LMFDB - Embedded newform 361.2.e.a.54.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			54.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	361.54
Dual form			361.2.e.a.234.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03209 + 0.866025i) q^{2} +(-2.70574 + 0.984808i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(-3.64543 - 1.32683i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +(4.05303 - 3.40090i) q^{9} +O(q^{10})$	\(q+(1.03209 + 0.866025i) q^{2} +(-2.70574 + 0.984808i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(-3.64543 - 1.32683i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +(4.05303 - 3.40090i) q^{9} +(0.907604 - 0.761570i) q^{10} +(1.11334 - 1.92836i) q^{11} +(0.266044 + 0.460802i) q^{12} +(2.41875 + 0.880352i) q^{13} +(0.0812519 - 0.460802i) q^{14} +(0.439693 + 2.49362i) q^{15} +(3.37939 - 1.23000i) q^{16} +(0.358441 + 0.300767i) q^{17} +7.12836 q^{18} -0.162504 q^{20} +(0.766044 + 0.642788i) q^{21} +(2.81908 - 1.02606i) q^{22} +(-0.467911 - 2.65366i) q^{23} +(-1.47178 + 8.34689i) q^{24} +(3.97178 + 1.44561i) q^{25} +(1.73396 + 3.00330i) q^{26} +(-3.29813 + 5.71253i) q^{27} +(-0.0491630 + 0.0412527i) q^{28} +(5.26991 - 4.42198i) q^{29} +(-1.70574 + 2.95442i) q^{30} +(-3.55303 - 6.15403i) q^{31} +(-0.979055 - 0.356347i) q^{32} +(-1.11334 + 6.31407i) q^{33} +(0.109470 + 0.620838i) q^{34} +(-0.286989 + 0.104455i) q^{35} +(-0.748970 - 0.628461i) q^{36} -4.94356 q^{37} -7.41147 q^{39} +(-1.98293 - 1.66387i) q^{40} +(2.32635 - 0.846723i) q^{41} +(0.233956 + 1.32683i) q^{42} +(0.677519 - 3.84240i) q^{43} +(-0.386659 - 0.140732i) q^{44} +(-2.32635 - 4.02936i) q^{45} +(1.81521 - 3.14403i) q^{46} +(-5.58512 + 4.68647i) q^{47} +(-7.93242 + 6.65609i) q^{48} +(3.43969 - 5.95772i) q^{49} +(2.84730 + 4.93166i) q^{50} +(-1.26604 - 0.460802i) q^{51} +(0.0825961 - 0.468426i) q^{52} +(0.492726 + 2.79439i) q^{53} +(-8.35117 + 3.03958i) q^{54} +(-1.50000 - 1.25865i) q^{55} -1.02229 q^{56} +9.26857 q^{58} +(4.83022 + 4.05304i) q^{59} +(0.439693 - 0.160035i) q^{60} +(1.58512 + 8.98968i) q^{61} +(1.66250 - 9.42853i) q^{62} +(-1.72668 - 0.628461i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(1.13176 - 1.96026i) q^{65} +(-6.61721 + 5.55250i) q^{66} +(-5.87939 + 4.93339i) q^{67} +(0.0432332 - 0.0748822i) q^{68} +(3.87939 + 6.71929i) q^{69} +(-0.386659 - 0.140732i) q^{70} +(1.61587 - 9.16404i) q^{71} +(-2.70439 - 15.3374i) q^{72} +(-1.30541 + 0.475129i) q^{73} +(-5.10220 - 4.28125i) q^{74} -12.1702 q^{75} -0.773318 q^{77} +(-7.64930 - 6.41852i) q^{78} +(-11.1309 + 4.05131i) q^{79} +(-0.549163 - 3.11446i) q^{80} +(0.541889 - 3.07321i) q^{81} +(3.13429 + 1.14079i) q^{82} +(7.41534 + 12.8438i) q^{83} +(0.0923963 - 0.160035i) q^{84} +(0.315207 - 0.264490i) q^{85} +(4.02687 - 3.37895i) q^{86} +(-9.90420 + 17.1546i) q^{87} +(-3.27719 - 5.67626i) q^{88} +(-9.67024 - 3.51968i) q^{89} +(1.08853 - 6.17334i) q^{90} +(-0.155230 - 0.880352i) q^{91} +(-0.467911 + 0.170306i) q^{92} +(15.6741 + 13.1521i) q^{93} -9.82295 q^{94} +3.00000 q^{96} +(-7.24170 - 6.07650i) q^{97} +(8.70961 - 3.17004i) q^{98} +(-2.04576 - 11.6021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9	$ 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9} + 9 q^{10} - 3 q^{12} + 12 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 12 q^{23} + 6 q^{24} + 9 q^{25} + 15 q^{26} - 6 q^{27} - 12 q^{28} + 3 q^{29} - 9 q^{31} - 9 q^{32} + 18 q^{34} + 6 q^{35} + 21 q^{36} - 24 q^{39} + 9 q^{40} + 15 q^{41} + 6 q^{42} - 21 q^{43} - 9 q^{44} - 15 q^{45} + 18 q^{46} - 12 q^{47} - 24 q^{48} + 15 q^{49} + 15 q^{50} - 3 q^{51} - 6 q^{52} - 15 q^{53} - 24 q^{54} - 9 q^{55} + 6 q^{56} + 36 q^{58} + 6 q^{59} - 3 q^{60} - 12 q^{61} + 15 q^{62} + 3 q^{63} - 12 q^{64} + 12 q^{65} - 9 q^{66} - 24 q^{67} - 15 q^{68} + 12 q^{69} - 9 q^{70} - 12 q^{71} - 15 q^{72} - 12 q^{73} - 30 q^{74} - 30 q^{75} - 18 q^{77} - 6 q^{78} - 15 q^{79} - 15 q^{80} - 3 q^{81} + 9 q^{82} - 3 q^{84} + 9 q^{85} + 48 q^{86} - 21 q^{87} - 9 q^{88} - 15 q^{89} + 27 q^{90} + 12 q^{91} - 12 q^{92} + 27 q^{93} - 18 q^{94} + 18 q^{96} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9 + 9 * q^10 - 3 * q^12 + 12 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 12 * q^23 + 6 * q^24 + 9 * q^25 + 15 * q^26 - 6 * q^27 - 12 * q^28 + 3 * q^29 - 9 * q^31 - 9 * q^32 + 18 * q^34 + 6 * q^35 + 21 * q^36 - 24 * q^39 + 9 * q^40 + 15 * q^41 + 6 * q^42 - 21 * q^43 - 9 * q^44 - 15 * q^45 + 18 * q^46 - 12 * q^47 - 24 * q^48 + 15 * q^49 + 15 * q^50 - 3 * q^51 - 6 * q^52 - 15 * q^53 - 24 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 - 12 * q^61 + 15 * q^62 + 3 * q^63 - 12 * q^64 + 12 * q^65 - 9 * q^66 - 24 * q^67 - 15 * q^68 + 12 * q^69 - 9 * q^70 - 12 * q^71 - 15 * q^72 - 12 * q^73 - 30 * q^74 - 30 * q^75 - 18 * q^77 - 6 * q^78 - 15 * q^79 - 15 * q^80 - 3 * q^81 + 9 * q^82 - 3 * q^84 + 9 * q^85 + 48 * q^86 - 21 * q^87 - 9 * q^88 - 15 * q^89 + 27 * q^90 + 12 * q^91 - 12 * q^92 + 27 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	1.03209	+	0.866025i	0.729797	+	0.612372i	0.930076	−	0.367366i	$-0.119740\pi$
$2$	1.03209	+	0.866025i	0.729797	+	0.612372i	−0.200279	+	0.979739i	$0.564185\pi$
$3$	−2.70574	+	0.984808i	−1.56216	+	0.568579i	−0.971230	−	0.238145i	$-0.923461\pi$
$3$	−2.70574	+	0.984808i	−1.56216	+	0.568579i	−0.590928	+	0.806724i	$0.701238\pi$
$4$	−0.0320889	−	0.181985i	−0.0160444	−	0.0909926i
$5$	0.152704	−	0.866025i	0.0682911	−	0.387298i	−0.931435	−	0.363907i	$-0.881443\pi$
$5$	0.152704	−	0.866025i	0.0682911	−	0.387298i	0.999726	−	0.0233912i	$-0.00744633\pi$
$6$	−3.64543	−	1.32683i	−1.48824	−	0.541675i
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	0.831342	−	0.555762i	$-0.187573\pi$
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	−0.896975	+	0.442082i	$0.854240\pi$
$8$	1.47178	−	2.54920i	0.520353	−	0.901278i
$9$	4.05303	−	3.40090i	1.35101	−	1.13363i
$10$	0.907604	−	0.761570i	0.287010	−	0.240830i
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$	0.266044	+	0.460802i	0.0768004	+	0.133022i
$13$	2.41875	+	0.880352i	0.670840	+	0.244166i	0.654910	−	0.755707i	$-0.272707\pi$
$13$	2.41875	+	0.880352i	0.670840	+	0.244166i	0.0159305	+	0.999873i	$0.494929\pi$
$14$	0.0812519	−	0.460802i	0.0217155	−	0.123155i
$15$	0.439693	+	2.49362i	0.113528	+	0.643850i
$16$	3.37939	−	1.23000i	0.844846	−	0.307499i
$17$	0.358441	+	0.300767i	0.0869346	+	0.0729468i	0.685219	−	0.728337i	$-0.259706\pi$
$17$	0.358441	+	0.300767i	0.0869346	+	0.0729468i	−0.598285	+	0.801284i	$0.704151\pi$
$18$	7.12836			1.68017
$19$		0			0
$19$		0			0
$20$	−0.162504			−0.0363370
$21$	0.766044	+	0.642788i	0.167165	+	0.140268i
$22$	2.81908	−	1.02606i	0.601029	−	0.218757i
$23$	−0.467911	−	2.65366i	−0.0975662	−	0.553325i	−0.993931	−	0.110008i	$-0.964912\pi$
$23$	−0.467911	−	2.65366i	−0.0975662	−	0.553325i	0.896365	−	0.443318i	$-0.146199\pi$
$24$	−1.47178	+	8.34689i	−0.300426	+	1.70380i
$25$	3.97178	+	1.44561i	0.794356	+	0.289122i
$26$	1.73396	+	3.00330i	0.340057	+	0.588995i
$27$	−3.29813	+	5.71253i	−0.634726	+	1.09938i
$28$	−0.0491630	+	0.0412527i	−0.00929094	+	0.00779602i
$29$	5.26991	−	4.42198i	0.978599	−	0.821142i	−0.00527877	−	0.999986i	$-0.501680\pi$
$29$	5.26991	−	4.42198i	0.978599	−	0.821142i	0.983877	+	0.178844i	$0.0572358\pi$
$30$	−1.70574	+	2.95442i	−0.311424	+	0.539401i
$31$	−3.55303	−	6.15403i	−0.638144	−	1.10530i	−0.985840	−	0.167690i	$-0.946369\pi$
$31$	−3.55303	−	6.15403i	−0.638144	−	1.10530i	0.347696	−	0.937607i	$-0.386964\pi$
$32$	−0.979055	−	0.356347i	−0.173074	−	0.0629939i
$33$	−1.11334	+	6.31407i	−0.193808	+	1.09914i
$34$	0.109470	+	0.620838i	0.0187740	+	0.106473i
$35$	−0.286989	+	0.104455i	−0.0485100	+	0.0176562i
$36$	−0.748970	−	0.628461i	−0.124828	−	0.104743i
$37$	−4.94356			−0.812717			−0.406358	−	0.913714i	$-0.633202\pi$
$37$	−4.94356			−0.812717			−0.406358	+	0.913714i	$0.633202\pi$
$38$		0			0
$39$	−7.41147			−1.18679
$40$	−1.98293	−	1.66387i	−0.313528	−	0.263081i
$41$	2.32635	−	0.846723i	0.363315	−	0.132236i	−0.153911	−	0.988085i	$-0.549187\pi$
$41$	2.32635	−	0.846723i	0.363315	−	0.132236i	0.517226	+	0.855849i	$0.326965\pi$
$42$	0.233956	+	1.32683i	0.0361001	+	0.204734i
$43$	0.677519	−	3.84240i	0.103321	−	0.585960i	−0.888557	−	0.458766i	$-0.848292\pi$
$43$	0.677519	−	3.84240i	0.103321	−	0.585960i	0.991878	−	0.127194i	$-0.0405972\pi$
$44$	−0.386659	−	0.140732i	−0.0582911	−	0.0212162i
$45$	−2.32635	−	4.02936i	−0.346792	−	0.600661i
$46$	1.81521	−	3.14403i	0.267638	−	0.463562i
$47$	−5.58512	+	4.68647i	−0.814674	+	0.683592i	−0.951718	−	0.306972i	$-0.900684\pi$
$47$	−5.58512	+	4.68647i	−0.814674	+	0.683592i	0.137045	+	0.990565i	$0.456240\pi$
$48$	−7.93242	+	6.65609i	−1.14495	+	0.960724i
$49$	3.43969	−	5.95772i	0.491385	−	0.851103i
$50$	2.84730	+	4.93166i	0.402669	+	0.697442i
$51$	−1.26604	−	0.460802i	−0.177282	−	0.0645253i
$52$	0.0825961	−	0.468426i	0.0114540	−	0.0649590i
$53$	0.492726	+	2.79439i	0.0676811	+	0.383839i	0.999767	+	0.0216005i	$0.00687620\pi$
$53$	0.492726	+	2.79439i	0.0676811	+	0.383839i	−0.932086	+	0.362238i	$0.882013\pi$
$54$	−8.35117	+	3.03958i	−1.13645	+	0.413634i
$55$	−1.50000	−	1.25865i	−0.202260	−	0.169716i
$56$	−1.02229			−0.136609
$57$		0			0
$58$	9.26857			1.21702
$59$	4.83022	+	4.05304i	0.628841	+	0.527661i	0.900569	−	0.434714i	$-0.143150\pi$
$59$	4.83022	+	4.05304i	0.628841	+	0.527661i	−0.271727	+	0.962374i	$0.587595\pi$
$60$	0.439693	−	0.160035i	0.0567641	−	0.0206604i
$61$	1.58512	+	8.98968i	0.202954	+	1.15101i	0.900627	+	0.434593i	$0.143108\pi$
$61$	1.58512	+	8.98968i	0.202954	+	1.15101i	−0.697673	+	0.716417i	$0.745781\pi$
