LMFDB - Embedded newform 135.2.p.a.124.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.12
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831033 - 0.990387i) q^{2} +(-0.768718 + 1.55212i) q^{3} +(0.0570464 + 0.323526i) q^{4} +(-0.122729 + 2.23270i) q^{5} +(0.898367 + 2.05119i) q^{6} +(-0.765094 - 0.134907i) q^{7} +(2.60712 + 1.50522i) q^{8} +(-1.81814 - 2.38628i) q^{9} +O(q^{10})$	\(q+(0.831033 - 0.990387i) q^{2} +(-0.768718 + 1.55212i) q^{3} +(0.0570464 + 0.323526i) q^{4} +(-0.122729 + 2.23270i) q^{5} +(0.898367 + 2.05119i) q^{6} +(-0.765094 - 0.134907i) q^{7} +(2.60712 + 1.50522i) q^{8} +(-1.81814 - 2.38628i) q^{9} +(2.10924 + 1.97700i) q^{10} +(3.66139 - 1.33264i) q^{11} +(-0.546003 - 0.160158i) q^{12} +(-3.28913 - 3.91983i) q^{13} +(-0.769429 + 0.645628i) q^{14} +(-3.37107 - 1.90681i) q^{15} +(3.03995 - 1.10645i) q^{16} +(3.38295 - 1.95315i) q^{17} +(-3.87428 - 0.182416i) q^{18} +(-1.51356 + 2.62156i) q^{19} +(-0.729337 + 0.0876612i) q^{20} +(0.797534 - 1.08381i) q^{21} +(1.72291 - 4.73366i) q^{22} +(3.17893 - 0.560532i) q^{23} +(-4.34042 + 2.88947i) q^{24} +(-4.96988 - 0.548034i) q^{25} -6.61553 q^{26} +(5.10144 - 0.987594i) q^{27} -0.255224i q^{28} +(-0.271790 - 0.228059i) q^{29} +(-4.68995 + 1.75404i) q^{30} +(-0.470061 - 2.66585i) q^{31} +(-0.628781 + 1.72756i) q^{32} +(-0.746168 + 6.70734i) q^{33} +(0.876974 - 4.97357i) q^{34} +(0.395105 - 1.69167i) q^{35} +(0.668307 - 0.724346i) q^{36} +(3.70101 - 2.13678i) q^{37} +(1.33854 + 3.67761i) q^{38} +(8.61246 - 2.09187i) q^{39} +(-3.68067 + 5.63618i) q^{40} +(-9.24182 + 7.75481i) q^{41} +(-0.410616 - 1.69055i) q^{42} +(0.120519 + 0.331124i) q^{43} +(0.640012 + 1.10853i) q^{44} +(5.55099 - 3.76650i) q^{45} +(2.08666 - 3.61420i) q^{46} +(-2.58307 - 0.455464i) q^{47} +(-0.619521 + 5.56890i) q^{48} +(-6.01068 - 2.18771i) q^{49} +(-4.67290 + 4.46667i) q^{50} +(0.430980 + 6.75217i) q^{51} +(1.08053 - 1.28773i) q^{52} -9.29215i q^{53} +(3.26136 - 5.87312i) q^{54} +(2.52602 + 8.33833i) q^{55} +(-1.79163 - 1.50335i) q^{56} +(-2.90547 - 4.36446i) q^{57} +(-0.451732 + 0.0796526i) q^{58} +(12.4304 + 4.52430i) q^{59} +(0.424594 - 1.19940i) q^{60} +(1.14463 - 6.49154i) q^{61} +(-3.03086 - 1.74987i) q^{62} +(1.06913 + 2.07101i) q^{63} +(4.42346 + 7.66166i) q^{64} +(9.15547 - 6.86255i) q^{65} +(6.02277 + 6.31302i) q^{66} +(2.55913 + 3.04985i) q^{67} +(0.824880 + 0.983053i) q^{68} +(-1.57369 + 5.36497i) q^{69} +(-1.34706 - 1.79714i) q^{70} +(-6.06946 - 10.5126i) q^{71} +(-1.14823 - 8.95804i) q^{72} +(-12.2022 - 7.04497i) q^{73} +(0.959425 - 5.44117i) q^{74} +(4.67105 - 7.29255i) q^{75} +(-0.934485 - 0.340125i) q^{76} +(-2.98109 + 0.525647i) q^{77} +(5.08548 - 10.2681i) q^{78} +(8.85574 + 7.43085i) q^{79} +(2.09728 + 6.92307i) q^{80} +(-2.38871 + 8.67722i) q^{81} +15.5975i q^{82} +(-3.57428 + 4.25966i) q^{83} +(0.396138 + 0.196195i) q^{84} +(3.94560 + 7.79282i) q^{85} +(0.428097 + 0.155815i) q^{86} +(0.562904 - 0.246537i) q^{87} +(11.5516 + 2.03686i) q^{88} +(-2.60530 + 4.51251i) q^{89} +(0.882767 - 8.62771i) q^{90} +(1.98768 + 3.44277i) q^{91} +(0.362693 + 0.996492i) q^{92} +(4.49906 + 1.31970i) q^{93} +(-2.59770 + 2.17973i) q^{94} +(-5.66739 - 3.70106i) q^{95} +(-2.19803 - 2.30395i) q^{96} +(2.43160 + 6.68077i) q^{97} +(-7.16175 + 4.13484i) q^{98} +(-9.83699 - 6.31420i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	0.831033	−	0.990387i	0.587629	−	0.700309i	−0.387519	−	0.921862i	$-0.626668\pi$
$2$	0.831033	−	0.990387i	0.587629	−	0.700309i	0.975149	+	0.221552i	$0.0711123\pi$
$3$	−0.768718	+	1.55212i	−0.443820	+	0.896116i
$3$	−0.768718	+	1.55212i	−0.443820	+	0.896116i
$4$	0.0570464	+	0.323526i	0.0285232	+	0.161763i
$5$	−0.122729	+	2.23270i	−0.0548861	+	0.998493i
$5$	−0.122729	+	2.23270i	−0.0548861	+	0.998493i
$6$	0.898367	+	2.05119i	0.366757	+	0.837395i
$7$	−0.765094	−	0.134907i	−0.289179	−	0.0509900i	0.0271771	−	0.999631i	$-0.491348\pi$
$7$	−0.765094	−	0.134907i	−0.289179	−	0.0509900i	−0.316356	+	0.948641i	$0.602459\pi$
$8$	2.60712	+	1.50522i	0.921756	+	0.532176i
$9$	−1.81814	−	2.38628i	−0.606048	−	0.795428i
$10$	2.10924	+	1.97700i	0.667001	+	0.625181i
$11$	3.66139	−	1.33264i	1.10395	−	0.401805i	0.275180	−	0.961393i	$-0.411263\pi$
$11$	3.66139	−	1.33264i	1.10395	−	0.401805i	0.828771	+	0.559587i	$0.189040\pi$
$12$	−0.546003	−	0.160158i	−0.157618	−	0.0462335i
$13$	−3.28913	−	3.91983i	−0.912240	−	1.08717i	−0.995881	−	0.0906695i	$-0.971099\pi$
$13$	−3.28913	−	3.91983i	−0.912240	−	1.08717i	0.0836409	−	0.996496i	$-0.473345\pi$
$14$	−0.769429	+	0.645628i	−0.205639	+	0.172551i
$15$	−3.37107	−	1.90681i	−0.870406	−	0.492335i
$16$	3.03995	−	1.10645i	0.759986	−	0.276612i
$17$	3.38295	−	1.95315i	0.820487	−	0.473708i	−0.0300976	−	0.999547i	$-0.509582\pi$
$17$	3.38295	−	1.95315i	0.820487	−	0.473708i	0.850584	+	0.525839i	$0.176248\pi$
$18$	−3.87428	−	0.182416i	−0.913177	−	0.0429959i
$19$	−1.51356	+	2.62156i	−0.347234	+	0.601427i	−0.985757	−	0.168176i	$-0.946212\pi$
$19$	−1.51356	+	2.62156i	−0.347234	+	0.601427i	0.638523	+	0.769603i	$0.279546\pi$
$20$	−0.729337	+	0.0876612i	−0.163085	+	0.0196016i
$21$	0.797534	−	1.08381i	0.174036	−	0.236507i
$22$	1.72291	−	4.73366i	0.367326	−	1.00922i
$23$	3.17893	−	0.560532i	0.662854	−	0.116879i	0.167908	−	0.985803i	$-0.446299\pi$
$23$	3.17893	−	0.560532i	0.662854	−	0.116879i	0.494946	+	0.868924i	$0.335188\pi$
$24$	−4.34042	+	2.88947i	−0.885985	+	0.589810i
$25$	−4.96988	−	0.548034i	−0.993975	−	0.109607i
$26$	−6.61553			−1.29741
$27$	5.10144	−	0.987594i	0.981772	−	0.190062i
$28$		−	0.255224i		−	0.0482328i
$29$	−0.271790	−	0.228059i	−0.0504701	−	0.0423494i	0.617204	−	0.786803i	$-0.288265\pi$
$29$	−0.271790	−	0.228059i	−0.0504701	−	0.0423494i	−0.667674	+	0.744454i	$0.732710\pi$
$30$	−4.68995	+	1.75404i	−0.856263	+	0.320243i
$31$	−0.470061	−	2.66585i	−0.0844255	−	0.478801i	−0.997479	−	0.0709611i	$-0.977393\pi$
$31$	−0.470061	−	2.66585i	−0.0844255	−	0.478801i	0.913054	−	0.407840i	$-0.133718\pi$
$32$	−0.628781	+	1.72756i	−0.111154	+	0.305393i
$33$	−0.746168	+	6.70734i	−0.129891	+	1.16760i
$34$	0.876974	−	4.97357i	0.150400	−	0.852959i
$35$	0.395105	−	1.69167i	0.0667850	−	0.285944i
$36$	0.668307	−	0.724346i	0.111384	−	0.120724i
$37$	3.70101	−	2.13678i	0.608443	−	0.351285i	−0.163913	−	0.986475i	$-0.552412\pi$
$37$	3.70101	−	2.13678i	0.608443	−	0.351285i	0.772356	+	0.635190i	$0.219078\pi$
$38$	1.33854	+	3.67761i	0.217140	+	0.596587i
$39$	8.61246	−	2.09187i	1.37910	−	0.334967i
$40$	−3.68067	+	5.63618i	−0.581966	+	0.891158i
$41$	−9.24182	+	7.75481i	−1.44333	+	1.21110i	−0.506059	+	0.862499i	$0.668898\pi$
$41$	−9.24182	+	7.75481i	−1.44333	+	1.21110i	−0.937272	+	0.348599i	$0.886658\pi$
$42$	−0.410616	−	1.69055i	−0.0633595	−	0.260858i
$43$	0.120519	+	0.331124i	0.0183790	+	0.0504960i	0.948543	−	0.316649i	$-0.102558\pi$
$43$	0.120519	+	0.331124i	0.0183790	+	0.0504960i	−0.930164	+	0.367145i	$0.880335\pi$
$44$	0.640012	+	1.10853i	0.0964854	+	0.167118i
$45$	5.55099	−	3.76650i	0.827493	−	0.561476i
$46$	2.08666	−	3.61420i	0.307661	−	0.532884i
$47$	−2.58307	−	0.455464i	−0.376779	−	0.0664363i	−0.0179481	−	0.999839i	$-0.505713\pi$
$47$	−2.58307	−	0.455464i	−0.376779	−	0.0664363i	−0.358831	+	0.933403i	$0.616824\pi$
$48$	−0.619521	+	5.56890i	−0.0894202	+	0.803802i
$49$	−6.01068	−	2.18771i	−0.858668	−	0.312530i
$50$	−4.67290	+	4.46667i	−0.660848	+	0.631682i
$51$	0.430980	+	6.75217i	0.0603493	+	0.945492i
$52$	1.08053	−	1.28773i	0.149843	−	0.178576i
$53$		−	9.29215i		−	1.27637i	−0.769881	−	0.638187i	$-0.779685\pi$
$53$		−	9.29215i		−	1.27637i	0.769881	−	0.638187i	$-0.220315\pi$
$54$	3.26136	−	5.87312i	0.443816	−	0.799230i
$55$	2.52602	+	8.33833i	0.340608	+	1.12434i
$56$	−1.79163	−	1.50335i	−0.239416	−	0.200894i
$57$	−2.90547	−	4.36446i	−0.384839	−	0.578087i
$58$	−0.451732	+	0.0796526i	−0.0593154	+	0.0104589i
$59$	12.4304	+	4.52430i	1.61830	+	0.589014i	0.983058	−	0.183296i	$-0.0586768\pi$
$59$	12.4304	+	4.52430i	1.61830	+	0.589014i	0.635245	+	0.772311i	$0.280899\pi$
$60$	0.424594	−	1.19940i	0.0548149	−	0.154842i
$61$	1.14463	−	6.49154i	0.146555	−	0.831156i	−0.819550	−	0.573008i	$-0.805777\pi$
$61$	1.14463	−	6.49154i	0.146555	−	0.831156i	0.966105	−	0.258148i	$-0.0831123\pi$
$62$	−3.03086	−	1.74987i	−0.384920	−	0.222233i
$63$	1.06913	+	2.07101i	0.134697	+	0.260923i
$64$	4.42346	+	7.66166i	0.552932	+	0.957707i
$65$	9.15547	−	6.86255i	1.13560	−	0.851195i
$66$	6.02277	+	6.31302i	0.741352	+	0.777079i
$67$	2.55913	+	3.04985i	0.312647	+	0.372599i	0.899369	−	0.437190i	$-0.144026\pi$
$67$	2.55913	+	3.04985i	0.312647	+	0.372599i	−0.586722	+	0.809789i	$0.699582\pi$
$68$	0.824880	+	0.983053i	0.100031	+	0.119213i
$69$	−1.57369	+	5.36497i	−0.189450	+	0.645867i
$70$	−1.34706	−	1.79714i	−0.161004	−	0.214799i
$71$	−6.06946	−	10.5126i	−0.720312	−	1.24762i	−0.960875	−	0.276983i	$-0.910665\pi$
$71$	−6.06946	−	10.5126i	−0.720312	−	1.24762i	0.240563	−	0.970634i	$-0.422668\pi$
$72$	−1.14823	−	8.95804i	−0.135320	−	1.05571i
$73$	−12.2022	−	7.04497i	−1.42816	−	0.824551i	−0.431189	−	0.902262i	$-0.641906\pi$
$73$	−12.2022	−	7.04497i	−1.42816	−	0.824551i	−0.996976	+	0.0777105i	$0.975239\pi$
$74$	0.959425	−	5.44117i	0.111531	−	0.632523i
$75$	4.67105	−	7.29255i	0.539366	−	0.842071i
$76$	−0.934485	−	0.340125i	−0.107193	−	0.0390150i
$77$	−2.98109	+	0.525647i	−0.339727	+	0.0599030i
