	+	6.58174i	−0.512906	+	0.296126i
$495$	1.57776	−	0.0894771i	0.0709149	−	0.00402170i
$496$	1.29038	−	0.745003i	0.0579399	−	0.0334516i
$497$	−0.199037	+	1.12384i	−0.00892805	+	0.0504110i
$498$	10.0611	−	5.04324i	0.450847	−	0.225993i
$499$	6.49963	+	36.8612i	0.290963	+	1.65013i	0.683172	+	0.730258i	$0.260600\pi$
$499$	6.49963	+	36.8612i	0.290963	+	1.65013i	−0.392208	+	0.919876i	$0.628289\pi$
$500$	−1.20382	+	1.01013i	−0.0538365	+	0.0451742i
$501$	−4.17621	+	6.33907i	−0.186579	+	0.283209i
$502$	2.01759	+	5.54328i	0.0900494	+	0.247409i
$503$	8.72136	+	15.1058i	0.388866	+	0.673536i	0.992297	−	0.123879i	$-0.0395335\pi$
$503$	8.72136	+	15.1058i	0.388866	+	0.673536i	−0.603431	+	0.797415i	$0.706200\pi$
$504$	8.95721	+	20.8961i	0.398986	+	0.930787i
$505$	−0.248072	+	0.429673i	−0.0110391	+	0.0191202i
$506$	22.5339	+	3.97333i	1.00175	+	0.176636i
$507$	0.799151	+	6.88273i	0.0354915	+	0.305673i
$508$	10.2918	+	3.74591i	0.456625	+	0.166198i
$509$	26.2302	+	9.54701i	1.16263	+	0.423164i	0.850037	−	0.526723i	$-0.176579\pi$
$509$	26.2302	+	9.54701i	1.16263	+	0.423164i	0.312595	+	0.949886i	$0.398802\pi$
$510$	0.0482719	−	0.0510871i	0.00213752	−	0.00226217i
$511$	−0.703004	+	3.96941i	−0.0310991	+	0.175596i
$512$		−	1.92969i		−	0.0852812i
$513$	−19.4605	−	16.4054i	−0.859204	−	0.724317i
$514$	−22.4597	−	12.9671i	−0.990655	−	0.571955i
$515$	−1.29582	−	0.228489i	−0.0571008	−	0.0100684i
$516$	3.04439	+	2.87663i	0.134022	+	0.126636i
$517$	−11.4483	−	13.6436i	−0.503496	−	0.600043i
$518$	−16.2222	−	5.91825i	−0.712761	−	0.260033i
$519$	−26.3801	−	11.4031i	−1.15796	−	0.500543i
$520$	−0.196139	+	1.11236i	−0.00860127	+	0.0487802i
$521$	3.13445	+	5.42902i	0.137323	+	0.237850i	0.926482	−	0.376338i	$-0.122817\pi$
$521$	3.13445	+	5.42902i	0.137323	+	0.237850i	−0.789160	+	0.614188i	$0.789484\pi$
$522$	5.20610	−	17.2935i	0.227865	−	0.756914i
$523$	5.33996	+	3.08303i	0.233500	+	0.134811i	0.612186	−	0.790714i	$-0.290290\pi$
$523$	5.33996	+	3.08303i	0.233500	+	0.134811i	−0.378686	+	0.925525i	$0.623624\pi$
$524$	1.15938	−	6.57518i	0.0506478	−	0.287238i
$525$	1.36226	−	22.7930i	0.0594541	−	0.994769i
$526$	19.5450	+	7.11378i	0.852200	+	0.310176i
$527$	−2.96239	+	0.522349i	−0.129044	+	0.0227539i
$528$	1.05921	−	0.530943i	0.0460962	−	0.0231063i
$529$	−13.5054	−	11.3324i	−0.587190	−	0.492711i
$530$	−0.373862	+	0.647548i	−0.0162395	+	0.0281277i
$531$	−0.153887	+	0.511176i	−0.00667812	+	0.0221832i
$532$	7.77036	−	13.4352i	0.336888	−	0.582491i
$533$	−18.5593	+	22.1181i	−0.803890	+	0.958039i
$534$	23.7622	−	2.75902i	1.02829	−	0.119395i
$535$	−0.207850	+	0.571064i	−0.00898615	+	0.0246892i
$536$	−32.5172	+	5.73367i	−1.40453	+	0.247657i
$537$	12.3813	−	13.1034i	0.534294	−	0.565454i
$538$	−2.82420	−	7.75944i	−0.121760	−	0.334533i
$539$	−24.2720	−	14.0623i	−1.04547	−	0.605708i
$540$	−0.805873	+	0.140195i	−0.0346792	+	0.00603304i
$541$	−10.3506	−	17.9278i	−0.445008	−	0.770777i	0.553045	−	0.833152i	$-0.313466\pi$
$541$	−10.3506	−	17.9278i	−0.445008	−	0.770777i	−0.998053	+	0.0623747i	$0.980133\pi$
$542$	−4.58267	+	25.9896i	−0.196843	+	1.11635i
$543$	8.20827	+	27.4939i	0.352250	+	1.17988i
$544$	−0.657200	+	1.80564i	−0.0281772	+	0.0774163i
$545$	0.272010	+	1.54264i	0.0116516	+	0.0660796i
$546$	−7.33884	−	9.88908i	−0.314073	−	0.423214i
$547$	−12.9704	−	10.8834i	−0.554573	−	0.465342i	0.321913	−	0.946769i	$-0.395674\pi$
$547$	−12.9704	−	10.8834i	−0.554573	−	0.465342i	−0.876486	+	0.481427i	$0.840118\pi$
$548$			17.3235i			0.740022i
$549$	1.64807	−	13.9158i	0.0703378	−	0.593914i
$550$	−17.8866			−0.762687
$551$	−30.9340	+	11.2590i	−1.31783	+	0.479651i
$552$	−31.5685	−	1.86283i	−1.34364	−	0.0792875i
$553$	−6.16415	+	1.08211i	−0.262126	+	0.0460160i
$554$	0.933281	−	2.56417i	0.0396513	−	0.108941i
$555$	0.912614	−	1.38526i	0.0387383	−	0.0588009i
$556$	10.5408	−	12.5620i	0.447030	−	0.532749i
$557$			42.9293i			1.81897i	0.415735	+	0.909486i	$0.363524\pi$
$557$			42.9293i			1.81897i	−0.415735	+	0.909486i	$0.636476\pi$
$558$	−20.9459	−	10.5595i	−0.886712	−	0.447020i
$559$	−5.24610	−	3.02883i	−0.221886	−	0.128106i
$560$	0.0202627	+	0.0558024i	0.000856257	+	0.00235808i
$561$	−2.37602	+	0.275879i	−0.100316	+	0.0116476i
$562$	−17.2001	+	14.4326i	−0.725544	+	0.608804i
$563$	0.471251	+	2.67260i	0.0198609	+	0.112637i	0.993127	−	0.117046i	$-0.0373424\pi$
$563$	0.471251	+	2.67260i	0.0198609	+	0.112637i	−0.973266	+	0.229682i	$0.926231\pi$
$564$	6.70073	+	6.33148i	0.282151	+	0.266604i
$565$	−0.257967	+	0.307433i	−0.0108527	+	0.0129338i
$566$	−10.0043			−0.420513
$567$	13.1604	−	19.8445i	0.552687	−	0.833389i
$568$	−1.23562			−0.0518454
