LMFDB - Embedded newform 162.2.g.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	162.7
Dual form			162.2.g.b.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597159 + 0.802123i) q^{2} +(0.156275 + 1.72499i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(3.59342 - 2.36343i) q^{5} +(-1.29033 + 1.15544i) q^{6} +(-0.0885835 + 0.0938930i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.95116 + 0.539145i) q^{9} +O(q^{10})$	\(q+(0.597159 + 0.802123i) q^{2} +(0.156275 + 1.72499i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(3.59342 - 2.36343i) q^{5} +(-1.29033 + 1.15544i) q^{6} +(-0.0885835 + 0.0938930i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.95116 + 0.539145i) q^{9} +(4.04160 + 1.47102i) q^{10} +(-2.32463 + 1.16747i) q^{11} +(-1.69734 - 0.345022i) q^{12} +(-1.86292 - 4.31874i) q^{13} +(-0.128212 - 0.0149858i) q^{14} +(4.63844 + 5.82925i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-3.83323 + 3.21646i) q^{17} +(-2.19477 - 2.04524i) q^{18} +(-1.93631 - 1.62476i) q^{19} +(1.23353 + 4.12029i) q^{20} +(-0.175808 - 0.138132i) q^{21} +(-2.32463 - 1.16747i) q^{22} +(3.20000 + 3.39181i) q^{23} +(-0.736831 - 1.56751i) q^{24} +(5.34645 - 12.3945i) q^{25} +(2.35170 - 4.07326i) q^{26} +(-1.39121 - 5.00645i) q^{27} +(-0.0645425 - 0.111791i) q^{28} +(3.33811 - 0.390169i) q^{29} +(-1.90589 + 7.20159i) q^{30} +(3.45836 - 0.819647i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(-2.37716 - 3.82750i) q^{33} +(-4.86905 - 1.15398i) q^{34} +(-0.0964080 + 0.546757i) q^{35} +(0.329906 - 2.98181i) q^{36} +(-0.386950 - 2.19450i) q^{37} +(0.146971 - 2.52339i) q^{38} +(7.15863 - 3.88842i) q^{39} +(-2.56837 + 3.44992i) q^{40} +(0.110999 - 0.149098i) q^{41} +(0.00581401 - 0.223506i) q^{42} +(-0.211858 + 3.63746i) q^{43} +(-0.451715 - 2.56180i) q^{44} +(-9.33050 + 8.91222i) q^{45} +(-0.809736 + 4.59224i) q^{46} +(-7.75700 - 1.83844i) q^{47} +(0.817329 - 1.52708i) q^{48} +(0.406045 + 6.97152i) q^{49} +(13.1346 - 3.11295i) q^{50} +(-6.14739 - 6.10962i) q^{51} +(4.67160 - 0.546031i) q^{52} +(6.41895 + 11.1179i) q^{53} +(3.18502 - 4.10557i) q^{54} +(-5.59412 + 9.68930i) q^{55} +(0.0511279 - 0.118528i) q^{56} +(2.50008 - 3.59401i) q^{57} +(2.30634 + 2.44458i) q^{58} +(-4.61669 - 2.31859i) q^{59} +(-6.91468 + 2.77173i) q^{60} +(-1.75607 - 5.86569i) q^{61} +(2.72265 + 2.28457i) q^{62} +(0.210802 - 0.324852i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-16.9013 - 11.1161i) q^{65} +(1.65059 - 4.19240i) q^{66} +(-3.54382 - 0.414214i) q^{67} +(-1.98195 - 4.59469i) q^{68} +(-5.35074 + 6.05002i) q^{69} +(-0.496138 + 0.249170i) q^{70} +(15.2792 + 5.56117i) q^{71} +(2.58878 - 1.51599i) q^{72} +(2.39884 - 0.873108i) q^{73} +(1.52919 - 1.62085i) q^{74} +(22.2158 + 7.28561i) q^{75} +(2.11184 - 1.38898i) q^{76} +(0.0963062 - 0.321685i) q^{77} +(7.39383 + 3.42010i) q^{78} +(-9.01273 - 12.1062i) q^{79} -4.30098 q^{80} +(8.41864 - 3.18220i) q^{81} +0.185879 q^{82} +(8.26834 + 11.1063i) q^{83} +(0.182751 - 0.128805i) q^{84} +(-6.17252 + 20.6176i) q^{85} +(-3.04421 + 2.00221i) q^{86} +(1.19470 + 5.69722i) q^{87} +(1.78514 - 1.89213i) q^{88} +(-10.3572 + 3.76972i) q^{89} +(-12.7205 - 2.16221i) q^{90} +(0.570523 + 0.207653i) q^{91} +(-4.16709 + 2.09279i) q^{92} +(1.95434 + 5.83754i) q^{93} +(-3.15750 - 7.31991i) q^{94} +(-10.7979 - 1.26210i) q^{95} +(1.71298 - 0.256310i) q^{96} +(6.37553 + 4.19325i) q^{97} +(-5.34955 + 4.48880i) q^{98} +(6.23090 - 4.69870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

Coefficient data

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

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

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

$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$3$	0.156275	+	1.72499i	0.0902255	+	0.995921i
$3$	0.156275	+	1.72499i	0.0902255	+	0.995921i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	3.59342	−	2.36343i	1.60702	−	1.05696i	0.652944	−	0.757406i	$-0.273534\pi$
$5$	3.59342	−	2.36343i	1.60702	−	1.05696i	0.954080	−	0.299551i	$-0.0968368\pi$
$6$	−1.29033	+	1.15544i	−0.526775	+	0.471707i
$7$	−0.0885835	+	0.0938930i	−0.0334814	+	0.0354882i	−0.743898	−	0.668293i	$-0.767025\pi$
$7$	−0.0885835	+	0.0938930i	−0.0334814	+	0.0354882i	0.710416	+	0.703782i	$0.248507\pi$
$8$	−0.939693	+	0.342020i	−0.332232	+	0.120922i
$9$	−2.95116	+	0.539145i	−0.983719	+	0.179715i
$10$	4.04160	+	1.47102i	1.27807	+	0.465178i
$11$	−2.32463	+	1.16747i	−0.700902	+	0.352006i	−0.763299	−	0.646045i	$-0.776422\pi$
$11$	−2.32463	+	1.16747i	−0.700902	+	0.352006i	0.0623973	+	0.998051i	$0.480125\pi$
$12$	−1.69734	−	0.345022i	−0.489980	−	0.0995992i
$13$	−1.86292	−	4.31874i	−0.516681	−	1.19780i	−0.954357	−	0.298669i	$-0.903457\pi$
$13$	−1.86292	−	4.31874i	−0.516681	−	1.19780i	0.437676	−	0.899133i	$-0.355802\pi$
$14$	−0.128212	−	0.0149858i	−0.0342661	−	0.00400514i
$15$	4.63844	+	5.82925i	1.19764	+	1.50511i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	−3.83323	+	3.21646i	−0.929695	+	0.780107i	−0.975763	−	0.218832i	$-0.929775\pi$
$17$	−3.83323	+	3.21646i	−0.929695	+	0.780107i	0.0460677	+	0.998938i	$0.485331\pi$
$18$	−2.19477	−	2.04524i	−0.517312	−	0.482067i
$19$	−1.93631	−	1.62476i	−0.444219	−	0.372744i	0.393066	−	0.919510i	$-0.371414\pi$
$19$	−1.93631	−	1.62476i	−0.444219	−	0.372744i	−0.837286	+	0.546766i	$0.815859\pi$
$20$	1.23353	+	4.12029i	0.275827	+	0.921326i
$21$	−0.175808	−	0.138132i	−0.0383644	−	0.0301429i
$22$	−2.32463	−	1.16747i	−0.495612	−	0.248906i
$23$	3.20000	+	3.39181i	0.667247	+	0.707240i	0.969253	−	0.246066i	$-0.0791379\pi$
$23$	3.20000	+	3.39181i	0.667247	+	0.707240i	−0.302006	+	0.953306i	$0.597656\pi$
$24$	−0.736831	−	1.56751i	−0.150405	−	0.319966i
$25$	5.34645	−	12.3945i	1.06929	−	2.47890i
$26$	2.35170	−	4.07326i	0.461206	−	0.798832i
$27$	−1.39121	−	5.00645i	−0.267739	−	0.963492i
$28$	−0.0645425	−	0.111791i	−0.0121974	−	0.0211265i
$29$	3.33811	−	0.390169i	0.619871	−	0.0724526i	0.199640	−	0.979869i	$-0.436023\pi$
$29$	3.33811	−	0.390169i	0.619871	−	0.0724526i	0.420232	+	0.907417i	$0.361949\pi$
$30$	−1.90589	+	7.20159i	−0.347966	+	1.31482i
$31$	3.45836	−	0.819647i	0.621140	−	0.147213i	0.0920163	−	0.995757i	$-0.470669\pi$
$31$	3.45836	−	0.819647i	0.621140	−	0.147213i	0.529124	+	0.848545i	$0.322521\pi$
$32$	−0.0581448	−	0.998308i	−0.0102787	−	0.176478i
$33$	−2.37716	−	3.82750i	−0.413810	−	0.666283i
$34$	−4.86905	−	1.15398i	−0.835034	−	0.197907i
$35$	−0.0964080	+	0.546757i	−0.0162959	+	0.0924188i
$36$	0.329906	−	2.98181i	0.0549843	−	0.496968i
$37$	−0.386950	−	2.19450i	−0.0636141	−	0.360774i	−0.999953	−	0.00967658i	$-0.996920\pi$
$37$	−0.386950	−	2.19450i	−0.0636141	−	0.360774i	0.936339	−	0.351097i	$-0.114191\pi$
$38$	0.146971	−	2.52339i	0.0238418	−	0.409349i
$39$	7.15863	−	3.88842i	1.14630	−	0.622646i
$40$	−2.56837	+	3.44992i	−0.406095	+	0.545480i
$41$	0.110999	−	0.149098i	0.0173351	−	0.0232851i	−0.793371	−	0.608738i	$-0.791676\pi$
$41$	0.110999	−	0.149098i	0.0173351	−	0.0232851i	0.810706	+	0.585453i	$0.199083\pi$
$42$	0.00581401	−	0.223506i	0.000897121	−	0.0344877i
$43$	−0.211858	+	3.63746i	−0.0323081	+	0.554708i	0.942853	+	0.333210i	$0.108132\pi$
$43$	−0.211858	+	3.63746i	−0.0323081	+	0.554708i	−0.975161	+	0.221498i	$0.928905\pi$
$44$	−0.451715	−	2.56180i	−0.0680986	−	0.386206i
$45$	−9.33050	+	8.91222i	−1.39091	+	1.32855i
$46$	−0.809736	+	4.59224i	−0.119389	+	0.677089i
$47$	−7.75700	−	1.83844i	−1.13147	−	0.268164i	−0.378106	−	0.925762i	$-0.623424\pi$
$47$	−7.75700	−	1.83844i	−1.13147	−	0.268164i	−0.753369	+	0.657598i	$0.771573\pi$
$48$	0.817329	−	1.52708i	0.117971	−	0.220415i
$49$	0.406045	+	6.97152i	0.0580064	+	0.995932i
$50$	13.1346	−	3.11295i	1.85751	−	0.440238i
$51$	−6.14739	−	6.10962i	−0.860807	−	0.855518i
$52$	4.67160	−	0.546031i	0.647834	−	0.0757209i
$53$	6.41895	+	11.1179i	0.881710	+	1.52717i	0.849438	+	0.527688i	$0.176941\pi$
$53$	6.41895	+	11.1179i	0.881710	+	1.52717i	0.0322723	+	0.999479i	$0.489726\pi$
$54$	3.18502	−	4.10557i	0.433426	−	0.558697i
$55$	−5.59412	+	9.68930i	−0.754311	+	1.30651i
$56$	0.0511279	−	0.118528i	0.00683226	−	0.0158390i
$57$	2.50008	−	3.59401i	0.331144	−	0.476039i
$58$	2.30634	+	2.44458i	0.302838	+	0.320989i
$59$	−4.61669	−	2.31859i	−0.601042	−	0.301855i	0.122139	−	0.992513i	$-0.461025\pi$
$59$	−4.61669	−	2.31859i	−0.601042	−	0.301855i	−0.723181	+	0.690658i	$0.757321\pi$
$60$	−6.91468	+	2.77173i	−0.892681	+	0.357829i
$61$	−1.75607	−	5.86569i	−0.224842	−	0.751025i	−0.993746	−	0.111661i	$-0.964383\pi$
$61$	−1.75607	−	5.86569i	−0.224842	−	0.751025i	0.768904	−	0.639364i	$-0.220802\pi$
$62$	2.72265	+	2.28457i	0.345777	+	0.290141i
$63$	0.210802	−	0.324852i	0.0265585	−	0.0409275i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	−16.9013	−	11.1161i	−2.09634	−	1.37879i
$66$	1.65059	−	4.19240i	0.203174	−	0.516049i
$67$	−3.54382	−	0.414214i	−0.432947	−	0.0506042i	−0.103171	−	0.994664i	$-0.532899\pi$
$67$	−3.54382	−	0.414214i	−0.432947	−	0.0506042i	−0.329776	+	0.944059i	$0.606973\pi$
$68$	−1.98195	−	4.59469i	−0.240347	−	0.557188i
$69$	−5.35074	+	6.05002i	−0.644153	+	0.728336i
$70$	−0.496138	+	0.249170i	−0.0592998	+	0.0297815i
$71$	15.2792	+	5.56117i	1.81331	+	0.659990i	0.996549	+	0.0830097i	$0.0264533\pi$
$71$	15.2792	+	5.56117i	1.81331	+	0.659990i	0.816758	+	0.576980i	$0.195769\pi$
$72$	2.58878	−	1.51599i	0.305091	−	0.178661i
$73$	2.39884	−	0.873108i	0.280764	−	0.102190i	−0.197800	−	0.980242i	$-0.563380\pi$
