LMFDB - Embedded newform 216.2.t.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28352 + 0.593791i) q^{2} +(-1.30914 - 1.13409i) q^{3} +(1.29483 - 1.52428i) q^{4} +(-0.508621 + 0.606151i) q^{5} +(2.35371 + 0.678272i) q^{6} +(-3.72062 - 1.35420i) q^{7} +(-0.756827 + 2.72529i) q^{8} +(0.427672 + 2.96936i) q^{9} +O(q^{10})$	\(q+(-1.28352 + 0.593791i) q^{2} +(-1.30914 - 1.13409i) q^{3} +(1.29483 - 1.52428i) q^{4} +(-0.508621 + 0.606151i) q^{5} +(2.35371 + 0.678272i) q^{6} +(-3.72062 - 1.35420i) q^{7} +(-0.756827 + 2.72529i) q^{8} +(0.427672 + 2.96936i) q^{9} +(0.292896 - 1.08002i) q^{10} +(2.92987 + 3.49168i) q^{11} +(-3.42377 + 0.527037i) q^{12} +(3.31770 + 0.585000i) q^{13} +(5.57959 - 0.471139i) q^{14} +(1.35328 - 0.216711i) q^{15} +(-0.646853 - 3.94735i) q^{16} +(-2.50743 + 4.34299i) q^{17} +(-2.31210 - 3.55727i) q^{18} +(-6.10844 + 3.52671i) q^{19} +(0.265368 + 1.56014i) q^{20} +(3.33502 + 5.99236i) q^{21} +(-5.83385 - 2.74190i) q^{22} +(-4.33163 + 1.57658i) q^{23} +(4.08152 - 2.70947i) q^{24} +(0.759517 + 4.30744i) q^{25} +(-4.60569 + 1.21916i) q^{26} +(2.80765 - 4.37231i) q^{27} +(-6.88173 + 3.91782i) q^{28} +(-3.32150 + 0.585669i) q^{29} +(-1.60828 + 1.08172i) q^{30} +(7.51376 - 2.73478i) q^{31} +(3.17415 + 4.68239i) q^{32} +(0.124291 - 7.89382i) q^{33} +(0.639495 - 7.06318i) q^{34} +(2.71323 - 1.56649i) q^{35} +(5.07989 + 3.19291i) q^{36} +(-3.56434 - 2.05787i) q^{37} +(5.74615 - 8.15372i) q^{38} +(-3.67987 - 4.52842i) q^{39} +(-1.26700 - 1.84489i) q^{40} +(0.333012 - 1.88860i) q^{41} +(-7.83875 - 5.71098i) q^{42} +(3.66311 + 4.36553i) q^{43} +(9.11596 + 0.0551814i) q^{44} +(-2.01740 - 1.25104i) q^{45} +(4.62355 - 4.59565i) q^{46} +(-7.37860 - 2.68559i) q^{47} +(-3.62984 + 5.90121i) q^{48} +(6.64689 + 5.57740i) q^{49} +(-3.53257 - 5.07767i) q^{50} +(8.20791 - 2.84191i) q^{51} +(5.18754 - 4.29963i) q^{52} -1.95507i q^{53} +(-1.00742 + 7.27909i) q^{54} -3.60667 q^{55} +(6.50645 - 9.11489i) q^{56} +(11.9964 + 2.31059i) q^{57} +(3.91543 - 2.72399i) q^{58} +(3.02793 - 3.60855i) q^{59} +(1.42194 - 2.34339i) q^{60} +(-1.87567 + 5.15337i) q^{61} +(-8.02014 + 7.97174i) q^{62} +(2.42989 - 11.6270i) q^{63} +(-6.85443 - 4.12515i) q^{64} +(-2.04205 + 1.71348i) q^{65} +(4.52774 + 10.2056i) q^{66} +(-5.36107 - 0.945302i) q^{67} +(3.37325 + 9.44544i) q^{68} +(7.45868 + 2.84850i) q^{69} +(-2.55231 + 3.62170i) q^{70} +(-5.56518 + 9.63918i) q^{71} +(-8.41604 - 1.08176i) q^{72} +(-1.32161 - 2.28909i) q^{73} +(5.79683 + 0.524840i) q^{74} +(3.89072 - 6.50038i) q^{75} +(-2.53367 + 13.8774i) q^{76} +(-6.17251 - 16.9588i) q^{77} +(7.41211 + 3.62722i) q^{78} +(-0.150274 - 0.852245i) q^{79} +(2.72169 + 1.61561i) q^{80} +(-8.63419 + 2.53982i) q^{81} +(0.694009 + 2.62179i) q^{82} +(-0.0489550 + 0.00863210i) q^{83} +(13.4523 + 2.67556i) q^{84} +(-1.35718 - 3.72882i) q^{85} +(-7.29387 - 3.42810i) q^{86} +(5.01249 + 3.00016i) q^{87} +(-11.7332 + 5.34214i) q^{88} +(-2.15515 - 3.73283i) q^{89} +(3.33223 + 0.407821i) q^{90} +(-11.5517 - 6.66938i) q^{91} +(-3.20555 + 8.64401i) q^{92} +(-12.9380 - 4.94109i) q^{93} +(11.0652 - 0.934344i) q^{94} +(0.969162 - 5.49639i) q^{95} +(1.15487 - 9.72966i) q^{96} +(5.00174 - 4.19696i) q^{97} +(-11.8432 - 3.21182i) q^{98} +(-9.11503 + 10.1931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−1.28352	+	0.593791i	−0.907583	+	0.419873i
$2$	−1.28352	+	0.593791i	−0.907583	+	0.419873i
$3$	−1.30914	−	1.13409i	−0.755830	−	0.654768i
$3$	−1.30914	−	1.13409i	−0.755830	−	0.654768i
$4$	1.29483	−	1.52428i	0.647413	−	0.762140i
$5$	−0.508621	+	0.606151i	−0.227462	+	0.271079i	−0.867689	−	0.497107i	$-0.834396\pi$
$5$	−0.508621	+	0.606151i	−0.227462	+	0.271079i	0.640227	+	0.768186i	$0.278840\pi$
$6$	2.35371	+	0.678272i	0.960898	+	0.276904i
$7$	−3.72062	−	1.35420i	−1.40626	−	0.511838i	−0.476233	−	0.879319i	$-0.657998\pi$
$7$	−3.72062	−	1.35420i	−1.40626	−	0.511838i	−0.930031	+	0.367481i	$0.880220\pi$
$8$	−0.756827	+	2.72529i	−0.267579	+	0.963536i
$9$	0.427672	+	2.96936i	0.142557	+	0.989787i
$10$	0.292896	−	1.08002i	0.0926220	−	0.341532i
$11$	2.92987	+	3.49168i	0.883388	+	1.05278i	0.998234	+	0.0593973i	$0.0189179\pi$
$11$	2.92987	+	3.49168i	0.883388	+	1.05278i	−0.114847	+	0.993383i	$0.536638\pi$
$12$	−3.42377	+	0.527037i	−0.988359	+	0.152142i
$13$	3.31770	+	0.585000i	0.920164	+	0.162250i	0.613615	−	0.789605i	$-0.289715\pi$
$13$	3.31770	+	0.585000i	0.920164	+	0.162250i	0.306549	+	0.951855i	$0.400826\pi$
$14$	5.57959	−	0.471139i	1.49121	−	0.125917i
$15$	1.35328	−	0.216711i	0.349417	−	0.0559545i
$16$	−0.646853	−	3.94735i	−0.161713	−	0.986838i
$17$	−2.50743	+	4.34299i	−0.608140	+	1.05333i	0.383406	+	0.923580i	$0.374751\pi$
$17$	−2.50743	+	4.34299i	−0.608140	+	1.05333i	−0.991547	+	0.129750i	$0.958582\pi$
$18$	−2.31210	−	3.55727i	−0.544968	−	0.838457i
$19$	−6.10844	+	3.52671i	−1.40137	+	0.809082i	−0.994533	−	0.104418i	$-0.966702\pi$
$19$	−6.10844	+	3.52671i	−1.40137	+	0.809082i	−0.406838	+	0.913500i	$0.633369\pi$
$20$	0.265368	+	1.56014i	0.0593380	+	0.348858i
$21$	3.33502	+	5.99236i	0.727761	+	1.30764i
$22$	−5.83385	−	2.74190i	−1.24378	−	0.584574i
$23$	−4.33163	+	1.57658i	−0.903207	+	0.328740i	−0.751537	−	0.659691i	$-0.770687\pi$
$23$	−4.33163	+	1.57658i	−0.903207	+	0.328740i	−0.151670	+	0.988431i	$0.548465\pi$
$24$	4.08152	−	2.70947i	0.833137	−	0.553067i
$25$	0.759517	+	4.30744i	0.151903	+	0.861487i
$26$	−4.60569	+	1.21916i	−0.903249	+	0.239097i
$27$	2.80765	−	4.37231i	0.540332	−	0.841452i
$28$	−6.88173	+	3.91782i	−1.30053	+	0.740399i
$29$	−3.32150	+	0.585669i	−0.616786	+	0.108756i	−0.473307	−	0.880897i	$-0.656940\pi$
$29$	−3.32150	+	0.585669i	−0.616786	+	0.108756i	−0.143479	+	0.989653i	$0.545829\pi$
$30$	−1.60828	+	1.08172i	−0.293631	+	0.197494i
$31$	7.51376	−	2.73478i	1.34951	−	0.491182i	0.436716	−	0.899600i	$-0.356142\pi$
$31$	7.51376	−	2.73478i	1.34951	−	0.491182i	0.912795	+	0.408418i	$0.133919\pi$
$32$	3.17415	+	4.68239i	0.561115	+	0.827738i
$33$	0.124291	−	7.89382i	0.0216364	−	1.37414i
$34$	0.639495	−	7.06318i	0.109673	−	1.21133i
$35$	2.71323	−	1.56649i	0.458620	−	0.264785i
$36$	5.07989	+	3.19291i	0.846649	+	0.532152i
$37$	−3.56434	−	2.05787i	−0.585973	−	0.338312i	0.177530	−	0.984115i	$-0.443189\pi$
$37$	−3.56434	−	2.05787i	−0.585973	−	0.338312i	−0.763504	+	0.645803i	$0.776523\pi$
$38$	5.74615	−	8.15372i	0.932148	−	1.32271i
$39$	−3.67987	−	4.52842i	−0.589251	−	0.725127i
$40$	−1.26700	−	1.84489i	−0.200330	−	0.291703i
$41$	0.333012	−	1.88860i	0.0520077	−	0.294950i	−0.947699	−	0.319165i	$-0.896597\pi$
$41$	0.333012	−	1.88860i	0.0520077	−	0.294950i	0.999707	+	0.0242149i	$0.00770860\pi$
$42$	−7.83875	−	5.71098i	−1.20955	−	0.881224i
$43$	3.66311	+	4.36553i	0.558619	+	0.665737i	0.969254	−	0.246064i	$-0.0791372\pi$
$43$	3.66311	+	4.36553i	0.558619	+	0.665737i	−0.410634	+	0.911800i	$0.634693\pi$
$44$	9.11596	+	0.0551814i	1.37428	+	0.00831891i
$45$	−2.01740	−	1.25104i	−0.300737	−	0.186495i
$46$	4.62355	−	4.59565i	0.681706	−	0.677592i
$47$	−7.37860	−	2.68559i	−1.07628	−	0.391733i	−0.257757	−	0.966210i	$-0.582984\pi$
$47$	−7.37860	−	2.68559i	−1.07628	−	0.391733i	−0.818521	+	0.574476i	$0.805206\pi$
$48$	−3.62984	+	5.90121i	−0.523922	+	0.851766i
$49$	6.64689	+	5.57740i	0.949555	+	0.796771i
$50$	−3.53257	−	5.07767i	−0.499581	−	0.718091i
$51$	8.20791	−	2.84191i	1.14934	−	0.397947i
$52$	5.18754	−	4.29963i	0.719383	−	0.596251i
$53$		−	1.95507i		−	0.268550i	−0.990944	−	0.134275i	$-0.957129\pi$
$53$		−	1.95507i		−	0.268550i	0.990944	−	0.134275i	$-0.0428705\pi$
$54$	−1.00742	+	7.27909i	−0.137092	+	0.990558i
$55$	−3.60667			−0.486324
$56$	6.50645	−	9.11489i	0.869461	−	1.21803i
$57$	11.9964	+	2.31059i	1.58896	+	0.306045i
$58$	3.91543	−	2.72399i	0.514121	−	0.357677i
$59$	3.02793	−	3.60855i	0.394203	−	0.469793i	−0.532040	−	0.846719i	$-0.678574\pi$
$59$	3.02793	−	3.60855i	0.394203	−	0.469793i	0.926243	+	0.376926i	$0.123019\pi$
$60$	1.42194	−	2.34339i	0.183572	−	0.302530i
$61$	−1.87567	+	5.15337i	−0.240156	+	0.659822i	0.759798	+	0.650159i	$0.225298\pi$
$61$	−1.87567	+	5.15337i	−0.240156	+	0.659822i	−0.999953	+	0.00966241i	$0.996924\pi$
$62$	−8.02014	+	7.97174i	−1.01856	+	1.01241i
$63$	2.42989	−	11.6270i	0.306137	−	1.46487i
$64$	−6.85443	−	4.12515i	−0.856803	−	0.515643i
$65$	−2.04205	+	1.71348i	−0.253285	+	0.212531i
$66$	4.52774	+	10.2056i	0.557327	+	1.25623i
$67$	−5.36107	−	0.945302i	−0.654959	−	0.115487i	−0.163713	−	0.986508i	$-0.552347\pi$
$67$	−5.36107	−	0.945302i	−0.654959	−	0.115487i	−0.491246	+	0.871021i	$0.663458\pi$
$68$	3.37325	+	9.44544i	0.409067	+	1.14543i
$69$	7.45868	+	2.84850i	0.897919	+	0.342919i
$70$	−2.55231	+	3.62170i	−0.305060	+	0.432876i
$71$	−5.56518	+	9.63918i	−0.660465	+	1.14396i	0.320028	+	0.947408i	$0.396308\pi$
$71$	−5.56518	+	9.63918i	−0.660465	+	1.14396i	−0.980493	+	0.196552i	$0.937026\pi$
$72$	−8.41604	−	1.08176i	−0.991840	−	0.127487i
$73$	−1.32161	−	2.28909i	−0.154683	−	0.267918i	0.778261	−	0.627941i	$-0.216102\pi$
$73$	−1.32161	−	2.28909i	−0.154683	−	0.267918i	−0.932943	+	0.360023i	$0.882769\pi$
$74$	5.79683	+	0.524840i	0.673867	+	0.0610115i
$75$	3.89072	−	6.50038i	0.449261	−	0.750599i
$76$	−2.53367	+	13.8774i	−0.290632	+	1.59185i
$77$	−6.17251	−	16.9588i	−0.703423	−	1.93264i
$78$	7.41211	+	3.62722i	0.839256	+	0.410702i
$79$	−0.150274	−	0.852245i	−0.0169071	−	0.0958850i	0.975187	−	0.221385i	$-0.0710577\pi$