$569$	−21.3534	+	25.4480i	−0.895182	+	1.06684i	0.102217	+	0.994762i	$0.467406\pi$
$569$	−21.3534	+	25.4480i	−0.895182	+	1.06684i	−0.997399	+	0.0720743i	$0.977038\pi$
$570$	−0.726147	−	0.686133i	−0.0304150	−	0.0287390i
$571$	0.378167	+	2.14469i	0.0158258	+	0.0897526i	0.991698	−	0.128591i	$-0.0410456\pi$
$571$	0.378167	+	2.14469i	0.0158258	+	0.0897526i	−0.975872	+	0.218344i	$0.929934\pi$
$572$	11.0286	−	9.25410i	0.461129	−	0.386933i
$573$	−17.8494	+	2.07248i	−0.745669	+	0.0865793i
$574$	−3.97797	+	22.4610i	−0.166037	+	0.937505i
$575$	27.5056	+	15.8803i	1.14706	+	0.662256i
$576$	−13.3881	+	8.77627i	−0.557839	+	0.365678i
$577$		−	34.2253i		−	1.42482i	−0.701764	−	0.712410i	$-0.747604\pi$
$577$		−	34.2253i		−	1.42482i	0.701764	−	0.712410i	$-0.252396\pi$
$578$	9.72023	−	11.5841i	0.404308	−	0.481836i
$579$	−17.3728	+	26.3702i	−0.721989	+	1.09591i
$580$	−0.361830	+	0.994121i	−0.0150242	+	0.0412786i
$581$	6.57739	−	18.0289i	0.272876	−	0.747964i
$582$	19.1971	+	1.13281i	0.795746	+	0.0469564i
$583$	23.9122	−	8.70333i	0.990342	−	0.360455i
$584$	−4.36423			−0.180593
$585$	1.08698	−	0.466911i	0.0449411	−	0.0193044i
$586$			4.32377i			0.178613i
$587$	10.2925	+	8.63644i	0.424817	+	0.356464i	0.829992	−	0.557775i	$-0.188345\pi$
$587$	10.2925	+	8.63644i	0.424817	+	0.356464i	−0.405175	+	0.914239i	$0.632789\pi$
$588$	13.3191	+	5.78125i	0.549272	+	0.238415i
$589$	7.42462	+	42.1071i	0.305926	+	1.73499i
$590$	−0.00716644	+	0.0196896i	−0.000295038	+	0.000810609i
$591$	−10.8622	−	36.3833i	−0.446810	−	1.49661i
$592$	0.215972	−	1.22484i	0.00887641	−	0.0503406i
$593$	1.95066	+	3.37864i	0.0801039	+	0.138744i	0.903294	−	0.429021i	$-0.141141\pi$
$593$	1.95066	+	3.37864i	0.0801039	+	0.138744i	−0.823190	+	0.567765i	$0.807808\pi$
$594$	−16.1324	−	9.36334i	−0.661918	−	0.384183i
$595$	9.04589e−5	−	0.119853i	3.70846e−6	−	0.00491351i
$596$	6.66876	+	18.3223i	0.273163	+	0.750510i
$597$	−8.63075	+	9.13408i	−0.353233	+	0.373833i
$598$	16.8690	−	2.97447i	0.689826	−	0.121635i
$599$	−3.18327	+	8.74596i	−0.130065	+	0.357350i	−0.987582	−	0.157105i	$-0.949784\pi$
$599$	−3.18327	+	8.74596i	−0.130065	+	0.357350i	0.857517	+	0.514456i	$0.172006\pi$
$600$	24.5552	−	2.85109i	1.00246	−	0.116395i
$601$	−20.1709	+	24.0388i	−0.822789	+	0.980561i	−0.999993	−	0.00361252i	$-0.998850\pi$
$601$	−20.1709	+	24.0388i	−0.822789	+	0.980561i	0.177205	+	0.984174i	$0.443295\pi$
$602$	−4.78573	−	0.00361202i	−0.195052	−	0.000147215i
$603$	23.6937	+	25.1908i	0.964882	+	1.02585i
$604$	2.54020	−	4.39975i	0.103359	−	0.179023i
$605$	−0.509401	−	0.427438i	−0.0207101	−	0.0173778i
$606$	5.23526	−	2.62425i	0.212668	−	0.106603i
$607$	−7.05213	+	1.24348i	−0.286237	+	0.0504714i	−0.314923	−	0.949117i	$-0.601979\pi$
$607$	−7.05213	+	1.24348i	−0.286237	+	0.0504714i	0.0286860	+	0.999588i	$0.490868\pi$
$608$	25.6653	+	9.34139i	1.04086	+	0.378843i
$609$	−13.7797	−	27.5419i	−0.558383	−	1.11605i
$610$	0.0955096	−	0.541662i	0.00386707	−	0.0219312i
$611$	−11.5467	−	6.66650i	−0.467130	−	0.269698i
$612$	1.20518	−	0.283690i	0.0487165	−	0.0114675i
$613$	−17.4253	−	30.1815i	−0.703801	−	1.21902i	−0.967122	−	0.254311i	$-0.918151\pi$
$613$	−17.4253	−	30.1815i	−0.703801	−	1.21902i	0.263321	−	0.964708i	$-0.415182\pi$
$614$	3.18381	−	18.0563i	0.128488	−	0.728693i
$615$	−2.01143	−	0.869467i	−0.0811086	−	0.0350603i
$616$	10.4083	−	28.5296i	0.419363	−	1.14949i
$617$	4.32090	+	5.14944i	0.173953	+	0.207309i	0.845976	−	0.533222i	$-0.179019\pi$
$617$	4.32090	+	5.14944i	0.173953	+	0.207309i	−0.672023	+	0.740530i	$0.734574\pi$
$618$	11.2887	+	10.6667i	0.454099	+	0.429076i
$619$	−33.9380	−	5.98419i	−1.36408	−	0.240525i	−0.556780	−	0.830660i	$-0.687963\pi$
$619$	−33.9380	−	5.98419i	−1.36408	−	0.240525i	−0.807304	+	0.590135i	$0.799074\pi$
$620$	1.18998	+	0.687033i	0.0477906	+	0.0275919i
$621$	16.4948	+	28.7216i	0.661915	+	1.15256i
$622$			13.2143i			0.529846i
$623$	26.2444	−	31.2290i	1.05146	−	1.25116i
$624$	0.609170	−	0.644696i	0.0243863	−	0.0258085i
$625$	−23.2490	−	8.46196i	−0.929962	−	0.338478i
$626$	−9.99142	−	3.63658i	−0.399338	−	0.145347i
$627$	3.92132	+	33.7726i	0.156603	+	1.34875i
$628$	−5.39626	−	0.951506i	−0.215334	−	0.0379692i
$629$	−1.25545	+	2.17451i	−0.0500582	+	0.0867033i
$630$	0.559824	−	0.748404i	0.0223039	−	0.0298171i
$631$	13.2483	+	22.9468i	0.527407	+	0.913496i	0.999490	+	0.0319417i	$0.0101691\pi$
$631$	13.2483	+	22.9468i	0.527407	+	0.913496i	−0.472083	+	0.881554i	$0.656498\pi$
$632$	−2.31734	−	6.36685i	−0.0921790	−	0.253260i
$633$	−4.36842	+	6.63083i	−0.173629	+	0.263552i
$634$	14.0475	−	11.7873i	0.557899	−	0.468132i
$635$	−0.208754	−	1.18390i	−0.00828416	−	0.0469818i
