LMFDB - Embedded newform 378.2.v.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	378.67
Dual form			378.2.v.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.71753 - 0.223844i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0598945 - 0.339678i) q^{5} +(1.45959 - 0.932530i) q^{6} +(-1.66417 + 2.05683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.89979 + 0.768916i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.71753 - 0.223844i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0598945 - 0.339678i) q^{5} +(1.45959 - 0.932530i) q^{6} +(-1.66417 + 2.05683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.89979 + 0.768916i) q^{9} +(0.172459 + 0.298708i) q^{10} +(-0.151791 - 0.860851i) q^{11} +(-0.518689 + 1.65256i) q^{12} +(0.0309187 - 0.175349i) q^{13} +(-0.0472752 - 2.64533i) q^{14} +(-0.178905 + 0.569999i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-3.46292 - 5.99795i) q^{17} +(-2.71562 + 1.27492i) q^{18} +(1.67631 - 2.90346i) q^{19} +(-0.324117 - 0.117969i) q^{20} +(3.31866 - 3.16014i) q^{21} +(0.669623 + 0.561880i) q^{22} +(-5.77971 - 4.84976i) q^{23} +(-0.664908 - 1.59934i) q^{24} +(4.58667 + 1.66941i) q^{25} +(0.0890268 + 0.154199i) q^{26} +(-4.80834 - 1.96973i) q^{27} +(1.73660 + 1.99605i) q^{28} +(-0.470725 - 2.66961i) q^{29} +(-0.229339 - 0.551643i) q^{30} +(1.29691 - 7.35512i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.0680089 + 1.51251i) q^{33} +(6.50816 + 2.36878i) q^{34} +(0.598985 + 0.688475i) q^{35} +(1.26078 - 2.72221i) q^{36} +4.87044 q^{37} +(0.582178 + 3.30170i) q^{38} +(-0.0923544 + 0.294245i) q^{39} +(0.324117 - 0.117969i) q^{40} +(0.625127 - 3.54527i) q^{41} +(-0.510945 + 4.55400i) q^{42} +(-6.79190 + 5.69908i) q^{43} -0.874131 q^{44} +(0.434865 - 0.938942i) q^{45} +7.54488 q^{46} +(-0.295641 - 1.67666i) q^{47} +(1.53739 + 0.797773i) q^{48} +(-1.46108 - 6.84582i) q^{49} +(-4.58667 + 1.66941i) q^{50} +(4.60504 + 11.0768i) q^{51} +(-0.167316 - 0.0608979i) q^{52} +(5.57388 - 9.65424i) q^{53} +(4.94952 - 1.58184i) q^{54} -0.301504 q^{55} +(-2.61335 - 0.412800i) q^{56} +(-3.52904 + 4.61154i) q^{57} +(2.07659 + 1.74247i) q^{58} +(-4.70748 + 1.71338i) q^{59} +(0.530273 + 0.275167i) q^{60} +(0.0300348 + 0.170336i) q^{61} +(3.73429 + 6.46798i) q^{62} +(-6.40727 + 4.68476i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0577103 - 0.0210048i) q^{65} +(-1.02432 - 1.11494i) q^{66} +(4.93575 + 4.14159i) q^{67} +(-6.50816 + 2.36878i) q^{68} +(8.84122 + 9.62333i) q^{69} +(-0.901393 - 0.142382i) q^{70} +(-4.67546 + 8.09814i) q^{71} +(0.783993 + 2.89575i) q^{72} -11.8114 q^{73} +(-3.73097 + 3.13066i) q^{74} +(-7.50403 - 3.89395i) q^{75} +(-2.56826 - 2.15503i) q^{76} +(2.02323 + 1.12039i) q^{77} +(-0.118389 - 0.284769i) q^{78} +(-0.362377 + 0.304071i) q^{79} +(-0.172459 + 0.298708i) q^{80} +(7.81754 + 4.45939i) q^{81} +(1.79998 + 3.11766i) q^{82} +(-0.240849 - 1.36592i) q^{83} +(-2.53585 - 3.81700i) q^{84} +(-2.24478 + 0.817035i) q^{85} +(1.53960 - 8.73150i) q^{86} +(0.210905 + 4.69050i) q^{87} +(0.669623 - 0.561880i) q^{88} +(-6.60450 + 11.4393i) q^{89} +(0.270414 + 0.998797i) q^{90} +(0.309208 + 0.355404i) q^{91} +(-5.77971 + 4.84976i) q^{92} +(-3.87387 + 12.3423i) q^{93} +(1.30421 + 1.09436i) q^{94} +(-0.885842 - 0.743309i) q^{95} +(-1.69051 + 0.377084i) q^{96} +(-3.52644 + 2.95904i) q^{97} +(5.51966 + 4.30504i) q^{98} +(0.221760 - 2.61300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.71753	−	0.223844i	−0.991614	−	0.129236i
$3$	−1.71753	−	0.223844i	−0.991614	−	0.129236i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.0598945	−	0.339678i	0.0267856	−	0.151909i	−0.968482	−	0.249085i	$-0.919870\pi$
$5$	0.0598945	−	0.339678i	0.0267856	−	0.151909i	0.995267	+	0.0971765i	$0.0309811\pi$
$6$	1.45959	−	0.932530i	0.595873	−	0.380704i
$7$	−1.66417	+	2.05683i	−0.628997	+	0.777408i
$7$	−1.66417	+	2.05683i	−0.628997	+	0.777408i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.89979	+	0.768916i	0.966596	+	0.256305i
$10$	0.172459	+	0.298708i	0.0545364	+	0.0944598i
$11$	−0.151791	−	0.860851i	−0.0457668	−	0.259556i	0.953336	−	0.301912i	$-0.0976249\pi$
$11$	−0.151791	−	0.860851i	−0.0457668	−	0.259556i	−0.999103	+	0.0423556i	$0.986514\pi$
$12$	−0.518689	+	1.65256i	−0.149733	+	0.477054i
$13$	0.0309187	−	0.175349i	0.00857530	−	0.0486329i	−0.980220	−	0.197912i	$-0.936584\pi$
$13$	0.0309187	−	0.175349i	0.00857530	−	0.0486329i	0.988795	+	0.149279i	$0.0476952\pi$
$14$	−0.0472752	−	2.64533i	−0.0126348	−	0.706994i
$15$	−0.178905	+	0.569999i	−0.0461932	+	0.147173i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.46292	−	5.99795i	−0.839881	−	1.45472i	−0.889994	−	0.455973i	$-0.849291\pi$
$17$	−3.46292	−	5.99795i	−0.839881	−	1.45472i	0.0501126	−	0.998744i	$-0.484042\pi$
$18$	−2.71562	+	1.27492i	−0.640077	+	0.300502i
$19$	1.67631	−	2.90346i	0.384573	−	0.666100i	−0.607137	−	0.794597i	$-0.707682\pi$
$19$	1.67631	−	2.90346i	0.384573	−	0.666100i	0.991710	+	0.128497i	$0.0410154\pi$
$20$	−0.324117	−	0.117969i	−0.0724749	−	0.0263787i
$21$	3.31866	−	3.16014i	0.724192	−	0.689599i
$22$	0.669623	+	0.561880i	0.142764	+	0.119793i
$23$	−5.77971	−	4.84976i	−1.20515	−	1.01124i	−0.999468	−	0.0326259i	$-0.989613\pi$
$23$	−5.77971	−	4.84976i	−1.20515	−	1.01124i	−0.205686	−	0.978618i	$-0.565943\pi$
$24$	−0.664908	−	1.59934i	−0.135724	−	0.326464i
$25$	4.58667	+	1.66941i	0.917334	+	0.333882i
$26$	0.0890268	+	0.154199i	0.0174596	+	0.0302409i
$27$	−4.80834	−	1.96973i	−0.925366	−	0.379075i
$28$	1.73660	+	1.99605i	0.328186	+	0.377218i
$29$	−0.470725	−	2.66961i	−0.0874114	−	0.495735i	−0.996810	−	0.0798093i	$-0.974569\pi$
$29$	−0.470725	−	2.66961i	−0.0874114	−	0.495735i	0.909399	−	0.415925i	$-0.136542\pi$
$30$	−0.229339	−	0.551643i	−0.0418714	−	0.100716i
$31$	1.29691	−	7.35512i	0.232931	−	1.32102i	−0.613996	−	0.789309i	$-0.710439\pi$
$31$	1.29691	−	7.35512i	0.232931	−	1.32102i	0.846927	−	0.531709i	$-0.178450\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.0680089	+	1.51251i	0.0118388	+	0.263294i
$34$	6.50816	+	2.36878i	1.11614	+	0.406242i
$35$	0.598985	+	0.688475i	0.101247	+	0.116374i
$36$	1.26078	−	2.72221i	0.210130	−	0.453702i
$37$	4.87044			0.800695			0.400348	−	0.916363i	$-0.368889\pi$
$37$	4.87044			0.800695			0.400348	+	0.916363i	$0.368889\pi$
$38$	0.582178	+	3.30170i	0.0944417	+	0.535606i
$39$	−0.0923544	+	0.294245i	−0.0147885	+	0.0471169i
$40$	0.324117	−	0.117969i	0.0512475	−	0.0186526i
$41$	0.625127	−	3.54527i	0.0976285	−	0.553679i	−0.896282	−	0.443485i	$-0.853742\pi$
$41$	0.625127	−	3.54527i	0.0976285	−	0.553679i	0.993910	−	0.110193i	$-0.0351470\pi$
$42$	−0.510945	+	4.55400i	−0.0788405	+	0.702698i
$43$	−6.79190	+	5.69908i	−1.03575	+	0.869101i	−0.991524	−	0.129920i	$-0.958528\pi$
$43$	−6.79190	+	5.69908i	−1.03575	+	0.869101i	−0.0442302	+	0.999021i	$0.514084\pi$
$44$	−0.874131			−0.131780
$45$	0.434865	−	0.938942i	0.0648259	−	0.139969i
$46$	7.54488			1.11243
$47$	−0.295641	−	1.67666i	−0.0431236	−	0.244566i	0.955625	−	0.294587i	$-0.0951822\pi$
$47$	−0.295641	−	1.67666i	−0.0431236	−	0.244566i	−0.998748	+	0.0500212i	$0.984071\pi$
$48$	1.53739	+	0.797773i	0.221903	+	0.115149i
$49$	−1.46108	−	6.84582i	−0.208725	−	0.977974i
$50$	−4.58667	+	1.66941i	−0.648653	+	0.236090i
$51$	4.60504	+	11.0768i	0.644835	+	1.55106i
$52$	−0.167316	−	0.0608979i	−0.0232025	−	0.00844502i
$53$	5.57388	−	9.65424i	0.765631	−	1.32611i	−0.174281	−	0.984696i	$-0.555760\pi$
$53$	5.57388	−	9.65424i	0.765631	−	1.32611i	0.939912	−	0.341416i	$-0.110906\pi$
$54$	4.94952	−	1.58184i	0.673545	−	0.215261i
$55$	−0.301504			−0.0406548
$56$	−2.61335	−	0.412800i	−0.349224	−	0.0551627i
$57$	−3.52904	+	4.61154i	−0.467432	+	0.610813i
$58$	2.07659	+	1.74247i	0.272670	+	0.228797i
$59$	−4.70748	+	1.71338i	−0.612861	+	0.223063i	−0.629755	−	0.776794i	$-0.716845\pi$
$59$	−4.70748	+	1.71338i	−0.612861	+	0.223063i	0.0168936	+	0.999857i	$0.494622\pi$
$60$	0.530273	+	0.275167i	0.0684580	+	0.0355239i
$61$	0.0300348	+	0.170336i	0.00384556	+	0.0218093i	0.986670	−	0.162733i	$-0.0520309\pi$
$61$	0.0300348	+	0.170336i	0.00384556	+	0.0218093i	−0.982825	+	0.184542i	$0.940920\pi$
$62$	3.73429	+	6.46798i	0.474256	+	0.821435i
$63$	−6.40727	+	4.68476i	−0.807240	+	0.590224i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0577103	−	0.0210048i	−0.00715808	−	0.00260533i
$66$	−1.02432	−	1.11494i	−0.126085	−	0.137239i
$67$	4.93575	+	4.14159i	0.602998	+	0.505976i	0.892408	−	0.451230i	$-0.149014\pi$
$67$	4.93575	+	4.14159i	0.602998	+	0.505976i	−0.289409	+	0.957205i	$0.593459\pi$
$68$	−6.50816	+	2.36878i	−0.789230	+	0.287256i
$69$	8.84122	+	9.62333i	1.06436	+	1.15851i
$70$	−0.901393	−	0.142382i	−0.107737	−	0.0170179i
$71$	−4.67546	+	8.09814i	−0.554876	+	0.961073i	0.443038	+	0.896503i	$0.353901\pi$
$71$	−4.67546	+	8.09814i	−0.554876	+	0.961073i	−0.997913	+	0.0645697i	$0.979433\pi$
$72$	0.783993	+	2.89575i	0.0923945	+	0.341267i
$73$	−11.8114			−1.38242			−0.691210	−	0.722654i	$-0.742922\pi$
$73$	−11.8114			−1.38242			−0.691210	+	0.722654i	$0.742922\pi$
$74$	−3.73097	+	3.13066i	−0.433717	+	0.363932i
$75$	−7.50403	−	3.89395i	−0.866491	−	0.449635i
$76$	−2.56826	−	2.15503i	−0.294600	−	0.247199i
$77$	2.02323	+	1.12039i	0.230568	+	0.127681i
$78$	−0.118389	−	0.284769i	−0.0134049	−	0.0322437i
$79$	−0.362377	+	0.304071i	−0.0407706	+	0.0342106i	−0.662945	−	0.748668i	$-0.730694\pi$
