LMFDB - Embedded newform 189.2.bd.a.185.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (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			185.17
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65422 - 0.291684i) q^{2} +(-0.549790 - 1.64248i) q^{3} +(0.771989 - 0.280981i) q^{4} +(3.52188 - 1.28186i) q^{5} +(-1.38856 - 2.55666i) q^{6} +(-2.17331 + 1.50888i) q^{7} +(-1.71431 + 0.989760i) q^{8} +(-2.39546 + 1.80604i) q^{9} +O(q^{10})$	\(q+(1.65422 - 0.291684i) q^{2} +(-0.549790 - 1.64248i) q^{3} +(0.771989 - 0.280981i) q^{4} +(3.52188 - 1.28186i) q^{5} +(-1.38856 - 2.55666i) q^{6} +(-2.17331 + 1.50888i) q^{7} +(-1.71431 + 0.989760i) q^{8} +(-2.39546 + 1.80604i) q^{9} +(5.45209 - 3.14776i) q^{10} +(1.63515 - 4.49253i) q^{11} +(-0.885937 - 1.11349i) q^{12} +(1.10865 + 3.04598i) q^{13} +(-3.15503 + 3.12994i) q^{14} +(-4.04173 - 5.07986i) q^{15} +(-3.80582 + 3.19347i) q^{16} +(1.93415 + 3.35005i) q^{17} +(-3.43584 + 3.68630i) q^{18} +(-1.31749 - 0.760652i) q^{19} +(2.35868 - 1.97917i) q^{20} +(3.67316 + 2.74005i) q^{21} +(1.39450 - 7.90859i) q^{22} +(-0.358638 - 0.0632375i) q^{23} +(2.56817 + 2.27156i) q^{24} +(6.93028 - 5.81520i) q^{25} +(2.72242 + 4.71536i) q^{26} +(4.28337 + 2.94155i) q^{27} +(-1.25381 + 1.77550i) q^{28} +(-2.29492 + 6.30525i) q^{29} +(-8.16763 - 7.22431i) q^{30} +(-0.240377 - 0.660432i) q^{31} +(-2.81938 + 3.36000i) q^{32} +(-8.27786 - 0.215742i) q^{33} +(4.17668 + 4.97757i) q^{34} +(-5.71999 + 8.09998i) q^{35} +(-1.34181 + 2.06732i) q^{36} -5.50394 q^{37} +(-2.40129 - 0.873998i) q^{38} +(4.39343 - 3.49558i) q^{39} +(-4.76888 + 5.68333i) q^{40} +(-0.793900 + 0.288956i) q^{41} +(6.87546 + 3.46125i) q^{42} +(0.0136704 + 0.0775288i) q^{43} -3.92763i q^{44} +(-6.12145 + 9.43130i) q^{45} -0.611712 q^{46} +(3.34124 + 1.21611i) q^{47} +(7.33760 + 4.49524i) q^{48} +(2.44658 - 6.55852i) q^{49} +(9.76803 - 11.6411i) q^{50} +(4.43900 - 5.01863i) q^{51} +(1.71173 + 2.03996i) q^{52} +(-7.25668 - 4.18964i) q^{53} +(7.94366 + 3.61659i) q^{54} -17.9182i q^{55} +(2.23232 - 4.73775i) q^{56} +(-0.525011 + 2.58214i) q^{57} +(-1.95717 + 11.0997i) q^{58} +(1.11005 + 0.931445i) q^{59} +(-4.54752 - 2.78595i) q^{60} +(0.979516 - 2.69120i) q^{61} +(-0.590275 - 1.02239i) q^{62} +(2.48100 - 7.53954i) q^{63} +(1.28433 - 2.22452i) q^{64} +(7.80906 + 9.30647i) q^{65} +(-13.7564 + 2.05764i) q^{66} +(0.702586 - 3.98456i) q^{67} +(2.43445 + 2.04274i) q^{68} +(0.0933094 + 0.623821i) q^{69} +(-7.09950 + 15.0676i) q^{70} +(-14.1956 - 8.19580i) q^{71} +(2.31903 - 5.46704i) q^{72} -12.0494i q^{73} +(-9.10474 + 1.60541i) q^{74} +(-13.3615 - 8.18569i) q^{75} +(-1.23082 - 0.217026i) q^{76} +(3.22498 + 12.2309i) q^{77} +(6.24812 - 7.06396i) q^{78} +(0.228017 + 1.29315i) q^{79} +(-9.31009 + 16.1256i) q^{80} +(2.47647 - 8.65258i) q^{81} +(-1.22900 + 0.709566i) q^{82} +(12.7610 + 4.64462i) q^{83} +(3.60555 + 1.08320i) q^{84} +(11.1062 + 9.31918i) q^{85} +(0.0452278 + 0.124262i) q^{86} +(11.6180 + 0.302793i) q^{87} +(1.64337 + 9.32000i) q^{88} +(4.36439 - 7.55934i) q^{89} +(-7.37529 + 17.3870i) q^{90} +(-7.00545 - 4.94706i) q^{91} +(-0.294633 + 0.0519517i) q^{92} +(-0.952586 + 0.757913i) q^{93} +(5.88187 + 1.03713i) q^{94} +(-5.61509 - 0.990092i) q^{95} +(7.06880 + 2.78347i) q^{96} +(4.18960 - 0.738740i) q^{97} +(2.13418 - 11.5629i) q^{98} +(4.19674 + 13.7148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.65422	−	0.291684i	1.16971	−	0.206252i	0.445147	−	0.895458i	$-0.353152\pi$
$2$	1.65422	−	0.291684i	1.16971	−	0.206252i	0.724566	+	0.689206i	$0.242040\pi$
$3$	−0.549790	−	1.64248i	−0.317422	−	0.948285i
$3$	−0.549790	−	1.64248i	−0.317422	−	0.948285i
$4$	0.771989	−	0.280981i	0.385995	−	0.140491i
$5$	3.52188	−	1.28186i	1.57503	−	0.573266i	0.600918	−	0.799311i	$-0.294802\pi$
$5$	3.52188	−	1.28186i	1.57503	−	0.573266i	0.974117	+	0.226045i	$0.0725796\pi$
$6$	−1.38856	−	2.55666i	−0.566877	−	1.04375i
$7$	−2.17331	+	1.50888i	−0.821435	+	0.570302i
$7$	−2.17331	+	1.50888i	−0.821435	+	0.570302i
$8$	−1.71431	+	0.989760i	−0.606101	+	0.349933i
$9$	−2.39546	+	1.80604i	−0.798487	+	0.602012i
$10$	5.45209	−	3.14776i	1.72410	−	0.995410i
$11$	1.63515	−	4.49253i	0.493015	−	1.35455i	−0.404893	−	0.914364i	$-0.632691\pi$
$11$	1.63515	−	4.49253i	0.493015	−	1.35455i	0.897908	−	0.440184i	$-0.145087\pi$
$12$	−0.885937	−	1.11349i	−0.255748	−	0.321438i
$13$	1.10865	+	3.04598i	0.307483	+	0.844804i	0.993146	+	0.116884i	$0.0372905\pi$
$13$	1.10865	+	3.04598i	0.307483	+	0.844804i	−0.685662	+	0.727920i	$0.740487\pi$
$14$	−3.15503	+	3.12994i	−0.843217	+	0.836512i
$15$	−4.04173	−	5.07986i	−1.04357	−	1.31161i
$16$	−3.80582	+	3.19347i	−0.951456	+	0.798366i
$17$	1.93415	+	3.35005i	0.469101	+	0.812507i	0.999376	−	0.0353188i	$-0.0112446\pi$
$17$	1.93415	+	3.35005i	0.469101	+	0.812507i	−0.530275	+	0.847826i	$0.677911\pi$
$18$	−3.43584	+	3.68630i	−0.809834	+	0.868870i
$19$	−1.31749	−	0.760652i	−0.302252	−	0.174506i	0.341202	−	0.939990i	$-0.389166\pi$
$19$	−1.31749	−	0.760652i	−0.302252	−	0.174506i	−0.643454	+	0.765485i	$0.722499\pi$
$20$	2.35868	−	1.97917i	0.527417	−	0.442555i
$21$	3.67316	+	2.74005i	0.801550	+	0.597928i
$22$	1.39450	−	7.90859i	0.297308	−	1.68612i
$23$	−0.358638	−	0.0632375i	−0.0747811	−	0.0131859i	0.136132	−	0.990691i	$-0.456533\pi$
$23$	−0.358638	−	0.0632375i	−0.0747811	−	0.0131859i	−0.210914	+	0.977505i	$0.567644\pi$
$24$	2.56817	+	2.27156i	0.524226	+	0.463680i
$25$	6.93028	−	5.81520i	1.38606	−	1.16304i
$26$	2.72242	+	4.71536i	0.533910	+	0.924758i
$27$	4.28337	+	2.94155i	0.824336	+	0.566101i
$28$	−1.25381	+	1.77550i	−0.236948	+	0.335537i
$29$	−2.29492	+	6.30525i	−0.426157	+	1.17086i	0.521970	+	0.852964i	$0.325197\pi$
$29$	−2.29492	+	6.30525i	−0.426157	+	1.17086i	−0.948127	+	0.317892i	$0.897025\pi$
$30$	−8.16763	−	7.22431i	−1.49120	−	1.31897i
$31$	−0.240377	−	0.660432i	−0.0431731	−	0.118617i	0.916233	−	0.400647i	$-0.131215\pi$
$31$	−0.240377	−	0.660432i	−0.0431731	−	0.118617i	−0.959406	+	0.282030i	$0.908992\pi$
$32$	−2.81938	+	3.36000i	−0.498400	+	0.593970i
$33$	−8.27786	−	0.215742i	−1.44099	−	0.0375559i
$34$	4.17668	+	4.97757i	0.716294	+	0.853647i
$35$	−5.71999	+	8.09998i	−0.966855	+	1.36915i
$36$	−1.34181	+	2.06732i	−0.223635	+	0.344553i
$37$	−5.50394			−0.904841			−0.452421	−	0.891805i	$-0.649439\pi$
$37$	−5.50394			−0.904841			−0.452421	+	0.891805i	$0.649439\pi$
$38$	−2.40129	−	0.873998i	−0.389541	−	0.141781i
$39$	4.39343	−	3.49558i	0.703512	−	0.559741i
$40$	−4.76888	+	5.68333i	−0.754026	+	0.898614i
$41$	−0.793900	+	0.288956i	−0.123986	+	0.0451273i	−0.403268	−	0.915082i	$-0.632126\pi$
$41$	−0.793900	+	0.288956i	−0.123986	+	0.0451273i	0.279282	+	0.960209i	$0.409904\pi$
$42$	6.87546	+	3.46125i	1.06091	+	0.534083i
$43$	0.0136704	+	0.0775288i	0.00208472	+	0.0118230i	0.985832	−	0.167734i	$-0.0536448\pi$
$43$	0.0136704	+	0.0775288i	0.00208472	+	0.0118230i	−0.983748	+	0.179557i	$0.942534\pi$
$44$		−	3.92763i		−	0.592112i
$45$	−6.12145	+	9.43130i	−0.912532	+	1.40594i
$46$	−0.611712			−0.0901920
$47$	3.34124	+	1.21611i	0.487369	+	0.177388i	0.574004	−	0.818852i	$-0.305389\pi$
$47$	3.34124	+	1.21611i	0.487369	+	0.177388i	−0.0866351	+	0.996240i	$0.527611\pi$
$48$	7.33760	+	4.49524i	1.05909	+	0.648832i
$49$	2.44658	−	6.55852i	0.349512	−	0.936932i
$50$	9.76803	−	11.6411i	1.38141	−	1.64630i
$51$	4.43900	−	5.01863i	0.621585	−	0.702749i
$52$	1.71173	+	2.03996i	0.237374	+	0.282891i
$53$	−7.25668	−	4.18964i	−0.996781	−	0.575492i	−0.0894868	−	0.995988i	$-0.528523\pi$
$53$	−7.25668	−	4.18964i	−0.996781	−	0.575492i	−0.907294	+	0.420496i	$0.861856\pi$
$54$	7.94366	+	3.61659i	1.08100	+	0.492155i
$55$		−	17.9182i		−	2.41609i
$56$	2.23232	−	4.73775i	0.298306	−	0.633108i
$57$	−0.525011	+	2.58214i	−0.0695394	+	0.342013i
$58$	−1.95717	+	11.0997i	−0.256989	+	1.45746i
$59$	1.11005	+	0.931445i	0.144517	+	0.121264i	0.712180	−	0.701997i	$-0.247708\pi$
$59$	1.11005	+	0.931445i	0.144517	+	0.121264i	−0.567663	+	0.823261i	$0.692152\pi$
$60$	−4.54752	−	2.78595i	−0.587082	−	0.359665i
$61$	0.979516	−	2.69120i	0.125414	−	0.344573i	−0.861057	−	0.508509i	$-0.830197\pi$
$61$	0.979516	−	2.69120i	0.125414	−	0.344573i	0.986471	+	0.163936i	$0.0524191\pi$
$62$	−0.590275	−	1.02239i	−0.0749650	−	0.129843i
$63$	2.48100	−	7.53954i	0.312577	−	0.949892i
$64$	1.28433	−	2.22452i	0.160541	−	0.278066i
$65$	7.80906	+	9.30647i	0.968594	+	1.15433i
$66$	−13.7564	+	2.05764i	−1.69329	+	0.253277i
$67$	0.702586	−	3.98456i	0.0858345	−	0.486792i	−0.911339	−	0.411657i	$-0.864950\pi$
$67$	0.702586	−	3.98456i	0.0858345	−	0.486792i	0.997173	−	0.0751348i	$-0.0239387\pi$
$68$	2.43445	+	2.04274i	0.295220	+	0.247719i
$69$	0.0933094	+	0.623821i	0.0112331	+	0.0750993i
$70$	−7.09950	+	15.0676i	−0.848553	+	1.80092i
$71$	−14.1956	−	8.19580i	−1.68470	−	0.972663i	−0.958461	−	0.285222i	$-0.907933\pi$
$71$	−14.1956	−	8.19580i	−1.68470	−	0.972663i	−0.726240	−	0.687441i	$-0.758734\pi$
$72$	2.31903	−	5.46704i	0.273300	−	0.644297i
$73$		−	12.0494i		−	1.41027i	−0.709072	−	0.705136i	$-0.750886\pi$
$73$		−	12.0494i		−	1.41027i	0.709072	−	0.705136i	$-0.249114\pi$
$74$	−9.10474	+	1.60541i	−1.05840	+	0.186625i
$75$	−13.3615	−	8.18569i	−1.54286	−	0.945202i
$76$	−1.23082	−	0.217026i	−0.141184	−	0.0248946i
$77$	3.22498	+	12.2309i	0.367521	+	1.39384i
