LMFDB - Embedded newform 216.2.t.a.13.9

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			13.9
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.938269 + 1.05814i) q^{2} +(-0.0518114 + 1.73128i) q^{3} +(-0.239304 - 1.98563i) q^{4} +(-1.55117 + 1.84861i) q^{5} +(-1.78331 - 1.67923i) q^{6} +(-1.49685 - 0.544810i) q^{7} +(2.32560 + 1.60984i) q^{8} +(-2.99463 - 0.179400i) q^{9} +O(q^{10})$	\(q+(-0.938269 + 1.05814i) q^{2} +(-0.0518114 + 1.73128i) q^{3} +(-0.239304 - 1.98563i) q^{4} +(-1.55117 + 1.84861i) q^{5} +(-1.78331 - 1.67923i) q^{6} +(-1.49685 - 0.544810i) q^{7} +(2.32560 + 1.60984i) q^{8} +(-2.99463 - 0.179400i) q^{9} +(-0.500669 - 3.37584i) q^{10} +(0.102391 + 0.122025i) q^{11} +(3.45007 - 0.311423i) q^{12} +(-3.39140 - 0.597995i) q^{13} +(1.98093 - 1.07270i) q^{14} +(-3.12009 - 2.78128i) q^{15} +(-3.88547 + 0.950339i) q^{16} +(-1.43581 + 2.48690i) q^{17} +(2.99960 - 3.00040i) q^{18} +(3.75621 - 2.16865i) q^{19} +(4.04186 + 2.63767i) q^{20} +(1.02077 - 2.56324i) q^{21} +(-0.225190 - 0.00614850i) q^{22} +(2.14748 - 0.781619i) q^{23} +(-2.90757 + 3.94285i) q^{24} +(-0.142997 - 0.810974i) q^{25} +(3.81480 - 3.02748i) q^{26} +(0.465746 - 5.17524i) q^{27} +(-0.723589 + 3.10257i) q^{28} +(-8.60509 + 1.51731i) q^{29} +(5.87045 - 0.691889i) q^{30} +(-6.69129 + 2.43543i) q^{31} +(2.64002 - 5.00303i) q^{32} +(-0.216565 + 0.170946i) q^{33} +(-1.28430 - 3.85267i) q^{34} +(3.32901 - 1.92201i) q^{35} +(0.360405 + 5.98917i) q^{36} +(5.14590 + 2.97099i) q^{37} +(-1.22961 + 6.00935i) q^{38} +(1.21101 - 5.84046i) q^{39} +(-6.58336 + 1.80200i) q^{40} +(-1.74706 + 9.90807i) q^{41} +(1.75450 + 3.48512i) q^{42} +(7.59829 + 9.05529i) q^{43} +(0.217795 - 0.232513i) q^{44} +(4.97682 - 5.25763i) q^{45} +(-1.18785 + 3.00570i) q^{46} +(3.66367 + 1.33347i) q^{47} +(-1.44399 - 6.77605i) q^{48} +(-3.41856 - 2.86851i) q^{49} +(0.992290 + 0.609602i) q^{50} +(-4.23112 - 2.61464i) q^{51} +(-0.375823 + 6.87717i) q^{52} +9.80805i q^{53} +(5.03911 + 5.34859i) q^{54} -0.384404 q^{55} +(-2.60402 - 3.67670i) q^{56} +(3.55991 + 6.61539i) q^{57} +(6.46837 - 10.5290i) q^{58} +(-1.72220 + 2.05244i) q^{59} +(-4.77595 + 6.86091i) q^{60} +(0.492702 - 1.35369i) q^{61} +(3.70121 - 9.36539i) q^{62} +(4.38478 + 1.90004i) q^{63} +(2.81683 + 7.48769i) q^{64} +(6.36609 - 5.34178i) q^{65} +(0.0223122 - 0.389548i) q^{66} +(-0.225321 - 0.0397302i) q^{67} +(5.28167 + 2.25587i) q^{68} +(1.24193 + 3.75838i) q^{69} +(-1.08976 + 5.32591i) q^{70} +(2.82317 - 4.88987i) q^{71} +(-6.67551 - 5.23809i) q^{72} +(7.14574 + 12.3768i) q^{73} +(-7.97195 + 2.65748i) q^{74} +(1.41143 - 0.205549i) q^{75} +(-5.20501 - 6.93948i) q^{76} +(-0.0867843 - 0.238438i) q^{77} +(5.04375 + 6.76133i) q^{78} +(-2.18269 - 12.3786i) q^{79} +(4.27021 - 8.65685i) q^{80} +(8.93563 + 1.07447i) q^{81} +(-8.84487 - 11.1451i) q^{82} +(-11.1079 + 1.95862i) q^{83} +(-5.33392 - 1.41348i) q^{84} +(-2.37013 - 6.51187i) q^{85} +(-16.7110 - 0.456270i) q^{86} +(-2.18104 - 14.9764i) q^{87} +(0.0416802 + 0.448616i) q^{88} +(-3.73417 - 6.46777i) q^{89} +(0.893694 + 10.1992i) q^{90} +(4.75063 + 2.74278i) q^{91} +(-2.06591 - 4.07706i) q^{92} +(-3.86972 - 11.7107i) q^{93} +(-4.84850 + 2.62551i) q^{94} +(-1.81753 + 10.3077i) q^{95} +(8.52483 + 4.82982i) q^{96} +(5.17680 - 4.34385i) q^{97} +(6.24280 - 0.925866i) q^{98} +(-0.284733 - 0.383790i) 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 $

$2$	−0.938269	+	1.05814i	−0.663456	+	0.748215i
$2$	−0.938269	+	1.05814i	−0.663456	+	0.748215i
$3$	−0.0518114	+	1.73128i	−0.0299133	+	0.999552i
$3$	−0.0518114	+	1.73128i	−0.0299133	+	0.999552i
$4$	−0.239304	−	1.98563i	−0.119652	−	0.992816i
$5$	−1.55117	+	1.84861i	−0.693704	+	0.826724i	−0.991798	−	0.127812i	$-0.959204\pi$
$5$	−1.55117	+	1.84861i	−0.693704	+	0.826724i	0.298095	+	0.954536i	$0.403649\pi$
$6$	−1.78331	−	1.67923i	−0.728034	−	0.685541i
$7$	−1.49685	−	0.544810i	−0.565757	−	0.205919i	0.0432765	−	0.999063i	$-0.486220\pi$
$7$	−1.49685	−	0.544810i	−0.565757	−	0.205919i	−0.609034	+	0.793144i	$0.708443\pi$
$8$	2.32560	+	1.60984i	0.822224	+	0.569164i
$9$	−2.99463	−	0.179400i	−0.998210	−	0.0597999i
$10$	−0.500669	−	3.37584i	−0.158325	−	1.06753i
$11$	0.102391	+	0.122025i	0.0308722	+	0.0367920i	0.781260	−	0.624206i	$-0.214577\pi$
$11$	0.102391	+	0.122025i	0.0308722	+	0.0367920i	−0.750387	+	0.660998i	$0.770133\pi$
$12$	3.45007	−	0.311423i	0.995951	−	0.0899000i
$13$	−3.39140	−	0.597995i	−0.940604	−	0.165854i	−0.317735	−	0.948180i	$-0.602922\pi$
$13$	−3.39140	−	0.597995i	−0.940604	−	0.165854i	−0.622869	+	0.782326i	$0.714033\pi$
$14$	1.98093	−	1.07270i	0.529427	−	0.286690i
$15$	−3.12009	−	2.78128i	−0.805603	−	0.718123i
$16$	−3.88547	+	0.950339i	−0.971367	+	0.237585i
$17$	−1.43581	+	2.48690i	−0.348236	+	0.603163i	−0.985936	−	0.167122i	$-0.946553\pi$
$17$	−1.43581	+	2.48690i	−0.348236	+	0.603163i	0.637700	+	0.770285i	$0.279886\pi$
$18$	2.99960	−	3.00040i	0.707012	−	0.707202i
$19$	3.75621	−	2.16865i	0.861733	−	0.497522i	−0.00285908	−	0.999996i	$-0.500910\pi$
$19$	3.75621	−	2.16865i	0.861733	−	0.497522i	0.864592	+	0.502474i	$0.167577\pi$
$20$	4.04186	+	2.63767i	0.903788	+	0.589801i
$21$	1.02077	−	2.56324i	0.222750	−	0.559344i
$22$	−0.225190	−	0.00614850i	−0.0480107	−	0.00131087i
$23$	2.14748	−	0.781619i	0.447781	−	0.162979i	−0.108280	−	0.994120i	$-0.534534\pi$
$23$	2.14748	−	0.781619i	0.447781	−	0.162979i	0.556061	+	0.831142i	$0.312312\pi$
$24$	−2.90757	+	3.94285i	−0.593505	+	0.804830i
$25$	−0.142997	−	0.810974i	−0.0285993	−	0.162195i
$26$	3.81480	−	3.02748i	0.748144	−	0.593737i
$27$	0.465746	−	5.17524i	0.0896329	−	0.995975i
$28$	−0.723589	+	3.10257i	−0.136746	+	0.586331i
$29$	−8.60509	+	1.51731i	−1.59793	+	0.281757i	−0.900486	−	0.434886i	$-0.856789\pi$
$29$	−8.60509	+	1.51731i	−1.59793	+	0.281757i	−0.697440	+	0.716643i	$0.745678\pi$
$30$	5.87045	−	0.691889i	1.07179	−	0.126321i
$31$	−6.69129	+	2.43543i	−1.20179	+	0.437416i	−0.863849	−	0.503751i	$-0.831953\pi$
$31$	−6.69129	+	2.43543i	−1.20179	+	0.437416i	−0.337942	+	0.941167i	$0.609731\pi$
$32$	2.64002	−	5.00303i	0.466695	−	0.884418i
$33$	−0.216565	+	0.170946i	−0.0376991	+	0.0297578i
$34$	−1.28430	−	3.85267i	−0.220256	−	0.660727i
$35$	3.32901	−	1.92201i	0.562706	−	0.324878i
$36$	0.360405	+	5.98917i	0.0600676	+	0.998194i
$37$	5.14590	+	2.97099i	0.845981	+	0.488427i	0.859293	−	0.511484i	$-0.170904\pi$
$37$	5.14590	+	2.97099i	0.845981	+	0.488427i	−0.0133118	+	0.999911i	$0.504237\pi$
$38$	−1.22961	+	6.00935i	−0.199469	+	0.974846i
$39$	1.21101	−	5.84046i	0.193916	−	0.935222i
$40$	−6.58336	+	1.80200i	−1.04092	+	0.284921i
$41$	−1.74706	+	9.90807i	−0.272845	+	1.54738i	0.472880	+	0.881127i	$0.343214\pi$
$41$	−1.74706	+	9.90807i	−0.272845	+	1.54738i	−0.745725	+	0.666254i	$0.767897\pi$
$42$	1.75450	+	3.48512i	0.270725	+	0.537766i
$43$	7.59829	+	9.05529i	1.15873	+	1.38092i	0.911162	+	0.412048i	$0.135187\pi$
$43$	7.59829	+	9.05529i	1.15873	+	1.38092i	0.247567	+	0.968871i	$0.420369\pi$
$44$	0.217795	−	0.232513i	0.0328338	−	0.0350526i
$45$	4.97682	−	5.25763i	0.741900	−	0.783761i
$46$	−1.18785	+	3.00570i	−0.175140	+	0.443166i
$47$	3.66367	+	1.33347i	0.534402	+	0.194506i	0.595103	−	0.803650i	$-0.297111\pi$
$47$	3.66367	+	1.33347i	0.534402	+	0.194506i	−0.0607009	+	0.998156i	$0.519334\pi$
$48$	−1.44399	−	6.77605i	−0.208422	−	0.978039i
$49$	−3.41856	−	2.86851i	−0.488366	−	0.409788i
$50$	0.992290	+	0.609602i	0.140331	+	0.0862107i
$51$	−4.23112	−	2.61464i	−0.592476	−	0.366123i
$52$	−0.375823	+	6.87717i	−0.0521173	+	0.953691i
$53$			9.80805i			1.34724i	0.739078	+	0.673620i	$0.235262\pi$
$53$			9.80805i			1.34724i	−0.739078	+	0.673620i	$0.764738\pi$
$54$	5.03911	+	5.34859i	0.685736	+	0.727850i
$55$	−0.384404			−0.0518330
$56$	−2.60402	−	3.67670i	−0.347977	−	0.491320i
$57$	3.55991	+	6.61539i	0.471522	+	0.876230i
$58$	6.46837	−	10.5290i	0.849338	−	1.38253i
$59$	−1.72220	+	2.05244i	−0.224212	+	0.267205i	−0.866410	−	0.499334i	$-0.833578\pi$
$59$	−1.72220	+	2.05244i	−0.224212	+	0.267205i	0.642198	+	0.766539i	$0.278023\pi$
$60$	−4.77595	+	6.86091i	−0.616572	+	0.885740i
$61$	0.492702	−	1.35369i	0.0630841	−	0.173322i	−0.904146	−	0.427224i	$-0.859492\pi$
$61$	0.492702	−	1.35369i	0.0630841	−	0.173322i	0.967230	+	0.253902i	$0.0817139\pi$
$62$	3.70121	−	9.36539i	0.470054	−	1.18941i
$63$	4.38478	+	1.90004i	0.552431	+	0.239382i
$64$	2.81683	+	7.48769i	0.352104	+	0.935961i
$65$	6.36609	−	5.34178i	0.789616	−	0.662566i
$66$	0.0223122	−	0.389548i	0.00274644	−	0.0479500i
$67$	−0.225321	−	0.0397302i	−0.0275273	−	0.00485381i	0.159868	−	0.987138i	$-0.448893\pi$
$67$	−0.225321	−	0.0397302i	−0.0275273	−	0.00485381i	−0.187395	+	0.982285i	$0.560004\pi$
$68$	5.28167	+	2.25587i	0.640497	+	0.273565i
$69$	1.24193	+	3.75838i	0.149511	+	0.452456i
$70$	−1.08976	+	5.32591i	−0.130252	+	0.636568i
$71$	2.82317	−	4.88987i	0.335048	−	0.580320i	−0.648446	−	0.761261i	$-0.724581\pi$
$71$	2.82317	−	4.88987i	0.335048	−	0.580320i	0.983494	+	0.180940i	$0.0579141\pi$
$72$	−6.67551	−	5.23809i	−0.786716	−	0.617315i
$73$	7.14574	+	12.3768i	0.836346	+	1.44859i	0.892930	+	0.450196i	$0.148646\pi$
$73$	7.14574	+	12.3768i	0.836346	+	1.44859i	−0.0565836	+	0.998398i	$0.518021\pi$
$74$	−7.97195	+	2.65748i	−0.926720	+	0.308926i
$75$	1.41143	−	0.205549i	0.162978	−	0.0237347i
$76$	−5.20501	−	6.93948i	−0.597056	−	0.796013i
$77$	−0.0867843	−	0.238438i	−0.00988999	−	0.0271725i
$78$	5.04375	+	6.76133i	0.571092	+	0.765570i