$636$	−11.7751	+	5.90240i	−0.466911	+	0.234046i
$637$	−20.6749	−	3.67773i	−0.819170	−	0.145717i
$638$	−20.8923	+	12.0622i	−0.827133	+	0.477546i
$639$	0.709491	+	1.08232i	0.0280670	+	0.0428161i
$640$	0.725326	−	0.418767i	0.0286710	−	0.0165532i
$641$	0.814710	+	2.23840i	0.0321791	+	0.0884114i	0.954742	−	0.297436i	$-0.0961314\pi$
$641$	0.814710	+	2.23840i	0.0321791	+	0.0884114i	−0.922563	+	0.385847i	$0.873909\pi$
$642$	5.75695	−	4.27906i	0.227209	−	0.168881i
$643$	9.49012	−	1.67336i	0.374254	−	0.0659911i	0.0166424	−	0.999862i	$-0.494702\pi$
$643$	9.49012	−	1.67336i	0.374254	−	0.0659911i	0.357612	+	0.933870i	$0.383591\pi$
$644$	−15.4811	+	12.9703i	−0.610039	+	0.511100i
$645$	0.106365	−	0.447269i	0.00418814	−	0.0176112i
$646$	1.15839	+	0.972007i	0.0455764	+	0.0382431i
$647$	−1.16581	+	2.01925i	−0.0458328	+	0.0793847i	−0.888032	−	0.459782i	$-0.847927\pi$
$647$	−1.16581	+	2.01925i	−0.0458328	+	0.0793847i	0.842199	+	0.539167i	$0.181261\pi$
$648$	23.6394	+	10.2828i	0.928645	+	0.403946i
$649$	0.617553	−	0.356545i	0.0242411	−	0.0139956i
$650$	−12.5825	+	4.57966i	−0.493527	+	0.179629i
$651$	−38.3368	+	11.4139i	−1.50254	+	0.447346i
$652$	7.60572	−	6.38196i	0.297863	−	0.249937i
$653$	12.3603	+	14.7305i	0.483698	+	0.576448i	0.951603	−	0.307330i	$-0.0994356\pi$
$653$	12.3603	+	14.7305i	0.483698	+	0.576448i	−0.467905	+	0.883779i	$0.654991\pi$
$654$	7.33618	−	16.9715i	0.286867	−	0.663640i
$655$	−0.688655	+	0.250650i	−0.0269080	+	0.00979370i
$656$	−1.64294			−0.0641460
$657$	2.50594	+	3.82279i	0.0977658	+	0.149141i
$658$	−10.5334	−	0.00795009i	−0.410637	−	0.000309927i
$659$	38.6246	+	6.81055i	1.50460	+	0.265301i	0.864360	−	0.502874i	$-0.167724\pi$
$659$	38.6246	+	6.81055i	1.50460	+	0.265301i	0.640239	+	0.768176i	$0.278835\pi$
$660$	0.912427	+	0.601111i	0.0355162	+	0.0233982i
$661$	−22.2105	−	26.4694i	−0.863888	−	1.02954i	−0.999249	−	0.0387452i	$-0.987664\pi$
$661$	−22.2105	−	26.4694i	−0.863888	−	1.02954i	0.135361	−	0.990796i	$-0.456781\pi$
$662$	−7.92573	−	9.44552i	−0.308042	−	0.367110i
$663$	−1.60080	+	0.802425i	−0.0621701	+	0.0311636i
$664$	20.4611	+	3.60784i	0.794044	+	0.140011i
$665$	−1.70359	−	0.00128578i	−0.0660622	−	4.98602e-5i
$666$	−17.9906	+	7.72782i	−0.697120	+	0.299447i
$667$	42.8369			1.65865
$668$	−4.93206	+	1.79512i	−0.190827	+	0.0694554i
$669$	40.5737	−	4.71099i	1.56867	−	0.182138i
$670$	0.872509	+	1.03982i	0.0337079	+	0.0401716i
$671$	−14.3391	+	12.0320i	−0.553556	+	0.464489i
$672$	−5.93028	+	24.8536i	−0.228766	+	0.958750i
$673$	13.9024	−	5.06006i	0.535898	−	0.195051i	−0.0598720	−	0.998206i	$-0.519069\pi$
$673$	13.9024	−	5.06006i	0.535898	−	0.195051i	0.595770	+	0.803155i	$0.296847\pi$
$674$	9.80042	−	5.65828i	0.377498	−	0.217949i
$675$	−16.5969	−	19.8717i	−0.638816	−	0.764862i
$676$	−2.39540	+	4.14895i	−0.0921307	+	0.159575i
$677$	14.3500	+	12.0411i	0.551516	+	0.462777i	0.875454	−	0.483302i	$-0.160563\pi$
$677$	14.3500	+	12.0411i	0.551516	+	0.462777i	−0.323938	+	0.946078i	$0.605007\pi$
$678$	4.53902	−	1.35512i	0.174320	−	0.0520430i
$679$	25.1364	−	21.0596i	0.964647	−	0.808195i
$680$	0.127784	−	0.0225318i	0.00490030	−	0.000864055i
$681$	−0.489216	−	4.21340i	−0.0187468	−	0.161458i
$682$	10.7167	+	29.4439i	0.410364	+	1.12746i
$683$	−19.2619	+	11.1209i	−0.737037	+	0.425529i	−0.820991	−	0.570941i	$-0.806579\pi$
$683$	−19.2619	+	11.1209i	−0.737037	+	0.425529i	0.0839538	+	0.996470i	$0.473245\pi$
$684$	−4.03235	−	17.1303i	−0.154181	−	0.654995i
$685$	1.64674	−	0.950746i	0.0629187	−	0.0363261i
$686$	−15.6025	+	5.63887i	−0.595706	+	0.215293i
$687$	0.378946	+	0.249651i	0.0144577	+	0.00952479i
$688$	−0.0598556	−	0.339458i	−0.00228197	−	0.0129417i
$689$	14.5929	−	12.2449i	0.555946	−	0.466494i
$690$	0.582558	+	1.16218i	0.0221776	+	0.0442434i
$691$	0.935144	+	2.56929i	0.0355745	+	0.0977403i	0.956208	−	0.292687i	$-0.0945495\pi$
$691$	0.935144	+	2.56929i	0.0355745	+	0.0977403i	−0.920634	+	0.390427i	$0.872327\pi$
$692$	−9.93535	−	17.2085i	−0.377685	−	0.654170i
$693$	−30.9666	+	7.26464i	−1.17632	+	0.275961i
$694$	−8.11734	+	14.0597i	−0.308130	+	0.533697i
$695$	−1.77263	−	0.312562i	−0.0672396	−	0.0118562i
$696$	26.7588	−	19.8895i	1.01429	−	0.753908i
$697$	3.11681	+	1.13443i	0.118058	+	0.0429694i
$698$	15.1969	+	5.53123i	0.575212	+	0.209360i
$699$	−14.3851	−	48.1835i	−0.544096	−	1.82247i
$700$	10.1572	−	12.0863i	0.383905	−	0.456820i
$701$		−	7.89910i		−	0.298345i	−0.988811	−	0.149173i	$-0.952339\pi$
$701$		−	7.89910i		−	0.298345i	0.988811	−	0.149173i	$-0.0476610\pi$
$702$	−13.7459	−	2.45624i	−0.518804	−	0.0927047i
$703$	30.9083	+	17.8449i	1.16573	+	0.673033i
$704$	21.0587	+	3.71322i	0.793680	+	0.139947i