$78$	5.08548	−	10.2681i	0.575817	−	1.16263i
$79$	8.85574	+	7.43085i	0.996349	+	0.836036i	0.986474	−	0.163916i	$-0.0524125\pi$
$79$	8.85574	+	7.43085i	0.996349	+	0.836036i	0.00987418	+	0.999951i	$0.496857\pi$
$80$	2.09728	+	6.92307i	0.234483	+	0.774023i
$81$	−2.38871	+	8.67722i	−0.265412	+	0.964135i
$82$			15.5975i			1.72245i
$83$	−3.57428	+	4.25966i	−0.392328	+	0.467558i	−0.925665	−	0.378345i	$-0.876493\pi$
$83$	−3.57428	+	4.25966i	−0.392328	+	0.467558i	0.533337	+	0.845903i	$0.320938\pi$
$84$	0.396138	+	0.196195i	0.0432222	+	0.0214067i
$85$	3.94560	+	7.79282i	0.427961	+	0.845250i
$86$	0.428097	+	0.155815i	0.0461629	+	0.0168019i
$87$	0.562904	−	0.246537i	0.0603496	−	0.0264315i
$88$	11.5516	+	2.03686i	1.23141	+	0.217130i
$89$	−2.60530	+	4.51251i	−0.276161	+	0.478325i	−0.970427	−	0.241393i	$-0.922396\pi$
$89$	−2.60530	+	4.51251i	−0.276161	+	0.478325i	0.694266	+	0.719718i	$0.255729\pi$
$90$	0.882767	−	8.62771i	0.0930518	−	0.909441i
$91$	1.98768	+	3.44277i	0.208366	+	0.360900i
$92$	0.362693	+	0.996492i	0.0378134	+	0.103891i
$93$	4.49906	+	1.31970i	0.466531	+	0.136846i
$94$	−2.59770	+	2.17973i	−0.267932	+	0.224822i
$95$	−5.66739	−	3.70106i	−0.581462	−	0.379720i
$96$	−2.19803	−	2.30395i	−0.224335	−	0.235146i
$97$	2.43160	+	6.68077i	0.246892	+	0.678330i	0.999796	+	0.0201995i	$0.00643015\pi$
$97$	2.43160	+	6.68077i	0.246892	+	0.678330i	−0.752904	+	0.658130i	$0.771348\pi$
$98$	−7.16175	+	4.13484i	−0.723446	+	0.417682i
$99$	−9.83699	−	6.31420i	−0.988655	−	0.634601i
$100$	−0.106210	−	1.63915i	−0.0106210	−	0.163915i
$101$	0.306182	−	1.73645i	0.0304663	−	0.172783i	−0.965778	−	0.259370i	$-0.916485\pi$
$101$	0.306182	−	1.73645i	0.0304663	−	0.172783i	0.996244	+	0.0865873i	$0.0275962\pi$
$102$	7.04542	+	5.18444i	0.697600	+	0.513336i
$103$	−6.55464	+	18.0087i	−0.645848	+	1.77445i	−0.0133237	+	0.999911i	$0.504241\pi$
$103$	−6.55464	+	18.0087i	−0.645848	+	1.77445i	−0.632524	+	0.774541i	$0.717981\pi$
$104$	−2.67494	−	15.1703i	−0.262299	−	1.48757i
$105$	2.32194	+	1.91367i	0.226598	+	0.186755i
$106$	−9.20282	−	7.72208i	−0.893857	−	0.750035i
$107$			5.51306i			0.532968i	0.963839	+	0.266484i	$0.0858619\pi$
$107$			5.51306i			0.532968i	−0.963839	+	0.266484i	$0.914138\pi$
$108$	0.610531	+	1.59411i	0.0587483	+	0.153393i
$109$	−14.2674			−1.36657			−0.683287	−	0.730150i	$-0.739450\pi$
$109$	−14.2674			−1.36657			−0.683287	+	0.730150i	$0.739450\pi$
$110$	10.3574	+	4.42770i	0.987538	+	0.422165i
$111$	0.471500	+	7.38699i	0.0447528	+	0.701142i
$112$	−2.47511	+	0.436429i	−0.233876	+	0.0412387i
$113$	2.12228	−	5.83093i	0.199648	−	0.548527i	−0.798954	−	0.601392i	$-0.794613\pi$
$113$	2.12228	−	5.83093i	0.199648	−	0.548527i	0.998602	+	0.0528647i	$0.0168352\pi$
$114$	−6.73705	−	0.749473i	−0.630982	−	0.0701946i
$115$	0.861350	+	7.16639i	0.0803213	+	0.668269i
$116$	0.0582783	−	0.100941i	0.00541100	−	0.00937213i
$117$	−3.37372	+	14.9756i	−0.311901	+	1.38450i
$118$	14.8109	−	8.55108i	1.36345	−	0.787191i
$119$	−2.85177	+	1.03796i	−0.261421	+	0.0951496i
$120$	−5.91861	−	10.0455i	−0.540293	−	0.917022i
$121$	3.20338	−	2.68795i	0.291216	−	0.244359i
$122$	−5.47790	−	6.52831i	−0.495946	−	0.591046i
$123$	−4.93203	−	20.3057i	−0.444706	−	1.83090i
$124$	0.835656	−	0.304154i	0.0750442	−	0.0273138i
$125$	1.83354	−	11.0290i	0.163997	−	0.986461i
$126$	2.93958	+	0.662233i	0.261879	+	0.0589964i
$127$	−10.4623	−	6.04043i	−0.928382	−	0.536002i	−0.0420828	−	0.999114i	$-0.513399\pi$
$127$	−10.4623	−	6.04043i	−0.928382	−	0.536002i	−0.886300	+	0.463112i	$0.846733\pi$
$128$	7.64304	+	1.34767i	0.675556	+	0.119119i
$129$	−0.606590	−	0.0674810i	−0.0534072	−	0.00594137i
$130$	0.811917	−	14.7705i	0.0712099	−	1.29546i
$131$	0.140206	+	0.795145i	0.0122498	+	0.0694722i	0.990320	−	0.138804i	$-0.0443258\pi$
$131$	0.140206	+	0.795145i	0.0122498	+	0.0694722i	−0.978070	+	0.208276i	$0.933215\pi$
$132$	−2.21256	+	0.141224i	−0.192579	+	0.0122920i
$133$	1.51168	−	1.80155i	0.131079	−	0.156214i
$134$	5.14726			0.444655
$135$	1.57890	+	11.5112i	0.135890	+	0.990724i
$136$	11.7597			1.00838
$137$	0.458752	−	0.546720i	0.0391939	−	0.0467094i	−0.746091	−	0.665844i	$-0.768072\pi$
$137$	0.458752	−	0.546720i	0.0391939	−	0.0467094i	0.785285	+	0.619134i	$0.212516\pi$
$138$	4.00561	+	6.01704i	0.340980	+	0.512204i
$139$	−2.29439	−	13.0121i	−0.194607	−	1.10367i	−0.912977	−	0.408011i	$-0.866222\pi$
$139$	−2.29439	−	13.0121i	−0.194607	−	1.10367i	0.718370	−	0.695662i	$-0.244889\pi$
$140$	0.569838	+	0.0313234i	0.0481601	+	0.00264731i
$141$	2.69258	−	3.65910i	0.226756	−	0.308152i
$142$	−15.4555	−	2.72522i	−1.29699	−	0.228695i
$143$	−17.2665	−	9.96882i	−1.44390	−	0.833635i
$144$	−8.16736	−	5.24249i	−0.680614	−	0.436874i
$145$	0.542542	−	0.578834i	0.0450557	−	0.0480696i
$146$	−17.1177	+	6.23034i	−1.41667	+	0.515627i
$147$	8.01610	−	7.64755i	0.661157	−	0.630760i
$148$	0.902433	+	1.07548i	0.0741796	+	0.0884038i
$149$	−4.06706	+	3.41267i	−0.333187	+	0.279577i	−0.793997	−	0.607922i	$-0.792003\pi$
$149$	−4.06706	+	3.41267i	−0.333187	+	0.279577i	0.460810	+	0.887499i	$0.347559\pi$
$150$	−3.34065	−	10.6865i	−0.272763	−	0.872549i
$151$	5.48224	−	1.99537i	0.446138	−	0.162381i	−0.109174	−	0.994023i	$-0.534821\pi$
$151$	5.48224	−	1.99537i	0.446138	−	0.162381i	0.555313	+	0.831641i	$0.312598\pi$
$152$	−7.89205	+	4.55648i	−0.640130	+	0.369579i
$153$	−10.8115	−	4.52158i	−0.874055	−	0.365548i
$154$	−1.95679	+	3.38927i	−0.157683	+	0.273115i
$155$	6.00973	−	0.722327i	0.482713	−	0.0580187i
$156$	1.16808	+	2.66702i	0.0935216	+	0.213532i
$157$	−0.552860	+	1.51897i	−0.0441230	+	0.121227i	−0.959797	−	0.280694i	$-0.909435\pi$
$157$	−0.552860	+	1.51897i	−0.0441230	+	0.121227i	0.915674	+	0.401921i	$0.131657\pi$
$158$	14.7188	−	2.59533i	1.17097	−	0.206473i
$159$	14.4225	+	7.14304i	1.14378	+	0.566480i
$160$	−3.77995	−	1.61590i	−0.298832	−	0.127748i
$161$	−2.50780			−0.197643
$162$	6.60871	+	9.57680i	0.519229	+	0.752425i
$163$		−	3.19497i		−	0.250249i	−0.992141	−	0.125125i	$-0.960067\pi$
$163$		−	3.19497i		−	0.250249i	0.992141	−	0.125125i	$-0.0399331\pi$
$164$	−3.03610	−	2.54759i	−0.237079	−	0.198933i
$165$	−14.8839	−	2.48915i	−1.15871	−	0.193780i
$166$	1.24837	+	7.07983i	0.0968920	+	0.549502i
$167$	−1.88938	+	5.19103i	−0.146205	+	0.401694i	−0.991080	−	0.133270i	$-0.957452\pi$
$167$	−1.88938	+	5.19103i	−0.146205	+	0.401694i	0.844875	+	0.534963i	$0.179675\pi$
$168$	3.71064	−	1.62516i	0.286282	−	0.125384i
$169$	−2.28928	+	12.9832i	−0.176099	+	0.998704i
$170$	10.9968	+	2.56842i	0.843419	+	0.196989i
$171$	9.00765	−	1.15459i	0.688832	−	0.0882938i
$172$	−0.100252	+	0.0578806i	−0.00764415	+	0.00441335i
$173$	3.64550	+	10.0159i	0.277162	+	0.761497i	0.997681	+	0.0680619i	$0.0216815\pi$
$173$	3.64550	+	10.0159i	0.277162	+	0.761497i	−0.720519	+	0.693435i	$0.756096\pi$
$174$	0.223625	−	0.762373i	0.0169530	−	0.0577953i
$175$	3.72849	+	1.08977i	0.281847	+	0.0823787i
$176$	9.65594	−	8.10229i	0.727844	−	0.610733i
$177$	−16.5777	+	15.8156i	−1.24606	+	1.18877i
$178$	2.30404	+	6.33030i	0.172695	+	0.474476i
$179$	7.01872	+	12.1568i	0.524604	+	0.908640i	0.999590	+	0.0286466i	$0.00911976\pi$
$179$	7.01872	+	12.1568i	0.524604	+	0.908640i	−0.474986	+	0.879993i	$0.657547\pi$
$180$	1.53522	+	1.58102i	0.114429	+	0.117843i
$181$	7.75754	−	13.4365i	0.576613	−	0.998723i	−0.419251	−	0.907870i	$-0.637707\pi$
$181$	7.75754	−	13.4365i	0.576613	−	0.998723i	0.995864	−	0.0908531i	$-0.0289594\pi$
$182$	5.06150	+	0.892479i	0.375183	+	0.0661550i
$183$	9.19573	+	6.76677i	0.679768	+	0.500214i
$184$	9.13159	+	3.32363i	0.673190	+	0.245021i
$185$	4.31656	+	8.52549i	0.317360	+	0.626806i
$186$	5.04588	−	3.35910i	0.369982	−	0.246301i
$187$	9.78348	−	11.6595i	0.715439	−	0.852627i
$188$		−	0.861671i		−	0.0628438i
$189$	−4.03631	+	0.0673839i	−0.293599	+	0.00490145i
$190$	−8.37527	+	2.53721i	−0.607606	+	0.184068i
$191$	3.34632	+	2.80790i	0.242131	+	0.203172i	0.755775	−	0.654831i	$-0.227260\pi$
$191$	3.34632	+	2.80790i	0.242131	+	0.203172i	−0.513644	+	0.858004i	$0.671705\pi$
$192$	−15.2922	+	0.976076i	−1.10362	+	0.0704422i
$193$	−3.24089	+	0.571456i	−0.233284	+	0.0411343i	−0.289068	−	0.957309i	$-0.593345\pi$
$193$	−3.24089	+	0.571456i	−0.233284	+	0.0411343i	0.0557838	+	0.998443i	$0.482234\pi$
$194$	8.63729	+	3.14372i	0.620122	+	0.225706i
$195$	3.61352	+	19.4857i	0.258769	+	1.39540i
$196$	0.364893	−	2.06941i	0.0260638	−	0.147815i
$197$	18.5561	+	10.7134i	1.32207	+	0.763297i	0.984059	−	0.177845i	$-0.0569125\pi$
$197$	18.5561	+	10.7134i	1.32207	+	0.763297i	0.338011	+	0.941142i	$0.390246\pi$
$198$	−14.4284	+	4.49512i	−1.02538	+	0.319454i
$199$	−7.03013	−	12.1765i	−0.498353	−	0.863172i	0.501645	−	0.865073i	$-0.332728\pi$
$199$	−7.03013	−	12.1765i	−0.498353	−	0.863172i	−0.999998	+	0.00190098i	$0.999395\pi$
$200$	−12.1321	−	8.90955i	−0.857872	−	0.630000i
$201$	−6.70098	+	1.62760i	−0.472651	+	0.114802i
$202$	−1.46531	−	1.74628i	−0.103099	−	0.122868i
$203$	0.177178	+	0.211153i	0.0124355	+	0.0148200i
$204$	−2.15992	+	0.524620i	−0.151224	+	0.0367307i
$205$	−16.1799	−	21.5859i	−1.13005	−	1.50763i
$206$	12.3885	+	21.4575i	0.863146	+	1.49501i
$207$	−7.11735	−	6.56671i	−0.494690	−	0.456418i
$208$	−14.3359	−	8.27682i	−0.994014	−	0.573894i
$209$	−2.04814	+	11.6156i	−0.141673	+	0.803466i
$210$	3.82488	−	0.709302i	0.263942	−	0.0489465i
$211$	3.90781	+	1.42233i	0.269025	+	0.0979170i	0.473010	−	0.881057i	$-0.343167\pi$
