LMFDB - Embedded newform 189.2.ba.a.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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			101.14
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.572822 - 0.682663i) q^{2} +(-1.73140 + 0.0474030i) q^{3} +(0.209393 + 1.18753i) q^{4} +(-1.06212 + 0.891222i) q^{5} +(-0.959425 + 1.20912i) q^{6} +(-1.58403 + 2.11916i) q^{7} +(2.47415 + 1.42845i) q^{8} +(2.99551 - 0.164147i) q^{9} +O(q^{10})$	\(q+(0.572822 - 0.682663i) q^{2} +(-1.73140 + 0.0474030i) q^{3} +(0.209393 + 1.18753i) q^{4} +(-1.06212 + 0.891222i) q^{5} +(-0.959425 + 1.20912i) q^{6} +(-1.58403 + 2.11916i) q^{7} +(2.47415 + 1.42845i) q^{8} +(2.99551 - 0.164147i) q^{9} +1.23558i q^{10} +(-0.371978 + 0.443306i) q^{11} +(-0.418836 - 2.04616i) q^{12} +(-1.85992 + 5.11010i) q^{13} +(0.539301 + 2.29526i) q^{14} +(1.79671 - 1.59341i) q^{15} +(0.126145 - 0.0459131i) q^{16} +2.31232 q^{17} +(1.60383 - 2.13895i) q^{18} -3.42394i q^{19} +(-1.28075 - 1.07468i) q^{20} +(2.64215 - 3.74420i) q^{21} +(0.0895514 + 0.507871i) q^{22} +(2.28843 - 6.28742i) q^{23} +(-4.35146 - 2.35594i) q^{24} +(-0.534425 + 3.03087i) q^{25} +(2.42307 + 4.19688i) q^{26} +(-5.17864 + 0.426201i) q^{27} +(-2.84824 - 1.43735i) q^{28} +(-0.224543 - 0.616928i) q^{29} +(-0.0585702 - 2.13929i) q^{30} +(1.71407 - 0.302237i) q^{31} +(-1.91332 + 5.25680i) q^{32} +(0.623030 - 0.785175i) q^{33} +(1.32455 - 1.57853i) q^{34} +(-0.206211 - 3.66252i) q^{35} +(0.822168 + 3.52287i) q^{36} +(0.542537 - 0.939702i) q^{37} +(-2.33740 - 1.96131i) q^{38} +(2.97804 - 8.93580i) q^{39} +(-3.90090 + 0.687834i) q^{40} +(1.37400 + 0.500093i) q^{41} +(-1.04255 - 3.94846i) q^{42} +(-0.681623 + 3.86568i) q^{43} +(-0.604328 - 0.348909i) q^{44} +(-3.03529 + 2.84401i) q^{45} +(-2.98132 - 5.16380i) q^{46} +(1.07027 - 6.06980i) q^{47} +(-0.216232 + 0.0854738i) q^{48} +(-1.98167 - 6.71364i) q^{49} +(1.76293 + 2.10098i) q^{50} +(-4.00355 + 0.109611i) q^{51} +(-6.45784 - 1.13869i) q^{52} +(8.16395 + 4.71346i) q^{53} +(-2.67549 + 3.77940i) q^{54} -0.802359i q^{55} +(-6.94625 + 2.98040i) q^{56} +(0.162305 + 5.92822i) q^{57} +(-0.549777 - 0.200103i) q^{58} +(4.76072 + 1.73276i) q^{59} +(2.26844 + 1.79999i) q^{60} +(13.3184 + 2.34839i) q^{61} +(0.775532 - 1.34326i) q^{62} +(-4.39713 + 6.60797i) q^{63} +(2.62687 + 4.54987i) q^{64} +(-2.57878 - 7.08513i) q^{65} +(-0.179124 - 0.875085i) q^{66} +(-6.31050 + 5.29514i) q^{67} +(0.484183 + 2.74594i) q^{68} +(-3.66415 + 10.9945i) q^{69} +(-2.61839 - 1.95720i) q^{70} +(13.6154 - 7.86086i) q^{71} +(7.64580 + 3.87280i) q^{72} +(2.07131 - 1.19587i) q^{73} +(-0.330722 - 0.908652i) q^{74} +(0.781631 - 5.27299i) q^{75} +(4.06603 - 0.716950i) q^{76} +(-0.350210 - 1.49049i) q^{77} +(-4.39425 - 7.15162i) q^{78} +(-2.05377 - 1.72332i) q^{79} +(-0.0930623 + 0.161189i) q^{80} +(8.94611 - 0.983409i) q^{81} +(1.12845 - 0.651511i) q^{82} +(-11.2771 + 4.10455i) q^{83} +(4.99959 + 2.35361i) q^{84} +(-2.45595 + 2.06079i) q^{85} +(2.24850 + 2.67966i) q^{86} +(0.418019 + 1.05751i) q^{87} +(-1.55357 + 0.565453i) q^{88} -11.8321 q^{89} +(0.202817 + 3.70119i) q^{90} +(-7.88293 - 12.0361i) q^{91} +(7.94566 + 1.40103i) q^{92} +(-2.95342 + 0.604546i) q^{93} +(-3.53055 - 4.20755i) q^{94} +(3.05150 + 3.63663i) q^{95} +(3.06354 - 9.19233i) q^{96} +(18.3532 + 3.23616i) q^{97} +(-5.71830 - 2.49291i) q^{98} +(-1.04150 + 1.38899i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.572822	−	0.682663i	0.405046	−	0.482715i	−0.524505	−	0.851407i	$-0.675750\pi$
$2$	0.572822	−	0.682663i	0.405046	−	0.482715i	0.929552	+	0.368692i	$0.120194\pi$
$3$	−1.73140	+	0.0474030i	−0.999625	+	0.0273681i
$3$	−1.73140	+	0.0474030i	−0.999625	+	0.0273681i
$4$	0.209393	+	1.18753i	0.104697	+	0.593764i
$5$	−1.06212	+	0.891222i	−0.474993	+	0.398567i	−0.848612	−	0.529016i	$-0.822561\pi$
$5$	−1.06212	+	0.891222i	−0.474993	+	0.398567i	0.373619	+	0.927582i	$0.378117\pi$
$6$	−0.959425	+	1.20912i	−0.391684	+	0.493620i
$7$	−1.58403	+	2.11916i	−0.598709	+	0.800967i
$7$	−1.58403	+	2.11916i	−0.598709	+	0.800967i
$8$	2.47415	+	1.42845i	0.874743	+	0.505033i
$9$	2.99551	−	0.164147i	0.998502	−	0.0547158i
$10$			1.23558i			0.390725i
$11$	−0.371978	+	0.443306i	−0.112156	+	0.133662i	−0.819201	−	0.573506i	$-0.805583\pi$
$11$	−0.371978	+	0.443306i	−0.112156	+	0.133662i	0.707046	+	0.707168i	$0.250027\pi$
$12$	−0.418836	−	2.04616i	−0.120908	−	0.590676i
$13$	−1.85992	+	5.11010i	−0.515850	+	1.41729i	0.359203	+	0.933260i	$0.383049\pi$
$13$	−1.85992	+	5.11010i	−0.515850	+	1.41729i	−0.875053	+	0.484027i	$0.839174\pi$
$14$	0.539301	+	2.29526i	0.144134	+	0.613435i
$15$	1.79671	−	1.59341i	0.463907	−	0.411417i
$16$	0.126145	−	0.0459131i	0.0315363	−	0.0114783i
$17$	2.31232			0.560820			0.280410	−	0.959880i	$-0.409530\pi$
$17$	2.31232			0.560820			0.280410	+	0.959880i	$0.409530\pi$
$18$	1.60383	−	2.13895i	0.378027	−	0.504155i
$19$		−	3.42394i		−	0.785506i	−0.919644	−	0.392753i	$-0.871523\pi$
$19$		−	3.42394i		−	0.785506i	0.919644	−	0.392753i	$-0.128477\pi$
$20$	−1.28075	−	1.07468i	−0.286385	−	0.240305i
$21$	2.64215	−	3.74420i	0.576564	−	0.817052i
$22$	0.0895514	+	0.507871i	0.0190924	+	0.108279i
$23$	2.28843	−	6.28742i	0.477171	−	1.31102i	−0.434713	−	0.900569i	$-0.643150\pi$
$23$	2.28843	−	6.28742i	0.477171	−	1.31102i	0.911884	−	0.410448i	$-0.134628\pi$
$24$	−4.35146	−	2.35594i	−0.888237	−	0.480904i
$25$	−0.534425	+	3.03087i	−0.106885	+	0.606175i
$26$	2.42307	+	4.19688i	0.475203	+	0.823076i
$27$	−5.17864	+	0.426201i	−0.996630	+	0.0820224i
$28$	−2.84824	−	1.43735i	−0.538268	−	0.271633i
$29$	−0.224543	−	0.616928i	−0.0416967	−	0.114561i	0.917097	−	0.398664i	$-0.130526\pi$
$29$	−0.224543	−	0.616928i	−0.0416967	−	0.114561i	−0.958794	+	0.284104i	$0.908304\pi$
$30$	−0.0585702	−	2.13929i	−0.0106934	−	0.390578i
$31$	1.71407	−	0.302237i	0.307857	−	0.0542834i	−0.0175856	−	0.999845i	$-0.505598\pi$
$31$	1.71407	−	0.302237i	0.307857	−	0.0542834i	0.325442	+	0.945562i	$0.394487\pi$
$32$	−1.91332	+	5.25680i	−0.338230	+	0.929280i
$33$	0.623030	−	0.785175i	0.108456	−	0.136681i
$34$	1.32455	−	1.57853i	0.227158	−	0.270716i
$35$	−0.206211	−	3.66252i	−0.0348560	−	0.619079i
$36$	0.822168	+	3.52287i	0.137028	+	0.587145i
$37$	0.542537	−	0.939702i	0.0891925	−	0.154486i	−0.817978	−	0.575250i	$-0.804905\pi$
$37$	0.542537	−	0.939702i	0.0891925	−	0.154486i	0.907170	+	0.420764i	$0.138238\pi$
$38$	−2.33740	−	1.96131i	−0.379176	−	0.318167i
$39$	2.97804	−	8.93580i	0.476869	−	1.43087i
$40$	−3.90090	+	0.687834i	−0.616787	+	0.108756i
$41$	1.37400	+	0.500093i	0.214582	+	0.0781015i	0.447074	−	0.894497i	$-0.352466\pi$
$41$	1.37400	+	0.500093i	0.214582	+	0.0781015i	−0.232492	+	0.972598i	$0.574688\pi$
$42$	−1.04255	−	3.94846i	−0.160869	−	0.609260i
$43$	−0.681623	+	3.86568i	−0.103947	+	0.589510i	0.887689	+	0.460443i	$0.152309\pi$
$43$	−0.681623	+	3.86568i	−0.103947	+	0.589510i	−0.991636	+	0.129067i	$0.958802\pi$
$44$	−0.604328	−	0.348909i	−0.0911059	−	0.0526000i
$45$	−3.03529	+	2.84401i	−0.452474	+	0.423959i
$46$	−2.98132	−	5.16380i	−0.439572	−	0.761361i
$47$	1.07027	−	6.06980i	0.156115	−	0.885372i	−0.801645	−	0.597801i	$-0.796041\pi$
$47$	1.07027	−	6.06980i	0.156115	−	0.885372i	0.957759	−	0.287571i	$-0.0928476\pi$
$48$	−0.216232	+	0.0854738i	−0.0312104	+	0.0123371i
$49$	−1.98167	−	6.71364i	−0.283095	−	0.959092i
$50$	1.76293	+	2.10098i	0.249316	+	0.297124i
$51$	−4.00355	+	0.109611i	−0.560610	+	0.0153486i
$52$	−6.45784	−	1.13869i	−0.895541	−	0.157908i
$53$	8.16395	+	4.71346i	1.12141	+	0.647444i	0.941759	−	0.336288i	$-0.109171\pi$
$53$	8.16395	+	4.71346i	1.12141	+	0.647444i	0.179646	+	0.983731i	$0.442505\pi$
$54$	−2.67549	+	3.77940i	−0.364088	+	0.514312i
$55$		−	0.802359i		−	0.108190i
$56$	−6.94625	+	2.98040i	−0.928231	+	0.398272i
$57$	0.162305	+	5.92822i	0.0214979	+	0.785212i
$58$	−0.549777	−	0.200103i	−0.0721893	−	0.0262748i
$59$	4.76072	+	1.73276i	0.619792	+	0.225586i	0.632782	−	0.774330i	$-0.281913\pi$
