LMFDB - Embedded newform 95.2.p.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(4,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("95.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.p (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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			4.2
Character	$\chi$	$=$	95.4
Dual form			95.2.p.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795068 + 2.18443i) q^{2} +(-1.13113 + 0.199449i) q^{3} +(-2.60752 - 2.18797i) q^{4} +(-2.16840 + 0.545927i) q^{5} +(0.463643 - 2.62945i) q^{6} +(-0.124103 - 0.0716510i) q^{7} +(2.82626 - 1.63174i) q^{8} +(-1.57940 + 0.574856i) q^{9} +O(q^{10})$	\(q+(-0.795068 + 2.18443i) q^{2} +(-1.13113 + 0.199449i) q^{3} +(-2.60752 - 2.18797i) q^{4} +(-2.16840 + 0.545927i) q^{5} +(0.463643 - 2.62945i) q^{6} +(-0.124103 - 0.0716510i) q^{7} +(2.82626 - 1.63174i) q^{8} +(-1.57940 + 0.574856i) q^{9} +(0.531485 - 5.17077i) q^{10} +(1.40779 + 2.43836i) q^{11} +(3.38583 + 1.95481i) q^{12} +(1.68258 + 0.296685i) q^{13} +(0.255187 - 0.214128i) q^{14} +(2.34386 - 1.05000i) q^{15} +(0.135204 + 0.766781i) q^{16} +(-1.21720 + 3.34424i) q^{17} -3.90715i q^{18} +(-2.82087 + 3.32305i) q^{19} +(6.84862 + 3.32088i) q^{20} +(0.154668 + 0.0562944i) q^{21} +(-6.44571 + 1.13655i) q^{22} +(-4.62417 + 5.51088i) q^{23} +(-2.87141 + 2.40940i) q^{24} +(4.40393 - 2.36758i) q^{25} +(-1.98586 + 3.43960i) q^{26} +(4.65595 - 2.68812i) q^{27} +(0.166831 + 0.458365i) q^{28} +(7.11492 - 2.58962i) q^{29} +(0.430125 + 5.95482i) q^{30} +(-2.42343 + 4.19751i) q^{31} +(4.64532 + 0.819095i) q^{32} +(-2.07872 - 2.47732i) q^{33} +(-6.33750 - 5.31779i) q^{34} +(0.308222 + 0.0876168i) q^{35} +(5.37609 + 1.95674i) q^{36} -9.49127i q^{37} +(-5.01619 - 8.80406i) q^{38} -1.96239 q^{39} +(-5.23764 + 5.08120i) q^{40} +(-0.0325278 - 0.184474i) q^{41} +(-0.245943 + 0.293103i) q^{42} +(7.06701 + 8.42213i) q^{43} +(1.66422 - 9.43825i) q^{44} +(3.11095 - 2.10876i) q^{45} +(-8.36160 - 14.4827i) q^{46} +(-1.25532 - 3.44897i) q^{47} +(-0.305867 - 0.840363i) q^{48} +(-3.48973 - 6.04439i) q^{49} +(1.67039 + 11.5025i) q^{50} +(0.709811 - 4.02554i) q^{51} +(-3.73823 - 4.45505i) q^{52} +(-1.05624 + 1.25878i) q^{53} +(2.17020 + 12.3078i) q^{54} +(-4.38381 - 4.51879i) q^{55} -0.467663 q^{56} +(2.52800 - 4.32142i) q^{57} +17.6010i q^{58} +(-5.04274 - 1.83541i) q^{59} +(-8.40902 - 2.39039i) q^{60} +(7.74681 + 6.50035i) q^{61} +(-7.24237 - 8.63112i) q^{62} +(0.237198 + 0.0418244i) q^{63} +(-6.26121 + 10.8447i) q^{64} +(-3.81049 + 0.275237i) q^{65} +(7.06425 - 2.57118i) q^{66} +(2.05488 + 5.64572i) q^{67} +(10.4910 - 6.05696i) q^{68} +(4.13141 - 7.15580i) q^{69} +(-0.436450 + 0.603628i) q^{70} +(0.414414 - 0.347735i) q^{71} +(-3.52578 + 4.20186i) q^{72} +(-10.3084 + 1.81765i) q^{73} +(20.7330 + 7.54620i) q^{74} +(-4.50920 + 3.55640i) q^{75} +(14.6262 - 2.49294i) q^{76} -0.403477i q^{77} +(1.56024 - 4.28672i) q^{78} +(2.01585 + 11.4325i) q^{79} +(-0.711784 - 1.58888i) q^{80} +(-0.867724 + 0.728107i) q^{81} +(0.428833 + 0.0756149i) q^{82} +(-6.57815 - 3.79789i) q^{83} +(-0.280128 - 0.485197i) q^{84} +(0.813673 - 7.91615i) q^{85} +(-24.0163 + 8.74123i) q^{86} +(-7.53141 + 4.34826i) q^{87} +(7.95753 + 4.59428i) q^{88} +(-0.251241 + 1.42486i) q^{89} +(2.13302 + 8.47226i) q^{90} +(-0.187556 - 0.157378i) q^{91} +(24.1152 - 4.25217i) q^{92} +(1.90403 - 5.23127i) q^{93} +8.53210 q^{94} +(4.30264 - 8.74570i) q^{95} -5.41783 q^{96} +(-3.01050 + 8.27128i) q^{97} +(15.9781 - 2.81738i) q^{98} +(-3.62516 - 3.04187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9}+O(q^{10}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34} + 6 q^{35} + 18 q^{36} - 48 q^{39} + 66 q^{40} + 6 q^{41} - 6 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{49} - 18 q^{50} + 108 q^{51} + 24 q^{54} + 36 q^{56} - 36 q^{59} - 114 q^{60} + 48 q^{61} - 18 q^{65} + 180 q^{66} + 66 q^{69} - 123 q^{70} - 24 q^{71} + 84 q^{74} + 72 q^{75} + 66 q^{76} + 48 q^{79} - 39 q^{80} - 78 q^{81} - 54 q^{84} - 84 q^{85} - 42 q^{86} - 12 q^{89} + 18 q^{90} - 30 q^{91} - 72 q^{94} - 63 q^{95} - 240 q^{96} - 36 q^{99}+O(q^{100}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−0.795068	+	2.18443i	−0.562198	+	1.54463i	0.254209	+	0.967149i	$0.418185\pi$
$2$	−0.795068	+	2.18443i	−0.562198	+	1.54463i	−0.816407	+	0.577477i	$0.804037\pi$
$3$	−1.13113	+	0.199449i	−0.653058	+	0.115152i	−0.490354	−	0.871523i	$-0.663133\pi$
$3$	−1.13113	+	0.199449i	−0.653058	+	0.115152i	−0.162704	+	0.986675i	$0.552022\pi$
$4$	−2.60752	−	2.18797i	−1.30376	−	1.09398i
$5$	−2.16840	+	0.545927i	−0.969738	+	0.244146i
$5$	−2.16840	+	0.545927i	−0.969738	+	0.244146i
$6$	0.463643	−	2.62945i	0.189282	−	1.07347i
$7$	−0.124103	−	0.0716510i	−0.0469066	−	0.0270816i	0.476363	−	0.879249i	$-0.341955\pi$
$7$	−0.124103	−	0.0716510i	−0.0469066	−	0.0270816i	−0.523270	+	0.852167i	$0.675288\pi$
$8$	2.82626	−	1.63174i	0.999232	−	0.576907i
$9$	−1.57940	+	0.574856i	−0.526468	+	0.191619i
$10$	0.531485	−	5.17077i	0.168070	−	1.63514i
$11$	1.40779	+	2.43836i	0.424463	+	0.735192i	0.996370	−	0.0851264i	$-0.0271294\pi$
$11$	1.40779	+	2.43836i	0.424463	+	0.735192i	−0.571907	+	0.820319i	$0.693796\pi$
$12$	3.38583	+	1.95481i	0.977405	+	0.564305i
$13$	1.68258	+	0.296685i	0.466665	+	0.0822856i	0.402036	−	0.915624i	$-0.368303\pi$
$13$	1.68258	+	0.296685i	0.466665	+	0.0822856i	0.0646286	+	0.997909i	$0.479414\pi$
$14$	0.255187	−	0.214128i	0.0682017	−	0.0572280i
$15$	2.34386	−	1.05000i	0.605182	−	0.271109i
$16$	0.135204	+	0.766781i	0.0338011	+	0.191695i
$17$	−1.21720	+	3.34424i	−0.295215	+	0.811097i	0.700067	+	0.714077i	$0.253153\pi$
$17$	−1.21720	+	3.34424i	−0.295215	+	0.811097i	−0.995282	+	0.0970200i	$0.969069\pi$
$18$		−	3.90715i		−	0.920923i
$19$	−2.82087	+	3.32305i	−0.647153	+	0.762360i
$19$	−2.82087	+	3.32305i	−0.647153	+	0.762360i
$20$	6.84862	+	3.32088i	1.53140	+	0.742571i
$21$	0.154668	+	0.0562944i	0.0337512	+	0.0122844i
$22$	−6.44571	+	1.13655i	−1.37423	+	0.242314i
$23$	−4.62417	+	5.51088i	−0.964207	+	1.14910i	0.0245699	+	0.999698i	$0.492178\pi$
$23$	−4.62417	+	5.51088i	−0.964207	+	1.14910i	−0.988777	+	0.149399i	$0.952266\pi$
$24$	−2.87141	+	2.40940i	−0.586125	+	0.491817i
$25$	4.40393	−	2.36758i	0.880785	−	0.473516i
$26$	−1.98586	+	3.43960i	−0.389459	+	0.674562i
$27$	4.65595	−	2.68812i	0.896038	−	0.517328i
$28$	0.166831	+	0.458365i	0.0315282	+	0.0866229i
$29$	7.11492	−	2.58962i	1.32121	−	0.480880i	0.417363	−	0.908740i	$-0.362954\pi$
$29$	7.11492	−	2.58962i	1.32121	−	0.480880i	0.903845	+	0.427860i	$0.140732\pi$
$30$	0.430125	+	5.95482i	0.0785297	+	1.08720i
$31$	−2.42343	+	4.19751i	−0.435261	+	0.753894i	−0.997317	−	0.0732050i	$-0.976677\pi$
$31$	−2.42343	+	4.19751i	−0.435261	+	0.753894i	0.562056	+	0.827099i	$0.310011\pi$
$32$	4.64532	+	0.819095i	0.821184	+	0.144797i
$33$	−2.07872	−	2.47732i	−0.361858	−	0.431246i
$34$	−6.33750	−	5.31779i	−1.08687	−	0.911994i
$35$	0.308222	+	0.0876168i	0.0520990	+	0.0148099i
$36$	5.37609	+	1.95674i	0.896015	+	0.326123i
$37$		−	9.49127i		−	1.56035i	−0.625559	−	0.780177i	$-0.715129\pi$
$37$		−	9.49127i		−	1.56035i	0.625559	−	0.780177i	$-0.284871\pi$
$38$	−5.01619	−	8.80406i	−0.813734	−	1.42821i
$39$	−1.96239			−0.314235
$40$	−5.23764	+	5.08120i	−0.828144	+	0.803407i
$41$	−0.0325278	−	0.184474i	−0.00507999	−	0.0288100i	0.982162	−	0.188035i	$-0.0602117\pi$
$41$	−0.0325278	−	0.184474i	−0.00507999	−	0.0288100i	−0.987242	+	0.159225i	$0.949101\pi$
$42$	−0.245943	+	0.293103i	−0.0379498	+	0.0452268i
$43$	7.06701	+	8.42213i	1.07771	+	1.28436i	0.956499	+	0.291736i	$0.0942330\pi$
$43$	7.06701	+	8.42213i	1.07771	+	1.28436i	0.121210	+	0.992627i	$0.461323\pi$
$44$	1.66422	−	9.43825i	0.250890	−	1.42287i
$45$	3.11095	−	2.10876i	0.463753	−	0.314355i
$46$	−8.36160	−	14.4827i	−1.23285	−	2.13536i
$47$	−1.25532	−	3.44897i	−0.183108	−	0.503084i	0.813846	−	0.581080i	$-0.197370\pi$
$47$	−1.25532	−	3.44897i	−0.183108	−	0.503084i	−0.996954	+	0.0779967i	$0.975148\pi$
$48$	−0.305867	−	0.840363i	−0.0441481	−	0.121296i
$49$	−3.48973	−	6.04439i	−0.498533	−	0.863485i
$50$	1.67039	+	11.5025i	0.236229	+	1.62669i
$51$	0.709811	−	4.02554i	0.0993934	−	0.563688i
$52$	−3.73823	−	4.45505i	−0.518399	−	0.617804i
$53$	−1.05624	+	1.25878i	−0.145086	+	0.172907i	−0.833693	−	0.552228i	$-0.813778\pi$
$53$	−1.05624	+	1.25878i	−0.145086	+	0.172907i	0.688607	+	0.725134i	$0.258222\pi$
$54$	2.17020	+	12.3078i	0.295327	+	1.67489i
$55$	−4.38381	−	4.51879i	−0.591113	−	0.609313i
$56$	−0.467663			−0.0624941
$57$	2.52800	−	4.32142i	0.334841	−	0.572386i
$58$			17.6010i			2.31112i
$59$	−5.04274	−	1.83541i	−0.656509	−	0.238950i	−0.00778043	−	0.999970i	$-0.502477\pi$
$59$	−5.04274	−	1.83541i	−0.656509	−	0.238950i	−0.648728	+	0.761020i	$0.724699\pi$
$60$	−8.40902	−	2.39039i	−1.08560	−	0.308599i
$61$	7.74681	+	6.50035i	0.991878	+	0.832284i	0.985839	−	0.167697i	$-0.0536331\pi$
$61$	7.74681	+	6.50035i	0.991878	+	0.832284i	0.00603938	+	0.999982i	$0.498078\pi$
$62$	−7.24237	−	8.63112i	−0.919782	−	1.09615i
$63$	0.237198	+	0.0418244i	0.0298841	+	0.00526938i
$64$	−6.26121	+	10.8447i	−0.782652	+	1.35559i
$65$	−3.81049	+	0.275237i	−0.472633	+	0.0341389i
$66$	7.06425	−	2.57118i	0.869549	−	0.316490i
$67$	2.05488	+	5.64572i	0.251043	+	0.689735i	0.999643	+	0.0267132i	$0.00850410\pi$
$67$	2.05488	+	5.64572i	0.251043	+	0.689735i	−0.748600	+	0.663022i	$0.769274\pi$
$68$	10.4910	−	6.05696i	1.27222	−	0.734514i
$69$	4.13141	−	7.15580i	0.497363	−	0.861457i
$70$	−0.436450	+	0.603628i	−0.0521658	+	0.0721474i
