LMFDB - Embedded newform 392.2.z.a.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24676 + 0.667524i) q^{2} +(-0.0948478 - 0.629274i) q^{3} +(1.10882 - 1.66448i) q^{4} +(2.70840 + 1.06297i) q^{5} +(0.538308 + 0.721241i) q^{6} +(2.24180 + 1.40511i) q^{7} +(-0.271356 + 2.81538i) q^{8} +(2.47973 - 0.764895i) q^{9} +O(q^{10})$	\(q+(-1.24676 + 0.667524i) q^{2} +(-0.0948478 - 0.629274i) q^{3} +(1.10882 - 1.66448i) q^{4} +(2.70840 + 1.06297i) q^{5} +(0.538308 + 0.721241i) q^{6} +(2.24180 + 1.40511i) q^{7} +(-0.271356 + 2.81538i) q^{8} +(2.47973 - 0.764895i) q^{9} +(-4.08629 + 0.482654i) q^{10} +(0.936484 - 3.03601i) q^{11} +(-1.15259 - 0.539882i) q^{12} +(-5.16780 + 1.17952i) q^{13} +(-3.73293 - 0.255388i) q^{14} +(0.412013 - 1.80515i) q^{15} +(-1.54102 - 3.69124i) q^{16} +(-5.63658 + 3.84296i) q^{17} +(-2.58104 + 2.60892i) q^{18} +(5.23520 - 3.02254i) q^{19} +(4.77244 - 3.32945i) q^{20} +(0.671572 - 1.54398i) q^{21} +(0.859035 + 4.41030i) q^{22} +(5.81948 + 3.96766i) q^{23} +(1.79738 - 0.0962755i) q^{24} +(2.54027 + 2.35703i) q^{25} +(5.65565 - 4.92020i) q^{26} +(-1.54487 - 3.20796i) q^{27} +(4.82455 - 2.17341i) q^{28} +(0.370156 - 0.768637i) q^{29} +(0.691297 + 2.52562i) q^{30} +(0.493832 - 0.855342i) q^{31} +(4.38527 + 3.57343i) q^{32} +(-1.99930 - 0.301347i) q^{33} +(4.46221 - 8.55380i) q^{34} +(4.57809 + 6.18857i) q^{35} +(1.47643 - 4.97560i) q^{36} +(-2.91688 + 0.218590i) q^{37} +(-4.50942 + 7.26300i) q^{38} +(1.23239 + 3.14009i) q^{39} +(-3.72760 + 7.33674i) q^{40} +(4.33675 + 5.43812i) q^{41} +(0.193352 + 2.37326i) q^{42} +(-6.83848 - 5.45350i) q^{43} +(-4.01499 - 4.92516i) q^{44} +(7.52916 + 0.564233i) q^{45} +(-9.90400 - 1.06207i) q^{46} +(3.55223 - 3.29599i) q^{47} +(-2.17664 + 1.31983i) q^{48} +(3.05131 + 6.29996i) q^{49} +(-4.74049 - 1.24296i) q^{50} +(2.95289 + 3.18246i) q^{51} +(-3.76689 + 9.90959i) q^{52} +(9.02242 + 0.676137i) q^{53} +(4.06748 + 2.96832i) q^{54} +(5.76356 - 7.22727i) q^{55} +(-4.56425 + 5.93023i) q^{56} +(-2.39855 - 3.00769i) q^{57} +(0.0515874 + 1.20539i) q^{58} +(-8.03090 + 3.15190i) q^{59} +(-2.54779 - 2.68738i) q^{60} +(2.18769 - 0.163945i) q^{61} +(-0.0447292 + 1.39605i) q^{62} +(6.63381 + 1.76956i) q^{63} +(-7.85273 - 1.52794i) q^{64} +(-15.2503 - 2.29861i) q^{65} +(2.69381 - 0.958876i) q^{66} +(-6.38483 - 3.68628i) q^{67} +(0.146563 + 13.6432i) q^{68} +(1.94478 - 4.03837i) q^{69} +(-9.83881 - 4.65968i) q^{70} +(-1.19860 + 0.577216i) q^{71} +(1.48058 + 7.18894i) q^{72} +(-6.22593 - 5.77682i) q^{73} +(3.49074 - 2.21962i) q^{74} +(1.24228 - 1.82209i) q^{75} +(0.773939 - 12.0654i) q^{76} +(6.36534 - 5.49025i) q^{77} +(-3.63258 - 3.09228i) q^{78} +(-2.59085 - 4.48748i) q^{79} +(-0.250017 - 11.6354i) q^{80} +(4.56015 - 3.10906i) q^{81} +(-9.03697 - 3.88515i) q^{82} +(4.68565 + 1.06947i) q^{83} +(-1.82527 - 2.82982i) q^{84} +(-19.3511 + 4.41676i) q^{85} +(12.1663 + 2.23437i) q^{86} +(-0.518792 - 0.160026i) q^{87} +(8.29340 + 3.46040i) q^{88} +(-10.4950 + 3.23727i) q^{89} +(-9.76370 + 4.32243i) q^{90} +(-13.2425 - 4.61711i) q^{91} +(13.0569 - 5.28700i) q^{92} +(-0.585083 - 0.229628i) q^{93} +(-2.22863 + 6.48050i) q^{94} +(17.3919 - 2.62140i) q^{95} +(1.83273 - 3.09847i) q^{96} -8.77219 q^{97} +(-8.00963 - 5.81772i) q^{98} -8.24479i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

Coefficient data

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

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

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

$2$	−1.24676	+	0.667524i	−0.881593	+	0.472011i
$2$	−1.24676	+	0.667524i	−0.881593	+	0.472011i
$3$	−0.0948478	−	0.629274i	−0.0547604	−	0.363312i	−0.999382	−	0.0351501i	$-0.988809\pi$
$3$	−0.0948478	−	0.629274i	−0.0547604	−	0.363312i	0.944622	−	0.328162i	$-0.106429\pi$
$4$	1.10882	−	1.66448i	0.554412	−	0.832242i
$5$	2.70840	+	1.06297i	1.21123	+	0.475374i	0.883068	−	0.469246i	$-0.155474\pi$
$5$	2.70840	+	1.06297i	1.21123	+	0.475374i	0.328166	+	0.944620i	$0.393569\pi$
$6$	0.538308	+	0.721241i	0.219763	+	0.294445i
$7$	2.24180	+	1.40511i	0.847320	+	0.531083i
$7$	2.24180	+	1.40511i	0.847320	+	0.531083i
$8$	−0.271356	+	2.81538i	−0.0959387	+	0.995387i
$9$	2.47973	−	0.764895i	0.826576	−	0.254965i
$10$	−4.08629	+	0.482654i	−1.29220	+	0.152629i
$11$	0.936484	−	3.03601i	0.282361	−	0.915391i	−0.697649	−	0.716440i	$-0.745770\pi$
$11$	0.936484	−	3.03601i	0.282361	−	0.915391i	0.980009	−	0.198951i	$-0.0637534\pi$
$12$	−1.15259	−	0.539882i	−0.332723	−	0.155850i
$13$	−5.16780	+	1.17952i	−1.43329	+	0.327139i	−0.867511	−	0.497419i	$-0.834281\pi$
$13$	−5.16780	+	1.17952i	−1.43329	+	0.327139i	−0.565778	+	0.824557i	$0.691424\pi$
$14$	−3.73293	−	0.255388i	−0.997668	−	0.0682552i
$15$	0.412013	−	1.80515i	0.106381	−	0.466087i
$16$	−1.54102	−	3.69124i	−0.385254	−	0.922810i
$17$	−5.63658	+	3.84296i	−1.36707	+	0.932054i	−0.367074	+	0.930192i	$0.619641\pi$
$17$	−5.63658	+	3.84296i	−1.36707	+	0.932054i	−0.999998	+	0.00186277i	$0.999407\pi$
$18$	−2.58104	+	2.60892i	−0.608358	+	0.614928i
$19$	5.23520	−	3.02254i	1.20104	−	0.693419i	0.240251	−	0.970711i	$-0.422770\pi$
$19$	5.23520	−	3.02254i	1.20104	−	0.693419i	0.960786	+	0.277292i	$0.0894370\pi$
$20$	4.77244	−	3.32945i	1.06715	−	0.744487i
$21$	0.671572	−	1.54398i	0.146549	−	0.336923i
$22$	0.859035	+	4.41030i	0.183147	+	0.940279i
$23$	5.81948	+	3.96766i	1.21345	+	0.827313i	0.989107	−	0.147198i	$-0.0470254\pi$
$23$	5.81948	+	3.96766i	1.21345	+	0.827313i	0.224339	+	0.974511i	$0.427978\pi$
$24$	1.79738	−	0.0962755i	0.366889	−	0.0196522i
$25$	2.54027	+	2.35703i	0.508055	+	0.471406i
$26$	5.65565	−	4.92020i	1.10916	−	0.964931i
$27$	−1.54487	−	3.20796i	−0.297311	−	0.617373i
$28$	4.82455	−	2.17341i	0.911754	−	0.410736i
$29$	0.370156	−	0.768637i	0.0687363	−	0.142732i	−0.863770	−	0.503887i	$-0.831903\pi$
$29$	0.370156	−	0.768637i	0.0687363	−	0.142732i	0.932506	+	0.361154i	$0.117617\pi$
$30$	0.691297	+	2.52562i	0.126213	+	0.461112i
$31$	0.493832	−	0.855342i	0.0886948	−	0.153624i	−0.818265	−	0.574841i	$-0.805064\pi$
$31$	0.493832	−	0.855342i	0.0886948	−	0.153624i	0.906960	+	0.421217i	$0.138397\pi$
$32$	4.38527	+	3.57343i	0.775214	+	0.631699i
$33$	−1.99930	−	0.301347i	−0.348034	−	0.0524577i
$34$	4.46221	−	8.55380i	0.765262	−	1.46697i
$35$	4.57809	+	6.18857i	0.773839	+	1.04606i
$36$	1.47643	−	4.97560i	0.246071	−	0.829267i
$37$	−2.91688	+	0.218590i	−0.479532	+	0.0359360i	−0.312304	−	0.949982i	$-0.601101\pi$
$37$	−2.91688	+	0.218590i	−0.479532	+	0.0359360i	−0.167228	+	0.985918i	$0.553482\pi$
$38$	−4.50942	+	7.26300i	−0.731524	+	1.17821i
$39$	1.23239	+	3.14009i	0.197341	+	0.502816i
$40$	−3.72760	+	7.33674i	−0.589386	+	1.16004i
$41$	4.33675	+	5.43812i	0.677287	+	0.849291i	0.995101	−	0.0988617i	$-0.0315202\pi$
$41$	4.33675	+	5.43812i	0.677287	+	0.849291i	−0.317814	+	0.948153i	$0.602949\pi$
$42$	0.193352	+	2.37326i	0.0298348	+	0.366202i
$43$	−6.83848	−	5.45350i	−1.04286	−	0.831652i	−0.0568556	−	0.998382i	$-0.518107\pi$
$43$	−6.83848	−	5.45350i	−1.04286	−	0.831652i	−0.986002	+	0.166731i	$0.946679\pi$
$44$	−4.01499	−	4.92516i	−0.605283	−	0.742496i
$45$	7.52916	+	0.564233i	1.12238	+	0.0841108i
$46$	−9.90400	−	1.06207i	−1.46027	−	0.156594i
$47$	3.55223	−	3.29599i	0.518146	−	0.480769i	−0.377206	−	0.926130i	$-0.623115\pi$
$47$	3.55223	−	3.29599i	0.518146	−	0.480769i	0.895351	+	0.445361i	$0.146924\pi$
$48$	−2.17664	+	1.31983i	−0.314171	+	0.190501i
$49$	3.05131	+	6.29996i	0.435902	+	0.899994i
$50$	−4.74049	−	1.24296i	−0.670406	−	0.175781i
$51$	2.95289	+	3.18246i	0.413488	+	0.445634i
$52$	−3.76689	+	9.90959i	−0.522374	+	1.37421i
$53$	9.02242	+	0.676137i	1.23933	+	0.0928746i	0.678213	−	0.734865i	$-0.262755\pi$
$53$	9.02242	+	0.676137i	1.23933	+	0.0928746i	0.561112	+	0.827740i	$0.310374\pi$
$54$	4.06748	+	2.96832i	0.553514	+	0.403937i
$55$	5.76356	−	7.22727i	0.777158	−	0.974525i
$56$	−4.56425	+	5.93023i	−0.609924	+	0.792460i
$57$	−2.39855	−	3.00769i	−0.317696	−	0.398379i
$58$	0.0515874	+	1.20539i	0.00677376	+	0.158276i
$59$	−8.03090	+	3.15190i	−1.04553	+	0.410342i	−0.825056	−	0.565050i	$-0.808857\pi$
$59$	−8.03090	+	3.15190i	−1.04553	+	0.410342i	−0.220477	+	0.975392i	$0.570762\pi$
$60$	−2.54779	−	2.68738i	−0.328918	−	0.346939i
$61$	2.18769	−	0.163945i	0.280105	−	0.0209910i	0.0660633	−	0.997815i	$-0.478956\pi$
$61$	2.18769	−	0.163945i	0.280105	−	0.0209910i	0.214042	+	0.976824i	$0.431337\pi$
$62$	−0.0447292	+	1.39605i	−0.00568061	+	0.177299i
$63$	6.63381	+	1.76956i	0.835782	+	0.222944i
$64$	−7.85273	−	1.52794i	−0.981592	−	0.190992i
$65$	−15.2503	−	2.29861i	−1.89156	−	0.285107i
$66$	2.69381	−	0.958876i	0.331585	−	0.118029i
$67$	−6.38483	−	3.68628i	−0.780031	−	0.450351i	0.0564103	−	0.998408i	$-0.482035\pi$
$67$	−6.38483	−	3.68628i	−0.780031	−	0.450351i	−0.836441	+	0.548057i	$0.815368\pi$
$68$	0.146563	+	13.6432i	0.0177733	+	1.65448i
$69$	1.94478	−	4.03837i	0.234124	−	0.486163i
$70$	−9.83881	−	4.65968i	−1.17596	−	0.556939i
$71$	−1.19860	+	0.577216i	−0.142248	+	0.0685029i	−0.503654	−	0.863906i	$-0.668011\pi$
$71$	−1.19860	+	0.577216i	−0.142248	+	0.0685029i	0.361406	+	0.932409i	$0.382297\pi$
$72$	1.48058	+	7.18894i	0.174488	+	0.847224i
$73$	−6.22593	−	5.77682i	−0.728690	−	0.676126i	0.225865	−	0.974159i	$-0.427479\pi$
$73$	−6.22593	−	5.77682i	−0.728690	−	0.676126i	−0.954556	+	0.298033i	$0.903670\pi$
$74$	3.49074	−	2.21962i	0.405790	−	0.258025i