$705$	0.234112	−	0.984445i	0.00881715	−	0.0370763i
$706$	−9.00125	−	10.7273i	−0.338766	−	0.403726i
$707$	3.42254	−	9.38131i	0.128718	−	0.352820i
$708$	−0.296234	+	0.220187i	−0.0111332	+	0.00827514i
$709$	6.03163	−	34.2071i	0.226523	−	1.28467i	−0.633230	−	0.773964i	$-0.718271\pi$
$709$	6.03163	−	34.2071i	0.226523	−	1.28467i	0.859753	−	0.510711i	$-0.170618\pi$
$710$	0.0253977	+	0.0439901i	0.000953159	+	0.00165092i
$711$	−4.24634	+	5.68568i	−0.159250	+	0.213230i
$712$	38.2459	+	22.0813i	1.43332	+	0.827531i
$713$	9.66145	−	54.7928i	0.361824	−	2.05201i
$714$	−0.779169	+	1.18076i	−0.0291597	+	0.0441888i
$715$	−1.48495	−	0.540478i	−0.0555340	−	0.0202127i
$716$	12.2752	−	2.16446i	0.458747	−	0.0808895i
$717$	−0.192610	+	3.26406i	−0.00719314	+	0.121898i
$718$	6.94020	+	5.82352i	0.259006	+	0.217332i
$719$	−1.44565	+	2.50394i	−0.0539137	+	0.0933812i	−0.891723	−	0.452582i	$-0.850503\pi$
$719$	−1.44565	+	2.50394i	−0.0539137	+	0.0933812i	0.837809	+	0.545963i	$0.183836\pi$
$720$	0.0601098	+	0.0303033i	0.00224016	+	0.00112934i
$721$	26.4840	+	0.0199887i	0.986317	+	0.000744419i
$722$	2.87581	−	3.42726i	0.107027	−	0.127549i
$723$	18.9413	+	25.4831i	0.704433	+	0.947728i
$724$	−6.78527	+	18.6424i	−0.252172	+	0.692838i
$725$	−32.9771	+	5.81475i	−1.22474	+	0.215954i
$726$	2.24536	+	7.52093i	0.0833332	+	0.279128i
$727$	8.56203	+	23.5240i	0.317548	+	0.872456i	0.991076	+	0.133295i	$0.0425557\pi$
$727$	8.56203	+	23.5240i	0.317548	+	0.872456i	−0.673528	+	0.739161i	$0.735222\pi$
$728$	0.0171587	−	22.7344i	0.000635945	−	0.842593i
$729$	−4.56667	−	26.6110i	−0.169136	−	0.985593i
$730$	0.0897052	+	0.155374i	0.00332014	+	0.00575065i
$731$	−0.120839	+	0.685312i	−0.00446939	+	0.0253472i
$732$	6.65428	−	7.04235i	0.245949	−	0.260293i
$733$	6.23827	−	17.1395i	0.230416	−	0.633062i	−0.769569	−	0.638563i	$-0.779529\pi$
$733$	6.23827	−	17.1395i	0.230416	−	0.633062i	0.999985	+	0.00550162i	$0.00175123\pi$
$734$	−4.33397	−	24.5792i	−0.159970	−	0.907234i
$735$	−0.181424	−	1.58338i	−0.00669192	−	0.0584039i
$736$	−27.2259	−	22.8452i	−1.00356	−	0.842086i
$737$		−	46.1950i		−	1.70161i
$738$	14.1799	+	21.6314i	0.521969	+	0.796261i
$739$	23.7495			0.873641			0.436821	−	0.899549i	$-0.356104\pi$
$739$	23.7495			0.873641			0.436821	+	0.899549i	$0.356104\pi$
$740$	1.07779	−	0.392283i	0.0396203	−	0.0144206i
$741$	11.4056	+	22.7537i	0.418995	+	0.835878i
$742$	5.15801	−	14.1383i	0.189357	−	0.519034i
$743$	3.47920	−	9.55903i	0.127640	−	0.350687i	−0.859369	−	0.511357i	$-0.829143\pi$
$743$	3.47920	−	9.55903i	0.127640	−	0.350687i	0.987008	+	0.160670i	$0.0513654\pi$
$744$	−19.4055	−	38.7132i	−0.711440	−	1.41929i
$745$	1.37569	−	1.63949i	0.0504014	−	0.0600661i
$746$			17.6751i			0.647132i
$747$	−8.58849	−	19.9942i	−0.314236	−	0.731551i
$748$	−1.43228	−	0.826928i	−0.0523694	−	0.0302355i
$749$	2.13311	−	12.0443i	0.0779422	−	0.440090i
$750$	−1.21456	−	1.63403i	−0.0443493	−	0.0596665i
$751$	−10.6919	+	8.97158i	−0.390153	+	0.327378i	−0.816673	−	0.577101i	$-0.804184\pi$
$751$	−10.6919	+	8.97158i	−0.390153	+	0.327378i	0.426520	+	0.904478i	$0.359740\pi$
$752$	−0.131743	−	0.747150i	−0.00480416	−	0.0272458i
$753$	10.9294	−	3.26296i	0.398290	−	0.118909i
$754$	−11.6085	+	13.8345i	−0.422757	+	0.503823i
$755$	−0.557645			−0.0202948
$756$	15.4880	−	5.58383i	0.563293	−	0.203082i
$757$	−23.1271			−0.840570			−0.420285	−	0.907392i	$-0.638070\pi$
$757$	−23.1271			−0.840570			−0.420285	+	0.907392i	$0.638070\pi$
$758$	−1.89803	+	2.26198i	−0.0689395	+	0.0821589i
$759$	10.2359	−	43.0422i	0.371540	−	1.56233i
$760$	−0.320265	−	1.81631i	−0.0116172	−	0.0658846i
$761$	12.8791	−	10.8068i	0.466866	−	0.391747i	−0.378784	−	0.925485i	$-0.623658\pi$
$761$	12.8791	−	10.8068i	0.466866	−	0.391747i	0.845650	+	0.533738i	$0.179213\pi$
$762$	−5.63017	+	13.0248i	−0.203959	+	0.471841i
$763$	−10.7610	−	29.6352i	−0.389575	−	1.07287i
$764$	−10.7597	−	6.21212i	−0.389273	−	0.224747i
$765$	−0.0931099	−	0.0989930i	−0.00336639	−	0.00357910i
$766$		−	27.6411i		−	0.998715i
$767$	0.343135	−	0.408933i	0.0123899	−	0.0147657i
$768$	−28.3212	−	1.67122i	−1.02195	−	0.0603048i
$769$	−5.01510	+	13.7789i	−0.180849	+	0.496879i	−0.996681	−	0.0814109i	$-0.974057\pi$
$769$	−5.01510	+	13.7789i	−0.180849	+	0.496879i	0.815832	+	0.578290i	$0.196280\pi$
$770$	−1.22964	+	0.215862i	−0.0443132	+	0.00777913i
$771$	−27.5872	+	41.8747i	−0.993530	+	1.50808i
$772$	−20.5171	+	7.46762i	−0.738427	+	0.268765i
$773$	−48.1829			−1.73302			−0.866508	−	0.499163i	$-0.833641\pi$
$773$	−48.1829			−1.73302			−0.866508	+	0.499163i	$0.833641\pi$
$774$	−3.95278	+	3.71787i	−0.142080	+	0.133636i
$775$			43.4926i			1.56230i
