LMFDB - Embedded newform 189.2.w.a.25.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.20
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03199 - 0.739583i) q^{2} +(-0.528499 - 1.64945i) q^{3} +(2.04991 - 1.72008i) q^{4} +(3.15692 + 1.14902i) q^{5} +(-2.29381 - 2.96080i) q^{6} +(-2.22776 + 1.42726i) q^{7} +(0.730849 - 1.26587i) q^{8} +(-2.44138 + 1.74347i) q^{9} +O(q^{10})$	\(q+(2.03199 - 0.739583i) q^{2} +(-0.528499 - 1.64945i) q^{3} +(2.04991 - 1.72008i) q^{4} +(3.15692 + 1.14902i) q^{5} +(-2.29381 - 2.96080i) q^{6} +(-2.22776 + 1.42726i) q^{7} +(0.730849 - 1.26587i) q^{8} +(-2.44138 + 1.74347i) q^{9} +7.26462 q^{10} +(-4.33921 + 1.57934i) q^{11} +(-3.92055 - 2.47216i) q^{12} +(-0.768974 - 4.36107i) q^{13} +(-3.47120 + 4.54780i) q^{14} +(0.226832 - 5.81444i) q^{15} +(-0.380489 + 2.15786i) q^{16} +2.95237 q^{17} +(-3.67141 + 5.34831i) q^{18} -0.839101 q^{19} +(8.44779 - 3.07474i) q^{20} +(3.53157 + 2.92027i) q^{21} +(-7.64917 + 6.41842i) q^{22} +(-0.430416 - 2.44101i) q^{23} +(-2.47424 - 0.536490i) q^{24} +(4.81565 + 4.04081i) q^{25} +(-4.78792 - 8.29293i) q^{26} +(4.16603 + 3.10551i) q^{27} +(-2.11170 + 6.75767i) q^{28} +(0.980067 - 5.55823i) q^{29} +(-3.83934 - 11.9826i) q^{30} +(2.29231 - 1.92348i) q^{31} +(1.33041 + 7.54514i) q^{32} +(4.89832 + 6.32263i) q^{33} +(5.99918 - 2.18352i) q^{34} +(-8.67282 + 1.94601i) q^{35} +(-2.00570 + 7.77329i) q^{36} +(-3.93660 + 6.81839i) q^{37} +(-1.70504 + 0.620585i) q^{38} +(-6.78697 + 3.57321i) q^{39} +(3.76174 - 3.15648i) q^{40} +(-0.459534 - 2.60615i) q^{41} +(9.33590 + 3.32207i) q^{42} +(6.80164 + 5.70725i) q^{43} +(-6.17838 + 10.7013i) q^{44} +(-9.71051 + 2.69878i) q^{45} +(-2.67993 - 4.64178i) q^{46} +(-1.04660 - 0.878199i) q^{47} +(3.76038 - 0.512829i) q^{48} +(2.92583 - 6.35921i) q^{49} +(12.7739 + 4.64931i) q^{50} +(-1.56032 - 4.86979i) q^{51} +(-9.07769 - 7.61709i) q^{52} +(5.27760 - 9.14106i) q^{53} +(10.7621 + 3.22925i) q^{54} -15.5132 q^{55} +(0.178572 + 3.86317i) q^{56} +(0.443464 + 1.38406i) q^{57} +(-2.11929 - 12.0191i) q^{58} +(-1.40366 - 7.96053i) q^{59} +(-9.53629 - 12.3092i) q^{60} +(5.67839 + 4.76474i) q^{61} +(3.23538 - 5.60384i) q^{62} +(2.95042 - 7.36852i) q^{63} +(6.09249 + 10.5525i) q^{64} +(2.58339 - 14.6511i) q^{65} +(14.6294 + 9.22481i) q^{66} +(-1.96099 - 0.713741i) q^{67} +(6.05208 - 5.07829i) q^{68} +(-3.79886 + 2.00002i) q^{69} +(-16.1838 + 10.3685i) q^{70} +(-2.56447 - 4.44179i) q^{71} +(0.422718 + 4.36467i) q^{72} +(1.30884 + 2.26698i) q^{73} +(-2.95636 + 16.7663i) q^{74} +(4.12005 - 10.0787i) q^{75} +(-1.72008 + 1.44332i) q^{76} +(7.41258 - 9.71160i) q^{77} +(-11.1484 + 12.2802i) q^{78} +(-8.45408 + 3.07703i) q^{79} +(-3.68061 + 6.37500i) q^{80} +(2.92065 - 8.51292i) q^{81} +(-2.86123 - 4.95580i) q^{82} +(-1.36872 + 7.76242i) q^{83} +(12.2625 - 0.0882838i) q^{84} +(9.32038 + 3.39234i) q^{85} +(18.0418 + 6.56670i) q^{86} +(-9.68600 + 1.32095i) q^{87} +(-1.17207 + 6.64713i) q^{88} -9.36279 q^{89} +(-17.7357 + 12.6656i) q^{90} +(7.93749 + 8.61789i) q^{91} +(-5.08104 - 4.26350i) q^{92} +(-4.38416 - 2.76450i) q^{93} +(-2.77617 - 1.01044i) q^{94} +(-2.64897 - 0.964148i) q^{95} +(11.7422 - 6.18205i) q^{96} +(-8.71278 - 7.31089i) q^{97} +(1.24209 - 15.0857i) q^{98} +(7.84012 - 11.4210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.03199	−	0.739583i	1.43683	−	0.522964i	0.497952	−	0.867205i	$-0.334086\pi$
$2$	2.03199	−	0.739583i	1.43683	−	0.522964i	0.938882	+	0.344240i	$0.111864\pi$
$3$	−0.528499	−	1.64945i	−0.305129	−	0.952311i
$3$	−0.528499	−	1.64945i	−0.305129	−	0.952311i
$4$	2.04991	−	1.72008i	1.02495	−	0.860038i
$5$	3.15692	+	1.14902i	1.41182	+	0.513859i	0.931662	−	0.363325i	$-0.118359\pi$
$5$	3.15692	+	1.14902i	1.41182	+	0.513859i	0.480154	+	0.877184i	$0.340581\pi$
$6$	−2.29381	−	2.96080i	−0.936444	−	1.20874i
$7$	−2.22776	+	1.42726i	−0.842014	+	0.539455i
$7$	−2.22776	+	1.42726i	−0.842014	+	0.539455i
$8$	0.730849	−	1.26587i	0.258394	−	0.447552i
$9$	−2.44138	+	1.74347i	−0.813793	+	0.581155i
$10$	7.26462			2.29727
$11$	−4.33921	+	1.57934i	−1.30832	+	0.476190i	−0.899698	−	0.436513i	$-0.856213\pi$
$11$	−4.33921	+	1.57934i	−1.30832	+	0.476190i	−0.408623	+	0.912703i	$0.633991\pi$
$12$	−3.92055	−	2.47216i	−1.13177	−	0.713652i
$13$	−0.768974	−	4.36107i	−0.213275	−	1.20954i	−0.883875	−	0.467724i	$-0.845074\pi$
$13$	−0.768974	−	4.36107i	−0.213275	−	1.20954i	0.670600	−	0.741820i	$-0.266037\pi$
$14$	−3.47120	+	4.54780i	−0.927718	+	1.21545i
$15$	0.226832	−	5.81444i	0.0585678	−	1.50128i
$16$	−0.380489	+	2.15786i	−0.0951224	+	0.539466i
$17$	2.95237			0.716054			0.358027	−	0.933711i	$-0.383450\pi$
$17$	2.95237			0.716054			0.358027	+	0.933711i	$0.383450\pi$
$18$	−3.67141	+	5.34831i	−0.865361	+	1.26061i
$19$	−0.839101			−0.192503			−0.0962515	−	0.995357i	$-0.530685\pi$
$19$	−0.839101			−0.192503			−0.0962515	+	0.995357i	$0.530685\pi$
$20$	8.44779	−	3.07474i	1.88898	−	0.687534i
$21$	3.53157	+	2.92027i	0.770652	+	0.637256i
$22$	−7.64917	+	6.41842i	−1.63081	+	1.36841i
$23$	−0.430416	−	2.44101i	−0.0897480	−	0.508986i	−0.996231	−	0.0867432i	$-0.972354\pi$
$23$	−0.430416	−	2.44101i	−0.0897480	−	0.508986i	0.906483	−	0.422243i	$-0.138757\pi$
$24$	−2.47424	−	0.536490i	−0.505052	−	0.109511i
$25$	4.81565	+	4.04081i	0.963130	+	0.808162i
$26$	−4.78792	−	8.29293i	−0.938989	−	1.62638i
$27$	4.16603	+	3.10551i	0.801752	+	0.597657i
$28$	−2.11170	+	6.75767i	−0.399073	+	1.27708i
$29$	0.980067	−	5.55823i	0.181994	−	1.03214i	−0.747764	−	0.663965i	$-0.768872\pi$
$29$	0.980067	−	5.55823i	0.181994	−	1.03214i	0.929757	−	0.368173i	$-0.120017\pi$
$30$	−3.83934	−	11.9826i	−0.700965	−	2.18772i
$31$	2.29231	−	1.92348i	0.411711	−	0.345467i	−0.413288	−	0.910600i	$-0.635620\pi$
$31$	2.29231	−	1.92348i	0.411711	−	0.345467i	0.824999	+	0.565134i	$0.191175\pi$
$32$	1.33041	+	7.54514i	0.235186	+	1.33381i
$33$	4.89832	+	6.32263i	0.852688	+	1.10063i
$34$	5.99918	−	2.18352i	1.02885	−	0.374471i
$35$	−8.67282	+	1.94601i	−1.46597	+	0.328935i
$36$	−2.00570	+	7.77329i	−0.334284	+	1.29555i
$37$	−3.93660	+	6.81839i	−0.647173	+	1.12094i	0.336622	+	0.941640i	$0.390716\pi$
$37$	−3.93660	+	6.81839i	−0.647173	+	1.12094i	−0.983795	+	0.179297i	$0.942618\pi$
$38$	−1.70504	+	0.620585i	−0.276595	+	0.100672i
$39$	−6.78697	+	3.57321i	−1.08679	+	0.572171i
$40$	3.76174	−	3.15648i	0.594784	−	0.499083i
$41$	−0.459534	−	2.60615i	−0.0717671	−	0.407012i	−0.999435	−	0.0336057i	$-0.989301\pi$
$41$	−0.459534	−	2.60615i	−0.0717671	−	0.407012i	0.927668	−	0.373406i	$-0.121810\pi$
$42$	9.33590	+	3.32207i	1.44056	+	0.512607i
$43$	6.80164	+	5.70725i	1.03724	+	0.870348i	0.991695	−	0.128614i	$-0.0410529\pi$
$43$	6.80164	+	5.70725i	1.03724	+	0.870348i	0.0455457	+	0.998962i	$0.485497\pi$
$44$	−6.17838	+	10.7013i	−0.931426	+	1.61328i
$45$	−9.71051	+	2.69878i	−1.44756	+	0.402310i
$46$	−2.67993	−	4.64178i	−0.395135	−	0.684393i
$47$	−1.04660	−	0.878199i	−0.152662	−	0.128098i	0.563258	−	0.826281i	$-0.309548\pi$
$47$	−1.04660	−	0.878199i	−0.152662	−	0.128098i	−0.715920	+	0.698183i	$0.753992\pi$
$48$	3.76038	−	0.512829i	0.542764	−	0.0740205i
$49$	2.92583	−	6.35921i	0.417976	−	0.908458i
$50$	12.7739	+	4.64931i	1.80650	+	0.657511i
$51$	−1.56032	−	4.86979i	−0.218489	−	0.681907i
$52$	−9.07769	−	7.61709i	−1.25885	−	1.05630i
$53$	5.27760	−	9.14106i	0.724934	−	1.25562i	−0.234068	−	0.972220i	$-0.575204\pi$
$53$	5.27760	−	9.14106i	0.724934	−	1.25562i	0.959001	−	0.283402i	$-0.0914629\pi$
$54$	10.7621	+	3.22925i	1.46454	+	0.439445i
$55$	−15.5132			−2.09180
$56$	0.178572	+	3.86317i	0.0238627	+	0.516237i
$57$	0.443464	+	1.38406i	0.0587382	+	0.183323i
$58$	−2.11929	−	12.0191i	−0.278277	−	1.57819i
$59$	−1.40366	−	7.96053i	−0.182740	−	1.03637i	−0.928824	−	0.370520i	$-0.879179\pi$
$59$	−1.40366	−	7.96053i	−0.182740	−	1.03637i	0.746084	−	0.665852i	$-0.231932\pi$
$60$	−9.53629	−	12.3092i	−1.23113	−	1.58911i
$61$	5.67839	+	4.76474i	0.727044	+	0.610062i	0.929324	−	0.369265i	$-0.120391\pi$
$61$	5.67839	+	4.76474i	0.727044	+	0.610062i	−0.202280	+	0.979328i	$0.564835\pi$
$62$	3.23538	−	5.60384i	0.410893	−	0.711688i
$63$	2.95042	−	7.36852i	0.371718	−	0.928346i
$64$	6.09249	+	10.5525i	0.761561	+	1.31906i
$65$	2.58339	−	14.6511i	0.320430	−	1.81725i
$66$	14.6294	+	9.22481i	1.80076	+	1.13550i
$67$	−1.96099	−	0.713741i	−0.239573	−	0.0871973i	0.219444	−	0.975625i	$-0.429576\pi$
$67$	−1.96099	−	0.713741i	−0.239573	−	0.0871973i	−0.459016	+	0.888428i	$0.651798\pi$
$68$	6.05208	−	5.07829i	0.733922	−	0.615834i
$69$	−3.79886	+	2.00002i	−0.457328	+	0.240774i
$70$	−16.1838	+	10.3685i	−1.93434	+	1.23928i
$71$	−2.56447	−	4.44179i	−0.304347	−	0.527144i	0.672769	−	0.739853i	$-0.265105\pi$
$71$	−2.56447	−	4.44179i	−0.304347	−	0.527144i	−0.977116	+	0.212709i	$0.931771\pi$
$72$	0.422718	+	4.36467i	0.0498178	+	0.514382i
$73$	1.30884	+	2.26698i	0.153188	+	0.265330i	0.932398	−	0.361434i	$-0.117713\pi$
$73$	1.30884	+	2.26698i	0.153188	+	0.265330i	−0.779210	+	0.626763i	$0.784379\pi$
$74$	−2.95636	+	16.7663i	−0.343670	+	1.94905i
$75$	4.12005	−	10.0787i	0.475743	−	1.16379i
$76$	−1.72008	+	1.44332i	−0.197307	+	0.165560i
$77$	7.41258	−	9.71160i	0.844742	−	1.10674i
$78$	−11.1484	+	12.2802i	−1.26230	+	1.39046i