$78$	6.24812	−	7.06396i	0.707460	−	0.799836i
$79$	0.228017	+	1.29315i	0.0256539	+	0.145491i	0.994944	−	0.100428i	$-0.0320214\pi$
$79$	0.228017	+	1.29315i	0.0256539	+	0.145491i	−0.969290	+	0.245919i	$0.920910\pi$
$80$	−9.31009	+	16.1256i	−1.04090	+	1.80289i
$81$	2.47647	−	8.65258i	0.275163	−	0.961398i
$82$	−1.22900	+	0.709566i	−0.135721	+	0.0783584i
$83$	12.7610	+	4.64462i	1.40070	+	0.509814i	0.928386	−	0.371616i	$-0.121196\pi$
$83$	12.7610	+	4.64462i	1.40070	+	0.509814i	0.472315	+	0.881430i	$0.343419\pi$
$84$	3.60555	+	1.08320i	0.393397	+	0.118187i
$85$	11.1062	+	9.31918i	1.20463	+	1.01081i
$86$	0.0452278	+	0.124262i	0.00487704	+	0.0133996i
$87$	11.6180	+	0.302793i	1.24558	+	0.0324628i
$88$	1.64337	+	9.32000i	0.175184	+	0.993516i
$89$	4.36439	−	7.55934i	0.462624	−	0.801289i	−0.536467	−	0.843922i	$-0.680241\pi$
$89$	4.36439	−	7.55934i	0.462624	−	0.801289i	0.999091	+	0.0426330i	$0.0135746\pi$
$90$	−7.37529	+	17.3870i	−0.777423	+	1.83275i
$91$	−7.00545	−	4.94706i	−0.734371	−	0.518593i
$92$	−0.294633	+	0.0519517i	−0.0307176	+	0.00541634i
$93$	−0.952586	+	0.757913i	−0.0987786	+	0.0785919i
$94$	5.88187	+	1.03713i	0.606669	+	0.106972i
$95$	−5.61509	−	0.990092i	−0.576096	−	0.101581i
$96$	7.06880	+	2.78347i	0.721456	+	0.284086i
$97$	4.18960	−	0.738740i	0.425390	−	0.0750077i	0.0431451	−	0.999069i	$-0.486262\pi$
$97$	4.18960	−	0.738740i	0.425390	−	0.0750077i	0.382245	+	0.924061i	$0.375151\pi$
$98$	2.13418	−	11.5629i	0.215584	−	1.16803i
$99$	4.19674	+	13.7148i	0.421788	+	1.37839i
$100$	3.71614	−	6.43655i	0.371614	−	0.643655i
$101$	−1.21735	−	6.90392i	−0.121131	−	0.686966i	−0.983531	−	0.180739i	$-0.942151\pi$
$101$	−1.21735	−	6.90392i	−0.121131	−	0.686966i	0.862400	−	0.506227i	$-0.168960\pi$
$102$	5.87925	−	9.59672i	0.582132	−	0.950217i
$103$	−2.45182	−	6.73632i	−0.241585	−	0.663749i	−0.999929	−	0.0118948i	$-0.996214\pi$
$103$	−2.45182	−	6.73632i	−0.241585	−	0.663749i	0.758344	−	0.651854i	$-0.226009\pi$
$104$	−4.91536	−	4.12448i	−0.481991	−	0.404438i
$105$	16.4488	+	4.94166i	1.60524	+	0.482257i
$106$	−13.2262	−	4.81395i	−1.28464	−	0.467572i
$107$	−15.4107	+	8.89738i	−1.48981	+	0.860142i	−0.999932	−	0.0116497i	$-0.996292\pi$
$107$	−15.4107	+	8.89738i	−1.48981	+	0.860142i	−0.489877	+	0.871792i	$0.662958\pi$
$108$	4.13324	+	1.06730i	0.397721	+	0.102701i
$109$	−8.73677	+	15.1325i	−0.836831	+	1.44943i	0.0557007	+	0.998448i	$0.482261\pi$
$109$	−8.73677	+	15.1325i	−0.836831	+	1.44943i	−0.892531	+	0.450986i	$0.851073\pi$
$110$	−5.22645	−	29.6407i	−0.498323	−	2.82613i
$111$	3.02601	+	9.04009i	0.287216	+	0.858047i
$112$	3.45270	−	12.6829i	0.326250	−	1.19842i
$113$	11.6574	+	2.05551i	1.09663	+	0.193366i	0.692561	−	0.721360i	$-0.256483\pi$
$113$	11.6574	+	2.05551i	1.09663	+	0.193366i	0.404074	+	0.914726i	$0.367594\pi$
$114$	−0.115316	+	4.42458i	−0.0108003	+	0.414400i
$115$	−1.34414	+	0.237008i	−0.125342	+	0.0221012i
$116$			5.51242i			0.511815i
$117$	−8.15688	−	5.29428i	−0.754104	−	0.489456i
$118$	2.10796	+	1.21703i	0.194054	+	0.112037i
$119$	−9.25834	−	4.36231i	−0.848710	−	0.399893i
$120$	11.9566	+	4.70814i	1.09149	+	0.429792i
$121$	−9.08261	−	7.62122i	−0.825692	−	0.692838i
$122$	0.835358	−	4.73755i	0.0756298	−	0.428918i
$123$	0.911082	+	1.14510i	0.0821495	+	0.103250i
$124$	−0.371138	−	0.442305i	−0.0333291	−	0.0397201i
$125$	7.58360	−	13.1352i	0.678298	−	1.17485i
$126$	1.90497	−	13.1957i	0.169708	−	1.17557i
$127$	−0.317649	−	0.550185i	−0.0281868	−	0.0488210i	0.851588	−	0.524212i	$-0.175640\pi$
$127$	−0.317649	−	0.550185i	−0.0281868	−	0.0488210i	−0.879775	+	0.475391i	$0.842307\pi$
$128$	4.47603	−	12.2978i	0.395629	−	1.08698i
$129$	0.119823	−	0.0650779i	0.0105499	−	0.00572979i
$130$	15.6325	+	13.1172i	1.37106	+	1.15045i
$131$	0.356411	−	2.02131i	0.0311398	−	0.176603i	−0.965271	−	0.261250i	$-0.915865\pi$
$131$	0.356411	−	2.02131i	0.0311398	−	0.176603i	0.996411	+	0.0846475i	$0.0269764\pi$
$132$	−6.45104	+	2.15937i	−0.561491	+	0.187949i
$133$	4.01104	−	0.334791i	0.347802	−	0.0290301i
$134$		−	6.79629i		−	0.587110i
$135$	18.8562	+	4.86911i	1.62288	+	0.419066i
$136$	−6.63149	−	3.82869i	−0.568646	−	0.328308i
$137$	10.0677	+	11.9983i	0.860145	+	1.02508i	0.999393	+	0.0348229i	$0.0110867\pi$
$137$	10.0677	+	11.9983i	0.860145	+	1.02508i	−0.139249	+	0.990257i	$0.544469\pi$
$138$	0.336313	+	1.00472i	0.0286289	+	0.0855277i
$139$	−14.5992	+	17.3986i	−1.23829	+	1.47573i	−0.413288	+	0.910600i	$0.635620\pi$
$139$	−14.5992	+	17.3986i	−1.23829	+	1.47573i	−0.824999	+	0.565133i	$0.808825\pi$
$140$	−2.13983	+	7.86031i	−0.180849	+	0.664317i
$141$	0.160454	−	6.15651i	0.0135127	−	0.518472i
$142$	−25.8732	−	9.41707i	−2.17123	−	0.790263i
$143$	15.4970			1.29592
$144$	3.34919	−	14.5233i	0.279099	−	1.21027i
$145$			25.1481i			2.08844i
$146$	−3.51461	−	19.9323i	−0.290871	−	1.64961i
$147$	−12.1173	−	0.412643i	−0.999421	−	0.0340342i
$148$	−4.24898	+	1.54650i	−0.349264	+	0.127122i
$149$	7.54861	−	8.99609i	0.618406	−	0.736988i	−0.362389	−	0.932027i	$-0.618039\pi$
$149$	7.54861	−	8.99609i	0.618406	−	0.736988i	0.980796	+	0.195039i	$0.0624833\pi$
$150$	−24.4906	−	9.64361i	−1.99965	−	0.787398i
$151$	−1.47688	−	0.537540i	−0.120187	−	0.0437444i	0.281227	−	0.959641i	$-0.409259\pi$
$151$	−1.47688	−	0.537540i	−0.120187	−	0.0437444i	−0.401413	+	0.915897i	$0.631481\pi$
$152$	3.01145			0.244261
$153$	−10.6835	−	4.53177i	−0.863710	−	0.366372i
$154$	8.90241	+	19.2920i	0.717376	+	1.55459i
$155$	−1.69316	−	2.01783i	−0.135998	−	0.162076i
$156$	2.40949	−	3.93302i	0.192914	−	0.314894i
$157$	6.00836	−	7.16049i	0.479520	−	0.571469i	−0.471000	−	0.882133i	$-0.656107\pi$
$157$	6.00836	−	7.16049i	0.479520	−	0.571469i	0.950520	+	0.310664i	$0.100551\pi$
$158$	0.754382	+	2.07265i	0.0600154	+	0.164891i
$159$	−2.89174	+	14.2223i	−0.229330	+	1.12791i
$160$	−5.62247	+	15.4476i	−0.444495	+	1.22124i
$161$	0.874849	−	0.403705i	0.0689478	−	0.0318164i
$162$	1.57281	−	15.0356i	0.123572	−	1.18131i
$163$	7.03192	+	12.1796i	0.550783	+	0.953983i	0.998218	+	0.0596673i	$0.0190040\pi$
$163$	7.03192	+	12.1796i	0.550783	+	0.953983i	−0.447436	+	0.894316i	$0.647663\pi$
$164$	−0.531691	+	0.446142i	−0.0415181	+	0.0348378i
$165$	−29.4302	+	9.85125i	−2.29114	+	0.766919i
$166$	22.4643	+	3.96106i	1.74357	+	0.307438i
$167$	−0.663852	+	3.76489i	−0.0513704	+	0.291336i	−0.999660	−	0.0260700i	$-0.991701\pi$
$167$	−0.663852	+	3.76489i	−0.0513704	+	0.291336i	0.948290	+	0.317406i	$0.102812\pi$
$168$	−9.00894	−	1.06176i	−0.695055	−	0.0819167i
$169$	1.90966	−	1.60240i	0.146897	−	0.123261i
$170$	21.0903	+	12.1765i	1.61756	+	0.933896i
$171$	4.52976	−	0.557318i	0.346399	−	0.0426192i
$172$	0.0323376	+	0.0560103i	0.00246572	+	0.00427074i
$173$	−8.86502	+	7.43864i	−0.673995	+	0.565549i	−0.914245	−	0.405162i	$-0.867215\pi$
$173$	−8.86502	+	7.43864i	−0.673995	+	0.565549i	0.240250	+	0.970711i	$0.422771\pi$
$174$	19.3070	−	2.88789i	1.46366	−	0.218930i
$175$	−6.28726	+	23.0952i	−0.475272	+	1.74583i
$176$	8.12365	+	22.3196i	0.612343	+	1.68240i
$177$	0.919581	−	2.33534i	0.0691199	−	0.175535i
$178$	5.01473	−	13.7779i	0.375870	−	1.03269i
$179$	7.89281	−	4.55692i	0.589937	−	0.340600i	−0.175136	−	0.984544i	$-0.556036\pi$
$179$	7.89281	−	4.55692i	0.589937	−	0.340600i	0.765072	+	0.643944i	$0.222703\pi$
$180$	−2.07568	+	9.00088i	−0.154712	+	0.670886i
$181$	−6.15516	+	3.55368i	−0.457509	+	0.264143i	−0.710996	−	0.703196i	$-0.751756\pi$
$181$	−6.15516	+	3.55368i	−0.457509	+	0.264143i	0.253487	+	0.967339i	$0.418422\pi$
$182$	−13.0316	−	6.14017i	−0.965963	−	0.455140i
$183$	−4.95876	−	0.129238i	−0.366562	−	0.00955354i
$184$	0.677407	−	0.246556i	0.0499391	−	0.0181764i
$185$	−19.3842	+	7.05528i	−1.42516	+	0.518715i
$186$	−1.35472	+	1.53161i	−0.0993328	+	0.112303i
$187$	18.2128	−	3.21141i	1.33185	−	0.234842i
$188$	2.92110			0.213043
$189$	−13.7475	+	0.0701746i	−0.999987	+	0.00510445i
$190$	−9.57741			−0.694818
$191$	−12.0621	+	2.12687i	−0.872783	+	0.153895i	−0.592060	−	0.805894i	$-0.701685\pi$
$191$	−12.0621	+	2.12687i	−0.872783	+	0.153895i	−0.280723	+	0.959789i	$0.590574\pi$
$192$	−4.35984	−	0.886460i	−0.314644	−	0.0639747i
$193$	15.5979	−	5.67717i	1.12276	−	0.408652i	0.287102	−	0.957900i	$-0.407308\pi$
$193$	15.5979	−	5.67717i	1.12276	−	0.408652i	0.835659	+	0.549248i	$0.185086\pi$
$194$	6.71506	−	2.44408i	0.482113	−	0.175475i
$195$	10.9923	−	17.9428i	0.787176	−	1.28491i
$196$	0.0459144	−	5.75056i	0.00327960	−	0.410754i
$197$	7.93030	−	4.57856i	0.565011	−	0.326209i	−0.190144	−	0.981756i	$-0.560895\pi$
$197$	7.93030	−	4.57856i	0.565011	−	0.326209i	0.755154	+	0.655547i	$0.227562\pi$
$198$	10.9427	+	21.4632i	0.777666	+	1.52533i
$199$	−5.68127	+	3.28009i	−0.402735	+	0.232519i	−0.687663	−	0.726030i	$-0.741363\pi$
$199$	−5.68127	+	3.28009i	−0.402735	+	0.232519i	0.284928	+	0.958549i	$0.408030\pi$
$200$	−6.12503	+	16.8284i	−0.433105	+	1.18995i
$201$	−6.93083	+	1.03669i	−0.488863	+	0.0731227i
$202$	−4.02753	−	11.0655i	−0.283376	−	0.778569i
$203$	−4.52626	−	17.1660i	−0.317681	−	1.20482i
$204$	2.01672	−	5.12161i	0.141199	−	0.358584i
$205$	−2.42562	+	2.03534i	−0.169413	+	0.142154i
$206$	−6.02073	−	10.4282i	−0.419484	−	0.726568i
$207$	0.973312	−	0.496229i	0.0676498	−	0.0344903i
$208$	−13.9466	−	8.05205i	−0.967020	−	0.558309i
$209$	−5.57154	+	4.67507i	−0.385391	+	0.323382i
$210$	28.6514	+	3.37675i	1.97714	+	0.233018i