$211$	3.90781	+	1.42233i	0.269025	+	0.0979170i	−0.203986	+	0.978974i	$0.565390\pi$
$212$	3.00625	−	0.530083i	0.206470	−	0.0364063i
$213$	20.9825	−	1.33928i	1.43770	−	0.0917660i
$214$	5.46007	+	4.58154i	0.373242	+	0.313188i
$215$	−0.754092	+	0.228445i	−0.0514286	+	0.0155798i
$216$	14.7866	+	5.10402i	1.00610	+	0.347284i
$217$			2.10304i			0.142764i
$218$	−11.8567	+	14.1303i	−0.803039	+	0.957024i
$219$	20.3147	−	13.5237i	1.37274	−	0.913849i
$220$	−2.55357	+	1.29290i	−0.172162	+	0.0871676i
$221$	−18.7830	−	6.83645i	−1.26348	−	0.459869i
$222$	7.70781	+	5.67187i	0.517315	+	0.380671i
$223$	16.3593	+	2.88459i	1.09550	+	0.193167i	0.692061	−	0.721839i	$-0.256703\pi$
$223$	16.3593	+	2.88459i	1.09550	+	0.193167i	0.403441	+	0.915006i	$0.367814\pi$
$224$	0.714137	−	1.23692i	0.0477153	−	0.0826453i
$225$	7.72818	+	12.8559i	0.515212	+	0.857063i
$226$	−4.01118	−	6.94758i	−0.266820	−	0.462146i
$227$	−1.81156	−	4.97722i	−0.120238	−	0.330350i	0.864943	−	0.501870i	$-0.167354\pi$
$227$	−1.81156	−	4.97722i	−0.120238	−	0.330350i	−0.985181	+	0.171520i	$0.945132\pi$
$228$	1.24627	−	1.18897i	0.0825362	−	0.0787415i
$229$	15.6135	−	13.1012i	1.03177	−	0.865754i	0.0407059	−	0.999171i	$-0.487039\pi$
$229$	15.6135	−	13.1012i	1.03177	−	0.865754i	0.991060	+	0.133417i	$0.0425949\pi$
$230$	7.81331	+	5.10244i	0.515195	+	0.336445i
$231$	1.47575	−	5.03108i	0.0970975	−	0.331021i
$232$	−0.365309	−	1.00368i	−0.0239837	−	0.0658948i
$233$	1.06238	−	0.613363i	0.0695985	−	0.0401827i	−0.464797	−	0.885417i	$-0.653873\pi$
$233$	1.06238	−	0.613363i	0.0695985	−	0.0401827i	0.534395	+	0.845235i	$0.320539\pi$
$234$	12.0280	+	15.7865i	0.786293	+	1.03200i
$235$	1.33393	−	5.71130i	0.0870160	−	0.372564i
$236$	−0.754619	+	4.27966i	−0.0491215	+	0.278582i
$237$	−18.3411	+	8.03293i	−1.19138	+	0.521795i
$238$	−1.34194	+	3.68694i	−0.0869848	+	0.238989i
$239$	−2.66890	−	15.1361i	−0.172637	−	0.979073i	−0.940836	−	0.338862i	$-0.889958\pi$
$239$	−2.66890	−	15.1361i	−0.172637	−	0.979073i	0.768199	−	0.640211i	$-0.221153\pi$
$240$	−12.3576	−	2.06667i	−0.797683	−	0.133403i
$241$	14.2379	+	11.9470i	0.917146	+	0.769577i	0.973465	−	0.228836i	$-0.0734920\pi$
$241$	14.2379	+	11.9470i	0.917146	+	0.769577i	−0.0563190	+	0.998413i	$0.517936\pi$
$242$		−	5.40637i		−	0.347534i
$243$	−11.6318	−	10.3779i	−0.746182	−	0.665742i
$244$	2.16548			0.138630
$245$	5.62218	−	13.1515i	0.359188	−	0.840221i
$246$	−24.2092	−	11.9901i	−1.54352	−	0.764460i
$247$	15.2543	−	2.68975i	0.970611	−	0.171145i
$248$	2.78719	−	7.65774i	0.176987	−	0.486267i
$249$	−3.86388	−	8.82218i	−0.244863	−	0.559083i
$250$	−9.39921	−	10.9814i	−0.594458	−	0.694522i
$251$	3.10032	−	5.36991i	0.195691	−	0.338946i	−0.751436	−	0.659806i	$-0.770639\pi$
$251$	3.10032	−	5.36991i	0.195691	−	0.338946i	0.947127	+	0.320860i	$0.103972\pi$
$252$	−0.609037	+	0.464034i	−0.0383657	+	0.0292314i
$253$	10.8923	−	6.28869i	0.684795	−	0.395367i
$254$	−14.6769	+	5.34196i	−0.920912	+	0.335185i
$255$	−15.1284	+	0.133561i	−0.947380	+	0.00836389i
$256$	−5.86792	+	4.92377i	−0.366745	+	0.307736i
$257$	12.7173	+	15.1559i	0.793285	+	0.945401i	0.999452	−	0.0331163i	$-0.0105432\pi$
$257$	12.7173	+	15.1559i	0.793285	+	0.945401i	−0.206166	+	0.978517i	$0.566099\pi$
$258$	−0.570929	+	0.544680i	−0.0355445	+	0.0339103i
$259$	−3.11989	+	1.13555i	−0.193861	+	0.0705595i
$260$	2.74250	+	2.57055i	0.170083	+	0.159419i
$261$	−0.0500600	+	1.06321i	−0.00309864	+	0.0658111i
$262$	0.904017	+	0.521935i	0.0558504	+	0.0322452i
$263$	−16.7623	−	2.95564i	−1.03360	−	0.182252i	−0.368986	−	0.929435i	$-0.620295\pi$
$263$	−16.7623	−	2.95564i	−1.03360	−	0.182252i	−0.664619	+	0.747183i	$0.731406\pi$
$264$	−12.0414	+	16.3637i	−0.741096	+	1.00712i
$265$	20.7465	+	1.14042i	1.27445	+	0.0700552i
$266$	−0.527975	−	2.99430i	−0.0323722	−	0.183592i
$267$	−5.00121	−	7.51258i	−0.306069	−	0.459762i
$268$	−0.840718	+	1.00193i	−0.0513550	+	0.0612025i
$269$	6.07723			0.370535			0.185268	−	0.982688i	$-0.440685\pi$
$269$	6.07723			0.370535			0.185268	+	0.982688i	$0.440685\pi$
$270$	12.7126	+	8.00244i	0.773666	+	0.487013i
$271$	−30.8933			−1.87664			−0.938318	−	0.345774i	$-0.887617\pi$
$271$	−30.8933			−1.87664			−0.938318	+	0.345774i	$0.887617\pi$
$272$	8.12293	−	9.68054i	0.492525	−	0.586969i
$273$	−6.87155	+	0.438600i	−0.415885	+	0.0265453i
$274$	−0.160226	−	0.908685i	−0.00967958	−	0.0548956i
$275$	−18.9270	+	4.61648i	−1.14134	+	0.278384i
$276$	−1.82548	−	0.203079i	−0.109881	−	0.0122239i
$277$	−24.3118	−	4.28682i	−1.46075	−	0.257570i	−0.613895	−	0.789388i	$-0.710398\pi$
$277$	−24.3118	−	4.28682i	−1.46075	−	0.257570i	−0.846859	+	0.531818i	$0.821509\pi$
$278$	−14.7937	−	8.54117i	−0.887269	−	0.512265i
$279$	−5.50684	+	5.96860i	−0.329686	+	0.357331i
$280$	3.57642	−	3.81566i	0.213732	−	0.228029i
$281$	16.7164	−	6.08427i	0.997216	−	0.362957i	0.208706	−	0.977979i	$-0.433075\pi$
$281$	16.7164	−	6.08427i	0.997216	−	0.362957i	0.788510	+	0.615022i	$0.210853\pi$
$282$	−1.38630	−	5.70753i	−0.0825528	−	0.339879i
$283$	1.86958	+	2.22808i	0.111135	+	0.132446i	0.818744	−	0.574158i	$-0.194671\pi$
$283$	1.86958	+	2.22808i	0.111135	+	0.132446i	−0.707609	+	0.706604i	$0.750226\pi$
$284$	3.05486	−	2.56333i	0.181273	−	0.152106i
$285$	10.1011	−	5.95139i	0.598338	−	0.352530i
$286$	−24.2220	+	8.81610i	−1.43228	+	0.521307i
$287$	8.11705	−	4.68638i	0.479134	−	0.276628i
$288$	5.26567	−	1.64051i	0.310283	−	0.0966677i
$289$	−0.870418	+	1.50761i	−0.0512011	+	0.0886828i
$290$	−0.122399	−	1.01836i	−0.00718755	−	0.0598000i
$291$	−12.2386	−	1.36150i	−0.717438	−	0.0798125i
$292$	1.58314	−	4.34963i	0.0926461	−	0.254543i
$293$	6.09217	−	1.07421i	0.355908	−	0.0627563i	0.00716458	−	0.999974i	$-0.497719\pi$
$293$	6.09217	−	1.07421i	0.355908	−	0.0627563i	0.348744	+	0.937218i	$0.386608\pi$
$294$	−0.912390	−	14.2944i	−0.0532116	−	0.833667i
$295$	−11.6270	+	27.1981i	−0.676949	+	1.58353i
$296$	12.8653			0.747781
$297$	17.3623	−	10.4143i	1.00746	−	0.604301i
$298$			6.86401i			0.397621i
$299$	−12.6531	−	10.6172i	−0.731748	−	0.614010i
$300$	2.62580	+	1.09519i	0.151600	+	0.0632309i
$301$	−0.0475378	−	0.269600i	−0.00274003	−	0.0155395i
$302$	2.57973	−	7.08776i	0.148447	−	0.407855i
$303$	2.45980	+	1.81007i	0.141312	+	0.103986i
$304$	−1.70051	+	9.64407i	−0.0975309	+	0.553125i
$305$	14.3532	+	3.35232i	0.821859	+	0.191953i
$306$	−13.4628	+	6.94995i	−0.769617	+	0.397302i
$307$	24.1159	−	13.9233i	1.37637	−	0.794645i	0.384646	−	0.923064i	$-0.374324\pi$
$307$	24.1159	−	13.9233i	1.37637	−	0.794645i	0.991720	+	0.128419i	$0.0409903\pi$
$308$	−0.340121	−	0.934475i	−0.0193802	−	0.0532466i
$309$	−22.9130	−	24.0172i	−1.30347	−	1.36629i
$310$	4.27890	−	6.55223i	0.243025	−	0.372142i
$311$	13.2628	−	11.1288i	0.752062	−	0.631055i	−0.183986	−	0.982929i	$-0.558900\pi$
$311$	13.2628	−	11.1288i	0.752062	−	0.631055i	0.936047	+	0.351874i	$0.114456\pi$
$312$	25.6024	+	7.50990i	1.44945	+	0.425164i
$313$	3.42361	+	9.40628i	0.193514	+	0.531675i	0.998063	−	0.0622113i	$-0.0198153\pi$
$313$	3.42361	+	9.40628i	0.193514	+	0.531675i	−0.804549	+	0.593886i	$0.797593\pi$
$314$	1.04492	+	1.80986i	0.0589684	+	0.102136i
$315$	−4.75516	+	2.13286i	−0.267923	+	0.120173i
$316$	−1.89888	+	3.28897i	−0.106821	+	0.185019i
$317$	−7.89475	−	1.39206i	−0.443413	−	0.0781857i	−0.0525162	−	0.998620i	$-0.516724\pi$
$317$	−7.89475	−	1.39206i	−0.443413	−	0.0781857i	−0.390897	+	0.920434i	$0.627835\pi$
$318$	19.0600	−	8.34776i	1.06883	−	0.468119i
$319$	−1.29905	−	0.472815i	−0.0727327	−	0.0264725i
$320$	−17.6490	+	8.93594i	−0.986612	+	0.499534i
$321$	−8.55693	−	4.23799i	−0.477601	−	0.236542i
$322$	−2.08407	+	2.48370i	−0.116141	+	0.138411i
$323$			11.8248i			0.657950i
$324$	−2.94357	−	0.277805i	−0.163532	−	0.0154336i
$325$	14.1984	+	21.2836i	0.787583	+	1.18060i
$326$	−3.16426	−	2.65513i	−0.175252	−	0.147054i
$327$	10.9677	−	22.1448i	0.606513	−	1.22461i
$328$	−35.7673	+	6.30673i	−1.97492	+	0.348231i
$329$	1.91484	+	0.696946i	0.105569	+	0.0384239i
$330$	−14.8342	+	12.6722i	−0.816597	+	0.697583i
$331$	−4.48752	+	25.4500i	−0.246656	+	1.39886i	0.569958	+	0.821674i	$0.306959\pi$
$331$	−4.48752	+	25.4500i	−0.246656	+	1.39886i	−0.816615	+	0.577183i	$0.804152\pi$
$332$	−1.58201	−	0.913374i	−0.0868240	−	0.0501279i
$333$	−11.8279	−	4.94669i	−0.648167	−	0.271077i
$334$	3.57099	+	6.18513i	0.195396	+	0.338435i
$335$	−7.12348	+	5.33946i	−0.389197	+	0.291726i
$336$	1.22528	−	4.17716i	0.0668443	−	0.227883i
$337$	−12.6980	−	15.1328i	−0.691702	−	0.824338i	0.299859	−	0.953984i	$-0.403060\pi$
$337$	−12.6980	−	15.1328i	−0.691702	−	0.824338i	−0.991560	+	0.129646i	$0.958616\pi$
$338$	10.9559	+	13.0567i	0.595921	+	0.710191i
$339$	7.41885	+	7.77638i	0.402937	+	0.422355i
$340$	−2.29610	+	1.72106i	−0.124523	+	0.0933374i
$341$	−5.27369	−	9.13430i	−0.285586	−	0.494650i
$342$	6.34216	−	9.88056i	0.342945	−	0.534279i
$343$	9.01329	+	5.20383i	0.486672	+	0.280980i
$344$	−0.184207	+	1.04469i	−0.00993177	+	0.0563259i
$345$	−11.7852	−	4.17202i	−0.634495	−	0.224614i
$346$	12.9492	+	4.71312i	0.696153	+	0.253379i
$347$	−24.8142	+	4.37541i	−1.33210	+	0.234884i	−0.793958	−	0.607973i	$-0.791983\pi$
$347$	−24.8142	+	4.37541i	−1.33210	+	0.234884i	−0.538138	+	0.842857i	$0.680872\pi$
$348$	0.111873	+	0.168050i	0.00599701	+	0.00900842i
$349$	−22.8639	−	19.1851i	−1.22388	−	1.02695i	−0.998613	−	0.0526561i	$-0.983231\pi$
$349$	−22.8639	−	19.1851i	−1.22388	−	1.02695i	−0.225263	−	0.974298i	$-0.572324\pi$