$79$	−2.18269	−	12.3786i	−0.245572	−	1.39271i	−0.819161	−	0.573563i	$-0.805561\pi$
$79$	−2.18269	−	12.3786i	−0.245572	−	1.39271i	0.573590	−	0.819143i	$-0.305550\pi$
$80$	4.27021	−	8.65685i	0.477424	−	0.967865i
$81$	8.93563	+	1.07447i	0.992848	+	0.119386i
$82$	−8.84487	−	11.1451i	−0.976753	−	1.23077i
$83$	−11.1079	+	1.95862i	−1.21925	+	0.214987i	−0.746003	−	0.665942i	$-0.768030\pi$
$83$	−11.1079	+	1.95862i	−1.21925	+	0.214987i	−0.473248	+	0.880929i	$0.656919\pi$
$84$	−5.33392	−	1.41348i	−0.581978	−	0.154223i
$85$	−2.37013	−	6.51187i	−0.257076	−	0.706311i
$86$	−16.7110	−	0.456270i	−1.80199	−	0.0492008i
$87$	−2.18104	−	14.9764i	−0.233832	−	1.60564i
$88$	0.0416802	+	0.448616i	0.00444313	+	0.0478226i
$89$	−3.73417	−	6.46777i	−0.395821	−	0.685582i	0.597385	−	0.801955i	$-0.296207\pi$
$89$	−3.73417	−	6.46777i	−0.395821	−	0.685582i	−0.993206	+	0.116373i	$0.962873\pi$
$90$	0.893694	+	10.1992i	0.0942036	+	1.07509i
$91$	4.75063	+	2.74278i	0.498001	+	0.287521i
$92$	−2.06591	−	4.07706i	−0.215386	−	0.425063i
$93$	−3.86972	−	11.7107i	−0.401271	−	1.21434i
$94$	−4.84850	+	2.62551i	−0.500085	+	0.270801i
$95$	−1.81753	+	10.3077i	−0.186474	+	1.05755i
$96$	8.52483	+	4.82982i	0.870062	+	0.492942i
$97$	5.17680	−	4.34385i	0.525624	−	0.441051i	−0.340963	−	0.940077i	$-0.610753\pi$
$97$	5.17680	−	4.34385i	0.525624	−	0.441051i	0.866587	+	0.499026i	$0.166309\pi$
$98$	6.24280	−	0.925866i	0.630618	−	0.0935266i
$99$	−0.284733	−	0.383790i	−0.0286168	−	0.0385724i
$100$	−1.57608	+	0.478008i	−0.157608	+	0.0478008i
$101$	−0.582767	+	1.60114i	−0.0579875	+	0.159319i	−0.965304	−	0.261129i	$-0.915905\pi$
$101$	−0.582767	+	1.60114i	−0.0579875	+	0.159319i	0.907316	+	0.420449i	$0.138127\pi$
$102$	6.73658	−	2.02387i	0.667020	−	0.200393i
$103$	9.82235	+	8.24193i	0.967825	+	0.812102i	0.982208	−	0.187795i	$-0.0601340\pi$
$103$	9.82235	+	8.24193i	0.967825	+	0.812102i	−0.0143832	+	0.999897i	$0.504578\pi$
$104$	−6.92435	−	6.85030i	−0.678989	−	0.671727i
$105$	3.15504	+	5.86302i	0.307901	+	0.572172i
$106$	−10.3783	−	9.20259i	−1.00803	−	0.893835i
$107$		−	15.7558i		−	1.52317i	−0.648065	−	0.761585i	$-0.724421\pi$
$107$		−	15.7558i		−	1.52317i	0.648065	−	0.761585i	$-0.275579\pi$
$108$	−10.3876	+	0.313654i	−0.999544	+	0.0301814i
$109$		−	4.23854i		−	0.405978i	−0.979181	−	0.202989i	$-0.934934\pi$
$109$		−	4.23854i		−	0.405978i	0.979181	−	0.202989i	$-0.0650656\pi$
$110$	0.360674	−	0.406752i	0.0343889	−	0.0387822i
$111$	−5.41021	+	8.75504i	−0.513515	+	0.830992i
$112$	6.33373	+	0.694324i	0.598481	+	0.0656074i
$113$	−5.72871	−	4.80696i	−0.538912	−	0.452201i	0.332254	−	0.943190i	$-0.392191\pi$
$113$	−5.72871	−	4.80696i	−0.538912	−	0.452201i	−0.871166	+	0.490989i	$0.836635\pi$
$114$	−10.3401	−	2.44014i	−0.968443	−	0.228540i
$115$	−1.88620	+	5.18228i	−0.175889	+	0.483250i
$116$	5.07205	+	16.7234i	0.470928	+	1.55273i
$117$	10.0487	+	2.39919i	0.929003	+	0.221805i
$118$	−0.555873	−	3.74807i	−0.0511723	−	0.345037i
$119$	3.50409	−	2.94028i	0.321220	−	0.269535i
$120$	−2.77866	−	11.4910i	−0.253656	−	1.04898i
$121$	1.90572	−	10.8079i	0.173248	−	0.982536i
$122$	0.970099	+	1.79147i	0.0878287	+	0.162192i
$123$	−17.0631	−	3.53799i	−1.53853	−	0.319010i
$124$	6.43712	+	12.7036i	0.578071	+	1.14082i
$125$	−8.72843	−	5.03936i	−0.780695	−	0.450734i
$126$	−6.12461	+	2.85695i	−0.545623	+	0.254517i
$127$	6.92735	+	11.9985i	0.614703	+	1.06470i	0.990437	+	0.137969i	$0.0440574\pi$
$127$	6.92735	+	11.9985i	0.614703	+	1.06470i	−0.375734	+	0.926728i	$0.622609\pi$
$128$	−10.5659	−	4.04487i	−0.933906	−	0.357520i
$129$	−16.0709	+	12.6856i	−1.41496	+	1.11690i
$130$	−0.320768	+	11.7482i	−0.0281332	+	1.03039i
$131$	1.76657	+	4.85361i	0.154346	+	0.424061i	0.992632	−	0.121169i	$-0.0386643\pi$
$131$	1.76657	+	4.85361i	0.154346	+	0.424061i	−0.838286	+	0.545231i	$0.816442\pi$
$132$	0.391260	+	0.389110i	0.0340548	+	0.0338677i
$133$	−6.80399	+	1.19973i	−0.589981	+	0.104030i
$134$	0.253452	−	0.201143i	0.0218949	−	0.0173761i
$135$	8.84455	+	8.88865i	0.761217	+	0.765013i
$136$	−7.34265	+	3.47211i	−0.629627	+	0.297731i
$137$	−3.27446	−	18.5704i	−0.279756	−	1.58658i	−0.723436	−	0.690391i	$-0.757438\pi$
$137$	−3.27446	−	18.5704i	−0.279756	−	1.58658i	0.443680	−	0.896185i	$-0.353673\pi$
$138$	−5.14214	−	2.21223i	−0.437728	−	0.188318i
$139$	5.53623	+	15.2107i	0.469577	+	1.29015i	0.918089	+	0.396375i	$0.129732\pi$
$139$	5.53623	+	15.2107i	0.469577	+	1.29015i	−0.448512	+	0.893777i	$0.648046\pi$
$140$	−4.61304	−	6.15025i	−0.389873	−	0.519791i
$141$	−2.49842	+	6.27374i	−0.210405	+	0.528344i
$142$	2.52526	+	7.57530i	0.211915	+	0.635705i
$143$	−0.274279	−	0.475066i	−0.0229364	−	0.0397270i
$144$	11.8060	−	2.14886i	0.983836	−	0.179072i
$145$	10.5430	−	18.2611i	0.875551	−	1.51650i
$146$	−19.8010	−	4.05159i	−1.63874	−	0.335312i
$147$	5.14331	−	5.76985i	0.424213	−	0.475889i
$148$	4.66785	−	10.9288i	0.383695	−	0.898345i
$149$	12.7731	+	2.25224i	1.04641	+	0.184511i	0.670321	−	0.742071i	$-0.266157\pi$
$149$	12.7731	+	2.25224i	1.04641	+	0.184511i	0.376092	+	0.926582i	$0.377268\pi$
$150$	−1.10680	+	1.68634i	−0.0903699	+	0.137689i
$151$	2.57721	−	2.16253i	0.209730	−	0.175985i	−0.531871	−	0.846825i	$-0.678511\pi$
$151$	2.57721	−	2.16253i	0.209730	−	0.175985i	0.741602	+	0.670841i	$0.234067\pi$
$152$	12.2266	+	1.00349i	0.991709	+	0.0813935i
$153$	4.74588	−	7.18977i	0.383682	−	0.581259i
$154$	0.333727	+	0.131889i	0.0268925	+	0.0106279i
$155$	5.87716	−	16.1474i	0.472065	−	1.29699i
$156$	−11.8868	−	1.00697i	−0.951706	−	0.0806220i
$157$	0.320529	−	0.381992i	0.0255810	−	0.0304863i	−0.753102	−	0.657903i	$-0.771443\pi$
$157$	0.320529	−	0.381992i	0.0255810	−	0.0304863i	0.778683	+	0.627417i	$0.215888\pi$
$158$	15.1462	+	9.30491i	1.20497	+	0.740259i
$159$	−16.9804	−	0.508169i	−1.34664	−	0.0403004i
$160$	5.15352	+	12.6409i	0.407422	+	0.999352i
$161$	−3.64030			−0.286896
$162$	−9.52096	+	8.44697i	−0.748037	+	0.663657i
$163$		−	11.3041i		−	0.885405i	−0.896669	−	0.442703i	$-0.854020\pi$
$163$		−	11.3041i		−	0.885405i	0.896669	−	0.442703i	$-0.145980\pi$
$164$	20.0919	+	1.09798i	1.56891	+	0.0857377i
$165$	0.0199165	−	0.665509i	0.00155050	−	0.0518098i
$166$	8.34971	−	13.5914i	0.648063	−	1.05490i
$167$	10.0898	+	8.46632i	0.780770	+	0.655144i	0.943442	−	0.331536i	$-0.107567\pi$
$167$	10.0898	+	8.46632i	0.780770	+	0.655144i	−0.162673	+	0.986680i	$0.552011\pi$
$168$	6.50031	−	4.31779i	0.501509	−	0.333125i
$169$	−1.07204	−	0.390189i	−0.0824644	−	0.0300146i
$170$	9.11426	+	3.60197i	0.699032	+	0.276258i
$171$	−11.6375	+	5.82044i	−0.889943	+	0.445100i
$172$	16.1622	−	17.2544i	1.23235	−	1.31563i
$173$	10.5281	+	12.5470i	0.800440	+	0.953928i	0.999661	−	0.0260269i	$-0.00828556\pi$
$173$	10.5281	+	12.5470i	0.800440	+	0.953928i	−0.199221	+	0.979955i	$0.563841\pi$
$174$	17.8935	+	11.7440i	1.35650	+	0.890314i
$175$	−0.227782	+	1.29182i	−0.0172187	+	0.0976521i
$176$	−0.513804	−	0.376819i	−0.0387294	−	0.0284038i
$177$	−3.46411	−	3.08795i	−0.260379	−	0.232104i
$178$	10.3474	+	2.11725i	0.775572	+	0.158694i
$179$	5.13398	+	2.96410i	0.383731	+	0.221547i	0.679441	−	0.733731i	$-0.262223\pi$
$179$	5.13398	+	2.96410i	0.383731	+	0.221547i	−0.295709	+	0.955278i	$0.595556\pi$
$180$	−11.6307	−	8.62396i	−0.866900	−	0.642792i
$181$	−1.50802	+	0.870656i	−0.112090	+	0.0647154i	−0.554997	−	0.831852i	$-0.687281\pi$
$181$	−1.50802	+	0.870656i	−0.112090	+	0.0647154i	0.442907	+	0.896568i	$0.353947\pi$
$182$	−7.35960	+	2.45335i	−0.545529	+	0.181854i
$183$	2.31808	+	0.923140i	0.171357	+	0.0682405i
$184$	6.25246	+	1.63937i	0.460938	+	0.120856i
$185$	−13.4744	+	4.90427i	−0.990655	+	0.360569i
$186$	16.0223	+	6.89305i	1.17481	+	0.505423i
$187$	−0.450481	+	0.0794319i	−0.0329424	+	0.00580863i
$188$	1.77105	−	7.59381i	0.129167	−	0.553836i
$189$	−3.51667	+	7.49283i	−0.255800	+	0.545023i
$190$	−9.20163	−	11.5946i	−0.667556	−	0.841160i
$191$	1.88621	+	10.6972i	0.136481	+	0.774023i	0.973817	+	0.227334i	$0.0730008\pi$
$191$	1.88621	+	10.6972i	0.136481	+	0.774023i	−0.837336	+	0.546689i	$0.815888\pi$
$192$	−13.1092	+	4.48876i	−0.946075	+	0.323949i
$193$	−13.6021	+	4.95075i	−0.979100	+	0.356363i	−0.781490	−	0.623918i	$-0.785540\pi$
$193$	−13.6021	+	4.95075i	−0.979100	+	0.356363i	−0.197609	+	0.980281i	$0.563318\pi$
$194$	−0.260844	+	9.55346i	−0.0187275	+	0.685898i
$195$	8.91826	+	11.2982i	0.638650	+	0.809082i
$196$	−4.87774	+	7.47445i	−0.348410	+	0.533889i
$197$	−7.36911	+	4.25456i	−0.525027	+	0.303125i	−0.738989	−	0.673717i	$-0.764697\pi$
$197$	−7.36911	+	4.25456i	−0.525027	+	0.303125i	0.213962	+	0.976842i	$0.431363\pi$
$198$	0.673259	+	0.0588115i	0.0478464	+	0.00417955i
$199$	−6.17939	+	10.7030i	−0.438045	+	0.758716i	−0.997539	−	0.0701183i	$-0.977662\pi$
$199$	−6.17939	+	10.7030i	−0.438045	+	0.758716i	0.559494	+	0.828835i	$0.310996\pi$
$200$	0.972986	−	2.11620i	0.0688005	−	0.149638i
$201$	0.0804581	−	0.388034i	0.00567508	−	0.0273698i
$202$	−1.14743	−	2.11895i	−0.0807330	−	0.149089i
$203$	13.7072	+	2.41695i	0.962057	+	0.169637i
$204$	−4.17919	+	9.02715i	−0.292602	+	0.632027i
$205$	−15.6062	−	18.5987i	−1.08998	−	1.29899i
$206$	−17.9371	+	2.66024i	−1.24974	+	0.185348i
$207$	−6.57114	+	1.95540i	−0.456726	+	0.135910i
$208$	13.7455	−	0.899487i	0.953076	−	0.0623682i
$209$	0.649234	+	0.236302i	0.0449084	+	0.0163453i
$210$	−9.16415	−	2.16262i	−0.632386	−	0.149235i
$211$	−1.13641	+	1.35433i	−0.0782339	+	0.0932356i	−0.803742	−	0.594978i	$-0.797161\pi$