$59$	4.76072	+	1.73276i	0.619792	+	0.225586i	−0.0129900	+	0.999916i	$0.504135\pi$
$60$	2.26844	+	1.79999i	0.292854	+	0.232377i
$61$	13.3184	+	2.34839i	1.70524	+	0.300680i	0.939521	−	0.342491i	$-0.111271\pi$
$61$	13.3184	+	2.34839i	1.70524	+	0.300680i	0.765722	+	0.643171i	$0.222382\pi$
$62$	0.775532	−	1.34326i	0.0984927	−	0.170594i
$63$	−4.39713	+	6.60797i	−0.553986	+	0.832526i
$64$	2.62687	+	4.54987i	0.328359	+	0.568734i
$65$	−2.57878	−	7.08513i	−0.319858	−	0.878803i
$66$	−0.179124	−	0.875085i	−0.0220487	−	0.107715i
$67$	−6.31050	+	5.29514i	−0.770950	+	0.646904i	−0.940952	−	0.338540i	$-0.890067\pi$
$67$	−6.31050	+	5.29514i	−0.770950	+	0.646904i	0.170002	+	0.985444i	$0.445623\pi$
$68$	0.484183	+	2.74594i	0.0587159	+	0.332994i
$69$	−3.66415	+	10.9945i	−0.441112	+	1.32359i
$70$	−2.61839	−	1.95720i	−0.312957	−	0.233930i
$71$	13.6154	−	7.86086i	1.61585	−	0.932913i	0.627875	−	0.778314i	$-0.283925\pi$
$71$	13.6154	−	7.86086i	1.61585	−	0.932913i	0.987977	−	0.154599i	$-0.0494085\pi$
$72$	7.64580	+	3.87280i	0.901066	+	0.456414i
$73$	2.07131	−	1.19587i	0.242429	−	0.139966i	−0.373864	−	0.927484i	$-0.621967\pi$
$73$	2.07131	−	1.19587i	0.242429	−	0.139966i	0.616292	+	0.787517i	$0.288634\pi$
$74$	−0.330722	−	0.908652i	−0.0384457	−	0.105629i
$75$	0.781631	−	5.27299i	0.0902550	−	0.608873i
$76$	4.06603	−	0.716950i	0.466405	−	0.0822398i
$77$	−0.350210	−	1.49049i	−0.0399102	−	0.169858i
$78$	−4.39425	−	7.15162i	−0.497551	−	0.809762i
$79$	−2.05377	−	1.72332i	−0.231067	−	0.193889i	0.519901	−	0.854226i	$-0.325969\pi$
$79$	−2.05377	−	1.72332i	−0.231067	−	0.193889i	−0.750969	+	0.660338i	$0.770413\pi$
$80$	−0.0930623	+	0.161189i	−0.0104047	+	0.0180214i
$81$	8.94611	−	0.983409i	0.994012	−	0.109268i
$82$	1.12845	−	0.651511i	0.124616	−	0.0719473i
$83$	−11.2771	+	4.10455i	−1.23783	+	0.450532i	−0.876271	−	0.481818i	$-0.839977\pi$
$83$	−11.2771	+	4.10455i	−1.23783	+	0.450532i	−0.361556	+	0.932350i	$0.617754\pi$
$84$	4.99959	+	2.35361i	0.545500	+	0.256800i
$85$	−2.45595	+	2.06079i	−0.266386	+	0.223524i
$86$	2.24850	+	2.67966i	0.242462	+	0.288956i
$87$	0.418019	+	1.05751i	0.0448164	+	0.113377i
$88$	−1.55357	+	0.565453i	−0.165611	+	0.0602775i
$89$	−11.8321			−1.25420			−0.627099	−	0.778940i	$-0.715758\pi$
$89$	−11.8321			−1.25420			−0.627099	+	0.778940i	$0.715758\pi$
$90$	0.202817	+	3.70119i	0.0213788	+	0.390139i
$91$	−7.88293	−	12.0361i	−0.826356	−	1.26172i
$92$	7.94566	+	1.40103i	0.828392	+	0.146068i
$93$	−2.95342	+	0.604546i	−0.306256	+	0.0626885i
$94$	−3.53055	−	4.20755i	−0.364149	−	0.433976i
$95$	3.05150	+	3.63663i	0.313077	+	0.373110i
$96$	3.06354	−	9.19233i	0.312671	−	0.938188i
$97$	18.3532	+	3.23616i	1.86348	+	0.328582i	0.987974	−	0.154618i	$-0.0494148\pi$
$97$	18.3532	+	3.23616i	1.86348	+	0.328582i	0.875510	+	0.483201i	$0.160526\pi$
$98$	−5.71830	−	2.49291i	−0.577635	−	0.251822i
$99$	−1.04150	+	1.38899i	−0.104674	+	0.139598i
$100$	−3.71115			−0.371115
$101$	11.4438	−	4.16521i	1.13870	−	0.414454i	0.297259	−	0.954797i	$-0.403928\pi$
$101$	11.4438	−	4.16521i	1.13870	−	0.414454i	0.841445	+	0.540343i	$0.181705\pi$
$102$	−2.21850	+	2.79586i	−0.219664	+	0.276832i
$103$	8.26065	+	9.84467i	0.813947	+	0.970024i	0.999921	−	0.0125308i	$-0.00398878\pi$
$103$	8.26065	+	9.84467i	0.813947	+	0.970024i	−0.185975	+	0.982554i	$0.559544\pi$
$104$	−11.9012	+	9.98633i	−1.16701	+	0.979241i
$105$	0.530649	+	6.33152i	0.0517860	+	0.617894i
$106$	7.89420	−	2.87325i	0.766752	−	0.279075i
$107$	−8.97631	+	5.18247i	−0.867772	+	0.501009i	−0.866607	−	0.498991i	$-0.833704\pi$
$107$	−8.97631	+	5.18247i	−0.867772	+	0.501009i	−0.00116512	+	0.999999i	$0.500371\pi$
$108$	−1.59050	−	6.06054i	−0.153046	−	0.583175i
$109$	8.42552	−	14.5934i	0.807019	−	1.39780i	−0.107901	−	0.994162i	$-0.534413\pi$
$109$	8.42552	−	14.5934i	0.807019	−	1.39780i	0.914920	−	0.403636i	$-0.132254\pi$
$110$	−0.547741	−	0.459609i	−0.0522250	−	0.0438220i
$111$	−0.894805	+	1.65272i	−0.0849311	+	0.156869i
$112$	−0.102521	+	0.340050i	−0.00968735	+	0.0321317i
$113$	−20.0144	+	3.52907i	−1.88279	+	0.331987i	−0.992385	−	0.123174i	$-0.960693\pi$
$113$	−20.0144	+	3.52907i	−1.88279	+	0.331987i	−0.890409	+	0.455162i	$0.849581\pi$
$114$	4.13995	+	3.28502i	0.387742	+	0.307670i
$115$	3.17290	+	8.71748i	0.295875	+	0.812909i
$116$	0.685601	−	0.395832i	0.0636564	−	0.0367521i
$117$	−4.73261	+	15.6126i	−0.437530	+	1.44339i
$118$	3.90993	−	2.25740i	0.359939	−	0.207811i
$119$	−3.66279	+	4.90017i	−0.335768	+	0.449198i
$120$	6.72142	−	1.37583i	0.613579	−	0.125596i
$121$	1.85198	+	10.5031i	0.168362	+	0.954826i
$122$	9.23222	−	7.74675i	0.835846	−	0.701358i
$123$	−2.40264	−	0.800731i	−0.216639	−	0.0721995i
$124$	0.717830	+	1.97222i	0.0644630	+	0.177111i
$125$	−5.59980	−	9.69914i	−0.500861	−	0.867517i
$126$	1.99224	+	6.78695i	0.177483	+	0.604629i
$127$	−0.987545	+	1.71048i	−0.0876305	+	0.151780i	−0.906509	−	0.422186i	$-0.861263\pi$
$127$	−0.987545	+	1.71048i	−0.0876305	+	0.151780i	0.818879	+	0.573967i	$0.194596\pi$
$128$	−6.40760	−	1.12983i	−0.566358	−	0.0998641i
$129$	0.996919	−	6.72535i	0.0877738	−	0.592134i
$130$	−6.31394	−	2.29809i	−0.553769	−	0.201555i
$131$	−2.09647	−	0.763054i	−0.183170	−	0.0666683i	0.248807	−	0.968553i	$-0.419962\pi$
$131$	−2.09647	−	0.763054i	−0.183170	−	0.0666683i	−0.431977	+	0.901885i	$0.642184\pi$
$132$	1.06287	+	0.575455i	0.0925113	+	0.0500869i
$133$	7.25588	+	5.42365i	0.629165	+	0.470290i
$134$			7.34111i			0.634176i
$135$	5.12049	−	5.06800i	0.440701	−	0.436184i
$136$	5.72102	+	3.30303i	0.490573	+	0.283233i
$137$	1.31325	+	0.231561i	0.112198	+	0.0197836i	0.229465	−	0.973317i	$-0.426302\pi$
$137$	1.31325	+	0.231561i	0.112198	+	0.0197836i	−0.117267	+	0.993100i	$0.537413\pi$
$138$	5.40664	+	8.79929i	0.460244	+	0.749045i
$139$	−9.79765	−	11.6764i	−0.831026	−	0.990378i	−0.999989	−	0.00475527i	$-0.998486\pi$
$139$	−9.79765	−	11.6764i	−0.831026	−	0.990378i	0.168963	−	0.985622i	$-0.445958\pi$
$140$	4.30617	−	1.01179i	0.363937	−	0.0855117i
$141$	−1.56534	+	10.5600i	−0.131825	+	0.889313i
$142$	2.43289	−	13.7976i	0.204164	−	1.15787i
$143$	−1.57349	−	2.72536i	−0.131582	−	0.227906i
$144$	0.370332	−	0.158239i	0.0308610	−	0.0131866i
$145$	0.788312	+	0.455132i	0.0654657	+	0.0377967i
$146$	0.370115	−	2.09903i	0.0306310	−	0.173717i
$147$	3.74931	+	11.5301i	0.309238	+	0.950985i
$148$	1.22952	+	0.447510i	0.101066	+	0.0367851i
$149$	−19.6318	+	3.46162i	−1.60830	+	0.283587i	−0.904392	−	0.426703i	$-0.859675\pi$
$149$	−19.6318	+	3.46162i	−1.60830	+	0.283587i	−0.703909	+	0.710290i	$0.748564\pi$
$150$	−3.15194	−	3.55408i	−0.257355	−	0.290189i
$151$	−2.21309	−	1.85701i	−0.180099	−	0.151121i	0.548282	−	0.836294i	$-0.315282\pi$
$151$	−2.21309	−	1.85701i	−0.180099	−	0.151121i	−0.728381	+	0.685173i	$0.759727\pi$
$152$	4.89093	−	8.47134i	0.396707	−	0.687116i
$153$	6.92656	−	0.379561i	0.559980	−	0.0306857i
$154$	−1.21811	−	0.614712i	−0.0981583	−	0.0495349i
$155$	−1.55119	+	1.84863i	−0.124594	+	0.148486i
$156$	11.2351	+	1.66541i	0.899527	+	0.133340i
$157$	−2.77826	+	7.63321i	−0.221729	+	0.609197i	−0.999820	−	0.0189550i	$-0.993966\pi$
$157$	−2.77826	+	7.63321i	−0.221729	+	0.609197i	0.778091	+	0.628152i	$0.216188\pi$
$158$	−2.35289	+	0.414878i	−0.187186	+	0.0330059i
$159$	−14.3585	−	7.77390i	−1.13870	−	0.616510i
$160$	−2.65281	−	7.28853i	−0.209723	−	0.576209i
$161$	9.69908	+	14.8090i	0.764394	+	1.16712i
$162$	4.45319	−	6.67049i	0.349876	−	0.524084i
$163$	0.518631	+	0.898295i	0.0406223	+	0.0703599i	0.885622	−	0.464407i	$-0.153733\pi$
$163$	0.518631	+	0.898295i	0.0406223	+	0.0703599i	−0.844999	+	0.534767i	$0.820399\pi$
$164$	−0.306169	+	1.73637i	−0.0239078	+	0.135588i
$165$	0.0380342	+	1.38921i	0.00296096	+	0.108150i
$166$	−3.65778	+	10.0497i	−0.283899	+	0.780005i
$167$	−2.43922	−	13.8335i	−0.188753	−	1.07047i	−0.921038	−	0.389472i	$-0.872658\pi$
$167$	−2.43922	−	13.8335i	−0.188753	−	1.07047i	0.732286	−	0.680998i	$-0.238454\pi$
$168$	11.8855	−	5.48954i	0.916984	−	0.423527i
$169$	−12.6952	−	10.6526i	−0.976556	−	0.819428i