$79$	−8.45408	+	3.07703i	−0.951158	+	0.346193i	−0.770563	−	0.637364i	$-0.780025\pi$
$79$	−8.45408	+	3.07703i	−0.951158	+	0.346193i	−0.180595	+	0.983557i	$0.557802\pi$
$80$	−3.68061	+	6.37500i	−0.411505	+	0.712747i
$81$	2.92065	−	8.51292i	0.324517	−	0.945880i
$82$	−2.86123	−	4.95580i	−0.315970	−	0.547276i
$83$	−1.36872	+	7.76242i	−0.150237	+	0.852036i	0.812775	+	0.582578i	$0.197956\pi$
$83$	−1.36872	+	7.76242i	−0.150237	+	0.852036i	−0.963012	+	0.269459i	$0.913155\pi$
$84$	12.2625	−	0.0882838i	1.33795	−	0.00963255i
$85$	9.32038	+	3.39234i	1.01094	+	0.367951i
$86$	18.0418	+	6.56670i	1.94550	+	0.708105i
$87$	−9.68600	+	1.32095i	−1.03845	+	0.141620i
$88$	−1.17207	+	6.64713i	−0.124943	+	0.708586i
$89$	−9.36279			−0.992454			−0.496227	−	0.868193i	$-0.665282\pi$
$89$	−9.36279			−0.992454			−0.496227	+	0.868193i	$0.665282\pi$
$90$	−17.7357	+	12.6656i	−1.86951	+	1.33507i
$91$	7.93749	+	8.61789i	0.832075	+	0.903400i
$92$	−5.08104	−	4.26350i	−0.529735	−	0.444500i
$93$	−4.38416	−	2.76450i	−0.454617	−	0.286665i
$94$	−2.77617	−	1.01044i	−0.286340	−	0.104219i
$95$	−2.64897	−	0.964148i	−0.271779	−	0.0989195i
$96$	11.7422	−	6.18205i	1.19844	−	0.630952i
$97$	−8.71278	−	7.31089i	−0.884649	−	0.742308i	0.0824809	−	0.996593i	$-0.473716\pi$
$97$	−8.71278	−	7.31089i	−0.884649	−	0.742308i	−0.967130	+	0.254284i	$0.918160\pi$
$98$	1.24209	−	15.0857i	0.125470	−	1.52389i
$99$	7.84012	−	11.4210i	0.787962	−	1.14786i
$100$	16.8221			1.68221
$101$	−1.61803	+	9.17628i	−0.161000	+	0.913074i	0.792094	+	0.610399i	$0.208991\pi$
$101$	−1.61803	+	9.17628i	−0.161000	+	0.913074i	−0.953094	+	0.302675i	$0.902120\pi$
$102$	−6.77217	−	8.74136i	−0.670545	−	0.865524i
$103$	6.29019	+	2.28944i	0.619791	+	0.225585i	0.632782	−	0.774330i	$-0.281913\pi$
$103$	6.29019	+	2.28944i	0.619791	+	0.225585i	−0.0129911	+	0.999916i	$0.504135\pi$
$104$	−6.08254	−	2.21386i	−0.596442	−	0.217087i
$105$	7.79342	+	13.2769i	0.760560	+	1.29570i
$106$	3.96344	−	22.4778i	0.384963	−	2.18323i
$107$	3.06775	+	5.31350i	0.296571	+	0.513676i	0.975349	−	0.220667i	$-0.0708236\pi$
$107$	3.06775	+	5.31350i	0.296571	+	0.513676i	−0.678778	+	0.734343i	$0.737490\pi$
$108$	13.8817	−	0.799867i	1.33577	−	0.0769672i
$109$	−7.83322	+	13.5675i	−0.750286	+	1.29953i	0.197398	+	0.980324i	$0.436751\pi$
$109$	−7.83322	+	13.5675i	−0.750286	+	1.29953i	−0.947684	+	0.319210i	$0.896582\pi$
$110$	−31.5227	+	11.4733i	−3.00557	+	1.09394i
$111$	13.3271	+	2.88972i	1.26495	+	0.274280i
$112$	−2.23220	−	5.35026i	−0.210923	−	0.505552i
$113$	−7.99538	+	6.70892i	−0.752142	+	0.631122i	−0.936069	−	0.351818i	$-0.885564\pi$
$113$	−7.99538	+	6.70892i	−0.752142	+	0.631122i	0.183926	+	0.982940i	$0.441119\pi$
$114$	1.92474	+	2.48441i	0.180268	+	0.232686i
$115$	1.44599	−	8.20063i	0.134840	−	0.764713i
$116$	−7.55154	−	13.0796i	−0.701143	−	1.21441i
$117$	9.48073	+	9.30634i	0.876494	+	0.860372i
$118$	−8.73969	−	15.1376i	−0.804553	−	1.39353i
$119$	−6.57717	+	4.21381i	−0.602928	+	0.386279i
$120$	−7.19453	−	4.53662i	−0.656768	−	0.414135i
$121$	7.90793	−	6.63554i	0.718903	−	0.603231i
$122$	15.0624	+	5.48225i	1.36368	+	0.496339i
$123$	−4.05585	+	2.13532i	−0.365703	+	0.192536i
$124$	1.39050	−	7.88589i	0.124870	−	0.708174i
$125$	2.16082	+	3.74265i	0.193270	+	0.334753i
$126$	0.545582	−	17.1548i	0.0486043	−	1.52827i
$127$	0.0905653	−	0.156864i	0.00803637	−	0.0139194i	−0.861979	−	0.506944i	$-0.830775\pi$
$127$	0.0905653	−	0.156864i	0.00803637	−	0.0139194i	0.870016	+	0.493024i	$0.164109\pi$
$128$	8.44618	+	7.08718i	0.746544	+	0.626424i
$129$	5.81918	−	14.2352i	0.512350	−	1.25334i
$130$	−5.58631	−	31.6815i	−0.489952	−	2.77865i
$131$	−2.41431	−	13.6922i	−0.210939	−	1.19630i	−0.887816	−	0.460199i	$-0.847778\pi$
$131$	−2.41431	−	13.6922i	−0.210939	−	1.19630i	0.676876	−	0.736097i	$-0.263333\pi$
$132$	20.9165	+	4.53533i	1.82055	+	0.394750i
$133$	1.86932	−	1.19762i	0.162090	−	0.103847i
$134$	−4.51257			−0.389827
$135$	9.58349	+	14.5907i	0.824816	+	1.25577i
$136$	2.15774	−	3.73731i	0.185024	−	0.320471i
$137$	0.125556	+	0.105354i	0.0107269	+	0.00900098i	0.648135	−	0.761525i	$-0.275549\pi$
$137$	0.125556	+	0.105354i	0.0107269	+	0.00900098i	−0.637408	+	0.770526i	$0.719994\pi$
$138$	−6.24005	+	6.87359i	−0.531188	+	0.585119i
$139$	1.63872	+	0.596444i	0.138994	+	0.0505897i	0.410581	−	0.911824i	$-0.365326\pi$
$139$	1.63872	+	0.596444i	0.138994	+	0.0505897i	−0.271586	+	0.962414i	$0.587548\pi$
$140$	−14.4312	+	18.9070i	−1.21966	+	1.59794i
$141$	−0.895421	+	2.19044i	−0.0754081	+	0.184468i
$142$	−8.49605	−	7.12903i	−0.712973	−	0.598255i
$143$	10.2244	+	17.7091i	0.855005	+	1.48091i
$144$	−2.83324	−	5.93153i	−0.236103	−	0.494294i
$145$	9.48053	−	16.4208i	0.787316	−	1.36367i
$146$	4.33617	+	3.63848i	0.358864	+	0.301123i
$147$	−12.0355	−	1.46518i	−0.992671	−	0.120846i
$148$	3.65849	+	20.7483i	0.300726	+	1.70550i
$149$	−8.11180	+	6.80661i	−0.664544	+	0.557619i	−0.911445	−	0.411422i	$-0.865032\pi$
$149$	−8.11180	+	6.80661i	−0.664544	+	0.557619i	0.246901	+	0.969041i	$0.420588\pi$
$150$	0.917833	−	23.5270i	0.0749407	−	1.92097i
$151$	22.4583	−	8.17415i	1.82763	−	0.665203i	0.834103	−	0.551609i	$-0.185986\pi$
$151$	22.4583	−	8.17415i	1.82763	−	0.665203i	0.993527	−	0.113594i	$-0.0362363\pi$
$152$	−0.613256	+	1.06219i	−0.0497417	+	0.0861551i
$153$	−7.20785	+	5.14735i	−0.582720	+	0.416139i
$154$	7.87974	−	25.2161i	0.634967	−	2.03197i
$155$	9.44675	−	3.43834i	0.758782	−	0.276174i
$156$	−7.76647	+	18.9988i	−0.621815	+	1.52112i
$157$	3.40588	+	19.3157i	0.271819	+	1.54156i	0.748889	+	0.662696i	$0.230588\pi$
$157$	3.40588	+	19.3157i	0.271819	+	1.54156i	−0.477070	+	0.878865i	$0.658301\pi$
$158$	−14.9029	+	12.5050i	−1.18561	+	0.994843i
$159$	−17.8669	−	3.87410i	−1.41694	−	0.307236i
$160$	−4.46955	+	25.3481i	−0.353349	+	2.00394i
$161$	4.44283	+	4.82367i	0.350144	+	0.380158i
$162$	−0.361275	−	19.4582i	−0.0283845	−	1.52878i
$163$	3.91324	+	6.77793i	0.306509	+	0.530889i	0.977596	−	0.210490i	$-0.0675058\pi$
$163$	3.91324	+	6.77793i	0.306509	+	0.530889i	−0.671087	+	0.741378i	$0.734173\pi$
$164$	−5.42477	−	4.55192i	−0.423603	−	0.355445i
$165$	8.19872	+	25.5883i	0.638270	+	1.99205i
$166$	2.95973	+	16.7854i	0.229719	+	1.30280i
$167$	12.9718	−	10.8846i	1.00379	−	0.842279i	0.0162837	−	0.999867i	$-0.494817\pi$
$167$	12.9718	−	10.8846i	1.00379	−	0.842279i	0.987505	+	0.157589i	$0.0503721\pi$
$168$	6.27773	−	2.33622i	0.484337	−	0.180244i
$169$	−6.21161	+	2.26084i	−0.477816	+	0.173911i
$170$	21.4478			1.64497
$171$	2.04856	−	1.46294i	0.156658	−	0.111874i
$172$	23.7596			1.81165
$173$	1.23851	−	7.02395i	0.0941623	−	0.534021i	−0.900839	−	0.434154i	$-0.857047\pi$
$173$	1.23851	−	7.02395i	0.0941623	−	0.534021i	0.995001	−	0.0998666i	$-0.0318416\pi$
$174$	−18.7049	+	9.84776i	−1.41801	+	0.746556i
$175$	−16.4954	−	2.12875i	−1.24694	−	0.160918i
$176$	−1.75698	−	9.96434i	−0.132438	−	0.751091i
$177$	−12.3887	+	6.52239i	−0.931189	+	0.490253i
$178$	−19.0251	+	6.92456i	−1.42599	+	0.519018i
$179$	4.54332			0.339583			0.169792	−	0.985480i	$-0.445690\pi$
$179$	4.54332			0.339583			0.169792	+	0.985480i	$0.445690\pi$
$180$	−15.2635	+	22.2350i	−1.13768	+	1.65730i
$181$	4.52457	−	7.83678i	0.336308	−	0.582503i	−0.647427	−	0.762128i	$-0.724155\pi$
$181$	4.52457	−	7.83678i	0.336308	−	0.582503i	0.983735	+	0.179624i	$0.0574882\pi$
$182$	22.5025	+	11.6410i	1.66800	+	0.862889i
$183$	4.85818	−	11.8844i	0.359127	−	0.878520i
$184$	−3.40457	−	1.23916i	−0.250988	−	0.0913522i
$185$	−20.2620	+	17.0019i	−1.48969	+	1.25000i
$186$	−10.9531	−	2.37498i	−0.803124	−	0.174142i
$187$	−12.8109	+	4.66280i	−0.936829	+	0.340978i
$188$	−3.65599			−0.266641
$189$	−13.7133	−	0.972318i	−0.997496	−	0.0707257i
$190$	−6.09575			−0.442232
$191$	−3.09289	+	1.12572i	−0.223794	+	0.0814542i	−0.451483	−	0.892280i	$-0.649105\pi$
$191$	−3.09289	+	1.12572i	−0.223794	+	0.0814542i	0.227690	+	0.973734i	$0.426883\pi$
$192$	14.1860	−	15.6263i	1.02378	−	1.12773i
$193$	8.65087	−	7.25894i	0.622703	−	0.522510i	−0.275949	−	0.961172i	$-0.588992\pi$
$193$	8.65087	−	7.25894i	0.622703	−	0.522510i	0.898652	+	0.438662i	$0.144548\pi$
$194$	−23.1113	−	8.41182i	−1.65929	−	0.603933i
$195$	−25.5316	+	3.48192i	−1.82836	+	0.249346i
$196$	−4.94064	−	18.0684i	−0.352903	−	1.29060i
$197$	−8.04334	+	13.9315i	−0.573064	+	0.992576i	0.423185	+	0.906043i	$0.360912\pi$
$197$	−8.04334	+	13.9315i	−0.573064	+	0.992576i	−0.996249	+	0.0865328i	$0.972421\pi$
$198$	7.48423	−	29.0058i	0.531881	−	2.06136i
$199$	−5.07815			−0.359980			−0.179990	−	0.983668i	$-0.557607\pi$
$199$	−5.07815			−0.359980			−0.179990	+	0.983668i	$0.557607\pi$
$200$	8.63465	−	3.14275i	0.610562	−	0.222226i
$201$	−0.140902	+	3.61176i	−0.00993843	+	0.254754i
$202$	3.49881	+	19.8428i	0.246176	+	1.39613i
$203$	5.74972	+	13.7812i	0.403551	+	0.967252i
$204$	−11.5749	−	7.29873i	−0.810406	−	0.511013i
$205$	1.54381	−	8.75540i	0.107825	−	0.611504i
$206$	14.4748			1.00851
$207$	5.30663	+	5.20902i	0.368836	+	0.362052i
$208$	9.70318			0.672794
$209$	3.64104	−	1.32523i	0.251856	−	0.0916680i
$210$	25.6555	+	21.2147i	1.77040	+	1.46395i
$211$	2.49358	−	2.09236i	0.171665	−	0.144044i	−0.552907	−	0.833243i	$-0.686482\pi$
$211$	2.49358	−	2.09236i	0.171665	−	0.144044i	0.724572	+	0.689199i	$0.242037\pi$