$211$	−1.13641	+	1.35433i	−0.0782339	+	0.0932356i	0.725508	+	0.688214i	$0.241605\pi$
$212$	19.4752	−	2.34711i	1.33756	−	0.161200i
$213$	8.31943	+	5.14103i	0.570038	+	0.352257i
$214$	16.6718	+	14.7832i	1.13966	+	1.01056i
$215$	−28.5259			−1.94545
$216$	9.41444	−	11.2858i	0.640572	−	0.767898i
$217$	11.3427			0.769994
$218$	4.48495	+	3.97689i	0.303759	+	0.269349i
$219$	−21.7979	+	11.7300i	−1.47296	+	0.792640i
$220$	0.0919893	+	0.763285i	0.00620192	+	0.0514606i
$221$	6.35657	−	7.57546i	0.427589	−	0.509581i
$222$	−4.18779	−	13.9393i	−0.281066	−	0.935546i
$223$	−2.82725	−	1.02903i	−0.189327	−	0.0689092i	0.245617	−	0.969367i	$-0.421009\pi$
$223$	−2.82725	−	1.02903i	−0.189327	−	0.0689092i	−0.434944	+	0.900458i	$0.643232\pi$
$224$	−6.67743	+	6.05048i	−0.446154	+	0.404265i
$225$	0.282734	+	2.45422i	0.0188489	+	0.163615i
$226$	10.4615	−	1.55154i	0.695888	−	0.103207i
$227$	−3.65533	−	4.35626i	−0.242613	−	0.289135i	0.630973	−	0.775805i	$-0.282656\pi$
$227$	−3.65533	−	4.35626i	−0.242613	−	0.289135i	−0.873586	+	0.486670i	$0.838211\pi$
$228$	12.2838	−	8.65177i	0.813517	−	0.572977i
$229$	21.4459	+	3.78149i	1.41718	+	0.249888i	0.829185	−	0.558974i	$-0.188805\pi$
$229$	21.4459	+	3.78149i	1.41718	+	0.249888i	0.587998	+	0.808862i	$0.299916\pi$
$230$	−3.71380	−	6.85822i	−0.244881	−	0.452218i
$231$	0.417298	−	0.137894i	0.0274562	−	0.00907275i
$232$	−22.4546	−	10.3242i	−1.47422	−	0.677815i
$233$	−11.7482	+	20.3485i	−0.769650	+	1.33307i	0.168103	+	0.985769i	$0.446236\pi$
$233$	−11.7482	+	20.3485i	−0.769650	+	1.33307i	−0.937753	+	0.347303i	$0.887097\pi$
$234$	−11.9670	+	8.38181i	−0.782310	+	0.547936i
$235$	−8.14804	+	4.70427i	−0.531520	+	0.306873i
$236$	4.48752	+	2.92850i	0.292113	+	0.190629i
$237$	21.5439	−	3.13748i	1.39943	−	0.203801i
$238$	−0.176561	+	6.46658i	−0.0114447	+	0.419166i
$239$	21.9880	−	8.00297i	1.42228	−	0.517669i	0.487574	−	0.873082i	$-0.337882\pi$
$239$	21.9880	−	8.00297i	1.42228	−	0.517669i	0.934710	+	0.355413i	$0.115660\pi$
$240$	14.7662	+	7.84143i	0.953151	+	0.506162i
$241$	0.682320	+	3.86963i	0.0439521	+	0.249265i	0.998866	−	0.0476196i	$-0.0151635\pi$
$241$	0.682320	+	3.86963i	0.0439521	+	0.249265i	−0.954913	+	0.296884i	$0.904052\pi$
$242$	9.64814	+	12.1572i	0.620206	+	0.781496i
$243$	−2.32317	+	15.4144i	−0.149032	+	0.988832i
$244$	−2.80583	−	0.654382i	−0.179625	−	0.0418925i
$245$	10.6055	−	1.87004i	0.677562	−	0.119472i
$246$	19.7534	−	14.7355i	1.25943	−	0.939499i
$247$	−14.0356	+	5.10855i	−0.893066	+	0.325049i
$248$	−19.4819	−	5.10807i	−1.23710	−	0.324363i
$249$	−2.81540	−	19.3323i	−0.178419	−	1.22514i
$250$	13.5219	−	4.50759i	0.855203	−	0.285085i
$251$	−0.431970	+	0.249398i	−0.0272657	+	0.0157419i	−0.513571	−	0.858047i	$-0.671678\pi$
$251$	−0.431970	+	0.249398i	−0.0272657	+	0.0157419i	0.486305	+	0.873789i	$0.338344\pi$
$252$	2.72348	−	9.16125i	0.171563	−	0.577105i
$253$	0.315261	+	0.182016i	0.0198203	+	0.0114433i
$254$	−19.1958	−	3.92776i	−1.20445	−	0.246449i
$255$	11.3966	−	3.76595i	0.713685	−	0.235833i
$256$	14.1937	−	7.38502i	0.887107	−	0.461564i
$257$	0.156179	−	0.885735i	0.00974218	−	0.0552506i	−0.979549	−	0.201205i	$-0.935514\pi$
$257$	0.156179	−	0.885735i	0.00974218	−	0.0552506i	0.989291	+	0.145955i	$0.0466253\pi$
$258$	1.65575	−	28.9077i	0.103082	−	1.79971i
$259$	−6.08403	−	7.25067i	−0.378043	−	0.450535i
$260$	−12.1302	−	11.3624i	−0.752285	−	0.704666i
$261$	26.0413	−	3.00003i	1.61191	−	0.185697i
$262$	−6.79329	−	2.68472i	−0.419691	−	0.165862i
$263$	−9.42004	−	3.42861i	−0.580864	−	0.211417i	0.0348423	−	0.999393i	$-0.488907\pi$
$263$	−9.42004	−	3.42861i	−0.580864	−	0.211417i	−0.615707	+	0.787976i	$0.711129\pi$
$264$	−0.778838	+	0.0489165i	−0.0479342	+	0.00301060i
$265$	−18.1313	−	15.2139i	−1.11380	−	0.934585i
$266$	5.11450	−	8.32522i	0.313590	−	0.510452i
$267$	11.3910	−	6.12977i	0.697115	−	0.375136i
$268$	−0.0249693	+	0.456912i	−0.00152524	+	0.0279104i
$269$		−	1.04059i		−	0.0634460i	−0.999497	−	0.0317230i	$-0.989901\pi$
$269$		−	1.04059i		−	0.0634460i	0.999497	−	0.0317230i	$-0.0100994\pi$
$270$	−17.7040	+	1.01880i	−1.07743	+	0.0620019i
$271$	−30.0408			−1.82485			−0.912423	−	0.409248i	$-0.865791\pi$
$271$	−30.0408			−1.82485			−0.912423	+	0.409248i	$0.865791\pi$
$272$	3.21541	−	11.0273i	0.194963	−	0.668628i
$273$	−4.99464	+	8.08254i	−0.302289	+	0.489178i
$274$	22.7223	+	13.9592i	1.37271	+	0.843306i
$275$	0.0843178	−	0.100486i	0.00508456	−	0.00605954i
$276$	7.16556	−	3.36542i	0.431316	−	0.202574i
$277$	−6.71914	+	18.4607i	−0.403714	+	1.10920i	0.556723	+	0.830698i	$0.312059\pi$
$277$	−6.71914	+	18.4607i	−0.403714	+	1.10920i	−0.960437	+	0.278497i	$0.910164\pi$
$278$	−21.2894	−	8.41361i	−1.27686	−	0.504615i
$279$	20.4749	−	6.09280i	1.22580	−	0.364767i
$280$	10.8361	+	0.889360i	0.647579	+	0.0531494i
$281$	21.2698	−	17.8475i	1.26885	−	1.06469i	0.274167	−	0.961682i	$-0.411598\pi$
$281$	21.2698	−	17.8475i	1.26885	−	1.06469i	0.994681	−	0.103008i	$-0.0328467\pi$
$282$	−4.29428	−	8.53012i	−0.255721	−	0.507962i
$283$	−24.5768	−	4.33356i	−1.46094	−	0.257603i	−0.614007	−	0.789301i	$-0.710443\pi$
$283$	−24.5768	−	4.33356i	−1.46094	−	0.257603i	−0.846934	+	0.531698i	$0.821554\pi$
$284$	−10.3851	−	4.43560i	−0.616240	−	0.263205i
$285$	−17.7513	−	3.68070i	−1.05150	−	0.218026i
$286$	0.760032	+	0.155515i	0.0449417	+	0.00919577i
$287$	8.01310	−	13.8791i	0.472999	−	0.819258i
$288$	−8.80344	+	14.5086i	−0.518748	+	0.854927i
$289$	4.37687	+	7.58097i	0.257463	+	0.445939i
$290$	9.43050	+	28.2897i	0.553778	+	1.66123i
$291$	7.25219	+	9.18753i	0.425131	+	0.538582i
$292$	22.8657	−	17.1506i	1.33812	−	1.00366i
$293$	−2.79279	−	7.67312i	−0.163156	−	0.448268i	0.830993	−	0.556283i	$-0.187773\pi$
$293$	−2.79279	−	7.67312i	−0.163156	−	0.448268i	−0.994149	+	0.108015i	$0.965551\pi$
$294$	1.27948	+	10.8560i	0.0746209	+	0.633134i
$295$	−1.12274	−	6.36736i	−0.0653683	−	0.370722i
$296$	7.18449	+	15.1934i	0.417590	+	0.883099i
$297$	0.679199	−	0.473067i	0.0394111	−	0.0274501i
$298$	−14.3678	+	11.4025i	−0.832303	+	0.660527i
$299$	−7.75036	+	1.36660i	−0.448215	+	0.0790324i
$300$	−0.745905	−	2.75339i	−0.0430648	−	0.158967i
$301$	−6.44011	−	17.6941i	−0.371202	−	1.01987i
$302$	−0.129858	+	4.75607i	−0.00747248	+	0.273681i
$303$	−2.74182	−	1.09189i	−0.157513	−	0.0627273i
$304$	−12.5337	+	11.9959i	−0.718855	+	0.688011i
$305$	1.73818	+	3.01061i	0.0995278	+	0.172387i
$306$	3.15484	+	11.7677i	0.180350	+	0.672716i
$307$	−16.1236	−	9.30896i	−0.920222	−	0.531290i	−0.0365160	−	0.999333i	$-0.511626\pi$
$307$	−16.1236	−	9.30896i	−0.920222	−	0.531290i	−0.883706	+	0.468043i	$0.844959\pi$
$308$	−0.452682	+	0.229381i	−0.0257940	+	0.0130702i
$309$	−14.7780	+	16.5782i	−0.840689	+	0.943099i
$310$	11.5717	+	21.3694i	0.657231	+	1.21370i
$311$	−0.851609	+	4.82971i	−0.0482903	+	0.273868i	−0.999386	−	0.0350274i	$-0.988848\pi$
$311$	−0.851609	+	4.82971i	−0.0482903	+	0.273868i	0.951096	+	0.308895i	$0.0999593\pi$
$312$	12.2185	−	11.6330i	0.691737	−	0.658591i
$313$	−7.88890	+	6.61958i	−0.445907	+	0.374161i	−0.837914	−	0.545802i	$-0.816225\pi$
$313$	−7.88890	+	6.61958i	−0.445907	+	0.374161i	0.392007	+	0.919962i	$0.371781\pi$
$314$	0.103457	+	0.697574i	0.00583840	+	0.0393664i
$315$	−10.3140	+	5.15848i	−0.581126	+	0.290647i
$316$	−24.0571	+	7.29627i	−1.35332	+	0.410447i
$317$	7.72259	−	21.2177i	0.433744	−	1.19170i	−0.509753	−	0.860321i	$-0.670263\pi$
$317$	7.72259	−	21.2177i	0.433744	−	1.19170i	0.943497	−	0.331381i	$-0.107515\pi$
$318$	16.4699	−	17.4908i	0.923588	−	0.980837i
$319$	−1.06624	−	0.894680i	−0.0596979	−	0.0500925i
$320$	−18.2112	−	6.40744i	−1.01804	−	0.358187i
$321$	27.2776	+	0.816330i	1.52249	+	0.0455631i
$322$	3.41558	−	3.85193i	0.190343	−	0.214660i
$323$			12.4551i			0.693020i
$324$	−0.00482748	−	18.0000i	−0.000268193	−	1.00000i
$325$			2.83585i			0.157304i
$326$	11.9613	+	10.6063i	0.662474	+	0.587427i
$327$	7.33808	+	0.219605i	0.405797	+	0.0121442i
$328$	−20.0134	+	20.2297i	−1.10505	+	1.11700i
$329$	−4.75749	−	3.99201i	−0.262289	−	0.220087i
$330$	0.685512	+	0.645501i	0.0377362	+	0.0355336i
$331$	8.06296	−	22.1528i	0.443180	−	1.21763i	−0.494209	−	0.869343i	$-0.664542\pi$
$331$	8.06296	−	22.1528i	0.443180	−	1.21763i	0.937389	−	0.348284i	$-0.113236\pi$
$332$	6.54727	+	21.5875i	0.359328	+	1.18477i
$333$	−14.8771	−	9.82018i	−0.815259	−	0.538143i
$334$	−18.4254	+	2.73266i	−1.00819	+	0.149525i
$335$	0.422957	−	0.354903i	0.0231086	−	0.0193904i
$336$	−1.53022	+	10.9295i	−0.0834806	+	0.596251i
$337$	−5.70981	+	32.3820i	−0.311033	+	1.76396i	0.282615	+	0.959233i	$0.408798\pi$
$337$	−5.70981	+	32.3820i	−0.311033	+	1.76396i	−0.593649	+	0.804724i	$0.702313\pi$
$338$	1.41873	−	0.768258i	0.0771688	−	0.0417877i
$339$	8.61898	−	9.66892i	0.468119	−	0.525144i
$340$	−12.3630	+	6.26451i	−0.670477	+	0.339741i
$341$	−0.982316	−	0.567140i	−0.0531954	−	0.0307124i
$342$	4.76030	−	17.7752i	0.257407	−	0.961173i
$343$	9.12950	+	15.8128i	0.492947	+	0.853809i
$344$	3.09302	+	33.2910i	0.166764	+	1.79493i
$345$	−8.87423	−	3.53403i	−0.477772	−	0.190266i
$346$	−23.1546	−	0.632204i	−1.24480	−	0.0339875i
$347$	−0.288638	−	0.793027i	−0.0154949	−	0.0425719i	0.931704	−	0.363218i	$-0.118322\pi$
$347$	−0.288638	−	0.793027i	−0.0154949	−	0.0425719i	−0.947199	+	0.320646i	$0.896100\pi$
$348$	−29.2157	+	7.91465i	−1.56613	+	0.424270i
$349$	−13.8072	+	2.43459i	−0.739085	+	0.130321i	−0.530501	−	0.847684i	$-0.677996\pi$
$349$	−13.8072	+	2.43459i	−0.739085	+	0.130321i	−0.208583	+	0.978005i	$0.566885\pi$