$79$	−0.150274	−	0.852245i	−0.0169071	−	0.0958850i	−0.992094	+	0.125500i	$0.959947\pi$
$80$	2.72169	+	1.61561i	0.304295	+	0.180631i
$81$	−8.63419	+	2.53982i	−0.959355	+	0.282203i
$82$	0.694009	+	2.62179i	0.0766405	+	0.289529i
$83$	−0.0489550	+	0.00863210i	−0.00537351	+	0.000947496i	−0.176334	−	0.984330i	$-0.556424\pi$
$83$	−0.0489550	+	0.00863210i	−0.00537351	+	0.000947496i	0.170961	+	0.985278i	$0.445313\pi$
$84$	13.4523	+	2.67556i	1.46777	+	0.291927i
$85$	−1.35718	−	3.72882i	−0.147207	−	0.404447i
$86$	−7.29387	−	3.42810i	−0.786518	−	0.369662i
$87$	5.01249	+	3.00016i	0.537395	+	0.321651i
$88$	−11.7332	+	5.34214i	−1.25077	+	0.569474i
$89$	−2.15515	−	3.73283i	−0.228445	−	0.395679i	0.728902	−	0.684618i	$-0.240031\pi$
$89$	−2.15515	−	3.73283i	−0.228445	−	0.395679i	−0.957348	+	0.288939i	$0.906698\pi$
$90$	3.33223	+	0.407821i	0.351248	+	0.0429881i
$91$	−11.5517	−	6.66938i	−1.21095	−	0.699141i
$92$	−3.20555	+	8.64401i	−0.334202	+	0.901200i
$93$	−12.9380	−	4.94109i	−1.34161	−	0.512367i
$94$	11.0652	−	0.934344i	1.14129	−	0.0963702i
$95$	0.969162	−	5.49639i	0.0994339	−	0.563918i
$96$	1.15487	−	9.72966i	0.117869	−	0.993029i
$97$	5.00174	−	4.19696i	0.507850	−	0.426137i	−0.352522	−	0.935804i	$-0.614676\pi$
$97$	5.00174	−	4.19696i	0.507850	−	0.426137i	0.860372	+	0.509667i	$0.170231\pi$
$98$	−11.8432	−	3.21182i	−1.19634	−	0.324443i
$99$	−9.11503	+	10.1931i	−0.916095	+	1.02445i
$100$	7.54918	+	4.41966i	0.754918	+	0.441966i
$101$	−1.65905	+	4.55822i	−0.165082	+	0.453559i	−0.994458	−	0.105131i	$-0.966474\pi$
$101$	−1.65905	+	4.55822i	−0.165082	+	0.453559i	0.829376	+	0.558690i	$0.188696\pi$
$102$	−8.84749	+	8.52142i	−0.876032	+	0.843746i
$103$	2.89374	+	2.42813i	0.285128	+	0.239251i	0.774122	−	0.633036i	$-0.218192\pi$
$103$	2.89374	+	2.42813i	0.285128	+	0.239251i	−0.488994	+	0.872287i	$0.662636\pi$
$104$	−4.10522	+	8.59895i	−0.402550	+	0.843197i
$105$	−5.32853	−	1.02631i	−0.520011	−	0.100158i
$106$	1.16090	+	2.50937i	0.112757	+	0.243731i
$107$			6.44327i			0.622894i	0.950263	+	0.311447i	$0.100814\pi$
$107$			6.44327i			0.622894i	−0.950263	+	0.311447i	$0.899186\pi$
$108$	−3.02922	−	9.94102i	−0.291486	−	0.956575i
$109$		−	1.86527i		−	0.178660i	−0.996002	−	0.0893301i	$-0.971527\pi$
$109$		−	1.86527i		−	0.178660i	0.996002	−	0.0893301i	$-0.0284726\pi$
$110$	4.62922	−	2.14161i	0.441379	−	0.204194i
$111$	2.33239	+	6.73632i	0.221380	+	0.639383i
$112$	−2.93879	+	15.5626i	−0.277690	+	1.47053i
$113$	4.03671	+	3.38720i	0.379741	+	0.318641i	0.812601	−	0.582821i	$-0.198051\pi$
$113$	4.03671	+	3.38720i	0.379741	+	0.318641i	−0.432859	+	0.901461i	$0.642495\pi$
$114$	−16.7695	+	4.15766i	−1.57061	+	0.389401i
$115$	1.24751	−	3.42750i	0.116331	−	0.319616i
$116$	−3.40803	+	5.82123i	−0.316428	+	0.540487i
$117$	−0.318188	+	10.1016i	−0.0294165	+	0.933896i
$118$	−1.74368	+	6.42959i	−0.160519	+	0.591892i
$119$	15.2105	−	12.7631i	1.39434	−	1.16999i
$120$	−0.433602	+	3.85211i	−0.0395822	+	0.351648i
$121$	−1.69757	+	9.62741i	−0.154325	+	0.875219i
$122$	−0.652566	−	7.72819i	−0.0590806	−	0.699678i
$123$	−2.57781	+	2.09477i	−0.232433	+	0.188879i
$124$	5.56043	−	14.9941i	0.499342	−	1.34651i
$125$	−6.42358	−	3.70865i	−0.574542	−	0.331712i
$126$	3.78522	+	16.3663i	0.337214	+	1.45803i
$127$	8.80265	+	15.2466i	0.781109	+	1.35292i	0.931296	+	0.364263i	$0.118679\pi$
$127$	8.80265	+	15.2466i	0.781109	+	1.35292i	−0.150187	+	0.988658i	$0.547988\pi$
$128$	11.2472	+	1.22460i	0.994125	+	0.108240i
$129$	0.155397	−	9.86937i	0.0136820	−	0.868950i
$130$	1.60355	−	3.41183i	0.140641	−	0.299237i
$131$	−3.58706	−	9.85536i	−0.313403	−	0.861067i	−0.991964	−	0.126523i	$-0.959618\pi$
$131$	−3.58706	−	9.85536i	−0.313403	−	0.861067i	0.678561	−	0.734544i	$-0.262604\pi$
$132$	−11.8714	−	10.4106i	−1.03328	−	0.906124i
$133$	27.5031	−	4.84953i	2.38482	−	0.420508i
$134$	7.44233	−	1.97004i	0.642920	−	0.170186i
$135$	1.22225	+	3.92571i	0.105195	+	0.337871i
$136$	−9.93823	−	10.1204i	−0.852196	−	0.867814i
$137$	−1.18700	−	6.73181i	−0.101412	−	0.575137i	−0.992593	−	0.121489i	$-0.961233\pi$
$137$	−1.18700	−	6.73181i	−0.101412	−	0.575137i	0.891181	−	0.453649i	$-0.149878\pi$
$138$	−11.2647	+	0.772796i	−0.958919	+	0.0657848i
$139$	3.94000	+	10.8251i	0.334187	+	0.918171i	0.987010	+	0.160660i	$0.0513623\pi$
$139$	3.94000	+	10.8251i	0.334187	+	0.918171i	−0.652823	+	0.757510i	$0.726415\pi$
$140$	1.12540	−	6.16405i	0.0951139	−	0.520958i
$141$	6.61388	+	11.8838i	0.556989	+	1.00080i
$142$	1.41935	−	15.6766i	0.119109	−	1.31555i
$143$	7.67778	+	13.2983i	0.642048	+	1.11206i
$144$	11.4445	−	3.60891i	0.953705	−	0.300743i
$145$	1.33438	−	2.31121i	0.110814	−	0.191936i
$146$	3.05555	+	2.15333i	0.252879	+	0.178211i
$147$	−2.37639	−	14.8398i	−0.196002	−	1.22396i
$148$	−7.75196	+	2.76846i	−0.637208	+	0.227566i
$149$	−10.7148	−	1.88931i	−0.877789	−	0.154778i	−0.283445	−	0.958989i	$-0.591477\pi$
$149$	−10.7148	−	1.88931i	−0.877789	−	0.154778i	−0.594344	+	0.804211i	$0.702588\pi$
$150$	−1.13393	+	10.6536i	−0.0925852	+	0.869864i
$151$	−13.6914	+	11.4884i	−1.11419	+	0.934917i	−0.998296	−	0.0583451i	$-0.981418\pi$
$151$	−13.6914	+	11.4884i	−1.11419	+	0.934917i	−0.115894	+	0.993262i	$0.536973\pi$
$152$	−4.98828	−	19.3164i	−0.404603	−	1.56676i
$153$	−13.9683	−	5.58808i	−1.12927	−	0.451769i
$154$	17.9925	+	18.1018i	1.44988	+	1.45868i
$155$	−2.16396	+	5.94544i	−0.173814	+	0.477549i
$156$	−11.6674	−	0.254358i	−0.934137	−	0.0203649i
$157$	5.09556	−	6.07265i	0.406670	−	0.484650i	−0.523372	−	0.852104i	$-0.675326\pi$
$157$	5.09556	−	6.07265i	0.406670	−	0.484650i	0.930042	+	0.367454i	$0.119771\pi$
$158$	0.698934	+	1.00464i	0.0556042	+	0.0799247i
$159$	−2.21723	+	2.55946i	−0.175838	+	0.202978i
$160$	−4.45267	−	0.457552i	−0.352015	−	0.0361726i
$161$	18.2514			1.43841
$162$	9.57400	−	8.38681i	0.752204	−	0.658930i
$163$			16.2608i			1.27365i	0.771009	+	0.636824i	$0.219752\pi$
$163$			16.2608i			1.27365i	−0.771009	+	0.636824i	$0.780248\pi$
$164$	−2.44757	−	2.95302i	−0.191123	−	0.230592i
$165$	4.72163	+	4.09030i	0.367578	+	0.318429i
$166$	0.0577089	−	0.0401485i	0.00447908	−	0.00311613i
$167$	−9.24890	−	7.76075i	−0.715701	−	0.600545i	0.210491	−	0.977596i	$-0.432494\pi$
$167$	−9.24890	−	7.76075i	−0.715701	−	0.600545i	−0.926193	+	0.377051i	$0.876938\pi$
$168$	−18.8549	+	4.55372i	−1.45469	+	0.351327i
$169$	−1.55110	−	0.564555i	−0.119316	−	0.0434273i
$170$	3.95609	+	3.98011i	0.303419	+	0.305261i
$171$	−13.0845	−	16.6299i	−1.00059	−	1.27172i
$172$	11.3974	+	0.0689914i	0.869041	+	0.00526055i
$173$	2.11267	+	2.51778i	0.160623	+	0.191423i	0.840353	−	0.542039i	$-0.182348\pi$
$173$	2.11267	+	2.51778i	0.160623	+	0.191423i	−0.679730	+	0.733462i	$0.737903\pi$
$174$	−8.21508	−	0.874383i	−0.622784	−	0.0662868i
$175$	3.00724	−	17.0549i	0.227326	−	1.28923i
$176$	11.8877	−	13.8238i	0.896068	−	1.04201i
$177$	−8.05640	+	1.29013i	−0.605556	+	0.0969720i
$178$	4.98268	+	3.51144i	0.373468	+	0.263193i
$179$	7.43771	+	4.29416i	0.555920	+	0.320961i	0.751506	−	0.659726i	$-0.229328\pi$
$179$	7.43771	+	4.29416i	0.555920	+	0.320961i	−0.195586	+	0.980687i	$0.562661\pi$
$180$	−4.51913	+	1.45520i	−0.336836	+	0.108464i
$181$	10.0107	−	5.77968i	0.744089	−	0.429600i	−0.0794649	−	0.996838i	$-0.525321\pi$
$181$	10.0107	−	5.77968i	0.744089	−	0.429600i	0.823554	+	0.567237i	$0.191988\pi$
$182$	18.7870	+	1.70096i	1.39259	+	0.126084i
$183$	8.29991	−	4.61928i	0.613547	−	0.341467i
$184$	−1.01836	−	12.9981i	−0.0750743	−	0.958236i
$185$	3.06028	−	1.11385i	0.224996	−	0.0818918i
$186$	19.5401	−	1.34051i	1.43275	−	0.0982912i
$187$	−22.5108	+	3.96925i	−1.64615	+	0.290261i
$188$	−13.6476	+	7.76967i	−0.995352	+	0.566661i
$189$	−16.3672	+	12.4656i	−1.19054	+	0.906741i
$190$	2.01977	+	7.63018i	0.146530	+	0.553552i
$191$	4.01620	+	22.7770i	0.290602	+	1.64809i	0.684558	+	0.728958i	$0.259995\pi$
$191$	4.01620	+	22.7770i	0.290602	+	1.64809i	−0.393956	+	0.919129i	$0.628894\pi$
$192$	4.29508	+	13.1739i	0.309971	+	0.950746i
$193$	2.47922	−	0.902363i	0.178458	−	0.0649535i	−0.251246	−	0.967923i	$-0.580840\pi$
$193$	2.47922	−	0.902363i	0.178458	−	0.0649535i	0.429704	+	0.902970i	$0.358618\pi$
$194$	−3.92770	+	8.35685i	−0.281992	+	0.599987i
$195$	4.61657	+	0.0726898i	0.330599	+	0.00520542i
$196$	17.1081	−	2.90995i	1.22201	−	0.207853i
$197$	13.8978	−	8.02392i	0.990180	−	0.571680i	0.0848516	−	0.996394i	$-0.472958\pi$
$197$	13.8978	−	8.02392i	0.990180	−	0.571680i	0.905328	+	0.424713i	$0.139625\pi$
$198$	5.64670	−	18.4954i	0.401294	−	1.31441i
$199$	9.62310	−	16.6677i	0.682164	−	1.18154i	−0.292156	−	0.956371i	$-0.594373\pi$
$199$	9.62310	−	16.6677i	0.682164	−	1.18154i	0.974319	−	0.225171i	$-0.0722941\pi$
$200$	−12.3138	−	1.19008i	−0.870720	−	0.0841512i
$201$	5.94631	+	7.31748i	0.419421	+	0.516135i
$202$	−0.577202	−	6.83567i	−0.0406118	−	0.480956i
$203$	13.1512	+	2.31890i	0.923030	+	0.162755i
$204$	6.29595	−	16.1909i	0.440805	−	1.13359i
$205$	0.975402	+	1.16244i	0.0681250	+	0.0811883i
$206$	−5.15596	−	1.39827i	−0.359233	−	0.0974223i
$207$	−6.53396	−	12.1879i	−0.454142	−	0.847118i
$208$	0.163136	−	13.4745i	0.0113114	−	0.934291i
$209$	−30.2110	−	10.9959i	−2.08974	−	0.760603i
$210$	7.44867	−	1.84674i	0.514007	−	0.127437i
$211$	13.9505	−	16.6256i	0.960392	−	1.14455i	−0.0290432	−	0.999578i	$-0.509246\pi$
$211$	13.9505	−	16.6256i	0.960392	−	1.14455i	0.989436	−	0.144973i	$-0.0463095\pi$
