LMFDB - Embedded newform 135.2.k.a.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(16,135)]

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([4, 0]))

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

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

chi := DirichletCharacter("135.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.k (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	135.61
Dual form			135.2.k.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.282715 + 0.102900i) q^{2} +(-0.864728 - 1.50075i) q^{3} +(-1.46275 + 1.22739i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.398898 + 0.335304i) q^{6} +(-3.28585 - 2.75715i) q^{7} +(0.588102 - 1.01862i) q^{8} +(-1.50449 + 2.59548i) q^{9} +O(q^{10})$	\(q+(-0.282715 + 0.102900i) q^{2} +(-0.864728 - 1.50075i) q^{3} +(-1.46275 + 1.22739i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.398898 + 0.335304i) q^{6} +(-3.28585 - 2.75715i) q^{7} +(0.588102 - 1.01862i) q^{8} +(-1.50449 + 2.59548i) q^{9} +(0.150430 + 0.260552i) q^{10} +(0.307813 - 1.74570i) q^{11} +(3.10689 + 1.13386i) q^{12} +(-3.80087 - 1.38340i) q^{13} +(1.21267 + 0.441375i) q^{14} +(-1.32779 + 1.11219i) q^{15} +(0.601708 - 3.41245i) q^{16} +(1.95214 + 3.38121i) q^{17} +(0.158267 - 0.888593i) q^{18} +(-0.556845 + 0.964484i) q^{19} +(1.46275 + 1.22739i) q^{20} +(-1.29643 + 7.31542i) q^{21} +(0.0926084 + 0.525208i) q^{22} +(6.60755 - 5.54440i) q^{23} +(-2.03724 - 0.00176120i) q^{24} +(-0.939693 + 0.342020i) q^{25} +1.21692 q^{26} +(5.19613 + 0.0134762i) q^{27} +8.19048 q^{28} +(-0.562260 + 0.204646i) q^{29} +(0.260942 - 0.451063i) q^{30} +(1.24781 - 1.04704i) q^{31} +(0.589520 + 3.34334i) q^{32} +(-2.88602 + 1.04760i) q^{33} +(-0.899826 - 0.755043i) q^{34} +(-2.14468 + 3.71470i) q^{35} +(-0.984980 - 5.64313i) q^{36} +(-2.60857 - 4.51818i) q^{37} +(0.0581832 - 0.329973i) q^{38} +(1.21058 + 6.90042i) q^{39} +(-1.10527 - 0.402285i) q^{40} +(-0.711333 - 0.258904i) q^{41} +(-0.386236 - 2.20158i) q^{42} +(-1.25194 + 7.10010i) q^{43} +(1.69240 + 2.93132i) q^{44} +(2.81730 + 1.03093i) q^{45} +(-1.29754 + 2.24740i) q^{46} +(-9.00022 - 7.55208i) q^{47} +(-5.64155 + 2.04783i) q^{48} +(1.97936 + 11.2255i) q^{49} +(0.230471 - 0.193388i) q^{50} +(3.38627 - 5.85350i) q^{51} +(7.25771 - 2.64159i) q^{52} +3.97724 q^{53} +(-1.47041 + 0.530872i) q^{54} -1.77263 q^{55} +(-4.74091 + 1.72555i) q^{56} +(1.92897 + 0.00166759i) q^{57} +(0.137901 - 0.115713i) q^{58} +(-2.39974 - 13.6096i) q^{59} +(0.577126 - 3.25658i) q^{60} +(-6.49619 - 5.45095i) q^{61} +(-0.245035 + 0.424413i) q^{62} +(12.0997 - 4.38024i) q^{63} +(2.95440 + 5.11717i) q^{64} +(-0.702373 + 3.98336i) q^{65} +(0.708124 - 0.593144i) q^{66} +(-7.36217 - 2.67961i) q^{67} +(-7.00557 - 2.54982i) q^{68} +(-14.0345 - 5.12188i) q^{69} +(0.224092 - 1.27089i) q^{70} +(2.59176 + 4.48907i) q^{71} +(1.75902 + 3.05891i) q^{72} +(2.18764 - 3.78911i) q^{73} +(1.20240 + 1.00894i) q^{74} +(1.32586 + 1.11449i) q^{75} +(-0.369276 - 2.09427i) q^{76} +(-5.82458 + 4.88740i) q^{77} +(-1.05230 - 1.82628i) q^{78} +(12.1133 - 4.40888i) q^{79} -3.46510 q^{80} +(-4.47302 - 7.80974i) q^{81} +0.227746 q^{82} +(-7.43037 + 2.70443i) q^{83} +(-7.08254 - 12.2918i) q^{84} +(2.99086 - 2.50963i) q^{85} +(-0.376657 - 2.13613i) q^{86} +(0.793324 + 0.666848i) q^{87} +(-1.59718 - 1.34019i) q^{88} +(1.62783 - 2.81949i) q^{89} +(-0.902576 - 0.00156056i) q^{90} +(8.67483 + 15.0252i) q^{91} +(-2.86005 + 16.2201i) q^{92} +(-2.65036 - 0.967248i) q^{93} +(3.32160 + 1.20896i) q^{94} +(1.04653 + 0.380904i) q^{95} +(4.50773 - 3.77580i) q^{96} +(-0.345856 + 1.96145i) q^{97} +(-1.71470 - 2.96995i) q^{98} +(4.06782 + 3.42530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + 3 q^{13} - 9 q^{14} - 6 q^{15} + 12 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{19} - 36 q^{21} - 51 q^{22} + 18 q^{23} + 45 q^{24} - 18 q^{26} - 9 q^{27} - 60 q^{28} + 18 q^{29} - 3 q^{30} + 12 q^{31} + 36 q^{32} + 27 q^{33} - 69 q^{34} - 12 q^{35} - 42 q^{36} + 24 q^{37} - 24 q^{38} + 6 q^{39} + 9 q^{40} - 75 q^{41} - 18 q^{42} + 6 q^{43} + 12 q^{44} - 6 q^{45} + 30 q^{46} + 45 q^{47} - 27 q^{48} - 36 q^{49} + 21 q^{51} + 30 q^{52} + 36 q^{53} + 18 q^{54} + 30 q^{56} + 30 q^{57} + 27 q^{58} - 27 q^{59} - 12 q^{61} + 36 q^{62} + 18 q^{63} + 27 q^{64} + 6 q^{65} + 78 q^{66} - 30 q^{67} + 69 q^{68} - 117 q^{69} + 27 q^{70} + 12 q^{71} + 9 q^{72} + 21 q^{73} - 30 q^{76} - 36 q^{77} + 66 q^{78} + 54 q^{79} + 6 q^{80} - 27 q^{81} - 48 q^{82} - 87 q^{83} + 45 q^{84} + 27 q^{85} + 18 q^{86} - 27 q^{87} - 18 q^{88} + 9 q^{89} - 6 q^{90} + 51 q^{91} + 24 q^{92} + 36 q^{93} + 15 q^{94} + 21 q^{95} - 15 q^{96} - 75 q^{97} - 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + 3 * q^13 - 9 * q^14 - 6 * q^15 + 12 * q^16 - 12 * q^17 + 6 * q^18 + 24 * q^19 - 36 * q^21 - 51 * q^22 + 18 * q^23 + 45 * q^24 - 18 * q^26 - 9 * q^27 - 60 * q^28 + 18 * q^29 - 3 * q^30 + 12 * q^31 + 36 * q^32 + 27 * q^33 - 69 * q^34 - 12 * q^35 - 42 * q^36 + 24 * q^37 - 24 * q^38 + 6 * q^39 + 9 * q^40 - 75 * q^41 - 18 * q^42 + 6 * q^43 + 12 * q^44 - 6 * q^45 + 30 * q^46 + 45 * q^47 - 27 * q^48 - 36 * q^49 + 21 * q^51 + 30 * q^52 + 36 * q^53 + 18 * q^54 + 30 * q^56 + 30 * q^57 + 27 * q^58 - 27 * q^59 - 12 * q^61 + 36 * q^62 + 18 * q^63 + 27 * q^64 + 6 * q^65 + 78 * q^66 - 30 * q^67 + 69 * q^68 - 117 * q^69 + 27 * q^70 + 12 * q^71 + 9 * q^72 + 21 * q^73 - 30 * q^76 - 36 * q^77 + 66 * q^78 + 54 * q^79 + 6 * q^80 - 27 * q^81 - 48 * q^82 - 87 * q^83 + 45 * q^84 + 27 * q^85 + 18 * q^86 - 27 * q^87 - 18 * q^88 + 9 * q^89 - 6 * q^90 + 51 * q^91 + 24 * q^92 + 36 * q^93 + 15 * q^94 + 21 * q^95 - 15 * q^96 - 75 * q^97 - 15 * q^98 + 123 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	−0.282715	+	0.102900i	−0.199910	+	0.0727612i	−0.440035	−	0.897981i	$-0.645034\pi$
$2$	−0.282715	+	0.102900i	−0.199910	+	0.0727612i	0.240125	+	0.970742i	$0.422812\pi$
$3$	−0.864728	−	1.50075i	−0.499251	−	0.866457i
$3$	−0.864728	−	1.50075i	−0.499251	−	0.866457i
$4$	−1.46275	+	1.22739i	−0.731375	+	0.613696i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	0.398898	+	0.335304i	0.162850	+	0.136887i
$7$	−3.28585	−	2.75715i	−1.24193	−	1.04211i	−0.997370	−	0.0724727i	$-0.976911\pi$
$7$	−3.28585	−	2.75715i	−1.24193	−	1.04211i	−0.244563	−	0.969633i	$-0.578645\pi$
$8$	0.588102	−	1.01862i	0.207925	−	0.360137i
$9$	−1.50449	+	2.59548i	−0.501497	+	0.865160i
$10$	0.150430	+	0.260552i	0.0475700	+	0.0823936i
$11$	0.307813	−	1.74570i	0.0928092	−	0.526347i	−0.902587	−	0.430506i	$-0.858335\pi$
$11$	0.307813	−	1.74570i	0.0928092	−	0.526347i	0.995397	−	0.0958407i	$-0.0305539\pi$
$12$	3.10689	+	1.13386i	0.896881	+	0.327316i
$13$	−3.80087	−	1.38340i	−1.05417	−	0.383687i	−0.243937	−	0.969791i	$-0.578439\pi$
$13$	−3.80087	−	1.38340i	−1.05417	−	0.383687i	−0.810236	+	0.586104i	$0.800661\pi$
$14$	1.21267	+	0.441375i	0.324099	+	0.117963i
$15$	−1.32779	+	1.11219i	−0.342834	+	0.287167i
$16$	0.601708	−	3.41245i	0.150427	−	0.853113i
$17$	1.95214	+	3.38121i	0.473464	+	0.820064i	0.999539	−	0.0303747i	$-0.00967005\pi$
$17$	1.95214	+	3.38121i	0.473464	+	0.820064i	−0.526075	+	0.850438i	$0.676337\pi$
$18$	0.158267	−	0.888593i	0.0373040	−	0.209443i
$19$	−0.556845	+	0.964484i	−0.127749	+	0.221268i	−0.922804	−	0.385269i	$-0.874109\pi$
$19$	−0.556845	+	0.964484i	−0.127749	+	0.221268i	0.795055	+	0.606537i	$0.207442\pi$
$20$	1.46275	+	1.22739i	0.327081	+	0.274453i
$21$	−1.29643	+	7.31542i	−0.282904	+	1.59636i
$22$	0.0926084	+	0.525208i	0.0197442	+	0.111975i
$23$	6.60755	−	5.54440i	1.37777	−	1.15609i	0.407741	−	0.913098i	$-0.366317\pi$
$23$	6.60755	−	5.54440i	1.37777	−	1.15609i	0.970029	−	0.242989i	$-0.0781278\pi$
$24$	−2.03724	−	0.00176120i	−0.415851	−	0.000359503i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	1.21692			0.238657
$27$	5.19613	+	0.0134762i	0.999997	+	0.00259350i
$28$	8.19048			1.54786
$29$	−0.562260	+	0.204646i	−0.104409	+	0.0380018i	−0.393696	−	0.919240i	$-0.628804\pi$
$29$	−0.562260	+	0.204646i	−0.104409	+	0.0380018i	0.289287	+	0.957242i	$0.406582\pi$
$30$	0.260942	−	0.451063i	0.0476412	−	0.0823525i
$31$	1.24781	−	1.04704i	0.224114	−	0.188054i	−0.523816	−	0.851831i	$-0.675492\pi$
$31$	1.24781	−	1.04704i	0.224114	−	0.188054i	0.747930	+	0.663777i	$0.231048\pi$
$32$	0.589520	+	3.34334i	0.104213	+	0.591024i
$33$	−2.88602	+	1.04760i	−0.502392	+	0.182364i
$34$	−0.899826	−	0.755043i	−0.154319	−	0.129489i
$35$	−2.14468	+	3.71470i	−0.362518	+	0.627899i
$36$	−0.984980	−	5.64313i	−0.164163	−	0.940522i
$37$	−2.60857	−	4.51818i	−0.428847	−	0.742785i	0.567924	−	0.823081i	$-0.307747\pi$
$37$	−2.60857	−	4.51818i	−0.428847	−	0.742785i	−0.996771	+	0.0802963i	$0.974413\pi$
$38$	0.0581832	−	0.329973i	0.00943856	−	0.0535287i
$39$	1.21058	+	6.90042i	0.193848	+	1.10495i
$40$	−1.10527	−	0.402285i	−0.174758	−	0.0636069i
$41$	−0.711333	−	0.258904i	−0.111092	−	0.0404340i	0.285876	−	0.958267i	$-0.407715\pi$
$41$	−0.711333	−	0.258904i	−0.111092	−	0.0404340i	−0.396968	+	0.917833i	$0.629938\pi$
$42$	−0.386236	−	2.20158i	−0.0595975	−	0.339711i
$43$	−1.25194	+	7.10010i	−0.190919	+	1.08276i	0.727193	+	0.686434i	$0.240825\pi$
$43$	−1.25194	+	7.10010i	−0.190919	+	1.08276i	−0.918112	+	0.396322i	$0.870286\pi$
$44$	1.69240	+	2.93132i	0.255139	+	0.441914i
$45$	2.81730	+	1.03093i	0.419978	+	0.153682i
$46$	−1.29754	+	2.24740i	−0.191311	+	0.331361i
$47$	−9.00022	−	7.55208i	−1.31282	−	1.10158i	−0.987775	−	0.155884i	$-0.950177\pi$
$47$	−9.00022	−	7.55208i	−1.31282	−	1.10158i	−0.325041	−	0.945700i	$-0.605378\pi$
$48$	−5.64155	+	2.04783i	−0.814287	+	0.295579i
$49$	1.97936	+	11.2255i	0.282766	+	1.60365i
$50$	0.230471	−	0.193388i	0.0325936	−	0.0273493i
$51$	3.38627	−	5.85350i	0.474173	−	0.819654i
$52$	7.25771	−	2.64159i	1.00646	−	0.366323i
$53$	3.97724			0.546316			0.273158	−	0.961969i	$-0.411932\pi$