$350$	−1.15320	−	1.45309i	−0.0616409	−	0.0776711i
$351$	−4.67429	+	17.2728i	−0.249495	+	0.921952i
$352$	0.880812	−	0.190117i	0.0469475	−	0.0101333i
$353$	4.09441	+	23.2205i	0.217923	+	1.23590i	0.875761	+	0.482744i	$0.160360\pi$
$353$	4.09441	+	23.2205i	0.217923	+	1.23590i	−0.657838	+	0.753159i	$0.728529\pi$
$354$	6.51774	−	0.768178i	0.346414	−	0.0408282i
$355$	4.66025	+	12.8039i	0.247341	+	0.679562i
$356$	−11.9490	+	8.96244i	−0.633296	+	0.475008i
$357$	4.90889	+	6.21889i	0.259806	+	0.329139i
$358$	−7.95347	+	2.65132i	−0.420354	+	0.140127i
$359$	−13.4957	−	23.3753i	−0.712277	−	1.23370i	−0.964001	−	0.265900i	$-0.914331\pi$
$359$	−13.4957	−	23.3753i	−0.712277	−	1.23370i	0.251724	−	0.967799i	$-0.419003\pi$
$360$	20.0380	−	4.21526i	1.05610	−	0.222164i
$361$	−0.0939335	+	0.162698i	−0.00494387	+	0.00856303i
$362$	0.493656	−	2.41260i	0.0259460	−	0.126804i
$363$	18.6127	+	3.85931i	0.976914	+	0.202561i
$364$	4.30930	−	10.0894i	0.225869	−	0.528826i
$365$	−33.9641	−	5.98879i	−1.77776	−	0.313468i
$366$	−3.15179	+	1.58669i	−0.164747	+	0.0829377i
$367$	22.3181	−	18.7271i	1.16500	−	0.977547i	0.165033	−	0.986288i	$-0.447227\pi$
$367$	22.3181	−	18.7271i	1.16500	−	0.977547i	0.999962	+	0.00874090i	$0.00278235\pi$
$368$	−7.60116	+	5.07779i	−0.396238	+	0.264698i
$369$	7.00930	−	29.3576i	0.364890	−	1.52829i
$370$	7.45319	−	18.8592i	0.387473	−	0.980444i
$371$	5.34353	−	14.6812i	0.277422	−	0.762211i
$372$	−22.3270	+	10.4862i	−1.15760	+	0.543686i
$373$	0.738799	−	0.880467i	0.0382536	−	0.0455888i	−0.746578	−	0.665297i	$-0.768305\pi$
$373$	0.738799	−	0.880467i	0.0382536	−	0.0455888i	0.784832	+	0.619709i	$0.212749\pi$
$374$	0.338622	−	0.551198i	0.0175097	−	0.0285018i
$375$	9.17676	−	14.8502i	0.473886	−	0.766862i
$376$	6.37357	+	8.99904i	0.328692	+	0.464090i
$377$	30.0906			1.54975
$378$	−4.62884	−	10.7514i	−0.238082	−	0.552993i
$379$		−	16.9124i		−	0.868731i	−0.900737	−	0.434365i	$-0.856973\pi$
$379$		−	16.9124i		−	0.868731i	0.900737	−	0.434365i	$-0.143027\pi$
$380$	20.9022	+	1.14226i	1.07226	+	0.0585969i
$381$	−21.1317	+	11.3715i	−1.08261	+	0.582579i
$382$	−13.0889	−	8.04099i	−0.669685	−	0.411413i
$383$	15.4572	+	12.9701i	0.789826	+	0.662743i	0.945702	−	0.325034i	$-0.105376\pi$
$383$	15.4572	+	12.9701i	0.789826	+	0.662743i	−0.155876	+	0.987777i	$0.549820\pi$
$384$	7.55023	−	18.0830i	0.385296	−	0.922793i
$385$	0.575396	+	0.209427i	0.0293249	+	0.0106734i
$386$	7.52384	−	19.0380i	0.382953	−	0.969008i
$387$	−21.1296	−	28.4804i	−1.07408	−	1.44774i
$388$	−9.86412	−	9.23972i	−0.500775	−	0.469076i
$389$	18.7454	+	22.3399i	0.950428	+	1.13268i	0.991049	+	0.133502i	$0.0426221\pi$
$389$	18.7454	+	22.3399i	0.950428	+	1.13268i	−0.0406204	+	0.999175i	$0.512933\pi$
$390$	−20.3228	−	1.16403i	−1.02908	−	0.0589429i
$391$	−1.13957	+	6.46284i	−0.0576307	+	0.326840i
$392$	−3.33236	−	12.1743i	−0.168309	−	0.614897i
$393$	−8.49446	+	2.80694i	−0.428489	+	0.141592i
$394$	2.41230	−	11.7894i	0.121530	−	0.593943i
$395$	26.2690	+	15.1664i	1.32174	+	0.763105i
$396$	−0.693928	+	0.657218i	−0.0348712	+	0.0330265i
$397$	−10.3158	+	5.95584i	−0.517736	+	0.298915i	−0.736008	−	0.676973i	$-0.763291\pi$
$397$	−10.3158	+	5.95584i	−0.517736	+	0.298915i	0.218272	+	0.975888i	$0.429958\pi$
$398$	−5.52732	−	16.5809i	−0.277059	−	0.831127i
$399$	−1.72453	−	11.8417i	−0.0863347	−	0.592829i
$400$	1.32631	+	3.01512i	0.0663155	+	0.150756i
$401$	2.23681	−	0.814132i	0.111701	−	0.0406558i	−0.285565	−	0.958359i	$-0.592181\pi$
$401$	2.23681	−	0.814132i	0.111701	−	0.0406558i	0.397266	+	0.917704i	$0.369959\pi$
$402$	0.335102	+	0.449216i	0.0167134	+	0.0224049i
$403$	24.1492	−	4.25815i	1.20296	−	0.212114i
$404$	3.31873	+	0.774002i	0.165113	+	0.0385080i
$405$	−15.8469	+	14.8518i	−0.787441	+	0.737993i
$406$	−15.4185	+	12.2363i	−0.765207	+	0.607279i
$407$	0.164360	+	0.932134i	0.00814705	+	0.0462042i
$408$	−5.63075	−	12.8920i	−0.278764	−	0.638251i
$409$	12.0885	−	4.39986i	0.597739	−	0.217559i	−0.0253911	−	0.999678i	$-0.508083\pi$
$409$	12.0885	−	4.39986i	0.597739	−	0.217559i	0.623130	+	0.782119i	$0.285861\pi$
$410$	34.3228	+	0.937135i	1.69508	+	0.0462818i
$411$	32.3201	−	4.70684i	1.59424	−	0.232171i
$412$	14.0149	−	21.4759i	0.690465	−	1.05804i
$413$	3.69607	−	2.13393i	0.181872	−	0.105004i
$414$	4.09641	−	8.78785i	0.201327	−	0.431899i
$415$	13.6095	−	23.5724i	0.668064	−	1.15712i
$416$	−11.9451	+	15.3885i	−0.585659	+	0.754484i
$417$	−26.6207	+	8.79666i	−1.30362	+	0.430774i
$418$	−0.859195	+	0.465263i	−0.0420246	+	0.0227568i
$419$	−7.38244	−	1.30172i	−0.360656	−	0.0635933i	−0.00961568	−	0.999954i	$-0.503061\pi$
$419$	−7.38244	−	1.30172i	−0.360656	−	0.0635933i	−0.351040	+	0.936360i	$0.614172\pi$
$420$	10.8868	−	7.66780i	0.531221	−	0.374150i
$421$	5.15270	+	6.14075i	0.251127	+	0.299282i	0.876850	−	0.480763i	$-0.159640\pi$
$421$	5.15270	+	6.14075i	0.251127	+	0.299282i	−0.625723	+	0.780045i	$0.715196\pi$
$422$	−0.366799	−	2.47320i	−0.0178555	−	0.120394i
$423$	−10.7321	−	4.65051i	−0.521814	−	0.226115i
$424$	−15.7894	+	22.8096i	−0.766801	+	1.10773i
$425$	2.22213	+	0.808790i	0.107789	+	0.0392321i
$426$	−13.2458	+	3.97943i	−0.641760	+	0.192804i
$427$	−1.47501	+	1.75784i	−0.0713805	+	0.0850680i
$428$	−31.2852	+	3.77042i	−1.51223	+	0.182250i
$429$	0.836681	−	0.450240i	0.0403953	−	0.0217378i
$430$	26.7650	−	30.1843i	1.29072	−	1.45562i
$431$	−4.63698			−0.223356			−0.111678	−	0.993744i	$-0.535622\pi$
$431$	−4.63698			−0.223356			−0.111678	+	0.993744i	$0.535622\pi$
$432$	3.10859	+	20.5508i	0.149562	+	0.988752i
$433$	−0.0678381			−0.00326009			−0.00163005	−	0.999999i	$-0.500519\pi$
$433$	−0.0678381			−0.00326009			−0.00163005	+	0.999999i	$0.500519\pi$
$434$	−10.6425	+	12.0021i	−0.510858	+	0.576122i
$435$	31.0687	+	19.1990i	1.48963	+	0.920523i
$436$	−8.41618	+	1.01430i	−0.403062	+	0.0485761i
$437$	6.37133	−	7.59305i	0.304782	−	0.363225i
$438$	8.04033	−	34.0710i	0.384182	−	1.62798i
$439$	12.9530	+	4.71449i	0.618211	+	0.225010i	0.632092	−	0.774893i	$-0.282196\pi$
$439$	12.9530	+	4.71449i	0.618211	+	0.225010i	−0.0138813	+	0.999904i	$0.504419\pi$
$440$	−0.893970	−	0.618829i	−0.0426183	−	0.0295015i
$441$	9.72272	+	9.20343i	0.462987	+	0.438258i
$442$	2.05170	+	13.8339i	0.0975895	+	0.658013i
$443$	8.58044	+	10.2258i	0.407669	+	0.485841i	0.930342	−	0.366692i	$-0.119510\pi$
$443$	8.58044	+	10.2258i	0.407669	+	0.485841i	−0.522673	+	0.852533i	$0.675065\pi$
$444$	18.6790	+	8.64758i	0.886465	+	0.410396i
$445$	17.7487	+	3.12957i	0.841369	+	0.148356i
$446$	3.74158	−	2.02610i	0.177169	−	0.0959388i
$447$	−4.56104	+	21.9971i	−0.215730	+	1.04043i
$448$	−0.137014	−	12.7426i	−0.00647332	−	0.602031i
$449$	6.26480	−	10.8509i	0.295654	−	0.512088i	−0.679483	−	0.733692i	$-0.737796\pi$
$449$	6.26480	−	10.8509i	0.295654	−	0.512088i	0.975137	+	0.221604i	$0.0711291\pi$
$450$	−2.86218	−	2.00355i	−0.134925	−	0.0944482i
$451$	−1.38792	+	0.801316i	−0.0653546	+	0.0377325i
$452$	−8.17395	+	12.5254i	−0.384470	+	0.589147i
$453$	3.61041	+	4.57390i	0.169632	+	0.214901i
$454$	8.03919	+	0.219499i	0.377298	+	0.0103016i
$455$	−12.4393	+	4.52755i	−0.583166	+	0.212255i
$456$	−2.37079	+	21.1156i	−0.111022	+	0.988831i
$457$	3.14504	+	17.8364i	0.147119	+	0.834352i	0.965642	+	0.259878i	$0.0836822\pi$
$457$	3.14504	+	17.8364i	0.147119	+	0.834352i	−0.818523	+	0.574474i	$0.805207\pi$
$458$	−24.1233	+	19.1446i	−1.12721	+	0.894569i
$459$	12.2016	+	8.58894i	0.569521	+	0.400898i
$460$	10.7415	+	2.50515i	0.500824	+	0.116803i
$461$	−6.87340	+	1.21197i	−0.320126	+	0.0564469i	−0.331402	−	0.943490i	$-0.607522\pi$
$461$	−6.87340	+	1.21197i	−0.320126	+	0.0564469i	0.0112760	+	0.999936i	$0.496411\pi$
$462$	−0.245628	+	0.570940i	−0.0114276	+	0.0265625i
$463$	26.8210	−	9.76206i	1.24648	−	0.453681i	0.367269	−	0.930115i	$-0.380293\pi$
$463$	26.8210	−	9.76206i	1.24648	−	0.453681i	0.879210	+	0.476434i	$0.158071\pi$
$464$	31.9928	−	14.0732i	1.48523	−	0.653332i
$465$	27.6510	+	11.0116i	1.28229	+	0.510651i
$466$	−10.5085	−	31.5235i	−0.486796	−	1.46030i
$467$	−0.471619	+	0.272289i	−0.0218239	+	0.0126000i	−0.510872	−	0.859657i	$-0.670677\pi$
$467$	−0.471619	+	0.272289i	−0.0218239	+	0.0126000i	0.489048	+	0.872257i	$0.337344\pi$
$468$	2.35921	−	20.5272i	0.109055	−	0.948868i
$469$	0.315627	+	0.182227i	0.0145743	+	0.00841448i
$470$	2.66729	−	13.0356i	0.123033	−	0.601288i
$471$	0.644726	+	0.574716i	0.0297074	+	0.0264815i
$472$	−7.30926	+	2.00069i	−0.336436	+	0.0920891i
$473$	−0.326975	+	1.85437i	−0.0150343	+	0.0852640i
$474$	−16.8941	+	25.7402i	−0.775972	+	1.18229i
$475$	−2.29584	−	2.73608i	−0.105340	−	0.125540i
$476$	−6.67686	−	6.25422i	−0.306033	−	0.286662i
$477$	1.75956	−	29.3715i	0.0805647	−	1.34483i
$478$	−12.1624	+	30.7752i	−0.556295	+	1.40762i
$479$	7.93244	+	2.88717i	0.362442	+	0.131918i	0.516821	−	0.856094i	$-0.327115\pi$
$479$	7.93244	+	2.88717i	0.362442	+	0.131918i	−0.154379	+	0.988012i	$0.549338\pi$
$480$	−22.1519	+	8.26723i	−1.01109	+	0.377346i
$481$	−15.6752	−	13.1530i	−0.714725	−	0.599726i
$482$	−4.73479	−	2.90877i	−0.215664	−	0.132491i
$483$	0.188609	−	6.30236i	0.00858200	−	0.286767i
$484$	−21.9166	−	1.19769i	−0.996207	−	0.0544406i
$485$			16.3079i			0.740505i
$486$	−14.1307	−	16.9211i	−0.640984	−	0.767555i
$487$	−15.0013			−0.679775			−0.339888	−	0.940466i	$-0.610389\pi$
$487$	−15.0013			−0.679775			−0.339888	+	0.940466i	$0.610389\pi$
$488$	3.32505	−	2.35497i	0.150518	−	0.106604i
$489$	19.5705	+	0.585681i	0.885009	+	0.0264854i