$212$	−2.98008	−	2.53148i	−0.204673	−	0.173863i
$213$	18.2173	−	6.30756i	1.24823	−	0.432187i
$214$	−3.82595	−	8.27004i	−0.261537	−	0.565328i
$215$	−4.50930			−0.307532
$216$	9.79093	+	10.9607i	0.666188	+	0.745784i
$217$	−31.6593			−2.14917
$218$	1.10758	+	2.39410i	0.0750146	+	0.162149i
$219$	−0.865877	+	4.49556i	−0.0585106	+	0.303782i
$220$	−4.67001	+	5.49758i	−0.314852	+	0.370647i
$221$	−10.8595	+	12.9419i	−0.730492	+	0.870566i
$222$	−6.99362	−	7.26122i	−0.469381	−	0.487341i
$223$	−5.73818	−	2.08853i	−0.384257	−	0.139858i	0.142666	−	0.989771i	$-0.454432\pi$
$223$	−5.73818	−	2.08853i	−0.384257	−	0.139858i	−0.526924	+	0.849913i	$0.676655\pi$
$224$	−5.46892	−	21.7198i	−0.365408	−	1.45122i
$225$	−12.4655	+	4.09745i	−0.831034	+	0.273163i
$226$	−7.19246	−	1.95057i	−0.478436	−	0.129750i
$227$	18.6090	+	22.1773i	1.23512	+	1.47196i	0.830063	+	0.557670i	$0.188305\pi$
$227$	18.6090	+	22.1773i	1.23512	+	1.47196i	0.405059	+	0.914291i	$0.367251\pi$
$228$	19.0552	−	15.2940i	1.26196	−	1.01287i
$229$	12.6630	+	2.23282i	0.836791	+	0.147549i	0.575593	−	0.817736i	$-0.304771\pi$
$229$	12.6630	+	2.23282i	0.836791	+	0.147549i	0.261198	+	0.965285i	$0.415882\pi$
$230$	0.434021	+	5.14001i	0.0286185	+	0.338922i
$231$	−11.1522	+	29.2016i	−0.733762	+	1.92132i
$232$	0.917677	−	9.49529i	0.0602485	−	0.623397i
$233$	13.9217	−	24.1131i	0.912041	−	1.57970i	0.100865	−	0.994900i	$-0.467839\pi$
$233$	13.9217	−	24.1131i	0.912041	−	1.57970i	0.811176	−	0.584802i	$-0.198828\pi$
$234$	−5.58985	−	13.1545i	−0.365420	−	0.859939i
$235$	5.38078	−	3.10659i	0.351003	−	0.202652i
$236$	−1.57979	−	9.28786i	−0.102836	−	0.604588i
$237$	−0.769795	+	1.28613i	−0.0500036	+	0.0835430i
$238$	−11.9443	+	25.4135i	−0.774232	+	1.64731i
$239$	3.89187	−	1.41652i	0.251744	−	0.0916273i	−0.213066	−	0.977038i	$-0.568345\pi$
$239$	3.89187	−	1.41652i	0.251744	−	0.0916273i	0.464810	+	0.885411i	$0.346123\pi$
$240$	−1.73081	−	5.20171i	−0.111723	−	0.335769i
$241$	−3.28233	−	18.6150i	−0.211434	−	1.19910i	−0.886989	−	0.461791i	$-0.847207\pi$
$241$	−3.28233	−	18.6150i	−0.211434	−	1.19910i	0.675555	−	0.737309i	$-0.263904\pi$
$242$	−3.53780	−	13.3649i	−0.227419	−	0.859131i
$243$	14.1837	+	6.46699i	0.909886	+	0.414858i
$244$	5.42651	+	9.53177i	0.347397	+	0.610209i
$245$	−6.76149	+	1.19223i	−0.431976	+	0.0761690i
$246$	2.06480	−	4.21935i	0.131647	−	0.269016i
$247$	−22.3291	+	8.12712i	−1.42076	+	0.517116i
$248$	1.76647	+	22.5469i	0.112171	+	1.43173i
$249$	0.0738784	+	0.0442189i	0.00468185	+	0.00280226i
$250$	10.4469	+	0.945857i	0.660722	+	0.0598212i
$251$	2.74444	−	1.58450i	0.173228	−	0.100013i	−0.410879	−	0.911690i	$-0.634778\pi$
$251$	2.74444	−	1.58450i	0.173228	−	0.100013i	0.584107	+	0.811677i	$0.301445\pi$
$252$	−14.5765	−	18.7588i	−0.918236	−	1.18169i
$253$	−18.1960	−	10.5055i	−1.14397	−	0.660473i
$254$	−20.3517	−	14.3424i	−1.27698	−	0.899921i
$255$	−2.45209	+	6.42069i	−0.153556	+	0.402079i
$256$	−15.1632	+	5.10671i	−0.947698	+	0.319170i
$257$	−0.803738	+	4.55822i	−0.0501358	+	0.284334i	−0.999560	−	0.0296622i	$-0.990557\pi$
$257$	−0.803738	+	4.55822i	−0.0501358	+	0.284334i	0.949424	+	0.313996i	$0.101668\pi$
$258$	5.66088	+	12.7598i	0.352431	+	0.794388i
$259$	10.4748	+	12.4834i	0.650872	+	0.775679i
$260$	−0.0322719	+	5.33131i	−0.00200142	+	0.330634i
$261$	−3.15957	−	9.61224i	−0.195573	−	0.594983i
$262$	10.4561	+	10.5196i	0.645978	+	0.649900i
$263$	16.1355	+	5.87284i	0.994957	+	0.362135i	0.787638	−	0.616139i	$-0.211304\pi$
$263$	16.1355	+	5.87284i	0.994957	+	0.362135i	0.207319	+	0.978273i	$0.433526\pi$
$264$	21.4189	+	6.31298i	1.31824	+	0.388537i
$265$	1.18507	+	0.994391i	0.0727982	+	0.0610850i
$266$	−32.4210	+	22.5555i	−1.98786	+	1.38297i
$267$	−1.41199	+	7.33091i	−0.0864121	+	0.448645i
$268$	−8.38256	+	6.94777i	−0.512046	+	0.424403i
$269$			2.41197i			0.147060i	0.997293	+	0.0735302i	$0.0234265\pi$
$269$			2.41197i			0.147060i	−0.997293	+	0.0735302i	$0.976573\pi$
$270$	−3.89983	−	4.31294i	−0.237336	−	0.262477i
$271$	17.5762			1.06768			0.533839	−	0.845586i	$-0.320749\pi$
$271$	17.5762			1.06768			0.533839	+	0.845586i	$0.320749\pi$
$272$	18.7652	+	7.08842i	1.13781	+	0.429798i
$273$	7.55906	+	21.8318i	0.457495	+	1.32132i
$274$	5.52082	+	7.93556i	0.333525	+	0.479404i
$275$	−12.8149	+	15.2722i	−0.772767	+	0.920948i
$276$	13.9996	−	7.68079i	0.842677	−	0.462329i
$277$	−5.51804	+	15.1607i	−0.331547	+	0.910917i	0.656163	+	0.754619i	$0.272178\pi$
$277$	−5.51804	+	15.1607i	−0.331547	+	0.910917i	−0.987710	+	0.156298i	$0.950044\pi$
$278$	−11.4849	−	11.5546i	−0.688817	−	0.693000i
$279$	11.3340	+	21.1415i	0.678548	+	1.26571i
$280$	2.21568	+	8.57991i	0.132412	+	0.512748i
$281$	−7.03652	+	5.90434i	−0.419764	+	0.352223i	−0.828073	−	0.560620i	$-0.810563\pi$
$281$	−7.03652	+	5.90434i	−0.419764	+	0.352223i	0.408310	+	0.912843i	$0.366118\pi$
$282$	−15.5455	−	11.3258i	−0.925721	−	0.674441i
$283$	0.0113336	+	0.00199842i	0.000673713	+	0.000118794i	0.173985	−	0.984748i	$-0.444336\pi$
$283$	0.0113336	+	0.00199842i	0.000673713	+	0.000118794i	−0.173311	+	0.984867i	$0.555447\pi$
$284$	7.48686	+	20.9639i	0.444263	+	1.24398i
$285$	−7.50218	+	6.09640i	−0.444390	+	0.361120i
$286$	−17.7510	−	12.5096i	−1.04964	−	0.739708i
$287$	−3.79655	+	6.57582i	−0.224103	+	0.388159i
$288$	−12.5462	+	11.4277i	−0.739293	+	0.673384i
$289$	−4.07438	−	7.05704i	−0.239670	−	0.415120i
$290$	−0.340320	+	3.75882i	−0.0199843	+	0.220725i
$291$	−11.3077	−	0.178044i	−0.662869	−	0.0104371i
$292$	−5.20047	−	0.949477i	−0.304335	−	0.0555639i
$293$	5.21237	+	14.3209i	0.304510	+	0.836634i	0.993702	+	0.112055i	$0.0357434\pi$
$293$	5.21237	+	14.3209i	0.304510	+	0.836634i	−0.689192	+	0.724579i	$0.742034\pi$
$294$	11.8618	+	17.6360i	0.691797	+	1.02855i
$295$	0.647256	+	3.67077i	0.0376847	+	0.213720i
$296$	8.30588	−	8.15640i	0.482770	−	0.474081i
$297$	23.4927	−	3.00690i	1.36319	−	0.174478i
$298$	14.8744	−	3.93738i	0.861654	−	0.228087i
$299$	−15.2933	+	2.69663i	−0.884437	+	0.155950i
$300$	−4.87059	−	14.3474i	−0.281204	−	0.828347i
$301$	−7.71728	−	21.2031i	−0.444817	−	1.22212i
$302$	10.7514	−	22.8754i	0.618673	−	1.31633i
$303$	7.34136	−	4.08580i	0.421750	−	0.234723i
$304$	17.8724	+	21.8309i	1.02505	+	1.25209i
$305$	−2.16971	−	3.75806i	−0.124237	−	0.215186i
$306$	21.2466	−	1.12184i	1.21459	−	0.0641310i
$307$	−13.5691	−	7.83415i	−0.774432	−	0.447119i	0.0600213	−	0.998197i	$-0.480883\pi$
$307$	−13.5691	−	7.83415i	−0.774432	−	0.447119i	−0.834453	+	0.551079i	$0.814216\pi$
$308$	−33.8423	−	12.5501i	−1.92835	−	0.715109i
$309$	−1.03457	−	6.46052i	−0.0588545	−	0.367526i
$310$	−0.752865	−	8.91601i	−0.0427598	−	0.506395i
$311$	5.64104	−	31.9919i	0.319874	−	1.81410i	−0.223612	−	0.974678i	$-0.571785\pi$
$311$	5.64104	−	31.9919i	0.319874	−	1.81410i	0.543486	−	0.839418i	$-0.317104\pi$
$312$	15.1263	−	6.60150i	0.856357	−	0.373736i
$313$	9.73885	−	8.17186i	0.550472	−	0.461901i	−0.324629	−	0.945842i	$-0.605239\pi$
$313$	9.73885	−	8.17186i	0.550472	−	0.461901i	0.875101	+	0.483941i	$0.160795\pi$
$314$	−2.93435	+	10.8200i	−0.165595	+	0.610610i
$315$	5.81184	+	7.38663i	0.327460	+	0.416189i
$316$	−1.49364	−	0.874449i	−0.0840237	−	0.0491916i
$317$	6.57901	−	18.0757i	0.369514	−	1.01523i	−0.606033	−	0.795440i	$-0.707240\pi$
$317$	6.57901	−	18.0757i	0.369514	−	1.01523i	0.975547	−	0.219792i	$-0.0705379\pi$
$318$	1.32607	−	4.60167i	0.0743624	−	0.258049i
$319$	−11.7765	−	9.88166i	−0.659358	−	0.553267i
$320$	5.98677	−	2.05668i	0.334670	−	0.114972i
$321$	7.30726	−	8.43511i	0.407851	−	0.470802i
$322$	−23.4259	+	10.8375i	−1.30548	+	0.603949i
$323$		−	35.3718i		−	1.96814i
$324$	−7.30837	+	16.4495i	−0.406021	+	0.913864i
$325$			14.7351i			0.817356i
$326$	−9.65553	−	20.8710i	−0.534771	−	1.15594i
$327$	−2.11538	+	2.44189i	−0.116981	+	0.135037i
$328$	4.89496	+	2.33690i	0.270279	+	0.129034i
$329$	23.8162	+	19.9841i	1.31303	+	1.10176i
$330$	−8.48906	−	2.44631i	−0.467308	−	0.134665i
$331$	1.10235	−	3.02867i	0.0605905	−	0.166471i	−0.905704	−	0.423911i	$-0.860657\pi$
$331$	1.10235	−	3.02867i	0.0605905	−	0.166471i	0.966294	+	0.257440i	$0.0828791\pi$
$332$	−0.0502305	+	0.0857982i	−0.00275676	+	0.00470879i
$333$	4.58619	−	11.4639i	0.251322	−	0.628217i
$334$	16.4794	+	4.46913i	0.901711	+	0.244540i
$335$	3.29975	−	2.76882i	0.180285	−	0.151277i
$336$	21.4967	−	17.0407i	1.17274	−	0.929644i
$337$	−5.11170	+	28.9899i	−0.278452	+	1.57918i	0.449326	+	0.893368i	$0.351664\pi$
$337$	−5.11170	+	28.9899i	−0.278452	+	1.57918i	−0.727778	+	0.685813i	$0.759447\pi$
$338$	2.32609	−	0.196415i	0.126523	−	0.0106835i
$339$	−1.44320	−	9.01230i	−0.0783840	−	0.489481i
$340$	−7.44106	−	2.75945i	−0.403548	−	0.149652i
$341$	31.5633	+	18.2231i	1.70925	+	0.986835i
$342$	26.6688	+	13.5753i	1.44208	+	0.734066i
$343$	−3.31975	−	5.74998i	−0.179250	−	0.310470i
$344$	−14.6697	+	6.67910i	−0.790936	+	0.360113i
$345$	−5.52026	+	3.07228i	−0.297201	+	0.165406i
$346$	−4.20668	−	1.97713i	−0.226152	−	0.106291i
$347$	−0.677943	−	1.86263i	−0.0363939	−	0.0999914i	0.920165	−	0.391531i	$-0.128055\pi$
$347$	−0.677943	−	1.86263i	−0.0363939	−	0.0999914i	−0.956559	+	0.291540i	$0.905832\pi$
$348$	11.0634	−	3.75575i	0.593060	−	0.201329i
$349$	−31.3630	+	5.53015i	−1.67882	+	0.296022i	−0.930222	−	0.366997i	$-0.880386\pi$
$349$	−31.3630	+	5.53015i	−1.67882	+	0.296022i	−0.748603	+	0.663019i	$0.769275\pi$
$350$	6.26720	+	23.6759i	0.334996	+	1.26553i
