LMFDB - Embedded newform 378.2.u.e.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	378.169
Dual form			378.2.u.e.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.873169 + 1.49585i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.605889 - 3.43617i) q^{5} +(1.33212 + 1.10700i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.47515 + 2.61227i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.873169 + 1.49585i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.605889 - 3.43617i) q^{5} +(1.33212 + 1.10700i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.47515 + 2.61227i) q^{9} +(-1.74459 - 3.02172i) q^{10} +(0.791459 - 4.48859i) q^{11} +(1.63040 + 0.584627i) q^{12} +(5.50344 + 2.00309i) q^{13} +(0.939693 + 0.342020i) q^{14} +(4.61096 - 3.90668i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.614096 + 1.06365i) q^{17} +(-0.492740 + 2.95926i) q^{18} +(-0.418950 + 0.725643i) q^{19} +(-2.67286 - 2.24280i) q^{20} +(-0.292629 + 1.70715i) q^{21} +(-0.791459 - 4.48859i) q^{22} +(-5.66011 + 4.74939i) q^{23} +(1.73203 - 0.00826063i) q^{24} +(-6.74169 + 2.45378i) q^{25} +5.85663 q^{26} +(-5.19562 + 0.0743434i) q^{27} +1.00000 q^{28} +(0.897215 - 0.326560i) q^{29} +(2.99672 - 5.24812i) q^{30} +(-6.47125 + 5.43002i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(7.40534 - 2.73539i) q^{33} +(0.940850 + 0.789467i) q^{34} +(1.74459 - 3.02172i) q^{35} +(0.549101 + 2.94932i) q^{36} +(-0.215229 - 0.372787i) q^{37} +(-0.145500 + 0.825171i) q^{38} +(1.80911 + 9.98136i) q^{39} +(-3.27875 - 1.19337i) q^{40} +(6.55650 + 2.38637i) q^{41} +(0.308899 + 1.70428i) q^{42} +(1.23170 - 6.98532i) q^{43} +(-2.27891 - 3.94720i) q^{44} +(9.86996 + 3.48612i) q^{45} +(-3.69437 + 6.39884i) q^{46} +(-6.64681 - 5.57734i) q^{47} +(1.62475 - 0.600152i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-5.49588 + 4.61159i) q^{50} +(-1.05485 + 1.84734i) q^{51} +(5.50344 - 2.00309i) q^{52} -7.79142 q^{53} +(-4.85686 + 1.84687i) q^{54} -15.9031 q^{55} +(0.939693 - 0.342020i) q^{56} +(-1.45127 + 0.00692158i) q^{57} +(0.731416 - 0.613731i) q^{58} +(1.92214 + 10.9010i) q^{59} +(1.02103 - 5.95656i) q^{60} +(8.16278 + 6.84939i) q^{61} +(-4.22381 + 7.31585i) q^{62} +(-2.80916 + 1.05290i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.54847 - 20.1244i) q^{65} +(6.02319 - 5.10320i) q^{66} +(-13.7773 - 5.01453i) q^{67} +(1.15412 + 0.420066i) q^{68} +(-12.0466 - 4.31966i) q^{69} +(0.605889 - 3.43617i) q^{70} +(0.0121983 + 0.0211281i) q^{71} +(1.52471 + 2.58365i) q^{72} +(1.20574 - 2.08840i) q^{73} +(-0.329750 - 0.276693i) q^{74} +(-9.55712 - 7.94202i) q^{75} +(0.145500 + 0.825171i) q^{76} +(3.49150 - 2.92972i) q^{77} +(5.11383 + 8.76066i) q^{78} +(-1.95673 + 0.712191i) q^{79} -3.48918 q^{80} +(-4.64786 - 7.70697i) q^{81} +6.97728 q^{82} +(15.8118 - 5.75502i) q^{83} +(0.873169 + 1.49585i) q^{84} +(3.28279 - 2.75459i) q^{85} +(-1.23170 - 6.98532i) q^{86} +(1.27191 + 1.05696i) q^{87} +(-3.49150 - 2.92972i) q^{88} +(-3.51410 + 6.08660i) q^{89} +(10.4671 - 0.0998439i) q^{90} +(2.92832 + 5.07199i) q^{91} +(-1.28304 + 7.27649i) q^{92} +(-13.7730 - 4.93871i) q^{93} +(-8.15352 - 2.96764i) q^{94} +(2.74727 + 0.999925i) q^{95} +(1.32150 - 1.11966i) q^{96} +(-2.34715 + 13.3113i) q^{97} +(0.500000 + 0.866025i) q^{98} +(10.5579 + 8.68884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.873169	+	1.49585i	0.504125	+	0.863631i
$3$	0.873169	+	1.49585i	0.504125	+	0.863631i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.605889	−	3.43617i	−0.270962	−	1.53670i	−0.751503	−	0.659729i	$-0.770671\pi$
$5$	−0.605889	−	3.43617i	−0.270962	−	1.53670i	0.480541	−	0.876972i	$-0.340440\pi$
$6$	1.33212	+	1.10700i	0.543837	+	0.451931i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.47515	+	2.61227i	−0.491717	+	0.870755i
$10$	−1.74459	−	3.02172i	−0.551687	−	0.955551i
$11$	0.791459	−	4.48859i	0.238634	−	1.35336i	−0.596190	−	0.802843i	$-0.703320\pi$
$11$	0.791459	−	4.48859i	0.238634	−	1.35336i	0.834824	−	0.550517i	$-0.185569\pi$
$12$	1.63040	+	0.584627i	0.470657	+	0.168767i
$13$	5.50344	+	2.00309i	1.52638	+	0.555556i	0.962731	−	0.270459i	$-0.0871756\pi$
$13$	5.50344	+	2.00309i	1.52638	+	0.555556i	0.563647	+	0.826016i	$0.309398\pi$
$14$	0.939693	+	0.342020i	0.251143	+	0.0914087i
$15$	4.61096	−	3.90668i	1.19054	−	1.00870i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.614096	+	1.06365i	0.148940	+	0.257972i	0.930836	−	0.365437i	$-0.119080\pi$
$17$	0.614096	+	1.06365i	0.148940	+	0.257972i	−0.781896	+	0.623409i	$0.785747\pi$
$18$	−0.492740	+	2.95926i	−0.116140	+	0.697504i
$19$	−0.418950	+	0.725643i	−0.0961138	+	0.166474i	−0.910073	−	0.414448i	$-0.863975\pi$
$19$	−0.418950	+	0.725643i	−0.0961138	+	0.166474i	0.813959	+	0.580922i	$0.197308\pi$
$20$	−2.67286	−	2.24280i	−0.597671	−	0.501505i
$21$	−0.292629	+	1.70715i	−0.0638569	+	0.372531i
$22$	−0.791459	−	4.48859i	−0.168740	−	0.956970i
$23$	−5.66011	+	4.74939i	−1.18021	+	0.990317i	−0.180236	+	0.983623i	$0.557686\pi$
$23$	−5.66011	+	4.74939i	−1.18021	+	0.990317i	−0.999978	+	0.00669339i	$0.997869\pi$
$24$	1.73203	−	0.00826063i	0.353549	−	0.00168619i
$25$	−6.74169	+	2.45378i	−1.34834	+	0.490755i
$26$	5.85663			1.14858
$27$	−5.19562	+	0.0743434i	−0.999898	+	0.0143074i
$28$	1.00000			0.188982
$29$	0.897215	−	0.326560i	0.166609	−	0.0606406i	−0.257369	−	0.966313i	$-0.582856\pi$
$29$	0.897215	−	0.326560i	0.166609	−	0.0606406i	0.423978	+	0.905673i	$0.360633\pi$
$30$	2.99672	−	5.24812i	0.547124	−	0.958171i
$31$	−6.47125	+	5.43002i	−1.16227	+	0.975261i	−0.999934	−	0.0114744i	$-0.996348\pi$
$31$	−6.47125	+	5.43002i	−1.16227	+	0.975261i	−0.162337	+	0.986735i	$0.551903\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	7.40534	−	2.73539i	1.28910	−	0.476170i
$34$	0.940850	+	0.789467i	0.161354	+	0.135392i
$35$	1.74459	−	3.02172i	0.294889	−	0.510763i
$36$	0.549101	+	2.94932i	0.0915169	+	0.491553i
$37$	−0.215229	−	0.372787i	−0.0353834	−	0.0612859i	0.847791	−	0.530330i	$-0.177932\pi$
$37$	−0.215229	−	0.372787i	−0.0353834	−	0.0612859i	−0.883175	+	0.469044i	$0.844599\pi$
$38$	−0.145500	+	0.825171i	−0.0236032	+	0.133860i
$39$	1.80911	+	9.98136i	0.289689	+	1.59830i
$40$	−3.27875	−	1.19337i	−0.518417	−	0.188688i
$41$	6.55650	+	2.38637i	1.02395	+	0.372689i	0.798776	−	0.601629i	$-0.205481\pi$
$41$	6.55650	+	2.38637i	1.02395	+	0.372689i	0.225178	+	0.974318i	$0.427704\pi$
$42$	0.308899	+	1.70428i	0.0476642	+	0.262977i
$43$	1.23170	−	6.98532i	0.187832	−	1.06525i	−0.734429	−	0.678685i	$-0.762550\pi$
$43$	1.23170	−	6.98532i	0.187832	−	1.06525i	0.922262	−	0.386566i	$-0.126339\pi$
$44$	−2.27891	−	3.94720i	−0.343559	−	0.595062i
$45$	9.86996	+	3.48612i	1.47133	+	0.519680i
$46$	−3.69437	+	6.39884i	−0.544705	+	0.943457i
$47$	−6.64681	−	5.57734i	−0.969537	−	0.813538i	0.0129410	−	0.999916i	$-0.495881\pi$
$47$	−6.64681	−	5.57734i	−0.969537	−	0.813538i	−0.982478	+	0.186378i	$0.940325\pi$
$48$	1.62475	−	0.600152i	0.234513	−	0.0866245i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	−5.49588	+	4.61159i	−0.777234	+	0.652177i
$51$	−1.05485	+	1.84734i	−0.147708	+	0.258679i
$52$	5.50344	−	2.00309i	0.763189	−	0.277778i
$53$	−7.79142			−1.07023			−0.535117	−	0.844778i	$-0.679732\pi$
$53$	−7.79142			−1.07023			−0.535117	+	0.844778i	$0.679732\pi$
$54$	−4.85686	+	1.84687i	−0.660935	+	0.251327i
$55$	−15.9031			−2.14437
$56$	0.939693	−	0.342020i	0.125572	−	0.0457044i
$57$	−1.45127	+	0.00692158i	−0.192225	+	0.000916786i
$58$	0.731416	−	0.613731i	0.0960397	−	0.0805869i
$59$	1.92214	+	10.9010i	0.250241	+	1.41919i	0.807998	+	0.589185i	$0.200551\pi$
$59$	1.92214	+	10.9010i	0.250241	+	1.41919i	−0.557757	+	0.830004i	$0.688338\pi$
$60$	1.02103	−	5.95656i	0.131815	−	0.768988i
$61$	8.16278	+	6.84939i	1.04514	+	0.876974i	0.992574	−	0.121644i	$-0.0388165\pi$
$61$	8.16278	+	6.84939i	1.04514	+	0.876974i	0.0525632	+	0.998618i	$0.483261\pi$
$62$	−4.22381	+	7.31585i	−0.536424	+	0.929114i
$63$	−2.80916	+	1.05290i	−0.353921	+	0.132653i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.54847	−	20.1244i	0.440134	−	2.49612i
$66$	6.02319	−	5.10320i	0.741403	−	0.628161i
$67$	−13.7773	−	5.01453i	−1.68316	−	0.612622i	−0.689426	−	0.724356i	$-0.742137\pi$
$67$	−13.7773	−	5.01453i	−1.68316	−	0.612622i	−0.993738	+	0.111734i	$0.964360\pi$
$68$	1.15412	+	0.420066i	0.139958	+	0.0509405i
$69$	−12.0466	−	4.31966i	−1.45024	−	0.520026i
$70$	0.605889	−	3.43617i	0.0724176	−	0.410701i
$71$	0.0121983	+	0.0211281i	0.00144767	+	0.00250745i	0.866748	−	0.498746i	$-0.166206\pi$
$71$	0.0121983	+	0.0211281i	0.00144767	+	0.00250745i	−0.865301	+	0.501253i	$0.832873\pi$
$72$	1.52471	+	2.58365i	0.179689	+	0.304486i
$73$	1.20574	−	2.08840i	0.141121	−	0.244428i	−0.786798	−	0.617210i	$-0.788263\pi$
$73$	1.20574	−	2.08840i	0.141121	−	0.244428i	0.927919	+	0.372782i	$0.121596\pi$
$74$	−0.329750	−	0.276693i	−0.0383326	−	0.0321649i
$75$	−9.55712	−	7.94202i	−1.10356	−	0.917065i
$76$	0.145500	+	0.825171i	0.0166900	+	0.0946536i
$77$	3.49150	−	2.92972i	0.397893	−	0.333872i
$78$	5.11383	+	8.76066i	0.579028	+	0.991950i
$79$	−1.95673	+	0.712191i	−0.220149	+	0.0801278i	−0.449740	−	0.893159i	$-0.648483\pi$