$62$	1.66250	−	9.42853i	0.211138	−	1.19742i
$63$	−1.72668	−	0.628461i	−0.217541	−	0.0791786i
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	1.13176	−	1.96026i	0.140377	−	0.243141i
$66$	−6.61721	+	5.55250i	−0.814522	+	0.683465i
$67$	−5.87939	+	4.93339i	−0.718281	+	0.602710i	−0.926909	−	0.375286i	$-0.877545\pi$
$67$	−5.87939	+	4.93339i	−0.718281	+	0.602710i	0.208628	+	0.977995i	$0.433100\pi$
$68$	0.0432332	−	0.0748822i	0.00524280	−	0.00908080i
$69$	3.87939	+	6.71929i	0.467023	+	0.808908i
$70$	−0.386659	−	0.140732i	−0.0462146	−	0.0168207i
$71$	1.61587	−	9.16404i	0.191768	−	1.08757i	−0.725178	−	0.688561i	$-0.758243\pi$
$71$	1.61587	−	9.16404i	0.191768	−	1.08757i	0.916947	−	0.399010i	$-0.130646\pi$
$72$	−2.70439	−	15.3374i	−0.318716	−	1.80753i
$73$	−1.30541	+	0.475129i	−0.152786	+	0.0556097i	−0.417281	−	0.908777i	$-0.637017\pi$
$73$	−1.30541	+	0.475129i	−0.152786	+	0.0556097i	0.264495	+	0.964387i	$0.414795\pi$
$74$	−5.10220	−	4.28125i	−0.593118	−	0.497685i
$75$	−12.1702			−1.40530
$76$		0			0
$77$	−0.773318			−0.0881278
$78$	−7.64930	−	6.41852i	−0.866113	−	0.726755i
$79$	−11.1309	+	4.05131i	−1.25232	+	0.455808i	−0.881186	−	0.472770i	$-0.843254\pi$
$79$	−11.1309	+	4.05131i	−1.25232	+	0.455808i	−0.371136	+	0.928578i	$0.621032\pi$
$80$	−0.549163	−	3.11446i	−0.0613983	−	0.348207i
$81$	0.541889	−	3.07321i	0.0602099	−	0.341467i
$82$	3.13429	+	1.14079i	0.346124	+	0.125979i
$83$	7.41534	+	12.8438i	0.813940	+	1.40979i	0.910087	+	0.414418i	$0.136015\pi$
$83$	7.41534	+	12.8438i	0.813940	+	1.40979i	−0.0961469	+	0.995367i	$0.530652\pi$
$84$	0.0923963	−	0.160035i	0.0100813	−	0.0174613i
$85$	0.315207	−	0.264490i	0.0341891	−	0.0286880i
$86$	4.02687	−	3.37895i	0.434229	−	0.364361i
$87$	−9.90420	+	17.1546i	−1.06184	+	1.83916i
$88$	−3.27719	−	5.67626i	−0.349349	−	0.605091i
$89$	−9.67024	−	3.51968i	−1.02504	−	0.373085i	−0.225852	−	0.974162i	$-0.572517\pi$
$89$	−9.67024	−	3.51968i	−1.02504	−	0.373085i	−0.799192	+	0.601076i	$0.794739\pi$
$90$	1.08853	−	6.17334i	0.114741	−	0.650727i
$91$	−0.155230	−	0.880352i	−0.0162725	−	0.0922860i
$92$	−0.467911	+	0.170306i	−0.0487831	+	0.0177556i
$93$	15.6741	+	13.1521i	1.62533	+	1.36381i
$94$	−9.82295			−1.01316
$95$		0			0
$96$	3.00000			0.306186
$97$	−7.24170	−	6.07650i	−0.735283	−	0.616976i	0.196283	−	0.980547i	$-0.437113\pi$
$97$	−7.24170	−	6.07650i	−0.735283	−	0.616976i	−0.931566	+	0.363572i	$0.881557\pi$
$98$	8.70961	−	3.17004i	0.879803	−	0.320222i
$99$	−2.04576	−	11.6021i	−0.205607	−	1.16605i
$100$	0.135630	−	0.769193i	0.0135630	−	0.0769193i
$101$	8.69119	+	3.16333i	0.864806	+	0.314764i	0.736062	−	0.676914i	$-0.236683\pi$
$101$	8.69119	+	3.16333i	0.864806	+	0.314764i	0.128744	+	0.991678i	$0.458905\pi$
$102$	−0.907604	−	1.57202i	−0.0898662	−	0.155653i
$103$	−2.75490	+	4.77163i	−0.271448	+	0.470162i	−0.969233	−	0.246145i	$-0.920836\pi$
$103$	−2.75490	+	4.77163i	−0.271448	+	0.470162i	0.697785	+	0.716308i	$0.254169\pi$
$104$	5.80406	−	4.87019i	0.569135	−	0.477561i
$105$	0.673648	−	0.565258i	0.0657413	−	0.0551635i
$106$	−1.91147	+	3.31077i	−0.185659	+	0.321570i
$107$	5.11721	+	8.86327i	0.494699	+	0.856845i	0.999981	−	0.00610974i	$-0.00194480\pi$
$107$	5.11721	+	8.86327i	0.494699	+	0.856845i	−0.505282	+	0.862954i	$0.668611\pi$
$108$	1.14543	+	0.416902i	0.110219	+	0.0401164i
$109$	0.316552	−	1.79525i	0.0303201	−	0.171954i	−0.965887	−	0.258962i	$-0.916619\pi$
$109$	0.316552	−	1.79525i	0.0303201	−	0.171954i	0.996208	+	0.0870081i	$0.0277306\pi$
$110$	−0.458111	−	2.59808i	−0.0436792	−	0.247717i
$111$	13.3760	−	4.86846i	1.26959	−	0.462094i
$112$	−0.956767	−	0.802823i	−0.0904060	−	0.0758596i
$113$	17.6878			1.66393			0.831963	−	0.554830i	$-0.187217\pi$
$113$	17.6878			1.66393			0.831963	+	0.554830i	$0.187217\pi$
$114$		0			0
$115$	−2.36959			−0.220965
$116$	−0.973841	−	0.817150i	−0.0904189	−	0.0758704i
$117$	12.7973	−	4.65782i	1.18311	−	0.430616i
$118$	1.47519	+	8.36619i	0.135802	+	0.770170i
$119$	0.0282185	−	0.160035i	0.00258679	−	0.0146704i
$120$	7.00387	+	2.54920i	0.639363	+	0.232709i
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$	−6.14930	+	10.6509i	−0.556731	+	0.964287i
$123$	−5.46064	+	4.58202i	−0.492369	+	0.413147i
$124$	−1.00593	+	0.844075i	−0.0903352	+	0.0758002i
$125$	4.05690	−	7.02676i	0.362861	−	0.628493i
$126$	−1.23783	−	2.14398i	−0.110274	−	0.191001i
$127$	10.9042	+	3.96880i	0.967591	+	0.352174i	0.777004	−	0.629496i	$-0.216739\pi$
$127$	10.9042	+	3.96880i	0.967591	+	0.352174i	0.190587	+	0.981670i	$0.438961\pi$
$128$	1.64930	−	9.35365i	0.145779	−	0.826753i
$129$	1.95084	+	11.0637i	0.171762	+	0.974109i
$130$	2.86571	−	1.04303i	0.251340	−	0.0914802i
$131$	1.41353	+	1.18610i	0.123501	+	0.103630i	0.702446	−	0.711737i	$-0.252091\pi$
$131$	1.41353	+	1.18610i	0.123501	+	0.103630i	−0.578945	+	0.815366i	$0.696536\pi$
$132$	1.18479			0.103123
$133$		0			0
$134$	−10.3405			−0.893282
$135$	4.44356	+	3.72859i	0.382441	+	0.320906i
$136$	1.29426	−	0.471073i	0.110982	−	0.0403942i
$137$	0.0444153	+	0.251892i	0.00379465	+	0.0215206i	0.986646	−	0.162878i	$-0.0520775\pi$
$137$	0.0444153	+	0.251892i	0.00379465	+	0.0215206i	−0.982852	+	0.184398i	$0.940966\pi$
$138$	−1.81521	+	10.2946i	−0.154521	+	0.876331i
$139$	−4.00640	−	1.45821i	−0.339818	−	0.123684i	0.166474	−	0.986046i	$-0.446762\pi$
$139$	−4.00640	−	1.45821i	−0.339818	−	0.123684i	−0.506292	+	0.862362i	$0.668984\pi$
$140$	0.0282185	+	0.0488759i	0.00238490	+	0.00413076i
$141$	10.4966	−	18.1806i	0.883973	−	1.53109i
$142$	9.60401	−	8.05872i	0.805950	−	0.676273i
$143$	4.39053	−	3.68409i	0.367155	−	0.308079i
$144$	9.51367	−	16.4782i	0.792806	−	1.37318i
$145$	−3.02481	−	5.23913i	−0.251197	−	0.435086i
$146$	−1.75877	−	0.640140i	−0.145557	−	0.0529784i
$147$	−3.43969	+	19.5075i	−0.283701	+	1.60895i
$148$	0.158633	+	0.899655i	0.0130396	+	0.0739512i
$149$	−15.5608	+	5.66366i	−1.27479	+	0.463985i	−0.888705	−	0.458479i	$-0.848394\pi$
$149$	−15.5608	+	5.66366i	−1.27479	+	0.463985i	−0.386083	+	0.922464i	$0.626172\pi$
$150$	−12.5608	−	10.5397i	−1.02558	−	0.860566i
$151$	4.36184			0.354962			0.177481	−	0.984124i	$-0.443205\pi$
$151$	4.36184			0.354962			0.177481	+	0.984124i	$0.443205\pi$
$152$		0			0
$153$	2.47565			0.200145
$154$	−0.798133	−	0.669713i	−0.0643154	−	0.0539670i
$155$	−5.87211	+	2.13727i	−0.471659	+	0.171670i
$156$	0.237826	+	1.34878i	0.0190413	+	0.107989i
$157$	−1.67024	+	9.47243i	−0.133300	+	0.755982i	0.842728	+	0.538339i	$0.180948\pi$
$157$	−1.67024	+	9.47243i	−0.133300	+	0.755982i	−0.976028	+	0.217643i	$0.930163\pi$
$158$	−14.9966	−	5.45831i	−1.19307	−	0.434240i
$159$	−4.08512	−	7.07564i	−0.323971	−	0.561135i
$160$	−0.458111	+	0.793471i	−0.0362168	+	0.0627294i
$161$	−0.716881	+	0.601535i	−0.0564982	+	0.0474076i
$162$	3.22075	−	2.70253i	0.253046	−	0.212331i
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	−0.981957	−	0.189105i	$-0.939441\pi$
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	0.654748	+	0.755847i	$0.272775\pi$
$164$	−0.228741	−	0.396191i	−0.0178617	−	0.0309373i
$165$	5.29813	+	1.92836i	0.412459	+	0.150123i
$166$	−3.46972	+	19.6778i	−0.269303	+	1.52729i
$167$	−0.700685	−	3.97378i	−0.0542206	−	0.307500i	0.945622	−	0.325269i	$-0.105455\pi$
$167$	−0.700685	−	3.97378i	−0.0542206	−	0.307500i	−0.999842	+	0.0177687i	$0.994344\pi$
$168$	2.76604	−	1.00676i	0.213405	−	0.0776731i
$169$	−4.88326	−	4.09754i	−0.375635	−	0.315195i
$170$	0.554378			0.0425188
$171$		0			0
$172$	−0.721000			−0.0549758
$173$	15.4311	+	12.9482i	1.17320	+	0.984434i	1.00000		0.000452057i	$-0.000143894\pi$
$173$	15.4311	+	12.9482i	1.17320	+	0.984434i	0.173203	+	0.984886i	$0.444588\pi$
$174$	−25.0783	+	9.12776i	−1.90118	+	0.691974i
$175$	−0.254900	−	1.44561i	−0.0192686	−	0.109278i
$176$	1.39053	−	7.88609i	0.104815	−	0.594436i
$177$	−17.0608	−	6.20961i	−1.28237	−	0.466743i
$178$	−6.93242	−	12.0073i	−0.519607	−	0.899985i
$179$	−5.75624	+	9.97011i	−0.430242	+	0.745201i	−0.996894	−	0.0787564i	$-0.974905\pi$
$179$	−5.75624	+	9.97011i	−0.430242	+	0.745201i	0.566652	+	0.823957i	$0.308238\pi$
$180$	−0.658633	+	0.552659i	−0.0490916	+	0.0411928i
$181$	−6.53983	+	5.48757i	−0.486102	+	0.407888i	−0.852627	−	0.522520i	$-0.824992\pi$
$181$	−6.53983	+	5.48757i	−0.486102	+	0.407888i	0.366525	+	0.930408i	$0.380547\pi$
$182$	0.602196	−	1.04303i	0.0446378	−	0.0773149i
$183$	−13.1420	−	22.7627i	−0.971487	−	1.68266i
$184$	−7.45336	−	2.71280i	−0.549469	−	0.199990i
$185$	−0.754900	+	4.28125i	−0.0555014	+	0.314764i
$186$	4.78699	+	27.1484i	0.350999	+	1.99061i
$187$	0.979055	−	0.356347i	0.0715956	−	0.0260587i
$188$	1.03209	+	0.866025i	0.0752728	+	0.0631614i
$189$	2.29086			0.166635
$190$		0			0
$191$	18.3354			1.32671			0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354			1.32671			0.663353	+	0.748307i	$0.269133\pi$
$192$	18.9611	+	15.9103i	1.36840	+	1.14822i
$193$	0.279715	−	0.101808i	0.0201343	−	0.00732830i	−0.331933	−	0.943303i	$-0.607701\pi$
$193$	0.279715	−	0.101808i	0.0201343	−	0.00732830i	0.352068	+	0.935975i	$0.385479\pi$
$194$	−2.21167	−	12.5430i	−0.158788	−	0.900534i
$195$	−1.13176	+	6.41852i	−0.0810470	+	0.459640i
$196$	−1.19459	−	0.434796i	−0.0853281	−	0.0310569i
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	0.531203	−	0.847245i	$-0.321740\pi$
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	−0.999337	+	0.0364128i	$0.988407\pi$
$198$	7.93629	−	13.7461i	0.564008	−	0.976890i
$199$	−0.196652	+	0.165011i	−0.0139403	+	0.0116973i	−0.649731	−	0.760164i	$-0.725119\pi$
$199$	−0.196652	+	0.165011i	−0.0139403	+	0.0116973i	0.635791	+	0.771861i	$0.280674\pi$
$200$	9.53074	−	7.99724i	0.673925	−	0.565491i
$201$	11.0496	−	19.1385i	0.779381	−	1.34993i