$79$	−0.362377	+	0.304071i	−0.0407706	+	0.0342106i	0.622175	+	0.782878i	$0.286249\pi$
$80$	−0.172459	+	0.298708i	−0.0192815	+	0.0333966i
$81$	7.81754	+	4.45939i	0.868615	+	0.495487i
$82$	1.79998	+	3.11766i	0.198775	+	0.344288i
$83$	−0.240849	−	1.36592i	−0.0264366	−	0.149929i	0.968732	−	0.248109i	$-0.0798091\pi$
$83$	−0.240849	−	1.36592i	−0.0264366	−	0.149929i	−0.995169	+	0.0981796i	$0.968698\pi$
$84$	−2.53585	−	3.81700i	−0.276684	−	0.416469i
$85$	−2.24478	+	0.817035i	−0.243481	+	0.0886198i
$86$	1.53960	−	8.73150i	0.166019	−	0.941541i
$87$	0.210905	+	4.69050i	0.0226113	+	0.502874i
$88$	0.669623	−	0.561880i	0.0713821	−	0.0598967i
$89$	−6.60450	+	11.4393i	−0.700076	+	1.21257i	0.268363	+	0.963318i	$0.413517\pi$
$89$	−6.60450	+	11.4393i	−0.700076	+	1.21257i	−0.968439	+	0.249250i	$0.919816\pi$
$90$	0.270414	+	0.998797i	0.0285041	+	0.105282i
$91$	0.309208	+	0.355404i	0.0324138	+	0.0372565i
$92$	−5.77971	+	4.84976i	−0.602577	+	0.505622i
$93$	−3.87387	+	12.3423i	−0.401702	+	1.27984i
$94$	1.30421	+	1.09436i	0.134519	+	0.112875i
$95$	−0.885842	−	0.743309i	−0.0908854	−	0.0762619i
$96$	−1.69051	+	0.377084i	−0.172536	+	0.0384859i
$97$	−3.52644	+	2.95904i	−0.358056	+	0.300445i	−0.804015	−	0.594609i	$-0.797307\pi$
$97$	−3.52644	+	2.95904i	−0.358056	+	0.300445i	0.445959	+	0.895053i	$0.352863\pi$
$98$	5.51966	+	4.30504i	0.557570	+	0.434875i
$99$	0.221760	−	2.61300i	0.0222877	−	0.262616i
$100$	2.44052	−	4.22710i	0.244052	−	0.422710i
$101$	12.7080	−	10.6633i	1.26450	−	1.06104i	0.269308	−	0.963054i	$-0.413205\pi$
$101$	12.7080	−	10.6633i	1.26450	−	1.06104i	0.995188	−	0.0979837i	$-0.0312393\pi$
$102$	−10.6477	−	5.52525i	−1.05428	−	0.547081i
$103$	2.69593	−	15.2894i	0.265637	−	1.50650i	−0.501577	−	0.865113i	$-0.667246\pi$
$103$	2.69593	−	15.2894i	0.265637	−	1.50650i	0.767214	−	0.641391i	$-0.221642\pi$
$104$	0.167316	−	0.0608979i	0.0164067	−	0.00597153i
$105$	−0.874662	−	1.31655i	−0.0853582	−	0.128482i
$106$	1.93579	+	10.9784i	0.188020	+	1.06632i
$107$	7.31071	+	12.6625i	0.706753	+	1.22413i	0.966055	+	0.258336i	$0.0831741\pi$
$107$	7.31071	+	12.6625i	0.706753	+	1.22413i	−0.259302	+	0.965796i	$0.583493\pi$
$108$	−2.77477	+	4.39325i	−0.267002	+	0.422741i
$109$	−2.18827	+	3.79020i	−0.209598	+	0.363035i	−0.951588	−	0.307376i	$-0.900549\pi$
$109$	−2.18827	+	3.79020i	−0.209598	+	0.363035i	0.741990	+	0.670411i	$0.233882\pi$
$110$	0.230965	−	0.193803i	0.0220217	−	0.0184784i
$111$	−8.36510	−	1.09022i	−0.793980	−	0.103479i
$112$	2.26728	−	1.36361i	0.214238	−	0.128849i
$113$	−7.48470	−	6.28041i	−0.704101	−	0.590811i	0.218836	−	0.975762i	$-0.429774\pi$
$113$	−7.48470	−	6.28041i	−0.704101	−	0.590811i	−0.922937	+	0.384951i	$0.874218\pi$
$114$	−0.260840	−	5.80106i	−0.0244299	−	0.543319i
$115$	−1.99353	+	1.67277i	−0.185898	+	0.155987i
$116$	−2.71080			−0.251691
$117$	0.224486	−	0.484700i	0.0207537	−	0.0448105i
$118$	2.50480	−	4.33843i	0.230585	−	0.399385i
$119$	18.0996	+	2.85898i	1.65919	+	0.262082i
$120$	−0.583087	+	0.130063i	−0.0532283	+	0.0118731i
$121$	9.61860	−	3.50088i	0.874418	−	0.318262i
$122$	−0.132498	−	0.111179i	−0.0119958	−	0.0100657i
$123$	−1.86726	+	5.94917i	−0.168365	+	0.536418i
$124$	−7.01817	−	2.55441i	−0.630251	−	0.229392i
$125$	1.70408	−	2.95155i	0.152417	−	0.263994i
$126$	1.89695	−	7.70724i	0.168994	−	0.686616i
$127$	−4.76761	−	8.25775i	−0.423057	−	0.732757i	0.573180	−	0.819430i	$-0.305710\pi$
$127$	−4.76761	−	8.25775i	−0.423057	−	0.732757i	−0.996237	+	0.0866732i	$0.972376\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	12.9410	−	8.26799i	1.13939	−	0.727956i
$130$	0.0577103	−	0.0210048i	0.00506153	−	0.00184224i
$131$	0.329501	+	0.276484i	0.0287886	+	0.0241565i	0.657068	−	0.753831i	$-0.271796\pi$
$131$	0.329501	+	0.276484i	0.0287886	+	0.0241565i	−0.628280	+	0.777987i	$0.716241\pi$
$132$	1.50134	+	0.195669i	0.130675	+	0.0170308i
$133$	3.18225	+	8.27974i	0.275936	+	0.717945i
$134$	−6.44317			−0.556605
$135$	−0.957069	+	1.51531i	−0.0823714	+	0.130417i
$136$	3.46292	−	5.99795i	0.296943	−	0.514320i
$137$	−2.55930	−	0.931510i	−0.218656	−	0.0795842i	0.230369	−	0.973103i	$-0.426007\pi$
$137$	−2.55930	−	0.931510i	−0.218656	−	0.0795842i	−0.449025	+	0.893519i	$0.648229\pi$
$138$	−12.9585	−	1.68888i	−1.10310	−	0.143767i
$139$	2.29383	−	0.834887i	0.194560	−	0.0708142i	−0.242902	−	0.970051i	$-0.578099\pi$
$139$	2.29383	−	0.834887i	0.194560	−	0.0708142i	0.437463	+	0.899237i	$0.355877\pi$
$140$	0.782028	−	0.470333i	0.0660935	−	0.0397504i
$141$	0.132459	+	2.94589i	0.0111551	+	0.248088i
$142$	−1.62377	−	9.20887i	−0.136264	−	0.772791i
$143$	−0.155642			−0.0130155
$144$	−2.46192	−	1.71433i	−0.205160	−	0.142861i
$145$	−0.935004			−0.0776478
$146$	9.04806	−	7.59222i	0.748823	−	0.628337i
$147$	0.977042	+	12.0849i	0.0805851	+	0.996748i
$148$	0.845743	−	4.79645i	0.0695196	−	0.394265i
$149$	−8.11492	+	2.95359i	−0.664800	+	0.241967i	−0.652307	−	0.757955i	$-0.726199\pi$
$149$	−8.11492	+	2.95359i	−0.664800	+	0.241967i	−0.0124925	+	0.999922i	$0.503977\pi$
$150$	8.25141	−	1.84056i	0.673725	−	0.150281i
$151$	0.0480257	+	0.272367i	0.00390827	+	0.0221649i	0.986700	−	0.162555i	$-0.0519734\pi$
$151$	0.0480257	+	0.272367i	0.00390827	+	0.0221649i	−0.982791	+	0.184720i	$0.940862\pi$
$152$	3.35263			0.271934
$153$	−5.42981	−	20.0555i	−0.438974	−	1.62139i
$154$	−2.27006	+	0.442235i	−0.182926	+	0.0356363i
$155$	−2.42070	−	0.881062i	−0.194435	−	0.0707686i
$156$	0.273737	+	0.142046i	0.0219165	+	0.0113728i
$157$	−15.4171	+	5.61136i	−1.23042	+	0.447835i	−0.873740	−	0.486393i	$-0.838312\pi$
$157$	−15.4171	+	5.61136i	−1.23042	+	0.447835i	−0.356677	+	0.934228i	$0.616090\pi$
$158$	0.0821443	−	0.465863i	0.00653505	−	0.0370621i
$159$	−11.7343	+	15.3337i	−0.930592	+	1.21604i
$160$	−0.0598945	−	0.339678i	−0.00473507	−	0.0268539i
$161$	19.5935	−	3.81706i	1.54419	−	0.300826i
$162$	−8.85502	+	1.60893i	−0.695716	+	0.126409i
$163$	10.6016	+	18.3625i	0.830380	+	1.43826i	0.897737	+	0.440531i	$0.145210\pi$
$163$	10.6016	+	18.3625i	0.830380	+	1.43826i	−0.0673579	+	0.997729i	$0.521457\pi$
$164$	−3.38286	−	1.23126i	−0.264157	−	0.0961453i
$165$	0.517841	+	0.0674899i	0.0403138	+	0.00525408i
$166$	1.06250	+	0.891542i	0.0824659	+	0.0691971i
$167$	−0.717784	−	0.602292i	−0.0555438	−	0.0466068i	0.614593	−	0.788844i	$-0.289320\pi$
$167$	−0.717784	−	0.602292i	−0.0555438	−	0.0466068i	−0.670137	+	0.742237i	$0.733765\pi$
$168$	4.39609	+	1.29398i	0.339166	+	0.0998325i
$169$	12.1862	+	4.43542i	0.937401	+	0.341186i
$170$	1.19442	−	2.06880i	0.0916082	−	0.158670i
$171$	7.09348	−	7.13048i	0.542452	−	0.545281i
$172$	4.43310	+	7.67835i	0.338020	+	0.585469i
$173$	11.6332	+	4.23412i	0.884452	+	0.321914i	0.744005	−	0.668174i	$-0.232924\pi$
$173$	11.6332	+	4.23412i	0.884452	+	0.321914i	0.140447	+	0.990088i	$0.455146\pi$
$174$	−3.17656	−	3.45756i	−0.240814	−	0.262117i
$175$	−11.0667	+	6.65580i	−0.836563	+	0.503131i
$176$	−0.151791	+	0.860851i	−0.0114417	+	0.0648891i
$177$	8.46874	−	1.88903i	0.636549	−	0.141989i
$178$	−2.29372	−	13.0083i	−0.171922	−	0.975016i
$179$	−4.24620	−	7.35464i	−0.317376	−	0.549712i	0.662564	−	0.749006i	$-0.269468\pi$
$179$	−4.24620	−	7.35464i	−0.317376	−	0.549712i	−0.979940	+	0.199294i	$0.936135\pi$
$180$	−0.849163	−	0.591304i	−0.0632929	−	0.0440732i
$181$	2.84630	+	4.92994i	0.211564	+	0.366439i	0.952204	−	0.305462i	$-0.0988110\pi$
$181$	2.84630	+	4.92994i	0.211564	+	0.366439i	−0.740640	+	0.671902i	$0.765478\pi$
$182$	−0.465316	−	0.0735005i	−0.0344915	−	0.00544822i
$183$	−0.0134569	−	0.299279i	−0.000994760	−	0.0221234i
$184$	1.31015	−	7.43026i	0.0965859	−	0.547766i
$185$	0.291712	−	1.65438i	0.0214471	−	0.121633i
$186$	−4.96592	−	11.9448i	−0.364119	−	0.875837i
$187$	−4.63770	+	3.89149i	−0.339142	+	0.284574i
$188$	−1.70253			−0.124169
$189$	12.0533	−	6.61196i	0.876748	−	0.480949i
$190$	1.15638			0.0838929
$191$	12.5320	−	10.5156i	0.906787	−	0.760884i	−0.0647182	−	0.997904i	$-0.520615\pi$
$191$	12.5320	−	10.5156i	0.906787	−	0.760884i	0.971505	+	0.237019i	$0.0761704\pi$
$192$	1.05262	−	1.37550i	0.0759661	−	0.0992681i
$193$	3.48754	−	19.7788i	0.251038	−	1.42371i	−0.555002	−	0.831849i	$-0.687282\pi$
$193$	3.48754	−	19.7788i	0.251038	−	1.42371i	0.806040	−	0.591861i	$-0.201606\pi$
$194$	0.799380	−	4.53351i	0.0573921	−	0.325487i
$195$	0.0944171	+	0.0489944i	0.00676135	+	0.00350856i
$196$	−6.99553	+	0.250117i	−0.499681	+	0.0178655i
$197$	4.50532	+	7.80344i	0.320991	+	0.555972i	0.980693	−	0.195555i	$-0.0626508\pi$
$197$	4.50532	+	7.80344i	0.320991	+	0.555972i	−0.659702	+	0.751527i	$0.729318\pi$
$198$	1.50973	+	2.14422i	0.107292	+	0.152383i
$199$	−10.5427	−	18.2605i	−0.747351	−	1.29445i	−0.949088	−	0.315011i	$-0.897992\pi$
$199$	−10.5427	−	18.2605i	−0.747351	−	1.29445i	0.201737	−	0.979440i	$-0.435342\pi$
$200$	0.847582	+	4.80688i	0.0599331	+	0.339898i
$201$	−7.55021	−	8.21813i	−0.532551	−	0.579662i
$202$	−2.88068	+	16.3371i	−0.202684	+	1.14948i
$203$	6.27430	+	3.47449i	0.440369	+	0.243861i
$204$	11.7082	−	2.61162i	0.819735	−	0.182850i
$205$	−1.16681	−	0.424685i	−0.0814936	−	0.0296613i
$206$	7.76261	+	13.4452i	0.540846	+	0.936774i
$207$	−13.0309	−	18.5074i	−0.905709	−	1.28635i
$208$	−0.0890268	+	0.154199i	−0.00617290	+	0.0106918i
$209$	−2.75390	−	1.00234i	−0.190491	−	0.0693331i
$210$	1.51629	+	0.446317i	0.104634	+	0.0307988i