$73$	2.39884	−	0.873108i	0.280764	−	0.102190i	0.478564	+	0.878053i	$0.341158\pi$
$74$	1.52919	−	1.62085i	0.177765	−	0.188420i
$75$	22.2158	+	7.28561i	2.56526	+	0.841270i
$76$	2.11184	−	1.38898i	0.242244	−	0.159327i
$77$	0.0963062	−	0.321685i	0.0109751	−	0.0366594i
$78$	7.39383	+	3.42010i	0.837187	+	0.387250i
$79$	−9.01273	−	12.1062i	−1.01401	−	1.36205i	−0.930803	−	0.365522i	$-0.880890\pi$
$79$	−9.01273	−	12.1062i	−1.01401	−	1.36205i	−0.0832090	−	0.996532i	$-0.526517\pi$
$80$	−4.30098			−0.480864
$81$	8.41864	−	3.18220i	0.935405	−	0.353578i
$82$	0.185879			0.0205269
$83$	8.26834	+	11.1063i	0.907568	+	1.21908i	0.975191	+	0.221365i	$0.0710512\pi$
$83$	8.26834	+	11.1063i	0.907568	+	1.21908i	−0.0676225	+	0.997711i	$0.521541\pi$
$84$	0.182751	−	0.128805i	0.0199398	−	0.0140538i
$85$	−6.17252	+	20.6176i	−0.669504	+	2.23630i
$86$	−3.04421	+	2.00221i	−0.328265	+	0.215903i
$87$	1.19470	+	5.69722i	0.128085	+	0.610806i
$88$	1.78514	−	1.89213i	0.190296	−	0.201702i
$89$	−10.3572	+	3.76972i	−1.09786	+	0.399589i	−0.826528	−	0.562896i	$-0.809687\pi$
$89$	−10.3572	+	3.76972i	−1.09786	+	0.399589i	−0.271335	+	0.962485i	$0.587465\pi$
$90$	−12.7205	−	2.16221i	−1.34086	−	0.227917i
$91$	0.570523	+	0.207653i	0.0598071	+	0.0217680i
$92$	−4.16709	+	2.09279i	−0.434449	+	0.218188i
$93$	1.95434	+	5.83754i	0.202655	+	0.605325i
$94$	−3.15750	−	7.31991i	−0.325671	−	0.754991i
$95$	−10.7979	−	1.26210i	−1.10785	−	0.129489i
$96$	1.71298	−	0.256310i	0.174830	−	0.0261595i
$97$	6.37553	+	4.19325i	0.647337	+	0.425760i	0.830267	−	0.557366i	$-0.188188\pi$
$97$	6.37553	+	4.19325i	0.647337	+	0.425760i	−0.182930	+	0.983126i	$0.558558\pi$
$98$	−5.34955	+	4.48880i	−0.540386	+	0.453438i
$99$	6.23090	−	4.69870i	0.626229	−	0.472238i
$100$	10.3404	+	8.67662i	1.03404	+	0.867662i
$101$	−3.24933	−	10.8535i	−0.323320	−	1.07996i	−0.952965	−	0.303081i	$-0.901985\pi$
$101$	−3.24933	−	10.8535i	−0.323320	−	1.07996i	0.629645	−	0.776883i	$-0.283200\pi$
$102$	1.22970	−	8.57938i	0.121758	−	0.849485i
$103$	0.651479	+	0.327185i	0.0641921	+	0.0322385i	0.480606	−	0.876937i	$-0.340417\pi$
$103$	0.651479	+	0.327185i	0.0641921	+	0.0322385i	−0.416414	+	0.909175i	$0.636713\pi$
$104$	3.22767	+	3.42113i	0.316499	+	0.335469i
$105$	−0.958215	−	0.0808580i	−0.0935122	−	0.00789093i
$106$	−5.08483	+	11.7880i	−0.493882	+	1.14495i
$107$	−2.55359	+	4.42294i	−0.246865	+	0.427582i	−0.962654	−	0.270734i	$-0.912734\pi$
$107$	−2.55359	+	4.42294i	−0.246865	+	0.427582i	0.715790	+	0.698316i	$0.246067\pi$
$108$	5.19513	+	0.103100i	0.499902	+	0.00992084i
$109$	0.870428	+	1.50763i	0.0833719	+	0.144404i	0.904696	−	0.426057i	$-0.140098\pi$
$109$	0.870428	+	1.50763i	0.0833719	+	0.144404i	−0.821324	+	0.570461i	$0.806764\pi$
$110$	−11.1126	+	1.29888i	−1.05954	+	0.123843i
$111$	3.72501	−	1.01043i	0.353563	−	0.0959057i
$112$	0.125605	−	0.0297690i	0.0118686	−	0.00281291i
$113$	−0.0928637	−	1.59441i	−0.00873588	−	0.149989i	−0.999855	−	0.0170141i	$-0.994584\pi$
$113$	−0.0928637	−	1.59441i	−0.00873588	−	0.149989i	0.991119	−	0.132975i	$-0.0424531\pi$
$114$	4.37579	−	0.140821i	0.409830	−	0.0131891i
$115$	19.5152	+	4.62519i	1.81980	+	0.431302i
$116$	−0.583603	+	3.30978i	−0.0541862	+	0.307305i
$117$	7.82620	+	11.7409i	0.723532	+	1.08544i
$118$	−0.897102	−	5.08772i	−0.0825849	−	0.468362i
$119$	0.0375576	−	0.644839i	0.00344290	−	0.0591123i
$120$	−6.35243	−	3.89126i	−0.579895	−	0.355222i
$121$	−2.52784	+	3.39548i	−0.229804	+	0.308680i
$122$	3.65635	−	4.91134i	0.331031	−	0.444651i
$123$	0.274538	+	0.168172i	0.0247542	+	0.0151635i
$124$	−0.206656	+	3.54815i	−0.0185583	+	0.318634i
$125$	−6.34711	−	35.9963i	−0.567703	−	3.21960i
$126$	0.386454	−	0.0248994i	0.0344280	−	0.00221821i
$127$	−0.937505	+	5.31685i	−0.0831901	+	0.471795i	0.914542	+	0.404490i	$0.132551\pi$
$127$	−0.937505	+	5.31685i	−0.0831901	+	0.471795i	−0.997732	+	0.0673044i	$0.978560\pi$
$128$	0.973045	+	0.230616i	0.0860058	+	0.0203838i
$129$	−6.30768	+	0.202993i	−0.555361	+	0.0178725i
$130$	−1.17622	−	20.1950i	−0.103162	−	1.77122i
$131$	5.79791	−	1.37413i	0.506566	−	0.120058i	0.0306167	−	0.999531i	$-0.490253\pi$
$131$	5.79791	−	1.37413i	0.506566	−	0.120058i	0.475949	+	0.879473i	$0.342105\pi$
$132$	4.34849	−	1.17955i	0.378487	−	0.102667i
$133$	0.324078	−	0.0378793i	0.0281011	−	0.00328455i
$134$	−1.78397	−	3.08993i	−0.154112	−	0.266930i
$135$	−16.8316	−	14.7022i	−1.44863	−	1.26537i
$136$	2.50196	−	4.33353i	0.214542	−	0.371597i
$137$	−1.45806	+	3.38015i	−0.124570	+	0.288786i	−0.969077	−	0.246759i	$-0.920634\pi$
$137$	−1.45806	+	3.38015i	−0.124570	+	0.288786i	0.844507	+	0.535545i	$0.179894\pi$
$138$	−8.04810	−	0.679130i	−0.685100	−	0.0578114i
$139$	−7.64725	−	8.10561i	−0.648631	−	0.687509i	0.316703	−	0.948525i	$-0.397424\pi$
$139$	−7.64725	−	8.10561i	−0.648631	−	0.687509i	−0.965335	+	0.261016i	$0.915943\pi$
$140$	−0.496138	−	0.249170i	−0.0419313	−	0.0210587i
$141$	1.95906	−	13.6680i	0.164983	−	1.15106i
$142$	4.66336	+	15.5767i	0.391340	+	1.30717i
$143$	9.37260	+	7.86455i	0.783776	+	0.657666i
$144$	2.76192	+	1.17124i	0.230160	+	0.0976031i
$145$	11.0731	−	9.29142i	0.919570	−	0.771610i
$146$	2.13283	+	1.40278i	0.176514	+	0.116095i
$147$	−11.9623	+	1.78990i	−0.986636	+	0.147628i
$148$	2.21329	+	0.258696i	0.181931	+	0.0212647i
$149$	−2.21381	−	5.13219i	−0.181363	−	0.420446i	0.803146	−	0.595782i	$-0.203158\pi$
$149$	−2.21381	−	5.13219i	−0.181363	−	0.420446i	−0.984509	+	0.175337i	$0.943899\pi$
$150$	7.42241	+	22.1705i	0.606037	+	1.81021i
$151$	−13.6408	+	6.85066i	−1.11007	+	0.557499i	−0.906774	−	0.421618i	$-0.861462\pi$
$151$	−13.6408	+	6.85066i	−1.11007	+	0.557499i	−0.203298	+	0.979117i	$0.565166\pi$
$152$	2.37523	+	0.864514i	0.192657	+	0.0701214i
$153$	9.57832	−	11.5590i	0.774361	−	0.934486i
$154$	0.315541	−	0.114848i	0.0254270	−	0.00925468i
$155$	10.4902	−	11.1189i	0.842590	−	0.893093i
$156$	1.67195	+	7.97311i	0.133863	+	0.638360i
$157$	1.59945	−	1.05197i	0.127650	−	0.0839567i	−0.484078	−	0.875025i	$-0.660845\pi$
$157$	1.59945	−	1.05197i	0.127650	−	0.0839567i	0.611728	+	0.791068i	$0.290475\pi$
$158$	4.32863	−	14.4586i	0.344368	−	1.15027i
$159$	−18.1752	+	12.8101i	−1.44139	+	1.01590i
$160$	−2.56837	−	3.44992i	−0.203047	−	0.272740i
$161$	−0.601934			−0.0474391
$162$	7.57979	+	4.85251i	0.595524	+	0.381249i
$163$	7.13549			0.558895			0.279447	−	0.960161i	$-0.409849\pi$
$163$	7.13549			0.558895			0.279447	+	0.960161i	$0.409849\pi$
$164$	0.110999	+	0.149098i	0.00866757	+	0.0116426i
$165$	−17.5881	−	8.13559i	−1.36923	−	0.633354i
$166$	−3.97112	+	13.2645i	−0.308219	+	1.02952i
$167$	−16.8839	+	11.1047i	−1.30652	+	0.859310i	−0.995832	−	0.0912023i	$-0.970929\pi$
$167$	−16.8839	+	11.1047i	−1.30652	+	0.859310i	−0.310686	+	0.950513i	$0.600559\pi$
$168$	0.212449	+	0.0696720i	0.0163908	+	0.00537531i
$169$	−6.25987	+	6.63507i	−0.481528	+	0.510390i
$170$	−20.2239	+	7.36089i	−1.55110	+	0.564554i
$171$	6.59033	+	3.75095i	0.503975	+	0.286843i
$172$	−3.42389	−	1.24619i	−0.261069	−	0.0950214i
$173$	18.8952	−	9.48953i	1.43658	−	0.721476i	0.451289	−	0.892378i	$-0.350965\pi$
$173$	18.8952	−	9.48953i	1.43658	−	0.721476i	0.985288	+	0.170902i	$0.0546682\pi$
$174$	−3.85645	+	4.36044i	−0.292357	+	0.330564i
$175$	0.690147	+	1.59994i	0.0521702	+	0.120944i
$176$	2.58373	+	0.301995i	0.194756	+	0.0227638i
$177$	3.27806	−	8.32606i	0.246394	−	0.625825i
$178$	−9.20868	−	6.05664i	−0.690220	−	0.453965i
$179$	3.78877	−	3.17915i	0.283186	−	0.237621i	−0.490119	−	0.871655i	$-0.663047\pi$
$179$	3.78877	−	3.17915i	0.283186	−	0.237621i	0.773305	+	0.634035i	$0.218602\pi$
$180$	−5.86179	−	11.4946i	−0.436912	−	0.856755i
$181$	12.3131	+	10.3319i	0.915222	+	0.767963i	0.973105	−	0.230361i	$-0.0739906\pi$
$181$	12.3131	+	10.3319i	0.915222	+	0.767963i	−0.0578832	+	0.998323i	$0.518435\pi$
$182$	0.174129	+	0.581632i	0.0129073	+	0.0431134i
$183$	9.84381	−	3.94586i	0.727675	−	0.291687i
$184$	−4.16709	−	2.09279i	−0.307202	−	0.154282i
$185$	−6.57701	−	6.97123i	−0.483552	−	0.512535i
$186$	−3.51538	+	5.05355i	−0.257760	+	0.370545i
$187$	5.15571	−	11.9523i	0.377022	−	0.874036i
$188$	3.98594	−	6.90385i	0.290705	−	0.503515i
$189$	0.593309	+	0.312864i	0.0431569	+	0.0227575i
$190$	−5.43573	−	9.41496i	−0.394349	−	0.683033i
$191$	−8.08475	+	0.944972i	−0.584992	+	0.0683758i	−0.403441	−	0.915006i	$-0.632186\pi$
$191$	−8.08475	+	0.944972i	−0.584992	+	0.0683758i	−0.181551	+	0.983381i	$0.558112\pi$
$192$	1.22851	+	1.22096i	0.0886603	+	0.0881155i
$193$	−3.60456	+	0.854296i	−0.259462	+	0.0614936i	−0.358288	−	0.933611i	$-0.616639\pi$
$193$	−3.60456	+	0.854296i	−0.259462	+	0.0614936i	0.0988261	+	0.995105i	$0.468491\pi$
$194$	0.443698	+	7.61800i	0.0318556	+	0.546940i
$195$	16.5339	−	30.8916i	1.18402	−	2.21220i
$196$	−6.79510	−	1.61047i	−0.485364	−	0.115033i
$197$	−2.86709	+	16.2601i	−0.204272	+	1.15848i	0.694310	+	0.719676i	$0.255710\pi$
$197$	−2.86709	+	16.2601i	−0.204272	+	1.15848i	−0.898582	+	0.438806i	$0.855401\pi$
$198$	7.48978	+	2.19208i	0.532275	+	0.155784i
$199$	−2.95094	−	16.7356i	−0.209187	−	1.18636i	−0.890714	−	0.454564i	$-0.849795\pi$
$199$	−2.95094	−	16.7356i	−0.209187	−	1.18636i	0.681527	−	0.731793i	$-0.261316\pi$
$200$	−0.784864	+	13.4756i	−0.0554983	+	0.952868i
$201$	0.160701	−	6.17778i	0.0113350	−	0.435747i
$202$	6.76548	−	9.08762i	0.476018	−	0.639403i
$203$	−0.259067	+	0.347988i	−0.0181830	+	0.0244239i
$204$	7.61604	−	4.13688i	0.533230	−	0.289640i
$205$	0.0464845	−	0.798108i	0.00324662	−	0.0557423i
$206$	0.126594	+	0.717948i	0.00882019	+	0.0500218i
$207$	−11.2724	−	8.28448i	−0.783485	−	0.575811i
