LMFDB - Embedded newform 162.2.g.b.13.2

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			13.2
Character	$\chi$	$=$	162.13
Dual form			162.2.g.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 + 0.448799i) q^{2} +(-0.977769 - 1.42967i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-1.15296 - 3.85116i) q^{5} +(-0.232129 - 1.71643i) q^{6} +(-0.663579 - 1.53835i) q^{7} +(0.173648 + 0.984808i) q^{8} +(-1.08794 + 2.79578i) q^{9} +O(q^{10})$	\(q+(0.893633 + 0.448799i) q^{2} +(-0.977769 - 1.42967i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-1.15296 - 3.85116i) q^{5} +(-0.232129 - 1.71643i) q^{6} +(-0.663579 - 1.53835i) q^{7} +(0.173648 + 0.984808i) q^{8} +(-1.08794 + 2.79578i) q^{9} +(0.698073 - 3.95897i) q^{10} +(0.0131573 - 0.00311835i) q^{11} +(0.562892 - 1.63803i) q^{12} +(3.84080 + 2.52614i) q^{13} +(0.0974140 - 1.67253i) q^{14} +(-4.37857 + 5.41390i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(4.83704 - 1.76054i) q^{17} +(-2.22696 + 2.01014i) q^{18} +(2.66092 + 0.968497i) q^{19} +(2.40060 - 3.22457i) q^{20} +(-1.55051 + 2.45285i) q^{21} +(0.0131573 + 0.00311835i) q^{22} +(-0.253001 + 0.586523i) q^{23} +(1.23817 - 1.21117i) q^{24} +(-9.32465 + 6.13292i) q^{25} +(2.29854 + 3.98119i) q^{26} +(5.06081 - 1.17823i) q^{27} +(0.837684 - 1.45091i) q^{28} +(-0.262835 - 4.51270i) q^{29} +(-6.34259 + 2.87294i) q^{30} +(-9.48738 + 1.10892i) q^{31} +(-0.686242 + 0.727374i) q^{32} +(-0.0173231 - 0.0157617i) q^{33} +(5.11267 + 0.597585i) q^{34} +(-5.15935 + 4.32920i) q^{35} +(-2.89223 + 0.796865i) q^{36} +(6.03321 + 5.06246i) q^{37} +(1.94323 + 2.05970i) q^{38} +(-0.143865 - 7.96107i) q^{39} +(3.59244 - 1.80419i) q^{40} +(6.30010 - 3.16403i) q^{41} +(-2.48643 + 1.49608i) q^{42} +(4.34864 + 4.60929i) q^{43} +(0.0103583 + 0.00869166i) q^{44} +(12.0213 + 0.966392i) q^{45} +(-0.489321 + 0.410589i) q^{46} +(-11.3730 - 1.32931i) q^{47} +(1.65004 - 0.526657i) q^{48} +(2.87751 - 3.04998i) q^{49} +(-11.0853 + 1.29568i) q^{50} +(-7.24650 - 5.19399i) q^{51} +(0.267296 + 4.58930i) q^{52} +(-2.96943 + 5.14321i) q^{53} +(5.05129 + 1.21838i) q^{54} +(-0.0271791 - 0.0470757i) q^{55} +(1.39975 - 0.920630i) q^{56} +(-1.21713 - 4.75122i) q^{57} +(1.79042 - 4.15065i) q^{58} +(-2.42002 - 0.573555i) q^{59} +(-6.95732 - 0.279198i) q^{60} +(1.39556 - 1.87456i) q^{61} +(-8.97591 - 3.26697i) q^{62} +(5.02282 - 0.181594i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(5.30025 - 17.7041i) q^{65} +(-0.00840662 - 0.0218597i) q^{66} +(0.232730 - 3.99581i) q^{67} +(4.30065 + 2.82858i) q^{68} +(1.08591 - 0.211774i) q^{69} +(-6.55350 + 1.55321i) q^{70} +(-1.01165 + 5.73737i) q^{71} +(-2.94223 - 0.585927i) q^{72} +(1.45371 + 8.24441i) q^{73} +(3.11944 + 7.23168i) q^{74} +(17.8854 + 7.33464i) q^{75} +(0.812139 + 2.71273i) q^{76} +(-0.0135280 - 0.0181713i) q^{77} +(3.44436 - 7.17884i) q^{78} +(-4.39144 - 2.20546i) q^{79} +4.02004 q^{80} +(-6.63278 - 6.08327i) q^{81} +7.04998 q^{82} +(13.5542 + 6.80719i) q^{83} +(-2.89339 + 0.221040i) q^{84} +(-12.3570 - 16.5984i) q^{85} +(1.81744 + 6.07068i) q^{86} +(-6.19470 + 4.78814i) q^{87} +(0.00535572 + 0.0124160i) q^{88} +(1.34899 + 7.65049i) q^{89} +(10.3089 + 6.25877i) q^{90} +(1.33740 - 7.58479i) q^{91} +(-0.621545 + 0.147309i) q^{92} +(10.8619 + 12.4796i) q^{93} +(-9.56667 - 6.29210i) q^{94} +(0.661893 - 11.3643i) q^{95} +(1.71089 + 0.269899i) q^{96} +(0.923670 - 3.08527i) q^{97} +(3.94027 - 1.43414i) q^{98} +(-0.00559615 + 0.0401776i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	0.893633	+	0.448799i	0.631894	+	0.317349i
$2$	0.893633	+	0.448799i	0.631894	+	0.317349i
$3$	−0.977769	−	1.42967i	−0.564515	−	0.825423i
$3$	−0.977769	−	1.42967i	−0.564515	−	0.825423i
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	−1.15296	−	3.85116i	−0.515620	−	1.72229i	−0.677540	−	0.735486i	$-0.736954\pi$
$5$	−1.15296	−	3.85116i	−0.515620	−	1.72229i	0.161920	−	0.986804i	$-0.448231\pi$
$6$	−0.232129	−	1.71643i	−0.0947664	−	0.700728i
$7$	−0.663579	−	1.53835i	−0.250809	−	0.581441i	0.745573	−	0.666424i	$-0.232176\pi$
$7$	−0.663579	−	1.53835i	−0.250809	−	0.581441i	−0.996382	+	0.0849824i	$0.972917\pi$
$8$	0.173648	+	0.984808i	0.0613939	+	0.348182i
$9$	−1.08794	+	2.79578i	−0.362646	+	0.931927i
$10$	0.698073	−	3.95897i	0.220750	−	1.25194i
$11$	0.0131573	−	0.00311835i	0.00396709	−	0.000940217i	−0.228632	−	0.973513i	$-0.573425\pi$
$11$	0.0131573	−	0.00311835i	0.00396709	−	0.000940217i	0.232599	+	0.972573i	$0.425277\pi$
$12$	0.562892	−	1.63803i	0.162493	−	0.472859i
$13$	3.84080	+	2.52614i	1.06525	+	0.700624i	0.955993	−	0.293390i	$-0.0947834\pi$
$13$	3.84080	+	2.52614i	1.06525	+	0.700624i	0.109254	+	0.994014i	$0.465154\pi$
$14$	0.0974140	−	1.67253i	0.0260350	−	0.447003i
$15$	−4.37857	+	5.41390i	−1.13054	+	1.39786i
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	4.83704	−	1.76054i	1.17315	−	0.426993i	0.319375	−	0.947628i	$-0.396527\pi$
$17$	4.83704	−	1.76054i	1.17315	−	0.426993i	0.853779	+	0.520635i	$0.174305\pi$
$18$	−2.22696	+	2.01014i	−0.524900	+	0.473794i
$19$	2.66092	+	0.968497i	0.610457	+	0.222188i	0.628703	−	0.777645i	$-0.283586\pi$
$19$	2.66092	+	0.968497i	0.610457	+	0.222188i	−0.0182459	+	0.999834i	$0.505808\pi$
$20$	2.40060	−	3.22457i	0.536791	−	0.721035i
$21$	−1.55051	+	2.45285i	−0.338349	+	0.535256i
$22$	0.0131573	+	0.00311835i	0.00280516	+	0.000664834i
$23$	−0.253001	+	0.586523i	−0.0527544	+	0.122298i	−0.942555	−	0.334051i	$-0.891584\pi$
$23$	−0.253001	+	0.586523i	−0.0527544	+	0.122298i	0.889801	+	0.456350i	$0.150843\pi$
$24$	1.23817	−	1.21117i	0.252740	−	0.247230i
$25$	−9.32465	+	6.13292i	−1.86493	+	1.22658i
$26$	2.29854	+	3.98119i	0.450781	+	0.780775i
$27$	5.06081	−	1.17823i	0.973953	−	0.226751i
$28$	0.837684	−	1.45091i	0.158307	−	0.274196i
$29$	−0.262835	−	4.51270i	−0.0488072	−	0.837987i	−0.930529	−	0.366218i	$-0.880653\pi$
$29$	−0.262835	−	4.51270i	−0.0488072	−	0.837987i	0.881722	−	0.471769i	$-0.156384\pi$
$30$	−6.34259	+	2.87294i	−1.15799	+	0.524524i
$31$	−9.48738	+	1.10892i	−1.70398	+	0.199167i	−0.911663	−	0.410938i	$-0.865201\pi$
$31$	−9.48738	+	1.10892i	−1.70398	+	0.199167i	−0.792321	+	0.610105i	$0.791127\pi$
$32$	−0.686242	+	0.727374i	−0.121312	+	0.128583i
$33$	−0.0173231	−	0.0157617i	−0.00301556	−	0.00274376i
$34$	5.11267	+	0.597585i	0.876815	+	0.102485i
$35$	−5.15935	+	4.32920i	−0.872088	+	0.731769i
$36$	−2.89223	+	0.796865i	−0.482039	+	0.132811i
$37$	6.03321	+	5.06246i	0.991853	+	0.832264i	0.985835	−	0.167718i	$-0.0536398\pi$
$37$	6.03321	+	5.06246i	0.991853	+	0.832264i	0.00601844	+	0.999982i	$0.498084\pi$
$38$	1.94323	+	2.05970i	0.315233	+	0.334127i
$39$	−0.143865	−	7.96107i	−0.0230368	−	1.27479i
$40$	3.59244	−	1.80419i	0.568015	−	0.285268i
$41$	6.30010	−	3.16403i	0.983910	−	0.494138i	0.117285	−	0.993098i	$-0.462581\pi$
$41$	6.30010	−	3.16403i	0.983910	−	0.494138i	0.866625	+	0.498960i	$0.166285\pi$
$42$	−2.48643	+	1.49608i	−0.383664	+	0.230850i
$43$	4.34864	+	4.60929i	0.663162	+	0.702911i	0.968410	−	0.249362i	$-0.0802209\pi$
$43$	4.34864	+	4.60929i	0.663162	+	0.702911i	−0.305248	+	0.952273i	$0.598739\pi$
$44$	0.0103583	+	0.00869166i	0.00156158	+	0.00131032i
$45$	12.0213	+	0.966392i	1.79204	+	0.144061i
$46$	−0.489321	+	0.410589i	−0.0721465	+	0.0605381i
$47$	−11.3730	−	1.32931i	−1.65892	−	0.193900i	−0.765598	−	0.643319i	$-0.777557\pi$
$47$	−11.3730	−	1.32931i	−1.65892	−	0.193900i	−0.893321	+	0.449419i	$0.851631\pi$
$48$	1.65004	−	0.526657i	0.238163	−	0.0760164i
$49$	2.87751	−	3.04998i	0.411073	−	0.435712i
$50$	−11.0853	+	1.29568i	−1.56769	+	0.183237i
$51$	−7.24650	−	5.19399i	−1.01471	−	0.727305i
$52$	0.267296	+	4.58930i	0.0370673	+	0.636421i
$53$	−2.96943	+	5.14321i	−0.407883	+	0.706474i	−0.994652	−	0.103280i	$-0.967066\pi$
$53$	−2.96943	+	5.14321i	−0.407883	+	0.706474i	0.586769	+	0.809754i	$0.300399\pi$
$54$	5.05129	+	1.21838i	0.687394	+	0.165801i
$55$	−0.0271791	−	0.0470757i	−0.00366484	−	0.00634768i
$56$	1.39975	−	0.920630i	0.187049	−	0.123024i
$57$	−1.21713	−	4.75122i	−0.161213	−	0.629314i
$58$	1.79042	−	4.15065i	0.235093	−	0.545007i
$59$	−2.42002	−	0.573555i	−0.315060	−	0.0746705i	0.0700438	−	0.997544i	$-0.477686\pi$
$59$	−2.42002	−	0.573555i	−0.315060	−	0.0746705i	−0.385103	+	0.922873i	$0.625834\pi$
$60$	−6.95732	−	0.279198i	−0.898186	−	0.0360443i
$61$	1.39556	−	1.87456i	0.178683	−	0.240013i	−0.703754	−	0.710444i	$-0.748494\pi$
$61$	1.39556	−	1.87456i	0.178683	−	0.240013i	0.882437	+	0.470431i	$0.155902\pi$
$62$	−8.97591	−	3.26697i	−1.13994	−	0.414905i
$63$	5.02282	−	0.181594i	0.632816	−	0.0228787i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	5.30025	−	17.7041i	0.657415	−	2.19592i
$66$	−0.00840662	−	0.0218597i	−0.00103478	−	0.00269075i
$67$	0.232730	−	3.99581i	0.0284324	−	0.488166i	−0.953793	−	0.300463i	$-0.902859\pi$
$67$	0.232730	−	3.99581i	0.0284324	−	0.488166i	0.982226	−	0.187703i	$-0.0601042\pi$
$68$	4.30065	+	2.82858i	0.521530	+	0.343016i
$69$	1.08591	−	0.211774i	0.130729	−	0.0254946i
$70$	−6.55350	+	1.55321i	−0.783293	+	0.185644i
$71$	−1.01165	+	5.73737i	−0.120061	+	0.680901i	0.864058	+	0.503392i	$0.167915\pi$
$71$	−1.01165	+	5.73737i	−0.120061	+	0.680901i	−0.984119	+	0.177509i	$0.943196\pi$
$72$	−2.94223	−	0.585927i	−0.346745	−	0.0690521i
$73$	1.45371	+	8.24441i	0.170144	+	0.964935i	0.943601	+	0.331086i	$0.107415\pi$
$73$	1.45371	+	8.24441i	0.170144	+	0.964935i	−0.773457	+	0.633849i	$0.781474\pi$
$74$	3.11944	+	7.23168i	0.362628	+	0.840666i