$202$	6.23055	+	10.7916i	0.438380	+	0.759297i
$203$	−2.24510	−	0.817150i	−0.157575	−	0.0573527i
$204$	−0.0432332	+	0.245188i	−0.00302693	+	0.0171666i
$205$	−0.378041	−	2.14398i	−0.0264035	−	0.149742i
$206$	−6.97565	+	2.53893i	−0.486017	+	0.176896i
$207$	−10.9213	−	9.16404i	−0.759081	−	0.636945i
$208$	9.25671			0.641837
$209$		0			0
$210$	1.18479			0.0817585
$211$	−1.87551	−	1.57374i	−0.129116	−	0.108341i	0.575943	−	0.817490i	$-0.304635\pi$
$211$	−1.87551	−	1.57374i	−0.129116	−	0.108341i	−0.705059	+	0.709149i	$0.749079\pi$
$212$	0.492726	−	0.179338i	0.0338406	−	0.0123170i
$213$	4.65270	+	26.3868i	0.318798	+	1.80799i
$214$	−2.39440	+	13.5793i	−0.163678	+	0.928263i
$215$	−3.22416	−	1.17350i	−0.219886	−	0.0800318i
$216$	9.70826	+	16.8152i	0.660564	+	1.14413i
$217$	−1.23396	+	2.13727i	−0.0837664	+	0.145088i
$218$	1.88144	−	1.57872i	0.127428	−	0.106924i
$219$	3.06418	−	2.57115i	0.207058	−	0.173742i
$220$	−0.180922	+	0.313366i	−0.0121978	+	0.0211272i
$221$	0.602196	+	1.04303i	0.0405081	+	0.0701621i
$222$	18.0214	+	6.55926i	1.20952	+	0.440229i
$223$	1.47771	−	8.38052i	0.0989549	−	0.561201i	−0.894509	−	0.447051i	$-0.852474\pi$
$223$	1.47771	−	8.38052i	0.0989549	−	0.561201i	0.993463	−	0.114150i	$-0.0364145\pi$
$224$	0.0628336	+	0.356347i	0.00419825	+	0.0238094i
$225$	21.0141	−	7.64852i	1.40094	−	0.509901i
$226$	18.2554	+	15.3181i	1.21433	+	1.01894i
$227$	14.1506			0.939211			0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506			0.939211			0.469606	+	0.882876i	$0.344396\pi$
$228$		0			0
$229$	−20.5330			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$	−2.44562	−	2.05212i	−0.161260	−	0.135313i
$231$	2.09240	−	0.761570i	0.137670	−	0.0501076i
$232$	−3.51636	−	19.9423i	−0.230860	−	1.30927i
$233$	3.06506	−	17.3828i	0.200798	−	1.13878i	−0.703117	−	0.711074i	$-0.748209\pi$
$233$	3.06506	−	17.3828i	0.200798	−	1.13878i	0.903916	−	0.427711i	$-0.140680\pi$
$234$	17.2417	+	6.27546i	1.12712	+	0.410240i
$235$	3.20574	+	5.55250i	0.209119	+	0.362205i
$236$	0.582596	−	1.00909i	0.0379238	−	0.0656859i
$237$	26.1275	−	21.9236i	1.69716	−	1.42409i
$238$	0.167718	−	0.140732i	0.0108716	−	0.00912233i
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	−0.901556	−	0.432663i	$-0.857574\pi$
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	0.825475	+	0.564438i	$0.190907\pi$
$240$	4.55303	+	7.88609i	0.293897	+	0.509045i
$241$	12.9684	+	4.72010i	0.835367	+	0.304049i	0.724060	−	0.689737i	$-0.242274\pi$
$241$	12.9684	+	4.72010i	0.835367	+	0.304049i	0.111307	+	0.993786i	$0.464496\pi$
$242$	−1.41353	+	8.01655i	−0.0908654	+	0.515323i
$243$	−1.87598	−	10.6392i	−0.120344	−	0.682506i
$244$	1.58512	−	0.576937i	0.101477	−	0.0369346i
$245$	−4.63429	−	3.88863i	−0.296074	−	0.248435i
$246$	−9.60401			−0.612329
$247$		0			0
$248$	−20.9172			−1.32824
$249$	−32.7126	−	27.4491i	−2.07308	−	1.73952i
$250$	10.2724	−	3.73886i	0.649686	−	0.236466i
$251$	−0.723278	−	4.10191i	−0.0456529	−	0.258910i	0.953436	−	0.301597i	$-0.0975196\pi$
$251$	−0.723278	−	4.10191i	−0.0456529	−	0.258910i	−0.999089	+	0.0426861i	$0.986408\pi$
$252$	−0.0589632	+	0.334397i	−0.00371433	+	0.0210650i
$253$	−5.63816	−	2.05212i	−0.354468	−	0.129016i
$254$	7.81702	+	13.5395i	0.490483	+	0.849542i
$255$	−0.592396	+	1.02606i	−0.0370973	+	0.0642544i
$256$	−3.36753	+	2.82569i	−0.210470	+	0.176606i
$257$	−0.511144	+	0.428901i	−0.0318843	+	0.0267541i	−0.658591	−	0.752501i	$-0.728847\pi$
$257$	−0.511144	+	0.428901i	−0.0318843	+	0.0267541i	0.626706	+	0.779256i	$0.284403\pi$
$258$	−7.56805	+	13.1082i	−0.471166	+	0.816084i
$259$	0.858441	+	1.48686i	0.0533409	+	0.0923892i
$260$	−0.393056	−	0.143061i	−0.0243763	−	0.00887224i
$261$	6.32042	−	35.8449i	0.391224	−	2.21874i
$262$	0.431703	+	2.44831i	0.0266707	+	0.151257i
$263$	−10.7121	+	3.89890i	−0.660538	+	0.240416i	−0.650469	−	0.759533i	$-0.725428\pi$
$263$	−10.7121	+	3.89890i	−0.660538	+	0.240416i	−0.0100696	+	0.999949i	$0.503205\pi$
$264$	14.4572	+	12.1311i	0.889781	+	0.746615i
$265$	2.49525			0.153282
$266$		0			0
$267$	29.6313			1.81341
$268$	1.08647	+	0.911654i	0.0663665	+	0.0556881i
$269$	18.2208	−	6.63181i	1.11094	−	0.404349i	0.279601	−	0.960116i	$-0.409798\pi$
$269$	18.2208	−	6.63181i	1.11094	−	0.404349i	0.831338	+	0.555768i	$0.187576\pi$
$270$	1.35710	+	7.69648i	0.0825903	+	0.468393i
$271$	−2.32588	+	13.1907i	−0.141287	+	0.801281i	0.828986	+	0.559269i	$0.188918\pi$
$271$	−2.32588	+	13.1907i	−0.141287	+	0.801281i	−0.970273	+	0.242011i	$0.922193\pi$
$272$	1.58125	+	0.575529i	0.0958775	+	0.0348965i
$273$	1.28699	+	2.22913i	0.0778921	+	0.134913i
$274$	−0.172304	+	0.298439i	−0.0104093	+	0.0180294i
$275$	7.20961	−	6.04958i	0.434756	−	0.364803i
$276$	1.09833	−	0.921605i	0.0661115	−	0.0554741i
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	0.466096	+	0.884734i	$0.345660\pi$
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	−0.999250	+	0.0387161i	$0.987673\pi$
$278$	−2.87211	−	4.97464i	−0.172258	−	0.298359i
$279$	−35.3298	−	12.8590i	−2.11514	−	0.769848i
$280$	−0.156107	+	0.885328i	−0.00932919	+	0.0529085i
$281$	−3.17412	−	18.0013i	−0.189352	−	1.07387i	−0.920235	−	0.391365i	$-0.872003\pi$
$281$	−3.17412	−	18.0013i	−0.189352	−	1.07387i	0.730884	−	0.682502i	$-0.239108\pi$
$282$	26.5783	−	9.67372i	1.58272	−	0.576061i
$283$	5.88919	+	4.94161i	0.350076	+	0.293748i	0.800820	−	0.598904i	$-0.204397\pi$
$283$	5.88919	+	4.94161i	0.350076	+	0.293748i	−0.450745	+	0.892653i	$0.648842\pi$
$284$	−1.71957			−0.102038
$285$		0			0
$286$	7.72193			0.456608
$287$	−0.658633	−	0.552659i	−0.0388779	−	0.0326224i
$288$	−5.18004	+	1.88538i	−0.305237	+	0.111097i
$289$	−2.91400	−	16.5261i	−0.171412	−	0.972125i
$290$	1.41534	−	8.02682i	0.0831119	−	0.471351i
$291$	25.5783	+	9.30975i	1.49943	+	0.545747i
$292$	0.128356	+	0.222318i	0.00751144	+	0.0130102i
$293$	−5.25150	+	9.09586i	−0.306796	+	0.531386i	−0.977660	−	0.210195i	$-0.932590\pi$
$293$	−5.25150	+	9.09586i	−0.306796	+	0.531386i	0.670864	+	0.741581i	$0.265924\pi$
$294$	−20.4440	+	17.1546i	−1.19232	+	1.00048i
$295$	4.24763	−	3.56418i	0.247306	−	0.207515i
$296$	−7.27584	+	12.6021i	−0.422900	+	0.732484i
$297$	7.34389	+	12.7200i	0.426136	+	0.738089i
$298$	−20.9650	−	7.63063i	−1.21447	−	0.442030i
$299$	1.20439	−	6.83045i	0.0696518	−	0.395015i
$300$	0.390530	+	2.21480i	0.0225472	+	0.127872i
$301$	−1.27332	+	0.463450i	−0.0733929	+	0.0267128i
$302$	4.50181	+	3.77747i	0.259050	+	0.217369i
$303$	−26.6313			−1.52993
$304$		0			0
$305$	8.02734			0.459644
$306$	2.55509	+	2.14398i	0.146065	+	0.122563i
$307$	−10.9902	+	4.00011i	−0.627244	+	0.228298i	−0.636031	−	0.771663i	$-0.719425\pi$
$307$	−10.9902	+	4.00011i	−0.627244	+	0.228298i	0.00878741	+	0.999961i	$0.497203\pi$
$308$	0.0248149	+	0.140732i	0.00141396	+	0.00801898i
$309$	2.75490	−	15.6238i	0.156721	−	0.888808i
$310$	−7.91147	−	2.87954i	−0.449342	−	0.163547i
$311$	−7.98293	−	13.8268i	−0.452670	−	0.784048i	0.545881	−	0.837863i	$-0.316195\pi$
$311$	−7.98293	−	13.8268i	−0.452670	−	0.784048i	−0.998551	+	0.0538151i	$0.982862\pi$
$312$	−10.9081	+	18.8933i	−0.617548	+	1.06962i
$313$	−20.3987	+	17.1166i	−1.15300	+	0.967486i	−0.999786	−	0.0207063i	$-0.993409\pi$
$313$	−20.3987	+	17.1166i	−1.15300	+	0.967486i	−0.153219	+	0.988192i	$0.548964\pi$
$314$	−9.92720	+	8.32991i	−0.560225	+	0.470084i
$315$	−0.807934	+	1.39938i	−0.0455219	+	0.0788462i
$316$	1.09446	+	1.89565i	0.0615679	+	0.106639i
$317$	27.7511	+	10.1006i	1.55866	+	0.567304i	0.970428	−	0.241390i	$-0.0776035\pi$
$317$	27.7511	+	10.1006i	1.55866	+	0.567304i	0.588228	+	0.808695i	$0.299826\pi$
$318$	1.91147	−	10.8405i	0.107190	−	0.607906i
$319$	−2.65998	−	15.0855i	−0.148930	−	0.844625i
$320$	−7.10354	+	2.58548i	−0.397100	+	0.144533i
$321$	−22.5744	−	18.9422i	−1.25998	−	1.05725i
$322$	−1.26083			−0.0702633
$323$		0			0
$324$	−0.576666			−0.0320370
$325$	8.33409	+	6.99313i	0.462292	+	0.387909i
$326$	−10.5778	+	3.85002i	−0.585853	+	0.213233i
$327$	0.911474	+	5.16923i	0.0504046	+	0.285859i
$328$	1.26542	−	7.17653i	0.0698709	−	0.396257i
$329$	2.37939	+	0.866025i	0.131180	+	0.0477455i
$330$	3.79813	+	6.57856i	0.209080	+	0.362138i
$331$	13.8327	−	23.9590i	0.760317	−	1.31691i	−0.182371	−	0.983230i	$-0.558377\pi$
$331$	13.8327	−	23.9590i	0.760317	−	1.31691i	0.942687	−	0.333677i	$-0.108290\pi$
$332$	2.09942	−	1.76162i	0.115221	−	0.0966817i
$333$	−20.0364	+	16.8126i	−1.09799	+	0.921322i
$334$	2.71823	−	4.70810i	0.148735	−	0.257616i
$335$	3.37464	+	5.84504i	0.184376	+	0.319349i
$336$	3.37939	+	1.23000i	0.184361	+	0.0671018i
$337$	−3.10132	+	17.5885i	−0.168940	+	0.958104i	0.775969	+	0.630771i	$0.217261\pi$
$337$	−3.10132	+	17.5885i	−0.168940	+	0.958104i	−0.944909	+	0.327333i	$0.893850\pi$
$338$	−1.49138	−	8.45805i	−0.0811205	−	0.460057i
$339$	−47.8585	+	17.4191i	−2.59932	+	0.946074i
$340$	−0.0582480	−	0.0488759i	−0.00315894	−	0.00265067i
$341$	−15.8229			−0.856861
$342$		0			0
$343$	−4.82026			−0.260270
$344$	−8.79788	−	7.38230i	−0.474350	−	0.398027i
$345$	6.41147	−	2.33359i	0.345182	−	0.125636i
$346$	4.71276	+	26.7274i	0.253360	+	1.43687i
$347$	−1.00727	+	5.71253i	−0.0540733	+	0.306665i	−0.999834	−	0.0181980i	$-0.994207\pi$
$347$	−1.00727	+	5.71253i	−0.0540733	+	0.306665i	0.945761	+	0.324863i	$0.105318\pi$
$348$	3.43969	+	1.25195i	0.184387	+	0.0671113i
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	0.785134	−	0.619326i	$-0.212594\pi$
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	−0.928919	+	0.370282i	$0.879261\pi$
$350$	0.988856	−	1.71275i	0.0528566	−	0.0915502i
$351$	−13.0064	+	10.9137i	−0.694230	+	0.582528i
$352$	−1.77719	+	1.49124i	−0.0947245	+	0.0794833i
$353$	12.6172	−	21.8537i	0.671546	−	1.16315i	−0.305919	−	0.952057i	$-0.598964\pi$