$75$	1.24228	−	1.82209i	0.143446	−	0.210397i
$76$	0.773939	−	12.0654i	0.0887768	−	1.38399i
$77$	6.36534	−	5.49025i	0.725398	−	0.625672i
$78$	−3.63258	−	3.09228i	−0.411309	−	0.350132i
$79$	−2.59085	−	4.48748i	−0.291493	−	0.504880i	0.682670	−	0.730727i	$-0.260819\pi$
$79$	−2.59085	−	4.48748i	−0.291493	−	0.504880i	−0.974163	+	0.225846i	$0.927485\pi$
$80$	−0.250017	−	11.6354i	−0.0279528	−	1.30088i
$81$	4.56015	−	3.10906i	0.506684	−	0.345451i
$82$	−9.03697	−	3.88515i	−0.997966	−	0.429043i
$83$	4.68565	+	1.06947i	0.514317	+	0.117389i	0.471799	−	0.881706i	$-0.343605\pi$
$83$	4.68565	+	1.06947i	0.514317	+	0.117389i	0.0425179	+	0.999096i	$0.486462\pi$
$84$	−1.82527	−	2.82982i	−0.199153	−	0.308759i
$85$	−19.3511	+	4.41676i	−2.09892	+	0.479065i
$86$	12.1663	+	2.23437i	1.31192	+	0.240938i
$87$	−0.518792	−	0.160026i	−0.0556204	−	0.0171566i
$88$	8.29340	+	3.46040i	0.884079	+	0.368880i
$89$	−10.4950	+	3.23727i	−1.11246	+	0.343150i	−0.795904	−	0.605423i	$-0.793004\pi$
$89$	−10.4950	+	3.23727i	−1.11246	+	0.343150i	−0.316560	+	0.948573i	$0.602528\pi$
$90$	−9.76370	+	4.32243i	−1.02918	+	0.455624i
$91$	−13.2425	−	4.61711i	−1.38819	−	0.484004i
$92$	13.0569	−	5.28700i	1.36127	−	0.551208i
$93$	−0.585083	−	0.229628i	−0.0606703	−	0.0238114i
$94$	−2.22863	+	6.48050i	−0.229866	+	0.668413i
$95$	17.3919	−	2.62140i	1.78437	−	0.268950i
$96$	1.83273	−	3.09847i	0.187053	−	0.316236i
$97$	−8.77219			−0.890681			−0.445341	−	0.895361i	$-0.646917\pi$
$97$	−8.77219			−0.890681			−0.445341	+	0.895361i	$0.646917\pi$
$98$	−8.00963	−	5.81772i	−0.809095	−	0.587679i
$99$		−	8.24479i		−	0.828632i
$100$	6.73996	−	1.61472i	0.673996	−	0.161472i
$101$	−0.316577	−	2.10035i	−0.0315006	−	0.208993i	0.967544	−	0.252704i	$-0.0813199\pi$
$101$	−0.316577	−	2.10035i	−0.0315006	−	0.208993i	−0.999044	+	0.0437114i	$0.986082\pi$
$102$	−5.80592	−	1.99664i	−0.574872	−	0.197697i
$103$	1.51846	−	3.86898i	0.149618	−	0.381221i	−0.836340	−	0.548211i	$-0.815309\pi$
$103$	1.51846	−	3.86898i	0.149618	−	0.381221i	0.985959	+	0.166989i	$0.0534045\pi$
$104$	−1.91847	−	14.8694i	−0.188122	−	1.45806i
$105$	3.46009	−	3.46785i	0.337670	−	0.338427i
$106$	−11.7001	+	5.17970i	−1.13642	+	0.503097i
$107$	3.04528	+	9.87256i	0.294398	+	0.954416i	0.975083	+	0.221840i	$0.0712062\pi$
$107$	3.04528	+	9.87256i	0.294398	+	0.954416i	−0.680685	+	0.732576i	$0.738318\pi$
$108$	−7.05260	−	0.985649i	−0.678636	−	0.0948441i
$109$	−3.71565	+	12.0458i	−0.355894	+	1.15378i	0.583838	+	0.811870i	$0.301550\pi$
$109$	−3.71565	+	12.0458i	−0.355894	+	1.15378i	−0.939732	+	0.341911i	$0.888926\pi$
$110$	−2.36140	+	12.8580i	−0.225151	+	1.22596i
$111$	0.414213	+	1.81479i	0.0393154	+	0.172252i
$112$	1.73197	−	10.4403i	0.163655	−	0.986518i
$113$	3.71411	−	16.2726i	0.349394	−	1.53079i	−0.429167	−	0.903225i	$-0.641193\pi$
$113$	3.71411	−	16.2726i	0.349394	−	1.53079i	0.778561	−	0.627569i	$-0.215950\pi$
$114$	4.99813	+	2.14878i	0.468118	+	0.201252i
$115$	11.5440	+	16.9319i	1.07648	+	1.57891i
$116$	−0.868947	−	1.46840i	−0.0806797	−	0.136338i
$117$	−11.9125	+	6.87770i	−1.10131	+	0.635844i
$118$	7.90864	−	9.29047i	0.728050	−	0.855257i
$119$	−18.0359	+	0.695091i	−1.65335	+	0.0637189i
$120$	4.97037	+	1.64981i	0.453731	+	0.150606i
$121$	0.748287	+	0.510173i	0.0680261	+	0.0463794i
$122$	−2.61809	+	1.66474i	−0.237031	+	0.150718i
$123$	3.01074	−	3.24480i	0.271469	−	0.292574i
$124$	−0.876131	−	1.77040i	−0.0786788	−	0.158987i
$125$	−1.93735	−	4.02294i	−0.173282	−	0.359823i
$126$	−9.45200	+	2.22201i	−0.842051	+	0.197952i
$127$	−4.98521	−	2.40075i	−0.442366	−	0.213032i	0.199423	−	0.979914i	$-0.436093\pi$
$127$	−4.98521	−	2.40075i	−0.442366	−	0.213032i	−0.641789	+	0.766881i	$0.721808\pi$
$128$	10.8104	−	3.33691i	0.955515	−	0.294944i
$129$	−2.78313	+	4.82053i	−0.245041	+	0.424424i
$130$	20.5478	−	7.31409i	1.80216	−	0.641489i
$131$	−1.25389	+	8.31905i	−0.109553	+	0.726839i	0.864850	+	0.502031i	$0.167414\pi$
$131$	−1.25389	+	8.31905i	−0.109553	+	0.726839i	−0.974403	+	0.224808i	$0.927825\pi$
$132$	−2.71846	+	2.99367i	−0.236612	+	0.260566i
$133$	15.9833	+	0.580120i	1.38592	+	0.0503027i
$134$	10.4210	+	0.333888i	0.900240	+	0.0288435i
$135$	−0.774171	−	10.3306i	−0.0666301	−	0.889116i
$136$	−9.28987	−	16.9119i	−0.796600	−	1.45019i
$137$	0.705751	+	1.79822i	0.0602964	+	0.153633i	0.957847	−	0.287279i	$-0.0927506\pi$
$137$	0.705751	+	1.79822i	0.0602964	+	0.153633i	−0.897551	+	0.440911i	$0.854655\pi$
$138$	0.271037	+	6.33307i	0.0230722	+	0.539107i
$139$	−11.4772	+	9.15277i	−0.973484	+	0.776328i	−0.974665	−	0.223672i	$-0.928196\pi$
$139$	−11.4772	+	9.15277i	−0.973484	+	0.776328i	0.00118037	+	0.999999i	$0.499624\pi$
$140$	15.3771	−	0.758126i	1.29960	−	0.0640734i
$141$	−2.41100	−	1.92271i	−0.203043	−	0.161921i
$142$	1.10906	−	1.51974i	0.0930705	−	0.127534i
$143$	−1.25854	+	16.7941i	−0.105245	+	1.40439i
$144$	−6.64472	−	7.97456i	−0.553726	−	0.664547i
$145$	1.81957	−	1.68831i	0.151107	−	0.140207i
$146$	11.6184	+	3.04636i	0.961547	+	0.252118i
$147$	3.67499	−	2.51765i	0.303108	−	0.207652i
$148$	−2.87047	+	5.09748i	−0.235951	+	0.419011i
$149$	−8.05512	−	8.68135i	−0.659901	−	0.711204i	0.311074	−	0.950386i	$-0.399311\pi$
$149$	−8.05512	−	8.68135i	−0.659901	−	0.711204i	−0.970975	+	0.239182i	$0.923121\pi$
$150$	−0.332537	+	3.10096i	−0.0271516	+	0.253192i
$151$	0.0990382	−	1.32157i	0.00805961	−	0.107548i	−0.991723	−	0.128395i	$-0.959017\pi$
$151$	0.0990382	−	1.32157i	0.00805961	−	0.107548i	0.999783	+	0.0208473i	$0.00663640\pi$
$152$	7.08900	+	15.5593i	0.574994	+	1.26202i
$153$	−11.0377	+	13.8409i	−0.892348	+	1.11897i
$154$	−4.27119	+	11.0940i	−0.344182	+	0.893983i
$155$	2.24670	−	1.79168i	0.180459	−	0.143911i
$156$	6.59313	+	1.43050i	0.527873	+	0.114532i
$157$	−5.35108	+	2.10014i	−0.427063	+	0.167610i	−0.569131	−	0.822247i	$-0.692720\pi$
$157$	−5.35108	+	2.10014i	−0.427063	+	0.167610i	0.142068	+	0.989857i	$0.454625\pi$
$158$	6.22566	+	3.86536i	0.495287	+	0.307511i
$159$	−0.430282	−	5.74171i	−0.0341236	−	0.455347i
$160$	8.07863	+	14.3397i	0.638672	+	1.13365i
$161$	7.47109	+	17.0717i	0.588804	+	1.34544i
$162$	−3.61005	+	6.92026i	−0.283632	+	0.543707i
$163$	2.50210	−	16.6003i	0.195979	−	1.30024i	−0.647081	−	0.762421i	$-0.724011\pi$
$163$	2.50210	−	16.6003i	0.195979	−	1.30024i	0.843061	−	0.537818i	$-0.180751\pi$
$164$	13.8604	−	1.18854i	1.08231	−	0.0928096i
$165$	−5.09460	−	2.94137i	−0.396614	−	0.228985i
$166$	−6.55578	+	1.79441i	−0.508827	+	0.139273i
$167$	−15.3464	−	7.39045i	−1.18754	−	0.571890i	−0.267443	−	0.963574i	$-0.586179\pi$
$167$	−15.3464	−	7.39045i	−1.18754	−	0.571890i	−0.920100	+	0.391683i	$0.871893\pi$
$168$	4.16465	+	2.30970i	0.321310	+	0.178197i
$169$	13.6023	−	6.55051i	1.04633	−	0.503885i
$170$	21.1779	−	18.4239i	1.62427	−	1.41305i
$171$	10.6699	−	11.4995i	0.815951	−	0.879386i
$172$	−16.6599	+	5.33556i	−1.27031	+	0.406833i
$173$	−9.03398	+	13.2504i	−0.686841	+	1.00741i	0.311524	+	0.950238i	$0.399161\pi$
$173$	−9.03398	+	13.2504i	−0.686841	+	1.00741i	−0.998364	+	0.0571717i	$0.981792\pi$
$174$	0.753631	−	0.146792i	0.0571326	−	0.0111282i
$175$	2.38289	+	8.85336i	0.180129	+	0.669251i
$176$	−12.6498	+	1.22175i	−0.953513	+	0.0920929i
$177$	2.74512	+	4.75469i	0.206336	+	0.357384i
$178$	10.9238	−	11.0417i	0.818770	−	0.827613i
$179$	−11.7702	−	17.2637i	−0.879747	−	1.29035i	−0.956031	−	0.293266i	$-0.905258\pi$
$179$	−11.7702	−	17.2637i	−0.879747	−	1.29035i	0.0762836	−	0.997086i	$-0.475695\pi$
$180$	9.28767	−	11.9065i	0.692262	−	0.887461i
$181$	14.1848	+	3.23758i	1.05435	+	0.240648i	0.714357	−	0.699782i	$-0.246719\pi$
$181$	14.1848	+	3.23758i	1.05435	+	0.240648i	0.339990	+	0.940429i	$0.389576\pi$
$182$	19.5923	−	3.08326i	1.45228	−	0.228546i
$183$	−0.310664	−	1.36111i	−0.0229650	−	0.100616i
$184$	−12.7496	+	15.3074i	−0.939914	+	1.12848i
$185$	−8.13244	−	2.50853i	−0.597909	−	0.184431i
$186$	0.882741	−	0.104265i	0.0647257	−	0.00764512i
$187$	6.38868	+	20.7116i	0.467186	+	1.51458i
$188$	−1.54732	−	9.56730i	−0.112850	−	0.697767i
$189$	1.04426	−	9.36232i	0.0759587	−	0.681009i
$190$	−19.9337	+	14.8778i	−1.44614	+	1.07935i
$191$	−7.28809	+	18.5697i	−0.527348	+	1.34366i	0.380663	+	0.924714i	$0.375696\pi$
$191$	−7.28809	+	18.5697i	−0.527348	+	1.34366i	−0.908011	+	0.418946i	$0.862400\pi$
$192$	−0.216678	+	5.08644i	−0.0156374	+	0.367082i
$193$	−15.8384	+	2.38726i	−1.14007	+	0.171839i	−0.691822	−	0.722068i	$-0.743192\pi$
$193$	−15.8384	+	2.38726i	−1.14007	+	0.171839i	−0.448253	+	0.893907i	$0.647954\pi$
$194$	10.9368	−	5.85565i	0.785218	−	0.420411i
$195$			9.81461i			0.702839i
$196$	13.8696	+	1.90669i	0.990682	+	0.136192i
$197$			20.2766i			1.44465i	0.691555	+	0.722324i	$0.256926\pi$
$197$			20.2766i			1.44465i	−0.691555	+	0.722324i	$0.743074\pi$
$198$	5.50359	+	10.2793i	0.391123	+	0.730516i
$199$	5.56081	−	0.838157i	0.394195	−	0.0594154i	0.0510461	−	0.998696i	$-0.483744\pi$
$199$	5.56081	−	0.838157i	0.394195	−	0.0594154i	0.343149	+	0.939281i	$0.388506\pi$
$200$	−7.32525	+	6.51224i	−0.517974	+	0.460485i
$201$	−1.71410	+	4.36744i	−0.120903	+	0.308056i
$202$	1.79673	+	2.40731i	0.126417	+	0.169378i
$203$	1.90984	−	1.20302i	0.134044	−	0.0844353i
$204$	8.57140	−	1.38625i	0.600118	−	0.0970572i
$205$	5.96512	+	19.3384i	0.416622	+	1.35066i
$206$	0.689475	+	5.83729i	0.0480380	+	0.406704i
$207$	17.4656	+	5.38742i	1.21394	+	0.374451i
$208$	12.3175	+	17.2579i	0.854068	+	1.19662i
$209$	−4.27378	−	18.7247i	−0.295624	−	1.29521i