$71$	0.414414	−	0.347735i	0.0491819	−	0.0412685i	−0.617865	−	0.786284i	$-0.712002\pi$
$71$	0.414414	−	0.347735i	0.0491819	−	0.0412685i	0.667047	+	0.745015i	$0.267558\pi$
$72$	−3.52578	+	4.20186i	−0.415517	+	0.495194i
$73$	−10.3084	+	1.81765i	−1.20651	+	0.212740i	−0.740509	−	0.672047i	$-0.765415\pi$
$73$	−10.3084	+	1.81765i	−1.20651	+	0.212740i	−0.465997	+	0.884786i	$0.654304\pi$
$74$	20.7330	+	7.54620i	2.41016	+	0.877228i
$75$	−4.50920	+	3.55640i	−0.520678	+	0.410657i
$76$	14.6262	−	2.49294i	1.67774	−	0.285960i
$77$		−	0.403477i		−	0.0459805i
$78$	1.56024	−	4.28672i	0.176662	−	0.485375i
$79$	2.01585	+	11.4325i	0.226801	+	1.28625i	0.859212	+	0.511620i	$0.170954\pi$
$79$	2.01585	+	11.4325i	0.226801	+	1.28625i	−0.632411	+	0.774633i	$0.717935\pi$
$80$	−0.711784	−	1.58888i	−0.0795799	−	0.177642i
$81$	−0.867724	+	0.728107i	−0.0964137	+	0.0809007i
$82$	0.428833	+	0.0756149i	0.0473567	+	0.00835027i
$83$	−6.57815	−	3.79789i	−0.722045	−	0.416873i	0.0934597	−	0.995623i	$-0.470207\pi$
$83$	−6.57815	−	3.79789i	−0.722045	−	0.416873i	−0.815505	+	0.578750i	$0.803541\pi$
$84$	−0.280128	−	0.485197i	−0.0305645	−	0.0529393i
$85$	0.813673	−	7.91615i	0.0882553	−	0.858627i
$86$	−24.0163	+	8.74123i	−2.58975	+	0.942591i
$87$	−7.53141	+	4.34826i	−0.807452	+	0.466182i
$88$	7.95753	+	4.59428i	0.848275	+	0.489752i
$89$	−0.251241	+	1.42486i	−0.0266315	+	0.151035i	−0.995224	−	0.0976195i	$-0.968877\pi$
$89$	−0.251241	+	1.42486i	−0.0266315	+	0.151035i	0.968592	+	0.248654i	$0.0799883\pi$
$90$	2.13302	+	8.47226i	0.224840	+	0.893055i
$91$	−0.187556	−	0.157378i	−0.0196612	−	0.0164977i
$92$	24.1152	−	4.25217i	2.51419	−	0.443319i
$93$	1.90403	−	5.23127i	0.197439	−	0.542458i
$94$	8.53210			0.880019
$95$	4.30264	−	8.74570i	0.441442	−	0.897290i
$96$	−5.41783			−0.552955
$97$	−3.01050	+	8.27128i	−0.305670	+	0.839822i	0.687818	+	0.725883i	$0.258569\pi$
$97$	−3.01050	+	8.27128i	−0.305670	+	0.839822i	−0.993488	+	0.113938i	$0.963653\pi$
$98$	15.9781	−	2.81738i	1.61404	−	0.284598i
$99$	−3.62516	−	3.04187i	−0.364343	−	0.305720i
$100$	−16.6635	−	3.46214i	−1.66635	−	0.346214i
$101$	−0.499751	+	2.83423i	−0.0497270	+	0.282016i	−0.999524	−	0.0308509i	$-0.990178\pi$
$101$	−0.499751	+	2.83423i	−0.0497270	+	0.282016i	0.949797	+	0.312867i	$0.101289\pi$
$102$	8.22916	+	4.75111i	0.814808	+	0.470430i
$103$	1.03894	−	0.599832i	0.102370	−	0.0591032i	−0.447941	−	0.894063i	$-0.647843\pi$
$103$	1.03894	−	0.599832i	0.102370	−	0.0591032i	0.550311	+	0.834960i	$0.314509\pi$
$104$	5.23952	−	1.90703i	0.513778	−	0.187000i
$105$	−0.366114	−	0.0376316i	−0.0357291	−	0.00367246i
$106$	−1.90994	−	3.30811i	−0.185509	−	0.321312i
$107$	−3.54668	−	2.04768i	−0.342871	−	0.197957i	0.318670	−	0.947866i	$-0.396764\pi$
$107$	−3.54668	−	2.04768i	−0.342871	−	0.197957i	−0.661541	+	0.749909i	$0.730097\pi$
$108$	−18.0220	−	3.17776i	−1.73417	−	0.305780i
$109$	12.4054	−	10.4093i	1.18822	−	0.997034i	0.188331	−	0.982106i	$-0.439692\pi$
$109$	12.4054	−	10.4093i	1.18822	−	0.997034i	0.999889	−	0.0149287i	$-0.00475214\pi$
$110$	13.3564	−	5.98339i	1.27348	−	0.570494i
$111$	1.89302	+	10.7359i	0.179678	+	1.01900i
$112$	0.0381614	−	0.104848i	0.00360591	−	0.00990716i
$113$			3.11845i			0.293359i	0.989184	+	0.146680i	$0.0468586\pi$
$113$			3.11845i			0.293359i	−0.989184	+	0.146680i	$0.953141\pi$
$114$	7.42992	+	8.95806i	0.695876	+	0.838999i
$115$	7.01853	−	14.4743i	0.654481	−	1.34973i
$116$	−24.2183	−	8.81474i	−2.24861	−	0.818428i
$117$	−2.82803	+	0.498658i	−0.261451	+	0.0461009i
$118$	8.01864	−	9.55625i	0.738176	−	0.879724i
$119$	0.390677	−	0.327817i	0.0358133	−	0.0300509i
$120$	4.91102	−	6.79213i	0.448313	−	0.620034i
$121$	1.53628	−	2.66091i	0.139661	−	0.241901i
$122$	−20.3588	+	11.7542i	−1.84320	+	1.06417i
$123$	0.0735863	+	0.202177i	0.00663506	+	0.0182297i
$124$	15.5031	−	5.64268i	1.39222	−	0.506728i
$125$	−8.25695	+	7.53809i	−0.738524	+	0.674227i
$126$	−0.279951	+	0.484890i	−0.0249400	+	0.0431974i
$127$	8.03622	+	1.41700i	0.713099	+	0.125739i	0.518417	−	0.855128i	$-0.326521\pi$
$127$	8.03622	+	1.41700i	0.713099	+	0.125739i	0.194682	+	0.980866i	$0.437633\pi$
$128$	−12.6475	−	15.0727i	−1.11789	−	1.33225i
$129$	−9.67349	−	8.11702i	−0.851703	−	0.714664i
$130$	2.42836	−	8.54258i	0.212981	−	0.749233i
$131$	−2.46196	−	0.896079i	−0.215102	−	0.0782908i	0.232222	−	0.972663i	$-0.425401\pi$
$131$	−2.46196	−	0.896079i	−0.215102	−	0.0782908i	−0.447324	+	0.894372i	$0.647623\pi$
$132$			11.0078i			0.958108i
$133$	0.588180	−	0.210283i	0.0510017	−	0.0182338i
$134$	−13.9665			−1.20652
$135$	−8.62846	+	8.37072i	−0.742619	+	0.720437i
$136$	2.01680	+	11.4378i	0.172939	+	0.980786i
$137$	−7.91946	+	9.43805i	−0.676605	+	0.806347i	−0.989667	−	0.143386i	$-0.954201\pi$
$137$	−7.91946	+	9.43805i	−0.676605	+	0.806347i	0.313062	+	0.949733i	$0.398645\pi$
$138$	12.3466	+	14.7141i	1.05101	+	1.25255i
$139$	−1.38116	+	7.83292i	−0.117148	+	0.664380i	0.868516	+	0.495661i	$0.165074\pi$
$139$	−1.38116	+	7.83292i	−0.117148	+	0.664380i	−0.985664	+	0.168719i	$0.946037\pi$
$140$	−0.611992	−	0.902842i	−0.0517227	−	0.0763041i
$141$	2.10782	+	3.65086i	0.177511	+	0.307458i
$142$	0.430115	+	1.18173i	0.0360945	+	0.0991687i
$143$	1.64529	+	4.52041i	0.137586	+	0.378016i
$144$	−0.654330	−	1.13333i	−0.0545275	−	0.0944445i
$145$	−14.0143	+	9.49957i	−1.16382	+	0.788896i
$146$	4.22535	−	23.9631i	0.349692	−	1.98320i
$147$	5.15289	+	6.14097i	0.425003	+	0.506499i
$148$	−20.7666	+	24.7487i	−1.70700	+	2.03433i
$149$	0.728662	+	4.13245i	0.0596943	+	0.338543i	0.999998	−	0.00179219i	$-0.000570472\pi$
$149$	0.728662	+	4.13245i	0.0596943	+	0.338543i	−0.940304	+	0.340335i	$0.889459\pi$
$150$	−4.18358	−	12.6776i	−0.341588	−	1.03512i
$151$	−2.86140			−0.232857			−0.116429	−	0.993199i	$-0.537145\pi$
$151$	−2.86140			−0.232857			−0.116429	+	0.993199i	$0.537145\pi$
$152$	−2.55015	+	13.9947i	−0.206845	+	1.13512i
$153$		−	5.98161i		−	0.483585i
$154$	0.881369	+	0.320792i	0.0710227	+	0.0258502i
$155$	2.96344	−	10.4249i	0.238029	−	0.837348i
$156$	5.11698	+	4.29366i	0.409686	+	0.343768i
$157$	7.40771	+	8.82817i	0.591200	+	0.704565i	0.975836	−	0.218504i	$-0.0701175\pi$
$157$	7.40771	+	8.82817i	0.591200	+	0.704565i	−0.384636	+	0.923068i	$0.625673\pi$
$158$	−26.5762	−	4.68610i	−2.11429	−	0.372806i
$159$	0.943685	−	1.63451i	0.0748391	−	0.129625i
$160$	−10.5201	+	0.759880i	−0.831686	+	0.0600738i
$161$	0.968735	−	0.352591i	0.0763470	−	0.0277880i
$162$	−0.900600	−	2.47438i	−0.0707578	−	0.194405i
$163$	16.3847	−	9.45974i	1.28335	−	0.740944i	0.305892	−	0.952066i	$-0.401045\pi$
$163$	16.3847	−	9.45974i	1.28335	−	0.740944i	0.977460	+	0.211122i	$0.0677119\pi$
$164$	−0.318807	+	0.552190i	−0.0248946	+	0.0431188i
$165$	5.85993	+	4.23699i	0.456195	+	0.329849i
$166$	13.5263	−	11.3499i	1.04985	−	0.880925i
$167$	9.68614	−	11.5435i	0.749536	−	0.893262i	−0.247602	−	0.968862i	$-0.579643\pi$
$167$	9.68614	−	11.5435i	0.749536	−	0.893262i	0.997138	+	0.0755996i	$0.0240871\pi$
$168$	0.528988	−	0.0932748i	0.0408123	−	0.00719631i
$169$	−9.47294	−	3.44787i	−0.728688	−	0.265221i
$170$	16.6454	+	8.07129i	1.27664	+	0.619040i
$171$	2.54502	−	6.87003i	0.194623	−	0.525364i
$172$		−	37.4233i		−	2.85350i
$173$	7.42012	−	20.3866i	0.564141	−	1.54997i	−0.249365	−	0.968410i	$-0.580222\pi$
$173$	7.42012	−	20.3866i	0.564141	−	1.54997i	0.813506	−	0.581556i	$-0.197556\pi$
$174$	−3.51049	−	19.9090i	−0.266130	−	1.50930i
$175$	−0.716181	−	0.0217217i	−0.0541382	−	0.00164200i
$176$	−1.67935	+	1.40914i	−0.126586	+	0.106218i
$177$	6.07006	+	1.07032i	0.456254	+	0.0804499i
$178$	−2.91275	−	1.68168i	−0.218320	−	0.126047i
$179$	11.4395	+	19.8138i	0.855028	+	1.48095i	0.876619	+	0.481185i	$0.159794\pi$
$179$	11.4395	+	19.8138i	0.855028	+	1.48095i	−0.0215906	+	0.999767i	$0.506873\pi$
$180$	−12.7257	−	1.30803i	−0.948521	−	0.0974951i
$181$	10.8685	−	3.95580i	0.807847	−	0.294032i	0.0951131	−	0.995466i	$-0.469679\pi$
$181$	10.8685	−	3.95580i	0.807847	−	0.294032i	0.712734	+	0.701434i	$0.247457\pi$
$182$	0.492903	−	0.284577i	0.0365364	−	0.0210943i
$183$	−10.0591	−	5.80765i	−0.743593	−	0.429314i
$184$	−4.07678	+	23.1206i	−0.300544	+	1.70447i
$185$	5.18154	+	20.5809i	0.380955	+	1.51314i
$186$	9.91353	+	8.31844i	0.726895	+	0.609937i
$187$	−9.86801	+	1.74000i	−0.721620	+	0.127241i
$188$	−4.27296	+	11.7399i	−0.311637	+	0.856217i
$189$	−0.770425			−0.0560402
$190$	15.6835	+	16.3523i	1.13780	+	1.18632i
$191$	7.28958			0.527455			0.263728	−	0.964597i	$-0.415048\pi$
$191$	7.28958			0.527455			0.263728	+	0.964597i	$0.415048\pi$
$192$	4.91928	−	13.5156i	0.355018	−	0.975404i
$193$	25.7884	−	4.54719i	1.85629	−	0.327314i	0.870094	−	0.492887i	$-0.164058\pi$
$193$	25.7884	−	4.54719i	1.85629	−	0.327314i	0.986198	+	0.165572i	$0.0529472\pi$
$194$	−15.6745	−	13.1525i	−1.12536	−	0.944292i
$195$	4.25526	−	1.07132i	0.304725	−	0.0767192i
$196$	−4.12540	+	23.3963i	−0.294671	+	1.67116i
$197$	−1.98164	−	1.14410i	−0.141186	−	0.0815136i	0.427743	−	0.903900i	$-0.359309\pi$
$197$	−1.98164	−	1.14410i	−0.141186	−	0.0815136i	−0.568929	+	0.822387i	$0.692642\pi$
$198$	9.52702	−	5.50043i	0.677056	−	0.390898i
$199$	−11.5083	+	4.18868i	−0.815802	+	0.296928i	−0.716018	−	0.698081i	$-0.754037\pi$
$199$	−11.5083	+	4.18868i	−0.815802	+	0.296928i	−0.0997838	+	0.995009i	$0.531815\pi$
$200$	8.58335	−	13.8774i	0.606934	−	0.981283i
$201$	−3.45036	−	5.97621i	−0.243370	−	0.421529i
$202$	−5.79384	−	3.34507i	−0.407653	−	0.235359i
$203$	−1.06853	−	0.188411i	−0.0749964	−	0.0132239i
$204$	−10.6586	+	8.94362i	−0.746251	+	0.626179i
$205$	0.171243	+	0.382256i	0.0119601	+	0.0266979i