$170$			2.85705i			0.219126i
$171$	−0.562031	−	10.2564i	−0.0429796	−	0.784330i
$172$	−4.73332			−0.360912
$173$	−5.50262	+	2.00279i	−0.418356	+	0.152269i	−0.542617	−	0.839980i	$-0.682566\pi$
$173$	−5.50262	+	2.00279i	−0.418356	+	0.152269i	0.124260	+	0.992250i	$0.460344\pi$
$174$	0.961371	+	0.320397i	0.0728813	+	0.0242892i
$175$	−5.57635	−	5.93354i	−0.421533	−	0.448533i
$176$	−0.0265697	+	0.0729997i	−0.00200277	+	0.00550256i
$177$	−8.32485	−	2.77443i	−0.625734	−	0.208539i
$178$	−6.77767	+	8.07732i	−0.508008	+	0.605420i
$179$		−	8.49786i		−	0.635160i	−0.948232	−	0.317580i	$-0.897130\pi$
$179$		−	8.49786i		−	0.635160i	0.948232	−	0.317580i	$-0.102870\pi$
$180$	−4.01290	−	3.00897i	−0.299104	−	0.224275i
$181$	5.00733	+	2.89098i	0.372192	+	0.214885i	0.674416	−	0.738352i	$-0.264396\pi$
$181$	5.00733	+	2.89098i	0.372192	+	0.214885i	−0.302224	+	0.953237i	$0.597729\pi$
$182$	−12.7321	−	1.51313i	−0.943765	−	0.112161i
$183$	−23.1708	−	3.43468i	−1.71283	−	0.253898i
$184$	14.6432	−	12.2871i	1.07951	−	0.905816i
$185$	0.261245	+	1.48159i	0.0192071	+	0.108929i
$186$	−1.27908	+	2.36249i	−0.0937870	+	0.173226i
$187$	−0.860132	+	1.02507i	−0.0628991	+	0.0749602i
$188$	7.43216			0.542046
$189$	7.29996	−	11.6495i	0.530994	−	0.847375i
$190$	4.23056			0.306917
$191$	15.2886	−	18.2202i	1.10624	−	1.31837i	0.162864	−	0.986649i	$-0.447927\pi$
$191$	15.2886	−	18.2202i	1.10624	−	1.31837i	0.943378	−	0.331719i	$-0.107629\pi$
$192$	−4.76385	−	7.75314i	−0.343801	−	0.559535i
$193$	−3.28572	−	18.6342i	−0.236511	−	1.34132i	−0.839408	−	0.543502i	$-0.817098\pi$
$193$	−3.28572	−	18.6342i	−0.236511	−	1.34132i	0.602897	−	0.797819i	$-0.294013\pi$
$194$	12.7223	−	10.6753i	0.913409	−	0.766441i
$195$	4.80076	+	12.1450i	0.343789	+	0.869720i
$196$	7.55768	−	3.75907i	0.539835	−	0.268505i
$197$	−9.22224	−	5.32447i	−0.657058	−	0.379352i	0.134097	−	0.990968i	$-0.457187\pi$
$197$	−9.22224	−	5.32447i	−0.657058	−	0.379352i	−0.791155	+	0.611616i	$0.790520\pi$
$198$	0.351618	+	1.50663i	0.0249884	+	0.107072i
$199$			10.0273i			0.710813i	0.934712	+	0.355407i	$0.115658\pi$
$199$			10.0273i			0.710813i	−0.934712	+	0.355407i	$0.884342\pi$
$200$	−5.65169	+	6.73543i	−0.399635	+	0.476267i
$201$	10.6750	−	9.46715i	0.752957	−	0.667761i
$202$	3.71184	−	10.1982i	0.261164	−	0.717543i
$203$	1.66305	+	0.501392i	0.116723	+	0.0351908i
$204$	−0.968482	−	4.73138i	−0.0678073	−	0.331263i
$205$	−1.90504	+	0.693377i	−0.133054	+	0.0484276i
$206$	11.4525			0.797931
$207$	5.82295	−	19.2096i	0.404723	−	1.33516i
$208$			0.730010i			0.0506171i
$209$	1.51786	+	1.27363i	0.104992	+	0.0880990i
$210$	4.62626	+	3.26458i	0.319242	+	0.225278i
$211$	−1.04018	−	5.89915i	−0.0716089	−	0.406114i	−0.999451	−	0.0331403i	$-0.989449\pi$
$211$	−1.04018	−	5.89915i	−0.0716089	−	0.406114i	0.927842	−	0.372974i	$-0.121662\pi$
$212$	−3.88789	+	10.6819i	−0.267021	+	0.733635i
$213$	−23.2011	+	14.2557i	−1.58972	+	0.976786i
$214$	−1.60395	+	9.09643i	−0.109643	+	0.621819i
$215$	−2.72121	−	4.71328i	−0.185585	−	0.321443i
$216$	−13.4215	−	6.34295i	−0.913220	−	0.431583i
$217$	−2.07466	+	4.11115i	−0.140837	+	0.279083i
$218$	−5.13607	−	14.1112i	−0.347858	−	0.955733i
$219$	−3.52958	+	2.16872i	−0.238507	+	0.146549i
$220$	0.952823	−	0.168008i	0.0642393	−	0.0113271i
$221$	−4.30074	+	11.8162i	−0.289299	+	0.794842i
$222$	0.615686	+	1.55756i	0.0413221	+	0.104537i
$223$	3.68146	−	4.38739i	0.246528	−	0.293801i	−0.628563	−	0.777759i	$-0.716357\pi$
$223$	3.68146	−	4.38739i	0.246528	−	0.293801i	0.875092	+	0.483957i	$0.160801\pi$
$224$	−8.10923	−	12.3816i	−0.541821	−	0.827279i
$225$	−1.10336	+	9.16672i	−0.0735575	+	0.611115i
$226$	−9.05551	+	15.6846i	−0.602363	+	1.04332i
$227$	13.5450	+	11.3656i	0.899011	+	0.754359i	0.969997	−	0.243118i	$-0.0781702\pi$
$227$	13.5450	+	11.3656i	0.899011	+	0.754359i	−0.0709862	+	0.997477i	$0.522615\pi$
$228$	−7.00594	+	1.43407i	−0.463980	+	0.0949736i
$229$	13.5151	−	2.38308i	0.893103	−	0.157478i	0.291781	−	0.956485i	$-0.405752\pi$
$229$	13.5151	−	2.38308i	0.893103	−	0.157478i	0.601322	+	0.799007i	$0.294641\pi$
$230$	7.76861	+	2.82754i	0.512247	+	0.186443i
$231$	0.677009	+	2.56404i	0.0445439	+	0.168702i
$232$	0.325697	−	1.84712i	0.0213831	−	0.121269i
$233$	7.92072	+	4.57303i	0.518904	+	0.299589i	0.736486	−	0.676453i	$-0.236484\pi$
$233$	7.92072	+	4.57303i	0.518904	+	0.299589i	−0.217582	+	0.976042i	$0.569817\pi$
$234$	7.94723	+	12.1740i	0.519526	+	0.795842i
$235$	4.27279	+	7.40069i	0.278726	+	0.482768i
$236$	−1.06084	+	6.01631i	−0.0690546	+	0.391628i
$237$	3.63759	+	2.88640i	0.236287	+	0.187492i
$238$	1.24704	+	5.30738i	0.0808333	+	0.344026i
$239$	1.62286	+	1.93405i	0.104974	+	0.125103i	0.815973	−	0.578089i	$-0.196202\pi$
$239$	1.62286	+	1.93405i	0.104974	+	0.125103i	−0.710999	+	0.703193i	$0.751757\pi$
$240$	0.153487	−	0.283494i	0.00990757	−	0.0182994i
$241$	7.08366	+	1.24904i	0.456299	+	0.0804578i	0.397073	−	0.917787i	$-0.370026\pi$
$241$	7.08366	+	1.24904i	0.456299	+	0.0804578i	0.0592254	+	0.998245i	$0.481137\pi$
$242$	8.23092	+	4.75212i	0.529103	+	0.305478i
$243$	−15.4427	+	2.12675i	−0.990650	+	0.136431i
$244$			16.3077i			1.04399i
$245$	8.08811	+	5.36457i	0.516731	+	0.342730i
$246$	−1.92292	+	1.18152i	−0.122601	+	0.0753309i
$247$	17.4967	+	6.36828i	1.11329	+	0.405204i
$248$	4.67260	+	1.70069i	0.296710	+	0.107994i
$249$	19.3307	−	7.64119i	1.22503	−	0.484241i
$250$	−9.82893	−	1.73311i	−0.621636	−	0.109611i
$251$	−0.469593	+	0.813359i	−0.0296405	+	0.0513388i	−0.880465	−	0.474111i	$-0.842770\pi$
$251$	−0.469593	+	0.813359i	−0.0296405	+	0.0513388i	0.850825	+	0.525450i	$0.176103\pi$
$252$	−8.76787	−	3.83805i	−0.552324	−	0.241774i
$253$	1.93601	+	3.35326i	0.121716	+	0.210818i
$254$	0.601992	+	1.65396i	0.0377724	+	0.103779i
$255$	4.15456	−	3.68448i	0.260168	−	0.230731i
$256$	−12.4909	+	10.4811i	−0.780682	+	0.655070i
$257$	−3.40273	−	19.2978i	−0.212256	−	1.20377i	−0.885604	−	0.464441i	$-0.846255\pi$
$257$	−3.40273	−	19.2978i	−0.212256	−	1.20377i	0.673348	−	0.739326i	$-0.264856\pi$
$258$	−4.02009	−	4.53299i	−0.250280	−	0.282212i
$259$	1.13198	+	2.63824i	0.0703378	+	0.163932i
$260$	7.87381	−	4.54595i	0.488313	−	0.281928i
$261$	−0.773888	−	1.81115i	−0.0479025	−	0.112108i
$262$	−1.72181	+	0.994090i	−0.106374	+	0.0614151i
$263$	4.07910	+	11.2072i	0.251528	+	0.691068i	0.999622	+	0.0274758i	$0.00874693\pi$
$263$	4.07910	+	11.2072i	0.251528	+	0.691068i	−0.748094	+	0.663593i	$0.769031\pi$
$264$	2.66305	−	1.05267i	0.163899	−	0.0647874i
$265$	−12.8718	+	2.26965i	−0.790710	+	0.139423i
$266$	7.85885	−	1.84654i	0.481857	−	0.113218i
$267$	20.4861	−	0.560876i	1.25373	−	0.0343251i
$268$	−7.60949	−	6.38512i	−0.464824	−	0.390033i
$269$	−8.21836	+	14.2346i	−0.501082	+	0.867900i	0.498917	+	0.866650i	$0.333731\pi$
$269$	−8.21836	+	14.2346i	−0.501082	+	0.867900i	−0.999999	+	0.00125014i	$0.999602\pi$
$270$	−0.526605	−	6.39863i	−0.0320482	−	0.389408i
$271$	−12.7971	+	7.38840i	−0.777367	+	0.448813i	−0.835496	−	0.549496i	$-0.814820\pi$
$271$	−12.7971	+	7.38840i	−0.777367	+	0.448813i	0.0581291	+	0.998309i	$0.481487\pi$
$272$	0.291688	−	0.106166i	0.0176862	−	0.00643725i
$273$	14.2191	+	20.4656i	0.860577	+	1.23863i
$274$	0.910336	−	0.763863i	0.0549954	−	0.0461466i
$275$	−1.14481	−	1.36433i	−0.0690347	−	0.0822724i
$276$	−13.8235	−	2.04911i	−0.832080	−	0.123342i
$277$	−26.0466	+	9.48020i	−1.56499	+	0.569610i	−0.971873	−	0.235506i	$-0.924325\pi$
$277$	−26.0466	+	9.48020i	−1.56499	+	0.569610i	−0.593118	+	0.805116i	$0.702103\pi$
$278$	−13.5833			−0.814674
$279$	5.08490	−	1.18671i	0.304425	−	0.0710467i
$280$	4.72153	−	9.35618i	0.282166	−	0.559139i
$281$	6.13171	+	1.08119i	0.365787	+	0.0644981i	0.353521	−	0.935427i	$-0.384984\pi$
$281$	6.13171	+	1.08119i	0.365787	+	0.0644981i	0.0122663	+	0.999925i	$0.496095\pi$
$282$	6.31226	+	7.11760i	0.375889	+	0.423847i
$283$	3.53087	+	4.20792i	0.209888	+	0.250135i	0.860710	−	0.509095i	$-0.170020\pi$
$283$	3.53087	+	4.20792i	0.209888	+	0.250135i	−0.650822	+	0.759230i	$0.725576\pi$