$53$	3.97724			0.546316			0.273158	+	0.961969i	$0.411932\pi$
$54$	−1.47041	+	0.530872i	−0.200098	+	0.0722425i
$55$	−1.77263			−0.239021
$56$	−4.74091	+	1.72555i	−0.633531	+	0.230586i
$57$	1.92897	+	0.00166759i	0.255498	+	0.000220878i
$58$	0.137901	−	0.115713i	0.0181073	−	0.0151939i
$59$	−2.39974	−	13.6096i	−0.312419	−	1.77182i	−0.586339	−	0.810066i	$-0.699431\pi$
$59$	−2.39974	−	13.6096i	−0.312419	−	1.77182i	0.273919	−	0.961753i	$-0.411680\pi$
$60$	0.577126	−	3.25658i	0.0745067	−	0.420423i
$61$	−6.49619	−	5.45095i	−0.831752	−	0.697923i	0.123940	−	0.992290i	$-0.460447\pi$
$61$	−6.49619	−	5.45095i	−0.831752	−	0.697923i	−0.955693	+	0.294366i	$0.904891\pi$
$62$	−0.245035	+	0.424413i	−0.0311195	+	0.0539006i
$63$	12.0997	−	4.38024i	1.52441	−	0.551858i
$64$	2.95440	+	5.11717i	0.369300	+	0.639647i
$65$	−0.702373	+	3.98336i	−0.0871187	+	0.494074i
$66$	0.708124	−	0.593144i	0.0871641	−	0.0730110i
$67$	−7.36217	−	2.67961i	−0.899432	−	0.327367i	−0.149407	−	0.988776i	$-0.547736\pi$
$67$	−7.36217	−	2.67961i	−0.899432	−	0.327367i	−0.750025	+	0.661409i	$0.769959\pi$
$68$	−7.00557	−	2.54982i	−0.849550	−	0.309211i
$69$	−14.0345	−	5.12188i	−1.68955	−	0.616602i
$70$	0.224092	−	1.27089i	0.0267841	−	0.151900i
$71$	2.59176	+	4.48907i	0.307586	+	0.532754i	0.977834	−	0.209383i	$-0.0671456\pi$
$71$	2.59176	+	4.48907i	0.307586	+	0.532754i	−0.670248	+	0.742137i	$0.733812\pi$
$72$	1.75902	+	3.05891i	0.207302	+	0.360496i
$73$	2.18764	−	3.78911i	0.256044	−	0.443481i	−0.709135	−	0.705073i	$-0.750914\pi$
$73$	2.18764	−	3.78911i	0.256044	−	0.443481i	0.965179	+	0.261592i	$0.0842474\pi$
$74$	1.20240	+	1.00894i	0.139777	+	0.117286i
$75$	1.32586	+	1.11449i	0.153098	+	0.128690i
$76$	−0.369276	−	2.09427i	−0.0423588	−	0.240229i
$77$	−5.82458	+	4.88740i	−0.663772	+	0.556971i
$78$	−1.05230	−	1.82628i	−0.119150	−	0.206786i
$79$	12.1133	−	4.40888i	1.36285	−	0.496038i	0.445917	−	0.895074i	$-0.352877\pi$
$79$	12.1133	−	4.40888i	1.36285	−	0.496038i	0.916935	+	0.399036i	$0.130655\pi$
$80$	−3.46510			−0.387410
$81$	−4.47302	−	7.80974i	−0.497002	−	0.867749i
$82$	0.227746			0.0251503
$83$	−7.43037	+	2.70443i	−0.815589	+	0.296850i	−0.715930	−	0.698172i	$-0.753997\pi$
$83$	−7.43037	+	2.70443i	−0.815589	+	0.296850i	−0.0996585	+	0.995022i	$0.531775\pi$
$84$	−7.08254	−	12.2918i	−0.772769	−	1.34115i
$85$	2.99086	−	2.50963i	0.324404	−	0.272207i
$86$	−0.376657	−	2.13613i	−0.0406160	−	0.230345i
$87$	0.793324	+	0.666848i	0.0850533	+	0.0714936i
$88$	−1.59718	−	1.34019i	−0.170260	−	0.142865i
$89$	1.62783	−	2.81949i	0.172550	−	0.298865i	−0.766761	−	0.641933i	$-0.778133\pi$
$89$	1.62783	−	2.81949i	0.172550	−	0.298865i	0.939311	+	0.343068i	$0.111466\pi$
$90$	−0.902576	−	0.00156056i	−0.0951398	−	0.000164497i
$91$	8.67483	+	15.0252i	0.909369	+	1.57507i
$92$	−2.86005	+	16.2201i	−0.298180	+	1.69106i
$93$	−2.65036	−	0.967248i	−0.274830	−	0.100299i
$94$	3.32160	+	1.20896i	0.342597	+	0.124695i
$95$	1.04653	+	0.380904i	0.107371	+	0.0390800i
$96$	4.50773	−	3.77580i	0.460068	−	0.385366i
$97$	−0.345856	+	1.96145i	−0.0351164	+	0.199155i	−0.997319	−	0.0731807i	$-0.976685\pi$
$97$	−0.345856	+	1.96145i	−0.0351164	+	0.199155i	0.962202	+	0.272336i	$0.0877961\pi$
$98$	−1.71470	−	2.96995i	−0.173211	−	0.300010i
$99$	4.06782	+	3.42530i	0.408831	+	0.344256i
$100$	0.954742	−	1.65366i	0.0954742	−	0.165366i
$101$	7.02258	+	5.89264i	0.698773	+	0.586340i	0.921424	−	0.388558i	$-0.127027\pi$
$101$	7.02258	+	5.89264i	0.698773	+	0.586340i	−0.222652	+	0.974898i	$0.571471\pi$
$102$	−0.355025	+	2.00332i	−0.0351527	+	0.198358i
$103$	0.314812	+	1.78539i	0.0310193	+	0.175919i	0.996381	−	0.0849945i	$-0.0270873\pi$
$103$	0.314812	+	1.78539i	0.0310193	+	0.175919i	−0.965362	+	0.260914i	$0.915976\pi$
$104$	−3.64447	+	3.05807i	−0.357369	+	0.299869i
$105$	7.42940	+	0.00642272i	0.725035	+	0.000626794i
$106$	−1.12442	+	0.409257i	−0.109214	+	0.0397506i
$107$	3.71297			0.358946			0.179473	−	0.983763i	$-0.442561\pi$
$107$	3.71297			0.358946			0.179473	+	0.983763i	$0.442561\pi$
$108$	−7.61718	+	6.35799i	−0.732964	+	0.611797i
$109$	−3.24138			−0.310468			−0.155234	−	0.987878i	$-0.549613\pi$
$109$	−3.24138			−0.310468			−0.155234	+	0.987878i	$0.549613\pi$
$110$	0.501148	−	0.182403i	0.0477826	−	0.0173914i
$111$	−4.52495	+	7.82181i	−0.429489	+	0.742414i
$112$	−11.3858	+	9.55380i	−1.07585	+	0.902749i
$113$	2.13575	+	12.1124i	0.200914	+	1.13944i	0.903741	+	0.428080i	$0.140810\pi$
$113$	2.13575	+	12.1124i	0.200914	+	1.13944i	−0.702827	+	0.711361i	$0.748079\pi$
$114$	−0.545520	+	0.198019i	−0.0510926	+	0.0185462i
$115$	−6.60755	−	5.54440i	−0.616157	−	0.517018i
$116$	0.571265	−	0.989460i	0.0530406	−	0.0918690i
$117$	9.30897	−	7.78377i	0.860615	−	0.719610i
$118$	2.07887	+	3.60070i	0.191375	+	0.331472i
$119$	2.90807	−	16.4925i	0.266583	−	1.51186i
$120$	0.352029	+	2.00660i	0.0321357	+	0.183177i
$121$	7.38391	+	2.68752i	0.671265	+	0.244320i
$122$	2.39747	+	0.872609i	0.217057	+	0.0790023i
$123$	0.226560	+	1.29141i	0.0204282	+	0.116443i
$124$	−0.540109	+	3.06311i	−0.0485033	+	0.275076i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−2.97003	+	2.48341i	−0.264591	+	0.221240i
$127$	5.50593	−	9.53655i	0.488572	−	0.846232i	−0.511341	−	0.859378i	$-0.670851\pi$
$127$	5.50593	−	9.53655i	0.488572	−	0.846232i	0.999914	+	0.0131457i	$0.00418454\pi$
$128$	−6.56312	−	5.50711i	−0.580103	−	0.486764i
$129$	11.7381	−	4.26081i	1.03348	−	0.375144i
$130$	−0.211315	−	1.19843i	−0.0185336	−	0.105109i
$131$	13.4406	−	11.2780i	1.17431	−	0.985361i	0.174307	−	0.984691i	$-0.444231\pi$
$131$	13.4406	−	11.2780i	1.17431	−	0.985361i	1.00000		0.000669520i	$-0.000213115\pi$
$132$	2.93571	−	5.07467i	0.255521	−	0.441693i
$133$	4.48894	−	1.63384i	0.389240	−	0.141672i
$134$	2.35713			0.203625
$135$	−0.889028	−	5.11953i	−0.0765153	−	0.440619i
$136$	4.59223			0.393781
$137$	−0.335210	+	0.122007i	−0.0286389	+	0.0104237i	−0.356300	−	0.934372i	$-0.615962\pi$
$137$	−0.335210	+	0.122007i	−0.0286389	+	0.0104237i	0.327661	+	0.944795i	$0.393740\pi$
$138$	4.49480	+	0.00388575i	0.382623	+	0.000330777i
$139$	−1.14234	+	0.958535i	−0.0968918	+	0.0813019i	−0.689947	−	0.723860i	$-0.742366\pi$
$139$	−1.14234	+	0.958535i	−0.0968918	+	0.0813019i	0.593055	+	0.805162i	$0.297922\pi$
$140$	−1.42226	−	8.06605i	−0.120203	−	0.681706i
$141$	−3.55102	+	20.0376i	−0.299050	+	1.68747i
$142$	−1.19465	−	1.00243i	−0.100253	−	0.0841224i
$143$	−3.58496	+	6.20934i	−0.299790	+	0.519251i
$144$	7.95169	+	6.69572i	0.662641	+	0.557977i
$145$	0.299172	+	0.518182i	0.0248449	+	0.0430326i
$146$	−0.228581	+	1.29635i	−0.0189175	+	0.107286i
$147$	15.1351	−	12.6775i	1.24832	−	1.04563i
$148$	9.36127	+	3.40722i	0.769492	+	0.280072i
$149$	17.0077	+	6.19029i	1.39332	+	0.507128i	0.926190	−	0.377058i	$-0.123064\pi$
$149$	17.0077	+	6.19029i	1.39332	+	0.507128i	0.467134	+	0.884186i	$0.345286\pi$
$150$	−0.489522	−	0.178651i	−0.0399693	−	0.0145868i
$151$	−3.68305	+	20.8876i	−0.299723	+	1.69981i	0.347638	+	0.937629i	$0.386984\pi$
$151$	−3.68305	+	20.8876i	−0.299723	+	1.69981i	−0.647361	+	0.762183i	$0.724127\pi$
$152$	0.654963	+	1.13443i	0.0531245	+	0.0920144i
$153$	−11.7128	−	0.0202515i	−0.946927	−	0.00163724i
$154$	1.14378	−	1.98109i	0.0921687	−	0.159641i
$155$	−1.24781	−	1.04704i	−0.100227	−	0.0841002i
$156$	−10.2403	−	8.60773i	−0.819881	−	0.689170i
$157$	−0.950859	−	5.39259i	−0.0758868	−	0.430375i	−0.998954	−	0.0457357i	$-0.985437\pi$
$157$	−0.950859	−	5.39259i	−0.0758868	−	0.430375i	0.923067	−	0.384640i	$-0.125674\pi$
$158$	−2.97094	+	2.49291i	−0.236355	+	0.198326i
$159$	−3.43923	−	5.96883i	−0.272749	−	0.473359i
$160$	3.19017	−	1.16113i	0.252205	−	0.0917953i
$161$	−36.9982			−2.91586
$162$	2.06821	+	1.74766i	0.162494	+	0.137309i
$163$	−17.9869			−1.40884			−0.704420	−	0.709783i	$-0.748793\pi$
$163$	−17.9869			−1.40884			−0.704420	+	0.709783i	$0.748793\pi$
$164$	1.35828	−	0.494373i	0.106064	−	0.0386040i
$165$	1.53284	+	2.66027i	0.119331	+	0.207101i
$166$	1.82239	−	1.52917i	0.141445	−	0.118686i
$167$	3.46215	+	19.6348i	0.267909	+	1.51939i	0.760620	+	0.649197i	$0.224895\pi$
$167$	3.46215	+	19.6348i	0.267909	+	1.51939i	−0.492711	+	0.870193i	$0.663994\pi$
$168$	6.68922	+	5.62278i	0.516084	+	0.433807i
$169$	2.57425	+	2.16006i	0.198019	+	0.166158i
$170$	−0.587320	+	1.01727i	−0.0450454	+	0.0780208i
$171$	−1.66553	−	2.89634i	−0.127366	−	0.221488i
$172$	−6.88334	−	11.9223i	−0.524850	−	0.909066i
$173$	1.17486	−	6.66294i	0.0893226	−	0.506574i	−0.907017	−	0.421094i	$-0.861646\pi$
$173$	1.17486	−	6.66294i	0.0893226	−	0.506574i	0.996340	−	0.0854803i	$-0.0272425\pi$
$174$	−0.292903	−	0.106895i	−0.0222049	−	0.00810368i
$175$	4.03069	+	1.46705i	0.304691	+	0.110899i
$176$	−5.77189	−	2.10080i	−0.435073	−	0.158354i
$177$	−18.3495	+	15.3700i	−1.37923	+	1.15528i
$178$	−0.170088	+	0.964615i	−0.0127486	+	0.0723009i
$179$	−4.71985	−	8.17503i	−0.352778	−	0.611030i	0.633957	−	0.773369i	$-0.281430\pi$
$179$	−4.71985	−	8.17503i	−0.352778	−	0.611030i	−0.986735	+	0.162338i	$0.948096\pi$
$180$	−5.38636	+	1.94994i	−0.401476	+	0.145340i
$181$	−0.566202	+	0.980691i	−0.0420855	+	0.0728942i	−0.886301	−	0.463110i	$-0.846734\pi$
$181$	−0.566202	+	0.980691i	−0.0420855	+	0.0728942i	0.844215	+	0.536004i	$0.180067\pi$
$182$	−3.99860	−	3.35522i	−0.296396	−	0.248706i
$183$	−2.56307	+	14.4627i	−0.189467	+	1.06912i
$184$	−1.76173	−	9.99127i	−0.129876	−	0.736566i
$185$	−3.99657	+	3.35352i	−0.293833	+	0.246556i
$186$	0.848827		0.000733811i	0.0622390		5.38056e-5i
$187$	6.50346	−	2.36707i	0.475580	−	0.173097i
$188$	22.4344			1.63620
$189$	−17.0366	−	14.3708i	−1.23923	−	1.04532i
$190$	−0.335064			−0.0243081
$191$	22.1994	−	8.07991i	1.60629	−	0.584642i	0.625588	−	0.780153i	$-0.284859\pi$
$191$	22.1994	−	8.07991i	1.60629	−	0.584642i	0.980701	+	0.195512i	$0.0626368\pi$
$192$	5.12483	−	8.85878i	0.369853	−	0.639327i
$193$	−2.08055	+	1.74579i	−0.149761	+	0.125665i	−0.714590	−	0.699544i	$-0.753387\pi$