$206$	0.484264	+	2.74640i	0.0337403	+	0.191351i
$207$	4.13548	−	11.3621i	0.287435	−	0.789722i
$208$			1.33029i			0.0922388i
$209$	−12.0740	−	2.20015i	−0.835174	−	0.152188i
$210$	0.373289	−	0.769832i	0.0257594	−	0.0531234i
$211$	−2.82198	−	1.02712i	−0.194273	−	0.0707097i	0.243051	−	0.970013i	$-0.421852\pi$
$211$	−2.82198	−	1.02712i	−0.194273	−	0.0707097i	−0.437325	+	0.899304i	$0.644074\pi$
$212$	5.50834	−	0.971270i	0.378315	−	0.0667071i
$213$	−0.399401	+	0.475987i	−0.0273665	+	0.0326141i
$214$	7.29287	−	6.11944i	0.498530	−	0.418316i
$215$	−19.9220	−	14.4045i	−1.35867	−	0.982378i
$216$	8.77261	−	15.1946i	0.596900	−	1.03386i
$217$	0.601511	−	0.347283i	0.0408332	−	0.0235751i
$218$	12.8754	+	35.3748i	0.872031	+	2.39589i
$219$	11.2976	−	4.11199i	0.763421	−	0.277863i
$220$	1.54391	+	21.3745i	0.104090	+	1.44107i
$221$	−3.04023	+	5.26583i	−0.204508	+	0.354218i
$222$	−24.9568	−	4.40056i	−1.67499	−	0.295346i
$223$	1.41004	+	1.68042i	0.0944233	+	0.112529i	0.811187	−	0.584787i	$-0.198822\pi$
$223$	1.41004	+	1.68042i	0.0944233	+	0.112529i	−0.716764	+	0.697316i	$0.754377\pi$
$224$	−0.517810	−	0.434494i	−0.0345977	−	0.0290309i
$225$	−5.59456	+	6.27098i	−0.372970	+	0.418065i
$226$	−6.81204	−	2.47938i	−0.453130	−	0.164926i
$227$			6.44357i			0.427675i	0.976869	+	0.213838i	$0.0685963\pi$
$227$			6.44357i			0.427675i	−0.976869	+	0.213838i	$0.931404\pi$
$228$	−16.0469	+	5.73702i	−1.06273	+	0.379943i
$229$	1.54321			0.101978			0.0509892	−	0.998699i	$-0.483763\pi$
$229$	1.54321			0.101978			0.0509892	+	0.998699i	$0.483763\pi$
$230$	26.0378	+	26.8395i	1.71688	+	1.76974i
$231$	0.0804731	+	0.456385i	0.00529474	+	0.0300280i
$232$	15.8830	−	18.9286i	1.04277	−	1.24273i
$233$	13.1522	+	15.6742i	0.861629	+	1.02685i	0.999338	+	0.0363763i	$0.0115815\pi$
$233$	13.1522	+	15.6742i	0.861629	+	1.02685i	−0.137710	+	0.990473i	$0.543974\pi$
$234$	1.15919	−	6.57410i	0.0757787	−	0.429762i
$235$	4.60493	+	6.79343i	0.300392	+	0.443155i
$236$	9.13323	+	15.8192i	0.594522	+	1.02974i
$237$	−4.56038	−	12.5295i	−0.296229	−	0.813881i
$238$	0.405479	+	1.11404i	0.0262833	+	0.0722127i
$239$	3.12033	+	5.40457i	0.201837	+	0.349592i	0.949120	−	0.314913i	$-0.101975\pi$
$239$	3.12033	+	5.40457i	0.201837	+	0.349592i	−0.747283	+	0.664506i	$0.768642\pi$
$240$	1.12202	+	1.65526i	0.0724261	+	0.106847i
$241$	−4.56951	+	25.9150i	−0.294348	+	1.66933i	0.375491	+	0.926826i	$0.377474\pi$
$241$	−4.56951	+	25.9150i	−0.294348	+	1.66933i	−0.669839	+	0.742506i	$0.733637\pi$
$242$	4.59113	+	5.47149i	0.295129	+	0.351721i
$243$	−9.53104	+	11.3586i	−0.611416	+	0.728657i
$244$	−5.97741	−	33.8996i	−0.382664	−	2.17020i
$245$	10.8669	+	11.2015i	0.694263	+	0.715639i
$246$	−0.500147			−0.0318882
$247$	−5.73226	+	4.75440i	−0.364735	+	0.302515i
$248$			15.8176i			1.00442i
$249$	8.19822	+	2.98391i	0.519541	+	0.189098i
$250$	−9.90159	−	24.0300i	−0.626232	−	1.51979i
$251$	−8.20154	−	6.88191i	−0.517677	−	0.434382i	0.346144	−	0.938181i	$-0.387491\pi$
$251$	−8.20154	−	6.88191i	−0.517677	−	0.434382i	−0.863821	+	0.503799i	$0.831935\pi$
$252$	−0.526988	−	0.628040i	−0.0331971	−	0.0395628i
$253$	−19.9473	−	3.51725i	−1.25408	−	0.221128i
$254$	−9.48469	+	16.4280i	−0.595122	+	1.03078i
$255$	0.658497	+	9.11648i	0.0412367	+	0.570896i
$256$	19.4463	−	7.07788i	1.21540	−	0.442368i
$257$	−4.62548	−	12.7084i	−0.288529	−	0.792728i	−0.996273	−	0.0862582i	$-0.972509\pi$
$257$	−4.62548	−	12.7084i	−0.288529	−	0.792728i	0.707744	−	0.706469i	$-0.249713\pi$
$258$	25.4222	−	14.6775i	1.58271	−	0.913781i
$259$	−0.680059	+	1.17790i	−0.0422568	+	0.0731910i
$260$	10.5381	+	7.61953i	0.653546	+	0.472543i
$261$	−9.74867	+	8.18011i	−0.603428	+	0.506336i
$262$	3.91485	−	4.66553i	0.241860	−	0.288238i
$263$	6.44120	−	1.13576i	0.397181	−	0.0700337i	0.0285097	−	0.999594i	$-0.490924\pi$
$263$	6.44120	−	1.13576i	0.397181	−	0.0700337i	0.368671	+	0.929560i	$0.379813\pi$
$264$	−9.91732	−	3.60961i	−0.610369	−	0.222156i
$265$	1.60315	−	3.30617i	0.0984810	−	0.203097i
$266$	−0.00829414	+	1.45203i	−0.000508546	+	0.0890295i
$267$		−	1.66181i		−	0.101701i
$268$	6.99454	−	19.2173i	0.427259	−	1.17389i
$269$	−2.50436	−	14.2029i	−0.152693	−	0.865968i	−0.960864	−	0.277020i	$-0.910653\pi$
$269$	−2.50436	−	14.2029i	−0.152693	−	0.865968i	0.808171	−	0.588948i	$-0.200458\pi$
$270$	−11.4251	−	25.5036i	−0.695307	−	1.55210i
$271$	−1.67326	+	1.40404i	−0.101644	+	0.0852891i	−0.692193	−	0.721712i	$-0.743355\pi$
$271$	−1.67326	+	1.40404i	−0.101644	+	0.0852891i	0.590550	+	0.807001i	$0.298911\pi$
$272$	−2.72887	−	0.481173i	−0.165462	−	0.0291754i
$273$	0.243540	+	0.140608i	0.0147397	+	0.00850996i
$274$	−14.3203	−	24.8034i	−0.865118	−	1.49843i
$275$	11.9728	+	7.40530i	0.721986	+	0.446556i
$276$	−26.4294	+	9.61951i	−1.59086	+	0.579026i
$277$	−13.8344	+	7.98732i	−0.831231	+	0.479911i	−0.854274	−	0.519823i	$-0.825998\pi$
$277$	−13.8344	+	7.98732i	−0.831231	+	0.479911i	0.0230432	+	0.999734i	$0.492664\pi$
$278$	−16.0124	−	9.24475i	−0.960358	−	0.554463i
$279$	1.41461	−	8.02267i	0.0846907	−	0.480305i
$280$	1.01408	−	0.255310i	0.0606030	−	0.0152577i
$281$	−10.9214	−	9.16416i	−0.651517	−	0.546688i	0.256014	−	0.966673i	$-0.417591\pi$
$281$	−10.9214	−	9.16416i	−0.651517	−	0.546688i	−0.907531	+	0.419985i	$0.862035\pi$
$282$	−9.65092	+	1.70172i	−0.574704	+	0.101336i
$283$	2.41716	−	6.64111i	0.143686	−	0.394773i	−0.846885	−	0.531776i	$-0.821525\pi$
$283$	2.41716	−	6.64111i	0.143686	−	0.394773i	0.990571	+	0.137003i	$0.0437471\pi$
$284$	−1.84142			−0.109268
$285$	−3.12253	+	10.7507i	−0.184963	+	0.636815i
$286$	−11.1826			−0.661244
$287$	−0.00918097	+	0.0252245i	−0.000541936	+	0.00148896i
$288$	−7.80769	+	1.37671i	−0.460073	+	0.0811232i
$289$	3.32041	+	2.78616i	0.195318	+	0.163892i
$290$	−9.60886	−	38.1660i	−0.564252	−	2.24118i
$291$	1.75557	−	9.95634i	0.102913	−	0.583651i
$292$	30.8563	+	17.8149i	1.80573	+	1.04254i
$293$	−0.845886	+	0.488373i	−0.0494172	+	0.0285310i	−0.524505	−	0.851407i	$-0.675750\pi$
$293$	−0.845886	+	0.488373i	−0.0494172	+	0.0285310i	0.475088	+	0.879938i	$0.342416\pi$
$294$	−17.5114	+	6.37364i	−1.02129	+	0.371718i
$295$	11.9367	+	1.22693i	0.694980	+	0.0714346i
$296$	−15.4873	−	26.8247i	−0.900179	−	1.55916i
$297$	13.1092	+	7.56858i	0.760671	+	0.439174i
$298$	−9.60638	−	1.69386i	−0.556483	−	0.0981230i
$299$	−9.41556	+	7.90059i	−0.544516	+	0.456903i
$300$	19.5391	+	0.592619i	1.12809	+	0.0342148i
$301$	−0.273584	−	1.55157i	−0.0157691	−	0.0894312i
$302$	2.27500	−	6.25052i	0.130912	−	0.359677i
$303$		−	3.30555i		−	0.189899i
$304$	−2.92945	−	1.71370i	−0.168015	−	0.0982876i
$305$	−20.3469	−	9.86617i	−1.16506	−	0.564935i
$306$	13.0664	+	4.75579i	0.746958	+	0.271870i
$307$	−28.0346	+	4.94325i	−1.60002	+	0.282126i	−0.901275	−	0.433248i	$-0.857367\pi$
$307$	−28.0346	+	4.94325i	−1.60002	+	0.282126i	−0.698742	+	0.715374i	$0.746256\pi$
$308$	−0.882796	+	1.05207i	−0.0503020	+	0.0599475i
$309$	−1.05554	+	0.885703i	−0.0600475	+	0.0503859i
$310$	20.4163	+	14.7619i	1.15957	+	0.838421i
$311$	12.7730	−	22.1235i	0.724292	−	1.25451i	−0.234972	−	0.972002i	$-0.575500\pi$
$311$	12.7730	−	22.1235i	0.724292	−	1.25451i	0.959265	−	0.282509i	$-0.0911668\pi$
$312$	−5.54623	+	3.20212i	−0.313993	+	0.181284i
$313$	−5.11365	−	14.0496i	−0.289041	−	0.794133i	−0.996201	−	0.0870798i	$-0.972246\pi$
$313$	−5.11365	−	14.0496i	−0.289041	−	0.794133i	0.707161	−	0.707053i	$-0.249976\pi$
$314$	−25.1742	+	9.16265i	−1.42066	+	0.517078i
$315$	−0.537174	+	0.0388008i	−0.0302663	+	0.00218618i
$316$	19.7575	−	34.2210i	1.11145	−	1.92508i
$317$	22.1977	+	3.91406i	1.24675	+	0.219835i	0.757805	−	0.652481i	$-0.226272\pi$
$317$	22.1977	+	3.91406i	1.24675	+	0.219835i	0.488943	+	0.872316i	$0.337383\pi$
$318$	2.82018	+	3.36096i	0.158148	+	0.188473i
$319$	16.3307	+	13.7031i	0.914344	+	0.767226i
$320$	7.65638	−	26.9339i	0.428005	−	1.50565i
$321$	4.42017	+	1.60881i	0.246710	+	0.0897950i
$322$			2.39647i			0.133550i
$323$	−7.67950	−	13.4785i	−0.427299	−	0.749964i
$324$	3.85568			0.214204
$325$	8.11240	−	2.67707i	0.449995	−	0.148497i
$326$	7.63716	+	43.3125i	0.422983	+	2.39886i
$327$	−11.9560	+	14.2486i	−0.661166	+	0.787947i
$328$	−0.392946	−	0.468295i	−0.0216968	−	0.0258572i
$329$	−0.0913327	+	0.517973i	−0.00503533	+	0.0285568i
$330$	−13.9145	+	9.43191i	−0.765966	+	0.519210i
$331$	5.43405	+	9.41205i	0.298682	+	0.517333i	0.975835	−	0.218510i	$-0.0701196\pi$
$331$	5.43405	+	9.41205i	0.298682	+	0.517333i	−0.677152	+	0.735843i	$0.736786\pi$
$332$	8.84297	+	24.2959i	0.485321	+	1.33341i
$333$	5.45611	+	14.9905i	0.298993	+	0.821476i
$334$	17.5148	+	30.3366i	0.958369	+	1.65994i
$335$	−7.53795	−	11.1204i	−0.411842	−	0.607571i
$336$	−0.0222538	+	0.126207i	−0.00121404	+	0.00688518i
$337$	−4.95529	−	5.90548i	−0.269932	−	0.321692i	0.614002	−	0.789305i	$-0.289559\pi$
$337$	−4.95529	−	5.90548i	−0.269932	−	0.321692i	−0.883934	+	0.467612i	$0.845114\pi$
$338$	15.0633	−	17.9517i	0.819333	−	0.976443i
$339$	−0.621971	−	3.52737i	−0.0337808	−	0.191581i
$340$	−19.4420	+	18.8612i	−1.05439	+	1.02289i
$341$	−13.6467			−0.739010
$342$	12.9836	+	11.0216i	0.702075	+	0.595978i
$343$			2.00329i			0.108167i
$344$	33.7159	+	12.2716i	1.81784	+	0.661639i
$345$	−5.05199	+	17.7721i	−0.271990	+	0.956818i
$346$	38.6337	+	32.4175i	2.07696	+	1.74278i
$347$	−13.0292	−	15.5276i	−0.699445	−	0.833566i	0.293018	−	0.956107i	$-0.405340\pi$
$347$	−13.0292	−	15.5276i	−0.699445	−	0.833566i	−0.992464	+	0.122540i	$0.960896\pi$
$348$	29.1521	+	5.14031i	1.56272	+	0.275549i
$349$	9.52515	−	16.4981i	0.509870	−	0.883120i	−0.490065	−	0.871686i	$-0.663027\pi$