$210$	−1.99903	+	6.63327i	−0.137946	+	0.457739i
$211$	0.909047	+	0.207484i	0.0625814	+	0.0142838i	0.253697	−	0.967284i	$-0.418353\pi$
$211$	0.909047	+	0.207484i	0.0625814	+	0.0142838i	−0.191116	+	0.981568i	$0.561211\pi$
$212$	11.1297	−	14.2680i	0.764391	−	0.979928i
$213$	0.476912	+	0.699501i	0.0326774	+	0.0479290i
$214$	−10.3869	−	10.2759i	−0.710034	−	0.702447i
$215$	−12.7244	−	22.0394i	−0.867799	−	1.50307i
$216$	9.45084	−	3.47891i	0.643048	−	0.236710i
$217$	2.30892	−	1.22361i	0.156740	−	0.0830643i
$218$	−3.40836	−	17.4986i	−0.230843	−	1.18515i
$219$	−3.04469	+	4.46574i	−0.205741	+	0.301767i
$220$	−5.63891	−	17.6071i	−0.380175	−	1.18707i
$221$	24.5959	−	26.5081i	1.65450	−	1.78313i
$222$	−1.72784	−	1.98611i	−0.115965	−	0.133299i
$223$	−7.10847	+	3.42326i	−0.476019	+	0.229238i	−0.656480	−	0.754344i	$-0.727955\pi$
$223$	−7.10847	+	3.42326i	−0.476019	+	0.229238i	0.180461	+	0.983582i	$0.442241\pi$
$224$	4.80981	+	14.1727i	0.321369	+	0.946954i
$225$	8.10207	+	3.90175i	0.540138	+	0.260117i
$226$	6.23172	+	22.7672i	0.414528	+	1.51445i
$227$	7.60166	+	4.38882i	0.504540	+	0.291296i	0.730586	−	0.682820i	$-0.239247\pi$
$227$	7.60166	+	4.38882i	0.504540	+	0.291296i	−0.226046	+	0.974117i	$0.572580\pi$
$228$	−7.66583	+	0.657355i	−0.507682	+	0.0435344i
$229$	1.82259	−	12.0921i	0.120440	−	0.799069i	−0.844301	−	0.535869i	$-0.819984\pi$
$229$	1.82259	−	12.0921i	0.120440	−	0.799069i	0.964741	−	0.263200i	$-0.0847779\pi$
$230$	−25.6951	−	13.4042i	−1.69428	−	0.883845i
$231$	−4.05861	−	3.48481i	−0.267037	−	0.229284i
$232$	2.06356	+	1.25070i	0.135480	+	0.0821128i
$233$	−1.28959	−	17.2084i	−0.0844841	−	1.12736i	−0.864847	−	0.502035i	$-0.832585\pi$
$233$	−1.28959	−	17.2084i	−0.0844841	−	1.12736i	0.780363	−	0.625326i	$-0.215034\pi$
$234$	10.2610	−	16.5267i	0.670785	−	1.08039i
$235$	13.1244	−	5.15094i	0.856141	−	0.336011i
$236$	−3.65857	+	16.8622i	−0.238153	+	1.09764i
$237$	−2.57812	+	2.05598i	−0.167467	+	0.133550i
$238$	22.0224	−	12.9060i	1.42750	−	0.836571i
$239$	10.4519	−	13.1062i	0.676075	−	0.847771i	−0.318911	−	0.947785i	$-0.603317\pi$
$239$	10.4519	−	13.1062i	0.676075	−	0.847771i	0.994986	+	0.100013i	$0.0318886\pi$
$240$	−7.29815	+	1.26092i	−0.471094	+	0.0813923i
$241$	0.513499	−	6.85217i	0.0330774	−	0.441387i	−0.955937	−	0.293570i	$-0.905156\pi$
$241$	0.513499	−	6.85217i	0.0330774	−	0.441387i	0.989015	−	0.147816i	$-0.0472245\pi$
$242$	−1.27349	−	0.136565i	−0.0818629	−	0.00877872i
$243$	−9.65438	−	10.4049i	−0.619329	−	0.667478i
$244$	2.15288	−	3.82317i	0.137824	−	0.244753i
$245$	1.56751	+	20.3063i	0.100145	+	1.29732i
$246$	−1.58769	+	6.05523i	−0.101227	+	0.386067i
$247$	−23.4893	+	21.7949i	−1.49459	+	1.38677i
$248$	2.27411	+	1.62243i	0.144406	+	0.103024i
$249$	0.228565	−	3.04999i	0.0144847	−	0.193285i
$250$	5.10082	+	3.72242i	0.322604	+	0.235427i
$251$	4.09859	+	3.26852i	0.258701	+	0.206307i	0.744248	−	0.667904i	$-0.232808\pi$
$251$	4.09859	+	3.26852i	0.258701	+	0.206307i	−0.485547	+	0.874210i	$0.661380\pi$
$252$	10.3011	−	9.07975i	0.648911	−	0.571970i
$253$	17.4957	−	13.9523i	1.09994	−	0.877176i
$254$	7.81793	−	0.334584i	0.490540	−	0.0209937i
$255$	4.61476	+	11.7582i	0.288987	+	0.736328i
$256$	−11.2505	+	11.3765i	−0.703158	+	0.711033i
$257$	0.933247	+	12.4533i	0.0582143	+	0.776816i	0.947559	+	0.319580i	$0.103542\pi$
$257$	0.933247	+	12.4533i	0.0582143	+	0.776816i	−0.889345	+	0.457237i	$0.848839\pi$
$258$	0.252085	−	7.86786i	0.0156941	−	0.489831i
$259$	−6.84620	−	3.60852i	−0.425402	−	0.224222i
$260$	−20.7358	+	22.8351i	−1.28598	+	1.41617i
$261$	0.329960	−	2.18914i	0.0204240	−	0.135505i
$262$	−3.98985	−	11.2089i	−0.246494	−	0.692486i
$263$	10.6284	−	18.4090i	0.655378	−	1.13515i	−0.326421	−	0.945224i	$-0.605843\pi$
$263$	10.6284	−	18.4090i	0.655378	−	1.13515i	0.981799	−	0.189923i	$-0.0608239\pi$
$264$	1.39093	−	5.54703i	0.0856057	−	0.341396i
$265$	23.7176	+	11.4218i	1.45696	+	0.701636i
$266$	−20.3145	+	9.94594i	−1.24556	+	0.609825i
$267$	3.03255	+	6.29716i	0.185589	+	0.385380i
$268$	−13.2154	+	6.54001i	−0.807260	+	0.399495i
$269$	−14.9005	+	16.0589i	−0.908498	+	0.979128i	−0.999861	−	0.0166897i	$-0.994687\pi$
$269$	−14.9005	+	16.0589i	−0.908498	+	0.979128i	0.0913628	+	0.995818i	$0.470878\pi$
$270$	7.86113	+	12.3630i	0.478413	+	0.752389i
$271$	−7.34486	−	5.00764i	−0.446168	−	0.304192i	0.319314	−	0.947649i	$-0.396547\pi$
$271$	−7.34486	−	5.00764i	−0.446168	−	0.304192i	−0.765483	+	0.643456i	$0.777500\pi$
$272$	22.8714	+	14.8839i	1.38678	+	0.902471i
$273$	−1.64940	+	8.77109i	−0.0998264	+	0.530851i
$274$	−2.08026	−	1.77085i	−0.125673	−	0.106981i
$275$	9.53489	−	5.50497i	0.574975	−	0.331962i
$276$	−4.56539	−	7.71490i	−0.274804	−	0.464382i
$277$	−8.79473	−	12.8995i	−0.528424	−	0.775055i	0.465509	−	0.885043i	$-0.345871\pi$
$277$	−8.79473	−	12.8995i	−0.528424	−	0.775055i	−0.993933	+	0.109988i	$0.964919\pi$
$278$	8.19964	−	19.0726i	0.491782	−	1.14390i
$279$	0.570322	−	2.49875i	0.0341443	−	0.149596i
$280$	−18.6655	+	11.2098i	−1.11548	+	0.669912i
$281$	3.45910	+	15.1553i	0.206353	+	0.904090i	0.966970	+	0.254890i	$0.0820391\pi$
$281$	3.45910	+	15.1553i	0.206353	+	0.904090i	−0.760618	+	0.649200i	$0.775104\pi$
$282$	4.28939	+	0.787758i	0.255430	+	0.0469103i
$283$	1.00678	−	3.26389i	0.0598467	−	0.194018i	−0.920713	−	0.390241i	$-0.872392\pi$
$283$	1.00678	−	3.26389i	0.0598467	−	0.194018i	0.980559	+	0.196223i	$0.0628677\pi$
$284$	−0.368271	+	2.63508i	−0.0218529	+	0.156363i
$285$	−3.29916	−	10.6956i	−0.195426	−	0.633554i
$286$	−9.64134	−	21.7783i	−0.570104	−	1.28778i
$287$	2.08095	+	18.2848i	0.122835	+	1.07932i
$288$	13.6076	+	5.50686i	0.801834	+	0.324495i
$289$	10.7920	−	27.4975i	0.634821	−	1.61750i
$290$	−1.14158	+	3.31953i	−0.0670358	+	0.194929i
$291$	0.832023	+	5.52012i	0.0487741	+	0.323595i
$292$	−16.5189	+	3.95749i	−0.966695	+	0.231595i
$293$			11.3752i			0.664544i	0.943184	+	0.332272i	$0.107815\pi$
$293$			11.3752i			0.664544i	−0.943184	+	0.332272i	$0.892185\pi$
$294$	−2.90125	+	5.59205i	−0.169204	+	0.326135i
$295$	−25.1013			−1.46145
$296$	0.176098	−	8.27145i	0.0102355	−	0.480768i
$297$	−11.1861	+	1.68604i	−0.649086	+	0.0978340i
$298$	15.8378	+	5.44659i	0.917460	+	0.315512i
$299$	−34.7538	−	13.6399i	−2.00986	−	0.788814i
$300$	−1.65537	−	4.08813i	−0.0955728	−	0.236028i
$301$	−7.66769	−	21.8345i	−0.441958	−	1.25852i
$302$	0.758704	+	1.71379i	0.0436585	+	0.0986178i
$303$	−1.29167	+	0.398427i	−0.0742044	+	0.0228890i
$304$	−19.2245	−	14.6666i	−1.10260	−	0.841186i
$305$	6.09942	+	1.88142i	0.349252	+	0.107730i
$306$	4.52230	−	24.6242i	0.258523	−	1.40767i
$307$	6.04354	−	1.37940i	0.344923	−	0.0787264i	−0.0465502	−	0.998916i	$-0.514823\pi$
$307$	6.04354	−	1.37940i	0.344923	−	0.0787264i	0.391473	+	0.920190i	$0.371966\pi$
$308$	−2.08038	−	16.6827i	−0.118541	−	0.950587i
$309$	−2.57867	−	0.588564i	−0.146695	−	0.0334823i
$310$	−1.60510	+	3.73352i	−0.0911638	+	0.212050i
$311$	−8.72802	+	5.95066i	−0.494921	+	0.337431i	−0.784922	−	0.619595i	$-0.787297\pi$
$311$	−8.72802	+	5.95066i	−0.494921	+	0.337431i	0.290001	+	0.957026i	$0.406344\pi$
$312$	−9.17495	+	2.61757i	−0.519429	+	0.148191i
$313$	−7.53272	−	13.0471i	−0.425775	−	0.737463i	0.570718	−	0.821146i	$-0.306665\pi$
$313$	−7.53272	−	13.0471i	−0.425775	−	0.737463i	−0.996492	+	0.0836831i	$0.973332\pi$
$314$	5.26962	−	6.19035i	0.297382	−	0.349342i
$315$	16.0860	+	11.8442i	0.906346	+	0.667346i
$316$	−10.3421	−	0.663400i	−0.581790	−	0.0373192i
$317$	13.5531	−	19.8787i	0.761216	−	1.11650i	−0.228513	−	0.973541i	$-0.573386\pi$
$317$	13.5531	−	19.8787i	0.761216	−	1.11650i	0.989729	−	0.142957i	$-0.0456612\pi$
$318$	4.36919	+	6.87131i	0.245012	+	0.385324i
$319$	−1.98694	−	1.84361i	−0.111247	−	0.103223i
$320$	−19.6442	−	12.4855i	−1.09814	−	0.697960i
$321$	5.92371	−	2.85271i	0.330629	−	0.159223i
$322$	−20.7104	−	16.2972i	−1.15415	−	0.908208i
$323$	−17.8931	+	37.1555i	−0.995600	+	2.06739i
$324$	−0.118573	−	11.0377i	−0.00658740	−	0.613206i
$325$	−15.9078	−	9.18436i	−0.882405	−	0.509457i
$326$	7.96160	+	22.3669i	0.440952	+	1.23879i
$327$	7.93255	+	1.19564i	0.438671	+	0.0661190i
$328$	−16.4872	+	10.7339i	−0.910352	+	0.592683i
$329$	12.5946	−	2.39765i	0.694363	−	0.132187i
$330$	8.31518	+	0.266417i	0.457735	+	0.0146657i
$331$	−14.8390	+	1.11203i	−0.815626	+	0.0611227i	−0.476008	−	0.879441i	$-0.657917\pi$
$331$	−14.8390	+	1.11203i	−0.815626	+	0.0611227i	−0.339618	+	0.940564i	$0.610298\pi$
$332$	6.97567	−	6.61333i	0.382840	−	0.362954i
$333$	−7.06588	+	2.77315i	−0.387208	+	0.151968i
$334$	24.0666	−	1.02998i	1.31687	−	0.0563581i
$335$	−13.3743	−	16.7708i	−0.730715	−	0.916287i
$336$	−6.73410	−	0.0996397i	−0.367375	−	0.00543579i
$337$	21.8957	−	27.4564i	1.19274	−	1.49564i	0.368285	−	0.929713i	$-0.379945\pi$
$337$	21.8957	−	27.4564i	1.19274	−	1.49564i	0.824452	−	0.565932i	$-0.191483\pi$
$338$	−12.5862	+	17.2467i	−0.684596	+	0.938099i
$339$	−10.5922	−	0.793774i	−0.575288	−	0.0431119i
$340$	−14.1053	+	37.1070i	−0.764969	+	2.01241i
$341$	−2.13436	−	2.30029i	−0.115582	−	0.124568i
$342$	−5.62670	+	21.4595i	−0.304257	+	1.16040i
$343$	−2.01174	+	18.4107i	−0.108624	+	0.994083i
$344$	17.2093	−	17.7731i	0.927866	−	0.958260i
$345$	9.55991	−	8.87030i	0.514688	−	0.477561i
$346$	2.41824	−	22.5505i	0.130006	−	1.21232i
$347$	−19.1289	−	1.43351i	−1.02689	−	0.0769550i	−0.449384	−	0.893339i	$-0.648356\pi$
$347$	−19.1289	−	1.43351i	−1.02689	−	0.0769550i	−0.577510	+	0.816384i	$0.695975\pi$