$351$	11.8727	−	12.8635i	0.633719	−	0.686605i
$352$	−7.04959	+	24.8019i	−0.375744	+	1.32194i
$353$	6.25698	+	35.4851i	0.333025	+	1.88868i	0.445917	+	0.895074i	$0.352878\pi$
$353$	6.25698	+	35.4851i	0.333025	+	1.88868i	−0.112892	+	0.993607i	$0.536011\pi$
$354$	9.57446	−	6.43972i	0.508877	−	0.342267i
$355$	−3.01223	−	8.27603i	−0.159872	−	0.439246i
$356$	−8.48041	−	1.54831i	−0.449461	−	0.0820604i
$357$	−34.3871	−	0.541439i	−1.81996	−	0.0286560i
$358$	−12.0962	−	1.09519i	−0.639307	−	0.0578823i
$359$	8.08048	+	13.9958i	0.426472	+	0.738670i	0.996557	−	0.0829153i	$-0.0264231\pi$
$359$	8.08048	+	13.9958i	0.426472	+	0.738670i	−0.570085	+	0.821586i	$0.693090\pi$
$360$	4.93629	−	4.55119i	0.260165	−	0.239869i
$361$	15.3753	−	26.6308i	0.809228	−	1.40162i
$362$	−9.41697	+	13.3626i	−0.494945	+	0.702321i
$363$	13.1407	−	10.6784i	0.689709	−	0.560470i
$364$	−25.1234	+	8.97234i	−1.31683	+	0.470278i
$365$	2.05973	+	0.363187i	0.107811	+	0.0190101i
$366$	−7.91018	+	10.8573i	−0.413472	+	0.567521i
$367$	−15.7119	+	13.1839i	−0.820156	+	0.688193i	−0.953009	−	0.302943i	$-0.902031\pi$
$367$	−15.7119	+	13.1839i	−0.820156	+	0.688193i	0.132853	+	0.991136i	$0.457586\pi$
$368$	9.02526	+	16.0786i	0.470474	+	0.838157i
$369$	5.75036	+	0.181129i	0.299352	+	0.00942918i
$370$	−3.26652	+	3.24681i	−0.169818	+	0.168793i
$371$	−2.64755	+	7.27409i	−0.137454	+	0.377652i
$372$	−24.2841	+	13.3233i	−1.25907	+	0.690782i
$373$	−16.8068	+	20.0295i	−0.870221	+	1.03709i	0.128748	+	0.991677i	$0.458904\pi$
$373$	−16.8068	+	20.0295i	−0.870221	+	1.03709i	−0.998968	+	0.0454111i	$0.985540\pi$
$374$	26.5360	−	18.4613i	1.37214	−	0.954610i
$375$	4.20338	+	12.1401i	0.217062	+	0.626910i
$376$	12.9033	−	18.0763i	0.665438	−	0.932214i
$377$	−11.3623			−0.585190
$378$	13.6055	−	25.7185i	0.699793	−	1.32282i
$379$		−	6.99042i		−	0.359074i	−0.983751	−	0.179537i	$-0.942540\pi$
$379$		−	6.99042i		−	0.359074i	0.983751	−	0.179537i	$-0.0574599\pi$
$380$	−7.12314	−	8.59414i	−0.365409	−	0.440870i
$381$	5.76722	−	29.9429i	0.295464	−	1.53402i
$382$	−18.6796	−	26.8499i	−0.955733	−	1.37376i
$383$	−7.84570	−	6.58332i	−0.400896	−	0.336392i	0.419944	−	0.907550i	$-0.362050\pi$
$383$	−7.84570	−	6.58332i	−0.400896	−	0.336392i	−0.820840	+	0.571158i	$0.806494\pi$
$384$	−13.3354	−	14.3586i	−0.680517	−	0.732732i
$385$	13.4191	+	4.88415i	0.683900	+	0.248919i
$386$	−2.64631	+	2.63034i	−0.134693	+	0.133881i
$387$	−11.3962	+	12.7441i	−0.579302	+	0.647819i
$388$	0.0790459	−	13.0584i	0.00401295	−	0.662939i
$389$	7.20890	+	8.59123i	0.365506	+	0.435593i	0.917184	−	0.398464i	$-0.130457\pi$
$389$	7.20890	+	8.59123i	0.365506	+	0.435593i	−0.551678	+	0.834057i	$0.686012\pi$
$390$	−5.96860	+	2.64797i	−0.302232	+	0.134085i
$391$	4.01415	−	22.7654i	0.203004	−	1.15130i
$392$	−20.2306	+	13.8936i	−1.02180	+	0.701732i
$393$	−6.48094	+	16.9701i	−0.326920	+	0.856026i
$394$	−13.0736	+	18.5512i	−0.658637	+	0.934597i
$395$	0.593021	+	0.342381i	0.0298381	+	0.0172271i
$396$	3.73479	+	27.0922i	0.187680	+	1.36143i
$397$	3.99340	−	2.30559i	0.200423	−	0.115714i	−0.396430	−	0.918065i	$-0.629751\pi$
$397$	3.99340	−	2.30559i	0.200423	−	0.115714i	0.596853	+	0.802351i	$0.296418\pi$
$398$	−2.45428	+	27.1074i	−0.123022	+	1.35877i
$399$	−41.5050	−	24.8423i	−2.07785	−	1.24367i
$400$	16.5117	−	5.78436i	0.825583	−	0.289218i
$401$	14.3732	−	5.23142i	0.717764	−	0.261245i	0.0427879	−	0.999084i	$-0.486376\pi$
$401$	14.3732	−	5.23142i	0.717764	−	0.261245i	0.674976	+	0.737839i	$0.264154\pi$
$402$	−11.9772	−	5.86123i	−0.597370	−	0.292332i
$403$	26.5282	−	4.67764i	1.32147	−	0.233010i
$404$	4.79981	+	8.43096i	0.238799	+	0.419456i
$405$	2.85201	−	6.52543i	0.141718	−	0.324251i
$406$	−18.2567	+	4.83268i	−0.906062	+	0.239842i
$407$	−3.25761	−	18.4748i	−0.161474	−	0.915762i
$408$	1.53307	+	24.5198i	0.0758983	+	1.21391i
$409$	0.943481	−	0.343399i	0.0466521	−	0.0169800i	−0.318589	−	0.947893i	$-0.603209\pi$
$409$	0.943481	−	0.343399i	0.0466521	−	0.0169800i	0.365241	+	0.930913i	$0.380987\pi$
$410$	−1.94219	−	0.912824i	−0.0959179	−	0.0450812i
$411$	−6.08055	+	10.1590i	−0.299931	+	0.501107i
$412$	7.44803	−	1.26685i	0.366938	−	0.0624133i
$413$	−16.1525	+	9.32565i	−0.794812	+	0.458885i
$414$	15.6235	+	11.7636i	0.767853	+	0.578147i
$415$	0.0196672	−	0.0340646i	0.000965425	−	0.00167217i
$416$	7.79166	+	17.3916i	0.382018	+	0.852695i
$417$	7.11862	−	18.6398i	0.348601	−	0.912796i
$418$	45.3056	−	3.82559i	2.21597	−	0.187116i
$419$	−23.6393	−	4.16825i	−1.15486	−	0.203633i	−0.436762	−	0.899577i	$-0.643875\pi$
$419$	−23.6393	−	4.16825i	−1.15486	−	0.203633i	−0.718096	+	0.695944i	$0.754986\pi$
$420$	−8.46391	+	6.79327i	−0.412996	+	0.331478i
$421$	4.34097	+	5.17337i	0.211566	+	0.252135i	0.861383	−	0.507956i	$-0.169599\pi$
$421$	4.34097	+	5.17337i	0.211566	+	0.252135i	−0.649817	+	0.760091i	$0.725154\pi$
$422$	−8.03359	+	29.6229i	−0.391069	+	1.44202i
$423$	4.81886	−	23.0583i	0.234301	−	1.12113i
$424$	5.32814	+	1.47965i	0.258758	+	0.0718582i
$425$	−20.6116	−	7.50201i	−0.999809	−	0.363901i
$426$	−19.6368	+	18.9131i	−0.951406	+	0.916343i
$427$	13.9574	−	16.6337i	0.675444	−	0.804963i
$428$	9.82134	+	8.34291i	0.474732	+	0.403270i
$429$	5.03024	−	26.1166i	0.242862	−	1.26092i
$430$	5.78776	−	2.67758i	0.279111	−	0.129124i
$431$	−29.2021			−1.40662			−0.703309	−	0.710884i	$-0.748295\pi$
$431$	−29.2021			−1.40662			−0.703309	+	0.710884i	$0.748295\pi$
$432$	−19.0752	−	8.25452i	−0.917756	−	0.397146i
$433$	−11.3701			−0.546412			−0.273206	−	0.961956i	$-0.588084\pi$
$433$	−11.3701			−0.546412			−0.273206	+	0.961956i	$0.588084\pi$
$434$	40.6352	−	18.7990i	1.95055	−	0.902381i
$435$	−4.36801	+	1.51238i	−0.209430	+	0.0725131i
$436$	−2.84319	−	2.41520i	−0.136164	−	0.115667i
$437$	20.8993	−	24.9068i	0.999750	−	1.19146i
$438$	−1.55805	−	6.28427i	−0.0744467	−	0.300274i
$439$	−8.53681	−	3.10714i	−0.407440	−	0.148296i	0.130166	−	0.991492i	$-0.458449\pi$
$439$	−8.53681	−	3.10714i	−0.407440	−	0.148296i	−0.537606	+	0.843196i	$0.680671\pi$
$440$	2.72963	−	9.82924i	0.130130	−	0.468591i
$441$	−13.7186	+	22.1223i	−0.653268	+	1.05344i
$442$	6.25361	−	23.0594i	0.297454	−	1.09682i
$443$	−17.5098	−	20.8674i	−0.831917	−	0.991440i	−0.999984	−	0.00566416i	$-0.998197\pi$
$443$	−17.5098	−	20.8674i	−0.831917	−	0.991440i	0.168067	−	0.985776i	$-0.446247\pi$
$444$	13.2881	+	5.16715i	0.630623	+	0.245222i
$445$	3.35881	+	0.592249i	0.159223	+	0.0280753i
$446$	8.60520	−	0.726620i	0.407468	−	0.0344065i
$447$	11.8845	+	14.6249i	0.562116	+	0.691734i
$448$	19.9165	+	24.6304i	0.940966	+	1.16368i
$449$	3.83919	−	6.64967i	0.181183	−	0.313818i	−0.761101	−	0.648633i	$-0.775341\pi$
$449$	3.83919	−	6.64967i	0.181183	−	0.313818i	0.942284	+	0.334816i	$0.108674\pi$
$450$	13.5666	−	12.6610i	0.639538	−	0.596847i
$451$	7.57008	−	4.37059i	0.356461	−	0.205803i
$452$	10.3899	−	1.76724i	0.488698	−	0.0831237i
$453$	30.9528	+	0.487366i	1.45429	+	0.0228984i
$454$	−37.0536	−	17.4151i	−1.73901	−	0.817331i
$455$	9.91809	−	3.60989i	0.464967	−	0.169234i
$456$	−15.3762	+	30.9449i	−0.720057	+	1.44913i
$457$	2.12889	+	12.0735i	0.0995853	+	0.564776i	0.993245	+	0.116032i	$0.0370175\pi$
$457$	2.12889	+	12.0735i	0.0995853	+	0.564776i	−0.893660	+	0.448744i	$0.851871\pi$
$458$	−17.5789	+	4.65328i	−0.821409	+	0.217434i
$459$	11.9490	+	23.1568i	0.557729	+	1.08087i
$460$	−3.60916	−	6.33957i	−0.168278	−	0.295584i
$461$	−16.2573	+	2.86660i	−0.757177	+	0.133511i	−0.538893	−	0.842374i	$-0.681157\pi$
$461$	−16.2573	+	2.86660i	−0.757177	+	0.133511i	−0.218285	+	0.975885i	$0.570046\pi$
$462$	−3.02559	−	44.1028i	−0.140763	−	2.05185i
$463$	37.1376	−	13.5170i	1.72593	−	0.628187i	0.727601	−	0.686001i	$-0.240635\pi$
$463$	37.1376	−	13.5170i	1.72593	−	0.628187i	0.998327	+	0.0578141i	$0.0184131\pi$
$464$	4.46036	+	12.7323i	0.207067	+	0.591081i
$465$	9.57559	−	5.32925i	0.444058	−	0.247138i
$466$	−3.55060	+	39.2161i	−0.164478	+	1.81665i
$467$	−4.76538	+	2.75129i	−0.220516	+	0.127315i	−0.606189	−	0.795321i	$-0.707302\pi$
$467$	−4.76538	+	2.75129i	−0.220516	+	0.127315i	0.385673	+	0.922635i	$0.373969\pi$
$468$	14.9857	+	13.5649i	0.692714	+	0.627036i
$469$	18.6664	+	10.7771i	0.861935	+	0.497638i
$470$	−5.06165	+	7.18242i	−0.233476	+	0.331300i
$471$	−13.5577	+	2.17109i	−0.624707	+	0.100039i
$472$	7.54273	+	10.9830i	0.347182	+	0.505536i
$473$	−4.51059	+	25.5808i	−0.207397	+	1.17621i
$474$	0.224353	−	2.10786i	0.0103049	−	0.0968173i
$475$	−19.8305	−	23.6331i	−0.909887	−	1.08436i
$476$	0.240381	−	39.7110i	0.0110179	−	1.82015i
$477$	5.80532	−	0.836130i	0.265807	−	0.0382838i
$478$	−4.15415	+	4.12908i	−0.190007	+	0.188860i
$479$	−15.7910	−	5.74745i	−0.721508	−	0.262608i	−0.0449423	−	0.998990i	$-0.514310\pi$
$479$	−15.7910	−	5.74745i	−0.721508	−	0.262608i	−0.676566	+	0.736382i	$0.736533\pi$
$480$	5.31025	+	5.64874i	0.242379	+	0.257828i
$481$	−10.6215	−	8.91253i	−0.484301	−	0.406377i
$482$	15.2664	+	21.9437i	0.695363	+	0.999507i
$483$	−23.8935	−	20.6987i	−1.08719	−	0.941824i
$484$	12.4768	+	15.0534i	0.567127	+	0.684245i
$485$			5.16647i			0.234597i
$486$	−22.0451	+	0.121674i	−0.999985	+	0.00551925i
$487$	−6.70956			−0.304039			−0.152020	−	0.988377i	$-0.548578\pi$
$487$	−6.70956			−0.304039			−0.152020	+	0.988377i	$0.548578\pi$
$488$	−12.6249	−	9.01197i	−0.571502	−	0.407953i
$489$	18.4413	−	21.2876i	0.833944	−	0.962661i
$490$	7.97054	−	5.54516i	0.360072	−	0.250505i