$193$	−2.08055	+	1.74579i	−0.149761	+	0.125665i	0.564829	+	0.825208i	$0.308942\pi$
$194$	−0.104054	−	0.590120i	−0.00747064	−	0.0423681i
$195$	6.58538	−	2.39044i	0.471589	−	0.171183i
$196$	−16.6734	−	13.9907i	−1.19096	−	0.999333i
$197$	7.13716	−	12.3619i	0.508501	−	0.880750i	−0.491450	−	0.870906i	$-0.663533\pi$
$197$	7.13716	−	12.3619i	0.508501	−	0.880750i	0.999952	−	0.00984437i	$-0.00313361\pi$
$198$	−1.50250	−	0.549807i	−0.106778	−	0.0390731i
$199$	−10.6351	−	18.4206i	−0.753905	−	1.30580i	−0.945917	−	0.324409i	$-0.894835\pi$
$199$	−10.6351	−	18.4206i	−0.753905	−	1.30580i	0.192012	−	0.981393i	$-0.438499\pi$
$200$	−0.204246	+	1.15833i	−0.0144423	+	0.0819066i
$201$	2.34486	+	13.3659i	0.165393	+	0.942758i
$202$	−2.59174	−	0.943316i	−0.182354	−	0.0663715i
$203$	2.41174	+	0.877802i	0.169271	+	0.0616096i
$204$	2.23128	+	12.7185i	0.156221	+	0.890472i
$205$	−0.131449	+	0.745484i	−0.00918080	+	0.0520669i
$206$	−0.272718	−	0.472361i	−0.0190012	−	0.0329110i
$207$	4.44936	+	25.4913i	0.309252	+	1.77176i
$208$	−7.00782	+	12.1379i	−0.485905	+	0.841612i
$209$	1.51229	+	1.26896i	0.104607	+	0.0877760i
$210$	−2.10106	+	0.762669i	−0.144987	+	0.0526291i
$211$	−3.49805	−	19.8384i	−0.240815	−	1.36573i	−0.830013	−	0.557743i	$-0.811667\pi$
$211$	−3.49805	−	19.8384i	−0.240815	−	1.36573i	0.589198	−	0.807989i	$-0.299444\pi$
$212$	−5.81770	+	4.88163i	−0.399562	+	0.335272i
$213$	4.49579	−	7.77141i	0.308046	−	0.532488i
$214$	−1.04971	+	0.382064i	−0.0717568	+	0.0261173i
$215$	7.20963			0.491693
$216$	3.06958	−	5.28497i	0.208859	−	0.359597i
$217$	−6.98697			−0.474306
$218$	0.916386	−	0.333537i	0.0620655	−	0.0225900i
$219$	−7.57821	−	0.00655137i	−0.512088	−	0.000442700i
$220$	2.59291	−	2.17571i	0.174814	−	0.146686i
$221$	−2.74226	−	15.5522i	−0.184465	−	1.04615i
$222$	0.474407	−	2.67696i	0.0318401	−	0.179666i
$223$	−4.43003	−	3.71723i	−0.296657	−	0.248924i	0.482294	−	0.876009i	$-0.339804\pi$
$223$	−4.43003	−	3.71723i	−0.296657	−	0.248924i	−0.778951	+	0.627085i	$0.784248\pi$
$224$	7.28102	−	12.6111i	0.486483	−	0.842614i
$225$	0.526052	−	2.95352i	0.0350701	−	0.196901i
$226$	−1.85017	−	3.20460i	−0.123072	−	0.213167i
$227$	2.65839	−	15.0765i	0.176443	−	1.00066i	−0.760021	−	0.649898i	$-0.774812\pi$
$227$	2.65839	−	15.0765i	0.176443	−	1.00066i	0.936465	−	0.350762i	$-0.114077\pi$
$228$	−2.82364	+	2.36516i	−0.187000	+	0.156637i
$229$	−2.31831	−	0.843797i	−0.153198	−	0.0557596i	0.264283	−	0.964445i	$-0.414865\pi$
$229$	−2.31831	−	0.843797i	−0.153198	−	0.0557596i	−0.417481	+	0.908686i	$0.637087\pi$
$230$	2.43857	+	0.887567i	0.160795	+	0.0585245i
$231$	12.3714	+	4.51495i	0.813981	+	0.297062i
$232$	−0.122209	+	0.693083i	−0.00802343	+	0.0455031i
$233$	−4.21427	−	7.29932i	−0.276086	−	0.478195i	0.694323	−	0.719664i	$-0.255704\pi$
$233$	−4.21427	−	7.29932i	−0.276086	−	0.478195i	−0.970408	+	0.241469i	$0.922371\pi$
$234$	−1.83084	+	3.15848i	−0.119686	+	0.206476i
$235$	−5.87447	+	10.1749i	−0.383208	+	0.663736i
$236$	20.2145	+	16.9620i	1.31585	+	1.10413i
$237$	−17.0913	−	14.3665i	−1.11020	−	0.933206i
$238$	0.874920	+	4.96192i	0.0567126	+	0.321633i
$239$	−11.6818	+	9.80219i	−0.755633	+	0.634051i	−0.936986	−	0.349367i	$-0.886397\pi$
$239$	−11.6818	+	9.80219i	−0.755633	+	0.634051i	0.181353	+	0.983418i	$0.441952\pi$
$240$	2.99637	+	5.20024i	0.193415	+	0.335674i
$241$	0.611555	−	0.222588i	0.0393937	−	0.0143381i	−0.322248	−	0.946655i	$-0.604439\pi$
$241$	0.611555	−	0.222588i	0.0393937	−	0.0143381i	0.361642	+	0.932317i	$0.382216\pi$
$242$	−2.36409			−0.151969
$243$	−7.85251	+	13.4662i	−0.503739	+	0.863856i
$244$	16.1928			1.03664
$245$	10.7113	−	3.89858i	0.684318	−	0.249071i
$246$	−0.196938	−	0.341789i	−0.0125563	−	0.0217917i
$247$	3.45077	−	2.89554i	0.219567	−	0.184239i
$248$	−0.332696	−	1.88682i	−0.0211262	−	0.119813i
$249$	10.4839	+	8.81251i	0.664392	+	0.558470i
$250$	−0.230471	−	0.193388i	−0.0145763	−	0.0122310i
$251$	−3.07930	+	5.33350i	−0.194364	+	0.336648i	−0.946692	−	0.322141i	$-0.895597\pi$
$251$	−3.07930	+	5.33350i	−0.194364	+	0.336648i	0.752328	+	0.658789i	$0.228931\pi$
$252$	−12.3225	+	21.2582i	−0.776244	+	1.33914i
$253$	−7.64494	−	13.2414i	−0.480633	−	0.832481i
$254$	−0.575299	+	3.26268i	−0.0360975	+	0.204719i
$255$	−6.35259	−	2.31838i	−0.397815	−	0.145182i
$256$	−8.68274	−	3.16026i	−0.542672	−	0.197516i
$257$	−6.58933	−	2.39832i	−0.411031	−	0.149603i	0.128225	−	0.991745i	$-0.459072\pi$
$257$	−6.58933	−	2.39832i	−0.411031	−	0.149603i	−0.539256	+	0.842142i	$0.681294\pi$
$258$	−2.88009	+	2.41244i	−0.179306	+	0.150192i
$259$	−3.88595	+	22.0383i	−0.241461	+	1.36939i
$260$	−3.86175	−	6.68874i	−0.239495	−	0.414818i
$261$	0.314760	−	1.76722i	0.0194832	−	0.109388i
$262$	−2.63935	+	4.57148i	−0.163059	+	0.282427i
$263$	14.9017	+	12.5040i	0.918880	+	0.771032i	0.973788	−	0.227459i	$-0.0730419\pi$
$263$	14.9017	+	12.5040i	0.918880	+	0.771032i	−0.0549074	+	0.998491i	$0.517486\pi$
$264$	−0.630165	+	3.55587i	−0.0387840	+	0.218848i
$265$	−0.690640	−	3.91682i	−0.0424257	−	0.240608i
$266$	−1.10097	+	0.923822i	−0.0675047	+	0.0566432i
$267$	−5.63897	−	0.00487489i	−0.345099	−	0.000298339i
$268$	14.0579	−	5.11667i	0.858726	−	0.312551i
$269$	10.1856			0.621026			0.310513	−	0.950569i	$-0.399499\pi$
$269$	10.1856			0.621026			0.310513	+	0.950569i	$0.399499\pi$
$270$	0.778141	+	1.35589i	0.0473561	+	0.0825167i
$271$	−6.87083			−0.417373			−0.208687	−	0.977983i	$-0.566919\pi$
$271$	−6.87083			−0.417373			−0.208687	+	0.977983i	$0.566919\pi$
$272$	12.7128	−	4.62710i	0.770829	−	0.280559i
$273$	15.0477	−	26.0115i	0.910731	−	1.57429i
$274$	0.0822145	−	0.0689862i	0.00496676	−	0.00416761i
$275$	0.307813	+	1.74570i	0.0185618	+	0.105269i
$276$	26.8155	−	9.73379i	1.61410	−	0.585905i
$277$	20.3488	+	17.0747i	1.22264	+	1.02592i	0.998682	+	0.0513192i	$0.0163426\pi$
$277$	20.3488	+	17.0747i	1.22264	+	1.02592i	0.223959	+	0.974599i	$0.428102\pi$
$278$	0.224323	−	0.388539i	0.0134540	−	0.0233030i
$279$	0.840247	+	4.81393i	0.0503042	+	0.288203i
$280$	2.52259	+	4.36925i	0.150753	+	0.261112i
$281$	−4.15446	+	23.5611i	−0.247834	+	1.40554i	0.565983	+	0.824417i	$0.308497\pi$
$281$	−4.15446	+	23.5611i	−0.247834	+	1.40554i	−0.813817	+	0.581121i	$0.802614\pi$
$282$	−1.05793	−	6.03032i	−0.0629990	−	0.359100i
$283$	12.6874	+	4.61782i	0.754186	+	0.274501i	0.690366	−	0.723460i	$-0.257450\pi$
$283$	12.6874	+	4.61782i	0.754186	+	0.274501i	0.0638197	+	0.997961i	$0.479672\pi$
$284$	−9.30095	−	3.38527i	−0.551910	−	0.200879i
$285$	−0.333319	−	1.89995i	−0.0197441	−	0.112543i
$286$	0.374583	−	2.12437i	0.0221496	−	0.125616i
$287$	1.62349	+	2.81197i	0.0958318	+	0.165985i
$288$	−9.56448	−	3.49993i	−0.563593	−	0.206235i
$289$	0.878281	−	1.52123i	0.0516636	−	0.0894840i
$290$	−0.137901	−	0.115713i	−0.00809784	−	0.00679490i
$291$	3.24271	−	1.17708i	0.190091	−	0.0690015i
$292$	1.45075	+	8.22761i	0.0848987	+	0.481484i
$293$	−4.22408	+	3.54442i	−0.246773	+	0.207067i	−0.757781	−	0.652508i	$-0.773717\pi$
$293$	−4.22408	+	3.54442i	−0.246773	+	0.207067i	0.511008	+	0.859576i	$0.329272\pi$
$294$	−2.97439	+	5.14153i	−0.173470	+	0.299860i
$295$	−12.9861	+	4.72656i	−0.756082	+	0.275191i
$296$	−6.13643			−0.356673
$297$	1.62296	−	9.06672i	0.0941740	−	0.526105i
$298$	−5.44531			−0.315438
$299$	−32.7846	+	11.9326i	−1.89598	+	0.690082i
$300$	−3.30732	−	0.00285918i	−0.190948	−	0.000165075i
$301$	23.6898	−	19.8781i	1.36545	−	1.14575i
$302$	−1.10808	−	6.28424i	−0.0637628	−	0.361617i
$303$	2.77075	−	15.6347i	0.159175	−	0.898187i
$304$	2.95620	+	2.48055i	0.169550	+	0.142269i
$305$	−4.24009	+	7.34405i	−0.242787	+	0.420519i
$306$	3.31348	−	1.19952i	0.189419	−	0.0685722i
$307$	−2.38360	−	4.12852i	−0.136039	−	0.235627i	0.789955	−	0.613165i	$-0.210104\pi$
$307$	−2.38360	−	4.12852i	−0.136039	−	0.235627i	−0.925994	+	0.377538i	$0.876771\pi$
$308$	2.52114	−	14.2981i	0.143655	−	0.814709i
$309$	2.40719	−	2.01633i	0.136940	−	0.114705i
$310$	0.460516	+	0.167614i	0.0261555	+	0.00951983i
$311$	−10.2196	−	3.71963i	−0.579500	−	0.210921i	0.0356051	−	0.999366i	$-0.488664\pi$
$311$	−10.2196	−	3.71963i	−0.579500	−	0.210921i	−0.615105	+	0.788445i	$0.710886\pi$
$312$	7.74087	+	2.82503i	0.438240	+	0.159936i
$313$	−2.15639	+	12.2295i	−0.121887	+	0.691253i	0.861222	+	0.508229i	$0.169700\pi$
$313$	−2.15639	+	12.2295i	−0.121887	+	0.691253i	−0.983108	+	0.183024i	$0.941411\pi$
$314$	0.823719	+	1.42672i	0.0464851	+	0.0805146i
$315$	−6.41478	−	11.1552i	−0.361432	−	0.628525i
$316$	−12.3073	+	21.3169i	−0.692339	+	1.19917i
$317$	−8.45181	−	7.09191i	−0.474701	−	0.398321i	0.373805	−	0.927507i	$-0.378053\pi$
$317$	−8.45181	−	7.09191i	−0.474701	−	0.398321i	−0.848506	+	0.529186i	$0.822497\pi$
$318$	1.58651	+	1.33358i	0.0889673	+	0.0747836i
$319$	0.184178	+	1.04453i	0.0103120	+	0.0584823i
$320$	4.52641	−	3.79811i	0.253034	−	0.212321i
$321$	−3.21071	−	5.57223i	−0.179204	−	0.311011i
$322$	10.4599	−	3.80710i	0.582909	−	0.212162i
$323$	−4.34816			−0.241938
$324$	16.1285	+	5.93355i	0.896029	+	0.329641i
$325$	4.04481			0.224365
$326$	5.08516	−	1.85085i	0.281641	−	0.102509i
$327$	2.80291	+	4.86449i	0.155001	+	0.269007i
$328$	−0.682061	+	0.572317i	−0.0376605	+	0.0316009i
$329$	8.75110	+	49.6300i	0.482464	+	2.73619i
$330$	−0.707098	−	0.594368i	−0.0389244	−	0.0327189i
$331$	1.55201	+	1.30229i	0.0853061	+	0.0715803i	0.684443	−	0.729066i	$-0.260045\pi$
$331$	1.55201	+	1.30229i	0.0853061	+	0.0715803i	−0.599137	+	0.800646i	$0.704490\pi$
$332$	7.54937	−	13.0759i	0.414325	−	0.717633i
$333$	15.6514	+	0.0270613i	0.857693	+	0.00148295i
$334$	−2.99923	−	5.19481i	−0.164110	−	0.284247i
$335$	−1.36047	+	7.71563i	−0.0743306	+	0.421550i
$336$	24.1835	+	8.82574i	1.31932	+	0.481484i
$337$	14.4525	+	5.26029i	0.787280	+	0.286546i	0.704205	−	0.709997i	$-0.251304\pi$
$337$	14.4525	+	5.26029i	0.787280	+	0.286546i	0.0830749	+	0.996543i	$0.473526\pi$
$338$	−0.950049	−	0.345790i	−0.0516759	−	0.0188085i
$339$	16.3309	−	13.6792i	0.886970	−	0.742951i