$348$	−0.841610	+	0.686081i	−0.0451151	+	0.0367778i
$349$	1.12697	+	0.898725i	0.0603251	+	0.0481077i	0.653188	−	0.757196i	$-0.273431\pi$
$349$	1.12697	+	0.898725i	0.0603251	+	0.0481077i	−0.592863	+	0.805303i	$0.702002\pi$
$350$	−8.88071	−	9.44739i	−0.474694	−	0.504984i
$351$	11.7674	+	14.7559i	0.628099	+	0.787611i
$352$	14.9557	−	9.96726i	0.797141	−	0.531257i
$353$	4.51914	+	11.5146i	0.240530	+	0.612860i	0.999257	−	0.0385489i	$-0.0122735\pi$
$353$	4.51914	+	11.5146i	0.240530	+	0.612860i	−0.758727	+	0.651409i	$0.774178\pi$
$354$	−6.59637	−	4.09552i	−0.350593	−	0.217675i
$355$	−3.85985	+	0.289256i	−0.204860	+	0.0153521i
$356$	−6.24869	+	21.0583i	−0.331180	+	1.11609i
$357$	2.14807	+	11.2836i	0.113688	+	0.597191i
$358$	26.1986	+	13.6668i	1.38464	+	0.722315i
$359$	1.26301	+	0.190367i	0.0666589	+	0.0100472i	0.182287	−	0.983245i	$-0.441650\pi$
$359$	1.26301	+	0.190367i	0.0666589	+	0.0100472i	−0.115628	+	0.993293i	$0.536888\pi$
$360$	−3.63161	+	21.0443i	−0.191403	+	1.10913i
$361$	8.77152	−	15.1927i	0.461659	−	0.799617i
$362$	−19.8462	+	5.43218i	−1.04309	+	0.285509i
$363$	0.250066	−	0.519266i	0.0131250	−	0.0272544i
$364$	−22.3687	+	16.9224i	−1.17244	+	0.886974i
$365$	−10.7217	−	22.2639i	−0.561202	−	1.16535i
$366$	1.29590	+	1.48960i	0.0677376	+	0.0778627i
$367$	16.2844	+	15.1098i	0.850041	+	0.788723i	0.979199	−	0.202901i	$-0.0650370\pi$
$367$	16.2844	+	15.1098i	0.850041	+	0.788723i	−0.129158	+	0.991624i	$0.541227\pi$
$368$	5.67765	−	27.5953i	0.295968	−	1.43851i
$369$	14.9136	+	10.1679i	0.776369	+	0.529319i
$370$	11.8137	−	2.30107i	0.614165	−	0.119627i
$371$	19.2764	+	14.1933i	1.00078	+	0.736879i
$372$	−1.03097	+	0.719245i	−0.0534532	+	0.0372911i
$373$	−13.9158	+	8.03427i	−0.720531	+	0.415999i	−0.814948	−	0.579534i	$-0.803235\pi$
$373$	−13.9158	+	8.03427i	−0.720531	+	0.415999i	0.0944170	+	0.995533i	$0.469901\pi$
$374$	−21.7906	−	21.5578i	−1.12677	−	1.11473i
$375$	−2.34778	+	1.60069i	−0.121239	+	0.0826593i
$376$	8.31554	+	10.8953i	0.428841	+	0.561880i
$377$	−1.00627	+	4.40877i	−0.0518257	+	0.227063i
$378$	4.94763	+	12.3696i	0.254479	+	0.636226i
$379$	35.3013	−	8.05729i	1.81331	−	0.413875i	0.824846	−	0.565358i	$-0.191262\pi$
$379$	35.3013	−	8.05729i	1.81331	−	0.413875i	0.988460	+	0.151483i	$0.0484048\pi$
$380$	14.9213	−	31.8552i	0.765444	−	1.63414i
$381$	−1.03789	+	3.36477i	−0.0531730	+	0.172383i
$382$	−3.30924	−	28.0170i	−0.169316	−	1.43347i
$383$	15.8388	−	4.88561i	0.809323	−	0.249643i	0.137640	−	0.990482i	$-0.456048\pi$
$383$	15.8388	−	4.88561i	0.809323	−	0.249643i	0.671682	+	0.740839i	$0.265572\pi$
$384$	−3.12518	−	6.48622i	−0.159481	−	0.330998i
$385$	23.0759	−	8.10363i	1.17606	−	0.412999i
$386$	18.1532	−	13.5489i	0.923972	−	0.689619i
$387$	−21.1289	−	8.29249i	−1.07404	−	0.421531i
$388$	−9.72682	+	14.6012i	−0.493805	+	0.741263i
$389$	3.65238	+	24.2320i	0.185183	+	1.22861i	0.867456	+	0.497513i	$0.165753\pi$
$389$	3.65238	+	24.2320i	0.185183	+	1.22861i	−0.682273	+	0.731097i	$0.739009\pi$
$390$	−6.55148	−	12.2365i	−0.331747	−	0.619618i
$391$	−48.0495			−2.42997
$392$	−18.5648	+	6.88107i	−0.937663	+	0.347547i
$393$	5.35389			0.270068
$394$	−13.5351	−	25.2801i	−0.681889	−	1.27359i
$395$	−2.24700	−	14.9079i	−0.113059	−	0.750097i
$396$	−13.7233	−	9.14202i	−0.689623	−	0.459404i
$397$	26.1090	+	10.2470i	1.31037	+	0.514284i	0.914710	−	0.404111i	$-0.132419\pi$
$397$	26.1090	+	10.2470i	1.31037	+	0.514284i	0.395665	+	0.918395i	$0.370514\pi$
$398$	−6.37351	+	4.75695i	−0.319475	+	0.238444i
$399$	−1.15092	−	10.1129i	−0.0576182	−	0.506277i
$400$	4.78576	−	13.0090i	0.239288	−	0.650450i
$401$	−20.6353	+	6.36515i	−1.03048	+	0.317860i	−0.763476	−	0.645836i	$-0.776509\pi$
$401$	−20.6353	+	6.36515i	−1.03048	+	0.317860i	−0.267001	+	0.963696i	$0.586033\pi$
$402$	−0.778305	−	6.58936i	−0.0388183	−	0.328647i
$403$	−1.54313	+	5.00272i	−0.0768689	+	0.249203i
$404$	−3.84703	−	1.80198i	−0.191397	−	0.0896519i
$405$	15.6556	−	3.57328i	0.777931	−	0.177558i
$406$	−1.57807	+	2.77474i	−0.0783182	+	0.137708i
$407$	−2.06797	+	9.06038i	−0.102506	+	0.449106i
$408$	−9.76112	+	7.44994i	−0.483248	+	0.368827i
$409$	4.60603	−	3.14034i	0.227753	−	0.155280i	−0.444067	−	0.895993i	$-0.646465\pi$
$409$	4.60603	−	3.14034i	0.227753	−	0.155280i	0.671821	+	0.740714i	$0.265513\pi$
$410$	−20.3459	−	20.1286i	−1.00481	−	0.994078i
$411$	1.06464	−	0.614669i	0.0525147	−	0.0303194i
$412$	−4.75614	−	6.81747i	−0.234318	−	0.335873i
$413$	−22.4324	−	4.21841i	−1.10383	−	0.207575i
$414$	−25.3716	+	4.94187i	−1.24695	+	0.242879i
$415$	11.5538	+	7.87725i	0.567154	+	0.386679i
$416$	−26.8771	−	13.2943i	−1.31776	−	0.651805i
$417$	6.84819	+	6.35419i	0.335357	+	0.311166i
$418$	17.8275	+	20.4923i	0.871973	+	1.00231i
$419$	−14.3133	−	29.7218i	−0.699248	−	1.45200i	−0.883165	−	0.469062i	$-0.844592\pi$
$419$	−14.3133	−	29.7218i	−0.699248	−	1.45200i	0.183917	−	0.982942i	$-0.441122\pi$
$420$	−1.93555	−	9.60450i	−0.0944453	−	0.468651i
$421$	7.75864	−	16.1110i	0.378133	−	0.785201i	−0.621865	−	0.783124i	$-0.713625\pi$
$421$	7.75864	−	16.1110i	0.378133	−	0.785201i	0.999998	−	0.00207646i	$-0.000660957\pi$
$422$	−1.27186	+	0.348127i	−0.0619134	+	0.0169466i
$423$	6.28748	−	10.8902i	0.305708	−	0.529501i
$424$	−4.35187	+	25.2181i	−0.211345	+	1.22470i
$425$	−23.3764	−	3.52343i	−1.13392	−	0.170912i
$426$	−1.06153	−	0.553760i	−0.0514312	−	0.0268298i
$427$	5.13473	+	2.70643i	0.248487	+	0.130973i
$428$	19.8094	+	5.87811i	0.957523	+	0.284129i
$429$	10.6874	−	0.800913i	0.515995	−	0.0386685i
$430$	30.5761	+	18.9840i	1.47451	+	0.915488i
$431$	7.57189	+	19.2929i	0.364725	+	0.929305i	0.988975	+	0.148080i	$0.0473094\pi$
$431$	7.57189	+	19.2929i	0.364725	+	0.929305i	−0.624250	+	0.781225i	$0.714595\pi$
$432$	−9.46069	+	10.6460i	−0.455177	+	0.512207i
$433$	20.6892	+	25.9435i	0.994261	+	1.24676i	0.968994	+	0.247084i	$0.0794722\pi$
$433$	20.6892	+	25.9435i	0.994261	+	1.24676i	0.0252672	+	0.999681i	$0.491956\pi$
$434$	−2.06188	+	3.06681i	−0.0989736	+	0.147212i
$435$	−1.23499	−	0.984875i	−0.0592134	−	0.0472212i
$436$	15.9301	+	19.5413i	0.762914	+	0.935861i
$437$	42.4585	+	3.18183i	2.03107	+	0.152207i
$438$	0.815012	−	7.60011i	0.0389428	−	0.363147i
$439$	6.41147	−	5.94897i	0.306003	−	0.283929i	−0.512191	−	0.858871i	$-0.671166\pi$
$439$	6.41147	−	5.94897i	0.306003	−	0.283929i	0.818194	+	0.574943i	$0.194976\pi$
$440$	18.7835	+	18.1878i	0.895470	+	0.867068i
$441$	12.3852	+	13.2883i	0.589773	+	0.632774i
$442$	−12.9704	+	49.4676i	−0.616940	+	2.35293i
$443$	13.2655	+	14.2968i	0.630262	+	0.679261i	0.964759	−	0.263136i	$-0.0847568\pi$
$443$	13.2655	+	14.2968i	0.630262	+	0.679261i	−0.334497	+	0.942397i	$0.608566\pi$
$444$	3.47997	+	1.32283i	0.165152	+	0.0627786i
$445$	−31.8657	−	2.38800i	−1.51058	−	0.113202i
$446$	6.57746	−	9.01306i	0.311452	−	0.426781i
$447$	−4.69894	+	5.89229i	−0.222252	+	0.278696i
$448$	−15.4573	−	14.4593i	−0.730289	−	0.683138i
$449$	−1.48103	−	1.85716i	−0.0698943	−	0.0876446i	0.745655	−	0.666332i	$-0.232137\pi$
$449$	−1.48103	−	1.85716i	−0.0698943	−	0.0876446i	−0.815550	+	0.578687i	$0.803565\pi$
$450$	−12.7059	+	0.543774i	−0.598960	+	0.0256337i
$451$	20.5715	−	8.07371i	0.968673	−	0.380176i
$452$	−22.9671	−	24.2255i	−1.08028	−	1.13947i
$453$	−0.841025	+	0.0630261i	−0.0395148	+	0.00296122i
$454$	−12.4071	−	0.397521i	−0.582294	−	0.0186566i
$455$	−30.9582	−	26.5814i	−1.45134	−	1.24615i
$456$	9.11866	−	5.93669i	0.427020	−	0.278011i
$457$	17.3257	+	2.61144i	0.810464	+	0.122158i	0.541184	−	0.840904i	$-0.317976\pi$
$457$	17.3257	+	2.61144i	0.810464	+	0.122158i	0.269280	+	0.963062i	$0.413214\pi$
$458$	5.79943	+	16.2926i	0.270990	+	0.761303i
$459$	21.0359	+	12.1451i	0.981870	+	0.566883i
$460$	40.9832	−	0.440264i	1.91085	−	0.0205274i
$461$	−15.8243	+	32.8596i	−0.737013	+	1.53042i	0.107095	+	0.994249i	$0.465845\pi$
$461$	−15.8243	+	32.8596i	−0.737013	+	1.53042i	−0.844107	+	0.536174i	$0.819869\pi$
$462$	7.38631	+	1.63550i	0.343642	+	0.0760906i
$463$	−13.2399	+	6.37599i	−0.615310	+	0.296318i	−0.715459	−	0.698655i	$-0.753782\pi$
$463$	−13.2399	+	6.37599i	−0.615310	+	0.296318i	0.100149	+	0.994972i	$0.468068\pi$
$464$	−3.40764	−	0.181853i	−0.158196	−	0.00844230i
$465$	−1.34055	−	1.24385i	−0.0621667	−	0.0576822i
$466$	13.0948	+	20.5940i	0.606607	+	0.953996i
$467$	2.92811	−	4.29476i	0.135497	−	0.198738i	−0.752493	−	0.658600i	$-0.771149\pi$
$467$	2.92811	−	4.29476i	0.135497	−	0.198738i	0.887990	+	0.459862i	$0.152101\pi$
$468$	−1.76107	+	27.4544i	−0.0814056	+	1.26908i
$469$	−9.13385	−	17.2353i	−0.421762	−	0.795853i
$470$	−12.9246	+	15.1828i	−0.596167	+	0.700332i
$471$	1.82910	+	3.16810i	0.0842807	+	0.145978i
$472$	−6.69455	−	23.4653i	−0.308142	−	1.08008i
$473$	−22.9610	+	15.6545i	−1.05575	+	0.719797i
$474$	1.84188	−	4.28427i	0.0846003	−	0.196783i
$475$	20.4231	+	4.66143i	0.937074	+	0.213881i
$476$	−18.8416	+	30.7912i	−0.863606	+	1.41131i
$477$	22.8903	−	5.22457i	1.04808	−	0.239217i
$478$	−4.28226	+	23.3172i	−0.195866	+	1.06650i
$479$	13.2161	+	4.07664i	0.603861	+	0.186266i	0.581585	−	0.813485i	$-0.302433\pi$
$479$	13.2161	+	4.07664i	0.603861	+	0.186266i	0.0222757	+	0.999752i	$0.492909\pi$
$480$	8.25736	−	6.44376i	0.376895	−	0.294116i
$481$	14.8160	−	4.57014i	0.675552	−	0.208380i
$482$	3.93377	+	8.88578i	0.179178	+	0.404736i
$483$	10.0342	−	6.32058i	0.456571	−	0.287596i
$484$	1.67889	−	0.679819i	0.0763134	−	0.0309009i