$211$	−17.9188	−	15.0357i	−1.23358	−	1.03510i	−0.997998	−	0.0632469i	$-0.979854\pi$
$211$	−17.9188	−	15.0357i	−1.23358	−	1.03510i	−0.235587	−	0.971853i	$-0.575701\pi$
$212$	−8.53968	−	7.16564i	−0.586507	−	0.492138i
$213$	9.84295	−	12.8622i	0.674428	−	0.881303i
$214$	−13.7396	−	5.00082i	−0.939222	−	0.341849i
$215$	1.52906	+	2.64840i	0.104281	+	0.180620i
$216$	−0.698332	−	5.14901i	−0.0475155	−	0.350346i
$217$	12.9699	+	14.9077i	0.880457	+	1.01200i
$218$	−0.759978	−	4.31005i	−0.0514722	−	0.291914i
$219$	20.2864	+	2.64391i	1.37083	+	0.178659i
$220$	−0.0523556	+	0.296923i	−0.00352981	+	0.0200186i
$221$	−1.15880	+	0.421769i	−0.0779494	+	0.0283713i
$222$	7.10882	−	4.54183i	0.477113	−	0.304828i
$223$	3.54993	+	1.29207i	0.237721	+	0.0865234i	0.458134	−	0.888883i	$-0.348518\pi$
$223$	3.54993	+	1.29207i	0.237721	+	0.0865234i	−0.220412	+	0.975407i	$0.570740\pi$
$224$	−0.860332	+	2.50197i	−0.0574833	+	0.167170i
$225$	12.0167	+	8.36770i	0.801115	+	0.557847i
$226$	9.77058			0.649929
$227$	3.46307	+	19.6401i	0.229852	+	1.30356i	0.853188	+	0.521603i	$0.174666\pi$
$227$	3.46307	+	19.6401i	0.229852	+	1.30356i	−0.623336	+	0.781954i	$0.714223\pi$
$228$	3.92867	+	4.27621i	0.260182	+	0.283199i
$229$	4.51329	−	1.64270i	0.298246	−	0.108553i	−0.188563	−	0.982061i	$-0.560383\pi$
$229$	4.51329	−	1.64270i	0.298246	−	0.108553i	0.486809	+	0.873508i	$0.338161\pi$
$230$	0.451897	−	2.56283i	0.0297972	−	0.168988i
$231$	−3.22415	−	2.37719i	−0.212134	−	0.156408i
$232$	2.07659	−	1.74247i	0.136335	−	0.114398i
$233$	−24.2405			−1.58805			−0.794024	−	0.607887i	$-0.792017\pi$
$233$	−24.2405			−1.58805			−0.794024	+	0.607887i	$0.792017\pi$
$234$	0.139593	+	0.515598i	0.00912547	+	0.0337057i
$235$	−0.587233			−0.0383069
$236$	0.869906	+	4.93348i	0.0566261	+	0.321142i
$237$	0.690457	−	0.441133i	0.0448500	−	0.0286547i
$238$	−15.7028	+	9.44411i	−1.01786	+	0.612171i
$239$	−2.10441	+	0.765942i	−0.136123	+	0.0495447i	−0.409183	−	0.912452i	$-0.634186\pi$
$239$	−2.10441	+	0.765942i	−0.136123	+	0.0495447i	0.273060	+	0.961997i	$0.411964\pi$
$240$	0.363067	−	0.474435i	0.0234359	−	0.0306246i
$241$	−26.2448	−	9.55231i	−1.69057	−	0.615318i	−0.695876	−	0.718162i	$-0.744984\pi$
$241$	−26.2448	−	9.55231i	−1.69057	−	0.615318i	−0.994697	+	0.102844i	$0.967206\pi$
$242$	−5.11795	+	8.86455i	−0.328994	+	0.569835i
$243$	−12.4286	−	9.40902i	−0.797296	−	0.603589i
$244$	0.172964			0.0110729
$245$	−2.41289	+	0.0862699i	−0.154154	+	0.00551158i
$246$	−2.39365	−	5.75758i	−0.152613	−	0.367090i
$247$	−0.457289	−	0.383711i	−0.0290966	−	0.0244149i
$248$	7.01817	−	2.55441i	0.445654	−	0.162205i
$249$	0.107910	+	2.39992i	0.00683855	+	0.152089i
$250$	0.591819	+	3.35637i	0.0374299	+	0.212276i
$251$	−6.50629	−	11.2692i	−0.410673	−	0.711307i	0.584290	−	0.811545i	$-0.301373\pi$
$251$	−6.50629	−	11.2692i	−0.410673	−	0.711307i	−0.994963	+	0.100238i	$0.968040\pi$
$252$	3.50097	+	7.12342i	0.220541	+	0.448734i
$253$	−3.29761	+	5.71162i	−0.207319	+	0.359087i
$254$	8.96018	+	3.26124i	0.562212	+	0.204628i
$255$	4.03836	−	0.900796i	0.252892	−	0.0564100i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.40982	−	2.33298i	0.399833	−	0.145527i	−0.134274	−	0.990944i	$-0.542870\pi$
$257$	6.40982	−	2.33298i	0.399833	−	0.145527i	0.534107	+	0.845417i	$0.320648\pi$
$258$	−4.59879	+	14.6519i	−0.286308	+	0.912190i
$259$	−8.10524	+	10.0177i	−0.503635	+	0.622467i
$260$	−0.0307070	+	0.0531861i	−0.00190437	+	0.00329846i
$261$	0.687706	−	8.10326i	0.0425679	−	0.501579i
$262$	−0.430132			−0.0265737
$263$	9.36461	−	7.85784i	0.577446	−	0.484535i	−0.306661	−	0.951819i	$-0.599212\pi$
$263$	9.36461	−	7.85784i	0.577446	−	0.484535i	0.884107	+	0.467284i	$0.154767\pi$
$264$	−1.27587	+	0.815153i	−0.0785243	+	0.0501692i
$265$	−2.94549	−	2.47156i	−0.180940	−	0.151827i
$266$	−7.75986	−	4.29714i	−0.475788	−	0.263475i
$267$	13.9040	−	18.1690i	0.850913	−	1.11192i
$268$	4.93575	−	4.14159i	0.301499	−	0.252988i
$269$	−12.8210	+	22.2066i	−0.781711	+	1.35396i	0.149234	+	0.988802i	$0.452319\pi$
$269$	−12.8210	+	22.2066i	−0.781711	+	1.35396i	−0.930945	+	0.365161i	$0.881014\pi$
$270$	−0.240868	−	1.77599i	−0.0146587	−	0.108083i
$271$	−8.25642	−	14.3005i	−0.501542	−	0.868696i	−0.999998	−	0.00178119i	$-0.999433\pi$
$271$	−8.25642	−	14.3005i	−0.501542	−	0.868696i	0.498457	−	0.866915i	$-0.333900\pi$
$272$	1.20266	+	6.82062i	0.0729219	+	0.413561i
$273$	−0.451517	−	0.679630i	−0.0273271	−	0.0411331i
$274$	2.55930	−	0.931510i	0.154613	−	0.0562746i
$275$	0.740898	−	4.20184i	0.0446778	−	0.253380i
$276$	11.0124	−	7.03582i	0.662868	−	0.423507i
$277$	−17.9371	+	15.0510i	−1.07774	+	0.904328i	−0.995731	−	0.0923035i	$-0.970577\pi$
$277$	−17.9371	+	15.0510i	−1.07774	+	0.904328i	−0.0820056	+	0.996632i	$0.526133\pi$
$278$	−1.22052	+	2.11401i	−0.0732021	+	0.126790i
$279$	9.41622	−	20.3311i	0.563734	−	1.21719i
$280$	−0.296744	+	0.862974i	−0.0177339	+	0.0515726i
$281$	−0.782905	+	0.656935i	−0.0467042	+	0.0391895i	−0.665841	−	0.746094i	$-0.731927\pi$
$281$	−0.782905	+	0.656935i	−0.0467042	+	0.0391895i	0.619137	+	0.785283i	$0.287483\pi$
$282$	−1.99505	−	2.17154i	−0.118803	−	0.129313i
$283$	7.62226	+	6.39584i	0.453097	+	0.380193i	0.840583	−	0.541682i	$-0.182212\pi$
$283$	7.62226	+	6.39584i	0.453097	+	0.380193i	−0.387487	+	0.921875i	$0.626657\pi$
$284$	7.16323	+	6.01066i	0.425059	+	0.356667i
$285$	1.35507	+	1.47494i	0.0802674	+	0.0873681i
$286$	0.119229	−	0.100045i	0.00705015	−	0.00591578i
$287$	6.25170	+	7.18572i	0.369026	+	0.424159i
$288$	2.98789	−	0.269241i	0.176063	−	0.0158652i
$289$	−15.4836	+	26.8184i	−0.910800	+	1.57755i
$290$	0.716254	−	0.601009i	0.0420599	−	0.0352925i
$291$	6.71912	−	4.29285i	0.393882	−	0.251651i
$292$	−2.05103	+	11.6320i	−0.120027	+	0.680709i
$293$	−5.48906	+	1.99786i	−0.320675	+	0.116716i	−0.497342	−	0.867555i	$-0.665691\pi$
$293$	−5.48906	+	1.99786i	−0.320675	+	0.116716i	0.176667	+	0.984271i	$0.443468\pi$
$294$	−8.51650	−	8.62956i	−0.496692	−	0.503286i
$295$	0.300047	+	1.70165i	0.0174694	+	0.0990739i
$296$	2.43522	+	4.21792i	0.141544	+	0.245162i
$297$	−0.965783	+	4.43825i	−0.0560404	+	0.257534i
$298$	4.31786	−	7.47875i	0.250127	−	0.433232i
$299$	−1.02910	+	0.863516i	−0.0595143	+	0.0499384i
$300$	−5.13786	+	6.71385i	−0.296634	+	0.387624i
$301$	−0.419151	−	23.4540i	−0.0241595	−	1.35187i
$302$	−0.211864	−	0.177775i	−0.0121914	−	0.0102298i
$303$	−24.2133	+	15.4699i	−1.39102	+	0.888721i
$304$	−2.56826	+	2.15503i	−0.147300	+	0.123599i
$305$	0.0596583			0.00341603
$306$	17.0509	+	11.8732i	0.974734	+	0.678744i
$307$	5.06341	−	8.77008i	0.288984	−	0.500535i	−0.684584	−	0.728934i	$-0.740016\pi$
$307$	5.06341	−	8.77008i	0.288984	−	0.500535i	0.973567	+	0.228400i	$0.0733492\pi$
$308$	1.45470	−	1.79794i	0.0828893	−	0.102447i
$309$	−8.05275	+	25.6564i	−0.458105	+	1.45954i
$310$	2.42070	−	0.881062i	0.137486	−	0.0500410i
$311$	20.7624	+	17.4217i	1.17733	+	0.987895i	0.999993	+	0.00374399i	$0.00119175\pi$
$311$	20.7624	+	17.4217i	1.17733	+	0.987895i	0.177334	+	0.984151i	$0.443253\pi$
$312$	−0.301001	+	0.0671411i	−0.0170408	+	0.00380112i
$313$	29.3814	+	10.6940i	1.66073	+	0.604458i	0.990478	−	0.137672i	$-0.0439619\pi$
$313$	29.3814	+	10.6940i	1.66073	+	0.604458i	0.670256	+	0.742130i	$0.266184\pi$
$314$	8.20326	−	14.2085i	0.462937	−	0.801830i
$315$	1.20755	+	2.45700i	0.0680378	+	0.138436i
$316$	0.236525	+	0.409673i	0.0133056	+	0.0230459i
$317$	−3.15222	−	17.8771i	−0.177046	−	1.00408i	−0.935755	−	0.352650i	$-0.885281\pi$
$317$	−3.15222	−	17.8771i	−0.177046	−	1.00408i	0.758709	−	0.651430i	$-0.225830\pi$
$318$	−0.867315	−	19.2890i	−0.0486366	−	1.08167i
$319$	−2.22669	+	0.810448i	−0.124671	+	0.0453764i
$320$	0.264223	+	0.221709i	0.0147705	+	0.0123939i
$321$	−9.72190	−	23.3847i	−0.542623	−	1.30520i
$322$	−12.5560	+	15.5185i	−0.699716	+	0.864813i
$323$	−23.2198			−1.29198
$324$	5.74914	−	6.92441i	0.319397	−	0.384689i
$325$	0.434543	−	0.752650i	0.0241041	−	0.0417495i
$326$	−19.9244	−	7.25191i	−1.10351	−	0.401646i
$327$	4.60682	−	6.01993i	0.254758	−	0.332903i
$328$	3.38286	−	1.23126i	0.186787	−	0.0679850i
$329$	3.94060	+	2.18217i	0.217252	+	0.120307i
$330$	−0.440071	+	0.281161i	−0.0242251	+	0.0154774i
$331$	−2.61440	−	14.8270i	−0.143700	−	0.814964i	−0.968402	−	0.249396i	$-0.919768\pi$
$331$	−2.61440	−	14.8270i	−0.143700	−	0.814964i	0.824701	−	0.565568i	$-0.191343\pi$
$332$	−1.38699			−0.0761212
$333$	14.1232	+	3.74496i	0.773949	+	0.205222i
$334$	0.937000			0.0512704
$335$	1.70243	−	1.42851i	0.0930139	−	0.0780479i
$336$	−4.19935	+	1.83451i	−0.229094	+	0.100081i
$337$	−1.67610	+	9.50563i	−0.0913030	+	0.517805i	0.904515	+	0.426442i	$0.140233\pi$
$337$	−1.67610	+	9.50563i	−0.0913030	+	0.517805i	−0.995818	+	0.0913625i	$0.970878\pi$
$338$	−12.1862	+	4.43542i	−0.662843	+	0.241255i
$339$	11.4493	+	12.4622i	0.621842	+	0.676852i
$340$	0.414819	+	2.35256i	0.0224967	+	0.127585i
$341$	−6.52852			−0.353539
$342$	−0.850534	+	10.0219i	−0.0459916	+	0.541920i
$343$	16.5122	+	8.38742i	0.891572	+	0.452878i
$344$	−8.33150	−	3.03242i	−0.449204	−	0.163497i
$345$	3.79838	−	2.42679i	0.204498	−	0.130654i
$346$	−11.6332	+	4.23412i	−0.625402	+	0.227628i
$347$	−4.67771	+	26.5286i	−0.251113	+	1.42413i	0.554744	+	0.832021i	$0.312816\pi$
$347$	−4.67771	+	26.5286i	−0.251113	+	1.42413i	−0.805857	+	0.592110i	$0.798295\pi$
$348$	4.65586	+	0.606796i	0.249580	+	0.0325277i