$75$	17.8854	+	7.33464i	2.06523	+	0.846931i
$76$	0.812139	+	2.71273i	0.0931587	+	0.311172i
$77$	−0.0135280	−	0.0181713i	−0.00154166	−	0.00207081i
$78$	3.44436	−	7.17884i	0.389997	−	0.812844i
$79$	−4.39144	−	2.20546i	−0.494076	−	0.248134i	0.184272	−	0.982875i	$-0.441007\pi$
$79$	−4.39144	−	2.20546i	−0.494076	−	0.248134i	−0.678348	+	0.734741i	$0.737304\pi$
$80$	4.02004			0.449454
$81$	−6.63278	−	6.08327i	−0.736976	−	0.675919i
$82$	7.04998			0.778541
$83$	13.5542	+	6.80719i	1.48777	+	0.747186i	0.992579	−	0.121598i	$-0.0388018\pi$
$83$	13.5542	+	6.80719i	1.48777	+	0.747186i	0.495191	+	0.868784i	$0.335098\pi$
$84$	−2.89339	+	0.221040i	−0.315695	+	0.0241174i
$85$	−12.3570	−	16.5984i	−1.34031	−	1.80035i
$86$	1.81744	+	6.07068i	0.195980	+	0.654619i
$87$	−6.19470	+	4.78814i	−0.664141	+	0.513343i
$88$	0.00535572	+	0.0124160i	0.000570922	+	0.00132355i
$89$	1.34899	+	7.65049i	0.142992	+	0.810950i	0.968957	+	0.247229i	$0.0795199\pi$
$89$	1.34899	+	7.65049i	0.142992	+	0.810950i	−0.825965	+	0.563722i	$0.809369\pi$
$90$	10.3089	+	6.25877i	1.08666	+	0.659732i
$91$	1.33740	−	7.58479i	0.140198	−	0.795102i
$92$	−0.621545	+	0.147309i	−0.0648006	+	0.0153580i
$93$	10.8619	+	12.4796i	1.12632	+	1.29407i
$94$	−9.56667	−	6.29210i	−0.986726	−	0.648980i
$95$	0.661893	−	11.3643i	0.0679088	−	1.16595i
$96$	1.71089	+	0.269899i	0.174617	+	0.0275464i
$97$	0.923670	−	3.08527i	0.0937845	−	0.313262i	−0.898206	−	0.439575i	$-0.855129\pi$
$97$	0.923670	−	3.08527i	0.0937845	−	0.313262i	0.991990	+	0.126313i	$0.0403143\pi$
$98$	3.94027	−	1.43414i	0.398027	−	0.144870i
$99$	−0.00559615	+	0.0401776i	−0.000562434	+	0.00403800i
$100$	−10.4877	−	3.81719i	−1.04877	−	0.381719i
$101$	2.80596	−	3.76905i	0.279203	−	0.375035i	−0.640295	−	0.768129i	$-0.721188\pi$
$101$	2.80596	−	3.76905i	0.279203	−	0.375035i	0.919498	+	0.393094i	$0.128595\pi$
$102$	−4.14465	−	7.89375i	−0.410382	−	0.781598i
$103$	−0.976984	−	0.231550i	−0.0962651	−	0.0228153i	0.182201	−	0.983261i	$-0.441678\pi$
$103$	−0.976984	−	0.231550i	−0.0962651	−	0.0228153i	−0.278466	+	0.960446i	$0.589826\pi$
$104$	−1.82081	+	4.22111i	−0.178545	+	0.413914i
$105$	11.2340	+	3.14322i	1.09633	+	0.306747i
$106$	−4.96185	+	3.26346i	−0.481937	+	0.316975i
$107$	−2.95229	−	5.11352i	−0.285409	−	0.494343i	0.687299	−	0.726374i	$-0.258796\pi$
$107$	−2.95229	−	5.11352i	−0.285409	−	0.494343i	−0.972708	+	0.232032i	$0.925463\pi$
$108$	3.96719	+	3.35580i	0.381743	+	0.322912i
$109$	4.08609	−	7.07731i	0.391376	−	0.677883i	−0.601255	−	0.799057i	$-0.705333\pi$
$109$	4.08609	−	7.07731i	0.391376	−	0.677883i	0.992631	+	0.121174i	$0.0386659\pi$
$110$	−0.00316065	−	0.0542663i	−0.000301357	−	0.00517409i
$111$	1.33859	−	13.5754i	0.127054	−	1.28852i
$112$	1.66404	−	0.194498i	0.157237	−	0.0183784i
$113$	−14.2211	+	15.0735i	−1.33781	+	1.41800i	−0.506445	+	0.862272i	$0.669041\pi$
$113$	−14.2211	+	15.0735i	−1.33781	+	1.41800i	−0.831366	+	0.555725i	$0.812441\pi$
$114$	1.04467	−	4.79209i	0.0978427	−	0.448820i
$115$	2.55049	+	0.298110i	0.237835	+	0.0277989i
$116$	3.46278	−	2.90562i	0.321511	−	0.269780i
$117$	−11.2411	+	7.98977i	−1.03924	+	0.738654i
$118$	−1.90520	−	1.59865i	−0.175388	−	0.147168i
$119$	−5.91808	−	6.27280i	−0.542510	−	0.575027i
$120$	−6.09198	−	3.37194i	−0.556119	−	0.307814i
$121$	−9.82980	+	4.93671i	−0.893618	+	0.448792i
$122$	2.08842	−	1.04884i	0.189077	−	0.0949579i
$123$	−10.6836	−	5.91340i	−0.963305	−	0.533193i
$124$	−6.55496	−	6.94785i	−0.588653	−	0.623935i
$125$	18.9722	+	15.9195i	1.69692	+	1.42389i
$126$	4.57006	+	2.09196i	0.407133	+	0.186367i
$127$	6.11180	−	5.12841i	0.542334	−	0.455072i	−0.330001	−	0.943981i	$-0.607049\pi$
$127$	6.11180	−	5.12841i	0.542334	−	0.455072i	0.872335	+	0.488908i	$0.162605\pi$
$128$	−0.993238	−	0.116093i	−0.0877907	−	0.0102613i
$129$	2.33782	−	10.7240i	0.205834	−	0.944193i
$130$	12.6820	−	13.4422i	1.11229	−	1.17896i
$131$	−8.15164	+	0.952790i	−0.712212	+	0.0832456i	−0.464481	−	0.885583i	$-0.653759\pi$
$131$	−8.15164	+	0.952790i	−0.712212	+	0.0832456i	−0.247731	+	0.968829i	$0.579685\pi$
$132$	0.00229821	−	0.0233075i	0.000200033	−	0.00202865i
$133$	−0.275847	−	4.73610i	−0.0239189	−	0.410672i
$134$	2.00129	−	3.46634i	0.172885	−	0.299446i
$135$	−10.3725	−	18.1315i	−0.892720	−	1.56051i
$136$	2.57374	+	4.45784i	0.220696	+	0.382257i
$137$	−10.6949	+	7.03413i	−0.913725	+	0.600967i	−0.916939	−	0.399028i	$-0.869348\pi$
$137$	−10.6949	+	7.03413i	−0.913725	+	0.600967i	0.00321342	+	0.999995i	$0.498977\pi$
$138$	1.06545	+	0.298109i	0.0906973	+	0.0253767i
$139$	−7.43815	+	17.2436i	−0.630896	+	1.46258i	0.239832	+	0.970814i	$0.422908\pi$
$139$	−7.43815	+	17.2436i	−0.630896	+	1.46258i	−0.870727	+	0.491766i	$0.836352\pi$
$140$	−6.55350	−	1.55321i	−0.553872	−	0.131270i
$141$	9.21966	+	17.5594i	0.776435	+	1.47877i
$142$	−3.47898	+	4.67307i	−0.291949	+	0.392156i
$143$	0.0584121	+	0.0212603i	0.00488467	+	0.00177787i
$144$	−2.36631	−	1.84407i	−0.197192	−	0.153673i
$145$	−17.0761	+	6.21518i	−1.41809	+	0.516143i
$146$	−2.40100	+	8.01990i	−0.198708	+	0.663731i
$147$	−7.17402	−	1.13173i	−0.591703	−	0.0933431i
$148$	−0.457937	+	7.86247i	−0.0376422	+	0.646291i
$149$	−1.82353	−	1.19935i	−0.149389	−	0.0982549i	0.472614	−	0.881270i	$-0.343311\pi$
$149$	−1.82353	−	1.19935i	−0.149389	−	0.0982549i	−0.622003	+	0.783015i	$0.713681\pi$
$150$	12.6912	+	14.5814i	1.03623	+	1.19057i
$151$	14.4265	−	3.41914i	1.17401	−	0.278245i	0.403079	−	0.915165i	$-0.367940\pi$
$151$	14.4265	−	3.41914i	1.17401	−	0.278245i	0.770930	+	0.636920i	$0.219792\pi$
$152$	−0.491719	+	2.78867i	−0.0398836	+	0.226191i
$153$	−0.340316	+	15.4387i	−0.0275129	+	1.24814i
$154$	−0.00393383	−	0.0223099i	−0.000316997	−	0.00179778i
$155$	15.2092	+	35.2589i	1.22163	+	2.83206i
$156$	6.29985	−	4.86942i	0.504392	−	0.389866i
$157$	−2.31347	−	7.72751i	−0.184635	−	0.616723i	−0.999322	−	0.0368220i	$-0.988277\pi$
$157$	−2.31347	−	7.72751i	−0.184635	−	0.616723i	0.814687	−	0.579901i	$-0.196909\pi$
$158$	−2.93452	−	3.94175i	−0.233458	−	0.313589i
$159$	10.2565	−	0.783545i	0.813395	−	0.0621392i
$160$	3.59244	+	1.80419i	0.284007	+	0.142634i
$161$	1.07016			0.0843407
$162$	−3.19711	−	8.41300i	−0.251188	−	0.660987i
$163$	17.6946			1.38595			0.692973	−	0.720964i	$-0.256300\pi$
$163$	17.6946			1.38595			0.692973	+	0.720964i	$0.256300\pi$
$164$	6.30010	+	3.16403i	0.491955	+	0.247069i
$165$	−0.0407280	+	0.0848864i	−0.00317067	+	0.00660840i
$166$	9.05744	+	12.1663i	0.702994	+	0.944285i
$167$	2.41890	+	8.07967i	0.187180	+	0.625224i	0.999138	+	0.0415086i	$0.0132164\pi$
$167$	2.41890	+	8.07967i	0.187180	+	0.625224i	−0.811958	+	0.583715i	$0.801598\pi$
$168$	−2.68483	−	1.10102i	−0.207139	−	0.0849458i
$169$	3.22137	+	7.46796i	0.247797	+	0.574459i
$170$	−3.59331	−	20.3787i	−0.275594	−	1.56297i
$171$	−5.60262	+	6.38569i	−0.428443	+	0.488326i
$172$	−1.10039	+	6.24063i	−0.0839040	+	0.475843i
$173$	−7.51741	+	1.78166i	−0.571538	+	0.135457i	−0.506215	−	0.862407i	$-0.668956\pi$
$173$	−7.51741	+	1.78166i	−0.571538	+	0.135457i	−0.0653230	+	0.997864i	$0.520808\pi$
$174$	−7.68470	+	1.49866i	−0.582575	+	0.113613i
$175$	15.6222	+	10.2749i	1.18093	+	0.776709i
$176$	−0.000786224		0.0134989i	−5.92639e−5		0.00101752i
$177$	1.54622	+	4.02064i	0.116221	+	0.302210i
$178$	−2.22803	+	7.44215i	−0.166998	+	0.557813i
$179$	−16.7997	+	6.11459i	−1.25567	+	0.457026i	−0.882313	−	0.470663i	$-0.844015\pi$
$179$	−16.7997	+	6.11459i	−1.25567	+	0.457026i	−0.373355	+	0.927689i	$0.621793\pi$
$180$	6.40348	+	10.2197i	0.477287	+	0.761730i
$181$	−12.8524	−	4.67788i	−0.955309	−	0.347704i	−0.183115	−	0.983091i	$-0.558618\pi$
$181$	−12.8524	−	4.67788i	−0.955309	−	0.347704i	−0.772193	+	0.635388i	$0.780840\pi$
$182$	4.59919	−	6.17779i	0.340915	−	0.457928i
$183$	−4.04455	−	0.162308i	−0.298982	−	0.0119982i
$184$	−0.621545	−	0.147309i	−0.0458209	−	0.0108598i
$185$	12.5403	−	29.0717i	0.921980	−	2.13739i
$186$	4.10567	+	16.0270i	0.301042	+	1.17515i
$187$	0.0581526	−	0.0382476i	0.00425254	−	0.00279694i
$188$	−5.72520	−	9.91634i	−0.417553	−	0.723223i
$189$	−5.17078	−	7.00344i	−0.376119	−	0.509425i
$190$	5.69176	−	9.85842i	0.412924	−	0.715205i
$191$	−0.157227	−	2.69948i	−0.0113765	−	0.195327i	−0.999208	−	0.0397977i	$-0.987329\pi$
$191$	−0.157227	−	2.69948i	−0.0113765	−	0.195327i	0.987831	−	0.155530i	$-0.0497084\pi$
$192$	1.40778	+	1.00904i	0.101598	+	0.0728210i
$193$	−9.73944	+	1.13838i	−0.701060	+	0.0819422i	−0.459153	−	0.888357i	$-0.651847\pi$
$193$	−9.73944	+	1.13838i	−0.701060	+	0.0819422i	−0.241907	+	0.970299i	$0.577773\pi$
$194$	2.21009	−	2.34256i	0.158675	−	0.168186i
$195$	−30.4935	+	9.73285i	−2.18368	+	0.696984i
$196$	4.16479	+	0.486794i	0.297485	+	0.0347710i
$197$	−1.84963	+	1.55203i	−0.131781	+	0.110577i	−0.706296	−	0.707917i	$-0.749635\pi$
$197$	−1.84963	+	1.55203i	−0.131781	+	0.110577i	0.574515	+	0.818494i	$0.305191\pi$
$198$	−0.0230326	+	0.0333925i	−0.00163685	+	0.00237310i
$199$	−10.4578	−	8.77512i	−0.741332	−	0.622052i	0.191863	−	0.981422i	$-0.438547\pi$
$199$	−10.4578	−	8.77512i	−0.741332	−	0.622052i	−0.933195	+	0.359370i	$0.882992\pi$
$200$	−7.65896	−	8.11802i	−0.541570	−	0.574031i
$201$	−5.94027	+	3.57425i	−0.418994	+	0.252108i
$202$	4.19904	−	2.10884i	0.295443	−	0.148377i
$203$	−6.76769	+	3.39886i	−0.474999	+	0.238553i
$204$	−0.161089	−	8.91423i	−0.0112785	−	0.624121i
$205$	−19.4489	−	20.6147i	−1.35837	−	1.43979i
$206$	−0.769146	−	0.645390i	−0.0535889	−	0.0449664i
$207$	−1.36454	−	1.34544i	−0.0948421	−	0.0935143i
$208$	−3.52157	+	2.95494i	−0.244177	+	0.204889i