$211$	2.58385	−	14.6538i	0.177880	−	1.00881i	−0.756888	−	0.653545i	$-0.773281\pi$
$211$	2.58385	−	14.6538i	0.177880	−	1.00881i	0.934767	−	0.355261i	$-0.115608\pi$
$212$	−6.77929	−	1.19537i	−0.465603	−	0.0820985i
$213$	−5.65684	+	27.8218i	−0.387601	+	1.90632i
$214$	−22.8975	+	19.2133i	−1.56524	+	1.31339i
$215$	0.147527	+	0.255524i	0.0100612	+	0.0174266i
$216$	−10.2545	−	0.803228i	−0.697728	−	0.0546527i
$217$	1.51893	+	1.07262i	0.103111	+	0.0728145i
$218$	−10.0386	+	27.5810i	−0.679903	+	1.86802i
$219$	−19.7908	+	6.62462i	−1.33734	+	0.447651i
$220$	−5.03468	−	13.8327i	−0.339438	−	0.932598i
$221$	−8.05991	+	9.60542i	−0.542168	+	0.646131i
$222$	7.64255	+	14.0717i	0.512934	+	0.944429i
$223$	−0.651794	−	0.776778i	−0.0436474	−	0.0520169i	0.743779	−	0.668425i	$-0.233031\pi$
$223$	−0.651794	−	0.776778i	−0.0436474	−	0.0520169i	−0.787426	+	0.616409i	$0.788587\pi$
$224$	1.05756	−	11.5564i	0.0706613	−	0.772147i
$225$	−6.09877	+	26.4464i	−0.406585	+	1.76309i
$226$	19.8835			1.32263
$227$	21.5947	+	7.85982i	1.43329	+	0.521675i	0.937872	−	0.346981i	$-0.112793\pi$
$227$	21.5947	+	7.85982i	1.43329	+	0.521675i	0.495417	+	0.868655i	$0.335015\pi$
$228$	0.320230	+	2.14091i	0.0212078	+	0.141785i
$229$	0.229944	−	0.274037i	0.0151951	−	0.0181089i	−0.758393	−	0.651797i	$-0.774015\pi$
$229$	0.229944	−	0.274037i	0.0151951	−	0.0181089i	0.773589	+	0.633688i	$0.218460\pi$
$230$	−2.15438	+	0.784130i	−0.142056	+	0.0517040i
$231$	18.3159	−	12.0214i	1.20510	−	0.790950i
$232$	−2.30646	−	13.0806i	−0.151427	−	0.858783i
$233$			19.9280i			1.30553i	0.757561	+	0.652764i	$0.226391\pi$
$233$			19.9280i			1.30553i	−0.757561	+	0.652764i	$0.773609\pi$
$234$	−15.0376	−	6.37869i	−0.983036	−	0.416988i
$235$	13.3263			0.869314
$236$	1.11867	+	0.407162i	0.0728191	+	0.0265040i
$237$	1.99861	−	1.08547i	0.129823	−	0.0705091i
$238$	−16.5878	−	4.51573i	−1.07523	−	0.292711i
$239$	−8.88553	+	10.5894i	−0.574757	+	0.684969i	−0.972600	−	0.232485i	$-0.925314\pi$
$239$	−8.88553	+	10.5894i	−0.574757	+	0.684969i	0.397843	+	0.917454i	$0.369759\pi$
$240$	31.6045	+	6.42594i	2.04006	+	0.414793i
$241$	−2.17087	−	2.58714i	−0.139838	−	0.166652i	0.691580	−	0.722300i	$-0.256915\pi$
$241$	−2.17087	−	2.58714i	−0.139838	−	0.166652i	−0.831418	+	0.555647i	$0.812470\pi$
$242$	−17.2477	−	9.95794i	−1.10872	−	0.640121i
$243$	−15.5732	+	0.689560i	−0.999021	+	0.0442353i
$244$		−	2.35280i		−	0.150623i
$245$	0.209466	−	26.2345i	0.0133823	−	1.67606i
$246$	1.84114	+	1.62850i	0.117387	+	0.103829i
$247$	0.856304	−	4.85634i	0.0544853	−	0.309002i
$248$	1.06575	+	0.894271i	0.0676752	+	0.0567863i
$249$	0.612814	−	23.5132i	0.0388355	−	1.49009i
$250$	8.71365	−	23.9405i	0.551099	−	1.51413i
$251$	−0.197747	−	0.342507i	−0.0124817	−	0.0216189i	0.859717	−	0.510770i	$-0.170640\pi$
$251$	−0.197747	−	0.342507i	−0.0124817	−	0.0216189i	−0.872199	+	0.489152i	$0.837306\pi$
$252$	−0.203160	−	6.51756i	−0.0127979	−	0.410568i
$253$	−0.870521	+	1.50779i	−0.0547292	+	0.0947937i
$254$	−0.685943	−	0.817475i	−0.0430399	−	0.0512929i
$255$	9.20048	−	23.3652i	0.576156	−	1.46319i
$256$	2.92519	−	16.5896i	0.182825	−	1.03685i
$257$	22.7517	+	19.0909i	1.41921	+	1.19086i	0.951760	+	0.306842i	$0.0992723\pi$
$257$	22.7517	+	19.0909i	1.41921	+	1.19086i	0.467452	+	0.884019i	$0.345172\pi$
$258$	0.179232	−	0.142604i	0.0111585	−	0.00887814i
$259$	11.9618	−	8.30476i	0.743269	−	0.516033i
$260$	8.64345	+	4.99030i	0.536044	+	0.309485i
$261$	−5.89011	−	19.2487i	−0.364588	−	1.19146i
$262$		−	3.44766i		−	0.212997i
$263$	11.8805	−	2.09484i	0.732580	−	0.129174i	0.205100	−	0.978741i	$-0.434248\pi$
$263$	11.8805	−	2.09484i	0.732580	−	0.129174i	0.527480	+	0.849567i	$0.323137\pi$
$264$	14.4044	−	7.82324i	0.886529	−	0.481487i
$265$	−30.9277	−	5.45339i	−1.89987	−	0.334999i
$266$	6.53751	−	1.72378i	0.400840	−	0.105692i
$267$	−14.8155	−	3.01235i	−0.906696	−	0.184353i
$268$	−0.577198	−	3.27345i	−0.0352580	−	0.199958i
$269$	1.78062	−	3.08412i	0.108566	−	0.188042i	−0.806624	−	0.591066i	$-0.798707\pi$
$269$	1.78062	−	3.08412i	0.108566	−	0.188042i	0.915190	+	0.403024i	$0.132041\pi$
$270$	32.6126	+	2.55453i	1.98474	+	0.155464i
$271$	6.59196	−	3.80587i	0.400433	−	0.231190i	−0.286238	−	0.958159i	$-0.592405\pi$
$271$	6.59196	−	3.80587i	0.400433	−	0.231190i	0.686671	+	0.726969i	$0.259071\pi$
$272$	−18.0593	−	6.57306i	−1.09501	−	0.398550i
$273$	−4.27391	+	14.2261i	−0.258669	+	0.861005i
$274$	20.1540	+	16.9112i	1.21755	+	1.02164i
$275$	−14.7929	−	40.6432i	−0.892046	−	2.45088i
$276$	0.247316	+	0.455365i	0.0148867	+	0.0274098i
$277$	−1.87641	−	10.6416i	−0.112742	−	0.639394i	−0.987843	−	0.155454i	$-0.950316\pi$
$277$	−1.87641	−	10.6416i	−0.112742	−	0.639394i	0.875101	−	0.483941i	$-0.160795\pi$
$278$	−19.0754	+	33.0396i	−1.14407	+	1.98158i
$279$	1.76858	+	1.14791i	0.105882	+	0.0687235i
$280$	1.78883	−	19.5473i	0.106903	−	1.16818i
$281$	3.59151	−	0.633280i	0.214252	−	0.0377783i	−0.0654920	−	0.997853i	$-0.520862\pi$
$281$	3.59151	−	0.633280i	0.214252	−	0.0377783i	0.279744	+	0.960075i	$0.409751\pi$
$282$	−1.53033	−	10.2310i	−0.0911298	−	0.609250i
$283$	24.6264	+	4.34229i	1.46389	+	0.258123i	0.848119	−	0.529806i	$-0.177735\pi$
$283$	24.6264	+	4.34229i	1.46389	+	0.258123i	0.615767	+	0.787928i	$0.288846\pi$
$284$	−13.2617	−	2.33839i	−0.786936	−	0.138758i
$285$	1.46092	+	9.76700i	0.0865374	+	0.578547i
$286$	25.6354	−	4.52022i	1.51586	−	0.267286i
$287$	1.28939	−	1.82589i	0.0761106	−	0.107779i
$288$	0.685423	−	13.1407i	0.0403889	−	0.774321i
$289$	1.01810	−	1.76340i	0.0598883	−	0.103730i
$290$	7.33531	+	41.6006i	0.430744	+	2.44287i
$291$	−3.51677	−	6.47518i	−0.206157	−	0.379582i
$292$	−3.38565	−	9.30198i	−0.198130	−	0.544357i
$293$	23.0690	+	19.3572i	1.34770	+	1.13086i	0.979574	+	0.201084i	$0.0644465\pi$
$293$	23.0690	+	19.3572i	1.34770	+	1.13086i	0.368131	+	0.929774i	$0.379998\pi$
$294$	−20.1651	+	2.85183i	−1.17605	+	0.166322i
$295$	5.10346	+	1.85751i	0.297135	+	0.108148i
$296$	9.43547	−	5.44757i	0.548426	−	0.316634i
$297$	20.2189	−	14.4333i	1.17322	−	0.837506i
$298$	9.86307	−	17.0833i	0.571352	−	0.989612i
$299$	−0.204982	−	1.16251i	−0.0118544	−	0.0672298i
$300$	−12.6150	−	2.56493i	−0.728327	−	0.148086i
$301$	−0.146691	−	0.147867i	−0.00845516	−	0.00852294i
$302$	−2.59988	−	0.458429i	−0.149606	−	0.0263796i
$303$	−10.6702	+	5.79517i	−0.612989	+	0.332924i
$304$	7.44324	−	1.31244i	0.426899	−	0.0752738i
$305$		−	10.7337i		−	0.614610i
$306$	−18.9947	−	4.38035i	−1.08586	−	0.250408i
$307$	−21.5000	−	12.4130i	−1.22707	−	0.708449i	−0.260654	−	0.965432i	$-0.583938\pi$
$307$	−21.5000	−	12.4130i	−1.22707	−	0.708449i	−0.966416	+	0.256983i	$0.917272\pi$
$308$	5.92631	+	8.53597i	0.337683	+	0.486382i
$309$	−9.71626	+	7.73062i	−0.552739	+	0.439779i
$310$	−3.38944	−	2.84408i	−0.192507	−	0.161533i
$311$	−1.37130	+	7.77704i	−0.0777594	+	0.440995i	0.920926	+	0.389737i	$0.127434\pi$
$311$	−1.37130	+	7.77704i	−0.0777594	+	0.440995i	−0.998685	+	0.0512580i	$0.983677\pi$
$312$	−4.07194	+	10.3410i	−0.230528	+	0.585442i
$313$	−12.4235	−	14.8057i	−0.702216	−	0.836868i	0.290559	−	0.956857i	$-0.406159\pi$
$313$	−12.4235	−	14.8057i	−0.702216	−	0.836868i	−0.992775	+	0.119989i	$0.961714\pi$
$314$	7.85057	−	13.5976i	0.443033	−	0.767356i
$315$	−0.926835	−	29.7337i	−0.0522212	−	1.67530i
$316$	0.539377	+	0.934229i	0.0303424	+	0.0525545i
$317$	−4.83449	+	13.2826i	−0.271532	+	0.746028i	0.726720	+	0.686933i	$0.241044\pi$
$317$	−4.83449	+	13.2826i	−0.271532	+	0.746028i	−0.998252	+	0.0590945i	$0.981179\pi$
$318$	−0.635155	+	24.3704i	−0.0356177	+	1.36662i
$319$	24.5740	+	20.6200i	1.37588	+	1.15450i
$320$	1.67173	−	9.48085i	0.0934525	−	0.529996i
$321$	23.0864	+	20.4200i	1.28856	+	1.13974i
$322$	1.32944	−	0.922998i	0.0740869	−	0.0514367i
$323$		−	5.88487i		−	0.327443i
$324$	−0.519404	−	7.37554i	−0.0288558	−	0.409752i
$325$	25.3962	+	14.6625i	1.40873	+	0.813330i
$326$	15.1850	+	18.0967i	0.841018	+	1.00229i
$327$	29.6582	+	6.03022i	1.64010	+	0.333472i
$328$	1.07500	−	1.28113i	0.0593568	−	0.0707386i
$329$	−9.09651	+	2.39852i	−0.501507	+	0.132235i
$330$	−45.8107	+	24.8805i	−2.52180	+	1.36963i
$331$	13.6983	+	4.98578i	0.752928	+	0.274043i	0.689837	−	0.723964i	$-0.257682\pi$
$331$	13.6983	+	4.98578i	0.752928	+	0.274043i	0.0630908	+	0.998008i	$0.479904\pi$
$332$	11.1564			0.612287
$333$	13.1845	−	9.94030i	0.722504	−	0.544725i
$334$			6.42161i			0.351375i
$335$	−2.63323	−	14.9338i	−0.143869	−	0.815920i
$336$	−22.7297	+	1.30196i	−1.24000	+	0.0710278i
$337$	−25.3341	+	9.22085i	−1.38003	+	0.502291i	−0.922189	−	0.386740i	$-0.873601\pi$
$337$	−25.3341	+	9.22085i	−1.38003	+	0.502291i	−0.457846	+	0.889032i	$0.651379\pi$
$338$	2.69161	−	3.20774i	0.146404	−	0.174478i
$339$	−3.03299	−	20.2771i	−0.164729	−	1.10130i
$340$	11.1924	+	4.07369i	0.606991	+	0.220927i
$341$	−3.36006			−0.181957
$342$	7.33067	−	2.24319i	0.396397	−	0.121298i
$343$	4.57881	+	17.9453i	0.247233	+	0.968956i
$344$	−0.100170	−	0.119378i	−0.00540082	−	0.00643644i
$345$	1.12828	+	2.07742i	0.0607444	+	0.111844i
$346$	−12.4950	+	14.8910i	−0.671735	+	0.800543i
$347$	−6.84951	−	18.8189i	−0.367701	−	1.01025i	−0.976233	−	0.216721i	$-0.930464\pi$
$347$	−6.84951	−	18.8189i	−0.367701	−	1.01025i	0.608532	−	0.793529i	$-0.291759\pi$
$348$	9.05402	−	3.03067i	0.485346	−	0.162461i