$350$	4.17779	−	2.78702i	0.223312	−	0.148972i
$351$	−20.6505	−	16.7484i	−1.10224	−	0.893966i
$352$			7.16322i			0.381801i
$353$	−8.34269	+	9.94244i	−0.444037	+	0.529182i	−0.940917	−	0.338637i	$-0.890034\pi$
$353$	−8.34269	+	9.94244i	−0.444037	+	0.529182i	0.496880	+	0.867819i	$0.334479\pi$
$354$	1.88687	+	29.5617i	0.100286	+	1.57118i
$355$	24.2164	−	12.2611i	1.28527	−	0.650749i
$356$	−1.60854	−	0.585459i	−0.0852523	−	0.0310293i
$357$	0.581173	−	5.22419i	0.0307589	−	0.276493i
$358$	17.8727	+	3.15144i	0.944602	+	0.166559i
$359$	−6.77215	+	11.7297i	−0.357421	+	0.619071i	−0.987529	−	0.157436i	$-0.949677\pi$
$359$	−6.77215	+	11.7297i	−0.357421	+	0.619071i	0.630109	+	0.776507i	$0.283010\pi$
$360$	20.1415	−	1.46424i	1.06155	−	0.0771724i
$361$	4.91829	+	8.51873i	0.258857	+	0.448354i
$362$	−6.86051	−	18.8491i	−0.360581	−	0.990687i
$363$	1.70953	+	7.03830i	0.0897269	+	0.369415i
$364$	−1.00043	+	0.839464i	−0.0524370	+	0.0439999i
$365$	17.2269	−	26.3793i	0.901695	−	1.38076i
$366$	14.3437	−	3.48392i	0.749756	−	0.182108i
$367$	8.56238	+	23.5250i	0.446953	+	1.22799i	0.934835	+	0.355083i	$0.115547\pi$
$367$	8.56238	+	23.5250i	0.446953	+	1.22799i	−0.487882	+	0.872910i	$0.662230\pi$
$368$	9.04359	−	5.22132i	0.471430	−	0.272180i
$369$	35.3082	+	7.95426i	1.83807	+	0.414082i
$370$	12.0307	+	2.80990i	0.625448	+	0.146080i
$371$	−1.25357	+	7.10937i	−0.0650823	+	0.369100i
$372$	−0.170301	+	1.53085i	−0.00882972	+	0.0793707i
$373$	−0.713033	+	1.95904i	−0.0369195	+	0.101435i	−0.956783	−	0.290804i	$-0.906077\pi$
$373$	−0.713033	+	1.95904i	−0.0369195	+	0.101435i	0.919863	+	0.392239i	$0.128299\pi$
$374$	−3.41702	−	19.3789i	−0.176690	−	1.00206i
$375$	15.7088	+	11.3240i	0.811198	+	0.584771i
$376$	−6.04879	−	5.07553i	−0.311942	−	0.261751i
$377$			1.81548i			0.0935021i
$378$	−3.28758	+	4.05351i	−0.169095	+	0.208490i
$379$	−9.13522			−0.469245			−0.234622	−	0.972087i	$-0.575385\pi$
$379$	−9.13522			−0.469245			−0.234622	+	0.972087i	$0.575385\pi$
$380$	0.874084	−	2.04468i	0.0448396	−	0.104890i
$381$	17.4181	−	11.5954i	0.892354	−	0.594050i
$382$	5.56181	−	0.980698i	0.284567	−	0.0501769i
$383$	3.49449	−	9.60103i	0.178560	−	0.490590i	−0.817832	−	0.575457i	$-0.804824\pi$
$383$	3.49449	−	9.60103i	0.178560	−	0.490590i	0.996392	+	0.0848669i	$0.0270465\pi$
$384$	−7.96710	+	10.8269i	−0.406569	+	0.552509i
$385$	−0.807744	−	6.72039i	−0.0411664	−	0.342503i
$386$	−2.12732	+	3.68463i	−0.108278	+	0.187543i
$387$	0.571035	−	0.889625i	0.0290274	−	0.0452222i
$388$	−2.02269	+	1.16780i	−0.102687	+	0.0592861i
$389$	16.4031	−	5.97024i	0.831670	−	0.302703i	0.109126	−	0.994028i	$-0.465195\pi$
$389$	16.4031	−	5.97024i	0.831670	−	0.302703i	0.722544	+	0.691325i	$0.242973\pi$
$390$	22.3014	+	12.6145i	1.12927	+	0.638761i
$391$	9.65938	−	8.10519i	0.488496	−	0.409897i
$392$	−12.3776	−	14.7510i	−0.625162	−	0.745039i
$393$	−1.34194	−	0.393627i	−0.0676918	−	0.0198559i
$394$	26.0312	−	9.47457i	1.31143	−	0.477322i
$395$	−17.6777	+	18.8602i	−0.889461	+	0.948960i
$396$	1.48164	−	3.54272i	0.0744553	−	0.178029i
$397$	11.4657	+	6.61971i	0.575445	+	0.332233i	0.759321	−	0.650716i	$-0.225531\pi$
$397$	11.4657	+	6.61971i	0.575445	+	0.332233i	−0.183876	+	0.982949i	$0.558864\pi$
$398$	−17.9018	−	3.15656i	−0.897334	−	0.158224i
$399$	1.63416	+	3.73119i	0.0818105	+	0.186793i
$400$	−15.7145	+	3.83292i	−0.785726	+	0.191646i
$401$	6.80556	+	38.5962i	0.339853	+	1.92740i	0.372717	+	0.927945i	$0.378426\pi$
$401$	6.80556	+	38.5962i	0.339853	+	1.92740i	−0.0328639	+	0.999460i	$0.510463\pi$
$402$	−3.95679	+	7.98915i	−0.197347	+	0.398463i
$403$	−8.90359	+	10.6109i	−0.443519	+	0.528566i
$404$	0.579252			0.0288189
$405$	−19.0804	−	6.39821i	−0.948114	−	0.317929i
$406$	0.356364			0.0176860
$407$	10.7033	−	12.7557i	0.530543	−	0.632277i
$408$	−9.03989	+	18.2524i	−0.447541	+	0.903630i
$409$	3.44309	+	19.5268i	0.170250	+	0.965536i	0.943485	+	0.331416i	$0.107526\pi$
$409$	3.44309	+	19.5268i	0.170250	+	0.965536i	−0.773235	+	0.634120i	$0.781363\pi$
$410$	−34.8245	−	1.91427i	−1.71986	−	0.0945388i
$411$	0.495922	+	1.13231i	0.0244620	+	0.0558528i
$412$	−6.20021	−	1.09326i	−0.305462	−	0.0538612i
$413$	−8.90009	−	5.13847i	−0.437945	−	0.252847i
$414$	−12.4183	+	1.59177i	−0.610328	+	0.0782313i
$415$	−9.07186	−	8.50306i	−0.445320	−	0.417399i
$416$	8.83989	−	3.21746i	0.433411	−	0.157749i
$417$	21.9601	+	6.44149i	1.07539	+	0.315441i
$418$	9.80184	+	11.6814i	0.479424	+	0.571355i
$419$	−20.8598	+	17.5035i	−1.01907	+	0.855101i	−0.989510	−	0.144462i	$-0.953855\pi$
$419$	−20.8598	+	17.5035i	−1.01907	+	0.855101i	−0.0295598	+	0.999563i	$0.509411\pi$
$420$	−0.486662	+	0.860377i	−0.0237467	+	0.0419821i
$421$	−2.12407	+	0.773098i	−0.103521	+	0.0376785i	−0.393261	−	0.919427i	$-0.628653\pi$
$421$	−2.12407	+	0.773098i	−0.103521	+	0.0376785i	0.289740	+	0.957105i	$0.406431\pi$
$422$	4.65617	−	2.68824i	0.226659	−	0.130862i
$423$	3.60952	+	6.99203i	0.175501	+	0.339964i
$424$	13.9867	−	24.2257i	0.679256	−	1.17651i
$425$	−17.8832	+	7.85293i	−0.867465	+	0.380923i
$426$	16.1108	−	21.8938i	0.780569	−	1.06076i
$427$	−1.75150	+	4.81222i	−0.0847612	+	0.232880i
$428$	−1.78362	+	0.314500i	−0.0862145	+	0.0152019i
$429$	28.7459	−	19.1364i	1.38786	−	0.923916i
$430$	−0.400427	+	0.936688i	−0.0193103	+	0.0451711i
$431$	9.69510			0.466996			0.233498	−	0.972357i	$-0.424983\pi$
$431$	9.69510			0.466996			0.233498	+	0.972357i	$0.424983\pi$
$432$	14.4154	−	8.64671i	0.693560	−	0.416015i
$433$		−	32.3437i		−	1.55434i	−0.629292	−	0.777169i	$-0.716655\pi$
$433$		−	32.3437i		−	1.55434i	0.629292	−	0.777169i	$-0.283345\pi$
$434$	2.08282	+	1.74770i	0.0999788	+	0.0838922i
$435$	0.481358	+	1.28705i	0.0230793	+	0.0617094i
$436$	−0.813906	−	4.61589i	−0.0389790	−	0.221061i
$437$	−3.34203	+	9.18216i	−0.159871	+	0.439242i
$438$	3.48848	−	31.3581i	0.166686	−	1.49835i
$439$	1.71544	−	9.72872i	0.0818733	−	0.464327i	−0.916114	−	0.400917i	$-0.868692\pi$
$439$	1.71544	−	9.72872i	0.0818733	−	0.464327i	0.997988	−	0.0634094i	$-0.0201974\pi$
$440$	−5.96541	+	25.5413i	−0.284390	+	1.21763i
$441$	5.70778	+	18.3208i	0.271799	+	0.872417i
$442$	−22.3800	+	12.9211i	−1.06451	+	0.614594i
$443$	8.94805	+	24.5846i	0.425135	+	1.16805i	0.948732	+	0.316082i	$0.102368\pi$
$443$	8.94805	+	24.5846i	0.425135	+	1.16805i	−0.523597	+	0.851966i	$0.675410\pi$
$444$	−2.36299	+	0.573944i	−0.112142	+	0.0272382i
$445$	−9.75532	−	6.37066i	−0.462446	−	0.301998i
$446$	16.4520	−	13.8049i	0.779025	−	0.653680i
$447$	−2.17044	−	8.93594i	−0.102658	−	0.422656i
$448$	−2.35075	−	6.45865i	−0.111063	−	0.305142i
$449$	−8.04462	−	13.9337i	−0.379649	−	0.657572i	0.611362	−	0.791351i	$-0.290622\pi$
$449$	−8.04462	−	13.9337i	−0.379649	−	0.657572i	−0.991011	+	0.133779i	$0.957289\pi$
$450$	19.1547	+	3.02982i	0.902963	+	0.142827i
$451$	−23.5036	+	40.7094i	−1.10674	+	1.91693i
$452$	2.00752	+	0.353981i	0.0944260	+	0.0166499i
$453$	−1.11725	+	10.0430i	−0.0524928	+	0.471860i
$454$	−6.43484	−	2.34209i	−0.302002	−	0.109920i
$455$	−7.93060	+	4.01537i	−0.371792	+	0.188243i
$456$	−1.00543	−	15.7520i	−0.0470835	−	0.737657i
$457$	19.5646	−	23.3162i	0.915193	−	1.09068i	−0.0803867	−	0.996764i	$-0.525616\pi$
$457$	19.5646	−	23.3162i	0.915193	−	1.09068i	0.995580	−	0.0939208i	$-0.0299400\pi$
$458$		−	26.3509i		−	1.23130i
$459$	15.3290	−	13.3048i	0.715497	−	0.621017i
$460$	−2.26938	+	0.687486i	−0.105810	+	0.0320542i
$461$	12.5270	+	10.5114i	0.583438	+	0.489563i	0.886074	−	0.463543i	$-0.153422\pi$
$461$	12.5270	+	10.5114i	0.583438	+	0.489563i	−0.302636	+	0.953106i	$0.597867\pi$
$462$	−3.75632	−	5.64257i	−0.174760	−	0.262516i
$463$	7.19625	−	1.26889i	0.334438	−	0.0589705i	−0.00390751	−	0.999992i	$-0.501244\pi$
$463$	7.19625	−	1.26889i	0.334438	−	0.0589705i	0.338346	+	0.941022i	$0.390133\pi$
$464$	−1.07856	−	0.392564i	−0.0500709	−	0.0182243i
$465$	−3.49865	+	9.88307i	−0.162246	+	0.458317i
$466$	0.275403	−	1.56189i	0.0127578	−	0.0723531i
$467$	−8.71268	−	5.03027i	−0.403175	−	0.232773i	0.284678	−	0.958623i	$-0.408113\pi$
$467$	−8.71268	−	5.03027i	−0.403175	−	0.232773i	−0.687853	+	0.725850i	$0.741447\pi$
$468$	−5.03746	−	0.237183i	−0.232857	−	0.0109638i
$469$	−1.54653	−	2.67867i	−0.0714121	−	0.123689i
$470$	−4.54786	−	6.06739i	−0.209777	−	0.279868i
$471$	−1.93263	−	2.02576i	−0.0890508	−	0.0933423i
$472$	25.5975	+	30.5059i	1.17822	+	1.40415i
$473$	0.882537	+	1.05177i	0.0405791	+	0.0483603i
$474$	−7.28638	+	24.8404i	−0.334675	+	1.14096i
$475$	8.95889	−	12.1993i	0.411062	−	0.559744i
$476$	−0.498490	−	0.863411i	−0.0228483	−	0.0395744i
$477$	−22.1737	+	16.8945i	−1.01526	+	0.773544i
$478$	−17.2085	−	9.93536i	−0.787100	−	0.454433i
$479$	−1.39286	+	7.89931i	−0.0636415	+	0.360929i	0.936311	+	0.351172i	$0.114217\pi$
$479$	−1.39286	+	7.89931i	−0.0636415	+	0.360929i	−0.999952	+	0.00975657i	$0.996894\pi$
$480$	5.41379	−	4.62476i	0.247105	−	0.211091i
$481$	−20.5489	−	7.47920i	−0.936950	−	0.341022i
$482$	23.6644	−	4.17267i	1.07788	−	0.190060i
$483$	1.92780	−	3.89241i	0.0877177	−	0.177111i
$484$	1.05236	+	0.883038i	0.0478347	+	0.0401381i
$485$	−15.2146	+	4.60911i	−0.690858	+	0.209289i
$486$	−19.9446	+	2.89563i	−0.904704	+	0.131349i
$487$			1.30014i			0.0589151i	0.999566	+	0.0294575i	$0.00937799\pi$
$487$			1.30014i			0.0589151i	−0.999566	+	0.0294575i	$0.990622\pi$
$488$	12.7554	−	15.2013i	0.577409	−	0.688130i