$340$	−1.29458	+	7.34191i	−0.0702083	+	0.398171i
$341$	−1.44372	−	2.50059i	−0.0781818	−	0.135415i
$342$	0.768903	+	0.647455i	0.0415775	+	0.0350103i
$343$	9.43380	−	16.3398i	0.509377	−	0.882267i
$344$	6.49605	+	5.45084i	0.350244	+	0.293889i
$345$	−2.60700	+	14.7107i	−0.140356	+	0.791996i
$346$	0.353466	+	2.00461i	0.0190024	+	0.107768i
$347$	0.887983	−	0.745107i	0.0476695	−	0.0399994i	−0.618642	−	0.785673i	$-0.712317\pi$
$347$	0.887983	−	0.745107i	0.0476695	−	0.0399994i	0.666311	+	0.745674i	$0.267872\pi$
$348$	−1.97892	−	0.00171078i	−0.106081	−	9.17072e-5i
$349$	4.85238	−	1.76612i	0.259742	−	0.0945383i	−0.208867	−	0.977944i	$-0.566978\pi$
$349$	4.85238	−	1.76612i	0.259742	−	0.0945383i	0.468609	+	0.883406i	$0.344755\pi$
$350$	−1.29050			−0.0689799
$351$	−19.7312	−	7.23958i	−1.05317	−	0.386420i
$352$	6.01791			0.320756
$353$	11.4102	−	4.15296i	0.607301	−	0.221040i	−0.0200207	−	0.999800i	$-0.506373\pi$
$353$	11.4102	−	4.15296i	0.607301	−	0.221040i	0.627322	+	0.778760i	$0.284151\pi$
$354$	3.60609	−	6.23349i	0.191662	−	0.331306i
$355$	3.97081	−	3.33191i	0.210749	−	0.176839i
$356$	1.07951	+	6.12219i	0.0572138	+	0.324475i
$357$	−27.2658	+	9.89724i	−1.44306	+	0.523818i
$358$	2.17558	+	1.82553i	0.114983	+	0.0964823i
$359$	−4.44707	+	7.70256i	−0.234708	+	0.406525i	−0.959188	−	0.282770i	$-0.908747\pi$
$359$	−4.44707	+	7.70256i	−0.234708	+	0.406525i	0.724480	+	0.689296i	$0.242080\pi$
$360$	2.70699	−	2.26347i	0.142671	−	0.119295i
$361$	8.87985	+	15.3803i	0.467360	+	0.809492i
$362$	0.0591609	−	0.335518i	0.00310943	−	0.0176344i
$363$	−2.35178	−	13.4054i	−0.123437	−	0.703600i
$364$	−31.1310	−	11.3308i	−1.63171	−	0.593893i
$365$	−4.11142	−	1.49643i	−0.215202	−	0.0783270i
$366$	−0.763597	−	4.35257i	−0.0399139	−	0.227513i
$367$	−4.79749	+	27.2079i	−0.250427	+	1.42024i	0.557117	+	0.830434i	$0.311907\pi$
$367$	−4.79749	+	27.2079i	−0.250427	+	1.42024i	−0.807544	+	0.589807i	$0.799204\pi$
$368$	−14.9442	−	25.8841i	−0.779019	−	1.34930i
$369$	1.74217	−	1.45673i	0.0906939	−	0.0758344i
$370$	0.784813	−	1.35934i	0.0408005	−	0.0706685i
$371$	−13.0686	−	10.9659i	−0.678488	−	0.569319i
$372$	5.06401	−	1.83819i	0.262557	−	0.0953058i
$373$	−5.35646	−	30.3780i	−0.277347	−	1.57291i	−0.731407	−	0.681942i	$-0.761136\pi$
$373$	−5.35646	−	30.3780i	−0.277347	−	1.57291i	0.454060	−	0.890971i	$-0.349975\pi$
$374$	−1.59505	+	1.33841i	−0.0824783	+	0.0692075i
$375$	0.867322	−	1.49925i	0.0447883	−	0.0774210i
$376$	−12.9858	+	4.72643i	−0.669689	+	0.243747i
$377$	2.42019			0.124646
$378$	6.29524	+	2.30979i	0.323792	+	0.118803i
$379$	−21.0219			−1.07982			−0.539911	−	0.841722i	$-0.681542\pi$
$379$	−21.0219			−1.07982			−0.539911	+	0.841722i	$0.681542\pi$
$380$	−1.99833	+	0.727331i	−0.102512	+	0.0373113i
$381$	−19.0731	−	0.0164887i	−0.977144	−	0.000844742i
$382$	−5.44467	+	4.56862i	−0.278574	+	0.233751i
$383$	−3.73782	−	21.1982i	−0.190994	−	1.08318i	−0.918009	−	0.396559i	$-0.870204\pi$
$383$	−3.73782	−	21.1982i	−0.190994	−	1.08318i	0.727016	−	0.686621i	$-0.240907\pi$
$384$	−2.58947	+	14.6117i	−0.132143	+	0.745652i
$385$	5.82458	+	4.88740i	0.296848	+	0.249085i
$386$	0.408561	−	0.707648i	0.0207952	−	0.0360184i
$387$	−16.5446	−	13.9314i	−0.841011	−	0.708174i
$388$	−1.90157	−	3.29361i	−0.0965374	−	0.167208i
$389$	2.32909	−	13.2089i	0.118089	−	0.669718i	−0.867085	−	0.498161i	$-0.834009\pi$
$389$	2.32909	−	13.2089i	0.118089	−	0.669718i	0.985174	−	0.171558i	$-0.0548799\pi$
$390$	−1.61581	+	1.35345i	−0.0818197	+	0.0685344i
$391$	31.6456	+	11.5181i	1.60039	+	0.582494i
$392$	12.5986	+	4.58552i	0.636327	+	0.231604i
$393$	−28.5478	−	10.4185i	−1.44005	−	0.525545i
$394$	−0.745742	+	4.22931i	−0.0375699	+	0.213070i
$395$	−6.44535	−	11.1637i	−0.324301	−	0.561706i
$396$	−10.1544	−	0.0175570i	−0.510277	−	0.000882270i
$397$	8.50299	−	14.7276i	0.426753	−	0.739158i	−0.569829	−	0.821763i	$-0.692991\pi$
$397$	8.50299	−	14.7276i	0.426753	−	0.739158i	0.996582	+	0.0826052i	$0.0263241\pi$
$398$	4.90219	+	4.11343i	0.245725	+	0.206187i
$399$	−6.33369	−	5.32394i	−0.317081	−	0.266530i
$400$	0.601708	+	3.41245i	0.0300854	+	0.170623i
$401$	4.77991	−	4.01082i	0.238697	−	0.200291i	−0.515590	−	0.856836i	$-0.672427\pi$
$401$	4.77991	−	4.01082i	0.238697	−	0.200291i	0.754287	+	0.656545i	$0.227983\pi$
$402$	−2.03827	−	3.53745i	−0.101660	−	0.176432i
$403$	−6.19126	+	2.25343i	−0.308409	+	0.112252i
$404$	−17.5049			−0.870899
$405$	−6.91436	+	5.76121i	−0.343577	+	0.286277i
$406$	−0.772161			−0.0383217
$407$	−8.69033	+	3.16302i	−0.430764	+	0.156785i
$408$	−3.97103	−	6.89178i	−0.196595	−	0.341194i
$409$	7.35423	−	6.17093i	0.363643	−	0.305133i	−0.442598	−	0.896720i	$-0.645943\pi$
$409$	7.35423	−	6.17093i	0.363643	−	0.305133i	0.806241	+	0.591587i	$0.201499\pi$
$410$	−0.0395476	−	0.224286i	−0.00195312	−	0.0110767i
$411$	0.472967	+	0.397564i	0.0233297	+	0.0196104i
$412$	−2.65186	−	2.22517i	−0.130648	−	0.109626i
$413$	−29.6386	+	51.3355i	−1.45842	+	2.52606i
$414$	−3.88095	−	6.74892i	−0.190738	−	0.331691i
$415$	3.95362	+	6.84787i	0.194075	+	0.336149i
$416$	2.38449	−	13.5231i	0.116909	−	0.663027i
$417$	2.42633	+	0.885489i	0.118818	+	0.0433626i
$418$	−0.558124	−	0.203140i	−0.0272987	−	0.00993592i
$419$	−14.1004	−	5.13212i	−0.688849	−	0.250721i	−0.0262069	−	0.999657i	$-0.508343\pi$
$419$	−14.1004	−	5.13212i	−0.688849	−	0.250721i	−0.662642	+	0.748936i	$0.730565\pi$
$420$	−10.8752	+	9.10940i	−0.530657	+	0.444493i
$421$	6.43175	−	36.4763i	0.313464	−	1.77774i	−0.267240	−	0.963630i	$-0.586112\pi$
$421$	6.43175	−	36.4763i	0.313464	−	1.77774i	0.580705	−	0.814114i	$-0.302777\pi$
$422$	3.03032	+	5.24867i	0.147514	+	0.255501i
$423$	33.1420	−	11.9978i	1.61142	−	0.583355i
$424$	2.33902	−	4.05130i	0.113593	−	0.196749i
$425$	−2.99086	−	2.50963i	−0.145078	−	0.121735i
$426$	−0.471350	+	2.65971i	−0.0228370	+	0.128863i
$427$	6.31639	+	35.8220i	0.305671	+	1.73355i
$428$	−5.43114	+	4.55727i	−0.262524	+	0.220284i
$429$	12.4187	+	0.0107359i	0.599579	+	0.000518337i
$430$	−2.03827	+	0.741870i	−0.0982942	+	0.0357762i
$431$	−14.3326			−0.690378			−0.345189	−	0.938533i	$-0.612185\pi$
$431$	−14.3326			−0.690378			−0.345189	+	0.938533i	$0.612185\pi$
$432$	3.17254	−	17.7235i	0.152639	−	0.852720i
$433$	14.4669			0.695233			0.347616	−	0.937637i	$-0.386991\pi$
$433$	14.4669			0.695233			0.347616	+	0.937637i	$0.386991\pi$
$434$	1.97532	−	0.718958i	0.0948185	−	0.0345111i
$435$	0.518957	−	0.897069i	0.0248821	−	0.0430112i
$436$	4.74132	−	3.97844i	0.227068	−	0.190533i
$437$	1.66810	+	9.46025i	0.0797959	+	0.452545i
$438$	2.14315	−	0.777944i	0.102404	−	0.0371716i
$439$	−11.4536	−	9.61070i	−0.546650	−	0.458694i	0.327155	−	0.944971i	$-0.393910\pi$
$439$	−11.4536	−	9.61070i	−0.546650	−	0.458694i	−0.873805	+	0.486277i	$0.838355\pi$
$440$	−1.04248	+	1.80564i	−0.0496985	+	0.0860803i
$441$	−32.1135	−	11.7513i	−1.52922	−	0.559585i
$442$	2.37559	+	4.11465i	0.112995	+	0.195714i
$443$	−6.01661	+	34.1219i	−0.285858	+	1.62118i	0.416348	+	0.909205i	$0.363310\pi$
$443$	−6.01661	+	34.1219i	−0.285858	+	1.62118i	−0.702206	+	0.711974i	$0.747801\pi$
$444$	−2.98157	−	16.9952i	−0.141499	−	0.806558i
$445$	−3.05932	−	1.11350i	−0.145026	−	0.0527851i
$446$	1.63494	+	0.595069i	0.0774166	+	0.0281773i
$447$	−5.41696	−	30.8772i	−0.256213	−	1.46044i
$448$	4.40112	−	24.9600i	0.207933	−	1.17925i
$449$	12.7777	+	22.1315i	0.603015	+	1.04445i	0.992362	+	0.123361i	$0.0393673\pi$
$449$	12.7777	+	22.1315i	0.603015	+	1.04445i	−0.389347	+	0.921091i	$0.627299\pi$
$450$	0.155194	+	0.889135i	0.00731590	+	0.0419142i
$451$	−0.670925	+	1.16208i	−0.0315926	+	0.0547201i
$452$	−17.9908	−	15.0960i	−0.846214	−	0.710058i
$453$	34.5319	−	12.5348i	1.62245	−	0.588936i
$454$	0.799800	+	4.53589i	0.0375365	+	0.212880i
$455$	13.2906	−	11.1521i	0.623074	−	0.522821i
$456$	1.13613	−	1.96391i	0.0532041	−	0.0919684i
$457$	18.0578	−	6.57250i	0.844707	−	0.307448i	0.116827	−	0.993152i	$-0.462728\pi$
$457$	18.0578	−	6.57250i	0.844707	−	0.307448i	0.727881	+	0.685704i	$0.240506\pi$
$458$	0.742248			0.0346830
$459$	10.0980	+	17.5955i	0.471336	+	0.821289i
$460$	16.4703			0.767934
$461$	10.5314	−	3.83312i	0.490497	−	0.178526i	−0.0849181	−	0.996388i	$-0.527063\pi$
$461$	10.5314	−	3.83312i	0.490497	−	0.178526i	0.575415	+	0.817862i	$0.304841\pi$
$462$	−3.96218	−	0.00342531i	−0.184337	−	0.000159360i
$463$	−9.75323	+	8.18393i	−0.453271	+	0.380340i	−0.840648	−	0.541582i	$-0.817826\pi$
$463$	−9.75323	+	8.18393i	−0.453271	+	0.380340i	0.387377	+	0.921921i	$0.373381\pi$
$464$	0.360029	+	2.04182i	0.0167139	+	0.0947893i
$465$	−0.492323	+	2.77806i	−0.0228309	+	0.128829i
$466$	1.94254	+	1.62998i	0.0899862	+	0.0755074i
$467$	16.4688	−	28.5249i	0.762087	−	1.31997i	−0.179687	−	0.983724i	$-0.557508\pi$
$467$	16.4688	−	28.5249i	0.762087	−	1.31997i	0.941773	−	0.336249i	$-0.109158\pi$
$468$	−4.06296	+	22.8115i	−0.187810	+	1.05446i
$469$	16.8029	+	29.1034i	0.775884	+	1.34387i
$470$	0.613808	−	3.48108i	0.0283128	−	0.160570i
$471$	−7.27068	+	6.09012i	−0.335015	+	0.280618i
$472$	−15.2743	−	5.55940i	−0.703058	−	0.255892i
$473$	12.0093	+	4.37101i	0.552186	+	0.200979i
$474$	6.31029	+	2.30294i	0.289841	+	0.105777i
$475$	0.193390	−	1.09677i	0.00887335	−	0.0503233i
$476$	15.9890	+	27.6937i	0.732854	+	1.26934i
$477$	−5.98371	+	10.3228i	−0.273975	+	0.472650i
$478$	2.29398	−	3.97328i	0.104924	−	0.181734i
$479$	−16.9755	−	14.2441i	−0.775628	−	0.650829i	0.166515	−	0.986039i	$-0.446748\pi$
$479$	−16.9755	−	14.2441i	−0.775628	−	0.650829i	−0.942144	+	0.335209i	$0.891193\pi$
$480$	−4.50120	−	3.78359i	−0.205451	−	0.172696i
$481$	3.66438	+	20.7818i	0.167082	+	0.947566i
$482$	−0.149992	+	0.125858i	−0.00683193	+	0.00573267i
$483$	31.9934	+	55.5249i	1.45575	+	2.52647i
$484$	−14.0995	+	5.13178i	−0.640885	+	0.233263i
$485$	1.99171			0.0904388
$486$	0.834354	−	4.61511i	0.0378471	−	0.209346i
$487$	−15.7072			−0.711761			−0.355881	−	0.934531i	$-0.615819\pi$