$349$	9.52515	−	16.4981i	0.509870	−	0.883120i	0.999935	−	0.0114345i	$-0.00363978\pi$
$350$	0.616862	−	1.54718i	0.0329727	−	0.0827002i
$351$	8.63155	−	3.14163i	0.460718	−	0.167688i
$352$	4.54237	+	12.4801i	0.242109	+	0.665189i
$353$	−15.7328	+	9.08336i	−0.837375	+	0.483459i	−0.856371	−	0.516361i	$-0.827286\pi$
$353$	−15.7328	+	9.08336i	−0.837375	+	0.483459i	0.0189962	+	0.999820i	$0.493953\pi$
$354$	−7.16414	+	12.4087i	−0.380770	+	0.659513i
$355$	−0.708778	+	0.980268i	−0.0376180	+	0.0520272i
$356$	3.77266	−	3.16564i	0.199951	−	0.167778i
$357$	−0.376524	+	0.448724i	−0.0199278	+	0.0237490i
$358$	−52.3771	+	9.23549i	−2.76821	+	0.488111i
$359$	−15.1590	−	5.51741i	−0.800060	−	0.291198i	−0.0905485	−	0.995892i	$-0.528862\pi$
$359$	−15.1590	−	5.51741i	−0.800060	−	0.291198i	−0.709511	+	0.704694i	$0.751084\pi$
$360$	5.35139	−	11.0361i	0.282043	−	0.581656i
$361$	−3.08534	−	18.7478i	−0.162387	−	0.986727i
$362$			26.8866i			1.41313i
$363$	−1.20701	+	3.31624i	−0.0633518	+	0.174058i
$364$	0.144718	+	0.820735i	0.00758527	+	0.0430182i
$365$	21.3604	−	9.56902i	1.11806	−	0.500865i
$366$	20.6841	−	17.3560i	1.08118	−	0.907214i
$367$	31.7715	+	5.60217i	1.65846	+	0.292431i	0.922902	−	0.385034i	$-0.125810\pi$
$367$	31.7715	+	5.60217i	1.65846	+	0.292431i	0.735555	+	0.677465i	$0.236921\pi$
$368$	−4.85084	−	2.80064i	−0.252868	−	0.145993i
$369$	0.157421	+	0.272660i	0.00819499	+	0.0141941i
$370$	−49.0772	−	5.04447i	−2.55140	−	0.262249i
$371$	0.221276	−	0.0805379i	0.0114881	−	0.00418132i
$372$	−16.4106	+	9.47469i	−0.850853	+	0.491240i
$373$	2.06146	+	1.19018i	0.106738	+	0.0616253i	0.552419	−	0.833567i	$-0.313705\pi$
$373$	2.06146	+	1.19018i	0.106738	+	0.0616253i	−0.445681	+	0.895192i	$0.647038\pi$
$374$	4.04484	−	22.9394i	0.209153	−	1.18617i
$375$	7.83623	−	10.1734i	0.404661	−	0.525352i
$376$	−9.17568	−	7.69931i	−0.473199	−	0.397061i
$377$	12.7398	−	2.24636i	0.656131	−	0.115694i
$378$	0.612540	−	1.68294i	0.0315057	−	0.0865611i
$379$	−17.7215			−0.910291			−0.455145	−	0.890417i	$-0.650413\pi$
$379$	−17.7215			−0.910291			−0.455145	+	0.890417i	$0.650413\pi$
$380$	−30.3545	+	13.3905i	−1.55715	+	0.686920i
$381$	−9.37263			−0.480174
$382$	−5.79571	+	15.9236i	−0.296534	+	0.814722i
$383$	10.5025	−	1.85188i	0.536655	−	0.0946268i	0.101249	−	0.994861i	$-0.467716\pi$
$383$	10.5025	−	1.85188i	0.536655	−	0.0946268i	0.435406	+	0.900234i	$0.356605\pi$
$384$	17.3121	+	14.5266i	0.883457	+	0.741308i
$385$	0.220269	+	0.874901i	0.0112260	+	0.0445891i
$386$	−10.5705	+	59.9484i	−0.538025	+	3.05129i
$387$	−16.0032	−	9.23943i	−0.813486	−	0.469667i
$388$	25.9472	−	14.9806i	1.31727	−	0.760527i
$389$	21.3605	−	7.77458i	1.08302	−	0.394187i	0.261989	−	0.965071i	$-0.415622\pi$
$389$	21.3605	−	7.77458i	1.08302	−	0.394187i	0.821031	+	0.570884i	$0.193400\pi$
$390$	−1.04298	+	10.1471i	−0.0528135	+	0.513818i
$391$	−12.8011	−	22.1722i	−0.647381	−	1.12130i
$392$	−19.7257	−	11.3887i	−0.996301	−	0.575214i
$393$	2.96351	+	0.522548i	0.149490	+	0.0263590i
$394$	4.07474	−	3.41911i	0.205282	−	0.172252i
$395$	−10.6125	−	23.6897i	−0.533971	−	1.19196i
$396$	2.79716	+	15.8635i	0.140563	+	0.797170i
$397$	−6.99106	+	19.2078i	−0.350871	+	0.964011i	0.631220	+	0.775604i	$0.282555\pi$
$397$	−6.99106	+	19.2078i	−0.350871	+	0.964011i	−0.982091	+	0.188407i	$0.939668\pi$
$398$		−	28.4694i		−	1.42704i
$399$	−0.623367	+	0.355169i	−0.0312074	+	0.0177807i
$400$	2.41084	+	3.05674i	0.120542	+	0.152837i
$401$	−15.6902	−	5.71077i	−0.783531	−	0.285182i	−0.0808870	−	0.996723i	$-0.525775\pi$
$401$	−15.6902	−	5.71077i	−0.783531	−	0.285182i	−0.702644	+	0.711541i	$0.747998\pi$
$402$	15.7979	−	2.78559i	0.787927	−	0.138933i
$403$	−5.32296	+	6.34366i	−0.265156	+	0.316000i
$404$	7.50431	−	6.29686i	0.373353	−	0.313281i
$405$	1.48408	−	2.05254i	0.0737445	−	0.101992i
$406$	1.26113	−	2.18434i	0.0625888	−	0.108407i
$407$	23.1431	−	13.3617i	1.14716	−	0.662313i
$408$	−4.56252	−	12.5354i	−0.225878	−	0.620596i
$409$	−16.6181	+	6.04849i	−0.821712	+	0.299079i	−0.718453	−	0.695576i	$-0.755149\pi$
$409$	−16.6181	+	6.04849i	−0.821712	+	0.299079i	−0.103259	+	0.994655i	$0.532927\pi$
$410$	−0.971163	+	0.0701485i	−0.0479623	+	0.00346439i
$411$	7.07553	−	12.2552i	0.349010	−	0.604504i
$412$	−4.02147	−	0.709093i	−0.198123	−	0.0349345i
$413$	0.494312	+	0.589098i	0.0243235	+	0.0289876i
$414$	21.5318	+	18.0673i	1.05823	+	0.887961i
$415$	16.3374	+	4.64417i	0.801973	+	0.227973i
$416$	7.57313	+	2.75639i	0.371303	+	0.135143i
$417$		−	9.13552i		−	0.447369i
$418$	14.4057	−	24.6255i	0.704606	−	1.20447i
$419$	37.9339			1.85319			0.926596	−	0.376059i	$-0.122721\pi$
$419$	37.9339			1.85319			0.926596	+	0.376059i	$0.122721\pi$
$420$	0.872313	+	0.899171i	0.0425645	+	0.0438751i
$421$	2.01122	+	11.4062i	0.0980211	+	0.555905i	0.993780	+	0.111364i	$0.0355221\pi$
$421$	2.01122	+	11.4062i	0.0980211	+	0.555905i	−0.895759	+	0.444541i	$0.853367\pi$
$422$	4.48734	−	5.34780i	0.218440	−	0.260327i
$423$	3.96532	+	4.72568i	0.192800	+	0.229770i
$424$	−0.931209	+	5.28115i	−0.0452235	+	0.256475i
$425$	2.55728	+	17.6096i	0.124046	+	0.854191i
$426$	−0.722211	−	1.25091i	−0.0349912	−	0.0606066i
$427$	−0.495648	−	1.36178i	−0.0239861	−	0.0659012i
$428$	4.76779	+	13.0994i	0.230460	+	0.633183i
$429$	−2.76263	−	4.78502i	−0.133381	−	0.231023i
$430$	47.3049	−	32.0657i	2.28125	−	1.54634i
$431$	5.52023	−	31.3068i	0.265900	−	1.50800i	−0.500559	−	0.865702i	$-0.666872\pi$
$431$	5.52023	−	31.3068i	0.265900	−	1.50800i	0.766459	−	0.642293i	$-0.222017\pi$
$432$	2.69070	+	3.20665i	0.129456	+	0.154280i
$433$	−2.62802	+	3.13196i	−0.126295	+	0.150512i	−0.825486	−	0.564422i	$-0.809099\pi$
$433$	−2.62802	+	3.13196i	−0.126295	+	0.150512i	0.699192	+	0.714934i	$0.253543\pi$
$434$	0.280373	+	1.59007i	0.0134583	+	0.0763260i
$435$	13.9573	−	13.5404i	0.669200	−	0.649211i
$436$	−55.1226			−2.63989
$437$	−5.26872	−	30.9119i	−0.252037	−	1.47871i
$438$			27.9481i			1.33541i
$439$	−11.0468	−	4.02069i	−0.527233	−	0.191897i	0.0646692	−	0.997907i	$-0.479401\pi$
$439$	−11.0468	−	4.02069i	−0.527233	−	0.191897i	−0.591903	+	0.806009i	$0.701623\pi$
$440$	−19.7633	−	5.61801i	−0.942176	−	0.267828i
$441$	8.98635	+	7.54044i	0.427921	+	0.359069i
$442$	−9.08566	−	10.8279i	−0.432161	−	0.515029i
$443$	7.76677	+	1.36949i	0.369010	+	0.0650665i	0.355079	−	0.934836i	$-0.384454\pi$
$443$	7.76677	+	1.36949i	0.369010	+	0.0650665i	0.0139318	+	0.999903i	$0.495565\pi$
$444$	18.5536	−	32.1358i	0.880516	−	1.52510i
$445$	−0.233078	−	3.22682i	−0.0110490	−	0.152966i
$446$	−4.79184	+	1.74409i	−0.226900	+	0.0825850i
$447$	−1.64842	−	4.52900i	−0.0779677	−	0.214215i
$448$	1.55407	−	0.897245i	0.0734231	−	0.0423908i
$449$	−0.580397	+	1.00528i	−0.0273906	+	0.0474419i	−0.879396	−	0.476091i	$-0.842053\pi$
$449$	−0.580397	+	1.00528i	−0.0273906	+	0.0474419i	0.852005	+	0.523533i	$0.175386\pi$
$450$	−9.25048	−	17.2068i	−0.436072	−	0.811136i
$451$	0.404022	−	0.339015i	0.0190247	−	0.0159636i
$452$	6.82307	−	8.13142i	0.320930	−	0.382470i
$453$	3.23661	−	0.570702i	0.152069	−	0.0268139i
$454$	−14.0755	−	5.12308i	−0.660598	−	0.240438i
$455$	0.492615	+	0.238867i	0.0230941	+	0.0111983i
$456$	0.0933272	−	16.3385i	0.00437045	−	0.765119i
$457$			38.6888i			1.80978i	0.425641	+	0.904892i	$0.360049\pi$
$457$			38.6888i			1.80978i	−0.425641	+	0.904892i	$0.639951\pi$
$458$	−1.22696	+	3.37105i	−0.0573321	+	0.157519i
$459$	3.32246	+	18.8426i	0.155079	+	0.879497i
$460$	−49.9701	+	22.3856i	−2.32987	+	1.04373i
$461$	−18.7676	+	15.7479i	−0.874096	+	0.733453i	−0.964956	−	0.262410i	$-0.915483\pi$
$461$	−18.7676	+	15.7479i	−0.874096	+	0.733453i	0.0908609	+	0.995864i	$0.471038\pi$
$462$	−1.06092	−	0.187070i	−0.0493587	−	0.00870326i
$463$	−28.1328	−	16.2425i	−1.30744	−	0.754852i	−0.325773	−	0.945448i	$-0.605625\pi$
$463$	−28.1328	−	16.2425i	−1.30744	−	0.754852i	−0.981669	+	0.190596i	$0.938958\pi$
$464$	2.94764	+	5.10546i	0.136841	+	0.237015i
$465$	−1.27280	+	12.3830i	−0.0590247	+	0.574246i
$466$	−44.6960	+	16.2680i	−2.07050	+	0.753602i
$467$	12.7323	−	7.35099i	0.589180	−	0.340163i	−0.175593	−	0.984463i	$-0.556184\pi$
$467$	12.7323	−	7.35099i	0.589180	−	0.340163i	0.764773	+	0.644299i	$0.222851\pi$
$468$	8.46518	+	4.88738i	0.391303	+	0.225919i
$469$	0.149505	−	0.847887i	0.00690351	−	0.0391518i
$470$	−18.5010	+	4.65791i	−0.853388	+	0.214853i
$471$	−10.1399	−	8.50835i	−0.467220	−	0.392044i
$472$	−17.2470	+	3.04111i	−0.793856	+	0.139978i
$473$	−10.5873	+	29.0885i	−0.486806	+	1.33749i
$474$	30.9957			1.42368
$475$	−4.55533	+	21.3131i	−0.209013	+	0.977913i
$476$	−1.73595			−0.0795672
$477$	0.944615	−	2.59531i	0.0432510	−	0.118831i
$478$	−14.2868	+	2.51915i	−0.653462	+	0.115223i
$479$	10.1268	+	8.49741i	0.462706	+	0.388256i	0.844125	−	0.536146i	$-0.180120\pi$
$479$	10.1268	+	8.49741i	0.462706	+	0.388256i	−0.381420	+	0.924402i	$0.624565\pi$
$480$	11.7480	−	2.95774i	0.536221	−	0.135002i
$481$	2.81592	−	15.9699i	0.128395	−	0.728162i
$482$	−52.9765	−	30.5860i	−2.41301	−	1.39315i
$483$	−1.02544	+	0.592039i	−0.0466592	+	0.0269387i
$484$	−9.82785	+	3.57705i	−0.446721	+	0.162593i
$485$	2.01245	−	19.5790i	0.0913808	−	0.889036i
$486$	−17.2344	−	29.8508i	−0.781767	−	1.35406i
$487$	8.36642	+	4.83036i	0.379119	+	0.218884i	0.677435	−	0.735583i	$-0.263092\pi$
$487$	8.36642	+	4.83036i	0.379119	+	0.218884i	−0.298316	+	0.954467i	$0.596425\pi$
$488$	32.5013	+	5.73086i	1.47127	+	0.259424i
$489$	−16.6465	+	13.9681i	−0.752783	+	0.631660i
$490$	−33.1089	+	14.8321i	−1.49571	+	0.670046i
$491$	0.466479	+	2.64553i	0.0210519	+	0.119391i	0.993523	−	0.113633i	$-0.0362489\pi$