$209$	0.0380308	+	0.00444516i	0.00263064	+	0.000307478i
$210$	8.62839	+	7.85070i	0.595416	+	0.541749i
$211$	4.10053	−	4.34631i	0.282292	−	0.299212i	−0.570676	−	0.821175i	$-0.693319\pi$
$211$	4.10053	−	4.34631i	0.282292	−	0.299212i	0.852968	+	0.521963i	$0.174800\pi$
$212$	−5.89871	+	0.689460i	−0.405125	+	0.0473523i
$213$	9.19174	−	4.16349i	0.629808	−	0.285277i
$214$	−0.343321	−	5.89460i	−0.0234690	−	0.402946i
$215$	12.7373	−	22.0616i	0.868677	−	1.50459i
$216$	2.03913	+	4.77932i	0.138745	+	0.325192i
$217$	8.00153	+	13.8591i	0.543179	+	0.940814i
$218$	6.82775	−	4.49068i	0.462434	−	0.304147i
$219$	10.3654	−	10.1395i	0.700430	−	0.685161i
$220$	0.0215302	−	0.0499127i	0.00145157	−	0.00336511i
$221$	23.0255	+	5.45714i	1.54886	+	0.367087i
$222$	7.28886	−	11.5307i	0.489196	−	0.773890i
$223$	7.99100	−	10.7338i	0.535117	−	0.718787i	−0.449545	−	0.893258i	$-0.648414\pi$
$223$	7.99100	−	10.7338i	0.535117	−	0.718787i	0.984662	+	0.174470i	$0.0558213\pi$
$224$	1.57433	+	0.573009i	0.105189	+	0.0382858i
$225$	−7.00167	−	32.7419i	−0.466778	−	2.18280i
$226$	−19.4734	+	7.08776i	−1.29535	+	0.471470i
$227$	6.69929	−	22.3772i	0.444647	−	1.48523i	−0.382879	−	0.923798i	$-0.625067\pi$
$227$	6.69929	−	22.3772i	0.444647	−	1.48523i	0.827526	−	0.561427i	$-0.189747\pi$
$228$	3.08424	−	3.81352i	0.204259	−	0.252557i
$229$	0.586644	−	10.0723i	0.0387665	−	0.665596i	−0.921821	−	0.387617i	$-0.873298\pi$
$229$	0.586644	−	10.0723i	0.0387665	−	0.665596i	0.960587	−	0.277979i	$-0.0896646\pi$
$230$	2.14541	+	1.41106i	0.141464	+	0.0930425i
$231$	−0.0127518	+	0.0371081i	−0.000839005	+	0.00244153i
$232$	4.39850	−	1.04246i	0.288776	−	0.0684411i
$233$	−0.251712	+	1.42753i	−0.0164902	+	0.0935207i	−0.991942	−	0.126692i	$-0.959564\pi$
$233$	−0.251712	+	1.42753i	−0.0164902	+	0.0935207i	0.975452	+	0.220213i	$0.0706751\pi$
$234$	−13.6312	+	2.09493i	−0.891099	+	0.136950i
$235$	7.99321	+	45.3318i	0.521420	+	2.95712i
$236$	−0.985073	−	2.28366i	−0.0641228	−	0.148653i
$237$	1.14072	+	8.43477i	0.0740975	+	0.547897i
$238$	−2.47336	−	8.26161i	−0.160324	−	0.535521i
$239$	12.7023	+	17.0622i	0.821644	+	1.10366i	0.992961	+	0.118443i	$0.0377904\pi$
$239$	12.7023	+	17.0622i	0.821644	+	1.10366i	−0.171317	+	0.985216i	$0.554802\pi$
$240$	−3.93067	−	5.74735i	−0.253724	−	0.370990i
$241$	8.20274	+	4.11957i	0.528385	+	0.265365i	0.692930	−	0.721005i	$-0.256319\pi$
$241$	8.20274	+	4.11957i	0.528385	+	0.265365i	−0.164545	+	0.986369i	$0.552616\pi$
$242$	−10.9998			−0.707095
$243$	−2.21177	+	15.4308i	−0.141885	+	0.989883i
$244$	2.33700			0.149611
$245$	−15.0636	−	7.56523i	−0.962379	−	0.483325i
$246$	−6.89325	−	10.0792i	−0.439498	−	0.642625i
$247$	7.77352	+	10.4417i	0.494617	+	0.664387i
$248$	−2.73954	−	9.15069i	−0.173961	−	0.581069i
$249$	−3.52084	−	26.0340i	−0.223124	−	1.64984i
$250$	9.80946	+	22.7409i	0.620405	+	1.43826i
$251$	−1.06851	−	6.05983i	−0.0674439	−	0.382493i	−0.999781	−	0.0209042i	$-0.993345\pi$
$251$	−1.06851	−	6.05983i	−0.0674439	−	0.382493i	0.932338	−	0.361589i	$-0.117766\pi$
$252$	3.14508	+	3.92048i	0.198122	+	0.246967i
$253$	−0.00149984	+	0.00850603i	−9.42943e−5	+	0.000534769i
$254$	7.76333	−	1.83994i	0.487114	−	0.115448i
$255$	−11.6480	+	33.8959i	−0.729423	+	2.12264i
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	0.554373	−	9.51822i	0.0345808	−	0.593730i	−0.935857	−	0.352380i	$-0.885373\pi$
$257$	0.554373	−	9.51822i	0.0345808	−	0.593730i	0.970438	−	0.241350i	$-0.0775903\pi$
$258$	6.90206	−	8.53408i	0.429704	−	0.531308i
$259$	3.78433	−	12.6405i	0.235147	−	0.785444i
$260$	17.3659	−	6.32068i	1.07699	−	0.391992i
$261$	12.9025	+	4.17470i	0.798642	+	0.258408i
$262$	−7.71218	−	2.80700i	−0.476460	−	0.173417i
$263$	−9.89545	+	13.2919i	−0.610180	+	0.819613i	−0.994626	−	0.103534i	$-0.966985\pi$
$263$	−9.89545	+	13.2919i	−0.610180	+	0.819613i	0.384446	+	0.923147i	$0.374392\pi$
$264$	0.0125141	−	0.0197969i	0.000770191	−	0.00121841i
$265$	23.2309	+	5.50583i	1.42706	+	0.338221i
$266$	1.87905	−	4.35614i	0.115212	−	0.267092i
$267$	9.61871	−	9.40902i	0.588656	−	0.575823i
$268$	3.34411	−	2.19946i	0.204274	−	0.134353i
$269$	−10.1199	−	17.5282i	−0.617023	−	1.06871i	−0.990026	−	0.140885i	$-0.955005\pi$
$269$	−10.1199	−	17.5282i	−0.617023	−	1.06871i	0.373003	−	0.927830i	$-0.378328\pi$
$270$	−1.13177	−	20.8581i	−0.0688771	−	1.26938i
$271$	6.66484	−	11.5438i	0.404860	−	0.701239i	−0.589445	−	0.807809i	$-0.700654\pi$
$271$	6.66484	−	11.5438i	0.404860	−	0.701239i	0.994305	+	0.106570i	$0.0339868\pi$
$272$	0.299299	+	5.13876i	0.0181477	+	0.311583i
$273$	−12.1514	+	5.50412i	−0.735439	+	0.333124i
$274$	−12.7142	+	1.48608i	−0.768093	+	0.0897772i
$275$	−0.103563	+	0.109770i	−0.00624509	+	0.00661941i
$276$	0.818331	+	0.744573i	0.0492578	+	0.0448181i
$277$	29.4197	+	3.43867i	1.76766	+	0.206610i	0.936798	−	0.349870i	$-0.113774\pi$
$277$	29.4197	+	3.43867i	1.76766	+	0.206610i	0.830861	+	0.556480i	$0.187848\pi$
$278$	−14.3859	+	12.0712i	−0.862807	+	0.723981i
$279$	7.22139	−	27.7311i	0.432333	−	1.66022i
$280$	−5.15935	−	4.32920i	−0.308330	−	0.258719i
$281$	1.06165	+	1.12528i	0.0633324	+	0.0671285i	0.758265	−	0.651946i	$-0.226047\pi$
$281$	1.06165	+	1.12528i	0.0633324	+	0.0671285i	−0.694933	+	0.719075i	$0.744566\pi$
$282$	0.358338	+	19.8294i	0.0213387	+	1.18083i
$283$	−5.12108	+	2.57190i	−0.304417	+	0.152884i	−0.594450	−	0.804133i	$-0.702630\pi$
$283$	−5.12108	+	2.57190i	−0.304417	+	0.152884i	0.290033	+	0.957017i	$0.406334\pi$
$284$	−5.20620	+	2.61465i	−0.308931	+	0.155151i
$285$	−16.8944	+	10.1653i	−1.00074	+	0.602142i
$286$	0.0426574	+	0.0452142i	0.00252238	+	0.00267357i
$287$	−9.04799	−	7.59217i	−0.534086	−	0.448151i
$288$	−1.28699	−	2.70992i	−0.0758366	−	0.159683i
$289$	7.27472	−	6.10421i	0.427925	−	0.359071i
$290$	−18.0491	−	2.10964i	−1.05988	−	0.123882i
$291$	−5.31407	+	1.69614i	−0.311516	+	0.0994292i
$292$	−5.74493	+	6.08927i	−0.336197	+	0.356348i
$293$	1.24181	−	0.145147i	0.0725476	−	0.00847960i	−0.0797417	−	0.996816i	$-0.525410\pi$
$293$	1.24181	−	0.145147i	0.0725476	−	0.00847960i	0.152289	+	0.988336i	$0.451335\pi$
$294$	−5.90302	−	4.23104i	−0.344271	−	0.246759i
$295$	0.581336	+	9.98116i	0.0338467	+	0.581126i
$296$	−3.93790	+	6.82064i	−0.228886	+	0.396442i
$297$	0.0629127	−	0.0312837i	0.00365056	−	0.00181527i
$298$	−1.09130	−	1.89018i	−0.0632171	−	0.109495i
$299$	−2.45336	+	1.61360i	−0.141882	+	0.0933171i
$300$	4.79715	+	18.7263i	0.276964	+	1.08116i
$301$	4.20504	−	9.74837i	0.242374	−	0.561887i
$302$	14.4265	+	3.41914i	0.830150	+	0.196749i
$303$	−8.13209	−	0.326342i	−0.467176	−	0.0187478i
$304$	−1.69097	+	2.27137i	−0.0969838	+	0.130272i
$305$	−8.82826	−	3.21322i	−0.505505	−	0.183989i
$306$	−7.23298	+	13.6438i	−0.413482	+	0.779962i
$307$	17.2059	−	6.26242i	0.981990	−	0.357415i	0.199376	−	0.979923i	$-0.436108\pi$
$307$	17.2059	−	6.26242i	0.981990	−	0.357415i	0.782614	+	0.622508i	$0.213886\pi$
$308$	0.00649725	−	0.0217023i	0.000370215	−	0.00123660i
$309$	0.624224	+	1.62317i	0.0355109	+	0.0923390i
$310$	−2.23272	+	38.3343i	−0.126810	+	2.17724i
$311$	13.9855	+	9.19840i	0.793044	+	0.521593i	0.880201	−	0.474601i	$-0.157408\pi$
$311$	13.9855	+	9.19840i	0.793044	+	0.521593i	−0.0871569	+	0.996195i	$0.527778\pi$
$312$	7.81514	−	1.52410i	0.442445	−	0.0862854i
$313$	12.0680	−	2.86018i	0.682126	−	0.161667i	0.125078	−	0.992147i	$-0.460082\pi$
$313$	12.0680	−	2.86018i	0.682126	−	0.161667i	0.557048	+	0.830480i	$0.311934\pi$
$314$	1.40071	−	7.94384i	0.0790468	−	0.448297i
$315$	−6.49046	−	19.1343i	−0.365696	−	1.07810i
$316$	−0.853333	−	4.83949i	−0.0480037	−	0.272243i
$317$	−8.84525	−	20.5056i	−0.496799	−	1.15171i	−0.963600	−	0.267347i	$-0.913853\pi$
$317$	−8.84525	−	20.5056i	−0.496799	−	1.15171i	0.466801	−	0.884362i	$-0.345406\pi$
$318$	9.51722	+	3.90292i	0.533699	+	0.218865i
$319$	−0.0175304	−	0.0585555i	−0.000981512	−	0.00327848i
$320$	2.40060	+	3.22457i	0.134198	+	0.180259i
$321$	−4.42401	+	9.22066i	−0.246924	+	0.514647i
$322$	0.956333	+	0.480288i	0.0532944	+	0.0267654i
$323$	14.5761			0.811034
$324$	0.918707	−	8.95299i	0.0510393	−	0.497388i
$325$	−51.3067			−2.84599
$326$	15.8124	+	7.94131i	0.875771	+	0.439829i
$327$	−14.1135	+	1.07820i	−0.780478	+	0.0596245i
$328$	4.20996	+	5.65496i	0.232456	+	0.312243i
$329$	5.50193	+	18.3777i	0.303331	+	1.01320i
$330$	−0.0744928	+	0.0575786i	−0.00410069	+	0.00316960i
$331$	−7.60331	−	17.6265i	−0.417916	−	0.968838i	−0.988996	−	0.147944i	$-0.952735\pi$
$331$	−7.60331	−	17.6265i	−0.417916	−	0.968838i	0.571080	−	0.820895i	$-0.306525\pi$
$332$	2.63382	+	14.9371i	0.144550	+	0.819782i
$333$	−20.7173	+	11.3599i	−1.13530	+	0.622518i
$334$	−1.46455	+	8.30586i	−0.0801364	+	0.454476i
$335$	−15.6568	+	3.71074i	−0.855424	+	0.202739i
$336$	−1.90511	−	2.18886i	−0.103933	−	0.119412i
$337$	12.3063	+	8.09396i	0.670365	+	0.440906i	0.838532	−	0.544853i	$-0.183414\pi$
$337$	12.3063	+	8.09396i	0.670365	+	0.440906i	−0.168167	+	0.985759i	$0.553785\pi$
$338$	−0.472899	+	8.11936i	−0.0257223	+	0.441635i
$339$	35.4552	+	5.59317i	1.92566	+	0.303779i
$340$	5.93483	−	19.8237i	0.321862	−	1.07509i
$341$	−0.121371	+	0.0441753i	−0.00657260	+	0.00239223i
$342$	−7.87258	+	3.19201i	−0.425700	+	0.172604i
$343$	−17.6217	−	6.41378i	−0.951483	−	0.346311i
$344$	−3.78413	+	5.08297i	−0.204027	+	0.274056i
$345$	−2.06759	−	3.93786i	−0.111315	−	0.212007i
$346$	−7.51741	−	1.78166i	−0.404139	−	0.0957826i
$347$	−3.89123	+	9.02089i	−0.208892	+	0.484267i	−0.990162	−	0.139927i	$-0.955313\pi$
$347$	−3.89123	+	9.02089i	−0.208892	+	0.484267i	0.781269	+	0.624194i	$0.214572\pi$