$485$	−23.7586	−	9.32457i	−1.07882	−	0.423407i
$486$	18.9822	+	6.52795i	0.861052	+	0.296114i
$487$	15.9227	−	2.39996i	0.721526	−	0.108752i	0.221994	−	0.975048i	$-0.428744\pi$
$487$	15.9227	−	2.39996i	0.721526	−	0.108752i	0.499532	+	0.866296i	$0.333505\pi$
$488$	−0.132076	+	6.20368i	−0.00597879	+	0.280827i
$489$	−10.6835			−0.483124
$490$	−15.5092	−	24.2707i	−0.700635	−	1.09644i
$491$		−	15.5794i		−	0.703089i	−0.936171	−	0.351544i	$-0.885657\pi$
$491$		−	15.5794i		−	0.703089i	0.936171	−	0.351544i	$-0.114343\pi$
$492$	−2.06254	−	8.60924i	−0.0929867	−	0.388134i
$493$	0.867424	+	5.75498i	0.0390668	+	0.259191i
$494$	14.7369	−	42.8527i	0.663046	−	1.92803i
$495$	8.76395	−	22.3302i	0.393910	−	1.00367i
$496$	−3.91828	−	0.504756i	−0.175936	−	0.0226642i
$497$	−3.49807	−	0.390170i	−0.156910	−	0.0175015i
$498$	1.75098	+	3.95518i	0.0784631	+	0.177236i
$499$	6.14210	+	19.9122i	0.274958	+	0.891392i	0.982745	+	0.184966i	$0.0592175\pi$
$499$	6.14210	+	19.9122i	0.274958	+	0.891392i	−0.707787	+	0.706426i	$0.750306\pi$
$500$	−8.84431	−	1.23605i	−0.395529	−	0.0552780i
$501$	−3.19505	+	10.3581i	−0.142744	+	0.462765i
$502$	−7.29177	−	1.33915i	−0.325448	−	0.0597693i
$503$	−4.30226	−	18.8494i	−0.191828	−	0.840454i	−0.975626	−	0.219438i	$-0.929577\pi$
$503$	−4.30226	−	18.8494i	−0.191828	−	0.840454i	0.783798	−	0.621016i	$-0.213280\pi$
$504$	−6.78211	+	18.1965i	−0.302099	+	0.810538i
$505$	1.37519	−	6.02510i	0.0611951	−	0.268113i
$506$	−12.4994	+	29.0740i	−0.555667	+	1.29250i
$507$	−5.41221	−	7.93825i	−0.240365	−	0.352550i
$508$	−9.52374	+	5.63580i	−0.422548	+	0.250048i
$509$	−20.0491	+	11.5754i	−0.888662	+	0.513069i	−0.873504	−	0.486816i	$-0.838158\pi$
$509$	−20.0491	+	11.5754i	−0.888662	+	0.513069i	−0.0151571	+	0.999885i	$0.504825\pi$
$510$	−13.6024	−	11.5792i	−0.602324	−	0.512736i
$511$	−5.84019	−	21.6986i	−0.258355	−	0.959890i
$512$	6.43261	−	21.6938i	0.284284	−	0.958740i
$513$	−17.7839	−	12.1249i	−0.785179	−	0.535326i
$514$	−9.47641	−	14.9033i	−0.417987	−	0.657358i
$515$	8.22520	−	8.86466i	0.362446	−	0.390624i
$516$	4.93769	+	9.97761i	0.217370	+	0.439240i
$517$	−6.68003	−	13.8712i	−0.293788	−	0.610056i
$518$	10.9443	−	0.0710459i	0.480867	−	0.00312158i
$519$	9.19499	+	4.42808i	0.403615	+	0.194371i
$520$	10.6097	−	42.3115i	0.465266	−	1.85548i
$521$	10.4349	−	18.0738i	0.457163	−	0.791829i	−0.541647	−	0.840606i	$-0.682199\pi$
$521$	10.4349	−	18.0738i	0.457163	−	0.791829i	0.998810	+	0.0487770i	$0.0155324\pi$
$522$	1.04992	+	2.94959i	0.0459539	+	0.129100i
$523$	0.131124	−	0.869949i	0.00573364	−	0.0380402i	−0.985781	−	0.168035i	$-0.946258\pi$
$523$	0.131124	−	0.869949i	0.00573364	−	0.0380402i	0.991515	+	0.129995i	$0.0414960\pi$
$524$	12.4566	+	11.3115i	0.544168	+	0.494143i
$525$	5.34518	−	2.33921i	0.233283	−	0.102091i
$526$	−0.962679	+	30.0464i	−0.0419748	+	1.31008i
$527$	0.503518	+	6.71898i	0.0219336	+	0.292683i
$528$	1.96862	+	7.84430i	0.0856732	+	0.341379i
$529$	9.72123	+	24.7693i	0.422662	+	1.07693i
$530$	−37.1945	+	1.59182i	−1.61563	+	0.0691442i
$531$	−17.5036	+	13.9586i	−0.759591	+	0.605753i
$532$	18.6882	−	25.9606i	0.810238	−	1.12554i
$533$	−28.8258	−	22.9878i	−1.24858	−	0.995713i
$534$	−7.98437	−	5.82675i	−0.345518	−	0.252148i
$535$	−2.24638	+	29.9759i	−0.0971196	+	1.29597i
$536$	12.1108	−	16.9754i	0.523109	−	0.733227i
$537$	−9.74724	+	9.04412i	−0.420625	+	0.390283i
$538$	7.85763	−	29.9680i	0.338767	−	1.29201i
$539$	21.9842	−	3.36399i	0.946928	−	0.144897i
$540$	−18.0535	−	10.1662i	−0.776901	−	0.437485i
$541$	21.8089	+	23.5044i	0.937638	+	1.01053i	0.999922	+	0.0124754i	$0.00397115\pi$
$541$	21.8089	+	23.5044i	0.937638	+	1.01053i	−0.0622838	+	0.998058i	$0.519838\pi$
$542$	12.5000	+	1.34046i	0.536921	+	0.0575777i
$543$	0.691932	−	9.23319i	0.0296937	−	0.396234i
$544$	−38.4505	−	3.28952i	−1.64855	−	0.141037i
$545$	−22.8678	+	28.6753i	−0.979549	+	1.22832i
$546$	−3.79850	−	12.0365i	−0.162561	−	0.515113i
$547$	12.8401	−	10.2397i	0.549004	−	0.437816i	−0.309295	−	0.950966i	$-0.600093\pi$
$547$	12.8401	−	10.2397i	0.549004	−	0.437816i	0.858299	+	0.513150i	$0.171522\pi$
$548$	3.77567	+	0.819203i	0.161289	+	0.0349946i
$549$	5.29948	−	2.07989i	0.226176	−	0.0887677i
$550$	−8.21303	+	13.2281i	−0.350205	+	0.564050i
$551$	−0.385398	−	5.14278i	−0.0164185	−	0.219090i
$552$	10.8418	+	6.57113i	0.461459	+	0.279686i
$553$	0.497264	−	13.7004i	0.0211458	−	0.582602i
$554$	19.5756	+	10.2119i	0.831689	+	0.433862i
$555$	−0.807206	+	5.35546i	−0.0342640	+	0.227327i
$556$	2.50843	+	29.2525i	0.106381	+	1.24058i
$557$	4.03639	+	2.33041i	0.171027	+	0.0987427i	0.583070	−	0.812422i	$-0.301851\pi$
$557$	4.03639	+	2.33041i	0.171027	+	0.0987427i	−0.412043	+	0.911164i	$0.635185\pi$
$558$	0.956916	+	3.49604i	0.0405095	+	0.147999i
$559$	41.7724	+	20.1165i	1.76678	+	0.850838i
$560$	15.7886	−	26.4356i	0.667190	−	1.11711i
$561$	12.4273	−	5.98468i	0.524682	−	0.252673i
$562$	−14.4292	−	16.5860i	−0.608659	−	0.699639i
$563$	−2.64434	+	2.84992i	−0.111446	+	0.120110i	−0.786311	−	0.617831i	$-0.788011\pi$
$563$	−2.64434	+	2.84992i	−0.111446	+	0.120110i	0.674865	+	0.737941i	$0.264202\pi$
$564$	−5.87369	+	1.88113i	−0.247327	+	0.0792097i
$565$	27.3565	−	40.1246i	1.15090	−	1.68806i
$566$	0.923514	+	4.74134i	0.0388182	+	0.199293i
$567$	14.5915	−	0.562348i	0.612786	−	0.0236164i
$568$	−1.29983	−	3.53115i	−0.0545398	−	0.148164i
$569$	−10.3143	−	17.8648i	−0.432396	−	0.748933i	0.564683	−	0.825308i	$-0.308999\pi$
$569$	−10.3143	−	17.8648i	−0.432396	−	0.748933i	−0.997079	+	0.0763755i	$0.975665\pi$
$570$	11.2529	+	11.1326i	0.471330	+	0.466294i
$571$	3.87970	+	5.69048i	0.162360	+	0.238139i	0.898794	−	0.438370i	$-0.144444\pi$
$571$	3.87970	+	5.69048i	0.162360	+	0.238139i	−0.736434	+	0.676509i	$0.763492\pi$
$572$	26.5580	+	20.7165i	1.11044	+	0.866200i
$573$	12.3767	+	2.82491i	0.517045	+	0.118012i
$574$	−14.8000	−	21.4077i	−0.617739	−	0.893539i
$575$	5.43120	+	23.7956i	0.226497	+	0.992346i
$576$	−20.6414	+	2.21764i	−0.860057	+	0.0924017i
$577$	18.2922	+	5.64241i	0.761516	+	0.234897i	0.651103	−	0.758989i	$-0.274307\pi$
$577$	18.2922	+	5.64241i	0.761516	+	0.234897i	0.110413	+	0.993886i	$0.464783\pi$
$578$	4.90022	+	41.4867i	0.203822	+	1.72562i
$579$	3.00448	+	9.74029i	0.124862	+	0.404793i
$580$	−0.792589	−	4.90069i	−0.0329105	−	0.203490i
$581$	9.00155	+	8.98140i	0.373447	+	0.372611i
$582$	−4.72214	−	6.32687i	−0.195739	−	0.262257i
$583$	10.5021	−	26.7590i	0.434953	−	1.10824i
$584$	17.9534	−	15.9608i	0.742917	−	0.660462i
$585$	−39.5747	+	5.96492i	−1.63621	+	0.246619i
$586$	−7.59319	−	14.1821i	−0.313672	−	0.585857i
$587$		−	9.85717i		−	0.406849i	−0.979091	−	0.203425i	$-0.934793\pi$
$587$		−	9.85717i		−	0.406849i	0.979091	−	0.203425i	$-0.0652072\pi$
$588$	−0.115666	−	8.90860i	−0.00477000	−	0.367384i
$589$		−	5.97051i		−	0.246011i
$590$	31.2953	−	16.7557i	1.28841	−	0.689821i
$591$	12.7595	−	1.92319i	0.524857	−	0.0791095i
$592$	5.30183	+	10.4301i	0.217904	+	0.428673i
$593$	8.20121	−	20.8963i	0.336783	−	0.858110i	−0.657706	−	0.753275i	$-0.728473\pi$
$593$	8.20121	−	20.8963i	0.336783	−	0.858110i	0.994490	−	0.104835i	$-0.0334316\pi$
$594$	12.8210	−	9.56911i	0.526051	−	0.392625i
$595$	−49.5872	−	17.2890i	−2.03288	−	0.708780i
$596$	−23.3817	+	3.78153i	−0.957751	+	0.154897i
$597$	−1.05486	−	3.41978i	−0.0431726	−	0.139962i
$598$	52.4346	−	6.19334i	2.14421	−	0.253265i
$599$	4.40200	+	1.35784i	0.179861	+	0.0554797i	0.383377	−	0.923592i	$-0.374761\pi$
$599$	4.40200	+	1.35784i	0.179861	+	0.0554797i	−0.203517	+	0.979072i	$0.565237\pi$
$600$	4.79277	+	3.99192i	0.195664	+	0.162970i
$601$	7.94593	+	34.8134i	0.324121	+	1.42007i	0.830145	+	0.557548i	$0.188258\pi$
$601$	7.94593	+	34.8134i	0.324121	+	1.42007i	−0.506024	+	0.862520i	$0.668885\pi$
$602$	24.1348	+	22.1040i	0.983661	+	0.900893i
$603$	−18.6523	−	4.25726i	−0.759579	−	0.173369i
$604$	−2.08992	−	1.63024i	−0.0850377	−	0.0663335i
$605$	1.48436	+	2.17716i	0.0603479	+	0.0885141i
$606$	1.34444	−	1.35896i	0.0546142	−	0.0552041i
$607$	8.70708	+	15.0811i	0.353409	+	0.612123i	0.986844	−	0.161673i	$-0.0516890\pi$
$607$	8.70708	+	15.0811i	0.353409	+	0.612123i	−0.633435	+	0.773796i	$0.718356\pi$
$608$	33.7586	+	5.45294i	1.36909	+	0.221146i
$609$	−0.938172	−	1.08771i	−0.0380166	−	0.0440762i
$610$	−8.86041	+	1.72582i	−0.358748	+	0.0698766i
$611$	−14.4695	+	21.2229i	−0.585374	+	0.858586i
$612$	10.7990	+	33.7193i	0.436525	+	1.36302i
$613$	−6.91123	+	7.44853i	−0.279142	+	0.300843i	−0.857024	−	0.515277i	$-0.827689\pi$
$613$	−6.91123	+	7.44853i	−0.279142	+	0.300843i	0.577882	+	0.816120i	$0.303879\pi$
$614$	−6.61407	+	5.75399i	−0.266922	+	0.232212i
$615$	11.6034	−	5.58790i	0.467894	−	0.225326i
$616$	13.7299	+	19.4107i	0.553192	+	0.782078i
$617$	−16.8479	−	8.11350i	−0.678270	−	0.326637i	0.0628380	−	0.998024i	$-0.479985\pi$
$617$	−16.8479	−	8.11350i	−0.678270	−	0.326637i	−0.741108	+	0.671386i	$0.765699\pi$
$618$	3.60786	−	0.987524i	0.145130	−	0.0397240i
$619$	−34.4354	−	19.8813i	−1.38408	−	0.799096i	−0.391436	−	0.920205i	$-0.628022\pi$
$619$	−34.4354	−	19.8813i	−1.38408	−	0.799096i	−0.992639	+	0.121109i	$0.961355\pi$
$620$	−0.491033	−	5.72625i	−0.0197204	−	0.229972i
$621$	3.73773	−	24.7982i	0.149990	−	0.995117i
$622$	6.90954	−	13.2452i	0.277047	−	0.531085i
$623$	−28.0763	−	7.48932i	−1.12485	−	0.300053i
$624$	9.69168	−	9.38799i	0.387978	−	0.375820i
$625$	−2.26568	−	30.2333i	−0.0906270	−	1.20933i
$626$	18.1007	+	11.2383i	0.723450	+	0.449172i