$79$	−1.95673	+	0.712191i	−0.220149	+	0.0801278i	0.229591	+	0.973287i	$0.426261\pi$
$80$	−3.48918			−0.390102
$81$	−4.64786	−	7.70697i	−0.516429	−	0.856330i
$82$	6.97728			0.770512
$83$	15.8118	−	5.75502i	1.73557	−	0.631695i	0.736566	−	0.676365i	$-0.236446\pi$
$83$	15.8118	−	5.75502i	1.73557	−	0.631695i	0.999002	+	0.0446700i	$0.0142236\pi$
$84$	0.873169	+	1.49585i	0.0952706	+	0.163211i
$85$	3.28279	−	2.75459i	0.356069	−	0.298777i
$86$	−1.23170	−	6.98532i	−0.132818	−	0.753246i
$87$	1.27191	+	1.05696i	0.136363	+	0.113318i
$88$	−3.49150	−	2.92972i	−0.372195	−	0.312309i
$89$	−3.51410	+	6.08660i	−0.372494	+	0.645179i	−0.989949	−	0.141428i	$-0.954831\pi$
$89$	−3.51410	+	6.08660i	−0.372494	+	0.645179i	0.617455	+	0.786607i	$0.288164\pi$
$90$	10.4671	−	0.0998439i	1.10332	−	0.0105245i
$91$	2.92832	+	5.07199i	0.306971	+	0.531689i
$92$	−1.28304	+	7.27649i	−0.133766	+	0.758627i
$93$	−13.7730	−	4.93871i	−1.42819	−	0.512120i
$94$	−8.15352	−	2.96764i	−0.840971	−	0.306089i
$95$	2.74727	+	0.999925i	0.281864	+	0.102590i
$96$	1.32150	−	1.11966i	0.134875	−	0.114274i
$97$	−2.34715	+	13.3113i	−0.238317	+	1.35156i	0.597198	+	0.802094i	$0.296281\pi$
$97$	−2.34715	+	13.3113i	−0.238317	+	1.35156i	−0.835515	+	0.549468i	$0.814831\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	10.5579	+	8.68884i	1.06110	+	0.873261i
$100$	−3.58718	+	6.21318i	−0.358718	+	0.621318i
$101$	−6.54854	−	5.49488i	−0.651604	−	0.546761i	0.255953	−	0.966689i	$-0.417611\pi$
$101$	−6.54854	−	5.49488i	−0.651604	−	0.546761i	−0.907557	+	0.419928i	$0.862055\pi$
$102$	−0.359405	+	2.09671i	−0.0355864	+	0.207605i
$103$	1.56684	+	8.88600i	0.154385	+	0.875563i	0.959345	+	0.282234i	$0.0910756\pi$
$103$	1.56684	+	8.88600i	0.154385	+	0.875563i	−0.804960	+	0.593329i	$0.797813\pi$
$104$	4.48644	−	3.76457i	0.439932	−	0.369147i
$105$	6.04336	−	0.0288228i	0.589772	−	0.00281282i
$106$	−7.32154	+	2.66482i	−0.711131	+	0.258830i
$107$	2.48999			0.240716			0.120358	−	0.992731i	$-0.461596\pi$
$107$	2.48999			0.240716			0.120358	+	0.992731i	$0.461596\pi$
$108$	−3.93229	+	3.39663i	−0.378385	+	0.326841i
$109$	−1.02333			−0.0980171			−0.0490086	−	0.998798i	$-0.515606\pi$
$109$	−1.02333			−0.0980171			−0.0490086	+	0.998798i	$0.515606\pi$
$110$	−14.9440	+	5.43917i	−1.42485	+	0.518605i
$111$	0.369704	−	0.647457i	0.0350907	−	0.0614539i
$112$	0.766044	−	0.642788i	0.0723844	−	0.0607377i
$113$	−1.28893	−	7.30990i	−0.121253	−	0.687657i	−0.983463	−	0.181108i	$-0.942032\pi$
$113$	−1.28893	−	7.30990i	−0.121253	−	0.687657i	0.862211	−	0.506550i	$-0.169079\pi$
$114$	−1.36138	+	0.502868i	−0.127505	+	0.0470979i
$115$	19.7491	+	16.5715i	1.84161	+	1.54530i
$116$	0.477398	−	0.826878i	0.0443253	−	0.0767737i
$117$	−13.3510	+	11.4216i	−1.23430	+	1.05593i
$118$	5.53458	+	9.58618i	0.509499	+	0.882479i
$119$	−0.213273	+	1.20953i	−0.0195507	+	0.110878i
$120$	−1.07780	−	5.94655i	−0.0983896	−	0.542843i
$121$	−9.18438	−	3.34284i	−0.834943	−	0.303895i
$122$	10.0131	+	3.64448i	0.906546	+	0.329956i
$123$	2.15528	+	11.8913i	0.194335	+	1.07220i
$124$	−1.46691	+	8.31928i	−0.131733	+	0.747093i
$125$	3.79336	+	6.57029i	0.339288	+	0.587665i
$126$	−2.27964	+	1.95020i	−0.203086	+	0.173737i
$127$	−3.30173	+	5.71876i	−0.292981	+	0.507458i	−0.974513	−	0.224330i	$-0.927981\pi$
$127$	−3.30173	+	5.71876i	−0.292981	+	0.507458i	0.681532	+	0.731788i	$0.261314\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	11.5245	−	4.25692i	1.01467	−	0.374801i
$130$	−3.54847	−	20.1244i	−0.311222	−	1.76503i
$131$	−7.48189	+	6.27805i	−0.653696	+	0.548516i	−0.908190	−	0.418558i	$-0.862535\pi$
$131$	−7.48189	+	6.27805i	−0.653696	+	0.548516i	0.254494	+	0.967074i	$0.418091\pi$
$132$	3.91455	−	6.85549i	0.340717	−	0.596694i
$133$	−0.787369	+	0.286579i	−0.0682736	+	0.0248495i
$134$	−14.6615			−1.26656
$135$	3.40343	+	17.8080i	0.292920	+	1.53267i
$136$	1.22819			0.105317
$137$	14.2949	−	5.20293i	1.22130	−	0.444516i	0.350690	−	0.936492i	$-0.385947\pi$
$137$	14.2949	−	5.20293i	1.22130	−	0.444516i	0.870609	+	0.491975i	$0.163725\pi$
$138$	−12.7975	+	0.0610356i	−1.08940	+	0.00519570i
$139$	9.21108	−	7.72901i	0.781274	−	0.655566i	−0.162295	−	0.986742i	$-0.551890\pi$
$139$	9.21108	−	7.72901i	0.781274	−	0.655566i	0.943569	+	0.331176i	$0.107445\pi$
$140$	−0.605889	−	3.43617i	−0.0512070	−	0.290409i
$141$	2.53908	−	14.8126i	0.213829	−	1.24745i
$142$	0.0186889	+	0.0156819i	0.00156834	+	0.00131599i
$143$	13.3468	−	23.1173i	1.11611	−	1.93316i
$144$	2.31642	+	1.90635i	0.193035	+	0.158863i
$145$	−1.66573	−	2.88512i	−0.138331	−	0.239596i
$146$	0.418748	−	2.37484i	0.0346558	−	0.196543i
$147$	−1.32150	+	1.11966i	−0.108996	+	0.0923477i
$148$	−0.404498	−	0.147225i	−0.0332495	−	0.0121018i
$149$	2.58540	+	0.941009i	0.211804	+	0.0770904i	0.445743	−	0.895161i	$-0.352939\pi$
$149$	2.58540	+	0.941009i	0.211804	+	0.0770904i	−0.233939	+	0.972251i	$0.575162\pi$
$150$	−11.6971	−	4.19432i	−0.955063	−	0.342465i
$151$	0.411684	−	2.33477i	0.0335023	−	0.190001i	−0.963464	−	0.267839i	$-0.913690\pi$
$151$	0.411684	−	2.33477i	0.0335023	−	0.190001i	0.996966	+	0.0778377i	$0.0248016\pi$
$152$	0.418950	+	0.725643i	0.0339814	+	0.0588574i
$153$	−3.68441	+	0.0351451i	−0.297867	+	0.00284131i
$154$	2.27891	−	3.94720i	0.183640	−	0.318074i
$155$	22.5793	+	18.9463i	1.81362	+	1.52180i
$156$	7.80176	+	6.48329i	0.624640	+	0.519079i
$157$	−1.38428	−	7.85064i	−0.110478	−	0.626550i	−0.988890	−	0.148647i	$-0.952508\pi$
$157$	−1.38428	−	7.85064i	−0.110478	−	0.626550i	0.878413	−	0.477903i	$-0.158603\pi$
$158$	−1.59514	+	1.33848i	−0.126903	+	0.106484i
$159$	−6.80323	−	11.6548i	−0.539531	−	0.924287i
$160$	−3.27875	+	1.19337i	−0.259208	+	0.0943441i
$161$	−7.38874			−0.582315
$162$	−7.00350	−	5.65252i	−0.550247	−	0.444104i
$163$	2.89741			0.226942			0.113471	−	0.993541i	$-0.463803\pi$
$163$	2.89741			0.226942			0.113471	+	0.993541i	$0.463803\pi$
$164$	6.55650	−	2.38637i	0.511977	−	0.186344i
$165$	−13.8861	−	23.7887i	−1.08103	−	1.85194i
$166$	12.8899	−	10.8159i	1.00045	−	0.839476i
$167$	−0.790091	−	4.48083i	−0.0611391	−	0.346737i	−0.999997	−	0.00243227i	$-0.999226\pi$
$167$	−0.790091	−	4.48083i	−0.0611391	−	0.346737i	0.938858	−	0.344305i	$-0.111885\pi$
$168$	1.33212	+	1.10700i	0.102775	+	0.0854069i
$169$	16.3169	+	13.6915i	1.25514	+	1.05319i
$170$	2.14269	−	3.71125i	0.164337	−	0.284640i
$171$	−1.27756	−	2.16484i	−0.0976973	−	0.165550i
$172$	−3.54654	−	6.14278i	−0.270421	−	0.468383i
$173$	1.59882	−	9.06736i	0.121556	−	0.689379i	−0.861738	−	0.507354i	$-0.830624\pi$
$173$	1.59882	−	9.06736i	0.121556	−	0.689379i	0.983294	−	0.182025i	$-0.0582652\pi$
$174$	1.55670	+	0.558200i	0.118013	+	0.0423170i
$175$	−6.74169	−	2.45378i	−0.509624	−	0.185488i
$176$	−4.28296	−	1.55887i	−0.322840	−	0.117504i
$177$	−14.6279	+	12.3937i	−1.09950	+	0.931564i
$178$	−1.22043	+	6.92143i	−0.0914754	+	0.518783i
$179$	4.47684	+	7.75412i	0.334615	+	0.579570i	0.983411	−	0.181392i	$-0.0580604\pi$
$179$	4.47684	+	7.75412i	0.334615	+	0.579570i	−0.648796	+	0.760963i	$0.724727\pi$
$180$	9.80167	−	3.67377i	0.730573	−	0.273826i
$181$	8.20062	−	14.2039i	0.609547	−	1.05577i	−0.381768	−	0.924258i	$-0.624685\pi$
$181$	8.20062	−	14.2039i	0.609547	−	1.05577i	0.991315	−	0.131508i	$-0.0419820\pi$
$182$	4.48644	+	3.76457i	0.332557	+	0.279049i
$183$	−3.11818	+	18.1910i	−0.230503	+	1.34472i
$184$	1.28304	+	7.27649i	0.0945871	+	0.536430i
$185$	−1.15056	+	0.965431i	−0.0845905	+	0.0709799i
$186$	−14.6315	+	0.0697826i	−1.07284	+	0.00511671i
$187$	5.26030	−	1.91459i	0.384671	−	0.140009i
$188$	−8.67680			−0.632820
$189$	−4.02786	−	3.28273i	−0.292984	−	0.238783i
$190$	2.92358			0.212099
$191$	1.65647	−	0.602906i	0.119858	−	0.0436248i	−0.281395	−	0.959592i	$-0.590797\pi$
$191$	1.65647	−	0.602906i	0.119858	−	0.0436248i	0.401253	+	0.915967i	$0.368575\pi$
$192$	0.858862	−	1.50411i	0.0619830	−	0.108550i
$193$	4.80848	−	4.03479i	0.346122	−	0.290431i	−0.453109	−	0.891455i	$-0.649685\pi$
$193$	4.80848	−	4.03479i	0.346122	−	0.290431i	0.799231	+	0.601025i	$0.205241\pi$
$194$	2.34715	+	13.3113i	0.168515	+	0.955698i
$195$	33.2015	−	12.2640i	2.37761	−	0.878244i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	−10.0278	+	17.3687i	−0.714455	+	1.23747i	0.248715	+	0.968577i	$0.419992\pi$
$197$	−10.0278	+	17.3687i	−0.714455	+	1.23747i	−0.963169	+	0.268895i	$0.913342\pi$
$198$	12.8929	+	4.55384i	0.916258	+	0.323627i
$199$	−5.22507	−	9.05009i	−0.370396	−	0.641544i	0.619231	−	0.785209i	$-0.287445\pi$
$199$	−5.22507	−	9.05009i	−0.370396	−	0.641544i	−0.989626	+	0.143665i	$0.954111\pi$
$200$	−1.24581	+	7.06536i	−0.0880924	+	0.499597i
$201$	−4.52892	−	24.9873i	−0.319446	−	1.76247i
$202$	−8.03298	−	2.92376i	−0.565198	−	0.205715i
$203$	0.897215	+	0.326560i	0.0629722	+	0.0229200i
$204$	0.379388	+	2.09319i	0.0265624	+	0.146552i
$205$	4.22746	−	23.9751i	0.295259	−	1.67450i
$206$	4.51154	+	7.81422i	0.314334	+	0.544442i
$207$	−4.05717	−	21.7918i	−0.281993	−	1.51463i
$208$	2.92832	−	5.07199i	0.203042	−	0.351680i
$209$	2.92553	+	2.45481i	0.202363	+	0.169803i
$210$	5.66905	−	2.09404i	0.391201	−	0.144502i
$211$	−3.46152	−	19.6313i	−0.238301	−	1.35147i	−0.835549	−	0.549415i	$-0.814850\pi$
$211$	−3.46152	−	19.6313i	−0.238301	−	1.35147i	0.597248	−	0.802056i	$-0.296261\pi$