$491$	0.466479	+	2.64553i	0.0210519	+	0.119391i	−0.972471	+	0.233024i	$0.925138\pi$
$492$	0.250479	−	0.688184i	0.0112924	−	0.0310257i
$493$			26.9461i			1.21359i
$494$	−5.82813	−	16.3018i	−0.262220	−	0.733452i
$495$	9.52145	+	4.61693i	0.427957	+	0.207515i
$496$	−3.54623	−	1.29072i	−0.159230	−	0.0579551i
$497$	−0.0763457	+	0.0134618i	−0.00342457	+	0.000603844i
$498$	−13.0363	+	15.5360i	−0.584170	+	0.696187i
$499$	−1.80438	+	1.51406i	−0.0807753	+	0.0677786i	−0.682281	−	0.731090i	$-0.739012\pi$
$499$	−1.80438	+	1.51406i	−0.0807753	+	0.0677786i	0.601506	+	0.798868i	$0.294568\pi$
$500$	38.0232	−	1.58975i	1.70045	−	0.0710958i
$501$	−8.65395	+	14.9891i	−0.386630	+	0.669663i
$502$	21.5538	−	12.4441i	0.961995	−	0.555408i
$503$	4.69900	+	12.9104i	0.209518	+	0.575646i	0.999287	−	0.0377584i	$-0.0120217\pi$
$503$	4.69900	+	12.9104i	0.209518	+	0.575646i	−0.789769	+	0.613405i	$0.789799\pi$
$504$	0.738629	−	0.268839i	0.0329011	−	0.0119750i
$505$	−0.463622	−	6.41857i	−0.0206309	−	0.285623i
$506$	23.5427	−	40.7771i	1.04660	−	1.81276i
$507$	11.4028	+	2.01062i	0.506416	+	0.0892948i
$508$	−17.8542	−	21.2779i	−0.792154	−	0.944052i
$509$	27.8684	+	23.3844i	1.23524	+	1.03649i	0.997881	+	0.0650727i	$0.0207279\pi$
$509$	27.8684	+	23.3844i	1.23524	+	1.03649i	0.237364	+	0.971421i	$0.423717\pi$
$510$	−20.4379	−	5.80978i	−0.905005	−	0.257262i
$511$	1.40954	+	0.513031i	0.0623544	+	0.0226952i
$512$			8.75464i			0.386904i
$513$	−4.20111	+	23.0548i	−0.185483	+	1.01789i
$514$	31.4382			1.38668
$515$	−1.92537	+	1.86786i	−0.0848420	+	0.0823078i
$516$	7.46402	+	42.3306i	0.328585	+	1.86350i
$517$	6.64259	−	7.91633i	0.292141	−	0.348160i
$518$	−2.03234	−	2.42205i	−0.0892960	−	0.106419i
$519$	−4.32704	+	24.5398i	−0.189936	+	1.07718i
$520$	−10.3203	+	6.99561i	−0.452575	+	0.306778i
$521$	−0.290212	−	0.502661i	−0.0127144	−	0.0220220i	0.859598	−	0.510971i	$-0.170714\pi$
$521$	−0.290212	−	0.502661i	−0.0127144	−	0.0220220i	−0.872313	+	0.488949i	$0.837381\pi$
$522$	−10.1180	−	27.7990i	−0.442854	−	1.21673i
$523$	−6.58262	−	18.0856i	−0.287838	−	0.790828i	−0.996368	−	0.0851478i	$-0.972864\pi$
$523$	−6.58262	−	18.0856i	−0.287838	−	0.790828i	0.708530	−	0.705680i	$-0.249358\pi$
$524$	4.45901	+	7.72322i	0.194793	+	0.337391i
$525$	0.814426	−	0.118271i	0.0355445	−	0.00516179i
$526$	−2.64021	+	14.9734i	−0.115118	+	0.652869i
$527$	−11.0876	−	13.2137i	−0.482986	−	0.575600i
$528$	1.61851	−	1.92886i	0.0704366	−	0.0839431i
$529$	−4.99286	−	28.3159i	−0.217081	−	1.23113i
$530$	5.94749	+	6.13061i	0.258343	+	0.266297i
$531$	9.01961			0.391418
$532$	−1.99378	−	0.738602i	−0.0864414	−	0.0320224i
$533$		−	0.320044i		−	0.0138626i
$534$	3.63011	+	1.32125i	0.157090	+	0.0571762i
$535$	8.80851	+	2.50396i	0.380825	+	0.108255i
$536$	15.0200	+	12.6032i	0.648763	+	0.544377i
$537$	−16.8914	−	20.1304i	−0.728918	−	0.868690i
$538$	33.0165	+	5.82169i	1.42344	+	0.250991i
$539$	9.82559	−	17.0184i	0.423218	−	0.733036i
$540$	40.8137	−	2.94803i	1.75634	−	0.126863i
$541$	29.9824	−	10.9127i	1.28904	−	0.469174i	0.395631	−	0.918410i	$-0.370526\pi$
$541$	29.9824	−	10.9127i	1.28904	−	0.469174i	0.893413	+	0.449236i	$0.148304\pi$
$542$	−1.73666	−	4.77143i	−0.0745959	−	0.204951i
$543$	−11.5047	+	6.64223i	−0.493713	+	0.285045i
$544$	−8.39355	+	14.5380i	−0.359870	+	0.623314i
$545$	−21.2171	+	29.3441i	−0.908840	+	1.25696i
$546$	−0.500778	+	0.420203i	−0.0214313	+	0.0179830i
$547$	−2.20766	+	2.63099i	−0.0943929	+	0.112493i	−0.811173	−	0.584806i	$-0.801171\pi$
$547$	−2.20766	+	2.63099i	−0.0943929	+	0.112493i	0.716780	+	0.697299i	$0.245615\pi$
$548$	41.3003	−	7.28235i	1.76426	−	0.311087i
$549$	−15.9721	−	5.81337i	−0.681673	−	0.248109i
$550$	−25.6956	+	20.2660i	−1.09566	+	0.864146i
$551$	−11.4649	+	30.9482i	−0.488419	+	1.31844i
$552$		−	26.9655i		−	1.14773i
$553$	0.568974	−	1.56324i	0.0241952	−	0.0664759i
$554$	−6.44843	−	36.5708i	−0.273967	−	1.55375i
$555$	−9.96583	−	22.2462i	−0.423026	−	0.944298i
$556$	20.7396	−	17.4026i	0.879554	−	0.738033i
$557$	−6.72634	−	1.18604i	−0.285004	−	0.0502539i	0.0293185	−	0.999570i	$-0.490666\pi$
$557$	−6.72634	−	1.18604i	−0.285004	−	0.0502539i	−0.314323	+	0.949316i	$0.601777\pi$
$558$	16.4003	+	9.46870i	0.694279	+	0.400842i
$559$	9.39211	+	16.2676i	0.397244	+	0.688047i
$560$	−0.0255100	+	0.248185i	−0.00107800	+	0.0104877i
$561$	10.8150	−	3.93632i	0.456608	−	0.166192i
$562$	28.7018	−	16.5710i	1.21071	−	0.699004i
$563$	10.8797	+	6.28141i	0.458526	+	0.264730i	0.711424	−	0.702763i	$-0.248051\pi$
$563$	10.8797	+	6.28141i	0.458526	+	0.264730i	−0.252898	+	0.967493i	$0.581384\pi$
$564$	2.49177	−	14.1315i	0.104922	−	0.595045i
$565$	−1.70245	−	6.76205i	−0.0716225	−	0.284482i
$566$	12.5852	+	10.5603i	0.528997	+	0.443881i
$567$	0.159857	−	0.0281871i	0.00671336	−	0.00118375i
$568$	0.603827	−	1.65900i	0.0253360	−	0.0696102i
$569$	−3.47978			−0.145880			−0.0729400	−	0.997336i	$-0.523238\pi$
$569$	−3.47978			−0.145880			−0.0729400	+	0.997336i	$0.523238\pi$
$570$	−21.0015	−	15.3685i	−0.879656	−	0.643714i
$571$	−0.621524			−0.0260100			−0.0130050	−	0.999915i	$-0.504140\pi$
$571$	−0.621524			−0.0260100			−0.0130050	+	0.999915i	$0.504140\pi$
$572$	5.60037	−	15.3869i	0.234163	−	0.643359i
$573$	−8.24546	+	1.45390i	−0.344459	+	0.0607374i
$574$	−0.0478017	−	0.0401104i	−0.00199521	−	0.00167418i
$575$	−7.31709	+	35.2176i	−0.305144	+	1.46868i
$576$	3.65482	−	20.7275i	0.152284	−	0.863646i
$577$	3.33567	+	1.92585i	0.138866	+	0.0801742i	0.567823	−	0.823150i	$-0.307786\pi$
$577$	3.33567	+	1.92585i	0.138866	+	0.0801742i	−0.428958	+	0.903325i	$0.641119\pi$
$578$	−8.72612	+	5.03803i	−0.362959	+	0.209554i
$579$	−28.2631	+	10.2869i	−1.17458	+	0.427510i
$580$	57.3272	+	5.89246i	2.38038	+	0.244671i
$581$	0.544246	+	0.942662i	0.0225791	+	0.0391082i
$582$	20.3531	+	11.7509i	0.843665	+	0.487090i
$583$	−4.55632	−	0.803402i	−0.188704	−	0.0332735i
$584$	−26.1682	+	21.9577i	−1.08285	+	0.908618i
$585$	5.86007	−	2.62519i	0.242284	−	0.108538i
$586$	−0.394279	−	2.23607i	−0.0162875	−	0.0923712i
$587$	−13.8290	+	37.9949i	−0.570784	+	1.56822i	0.232485	+	0.972600i	$0.425314\pi$
$587$	−13.8290	+	37.9949i	−0.570784	+	1.56822i	−0.803269	+	0.595616i	$0.796908\pi$
$588$		−	27.2871i		−	1.12530i
$589$	−7.11233	−	19.8938i	−0.293059	−	0.819710i
$590$	−12.1706	+	25.0994i	−0.501056	+	1.03332i
$591$	2.46968	+	0.898889i	0.101589	+	0.0369753i
$592$	7.27772	−	1.28326i	0.299113	−	0.0527416i
$593$	3.77549	−	4.49946i	0.155041	−	0.184771i	−0.682933	−	0.730481i	$-0.739296\pi$
$593$	3.77549	−	4.49946i	0.155041	−	0.184771i	0.837974	+	0.545711i	$0.183740\pi$
$594$	−26.9557	+	22.6185i	−1.10601	+	0.928050i
$595$	−0.668180	+	0.924120i	−0.0273927	+	0.0378852i
$596$	7.14166	−	12.3697i	0.292534	−	0.506684i
$597$	12.1820	−	7.03326i	0.498575	−	0.287852i
$598$	−9.77229	−	26.8491i	−0.399619	−	1.09794i
$599$	−12.5080	+	4.55254i	−0.511063	+	0.186012i	−0.584663	−	0.811276i	$-0.698773\pi$
$599$	−12.5080	+	4.55254i	−0.511063	+	0.186012i	0.0736001	+	0.997288i	$0.476551\pi$
$600$	−6.94104	+	17.4091i	−0.283367	+	0.710725i
$601$	−2.58008	+	4.46883i	−0.105244	+	0.182287i	−0.913838	−	0.406079i	$-0.866896\pi$
$601$	−2.58008	+	4.46883i	−0.105244	+	0.182287i	0.808594	+	0.588367i	$0.200229\pi$
$602$	3.60682	+	0.635980i	0.147003	+	0.0259206i
$603$	−6.49095	−	7.73561i	−0.264332	−	0.315019i
$604$	7.46114	+	6.26064i	0.303590	+	0.254742i
$605$	−1.87860	+	6.60861i	−0.0763760	+	0.268678i
$606$	7.22076	+	2.62814i	0.293323	+	0.106761i
$607$		−	30.5069i		−	1.23824i	−0.785297	−	0.619119i	$-0.787490\pi$
$607$		−	30.5069i		−	1.23824i	0.785297	−	0.619119i	$-0.212510\pi$
$608$	−15.8258	+	13.1261i	−0.641819	+	0.532333i
$609$	1.24623			0.0504998
$610$	37.7291	−	36.6022i	1.52761	−	1.48198i
$611$	−1.08893	−	6.17561i	−0.0440533	−	0.249839i
$612$	−13.0876	+	15.5972i	−0.529034	+	0.630478i
$613$	−29.2473	−	34.8556i	−1.18129	−	1.40780i	−0.892879	−	0.450297i	$-0.851318\pi$
$613$	−29.2473	−	34.8556i	−1.18129	−	1.40780i	−0.288409	−	0.957507i	$-0.593126\pi$
$614$	11.4912	−	65.1698i	0.463747	−	2.63004i
$615$	−0.269939	−	0.398228i	−0.0108850	−	0.0160581i
$616$	−0.658370	−	1.14033i	−0.0265265	−	0.0459452i
$617$	0.849053	+	2.33275i	0.0341816	+	0.0939131i	0.955609	−	0.294636i	$-0.0951985\pi$
$617$	0.849053	+	2.33275i	0.0341816	+	0.0939131i	−0.921428	+	0.388549i	$0.872976\pi$
$618$	−1.09553	−	3.00995i	−0.0440687	−	0.121078i
$619$	11.7473	+	20.3469i	0.472162	+	0.817809i	0.999493	−	0.0318512i	$-0.0101403\pi$
$619$	11.7473	+	20.3469i	0.472162	+	0.817809i	−0.527330	+	0.849660i	$0.676807\pi$
$620$	−30.5365	+	20.6992i	−1.22638	+	0.831300i
$621$	−6.71606	+	38.0887i	−0.269506	+	1.52845i
$622$	38.1719	+	45.4915i	1.53056	+	1.82404i
$623$	0.133272	−	0.158828i	0.00533945	−	0.00636330i
$624$	−0.265324	−	1.50473i	−0.0106215	−	0.0602373i
$625$	13.7891	−	20.8533i	0.551566	−	0.834132i
$626$	34.7562			1.38914
$627$	14.0961	+	0.0805182i	0.562942	+	0.00321559i
$628$		−	39.2275i		−	1.56535i
$629$	31.7410	+	11.5528i	1.26560	+	0.460640i
$630$	0.342332	−	1.20427i	0.0136388	−	0.0479792i
$631$	−13.6507	−	11.4543i	−0.543426	−	0.455989i	0.329282	−	0.944232i	$-0.393193\pi$
$631$	−13.6507	−	11.4543i	−0.543426	−	0.455989i	−0.872708	+	0.488243i	$0.837638\pi$
$632$	24.3521	+	29.0217i	0.968675	+	1.15442i
$633$	3.39689	+	0.598963i	0.135014	+	0.0238066i
$634$	−26.1987	+	45.3774i	−1.04048	+	1.80217i
$635$	−18.1993	+	1.31456i	−0.722218	+	0.0521668i
$636$	−6.03693	+	2.19726i	−0.239380	+	0.0871272i
$637$	−4.07849	−	11.2056i	−0.161596	−	0.443980i
$638$	−42.9175	+	24.7784i	−1.69912	+	0.980987i
$639$	−0.454629	+	0.787441i	−0.0179849	+	0.0311507i