$353$	12.6172	−	21.8537i	0.671546	−	1.16315i	0.977466	−	0.211095i	$-0.0677029\pi$
$354$	−12.2306	−	21.1839i	−0.650047	−	1.12591i
$355$	−7.68954	−	2.79876i	−0.408118	−	0.148543i
$356$	−0.330222	+	1.87278i	−0.0175017	+	0.0992573i
$357$	0.0812519	+	0.460802i	0.00430031	+	0.0243883i
$358$	−14.5753	+	5.30498i	−0.770330	+	0.280377i
$359$	5.12243	+	4.29823i	0.270351	+	0.226852i	0.767877	−	0.640598i	$-0.221313\pi$
$359$	5.12243	+	4.29823i	0.270351	+	0.226852i	−0.497525	+	0.867449i	$0.665758\pi$
$360$	−13.6955			−0.721818
$361$		0			0
$362$	−11.5021			−0.604535
$363$	−13.3268	−	11.1825i	−0.699477	−	0.586931i
$364$	−0.155230	+	0.0564991i	−0.00813626	+	0.00296135i
$365$	0.212134	+	1.20307i	0.0111036	+	0.0629716i
$366$	6.14930	−	34.8744i	0.321429	−	1.82291i
$367$	−7.62923	−	2.77681i	−0.398243	−	0.144948i	0.135132	−	0.990828i	$-0.456854\pi$
$367$	−7.62923	−	2.77681i	−0.398243	−	0.144948i	−0.533375	+	0.845879i	$0.679076\pi$
$368$	−4.84524	−	8.39220i	−0.252575	−	0.437473i
$369$	6.54916	−	11.3435i	0.340936	−	0.590518i
$370$	−4.48680	+	3.76487i	−0.233257	+	0.195726i
$371$	0.754900	−	0.633436i	0.0391925	−	0.0328864i
$372$	1.89053	−	3.27449i	0.0980194	−	0.169775i
$373$	17.4488	+	30.2222i	0.903463	+	1.56484i	0.822967	+	0.568090i	$0.192317\pi$
$373$	17.4488	+	30.2222i	0.903463	+	1.56484i	0.0804968	+	0.996755i	$0.474349\pi$
$374$	1.31908	+	0.480105i	0.0682079	+	0.0248256i
$375$	−4.05690	+	23.0078i	−0.209498	+	1.18812i
$376$	3.72668	+	21.1351i	0.192189	+	1.08996i
$377$	16.6395	−	6.05628i	0.856978	−	0.311914i
$378$	2.36437	+	1.98394i	0.121610	+	0.102043i
$379$	−1.70140			−0.0873950			−0.0436975	−	0.999045i	$-0.513914\pi$
$379$	−1.70140			−0.0873950			−0.0436975	+	0.999045i	$0.513914\pi$
$380$		0			0
$381$	−33.4124			−1.71177
$382$	18.9238	+	15.8790i	0.968226	+	0.812438i
$383$	2.75965	−	1.00443i	0.141011	−	0.0513240i	−0.270550	−	0.962706i	$-0.587206\pi$
$383$	2.75965	−	1.00443i	0.141011	−	0.0513240i	0.411562	+	0.911382i	$0.364983\pi$
$384$	4.74897	+	26.9327i	0.242345	+	1.37441i
$385$	−0.118089	+	0.669713i	−0.00601835	+	0.0341318i
$386$	0.376859	+	0.137165i	0.0191816	+	0.00698154i
$387$	−10.3216	−	17.8775i	−0.524677	−	0.908767i
$388$	−0.873455	+	1.51287i	−0.0443430	+	0.0768043i
$389$	−18.8195	+	15.7915i	−0.954189	+	0.800659i	−0.979998	−	0.199007i	$-0.936228\pi$
$389$	−18.8195	+	15.7915i	−0.954189	+	0.800659i	0.0258092	+	0.999667i	$0.491784\pi$
$390$	−6.72668	+	5.64436i	−0.340619	+	0.285813i
$391$	0.630415	−	1.09191i	0.0318815	−	0.0552203i
$392$	−10.1250	−	17.5369i	−0.511387	−	0.885749i
$393$	−4.99273	−	1.81720i	−0.251850	−	0.0916658i
$394$	3.07444	−	17.4360i	0.154888	−	0.878415i
$395$	1.80881	+	10.2583i	0.0910112	+	0.516150i
$396$	−2.04576	+	0.744596i	−0.102803	+	0.0374173i
$397$	−24.3876	−	20.4636i	−1.22398	−	1.02704i	−0.998607	−	0.0527667i	$-0.983196\pi$
$397$	−24.3876	−	20.4636i	−1.22398	−	1.02704i	−0.225371	−	0.974273i	$-0.572360\pi$
$398$	−0.345866			−0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	0.0662372	+	0.0555796i	0.00330773	+	0.00277551i	0.644440	−	0.764655i	$-0.277091\pi$
$401$	0.0662372	+	0.0555796i	0.00330773	+	0.00277551i	−0.641132	+	0.767430i	$0.721535\pi$
$402$	27.9786	−	10.1834i	1.39545	−	0.507902i
$403$	−3.17617	−	18.0130i	−0.158217	−	0.897290i
$404$	0.296789	−	1.68317i	0.0147658	−	0.0837411i
$405$	−2.57873	−	0.938579i	−0.128138	−	0.0466384i
$406$	−1.60947	−	2.78768i	−0.0798767	−	0.138350i
$407$	−5.50387	+	9.53298i	−0.272817	+	0.472532i
$408$	−3.03802	+	2.54920i	−0.150404	+	0.126204i
$409$	−15.3255	+	12.8596i	−0.757796	+	0.635866i	−0.937552	−	0.347845i	$-0.886914\pi$
$409$	−15.3255	+	12.8596i	−0.757796	+	0.635866i	0.179756	+	0.983711i	$0.442469\pi$
$410$	1.46657	−	2.54017i	0.0724286	−	0.125450i
$411$	−0.368241	−	0.637812i	−0.0181640	−	0.0314609i
$412$	0.956767	+	0.348235i	0.0471365	+	0.0171563i
$413$	0.380263	−	2.15658i	0.0187115	−	0.106118i
$414$	−3.33544	−	18.9162i	−0.163928	−	0.929681i
$415$	12.2554	−	4.46059i	0.601592	−	0.218962i
$416$	−2.05438	−	1.72383i	−0.100724	−	0.0845176i
$417$	12.2763			0.601174
$418$		0			0
$419$	25.4097			1.24135			0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$	−0.124485	−	0.104455i	−0.00607425	−	0.00509690i
$421$	4.10607	−	1.49449i	0.200117	−	0.0728368i	−0.240017	−	0.970769i	$-0.577153\pi$
$421$	4.10607	−	1.49449i	0.200117	−	0.0728368i	0.440134	+	0.897932i	$0.354931\pi$
$422$	−0.572796	−	3.24849i	−0.0278833	−	0.158134i
$423$	−6.69846	+	37.9889i	−0.325690	+	1.84708i
$424$	7.84864	+	2.85667i	0.381164	+	0.138732i
$425$	0.988856	+	1.71275i	0.0479665	+	0.0830805i
$426$	−18.0496	+	31.2629i	−0.874507	+	1.51469i
$427$	2.42855	−	2.03779i	0.117526	−	0.0986158i
$428$	1.44878	−	1.21567i	0.0700293	−	0.0587616i
$429$	−8.25150	+	14.2920i	−0.398386	+	0.690025i
$430$	−2.31134	−	4.00335i	−0.111463	−	0.193059i
$431$	−35.9962	−	13.1015i	−1.73388	−	0.631079i	−0.734981	−	0.678088i	$-0.762809\pi$
$431$	−35.9962	−	13.1015i	−1.73388	−	0.631079i	−0.998894	+	0.0470089i	$0.985031\pi$
$432$	−4.11927	+	23.3615i	−0.198188	+	1.12398i
$433$	3.14842	+	17.8556i	0.151304	+	0.858085i	0.962088	+	0.272740i	$0.0879299\pi$
$433$	3.14842	+	17.8556i	0.151304	+	0.858085i	−0.810784	+	0.585345i	$0.800959\pi$
$434$	−3.12449	+	1.13722i	−0.149980	+	0.0545883i
$435$	13.3439	+	11.1969i	0.639791	+	0.536848i
$436$	−0.336867			−0.0161330
$437$		0			0
$438$	5.38919			0.257505
$439$	4.66566	+	3.91495i	0.222680	+	0.186850i	0.747302	−	0.664485i	$-0.231349\pi$
$439$	4.66566	+	3.91495i	0.222680	+	0.186850i	−0.524622	+	0.851335i	$0.675793\pi$
$440$	−5.41622	+	1.97134i	−0.258208	+	0.0939801i
$441$	−6.32042	−	35.8449i	−0.300972	−	1.70690i
$442$	−0.281774	+	1.59802i	−0.0134026	+	0.0760102i
$443$	28.0903	+	10.2240i	1.33461	+	0.485759i	0.908112	−	0.418728i	$-0.137524\pi$
$443$	28.0903	+	10.2240i	1.33461	+	0.485759i	0.426501	+	0.904487i	$0.359746\pi$
$444$	−1.31521	−	2.27801i	−0.0624170	−	0.108109i
$445$	−4.52481	+	7.83721i	−0.214497	+	0.371519i
$446$	8.78287	−	7.36970i	0.415881	−	0.348966i
$447$	36.5257	−	30.6487i	1.72761	−	1.44964i
$448$	−1.49273	+	2.58548i	−0.0705247	+	0.122152i
$449$	−5.62495	−	9.74270i	−0.265458	−	0.459787i	0.702226	−	0.711955i	$-0.252190\pi$
$449$	−5.62495	−	9.74270i	−0.265458	−	0.459787i	−0.967683	+	0.252168i	$0.918856\pi$
$450$	28.3123	+	10.3048i	1.33465	+	0.485774i
$451$	0.957234	−	5.42874i	0.0450744	−	0.255629i
$452$	−0.567581	−	3.21891i	−0.0266968	−	0.151405i
$453$	−11.8020	+	4.29558i	−0.554507	+	0.201824i
$454$	14.6047	+	12.2548i	0.685434	+	0.575147i
$455$	−0.786112			−0.0368535
$456$		0			0
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$	−21.1919	−	17.7821i	−0.990233	−	0.830904i
$459$	−2.90033	+	1.05563i	−0.135376	+	0.0492728i
$460$	0.0760373	+	0.431229i	0.00354526	+	0.0201062i
$461$	−6.35962	+	36.0672i	−0.296197	+	1.67982i	0.366099	+	0.930576i	$0.380693\pi$
$461$	−6.35962	+	36.0672i	−0.296197	+	1.67982i	−0.662297	+	0.749242i	$0.730418\pi$
$462$	2.81908	+	1.02606i	0.131155	+	0.0477367i
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.540534	+	0.841322i	$0.318222\pi$
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.458340	+	0.888777i	$0.348444\pi$
$464$	12.3701	−	21.4256i	0.574265	−	0.994657i
$465$	13.7836	−	11.5658i	0.639198	−	0.536351i
$466$	18.2173	−	15.2862i	0.843902	−	0.708118i
$467$	−12.7981	+	22.1670i	−0.592227	+	1.02577i	0.401705	+	0.915769i	$0.368418\pi$
$467$	−12.7981	+	22.1670i	−0.592227	+	1.02577i	−0.993932	+	0.109998i	$0.964916\pi$
$468$	−1.25830	−	2.17945i	−0.0581651	−	0.100745i
$469$	2.50475	+	0.911654i	0.115659	+	0.0420963i
$470$	−1.50000	+	8.50692i	−0.0691898	+	0.392395i
$471$	−4.80928	−	27.2748i	−0.221600	−	1.25676i
$472$	17.4410	−	6.34802i	0.802789	−	0.292191i
$473$	−6.65523	−	5.58440i	−0.306008	−	0.256771i
$474$	45.9522			2.11066
$475$		0			0
$476$	−0.0300295			−0.00137640
$477$	11.5005	+	9.65004i	0.526570	+	0.441845i
$478$	−2.97818	+	1.08397i	−0.136219	+	0.0495796i
$479$	6.62923	+	37.5962i	0.302897	+	1.71782i	0.633240	+	0.773955i	$0.281725\pi$
$479$	6.62923	+	37.5962i	0.302897	+	1.71782i	−0.330343	+	0.943861i	$0.607164\pi$
$480$	0.458111	−	2.59808i	0.0209098	−	0.118585i
$481$	−11.9572	−	4.35208i	−0.545203	−	0.198438i
$482$	9.29679	+	16.1025i	0.423457	+	0.733449i
$483$	1.34730	−	2.33359i	0.0613041	−	0.106182i
$484$	0.855286	−	0.717670i	0.0388766	−	0.0326214i
$485$	−6.36824	+	5.34359i	−0.289167	+	0.242640i
$486$	7.27766	−	12.6053i	0.330121	−	0.571787i
$487$	3.88191	+	6.72367i	0.175906	+	0.304678i	0.940475	−	0.339864i	$-0.110381\pi$
$487$	3.88191	+	6.72367i	0.175906	+	0.304678i	−0.764568	+	0.644543i	$0.777048\pi$
$488$	25.2494	+	9.19004i	1.14299	+	0.416014i
$489$	4.17752	−	23.6919i	0.188914	−	1.07138i
$490$	−1.41534	−	8.02682i	−0.0639387	−	0.362615i
$491$	34.5082	−	12.5600i	1.55733	−	0.566823i	0.587210	−	0.809435i	$-0.300226\pi$
$491$	34.5082	−	12.5600i	1.55733	−	0.566823i	0.970124	+	0.242611i	$0.0780040\pi$
$492$	1.00908	+	0.846723i	0.0454931	+	0.0381732i
$493$	3.21894			0.144974
$494$		0			0
$495$	−10.3601			−0.465651
$496$	−19.5765	−	16.4266i	−0.879011	−	0.737578i
$497$	−3.03684	+	1.10532i	−0.136221	+	0.0495803i
$498$	−9.99067	−	56.6599i	−0.447692	−	2.53899i
$499$	0.855448	−	4.85148i	0.0382951	−	0.217182i	−0.959655	−	0.281180i	$-0.909274\pi$
$499$	0.855448	−	4.85148i	0.0382951	−	0.217182i	0.997950	+	0.0639981i	$0.0203852\pi$
$500$	−1.40895	−	0.512815i	−0.0630101	−	0.0229338i
$501$	5.80928	+	10.0620i	0.259539	+	0.449535i
$502$	2.80587	−	4.85992i	0.125232	−	0.216909i
$503$	25.2408	−	21.1796i	1.12543	−	0.944350i	0.126566	−	0.991958i	$-0.459604\pi$
$503$	25.2408	−	21.1796i	1.12543	−	0.944350i	0.998866	+	0.0476081i	$0.0151599\pi$