$349$	4.71314	+	26.7296i	0.252289	+	1.43080i	0.802937	+	0.596063i	$0.203269\pi$
$349$	4.71314	+	26.7296i	0.252289	+	1.43080i	−0.550649	+	0.834737i	$0.685620\pi$
$350$	4.19931	−	12.2122i	0.224462	−	0.652768i
$351$	−0.494058	+	0.782234i	−0.0263708	+	0.0417526i
$352$	−0.437065	−	0.757020i	−0.0232957	−	0.0403493i
$353$	6.24891	+	2.27442i	0.332596	+	0.121055i	0.502920	−	0.864333i	$-0.332259\pi$
$353$	6.24891	+	2.27442i	0.332596	+	0.121055i	−0.170324	+	0.985388i	$0.554481\pi$
$354$	−5.27318	+	6.89069i	−0.280266	+	0.366236i
$355$	2.47073	+	2.07319i	0.131133	+	0.110033i
$356$	10.1187	+	8.49059i	0.536289	+	0.450000i
$357$	−30.4466	−	8.96187i	−1.61141	−	0.474313i
$358$	7.98025	+	2.90457i	0.421769	+	0.153512i
$359$	−1.16184	+	2.01237i	−0.0613196	+	0.106209i	−0.895055	−	0.445955i	$-0.852864\pi$
$359$	−1.16184	+	2.01237i	−0.0613196	+	0.106209i	0.833736	+	0.552163i	$0.186198\pi$
$360$	1.03058	−	0.0928662i	0.0543163	−	0.00489448i
$361$	3.87994	+	6.72025i	0.204207	+	0.353697i
$362$	−5.34929	−	1.94698i	−0.281153	−	0.102331i
$363$	−17.3038	+	3.85979i	−0.908216	+	0.202586i
$364$	0.403698	−	0.242795i	0.0211595	−	0.0127259i
$365$	−0.707438	+	4.01208i	−0.0370290	+	0.210002i
$366$	0.202682	+	0.220611i	0.0105943	+	0.0115315i
$367$	−2.99549	−	16.9883i	−0.156363	−	0.886781i	−0.957529	−	0.288338i	$-0.906897\pi$
$367$	−2.99549	−	16.9883i	−0.156363	−	0.886781i	0.801165	−	0.598443i	$-0.204214\pi$
$368$	3.77244	+	6.53406i	0.196652	+	0.340611i
$369$	4.53875	−	9.79987i	0.236278	−	0.510161i
$370$	0.839952	+	1.45484i	0.0436670	+	0.0756335i
$371$	10.5812	+	27.5308i	0.549350	+	1.42933i
$372$	11.4821	+	5.95824i	0.595319	+	0.308920i
$373$	1.71387	−	9.71987i	0.0887411	−	0.503276i	−0.907745	−	0.419522i	$-0.862198\pi$
$373$	1.71387	−	9.71987i	0.0887411	−	0.503276i	0.996486	−	0.0837541i	$-0.0266910\pi$
$374$	1.05128	−	5.96211i	0.0543605	−	0.308293i
$375$	−3.58748	+	4.68791i	−0.185257	+	0.242082i
$376$	1.30421	−	1.09436i	0.0672595	−	0.0564375i
$377$	−0.482667			−0.0248586
$378$	−4.98328	+	12.8128i	−0.256312	+	0.659018i
$379$	3.71099			0.190621			0.0953104	−	0.995448i	$-0.469616\pi$
$379$	3.71099			0.190621			0.0953104	+	0.995448i	$0.469616\pi$
$380$	−0.885842	+	0.743309i	−0.0454427	+	0.0381310i
$381$	6.34005	+	15.2501i	0.324810	+	0.781286i
$382$	−2.84078	+	16.1109i	−0.145347	+	0.824305i
$383$	−1.61079	+	9.13525i	−0.0823076	+	0.466790i	0.915598	+	0.402096i	$0.131718\pi$
$383$	−1.61079	+	9.13525i	−0.0823076	+	0.466790i	−0.997905	+	0.0646938i	$0.979393\pi$
$384$	0.0778017	+	1.73030i	0.00397030	+	0.0882991i
$385$	0.501754	−	0.620142i	0.0255717	−	0.0316053i
$386$	10.0420	+	17.3932i	0.511123	+	0.885290i
$387$	−24.0772	+	11.3037i	−1.22391	+	0.574600i
$388$	2.30172	+	3.98670i	0.116852	+	0.202394i
$389$	−0.351801	−	1.99516i	−0.0178370	−	0.101159i	0.974590	−	0.223998i	$-0.0719110\pi$
$389$	−0.351801	−	1.99516i	−0.0178370	−	0.101159i	−0.992427	+	0.122840i	$0.960800\pi$
$390$	−0.103821	+	0.0231582i	−0.00525716	+	0.00117266i
$391$	−9.07392	+	51.4607i	−0.458888	+	2.60248i
$392$	5.19812	−	4.68824i	0.262544	−	0.236792i
$393$	−0.504036	−	0.548625i	−0.0254253	−	0.0276745i
$394$	−8.46723	−	3.08182i	−0.426573	−	0.155260i
$395$	0.0815819	+	0.141304i	0.00410483	+	0.00710977i
$396$	−2.53479	−	0.672133i	−0.127378	−	0.0337760i
$397$	8.68241	−	15.0384i	0.435758	−	0.754755i	−0.561599	−	0.827409i	$-0.689814\pi$
$397$	8.68241	−	15.0384i	0.435758	−	0.754755i	0.997357	+	0.0726545i	$0.0231471\pi$
$398$	19.8138	+	7.21162i	0.993175	+	0.361486i
$399$	−3.61222	−	14.9330i	−0.180837	−	0.747585i
$400$	−3.73909	−	3.13747i	−0.186954	−	0.156873i
$401$	−13.1901	−	11.0678i	−0.658681	−	0.552699i	0.251010	−	0.967984i	$-0.419237\pi$
$401$	−13.1901	−	11.0678i	−0.658681	−	0.552699i	−0.909691	+	0.415285i	$0.863682\pi$
$402$	11.0663	+	1.44227i	0.551937	+	0.0719337i
$403$	−1.24961	−	0.454821i	−0.0622476	−	0.0226563i
$404$	−8.29457	−	14.3666i	−0.412670	−	0.714766i
$405$	1.98298	−	2.38836i	0.0985353	−	0.118678i
$406$	−7.03975	+	1.37143i	−0.349377	+	0.0680628i
$407$	−0.739290	−	4.19272i	−0.0366452	−	0.207825i
$408$	−7.29026	+	9.52648i	−0.360921	+	0.471631i
$409$	−2.82313	+	16.0107i	−0.139595	+	0.791680i	0.831955	+	0.554843i	$0.187222\pi$
$409$	−2.82313	+	16.0107i	−0.139595	+	0.791680i	−0.971549	+	0.236837i	$0.923889\pi$
$410$	1.16681	−	0.424685i	0.0576247	−	0.0209737i
$411$	4.18715	+	2.17278i	0.206537	+	0.107175i
$412$	−14.5889	−	5.30994i	−0.718745	−	0.261602i
$413$	4.30991	−	12.5338i	0.212077	−	0.616749i
$414$	21.8785	+	5.80138i	1.07527	+	0.285122i
$415$	−0.478400			−0.0234837
$416$	−0.0309187	−	0.175349i	−0.00151591	−	0.00859717i
$417$	−4.12660	+	0.920479i	−0.202081	+	0.0450760i
$418$	2.75390	−	1.00234i	0.134698	−	0.0490259i
$419$	3.14062	−	17.8113i	0.153429	−	0.870141i	−0.806778	−	0.590854i	$-0.798791\pi$
$419$	3.14062	−	17.8113i	0.153429	−	0.870141i	0.960208	−	0.279287i	$-0.0900980\pi$
$420$	−1.44844	+	0.632756i	−0.0706764	+	0.0308754i
$421$	11.5132	−	9.66070i	0.561118	−	0.470834i	−0.317567	−	0.948236i	$-0.602866\pi$
$421$	11.5132	−	9.66070i	0.561118	−	0.470834i	0.878685	+	0.477402i	$0.158421\pi$
$422$	23.3914			1.13868
$423$	0.431917	−	5.08928i	0.0210005	−	0.247449i
$424$	11.1478			0.541383
$425$	−5.87022	−	33.2916i	−0.284747	−	1.61488i
$426$	0.727518	+	16.1799i	0.0352484	+	0.783920i
$427$	−0.400334	−	0.221691i	−0.0193735	−	0.0107284i
$428$	13.7396	−	5.00082i	0.664130	−	0.241724i
$429$	0.267319	+	0.0348396i	0.0129063	+	0.00168207i
$430$	−2.87369	−	1.04594i	−0.138582	−	0.0504395i
$431$	14.4158	−	24.9690i	0.694387	−	1.20271i	−0.276000	−	0.961158i	$-0.589009\pi$
$431$	14.4158	−	24.9690i	0.694387	−	1.20271i	0.970387	−	0.241556i	$-0.0776576\pi$
$432$	3.84467	+	3.49549i	0.184977	+	0.168177i
$433$	−8.60887			−0.413716			−0.206858	−	0.978371i	$-0.566324\pi$
$433$	−8.60887			−0.413716			−0.206858	+	0.978371i	$0.566324\pi$
$434$	−19.5180	−	3.08303i	−0.936895	−	0.147990i
$435$	1.60589	+	0.209295i	0.0769967	+	0.0100349i
$436$	3.35263	+	2.81319i	0.160562	+	0.134727i
$437$	−23.7697	+	8.65146i	−1.13706	+	0.413856i
$438$	−17.2397	+	11.0145i	−0.823747	+	0.526292i
$439$	−4.28228	−	24.2860i	−0.204382	−	1.15911i	−0.898409	−	0.439159i	$-0.855277\pi$
$439$	−4.28228	−	24.2860i	−0.204382	−	1.15911i	0.694028	−	0.719948i	$-0.255835\pi$
$440$	−0.150752	−	0.261110i	−0.00718682	−	0.0124479i
$441$	1.02705	−	20.9749i	0.0489069	−	0.998803i
$442$	0.616585	−	1.06796i	0.0293280	−	0.0507975i
$443$	−8.91469	−	3.24468i	−0.423550	−	0.154160i	0.121446	−	0.992598i	$-0.461247\pi$
$443$	−8.91469	−	3.24468i	−0.423550	−	0.154160i	−0.544996	+	0.838438i	$0.683469\pi$
$444$	−2.52624	+	8.04870i	−0.119890	+	0.381975i
$445$	3.49012	+	2.92856i	0.165448	+	0.138827i
$446$	−3.54993	+	1.29207i	−0.168094	+	0.0611813i
$447$	14.5987	−	3.25639i	0.690496	−	0.154022i
$448$	−0.949180	−	2.46963i	−0.0448445	−	0.116679i
$449$	−9.94850	+	17.2313i	−0.469499	+	0.813196i	−0.999392	−	0.0348687i	$-0.988899\pi$
$449$	−9.94850	+	17.2313i	−0.469499	+	0.813196i	0.529893	+	0.848064i	$0.322232\pi$
$450$	−14.5840	+	1.31417i	−0.687496	+	0.0619507i
$451$	−3.14684			−0.148179
$452$	−7.48470	+	6.28041i	−0.352050	+	0.295405i
$453$	−0.0215175	−	0.478548i	−0.00101098	−	0.0224841i
$454$	−15.2773	−	12.8191i	−0.716998	−	0.601632i
$455$	0.139243	−	0.0837445i	0.00652781	−	0.00392600i
$456$	−5.75823	−	0.750466i	−0.269654	−	0.0351438i
$457$	21.0765	−	17.6853i	0.985918	−	0.827283i	0.000946120	−	1.00000i	$-0.499699\pi$
$457$	21.0765	−	17.6853i	0.985918	−	0.827283i	0.984972	+	0.172716i	$0.0552544\pi$
$458$	−2.40147	+	4.15947i	−0.112213	+	0.194359i
$459$	4.83653	+	35.6612i	0.225750	+	1.66452i
$460$	1.30118	+	2.25372i	0.0606680	+	0.105080i
$461$	1.54638	+	8.76995i	0.0720220	+	0.408457i	0.999410	+	0.0343554i	$0.0109378\pi$
$461$	1.54638	+	8.76995i	0.0720220	+	0.408457i	−0.927388	+	0.374102i	$0.877951\pi$
$462$	3.99787	−	0.251410i	0.185998	−	0.0116967i
$463$	37.9447	−	13.8107i	1.76344	−	0.641840i	0.763448	−	0.645869i	$-0.223505\pi$
$463$	37.9447	−	13.8107i	1.76344	−	0.641840i	0.999992	+	0.00402929i	$0.00128257\pi$
$464$	−0.470725	+	2.66961i	−0.0218528	+	0.123934i
$465$	3.96039	+	2.05511i	0.183659	+	0.0953033i
$466$	18.5693	−	15.5815i	0.860206	−	0.721799i
$467$	11.5364	−	19.9816i	0.533840	−	0.924637i	−0.465379	−	0.885112i	$-0.654082\pi$
$467$	11.5364	−	19.9816i	0.533840	−	0.924637i	0.999219	−	0.0395259i	$-0.0125848\pi$
$468$	−0.438355	−	0.305243i	−0.0202629	−	0.0141099i
$469$	−16.7325	+	3.25969i	−0.772634	+	0.150518i
$470$	0.449846	−	0.377466i	0.0207499	−	0.0174112i
$471$	27.7353	−	6.18663i	1.27798	−	0.285065i
$472$	−3.83757	−	3.22010i	−0.176638	−	0.148217i
$473$	5.93701	+	4.98174i	0.272984	+	0.229061i
$474$	−0.245366	+	0.781745i	−0.0112700	+	0.0359067i
$475$	12.5358	−	10.5188i	0.575181	−	0.482634i
$476$	5.95852	−	17.3282i	0.273108	−	0.794237i
$477$	23.5864	−	23.7094i	1.07995	−	1.08558i
$478$	1.11973	−	1.93943i	0.0512154	−	0.0887076i
$479$	−3.38656	+	2.84166i	−0.154736	+	0.129839i	−0.716869	−	0.697208i	$-0.754425\pi$
$479$	−3.38656	+	2.84166i	−0.154736	+	0.129839i	0.562133	+	0.827047i	$0.309981\pi$
$480$	0.0268353	+	0.596813i	0.00122486	+	0.0272407i
$481$	0.150588	−	0.854025i	0.00686620	−	0.0389402i
$482$	26.2448	−	9.55231i	1.19542	−	0.435096i
$483$	−34.5068	+	2.16999i	−1.57011	+	0.0987382i
$484$	−1.77744	−	10.0804i	−0.0807929	−	0.458200i
$485$	0.793907	+	1.37509i	0.0360494	+	0.0624395i