$349$	3.59306	−	9.87186i	0.192332	−	0.528429i	−0.805617	−	0.592437i	$-0.798166\pi$
$349$	3.59306	−	9.87186i	0.192332	−	0.528429i	0.997949	+	0.0640080i	$0.0203883\pi$
$350$	−3.66403	+	40.0385i	−0.195851	+	2.14015i
$351$	−4.21116	+	16.3082i	−0.224775	+	0.870469i
$352$	10.4848	+	18.1602i	0.558842	+	0.967944i
$353$	2.52612	−	2.11967i	0.134452	−	0.112819i	−0.573082	−	0.819498i	$-0.694252\pi$
$353$	2.52612	−	2.11967i	0.134452	−	0.112819i	0.707534	+	0.706680i	$0.249808\pi$
$354$	0.840011	−	4.13139i	0.0446461	−	0.219581i
$355$	−60.5010	−	10.6680i	−3.21106	−	0.566196i
$356$	1.24523	−	7.06204i	0.0659970	−	0.374288i
$357$	−2.07486	+	17.6050i	−0.109813	+	0.931753i
$358$	11.7273	−	9.84037i	0.619807	−	0.520080i
$359$	9.58505	+	5.53393i	0.505880	+	0.292070i	0.731138	−	0.682229i	$-0.238989\pi$
$359$	9.58505	+	5.53393i	0.505880	+	0.292070i	−0.225259	+	0.974299i	$0.572323\pi$
$360$	1.15937	−	22.2270i	0.0611042	−	1.17146i
$361$	−8.34282	−	14.4502i	−0.439096	−	0.760536i
$362$	−9.14545	+	7.67395i	−0.480674	+	0.403334i
$363$	−7.52414	+	19.1081i	−0.394915	+	1.00291i
$364$	−6.79817	−	1.85068i	−0.356321	−	0.0970021i
$365$	−15.4456	−	42.4365i	−0.808461	−	2.22123i
$366$	−8.24059	+	1.23260i	−0.430743	+	0.0644292i
$367$	−6.76907	+	18.5979i	−0.353342	+	0.970800i	0.627946	+	0.778257i	$0.283896\pi$
$367$	−6.76907	+	18.5979i	−0.353342	+	0.970800i	−0.981288	+	0.192543i	$0.938326\pi$
$368$	1.56686	−	0.904626i	0.0816781	−	0.0471569i
$369$	1.37989	−	2.12599i	0.0718343	−	0.110675i
$370$	−30.0079	+	17.3251i	−1.56004	+	0.900688i
$371$	22.0927	−	1.84402i	1.14700	−	0.0957367i
$372$	−0.522427	+	0.852760i	−0.0270866	+	0.0442135i
$373$	4.10447	−	1.49390i	0.212521	−	0.0773514i	−0.233566	−	0.972341i	$-0.575039\pi$
$373$	4.10447	−	1.49390i	0.212521	−	0.0773514i	0.446087	+	0.894990i	$0.352817\pi$
$374$	29.1914	−	10.6248i	1.50945	−	0.549395i
$375$	−25.7436	−	5.23430i	−1.32940	−	0.270298i
$376$	−6.93158	+	1.22223i	−0.357469	+	0.0630315i
$377$	−21.7499			−1.12018
$378$	−22.7210	+	4.12603i	−1.16864	+	0.212220i
$379$	−5.24775			−0.269559			−0.134780	−	0.990876i	$-0.543033\pi$
$379$	−5.24775			−0.269559			−0.134780	+	0.990876i	$0.543033\pi$
$380$	−4.61299	+	0.813394i	−0.236641	+	0.0417262i
$381$	−0.729025	+	0.824218i	−0.0373491	+	0.0422259i
$382$	−19.3330	+	7.03664i	−0.989163	+	0.360026i
$383$	−3.81324	+	1.38790i	−0.194847	+	0.0709186i	−0.437601	−	0.899169i	$-0.644172\pi$
$383$	−3.81324	+	1.38790i	−0.194847	+	0.0709186i	0.242753	+	0.970088i	$0.421949\pi$
$384$	−22.6597	−	0.590569i	−1.15635	−	0.0301374i
$385$	27.0363	+	38.9419i	1.37790	+	1.98466i
$386$	24.1465	−	13.9410i	1.22902	−	0.709577i
$387$	−0.172767	−	0.161028i	−0.00878223	−	0.00818551i
$388$	3.02676	−	1.74750i	0.153660	−	0.0887159i
$389$	−2.79942	+	7.69133i	−0.141936	+	0.389966i	−0.990209	−	0.139593i	$-0.955420\pi$
$389$	−2.79942	+	7.69133i	−0.141936	+	0.389966i	0.848273	+	0.529559i	$0.177643\pi$
$390$	12.9501	−	32.8877i	0.655755	−	1.66533i
$391$	−0.481811	−	1.32377i	−0.0243662	−	0.0669457i
$392$	2.29715	+	13.6649i	0.116024	+	0.690181i
$393$	−3.51590	+	0.525899i	−0.177354	+	0.0265281i
$394$	11.7830	−	9.88711i	0.593619	−	0.498105i
$395$	2.46069	+	4.26204i	0.123811	+	0.214446i
$396$	7.09344	+	9.40848i	0.356459	+	0.472794i
$397$	5.86290	+	3.38495i	0.294251	+	0.169886i	0.639857	−	0.768494i	$-0.278993\pi$
$397$	5.86290	+	3.38495i	0.294251	+	0.169886i	−0.345607	+	0.938380i	$0.612327\pi$
$398$	−8.44135	+	7.08313i	−0.423127	+	0.355045i
$399$	−2.75512	−	6.40398i	−0.137929	−	0.320600i
$400$	−7.80480	+	44.2632i	−0.390240	+	2.21316i
$401$	−3.58143	−	0.631503i	−0.178848	−	0.0315357i	0.0835068	−	0.996507i	$-0.473388\pi$
$401$	−3.58143	−	0.631503i	−0.178848	−	0.0315357i	−0.262355	+	0.964971i	$0.584499\pi$
$402$	−11.1627	+	3.73653i	−0.556747	+	0.186361i
$403$	1.74517	−	1.46437i	0.0869331	−	0.0729455i
$404$	−2.87965	−	4.98770i	−0.143268	−	0.248147i
$405$	−2.36957	−	33.6479i	−0.117745	−	1.67198i
$406$	−12.4945	−	27.0762i	−0.620092	−	1.34377i
$407$	−8.99974	+	24.7266i	−0.446101	+	1.22565i
$408$	−2.64261	+	12.9971i	−0.130829	+	0.643450i
$409$	−12.5707	−	34.5376i	−0.621580	−	1.70778i	−0.703088	−	0.711103i	$-0.748196\pi$
$409$	−12.5707	−	34.5376i	−0.621580	−	1.70778i	0.0815082	−	0.996673i	$-0.474026\pi$
$410$	−3.41885	+	4.07442i	−0.168845	+	0.201221i
$411$	14.1717	−	23.1325i	0.699039	−	1.14104i
$412$	−3.78556	−	4.51145i	−0.186501	−	0.222263i
$413$	−3.81793	−	0.349389i	−0.187868	−	0.0171923i
$414$	1.46533	−	1.10477i	0.0720172	−	0.0542967i
$415$	50.8965			2.49841
$416$	−13.3602	−	4.86272i	−0.655038	−	0.238414i
$417$	36.6034	+	14.4132i	1.79247	+	0.705819i
$418$	−7.85292	+	9.35874i	−0.384099	+	0.457751i
$419$	−11.4760	+	4.17694i	−0.560642	+	0.204057i	−0.606768	−	0.794879i	$-0.707534\pi$
$419$	−11.4760	+	4.17694i	−0.560642	+	0.204057i	0.0461267	+	0.998936i	$0.485312\pi$
$420$	14.0868	−	0.806897i	0.687367	−	0.0393726i
$421$	0.755733	+	4.28598i	0.0368322	+	0.208886i	0.997670	−	0.0682260i	$-0.0217339\pi$
$421$	0.755733	+	4.28598i	0.0368322	+	0.208886i	−0.960838	+	0.277112i	$0.910623\pi$
$422$		−	24.9942i		−	1.21670i
$423$	−10.2001	+	3.12125i	−0.495948	+	0.151760i
$424$	16.5870			0.805534
$425$	32.8854	+	11.9693i	1.59518	+	0.580597i
$426$	−1.24249	+	47.6735i	−0.0601990	+	2.30979i
$427$	1.93189	+	7.32679i	0.0934908	+	0.354568i
$428$	−9.39691	+	11.1988i	−0.454217	+	0.541314i
$429$	−8.52008	−	25.4534i	−0.411353	−	1.22890i
$430$	0.318575	+	0.379662i	0.0153630	+	0.0183089i
$431$	7.21480	+	4.16547i	0.347525	+	0.200644i	0.663595	−	0.748092i	$-0.269030\pi$
$431$	7.21480	+	4.16547i	0.347525	+	0.200644i	−0.316070	+	0.948736i	$0.602363\pi$
$432$	−25.6955	+	2.48379i	−1.23628	+	0.119501i
$433$		−	23.0129i		−	1.10593i	−0.833205	−	0.552965i	$-0.813496\pi$
$433$		−	23.0129i		−	1.10593i	0.833205	−	0.552965i	$-0.186504\pi$
$434$	2.82551	+	1.33131i	0.135629	+	0.0639051i
$435$	41.3052	−	13.8262i	1.98043	−	0.662916i
$436$	−2.49274	+	14.1370i	−0.119380	+	0.677040i
$437$	0.424399	+	0.356113i	0.0203018	+	0.0170352i
$438$	−30.8061	+	16.7313i	−1.47197	+	0.799451i
$439$	−6.23322	+	17.1256i	−0.297495	+	0.817361i	0.697422	+	0.716661i	$0.254331\pi$
$439$	−6.23322	+	17.1256i	−0.297495	+	0.817361i	−0.994917	+	0.100700i	$0.967892\pi$
$440$	17.7347	+	30.7174i	0.845469	+	1.46440i
$441$	5.98423	+	20.1293i	0.284964	+	0.958538i
$442$	−10.5311	+	18.2405i	−0.500915	+	0.867610i
$443$	−9.71170	−	11.5739i	−0.461417	−	0.549895i	0.484294	−	0.874905i	$-0.339077\pi$
$443$	−9.71170	−	11.5739i	−0.461417	−	0.549895i	−0.945710	+	0.325011i	$0.894632\pi$
$444$	4.87614	+	6.12860i	0.231411	+	0.290850i
$445$	5.68084	−	32.2177i	0.269298	−	1.52726i
$446$	−1.30479	−	1.09485i	−0.0617835	−	0.0518425i
$447$	−18.9260	−	7.45246i	−0.895170	−	0.352489i
$448$	0.565282	+	6.77248i	0.0267070	+	0.319970i
$449$	−19.1172	−	11.0373i	−0.902197	−	0.520884i	−0.0242848	−	0.999705i	$-0.507731\pi$
$449$	−19.1172	−	11.0373i	−0.902197	−	0.520884i	−0.877912	+	0.478821i	$0.841064\pi$
$450$	−2.37472	+	45.5272i	−0.111945	+	2.14617i
$451$			4.03910i			0.190194i
$452$	9.57694	−	1.68867i	0.450461	−	0.0794285i
$453$	−0.0709233	+	2.72128i	−0.00333227	+	0.127857i
$454$	38.0150	+	6.70307i	1.78413	+	0.314591i
$455$	−31.0138	−	8.44298i	−1.45395	−	0.395813i
$456$	−1.65567	−	4.94624i	−0.0775337	−	0.231629i
$457$	−6.75113	−	38.2875i	−0.315804	−	1.79102i	−0.567673	−	0.823254i	$-0.692156\pi$
$457$	−6.75113	−	38.2875i	−0.315804	−	1.79102i	0.251869	−	0.967761i	$-0.418955\pi$
$458$	0.300447	−	0.520389i	0.0140390	−	0.0243162i
$459$	−1.56964	+	20.0389i	−0.0732645	+	0.935337i
$460$	−0.971069	+	0.560647i	−0.0452763	+	0.0261403i
$461$	−6.46360	−	2.35256i	−0.301040	−	0.109570i	0.187084	−	0.982344i	$-0.440096\pi$
$461$	−6.46360	−	2.35256i	−0.301040	−	0.109570i	−0.488124	+	0.872774i	$0.662319\pi$
$462$	26.7922	−	25.2285i	1.24648	−	1.17374i
$463$	7.23069	+	6.06727i	0.336039	+	0.281970i	0.795155	−	0.606406i	$-0.207389\pi$
$463$	7.23069	+	6.06727i	0.336039	+	0.281970i	−0.459116	+	0.888376i	$0.651834\pi$
$464$	−11.4015	−	31.3254i	−0.529302	−	1.45425i
$465$	−2.38336	+	3.89037i	−0.110526	+	0.180411i
$466$	5.81269	+	32.9654i	0.269268	+	1.52709i
$467$	−9.67014	+	16.7492i	−0.447481	+	0.775060i	−0.998221	−	0.0596169i	$-0.981012\pi$
$467$	−9.67014	+	16.7492i	−0.447481	+	0.775060i	0.550740	+	0.834677i	$0.314345\pi$
$468$	−7.78462	−	1.79520i	−0.359844	−	0.0829831i
$469$	4.48527	+	9.71982i	0.207111	+	0.448819i
$470$	22.0447	−	3.88708i	1.01685	−	0.179298i
$471$	−15.0643	−	5.93183i	−0.694125	−	0.273324i
$472$	−2.82489	−	0.498104i	−0.130026	−	0.0229271i
$473$	0.370653	+	0.0653562i	0.0170427	+	0.00300508i
$474$	2.98953	−	2.37858i	0.137313	−	0.109252i
$475$	−13.5539	+	2.38992i	−0.621896	+	0.109657i
$476$	−8.37307	−	0.766242i	−0.383779	−	0.0351207i
$477$	24.9497	−	3.06969i	1.14237	−	0.140551i
$478$	−11.6099	+	20.1089i	−0.531024	+	0.919761i
$479$	−2.97359	−	16.8641i	−0.135867	−	0.770540i	−0.974252	−	0.225461i	$-0.927611\pi$
$479$	−2.97359	−	16.8641i	−0.135867	−	0.770540i	0.838385	−	0.545078i	$-0.183500\pi$
$480$	28.4635	+	0.741831i	1.29918	+	0.0338598i
$481$	−6.10192	−	16.7649i	−0.278224	−	0.764413i
$482$	−4.34573	−	3.64650i	−0.197943	−	0.166094i
$483$	−1.14406	−	1.21497i	−0.0520565	−	0.0552829i
$484$	−9.15310	−	3.33146i	−0.416050	−	0.151430i
$485$	13.8083	−	7.97225i	0.627005	−	0.362001i
$486$	−25.5604	+	5.68314i	−1.15944	+	0.257793i