$212$	−5.96857	+	5.00823i	−0.409923	+	0.343967i
$213$	−0.0209533	+	0.0366953i	−0.00143570	+	0.00251432i
$214$	2.33982	−	0.851625i	0.159947	−	0.0582159i
$215$	−24.7490			−1.68787
$216$	−2.53343	+	4.53671i	−0.172378	+	0.308684i
$217$	−8.44762			−0.573462
$218$	−0.961614	+	0.349999i	−0.0651287	+	0.0237049i
$219$	4.17674	−	0.0199203i	0.282238	−	0.00134609i
$220$	−12.1825	+	10.2223i	−0.821341	+	0.689187i
$221$	1.24906	+	7.08379i	0.0840211	+	0.476507i
$222$	0.125964	−	0.734857i	0.00845418	−	0.0493204i
$223$	−3.78851	−	3.17894i	−0.253698	−	0.212878i	0.507065	−	0.861908i	$-0.330730\pi$
$223$	−3.78851	−	3.17894i	−0.253698	−	0.212878i	−0.760763	+	0.649030i	$0.775175\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	3.53510	−	21.2308i	0.235673	−	1.41539i
$226$	−3.71133	−	6.42822i	−0.246874	−	0.427599i
$227$	−0.785748	+	4.45620i	−0.0521519	+	0.295768i	−0.999717	−	0.0237950i	$-0.992425\pi$
$227$	−0.785748	+	4.45620i	−0.0521519	+	0.295768i	0.947565	+	0.319563i	$0.103536\pi$
$228$	−1.10729	+	0.938161i	−0.0733320	+	0.0621312i
$229$	16.4995	+	6.00532i	1.09032	+	0.396843i	0.823738	−	0.566971i	$-0.191885\pi$
$229$	16.4995	+	6.00532i	1.09032	+	0.396843i	0.266578	+	0.963813i	$0.414107\pi$
$230$	24.2259	+	8.81750i	1.59741	+	0.581408i
$231$	7.43110	+	2.66463i	0.488930	+	0.175320i
$232$	0.165799	−	0.940291i	0.0108852	−	0.0617331i
$233$	0.652915	+	1.13088i	0.0427739	+	0.0740866i	0.886620	−	0.462499i	$-0.153047\pi$
$233$	0.652915	+	1.13088i	0.0427739	+	0.0740866i	−0.843846	+	0.536586i	$0.819714\pi$
$234$	−8.63942	+	15.2991i	−0.564776	+	1.00013i
$235$	−15.1374	+	26.2188i	−0.987458	+	1.71033i
$236$	8.47947	+	7.11512i	0.551966	+	0.463155i
$237$	−2.77389	−	2.30512i	−0.180183	−	0.149733i
$238$	0.213273	+	1.20953i	0.0138245	+	0.0784024i
$239$	4.82758	−	4.05082i	0.312270	−	0.262026i	−0.473160	−	0.880977i	$-0.656887\pi$
$239$	4.82758	−	4.05082i	0.312270	−	0.262026i	0.785429	+	0.618951i	$0.212442\pi$
$240$	−3.04664	−	5.21930i	−0.196660	−	0.336904i
$241$	22.4922	−	8.18649i	1.44885	−	0.527338i	0.506579	−	0.862193i	$-0.330910\pi$
$241$	22.4922	−	8.18649i	1.44885	−	0.527338i	0.942270	+	0.334855i	$0.108687\pi$
$242$	−9.77381			−0.628284
$243$	7.47012	−	13.6820i	0.479208	−	0.877701i
$244$	10.6558			0.682165
$245$	3.27875	−	1.19337i	0.209472	−	0.0762415i
$246$	6.09235	+	10.4370i	0.388434	+	0.665438i
$247$	−3.75919	+	3.15434i	−0.239192	+	0.200706i
$248$	1.46691	+	8.31928i	0.0931491	+	0.528275i
$249$	22.4150	+	18.6270i	1.42049	+	1.18044i
$250$	5.81177	+	4.87665i	0.367568	+	0.308426i
$251$	−6.86570	+	11.8917i	−0.433359	+	0.750600i	−0.997160	−	0.0753105i	$-0.976005\pi$
$251$	−6.86570	+	11.8917i	−0.433359	+	0.750600i	0.563801	+	0.825911i	$0.309339\pi$
$252$	−1.47515	+	2.61227i	−0.0929257	+	0.164557i
$253$	16.8383	+	29.1648i	1.05862	+	1.83358i
$254$	−1.14668	+	6.50313i	−0.0719489	+	0.408043i
$255$	6.98689	+	2.50535i	0.437536	+	0.156891i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−9.58938	−	3.49025i	−0.598169	−	0.217716i	0.0251494	−	0.999684i	$-0.491994\pi$
$257$	−9.58938	−	3.49025i	−0.598169	−	0.217716i	−0.623319	+	0.781968i	$0.714216\pi$
$258$	9.37352	−	7.94181i	0.583570	−	0.494435i
$259$	0.0747482	−	0.423918i	0.00464463	−	0.0263410i
$260$	−10.2174	−	17.6971i	−0.633657	−	1.09753i
$261$	−0.470467	+	2.82549i	−0.0291211	+	0.174893i
$262$	−4.88346	+	8.45840i	−0.301701	+	0.522561i
$263$	−2.62569	−	2.20322i	−0.161907	−	0.135856i	0.558235	−	0.829683i	$-0.311479\pi$
$263$	−2.62569	−	2.20322i	−0.161907	−	0.135856i	−0.720142	+	0.693827i	$0.755923\pi$
$264$	1.33375	−	7.78091i	0.0820868	−	0.478882i
$265$	4.72074	+	26.7726i	0.289993	+	1.64463i
$266$	−0.641869	+	0.538592i	−0.0393555	+	0.0330232i
$267$	−12.1731	+	0.0580573i	−0.744980	+	0.00355305i
$268$	−13.7773	+	5.01453i	−0.841582	+	0.306311i
$269$	−3.36486			−0.205159			−0.102579	−	0.994725i	$-0.532710\pi$
$269$	−3.36486			−0.205159			−0.102579	+	0.994725i	$0.532710\pi$
$270$	9.28887	+	15.5700i	0.565302	+	0.947560i
$271$	9.07619			0.551339			0.275670	−	0.961252i	$-0.411100\pi$
$271$	9.07619			0.551339			0.275670	+	0.961252i	$0.411100\pi$
$272$	1.15412	−	0.420066i	0.0699790	−	0.0254703i
$273$	−5.03004	+	8.80904i	−0.304432	+	0.533147i
$274$	11.6533	−	9.77831i	0.704004	−	0.590729i
$275$	5.67821	+	32.2027i	0.342409	+	1.94190i
$276$	−12.0049	+	4.43437i	−0.722608	+	0.266918i
$277$	−9.56560	−	8.02649i	−0.574741	−	0.482265i	0.308474	−	0.951233i	$-0.400182\pi$
$277$	−9.56560	−	8.02649i	−0.574741	−	0.482265i	−0.883215	+	0.468968i	$0.844626\pi$
$278$	6.01211	−	10.4133i	0.360582	−	0.624547i
$279$	−4.63860	−	24.9147i	−0.277706	−	1.49161i
$280$	−1.74459	−	3.02172i	−0.104259	−	0.180582i
$281$	3.51004	−	19.9064i	0.209391	−	1.18752i	−0.680987	−	0.732296i	$-0.738449\pi$
$281$	3.51004	−	19.9064i	0.209391	−	1.18752i	0.890378	−	0.455222i	$-0.150440\pi$
$282$	−2.68026	−	14.7877i	−0.159607	−	0.880596i
$283$	−7.69188	−	2.79961i	−0.457235	−	0.166420i	0.103126	−	0.994668i	$-0.467115\pi$
$283$	−7.69188	−	2.79961i	−0.457235	−	0.166420i	−0.560361	+	0.828248i	$0.689338\pi$
$284$	0.0229253	+	0.00834414i	0.00136037	+	0.000495134i
$285$	0.903093	+	4.98261i	0.0534946	+	0.295145i
$286$	4.63528	−	26.2880i	0.274090	−	1.55444i
$287$	3.48864	+	6.04250i	0.205928	+	0.356678i
$288$	2.82874	+	0.999124i	0.166685	+	0.0588740i
$289$	7.74577	−	13.4161i	0.455634	−	0.789181i
$290$	−2.55204	−	2.14142i	−0.149861	−	0.125748i
$291$	−21.9613	+	8.11206i	−1.28739	+	0.475538i
$292$	−0.418748	−	2.37484i	−0.0245054	−	0.138977i
$293$	−8.37145	+	7.02448i	−0.489065	+	0.410375i	−0.853691	−	0.520779i	$-0.825641\pi$
$293$	−8.37145	+	7.02448i	−0.489065	+	0.410375i	0.364626	+	0.931154i	$0.381197\pi$
$294$	−0.858862	+	1.50411i	−0.0500898	+	0.0877217i
$295$	36.2931	−	13.2096i	2.11306	−	0.769092i
$296$	−0.430458			−0.0250199
$297$	−3.77842	+	23.3798i	−0.219246	+	1.35664i
$298$	2.75133			0.159380
$299$	−40.6635	+	14.8003i	−2.35163	+	0.855923i
$300$	−12.4262	+	0.0592647i	−0.717428	+	0.00342165i
$301$	5.43361	−	4.55934i	0.313188	−	0.262796i
$302$	−0.411684	−	2.33477i	−0.0236897	−	0.134351i
$303$	2.50154	−	14.5936i	0.143710	−	0.838381i
$304$	0.641869	+	0.538592i	0.0368137	+	0.0308904i
$305$	18.5899	−	32.1987i	1.06445	−	1.84369i
$306$	−3.45019	+	1.29317i	−0.197234	+	0.0739255i
$307$	1.82256	+	3.15677i	0.104019	+	0.180166i	0.913337	−	0.407205i	$-0.133496\pi$
$307$	1.82256	+	3.15677i	0.104019	+	0.180166i	−0.809318	+	0.587371i	$0.800163\pi$
$308$	0.791459	−	4.48859i	0.0450976	−	0.255761i
$309$	−11.9240	+	10.1027i	−0.678334	+	0.574725i
$310$	27.6977	+	10.0811i	1.57312	+	0.572569i
$311$	−18.8905	−	6.87559i	−1.07118	−	0.389879i	−0.254564	−	0.967056i	$-0.581932\pi$
$311$	−18.8905	−	6.87559i	−1.07118	−	0.389879i	−0.816619	+	0.577177i	$0.804154\pi$
$312$	9.54867	+	3.42395i	0.540587	+	0.193843i
$313$	5.77083	−	32.7280i	0.326187	−	1.84990i	−0.175014	−	0.984566i	$-0.555997\pi$
$313$	5.77083	−	32.7280i	0.326187	−	1.84990i	0.501200	−	0.865331i	$-0.332892\pi$
$314$	−3.98588	−	6.90374i	−0.224936	−	0.389601i
$315$	5.32000	+	9.01481i	0.299748	+	0.507927i
$316$	−1.04115	+	1.80333i	−0.0585695	+	0.101445i
$317$	−21.1190	−	17.7209i	−1.18616	−	0.995307i	−0.999918	−	0.0128027i	$-0.995925\pi$
$317$	−21.1190	−	17.7209i	−1.18616	−	0.995307i	−0.186242	−	0.982504i	$-0.559631\pi$
$318$	−10.3791	−	8.62510i	−0.582033	−	0.483672i
$319$	−0.755682	−	4.28569i	−0.0423101	−	0.239952i
$320$	−2.67286	+	2.24280i	−0.149418	+	0.125376i
$321$	2.17418	+	3.72465i	0.121351	+	0.207890i
$322$	−6.94315	+	2.52710i	−0.386926	+	0.140830i
$323$	−1.02910			−0.0572608
$324$	−8.51441	−	2.91629i	−0.473023	−	0.162016i
$325$	−42.0176			−2.33072
$326$	2.72267	−	0.990971i	0.150795	−	0.0548848i
$327$	−0.893539	−	1.53075i	−0.0494128	−	0.0846506i
$328$	5.34491	−	4.48491i	0.295123	−	0.247638i
$329$	−1.50671	−	8.54498i	−0.0830676	−	0.471100i
$330$	−21.1848	−	17.6047i	−1.16619	−	0.969107i
$331$	17.4897	+	14.6756i	0.961320	+	0.806644i	0.981167	−	0.193159i	$-0.0618735\pi$
$331$	17.4897	+	14.6756i	0.961320	+	0.806644i	−0.0198470	+	0.999803i	$0.506318\pi$
$332$	8.41327	−	14.5722i	0.461738	−	0.799754i
$333$	1.29131	−	0.0123177i	0.0707636	−	0.000675005i
$334$	−2.27498	−	3.94038i	−0.124481	−	0.215608i
$335$	−8.88324	+	50.3794i	−0.485343	+	2.75252i
$336$	1.63040	+	0.584627i	0.0889457	+	0.0318940i
$337$	26.1265	+	9.50926i	1.42320	+	0.518002i	0.934974	−	0.354715i	$-0.115422\pi$
$337$	26.1265	+	9.50926i	1.42320	+	0.518002i	0.488225	+	0.872718i	$0.337644\pi$
$338$	20.0156	+	7.28509i	1.08871	+	0.396256i
$339$	9.80908	−	8.31083i	0.532756	−	0.451383i
$340$	0.744148	−	4.22028i	0.0403571	−	0.228877i
$341$	19.2514	+	33.3444i	1.04252	+	1.80570i
$342$	−1.94093	−	1.59734i	−0.104954	−	0.0863740i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−5.43361	−	4.55934i	−0.292961	−	0.245823i
$345$	−7.54416	+	44.0115i	−0.406164	+	2.36950i
$346$	−1.59882	−	9.06736i	−0.0859531	−	0.487464i
$347$	4.50344	−	3.77883i	0.241757	−	0.202858i	−0.513856	−	0.857876i	$-0.671783\pi$
$347$	4.50344	−	3.77883i	0.241757	−	0.202858i	0.755613	+	0.655018i	$0.227339\pi$
$348$	1.65374	−	0.00788721i	0.0886496	−	0.000422799i
$349$	−11.7340	+	4.27083i	−0.628107	+	0.228612i	−0.636407	−	0.771353i	$-0.719580\pi$