$284$	12.1860	+	14.5227i	0.723104	+	0.861762i
$285$	−5.45575	−	6.15182i	−0.323171	−	0.364402i
$286$	−2.76183	−	0.486986i	−0.163311	−	0.0287961i
$287$	−3.23623	+	2.11955i	−0.191029	+	0.125113i
$288$	−4.86847	+	16.0608i	−0.286877	+	0.946394i
$289$	−11.6532			−0.685481
$290$	0.762264	−	0.277441i	0.0447617	−	0.0162919i
$291$	−31.9301	−	4.73310i	−1.87178	−	0.277459i
$292$	1.85385	+	2.20933i	0.108488	+	0.129291i
$293$	17.8320	−	14.9629i	1.04176	−	0.874140i	0.0495561	−	0.998771i	$-0.484219\pi$
$293$	17.8320	−	14.9629i	1.04176	−	0.874140i	0.992203	+	0.124632i	$0.0397749\pi$
$294$	10.0188	+	4.04517i	0.584311	+	0.235919i
$295$	−6.60071	+	2.40246i	−0.384308	+	0.139877i
$296$	2.68463	−	1.54997i	0.156041	−	0.0900904i
$297$	1.73741	−	2.45426i	0.100814	−	0.142411i
$298$	−8.88242	+	15.3848i	−0.514545	+	0.891218i
$299$	27.8730	+	23.3882i	1.61194	+	1.35258i
$300$	6.42549	−	0.175920i	0.370976	−	0.0101567i
$301$	−7.11227	−	7.56783i	−0.409944	−	0.436203i
$302$	−2.53542	+	0.447062i	−0.145897	+	0.0257255i
$303$	−19.6164	+	7.75413i	−1.12693	+	0.445463i
$304$	−0.157204	−	0.431914i	−0.00901627	−	0.0247720i
$305$	−16.2386	+	9.37537i	−0.929821	+	0.536832i
$306$	3.70858	−	4.94593i	0.212005	−	0.282740i
$307$	15.1010	−	8.71859i	0.861862	−	0.497596i	−0.00277334	−	0.999996i	$-0.500883\pi$
$307$	15.1010	−	8.71859i	0.861862	−	0.497596i	0.864635	+	0.502400i	$0.167549\pi$
$308$	1.69667	−	0.727983i	0.0966768	−	0.0414807i
$309$	−14.7692	−	16.6535i	−0.840189	−	0.947384i
$310$	0.373438	+	2.11787i	0.0212099	+	0.120287i
$311$	−1.15637	+	0.970311i	−0.0655718	+	0.0550213i	−0.674985	−	0.737832i	$-0.735850\pi$
$311$	−1.15637	+	0.970311i	−0.0655718	+	0.0550213i	0.609413	+	0.792853i	$0.291405\pi$
$312$	20.1325	−	17.8545i	1.13978	−	1.01081i
$313$	−9.95908	−	27.3624i	−0.562921	−	1.54661i	−0.815333	−	0.578992i	$-0.803446\pi$
$313$	−9.95908	−	27.3624i	−0.562921	−	1.54661i	0.252413	−	0.967620i	$-0.418776\pi$
$314$	3.61946	+	6.26909i	0.204258	+	0.353785i
$315$	−1.21890	−	10.9373i	−0.0686772	−	0.616245i
$316$	1.61644	−	2.79976i	0.0909320	−	0.157499i
$317$	29.9400	+	5.27923i	1.68160	+	0.296511i	0.931209	−	0.364486i	$-0.118755\pi$
$317$	29.9400	+	5.27923i	1.68160	+	0.296511i	0.750388	+	0.660997i	$0.229866\pi$
$318$	−13.5318	+	5.34896i	−0.758827	+	0.299955i
$319$	0.357014	+	0.129942i	0.0199889	+	0.00727537i
$320$	−6.84500	−	2.49137i	−0.382647	−	0.139272i
$321$	15.2959	−	9.39845i	0.853736	−	0.524570i
$322$	15.6654	+	1.86174i	0.873000	+	0.103751i
$323$		−	7.91725i		−	0.440527i
$324$	3.04108	+	10.4178i	0.168949	+	0.578768i
$325$	−14.4941	−	8.36816i	−0.803987	−	0.464182i
$326$	0.910316	+	0.160513i	0.0504177	+	0.00889000i
$327$	−13.8962	+	25.6665i	−0.768461	+	1.41936i
$328$	2.68511	+	3.19999i	0.148260	+	0.176690i
$329$	11.1675	+	11.8828i	0.615686	+	0.655123i
$330$	0.970146	+	0.769803i	0.0534048	+	0.0423763i
$331$	−4.91465	+	27.8723i	−0.270133	+	1.53200i	0.483875	+	0.875137i	$0.339229\pi$
$331$	−4.91465	+	27.8723i	−0.270133	+	1.53200i	−0.754008	+	0.656865i	$0.771882\pi$
$332$	−7.23562	−	12.5325i	−0.397106	−	0.687808i
$333$	1.47092	−	2.90394i	0.0806061	−	0.159135i
$334$	−10.8409	−	6.25898i	−0.593186	−	0.342476i
$335$	1.98335	−	11.2481i	0.108362	−	0.614550i
$336$	0.161386	−	0.593623i	0.00880434	−	0.0323848i
$337$	7.63576	+	2.77919i	0.415946	+	0.151392i	0.541512	−	0.840693i	$-0.317852\pi$
$337$	7.63576	+	2.77919i	0.415946	+	0.151392i	−0.125565	+	0.992085i	$0.540074\pi$
$338$	−14.5442	+	2.56454i	−0.791101	+	0.139492i
$339$	34.4856	−	7.05899i	1.87300	−	0.383392i
$340$	−2.96150	−	2.48500i	−0.160610	−	0.134768i
$341$	−0.503614	+	0.872285i	−0.0272722	+	0.0472369i
$342$	−7.32363	−	5.49144i	−0.396017	−	0.296943i
$343$	17.3663	+	6.43517i	0.937692	+	0.347467i
$344$	−7.20836	+	8.59059i	−0.388649	+	0.463174i
$345$	−5.90680	−	14.9431i	−0.318012	−	0.804507i
$346$	−1.78479	+	4.90368i	−0.0959510	+	0.263623i
$347$	13.5586	−	2.39075i	0.727863	−	0.128342i	0.202576	−	0.979267i	$-0.435069\pi$
$347$	13.5586	−	2.39075i	0.727863	−	0.128342i	0.525288	+	0.850925i	$0.323958\pi$
$348$	−1.16829	+	0.717844i	−0.0626268	+	0.0384805i
$349$	0.460133	+	1.26420i	0.0246303	+	0.0676713i	0.951398	−	0.307963i	$-0.0996472\pi$
$349$	0.460133	+	1.26420i	0.0246303	+	0.0676713i	−0.926768	+	0.375634i	$0.877425\pi$
$350$	−7.24486	+	0.407907i	−0.387254	+	0.0218036i
$351$	7.45396	−	27.2561i	0.397863	−	1.45482i
$352$	−1.61866	−	2.80360i	−0.0862749	−	0.149432i
$353$	2.73545	−	15.5135i	0.145593	−	0.825701i	−0.821295	−	0.570503i	$-0.806748\pi$
$353$	2.73545	−	15.5135i	0.145593	−	0.825701i	0.966889	−	0.255198i	$-0.0821407\pi$
$354$	−6.66266	+	4.09381i	−0.354116	+	0.217584i
$355$	−7.45539	+	20.4835i	−0.395691	+	1.08715i
$356$	−2.47755	−	14.0509i	−0.131310	−	0.744697i
$357$	6.10948	−	8.65779i	0.323348	−	0.458219i
$358$	−5.80117	−	4.86776i	−0.306601	−	0.257269i
$359$			29.9732i			1.58192i	0.611866	+	0.790962i	$0.290419\pi$
$359$			29.9732i			1.58192i	−0.611866	+	0.790962i	$0.709581\pi$
$360$	−11.5723	+	2.70073i	−0.609912	+	0.142341i
$361$	7.27661			0.382980
$362$	4.84188	−	1.76230i	0.254483	−	0.0926244i
$363$	−3.70439	−	18.0973i	−0.194430	−	0.949860i
$364$	12.6425	−	11.8815i	0.662647	−	0.622758i
$365$	−1.13419	+	3.11616i	−0.0593661	+	0.163107i
$366$	−15.6175	+	13.8504i	−0.816338	+	0.723971i
$367$	−3.07129	+	3.66022i	−0.160320	+	0.191062i	−0.840225	−	0.542239i	$-0.817577\pi$
$367$	−3.07129	+	3.66022i	−0.160320	+	0.191062i	0.679904	+	0.733301i	$0.262021\pi$
$368$		−	0.898197i		−	0.0468218i
$369$	4.19790	+	1.27249i	0.218534	+	0.0662434i
$370$	1.16108	+	0.670348i	0.0603615	+	0.0348497i
$371$	−22.9206	+	9.83443i	−1.18998	+	0.510578i
$372$	−1.33634	−	3.38068i	−0.0692861	−	0.175280i
$373$	10.5947	−	8.89000i	0.548572	−	0.460307i	−0.325885	−	0.945409i	$-0.605662\pi$
$373$	10.5947	−	8.89000i	0.548572	−	0.460307i	0.874457	+	0.485103i	$0.161218\pi$
$374$	0.207071	+	1.17436i	0.0107074	+	0.0607247i
$375$	10.1553	+	16.5277i	0.524416	+	0.853485i
$376$	11.3184	−	13.4888i	0.583703	−	0.695630i
$377$	3.57020			0.183875
$378$	−3.77109	−	11.6565i	−0.193964	−	0.599545i
$379$	−8.84194			−0.454180			−0.227090	−	0.973874i	$-0.572921\pi$
$379$	−8.84194			−0.454180			−0.227090	+	0.973874i	$0.572921\pi$
$380$	−3.67963	+	4.38522i	−0.188761	+	0.224957i
$381$	1.62876	−	3.00834i	0.0834437	−	0.154122i
$382$	−3.68063	−	20.8739i	−0.188317	−	1.06800i
$383$	23.0477	−	19.3393i	1.17768	−	0.988193i	0.177691	−	0.984086i	$-0.443137\pi$
$383$	23.0477	−	19.3393i	1.17768	−	0.988193i	0.999992	−	0.00410677i	$-0.00130723\pi$
$384$	11.1477	+	1.65246i	0.568878	+	0.0843265i
$385$	1.70033	+	1.27096i	0.0866566	+	0.0647743i
$386$	−14.6030	−	8.43106i	−0.743274	−	0.429130i
$387$	−1.40727	+	11.6915i	−0.0715353	+	0.594315i
$388$			22.4725i			1.14087i
$389$	6.35574	−	7.57448i	0.322249	−	0.384041i	−0.580463	−	0.814286i	$-0.697128\pi$
$389$	6.35574	−	7.57448i	0.322249	−	0.384041i	0.902712	+	0.430245i	$0.141573\pi$
$390$	11.0409	+	3.67961i	0.559078	+	0.186324i
$391$	5.29159	−	14.5385i	0.267607	−	0.735244i
$392$	4.68716	−	19.4413i	0.236737	−	0.981932i
$393$	3.66601	+	1.22177i	0.184926	+	0.0616303i
$394$	−8.91752	+	3.24571i	−0.449258	+	0.163517i
$395$	3.71721			0.187033
$396$	−1.86754	−	0.945960i	−0.0938475	−	0.0475363i
$397$		−	11.4899i		−	0.576660i	−0.957531	−	0.288330i	$-0.906900\pi$
$397$		−	11.4899i		−	0.576660i	0.957531	−	0.288330i	$-0.0931000\pi$
$398$	6.84523	+	5.74383i	0.343121	+	0.287912i
$399$	−12.8199	−	9.04656i	−0.641800	−	0.452894i
$400$	0.0717417	+	0.406867i	0.00358709	+	0.0203434i
$401$	5.63819	−	15.4908i	0.281558	−	0.773573i	−0.715620	−	0.698490i	$-0.753856\pi$
$401$	5.63819	−	15.4908i	0.281558	−	0.773573i	0.997177	−	0.0750829i	$-0.0239221\pi$
$402$	−0.347991	−	12.7104i	−0.0173562	−	0.633938i
$403$	−1.64358	+	9.32122i	−0.0818727	+	0.464323i
$404$	7.34256	+	12.7177i	0.365306	+	0.632729i
$405$	−8.62539	+	9.01747i	−0.428599	+	0.448082i
$406$	1.29492	−	0.848096i	0.0642656	−	0.0420903i