$208$	−0.816737	+	4.63194i	−0.0566305	+	0.321167i
$209$	6.39805	+	1.51637i	0.442562	+	0.104889i
$210$	−0.507348	−	0.816891i	−0.0350104	−	0.0563709i
$211$	−1.07432	−	18.4454i	−0.0739595	−	1.26984i	−0.807368	−	0.590048i	$-0.799109\pi$
$211$	−1.07432	−	18.4454i	−0.0739595	−	1.26984i	0.733409	−	0.679788i	$-0.237928\pi$
$212$	−12.4919	+	2.96062i	−0.857944	+	0.203336i
$213$	−7.20519	+	27.2255i	−0.493691	+	1.86546i
$214$	−5.07264	+	0.592907i	−0.346759	+	0.0405303i
$215$	7.83559	+	13.5716i	0.534383	+	0.925578i
$216$	3.01962	+	4.22870i	0.205459	+	0.287727i
$217$	−0.229395	+	0.397323i	−0.0155723	+	0.0269721i
$218$	−0.689518	+	1.59848i	−0.0467000	+	0.108263i
$219$	1.88098	+	4.00153i	0.127105	+	0.270398i
$220$	−7.67784	−	8.13803i	−0.517640	−	0.548666i
$221$	21.0321	+	10.5627i	1.41477	+	0.710524i
$222$	3.03491	+	2.38453i	0.203690	+	0.160039i
$223$	0.491439	+	1.64152i	0.0329092	+	0.109924i	0.972866	−	0.231369i	$-0.0743203\pi$
$223$	0.491439	+	1.64152i	0.0329092	+	0.109924i	−0.939957	+	0.341293i	$0.889135\pi$
$224$	0.0988848	+	0.0829742i	0.00660702	+	0.00554395i
$225$	−9.09580	+	39.4605i	−0.606387	+	2.63070i
$226$	1.22346	−	1.02660i	0.0813831	−	0.0682886i
$227$	5.05674	+	3.32587i	0.335628	+	0.220746i	0.706124	−	0.708088i	$-0.250442\pi$
$227$	5.05674	+	3.32587i	0.335628	+	0.220746i	−0.370496	+	0.928834i	$0.620812\pi$
$228$	2.72600	+	3.42583i	0.180533	+	0.226881i
$229$	0.417308	+	0.0487763i	0.0275765	+	0.00322323i	0.129870	−	0.991531i	$-0.458544\pi$
$229$	0.417308	+	0.0487763i	0.0275765	+	0.00322323i	−0.102293	+	0.994754i	$0.532618\pi$
$230$	7.94371	+	18.4156i	0.523793	+	1.21429i
$231$	0.569953	+	0.115855i	0.0375001	+	0.00762273i
$232$	−3.00335	+	1.50834i	−0.197180	+	0.0990274i
$233$	6.14840	+	2.23784i	0.402795	+	0.146606i	0.535470	−	0.844554i	$-0.320134\pi$
$233$	6.14840	+	2.23784i	0.402795	+	0.146606i	−0.132675	+	0.991160i	$0.542357\pi$
$234$	−4.74415	+	13.2887i	−0.310135	+	0.868712i
$235$	−32.2192	+	11.7268i	−2.10175	+	0.764973i
$236$	3.54527	−	3.75776i	0.230777	−	0.244609i
$237$	19.4746	−	17.4387i	1.26501	−	1.13277i
$238$	0.539668	−	0.354945i	0.0349815	−	0.0230077i
$239$	−2.00176	+	6.68634i	−0.129483	+	0.432504i	−0.998004	−	0.0631487i	$-0.979886\pi$
$239$	−2.00176	+	6.68634i	−0.129483	+	0.432504i	0.868521	+	0.495652i	$0.165071\pi$
$240$	−0.672137	−	7.41913i	−0.0433862	−	0.478903i
$241$	11.5020	+	15.4499i	0.740911	+	0.995216i	0.999572	+	0.0292479i	$0.00931123\pi$
$241$	11.5020	+	15.4499i	0.740911	+	0.995216i	−0.258661	+	0.965968i	$0.583281\pi$
$242$	−4.23311			−0.272115
$243$	6.80488	+	14.0247i	0.436533	+	0.899688i
$244$	6.12292			0.391980
$245$	17.9358	+	24.0919i	1.14587	+	1.53918i
$246$	0.0290482	+	0.320638i	0.00185205	+	0.0204431i
$247$	−3.40970	+	11.3892i	−0.216954	+	0.724677i
$248$	−2.96946	+	1.95305i	−0.188561	+	0.124019i
$249$	−17.8661	+	15.9984i	−1.13222	+	1.01386i
$250$	25.0832	−	26.5867i	1.58640	−	1.68149i
$251$	21.8782	−	7.96302i	1.38094	−	0.502621i	0.458477	−	0.888706i	$-0.348395\pi$
$251$	21.8782	−	7.96302i	1.38094	−	0.502621i	0.922463	+	0.386085i	$0.126173\pi$
$252$	0.250746	+	0.295114i	0.0157955	+	0.0185905i
$253$	−11.3987	−	4.14877i	−0.716627	−	0.260831i
$254$	−4.82461	+	2.42301i	−0.302723	+	0.152033i
$255$	−36.5298	−	7.42548i	−2.28758	−	0.465002i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	−0.643249	−	0.0751851i	−0.0401248	−	0.00468992i	0.0960068	−	0.995381i	$-0.469393\pi$
$257$	−0.643249	−	0.0751851i	−0.0401248	−	0.00468992i	−0.136132	+	0.990691i	$0.543467\pi$
$258$	−3.92951	−	4.93832i	−0.244641	−	0.307446i
$259$	0.240326	+	0.158065i	0.0149331	+	0.00982166i
$260$	15.4965	−	13.0031i	0.961051	−	0.806418i
$261$	−9.64093	+	2.95118i	−0.596758	+	0.182673i
$262$	4.56449	+	3.83006i	0.281995	+	0.236622i
$263$	−2.76626	−	9.23995i	−0.170575	−	0.569760i	−0.999939	−	0.0110512i	$-0.996482\pi$
$263$	−2.76626	−	9.23995i	−0.170575	−	0.569760i	0.829364	−	0.558709i	$-0.188703\pi$
$264$	3.54288	+	2.78364i	0.218049	+	0.171321i
$265$	49.3424	+	24.7807i	3.03108	+	1.52227i
$266$	0.223910	+	0.237331i	0.0137288	+	0.0145517i
$267$	−8.12129	−	17.2769i	−0.497015	−	1.05733i
$268$	1.41319	−	3.27615i	0.0863244	−	0.200123i
$269$	5.84034	−	10.1158i	0.356092	−	0.616770i	−0.631212	−	0.775610i	$-0.717442\pi$
$269$	5.84034	−	10.1158i	0.356092	−	0.616770i	0.987304	+	0.158841i	$0.0507756\pi$
$270$	1.74188	−	22.2806i	0.106007	−	1.35595i
$271$	−9.53060	−	16.5075i	−0.578943	−	1.00276i	−0.995601	−	0.0936948i	$-0.970132\pi$
$271$	−9.53060	−	16.5075i	−0.578943	−	1.00276i	0.416658	−	0.909063i	$-0.363201\pi$
$272$	4.97009	−	0.580920i	0.301356	−	0.0352235i
$273$	−0.269041	+	1.01660i	−0.0162831	+	0.0615272i
$274$	−3.58199	+	0.848948i	−0.216396	+	0.0512868i
$275$	2.04169	+	35.0544i	0.123118	+	2.11386i
$276$	−4.26124	−	6.86111i	−0.256497	−	0.412991i
$277$	8.76422	+	2.07716i	0.526591	+	0.124804i	0.485308	−	0.874343i	$-0.338707\pi$
$277$	8.76422	+	2.07716i	0.526591	+	0.124804i	0.0412827	+	0.999148i	$0.486856\pi$
$278$	1.93508	−	10.9744i	0.116058	−	0.658199i
$279$	−9.76426	+	4.28347i	−0.584571	+	0.256444i
$280$	−0.0964080	−	0.546757i	−0.00576148	−	0.0326750i
$281$	0.572120	−	9.82292i	0.0341298	−	0.585986i	−0.937280	−	0.348577i	$-0.886665\pi$
$281$	0.572120	−	9.82292i	0.0341298	−	0.585986i	0.971410	−	0.237409i	$-0.0762981\pi$
$282$	12.1333	−	6.59057i	0.722528	−	0.392463i
$283$	3.98496	−	5.35274i	0.236882	−	0.318187i	−0.667747	−	0.744388i	$-0.732741\pi$
$283$	3.98496	−	5.35274i	0.236882	−	0.318187i	0.904628	+	0.426201i	$0.140149\pi$
$284$	−9.70967	+	13.0423i	−0.576163	+	0.773921i
$285$	0.489652	−	18.8236i	0.0290045	−	1.11501i
$286$	−0.711406	+	12.2144i	−0.0420663	+	0.722250i
$287$	0.00416654	+	0.0236296i	0.000245943	+	0.00139481i
$288$	0.709828	+	2.91481i	0.0418270	+	0.171757i
$289$	1.39601	−	7.91715i	0.0821181	−	0.465715i
$290$	14.0653	+	3.33353i	0.825940	+	0.195751i
$291$	−6.23696	+	11.6530i	−0.365617	+	0.683111i
$292$	0.148432	+	2.54848i	0.00868632	+	0.149138i
$293$	−1.12297	+	0.266149i	−0.0656047	+	0.0155486i	−0.263287	−	0.964718i	$-0.584807\pi$
$293$	−1.12297	+	0.266149i	−0.0656047	+	0.0155486i	0.197682	+	0.980266i	$0.436659\pi$
$294$	−8.57912	−	8.52641i	−0.500345	−	0.497270i
$295$	−22.0695	+	2.57955i	−1.28494	+	0.150187i
$296$	1.11418	+	1.92981i	0.0647602	+	0.112168i
$297$	9.07894	+	10.0139i	0.526813	+	0.581067i
$298$	2.79465	−	4.84048i	0.161890	−	0.280402i
$299$	8.68696	−	20.1386i	0.502380	−	1.16465i
$300$	−13.3511	+	19.1930i	−0.770827	+	1.10811i
$301$	−0.322765	−	0.342111i	−0.0186039	−	0.0197190i
$302$	−13.6408	−	6.85066i	−0.784939	−	0.394211i
$303$	18.2144	−	7.30118i	1.04639	−	0.419442i
$304$	0.724944	+	2.42148i	0.0415784	+	0.138881i
$305$	−20.1734	−	16.9275i	−1.15513	−	0.969267i
$306$	14.9915	+	0.780467i	0.857006	+	0.0446163i
$307$	2.95975	−	2.48353i	0.168922	−	0.141742i	−0.554408	−	0.832245i	$-0.687055\pi$
$307$	2.95975	−	2.48353i	0.168922	−	0.141742i	0.723330	+	0.690503i	$0.242611\pi$
$308$	0.280550	+	0.184521i	0.0159858	+	0.0105140i
$309$	−0.462580	+	1.17492i	−0.0263152	+	0.0668391i
$310$	15.1830	+	1.77464i	0.862338	+	0.100793i
$311$	−13.5167	−	31.3353i	−0.766462	−	1.77686i	−0.615209	−	0.788364i	$-0.710928\pi$
$311$	−13.5167	−	31.3353i	−0.766462	−	1.77686i	−0.151253	−	0.988495i	$-0.548331\pi$
$312$	−5.39699	+	6.10232i	−0.305545	+	0.345476i
$313$	17.5353	−	8.80654i	0.991152	−	0.497775i	0.122112	−	0.992516i	$-0.461033\pi$
$313$	17.5353	−	8.80654i	0.991152	−	0.497775i	0.869040	+	0.494741i	$0.164737\pi$
$314$	1.79894	+	0.654760i	0.101520	+	0.0369503i
$315$	−0.0102664	−	1.66554i	−0.000578444	−	0.0938428i
$316$	14.1825	−	5.16201i	0.797828	−	0.290386i
$317$	−6.58735	+	6.98219i	−0.369983	+	0.392159i	−0.885438	−	0.464758i	$-0.846141\pi$
$317$	−6.58735	+	6.98219i	−0.369983	+	0.392159i	0.515455	+	0.856917i	$0.327623\pi$
$318$	−21.1287	−	6.92910i	−1.18484	−	0.388565i
$319$	−7.30435	+	4.80415i	−0.408965	+	0.268981i
$320$	1.23353	−	4.12029i	0.0689567	−	0.230331i
$321$	−8.02858	−	3.71371i	−0.448112	−	0.207279i
$322$	−0.359450	−	0.482825i	−0.0200314	−	0.0269068i
$323$	12.6483			0.703769
$324$	0.634023	+	8.97764i	0.0352235	+	0.498758i
$325$	−63.4885			−3.52171
$326$	4.26102	+	5.72354i	0.235996	+	0.316998i
$327$	−2.46461	+	1.73708i	−0.136293	+	0.0960608i
$328$	−0.0533106	+	0.178070i	−0.00294359	+	0.00983226i
$329$	0.859759	−	0.565472i	0.0474000	−	0.0311755i
$330$	−3.97717	−	18.9661i	−0.218936	−	1.04405i
$331$	−17.4695	+	18.5166i	−0.960212	+	1.01776i	0.0396163	+	0.999215i	$0.487386\pi$
$331$	−17.4695	+	18.5166i	−0.960212	+	1.01776i	−0.999828	+	0.0185499i	$0.994095\pi$
$332$	−13.0111	+	4.73566i	−0.714078	+	0.259903i
$333$	2.32510	+	6.26769i	0.127415	+	0.343467i
$334$	−18.9898	−	6.91171i	−1.03907	−	0.378192i
$335$	−13.7134	+	6.88713i	−0.749243	+	0.376284i
$336$	0.0709802	+	0.212016i	0.00387229	+	0.0115664i
$337$	−9.74332	−	22.5875i	−0.530752	−	1.23042i	−0.947018	−	0.321179i	$-0.895921\pi$
$337$	−9.74332	−	22.5875i	−0.530752	−	1.23042i	0.416266	−	0.909243i	$-0.363338\pi$
$338$	−9.06028	−	1.05899i	−0.492814	−	0.0576017i
$339$	2.73582	−	0.409355i	0.148589	−	0.0222331i
$340$	−17.9812	−	11.8264i	−0.975167	−	0.641378i
$341$	−7.08249	+	5.94292i	−0.383538	+	0.321827i
$342$	0.926742	+	7.52617i	0.0501124	+	0.406969i
$343$	−1.38274	−	1.16026i	−0.0746609	−	0.0626480i
$344$	−1.04500	−	3.49056i	−0.0563429	−	0.188198i
$345$	−4.92865	+	34.3863i	−0.265350	+	1.85130i
$346$	18.8952	+	9.48953i	1.01581	+	0.510160i
$347$	16.0265	+	16.9871i	0.860346	+	0.911913i	0.996897	−	0.0787200i	$-0.0250833\pi$