$212$	−4.90474	−	27.8162i	−0.336859	−	1.91042i
$213$	−5.97120	+	6.57745i	−0.409140	+	0.450679i
$214$	10.1634	+	8.52812i	0.694757	+	0.582970i
$215$	14.9144	+	25.8326i	1.01716	+	1.76177i
$216$	6.97591	−	3.00398i	0.474650	−	0.204395i
$217$	−2.36141	+	7.55678i	−0.160303	+	0.512987i
$218$	−5.88269	+	33.3624i	−0.398426	+	2.25959i
$219$	3.04755	−	3.35696i	0.205934	−	0.226843i
$220$	−31.8007	+	26.6839i	−2.14400	+	1.79903i
$221$	−2.27030	−	12.8755i	−0.152717	−	0.866099i
$222$	29.2177	−	3.98462i	1.96096	−	0.267430i
$223$	−15.2986	+	5.56824i	−1.02447	+	0.372877i	−0.798973	−	0.601367i	$-0.794623\pi$
$223$	−15.2986	+	5.56824i	−1.02447	+	0.372877i	−0.225498	+	0.974244i	$0.572401\pi$
$224$	−13.7328	−	14.9099i	−0.917558	−	0.996210i
$225$	−18.8018	−	1.46923i	−1.25346	−	0.0979484i
$226$	−11.2847	+	19.5457i	−0.750648	+	1.30016i
$227$	−12.1842	+	4.43470i	−0.808696	+	0.294341i	−0.713085	−	0.701077i	$-0.752703\pi$
$227$	−12.1842	+	4.43470i	−0.808696	+	0.294341i	−0.0956111	+	0.995419i	$0.530481\pi$
$228$	3.28974	+	2.07439i	0.217868	+	0.137380i
$229$	−2.56403	+	2.15148i	−0.169436	+	0.142174i	−0.723563	−	0.690259i	$-0.757497\pi$
$229$	−2.56403	+	2.15148i	−0.169436	+	0.142174i	0.554127	+	0.832432i	$0.313052\pi$
$230$	−3.12681	−	17.7330i	−0.206176	−	1.16928i
$231$	−19.9363	−	7.09412i	−1.31172	−	0.466759i
$232$	−6.31971	−	5.30287i	−0.414909	−	0.348150i
$233$	−4.81070	+	8.33238i	−0.315159	+	0.545872i	−0.979471	−	0.201583i	$-0.935391\pi$
$233$	−4.81070	+	8.33238i	−0.315159	+	0.545872i	0.664312	+	0.747455i	$0.268725\pi$
$234$	26.1476	+	11.8986i	1.70932	+	0.777835i
$235$	−2.29495	−	3.97497i	−0.149706	−	0.259298i
$236$	−16.5701	−	13.9039i	−1.07862	−	0.905069i
$237$	9.54338	+	12.3184i	0.619909	+	0.800165i
$238$	−10.2483	+	13.4268i	−0.664296	+	0.870329i
$239$	22.0937	+	8.04146i	1.42913	+	0.520159i	0.936681	−	0.350185i	$-0.113881\pi$
$239$	22.0937	+	8.04146i	1.42913	+	0.520159i	0.492444	+	0.870344i	$0.336103\pi$
$240$	12.4605	+	2.70181i	0.804319	+	0.174401i
$241$	11.6680	+	9.79063i	0.751603	+	0.630670i	0.935926	−	0.352196i	$-0.114565\pi$
$241$	11.6680	+	9.79063i	0.751603	+	0.630670i	−0.184323	+	0.982866i	$0.559009\pi$
$242$	11.1613	−	19.3319i	0.717475	−	1.24270i
$243$	−15.5852	−	0.318411i	−0.999791	−	0.0204261i
$244$	19.8359			1.26986
$245$	16.5435	−	16.7136i	1.05692	−	1.06780i
$246$	−6.66219	+	7.33859i	−0.424766	+	0.467891i
$247$	0.645247	+	3.65938i	0.0410561	+	0.232841i
$248$	−0.759534	−	4.30753i	−0.0482305	−	0.273529i
$249$	13.5271	−	1.84479i	0.857245	−	0.116909i
$250$	7.15876	+	6.00692i	0.452760	+	0.379911i
$251$	14.5049	−	25.1232i	0.915540	−	1.58576i	0.109431	−	0.993994i	$-0.465097\pi$
$251$	14.5049	−	25.1232i	0.915540	−	1.58576i	0.806109	−	0.591767i	$-0.201570\pi$
$252$	−6.62633	−	20.1797i	−0.417419	−	1.27120i
$253$	5.72286	+	9.91229i	0.359793	+	0.623180i
$254$	0.0680139	−	0.385726i	0.00426757	−	0.0242026i
$255$	0.669692	−	17.1664i	0.0419377	−	1.07500i
$256$	−0.496177	−	0.180594i	−0.0310111	−	0.0112871i
$257$	13.7665	−	11.5515i	0.858733	−	0.720563i	−0.102962	−	0.994685i	$-0.532832\pi$
$257$	13.7665	−	11.5515i	0.858733	−	0.720563i	0.961695	+	0.274123i	$0.0883874\pi$
$258$	1.29635	−	33.2296i	0.0807072	−	2.06879i
$259$	−0.961851	−	20.8083i	−0.0597665	−	1.29297i
$260$	−19.9053	−	34.4770i	−1.23448	−	2.13817i
$261$	7.29788	+	15.2785i	0.451727	+	0.945713i
$262$	−15.0324	−	26.0369i	−0.928705	−	1.60856i
$263$	3.79793	−	21.5391i	0.234190	−	1.32816i	−0.610122	−	0.792308i	$-0.708879\pi$
$263$	3.79793	−	21.5391i	0.234190	−	1.32816i	0.844312	−	0.535852i	$-0.180009\pi$
$264$	11.5836	−	1.57973i	0.712918	−	0.0972257i
$265$	27.1642	−	22.7935i	1.66869	−	1.40019i
$266$	2.91269	−	3.81607i	0.178588	−	0.233978i
$267$	4.94822	+	15.4435i	0.302826	+	0.945125i
$268$	−5.24752	+	1.90994i	−0.320544	+	0.116668i
$269$	7.08887	−	12.2783i	0.432216	−	0.748621i	−0.564848	−	0.825195i	$-0.691065\pi$
$269$	7.08887	−	12.2783i	0.432216	−	0.748621i	0.997064	+	0.0765747i	$0.0243984\pi$
$270$	30.2646	+	22.5604i	1.84185	+	1.37298i
$271$	−8.14156	−	14.1016i	−0.494565	−	0.856611i	0.505416	−	0.862876i	$-0.331339\pi$
$271$	−8.14156	−	14.1016i	−0.494565	−	0.856611i	−0.999980	+	0.00626473i	$0.998006\pi$
$272$	−1.12334	+	6.37081i	−0.0681128	+	0.386287i
$273$	10.0198	−	17.6471i	0.606428	−	1.06805i
$274$	0.333046	+	0.121219i	0.0201200	+	0.00732309i
$275$	−27.2779	−	9.92836i	−1.64492	−	0.598703i
$276$	−4.34711	+	10.6342i	−0.261665	+	0.640102i
$277$	−4.98026	+	28.2444i	−0.299235	+	1.69704i	0.350240	+	0.936660i	$0.386100\pi$
$277$	−4.98026	+	28.2444i	−0.299235	+	1.69704i	−0.649474	+	0.760383i	$0.725011\pi$
$278$	3.77097			0.226168
$279$	−2.24288	+	8.69250i	−0.134278	+	0.520406i
$280$	−3.87513	+	12.4009i	−0.231583	+	0.741094i
$281$	−0.494621	−	0.415036i	−0.0295066	−	0.0247590i	0.627915	−	0.778282i	$-0.283909\pi$
$281$	−0.494621	−	0.415036i	−0.0295066	−	0.0247590i	−0.657422	+	0.753523i	$0.728353\pi$
$282$	−0.199475	+	5.11318i	−0.0118785	+	0.304486i
$283$	−10.5590	−	3.84316i	−0.627667	−	0.228452i	0.00854867	−	0.999963i	$-0.497279\pi$
$283$	−10.5590	−	3.84316i	−0.627667	−	0.228452i	−0.636215	+	0.771511i	$0.719501\pi$
$284$	−12.8971	−	4.69417i	−0.765304	−	0.278548i
$285$	−0.190335	+	4.87890i	−0.0112745	+	0.289001i
$286$	33.8732	+	28.4230i	2.00296	+	1.68069i
$287$	4.74339	+	5.14999i	0.279994	+	0.303994i
$288$	−16.4027	−	16.1010i	−0.966540	−	0.948761i
$289$	−8.28352			−0.487266
$290$	7.11981	−	40.3785i	0.418090	−	2.37110i
$291$	−7.45426	+	18.2351i	−0.436977	+	1.06896i
$292$	6.58237	+	2.39579i	0.385204	+	0.140203i
$293$	−12.0370	−	4.38110i	−0.703207	−	0.255947i	−0.0344277	−	0.999407i	$-0.510961\pi$
$293$	−12.0370	−	4.38110i	−0.703207	−	0.255947i	−0.668780	+	0.743461i	$0.733183\pi$
$294$	−25.5396	+	5.92403i	−1.48950	+	0.345496i
$295$	4.71561	−	26.7436i	0.274553	−	1.55707i
$296$	5.75412	+	9.96643i	0.334452	+	0.579287i
$297$	−22.9819	−	6.89589i	−1.33355	−	0.400140i
$298$	−11.4490	+	19.8303i	−0.663224	+	1.14874i
$299$	−10.3144	+	3.75415i	−0.596500	+	0.217108i
$300$	−8.89047	−	27.7473i	−0.513292	−	1.60199i
$301$	−23.2982	−	3.00665i	−1.34289	−	0.173300i
$302$	39.5895	−	33.2196i	2.27812	−	1.91157i
$303$	15.9910	−	2.18080i	0.918656	−	0.125284i
$304$	0.319269	−	1.81067i	0.0183113	−	0.103849i
$305$	12.4514	+	21.5665i	0.712966	+	1.23489i
$306$	−10.8394	+	15.7902i	−0.619645	+	0.902664i
$307$	−3.20676	−	5.55428i	−0.183020	−	0.316999i	0.759888	−	0.650054i	$-0.225254\pi$
$307$	−3.20676	−	5.55428i	−0.183020	−	0.316999i	−0.942907	+	0.333055i	$0.891921\pi$
$308$	−1.50960	−	32.6581i	−0.0860173	−	1.86087i
$309$	0.451965	−	11.5853i	0.0257114	−	0.659066i
$310$	16.6528	−	13.9733i	0.945813	−	0.793632i
$311$	18.6443	+	6.78599i	1.05722	+	0.384798i	0.811385	−	0.584513i	$-0.198714\pi$
$311$	18.6443	+	6.78599i	1.05722	+	0.384798i	0.245839	+	0.969311i	$0.420936\pi$
$312$	−0.437045	+	11.2029i	−0.0247428	+	0.634238i
$313$	−2.04149	+	11.5778i	−0.115392	+	0.654418i	0.871164	+	0.490992i	$0.163366\pi$
$313$	−2.04149	+	11.5778i	−0.115392	+	0.654418i	−0.986556	+	0.163426i	$0.947745\pi$
$314$	21.2063	+	36.7304i	1.19674	+	2.07281i
$315$	17.7808	−	19.8717i	1.00184	−	1.11964i
$316$	−12.0373	+	20.8493i	−0.677153	+	1.17286i
$317$	1.81873	+	1.52610i	0.102150	+	0.0857141i	0.692432	−	0.721483i	$-0.256539\pi$
$317$	1.81873	+	1.52610i	0.102150	+	0.0857141i	−0.590282	+	0.807197i	$0.700984\pi$
$318$	−39.1706	+	5.34198i	−2.19658	+	0.299563i
$319$	4.52564	+	25.6662i	0.253387	+	1.43703i
$320$	7.10841	+	40.3138i	0.397372	+	2.25361i
$321$	7.14306	−	7.86829i	0.398687	−	0.439165i
$322$	12.5953	+	6.51580i	0.701908	+	0.363111i
$323$	−2.47734			−0.137843
$324$	−8.65579	−	22.4744i	−0.480877	−	1.24858i
$325$	13.9191	−	24.1087i	0.772095	−	1.33731i
$326$	12.9645	+	10.8785i	0.718038	+	0.602505i
$327$	26.5188	+	5.75009i	1.46649	+	0.317981i
$328$	−3.63489	−	1.32299i	−0.200703	−	0.0730499i
$329$	3.58499	+	0.462646i	0.197647	+	0.0255065i
$330$	35.5844	+	45.9315i	1.95886	+	2.52845i
$331$	−4.06744	−	3.41298i	−0.223567	−	0.187595i	0.524124	−	0.851642i	$-0.324393\pi$
$331$	−4.06744	−	3.41298i	−0.223567	−	0.187595i	−0.747690	+	0.664047i	$0.768837\pi$
$332$	10.5462	+	18.2665i	0.578797	+	1.00251i
$333$	−2.27690	−	23.5096i	−0.124773	−	1.28832i
$334$	18.3085	−	31.7112i	1.00179	−	1.73516i
$335$	−5.37057	−	4.50644i	−0.293425	−	0.246213i
$336$	−7.64528	+	6.50952i	−0.417084	+	0.355123i
$337$	3.26895	+	18.5391i	0.178071	+	1.00989i	0.934539	+	0.355860i	$0.115812\pi$
$337$	3.26895	+	18.5391i	0.178071	+	1.00989i	−0.756468	+	0.654031i	$0.773077\pi$
$338$	−10.9498	+	9.18801i	−0.595593	+	0.499762i
$339$	15.2916	+	9.64234i	0.830525	+	0.523700i
$340$	24.9410	−	9.07778i	1.35262	−	0.492312i
$341$	−6.90899	+	11.9667i	−0.374143	+	0.648034i
$342$	3.08069	−	4.48777i	0.166585	−	0.242671i
$343$	2.55823	+	18.3427i	0.138131	+	0.990414i
$344$	12.1956	−	4.43884i	0.657543	−	0.239326i
$345$	−14.2907	+	1.94893i	−0.769388	+	0.104927i
$346$	−2.67815	−	15.1886i	−0.143978	−	0.816542i
$347$	4.52329	−	3.79549i	0.242823	−	0.203753i	−0.513252	−	0.858238i	$-0.671559\pi$
$347$	4.52329	−	3.79549i	0.242823	−	0.203753i	0.756074	+	0.654486i	$0.227115\pi$
$348$	−17.5833	+	19.3685i	−0.942562	+	1.03826i