$489$	4.95897	+	2.45603i	0.224253	+	0.111066i
$490$	−8.35289	−	16.4975i	−0.377345	−	0.745281i
$491$	10.4561	+	3.80573i	0.471879	+	0.171750i	0.567003	−	0.823715i	$-0.308103\pi$
$491$	10.4561	+	3.80573i	0.471879	+	0.171750i	−0.0951242	+	0.995465i	$0.530325\pi$
$492$	6.28806	−	2.75400i	0.283488	−	0.124160i
$493$	−1.36488	−	0.240666i	−0.0614713	−	0.0108390i
$494$	10.0130	−	17.3430i	0.450505	−	0.780298i
$495$	15.3050	−	21.1881i	0.687907	−	0.952334i
$496$	−4.37859	−	7.58394i	−0.196604	−	0.340529i
$497$	3.22548	+	8.86195i	0.144683	+	0.397513i
$498$	−11.9484	−	3.50479i	−0.535420	−	0.157053i
$499$	−13.6131	+	11.4227i	−0.609404	+	0.511351i	−0.894453	−	0.447162i	$-0.852435\pi$
$499$	−13.6131	+	11.4227i	−0.609404	+	0.511351i	0.285049	+	0.958513i	$0.407990\pi$
$500$	3.67275	−	0.0359640i	0.164251	−	0.00160836i
$501$	−6.60469	−	6.92298i	−0.295076	−	0.309296i
$502$	−2.74182	−	7.53309i	−0.122374	−	0.336218i
$503$	−11.2798	+	6.51241i	−0.502942	+	0.290374i	−0.729928	−	0.683524i	$-0.760446\pi$
$503$	−11.2798	+	6.51241i	−0.502942	+	0.290374i	0.226985	+	0.973898i	$0.427113\pi$
$504$	−0.329994	+	7.00865i	−0.0146991	+	0.312190i
$505$	3.83938	+	0.896725i	0.170850	+	0.0399037i
$506$	2.82366	−	16.0137i	0.125527	−	0.711898i
$507$	−18.3916	−	13.5336i	−0.816799	−	0.601050i
$508$	1.35740	−	3.72942i	0.0602248	−	0.165466i
$509$	3.60691	+	20.4558i	0.159873	+	0.906687i	0.954194	+	0.299188i	$0.0967159\pi$
$509$	3.60691	+	20.4558i	0.159873	+	0.906687i	−0.794321	+	0.607499i	$0.792173\pi$
$510$	−12.4400	+	15.0940i	−0.550851	+	0.668374i
$511$	8.38545	+	7.03623i	0.370951	+	0.311265i
$512$			25.4252i			1.12365i
$513$	−5.13228	+	14.8685i	−0.226596	+	0.656460i
$514$	25.5788			1.12823
$515$	−39.4036	−	16.8447i	−1.73633	−	0.742267i
$516$	−0.0127719	−	0.200097i	−0.000562250	−	0.00880878i
$517$	−10.0646	+	1.77466i	−0.442640	+	0.0780493i
$518$	−1.46810	+	4.03358i	−0.0645047	+	0.177225i
$519$	−18.3483	−	2.04118i	−0.805400	−	0.0895980i
$520$	34.1991	−	4.11049i	1.49973	−	0.180257i
$521$	12.5826	−	21.7937i	0.551255	−	0.954801i	−0.446930	−	0.894569i	$-0.647483\pi$
$521$	12.5826	−	21.7937i	0.551255	−	0.954801i	0.998184	−	0.0602320i	$-0.0191841\pi$
$522$	1.01139	+	0.933142i	0.0442673	+	0.0408425i
$523$	−21.4096	+	12.3608i	−0.936177	+	0.540502i	−0.888760	−	0.458373i	$-0.848432\pi$
$523$	−21.4096	+	12.3608i	−0.936177	+	0.540502i	−0.0474173	+	0.998875i	$0.515099\pi$
$524$	−0.249252	+	0.0907203i	−0.0108886	+	0.00396313i
$525$	−4.55761	+	4.94933i	−0.198910	+	0.216007i
$526$	−16.8572	+	14.1449i	−0.735010	+	0.616746i
$527$	−6.79700	−	8.10034i	−0.296082	−	0.352857i
$528$	5.15302	+	21.2155i	0.224256	+	0.923288i
$529$	−11.8215	+	4.30268i	−0.513978	+	0.187073i
$530$	18.3705	−	19.5994i	0.797965	−	0.851343i
$531$	−11.8040	−	37.8884i	−0.512251	−	1.64421i
$532$	0.669084	+	0.386296i	0.0290085	+	0.0167481i
$533$	60.7951	+	10.7198i	2.63333	+	0.464327i
$534$	−11.5965	−	1.29007i	−0.501831	−	0.0558270i
$535$	−12.3090	−	0.676613i	−0.532165	−	0.0292525i
$536$	2.08126	+	11.8034i	0.0898966	+	0.509829i
$537$	−24.2642	+	1.54874i	−1.04708	+	0.0668332i
$538$	5.05038	−	6.01881i	0.217737	−	0.259489i
$539$	−24.9229			−1.07350
$540$	−3.63409	+	1.16749i	−0.156386	+	0.0502406i
$541$	16.9208			0.727482			0.363741	−	0.931500i	$-0.381499\pi$
$541$	16.9208			0.727482			0.363741	+	0.931500i	$0.381499\pi$
$542$	−25.6734	+	30.5964i	−1.10277	+	1.31423i
$543$	14.8916	+	22.3695i	0.639060	+	0.959966i
$544$	1.24705	+	7.07237i	0.0534668	+	0.303225i
$545$	1.75103	−	31.8549i	0.0750059	−	1.36451i
$546$	−5.27610	+	7.16999i	−0.225796	+	0.306847i
$547$	1.40276	+	0.247344i	0.0599776	+	0.0105757i	0.203556	−	0.979063i	$-0.434750\pi$
$547$	1.40276	+	0.247344i	0.0599776	+	0.0105757i	−0.143579	+	0.989639i	$0.545861\pi$
$548$	0.203048	+	0.117230i	0.00867379	+	0.00500781i
$549$	−17.5718	+	9.07112i	−0.749944	+	0.387146i
$550$	−11.1569	+	22.5815i	−0.475730	+	0.962878i
$551$	1.00924	−	0.367332i	0.0429950	−	0.0156489i
$552$	−12.1783	+	11.6184i	−0.518342	+	0.494511i
$553$	−5.77301	−	6.88000i	−0.245493	−	0.292567i
$554$	−24.4495	+	20.5156i	−1.03876	+	0.871624i
$555$	−16.5508	+	0.146118i	−0.702542	+	0.00620235i
$556$	4.07887	−	1.48459i	0.172983	−	0.0629605i
$557$	−8.38178	+	4.83922i	−0.355147	+	0.205044i	−0.666950	−	0.745102i	$-0.732401\pi$
$557$	−8.38178	+	4.83922i	−0.355147	+	0.205044i	0.311803	+	0.950147i	$0.399067\pi$
$558$	1.33486	+	10.4140i	0.0565090	+	0.440860i
$559$	0.901548	−	1.56153i	0.0381314	−	0.0660455i
$560$	−0.670646	−	5.57974i	−0.0283400	−	0.235787i
$561$	10.5762	+	24.1480i	0.446527	+	1.01953i
$562$	7.86609	−	21.6119i	0.331811	−	0.911644i
$563$	37.5918	−	6.62845i	1.58431	−	0.279356i	0.688985	−	0.724776i	$-0.258057\pi$
$563$	37.5918	−	6.62845i	1.58431	−	0.279356i	0.895322	+	0.445420i	$0.146945\pi$
$564$	1.33742	+	0.662383i	0.0563154	+	0.0278913i
$565$	12.7582	+	5.45404i	0.536743	+	0.229453i
$566$	3.76035			0.158059
$567$	2.99820	−	6.31664i	0.125913	−	0.265274i
$568$		−	36.5435i		−	1.53333i
$569$	25.8444	+	21.6860i	1.08345	+	0.909126i	0.996203	−	0.0870599i	$-0.0277472\pi$
$569$	25.8444	+	21.6860i	1.08345	+	0.909126i	0.0872516	+	0.996186i	$0.472192\pi$
$570$	2.50018	−	14.9498i	0.104721	−	0.626178i
$571$	0.954517	+	5.41334i	0.0399453	+	0.226541i	0.998245	−	0.0592252i	$-0.0188630\pi$
$571$	0.954517	+	5.41334i	0.0399453	+	0.226541i	−0.958299	+	0.285766i	$0.907752\pi$
$572$	2.24018	−	6.15485i	0.0936667	−	0.257347i
$573$	−6.93057	+	3.03541i	−0.289529	+	0.126806i
$574$	2.10421	−	11.9336i	0.0878279	−	0.498097i
$575$	−16.1061	+	1.04361i	−0.671671	+	0.0435215i
$576$	10.2404	−	24.4856i	0.426684	−	1.02023i
$577$	−23.6596	+	13.6599i	−0.984962	+	0.568668i	−0.903765	−	0.428030i	$-0.859208\pi$
$577$	−23.6596	+	13.6599i	−0.984962	+	0.568668i	−0.0811975	+	0.996698i	$0.525874\pi$
$578$	0.769769	+	2.11492i	0.0320182	+	0.0879692i
$579$	1.60436	−	5.46953i	0.0666750	−	0.227306i
$580$	0.218218	+	0.142506i	0.00906101	+	0.00591724i
$581$	3.30932	−	2.77685i	0.137294	−	0.115203i
$582$	−11.5191	+	10.9895i	−0.477481	+	0.455528i
$583$	−12.3831	−	34.0222i	−0.512854	−	1.40906i
$584$	−21.2085	−	36.7342i	−0.877613	−	1.52007i
$585$	−33.0220	−	9.37045i	−1.36529	−	0.387420i
$586$	3.99891	−	6.92632i	0.165193	−	0.286123i
$587$	11.7130	+	2.06533i	0.483449	+	0.0852451i	0.410061	−	0.912058i	$-0.365508\pi$
$587$	11.7130	+	2.06533i	0.483449	+	0.0852451i	0.0733885	+	0.997303i	$0.476619\pi$
$588$	2.93147	+	2.15715i	0.120892	+	0.0889595i
$589$	7.70014	+	2.80262i	0.317279	+	0.115480i
$590$	17.2742	+	34.1177i	0.711169	+	1.40460i
$591$	−30.8929	+	20.5657i	−1.27076	+	0.845961i
$592$	8.88664	−	10.5907i	0.365239	−	0.435274i
$593$		−	9.14301i		−	0.375459i	−0.982221	−	0.187729i	$-0.939887\pi$
$593$		−	9.14301i		−	0.375459i	0.982221	−	0.187729i	$-0.0601128\pi$
$594$	4.11439	−	25.8500i	0.168816	−	1.06064i
$595$	−1.96746	−	6.49453i	−0.0806578	−	0.266250i
$596$	−1.33610	−	1.12112i	−0.0547287	−	0.0459229i
$597$	24.3036	−	1.55126i	0.994681	−	0.0634889i
$598$	−21.0303	+	3.70821i	−0.859994	+	0.151640i
$599$	24.8634	+	9.04955i	1.01589	+	0.369755i	0.795693	−	0.605700i	$-0.207107\pi$
$599$	24.8634	+	9.04955i	1.01589	+	0.369755i	0.220200	+	0.975455i	$0.429329\pi$
$600$	23.1549	−	11.9816i	0.945294	−	0.489147i
$601$	3.19159	−	18.1004i	0.130188	−	0.738330i	−0.847903	−	0.530151i	$-0.822135\pi$
$601$	3.19159	−	18.1004i	0.130188	−	0.738330i	0.978091	−	0.208179i	$-0.0667537\pi$
$602$	−0.306514	−	0.176966i	−0.0124926	−	0.00721260i
$603$	2.62495	−	11.6519i	0.106896	−	0.474501i
$604$	0.958297	+	1.65982i	0.0389925	+	0.0675371i
$605$	5.60824	+	7.48207i	0.228007	+	0.304189i
$606$	3.83685	−	0.931928i	0.155861	−	0.0378570i
$607$	−19.6443	−	23.4111i	−0.797336	−	0.950228i	0.202240	−	0.979336i	$-0.435178\pi$
$607$	−19.6443	−	23.4111i	−0.797336	−	0.950228i	−0.999576	+	0.0291076i	$0.990733\pi$
$608$	−3.57721	−	4.26315i	−0.145075	−	0.172894i
$609$	−0.463934	+	0.112684i	−0.0187995	+	0.00456620i
$610$	15.2480	−	11.4293i	0.617375	−	0.462758i
$611$	6.71069	+	11.6233i	0.271486	+	0.470227i
$612$	0.846095	−	3.75573i	0.0342014	−	0.151816i
$613$	17.3635	+	10.0248i	0.701304	+	0.404898i	0.807833	−	0.589411i	$-0.200640\pi$
$613$	17.3635	+	10.0248i	0.701304	+	0.404898i	−0.106529	+	0.994310i	$0.533974\pi$
$614$	6.25164	−	35.4548i	0.252295	−	1.43084i
$615$	45.9417	−	8.51962i	1.85255	−	0.343544i
$616$	−8.56328	−	3.11678i	−0.345024	−	0.125579i
$617$	−24.8810	+	4.38720i	−1.00167	+	0.176622i	−0.650352	−	0.759633i	$-0.725379\pi$
$617$	−24.8810	+	4.38720i	−1.00167	+	0.176622i	−0.351321	+	0.936255i	$0.614267\pi$
$618$	−42.8278	+	2.73363i	−1.72279	+	0.109963i
$619$	−13.4670	−	11.3002i	−0.541285	−	0.454192i	0.330692	−	0.943739i	$-0.392718\pi$
$619$	−13.4670	−	11.3002i	−0.541285	−	0.454192i	−0.871977	+	0.489547i	$0.837162\pi$
$620$	0.576525	+	1.90310i	0.0231538	+	0.0764302i
$621$	15.6636	−	5.99901i	0.628557	−	0.240732i
$622$		−	22.3836i		−	0.897502i
$623$	2.60207	−	3.10102i	0.104250	−	0.124240i
$624$	23.8669	−	15.8884i	0.955439	−	0.636046i
$625$	24.3993	+	5.44732i	0.975973	+	0.217893i
$626$	12.1610	+	4.42624i	0.486051	+	0.176908i
$627$	−16.4543	−	12.1081i	−0.657122	−	0.483549i
$628$	−0.522965	−	0.0922128i	−0.0208686	−	0.00367969i
$629$	8.34690	−	14.4573i	0.332813	−	0.576449i
$630$	−1.83934	+	6.48193i	−0.0732810	+	0.258246i
$631$	15.3587	+	26.6020i	0.611420	+	1.05901i	0.991001	+	0.133852i	$0.0427347\pi$
$631$	15.3587	+	26.6020i	0.611420	+	1.05901i	−0.379581	+	0.925158i	$0.623932\pi$