$407$	0.214764	+	0.590059i	0.0106454	+	0.0292481i
$408$	−10.0620	−	5.44768i	−0.498141	−	0.269700i
$409$	8.98833	−	1.58489i	0.444444	−	0.0783675i	0.0530527	−	0.998592i	$-0.483105\pi$
$409$	8.98833	−	1.58489i	0.444444	−	0.0783675i	0.391392	+	0.920224i	$0.371994\pi$
$410$	−0.617905	+	1.69768i	−0.0305162	+	0.0838425i
$411$	−2.28474	−	0.338674i	−0.112698	−	0.0167055i
$412$	−9.96108	+	11.8712i	−0.490747	+	0.584850i
$413$	−11.2131	+	7.34396i	−0.551762	+	0.361373i
$414$	−9.77819	−	14.9788i	−0.480572	−	0.736169i
$415$	8.31959	−	14.4100i	0.408393	−	0.707357i
$416$	−23.3041	−	19.5545i	−1.14258	−	0.958738i
$417$	17.5172	+	19.7521i	0.857819	+	0.967263i
$418$	1.73892	−	0.306619i	0.0850535	−	0.0149972i
$419$	−27.5287	−	10.0196i	−1.34487	−	0.489492i	−0.433525	−	0.901142i	$-0.642730\pi$
$419$	−27.5287	−	10.0196i	−1.34487	−	0.489492i	−0.911342	+	0.411650i	$0.864953\pi$
$420$	−7.40774	+	1.95594i	−0.361461	+	0.0954399i
$421$	2.05835	−	11.6735i	0.100318	−	0.568930i	−0.892670	−	0.450711i	$-0.851171\pi$
$421$	2.05835	−	11.6735i	0.100318	−	0.568930i	0.992988	−	0.118219i	$-0.0377184\pi$
$422$	−4.62297	−	2.66907i	−0.225042	−	0.129928i
$423$	2.20966	−	18.3578i	0.107437	−	0.892587i
$424$	13.4659	+	23.3236i	0.653961	+	1.13269i
$425$	−1.23576	+	7.00834i	−0.0599432	+	0.339955i
$426$	−3.55826	+	24.0045i	−0.172398	+	1.16302i
$427$	−26.0734	+	24.5038i	−1.26178	+	1.18582i
$428$	−8.03390	−	9.57443i	−0.388333	−	0.462798i
$429$	2.85353	+	4.64411i	0.137770	+	0.224220i
$430$	−4.77635	−	0.842200i	−0.230336	−	0.0406145i
$431$	−10.4044	−	6.00699i	−0.501163	−	0.289347i	0.228031	−	0.973654i	$-0.426771\pi$
$431$	−10.4044	−	6.00699i	−0.501163	−	0.289347i	−0.729194	+	0.684307i	$0.760105\pi$
$432$	−0.633693	+	0.291531i	−0.0304886	+	0.0140263i
$433$			1.86378i			0.0895673i	0.998997	+	0.0447837i	$0.0142599\pi$
$433$			1.86378i			0.0895673i	−0.998997	+	0.0447837i	$0.985740\pi$
$434$	1.61811	+	3.77125i	0.0776720	+	0.181026i
$435$	−1.38646	−	0.750648i	−0.0664756	−	0.0359908i
$436$	19.0943	+	6.94977i	0.914453	+	0.332834i
$437$	−21.5278	−	7.83546i	−1.02981	−	0.374821i
$438$	−0.541318	+	3.65181i	−0.0258652	+	0.174490i
$439$	25.7176	+	4.53471i	1.22744	+	0.216430i	0.749524	−	0.661978i	$-0.230283\pi$
$439$	25.7176	+	4.53471i	1.22744	+	0.216430i	0.477912	+	0.878408i	$0.341394\pi$
$440$	1.14613	−	1.98515i	0.0546396	−	0.0946385i
$441$	−7.03813	−	19.7855i	−0.335149	−	0.942165i
$442$	5.60291	+	9.70452i	0.266503	+	0.461597i
$443$	−2.67757	−	7.35657i	−0.127215	−	0.349521i	0.859691	−	0.510814i	$-0.170656\pi$
$443$	−2.67757	−	7.35657i	−0.127215	−	0.349521i	−0.986907	+	0.161293i	$0.948434\pi$
$444$	−2.15001	−	0.716537i	−0.102035	−	0.0340053i
$445$	12.5671	−	10.5450i	0.595735	−	0.499881i
$446$	−0.886287	−	5.02638i	−0.0419669	−	0.238006i
$447$	33.8265	−	6.92406i	1.59994	−	0.327497i
$448$	−13.8030	−	1.64040i	−0.652129	−	0.0775017i
$449$	2.53492	−	1.46354i	0.119630	−	0.0690687i	−0.438991	−	0.898492i	$-0.644664\pi$
$449$	2.53492	−	1.46354i	0.119630	−	0.0690687i	0.558621	+	0.829423i	$0.311331\pi$
$450$	5.62575	+	6.00412i	0.265200	+	0.283037i
$451$	−0.732791	+	0.423077i	−0.0345058	+	0.0199219i
$452$	−8.38174	−	23.0286i	−0.394244	−	1.08318i
$453$	3.91978	+	3.11032i	0.184167	+	0.146135i
$454$	15.5177	−	2.73619i	0.728282	−	0.128416i
$455$	19.0994	+	5.75826i	0.895394	+	0.269951i
$456$	−8.06660	+	14.8991i	−0.377753	+	0.697716i
$457$	−18.8614	−	15.8266i	−0.882297	−	0.740335i	0.0843528	−	0.996436i	$-0.473118\pi$
$457$	−18.8614	−	15.8266i	−0.882297	−	0.740335i	−0.966650	+	0.256101i	$0.917562\pi$
$458$	6.11491	−	10.5913i	0.285731	−	0.494900i
$459$	−11.9747	+	0.985513i	−0.558930	+	0.0459998i
$460$	−9.68786	+	5.59329i	−0.451699	+	0.260788i
$461$	−35.5416	+	12.9361i	−1.65534	+	0.602493i	−0.989620	−	0.143711i	$-0.954096\pi$
$461$	−35.5416	+	12.9361i	−1.65534	+	0.602493i	−0.665717	+	0.746204i	$0.731874\pi$
$462$	2.13818	+	1.00657i	0.0994772	+	0.0468300i
$463$	−8.27501	+	6.94356i	−0.384572	+	0.322695i	−0.814494	−	0.580171i	$-0.802986\pi$
$463$	−8.27501	+	6.94356i	−0.384572	+	0.322695i	0.429922	+	0.902866i	$0.358541\pi$
$464$	−0.0566502	−	0.0675131i	−0.00262992	−	0.00313422i
$465$	2.59810	−	3.27425i	0.120484	−	0.151840i
$466$	7.65900	−	2.78765i	0.354796	−	0.129135i
$467$	−29.0369			−1.34367			−0.671833	−	0.740702i	$-0.734493\pi$
$467$	−29.0369			−1.34367			−0.671833	+	0.740702i	$0.734493\pi$
$468$	−19.5314	−	2.35092i	−0.902840	−	0.108671i
$469$	−1.22519	−	21.7606i	−0.0565739	−	1.00481i
$470$	7.49973	+	1.32240i	0.345937	+	0.0609979i
$471$	4.44845	−	13.3479i	0.204974	−	0.615037i
$472$	9.30356	+	11.0875i	0.428231	+	0.510346i
$473$	−1.46013	−	1.74012i	−0.0671369	−	0.0800106i
$474$	4.05413	−	0.829855i	0.186213	−	0.0381165i
$475$	10.3775	+	1.82984i	0.476154	+	0.0839588i
$476$	−6.58605	−	3.32360i	−0.301871	−	0.152337i
$477$	25.2289	+	12.7791i	1.15515	+	0.585115i
$478$	2.24991			0.102909
$479$	−12.8160	+	4.66466i	−0.585580	+	0.213134i	−0.617784	−	0.786348i	$-0.711969\pi$
$479$	−12.8160	+	4.66466i	−0.585580	+	0.213134i	0.0322044	+	0.999481i	$0.489747\pi$
$480$	4.93858	+	12.4936i	0.225414	+	0.570253i
$481$	3.79289	+	4.52019i	0.172941	+	0.206103i
$482$	4.91035	−	4.12027i	0.223660	−	0.187673i
$483$	−17.4950	−	25.1806i	−0.796050	−	1.14576i
$484$	−12.0849	+	4.39855i	−0.549314	+	0.199934i
$485$	−22.3774	+	12.9196i	−1.01610	+	0.586648i
$486$	−7.39407	+	11.7604i	−0.335402	+	0.533463i
$487$	16.0866	−	27.8628i	0.728954	−	1.26259i	−0.228371	−	0.973574i	$-0.573340\pi$
$487$	16.0866	−	27.8628i	0.728954	−	1.26259i	0.957325	−	0.289012i	$-0.0933267\pi$
$488$	29.5971	+	24.8349i	1.33980	+	1.12422i
$489$	−0.940540	−	1.53072i	−0.0425327	−	0.0692218i
$490$	8.29524	−	2.44851i	0.374741	−	0.110612i
$491$	24.2362	−	4.27350i	1.09377	−	0.192860i	0.402470	−	0.915433i	$-0.368152\pi$
$491$	24.2362	−	4.27350i	1.09377	−	0.192860i	0.691295	+	0.722573i	$0.257041\pi$
$492$	0.447793	−	3.02087i	0.0201881	−	0.136191i
$493$	−0.519216	−	1.42653i	−0.0233843	−	0.0642479i
$494$	14.3699	−	8.29645i	0.646531	−	0.373275i
$495$	−0.131705	−	2.40347i	−0.00591970	−	0.108028i
$496$	0.202346	−	0.116824i	0.00908558	−	0.00524556i
$497$	−4.90887	+	41.3051i	−0.220193	+	1.85279i
$498$	5.85670	−	17.5734i	0.262445	−	0.787483i
$499$	−4.54776	−	25.7916i	−0.203586	−	1.15459i	−0.899650	−	0.436613i	$-0.856178\pi$
$499$	−4.54776	−	25.7916i	−0.203586	−	1.15459i	0.696064	−	0.717980i	$-0.254933\pi$
$500$	10.3454	−	8.68085i	0.462662	−	0.388219i
$501$	4.87902	+	23.8358i	0.217979	+	1.06490i
$502$	0.286257	+	0.786484i	0.0127763	+	0.0351025i
$503$	3.69643	+	6.40240i	0.164815	+	0.285469i	0.936590	−	0.350428i	$-0.113964\pi$
$503$	3.69643	+	6.40240i	0.164815	+	0.285469i	−0.771774	+	0.635897i	$0.780630\pi$
$504$	−20.3183	+	10.0680i	−0.905049	+	0.448465i
$505$	−8.44256	+	14.6229i	−0.375689	+	0.650713i
$506$	3.39813	+	0.599182i	0.151065	+	0.0266369i
$507$	22.4855	+	17.8421i	0.998617	+	0.792395i
$508$	−2.23803	−	0.814575i	−0.0992963	−	0.0361409i
$509$	−15.1126	−	5.50053i	−0.669853	−	0.243807i	−0.0153687	−	0.999882i	$-0.504892\pi$
$509$	−15.1126	−	5.50053i	−0.669853	−	0.243807i	−0.654485	+	0.756075i	$0.727114\pi$
$510$	−0.135433	−	4.94671i	−0.00599707	−	0.219044i
$511$	−0.746786	+	6.28374i	−0.0330359	+	0.277976i
$512$			1.51799i			0.0670865i
$513$	1.45929	+	17.7314i	0.0644292	+	0.782860i
$514$	−15.1231	−	8.73131i	−0.667050	−	0.385122i
$515$	−17.5476	−	3.09411i	−0.773238	−	0.136343i
$516$	8.19528	−	0.224374i	0.360777	−	0.00987750i
$517$	2.29267	+	2.73229i	0.100831	+	0.120166i
$518$	2.44945	+	0.738483i	0.107623	+	0.0324471i
$519$	9.43231	−	3.72848i	0.414032	−	0.163662i
$520$	3.74048	−	21.2133i	0.164031	−	0.930266i
$521$	8.46473	+	14.6613i	0.370847	+	0.642325i	0.989696	−	0.143184i	$-0.0457342\pi$
$521$	8.46473	+	14.6613i	0.370847	+	0.642325i	−0.618849	+	0.785510i	$0.712401\pi$
$522$	−1.67971	−	0.509164i	−0.0735188	−	0.0222855i
$523$	−8.72367	−	5.03662i	−0.381460	−	0.220236i	0.296994	−	0.954879i	$-0.404016\pi$
$523$	−8.72367	−	5.03662i	−0.381460	−	0.220236i	−0.678453	+	0.734644i	$0.737349\pi$