$487$	−15.7072			−0.711761			−0.355881	+	0.934531i	$0.615819\pi$
$488$	−9.37289	+	3.41145i	−0.424291	+	0.154429i
$489$	15.5538	+	26.9938i	0.703365	+	1.22070i
$490$	−2.62707	+	2.20437i	−0.118679	+	0.0995835i
$491$	−4.61638	−	26.1808i	−0.208334	−	1.18152i	−0.892106	−	0.451826i	$-0.850773\pi$
$491$	−4.61638	−	26.1808i	−0.208334	−	1.18152i	0.683772	−	0.729696i	$-0.260338\pi$
$492$	−1.91647	−	1.61094i	−0.0864012	−	0.0726266i
$493$	−1.78956	−	1.50162i	−0.0805978	−	0.0676296i
$494$	−0.677634	+	1.17370i	−0.0304882	+	0.0528071i
$495$	2.66690	−	4.60081i	0.119868	−	0.206791i
$496$	−2.82215	−	4.88811i	−0.126718	−	0.219483i
$497$	3.86090	−	21.8963i	0.173185	−	0.982182i
$498$	−3.87077	−	1.41264i	−0.173453	−	0.0633017i
$499$	1.98733	+	0.723329i	0.0889652	+	0.0323807i	0.386119	−	0.922449i	$-0.373815\pi$
$499$	1.98733	+	0.723329i	0.0889652	+	0.0323807i	−0.297154	+	0.954830i	$0.596038\pi$
$500$	−1.79433	−	0.653082i	−0.0802448	−	0.0292067i
$501$	26.4731	−	22.1746i	1.18273	−	0.990689i
$502$	0.321747	−	1.82472i	0.0143603	−	0.0814412i
$503$	−4.80026	−	8.31430i	−0.214033	−	0.370716i	0.738940	−	0.673771i	$-0.235327\pi$
$503$	−4.80026	−	8.31430i	−0.214033	−	0.370716i	−0.952973	+	0.303055i	$0.901993\pi$
$504$	2.65402	−	14.9010i	0.118220	−	0.663743i
$505$	4.58366	−	7.93914i	0.203970	−	0.353287i
$506$	3.52388	+	2.95688i	0.156655	+	0.131450i
$507$	1.01567	−	5.73117i	0.0451074	−	0.254530i
$508$	3.65129	+	20.7075i	0.162000	+	0.918748i
$509$	−3.02405	+	2.53748i	−0.134039	+	0.112472i	−0.707342	−	0.706871i	$-0.750106\pi$
$509$	−3.02405	+	2.53748i	−0.134039	+	0.112472i	0.573304	+	0.819343i	$0.305662\pi$
$510$	2.03453	+	0.00175886i	0.0900907	+	7.78834e-5i
$511$	−17.6354	+	6.41876i	−0.780144	+	0.283949i
$512$	19.9150			0.880128
$513$	−2.90644	+	5.00408i	−0.128322	+	0.220936i
$514$	2.10969			0.0930544
$515$	1.70359	−	0.620058i	0.0750694	−	0.0273230i
$516$	−11.9401	+	20.6397i	−0.525635	+	0.908612i
$517$	−15.9540	+	13.3870i	−0.701657	+	0.588760i
$518$	−1.16912	−	6.63042i	−0.0513683	−	0.291324i
$519$	−11.0153	+	3.99847i	−0.483519	+	0.175513i
$520$	3.64447	+	3.05807i	0.159820	+	0.134105i
$521$	12.6619	−	21.9311i	0.554729	−	0.960818i	−0.443196	−	0.896425i	$-0.646155\pi$
$521$	12.6619	−	21.9311i	0.554729	−	0.960818i	0.997925	−	0.0643933i	$-0.0205112\pi$
$522$	0.0928594	+	0.532009i	0.00406434	+	0.0232854i
$523$	7.76052	+	13.4416i	0.339344	+	0.587761i	0.984309	−	0.176451i	$-0.0564617\pi$
$523$	7.76052	+	13.4416i	0.339344	+	0.587761i	−0.644966	+	0.764211i	$0.723128\pi$
$524$	−5.81768	+	32.9937i	−0.254146	+	1.44134i
$525$	−1.28378	−	7.31765i	−0.0560286	−	0.319368i
$526$	−5.49961	−	2.00169i	−0.239794	−	0.0872780i
$527$	5.97617	+	2.17515i	0.260326	+	0.0947509i
$528$	1.83835	+	10.4788i	0.0800040	+	0.456030i
$529$	8.92553	−	50.6192i	0.388066	−	2.20083i
$530$	0.598294	+	1.03628i	0.0259882	+	0.0450129i
$531$	38.9338	+	14.2470i	1.68958	+	0.618268i
$532$	−4.56083	+	7.89959i	−0.197737	+	0.342491i
$533$	2.34552	+	1.96812i	0.101596	+	0.0852488i
$534$	1.59472	−	0.578871i	0.0690104	−	0.0250502i
$535$	−0.644750	−	3.65656i	−0.0278750	−	0.158087i
$536$	−7.05922	+	5.92338i	−0.304912	+	0.255851i
$537$	−8.18727	+	14.1525i	−0.353307	+	0.610725i
$538$	−2.87962	+	1.04810i	−0.124149	+	0.0451866i
$539$	20.2056			0.870317
$540$	7.58410	+	6.39741i	0.326368	+	0.275301i
$541$	11.7630			0.505730			0.252865	−	0.967502i	$-0.418627\pi$
$541$	11.7630			0.505730			0.252865	+	0.967502i	$0.418627\pi$
$542$	1.94249	−	0.707008i	0.0834370	−	0.0303686i
$543$	1.96138	+	0.00169561i	0.0841709	+	7.27658e-5i
$544$	−10.1537	+	8.51996i	−0.435336	+	0.365290i
$545$	0.562859	+	3.19213i	0.0241102	+	0.136736i
$546$	−1.57764	+	8.90225i	−0.0675169	+	0.380981i
$547$	13.8145	+	11.5917i	0.590665	+	0.495627i	0.888430	−	0.459012i	$-0.151797\pi$
$547$	13.8145	+	11.5917i	0.590665	+	0.495627i	−0.297765	+	0.954639i	$0.596241\pi$
$548$	0.340579	−	0.589900i	0.0145488	−	0.0251993i
$549$	23.9213	−	8.65983i	1.02094	−	0.369593i
$550$	−0.266655	−	0.461860i	−0.0113702	−	0.0196938i
$551$	0.115714	−	0.656247i	0.00492958	−	0.0279571i
$552$	−13.4710	+	11.2836i	−0.573362	+	0.480264i
$553$	−51.9584	−	18.9113i	−2.20950	−	0.804191i
$554$	−7.50989	−	2.73338i	−0.319065	−	0.116130i
$555$	8.48873	+	3.09796i	0.360327	+	0.131501i
$556$	0.494455	−	2.80419i	0.0209696	−	0.118924i
$557$	−4.95446	−	8.58137i	−0.209927	−	0.363604i	0.741764	−	0.670661i	$-0.233989\pi$
$557$	−4.95446	−	8.58137i	−0.209927	−	0.363604i	−0.951691	+	0.307056i	$0.900656\pi$
$558$	−0.732903	−	1.27451i	−0.0310263	−	0.0539543i
$559$	14.5808	−	25.2547i	0.616701	−	1.06816i
$560$	11.3858	+	9.55380i	0.481137	+	0.403722i
$561$	−9.17609	−	7.71319i	−0.387415	−	0.325651i
$562$	−1.24991	−	7.08857i	−0.0527241	−	0.299013i
$563$	−0.891731	+	0.748251i	−0.0375820	+	0.0315350i	−0.661385	−	0.750046i	$-0.730031\pi$
$563$	−0.891731	+	0.748251i	−0.0375820	+	0.0315350i	0.623803	+	0.781581i	$0.285587\pi$
$564$	−19.3997	−	33.6684i	−0.816874	−	1.41770i
$565$	11.5575	−	4.20660i	0.486229	−	0.176973i
$566$	−4.06208			−0.170742
$567$	−6.83500	+	37.9944i	−0.287043	+	1.59562i
$568$	6.09688			0.255820
$569$	4.81240	−	1.75157i	0.201746	−	0.0734296i	−0.239171	−	0.970978i	$-0.576876\pi$
$569$	4.81240	−	1.75157i	0.201746	−	0.0734296i	0.440917	+	0.897548i	$0.354653\pi$
$570$	0.289739	+	0.502846i	0.0121358	+	0.0210619i
$571$	−11.3635	+	9.53515i	−0.475550	+	0.399033i	−0.848814	−	0.528691i	$-0.822683\pi$
$571$	−11.3635	+	9.53515i	−0.475550	+	0.399033i	0.373264	+	0.927725i	$0.378238\pi$
$572$	−2.37739	−	13.4829i	−0.0994038	−	0.563747i
$573$	−31.3223	−	26.3287i	−1.30851	−	1.09990i
$574$	−0.748337	−	0.627930i	−0.0312350	−	0.0262093i
$575$	−4.31277	+	7.46994i	−0.179855	+	0.311518i
$576$	−17.7264	−	0.0306490i	−0.738599	−	0.00127704i
$577$	15.7817	+	27.3347i	0.657001	+	1.13796i	0.981388	+	0.192035i	$0.0615086\pi$
$577$	15.7817	+	27.3347i	0.657001	+	1.13796i	−0.324387	+	0.945924i	$0.605158\pi$
$578$	−0.0917692	+	0.520449i	−0.00381710	+	0.0216478i
$579$	4.41910	+	1.61275i	0.183651	+	0.0670235i
$580$	−1.07363	−	0.390768i	−0.0445799	−	0.0162258i
$581$	31.8716	+	11.6003i	1.32226	+	0.481262i
$582$	−0.795643	+	0.666452i	−0.0329804	+	0.0276253i
$583$	1.22425	−	6.94305i	0.0507031	−	0.287552i
$584$	−2.57311	−	4.45676i	−0.106476	−	0.184422i
$585$	−9.28200	−	7.81591i	−0.383764	−	0.323148i
$586$	0.829490	−	1.43672i	0.0342659	−	0.0593503i
$587$	13.0278	+	10.9316i	0.537713	+	0.451195i	0.870755	−	0.491717i	$-0.163631\pi$
$587$	13.0278	+	10.9316i	0.537713	+	0.451195i	−0.333042	+	0.942912i	$0.608075\pi$
$588$	−6.57848	+	37.1207i	−0.271292	+	1.53083i
$589$	0.315014	+	1.78653i	0.0129799	+	0.0736129i
$590$	3.18501	−	2.67254i	0.131125	−	0.110027i
$591$	−24.7238	−	0.0213738i	−1.01700	−	0.000879199i
$592$	−16.9877	+	6.18301i	−0.698190	+	0.254120i
$593$	42.7865			1.75703			0.878517	−	0.477712i	$-0.158534\pi$
$593$	42.7865			1.75703			0.878517	+	0.477712i	$0.158534\pi$
$594$	0.474128	+	2.73030i	0.0194537	+	0.112026i
$595$	−16.7469			−0.686557
$596$	−32.4759	+	11.8203i	−1.33026	+	0.484177i
$597$	−18.4482	+	31.8895i	−0.755034	+	1.30515i
$598$	8.04084	−	6.74706i	0.328814	−	0.275908i
$599$	−0.336622	−	1.90908i	−0.0137540	−	0.0780029i	0.977158	−	0.212513i	$-0.0681649\pi$
$599$	−0.336622	−	1.90908i	−0.0137540	−	0.0780029i	−0.990912	+	0.134511i	$0.957054\pi$
$600$	1.91498	−	0.695123i	0.0781789	−	0.0283783i
$601$	−15.1011	−	12.6713i	−0.615986	−	0.516874i	0.280553	−	0.959839i	$-0.409482\pi$
$601$	−15.1011	−	12.6713i	−0.615986	−	0.516874i	−0.896539	+	0.442965i	$0.853927\pi$
$602$	−4.65200	+	8.05750i	−0.189601	+	0.328399i
$603$	18.0312	−	15.0769i	0.734287	−	0.613979i
$604$	−20.2499	−	35.0739i	−0.823959	−	1.42714i
$605$	1.36449	−	7.73842i	0.0554745	−	0.314611i
$606$	0.825471	+	4.70526i	0.0335325	+	0.191138i
$607$	10.8522	+	3.94987i	0.440477	+	0.160320i	0.552732	−	0.833359i	$-0.313585\pi$
$607$	10.8522	+	3.94987i	0.440477	+	0.160320i	−0.112255	+	0.993679i	$0.535807\pi$
$608$	−3.55287	−	1.29314i	−0.144088	−	0.0524436i
$609$	−0.768141	−	4.37848i	−0.0311267	−	0.177425i
$610$	0.443035	−	2.51258i	0.0179380	−	0.101731i
$611$	23.7611	+	41.1554i	0.961271	+	1.66497i
$612$	17.1578	−	14.3466i	0.693563	−	0.579928i
$613$	−5.95138	+	10.3081i	−0.240374	+	0.416340i	−0.960821	−	0.277170i	$-0.910603\pi$
$613$	−5.95138	+	10.3081i	−0.240374	+	0.416340i	0.720447	+	0.693510i	$0.243937\pi$
$614$	1.09870	+	0.921923i	0.0443401	+	0.0372058i
$615$	1.23245	−	0.447370i	0.0496972	−	0.0180397i
$616$	1.55297	+	8.80733i	0.0625710	+	0.354858i
$617$	22.1687	−	18.6018i	0.892480	−	0.748879i	−0.0762262	−	0.997091i	$-0.524287\pi$
$617$	22.1687	−	18.6018i	0.892480	−	0.748879i	0.968706	+	0.248211i	$0.0798427\pi$
$618$	−0.473068	+	0.817745i	−0.0190296	+	0.0328945i
$619$	5.52194	−	2.00982i	0.221946	−	0.0807816i	−0.228654	−	0.973508i	$-0.573432\pi$
$619$	5.52194	−	2.00982i	0.221946	−	0.0807816i	0.450600	+	0.892726i	$0.351210\pi$
$620$	3.11037			0.124915
$621$	34.4085	−	28.7204i	1.38076	−	1.15251i
$622$	3.27198			0.131194
$623$	−13.1226	+	4.77622i	−0.525744	+	0.191355i
$624$	24.2758	+	0.0209864i	0.971809	+	0.000840130i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−0.648770	−	3.67936i	−0.0259301	−	0.147057i
$627$	0.596673	−	3.36688i	0.0238288	−	0.134460i
$628$	8.00969	+	6.72093i	0.319621	+	0.268194i
$629$	10.1846	−	17.6403i	0.406087	−	0.703364i
$630$	2.96142	+	2.49367i	0.117986	+	0.0993501i
$631$	−10.1424	−	17.5671i	−0.403761	−	0.699335i	0.590415	−	0.807100i	$-0.298964\pi$
$631$	−10.1424	−	17.5671i	−0.403761	−	0.699335i	−0.994176	+	0.107765i	$0.965631\pi$
$632$	2.63287	−	14.9317i	0.104730	−	0.593953i
$633$	−26.7476	+	22.4045i	−1.06312	+	0.890499i
$634$	3.11921	+	1.13530i	0.123880	+	0.0450885i
$635$	−10.3478	−	3.76628i	−0.410638	−	0.149460i
$636$	12.3568	+	4.50962i	0.489980	+	0.178818i
$637$	8.00613	−	45.4050i	0.317214	−	1.79901i
$638$	−0.159552	−	0.276352i	−0.00631671	−	0.0109409i
$639$	−15.5506	−	0.0268870i	−0.615171	−	0.00106363i