$491$	19.8688	−	23.6787i	0.896667	−	1.06861i	−0.100615	−	0.994925i	$-0.532081\pi$
$491$	19.8688	−	23.6787i	0.896667	−	1.06861i	0.997282	−	0.0736810i	$-0.0234747\pi$
$492$	−0.144793	+	6.64166i	−0.00652779	+	0.299429i
$493$	5.78485	−	15.8938i	0.260537	−	0.715819i
$494$	23.8339	−	23.6901i	1.07234	−	1.06587i
$495$	−1.54247	−	10.7095i	−0.0693290	−	0.481357i
$496$	−15.6555	−	27.8904i	−0.702951	−	1.25232i
$497$	33.7593	−	28.3274i	1.51431	−	1.27066i
$498$	−0.121081	−	0.0128874i	−0.00542576	−	0.000577499i
$499$	−13.9388	−	2.45779i	−0.623986	−	0.110026i	−0.147289	−	0.989093i	$-0.547055\pi$
$499$	−13.9388	−	2.45779i	−0.623986	−	0.110026i	−0.476697	+	0.879068i	$0.658166\pi$
$500$	−13.9704	+	4.98926i	−0.624777	+	0.223127i
$501$	3.30666	+	20.6490i	0.147731	+	0.922528i
$502$	−2.58167	+	3.66336i	−0.115226	+	0.163504i
$503$	9.87132	−	17.0976i	0.440140	−	0.762346i	−0.557559	−	0.830137i	$-0.688262\pi$
$503$	9.87132	−	17.0976i	0.440140	−	0.762346i	0.997699	+	0.0677917i	$0.0215953\pi$
$504$	29.8480	+	15.4218i	1.32954	+	0.686942i
$505$	−1.91914	−	3.32404i	−0.0854004	−	0.147918i
$506$	29.5929	+	2.67932i	1.31557	+	0.119110i
$507$	1.39035	+	2.49817i	0.0617475	+	0.110948i
$508$	34.6380	+	6.32404i	1.53681	+	0.280584i
$509$	11.0783	+	30.4374i	0.491037	+	1.34911i	0.899733	+	0.436442i	$0.143761\pi$
$509$	11.0783	+	30.4374i	0.491037	+	1.34911i	−0.408696	+	0.912671i	$0.634016\pi$
$510$	−0.665250	−	9.69708i	−0.0294577	−	0.429394i
$511$	1.81733	+	10.3066i	0.0803939	+	0.455936i
$512$	16.4298	−	15.5583i	0.726103	−	0.687586i
$513$	−1.73045	+	36.6097i	−0.0764013	+	1.61636i
$514$	−1.67502	−	6.32780i	−0.0738819	−	0.279107i
$515$	−2.94363	+	0.519041i	−0.129712	+	0.0228717i
$516$	−14.8425	−	13.0160i	−0.653403	−	0.572997i
$517$	−12.2411	−	33.6321i	−0.538362	−	1.47914i
$518$	−20.8571	−	9.80278i	−0.916407	−	0.430709i
$519$	0.0896241	−	5.69208i	0.00393406	−	0.249854i
$520$	−3.12426	−	6.86199i	−0.137008	−	0.300918i
$521$	−3.03183	−	5.25129i	−0.132827	−	0.230063i	0.791938	−	0.610601i	$-0.209072\pi$
$521$	−3.03183	−	5.25129i	−0.132827	−	0.230063i	−0.924765	+	0.380538i	$0.875739\pi$
$522$	9.76302	+	10.4613i	0.427316	+	0.457880i
$523$	36.4139	+	21.0236i	1.59227	+	0.919298i	0.992917	+	0.118814i	$0.0379091\pi$
$523$	36.4139	+	21.0236i	1.59227	+	0.919298i	0.599354	+	0.800484i	$0.295424\pi$
$524$	−19.6669	−	7.29330i	−0.859154	−	0.318609i
$525$	−23.2787	+	18.9167i	−1.01597	+	0.825592i
$526$	−24.1974	+	2.04322i	−1.05506	+	0.0890886i
$527$	−6.96306	+	39.4895i	−0.303316	+	1.72019i
$528$	−31.2401	+	4.61552i	−1.35955	+	0.200865i
$529$	−1.34164	+	1.12577i	−0.0583322	+	0.0489465i
$530$	−2.11152	−	0.572634i	−0.0917184	−	0.0248736i
$531$	12.0100	+	7.44775i	0.521192	+	0.323205i
$532$	28.2196	−	48.2016i	1.22348	−	2.08981i
$533$	2.20967	−	6.07101i	0.0957113	−	0.262965i
$534$	−2.54072	−	10.2478i	−0.109948	−	0.443464i
$535$	−3.90559	−	3.27718i	−0.168853	−	0.141685i
$536$	6.63363	−	13.8951i	0.286529	−	0.600175i
$537$	−4.86699	−	14.0567i	−0.210026	−	0.606591i
$538$	−1.43221	−	3.09580i	−0.0617468	−	0.133470i
$539$			39.5498i			1.70353i
$540$	7.56648	+	3.22005i	0.325609	+	0.138569i
$541$		−	10.0195i		−	0.430773i	−0.976529	−	0.215387i	$-0.930899\pi$
$541$		−	10.0195i		−	0.430773i	0.976529	−	0.215387i	$-0.0691012\pi$
$542$	−22.5593	+	10.4366i	−0.969005	+	0.448289i
$543$	−19.6600	−	3.78667i	−0.843693	−	0.162501i
$544$	−28.2945	+	2.04453i	−1.21312	+	0.0876585i
$545$	1.13063	+	0.948714i	0.0484310	+	0.0406384i
$546$	−22.6657	−	23.5330i	−0.970002	−	1.00712i
$547$	−3.01183	+	8.27494i	−0.128777	+	0.353811i	−0.987279	−	0.158999i	$-0.949173\pi$
$547$	−3.01183	+	8.27494i	−0.128777	+	0.353811i	0.858502	+	0.512810i	$0.171395\pi$
$548$	−11.7981	−	6.90720i	−0.503990	−	0.295061i
$549$	−16.1044	−	3.36560i	−0.687319	−	0.143640i
$550$	7.37964	−	27.2115i	0.314669	−	1.16030i
$551$	18.2237	−	15.2915i	0.776354	−	0.651438i
$552$	−13.4079	+	18.1712i	−0.570679	+	0.773420i
$553$	−0.594995	+	3.37438i	−0.0253017	+	0.143493i
$554$	−1.91978	−	22.7355i	−0.0815637	−	0.965940i
$555$	−5.26952	−	2.01245i	−0.223679	−	0.0854239i
$556$	21.6020	+	8.01092i	0.916131	+	0.339738i
$557$	−3.90866	−	2.25666i	−0.165615	−	0.0956179i	0.414901	−	0.909866i	$-0.363816\pi$
$557$	−3.90866	−	2.25666i	−0.165615	−	0.0956179i	−0.580517	+	0.814248i	$0.697149\pi$
$558$	−27.1009	−	20.4054i	−1.14727	−	0.863829i
$559$	9.59927	+	16.6264i	0.406006	+	0.703223i
$560$	−7.93854	−	9.69680i	−0.335464	−	0.409765i
$561$	33.9711	+	20.3330i	1.43426	+	0.858459i
$562$	5.52554	−	11.7565i	0.233081	−	0.495919i
$563$	5.14318	+	14.1308i	0.216759	+	0.595541i	0.999646	−	0.0266239i	$-0.00847564\pi$
$563$	5.14318	+	14.1308i	0.216759	+	0.595541i	−0.782886	+	0.622165i	$0.786253\pi$
$564$	26.6781	+	5.30606i	1.12335	+	0.223425i
$565$	−4.10631	+	0.724053i	−0.172754	+	0.0304611i
$566$	−0.0157335	+	0.00416479i	−0.000661329	+	0.000175059i
$567$	35.5640	+	2.24266i	1.49355	+	0.0941829i
$568$	−22.0577	−	22.4619i	−0.925520	−	0.942482i
$569$	4.81063	+	27.2824i	0.201672	+	1.14374i	0.902591	+	0.430499i	$0.141662\pi$
$569$	4.81063	+	27.2824i	0.201672	+	1.14374i	−0.700919	+	0.713241i	$0.747227\pi$
$570$	6.00917	−	12.2795i	0.251697	−	0.514334i
$571$	13.0209	+	35.7745i	0.544906	+	1.49712i	0.840504	+	0.541805i	$0.182259\pi$
$571$	13.0209	+	35.7745i	0.544906	+	1.49712i	−0.295598	+	0.955312i	$0.595519\pi$
$572$	30.2117	+	5.51591i	1.26322	+	0.230632i
$573$	20.5735	−	34.3730i	0.859469	−	1.43595i
$574$	0.968275	−	10.6945i	0.0404150	−	0.446381i
$575$	−10.0810	−	17.4608i	−0.420406	−	0.728164i
$576$	9.31760	−	22.1175i	0.388233	−	0.921561i
$577$	−5.45660	+	9.45110i	−0.227161	+	0.393454i	−0.956966	−	0.290201i	$-0.906278\pi$
$577$	−5.45660	+	9.45110i	−0.227161	+	0.393454i	0.729805	+	0.683656i	$0.239611\pi$
$578$	9.41994	+	6.63849i	0.391818	+	0.276125i
$579$	−4.26900	−	1.63035i	−0.177414	−	0.0677550i
$580$	−1.79514	−	5.02658i	−0.0745393	−	0.208717i
$581$	0.193833	+	0.0341780i	0.00804154	+	0.00141794i
$582$	14.6193	−	6.48588i	0.605991	−	0.268848i
$583$	6.82649	−	5.72810i	0.282724	−	0.237234i
$584$	7.23868	−	1.86932i	0.299539	−	0.0773531i
$585$	−5.96127	−	5.33077i	−0.246468	−	0.220400i
$586$	−15.1938	−	15.2860i	−0.627648	−	0.631459i
$587$	15.6970	−	43.1271i	0.647883	−	1.78004i	0.0224745	−	0.999747i	$-0.492846\pi$
$587$	15.6970	−	43.1271i	0.647883	−	1.78004i	0.625409	−	0.780297i	$-0.284932\pi$
$588$	−25.6969	−	15.5926i	−1.05972	−	0.643028i
$589$	−36.2525	+	43.2041i	−1.49376	+	1.78019i
$590$	−3.01043	−	4.32716i	−0.123937	−	0.178146i
$591$	−27.2940	−	5.25702i	−1.12273	−	0.216245i
$592$	−5.81754	+	15.4008i	−0.239099	+	0.632970i
$593$	−15.2625			−0.626755			−0.313378	−	0.949629i	$-0.601461\pi$
$593$	−15.2625			−0.626755			−0.313378	+	0.949629i	$0.601461\pi$
$594$	−28.3678	+	17.8092i	−1.16395	+	0.730719i
$595$			15.7114i			0.644105i
$596$	−16.7536	+	13.8860i	−0.686254	+	0.568793i
$597$	−31.5006	+	10.9068i	−1.28924	+	0.446386i
$598$	18.0280	−	12.5422i	0.737220	−	0.512889i
$599$	−0.191609	−	0.160779i	−0.00782893	−	0.00656925i	0.638865	−	0.769319i	$-0.279404\pi$
$599$	−0.191609	−	0.160779i	−0.00782893	−	0.00656925i	−0.646694	+	0.762750i	$0.723849\pi$
$600$	14.7708	+	15.5230i	0.603017	+	0.633724i
$601$	40.8905	+	14.8829i	1.66796	+	0.607087i	0.991583	−	0.129472i	$-0.0413282\pi$
$601$	40.8905	+	14.8829i	1.66796	+	0.607087i	0.676374	+	0.736559i	$0.263550\pi$
$602$	22.4954	+	22.6320i	0.916845	+	0.922412i
$603$	0.514160	−	16.3232i	0.0209382	−	0.664734i
$604$	−0.216375	+	35.7450i	−0.00880416	+	1.45445i
$605$	−4.97224	−	5.92569i	−0.202150	−	0.240913i
$606$	−6.99664	+	9.60342i	−0.284219	+	0.390112i
$607$	−4.64267	+	26.3299i	−0.188440	+	1.06870i	0.733015	+	0.680213i	$0.238113\pi$
$607$	−4.64267	+	26.3299i	−0.188440	+	1.06870i	−0.921455	+	0.388485i	$0.872999\pi$
$608$	−35.9025	−	17.4078i	−1.45604	−	0.705980i
$609$	−14.5868	−	17.9504i	−0.591087	−	0.727386i
$610$	5.01636	+	3.53517i	0.203106	+	0.143135i
$611$	−22.9089	−	13.2265i	−0.926794	−	0.535085i
$612$	−26.6042	+	14.0559i	−1.07541	+	0.568178i
$613$	−20.7249	+	11.9655i	−0.837070	+	0.483283i	−0.856267	−	0.516533i	$-0.827222\pi$
$613$	−20.7249	+	11.9655i	−0.837070	+	0.483283i	0.0191971	+	0.999816i	$0.493889\pi$
$614$	22.0681	+	1.99803i	0.890594	+	0.0806337i
$615$	0.0413787	−	2.62799i	0.00166855	−	0.105971i
$616$	50.8893	−	3.98699i	2.05039	−	0.160640i
$617$	7.04370	−	2.56370i	0.283569	−	0.103210i	−0.196320	−	0.980540i	$-0.562899\pi$
$617$	7.04370	−	2.56370i	0.283569	−	0.103210i	0.479889	+	0.877329i	$0.340677\pi$
$618$	5.16408	+	7.67786i	0.207730	+	0.308849i
$619$	14.0173	−	2.47163i	0.563402	−	0.0993430i	0.115309	−	0.993330i	$-0.463214\pi$
$619$	14.0173	−	2.47163i	0.563402	−	0.0993430i	0.448094	+	0.893987i	$0.352103\pi$
$620$	6.26055	+	10.9968i	0.251430	+	0.441642i
$621$	−5.26836	+	23.3657i	−0.211412	+	0.937634i
$622$	11.7561	+	44.4118i	0.471378	+	1.78075i
$623$	2.96352	+	16.8069i	0.118731	+	0.673356i
$624$	−15.4949	+	17.4550i	−0.620293	+	0.698758i
$625$	−15.0354	+	5.47243i	−0.601415	+	0.218897i
$626$	−7.64759	+	16.2715i	−0.305659	+	0.650342i
$627$	27.0800	+	48.6572i	1.08147	+	1.94318i
$628$	−2.65855	−	15.6301i	−0.106088	−	0.623708i
$629$	17.8746	−	10.3199i	0.712708	−	0.411482i
$630$	−11.8457	−	6.02984i	−0.471944	−	0.240235i
$631$	−22.2070	+	38.4637i	−0.884048	+	1.53122i	−0.0372471	+	0.999306i	$0.511859\pi$
$631$	−22.2070	+	38.4637i	−0.884048	+	1.53122i	−0.846801	+	0.531910i	$0.821474\pi$