$349$	1.98947	−	11.2829i	0.106494	−	0.603958i	−0.884119	−	0.467262i	$-0.845240\pi$
$349$	1.98947	−	11.2829i	0.106494	−	0.603958i	0.990613	−	0.136696i	$-0.0436484\pi$
$350$	−35.0929	+	7.87415i	−1.87579	+	0.420891i
$351$	10.3398	−	20.5564i	0.551898	−	1.09722i
$352$	−17.6893	−	30.6388i	−0.942843	−	1.63305i
$353$	−10.3800	−	8.70988i	−0.552473	−	0.463580i	0.323304	−	0.946295i	$-0.395206\pi$
$353$	−10.3800	−	8.70988i	−0.552473	−	0.463580i	−0.875778	+	0.482715i	$0.839651\pi$
$354$	−20.3498	+	22.4159i	−1.08158	+	1.19139i
$355$	−2.99209	−	16.9690i	−0.158804	−	0.900621i
$356$	−19.1928	+	16.1047i	−1.01722	+	0.853547i
$357$	10.4265	+	8.62172i	0.551829	+	0.456310i
$358$	9.23197	−	3.36016i	0.487925	−	0.177590i
$359$	−26.8362			−1.41636			−0.708181	−	0.706031i	$-0.750484\pi$
$359$	−26.8362			−1.41636			−0.708181	+	0.706031i	$0.750484\pi$
$360$	−3.68063	+	14.2646i	−0.193986	+	0.751812i
$361$	−18.2959			−0.962943
$362$	3.39792	−	19.2705i	0.178591	−	1.01284i
$363$	−15.1243	−	9.53687i	−0.793822	−	0.500556i
$364$	31.0945	+	4.01277i	1.62980	+	0.210326i
$365$	1.52709	+	8.66055i	0.0799315	+	0.453314i
$366$	1.08227	−	27.7420i	0.0565710	−	1.45010i
$367$	2.46698	−	0.897909i	0.128776	−	0.0468705i	−0.276829	−	0.960919i	$-0.589283\pi$
$367$	2.46698	−	0.897909i	0.128776	−	0.0468705i	0.405604	+	0.914049i	$0.367061\pi$
$368$	5.43114			0.283118
$369$	5.66562	+	5.56141i	0.294941	+	0.289515i
$370$	−28.5979	+	49.5330i	−1.48673	+	2.57510i
$371$	1.28950	+	27.8966i	0.0669477	+	1.44832i
$372$	−13.7423	+	1.87413i	−0.712503	+	0.0971691i
$373$	5.42720	+	1.97534i	0.281010	+	0.102279i	0.478680	−	0.877989i	$-0.341115\pi$
$373$	5.42720	+	1.97534i	0.281010	+	0.102279i	−0.197670	+	0.980269i	$0.563338\pi$
$374$	−22.5832	+	18.9495i	−1.16775	+	0.979857i
$375$	5.03133	−	5.54215i	0.259817	−	0.286196i
$376$	−1.87659	+	0.683022i	−0.0967776	+	0.0352242i
$377$	−24.9935			−1.28723
$378$	−28.5844	+	8.16639i	−1.47022	+	0.420034i
$379$	−2.35232			−0.120830			−0.0604152	−	0.998173i	$-0.519242\pi$
$379$	−2.35232			−0.120830			−0.0604152	+	0.998173i	$0.519242\pi$
$380$	−7.08855	+	2.58002i	−0.363635	+	0.132352i
$381$	−0.306603	−	0.0664807i	−0.0157077	−	0.00340591i
$382$	−5.45215	+	4.57490i	−0.278956	+	0.234072i
$383$	19.9989	+	7.27901i	1.02190	+	0.371940i	0.797990	−	0.602670i	$-0.205897\pi$
$383$	19.9989	+	7.27901i	1.02190	+	0.371940i	0.223907	+	0.974611i	$0.428119\pi$
$384$	7.22617	−	17.6771i	0.368759	−	0.902082i
$385$	34.5598	−	22.1415i	1.76133	−	1.12844i
$386$	12.2099	−	21.1481i	0.621466	−	1.07641i
$387$	−26.5558	−	2.07514i	−1.34991	−	0.105485i
$388$	−30.4357			−1.54514
$389$	13.9139	−	5.06425i	0.705464	−	0.256768i	0.0357219	−	0.999362i	$-0.488627\pi$
$389$	13.9139	−	5.06425i	0.705464	−	0.256768i	0.669742	+	0.742594i	$0.266405\pi$
$390$	−49.3048	+	25.9580i	−2.49664	+	1.31443i
$391$	−1.27075	−	7.20676i	−0.0642644	−	0.364462i
$392$	−5.91158	−	8.35134i	−0.298580	−	0.421806i
$393$	−21.3087	+	11.2186i	−1.07488	+	0.565904i
$394$	−6.04049	+	34.2573i	−0.304315	+	1.72586i
$395$	−30.2244			−1.52075
$396$	−3.57353	−	36.8977i	−0.179577	−	1.85418i
$397$	−37.9255			−1.90343			−0.951713	−	0.306991i	$-0.900678\pi$
$397$	−37.9255			−1.90343			−0.951713	+	0.306991i	$0.900678\pi$
$398$	−10.3187	+	3.75572i	−0.517232	+	0.188257i
$399$	−2.96335	−	2.45041i	−0.148353	−	0.122674i
$400$	−10.5518	+	8.85403i	−0.527591	+	0.442701i
$401$	1.52015	+	8.62118i	0.0759125	+	0.430521i	0.998950	+	0.0458115i	$0.0145874\pi$
$401$	1.52015	+	8.62118i	0.0759125	+	0.430521i	−0.923038	+	0.384710i	$0.874302\pi$
$402$	2.38489	+	7.44327i	0.118947	+	0.371236i
$403$	−10.1511	−	8.51782i	−0.505665	−	0.424303i
$404$	12.4671	+	21.5936i	0.620261	+	1.07432i
$405$	19.0018	−	23.5187i	0.944208	−	1.16865i
$406$	21.8757	+	23.7509i	1.08567	+	1.17874i
$407$	6.31316	−	35.8037i	0.312931	−	1.77472i
$408$	−7.30487	−	1.58392i	−0.361645	−	0.0784156i
$409$	25.7459	−	21.6034i	1.27305	−	1.06822i	0.278890	−	0.960323i	$-0.410033\pi$
$409$	25.7459	−	21.6034i	1.27305	−	1.06822i	0.994162	−	0.107895i	$-0.0344110\pi$
$410$	−3.33834	−	18.9327i	−0.164869	−	0.935018i
$411$	0.107420	−	0.262777i	0.00529863	−	0.0129618i
$412$	16.8323	−	6.12646i	0.829268	−	0.301829i
$413$	14.4888	+	15.7308i	0.712947	+	0.774060i
$414$	14.6355	+	6.65997i	0.719296	+	0.327320i
$415$	−13.2402	+	22.9326i	−0.649934	+	1.12572i
$416$	31.8818	−	11.6040i	1.56314	−	0.568935i
$417$	0.117746	−	3.01820i	0.00576603	−	0.147802i
$418$	6.41843	−	5.38570i	0.313936	−	0.263423i
$419$	−0.518619	−	2.94123i	−0.0253362	−	0.143689i	0.969516	−	0.245030i	$-0.0787977\pi$
$419$	−0.518619	−	2.94123i	−0.0253362	−	0.143689i	−0.994852	+	0.101341i	$0.967687\pi$
$420$	38.8131	+	13.8112i	1.89388	+	0.673917i
$421$	−9.26236	−	7.77205i	−0.451420	−	0.378786i	0.388542	−	0.921431i	$-0.372979\pi$
$421$	−9.26236	−	7.77205i	−0.451420	−	0.378786i	−0.839963	+	0.542644i	$0.817423\pi$
$422$	3.51945	−	6.09586i	0.171324	−	0.296742i
$423$	4.08625	+	0.319310i	0.198680	+	0.0155254i
$424$	−7.71425	−	13.3615i	−0.374637	−	0.648891i
$425$	14.2176	+	11.9300i	0.689654	+	0.578688i
$426$	−7.26884	+	17.7815i	−0.352176	+	0.861517i
$427$	−19.4506	−	2.51012i	−0.941283	−	0.121473i
$428$	15.4282	+	5.61542i	0.745752	+	0.271431i
$429$	23.8068	−	26.2239i	1.14940	−	1.26610i
$430$	49.4113	+	41.4610i	2.38283	+	1.99943i
$431$	12.5494	−	21.7362i	0.604484	−	1.04700i	−0.387648	−	0.921807i	$-0.626712\pi$
$431$	12.5494	−	21.7362i	0.604484	−	1.04700i	0.992133	−	0.125190i	$-0.0399542\pi$
$432$	−8.28640	+	7.80810i	−0.398680	+	0.375667i
$433$	38.7840			1.86384			0.931919	−	0.362667i	$-0.118134\pi$
$433$	38.7840			1.86384			0.931919	+	0.362667i	$0.118134\pi$
$434$	0.790517	+	17.1017i	0.0379460	+	0.820910i
$435$	−32.0957	−	6.95932i	−1.53887	−	0.333674i
$436$	7.27982	+	41.2859i	0.348640	+	1.97724i
$437$	0.361163	+	2.04826i	0.0172768	+	0.0979814i
$438$	3.70983	−	9.07523i	0.177263	−	0.433631i
$439$	5.84735	+	4.90651i	0.279079	+	0.234175i	0.771573	−	0.636141i	$-0.219470\pi$
$439$	5.84735	+	4.90651i	0.279079	+	0.234175i	−0.492494	+	0.870316i	$0.663915\pi$
$440$	−11.3378	+	19.6377i	−0.540510	+	0.936191i
$441$	3.94400	+	20.6263i	0.187810	+	0.982205i
$442$	−14.1357	−	24.4838i	−0.672367	−	1.16457i
$443$	0.975535	−	5.53253i	0.0463490	−	0.262859i	−0.952824	−	0.303524i	$-0.901837\pi$
$443$	0.975535	−	5.53253i	0.0463490	−	0.262859i	0.999173	+	0.0406656i	$0.0129478\pi$
$444$	32.2898	−	17.0000i	1.53241	−	0.806782i
$445$	−29.5576	−	10.7581i	−1.40116	−	0.509981i
$446$	−26.9684	+	22.6292i	−1.27699	+	1.07152i
$447$	15.5142	+	9.78273i	0.733798	+	0.462707i
$448$	−28.6338	−	14.8128i	−1.35282	−	0.699841i
$449$	−15.4853	−	26.8214i	−0.730798	−	1.26578i	−0.956542	−	0.291593i	$-0.905815\pi$
$449$	−15.4853	−	26.8214i	−0.730798	−	1.26578i	0.225744	−	0.974187i	$-0.427519\pi$
$450$	−39.2917	+	10.9201i	−1.85223	+	0.514777i
$451$	6.11001	+	10.5829i	0.287709	+	0.498327i
$452$	−4.84993	+	27.5053i	−0.228121	+	1.29374i
$453$	−25.3520	−	32.7238i	−1.19114	−	1.53750i
$454$	−21.4784	+	18.0225i	−1.00803	+	0.845839i
$455$	15.1559	+	36.3263i	0.710517	+	1.70300i
$456$	2.07614	+	0.450170i	0.0972241	+	0.0210811i
$457$	3.44394	−	1.25349i	0.161101	−	0.0586358i	−0.260211	−	0.965552i	$-0.583792\pi$
$457$	3.44394	−	1.25349i	0.161101	−	0.0586358i	0.421312	+	0.906916i	$0.361570\pi$
$458$	−3.61888	+	6.26809i	−0.169099	+	0.292889i
$459$	12.2996	+	9.16862i	0.574098	+	0.427955i
$460$	−11.1416	−	19.2977i	−0.519478	−	0.899762i
$461$	−2.83706	+	16.0897i	−0.132135	+	0.749374i	0.844677	+	0.535276i	$0.179792\pi$
$461$	−2.83706	+	16.0897i	−0.132135	+	0.749374i	−0.976812	+	0.214098i	$0.931319\pi$
$462$	−45.7571	+	0.329429i	−2.12881	+	0.0153264i
$463$	0.873706	+	0.318003i	0.0406046	+	0.0147789i	0.362243	−	0.932084i	$-0.382011\pi$
$463$	0.873706	+	0.318003i	0.0406046	+	0.0147789i	−0.321638	+	0.946863i	$0.604233\pi$
$464$	11.6210	+	4.22970i	0.539491	+	0.196359i
$465$	−10.6640	−	13.7648i	−0.494530	−	0.638327i
$466$	−3.61280	+	20.4892i	−0.167360	+	0.949144i
$467$	6.04307			0.279640			0.139820	−	0.990177i	$-0.455348\pi$
$467$	6.04307			0.279640			0.139820	+	0.990177i	$0.455348\pi$
$468$	35.4422	+	2.76955i	1.63832	+	0.128022i
$469$	5.38730	−	1.20880i	0.248763	−	0.0558174i
$470$	−7.60313	−	6.37978i	−0.350706	−	0.294277i
$471$	30.0603	−	15.8262i	1.38511	−	0.729231i
$472$	−11.1028	−	4.04110i	−0.511049	−	0.186007i
$473$	−38.5275	−	14.0228i	−1.77149	−	0.644771i
$474$	28.5025	+	17.9727i	1.30916	+	0.825512i
$475$	−4.04082	−	3.39065i	−0.185405	−	0.155574i
$476$	−6.23450	+	19.9511i	−0.285758	+	0.914459i
$477$	3.05252	+	31.5181i	0.139765	+	1.44311i
$478$	50.8416			2.32544
$479$	−3.10382	+	17.6026i	−0.141817	+	0.804285i	0.828051	+	0.560653i	$0.189450\pi$
$479$	−3.10382	+	17.6026i	−0.141817	+	0.804285i	−0.969868	+	0.243632i	$0.921661\pi$
$480$	44.1725	−	6.02412i	2.01619	−	0.274962i
$481$	32.7626	+	11.9246i	1.49385	+	0.543716i
$482$	30.9503	+	11.2650i	1.40975	+	0.513106i
$483$	5.60838	−	9.87754i	0.255190	−	0.449444i
$484$	4.79688	−	27.2045i	0.218040	−	1.23657i
$485$	−19.1051	−	33.0911i	−0.867520	−	1.50259i
$486$	−31.9045	+	10.8796i	−1.44722	+	0.493506i
$487$	10.5234	−	18.2271i	0.476861	−	0.825947i	−0.522788	−	0.852463i	$-0.675108\pi$
$487$	10.5234	−	18.2271i	0.476861	−	0.825947i	0.999648	+	0.0265160i	$0.00844128\pi$