$640$	−4.28377	+	7.41971i	−0.169331	+	0.293290i
$641$	7.37134	+	6.18529i	0.291151	+	0.244304i	0.776650	−	0.629933i	$-0.216918\pi$
$641$	7.37134	+	6.18529i	0.291151	+	0.244304i	−0.485499	+	0.874237i	$0.661362\pi$
$642$	1.48110	+	1.24497i	0.0584542	+	0.0491351i
$643$	−1.13466	−	6.43500i	−0.0447468	−	0.253772i	0.954226	−	0.299087i	$-0.0966819\pi$
$643$	−1.13466	−	6.43500i	−0.0447468	−	0.253772i	−0.998973	+	0.0453151i	$0.985571\pi$
$644$	54.1190	−	45.4113i	2.13259	−	1.78945i
$645$	−6.23437	−	10.8198i	−0.245478	−	0.426031i
$646$	1.22929	−	0.447425i	0.0483658	−	0.0176037i
$647$	−4.88147			−0.191910			−0.0959551	−	0.995386i	$-0.530591\pi$
$647$	−4.88147			−0.191910			−0.0959551	+	0.995386i	$0.530591\pi$
$648$	−10.5858	−	0.0366057i	−0.415848	−	0.00143801i
$649$	−24.4969			−0.961587
$650$	−1.14353	+	0.416210i	−0.0448528	+	0.0163251i
$651$	6.04183	+	10.4857i	0.236798	+	0.410966i
$652$	26.3103	−	22.0769i	1.03039	−	0.864600i
$653$	1.09046	+	6.18430i	0.0426730	+	0.242010i	0.998682	−	0.0513272i	$-0.0163451\pi$
$653$	1.09046	+	6.18430i	0.0426730	+	0.242010i	−0.956009	+	0.293338i	$0.905234\pi$
$654$	−1.29298	−	1.08685i	−0.0505595	−	0.0424990i
$655$	−13.4406	−	11.2780i	−0.525166	−	0.440667i
$656$	−1.31151	+	2.27161i	−0.0512059	+	0.0886913i
$657$	6.54326	+	11.3786i	0.255277	+	0.443923i
$658$	−7.58098	−	13.1306i	−0.295537	−	0.511886i
$659$	1.25353	−	7.10913i	0.0488307	−	0.276933i	−0.950609	−	0.310389i	$-0.899541\pi$
$659$	1.25353	−	7.10913i	0.0488307	−	0.276933i	0.999440	+	0.0334569i	$0.0106517\pi$
$660$	−5.50735	−	2.00991i	−0.214373	−	0.0782355i
$661$	−41.0593	−	14.9444i	−1.59702	−	0.581268i	−0.618206	−	0.786016i	$-0.712140\pi$
$661$	−41.0593	−	14.9444i	−1.59702	−	0.581268i	−0.978815	+	0.204748i	$0.934363\pi$
$662$	−0.572781	−	0.208475i	−0.0222618	−	0.00810263i
$663$	−20.9686	+	17.5638i	−0.814351	+	0.682123i
$664$	−1.61502	+	9.15922i	−0.0626748	+	0.355447i
$665$	−2.38851	−	4.13703i	−0.0926226	−	0.160427i
$666$	−4.42768	+	1.60288i	−0.171569	+	0.0621103i
$667$	−2.58053	+	4.46960i	−0.0999183	+	0.173064i
$668$	−29.1639	−	24.4714i	−1.12839	−	0.946828i
$669$	−1.74786	+	9.86275i	−0.0675763	+	0.381316i
$670$	−0.409311	−	2.32132i	−0.0158131	−	0.0896803i
$671$	−11.5153	+	9.66250i	−0.444544	+	0.373017i
$672$	−25.2222	−	0.0218046i	−0.972966	−	0.000841130i
$673$	−33.3471	+	12.1373i	−1.28543	+	0.467860i	−0.892226	−	0.451589i	$-0.850857\pi$
$673$	−33.3471	+	12.1373i	−1.28543	+	0.467860i	−0.393209	+	0.919449i	$0.628635\pi$
$674$	−4.62723			−0.178234
$675$	−4.88738	+	1.76452i	−0.188115	+	0.0679164i
$676$	−6.41672			−0.246797
$677$	−13.4876	+	4.90907i	−0.518369	+	0.188671i	−0.587937	−	0.808906i	$-0.700060\pi$
$677$	−13.4876	+	4.90907i	−0.518369	+	0.188671i	0.0695687	+	0.997577i	$0.477838\pi$
$678$	−3.20939	+	5.54775i	−0.123256	+	0.213060i
$679$	6.54445	−	5.49144i	0.251153	−	0.210742i
$680$	−0.797433	−	4.52247i	−0.0305802	−	0.173429i
$681$	−24.9248	+	9.04747i	−0.955119	+	0.346700i
$682$	0.665472	+	0.558397i	0.0254822	+	0.0213821i
$683$	−7.28683	+	12.6212i	−0.278823	+	0.482935i	−0.971092	−	0.238704i	$-0.923278\pi$
$683$	−7.28683	+	12.6212i	−0.278823	+	0.482935i	0.692270	+	0.721639i	$0.256611\pi$
$684$	5.99119	+	2.19235i	0.229079	+	0.0838268i
$685$	0.178362	+	0.308931i	0.00681485	+	0.0118037i
$686$	−0.985712	+	5.59025i	−0.0376346	+	0.213437i
$687$	0.738384	+	4.20886i	0.0281711	+	0.160578i
$688$	23.4755	+	8.54437i	0.894994	+	0.325751i
$689$	−15.1170	−	5.50213i	−0.575911	−	0.209614i
$690$	−0.776687	−	4.42719i	−0.0295680	−	0.168540i
$691$	−4.75235	+	26.9519i	−0.180788	+	1.02530i	0.750461	+	0.660915i	$0.229832\pi$
$691$	−4.75235	+	26.9519i	−0.180788	+	1.02530i	−0.931249	+	0.364384i	$0.881280\pi$
$692$	6.45952	+	11.1882i	0.245554	+	0.425312i
$693$	−3.92213	−	22.4706i	−0.148989	−	0.853588i
$694$	−0.174375	+	0.302026i	−0.00661918	+	0.0114648i
$695$	1.14234	+	0.958535i	0.0433313	+	0.0363593i
$696$	1.14582	−	0.415923i	0.0434322	−	0.0157655i
$697$	−0.513214	−	2.91058i	−0.0194394	−	0.110246i
$698$	−1.19011	+	0.998618i	−0.0450462	+	0.0377983i
$699$	−7.31025	+	12.6365i	−0.276499	+	0.477956i
$700$	−7.69653	+	2.80131i	−0.290902	+	0.105880i
$701$	−30.5667			−1.15449			−0.577243	−	0.816572i	$-0.695872\pi$
$701$	−30.5667			−1.15449			−0.577243	+	0.816572i	$0.695872\pi$
$702$	6.32326	+	0.0163994i	0.238656	+	0.000618956i
$703$	5.81029			0.219139
$704$	9.84243	−	3.58235i	0.370951	−	0.135015i
$705$	20.3498	+	0.0175924i	0.766417	+	0.000662567i
$706$	−2.79848	+	2.34821i	−0.105322	+	0.0883759i
$707$	−6.82820	−	38.7246i	−0.256801	−	1.45639i
$708$	7.97562	−	45.0045i	0.299742	−	1.69137i
$709$	11.3456	+	9.52012i	0.426094	+	0.357536i	0.830476	−	0.557055i	$-0.188069\pi$
$709$	11.3456	+	9.52012i	0.426094	+	0.357536i	−0.404381	+	0.914590i	$0.632513\pi$
$710$	−0.779756	+	1.35058i	−0.0292637	+	0.0506862i
$711$	−6.78118	+	38.0729i	−0.254314	+	1.42785i
$712$	−1.91466	−	3.31629i	−0.0717549	−	0.124283i
$713$	2.43979	−	13.8367i	0.0913708	−	0.518190i
$714$	6.69002	−	5.60374i	0.250368	−	0.209715i
$715$	6.73753	+	2.45226i	0.251969	+	0.0917093i
$716$	16.9379	+	6.16490i	0.633000	+	0.230393i
$717$	24.8122	+	9.05520i	0.926629	+	0.338173i
$718$	0.464662	−	2.63523i	0.0173410	−	0.0983460i
$719$	−2.62426	−	4.54535i	−0.0978684	−	0.169513i	0.812934	−	0.582356i	$-0.197869\pi$
$719$	−2.62426	−	4.54535i	−0.0978684	−	0.169513i	−0.910802	+	0.412843i	$0.864536\pi$
$720$	5.21320	−	8.99358i	0.194285	−	0.335171i
$721$	3.88816	−	6.73449i	0.144803	−	0.250805i
$722$	−4.09310	−	3.43452i	−0.152329	−	0.127820i
$723$	−0.862878	−	0.725312i	−0.0320908	−	0.0269747i
$724$	−0.375481	−	2.12946i	−0.0139546	−	0.0791407i
$725$	0.458359	−	0.384609i	0.0170230	−	0.0142840i
$726$	2.04429	+	3.54790i	0.0758709	+	0.131675i
$727$	−44.6043	+	16.2347i	−1.65428	+	0.602110i	−0.989449	−	0.144881i	$-0.953720\pi$
$727$	−44.6043	+	16.2347i	−1.65428	+	0.602110i	−0.664834	+	0.746991i	$0.731498\pi$
$728$	20.4067			0.756324
$729$	26.9996	+	0.140048i	0.999987	+	0.00518698i
$730$	1.31634			0.0487200
$731$	−26.4509	+	9.62734i	−0.978322	+	0.356080i
$732$	−14.0023	−	24.3013i	−0.517542	−	0.898201i
$733$	−29.7170	+	24.9355i	−1.09762	+	0.921014i	−0.997263	−	0.0739377i	$-0.976443\pi$
$733$	−29.7170	+	24.9355i	−1.09762	+	0.921014i	−0.100358	+	0.994951i	$0.531999\pi$
$734$	−1.44337	−	8.18574i	−0.0532757	−	0.302141i
$735$	−15.1131	−	12.7037i	−0.557456	−	0.468583i
$736$	22.4321	+	18.8227i	0.826857	+	0.693815i
$737$	−6.94396	+	12.0273i	−0.255784	+	0.443031i
$738$	−0.342641	+	0.591109i	−0.0126128	+	0.0217590i
$739$	7.71235	+	13.3582i	0.283704	+	0.491389i	0.972294	−	0.233762i	$-0.0751035\pi$
$739$	7.71235	+	13.3582i	0.283704	+	0.491389i	−0.688590	+	0.725150i	$0.741770\pi$
$740$	1.72989	−	9.81071i	0.0635921	−	0.360649i
$741$	−7.32945	−	2.67488i	−0.269254	−	0.0982642i
$742$	4.82307	+	1.75546i	0.177061	+	0.0644448i
$743$	38.6448	+	14.0656i	1.41774	+	0.516015i	0.933391	−	0.358860i	$-0.116834\pi$
$743$	38.6448	+	14.0656i	1.41774	+	0.516015i	0.484349	+	0.874875i	$0.339057\pi$
$744$	−2.54394	+	2.13088i	−0.0932654	+	0.0781217i
$745$	3.14289	−	17.8242i	0.115147	−	0.653029i
$746$	4.64024	+	8.03714i	0.169891	+	0.294260i
$747$	4.15962	−	23.3542i	0.152192	−	0.854484i
$748$	−6.60761	+	11.4447i	−0.241598	+	0.418460i
$749$	−12.2002	−	10.2372i	−0.445787	−	0.374060i
$750$	−0.0909322	+	0.513108i	−0.00332038	+	0.0187361i
$751$	−8.93875	−	50.6942i	−0.326180	−	1.84986i	−0.501253	−	0.865301i	$-0.667128\pi$
$751$	−8.93875	−	50.6942i	−0.326180	−	1.84986i	0.175074	−	0.984555i	$-0.443984\pi$
$752$	−31.1866	+	26.1687i	−1.13726	+	0.954273i
$753$	10.6670	+	0.00922162i	0.388727	+	0.000336055i
$754$	−0.684223	+	0.249037i	−0.0249179	+	0.00906939i
$755$	21.2099			0.771906
$756$	42.5588	+	0.110377i	1.54785	+	0.00401436i
$757$	36.7855			1.33699			0.668497	−	0.743715i	$-0.266938\pi$
$757$	36.7855			1.33699			0.668497	+	0.743715i	$0.266938\pi$
$758$	5.94321	−	2.16315i	0.215867	−	0.0785691i
$759$	−13.2612	+	22.9234i	−0.481353	+	0.832065i
$760$	1.00346	−	0.842004i	0.0363994	−	0.0305427i
$761$	−4.11655	−	23.3461i	−0.149225	−	0.846295i	−0.963877	−	0.266346i	$-0.914184\pi$
$761$	−4.11655	−	23.3461i	−0.149225	−	0.846295i	0.814653	−	0.579949i	$-0.196928\pi$
$762$	5.39395	−	1.95796i	0.195402	−	0.0709293i
$763$	10.6507	+	8.93697i	0.385580	+	0.323540i
$764$	−22.5549	+	39.0662i	−0.816007	+	1.41337i
$765$	2.01397	+	11.5384i	0.0728152	+	0.417172i
$766$	3.23803	+	5.60844i	0.116995	+	0.202641i
$767$	−9.70648	+	55.0482i	−0.350481	+	1.98767i
$768$	2.76546	+	15.7634i	0.0997899	+	0.568812i
$769$	10.3649	+	3.77252i	0.373768	+	0.136040i	0.522072	−	0.852901i	$-0.325159\pi$
$769$	10.3649	+	3.77252i	0.373768	+	0.136040i	−0.148304	+	0.988942i	$0.547381\pi$
$770$	−2.14961	−	0.782394i	−0.0774665	−	0.0281955i
$771$	2.09871	+	11.9628i	0.0755830	+	0.430830i
$772$	0.900555	−	5.10730i	0.0324117	−	0.183816i
$773$	−22.1299	−	38.3301i	−0.795958	−	1.37864i	−0.922229	−	0.386644i	$-0.873634\pi$
$773$	−22.1299	−	38.3301i	−0.795958	−	1.37864i	0.126272	−	0.991996i	$-0.459699\pi$
$774$	6.11096	+	2.23618i	0.219654	+	0.0803778i
$775$	−0.814452	+	1.41067i	−0.0292560	+	0.0506728i
$776$	1.79458	+	1.50583i	0.0644216	+	0.0540561i
$777$	36.4342	−	13.2253i	1.30707	−	0.474455i
$778$	0.700727	+	3.97402i	0.0251223	+	0.142475i
$779$	0.645811	−	0.541900i	0.0231386	−	0.0194156i
$780$	−6.69875	+	11.5794i	−0.239854	+	0.414611i
$781$	8.63433	−	3.14264i	0.308960	−	0.112452i
$782$	−10.1319			−0.362316
$783$	−2.92434	+	1.05579i	−0.104507	+	0.0377309i
$784$	39.4976			1.41063
$785$	−5.14555	+	1.87283i	−0.183652	+	0.0668440i
$786$	9.14296	+	0.00790409i	0.326119	+	0.000281930i
$787$	−31.5179	+	26.4467i	−1.12349	+	0.942722i	−0.998776	−	0.0494704i	$-0.984247\pi$
$787$	−31.5179	+	26.4467i	−1.12349	+	0.942722i	−0.124717	+	0.992192i	$0.539802\pi$
$788$	4.73305	+	26.8425i	0.168608	+	0.956224i
$789$	5.87946	−	33.1763i	0.209314	−	1.18111i