$776$	27.1959	+	22.8201i	0.976276	+	0.819193i
$777$	−13.2711	+	30.6378i	−0.476097	+	1.09913i
$778$	−2.09088	−	11.8580i	−0.0749617	−	0.425129i
$779$	16.1246	−	44.3020i	0.577725	−	1.58729i
$780$	0.795764	+	0.189241i	0.0284929	+	0.00677592i
$781$	0.300184	−	1.70243i	0.0107414	−	0.0609176i
$782$	−0.983875	−	1.70412i	−0.0351833	−	0.0609393i
$783$	−32.7868	−	12.0185i	−1.17170	−	0.429506i
$784$	−0.595895	−	1.03573i	−0.0212820	−	0.0369903i
$785$	0.205709	+	0.565180i	0.00734206	+	0.0201722i
$786$	8.41542	+	2.00128i	0.300168	+	0.0713832i
$787$	−24.8204	+	4.37651i	−0.884753	+	0.156006i	−0.597519	−	0.801855i	$-0.703847\pi$
$787$	−24.8204	+	4.37651i	−0.884753	+	0.156006i	−0.287234	+	0.957860i	$0.592736\pi$
$788$	8.97909	−	24.6698i	0.319867	−	0.878827i
$789$	15.9571	−	36.9153i	0.568089	−	1.31422i
$790$	−0.179038	+	0.213370i	−0.00636990	+	0.00759135i
$791$	4.04411	−	6.99242i	0.143792	−	0.248622i
$792$	−13.5908	−	31.6397i	−0.482927	−	1.12427i
$793$	−7.00637	+	12.1354i	−0.248804	+	0.430940i
$794$	22.2012	+	18.6290i	0.787892	+	0.661120i
$795$	1.20731	+	0.795382i	0.0428189	+	0.0282093i
$796$	−8.55679	+	1.50879i	−0.303287	+	0.0534777i
$797$	−48.1785	−	17.5355i	−1.70657	−	0.621140i	−0.710022	−	0.704179i	$-0.751315\pi$
$797$	−48.1785	−	17.5355i	−1.70657	−	0.621140i	−0.996546	+	0.0830393i	$0.973537\pi$
$798$	16.7832	+	11.0750i	0.594120	+	0.392052i
$799$	−0.265968	+	1.50838i	−0.00940927	+	0.0533626i
$800$	24.0603	+	13.8912i	0.850661	+	0.491129i
$801$	−2.61894	−	46.1800i	−0.0925358	−	1.63169i
$802$	17.0847	+	29.5916i	0.603283	+	1.04492i
$803$	1.06025	−	6.01300i	0.0374156	−	0.212194i
$804$	2.75777	+	23.7515i	0.0972591	+	0.837650i
$805$	2.08256	+	0.759772i	0.0734007	+	0.0267784i
$806$	15.0776	+	17.9687i	0.531084	+	0.632922i
$807$	−15.2989	+	4.56747i	−0.538547	+	0.160783i
$808$	10.6469	+	1.87734i	0.374557	+	0.0660445i
$809$	−17.0109	−	9.82125i	−0.598072	−	0.345297i	0.170211	−	0.985408i	$-0.445555\pi$
$809$	−17.0109	−	9.82125i	−0.598072	−	0.345297i	−0.768283	+	0.640111i	$0.778888\pi$
$810$	−0.119816	−	1.05296i	−0.00420990	−	0.0369973i
$811$			18.4996i			0.649608i	0.945781	+	0.324804i	$0.105298\pi$
$811$			18.4996i			0.649608i	−0.945781	+	0.324804i	$0.894702\pi$
$812$	3.71337	−	20.9670i	0.130314	−	0.735798i
$813$	49.6431	+	11.8057i	1.74106	+	0.414043i
$814$	24.5774	+	8.94543i	0.861436	+	0.313537i
$815$	−1.02408	−	0.372733i	−0.0358718	−	0.0130563i
$816$	−0.0935284	−	0.0404289i	−0.00327415	−	0.00141530i
$817$	9.74096	+	1.71759i	0.340793	+	0.0600910i
$818$	10.1493	−	17.5791i	0.354862	−	0.614639i
$819$	−19.9237	+	13.0390i	−0.696192	+	0.455621i
$820$	−0.757550	−	1.31212i	−0.0264548	−	0.0458211i
$821$	−10.8254	−	29.7424i	−0.377808	−	1.03802i	−0.972263	−	0.233889i	$-0.924855\pi$
$821$	−10.8254	−	29.7424i	−0.377808	−	1.03802i	0.594456	−	0.804128i	$-0.297368\pi$
$822$	−22.4050	−	1.32211i	−0.781465	−	0.0461137i
$823$	21.5880	−	18.1145i	0.752509	−	0.631430i	−0.183656	−	0.982991i	$-0.558793\pi$
$823$	21.5880	−	18.1145i	0.752509	−	0.631430i	0.936165	+	0.351560i	$0.114349\pi$
$824$	4.97885	+	28.2365i	0.173447	+	0.983665i
$825$	−2.03727	+	34.5246i	−0.0709288	+	1.20199i
$826$	0.0735472	−	0.415274i	0.00255903	−	0.0144492i
$827$	−26.8439	+	15.4983i	−0.933454	+	0.538930i	−0.887902	−	0.460032i	$-0.847838\pi$
$827$	−26.8439	+	15.4983i	−0.933454	+	0.538930i	−0.0455515	+	0.998962i	$0.514505\pi$
$828$	−2.69330	+	22.7415i	−0.0935988	+	0.790323i
$829$	−8.33259	+	4.81082i	−0.289403	+	0.167087i	−0.637672	−	0.770308i	$-0.720103\pi$
$829$	−8.33259	+	4.81082i	−0.289403	+	0.167087i	0.348270	+	0.937394i	$0.386769\pi$
$830$	−0.292125	−	0.802607i	−0.0101398	−	0.0278589i
$831$	−4.84304	−	2.09347i	−0.168003	−	0.0726217i
$832$	15.7647	−	2.77974i	0.546543	−	0.0963702i
$833$	0.415313	+	2.37633i	0.0143897	+	0.0823349i
$834$	15.4425	+	14.5915i	0.534729	+	0.505262i
$835$	0.441323	+	0.370314i	0.0152726	+	0.0128152i
$836$	−11.7539	+	20.3583i	−0.406517	+	0.704107i
$837$	−22.7677	+	39.2270i	−0.786965	+	1.35588i
$838$	−1.03063	+	0.595033i	−0.0356024	+	0.0205551i
$839$	46.3318	−	16.8634i	1.59955	−	0.582189i	0.620216	−	0.784431i	$-0.287045\pi$
$839$	46.3318	−	16.8634i	1.59955	−	0.582189i	0.979335	+	0.202242i	$0.0648229\pi$
$840$	1.65368	−	0.492344i	0.0570573	−	0.0169875i
$841$	−12.3820	+	10.3898i	−0.426967	+	0.358268i
$842$	−2.64909	−	3.15707i	−0.0912938	−	0.108800i
$843$	25.8987	+	34.8435i	0.891998	+	1.20007i
$844$	−5.15906	+	1.87774i	−0.177582	+	0.0646346i
$845$	0.525857			0.0180900
$846$	−8.70012	+	8.18307i	−0.299116	+	0.281340i
$847$	11.5861	+	6.70089i	0.398102	+	0.230245i
$848$	1.06750	+	0.188229i	0.0366581	+	0.00646382i