$349$	−11.7340	+	4.27083i	−0.628107	+	0.228612i	0.00830009	+	0.999966i	$0.497358\pi$
$350$	−7.17436			−0.383486
$351$	−28.7427	−	9.99814i	−1.53417	−	0.533661i
$352$	−4.55783			−0.242933
$353$	0.0127909	−	0.00465551i	0.000680792	−	0.000247788i	−0.341680	−	0.939816i	$-0.610996\pi$
$353$	0.0127909	−	0.00465551i	0.000680792	−	0.000247788i	0.342361	+	0.939569i	$0.388774\pi$
$354$	−9.50688	+	16.6493i	−0.505285	+	0.884899i
$355$	0.0652089	−	0.0547168i	0.00346093	−	0.00290407i
$356$	1.22043	+	6.92143i	0.0646829	+	0.366835i
$357$	−1.99551	+	0.737102i	−0.105613	+	0.0390116i
$358$	6.85892	+	5.75532i	0.362505	+	0.304178i
$359$	−15.9100	+	27.5569i	−0.839696	+	1.45440i	0.0504524	+	0.998726i	$0.483934\pi$
$359$	−15.9100	+	27.5569i	−0.839696	+	1.45440i	−0.890149	+	0.455670i	$0.849400\pi$
$360$	7.95405	−	6.80458i	0.419215	−	0.358633i
$361$	9.14896	+	15.8465i	0.481524	+	0.834025i
$362$	2.84804	−	16.1521i	0.149690	−	0.848934i
$363$	−3.01912	−	16.6573i	−0.158463	−	0.874284i
$364$	5.50344	+	2.00309i	0.288458	+	0.104990i
$365$	−7.90662	−	2.87778i	−0.413852	−	0.150630i
$366$	3.29155	+	18.1604i	0.172052	+	0.949260i
$367$	6.51601	−	36.9541i	0.340133	−	1.92899i	−0.0289189	−	0.999582i	$-0.509206\pi$
$367$	6.51601	−	36.9541i	0.340133	−	1.92899i	0.369052	−	0.929409i	$-0.379682\pi$
$368$	3.69437	+	6.39884i	0.192582	+	0.333563i
$369$	−15.9057	+	13.6071i	−0.828016	+	0.708356i
$370$	−0.750972	+	1.30072i	−0.0390412	+	0.0676213i
$371$	−5.96857	−	5.00823i	−0.309873	−	0.260014i
$372$	−13.7253	+	5.06985i	−0.711623	+	0.262860i
$373$	−0.946384	−	5.36721i	−0.0490019	−	0.277904i	0.950455	−	0.310863i	$-0.100618\pi$
$373$	−0.946384	−	5.36721i	−0.0490019	−	0.277904i	−0.999457	+	0.0329592i	$0.989507\pi$
$374$	4.28823	−	3.59825i	0.221739	−	0.186061i
$375$	−6.51594	+	11.4113i	−0.336482	+	0.589276i
$376$	−8.15352	+	2.96764i	−0.420486	+	0.153044i
$377$	5.59189			0.287997
$378$	−4.90771	−	1.70715i	−0.252426	−	0.0878062i
$379$	−17.4571			−0.896712			−0.448356	−	0.893855i	$-0.647990\pi$
$379$	−17.4571			−0.896712			−0.448356	+	0.893855i	$0.647990\pi$
$380$	2.74727	−	0.999925i	0.140932	−	0.0512950i
$381$	−11.4374	+	0.0545486i	−0.585955	+	0.00279461i
$382$	1.35037	−	1.13309i	0.0690908	−	0.0579741i
$383$	4.08862	+	23.1877i	0.208919	+	1.18484i	0.891153	+	0.453703i	$0.149897\pi$
$383$	4.08862	+	23.1877i	0.208919	+	1.18484i	−0.682234	+	0.731134i	$0.738992\pi$
$384$	0.292629	−	1.70715i	0.0149332	−	0.0871177i
$385$	−12.1825	−	10.2223i	−0.620876	−	0.520977i
$386$	3.13851	−	5.43606i	0.159746	−	0.276688i
$387$	16.4306	+	13.5219i	0.835212	+	0.687358i
$388$	6.75834	+	11.7058i	0.343103	+	0.594271i
$389$	1.51951	−	8.61757i	0.0770422	−	0.436928i	−0.921750	−	0.387786i	$-0.873240\pi$
$389$	1.51951	−	8.61757i	0.0770422	−	0.436928i	0.998792	−	0.0491424i	$-0.0156488\pi$
$390$	27.0047	−	22.8800i	1.36744	−	1.15857i
$391$	−8.52752	−	3.10376i	−0.431255	−	0.156964i
$392$	0.939693	+	0.342020i	0.0474616	+	0.0172746i
$393$	−15.9240	−	5.71000i	−0.803259	−	0.288032i
$394$	−3.48264	+	19.7510i	−0.175453	+	0.995041i
$395$	3.63277	+	6.29214i	0.182785	+	0.316592i
$396$	13.6729	−	0.130424i	0.687087	−	0.00655404i
$397$	−7.51055	+	13.0087i	−0.376944	+	0.652886i	−0.990616	−	0.136675i	$-0.956358\pi$
$397$	−7.51055	+	13.0087i	−0.376944	+	0.652886i	0.613672	+	0.789561i	$0.289692\pi$
$398$	−8.00527	−	6.71722i	−0.401268	−	0.336704i
$399$	−1.11619	−	0.927556i	−0.0558792	−	0.0464359i
$400$	1.24581	+	7.06536i	0.0622907	+	0.353268i
$401$	26.7772	−	22.4688i	1.33719	−	1.12204i	0.354853	−	0.934922i	$-0.384531\pi$
$401$	26.7772	−	22.4688i	1.33719	−	1.12204i	0.982338	−	0.187115i	$-0.0599136\pi$
$402$	−12.8020	−	21.9314i	−0.638504	−	1.09384i
$403$	−46.4909	+	16.9213i	−2.31588	+	0.842911i
$404$	−8.54851			−0.425304
$405$	−23.6664	+	20.6404i	−1.17599	+	1.02563i
$406$	0.954796			0.0473857
$407$	−1.84363	+	0.671028i	−0.0913855	+	0.0332616i
$408$	1.07242	+	1.83719i	0.0530927	+	0.0909547i
$409$	−12.9586	+	10.8736i	−0.640762	+	0.537663i	−0.904252	−	0.426999i	$-0.859571\pi$
$409$	−12.9586	+	10.8736i	−0.640762	+	0.537663i	0.263490	+	0.964662i	$0.415126\pi$
$410$	−4.22746	−	23.9751i	−0.208779	−	1.18405i
$411$	20.2647	+	16.8401i	0.999585	+	0.830660i
$412$	6.91208	+	5.79992i	0.340534	+	0.285742i
$413$	−5.53458	+	9.58618i	−0.272339	+	0.471705i
$414$	−11.2657	−	19.0899i	−0.553680	−	0.938219i
$415$	−29.3554	−	50.8450i	−1.44100	−	2.49588i
$416$	1.01699	−	5.76766i	0.0498622	−	0.282783i
$417$	19.6043	+	7.02968i	0.960027	+	0.344245i
$418$	3.58869	+	1.30618i	0.175529	+	0.0638872i
$419$	−29.3761	−	10.6920i	−1.43512	−	0.522340i	−0.496725	−	0.867908i	$-0.665464\pi$
$419$	−29.3761	−	10.6920i	−1.43512	−	0.522340i	−0.938394	+	0.345568i	$0.887686\pi$
$420$	4.61096	−	3.90668i	0.224992	−	0.190626i
$421$	−1.81909	+	10.3166i	−0.0886571	+	0.502799i	0.907850	+	0.419295i	$0.137723\pi$
$421$	−1.81909	+	10.3166i	−0.0886571	+	0.502799i	−0.996507	+	0.0835049i	$0.973389\pi$
$422$	−9.96705	−	17.2634i	−0.485189	−	0.840371i
$423$	24.3745	−	9.13583i	1.18513	−	0.444199i
$424$	−3.89571	+	6.74757i	−0.189192	+	0.327691i
$425$	−6.74999	−	5.66392i	−0.327423	−	0.274740i
$426$	−0.00713916	+	0.0416488i	−0.000345894	+	0.00201789i
$427$	1.85035	+	10.4939i	0.0895448	+	0.507834i
$428$	1.90744	−	1.60053i	0.0921996	−	0.0773646i
$429$	46.2340	−	0.220505i	2.23220	−	0.0106461i
$430$	−23.2565	+	8.46466i	−1.12153	+	0.408202i
$431$	27.4019			1.31990			0.659950	−	0.751309i	$-0.270577\pi$
$431$	27.4019			1.31990			0.659950	+	0.751309i	$0.270577\pi$
$432$	−0.828996	+	5.12960i	−0.0398851	+	0.246798i
$433$	−10.5172			−0.505424			−0.252712	−	0.967541i	$-0.581323\pi$
$433$	−10.5172			−0.505424			−0.252712	+	0.967541i	$0.581323\pi$
$434$	−7.93816	+	2.88926i	−0.381044	+	0.138689i
$435$	2.86126	−	5.01088i	0.137187	−	0.240253i
$436$	−0.783915	+	0.657783i	−0.0375427	+	0.0315021i
$437$	−1.07506	−	6.09698i	−0.0514272	−	0.291658i
$438$	3.91804	−	1.44725i	0.187211	−	0.0691523i
$439$	−3.60794	−	3.02742i	−0.172198	−	0.144491i	0.552616	−	0.833436i	$-0.313630\pi$
$439$	−3.60794	−	3.02742i	−0.172198	−	0.144491i	−0.724814	+	0.688945i	$0.758074\pi$
$440$	−7.95154	+	13.7725i	−0.379075	+	0.656577i
$441$	−2.82874	−	0.999124i	−0.134702	−	0.0475773i
$442$	3.59654	+	6.22938i	0.171070	+	0.296302i
$443$	3.71847	−	21.0885i	0.176670	−	1.00195i	−0.759529	−	0.650474i	$-0.774570\pi$
$443$	3.71847	−	21.0885i	0.176670	−	1.00195i	0.936199	−	0.351472i	$-0.114319\pi$
$444$	−0.132968	−	0.733622i	−0.00631039	−	0.0348162i
$445$	23.0437	+	8.38724i	1.09238	+	0.397593i
$446$	−4.64730	−	1.69148i	−0.220056	−	0.0800938i
$447$	0.849882	+	4.68904i	0.0401980	+	0.221784i
$448$	0.173648	−	0.984808i	0.00820411	−	0.0465278i
$449$	−18.0411	−	31.2481i	−0.851411	−	1.47469i	−0.879935	−	0.475094i	$-0.842414\pi$
$449$	−18.0411	−	31.2481i	−0.851411	−	1.47469i	0.0285244	−	0.999593i	$-0.490919\pi$
$450$	−3.93945	−	21.1595i	−0.185707	−	0.997467i
$451$	15.9006	−	27.5407i	0.748732	−	1.29684i
$452$	−5.68609	−	4.77120i	−0.267451	−	0.224418i
$453$	3.85195	−	1.42284i	0.180980	−	0.0668506i
$454$	0.785748	+	4.45620i	0.0368770	+	0.209140i
$455$	15.6540	−	13.1353i	0.733870	−	0.615790i
$456$	−0.719641	+	1.26030i	−0.0337003	+	0.0590188i
$457$	−29.7643	+	10.8333i	−1.39231	+	0.506761i	−0.925888	−	0.377799i	$-0.876681\pi$
$457$	−29.7643	+	10.8333i	−1.39231	+	0.506761i	−0.466427	+	0.884560i	$0.654459\pi$
$458$	17.5584			0.820449
$459$	−3.26969	−	5.48064i	−0.152616	−	0.255815i
$460$	25.7806			1.20203
$461$	−6.97397	+	2.53832i	−0.324810	+	0.118221i	−0.499279	−	0.866442i	$-0.666402\pi$
$461$	−6.97397	+	2.53832i	−0.324810	+	0.118221i	0.174468	+	0.984663i	$0.444179\pi$
$462$	7.89430	−	0.0376505i	0.367276	−	0.00175166i
$463$	−19.1851	+	16.0982i	−0.891607	+	0.748147i	−0.968532	−	0.248890i	$-0.919934\pi$
$463$	−19.1851	+	16.0982i	−0.891607	+	0.748147i	0.0769251	+	0.997037i	$0.475490\pi$
$464$	−0.165799	−	0.940291i	−0.00769701	−	0.0436519i
$465$	−8.62531	+	50.3187i	−0.399989	+	2.33347i
$466$	1.00032	+	0.839372i	0.0463391	+	0.0388831i
$467$	−16.7076	+	28.9384i	−0.773136	+	1.33911i	0.162700	+	0.986676i	$0.447980\pi$
$467$	−16.7076	+	28.9384i	−0.773136	+	1.33911i	−0.935836	+	0.352436i	$0.885354\pi$
$468$	−2.88580	+	17.3313i	−0.133396	+	0.801139i
$469$	−7.33075	−	12.6972i	−0.338502	−	0.586303i
$470$	−5.25718	+	29.8149i	−0.242496	+	1.37526i
$471$	10.5347	−	8.92562i	0.485413	−	0.411271i
$472$	10.4016	+	3.78588i	0.478773	+	0.174259i
$473$	−30.3794	−	11.0572i	−1.39684	−	0.508410i
$474$	−3.39500	−	1.21737i	−0.155937	−	0.0559158i
$475$	1.04387	−	5.92007i	0.0478960	−	0.271632i
$476$	0.614096	+	1.06365i	0.0281470	+	0.0487521i
$477$	11.4935	−	20.3533i	0.526252	−	0.931912i
$478$	3.15098	−	5.45765i	0.144122	−	0.249627i
$479$	12.4361	+	10.4351i	0.568219	+	0.476792i	0.881054	−	0.473015i	$-0.156834\pi$
$479$	12.4361	+	10.4351i	0.568219	+	0.476792i	−0.312836	+	0.949807i	$0.601279\pi$
$480$	−4.64801	−	3.86252i	−0.212152	−	0.176299i
$481$	−0.437773	−	2.48273i	−0.0199607	−	0.113203i
$482$	18.3358	−	15.3856i	0.835173	−	0.700793i
$483$	−6.45162	−	11.0525i	−0.293559	−	0.502905i
$484$	−9.18438	+	3.34284i	−0.417472	+	0.151947i
$485$	47.1621			2.14152
$486$	2.34009	−	15.4118i	0.106149	−	0.699094i