$487$	−20.1639	+	34.9249i	−0.913713	+	1.58260i	−0.104939	+	0.994479i	$0.533465\pi$
$487$	−20.1639	+	34.9249i	−0.913713	+	1.58260i	−0.808774	+	0.588119i	$0.799869\pi$
$488$	0.984441	+	5.58304i	0.0445636	+	0.252733i
$489$	16.1387	−	18.2460i	0.729817	−	0.825113i
$490$	−7.30570	−	43.4589i	−0.330038	−	1.96327i
$491$	4.14445	+	0.730778i	0.187036	+	0.0329795i	0.266382	−	0.963868i	$-0.414172\pi$
$491$	4.14445	+	0.730778i	0.187036	+	0.0329795i	−0.0793453	+	0.996847i	$0.525283\pi$
$492$	1.02510	+	0.628006i	0.0462149	+	0.0283127i
$493$	−25.5616	+	4.50721i	−1.15124	+	0.202994i
$494$		−	8.28324i		−	0.372681i
$495$	32.3609	+	42.9223i	1.45451	+	1.92922i
$496$	3.02390	+	1.74585i	0.135777	+	0.0783909i
$497$	43.2178	−	3.60728i	1.93858	−	0.161809i
$498$	−5.84470	−	39.0748i	−0.261907	−	1.75099i
$499$	9.58989	+	8.04687i	0.429302	+	0.360227i	0.831688	−	0.555243i	$-0.187375\pi$
$499$	9.58989	+	8.04687i	0.429302	+	0.360227i	−0.402386	+	0.915470i	$0.631819\pi$
$500$	2.16372	−	12.2711i	0.0967646	−	0.548779i
$501$	6.54873	−	0.979539i	0.292576	−	0.0437626i
$502$	−0.427021	−	0.508904i	−0.0190589	−	0.0227135i
$503$	17.2248	−	29.8343i	0.768016	−	1.33024i	−0.170621	−	0.985337i	$-0.554577\pi$
$503$	17.2248	−	29.8343i	0.768016	−	1.33024i	0.938637	−	0.344907i	$-0.112089\pi$
$504$	3.20911	+	15.3807i	0.142945	+	0.685112i
$505$	−13.1372	−	22.7543i	−0.584599	−	1.01255i
$506$	−1.00024	+	2.74813i	−0.0444660	+	0.122169i
$507$	−3.68181	−	2.25559i	−0.163515	−	0.100174i
$508$	−0.399813	−	0.335483i	−0.0177388	−	0.0148847i
$509$	1.74125	−	9.87512i	0.0771796	−	0.437707i	−0.921592	−	0.388160i	$-0.873111\pi$
$509$	1.74125	−	9.87512i	0.0771796	−	0.437707i	0.998772	−	0.0495476i	$-0.0157779\pi$
$510$	8.40438	−	41.3349i	0.372152	−	1.83034i
$511$	18.1810	+	26.1870i	0.804280	+	1.15845i
$512$		−	2.12207i		−	0.0937832i
$513$	−3.40580	−	7.13361i	−0.150370	−	0.314957i
$514$	43.2049	+	24.9444i	1.90569	+	1.10025i
$515$	−17.2700	−	20.5816i	−0.761009	−	0.906935i
$516$	0.0742167	−	0.0839076i	0.00326721	−	0.00369383i
$517$	10.9268	−	13.0221i	0.480561	−	0.572710i
$518$	17.3651	−	17.2270i	0.762978	−	0.756910i
$519$	17.0917	+	10.4709i	0.750242	+	0.459622i
$520$	−22.5983	−	8.22512i	−0.991003	−	0.360696i
$521$	32.0592			1.40454			0.702270	−	0.711911i	$-0.252170\pi$
$521$	32.0592			1.40454			0.702270	+	0.711911i	$0.252170\pi$
$522$	−15.3581	−	30.1236i	−0.672205	−	1.31847i
$523$			4.17931i			0.182748i	0.995817	+	0.0913742i	$0.0291259\pi$
$523$			4.17931i			0.182748i	−0.995817	+	0.0913742i	$0.970874\pi$
$524$	−0.292804	−	1.66057i	−0.0127912	−	0.0725425i
$525$	41.3900	−	2.37083i	1.80641	−	0.103471i
$526$	19.0419	−	6.93068i	0.830266	−	0.302192i
$527$	1.74755	−	2.08265i	0.0761246	−	0.0907218i
$528$	32.1930	−	25.6140i	1.40102	−	1.11471i
$529$	−21.4883	−	7.82110i	−0.934274	−	0.340048i
$530$	−52.7520			−2.29140
$531$	−4.34131	−	0.226445i	−0.188397	−	0.00982688i
$532$	3.00241	−	1.38548i	0.130171	−	0.0600683i
$533$	−1.76031	−	2.09786i	−0.0762475	−	0.0908682i
$534$	−25.3869	−	0.661646i	−1.09860	−	0.0286322i
$535$	−42.8695	+	51.0899i	−1.85341	+	2.20881i
$536$	2.73931	+	7.52618i	0.118320	+	0.325081i
$537$	−11.8240	−	10.4584i	−0.510244	−	0.451314i
$538$	2.04595	−	5.62119i	0.0882070	−	0.242347i
$539$	−25.4638	−	21.7155i	−1.09680	−	0.935352i
$540$	15.9249	−	1.53934i	0.685299	−	0.0662427i
$541$	−1.91792	−	3.32193i	−0.0824578	−	0.142821i	0.821847	−	0.569708i	$-0.192944\pi$
$541$	−1.91792	−	3.32193i	−0.0824578	−	0.142821i	−0.904305	+	0.426887i	$0.859610\pi$
$542$	9.79445	−	8.21852i	0.420708	−	0.353016i
$543$	9.22089	+	8.15593i	0.395706	+	0.350004i
$544$	−16.7093	−	2.94630i	−0.716405	−	0.126322i
$545$	−11.3721	+	64.4943i	−0.487127	+	2.76263i
$546$	−2.92046	+	24.7798i	−0.124984	+	1.06048i
$547$	3.29856	−	2.76782i	0.141036	−	0.118344i	−0.569540	−	0.821964i	$-0.692879\pi$
$547$	3.29856	−	2.76782i	0.141036	−	0.118344i	0.710576	+	0.703620i	$0.248434\pi$
$548$	11.1435	+	6.43368i	0.476025	+	0.274833i
$549$	2.51401	+	8.21570i	0.107295	+	0.350638i
$550$	−36.3258	−	62.9180i	−1.54894	−	2.68283i
$551$	7.81963	−	6.56145i	0.333128	−	0.279527i
$552$	−0.777395	−	0.977072i	−0.0330881	−	0.0415869i
$553$	−2.44676	−	2.46637i	−0.104047	−	0.104881i
$554$	−6.20800	−	17.0563i	−0.263753	−	0.724654i
$555$	22.2454	+	27.9592i	0.944264	+	1.18680i
$556$	−6.38173	+	17.5337i	−0.270646	+	0.743593i
$557$	−29.3284	+	16.9328i	−1.24269	+	0.717465i	−0.969640	−	0.244536i	$-0.921364\pi$
$557$	−29.3284	+	16.9328i	−1.24269	+	0.717465i	−0.273046	+	0.962001i	$0.588031\pi$
$558$	3.26045	+	1.38303i	0.138026	+	0.0585483i
$559$	−0.220996	+	0.127592i	−0.00934712	+	0.00539656i
$560$	−4.09772	−	49.0937i	−0.173160	−	2.07459i
$561$	−15.2879	−	28.1485i	−0.645456	−	1.18843i
$562$	5.75644	−	2.09517i	0.242821	−	0.0883796i
$563$	−4.22574	+	1.53805i	−0.178094	+	0.0648209i	−0.429528	−	0.903054i	$-0.641320\pi$
$563$	−4.22574	+	1.53805i	−0.178094	+	0.0648209i	0.251434	+	0.967874i	$0.419098\pi$
$564$	−1.60599	−	4.79785i	−0.0676246	−	0.202026i
$565$	43.6909	−	7.70388i	1.83809	−	0.324105i
$566$	42.0041			1.76556
$567$	7.67353	+	22.5414i	0.322258	+	0.946652i
$568$	32.4475			1.36147
$569$	−3.32912	+	0.587013i	−0.139564	+	0.0246089i	−0.242994	−	0.970028i	$-0.578129\pi$
$569$	−3.32912	+	0.587013i	−0.139564	+	0.0246089i	0.103430	+	0.994637i	$0.467018\pi$
$570$	5.26557	+	15.7307i	0.220550	+	0.658885i
$571$	−18.0028	+	6.55249i	−0.753394	+	0.274213i	−0.690033	−	0.723778i	$-0.742404\pi$
$571$	−18.0028	+	6.55249i	−0.753394	+	0.274213i	−0.0633608	+	0.997991i	$0.520182\pi$
$572$	11.9635	−	4.35436i	0.500219	−	0.182065i
$573$	10.1250	+	18.6424i	0.422976	+	0.778797i
$574$	1.60036	−	3.39652i	0.0667979	−	0.141768i
$575$	−2.85320	+	1.64729i	−0.118987	+	0.0686969i
$576$	0.941009	+	7.64831i	0.0392087	+	0.318679i
$577$	−39.7257	+	22.9356i	−1.65380	+	0.954823i	−0.678313	+	0.734773i	$0.737289\pi$
$577$	−39.7257	+	22.9356i	−1.65380	+	0.954823i	−0.975489	+	0.220050i	$0.929378\pi$
$578$	1.16981	−	3.21403i	0.0486577	−	0.133686i
$579$	−17.9002	−	22.4979i	−0.743907	−	0.934982i
$580$	7.06615	+	19.4141i	0.293406	+	0.806127i
$581$	−34.7418	+	9.16055i	−1.44133	+	0.380044i
$582$	−7.70623	−	9.68560i	−0.319433	−	0.401481i
$583$	−30.6878	+	25.7501i	−1.27096	+	1.06646i
$584$	11.9260	+	20.6564i	0.493500	+	0.854768i
$585$	−35.5141	−	8.18985i	−1.46833	−	0.338609i
$586$	43.8074	+	25.2922i	1.80967	+	1.04481i
$587$	−30.9328	+	25.9557i	−1.27673	+	1.07131i	−0.283048	+	0.959106i	$0.591346\pi$
$587$	−30.9328	+	25.9557i	−1.27673	+	1.07131i	−0.993686	+	0.112201i	$0.964210\pi$
$588$	−9.47040	+	3.08619i	−0.390553	+	0.127272i
$589$	−0.185664	+	1.05295i	−0.00765016	+	0.0433862i
$590$	8.98407	+	1.58413i	0.369868	+	0.0652178i
$591$	−11.8802	−	10.5081i	−0.488686	−	0.432245i
$592$	20.9470	−	17.5766i	0.860917	−	0.722395i
$593$	2.27065	+	3.93289i	0.0932446	+	0.161504i	0.908875	−	0.417069i	$-0.136943\pi$
$593$	2.27065	+	3.93289i	0.0932446	+	0.161504i	−0.815630	+	0.578574i	$0.803609\pi$
$594$	29.2367	−	29.7735i	1.19959	−	1.22162i
$595$	−38.1987	−	3.49567i	−1.56599	−	0.143308i
$596$	3.29972	−	9.06590i	0.135162	−	0.371354i
$597$	8.51097	+	7.52800i	0.348331	+	0.308101i
$598$	−0.678173	−	1.86326i	−0.0277325	−	0.0761945i
$599$	6.32849	−	7.54200i	0.258575	−	0.308158i	−0.621101	−	0.783730i	$-0.713315\pi$
$599$	6.32849	−	7.54200i	0.258575	−	0.308158i	0.879677	+	0.475572i	$0.157759\pi$
$600$	31.0077	+	0.808140i	1.26588	+	0.0329922i
$601$	13.1479	+	15.6690i	0.536313	+	0.639153i	0.964357	−	0.264605i	$-0.0852416\pi$
$601$	13.1479	+	15.6690i	0.536313	+	0.639153i	−0.428044	+	0.903758i	$0.640797\pi$
$602$	−0.285791	−	0.201818i	−0.0116480	−	0.00822549i
$603$	5.51324	+	10.8138i	0.224517	+	0.440370i
$604$	−1.29117			−0.0525371
$605$	−41.7573	−	15.1984i	−1.69767	−	0.617903i
$606$	−15.9606	+	12.6989i	−0.648355	+	0.515856i
$607$	10.8208	−	12.8957i	0.439203	−	0.523421i	−0.500351	−	0.865823i	$-0.666796\pi$
$607$	10.8208	−	12.8957i	0.439203	−	0.523421i	0.939554	+	0.342401i	$0.111240\pi$
$608$	6.27029	−	2.28220i	0.254294	−	0.0925554i
$609$	−25.7063	+	16.8720i	−1.04167	+	0.683688i
$610$	−3.13085	−	17.7559i	−0.126764	−	0.718917i
$611$			11.5256i			0.466275i
$612$	−9.52089	−	0.496615i	−0.384859	−	0.0200745i
$613$	−14.5656			−0.588299			−0.294150	−	0.955759i	$-0.595036\pi$
$613$	−14.5656			−0.588299			−0.294150	+	0.955759i	$0.595036\pi$
$614$	−39.1865	−	14.2627i	−1.58144	−	0.575596i
$615$	4.67658	+	2.86502i	0.188578	+	0.115529i
$616$	−17.6343	−	17.7756i	−0.710506	−	0.716201i
$617$	6.20042	−	7.38938i	0.249620	−	0.297485i	−0.626655	−	0.779297i	$-0.715577\pi$
$617$	6.20042	−	7.38938i	0.249620	−	0.297485i	0.876275	+	0.481811i	$0.160021\pi$
$618$	−13.8180	+	15.6222i	−0.555840	+	0.628419i
$619$	−20.8566	−	24.8559i	−0.838298	−	0.999044i	−0.999926	−	0.0121927i	$-0.996119\pi$
$619$	−20.8566	−	24.8559i	−0.838298	−	0.999044i	0.161628	−	0.986852i	$-0.448326\pi$
$620$	−1.87408	−	1.08200i	−0.0752648	−	0.0434541i
$621$	−1.35016	−	1.32582i	−0.0541802	−	0.0532033i
$622$			13.2649i			0.531876i
$623$	1.92093	+	23.0141i	0.0769605	+	0.922042i
$624$	−5.55762	+	27.3338i	−0.222483	+	1.09423i
$625$	2.01625	−	11.4347i	0.0806501	−	0.457390i
$626$	−24.8698	−	20.8682i	−0.993996	−	0.834062i
$627$	10.7419	+	6.58081i	0.428989	+	0.262812i
$628$	2.62643	−	7.21606i	0.104806	−	0.287952i