$488$	10.1816	−	3.70579i	0.460898	−	0.167753i
$489$	9.11172	−	10.0368i	0.412046	−	0.453881i
$490$	21.2550	−	46.1972i	0.960205	−	2.08698i
$491$	−19.1658	+	16.0820i	−0.864942	+	0.725773i	−0.963027	−	0.269405i	$-0.913173\pi$
$491$	−19.1658	+	16.0820i	−0.864942	+	0.725773i	0.0980847	+	0.995178i	$0.468728\pi$
$492$	−4.64119	+	11.3536i	−0.209241	+	0.511859i
$493$	2.89352	−	16.4100i	0.130317	−	0.739067i
$494$	4.01755	+	6.95860i	0.180758	+	0.313082i
$495$	37.8737	−	27.0468i	1.70229	−	1.21566i
$496$	3.27840	+	5.67835i	0.147204	+	0.254966i
$497$	12.0526	+	6.23507i	0.540635	+	0.279681i
$498$	26.1225	−	13.7530i	1.17058	−	0.616287i
$499$	−16.9122	+	14.1910i	−0.757093	+	0.635276i	−0.937368	−	0.348340i	$-0.886745\pi$
$499$	−16.9122	+	14.1910i	−0.757093	+	0.635276i	0.180276	+	0.983616i	$0.442301\pi$
$500$	10.8671	+	3.95531i	0.485992	+	0.176887i
$501$	−24.8093	−	15.6438i	−1.10840	−	0.698915i
$502$	10.8931	−	61.7776i	0.486181	−	2.75727i
$503$	15.6150	+	27.0460i	0.696238	+	1.20592i	0.969762	+	0.244054i	$0.0784775\pi$
$503$	15.6150	+	27.0460i	0.696238	+	1.20592i	−0.273524	+	0.961865i	$0.588189\pi$
$504$	−7.17126	−	9.12011i	−0.319433	−	0.406242i
$505$	−15.6517	+	27.1096i	−0.696493	+	1.20636i
$506$	18.9598	+	15.9091i	0.842864	+	0.707247i
$507$	7.01198	+	9.05090i	0.311413	+	0.401964i
$508$	−0.0841670	−	0.477335i	−0.00373431	−	0.0211783i
$509$	−7.13189	−	40.4469i	−0.316115	−	1.79278i	−0.565896	−	0.824476i	$-0.691470\pi$
$509$	−7.13189	−	40.4469i	−0.316115	−	1.79278i	0.249781	−	0.968302i	$-0.419641\pi$
$510$	−11.3352	−	35.3772i	−0.501929	−	1.56653i
$511$	−6.15136	−	3.18222i	−0.272120	−	0.140773i
$512$	−23.1932			−1.02500
$513$	−3.49572	−	2.60584i	−0.154340	−	0.115051i
$514$	19.4302	−	33.6540i	0.857027	−	1.48442i
$515$	17.2270	+	14.4552i	0.759111	+	0.636970i
$516$	−12.5569	−	39.1903i	−0.552788	−	1.72526i
$517$	5.92838	+	2.15775i	0.260730	+	0.0948979i
$518$	−17.3440	−	41.5709i	−0.762050	−	1.82652i
$519$	−12.2402	+	1.66928i	−0.537286	+	0.0732734i
$520$	−16.6583	−	13.9780i	−0.730515	−	0.612975i
$521$	−8.41822	−	14.5808i	−0.368809	−	0.638796i	0.620571	−	0.784151i	$-0.286901\pi$
$521$	−8.41822	−	14.5808i	−0.368809	−	0.638796i	−0.989380	+	0.145355i	$0.953568\pi$
$522$	26.1289	+	25.6483i	1.14363	+	1.12259i
$523$	−15.2717	+	26.4514i	−0.667786	+	1.15664i	0.310736	+	0.950496i	$0.399425\pi$
$523$	−15.2717	+	26.4514i	−0.667786	+	1.15664i	−0.978522	+	0.206143i	$0.933909\pi$
$524$	−28.5008	−	23.9150i	−1.24506	−	1.04473i
$525$	5.20654	+	28.3334i	0.227232	+	1.23657i
$526$	−8.21263	−	46.5762i	−0.358088	−	2.03082i
$527$	6.76774	−	5.67881i	0.294807	−	0.247373i
$528$	−15.5071	+	8.16420i	−0.674862	+	0.355301i
$529$	15.8397	−	5.76516i	0.688680	−	0.250659i
$530$	38.3397	−	66.4064i	1.66537	−	2.88451i
$531$	17.3058	+	16.9874i	0.751006	+	0.737192i
$532$	1.77193	−	5.67037i	0.0768227	−	0.245842i
$533$	−11.0122	+	4.00812i	−0.476992	+	0.173611i
$534$	21.4765	+	27.7213i	0.929377	+	1.19962i
$535$	3.57930	+	20.2992i	0.154747	+	0.877612i
$536$	−2.33669	+	1.96071i	−0.100929	+	0.0846899i
$537$	−2.40114	−	7.49398i	−0.103617	−	0.323389i
$538$	5.32369	−	30.1922i	0.229521	−	1.30168i
$539$	−2.65242	+	32.2148i	−0.114248	+	1.38759i
$540$	44.7424	+	13.4253i	1.92541	+	0.577732i
$541$	2.15170	+	3.72686i	0.0925089	+	0.160230i	0.908566	−	0.417741i	$-0.137178\pi$
$541$	2.15170	+	3.72686i	0.0925089	+	0.160230i	−0.816057	+	0.577971i	$0.803845\pi$
$542$	−26.9729	−	22.6329i	−1.15858	−	0.972168i
$543$	−15.3176	−	3.32132i	−0.657342	−	0.142532i
$544$	3.92787	+	22.2760i	0.168406	+	0.955077i
$545$	−40.3182	+	33.8310i	−1.72704	+	1.44916i
$546$	7.30872	−	43.2691i	0.312784	−	1.85175i
$547$	−28.9084	+	10.5218i	−1.23603	+	0.449880i	−0.875660	−	0.482928i	$-0.839573\pi$
$547$	−28.9084	+	10.5218i	−1.23603	+	0.449880i	−0.360374	+	0.932808i	$0.617351\pi$
$548$	0.438594			0.0187358
$549$	−22.1703	−	1.73244i	−0.946204	−	0.0739389i
$550$	−62.7713			−2.67658
$551$	−0.822375	+	4.66392i	−0.0350344	+	0.198690i
$552$	−0.244626	+	6.27056i	−0.0104120	+	0.266893i
$553$	14.4419	−	18.9211i	0.614133	−	0.804607i
$554$	10.7693	+	61.0757i	0.457543	+	2.59486i
$555$	38.7522	+	24.4358i	1.64494	+	1.03724i
$556$	4.38514	−	1.59606i	0.185971	−	0.0676881i
$557$	−31.5974			−1.33882			−0.669412	−	0.742892i	$-0.733454\pi$
$557$	−31.5974			−1.33882			−0.669412	+	0.742892i	$0.733454\pi$
$558$	1.87132	+	19.3219i	0.0792193	+	0.817959i
$559$	19.6594	−	34.0512i	0.831506	−	1.44021i
$560$	−0.899303	−	19.4552i	−0.0380025	−	0.822132i
$561$	14.4616	+	18.6667i	0.610571	+	0.788111i
$562$	−1.31202	−	0.477535i	−0.0553441	−	0.0201436i
$563$	−1.86377	+	1.56389i	−0.0785485	+	0.0659100i	−0.681217	−	0.732082i	$-0.738549\pi$
$563$	−1.86377	+	1.56389i	−0.0785485	+	0.0659100i	0.602668	+	0.797992i	$0.294104\pi$
$564$	1.93219	+	6.03038i	0.0813598	+	0.253925i
$565$	−32.9495	+	11.9926i	−1.38619	+	0.504534i
$566$	−24.2981			−1.02132
$567$	5.64367	+	23.1333i	0.237012	+	0.971507i
$568$	−7.49696			−0.314566
$569$	17.5346	−	6.38206i	0.735087	−	0.267550i	0.0527708	−	0.998607i	$-0.483195\pi$
$569$	17.5346	−	6.38206i	0.735087	−	0.267550i	0.682317	+	0.731057i	$0.260973\pi$
$570$	3.22160	+	10.0546i	0.134938	+	0.421143i
$571$	−15.6380	+	13.1218i	−0.654428	+	0.549130i	−0.908411	−	0.418078i	$-0.862704\pi$
$571$	−15.6380	+	13.1218i	−0.654428	+	0.549130i	0.253983	+	0.967209i	$0.418259\pi$
$572$	51.4200	+	18.7154i	2.14998	+	0.782528i
$573$	3.49141	+	4.50663i	0.145856	+	0.188267i
$574$	13.4474	+	6.95659i	0.561282	+	0.290362i
$575$	7.79093	−	13.4943i	0.324904	−	0.562751i
$576$	−33.2720	−	15.1406i	−1.38633	−	0.630859i
$577$	0.0811997			0.00338039			0.00169019	−	0.999999i	$-0.499462\pi$
$577$	0.0811997			0.00338039			0.00169019	+	0.999999i	$0.499462\pi$
$578$	−16.8320	+	6.12636i	−0.700120	+	0.254823i
$579$	−16.5452	−	10.4328i	−0.687597	−	0.433574i
$580$	−8.81075	−	49.9683i	−0.365847	−	2.07482i
$581$	−8.02984	−	19.2463i	−0.333134	−	0.798473i
$582$	−1.66060	+	42.5666i	−0.0688341	+	1.76444i
$583$	−8.46372	+	48.0001i	−0.350531	+	1.98796i
$584$	3.82626			0.158332
$585$	19.2367	+	40.2729i	0.795339	+	1.66508i
$586$	−27.6992			−1.14424
$587$	−4.39620	+	1.60009i	−0.181451	+	0.0660426i	−0.431148	−	0.902281i	$-0.641891\pi$
$587$	−4.39620	+	1.60009i	−0.181451	+	0.0660426i	0.249697	+	0.968324i	$0.419669\pi$
$588$	−27.1919	+	17.6985i	−1.12137	+	0.729873i
$589$	−1.92348	+	1.61399i	−0.0792556	+	0.0665034i
$590$	−10.1970	−	57.8302i	−0.419805	−	2.38083i
$591$	27.2302	+	5.90433i	1.12010	+	0.242872i
$592$	−13.2153	−	11.0890i	−0.543146	−	0.455754i
$593$	4.66656	+	8.08272i	0.191633	+	0.331918i	0.945791	−	0.324775i	$-0.105288\pi$
$593$	4.66656	+	8.08272i	0.191633	+	0.331918i	−0.754159	+	0.656692i	$0.771955\pi$
$594$	−51.7991	+	2.98468i	−2.12534	+	0.122463i
$595$	−25.6053	+	5.74533i	−1.04972	+	0.235536i
$596$	−4.92055	+	27.9058i	−0.201553	+	1.14307i
$597$	2.68380	+	8.37616i	0.109840	+	0.342813i
$598$	−18.1823	+	15.2568i	−0.743531	+	0.623896i
$599$	4.12966	+	23.4205i	0.168733	+	0.956935i	0.945131	+	0.326691i	$0.105934\pi$
$599$	4.12966	+	23.4205i	0.168733	+	0.956935i	−0.776398	+	0.630243i	$0.782955\pi$
$600$	−9.74722	−	12.5815i	−0.397929	−	0.513637i
$601$	−30.6186	+	11.1443i	−1.24896	+	0.454584i	−0.880050	−	0.474881i	$-0.842491\pi$
$601$	−30.6186	+	11.1443i	−1.24896	+	0.454584i	−0.368910	+	0.929465i	$0.620269\pi$
$602$	−49.5653	+	11.1215i	−2.02013	+	0.453277i
$603$	6.03189	−	1.67640i	0.245638	−	0.0682683i
$604$	31.9772	−	55.3862i	1.30114	−	2.25363i
$605$	32.5891	−	11.8615i	1.32493	−	0.482237i
$606$	30.8806	−	16.2580i	1.25444	−	0.660436i
$607$	−0.808607	+	0.678502i	−0.0328203	+	0.0275395i	−0.659050	−	0.752099i	$-0.729042\pi$
$607$	−0.808607	+	0.678502i	−0.0328203	+	0.0275395i	0.626230	+	0.779638i	$0.284597\pi$
$608$	−1.11635	−	6.33114i	−0.0452740	−	0.256762i
$609$	19.6927	−	16.7672i	0.797990	−	0.679443i
$610$	41.2514	+	34.6140i	1.67022	+	1.40148i
$611$	−3.02508	+	5.23959i	−0.122382	+	0.211971i
$612$	−5.92157	+	22.9496i	−0.239365	+	0.927684i
$613$	0.576889	+	0.999202i	0.0233003	+	0.0403574i	0.877440	−	0.479686i	$-0.159249\pi$
$613$	0.576889	+	0.999202i	0.0233003	+	0.0403574i	−0.854140	+	0.520043i	$0.825916\pi$
$614$	−10.6240	−	8.91456i	−0.428748	−	0.359762i
$615$	−15.2575	+	2.08077i	−0.615242	+	0.0839049i
$616$	−6.87613	−	16.4811i	−0.277047	−	0.664041i
$617$	−36.6671	−	13.3457i	−1.47616	−	0.537278i	−0.526395	−	0.850240i	$-0.676457\pi$
$617$	−36.6671	−	13.3457i	−1.47616	−	0.537278i	−0.949766	+	0.312962i	$0.898679\pi$
$618$	−7.64992	−	23.8755i	−0.307725	−	0.960414i
$619$	12.9710	+	10.8839i	0.521347	+	0.437462i	0.865101	−	0.501597i	$-0.167254\pi$
$619$	12.9710	+	10.8839i	0.521347	+	0.437462i	−0.343754	+	0.939060i	$0.611699\pi$
$620$	13.4508	−	23.2974i	0.540195	−	0.935646i
$621$	5.78747	−	11.5060i	0.232243	−	0.461719i
$622$	42.9039			1.72029
$623$	20.8580	−	13.3632i	0.835660	−	0.535385i
$624$	−5.12812	−	16.0049i	−0.205289	−	0.640710i
$625$	−2.93696	−	16.6563i	−0.117478	−	0.666253i
$626$	4.41450	+	25.0359i	0.176439	+	1.00064i
$627$	−4.11018	−	5.30533i	−0.164145	−	0.211874i
$628$	40.2062	+	33.7370i	1.60440	+	1.34625i
$629$	−11.6223	+	20.1304i	−0.463411	+	0.802652i
$630$	21.4337	−	53.5295i	0.853938	−	2.13267i