$524$	0.467160	−	2.64940i	0.0204080	−	0.115739i
$525$	9.93618	+	10.0090i	0.433650	+	0.436829i
$526$	9.98737	+	3.63511i	0.435470	+	0.158498i
$527$	3.96348	−	0.698869i	0.172652	−	0.0304432i
$528$	0.0425425	−	0.127651i	0.00185142	−	0.00555531i
$529$	−16.6757	−	13.9925i	−0.725029	−	0.608372i
$530$	−5.82386	+	10.0872i	−0.252972	+	0.438161i
$531$	14.5452	+	4.40903i	0.631207	+	0.191336i
$532$	−4.92139	+	9.75223i	−0.213370	+	0.422813i
$533$	−5.11105	+	6.09112i	−0.221384	+	0.263836i
$534$	11.3520	−	14.3064i	0.491249	−	0.619097i
$535$	4.91516	−	13.5043i	0.212501	−	0.583841i
$536$	−23.1769	+	4.08672i	−1.00109	+	0.176519i
$537$	0.402824	+	14.7132i	0.0173831	+	0.634922i
$538$	5.00978	+	13.7643i	0.215987	+	0.593420i
$539$	3.71334	+	1.61884i	0.159945	+	0.0697285i
$540$	7.09058	+	5.01951i	0.305130	+	0.216006i
$541$	9.39785	+	16.2776i	0.404045	+	0.699827i	0.994210	−	0.107456i	$-0.0342705\pi$
$541$	9.39785	+	16.2776i	0.404045	+	0.699827i	−0.590165	+	0.807283i	$0.700937\pi$
$542$	−2.28667	+	12.9683i	−0.0982207	+	0.557037i
$543$	−8.80674	−	4.76809i	−0.377934	−	0.204618i
$544$	−4.42420	+	12.1554i	−0.189686	+	0.521158i
$545$	4.05710	+	23.0090i	0.173787	+	0.985595i
$546$	22.1161	+	2.01630i	0.946481	+	0.0862898i
$547$	−9.76636	−	8.19495i	−0.417579	−	0.350391i	0.409662	−	0.912237i	$-0.365647\pi$
$547$	−9.76636	−	8.19495i	−0.417579	−	0.350391i	−0.827241	+	0.561847i	$0.810091\pi$
$548$			1.60801i			0.0686906i
$549$	40.2808	+	4.84844i	1.71914	+	0.206926i
$550$	−1.58715			−0.0676764
$551$	−2.11233	+	0.768824i	−0.0899881	+	0.0327530i
$552$	−24.7708	+	21.9680i	−1.05431	+	0.935021i
$553$	6.90523	−	1.62247i	0.293640	−	0.0689945i
$554$	−8.44831	+	23.2115i	−0.358934	+	0.986164i
$555$	−0.522552	−	2.55285i	−0.0221811	−	0.108363i
$556$	11.8145	−	14.0799i	0.501045	−	0.597122i
$557$		−	27.3089i		−	1.15711i	−0.815642	−	0.578557i	$-0.803616\pi$
$557$		−	27.3089i		−	1.15711i	0.815642	−	0.578557i	$-0.196384\pi$
$558$	2.10262	−	4.15105i	0.0890110	−	0.175728i
$559$	−18.4862	−	10.6730i	−0.781884	−	0.451421i
$560$	−0.194170	−	0.452542i	−0.00820520	−	0.0191234i
$561$	1.44064	−	1.81557i	0.0608240	−	0.0766536i
$562$	4.25046	−	3.56656i	0.179295	−	0.150446i
$563$	4.09167	+	23.2050i	0.172443	+	0.977974i	0.941054	+	0.338257i	$0.109837\pi$
$563$	4.09167	+	23.2050i	0.172443	+	0.977974i	−0.768611	+	0.639717i	$0.779052\pi$
$564$	−12.8681	+	0.352307i	−0.541843	+	0.0148348i
$565$	18.1124	−	21.5855i	0.761996	−	0.908111i
$566$	4.89515			0.205759
$567$	−12.0870	+	20.5160i	−0.507604	+	0.861590i
$568$	44.9154			1.88461
$569$	8.50590	−	10.1369i	0.356586	−	0.424963i	−0.557693	−	0.830047i	$-0.688313\pi$
$569$	8.50590	−	10.1369i	0.356586	−	0.424963i	0.914279	+	0.405084i	$0.132758\pi$
$570$	−7.32479	+	0.200541i	−0.306802	+	0.00839974i
$571$	1.15073	+	6.52612i	0.0481566	+	0.273110i	0.999373	−	0.0354159i	$-0.0112756\pi$
$571$	1.15073	+	6.52612i	0.0481566	+	0.273110i	−0.951216	+	0.308525i	$0.900164\pi$
$572$	2.90696	−	2.43923i	0.121546	−	0.101989i
$573$	−25.6070	+	32.2712i	−1.06975	+	1.34815i
$574$	−0.406849	+	3.42338i	−0.0169815	+	0.142889i
$575$	17.8334	+	10.2961i	0.743703	+	0.429377i
$576$	8.61566	+	13.1980i	0.358986	+	0.549916i
$577$		−	1.50126i		−	0.0624981i	−0.999512	−	0.0312490i	$-0.990052\pi$
$577$		−	1.50126i		−	0.0624981i	0.999512	−	0.0312490i	$-0.00994850\pi$
$578$	−6.67520	+	7.95519i	−0.277652	+	0.330892i
$579$	6.57221	+	32.1076i	0.273132	+	1.33435i
$580$	−0.375415	+	1.03144i	−0.0155882	+	0.0428283i
$581$	9.16521	−	30.3998i	0.380237	−	1.26120i
$582$	−21.5214	+	19.0863i	−0.892091	+	0.791152i
$583$	−5.12632	+	1.86583i	−0.212311	+	0.0772747i
$584$	6.83297			0.282750
$585$	−8.88775	−	20.8003i	−0.367463	−	0.859985i
$586$		−	20.7443i		−	0.856940i
$587$	−2.83790	−	2.38128i	−0.117133	−	0.0982861i	0.582340	−	0.812945i	$-0.302137\pi$
$587$	−2.83790	−	2.38128i	−0.117133	−	0.0982861i	−0.699473	+	0.714659i	$0.746582\pi$
$588$	−12.9072	+	6.86673i	−0.532284	+	0.283179i
$589$	−1.03484	−	5.86889i	−0.0426400	−	0.241823i
$590$	−2.14096	+	5.88225i	−0.0881420	+	0.242168i
$591$	16.2198	+	8.78163i	0.667194	+	0.361228i
$592$	0.0252938	−	0.143449i	0.00103957	−	0.00589570i
$593$	−13.5970	−	23.5507i	−0.558362	−	0.967112i	−0.997633	−	0.0687572i	$-0.978097\pi$
$593$	−13.5970	−	23.5507i	−0.558362	−	0.967112i	0.439271	−	0.898355i	$-0.355237\pi$
$594$	−0.680210	−	2.59192i	−0.0279094	−	0.106348i
$595$	−0.476825	−	8.46892i	−0.0195479	−	0.347192i
$596$	−8.22153	−	22.5885i	−0.336767	−	0.925260i
$597$	−0.475322	−	17.3612i	−0.0194536	−	0.710547i
$598$	31.9326	−	5.63057i	1.30582	−	0.230251i
$599$	0.718887	−	1.97512i	0.0293729	−	0.0807014i	−0.924139	−	0.382055i	$-0.875216\pi$
$599$	0.718887	−	1.97512i	0.0293729	−	0.0807014i	0.953512	+	0.301354i	$0.0974386\pi$
$600$	9.46608	−	11.9296i	0.386451	−	0.487026i
$601$	−6.40627	+	7.63469i	−0.261317	+	0.311426i	−0.880710	−	0.473655i	$-0.842934\pi$
$601$	−6.40627	+	7.63469i	−0.261317	+	0.311426i	0.619393	+	0.785081i	$0.287379\pi$
$602$	−9.24034	+	0.520259i	−0.376608	+	0.0212042i
$603$	−18.0340	+	16.8975i	−0.734399	+	0.688118i
$604$	1.74184	−	3.01695i	0.0708744	−	0.122758i
$605$	−11.3276	−	9.50499i	−0.460532	−	0.386433i
$606$	−5.94327	+	17.8331i	−0.241429	+	0.724422i
$607$	−22.3484	+	3.94062i	−0.907092	+	0.159945i	−0.607683	−	0.794180i	$-0.707901\pi$
$607$	−22.3484	+	3.94062i	−0.907092	+	0.159945i	−0.299409	+	0.954125i	$0.596790\pi$
$608$	17.9990	+	6.55109i	0.729955	+	0.265682i
$609$	−2.90318	−	0.789278i	−0.117643	−	0.0319831i
$610$	−2.90162	+	16.4559i	−0.117483	+	0.666281i
$611$	29.0267	+	16.7586i	1.17429	+	0.677979i
$612$	1.90111	+	8.14600i	0.0768480	+	0.329283i
$613$	14.3002	+	24.7687i	0.577581	+	1.00040i	0.995756	+	0.0920328i	$0.0293365\pi$
$613$	14.3002	+	24.7687i	0.577581	+	1.00040i	−0.418175	+	0.908366i	$0.637330\pi$
$614$	2.69835	−	15.3031i	0.108897	−	0.617584i
$615$	3.26552	−	1.29082i	0.131678	−	0.0520509i
$616$	1.26262	−	4.18796i	0.0508726	−	0.168738i
$617$	0.142287	+	0.169571i	0.00572826	+	0.00682668i	0.768901	−	0.639368i	$-0.220804\pi$
$617$	0.142287	+	0.169571i	0.00572826	+	0.00682668i	−0.763173	+	0.646195i	$0.776359\pi$
$618$	−19.8288	+	0.542882i	−0.797633	+	0.0218379i
$619$	−23.5424	−	4.15115i	−0.946247	−	0.166849i	−0.320828	−	0.947138i	$-0.603961\pi$
$619$	−23.5424	−	4.15115i	−0.946247	−	0.166849i	−0.625420	+	0.780289i	$0.715072\pi$
$620$	−2.52011	−	1.45498i	−0.101210	−	0.0584336i
$621$	−9.17127	+	33.5356i	−0.368031	+	1.34574i
$622$			1.34523i			0.0539387i
$623$	18.7424	−	25.0740i	0.750899	−	1.00457i
$624$	−0.0346047	−	1.26394i	−0.00138530	−	0.0505981i
$625$	0.131608	+	0.0479015i	0.00526433	+	0.00191606i
$626$	−24.3840	−	8.87506i	−0.974582	−	0.354719i
$627$	−2.68839	−	2.13322i	−0.107364	−	0.0851926i
$628$	−9.64640	−	1.70092i	−0.384933	−	0.0678741i
$629$	1.25452	−	2.17289i	0.0500209	−	0.0866388i
$630$	−8.16467	−	5.43301i	−0.325288	−	0.216456i
$631$	8.84858	+	15.3262i	0.352256	+	0.610126i	0.986644	−	0.162889i	$-0.0520812\pi$
$631$	8.84858	+	15.3262i	0.352256	+	0.610126i	−0.634388	+	0.773015i	$0.718748\pi$
$632$	−2.61966	−	7.19745i	−0.104204	−	0.286299i
$633$	2.08061	+	10.1645i	0.0826967	+	0.404002i
$634$	20.7542	−	17.4149i	0.824255	−	0.691632i
$635$	−0.475528	−	2.69685i	−0.0188707	−	0.107021i
$636$	6.22514	−	18.6789i	0.246843	−	0.740668i
$637$	37.9931	+	2.36034i	1.50534	+	0.0935202i
$638$	0.293212	−	0.169286i	0.0116084	−	0.00670210i
$639$	39.4947	−	25.7822i	1.56239	−	1.01993i
$640$	7.81256	−	4.51058i	0.308819	−	0.178296i
$641$	−6.54891	−	17.9930i	−0.258666	−	0.710680i	−0.999250	−	0.0387161i	$-0.987673\pi$
$641$	−6.54891	−	17.9930i	−0.258666	−	0.710680i	0.740584	−	0.671964i	$-0.234549\pi$
$642$	2.34588	−	15.8256i	0.0925844	−	0.624587i
$643$	−29.5375	+	5.20825i	−1.16484	+	0.205393i	−0.722447	−	0.691426i	$-0.756983\pi$
$643$	−29.5375	+	5.20825i	−1.16484	+	0.205393i	−0.442396	+	0.896820i	$0.645872\pi$
$644$	−15.5552	+	14.6188i	−0.612961	+	0.576063i
$645$	4.93494	+	8.03159i	0.194313	+	0.316244i