$632$	11.9029	+	32.7030i	0.473472	+	1.30085i
$633$	−5.21163	+	4.97202i	−0.207143	+	0.197620i
$634$	−7.93948	+	6.66201i	−0.315317	+	0.264582i
$635$	14.7705	−	22.6179i	0.586149	−	0.897564i
$636$	−1.48821	+	5.07354i	−0.0590113	+	0.201179i
$637$	11.1944	+	30.7565i	0.443540	+	1.21862i
$638$	−1.54782	+	0.893635i	−0.0612788	+	0.0353794i
$639$	−14.0509	+	33.5969i	−0.555846	+	1.32907i
$640$	−3.94697	+	16.8992i	−0.156018	+	0.668000i
$641$	1.59110	−	9.02357i	0.0628446	−	0.356409i	−0.937128	−	0.348986i	$-0.886526\pi$
$641$	1.59110	−	9.02357i	0.0628446	−	0.356409i	0.999972	−	0.00742320i	$-0.00236290\pi$
$642$	−11.3083	+	4.95276i	−0.446305	+	0.195470i
$643$	4.97910	−	13.6800i	0.196357	−	0.539486i	−0.801967	−	0.597369i	$-0.796213\pi$
$643$	4.97910	−	13.6800i	0.196357	−	0.539486i	0.998323	+	0.0578831i	$0.0184351\pi$
$644$	−0.143061	−	0.811340i	−0.00563740	−	0.0319713i
$645$	0.225111	−	1.34605i	0.00886373	−	0.0530006i
$646$	11.7111	+	9.82681i	0.460769	+	0.386631i
$647$		−	16.6946i		−	0.656331i	−0.944620	−	0.328165i	$-0.893570\pi$
$647$		−	16.6946i		−	0.656331i	0.944620	−	0.328165i	$-0.106430\pi$
$648$	−19.2888	+	19.0270i	−0.757735	+	0.747452i
$649$	51.5419			2.02320
$650$	32.8783	+	3.62553i	1.28959	+	0.142205i
$651$	−3.26417	−	1.61665i	−0.127933	−	0.0633614i
$652$	1.03366	−	0.182262i	0.0404811	−	0.00713791i
$653$	6.31264	−	17.3438i	0.247033	−	0.678716i	−0.752759	−	0.658296i	$-0.771277\pi$
$653$	6.31264	−	17.3438i	0.247033	−	0.678716i	0.999791	−	0.0204201i	$-0.00650038\pi$
$654$	−12.8174	−	29.2653i	−0.501200	−	1.14436i
$655$	−1.79253	+	0.215449i	−0.0700398	+	0.00841830i
$656$	−19.5143	+	33.7998i	−0.761907	+	1.31966i
$657$	5.37413	+	41.9268i	0.209665	+	1.63572i
$658$	2.28155	−	1.31725i	0.0889439	−	0.0513518i
$659$	8.26055	−	3.00660i	0.321785	−	0.117120i	−0.176077	−	0.984376i	$-0.556341\pi$
$659$	8.26055	−	3.00660i	0.321785	−	0.117120i	0.497862	+	0.867256i	$0.334118\pi$
$660$	−0.0437654	−	4.95732i	−0.00170357	−	0.192963i
$661$	−13.7931	+	11.5737i	−0.536487	+	0.450166i	−0.870335	−	0.492461i	$-0.836097\pi$
$661$	−13.7931	+	11.5737i	−0.536487	+	0.450166i	0.333847	+	0.942627i	$0.391653\pi$
$662$	21.4760	+	25.5942i	0.834690	+	0.994745i
$663$	25.0498	−	23.8981i	0.972854	−	0.928126i
$664$	−15.7303	+	5.72536i	−0.610454	+	0.222187i
$665$	3.83679	+	3.59623i	0.148784	+	0.139456i
$666$	−14.7286	+	7.60337i	−0.570720	+	0.294625i
$667$	−0.991835	−	0.572636i	−0.0384040	−	0.0221726i
$668$	−1.78721	−	0.315134i	−0.0691494	−	0.0121929i
$669$	−17.0529	+	23.1742i	−0.659305	+	0.895966i
$670$	−0.631718	+	11.4923i	−0.0244054	+	0.443985i
$671$	−4.45992	−	25.2934i	−0.172173	−	0.976442i
$672$	1.37088	+	2.05927i	0.0528828	+	0.0794380i
$673$	5.25324	−	6.26057i	0.202498	−	0.241327i	−0.655233	−	0.755427i	$-0.727429\pi$
$673$	5.25324	−	6.26057i	0.202498	−	0.241327i	0.857730	+	0.514100i	$0.171874\pi$
$674$	−25.5398			−0.983756
$675$	−25.8947	+	2.11246i	−0.996689	+	0.0813085i
$676$	−4.33098			−0.166576
$677$	−0.529394	+	0.630907i	−0.0203462	+	0.0242477i	−0.776122	−	0.630583i	$-0.782816\pi$
$677$	−0.529394	+	0.630907i	−0.0203462	+	0.0242477i	0.755775	+	0.654831i	$0.227260\pi$
$678$	13.8669	−	0.885104i	0.532556	−	0.0339922i
$679$	−0.959124	−	5.43946i	−0.0368078	−	0.208747i
$680$	−1.44326	+	26.2558i	−0.0553463	+	1.00686i
$681$	9.11782	+	1.01433i	0.349396	+	0.0388690i
$682$	−13.4291	−	2.36791i	−0.514227	−	0.0906721i
$683$	33.6587	+	19.4328i	1.28791	+	0.743577i	0.978282	−	0.207280i	$-0.0664611\pi$
$683$	33.6587	+	19.4328i	1.28791	+	0.743577i	0.309631	+	0.950857i	$0.399794\pi$
$684$	0.887394	+	2.84834i	0.0339303	+	0.108909i
$685$	1.16436	+	1.09135i	0.0444878	+	0.0416985i
$686$	12.6441	−	4.60209i	0.482756	−	0.175709i
$687$	8.33233	+	34.3051i	0.317898	+	1.30882i
$688$	0.732745	+	0.873251i	0.0279356	+	0.0332924i
$689$	−36.4236	+	30.5631i	−1.38763	+	1.16436i
$690$	−13.9258	+	8.20485i	−0.530147	+	0.312353i
$691$	33.1809	−	12.0769i	1.26226	−	0.459426i	0.377734	−	0.925914i	$-0.376703\pi$
$691$	33.1809	−	12.0769i	1.26226	−	0.459426i	0.884527	+	0.466488i	$0.154481\pi$
$692$	−3.03245	+	1.75079i	−0.115277	+	0.0665549i
$693$	6.67440	+	6.15803i	0.253539	+	0.233924i
$694$	−16.2881	+	28.2118i	−0.618287	+	1.07090i
$695$	29.3337	−	3.52571i	1.11269	−	0.133738i
$696$	1.83865	+	0.204543i	0.0696938	+	0.00775320i
$697$	−16.1184	+	44.2848i	−0.610526	+	1.67741i
$698$	−38.0013	+	6.70066i	−1.43837	+	0.253624i
$699$	0.135344	+	2.12044i	0.00511918	+	0.0802023i
$700$	−0.139871	+	1.26843i	−0.00528664	+	0.0479422i
$701$	−26.7698			−1.01108			−0.505541	−	0.862803i	$-0.668707\pi$
$701$	−26.7698			−1.01108			−0.505541	+	0.862803i	$0.668707\pi$
$702$	−33.7487	+	6.53345i	−1.27376	+	0.246589i
$703$			12.9366i			0.487912i
$704$	26.4062	+	22.1575i	0.995222	+	0.835091i
$705$	7.83920	+	6.46080i	0.295241	+	0.243328i
$706$	2.91380	+	16.5250i	0.109662	+	0.621926i
$707$	−0.468517	+	1.28724i	−0.0176204	+	0.0484116i
$708$	−6.06245	−	4.46111i	−0.227841	−	0.167659i
$709$	5.90817	−	33.5069i	0.221886	−	1.25838i	−0.646664	−	0.762775i	$-0.723836\pi$
$709$	5.90817	−	33.5069i	0.221886	−	1.25838i	0.868550	−	0.495602i	$-0.165053\pi$
$710$	7.98142	−	34.1729i	0.299537	−	1.28249i
$711$	1.63111	−	34.6427i	0.0611714	−	1.29920i
$712$	−13.5846	+	7.84310i	−0.509106	+	0.293933i
$713$	−2.98859	−	8.21108i	−0.111923	−	0.307507i
$714$	−4.69099	−	4.91706i	−0.175556	−	0.184016i
$715$	24.3765	−	37.3274i	0.911628	−	1.39597i
$716$	−3.53264	+	2.96424i	−0.132021	+	0.110779i
$717$	25.5447	+	7.49295i	0.953983	+	0.279829i
$718$	5.98907	+	16.4548i	0.223510	+	0.614089i
$719$	3.78251	+	6.55150i	0.141064	+	0.244330i	0.927898	−	0.372835i	$-0.121614\pi$
$719$	3.78251	+	6.55150i	0.141064	+	0.244330i	−0.786834	+	0.617165i	$0.788281\pi$
$720$	12.7073	−	17.5918i	0.473572	−	0.655609i
$721$	7.44442	−	12.8941i	0.277245	−	0.480202i
$722$	12.5241	+	2.20834i	0.466099	+	0.0821858i
$723$	−29.4882	+	12.9150i	−1.09668	+	0.480316i
$724$	4.78958	+	1.74326i	0.178003	+	0.0647879i
$725$	1.22578	+	1.28237i	0.0455242	+	0.0476261i
$726$	8.39132	+	4.15597i	0.311431	+	0.154243i
$727$	−18.7705	+	22.3698i	−0.696158	+	0.829649i	−0.992086	−	0.125561i	$-0.959927\pi$
$727$	−18.7705	+	22.3698i	−0.696158	+	0.829649i	0.295927	+	0.955210i	$0.404371\pi$
$728$			11.9676i			0.443549i
$729$	25.0493	−	10.0763i	0.927753	−	0.373196i
$730$	−11.8096	−	38.9833i	−0.437094	−	1.44284i
$731$	1.05445	+	0.884786i	0.0390001	+	0.0327250i
$732$	−1.66464	+	3.36108i	−0.0615270	+	0.124229i
$733$	21.0725	−	3.71565i	0.778330	−	0.137241i	0.229650	−	0.973273i	$-0.426242\pi$
$733$	21.0725	−	3.71565i	0.778330	−	0.137241i	0.548680	+	0.836033i	$0.315131\pi$
$734$	30.4144	+	11.0699i	1.12262	+	0.408599i
$735$	16.0909	+	18.8361i	0.593520	+	0.694780i
$736$	−1.03050	+	5.84426i	−0.0379847	+	0.215422i
$737$	13.4343	+	7.75631i	0.494860	+	0.285707i
$738$	37.2201	−	28.3585i	1.37009	−	1.04389i
$739$	−1.12801	−	1.95377i	−0.0414944	−	0.0718704i	0.844532	−	0.535505i	$-0.179879\pi$
$739$	−1.12801	−	1.95377i	−0.0414944	−	0.0718704i	−0.886027	+	0.463634i	$0.846545\pi$
$740$	−2.51197	+	1.88287i	−0.0923419	+	0.0692156i
$741$	−7.55148	+	25.7442i	−0.277411	+	0.945737i
$742$	5.99927	+	7.14965i	0.220240	+	0.262472i
$743$	−2.12019	−	2.52675i	−0.0777823	−	0.0926974i	0.725750	−	0.687959i	$-0.241493\pi$
$743$	−2.12019	−	2.52675i	−0.0777823	−	0.0926974i	−0.803532	+	0.595261i	$0.797049\pi$
$744$	9.74315	+	10.2127i	0.357201	+	0.374415i
$745$	−7.12031	−	9.49935i	−0.260868	−	0.348029i
$746$	1.34766	+	2.33421i	0.0493412	+	0.0854615i
$747$	16.6633	+	0.784572i	0.609678	+	0.0287060i
$748$	4.33026	+	2.50008i	0.158330	+	0.0914119i
$749$	0.743750	−	4.21801i	0.0271760	−	0.154123i
$750$	24.2697	−	6.14712i	0.886205	−	0.224461i
$751$	−29.9156	−	10.8884i	−1.09164	−	0.397323i	−0.267410	−	0.963583i	$-0.586168\pi$
$751$	−29.9156	−	10.8884i	−1.09164	−	0.397323i	−0.824227	+	0.566260i	$0.808390\pi$
$752$	−8.35633	+	1.47345i	−0.304724	+	0.0537310i
$753$	5.95147	+	8.94002i	0.216884	+	0.325792i
$754$	1.79803	+	1.50873i	0.0654804	+	0.0549446i
$755$	3.78223	+	12.4851i	0.137650	+	0.454378i
$756$	−0.252057	−	1.30201i	−0.00916724	−	0.0473536i
$757$		−	18.5287i		−	0.673436i	−0.941605	−	0.336718i	$-0.890683\pi$
$757$		−	18.5287i		−	0.673436i	0.941605	−	0.336718i	$-0.109317\pi$
$758$	−7.59167	+	9.04740i	−0.275742	+	0.328616i
$759$	1.38766	+	21.7404i	0.0503688	+	0.789128i
$760$	−9.20465	−	18.1798i	−0.333888	−	0.659450i
$761$	−38.6363	−	14.0625i	−1.40057	−	0.509764i	−0.472219	−	0.881481i	$-0.656547\pi$
$761$	−38.6363	−	14.0625i	−1.40057	−	0.509764i	−0.928346	+	0.371717i	$0.878769\pi$
$762$	2.99106	−	26.8868i	0.108355	−	0.974005i
$763$	10.9159	+	1.92478i	0.395184	+	0.0696816i
$764$	−0.717533	+	1.24280i	−0.0259594	+	0.0449630i
$765$	11.4222	−	23.5838i	0.412971	−	0.852674i
$766$	−6.60470	−	11.4397i	−0.238638	−	0.413332i
$767$	−23.1507	−	63.6062i	−0.835925	−	2.29669i
$768$	−3.13150	−	12.8927i	−0.112998	−	0.465226i
$769$	−26.1339	+	21.9289i	−0.942412	+	0.790777i	−0.978003	−	0.208589i	$-0.933113\pi$
$769$	−26.1339	+	21.9289i	−0.942412	+	0.790777i	0.0355917	+	0.999366i	$0.488668\pi$
$770$	−7.32705	−	4.78489i	−0.264049	−	0.172435i
$771$	−33.2998	+	8.08817i	−1.19926	+	0.291288i
$772$	−0.369762	−	1.01591i	−0.0133080	−	0.0365635i
$773$	−4.57453	+	2.64111i	−0.164534	+	0.0949940i	−0.580006	−	0.814612i	$-0.696950\pi$