$487$	5.01634			0.227312			0.113656	−	0.993520i	$-0.463744\pi$
$487$	5.01634			0.227312			0.113656	+	0.993520i	$0.463744\pi$
$488$	10.0131	−	3.64448i	0.453273	−	0.164978i
$489$	2.52993	+	4.33409i	0.114407	+	0.195994i
$490$	2.67286	−	2.24280i	0.120748	−	0.101319i
$491$	5.09109	+	28.8730i	0.229758	+	1.30302i	0.853378	+	0.521293i	$0.174550\pi$
$491$	5.09109	+	28.8730i	0.229758	+	1.30302i	−0.623620	+	0.781728i	$0.714339\pi$
$492$	9.29460	+	7.72385i	0.419033	+	0.348218i
$493$	0.898320	+	0.753780i	0.0404583	+	0.0339485i
$494$	−2.45364	+	4.24983i	−0.110394	+	0.191209i
$495$	23.4594	−	41.5431i	1.05442	−	1.86722i
$496$	4.22381	+	7.31585i	0.189655	+	0.328491i
$497$	−0.00423643	+	0.0240260i	−0.000190030	+	0.00107771i
$498$	27.4340	+	9.83725i	1.22935	+	0.440818i
$499$	−12.8185	−	4.66554i	−0.573833	−	0.208858i	0.0387710	−	0.999248i	$-0.487656\pi$
$499$	−12.8185	−	4.66554i	−0.573833	−	0.208858i	−0.612604	+	0.790390i	$0.709878\pi$
$500$	7.12919	+	2.59481i	0.318827	+	0.116043i
$501$	6.01278	−	5.09438i	0.268631	−	0.227600i
$502$	−2.38443	+	13.5228i	−0.106422	+	0.603552i
$503$	−17.1288	−	29.6679i	−0.763734	−	1.32283i	−0.940913	−	0.338647i	$-0.890031\pi$
$503$	−17.1288	−	29.6679i	−0.763734	−	1.32283i	0.177180	−	0.984179i	$-0.443303\pi$
$504$	−0.492740	+	2.95926i	−0.0219484	+	0.131816i
$505$	−14.9136	+	25.8312i	−0.663648	+	1.14947i
$506$	25.7978	+	21.6469i	1.14685	+	0.962323i
$507$	−6.23304	+	36.3626i	−0.276819	+	1.61492i
$508$	1.14668	+	6.50313i	0.0508756	+	0.288530i
$509$	8.68647	−	7.28881i	0.385021	−	0.323071i	−0.429649	−	0.902996i	$-0.641363\pi$
$509$	8.68647	−	7.28881i	0.385021	−	0.323071i	0.814670	+	0.579925i	$0.196918\pi$
$510$	7.42241	−	0.0353999i	0.328670	−	0.00156753i
$511$	2.26604	−	0.824772i	0.100244	−	0.0364858i
$512$	−1.00000			−0.0441942
$513$	2.12276	−	3.80131i	0.0937221	−	0.167832i
$514$	−10.2048			−0.450115
$515$	29.5845	−	10.7679i	1.30365	−	0.474489i
$516$	6.09197	−	10.6688i	0.268184	−	0.469667i
$517$	−30.2950	+	25.4206i	−1.33237	+	1.11799i
$518$	−0.0747482	−	0.423918i	−0.00328425	−	0.0186259i
$519$	14.9595	−	5.52574i	0.656648	−	0.242553i
$520$	−15.6540	−	13.1353i	−0.686473	−	0.576019i
$521$	7.80766	−	13.5233i	0.342060	−	0.592465i	−0.642755	−	0.766071i	$-0.722209\pi$
$521$	7.80766	−	13.5233i	0.342060	−	0.592465i	0.984815	+	0.173607i	$0.0555422\pi$
$522$	0.524280	+	2.81600i	0.0229471	+	0.123253i
$523$	10.3068	+	17.8520i	0.450687	+	0.780612i	0.998429	−	0.0560349i	$-0.0178458\pi$
$523$	10.3068	+	17.8520i	0.450687	+	0.780612i	−0.547742	+	0.836647i	$0.684512\pi$
$524$	−1.69601	+	9.61853i	−0.0740904	+	0.420188i
$525$	−2.21615	−	12.2271i	−0.0967209	−	0.533636i
$526$	−3.22089	−	1.17231i	−0.140437	−	0.0511151i
$527$	−9.74959	−	3.54856i	−0.424699	−	0.154578i
$528$	−1.40791	−	7.76783i	−0.0612714	−	0.338052i
$529$	5.48616	−	31.1135i	0.238529	−	1.35276i
$530$	13.5928	+	23.5435i	0.590435	+	1.02266i
$531$	−31.3117	−	11.0595i	−1.35881	−	0.479940i
$532$	−0.418950	+	0.725643i	−0.0181638	+	0.0314606i
$533$	31.3032	+	26.2665i	1.35589	+	1.13773i
$534$	−11.4191	+	4.21799i	−0.494152	+	0.182530i
$535$	−1.50866	−	8.55601i	−0.0652249	−	0.369909i
$536$	−11.2314	+	9.42423i	−0.485121	+	0.407065i
$537$	−7.68998	+	13.4674i	−0.331847	+	0.581159i
$538$	−3.16193	+	1.15085i	−0.136320	+	0.0496166i
$539$	4.55783			0.196320
$540$	14.0539	+	11.4540i	0.604785	+	0.492903i
$541$	21.5756			0.927606			0.463803	−	0.885938i	$-0.346485\pi$
$541$	21.5756			0.927606			0.463803	+	0.885938i	$0.346485\pi$
$542$	8.52882	−	3.10424i	0.366344	−	0.133338i
$543$	28.4074	−	0.135484i	1.21908	−	0.00581419i
$544$	0.940850	−	0.789467i	0.0403386	−	0.0338481i
$545$	0.620024	+	3.51633i	0.0265589	+	0.150623i
$546$	−1.71382	+	9.99817i	−0.0733447	+	0.427882i
$547$	11.9267	+	10.0077i	0.509951	+	0.427900i	0.861112	−	0.508415i	$-0.169769\pi$
$547$	11.9267	+	10.0077i	0.509951	+	0.427900i	−0.351161	+	0.936315i	$0.614213\pi$
$548$	7.60618	−	13.1743i	0.324920	−	0.562777i
$549$	−29.9337	+	11.2195i	−1.27754	+	0.478836i
$550$	16.3498	+	28.3186i	0.697156	+	1.20751i
$551$	−0.138923	+	0.787870i	−0.00591831	+	0.0335644i
$552$	−9.76425	+	8.27285i	−0.415594	+	0.352116i
$553$	−1.95673	−	0.712191i	−0.0832086	−	0.0302855i
$554$	−11.7339	−	4.27081i	−0.498528	−	0.181449i
$555$	−2.44877	−	0.878077i	−0.103945	−	0.0372723i
$556$	2.08798	−	11.8415i	0.0885502	−	0.502193i
$557$	17.5941	+	30.4738i	0.745484	+	1.29122i	0.949968	+	0.312346i	$0.101115\pi$
$557$	17.5941	+	30.4738i	0.745484	+	1.29122i	−0.204484	+	0.978870i	$0.565552\pi$
$558$	−12.8802	−	21.8257i	−0.545262	−	0.923955i
$559$	20.7708	−	35.9760i	0.878510	−	1.52162i
$560$	−2.67286	−	2.24280i	−0.112949	−	0.0947756i
$561$	7.45708	+	6.19687i	0.314838	+	0.261632i
$562$	−3.51004	−	19.9064i	−0.148062	−	0.839702i
$563$	13.6284	−	11.4356i	0.574369	−	0.481953i	−0.308723	−	0.951152i	$-0.599902\pi$
$563$	13.6284	−	11.4356i	0.574369	−	0.481953i	0.883093	+	0.469199i	$0.155457\pi$
$564$	−7.57631	−	12.9792i	−0.319020	−	0.546523i
$565$	−24.3371	+	8.85798i	−1.02387	+	0.372658i
$566$	−8.18552			−0.344063
$567$	1.39347	−	8.89147i	0.0585204	−	0.373407i
$568$	0.0243966			0.00102366
$569$	−8.69197	+	3.16362i	−0.364386	+	0.132626i	−0.517723	−	0.855548i	$-0.673220\pi$
$569$	−8.69197	+	3.16362i	−0.364386	+	0.132626i	0.153337	+	0.988174i	$0.450998\pi$
$570$	2.55278	+	4.37325i	0.106924	+	0.183175i
$571$	25.2211	−	21.1630i	1.05547	−	0.885646i	0.0618132	−	0.998088i	$-0.480312\pi$
$571$	25.2211	−	21.1630i	1.05547	−	0.885646i	0.993658	+	0.112442i	$0.0358672\pi$
$572$	−4.63528	−	26.2880i	−0.193811	−	1.09916i
$573$	2.34824	+	1.95140i	0.0980991	+	0.0815208i
$574$	5.34491	+	4.48491i	0.223092	+	0.187197i
$575$	26.5047	−	45.9076i	1.10532	−	1.91448i
$576$	2.99986	−	0.0286153i	0.124994	−	0.00119230i
$577$	−0.102627	−	0.177755i	−0.00427242	−	0.00740005i	0.863881	−	0.503695i	$-0.168027\pi$
$577$	−0.102627	−	0.177755i	−0.00427242	−	0.00740005i	−0.868154	+	0.496295i	$0.834693\pi$
$578$	2.69008	−	15.2562i	0.111893	−	0.634574i
$579$	10.2341	+	3.66972i	0.425313	+	0.152508i
$580$	−3.13054	−	1.13942i	−0.129989	−	0.0473120i
$581$	15.8118	+	5.75502i	0.655983	+	0.238758i
$582$	−17.8623	+	15.1340i	−0.740418	+	0.627326i
$583$	−6.16659	+	34.9725i	−0.255394	+	1.44841i
$584$	−1.20574	−	2.08840i	−0.0498937	−	0.0864185i
$585$	47.3357	+	38.9560i	1.95709	+	1.61063i
$586$	−5.46408	+	9.46406i	−0.225719	+	0.390957i
$587$	−12.6791	−	10.6390i	−0.523322	−	0.439119i	0.342466	−	0.939530i	$-0.388738\pi$
$587$	−12.6791	−	10.6390i	−0.523322	−	0.439119i	−0.865788	+	0.500411i	$0.833182\pi$
$588$	−0.292629	+	1.70715i	−0.0120678	+	0.0704018i
$589$	−1.22913	−	6.97073i	−0.0506453	−	0.287224i
$590$	29.5864	−	24.8259i	1.21805	−	1.02207i
$591$	−34.7371	+	0.165673i	−1.42889	+	0.00681486i
$592$	−0.404498	+	0.147225i	−0.0166248	+	0.00605092i
$593$	−15.3451			−0.630147			−0.315074	−	0.949067i	$-0.602029\pi$
$593$	−15.3451			−0.630147			−0.315074	+	0.949067i	$0.602029\pi$
$594$	4.44582	+	23.2622i	0.182414	+	0.954458i
$595$	4.28538			0.175683
$596$	2.58540	−	0.941009i	0.105902	−	0.0385452i
$597$	8.97523	−	15.7182i	0.367332	−	0.643303i
$598$	−33.1492	+	27.8155i	−1.35557	+	1.13746i
$599$	−0.816771	−	4.63214i	−0.0333724	−	0.189264i	0.963564	−	0.267477i	$-0.0861898\pi$
$599$	−0.816771	−	4.63214i	−0.0333724	−	0.189264i	−0.996937	+	0.0782126i	$0.975079\pi$
$600$	−11.6565	+	4.30571i	−0.475877	+	0.175780i
$601$	6.76569	+	5.67709i	0.275978	+	0.231573i	0.770262	−	0.637727i	$-0.220125\pi$
$601$	6.76569	+	5.67709i	0.275978	+	0.231573i	−0.494284	+	0.869300i	$0.664570\pi$
$602$	3.54654	−	6.14278i	0.144546	−	0.250361i
$603$	33.4229	−	28.5928i	1.36108	−	1.16439i
$604$	−1.18540	−	2.05317i	−0.0482331	−	0.0835421i
$605$	−5.92185	+	33.5845i	−0.240757	+	1.36540i
$606$	−2.64063	−	14.5691i	−0.107268	−	0.591829i
$607$	19.4386	+	7.07507i	0.788988	+	0.287168i	0.704915	−	0.709291i	$-0.250985\pi$
$607$	19.4386	+	7.07507i	0.788988	+	0.287168i	0.0840729	+	0.996460i	$0.473207\pi$
$608$	0.787369	+	0.286579i	0.0319320	+	0.0116223i
$609$	0.294936	+	1.62724i	0.0119514	+	0.0659392i
$610$	6.45621	−	36.6150i	0.261404	−	1.48250i
$611$	−25.4084	−	44.0087i	−1.02791	−	1.78040i
$612$	−2.79983	+	2.39521i	−0.113176	+	0.0968208i
$613$	6.82664	−	11.8241i	0.275726	−	0.477571i	−0.694592	−	0.719404i	$-0.744415\pi$
$613$	6.82664	−	11.8241i	0.275726	−	0.477571i	0.970318	+	0.241833i	$0.0777486\pi$
$614$	2.79232	+	2.34304i	0.112689	+	0.0945573i
$615$	39.5545	−	14.6107i	1.59499	−	0.589160i
$616$	−0.791459	−	4.48859i	−0.0318888	−	0.180850i
$617$	−32.6841	+	27.4252i	−1.31581	+	1.10410i	−0.328637	+	0.944456i	$0.606589\pi$
$617$	−32.6841	+	27.4252i	−1.31581	+	1.10410i	−0.987175	+	0.159641i	$0.948966\pi$
$618$	−7.74958	+	13.5717i	−0.311734	+	0.545935i
$619$	−12.5311	+	4.56096i	−0.503669	+	0.183321i	−0.581343	−	0.813658i	$-0.697473\pi$
$619$	−12.5311	+	4.56096i	−0.503669	+	0.183321i	0.0776745	+	0.996979i	$0.475251\pi$
$620$	29.4752			1.18375
$621$	29.0547	−	25.0968i	1.16592	−	1.00710i
$622$	−20.1029			−0.806052
$623$	−6.60435	+	2.40379i	−0.264598	+	0.0963057i
$624$	10.1439	−	0.0483795i	0.406080	−	0.00193673i
$625$	−7.20111	+	6.04244i	−0.288044	+	0.241698i
$626$	−5.77083	−	32.7280i	−0.230649	−	1.30807i