$348$	−7.53989	−	2.10963i	−0.404181	−	0.113088i
$349$	−21.6854	+	14.2627i	−1.16079	+	0.763464i	−0.975668	−	0.219252i	$-0.929638\pi$
$349$	−21.6854	+	14.2627i	−1.16079	+	0.763464i	−0.185122	+	0.982716i	$0.559268\pi$
$350$	9.34916	+	16.1932i	0.499734	+	0.865564i
$351$	22.4139	+	8.25893i	1.19637	+	0.440829i
$352$	−0.00676091	+	0.0117102i	−0.000360358	+	0.000624158i
$353$	0.0720294	+	1.23670i	0.00383374	+	0.0658227i	0.999682	−	0.0252019i	$-0.00802285\pi$
$353$	0.0720294	+	1.23670i	0.00383374	+	0.0658227i	−0.995849	+	0.0910246i	$0.970986\pi$
$354$	−0.422707	+	4.28692i	−0.0224666	+	0.227847i
$355$	23.2619	−	2.71893i	1.23461	−	0.144306i
$356$	−5.33108	+	5.65061i	−0.282546	+	0.299482i
$357$	−3.18155	+	14.5943i	−0.168385	+	0.772411i
$358$	−17.7570	−	2.07549i	−0.938485	−	0.109693i
$359$	9.38496	−	7.87492i	0.495319	−	0.415622i	−0.360609	−	0.932717i	$-0.617431\pi$
$359$	9.38496	−	7.87492i	0.495319	−	0.415622i	0.855928	+	0.517095i	$0.172987\pi$
$360$	1.13577	+	12.0065i	0.0598606	+	0.632799i
$361$	−8.41232	−	7.05878i	−0.442754	−	0.371515i
$362$	−9.38586	−	9.94843i	−0.493310	−	0.522878i
$363$	16.6692	+	9.22645i	0.874904	+	0.484263i
$364$	6.88258	−	3.45656i	0.360745	−	0.181173i
$365$	30.0744	−	15.1040i	1.57417	−	0.790577i
$366$	−3.54150	−	1.96023i	−0.185117	−	0.102463i
$367$	6.89289	+	7.30603i	0.359806	+	0.381372i	0.881837	−	0.471555i	$-0.156307\pi$
$367$	6.89289	+	7.30603i	0.359806	+	0.381372i	−0.522031	+	0.852926i	$0.674825\pi$
$368$	−0.489321	−	0.410589i	−0.0255076	−	0.0214034i
$369$	1.99182	+	21.0560i	0.103690	+	1.09613i
$370$	24.2537	−	20.3513i	1.26089	−	1.05801i
$371$	9.88250	+	1.15510i	0.513074	+	0.0599697i
$372$	−3.52393	+	16.1648i	−0.182707	+	0.838108i
$373$	−23.8751	+	25.3061i	−1.23620	+	1.31030i	−0.302110	+	0.953273i	$0.597691\pi$
$373$	−23.8751	+	25.3061i	−1.23620	+	1.31030i	−0.934094	+	0.357026i	$0.883791\pi$
$374$	0.0691326	−	0.00808044i	0.00357476	−	0.000417830i
$375$	4.20936	−	42.6896i	0.217371	−	2.20448i
$376$	−0.665781	−	11.4310i	−0.0343351	−	0.589510i
$377$	10.3902	−	17.9963i	0.535122	−	0.926858i
$378$	−1.47764	−	8.57914i	−0.0760014	−	0.441264i
$379$	4.86589	+	8.42796i	0.249944	+	0.432915i	0.963510	−	0.267672i	$-0.0862545\pi$
$379$	4.86589	+	8.42796i	0.249944	+	0.432915i	−0.713566	+	0.700588i	$0.752921\pi$
$380$	9.51080	−	6.25535i	0.487894	−	0.320893i
$381$	−13.3079	−	3.72348i	−0.681783	−	0.190760i
$382$	1.07102	−	2.48290i	0.0547982	−	0.127036i
$383$	10.4713	+	2.48175i	0.535061	+	0.126812i	0.489258	−	0.872139i	$-0.337267\pi$
$383$	10.4713	+	2.48175i	0.535061	+	0.126812i	0.0458021	+	0.998951i	$0.485416\pi$
$384$	0.805182	+	1.53352i	0.0410893	+	0.0782571i
$385$	−0.0543833	+	0.0730495i	−0.00277163	+	0.00372295i
$386$	−9.21438	−	3.35376i	−0.469000	−	0.170702i
$387$	−17.6176	+	7.14324i	−0.895554	+	0.363111i
$388$	3.02635	−	1.10150i	0.153639	−	0.0559202i
$389$	−7.51883	+	25.1147i	−0.381220	+	1.27336i	0.525197	+	0.850980i	$0.323992\pi$
$389$	−7.51883	+	25.1147i	−0.381220	+	1.27336i	−0.906417	+	0.422383i	$0.861194\pi$
$390$	−31.6181	−	4.98785i	−1.60104	−	0.252570i
$391$	−0.191181	+	3.28245i	−0.00966845	+	0.166001i
$392$	3.50332	+	2.30417i	0.176944	+	0.116378i
$393$	9.33259	+	10.7226i	0.470767	+	0.540882i
$394$	−2.34944	+	0.556827i	−0.118363	+	0.0280526i
$395$	−3.43043	+	19.4549i	−0.172604	+	0.978885i
$396$	−0.0355692	+	0.0195036i	−0.00178742	+	0.000980093i
$397$	2.93006	+	16.6172i	0.147056	+	0.833995i	0.965694	+	0.259684i	$0.0836185\pi$
$397$	2.93006	+	16.6172i	0.147056	+	0.833995i	−0.818638	+	0.574310i	$0.805270\pi$
$398$	−5.40715	−	12.5352i	−0.271036	−	0.628332i
$399$	−6.50137	+	5.02518i	−0.325476	+	0.251574i
$400$	−3.20093	−	10.6919i	−0.160047	−	0.534593i
$401$	−7.78193	−	10.4529i	−0.388611	−	0.521995i	0.564168	−	0.825660i	$-0.309197\pi$
$401$	−7.78193	−	10.4529i	−0.388611	−	0.521995i	−0.952779	+	0.303665i	$0.901790\pi$
$402$	−6.91254	+	0.528082i	−0.344766	+	0.0263383i
$403$	−39.2404	−	19.7073i	−1.95471	−	0.981690i
$404$	4.69884			0.233776
$405$	−15.7803	+	32.5577i	−0.784129	+	1.61780i
$406$	−7.57324			−0.375854
$407$	0.0951675	+	0.0477949i	0.00471728	+	0.00236911i
$408$	3.85674	−	8.03834i	0.190937	−	0.397957i
$409$	−15.4125	−	20.7026i	−0.762101	−	1.02368i	−0.998644	−	0.0520579i	$-0.983422\pi$
$409$	−15.4125	−	20.7026i	−0.762101	−	1.02368i	0.236543	−	0.971621i	$-0.423985\pi$
$410$	−8.12836	−	27.1506i	−0.401431	−	1.34087i
$411$	20.5136	+	8.41244i	1.01186	+	0.414955i
$412$	−0.397683	−	0.921933i	−0.0195924	−	0.0454204i
$413$	0.723546	+	4.10343i	0.0356034	+	0.201917i
$414$	−0.615567	−	1.81473i	−0.0302535	−	0.0891891i
$415$	10.5881	−	60.0479i	0.519748	−	2.94764i
$416$	−4.47316	+	1.06016i	−0.219315	+	0.0519786i
$417$	31.9255	−	6.22609i	1.56340	−	0.304893i
$418$	0.0319906	+	0.0210405i	0.00156471	+	0.00102913i
$419$	0.0325942	−	0.559620i	0.00159233	−	0.0273392i	−0.997418	−	0.0718090i	$-0.977123\pi$
$419$	0.0325942	−	0.559620i	0.00159233	−	0.0273392i	0.999011	+	0.0444698i	$0.0141598\pi$
$420$	4.18723	+	10.8881i	0.204316	+	0.531283i
$421$	−0.596418	+	1.99217i	−0.0290676	+	0.0970926i	−0.971292	−	0.237888i	$-0.923545\pi$
$421$	−0.596418	+	1.99217i	−0.0290676	+	0.0970926i	0.942225	+	0.334981i	$0.108730\pi$
$422$	5.61499	−	2.04369i	0.273333	−	0.0994852i
$423$	16.0895	−	30.3501i	0.782300	−	1.47567i
$424$	−5.58071	−	2.03121i	−0.271023	−	0.0986443i
$425$	−34.3065	+	46.0816i	−1.66411	+	2.23529i
$426$	10.0826	+	0.404616i	0.488504	+	0.0196037i
$427$	−3.80980	−	0.902938i	−0.184369	−	0.0436962i
$428$	2.33869	−	5.42169i	0.113045	−	0.262067i
$429$	−0.0267183	−	0.104298i	−0.00128997	−	0.00503555i
$430$	21.2837	−	13.9985i	1.02639	−	0.675069i
$431$	4.95301	+	8.57886i	0.238578	+	0.413229i	0.960306	−	0.278947i	$-0.0899854\pi$
$431$	4.95301	+	8.57886i	0.238578	+	0.413229i	−0.721729	+	0.692176i	$0.756652\pi$
$432$	−0.322723	+	5.18612i	−0.0155270	+	0.249517i
$433$	−1.14206	+	1.97810i	−0.0548838	+	0.0950615i	−0.892162	−	0.451716i	$-0.850812\pi$
$433$	−1.14206	+	1.97810i	−0.0548838	+	0.0950615i	0.837278	+	0.546777i	$0.184145\pi$
$434$	0.930495	+	15.9760i	0.0446652	+	0.766872i
$435$	25.5821	+	18.3362i	1.22657	+	0.879154i
$436$	8.11691	−	0.948731i	0.388730	−	0.0454360i
$437$	−1.24126	+	1.31566i	−0.0593776	+	0.0629366i
$438$	13.8135	−	4.40896i	0.660033	−	0.210668i
$439$	−32.2822	−	3.77325i	−1.54074	−	0.180087i	−0.697094	−	0.716980i	$-0.745524\pi$
$439$	−32.2822	−	3.77325i	−1.54074	−	0.180087i	−0.843650	+	0.536893i	$0.819598\pi$
$440$	0.0416409	−	0.0349408i	0.00198515	−	0.00166574i
$441$	5.39653	+	11.3631i	0.256978	+	0.541099i
$442$	18.1272	+	15.2105i	0.862221	+	0.723489i
$443$	13.4623	+	14.2692i	0.639613	+	0.677950i	0.963366	−	0.268192i	$-0.0864260\pi$
$443$	13.4623	+	14.2692i	0.639613	+	0.677950i	−0.323753	+	0.946142i	$0.604945\pi$
$444$	11.6885	−	7.03298i	0.554713	−	0.333770i
$445$	27.9079	−	14.0159i	1.32296	−	0.664416i
$446$	11.9583	−	6.00570i	0.566244	−	0.284378i
$447$	0.0683038	+	3.77974i	0.00323066	+	0.178776i
$448$	1.14971	+	1.21862i	0.0543186	+	0.0575743i
$449$	−7.24842	−	6.08214i	−0.342074	−	0.287034i	0.455524	−	0.890223i	$-0.349452\pi$
$449$	−7.24842	−	6.08214i	−0.342074	−	0.287034i	−0.797598	+	0.603189i	$0.793896\pi$
$450$	8.43763	−	32.4016i	0.397754	−	1.52743i
$451$	0.0730260	−	0.0612761i	0.00343866	−	0.00288538i
$452$	−20.5831	−	2.40582i	−0.968147	−	0.113160i
$453$	−18.9940	−	17.2820i	−0.892416	−	0.811981i
$454$	16.0296	−	16.9903i	0.752304	−	0.797396i
$455$	−30.7522	+	3.59441i	−1.44168	+	0.168509i
$456$	4.46768	−	2.02368i	0.209218	−	0.0947675i
$457$	1.42592	+	24.4821i	0.0667017	+	1.14522i	0.851113	+	0.524983i	$0.175928\pi$
$457$	1.42592	+	24.4821i	0.0667017	+	1.14522i	−0.784411	+	0.620242i	$0.787035\pi$
$458$	5.04468	−	8.73764i	0.235722	−	0.408283i
$459$	22.4050	−	14.6089i	1.04578	−	0.681885i
$460$	1.28393	+	2.22383i	0.0598634	+	0.103686i
$461$	18.8285	−	12.3837i	0.876932	−	0.576767i	−0.0292894	−	0.999571i	$-0.509324\pi$
$461$	18.8285	−	12.3837i	0.876932	−	0.576767i	0.906221	+	0.422804i	$0.138954\pi$
$462$	−0.0280495	+	0.0274380i	−0.00130498	+	0.00127653i
$463$	−7.14555	+	16.5652i	−0.332082	+	0.769852i	0.667597	+	0.744522i	$0.267323\pi$
$463$	−7.14555	+	16.5652i	−0.332082	+	0.769852i	−0.999679	+	0.0253295i	$0.991936\pi$
$464$	4.39850	+	1.04246i	0.204195	+	0.0483951i
$465$	35.5376	−	56.2192i	1.64802	−	2.60710i
$466$	−0.865613	+	1.16272i	−0.0400988	+	0.0538620i
$467$	5.17094	+	1.88207i	0.239283	+	0.0870918i	0.458878	−	0.888499i	$-0.348251\pi$
$467$	5.17094	+	1.88207i	0.239283	+	0.0870918i	−0.219595	+	0.975591i	$0.570474\pi$
$468$	−13.1215	−	4.24557i	−0.606541	−	0.196251i
$469$	−6.30139	+	2.29352i	−0.290971	+	0.105905i
$470$	−13.2019	+	44.0973i	−0.608956	+	2.03406i
$471$	−8.78579	+	10.8632i	−0.404828	+	0.500551i
$472$	0.144610	−	2.48285i	0.00665620	−	0.114282i
$473$	0.0715900	+	0.0470855i	0.00329171	+	0.00216499i
$474$	−2.76613	+	8.04953i	−0.127053	+	0.369727i
$475$	−30.7519	+	7.28833i	−1.41099	+	0.334412i
$476$	1.49753	−	8.49289i	0.0686390	−	0.389271i
$477$	−11.1487	−	13.8974i	−0.510465	−	0.636317i
$478$	3.69371	+	20.9481i	0.168946	+	0.958143i
$479$	−15.6255	−	36.2239i	−0.713946	−	1.65511i	−0.754807	−	0.655947i	$-0.772269\pi$
$479$	−15.6255	−	36.2239i	−0.713946	−	1.65511i	0.0408608	−	0.999165i	$-0.486990\pi$
$480$	−0.933169	−	6.90010i	−0.0425931	−	0.314945i
$481$	10.3839	+	34.6846i	0.473465	+	1.58148i
$482$	5.48137	+	7.36276i	0.249670	+	0.335365i
$483$	−1.04637	−	1.52999i	−0.0476116	−	0.0696167i
