LMFDB - Embedded newform 189.2.be.a.41.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(20,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

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

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

chi := DirichletCharacter("189.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.14
Character	$\chi$	$=$	189.41
Dual form			189.2.be.a.83.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.128087 - 0.0225853i) q^{2} +(0.167661 + 1.72392i) q^{3} +(-1.86349 + 0.678255i) q^{4} +(0.718615 + 0.602989i) q^{5} +(0.0604104 + 0.217025i) q^{6} +(-2.40304 + 1.10697i) q^{7} +(-0.448647 + 0.259026i) q^{8} +(-2.94378 + 0.578068i) q^{9} +O(q^{10})$	\(q+(0.128087 - 0.0225853i) q^{2} +(0.167661 + 1.72392i) q^{3} +(-1.86349 + 0.678255i) q^{4} +(0.718615 + 0.602989i) q^{5} +(0.0604104 + 0.217025i) q^{6} +(-2.40304 + 1.10697i) q^{7} +(-0.448647 + 0.259026i) q^{8} +(-2.94378 + 0.578068i) q^{9} +(0.105664 + 0.0610052i) q^{10} +(-0.371473 - 0.442704i) q^{11} +(-1.48169 - 3.09878i) q^{12} +(3.20694 + 0.565471i) q^{13} +(-0.282798 + 0.196062i) q^{14} +(-0.919020 + 1.33993i) q^{15} +(2.98664 - 2.50609i) q^{16} +(-3.53412 + 6.12128i) q^{17} +(-0.364005 + 0.140529i) q^{18} +(2.90929 - 1.67968i) q^{19} +(-1.74811 - 0.636260i) q^{20} +(-2.31122 - 3.95705i) q^{21} +(-0.0575796 - 0.0483150i) q^{22} +(2.98885 + 8.21179i) q^{23} +(-0.521761 - 0.730002i) q^{24} +(-0.715430 - 4.05740i) q^{25} +0.423540 q^{26} +(-1.49010 - 4.97791i) q^{27} +(3.72724 - 3.69270i) q^{28} +(6.54588 - 1.15422i) q^{29} +(-0.0874521 + 0.192384i) q^{30} +(2.37961 + 6.53791i) q^{31} +(0.991947 - 1.18216i) q^{32} +(0.700904 - 0.714613i) q^{33} +(-0.314426 + 0.863877i) q^{34} +(-2.39435 - 0.653523i) q^{35} +(5.09362 - 3.07385i) q^{36} +(4.05278 - 7.01962i) q^{37} +(0.334708 - 0.280853i) q^{38} +(-0.437145 + 5.62331i) q^{39} +(-0.478595 - 0.0843891i) q^{40} +(0.0788958 - 0.447440i) q^{41} +(-0.385409 - 0.454648i) q^{42} +(-2.01301 + 1.68912i) q^{43} +(0.992502 + 0.573021i) q^{44} +(-2.46401 - 1.35966i) q^{45} +(0.568299 + 0.984323i) q^{46} +(-7.41908 - 2.70032i) q^{47} +(4.82104 + 4.72855i) q^{48} +(4.54923 - 5.32020i) q^{49} +(-0.183275 - 0.503544i) q^{50} +(-11.1451 - 5.06623i) q^{51} +(-6.35964 + 1.12138i) q^{52} -1.29237i q^{53} +(-0.303290 - 0.603953i) q^{54} -0.542128i q^{55} +(0.791383 - 1.11909i) q^{56} +(3.38341 + 4.73376i) q^{57} +(0.812376 - 0.295681i) q^{58} +(5.65096 + 4.74172i) q^{59} +(0.803770 - 3.12027i) q^{60} +(1.72106 - 4.72858i) q^{61} +(0.452458 + 0.783680i) q^{62} +(6.43412 - 4.64780i) q^{63} +(-3.79843 + 6.57908i) q^{64} +(1.96358 + 2.34011i) q^{65} +(0.0736372 - 0.107363i) q^{66} +(-0.858343 + 4.86791i) q^{67} +(2.43401 - 13.8040i) q^{68} +(-13.6553 + 6.52932i) q^{69} +(-0.321446 - 0.0296310i) q^{70} +(-9.76878 - 5.64001i) q^{71} +(1.17098 - 1.02187i) q^{72} +(2.28636 - 1.32003i) q^{73} +(0.360570 - 0.990657i) q^{74} +(6.87468 - 1.91361i) q^{75} +(-4.28219 + 5.10331i) q^{76} +(1.38273 + 0.652627i) q^{77} +(0.0710112 + 0.730148i) q^{78} +(-0.885790 - 5.02356i) q^{79} +3.65739 q^{80} +(8.33168 - 3.40341i) q^{81} -0.0590933i q^{82} +(1.48382 + 8.41518i) q^{83} +(6.99083 + 5.80632i) q^{84} +(-6.23074 + 2.26780i) q^{85} +(-0.219692 + 0.261819i) q^{86} +(3.08726 + 11.0910i) q^{87} +(0.281332 + 0.102397i) q^{88} +(6.34396 + 10.9881i) q^{89} +(-0.346317 - 0.118505i) q^{90} +(-8.33238 + 2.19114i) q^{91} +(-11.1394 - 13.2754i) q^{92} +(-10.8719 + 5.19840i) q^{93} +(-1.01128 - 0.178316i) q^{94} +(3.10349 + 0.547229i) q^{95} +(2.20425 + 1.51183i) q^{96} +(0.827435 + 0.986099i) q^{97} +(0.462541 - 0.784196i) q^{98} +(1.34945 + 1.08849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	0.128087	−	0.0225853i	0.0905714	−	0.0159702i	−0.128179	−	0.991751i	$-0.540913\pi$
$2$	0.128087	−	0.0225853i	0.0905714	−	0.0159702i	0.218750	+	0.975781i	$0.429802\pi$
$3$	0.167661	+	1.72392i	0.0967992	+	0.995304i
$3$	0.167661	+	1.72392i	0.0967992	+	0.995304i
$4$	−1.86349	+	0.678255i	−0.931744	+	0.339127i
$5$	0.718615	+	0.602989i	0.321374	+	0.269665i	0.789174	−	0.614169i	$-0.210509\pi$
$5$	0.718615	+	0.602989i	0.321374	+	0.269665i	−0.467800	+	0.883834i	$0.654953\pi$
$6$	0.0604104	+	0.217025i	0.0246624	+	0.0886002i
$7$	−2.40304	+	1.10697i	−0.908265	+	0.418396i
$7$	−2.40304	+	1.10697i	−0.908265	+	0.418396i
$8$	−0.448647	+	0.259026i	−0.158621	+	0.0915797i
$9$	−2.94378	+	0.578068i	−0.981260	+	0.192689i
$10$	0.105664	+	0.0610052i	0.0334139	+	0.0192915i
$11$	−0.371473	−	0.442704i	−0.112003	−	0.133480i	0.707130	−	0.707084i	$-0.249990\pi$
$11$	−0.371473	−	0.442704i	−0.112003	−	0.133480i	−0.819133	+	0.573603i	$0.805545\pi$
$12$	−1.48169	−	3.09878i	−0.427727	−	0.894542i
$13$	3.20694	+	0.565471i	0.889446	+	0.156833i	0.599657	−	0.800257i	$-0.295304\pi$
$13$	3.20694	+	0.565471i	0.889446	+	0.156833i	0.289789	+	0.957091i	$0.406415\pi$
$14$	−0.282798	+	0.196062i	−0.0755810	+	0.0523999i
$15$	−0.919020	+	1.33993i	−0.237290	+	0.345968i
$16$	2.98664	−	2.50609i	0.746661	−	0.626523i
$17$	−3.53412	+	6.12128i	−0.857150	+	1.48463i	0.0174852	+	0.999847i	$0.494434\pi$
$17$	−3.53412	+	6.12128i	−0.857150	+	1.48463i	−0.874636	+	0.484781i	$0.838899\pi$
$18$	−0.364005	+	0.140529i	−0.0857968	+	0.0331230i
$19$	2.90929	−	1.67968i	0.667438	−	0.385345i	−0.127667	−	0.991817i	$-0.540749\pi$
$19$	2.90929	−	1.67968i	0.667438	−	0.385345i	0.795105	+	0.606472i	$0.207416\pi$
$20$	−1.74811	−	0.636260i	−0.390889	−	0.142272i
$21$	−2.31122	−	3.95705i	−0.504350	−	0.863499i
$22$	−0.0575796	−	0.0483150i	−0.0122760	−	0.0103008i
$23$	2.98885	+	8.21179i	0.623218	+	1.71228i	0.698971	+	0.715150i	$0.253642\pi$
$23$	2.98885	+	8.21179i	0.623218	+	1.71228i	−0.0757526	+	0.997127i	$0.524136\pi$
$24$	−0.521761	−	0.730002i	−0.106504	−	0.149011i
$25$	−0.715430	−	4.05740i	−0.143086	−	0.811481i
$26$	0.423540			0.0830630
$27$	−1.49010	−	4.97791i	−0.286769	−	0.958000i
$28$	3.72724	−	3.69270i	0.704381	−	0.697855i
$29$	6.54588	−	1.15422i	1.21554	−	0.214332i	0.471135	−	0.882061i	$-0.343844\pi$
$29$	6.54588	−	1.15422i	1.21554	−	0.214332i	0.744405	+	0.667729i	$0.232733\pi$
$30$	−0.0874521	+	0.192384i	−0.0159665	+	0.0351244i
$31$	2.37961	+	6.53791i	0.427390	+	1.17424i	0.947391	+	0.320078i	$0.103709\pi$
$31$	2.37961	+	6.53791i	0.427390	+	1.17424i	−0.520001	+	0.854165i	$0.674069\pi$
$32$	0.991947	−	1.18216i	0.175353	−	0.208978i
$33$	0.700904	−	0.714613i	0.122012	−	0.124398i
$34$	−0.314426	+	0.863877i	−0.0539236	+	0.148154i
$35$	−2.39435	−	0.653523i	−0.404720	−	0.110466i
$36$	5.09362	−	3.07385i	0.848937	−	0.512309i
$37$	4.05278	−	7.01962i	0.666273	−	1.15402i	−0.312666	−	0.949863i	$-0.601222\pi$
$37$	4.05278	−	7.01962i	0.666273	−	1.15402i	0.978939	−	0.204155i	$-0.0654447\pi$
$38$	0.334708	−	0.280853i	0.0542968	−	0.0455604i
$39$	−0.437145	+	5.62331i	−0.0699992	+	0.900450i
$40$	−0.478595	−	0.0843891i	−0.0756724	−	0.0133431i
$41$	0.0788958	−	0.447440i	0.0123215	−	0.0698785i	−0.978027	−	0.208478i	$-0.933149\pi$
$41$	0.0788958	−	0.447440i	0.0123215	−	0.0698785i	0.990348	+	0.138600i	$0.0442601\pi$
$42$	−0.385409	−	0.454648i	−0.0594700	−	0.0701538i
$43$	−2.01301	+	1.68912i	−0.306981	+	0.257588i	−0.783243	−	0.621716i	$-0.786436\pi$
$43$	−2.01301	+	1.68912i	−0.306981	+	0.257588i	0.476262	+	0.879303i	$0.341991\pi$
$44$	0.992502	+	0.573021i	0.149625	+	0.0863862i
$45$	−2.46401	−	1.35966i	−0.367313	−	0.202686i
$46$	0.568299	+	0.984323i	0.0837911	+	0.145130i
$47$	−7.41908	−	2.70032i	−1.08218	−	0.393883i	−0.261464	−	0.965213i	$-0.584205\pi$
$47$	−7.41908	−	2.70032i	−1.08218	−	0.393883i	−0.820720	+	0.571331i	$0.806427\pi$
$48$	4.82104	+	4.72855i	0.695857	+	0.682508i
$49$	4.54923	−	5.32020i	0.649890	−	0.760028i
$50$	−0.183275	−	0.503544i	−0.0259190	−	0.0712119i
$51$	−11.1451	−	5.06623i	−1.56063	−	0.709414i
$52$	−6.35964	+	1.12138i	−0.881923	+	0.155507i
$53$		−	1.29237i		−	0.177520i	−0.996053	−	0.0887602i	$-0.971710\pi$
$53$		−	1.29237i		−	0.177520i	0.996053	−	0.0887602i	$-0.0282905\pi$
$54$	−0.303290	−	0.603953i	−0.0412726	−	0.0821876i
$55$		−	0.542128i		−	0.0731005i
$56$	0.791383	−	1.11909i	0.105753	−	0.149545i
$57$	3.38341	+	4.73376i	0.448143	+	0.627002i
$58$	0.812376	−	0.295681i	0.106670	−	0.0388248i
$59$	5.65096	+	4.74172i	0.735692	+	0.617319i	0.931677	−	0.363288i	$-0.118346\pi$
$59$	5.65096	+	4.74172i	0.735692	+	0.617319i	−0.195985	+	0.980607i	$0.562790\pi$
$60$	0.803770	−	3.12027i	0.103766	−	0.402826i
$61$	1.72106	−	4.72858i	0.220359	−	0.605432i	−0.779419	−	0.626503i	$-0.784485\pi$
$61$	1.72106	−	4.72858i	0.220359	−	0.605432i	0.999778	+	0.0210711i	$0.00670765\pi$
$62$	0.452458	+	0.783680i	0.0574622	+	0.0995274i
$63$	6.43412	−	4.64780i	0.810623	−	0.585568i
$64$	−3.79843	+	6.57908i	−0.474804	+	0.822384i
$65$	1.96358	+	2.34011i	0.243553	+	0.290255i
$66$	0.0736372	−	0.107363i	0.00906412	−	0.0132155i
$67$	−0.858343	+	4.86791i	−0.104863	+	0.594710i	0.886411	+	0.462898i	$0.153190\pi$
$67$	−0.858343	+	4.86791i	−0.104863	+	0.594710i	−0.991275	+	0.131811i	$0.957921\pi$
$68$	2.43401	−	13.8040i	0.295167	−	1.67398i
$69$	−13.6553	+	6.52932i	−1.64391	+	0.786038i
$70$	−0.321446	−	0.0296310i	−0.0384202	−	0.00354158i
$71$	−9.76878	−	5.64001i	−1.15934	−	0.669346i	−0.208195	−	0.978087i	$-0.566759\pi$
$71$	−9.76878	−	5.64001i	−1.15934	−	0.669346i	−0.951146	+	0.308741i	$0.900092\pi$
$72$	1.17098	−	1.02187i	0.138002	−	0.120428i
$73$	2.28636	−	1.32003i	0.267598	−	0.154498i	−0.360198	−	0.932876i	$-0.617291\pi$