$773$	−4.57453	+	2.64111i	−0.164534	+	0.0949940i	0.415472	+	0.909606i	$0.363617\pi$
$774$	−0.406524	−	1.30485i	−0.0146122	−	0.0469020i
$775$	0.875170	+	13.5065i	0.0314370	+	0.485170i
$776$	−3.71656	+	21.0777i	−0.133417	+	0.756645i
$777$	0.635814	−	5.71536i	0.0228097	−	0.205037i
$778$	7.71867	−	21.2069i	0.276728	−	0.760303i
$779$	−6.34166	−	35.9653i	−0.227213	−	1.28859i
$780$	−6.09801	+	2.28066i	−0.218344	+	0.0816606i
$781$	−36.2321	−	30.4024i	−1.29649	−	1.08788i
$782$		−	16.3022i		−	0.582966i
$783$	−1.61175	−	0.895009i	−0.0575991	−	0.0319850i
$784$	−20.6927			−0.739026
$785$	−3.32355	−	1.42079i	−0.118623	−	0.0507102i
$786$	−1.50504	+	1.00192i	−0.0536830	+	0.0357373i
$787$	−11.5446	+	2.03562i	−0.411520	+	0.0725620i	−0.375575	−	0.926792i	$-0.622555\pi$
$787$	−11.5446	+	2.03562i	−0.411520	+	0.0725620i	−0.0359440	+	0.999354i	$0.511444\pi$
$788$	−2.40750	+	6.61455i	−0.0857636	+	0.235634i
$789$	17.4730	−	23.7450i	0.622054	−	0.845343i
$790$	3.98815	+	33.1812i	0.141892	+	1.18053i
$791$	−2.41038	+	4.17490i	−0.0857032	+	0.148442i
$792$	−16.1419	−	31.2687i	−0.573579	−	1.11109i
$793$	−29.2106	+	16.8647i	−1.03730	+	0.598884i
$794$	16.0844	−	5.85425i	0.570815	−	0.207760i
$795$	−17.7183	+	31.3244i	−0.628404	+	1.11096i
$796$	3.53839	−	2.96906i	0.125415	−	0.105235i
$797$	−15.6442	−	18.6441i	−0.554147	−	0.660406i	0.414150	−	0.910209i	$-0.364079\pi$
$797$	−15.6442	−	18.6441i	−0.554147	−	0.660406i	−0.968297	+	0.249802i	$0.919634\pi$
$798$	5.05337	+	1.48229i	0.178887	+	0.0524725i
$799$	−9.62798	+	3.50430i	−0.340613	+	0.123973i
$800$	4.07173	−	8.24117i	0.143957	−	0.291370i
$801$	15.5049	−	1.98741i	0.547840	−	0.0702216i
$802$	43.8809	+	25.3346i	1.54949	+	0.894597i
$803$	−54.0656	−	9.53322i	−1.90793	−	0.336420i
$804$	−0.908836	−	2.07509i	−0.0320522	−	0.0731829i
$805$	0.307781	−	5.59917i	0.0108478	−	0.197345i
$806$	3.10970	+	17.6360i	0.109535	+	0.621201i
$807$	−4.67168	+	9.43258i	−0.164451	+	0.332042i
$808$	3.41199	−	4.06625i	0.120033	−	0.143050i
$809$	2.84260			0.0999405			0.0499703	−	0.998751i	$-0.484087\pi$
$809$	2.84260			0.0999405			0.0499703	+	0.998751i	$0.484087\pi$
$810$	−22.1932	+	13.5799i	−0.779789	+	0.477149i
$811$	25.2940			0.888194			0.444097	−	0.895979i	$-0.353525\pi$
$811$	25.2940			0.888194			0.444097	+	0.895979i	$0.353525\pi$
$812$	−0.0582060	+	0.0693672i	−0.00204263	+	0.00243431i
$813$	23.7483	−	47.9501i	0.832888	−	1.68168i
$814$	−3.73828	−	21.2008i	−0.131027	−	0.743089i
$815$	7.13341	+	0.392116i	0.249872	+	0.0137352i
$816$	8.78109	+	20.0494i	0.307400	+	0.701868i
$817$	−1.05047	−	0.185227i	−0.0367514	−	0.00648027i
$818$	22.2004	+	12.8174i	0.776218	+	0.448149i
$819$	4.60153	−	11.0026i	0.160790	−	0.384463i
$820$	6.06061	−	6.46602i	0.211646	−	0.225803i
$821$	−39.7487	+	14.4673i	−1.38724	+	0.504914i	−0.924365	−	0.381510i	$-0.875404\pi$
$821$	−39.7487	+	14.4673i	−1.38724	+	0.504914i	−0.462874	+	0.886424i	$0.653182\pi$
$822$	1.53355	+	0.449834i	0.0534889	+	0.0156897i
$823$	−1.42693	−	1.70055i	−0.0497397	−	0.0592774i	0.740601	−	0.671945i	$-0.234541\pi$
$823$	−1.42693	−	1.70055i	−0.0497397	−	0.0592774i	−0.790341	+	0.612668i	$0.790096\pi$
$824$	−44.1958	+	37.0847i	−1.53964	+	1.29191i
$825$	7.38421	−	32.9257i	0.257085	−	1.14633i
$826$	−12.4853	+	4.54429i	−0.434421	+	0.158116i
$827$	15.7822	−	9.11184i	0.548800	−	0.316850i	−0.199838	−	0.979829i	$-0.564042\pi$
$827$	15.7822	−	9.11184i	0.548800	−	0.316850i	0.748638	+	0.662979i	$0.230708\pi$
$828$	1.71848	−	2.67725i	0.0597214	−	0.0930410i
$829$	15.8943	−	27.5298i	0.552033	−	0.956149i	−0.446095	−	0.894986i	$-0.647186\pi$
$829$	15.8943	−	27.5298i	0.552033	−	0.956149i	0.998128	−	0.0611633i	$-0.0194810\pi$
$830$	−15.9603	+	1.91832i	−0.553991	+	0.0665859i
$831$	25.3426	−	34.4394i	0.879124	−	1.19469i
$832$	15.4831	−	42.5394i	0.536779	−	1.47479i
$833$	−24.6068	+	4.33884i	−0.852574	+	0.150332i
$834$	24.6291	−	16.3959i	0.852837	−	0.567743i
$835$	−11.3581	−	4.85550i	−0.393064	−	0.168032i
$836$	−3.87478			−0.134012
$837$	−5.03076	−	13.1354i	−0.173889	−	0.454027i
$838$			35.2053i			1.21615i
$839$	−14.1865	−	11.9039i	−0.489772	−	0.410968i	0.364173	−	0.931331i	$-0.381352\pi$
$839$	−14.1865	−	11.9039i	−0.489772	−	0.410968i	−0.853945	+	0.520364i	$0.825796\pi$
$840$	3.17309	+	8.48420i	0.109482	+	0.292733i
$841$	−5.01394	−	28.4355i	−0.172894	−	0.980533i
$842$	−0.999506	+	2.74612i	−0.0344453	+	0.0946376i
$843$	−3.40669	+	30.6229i	−0.117333	+	1.05471i
$844$	−0.237233	+	1.34542i	−0.00816591	+	0.0463112i
$845$	−28.7065	−	6.70468i	−0.987534	−	0.230648i
$846$	9.92444	+	2.23579i	0.341209	+	0.0768680i
$847$	−2.81351	+	1.62438i	−0.0966734	+	0.0558144i
$848$	−10.2813	−	28.2476i	−0.353061	−	0.970027i
$849$	−4.89543	+	1.18905i	−0.168011	+	0.0408080i
$850$	−7.08413	+	24.2374i	−0.242984	+	0.831336i
$851$	10.5675	−	8.86722i	0.362251	−	0.303964i
$852$	1.63027	+	6.71199i	0.0558521	+	0.229949i
$853$	7.92056	+	21.7616i	0.271195	+	0.745102i	0.998284	+	0.0585587i	$0.0186505\pi$
$853$	7.92056	+	21.7616i	0.271195	+	0.745102i	−0.727089	+	0.686543i	$0.759127\pi$
$854$	3.31040	+	5.73378i	0.113280	+	0.196206i
$855$	1.47235	+	20.2530i	0.0503534	+	0.692640i
$856$	−8.29838	+	14.3732i	−0.283633	+	0.491266i
$857$	−23.4792	−	4.14002i	−0.802035	−	0.141420i	−0.242418	−	0.970172i	$-0.577941\pi$
$857$	−23.4792	−	4.14002i	−0.802035	−	0.141420i	−0.559617	+	0.828751i	$0.689052\pi$
$858$	4.93629	−	44.3726i	0.168522	−	1.51485i
$859$	−7.58350	−	2.76017i	−0.258746	−	0.0941757i	0.209390	−	0.977832i	$-0.432852\pi$
$859$	−7.58350	−	2.76017i	−0.258746	−	0.0941757i	−0.468136	+	0.883656i	$0.655074\pi$
$860$	−0.116926	−	0.230936i	−0.00398714	−	0.00787486i
$861$	1.03409	+	16.2011i	0.0352417	+	0.552133i
$862$	8.05695	−	9.60190i	0.274421	−	0.327042i
$863$		−	18.5552i		−	0.631628i	−0.948821	−	0.315814i	$-0.897723\pi$
$863$		−	18.5552i		−	0.631628i	0.948821	−	0.315814i	$-0.102277\pi$
$864$	−1.50156	+	9.43403i	−0.0510841	+	0.320952i
$865$	−22.8100	+	6.91006i	−0.775562	+	0.234949i
$866$	−32.0328	−	26.8787i	−1.08852	−	0.913375i
$867$	−1.67088	−	2.50992i	−0.0567461	−	0.0852413i
$868$	−0.680388	+	0.119971i	−0.0230939	+	0.00407208i
$869$	42.3270	+	15.4058i	1.43584	+	0.522604i
$870$	1.67470	+	0.592852i	0.0567777	+	0.0200996i
$871$	3.53760	−	20.0627i	0.119867	−	0.679799i
$872$	−37.1970	−	21.4757i	−1.25965	−	0.727258i
$873$	11.5212	−	17.9491i	0.389934	−	0.607485i
$874$	6.31655	+	10.9406i	0.213660	+	0.370071i
$875$	−2.89072	+	8.19084i	−0.0977240	+	0.276901i
$876$	5.53416	+	5.80086i	0.186982	+	0.195993i
$877$	−6.79778	−	8.10128i	−0.229545	−	0.273561i	0.638962	−	0.769238i	$-0.279364\pi$
$877$	−6.79778	−	8.10128i	−0.229545	−	0.273561i	−0.868507	+	0.495678i	$0.834920\pi$
$878$	−8.20962	−	9.78384i	−0.277061	−	0.330189i
$879$	−3.01586	+	10.2815i	−0.101722	+	0.346788i
$880$	16.9049	+	22.5532i	0.569864	+	0.760267i
$881$	−5.52419	−	9.56817i	−0.186115	−	0.322360i	0.757837	−	0.652444i	$-0.226256\pi$
$881$	−5.52419	−	9.56817i	−0.186115	−	0.322360i	−0.943952	+	0.330084i	$0.892923\pi$
$882$	22.8880	+	9.57225i	0.770679	+	0.322314i
$883$	45.6600	+	26.3618i	1.53658	+	0.887146i	0.999035	+	0.0439118i	$0.0139821\pi$
$883$	45.6600	+	26.3618i	1.53658	+	0.887146i	0.537546	+	0.843234i	$0.319351\pi$
$884$	1.14027	−	6.46678i	0.0383513	−	0.217501i
$885$	−33.2768	−	38.9541i	−1.11859	−	1.30943i
$886$	31.7844	+	11.5686i	1.06782	+	0.388654i
$887$	41.4529	−	7.30927i	1.39185	−	0.245421i	0.573062	−	0.819512i	$-0.305755\pi$
$887$	41.4529	−	7.30927i	1.39185	−	0.245421i	0.818792	+	0.574091i	$0.194644\pi$
$888$	−9.88980	+	19.9685i	−0.331880	+	0.670099i
$889$	7.18978	+	6.03294i	0.241138	+	0.202338i
$890$	−14.4164	+	4.36731i	−0.483239	+	0.146393i
$891$	2.81759	+	34.9540i	0.0943929	+	1.17100i
$892$			5.45722i			0.182721i
$893$	5.10364	−	6.08228i	0.170787	−	0.203536i
$894$	−10.6538	−	5.27649i	−0.356315	−	0.176472i
$895$	−28.0038	+	14.1787i	−0.936064	+	0.473941i
$896$	−5.66584	−	2.06220i	−0.189282	−	0.0688932i
$897$	26.2059	−	11.4775i	0.874989	−	0.383222i
$898$	−20.4851	−	3.61208i	−0.683597	−	0.120537i
$899$	−0.480212	+	0.831752i	−0.0160160	+	0.0277405i
$900$	−3.71837	+	3.23365i	−0.123946	+	0.107788i
$901$	−18.1489	−	31.4349i	−0.604629	−	1.04725i
$902$	20.7858	+	57.1085i	0.692092	+	1.90151i
$903$	0.454995	+	0.133462i	0.0151413	+	0.00444135i
$904$	14.3099	−	12.0074i	0.475940	−	0.399361i
$905$	29.0475	+	18.9693i	0.965570	+	0.630560i
$906$	9.01796	+	9.45255i	0.299602	+	0.314040i
$907$	0.214958	+	0.590592i	0.00713756	+	0.0196103i	0.943210	−	0.332196i	$-0.107790\pi$
$907$	0.214958	+	0.590592i	0.00713756	+	0.0196103i	−0.936073	+	0.351807i	$0.885567\pi$
$908$	1.50692	−	0.870019i	0.0500088	−	0.0288726i
$909$	−4.70034	+	2.42647i	−0.155900	+	0.0804810i
$910$	−2.61383	+	11.1913i	−0.0866476	+	0.370987i
$911$	4.64690	−	26.3539i	0.153959	−	0.873144i	−0.805773	−	0.592225i	$-0.798250\pi$
$911$	4.64690	−	26.3539i	0.153959	−	0.873144i	0.959731	−	0.280919i	$-0.0906392\pi$
$912$	−13.6615	−	10.0530i	−0.452378	−	0.332887i
$913$	−7.41025	+	20.3595i	−0.245243	+	0.673801i
$914$	−6.83321	−	38.7530i	−0.226022	−	1.28184i
$915$	−16.2367	+	19.7008i	−0.536770	+	0.651289i
$916$	5.12928	+	4.30398i	0.169476	+	0.142207i
$917$		−	0.627276i		−	0.0207145i
$918$	−0.438035	−	26.2384i	−0.0144573	−	0.865997i
$919$	−8.32555			−0.274634			−0.137317	−	0.990527i	$-0.543848\pi$
$919$	−8.32555			−0.274634			−0.137317	+	0.990527i	$0.543848\pi$
$920$	−8.54136	+	19.9802i	−0.281600	+	0.658727i