$347$	16.0265	+	16.9871i	0.860346	+	0.911913i	−0.136551	+	0.990633i	$0.543602\pi$
$348$	−5.80052	−	0.489471i	−0.310941	−	0.0262384i
$349$	−1.81659	+	4.21134i	−0.0972400	+	0.225428i	−0.959892	−	0.280370i	$-0.909543\pi$
$349$	−1.81659	+	4.21134i	−0.0972400	+	0.225428i	0.862652	+	0.505798i	$0.168802\pi$
$350$	−0.871222	+	1.50900i	−0.0465688	+	0.0806595i
$351$	−19.0298	+	15.3349i	−1.01574	+	0.818516i
$352$	1.30066	+	2.25281i	0.0693255	+	0.120075i
$353$	−15.3993	+	1.79993i	−0.819624	+	0.0958004i	−0.515563	−	0.856852i	$-0.672417\pi$
$353$	−15.3993	+	1.79993i	−0.819624	+	0.0958004i	−0.304062	+	0.952652i	$0.598343\pi$
$354$	8.63605	−	2.34257i	0.459001	−	0.124506i
$355$	68.0479	−	16.1277i	3.61161	−	0.855967i
$356$	−0.640868	−	11.0033i	−0.0339659	−	0.583172i
$357$	1.11821	−	0.0359860i	0.0591818	−	0.00190458i
$358$	4.81257	+	1.14060i	0.254352	+	0.0602825i
$359$	1.42766	−	8.09664i	0.0753488	−	0.427324i	−0.923676	−	0.383174i	$-0.874831\pi$
$359$	1.42766	−	8.09664i	0.0753488	−	0.427324i	0.999025	−	0.0441501i	$-0.0140580\pi$
$360$	5.71965	−	11.5660i	0.301452	−	0.609580i
$361$	−2.18986	−	12.4193i	−0.115256	−	0.653647i
$362$	−0.934594	+	16.0464i	−0.0491212	+	0.843378i
$363$	−6.25219	−	3.82986i	−0.328155	−	0.201016i
$364$	−0.362558	+	0.486999i	−0.0190032	+	0.0255257i
$365$	6.55652	−	8.80693i	0.343184	−	0.460976i
$366$	9.04338	+	5.53964i	0.472705	+	0.289562i
$367$	−0.377069	+	6.47402i	−0.0196828	+	0.337941i	0.974063	+	0.226277i	$0.0726553\pi$
$367$	−0.377069	+	6.47402i	−0.0196828	+	0.337941i	−0.993746	+	0.111665i	$0.964382\pi$
$368$	−0.809736	−	4.59224i	−0.0422104	−	0.239387i
$369$	−0.247190	+	0.499855i	−0.0128682	+	0.0260214i
$370$	1.66426	−	9.43850i	0.0865209	−	0.490684i
$371$	−1.61251	−	0.382172i	−0.0837173	−	0.0198414i
$372$	−6.15281	+	0.198009i	−0.319008	+	0.0102663i
$373$	−1.27421	−	21.8773i	−0.0659759	−	1.13276i	−0.855078	−	0.518500i	$-0.826491\pi$
$373$	−1.27421	−	21.8773i	−0.0659759	−	1.13276i	0.789102	−	0.614262i	$-0.210546\pi$
$374$	12.6660	−	3.00189i	0.654941	−	0.155224i
$375$	61.1012	−	16.5740i	3.15525	−	0.855878i
$376$	7.91798	−	0.925479i	0.408339	−	0.0477279i
$377$	−7.90367	−	13.6896i	−0.407060	−	0.705048i
$378$	0.103344	+	0.662736i	0.00531545	+	0.0340875i
$379$	−10.8576	+	18.8060i	−0.557719	+	0.965997i	0.439968	+	0.898014i	$0.354990\pi$
$379$	−10.8576	+	18.8060i	−0.557719	+	0.965997i	−0.997686	+	0.0679836i	$0.978343\pi$
$380$	4.30596	−	9.98235i	0.220891	−	0.512084i
$381$	−9.31801	−	0.786290i	−0.477376	−	0.0402829i
$382$	−5.58586	−	5.92067i	−0.285798	−	0.302928i
$383$	−7.80811	−	3.92138i	−0.398976	−	0.200373i	0.237986	−	0.971269i	$-0.423513\pi$
$383$	−7.80811	−	3.92138i	−0.398976	−	0.200373i	−0.636962	+	0.770896i	$0.719809\pi$
$384$	−0.245746	+	1.71453i	−0.0125407	+	0.0874942i
$385$	−0.414211	−	1.38356i	−0.0211101	−	0.0705128i
$386$	−2.83775	−	2.38115i	−0.144437	−	0.121197i
$387$	−1.33590	−	10.8489i	−0.0679074	−	0.551483i
$388$	−5.84561	+	4.90505i	−0.296766	+	0.249016i
$389$	−0.601325	−	0.395498i	−0.0304884	−	0.0200525i	0.534173	−	0.845375i	$-0.320623\pi$
$389$	−0.601325	−	0.395498i	−0.0304884	−	0.0200525i	−0.564662	+	0.825322i	$0.690993\pi$
$390$	34.6523	−	5.18495i	1.75469	−	0.262550i
$391$	−23.1760	−	2.70888i	−1.17206	−	0.136994i
$392$	−2.76596	−	6.41221i	−0.139702	−	0.323866i
$393$	3.27642	+	9.78657i	0.165274	+	0.493667i
$394$	−14.7547	+	7.41008i	−0.743330	+	0.373315i
$395$	−60.9986	−	22.2017i	−3.06917	−	1.11709i
$396$	2.71427	+	7.31674i	0.136397	+	0.367680i
$397$	31.6900	−	11.5342i	1.59048	−	0.578886i	0.613028	−	0.790061i	$-0.289951\pi$
$397$	31.6900	−	11.5342i	1.59048	−	0.578886i	0.977448	+	0.211175i	$0.0677291\pi$
$398$	11.6618	−	12.3608i	0.584556	−	0.619593i
$399$	0.115987	+	0.553110i	0.00580659	+	0.0276902i
$400$	−11.2778	+	7.41751i	−0.563889	+	0.370875i
$401$	−0.644453	+	2.15262i	−0.0321825	+	0.107497i	−0.972572	−	0.232603i	$-0.925276\pi$
$401$	−0.644453	+	2.15262i	−0.0321825	+	0.107497i	0.940389	+	0.340100i	$0.110461\pi$
$402$	5.05130	−	3.56021i	0.251936	−	0.177567i
$403$	−9.98250	−	13.4088i	−0.497264	−	0.667941i
$404$	11.3295			0.563662
$405$	22.7308	−	31.3318i	1.12950	−	1.55689i
$406$	−0.433833			−0.0215308
$407$	3.46153	+	4.64965i	0.171582	+	0.230474i
$408$	7.86627	+	3.63863i	0.389438	+	0.180139i
$409$	2.12519	−	7.09864i	0.105084	−	0.351005i	−0.889234	−	0.457452i	$-0.848762\pi$
$409$	2.12519	−	7.09864i	0.105084	−	0.351005i	0.994318	+	0.106447i	$0.0339474\pi$
$410$	0.667939	−	0.439311i	0.0329872	−	0.0216960i
$411$	−6.05858	−	1.98689i	−0.298848	−	0.0980062i
$412$	−0.500286	+	0.530272i	−0.0246473	+	0.0261246i
$413$	0.626662	−	0.228086i	0.0308360	−	0.0112234i
$414$	−0.0862277	−	13.9890i	−0.00423786	−	0.687521i
$415$	55.9606	+	20.3680i	2.74700	+	0.999825i
$416$	−4.20311	+	2.11088i	−0.206074	+	0.103494i
$417$	12.7870	−	14.4581i	0.626182	−	0.708017i
$418$	2.60434	+	6.03754i	0.127382	+	0.295306i
$419$	−11.6845	−	1.36572i	−0.570826	−	0.0667200i	−0.174216	−	0.984707i	$-0.555739\pi$
$419$	−11.6845	−	1.36572i	−0.570826	−	0.0667200i	−0.396610	+	0.917987i	$0.629813\pi$
$420$	0.352280	−	0.894770i	0.0171895	−	0.0436603i
$421$	28.8363	+	18.9659i	1.40539	+	0.924342i	0.999948	+	0.0102236i	$0.00325433\pi$
$421$	28.8363	+	18.9659i	1.40539	+	0.924342i	0.405447	+	0.914119i	$0.367116\pi$
$422$	14.1540	−	11.8766i	0.689004	−	0.578143i
$423$	23.8833	+	1.24338i	1.16125	+	0.0604553i
$424$	−9.83440	−	8.25204i	−0.477601	−	0.400755i
$425$	19.3722	+	64.7076i	0.939688	+	3.13878i
$426$	−26.1408	+	10.4785i	−1.26653	+	0.507684i
$427$	0.706306	+	0.354720i	0.0341806	+	0.0171661i
$428$	−3.50476	−	3.71482i	−0.169409	−	0.179563i
$429$	−12.1015	+	17.3966i	−0.584267	+	0.839918i
$430$	−6.20704	+	14.3895i	−0.299330	+	0.693924i
$431$	−12.4412	+	21.5489i	−0.599273	+	1.03797i	0.393655	+	0.919258i	$0.371210\pi$
$431$	−12.4412	+	21.5489i	−0.599273	+	1.03797i	−0.992929	+	0.118714i	$0.962123\pi$
$432$	−1.58875	+	4.94731i	−0.0764387	+	0.238028i
$433$	6.47692	+	11.2184i	0.311261	+	0.539120i	0.978636	−	0.205603i	$-0.0659154\pi$
$433$	6.47692	+	11.2184i	0.311261	+	0.539120i	−0.667375	+	0.744722i	$0.732582\pi$
$434$	−0.455687	+	0.0532622i	−0.0218737	+	0.00255667i
$435$	17.7580	+	17.6489i	0.851432	+	0.846200i
$436$	−1.69393	+	0.401469i	−0.0811246	+	0.0192269i
$437$	−0.685338	−	11.7668i	−0.0327842	−	0.562882i
$438$	−2.08648	+	3.89832i	−0.0996957	+	0.186269i
$439$	−5.32817	−	1.26280i	−0.254300	−	0.0602701i	0.101489	−	0.994837i	$-0.467639\pi$
$439$	−5.32817	−	1.26280i	−0.254300	−	0.0602701i	−0.355788	+	0.934567i	$0.615788\pi$
$440$	1.94282	−	11.0183i	0.0926202	−	0.525275i
$441$	−4.95697	−	20.3551i	−0.236046	−	0.969292i
$442$	4.08689	+	23.1779i	0.194394	+	1.10246i
$443$	0.286132	−	4.91270i	0.0135946	−	0.233409i	−0.984666	−	0.174451i	$-0.944185\pi$
$443$	0.286132	−	4.91270i	0.0135946	−	0.233409i	0.998260	−	0.0589586i	$-0.0187780\pi$
$444$	−0.100365	+	3.85832i	−0.00476313	+	0.183108i
$445$	−28.3083	+	38.0247i	−1.34194	+	1.80254i
$446$	−1.02323	+	1.37444i	−0.0484516	+	0.0650818i
$447$	8.50700	−	4.62083i	0.402367	−	0.218558i
$448$	−0.00750562	+	0.128867i	−0.000354607	+	0.00608837i
$449$	1.95809	+	11.1049i	0.0924078	+	0.524071i	0.995511	+	0.0946469i	$0.0301722\pi$
$449$	1.95809	+	11.1049i	0.0924078	+	0.524071i	−0.903103	+	0.429424i	$0.858717\pi$
$450$	−37.0839	+	16.2683i	−1.74815	+	0.766893i
$451$	−0.0839642	+	0.476185i	−0.00395372	+	0.0224227i
$452$	1.55406	+	0.368319i	0.0730968	+	0.0173243i
$453$	−13.9490	−	22.4596i	−0.655382	−	1.05524i
$454$	0.351918	+	6.04220i	0.0165163	+	0.283575i
$455$	2.54090	−	0.602205i	0.119119	−	0.0282318i
$456$	−1.12008	+	4.23235i	−0.0524528	+	0.198198i
$457$	13.0568	−	1.52612i	0.610770	−	0.0713888i	0.194916	−	0.980820i	$-0.437557\pi$
$457$	13.0568	−	1.52612i	0.610770	−	0.0713888i	0.415854	+	0.909431i	$0.363483\pi$
$458$	0.210074	+	0.363859i	0.00981613	+	0.0170020i
$459$	21.4359	+	14.7161i	1.00054	+	0.686889i
$460$	−10.0279	+	17.3689i	−0.467554	+	0.809827i
$461$	−4.80181	+	11.1318i	−0.223642	+	0.518462i	−0.992685	−	0.120737i	$-0.961474\pi$
$461$	−4.80181	+	11.1318i	−0.223642	+	0.518462i	0.769042	+	0.639198i	$0.220734\pi$
$462$	0.247422	+	0.526356i	0.0115111	+	0.0244883i
$463$	−3.56649	−	3.78026i	−0.165749	−	0.175684i	0.639176	−	0.769061i	$-0.279276\pi$
$463$	−3.56649	−	3.78026i	−0.165749	−	0.175684i	−0.804925	+	0.593377i	$0.797794\pi$
$464$	−3.00335	−	1.50834i	−0.139427	−	0.0700229i
$465$	20.8193	+	16.3578i	0.965474	+	0.758574i
$466$	1.87655	+	6.26812i	0.0869296	+	0.290365i
$467$	−27.4382	−	23.0233i	−1.26969	−	1.06539i	−0.994579	−	0.103980i	$-0.966842\pi$
$467$	−27.4382	−	23.0233i	−1.26969	−	1.06539i	−0.275107	−	0.961414i	$-0.588713\pi$
$468$	−13.4922	+	4.13009i	−0.623678	+	0.190914i
$469$	0.352816	−	0.296048i	0.0162915	−	0.0136702i
$470$	−28.6463	−	18.8410i	−1.32136	−	0.869069i
$471$	2.06460	+	2.59463i	0.0951316	+	0.119554i
$472$	5.13127	+	0.599760i	0.236186	+	0.0276062i
$473$	−3.75415	−	8.70309i	−0.172616	−	0.400168i
$474$	25.6174	+	5.20731i	1.17665	+	0.239180i
$475$	−30.4904	+	15.3128i	−1.39899	+	0.702601i
$476$	0.606977	+	0.220922i	0.0278208	+	0.0101259i
$477$	−24.9375	−	29.3500i	−1.14181	−	1.34385i
$478$	−6.55864	+	2.38715i	−0.299985	+	0.109186i
$479$	6.22004	−	6.59286i	0.284201	−	0.301235i	−0.569508	−	0.821986i	$-0.692866\pi$
$479$	6.22004	−	6.59286i	0.284201	−	0.301235i	0.853709	+	0.520750i	$0.174348\pi$
$480$	5.54969	−	4.96953i	0.253307	−	0.226827i
$481$	−8.75661	+	5.75932i	−0.399267	+	0.262602i
$482$	−5.52419	+	18.4521i	−0.251620	+	0.840470i