$73$	2.28636	−	1.32003i	0.267598	−	0.154498i	0.627796	+	0.778378i	$0.283957\pi$
$74$	0.360570	−	0.990657i	0.0419154	−	0.115162i
$75$	6.87468	−	1.91361i	0.793820	−	0.220965i
$76$	−4.28219	+	5.10331i	−0.491200	+	0.585390i
$77$	1.38273	+	0.652627i	0.157576	+	0.0743738i
$78$	0.0710112	+	0.730148i	0.00804044	+	0.0826730i
$79$	−0.885790	−	5.02356i	−0.0996592	−	0.565195i	−0.993220	−	0.116252i	$-0.962912\pi$
$79$	−0.885790	−	5.02356i	−0.0996592	−	0.565195i	0.893561	−	0.448943i	$-0.148199\pi$
$80$	3.65739			0.408909
$81$	8.33168	−	3.40341i	0.925742	−	0.378156i
$82$		−	0.0590933i		−	0.00652577i
$83$	1.48382	+	8.41518i	0.162871	+	0.923686i	0.951233	+	0.308474i	$0.0998184\pi$
$83$	1.48382	+	8.41518i	0.162871	+	0.923686i	−0.788362	+	0.615212i	$0.789070\pi$
$84$	6.99083	+	5.80632i	0.762762	+	0.633522i
$85$	−6.23074	+	2.26780i	−0.675818	+	0.245978i
$86$	−0.219692	+	0.261819i	−0.0236900	+	0.0282326i
$87$	3.08726	+	11.0910i	0.330989	+	1.18908i
$88$	0.281332	+	0.102397i	0.0299901	+	0.0109155i
$89$	6.34396	+	10.9881i	0.672458	+	1.16473i	0.977205	+	0.212298i	$0.0680948\pi$
$89$	6.34396	+	10.9881i	0.672458	+	1.16473i	−0.304747	+	0.952433i	$0.598572\pi$
$90$	−0.346317	−	0.118505i	−0.0365050	−	0.0124915i
$91$	−8.33238	+	2.19114i	−0.873471	+	0.229694i
$92$	−11.1394	−	13.2754i	−1.16136	−	1.38405i
$93$	−10.8719	+	5.19840i	−1.12736	+	0.539049i
$94$	−1.01128	−	0.178316i	−0.104305	−	0.0183918i
$95$	3.10349	+	0.547229i	0.318412	+	0.0561445i
$96$	2.20425	+	1.51183i	0.224970	+	0.154301i
$97$	0.827435	+	0.986099i	0.0840133	+	0.100123i	0.806414	−	0.591352i	$-0.201406\pi$
$97$	0.827435	+	0.986099i	0.0840133	+	0.100123i	−0.722400	+	0.691475i	$0.756961\pi$
$98$	0.462541	−	0.784196i	0.0467236	−	0.0792157i
$99$	1.34945	+	1.08849i	0.135625	+	0.109397i
$100$	4.08515	+	7.07569i	0.408515	+	0.707569i
$101$	−10.6757	−	3.88564i	−1.06227	−	0.386635i	−0.248991	−	0.968506i	$-0.580099\pi$
$101$	−10.6757	−	3.88564i	−1.06227	−	0.386635i	−0.813281	+	0.581871i	$0.802321\pi$
$102$	−1.54197	−	0.397205i	−0.152678	−	0.0393292i
$103$	−6.15902	+	7.34003i	−0.606866	+	0.723235i	−0.978753	−	0.205043i	$-0.934267\pi$
$103$	−6.15902	+	7.34003i	−0.606866	+	0.723235i	0.371887	+	0.928278i	$0.378711\pi$
$104$	−1.58526	+	0.576986i	−0.155447	+	0.0565782i
$105$	0.725180	−	4.23724i	0.0707703	−	0.413512i
$106$	−0.0291885	−	0.165536i	−0.00283503	−	0.0160783i
$107$			9.37225i			0.906049i	0.891498	+	0.453025i	$0.149655\pi$
$107$			9.37225i			0.906049i	−0.891498	+	0.453025i	$0.850345\pi$
$108$	6.15307	+	8.26562i	0.592080	+	0.795360i
$109$	0.504705			0.0483419			0.0241710	−	0.999708i	$-0.492305\pi$
$109$	0.504705			0.0483419			0.0241710	+	0.999708i	$0.492305\pi$
$110$	−0.0122441	−	0.0694398i	−0.00116743	−	0.00662082i
$111$	12.7807	+	5.80974i	1.21309	+	0.551436i
$112$	−4.40286	+	9.32838i	−0.416031	+	0.881449i
$113$	1.27258	−	1.51660i	0.119714	−	0.142669i	−0.702859	−	0.711329i	$-0.748093\pi$
$113$	1.27258	−	1.51660i	0.119714	−	0.142669i	0.822573	+	0.568660i	$0.192538\pi$
$114$	0.540285	+	0.529920i	0.0506023	+	0.0496316i
$115$	−2.80379	+	7.70336i	−0.261455	+	0.718342i
$116$	−11.4153	+	6.59064i	−1.05989	+	0.611926i
$117$	−9.76741	+	0.189209i	−0.902998	+	0.0174924i
$118$	0.830909	+	0.479726i	0.0764914	+	0.0441623i
$119$	1.71657	−	18.6219i	0.157357	−	1.70706i
$120$	0.0652382	−	0.839206i	0.00595540	−	0.0766087i
$121$	1.85214	−	10.5040i	0.168376	−	0.954907i
$122$	0.113650	−	0.644542i	0.0102894	−	0.0583540i
$123$	0.784578	+	0.0609915i	0.0707430	+	0.00549942i
$124$	−8.86874	−	10.5693i	−0.796436	−	0.949156i
$125$	4.27767	−	7.40913i	0.382606	−	0.662693i
$126$	0.719158	−	0.740641i	0.0640677	−	0.0659815i
$127$	0.193218	+	0.334663i	0.0171453	+	0.0296965i	0.874471	−	0.485078i	$-0.161209\pi$
$127$	0.193218	+	0.334663i	0.0171453	+	0.0296965i	−0.857325	+	0.514775i	$0.827876\pi$
$128$	−1.39355	+	3.82874i	−0.123173	+	0.338416i
$129$	−3.24940	−	3.18706i	−0.286094	−	0.280605i
$130$	0.304362	+	0.255390i	0.0266943	+	0.0223992i
$131$	7.17503	−	2.61150i	0.626886	−	0.228168i	−0.00898960	−	0.999960i	$-0.502862\pi$
$131$	7.17503	−	2.61150i	0.626886	−	0.228168i	0.635875	+	0.771792i	$0.280639\pi$
$132$	−0.821437	+	1.80706i	−0.0714969	+	0.157285i
$133$	−5.13180	+	7.25685i	−0.444983	+	0.629249i
$134$			0.642903i			0.0555384i
$135$	1.93082	−	4.47571i	0.166179	−	0.385208i
$136$		−	3.66172i		−	0.313990i
$137$	11.1706	−	1.96969i	0.954373	−	0.168282i	0.325285	−	0.945616i	$-0.394540\pi$
$137$	11.1706	−	1.96969i	0.954373	−	0.168282i	0.629088	+	0.777334i	$0.283429\pi$
$138$	−1.60161	+	1.14473i	−0.136338	+	0.0974461i
$139$	−4.55002	−	12.5011i	−0.385928	−	1.06033i	−0.968817	−	0.247776i	$-0.920300\pi$
$139$	−4.55002	−	12.5011i	−0.385928	−	1.06033i	0.582890	−	0.812551i	$-0.301922\pi$
$140$	4.90511	−	0.406148i	0.414557	−	0.0343258i
$141$	3.41124	−	13.2426i	0.287278	−	1.11523i
$142$	−1.37864	−	0.501783i	−0.115693	−	0.0421087i
$143$	−0.940957	−	1.62978i	−0.0786868	−	0.136289i
$144$	−7.34333	+	9.10387i	−0.611944	+	0.758655i
$145$	5.39995	+	3.11766i	0.448441	+	0.258908i
$146$	0.263040	−	0.220717i	0.0217694	−	0.0182667i
$147$	9.93431	+	6.95050i	0.819368	+	0.573268i
$148$	−2.79122	+	15.8298i	−0.229437	+	1.30120i
$149$	3.08342	+	0.543690i	0.252603	+	0.0445408i	0.298516	−	0.954405i	$-0.403508\pi$
$149$	3.08342	+	0.543690i	0.252603	+	0.0445408i	−0.0459125	+	0.998945i	$0.514620\pi$
$150$	0.837340	−	0.400376i	0.0683685	−	0.0326905i
$151$	4.62183	−	3.87817i	0.376119	−	0.315601i	−0.435058	−	0.900403i	$-0.643272\pi$
$151$	4.62183	−	3.87817i	0.376119	−	0.315601i	0.811177	+	0.584801i	$0.198828\pi$
$152$	−0.870164	+	1.50717i	−0.0705796	+	0.122248i
$153$	6.86516	−	20.0627i	0.555015	−	1.62197i
$154$	0.191850	+	0.0523641i	0.0154597	+	0.00421962i
$155$	−2.23227	+	6.13312i	−0.179300	+	0.492624i
$156$	−2.99942	−	10.7755i	−0.240146	−	0.862728i
$157$	6.23925	−	7.43565i	0.497947	−	0.593430i	−0.457273	−	0.889326i	$-0.651174\pi$
$157$	6.23925	−	7.43565i	0.497947	−	0.593430i	0.955220	+	0.295897i	$0.0956184\pi$
$158$	−0.226917	−	0.623449i	−0.0180525	−	0.0495990i
$159$	2.22793	−	0.216680i	0.176687	−	0.0171838i
$160$	1.42565	−	0.251381i	0.112708	−	0.0198734i
$161$	−16.2725	−	16.4247i	−1.28246	−	1.29445i
$162$	0.990315	−	0.624106i	0.0778065	−	0.0490344i
$163$	10.0073			0.783832			0.391916	−	0.920001i	$-0.371812\pi$
$163$	10.0073			0.783832			0.391916	+	0.920001i	$0.371812\pi$
$164$	0.156457	+	0.887312i	0.0122172	+	0.0692874i
$165$	0.934584	−	0.0908938i	0.0727573	−	0.00707607i
$166$	0.380118	+	1.04437i	0.0295029	+	0.0810585i
$167$	−9.99883	−	8.39002i	−0.773733	−	0.649239i	0.167929	−	0.985799i	$-0.446292\pi$
$167$	−9.99883	−	8.39002i	−0.773733	−	0.649239i	−0.941662	+	0.336560i	$0.890737\pi$
$168$	2.06190	+	1.17665i	0.159079	+	0.0907806i
$169$	−2.25128	−	0.819398i	−0.173175	−	0.0630306i
$170$	−0.746860	+	0.431200i	−0.0572815	+	0.0330715i
$171$	−7.59335	+	6.62638i	−0.580678	+	0.506732i
$172$	2.60557	−	4.51298i	0.198673	−	0.344112i
$173$	0.179663	−	0.150755i	0.0136595	−	0.0114617i	−0.635932	−	0.771745i	$-0.719384\pi$
$173$	0.179663	−	0.150755i	0.0136595	−	0.0114617i	0.649592	+	0.760283i	$0.274940\pi$
$174$	0.645933	+	1.35090i	0.0489681	+	0.102411i
$175$	6.21064	+	8.95816i	0.469480	+	0.677173i
$176$	−2.21892	−	0.391255i	−0.167257	−	0.0294919i
$177$	−7.22688	+	10.5368i	−0.543206	+	0.791993i
$178$	1.06075	+	1.26415i	0.0795065	+	0.0947521i
$179$	4.00486	+	2.31221i	0.299338	+	0.172823i	0.642145	−	0.766583i	$-0.278045\pi$
$179$	4.00486	+	2.31221i	0.299338	+	0.172823i	−0.342808	+	0.939406i	$0.611378\pi$
$180$	5.51385	+	0.862484i	0.410978	+	0.0642857i
$181$	−9.24646	+	5.33844i	−0.687284	+	0.396803i	−0.802594	−	0.596526i	$-0.796547\pi$
$181$	−9.24646	+	5.33844i	−0.687284	+	0.396803i	0.115310	+	0.993330i	$0.463214\pi$
$182$	−1.01778	+	0.468847i	−0.0754432	+	0.0347532i
$183$	8.44023	+	2.17417i	0.623920	+	0.160719i
$184$	−3.46801	−	2.91001i	−0.255665	−	0.214528i
$185$	7.14514	−	2.60062i	0.525321	−	0.191201i
$186$	−1.27514	+	0.911392i	−0.0934978	+	0.0668265i
$187$	4.02275	−	0.709319i	0.294172	−	0.0518705i
$188$	15.6569			1.14190
$189$	9.09118	+	10.3126i	0.661286	+	0.750134i
$190$	0.409877			0.0297356
$191$	11.9839	−	2.11308i	0.867124	−	0.152897i	0.277648	−	0.960683i	$-0.410445\pi$
$191$	11.9839	−	2.11308i	0.867124	−	0.152897i	0.589477	+	0.807786i	$0.299334\pi$
$192$	−11.9786	−	5.44512i	−0.864483	−	0.392968i
$193$	10.4601	−	3.80716i	0.752933	−	0.274045i	0.0630935	−	0.998008i	$-0.479903\pi$
$193$	10.4601	−	3.80716i	0.752933	−	0.274045i	0.689839	+	0.723963i	$0.257681\pi$
$194$	0.128255	+	0.107619i	0.00920819	+	0.00772659i
$195$	−3.70493	+	3.77740i	−0.265316	+	0.270505i
$196$	−4.86899	+	12.9997i	−0.347785	+	0.928548i
$197$	16.2149	−	9.36166i	1.15526	−	0.666991i	0.205098	−	0.978741i	$-0.434249\pi$
$197$	16.2149	−	9.36166i	1.15526	−	0.666991i	0.950164	+	0.311751i	$0.100915\pi$
$198$	0.197431	+	0.108944i	0.0140308	+	0.00774230i
$199$	−9.79495	−	5.65512i	−0.694346	−	0.400881i	0.110892	−	0.993832i	$-0.464629\pi$
$199$	−9.79495	−	5.65512i	−0.694346	−	0.400881i	−0.805238	+	0.592952i	$0.797962\pi$
$200$	1.37195	+	1.63503i	0.0970116	+	0.115614i
$201$	−8.53578	−	0.663554i	−0.602067	−	0.0468035i
$202$	−1.45518	−	0.256588i	−0.102386	−	0.0180534i
$203$	−14.4524	+	10.0197i	−1.01436	+	0.703248i
$204$	24.2050	+	1.88165i	1.69469	+	0.131742i
$205$	0.326497	−	0.273964i	0.0228036	−	0.0191345i
$206$	−0.623116	+	1.07927i	−0.0434145	+	0.0751962i
$207$	−13.5455	−	22.4460i	−0.941476	−	1.56010i