$627$	−1.11755	+	6.51963i	−0.0446307	+	0.260369i
$628$	−6.10672	−	5.12414i	−0.243685	−	0.204476i
$629$	0.264342	−	0.457855i	0.0105400	−	0.0182559i
$630$	8.08241	+	6.65161i	0.322011	+	0.265006i
$631$	−13.4869	−	23.3600i	−0.536904	−	0.929945i	−0.999069	−	0.0431512i	$-0.986260\pi$
$631$	−13.4869	−	23.3600i	−0.536904	−	0.929945i	0.462164	−	0.886794i	$-0.347073\pi$
$632$	−0.361589	+	2.05067i	−0.0143832	+	0.0815714i
$633$	26.3430	−	22.3193i	1.04704	−	0.887114i
$634$	−25.9063	−	9.42911i	−1.02887	−	0.374478i
$635$	21.6511	+	7.88035i	0.859197	+	0.312722i
$636$	−12.7031	−	4.55508i	−0.503713	−	0.180621i
$637$	−1.01699	+	5.76766i	−0.0402948	+	0.228523i
$638$	−2.17590	−	3.76877i	−0.0861447	−	0.149207i
$639$	−0.0731866		0.000698118i	−0.00289522		2.76171e-5i
$640$	−1.74459	+	3.02172i	−0.0689609	+	0.119444i
$641$	10.3416	+	8.67764i	0.408469	+	0.342746i	0.823756	−	0.566944i	$-0.191874\pi$
$641$	10.3416	+	8.67764i	0.408469	+	0.342746i	−0.415287	+	0.909690i	$0.636319\pi$
$642$	3.31697	+	2.75641i	0.130910	+	0.108787i
$643$	5.47398	+	31.0445i	0.215873	+	1.22427i	0.879386	+	0.476110i	$0.157953\pi$
$643$	5.47398	+	31.0445i	0.215873	+	1.22427i	−0.663513	+	0.748164i	$0.730935\pi$
$644$	−5.66011	+	4.74939i	−0.223039	+	0.187152i
$645$	−21.6101	−	37.0209i	−0.850896	−	1.45769i
$646$	−0.967040	+	0.351974i	−0.0380477	+	0.0138482i
$647$	−44.3345			−1.74297			−0.871484	−	0.490423i	$-0.836842\pi$
$647$	−44.3345			−1.74297			−0.871484	+	0.490423i	$0.836842\pi$
$648$	−8.99836	+	0.171684i	−0.353489	+	0.00674439i
$649$	50.4514			1.98039
$650$	−39.4836	+	14.3709i	−1.54868	+	0.563672i
$651$	−7.37620	−	12.6364i	−0.289096	−	0.495259i
$652$	2.21954	−	1.86242i	0.0869240	−	0.0729379i
$653$	−5.23455	−	29.6866i	−0.204844	−	1.16173i	−0.897686	−	0.440637i	$-0.854753\pi$
$653$	−5.23455	−	29.6866i	−0.204844	−	1.16173i	0.692842	−	0.721089i	$-0.256358\pi$
$654$	−1.36320	−	1.13283i	−0.0533053	−	0.0442970i
$655$	26.1056	+	21.9052i	1.02003	+	0.855908i
$656$	3.48864	−	6.04250i	0.136209	−	0.235920i
$657$	3.67680	+	6.23040i	0.143446	+	0.243071i
$658$	−4.33840	−	7.51433i	−0.169128	−	0.292939i
$659$	0.176928	−	1.00341i	0.00689212	−	0.0390871i	−0.981168	−	0.193158i	$-0.938127\pi$
$659$	0.176928	−	1.00341i	0.00689212	−	0.0390871i	0.988060	+	0.154070i	$0.0492383\pi$
$660$	−25.9284	−	9.29737i	−1.00926	−	0.361900i
$661$	38.7460	+	14.1024i	1.50704	+	0.548519i	0.957873	−	0.287192i	$-0.0927217\pi$
$661$	38.7460	+	14.1024i	1.50704	+	0.548519i	0.549170	+	0.835711i	$0.314944\pi$
$662$	21.4543	+	7.80872i	0.833844	+	0.303495i
$663$	−9.50567	+	8.05377i	−0.369169	+	0.312782i
$664$	2.92190	−	16.5709i	0.113392	−	0.643076i
$665$	1.46179	+	2.53190i	0.0566859	+	0.0981828i
$666$	1.20923	−	0.453231i	0.0468566	−	0.0175623i
$667$	−3.52737	+	6.10959i	−0.136580	+	0.236564i
$668$	−3.48547	−	2.92465i	−0.134857	−	0.113158i
$669$	1.44721	−	8.44281i	0.0559524	−	0.326418i
$670$	8.88324	+	50.3794i	0.343190	+	1.94632i
$671$	37.2046	−	31.2183i	1.43627	−	1.20517i
$672$	1.73203	−	0.00826063i	0.0668146	−	0.000318661i
$673$	−3.71215	+	1.35111i	−0.143093	+	0.0520816i	−0.412574	−	0.910924i	$-0.635370\pi$
$673$	−3.71215	+	1.35111i	−0.143093	+	0.0520816i	0.269481	+	0.963006i	$0.413148\pi$
$674$	27.8032			1.07094
$675$	34.8448	−	13.2501i	1.34118	−	0.509996i
$676$	21.3002			0.819237
$677$	21.7634	−	7.92124i	0.836436	−	0.304438i	0.111939	−	0.993715i	$-0.464294\pi$
$677$	21.7634	−	7.92124i	0.836436	−	0.304438i	0.724498	+	0.689277i	$0.242072\pi$
$678$	6.37504	−	11.1645i	0.244832	−	0.428771i
$679$	−10.3544	+	8.68836i	−0.397365	+	0.333429i
$680$	−0.744148	−	4.22028i	−0.0285368	−	0.161840i
$681$	−7.35191	+	2.71565i	−0.281726	+	0.104064i
$682$	29.4949	+	24.7491i	1.12942	+	0.947693i
$683$	6.84387	−	11.8539i	0.261873	−	0.453578i	−0.704866	−	0.709340i	$-0.748993\pi$
$683$	6.84387	−	11.8539i	0.261873	−	0.453578i	0.966740	+	0.255762i	$0.0823264\pi$
$684$	−2.37020	−	0.837167i	−0.0906269	−	0.0320099i
$685$	−26.5393	−	45.9674i	−1.01401	−	1.75632i
$686$	−0.173648	+	0.984808i	−0.00662992	+	0.0376001i
$687$	5.42377	+	29.9244i	0.206930	+	1.14169i
$688$	−6.66531	−	2.42597i	−0.254113	−	0.0924894i
$689$	−42.8796	−	15.6069i	−1.63358	−	0.594575i
$690$	7.96362	+	43.9375i	0.303170	+	1.67267i
$691$	0.0991261	−	0.562172i	0.00377093	−	0.0213860i	−0.982864	−	0.184331i	$-0.940988\pi$
$691$	0.0991261	−	0.562172i	0.00377093	−	0.0213860i	0.986635	+	0.162945i	$0.0520993\pi$
$692$	−4.60362	−	7.97370i	−0.175003	−	0.303115i
$693$	2.50271	+	13.4425i	0.0950701	+	0.510638i
$694$	2.93941	−	5.09121i	0.111578	−	0.193260i
$695$	−32.1391	−	26.9679i	−1.21911	−	1.02295i
$696$	1.55131	−	0.573023i	0.0588021	−	0.0217204i
$697$	1.48807	+	8.43925i	0.0563646	+	0.319660i
$698$	−9.56565	+	8.02654i	−0.362065	+	0.303809i
$699$	−1.12153	+	1.96412i	−0.0424201	+	0.0742897i
$700$	−6.74169	+	2.45378i	−0.254812	+	0.0927440i
$701$	−7.18650			−0.271430			−0.135715	−	0.990748i	$-0.543333\pi$
$701$	−7.18650			−0.271430			−0.135715	+	0.990748i	$0.543333\pi$
$702$	−30.4288	+	0.435402i	−1.14846	+	0.0164332i
$703$	0.360681			0.0136033
$704$	−4.28296	+	1.55887i	−0.161420	+	0.0587521i
$705$	−52.4370	+	0.250089i	−1.97489	+	0.00941891i
$706$	0.0104273	−	0.00874950i	0.000392435	−	0.000329292i
$707$	−1.48443	−	8.41864i	−0.0558279	−	0.316616i
$708$	−3.23916	+	18.8967i	−0.121735	+	0.710183i
$709$	−17.6393	−	14.8011i	−0.662458	−	0.555868i	0.248365	−	0.968667i	$-0.420107\pi$
$709$	−17.6393	−	14.8011i	−0.662458	−	0.555868i	−0.910822	+	0.412799i	$0.864551\pi$
$710$	0.0425621	−	0.0737197i	0.00159733	−	0.00276665i
$711$	1.02604	−	6.16209i	0.0384794	−	0.231096i
$712$	3.51410	+	6.08660i	0.131697	+	0.228105i
$713$	10.8386	−	61.4690i	0.405910	−	2.30203i
$714$	−1.62306	+	1.37515i	−0.0607415	+	0.0514638i
$715$	−87.5216	−	31.8552i	−3.27312	−	1.19132i
$716$	8.41371	+	3.06234i	0.314435	+	0.114445i
$717$	10.2747	+	3.68429i	0.383716	+	0.137592i
$718$	−5.52548	+	31.3365i	−0.206209	+	1.16947i
$719$	11.3764	+	19.7046i	0.424270	+	0.734857i	0.996352	−	0.0853396i	$-0.0271975\pi$
$719$	11.3764	+	19.7046i	0.424270	+	0.734857i	−0.572082	+	0.820196i	$0.693864\pi$
$720$	5.14706	−	9.11466i	0.191820	−	0.339683i
$721$	−4.51154	+	7.81422i	−0.168019	+	0.291017i
$722$	14.0170	+	11.7617i	0.521660	+	0.437724i
$723$	31.8853	+	26.4968i	1.18583	+	0.985427i
$724$	−2.84804	−	16.1521i	−0.105847	−	0.600287i
$725$	−5.24744	+	4.40313i	−0.194885	+	0.163528i
$726$	−8.53419	−	14.6202i	−0.316734	−	0.542606i
$727$	−37.4420	+	13.6278i	−1.38865	+	0.505427i	−0.924788	−	0.380482i	$-0.875758\pi$
$727$	−37.4420	+	13.6278i	−1.38865	+	0.505427i	−0.463860	+	0.885909i	$0.653536\pi$
$728$	5.85663			0.217061
$729$	26.9889	−	0.772520i	0.999591	−	0.0286118i
$730$	−8.41405			−0.311418
$731$	8.18628	−	2.97956i	0.302781	−	0.110203i
$732$	9.30428	+	15.9394i	0.343896	+	0.589139i
$733$	3.13291	−	2.62883i	0.115717	−	0.0970979i	−0.583093	−	0.812405i	$-0.698158\pi$
$733$	3.13291	−	2.62883i	0.115717	−	0.0970979i	0.698810	+	0.715307i	$0.253713\pi$
$734$	−6.51601	−	36.9541i	−0.240510	−	1.36400i
$735$	4.64801	+	3.86252i	0.171445	+	0.142471i
$736$	5.66011	+	4.74939i	0.208634	+	0.175065i
$737$	−33.4123	+	57.8718i	−1.23076	+	2.13173i
$738$	−10.2925	+	18.2265i	−0.378874	+	0.670927i
$739$	−11.4550	−	19.8407i	−0.421380	−	0.729852i	0.574694	−	0.818368i	$-0.305121\pi$
$739$	−11.4550	−	19.8407i	−0.421380	−	0.729852i	−0.996075	+	0.0885160i	$0.971788\pi$
$740$	−0.260810	+	1.47913i	−0.00958756	+	0.0543737i
$741$	−8.00084	−	2.86893i	−0.293918	−	0.105393i
$742$	−7.32154	−	2.66482i	−0.268782	−	0.0978287i
$743$	−22.3169	−	8.12269i	−0.818728	−	0.297993i	−0.101504	−	0.994835i	$-0.532365\pi$
$743$	−22.3169	−	8.12269i	−0.818728	−	0.297993i	−0.717224	+	0.696843i	$0.754588\pi$
$744$	−11.1636	+	9.45843i	−0.409276	+	0.346763i
$745$	1.66700	−	9.45402i	0.0610741	−	0.346368i
$746$	−2.72500	−	4.71984i	−0.0997695	−	0.172806i
$747$	−8.29112	+	49.7941i	−0.303356	+	1.82187i
$748$	2.79895	−	4.84792i	0.102340	−	0.177257i
$749$	1.90744	+	1.60053i	0.0696963	+	0.0584822i
$750$	−2.22009	+	12.9517i	−0.0810664	+	0.472929i
$751$	4.93248	+	27.9735i	0.179989	+	1.02077i	0.932227	+	0.361875i	$0.117863\pi$
$751$	4.93248	+	27.9735i	0.179989	+	1.02077i	−0.752238	+	0.658892i	$0.771026\pi$
$752$	−6.64681	+	5.57734i	−0.242384	+	0.203385i
$753$	−23.7832	+	0.113430i	−0.866709	+	0.00413362i
$754$	5.25466	−	1.91254i	0.191363	−	0.0696506i
$755$	−8.27211			−0.301053
$756$	−5.19562	+	0.0743434i	−0.188963	+	0.00270384i
$757$	13.3407			0.484876			0.242438	−	0.970167i	$-0.422053\pi$
$757$	13.3407			0.484876			0.242438	+	0.970167i	$0.422053\pi$
$758$	−16.4043	+	5.97069i	−0.595832	+	0.216865i
$759$	−28.9236	+	50.6535i	−1.04986	+	1.83860i
$760$	2.23960	−	1.87924i	0.0812387	−	0.0681673i
$761$	−0.590272	−	3.34760i	−0.0213973	−	0.121350i	0.972238	−	0.233993i	$-0.0751794\pi$
$761$	−0.590272	−	3.34760i	−0.0213973	−	0.121350i	−0.993636	+	0.112643i	$0.964068\pi$
$762$	−10.7290	+	3.96307i	−0.388669	+	0.143567i
$763$	−0.783915	−	0.657783i	−0.0283796	−	0.0238133i
$764$	0.881390	−	1.52661i	0.0318876	−	0.0552309i
$765$	2.35311	+	12.6390i	0.0850768	+	0.456962i
$766$	11.7727	+	20.3909i	0.425365	+	0.736754i
$767$	−11.2573	+	63.8432i	−0.406476	+	2.30524i