$849$	−1.13949	+	19.3103i	−0.0391071	+	0.662727i
$850$	0.988736	+	1.17833i	0.0339134	+	0.0404164i
$851$	−29.8524	−	35.5767i	−1.02333	−	1.21955i
$852$	−0.0527092	+	0.893236i	−0.00180579	+	0.0306017i
$853$	15.1514	+	2.67160i	0.518774	+	0.0914738i	0.426903	−	0.904297i	$-0.359604\pi$
$853$	15.1514	+	2.67160i	0.518774	+	0.0914738i	0.0918701	+	0.995771i	$0.470716\pi$
$854$	−0.00835540	+	11.0705i	−0.000285916	+	0.378824i
$855$	−1.40708	+	1.32346i	−0.0481211	+	0.0452612i
$856$	13.2423			0.452613
$857$	−2.89686	+	1.05437i	−0.0989548	+	0.0360166i	−0.391023	−	0.920381i	$-0.627879\pi$
$857$	−2.89686	+	1.05437i	−0.0989548	+	0.0360166i	0.292068	+	0.956397i	$0.405657\pi$
$858$	11.1270	+	14.9699i	0.379868	+	0.511065i
$859$	−20.1100	−	23.9661i	−0.686143	−	0.817713i	0.304741	−	0.952435i	$-0.401430\pi$
$859$	−20.1100	−	23.9661i	−0.686143	−	0.817713i	−0.990883	+	0.134722i	$0.956986\pi$
$860$	0.243505	−	0.204325i	0.00830345	−	0.00696742i
$861$	42.9011	+	10.2366i	1.46206	+	0.348861i
$862$	−14.9384	+	5.43713i	−0.508804	+	0.185189i
$863$	−5.09715	+	2.94284i	−0.173509	+	0.100176i	−0.584239	−	0.811581i	$-0.698607\pi$
$863$	−5.09715	+	2.94284i	−0.173509	+	0.100176i	0.410730	+	0.911757i	$0.365274\pi$
$864$	14.4288	+	25.1240i	0.490876	+	0.854737i
$865$	−1.09054	+	1.88888i	−0.0370796	+	0.0642238i
$866$	0.838783	+	0.703822i	0.0285030	+	0.0239168i
$867$	−21.2525	−	20.0814i	−0.721772	−	0.681999i
$868$	−25.9815	−	9.47869i	−0.881868	−	0.321728i
$869$	9.33518	−	1.64604i	0.316674	−	0.0558382i
$870$	−1.25812	−	0.543838i	−0.0426541	−	0.0184378i
$871$	−11.8277	−	32.4963i	−0.400766	−	1.10110i
$872$	29.5603	−	17.0667i	1.00104	−	0.577950i
$873$	4.37308	−	36.9251i	0.148006	−	1.24973i
$874$	−24.2222	+	13.9847i	−0.819329	+	0.473040i
$875$	−3.41862	−	0.605456i	−0.115570	−	0.0204681i
$876$	−0.186170	+	3.15492i	−0.00629010	+	0.106595i
$877$	2.60088	+	14.7504i	0.0878256	+	0.498084i	0.996711	+	0.0810379i	$0.0258235\pi$
$877$	2.60088	+	14.7504i	0.0878256	+	0.498084i	−0.908885	+	0.417046i	$0.863065\pi$
$878$	−3.34257	+	2.80475i	−0.112806	+	0.0946556i
$879$	8.34573	+	0.492476i	0.281494	+	0.0166108i
$880$	−0.0307544	−	0.0844970i	−0.00103673	−	0.00284839i
$881$	11.8885	+	20.5915i	0.400533	+	0.693744i	0.993790	−	0.111269i	$-0.0354915\pi$
$881$	11.8885	+	20.5915i	0.400533	+	0.693744i	−0.593257	+	0.805013i	$0.702158\pi$
$882$	−8.49360	+	16.7849i	−0.285994	+	0.565176i
$883$	−11.3387	+	19.6392i	−0.381578	+	0.660913i	−0.991288	−	0.131712i	$-0.957953\pi$
$883$	−11.3387	+	19.6392i	−0.381578	+	0.660913i	0.609710	+	0.792625i	$0.291286\pi$
$884$	−1.21928	−	0.214992i	−0.0410088	−	0.00723096i
$885$	0.0371886	+	0.0160753i	0.00125008	+	0.000540364i
$886$	−19.5794	−	7.12631i	−0.657782	−	0.239413i
$887$	−10.8540	−	3.95053i	−0.364442	−	0.132646i	0.153307	−	0.988179i	$-0.451008\pi$
$887$	−10.8540	−	3.95053i	−0.364442	−	0.132646i	−0.517749	+	0.855533i	$0.673230\pi$
$888$	−35.1664	−	8.36294i	−1.18011	−	0.280642i
$889$	8.25857	+	22.7436i	0.276984	+	0.762797i
$890$		−	1.81549i		−	0.0608554i
$891$	−19.9105	+	30.0721i	−0.667028	+	1.00745i
$892$	24.4581	+	14.1209i	0.818917	+	0.472802i
$893$	21.4400	+	3.78044i	0.717461	+	0.126508i
$894$	−24.2058	+	7.22661i	−0.809562	+	0.241694i
$895$	−0.879440	−	1.04808i	−0.0293964	−	0.0350333i
$896$	−12.9217	+	10.8260i	−0.431685	+	0.361672i
$897$	−3.81992	−	32.8993i	−0.127544	−	1.09848i
$898$	−3.58033	+	20.3051i	−0.119477	+	0.677589i
$899$	29.3300	+	50.8011i	0.978212	+	1.69431i
$900$	−1.01359	−	17.8727i	−0.0337863	−	0.595757i
$901$	−1.89518	−	1.09418i	−0.0631375	−	0.0364525i
$902$	5.99948	−	34.0247i	0.199761	−	1.13290i
$903$	−0.552065	+	9.23699i	−0.0183716	+	0.307388i
$904$	8.21764	+	2.99098i	0.273315	+	0.0994784i
$905$	2.14450	−	0.378134i	0.0712857	−	0.0125696i
$906$	5.49649	+	3.62111i	0.182609	+	0.120303i
$907$	−17.1444	−	14.3858i	−0.569269	−	0.477673i	0.312134	−	0.950038i	$-0.398956\pi$
$907$	−17.1444	−	14.3858i	−0.569269	−	0.477673i	−0.881403	+	0.472365i	$0.843401\pi$
$908$	1.46639	−	2.53986i	0.0486639	−	0.0842883i
$909$	−4.46901	−	10.4040i	−0.148228	−	0.345078i
$910$	−0.809736	+	0.466687i	−0.0268425	+	0.0154705i
$911$	−29.6477	+	35.3327i	−0.982271	+	1.17063i	0.00306421	+	0.999995i	$0.499025\pi$
$911$	−29.6477	+	35.3327i	−0.982271	+	1.17063i	−0.985335	+	0.170630i	$0.945420\pi$
$912$	−0.574653	+	1.32941i	−0.0190287	+	0.0440210i
$913$	−9.94171	+	27.3146i	−0.329023	+	0.903982i
$914$	−23.4670	+	4.13787i	−0.776221	+	0.136869i
$915$	−1.03463	−	0.246047i	−0.0342040	−	0.00813407i
$916$	0.107311	+	0.294836i	0.00354567	+	0.00974165i
$917$	12.7798	−	7.36558i	0.422027	−	0.243233i
$918$	0.274929	+	1.58035i	0.00907400	+	0.0521594i