$208$	10.9951	−	6.34804i	0.762374	−	0.440157i
$209$	−1.82433	−	0.664001i	−0.126191	−	0.0459299i
$210$	−0.00281275	−	0.559115i	−0.000194098	−	0.0385826i
$211$	3.41059	+	2.86182i	0.234795	+	0.197016i	0.752592	−	0.658487i	$-0.228803\pi$
$211$	3.41059	+	2.86182i	0.234795	+	0.197016i	−0.517797	+	0.855503i	$0.673248\pi$
$212$	0.876554	+	2.40831i	0.0602020	+	0.165404i
$213$	8.08506	−	17.7862i	0.553979	−	1.21869i
$214$	0.211675	+	1.20047i	0.0144698	+	0.0820622i
$215$	−2.46510			−0.168118
$216$	1.95794	+	1.84735i	0.133221	+	0.125696i
$217$	−12.9556	−	13.0767i	−0.879482	−	0.887706i
$218$	0.0646463	−	0.0113989i	0.00437840	−	0.000772030i
$219$	2.65896	+	3.72017i	0.179676	+	0.251386i
$220$	0.367701	+	1.01025i	0.0247904	+	0.0681110i
$221$	−14.7951	+	17.6321i	−0.995228	+	1.18607i
$222$	1.76826	+	0.455498i	0.118678	+	0.0305710i
$223$	4.90848	−	13.4859i	0.328696	−	0.903085i	−0.659747	−	0.751488i	$-0.729336\pi$
$223$	4.90848	−	13.4859i	0.328696	−	0.903085i	0.988442	−	0.151596i	$-0.0484414\pi$
$224$	−1.07508	+	3.93883i	−0.0718316	+	0.263174i
$225$	4.45152	+	11.5305i	0.296768	+	0.768703i
$226$	0.128748	−	0.222998i	0.00856420	−	0.0148336i
$227$	19.7550	−	16.5764i	1.31119	−	1.10022i	0.323092	−	0.946368i	$-0.395278\pi$
$227$	19.7550	−	16.5764i	1.31119	−	1.10022i	0.988095	−	0.153848i	$-0.0491666\pi$
$228$	−9.51564	−	6.52651i	−0.630189	−	0.432228i
$229$	−12.9346	−	2.28072i	−0.854743	−	0.150714i	−0.270927	−	0.962600i	$-0.587330\pi$
$229$	−12.9346	−	2.28072i	−0.854743	−	0.150714i	−0.583817	+	0.811886i	$0.698441\pi$
$230$	−0.185148	+	1.05003i	−0.0122083	+	0.0692367i
$231$	−0.893246	+	2.49313i	−0.0587713	+	0.164036i
$232$	−2.63782	+	2.21339i	−0.173181	+	0.145316i
$233$	6.21683	+	3.58929i	0.407278	+	0.235142i	0.689620	−	0.724172i	$-0.257778\pi$
$233$	6.21683	+	3.58929i	0.407278	+	0.235142i	−0.282341	+	0.959314i	$0.591111\pi$
$234$	−1.24681	+	0.244835i	−0.0815064	+	0.0160054i
$235$	−3.70319	−	6.41412i	−0.241570	−	0.418411i
$236$	−13.7466	−	5.00335i	−0.894827	−	0.325690i
$237$	8.51170	−	2.36928i	0.552894	−	0.153902i
$238$	−0.200709	−	2.42399i	−0.0130101	−	0.157124i
$239$	−4.68155	−	12.8625i	−0.302824	−	0.832003i	−0.994006	−	0.109322i	$-0.965132\pi$
$239$	−4.68155	−	12.8625i	−0.302824	−	0.832003i	0.691182	−	0.722681i	$-0.257090\pi$
$240$	0.613203	+	6.30504i	0.0395821	+	0.406989i
$241$	0.483890	−	0.0853229i	0.0311701	−	0.00549613i	−0.158041	−	0.987432i	$-0.550518\pi$
$241$	0.483890	−	0.0853229i	0.0311701	−	0.00549613i	0.189211	+	0.981936i	$0.439407\pi$
$242$		−	1.38726i		−	0.0891763i
$243$	7.26409	+	13.7925i	0.465992	+	0.884789i
$244$			9.97897i			0.638838i
$245$	6.47717	−	1.08004i	0.413811	−	0.0690010i
$246$	0.101872	−	0.00990765i	0.00649512	−	0.000631689i
$247$	10.2798	−	3.74152i	0.654085	−	0.238067i
$248$	−2.76110	−	2.31683i	−0.175330	−	0.147119i
$249$	−14.2583	+	3.96889i	−0.903583	+	0.251518i
$250$	0.380578	−	1.04563i	0.0240698	−	0.0661313i
$251$	−2.82550	−	4.89390i	−0.178344	−	0.308900i	0.762970	−	0.646434i	$-0.223741\pi$
$251$	−2.82550	−	4.89390i	−0.178344	−	0.308900i	−0.941313	+	0.337534i	$0.890407\pi$
$252$	−8.83753	+	13.0251i	−0.556712	+	0.820504i
$253$	2.52512	−	4.37364i	0.158753	−	0.274968i
$254$	0.0323072	+	0.0385022i	0.00202713	+	0.00241584i
$255$	−4.95416	−	10.3611i	−0.310241	−	0.648834i
$256$	2.54634	−	14.4410i	0.159146	−	0.902563i
$257$	−3.07910	+	17.4625i	−0.192069	+	1.08928i	0.724462	+	0.689315i	$0.242088\pi$
$257$	−3.07910	+	17.4625i	−0.192069	+	1.08928i	−0.916531	+	0.399964i	$0.869023\pi$
$258$	−0.488187	−	0.334834i	−0.0303932	−	0.0208458i
$259$	−1.96848	+	21.3548i	−0.122316	+	1.32692i
$260$	−5.24630	−	3.02896i	−0.325362	−	0.187848i
$261$	−18.6024	+	7.18172i	−1.15146	+	0.444537i
$262$	0.860050	−	0.496550i	0.0531340	−	0.0306770i
$263$	−8.48074	+	23.3006i	−0.522945	+	1.43678i	0.344282	+	0.938866i	$0.388122\pi$
$263$	−8.48074	+	23.3006i	−0.522945	+	1.43678i	−0.867227	+	0.497913i	$0.834100\pi$
$264$	−0.129355	+	0.502162i	−0.00796124	+	0.0309059i
$265$	0.779284	−	0.928714i	0.0478710	−	0.0570505i
$266$	−0.493421	+	1.04541i	−0.0302536	+	0.0640985i
$267$	−17.8789	+	12.7787i	−1.09417	+	0.782045i
$268$	−1.70217	−	9.65347i	−0.103976	−	0.589679i
$269$	−19.8594			−1.21085			−0.605424	−	0.795903i	$-0.706996\pi$
$269$	−19.8594			−1.21085			−0.605424	+	0.795903i	$0.706996\pi$
$270$	0.146229	−	0.616890i	0.00889919	−	0.0375428i
$271$			30.9766i			1.88169i	0.338831	+	0.940847i	$0.389969\pi$
$271$			30.9766i			1.88169i	−0.338831	+	0.940847i	$0.610031\pi$
$272$	4.78532	+	27.1389i	0.290153	+	1.64554i
$273$	−5.17437	−	13.9970i	−0.313167	−	0.847135i
$274$	1.38633	−	0.504584i	0.0837514	−	0.0304830i
$275$	−1.53047	+	1.82394i	−0.0922907	+	0.109988i
$276$	21.0180	−	21.4291i	1.26514	−	1.28988i
$277$	−0.903294	−	0.328772i	−0.0542737	−	0.0197540i	0.314741	−	0.949178i	$-0.398082\pi$
$277$	−0.903294	−	0.328772i	−0.0542737	−	0.0197540i	−0.369014	+	0.929424i	$0.620305\pi$
$278$	−0.865140	−	1.49847i	−0.0518876	−	0.0898720i
$279$	−10.7844	−	17.8706i	−0.645644	−	1.06988i
$280$	1.24350	−	0.327000i	0.0743133	−	0.0195420i
$281$	4.40231	+	5.24646i	0.262620	+	0.312978i	0.881200	−	0.472744i	$-0.156736\pi$
$281$	4.40231	+	5.24646i	0.262620	+	0.312978i	−0.618580	+	0.785722i	$0.712292\pi$
$282$	0.137849	−	1.77326i	0.00820880	−	0.105596i
$283$	24.5783	+	4.33382i	1.46103	+	0.257619i	0.846970	−	0.531640i	$-0.178424\pi$
$283$	24.5783	+	4.33382i	1.46103	+	0.257619i	0.614060	+	0.789259i	$0.289535\pi$
$284$	22.0294	+	3.88437i	1.30720	+	0.230495i
$285$	−0.423043	+	5.44191i	−0.0250589	+	0.322351i
$286$	−0.157334	−	0.187503i	−0.00930334	−	0.0110873i
$287$	0.305714	+	1.16255i	0.0180457	+	0.0686234i
$288$	−2.23671	+	4.05342i	−0.131799	+	0.238850i
$289$	−16.4800	−	28.5443i	−0.969414	−	1.67907i
$290$	0.762078	+	0.277374i	0.0447508	+	0.0162879i
$291$	−1.56122	+	1.59176i	−0.0915206	+	0.0933106i
$292$	−3.36529	+	4.01059i	−0.196939	+	0.234702i
$293$	−14.9838	+	5.45364i	−0.875361	+	0.318605i	−0.740336	−	0.672237i	$-0.765334\pi$
$293$	−14.9838	+	5.45364i	−0.875361	+	0.318605i	−0.135025	+	0.990842i	$0.543111\pi$
$294$	1.42944	+	0.665902i	0.0833665	+	0.0388362i
$295$	1.20166	+	6.81493i	0.0699632	+	0.396781i
$296$			4.19911i			0.244068i
$297$	−1.65021	+	2.50883i	−0.0957550	+	0.145577i
$298$	0.407226			0.0235900
$299$	4.94154	+	28.0249i	0.285777	+	1.62072i
$300$	−11.5130	+	8.22878i	−0.664702	+	0.475089i
$301$	2.96754	−	6.28736i	0.171046	−	0.362397i
$302$	0.504408	−	0.601130i	0.0290254	−	0.0345911i
$303$	4.90862	−	19.0555i	0.281993	−	1.09471i
$304$	4.47959	−	12.3076i	0.256922	−	0.705888i
$305$	4.08806	−	2.36024i	0.234082	−	0.135147i
$306$	0.426220	−	2.72482i	0.0243654	−	0.155768i
$307$	19.7380	+	11.3958i	1.12651	+	0.650391i	0.943055	−	0.332637i	$-0.107939\pi$
$307$	19.7380	+	11.3958i	1.12651	+	0.650391i	0.183455	+	0.983028i	$0.441272\pi$
$308$	−3.01934	−	0.278323i	−0.172043	−	0.0158589i
$309$	−13.6862	−	9.38700i	−0.778583	−	0.534008i
$310$	−0.147408	+	0.835991i	−0.00837220	+	0.0474811i
$311$	−2.66176	+	15.0956i	−0.150935	+	0.855993i	0.811474	+	0.584388i	$0.198666\pi$
$311$	−2.66176	+	15.0956i	−0.150935	+	0.855993i	−0.962409	+	0.271605i	$0.912446\pi$
$312$	−1.26046	−	2.63611i	−0.0713597	−	0.149241i
$313$	16.0804	+	19.1639i	0.908918	+	1.08321i	0.996206	+	0.0870231i	$0.0277354\pi$
$313$	16.0804	+	19.1639i	0.908918	+	1.08321i	−0.0872884	+	0.996183i	$0.527820\pi$
$314$	0.631233	−	1.09333i	0.0356226	−	0.0617001i
$315$	7.42623	+	0.539730i	0.418421	+	0.0304103i
$316$	5.05791	+	8.76057i	0.284530	+	0.492820i
$317$	−8.79594	+	24.1666i	−0.494029	+	1.35733i	0.402934	+	0.915229i	$0.367990\pi$
$317$	−8.79594	+	24.1666i	−0.494029	+	1.35733i	−0.896963	+	0.442105i	$0.854232\pi$
$318$	0.280476	−	0.0780724i	0.0157283	−	0.00437808i
$319$	−2.94260	−	2.46913i	−0.164754	−	0.138245i
$320$	−6.69672	+	2.43741i	−0.374358	+	0.136255i
$321$	−16.1570	+	1.57136i	−0.901794	+	0.0877048i
$322$	−2.45526	−	1.73628i	−0.136827	−	0.0967590i
$323$			23.7448i			1.32120i
$324$	−13.2176	+	11.9932i	−0.734312	+	0.666289i
$325$		−	13.4164i		−	0.744209i
$326$	1.28181	−	0.226017i	0.0709928	−	0.0125179i
$327$	0.0846193	+	0.870069i	0.00467946	+	0.0481149i
$328$	0.0805025	+	0.221179i	0.00444501	+	0.0122126i
$329$	20.8175	−	1.72371i	1.14771	−	0.0950315i
$330$	0.117656	−	0.0327502i	0.00647672	−	0.00180284i
$331$	16.4139	+	5.97417i	0.902189	+	0.328370i	0.751130	−	0.660155i	$-0.229509\pi$
$331$	16.4139	+	5.97417i	0.902189	+	0.328370i	0.151059	+	0.988525i	$0.451732\pi$
$332$	−8.47272	−	14.6752i	−0.465001	−	0.805406i
$333$	−7.87267	+	23.0070i	−0.431420	+	1.26078i
$334$	−1.47021	−	0.848829i	−0.0804466	−	0.0464459i
$335$	−3.55211	+	2.98058i	−0.194073	+	0.162846i
$336$	−16.8195	−	6.02616i	−0.917581	−	0.328754i
$337$	3.83200	−	21.7323i	0.208742	−	1.18384i	−0.682699	−	0.730700i	$-0.739194\pi$
$337$	3.83200	−	21.7323i	0.208742	−	1.18384i	0.891441	−	0.453136i	$-0.149695\pi$
$338$	−0.306867	−	0.0541089i	−0.0166913	−	0.00294313i
$339$	2.82785	+	1.93954i	0.153588	+	0.105341i
$340$	10.0728	−	8.45205i	0.546272	−	0.458377i
$341$	2.01040	−	3.48212i	0.108869	−	0.188567i
$342$	−0.822954	+	1.02025i	−0.0445002	+	0.0551690i
$343$	−5.04268	+	17.8205i	−0.272279	+	0.962218i
$344$	0.465605	−	1.27924i	0.0251037	−	0.0689720i
$345$	−13.7500	−	3.54195i	−0.740277	−	0.190692i
$346$	0.0196077	−	0.0233676i	0.00105412	−	0.00125625i
$347$	−10.7646	−	29.5756i	−0.577876	−	1.58770i	−0.791753	−	0.610841i	$-0.790831\pi$