$640$	35.6534	+	25.7790i	1.40932	+	1.01900i
$641$	28.6984	−	24.0808i	1.13352	−	0.951135i	0.134311	−	0.990939i	$-0.457118\pi$
$641$	28.6984	−	24.0808i	1.13352	−	0.951135i	0.999207	+	0.0398045i	$0.0126735\pi$
$642$	−7.02867	+	8.37644i	−0.277399	+	0.330592i
$643$	19.5865	−	3.45362i	0.772415	−	0.136198i	0.226469	−	0.974018i	$-0.427282\pi$
$643$	19.5865	−	3.45362i	0.772415	−	0.136198i	0.545946	+	0.837821i	$0.316171\pi$
$644$	−3.29745	−	1.20017i	−0.129938	−	0.0472935i
$645$	25.4073	+	12.3199i	1.00041	+	0.485097i
$646$	35.5486	−	6.05901i	1.39864	−	0.238389i
$647$			23.0645i			0.906759i	0.891318	+	0.453380i	$0.149782\pi$
$647$			23.0645i			0.906759i	−0.891318	+	0.453380i	$0.850218\pi$
$648$	−1.26433	+	3.47371i	−0.0496675	+	0.136460i
$649$	−2.62372	−	14.8799i	−0.102990	−	0.584086i
$650$	−0.602031	+	19.8494i	−0.0236136	+	0.778559i
$651$	−0.611122	+	0.512793i	−0.0239518	+	0.0200979i
$652$	−63.4211	−	11.1829i	−2.48376	−	0.437954i
$653$	23.3687	+	13.4919i	0.914489	+	0.527981i	0.881873	−	0.471487i	$-0.156283\pi$
$653$	23.3687	+	13.4919i	0.914489	+	0.527981i	0.0326165	+	0.999468i	$0.489616\pi$
$654$	−21.6192	−	37.4455i	−0.845377	−	1.46424i
$655$	5.82770	+	0.599009i	0.227707	+	0.0234052i
$656$	0.137054	−	0.0498834i	0.00535104	−	0.00194762i
$657$	15.2362	−	8.79663i	0.594421	−	0.343189i
$658$	−1.05886	−	0.611334i	−0.0412787	−	0.0238323i
$659$	−2.34217	+	13.2831i	−0.0912379	+	0.517436i	0.904598	+	0.426267i	$0.140171\pi$
$659$	−2.34217	+	13.2831i	−0.0912379	+	0.517436i	−0.995835	+	0.0911691i	$0.970940\pi$
$660$	−6.00947	−	23.8694i	−0.233918	−	0.929114i
$661$	−16.8359	−	14.1270i	−0.654842	−	0.549477i	0.253694	−	0.967284i	$-0.418354\pi$
$661$	−16.8359	−	14.1270i	−0.654842	−	0.549477i	−0.908536	+	0.417807i	$0.862799\pi$
$662$	−24.8804	+	4.38709i	−0.967005	+	0.170509i
$663$	2.38863	−	6.56271i	0.0927668	−	0.254875i
$664$	−24.7887			−0.961988
$665$	−1.16061	+	0.777081i	−0.0450065	+	0.0301339i
$666$	−37.0838			−1.43697
$667$	−18.6296	+	51.1843i	−0.721340	+	1.98186i
$668$	−50.5136	+	8.90691i	−1.95443	+	0.344619i
$669$	−1.93010	−	1.61954i	−0.0746219	−	0.0626152i
$670$	30.2849	−	7.62467i	1.17001	−	0.294567i
$671$	−4.94431	+	28.0406i	−0.190873	+	1.08250i
$672$	0.672370	+	0.388193i	0.0259372	+	0.0149749i
$673$	−20.0916	+	11.5999i	−0.774475	+	0.447143i	−0.834468	−	0.551056i	$-0.814225\pi$
$673$	−20.0916	+	11.5999i	−0.774475	+	0.447143i	0.0599940	+	0.998199i	$0.480892\pi$
$674$	16.8399	−	6.12923i	0.648649	−	0.236089i
$675$	14.1401	−	22.8616i	0.544254	−	0.879943i
$676$	17.1570	+	29.7169i	0.659886	+	1.14296i
$677$	24.8804	+	14.3647i	0.956232	+	0.552081i	0.895011	−	0.446043i	$-0.147167\pi$
$677$	24.8804	+	14.3647i	0.956232	+	0.552081i	0.0612208	+	0.998124i	$0.480501\pi$
$678$	8.19981	+	1.44585i	0.314912	+	0.0555275i
$679$	0.966259	−	0.810788i	0.0370816	−	0.0311152i
$680$	−10.6174	−	23.7008i	−0.407161	−	0.908883i
$681$	−1.28516	−	7.28852i	−0.0492475	−	0.279297i
$682$	10.8500	−	29.8103i	0.415470	−	1.14149i
$683$			24.0010i			0.918374i	0.888340	+	0.459187i	$0.151859\pi$
$683$			24.0010i			0.918374i	−0.888340	+	0.459187i	$0.848141\pi$
$684$	−21.6676	+	12.3453i	−0.828481	+	0.472035i
$685$	12.0201	−	24.7889i	0.459264	−	0.947136i
$686$	−4.37604	−	1.59275i	−0.167078	−	0.0608114i
$687$	−1.74558	+	0.307792i	−0.0665979	+	0.0117430i
$688$	−5.50244	+	6.55756i	−0.209779	+	0.250005i
$689$	−2.15068	+	1.80463i	−0.0819343	+	0.0687510i
$690$	−34.8053	−	25.1658i	−1.32501	−	0.958044i
$691$	−18.6933	+	32.3778i	−0.711128	+	1.23171i	0.253307	+	0.967386i	$0.418482\pi$
$691$	−18.6933	+	32.3778i	−0.711128	+	1.23171i	−0.964434	+	0.264323i	$0.914851\pi$
$692$	−63.9534	+	36.9235i	−2.43114	+	1.40362i
$693$	0.231941	+	0.637253i	0.00881072	+	0.0242073i
$694$	44.2781	−	16.1159i	1.68078	−	0.611752i
$695$	−1.28131	−	17.7389i	−0.0486028	−	0.672876i
$696$	−14.1905	+	24.5786i	−0.537888	+	0.931649i
$697$	0.656519	+	0.115762i	0.0248674	+	0.00438480i
$698$	28.4657	+	33.9241i	1.07744	+	1.28405i
$699$	−18.0030	−	15.1063i	−0.680937	−	0.571374i
$700$	1.81993	+	1.62362i	0.0687869	+	0.0613671i
$701$	2.18595	+	0.795621i	0.0825622	+	0.0300502i	0.382971	−	0.923760i	$-0.374901\pi$
$701$	2.18595	+	0.795621i	0.0825622	+	0.0300502i	−0.300409	+	0.953811i	$0.597123\pi$
$702$			21.3528i			0.805911i
$703$	31.5400	+	26.7737i	1.18955	+	1.00979i
$704$	−35.2578			−1.32883
$705$	−6.56371	−	6.76581i	−0.247204	−	0.254815i
$706$	−7.33330	−	41.5892i	−0.275992	−	1.56523i
$707$	0.265096	−	0.315929i	0.00996996	−	0.0118817i
$708$	−13.4860	−	16.0720i	−0.506834	−	0.604022i
$709$	4.22872	−	23.9823i	0.158813	−	0.900674i	−0.796403	−	0.604766i	$-0.793267\pi$
$709$	4.22872	−	23.9823i	0.158813	−	0.900674i	0.955216	−	0.295908i	$-0.0956222\pi$
$710$	−1.57780	−	2.32766i	−0.0592138	−	0.0873554i
$711$	−9.75586	−	16.8976i	−0.365873	−	0.633711i
$712$	1.61493	+	4.43697i	0.0605219	+	0.166283i
$713$	−11.9256	−	32.7652i	−0.446616	−	1.22707i
$714$	−0.680844	−	1.17926i	−0.0254799	−	0.0441326i
$715$	−6.03547	−	8.90385i	−0.225714	−	0.332985i
$716$	13.5232	−	76.6941i	0.505387	−	2.86619i
$717$	−4.60743	−	5.49092i	−0.172068	−	0.205062i
$718$	24.1048	−	28.7270i	0.899584	−	1.07208i
$719$	−2.96281	−	16.8029i	−0.110494	−	0.626644i	−0.988883	−	0.148697i	$-0.952492\pi$
$719$	−2.96281	−	16.8029i	−0.110494	−	0.626644i	0.878389	−	0.477947i	$-0.158619\pi$
$720$	2.03757	+	2.10030i	0.0759357	+	0.0782737i
$721$	−0.171914			−0.00640242
$722$	43.4064	+	8.16607i	1.61542	+	0.303910i
$723$		−	30.2246i		−	1.12407i
$724$	−36.9949	−	13.4650i	−1.37491	−	0.500425i
$725$	25.2025	−	28.2496i	0.935996	−	1.04917i
$726$	−6.28445	−	5.27328i	−0.233238	−	0.195710i
$727$	9.40083	+	11.2035i	0.348657	+	0.415514i	0.911663	−	0.410940i	$-0.134799\pi$
$727$	9.40083	+	11.2035i	0.348657	+	0.415514i	−0.563005	+	0.826453i	$0.690355\pi$
$728$	−0.786883	−	0.138749i	−0.0291638	−	0.00514237i
$729$	10.2145	−	17.6920i	0.378314	−	0.655259i
$730$	3.91988	+	54.2684i	0.145081	+	2.00856i
$731$	−36.7676	+	13.3823i	−1.35990	+	0.494963i
$732$	13.5224	+	37.1526i	0.499804	+	1.37320i
$733$	29.0344	−	16.7630i	1.07241	−	0.619156i	0.143570	−	0.989640i	$-0.454142\pi$
$733$	29.0344	−	16.7630i	1.07241	−	0.619156i	0.928839	+	0.370484i	$0.120808\pi$
$734$	−37.4980	+	64.9485i	−1.38408	+	2.39729i
$735$	−14.5261	−	10.5030i	−0.535801	−	0.387409i
$736$	−25.9947	+	21.8121i	−0.958177	+	0.804006i
$737$	−10.8735	+	12.9585i	−0.400529	+	0.477332i
$738$	−0.720768	+	0.127091i	−0.0265318	+	0.00467828i
$739$	−14.2925	−	5.20205i	−0.525759	−	0.191361i	0.0654847	−	0.997854i	$-0.479141\pi$
$739$	−14.2925	−	5.20205i	−0.525759	−	0.191361i	−0.591244	+	0.806493i	$0.701363\pi$
$740$	31.5193	−	65.0021i	1.15867	−	2.38952i
$741$	5.53567	−	6.52114i	0.203358	−	0.239560i
$742$			0.547396i			0.0200955i
$743$	2.27717	−	6.25647i	0.0835412	−	0.229528i	−0.890888	−	0.454224i	$-0.849917\pi$
$743$	2.27717	−	6.25647i	0.0835412	−	0.229528i	0.974429	+	0.224696i	$0.0721389\pi$
$744$	−3.15481	−	17.8918i	−0.115661	−	0.655945i
$745$	−3.83605	−	8.56301i	−0.140542	−	0.313724i
$746$	−4.23887	+	3.55684i	−0.155196	+	0.130225i
$747$	12.5728	+	2.21692i	0.460014	+	0.0811129i
$748$	29.5381	+	17.0538i	1.08002	+	0.623549i
$749$	0.293437	+	0.508247i	0.0107219	+	0.0185709i
$750$	15.9927	+	25.2062i	0.583973	+	0.920402i
$751$	−7.34004	+	2.67155i	−0.267842	+	0.0974864i	−0.472450	−	0.881358i	$-0.656630\pi$
$751$	−7.34004	+	2.67155i	−0.267842	+	0.0974864i	0.204608	+	0.978844i	$0.434408\pi$
$752$	2.47488	−	1.42887i	0.0902496	−	0.0521056i
$753$	10.6496	+	6.14855i	0.388093	+	0.224066i
$754$	−5.22195	+	29.6151i	−0.190172	+	1.07852i
$755$	6.20465	−	1.56211i	0.225810	−	0.0568512i
$756$	2.00890	+	1.68567i	0.0730629	+	0.0613071i
$757$	−18.1053	+	3.19246i	−0.658049	+	0.116032i	−0.492695	−	0.870202i	$-0.663988\pi$
$757$	−18.1053	+	3.19246i	−0.658049	+	0.116032i	−0.165355	+	0.986234i	$0.552877\pi$
$758$	14.0898	−	38.7113i	0.511764	−	1.40606i
$759$	23.2645			0.844449
$760$	−2.11034	−	31.7384i	−0.0765502	−	1.15127i
$761$	22.4779			0.814822			0.407411	−	0.913245i	$-0.366432\pi$
$761$	22.4779			0.814822			0.407411	+	0.913245i	$0.366432\pi$
$762$	7.45188	−	20.4739i	0.269953	−	0.741690i
$763$	−2.28539	+	0.402976i	−0.0827366	+	0.0145887i
$764$	−19.0077	−	15.9494i	−0.687675	−	0.577028i
$765$	3.26553	+	12.9705i	0.118065	+	0.468951i
$766$	−4.30493	+	24.4145i	−0.155543	+	0.882131i
$767$	−7.94029	−	4.58433i	−0.286707	−	0.165531i
$768$	−20.5846	+	11.8846i	−0.742784	+	0.428847i
$769$	5.18597	−	1.88754i	0.187011	−	0.0680664i	−0.246817	−	0.969062i	$-0.579385\pi$
$769$	5.18597	−	1.88754i	0.187011	−	0.0680664i	0.433828	+	0.900996i	$0.357162\pi$
$770$	−2.08629	−	0.214442i	−0.0751847	−	0.00772797i
$771$	7.76669	+	13.4523i	0.279710	+	0.484473i
$772$	−77.1929	−	44.5673i	−2.77823	−	1.60401i
$773$	−32.6839	−	5.76305i	−1.17556	−	0.207283i	−0.448451	−	0.893807i	$-0.648024\pi$
$773$	−32.6839	−	5.76305i	−1.17556	−	0.207283i	−0.727106	+	0.686525i	$0.759135\pi$
$774$	32.9065	−	27.6118i	1.18280	−	0.992487i
$775$	−0.734685	+	24.2232i	−0.0263907	+	0.870122i
$776$	4.98813	+	28.2891i	0.179064	+	1.01552i
$777$	0.534305	−	1.46799i	0.0191681	−	0.0526639i
$778$			52.8418i			1.89447i
$779$	0.704774	+	0.412287i	0.0252512	+	0.0147717i
$780$	−13.4397	−	6.51687i	−0.481218	−	0.233341i
$781$	1.43131	+	0.520953i	0.0512162	+	0.0186412i
$782$	58.6114	−	10.3348i	2.09594	−	0.369571i
$783$	26.1655	−	31.1829i	0.935080	−	1.11439i
$784$	4.16290	−	3.49309i	0.148675	−	0.124753i
$785$	−20.8824	−	15.0989i	−0.745326	−	0.538904i
$786$	−3.49767	+	6.05813i	−0.124758	+	0.216086i
$787$	42.1279	−	24.3225i	1.50170	−	0.867005i	0.501698	−	0.865043i	$-0.332709\pi$