$504$	−4.14337	+	3.47670i	−0.184560	+	0.154865i
$505$	4.06670	−	7.04374i	0.180966	−	0.313442i
$506$	−4.04189	−	7.00076i	−0.179684	−	0.311222i
$507$	17.2481	+	6.27779i	0.766015	+	0.278807i
$508$	0.372360	−	2.11176i	0.0165208	−	0.0936941i
$509$	6.41370	+	36.3739i	0.284282	+	1.61224i	0.707839	+	0.706374i	$0.249670\pi$
$509$	6.41370	+	36.3739i	0.284282	+	1.61224i	−0.423557	+	0.905870i	$0.639219\pi$
$510$	−1.50000	+	0.545955i	−0.0664211	+	0.0241753i
$511$	0.369585	+	0.310119i	0.0163495	+	0.0137188i
$512$	−24.9186			−1.10126
$513$		0			0
$514$	−0.898986			−0.0396526
$515$	3.71167	+	3.11446i	0.163556	+	0.137239i
$516$	1.95084	−	0.710047i	0.0858808	−	0.0312581i
$517$	2.81908	+	15.9878i	0.123983	+	0.703142i
$518$	−0.401674	+	2.27801i	−0.0176485	+	0.100090i
$519$	−54.5039	−	19.8378i	−2.39246	−	0.870783i
$520$	−3.33140	−	5.77016i	−0.146092	−	0.253038i
$521$	4.64590	−	8.04693i	0.203540	−	0.352542i	−0.746126	−	0.665804i	$-0.768088\pi$
$521$	4.64590	−	8.04693i	0.203540	−	0.352542i	0.949667	+	0.313262i	$0.101422\pi$
$522$	37.5658	−	31.5215i	1.64421	−	1.37966i
$523$	21.7672	−	18.2649i	0.951814	−	0.798667i	−0.0277878	−	0.999614i	$-0.508846\pi$
$523$	21.7672	−	18.2649i	0.951814	−	0.798667i	0.979602	+	0.200947i	$0.0644018\pi$
$524$	0.170493	−	0.295303i	0.00744802	−	0.0129004i
$525$	2.11334	+	3.66041i	0.0922338	+	0.159754i
$526$	−14.4324	−	5.25297i	−0.629283	−	0.229040i
$527$	0.577382	−	3.27449i	0.0251511	−	0.142639i
$528$	4.00387	+	22.7071i	0.174246	+	0.988199i
$529$	14.7900	−	5.38311i	0.643043	−	0.234048i
$530$	2.57532	+	2.16095i	0.111865	+	0.0938657i
$531$	33.3610			1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$	30.5822	+	25.6615i	1.32342	+	1.11048i
$535$	8.45723	−	3.07818i	0.365638	−	0.133081i
$536$	3.92303	+	22.2486i	0.169449	+	0.960993i
$537$	5.75624	−	32.6453i	0.248400	−	1.40875i
$538$	24.5488	+	8.93502i	1.05837	+	0.385216i
$539$	−7.65910	−	13.2660i	−0.329901	−	0.571405i
$540$	0.535959	−	0.928309i	0.0230640	−	0.0399480i
$541$	11.4795	−	9.63246i	0.493543	−	0.414132i	−0.361751	−	0.932275i	$-0.617821\pi$
$541$	11.4795	−	9.63246i	0.493543	−	0.414132i	0.855294	+	0.518143i	$0.173376\pi$
$542$	−13.8240	+	11.5998i	−0.593794	+	0.498252i
$543$	12.2909	−	21.2884i	0.527451	−	0.913572i
$544$	−0.243756	−	0.422197i	−0.0104509	−	0.0181016i
$545$	−1.50640	−	0.548284i	−0.0645269	−	0.0234859i
$546$	−0.602196	+	3.41523i	−0.0257716	+	0.146158i
$547$	0.674992	+	3.82807i	0.0288606	+	0.163677i	0.995832	−	0.0912093i	$-0.0290732\pi$
$547$	0.674992	+	3.82807i	0.0288606	+	0.163677i	−0.966971	+	0.254886i	$0.917962\pi$
$548$	0.0444153	−	0.0161658i	0.00189733	−	0.000690571i
$549$	36.9975	+	31.0446i	1.57902	+	1.32495i
$550$	12.6800			0.540679
$551$		0			0
$552$	22.8384			0.972068
$553$	3.15136	+	2.64430i	0.134009	+	0.112447i
$554$	−22.4684	+	8.17782i	−0.954590	+	0.347442i
$555$	−2.17365	−	12.3274i	−0.0922662	−	0.523268i
$556$	−0.136812	+	0.775897i	−0.00580210	+	0.0329054i
$557$	−12.4081	−	4.51617i	−0.525747	−	0.191356i	0.0654914	−	0.997853i	$-0.479138\pi$
$557$	−12.4081	−	4.51617i	−0.525747	−	0.191356i	−0.591238	+	0.806497i	$0.701361\pi$
$558$	−25.3273	−	43.8681i	−1.07219	−	1.85709i
$559$	5.02141	−	8.69734i	0.212383	−	0.367858i
$560$	−0.841367	+	0.705990i	−0.0355542	+	0.0298335i
$561$	−2.29813	+	1.92836i	−0.0970273	+	0.0814155i
$562$	12.3136	−	21.3278i	0.519418	−	0.899659i
$563$	5.35638	+	9.27752i	0.225745	+	0.391001i	0.956543	−	0.291593i	$-0.0941852\pi$
$563$	5.35638	+	9.27752i	0.225745	+	0.391001i	−0.730798	+	0.682594i	$0.760852\pi$
$564$	−3.64543	−	1.32683i	−0.153500	−	0.0558695i
$565$	2.70099	−	15.3181i	0.113631	−	0.644436i
$566$	1.79860	+	10.2004i	0.0756008	+	0.428753i
$567$	−1.01842	+	0.370674i	−0.0427695	+	0.0155668i
$568$	−20.9828	−	17.6066i	−0.880417	−	0.738758i
$569$	13.4706			0.564717			0.282358	−	0.959309i	$-0.408883\pi$
$569$	13.4706			0.564717			0.282358	+	0.959309i	$0.408883\pi$
$570$		0			0
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	−0.811337	−	0.680793i	−0.0339237	−	0.0284654i
$573$	−49.6109	+	18.0569i	−2.07252	+	0.754337i
$574$	−0.201151	−	1.14079i	−0.00839590	−	0.0476155i
$575$	1.97771	−	11.2162i	0.0824763	−	0.467746i
$576$	−42.7388	−	15.5556i	−1.78078	−	0.648152i
$577$	5.27719	+	9.14036i	0.219692	+	0.380518i	0.954714	−	0.297526i	$-0.0961613\pi$
$577$	5.27719	+	9.14036i	0.219692	+	0.380518i	−0.735022	+	0.678044i	$0.762828\pi$
$578$	11.3045	−	19.5800i	0.470206	−	0.814421i
$579$	−0.656574	+	0.550931i	−0.0272863	+	0.0228959i
$580$	−0.856381	+	0.718589i	−0.0355593	+	0.0298378i
$581$	2.57532	−	4.46059i	0.106842	−	0.185056i
$582$	18.3366	+	31.7600i	0.760077	+	1.31649i
$583$	5.93717	+	2.16095i	0.245892	+	0.0894975i
$584$	−0.710074	+	4.02703i	−0.0293831	+	0.166640i
$585$	−2.07960	−	11.7940i	−0.0859810	−	0.487623i
$586$	−13.2973	+	4.83981i	−0.549305	+	0.199931i
$587$	−14.6734	−	12.3124i	−0.605636	−	0.508189i	0.287616	−	0.957746i	$-0.407137\pi$
$587$	−14.6734	−	12.3124i	−0.605636	−	0.508189i	−0.893252	+	0.449557i	$0.851582\pi$
$588$	3.66044			0.150954
$589$		0			0
$590$	7.47060			0.307560
$591$	28.9859	+	24.3221i	1.19232	+	1.00048i
$592$	−16.7062	+	6.08056i	−0.686621	+	0.249910i
$593$	−1.50980	−	8.56250i	−0.0620001	−	0.351620i	−0.999988	−	0.00495124i	$-0.998424\pi$
$593$	−1.50980	−	8.56250i	−0.0620001	−	0.351620i	0.937988	−	0.346669i	$-0.112687\pi$
$594$	−3.43629	+	19.4882i	−0.140993	+	0.799609i
$595$	−0.134285	−	0.0488759i	−0.00550516	−	0.00200372i
$596$	1.53003	+	2.65009i	0.0626724	+	0.108552i
$597$	0.369585	−	0.640140i	0.0151261	−	0.0261992i
$598$	7.15839	−	6.00660i	0.292728	−	0.245628i
$599$	−15.1919	+	12.7475i	−0.620724	+	0.520850i	−0.898031	−	0.439932i	$-0.855003\pi$
$599$	−15.1919	+	12.7475i	−0.620724	+	0.520850i	0.277307	+	0.960781i	$0.410558\pi$
$600$	−17.9119	+	31.0244i	−0.731252	+	1.26657i
$601$	−16.8807	−	29.2383i	−0.688579	−	1.19265i	−0.972298	−	0.233747i	$-0.924901\pi$
$601$	−16.8807	−	29.2383i	−0.688579	−	1.19265i	0.283718	−	0.958908i	$-0.408432\pi$
$602$	−1.71554	−	0.624404i	−0.0699201	−	0.0254488i
$603$	−7.05138	+	39.9904i	−0.287155	+	1.62853i
$604$	−0.139967	−	0.793791i	−0.00569517	−	0.0322989i
$605$	4.99273	−	1.81720i	0.202983	−	0.0738798i
$606$	−27.4859	−	23.0634i	−1.11654	−	0.936888i
$607$	−35.2850			−1.43217			−0.716087	−	0.698011i	$-0.754068\pi$
$607$	−35.2850			−1.43217			−0.716087	+	0.698011i	$0.754068\pi$
$608$		0			0
$609$	6.87939			0.278767
$610$	8.28493	+	6.95188i	0.335447	+	0.281473i
$611$	−17.6348	+	6.41852i	−0.713426	+	0.259666i
$612$	−0.0794409	−	0.450532i	−0.00321121	−	0.0182117i
$613$	3.20439	−	18.1730i	0.129424	−	0.734001i	−0.849157	−	0.528140i	$-0.822889\pi$
$613$	3.20439	−	18.1730i	0.129424	−	0.734001i	0.978581	−	0.205861i	$-0.0659994\pi$
$614$	−14.8071	−	5.38933i	−0.597564	−	0.217496i
$615$	3.13429	+	5.42874i	0.126387	+	0.218908i
$616$	−1.13816	+	1.97134i	−0.0458576	+	0.0794277i
$617$	−27.3366	+	22.9381i	−1.10053	+	0.923455i	−0.997461	−	0.0712191i	$-0.977311\pi$
$617$	−27.3366	+	22.9381i	−1.10053	+	0.923455i	−0.103070	+	0.994674i	$0.532867\pi$
$618$	16.3739	−	13.7394i	0.658656	−	0.552678i
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	−0.900452	−	0.434955i	$-0.856764\pi$
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	0.826908	+	0.562337i	$0.190098\pi$
$620$	0.577382	+	1.00005i	0.0231882	+	0.0401631i
$621$	16.7023	+	6.07915i	0.670242	+	0.243948i
$622$	3.73530	−	21.1839i	0.149772	−	0.849399i
$623$	0.620615	+	3.51968i	0.0248644	+	0.141013i
$624$	−25.0462	+	9.11608i	−1.00265	+	0.364935i
$625$	10.7233	+	8.99790i	0.428931	+	0.359916i
$626$	−35.8767			−1.43392
$627$		0			0
$628$	1.77744			0.0709275
$629$	−1.77197	−	1.48686i	−0.0706532	−	0.0592851i
$630$	−2.04576	+	0.744596i	−0.0815050	+	0.0296654i
$631$	−0.137851	−	0.781792i	−0.00548776	−	0.0311226i	0.981941	−	0.189188i	$-0.0605855\pi$
$631$	−0.137851	−	0.781792i	−0.00548776	−	0.0311226i	−0.987429	+	0.158065i	$0.949474\pi$
$632$	−6.05463	+	34.3375i	−0.240840	+	1.36587i
$633$	6.62449	+	2.41112i	0.263300	+	0.0958332i
$634$	19.8942	+	34.4578i	0.790101	+	1.36850i
$635$	5.10220	−	8.83726i	0.202474	−	0.350696i
$636$	−1.15657	+	0.970481i	−0.0458611	+	0.0384821i
$637$	13.5646	−	11.3821i	0.537451	−	0.450975i
$638$	10.3191	−	17.8732i	0.408536	−	0.707605i
$639$	−24.6168	−	42.6375i	−0.973826	−	1.68672i
$640$	−7.84864	−	2.85667i	−0.310245	−	0.112920i
$641$	−5.10220	+	28.9360i	−0.201525	+	1.14290i	0.701291	+	0.712875i	$0.252607\pi$
$641$	−5.10220	+	28.9360i	−0.201525	+	1.14290i	−0.902816	+	0.430028i	$0.858504\pi$
$642$	−6.89440	−	39.1001i	−0.272100	−	1.54316i
$643$	−20.8742	+	7.59760i	−0.823199	+	0.299620i	−0.719065	−	0.694943i	$-0.755429\pi$
$643$	−20.8742	+	7.59760i	−0.823199	+	0.299620i	−0.104135	+	0.994563i	$0.533207\pi$
$644$	0.132474	+	0.111159i	0.00522022	+	0.00438028i
$645$	9.87939			0.389000
$646$		0			0
$647$	11.2591			0.442640			0.221320	−	0.975201i	$-0.428963\pi$
$647$	11.2591			0.442640			0.221320	+	0.975201i	$0.428963\pi$
$648$	−7.03667	−	5.90447i	−0.276427	−	0.231950i
$649$	13.1934	−	4.80201i	0.517887	−	0.188495i
$650$	2.54529	+	14.4351i	0.0998346	+	0.566190i
$651$	1.23396	−	6.99811i	0.0483625	−	0.274278i
$652$	1.45084	+	0.528061i	0.0568192	+	0.0206805i
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	−0.999456	−	0.0329874i	$-0.989498\pi$
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	0.471160	−	0.882048i	$-0.343835\pi$
$654$	−3.53596	+	6.12446i	−0.138267	+	0.239485i
$655$	1.24304	−	1.04303i	0.0485696	−	0.0407547i
$656$	6.82017	−	5.72281i	0.266283	−	0.223438i
$657$	−3.67499	+	6.36527i	−0.143375	+	0.248333i
$658$	1.70574	+	2.95442i	0.0664966	+	0.115175i
$659$	26.3357	+	9.58543i	1.02589	+	0.373395i	0.799516	−	0.600644i	$-0.205089\pi$