$631$	−19.1743	−	33.2108i	−0.763315	−	1.32210i	−0.941133	−	0.338037i	$-0.890237\pi$
$631$	−19.1743	−	33.2108i	−0.763315	−	1.32210i	0.177818	−	0.984063i	$-0.443096\pi$
$632$	−2.28354	+	12.9506i	−0.0908343	+	0.515147i
$633$	−4.76910	−	3.00723i	−0.189555	−	0.119526i
$634$	4.82432	+	1.75591i	0.191598	+	0.0697360i
$635$	0.466147	−	0.391144i	0.0184985	−	0.0155221i
$636$	−43.2893	+	22.7910i	−1.71653	+	0.903720i
$637$	−29.9828	−	7.86968i	−1.18796	−	0.311808i
$638$	28.1784	+	48.8064i	1.11559	+	1.93226i
$639$	14.0050	+	6.37303i	0.554027	+	0.252113i
$640$	18.5205	+	32.0785i	0.732089	+	1.26801i
$641$	7.29587	−	41.3769i	0.288169	−	1.63429i	−0.405570	−	0.914064i	$-0.632927\pi$
$641$	7.29587	−	41.3769i	0.288169	−	1.63429i	0.693740	−	0.720226i	$-0.255962\pi$
$642$	8.69537	−	21.2712i	0.343179	−	0.839506i
$643$	−26.6672	+	22.3764i	−1.05165	+	0.882441i	−0.993266	−	0.115853i	$-0.963040\pi$
$643$	−26.6672	+	22.3764i	−1.05165	+	0.882441i	−0.0583856	+	0.998294i	$0.518595\pi$
$644$	17.4045	+	2.24606i	0.685832	+	0.0885072i
$645$	34.7273	−	38.2531i	1.36739	−	1.50622i
$646$	−5.03392	+	1.83220i	−0.198057	+	0.0720868i
$647$	8.24077	−	14.2734i	0.323978	−	0.561146i	−0.657327	−	0.753605i	$-0.728313\pi$
$647$	8.24077	−	14.2734i	0.323978	−	0.561146i	0.981305	+	0.192459i	$0.0616463\pi$
$648$	−8.64167	−	9.91882i	−0.339477	−	0.389648i
$649$	18.6632	+	32.3255i	0.732593	+	1.26889i
$650$	10.4532	−	59.2829i	0.410007	−	2.32527i
$651$	13.7125	−	0.0987235i	0.537437	−	0.00386928i
$652$	19.6803	+	7.16305i	0.770741	+	0.280527i
$653$	27.2755	+	9.92746i	1.06737	+	0.388492i	0.815193	−	0.579189i	$-0.196631\pi$
$653$	27.2755	+	9.92746i	1.06737	+	0.388492i	0.252179	+	0.967681i	$0.418853\pi$
$654$	58.1386	−	7.92877i	2.27340	−	0.310040i
$655$	8.11093	−	45.9994i	0.316920	−	1.79734i
$656$	5.79855			0.226396
$657$	−7.14777	−	3.25263i	−0.278861	−	0.126897i
$658$	7.62682	−	1.71131i	0.297324	−	0.0667137i
$659$	7.69234	+	6.45464i	0.299651	+	0.251437i	0.780199	−	0.625531i	$-0.215118\pi$
$659$	7.69234	+	6.45464i	0.299651	+	0.251437i	−0.480548	+	0.876968i	$0.659562\pi$
$660$	60.8204	+	38.3512i	2.36743	+	1.49282i
$661$	−34.1281	−	12.4216i	−1.32743	−	0.483145i	−0.421598	−	0.906783i	$-0.638531\pi$
$661$	−34.1281	−	12.4216i	−1.32743	−	0.483145i	−0.905831	+	0.423638i	$0.860753\pi$
$662$	−10.7892	−	3.92694i	−0.419333	−	0.152625i
$663$	−20.0376	+	10.5494i	−0.778197	+	0.409705i
$664$	8.82587	+	7.40578i	0.342510	+	0.287400i
$665$	7.27737	−	1.63290i	0.282204	−	0.0633211i
$666$	−22.0140	−	46.0873i	−0.853023	−	1.78585i
$667$	−13.9896			−0.541678
$668$	7.86858	−	44.6250i	0.304445	−	1.72659i
$669$	17.2698	+	22.2915i	0.667690	+	0.861839i
$670$	−14.2458	−	5.18505i	−0.550364	−	0.200316i
$671$	−32.1649	−	11.7071i	−1.24171	−	0.451946i
$672$	−17.3354	+	30.5314i	−0.668729	+	1.17777i
$673$	−0.279493	+	1.58508i	−0.0107737	+	0.0611005i	−0.989721	−	0.143014i	$-0.954320\pi$
$673$	−0.279493	+	1.58508i	−0.0107737	+	0.0611005i	0.978947	+	0.204115i	$0.0654316\pi$
$674$	20.3537	+	35.2536i	0.783995	+	1.35792i
$675$	7.51333	+	31.7892i	0.289188	+	1.22357i
$676$	−8.84440	+	15.3190i	−0.340169	+	0.589190i
$677$	−26.9891	+	9.82324i	−1.03728	+	0.377538i	−0.803847	−	0.594836i	$-0.797217\pi$
$677$	−26.9891	+	9.82324i	−1.03728	+	0.377538i	−0.233429	+	0.972374i	$0.574995\pi$
$678$	38.2036	+	8.28371i	1.46720	+	0.318134i
$679$	29.8446	+	3.85146i	1.14533	+	0.147806i
$680$	11.1061	−	9.31908i	0.425898	−	0.357371i
$681$	13.7542	+	17.7536i	0.527061	+	0.680318i
$682$	−5.18860	+	29.4260i	−0.198682	+	1.12678i
$683$	16.0850	+	27.8600i	0.615475	+	1.06603i	0.990301	+	0.138939i	$0.0443692\pi$
$683$	16.0850	+	27.8600i	0.615475	+	1.06603i	−0.374826	+	0.927095i	$0.622297\pi$
$684$	1.68299	−	6.52258i	0.0643507	−	0.249397i
$685$	0.275315	+	0.476860i	0.0105192	+	0.0182199i
$686$	18.7643	+	35.3802i	0.716423	+	1.35082i
$687$	4.90384	+	3.09219i	0.187093	+	0.117974i
$688$	−14.9034	+	12.5055i	−0.568188	+	0.476766i
$689$	−43.9232	−	15.9867i	−1.67334	−	0.609046i
$690$	−27.5972	+	14.5294i	−1.05061	+	0.553125i
$691$	5.43752	−	30.8377i	0.206853	−	1.17312i	−0.687644	−	0.726048i	$-0.741355\pi$
$691$	5.43752	−	30.8377i	0.206853	−	1.17312i	0.894497	−	0.447074i	$-0.147534\pi$
$692$	−9.54289	−	16.5288i	−0.362766	−	0.628329i
$693$	−1.16506	+	36.6333i	−0.0442571	+	1.39158i
$694$	6.38419	−	11.0577i	0.242341	−	0.419746i
$695$	4.48796	+	3.76585i	0.170238	+	0.142847i
$696$	−5.40686	+	13.2266i	−0.204946	+	0.501353i
$697$	−1.35671	−	7.69430i	−0.0513892	−	0.291442i
$698$	−4.30203	−	24.3980i	−0.162834	−	0.923480i
$699$	16.2863	+	3.53136i	0.616004	+	0.133568i
$700$	−37.4757	+	24.0096i	−1.41645	+	0.907479i
$701$	41.0228			1.54941			0.774705	−	0.632323i	$-0.217898\pi$
$701$	41.0228			1.54941			0.774705	+	0.632323i	$0.217898\pi$
$702$	5.80719	−	49.4175i	0.219178	−	1.86514i
$703$	3.30321	−	5.72132i	0.124583	−	0.215784i
$704$	−43.1026	−	36.1674i	−1.62449	−	1.36311i
$705$	−5.34363	+	5.88617i	−0.201253	+	0.221686i
$706$	−27.5338	−	10.0215i	−1.03625	−	0.377163i
$707$	−9.49241	−	22.7519i	−0.356999	−	0.855673i
$708$	−14.1766	+	34.6797i	−0.532789	+	1.30334i
$709$	12.2501	+	10.2790i	0.460062	+	0.386038i	0.843154	−	0.537672i	$-0.180696\pi$
$709$	12.2501	+	10.2790i	0.460062	+	0.386038i	−0.383092	+	0.923710i	$0.625141\pi$
$710$	−18.6299	−	32.2679i	−0.699168	−	1.21099i
$711$	15.2749	−	22.2516i	0.572853	−	0.834500i
$712$	−6.84279	+	11.8521i	−0.256444	+	0.444174i
$713$	−5.68188	−	4.76766i	−0.212788	−	0.178550i
$714$	27.5630	+	9.80798i	1.03152	+	0.367054i
$715$	11.9293	+	67.6543i	0.446130	+	2.53013i
$716$	9.31337	−	7.81485i	0.348057	−	0.292055i
$717$	1.58749	−	40.6924i	0.0592858	−	1.51969i
$718$	−54.5309	+	19.8476i	−2.03508	+	0.740707i
$719$	9.90454	−	17.1552i	0.369377	−	0.639779i	−0.620091	−	0.784530i	$-0.712904\pi$
$719$	9.90454	−	17.1552i	0.369377	−	0.639779i	0.989468	+	0.144750i	$0.0462378\pi$
$720$	−2.12884	−	21.9808i	−0.0793371	−	0.819177i
$721$	−17.2807	+	3.87744i	−0.643566	+	0.144403i
$722$	−37.1771	+	13.5314i	−1.38359	+	0.503585i
$723$	9.98263	−	24.4202i	0.371258	−	0.908196i
$724$	−4.20491	−	23.8473i	−0.156274	−	0.886276i
$725$	27.1794	−	22.8062i	1.00942	−	0.847003i
$726$	−37.7858	−	8.19311i	−1.40236	−	0.304075i
$727$	−3.88585	+	22.0377i	−0.144118	+	0.817334i	0.823953	+	0.566658i	$0.191764\pi$
$727$	−3.88585	+	22.0377i	−0.144118	+	0.817334i	−0.968071	+	0.250676i	$0.919347\pi$
$728$	16.7102	−	3.74944i	0.619322	−	0.138964i
$729$	7.71156	+	25.8753i	0.285613	+	0.958345i
$730$	9.50823	+	16.4687i	0.351915	+	0.609535i
$731$	20.0809	+	16.8499i	0.742721	+	0.623217i
$732$	−10.4832	−	32.7183i	−0.387472	−	1.20930i
$733$	2.12104	+	12.0290i	0.0783424	+	0.444302i	0.998596	+	0.0529786i	$0.0168715\pi$
$733$	2.12104	+	12.0290i	0.0783424	+	0.444302i	−0.920253	+	0.391323i	$0.872017\pi$
$734$	4.34881	−	3.64908i	0.160517	−	0.134690i
$735$	−36.3116	−	18.4545i	−1.33937	−	0.680706i
$736$	17.8451	−	6.49510i	0.657781	−	0.239413i
$737$	9.63637			0.354960
$738$	15.6256	+	7.11052i	0.575186	+	0.261742i
$739$	23.3271			0.858102			0.429051	−	0.903280i	$-0.358848\pi$
$739$	23.3271			0.858102			0.429051	+	0.903280i	$0.358848\pi$
$740$	−12.2908	+	69.7044i	−0.451818	+	2.56238i
$741$	5.69496	−	2.99828i	0.209209	−	0.110145i
$742$	23.2521	+	55.7319i	0.853613	+	2.04598i
$743$	4.94730	+	28.0575i	0.181499	+	1.02933i	0.930372	+	0.366617i	$0.119484\pi$
$743$	4.94730	+	28.0575i	0.181499	+	1.02933i	−0.748873	+	0.662714i	$0.769405\pi$
$744$	−6.70365	+	3.52934i	−0.245768	+	0.129392i
$745$	−33.4292	+	12.1672i	−1.22475	+	0.445773i
$746$	12.4889			0.457252
$747$	−10.1919	−	21.3373i	−0.372904	−	0.780692i
$748$	−18.2409	+	31.5941i	−0.666952	+	1.15519i
$749$	−14.4180	−	7.45872i	−0.526822	−	0.272536i
$750$	6.12472	−	14.9827i	0.223643	−	0.547090i
$751$	19.7354	+	7.18311i	0.720156	+	0.262115i	0.675992	−	0.736909i	$-0.263715\pi$
$751$	19.7354	+	7.18311i	0.720156	+	0.262115i	0.0441639	+	0.999024i	$0.485938\pi$
$752$	2.29325	−	1.92427i	0.0836263	−	0.0701708i
$753$	−49.1053	−	10.6475i	−1.78950	−	0.388017i
$754$	−50.7865	+	18.4848i	−1.84954	+	0.673176i
$755$	80.2913			2.92210
$756$	−29.7834	+	21.5947i	−1.08321	+	0.785393i
$757$	51.2608			1.86310			0.931552	−	0.363608i	$-0.118455\pi$
$757$	51.2608			1.86310			0.931552	+	0.363608i	$0.118455\pi$
$758$	−4.77988	+	1.73974i	−0.173613	+	0.0631900i
$759$	13.3253	−	14.6782i	0.483678	−	0.532785i
$760$	−3.15648	+	2.64860i	−0.114498	+	0.0960750i
$761$	6.33254	+	2.30486i	0.229555	+	0.0835510i	0.454237	−	0.890881i	$-0.349912\pi$
$761$	6.33254	+	2.30486i	0.229555	+	0.0835510i	−0.224682	+	0.974432i	$0.572134\pi$
$762$	−0.672181	+	0.0916700i	−0.0243505	+	0.00332085i
$763$	−1.91393	−	41.4053i	−0.0692890	−	1.49897i
$764$	−4.40381	+	7.62762i	−0.159324	+	0.275958i
$765$	−28.6690	+	7.96778i	−1.03653	+	0.288076i
$766$	46.0210			1.66281
$767$	−33.6370	+	12.2429i	−1.21456	+	0.442065i
$768$	−0.0356515	+	0.913864i	−0.00128646	+	0.0329762i
$769$	−3.96380	−	22.4798i	−0.142938	−	0.810642i	−0.969000	−	0.247062i	$-0.920535\pi$
$769$	−3.96380	−	22.4798i	−0.142938	−	0.810642i	0.826061	−	0.563580i	$-0.190576\pi$
$770$	53.8496	−	70.5511i	1.94060	−	2.54248i
$771$	−26.3292	−	16.6023i	−0.948224	−	0.597917i
$772$	5.24754	−	29.7603i	0.188863	−	1.07110i