$486$	15.5689	−	0.781229i	0.706218	−	0.0354373i
$487$	11.4644	−	19.8569i	0.519502	−	0.899803i	−0.480242	−	0.877136i	$-0.659451\pi$
$487$	11.4644	−	19.8569i	0.519502	−	0.899803i	0.999743	−	0.0226668i	$-0.00721568\pi$
$488$	−0.132498	+	0.111179i	−0.00599789	+	0.00503283i
$489$	−14.0981	−	33.9111i	−0.637540	−	1.53351i
$490$	1.79293	−	1.61706i	0.0809962	−	0.0730514i
$491$	18.2266	+	15.2939i	0.822554	+	0.690205i	0.953569	−	0.301175i	$-0.0973790\pi$
$491$	18.2266	+	15.2939i	0.822554	+	0.690205i	−0.131014	+	0.991380i	$0.541823\pi$
$492$	5.53454	+	2.87195i	0.249516	+	0.129478i
$493$	−14.3821	+	12.0680i	−0.647738	+	0.543517i
$494$	0.596948			0.0268579
$495$	−0.874297	−	0.231831i	−0.0392967	−	0.0104200i
$496$	−3.73429	+	6.46798i	−0.167675	+	0.290421i
$497$	−8.87571	−	23.0933i	−0.398130	−	1.03588i
$498$	−1.62530	−	1.76908i	−0.0728315	−	0.0792744i
$499$	10.7247	−	3.90346i	0.480102	−	0.174743i	−0.0906208	−	0.995885i	$-0.528885\pi$
$499$	10.7247	−	3.90346i	0.480102	−	0.174743i	0.570723	+	0.821142i	$0.306663\pi$
$500$	−2.61080	−	2.19072i	−0.116758	−	0.0979719i
$501$	1.09799	+	1.19512i	0.0490547	+	0.0533942i
$502$	12.2278	+	4.45056i	0.545754	+	0.198638i
$503$	−6.01608	+	10.4202i	−0.268244	+	0.464612i	−0.968408	−	0.249370i	$-0.919777\pi$
$503$	−6.01608	+	10.4202i	−0.268244	+	0.464612i	0.700165	+	0.713981i	$0.253110\pi$
$504$	−7.26075	−	3.20648i	−0.323420	−	0.142828i
$505$	−2.86095	−	4.95531i	−0.127311	−	0.220509i
$506$	−1.14525	−	6.49502i	−0.0509124	−	0.288739i
$507$	−19.9373	−	10.3458i	−0.885446	−	0.459471i
$508$	−8.96018	+	3.26124i	−0.397544	+	0.144694i
$509$	25.5185	+	21.4125i	1.13109	+	0.949094i	0.999111	−	0.0421587i	$-0.0134235\pi$
$509$	25.5185	+	21.4125i	1.13109	+	0.949094i	0.131976	+	0.991253i	$0.457868\pi$
$510$	−2.51454	+	3.28586i	−0.111346	+	0.145500i
$511$	19.6562	−	24.2940i	0.869538	−	1.07470i
$512$	−1.00000			−0.0441942
$513$	−13.7793	+	10.6589i	−0.608373	+	0.470604i
$514$	−3.41059	+	5.90732i	−0.150435	+	0.260561i
$515$	−5.03199	−	1.83150i	−0.221736	−	0.0807053i
$516$	−5.89520	−	14.1801i	−0.259522	−	0.624243i
$517$	−1.39848	+	0.509005i	−0.0615051	+	0.0223860i
$518$	−0.230251	−	12.8839i	−0.0101166	−	0.566087i
$519$	−19.0325	−	9.87622i	−0.835432	−	0.433518i
$520$	−0.0106644	−	0.0604810i	−0.000467666	−	0.00265227i
$521$	−20.4974			−0.898007			−0.449003	−	0.893530i	$-0.648221\pi$
$521$	−20.4974			−0.898007			−0.449003	+	0.893530i	$0.648221\pi$
$522$	4.68186	+	6.64950i	0.204919	+	0.291041i
$523$	8.23498			0.360091			0.180045	−	0.983658i	$-0.442376\pi$
$523$	8.23498			0.360091			0.180045	+	0.983658i	$0.442376\pi$
$524$	0.329501	−	0.276484i	0.0143943	−	0.0120783i
$525$	20.4972	−	8.95430i	0.894570	−	0.390798i
$526$	−2.12278	+	12.0389i	−0.0925578	+	0.524921i
$527$	−48.6067	+	17.6914i	−2.11734	+	0.770650i
$528$	0.453402	−	1.44456i	0.0197318	−	0.0628662i
$529$	5.89105	+	33.4098i	0.256133	+	1.45260i
$530$	3.84507			0.167019
$531$	−14.9681	+	1.34879i	−0.649561	+	0.0585324i
$532$	8.70655	−	1.69614i	0.377477	−	0.0735370i
$533$	−0.602330	−	0.219230i	−0.0260898	−	0.00949592i
$534$	1.02768	+	22.8556i	0.0444722	+	0.989058i
$535$	4.73906	−	1.72488i	0.204887	−	0.0745729i
$536$	−1.11884	+	6.34528i	−0.0483267	+	0.274075i
$537$	5.64667	+	13.5823i	0.243672	+	0.586118i
$538$	−4.45269	−	25.2525i	−0.191969	−	1.08871i
$539$	−5.67145	+	2.29691i	−0.244287	+	0.0989347i
$540$	1.32610	+	1.20566i	0.0570662	+	0.0518834i
$541$	−15.8713	−	27.4898i	−0.682358	−	1.18188i	−0.974259	−	0.225431i	$-0.927621\pi$
$541$	−15.8713	−	27.4898i	−0.682358	−	1.18188i	0.291901	−	0.956449i	$-0.405712\pi$
$542$	15.5170	+	5.64772i	0.666512	+	0.242590i
$543$	−3.78506	−	9.10442i	−0.162432	−	0.390708i
$544$	−5.30550	−	4.45184i	−0.227471	−	0.190871i
$545$	1.15638	+	0.970320i	0.0495340	+	0.0415640i
$546$	0.782740	+	0.230397i	0.0334982	+	0.00986009i
$547$	9.28683	+	3.38013i	0.397076	+	0.144524i	0.532837	−	0.846218i	$-0.321126\pi$
$547$	9.28683	+	3.38013i	0.397076	+	0.144524i	−0.135761	+	0.990742i	$0.543348\pi$
$548$	−1.36178	+	2.35867i	−0.0581722	+	0.100757i
$549$	−0.0438794	+	0.517032i	−0.00187273	+	0.0220664i
$550$	2.13333	+	3.69504i	0.0909655	+	0.157557i
$551$	−8.54020	−	3.10838i	−0.363825	−	0.132421i
$552$	−3.91344	+	12.4684i	−0.166567	+	0.530690i
$553$	−0.0223635	−	1.25137i	−0.000950994	−	0.0532138i
$554$	4.06601	−	23.0595i	0.172748	−	0.979705i
$555$	−0.871347	+	2.77615i	−0.0369866	+	0.117841i
$556$	−0.423883	−	2.40396i	−0.0179767	−	0.101951i
$557$	−17.9401	−	31.0732i	−0.760147	−	1.31661i	−0.942775	−	0.333431i	$-0.891794\pi$
$557$	−17.9401	−	31.0732i	−0.760147	−	1.31661i	0.182628	−	0.983182i	$-0.441540\pi$
$558$	5.85532	+	21.6271i	0.247875	+	0.915550i
$559$	0.789329	+	1.36716i	0.0333851	+	0.0578246i
$560$	−0.327390	−	0.851820i	−0.0138347	−	0.0359960i
$561$	8.83646	−	5.64562i	0.373075	−	0.238358i
$562$	0.177470	−	1.00648i	0.00748613	−	0.0424559i
$563$	−5.13320	+	29.1118i	−0.216339	+	1.22692i	0.662229	+	0.749301i	$0.269610\pi$
$563$	−5.13320	+	29.1118i	−0.216339	+	1.22692i	−0.878568	+	0.477617i	$0.841501\pi$
$564$	2.92413	+	0.381101i	0.123128	+	0.0160472i
$565$	−2.58161	+	2.16623i	−0.108609	+	0.0911339i
$566$	−9.95016			−0.418236
$567$	−22.1819	+	8.65815i	−0.931552	+	0.363608i
$568$	−9.35093			−0.392356
$569$	−21.8287	+	18.3165i	−0.915108	+	0.767867i	−0.973084	−	0.230451i	$-0.925980\pi$
$569$	−21.8287	+	18.3165i	−0.915108	+	0.767867i	0.0579756	+	0.998318i	$0.481535\pi$
$570$	−1.98612	−	0.258850i	−0.0831894	−	0.0108420i
$571$	7.68634	−	43.5914i	0.321663	−	1.82424i	−0.210490	−	0.977596i	$-0.567506\pi$
$571$	7.68634	−	43.5914i	0.321663	−	1.82424i	0.532153	−	0.846648i	$-0.321383\pi$
$572$	−0.0270270	+	0.153278i	−0.00113005	+	0.00640886i
$573$	−23.8780	+	15.2556i	−0.997516	+	0.637314i
$574$	−9.40797	−	1.48606i	−0.392681	−	0.0620271i
$575$	−18.4134	−	31.8929i	−0.767892	−	1.33003i
$576$	−2.11579	+	2.12683i	−0.0881581	+	0.0886180i
$577$	−2.90041	−	5.02365i	−0.120746	−	0.209137i	0.799316	−	0.600910i	$-0.205195\pi$
$577$	−2.90041	−	5.02365i	−0.120746	−	0.209137i	−0.920062	+	0.391773i	$0.871862\pi$
$578$	−5.37740	−	30.4967i	−0.223670	−	1.26850i
$579$	−10.4173	+	33.1899i	−0.432928	+	1.37933i
$580$	−0.162362	+	0.920799i	−0.00674170	+	0.0382341i
$581$	3.21028	+	1.77774i	0.133185	+	0.0737532i
$582$	−2.38775	+	7.60748i	−0.0989756	+	0.315340i
$583$	−9.15693	−	3.33285i	−0.379241	−	0.138032i
$584$	−5.90570	−	10.2290i	−0.244380	−	0.423278i
$585$	−0.151197	−	0.105284i	−0.00625121	−	0.00435295i
$586$	2.92067	−	5.05875i	0.120652	−	0.208975i
$587$	25.5478	+	9.29864i	1.05447	+	0.383796i	0.810348	−	0.585949i	$-0.199278\pi$
$587$	25.5478	+	9.29864i	1.05447	+	0.383796i	0.244122	+	0.969744i	$0.421500\pi$
$588$	12.0710	+	1.13633i	0.497799	+	0.0468613i
$589$	−19.1813	−	16.0950i	−0.790351	−	0.663183i
$590$	−1.32365	−	1.11067i	−0.0544938	−	0.0457257i
$591$	−5.99125	−	14.4111i	−0.246447	−	0.592793i
$592$	−4.57672	−	1.66579i	−0.188102	−	0.0684635i
$593$	6.64686	+	11.5127i	0.272954	+	0.472770i	0.969617	−	0.244629i	$-0.0786661\pi$
$593$	6.64686	+	11.5127i	0.272954	+	0.472770i	−0.696663	+	0.717398i	$0.745333\pi$
$594$	−2.11302	−	4.02069i	−0.0866983	−	0.164971i
$595$	2.05520	−	5.97682i	0.0842551	−	0.245026i
$596$	1.49958	+	8.50452i	0.0614250	+	0.348359i
$597$	14.0198	+	33.7227i	0.573794	+	1.38018i
$598$	0.233278	−	1.32298i	0.00953944	−	0.0541008i
$599$	21.3867	−	7.78412i	0.873836	−	0.318050i	0.134117	−	0.990966i	$-0.457180\pi$
$599$	21.3867	−	7.78412i	0.873836	−	0.318050i	0.739720	+	0.672915i	$0.234958\pi$
$600$	−0.379753	−	8.44566i	−0.0155033	−	0.344793i
$601$	28.4675	+	10.3613i	1.16121	+	0.422647i	0.849531	−	0.527539i	$-0.176885\pi$
$601$	28.4675	+	10.3613i	1.16121	+	0.422647i	0.311683	+	0.950186i	$0.399107\pi$
$602$	15.3970	+	17.6974i	0.627536	+	0.721291i
$603$	11.1281	+	15.8049i	0.453171	+	0.643626i
$604$	0.276569			0.0112534
$605$	−0.613074	−	3.47691i	−0.0249250	−	0.141357i
$606$	8.60460	−	27.4146i	0.349538	−	1.11364i
$607$	−5.40211	+	1.96621i	−0.219265	+	0.0798058i	−0.449317	−	0.893372i	$-0.648333\pi$
$607$	−5.40211	+	1.96621i	−0.219265	+	0.0798058i	0.230052	+	0.973178i	$0.426110\pi$
$608$	0.582178	−	3.30170i	0.0236104	−	0.133901i
$609$	−9.99852	−	7.37199i	−0.405161	−	0.298728i
$610$	−0.0457009	+	0.0383476i	−0.00185038	+	0.00155265i
$611$	−0.303141			−0.0122638
$612$	−20.6937	+	1.86472i	−0.836492	+	0.0753768i
$613$	−6.92371			−0.279646			−0.139823	−	0.990177i	$-0.544653\pi$
$613$	−6.92371			−0.279646			−0.139823	+	0.990177i	$0.544653\pi$
$614$	1.75850	+	9.97297i	0.0709674	+	0.402476i
$615$	1.90896	+	0.990590i	0.0769769	+	0.0399445i
$616$	0.0413247	+	2.31236i	0.00166502	+	0.0931678i
$617$	45.8449	−	16.6862i	1.84565	−	0.671761i	0.858310	−	0.513132i	$-0.171515\pi$
$617$	45.8449	−	16.6862i	1.84565	−	0.671761i	0.987338	−	0.158629i	$-0.0507073\pi$
$618$	−10.3228	−	24.8301i	−0.415245	−	0.998815i
$619$	33.3547	+	12.1401i	1.34064	+	0.487953i	0.910014	−	0.414578i	$-0.136071\pi$
$619$	33.3547	+	12.1401i	1.34064	+	0.487953i	0.430625	+	0.902531i	$0.358293\pi$
$620$	−1.28803	+	2.23093i	−0.0517284	+	0.0895962i
$621$	18.2381	+	34.7038i	0.731870	+	1.39261i
$622$	−27.1034			−1.08675
$623$	−12.5377	−	32.6213i	−0.502313	−	1.30695i
$624$	0.187422	−	0.244913i	0.00750290	−	0.00980435i
$625$	17.7949	+	14.9317i	0.711797	+	0.597269i
$626$	−29.3814	+	10.6940i	−1.17432	+	0.427416i
$627$	4.50552	+	2.33798i	0.179933	+	0.0933700i