$919$	−8.95419	−	15.5091i	−0.295371	−	0.511598i	0.679700	−	0.733490i	$-0.262110\pi$
$919$	−8.95419	−	15.5091i	−0.295371	−	0.511598i	−0.975071	+	0.221892i	$0.928777\pi$
$920$	−0.416752	+	2.36352i	−0.0137399	+	0.0779228i
$921$	−34.4896	−	8.20199i	−1.13647	−	0.270265i
$922$	8.41101	−	23.1091i	0.277002	−	0.761056i
$923$	−0.224720	−	1.27445i	−0.00739674	−	0.0419490i
$924$	−20.1802	−	8.74125i	−0.663880	−	0.287566i
$925$	27.8105	+	23.3358i	0.914404	+	0.767276i
$926$			2.85879i			0.0939456i
$927$	21.8745	−	20.5745i	0.718453	−	0.675756i
$928$	37.4713			1.23005
$929$	−27.6851	+	10.0766i	−0.908320	+	0.330602i	−0.753582	−	0.657354i	$-0.771676\pi$
$929$	−27.6851	+	10.0766i	−0.908320	+	0.330602i	−0.154738	+	0.987955i	$0.549453\pi$
$930$	−0.979381	+	1.48660i	−0.0321152	+	0.0487476i
$931$	33.7769	−	5.90323i	1.10699	−	0.193470i
$932$	11.8913	−	32.6711i	0.389513	−	1.07018i
$933$	25.5062	+	1.50510i	0.835036	+	0.0492749i
$934$	−9.73256	+	11.5988i	−0.318459	+	0.379525i
$935$			0.181534i			0.00593679i
$936$	−17.6616	−	18.7775i	−0.577286	−	0.613762i
$937$	42.6087	+	24.6001i	1.39196	+	0.803651i	0.993533	−	0.113547i	$-0.0362211\pi$
$937$	42.6087	+	24.6001i	1.39196	+	0.803651i	0.398432	+	0.917198i	$0.369554\pi$
$938$	−20.9156	−	17.5772i	−0.682919	−	0.573916i
$939$	−8.15733	+	18.8712i	−0.266204	+	0.615838i
$940$	0.535957	−	0.449721i	0.0174810	−	0.0146683i
$941$	2.46173	+	13.9611i	0.0802500	+	0.455120i	0.998281	+	0.0586114i	$0.0186673\pi$
$941$	2.46173	+	13.9611i	0.0802500	+	0.455120i	−0.918031	+	0.396509i	$0.870222\pi$
$942$	1.64245	−	6.90655i	0.0535140	−	0.225028i
$943$	−39.4342	+	46.9959i	−1.28416	+	1.53040i
$944$	0.0303757			0.000988646
$945$	−1.38080	−	1.16581i	−0.0449175	−	0.0379239i
$946$	7.24863			0.235673
$947$	10.2975	−	12.2720i	0.334622	−	0.398787i	−0.572328	−	0.820025i	$-0.693960\pi$
$947$	10.2975	−	12.2720i	0.334622	−	0.398787i	0.906950	+	0.421237i	$0.138404\pi$
$948$	−4.70148	+	1.40362i	−0.152697	+	0.0455875i
$949$	−0.793715	−	4.50138i	−0.0257651	−	0.146121i
$950$	16.7487	−	14.0538i	0.543399	−	0.455966i
$951$	−21.1517	−	28.4570i	−0.685892	−	0.922783i
$952$	−2.45482	+	0.891384i	−0.0795612	+	0.0288899i
$953$	38.0570	+	21.9722i	1.23279	+	0.711750i	0.967610	−	0.252450i	$-0.0812363\pi$
$953$	38.0570	+	21.9722i	1.23279	+	0.711750i	0.265177	+	0.964200i	$0.414570\pi$
$954$	−6.73512	−	15.6795i	−0.218058	−	0.507644i
$955$			1.36374i			0.0441294i
$956$	−1.45318	+	1.73183i	−0.0469991	+	0.0560114i
$957$	20.9027	+	41.7001i	0.675689	+	1.34797i
$958$	−11.5588	+	31.7574i	−0.373446	+	1.02604i
$959$	−29.3368	+	24.5788i	−0.947335	+	0.793691i
$960$	0.544421	+	1.08610i	0.0175711	+	0.0350537i
$961$	42.4645	−	15.4558i	1.36982	−	0.498575i
$962$	19.5796			0.631272
$963$	−7.60371	−	11.5994i	−0.245026	−	0.373786i
$964$			21.9535i			0.707075i
$965$	1.83588	+	1.54049i	0.0590990	+	0.0495900i
$966$	−15.5934	−	21.0121i	−0.501709	−	0.676052i
$967$	−5.36073	−	30.4022i	−0.172389	−	0.977669i	−0.941114	−	0.338089i	$-0.890219\pi$
$967$	−5.36073	−	30.4022i	−0.172389	−	0.977669i	0.768725	−	0.639580i	$-0.220892\pi$
$968$	−4.95589	+	13.6162i	−0.159288	+	0.437642i
$969$	2.00810	−	2.12521i	0.0645096	−	0.0682717i
$970$	0.253431	−	1.43728i	0.00813718	−	0.0461482i
$971$	−26.8436	−	46.4945i	−0.861453	−	1.49208i	−0.870527	−	0.492121i	$-0.836222\pi$
$971$	−26.8436	−	46.4945i	−0.861453	−	1.49208i	0.00907360	−	0.999959i	$-0.497112\pi$
$972$	8.44189	−	16.6504i	0.270774	−	0.534063i
$973$	36.2289	+	0.0273437i	1.16145	+	0.000876598i
$974$	−5.62650	−	15.4587i	−0.180285	−	0.495328i
$975$	7.40650	+	24.8083i	0.237198	+	0.794503i
$976$	−0.785242	+	0.138459i	−0.0251350	+	0.00443198i
$977$	−8.60683	+	23.6471i	−0.275357	+	0.756537i	0.722517	+	0.691354i	$0.242985\pi$
$977$	−8.60683	+	23.6471i	−0.275357	+	0.756537i	−0.997873	+	0.0651829i	$0.979237\pi$
$978$	7.67354	+	10.3238i	0.245373	+	0.330119i
$979$	−39.7149	+	47.3304i	−1.26929	+	1.51269i
$980$	0.552409	−	0.953473i	0.0176461	−	0.0304576i
$981$	−31.9228	−	16.0933i	−1.01922	−	0.513820i
$982$	8.17359	−	14.1571i	0.260830	−	0.451771i
$983$	20.1305	+	16.8915i	0.642064	+	0.538756i	0.904651	−	0.426152i	$-0.140131\pi$
$983$	20.1305	+	16.8915i	0.642064	+	0.538756i	−0.262587	+	0.964908i	$0.584576\pi$
$984$	−2.81276	+	47.6664i	−0.0896676	+	1.51955i
$985$	−2.83787	+	0.500392i	−0.0904220	+	0.0159438i
$986$	1.94951	+	0.709565i	0.0620852	+	0.0225972i
$987$	−1.21510	+	20.3307i	−0.0386771	+	0.647134i
$988$	−3.05588	+	17.3307i	−0.0972204	+	0.551364i
$989$	−11.1468	−	6.43559i	−0.354447	−	0.204640i
$990$	−0.847072	+	1.13420i	−0.0269217	+	0.0360471i
$991$	−18.0463	−	31.2570i	−0.573258	−	0.992912i	−0.996228	−	0.0867687i	$-0.972346\pi$