$483$	−0.0940674	−	1.03833i	−0.00428021	−	0.0472456i
$484$	−2.52784	−	3.39548i	−0.114902	−	0.154340i
$485$	32.8204			1.49030
$486$	−7.18598	+	13.8334i	−0.325963	+	0.627494i
$487$	32.7270			1.48300			0.741500	−	0.670953i	$-0.234115\pi$
$487$	32.7270			1.48300			0.741500	+	0.670953i	$0.234115\pi$
$488$	3.65635	+	4.91134i	0.165515	+	0.222326i
$489$	1.11510	+	12.3086i	0.0504266	+	0.556615i
$490$	−8.61419	+	28.7734i	−0.389149	+	1.29985i
$491$	23.6314	−	15.5426i	1.06647	−	0.701429i	0.110200	−	0.993909i	$-0.464851\pi$
$491$	23.6314	−	15.5426i	1.06647	−	0.701429i	0.956272	+	0.292480i	$0.0944805\pi$
$492$	−0.239845	+	0.214772i	−0.0108130	+	0.00968267i
$493$	−11.5408	+	12.2325i	−0.519771	+	0.550925i
$494$	−11.1717	+	4.06615i	−0.502637	+	0.182945i
$495$	11.2852	−	31.6107i	0.507231	−	1.42079i
$496$	−3.33982	−	1.21560i	−0.149963	−	0.0545819i
$497$	−1.87564	+	0.941982i	−0.0841339	+	0.0422536i
$498$	−23.5016	−	4.77722i	−1.05313	−	0.214072i
$499$	−11.5296	−	26.7287i	−0.516138	−	1.19654i	−0.954627	−	0.297805i	$-0.903745\pi$
$499$	−11.5296	−	26.7287i	−0.516138	−	1.19654i	0.438489	−	0.898737i	$-0.355514\pi$
$500$	36.3044	+	4.24338i	1.62358	+	0.189770i
$501$	−21.7941	−	27.3892i	−0.973687	−	1.22366i
$502$	19.4521	+	12.7938i	0.868189	+	0.571017i
$503$	−7.81007	+	6.55343i	−0.348234	+	0.292203i	−0.800080	−	0.599893i	$-0.795210\pi$
$503$	−7.81007	+	6.55343i	−0.348234	+	0.292203i	0.451847	+	0.892096i	$0.350765\pi$
$504$	−0.0869828	+	0.377360i	−0.00387452	+	0.0168089i
$505$	−37.3276	−	31.3216i	−1.66106	−	1.39379i
$506$	−3.47898	−	11.6206i	−0.154659	−	0.516599i
$507$	−12.4237	−	9.76129i	−0.551754	−	0.433514i
$508$	−4.82461	−	2.42301i	−0.214057	−	0.107504i
$509$	−4.99886	−	5.29848i	−0.221571	−	0.234851i	0.607047	−	0.794666i	$-0.292354\pi$
$509$	−4.99886	−	5.29848i	−0.221571	−	0.234851i	−0.828618	+	0.559815i	$0.810872\pi$
$510$	−15.8579	−	33.7356i	−0.702200	−	1.49384i
$511$	−0.130519	+	0.302578i	−0.00577383	+	0.0133852i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−5.44044	+	11.9544i	−0.240201	+	0.527800i
$514$	−0.323814	−	0.560863i	−0.0142828	−	0.0247386i
$515$	3.11431	−	0.364011i	0.137233	−	0.0160402i
$516$	1.61460	−	6.10091i	0.0710788	−	0.268578i
$517$	20.1785	−	4.78239i	0.887448	−	0.210329i
$518$	0.0167252	+	0.287160i	0.000734863	+	0.0126171i
$519$	19.3222	+	31.1110i	0.848149	+	1.36562i
$520$	19.6839	+	4.66518i	0.863198	+	0.204582i
$521$	1.24150	−	7.04092i	0.0543913	−	0.308468i	−0.945460	−	0.325740i	$-0.894387\pi$
$521$	1.24150	−	7.04092i	0.0543913	−	0.308468i	0.999851	+	0.0172711i	$0.00549785\pi$
$522$	−8.12437	−	5.97089i	−0.355594	−	0.261339i
$523$	6.67445	+	37.8527i	0.291853	+	1.65518i	0.679724	+	0.733468i	$0.262100\pi$
$523$	6.67445	+	37.8527i	0.291853	+	1.65518i	−0.387870	+	0.921714i	$0.626789\pi$
$524$	−0.346457	+	5.94844i	−0.0151351	+	0.259859i
$525$	−2.65202	+	1.44053i	−0.115744	+	0.0628697i
$526$	5.75968	−	7.73660i	0.251134	−	0.337332i
$527$	−10.6203	+	14.2656i	−0.462629	+	0.621419i
$528$	−0.117164	+	4.50410i	−0.00509891	+	0.196016i
$529$	0.0730088	−	1.25351i	0.00317429	−	0.0545005i
$530$	9.58808	+	54.3767i	0.416480	+	2.36197i
$531$	14.8746	+	4.35345i	0.645504	+	0.188924i
$532$	−0.0566587	+	0.321327i	−0.00245646	+	0.0139313i
$533$	−0.850696	−	0.201619i	−0.0368477	−	0.00873307i
$534$	9.00854	−	16.8313i	0.389838	−	0.728364i
$535$	1.27720	+	21.9287i	0.0552182	+	0.948060i
$536$	3.47177	−	0.822825i	0.149958	−	0.0355406i
$537$	6.07608	+	6.03875i	0.262202	+	0.260591i
$538$	11.6017	−	1.35605i	0.500185	−	0.0584633i
$539$	−9.08296	−	15.7321i	−0.391231	−	0.677632i
$540$	18.9119	−	11.9078i	0.813840	−	0.512431i
$541$	6.57326	−	11.3852i	0.282607	−	0.489489i	−0.689419	−	0.724363i	$-0.742134\pi$
$541$	6.57326	−	11.3852i	0.282607	−	0.489489i	0.972026	+	0.234873i	$0.0754675\pi$
$542$	7.54975	−	17.5023i	0.324290	−	0.751788i
$543$	−15.8981	+	22.8545i	−0.682254	+	0.980779i
$544$	3.43390	+	3.63972i	0.147227	+	0.156052i
$545$	6.69097	+	3.36033i	0.286610	+	0.143941i
$546$	−0.976095	+	0.391265i	−0.0417730	+	0.0167446i
$547$	−6.14697	−	20.5323i	−0.262825	−	0.877898i	−0.982922	−	0.184024i	$-0.941088\pi$
$547$	−6.14697	−	20.5323i	−0.262825	−	0.877898i	0.720096	−	0.693874i	$-0.244098\pi$
$548$	−2.81998	−	2.36624i	−0.120463	−	0.101081i
$549$	8.34491	+	16.3638i	0.356152	+	0.698390i
$550$	−26.8987	+	22.5707i	−1.14697	+	0.962418i
$551$	−7.09754	−	4.66812i	−0.302365	−	0.198869i
$552$	2.95882	−	7.51522i	0.125936	−	0.319869i
$553$	1.93507	+	0.226177i	0.0822874	+	0.00961802i
$554$	3.56749	+	8.27037i	0.151568	+	0.351375i
$555$	10.9974	−	12.4347i	0.466816	−	0.527823i
$556$	9.95835	−	5.00127i	0.422328	−	0.212101i
$557$	−26.4493	−	9.62675i	−1.12069	−	0.407898i	−0.285787	−	0.958293i	$-0.592255\pi$
$557$	−26.4493	−	9.62675i	−1.12069	−	0.407898i	−0.834905	+	0.550395i	$0.814477\pi$
$558$	−9.26668	−	5.27423i	−0.392290	−	0.223276i
$559$	16.1039	−	5.86135i	0.681123	−	0.247909i
$560$	0.380996	−	0.403832i	0.0161000	−	0.0170650i
$561$	21.4232	+	7.02568i	0.904489	+	0.296624i
$562$	8.22084	−	5.40693i	0.346775	−	0.228078i
$563$	−5.96928	+	19.9388i	−0.251575	+	0.840320i	0.735148	+	0.677907i	$0.237113\pi$
$563$	−5.96928	+	19.9388i	−0.251575	+	0.840320i	−0.986723	+	0.162413i	$0.948072\pi$
$564$	12.5320	+	5.79679i	0.527691	+	0.244089i
$565$	−4.10196	−	5.50989i	−0.172571	−	0.231803i
$566$	6.67321			0.280496
$567$	−0.446966	+	1.07234i	−0.0187708	+	0.0450341i
$568$	−16.2598			−0.682245
$569$	−4.96037	−	6.66294i	−0.207950	−	0.279325i	0.685896	−	0.727700i	$-0.259410\pi$
$569$	−4.96037	−	6.66294i	−0.207950	−	0.279325i	−0.893846	+	0.448375i	$0.852003\pi$
$570$	15.3912	−	10.8479i	0.644667	−	0.454368i
$571$	−1.99571	+	6.66612i	−0.0835177	+	0.278969i	−0.989539	−	0.144263i	$-0.953919\pi$
$571$	−1.99571	+	6.66612i	−0.0835177	+	0.278969i	0.906022	+	0.423231i	$0.139104\pi$
$572$	−10.2222	+	6.72328i	−0.427414	+	0.281114i
$573$	−2.89351	−	13.7984i	−0.120878	−	0.576437i
$574$	−0.0164658	+	0.0174527i	−0.000687268	+	0.000728462i
$575$	59.1483	−	21.5282i	2.46666	−	0.897789i
$576$	−1.91416	+	2.30998i	−0.0797567	+	0.0962490i
$577$	−16.5719	−	6.03169i	−0.689898	−	0.251102i	−0.0268065	−	0.999641i	$-0.508534\pi$
$577$	−16.5719	−	6.03169i	−0.689898	−	0.251102i	−0.663092	+	0.748538i	$0.730756\pi$
$578$	7.18417	−	3.60802i	0.298822	−	0.150074i
$579$	−2.03695	−	6.08431i	−0.0846529	−	0.252855i
$580$	5.72529	+	13.2727i	0.237730	+	0.551119i
$581$	−1.77524	−	0.207496i	−0.0736495	−	0.00860839i
$582$	−13.0716	+	1.95588i	−0.541835	+	0.0810737i
$583$	−27.9016	−	18.3511i	−1.15556	−	0.760027i
$584$	−1.95556	+	1.64091i	−0.0809215	+	0.0679012i
$585$	55.8715	+	23.6932i	2.31000	+	0.979594i
$586$	−0.884077	−	0.741829i	−0.0365209	−	0.0306447i
$587$	−9.11225	−	30.4370i	−0.376103	−	1.25627i	−0.911370	−	0.411588i	$-0.864974\pi$
$587$	−9.11225	−	30.4370i	−0.376103	−	1.25627i	0.535267	−	0.844683i	$-0.320211\pi$
$588$	1.71613	−	11.9731i	0.0707720	−	0.493764i
$589$	−8.02818	−	4.03190i	−0.330795	−	0.166132i
$590$	−15.2481	−	16.1621i	−0.627755	−	0.665381i
$591$	−28.4965	−	2.40464i	−1.17219	−	0.0989138i
$592$	−0.882606	+	2.04611i	−0.0362749	+	0.0840946i
$593$	−3.64684	+	6.31651i	−0.149758	+	0.259388i	−0.931138	−	0.364667i	$-0.881183\pi$
$593$	−3.64684	+	6.31651i	−0.149758	+	0.259388i	0.781380	+	0.624055i	$0.214516\pi$
$594$	−2.61084	+	13.2623i	−0.107124	+	0.544160i
$595$	−1.38907	−	2.40594i	−0.0569463	−	0.0986339i
$596$	5.55152	−	0.648879i	0.227399	−	0.0265791i
$597$	28.4076	−	7.70569i	1.16264	−	0.315373i
$598$	21.3412	−	5.05795i	0.872705	−	0.206835i
$599$	−0.436839	−	7.50023i	−0.0178487	−	0.306451i	−0.995404	−	0.0957697i	$-0.969469\pi$
$599$	−0.436839	−	7.50023i	−0.0178487	−	0.306451i	0.977555	−	0.210681i	$-0.0675683\pi$
$600$	−23.3679	+	0.752022i	−0.953989	+	0.0307012i
$601$	−28.4597	−	6.74508i	−1.16090	−	0.275138i	−0.395358	−	0.918527i	$-0.629379\pi$
$601$	−28.4597	−	6.74508i	−1.16090	−	0.275138i	−0.765539	+	0.643390i	$0.777528\pi$
$602$	0.0816733	−	0.463192i	0.00332875	−	0.0188783i
$603$	10.6817	−	0.688227i	0.434992	−	0.0280268i
$604$	−2.65064	−	15.0325i	−0.107853	−	0.611665i
$605$	−1.05862	+	18.1757i	−0.0430389	+	0.738949i
$606$	16.7333	+	10.2502i	0.679744	+	0.416386i
$607$	−14.9376	+	20.0647i	−0.606300	+	0.814402i	−0.994228	−	0.107287i	$-0.965783\pi$
$607$	−14.9376	+	20.0647i	−0.606300	+	0.814402i	0.387928	+	0.921690i	$0.373191\pi$
$608$	−1.50942	+	2.02750i	−0.0612151	+	0.0822261i
$609$	−0.640760	−	0.392506i	−0.0259649	−	0.0159051i
$610$	1.53122	−	26.2900i	0.0619972	−	1.06445i
$611$	6.51093	+	36.9253i	0.263404	+	1.49384i
$612$	8.32626	+	12.4911i	0.336569	+	0.504922i
$613$	−1.53354	+	8.69717i	−0.0619393	+	0.351275i	0.938049	+	0.346502i	$0.112631\pi$
$613$	−1.53354	+	8.69717i	−0.0619393	+	0.351275i	−0.999989	+	0.00477341i	$0.998481\pi$
$614$	3.75954	+	0.891026i	0.151722	+	0.0359589i
$615$	1.38399	−	0.0445394i	0.0558078	−	0.00179600i
$616$	0.0195246	+	0.335224i	0.000786667	+	0.0135065i
$617$	−44.0323	+	10.4359i	−1.77267	+	0.420132i	−0.981501	−	0.191459i	$-0.938678\pi$
$617$	−44.0323	+	10.4359i	−1.77267	+	0.420132i	−0.791174	+	0.611591i	$0.790530\pi$
$618$	−1.21867	+	0.330570i	−0.0490220	+	0.0132975i
$619$	14.2900	−	1.67026i	0.574364	−	0.0671336i	0.176048	−	0.984382i	$-0.443669\pi$
$619$	14.2900	−	1.67026i	0.574364	−	0.0671336i	0.398316	+	0.917248i	$0.369595\pi$
$620$	7.64320	+	13.2384i	0.306958	+	0.531667i
$621$	12.5290	−	20.7394i	0.502772	−	0.832242i
$622$	17.0631	−	29.5542i	0.684169	−	1.18501i
$623$	0.563528	−	1.30640i	0.0225773	−	0.0523400i