$347$	−10.7646	−	29.5756i	−0.577876	−	1.58770i	0.213877	−	0.976861i	$-0.431391\pi$
$348$	−13.2756	−	18.5741i	−0.711648	−	0.995675i
$349$	36.2448	−	6.39093i	1.94014	−	0.342099i	0.940139	−	0.340791i	$-0.110695\pi$
$349$	36.2448	−	6.39093i	1.94014	−	0.342099i	0.999999	−	0.00130796i	$-0.000416336\pi$
$350$	0.997827	+	1.00716i	0.0533361	+	0.0538348i
$351$	−1.96380	−	16.8065i	−0.104820	−	0.897064i
$352$	−0.891827			−0.0475346
$353$	−2.51204	−	14.2465i	−0.133702	−	0.758264i	−0.975755	−	0.218868i	$-0.929764\pi$
$353$	−2.51204	−	14.2465i	−0.133702	−	0.758264i	0.842052	−	0.539396i	$-0.181347\pi$
$354$	−0.687696	+	1.51285i	−0.0365506	+	0.0804070i
$355$	−3.61913	−	9.94347i	−0.192083	−	0.527744i
$356$	−19.2746	−	16.1733i	−1.02155	−	0.857183i
$357$	32.3904	−	0.162947i	1.71428	−	0.00862406i
$358$	0.565194	+	0.205714i	0.0298714	+	0.0108723i
$359$	18.2325	−	10.5265i	0.962274	−	0.555569i	0.0654020	−	0.997859i	$-0.479167\pi$
$359$	18.2325	−	10.5265i	0.962274	−	0.555569i	0.896872	+	0.442290i	$0.145834\pi$
$360$	1.45766	−	0.0282370i	0.0768254	−	0.00148822i
$361$	−3.85734	+	6.68110i	−0.203018	+	0.351637i
$362$	−1.06378	+	0.892621i	−0.0559112	+	0.0469151i
$363$	18.4185	+	1.43182i	0.966722	+	0.0751510i
$364$	14.0411	−	9.73465i	0.735956	−	0.510234i
$365$	2.43897	+	0.430057i	0.127662	+	0.0225102i
$366$	1.13019	+	0.0878587i	0.0590760	+	0.00459245i
$367$	−8.19588	−	9.76747i	−0.427821	−	0.509858i	0.508471	−	0.861079i	$-0.330211\pi$
$367$	−8.19588	−	9.76747i	−0.427821	−	0.509858i	−0.936292	+	0.351221i	$0.885766\pi$
$368$	29.5061	+	17.0354i	1.53811	+	0.888030i
$369$	0.0263989	+	1.36277i	0.00137427	+	0.0709431i
$370$	0.856467	−	0.494481i	0.0445256	−	0.0257069i
$371$	1.43061	+	3.10561i	0.0742738	+	0.161235i
$372$	16.7337	−	17.0610i	0.867604	−	0.884573i
$373$	8.46332	+	7.10157i	0.438214	+	0.367705i	0.835041	−	0.550188i	$-0.185444\pi$
$373$	8.46332	+	7.10157i	0.438214	+	0.367705i	−0.396826	+	0.917894i	$0.629889\pi$
$374$	0.499243	−	0.181710i	0.0258152	−	0.00939598i
$375$	13.4899	+	6.13212i	0.696617	+	0.316661i
$376$	4.02800	−	0.710246i	0.207728	−	0.0366281i
$377$	21.6449			1.11477
$378$	1.39738	+	1.11559i	0.0718734	+	0.0573799i
$379$	−24.8691			−1.27744			−0.638720	−	0.769439i	$-0.720536\pi$
$379$	−24.8691			−1.27744			−0.638720	+	0.769439i	$0.720536\pi$
$380$	−6.15448	+	1.08520i	−0.315718	+	0.0556697i
$381$	−0.544536	+	0.389201i	−0.0278974	+	0.0199394i
$382$	1.48726	−	0.541319i	0.0760949	−	0.0276963i
$383$	−20.9018	−	17.5387i	−1.06803	−	0.896184i	−0.0731584	−	0.997320i	$-0.523308\pi$
$383$	−20.9018	−	17.5387i	−1.06803	−	0.896184i	−0.994873	+	0.101136i	$0.967752\pi$
$384$	−6.83408	−	1.76043i	−0.348750	−	0.0898366i
$385$	0.600120	+	1.30276i	0.0305850	+	0.0663947i
$386$	1.25382	−	0.723892i	0.0638176	−	0.0368451i
$387$	4.94943	−	6.13604i	0.251594	−	0.311912i
$388$	−2.21074	−	1.27637i	−0.112233	−	0.0647980i
$389$	−14.2352	−	16.9649i	−0.721755	−	0.860154i	0.273045	−	0.962001i	$-0.411969\pi$
$389$	−14.2352	−	16.9649i	−0.721755	−	0.860154i	−0.994800	+	0.101847i	$0.967525\pi$
$390$	−0.389242	+	0.567514i	−0.0197100	+	0.0287372i
$391$	−60.8296	−	10.7259i	−3.07629	−	0.542432i
$392$	−0.662925	+	3.56526i	−0.0334828	+	0.180073i
$393$	5.70498	+	11.9313i	0.287778	+	0.601855i
$394$	1.86548	−	1.56533i	0.0939818	−	0.0788601i
$395$	2.39261	−	4.14413i	0.120385	−	0.208514i
$396$	−3.25295	−	1.11312i	−0.163467	−	0.0559362i
$397$	−17.4954	+	10.1010i	−0.878068	+	0.506953i	−0.870021	−	0.493015i	$-0.835895\pi$
$397$	−17.4954	+	10.1010i	−0.878068	+	0.506953i	−0.00804683	+	0.999968i	$0.502561\pi$
$398$	−1.38233	−	0.503128i	−0.0692900	−	0.0252195i
$399$	−13.3706	−	7.63010i	−0.669368	−	0.381983i
$400$	−12.3050	−	10.3251i	−0.615248	−	0.516255i
$401$	6.04055	+	16.5963i	0.301651	+	0.828778i	0.994214	+	0.107421i	$0.0342592\pi$
$401$	6.04055	+	16.5963i	0.301651	+	0.828778i	−0.692563	+	0.721357i	$0.743519\pi$
$402$	−1.10831	+	0.107790i	−0.0552776	+	0.00537607i
$403$	3.93426	+	22.3123i	0.195980	+	1.11146i
$404$	22.5295			1.12088
$405$	8.03948	+	2.57817i	0.399485	+	0.128110i
$406$	−1.62487	+	1.60981i	−0.0806407	+	0.0798936i
$407$	−4.61311	+	0.813417i	−0.228664	+	0.0403196i
$408$	6.31251	−	0.613929i	0.312516	−	0.0303940i
$409$	−5.13628	−	14.1118i	−0.253973	−	0.697784i	−0.999509	−	0.0313196i	$-0.990029\pi$
$409$	−5.13628	−	14.1118i	−0.253973	−	0.697784i	0.745537	−	0.666464i	$-0.232193\pi$
$410$	0.0356326	−	0.0424653i	0.00175977	−	0.00209721i
$411$	5.26846	+	18.9270i	0.259874	+	0.933602i
$412$	6.49885	−	17.8555i	0.320176	−	0.879675i
$413$	−18.8284	−	5.13910i	−0.926487	−	0.252878i
$414$	−2.24195	−	2.56911i	−0.110186	−	0.126265i
$415$	−4.00797	+	6.94200i	−0.196743	+	0.340770i
$416$	3.84959	−	3.23019i	0.188742	−	0.158373i
$417$	20.7880	−	9.93980i	1.01799	−	0.486754i
$418$	−0.248670	−	0.0438472i	−0.0121628	−	0.00214464i
$419$	5.29545	−	30.0320i	0.258700	−	1.46716i	−0.527695	−	0.849434i	$-0.676944\pi$
$419$	5.29545	−	30.0320i	0.258700	−	1.46716i	0.786394	−	0.617725i	$-0.211945\pi$
$420$	1.52256	+	8.38790i	0.0742934	+	0.409288i
$421$	−3.25924	+	2.73483i	−0.158846	+	0.133287i	−0.718746	−	0.695272i	$-0.755284\pi$
$421$	−3.25924	+	2.73483i	−0.158846	+	0.133287i	0.559901	+	0.828560i	$0.310839\pi$
$422$	0.501488	+	0.289535i	0.0244121	+	0.0140943i
$423$	23.4011	+	3.66043i	1.13780	+	0.177976i
$424$	0.334757	+	0.579817i	0.0162573	+	0.0281584i
$425$	27.3649	+	9.96002i	1.32739	+	0.483132i
$426$	0.633889	−	2.46079i	0.0307120	−	0.119226i
$427$	1.09862	+	13.2681i	0.0531658	+	0.642090i
$428$	−6.35677	−	17.4651i	−0.307266	−	0.844206i
$429$	2.65185	−	1.89538i	0.128033	−	0.0915099i
$430$	−0.315748	+	0.0556748i	−0.0152267	+	0.00268488i
$431$		−	22.1449i		−	1.06668i	−0.845900	−	0.533342i	$-0.820936\pi$
$431$		−	22.1449i		−	1.06668i	0.845900	−	0.533342i	$-0.179064\pi$
$432$	−16.9255	−	11.1329i	−0.814328	−	0.535633i
$433$			31.7576i			1.52617i	0.646296	+	0.763087i	$0.276317\pi$
$433$			31.7576i			1.52617i	−0.646296	+	0.763087i	$0.723683\pi$
$434$	−1.95479	−	1.38236i	−0.0938328	−	0.0663553i
$435$	−4.46923	+	9.83177i	−0.214283	+	0.471397i
$436$	−0.940511	+	0.342318i	−0.0450423	+	0.0163941i
$437$	22.4886	+	18.8702i	1.07578	+	0.902685i
$438$	0.424600	+	0.416454i	0.0202882	+	0.0198989i
$439$	4.19861	−	11.5356i	0.200389	−	0.550564i	−0.798272	−	0.602297i	$-0.794252\pi$
$439$	4.19861	−	11.5356i	0.200389	−	0.550564i	0.998661	+	0.0517331i	$0.0164745\pi$
$440$	0.140426	+	0.243224i	0.00669453	+	0.0115953i
$441$	−10.3165	+	18.2913i	−0.491261	+	0.871012i
$442$	−1.49684	+	2.59261i	−0.0711975	+	0.123318i
$443$	−8.77298	−	10.4552i	−0.416817	−	0.496743i	0.516254	−	0.856435i	$-0.327326\pi$
$443$	−8.77298	−	10.4552i	−0.416817	−	0.496743i	−0.933071	+	0.359693i	$0.882882\pi$
$444$	−27.7572	−	2.15779i	−1.31730	−	0.102404i
$445$	−2.06682	+	11.7215i	−0.0979766	+	0.555653i
$446$	0.324131	−	1.83824i	0.0153480	−	0.0870430i
$447$	−0.420307	+	5.40671i	−0.0198798	+	0.255729i
$448$	1.84494	−	20.0146i	0.0871654	−	0.945599i
$449$	−17.8336	−	10.2962i	−0.841620	−	0.485909i	0.0161947	−	0.999869i	$-0.494845\pi$
$449$	−17.8336	−	10.2962i	−0.841620	−	0.485909i	−0.857814	+	0.513959i	$0.828178\pi$
$450$	0.830604	+	1.37638i	0.0391550	+	0.0648830i
$451$	−0.227392	+	0.131285i	−0.0107074	+	0.00618195i
$452$	−1.34279	+	3.68929i	−0.0631597	+	0.173530i
$453$	7.46055	+	7.31743i	0.350527	+	0.343803i
$454$	2.15598	−	2.56940i	0.101185	−	0.120588i
$455$	−7.30901	−	3.44975i	−0.342652	−	0.161727i
$456$	−2.74413	−	1.24740i	−0.128505	−	0.0584147i
$457$	2.71446	+	15.3945i	0.126977	+	0.720124i	0.980114	+	0.198436i	$0.0635862\pi$
$457$	2.71446	+	15.3945i	0.126977	+	0.720124i	−0.853137	+	0.521688i	$0.825303\pi$
$458$	−1.70827			−0.0798223
$459$	35.7374	+	8.47124i	1.66808	+	0.395404i
$460$		−	16.2568i		−	0.757978i
$461$	2.05310	+	11.6437i	0.0956224	+	0.542302i	0.994555	+	0.104214i	$0.0332328\pi$
$461$	2.05310	+	11.6437i	0.0956224	+	0.542302i	−0.898932	+	0.438087i	$0.855656\pi$
$462$	−0.0581056	+	0.339512i	−0.00270332	+	0.0157955i
$463$	15.6277	−	5.68803i	0.726283	−	0.264345i	0.0476923	−	0.998862i	$-0.484813\pi$
$463$	15.6277	−	5.68803i	0.726283	−	0.264345i	0.678591	+	0.734517i	$0.262591\pi$
$464$	16.6577	−	19.8518i	0.773312	−	0.921598i
$465$	−10.9472	−	2.81997i	−0.507666	−	0.130773i
$466$	0.877362	+	0.319334i	0.0406430	+	0.0147929i
$467$	−12.5881	−	21.8032i	−0.582506	−	1.00893i	−0.995181	−	0.0980518i	$-0.968739\pi$
$467$	−12.5881	−	21.8032i	−0.582506	−	1.00893i	0.412675	−	0.910878i	$-0.364594\pi$
$468$	18.0731	−	6.97738i	0.835431	−	0.322530i
$469$	−3.32600	−	12.6480i	−0.153580	−	0.584028i
$470$	−0.619196	−	0.737930i	−0.0285614	−	0.0340382i
$471$	13.8645	+	9.50928i	0.638844	+	0.438165i
$472$	−3.76352	−	0.663609i	−0.173230	−	0.0305451i
$473$	1.49556	+	0.263707i	0.0687658	+	0.0121253i
$474$	1.03673	−	0.495714i	0.0476186	−	0.0227689i
$475$	−8.89655	−	10.6025i	−0.408202	−	0.486476i
$476$	9.43156	+	35.8659i	0.432295	+	1.64391i
$477$	0.747076	+	3.80445i	0.0342063	+	0.174194i
$478$	−0.890149	−	1.54178i	−0.0407145	−	0.0705195i
$479$	−4.60847	−	1.67734i	−0.210566	−	0.0766398i	0.234584	−	0.972096i	$-0.424627\pi$
$479$	−4.60847	−	1.67734i	−0.210566	−	0.0766398i	−0.445150	+	0.895456i	$0.646850\pi$
$480$	0.672388	+	2.41556i	0.0306902	+	0.110255i
$481$	16.9664	−	20.2198i	0.773602	−	0.921943i
$482$	0.0600531	−	0.0218576i	0.00273535	−	0.000995584i
$483$	25.5866	−	30.8063i	1.16423	−	1.40174i
$484$	3.67294	+	20.8303i	0.166952	+	0.946830i
$485$			1.20756i			0.0548325i
$486$	1.24195	+	1.60258i	0.0563358	+	0.0726946i