$991$	−18.0463	−	31.2570i	−0.573258	−	0.992912i	0.422970	−	0.906144i	$-0.360987\pi$
$992$	8.45129	−	47.9296i	0.268329	−	1.52177i
$993$	−19.1344	+	14.2224i	−0.607213	+	0.451333i
$994$	−0.656585	−	0.783688i	−0.0208256	−	0.0248571i
$995$	0.613037	+	0.730589i	0.0194346	+	0.0231612i
$996$	3.48096	−	14.6375i	0.110298	−	0.463808i
$997$	−12.4645	−	2.19782i	−0.394754	−	0.0696058i	−0.0272522	−	0.999629i	$-0.508676\pi$
$997$	−12.4645	−	2.19782i	−0.394754	−	0.0696058i	−0.367502	+	0.930023i	$0.619787\pi$
$998$	−29.0371	−	16.7646i	−0.919153	−	0.530673i
$999$	12.8671	+	35.6055i	0.407096	+	1.12651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.9	✓	132
3.2	odd	2		567.2.ba.a.143.14		132
7.5	odd	6		189.2.bd.a.47.14	yes	132
21.5	even	6		567.2.bd.a.467.9		132
27.4	even	9		567.2.bd.a.17.9		132
27.23	odd	18		189.2.bd.a.185.14	yes	132
189.131	even	18	inner	189.2.ba.a.131.9	yes	132
189.166	odd	18		567.2.ba.a.341.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.9	✓	132	1.1	even	1	trivial
189.2.ba.a.131.9	yes	132	189.131	even	18	inner
189.2.bd.a.47.14	yes	132	7.5	odd	6
189.2.bd.a.185.14	yes	132	27.23	odd	18
567.2.ba.a.143.14		132	3.2	odd	2
567.2.ba.a.341.14		132	189.166	odd	18
567.2.bd.a.17.9		132	27.4	even	9
567.2.bd.a.467.9		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.575801 + 0.686212i) q^{2} +(1.25894 + 1.18957i) q^{3} +(0.207955 + 1.17937i) q^{4} +(0.100696 - 0.0844942i) q^{5} +(-1.54119 + 0.178947i) q^{6} +(-1.70219 + 2.02548i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(0.169862 + 2.99519i) q^{9} +O(q^{10})\)	\(q+(-0.575801 + 0.686212i) q^{2} +(1.25894 + 1.18957i) q^{3} +(0.207955 + 1.17937i) q^{4} +(0.100696 - 0.0844942i) q^{5} +(-1.54119 + 0.178947i) q^{6} +(-1.70219 + 2.02548i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(0.169862 + 2.99519i) q^{9} +0.117751i q^{10} +(2.57587 - 3.06980i) q^{11} +(-1.14114 + 1.73214i) q^{12} +(1.02604 - 2.81901i) q^{13} +(-0.409789 - 2.33433i) q^{14} +(0.227282 + 0.0134118i) q^{15} +(0.160408 - 0.0583836i) q^{16} -0.344621 q^{17} +(-2.15314 - 1.60807i) q^{18} +4.89841i q^{19} +(0.120590 + 0.101187i) q^{20} +(-4.55239 + 0.525094i) q^{21} +(0.623349 + 3.53519i) q^{22} +(2.18009 - 5.98976i) q^{23} +(-1.41925 - 4.75384i) q^{24} +(-0.865240 + 4.90702i) q^{25} +(1.34365 + 2.32726i) q^{26} +(-3.34913 + 3.97282i) q^{27} +(-2.74277 - 1.58630i) q^{28} +(2.29851 + 6.31510i) q^{29} +(-0.140072 + 0.148241i) q^{30} +(8.59607 - 1.51572i) q^{31} +(1.90702 - 5.23950i) q^{32} +(6.89460 - 0.800529i) q^{33} +(0.198433 - 0.236483i) q^{34} +(-0.000262488 + 0.347783i) q^{35} +(-3.49712 + 0.823195i) q^{36} +(3.64300 - 6.30985i) q^{37} +(-3.36135 - 2.82051i) q^{38} +(4.64512 - 2.32843i) q^{39} +(-0.370796 + 0.0653813i) q^{40} +(-9.04416 - 3.29180i) q^{41} +(2.26094 - 3.42626i) q^{42} +(0.350643 - 1.98860i) q^{43} +(4.15611 + 2.39953i) q^{44} +(0.270180 + 0.287252i) q^{45} +(2.85495 + 4.94491i) q^{46} +(0.771769 - 4.37692i) q^{47} +(0.271395 + 0.117314i) q^{48} +(-1.20513 - 6.89548i) q^{49} +(-2.86905 - 3.41920i) q^{50} +(-0.433857 - 0.409950i) q^{51} +(3.53803 + 0.623850i) q^{52} +(5.49931 + 3.17503i) q^{53} +(-0.797771 - 4.58577i) q^{54} -0.526764i q^{55} +(7.12325 - 2.58656i) q^{56} +(-5.82699 + 6.16681i) q^{57} +(-5.65698 - 2.05897i) q^{58} +(0.167214 + 0.0608610i) q^{59} +(0.0314470 + 0.270839i) q^{60} +(-4.60007 - 0.811116i) q^{61} +(-3.90952 + 6.77148i) q^{62} +(-6.35583 - 4.75431i) q^{63} +(2.66805 + 4.62120i) q^{64} +(-0.134872 - 0.370558i) q^{65} +(-3.42058 + 5.19210i) q^{66} +(8.83064 - 7.40979i) q^{67} +(-0.0716657 - 0.406437i) q^{68} +(9.86983 - 4.94738i) q^{69} +(-0.238502 - 0.200434i) q^{70} +(0.373587 - 0.215690i) q^{71} +(3.86826 - 7.67310i) q^{72} +(1.31951 - 0.761822i) q^{73} +(2.23226 + 6.13309i) q^{74} +(-6.92652 + 5.14839i) q^{75} +(-5.77706 + 1.01865i) q^{76} +(1.83321 + 10.4427i) q^{77} +(-1.07687 + 4.52825i) q^{78} +(1.81204 + 1.52049i) q^{79} +(0.0112194 - 0.0194325i) q^{80} +(-8.94229 + 1.01754i) q^{81} +(7.46651 - 4.31079i) q^{82} +(-6.81615 + 2.48087i) q^{83} +(-1.56598 - 5.25977i) q^{84} +(-0.0347021 + 0.0291185i) q^{85} +(1.16270 + 1.38565i) q^{86} +(-4.61855 + 10.6846i) q^{87} +(-10.7861 + 3.92584i) q^{88} -15.4181 q^{89} +(-0.352686 + 0.0200014i) q^{90} +(3.96334 + 6.87669i) q^{91} +(7.51752 + 1.32554i) q^{92} +(12.6250 + 8.31740i) q^{93} +(2.55911 + 3.04983i) q^{94} +(0.413888 + 0.493252i) q^{95} +(8.63357 - 4.32769i) q^{96} +(-12.2061 - 2.15226i) q^{97} +(5.42568 + 3.14345i) q^{98} +(9.63217 + 7.19377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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