$787$	42.1279	−	24.3225i	1.50170	−	0.867005i	0.999998	−	0.00196163i	$-0.000624406\pi$
$788$	2.66390	+	7.31901i	0.0948976	+	0.260729i
$789$	−7.05930	+	2.56938i	−0.251318	+	0.0914722i
$790$	60.1861	−	4.34733i	2.14132	−	0.154671i
$791$	0.223440	−	0.387010i	0.00794462	−	0.0137605i
$792$	−15.2092	−	2.68179i	−0.540435	−	0.0952932i
$793$	11.1061	+	13.2357i	0.394389	+	0.470015i
$794$	−36.3997	−	30.5430i	−1.29178	−	1.08393i
$795$	−1.15396	+	4.05946i	−0.0409269	+	0.143974i
$796$	39.1728	+	14.2577i	1.38844	+	0.505352i
$797$			1.06027i			0.0375567i	0.999824	+	0.0187784i	$0.00597769\pi$
$797$			1.06027i			0.0375567i	−0.999824	+	0.0187784i	$0.994022\pi$
$798$	−0.280223	−	1.64409i	−0.00991980	−	0.0582000i
$799$	13.0622			0.462106
$800$	22.3969	−	7.39093i	0.791851	−	0.261309i
$801$	−0.422277	−	2.39485i	−0.0149204	−	0.0846179i
$802$	24.9496	−	29.7337i	0.881000	−	1.04993i
$803$	−18.9441	−	22.5767i	−0.668522	−	0.796714i
$804$	−4.07886	+	23.1324i	−0.143850	+	0.815815i
$805$	−1.90812	+	1.29342i	−0.0672523	+	0.0455870i
$806$	−9.62517	−	16.6713i	−0.339032	−	0.587221i
$807$	5.66551	+	15.5659i	0.199435	+	0.547944i
$808$	3.21230	+	8.82571i	0.113008	+	0.310487i
$809$	−6.80960	−	11.7946i	−0.239413	−	0.414675i	0.721133	−	0.692797i	$-0.243622\pi$
$809$	−6.80960	−	11.7946i	−0.239413	−	0.414675i	−0.960546	+	0.278121i	$0.910288\pi$
$810$	3.30369	+	4.87378i	0.116080	+	0.171247i
$811$	3.88880	−	22.0545i	0.136554	−	0.774438i	−0.837210	−	0.546881i	$-0.815815\pi$
$811$	3.88880	−	22.0545i	0.136554	−	0.774438i	0.973765	−	0.227557i	$-0.0730738\pi$
$812$	2.37398	+	2.82920i	0.0833105	+	0.0992856i
$813$	1.61265	−	1.92188i	0.0565580	−	0.0674032i
$814$	10.7873	+	61.1779i	0.378095	+	2.14429i
$815$	−30.3644	+	29.4574i	−1.06362	+	1.03185i
$816$	3.18268			0.111416
$817$	−47.9223	−	0.273738i	−1.67659	−	0.00957687i
$818$		−	41.1100i		−	1.43738i
$819$	0.386697	+	0.140746i	0.0135123	+	0.00491807i
$820$	0.389846	−	1.37141i	0.0136140	−	0.0478919i
$821$	−4.22809	−	3.54778i	−0.147561	−	0.123819i	0.566019	−	0.824392i	$-0.308483\pi$
$821$	−4.22809	−	3.54778i	−0.147561	−	0.123819i	−0.713580	+	0.700574i	$0.752927\pi$
$822$	21.1451	+	25.1997i	0.737519	+	0.878941i
$823$	−22.0128	−	3.88144i	−0.767317	−	0.135299i	−0.223729	−	0.974651i	$-0.571823\pi$
$823$	−22.0128	−	3.88144i	−0.767317	−	0.135299i	−0.543587	+	0.839353i	$0.682934\pi$
$824$	1.95754	−	3.39055i	0.0681941	−	0.118116i
$825$	−15.0198	−	5.98840i	−0.522921	−	0.208489i
$826$	−1.67985	+	0.611417i	−0.0584496	+	0.0212739i
$827$	−1.53460	−	4.21627i	−0.0533632	−	0.146614i	0.910147	−	0.414285i	$-0.135968\pi$
$827$	−1.53460	−	4.21627i	−0.0533632	−	0.146614i	−0.963510	+	0.267671i	$0.913746\pi$
$828$	−35.6433	+	20.5787i	−1.23869	+	0.715158i
$829$	13.5156	−	23.4097i	0.469416	−	0.813052i	−0.529973	−	0.848015i	$-0.677798\pi$
$829$	13.5156	−	23.4097i	0.469416	−	0.813052i	0.999389	+	0.0349625i	$0.0111312\pi$
$830$	−23.1342	+	31.9956i	−0.803001	+	1.11058i
$831$	14.0555	−	11.7940i	0.487579	−	0.409128i
$832$	−13.7525	+	16.3896i	−0.476782	+	0.568206i
$833$	24.4616	−	4.31324i	0.847544	−	0.149445i
$834$	19.9559	+	7.26336i	0.691017	+	0.251510i
$835$	−14.7015	+	30.3188i	−0.508767	+	1.04923i
$836$	26.6693	+	32.1544i	0.922375	+	1.11208i
$837$			26.0578i			0.900691i
$838$	−30.1600	+	82.8640i	−1.04186	+	2.86249i
$839$	1.75648	+	9.96148i	0.0606404	+	0.343909i	1.00000		0.000973662i	$0.000309926\pi$
$839$	1.75648	+	9.96148i	0.0606404	+	0.343909i	−0.939359	+	0.342935i	$0.888579\pi$
$840$	−1.09614	+	0.491046i	−0.0378203	+	0.0169427i
$841$	21.7007	−	18.2091i	0.748300	−	0.627898i
$842$	−26.5152	−	4.67534i	−0.913773	−	0.161123i
$843$	14.1813	+	8.18759i	0.488431	+	0.281996i
$844$	5.11107	+	8.85264i	0.175930	+	0.304720i
$845$	22.4234	+	2.30482i	0.771389	+	0.0792883i
$846$	−13.4756	+	4.90473i	−0.463301	+	0.168628i
$847$	−0.381314	+	0.220152i	−0.0131021	+	0.00756450i
$848$	−1.10802	−	0.639714i	−0.0380495	−	0.0219679i
$849$	−1.40957	+	7.99405i	−0.0483762	+	0.274355i
$850$	−40.5002	−	8.41464i	−1.38914	−	0.288620i
$851$	52.3052	+	43.8893i	1.79300	+	1.50450i
$852$	2.08289	−	0.367270i	0.0713586	−	0.0125825i
$853$	9.44325	−	25.9451i	0.323331	−	0.888344i	−0.666425	−	0.745572i	$-0.732176\pi$
$853$	9.44325	−	25.9451i	0.323331	−	0.888344i	0.989756	−	0.142772i	$-0.0456015\pi$
$854$	3.36879			0.115278
$855$	−1.76809	+	16.2864i	−0.0604673	+	0.556982i
$856$	−13.3651			−0.456810
$857$	13.2079	−	36.2885i	0.451175	−	1.23959i	−0.480723	−	0.876872i	$-0.659626\pi$
$857$	13.2079	−	36.2885i	0.451175	−	1.23959i	0.931898	−	0.362720i	$-0.118152\pi$
$858$	12.6490	−	2.23036i	0.431831	−	0.0761434i
$859$	−43.7965	−	36.7496i	−1.49432	−	1.25388i	−0.889009	−	0.457889i	$-0.848606\pi$
$859$	−43.7965	−	36.7496i	−1.49432	−	1.25388i	−0.605307	−	0.795992i	$-0.706950\pi$
$860$	20.4304	+	81.1486i	0.696670	+	2.76715i
$861$	0.00535387	−	0.0303633i	0.000182460	−	0.00103478i
$862$	63.9986	+	36.9496i	2.17980	+	1.25851i
$863$	−24.6314	+	14.2209i	−0.838463	+	0.484087i	−0.856741	−	0.515746i	$-0.827515\pi$
$863$	−24.6314	+	14.2209i	−0.838463	+	0.484087i	0.0182787	+	0.999833i	$0.494181\pi$
$864$	23.8302	−	8.67349i	0.810720	−	0.295078i
$865$	−4.96019	+	48.2572i	−0.168651	+	1.64079i
$866$	−4.75209	−	8.23085i	−0.161482	−	0.279696i
$867$	−4.31151	−	2.48925i	−0.146427	−	0.0845395i
$868$	−2.32830	−	0.410541i	−0.0790275	−	0.0139347i
$869$	−25.0385	+	21.0098i	−0.849374	+	0.712710i
$870$	18.4810	+	41.2542i	0.626566	+	1.39865i
$871$	1.78250	+	10.1091i	0.0603977	+	0.342532i
$872$	18.0754	−	49.6618i	0.612111	−	1.68176i
$873$		−	14.7943i		−	0.500711i
$874$	71.7138	+	13.0679i	2.42576	+	0.442028i
$875$	1.56483	−	0.343882i	0.0529008	−	0.0116253i
$876$	−38.4556	−	13.9967i	−1.29929	−	0.472905i
$877$	−13.1274	+	2.31472i	−0.443282	+	0.0781626i	−0.390834	−	0.920461i	$-0.627813\pi$
$877$	−13.1274	+	2.31472i	−0.443282	+	0.0781626i	−0.0524480	+	0.998624i	$0.516702\pi$
$878$	17.5659	−	20.9342i	0.592819	−	0.706494i
$879$	0.859402	−	0.721124i	0.0289869	−	0.0243229i
$880$	2.87221	−	3.97238i	0.0968222	−	0.133909i
$881$	14.0692	−	24.3686i	0.474004	−	0.820999i	−0.525553	−	0.850761i	$-0.676142\pi$
$881$	14.0692	−	24.3686i	0.474004	−	0.820999i	0.999557	+	0.0297621i	$0.00947498\pi$
$882$	−23.6163	+	13.6349i	−0.795203	+	0.459111i
$883$	12.1840	+	33.4754i	0.410026	+	1.12654i	0.957177	+	0.289503i	$0.0934900\pi$
$883$	12.1840	+	33.4754i	0.410026	+	1.12654i	−0.547151	+	0.837034i	$0.684288\pi$
$884$	19.4489	−	7.07883i	0.654139	−	0.238087i
$885$	−13.7466	+	0.992940i	−0.462088	+	0.0333773i
$886$	−9.16667	+	15.8771i	−0.307960	+	0.533403i
$887$	−58.2732	−	10.2751i	−1.95662	−	0.345005i	−0.998224	−	0.0595725i	$-0.981026\pi$
$887$	−58.2732	−	10.2751i	−1.95662	−	0.345005i	−0.958399	−	0.285433i	$-0.907863\pi$
$888$	22.8683	+	27.2533i	0.767409	+	0.914562i
$889$	−0.895791	−	0.751658i	−0.0300439	−	0.0252098i
$890$	7.23409	+	2.05640i	0.242487	+	0.0689307i
$891$	−2.99695	−	1.09080i	−0.100402	−	0.0365432i
$892$		−	7.46685i		−	0.250009i
$893$	15.0022	+	5.55760i	0.502030	+	0.185978i
$894$	11.2039			0.374715
$895$	−35.6223	−	36.7191i	−1.19072	−	1.22738i
$896$	0.489620	+	2.77677i	0.0163570	+	0.0927654i
$897$	9.07445	−	10.8145i	0.302987	−	0.361086i
$898$	−1.73450	−	2.06710i	−0.0578811	−	0.0689800i
$899$	−6.37258	+	36.1407i	−0.212537	+	1.20536i
$900$	28.3086	−	4.11099i	0.943621	−	0.137033i
$901$	−2.92400	−	5.06452i	−0.0974126	−	0.168724i
$902$	0.419329	+	1.15210i	0.0139621	+	0.0383607i
$903$	0.618918	+	1.70046i	0.0205963	+	0.0565879i
$904$	5.08850	+	8.81354i	0.169241	+	0.293134i
$905$	−21.4076	+	14.5112i	−0.711614	+	0.482367i
$906$	−1.32667	+	7.52390i	−0.0440755	+	0.249965i
$907$	−29.7254	−	35.4253i	−0.987016	−	1.17628i	−0.984340	−	0.176283i	$-0.943593\pi$
$907$	−29.7254	−	35.4253i	−0.987016	−	1.17628i	−0.00267604	−	0.999996i	$-0.500852\pi$
$908$	14.0983	−	16.8017i	0.467870	−	0.557585i
$909$	−0.839964	−	4.76367i	−0.0278598	−	0.158001i
$910$	−0.913452	+	0.886167i	−0.0302806	+	0.0293761i
$911$	48.8276			1.61773			0.808866	−	0.587994i	$-0.200082\pi$
$911$	48.8276			1.61773			0.808866	+	0.587994i	$0.200082\pi$
$912$	3.65538	+	1.35415i	0.121042	+	0.0448402i
$913$		−	21.3865i		−	0.707790i
$914$	−84.5130	−	30.7602i	−2.79544	−	1.01746i
$915$	24.9828	+	7.10175i	0.825906	+	0.234777i
$916$	−4.02396	−	3.37650i	−0.132955	−	0.111563i
$917$	0.241332	+	0.287608i	0.00796948	+	0.00949766i
$918$	−43.8019	−	7.72346i	−1.44568	−	0.254912i
$919$	−4.80464	+	8.32189i	−0.158491	+	0.274514i	−0.934325	−	0.356423i	$-0.883996\pi$
$919$	−4.80464	+	8.32189i	−0.158491	+	0.274514i	0.775834	+	0.630937i	$0.217329\pi$
$920$	−3.78206	−	52.3603i	−0.124691	−	1.72627i
$921$	30.7248	−	11.1829i	1.01242	−	0.368490i
$922$	−19.4787	−	53.5173i	−0.641496	−	1.76250i
$923$	0.800454	−	0.462142i	0.0263473	−	0.0152116i
$924$	0.788722	−	1.36611i	0.0259470	−	0.0449416i
$925$	−22.4713	−	41.7988i	−0.738853	−	1.37434i
$926$	57.8481	−	48.5403i	1.90100	−	1.59513i
$927$	−1.29609	+	1.54462i	−0.0425691	+	0.0507318i
$928$	35.1722	−	6.20181i	1.15459	−	0.203585i
$929$	48.5984	+	17.6884i	1.59446	+	0.580337i	0.978284	−	0.207269i	$-0.0664577\pi$
$929$	48.5984	+	17.6884i	1.59446	+	0.580337i	0.616179	+	0.787606i	$0.288680\pi$
$930$	−26.0378	−	12.6256i	−0.853812	−	0.414011i
$931$	29.9299	+	5.45391i	0.980914	+	0.178745i
$932$		−	69.6473i		−	2.28137i
$933$	−10.0355	+	27.5722i	−0.328546	+	0.902672i
$934$	5.93470	+	33.6574i	0.194189	+	1.10130i
$935$	20.4479	−	9.16023i	0.668717	−	0.299571i
$936$	−7.17905	+	6.02394i	−0.234655	+	0.196899i
$937$	11.3148	+	1.99511i	0.369639	+	0.0651773i	0.355382	−	0.934721i	$-0.384351\pi$