$487$	−1.94654			−0.0882062			−0.0441031	−	0.999027i	$-0.514043\pi$
$487$	−1.94654			−0.0882062			−0.0441031	+	0.999027i	$0.514043\pi$
$488$	0.452678	+	2.56726i	0.0204918	+	0.116215i
$489$	1.67783	+	17.2518i	0.0758743	+	0.780151i
$490$	0.805250	−	0.284628i	0.0363775	−	0.0128582i
$491$	−13.1928	+	15.7225i	−0.595382	+	0.709549i	−0.976631	−	0.214924i	$-0.931050\pi$
$491$	−13.1928	+	15.7225i	−0.595382	+	0.709549i	0.381249	+	0.924472i	$0.375494\pi$
$492$	−1.50342	+	0.418487i	−0.0677794	+	0.0188668i
$493$	−16.0687	+	44.1483i	−0.723697	+	1.98834i
$494$	1.23220	−	0.711413i	0.0554394	−	0.0320080i
$495$	0.313387	+	1.59591i	0.0140857	+	0.0717306i
$496$	23.4916	+	13.5629i	1.05481	+	0.608993i
$497$	29.7181	+	2.73942i	1.33304	+	0.122880i
$498$	−1.73667	+	0.830392i	−0.0778220	+	0.0372107i
$499$	0.697421	−	3.95527i	0.0312209	−	0.177062i	−0.965210	−	0.261476i	$-0.915791\pi$
$499$	0.697421	−	3.95527i	0.0312209	−	0.177062i	0.996431	+	0.0844140i	$0.0269018\pi$
$500$	−2.94610	+	16.7082i	−0.131754	+	0.747213i
$501$	12.7873	−	18.6438i	0.571293	−	0.832945i
$502$	−0.472440	−	0.563032i	−0.0210860	−	0.0251294i
$503$	18.2052	−	31.5323i	0.811729	−	1.40596i	−0.0999240	−	0.994995i	$-0.531860\pi$
$503$	18.2052	−	31.5323i	0.811729	−	1.40596i	0.911653	−	0.410961i	$-0.134807\pi$
$504$	−1.68275	+	3.75183i	−0.0749555	+	0.167120i
$505$	−5.32872	−	9.22961i	−0.237125	−	0.410712i
$506$	0.224656	−	0.617238i	0.00998719	−	0.0274396i
$507$	1.03512	−	4.01840i	0.0459714	−	0.178463i
$508$	−0.587046	−	0.492590i	−0.0260459	−	0.0218551i
$509$	−12.0063	+	4.36995i	−0.532172	+	0.193695i	−0.594108	−	0.804385i	$-0.702495\pi$
$509$	−12.0063	+	4.36995i	−0.532172	+	0.193695i	0.0619358	+	0.998080i	$0.480273\pi$
$510$	−0.868572	−	1.21523i	−0.0384610	−	0.0538112i
$511$	−4.03298	+	5.70302i	−0.178409	+	0.252287i
$512$		−	10.0561i		−	0.444423i
$513$	−12.6964	−	11.9793i	−0.560562	−	0.528900i
$514$			2.30626i			0.101725i
$515$	−8.85192	+	1.56083i	−0.390062	+	0.0687785i
$516$	8.21686	+	3.73514i	0.361727	+	0.164430i
$517$	1.56054	+	4.28756i	0.0686326	+	0.188567i
$518$	0.230165	+	2.77973i	0.0101129	+	0.122134i
$519$	0.290012	+	0.284448i	0.0127301	+	0.0124859i
$520$	−1.48711	−	0.541262i	−0.0652139	−	0.0237359i
$521$	5.16170	+	8.94033i	0.226138	+	0.391683i	0.956660	−	0.291206i	$-0.0940566\pi$
$521$	5.16170	+	8.94033i	0.226138	+	0.391683i	−0.730522	+	0.682889i	$0.760723\pi$
$522$	−2.22053	+	1.34003i	−0.0971901	+	0.0586514i
$523$	−15.1595	−	8.75233i	−0.662878	−	0.382713i	0.130495	−	0.991449i	$-0.458343\pi$
$523$	−15.1595	−	8.75233i	−0.662878	−	0.382713i	−0.793373	+	0.608736i	$0.791677\pi$
$524$	−11.5993	+	9.73300i	−0.506719	+	0.425188i
$525$	−14.4018	+	12.2086i	−0.628548	+	0.532825i
$526$	−0.560024	+	3.17606i	−0.0244182	+	0.138483i
$527$	−48.4302	−	8.53955i	−2.10965	−	0.371989i
$528$	0.302465	−	3.89083i	0.0131631	−	0.169326i
$529$	−40.8813	+	34.3035i	−1.77745	+	1.49146i
$530$	0.0788411	−	0.136557i	0.00342464	−	0.00593165i
$531$	−19.3762	−	10.6919i	−0.840856	−	0.463990i
$532$	4.64106	−	17.0037i	0.201215	−	0.737205i
$533$	0.506029	−	1.39030i	0.0219185	−	0.0602207i
$534$	−2.00145	+	2.04059i	−0.0866110	+	0.0883050i
$535$	−5.65136	+	6.73503i	−0.244330	+	0.291181i
$536$	−0.875824	−	2.40631i	−0.0378298	−	0.103937i
$537$	−3.31460	+	7.29172i	−0.143035	+	0.314661i
$538$	−2.54374	+	0.448529i	−0.109668	+	0.0193375i
$539$	−4.04519	−	0.0376525i	−0.174239	−	0.00162181i
$540$	−0.562391	+	9.65003i	−0.0242015	+	0.415271i
$541$	−13.0613			−0.561548			−0.280774	−	0.959774i	$-0.590591\pi$
$541$	−13.0613			−0.561548			−0.280774	+	0.959774i	$0.590591\pi$
$542$	0.699614	+	3.96771i	0.0300510	+	0.170428i
$543$	−10.7533	−	15.0451i	−0.461469	−	0.645646i
$544$	3.73065	+	10.2499i	0.159950	+	0.439459i
$545$	0.362688	+	0.304331i	0.0155358	+	0.0130361i
$546$	−0.978896	−	1.67597i	−0.0418929	−	0.0717249i
$547$	−1.26839	−	0.461658i	−0.0542327	−	0.0197391i	0.314761	−	0.949171i	$-0.398076\pi$
$547$	−1.26839	−	0.461658i	−0.0542327	−	0.0197391i	−0.368994	+	0.929432i	$0.620298\pi$
$548$	−19.4804	+	11.2470i	−0.832163	+	0.480449i
$549$	−2.33299	+	14.9148i	−0.0995695	+	0.636547i
$550$	−0.154839	+	0.268190i	−0.00660238	+	0.0114356i
$551$	17.1052	−	14.3530i	0.728705	−	0.611456i
$552$	4.43516	−	6.46646i	0.188773	−	0.275231i
$553$	7.68953	+	11.0913i	0.326992	+	0.471650i
$554$	−0.123126	−	0.0217104i	−0.00523112	−	0.000922387i
$555$	5.68121	+	11.8816i	0.241154	+	0.504346i
$556$	16.9578	+	20.2095i	0.719172	+	0.857076i
$557$	−18.3052	−	10.5685i	−0.775617	−	0.447802i	0.0592580	−	0.998243i	$-0.481127\pi$
$557$	−18.3052	−	10.5685i	−0.775617	−	0.447802i	−0.834875	+	0.550440i	$0.814460\pi$
$558$	−1.78496	−	2.04543i	−0.0755632	−	0.0865899i
$559$	−7.41075	+	4.27860i	−0.313441	+	0.180965i
$560$	−8.78887	+	4.04863i	−0.371398	+	0.171086i
$561$	1.89727	+	6.81596i	0.0801026	+	0.287770i
$562$	0.682373	+	0.572579i	0.0287841	+	0.0241528i
$563$	4.13292	−	1.50426i	0.174182	−	0.0633969i	−0.253457	−	0.967347i	$-0.581568\pi$
$563$	4.13292	−	1.50426i	0.174182	−	0.0633969i	0.427639	+	0.903950i	$0.359345\pi$
$564$	2.62505	+	26.9912i	0.110535	+	1.13653i
$565$	1.82898	−	0.322499i	0.0769459	−	0.0135676i
$566$	3.24605			0.136442
$567$	−16.2539	+	17.4015i	−0.682600	+	0.730793i
$568$	5.84365			0.245194
$569$	20.6845	−	3.64724i	0.867139	−	0.152900i	0.277656	−	0.960681i	$-0.410442\pi$
$569$	20.6845	−	3.64724i	0.867139	−	0.152900i	0.589483	+	0.807780i	$0.299331\pi$
$570$	0.0687205	+	0.706595i	0.00287838	+	0.0295960i
$571$	−17.7802	+	6.47147i	−0.744079	+	0.270823i	−0.686112	−	0.727496i	$-0.740684\pi$
$571$	−17.7802	+	6.47147i	−0.744079	+	0.270823i	−0.0579669	+	0.998319i	$0.518462\pi$
$572$	2.85887	+	2.39888i	0.119535	+	0.100302i
$573$	5.65202	+	20.3050i	0.236116	+	0.848252i
$574$	0.0654146	+	0.142004i	0.00273035	+	0.00592712i
$575$	31.1803	−	18.0019i	1.30031	−	0.750732i
$576$	7.37859	−	21.5631i	0.307441	−	0.898462i
$577$	−20.6168	−	11.9031i	−0.858290	−	0.495534i	0.00514914	−	0.999987i	$-0.498361\pi$
$577$	−20.6168	−	11.9031i	−0.858290	−	0.495534i	−0.863439	+	0.504453i	$0.831694\pi$
$578$	−2.75556	−	3.28395i	−0.114616	−	0.136594i
$579$	8.31697	+	17.3940i	0.345641	+	0.722870i
$580$	−12.1773	−	2.14719i	−0.505635	−	0.0891571i
$581$	−12.8811	−	18.5795i	−0.534396	−	0.770807i
$582$	−0.164023	+	0.239145i	−0.00679896	+	0.00991288i
$583$	−0.572137	+	0.480080i	−0.0236955	+	0.0198829i
$584$	−0.683845	+	1.18445i	−0.0282977	+	0.0490131i
$585$	−7.13310	−	5.75368i	−0.294917	−	0.237885i
$586$	−1.79606	+	1.03696i	−0.0741945	+	0.0428362i
$587$	−8.37586	−	3.04856i	−0.345709	−	0.125828i	0.163329	−	0.986572i	$-0.447777\pi$
$587$	−8.37586	−	3.04856i	−0.345709	−	0.125828i	−0.509038	+	0.860744i	$0.669999\pi$
$588$	−23.2267	−	6.21419i	−0.957852	−	0.256269i
$589$	17.9046	+	15.0237i	0.737746	+	0.619042i
$590$	0.307834	+	0.845767i	0.0126733	+	0.0348197i
$591$	18.8573	+	26.3835i	0.775687	+	1.08527i
$592$	−5.48760	−	31.1217i	−0.225539	−	1.27910i
$593$	−13.7775			−0.565776			−0.282888	−	0.959153i	$-0.591292\pi$
$593$	−13.7775			−0.565776			−0.282888	+	0.959153i	$0.591292\pi$
$594$	−0.154709	+	0.358620i	−0.00634777	+	0.0147144i
$595$	12.4623	−	12.3469i	0.510906	−	0.506173i
$596$	−6.11468	+	1.07818i	−0.250467	+	0.0441641i
$597$	8.10672	−	17.8338i	0.331786	−	0.729890i
$598$	1.26590	+	3.47802i	0.0517664	+	0.142227i
$599$	−8.74946	+	10.4272i	−0.357493	+	0.426044i	−0.914577	−	0.404413i	$-0.867476\pi$
$599$	−8.74946	+	10.4272i	−0.357493	+	0.426044i	0.557083	+	0.830457i	$0.311920\pi$
$600$	−2.58863	+	2.63926i	−0.105680	+	0.107747i
$601$	10.7694	−	29.5886i	0.439292	−	1.20695i	−0.500661	−	0.865643i	$-0.666910\pi$
$601$	10.7694	−	29.5886i	0.439292	−	1.20695i	0.939953	−	0.341303i	$-0.110868\pi$
$602$	0.238103	−	0.872354i	0.00970437	−	0.0355545i
$603$	−0.287206	−	14.8262i	−0.0116959	−	0.603771i
$604$	−5.98233	+	10.3617i	−0.243418	+	0.421612i
$605$	7.66476	−	6.43150i	0.311617	−	0.261477i
$606$	0.198358	−	2.55163i	0.00805776	−	0.103653i
$607$	−5.82153	−	1.02649i	−0.236289	−	0.0416641i	0.0542498	−	0.998527i	$-0.482723\pi$
$607$	−5.82153	−	1.02649i	−0.236289	−	0.0416641i	−0.290538	+	0.956863i	$0.593834\pi$
$608$	0.900219	−	5.10540i	0.0365087	−	0.207051i
$609$	−19.6963	−	23.2347i	−0.798134	−	0.941519i
$610$	0.470322	−	0.394647i	0.0190428	−	0.0159788i
$611$	−22.2656	−	12.8551i	−0.900770	−	0.520060i
$612$	0.814433	+	42.0429i	0.0329215	+	1.69948i
$613$	5.86682	+	10.1616i	0.236959	+	0.410424i	0.959840	−	0.280548i	$-0.0905161\pi$
$613$	5.86682	+	10.1616i	0.236959	+	0.410424i	−0.722882	+	0.690972i	$0.757183\pi$
$614$	2.78557	+	1.01386i	0.112416	+	0.0409162i
$615$	0.527032	+	0.516921i	0.0212520	+	0.0208443i
$616$	−0.789404	+	0.0653635i	−0.0318060	+	0.00263357i
$617$	13.7308	+	37.7251i	0.552782	+	1.51876i	0.829895	+	0.557919i	$0.188400\pi$
$617$	13.7308	+	37.7251i	0.552782	+	1.51876i	−0.277113	+	0.960837i	$0.589378\pi$
$618$	−1.96504	−	0.893249i	−0.0790456	−	0.0359317i
$619$	−29.0524	+	5.12272i	−1.16771	+	0.205899i	−0.723696	−	0.690119i	$-0.757558\pi$
$619$	−29.0524	+	5.12272i	−1.16771	+	0.205899i	−0.444018	+	0.896018i	$0.646447\pi$
$620$		−	12.9430i		−	0.519805i
$621$	36.4239	−	27.1146i	1.46164	−	1.08807i
$622$			1.99367i			0.0799390i
$623$	−27.4083	−	19.3822i	−1.09809	−	0.776531i
$624$	12.7869	+	17.8904i	0.511887	+	0.716187i
$625$	−11.8160	+	4.30068i	−0.472641	+	0.172027i
$626$	2.49252	+	2.09147i	0.0996210	+	0.0835919i
$627$	0.838814	−	3.25632i	0.0334990	−	0.130045i