$790$	2.97094	+	2.49291i	0.105701	+	0.0886939i
$791$	26.3781	−	45.6882i	0.937896	−	1.62448i
$792$	5.88138	−	2.12914i	0.208986	−	0.0756556i
$793$	17.1503	+	29.7053i	0.609026	+	1.05486i
$794$	−0.888454	+	5.03867i	−0.0315301	+	0.178816i
$795$	−5.28094	+	4.42346i	−0.187296	+	0.156884i
$796$	38.1659	+	13.8912i	1.35275	+	0.492362i
$797$	−21.9590	−	7.99243i	−0.777828	−	0.283106i	−0.0775615	−	0.996988i	$-0.524713\pi$
$797$	−21.9590	−	7.99243i	−0.777828	−	0.283106i	−0.700267	+	0.713881i	$0.746936\pi$
$798$	2.33846	+	0.853421i	0.0827807	+	0.0302108i
$799$	7.96546	−	45.1743i	0.281798	−	1.59815i
$800$	−1.69746	−	2.94008i	−0.0600141	−	0.103948i
$801$	4.86886	+	8.46689i	0.172033	+	0.299163i
$802$	−0.938639	+	1.62577i	−0.0331445	+	0.0574080i
$803$	−5.94124	−	4.98529i	−0.209662	−	0.175927i
$804$	−19.8351	−	16.6729i	−0.699531	−	0.588008i
$805$	6.42466	+	36.4361i	0.226440	+	1.28420i
$806$	1.51848	−	1.27416i	0.0534863	−	0.0448803i
$807$	−8.80777	−	15.2860i	−0.310048	−	0.538093i
$808$	10.1324	−	3.68788i	0.356455	−	0.129739i
$809$	−16.4420			−0.578070			−0.289035	−	0.957319i	$-0.593334\pi$
$809$	−16.4420			−0.578070			−0.289035	+	0.957319i	$0.593334\pi$
$810$	1.36197	−	2.34027i	0.0478546	−	0.0822286i
$811$	49.2346			1.72886			0.864430	−	0.502753i	$-0.167679\pi$
$811$	49.2346			1.72886			0.864430	+	0.502753i	$0.167679\pi$
$812$	−4.60518	+	1.67615i	−0.161610	+	0.0588213i
$813$	5.94140	+	10.3114i	0.208374	+	0.361636i
$814$	2.13141	−	1.78847i	0.0747059	−	0.0626857i
$815$	3.12339	+	17.7136i	0.109407	+	0.620481i
$816$	−17.9373	−	15.0776i	−0.627930	−	0.527821i
$817$	−6.15080	−	5.16113i	−0.215189	−	0.180565i
$818$	−1.44416	+	2.50136i	−0.0504940	+	0.0874582i
$819$	−52.0489	−	0.0899927i	−1.81874	−	0.00314460i
$820$	−0.722725	−	1.25180i	−0.0252386	−	0.0437146i
$821$	−0.479682	+	2.72041i	−0.0167410	+	0.0949431i	−0.992033	−	0.125975i	$-0.959794\pi$
$821$	−0.479682	+	2.72041i	−0.0167410	+	0.0949431i	0.975292	+	0.220918i	$0.0709053\pi$
$822$	−0.174624	−	0.0637290i	−0.00609071	−	0.00222280i
$823$	31.0031	+	11.2842i	1.08070	+	0.393343i	0.820169	−	0.572122i	$-0.193880\pi$
$823$	31.0031	+	11.2842i	1.08070	+	0.393343i	0.260533	+	0.965465i	$0.416102\pi$
$824$	2.00377	+	0.729314i	0.0698048	+	0.0254069i
$825$	2.35368	−	1.97150i	0.0819444	−	0.0686389i
$826$	3.09685	−	17.5631i	0.107753	−	0.611099i
$827$	27.3913	+	47.4431i	0.952489	+	1.64976i	0.740013	+	0.672592i	$0.234819\pi$
$827$	27.3913	+	47.4431i	0.952489	+	1.64976i	0.212475	+	0.977166i	$0.431847\pi$
$828$	−37.7961	−	31.8262i	−1.31350	−	1.10604i
$829$	−25.5346	+	44.2272i	−0.886852	+	1.53607i	−0.0432768	+	0.999063i	$0.513780\pi$
$829$	−25.5346	+	44.2272i	−0.886852	+	1.53607i	−0.843576	+	0.537010i	$0.819554\pi$
$830$	−1.82239	−	1.52917i	−0.0632561	−	0.0530782i
$831$	8.02860	−	45.3034i	0.278509	−	1.57156i
$832$	−4.15018	−	23.5369i	−0.143882	−	0.815994i
$833$	−34.0918	+	28.6064i	−1.18121	+	0.991154i
$834$	−0.777077		0.000671783i	−0.0269080		2.32620e-5i
$835$	18.7354	−	6.81911i	0.648364	−	0.235985i
$836$	−3.76962			−0.130375
$837$	6.49791	−	5.42374i	0.224601	−	0.187472i
$838$	4.51449			0.155950
$839$	38.7316	−	14.0971i	1.33716	−	0.486688i	0.428245	−	0.903663i	$-0.359132\pi$
$839$	38.7316	−	14.0971i	1.33716	−	0.486688i	0.908918	+	0.416975i	$0.136910\pi$
$840$	4.37579	−	7.56398i	0.150979	−	0.260982i
$841$	−21.9410	+	18.4107i	−0.756587	+	0.634852i
$842$	1.93505	+	10.9742i	0.0666862	+	0.378196i
$843$	38.9518	−	14.1392i	1.34157	−	0.486979i
$844$	29.4663	+	24.7251i	1.01427	+	0.851074i
$845$	1.68022	−	2.91023i	0.0578015	−	0.100115i
$846$	−8.13516	+	6.80228i	−0.279693	+	0.233867i
$847$	−16.8525	−	29.1894i	−0.579059	−	1.00296i
$848$	2.39313	−	13.5721i	0.0821806	−	0.466069i
$849$	−4.04094	−	23.0337i	−0.138685	−	0.790515i
$850$	1.10380	+	0.401750i	0.0378600	+	0.0137799i
$851$	−42.2869	−	15.3912i	−1.44958	−	0.527602i
$852$	2.96236	+	16.8857i	0.101489	+	0.578495i
$853$	3.58449	−	20.3286i	0.122730	−	0.696039i	−0.859900	−	0.510463i	$-0.829474\pi$
$853$	3.58449	−	20.3286i	0.122730	−	0.696039i	0.982630	−	0.185576i	$-0.0594150\pi$
$854$	−5.47182	−	9.47746i	−0.187242	−	0.324312i
$855$	−2.56312	+	2.14317i	−0.0876568	+	0.0732949i
$856$	2.18360	−	3.78211i	0.0746339	−	0.129270i
$857$	28.2977	+	23.7446i	0.966630	+	0.811099i	0.982019	−	0.188783i	$-0.0604541\pi$
$857$	28.2977	+	23.7446i	0.966630	+	0.811099i	−0.0153887	+	0.999882i	$0.504899\pi$
$858$	−3.51205	+	1.27484i	−0.119899	+	0.0435225i
$859$	4.11514	+	23.3381i	0.140407	+	0.796286i	0.970941	+	0.239318i	$0.0769240\pi$
$859$	4.11514	+	23.3381i	0.140407	+	0.796286i	−0.830535	+	0.556967i	$0.811965\pi$
$860$	−10.5459	+	8.84905i	−0.359612	+	0.301750i
$861$	2.81618	−	4.86805i	0.0959752	−	0.165903i
$862$	4.05205	−	1.47482i	0.138013	−	0.0502327i
$863$	36.6147			1.24638			0.623189	−	0.782072i	$-0.285837\pi$
$863$	36.6147			1.24638			0.623189	+	0.782072i	$0.285837\pi$
$864$	3.01817	+	17.3804i	0.102680	+	0.591292i
$865$	−6.76573			−0.230042
$866$	−4.09000	+	1.48864i	−0.138984	+	0.0505859i
$867$	−3.04245	−	0.00263020i	−0.103327	−	8.93264e-5i
$868$	10.2202	−	8.57576i	0.346896	−	0.291080i
$869$	−3.96793	−	22.5032i	−0.134603	−	0.763370i
$870$	−0.0544088	+	0.307015i	−0.00184463	+	0.0104088i
$871$	24.2757	+	20.3697i	0.822550	+	0.690202i
$872$	−1.90626	+	3.30174i	−0.0645541	+	0.111811i
$873$	−4.57056	−	3.84864i	−0.154690	−	0.130257i
$874$	−1.44505	−	2.50291i	−0.0488797	−	0.0846621i
$875$	0.744841	−	4.22420i	0.0251802	−	0.142804i
$876$	11.0931	−	9.29185i	0.374800	−	0.313943i
$877$	−22.7520	−	8.28105i	−0.768280	−	0.279631i	−0.0720034	−	0.997404i	$-0.522939\pi$
$877$	−22.7520	−	8.28105i	−0.768280	−	0.279631i	−0.696277	+	0.717773i	$0.745161\pi$
$878$	4.22704	+	1.53852i	0.142656	+	0.0519224i
$879$	8.97197	+	3.27432i	0.302617	+	0.110440i
$880$	−1.06660	+	6.04900i	−0.0359552	+	0.203912i
$881$	−13.4734	−	23.3367i	−0.453931	−	0.786232i	0.544695	−	0.838634i	$-0.316646\pi$
$881$	−13.4734	−	23.3367i	−0.453931	−	0.786232i	−0.998626	+	0.0524023i	$0.983312\pi$
$882$	10.2882	+	0.0177883i	0.346421	+	0.000598963i
$883$	−0.494590	+	0.856656i	−0.0166443	+	0.0288288i	−0.874228	−	0.485516i	$-0.838632\pi$
$883$	−0.494590	+	0.856656i	−0.0166443	+	0.0288288i	0.857583	+	0.514345i	$0.171965\pi$
$884$	23.0998	+	19.3831i	0.776932	+	0.651923i
$885$	18.3229	+	15.4017i	0.615916	+	0.517723i
$886$	−1.81015	−	10.2659i	−0.0608132	−	0.344889i
$887$	19.0122	−	15.9532i	0.638368	−	0.535655i	−0.265148	−	0.964208i	$-0.585421\pi$
$887$	19.0122	−	15.9532i	0.638368	−	0.535655i	0.903517	+	0.428553i	$0.140976\pi$
$888$	5.30634	+	9.20923i	0.178069	+	0.309042i
$889$	−44.3854	+	16.1550i	−1.48864	+	0.541820i
$890$	0.979495			0.0328328
$891$	−15.0103	+	5.40459i	−0.502864	+	0.181061i
$892$	11.0425			0.369731
$893$	12.2956	−	4.47523i	0.411456	−	0.149758i
$894$	4.70871	+	8.17203i	0.157483	+	0.273314i
$895$	−7.23124	+	6.06773i	−0.241714	+	0.202822i
$896$	6.38146	+	36.1910i	0.213190	+	1.20906i
$897$	46.2577	+	38.8830i	1.54450	+	1.29826i
$898$	−5.88977	−	4.94210i	−0.196544	−	0.164920i
$899$	−0.487323	+	0.844068i	−0.0162531	+	0.0281512i
$900$	2.85564	+	4.96593i	0.0951881	+	0.165531i
$901$	7.76414	+	13.4479i	0.258661	+	0.448014i
$902$	0.0701031	−	0.397575i	0.00233418	−	0.0132378i
$903$	−50.3172	−	18.3632i	−1.67445	−	0.611090i
$904$	13.5940	+	4.94782i	0.452130	+	0.164562i
$905$	1.06411	+	0.387305i	0.0353723	+	0.0128745i
$906$	−8.47287	+	7.09711i	−0.281492	+	0.235786i
$907$	0.569479	−	3.22968i	0.0189092	−	0.107240i	−0.973892	−	0.227010i	$-0.927105\pi$
$907$	0.569479	−	3.22968i	0.0189092	−	0.107240i	0.992802	+	0.119771i	$0.0382160\pi$
$908$	14.6162	+	25.3160i	0.485055	+	0.840140i
$909$	−25.8596	+	9.36153i	−0.857710	+	0.310502i
$910$	−2.60990	+	4.52048i	−0.0865174	+	0.149853i
$911$	−30.1923	−	25.3344i	−1.00032	−	0.839365i	−0.0132884	−	0.999912i	$-0.504230\pi$
$911$	−30.1923	−	25.3344i	−1.00032	−	0.839365i	−0.987028	+	0.160546i	$0.948674\pi$
$912$	1.16637	−	6.58151i	0.0386222	−	0.217936i
$913$	2.43395	+	13.8036i	0.0805521	+	0.456833i
$914$	−4.42890	+	3.71629i	−0.146495	+	0.122924i
$915$	14.6881	+	0.0126979i	0.485574	+	0.000419779i
$916$	4.42678	−	1.61122i	0.146265	−	0.0532361i
$917$	−75.2587			−2.48526
$918$	−4.66544	−	3.93543i	−0.153983	−	0.129889i
$919$	−9.02247			−0.297624			−0.148812	−	0.988866i	$-0.547545\pi$
$919$	−9.02247			−0.297624			−0.148812	+	0.988866i	$0.547545\pi$
$920$	−9.53356	+	3.46993i	−0.314312	+	0.114400i
$921$	−4.13470	+	7.14724i	−0.136243	+	0.235509i
$922$	−2.58296	+	2.16736i	−0.0850653	+	0.0713782i
$923$	−3.64077	−	20.6478i	−0.119837	−	0.679632i
$924$	−23.6379	+	8.58037i	−0.777631	+	0.282273i
$925$	3.99657	+	3.35352i	0.131406	+	0.110263i
$926$	1.91526	−	3.31733i	0.0629393	−	0.109014i
$927$	−5.10756	−	1.86901i	−0.167754	−	0.0613862i
$928$	−1.01566	−	1.75918i	−0.0333408	−	0.0577480i
$929$	−4.32579	+	24.5328i	−0.141925	+	0.804894i	0.827861	+	0.560934i	$0.189558\pi$
$929$	−4.32579	+	24.5328i	−0.141925	+	0.804894i	−0.969785	+	0.243960i	$0.921553\pi$
$930$	−0.146675	−	0.836058i	−0.00480965	−	0.0274154i
$931$	−11.9290	−	4.34181i	−0.390958	−	0.142297i
$932$	15.1235	+	5.50452i	0.495388	+	0.180307i
$933$	3.25495	+	18.5535i	0.106562	+	0.607414i
$934$	−1.72078	+	9.75904i	−0.0563057	+	0.319326i
$935$	−3.46042	−	5.99362i	−0.113168	−	0.196012i
$936$	−2.45409	−	14.0600i	−0.0802146	−	0.459565i
$937$	12.7014	−	21.9995i	0.414938	−	0.718694i	−0.580484	−	0.814272i	$-0.697137\pi$
$937$	12.7014	−	21.9995i	0.414938	−	0.718694i	0.995422	+	0.0955779i	$0.0304699\pi$
$938$	−7.74516	−	6.49896i	−0.252888	−	0.212199i
$939$	20.2181	−	7.33900i	0.659793	−	0.239499i
$940$	−3.89570	−	22.0936i	−0.127064	−	0.720614i
$941$	18.5701	−	15.5822i	0.605368	−	0.507964i	−0.287798	−	0.957691i	$-0.592923\pi$
$941$	18.5701	−	15.5822i	0.605368	−	0.507964i	0.893166	+	0.449727i	$0.148479\pi$
$942$	1.42886	−	2.46992i	0.0465547	−	0.0804744i
$943$	−6.13563	+	2.23319i	−0.199804	+	0.0727226i
$944$	−47.8861			−1.55856