$484$	−9.82980	−	4.93671i	−0.446809	−	0.224396i
$485$	−12.9468			−0.587885
$486$	−8.90181	+	12.7968i	−0.403795	+	0.580474i
$487$	−6.31620			−0.286214			−0.143107	−	0.989707i	$-0.545709\pi$
$487$	−6.31620			−0.286214			−0.143107	+	0.989707i	$0.545709\pi$
$488$	2.08842	+	1.04884i	0.0945383	+	0.0474789i
$489$	−17.3012	−	25.2975i	−0.782387	−	1.14399i
$490$	−10.0661	−	13.5211i	−0.454739	−	0.610820i
$491$	−0.0319262	−	0.106641i	−0.00144081	−	0.00481264i	0.957266	−	0.289209i	$-0.0933921\pi$
$491$	−0.0319262	−	0.106641i	−0.00144081	−	0.00481264i	−0.958707	+	0.284396i	$0.908207\pi$
$492$	−1.63651	−	12.1008i	−0.0737795	−	0.545545i
$493$	−9.21612	−	21.3654i	−0.415073	−	0.962248i
$494$	2.26047	+	12.8198i	0.101703	+	0.576788i
$495$	0.161182	−	0.0247716i	0.00724461	−	0.00111340i
$496$	1.65868	−	9.40685i	0.0744770	−	0.422380i
$497$	9.49740	−	2.25092i	0.426017	−	0.100968i
$498$	8.53770	−	24.8450i	0.382584	−	1.11333i
$499$	9.41139	+	6.18997i	0.421312	+	0.277101i	0.742411	−	0.669944i	$-0.233682\pi$
$499$	9.41139	+	6.18997i	0.421312	+	0.277101i	−0.321100	+	0.947045i	$0.604052\pi$
$500$	−1.44004	+	24.7245i	−0.0644004	+	1.10571i
$501$	9.18618	−	11.3583i	0.410408	−	0.507451i
$502$	1.76479	−	5.89481i	0.0787664	−	0.263098i
$503$	−4.38661	+	1.59659i	−0.195589	+	0.0711886i	−0.437958	−	0.898996i	$-0.644298\pi$
$503$	−4.38661	+	1.59659i	−0.195589	+	0.0711886i	0.242368	+	0.970184i	$0.422076\pi$
$504$	1.05104	+	4.91498i	0.0468170	+	0.218931i
$505$	−17.7504	−	6.46061i	−0.789881	−	0.287493i
$506$	−0.00515781	+	0.00692814i	−0.000229292	+	0.000307993i
$507$	7.52701	−	11.9074i	0.334286	−	0.528828i
$508$	7.76333	+	1.83994i	0.344442	+	0.0816342i
$509$	5.23832	−	12.1438i	0.232184	−	0.538264i	−0.761797	−	0.647816i	$-0.775683\pi$
$509$	5.23832	−	12.1438i	0.232184	−	0.538264i	0.993981	+	0.109553i	$0.0349418\pi$
$510$	−25.6214	+	25.0629i	−1.13454	+	1.10980i
$511$	11.7181	−	7.70713i	0.518379	−	0.340944i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	14.6075	+	1.76619i	0.644938	+	0.0779793i
$514$	4.76717	−	8.25699i	0.210271	−	0.364200i
$515$	0.234691	+	4.02949i	0.0103417	+	0.177560i
$516$	9.99799	−	4.52869i	0.440137	−	0.199364i
$517$	−0.153783	+	0.0179747i	−0.00676339	+	0.000790526i
$518$	9.05486	−	9.59759i	0.397848	−	0.421694i
$519$	9.89748	+	9.00540i	0.434451	+	0.395293i
$520$	18.3555	+	2.14545i	0.804941	+	0.0940841i
$521$	−23.2776	+	19.5322i	−1.01981	+	0.855722i	−0.989604	−	0.143821i	$-0.954061\pi$
$521$	−23.2776	+	19.5322i	−1.01981	+	0.855722i	−0.0302066	+	0.999544i	$0.509617\pi$
$522$	9.65646	+	9.52126i	0.422652	+	0.416734i
$523$	12.9993	+	10.9077i	0.568418	+	0.476959i	0.881121	−	0.472892i	$-0.156790\pi$
$523$	12.9993	+	10.9077i	0.568418	+	0.476959i	−0.312702	+	0.949851i	$0.601234\pi$
$524$	−5.63207	−	5.96965i	−0.246038	−	0.260785i
$525$	−0.585161	−	32.3812i	−0.0255385	−	1.41323i
$526$	−14.8083	+	7.43700i	−0.645672	+	0.324269i
$527$	−43.9386	+	22.0668i	−1.91399	+	0.961244i
$528$	0.0200678	−	0.0120748i	0.000873341	−	0.000525488i
$529$	15.5036	+	16.4328i	0.674068	+	0.714470i
$530$	18.2889	+	15.3462i	0.794419	+	0.666597i
$531$	4.23636	−	6.14185i	0.183843	−	0.266534i
$532$	3.63421	−	3.04947i	0.157563	−	0.132211i
$533$	32.1902	+	3.76249i	1.39431	+	0.162972i
$534$	12.8184	−	4.09134i	0.554704	−	0.177050i
$535$	−16.2891	+	17.2654i	−0.704239	+	0.746450i
$536$	3.97552	−	0.464672i	0.171716	−	0.0200708i
$537$	25.1681	+	18.0394i	1.08608	+	0.778459i
$538$	−1.17684	−	20.2056i	−0.0507373	−	0.871125i
$539$	0.0283495	−	0.0491027i	0.00122110	−	0.00211500i
$540$	8.34970	−	19.1474i	0.359314	−	0.823972i
$541$	−19.9050	−	34.4764i	−0.855782	−	1.48226i	−0.875918	−	0.482460i	$-0.839743\pi$
$541$	−19.9050	−	34.4764i	−0.855782	−	1.48226i	0.0201362	−	0.999797i	$-0.493590\pi$
$542$	11.1368	−	7.32478i	0.478366	−	0.314626i
$543$	5.87880	+	22.9486i	0.252283	+	0.984818i
$544$	−2.03881	+	4.72649i	−0.0874132	+	0.202647i
$545$	−31.9669	−	7.57630i	−1.36931	−	0.324533i
$546$	−13.3292	−	0.534901i	−0.570436	−	0.0228916i
$547$	−2.53512	+	3.40526i	−0.108394	+	0.145598i	−0.853010	−	0.521895i	$-0.825225\pi$
$547$	−2.53512	+	3.40526i	−0.108394	+	0.145598i	0.744616	+	0.667493i	$0.232633\pi$
$548$	−12.0288	−	4.37812i	−0.513844	−	0.187024i
$549$	3.72258	+	5.94109i	0.158876	+	0.253559i
$550$	−0.141812	+	0.0516154i	−0.00604690	+	0.00220089i
$551$	3.67115	−	12.2625i	0.156396	−	0.522400i
$552$	0.397124	+	1.03264i	0.0169027	+	0.0439521i
$553$	−0.478707	+	8.21907i	−0.0203567	+	0.349511i
$554$	24.7471	+	16.2765i	1.05141	+	0.691520i
$555$	−53.8245	+	10.4968i	−2.28472	+	0.445565i
$556$	−18.2732	+	4.33083i	−0.774957	+	0.183668i
$557$	3.49887	−	19.8431i	0.148252	−	0.840778i	−0.816447	−	0.577421i	$-0.804059\pi$
$557$	3.49887	−	19.8431i	0.148252	−	0.840778i	0.964698	−	0.263357i	$-0.0848297\pi$
$558$	18.8990	−	21.5404i	0.800057	−	0.911880i
$559$	5.05858	+	28.6887i	0.213955	+	1.21340i
$560$	−2.66762	−	6.18423i	−0.112727	−	0.261331i
$561$	−0.111541	−	0.0457420i	−0.00470928	−	0.00193123i
$562$	0.443697	+	1.48205i	0.0187162	+	0.0625165i
$563$	−6.16547	−	8.28167i	−0.259844	−	0.349031i	0.652987	−	0.757369i	$-0.273516\pi$
$563$	−6.16547	−	8.28167i	−0.259844	−	0.349031i	−0.912831	+	0.408339i	$0.866108\pi$
$564$	−8.57921	+	17.8811i	−0.361250	+	0.752928i
$565$	74.4469	+	37.3886i	3.13200	+	1.57295i
$566$	−5.73063			−0.240876
$567$	−4.95682	+	14.2403i	−0.208167	+	0.598035i
$568$	−5.82588			−0.244449
$569$	−14.7778	−	7.42168i	−0.619517	−	0.311133i	0.111216	−	0.993796i	$-0.464525\pi$
$569$	−14.7778	−	7.42168i	−0.619517	−	0.311133i	−0.730733	+	0.682663i	$0.760822\pi$
$570$	−19.6596	+	1.50189i	−0.823449	+	0.0629072i
$571$	−11.7740	−	15.8152i	−0.492726	−	0.661846i	0.484316	−	0.874893i	$-0.339069\pi$
$571$	−11.7740	−	15.8152i	−0.492726	−	0.661846i	−0.977042	+	0.213047i	$0.931661\pi$
$572$	0.0178279	+	0.0595495i	0.000745424	+	0.00248989i
$573$	−3.70564	+	2.86425i	−0.154805	+	0.119656i
$574$	−4.67822	−	10.8453i	−0.195265	−	0.452676i
$575$	−1.23795	−	7.02076i	−0.0516260	−	0.292786i
$576$	0.0661132	−	2.99927i	0.00275472	−	0.124970i
$577$	4.46863	−	25.3429i	0.186031	−	1.05504i	−0.738591	−	0.674153i	$-0.764509\pi$
$577$	4.46863	−	25.3429i	0.186031	−	1.05504i	0.924623	−	0.380884i	$-0.124380\pi$
$578$	9.24049	−	2.19004i	0.384354	−	0.0910935i
$579$	11.1504	+	12.8112i	0.463396	+	0.532413i
$580$	−15.1825	−	9.98566i	−0.630417	−	0.414632i
$581$	1.47753	−	25.3683i	0.0612984	−	1.05245i
$582$	−5.51005	−	0.869229i	−0.228399	−	0.0360307i
$583$	−0.0230315	+	0.0769307i	−0.000953868	+	0.00318614i
$584$	−7.86672	+	2.86325i	−0.325527	+	0.118482i
$585$	43.7304	+	34.0793i	1.80803	+	1.40900i
$586$	1.17487	+	0.427617i	0.0485334	+	0.0176647i
$587$	20.5379	−	27.5872i	0.847690	−	1.13864i	−0.141198	−	0.989981i	$-0.545096\pi$
$587$	20.5379	−	27.5872i	0.847690	−	1.13864i	0.988888	−	0.148663i	$-0.0474971\pi$
$588$	−3.37624	−	6.43027i	−0.139234	−	0.265180i
$589$	−26.3192	−	6.23776i	−1.08446	−	0.257022i
$590$	−3.96004	+	9.18040i	−0.163032	+	0.377951i
$591$	4.02740	+	1.12685i	0.165665	+	0.0463524i
$592$	−6.58013	+	4.32782i	−0.270442	+	0.177872i
$593$	9.43328	+	16.3389i	0.387378	+	0.670959i	0.992096	−	0.125481i	$-0.0400474\pi$
$593$	9.43328	+	16.3389i	0.387378	+	0.670959i	−0.604718	+	0.796440i	$0.706714\pi$
$594$	0.0702609		0.000278969i	0.00288284		1.14462e-5i
$595$	−17.3342	+	30.0238i	−0.710634	+	1.23085i
$596$	−0.126906	−	2.17890i	−0.00519829	−	0.0892512i
$597$	−2.32027	+	23.5313i	−0.0949625	+	0.963070i
$598$	−2.91659	+	0.340900i	−0.119268	+	0.0139405i
$599$	−5.63271	+	5.97033i	−0.230146	+	0.243941i	−0.832148	−	0.554554i	$-0.812889\pi$
$599$	−5.63271	+	5.97033i	−0.230146	+	0.243941i	0.602001	+	0.798495i	$0.294370\pi$
$600$	−4.11744	+	18.8874i	−0.168094	+	0.771073i
$601$	5.46628	+	0.638917i	0.222974	+	0.0260620i	0.226846	−	0.973931i	$-0.427158\pi$
$601$	5.46628	+	0.638917i	0.222974	+	0.0260620i	−0.00387210	+	0.999993i	$0.501233\pi$
$602$	8.13282	−	6.82424i	0.331469	−	0.278135i
$603$	10.9182	+	4.99786i	0.444624	+	0.203528i
$604$	11.3575	+	9.53004i	0.462129	+	0.387772i
$605$	30.3454	+	32.1643i	1.23372	+	1.30766i
$606$	−7.12064	−	3.94131i	−0.289256	−	0.160105i
$607$	−5.82005	+	2.92294i	−0.236229	+	0.118638i	−0.562976	−	0.826473i	$-0.690344\pi$
$607$	−5.82005	+	2.92294i	−0.236229	+	0.118638i	0.326747	+	0.945112i	$0.394047\pi$
$608$	−2.53049	+	1.27086i	−0.102625	+	0.0515403i
$609$	11.4765	+	6.35230i	0.465051	+	0.257408i
$610$	−6.44713	−	6.83356i	−0.261037	−	0.276683i
$611$	−40.3233	−	33.8353i	−1.63131	−	1.36883i
$612$	−12.5869	+	8.94636i	−0.508797	+	0.361635i
$613$	15.4318	−	12.9488i	0.623283	−	0.522997i	−0.275550	−	0.961287i	$-0.588860\pi$
$613$	15.4318	−	12.9488i	0.623283	−	0.522997i	0.898834	+	0.438290i	$0.144416\pi$
$614$	18.1863	+	2.12567i	0.733939	+	0.0857851i
$615$	−10.4557	+	47.9620i	−0.421615	+	1.93401i
$616$	0.0155461	−	0.0164779i	0.000626372	−	0.000663915i
$617$	9.28251	−	1.08497i	0.373700	−	0.0436792i	0.0728296	−	0.997344i	$-0.476797\pi$
$617$	9.28251	−	1.08497i	0.373700	−	0.0436792i	0.300870	+	0.953665i	$0.402723\pi$
$618$	−0.170651	+	1.73067i	−0.00686458	+	0.0696177i
$619$	0.366677	+	6.29560i	0.0147380	+	0.253041i	0.997627	+	0.0688447i	$0.0219313\pi$
$619$	0.366677	+	6.29560i	0.0147380	+	0.253041i	−0.982889	+	0.184197i	$0.941032\pi$
$620$	−19.1997	+	33.2548i	−0.771077	+	1.33554i
$621$	−0.589331	+	3.26637i	−0.0236490	+	0.131075i
$622$	8.36965	+	14.4967i	0.335592	+	0.581263i
$623$	10.8740	−	7.15192i	0.435656	−	0.286536i
$624$	7.66788	+	2.14544i	0.306961	+	0.0858863i