$628$	2.84896	+	16.1573i	0.113686	+	0.644745i
$629$	−16.8659	−	29.2126i	−0.672489	−	1.16478i
$630$	−2.50437	−	1.10597i	−0.0997764	−	0.0440630i
$631$	10.1540	−	17.5873i	0.404226	−	0.700140i	−0.590005	−	0.807400i	$-0.700874\pi$
$631$	10.1540	−	17.5873i	0.404226	−	0.700140i	0.994231	+	0.107259i	$0.0342075\pi$
$632$	−0.444522	−	0.161793i	−0.0176821	−	0.00643577i
$633$	27.4104	+	29.8352i	1.08947	+	1.18584i
$634$	13.9059	+	11.6685i	0.552275	+	0.463414i
$635$	−3.09053	+	1.12486i	−0.122644	+	0.0446388i
$636$	13.0631	+	14.2187i	0.517987	+	0.563809i
$637$	−1.24558	+	0.0445342i	−0.0493517	+	0.00176451i
$638$	1.18480	−	2.05213i	0.0469065	−	0.0812444i
$639$	−19.7846	+	19.8879i	−0.782668	+	0.786751i
$640$	−0.344919			−0.0136341
$641$	−7.66981	+	6.43573i	−0.302939	+	0.254196i	−0.781566	−	0.623822i	$-0.785579\pi$
$641$	−7.66981	+	6.43573i	−0.302939	+	0.254196i	0.478627	+	0.878018i	$0.341135\pi$
$642$	22.4788	+	11.6646i	0.887166	+	0.460364i
$643$	34.3845	+	28.8520i	1.35599	+	1.13781i	0.977198	+	0.212331i	$0.0681054\pi$
$643$	34.3845	+	28.8520i	1.35599	+	1.13781i	0.378794	+	0.925481i	$0.376339\pi$
$644$	−0.356686	−	19.9587i	−0.0140554	−	0.786483i
$645$	−2.03336	−	4.89097i	−0.0800637	−	0.192582i
$646$	17.7874	−	14.9254i	0.699835	−	0.587231i
$647$	−3.03773	+	5.26150i	−0.119425	+	0.206851i	−0.919540	−	0.392996i	$-0.871439\pi$
$647$	−3.03773	+	5.26150i	−0.119425	+	0.206851i	0.800115	+	0.599847i	$0.204772\pi$
$648$	0.0468261	+	8.99988i	0.00183950	+	0.353549i
$649$	2.18952	+	3.79236i	0.0859461	+	0.148863i
$650$	0.150915	+	0.855882i	0.00591938	+	0.0335704i
$651$	−18.9392	−	28.5076i	−0.742286	−	1.11730i
$652$	19.9244	−	7.25191i	0.780302	−	0.284007i
$653$	6.55931	−	37.1997i	0.256686	−	1.45574i	−0.535023	−	0.844838i	$-0.679697\pi$
$653$	6.55931	−	37.1997i	0.256686	−	1.45574i	0.791709	−	0.610899i	$-0.209192\pi$
$654$	0.340502	+	7.57274i	0.0133147	+	0.296118i
$655$	0.113651	−	0.0953644i	0.00444071	−	0.00372620i
$656$	−1.79998	+	3.11766i	−0.0702775	+	0.121724i
$657$	−34.2506	−	9.08198i	−1.33624	−	0.354322i
$658$	−4.42134	+	0.861331i	−0.172362	+	0.0335782i
$659$	−5.02289	+	4.21470i	−0.195664	+	0.164181i	−0.735356	−	0.677681i	$-0.762985\pi$
$659$	−5.02289	+	4.21470i	−0.195664	+	0.164181i	0.539692	+	0.841862i	$0.318541\pi$
$660$	0.156387	−	0.498254i	0.00608734	−	0.0193945i
$661$	23.6753	+	19.8659i	0.920861	+	0.772694i	0.974154	−	0.225885i	$-0.0725274\pi$
$661$	23.6753	+	19.8659i	0.920861	+	0.772694i	−0.0532932	+	0.998579i	$0.516972\pi$
$662$	11.5333	+	9.67762i	0.448256	+	0.376131i
$663$	2.08468	−	0.465008i	0.0809623	−	0.0180594i
$664$	1.06250	−	0.891542i	0.0412330	−	0.0345986i
$665$	3.00305	−	0.585030i	0.116453	−	0.0226865i
$666$	−13.2262	+	6.20944i	−0.512506	+	0.240611i
$667$	−10.2263	+	17.7125i	−0.395964	+	0.685831i
$668$	−0.717784	+	0.602292i	−0.0277719	+	0.0233034i
$669$	−5.80788	−	3.01380i	−0.224546	−	0.116520i
$670$	−0.385910	+	2.18861i	−0.0149090	+	0.0845532i
$671$	0.142075	−	0.0517110i	0.00548473	−	0.00199628i
$672$	2.03769	−	4.10461i	0.0786057	−	0.158339i
$673$	−6.01881	−	34.1344i	−0.232008	−	1.31578i	−0.848824	−	0.528676i	$-0.822689\pi$
$673$	−6.01881	−	34.1344i	−0.232008	−	1.31578i	0.616815	−	0.787108i	$-0.288423\pi$
$674$	−4.82614	−	8.35911i	−0.185896	−	0.321981i
$675$	−18.7660	−	17.0616i	−0.722303	−	0.656702i
$676$	6.48415	−	11.2309i	0.249390	−	0.431957i
$677$	−27.5348	+	23.1045i	−1.05825	+	0.887977i	−0.993937	−	0.109953i	$-0.964930\pi$
$677$	−27.5348	+	23.1045i	−1.05825	+	0.887977i	−0.0643129	+	0.997930i	$0.520486\pi$
$678$	−16.7812	−	2.18709i	−0.644479	−	0.0839945i
$679$	−0.217629	−	12.1776i	−0.00835182	−	0.467334i
$680$	−1.82996	−	1.53552i	−0.0701759	−	0.0588846i
$681$	−1.55160	−	34.5075i	−0.0594576	−	1.32233i
$682$	5.00114	−	4.19645i	0.191503	−	0.160690i
$683$	35.8007			1.36987			0.684937	−	0.728602i	$-0.259830\pi$
$683$	35.8007			1.36987			0.684937	+	0.728602i	$0.259830\pi$
$684$	−5.79038	−	8.22390i	−0.221401	−	0.314449i
$685$	−0.469702	+	0.813547i	−0.0179464	+	0.0310841i
$686$	−18.0404	+	4.18867i	−0.688785	+	0.159924i
$687$	−8.11939	+	1.81111i	−0.309774	+	0.0690981i
$688$	8.33150	−	3.03242i	0.317635	−	0.115610i
$689$	−1.52052	−	1.27587i	−0.0579272	−	0.0486067i
$690$	−1.34982	+	4.30058i	−0.0513867	+	0.163720i
$691$	−3.84006	−	1.39767i	−0.146083	−	0.0531698i	0.267944	−	0.963434i	$-0.413656\pi$
$691$	−3.84006	−	1.39767i	−0.146083	−	0.0531698i	−0.414027	+	0.910265i	$0.635878\pi$
$692$	6.18987	−	10.7212i	0.235304	−	0.407558i
$693$	5.00544	+	4.80460i	0.190141	+	0.182512i
$694$	−13.4689	−	23.3289i	−0.511274	−	0.885552i
$695$	−0.146205	−	0.829171i	−0.00554588	−	0.0314523i
$696$	−3.95664	+	2.52790i	−0.149976	+	0.0958197i
$697$	−23.4291	+	8.52751i	−0.887442	+	0.323002i
$698$	−20.7919	−	17.4465i	−0.786985	−	0.660359i
$699$	41.6337	+	5.42609i	1.57473	+	0.205234i
$700$	4.63298	+	12.0543i	0.175110	+	0.455611i
$701$	35.0169			1.32257			0.661285	−	0.750135i	$-0.270011\pi$
$701$	35.0169			1.32257			0.661285	+	0.750135i	$0.270011\pi$
$702$	−0.124340	−	0.916800i	−0.00469293	−	0.0346024i
$703$	8.16439	−	14.1411i	0.307926	−	0.533343i
$704$	0.821414	+	0.298970i	0.0309582	+	0.0112679i
$705$	1.00859	+	0.131449i	0.0379856	+	0.00495064i
$706$	−6.24891	+	2.27442i	−0.235181	+	0.0855989i
$707$	0.784255	+	43.8838i	0.0294949	+	1.65042i
$708$	−0.389755	−	8.66811i	−0.0146479	−	0.325767i
$709$	−2.69963	−	15.3104i	−0.101387	−	0.574993i	−0.992602	−	0.121413i	$-0.961258\pi$
$709$	−2.69963	−	15.3104i	−0.101387	−	0.574993i	0.891215	−	0.453581i	$-0.149854\pi$
$710$	−3.22531			−0.121044
$711$	−1.28462	+	0.603103i	−0.0481771	+	0.0226181i
$712$	−13.2090			−0.495029
$713$	−43.1663	+	36.2208i	−1.61659	+	1.35648i
$714$	29.0840	−	12.7055i	1.08844	−	0.475492i
$715$	−0.00932211	+	0.0528683i	−0.000348627	+	0.00197716i
$716$	−7.98025	+	2.90457i	−0.298236	+	0.108549i
$717$	3.78583	−	0.844465i	0.141384	−	0.0315371i
$718$	−0.403503	−	2.28838i	−0.0150586	−	0.0854015i
$719$	−15.1960			−0.566715			−0.283357	−	0.959014i	$-0.591448\pi$
$719$	−15.1960			−0.566715			−0.283357	+	0.959014i	$0.591448\pi$
$720$	−0.729777	+	0.733584i	−0.0271972	+	0.0273391i
$721$	26.9611	+	30.9891i	1.00408	+	1.15410i
$722$	−7.29190	−	2.65403i	−0.271376	−	0.0987729i
$723$	42.9378	+	22.2811i	1.59687	+	0.828642i
$724$	5.34929	−	1.94698i	0.198805	−	0.0723591i
$725$	2.29762	−	13.0305i	0.0853315	−	0.483939i
$726$	10.7745	−	14.0795i	0.399879	−	0.522538i
$727$	−2.20445	−	12.5021i	−0.0817585	−	0.463676i	−0.998009	−	0.0630700i	$-0.979911\pi$
$727$	−2.20445	−	12.5021i	−0.0817585	−	0.463676i	0.916251	−	0.400606i	$-0.131200\pi$
$728$	−0.153185	+	0.445484i	−0.00567742	+	0.0165107i
$729$	19.2403	+	18.9423i	0.712604	+	0.701567i
$730$	−2.03699	−	3.52816i	−0.0753922	−	0.130583i
$731$	57.7026	+	21.0020i	2.13421	+	0.776788i
$732$	−0.297069	−	0.0387169i	−0.0109800	−	0.00143102i
$733$	18.9023	+	15.8609i	0.698173	+	0.585837i	0.921253	−	0.388963i	$-0.127167\pi$
$733$	18.9023	+	15.8609i	0.698173	+	0.585837i	−0.223080	+	0.974800i	$0.571611\pi$
$734$	13.2145	+	11.0883i	0.487757	+	0.409277i
$735$	4.16351	+	0.391940i	0.153573	+	0.0144569i
$736$	−7.08987	−	2.58050i	−0.261336	−	0.0951185i
$737$	2.81609	−	4.87761i	0.103732	−	0.179669i
$738$	2.82235	+	10.4246i	0.103892	+	0.383734i
$739$	25.1354	+	43.5358i	0.924621	+	1.60149i	0.792169	+	0.610302i	$0.208952\pi$
$739$	25.1354	+	43.5358i	0.924621	+	1.60149i	0.132452	+	0.991189i	$0.457715\pi$
$740$	−1.57859	−	0.574561i	−0.0580303	−	0.0211213i
$741$	0.699513	+	0.761394i	0.0256973	+	0.0279705i
$742$	−25.8021	−	14.2883i	−0.947226	−	0.524541i
$743$	3.50903	−	19.9007i	0.128734	−	0.730086i	−0.850286	−	0.526321i	$-0.823571\pi$
$743$	3.50903	−	19.9007i	0.128734	−	0.730086i	0.979020	−	0.203765i	$-0.0653178\pi$
$744$	−12.6257	+	2.81628i	−0.462880	+	0.103250i
$745$	0.517232	+	2.93337i	0.0189499	+	0.107470i
$746$	4.93491	+	8.54751i	0.180680	+	0.312947i
$747$	0.351869	−	4.14608i	0.0128742	−	0.151697i
$748$	3.02704	+	5.24299i	0.110680	+	0.191703i
$749$	−38.2109	−	6.03571i	−1.39620	−	0.220540i
$750$	−0.265160	−	5.89713i	−0.00968227	−	0.215333i
$751$	−2.59341	+	14.7079i	−0.0946347	+	0.536700i	0.900224	+	0.435427i	$0.143403\pi$
$751$	−2.59341	+	14.7079i	−0.0946347	+	0.536700i	−0.994859	+	0.101273i	$0.967708\pi$
$752$	−0.295641	+	1.67666i	−0.0107809	+	0.0611415i
$753$	8.65216	+	20.8116i	0.315302	+	0.758416i
$754$	0.369744	−	0.310252i	0.0134653	−	0.0112987i
$755$	0.0953937			0.00347173
$756$	−4.41847	−	13.0183i	−0.160698	−	0.473472i
$757$	−39.1056			−1.42132			−0.710658	−	0.703538i	$-0.751603\pi$
$757$	−39.1056			−1.42132			−0.710658	+	0.703538i	$0.751603\pi$
$758$	−2.84278	+	2.38538i	−0.103255	+	0.0866409i
$759$	6.94224	−	9.07171i	0.251987	−	0.329282i
$760$	0.200804	−	1.13882i	0.00728393	−	0.0413092i
$761$	−0.122854	+	0.696740i	−0.00445345	+	0.0252568i	−0.986954	−	0.161006i	$-0.948526\pi$
$761$	−0.122854	+	0.696740i	−0.00445345	+	0.0252568i	0.982500	+	0.186262i	$0.0596374\pi$
$762$	−14.6593	−	7.60694i	−0.531051	−	0.275571i
$763$	−4.15413	−	10.8084i	−0.150389	−	0.391291i
$764$	−8.17971	−	14.1677i	−0.295932	−	0.512568i
$765$	−7.13763	+	0.643176i	−0.258062	+	0.0232541i
$766$	−4.63809	−	8.03341i	−0.167581	−	0.290259i
$767$	0.154890	+	0.878425i	0.00559275	+	0.0317181i
$768$	−1.17182	−	1.27548i	−0.0422843	−	0.0460249i
$769$	−6.43977	+	36.5218i	−0.232224	+	1.31701i	0.616157	+	0.787623i	$0.288689\pi$