$624$	−8.11767	−	0.685001i	−0.324967	−	0.0274220i
$625$	−61.5665	−	65.2567i	−2.46266	−	2.61027i
$626$	17.5353	+	8.80654i	0.700850	+	0.351980i
$627$	−1.61585	+	11.2735i	−0.0645310	+	0.450221i
$628$	0.549053	+	1.83397i	0.0219096	+	0.0731832i
$629$	8.54180	+	7.16742i	0.340584	+	0.285784i
$630$	1.32984	−	1.00283i	0.0529821	−	0.0399537i
$631$	20.0903	−	16.8577i	0.799782	−	0.671096i	−0.148364	−	0.988933i	$-0.547401\pi$
$631$	20.0903	−	16.8577i	0.799782	−	0.671096i	0.948146	+	0.317836i	$0.102956\pi$
$632$	12.6098	+	8.29357i	0.501589	+	0.329901i
$633$	31.6502	−	4.73576i	1.25798	−	0.188229i
$634$	−9.53427	−	1.11440i	−0.378654	−	0.0442583i
$635$	9.19715	+	21.3214i	0.364978	+	0.846114i
$636$	−7.05920	−	21.0856i	−0.279916	−	0.836098i
$637$	29.3517	−	14.7410i	1.16296	−	0.584060i
$638$	−8.21538	−	2.99015i	−0.325250	−	0.118381i
$639$	−48.0896	−	8.17418i	−1.90239	−	0.323366i
$640$	4.04160	−	1.47102i	0.159758	−	0.0581472i
$641$	−13.7061	+	14.5276i	−0.541357	+	0.573805i	−0.939079	−	0.343701i	$-0.888319\pi$
$641$	−13.7061	+	14.5276i	−0.541357	+	0.573805i	0.397722	+	0.917506i	$0.369801\pi$
$642$	−1.81548	−	8.65758i	−0.0716515	−	0.341688i
$643$	−13.4723	+	8.86089i	−0.531297	+	0.349439i	−0.786641	−	0.617411i	$-0.788182\pi$
$643$	−13.4723	+	8.86089i	−0.531297	+	0.349439i	0.255344	+	0.966850i	$0.417811\pi$
$644$	0.172637	−	0.576647i	0.00680284	−	0.0227231i
$645$	−22.1864	+	15.6372i	−0.873588	+	0.615714i
$646$	7.55303	+	10.1455i	0.297170	+	0.399168i
$647$	8.30742			0.326598			0.163299	−	0.986577i	$-0.447786\pi$
$647$	8.30742			0.326598			0.163299	+	0.986577i	$0.447786\pi$
$648$	−6.82256	+	5.86964i	−0.268015	+	0.230581i
$649$	13.4390			0.527526
$650$	−37.9127	−	50.9256i	−1.48706	−	1.99747i
$651$	−0.721226	−	0.333611i	−0.0282671	−	0.0130752i
$652$	−2.04648	+	6.83573i	−0.0801464	+	0.267708i
$653$	−3.26132	+	2.14501i	−0.127625	+	0.0839406i	−0.611717	−	0.791077i	$-0.709521\pi$
$653$	−3.26132	+	2.14501i	−0.127625	+	0.0839406i	0.484091	+	0.875018i	$0.339150\pi$
$654$	−2.86511	−	0.939606i	−0.112035	−	0.0367415i
$655$	17.5866	−	18.6408i	0.687167	−	0.728355i
$656$	−0.174669	+	0.0635742i	−0.00681967	+	0.00248216i
$657$	−6.60863	+	3.87000i	−0.257827	+	0.150983i
$658$	0.966991	+	0.351956i	0.0376972	+	0.0137207i
$659$	30.2419	−	15.1881i	1.17806	−	0.591643i	0.251523	−	0.967851i	$-0.419069\pi$
$659$	30.2419	−	15.1881i	1.17806	−	0.591643i	0.926535	+	0.376209i	$0.122772\pi$
$660$	12.8381	−	14.5159i	0.499724	−	0.565032i
$661$	2.98024	+	6.90897i	0.115918	+	0.268728i	0.966291	−	0.257452i	$-0.0828830\pi$
$661$	2.98024	+	6.90897i	0.115918	+	0.268728i	−0.850373	+	0.526180i	$0.823624\pi$
$662$	−25.2847	−	2.95535i	−0.982717	−	0.114863i
$663$	−14.9337	+	37.9307i	−0.579978	+	1.47311i
$664$	−11.5683	−	7.60858i	−0.448936	−	0.295270i
$665$	1.07502	−	0.902051i	0.0416876	−	0.0349800i
$666$	−3.63901	+	5.60783i	−0.141009	+	0.217299i
$667$	12.0053	+	10.0737i	0.464849	+	0.390054i
$668$	−5.79586	−	19.3595i	−0.224248	−	0.749042i
$669$	−2.75480	+	1.10425i	−0.106507	+	0.0426930i
$670$	−13.7134	−	6.88713i	−0.529795	−	0.266073i
$671$	10.9302	+	11.5854i	0.421958	+	0.447249i
$672$	−0.127676	+	0.183542i	−0.00492521	+	0.00708028i
$673$	11.0938	−	25.7184i	0.427636	−	0.991371i	−0.559110	−	0.829094i	$-0.688857\pi$
$673$	11.0938	−	25.7184i	0.427636	−	0.991371i	0.986745	−	0.162277i	$-0.0518839\pi$
$674$	12.2997	−	21.3037i	0.473766	−	0.820587i
$675$	−69.4904	−	9.52343i	−2.67469	−	0.366557i
$676$	−4.56098	−	7.89985i	−0.175422	−	0.303840i
$677$	0.0924544	−	0.0108064i	0.00355331	−	0.000415323i	−0.114316	−	0.993444i	$-0.536468\pi$
$677$	0.0924544	−	0.0108064i	0.00355331	−	0.000415323i	0.117869	+	0.993029i	$0.462394\pi$
$678$	1.96207	+	1.95001i	0.0753529	+	0.0748898i
$679$	−0.958483	+	0.227165i	−0.0367832	+	0.00871778i
$680$	−1.25138	−	21.4854i	−0.0479883	−	0.823927i
$681$	−4.94684	+	9.24256i	−0.189563	+	0.354176i
$682$	−8.99632	−	2.13217i	−0.344487	−	0.0816449i
$683$	−6.87679	+	39.0002i	−0.263133	+	1.49230i	0.511165	+	0.859482i	$0.329214\pi$
$683$	−6.87679	+	39.0002i	−0.263133	+	1.49230i	−0.774299	+	0.632820i	$0.781897\pi$
$684$	−5.48350	+	5.23768i	−0.209667	+	0.200268i
$685$	2.74935	+	15.5923i	0.105047	+	0.595752i
$686$	0.104954	−	1.80198i	0.00400715	−	0.0688001i
$687$	−0.0189236	+	0.727473i	−0.000721979	+	0.0277548i
$688$	2.17582	−	2.92264i	0.0829525	−	0.111425i
$689$	36.0575	−	48.4336i	1.37368	−	1.84517i
$690$	−30.5252	+	16.5807i	−1.16208	+	0.631216i
$691$	2.24484	−	38.5425i	0.0853979	−	1.46623i	−0.634918	−	0.772580i	$-0.718966\pi$
$691$	2.24484	−	38.5425i	0.0853979	−	1.46623i	0.720316	−	0.693646i	$-0.243997\pi$
$692$	3.67166	+	20.8230i	0.139576	+	0.791573i
$693$	−0.110780	+	1.00127i	−0.00420817	+	0.0380349i
$694$	−4.05537	+	22.9992i	−0.153940	+	0.873036i
$695$	−46.6368	−	11.0531i	−1.76903	−	0.419269i
$696$	−3.07122	−	4.94502i	−0.116414	−	0.187441i
$697$	0.0540819	+	0.928550i	0.00204850	+	0.0351713i
$698$	−4.46281	+	1.05770i	−0.168920	+	0.0400347i
$699$	−2.89939	+	10.9556i	−0.109665	+	0.414380i
$700$	−1.73066	+	0.202285i	−0.0654129	+	0.00764567i
$701$	−14.9323	−	25.8636i	−0.563986	−	0.976853i	−0.997143	−	0.0755346i	$-0.975934\pi$
$701$	−14.9323	−	25.8636i	−0.563986	−	0.976853i	0.433157	−	0.901319i	$-0.357400\pi$
$702$	−23.6643	−	6.10690i	−0.893151	−	0.230490i
$703$	−2.81627	+	4.87793i	−0.106218	+	0.183975i
$704$	−1.03033	+	2.38858i	−0.0388321	+	0.0900229i
$705$	−25.2637	−	53.7450i	−0.951484	−	2.02415i
$706$	−10.6396	−	11.2773i	−0.400427	−	0.424428i
$707$	1.30690	+	0.656352i	0.0491512	+	0.0246847i
$708$	7.03612	+	5.52829i	0.264434	+	0.207766i
$709$	11.4938	+	38.3920i	0.431660	+	1.44184i	0.846715	+	0.532047i	$0.178577\pi$
$709$	11.4938	+	38.3920i	0.431660	+	1.44184i	−0.415055	+	0.909796i	$0.636238\pi$
$710$	53.5718	+	44.9521i	2.01051	+	1.68702i
$711$	33.1250	+	30.8681i	1.24228	+	1.15764i
$712$	8.44328	−	7.08475i	0.316425	−	0.265512i
$713$	13.8469	+	9.10722i	0.518569	+	0.341068i
$714$	0.696613	+	0.875451i	0.0260701	+	0.0327629i
$715$	52.2669	+	6.10913i	1.95467	+	0.228468i
$716$	1.95896	+	4.54139i	0.0732099	+	0.169720i
$717$	−11.8467	−	2.40810i	−0.442422	−	0.0899321i
$718$	7.34704	−	3.68982i	0.274189	−	0.137703i
$719$	43.5140	+	15.8378i	1.62280	+	0.590650i	0.983912	−	0.178652i	$-0.0571738\pi$
$719$	43.5140	+	15.8378i	1.62280	+	0.590650i	0.638885	+	0.769302i	$0.279396\pi$
$720$	12.6929	−	2.31885i	0.473035	−	0.0864186i
$721$	−0.0884307	+	0.0321861i	−0.00329333	+	0.00119867i
$722$	8.65411	−	9.17282i	0.322073	−	0.341377i
$723$	−24.8534	+	22.2553i	−0.924308	+	0.827683i
$724$	−13.4293	+	8.83256i	−0.499094	+	0.328260i
$725$	13.0111	−	43.4601i	0.483221	−	1.61407i
$726$	−0.661531	−	7.30206i	−0.0245517	−	0.271005i
$727$	22.3315	+	29.9964i	0.828228	+	1.11250i	0.992029	+	0.126010i	$0.0402173\pi$
$727$	22.3315	+	29.9964i	0.828228	+	1.11250i	−0.163800	+	0.986493i	$0.552375\pi$
$728$	−0.607138			−0.0225020
$729$	−23.1291	+	13.9301i	−0.856632	+	0.515928i
$730$	10.9795			0.406371
$731$	−10.8877	−	14.6247i	−0.402695	−	0.540913i
$732$	0.956861	+	10.5620i	0.0353666	+	0.390381i
$733$	−10.0486	+	33.5646i	−0.371152	+	1.23973i	0.544840	+	0.838540i	$0.316590\pi$
$733$	−10.0486	+	33.5646i	−0.371152	+	1.23973i	−0.915993	+	0.401195i	$0.868595\pi$
$734$	−5.41814	+	3.56356i	−0.199987	+	0.131534i
$735$	−38.7553	+	34.7039i	−1.42951	+	1.28007i
$736$	3.20000	−	3.39181i	0.117954	−	0.125024i
$737$	8.72165	−	3.17442i	0.321266	−	0.116931i
$738$	−0.548557	+	0.100216i	−0.0201927	+	0.00368899i
$739$	17.0975	+	6.22298i	0.628941	+	0.228916i	0.636771	−	0.771053i	$-0.280270\pi$
$739$	17.0975	+	6.22298i	0.628941	+	0.228916i	−0.00782904	+	0.999969i	$0.502492\pi$
$740$	8.56467	−	4.30134i	0.314844	−	0.158120i
$741$	−20.1791	−	4.10184i	−0.741296	−	0.150685i
$742$	−0.656375	−	1.52165i	−0.0240963	−	0.0558615i
$743$	25.9853	+	3.03725i	0.953308	+	0.111426i	0.578505	−	0.815679i	$-0.303636\pi$
$743$	25.9853	+	3.03725i	0.953308	+	0.111426i	0.374803	+	0.927104i	$0.377710\pi$
$744$	−3.83303	−	4.81707i	−0.140526	−	0.176602i
$745$	−20.0847	−	13.2099i	−0.735847	−	0.483974i
$746$	16.7874	−	14.0863i	0.614629	−	0.515735i
$747$	−30.3891	−	28.3186i	−1.11188	−	1.03612i
$748$	9.97147	+	8.36706i	0.364593	+	0.305930i
$749$	−0.189078	−	0.631564i	−0.00690875	−	0.0230768i
$750$	49.7815	+	39.1134i	1.81776	+	1.42822i
$751$	−5.79203	−	2.90887i	−0.211354	−	0.106146i	0.339973	−	0.940435i	$-0.389582\pi$
$751$	−5.79203	−	2.90887i	−0.211354	−	0.106146i	−0.551327	+	0.834289i	$0.685878\pi$
$752$	5.47064	+	5.79854i	0.199494	+	0.211451i
$753$	17.1551	+	36.4952i	0.625167	+	1.32996i
$754$	6.26097	−	14.5146i	0.228011	−	0.528589i
$755$	−32.8260	+	56.8563i	−1.19466	+	2.06921i
$756$	−0.469883	+	0.478653i	−0.0170895	+	0.0174085i
$757$	26.5187	+	45.9317i	0.963837	+	1.66941i	0.712708	+	0.701461i	$0.247468\pi$
$757$	26.5187	+	45.9317i	0.963837	+	1.66941i	0.251129	+	0.967954i	$0.419198\pi$
$758$	−21.5684	+	2.52099i	−0.783400	+	0.0915664i
$759$	5.37525	−	20.3109i	0.195109	−	0.737238i
$760$	10.5784	−	2.50713i	0.383720	−	0.0909432i
$761$	0.163665	+	2.81001i	0.00593284	+	0.101863i	0.999975	−	0.00713768i	$-0.00227201\pi$
$761$	0.163665	+	2.81001i	0.00593284	+	0.101863i	−0.994042	+	0.109001i	$0.965235\pi$
$762$	−4.93363	−	7.94373i	−0.178726	−	0.287771i
$763$	−0.218661	−	0.0518236i	−0.00791606	−	0.00187614i
$764$	1.41346	−	8.01613i	0.0511372	−	0.290013i
$765$	7.10016	−	64.1738i	0.256707	−	2.32021i
$766$	−1.51725	−	8.60475i	−0.0548204	−	0.310902i
$767$	−1.41284	+	24.2576i	−0.0510149	+	0.875892i