$490$	−7.97207	+	12.9767i	−0.360142	+	0.586227i
$491$	−9.43399	+	11.2430i	−0.425750	+	0.507389i	−0.935691	−	0.352820i	$-0.885223\pi$
$491$	−9.43399	+	11.2430i	−0.425750	+	0.507389i	0.509941	+	0.860209i	$0.329667\pi$
$492$	−2.94189	+	34.7276i	−0.132631	+	1.56564i
$493$	8.58191	−	23.5786i	0.386510	−	1.06193i
$494$	7.76365	−	19.6448i	0.349303	−	0.883861i
$495$	1.15115	+	0.0689619i	0.0517402	+	0.00309961i
$496$	23.6843	−	15.8218i	1.06346	−	0.710419i
$497$	−6.88991	+	5.78132i	−0.309055	+	0.259328i
$498$	23.0978	+	15.1598i	1.03504	+	0.679329i
$499$	−17.0588	−	3.00792i	−0.763655	−	0.134653i	−0.221762	−	0.975101i	$-0.571181\pi$
$499$	−17.0588	−	3.00792i	−0.763655	−	0.134653i	−0.541892	+	0.840448i	$0.682292\pi$
$500$	−7.91757	+	18.5374i	−0.354084	+	0.829017i
$501$	−15.1803	+	17.0295i	−0.678206	+	0.760823i
$502$	0.141407	−	0.691086i	0.00631131	−	0.0308447i
$503$	−2.40445	+	4.16463i	−0.107209	+	0.185692i	−0.914639	−	0.404272i	$-0.867525\pi$
$503$	−2.40445	+	4.16463i	−0.107209	+	0.185692i	0.807429	+	0.589964i	$0.200858\pi$
$504$	7.13849	+	11.4775i	0.317974	+	0.511250i
$505$	−2.05591	−	3.56095i	−0.0914870	−	0.158460i
$506$	−0.488397	+	0.162809i	−0.0217119	+	0.00723775i
$507$	0.731069	−	1.83577i	0.0324679	−	0.0815296i
$508$	22.1669	−	16.6265i	0.983497	−	0.737680i
$509$	−10.1785	−	27.9653i	−0.451155	−	1.23954i	−0.931912	−	0.362685i	$-0.881860\pi$
$509$	−10.1785	−	27.9653i	−0.451155	−	1.23954i	0.480757	−	0.876854i	$-0.340362\pi$
$510$	−6.70822	+	15.5927i	−0.297045	+	0.690455i
$511$	−3.95313	−	22.4193i	−0.174876	−	0.991772i
$512$	−5.50316	+	21.9480i	−0.243208	+	0.969974i
$513$	−9.47383	−	20.4493i	−0.418280	−	0.902859i
$514$	0.790690	+	0.996316i	0.0348759	+	0.0439456i
$515$	−30.4722	+	5.37308i	−1.34277	+	0.236766i
$516$	29.0347	+	28.8752i	1.27818	+	1.27116i
$517$	0.212412	+	0.583597i	0.00934187	+	0.0256666i
$518$	13.3807	+	0.365340i	0.587912	+	0.0160521i
$519$	−22.2677	+	17.5771i	−0.977445	+	0.771547i
$520$	23.4044	−	2.17446i	1.02635	−	0.0953566i
$521$	15.3931	+	26.6615i	0.674382	+	1.16806i	0.976649	+	0.214840i	$0.0689231\pi$
$521$	15.3931	+	26.6615i	0.674382	+	1.16806i	−0.302267	+	0.953223i	$0.597744\pi$
$522$	−21.2593	+	30.3701i	−0.930493	+	1.32926i
$523$	20.1716	+	11.6461i	0.882042	+	0.509247i	0.871331	−	0.490695i	$-0.163257\pi$
$523$	20.1716	+	11.6461i	0.882042	+	0.509247i	0.0107111	+	0.999943i	$0.496590\pi$
$524$	9.21473	−	4.66924i	0.402547	−	0.203977i
$525$	−2.22469	−	0.461284i	−0.0970933	−	0.0201321i
$526$	12.4665	−	6.75072i	0.543564	−	0.294345i
$527$	3.55077	−	20.1374i	0.154674	−	0.877200i
$528$	0.678999	−	0.870013i	0.0295496	−	0.0378625i
$529$	−13.6183	+	11.4271i	−0.592099	+	0.496830i
$530$	33.1104	−	4.91059i	1.43823	−	0.213302i
$531$	5.52557	−	5.83734i	0.239789	−	0.253319i
$532$	4.01044	+	13.2231i	0.173875	+	0.573295i
$533$	11.8499	−	32.5574i	0.513278	−	1.41022i
$534$	−4.20165	+	17.8046i	−0.181823	+	0.770478i
$535$	29.1263	+	24.4399i	1.25924	+	1.05663i
$536$	−0.460047	−	0.455127i	−0.0198710	−	0.0196585i
$537$	−5.39768	+	8.73475i	−0.232927	+	0.376932i
$538$	1.10109	+	0.976354i	0.0474712	+	0.0420936i
$539$		−	0.710862i		−	0.0306190i
$540$	15.5330	−	19.6891i	0.668436	−	0.847284i
$541$			29.0030i			1.24694i	0.781848	+	0.623469i	$0.214277\pi$
$541$			29.0030i			1.24694i	−0.781848	+	0.623469i	$0.785723\pi$
$542$	28.1863	−	31.7872i	1.21071	−	1.36538i
$543$	−1.42921	−	2.65591i	−0.0613334	−	0.113976i
$544$	8.65146	+	13.7489i	0.370928	+	0.589479i
$545$	7.83541	+	6.57469i	0.335632	+	0.281629i
$546$	−3.86611	−	12.8686i	−0.165454	−	0.550725i
$547$	−3.84045	+	10.5516i	−0.164206	+	0.451152i	−0.994319	−	0.106443i	$-0.966054\pi$
$547$	−3.84045	+	10.5516i	−0.164206	+	0.451152i	0.830113	+	0.557596i	$0.188276\pi$
$548$	−36.0904	+	10.9458i	−1.54171	+	0.467583i
$549$	−1.71831	+	3.96541i	−0.0733358	+	0.169239i
$550$	0.0272152	+	0.183503i	0.00116046	+	0.00782458i
$551$	−29.0320	+	24.3607i	−1.23681	+	1.03780i
$552$	−3.16215	+	10.7398i	−0.134590	+	0.457116i
$553$	−3.47684	+	19.7182i	−0.147850	+	0.838501i
$554$	−13.2296	−	24.4309i	−0.562070	−	1.03797i
$555$	−7.79251	−	23.5819i	−0.330774	−	1.00100i
$556$	28.8779	−	14.6329i	1.22470	−	0.620573i
$557$	−2.53413	−	1.46308i	−0.107374	−	0.0619927i	0.445351	−	0.895356i	$-0.353079\pi$
$557$	−2.53413	−	1.46308i	−0.107374	−	0.0619927i	−0.552726	+	0.833363i	$0.686412\pi$
$558$	−12.7639	+	27.3819i	−0.540339	+	1.15917i
$559$	−20.3538	−	35.2538i	−0.860874	−	1.49108i
$560$	−11.1082	+	10.6316i	−0.469408	+	0.449266i
$561$	−0.114178	−	0.784021i	−0.00482062	−	0.0331014i
$562$	−1.07172	+	39.2520i	−0.0452078	+	1.65575i
$563$	2.96778	+	8.15390i	0.125077	+	0.343646i	0.986389	−	0.164431i	$-0.0525788\pi$
$563$	2.96778	+	8.15390i	0.125077	+	0.343646i	−0.861312	+	0.508077i	$0.830357\pi$
$564$	13.0552	+	3.45961i	0.549724	+	0.145676i
$565$	17.7724	−	3.13375i	0.747690	−	0.131838i
$566$	27.6452	−	21.9396i	1.16201	−	0.922190i
$567$	−12.7899	−	6.47655i	−0.537127	−	0.271989i
$568$	14.4375	−	6.82703i	0.605782	−	0.286456i
$569$	−1.80356	−	10.2285i	−0.0756093	−	0.428802i	−0.998991	−	0.0449179i	$-0.985697\pi$
$569$	−1.80356	−	10.2285i	−0.0756093	−	0.428802i	0.923381	−	0.383884i	$-0.125414\pi$
$570$	20.5502	−	15.3298i	0.860752	−	0.642095i
$571$	−1.71537	−	4.71295i	−0.0717862	−	0.197231i	0.898611	−	0.438747i	$-0.144578\pi$
$571$	−1.71537	−	4.71295i	−0.0717862	−	0.197231i	−0.970397	+	0.241516i	$0.922355\pi$
$572$	−0.877670	+	0.658303i	−0.0366972	+	0.0275250i
$573$	−18.6175	+	2.71131i	−0.777759	+	0.113266i
$574$	7.16754	+	21.5013i	0.299167	+	0.897446i
$575$	−0.940956	−	1.62978i	−0.0392406	−	0.0679667i
$576$	−7.09208	−	22.9282i	−0.295503	−	0.955342i
$577$	4.43057	−	7.67398i	0.184447	−	0.319472i	−0.758943	−	0.651157i	$-0.774284\pi$
$577$	4.43057	−	7.67398i	0.184447	−	0.319472i	0.943390	+	0.331685i	$0.107617\pi$
$578$	−12.1284	−	2.48166i	−0.504474	−	0.103223i
$579$	−7.86638	−	23.8055i	−0.326915	−	0.989321i
$580$	−38.7827	−	16.5646i	−1.61037	−	0.687809i
$581$	17.6940	+	3.11993i	0.734070	+	0.129436i
$582$	−16.5262	−	0.946570i	−0.685031	−	0.0392366i
$583$	−1.19683	+	1.00426i	−0.0495677	+	0.0415922i
$584$	−3.30651	+	40.2870i	−0.136824	+	1.66709i
$585$	−20.0224	+	14.8546i	−0.827824	+	0.614162i
$586$	10.7396	+	4.24430i	0.443648	+	0.175330i
$587$	0.553940	−	1.52194i	0.0228636	−	0.0628171i	−0.927736	−	0.373238i	$-0.878248\pi$
$587$	0.553940	−	1.52194i	0.0228636	−	0.0628171i	0.950599	+	0.310420i	$0.100470\pi$
$588$	−12.6876	−	8.83197i	−0.523228	−	0.364224i
$589$	−19.8523	+	23.6590i	−0.817999	+	0.974854i
$590$	7.79097	+	4.78629i	0.320749	+	0.197048i
$591$	−6.98401	−	12.9784i	−0.287284	−	0.533860i
$592$	−22.8177	−	6.65333i	−0.937801	−	0.273450i
$593$	−16.7535			−0.687984			−0.343992	−	0.938973i	$-0.611779\pi$
$593$	−16.7535			−0.687984			−0.343992	+	0.938973i	$0.611779\pi$
$594$	−0.136701	+	1.16255i	−0.00560893	+	0.0477000i
$595$			11.0386i			0.452538i
$596$	1.41547	−	25.9016i	0.0579799	−	1.06097i
$597$	−18.2097	−	11.2528i	−0.745273	−	0.460545i
$598$	5.82588	−	9.48317i	0.238238	−	0.387796i
$599$	−31.3875	−	26.3372i	−1.28246	−	1.07611i	−0.992900	−	0.118949i	$-0.962048\pi$
$599$	−31.3875	−	26.3372i	−1.28246	−	1.07611i	−0.289557	−	0.957161i	$-0.593508\pi$
$600$	3.61332	+	1.79415i	0.147513	+	0.0732459i
$601$	−8.03176	−	2.92332i	−0.327622	−	0.119245i	0.172972	−	0.984927i	$-0.444663\pi$
$601$	−8.03176	−	2.92332i	−0.327622	−	0.119245i	−0.500594	+	0.865682i	$0.666885\pi$
$602$	24.7653	+	9.78727i	1.00936	+	0.398899i
$603$	0.667626	+	0.159400i	0.0271878	+	0.00649126i
$604$	−4.91073	−	4.59988i	−0.199815	−	0.187167i
$605$	17.0235	+	20.2878i	0.692103	+	0.824817i
$606$	3.72793	−	1.87673i	0.151437	−	0.0762371i
$607$	4.22098	−	23.9383i	0.171324	−	0.971627i	−0.770978	−	0.636862i	$-0.780232\pi$
$607$	4.22098	−	23.9383i	0.171324	−	0.971627i	0.942302	−	0.334765i	$-0.108657\pi$
$608$	−0.933321	−	24.5177i	−0.0378511	−	0.994324i
$609$	−4.89460	+	23.6057i	−0.198339	+	0.956552i
$610$	−4.81652	−	0.985535i	−0.195015	−	0.0399031i
$611$	−11.6276	−	6.71318i	−0.470401	−	0.271586i
$612$	−15.4120	−	7.70304i	−0.622991	−	0.311377i
$613$	−14.3628	+	8.29237i	−0.580108	+	0.334926i	−0.761176	−	0.648545i	$-0.775378\pi$
$613$	−14.3628	+	8.29237i	−0.580108	+	0.334926i	0.181068	+	0.983471i	$0.442045\pi$
$614$	24.9784	−	8.32665i	1.00805	−	0.336036i
$615$	33.0081	−	26.0550i	1.33101	−	1.05064i
$616$	0.182021	−	0.694220i	0.00733385	−	0.0279709i
$617$	−17.6023	+	6.40672i	−0.708642	+	0.257925i	−0.671096	−	0.741370i	$-0.734176\pi$
$617$	−17.6023	+	6.40672i	−0.708642	+	0.257925i	−0.0375461	+	0.999295i	$0.511954\pi$
$618$	−3.67626	−	31.1919i	−0.147881	−	1.25472i
$619$	4.87939	−	0.860368i	0.196119	−	0.0345811i	−0.0747256	−	0.997204i	$-0.523808\pi$
$619$	4.87939	−	0.860368i	0.196119	−	0.0345811i	0.270845	+	0.962623i	$0.412697\pi$
$620$	−33.4691	−	7.80575i	−1.34415	−	0.313486i
$621$	−3.04488	−	11.4778i	−0.122187	−	0.460587i
$622$	−4.31146	−	5.43269i	−0.172874	−	0.217831i
$623$	2.06579	+	11.7157i	0.0827643	+	0.469380i
$624$	0.845088	+	23.8438i	0.0338306	+	0.954515i
$625$	26.7242	−	9.72681i	1.06897	−	0.389072i
$626$	0.397499	−	14.5585i	0.0158872	−	0.581874i
$627$	−0.442741	+	1.11176i	−0.0176814	+	0.0443994i
$628$	−0.835199	−	0.545041i	−0.0333281	−	0.0217495i
$629$	−14.7771	+	8.53157i	−0.589202	+	0.340176i
$630$	4.21891	−	15.7536i	0.168085	−	0.627639i
$631$	−2.46788	+	4.27449i	−0.0982447	+	0.170165i	−0.910958	−	0.412499i	$-0.864656\pi$