$921$	3.07230	+	48.1338i	0.101236	+	1.58606i
$922$	20.8206	−	3.67124i	0.685691	−	0.120906i
$923$	−21.2444	+	58.3685i	−0.699268	+	1.92122i
$924$	1.71187	+	0.190440i	0.0563165	+	0.00626501i
$925$	−19.5646	+	8.59125i	−0.643280	+	0.282479i
$926$	4.72363	−	8.18157i	0.155228	−	0.268863i
$927$	54.8912	−	17.1012i	1.80286	−	0.561677i
$928$	0.564881	−	0.326134i	0.0185431	−	0.0107059i
$929$	20.0134	−	7.28427i	0.656618	−	0.238989i	0.00784221	−	0.999969i	$-0.497504\pi$
$929$	20.0134	−	7.28427i	0.656618	−	0.238989i	0.648775	+	0.760980i	$0.275281\pi$
$930$	6.88057	+	11.6782i	0.225623	+	0.382943i
$931$	14.8327	−	12.4461i	0.486122	−	0.407905i
$932$	0.259044	+	0.308716i	0.00848525	+	0.0101123i
$933$	7.07785	+	29.1403i	0.231718	+	0.954009i
$934$	−12.2224	+	4.44860i	−0.399930	+	0.145563i
$935$	24.8314	+	23.2745i	0.812074	+	0.761158i
$936$	−31.3373	+	33.9650i	−1.02429	+	1.11018i
$937$	−2.68331	−	1.54921i	−0.0876598	−	0.0506104i	0.455529	−	0.890221i	$-0.349450\pi$
$937$	−2.68331	−	1.54921i	−0.0876598	−	0.0506104i	−0.543189	+	0.839610i	$0.682783\pi$
$938$	−3.93814	−	0.694400i	−0.128585	−	0.0226730i
$939$	−17.2315	−	1.91694i	−0.562327	−	0.0625570i
$940$	1.92385	+	0.105752i	0.0627491	+	0.00344925i
$941$	−2.52290	−	14.3081i	−0.0822442	−	0.466430i	−0.997917	−	0.0645063i	$-0.979453\pi$
$941$	−2.52290	−	14.3081i	−0.0822442	−	0.466430i	0.915673	−	0.401924i	$-0.131658\pi$
$942$	−3.61237	+	0.230572i	−0.117697	+	0.00751243i
$943$	−25.0323	+	29.8324i	−0.815165	+	0.971476i
$944$	42.7937			1.39282
$945$	0.344925	−	9.02014i	0.0112204	−	0.293425i
$946$	1.77507			0.0577127
$947$	2.63542	−	3.14077i	0.0856396	−	0.102061i	−0.721523	−	0.692390i	$-0.756558\pi$
$947$	2.63542	−	3.14077i	0.0856396	−	0.102061i	0.807163	+	0.590329i	$0.201002\pi$
$948$	−3.64516	−	5.47558i	−0.118389	−	0.177839i
$949$	12.5197	+	71.0025i	0.406406	+	2.30484i
$950$	−4.63692	−	19.0108i	−0.150442	−	0.616793i
$951$	8.22948	−	11.1835i	0.266859	−	0.362649i
$952$	−8.99727	−	1.58646i	−0.291603	−	0.0514175i
$953$	−24.8072	−	14.3224i	−0.803584	−	0.463950i	0.0411387	−	0.999153i	$-0.486901\pi$
$953$	−24.8072	−	14.3224i	−0.803584	−	0.463950i	−0.844723	+	0.535204i	$0.820235\pi$
$954$	−1.69504	+	36.0004i	−0.0548788	+	1.16556i
$955$	−6.67988	+	7.12672i	−0.216156	+	0.230615i
$956$	4.74467	−	1.72692i	0.153454	−	0.0558525i
$957$	1.73247	−	1.65281i	0.0560027	−	0.0534279i
$958$	6.66586	+	7.94406i	0.215364	+	0.256661i
$959$	−0.424745	+	0.356403i	−0.0137157	+	0.0115089i
$960$	−0.302486	−	34.2626i	−0.00976269	−	1.10582i
$961$	22.2447	−	8.09640i	0.717570	−	0.261174i
$962$	−24.4841	+	14.1359i	−0.789401	+	0.455761i
$963$	13.1557	−	10.0235i	0.423938	−	0.323004i
$964$	−3.05296	+	5.28788i	−0.0983291	+	0.170311i
$965$	−0.878137	−	7.30605i	−0.0282682	−	0.235190i
$966$	−2.25293	−	5.14399i	−0.0724868	−	0.165505i
$967$	−7.35273	+	20.2015i	−0.236448	+	0.649635i	0.763545	+	0.645755i	$0.223457\pi$
$967$	−7.35273	+	20.2015i	−0.236448	+	0.649635i	−0.999992	+	0.00388011i	$0.998765\pi$
$968$	12.3976	−	2.18602i	0.398473	−	0.0702615i
$969$	−18.3535	−	9.08995i	−0.589600	−	0.292011i
$970$	−8.07902	+	18.8986i	−0.259402	+	0.606799i
$971$	39.3784			1.26371			0.631857	−	0.775085i	$-0.282293\pi$
$971$	39.3784			1.26371			0.631857	+	0.775085i	$0.282293\pi$
$972$	2.69396	−	4.35522i	0.0864090	−	0.139694i
$973$			10.2650i			0.329081i
$974$	1.28764	+	1.08046i	0.0412588	+	0.0346202i
$975$	−43.9492	+	5.67642i	−1.40750	+	0.181791i
$976$	−3.70294	−	21.0004i	−0.118528	−	0.672206i
$977$	−7.02896	+	19.3119i	−0.224876	+	0.617843i	−0.999901	−	0.0140884i	$-0.995515\pi$
$977$	−7.02896	+	19.3119i	−0.224876	+	0.617843i	0.775024	+	0.631931i	$0.217738\pi$
$978$	6.55350	−	2.87026i	0.209558	−	0.0917807i
$979$	−3.52548	+	19.9940i	−0.112675	+	0.639010i
$980$	4.57559	+	1.06867i	0.146162	+	0.0341375i
$981$	25.9403	+	34.0462i	0.828209	+	1.08701i
$982$	12.4585	−	7.19295i	0.397568	−	0.229536i
$983$	−7.78235	−	21.3818i	−0.248218	−	0.681975i	−0.999752	−	0.0222795i	$-0.992908\pi$
$983$	−7.78235	−	21.3818i	−0.248218	−	0.681975i	0.751533	−	0.659695i	$-0.229315\pi$
$984$	17.7062	−	60.3631i	0.564452	−	1.92431i
$985$	−26.1971	+	40.1154i	−0.834710	+	1.27818i
$986$	−1.37262	+	1.15176i	−0.0437130	+	0.0366796i
$987$	−2.55372	+	2.43631i	−0.0812858	+	0.0775486i
$988$	1.74041	+	4.78174i	0.0553698	+	0.152127i
$989$	0.568729	+	0.985067i	0.0180845	+	0.0313233i
$990$	−8.26546	−	32.7659i	−0.262694	−	1.04137i
$991$	−8.61401	+	14.9199i	−0.273633	+	0.473946i	−0.969789	−	0.243944i	$-0.921559\pi$
$991$	−8.61401	+	14.9199i	−0.273633	+	0.473946i	0.696156	+	0.717890i	$0.254892\pi$
$992$	4.90099	+	0.864176i	0.155606	+	0.0274376i
$993$	−36.0517	−	26.5290i	−1.14407	−	0.841873i
$994$	11.4572	+	4.17010i	0.363402	+	0.132267i
$995$	28.0493	−	14.2017i	0.889224	−	0.450225i
$996$	2.63378	−	1.75334i	0.0834546	−	0.0555567i
$997$	8.68705	−	10.3528i	0.275122	−	0.327877i	−0.610736	−	0.791834i	$-0.709126\pi$
$997$	8.68705	−	10.3528i	0.275122	−	0.327877i	0.885858	+	0.463957i	$0.153571\pi$
$998$			22.9749i			0.727256i
$999$	16.7702	−	14.5557i	0.530586	−	0.460524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.12	yes	96
3.2	odd	2		405.2.p.a.289.5		96
5.2	odd	4		675.2.l.h.151.12		96
5.3	odd	4		675.2.l.h.151.5		96
5.4	even	2	inner	135.2.p.a.124.5	yes	96
15.14	odd	2		405.2.p.a.289.12		96
27.5	odd	18		405.2.p.a.199.12		96
27.22	even	9	inner	135.2.p.a.49.5	✓	96
135.22	odd	36		675.2.l.h.76.12		96
135.49	even	18	inner	135.2.p.a.49.12	yes	96
135.59	odd	18		405.2.p.a.199.5		96
135.103	odd	36		675.2.l.h.76.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.5	✓	96	27.22	even	9	inner
135.2.p.a.49.12	yes	96	135.49	even	18	inner
135.2.p.a.124.5	yes	96	5.4	even	2	inner
135.2.p.a.124.12	yes	96	1.1	even	1	trivial
405.2.p.a.199.5		96	135.59	odd	18
405.2.p.a.199.12		96	27.5	odd	18
405.2.p.a.289.5		96	3.2	odd	2
405.2.p.a.289.12		96	15.14	odd	2
675.2.l.h.76.5		96	135.103	odd	36
675.2.l.h.76.12		96	135.22	odd	36
675.2.l.h.151.5		96	5.3	odd	4
675.2.l.h.151.12		96	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831033 - 0.990387i) q^{2} +(-0.768718 + 1.55212i) q^{3} +(0.0570464 + 0.323526i) q^{4} +(-0.122729 + 2.23270i) q^{5} +(0.898367 + 2.05119i) q^{6} +(-0.765094 - 0.134907i) q^{7} +(2.60712 + 1.50522i) q^{8} +(-1.81814 - 2.38628i) q^{9} +O(q^{10})\)	\(q+(0.831033 - 0.990387i) q^{2} +(-0.768718 + 1.55212i) q^{3} +(0.0570464 + 0.323526i) q^{4} +(-0.122729 + 2.23270i) q^{5} +(0.898367 + 2.05119i) q^{6} +(-0.765094 - 0.134907i) q^{7} +(2.60712 + 1.50522i) q^{8} +(-1.81814 - 2.38628i) q^{9} +(2.10924 + 1.97700i) q^{10} +(3.66139 - 1.33264i) q^{11} +(-0.546003 - 0.160158i) q^{12} +(-3.28913 - 3.91983i) q^{13} +(-0.769429 + 0.645628i) q^{14} +(-3.37107 - 1.90681i) q^{15} +(3.03995 - 1.10645i) q^{16} +(3.38295 - 1.95315i) q^{17} +(-3.87428 - 0.182416i) q^{18} +(-1.51356 + 2.62156i) q^{19} +(-0.729337 + 0.0876612i) q^{20} +(0.797534 - 1.08381i) q^{21} +(1.72291 - 4.73366i) q^{22} +(3.17893 - 0.560532i) q^{23} +(-4.34042 + 2.88947i) q^{24} +(-4.96988 - 0.548034i) q^{25} -6.61553 q^{26} +(5.10144 - 0.987594i) q^{27} -0.255224i q^{28} +(-0.271790 - 0.228059i) q^{29} +(-4.68995 + 1.75404i) q^{30} +(-0.470061 - 2.66585i) q^{31} +(-0.628781 + 1.72756i) q^{32} +(-0.746168 + 6.70734i) q^{33} +(0.876974 - 4.97357i) q^{34} +(0.395105 - 1.69167i) q^{35} +(0.668307 - 0.724346i) q^{36} +(3.70101 - 2.13678i) q^{37} +(1.33854 + 3.67761i) q^{38} +(8.61246 - 2.09187i) q^{39} +(-3.68067 + 5.63618i) q^{40} +(-9.24182 + 7.75481i) q^{41} +(-0.410616 - 1.69055i) q^{42} +(0.120519 + 0.331124i) q^{43} +(0.640012 + 1.10853i) q^{44} +(5.55099 - 3.76650i) q^{45} +(2.08666 - 3.61420i) q^{46} +(-2.58307 - 0.455464i) q^{47} +(-0.619521 + 5.56890i) q^{48} +(-6.01068 - 2.18771i) q^{49} +(-4.67290 + 4.46667i) q^{50} +(0.430980 + 6.75217i) q^{51} +(1.08053 - 1.28773i) q^{52} -9.29215i q^{53} +(3.26136 - 5.87312i) q^{54} +(2.52602 + 8.33833i) q^{55} +(-1.79163 - 1.50335i) q^{56} +(-2.90547 - 4.36446i) q^{57} +(-0.451732 + 0.0796526i) q^{58} +(12.4304 + 4.52430i) q^{59} +(0.424594 - 1.19940i) q^{60} +(1.14463 - 6.49154i) q^{61} +(-3.03086 - 1.74987i) q^{62} +(1.06913 + 2.07101i) q^{63} +(4.42346 + 7.66166i) q^{64} +(9.15547 - 6.86255i) q^{65} +(6.02277 + 6.31302i) q^{66} +(2.55913 + 3.04985i) q^{67} +(0.824880 + 0.983053i) q^{68} +(-1.57369 + 5.36497i) q^{69} +(-1.34706 - 1.79714i) q^{70} +(-6.06946 - 10.5126i) q^{71} +(-1.14823 - 8.95804i) q^{72} +(-12.2022 - 7.04497i) q^{73} +(0.959425 - 5.44117i) q^{74} +(4.67105 - 7.29255i) q^{75} +(-0.934485 - 0.340125i) q^{76} +(-2.98109 + 0.525647i) q^{77} +(5.08548 - 10.2681i) q^{78} +(8.85574 + 7.43085i) q^{79} +(2.09728 + 6.92307i) q^{80} +(-2.38871 + 8.67722i) q^{81} +15.5975i q^{82} +(-3.57428 + 4.25966i) q^{83} +(0.396138 + 0.196195i) q^{84} +(3.94560 + 7.79282i) q^{85} +(0.428097 + 0.155815i) q^{86} +(0.562904 - 0.246537i) q^{87} +(11.5516 + 2.03686i) q^{88} +(-2.60530 + 4.51251i) q^{89} +(0.882767 - 8.62771i) q^{90} +(1.98768 + 3.44277i) q^{91} +(0.362693 + 0.996492i) q^{92} +(4.49906 + 1.31970i) q^{93} +(-2.59770 + 2.17973i) q^{94} +(-5.66739 - 3.70106i) q^{95} +(-2.19803 - 2.30395i) q^{96} +(2.43160 + 6.68077i) q^{97} +(-7.16175 + 4.13484i) q^{98} +(-9.83699 - 6.31420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

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