$659$	26.3357	+	9.58543i	1.02589	+	0.373395i	0.226378	+	0.974039i	$0.427311\pi$
$660$	0.180922	−	1.02606i	0.00704238	−	0.0399393i
$661$	−1.97400	−	11.1951i	−0.0767798	−	0.435440i	−0.998830	−	0.0483686i	$-0.984598\pi$
$661$	−1.97400	−	11.1951i	−0.0767798	−	0.435440i	0.922050	−	0.387071i	$-0.126513\pi$
$662$	35.0257	−	12.7483i	1.36131	−	0.495478i
$663$	−2.65657	−	2.22913i	−0.103173	−	0.0865722i
$664$	43.6551			1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	−14.2003	−	11.9154i	−0.549837	−	0.461368i
$668$	−0.700685	+	0.255028i	−0.0271103	+	0.00986734i
$669$	4.25490	+	24.1307i	0.164504	+	0.932948i
$670$	−1.57903	+	8.95513i	−0.0610033	+	0.345967i
$671$	19.1001	+	6.95188i	0.737353	+	0.268374i
$672$	−0.520945	−	0.902302i	−0.0200959	−	0.0348071i
$673$	−8.28359	+	14.3476i	−0.319309	+	0.553059i	−0.980344	−	0.197296i	$-0.936784\pi$
$673$	−8.28359	+	14.3476i	−0.319309	+	0.553059i	0.661035	+	0.750355i	$0.270117\pi$
$674$	−18.4329	+	15.4670i	−0.710008	+	0.595768i
$675$	−21.3576	+	17.9211i	−0.822053	+	0.689784i
$676$	−0.588993	+	1.02017i	−0.0226536	+	0.0392371i
$677$	−4.52481	−	7.83721i	−0.173903	−	0.301208i	0.765878	−	0.642986i	$-0.222305\pi$
$677$	−4.52481	−	7.83721i	−0.173903	−	0.301208i	−0.939781	+	0.341777i	$0.888971\pi$
$678$	−64.4796	−	23.4686i	−2.47632	−	0.901308i
$679$	−0.570108	+	3.23324i	−0.0218787	+	0.124080i
$680$	−0.210323	−	1.19280i	−0.00806551	−	0.0457418i
$681$	−38.2879	+	13.9357i	−1.46720	+	0.534016i
$682$	−16.3307	−	13.7031i	−0.625334	−	0.524718i
$683$	−8.73143			−0.334099			−0.167049	−	0.985949i	$-0.553424\pi$
$683$	−8.73143			−0.334099			−0.167049	+	0.985949i	$0.553424\pi$
$684$		0			0
$685$	0.224927			0.00859402
$686$	−4.97494	−	4.17447i	−0.189944	−	0.159382i
$687$	55.5570	−	20.2211i	2.11963	−	0.771482i
$688$	−2.43654	−	13.8183i	−0.0928921	−	0.526817i
$689$	−1.26827	+	7.19269i	−0.0483171	+	0.274020i
$690$	8.63816	+	3.14403i	0.328849	+	0.119691i
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	−0.980508	−	0.196478i	$-0.937050\pi$
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	0.320099	−	0.947384i	$-0.396284\pi$
$692$	1.86122	−	3.22372i	0.0707528	−	0.122547i
$693$	−3.13429	+	2.62998i	−0.119062	+	0.0999046i
$694$	−5.98680	+	5.02352i	−0.227256	+	0.190690i
$695$	−1.87464	+	3.24697i	−0.0711091	+	0.123164i
$696$	29.1536	+	50.4956i	1.10507	+	1.91403i
$697$	1.08853	+	0.396191i	0.0412309	+	0.0150068i
$698$	1.25687	−	7.12808i	0.0475734	−	0.269802i
$699$	8.82547	+	50.0518i	0.333810	+	1.89313i
$700$	−0.254900	+	0.0927760i	−0.00963432	+	0.00350660i
$701$	30.1937	+	25.3355i	1.14040	+	0.956910i	0.999452	−	0.0331069i	$-0.0105402\pi$
$701$	30.1937	+	25.3355i	1.14040	+	0.956910i	0.140949	+	0.990017i	$0.454985\pi$
$702$	−22.8753			−0.863371
$703$		0			0
$704$	−19.1411			−0.721409
$705$	−14.1420	−	11.8666i	−0.532620	−	0.446921i
$706$	31.9479	−	11.6281i	1.20238	−	0.437629i
$707$	−0.557781	−	3.16333i	−0.0209775	−	0.118969i
$708$	−0.582596	+	3.30407i	−0.0218953	+	0.124174i
$709$	38.6416	+	14.0644i	1.45122	+	0.528200i	0.942931	−	0.332989i	$-0.108057\pi$
$709$	38.6416	+	14.0644i	1.45122	+	0.528200i	0.508286	+	0.861189i	$0.330279\pi$
$710$	−5.51249	−	9.54791i	−0.206880	−	0.358327i
$711$	−31.3357	+	54.2751i	−1.17518	+	2.03548i
$712$	−23.2049	+	19.4712i	−0.869639	+	0.729714i
$713$	−14.6682	+	12.3081i	−0.549328	+	0.460941i
$714$	−0.315207	+	0.545955i	−0.0117963	+	0.0204319i
$715$	−2.52007	−	4.36488i	−0.0942452	−	0.163237i
$716$	1.99912	+	0.727621i	0.0747107	+	0.0271925i
$717$	1.17617	−	6.67042i	0.0439250	−	0.249111i
$718$	1.56443	+	8.87230i	0.0583839	+	0.331111i
$719$	39.8387	−	14.5001i	1.48573	−	0.540763i	0.533411	−	0.845856i	$-0.320910\pi$
$719$	39.8387	−	14.5001i	1.48573	−	0.540763i	0.952323	+	0.305093i	$0.0986875\pi$
$720$	−12.8177	−	10.7554i	−0.477689	−	0.400828i
$721$	1.91353			0.0712637
$722$		0			0
$723$	−39.7374			−1.47785
$724$	1.20851	+	1.01406i	0.0449140	+	0.0376873i
$725$	27.3234	−	9.94491i	1.01477	−	0.369345i
$726$	−4.07011	−	23.0827i	−0.151056	−	0.856680i
$727$	8.97003	−	50.8715i	0.332680	−	1.88672i	−0.116356	−	0.993208i	$-0.537121\pi$
$727$	8.97003	−	50.8715i	0.332680	−	1.88672i	0.449036	−	0.893514i	$-0.351768\pi$
$728$	−2.47266	−	0.899974i	−0.0916428	−	0.0333553i
$729$	20.2344	+	35.0470i	0.749423	+	1.29804i
$730$	−0.822948	+	1.42539i	−0.0304587	+	0.0527560i
$731$	1.39852	−	1.17350i	0.0517261	−	0.0434033i
$732$	−3.72075	+	3.12208i	−0.137523	+	0.115395i
$733$	11.4581	−	19.8460i	0.423215	−	0.733030i	−0.573037	−	0.819530i	$-0.694235\pi$
$733$	11.4581	−	19.8460i	0.423215	−	0.733030i	0.996252	+	0.0864997i	$0.0275682\pi$
$734$	−5.46926	−	9.47303i	−0.201874	−	0.349656i
$735$	16.3687	+	5.95772i	0.603769	+	0.219754i
$736$	−0.487511	+	2.76481i	−0.0179699	+	0.101912i
$737$	2.96761	+	16.8301i	0.109313	+	0.619946i
$738$	16.5831	−	6.03574i	0.610431	−	0.222179i
$739$	21.5462	+	18.0794i	0.792591	+	0.665063i	0.946385	−	0.323040i	$-0.104705\pi$
$739$	21.5462	+	18.0794i	0.792591	+	0.665063i	−0.153794	+	0.988103i	$0.549149\pi$
$740$	0.803348			0.0295317
$741$		0			0
$742$	1.32770			0.0487413
$743$	−4.69775	−	3.94188i	−0.172344	−	0.144613i	0.552536	−	0.833489i	$-0.313660\pi$
$743$	−4.69775	−	3.94188i	−0.172344	−	0.144613i	−0.724880	+	0.688876i	$0.758105\pi$
$744$	56.5963	−	20.5994i	2.07492	−	0.755210i
$745$	2.52869	+	14.3409i	0.0926439	+	0.525409i
$746$	−8.16448	+	46.3030i	−0.298923	+	1.69528i
$747$	73.7349	+	26.8373i	2.69782	+	0.981926i
$748$	−0.0962667	−	0.166739i	−0.00351986	−	0.00609657i
$749$	1.77719	−	3.07818i	0.0649371	−	0.112474i
$750$	−24.1125	+	20.2328i	−0.880463	+	0.738796i
$751$	−4.32114	+	3.62586i	−0.157681	+	0.132310i	−0.718215	−	0.695822i	$-0.755040\pi$
$751$	−4.32114	+	3.62586i	−0.157681	+	0.132310i	0.560534	+	0.828131i	$0.310596\pi$
$752$	−13.1099	+	22.7071i	−0.478070	+	0.828042i
$753$	5.99660	+	10.3864i	0.218528	+	0.378502i
$754$	22.4183	+	8.15961i	0.816428	+	0.297155i
$755$	0.666070	−	3.77747i	0.0242408	−	0.137476i
$756$	−0.0735111	−	0.416902i	−0.00267357	−	0.0151626i
$757$	−14.7456	+	5.36695i	−0.535937	+	0.195065i	−0.595787	−	0.803142i	$-0.703160\pi$
$757$	−14.7456	+	5.36695i	−0.535937	+	0.195065i	0.0598505	+	0.998207i	$0.480938\pi$
$758$	−1.75600	−	1.47346i	−0.0637806	−	0.0535183i
$759$	17.2763			0.627090
$760$		0			0
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$	−34.4846	−	28.9360i	−1.24924	−	1.04824i
$763$	−0.594922	+	0.216534i	−0.0215376	+	0.00783906i
$764$	−0.588364	−	3.33678i	−0.0212863	−	0.120720i
$765$	0.378041	−	2.14398i	0.0136681	−	0.0775157i
$766$	3.71806	+	1.35326i	0.134339	+	0.0488954i
$767$	8.11499	+	14.0556i	0.293015	+	0.507517i
$768$	6.32888	−	10.9619i	0.228374	−	0.395555i
$769$	17.2606	−	14.4833i	0.622432	−	0.522283i	−0.276135	−	0.961119i	$-0.589054\pi$
$769$	17.2606	−	14.4833i	0.622432	−	0.522283i	0.898567	+	0.438836i	$0.144609\pi$
$770$	−0.701867	+	0.588936i	−0.0252935	+	0.0212238i
$771$	0.960637	−	1.66387i	0.0345965	−	0.0599229i
$772$	−0.0275033	−	0.0476371i	−0.000989864	−	0.00171450i
$773$	−24.8380	−	9.04028i	−0.893359	−	0.325156i	−0.145771	−	0.989318i	$-0.546566\pi$
$773$	−24.8380	−	9.04028i	−0.893359	−	0.325156i	−0.747589	+	0.664162i	$0.768788\pi$
$774$	4.82959	−	27.3900i	0.173596	−	0.984513i
$775$	−5.21554	−	29.5788i	−0.187348	−	1.06250i
$776$	−26.1484	+	9.51725i	−0.938674	+	0.341649i
$777$	−3.78699	−	3.17766i	−0.135857	−	0.113998i
$778$	−33.0993			−1.18667
$779$		0			0
$780$	1.20439			0.0431242
$781$	−15.8726	−	13.3187i	−0.567965	−	0.476580i
$782$	1.59627	−	0.580994i	0.0570824	−	0.0207763i
$783$	7.87985	+	44.6889i	0.281603	+	1.59705i
$784$	4.29607	−	24.3642i	0.153431	−	0.870152i
$785$	7.94831	+	2.89295i	0.283687	+	0.103254i
$786$	−3.57919	−	6.19934i	−0.127666	−	0.221123i
$787$	−7.77884	+	13.4733i	−0.277286	+	0.480273i	−0.970709	−	0.240257i	$-0.922768\pi$
$787$	−7.77884	+	13.4733i	−0.277286	+	0.480273i	0.693424	+	0.720530i	$0.256101\pi$
$788$	−1.86025	+	1.56094i	−0.0662687	+	0.0556061i
$789$	25.1446	−	21.0988i	0.895170	−	0.751137i
$790$	−7.01707	+	12.1539i	−0.249656	+	0.432417i
$791$	−3.07145	−	5.31991i	−0.109208	−	0.189154i
$792$	−32.5869	−	11.8607i	−1.15793	−	0.421451i
$793$	−4.08007	+	23.1392i	−0.144888	+	0.821698i
$794$	−7.44815	−	42.2405i	−0.264325	−	1.49906i
$795$	−6.75150	+	2.45734i	−0.239451	+	0.0871530i
$796$	0.0363398	+	0.0304927i	0.00128803	+	0.00108079i
$797$	−33.4935			−1.18640			−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935			−1.18640			−0.593200	+	0.805055i	$0.702136\pi$
$798$		0			0
$799$	−3.41147			−0.120689
$800$	−3.37346	−	2.83067i	−0.119270	−	0.100079i
$801$	−51.1639	+	18.6221i	−1.80779	+	0.657981i
$802$	0.0202293	+	0.114726i	0.000714322	+	0.00405112i
$803$	−0.537141	+	3.04628i	−0.0189553	+	0.107501i
$804$	−3.83750	−	1.39673i	−0.135338	−	0.0492590i
$805$	0.411474	+	0.712694i	0.0145026	+	0.0251192i
$806$	12.3216	−	21.3416i	0.434010	−	0.751727i
$807$	−42.7695	+	35.8879i	−1.50556	+	1.26331i
$808$	20.8555	−	17.4998i	0.733694	−	0.615642i
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	0.237096	+	0.971486i	$0.423804\pi$
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	−0.959880	+	0.280412i	$0.909529\pi$
$810$	−1.84864	−	3.20194i	−0.0649546	−	0.112505i
$811$	15.6814	+	5.70756i	0.550648	+	0.200419i	0.602334	−	0.798244i	$-0.294237\pi$
$811$	15.6814	+	5.70756i	0.550648	+	0.200419i	−0.0516864	+	0.998663i	$0.516460\pi$
$812$	−0.0766663	+	0.434796i	−0.00269046	+	0.0152584i
$813$	−6.69712	−	37.9812i	−0.234878	−	1.33206i
$814$	−13.9363	+	5.07239i	−0.488467	+	0.177787i
$815$	5.62836	+	4.72275i	0.197153	+	0.165431i
$816$	−4.84524			−0.169617
$817$		0			0
$818$	−26.9540			−0.942424