$625$	17.3318	−	40.1795i	0.693270	−	1.60718i
$626$	12.0680	+	2.86018i	0.482336	+	0.114316i
$627$	−0.0308302	−	0.0587180i	−0.00123124	−	0.00234497i
$628$	4.81691	−	6.47023i	0.192216	−	0.258190i
$629$	38.0955	+	13.8656i	1.51897	+	0.552859i
$630$	2.78737	−	20.0120i	0.111051	−	0.797295i
$631$	−34.1219	+	12.4194i	−1.35837	+	0.494407i	−0.915550	−	0.402203i	$-0.868244\pi$
$631$	−34.1219	+	12.4194i	−1.35837	+	0.494407i	−0.442821	+	0.896610i	$0.646022\pi$
$632$	1.40939	−	4.70770i	0.0560626	−	0.187262i
$633$	−10.2232	−	1.61274i	−0.406335	−	0.0641007i
$634$	1.29849	−	22.2942i	0.0515696	−	0.885416i
$635$	−26.7970	−	17.6246i	−1.06340	−	0.699412i
$636$	6.75327	+	7.75910i	0.267785	+	0.307668i
$637$	18.7566	−	4.44540i	0.743164	−	0.176133i
$638$	0.0106140	−	0.0601947i	0.000420210	−	0.00238313i
$639$	−14.9398	−	9.07026i	−0.591010	−	0.358814i
$640$	0.698073	+	3.95897i	0.0275938	+	0.156492i
$641$	−11.6086	−	26.9118i	−0.458513	−	1.06295i	−0.978025	−	0.208490i	$-0.933145\pi$
$641$	−11.6086	−	26.9118i	−0.458513	−	1.06295i	0.519511	−	0.854464i	$-0.326114\pi$
$642$	−8.09166	+	6.25439i	−0.319353	+	0.246841i
$643$	−10.6916	−	35.7124i	−0.421635	−	1.40836i	−0.860336	−	0.509727i	$-0.829746\pi$
$643$	−10.6916	−	35.7124i	−0.421635	−	1.40836i	0.438701	−	0.898633i	$-0.355439\pi$
$644$	0.639057	+	0.858403i	0.0251824	+	0.0338258i
$645$	−43.9951	+	3.36100i	−1.73231	+	0.132339i
$646$	13.0257	+	6.54173i	0.512487	+	0.257381i
$647$	7.10308			0.279251			0.139625	−	0.990204i	$-0.455410\pi$
$647$	7.10308			0.279251			0.139625	+	0.990204i	$0.455410\pi$
$648$	4.83908	−	7.58837i	0.190097	−	0.298099i
$649$	−0.0336296			−0.00132008
$650$	−45.8494	−	23.0264i	−1.79836	−	0.903171i
$651$	11.9903	−	24.9905i	0.469937	−	0.979456i
$652$	10.5665	+	14.1932i	0.413815	+	0.555850i
$653$	6.10772	+	20.4012i	0.239014	+	0.798361i	0.990368	+	0.138462i	$0.0442158\pi$
$653$	6.10772	+	20.4012i	0.239014	+	0.798361i	−0.751354	+	0.659899i	$0.770599\pi$
$654$	−13.0962	−	5.37061i	−0.512101	−	0.210008i
$655$	13.0679	+	30.2947i	0.510603	+	1.18371i
$656$	1.22422	+	6.94288i	0.0477976	+	0.271074i
$657$	−24.6311	−	4.90514i	−0.960951	−	0.191368i
$658$	−3.33120	+	18.8922i	−0.129864	+	0.736494i
$659$	5.77964	−	1.36980i	0.225143	−	0.0533599i	−0.116496	−	0.993191i	$-0.537166\pi$
$659$	5.77964	−	1.36980i	0.225143	−	0.0533599i	0.341639	+	0.939831i	$0.389018\pi$
$660$	−0.0924104	+	0.0180218i	−0.00359707	+	0.000701499i
$661$	−16.2750	−	10.7042i	−0.633023	−	0.416346i	0.192040	−	0.981387i	$-0.438490\pi$
$661$	−16.2750	−	10.7042i	−0.633023	−	0.416346i	−0.825062	+	0.565042i	$0.808860\pi$
$662$	1.11617	−	19.1639i	0.0433813	−	0.744828i
$663$	−14.7117	−	38.2548i	−0.571354	−	1.48569i
$664$	−4.35011	+	14.5304i	−0.168817	+	0.563888i
$665$	−17.9214	+	6.52287i	−0.694963	+	0.252946i
$666$	−23.6120	+	0.853664i	−0.914945	+	0.0330788i
$667$	2.71330	+	0.987559i	0.105059	+	0.0382384i
$668$	−5.03643	+	6.76510i	−0.194865	+	0.261749i
$669$	−23.1592	−	0.929379i	−0.895385	−	0.0359319i
$670$	−15.6568	−	3.71074i	−0.604876	−	0.143358i
$671$	0.0125163	−	0.0290161i	0.000483187	−	0.00112015i
$672$	−0.720114	−	2.81105i	−0.0277790	−	0.108439i
$673$	0.434211	−	0.285585i	0.0167376	−	0.0110085i	−0.541113	−	0.840950i	$-0.681997\pi$
$673$	0.434211	−	0.285585i	0.0167376	−	0.0110085i	0.557850	+	0.829942i	$0.311626\pi$
$674$	7.36472	+	12.7561i	0.283678	+	0.491345i
$675$	−39.9643	+	42.0241i	−1.53823	+	1.61751i
$676$	−4.06656	+	7.04349i	−0.156406	+	0.270903i
$677$	−1.17987	−	20.2575i	−0.0453460	−	0.778561i	−0.941955	−	0.335738i	$-0.891014\pi$
$677$	−1.17987	−	20.2575i	−0.0453460	−	0.778561i	0.896609	−	0.442822i	$-0.146023\pi$
$678$	29.1737	+	20.9105i	1.12041	+	0.803063i
$679$	−5.35916	+	0.626395i	−0.205666	+	0.0240389i
$680$	14.2004	−	15.0516i	0.544562	−	0.577202i
$681$	−38.5424	+	12.3019i	−1.47695	+	0.471410i
$682$	−0.128287	−	0.0149946i	−0.00491235	−	0.000574172i
$683$	33.8852	−	28.4331i	1.29658	−	1.08796i	0.305858	−	0.952077i	$-0.401057\pi$
$683$	33.8852	−	28.4331i	1.29658	−	1.08796i	0.990725	−	0.135885i	$-0.0433879\pi$
$684$	−8.46777	−	0.680721i	−0.323773	−	0.0260280i
$685$	39.4203	+	33.0776i	1.50617	+	1.26383i
$686$	−12.8688	−	13.6402i	−0.491334	−	0.520784i
$687$	−14.9737	+	9.00966i	−0.571282	+	0.343740i
$688$	−5.66286	+	2.84400i	−0.215895	+	0.108426i
$689$	−24.3974	+	12.2529i	−0.929468	+	0.466797i
$690$	−0.0803606	−	4.44693i	−0.00305928	−	0.169292i
$691$	18.3720	+	19.4732i	0.698904	+	0.740795i	0.975454	−	0.220205i	$-0.0706726\pi$
$691$	18.3720	+	19.4732i	0.698904	+	0.740795i	−0.276550	+	0.961000i	$0.589191\pi$
$692$	−5.91820	−	4.96596i	−0.224976	−	0.188777i
$693$	0.0655207	−	0.0180522i	0.00248893	−	0.000685747i
$694$	−7.52590	+	6.31498i	−0.285679	+	0.239713i
$695$	74.9836	+	8.76433i	2.84429	+	0.332450i
$696$	−5.79110	−	5.26913i	−0.219511	−	0.199726i
$697$	24.9034	−	26.3961i	0.943285	−	0.999824i
$698$	−25.7798	+	3.01323i	−0.975781	+	0.114052i
$699$	2.28702	−	1.03593i	0.0865031	−	0.0391824i
$700$	1.08721	+	18.6667i	0.0410927	+	0.705535i
$701$	−18.8061	+	32.5731i	−0.710295	+	1.23027i	0.254451	+	0.967086i	$0.418105\pi$
$701$	−18.8061	+	32.5731i	−0.710295	+	1.23027i	−0.964746	+	0.263182i	$0.915228\pi$
$702$	16.3232	+	17.4398i	0.616080	+	0.658223i
$703$	11.1509	+	19.3140i	0.420565	+	0.728440i
$704$	−0.0112973	+	0.00743037i	−0.000425784	+	0.000280042i
$705$	56.9941	−	55.7517i	2.14652	−	2.09973i
$706$	−0.490661	+	1.13748i	−0.0184663	+	0.0428096i
$707$	−7.66009	−	1.81548i	−0.288087	−	0.0682780i
$708$	−2.30171	+	3.64122i	−0.0865036	+	0.136846i
$709$	−14.3162	+	19.2300i	−0.537657	+	0.722198i	−0.985075	−	0.172127i	$-0.944936\pi$
$709$	−14.3162	+	19.2300i	−0.537657	+	0.722198i	0.447418	+	0.894325i	$0.352344\pi$
$710$	22.0079	+	8.01021i	0.825941	+	0.300618i
$711$	10.9436	−	9.87810i	0.410417	−	0.370458i
$712$	−7.30001	+	2.65699i	−0.273580	+	0.0995748i
$713$	1.74991	−	5.84512i	0.0655348	−	0.218902i
$714$	−9.39304	+	11.6141i	−0.351526	+	0.434645i
$715$	0.0145298	−	0.249467i	0.000543383	−	0.00932952i
$716$	−14.9367	−	9.82404i	−0.558212	−	0.367142i
$717$	11.9734	−	34.8430i	0.447155	−	1.30124i
$718$	11.9210	−	2.82532i	0.444887	−	0.105440i
$719$	1.44404	−	8.18958i	0.0538537	−	0.305420i	−0.945969	−	0.324258i	$-0.894886\pi$
$719$	1.44404	−	8.18958i	0.0538537	−	0.305420i	0.999823	+	0.0188379i	$0.00599664\pi$
$720$	−4.37355	+	11.2392i	−0.162993	+	0.418859i
$721$	0.292102	+	1.65659i	0.0108785	+	0.0616948i
$722$	−4.34955	−	10.0834i	−0.161874	−	0.375265i
$723$	−2.13074	−	15.7552i	−0.0792429	−	0.585943i
$724$	−3.92266	−	13.1026i	−0.145785	−	0.486955i
$725$	30.1269	+	40.4674i	1.11888	+	1.50292i
$726$	10.7553	+	15.7262i	0.399166	+	0.583652i
$727$	−42.7215	−	21.4555i	−1.58445	−	0.795742i	−0.584574	−	0.811340i	$-0.698738\pi$
$727$	−42.7215	−	21.4555i	−1.58445	−	0.795742i	−0.999878	+	0.0155984i	$0.995035\pi$
$728$	7.70179			0.285448
$729$	24.2235	−	11.9256i	0.897168	−	0.441689i
$730$	33.6541			1.24560
$731$	29.1494	+	14.6394i	1.07813	+	0.541457i
$732$	−2.28505	−	3.34115i	−0.0844577	−	0.123492i
$733$	12.3666	+	16.6112i	0.456771	+	0.613550i	0.969527	−	0.244984i	$-0.0787828\pi$
$733$	12.3666	+	16.6112i	0.456771	+	0.613550i	−0.512756	+	0.858535i	$0.671375\pi$
$734$	2.88077	+	9.62243i	0.106331	+	0.355170i
$735$	3.91291	+	28.9331i	0.144330	+	1.06721i
$736$	−0.253001	−	0.586523i	−0.00932575	−	0.0216195i
$737$	−0.00939823	−	0.0533000i	−0.000346188	−	0.00196333i
$738$	−7.66994	+	19.7102i	−0.282334	+	0.725543i
$739$	−4.41970	+	25.0654i	−0.162581	+	0.922045i	0.788942	+	0.614468i	$0.210629\pi$
$739$	−4.41970	+	25.0654i	−0.162581	+	0.922045i	−0.951523	+	0.307577i	$0.900482\pi$
$740$	30.8076	−	7.30153i	1.13251	−	0.268410i
$741$	7.32746	−	21.3231i	0.269181	−	0.783325i
$742$	8.31292	+	5.46749i	0.305177	+	0.200718i
$743$	−1.36294	+	23.4008i	−0.0500015	+	0.858492i	0.876313	+	0.481742i	$0.159996\pi$
$743$	−1.36294	+	23.4008i	−0.0500015	+	0.858492i	−0.926315	+	0.376751i	$0.877041\pi$
$744$	−10.4039	+	12.8639i	−0.381424	+	0.471613i
$745$	−2.51644	+	8.40550i	−0.0921953	+	0.307954i
$746$	−32.6929	+	11.8992i	−1.19697	+	0.435662i
$747$	−33.7776	+	30.4889i	−1.23586	+	1.11553i
$748$	0.0654056	+	0.0238057i	0.00239147	+	0.000870423i
$749$	−5.90730	+	7.93489i	−0.215848	+	0.289934i
$750$	22.9207	−	36.2597i	0.836945	−	1.32402i
$751$	21.6246	+	5.12511i	0.789091	+	0.187018i	0.605353	−	0.795957i	$-0.293032\pi$
$751$	21.6246	+	5.12511i	0.789091	+	0.187018i	0.183738	+	0.982975i	$0.441180\pi$
$752$	4.53527	−	10.5139i	0.165384	−	0.383404i
$753$	−7.61883	+	7.45274i	−0.277646	+	0.271593i
$754$	17.3617	−	11.4190i	0.632278	−	0.415856i
$755$	−29.8008	−	51.6165i	−1.08456	−	1.87852i
$756$	2.52985	−	8.32977i	0.0920097	−	0.302951i
$757$	6.59727	−	11.4268i	0.239782	−	0.415314i	−0.720870	−	0.693071i	$-0.756257\pi$
$757$	6.59727	−	11.4268i	0.239782	−	0.415314i	0.960652	+	0.277756i	$0.0895908\pi$
$758$	0.565852	+	9.71531i	0.0205527	+	0.352876i
$759$	0.0136273	−	0.00617264i	0.000494641	−	0.000224053i
$760$	11.3066	−	1.32155i	0.410132	−	0.0479375i
$761$	1.31639	−	1.39529i	0.0477190	−	0.0505792i	−0.703074	−	0.711116i	$-0.748190\pi$
$761$	1.31639	−	1.39529i	0.0477190	−	0.0505792i	0.750793	+	0.660537i	$0.229671\pi$
$762$	−10.2213	−	9.29999i	−0.370277	−	0.336903i
$763$	−13.5988	−	1.58947i	−0.492310	−	0.0575428i
$764$	2.07142	−	1.73813i	0.0749415	−	0.0628834i
$765$	59.8491	−	16.4896i	2.16385	−	0.596182i
$766$	8.24372	+	6.91731i	0.297858	+	0.249932i
$767$	−7.84594	−	8.31621i	−0.283300	−	0.300281i
$768$	0.0312948	+	1.73177i	0.00112926	+	0.0624898i