$629$	−10.6455	−	18.4385i	−0.424462	−	0.735190i
$630$	−10.2060	−	48.9158i	−0.406618	−	1.94885i
$631$	1.22037	−	2.11374i	0.0485821	−	0.0841467i	−0.840712	−	0.541483i	$-0.817863\pi$
$631$	1.22037	−	2.11374i	0.0485821	−	0.0841467i	0.889294	+	0.457336i	$0.151196\pi$
$632$	−1.67080	−	1.99118i	−0.0664608	−	0.0792049i
$633$	−25.4890	+	3.81257i	−1.01310	+	0.151536i
$634$	−4.12298	+	23.3826i	−0.163745	+	0.928642i
$635$	−1.82398	−	1.53050i	−0.0723826	−	0.0607362i
$636$	1.76382	+	11.7920i	0.0699399	+	0.467584i
$637$	22.6896	+	0.181161i	0.898993	+	0.00717787i
$638$	46.6654	+	26.9423i	1.84750	+	1.06665i
$639$	48.8068	−	6.00494i	1.93077	−	0.237552i
$640$		−	49.0490i		−	1.93883i
$641$	18.6803	−	3.29385i	0.737829	−	0.130099i	0.207911	−	0.978148i	$-0.433334\pi$
$641$	18.6803	−	3.29385i	0.737829	−	0.130099i	0.529918	+	0.848049i	$0.322223\pi$
$642$	44.1462	+	27.0454i	1.74231	+	1.06740i
$643$	30.7254	+	5.41772i	1.21169	+	0.213654i	0.742746	−	0.669573i	$-0.233523\pi$
$643$	30.7254	+	5.41772i	1.21169	+	0.213654i	0.468946	+	0.883227i	$0.344634\pi$
$644$	0.561941	−	0.557472i	0.0221436	−	0.0219675i
$645$	0.338583	−	0.382794i	0.0133317	−	0.0150725i
$646$	−1.71652	−	9.73489i	−0.0675357	−	0.383014i
$647$	18.3923	−	31.8564i	0.723076	−	1.25240i	−0.236685	−	0.971587i	$-0.576061\pi$
$647$	18.3923	−	31.8564i	0.723076	−	1.25240i	0.959761	−	0.280818i	$-0.0906058\pi$
$648$	4.31853	+	17.2843i	0.169648	+	0.678993i
$649$	5.99964	−	3.46390i	0.235507	−	0.135970i
$650$	46.2879	+	16.8474i	1.81556	+	0.660810i
$651$	0.926671	−	3.08452i	0.0363191	−	0.120892i
$652$	8.85082	+	7.42672i	0.346625	+	0.290853i
$653$	5.39569	+	14.8245i	0.211150	+	0.580129i	0.999378	−	0.0352534i	$-0.0112238\pi$
$653$	5.39569	+	14.8245i	0.211150	+	0.580129i	−0.788229	+	0.615382i	$0.789002\pi$
$654$	50.8202	+	1.32450i	1.98723	+	0.0517922i
$655$	−1.33580	−	7.57569i	−0.0521939	−	0.296007i
$656$	2.09867	−	3.63501i	0.0819394	−	0.141923i
$657$	21.7616	+	28.8638i	0.849000	+	1.12608i
$658$	−14.3481	+	6.62100i	−0.559345	+	0.258114i
$659$	−14.0350	+	2.47474i	−0.546725	+	0.0964023i	−0.440187	−	0.897906i	$-0.645088\pi$
$659$	−14.0350	+	2.47474i	−0.546725	+	0.0964023i	−0.106538	+	0.994309i	$0.533977\pi$
$660$	−19.9518	+	15.8744i	−0.776623	+	0.617910i
$661$	−23.5313	−	4.14920i	−0.915260	−	0.161385i	−0.303869	−	0.952714i	$-0.598279\pi$
$661$	−23.5313	−	4.14920i	−0.915260	−	0.161385i	−0.611391	+	0.791329i	$0.709390\pi$
$662$	24.1144	+	4.25201i	0.937231	+	0.165259i
$663$	20.2079	+	7.95724i	0.784812	+	0.309034i
$664$	−26.4734	+	4.66798i	−1.02737	+	0.181153i
$665$	13.6973	−	6.32070i	0.531158	−	0.245106i
$666$	18.9106	−	20.2892i	0.732771	−	0.786190i
$667$	1.22177	−	2.11617i	0.0473073	−	0.0819386i
$668$	0.545377	+	3.09299i	0.0211013	+	0.119671i
$669$	−0.917490	+	1.49762i	−0.0354722	+	0.0579014i
$670$	−8.71190	−	23.9357i	−0.336570	−	0.924718i
$671$	−10.4886	−	8.80101i	−0.404909	−	0.339759i
$672$	−19.5626	+	4.61660i	−0.754644	+	0.178089i
$673$	−2.30855	−	0.840244i	−0.0889881	−	0.0323890i	0.297142	−	0.954833i	$-0.403966\pi$
$673$	−2.30855	−	0.840244i	−0.0889881	−	0.0323890i	−0.386131	+	0.922444i	$0.626189\pi$
$674$	−39.2186	+	22.6429i	−1.51064	+	0.872171i
$675$	46.7907	−	4.52290i	1.80097	−	0.174086i
$676$	1.02400	−	1.77361i	0.0393845	−	0.0682159i
$677$	0.472088	+	2.67734i	0.0181438	+	0.102899i	0.992535	−	0.121962i	$-0.0389185\pi$
$677$	0.472088	+	2.67734i	0.0181438	+	0.102899i	−0.974391	+	0.224860i	$0.927807\pi$
$678$	−10.9317	−	32.6582i	−0.419831	−	1.25423i
$679$	−7.99066	+	7.92711i	−0.306653	+	0.304215i
$680$	−28.2632	−	4.98357i	−1.08384	−	0.191111i
$681$	1.03703	−	39.7900i	0.0397390	−	1.52476i
$682$	−5.55829	+	0.980076i	−0.212838	+	0.0375291i
$683$		−	21.7302i		−	0.831484i	−0.909483	−	0.415742i	$-0.863522\pi$
$683$		−	21.7302i		−	0.831484i	0.909483	−	0.415742i	$-0.136478\pi$
$684$	3.34033	−	1.70302i	0.127721	−	0.0651166i
$685$	50.8375	+	29.3510i	1.94240	+	1.12145i
$686$	12.8087	+	28.3500i	0.489040	+	1.08241i
$687$	−0.576520	−	0.227015i	−0.0219956	−	0.00866117i
$688$	−0.299613	−	0.251405i	−0.0114226	−	0.00958472i
$689$	4.71649	−	26.7486i	0.179684	−	1.01904i
$690$	2.47237	+	3.10741i	0.0941216	+	0.118297i
$691$	−8.16535	−	9.73108i	−0.310624	−	0.370188i	0.588034	−	0.808836i	$-0.299902\pi$
$691$	−8.16535	−	9.73108i	−0.310624	−	0.370188i	−0.898659	+	0.438648i	$0.855457\pi$
$692$	−4.75359	+	8.23345i	−0.180704	+	0.312989i
$693$	−29.8148	−	23.4742i	−1.13257	−	0.891712i
$694$	−16.8198	−	29.1327i	−0.638471	−	1.10586i
$695$	−29.1140	+	79.9902i	−1.10436	+	3.03420i
$696$	−20.2165	+	10.9799i	−0.766305	+	0.416192i
$697$	−2.50354	−	2.10072i	−0.0948284	−	0.0795705i
$698$	3.06426	−	17.3783i	0.115984	−	0.657778i
$699$	32.7313	−	10.9562i	1.23801	−	0.414403i
$700$	1.63561	+	19.5958i	0.0618204	+	0.740653i
$701$			23.3250i			0.880973i	0.897759	+	0.440487i	$0.145194\pi$
$701$			23.3250i			0.880973i	−0.897759	+	0.440487i	$0.854806\pi$
$702$	−2.20934	+	28.2058i	−0.0833863	+	1.06456i
$703$	7.25137	+	4.18658i	0.273490	+	0.157900i
$704$	−7.89367	−	9.40731i	−0.297504	−	0.354551i
$705$	−7.32669	−	21.8882i	−0.275939	−	0.824357i
$706$	3.56050	−	4.24323i	0.134001	−	0.159696i
$707$	13.0628	+	13.1676i	0.491279	+	0.495217i
$708$	0.0537211	−	2.06124i	0.00201896	−	0.0774661i
$709$	21.6133	+	7.86662i	0.811706	+	0.295437i	0.714328	−	0.699811i	$-0.246732\pi$
$709$	21.6133	+	7.86662i	0.811706	+	0.295437i	0.0973778	+	0.995247i	$0.468954\pi$
$710$	−103.194			−3.87279
$711$	−2.88168	−	2.68588i	−0.108071	−	0.100728i
$712$			17.2788i			0.647550i
$713$	0.0444444	+	0.252056i	0.00166445	+	0.00943959i
$714$	1.70281	+	29.7277i	0.0637262	+	1.11253i
$715$	54.5785	−	19.8650i	2.04112	−	0.742907i
$716$	4.81276	−	5.73562i	0.179861	−	0.214350i
$717$	22.2780	+	8.77235i	0.831986	+	0.327609i
$718$	17.4700	+	6.35855i	0.651973	+	0.237299i
$719$	18.4488			0.688025			0.344013	−	0.938965i	$-0.388214\pi$
$719$	18.4488			0.688025			0.344013	+	0.938965i	$0.388214\pi$
$720$	−6.82136	−	55.4425i	−0.254217	−	2.06622i
$721$	15.4928	+	10.9406i	0.576983	+	0.407450i
$722$	−18.0158	−	21.4704i	−0.670478	−	0.799044i
$723$	−3.05580	+	4.98799i	−0.113646	+	0.185505i
$724$	−3.75320	+	4.47289i	−0.139487	+	0.166234i
$725$	20.7618	+	57.0426i	0.771074	+	2.11851i
$726$	−6.87309	+	33.8037i	−0.255084	+	1.25457i
$727$	0.912501	−	2.50708i	0.0338428	−	0.0929823i	−0.921620	−	0.388092i	$-0.873134\pi$
$727$	0.912501	−	2.50708i	0.0338428	−	0.0929823i	0.955463	+	0.295110i	$0.0953564\pi$
$728$	16.9059	+	1.54711i	0.626576	+	0.0573397i
$729$	9.69458	+	25.1995i	0.359059	+	0.933315i
$730$	−37.9285	−	65.6942i	−1.40380	−	2.43145i
$731$	−0.233285	+	0.195749i	−0.00862835	+	0.00724005i
$732$	−3.86442	+	1.29355i	−0.142833	+	0.0478109i
$733$	34.5172	+	6.08631i	1.27492	+	0.224803i	0.769822	−	0.638259i	$-0.220345\pi$
$733$	34.5172	+	6.08631i	1.27492	+	0.224803i	0.505098	+	0.863062i	$0.331456\pi$
$734$	−5.77285	+	32.7394i	−0.213080	+	1.20843i
$735$	−43.2048	+	14.0795i	−1.59363	+	0.519329i
$736$	1.22361	−	1.02673i	0.0451030	−	0.0378459i
$737$	−16.7519	−	9.67173i	−0.617065	−	0.356263i
$738$	1.66253	−	3.91936i	0.0611986	−	0.144274i
$739$	3.42267	+	5.92824i	0.125905	+	0.218074i	0.922086	−	0.386984i	$-0.126483\pi$
$739$	3.42267	+	5.92824i	0.125905	+	0.218074i	−0.796181	+	0.605058i	$0.793150\pi$
$740$	−12.9820	+	10.8932i	−0.477228	+	0.400442i
$741$	−8.44721	+	1.26351i	−0.310316	+	0.0464162i
$742$	36.0084	−	9.49451i	1.32191	−	0.348554i
$743$	7.09106	+	19.4825i	0.260146	+	0.714744i	0.999157	+	0.0410513i	$0.0130707\pi$
$743$	7.09106	+	19.4825i	0.260146	+	0.714744i	−0.739011	+	0.673693i	$0.764707\pi$
$744$	0.882880	−	2.24213i	0.0323680	−	0.0822006i
$745$	15.0536	−	41.3595i	0.551522	−	1.51529i
$746$	6.35396	−	3.66846i	0.232635	−	0.134312i
$747$	−38.9568	+	11.9208i	−1.42536	+	0.436159i
$748$	13.1578	−	7.59664i	0.481095	−	0.277761i
$749$	20.0673	−	42.5896i	0.733242	−	1.55619i
$750$	−44.1125	−	1.14968i	−1.61076	−	0.0419805i
$751$	−27.6433	+	10.0614i	−1.00872	+	0.367144i	−0.792941	−	0.609298i	$-0.791451\pi$
$751$	−27.6433	+	10.0614i	−1.00872	+	0.367144i	−0.215779	+	0.976442i	$0.569229\pi$
$752$	−16.5998	+	6.04182i	−0.605331	+	0.220322i
$753$	−0.453841	+	0.513102i	−0.0165389	+	0.0186985i
$754$	−35.9793	+	6.34411i	−1.31029	+	0.231039i
$755$	−5.89045			−0.214376
$756$	−10.5932	+	3.91698i	−0.385273	+	0.142459i
$757$	−41.4656			−1.50709			−0.753546	−	0.657396i	$-0.771658\pi$
$757$	−41.4656			−1.50709			−0.753546	+	0.657396i	$0.771658\pi$
$758$	−8.68096	+	1.53069i	−0.315307	+	0.0555970i
$759$	2.95511	+	0.600844i	0.107264	+	0.0218093i
$760$	10.6060	−	3.86026i	0.384719	−	0.140026i
$761$	42.9346	−	15.6269i	1.55638	−	0.566476i	0.586476	−	0.809967i	$-0.300515\pi$
$761$	42.9346	−	15.6269i	1.55638	−	0.566476i	0.969903	+	0.243491i	$0.0782926\pi$
$762$	−0.965559	+	1.57608i	−0.0349785	+	0.0570955i
$763$	−3.84538	−	46.0704i	−0.139212	−	1.66786i
$764$	−8.71420	+	5.03115i	−0.315269	+	0.182020i
$765$	−43.4352	−	2.26560i	−1.57040	−	0.0819129i
$766$	−5.90311	+	3.40816i	−0.213288	+	0.123142i
$767$	−1.60651	+	4.41385i	−0.0580077	+	0.159375i
$768$	−28.8563	+	4.31624i	−1.04126	+	0.155749i
$769$	3.17805	+	8.73163i	0.114604	+	0.314871i	0.983712	−	0.179750i	$-0.0575290\pi$
$769$	3.17805	+	8.73163i	0.114604	+	0.314871i	−0.869109	+	0.494621i	$0.835307\pi$
$770$	56.0829	+	56.5324i	2.02109	+	2.03729i