$768$	−0.308899	−	1.70428i	−0.0111464	−	0.0614980i
$769$	33.2723	+	12.1101i	1.19983	+	0.436703i	0.863165	−	0.504921i	$-0.168478\pi$
$769$	33.2723	+	12.1101i	1.19983	+	0.436703i	0.336666	+	0.941624i	$0.390701\pi$
$770$	−14.9440	−	5.43917i	−0.538544	−	0.196014i
$771$	−3.15226	−	17.3919i	−0.113526	−	0.626353i
$772$	1.08999	−	6.18166i	0.0392297	−	0.222483i
$773$	−7.38369	−	12.7889i	−0.265573	−	0.459986i	0.702141	−	0.712038i	$-0.252228\pi$
$773$	−7.38369	−	12.7889i	−0.265573	−	0.459986i	−0.967714	+	0.252052i	$0.918894\pi$
$774$	20.0644	+	7.08686i	0.721202	+	0.254732i
$775$	30.3031	−	52.4865i	1.08852	−	1.88537i
$776$	10.3544	+	8.68836i	0.371701	+	0.311894i
$777$	0.699387	−	0.258340i	0.0250904	−	0.00926790i
$778$	−1.51951	−	8.61757i	−0.0544771	−	0.308955i
$779$	−4.47850	+	3.75791i	−0.160459	+	0.134641i
$780$	17.5507	−	30.7363i	0.628416	−	1.10054i
$781$	0.104490	−	0.0380312i	0.00373894	−	0.00136086i
$782$	−9.07480			−0.324514
$783$	−4.63731	+	1.76338i	−0.165724	+	0.0630181i
$784$	1.00000			0.0357143
$785$	−26.1374	+	9.51324i	−0.932885	+	0.339542i
$786$	−16.9166	+	0.0806808i	−0.603395	+	0.00287779i
$787$	21.5566	−	18.0881i	0.768409	−	0.644772i	−0.171892	−	0.985116i	$-0.554988\pi$
$787$	21.5566	−	18.0881i	0.768409	−	0.644772i	0.940301	+	0.340344i	$0.110544\pi$
$788$	3.48264	+	19.7510i	0.124064	+	0.703601i
$789$	1.00301	−	5.85143i	0.0357083	−	0.208317i
$790$	5.56573	+	4.67020i	0.198020	+	0.166158i
$791$	3.71133	−	6.42822i	0.131960	−	0.228561i
$792$	12.8037	−	4.79895i	0.454959	−	0.170523i
$793$	31.2034	+	54.0459i	1.10807	+	1.91923i
$794$	−2.60839	+	14.7929i	−0.0925682	+	0.524981i
$795$	−35.9259	+	30.4386i	−1.27416	+	1.07955i
$796$	−9.81992	−	3.57416i	−0.348058	−	0.126683i
$797$	−5.70104	−	2.07501i	−0.201941	−	0.0735006i	0.239069	−	0.971002i	$-0.423158\pi$
$797$	−5.70104	−	2.07501i	−0.201941	−	0.0735006i	−0.441011	+	0.897502i	$0.645380\pi$
$798$	−1.36612	−	0.489859i	−0.0483599	−	0.0173408i
$799$	1.85053	−	10.4949i	0.0654670	−	0.371282i
$800$	3.58718	+	6.21318i	0.126826	+	0.219669i
$801$	−10.7160	−	18.1584i	−0.378631	−	0.641596i
$802$	17.4776	−	30.2721i	0.617155	−	1.06894i
$803$	−8.41966	−	7.06493i	−0.297123	−	0.249316i
$804$	−19.5309	−	16.2303i	−0.688802	−	0.572398i
$805$	4.47676	+	25.3890i	0.157785	+	0.894844i
$806$	−37.8997	+	31.8017i	−1.33496	+	1.12017i
$807$	−2.93809	−	5.03333i	−0.103426	−	0.177182i
$808$	−8.03298	+	2.92376i	−0.282599	+	0.102858i
$809$	18.9454			0.666086			0.333043	−	0.942912i	$-0.391925\pi$
$809$	18.9454			0.666086			0.333043	+	0.942912i	$0.391925\pi$
$810$	−15.1797	+	27.4900i	−0.533359	+	0.965901i
$811$	53.4126			1.87557			0.937785	−	0.347217i	$-0.112873\pi$
$811$	53.4126			1.87557			0.937785	+	0.347217i	$0.112873\pi$
$812$	0.897215	−	0.326560i	0.0314861	−	0.0114600i
$813$	7.92505	+	13.5766i	0.277944	+	0.476153i
$814$	−1.50294	+	1.26112i	−0.0526781	+	0.0442022i
$815$	−1.75551	−	9.95598i	−0.0614927	−	0.348743i
$816$	1.63610	+	1.35961i	0.0572750	+	0.0475958i
$817$	4.55283	+	3.82028i	0.159283	+	0.133655i
$818$	−8.45814	+	14.6499i	−0.295732	+	0.512223i
$819$	−17.5691	+	0.167589i	−0.613914	+	0.00585605i
$820$	−12.1725	−	21.0834i	−0.425082	−	0.736263i
$821$	−7.56323	+	42.8932i	−0.263959	+	1.49698i	0.508025	+	0.861342i	$0.330376\pi$
$821$	−7.56323	+	42.8932i	−0.263959	+	1.49698i	−0.771984	+	0.635642i	$0.780736\pi$
$822$	24.8022	+	8.89355i	0.865078	+	0.310198i
$823$	−29.9706	−	10.9084i	−1.04471	−	0.380243i	−0.238045	−	0.971254i	$-0.576507\pi$
$823$	−29.9706	−	10.9084i	−1.04471	−	0.380243i	−0.806663	+	0.591012i	$0.798729\pi$
$824$	8.47892	+	3.08607i	0.295377	+	0.107509i
$825$	−43.2125	+	36.6122i	−1.50447	+	1.27467i
$826$	−1.92214	+	10.9010i	−0.0668798	+	0.379294i
$827$	17.9460	+	31.0835i	0.624045	+	1.08088i	0.988725	+	0.149745i	$0.0478452\pi$
$827$	17.9460	+	31.0835i	0.624045	+	1.08088i	−0.364680	+	0.931133i	$0.618821\pi$
$828$	−17.1154	−	14.0856i	−0.594803	−	0.489507i
$829$	−28.2608	+	48.9491i	−0.981537	+	1.70007i	−0.325122	+	0.945672i	$0.605405\pi$
$829$	−28.2608	+	48.9491i	−0.981537	+	1.70007i	−0.656415	+	0.754400i	$0.727928\pi$
$830$	−44.9751	−	37.7386i	−1.56111	−	1.30992i
$831$	3.65406	−	21.3172i	0.126758	−	0.739486i
$832$	−1.01699	−	5.76766i	−0.0352579	−	0.199958i
$833$	−0.940850	+	0.789467i	−0.0325985	+	0.0273534i
$834$	20.8263	−	0.0993275i	0.721156	−	0.00343943i
$835$	−14.9182	+	5.42977i	−0.516265	+	0.187905i
$836$	3.81901			0.132083
$837$	33.2185	−	28.6934i	1.14820	−	0.991790i
$838$	−31.2614			−1.07991
$839$	−5.29894	+	1.92866i	−0.182940	+	0.0665847i	−0.431866	−	0.901938i	$-0.642145\pi$
$839$	−5.29894	+	1.92866i	−0.182940	+	0.0665847i	0.248926	+	0.968523i	$0.419922\pi$
$840$	2.99672	−	5.24812i	0.103397	−	0.181077i
$841$	−21.5169	+	18.0549i	−0.741963	+	0.622581i
$842$	1.81909	+	10.3166i	0.0626900	+	0.355533i
$843$	32.8419	−	12.1312i	1.13114	−	0.417820i
$844$	−15.2704	−	12.8134i	−0.525629	−	0.441055i
$845$	37.1600	−	64.3631i	1.27834	−	2.21416i
$846$	19.7799	−	16.9215i	0.680048	−	0.581771i
$847$	−4.88691	−	8.46437i	−0.167916	−	0.290839i
$848$	−1.35297	+	7.67305i	−0.0464610	+	0.263494i
$849$	−2.52850	−	13.9505i	−0.0867780	−	0.478778i
$850$	−8.28009	−	3.01371i	−0.284005	−	0.103369i
$851$	2.98873	+	1.08781i	0.102452	+	0.0372896i
$852$	0.00753610	+	0.0415788i	0.000258183	+	0.00142447i
$853$	−3.33935	+	18.9384i	−0.114337	+	0.648439i	0.872739	+	0.488187i	$0.162342\pi$
$853$	−3.33935	+	18.9384i	−0.114337	+	0.648439i	−0.987076	+	0.160252i	$0.948769\pi$
$854$	5.32788	+	9.22815i	0.182316	+	0.315781i
$855$	−6.66470	+	5.70156i	−0.227928	+	0.194989i
$856$	1.24499	−	2.15639i	0.0425530	−	0.0737039i
$857$	29.3114	+	24.5952i	1.00126	+	0.840155i	0.987158	−	0.159745i	$-0.0510673\pi$
$857$	29.3114	+	24.5952i	1.00126	+	0.840155i	0.0141000	+	0.999901i	$0.495512\pi$
$858$	43.3704	−	16.0202i	1.48064	−	0.546920i
$859$	−2.86287	−	16.2361i	−0.0976799	−	0.553970i	−0.993893	−	0.110347i	$-0.964804\pi$
$859$	−2.86287	−	16.2361i	−0.0976799	−	0.553970i	0.896213	−	0.443623i	$-0.146307\pi$
$860$	−18.9588	+	15.9084i	−0.646491	+	0.542470i
$861$	−5.99252	+	10.4946i	−0.204225	+	0.357656i
$862$	25.7493	−	9.37199i	0.877025	−	0.319211i
$863$	47.7136			1.62419			0.812094	−	0.583526i	$-0.198327\pi$
$863$	47.7136			1.62419			0.812094	+	0.583526i	$0.198327\pi$
$864$	0.975424	+	5.10378i	0.0331846	+	0.173634i
$865$	−32.1257			−1.09231
$866$	−9.88294	+	3.59709i	−0.335836	+	0.122234i
$867$	26.8318	−	0.127970i	0.911257	−	0.00434608i
$868$	−6.47125	+	5.43002i	−0.219649	+	0.184307i
$869$	1.64806	+	9.34662i	0.0559066	+	0.317062i
$870$	0.974880	−	5.68730i	0.0330515	−	0.192817i
$871$	−65.7779	−	55.1942i	−2.22880	−	1.87019i
$872$	−0.511664	+	0.886229i	−0.0173271	+	0.0300115i
$873$	−31.3103	−	25.7676i	−1.05969	−	0.872101i
$874$	−3.09552	−	5.36159i	−0.104707	−	0.181359i
$875$	−1.31742	+	7.47146i	−0.0445369	+	0.252582i
$876$	3.18677	−	2.70002i	0.107671	−	0.0912252i
$877$	5.40825	+	1.96844i	0.182624	+	0.0664696i	0.431713	−	0.902011i	$-0.357909\pi$
$877$	5.40825	+	1.96844i	0.182624	+	0.0664696i	−0.249090	+	0.968480i	$0.580131\pi$
$878$	−4.42580	−	1.61086i	−0.149363	−	0.0543638i
$879$	−17.8173	−	6.38890i	−0.600962	−	0.215492i
$880$	−2.76154	+	15.6615i	−0.0930915	+	0.527948i
$881$	21.4627	+	37.1745i	0.723097	+	1.25244i	0.959753	+	0.280847i	$0.0906153\pi$
$881$	21.4627	+	37.1745i	0.723097	+	1.25244i	−0.236656	+	0.971594i	$0.576051\pi$
$882$	−2.99986	+	0.0286153i	−0.101011	+	0.000963528i
$883$	−11.0225	+	19.0915i	−0.370936	+	0.642480i	−0.989710	−	0.143089i	$-0.954296\pi$
$883$	−11.0225	+	19.0915i	−0.370936	+	0.642480i	0.618774	+	0.785569i	$0.287630\pi$
$884$	5.51021	+	4.62362i	0.185329	+	0.155509i
$885$	51.4496	+	42.7549i	1.72946	+	1.43719i
$886$	−3.71847	−	21.0885i	−0.124925	−	0.708483i
$887$	5.77474	−	4.84558i	0.193897	−	0.162699i	−0.540671	−	0.841234i	$-0.681830\pi$
$887$	5.77474	−	4.84558i	0.193897	−	0.162699i	0.734567	+	0.678536i	$0.237385\pi$
$888$	−0.375863	−	0.643902i	−0.0126131	−	0.0216079i
$889$	−6.20521	+	2.25851i	−0.208116	+	0.0757481i
$890$	24.5226			0.822001
$891$	−38.2720	+	14.7626i	−1.28216	+	0.494565i
$892$	−4.94555			−0.165589
$893$	6.83184	−	2.48659i	0.228619	−	0.0832104i
$894$	2.40237	+	4.11558i	0.0803474	+	0.137645i
$895$	23.9320	−	20.0813i	0.799958	−	0.671245i
$896$	−0.173648	−	0.984808i	−0.00580118	−	0.0329001i
$897$	−57.6452	−	47.9034i	−1.92472	−	1.59945i
$898$	−27.6405	−	23.1932i	−0.922376	−	0.773966i
$899$	−4.03288	+	6.98515i	−0.134504	+	0.232968i
$900$	−10.9388	−	18.5360i	−0.364628	−	0.617868i
$901$	−4.78468	−	8.28731i	−0.159401	−	0.276090i
$902$	5.52223	−	31.3181i	0.183870	−	1.04278i
$903$	11.5646	+	4.14680i	0.384845	+	0.137997i
$904$	−6.97502	−	2.53870i	−0.231986	−	0.0844360i
$905$	−53.7756	−	19.5727i	−1.78756	−	0.650619i
$906$	3.13301	−	2.65447i	0.104087	−	0.0881889i
$907$	3.26033	−	18.4902i	0.108257	−	0.613958i	−0.881612	−	0.471975i	$-0.843541\pi$
$907$	3.26033	−	18.4902i	0.108257	−	0.613958i	0.989869	−	0.141983i	$-0.0453478\pi$
$908$	2.26247	+	3.91871i	0.0750827	+	0.130047i
$909$	24.0142	−	9.00076i	0.796500	−	0.298536i
$910$	10.2174	−	17.6971i	0.338704	−	0.586653i
$911$	1.53361	+	1.28685i	0.0508107	+	0.0426353i	0.667839	−	0.744305i	$-0.267219\pi$