$628$	−6.58351	+	18.0881i	−0.262711	+	0.721792i
$629$	28.6460	+	49.6164i	1.14219	+	1.97833i
$630$	0.963396	−	0.0985908i	0.0383826	−	0.00392795i
$631$	6.72731	−	11.6520i	0.267810	−	0.463860i	−0.700486	−	0.713666i	$-0.747033\pi$
$631$	6.72731	−	11.6520i	0.267810	−	0.463860i	0.968296	+	0.249806i	$0.0803667\pi$
$632$	1.69864	+	2.02436i	0.0675684	+	0.0805249i
$633$	−4.36173	+	6.35939i	−0.173363	+	0.252763i
$634$	−0.580839	+	3.29410i	−0.0230681	+	0.130825i
$635$	−0.0629490	+	0.357002i	−0.00249806	+	0.0141672i
$636$	−4.00477	+	1.91489i	−0.158799	+	0.0759302i
$637$	17.5975	−	14.4891i	0.697240	−	0.574080i
$638$	−0.432675	−	0.249805i	−0.0171298	−	0.00988988i
$639$	32.0175	+	10.9559i	1.26659	+	0.433410i
$640$	−3.31012	+	1.91110i	−0.130844	+	0.0755427i
$641$	13.3652	−	36.7206i	0.527893	−	1.45037i	−0.333653	−	0.942696i	$-0.608281\pi$
$641$	13.3652	−	36.7206i	0.527893	−	1.45037i	0.861546	−	0.507679i	$-0.169496\pi$
$642$	−2.03401	+	0.566181i	−0.0802761	+	0.0223454i
$643$	−12.1819	+	14.5178i	−0.480405	+	0.572525i	−0.950750	−	0.309958i	$-0.899685\pi$
$643$	−12.1819	+	14.5178i	−0.480405	+	0.572525i	0.470345	+	0.882483i	$0.344130\pi$
$644$	41.4639	+	19.5704i	1.63390	+	0.771180i
$645$	−0.413301	−	4.24962i	−0.0162737	−	0.167329i
$646$	0.536282	+	3.04141i	0.0210997	+	0.119663i
$647$	−40.0251			−1.57355			−0.786775	−	0.617240i	$-0.788251\pi$
$647$	−40.0251			−1.57355			−0.786775	+	0.617240i	$0.788251\pi$
$648$	−2.85641	+	3.68505i	−0.112210	+	0.144763i
$649$		−	4.26312i		−	0.167342i
$650$	−0.303013	−	1.71847i	−0.0118852	−	0.0674041i
$651$	20.3710	−	24.5268i	0.798404	−	0.961281i
$652$	−18.6485	+	6.78750i	−0.730331	+	0.265819i
$653$	23.0194	−	27.4334i	0.900818	−	1.07355i	−0.0961205	−	0.995370i	$-0.530643\pi$
$653$	23.0194	−	27.4334i	0.900818	−	1.07355i	0.996939	−	0.0781839i	$-0.0249121\pi$
$654$	0.0304894	+	0.109534i	0.00119223	+	0.00428310i
$655$	6.73079	+	2.44981i	0.262994	+	0.0957219i
$656$	−0.885693	−	1.53407i	−0.0345805	−	0.0598952i
$657$	−5.96747	+	5.20755i	−0.232813	+	0.203166i
$658$	2.62753	−	0.690956i	0.102432	−	0.0269363i
$659$	10.7842	+	12.8521i	0.420093	+	0.500647i	0.934037	−	0.357177i	$-0.116261\pi$
$659$	10.7842	+	12.8521i	0.420093	+	0.500647i	−0.513944	+	0.857824i	$0.671816\pi$
$660$	−1.67994	+	0.803265i	−0.0653915	+	0.0312671i
$661$	41.5273	+	7.32238i	1.61522	+	0.284807i	0.906984	−	0.421165i	$-0.138379\pi$
$661$	41.5273	+	7.32238i	1.61522	+	0.284807i	0.708239	+	0.705973i	$0.249490\pi$
$662$	2.23734	+	0.394503i	0.0869567	+	0.0153328i
$663$	−32.8769	−	22.5493i	−1.27683	−	0.875744i
$664$	−2.84547	−	3.39110i	−0.110426	−	0.131600i
$665$	−8.06359	+	2.12046i	−0.312693	+	0.0822280i
$666$	−0.488771	+	3.12471i	−0.0189395	+	0.121080i
$667$	29.0428	+	50.3037i	1.12454	+	1.94777i
$668$	24.3233	+	8.85295i	0.941096	+	0.342531i
$669$	24.0716	+	6.20074i	0.930661	+	0.239734i
$670$	−0.387664	+	0.462000i	−0.0149768	+	0.0178486i
$671$	−2.73269	+	0.994618i	−0.105494	+	0.0383968i
$672$	−6.97046	−	1.19296i	−0.268891	−	0.0460193i
$673$	−6.73038	−	38.1699i	−0.259437	−	1.47134i	−0.784421	−	0.620228i	$-0.787040\pi$
$673$	−6.73038	−	38.1699i	−0.259437	−	1.47134i	0.524984	−	0.851112i	$-0.324071\pi$
$674$		−	2.87018i		−	0.110555i
$675$	−19.1313	+	9.60728i	−0.736366	+	0.369784i
$676$	4.75099			0.182731
$677$	−4.89108	−	27.7387i	−0.187980	−	1.06609i	−0.922067	−	0.387030i	$-0.873501\pi$
$677$	−4.89108	−	27.7387i	−0.187980	−	1.06609i	0.734087	−	0.679055i	$-0.237610\pi$
$678$	0.406017	+	0.184563i	0.0155930	+	0.00708810i
$679$	−3.07995	−	1.45369i	−0.118197	−	0.0557875i
$680$	2.20798	−	2.63137i	0.0846722	−	0.100908i
$681$	31.8885	+	31.2768i	1.22197	+	1.19853i
$682$	0.178863	−	0.491421i	0.00684900	−	0.0188175i
$683$	−16.4680	+	9.50782i	−0.630132	+	0.363807i	−0.780803	−	0.624777i	$-0.785190\pi$
$683$	−16.4680	+	9.50782i	−0.630132	+	0.363807i	0.150671	+	0.988584i	$0.451856\pi$
$684$	9.65575	−	17.4984i	0.369197	−	0.669069i
$685$	9.21509	+	5.32034i	0.352091	+	0.203280i
$686$	−0.243422	+	2.39647i	−0.00929391	+	0.0914978i
$687$	1.76314	−	22.6806i	0.0672681	−	0.865318i
$688$	−1.77906	+	10.0896i	−0.0678262	+	0.384661i
$689$	0.730796	−	4.14455i	0.0278411	−	0.157895i
$690$	−1.84120	−	0.143131i	−0.0700933	−	0.00544891i
$691$	−7.46991	−	8.90229i	−0.284169	−	0.338659i	0.605011	−	0.796217i	$-0.293169\pi$
$691$	−7.46991	−	8.90229i	−0.284169	−	0.338659i	−0.889180	+	0.457558i	$0.848724\pi$
$692$	−0.232550	+	0.402788i	−0.00884021	+	0.0153117i
$693$	−4.44771	−	1.12188i	−0.168954	−	0.0426168i
$694$	−2.04679	−	3.54514i	−0.0776950	−	0.134572i
$695$	4.26830	−	11.7271i	0.161906	−	0.444833i
$696$	−4.25796	−	4.17628i	−0.161398	−	0.158301i
$697$	2.46008	+	2.06425i	0.0931822	+	0.0781891i
$698$	4.49816	−	1.63719i	0.170258	−	0.0619687i
$699$	−5.14531	+	11.3191i	−0.194614	+	0.428127i
$700$	−17.6494	−	12.4810i	−0.667083	−	0.471739i
$701$			32.8178i			1.23951i	0.784795	+	0.619755i	$0.212768\pi$
$701$			32.8178i			1.23951i	−0.784795	+	0.619755i	$0.787232\pi$
$702$	−0.631116	−	2.10835i	−0.0238199	−	0.0795744i
$703$		−	27.2295i		−	1.02698i
$704$	4.32360	−	0.762367i	0.162952	−	0.0287328i
$705$	10.4365	−	7.45939i	0.393062	−	0.280937i
$706$	−0.643521	−	1.76806i	−0.0242192	−	0.0665418i
$707$	29.9555	−	2.48034i	1.12659	−	0.0932829i
$708$	6.32059	−	24.5368i	0.237542	−	0.922151i
$709$	−28.1037	−	10.2289i	−1.05546	−	0.384154i	−0.244736	−	0.969590i	$-0.578701\pi$
$709$	−28.1037	−	10.2289i	−1.05546	−	0.384154i	−0.810719	+	0.585435i	$0.800924\pi$
$710$	−0.688140	−	1.19189i	−0.0258254	−	0.0447310i
$711$	5.51153	+	14.2762i	0.206699	+	0.535400i
$712$	−5.69240	−	3.28651i	−0.213332	−	0.123167i
$713$	−46.5757	+	39.0817i	−1.74427	+	1.46362i
$714$	4.14511	−	0.752416i	0.155127	−	0.0281585i
$715$	0.306558	−	1.73857i	0.0114646	−	0.0650190i
$716$	−9.03129	−	1.59246i	−0.337515	−	0.0595130i
$717$	21.3889	−	10.2271i	0.798783	−	0.381939i
$718$	2.09761	−	1.76010i	0.0782820	−	0.0656864i
$719$	19.8104	−	34.3126i	0.738802	−	1.27964i	−0.214233	−	0.976783i	$-0.568725\pi$
$719$	19.8104	−	34.3126i	0.738802	−	1.27964i	0.953035	−	0.302860i	$-0.0979414\pi$
$720$	−10.7666	+	2.11422i	−0.401246	+	0.0787924i
$721$	6.67518	−	24.4563i	0.248597	−	0.910799i
$722$	−0.343182	+	0.942884i	−0.0127719	+	0.0350905i
$723$	0.228219	+	0.819881i	0.00848756	+	0.0304917i
$724$	13.6098	−	16.2196i	0.505806	−	0.602796i
$725$	−9.36624	−	25.7335i	−0.347853	−	0.955720i
$726$	2.39152	−	0.232589i	0.0887575	−	0.00863219i
$727$	−2.99121	+	0.527432i	−0.110938	+	0.0195614i	−0.228841	−	0.973464i	$-0.573494\pi$
$727$	−2.99121	+	0.527432i	−0.110938	+	0.0195614i	0.117904	+	0.993025i	$0.462383\pi$
$728$	3.17073	−	3.14136i	0.117515	−	0.116426i
$729$	−22.5592	+	14.8352i	−0.835527	+	0.549450i
$730$	0.322115			0.0119220
$731$	−3.22533	−	18.2917i	−0.119293	−	0.676544i
$732$	−17.2029	+	1.67309i	−0.635838	+	0.0618390i
$733$	−5.75131	−	15.8016i	−0.212429	−	0.583645i	0.787016	−	0.616932i	$-0.211625\pi$
$733$	−5.75131	−	15.8016i	−0.212429	−	0.583645i	−0.999446	+	0.0332869i	$0.989402\pi$
$734$	−1.27039	−	1.06598i	−0.0468909	−	0.0393462i
$735$	2.94786	+	10.9850i	0.108734	+	0.405188i
$736$	12.6724	+	4.61238i	0.467111	+	0.170014i
$737$	2.47390	−	1.42830i	0.0911271	−	0.0526123i
$738$	0.0341599	+	0.173958i	0.00125745	+	0.00640347i
$739$	1.52103	−	2.63450i	0.0559519	−	0.0969115i	−0.836693	−	0.547672i	$-0.815514\pi$
$739$	1.52103	−	2.63450i	0.0559519	−	0.0969115i	0.892645	+	0.450761i	$0.148847\pi$
$740$	−11.5510	+	9.69245i	−0.424624	+	0.356302i
$741$	8.17359	+	17.0941i	0.300264	+	0.627969i
$742$	0.253385	+	0.365479i	0.00930204	+	0.0134172i
$743$	34.6486	+	6.10948i	1.27113	+	0.224135i	0.768211	−	0.640197i	$-0.221147\pi$
$743$	34.6486	+	6.10948i	1.27113	+	0.224135i	0.502922	+	0.864332i	$0.332258\pi$
$744$	3.53110	−	5.14834i	0.129456	−	0.188747i
$745$	1.88795	+	2.24997i	0.0691691	+	0.0824326i
$746$	1.24444	+	0.718475i	0.0455620	+	0.0263052i
$747$	−9.23259	−	23.9147i	−0.337803	−	0.874993i
$748$	−7.01525	+	4.05026i	−0.256503	+	0.148092i
$749$	−10.3748	−	22.5219i	−0.379087	−	0.822933i
$750$	1.86638	+	0.480773i	0.0681507	+	0.0175553i
$751$	−11.0459	−	9.26863i	−0.403072	−	0.338217i	0.418608	−	0.908167i	$-0.362518\pi$
$751$	−11.0459	−	9.26863i	−0.403072	−	0.338217i	−0.821679	+	0.569950i	$0.806963\pi$
$752$	−28.9254	+	10.5280i	−1.05480	+	0.383916i
$753$	7.96296	−	5.69144i	0.290186	−	0.207408i
$754$	2.77244	−	0.488857i	0.100966	−	0.0178031i
$755$	5.65981			0.205982
$756$	−23.9359	−	13.0514i	−0.870540	−	0.474673i
$757$	47.8999			1.74095			0.870475	−	0.492212i	$-0.163812\pi$
$757$	47.8999			1.74095			0.870475	+	0.492212i	$0.163812\pi$
$758$	−3.18542	+	0.561675i	−0.115700	+	0.0204010i
$759$	7.96315	+	3.61981i	0.289044	+	0.131391i
$760$	−1.53412	+	0.558374i	−0.0556484	+	0.0202543i
$761$	20.9193	+	17.5534i	0.758324	+	0.636309i	0.937690	−	0.347473i	$-0.112960\pi$
$761$	20.9193	+	17.5534i	0.758324	+	0.636309i	−0.179366	+	0.983782i	$0.557405\pi$
$762$	−0.0609579	+	0.0621502i	−0.00220827	+	0.00225146i
$763$	−1.21283	+	0.558694i	−0.0439073	+	0.0202261i
$764$	−20.8987	+	12.0658i	−0.756087	+	0.436527i
$765$	17.0310	−	10.2777i	0.615756	−	0.371591i
$766$	−3.07337	−	1.77441i	−0.111045	−	0.0641121i
$767$	15.4410	+	18.4019i	0.557542	+	0.664453i
$768$	25.3220	+	1.96848i	0.913730	+	0.0710315i
$769$	−0.0501634	−	0.00884516i	−0.00180894	−	0.000318965i	0.172744	−	0.984967i	$-0.444737\pi$
$769$	−0.0501634	−	0.00884516i	−0.00180894	−	0.000318965i	−0.174553	+	0.984648i	$0.555848\pi$
$770$	0.106291	+	0.153313i	0.00383046	+	0.00552501i