$646$	−5.40481	−	4.53517i	−0.212649	−	0.178434i
$647$	0.0112934	−	0.0195607i	0.000443989	−	0.000769011i	−0.865803	−	0.500384i	$-0.833192\pi$
$647$	0.0112934	−	0.0195607i	0.000443989	−	0.000769011i	0.866247	+	0.499615i	$0.166525\pi$
$648$	23.5387	+	10.3460i	0.924689	+	0.406428i
$649$	−2.53903	+	1.46591i	−0.0996655	+	0.0575419i
$650$	−14.0152	+	5.10110i	−0.549720	+	0.200082i
$651$	3.39719	−	7.21639i	0.133146	−	0.282833i
$652$	−0.958152	+	0.803985i	−0.0375241	+	0.0314865i
$653$	−19.3776	−	23.0933i	−0.758304	−	0.903712i	0.239435	−	0.970912i	$-0.423038\pi$
$653$	−19.3776	−	23.0933i	−0.758304	−	0.903712i	−0.997739	+	0.0672006i	$0.978593\pi$
$654$	9.56151	+	24.1887i	0.373885	+	0.945855i
$655$	2.90675	−	1.05797i	0.113576	−	0.0413383i
$656$	0.196284			0.00766360
$657$	6.00833	−	3.92224i	0.234407	−	0.153021i
$658$	14.5090	−	0.816899i	0.565619	−	0.0318460i
$659$	17.6905	+	3.11932i	0.689126	+	0.121511i	0.507236	−	0.861807i	$-0.330667\pi$
$659$	17.6905	+	3.11932i	0.689126	+	0.121511i	0.181890	+	0.983319i	$0.441778\pi$
$660$	−1.64176	+	0.336057i	−0.0639052	+	0.0130810i
$661$	−22.0195	−	26.2418i	−0.856459	−	1.02069i	−0.999520	−	0.0309742i	$-0.990139\pi$
$661$	−22.0195	−	26.2418i	−0.856459	−	1.02069i	0.143061	−	0.989714i	$-0.454305\pi$
$662$	16.2122	+	19.3209i	0.630105	+	0.750929i
$663$	6.88618	−	20.6624i	0.267437	−	0.802462i
$664$	−33.7645	−	5.95359i	−1.31032	−	0.231044i
$665$	−12.5403	+	0.706054i	−0.486291	+	0.0273796i
$666$	−1.13983	−	2.66758i	−0.0441676	−	0.103367i
$667$	−4.39274			−0.170087
$668$	15.9169	−	5.79328i	0.615844	−	0.224149i
$669$	−6.16610	+	7.77084i	−0.238395	+	0.300438i
$670$	−6.54256	−	7.79712i	−0.252761	−	0.301229i
$671$	−5.99520	+	5.03057i	−0.231442	+	0.194203i
$672$	14.6273	+	21.0531i	0.564259	+	0.812141i
$673$	−16.8698	+	6.14009i	−0.650282	+	0.236683i	−0.646035	−	0.763308i	$-0.723574\pi$
$673$	−16.8698	+	6.14009i	−0.650282	+	0.236683i	−0.00424668	+	0.999991i	$0.501352\pi$
$674$	6.27118	−	3.62067i	0.241557	−	0.139463i
$675$	1.47583	−	15.9236i	0.0568049	−	0.612899i
$676$	9.99192	−	17.3065i	0.384304	−	0.665635i
$677$	2.57495	+	2.16064i	0.0989635	+	0.0830403i	0.690927	−	0.722925i	$-0.257203\pi$
$677$	2.57495	+	2.16064i	0.0989635	+	0.0830403i	−0.591963	+	0.805965i	$0.701647\pi$
$678$	14.9352	−	27.5856i	0.573584	−	1.05942i
$679$	−35.9300	+	33.7671i	−1.37887	+	1.29586i
$680$	−9.02013	+	1.59049i	−0.345906	+	0.0609926i
$681$	−23.9905	−	19.0363i	−0.919319	−	0.729473i
$682$	0.306995	+	0.843463i	0.0117555	+	0.0322979i
$683$	35.1068	−	20.2689i	1.34333	−	0.775570i	0.356032	−	0.934474i	$-0.384129\pi$
$683$	35.1068	−	20.2689i	1.34333	−	0.775570i	0.987294	+	0.158904i	$0.0507960\pi$
$684$	12.0621	−	2.81506i	0.461207	−	0.107636i
$685$	−1.60120	+	0.924452i	−0.0611786	+	0.0353215i
$686$	14.3409	−	8.16912i	0.547536	−	0.311898i
$687$	−23.2871	+	4.76672i	−0.888458	+	0.181862i
$688$	0.0915018	+	0.518932i	0.00348847	+	0.0197841i
$689$	−39.2706	+	32.9519i	−1.49609	+	1.25537i
$690$	−13.5846	−	4.52736i	−0.517157	−	0.172353i
$691$	14.3836	+	39.5186i	0.547178	+	1.50336i	0.837504	+	0.546431i	$0.184014\pi$
$691$	14.3836	+	39.5186i	0.547178	+	1.50336i	−0.290327	+	0.956928i	$0.593764\pi$
$692$	−3.53058	−	6.11514i	−0.134212	−	0.232463i
$693$	−1.29372	−	4.40730i	−0.0491443	−	0.167419i
$694$	6.13459	−	10.6254i	0.232866	−	0.403335i
$695$	20.8125	+	3.66981i	0.789463	+	0.139204i
$696$	−0.476354	+	3.21355i	−0.0180561	+	0.121809i
$697$	3.17711	+	1.15638i	0.120342	+	0.0438008i
$698$	1.12660	+	0.410049i	0.0426424	+	0.0155206i
$699$	−13.9307	−	7.54229i	−0.526908	−	0.285275i
$700$	5.87859	−	7.86451i	0.222190	−	0.297251i
$701$			33.4343i			1.26280i	0.775459	+	0.631398i	$0.217519\pi$
$701$			33.4343i			1.26280i	−0.775459	+	0.631398i	$0.782481\pi$
$702$	−14.3369	−	20.7014i	−0.541113	−	0.781325i
$703$	−3.21749	−	1.85762i	−0.121350	−	0.0700613i
$704$	−2.99413	−	0.527946i	−0.112845	−	0.0198977i
$705$	−7.74873	−	12.6110i	−0.291834	−	0.474959i
$706$	−9.02357	−	10.7539i	−0.339607	−	0.404727i
$707$	−9.30068	+	30.8491i	−0.349788	+	1.16020i
$708$	1.55154	−	10.4669i	0.0583106	−	0.393371i
$709$	6.70491	−	38.0254i	0.251808	−	1.42807i	−0.552327	−	0.833628i	$-0.686260\pi$
$709$	6.70491	−	38.0254i	0.251808	−	1.42807i	0.804135	−	0.594447i	$-0.202629\pi$
$710$	9.71272	+	16.8229i	0.364512	+	0.631353i
$711$	−6.43496	−	4.82509i	−0.241330	−	0.180955i
$712$	−29.2743	−	16.9015i	−1.09710	−	0.633411i
$713$	2.02225	−	11.4687i	0.0757338	−	0.429508i
$714$	−2.41070	−	9.13009i	−0.0902184	−	0.341685i
$715$	4.10014	+	1.49233i	0.153336	+	0.0558099i
$716$	10.0914	−	1.77939i	0.377135	−	0.0664990i
$717$	−2.90150	−	3.27169i	−0.108359	−	0.122183i
$718$	20.4616	+	17.1693i	0.763619	+	0.640752i
$719$	−10.3735	+	17.9674i	−0.386866	+	0.670072i	−0.992026	−	0.126032i	$-0.959776\pi$
$719$	−10.3735	+	17.9674i	−0.386866	+	0.670072i	0.605160	+	0.796104i	$0.293109\pi$
$720$	−0.252310	+	0.498118i	−0.00940304	+	0.0185637i
$721$	−33.9476	+	1.91135i	−1.26427	+	0.0711823i
$722$	4.16820	−	4.96747i	0.155124	−	0.184870i
$723$	−12.3239	−	1.82680i	−0.458330	−	0.0679396i
$724$	−2.38462	+	6.55169i	−0.0886237	+	0.243492i
$725$	1.98983	−	0.350861i	0.0739005	−	0.0130307i
$726$	−14.4763	−	7.83766i	−0.537266	−	0.290883i
$727$	6.23885	+	17.1411i	0.231386	+	0.635729i	0.999992	−	0.00399420i	$-0.00127140\pi$
$727$	6.23885	+	17.1411i	0.231386	+	0.635729i	−0.768606	+	0.639723i	$0.779049\pi$
$728$	−2.31064	−	41.0393i	−0.0856379	−	1.52102i
$729$	26.6367	−	4.41429i	0.986545	−	0.163492i
$730$	1.47760	+	2.55927i	0.0546883	+	0.0947228i
$731$	−1.57613	+	8.93868i	−0.0582953	+	0.330609i
$732$	−0.773033	−	28.2351i	−0.0285721	−	1.04360i
$733$	9.34633	−	25.6788i	0.345214	−	0.948469i	−0.638641	−	0.769505i	$-0.720503\pi$
$733$	9.34633	−	25.6788i	0.345214	−	0.948469i	0.983856	−	0.178964i	$-0.0572746\pi$
$734$	0.739395	+	4.19331i	0.0272916	+	0.154778i
$735$	−14.2581	−	8.90483i	−0.525917	−	0.328459i
$736$	28.6732	+	24.0597i	1.05691	+	0.886851i
$737$		−	4.76716i		−	0.175601i
$738$	3.27333	−	2.13684i	0.120493	−	0.0786580i
$739$	14.1363			0.520012			0.260006	−	0.965607i	$-0.416275\pi$
$739$	14.1363			0.520012			0.260006	+	0.965607i	$0.416275\pi$
$740$	−1.70473	+	0.620471i	−0.0626671	+	0.0228090i
$741$	−30.5957	−	10.1967i	−1.12396	−	0.374583i
$742$	−6.41580	+	21.2804i	−0.235532	+	0.781228i
$743$	3.05230	−	8.38613i	0.111978	−	0.307657i	−0.871027	−	0.491235i	$-0.836546\pi$
$743$	3.05230	−	8.38613i	0.111978	−	0.307657i	0.983005	+	0.183578i	$0.0587679\pi$
$744$	−8.17076	−	2.72308i	−0.299555	−	0.0998329i
$745$	17.7662	−	21.1730i	0.650904	−	0.775717i
$746$		−	12.3250i		−	0.451250i
$747$	−33.1070	+	14.1463i	−1.21132	+	0.517586i
$748$	−1.39740	−	0.806789i	−0.0510940	−	0.0294991i
$749$	3.23630	−	27.2314i	0.118252	−	0.995015i
$750$	17.1000	+	2.53478i	0.624403	+	0.0925571i
$751$	−2.72115	+	2.28332i	−0.0992962	+	0.0833194i	−0.691084	−	0.722774i	$-0.742867\pi$
$751$	−2.72115	+	2.28332i	−0.0992962	+	0.0833194i	0.591788	+	0.806094i	$0.298422\pi$
$752$	−0.143674	−	0.814816i	−0.00523926	−	0.0297133i
$753$	0.774499	−	1.43051i	0.0282243	−	0.0521308i
$754$	2.04509	−	2.43724i	0.0744777	−	0.0887591i
$755$	4.00557			0.145778
$756$	15.3626	+	6.22958i	0.558734	+	0.226568i
$757$	−21.6011			−0.785104			−0.392552	−	0.919730i	$-0.628408\pi$
$757$	−21.6011			−0.785104			−0.392552	+	0.919730i	$0.628408\pi$
$758$	−5.06486	+	6.03606i	−0.183964	+	0.219240i
$759$	−3.51096	−	5.71407i	−0.127440	−	0.207408i
$760$	2.35511	+	13.3565i	0.0854287	+	0.484490i
$761$	−7.74438	+	6.49831i	−0.280734	+	0.235563i	−0.772271	−	0.635293i	$-0.780879\pi$
$761$	−7.74438	+	6.49831i	−0.280734	+	0.235563i	0.491538	+	0.870856i	$0.336435\pi$
$762$	−1.12069	−	2.83513i	−0.0405984	−	0.102706i
$763$	17.5795	+	40.9715i	0.636420	+	1.48327i
$764$	24.8383	+	14.3404i	0.898618	+	0.518818i
$765$	−7.01855	+	6.57625i	−0.253756	+	0.237765i
$766$		−	26.8118i		−	0.968750i
$767$	−17.7091	+	21.1049i	−0.639440	+	0.762055i
$768$	21.1300	−	18.7391i	0.762462	−	0.676190i