$911$	1.53361	+	1.28685i	0.0508107	+	0.0426353i	−0.617029	+	0.786941i	$0.711664\pi$
$912$	−0.245194	+	1.43042i	−0.00811918	+	0.0473661i
$913$	−13.3175	−	75.5274i	−0.440745	−	2.49959i
$914$	−24.2641	+	20.3600i	−0.802584	+	0.673448i
$915$	64.3966	−	0.307129i	2.12889	−	0.0101534i
$916$	16.4995	−	6.00532i	0.545158	−	0.198421i
$917$	−9.76691			−0.322532
$918$	−4.94699	−	4.03182i	−0.163275	−	0.133070i
$919$	35.0413			1.15591			0.577953	−	0.816070i	$-0.303852\pi$
$919$	35.0413			1.15591			0.577953	+	0.816070i	$0.303852\pi$
$920$	24.2259	−	8.81750i	0.798703	−	0.290704i
$921$	−3.13065	+	5.48267i	−0.103159	+	0.180660i
$922$	−5.68523	+	4.77048i	−0.187233	+	0.157107i
$923$	0.0248112	+	0.140712i	0.000816672	+	0.00463158i
$924$	7.40534	−	2.73539i	0.243618	−	0.0899877i
$925$	2.36574	+	1.98509i	0.0777852	+	0.0652695i
$926$	−12.5222	+	21.6890i	−0.411504	+	0.712746i
$927$	−25.5239	−	9.01518i	−0.838315	−	0.296097i
$928$	−0.477398	−	0.826878i	−0.0156714	−	0.0271436i
$929$	3.54406	−	20.0994i	0.116277	−	0.659439i	−0.869833	−	0.493346i	$-0.835774\pi$
$929$	3.54406	−	20.0994i	0.116277	−	0.659439i	0.986110	−	0.166093i	$-0.0531153\pi$
$930$	9.10488	+	50.2341i	0.298561	+	1.64724i
$931$	−0.787369	−	0.286579i	−0.0258050	−	0.00939224i
$932$	1.22708	+	0.446620i	0.0401943	+	0.0146295i
$933$	−6.20976	−	34.2610i	−0.203298	−	1.12165i
$934$	−5.80249	+	32.9076i	−0.189863	+	1.07677i
$935$	−9.76602	−	16.9152i	−0.319383	−	0.553187i
$936$	3.21589	+	17.2731i	0.105115	+	0.564589i
$937$	14.7025	−	25.4654i	0.480309	−	0.831919i	−0.519436	−	0.854509i	$-0.673858\pi$
$937$	14.7025	−	25.4654i	0.480309	−	0.831919i	0.999745	+	0.0225901i	$0.00719126\pi$
$938$	−11.2314	−	9.42423i	−0.366717	−	0.307712i
$939$	53.9952	−	19.9448i	1.76207	−	0.650874i
$940$	5.25718	+	29.8149i	0.171470	+	0.972456i
$941$	−18.8660	+	15.8304i	−0.615014	+	0.516058i	−0.896232	−	0.443586i	$-0.853706\pi$
$941$	−18.8660	+	15.8304i	−0.615014	+	0.516058i	0.281218	+	0.959644i	$0.409262\pi$
$942$	6.84663	−	11.9904i	0.223075	−	0.390669i
$943$	−48.4443	+	17.6323i	−1.57756	+	0.574186i
$944$	11.0692			0.360271
$945$	−8.83958	+	15.8294i	−0.287551	+	0.514930i
$946$	−32.3290			−1.05111
$947$	44.9500	−	16.3604i	1.46068	−	0.531643i	0.515126	−	0.857115i	$-0.327745\pi$
$947$	44.9500	−	16.3604i	1.46068	−	0.531643i	0.945552	+	0.325471i	$0.105523\pi$
$948$	−3.60662	+	0.0172012i	−0.117138	+	0.000558668i
$949$	10.8189	−	9.07816i	0.351197	−	0.294690i
$950$	−1.04387	−	5.92007i	−0.0338676	−	0.192073i
$951$	8.06745	−	47.0643i	0.261605	−	1.52616i
$952$	0.940850	+	0.789467i	0.0304931	+	0.0255868i
$953$	−2.66478	+	4.61554i	−0.0863209	+	0.149512i	−0.905953	−	0.423378i	$-0.860844\pi$
$953$	−2.66478	+	4.61554i	−0.0863209	+	0.149512i	0.819632	+	0.572890i	$0.194178\pi$
$954$	3.83915	−	23.0568i	0.124297	−	0.746492i
$955$	−3.07532	−	5.32662i	−0.0995152	−	0.172365i
$956$	1.09432	−	6.20621i	0.0353929	−	0.200723i
$957$	5.75092	−	4.87252i	0.185901	−	0.157506i
$958$	15.2551	+	5.55240i	0.492870	+	0.179390i
$959$	14.2949	+	5.20293i	0.461607	+	0.168011i
$960$	−5.68876	−	2.03987i	−0.183604	−	0.0658364i
$961$	7.00883	−	39.7490i	0.226091	−	1.28223i
$962$	−1.26052	−	2.18328i	−0.0406407	−	0.0703918i
$963$	−3.67310	+	6.50450i	−0.118364	+	0.209605i
$964$	11.9678	−	20.7289i	0.385458	−	0.667633i
$965$	−16.7776	−	14.0781i	−0.540091	−	0.453190i
$966$	−9.84271	−	8.17934i	−0.316684	−	0.263166i
$967$	5.08495	+	28.8382i	0.163521	+	0.927374i	0.950576	+	0.310491i	$0.100494\pi$
$967$	5.08495	+	28.8382i	0.163521	+	0.927374i	−0.787055	+	0.616883i	$0.788395\pi$
$968$	−7.48717	+	6.28248i	−0.240647	+	0.201927i
$969$	−0.898581	−	1.53939i	−0.0288666	−	0.0494522i
$970$	44.3179	−	16.1304i	1.42296	−	0.517916i
$971$	25.3779			0.814414			0.407207	−	0.913336i	$-0.366503\pi$
$971$	25.3779			0.814414			0.407207	+	0.913336i	$0.366503\pi$
$972$	−3.07219	−	15.2827i	−0.0985404	−	0.490194i
$973$	12.0242			0.385479
$974$	4.71382	−	1.71569i	0.151040	−	0.0549742i
$975$	−36.6885	−	62.8521i	−1.17497	−	2.01288i
$976$	8.16278	−	6.84939i	0.261284	−	0.219244i
$977$	5.36097	+	30.4036i	0.171513	+	0.972696i	0.942093	+	0.335353i	$0.108856\pi$
$977$	5.36097	+	30.4036i	0.171513	+	0.972696i	−0.770580	+	0.637343i	$0.780033\pi$
$978$	3.85970	+	3.20743i	0.123420	+	0.102562i
$979$	24.5390	+	20.5906i	0.784269	+	0.658080i
$980$	1.74459	−	3.02172i	0.0557288	−	0.0965252i
$981$	1.50956	−	2.67321i	0.0481967	−	0.0853489i
$982$	14.6592	+	25.3905i	0.467794	+	0.810243i
$983$	−0.159466	+	0.904379i	−0.00508619	+	0.0288452i	−0.987245	−	0.159207i	$-0.949106\pi$
$983$	−0.159466	+	0.904379i	−0.00508619	+	0.0288452i	0.982159	+	0.188052i	$0.0602174\pi$
$984$	11.3758	+	4.07911i	0.362647	+	0.130037i
$985$	65.7577	+	23.9338i	2.09521	+	0.762596i
$986$	1.10195	+	0.401078i	0.0350933	+	0.0127729i
$987$	11.4664	−	9.71503i	0.364980	−	0.309233i
$988$	−0.852140	+	4.83273i	−0.0271102	+	0.153749i
$989$	26.2045	+	45.3875i	0.833253	+	1.44324i
$990$	7.83609	−	47.0613i	0.249047	−	1.49571i
$991$	−3.22919	+	5.59313i	−0.102579	+	0.177672i	−0.912746	−	0.408527i	$-0.866043\pi$
$991$	−3.22919	+	5.59313i	−0.102579	+	0.177672i	0.810168	+	0.586198i	$0.199376\pi$
$992$	6.47125	+	5.43002i	0.205462	+	0.172403i
$993$	−6.68106	+	38.9763i	−0.212017	+	1.23687i
$994$	0.00423643	+	0.0240260i	0.000134371	+	0.000762059i
$995$	−27.9318	+	23.4376i	−0.885498	+	0.743021i
$996$	29.1441	−	0.138998i	0.923466	−	0.00440431i
$997$	33.8987	−	12.3381i	1.07358	−	0.390752i	0.256067	−	0.966659i	$-0.417573\pi$
$997$	33.8987	−	12.3381i	1.07358	−	0.390752i	0.817515	+	0.575907i	$0.195351\pi$
$998$	−13.6411			−0.431802
$999$	1.14596	+	1.92086i	0.0362566	+	0.0607734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.169.3	yes	36
27.4	even	9	inner	378.2.u.e.85.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.3	✓	36	27.4	even	9	inner
378.2.u.e.169.3	yes	36	1.1	even	1	trivial

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.873169 + 1.49585i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.605889 - 3.43617i) q^{5} +(1.33212 + 1.10700i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.47515 + 2.61227i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.873169 + 1.49585i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.605889 - 3.43617i) q^{5} +(1.33212 + 1.10700i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.47515 + 2.61227i) q^{9} +(-1.74459 - 3.02172i) q^{10} +(0.791459 - 4.48859i) q^{11} +(1.63040 + 0.584627i) q^{12} +(5.50344 + 2.00309i) q^{13} +(0.939693 + 0.342020i) q^{14} +(4.61096 - 3.90668i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.614096 + 1.06365i) q^{17} +(-0.492740 + 2.95926i) q^{18} +(-0.418950 + 0.725643i) q^{19} +(-2.67286 - 2.24280i) q^{20} +(-0.292629 + 1.70715i) q^{21} +(-0.791459 - 4.48859i) q^{22} +(-5.66011 + 4.74939i) q^{23} +(1.73203 - 0.00826063i) q^{24} +(-6.74169 + 2.45378i) q^{25} +5.85663 q^{26} +(-5.19562 + 0.0743434i) q^{27} +1.00000 q^{28} +(0.897215 - 0.326560i) q^{29} +(2.99672 - 5.24812i) q^{30} +(-6.47125 + 5.43002i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(7.40534 - 2.73539i) q^{33} +(0.940850 + 0.789467i) q^{34} +(1.74459 - 3.02172i) q^{35} +(0.549101 + 2.94932i) q^{36} +(-0.215229 - 0.372787i) q^{37} +(-0.145500 + 0.825171i) q^{38} +(1.80911 + 9.98136i) q^{39} +(-3.27875 - 1.19337i) q^{40} +(6.55650 + 2.38637i) q^{41} +(0.308899 + 1.70428i) q^{42} +(1.23170 - 6.98532i) q^{43} +(-2.27891 - 3.94720i) q^{44} +(9.86996 + 3.48612i) q^{45} +(-3.69437 + 6.39884i) q^{46} +(-6.64681 - 5.57734i) q^{47} +(1.62475 - 0.600152i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-5.49588 + 4.61159i) q^{50} +(-1.05485 + 1.84734i) q^{51} +(5.50344 - 2.00309i) q^{52} -7.79142 q^{53} +(-4.85686 + 1.84687i) q^{54} -15.9031 q^{55} +(0.939693 - 0.342020i) q^{56} +(-1.45127 + 0.00692158i) q^{57} +(0.731416 - 0.613731i) q^{58} +(1.92214 + 10.9010i) q^{59} +(1.02103 - 5.95656i) q^{60} +(8.16278 + 6.84939i) q^{61} +(-4.22381 + 7.31585i) q^{62} +(-2.80916 + 1.05290i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.54847 - 20.1244i) q^{65} +(6.02319 - 5.10320i) q^{66} +(-13.7773 - 5.01453i) q^{67} +(1.15412 + 0.420066i) q^{68} +(-12.0466 - 4.31966i) q^{69} +(0.605889 - 3.43617i) q^{70} +(0.0121983 + 0.0211281i) q^{71} +(1.52471 + 2.58365i) q^{72} +(1.20574 - 2.08840i) q^{73} +(-0.329750 - 0.276693i) q^{74} +(-9.55712 - 7.94202i) q^{75} +(0.145500 + 0.825171i) q^{76} +(3.49150 - 2.92972i) q^{77} +(5.11383 + 8.76066i) q^{78} +(-1.95673 + 0.712191i) q^{79} -3.48918 q^{80} +(-4.64786 - 7.70697i) q^{81} +6.97728 q^{82} +(15.8118 - 5.75502i) q^{83} +(0.873169 + 1.49585i) q^{84} +(3.28279 - 2.75459i) q^{85} +(-1.23170 - 6.98532i) q^{86} +(1.27191 + 1.05696i) q^{87} +(-3.49150 - 2.92972i) q^{88} +(-3.51410 + 6.08660i) q^{89} +(10.4671 - 0.0998439i) q^{90} +(2.92832 + 5.07199i) q^{91} +(-1.28304 + 7.27649i) q^{92} +(-13.7730 - 4.93871i) q^{93} +(-8.15352 - 2.96764i) q^{94} +(2.74727 + 0.999925i) q^{95} +(1.32150 - 1.11966i) q^{96} +(-2.34715 + 13.3113i) q^{97} +(0.500000 + 0.866025i) q^{98} +(10.5579 + 8.68884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Introduction

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