$773$	31.5340			1.13420			0.567100	−	0.823649i	$-0.308065\pi$
$773$	31.5340			1.13420			0.567100	+	0.823649i	$0.308065\pi$
$774$	−55.4958	+	15.4236i	−1.99475	+	0.554388i
$775$	18.8114			0.675724
$776$	−15.6223	+	5.68607i	−0.560810	+	0.204118i
$777$	−33.8140	+	12.5837i	−1.21307	+	0.451437i
$778$	24.5275	−	20.5810i	0.879353	−	0.737865i
$779$	0.385595	+	2.18682i	0.0138154	+	0.0783510i
$780$	−46.3482	+	51.0539i	−1.65953	+	1.82802i
$781$	18.1429	+	15.2237i	0.649204	+	0.544746i
$782$	−7.91215	−	13.7042i	−0.282938	−	0.490063i
$783$	21.3442	−	20.1121i	0.762778	−	0.718749i
$784$	12.6091	+	8.73315i	0.450323	+	0.311898i
$785$	−11.4421	+	64.8915i	−0.408387	+	2.31608i
$786$	−35.0020	+	38.5557i	−1.24848	+	1.37524i
$787$	17.1396	−	14.3818i	0.610960	−	0.512656i	−0.283987	−	0.958828i	$-0.591657\pi$
$787$	17.1396	−	14.3818i	0.610960	−	0.512656i	0.894947	+	0.446172i	$0.147213\pi$
$788$	7.47509	+	42.3933i	0.266289	+	1.51020i
$789$	−37.5349	+	5.11890i	−1.33628	+	0.182238i
$790$	−61.4157	+	22.3535i	−2.18507	+	0.795301i
$791$	8.23638	−	26.3574i	0.292852	−	0.937161i
$792$	−8.72758	−	18.2716i	−0.310121	−	0.649254i
$793$	16.4128	−	28.4278i	0.582836	−	1.00950i
$794$	−77.0641	+	28.0491i	−2.73490	+	0.995424i
$795$	−51.9530	−	32.7597i	−1.84258	−	1.16187i
$796$	−10.4097	+	8.73480i	−0.368963	+	0.309597i
$797$	−0.872685	−	4.94924i	−0.0309121	−	0.175311i	0.965443	−	0.260615i	$-0.0839252\pi$
$797$	−0.872685	−	4.94924i	−0.0309121	−	0.175311i	−0.996355	+	0.0853034i	$0.972814\pi$
$798$	−7.83377	−	2.78755i	−0.277312	−	0.0986783i
$799$	−3.08994	−	2.59277i	−0.109314	−	0.0917255i
$800$	−24.0817	+	41.7107i	−0.851416	+	1.47470i
$801$	22.8581	−	16.3237i	0.807652	−	0.576770i
$802$	9.46501	+	16.3939i	0.334221	+	0.578888i
$803$	−9.25967	−	7.76979i	−0.326767	−	0.274190i
$804$	5.92367	+	7.64613i	0.208912	+	0.269658i
$805$	8.48315	+	20.3329i	0.298992	+	0.716639i
$806$	−26.9267	−	9.80050i	−0.948451	−	0.345208i
$807$	−23.9989	−	5.20369i	−0.844801	−	0.183179i
$808$	10.4334	+	8.75468i	0.367047	+	0.307989i
$809$	−17.3627	+	30.0732i	−0.610442	+	1.05732i	0.380724	+	0.924689i	$0.375675\pi$
$809$	−17.3627	+	30.0732i	−0.610442	+	1.05732i	−0.991166	+	0.132627i	$0.957659\pi$
$810$	21.2174	−	61.8431i	0.745505	−	2.17295i
$811$	−41.4471			−1.45541			−0.727703	−	0.685893i	$-0.759412\pi$
$811$	−41.4471			−1.45541			−0.727703	+	0.685893i	$0.759412\pi$
$812$	35.4911	+	18.3603i	1.24549	+	0.644319i
$813$	−18.9571	+	20.8818i	−0.664854	+	0.732356i
$814$	−13.6516	−	77.4218i	−0.478487	−	2.71363i
$815$	4.56577	+	25.8938i	0.159932	+	0.907019i
$816$	11.1020	−	1.51406i	0.388648	−	0.0530027i
$817$	−5.70727	−	4.78896i	−0.199672	−	0.167545i
$818$	36.3379	−	62.9390i	1.27052	−	2.20061i
$819$	−34.4034	−	7.20078i	−1.20215	−	0.251616i
$820$	−11.8953	−	20.6032i	−0.415401	−	0.719496i
$821$	−5.93815	+	33.6769i	−0.207243	+	1.17533i	0.686628	+	0.727009i	$0.259090\pi$
$821$	−5.93815	+	33.6769i	−0.207243	+	1.17533i	−0.893871	+	0.448325i	$0.852021\pi$
$822$	0.0239301	−	0.613406i	0.000834659	−	0.0213950i
$823$	40.5004	+	14.7409i	1.41175	+	0.513837i	0.931644	−	0.363371i	$-0.118374\pi$
$823$	40.5004	+	14.7409i	1.41175	+	0.513837i	0.480110	+	0.877208i	$0.340597\pi$
$824$	7.49531	−	6.28931i	0.261111	−	0.219098i
$825$	−1.95999	+	50.2408i	−0.0682380	+	1.74916i
$826$	41.0753	+	21.2490i	1.42919	+	0.739349i
$827$	−22.2920	−	38.6108i	−0.775168	−	1.34263i	−0.934700	−	0.355437i	$-0.884332\pi$
$827$	−22.2920	−	38.6108i	−0.775168	−	1.34263i	0.159532	−	0.987193i	$-0.449001\pi$
$828$	19.8380	+	1.55019i	0.689418	+	0.0538729i
$829$	14.4457	+	25.0206i	0.501719	+	0.869003i	0.999998	+	0.00198616i	$0.000632216\pi$
$829$	14.4457	+	25.0206i	0.501719	+	0.869003i	−0.498279	+	0.867017i	$0.666034\pi$
$830$	−9.94326	+	56.3910i	−0.345136	+	1.95736i
$831$	49.2199	−	6.71246i	1.70742	−	0.232853i
$832$	41.3352	−	34.6844i	1.43304	−	1.20246i
$833$	8.63813	−	18.7747i	0.299293	−	0.650506i
$834$	−1.99295	−	6.22003i	−0.0690103	−	0.215382i
$835$	53.4576	−	19.4570i	1.84998	−	0.673337i
$836$	5.18429	−	8.97945i	0.179302	−	0.310561i
$837$	15.5232	−	0.894452i	0.536561	−	0.0309168i
$838$	−3.22911	−	5.59299i	−0.111548	−	0.193207i
$839$	−6.36419	+	36.0931i	−0.219716	+	1.24607i	0.652816	+	0.757517i	$0.273588\pi$
$839$	−6.36419	+	36.0931i	−0.219716	+	1.24607i	−0.872532	+	0.488557i	$0.837523\pi$
$840$	22.5026	−	0.162008i	0.776415	−	0.00558980i
$841$	−2.68235	−	0.976295i	−0.0924948	−	0.0336653i
$842$	−24.5691	−	8.94242i	−0.846707	−	0.308176i
$843$	−0.423175	+	1.03520i	−0.0145749	+	0.0356541i
$844$	1.51258	−	8.57828i	0.0520652	−	0.295277i
$845$	−22.2073			−0.763955
$846$	8.53936	−	2.37329i	0.293589	−	0.0815953i
$847$	−8.14630	+	26.0691i	−0.279910	+	0.895745i
$848$	17.7171	+	14.8664i	0.608408	+	0.510515i
$849$	−0.758689	+	19.4476i	−0.0260381	+	0.667441i
$850$	37.7131	+	13.7265i	1.29355	+	0.470814i
$851$	18.3382	+	6.67454i	0.628624	+	0.228800i
$852$	−0.926690	+	23.7541i	−0.0317479	+	0.813801i
$853$	−1.52194	−	1.27706i	−0.0521104	−	0.0437258i	0.616360	−	0.787464i	$-0.288606\pi$
$853$	−1.52194	−	1.27706i	−0.0521104	−	0.0437258i	−0.668471	+	0.743738i	$0.733051\pi$
$854$	−41.3799	+	9.28484i	−1.41599	+	0.317721i
$855$	8.14810	−	2.26455i	0.278659	−	0.0774458i
$856$	8.96826			0.306529
$857$	1.40657	−	7.97707i	0.0480476	−	0.272492i	−0.951314	−	0.308224i	$-0.900265\pi$
$857$	1.40657	−	7.97707i	0.0480476	−	0.272492i	0.999361	+	0.0357325i	$0.0113764\pi$
$858$	28.9804	−	70.8937i	0.989374	−	2.42027i
$859$	−42.5686	−	15.4937i	−1.45242	−	0.528638i	−0.509155	−	0.860675i	$-0.670042\pi$
$859$	−42.5686	−	15.4937i	−1.45242	−	0.528638i	−0.943267	+	0.332036i	$0.892264\pi$
$860$	75.0072	+	27.3004i	2.55772	+	0.930935i
$861$	5.98778	−	10.5458i	0.204063	−	0.359398i
$862$	9.42453	−	53.4491i	0.321001	−	1.82048i
$863$	−22.7185	−	39.3497i	−0.773348	−	1.33948i	−0.935718	−	0.352749i	$-0.885247\pi$
$863$	−22.7185	−	39.3497i	−0.773348	−	1.33948i	0.162370	−	0.986730i	$-0.448086\pi$
$864$	−17.8890	+	35.5649i	−0.608597	+	1.20994i
$865$	11.9806	−	20.7509i	0.407351	−	0.705553i
$866$	78.8086	−	28.6840i	2.67802	−	0.974721i
$867$	4.37783	+	13.6633i	0.148679	+	0.464029i
$868$	8.15757	+	19.5525i	0.276886	+	0.663654i
$869$	31.8243	−	26.7038i	1.07957	−	0.905864i
$870$	−70.3651	+	9.59618i	−2.38560	+	0.325341i
$871$	−1.60472	+	9.10085i	−0.0543740	+	0.308370i
$872$	11.4498	+	19.8316i	0.387739	+	0.671584i
$873$	34.0175	+	2.65822i	1.15132	+	0.0899670i
$874$	2.24873	+	3.89492i	0.0760646	+	0.131748i
$875$	−10.1555	−	5.25366i	−0.343320	−	0.177606i
$876$	0.472959	−	12.1235i	0.0159798	−	0.409614i
$877$	18.3346	−	15.3846i	0.619116	−	0.519500i	−0.278410	−	0.960462i	$-0.589807\pi$
$877$	18.3346	−	15.3846i	0.619116	−	0.519500i	0.897525	+	0.440963i	$0.145363\pi$
$878$	15.5105	+	5.64537i	0.523455	+	0.190522i
$879$	−0.864885	+	22.1698i	−0.0291719	+	0.747769i
$880$	5.90262	−	33.4754i	0.198977	−	1.12846i
$881$	−22.7785	−	39.4536i	−0.767429	−	1.32923i	−0.938953	−	0.344045i	$-0.888203\pi$
$881$	−22.7785	−	39.4536i	−0.767429	−	1.32923i	0.171524	−	0.985180i	$-0.445131\pi$
$882$	23.2691	+	38.9955i	0.783510	+	1.31305i
$883$	9.34145	−	16.1799i	0.314365	−	0.544496i	−0.664937	−	0.746899i	$-0.731542\pi$
$883$	9.34145	−	16.1799i	0.314365	−	0.544496i	0.979302	+	0.202403i	$0.0648751\pi$
$884$	−26.8007	−	22.4885i	−0.901405	−	0.756368i
$885$	−46.6044	+	6.35577i	−1.56659	+	0.213647i
$886$	−2.10949	−	11.9635i	−0.0708698	−	0.401923i
$887$	9.76974	+	55.4070i	0.328036	+	1.86038i	0.487421	+	0.873167i	$0.337938\pi$
$887$	9.76974	+	55.4070i	0.328036	+	1.86038i	−0.159385	+	0.987216i	$0.550951\pi$
$888$	13.3981	−	14.7584i	0.449611	−	0.495259i
$889$	0.0221283	+	0.478715i	0.000742159	+	0.0160556i
$890$	−68.0171			−2.27994
$891$	0.771485	+	41.5521i	0.0258457	+	1.39205i
$892$	−21.7829	+	37.7291i	−0.729346	+	1.26326i
$893$	0.878200	+	0.736898i	0.0293879	+	0.0246593i
$894$	38.7599	+	8.40433i	1.29633	+	0.281083i
$895$	14.3429	+	5.22038i	0.479430	+	0.174498i
$896$	−28.9313	−	3.73361i	−0.966528	−	0.124731i
$897$	11.6435	+	15.0291i	0.388764	+	0.501807i
$898$	−51.3027	−	43.0481i	−1.71199	−	1.43653i
$899$	−8.44452	−	14.6263i	−0.281640	−	0.487815i
$900$	−41.0692	+	29.3288i	−1.36897	+	0.977627i
$901$	15.5814	−	26.9878i	0.519092	−	0.899094i
$902$	20.2424	+	16.9854i	0.673998	+	0.565551i
$903$	7.35374	+	40.0182i	0.244717	+	1.33172i
$904$	2.64919	+	15.0243i	0.0881108	+	0.499701i
$905$	23.2883	−	19.5412i	0.774130	−	0.649572i
$906$	−75.7171	−	47.7445i	−2.51553	−	1.58620i
$907$	−20.6872	+	7.52954i	−0.686909	+	0.250014i	−0.661811	−	0.749671i	$-0.730212\pi$
$907$	−20.6872	+	7.52954i	−0.686909	+	0.250014i	−0.0250976	+	0.999685i	$0.507990\pi$
$908$	−17.3485	+	30.0485i	−0.575731	+	0.997195i
$909$	−12.0483	−	25.2237i	−0.399617	−	0.836619i
$910$	57.6629	+	62.6057i	1.91151	+	2.07536i
$911$	−27.5675	+	10.0338i	−0.913353	+	0.332433i	−0.755591	−	0.655044i	$-0.772650\pi$
$911$	−27.5675	+	10.0338i	−0.913353	+	0.332433i	−0.157762	+	0.987477i	$0.550428\pi$
$912$	−3.15534	+	0.430316i	−0.104484	+	0.0142492i
$913$	−6.32035	−	35.8445i	−0.209173	−	1.18628i
$914$	6.07098	−	5.09416i	0.200810	−	0.168500i
$915$	28.9923	−	31.9359i	0.958457	−	1.05577i
$916$	−1.55532	+	8.82065i	−0.0513892	+	0.291442i
$917$	24.9210	+	27.0572i	0.822962	+	0.893506i