$771$	−30.6201	−	2.38034i	−1.10276	−	0.0857260i
$772$	−16.9100	+	14.1892i	−0.608605	+	0.510680i
$773$	−14.1938	+	24.5843i	−0.510514	+	0.884236i	0.489412	+	0.872053i	$0.337212\pi$
$773$	−14.1938	+	24.5843i	−0.510514	+	0.884236i	−0.999926	+	0.0121834i	$0.996122\pi$
$774$	0.495376	−	0.897733i	0.0178059	−	0.0322683i
$775$	24.8245	−	14.3324i	0.891723	−	0.514836i
$776$	−0.626652	−	0.228083i	−0.0224955	−	0.00818769i
$777$	−37.1439	+	0.186861i	−1.33253	+	0.00670358i
$778$	−2.20651	−	1.85148i	−0.0791072	−	0.0663788i
$779$	−0.522026	−	1.43426i	−0.0187035	−	0.0513876i
$780$	4.34207	−	9.55203i	0.155471	−	0.342018i
$781$	1.13198	+	6.41980i	0.0405055	+	0.229718i
$782$	−8.03375			−0.287286
$783$	−15.4996	−	30.8649i	−0.553910	−	1.10302i
$784$	0.254018	−	27.2903i	0.00907206	−	0.974655i
$785$	8.96724	−	1.58117i	0.320054	−	0.0564342i
$786$	1.00021	+	1.39940i	0.0356762	+	0.0499150i
$787$	18.0105	+	49.4833i	0.642004	+	1.76389i	0.645339	+	0.763896i	$0.276716\pi$
$787$	18.0105	+	49.4833i	0.642004	+	1.76389i	−0.00333553	+	0.999994i	$0.501062\pi$
$788$	−23.8667	+	28.4432i	−0.850214	+	1.01325i
$789$	−41.5903	−	10.7135i	−1.48065	−	0.381410i
$790$	0.212867	−	0.584848i	0.00757348	−	0.0208080i
$791$	−1.37923	+	5.05315i	−0.0490396	+	0.179669i
$792$	−0.887373	−	0.138804i	−0.0315314	−	0.00493218i
$793$	8.19322	−	14.1911i	0.290950	−	0.503940i
$794$	−2.01280	+	1.68894i	−0.0714317	+	0.0599383i
$795$	1.73168	+	1.18771i	0.0614164	+	0.0421238i
$796$	22.0884	+	3.89478i	0.782902	+	0.138047i
$797$	5.14985	−	29.2062i	0.182417	−	1.03454i	−0.746812	−	0.665035i	$-0.768417\pi$
$797$	5.14985	−	29.2062i	0.182417	−	1.03454i	0.929229	−	0.369503i	$-0.120472\pi$
$798$	−1.88493	−	0.675341i	−0.0667260	−	0.0239068i
$799$	42.7494	−	35.8710i	1.51236	−	1.26902i
$800$	−5.50615	−	3.17898i	−0.194672	−	0.112394i
$801$	−25.0271	−	28.6792i	−0.884287	−	1.01333i
$802$	1.14855	+	1.98934i	0.0405567	+	0.0702462i
$803$	−1.43370	−	0.521825i	−0.0505943	−	0.0184148i
$804$	16.3564	−	4.55291i	0.576845	−	0.160569i
$805$	−1.78976	−	21.6152i	−0.0630809	−	0.761836i
$806$	1.00786	+	2.76907i	0.0355003	+	0.0975363i
$807$	−3.32965	−	34.2359i	−0.117209	−	1.20516i
$808$	5.79610	−	1.02201i	0.203906	−	0.0359542i
$809$			15.0635i			0.529603i	0.964303	+	0.264802i	$0.0853065\pi$
$809$			15.0635i			0.529603i	−0.964303	+	0.264802i	$0.914694\pi$
$810$	1.08798	+	0.148658i	0.0382279	+	0.00522329i
$811$			10.9588i			0.384817i	0.981315	+	0.192409i	$0.0616299\pi$
$811$			10.9588i			0.384817i	−0.981315	+	0.192409i	$0.938370\pi$
$812$	20.1359	−	28.4740i	0.706630	−	0.999243i
$813$	−53.4011	+	5.19357i	−1.87286	+	0.182147i
$814$	−0.572510	+	0.208377i	−0.0200665	+	0.00730360i
$815$	7.19139	+	6.03429i	0.251903	+	0.211372i
$816$	−45.9829	+	12.7996i	−1.60972	+	0.448077i
$817$	−3.01926	+	8.29535i	−0.105631	+	0.290218i
$818$	−0.976611	−	1.69154i	−0.0341464	−	0.0591433i
$819$	23.2621	−	11.2669i	0.812842	−	0.393698i
$820$	−0.422607	+	0.731977i	−0.0147581	+	0.0255617i
$821$	−8.72275	−	10.3954i	−0.304426	−	0.362801i	0.592044	−	0.805906i	$-0.298321\pi$
$821$	−8.72275	−	10.3954i	−0.304426	−	0.362801i	−0.896470	+	0.443105i	$0.853877\pi$
$822$	1.10229	+	2.30532i	0.0384469	+	0.0804074i
$823$	3.74780	−	21.2549i	0.130640	−	0.740898i	−0.847157	−	0.531343i	$-0.821688\pi$
$823$	3.74780	−	21.2549i	0.130640	−	0.740898i	0.977797	−	0.209554i	$-0.0672014\pi$
$824$	0.861963	−	4.88843i	0.0300279	−	0.170297i
$825$	−3.40092	−	2.33260i	−0.118405	−	0.0812106i
$826$	−2.52775	−	0.233008i	−0.0879517	−	0.00810740i
$827$	20.9221	+	12.0794i	0.727534	+	0.420042i	0.817519	−	0.575901i	$-0.195349\pi$
$827$	20.9221	+	12.0794i	0.727534	+	0.420042i	−0.0899855	+	0.995943i	$0.528682\pi$
$828$	40.4659	+	32.6405i	1.40629	+	1.13434i
$829$	−1.59657	+	0.921782i	−0.0554513	+	0.0320148i	−0.527469	−	0.849574i	$-0.676859\pi$
$829$	−1.59657	+	0.921782i	−0.0554513	+	0.0320148i	0.472018	+	0.881589i	$0.343526\pi$
$830$	−0.356583	+	0.979704i	−0.0123772	+	0.0340060i
$831$	0.415328	−	1.61233i	0.0144076	−	0.0559310i
$832$	−15.9016	+	18.9508i	−0.551290	+	0.657001i
$833$	16.4889	+	46.6493i	0.571306	+	1.61630i
$834$	2.43818	−	1.74266i	0.0844273	−	0.0603435i
$835$	−2.12622	−	12.0584i	−0.0735808	−	0.417297i
$836$	3.84998			0.133154
$837$	28.9993	−	21.5876i	1.00236	−	0.746176i
$838$		−	3.96632i		−	0.137014i
$839$	2.42672	+	13.7626i	0.0837795	+	0.475137i	0.997613	+	0.0690488i	$0.0219964\pi$
$839$	2.42672	+	13.7626i	0.0837795	+	0.475137i	−0.913834	+	0.406089i	$0.866892\pi$
$840$	0.772207	+	2.08886i	0.0266437	+	0.0720727i
$841$	14.2653	−	5.19214i	0.491906	−	0.179039i
$842$	−0.355701	+	0.423908i	−0.0122583	+	0.0146088i
$843$	−8.30637	+	8.46884i	−0.286087	+	0.291682i
$844$	−8.29664	−	3.01973i	−0.285582	−	0.103943i
$845$	−1.12371	−	1.94633i	−0.0386569	−	0.0669557i
$846$	3.08006	−	0.0596653i	0.105895	−	0.00205133i
$847$	7.17685	+	27.2918i	0.246599	+	0.937756i
$848$	−3.23879	−	3.85984i	−0.111221	−	0.132548i
$849$	−3.35032	+	43.0976i	−0.114983	+	1.47911i
$850$	3.73005	+	0.657708i	0.127940	+	0.0225592i
$851$	69.7568	+	12.3000i	2.39123	+	0.421639i
$852$	−3.00287	+	38.6281i	−0.102877	+	1.32338i
$853$	−3.48262	−	4.15042i	−0.119243	−	0.142108i	0.703121	−	0.711070i	$-0.251789\pi$
$853$	−3.48262	−	4.15042i	−0.119243	−	0.142108i	−0.822363	+	0.568963i	$0.807345\pi$
$854$	0.440383	+	1.67467i	0.0150696	+	0.0573060i
$855$	−9.45233	+	0.183106i	−0.323263	+	0.00626208i
$856$	−2.42766	−	4.20483i	−0.0829757	−	0.143718i
$857$	−7.35667	−	2.67761i	−0.251299	−	0.0914654i	0.213299	−	0.976987i	$-0.431579\pi$
$857$	−7.35667	−	2.67761i	−0.251299	−	0.0914654i	−0.464598	+	0.885522i	$0.653801\pi$
$858$	0.296861	−	0.302667i	0.0101347	−	0.0103329i
$859$	−1.40560	+	1.67512i	−0.0479583	+	0.0571545i	−0.789490	−	0.613763i	$-0.789655\pi$
$859$	−1.40560	+	1.67512i	−0.0479583	+	0.0571545i	0.741532	+	0.670917i	$0.234100\pi$
$860$	4.59368	−	1.67196i	0.156643	−	0.0570135i
$861$	−1.95289	+	0.721940i	−0.0665543	+	0.0246037i
$862$	−0.500149	−	2.83648i	−0.0170351	−	0.0966110i
$863$		−	12.4864i		−	0.425040i	−0.977157	−	0.212520i	$-0.931833\pi$
$863$		−	12.4864i		−	0.425040i	0.977157	−	0.212520i	$-0.0681671\pi$
$864$	−7.36277	−	3.17630i	−0.250486	−	0.108060i
$865$	0.220012			0.00748064
$866$	0.717254	+	4.06775i	0.0243733	+	0.138228i
$867$	46.4449	−	33.1960i	1.57735	−	1.12739i
$868$	33.0119	+	15.5812i	1.12050	+	0.528859i
$869$	−1.89491	+	2.25826i	−0.0642803	+	0.0766063i
$870$	−0.350398	+	1.36026i	−0.0118796	+	0.0461173i
$871$	−5.50532	+	15.1257i	−0.186541	+	0.512516i
$872$	−0.226434	+	0.130732i	−0.00766803	+	0.00442714i
$873$	−3.00582	−	2.42454i	−0.101732	−	0.0820584i
$874$	3.30670	+	1.90912i	0.111851	+	0.0645771i
$875$	−2.07771	+	22.5397i	−0.0702395	+	0.761982i
$876$	−7.47816	−	5.12906i	−0.252664	−	0.173295i
$877$	−9.15553	+	51.9236i	−0.309160	+	1.75334i	0.294084	+	0.955779i	$0.404985\pi$
$877$	−9.15553	+	51.9236i	−0.309160	+	1.75334i	−0.603245	+	0.797556i	$0.706126\pi$
$878$	0.277255	−	1.57239i	0.00935690	−	0.0530656i
$879$	−11.9138	−	24.9164i	−0.401843	−	0.840409i
$880$	−1.35862	−	1.61914i	−0.0457992	−	0.0545813i
$881$	−13.0777	+	22.6513i	−0.440600	+	0.763141i	−0.997734	−	0.0672812i	$-0.978568\pi$
$881$	−13.0777	+	22.6513i	−0.440600	+	0.763141i	0.557134	+	0.830422i	$0.311901\pi$
$882$	−0.908299	+	2.57588i	−0.0305840	+	0.0867344i
$883$	−8.18042	−	14.1689i	−0.275293	−	0.476821i	0.694916	−	0.719091i	$-0.255442\pi$
$883$	−8.18042	−	14.1689i	−0.275293	−	0.476821i	−0.970209	+	0.242270i	$0.922108\pi$
$884$	15.6115	−	42.8922i	0.525071	−	1.44262i
$885$	−11.5469	+	3.21416i	−0.388145	+	0.108043i
$886$	−1.35984	−	1.14104i	−0.0456848	−	0.0383341i
$887$	−32.9621	+	11.9972i	−1.10676	+	0.402827i	−0.829804	−	0.558055i	$-0.811548\pi$
$887$	−32.9621	+	11.9972i	−1.10676	+	0.402827i	−0.276956	+	0.960883i	$0.589326\pi$
$888$	−7.23891	+	0.704027i	−0.242922	+	0.0236256i
$889$	−0.834772	−	0.590323i	−0.0279974	−	0.0197988i
$890$			1.54806i			0.0518910i
$891$	−4.60170	−	2.42420i	−0.154163	−	0.0812136i
$892$			28.4601i			0.952914i
$893$	−26.1200	+	4.60566i	−0.874071	+	0.154122i
$894$	0.0682760	+	0.702024i	0.00228349	+	0.0234792i
$895$	1.48372	+	4.07648i	0.0495952	+	0.136262i
$896$	−0.889553	−	10.7433i	−0.0297179	−	0.358907i
$897$	−47.4840	+	13.2175i	−1.58545	+	0.441319i
$898$	−2.51680	−	0.916041i	−0.0839868	−	0.0305687i
$899$	23.1228	+	40.0498i	0.771188	+	1.33574i
$900$	−16.1160	−	18.4678i	−0.537200	−	0.615592i
$901$	7.91094	+	4.56738i	0.263552	+	0.152162i
$902$	−0.0261609	+	0.0219516i	−0.000871062	+	0.000730908i
$903$	11.3364	+	4.06166i	0.377253	+	0.135163i
$904$	−0.178099	+	1.01005i	−0.00592347	+	0.0335937i
$905$	−9.86366	−	1.73923i	−0.327879	−	0.0578140i
$906$	1.12087	+	0.768771i	0.0372383	+	0.0255407i
$907$	40.1884	−	33.7220i	1.33443	−	1.11972i	0.351413	−	0.936220i	$-0.385701\pi$
$907$	40.1884	−	33.7220i	1.33443	−	1.11972i	0.983019	−	0.183502i	$-0.0587433\pi$
$908$	−25.5702	+	44.2889i	−0.848577	+	1.46978i
$909$	33.6731	+	5.26718i	1.11687	+	0.174701i
$910$	−1.01410	−	0.276793i	−0.0336172	−	0.00917561i
$911$	−0.452283	+	1.24264i	−0.0149848	+	0.0411704i	−0.946960	−	0.321353i	$-0.895862\pi$
$911$	−0.452283	+	1.24264i	−0.0149848	+	0.0411704i	0.931975	+	0.362523i	$0.118085\pi$
$912$	21.9683	+	5.65894i	0.727443	+	0.187386i
$913$	3.17424	−	3.78291i	0.105052	−	0.125196i
$914$	0.695377	+	1.91053i	0.0230010	+	0.0631948i
$915$	4.75427	+	6.65176i	0.157171	+	0.219900i
$916$	25.6504	−	4.52286i	0.847514	−	0.149440i