$769$	−6.43977	+	36.5218i	−0.232224	+	1.31701i	−0.848381	+	0.529386i	$0.822422\pi$
$770$	0.0142537	+	0.797577i	0.000513666	+	0.0287427i
$771$	−11.5313	+	2.57216i	−0.415288	+	0.0926340i
$772$	−18.8727	−	6.86911i	−0.679244	−	0.247225i
$773$	1.64340	+	2.84645i	0.0591089	+	0.102380i	0.894066	−	0.447936i	$-0.147841\pi$
$773$	1.64340	+	2.84645i	0.0591089	+	0.102380i	−0.834957	+	0.550316i	$0.814507\pi$
$774$	11.1783	−	24.1357i	0.401796	−	0.867538i
$775$	18.2272	−	31.5704i	0.654740	−	1.13404i
$776$	−4.32582	−	1.57447i	−0.155288	−	0.0565202i
$777$	16.1633	−	15.3913i	0.579857	−	0.552158i
$778$	1.55196	+	1.30225i	0.0556404	+	0.0466879i
$779$	−9.24566	−	7.75803i	−0.331260	−	0.277960i
$780$	0.0646454	−	0.0844749i	0.00231468	−	0.00302469i
$781$	7.68099	+	2.79565i	0.274847	+	0.100036i
$782$	−26.1273	−	45.2538i	−0.934310	−	1.61827i
$783$	−2.99502	+	13.7636i	−0.107033	+	0.491871i
$784$	−0.968444	+	6.93268i	−0.0345873	+	0.247596i
$785$	0.982660	+	5.57294i	0.0350726	+	0.198907i
$786$	0.738764	+	0.0962826i	0.0263508	+	0.00343429i
$787$	1.61519	−	9.16022i	0.0575754	−	0.326527i	−0.942393	−	0.334509i	$-0.891430\pi$
$787$	1.61519	−	9.16022i	0.0575754	−	0.326527i	0.999968	+	0.00798203i	$0.00254079\pi$
$788$	8.46723	−	3.08182i	0.301633	−	0.109785i
$789$	−17.8429	+	11.3998i	−0.635224	+	0.405845i
$790$	−0.153324	−	0.0558053i	−0.00545502	−	0.00198546i
$791$	25.3735	−	4.94307i	0.902178	−	0.175755i
$792$	2.37380	−	1.11445i	0.0843494	−	0.0396003i
$793$	0.0307968			0.00109363
$794$	3.01537	+	17.1010i	0.107012	+	0.606892i
$795$	4.50571	+	4.90430i	0.159801	+	0.173938i
$796$	−19.8138	+	7.21162i	−0.702281	+	0.255609i
$797$	5.26438	−	29.8558i	0.186474	−	1.05755i	−0.737573	−	0.675267i	$-0.764028\pi$
$797$	5.26438	−	29.8558i	0.186474	−	1.05755i	0.924047	−	0.382279i	$-0.124861\pi$
$798$	12.3659	+	9.11745i	0.437747	+	0.322754i
$799$	−9.03275	+	7.57938i	−0.319556	+	0.268139i
$800$	4.88103			0.172571
$801$	−27.9476	+	28.0933i	−0.987478	+	0.992629i
$802$	17.2184			0.608004
$803$	1.79287	+	10.1679i	0.0632689	+	0.358816i
$804$	−9.40435	+	6.00845i	−0.331666	+	0.211902i
$805$	−0.123027	−	6.88412i	−0.00433615	−	0.242633i
$806$	1.24961	−	0.454821i	0.0440157	−	0.0160204i
$807$	26.9912	−	35.2706i	0.950136	−	1.24158i
$808$	15.5887	+	5.67382i	0.548409	+	0.199604i
$809$	−0.598540	+	1.03670i	−0.0210435	+	0.0364485i	−0.876355	−	0.481665i	$-0.840032\pi$
$809$	−0.598540	+	1.03670i	−0.0210435	+	0.0364485i	0.855312	+	0.518114i	$0.173366\pi$
$810$	0.0161512	+	3.10422i	0.000567495	+	0.109071i
$811$	−47.3836			−1.66386			−0.831932	−	0.554878i	$-0.812765\pi$
$811$	−47.3836			−1.66386			−0.831932	+	0.554878i	$0.812765\pi$
$812$	4.51122	−	5.57564i	0.158313	−	0.195667i
$813$	10.9795	+	26.4097i	0.385069	+	0.926228i
$814$	3.26136	+	2.73660i	0.114311	+	0.0959179i
$815$	6.87231	−	2.50132i	0.240727	−	0.0876173i
$816$	−0.538842	−	11.9838i	−0.0188632	−	0.419517i
$817$	5.16170	+	29.2735i	0.180585	+	1.02415i
$818$	−8.12887	−	14.0796i	−0.284219	−	0.492282i
$819$	0.623361	+	1.26835i	0.0217820	+	0.0443198i
$820$	−0.620847	+	1.07534i	−0.0216809	+	0.0375525i
$821$	10.4607	+	3.80738i	0.365081	+	0.132879i	0.518045	−	0.855353i	$-0.326660\pi$
$821$	10.4607	+	3.80738i	0.365081	+	0.132879i	−0.152965	+	0.988232i	$0.548882\pi$
$822$	−4.60418	+	1.02701i	−0.160589	+	0.0358210i
$823$	−20.5272	−	17.2244i	−0.715534	−	0.600404i	0.210612	−	0.977570i	$-0.432454\pi$
$823$	−20.5272	−	17.2244i	−0.715534	−	0.600404i	−0.926146	+	0.377165i	$0.876899\pi$
$824$	14.5889	−	5.30994i	0.508229	−	0.184980i
$825$	−2.21307	+	7.05092i	−0.0770491	+	0.245482i
$826$	4.75500	+	12.3718i	0.165448	+	0.430471i
$827$	6.01479	−	10.4179i	0.209155	−	0.362267i	−0.742294	−	0.670075i	$-0.766262\pi$
$827$	6.01479	−	10.4179i	0.209155	−	0.362267i	0.951449	+	0.307808i	$0.0995954\pi$
$828$	−20.4890	+	9.61915i	−0.712042	+	0.334288i
$829$	−35.2177			−1.22316			−0.611580	−	0.791182i	$-0.709466\pi$
$829$	−35.2177			−1.22316			−0.611580	+	0.791182i	$0.709466\pi$
$830$	0.366476	−	0.307510i	0.0127206	−	0.0106738i
$831$	34.1765	−	21.8354i	1.18557	−	0.757462i
$832$	0.136397	+	0.114451i	0.00472871	+	0.00396786i
$833$	−36.0013	+	32.4700i	−1.24737	+	1.12502i
$834$	2.56949	−	3.35766i	0.0889741	−	0.116266i
$835$	−0.247577	+	0.207742i	−0.00856775	+	0.00718920i
$836$	−1.46532	+	2.53801i	−0.0506791	+	0.0877788i
$837$	−20.7236	+	32.8114i	−0.716312	+	1.13413i
$838$	9.04305	+	15.6630i	0.312387	+	0.541070i
$839$	9.00886	+	51.0918i	0.311021	+	1.76389i	0.593715	+	0.804675i	$0.297661\pi$
$839$	9.00886	+	51.0918i	0.311021	+	1.76389i	−0.282695	+	0.959210i	$0.591228\pi$
$840$	0.702838	−	1.41576i	0.0242502	−	0.0488482i
$841$	20.3458	−	7.40528i	0.701581	−	0.255354i
$842$	−2.60982	+	14.8010i	−0.0899405	+	0.510078i
$843$	1.49171	−	0.953054i	0.0513772	−	0.0328249i
$844$	−17.9188	+	15.0357i	−0.616792	+	0.517550i
$845$	2.23650	−	3.87374i	0.0769380	−	0.133261i
$846$	2.94046	+	4.17625i	0.101095	+	0.143582i
$847$	−8.80626	+	25.6099i	−0.302587	+	0.879965i
$848$	−8.53968	+	7.16564i	−0.293254	+	0.246069i
$849$	−11.6598	−	12.6912i	−0.400162	−	0.435561i
$850$	25.8963	+	21.7296i	0.888236	+	0.745318i
$851$	−28.1497	−	23.6204i	−0.964961	−	0.809698i
$852$	−10.9576	−	11.9269i	−0.375400	−	0.408609i
$853$	26.1780	−	21.9659i	0.896317	−	0.752100i	−0.0731497	−	0.997321i	$-0.523305\pi$
$853$	26.1780	−	21.9659i	0.896317	−	0.752100i	0.969467	+	0.245221i	$0.0788607\pi$
$854$	0.449174	−	0.0875046i	0.0153704	−	0.00299435i
$855$	−1.99721	−	2.83658i	−0.0683031	−	0.0970089i
$856$	−7.31071	+	12.6625i	−0.249875	+	0.432796i
$857$	−8.86376	+	7.43758i	−0.302780	+	0.254063i	−0.781500	−	0.623905i	$-0.785545\pi$
$857$	−8.86376	+	7.43758i	−0.302780	+	0.254063i	0.478720	+	0.877968i	$0.341101\pi$
$858$	−0.227173	+	0.145141i	−0.00775556	+	0.00495503i
$859$	−8.76392	+	49.7026i	−0.299021	+	1.69583i	0.351373	+	0.936235i	$0.385715\pi$
$859$	−8.76392	+	49.7026i	−0.299021	+	1.69583i	−0.650394	+	0.759597i	$0.725396\pi$
$860$	2.87369	−	1.04594i	0.0979919	−	0.0356661i
$861$	−9.12897	−	13.7411i	−0.311114	−	0.468294i
$862$	5.00657	+	28.3937i	0.170524	+	0.967092i
$863$	1.06132	+	1.83825i	0.0361276	+	0.0625748i	0.883524	−	0.468386i	$-0.155164\pi$
$863$	1.06132	+	1.83825i	0.0361276	+	0.0625748i	−0.847396	+	0.530961i	$0.821831\pi$
$864$	−5.19205	−	0.206394i	−0.176637	−	0.00702167i
$865$	2.13500	−	3.69793i	0.0725922	−	0.125733i
$866$	6.59477	−	5.53367i	0.224100	−	0.188042i
$867$	32.5966	−	42.5954i	1.10704	−	1.44661i
$868$	16.9334	−	10.1842i	0.574757	−	0.345674i
$869$	0.316765	+	0.265798i	0.0107455	+	0.00901657i
$870$	−1.36472	+	0.871919i	−0.0462683	+	0.0295608i
$871$	0.878829	−	0.737425i	0.0297780	−	0.0249867i
$872$	−4.37654			−0.148208
$873$	−12.5012	+	5.86904i	−0.423101	+	0.198637i
$874$	12.6476	−	21.9063i	0.427811	−	0.740991i
$875$	3.23495	+	8.41686i	0.109361	+	0.284542i
$876$	6.12644	−	19.5191i	0.206993	−	0.659489i
$877$	6.45299	−	2.34870i	0.217902	−	0.0793098i	−0.230763	−	0.973010i	$-0.574122\pi$
$877$	6.45299	−	2.34870i	0.217902	−	0.0793098i	0.448664	+	0.893700i	$0.351900\pi$
$878$	18.8911	+	15.8516i	0.637545	+	0.534964i
$879$	9.87482	−	2.20267i	0.333069	−	0.0742943i
$880$	0.283321	+	0.103120i	0.00955075	+	0.00347619i
$881$	−27.2296	+	47.1630i	−0.917388	+	1.58896i	−0.114022	+	0.993478i	$0.536373\pi$
$881$	−27.2296	+	47.1630i	−0.917388	+	1.58896i	−0.803367	+	0.595485i	$0.796960\pi$
$882$	12.6956	+	16.7279i	0.427484	+	0.563256i
$883$	−6.18561	−	10.7138i	−0.208162	−	0.360548i	0.742973	−	0.669321i	$-0.233415\pi$
$883$	−6.18561	−	10.7138i	−0.208162	−	0.360548i	−0.951136	+	0.308773i	$0.900082\pi$
$884$	0.214138	+	1.21444i	0.00720223	+	0.0408459i
$885$	−0.134434	−	2.98979i	−0.00451894	−	0.100501i
$886$	8.91469	−	3.24468i	0.299495	−	0.109007i
$887$	26.0682	+	21.8738i	0.875286	+	0.734452i	0.965204	−	0.261497i	$-0.0842163\pi$
$887$	26.0682	+	21.8738i	0.875286	+	0.734452i	−0.0899186	+	0.995949i	$0.528661\pi$
$888$	−3.23839	−	7.78950i	−0.108673	−	0.261399i
$889$	24.9189	+	3.93614i	0.835752	+	0.132014i
$890$	−4.55603			−0.152719
$891$	2.65223	−	7.40663i	0.0888532	−	0.248131i
$892$	1.88888	−	3.27164i	0.0632444	−	0.109543i
$893$	−5.36371	−	1.95223i	−0.179490	−	0.0653289i
$894$	−9.09010	+	11.8784i	−0.304018	+	0.397273i
$895$	−2.75254	+	1.00184i	−0.0920072	+	0.0334879i
$896$	2.31456	+	1.28172i	0.0773240	+	0.0428194i
$897$	1.96080	−	1.25275i	0.0654691	−	0.0418282i
$898$	−3.45508	−	19.5947i	−0.115297	−	0.653884i
$899$	−20.2458			−0.675235
$900$	10.3273	−	10.3811i	0.344242	−	0.346038i
$901$	−77.2075			−2.57216
$902$	2.41062	−	2.02275i	0.0802648	−	0.0673502i
$903$	−4.53014	+	40.3767i	−0.150754	+	1.34365i
$904$	1.69664	−	9.62214i	0.0564295	−	0.320028i
$905$	1.84507	−	0.671551i	0.0613322	−	0.0223231i
$906$	0.324088	+	0.352757i	0.0107671	+	0.0117196i
$907$	2.79319	+	15.8410i	0.0927464	+	0.525991i	0.995415	+	0.0956538i	$0.0304942\pi$
$907$	2.79319	+	15.8410i	0.0927464	+	0.525991i	−0.902668	+	0.430337i	$0.858395\pi$
$908$	19.9431			0.661833
$909$	45.0498	−	21.1499i	1.49421	−	0.701498i
$910$	−0.0528364	+	0.153656i	−0.00175151	+	0.00509364i
$911$	3.71447	+	1.35196i	0.123066	+	0.0447923i	0.402819	−	0.915280i	$-0.368030\pi$
$911$	3.71447	+	1.35196i	0.123066	+	0.0447923i	−0.279753	+	0.960072i	$0.590253\pi$
$912$	4.89345	−	3.12643i	0.162038	−	0.103526i
$913$	−1.13930	+	0.414670i	−0.0377052	+	0.0137236i