$918$	31.7737	+	9.53392i	1.04869	+	0.314666i
$919$	−17.5525	−	30.4018i	−0.579003	−	1.00286i	−0.995594	−	0.0937690i	$-0.970108\pi$
$919$	−17.5525	−	30.4018i	−0.579003	−	1.00286i	0.416591	−	0.909094i	$-0.363225\pi$
$920$	−9.32411	−	7.82386i	−0.307407	−	0.257945i
$921$	−7.46674	+	8.22483i	−0.246037	+	0.271017i
$922$	6.13484	+	34.7924i	0.202040	+	1.14583i
$923$	−17.3990	+	14.5995i	−0.572694	+	0.480547i
$924$	−53.0701	+	19.7497i	−1.74588	+	0.649719i
$925$	−46.5091	+	16.9279i	−1.52921	+	0.556587i
$926$	2.01055			0.0660708
$927$	−19.3483	+	5.37733i	−0.635481	+	0.176615i
$928$	43.2415			1.41947
$929$	0.0485920	−	0.275579i	0.00159425	−	0.00904144i	−0.984000	−	0.178167i	$-0.942983\pi$
$929$	0.0485920	−	0.275579i	0.00159425	−	0.00904144i	0.985595	+	0.169126i	$0.0540944\pi$
$930$	−31.8493	−	20.0830i	−1.04438	−	0.658549i
$931$	−2.45507	+	5.33602i	−0.0804616	+	0.174881i
$932$	4.47083	+	25.3554i	0.146447	+	0.830542i
$933$	1.33964	−	34.3393i	0.0438579	−	1.12422i
$934$	12.2794	−	4.46935i	0.401796	−	0.146242i
$935$	−45.8008			−1.49785
$936$	18.7096	−	5.19982i	0.611542	−	0.169962i
$937$	26.7259	−	46.2907i	0.873098	−	1.51225i	0.0143237	−	0.999897i	$-0.495440\pi$
$937$	26.7259	−	46.2907i	0.873098	−	1.51225i	0.858775	−	0.512353i	$-0.171226\pi$
$938$	10.0529	−	6.44064i	0.328240	−	0.210294i
$939$	20.1760	−	2.75154i	0.658419	−	0.0897932i
$940$	−11.5417	−	4.20082i	−0.376448	−	0.137016i
$941$	14.5850	−	12.2383i	0.475459	−	0.398957i	−0.373322	−	0.927702i	$-0.621781\pi$
$941$	14.5850	−	12.2383i	0.475459	−	0.398957i	0.848781	+	0.528744i	$0.177337\pi$
$942$	49.3774	−	54.3907i	1.60880	−	1.77214i
$943$	−6.16384	+	2.24346i	−0.200722	+	0.0730570i
$944$	17.7118			0.576470
$945$	−42.1745	−	18.8264i	−1.37194	−	0.612424i
$946$	−88.6584			−2.88253
$947$	2.73380	−	0.995023i	0.0888366	−	0.0323339i	−0.297220	−	0.954809i	$-0.596059\pi$
$947$	2.73380	−	0.995023i	0.0888366	−	0.0323339i	0.386056	+	0.922475i	$0.373837\pi$
$948$	40.7516	+	8.83618i	1.32355	+	0.286986i
$949$	8.87999	−	7.45119i	0.288257	−	0.241876i
$950$	−10.7186	−	3.90124i	−0.347756	−	0.126573i
$951$	1.55603	−	3.80645i	0.0504576	−	0.123433i
$952$	0.527211	+	11.4055i	0.0170870	+	0.369654i
$953$	6.98653	−	12.1010i	0.226316	−	0.391991i	−0.730398	−	0.683022i	$-0.760665\pi$
$953$	6.98653	−	12.1010i	0.226316	−	0.391991i	0.956713	+	0.291032i	$0.0939985\pi$
$954$	29.5130	+	61.7868i	0.955517	+	2.00042i
$955$	−11.0575			−0.357811
$956$	59.1220	−	21.5186i	1.91214	−	0.695963i
$957$	39.9434	−	21.0294i	1.29119	−	0.679784i
$958$	6.71169	+	38.0639i	0.216845	+	1.22979i
$959$	−0.430076	−	0.0555016i	−0.0138879	−	0.00179224i
$960$	62.7389	−	33.0308i	2.02489	−	1.06606i
$961$	−3.82817	+	21.7106i	−0.123489	+	0.700343i
$962$	75.3926			2.43075
$963$	−16.7535	−	7.62375i	−0.539873	−	0.245672i
$964$	40.7590			1.31276
$965$	35.6508	−	12.9758i	1.14764	−	0.417706i
$966$	4.09089	−	24.2189i	0.131622	−	0.779231i
$967$	30.3105	−	25.4335i	0.974720	−	0.817887i	−0.00856441	−	0.999963i	$-0.502726\pi$
$967$	30.3105	−	25.4335i	0.974720	−	0.817887i	0.983284	+	0.182076i	$0.0582817\pi$
$968$	−2.62022	−	14.8600i	−0.0842169	−	0.477618i
$969$	1.30927	+	4.08624i	0.0420598	+	0.131269i
$970$	−63.2950	−	53.1108i	−2.03228	−	1.70529i
$971$	−13.8858	−	24.0508i	−0.445615	−	0.771828i	0.552479	−	0.833526i	$-0.313682\pi$
$971$	−13.8858	−	24.0508i	−0.445615	−	0.771828i	−0.998095	+	0.0616980i	$0.980348\pi$
$972$	−32.4959	+	26.1550i	−1.04231	+	0.838922i
$973$	−4.50195	+	1.01015i	−0.144326	+	0.0323839i
$974$	7.90300	−	44.8201i	0.253228	−	1.43613i
$975$	−47.1223	−	10.2176i	−1.50912	−	0.327224i
$976$	−12.4422	+	10.4403i	−0.398266	+	0.334185i
$977$	−1.78465	−	10.1213i	−0.0570962	−	0.323808i	0.942860	−	0.333190i	$-0.108125\pi$
$977$	−1.78465	−	10.1213i	−0.0570962	−	0.323808i	−0.999956	+	0.00938123i	$0.997014\pi$
$978$	11.0918	−	27.1336i	0.354678	−	0.867637i
$979$	40.6271	−	14.7871i	1.29845	−	0.472596i
$980$	5.16386	−	62.7174i	0.164953	−	2.00344i
$981$	−4.53068	−	46.7804i	−0.144653	−	1.49358i
$982$	−27.0508	+	46.8533i	−0.863224	+	1.49515i
$983$	−7.65023	+	2.78446i	−0.244005	+	0.0888104i	−0.461128	−	0.887334i	$-0.652555\pi$
$983$	−7.65023	+	2.78446i	−0.244005	+	0.0888104i	0.217123	+	0.976144i	$0.430333\pi$
$984$	−0.261175	+	6.69477i	−0.00832596	+	0.213421i
$985$	−41.3998	+	34.7385i	−1.31911	+	1.10686i
$986$	−6.25693	−	35.4848i	−0.199261	−	1.13007i
$987$	−1.13155	−	6.15777i	−0.0360176	−	0.196004i
$988$	7.61710	+	6.39151i	0.242332	+	0.203341i
$989$	11.0039	−	19.0594i	0.349905	−	0.606053i
$990$	56.9555	−	82.9695i	1.81017	−	2.63694i
$991$	27.4363	+	47.5210i	0.871542	+	1.50955i	0.860402	+	0.509617i	$0.170213\pi$
$991$	27.4363	+	47.5210i	0.871542	+	1.50955i	0.0111402	+	0.999938i	$0.496454\pi$
$992$	17.5626	+	14.7368i	0.557614	+	0.467893i
$993$	−3.47992	+	8.51280i	−0.110432	+	0.270145i
$994$	29.1022	+	3.75566i	0.923065	+	0.119122i
$995$	−16.0313	−	5.83492i	−0.508226	−	0.184979i
$996$	24.5561	−	27.0493i	0.778090	−	0.857089i
$997$	16.5770	+	13.9098i	0.524999	+	0.440526i	0.866370	−	0.499402i	$-0.166447\pi$
$997$	16.5770	+	13.9098i	0.524999	+	0.440526i	−0.341371	+	0.939928i	$0.610891\pi$
$998$	−23.8699	+	41.3439i	−0.755589	+	1.30872i
$999$	−37.5746	+	16.1804i	−1.18881	+	0.511926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.20	yes	132
3.2	odd	2		567.2.w.a.235.3		132
7.2	even	3		189.2.u.a.79.3	yes	132
21.2	odd	6		567.2.u.a.478.20		132
27.13	even	9		189.2.u.a.67.3	✓	132
27.14	odd	18		567.2.u.a.172.20		132
189.121	even	9	inner	189.2.w.a.121.20	yes	132
189.149	odd	18		567.2.w.a.415.3		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.3	✓	132	27.13	even	9
189.2.u.a.79.3	yes	132	7.2	even	3
189.2.w.a.25.20	yes	132	1.1	even	1	trivial
189.2.w.a.121.20	yes	132	189.121	even	9	inner
567.2.u.a.172.20		132	27.14	odd	18
567.2.u.a.478.20		132	21.2	odd	6
567.2.w.a.235.3		132	3.2	odd	2
567.2.w.a.415.3		132	189.149	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03199 - 0.739583i) q^{2} +(-0.528499 - 1.64945i) q^{3} +(2.04991 - 1.72008i) q^{4} +(3.15692 + 1.14902i) q^{5} +(-2.29381 - 2.96080i) q^{6} +(-2.22776 + 1.42726i) q^{7} +(0.730849 - 1.26587i) q^{8} +(-2.44138 + 1.74347i) q^{9} +O(q^{10})\)	\(q+(2.03199 - 0.739583i) q^{2} +(-0.528499 - 1.64945i) q^{3} +(2.04991 - 1.72008i) q^{4} +(3.15692 + 1.14902i) q^{5} +(-2.29381 - 2.96080i) q^{6} +(-2.22776 + 1.42726i) q^{7} +(0.730849 - 1.26587i) q^{8} +(-2.44138 + 1.74347i) q^{9} +7.26462 q^{10} +(-4.33921 + 1.57934i) q^{11} +(-3.92055 - 2.47216i) q^{12} +(-0.768974 - 4.36107i) q^{13} +(-3.47120 + 4.54780i) q^{14} +(0.226832 - 5.81444i) q^{15} +(-0.380489 + 2.15786i) q^{16} +2.95237 q^{17} +(-3.67141 + 5.34831i) q^{18} -0.839101 q^{19} +(8.44779 - 3.07474i) q^{20} +(3.53157 + 2.92027i) q^{21} +(-7.64917 + 6.41842i) q^{22} +(-0.430416 - 2.44101i) q^{23} +(-2.47424 - 0.536490i) q^{24} +(4.81565 + 4.04081i) q^{25} +(-4.78792 - 8.29293i) q^{26} +(4.16603 + 3.10551i) q^{27} +(-2.11170 + 6.75767i) q^{28} +(0.980067 - 5.55823i) q^{29} +(-3.83934 - 11.9826i) q^{30} +(2.29231 - 1.92348i) q^{31} +(1.33041 + 7.54514i) q^{32} +(4.89832 + 6.32263i) q^{33} +(5.99918 - 2.18352i) q^{34} +(-8.67282 + 1.94601i) q^{35} +(-2.00570 + 7.77329i) q^{36} +(-3.93660 + 6.81839i) q^{37} +(-1.70504 + 0.620585i) q^{38} +(-6.78697 + 3.57321i) q^{39} +(3.76174 - 3.15648i) q^{40} +(-0.459534 - 2.60615i) q^{41} +(9.33590 + 3.32207i) q^{42} +(6.80164 + 5.70725i) q^{43} +(-6.17838 + 10.7013i) q^{44} +(-9.71051 + 2.69878i) q^{45} +(-2.67993 - 4.64178i) q^{46} +(-1.04660 - 0.878199i) q^{47} +(3.76038 - 0.512829i) q^{48} +(2.92583 - 6.35921i) q^{49} +(12.7739 + 4.64931i) q^{50} +(-1.56032 - 4.86979i) q^{51} +(-9.07769 - 7.61709i) q^{52} +(5.27760 - 9.14106i) q^{53} +(10.7621 + 3.22925i) q^{54} -15.5132 q^{55} +(0.178572 + 3.86317i) q^{56} +(0.443464 + 1.38406i) q^{57} +(-2.11929 - 12.0191i) q^{58} +(-1.40366 - 7.96053i) q^{59} +(-9.53629 - 12.3092i) q^{60} +(5.67839 + 4.76474i) q^{61} +(3.23538 - 5.60384i) q^{62} +(2.95042 - 7.36852i) q^{63} +(6.09249 + 10.5525i) q^{64} +(2.58339 - 14.6511i) q^{65} +(14.6294 + 9.22481i) q^{66} +(-1.96099 - 0.713741i) q^{67} +(6.05208 - 5.07829i) q^{68} +(-3.79886 + 2.00002i) q^{69} +(-16.1838 + 10.3685i) q^{70} +(-2.56447 - 4.44179i) q^{71} +(0.422718 + 4.36467i) q^{72} +(1.30884 + 2.26698i) q^{73} +(-2.95636 + 16.7663i) q^{74} +(4.12005 - 10.0787i) q^{75} +(-1.72008 + 1.44332i) q^{76} +(7.41258 - 9.71160i) q^{77} +(-11.1484 + 12.2802i) q^{78} +(-8.45408 + 3.07703i) q^{79} +(-3.68061 + 6.37500i) q^{80} +(2.92065 - 8.51292i) q^{81} +(-2.86123 - 4.95580i) q^{82} +(-1.36872 + 7.76242i) q^{83} +(12.2625 - 0.0882838i) q^{84} +(9.32038 + 3.39234i) q^{85} +(18.0418 + 6.56670i) q^{86} +(-9.68600 + 1.32095i) q^{87} +(-1.17207 + 6.64713i) q^{88} -9.36279 q^{89} +(-17.7357 + 12.6656i) q^{90} +(7.93749 + 8.61789i) q^{91} +(-5.08104 - 4.26350i) q^{92} +(-4.38416 - 2.76450i) q^{93} +(-2.77617 - 1.01044i) q^{94} +(-2.64897 - 0.964148i) q^{95} +(11.7422 - 6.18205i) q^{96} +(-8.71278 - 7.31089i) q^{97} +(1.24209 - 15.0857i) q^{98} +(7.84012 - 11.4210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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