$917$	−14.3511	+	14.2181i	−0.473914	+	0.469523i
$918$	4.76883	+	0.277921i	0.157395	+	0.00917277i
$919$	−37.3883			−1.23333			−0.616663	−	0.787227i	$-0.711516\pi$
$919$	−37.3883			−1.23333			−0.616663	+	0.787227i	$0.711516\pi$
$920$	−0.737460	−	4.18235i	−0.0243133	−	0.137888i
$921$	−16.3361	+	35.9374i	−0.538291	+	1.18418i
$922$	0.525952	+	1.44504i	0.0173213	+	0.0475899i
$923$	−28.1387	−	23.6111i	−0.926196	−	0.777170i
$924$	−0.0264202	−	5.25176i	−0.000869160	−	0.172770i
$925$	−31.3809	−	11.4217i	−1.03180	−	0.375544i
$926$	1.87325	−	1.08152i	0.0615588	−	0.0355410i
$927$	13.8878	−	25.1678i	0.456134	−	0.826618i
$928$	5.12870	−	8.88318i	0.168358	−	0.291605i
$929$	−24.0752	+	20.2015i	−0.789882	+	0.662790i	−0.945716	−	0.324993i	$-0.894638\pi$
$929$	−24.0752	+	20.2015i	−0.789882	+	0.662790i	0.155834	+	0.987783i	$0.450194\pi$
$930$	−1.46589	−	0.113956i	−0.0480685	−	0.00373675i
$931$	4.29880	−	23.1193i	0.140888	−	0.757704i
$932$	−14.0194	−	2.47201i	−0.459222	−	0.0809733i
$933$	−26.4699	−	2.05771i	−0.866584	−	0.0673665i
$934$	−2.10480	−	2.50840i	−0.0688712	−	0.0820775i
$935$	3.31852	+	1.91595i	0.108527	+	0.0626582i
$936$	4.33311	−	2.61491i	0.141632	−	0.0854709i
$937$	35.2543	−	20.3541i	1.15171	−	0.664939i	0.202405	−	0.979302i	$-0.435124\pi$
$937$	35.2543	−	20.3541i	1.15171	−	0.664939i	0.949303	+	0.314363i	$0.101791\pi$
$938$	−0.711676	−	1.54492i	−0.0232370	−	0.0504436i
$939$	−30.3409	+	30.9343i	−0.990137	+	1.00950i
$940$	11.2513	+	9.44093i	0.366976	+	0.307929i
$941$	41.5056	−	15.1068i	1.35305	−	0.492468i	0.439148	−	0.898415i	$-0.355280\pi$
$941$	41.5056	−	15.1068i	1.35305	−	0.492468i	0.913897	+	0.405946i	$0.133058\pi$
$942$	1.99064	+	0.904885i	0.0648586	+	0.0294827i
$943$	3.91010	−	0.689455i	0.127330	−	0.0224518i
$944$	28.7606			0.936077
$945$	0.314641	+	12.8927i	0.0102353	+	0.419399i
$946$	0.197518			0.00642186
$947$	−38.9031	+	6.85966i	−1.26418	+	0.222909i	−0.765250	−	0.643733i	$-0.777385\pi$
$947$	−38.9031	+	6.85966i	−1.26418	+	0.222909i	−0.498930	+	0.866642i	$0.666273\pi$
$948$	−14.2545	+	10.1882i	−0.462964	+	0.330898i
$949$	8.07866	−	2.94039i	0.262244	−	0.0954491i
$950$	−1.37899	−	1.15711i	−0.0447405	−	0.0375417i
$951$	−43.1360	−	11.1117i	−1.39878	−	0.360320i
$952$	4.05342	+	8.79928i	0.131372	+	0.285186i
$953$	−14.8344	+	8.56462i	−0.480532	+	0.277435i	−0.720638	−	0.693311i	$-0.756151\pi$
$953$	−14.8344	+	8.56462i	−0.480532	+	0.277435i	0.240106	+	0.970747i	$0.422818\pi$
$954$	0.181615	+	0.470428i	0.00588001	+	0.0152307i
$955$	9.88597	+	5.70767i	0.319903	+	0.184696i
$956$	17.4480	+	20.7938i	0.564310	+	0.672518i
$957$	3.76322	−	5.48677i	0.121648	−	0.177362i
$958$	−0.628169	−	0.110763i	−0.0202952	−	0.00357860i
$959$	−24.6632	+	17.0988i	−0.796415	+	0.552150i
$960$	−5.32467	−	11.1359i	−0.171853	−	0.359411i
$961$	−13.3344	+	11.1889i	−0.430142	+	0.360932i
$962$	1.71651	−	2.97309i	0.0553426	−	0.0958563i
$963$	−5.41779	−	27.5898i	−0.174586	−	0.889070i
$964$	−0.843853	+	0.487199i	−0.0271787	+	0.0156916i
$965$	9.81244	+	3.57144i	0.315874	+	0.114969i
$966$	2.58155	−	4.52378i	0.0830600	−	0.145550i
$967$	−38.3718	−	32.1978i	−1.23396	−	1.03541i	−0.997972	−	0.0636544i	$-0.979724\pi$
$967$	−38.3718	−	32.1978i	−1.23396	−	1.03541i	−0.235983	−	0.971757i	$-0.575831\pi$
$968$	1.88985	+	5.19233i	0.0607422	+	0.166888i
$969$	−40.9341	+	3.98108i	−1.31499	+	0.127891i
$970$	0.0272730	+	0.154673i	0.000875685	+	0.00496625i
$971$	38.1874			1.22549			0.612747	−	0.790279i	$-0.290065\pi$
$971$	38.1874			1.22549			0.612747	+	0.790279i	$0.290065\pi$
$972$	−22.8914	−	20.7753i	−0.734241	−	0.666367i
$973$	24.7722	+	25.0039i	0.794161	+	0.801588i
$974$	−0.249327	+	0.0439631i	−0.00798896	+	0.00140867i
$975$	23.1288	−	2.24941i	0.740714	−	0.0720388i
$976$	−6.71005	−	18.4357i	−0.214784	−	0.590113i
$977$	−29.1076	+	34.6891i	−0.931234	+	1.10980i	0.0625018	+	0.998045i	$0.480092\pi$
$977$	−29.1076	+	34.6891i	−0.931234	+	1.10980i	−0.993736	+	0.111756i	$0.964352\pi$
$978$	0.604545	+	2.17184i	0.0193312	+	0.0694477i
$979$	2.50785	−	6.89026i	0.0801513	−	0.220214i
$980$	−11.3376	+	6.40580i	−0.362166	+	0.204626i
$981$	−1.48574	+	0.291753i	−0.0474360	+	0.00931497i
$982$	−1.33473	+	2.31182i	−0.0425930	+	0.0737732i
$983$	−29.7743	+	24.9836i	−0.949652	+	0.796852i	−0.979239	−	0.202710i	$-0.935025\pi$
$983$	−29.7743	+	24.9836i	−0.949652	+	0.796852i	0.0295873	+	0.999562i	$0.490581\pi$
$984$	−0.367797	+	0.175863i	−0.0117249	+	0.00560630i
$985$	17.2972	+	3.04997i	0.551136	+	0.0971801i
$986$	−1.06109	+	6.01775i	−0.0337921	+	0.191644i
$987$	6.46183	+	35.5987i	0.205682	+	1.13312i
$988$	−16.6185	+	13.9446i	−0.528705	+	0.443636i
$989$	−19.8872	−	11.4819i	−0.632378	−	0.365103i
$990$	0.0761848	+	0.197337i	0.00242131	+	0.00627179i
$991$	7.00357	+	12.1305i	0.222476	+	0.385339i	0.955559	−	0.294799i	$-0.0952528\pi$
$991$	7.00357	+	12.1305i	0.222476	+	0.385339i	−0.733083	+	0.680139i	$0.761919\pi$
$992$	10.0893	+	3.67220i	0.320335	+	0.116592i
$993$	−7.54700	+	29.2978i	−0.239497	+	0.929738i
$994$	3.86839	−	0.320307i	0.122698	−	0.0101595i
$995$	−3.62882	−	9.97010i	−0.115041	−	0.316073i
$996$	23.8783	−	17.0667i	0.756612	−	0.540780i
$997$	−25.7904	+	4.54754i	−0.816790	+	0.144022i	−0.566408	−	0.824125i	$-0.691667\pi$
$997$	−25.7904	+	4.54754i	−0.816790	+	0.144022i	−0.250382	+	0.968147i	$0.580556\pi$
$998$		−	0.522372i		−	0.0165354i
$999$	−40.9821	−	9.71446i	−1.29662	−	0.307352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.41.14	yes	132
3.2	odd	2		567.2.be.a.314.9		132
7.6	odd	2	inner	189.2.be.a.41.13	✓	132
21.20	even	2		567.2.be.a.314.10		132
27.2	odd	18	inner	189.2.be.a.83.13	yes	132
27.25	even	9		567.2.be.a.251.10		132
189.83	even	18	inner	189.2.be.a.83.14	yes	132
189.160	odd	18		567.2.be.a.251.9		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.41.13	✓	132	7.6	odd	2	inner
189.2.be.a.41.14	yes	132	1.1	even	1	trivial
189.2.be.a.83.13	yes	132	27.2	odd	18	inner
189.2.be.a.83.14	yes	132	189.83	even	18	inner
567.2.be.a.251.9		132	189.160	odd	18
567.2.be.a.251.10		132	27.25	even	9
567.2.be.a.314.9		132	3.2	odd	2
567.2.be.a.314.10		132	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.128087 - 0.0225853i) q^{2} +(0.167661 + 1.72392i) q^{3} +(-1.86349 + 0.678255i) q^{4} +(0.718615 + 0.602989i) q^{5} +(0.0604104 + 0.217025i) q^{6} +(-2.40304 + 1.10697i) q^{7} +(-0.448647 + 0.259026i) q^{8} +(-2.94378 + 0.578068i) q^{9} +O(q^{10})\)	\(q+(0.128087 - 0.0225853i) q^{2} +(0.167661 + 1.72392i) q^{3} +(-1.86349 + 0.678255i) q^{4} +(0.718615 + 0.602989i) q^{5} +(0.0604104 + 0.217025i) q^{6} +(-2.40304 + 1.10697i) q^{7} +(-0.448647 + 0.259026i) q^{8} +(-2.94378 + 0.578068i) q^{9} +(0.105664 + 0.0610052i) q^{10} +(-0.371473 - 0.442704i) q^{11} +(-1.48169 - 3.09878i) q^{12} +(3.20694 + 0.565471i) q^{13} +(-0.282798 + 0.196062i) q^{14} +(-0.919020 + 1.33993i) q^{15} +(2.98664 - 2.50609i) q^{16} +(-3.53412 + 6.12128i) q^{17} +(-0.364005 + 0.140529i) q^{18} +(2.90929 - 1.67968i) q^{19} +(-1.74811 - 0.636260i) q^{20} +(-2.31122 - 3.95705i) q^{21} +(-0.0575796 - 0.0483150i) q^{22} +(2.98885 + 8.21179i) q^{23} +(-0.521761 - 0.730002i) q^{24} +(-0.715430 - 4.05740i) q^{25} +0.423540 q^{26} +(-1.49010 - 4.97791i) q^{27} +(3.72724 - 3.69270i) q^{28} +(6.54588 - 1.15422i) q^{29} +(-0.0874521 + 0.192384i) q^{30} +(2.37961 + 6.53791i) q^{31} +(0.991947 - 1.18216i) q^{32} +(0.700904 - 0.714613i) q^{33} +(-0.314426 + 0.863877i) q^{34} +(-2.39435 - 0.653523i) q^{35} +(5.09362 - 3.07385i) q^{36} +(4.05278 - 7.01962i) q^{37} +(0.334708 - 0.280853i) q^{38} +(-0.437145 + 5.62331i) q^{39} +(-0.478595 - 0.0843891i) q^{40} +(0.0788958 - 0.447440i) q^{41} +(-0.385409 - 0.454648i) q^{42} +(-2.01301 + 1.68912i) q^{43} +(0.992502 + 0.573021i) q^{44} +(-2.46401 - 1.35966i) q^{45} +(0.568299 + 0.984323i) q^{46} +(-7.41908 - 2.70032i) q^{47} +(4.82104 + 4.72855i) q^{48} +(4.54923 - 5.32020i) q^{49} +(-0.183275 - 0.503544i) q^{50} +(-11.1451 - 5.06623i) q^{51} +(-6.35964 + 1.12138i) q^{52} -1.29237i q^{53} +(-0.303290 - 0.603953i) q^{54} -0.542128i q^{55} +(0.791383 - 1.11909i) q^{56} +(3.38341 + 4.73376i) q^{57} +(0.812376 - 0.295681i) q^{58} +(5.65096 + 4.74172i) q^{59} +(0.803770 - 3.12027i) q^{60} +(1.72106 - 4.72858i) q^{61} +(0.452458 + 0.783680i) q^{62} +(6.43412 - 4.64780i) q^{63} +(-3.79843 + 6.57908i) q^{64} +(1.96358 + 2.34011i) q^{65} +(0.0736372 - 0.107363i) q^{66} +(-0.858343 + 4.86791i) q^{67} +(2.43401 - 13.8040i) q^{68} +(-13.6553 + 6.52932i) q^{69} +(-0.321446 - 0.0296310i) q^{70} +(-9.76878 - 5.64001i) q^{71} +(1.17098 - 1.02187i) q^{72} +(2.28636 - 1.32003i) q^{73} +(0.360570 - 0.990657i) q^{74} +(6.87468 - 1.91361i) q^{75} +(-4.28219 + 5.10331i) q^{76} +(1.38273 + 0.652627i) q^{77} +(0.0710112 + 0.730148i) q^{78} +(-0.885790 - 5.02356i) q^{79} +3.65739 q^{80} +(8.33168 - 3.40341i) q^{81} -0.0590933i q^{82} +(1.48382 + 8.41518i) q^{83} +(6.99083 + 5.80632i) q^{84} +(-6.23074 + 2.26780i) q^{85} +(-0.219692 + 0.261819i) q^{86} +(3.08726 + 11.0910i) q^{87} +(0.281332 + 0.102397i) q^{88} +(6.34396 + 10.9881i) q^{89} +(-0.346317 - 0.118505i) q^{90} +(-8.33238 + 2.19114i) q^{91} +(-11.1394 - 13.2754i) q^{92} +(-10.8719 + 5.19840i) q^{93} +(-1.01128 - 0.178316i) q^{94} +(3.10349 + 0.547229i) q^{95} +(2.20425 + 1.51183i) q^{96} +(0.827435 + 0.986099i) q^{97} +(0.462541 - 0.784196i) q^{98} +(1.34945 + 1.08849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

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