$914$	−4.77766	+	27.0954i	−0.158031	+	0.896238i
$915$	−0.102465	−	0.0133542i	−0.00338738	−	0.000441475i
$916$	−0.834022	−	4.72997i	−0.0275568	−	0.156283i
$917$	−1.11702	+	0.217610i	−0.0368874	+	0.00718611i
$918$	−26.6276	−	24.2092i	−0.878841	−	0.799023i
$919$	16.7643	+	29.0365i	0.553002	+	0.957827i	0.998056	+	0.0623234i	$0.0198510\pi$
$919$	16.7643	+	29.0365i	0.553002	+	0.957827i	−0.445054	+	0.895504i	$0.646816\pi$
$920$	−2.44543	−	0.890063i	−0.0806233	−	0.0293445i
$921$	−10.6597	+	13.9294i	−0.351248	+	0.458990i
$922$	−6.82181	−	5.72418i	−0.224664	−	0.188516i
$923$	1.27544	+	1.07022i	0.0419816	+	0.0352267i
$924$	−2.90095	+	2.76237i	−0.0954341	+	0.0908755i
$925$	22.3391	+	8.13076i	0.734505	+	0.267338i
$926$	−20.1900	+	34.9700i	−0.663483	+	1.14919i
$927$	19.5738	−	42.2629i	0.642889	−	1.38810i
$928$	−1.35540	−	2.34762i	−0.0444931	−	0.0770643i
$929$	−49.1039	−	17.8724i	−1.61105	−	0.586373i	−0.629400	−	0.777081i	$-0.716699\pi$
$929$	−49.1039	−	17.8724i	−1.61105	−	0.586373i	−0.981647	+	0.190708i	$0.938922\pi$
$930$	−4.35483	+	0.971388i	−0.142801	+	0.0318531i
$931$	−22.3258	−	7.23356i	−0.731699	−	0.237070i
$932$	−4.20932	+	23.8722i	−0.137881	+	0.781961i
$933$	−31.7602	−	34.5698i	−1.03978	−	1.13176i
$934$	4.00654	+	22.7222i	0.131098	+	0.743494i
$935$	1.04408	+	1.80841i	0.0341452	+	0.0591412i
$936$	0.532005	−	0.0479393i	0.0173891	−	0.00156695i
$937$	2.60312	+	4.50873i	0.0850401	+	0.147294i	0.905408	−	0.424542i	$-0.139565\pi$
$937$	2.60312	+	4.50873i	0.0850401	+	0.147294i	−0.820368	+	0.571836i	$0.806232\pi$
$938$	10.7225	−	13.2525i	0.350103	−	0.432709i
$939$	−48.0695	−	24.9440i	−1.56869	−	0.814016i
$940$	−0.101972	+	0.578312i	−0.00332596	+	0.0188624i
$941$	8.78770	−	49.8375i	0.286471	−	1.62466i	−0.413513	−	0.910498i	$-0.635698\pi$
$941$	8.78770	−	49.8375i	0.286471	−	1.62466i	0.699984	−	0.714159i	$-0.253191\pi$
$942$	−17.2698	+	22.5671i	−0.562680	+	0.735277i
$943$	−20.8068	+	17.4589i	−0.677561	+	0.568542i
$944$	5.00959			0.163048
$945$	−1.52401	−	4.49027i	−0.0495762	−	0.146068i
$946$	−7.75021			−0.251981
$947$	40.5386	−	34.0159i	1.31733	−	1.10537i	0.330462	−	0.943819i	$-0.392795\pi$
$947$	40.5386	−	34.0159i	1.31733	−	1.10537i	0.986865	−	0.161549i	$-0.0516490\pi$
$948$	−0.314535	−	0.756569i	−0.0102156	−	0.0245722i
$949$	−0.365193	+	2.07111i	−0.0118547	+	0.0672312i
$950$	−2.84163	+	16.1157i	−0.0921946	+	0.522862i
$951$	1.41233	+	31.4100i	0.0457979	+	1.01854i
$952$	6.57386	+	17.1042i	0.213060	+	0.554351i
$953$	12.1486	+	21.0420i	0.393531	+	0.681616i	0.992913	−	0.118848i	$-0.0379200\pi$
$953$	12.1486	+	21.0420i	0.393531	+	0.681616i	−0.599381	+	0.800464i	$0.704587\pi$
$954$	−2.82809	+	33.3235i	−0.0915629	+	1.07889i
$955$	−2.82133	−	4.88669i	−0.0912962	−	0.158130i
$956$	0.388879	+	2.20544i	0.0125772	+	0.0713291i
$957$	4.00580	−	0.893534i	0.129489	−	0.0288838i
$958$	0.767672	−	4.35368i	0.0248023	−	0.140661i
$959$	6.17507	−	3.71385i	0.199403	−	0.119927i
$960$	−0.404181	−	0.439936i	−0.0130449	−	0.0141989i
$961$	−23.2854	−	8.47518i	−0.751140	−	0.273393i
$962$	0.433600	+	0.751017i	0.0139798	+	0.0242137i
$963$	11.4631	+	42.3399i	0.369393	+	1.36439i
$964$	−13.9645	+	24.1873i	−0.449768	+	0.779020i
$965$	−6.50955	−	2.36928i	−0.209550	−	0.0762699i
$966$	25.0389	−	23.8429i	0.805614	−	0.767132i
$967$	11.7983	+	9.89991i	0.379406	+	0.318360i	0.812469	−	0.583004i	$-0.198123\pi$
$967$	11.7983	+	9.89991i	0.379406	+	0.318360i	−0.433063	+	0.901364i	$0.642567\pi$
$968$	7.84115	+	6.57951i	0.252024	+	0.211473i
$969$	39.8805	+	5.19761i	1.28115	+	0.166971i
$970$	−1.49206	−	0.543064i	−0.0479070	−	0.0174367i
$971$	5.50393	+	9.53309i	0.176630	+	0.305932i	0.940724	−	0.339173i	$-0.110147\pi$
$971$	5.50393	+	9.53309i	0.176630	+	0.305932i	−0.764094	+	0.645104i	$0.776814\pi$
$972$	−11.4243	+	10.6059i	−0.366434	+	0.340185i
$973$	−2.10011	+	6.10741i	−0.0673264	+	0.195795i
$974$	3.98154	+	22.5805i	0.127577	+	0.723525i
$975$	−0.914814	+	1.19543i	−0.0292975	+	0.0382843i
$976$	0.0300348	−	0.170336i	0.000961391	−	0.00545232i
$977$	−38.6691	+	14.0744i	−1.23713	+	0.450280i	−0.876035	−	0.482247i	$-0.839821\pi$
$977$	−38.6691	+	14.0744i	−1.23713	+	0.450280i	−0.361099	+	0.932527i	$0.617599\pi$
$978$	32.5975	+	16.9153i	1.04235	+	0.540892i
$979$	10.8501	+	3.94910i	0.346770	+	0.126214i
$980$	−0.334034	+	2.39121i	−0.0106703	+	0.0763845i
$981$	−9.25986	+	9.30817i	−0.295645	+	0.297187i
$982$	−23.7931			−0.759269
$983$	−6.51957	−	36.9743i	−0.207942	−	1.17930i	−0.892743	−	0.450567i	$-0.851222\pi$
$983$	−6.51957	−	36.9743i	−0.207942	−	1.17930i	0.684801	−	0.728730i	$-0.259889\pi$
$984$	−6.08576	+	1.35749i	−0.194007	+	0.0432751i
$985$	2.92050	−	1.06298i	0.0930550	−	0.0338693i
$986$	3.26016	−	18.4893i	0.103825	−	0.588819i
$987$	−6.27961	−	4.63001i	−0.199882	−	0.147375i
$988$	−0.457289	+	0.383711i	−0.0145483	+	0.0122075i
$989$	66.8944			2.12712
$990$	0.818769	−	0.384395i	0.0260222	−	0.0122169i
$991$	−56.7820			−1.80374			−0.901870	−	0.432008i	$-0.857805\pi$
$991$	−56.7820			−1.80374			−0.901870	+	0.432008i	$0.857805\pi$
$992$	−1.29691	−	7.35512i	−0.0411768	−	0.233525i
$993$	1.17136	+	26.0509i	0.0371720	+	0.826701i
$994$	21.6433	+	11.9853i	0.686483	+	0.380151i
$995$	−6.83414	+	2.48742i	−0.216657	+	0.0788566i
$996$	2.38220	+	0.310470i	0.0754828	+	0.00983763i
$997$	−31.2269	−	11.3657i	−0.988965	−	0.359954i	−0.203646	−	0.979045i	$-0.565279\pi$
$997$	−31.2269	−	11.3657i	−0.988965	−	0.359954i	−0.785319	+	0.619091i	$0.787501\pi$
$998$	−5.70648	+	9.88391i	−0.180635	+	0.312870i
$999$	−23.4187	−	9.59347i	−0.740936	−	0.303524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.67.1	✓	72
7.2	even	3		378.2.w.b.121.8	yes	72
27.25	even	9		378.2.w.b.25.8	yes	72
189.79	even	9	inner	378.2.v.a.79.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.1	✓	72	1.1	even	1	trivial
378.2.v.a.79.1	yes	72	189.79	even	9	inner
378.2.w.b.25.8	yes	72	27.25	even	9
378.2.w.b.121.8	yes	72	7.2	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.71753 - 0.223844i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0598945 - 0.339678i) q^{5} +(1.45959 - 0.932530i) q^{6} +(-1.66417 + 2.05683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.89979 + 0.768916i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.71753 - 0.223844i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0598945 - 0.339678i) q^{5} +(1.45959 - 0.932530i) q^{6} +(-1.66417 + 2.05683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.89979 + 0.768916i) q^{9} +(0.172459 + 0.298708i) q^{10} +(-0.151791 - 0.860851i) q^{11} +(-0.518689 + 1.65256i) q^{12} +(0.0309187 - 0.175349i) q^{13} +(-0.0472752 - 2.64533i) q^{14} +(-0.178905 + 0.569999i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-3.46292 - 5.99795i) q^{17} +(-2.71562 + 1.27492i) q^{18} +(1.67631 - 2.90346i) q^{19} +(-0.324117 - 0.117969i) q^{20} +(3.31866 - 3.16014i) q^{21} +(0.669623 + 0.561880i) q^{22} +(-5.77971 - 4.84976i) q^{23} +(-0.664908 - 1.59934i) q^{24} +(4.58667 + 1.66941i) q^{25} +(0.0890268 + 0.154199i) q^{26} +(-4.80834 - 1.96973i) q^{27} +(1.73660 + 1.99605i) q^{28} +(-0.470725 - 2.66961i) q^{29} +(-0.229339 - 0.551643i) q^{30} +(1.29691 - 7.35512i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.0680089 + 1.51251i) q^{33} +(6.50816 + 2.36878i) q^{34} +(0.598985 + 0.688475i) q^{35} +(1.26078 - 2.72221i) q^{36} +4.87044 q^{37} +(0.582178 + 3.30170i) q^{38} +(-0.0923544 + 0.294245i) q^{39} +(0.324117 - 0.117969i) q^{40} +(0.625127 - 3.54527i) q^{41} +(-0.510945 + 4.55400i) q^{42} +(-6.79190 + 5.69908i) q^{43} -0.874131 q^{44} +(0.434865 - 0.938942i) q^{45} +7.54488 q^{46} +(-0.295641 - 1.67666i) q^{47} +(1.53739 + 0.797773i) q^{48} +(-1.46108 - 6.84582i) q^{49} +(-4.58667 + 1.66941i) q^{50} +(4.60504 + 11.0768i) q^{51} +(-0.167316 - 0.0608979i) q^{52} +(5.57388 - 9.65424i) q^{53} +(4.94952 - 1.58184i) q^{54} -0.301504 q^{55} +(-2.61335 - 0.412800i) q^{56} +(-3.52904 + 4.61154i) q^{57} +(2.07659 + 1.74247i) q^{58} +(-4.70748 + 1.71338i) q^{59} +(0.530273 + 0.275167i) q^{60} +(0.0300348 + 0.170336i) q^{61} +(3.73429 + 6.46798i) q^{62} +(-6.40727 + 4.68476i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0577103 - 0.0210048i) q^{65} +(-1.02432 - 1.11494i) q^{66} +(4.93575 + 4.14159i) q^{67} +(-6.50816 + 2.36878i) q^{68} +(8.84122 + 9.62333i) q^{69} +(-0.901393 - 0.142382i) q^{70} +(-4.67546 + 8.09814i) q^{71} +(0.783993 + 2.89575i) q^{72} -11.8114 q^{73} +(-3.73097 + 3.13066i) q^{74} +(-7.50403 - 3.89395i) q^{75} +(-2.56826 - 2.15503i) q^{76} +(2.02323 + 1.12039i) q^{77} +(-0.118389 - 0.284769i) q^{78} +(-0.362377 + 0.304071i) q^{79} +(-0.172459 + 0.298708i) q^{80} +(7.81754 + 4.45939i) q^{81} +(1.79998 + 3.11766i) q^{82} +(-0.240849 - 1.36592i) q^{83} +(-2.53585 - 3.81700i) q^{84} +(-2.24478 + 0.817035i) q^{85} +(1.53960 - 8.73150i) q^{86} +(0.210905 + 4.69050i) q^{87} +(0.669623 - 0.561880i) q^{88} +(-6.60450 + 11.4393i) q^{89} +(0.270414 + 0.998797i) q^{90} +(0.309208 + 0.355404i) q^{91} +(-5.77971 + 4.84976i) q^{92} +(-3.87387 + 12.3423i) q^{93} +(1.30421 + 1.09436i) q^{94} +(-0.885842 - 0.743309i) q^{95} +(-1.69051 + 0.377084i) q^{96} +(-3.52644 + 2.95904i) q^{97} +(5.51966 + 4.30504i) q^{98} +(0.221760 - 2.61300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

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