$769$	1.31374	−	0.659788i	0.0473749	−	0.0237925i	−0.424954	−	0.905215i	$-0.639710\pi$
$769$	1.31374	−	0.659788i	0.0473749	−	0.0237925i	0.472329	+	0.881422i	$0.343413\pi$
$770$	−0.0813832	+	0.0408722i	−0.00293285	+	0.00147293i
$771$	−14.1500	+	8.51404i	−0.509600	+	0.306626i
$772$	−6.72911	−	7.13244i	−0.242186	−	0.256702i
$773$	28.7330	+	24.1099i	1.03345	+	0.867172i	0.991258	−	0.131938i	$-0.0421199\pi$
$773$	28.7330	+	24.1099i	1.03345	+	0.867172i	0.0421969	+	0.999109i	$0.486564\pi$
$774$	−18.9496	−	1.52335i	−0.681128	−	0.0547557i
$775$	81.6657	−	68.5256i	2.93352	−	2.46151i
$776$	3.19879	+	0.373885i	0.114830	+	0.0134217i
$777$	−21.7720	+	6.94916i	−0.781067	+	0.249300i
$778$	−17.9905	+	19.0688i	−0.644991	+	0.683651i
$779$	19.8284	−	2.31761i	0.710427	−	0.0830370i
$780$	−26.0164	−	18.6475i	−0.931536	−	0.667686i
$781$	0.00458045	+	0.0786433i	0.000163901	+	0.00281408i
$782$	−1.64401	+	2.84751i	−0.0587896	+	0.101827i
$783$	−6.64715	−	22.5282i	−0.237550	−	0.805093i
$784$	2.09657	+	3.63137i	0.0748776	+	0.129692i
$785$	−27.0925	+	17.8190i	−0.966974	+	0.635989i
$786$	3.52762	+	13.7705i	0.125826	+	0.491178i
$787$	13.4133	−	31.0956i	0.478133	−	1.10844i	−0.493028	−	0.870014i	$-0.664110\pi$
$787$	13.4133	−	31.0956i	0.478133	−	1.10844i	0.971161	−	0.238424i	$-0.0766309\pi$
$788$	−2.34944	−	0.556827i	−0.0836953	−	0.0198361i
$789$	28.6785	+	1.15087i	1.02098	+	0.0409722i
$790$	−11.7969	+	15.8460i	−0.419715	+	0.563775i
$791$	32.6252	+	11.8746i	1.16002	+	0.422212i
$792$	−0.0405390	+	0.00146564i	−0.00144049	+	5.20793e-5i
$793$	10.0955	−	3.67445i	0.358501	−	0.130484i
$794$	−4.83939	+	16.1647i	−0.171744	+	0.573664i
$795$	−14.8429	−	38.5961i	−0.526424	−	1.36886i
$796$	0.793774	−	13.6286i	0.0281346	−	0.483052i
$797$	−34.1497	−	22.4606i	−1.20965	−	0.795597i	−0.225723	−	0.974191i	$-0.572474\pi$
$797$	−34.1497	−	22.4606i	−1.20965	−	0.795597i	−0.983923	+	0.178595i	$0.942845\pi$
$798$	−8.06513	+	1.57286i	−0.285503	+	0.0556786i
$799$	−57.3519	+	13.5926i	−2.02896	+	0.480873i
$800$	1.93804	−	10.9912i	0.0685201	−	0.388597i
$801$	−22.8567	−	4.55178i	−0.807602	−	0.160829i
$802$	−2.26291	−	12.8336i	−0.0799063	−	0.453171i
$803$	0.0448359	+	0.103941i	0.00158223	+	0.00366801i
$804$	−6.41427	−	2.63043i	−0.226214	−	0.0927681i
$805$	−1.23386	−	4.12137i	−0.0434877	−	0.145259i
$806$	−26.2219	−	35.2221i	−0.923628	−	1.24065i
$807$	−15.1647	+	31.6067i	−0.533823	+	1.11261i
$808$	4.19904	+	2.10884i	0.147722	+	0.0741886i
$809$	−11.6068			−0.408075			−0.204037	−	0.978963i	$-0.565406\pi$
$809$	−11.6068			−0.408075			−0.204037	+	0.978963i	$0.565406\pi$
$810$	−28.7136	+	22.0124i	−1.00889	+	0.773437i
$811$	−27.5179			−0.966283			−0.483141	−	0.875542i	$-0.660504\pi$
$811$	−27.5179			−0.966283			−0.483141	+	0.875542i	$0.660504\pi$
$812$	−6.76769	−	3.39886i	−0.237499	−	0.119277i
$813$	−23.0206	+	1.75865i	−0.807368	+	0.0616787i
$814$	0.0635945	+	0.0854222i	0.00222899	+	0.00299405i
$815$	−20.4012	−	68.1446i	−0.714621	−	2.38700i
$816$	7.05411	−	5.45242i	0.246943	−	0.190873i
$817$	7.10732	+	16.4766i	0.248654	+	0.576444i
$818$	−4.48182	−	25.4177i	−0.156703	−	0.888708i
$819$	19.7504	+	11.9909i	0.690135	+	0.418994i
$820$	4.92140	−	27.9107i	0.171863	−	0.974683i
$821$	21.5317	−	5.10311i	0.751462	−	0.178100i	0.163001	−	0.986626i	$-0.447883\pi$
$821$	21.5317	−	5.10311i	0.751462	−	0.178100i	0.588460	+	0.808526i	$0.299734\pi$
$822$	14.5562	+	16.7241i	0.507704	+	0.583321i
$823$	−36.8962	−	24.2670i	−1.28612	−	0.845894i	−0.292238	−	0.956346i	$-0.594400\pi$
$823$	−36.8962	−	24.2670i	−1.28612	−	0.845894i	−0.993882	+	0.110452i	$0.964770\pi$
$824$	0.0583802	−	1.00235i	0.00203377	−	0.0349185i
$825$	0.258197	+	0.0407314i	0.00898926	+	0.00141808i
$826$	−1.19503	+	3.99169i	−0.0415805	+	0.138889i
$827$	26.0786	−	9.49183i	0.906841	−	0.330063i	0.153850	−	0.988094i	$-0.450833\pi$
$827$	26.0786	−	9.49183i	0.906841	−	0.330063i	0.752991	+	0.658031i	$0.228610\pi$
$828$	0.264359	−	1.89797i	0.00918710	−	0.0659589i
$829$	−18.5119	−	6.73779i	−0.642946	−	0.234013i	−8.97374e−5	−	1.00000i	$-0.500029\pi$
$829$	−18.5119	−	6.73779i	−0.642946	−	0.234013i	−0.642856	+	0.765987i	$0.722251\pi$
$830$	36.4113	−	48.9089i	1.26385	−	1.69765i
$831$	−23.8495	−	45.4228i	−0.827330	−	1.57570i
$832$	−4.47316	−	1.06016i	−0.155079	−	0.0367544i
$833$	8.54902	−	19.8189i	0.296206	−	0.686683i
$834$	31.3239	+	8.76429i	1.08466	+	0.303483i
$835$	28.3272	−	18.6311i	0.980303	−	0.644755i
$836$	0.0191448	+	0.0331598i	0.000662138	+	0.00114686i
$837$	−46.7073	+	16.7903i	−1.61444	+	0.580359i
$838$	0.280284	−	0.485466i	0.00968226	−	0.0167702i
$839$	1.67067	+	28.6843i	0.0576780	+	0.990292i	0.895701	+	0.444657i	$0.146675\pi$
$839$	1.67067	+	28.6843i	0.0576780	+	0.990292i	−0.838023	+	0.545635i	$0.816288\pi$
$840$	−1.14471	+	11.6091i	−0.0394961	+	0.400553i
$841$	8.50856	−	0.994508i	0.293399	−	0.0342934i
$842$	−1.42706	+	1.51260i	−0.0491799	+	0.0521276i
$843$	0.570738	−	2.61807i	0.0196573	−	0.0901711i
$844$	5.93494	+	0.693695i	0.204289	+	0.0238780i
$845$	25.0462	−	21.0163i	0.861615	−	0.722981i
$846$	27.9993	−	19.9009i	0.962634	−	0.684207i
$847$	14.1172	+	11.8458i	0.485074	+	0.407025i
$848$	−4.07550	−	4.31977i	−0.139953	−	0.148342i
$849$	8.68421	+	4.80675i	0.298041	+	0.164967i
$850$	−51.3388	+	25.7833i	−1.76091	+	0.884360i
$851$	−4.49566	+	2.25781i	−0.154109	+	0.0773966i
$852$	8.82856	+	4.88664i	0.302461	+	0.167414i
$853$	−5.52807	−	5.85941i	−0.189278	−	0.200622i	0.625785	−	0.779996i	$-0.284779\pi$
$853$	−5.52807	−	5.85941i	−0.189278	−	0.200622i	−0.815062	+	0.579373i	$0.803297\pi$
$854$	−2.99932	−	2.51673i	−0.102635	−	0.0861207i
$855$	31.0519	+	14.2141i	1.06195	+	0.486113i
$856$	4.52318	−	3.79539i	0.154599	−	0.129724i
$857$	−25.8580	−	3.02237i	−0.883292	−	0.103242i	−0.337661	−	0.941268i	$-0.609636\pi$
$857$	−25.8580	−	3.02237i	−0.883292	−	0.103242i	−0.545631	+	0.838026i	$0.683710\pi$
$858$	0.0229325	−	0.105195i	0.000782903	−	0.00359130i
$859$	6.85732	−	7.26833i	0.233969	−	0.247992i	−0.599742	−	0.800193i	$-0.704730\pi$
$859$	6.85732	−	7.26833i	0.233969	−	0.247992i	0.833711	+	0.552201i	$0.186212\pi$
$860$	25.3023	−	2.95742i	0.862803	−	0.100847i
$861$	−2.00748	+	20.3591i	−0.0684149	+	0.693835i
$862$	0.575983	+	9.88925i	0.0196181	+	0.336829i
$863$	13.8830	−	24.0461i	0.472584	−	0.818540i	−0.526923	−	0.849913i	$-0.676655\pi$
$863$	13.8830	−	24.0461i	0.472584	−	0.818540i	0.999508	+	0.0313727i	$0.00998787\pi$
$864$	−2.61592	+	4.48965i	−0.0889955	+	0.152741i
$865$	15.5287	+	26.8966i	0.527993	+	0.914510i
$866$	−1.90835	+	1.25514i	−0.0648484	+	0.0426514i
$867$	−15.8400	−	4.43197i	−0.537956	−	0.150518i
$868$	−6.33849	+	14.6943i	−0.215142	+	0.498756i
$869$	−0.0646571	−	0.0153240i	−0.00219334	−	0.000519832i
$870$	14.6317	+	27.8671i	0.496063	+	0.944782i
$871$	10.9878	−	14.7592i	0.372309	−	0.500097i
$872$	7.67933	+	2.79505i	0.260055	+	0.0946522i
$873$	7.62085	+	5.93896i	0.257927	+	0.201003i
$874$	−1.69970	+	0.618640i	−0.0574932	+	0.0209258i
$875$	11.9003	−	39.7497i	0.402303	−	1.34378i
$876$	14.3229	+	2.25948i	0.483926	+	0.0763409i
$877$	2.79485	−	47.9857i	0.0943754	−	1.62036i	−0.536100	−	0.844154i	$-0.680103\pi$
$877$	2.79485	−	47.9857i	0.0943754	−	1.62036i	0.630476	−	0.776209i	$-0.282860\pi$
$878$	−27.1550	−	17.8601i	−0.916436	−	0.602750i
$879$	−1.42172	−	1.63347i	−0.0479534	−	0.0550956i
$880$	0.0528931	−	0.0125359i	0.00178302	−	0.000422585i
$881$	−3.81442	+	21.6326i	−0.128511	+	0.728822i	0.850649	+	0.525734i	$0.176209\pi$
$881$	−3.81442	+	21.6326i	−0.128511	+	0.728822i	−0.979160	+	0.203089i	$0.934902\pi$
$882$	−0.277222	+	12.5764i	−0.00933455	+	0.423469i
$883$	−8.64270	−	49.0152i	−0.290850	−	1.64949i	−0.683607	−	0.729851i	$-0.739590\pi$
$883$	−8.64270	−	49.0152i	−0.290850	−	1.64949i	0.392757	−	0.919642i	$-0.371522\pi$
$884$	9.37257	+	21.7280i	0.315233	+	0.730793i
$885$	13.7014	−	10.5904i	0.460567	−	0.355992i
$886$	5.62634	+	18.7933i	0.189021	+	0.631373i
$887$	−6.07019	−	8.15368i	−0.203817	−	0.273774i	0.688448	−	0.725286i	$-0.258292\pi$
$887$	−6.07019	−	8.15368i	−0.203817	−	0.273774i	−0.892265	+	0.451512i	$0.850885\pi$
$888$	13.6016	−	1.03909i	0.456441	−	0.0348697i
$889$	−11.9449	−	5.99898i	−0.400621	−	0.201199i
$890$	31.2297			1.04682
$891$	−0.106240	−	0.0593563i	−0.00355916	−	0.00198851i
$892$	13.3817			0.448053
$893$	−28.9752	−	14.5519i	−0.969617	−	0.486960i
$894$	−1.63531	+	3.40836i	−0.0546928	+	0.113992i
$895$	42.9176	+	57.6484i	1.43458	+	1.92697i
$896$	0.480501	+	1.60498i	0.0160524	+	0.0536188i
$897$	4.70575	+	1.92978i	0.157120	+	0.0644335i
$898$	−3.74776	−	8.68829i	−0.125064	−	0.289932i
$899$	7.49781	+	42.5222i	0.250066	+	1.41820i
$900$	22.0820	−	25.1683i	0.736065	−	0.838944i
$901$	−5.30845	+	30.1057i	−0.176850	+	1.00297i
$902$	0.0927591	−	0.0219843i	0.00308854	−	0.000731997i
$903$	−18.0485	+	3.51982i	−0.600618	+	0.117132i
$904$	−17.3140	−	11.3876i	−0.575855	−	0.378746i
$905$	−3.19697	+	54.8899i	−0.106271	+	1.82460i
$906$	−9.21750	−	23.9683i	−0.306231	−	0.796293i
$907$	−13.1126	+	43.7992i	−0.435398	+	1.45433i	0.405980	+	0.913882i	$0.366930\pi$
$907$	−13.1126	+	43.7992i	−0.435398	+	1.45433i	−0.841378	+	0.540448i	$0.818255\pi$
$908$	21.9498	−	7.98907i	0.728429	−	0.265127i
$909$	7.48474	+	11.9453i	0.248253	+	0.396202i
$910$	−29.0943	−	10.5895i	−0.964467	−	0.351037i
$911$	−16.8453	+	22.6271i	−0.558109	+	0.749670i	−0.988209	−	0.153111i	$-0.951071\pi$
$911$	−16.8453	+	22.6271i	−0.558109	+	0.749670i	0.430100	+	0.902781i	$0.358478\pi$
$912$	4.90069	+	0.196665i	0.162278	+	0.00651224i