$771$	18.8478	−	47.8652i	0.678786	−	1.72382i
$772$	10.4462	−	8.76543i	0.375968	−	0.315475i
$773$	1.62756	+	2.81902i	0.0585393	+	0.101393i	0.893810	−	0.448446i	$-0.148022\pi$
$773$	1.62756	+	2.81902i	0.0585393	+	0.101393i	−0.835271	+	0.549839i	$0.814689\pi$
$774$	−0.332764	−	0.215983i	−0.0119610	−	0.00776334i
$775$	−5.50642	−	3.17914i	−0.197797	−	0.114198i
$776$	−6.45112	+	5.41313i	−0.231582	+	0.194320i
$777$	−20.2168	−	15.0811i	−0.725275	−	0.541030i
$778$	−2.38742	+	13.5397i	−0.0855931	+	0.485423i
$779$	1.26575	+	0.223186i	0.0453501	+	0.00799645i
$780$	3.44437	−	16.9403i	0.123328	−	0.606560i
$781$	−60.0317	+	50.3726i	−2.14810	+	1.80247i
$782$	−1.18314	−	2.04927i	−0.0423092	−	0.0732816i
$783$	−28.3772	+	20.2571i	−1.01412	+	0.723930i
$784$	11.6332	+	32.7737i	0.415470	+	1.17049i
$785$	11.9820	−	32.9203i	0.427656	−	1.17498i
$786$	−5.66269	+	1.89549i	−0.201982	+	0.0676098i
$787$	12.7488	+	35.0269i	0.454444	+	1.24858i	0.929566	+	0.368656i	$0.120182\pi$
$787$	12.7488	+	35.0269i	0.454444	+	1.24858i	−0.475122	+	0.879920i	$0.657596\pi$
$788$	4.83562	−	5.76287i	0.172262	−	0.205294i
$789$	−9.97249	−	18.3617i	−0.355030	−	0.653692i
$790$	5.31370	+	6.33262i	0.189053	+	0.225304i
$791$	−28.4367	+	13.1223i	−1.01109	+	0.466575i
$792$	−20.7689	−	19.3577i	−0.737990	−	0.687847i
$793$	9.28328			0.329659
$794$	10.6859	+	3.88934i	0.379228	+	0.138028i
$795$	8.04669	+	53.7963i	0.285387	+	1.90796i
$796$	−3.46424	+	4.12852i	−0.122787	+	0.146332i
$797$	24.8403	−	9.04114i	0.879889	−	0.320253i	0.137724	−	0.990471i	$-0.456021\pi$
$797$	24.8403	−	9.04114i	0.879889	−	0.320253i	0.742165	+	0.670217i	$0.233799\pi$
$798$	−6.42552	−	9.78999i	−0.227461	−	0.346562i
$799$	2.38843	+	13.5455i	0.0844966	+	0.479204i
$800$			39.6810i			1.40294i
$801$	3.19772	+	25.9903i	0.112986	+	0.918324i
$802$	−6.10868			−0.215705
$803$	−54.1321	−	19.7025i	−1.91028	−	0.695285i
$804$	−5.05923	+	2.74775i	−0.178425	+	0.0969056i
$805$	2.56363	−	2.54324i	0.0903559	−	0.0896374i
$806$	2.45977	−	2.93144i	0.0866416	−	0.103255i
$807$	−6.04455	−	1.22900i	−0.212778	−	0.0432629i
$808$	8.92014	+	10.6306i	0.313809	+	0.373983i
$809$	5.51222	+	3.18248i	0.193799	+	0.111890i	0.593760	−	0.804642i	$-0.297643\pi$
$809$	5.51222	+	3.18248i	0.193799	+	0.111890i	−0.399961	+	0.916532i	$0.630976\pi$
$810$	−13.7343	−	54.9699i	−0.482576	−	1.93145i
$811$		−	37.5618i		−	1.31897i	−0.751716	−	0.659487i	$-0.770773\pi$
$811$		−	37.5618i		−	1.31897i	0.751716	−	0.659487i	$-0.229227\pi$
$812$	−8.31756	−	11.9802i	−0.291889	−	0.420423i
$813$	−9.87524	−	8.73471i	−0.346340	−	0.306340i
$814$	−7.67523	+	43.5284i	−0.269017	+	1.52567i
$815$	40.3782	+	33.8814i	1.41439	+	1.18681i
$816$	−0.867252	+	33.2758i	−0.0303599	+	1.16489i
$817$	0.0409618	−	0.112542i	0.00143307	−	0.00393733i
$818$	−30.8688	−	53.4663i	−1.07930	−	1.86940i
$819$	25.7159	−	0.801594i	0.898585	−	0.0280100i
$820$	−1.30066	+	2.25282i	−0.0454211	+	0.0786717i
$821$	−28.0676	−	33.4496i	−0.979565	−	1.16740i	−0.985886	−	0.167421i	$-0.946456\pi$
$821$	−28.0676	−	33.4496i	−0.979565	−	1.16740i	0.00632015	−	0.999980i	$-0.497988\pi$
$822$	16.6958	−	42.4001i	0.582333	−	1.47887i
$823$	4.12887	−	23.4160i	0.143923	−	0.816230i	−0.824302	−	0.566150i	$-0.808432\pi$
$823$	4.12887	−	23.4160i	0.143923	−	0.816230i	0.968225	−	0.250079i	$-0.0804567\pi$
$824$	10.8705	+	9.12145i	0.378692	+	0.317761i
$825$	−58.6225	+	46.6422i	−2.04097	+	1.62387i
$826$	−6.41762	+	0.535662i	−0.223298	+	0.0186381i
$827$	1.91398	+	1.10504i	0.0665558	+	0.0384260i	0.532909	−	0.846173i	$-0.321099\pi$
$827$	1.91398	+	1.10504i	0.0665558	+	0.0384260i	−0.466353	+	0.884599i	$0.654432\pi$
$828$	0.611955	−	0.656566i	0.0212669	−	0.0228173i
$829$			8.72501i			0.303032i	0.988455	+	0.151516i	$0.0484155\pi$
$829$			8.72501i			0.303032i	−0.988455	+	0.151516i	$0.951584\pi$
$830$	84.1942	−	14.8457i	2.92242	−	0.515302i
$831$	−16.4470	+	8.93263i	−0.570541	+	0.309870i
$832$	8.19973	+	1.44583i	0.284275	+	0.0501253i
$833$	26.7035	−	4.48901i	0.925220	−	0.155535i
$834$	64.7543	+	13.1661i	2.24226	+	0.455904i
$835$	2.48806	+	14.1105i	0.0861028	+	0.488313i
$836$	−2.98756	+	5.17460i	−0.103327	+	0.178967i
$837$	0.913065	−	3.53596i	0.0315602	−	0.122221i
$838$	−17.7656	+	10.2570i	−0.613702	+	0.354321i
$839$	22.6010	+	8.22611i	0.780275	+	0.283997i	0.701287	−	0.712879i	$-0.252609\pi$
$839$	22.6010	+	8.22611i	0.780275	+	0.283997i	0.0789874	+	0.996876i	$0.474831\pi$
$840$	−33.0895	+	7.80882i	−1.14170	+	0.269430i
$841$	−12.2742	−	10.2993i	−0.423249	−	0.355148i
$842$	2.50030	+	6.86953i	0.0861661	+	0.236739i
$843$	−3.01473	−	5.55080i	−0.103833	−	0.191180i
$844$	−2.12272	−	12.0386i	−0.0730671	−	0.414384i
$845$	4.67156	−	8.09138i	0.160707	−	0.278352i
$846$	−15.9629	+	8.13846i	−0.548816	+	0.279806i
$847$	31.2388	+	2.85875i	1.07338	+	0.0982279i
$848$	40.9971	−	7.22890i	1.40785	−	0.248241i
$849$	−6.40722	−	42.8356i	−0.219895	−	1.47011i
$850$	57.8911	+	10.2078i	1.98565	+	0.350124i
$851$	1.97392	+	0.348055i	0.0676650	+	0.0119312i
$852$	3.45039	+	23.0676i	0.118208	+	0.790284i
$853$	−13.6366	+	2.40451i	−0.466910	+	0.0823287i	−0.402153	−	0.915572i	$-0.631738\pi$
$853$	−13.6366	+	2.40451i	−0.466910	+	0.0823287i	−0.0647563	+	0.997901i	$0.520627\pi$
$854$	5.33289	+	11.5566i	0.182488	+	0.395460i
$855$	15.2389	−	7.76933i	0.521158	−	0.265705i
$856$	17.6125	−	30.5058i	0.601984	−	1.04267i
$857$	−1.83530	−	10.4085i	−0.0626926	−	0.355547i	−0.999976	−	0.00697807i	$-0.997779\pi$
$857$	−1.83530	−	10.4085i	−0.0626926	−	0.355547i	0.937283	−	0.348569i	$-0.113332\pi$
$858$	−21.5185	−	39.6204i	−0.734629	−	1.35262i
$859$	15.5629	+	42.7586i	0.530998	+	1.45890i	0.857885	+	0.513841i	$0.171778\pi$
$859$	15.5629	+	42.7586i	0.530998	+	1.45890i	−0.326887	+	0.945063i	$0.606000\pi$
$860$	0.185687	+	0.155810i	0.00633186	+	0.00531306i
$861$	−3.70788	−	1.11395i	−0.126364	−	0.0379631i
$862$	13.1499	+	4.78617i	0.447887	+	0.163018i
$863$	42.6896	−	24.6469i	1.45317	−	0.838989i	0.454511	−	0.890741i	$-0.349814\pi$
$863$	42.6896	−	24.6469i	1.45317	−	0.838989i	0.998660	+	0.0517521i	$0.0164806\pi$
$864$	−21.9601	+	6.09881i	−0.747097	+	0.207486i
$865$	−21.6863	+	37.5618i	−0.737356	+	1.27714i
$866$	−6.71250	−	38.0685i	−0.228100	−	1.29362i
$867$	−3.45609	−	0.702706i	−0.117375	−	0.0238651i
$868$	1.47398	+	0.401266i	0.0500302	+	0.0136198i
$869$	6.18235	+	1.09012i	0.209722	+	0.0369796i
$870$	64.2952	−	34.9197i	2.17981	−	1.18389i
$871$	12.9158	−	2.27741i	0.437636	−	0.0771671i
$872$		−	34.5892i		−	1.17134i
$873$	−8.70184	+	9.33620i	−0.294513	+	0.315983i
$874$	0.805923	+	0.465300i	0.0272608	+	0.0157390i
$875$	3.33783	+	39.9896i	0.112839	+	1.35190i
$876$	−13.4169	+	10.6750i	−0.453315	+	0.360674i
$877$	30.1140	+	25.2687i	1.01688	+	0.853263i	0.989232	−	0.146355i	$-0.0467542\pi$
$877$	30.1140	+	25.2687i	1.01688	+	0.853263i	0.0276466	+	0.999618i	$0.491199\pi$
$878$	−5.31586	+	30.1477i	−0.179402	+	1.01744i
$879$	19.1106	−	48.5327i	0.644585	−	1.63697i
$880$	57.2211	+	68.1935i	1.92892	+	2.29880i
$881$	−20.9452	+	36.2781i	−0.705660	+	1.22224i	0.260792	+	0.965395i	$0.416016\pi$
$881$	−20.9452	+	36.2781i	−0.705660	+	1.22224i	−0.966453	+	0.256845i	$0.917317\pi$
$882$	15.7707	+	31.5529i	0.531026	+	1.06244i
$883$	3.31527	+	5.74221i	0.111568	+	0.193241i	0.916402	−	0.400258i	$-0.131080\pi$
$883$	3.31527	+	5.74221i	0.111568	+	0.193241i	−0.804835	+	0.593499i	$0.797746\pi$
$884$	−3.52322	+	9.67997i	−0.118499	+	0.325573i
$885$	0.245081	−	9.40356i	0.00823829	−	0.316097i
$886$	−19.4412	−	16.3131i	−0.653142	−	0.548051i
$887$	−6.95608	+	39.4499i	−0.233562	+	1.32460i	0.612058	+	0.790813i	$0.290342\pi$
$887$	−6.95608	+	39.4499i	−0.233562	+	1.32460i	−0.845620	+	0.533785i	$0.820769\pi$
$888$	−14.1350	−	12.5025i	−0.474341	−	0.419557i
$889$	1.52051	+	0.716430i	0.0509963	+	0.0240283i
$890$		−	54.9522i		−	1.84200i
$891$	−34.8226	−	25.2738i	−1.16660	−	0.846705i
$892$	−0.721438	−	0.416523i	−0.0241555	−	0.0139462i
$893$	−3.47700	−	4.14373i	−0.116353	−	0.138665i
$894$	−33.4816	−	6.80761i	−1.11979	−	0.227681i
$895$	21.9562	−	26.1664i	0.733916	−	0.874647i
$896$	8.82803	+	33.4807i	0.294924	+	1.11851i
$897$	−1.79670	+	0.975817i	−0.0599901	+	0.0325816i
$898$	−34.8436	−	12.6820i	−1.16274	−	0.423204i
$899$	4.71583			0.157282
$900$	2.72276	+	22.1300i	0.0907587	+	0.737667i
$901$		−	32.4137i		−	1.07986i
$902$	1.17814	+	6.68158i	0.0392279	+	0.222472i
$903$	−0.162219	+	0.322233i	−0.00539832	+	0.0107233i
$904$	−22.0189	+	8.01422i	−0.732337	+	0.266549i
$905$	−17.1224	+	20.4057i	−0.569169	+	0.678309i
$906$	0.676430	+	4.52228i	0.0224729	+	0.150243i
$907$	−43.8700	−	15.9674i	−1.45668	−	0.530187i	−0.512230	−	0.858848i	$-0.671180\pi$
$907$	−43.8700	−	15.9674i	−1.45668	−	0.530187i	−0.944448	+	0.328661i	$0.893403\pi$
$908$	18.8793			0.626532
$909$	15.3848	+	14.3395i	0.510283	+	0.475611i
$910$	−53.7665	−	4.92032i	−1.78234	−	0.163107i
$911$	−11.2903	−	13.4553i	−0.374066	−	0.445794i	0.545866	−	0.837872i	$-0.316201\pi$
$911$	−11.2903	−	13.4553i	−0.374066	−	0.445794i	−0.919932	+	0.392078i	$0.871756\pi$
$912$	−6.24788	−	11.5038i	−0.206888	−	0.380928i
$913$	41.7322	−	49.7345i	1.38113	−	1.64597i
$914$	−22.3357	−	61.3669i	−0.738800	−	2.02984i
$915$	−17.6298	+	5.90128i	−0.582825	+	0.195090i
$916$	0.100515	−	0.276164i	0.00332112	−	0.00912470i
$917$	2.27531	+	4.93072i	0.0751374	+	0.162827i