$627$	−11.3776	+	4.46537i	−0.454377	+	0.178330i
$628$	−2.43775	+	11.2355i	−0.0972768	+	0.448344i
$629$	15.6012	−	12.4416i	0.622061	−	0.496077i
$630$	−27.9617	−	4.02910i	−1.11402	−	0.160523i
$631$	−19.3359	+	24.2464i	−0.769748	+	0.965234i	−0.999969	−	0.00790452i	$-0.997484\pi$
$631$	−19.3359	+	24.2464i	−0.769748	+	0.965234i	0.230220	+	0.973139i	$0.426055\pi$
$632$	13.3370	−	6.07651i	0.530517	−	0.241711i
$633$	0.0443432	−	0.591719i	0.00176248	−	0.0235187i
$634$	−3.62793	+	33.8309i	−0.144083	+	1.34360i
$635$	−10.9500	−	11.8013i	−0.434539	−	0.468321i
$636$	−10.0341	−	5.65035i	−0.397878	−	0.224051i
$637$	−23.1995	−	28.9578i	−0.919196	−	1.14735i
$638$	3.70790	+	0.972214i	0.146797	+	0.0384903i
$639$	−2.53070	+	2.34814i	−0.100113	+	0.0928911i
$640$	32.8260	+	2.45344i	1.29756	+	0.0969809i
$641$	0.121272	−	1.61826i	0.00478995	−	0.0639175i	−0.994297	−	0.106650i	$-0.965987\pi$
$641$	0.121272	−	1.61826i	0.00478995	−	0.0639175i	0.999087	+	0.0427330i	$0.0136065\pi$
$642$	−5.48120	+	7.51086i	−0.216326	+	0.296430i
$643$	6.29064	+	5.01662i	0.248079	+	0.197836i	0.739632	−	0.673011i	$-0.234999\pi$
$643$	6.29064	+	5.01662i	0.248079	+	0.197836i	−0.491554	+	0.870847i	$0.663571\pi$
$644$	36.6997	+	6.49401i	1.44617	+	0.255900i
$645$	−12.6619	+	10.0975i	−0.498563	+	0.397590i
$646$	−2.49370	−	58.2680i	−0.0981134	−	2.29253i
$647$	−0.861650	−	2.19545i	−0.0338749	−	0.0863120i	0.912935	−	0.408104i	$-0.133810\pi$
$647$	−0.861650	−	2.19545i	−0.0338749	−	0.0863120i	−0.946810	+	0.321792i	$0.895715\pi$
$648$	7.51576	+	13.6822i	0.295247	+	0.537489i
$649$	2.04837	+	27.3336i	0.0804055	+	1.07294i
$650$	25.9640	+	0.831880i	1.01839	+	0.0326290i
$651$	−0.988985	−	1.33689i	−0.0387614	−	0.0523968i
$652$	−24.8566	−	22.5716i	−0.973460	−	0.883971i
$653$	−7.37784	+	48.9488i	−0.288717	+	1.91551i	0.101584	+	0.994827i	$0.467609\pi$
$653$	−7.37784	+	48.9488i	−0.288717	+	1.91551i	−0.390302	+	0.920687i	$0.627629\pi$
$654$	−10.6881	+	3.80449i	−0.417938	+	0.148767i
$655$	−12.2389	+	21.1985i	−0.478215	+	0.828293i
$656$	13.3904	−	24.3882i	0.522807	−	0.952201i
$657$	−19.8573	−	9.56277i	−0.774707	−	0.373079i
$658$	−14.1020	+	11.3965i	−0.549752	+	0.444282i
$659$	2.22156	+	4.61311i	0.0865396	+	0.179701i	0.939747	−	0.341870i	$-0.111060\pi$
$659$	2.22156	+	4.61311i	0.0865396	+	0.179701i	−0.853208	+	0.521571i	$0.825346\pi$
$660$	−10.5449	+	5.21842i	−0.410459	+	0.203127i
$661$	−4.60162	+	4.95936i	−0.178982	+	0.192897i	−0.816170	−	0.577811i	$-0.803907\pi$
$661$	−4.60162	+	4.95936i	−0.178982	+	0.192897i	0.637188	+	0.770708i	$0.280097\pi$
$662$	17.7584	−	11.2918i	0.690199	−	0.438869i
$663$	−19.0137	−	12.9633i	−0.738431	−	0.503454i
$664$	−4.28244	+	12.9017i	−0.166191	+	0.500682i
$665$	42.6724	+	18.5609i	1.65477	+	0.719761i
$666$	6.95831	−	8.17410i	0.269629	−	0.316740i
$667$	5.20381	−	3.00442i	0.201492	−	0.116332i
$668$	−29.3178	+	17.3492i	−1.13434	+	0.671260i
$669$	2.82839	+	4.14849i	0.109352	+	0.160390i
$670$	27.8694	+	11.9815i	1.07669	+	0.462887i
$671$	1.55100	−	6.79539i	0.0598758	−	0.262333i
$672$	8.46232	−	4.37094i	0.326441	−	0.168613i
$673$	0.700701	+	3.06997i	0.0270100	+	0.118339i	0.986636	−	0.162941i	$-0.0520982\pi$
$673$	0.700701	+	3.06997i	0.0270100	+	0.118339i	−0.959626	+	0.281280i	$0.909241\pi$
$674$	−8.97096	+	48.8475i	−0.345548	+	1.88153i
$675$	3.63686	−	11.7904i	0.139983	−	0.453813i
$676$	4.17931	−	29.9041i	0.160743	−	1.15016i
$677$	2.26464	+	7.34177i	0.0870371	+	0.282167i	0.988619	−	0.150441i	$-0.0480694\pi$
$677$	2.26464	+	7.34177i	0.0870371	+	0.282167i	−0.901582	+	0.432609i	$0.857593\pi$
$678$	13.7358	−	6.08088i	0.527519	−	0.233535i
$679$	−19.6655	−	12.3259i	−0.754692	−	0.473026i
$680$	−7.18383	−	55.6792i	−0.275487	−	2.13520i
$681$	2.04077	−	5.19980i	0.0782025	−	0.199257i
$682$	4.19653	+	1.44318i	0.160694	+	0.0552621i
$683$	4.34686	+	28.8396i	0.166328	+	1.10352i	0.903743	+	0.428075i	$0.140808\pi$
$683$	4.34686	+	28.8396i	0.166328	+	1.10352i	−0.737415	+	0.675440i	$0.763954\pi$
$684$	−7.30958	−	30.5108i	−0.279489	−	1.16661i
$685$			5.62051i			0.214749i
$686$	−9.78140	−	24.2966i	−0.373456	−	0.927648i
$687$	−7.78212			−0.296906
$688$	−9.59199	+	33.6464i	−0.365691	+	1.28276i
$689$	−47.4236	+	7.14795i	−1.80669	+	0.272315i
$690$	−5.99778	+	17.4406i	−0.228332	+	0.663952i
$691$	0.891323	+	0.349819i	0.0339075	+	0.0133077i	0.382234	−	0.924065i	$-0.375155\pi$
$691$	0.891323	+	0.349819i	0.0339075	+	0.0133077i	−0.348327	+	0.937373i	$0.613250\pi$
$692$	12.0380	+	29.7293i	0.457616	+	1.13014i
$693$	11.5849	−	18.4831i	0.440073	−	0.702116i
$694$	24.8061	−	10.9818i	0.941626	−	0.416862i
$695$	−40.8140	+	12.5895i	−1.54816	+	0.477545i
$696$	0.591312	−	1.41717i	0.0224136	−	0.0537178i
$697$	−45.3429	−	13.9864i	−1.71749	−	0.529774i
$698$	−2.00498	−	0.368219i	−0.0758895	−	0.0139373i
$699$	−10.7065	+	2.44369i	−0.404957	+	0.0924288i
$700$	17.3785	+	5.85054i	0.656845	+	0.221130i
$701$	27.9980	+	6.39035i	1.05747	+	0.241360i	0.715688	−	0.698420i	$-0.246113\pi$
$701$	27.9980	+	6.39035i	1.05747	+	0.241360i	0.341780	+	0.939780i	$0.388970\pi$
$702$	−24.5211	−	10.5420i	−0.925488	−	0.397883i
$703$	−14.6098	+	9.96076i	−0.551017	+	0.375677i
$704$	−11.9928	+	22.4101i	−0.451995	+	0.844611i
$705$	−4.48618	−	7.77029i	−0.168959	−	0.292646i
$706$	−13.3206	−	11.3393i	−0.501326	−	0.426760i
$707$	2.24153	−	5.15338i	0.0843014	−	0.193813i
$708$	10.9580	+	0.702903i	0.411825	+	0.0264167i
$709$	5.52903	−	8.10960i	0.207647	−	0.304562i	−0.708261	−	0.705951i	$-0.750520\pi$
$709$	5.52903	−	8.10960i	0.207647	−	0.304562i	0.915908	+	0.401389i	$0.131472\pi$
$710$	4.61923	−	2.93718i	0.173357	−	0.110230i
$711$	−9.85704	−	9.14600i	−0.369668	−	0.343002i
$712$	−6.26627	−	30.4258i	−0.234838	−	1.14025i
$713$	6.26755	−	3.01829i	0.234721	−	0.113036i
$714$	−10.2102	−	12.6340i	−0.382107	−	0.472817i
$715$	−21.2602	+	44.1473i	−0.795087	+	1.65101i
$716$	−41.7863	+	0.448892i	−1.56163	+	0.0167759i
$717$	−9.23875	−	5.33399i	−0.345027	−	0.199202i
$718$	−1.70174	+	0.605743i	−0.0635084	+	0.0226061i
$719$	36.1207	+	5.44431i	1.34707	+	0.203039i	0.782658	−	0.622452i	$-0.213863\pi$
$719$	36.1207	+	5.44431i	1.34707	+	0.203039i	0.564416	+	0.825491i	$0.309102\pi$
$720$	−9.51985	−	28.6614i	−0.354784	−	1.06815i
$721$	8.84043	−	6.53985i	0.329235	−	0.243557i
$722$	−0.794487	+	24.7969i	−0.0295678	+	0.922845i
$723$	−4.36060	+	0.326781i	−0.162172	+	0.0121531i
$724$	21.1173	−	20.0204i	0.784820	−	0.744054i
$725$	2.75200	−	1.08008i	0.102207	−	0.0401132i
$726$	0.0348508	+	0.814326i	0.00129343	+	0.0302225i
$727$	12.4766	+	15.6452i	0.462733	+	0.580249i	0.957375	−	0.288848i	$-0.0932722\pi$
$727$	12.4766	+	15.6452i	0.462733	+	0.580249i	−0.494642	+	0.869097i	$0.664701\pi$
$728$	16.5923	−	36.0298i	0.614953	−	1.33535i
$729$	4.69157	−	5.88305i	0.173762	−	0.217891i
$730$	28.2291	+	20.6008i	1.04481	+	0.762469i
$731$	59.5032	+	4.45915i	2.20081	+	0.164928i
$732$	−2.61002	−	0.992135i	−0.0964690	−	0.0366704i
$733$	26.8756	+	28.9650i	0.992674	+	1.06985i	0.997557	+	0.0698596i	$0.0222551\pi$
$733$	26.8756	+	28.9650i	0.992674	+	1.06985i	−0.00488327	+	0.999988i	$0.501554\pi$
$734$	−30.3889	−	7.96800i	−1.12168	−	0.294104i
$735$	12.6295	−	2.91240i	0.465847	−	0.107425i
$736$	11.3419	+	38.1948i	0.418067	+	1.40788i
$737$	−17.1709	+	15.9322i	−0.632497	+	0.586872i
$738$	−25.3810	−	2.72178i	−0.934286	−	0.100190i
$739$	30.5870	+	2.29218i	1.12516	+	0.0843191i	0.624282	−	0.781199i	$-0.285392\pi$
$739$	30.5870	+	2.29218i	1.12516	+	0.0843191i	0.500878	+	0.865518i	$0.333011\pi$
$740$	−13.1929	+	10.7548i	−0.484979	+	0.395355i
$741$	15.9429	+	12.7140i	0.585676	+	0.467061i
$742$	−33.5074	−	4.82819i	−1.23010	−	0.177248i
$743$	−28.7072	−	35.9977i	−1.05316	−	1.32063i	−0.945207	−	0.326471i	$-0.894140\pi$
$743$	−28.7072	−	35.9977i	−1.05316	−	1.32063i	−0.107957	−	0.994156i	$-0.534431\pi$
$744$	0.805257	−	1.58492i	0.0295221	−	0.0581060i
$745$	−12.5885	−	32.0749i	−0.461206	−	1.17513i
$746$	11.9866	−	19.3059i	0.438859	−	0.706840i
$747$	12.4372	−	0.932037i	0.455052	−	0.0341014i
$748$	41.5580	+	12.3317i	1.51951	+	0.450890i
$749$	−7.04516	+	26.4112i	−0.257425	+	0.965046i
$750$	1.85862	−	3.56288i	0.0678673	−	0.130098i
$751$	22.3684	+	3.37150i	0.816235	+	0.123028i	0.543874	−	0.839167i	$-0.316957\pi$
$751$	22.3684	+	3.37150i	0.816235	+	0.123028i	0.272362	+	0.962195i	$0.412195\pi$
$752$	−17.6403	−	8.03296i	−0.643277	−	0.292932i
$753$	1.66805	−	2.88915i	0.0607871	−	0.105286i
$754$	−1.68838	−	6.16839i	−0.0614870	−	0.224639i
$755$	1.67303	−	3.47407i	0.0608876	−	0.126434i
$756$	−14.4255	−	12.1193i	−0.524652	−	0.440776i
$757$	9.12241	+	18.9429i	0.331560	+	0.688491i	0.998390	−	0.0567188i	$-0.0180638\pi$
$757$	9.12241	+	18.9429i	0.331560	+	0.688491i	−0.666831	+	0.745209i	$0.732350\pi$
$758$	−38.6338	+	33.6100i	−1.40324	+	1.22077i
$759$	−10.4393	−	9.68623i	−0.378922	−	0.351588i
$760$	2.66086	+	49.6761i	0.0965197	+	1.80194i
$761$	33.4715	+	22.8205i	1.21334	+	0.827241i	0.989093	−	0.147292i	$-0.0470556\pi$
$761$	33.4715	+	22.8205i	1.21334	+	0.827241i	0.224246	+	0.974533i	$0.428008\pi$
$762$	−0.952059	−	4.88789i	−0.0344895	−	0.177069i
$763$	−25.2555	+	21.7834i	−0.914310	+	0.788612i
$764$	22.8278	+	32.7215i	0.825883	+	1.18382i
$765$	−44.6071	+	25.7539i	−1.61277	+	0.931134i
$766$	−16.4859	+	16.6639i	−0.595659	+	0.602092i
$767$	37.7843	−	25.7609i	1.36431	−	0.930173i
$768$	8.22605	+	6.00063i	0.296832	+	0.216529i