$632$	2.43635	+	0.235462i	0.0969127	+	0.00936617i
$633$	−37.1180	+	5.94397i	−1.47531	+	0.236251i
$634$	2.28891	+	27.1070i	0.0909041	+	1.07656i
$635$	−13.7190	−	2.41903i	−0.544421	−	0.0959961i
$636$	1.03040	+	6.69373i	0.0408579	+	0.265424i
$637$	18.7896	+	22.3926i	0.744471	+	0.887226i
$638$	20.9830	+	5.69049i	0.830724	+	0.225289i
$639$	−31.0023	−	12.4026i	−1.22643	−	0.490640i
$640$	−6.46287	+	6.19467i	−0.255467	+	0.244866i
$641$	−34.2487	−	12.4655i	−1.35274	−	0.492359i	−0.438941	−	0.898516i	$-0.644646\pi$
$641$	−34.2487	−	12.4655i	−1.35274	−	0.492359i	−0.913803	+	0.406157i	$0.866868\pi$
$642$	−4.37029	+	15.1656i	−0.172482	+	0.598538i
$643$	12.8834	−	15.3538i	0.508072	−	0.605496i	−0.449646	−	0.893207i	$-0.648450\pi$
$643$	12.8834	−	15.3538i	0.508072	−	0.605496i	0.957717	+	0.287711i	$0.0928942\pi$
$644$	23.6323	−	27.8202i	0.931244	−	1.09627i
$645$	5.90329	+	5.11396i	0.232442	+	0.201362i
$646$	21.0035	+	45.4003i	0.826370	+	1.78625i
$647$	24.2273			0.952475			0.476238	−	0.879317i	$-0.342000\pi$
$647$	24.2273			0.952475			0.476238	+	0.879317i	$0.342000\pi$
$648$	−0.387173	−	25.4529i	−0.0152096	−	0.999884i
$649$	21.4713			0.842824
$650$	−8.74956	−	18.9127i	−0.343186	−	0.741818i
$651$	41.4463	+	35.9046i	1.62441	+	1.40721i
$652$	24.7861	+	21.0550i	0.970697	+	0.824576i
$653$	−18.5592	+	22.1180i	−0.726277	+	0.865543i	−0.995225	−	0.0976117i	$-0.968880\pi$
$653$	−18.5592	+	22.1180i	−0.726277	+	0.865543i	0.268948	+	0.963155i	$0.413324\pi$
$654$	1.26516	−	4.39030i	0.0494716	−	0.171674i
$655$	7.79829	+	2.83834i	0.304704	+	0.110903i
$656$	−7.67039	−	0.0928654i	−0.299479	−	0.00362578i
$657$	6.23193	−	4.90331i	0.243131	−	0.191297i
$658$	−42.4348	−	11.5081i	−1.65428	−	0.448634i
$659$	−12.4603	−	14.8496i	−0.485384	−	0.578458i	0.466653	−	0.884440i	$-0.345460\pi$
$659$	−12.4603	−	14.8496i	−0.485384	−	0.578458i	−0.952037	+	0.305982i	$0.901015\pi$
$660$	12.3484	−	1.90085i	0.480662	−	0.0739905i
$661$	0.820430	+	0.144664i	0.0319110	+	0.00562677i	0.189581	−	0.981865i	$-0.439287\pi$
$661$	0.820430	+	0.144664i	0.0319110	+	0.00562677i	−0.157670	+	0.987492i	$0.550398\pi$
$662$	0.383518	+	4.54191i	0.0149058	+	0.176526i
$663$	28.8939	−	4.62698i	1.12215	−	0.179697i
$664$	0.0135255	−	0.139950i	0.000524892	−	0.00543110i
$665$	−11.0491	+	19.1376i	−0.428465	+	0.742123i
$666$	0.920701	+	17.4373i	0.0356765	+	0.675683i
$667$	13.4641	−	7.77352i	0.521333	−	0.300992i
$668$	−23.8053	+	4.04909i	−0.921053	+	0.156664i
$669$	5.14348	+	9.24179i	0.198858	+	0.357308i
$670$	−2.59118	+	5.51318i	−0.100106	+	0.212993i
$671$	−23.4894	+	8.54944i	−0.906798	+	0.330047i
$672$	−17.4727	+	34.6365i	−0.674025	+	1.33613i
$673$	4.69264	+	26.6133i	0.180888	+	1.02587i	0.931126	+	0.364698i	$0.118828\pi$
$673$	4.69264	+	26.6133i	0.180888	+	1.02587i	−0.750238	+	0.661168i	$0.770061\pi$
$674$	−10.6530	−	40.2443i	−0.410337	−	1.55015i
$675$	20.9659	+	8.77291i	0.806979	+	0.337669i
$676$	−2.86895	+	1.63331i	−0.110344	+	0.0628197i
$677$	3.65534	−	0.644536i	0.140486	−	0.0247715i	−0.102963	−	0.994685i	$-0.532832\pi$
$677$	3.65534	−	0.644536i	0.140486	−	0.0247715i	0.243449	+	0.969914i	$0.421721\pi$
$678$	7.20379	+	10.7105i	0.276660	+	0.411333i
$679$	−24.2931	+	8.84197i	−0.932284	+	0.339324i
$680$	11.1893	−	0.876638i	0.429088	−	0.0336175i
$681$	0.789435	−	50.1374i	0.0302512	−	1.92127i
$682$	−51.3327	−	4.64762i	−1.96563	−	0.177967i
$683$	−9.79814	+	5.65696i	−0.374916	+	0.216458i	−0.675604	−	0.737265i	$-0.736117\pi$
$683$	−9.79814	+	5.65696i	−0.374916	+	0.216458i	0.300688	+	0.953722i	$0.402784\pi$
$684$	−42.2907	−	1.58840i	−1.61702	−	0.0607339i
$685$	4.68423	+	2.70444i	0.178975	+	0.103331i
$686$	7.67524	+	5.40895i	0.293042	+	0.206515i
$687$	−14.0453	−	17.2840i	−0.535862	−	0.659426i
$688$	14.8628	−	17.2834i	0.566638	−	0.658925i
$689$	1.14372	−	6.48634i	0.0435722	−	0.247110i
$690$	5.26105	−	7.22119i	0.200285	−	0.274906i
$691$	−19.6465	−	23.4138i	−0.747388	−	0.890703i	0.249592	−	0.968351i	$-0.419703\pi$
$691$	−19.6465	−	23.4138i	−0.747388	−	0.890703i	−0.996981	+	0.0776481i	$0.975259\pi$
$692$	6.57334	+	0.0397902i	0.249881	+	0.00151260i
$693$	47.7171	−	25.5812i	1.81262	−	0.971750i
$694$	1.97616	+	1.98816i	0.0750142	+	0.0754696i
$695$	−8.56559	−	3.11762i	−0.324912	−	0.118258i
$696$	−11.9699	+	11.3899i	−0.453718	+	0.431733i
$697$	7.36719	+	6.18180i	0.279052	+	0.234153i
$698$	36.9712	−	25.7211i	1.39938	−	0.973558i
$699$	−45.5719	+	15.7788i	−1.72369	+	0.596810i
$700$	−22.1026	−	26.6670i	−0.835398	−	1.00792i
$701$		−	17.0117i		−	0.642524i	−0.946990	−	0.321262i	$-0.895893\pi$
$701$		−	17.0117i		−	0.642524i	0.946990	−	0.321262i	$-0.104107\pi$
$702$	−7.60058	+	23.5605i	−0.286865	+	0.889233i
$703$	29.0300			1.09489
$704$	−5.67886	−	36.0196i	−0.214030	−	1.35754i
$705$	−10.5673	−	2.03534i	−0.397989	−	0.0766555i
$706$	−29.1017	−	41.8304i	−1.09526	−	1.57431i
$707$	12.3454	−	14.7127i	0.464298	−	0.553329i
$708$	−8.46512	+	13.9507i	−0.318139	+	0.524299i
$709$	0.200362	−	0.550490i	0.00752475	−	0.0206741i	−0.935873	−	0.352336i	$-0.885387\pi$
$709$	0.200362	−	0.550490i	0.00752475	−	0.0206741i	0.943398	+	0.331662i	$0.107609\pi$
$710$	8.78047	+	8.83378i	0.329525	+	0.331526i
$711$	2.46635	−	0.810698i	0.0924955	−	0.0304036i
$712$	11.8041	−	3.04830i	0.442378	−	0.114240i
$713$	−28.2352	+	23.6921i	−1.05742	+	0.887277i
$714$	44.4578	−	19.7238i	1.66379	−	0.738144i
$715$	−11.9659	−	2.10990i	−0.447498	−	0.0789059i
$716$	16.1760	−	5.77695i	0.604527	−	0.215895i
$717$	−6.70145	−	2.55931i	−0.250270	−	0.0955792i
$718$	−18.6820	−	13.1657i	−0.697206	−	0.491340i
$719$	−20.6296	+	35.7316i	−0.769356	+	1.33256i	0.168557	+	0.985692i	$0.446089\pi$
$719$	−20.6296	+	35.7316i	−0.769356	+	1.33256i	−0.937913	+	0.346872i	$0.887244\pi$
$720$	−3.63335	+	8.77264i	−0.135407	+	0.326937i
$721$	−7.47833	−	12.9529i	−0.278508	−	0.482390i
$722$	−3.92133	+	43.3108i	−0.145937	+	1.61186i
$723$	−16.8141	+	28.0921i	−0.625324	+	1.04476i
$724$	4.15227	−	22.7428i	0.154318	−	0.845229i
$725$	−5.04547	−	13.8623i	−0.187384	−	0.514833i
$726$	−10.5256	+	21.5087i	−0.390642	+	0.798263i
$727$	1.56785	+	8.89170i	0.0581482	+	0.329775i	0.999980	−	0.00630954i	$-0.00200840\pi$
$727$	1.56785	+	8.89170i	0.0581482	+	0.329775i	−0.941832	+	0.336084i	$0.890897\pi$
$728$	26.9186	−	26.4342i	0.997671	−	0.979717i
$729$	−11.2343	−	24.5518i	−0.416084	−	0.909326i
$730$	−2.85936	+	0.756895i	−0.105830	+	0.0280139i
$731$	−28.1444	+	4.96262i	−1.04096	+	0.183549i
$732$	3.70587	−	18.6325i	0.136973	−	0.688678i
$733$	4.19617	+	11.5289i	0.154989	+	0.425829i	0.992748	−	0.120211i	$-0.0383570\pi$
$733$	4.19617	+	11.5289i	0.154989	+	0.425829i	−0.837759	+	0.546040i	$0.816135\pi$
$734$	12.3381	−	26.2513i	0.455406	−	0.968953i
$735$	10.2038	+	6.10736i	0.376373	+	0.225273i
$736$	−21.1314	−	15.2781i	−0.778914	−	0.563157i
$737$	−12.4065	−	21.4888i	−0.457001	−	0.791548i
$738$	−7.48824	+	3.18203i	−0.275646	+	0.117132i
$739$	−0.280828	−	0.162136i	−0.0103304	−	0.00596427i	0.494826	−	0.868992i	$-0.335232\pi$
$739$	−0.280828	−	0.162136i	−0.0103304	−	0.00596427i	−0.505156	+	0.863028i	$0.668565\pi$
$740$	2.26471	−	6.10696i	0.0832523	−	0.224496i
$741$	38.4487	+	14.6837i	1.41245	+	0.539420i
$742$	−0.921111	−	10.9085i	−0.0338150	−	0.400464i
$743$	2.52359	−	14.3120i	0.0925816	−	0.525056i	−0.902880	−	0.429893i	$-0.858551\pi$
$743$	2.52359	−	14.3120i	0.0925816	−	0.525056i	0.995462	−	0.0951637i	$-0.0303374\pi$
$744$	23.2577	−	31.5203i	0.852670	−	1.15559i
$745$	6.59497	−	5.53383i	0.241621	−	0.202744i
$746$	9.67840	−	35.6879i	0.354351	−	1.30663i
$747$	−0.0465685	−	0.141673i	−0.00170385	−	0.00518356i
$748$	−23.0973	+	39.4522i	−0.844519	+	1.44251i
$749$	8.72545	−	23.9730i	0.318821	−	0.875954i
$750$	−12.6038	−	13.0860i	−0.460224	−	0.477834i
$751$	29.4541	+	24.7149i	1.07480	+	0.901861i	0.995478	−	0.0949883i	$-0.0302814\pi$
$751$	29.4541	+	24.7149i	1.07480	+	0.901861i	0.0793178	+	0.996849i	$0.474726\pi$
$752$	−5.82810	+	30.8631i	−0.212529	+	1.12546i
$753$	−5.38982	−	1.03812i	−0.196416	−	0.0378311i
$754$	14.5837	−	6.74685i	0.531109	−	0.245706i
$755$		−	14.1423i		−	0.514692i
$756$	−2.19152	+	41.0889i	−0.0797049	+	1.49439i
$757$			18.0723i			0.656850i	0.944530	+	0.328425i	$0.106518\pi$
$757$			18.0723i			0.656850i	−0.944530	+	0.328425i	$0.893482\pi$
$758$	4.15084	+	8.97231i	0.150765	+	0.325889i
$759$	11.9069	+	34.3890i	0.432192	+	1.24824i
$760$	14.2458	+	6.80106i	0.516749	+	0.246701i
$761$	−28.4100	−	23.8388i	−1.02986	−	0.864157i	−0.0390275	−	0.999238i	$-0.512426\pi$
$761$	−28.4100	−	23.8388i	−1.02986	−	0.864157i	−0.990835	+	0.135081i	$0.956870\pi$
$762$	10.3775	+	41.8568i	0.375938	+	1.51631i
$763$	−2.52594	+	6.93996i	−0.0914451	+	0.251243i
$764$	39.9188	+	23.3705i	1.44421	+	0.845513i
$765$	10.4918	−	5.62466i	0.379331	−	0.203360i
$766$	13.9792	+	3.79110i	0.505089	+	0.136978i
$767$	12.1568	−	10.2007i	0.438956	−	0.368328i
$768$	25.6421	+	10.5110i	0.925280	+	0.379284i
$769$	3.69811	−	20.9730i	0.133357	−	0.756307i	−0.842632	−	0.538490i	$-0.818995\pi$
$769$	3.69811	−	20.9730i	0.133357	−	0.756307i	0.975989	−	0.217818i	$-0.0698938\pi$
$770$	−20.1238	+	1.69924i	−0.725210	+	0.0612365i
$771$	6.22164	−	5.05582i	0.224067	−	0.182081i
$772$	1.83471	−	4.94743i	0.0660326	−	0.178062i
$773$	−21.7593	−	12.5627i	−0.782627	−	0.451850i	0.0547332	−	0.998501i	$-0.482569\pi$
$773$	−21.7593	−	12.5627i	−0.782627	−	0.451850i	−0.837361	+	0.546651i	$0.815903\pi$