$768$	−1.52201	+	0.826727i	−0.0549209	+	0.0298319i
$769$	14.1497	−	19.0063i	0.510250	−	0.685385i	−0.470108	−	0.882609i	$-0.655785\pi$
$769$	14.1497	−	19.0063i	0.510250	−	0.685385i	0.980358	+	0.197224i	$0.0631926\pi$
$770$	0.862437	−	1.15845i	0.0310801	−	0.0417478i
$771$	0.0291693	−	1.12135i	0.00105051	−	0.0403843i
$772$	0.215392	−	3.69815i	0.00775214	−	0.133099i
$773$	3.87244	+	21.9617i	0.139282	+	0.789908i	0.971782	+	0.235882i	$0.0757979\pi$
$773$	3.87244	+	21.9617i	0.139282	+	0.789908i	−0.832500	+	0.554026i	$0.813091\pi$
$774$	7.90445	−	7.55009i	0.284120	−	0.271383i
$775$	8.33089	−	47.2468i	0.299254	−	1.69716i
$776$	−7.42521	−	1.75981i	−0.266550	−	0.0631734i
$777$	−0.235102	+	0.439260i	−0.00843425	+	0.0157584i
$778$	−0.0418486	−	0.718512i	−0.00150034	−	0.0257599i
$779$	−0.457175	+	0.108353i	−0.0163800	+	0.00388213i
$780$	24.8519	+	24.6992i	0.889840	+	0.884372i
$781$	−42.0110	+	4.91038i	−1.50327	+	0.175707i
$782$	−11.6669	−	20.2076i	−0.417206	−	0.722623i
$783$	−6.59738	−	16.1693i	−0.235771	−	0.577843i
$784$	3.49167	−	6.04775i	0.124702	−	0.215991i
$785$	3.26122	−	7.56037i	0.116398	−	0.269841i
$786$	−5.89349	+	8.47223i	−0.210214	+	0.302194i
$787$	−19.4259	−	20.5903i	−0.692460	−	0.733965i	0.281780	−	0.959479i	$-0.409075\pi$
$787$	−19.4259	−	20.5903i	−0.692460	−	0.733965i	−0.974240	+	0.225514i	$0.927594\pi$
$788$	−14.7547	−	7.41008i	−0.525614	−	0.263973i
$789$	15.5065	−	6.21573i	0.552046	−	0.221286i
$790$	−18.6174	−	62.1863i	−0.662376	−	2.21249i
$791$	0.157930	+	0.132519i	0.00561534	+	0.00471183i
$792$	−4.24808	+	6.54643i	−0.150949	+	0.232617i
$793$	−22.0610	+	18.5113i	−0.783407	+	0.657357i
$794$	28.1758	+	18.5315i	0.999923	+	0.657660i
$795$	−35.0354	+	88.9876i	−1.24258	+	3.15606i
$796$	16.8789	+	1.97286i	0.598256	+	0.0699261i
$797$	15.4920	+	35.9145i	0.548755	+	1.27216i	0.936590	+	0.350428i	$0.113964\pi$
$797$	15.4920	+	35.9145i	0.548755	+	1.27216i	−0.387834	+	0.921729i	$0.626777\pi$
$798$	−0.374400	+	0.423330i	−0.0132536	+	0.0149857i
$799$	35.6477	−	17.9029i	1.26112	−	0.633360i
$800$	−12.6844	−	4.61673i	−0.448460	−	0.163226i
$801$	28.5333	−	16.7091i	1.00818	−	0.590386i
$802$	−2.11151	+	0.768527i	−0.0745600	+	0.0271376i
$803$	−4.55709	+	4.83024i	−0.160816	+	0.170455i
$804$	5.87216	+	1.92576i	0.207095	+	0.0679162i
$805$	−2.16300	+	1.42263i	−0.0762357	+	0.0501410i
$806$	4.79439	−	16.0144i	0.168875	−	0.564083i
$807$	18.3623	+	8.49367i	0.646383	+	0.298991i
$808$	6.76548	+	9.08762i	0.238009	+	0.319701i
$809$	−50.7676			−1.78489			−0.892447	−	0.451151i	$-0.851013\pi$
$809$	−50.7676			−1.78489			−0.892447	+	0.451151i	$0.851013\pi$
$810$	38.7059	−	0.477182i	1.35999	−	0.0167665i
$811$	42.1411			1.47977			0.739887	−	0.672731i	$-0.234879\pi$
$811$	42.1411			1.47977			0.739887	+	0.672731i	$0.234879\pi$
$812$	−0.259067	−	0.347988i	−0.00909148	−	0.0122120i
$813$	26.9858	−	19.0199i	0.946433	−	0.667056i
$814$	−1.66250	+	5.55315i	−0.0582707	+	0.194638i
$815$	25.6408	−	16.8642i	0.898158	−	0.590728i
$816$	1.77878	+	8.48256i	0.0622698	+	0.296949i
$817$	6.32021	−	6.69903i	0.221116	−	0.234369i
$818$	6.96306	−	2.53435i	0.243458	−	0.0886113i
$819$	−1.79566	−	0.305223i	−0.0627454	−	0.0106653i
$820$	0.751247	+	0.273432i	0.0262347	+	0.00954864i
$821$	−34.3947	+	17.2737i	−1.20038	+	0.602855i	−0.932701	−	0.360651i	$-0.882554\pi$
$821$	−34.3947	+	17.2737i	−1.20038	+	0.602855i	−0.267683	+	0.963507i	$0.586258\pi$
$822$	−2.02420	−	6.04622i	−0.0706021	−	0.210886i
$823$	−6.44808	−	14.9483i	−0.224766	−	0.521066i	0.768096	−	0.640335i	$-0.221204\pi$
$823$	−6.44808	−	14.9483i	−0.224766	−	0.521066i	−0.992862	+	0.119269i	$0.961945\pi$
$824$	−0.724094	−	0.0846344i	−0.0252250	−	0.00294838i
$825$	−60.1493	+	9.00001i	−2.09413	+	0.313340i
$826$	0.557170	+	0.366456i	0.0193864	+	0.0127506i
$827$	24.8901	−	20.8853i	0.865514	−	0.726252i	−0.0976347	−	0.995222i	$-0.531128\pi$
$827$	24.8901	−	20.8853i	0.865514	−	0.726252i	0.963149	+	0.268970i	$0.0866832\pi$
$828$	11.1694	−	8.42281i	0.388164	−	0.292713i
$829$	0.215900	+	0.181162i	0.00749852	+	0.00629200i	0.646529	−	0.762889i	$-0.276220\pi$
$829$	0.215900	+	0.181162i	0.00749852	+	0.00629200i	−0.639031	+	0.769181i	$0.720664\pi$
$830$	17.0797	+	57.0502i	0.592845	+	1.98024i
$831$	−2.21344	+	15.4428i	−0.0767833	+	0.535704i
$832$	−4.20311	−	2.11088i	−0.145717	−	0.0731816i
$833$	−23.9801	−	25.4174i	−0.830861	−	0.880662i
$834$	19.2331	+	1.62296i	0.665986	+	0.0561985i
$835$	−34.4258	+	79.8079i	−1.19135	+	2.76187i
$836$	−3.28764	+	5.69437i	−0.113706	+	0.196944i
$837$	−8.91483	−	16.1738i	−0.308142	−	0.559049i
$838$	−5.88203	−	10.1880i	−0.203191	−	0.351938i
$839$	7.11295	−	0.831385i	0.245566	−	0.0287026i	0.00758076	−	0.999971i	$-0.497587\pi$
$839$	7.11295	−	0.831385i	0.245566	−	0.0287026i	0.237986	+	0.971269i	$0.423513\pi$
$840$	0.928083	−	0.251747i	0.0320219	−	0.00868610i
$841$	−17.2276	+	4.08301i	−0.594054	+	0.140793i
$842$	2.00683	+	34.4559i	0.0691599	+	1.18743i
$843$	17.0338	−	0.548180i	0.586676	−	0.0188803i
$844$	17.9786	+	4.26102i	0.618850	+	0.146670i
$845$	−6.81280	+	38.6373i	−0.234367	+	1.32916i
$846$	13.2648	+	19.8999i	0.456052	+	0.684171i
$847$	−0.0948868	−	0.538130i	−0.00326035	−	0.0184904i
$848$	0.746457	−	12.8162i	0.0256335	−	0.440109i
$849$	9.85615	+	6.03751i	0.338262	+	0.207207i
$850$	−40.3352	+	54.1795i	−1.38348	+	1.85834i
$851$	6.20508	−	8.33487i	0.212707	−	0.285716i
$852$	−24.0153	−	14.7108i	−0.822749	−	0.503985i
$853$	−2.46540	+	42.3294i	−0.0844138	+	1.44933i	0.644437	+	0.764657i	$0.277092\pi$
$853$	−2.46540	+	42.3294i	−0.0844138	+	1.44933i	−0.728851	+	0.684672i	$0.759945\pi$
$854$	0.137247	+	0.778369i	0.00469651	+	0.0266352i
$855$	32.5469	−	2.09701i	1.11308	−	0.0717163i
$856$	0.886852	−	5.02959i	0.0303120	−	0.171908i
$857$	−5.73925	−	1.36023i	−0.196049	−	0.0464645i	0.131418	−	0.991327i	$-0.458047\pi$
$857$	−5.73925	−	1.36023i	−0.196049	−	0.0464645i	−0.327467	+	0.944863i	$0.606195\pi$
$858$	−21.1808	+	0.681637i	−0.723100	+	0.0232707i
$859$	−1.91521	−	32.8830i	−0.0653463	−	1.12195i	−0.858461	−	0.512879i	$-0.828579\pi$
$859$	−1.91521	−	32.8830i	−0.0653463	−	1.12195i	0.793115	−	0.609073i	$-0.208458\pi$
$860$	−15.2488	+	3.61402i	−0.519978	+	0.123237i
$861$	−0.0401096	+	0.0108799i	−0.00136693	+	0.000370788i
$862$	−24.7142	+	2.88868i	−0.841770	+	0.0983888i
$863$	5.91413	+	10.2436i	0.201319	+	0.348695i	0.948954	−	0.315415i	$-0.102144\pi$
$863$	5.91413	+	10.2436i	0.201319	+	0.348695i	−0.747634	+	0.664110i	$0.768810\pi$
$864$	−4.91709	+	1.67996i	−0.167283	+	0.0571533i
$865$	45.4706	−	78.7573i	1.54605	−	2.67783i
$866$	−5.13075	+	11.8944i	−0.174350	+	0.404189i
$867$	13.8751	+	1.17084i	0.471224	+	0.0397638i
$868$	−0.314840	−	0.333711i	−0.0106864	−	0.0113269i
$869$	35.0849	+	17.6203i	1.19017	+	0.597728i
$870$	−3.55224	+	24.7833i	−0.120432	+	0.840233i
$871$	4.81298	+	16.0765i	0.163082	+	0.544731i
$872$	−1.33357	−	1.11900i	−0.0451605	−	0.0378941i
$873$	−21.0760	−	8.93760i	−0.713313	−	0.302492i
$874$	9.02917	−	7.57637i	0.305416	−	0.256275i
$875$	3.94205	+	2.59273i	0.133266	+	0.0876501i
$876$	−4.37289	+	0.654307i	−0.147746	+	0.0221070i
$877$	−3.99541	−	0.466996i	−0.134915	−	0.0157693i	0.0483672	−	0.998830i	$-0.484598\pi$
$877$	−3.99541	−	0.466996i	−0.134915	−	0.0157693i	−0.183283	+	0.983060i	$0.558672\pi$
$878$	−2.16884	−	5.02794i	−0.0731949	−	0.169685i
$879$	−0.634597	−	1.89552i	−0.0214044	−	0.0639343i
$880$	9.99818	−	5.02127i	0.337039	−	0.169267i
$881$	28.9518	+	10.5376i	0.975409	+	0.355020i	0.780054	−	0.625712i	$-0.215192\pi$
$881$	28.9518	+	10.5376i	0.975409	+	0.355020i	0.195356	+	0.980732i	$0.437414\pi$
$882$	13.3672	−	16.1313i	0.450098	−	0.543170i
$883$	−23.8873	+	8.69427i	−0.803872	+	0.292586i	−0.711090	−	0.703101i	$-0.751798\pi$
$883$	−23.8873	+	8.69427i	−0.803872	+	0.292586i	−0.0927821	+	0.995686i	$0.529576\pi$
$884$	−16.1510	+	17.1191i	−0.543217	+	0.575777i
$885$	−7.89861	−	37.6665i	−0.265509	−	1.26614i
$886$	4.11146	−	2.70415i	0.138127	−	0.0908476i
$887$	−2.56888	+	8.58064i	−0.0862544	+	0.288110i	−0.990224	−	0.139487i	$-0.955455\pi$
$887$	−2.56888	+	8.58064i	−0.0862544	+	0.288110i	0.903969	+	0.427597i	$0.140640\pi$
$888$	−3.15478	+	2.22352i	−0.105868	+	0.0746165i
$889$	−0.416168	−	0.559011i	−0.0139578	−	0.0187486i
$890$	−47.4051			−1.58902
$891$	−15.8551	+	17.2260i	−0.531165	+	0.577092i
$892$	−1.71351			−0.0573724
$893$	12.0329	+	16.1630i	0.402666	+	0.540875i
$894$	8.78650	+	4.06429i	0.293865	+	0.135930i
$895$	6.10092	−	20.3785i	0.203931	−	0.681178i
$896$	−0.107849	+	0.0709333i	−0.00360298	+	0.00236972i
$897$	36.0964	+	11.8377i	1.20522	+	0.395250i
$898$	−7.73818	+	8.20199i	−0.258226	+	0.273704i
$899$	11.2246	−	4.08542i	0.374361	−	0.136256i
$900$	−35.1941	−	20.0311i	−1.17314	−	0.667703i
$901$	−60.3658	−	21.9713i	−2.01108	−	0.731971i
$902$	−0.432099	+	0.217008i	−0.0143873	+	0.00722558i
$903$	0.539697	−	0.610229i	0.0179600	−	0.0203072i
$904$	0.632583	+	1.46649i	0.0210394	+	0.0487748i
$905$	68.6646	+	8.02574i	2.28249	+	0.266785i
$906$	9.68558	−	24.6008i	0.321782	−	0.817306i
$907$	20.6765	+	13.5992i	0.686553	+	0.451553i	0.844261	−	0.535933i	$-0.180040\pi$
$907$	20.6765	+	13.5992i	0.686553	+	0.451553i	−0.157708	+	0.987486i	$0.550410\pi$
$908$	−4.63644	+	3.89043i	−0.153866	+	0.129109i
$909$	15.4409	+	30.2785i	0.512142	+	1.00428i
$910$	2.00036	+	1.67850i	0.0663114	+	0.0556419i
$911$	−9.35350	−	31.2429i	−0.309895	−	1.03512i	−0.961095	−	0.276217i	$-0.910919\pi$
$911$	−9.35350	−	31.2429i	−0.309895	−	1.03512i	0.651200	−	0.758906i	$-0.274266\pi$