$769$	0.966728	−	4.23551i	0.0348611	−	0.152737i	−0.954502	−	0.298205i	$-0.903612\pi$
$769$	0.966728	−	4.23551i	0.0348611	−	0.152737i	0.989363	+	0.145469i	$0.0464691\pi$
$770$	−23.3607	+	25.5070i	−0.841862	+	0.919207i
$771$	7.74803	−	1.76844i	0.279038	−	0.0636887i
$772$	−13.5885	+	29.0099i	−0.489060	+	1.04409i
$773$	5.38031	−	17.4425i	0.193516	−	0.627364i	−0.805862	−	0.592103i	$-0.798298\pi$
$773$	5.38031	−	17.4425i	0.193516	−	0.627364i	0.999378	−	0.0352605i	$-0.0112261\pi$
$774$	31.8781	−	3.76530i	1.14584	−	0.135341i
$775$	3.27054	−	1.00883i	0.117481	−	0.0362381i
$776$	2.38038	−	24.6971i	0.0854508	−	0.886573i
$777$	−1.62140	+	4.65040i	−0.0581674	+	0.166832i
$778$	−20.7291	−	27.7734i	−0.743173	−	0.995726i
$779$	39.1407	+	15.3616i	1.40236	+	0.550386i
$780$	16.3363	+	10.8827i	0.584932	+	0.389662i
$781$	0.629961	+	4.17951i	0.0225418	+	0.149555i
$782$	59.9063	−	32.0742i	2.14224	−	1.14697i
$783$	−3.03760			−0.108555
$784$	18.5526	−	20.9715i	0.662591	−	0.748981i
$785$	−16.7253			−0.596950
$786$	−6.67502	+	3.57385i	−0.238090	+	0.127475i
$787$	−0.399210	−	2.64859i	−0.0142303	−	0.0944119i	0.980588	−	0.196078i	$-0.0628207\pi$
$787$	−0.399210	−	2.64859i	−0.0142303	−	0.0944119i	−0.994819	+	0.101666i	$0.967583\pi$
$788$	33.7501	+	22.4832i	1.20230	+	0.800930i
$789$	−12.5924	−	4.94215i	−0.448301	−	0.175945i
$790$	12.7528	+	17.0866i	0.453725	+	0.607915i
$791$	31.1911	−	31.2610i	1.10903	−	1.11151i
$792$	23.2122	+	2.23727i	0.824810	+	0.0794979i
$793$	−11.1122	+	3.42765i	−0.394605	+	0.121720i
$794$	−39.3918	+	4.65279i	−1.39796	+	0.165121i
$795$	4.93788	−	16.0082i	0.175129	−	0.567753i
$796$	4.77086	−	10.1852i	0.169099	−	0.361007i
$797$	−5.44093	+	1.24186i	−0.192728	+	0.0439888i	−0.317795	−	0.948159i	$-0.602942\pi$
$797$	−5.44093	+	1.24186i	−0.192728	+	0.0439888i	0.125067	+	0.992148i	$0.460085\pi$
$798$	8.18551	+	11.8401i	0.289764	+	0.419134i
$799$	−7.35610	+	32.2292i	−0.260240	+	1.14019i
$800$	2.71711	+	19.4137i	0.0960644	+	0.686378i
$801$	−23.5485	+	16.0551i	−0.832045	+	0.567279i
$802$	21.4784	−	21.7104i	0.758428	−	0.766620i
$803$	−23.3690	+	13.4921i	−0.824673	+	0.476125i
$804$	5.36891	+	7.69581i	0.189347	+	0.271410i
$805$	2.08801	+	54.1786i	0.0735927	+	1.90954i
$806$	−1.41551	−	7.26727i	−0.0498593	−	0.255979i
$807$	11.5187	+	7.85333i	0.405478	+	0.276450i
$808$	5.99919	−	0.321342i	0.211051	−	0.0113048i
$809$	−11.3457	−	10.5273i	−0.398894	−	0.370120i	0.455066	−	0.890457i	$-0.349616\pi$
$809$	−11.3457	−	10.5273i	−0.398894	−	0.370120i	−0.853960	+	0.520338i	$0.825806\pi$
$810$	−17.1335	+	14.9055i	−0.602009	+	0.523725i
$811$	−3.32561	−	6.90570i	−0.116778	−	0.242492i	0.834384	−	0.551183i	$-0.185823\pi$
$811$	−3.32561	−	6.90570i	−0.116778	−	0.242492i	−0.951162	+	0.308691i	$0.900109\pi$
$812$	0.115271	−	4.51283i	0.00404521	−	0.158369i
$813$	−2.45453	+	5.09689i	−0.0860843	+	0.178756i
$814$	−3.46975	−	12.6765i	−0.121615	−	0.444313i
$815$	24.4223	−	42.3007i	0.855477	−	1.48173i
$816$	7.19678	−	15.8041i	0.251938	−	0.553253i
$817$	−52.2842	−	7.88058i	−1.82919	−	0.275707i
$818$	−3.64636	+	6.98988i	−0.127492	+	0.244395i
$819$	−36.3694	−	1.32004i	−1.27085	−	0.0461261i
$820$	38.8028	+	11.5141i	1.35505	+	0.402089i
$821$	−4.33027	+	0.324509i	−0.151128	+	0.0113254i	−0.150079	−	0.988674i	$-0.547953\pi$
$821$	−4.33027	+	0.324509i	−0.151128	+	0.0113254i	−0.00104857	+	0.999999i	$0.500334\pi$
$822$	−0.917042	+	1.47702i	−0.0319855	+	0.0515168i
$823$	−16.7117	−	42.5808i	−0.582535	−	1.48427i	−0.853191	−	0.521598i	$-0.825336\pi$
$823$	−16.7117	−	42.5808i	−0.582535	−	1.48427i	0.270657	−	0.962676i	$-0.412759\pi$
$824$	10.4806	+	5.32491i	0.365109	+	0.185502i
$825$	−4.36850	−	5.47793i	−0.152092	−	0.190717i
$826$	30.7837	−	9.71482i	1.07110	−	0.338022i
$827$	−8.31148	−	6.62819i	−0.289019	−	0.230485i	0.468238	−	0.883603i	$-0.344889\pi$
$827$	−8.31148	−	6.62819i	−0.289019	−	0.230485i	−0.757256	+	0.653118i	$0.773461\pi$
$828$	28.3335	−	23.0975i	0.984658	−	0.802693i
$829$	−28.7603	−	2.15529i	−0.998886	−	0.0748562i	−0.434761	−	0.900546i	$-0.643167\pi$
$829$	−28.7603	−	2.15529i	−0.998886	−	0.0748562i	−0.564125	+	0.825690i	$0.690786\pi$
$830$	−19.6631	−	2.10861i	−0.682515	−	0.0731908i
$831$	−7.28316	+	6.75778i	−0.252650	+	0.234425i
$832$	42.3835	−	1.36634i	1.46939	−	0.0473694i
$833$	−41.4095	−	23.7842i	−1.43475	−	0.824074i
$834$	−12.7796	−	3.35083i	−0.442522	−	0.116030i
$835$	−33.7085	−	36.3291i	−1.16653	−	1.25722i
$836$	−35.9058	−	13.6487i	−1.24183	−	0.472051i
$837$	−3.50681	−	0.262799i	−0.121213	−	0.00908367i
$838$	37.6852	+	27.5015i	1.30181	+	0.950024i
$839$	−2.57672	+	3.23110i	−0.0889582	+	0.111550i	−0.824319	−	0.566126i	$-0.808441\pi$
$839$	−2.57672	+	3.23110i	−0.0889582	+	0.111550i	0.735360	+	0.677676i	$0.237013\pi$
$840$	8.82440	+	10.6825i	0.304471	+	0.368581i
$841$	17.6274	+	22.1041i	0.607842	+	0.762210i
$842$	1.08129	+	25.2656i	0.0372639	+	0.870710i
$843$	9.20876	−	3.61417i	0.317166	−	0.124479i
$844$	1.35333	−	1.28303i	0.0465834	−	0.0441638i
$845$	43.8034	−	3.28261i	1.50688	−	0.112925i
$846$	−0.569493	+	17.7746i	−0.0195796	+	0.611102i
$847$	0.960656	+	2.19513i	0.0330085	+	0.0754257i
$848$	−11.4079	−	34.3459i	−0.391750	−	1.17944i
$849$	−2.14937	−	0.323966i	−0.0737663	−	0.0111185i
$850$	31.4968	−	11.2115i	1.08033	−	0.384550i
$851$	−17.8420	−	10.3011i	−0.611617	−	0.353117i
$852$	1.69312	−	0.0181884i	0.0580053	−	0.000623126i
$853$	24.2764	−	50.4105i	0.831209	−	1.72602i	0.156847	−	0.987623i	$-0.449867\pi$
$853$	24.2764	−	50.4105i	0.831209	−	1.72602i	0.674362	−	0.738401i	$-0.264419\pi$
$854$	−8.20838	+	0.0532852i	−0.280885	+	0.00182338i
$855$	41.1220	−	19.8033i	1.40634	−	0.677260i
$856$	−28.6214	+	5.89465i	−0.978258	+	0.201475i
$857$	−21.8238	−	20.2495i	−0.745487	−	0.691711i	0.212934	−	0.977067i	$-0.431698\pi$
$857$	−21.8238	−	20.2495i	−0.745487	−	0.691711i	−0.958422	+	0.285355i	$0.907888\pi$
$858$	−12.7901	+	8.13267i	−0.436645	+	0.277645i
$859$	21.0858	−	30.9273i	0.719440	−	1.05522i	−0.276123	−	0.961122i	$-0.589050\pi$
$859$	21.0858	−	30.9273i	0.719440	−	1.05522i	0.995563	−	0.0941019i	$-0.0299980\pi$
$860$	−50.7933	−	3.25816i	−1.73204	−	0.111102i
$861$	11.3088	−	3.04376i	0.385402	−	0.103731i
$862$	−22.3188	−	18.9992i	−0.760181	−	0.647114i
$863$	6.28847	+	10.8919i	0.214062	+	0.370766i	0.952982	−	0.303027i	$-0.0979972\pi$
$863$	6.28847	+	10.8919i	0.214062	+	0.370766i	−0.738920	+	0.673793i	$0.764664\pi$
$864$	4.68874	−	19.5883i	0.159514	−	0.666407i
$865$	−38.5524	+	26.2846i	−1.31082	+	0.893703i
$866$	−43.1124	−	18.5348i	−1.46502	−	0.629837i
$867$	−18.3270	−	4.18303i	−0.622419	−	0.142063i
$868$	0.523505	−	5.19994i	0.0177689	−	0.176497i
$869$	−16.0503	+	3.66338i	−0.544469	+	0.124272i
$870$	2.19717	+	0.403516i	0.0744910	+	0.0136805i
$871$	37.3435	+	11.5190i	1.26534	+	0.390305i
$872$	−32.9053	−	13.7297i	−1.11432	−	0.464945i
$873$	−21.7527	+	6.70981i	−0.736216	+	0.227093i
$874$	−55.0596	+	24.3751i	−1.86242	+	0.824500i
$875$	1.30955	−	11.7408i	0.0442710	−	0.396912i
$876$	4.05713	+	10.0196i	0.137078	+	0.338529i
$877$	−9.90177	−	3.88616i	−0.334359	−	0.131226i	0.192221	−	0.981352i	$-0.438431\pi$
$877$	−9.90177	−	3.88616i	−0.334359	−	0.131226i	−0.526580	+	0.850125i	$0.676526\pi$
$878$	−4.02248	+	11.6967i	−0.135752	+	0.394746i
$879$	7.15809	−	1.07891i	0.241437	−	0.0363907i
$880$	−35.5594	−	10.1373i	−1.19871	−	0.341729i
$881$	10.8727			0.366311			0.183155	−	0.983084i	$-0.441369\pi$
$881$	10.8727			0.366311			0.183155	+	0.983084i	$0.441369\pi$
$882$	−24.3116	−	8.29984i	−0.818616	−	0.279470i
$883$		−	12.0187i		−	0.404462i	−0.979338	−	0.202231i	$-0.935181\pi$
$883$		−	12.0187i		−	0.404462i	0.979338	−	0.202231i	$-0.0648191\pi$
$884$	−16.8497	−	70.3323i	−0.566718	−	2.36553i
$885$	2.38080	+	15.7956i	0.0800297	+	0.530963i
$886$	−26.0823	−	8.96965i	−0.876253	−	0.301341i
$887$	15.5157	−	39.5334i	0.520967	−	1.32740i	−0.392224	−	0.919870i	$-0.628294\pi$
$887$	15.5157	−	39.5334i	0.520967	−	1.32740i	0.913191	−	0.407532i	$-0.133610\pi$
$888$	−5.22171	+	0.673715i	−0.175229	+	0.0226084i
$889$	−7.80251	−	12.3868i	−0.261688	−	0.415440i
$890$	41.3229	−	18.2938i	1.38515	−	0.613211i
$891$	−5.16862	−	16.7562i	−0.173155	−	0.561355i
$892$	−2.18408	+	15.6277i	−0.0731285	+	0.523255i
$893$	8.63436	−	27.9919i	0.288938	−	0.936713i
$894$	1.92521	−	10.4829i	0.0643888	−	0.350601i
$895$	−13.5276	−	59.2685i	−0.452179	−	1.98113i
$896$	28.9235	+	7.70918i	0.966266	+	0.257546i
$897$	−5.28689	+	23.1634i	−0.176524	+	0.773403i
$898$	3.08619	+	1.32681i	0.102987	+	0.0442761i
$899$	−0.474653	−	0.696188i	−0.0158306	−	0.0232192i
$900$	15.4782	−	9.15942i	0.515939	−	0.305314i
$901$	−53.4540	+	30.8617i	−1.78081	+	1.02815i
$902$	−20.2583	+	23.7979i	−0.674528	+	0.792384i
$903$	−13.0126	+	6.89603i	−0.433033	+	0.229486i
$904$	44.8056	+	14.8723i	1.49021	+	0.494644i
$905$	34.9766	+	23.8467i	1.16266	+	0.792690i
$906$	1.00649	−	0.639983i	0.0334382	−	0.0212620i
$907$	−30.1180	+	32.4595i	−1.00005	+	1.07780i	−0.00308255	+	0.999995i	$0.500981\pi$
$907$	−30.1180	+	32.4595i	−1.00005	+	1.07780i	−0.996969	+	0.0778037i	$0.975209\pi$
$908$	15.7340	−	7.78641i	0.522152	−	0.258401i
$909$	−2.39157	−	4.96615i	−0.0793234	−	0.164717i
$910$	56.3411	+	12.4753i	1.86769	+	0.413551i
$911$	−8.11052	−	3.90582i	−0.268713	−	0.129406i	0.294676	−	0.955597i	$-0.404788\pi$
$911$	−8.11052	−	3.90582i	−0.268713	−	0.129406i	−0.563389	+	0.826192i	$0.690503\pi$
$912$	−7.40591	+	13.4886i	−0.245234	+	0.446651i