$819$	−3.62314	−	3.04018i	−0.126603	−	0.106232i
$820$	−0.378041	+	0.137596i	−0.0132018	+	0.00480505i
$821$	−5.45084	−	30.9132i	−0.190236	−	1.07888i	−0.919042	−	0.394160i	$-0.871036\pi$
$821$	−5.45084	−	30.9132i	−0.190236	−	1.07888i	0.728807	−	0.684720i	$-0.240075\pi$
$822$	0.172304	−	0.977185i	0.00600979	−	0.0340832i
$823$	−43.5321	−	15.8444i	−1.51744	−	0.552301i	−0.556929	−	0.830560i	$-0.688020\pi$
$823$	−43.5321	−	15.8444i	−1.51744	−	0.552301i	−0.960506	+	0.278259i	$0.910243\pi$
$824$	8.10922	+	14.0456i	0.282498	+	0.489301i
$825$	−13.5496	+	23.4686i	−0.471738	+	0.817073i
$826$	2.26011	−	1.89646i	0.0786394	−	0.0659863i
$827$	−31.2230	+	26.1992i	−1.08573	+	0.911037i	−0.996384	−	0.0849640i	$-0.972922\pi$
$827$	−31.2230	+	26.1992i	−1.08573	+	0.911037i	−0.0893471	+	0.996001i	$0.528478\pi$
$828$	−1.31727	+	2.28157i	−0.0457782	+	0.0792901i
$829$	−17.7417	−	30.7295i	−0.616195	−	1.06728i	−0.990174	−	0.139843i	$-0.955340\pi$
$829$	−17.7417	−	30.7295i	−0.616195	−	1.06728i	0.373979	−	0.927437i	$-0.377993\pi$
$830$	16.5116	+	6.00973i	0.573126	+	0.208601i
$831$	8.87346	−	50.3239i	0.307817	−	1.74572i
$832$	−3.84224	−	21.7904i	−0.133206	−	0.755448i
$833$	3.02481	−	1.10094i	0.104804	−	0.0381454i
$834$	12.6702	+	10.6316i	0.438735	+	0.368142i
$835$	−3.54839			−0.122797
$836$		0			0
$837$	46.8735			1.62019
$838$	26.2251	+	22.0055i	0.905931	+	0.760166i
$839$	−35.8987	+	13.0661i	−1.23936	+	0.451091i	−0.876794	−	0.480866i	$-0.840322\pi$
$839$	−35.8987	+	13.0661i	−1.23936	+	0.451091i	−0.362568	+	0.931957i	$0.618100\pi$
$840$	−0.449493	−	2.54920i	−0.0155090	−	0.0879558i
$841$	3.18227	−	18.0475i	0.109733	−	0.622329i
$842$	5.53209	+	2.01352i	0.190648	+	0.0693903i
$843$	26.3161	+	45.5809i	0.906376	+	1.56989i
$844$	−0.226215	+	0.391815i	−0.00778663	+	0.0134868i
$845$	−4.29426	+	3.60331i	−0.147727	+	0.123958i
$846$	−39.8127	+	33.4069i	−1.36879	+	1.14855i
$847$	1.04916	−	1.81720i	0.0360497	−	0.0624399i
$848$	5.10220	+	8.83726i	0.175210	+	0.303473i
$849$	−20.8011	−	7.57099i	−0.713893	−	0.259836i
$850$	−0.462697	+	2.62408i	−0.0158704	+	0.0900053i
$851$	2.31315	+	13.1185i	0.0792937	+	0.449697i
$852$	4.65270	−	1.69345i	0.159399	−	0.0580165i
$853$	−19.6120	−	16.4564i	−0.671502	−	0.563457i	0.242008	−	0.970274i	$-0.422194\pi$
$853$	−19.6120	−	16.4564i	−0.671502	−	0.563457i	−0.913510	+	0.406817i	$0.866639\pi$
$854$	4.27126			0.146159
$855$		0			0
$856$	30.1257			1.02967
$857$	16.1532	+	13.5541i	0.551782	+	0.463000i	0.875544	−	0.483139i	$-0.160503\pi$
$857$	16.1532	+	13.5541i	0.551782	+	0.463000i	−0.323762	+	0.946139i	$0.604948\pi$
$858$	−20.8935	+	7.60462i	−0.713293	+	0.259617i
$859$	−3.39780	−	19.2699i	−0.115932	−	0.657481i	−0.986285	−	0.165053i	$-0.947221\pi$
$859$	−3.39780	−	19.2699i	−0.115932	−	0.657481i	0.870353	−	0.492428i	$-0.163890\pi$
$860$	−0.110099	+	0.624404i	−0.00375436	+	0.0212920i
$861$	2.32635	+	0.846723i	0.0792819	+	0.0288562i
$862$	−25.8050	−	44.6956i	−0.878922	−	1.52234i
$863$	2.47447	−	4.28591i	0.0842319	−	0.145894i	−0.820832	−	0.571170i	$-0.806490\pi$
$863$	2.47447	−	4.28591i	0.0842319	−	0.145894i	0.905064	+	0.425276i	$0.139823\pi$
$864$	5.26470	−	4.41761i	0.179109	−	0.150290i
$865$	13.5699	−	11.3865i	0.461389	−	0.387151i
$866$	−12.2139	+	21.1552i	−0.415047	+	0.718882i
$867$	24.1596	+	41.8456i	0.820502	+	1.42115i
$868$	0.428548	+	0.155979i	0.0145459	+	0.00529427i
$869$	−4.58007	+	25.9749i	−0.155368	+	0.881137i
$870$	4.07532	+	23.1123i	0.138166	+	0.783580i
$871$	−18.5639	+	6.75670i	−0.629013	+	0.228942i
$872$	−4.11057	−	3.44917i	−0.139201	−	0.116804i
$873$	−50.0164			−1.69280
$874$		0			0
$875$	−2.81790			−0.0952623
$876$	−0.566237	−	0.475129i	−0.0191314	−	0.0160531i
$877$	1.14631	−	0.417222i	0.0387080	−	0.0140886i	−0.322594	−	0.946538i	$-0.604555\pi$
$877$	1.14631	−	0.417222i	0.0387080	−	0.0140886i	0.361302	+	0.932449i	$0.382332\pi$
$878$	1.42493	+	8.08116i	0.0480889	+	0.272726i
$879$	5.25150	−	29.7827i	0.177129	−	1.00455i
$880$	−6.61721	−	2.40847i	−0.223066	−	0.0811894i
$881$	−23.2515	−	40.2728i	−0.783363	−	1.35682i	−0.929972	−	0.367630i	$-0.880169\pi$
$881$	−23.2515	−	40.2728i	−0.783363	−	1.35682i	0.146609	−	0.989194i	$-0.453164\pi$
$882$	24.5194	−	42.4688i	0.825610	−	1.43000i
$883$	9.90104	−	8.30796i	0.333197	−	0.279585i	−0.460804	−	0.887502i	$-0.652439\pi$
$883$	9.90104	−	8.30796i	0.333197	−	0.279585i	0.794001	+	0.607917i	$0.207995\pi$
$884$	0.170493	−	0.143061i	0.00573430	−	0.00481165i
$885$	−7.98293	+	13.8268i	−0.268343	+	0.464784i
$886$	20.1374	+	34.8791i	0.676531	+	1.17179i
$887$	−21.8237	−	7.94318i	−0.732769	−	0.266706i	−0.0514324	−	0.998676i	$-0.516379\pi$
$887$	−21.8237	−	7.94318i	−0.732769	−	0.266706i	−0.681336	+	0.731970i	$0.738601\pi$
$888$	7.27584	−	41.2634i	0.244161	−	1.38471i
$889$	−0.699807	−	3.96880i	−0.0234708	−	0.133109i
$890$	−11.4572	+	4.17009i	−0.384047	+	0.139782i
$891$	−5.32295	−	4.46648i	−0.178325	−	0.149633i
$892$	−1.57255			−0.0526528
$893$		0			0
$894$	64.2404			2.14852
$895$	7.75537	+	6.50753i	0.259233	+	0.217523i
$896$	−3.09967	+	1.12819i	−0.103553	+	0.0376901i
$897$	3.46791	+	19.6675i	0.115790	+	0.656679i
$898$	2.63198	−	14.9267i	0.0878302	−	0.498110i
$899$	−45.9372	−	16.7198i	−1.53209	−	0.557636i
$900$	−2.06624	−	3.57883i	−0.0688746	−	0.119294i
$901$	−0.663848	+	1.14982i	−0.0221160	+	0.0383060i
$902$	5.68938	−	4.77396i	0.189436	−	0.158955i
$903$	2.98886	−	2.50795i	0.0994629	−	0.0834593i
$904$	26.0326	−	45.0897i	0.865830	−	1.49966i
$905$	3.75372	+	6.50163i	0.124778	+	0.216122i
$906$	−15.9008	−	5.78742i	−0.528269	−	0.192274i
$907$	6.94537	−	39.3892i	0.230617	−	1.30790i	−0.621032	−	0.783785i	$-0.713287\pi$
$907$	6.94537	−	39.3892i	0.230617	−	1.30790i	0.851650	−	0.524111i	$-0.175602\pi$
$908$	−0.454078	−	2.57521i	−0.0150691	−	0.0854612i
$909$	45.9839	−	16.7368i	1.52519	−	0.555123i
$910$	−0.811337	−	0.680793i	−0.0268956	−	0.0225681i
$911$	18.7997			0.622863			0.311431	−	0.950269i	$-0.399192\pi$
$911$	18.7997			0.622863			0.311431	+	0.950269i	$0.399192\pi$
$912$		0			0
$913$	33.0232			1.09291
$914$	−24.1407	−	20.2564i	−0.798503	−	0.670023i
$915$	−21.7199	+	7.90539i	−0.718037	+	0.261344i
$916$	0.658882	+	3.73670i	0.0217701	+	0.123464i
$917$	0.111281	−	0.631108i	0.00367484	−	0.0208410i
$918$	−3.90760	−	1.42225i	−0.128970	−	0.0469413i
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	−0.981398	−	0.191984i	$-0.938508\pi$
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	0.324436	−	0.945908i	$-0.394825\pi$
$920$	−3.48751	+	6.04055i	−0.114980	+	0.199151i
$921$	25.7973	−	21.6465i	0.850048	−	0.713275i
$922$	−37.7988	+	31.7170i	−1.24484	+	1.04454i
$923$	11.9760	−	20.7430i	0.394193	−	0.682763i
$924$	−0.205737	−	0.356347i	−0.00676825	−	0.0117230i
$925$	−19.6348	−	7.14647i	−0.645587	−	0.234974i
$926$	−10.0569	+	57.0355i	−0.330490	+	1.87430i
$927$	5.06212	+	28.7087i	0.166262	+	0.942917i
$928$	−6.73530	+	2.45145i	−0.221097	+	0.0804727i
$929$	20.6480	+	17.3257i	0.677437	+	0.568438i	0.915256	−	0.402872i	$-0.131988\pi$
$929$	20.6480	+	17.3257i	0.677437	+	0.568438i	−0.237819	+	0.971310i	$0.576432\pi$
$930$	24.2422			0.794932
$931$		0			0
$932$	−3.26176			−0.106843
$933$	35.2165	+	29.5501i	1.15294	+	0.967428i
$934$	−32.4060	+	11.7948i	−1.06036	+	0.385938i
$935$	−0.159100	−	0.902302i	−0.00520313	−	0.0295084i
$936$	6.96105	−	39.4781i	0.227529	−	1.29038i
$937$	−2.46538	−	0.897327i	−0.0805406	−	0.0293144i	0.301436	−	0.953487i	$-0.402534\pi$
$937$	−2.46538	−	0.897327i	−0.0805406	−	0.0293144i	−0.381976	+	0.924172i	$0.624756\pi$
$938$	1.79561	+	3.11008i	0.0586287	+	0.101548i
$939$	38.3371	−	66.4018i	1.25108	−	2.16694i
$940$	0.907604	−	0.761570i	0.0296028	−	0.0248397i
$941$	14.3018	−	12.0006i	0.466224	−	0.391208i	−0.379191	−	0.925318i	$-0.623798\pi$
$941$	14.3018	−	12.0006i	0.466224	−	0.391208i	0.845415	+	0.534110i	$0.179353\pi$
$942$	18.6570	−	32.3149i	0.607879	−	1.05288i
$943$	−3.33544	−	5.77715i	−0.108617	−	0.188130i
$944$	21.3084	+	7.75562i	0.693529	+	0.252424i
$945$	0.349823	−	1.98394i	0.0113797	−	0.0645377i
$946$	−2.03256	−	11.5272i	−0.0660841	−	0.374781i
$947$	−7.89306	+	2.87284i	−0.256490	+	0.0933547i	−0.467065	−	0.884223i	$-0.654689\pi$
$947$	−7.89306	+	2.87284i	−0.256490	+	0.0933547i	0.210575	+	0.977578i	$0.432466\pi$
$948$	−4.82816	−	4.05131i	−0.156811	−	0.131580i
$949$	−3.57573			−0.116073
$950$		0			0
$951$	−85.0343			−2.75742
$952$	−0.366430	−	0.307471i	−0.0118761	−	0.00996520i
$953$	31.6609	−	11.5236i	1.02560	−	0.373287i	0.226195	−	0.974082i	$-0.427371\pi$
$953$	31.6609	−	11.5236i	1.02560	−	0.373287i	0.799403	+	0.600795i	$0.205149\pi$
$954$	3.51233	+	19.9194i	0.113716	+	0.644914i
$955$	2.79989	−	15.8790i	0.0906022	−	0.513831i
$956$	0.408481	+	0.148675i	0.0132112	+	0.00480849i
$957$	22.0535	+	38.1978i	0.712888	+	1.23476i
$958$	−25.7173	+	44.5438i	−0.830890	+	1.43914i
$959$	0.0680482	−	0.0570992i	0.00219739	−	0.00184383i
$960$	16.6741	−	13.9912i	0.538155	−	0.451565i
$961$	−9.74809	+	16.8842i	−0.314455	+	0.544651i
$962$	−8.57192	−	14.8470i	−0.276370	−	0.478686i
$963$	50.8833	+	18.5200i	1.63969	+	0.596799i
$964$	0.442848	−	2.51151i	0.0142632	−	0.0808904i
$965$	−0.0454548	−	0.257787i	−0.00146324	−	0.00829845i
$966$	3.41147	−	1.24168i	0.109762	−	0.0399502i
$967$	8.99588	+	7.54844i	0.289288	+	0.242741i	0.775869	−	0.630894i	$-0.217312\pi$
$967$	8.99588	+	7.54844i	0.289288	+	0.242741i	−0.486581	+	0.873635i	$0.661756\pi$
$968$	17.7847			0.571621
$969$		0			0
$970$	−11.2003			−0.359619
$971$	−9.81252	−	8.23368i	−0.314899	−	0.264231i	0.471615	−	0.881805i	$-0.343671\pi$
$971$	−9.81252	−	8.23368i	−0.314899	−	0.264231i	−0.786513	+	0.617573i	$0.788116\pi$
$972$	−1.87598	+	0.682801i	−0.0601721	+	0.0219009i