$912$	−4.06373	+	1.62894i	−0.134564	+	0.0539395i
$913$	−32.1871	−	16.1650i	−1.06524	−	0.534983i
$914$	9.02110	+	9.56181i	0.298392	+	0.316277i
$915$	26.0471	−	37.4443i	0.861092	−	1.23787i
$916$	−0.166412	+	0.385787i	−0.00549842	+	0.0127468i
$917$	−0.384578	+	0.666108i	−0.0126999	+	0.0219968i
$918$	0.996502	+	25.9821i	0.0328895	+	0.857536i
$919$	22.5768	+	39.1042i	0.744740	+	1.28993i	0.950316	+	0.311287i	$0.100760\pi$
$919$	22.5768	+	39.1042i	0.744740	+	1.28993i	−0.205576	+	0.978641i	$0.565907\pi$
$920$	−19.9202	+	2.32834i	−0.656750	+	0.0767631i
$921$	4.74659	+	4.71742i	0.156405	+	0.155444i
$922$	−11.7965	+	2.79583i	−0.388499	+	0.0920759i
$923$	−4.44670	−	76.3468i	−0.146365	−	2.51299i
$924$	−0.274453	+	0.512781i	−0.00902883	+	0.0168693i
$925$	−29.2685	−	6.93676i	−0.962342	−	0.228079i
$926$	0.902474	−	5.11818i	0.0296571	−	0.168194i
$927$	−2.09902	−	0.614332i	−0.0689408	−	0.0201773i
$928$	−0.583603	−	3.30978i	−0.0191577	−	0.108649i
$929$	2.70324	−	46.4129i	0.0886906	−	1.52276i	−0.601349	−	0.798987i	$-0.705370\pi$
$929$	2.70324	−	46.4129i	0.0886906	−	1.52276i	0.690039	−	0.723772i	$-0.257593\pi$
$930$	−0.688502	+	26.4679i	−0.0225769	+	0.867915i
$931$	10.5408	−	14.1587i	0.345460	−	0.464034i
$932$	−3.90721	+	5.24829i	−0.127985	+	0.171913i
$933$	51.9406	−	28.2131i	1.70046	−	0.923654i
$934$	2.08263	−	35.7574i	0.0681457	−	1.17002i
$935$	−9.72172	−	55.1346i	−0.317934	−	1.80309i
$936$	−11.3698	−	8.35610i	−0.371635	−	0.273128i
$937$	−6.79006	+	38.5083i	−0.221821	+	1.25801i	0.646848	+	0.762619i	$0.276087\pi$
$937$	−6.79006	+	38.5083i	−0.221821	+	1.25801i	−0.868669	+	0.495393i	$0.835024\pi$
$938$	0.448154	+	0.106214i	0.0146327	+	0.00346802i
$939$	17.9315	+	28.8719i	0.585172	+	0.942197i
$940$	−1.99361	−	34.2289i	−0.0650243	−	1.11642i
$941$	40.9789	−	9.71219i	1.33588	−	0.316608i	0.500237	−	0.865888i	$-0.333246\pi$
$941$	40.9789	−	9.71219i	1.33588	−	0.316608i	0.835638	+	0.549280i	$0.185098\pi$
$942$	−0.848323	+	3.20547i	−0.0276398	+	0.104440i
$943$	0.860907	−	0.100626i	0.0280350	−	0.00327682i
$944$	2.58310	+	4.47406i	0.0840728	+	0.145618i
$945$	2.87144	−	0.277993i	0.0934078	−	0.00904310i
$946$	4.73913	−	8.20841i	0.154082	−	0.266879i
$947$	−13.7574	+	31.8932i	−0.447055	+	1.03639i	0.534493	+	0.845173i	$0.320503\pi$
$947$	−13.7574	+	31.8932i	−0.447055	+	1.03639i	−0.981548	+	0.191217i	$0.938757\pi$
$948$	11.1208	+	23.6579i	0.361186	+	0.768373i
$949$	−8.23958	−	8.73345i	−0.267468	−	0.283500i
$950$	−30.4904	−	15.3128i	−0.989238	−	0.496814i
$951$	−13.0736	−	10.2720i	−0.423941	−	0.333091i
$952$	0.185255	+	0.618796i	0.00600416	+	0.0200553i
$953$	−29.3664	−	24.6414i	−0.951272	−	0.798212i	0.0282396	−	0.999601i	$-0.491010\pi$
$953$	−29.3664	−	24.6414i	−0.951272	−	0.798212i	−0.979511	+	0.201389i	$0.935454\pi$
$954$	8.65071	−	37.5296i	0.280077	−	1.21507i
$955$	−26.8185	+	22.5034i	−0.867826	+	0.728193i
$956$	−5.83134	−	3.83533i	−0.188599	−	0.124043i
$957$	−9.42858	−	11.8491i	−0.304783	−	0.383028i
$958$	9.00263	+	1.05226i	0.290862	+	0.0339969i
$959$	−0.188213	−	0.436327i	−0.00607772	−	0.0140897i
$960$	7.30022	+	1.48393i	0.235614	+	0.0478937i
$961$	−16.4142	+	8.24350i	−0.529489	+	0.265919i
$962$	−9.84877	−	3.58466i	−0.317537	−	0.115574i
$963$	5.15143	−	14.4296i	0.166002	−	0.464986i
$964$	−18.0997	+	6.58774i	−0.582951	+	0.212177i
$965$	−10.9336	+	11.5890i	−0.351966	+	0.373062i
$966$	0.776694	−	0.695500i	0.0249897	−	0.0223774i
$967$	−38.0854	+	25.0492i	−1.22475	+	0.805528i	−0.986193	−	0.165602i	$-0.947043\pi$
$967$	−38.0854	+	25.0492i	−1.22475	+	0.805528i	−0.238553	+	0.971130i	$0.576673\pi$
$968$	1.21407	−	4.05528i	0.0390217	−	0.130342i
$969$	1.97661	+	21.8181i	0.0634979	+	0.700899i
$970$	19.5990	+	26.3260i	0.629285	+	0.845276i
$971$	−12.7545			−0.409312			−0.204656	−	0.978834i	$-0.565608\pi$
$971$	−12.7545			−0.409312			−0.204656	+	0.978834i	$0.565608\pi$
$972$	−15.3872	+	2.49666i	−0.493545	+	0.0800805i
$973$	1.43848			0.0461156
$974$	19.5432	+	26.2511i	0.626204	+	0.841138i
$975$	−9.92168	−	109.517i	−0.317748	−	3.50734i
$976$	−1.75607	+	5.86569i	−0.0562105	+	0.187756i
$977$	9.34184	−	6.14423i	0.298872	−	0.196571i	−0.391212	−	0.920301i	$-0.627944\pi$
$977$	9.34184	−	6.14423i	0.298872	−	0.196571i	0.690084	+	0.723729i	$0.257574\pi$
$978$	−9.20714	+	8.24465i	−0.294412	+	0.263635i
$979$	19.6756	−	20.8550i	0.628836	−	0.666527i
$980$	−28.2238	+	10.2726i	−0.901578	+	0.328147i
$981$	−3.38160	−	3.97995i	−0.107966	−	0.127070i
$982$	26.5788	+	9.67390i	0.848164	+	0.308707i
$983$	39.0807	−	19.6271i	1.24648	−	0.626007i	0.301605	−	0.953433i	$-0.402477\pi$
$983$	39.0807	−	19.6271i	1.24648	−	0.626007i	0.944877	+	0.327426i	$0.106181\pi$
$984$	−0.315499	−	0.0641322i	−0.0100577	−	0.00204446i
$985$	28.1269	+	65.2054i	0.896196	+	2.07762i
$986$	−16.7037	−	1.95238i	−0.531953	−	0.0621764i
$987$	1.10979	+	1.39470i	0.0353250	+	0.0443939i
$988$	−9.93281	−	6.53291i	−0.316005	−	0.207840i
$989$	−13.0155	+	10.9213i	−0.413869	+	0.347278i
$990$	32.0947	−	9.82449i	1.02004	−	0.312243i
$991$	14.5001	+	12.1670i	0.460611	+	0.386499i	0.843356	−	0.537356i	$-0.180577\pi$
$991$	14.5001	+	12.1670i	0.460611	+	0.386499i	−0.382745	+	0.923854i	$0.625021\pi$
$992$	−1.01935	−	3.40485i	−0.0323643	−	0.108104i
$993$	−34.6710	−	27.2410i	−1.10025	−	0.864467i
$994$	−1.87564	−	0.941982i	−0.0594917	−	0.0298778i
$995$	−50.1574	−	53.1637i	−1.59010	−	1.68540i
$996$	−10.2023	−	21.7039i	−0.323271	−	0.687715i
$997$	8.85642	−	20.5315i	0.280486	−	0.650239i	−0.718488	−	0.695540i	$-0.755165\pi$
$997$	8.85642	−	20.5315i	0.280486	−	0.650239i	0.998973	+	0.0453008i	$0.0144246\pi$
$998$	14.5547	−	25.2095i	0.460721	−	0.797992i
$999$	−10.4483	+	4.99026i	−0.330570	+	0.157885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.7.2	✓	90
3.2	odd	2		486.2.g.b.343.1		90
81.23	odd	54		486.2.g.b.469.1		90
81.58	even	27	inner	162.2.g.b.139.2	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.7.2	✓	90	1.1	even	1	trivial
162.2.g.b.139.2	yes	90	81.58	even	27	inner
486.2.g.b.343.1		90	3.2	odd	2
486.2.g.b.469.1		90	81.23	odd	54

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.597159 + 0.802123i) q^{2} +(0.156275 + 1.72499i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(3.59342 - 2.36343i) q^{5} +(-1.29033 + 1.15544i) q^{6} +(-0.0885835 + 0.0938930i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.95116 + 0.539145i) q^{9} +O(q^{10})\)	\(q+(0.597159 + 0.802123i) q^{2} +(0.156275 + 1.72499i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(3.59342 - 2.36343i) q^{5} +(-1.29033 + 1.15544i) q^{6} +(-0.0885835 + 0.0938930i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.95116 + 0.539145i) q^{9} +(4.04160 + 1.47102i) q^{10} +(-2.32463 + 1.16747i) q^{11} +(-1.69734 - 0.345022i) q^{12} +(-1.86292 - 4.31874i) q^{13} +(-0.128212 - 0.0149858i) q^{14} +(4.63844 + 5.82925i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-3.83323 + 3.21646i) q^{17} +(-2.19477 - 2.04524i) q^{18} +(-1.93631 - 1.62476i) q^{19} +(1.23353 + 4.12029i) q^{20} +(-0.175808 - 0.138132i) q^{21} +(-2.32463 - 1.16747i) q^{22} +(3.20000 + 3.39181i) q^{23} +(-0.736831 - 1.56751i) q^{24} +(5.34645 - 12.3945i) q^{25} +(2.35170 - 4.07326i) q^{26} +(-1.39121 - 5.00645i) q^{27} +(-0.0645425 - 0.111791i) q^{28} +(3.33811 - 0.390169i) q^{29} +(-1.90589 + 7.20159i) q^{30} +(3.45836 - 0.819647i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(-2.37716 - 3.82750i) q^{33} +(-4.86905 - 1.15398i) q^{34} +(-0.0964080 + 0.546757i) q^{35} +(0.329906 - 2.98181i) q^{36} +(-0.386950 - 2.19450i) q^{37} +(0.146971 - 2.52339i) q^{38} +(7.15863 - 3.88842i) q^{39} +(-2.56837 + 3.44992i) q^{40} +(0.110999 - 0.149098i) q^{41} +(0.00581401 - 0.223506i) q^{42} +(-0.211858 + 3.63746i) q^{43} +(-0.451715 - 2.56180i) q^{44} +(-9.33050 + 8.91222i) q^{45} +(-0.809736 + 4.59224i) q^{46} +(-7.75700 - 1.83844i) q^{47} +(0.817329 - 1.52708i) q^{48} +(0.406045 + 6.97152i) q^{49} +(13.1346 - 3.11295i) q^{50} +(-6.14739 - 6.10962i) q^{51} +(4.67160 - 0.546031i) q^{52} +(6.41895 + 11.1179i) q^{53} +(3.18502 - 4.10557i) q^{54} +(-5.59412 + 9.68930i) q^{55} +(0.0511279 - 0.118528i) q^{56} +(2.50008 - 3.59401i) q^{57} +(2.30634 + 2.44458i) q^{58} +(-4.61669 - 2.31859i) q^{59} +(-6.91468 + 2.77173i) q^{60} +(-1.75607 - 5.86569i) q^{61} +(2.72265 + 2.28457i) q^{62} +(0.210802 - 0.324852i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-16.9013 - 11.1161i) q^{65} +(1.65059 - 4.19240i) q^{66} +(-3.54382 - 0.414214i) q^{67} +(-1.98195 - 4.59469i) q^{68} +(-5.35074 + 6.05002i) q^{69} +(-0.496138 + 0.249170i) q^{70} +(15.2792 + 5.56117i) q^{71} +(2.58878 - 1.51599i) q^{72} +(2.39884 - 0.873108i) q^{73} +(1.52919 - 1.62085i) q^{74} +(22.2158 + 7.28561i) q^{75} +(2.11184 - 1.38898i) q^{76} +(0.0963062 - 0.321685i) q^{77} +(7.39383 + 3.42010i) q^{78} +(-9.01273 - 12.1062i) q^{79} -4.30098 q^{80} +(8.41864 - 3.18220i) q^{81} +0.185879 q^{82} +(8.26834 + 11.1063i) q^{83} +(0.182751 - 0.128805i) q^{84} +(-6.17252 + 20.6176i) q^{85} +(-3.04421 + 2.00221i) q^{86} +(1.19470 + 5.69722i) q^{87} +(1.78514 - 1.89213i) q^{88} +(-10.3572 + 3.76972i) q^{89} +(-12.7205 - 2.16221i) q^{90} +(0.570523 + 0.207653i) q^{91} +(-4.16709 + 2.09279i) q^{92} +(1.95434 + 5.83754i) q^{93} +(-3.15750 - 7.31991i) q^{94} +(-10.7979 - 1.26210i) q^{95} +(1.71298 - 0.256310i) q^{96} +(6.37553 + 4.19325i) q^{97} +(-5.34955 + 4.48880i) q^{98} +(6.23090 - 4.69870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

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