$631$	−2.46788	+	4.27449i	−0.0982447	+	0.170165i	0.812713	+	0.582664i	$0.197989\pi$
$632$	14.8516	−	32.3015i	0.590764	−	1.28489i
$633$	−2.28583	−	2.03761i	−0.0908536	−	0.0809879i
$634$	15.2053	+	28.0794i	0.603879	+	1.11518i
$635$	−32.9261	−	5.80576i	−1.30663	−	0.230394i
$636$	3.05445	+	33.8385i	0.121117	+	1.34178i
$637$	9.87834	+	11.7725i	0.391394	+	0.466445i
$638$	1.94711	−	0.288775i	0.0770869	−	0.0114327i
$639$	−9.33158	+	14.1369i	−0.369152	+	0.559246i
$640$	23.8669	−	13.2580i	0.943424	−	0.524069i
$641$	1.74409	+	0.634798i	0.0688875	+	0.0250730i	0.376234	−	0.926525i	$-0.377219\pi$
$641$	1.74409	+	0.634798i	0.0688875	+	0.0250730i	−0.307347	+	0.951598i	$0.599441\pi$
$642$	−26.4575	+	28.0975i	−1.04420	+	1.10892i
$643$	21.2761	−	25.3559i	0.839048	−	0.999938i	−0.160868	−	0.986976i	$-0.551429\pi$
$643$	21.2761	−	25.3559i	0.839048	−	0.999938i	0.999916	−	0.0129623i	$-0.00412614\pi$
$644$	0.871137	+	7.22829i	0.0343276	+	0.284835i
$645$	1.47797	−	49.3863i	0.0581949	−	1.94458i
$646$	−13.1792	−	11.6862i	−0.518528	−	0.459789i
$647$	8.85391			0.348083			0.174042	−	0.984738i	$-0.444317\pi$
$647$	8.85391			0.348083			0.174042	+	0.984738i	$0.444317\pi$
$648$	19.0510	+	16.8837i	0.748393	+	0.663255i
$649$	−0.426789			−0.0167529
$650$	−3.00071	−	2.66079i	−0.117698	−	0.104365i
$651$	−0.587682	+	19.6374i	−0.0230331	+	0.769650i
$652$	−22.4458	+	2.70511i	−0.879044	+	0.105940i
$653$	6.38975	−	7.61501i	0.250050	−	0.297998i	−0.626389	−	0.779511i	$-0.715468\pi$
$653$	6.38975	−	7.61501i	0.250050	−	0.297998i	0.876439	+	0.481512i	$0.159912\pi$
$654$	−7.11746	+	7.55864i	−0.278315	+	0.295566i
$655$	−11.7127	−	4.26306i	−0.457652	−	0.166572i
$656$	−2.62788	−	40.1578i	−0.102601	−	1.56790i
$657$	−19.1785	−	38.3459i	−0.748224	−	1.49601i
$658$	8.68790	−	1.28850i	0.338690	−	0.0502308i
$659$	27.1973	+	32.4125i	1.05946	+	1.26261i	0.963637	+	0.267213i	$0.0861028\pi$
$659$	27.1973	+	32.4125i	1.05946	+	1.26261i	0.0958197	+	0.995399i	$0.469453\pi$
$660$	−1.32622	+	0.119712i	−0.0516231	+	0.00465979i
$661$	49.7307	+	8.76886i	1.93430	+	0.341069i	0.999886	−	0.0151198i	$-0.00481297\pi$
$661$	49.7307	+	8.76886i	1.93430	+	0.341069i	0.934414	+	0.356189i	$0.115924\pi$
$662$	15.8754	+	29.3170i	0.617017	+	1.13944i
$663$	12.7859	+	11.3975i	0.496562	+	0.442641i
$664$	−28.9856	−	13.3270i	−1.12486	−	0.517187i
$665$	8.33631	−	14.4389i	0.323268	−	0.559917i
$666$	24.3498	−	6.52801i	0.943535	−	0.252955i
$667$	−17.2933	+	9.98430i	−0.669600	+	0.386594i
$668$	14.3965	−	22.0606i	0.557016	−	0.853550i
$669$	1.92803	−	4.84143i	0.0745418	−	0.187181i
$670$	−0.0213115	+	0.780540i	−0.000823337	+	0.0301549i
$671$	0.215633	−	0.0784840i	0.00832442	−	0.00302984i
$672$	−10.1291	−	11.8740i	−0.390738	−	0.458048i
$673$	2.52619	+	14.3267i	0.0973775	+	0.552255i	0.993993	+	0.109445i	$0.0349074\pi$
$673$	2.52619	+	14.3267i	0.0973775	+	0.552255i	−0.896615	+	0.442810i	$0.853981\pi$
$674$	−28.9072	−	36.4247i	−1.11346	−	1.40303i
$675$	−4.26358	+	0.362334i	−0.164105	+	0.0139462i
$676$	−0.518230	+	2.22204i	−0.0199319	+	0.0854632i
$677$	−39.3485	+	6.93820i	−1.51229	+	0.266657i	−0.867396	−	0.497619i	$-0.834208\pi$
$677$	−39.3485	+	6.93820i	−1.51229	+	0.266657i	−0.644890	+	0.764276i	$0.723097\pi$
$678$	2.14411	+	18.1921i	0.0823442	+	0.698663i
$679$	−10.1155	+	3.68173i	−0.388197	+	0.141292i
$680$	4.97110	−	18.9595i	0.190633	−	0.727064i
$681$	7.73127	−	6.10268i	0.296263	−	0.233855i
$682$	1.52179	−	0.507294i	0.0582723	−	0.0194253i
$683$	−16.3031	+	9.41260i	−0.623821	+	0.360163i	−0.778355	−	0.627824i	$-0.783946\pi$
$683$	−16.3031	+	9.41260i	−0.623821	+	0.360163i	0.154534	+	0.987987i	$0.450612\pi$
$684$	14.3421	+	21.7150i	0.548386	+	0.830292i
$685$	39.4087	+	22.7526i	1.50573	+	0.869333i
$686$	−25.2980	−	5.17636i	−0.965881	−	0.197634i
$687$	−7.65794	+	36.9328i	−0.292168	+	1.40907i
$688$	−38.1285	−	27.9631i	−1.45364	−	1.06608i
$689$	5.86516	−	33.2630i	0.223445	−	1.26722i
$690$	12.0659	−	6.07428i	0.459341	−	0.231244i
$691$	7.33473	+	8.74119i	0.279026	+	0.332531i	0.887297	−	0.461199i	$-0.152581\pi$
$691$	7.33473	+	8.74119i	0.279026	+	0.332531i	−0.608270	+	0.793730i	$0.708136\pi$
$692$	22.3942	−	23.9076i	0.851300	−	0.908829i
$693$	0.217111	+	0.729603i	0.00824738	+	0.0277153i
$694$	1.10995	+	0.438654i	0.0421331	+	0.0166511i
$695$	−36.7062	−	13.3600i	−1.39235	−	0.506773i
$696$	19.0374	−	38.3402i	0.721610	−	1.45328i
$697$	−22.1320	−	18.5709i	−0.838307	−	0.703423i
$698$	10.3788	−	16.8942i	0.392842	−	0.639456i
$699$	−34.6201	−	21.3937i	−1.30945	−	0.809182i
$700$	2.61958	+	0.143155i	0.0990108	+	0.00541073i
$701$		−	29.8398i		−	1.12704i	−0.826104	−	0.563518i	$-0.809448\pi$
$701$		−	29.8398i		−	1.12704i	0.826104	−	0.563518i	$-0.190552\pi$
$702$	−13.8912	−	21.1525i	−0.524289	−	0.798351i
$703$	25.7721			0.972013
$704$	−0.625269	+	1.11040i	−0.0235657	+	0.0418498i
$705$	−7.72223	−	14.3502i	−0.290836	−	0.540461i
$706$	−28.4121	−	17.4547i	−1.06930	−	0.656915i
$707$	1.74463	−	2.07917i	0.0656137	−	0.0781954i
$708$	−5.30255	+	7.61741i	−0.199282	+	0.286280i
$709$	0.897749	−	2.46655i	0.0337157	−	0.0926331i	−0.921693	−	0.387921i	$-0.873193\pi$
$709$	0.897749	−	2.46655i	0.0337157	−	0.0926331i	0.955408	+	0.295288i	$0.0954156\pi$
$710$	−17.9209	−	7.08235i	−0.672559	−	0.265796i
$711$	4.31562	+	37.4610i	0.161849	+	1.40490i
$712$	1.72789	−	21.0528i	0.0647554	−	0.788989i
$713$	−12.4658	+	10.4601i	−0.466849	+	0.391733i
$714$	−11.1863	−	0.640718i	−0.418636	−	0.0239783i
$715$	1.30367	+	0.229871i	0.0487543	+	0.00859670i
$716$	4.65704	−	10.9035i	0.174042	−	0.407483i
$717$	12.7161	+	38.4819i	0.474892	+	1.43713i
$718$	37.3968	+	7.65198i	1.39564	+	0.285569i
$719$	−6.54404	+	11.3346i	−0.244051	+	0.422709i	−0.961864	−	0.273526i	$-0.911810\pi$
$719$	−6.54404	+	11.3346i	−0.244051	+	0.422709i	0.717813	+	0.696236i	$0.245143\pi$
$720$	−14.3407	+	25.1580i	−0.534448	+	0.937583i
$721$	−10.2123	−	17.6883i	−0.380327	−	0.658746i
$722$	−0.0840213	−	0.252049i	−0.00312695	−	0.00938027i
$723$	−6.73475	+	0.980794i	−0.250468	+	0.0364761i
$724$	2.08968	+	2.78602i	0.0776623	+	0.103542i
$725$	2.46100	+	6.76154i	0.0913992	+	0.251117i
$726$	−21.5474	+	16.0737i	−0.799699	+	0.596552i
$727$	6.97054	+	39.5319i	0.258523	+	1.46616i	0.786865	+	0.617125i	$0.211703\pi$
$727$	6.97054	+	39.5319i	0.258523	+	1.46616i	−0.528342	+	0.849031i	$0.677186\pi$
$728$	6.63263	+	14.0263i	0.245822	+	0.519851i
$729$	−26.5662	−	4.82069i	−0.983932	−	0.178544i
$730$	38.2044	−	30.3196i	1.41401	−	1.12218i
$731$	−33.4294	+	5.89450i	−1.23643	+	0.218016i
$732$	1.27829	−	4.82377i	0.0472470	−	0.178291i
$733$	−0.696450	−	1.91348i	−0.0257240	−	0.0706760i	0.926166	−	0.377116i	$-0.123084\pi$
$733$	−0.696450	−	1.91348i	−0.0257240	−	0.0706760i	−0.951890	+	0.306440i	$0.900862\pi$
$734$	−1.12454	+	41.1866i	−0.0415077	+	1.52023i
$735$	2.68807	+	18.4580i	0.0991509	+	0.680833i
$736$	1.75894	−	12.8074i	0.0648354	−	0.472087i
$737$	−0.0182229	−	0.0315629i	−0.000671248	−	0.00116264i
$738$	24.4877	+	34.9621i	0.901405	+	1.28697i
$739$	−30.6990	−	17.7241i	−1.12928	−	0.651990i	−0.185526	−	0.982639i	$-0.559399\pi$
$739$	−30.6990	−	17.7241i	−1.12928	−	0.651990i	−0.943754	+	0.330649i	$0.892732\pi$
$740$	12.9625	+	25.5815i	0.476512	+	0.940395i
$741$	−8.11710	−	24.5642i	−0.298189	−	0.902389i
$742$	10.5211	+	19.4291i	0.386240	+	0.713265i
$743$	9.22773	−	52.3330i	0.338532	−	1.91991i	−0.0505739	−	0.998720i	$-0.516105\pi$
$743$	9.22773	−	52.3330i	0.338532	−	1.91991i	0.389106	−	0.921193i	$-0.372784\pi$
$744$	9.85286	−	33.4639i	0.361224	−	1.22685i
$745$	−23.9767	+	20.1189i	−0.878440	+	0.737099i
$746$	0.238461	+	1.60786i	0.00873069	+	0.0588681i
$747$	33.6155	−	3.87260i	1.22993	−	0.141691i
$748$	0.265524	+	0.875480i	0.00970853	+	0.0320107i
$749$	−8.58392	+	23.5841i	−0.313649	+	0.861745i
$750$	7.10329	+	23.6438i	0.259376	+	0.863348i
$751$	6.58894	+	5.52878i	0.240434	+	0.201748i	0.755040	−	0.655679i	$-0.227617\pi$
$751$	6.58894	+	5.52878i	0.240434	+	0.201748i	−0.514606	+	0.857427i	$0.672062\pi$
$752$	−15.5023	−	1.69942i	−0.565312	−	0.0619713i
$753$	−0.409396	−	0.760782i	−0.0149192	−	0.0277244i
$754$	−28.2331	+	31.8400i	−1.02819	+	1.15954i
$755$			8.11871i			0.295470i
$756$	15.7195	+	5.18976i	0.571714	+	0.188750i
$757$			21.7216i			0.789484i	0.918792	+	0.394742i	$0.129166\pi$
$757$			21.7216i			0.789484i	−0.918792	+	0.394742i	$0.870834\pi$
$758$	17.8956	+	15.8684i	0.649998	+	0.576365i
$759$	−0.331454	+	0.536373i	−0.0120310	+	0.0194691i
$760$	−20.8206	+	21.0457i	−0.755242	+	0.763407i
$761$	−0.341041	−	0.286168i	−0.0123627	−	0.0103736i	0.636585	−	0.771206i	$-0.280346\pi$
$761$	−0.341041	−	0.286168i	−0.0123627	−	0.0103736i	−0.648948	+	0.760833i	$0.724791\pi$
$762$	7.79459	−	33.0297i	0.282368	−	1.19654i
$763$	−2.30920	+	6.34447i	−0.0835986	+	0.229685i
$764$	20.7893	−	6.30519i	0.752132	−	0.228114i
$765$	5.92943	+	19.9258i	0.214379	+	0.720420i
$766$	−28.2272	+	4.18636i	−1.01989	+	0.151259i
$767$	7.06802	−	5.93077i	0.255211	−	0.214148i
$768$	12.0501	+	24.9559i	0.434821	+	0.900517i
$769$	3.22004	−	18.2618i	0.116118	−	0.658536i	−0.870073	−	0.492923i	$-0.835928\pi$
$769$	3.22004	−	18.2618i	0.116118	−	0.658536i	0.986191	−	0.165614i	$-0.0529604\pi$
$770$	−0.761478	+	0.412349i	−0.0274418	+	0.0148600i
$771$	1.52536	+	0.316280i	0.0549345	+	0.0113905i
$772$	13.0854	+	25.8240i	0.470954	+	0.929426i
$773$	−1.50501	−	0.868919i	−0.0541315	−	0.0312528i	0.472690	−	0.881229i	$-0.343283\pi$