$973$	0.257122	+	1.45821i	0.00824294	+	0.0467480i
$974$	−1.81639	+	10.3013i	−0.0582009	+	0.330074i
$975$	−29.4368	−	10.7141i	−0.942731	−	0.343126i
$976$	16.4140	+	28.4299i	0.525399	+	0.910018i
$977$	7.26382	−	12.5813i	0.232390	−	0.402512i	−0.726121	−	0.687567i	$-0.758679\pi$
$977$	7.26382	−	12.5813i	0.232390	−	0.402512i	0.958511	+	0.285055i	$0.0920120\pi$
$978$	24.8293	−	20.8343i	0.793955	−	0.666207i
$979$	−17.5535	+	14.7291i	−0.561012	+	0.470745i
$980$	−0.558963	+	0.968153i	−0.0178554	+	0.0309265i
$981$	−4.82248	−	8.35278i	−0.153970	−	0.266684i
$982$	46.4928	+	16.9220i	1.48364	+	0.540002i
$983$	6.43371	−	36.4874i	0.205203	−	1.16377i	−0.691916	−	0.721978i	$-0.743233\pi$
$983$	6.43371	−	36.4874i	0.205203	−	1.16377i	0.897119	−	0.441788i	$-0.145656\pi$
$984$	3.64362	+	20.6640i	0.116154	+	0.658744i
$985$	−10.8592	+	3.95243i	−0.346003	+	0.125935i
$986$	3.32223	+	2.78768i	0.105801	+	0.0887780i
$987$	−7.29086			−0.232071
$988$		0			0
$989$	−10.5134			−0.334307
$990$	−10.6925	−	8.97210i	−0.339831	−	0.285152i
$991$	3.22446	−	1.17361i	0.102428	−	0.0372809i	−0.290298	−	0.956936i	$-0.593754\pi$
$991$	3.22446	−	1.17361i	0.102428	−	0.0372809i	0.392726	+	0.919656i	$0.371532\pi$
$992$	1.28564	+	7.29125i	0.0408193	+	0.231498i
$993$	−13.8327	+	78.4494i	−0.438969	+	2.48952i
$994$	−4.09152	−	1.48919i	−0.129775	−	0.0472343i
$995$	0.112874	+	0.195503i	0.00357835	+	0.00619788i
$996$	−3.94562	+	6.83402i	−0.125022	+	0.216544i
$997$	9.78699	−	8.21226i	0.309957	−	0.260085i	−0.474517	−	0.880246i	$-0.657377\pi$
$997$	9.78699	−	8.21226i	0.309957	−	0.260085i	0.784474	+	0.620161i	$0.212933\pi$
$998$	5.08441	−	4.26632i	0.160944	−	0.135048i
$999$	16.3045	−	28.2403i	0.515852	−	0.893483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.a.54.1		6
19.2	odd	18		361.2.c.i.292.2		6
19.3	odd	18		361.2.c.i.68.2		6
19.4	even	9		361.2.e.h.28.1		6
19.5	even	9		361.2.a.h.1.2		3
19.6	even	9	inner	361.2.e.a.234.1		6
19.7	even	3		361.2.e.b.62.1		6
19.8	odd	6		19.2.e.a.17.1	yes	6
19.9	even	9		361.2.e.b.99.1		6
19.10	odd	18		361.2.e.f.99.1		6
19.11	even	3		361.2.e.h.245.1		6
19.12	odd	6		361.2.e.f.62.1		6
19.13	odd	18		361.2.e.g.234.1		6
19.14	odd	18		361.2.a.g.1.2		3
19.15	odd	18		19.2.e.a.9.1	✓	6
19.16	even	9		361.2.c.h.68.2		6
19.17	even	9		361.2.c.h.292.2		6
19.18	odd	2		361.2.e.g.54.1		6
57.5	odd	18		3249.2.a.s.1.2		3
57.8	even	6		171.2.u.c.55.1		6
57.14	even	18		3249.2.a.z.1.2		3
57.53	even	18		171.2.u.c.28.1		6
76.15	even	18		304.2.u.b.161.1		6
76.27	even	6		304.2.u.b.17.1		6
76.43	odd	18		5776.2.a.bi.1.1		3
76.71	even	18		5776.2.a.br.1.3		3
95.8	even	12		475.2.u.a.74.2		12
95.14	odd	18		9025.2.a.bd.1.2		3
95.24	even	18		9025.2.a.x.1.2		3
95.27	even	12		475.2.u.a.74.1		12
95.34	odd	18		475.2.l.a.351.1		6
95.53	even	36		475.2.u.a.199.1		12
95.72	even	36		475.2.u.a.199.2		12
95.84	odd	6		475.2.l.a.226.1		6
133.27	even	6		931.2.w.a.834.1		6
133.34	even	18		931.2.w.a.883.1		6
133.46	odd	6		931.2.x.a.226.1		6
133.53	odd	18		931.2.v.b.275.1		6
133.65	odd	6		931.2.v.b.606.1		6
133.72	odd	18		931.2.x.a.655.1		6
133.103	even	6		931.2.v.a.606.1		6
133.110	even	18		931.2.x.b.655.1		6
133.122	even	6		931.2.x.b.226.1		6
133.129	even	18		931.2.v.a.275.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	19.15	odd	18
19.2.e.a.17.1	yes	6	19.8	odd	6
171.2.u.c.28.1		6	57.53	even	18
171.2.u.c.55.1		6	57.8	even	6
304.2.u.b.17.1		6	76.27	even	6
304.2.u.b.161.1		6	76.15	even	18
361.2.a.g.1.2		3	19.14	odd	18
361.2.a.h.1.2		3	19.5	even	9
361.2.c.h.68.2		6	19.16	even	9
361.2.c.h.292.2		6	19.17	even	9
361.2.c.i.68.2		6	19.3	odd	18
361.2.c.i.292.2		6	19.2	odd	18
361.2.e.a.54.1		6	1.1	even	1	trivial
361.2.e.a.234.1		6	19.6	even	9	inner
361.2.e.b.62.1		6	19.7	even	3
361.2.e.b.99.1		6	19.9	even	9
361.2.e.f.62.1		6	19.12	odd	6
361.2.e.f.99.1		6	19.10	odd	18
361.2.e.g.54.1		6	19.18	odd	2
361.2.e.g.234.1		6	19.13	odd	18
361.2.e.h.28.1		6	19.4	even	9
361.2.e.h.245.1		6	19.11	even	3
475.2.l.a.226.1		6	95.84	odd	6
475.2.l.a.351.1		6	95.34	odd	18
475.2.u.a.74.1		12	95.27	even	12
475.2.u.a.74.2		12	95.8	even	12
475.2.u.a.199.1		12	95.53	even	36
475.2.u.a.199.2		12	95.72	even	36
931.2.v.a.275.1		6	133.129	even	18
931.2.v.a.606.1		6	133.103	even	6
931.2.v.b.275.1		6	133.53	odd	18
931.2.v.b.606.1		6	133.65	odd	6
931.2.w.a.834.1		6	133.27	even	6
931.2.w.a.883.1		6	133.34	even	18
931.2.x.a.226.1		6	133.46	odd	6
931.2.x.a.655.1		6	133.72	odd	18
931.2.x.b.226.1		6	133.122	even	6
931.2.x.b.655.1		6	133.110	even	18
3249.2.a.s.1.2		3	57.5	odd	18
3249.2.a.z.1.2		3	57.14	even	18
5776.2.a.bi.1.1		3	76.43	odd	18
5776.2.a.br.1.3		3	76.71	even	18
9025.2.a.x.1.2		3	95.24	even	18
9025.2.a.bd.1.2		3	95.14	odd	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03209 + 0.866025i) q^{2} +(-2.70574 + 0.984808i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(-3.64543 - 1.32683i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +(4.05303 - 3.40090i) q^{9} +O(q^{10})\)	\(q+(1.03209 + 0.866025i) q^{2} +(-2.70574 + 0.984808i) q^{3} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(-3.64543 - 1.32683i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +(4.05303 - 3.40090i) q^{9} +(0.907604 - 0.761570i) q^{10} +(1.11334 - 1.92836i) q^{11} +(0.266044 + 0.460802i) q^{12} +(2.41875 + 0.880352i) q^{13} +(0.0812519 - 0.460802i) q^{14} +(0.439693 + 2.49362i) q^{15} +(3.37939 - 1.23000i) q^{16} +(0.358441 + 0.300767i) q^{17} +7.12836 q^{18} -0.162504 q^{20} +(0.766044 + 0.642788i) q^{21} +(2.81908 - 1.02606i) q^{22} +(-0.467911 - 2.65366i) q^{23} +(-1.47178 + 8.34689i) q^{24} +(3.97178 + 1.44561i) q^{25} +(1.73396 + 3.00330i) q^{26} +(-3.29813 + 5.71253i) q^{27} +(-0.0491630 + 0.0412527i) q^{28} +(5.26991 - 4.42198i) q^{29} +(-1.70574 + 2.95442i) q^{30} +(-3.55303 - 6.15403i) q^{31} +(-0.979055 - 0.356347i) q^{32} +(-1.11334 + 6.31407i) q^{33} +(0.109470 + 0.620838i) q^{34} +(-0.286989 + 0.104455i) q^{35} +(-0.748970 - 0.628461i) q^{36} -4.94356 q^{37} -7.41147 q^{39} +(-1.98293 - 1.66387i) q^{40} +(2.32635 - 0.846723i) q^{41} +(0.233956 + 1.32683i) q^{42} +(0.677519 - 3.84240i) q^{43} +(-0.386659 - 0.140732i) q^{44} +(-2.32635 - 4.02936i) q^{45} +(1.81521 - 3.14403i) q^{46} +(-5.58512 + 4.68647i) q^{47} +(-7.93242 + 6.65609i) q^{48} +(3.43969 - 5.95772i) q^{49} +(2.84730 + 4.93166i) q^{50} +(-1.26604 - 0.460802i) q^{51} +(0.0825961 - 0.468426i) q^{52} +(0.492726 + 2.79439i) q^{53} +(-8.35117 + 3.03958i) q^{54} +(-1.50000 - 1.25865i) q^{55} -1.02229 q^{56} +9.26857 q^{58} +(4.83022 + 4.05304i) q^{59} +(0.439693 - 0.160035i) q^{60} +(1.58512 + 8.98968i) q^{61} +(1.66250 - 9.42853i) q^{62} +(-1.72668 - 0.628461i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(1.13176 - 1.96026i) q^{65} +(-6.61721 + 5.55250i) q^{66} +(-5.87939 + 4.93339i) q^{67} +(0.0432332 - 0.0748822i) q^{68} +(3.87939 + 6.71929i) q^{69} +(-0.386659 - 0.140732i) q^{70} +(1.61587 - 9.16404i) q^{71} +(-2.70439 - 15.3374i) q^{72} +(-1.30541 + 0.475129i) q^{73} +(-5.10220 - 4.28125i) q^{74} -12.1702 q^{75} -0.773318 q^{77} +(-7.64930 - 6.41852i) q^{78} +(-11.1309 + 4.05131i) q^{79} +(-0.549163 - 3.11446i) q^{80} +(0.541889 - 3.07321i) q^{81} +(3.13429 + 1.14079i) q^{82} +(7.41534 + 12.8438i) q^{83} +(0.0923963 - 0.160035i) q^{84} +(0.315207 - 0.264490i) q^{85} +(4.02687 - 3.37895i) q^{86} +(-9.90420 + 17.1546i) q^{87} +(-3.27719 - 5.67626i) q^{88} +(-9.67024 - 3.51968i) q^{89} +(1.08853 - 6.17334i) q^{90} +(-0.155230 - 0.880352i) q^{91} +(-0.467911 + 0.170306i) q^{92} +(15.6741 + 13.1521i) q^{93} -9.82295 q^{94} +3.00000 q^{96} +(-7.24170 - 6.07650i) q^{97} +(8.70961 - 3.17004i) q^{98} +(-2.04576 - 11.6021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9	\( 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9} + 9 q^{10} - 3 q^{12} + 12 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 12 q^{23} + 6 q^{24} + 9 q^{25} + 15 q^{26} - 6 q^{27} - 12 q^{28} + 3 q^{29} - 9 q^{31} - 9 q^{32} + 18 q^{34} + 6 q^{35} + 21 q^{36} - 24 q^{39} + 9 q^{40} + 15 q^{41} + 6 q^{42} - 21 q^{43} - 9 q^{44} - 15 q^{45} + 18 q^{46} - 12 q^{47} - 24 q^{48} + 15 q^{49} + 15 q^{50} - 3 q^{51} - 6 q^{52} - 15 q^{53} - 24 q^{54} - 9 q^{55} + 6 q^{56} + 36 q^{58} + 6 q^{59} - 3 q^{60} - 12 q^{61} + 15 q^{62} + 3 q^{63} - 12 q^{64} + 12 q^{65} - 9 q^{66} - 24 q^{67} - 15 q^{68} + 12 q^{69} - 9 q^{70} - 12 q^{71} - 15 q^{72} - 12 q^{73} - 30 q^{74} - 30 q^{75} - 18 q^{77} - 6 q^{78} - 15 q^{79} - 15 q^{80} - 3 q^{81} + 9 q^{82} - 3 q^{84} + 9 q^{85} + 48 q^{86} - 21 q^{87} - 9 q^{88} - 15 q^{89} + 27 q^{90} + 12 q^{91} - 12 q^{92} + 27 q^{93} - 18 q^{94} + 18 q^{96} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9 + 9 * q^10 - 3 * q^12 + 12 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 12 * q^23 + 6 * q^24 + 9 * q^25 + 15 * q^26 - 6 * q^27 - 12 * q^28 + 3 * q^29 - 9 * q^31 - 9 * q^32 + 18 * q^34 + 6 * q^35 + 21 * q^36 - 24 * q^39 + 9 * q^40 + 15 * q^41 + 6 * q^42 - 21 * q^43 - 9 * q^44 - 15 * q^45 + 18 * q^46 - 12 * q^47 - 24 * q^48 + 15 * q^49 + 15 * q^50 - 3 * q^51 - 6 * q^52 - 15 * q^53 - 24 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 - 12 * q^61 + 15 * q^62 + 3 * q^63 - 12 * q^64 + 12 * q^65 - 9 * q^66 - 24 * q^67 - 15 * q^68 + 12 * q^69 - 9 * q^70 - 12 * q^71 - 15 * q^72 - 12 * q^73 - 30 * q^74 - 30 * q^75 - 18 * q^77 - 6 * q^78 - 15 * q^79 - 15 * q^80 - 3 * q^81 + 9 * q^82 - 3 * q^84 + 9 * q^85 + 48 * q^86 - 21 * q^87 - 9 * q^88 - 15 * q^89 + 27 * q^90 + 12 * q^91 - 12 * q^92 + 27 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^98 + 18 * q^99

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