$937$	11.3148	+	1.99511i	0.369639	+	0.0651773i	0.0142567	+	0.999898i	$0.495462\pi$
$938$	1.73328	+	1.00071i	0.0565937	+	0.0326744i
$939$	8.58639	+	14.8721i	0.280206	+	0.485331i
$940$	2.85638	−	27.7894i	0.0931648	−	0.906392i
$941$	−24.8922	+	9.06002i	−0.811462	+	0.295348i	−0.714228	−	0.699913i	$-0.753222\pi$
$941$	−24.8922	+	9.06002i	−0.811462	+	0.295348i	−0.0972346	+	0.995261i	$0.531000\pi$
$942$	26.6478	−	15.3851i	0.868232	−	0.501274i
$943$	1.16703	+	0.673785i	0.0380037	+	0.0219414i
$944$	0.725556	−	4.11483i	0.0236148	−	0.133926i
$945$	1.67059	−	0.420596i	0.0543443	−	0.0136820i
$946$	−55.1241	−	46.2546i	−1.79224	−	1.50387i
$947$	14.4785	−	2.55295i	0.470487	−	0.0829596i	0.0666224	−	0.997778i	$-0.478778\pi$
$947$	14.4785	−	2.55295i	0.470487	−	0.0829596i	0.403865	+	0.914819i	$0.367667\pi$
$948$	−15.5230	+	42.6490i	−0.504162	+	1.38517i
$949$	−17.8840			−0.580539
$950$	−42.9352	−	26.8962i	−1.39300	−	0.872628i
$951$	−25.8892			−0.839513
$952$	0.569241	−	1.56398i	0.0184492	−	0.0506888i
$953$	−5.76163	+	1.01593i	−0.186637	+	0.0329092i	−0.266186	−	0.963922i	$-0.585763\pi$
$953$	−5.76163	+	1.01593i	−0.186637	+	0.0329092i	0.0795481	+	0.996831i	$0.474652\pi$
$954$	4.91824	+	4.12689i	0.159234	+	0.133613i
$955$	−15.8067	+	3.97958i	−0.511494	+	0.128776i
$956$	3.68871	−	20.9197i	0.119301	−	0.676591i
$957$	−21.2052	−	12.2428i	−0.685467	−	0.395755i
$958$	−26.6135	+	15.3653i	−0.859843	+	0.496431i
$959$	1.65908	−	0.603855i	0.0535744	−	0.0194995i
$960$	−3.28843	+	31.9928i	−0.106134	+	1.03256i
$961$	3.75397	+	6.50206i	0.121096	+	0.209744i
$962$	32.6462	+	18.8483i	1.05256	+	0.607693i
$963$	6.77876	+	1.19528i	0.218442	+	0.0385173i
$964$	68.6163	−	57.5759i	2.20998	−	1.85440i
$965$	−53.4372	+	23.9387i	−1.72020	+	0.770616i
$966$	−0.477973	−	2.71072i	−0.0153785	−	0.0872159i
$967$	8.23258	−	22.6188i	0.264742	−	0.727373i	−0.734090	−	0.679052i	$-0.762391\pi$
$967$	8.23258	−	22.6188i	0.264742	−	0.727373i	0.998832	−	0.0483204i	$-0.0153869\pi$
$968$		−	10.0272i		−	0.322287i
$969$	11.3748	+	13.7143i	0.365411	+	0.440566i
$970$	41.1689	+	19.9627i	1.32185	+	0.640963i
$971$	−49.4859	−	18.0114i	−1.58808	−	0.578013i	−0.611137	−	0.791524i	$-0.709288\pi$
$971$	−49.4859	−	18.0114i	−1.58808	−	0.578013i	−0.976941	+	0.213511i	$0.931510\pi$
$972$	49.7047	−	8.76428i	1.59428	−	0.281114i
$973$	0.732643	−	0.873130i	0.0234875	−	0.0279913i
$974$	−17.2035	+	14.4354i	−0.551234	+	0.462540i
$975$	−8.64224	+	4.64612i	−0.276773	+	0.148795i
$976$	−3.93694	+	6.81899i	−0.126018	+	0.218270i
$977$	5.63672	−	3.25436i	0.180335	−	0.104116i	−0.407115	−	0.913377i	$-0.633465\pi$
$977$	5.63672	−	3.25436i	0.180335	−	0.104116i	0.587450	+	0.809261i	$0.300132\pi$
$978$	−17.2772	−	47.4688i	−0.552465	−	1.51789i
$979$	−3.82801	+	1.39328i	−0.122344	+	0.0445294i
$980$	−3.82716	−	52.9847i	−0.122254	−	1.69253i
$981$	−13.6092	+	23.5718i	−0.434509	+	0.752591i
$982$	−6.14987	−	1.08439i	−0.196250	−	0.0346042i
$983$	−0.803066	−	0.957057i	−0.0256138	−	0.0305254i	0.753085	−	0.657923i	$-0.228565\pi$
$983$	−0.803066	−	0.957057i	−0.0256138	−	0.0305254i	−0.778699	+	0.627397i	$0.784120\pi$
$984$	0.537873	+	0.451329i	0.0171468	+	0.0143879i
$985$	4.92157	+	1.39903i	0.156814	+	0.0445769i
$986$	−58.8619	−	21.4240i	−1.87454	−	0.682278i
$987$		−	0.604111i		−	0.0192291i
$988$	25.3494	+	0.144799i	0.806473	+	0.00460666i
$989$	−79.0924			−2.51499
$990$	−17.6556	+	17.1282i	−0.561131	+	0.544370i
$991$	6.52844	+	37.0246i	0.207383	+	1.17613i	0.893646	+	0.448772i	$0.148139\pi$
$991$	6.52844	+	37.0246i	0.207383	+	1.17613i	−0.686264	+	0.727353i	$0.740750\pi$
$992$	−14.6958	+	17.5137i	−0.466591	+	0.556062i
$993$	−8.02384	−	9.56244i	−0.254629	−	0.303455i
$994$	0.0312936	−	0.177475i	0.000992573	−	0.00562916i
$995$	22.6679	−	15.3654i	0.718621	−	0.487117i
$996$	−14.8483	−	25.7181i	−0.470487	−	0.814908i
$997$	10.2369	+	28.1257i	0.324207	+	0.890751i	0.989547	+	0.144211i	$0.0460643\pi$
$997$	10.2369	+	28.1257i	0.324207	+	0.890751i	−0.665340	+	0.746540i	$0.731713\pi$
$998$	−1.87275	−	5.14533i	−0.0592808	−	0.162873i
$999$	−25.5136	−	44.1909i	−0.807215	−	1.39814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.p.a.4.2	✓	48
3.2	odd	2		855.2.da.b.289.7		48
5.2	odd	4		475.2.l.f.251.2		48
5.3	odd	4		475.2.l.f.251.7		48
5.4	even	2	inner	95.2.p.a.4.7	yes	48
15.14	odd	2		855.2.da.b.289.2		48
19.5	even	9	inner	95.2.p.a.24.7	yes	48
19.9	even	9		1805.2.b.k.1084.3		24
19.10	odd	18		1805.2.b.l.1084.22		24
57.5	odd	18		855.2.da.b.784.2		48
95.9	even	18		1805.2.b.k.1084.22		24
95.24	even	18	inner	95.2.p.a.24.2	yes	48
95.28	odd	36		9025.2.a.cu.1.3		24
95.29	odd	18		1805.2.b.l.1084.3		24
95.43	odd	36		475.2.l.f.176.7		48
95.47	odd	36		9025.2.a.cu.1.22		24
95.48	even	36		9025.2.a.ct.1.22		24
95.62	odd	36		475.2.l.f.176.2		48
95.67	even	36		9025.2.a.ct.1.3		24
285.119	odd	18		855.2.da.b.784.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.2	✓	48	1.1	even	1	trivial
95.2.p.a.4.7	yes	48	5.4	even	2	inner
95.2.p.a.24.2	yes	48	95.24	even	18	inner
95.2.p.a.24.7	yes	48	19.5	even	9	inner
475.2.l.f.176.2		48	95.62	odd	36
475.2.l.f.176.7		48	95.43	odd	36
475.2.l.f.251.2		48	5.2	odd	4
475.2.l.f.251.7		48	5.3	odd	4
855.2.da.b.289.2		48	15.14	odd	2
855.2.da.b.289.7		48	3.2	odd	2
855.2.da.b.784.2		48	57.5	odd	18
855.2.da.b.784.7		48	285.119	odd	18
1805.2.b.k.1084.3		24	19.9	even	9
1805.2.b.k.1084.22		24	95.9	even	18
1805.2.b.l.1084.3		24	95.29	odd	18
1805.2.b.l.1084.22		24	19.10	odd	18
9025.2.a.ct.1.3		24	95.67	even	36
9025.2.a.ct.1.22		24	95.48	even	36
9025.2.a.cu.1.3		24	95.28	odd	36
9025.2.a.cu.1.22		24	95.47	odd	36

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795068 + 2.18443i) q^{2} +(-1.13113 + 0.199449i) q^{3} +(-2.60752 - 2.18797i) q^{4} +(-2.16840 + 0.545927i) q^{5} +(0.463643 - 2.62945i) q^{6} +(-0.124103 - 0.0716510i) q^{7} +(2.82626 - 1.63174i) q^{8} +(-1.57940 + 0.574856i) q^{9} +O(q^{10})\)	\(q+(-0.795068 + 2.18443i) q^{2} +(-1.13113 + 0.199449i) q^{3} +(-2.60752 - 2.18797i) q^{4} +(-2.16840 + 0.545927i) q^{5} +(0.463643 - 2.62945i) q^{6} +(-0.124103 - 0.0716510i) q^{7} +(2.82626 - 1.63174i) q^{8} +(-1.57940 + 0.574856i) q^{9} +(0.531485 - 5.17077i) q^{10} +(1.40779 + 2.43836i) q^{11} +(3.38583 + 1.95481i) q^{12} +(1.68258 + 0.296685i) q^{13} +(0.255187 - 0.214128i) q^{14} +(2.34386 - 1.05000i) q^{15} +(0.135204 + 0.766781i) q^{16} +(-1.21720 + 3.34424i) q^{17} -3.90715i q^{18} +(-2.82087 + 3.32305i) q^{19} +(6.84862 + 3.32088i) q^{20} +(0.154668 + 0.0562944i) q^{21} +(-6.44571 + 1.13655i) q^{22} +(-4.62417 + 5.51088i) q^{23} +(-2.87141 + 2.40940i) q^{24} +(4.40393 - 2.36758i) q^{25} +(-1.98586 + 3.43960i) q^{26} +(4.65595 - 2.68812i) q^{27} +(0.166831 + 0.458365i) q^{28} +(7.11492 - 2.58962i) q^{29} +(0.430125 + 5.95482i) q^{30} +(-2.42343 + 4.19751i) q^{31} +(4.64532 + 0.819095i) q^{32} +(-2.07872 - 2.47732i) q^{33} +(-6.33750 - 5.31779i) q^{34} +(0.308222 + 0.0876168i) q^{35} +(5.37609 + 1.95674i) q^{36} -9.49127i q^{37} +(-5.01619 - 8.80406i) q^{38} -1.96239 q^{39} +(-5.23764 + 5.08120i) q^{40} +(-0.0325278 - 0.184474i) q^{41} +(-0.245943 + 0.293103i) q^{42} +(7.06701 + 8.42213i) q^{43} +(1.66422 - 9.43825i) q^{44} +(3.11095 - 2.10876i) q^{45} +(-8.36160 - 14.4827i) q^{46} +(-1.25532 - 3.44897i) q^{47} +(-0.305867 - 0.840363i) q^{48} +(-3.48973 - 6.04439i) q^{49} +(1.67039 + 11.5025i) q^{50} +(0.709811 - 4.02554i) q^{51} +(-3.73823 - 4.45505i) q^{52} +(-1.05624 + 1.25878i) q^{53} +(2.17020 + 12.3078i) q^{54} +(-4.38381 - 4.51879i) q^{55} -0.467663 q^{56} +(2.52800 - 4.32142i) q^{57} +17.6010i q^{58} +(-5.04274 - 1.83541i) q^{59} +(-8.40902 - 2.39039i) q^{60} +(7.74681 + 6.50035i) q^{61} +(-7.24237 - 8.63112i) q^{62} +(0.237198 + 0.0418244i) q^{63} +(-6.26121 + 10.8447i) q^{64} +(-3.81049 + 0.275237i) q^{65} +(7.06425 - 2.57118i) q^{66} +(2.05488 + 5.64572i) q^{67} +(10.4910 - 6.05696i) q^{68} +(4.13141 - 7.15580i) q^{69} +(-0.436450 + 0.603628i) q^{70} +(0.414414 - 0.347735i) q^{71} +(-3.52578 + 4.20186i) q^{72} +(-10.3084 + 1.81765i) q^{73} +(20.7330 + 7.54620i) q^{74} +(-4.50920 + 3.55640i) q^{75} +(14.6262 - 2.49294i) q^{76} -0.403477i q^{77} +(1.56024 - 4.28672i) q^{78} +(2.01585 + 11.4325i) q^{79} +(-0.711784 - 1.58888i) q^{80} +(-0.867724 + 0.728107i) q^{81} +(0.428833 + 0.0756149i) q^{82} +(-6.57815 - 3.79789i) q^{83} +(-0.280128 - 0.485197i) q^{84} +(0.813673 - 7.91615i) q^{85} +(-24.0163 + 8.74123i) q^{86} +(-7.53141 + 4.34826i) q^{87} +(7.95753 + 4.59428i) q^{88} +(-0.251241 + 1.42486i) q^{89} +(2.13302 + 8.47226i) q^{90} +(-0.187556 - 0.157378i) q^{91} +(24.1152 - 4.25217i) q^{92} +(1.90403 - 5.23127i) q^{93} +8.53210 q^{94} +(4.30264 - 8.74570i) q^{95} -5.41783 q^{96} +(-3.01050 + 8.27128i) q^{97} +(15.9781 - 2.81738i) q^{98} +(-3.62516 - 3.04187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9}+O(q^{10}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34} + 6 q^{35} + 18 q^{36} - 48 q^{39} + 66 q^{40} + 6 q^{41} - 6 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{49} - 18 q^{50} + 108 q^{51} + 24 q^{54} + 36 q^{56} - 36 q^{59} - 114 q^{60} + 48 q^{61} - 18 q^{65} + 180 q^{66} + 66 q^{69} - 123 q^{70} - 24 q^{71} + 84 q^{74} + 72 q^{75} + 66 q^{76} + 48 q^{79} - 39 q^{80} - 78 q^{81} - 54 q^{84} - 84 q^{85} - 42 q^{86} - 12 q^{89} + 18 q^{90} - 30 q^{91} - 72 q^{94} - 63 q^{95} - 240 q^{96} - 36 q^{99}+O(q^{100}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Introduction

L-functions

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