$773$	−1.50501	−	0.868919i	−0.0541315	−	0.0312528i	−0.526822	+	0.849976i	$0.676616\pi$
$774$	49.9613	+	4.36430i	1.79582	+	0.156872i
$775$	2.93190	+	5.07821i	0.105317	+	0.182415i
$776$	19.0321	−	1.76824i	0.683211	−	0.0634761i
$777$	12.8681	−	10.1575i	0.461642	−	0.364397i
$778$	−41.2268	−	1.12564i	−1.47805	−	0.0403562i
$779$	14.9248	+	41.0055i	0.534736	+	1.46918i
$780$	20.2999	−	20.4121i	0.726854	−	0.730870i
$781$	0.885756	−	0.156183i	0.0316948	−	0.00558865i
$782$	−5.76934	−	7.26970i	−0.206311	−	0.259964i
$783$	3.84465	+	45.2401i	0.137397	+	1.61675i
$784$	16.0088	+	7.89672i	0.571742	+	0.282026i
$785$	0.208959	+	1.18507i	0.00745808	+	0.0422969i
$786$	4.99995	−	11.6220i	0.178342	−	0.414542i
$787$	12.6576	+	34.7764i	0.451193	+	1.23964i	0.931885	+	0.362754i	$0.118163\pi$
$787$	12.6576	+	34.7764i	0.451193	+	1.23964i	−0.480692	+	0.876890i	$0.659614\pi$
$788$	10.2114	+	13.6142i	0.363767	+	0.484986i
$789$	6.42394	−	16.1310i	0.228698	−	0.574280i
$790$	−40.6955	+	13.5660i	−1.44788	+	0.482657i
$791$	5.95616	+	10.3164i	0.211777	+	0.366808i
$792$	−0.0443354	−	1.35092i	−0.00157539	−	0.0480028i
$793$	−2.48045	+	4.29626i	−0.0880833	+	0.152565i
$794$	3.37692	−	16.5037i	0.119842	−	0.585695i
$795$	27.2789	−	30.6020i	0.967484	−	1.08534i
$796$	22.7310	+	9.70871i	0.805679	+	0.344116i
$797$	−11.7114	−	2.06503i	−0.414837	−	0.0731470i	−0.0376658	−	0.999290i	$-0.511992\pi$
$797$	−11.7114	−	2.06503i	−0.414837	−	0.0731470i	−0.377172	+	0.926143i	$0.623103\pi$
$798$	14.1483	+	9.28595i	0.500843	+	0.328719i
$799$	−8.57656	+	7.19659i	−0.303417	+	0.254597i
$800$	−4.43484	−	1.42558i	−0.156795	−	0.0504017i
$801$	10.0221	+	20.0385i	0.354115	+	0.708025i
$802$	−1.23727	+	3.13072i	−0.0436894	+	0.110550i
$803$	−0.778620	+	2.13924i	−0.0274769	+	0.0754922i
$804$	−0.789747	−	0.0669020i	−0.0278522	−	0.00235945i
$805$	5.64671	−	6.72949i	0.199021	−	0.237183i
$806$	−18.1527	+	29.5484i	−0.639402	+	1.04080i
$807$	1.80155	+	0.0539145i	0.0634176	+	0.00189788i
$808$	−3.93286	+	2.78545i	−0.138358	+	0.0979917i
$809$	13.6067			0.478385			0.239192	−	0.970972i	$-0.423117\pi$
$809$	13.6067			0.478385			0.239192	+	0.970972i	$0.423117\pi$
$810$	−0.846549	−	30.7032i	−0.0297447	−	1.07880i
$811$		−	23.1998i		−	0.814656i	−0.913282	−	0.407328i	$-0.866461\pi$
$811$		−	23.1998i		−	0.814656i	0.913282	−	0.407328i	$-0.133539\pi$
$812$	1.51899	−	27.7958i	0.0533059	−	0.975443i
$813$	1.55645	−	52.0088i	0.0545872	−	1.82403i
$814$	−1.14054	−	0.700677i	−0.0399759	−	0.0245587i
$815$	20.8969	+	17.5346i	0.731985	+	0.614209i
$816$	18.9247	+	6.13810i	0.662497	+	0.214876i
$817$	48.1785	+	17.5355i	1.68555	+	0.613491i
$818$	−6.68662	+	16.9195i	−0.233792	+	0.591578i
$819$	−13.7343	−	9.06586i	−0.479916	−	0.316787i
$820$	−33.1956	+	35.4389i	−1.15924	+	1.23758i
$821$	−18.9516	−	22.5856i	−0.661414	−	0.788243i	0.326174	−	0.945310i	$-0.394241\pi$
$821$	−18.9516	−	22.5856i	−0.661414	−	0.788243i	−0.987588	+	0.157067i	$0.949796\pi$
$822$	−25.3445	+	38.6154i	−0.883991	+	1.34687i
$823$	2.95142	−	16.7383i	0.102880	−	0.583462i	−0.889166	−	0.457585i	$-0.848715\pi$
$823$	2.95142	−	16.7383i	0.102880	−	0.583462i	0.992046	−	0.125877i	$-0.0401744\pi$
$824$	9.57467	+	34.9799i	0.333549	+	1.21858i
$825$	0.169600	+	0.151184i	0.00590473	+	0.00526354i
$826$	−1.20992	+	5.91315i	−0.0420986	+	0.205745i
$827$	−44.0488	−	25.4316i	−1.53173	−	0.884343i	−0.999282	−	0.0378772i	$-0.987940\pi$
$827$	−44.0488	−	25.4316i	−1.53173	−	0.884343i	−0.532444	−	0.846465i	$-0.678726\pi$
$828$	5.45521	+	12.5799i	0.189582	+	0.437182i
$829$	41.8595	−	24.1676i	1.45384	−	0.839374i	0.455143	−	0.890418i	$-0.349588\pi$
$829$	41.8595	−	24.1676i	1.45384	−	0.839374i	0.998696	+	0.0510440i	$0.0162549\pi$
$830$	12.1734	+	36.5179i	0.422544	+	1.26755i
$831$	−31.6124	−	12.5892i	−1.09662	−	0.436713i
$832$	−5.07539	−	27.0782i	−0.175957	−	0.938766i
$833$	12.0421	−	4.38298i	0.417235	−	0.151861i
$834$	15.6693	−	36.4220i	0.542584	−	1.26119i
$835$	−31.3019	+	5.51936i	−1.08325	+	0.191005i
$836$	0.313844	−	1.34569i	0.0108545	−	0.0465416i
$837$	9.48749	+	35.7633i	0.327936	+	1.23616i
$838$	8.30411	−	6.59026i	0.286861	−	0.227657i
$839$	4.93028	+	27.9610i	0.170212	+	0.965321i	0.943526	+	0.331298i	$0.107486\pi$
$839$	4.93028	+	27.9610i	0.170212	+	0.965321i	−0.773314	+	0.634023i	$0.781402\pi$
$840$	−2.10116	+	18.7142i	−0.0724969	+	0.645700i
$841$	44.4943	−	16.1946i	1.53429	−	0.558434i
$842$	−11.3324	−	0.309414i	−0.390539	−	0.0106631i
$843$	29.7968	+	37.7485i	1.02626	+	1.30013i
$844$	2.96114	+	1.93240i	0.101927	+	0.0665161i
$845$	2.38422	−	1.37653i	0.0820196	−	0.0473540i
$846$	14.9905	−	6.99263i	0.515384	−	0.240412i
$847$	−8.74084	+	15.1396i	−0.300339	+	0.520202i
$848$	−9.32097	−	38.1089i	−0.320084	−	1.30866i
$849$	8.77594	−	42.3247i	0.301190	−	1.45258i
$850$	−2.94077	+	1.59246i	−0.100867	+	0.0546208i
$851$	13.3729	+	2.35800i	0.458417	+	0.0808313i
$852$	8.21732	−	17.7496i	0.281521	−	0.608091i
$853$	17.3921	+	20.7271i	0.595495	+	0.709684i	0.976652	−	0.214827i	$-0.0689186\pi$
$853$	17.3921	+	20.7271i	0.595495	+	0.709684i	−0.381157	+	0.924510i	$0.624474\pi$
$854$	−0.476086	−	3.21009i	−0.0162913	−	0.109847i
$855$	7.29202	−	30.5417i	0.249382	−	1.04450i
$856$	25.3643	−	36.6417i	0.866934	−	1.25239i
$857$	1.73329	+	0.630867i	0.0592082	+	0.0215500i	0.371454	−	0.928451i	$-0.378859\pi$
$857$	1.73329	+	0.630867i	0.0592082	+	0.0215500i	−0.312246	+	0.950001i	$0.601081\pi$
$858$	−0.308617	+	1.30777i	−0.0105360	+	0.0446465i
$859$	11.6792	−	13.9187i	0.398489	−	0.474901i	−0.529070	−	0.848578i	$-0.677459\pi$
$859$	11.6792	−	13.9187i	0.398489	−	0.474901i	0.927559	+	0.373678i	$0.121903\pi$
$860$	6.82637	+	56.6420i	0.232777	+	1.93148i
$861$	23.6134	+	14.5920i	0.804742	+	0.497294i
$862$	4.35074	−	4.90656i	0.148187	−	0.167118i
$863$	49.6695			1.69077			0.845385	−	0.534157i	$-0.179371\pi$
$863$	49.6695			1.69077			0.845385	+	0.534157i	$0.179371\pi$
$864$	−24.6623	−	15.9929i	−0.839027	−	0.544089i
$865$	−39.5254			−1.34390
$866$	0.0636504	−	0.0717820i	0.00216293	−	0.00243925i
$867$	−13.3515	+	7.18480i	−0.453441	+	0.244008i
$868$	−2.71436	−	22.5225i	−0.0921313	−	0.764463i
$869$	1.28702	−	1.53381i	0.0436592	−	0.0520310i
$870$	−49.4660	+	14.8611i	−1.67705	+	0.503837i
$871$	0.740394	+	0.269482i	0.0250873	+	0.00913103i
$872$	6.82337	−	9.85715i	0.231068	−	0.333805i
$873$	−16.2819	+	12.0795i	−0.551059	+	0.408830i
$874$	2.05647	+	13.8661i	0.0695610	+	0.469026i
$875$	10.3197	+	12.2985i	0.348869	+	0.415766i
$876$	28.5078	+	40.4755i	0.963188	+	1.36754i
$877$	−22.9919	−	4.05410i	−0.776382	−	0.136897i	−0.228603	−	0.973520i	$-0.573416\pi$
$877$	−22.9919	−	4.05410i	−0.776382	−	0.136897i	−0.547779	+	0.836623i	$0.684527\pi$
$878$	−17.1419	+	9.28253i	−0.578512	+	0.313270i
$879$	13.4290	−	4.43753i	0.452948	−	0.149674i
$880$	1.49359	−	0.365314i	0.0503489	−	0.0123147i
$881$	−15.9640	+	27.6505i	−0.537842	+	0.931569i	0.461178	+	0.887307i	$0.347427\pi$
$881$	−15.9640	+	27.6505i	−0.537842	+	0.931569i	−0.999020	+	0.0442614i	$0.985907\pi$
$882$	−18.8610	+	1.65267i	−0.635083	+	0.0556484i
$883$	40.1101	−	23.1576i	1.34981	−	0.779315i	0.361590	−	0.932337i	$-0.382234\pi$
$883$	40.1101	−	23.1576i	1.34981	−	0.779315i	0.988223	+	0.153023i	$0.0489007\pi$
$884$	−16.5632	−	10.8090i	−0.557082	−	0.363545i
$885$	11.0818	−	1.61387i	0.372512	−	0.0542496i
$886$	−18.8710	−	0.515247i	−0.633984	−	0.0173101i
$887$	−32.0649	+	11.6707i	−1.07663	+	0.391863i	−0.818654	−	0.574288i	$-0.805279\pi$
$887$	−32.0649	+	11.6707i	−1.07663	+	0.391863i	−0.257980	+	0.966150i	$0.583057\pi$
$888$	−26.6762	+	11.6511i	−0.895195	+	0.390987i
$889$	−3.83231	−	21.7341i	−0.128532	−	0.728939i
$890$	−19.9646	+	15.8442i	−0.669214	+	0.531097i
$891$	0.783820	+	1.20039i	0.0262589	+	0.0402146i
$892$	−1.36671	+	5.86013i	−0.0457609	+	0.196212i
$893$	16.6533	−	2.93643i	0.557283	−	0.0982640i
$894$	−18.9964	−	25.4654i	−0.635335	−	0.851689i
$895$	−13.4431	+	4.89290i	−0.449354	+	0.163552i
$896$	13.6120	+	11.8110i	0.454744	+	0.394578i
$897$	−1.96440	−	13.4888i	−0.0655894	−	0.450379i
$898$	5.60372	+	16.8101i	0.186998	+	0.560961i
$899$	53.8839	−	31.1099i	1.79713	−	1.03757i
$900$	4.80552	−	1.14871i	0.160184	−	0.0382903i
$901$	−24.3917	−	14.0825i	−0.812605	−	0.469158i
$902$	0.454340	−	2.22046i	0.0151279	−	0.0739332i
$903$	30.9670	−	10.2329i	1.03052	−	0.340528i
$904$	−5.58425	−	20.4014i	−0.185730	−	0.678539i
$905$	0.729690	−	4.13828i	0.0242557	−	0.137561i
$906$	−8.22735	−	0.471239i	−0.273335	−	0.0156559i
$907$	−0.685743	−	0.817237i	−0.0227697	−	0.0271359i	0.754539	−	0.656255i	$-0.227860\pi$
$907$	−0.685743	−	0.817237i	−0.0227697	−	0.0271359i	−0.777309	+	0.629119i	$0.783416\pi$
$908$	−7.77518	+	8.30061i	−0.258029	+	0.275466i
$909$	2.03242	−	4.69028i	0.0674110	−	0.155567i
$910$	6.88068	−	17.4106i	0.228092	−	0.577155i
$911$	2.39685	+	0.872383i	0.0794113	+	0.0289033i	0.381420	−	0.924402i	$-0.375435\pi$
$911$	2.39685	+	0.872383i	0.0794113	+	0.0289033i	−0.302009	+	0.953305i	$0.597657\pi$
$912$	−20.1188	−	22.3208i	−0.666200	−	0.739114i
$913$	−1.37636	−	1.15490i	−0.0455508	−	0.0382216i
$914$	−21.8242	−	13.4075i	−0.721881	−	0.443479i
$915$	−5.30226	+	2.85328i	−0.175287	+	0.0943266i
$916$	2.37656	−	43.4885i	0.0785237	−	1.43690i
$917$		−	8.22758i		−	0.271699i
$918$	−20.5366	+	4.85220i	−0.677810	+	0.160147i
$919$	3.85703			0.127232			0.0636159	−	0.997974i	$-0.479737\pi$
$919$	3.85703			0.127232			0.0636159	+	0.997974i	$0.479737\pi$
$920$	−12.7292	+	9.01544i	−0.419669	+	0.297230i