$913$	0.199565	+	0.0472978i	0.00660463	+	0.00156533i
$914$	−9.71330	+	22.5180i	−0.321287	+	0.744828i
$915$	4.03813	+	15.7633i	0.133496	+	0.521119i
$916$	8.42954	−	5.54419i	0.278520	−	0.183185i
$917$	6.87498	+	11.9078i	0.227032	+	0.393231i
$918$	26.5783	−	2.99964i	0.877215	−	0.0990028i
$919$	14.5203	−	25.1498i	0.478979	−	0.829617i	−0.520730	−	0.853721i	$-0.674340\pi$
$919$	14.5203	−	25.1498i	0.478979	−	0.829617i	0.999709	+	0.0241047i	$0.00767352\pi$
$920$	0.149307	+	2.56351i	0.00492252	+	0.0845164i
$921$	−25.7766	−	18.4756i	−0.849367	−	0.608791i
$922$	22.3836	−	2.61627i	0.737164	−	0.0861621i
$923$	−18.3789	+	19.4805i	−0.604950	+	0.641210i
$924$	−0.0373801	+	0.0119309i	−0.00122971	+	0.000392498i
$925$	−87.3053	−	10.2045i	−2.87058	−	0.335523i
$926$	−13.8200	+	11.5963i	−0.454152	+	0.381079i
$927$	1.71026	−	2.47952i	0.0561723	−	0.0814382i
$928$	3.46278	+	2.90562i	0.113671	+	0.0953817i
$929$	−4.37340	−	4.63553i	−0.143487	−	0.152087i	0.651644	−	0.758525i	$-0.274079\pi$
$929$	−4.37340	−	4.63553i	−0.143487	−	0.152087i	−0.795131	+	0.606438i	$0.792598\pi$
$930$	56.9887	−	34.2900i	1.86873	−	1.12442i
$931$	10.6107	−	5.32891i	0.347753	−	0.174648i
$932$	−1.29537	+	0.650558i	−0.0424312	+	0.0213097i
$933$	−0.523854	−	28.9886i	−0.0171502	−	0.949044i
$934$	3.77625	+	4.00259i	0.123563	+	0.130969i
$935$	−0.214345	−	0.179857i	−0.00700984	−	0.00588195i
$936$	−9.82038	−	9.68289i	−0.320989	−	0.316495i
$937$	−4.00720	+	3.36244i	−0.130910	+	0.109846i	−0.705892	−	0.708320i	$-0.749453\pi$
$937$	−4.00720	+	3.36244i	−0.130910	+	0.109846i	0.574982	+	0.818166i	$0.305009\pi$
$938$	−6.66046	−	0.778496i	−0.217472	−	0.0254188i
$939$	−15.8889	−	14.4568i	−0.518514	−	0.471779i
$940$	−31.5884	+	33.4818i	−1.03030	+	1.09206i
$941$	43.5519	−	5.09049i	1.41975	−	0.165945i	0.628678	−	0.777665i	$-0.283596\pi$
$941$	43.5519	−	5.09049i	1.41975	−	0.165945i	0.791074	+	0.611720i	$0.209522\pi$
$942$	−12.7267	+	5.76467i	−0.414657	+	0.187823i
$943$	0.261842	+	4.49565i	0.00852675	+	0.146399i
$944$	1.24353	−	2.15386i	0.0404734	−	0.0701020i
$945$	−21.0096	+	27.9882i	−0.683444	+	0.910455i
$946$	0.0428432	+	0.0742067i	0.00139295	+	0.00241267i
$947$	−37.5241	+	24.6800i	−1.21937	+	0.801992i	−0.985401	−	0.170252i	$-0.945542\pi$
$947$	−37.5241	+	24.6800i	−1.21937	+	0.801992i	−0.233969	+	0.972244i	$0.575172\pi$
$948$	−6.08453	+	5.95189i	−0.197616	+	0.193308i
$949$	−15.2431	+	35.3374i	−0.494811	+	1.14710i
$950$	−30.7519	−	7.28833i	−0.997723	−	0.236465i
$951$	−20.6677	+	32.6956i	−0.670197	+	1.06023i
$952$	5.14984	−	6.91744i	0.166907	−	0.224195i
$953$	−39.4523	−	14.3595i	−1.27799	−	0.465149i	−0.388220	−	0.921567i	$-0.626910\pi$
$953$	−39.4523	−	14.3595i	−1.27799	−	0.465149i	−0.889765	+	0.456418i	$0.849132\pi$
$954$	−3.72574	−	17.4227i	−0.120625	−	0.564080i
$955$	−10.2148	+	3.71790i	−0.330544	+	0.120308i
$956$	−6.10066	+	20.3776i	−0.197309	+	0.659060i
$957$	−0.0665746	+	0.0823164i	−0.00215205	+	0.00266091i
$958$	2.29383	−	39.3836i	0.0741103	−	1.27242i
$959$	17.9179	+	11.7848i	0.578598	+	0.380550i
$960$	2.26285	−	6.58496i	0.0730331	−	0.212529i
$961$	58.6163	−	13.8923i	1.89085	−	0.448140i
$962$	−6.28704	+	35.6556i	−0.202702	+	1.14958i
$963$	17.5082	−	2.69077i	0.564194	−	0.0867090i
$964$	1.59393	+	9.03964i	0.0513371	+	0.291147i
$965$	15.6133	+	36.1956i	0.502609	+	1.16518i
$966$	−0.248416	−	1.83686i	−0.00799266	−	0.0590999i
$967$	10.8072	+	36.0986i	0.347537	+	1.16085i	0.935903	+	0.352259i	$0.114586\pi$
$967$	10.8072	+	36.0986i	0.347537	+	1.16085i	−0.588366	+	0.808595i	$0.700229\pi$
$968$	−6.56864	−	8.82321i	−0.211124	−	0.283589i
$969$	−14.2520	−	20.8390i	−0.457841	−	0.669446i
$970$	−11.5697	−	5.81052i	−0.371481	−	0.186565i
$971$	−27.7914			−0.891868			−0.445934	−	0.895066i	$-0.647128\pi$
$971$	−27.7914			−0.891868			−0.445934	+	0.895066i	$0.647128\pi$
$972$	−13.6981	+	7.44050i	−0.439368	+	0.238654i
$973$	31.4624			1.00864
$974$	−5.64436	−	2.83470i	−0.180857	−	0.0908298i
$975$	50.1661	+	73.3519i	1.60660	+	2.34914i
$976$	1.39556	+	1.87456i	0.0446708	+	0.0600033i
$977$	0.169752	+	0.567010i	0.00543084	+	0.0181403i	0.960662	−	0.277720i	$-0.0895788\pi$
$977$	0.169752	+	0.567010i	0.00543084	+	0.0181403i	−0.955231	+	0.295861i	$0.904394\pi$
$978$	−4.10743	−	30.3714i	−0.131341	−	0.971171i
$979$	0.0416060	+	0.0964535i	0.00132973	+	0.00308267i
$980$	−2.92712	−	16.6005i	−0.0935034	−	0.530284i
$981$	15.3412	+	19.1235i	0.489807	+	0.610565i
$982$	0.0193301	−	0.109626i	0.000616848	−	0.00349832i
$983$	−27.3129	+	6.47327i	−0.871145	+	0.206465i	−0.641792	−	0.766878i	$-0.721809\pi$
$983$	−27.3129	+	6.47327i	−0.871145	+	0.206465i	−0.229352	+	0.973343i	$0.573661\pi$
$984$	3.96838	−	11.5481i	0.126507	−	0.368140i
$985$	8.10965	+	5.33380i	0.258395	+	0.169949i
$986$	1.35293	−	23.2290i	0.0430862	−	0.739761i
$987$	20.8945	−	25.8351i	0.665080	−	0.822341i
$988$	−3.73347	+	12.4706i	−0.118777	+	0.396744i
$989$	−3.80367	+	1.38442i	−0.120950	+	0.0440221i
$990$	0.155155	+	0.0502019i	0.00493116	+	0.00159552i
$991$	−19.6354	−	7.14669i	−0.623738	−	0.227022i	0.0107653	−	0.999942i	$-0.496573\pi$
$991$	−19.6354	−	7.14669i	−0.623738	−	0.227022i	−0.634504	+	0.772920i	$0.718795\pi$
$992$	5.70404	−	7.66186i	0.181103	−	0.243264i
$993$	−17.7658	+	28.1049i	−0.563781	+	0.891881i
$994$	9.49740	+	2.25092i	0.301239	+	0.0713950i
$995$	−21.7370	+	50.3919i	−0.689108	+	1.59753i
$996$	18.7800	−	18.3706i	0.595066	−	0.582094i
$997$	17.6322	−	11.5969i	0.558416	−	0.367276i	−0.238708	−	0.971091i	$-0.576724\pi$
$997$	17.6322	−	11.5969i	0.558416	−	0.367276i	0.797124	+	0.603815i	$0.206353\pi$
$998$	5.63227	+	9.75538i	0.178286	+	0.308801i
$999$	36.4977	+	18.5116i	1.15473	+	0.585682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.13.2	✓	90
3.2	odd	2		486.2.g.b.253.5		90
81.25	even	27	inner	162.2.g.b.25.2	yes	90
81.56	odd	54		486.2.g.b.73.5		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.2	✓	90	1.1	even	1	trivial
162.2.g.b.25.2	yes	90	81.25	even	27	inner
486.2.g.b.73.5		90	81.56	odd	54
486.2.g.b.253.5		90	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.893633 + 0.448799i) q^{2} +(-0.977769 - 1.42967i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-1.15296 - 3.85116i) q^{5} +(-0.232129 - 1.71643i) q^{6} +(-0.663579 - 1.53835i) q^{7} +(0.173648 + 0.984808i) q^{8} +(-1.08794 + 2.79578i) q^{9} +O(q^{10})\)	\(q+(0.893633 + 0.448799i) q^{2} +(-0.977769 - 1.42967i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-1.15296 - 3.85116i) q^{5} +(-0.232129 - 1.71643i) q^{6} +(-0.663579 - 1.53835i) q^{7} +(0.173648 + 0.984808i) q^{8} +(-1.08794 + 2.79578i) q^{9} +(0.698073 - 3.95897i) q^{10} +(0.0131573 - 0.00311835i) q^{11} +(0.562892 - 1.63803i) q^{12} +(3.84080 + 2.52614i) q^{13} +(0.0974140 - 1.67253i) q^{14} +(-4.37857 + 5.41390i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(4.83704 - 1.76054i) q^{17} +(-2.22696 + 2.01014i) q^{18} +(2.66092 + 0.968497i) q^{19} +(2.40060 - 3.22457i) q^{20} +(-1.55051 + 2.45285i) q^{21} +(0.0131573 + 0.00311835i) q^{22} +(-0.253001 + 0.586523i) q^{23} +(1.23817 - 1.21117i) q^{24} +(-9.32465 + 6.13292i) q^{25} +(2.29854 + 3.98119i) q^{26} +(5.06081 - 1.17823i) q^{27} +(0.837684 - 1.45091i) q^{28} +(-0.262835 - 4.51270i) q^{29} +(-6.34259 + 2.87294i) q^{30} +(-9.48738 + 1.10892i) q^{31} +(-0.686242 + 0.727374i) q^{32} +(-0.0173231 - 0.0157617i) q^{33} +(5.11267 + 0.597585i) q^{34} +(-5.15935 + 4.32920i) q^{35} +(-2.89223 + 0.796865i) q^{36} +(6.03321 + 5.06246i) q^{37} +(1.94323 + 2.05970i) q^{38} +(-0.143865 - 7.96107i) q^{39} +(3.59244 - 1.80419i) q^{40} +(6.30010 - 3.16403i) q^{41} +(-2.48643 + 1.49608i) q^{42} +(4.34864 + 4.60929i) q^{43} +(0.0103583 + 0.00869166i) q^{44} +(12.0213 + 0.966392i) q^{45} +(-0.489321 + 0.410589i) q^{46} +(-11.3730 - 1.32931i) q^{47} +(1.65004 - 0.526657i) q^{48} +(2.87751 - 3.04998i) q^{49} +(-11.0853 + 1.29568i) q^{50} +(-7.24650 - 5.19399i) q^{51} +(0.267296 + 4.58930i) q^{52} +(-2.96943 + 5.14321i) q^{53} +(5.05129 + 1.21838i) q^{54} +(-0.0271791 - 0.0470757i) q^{55} +(1.39975 - 0.920630i) q^{56} +(-1.21713 - 4.75122i) q^{57} +(1.79042 - 4.15065i) q^{58} +(-2.42002 - 0.573555i) q^{59} +(-6.95732 - 0.279198i) q^{60} +(1.39556 - 1.87456i) q^{61} +(-8.97591 - 3.26697i) q^{62} +(5.02282 - 0.181594i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(5.30025 - 17.7041i) q^{65} +(-0.00840662 - 0.0218597i) q^{66} +(0.232730 - 3.99581i) q^{67} +(4.30065 + 2.82858i) q^{68} +(1.08591 - 0.211774i) q^{69} +(-6.55350 + 1.55321i) q^{70} +(-1.01165 + 5.73737i) q^{71} +(-2.94223 - 0.585927i) q^{72} +(1.45371 + 8.24441i) q^{73} +(3.11944 + 7.23168i) q^{74} +(17.8854 + 7.33464i) q^{75} +(0.812139 + 2.71273i) q^{76} +(-0.0135280 - 0.0181713i) q^{77} +(3.44436 - 7.17884i) q^{78} +(-4.39144 - 2.20546i) q^{79} +4.02004 q^{80} +(-6.63278 - 6.08327i) q^{81} +7.04998 q^{82} +(13.5542 + 6.80719i) q^{83} +(-2.89339 + 0.221040i) q^{84} +(-12.3570 - 16.5984i) q^{85} +(1.81744 + 6.07068i) q^{86} +(-6.19470 + 4.78814i) q^{87} +(0.00535572 + 0.0124160i) q^{88} +(1.34899 + 7.65049i) q^{89} +(10.3089 + 6.25877i) q^{90} +(1.33740 - 7.58479i) q^{91} +(-0.621545 + 0.147309i) q^{92} +(10.8619 + 12.4796i) q^{93} +(-9.56667 - 6.29210i) q^{94} +(0.661893 - 11.3643i) q^{95} +(1.71089 + 0.269899i) q^{96} +(0.923670 - 3.08527i) q^{97} +(3.94027 - 1.43414i) q^{98} +(-0.00559615 + 0.0401776i) 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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