$774$	7.05988	−	23.1242i	0.253762	−	0.831183i
$775$	17.4867	+	30.2879i	0.628142	+	1.08797i
$776$	7.65249	+	16.8076i	0.274708	+	0.603357i
$777$	0.444364	−	28.2218i	0.0159415	−	1.01245i
$778$	−14.3541	−	6.74640i	−0.514620	−	0.241870i
$779$	4.62637	+	12.7109i	0.165757	+	0.455414i
$780$	6.08845	−	6.94281i	0.218001	−	0.248593i
$781$	−49.9621	+	8.80967i	−1.78779	+	0.315235i
$782$	8.36564	+	31.6033i	0.299155	+	1.13013i
$783$	−6.76485	+	16.1670i	−0.241756	+	0.577761i
$784$	17.7164	−	29.8454i	0.632728	−	1.06591i
$785$	1.08923	+	6.17736i	0.0388764	+	0.220479i
$786$	−1.75827	−	25.6297i	−0.0627155	−	0.914180i
$787$	15.0107	+	41.2415i	0.535074	+	1.47010i	0.852961	+	0.521974i	$0.174804\pi$
$787$	15.0107	+	41.2415i	0.535074	+	1.47010i	−0.317888	+	0.948128i	$0.602974\pi$
$788$	5.76458	−	31.5737i	0.205355	−	1.12477i
$789$	−14.4632	−	25.9875i	−0.514904	−	0.925178i
$790$	−0.964455	−	0.0873210i	−0.0343138	−	0.00310674i
$791$	−10.4321	−	18.0690i	−0.370924	−	0.642459i
$792$	−20.8807	−	32.5555i	−0.741964	−	1.15681i
$793$	−9.23765	+	16.0001i	−0.328038	+	0.568179i
$794$	−3.75655	+	5.33050i	−0.133315	+	0.189172i
$795$	−0.423686	−	2.64577i	−0.0150266	−	0.0938358i
$796$	−12.9460	−	36.2501i	−0.458858	−	1.28485i
$797$	45.5449	+	8.03080i	1.61328	+	0.284466i	0.906259	−	0.422723i	$-0.138926\pi$
$797$	45.5449	+	8.03080i	1.61328	+	0.284466i	0.707025	+	0.707188i	$0.250037\pi$
$798$	68.0235	+	7.24017i	2.40801	+	0.256299i
$799$	30.1648	−	25.3113i	1.06715	−	0.895448i
$800$	−17.7583	+	17.2288i	−0.627850	+	0.609130i
$801$	10.1624	−	7.99584i	0.359071	−	0.282519i
$802$	−15.3419	+	15.2493i	−0.541741	+	0.538471i
$803$	4.12064	−	11.3214i	0.145414	−	0.399523i
$804$	18.8533	+	0.411017i	0.664905	+	0.0144954i
$805$	−9.28303	+	11.0631i	−0.327184	+	0.389922i
$806$	−31.2719	+	21.7560i	−1.10150	+	0.766324i
$807$	2.73540	−	3.15760i	0.0962905	−	0.111153i
$808$	−11.1668	−	7.97119i	−0.392848	−	0.280425i
$809$	16.8816			0.593524			0.296762	−	0.954951i	$-0.404093\pi$
$809$	16.8816			0.593524			0.296762	+	0.954951i	$0.404093\pi$
$810$	0.214133	+	10.0690i	0.00752387	+	0.353788i
$811$		−	30.5802i		−	1.07382i	−0.843640	−	0.536909i	$-0.819592\pi$
$811$		−	30.5802i		−	1.07382i	0.843640	−	0.536909i	$-0.180408\pi$
$812$	20.5631	−	17.0434i	0.721623	−	0.598108i
$813$	−23.0096	−	19.9330i	−0.806982	−	0.699081i
$814$	15.1514	+	21.7784i	0.531055	+	0.763331i
$815$	−9.85652	−	8.27060i	−0.345259	−	0.289707i
$816$	−16.5273	−	30.5612i	−0.578573	−	1.06986i
$817$	−37.7718	−	13.7478i	−1.32147	−	0.480975i
$818$	−1.00707	+	1.00099i	−0.0352112	+	0.0349987i
$819$	14.8634	−	37.1535i	0.519371	−	1.29825i
$820$	3.03486	+	0.0183708i	0.105982	+	0.000641537i
$821$	24.4506	+	29.1391i	0.853332	+	1.01696i	0.999616	+	0.0277185i	$0.00882419\pi$
$821$	24.4506	+	29.1391i	0.853332	+	1.01696i	−0.146284	+	0.989243i	$0.546731\pi$
$822$	1.77215	−	16.6498i	0.0618108	−	0.580730i
$823$	4.64180	−	26.3249i	0.161803	−	0.917629i	−0.790497	−	0.612466i	$-0.790178\pi$
$823$	4.64180	−	26.3249i	0.161803	−	0.917629i	0.952300	−	0.305164i	$-0.0987112\pi$
$824$	−8.80743	+	6.04860i	−0.306821	+	0.210713i
$825$	34.0965	−	5.46011i	1.18709	−	0.190097i
$826$	15.1945	−	21.5608i	0.528684	−	0.750197i
$827$	−42.2208	−	24.3762i	−1.46816	−	0.847643i	−0.468797	−	0.883306i	$-0.655313\pi$
$827$	−42.2208	−	24.3762i	−1.46816	−	0.847643i	−0.999364	+	0.0356625i	$0.988646\pi$
$828$	−27.0381	−	5.82163i	−0.939639	−	0.202316i
$829$	10.2346	−	5.90895i	0.355462	−	0.205226i	−0.311626	−	0.950205i	$-0.600874\pi$
$829$	10.2346	−	5.90895i	0.355462	−	0.205226i	0.667088	+	0.744979i	$0.267540\pi$
$830$	−0.00501593	+	0.0554007i	−0.000174106	+	0.00192299i
$831$	24.4175	−	13.5894i	0.847032	−	0.471412i
$832$	−20.3277	−	17.6958i	−0.704737	−	0.613493i
$833$	−40.8892	+	14.8824i	−1.41673	+	0.515646i
$834$	1.93128	+	28.1515i	0.0668746	+	0.974806i
$835$	9.40837	−	1.65895i	0.325590	−	0.0574103i
$836$	−55.8788	+	31.8122i	−1.93261	+	1.10025i
$837$	9.13863	−	40.5308i	0.315877	−	1.40095i
$838$	32.8165	−	8.68680i	1.13363	−	0.300080i
$839$	6.08118	+	34.4881i	0.209946	+	1.19066i	0.889465	+	0.457003i	$0.151077\pi$
$839$	6.08118	+	34.4881i	0.209946	+	1.19066i	−0.679520	+	0.733657i	$0.737812\pi$
$840$	6.82978	−	13.7451i	0.235650	−	0.474250i
$841$	−16.5618	+	6.02799i	−0.571095	+	0.207862i
$842$	−8.64360	−	4.06247i	−0.297878	−	0.140002i
$843$	15.9078	+	0.250475i	0.547894	+	0.00862683i
$844$	−7.27853	−	42.7917i	−0.250537	−	1.47295i
$845$	1.13113	−	0.653058i	0.0389120	−	0.0224659i
$846$	7.50669	+	32.4570i	0.258085	+	1.11590i
$847$	19.3534	−	33.5211i	0.664992	−	1.15180i
$848$	−7.71736	+	1.26465i	−0.265015	+	0.0434281i
$849$	−0.0125708	−	0.0154696i	−0.000431430	−	0.000530914i
$850$	30.9099	−	2.61002i	1.06020	−	0.0895231i
$851$	18.6838	+	3.29446i	0.640472	+	0.112932i
$852$	13.9737	−	35.9354i	0.478732	−	1.23113i
$853$	−37.0236	−	44.1231i	−1.26767	−	1.51074i	−0.761255	−	0.648452i	$-0.775417\pi$
$853$	−37.0236	−	44.1231i	−1.26767	−	1.51074i	−0.506410	−	0.862293i	$-0.669028\pi$
$854$	−8.03754	+	29.6374i	−0.275039	+	1.01417i
$855$	16.7352	+	0.527138i	0.572333	+	0.0180277i
$856$	−17.5598	−	4.87644i	−0.600181	−	0.166673i
$857$	40.8515	+	14.8687i	1.39546	+	0.507906i	0.926828	−	0.375486i	$-0.122524\pi$
$857$	40.8515	+	14.8687i	1.39546	+	0.507906i	0.468634	+	0.883393i	$0.344746\pi$
$858$	9.05139	+	36.5080i	0.309009	+	1.24636i
$859$	2.97958	−	3.55093i	0.101662	−	0.121156i	−0.712814	−	0.701353i	$-0.752580\pi$
$859$	2.97958	−	3.55093i	0.101662	−	0.121156i	0.814476	+	0.580197i	$0.197024\pi$
$860$	−5.83876	+	6.87343i	−0.199100	+	0.234382i
$861$	12.4278	−	4.30300i	0.423538	−	0.146646i
$862$	37.4814	−	17.3400i	1.27662	−	0.590601i
$863$	24.4317			0.831665			0.415832	−	0.909441i	$-0.363490\pi$
$863$	24.4317			0.831665			0.415832	+	0.909441i	$0.363490\pi$
$864$	29.3848	−	0.731865i	0.999690	−	0.0248985i
$865$	−2.60070			−0.0884265
$866$	14.5937	−	6.75145i	0.495914	−	0.229424i
$867$	−2.66941	+	13.8593i	−0.0906579	+	0.470688i
$868$	−40.9933	+	48.2576i	−1.39140	+	1.63797i
$869$	2.53548	−	3.02167i	0.0860103	−	0.102503i
$870$	4.70837	−	4.53485i	0.159629	−	0.153746i
$871$	−17.2334	−	6.27245i	−0.583932	−	0.212534i
$872$	5.08340	+	1.41168i	0.172146	+	0.0478057i
$873$	14.6014	+	13.0570i	0.494182	+	0.441914i
$874$	−12.0352	+	44.3781i	−0.407095	+	1.50111i
$875$	18.8775	+	22.4973i	0.638175	+	0.760547i
$876$	5.73133	+	7.14081i	0.193644	+	0.241265i
$877$	54.5573	+	9.61992i	1.84227	+	0.324842i	0.982560	−	0.185944i	$-0.0595342\pi$
$877$	54.5573	+	9.61992i	1.84227	+	0.324842i	0.859708	+	0.510785i	$0.170645\pi$
$878$	12.8021	−	1.08101i	0.432051	−	0.0364822i
$879$	9.41748	−	24.6593i	0.317644	−	0.831736i
$880$	2.33299	+	14.2368i	0.0786450	+	0.479923i
$881$	8.83907	−	15.3097i	0.297796	−	0.515798i	−0.677835	−	0.735214i	$-0.737082\pi$
$881$	8.83907	−	15.3097i	0.297796	−	0.515798i	0.975631	+	0.219416i	$0.0704152\pi$
$882$	4.47205	−	36.5403i	0.150582	−	1.23038i
$883$	−1.51759	+	0.876179i	−0.0510708	+	0.0294858i	−0.525318	−	0.850906i	$-0.676054\pi$
$883$	−1.51759	+	0.876179i	−0.0510708	+	0.0294858i	0.474247	+	0.880392i	$0.342720\pi$
$884$	5.66585	+	33.3105i	0.190563	+	1.12035i
$885$	3.31564	−	5.53958i	0.111454	−	0.186211i
$886$	34.8650	+	16.3865i	1.17131	+	0.550514i
$887$	−6.07325	+	2.21048i	−0.203920	+	0.0742207i	−0.441961	−	0.897034i	$-0.645717\pi$
$887$	−6.07325	+	2.21048i	−0.203920	+	0.0742207i	0.238041	+	0.971255i	$0.423495\pi$
$888$	−20.1236	+	1.25821i	−0.675305	+	0.0422227i
$889$	−12.1044	−	68.6475i	−0.405969	−	2.30236i
$890$	−4.66276	+	1.23427i	−0.156296	+	0.0413728i
$891$	−34.1653	−	22.7065i	−1.14458	−	0.760696i
$892$	−10.6134	+	6.04231i	−0.355364	+	0.202312i
$893$	54.5430	−	9.61740i	1.82521	−	0.321834i
$894$	−23.9380	−	11.7144i	−0.800607	−	0.391789i
$895$	−6.38588	+	2.32427i	−0.213457	+	0.0776918i
$896$	−40.1884	−	19.7872i	−1.34260	−	0.661045i
$897$	23.0793	+	13.8138i	0.770595	+	0.461229i
$898$	−0.979149	+	10.8146i	−0.0326746	+	0.360889i
$899$	−23.3552	+	13.4842i	−0.778941	+	0.449722i
$900$	−9.89500	+	24.3064i	−0.329833	+	0.810213i
$901$	8.49087	+	4.90220i	0.282872	+	0.163316i
$902$	−7.12110	+	10.1048i	−0.237107	+	0.336452i
$903$	−13.9432	+	36.5098i	−0.464002	+	1.21497i
$904$	−12.2862	+	8.43768i	−0.408633	+	0.280633i
$905$	−1.58829	+	9.00766i	−0.0527967	+	0.299425i
$906$	−40.0179	+	17.7540i	−1.32950	+	0.589836i
$907$	−2.37017	−	2.82465i	−0.0787001	−	0.0937911i	0.725258	−	0.688478i	$-0.241721\pi$
$907$	−2.37017	−	2.82465i	−0.0787001	−	0.0937911i	−0.803958	+	0.594686i	$0.797276\pi$
$908$	57.8998	+	0.350483i	1.92147	+	0.0116312i
$909$	−14.2445	−	2.97691i	−0.472461	−	0.0987378i
$910$	−10.5865	+	10.5226i	−0.350939	+	0.348821i
$911$	21.2057	+	7.71823i	0.702575	+	0.255716i	0.668510	−	0.743703i	$-0.266932\pi$
$911$	21.2057	+	7.71823i	0.702575	+	0.255716i	0.0340652	+	0.999420i	$0.489155\pi$
$912$	1.36081	−	48.8485i	0.0450609	−	1.61754i
$913$	−0.173572	−	0.145644i	−0.00574440	−	0.00482013i
$914$	−9.90162	−	14.2325i	−0.327516	−	0.470768i
$915$	−1.42153	+	7.38046i	−0.0469943	+	0.243990i
$916$	19.7998	−	16.4108i	0.654202	−	0.542227i
$917$			41.5257i			1.37130i
$918$	−29.0870	−	22.6270i	−0.960013	−	0.746802i
$919$	−18.6829			−0.616291			−0.308145	−	0.951339i	$-0.599708\pi$
$919$	−18.6829			−0.616291			−0.308145	+	0.951339i	$0.599708\pi$
$920$	8.39680	+	5.99385i	0.276834	+	0.197611i
$921$	8.87921	+	25.6446i	0.292580	+	0.845019i