$921$	16.9518	−	27.4321i	0.558579	−	0.903917i
$922$	5.16667	−	8.41015i	0.170155	−	0.276973i
$923$	−12.4986	+	14.8952i	−0.411396	+	0.490283i
$924$	−0.373667	−	0.795602i	−0.0122928	−	0.0261734i
$925$	1.67355	−	4.59804i	0.0550259	−	0.151182i
$926$	−14.8357	+	37.5397i	−0.487533	+	1.23363i
$927$	−27.9357	−	26.4437i	−0.917530	−	0.868524i
$928$	−15.1265	+	47.0572i	−0.496552	+	1.54473i
$929$	23.6191	−	19.8188i	0.774919	−	0.650234i	−0.167045	−	0.985949i	$-0.553422\pi$
$929$	23.6191	−	19.8188i	0.774919	−	0.650234i	0.941964	+	0.335715i	$0.108978\pi$
$930$	−37.5959	+	18.9267i	−1.23282	+	0.620631i
$931$	−19.0616	−	3.36108i	−0.624719	−	0.110155i
$932$	43.2160	+	18.4581i	1.41559	+	0.604616i
$933$	−8.31744	−	1.72460i	−0.272301	−	0.0564610i
$934$	0.154386	−	0.754517i	0.00505167	−	0.0246886i
$935$	0.551933	−	0.955975i	0.0180501	−	0.0312637i
$936$	19.5069	+	21.7563i	0.637604	+	0.711129i
$937$	3.69048	+	6.39210i	0.120563	+	0.208821i	0.919990	−	0.391942i	$-0.128197\pi$
$937$	3.69048	+	6.39210i	0.120563	+	0.208821i	−0.799427	+	0.600763i	$0.794863\pi$
$938$	−0.488964	+	0.162998i	−0.0159653	+	0.00532208i
$939$	−11.0516	−	14.0008i	−0.360655	−	0.456900i
$940$	11.2908	+	15.0533i	0.368266	+	0.490983i
$941$	13.1119	+	36.0246i	0.427435	+	1.17437i	0.947364	+	0.320158i	$0.103736\pi$
$941$	13.1119	+	36.0246i	0.427435	+	1.17437i	−0.519929	+	0.854209i	$0.674042\pi$
$942$	−1.21305	+	0.142970i	−0.0395234	+	0.00465821i
$943$	3.99256	+	22.6429i	0.130016	+	0.737355i
$944$	4.74105	−	9.61137i	0.154308	−	0.312823i
$945$	−8.39636	−	18.1236i	−0.273134	−	0.589561i
$946$	−1.65538	−	2.08588i	−0.0538212	−	0.0678178i
$947$	21.8272	−	3.84873i	0.709289	−	0.125067i	0.192647	−	0.981268i	$-0.438293\pi$
$947$	21.8272	−	3.84873i	0.709289	−	0.125067i	0.516642	+	0.856201i	$0.327182\pi$
$948$	−11.3854	−	42.0275i	−0.369781	−	1.36499i
$949$	−16.8328	−	46.2477i	−0.546416	−	1.50126i
$950$	5.04926	+	0.137863i	0.163820	+	0.00447287i
$951$	36.3335	+	14.4693i	1.17819	+	0.469198i
$952$	12.8825	−	1.19689i	0.417524	−	0.0387915i
$953$	22.3908	+	38.7819i	0.725308	+	1.25627i	0.958847	+	0.283922i	$0.0916358\pi$
$953$	22.3908	+	38.7819i	0.725308	+	1.25627i	−0.233540	+	0.972347i	$0.575031\pi$
$954$	29.4281	+	29.4202i	0.952770	+	0.952515i
$955$	−22.7008	−	13.1063i	−0.734580	−	0.424110i
$956$	−21.1528	−	41.7449i	−0.684129	−	1.35013i
$957$	1.60418	−	1.79960i	0.0518558	−	0.0581727i
$958$	−10.4978	+	5.68466i	−0.339168	+	0.183663i
$959$	−5.21595	+	29.5811i	−0.168432	+	0.955224i
$960$	12.0366	−	31.1966i	0.388480	−	1.00687i
$961$	15.0947	−	12.6659i	0.486925	−	0.408579i
$962$	28.6252	−	4.24538i	0.922913	−	0.136877i
$963$	−2.82658	+	47.1828i	−0.0910854	+	1.52044i
$964$	7.52038	−	2.28085i	0.242215	−	0.0734614i
$965$	11.9471	−	32.8244i	0.384591	−	1.05666i
$966$	6.49179	+	6.11288i	0.208870	+	0.196679i
$967$	32.4852	+	27.2583i	1.04465	+	0.876567i	0.992521	−	0.122073i	$-0.0389542\pi$
$967$	32.4852	+	27.2583i	1.04465	+	0.876567i	0.0521310	+	0.998640i	$0.483399\pi$
$968$	21.8309	−	22.0669i	0.701673	−	0.709258i
$969$	−21.5632	−	0.645316i	−0.692710	−	0.0207305i
$970$	−17.2560	−	15.3012i	−0.554057	−	0.491293i
$971$		−	9.33492i		−	0.299572i	−0.988718	−	0.149786i	$-0.952142\pi$
$971$		−	9.33492i		−	0.299572i	0.988718	−	0.149786i	$-0.0478584\pi$
$972$	31.1632	+	0.924247i	0.999560	+	0.0296452i
$973$		−	25.7843i		−	0.826608i
$974$	14.0753	−	15.8735i	0.451001	−	0.508618i
$975$	−4.90963	−	0.146929i	−0.157234	−	0.00470550i
$976$	−0.627916	+	5.72795i	−0.0200991	+	0.183347i
$977$	0.274142	+	0.230032i	0.00877057	+	0.00735938i	0.647162	−	0.762352i	$-0.275956\pi$
$977$	0.274142	+	0.230032i	0.00877057	+	0.00735938i	−0.638392	+	0.769712i	$0.720400\pi$
$978$	−18.9821	+	20.1587i	−0.606981	+	0.644605i
$979$	0.406885	−	1.11791i	0.0130041	−	0.0357285i
$980$	−6.25115	−	20.6112i	−0.199686	−	0.658399i
$981$	−0.760392	+	12.6929i	−0.0242774	+	0.405252i
$982$	−3.04500	−	20.5314i	−0.0971698	−	0.655183i
$983$	−6.53130	+	5.48041i	−0.208316	+	0.174798i	−0.740976	−	0.671531i	$-0.765637\pi$
$983$	−6.53130	+	5.48041i	−0.208316	+	0.174798i	0.532660	+	0.846329i	$0.321192\pi$
$984$	−33.9863	−	35.6968i	−1.08344	−	1.13797i
$985$	3.56571	−	20.2221i	0.113613	−	0.644331i
$986$	16.8972	+	31.2039i	0.538118	+	0.993734i
$987$	7.15777	−	8.02970i	0.227834	−	0.255588i
$988$	13.5025	+	26.6471i	0.429571	+	0.847757i
$989$	23.3950	+	13.5071i	0.743917	+	0.429501i
$990$	−1.15306	+	1.15337i	−0.0366466	+	0.0366564i
$991$	−25.9790	−	44.9969i	−0.825249	−	1.42937i	−0.901729	−	0.432302i	$-0.857701\pi$
$991$	−25.9790	−	44.9969i	−0.825249	−	1.42937i	0.0764798	−	0.997071i	$-0.475632\pi$
$992$	−5.48065	+	39.9063i	−0.174011	+	1.26703i
$993$	37.9348	+	15.1070i	1.20383	+	0.479405i
$994$	0.347162	−	12.7149i	0.0110113	−	0.403292i
$995$	−10.2004	−	28.0255i	−0.323375	−	0.888467i
$996$	−37.7132	+	10.2167i	−1.19499	+	0.323727i
$997$	−44.7921	+	7.89805i	−1.41858	+	0.250134i	−0.829755	−	0.558128i	$-0.811520\pi$
$997$	−44.7921	+	7.89805i	−1.41858	+	0.250134i	−0.588824	+	0.808262i	$0.700409\pi$
$998$	19.1885	−	15.2282i	0.607401	−	0.482042i
$999$	17.7722	−	25.2475i	0.562289	−	0.798797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.9	✓	204
3.2	odd	2		648.2.t.a.253.26		204
4.3	odd	2		864.2.bf.a.337.18		204
8.3	odd	2		864.2.bf.a.337.17		204
8.5	even	2	inner	216.2.t.a.13.31	yes	204
24.5	odd	2		648.2.t.a.253.4		204
27.2	odd	18		648.2.t.a.397.4		204
27.25	even	9	inner	216.2.t.a.133.31	yes	204
108.79	odd	18		864.2.bf.a.241.17		204
216.29	odd	18		648.2.t.a.397.26		204
216.133	even	18	inner	216.2.t.a.133.9	yes	204
216.187	odd	18		864.2.bf.a.241.18		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.9	✓	204	1.1	even	1	trivial
216.2.t.a.13.31	yes	204	8.5	even	2	inner
216.2.t.a.133.9	yes	204	216.133	even	18	inner
216.2.t.a.133.31	yes	204	27.25	even	9	inner
648.2.t.a.253.4		204	24.5	odd	2
648.2.t.a.253.26		204	3.2	odd	2
648.2.t.a.397.4		204	27.2	odd	18
648.2.t.a.397.26		204	216.29	odd	18
864.2.bf.a.241.17		204	108.79	odd	18
864.2.bf.a.241.18		204	216.187	odd	18
864.2.bf.a.337.17		204	8.3	odd	2
864.2.bf.a.337.18		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)

\(f(q)\)	\(=\)	\(q+(-0.938269 + 1.05814i) q^{2} +(-0.0518114 + 1.73128i) q^{3} +(-0.239304 - 1.98563i) q^{4} +(-1.55117 + 1.84861i) q^{5} +(-1.78331 - 1.67923i) q^{6} +(-1.49685 - 0.544810i) q^{7} +(2.32560 + 1.60984i) q^{8} +(-2.99463 - 0.179400i) q^{9} +O(q^{10})\)	\(q+(-0.938269 + 1.05814i) q^{2} +(-0.0518114 + 1.73128i) q^{3} +(-0.239304 - 1.98563i) q^{4} +(-1.55117 + 1.84861i) q^{5} +(-1.78331 - 1.67923i) q^{6} +(-1.49685 - 0.544810i) q^{7} +(2.32560 + 1.60984i) q^{8} +(-2.99463 - 0.179400i) q^{9} +(-0.500669 - 3.37584i) q^{10} +(0.102391 + 0.122025i) q^{11} +(3.45007 - 0.311423i) q^{12} +(-3.39140 - 0.597995i) q^{13} +(1.98093 - 1.07270i) q^{14} +(-3.12009 - 2.78128i) q^{15} +(-3.88547 + 0.950339i) q^{16} +(-1.43581 + 2.48690i) q^{17} +(2.99960 - 3.00040i) q^{18} +(3.75621 - 2.16865i) q^{19} +(4.04186 + 2.63767i) q^{20} +(1.02077 - 2.56324i) q^{21} +(-0.225190 - 0.00614850i) q^{22} +(2.14748 - 0.781619i) q^{23} +(-2.90757 + 3.94285i) q^{24} +(-0.142997 - 0.810974i) q^{25} +(3.81480 - 3.02748i) q^{26} +(0.465746 - 5.17524i) q^{27} +(-0.723589 + 3.10257i) q^{28} +(-8.60509 + 1.51731i) q^{29} +(5.87045 - 0.691889i) q^{30} +(-6.69129 + 2.43543i) q^{31} +(2.64002 - 5.00303i) q^{32} +(-0.216565 + 0.170946i) q^{33} +(-1.28430 - 3.85267i) q^{34} +(3.32901 - 1.92201i) q^{35} +(0.360405 + 5.98917i) q^{36} +(5.14590 + 2.97099i) q^{37} +(-1.22961 + 6.00935i) q^{38} +(1.21101 - 5.84046i) q^{39} +(-6.58336 + 1.80200i) q^{40} +(-1.74706 + 9.90807i) q^{41} +(1.75450 + 3.48512i) q^{42} +(7.59829 + 9.05529i) q^{43} +(0.217795 - 0.232513i) q^{44} +(4.97682 - 5.25763i) q^{45} +(-1.18785 + 3.00570i) q^{46} +(3.66367 + 1.33347i) q^{47} +(-1.44399 - 6.77605i) q^{48} +(-3.41856 - 2.86851i) q^{49} +(0.992290 + 0.609602i) q^{50} +(-4.23112 - 2.61464i) q^{51} +(-0.375823 + 6.87717i) q^{52} +9.80805i q^{53} +(5.03911 + 5.34859i) q^{54} -0.384404 q^{55} +(-2.60402 - 3.67670i) q^{56} +(3.55991 + 6.61539i) q^{57} +(6.46837 - 10.5290i) q^{58} +(-1.72220 + 2.05244i) q^{59} +(-4.77595 + 6.86091i) q^{60} +(0.492702 - 1.35369i) q^{61} +(3.70121 - 9.36539i) q^{62} +(4.38478 + 1.90004i) q^{63} +(2.81683 + 7.48769i) q^{64} +(6.36609 - 5.34178i) q^{65} +(0.0223122 - 0.389548i) q^{66} +(-0.225321 - 0.0397302i) q^{67} +(5.28167 + 2.25587i) q^{68} +(1.24193 + 3.75838i) q^{69} +(-1.08976 + 5.32591i) q^{70} +(2.82317 - 4.88987i) q^{71} +(-6.67551 - 5.23809i) q^{72} +(7.14574 + 12.3768i) q^{73} +(-7.97195 + 2.65748i) q^{74} +(1.41143 - 0.205549i) q^{75} +(-5.20501 - 6.93948i) q^{76} +(-0.0867843 - 0.238438i) q^{77} +(5.04375 + 6.76133i) q^{78} +(-2.18269 - 12.3786i) q^{79} +(4.27021 - 8.65685i) q^{80} +(8.93563 + 1.07447i) q^{81} +(-8.84487 - 11.1451i) q^{82} +(-11.1079 + 1.95862i) q^{83} +(-5.33392 - 1.41348i) q^{84} +(-2.37013 - 6.51187i) q^{85} +(-16.7110 - 0.456270i) q^{86} +(-2.18104 - 14.9764i) q^{87} +(0.0416802 + 0.448616i) q^{88} +(-3.73417 - 6.46777i) q^{89} +(0.893694 + 10.1992i) q^{90} +(4.75063 + 2.74278i) q^{91} +(-2.06591 - 4.07706i) q^{92} +(-3.86972 - 11.7107i) q^{93} +(-4.84850 + 2.62551i) q^{94} +(-1.81753 + 10.3077i) q^{95} +(8.52483 + 4.82982i) q^{96} +(5.17680 - 4.34385i) q^{97} +(6.24280 - 0.925866i) q^{98} +(-0.284733 - 0.383790i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more