$918$	3.24850	+	33.6067i	0.107217	+	1.10919i
$919$	−0.970359	−	1.68071i	−0.0320092	−	0.0554416i	0.849577	−	0.527465i	$-0.176857\pi$
$919$	−0.970359	−	1.68071i	−0.0320092	−	0.0554416i	−0.881586	+	0.472023i	$0.843524\pi$
$920$	2.06970	−	1.73668i	0.0682360	−	0.0572568i
$921$	−8.56763	+	42.1378i	−0.282313	+	1.38849i
$922$	−11.3784	−	2.00633i	−0.374729	−	0.0660749i
$923$	9.22643	−	52.3257i	0.303692	−	1.72232i
$924$	10.7619	−	14.4268i	0.354041	−	0.474607i
$925$	−38.1438	+	32.0065i	−1.25416	+	1.05237i
$926$	13.7309	+	7.92754i	0.451225	+	0.260515i
$927$	18.0393	+	11.7085i	0.592487	+	0.384558i
$928$	−14.7154	−	25.4878i	−0.483057	−	0.836679i
$929$	3.84326	−	3.22488i	0.126093	−	0.105805i	−0.577560	−	0.816348i	$-0.695995\pi$
$929$	3.84326	−	3.22488i	0.126093	−	0.105805i	0.703654	+	0.710543i	$0.251551\pi$
$930$	−2.80785	+	7.13072i	−0.0920731	+	0.233826i
$931$	−8.21210	+	6.77978i	−0.269141	+	0.222198i
$932$	5.59940	+	15.3842i	0.183415	+	0.503927i
$933$	13.5275	−	2.02341i	0.442872	−	0.0662434i
$934$	−11.1111	+	30.5275i	−0.363566	+	0.998891i
$935$	60.0269	−	34.6565i	1.96309	−	1.13339i
$936$	19.2235	+	1.00271i	0.628340	+	0.0327745i
$937$	−25.9158	+	14.9625i	−0.846632	+	0.488803i	−0.859513	−	0.511114i	$-0.829233\pi$
$937$	−25.9158	+	14.9625i	−0.846632	+	0.488803i	0.0128808	+	0.999917i	$0.495900\pi$
$938$	10.2548	+	14.7705i	0.334830	+	0.482273i
$939$	−17.4877	+	28.5453i	−0.570691	+	0.931541i
$940$	10.2878	−	3.74445i	0.335551	−	0.122130i
$941$	−38.6183	+	14.0559i	−1.25892	+	0.458210i	−0.883407	−	0.468606i	$-0.844756\pi$
$941$	−38.6183	+	14.0559i	−1.25892	+	0.458210i	−0.375515	+	0.926816i	$0.622534\pi$
$942$	−26.6499	−	5.41856i	−0.868301	−	0.176546i
$943$	0.302995	−	0.0534262i	0.00986688	−	0.00173980i
$944$	−7.19920			−0.234314
$945$	−48.3273	+	17.8696i	−1.57209	+	0.581298i
$946$	0.632207			0.0205548
$947$	19.3958	−	3.42001i	0.630279	−	0.111135i	0.150622	−	0.988591i	$-0.451872\pi$
$947$	19.3958	−	3.42001i	0.630279	−	0.111135i	0.479657	+	0.877456i	$0.340761\pi$
$948$	1.23791	−	1.39955i	0.0402053	−	0.0454551i
$949$	36.7022	−	13.3585i	1.19140	−	0.433635i
$950$	−21.7241	+	7.90692i	−0.704822	+	0.256534i
$951$	24.4744	+	0.637865i	0.793637	+	0.0206842i
$952$	20.1893	−	1.68515i	0.654340	−	0.0546161i
$953$	−11.1121	+	6.41558i	−0.359956	+	0.207821i	−0.669062	−	0.743207i	$-0.733304\pi$
$953$	−11.1121	+	6.41558i	−0.359956	+	0.207821i	0.309105	+	0.951028i	$0.399970\pi$
$954$	40.3770	−	12.3554i	1.30726	−	0.400021i
$955$	−39.7550	+	22.9525i	−1.28644	+	0.742727i
$956$	−3.88412	+	10.6715i	−0.125622	+	0.345142i
$957$	20.3574	−	51.6989i	0.658060	−	1.67119i
$958$	−9.83797	−	27.0296i	−0.317850	−	0.873287i
$959$	−39.9842	−	10.8850i	−1.29116	−	0.351495i
$960$	−16.4912	+	2.46670i	−0.532251	+	0.0796125i
$961$	23.3690	−	19.6089i	0.753838	−	0.632545i
$962$	−14.9840	−	25.9530i	−0.483103	−	0.836760i
$963$	20.8468	−	49.1456i	0.671778	−	1.58370i
$964$	−2.40283	−	1.38727i	−0.0773899	−	0.0446811i
$965$	47.6567	−	39.9887i	1.53412	−	1.28728i
$966$	−2.24692	−	1.67612i	−0.0722934	−	0.0539284i
$967$	10.1442	−	57.5307i	0.326216	−	1.85006i	−0.174771	−	0.984609i	$-0.555918\pi$
$967$	10.1442	−	57.5307i	0.326216	−	1.85006i	0.500987	−	0.865455i	$-0.332971\pi$
$968$	23.1136	+	4.07555i	0.742900	+	0.130993i
$969$	−9.66576	+	3.23544i	−0.310509	+	0.103937i
$970$	20.5167	−	17.2156i	0.658752	−	0.552758i
$971$	28.5180	+	49.3946i	0.915186	+	1.58515i	0.806629	+	0.591059i	$0.201290\pi$
$971$	28.5180	+	49.3946i	0.915186	+	1.58515i	0.108558	+	0.994090i	$0.465377\pi$
$972$	−11.8286	+	4.90811i	−0.379402	+	0.157428i
$973$	5.47622	−	59.8411i	0.175560	−	1.91842i
$974$	−23.1685	+	63.6551i	−0.742368	+	2.03964i
$975$	10.1203	−	49.7740i	0.324107	−	1.59405i
$976$	4.86638	+	13.3703i	0.155769	+	0.427972i
$977$	13.4091	−	15.9803i	0.428995	−	0.511256i	−0.507637	−	0.861571i	$-0.669481\pi$
$977$	13.4091	−	15.9803i	0.428995	−	0.511256i	0.936632	+	0.350315i	$0.113925\pi$
$978$	21.3749	−	34.8904i	0.683495	−	1.11567i
$979$	−26.8241	−	31.9678i	−0.857303	−	1.02169i
$980$	−7.20971	−	20.3116i	−0.230306	−	0.648832i
$981$	−6.40130	−	52.0283i	−0.204378	−	1.66114i
$982$	7.06900			0.225581
$983$	−36.4843	−	13.2792i	−1.16367	−	0.423540i	−0.313261	−	0.949667i	$-0.601422\pi$
$983$	−36.4843	−	13.2792i	−1.16367	−	0.423540i	−0.850406	+	0.526127i	$0.823644\pi$
$984$	−2.69525	−	1.06130i	−0.0859215	−	0.0338331i
$985$	22.0605	−	26.2907i	0.702907	−	0.837692i
$986$	−40.9700	+	14.9119i	−1.30475	+	0.474890i
$987$	8.94070	+	13.6221i	0.284585	+	0.433597i
$988$	−0.703483	−	3.98965i	−0.0223808	−	0.126928i
$989$		−	0.0286692i		−	0.000911628i
$990$	66.0519	+	61.5640i	2.09927	+	1.95663i
$991$	60.7317			1.92921			0.964603	−	0.263705i	$-0.0849447\pi$
$991$	60.7317			1.92921			0.964603	+	0.263705i	$0.0849447\pi$
$992$	2.89677	+	1.05434i	0.0919725	+	0.0334752i
$993$	0.657827	−	25.2403i	0.0208755	−	0.800977i
$994$	70.4398	−	18.5732i	2.23421	−	0.589106i
$995$	−15.8042	+	18.8347i	−0.501026	+	0.597100i
$996$	−6.13368	−	18.3241i	−0.194353	−	0.580623i
$997$	29.4246	+	35.0669i	0.931887	+	1.11058i	0.993653	+	0.112489i	$0.0358822\pi$
$997$	29.4246	+	35.0669i	0.931887	+	1.11058i	−0.0617663	+	0.998091i	$0.519673\pi$
$998$	18.2110	+	10.5141i	0.576458	+	0.332818i
$999$	−23.5754	−	16.1901i	−0.745893	−	0.512232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.17	yes	132
3.2	odd	2		567.2.bd.a.17.6		132
7.5	odd	6		189.2.ba.a.131.6	yes	132
21.5	even	6		567.2.ba.a.341.17		132
27.7	even	9		567.2.ba.a.143.17		132
27.20	odd	18		189.2.ba.a.101.6	✓	132
189.47	even	18	inner	189.2.bd.a.47.17	yes	132
189.61	odd	18		567.2.bd.a.467.6		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.6	✓	132	27.20	odd	18
189.2.ba.a.131.6	yes	132	7.5	odd	6
189.2.bd.a.47.17	yes	132	189.47	even	18	inner
189.2.bd.a.185.17	yes	132	1.1	even	1	trivial
567.2.ba.a.143.17		132	27.7	even	9
567.2.ba.a.341.17		132	21.5	even	6
567.2.bd.a.17.6		132	3.2	odd	2
567.2.bd.a.467.6		132	189.61	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.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65422 - 0.291684i) q^{2} +(-0.549790 - 1.64248i) q^{3} +(0.771989 - 0.280981i) q^{4} +(3.52188 - 1.28186i) q^{5} +(-1.38856 - 2.55666i) q^{6} +(-2.17331 + 1.50888i) q^{7} +(-1.71431 + 0.989760i) q^{8} +(-2.39546 + 1.80604i) q^{9} +O(q^{10})\)	\(q+(1.65422 - 0.291684i) q^{2} +(-0.549790 - 1.64248i) q^{3} +(0.771989 - 0.280981i) q^{4} +(3.52188 - 1.28186i) q^{5} +(-1.38856 - 2.55666i) q^{6} +(-2.17331 + 1.50888i) q^{7} +(-1.71431 + 0.989760i) q^{8} +(-2.39546 + 1.80604i) q^{9} +(5.45209 - 3.14776i) q^{10} +(1.63515 - 4.49253i) q^{11} +(-0.885937 - 1.11349i) q^{12} +(1.10865 + 3.04598i) q^{13} +(-3.15503 + 3.12994i) q^{14} +(-4.04173 - 5.07986i) q^{15} +(-3.80582 + 3.19347i) q^{16} +(1.93415 + 3.35005i) q^{17} +(-3.43584 + 3.68630i) q^{18} +(-1.31749 - 0.760652i) q^{19} +(2.35868 - 1.97917i) q^{20} +(3.67316 + 2.74005i) q^{21} +(1.39450 - 7.90859i) q^{22} +(-0.358638 - 0.0632375i) q^{23} +(2.56817 + 2.27156i) q^{24} +(6.93028 - 5.81520i) q^{25} +(2.72242 + 4.71536i) q^{26} +(4.28337 + 2.94155i) q^{27} +(-1.25381 + 1.77550i) q^{28} +(-2.29492 + 6.30525i) q^{29} +(-8.16763 - 7.22431i) q^{30} +(-0.240377 - 0.660432i) q^{31} +(-2.81938 + 3.36000i) q^{32} +(-8.27786 - 0.215742i) q^{33} +(4.17668 + 4.97757i) q^{34} +(-5.71999 + 8.09998i) q^{35} +(-1.34181 + 2.06732i) q^{36} -5.50394 q^{37} +(-2.40129 - 0.873998i) q^{38} +(4.39343 - 3.49558i) q^{39} +(-4.76888 + 5.68333i) q^{40} +(-0.793900 + 0.288956i) q^{41} +(6.87546 + 3.46125i) q^{42} +(0.0136704 + 0.0775288i) q^{43} -3.92763i q^{44} +(-6.12145 + 9.43130i) q^{45} -0.611712 q^{46} +(3.34124 + 1.21611i) q^{47} +(7.33760 + 4.49524i) q^{48} +(2.44658 - 6.55852i) q^{49} +(9.76803 - 11.6411i) q^{50} +(4.43900 - 5.01863i) q^{51} +(1.71173 + 2.03996i) q^{52} +(-7.25668 - 4.18964i) q^{53} +(7.94366 + 3.61659i) q^{54} -17.9182i q^{55} +(2.23232 - 4.73775i) q^{56} +(-0.525011 + 2.58214i) q^{57} +(-1.95717 + 11.0997i) q^{58} +(1.11005 + 0.931445i) q^{59} +(-4.54752 - 2.78595i) q^{60} +(0.979516 - 2.69120i) q^{61} +(-0.590275 - 1.02239i) q^{62} +(2.48100 - 7.53954i) q^{63} +(1.28433 - 2.22452i) q^{64} +(7.80906 + 9.30647i) q^{65} +(-13.7564 + 2.05764i) q^{66} +(0.702586 - 3.98456i) q^{67} +(2.43445 + 2.04274i) q^{68} +(0.0933094 + 0.623821i) q^{69} +(-7.09950 + 15.0676i) q^{70} +(-14.1956 - 8.19580i) q^{71} +(2.31903 - 5.46704i) q^{72} -12.0494i q^{73} +(-9.10474 + 1.60541i) q^{74} +(-13.3615 - 8.18569i) q^{75} +(-1.23082 - 0.217026i) q^{76} +(3.22498 + 12.2309i) q^{77} +(6.24812 - 7.06396i) q^{78} +(0.228017 + 1.29315i) q^{79} +(-9.31009 + 16.1256i) q^{80} +(2.47647 - 8.65258i) q^{81} +(-1.22900 + 0.709566i) q^{82} +(12.7610 + 4.64462i) q^{83} +(3.60555 + 1.08320i) q^{84} +(11.1062 + 9.31918i) q^{85} +(0.0452278 + 0.124262i) q^{86} +(11.6180 + 0.302793i) q^{87} +(1.64337 + 9.32000i) q^{88} +(4.36439 - 7.55934i) q^{89} +(-7.37529 + 17.3870i) q^{90} +(-7.00545 - 4.94706i) q^{91} +(-0.294633 + 0.0519517i) q^{92} +(-0.952586 + 0.757913i) q^{93} +(5.88187 + 1.03713i) q^{94} +(-5.61509 - 0.990092i) q^{95} +(7.06880 + 2.78347i) q^{96} +(4.18960 - 0.738740i) q^{97} +(2.13418 - 11.5629i) q^{98} +(4.19674 + 13.7148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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