$922$	19.1643	−	13.3327i	0.631144	−	0.439091i
$923$	−24.1025	+	28.7243i	−0.793344	+	0.945470i
$924$	30.0712	+	54.8101i	0.989271	+	1.80312i
$925$	6.15697	−	16.9161i	0.202440	−	0.556199i
$926$	−39.6404	+	39.4012i	−1.30266	+	1.29480i
$927$	−5.97243	+	9.63099i	−0.196160	+	0.316323i
$928$	−13.2852	−	13.6935i	−0.436110	−	0.449513i
$929$	28.8670	−	24.2223i	0.947094	−	0.794706i	−0.0317116	−	0.999497i	$-0.510096\pi$
$929$	28.8670	−	24.2223i	0.947094	−	0.794706i	0.978806	+	0.204791i	$0.0656514\pi$
$930$	−9.12597	+	12.5261i	−0.299252	+	0.410746i
$931$	−60.2719	−	10.6276i	−1.97533	−	0.348304i
$932$	−18.7289	−	52.4428i	−0.613486	−	1.71782i
$933$	−43.6667	+	35.4843i	−1.42958	+	1.16170i
$934$	4.48275	−	6.36097i	0.146680	−	0.208137i
$935$	9.04347	−	15.6638i	0.295753	−	0.512260i
$936$	−27.2891	−	8.51234i	−0.891971	−	0.278234i
$937$	9.22218	+	15.9733i	0.301275	+	0.521824i	0.976425	−	0.215856i	$-0.0692543\pi$
$937$	9.22218	+	15.9733i	0.301275	+	0.521824i	−0.675150	+	0.737681i	$0.735921\pi$
$938$	−30.3580	−	2.74859i	−0.991222	−	0.0897445i
$939$	−22.0171	−	0.346669i	−0.718501	−	0.0113131i
$940$	2.23185	−	12.2243i	0.0727951	−	0.398713i
$941$	2.21353	+	6.08164i	0.0721592	+	0.198256i	0.970529	−	0.240984i	$-0.0774701\pi$
$941$	2.21353	+	6.08164i	0.0721592	+	0.198256i	−0.898370	+	0.439240i	$0.855248\pi$
$942$	16.1124	−	10.8371i	0.524970	−	0.353091i
$943$	1.53506	+	8.70575i	0.0499884	+	0.283498i
$944$	−16.2028	−	9.61812i	−0.527358	−	0.313043i
$945$	0.768629	−	16.2613i	0.0250035	−	0.528979i
$946$	−9.40023	−	35.5117i	−0.305628	−	1.15459i
$947$	25.1285	−	4.43083i	0.816566	−	0.143983i	0.250261	−	0.968178i	$-0.419484\pi$
$947$	25.1285	−	4.43083i	0.816566	−	0.143983i	0.566305	+	0.824196i	$0.308373\pi$
$948$	0.963668	+	2.83869i	0.0312985	+	0.0921965i
$949$	−3.04558	−	8.36767i	−0.0988638	−	0.271626i
$950$	39.4859	+	18.5583i	1.28109	+	0.602110i
$951$	−29.1123	+	16.2023i	−0.944031	+	0.525396i
$952$	23.2715	+	51.1124i	0.754232	+	1.65656i
$953$	5.24734	+	9.08865i	0.169978	+	0.294410i	0.938412	−	0.345519i	$-0.112297\pi$
$953$	5.24734	+	9.08865i	0.169978	+	0.294410i	−0.768434	+	0.639929i	$0.778964\pi$
$954$	−6.95473	+	4.52033i	−0.225168	+	0.146351i
$955$	−15.8490	−	9.15044i	−0.512863	−	0.296101i
$956$	2.88011	−	7.76644i	0.0931494	−	0.251185i
$957$	4.21033	+	26.2921i	0.136101	+	0.849902i
$958$	23.6808	−	1.99960i	0.765090	−	0.0646040i
$959$	−4.69981	+	26.6540i	−0.151765	+	0.860702i
$960$	−10.1700	−	4.09707i	−0.328234	−	0.132232i
$961$	25.2301	−	21.1706i	0.813876	−	0.682923i
$962$	18.9251	+	5.13241i	0.610170	+	0.165475i
$963$	−19.1324	+	2.75561i	−0.616532	+	0.0887982i
$964$	−32.6246	−	19.1000i	−1.05077	−	0.615171i
$965$	−0.714016	+	1.96174i	−0.0229850	+	0.0631508i
$966$	42.9584	+	12.3794i	1.38216	+	0.398300i
$967$	−26.6055	−	22.3246i	−0.855574	−	0.717912i	0.105436	−	0.994426i	$-0.466376\pi$
$967$	−26.6055	−	22.3246i	−0.855574	−	0.717912i	−0.961010	+	0.276514i	$0.910821\pi$
$968$	−24.9527	−	11.9127i	−0.802011	−	0.382887i
$969$	−40.1149	+	46.3065i	−1.28868	+	1.48758i
$970$	−3.06780	−	6.63125i	−0.0985012	−	0.212917i
$971$		−	13.9739i		−	0.448445i	−0.974538	−	0.224223i	$-0.928016\pi$
$971$		−	13.9739i		−	0.448445i	0.974538	−	0.224223i	$-0.0719843\pi$
$972$	28.2229	−	13.2463i	0.905252	−	0.424876i
$973$		−	45.6116i		−	1.46224i
$974$	8.61183	−	3.98407i	0.275941	−	0.127658i
$975$	16.7109	−	19.2902i	0.535179	−	0.617782i
$976$	21.5555	+	4.07047i	0.689973	+	0.130293i
$977$	−11.1693	−	9.37218i	−0.357339	−	0.299843i	0.446390	−	0.894838i	$-0.352709\pi$
$977$	−11.1693	−	9.37218i	−0.357339	−	0.299843i	−0.803729	+	0.594996i	$0.797154\pi$
$978$	−11.0293	+	38.2733i	−0.352677	+	1.22385i
$979$	6.71953	−	18.4618i	0.214757	−	0.590041i
$980$	−6.93766	+	11.8501i	−0.221615	+	0.378539i
$981$	5.53865	−	0.797723i	0.176835	−	0.0254693i
$982$	−11.4417	+	42.1900i	−0.365120	+	1.34634i
$983$	8.62000	−	7.23304i	0.274935	−	0.230698i	−0.494885	−	0.868958i	$-0.664790\pi$
$983$	8.62000	−	7.23304i	0.274935	−	0.230698i	0.769821	+	0.638260i	$0.220346\pi$
$984$	−3.75791	−	8.61066i	−0.119798	−	0.274498i
$985$	−2.20502	+	12.5053i	−0.0702579	+	0.398452i
$986$	2.01261	+	23.8349i	0.0640945	+	0.759057i
$987$	−8.51475	−	53.1717i	−0.271027	−	1.69247i
$988$	−16.5243	+	44.5589i	−0.525707	+	1.41761i
$989$	−22.7499	−	13.1346i	−0.723403	−	0.417657i
$990$	8.33900	+	12.8299i	0.265031	+	0.407762i
$991$	−9.44162	−	16.3534i	−0.299923	−	0.519482i	0.676195	−	0.736723i	$-0.263628\pi$
$991$	−9.44162	−	16.3534i	−0.299923	−	0.519482i	−0.976118	+	0.217241i	$0.930294\pi$
$992$	36.6551	+	26.5018i	1.16380	+	0.841432i
$993$	−4.87792	+	2.71478i	−0.154796	+	0.0861510i
$994$	−26.5100	+	56.4046i	−0.840847	+	1.78905i
$995$	5.20863	+	14.3106i	0.165125	+	0.453676i
$996$	0.163062	−	0.0553555i	0.00516681	−	0.00175401i
$997$	29.3371	−	5.17293i	0.929117	−	0.163828i	0.311445	−	0.950264i	$-0.399187\pi$
$997$	29.3371	−	5.17293i	0.929117	−	0.163828i	0.617672	+	0.786436i	$0.288076\pi$
$998$	19.3501	−	5.12212i	0.612516	−	0.162138i
$999$	−19.0051	+	9.80663i	−0.601293	+	0.310268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.6	✓	204
3.2	odd	2		648.2.t.a.253.29		204
4.3	odd	2		864.2.bf.a.337.26		204
8.3	odd	2		864.2.bf.a.337.9		204
8.5	even	2	inner	216.2.t.a.13.33	yes	204
24.5	odd	2		648.2.t.a.253.2		204
27.2	odd	18		648.2.t.a.397.2		204
27.25	even	9	inner	216.2.t.a.133.33	yes	204
108.79	odd	18		864.2.bf.a.241.9		204
216.29	odd	18		648.2.t.a.397.29		204
216.133	even	18	inner	216.2.t.a.133.6	yes	204
216.187	odd	18		864.2.bf.a.241.26		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.6	✓	204	1.1	even	1	trivial
216.2.t.a.13.33	yes	204	8.5	even	2	inner
216.2.t.a.133.6	yes	204	216.133	even	18	inner
216.2.t.a.133.33	yes	204	27.25	even	9	inner
648.2.t.a.253.2		204	24.5	odd	2
648.2.t.a.253.29		204	3.2	odd	2
648.2.t.a.397.2		204	27.2	odd	18
648.2.t.a.397.29		204	216.29	odd	18
864.2.bf.a.241.9		204	108.79	odd	18
864.2.bf.a.241.26		204	216.187	odd	18
864.2.bf.a.337.9		204	8.3	odd	2
864.2.bf.a.337.26		204	4.3	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28352 + 0.593791i) q^{2} +(-1.30914 - 1.13409i) q^{3} +(1.29483 - 1.52428i) q^{4} +(-0.508621 + 0.606151i) q^{5} +(2.35371 + 0.678272i) q^{6} +(-3.72062 - 1.35420i) q^{7} +(-0.756827 + 2.72529i) q^{8} +(0.427672 + 2.96936i) q^{9} +O(q^{10})\)	\(q+(-1.28352 + 0.593791i) q^{2} +(-1.30914 - 1.13409i) q^{3} +(1.29483 - 1.52428i) q^{4} +(-0.508621 + 0.606151i) q^{5} +(2.35371 + 0.678272i) q^{6} +(-3.72062 - 1.35420i) q^{7} +(-0.756827 + 2.72529i) q^{8} +(0.427672 + 2.96936i) q^{9} +(0.292896 - 1.08002i) q^{10} +(2.92987 + 3.49168i) q^{11} +(-3.42377 + 0.527037i) q^{12} +(3.31770 + 0.585000i) q^{13} +(5.57959 - 0.471139i) q^{14} +(1.35328 - 0.216711i) q^{15} +(-0.646853 - 3.94735i) q^{16} +(-2.50743 + 4.34299i) q^{17} +(-2.31210 - 3.55727i) q^{18} +(-6.10844 + 3.52671i) q^{19} +(0.265368 + 1.56014i) q^{20} +(3.33502 + 5.99236i) q^{21} +(-5.83385 - 2.74190i) q^{22} +(-4.33163 + 1.57658i) q^{23} +(4.08152 - 2.70947i) q^{24} +(0.759517 + 4.30744i) q^{25} +(-4.60569 + 1.21916i) q^{26} +(2.80765 - 4.37231i) q^{27} +(-6.88173 + 3.91782i) q^{28} +(-3.32150 + 0.585669i) q^{29} +(-1.60828 + 1.08172i) q^{30} +(7.51376 - 2.73478i) q^{31} +(3.17415 + 4.68239i) q^{32} +(0.124291 - 7.89382i) q^{33} +(0.639495 - 7.06318i) q^{34} +(2.71323 - 1.56649i) q^{35} +(5.07989 + 3.19291i) q^{36} +(-3.56434 - 2.05787i) q^{37} +(5.74615 - 8.15372i) q^{38} +(-3.67987 - 4.52842i) q^{39} +(-1.26700 - 1.84489i) q^{40} +(0.333012 - 1.88860i) q^{41} +(-7.83875 - 5.71098i) q^{42} +(3.66311 + 4.36553i) q^{43} +(9.11596 + 0.0551814i) q^{44} +(-2.01740 - 1.25104i) q^{45} +(4.62355 - 4.59565i) q^{46} +(-7.37860 - 2.68559i) q^{47} +(-3.62984 + 5.90121i) q^{48} +(6.64689 + 5.57740i) q^{49} +(-3.53257 - 5.07767i) q^{50} +(8.20791 - 2.84191i) q^{51} +(5.18754 - 4.29963i) q^{52} -1.95507i q^{53} +(-1.00742 + 7.27909i) q^{54} -3.60667 q^{55} +(6.50645 - 9.11489i) q^{56} +(11.9964 + 2.31059i) q^{57} +(3.91543 - 2.72399i) q^{58} +(3.02793 - 3.60855i) q^{59} +(1.42194 - 2.34339i) q^{60} +(-1.87567 + 5.15337i) q^{61} +(-8.02014 + 7.97174i) q^{62} +(2.42989 - 11.6270i) q^{63} +(-6.85443 - 4.12515i) q^{64} +(-2.04205 + 1.71348i) q^{65} +(4.52774 + 10.2056i) q^{66} +(-5.36107 - 0.945302i) q^{67} +(3.37325 + 9.44544i) q^{68} +(7.45868 + 2.84850i) q^{69} +(-2.55231 + 3.62170i) q^{70} +(-5.56518 + 9.63918i) q^{71} +(-8.41604 - 1.08176i) q^{72} +(-1.32161 - 2.28909i) q^{73} +(5.79683 + 0.524840i) q^{74} +(3.89072 - 6.50038i) q^{75} +(-2.53367 + 13.8774i) q^{76} +(-6.17251 - 16.9588i) q^{77} +(7.41211 + 3.62722i) q^{78} +(-0.150274 - 0.852245i) q^{79} +(2.72169 + 1.61561i) q^{80} +(-8.63419 + 2.53982i) q^{81} +(0.694009 + 2.62179i) q^{82} +(-0.0489550 + 0.00863210i) q^{83} +(13.4523 + 2.67556i) q^{84} +(-1.35718 - 3.72882i) q^{85} +(-7.29387 - 3.42810i) q^{86} +(5.01249 + 3.00016i) q^{87} +(-11.7332 + 5.34214i) q^{88} +(-2.15515 - 3.73283i) q^{89} +(3.33223 + 0.407821i) q^{90} +(-11.5517 - 6.66938i) q^{91} +(-3.20555 + 8.64401i) q^{92} +(-12.9380 - 4.94109i) q^{93} +(11.0652 - 0.934344i) q^{94} +(0.969162 - 5.49639i) q^{95} +(1.15487 - 9.72966i) q^{96} +(5.00174 - 4.19696i) q^{97} +(-11.8432 - 3.21182i) q^{98} +(-9.11503 + 10.1931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

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