$945$	−11.1941	+	19.2732i	−0.364145	+	0.626957i
$946$	−3.84497			−0.125011
$947$	−10.2582	+	3.73369i	−0.333348	+	0.121329i	−0.503271	−	0.864129i	$-0.667870\pi$
$947$	−10.2582	+	3.73369i	−0.333348	+	0.121329i	0.169923	+	0.985457i	$0.445648\pi$
$948$	42.6337	+	0.0368569i	1.38468	+	0.00119706i
$949$	−13.5568	+	11.3755i	−0.440073	+	0.369265i
$950$	0.0581832	+	0.329973i	0.00188771	+	0.0107057i
$951$	−3.33465	+	18.8166i	−0.108134	+	0.610171i
$952$	−15.0894	−	12.6615i	−0.489050	−	0.410361i
$953$	7.28673	−	12.6210i	0.236040	−	0.408834i	−0.723534	−	0.690289i	$-0.757484\pi$
$953$	7.28673	−	12.6210i	0.236040	−	0.408834i	0.959575	+	0.281455i	$0.0908169\pi$
$954$	0.629467	−	3.53414i	0.0203798	−	0.114422i
$955$	−11.8120	−	20.4590i	−0.382228	−	0.662039i
$956$	5.05641	−	28.6763i	0.163536	−	0.927458i
$957$	1.40831	−	1.17964i	0.0455242	−	0.0381323i
$958$	6.26493	+	2.28025i	0.202411	+	0.0736715i
$959$	1.43784	+	0.523331i	0.0464303	+	0.0168992i
$960$	−9.61411	−	3.50867i	−0.310294	−	0.113242i
$961$	−4.92235	+	27.9160i	−0.158785	+	0.900517i
$962$	−3.17442	−	5.49825i	−0.102347	−	0.177271i
$963$	−5.58612	+	9.63692i	−0.180010	+	0.310545i
$964$	−0.621349	+	1.07621i	−0.0200123	+	0.0346623i
$965$	2.08055	+	1.74579i	0.0669752	+	0.0561989i
$966$	−14.7585	−	12.4056i	−0.474847	−	0.399144i
$967$	−8.32112	−	47.1914i	−0.267589	−	1.51757i	−0.761560	−	0.648095i	$-0.775566\pi$
$967$	−8.32112	−	47.1914i	−0.267589	−	1.51757i	0.493971	−	0.869478i	$-0.335545\pi$
$968$	7.08006	−	5.94088i	0.227562	−	0.190947i
$969$	3.75998	+	6.52550i	0.120788	+	0.209629i
$970$	−0.563086	+	0.204946i	−0.0180796	+	0.00658043i
$971$	10.0839			0.323608			0.161804	−	0.986823i	$-0.448269\pi$
$971$	10.0839			0.323608			0.161804	+	0.986823i	$0.448269\pi$
$972$	−5.04204	−	29.3358i	−0.161723	−	0.940945i
$973$	6.39638			0.205058
$974$	4.44066	−	1.61627i	0.142288	−	0.0517886i
$975$	−3.49766	−	6.07023i	−0.112015	−	0.194403i
$976$	−22.5099	+	18.8881i	−0.720526	+	0.604593i
$977$	5.59597	+	31.7363i	0.179031	+	1.01534i	0.933387	+	0.358870i	$0.116838\pi$
$977$	5.59597	+	31.7363i	0.179031	+	1.01534i	−0.754356	+	0.656465i	$0.772051\pi$
$978$	−7.17493	−	6.03106i	−0.229429	−	0.192852i
$979$	−4.42090	−	3.70957i	−0.141293	−	0.118558i
$980$	−10.8828	+	18.8496i	−0.347638	+	0.602128i
$981$	4.87662	−	8.41293i	0.155698	−	0.268604i
$982$	3.99912	+	6.92667i	0.127617	+	0.221039i
$983$	0.439376	−	2.49182i	0.0140139	−	0.0794768i	−0.976999	−	0.213245i	$-0.931597\pi$
$983$	0.439376	−	2.49182i	0.0140139	−	0.0794768i	0.991013	+	0.133768i	$0.0427078\pi$
$984$	1.44870	+	0.528703i	0.0461829	+	0.0168544i
$985$	−13.4135	−	4.88210i	−0.427388	−	0.155557i
$986$	0.660453	+	0.240385i	0.0210331	+	0.00765542i
$987$	66.9147	−	56.0496i	2.12992	−	1.78408i
$988$	−1.49365	+	8.47090i	−0.0475193	+	0.269495i
$989$	31.0935	+	53.8556i	0.988716	+	1.71251i
$990$	−0.280549	+	1.57514i	−0.00891643	+	0.0500613i
$991$	25.3489	−	43.9056i	0.805234	−	1.39471i	−0.110899	−	0.993832i	$-0.535373\pi$
$991$	25.3489	−	43.9056i	0.805234	−	1.39471i	0.916133	−	0.400875i	$-0.131294\pi$
$992$	4.23621	+	3.55461i	0.134500	+	0.112859i
$993$	0.612343	−	3.45530i	0.0194321	−	0.109651i
$994$	1.16159	+	6.58769i	0.0368433	+	0.208949i
$995$	−16.2940	+	13.6723i	−0.516554	+	0.433440i
$996$	−26.1518	−	0.0226082i	−0.828650	−	0.000716369i
$997$	−13.1297	+	4.77883i	−0.415822	+	0.151347i	−0.541455	−	0.840730i	$-0.682126\pi$
$997$	−13.1297	+	4.77883i	−0.415822	+	0.151347i	0.125632	+	0.992077i	$0.459904\pi$
$998$	−0.636279			−0.0201411
$999$	−13.4936	−	23.5122i	−0.426919	−	0.743894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.k.a.61.3	yes	30
3.2	odd	2		405.2.k.a.181.3		30
5.2	odd	4		675.2.u.c.574.5		60
5.3	odd	4		675.2.u.c.574.6		60
5.4	even	2		675.2.l.d.601.3		30
27.2	odd	18		3645.2.a.g.1.7		15
27.4	even	9	inner	135.2.k.a.31.3	✓	30
27.23	odd	18		405.2.k.a.226.3		30
27.25	even	9		3645.2.a.h.1.9		15
135.4	even	18		675.2.l.d.301.3		30
135.58	odd	36		675.2.u.c.274.5		60
135.112	odd	36		675.2.u.c.274.6		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.31.3	✓	30	27.4	even	9	inner
135.2.k.a.61.3	yes	30	1.1	even	1	trivial
405.2.k.a.181.3		30	3.2	odd	2
405.2.k.a.226.3		30	27.23	odd	18
675.2.l.d.301.3		30	135.4	even	18
675.2.l.d.601.3		30	5.4	even	2
675.2.u.c.274.5		60	135.58	odd	36
675.2.u.c.274.6		60	135.112	odd	36
675.2.u.c.574.5		60	5.2	odd	4
675.2.u.c.574.6		60	5.3	odd	4
3645.2.a.g.1.7		15	27.2	odd	18
3645.2.a.h.1.9		15	27.25	even	9

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.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.282715 + 0.102900i) q^{2} +(-0.864728 - 1.50075i) q^{3} +(-1.46275 + 1.22739i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.398898 + 0.335304i) q^{6} +(-3.28585 - 2.75715i) q^{7} +(0.588102 - 1.01862i) q^{8} +(-1.50449 + 2.59548i) q^{9} +O(q^{10})\)	\(q+(-0.282715 + 0.102900i) q^{2} +(-0.864728 - 1.50075i) q^{3} +(-1.46275 + 1.22739i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.398898 + 0.335304i) q^{6} +(-3.28585 - 2.75715i) q^{7} +(0.588102 - 1.01862i) q^{8} +(-1.50449 + 2.59548i) q^{9} +(0.150430 + 0.260552i) q^{10} +(0.307813 - 1.74570i) q^{11} +(3.10689 + 1.13386i) q^{12} +(-3.80087 - 1.38340i) q^{13} +(1.21267 + 0.441375i) q^{14} +(-1.32779 + 1.11219i) q^{15} +(0.601708 - 3.41245i) q^{16} +(1.95214 + 3.38121i) q^{17} +(0.158267 - 0.888593i) q^{18} +(-0.556845 + 0.964484i) q^{19} +(1.46275 + 1.22739i) q^{20} +(-1.29643 + 7.31542i) q^{21} +(0.0926084 + 0.525208i) q^{22} +(6.60755 - 5.54440i) q^{23} +(-2.03724 - 0.00176120i) q^{24} +(-0.939693 + 0.342020i) q^{25} +1.21692 q^{26} +(5.19613 + 0.0134762i) q^{27} +8.19048 q^{28} +(-0.562260 + 0.204646i) q^{29} +(0.260942 - 0.451063i) q^{30} +(1.24781 - 1.04704i) q^{31} +(0.589520 + 3.34334i) q^{32} +(-2.88602 + 1.04760i) q^{33} +(-0.899826 - 0.755043i) q^{34} +(-2.14468 + 3.71470i) q^{35} +(-0.984980 - 5.64313i) q^{36} +(-2.60857 - 4.51818i) q^{37} +(0.0581832 - 0.329973i) q^{38} +(1.21058 + 6.90042i) q^{39} +(-1.10527 - 0.402285i) q^{40} +(-0.711333 - 0.258904i) q^{41} +(-0.386236 - 2.20158i) q^{42} +(-1.25194 + 7.10010i) q^{43} +(1.69240 + 2.93132i) q^{44} +(2.81730 + 1.03093i) q^{45} +(-1.29754 + 2.24740i) q^{46} +(-9.00022 - 7.55208i) q^{47} +(-5.64155 + 2.04783i) q^{48} +(1.97936 + 11.2255i) q^{49} +(0.230471 - 0.193388i) q^{50} +(3.38627 - 5.85350i) q^{51} +(7.25771 - 2.64159i) q^{52} +3.97724 q^{53} +(-1.47041 + 0.530872i) q^{54} -1.77263 q^{55} +(-4.74091 + 1.72555i) q^{56} +(1.92897 + 0.00166759i) q^{57} +(0.137901 - 0.115713i) q^{58} +(-2.39974 - 13.6096i) q^{59} +(0.577126 - 3.25658i) q^{60} +(-6.49619 - 5.45095i) q^{61} +(-0.245035 + 0.424413i) q^{62} +(12.0997 - 4.38024i) q^{63} +(2.95440 + 5.11717i) q^{64} +(-0.702373 + 3.98336i) q^{65} +(0.708124 - 0.593144i) q^{66} +(-7.36217 - 2.67961i) q^{67} +(-7.00557 - 2.54982i) q^{68} +(-14.0345 - 5.12188i) q^{69} +(0.224092 - 1.27089i) q^{70} +(2.59176 + 4.48907i) q^{71} +(1.75902 + 3.05891i) q^{72} +(2.18764 - 3.78911i) q^{73} +(1.20240 + 1.00894i) q^{74} +(1.32586 + 1.11449i) q^{75} +(-0.369276 - 2.09427i) q^{76} +(-5.82458 + 4.88740i) q^{77} +(-1.05230 - 1.82628i) q^{78} +(12.1133 - 4.40888i) q^{79} -3.46510 q^{80} +(-4.47302 - 7.80974i) q^{81} +0.227746 q^{82} +(-7.43037 + 2.70443i) q^{83} +(-7.08254 - 12.2918i) q^{84} +(2.99086 - 2.50963i) q^{85} +(-0.376657 - 2.13613i) q^{86} +(0.793324 + 0.666848i) q^{87} +(-1.59718 - 1.34019i) q^{88} +(1.62783 - 2.81949i) q^{89} +(-0.902576 - 0.00156056i) q^{90} +(8.67483 + 15.0252i) q^{91} +(-2.86005 + 16.2201i) q^{92} +(-2.65036 - 0.967248i) q^{93} +(3.32160 + 1.20896i) q^{94} +(1.04653 + 0.380904i) q^{95} +(4.50773 - 3.77580i) q^{96} +(-0.345856 + 1.96145i) q^{97} +(-1.71470 - 2.96995i) q^{98} +(4.06782 + 3.42530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + 3 q^{13} - 9 q^{14} - 6 q^{15} + 12 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{19} - 36 q^{21} - 51 q^{22} + 18 q^{23} + 45 q^{24} - 18 q^{26} - 9 q^{27} - 60 q^{28} + 18 q^{29} - 3 q^{30} + 12 q^{31} + 36 q^{32} + 27 q^{33} - 69 q^{34} - 12 q^{35} - 42 q^{36} + 24 q^{37} - 24 q^{38} + 6 q^{39} + 9 q^{40} - 75 q^{41} - 18 q^{42} + 6 q^{43} + 12 q^{44} - 6 q^{45} + 30 q^{46} + 45 q^{47} - 27 q^{48} - 36 q^{49} + 21 q^{51} + 30 q^{52} + 36 q^{53} + 18 q^{54} + 30 q^{56} + 30 q^{57} + 27 q^{58} - 27 q^{59} - 12 q^{61} + 36 q^{62} + 18 q^{63} + 27 q^{64} + 6 q^{65} + 78 q^{66} - 30 q^{67} + 69 q^{68} - 117 q^{69} + 27 q^{70} + 12 q^{71} + 9 q^{72} + 21 q^{73} - 30 q^{76} - 36 q^{77} + 66 q^{78} + 54 q^{79} + 6 q^{80} - 27 q^{81} - 48 q^{82} - 87 q^{83} + 45 q^{84} + 27 q^{85} + 18 q^{86} - 27 q^{87} - 18 q^{88} + 9 q^{89} - 6 q^{90} + 51 q^{91} + 24 q^{92} + 36 q^{93} + 15 q^{94} + 21 q^{95} - 15 q^{96} - 75 q^{97} - 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + 3 * q^13 - 9 * q^14 - 6 * q^15 + 12 * q^16 - 12 * q^17 + 6 * q^18 + 24 * q^19 - 36 * q^21 - 51 * q^22 + 18 * q^23 + 45 * q^24 - 18 * q^26 - 9 * q^27 - 60 * q^28 + 18 * q^29 - 3 * q^30 + 12 * q^31 + 36 * q^32 + 27 * q^33 - 69 * q^34 - 12 * q^35 - 42 * q^36 + 24 * q^37 - 24 * q^38 + 6 * q^39 + 9 * q^40 - 75 * q^41 - 18 * q^42 + 6 * q^43 + 12 * q^44 - 6 * q^45 + 30 * q^46 + 45 * q^47 - 27 * q^48 - 36 * q^49 + 21 * q^51 + 30 * q^52 + 36 * q^53 + 18 * q^54 + 30 * q^56 + 30 * q^57 + 27 * q^58 - 27 * q^59 - 12 * q^61 + 36 * q^62 + 18 * q^63 + 27 * q^64 + 6 * q^65 + 78 * q^66 - 30 * q^67 + 69 * q^68 - 117 * q^69 + 27 * q^70 + 12 * q^71 + 9 * q^72 + 21 * q^73 - 30 * q^76 - 36 * q^77 + 66 * q^78 + 54 * q^79 + 6 * q^80 - 27 * q^81 - 48 * q^82 - 87 * q^83 + 45 * q^84 + 27 * q^85 + 18 * q^86 - 27 * q^87 - 18 * q^88 + 9 * q^89 - 6 * q^90 + 51 * q^91 + 24 * q^92 + 36 * q^93 + 15 * q^94 + 21 * q^95 - 15 * q^96 - 75 * q^97 - 15 * q^98 + 123 * q^99

Introduction

L-functions

Modular forms

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