$913$	7.63495	−	13.2241i	0.252680	−	0.437654i
$914$	−23.3442	+	8.30951i	−0.772159	+	0.274854i
$915$	0.605413	−	4.01666i	0.0200144	−	0.132787i
$916$	−18.1062	−	16.4417i	−0.598246	−	0.543249i
$917$	−14.5002	+	16.8878i	−0.478838	+	0.557683i
$918$	−34.3338	−	1.10005i	−1.13318	−	0.0363070i
$919$	0.739334	+	9.86572i	0.0243884	+	0.325440i	0.996032	+	0.0889916i	$0.0283644\pi$
$919$	0.739334	+	9.86572i	0.0243884	+	0.325440i	−0.971644	+	0.236449i	$0.924017\pi$
$920$	−50.8024	+	27.9062i	−1.67490	+	0.920039i
$921$	−1.44124	−	3.67221i	−0.0474904	−	0.121003i
$922$	−2.20538	−	51.5311i	−0.0726304	−	1.69709i
$923$	5.51329	−	4.39670i	0.181472	−	0.144719i
$924$	−10.3007	+	2.89145i	−0.338868	+	0.0951218i
$925$	−7.92490	−	6.31990i	−0.260569	−	0.207797i
$926$	12.2508	−	16.7873i	0.402588	−	0.551664i
$927$	0.806011	−	10.7555i	0.0264729	−	0.353256i
$928$	4.36991	−	2.04796i	0.143449	−	0.0672274i
$929$	2.89121	−	2.68265i	0.0948575	−	0.0880149i	−0.631319	−	0.775523i	$-0.717486\pi$
$929$	2.89121	−	2.68265i	0.0948575	−	0.0880149i	0.726176	+	0.687508i	$0.241296\pi$
$930$	2.50165	+	0.655934i	0.0820323	+	0.0215089i
$931$	35.0161	+	23.7588i	1.14761	+	0.778664i
$932$	−30.0731	−	16.9346i	−0.985077	−	0.554712i
$933$	4.57243	+	4.92791i	0.149695	+	0.161333i
$934$	−0.783807	+	7.30912i	−0.0256470	+	0.239162i
$935$	−4.71267	+	62.8863i	−0.154121	+	2.05660i
$936$	−16.1308	−	35.4046i	−0.527252	−	1.15724i
$937$	12.2304	−	15.3364i	0.399550	−	0.501019i	−0.540837	−	0.841128i	$-0.681892\pi$
$937$	12.2304	−	15.3364i	0.399550	−	0.501019i	0.940386	+	0.340108i	$0.110464\pi$
$938$	22.8927	+	15.3912i	0.747473	+	0.502542i
$939$	−7.49571	+	5.97763i	−0.244613	+	0.195073i
$940$	5.97898	−	27.5568i	0.195013	−	0.898805i
$941$	−3.61600	+	1.41918i	−0.117878	+	0.0462638i	−0.423547	−	0.905874i	$-0.639215\pi$
$941$	−3.61600	+	1.41918i	−0.117878	+	0.0462638i	0.305669	+	0.952138i	$0.401120\pi$
$942$	−4.39524	−	2.72889i	−0.143205	−	0.0889122i
$943$	3.66108	+	48.8538i	0.119221	+	1.59090i
$944$	24.0102	+	24.7869i	0.781464	+	0.806744i
$945$	12.7801	−	24.2469i	0.415738	−	0.788752i
$946$	18.1771	−	34.8445i	0.590988	−	1.13289i
$947$	6.42655	−	42.6374i	0.208835	−	1.38553i	−0.601177	−	0.799116i	$-0.705301\pi$
$947$	6.42655	−	42.6374i	0.208835	−	1.38553i	0.810012	−	0.586413i	$-0.199460\pi$
$948$	0.563468	+	6.57096i	0.0183006	+	0.213415i
$949$	38.9882	+	22.5099i	1.26561	+	0.730701i
$950$	−28.5743	+	7.82119i	−0.927072	+	0.253753i
$951$	−13.7946	−	6.64314i	−0.447321	−	0.215419i
$952$	2.93719	−	50.9665i	0.0951949	−	1.65183i
$953$	21.0366	−	10.1307i	0.681444	−	0.328166i	−0.0609395	−	0.998141i	$-0.519410\pi$
$953$	21.0366	−	10.1307i	0.681444	−	0.328166i	0.742383	+	0.669975i	$0.233695\pi$
$954$	−25.0512	+	21.7936i	−0.811064	+	0.705595i
$955$	−39.4781	+	42.5473i	−1.27748	+	1.37680i
$956$	−10.2258	−	31.9295i	−0.330727	−	1.03267i
$957$	−0.971681	+	1.42519i	−0.0314100	+	0.0460700i
$958$	−19.1986	+	3.73949i	−0.620279	+	0.120818i
$959$	−0.944559	+	5.02292i	−0.0305014	+	0.162198i
$960$	−5.99358	+	13.5458i	−0.193442	+	0.437189i
$961$	15.0123	+	26.0020i	0.484266	+	0.838774i
$962$	−15.4214	+	15.5879i	−0.497205	+	0.502574i
$963$	15.1029	+	22.1519i	0.486685	+	0.713836i
$964$	−10.8359	−	8.45256i	−0.349002	−	0.272239i
$965$	−45.4344	−	10.3701i	−1.46259	−	0.333826i
$966$	−8.29107	+	14.5783i	−0.266761	+	0.469049i
$967$	5.05741	+	22.1580i	0.162635	+	0.712552i	0.988815	+	0.149146i	$0.0476523\pi$
$967$	5.05741	+	22.1580i	0.162635	+	0.712552i	−0.826180	+	0.563406i	$0.809491\pi$
$968$	−1.63938	+	1.96827i	−0.0526918	+	0.0632627i
$969$	25.0781	+	7.73557i	0.805624	+	0.248502i
$970$	35.8457	−	4.23393i	1.15094	−	0.135943i
$971$	−9.91671	−	32.1492i	−0.318242	−	1.03172i	−0.963490	−	0.267743i	$-0.913722\pi$
$971$	−9.91671	−	32.1492i	−0.318242	−	1.03172i	0.645248	−	0.763973i	$-0.276754\pi$
$972$	−28.0239	+	4.53231i	−0.898866	+	0.145374i
$973$	−38.5903	+	4.39187i	−1.23715	+	0.140797i
$974$	−18.2497	+	13.6209i	−0.584760	+	0.436443i
$975$	−4.27066	+	10.8815i	−0.136771	+	0.348486i
$976$	−3.97643	−	7.82266i	−0.127283	−	0.250397i
$977$	23.4426	−	3.53341i	0.749997	−	0.113044i	0.237089	−	0.971488i	$-0.423807\pi$
$977$	23.4426	−	3.53341i	0.749997	−	0.113044i	0.512907	+	0.858444i	$0.328568\pi$
$978$	13.3197	−	7.13148i	0.425919	−	0.228040i
$979$			34.8944i			1.11523i
$980$	35.5376	+	19.9070i	1.13521	+	0.635905i
$981$			32.7125i			1.04443i
$982$	10.3996	+	19.4238i	0.331865	+	0.619838i
$983$	5.46813	−	0.824189i	0.174406	−	0.0262875i	−0.0612584	−	0.998122i	$-0.519511\pi$
$983$	5.46813	−	0.824189i	0.174406	−	0.0262875i	0.235665	+	0.971834i	$0.424273\pi$
$984$	8.31837	+	9.35686i	0.265180	+	0.298286i
$985$	−21.5534	+	54.9171i	−0.686748	+	1.74981i
$986$	−4.92306	−	6.59606i	−0.156782	−	0.210061i
$987$	−2.70335	−	7.69805i	−0.0860486	−	0.245032i
$988$	10.2317	+	63.2643i	0.325515	+	2.01270i
$989$	−18.1588	−	58.8693i	−0.577415	−	1.87193i
$990$	3.97938	+	33.6906i	0.126473	+	1.07076i
$991$	−56.0580	−	17.2916i	−1.78074	−	0.549286i	−0.783356	−	0.621573i	$-0.786494\pi$
$991$	−56.0580	−	17.2916i	−1.78074	−	0.549286i	−0.997384	+	0.0722873i	$0.976970\pi$
$992$	5.22209	−	1.98623i	0.165802	−	0.0630630i
$993$	2.10722	+	9.23233i	0.0668706	+	0.292979i
$994$	4.62171	−	1.84860i	0.146592	−	0.0586340i
$995$	15.9518	+	3.64090i	0.505707	+	0.115424i
$996$	−4.82323	−	3.76235i	−0.152830	−	0.119215i
$997$	−1.86886	−	2.74111i	−0.0591872	−	0.0868117i	0.795504	−	0.605948i	$-0.207206\pi$
$997$	−1.86886	−	2.74111i	−0.0591872	−	0.0868117i	−0.854691	+	0.519136i	$0.826254\pi$
$998$	−20.9496	−	20.7257i	−0.663148	−	0.656062i
$999$	5.20744	+	9.01955i	0.164756	+	0.285366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.9	✓	648
8.5	even	2	inner	392.2.z.a.109.18	yes	648
49.9	even	21	inner	392.2.z.a.205.18	yes	648
392.205	even	42	inner	392.2.z.a.205.9	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.9	✓	648	1.1	even	1	trivial
392.2.z.a.109.18	yes	648	8.5	even	2	inner
392.2.z.a.205.9	yes	648	392.205	even	42	inner
392.2.z.a.205.18	yes	648	49.9	even	21	inner

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24676 + 0.667524i) q^{2} +(-0.0948478 - 0.629274i) q^{3} +(1.10882 - 1.66448i) q^{4} +(2.70840 + 1.06297i) q^{5} +(0.538308 + 0.721241i) q^{6} +(2.24180 + 1.40511i) q^{7} +(-0.271356 + 2.81538i) q^{8} +(2.47973 - 0.764895i) q^{9} +O(q^{10})\)	\(q+(-1.24676 + 0.667524i) q^{2} +(-0.0948478 - 0.629274i) q^{3} +(1.10882 - 1.66448i) q^{4} +(2.70840 + 1.06297i) q^{5} +(0.538308 + 0.721241i) q^{6} +(2.24180 + 1.40511i) q^{7} +(-0.271356 + 2.81538i) q^{8} +(2.47973 - 0.764895i) q^{9} +(-4.08629 + 0.482654i) q^{10} +(0.936484 - 3.03601i) q^{11} +(-1.15259 - 0.539882i) q^{12} +(-5.16780 + 1.17952i) q^{13} +(-3.73293 - 0.255388i) q^{14} +(0.412013 - 1.80515i) q^{15} +(-1.54102 - 3.69124i) q^{16} +(-5.63658 + 3.84296i) q^{17} +(-2.58104 + 2.60892i) q^{18} +(5.23520 - 3.02254i) q^{19} +(4.77244 - 3.32945i) q^{20} +(0.671572 - 1.54398i) q^{21} +(0.859035 + 4.41030i) q^{22} +(5.81948 + 3.96766i) q^{23} +(1.79738 - 0.0962755i) q^{24} +(2.54027 + 2.35703i) q^{25} +(5.65565 - 4.92020i) q^{26} +(-1.54487 - 3.20796i) q^{27} +(4.82455 - 2.17341i) q^{28} +(0.370156 - 0.768637i) q^{29} +(0.691297 + 2.52562i) q^{30} +(0.493832 - 0.855342i) q^{31} +(4.38527 + 3.57343i) q^{32} +(-1.99930 - 0.301347i) q^{33} +(4.46221 - 8.55380i) q^{34} +(4.57809 + 6.18857i) q^{35} +(1.47643 - 4.97560i) q^{36} +(-2.91688 + 0.218590i) q^{37} +(-4.50942 + 7.26300i) q^{38} +(1.23239 + 3.14009i) q^{39} +(-3.72760 + 7.33674i) q^{40} +(4.33675 + 5.43812i) q^{41} +(0.193352 + 2.37326i) q^{42} +(-6.83848 - 5.45350i) q^{43} +(-4.01499 - 4.92516i) q^{44} +(7.52916 + 0.564233i) q^{45} +(-9.90400 - 1.06207i) q^{46} +(3.55223 - 3.29599i) q^{47} +(-2.17664 + 1.31983i) q^{48} +(3.05131 + 6.29996i) q^{49} +(-4.74049 - 1.24296i) q^{50} +(2.95289 + 3.18246i) q^{51} +(-3.76689 + 9.90959i) q^{52} +(9.02242 + 0.676137i) q^{53} +(4.06748 + 2.96832i) q^{54} +(5.76356 - 7.22727i) q^{55} +(-4.56425 + 5.93023i) q^{56} +(-2.39855 - 3.00769i) q^{57} +(0.0515874 + 1.20539i) q^{58} +(-8.03090 + 3.15190i) q^{59} +(-2.54779 - 2.68738i) q^{60} +(2.18769 - 0.163945i) q^{61} +(-0.0447292 + 1.39605i) q^{62} +(6.63381 + 1.76956i) q^{63} +(-7.85273 - 1.52794i) q^{64} +(-15.2503 - 2.29861i) q^{65} +(2.69381 - 0.958876i) q^{66} +(-6.38483 - 3.68628i) q^{67} +(0.146563 + 13.6432i) q^{68} +(1.94478 - 4.03837i) q^{69} +(-9.83881 - 4.65968i) q^{70} +(-1.19860 + 0.577216i) q^{71} +(1.48058 + 7.18894i) q^{72} +(-6.22593 - 5.77682i) q^{73} +(3.49074 - 2.21962i) q^{74} +(1.24228 - 1.82209i) q^{75} +(0.773939 - 12.0654i) q^{76} +(6.36534 - 5.49025i) q^{77} +(-3.63258 - 3.09228i) q^{78} +(-2.59085 - 4.48748i) q^{79} +(-0.250017 - 11.6354i) q^{80} +(4.56015 - 3.10906i) q^{81} +(-9.03697 - 3.88515i) q^{82} +(4.68565 + 1.06947i) q^{83} +(-1.82527 - 2.82982i) q^{84} +(-19.3511 + 4.41676i) q^{85} +(12.1663 + 2.23437i) q^{86} +(-0.518792 - 0.160026i) q^{87} +(8.29340 + 3.46040i) q^{88} +(-10.4950 + 3.23727i) q^{89} +(-9.76370 + 4.32243i) q^{90} +(-13.2425 - 4.61711i) q^{91} +(13.0569 - 5.28700i) q^{92} +(-0.585083 - 0.229628i) q^{93} +(-2.22863 + 6.48050i) q^{94} +(17.3919 - 2.62140i) q^{95} +(1.83273 - 3.09847i) q^{96} -8.77219 q^{97} +(-8.00963 - 5.81772i) q^{98} -8.24479i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

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