$769$	−12.2720	+	33.7171i	−0.442540	+	1.21587i	0.495276	+	0.868736i	$0.335067\pi$
$769$	−12.2720	+	33.7171i	−0.442540	+	1.21587i	−0.937816	+	0.347133i	$0.887155\pi$
$770$	1.84162	−	0.432713i	0.0663675	−	0.0155939i
$771$	6.80627	+	33.2510i	0.245122	+	1.19751i
$772$	21.4406	−	7.80375i	0.771665	−	0.280863i
$773$	−35.8360			−1.28893			−0.644466	−	0.764633i	$-0.722920\pi$
$773$	−35.8360			−1.28893			−0.644466	+	0.764633i	$0.722920\pi$
$774$	7.17527	+	7.65786i	0.257910	+	0.275256i
$775$			5.35666i			0.192417i
$776$	40.7858	+	34.2233i	1.46412	+	1.22855i
$777$	−2.08497	−	4.51420i	−0.0747980	−	0.161946i
$778$	−1.53010	−	8.67765i	−0.0548569	−	0.311109i
$779$	1.71229	−	4.70448i	0.0613492	−	0.168556i
$780$	−13.4172	+	8.24410i	−0.480414	+	0.295186i
$781$	−1.57987	+	8.95987i	−0.0565321	+	0.320609i
$782$	−6.89376	−	11.9403i	−0.246520	−	0.426986i
$783$	1.42577	+	3.09915i	0.0509527	+	0.110755i
$784$	−0.558222	−	0.755910i	−0.0199365	−	0.0269968i
$785$	−3.85205	−	10.5834i	−0.137486	−	0.377738i
$786$	2.93403	−	1.80279i	0.104653	−	0.0643033i
$787$	−23.3675	+	4.12032i	−0.832962	+	0.146874i	−0.573836	−	0.818970i	$-0.694545\pi$
$787$	−23.3675	+	4.12032i	−0.832962	+	0.146874i	−0.259125	+	0.965844i	$0.583434\pi$
$788$	4.39187	−	12.0666i	0.156454	−	0.429854i
$789$	−7.59383	−	19.2109i	−0.270347	−	0.683926i
$790$	2.12930	−	2.53760i	0.0757570	−	0.0902837i
$791$	24.2248	−	48.0038i	0.861335	−	1.70682i
$792$	−4.56091	+	1.94883i	−0.162065	+	0.0692488i
$793$	−36.7717	+	63.6904i	−1.30580	+	2.26171i
$794$	−7.84370	−	6.58165i	−0.278363	−	0.233574i
$795$	22.1787	−	4.53984i	0.786598	−	0.161011i
$796$	−11.9076	+	2.09964i	−0.422055	+	0.0744197i
$797$	25.1031	+	9.13677i	0.889196	+	0.323641i	0.745915	−	0.666041i	$-0.232012\pi$
$797$	25.1031	+	9.13677i	0.889196	+	0.323641i	0.143281	+	0.989682i	$0.454235\pi$
$798$	−13.5193	+	3.56963i	−0.478578	+	0.126363i
$799$	2.47481	−	14.0353i	0.0875523	−	0.496534i
$800$	−14.9102	−	8.60839i	−0.527154	−	0.304353i
$801$	−35.4430	+	1.94220i	−1.25232	+	0.0686244i
$802$	−7.34531	−	12.7224i	−0.259372	−	0.449245i
$803$	−0.240345	+	1.36306i	−0.00848159	+	0.0481015i
$804$	13.4778	+	10.6945i	0.475324	+	0.377166i
$805$	−23.4997	−	7.08490i	−0.828256	−	0.249710i
$806$	5.42177	+	6.46141i	0.190974	+	0.227594i
$807$	13.5545	−	25.0354i	0.477142	−	0.881289i
$808$	34.2635	+	6.04158i	1.20539	+	0.212542i
$809$	17.2909	+	9.98289i	0.607915	+	0.350980i	0.772149	−	0.635442i	$-0.219182\pi$
$809$	17.2909	+	9.98289i	0.607915	+	0.350980i	−0.164234	+	0.986421i	$0.552515\pi$
$810$	1.21508	+	11.0536i	0.0426936	+	0.388385i
$811$			13.5611i			0.476196i	0.971241	+	0.238098i	$0.0765239\pi$
$811$			13.5611i			0.476196i	−0.971241	+	0.238098i	$0.923476\pi$
$812$	−0.247185	+	2.07991i	−0.00867449	+	0.0729905i
$813$	21.8067	−	13.3989i	0.764793	−	0.469920i
$814$	0.525833	+	0.191387i	0.0184304	+	0.00670813i
$815$	−1.35143	−	0.491879i	−0.0473384	−	0.0172298i
$816$	−0.499997	+	0.197643i	−0.0175034	+	0.00691887i
$817$	13.2359	+	2.33384i	0.463064	+	0.0816507i
$818$	4.06677	−	7.04386i	0.142191	−	0.246283i
$819$	−25.5891	−	34.7601i	−0.894154	−	1.21462i
$820$	−1.22231	−	2.11710i	−0.0426848	−	0.0739322i
$821$	−11.6528	−	32.0157i	−0.406684	−	1.11735i	−0.958922	−	0.283669i	$-0.908448\pi$
$821$	−11.6528	−	32.0157i	−0.406684	−	1.11735i	0.552238	−	0.833686i	$-0.313774\pi$
$822$	−1.53995	+	1.36571i	−0.0537119	+	0.0476345i
$823$	6.62637	−	5.56019i	0.230981	−	0.193816i	−0.519950	−	0.854197i	$-0.674050\pi$
$823$	6.62637	−	5.56019i	0.230981	−	0.193816i	0.750931	+	0.660381i	$0.229605\pi$
$824$	6.37547	+	36.1571i	0.222100	+	1.25959i
$825$	2.04680	+	2.30794i	0.0712605	+	0.0803522i
$826$	−1.40968	+	11.8616i	−0.0490490	+	0.412717i
$827$	−34.8581	+	20.1253i	−1.21213	+	0.699826i	−0.963224	−	0.268700i	$-0.913406\pi$
$827$	−34.8581	+	20.1253i	−1.21213	+	0.699826i	−0.248911	+	0.968526i	$0.580073\pi$
$828$	24.0312	+	2.89255i	0.835144	+	0.100523i
$829$	35.8294	−	20.6861i	1.24441	−	0.718458i	0.274417	−	0.961611i	$-0.411515\pi$
$829$	35.8294	−	20.6861i	1.24441	−	0.718458i	0.969988	+	0.243153i	$0.0781817\pi$
$830$	−5.07149	−	13.9338i	−0.176034	−	0.483650i
$831$	44.6478	−	17.6487i	1.54882	−	0.612228i
$832$	−28.1361	+	4.96115i	−0.975444	+	0.171997i
$833$	−4.58225	−	15.5241i	−0.158766	−	0.537877i
$834$	23.5182	−	0.643891i	0.814369	−	0.0222961i
$835$	14.9195	+	12.5189i	0.516310	+	0.433235i
$836$	−1.19464	+	2.06919i	−0.0413176	+	0.0715643i
$837$	−8.74776	+	2.29572i	−0.302367	+	0.0793516i
$838$	−22.6091	+	13.0534i	−0.781019	+	0.450921i
$839$	−25.4475	+	9.26215i	−0.878547	+	0.319765i	−0.741623	−	0.670817i	$-0.765944\pi$
$839$	−25.4475	+	9.26215i	−0.878547	+	0.319765i	−0.136924	+	0.990582i	$0.543722\pi$
$840$	−7.73136	+	16.4231i	−0.266757	+	0.566652i
$841$	21.8851	−	18.3638i	0.754659	−	0.633234i
$842$	−6.78997	−	8.09197i	−0.233998	−	0.278868i
$843$	−10.6677	−	1.58131i	−0.367415	−	0.0544631i
$844$	6.78759	−	2.47048i	0.233639	−	0.0850375i
$845$	22.9776			0.790455
$846$	−11.2665	−	12.0242i	−0.387349	−	0.413401i
$847$	−25.1913	−	12.7126i	−0.865583	−	0.436811i
$848$	1.24625	+	0.219748i	0.0427965	+	0.00754619i
$849$	−6.31282	−	7.11823i	−0.216655	−	0.244297i
$850$	4.07646	+	4.85814i	0.139822	+	0.166633i
$851$	−4.66674	−	5.56160i	−0.159974	−	0.190649i
$852$	−21.7872	−	24.5669i	−0.746418	−	0.841649i
$853$	−19.5183	−	3.44160i	−0.668293	−	0.117838i	−0.170800	−	0.985306i	$-0.554635\pi$
$853$	−19.5183	−	3.44160i	−0.668293	−	0.117838i	−0.497494	+	0.867468i	$0.665746\pi$
$854$	1.79244	+	31.8357i	0.0613361	+	1.08939i
$855$	9.73771	+	10.3927i	0.333023	+	0.355421i
$856$	−29.6116			−1.01210
$857$	29.8153	−	10.8519i	1.01847	−	0.370693i	0.221790	−	0.975094i	$-0.428810\pi$
$857$	29.8153	−	10.8519i	1.01847	−	0.370693i	0.796680	+	0.604402i	$0.206588\pi$
$858$	4.80493	+	0.712249i	0.164038	+	0.0243158i
$859$	1.68873	+	2.01255i	0.0576187	+	0.0686673i	0.794084	−	0.607808i	$-0.207951\pi$
$859$	1.68873	+	2.01255i	0.0576187	+	0.0686673i	−0.736465	+	0.676475i	$0.763507\pi$
$860$	5.02734	−	4.21844i	0.171431	−	0.143848i
$861$	5.50275	−	3.82320i	0.187533	−	0.130294i
$862$	−10.0606	+	3.66177i	−0.342666	+	0.124720i
$863$	32.4638	−	18.7430i	1.10508	−	0.638018i	0.167529	−	0.985867i	$-0.446421\pi$
$863$	32.4638	−	18.7430i	1.10508	−	0.638018i	0.937551	+	0.347849i	$0.113088\pi$
$864$	7.66794	−	28.0386i	0.260869	−	0.953891i
$865$	4.05950	−	7.03126i	0.138027	−	0.239070i
$866$	1.27233	+	1.06761i	0.0432355	+	0.0362789i
$867$	20.1763	−	0.552396i	0.685225	−	0.0187604i
$868$	−5.31652	−	1.60287i	−0.180454	−	0.0544050i
$869$	1.52792	−	0.269413i	0.0518310	−	0.00913921i
$870$	−1.30663	+	0.516496i	−0.0442990	+	0.0175109i
$871$	−15.3216	−	42.0958i	−0.519154	−	1.42636i
$872$	41.6920	−	24.0709i	1.41187	−	0.815142i
$873$	55.5083	+	6.68132i	1.87867	+	0.226128i
$874$	−17.6806	+	10.2079i	−0.598054	+	0.345286i
$875$	29.4243	+	3.49691i	0.994723	+	0.118217i
$876$	−3.31449	−	3.73736i	−0.111986	−	0.126274i
$877$	6.49296	+	36.8234i	0.219252	+	1.24344i	0.873374	+	0.487049i	$0.161927\pi$
$877$	6.49296	+	36.8234i	0.219252	+	1.24344i	−0.654123	+	0.756388i	$0.726962\pi$
$878$	17.8273	−	14.9589i	0.601642	−	0.504838i
$879$	−30.1652	+	26.7520i	−1.01745	+	0.902323i
$880$	−0.0368388	−	0.101214i	−0.00124184	−	0.00341192i
$881$	3.30548	+	5.72527i	0.111365	+	0.192889i	0.916321	−	0.400445i	$-0.131145\pi$
$881$	3.30548	+	5.72527i	0.111365	+	0.192889i	−0.804956	+	0.593334i	$0.797811\pi$
$882$	−17.5384	−	6.52889i	−0.590548	−	0.219839i
$883$	27.7285	−	48.0272i	0.933140	−	1.61625i	0.155222	−	0.987880i	$-0.450391\pi$
$883$	27.7285	−	48.0272i	0.933140	−	1.61625i	0.777918	−	0.628366i	$-0.216276\pi$
$884$	−14.9326	−	2.63302i	−0.502237	−	0.0885579i
$885$	11.3146	−	4.47252i	0.380336	−	0.150342i
$886$	−6.55582	−	2.38613i	−0.220247	−	0.0801634i
$887$	25.8689	+	9.41552i	0.868594	+	0.316142i	0.737598	−	0.675241i	$-0.235960\pi$
$887$	25.8689	+	9.41552i	0.868594	+	0.316142i	0.130996	+	0.991383i	$0.458182\pi$
$888$	−4.57471	+	2.81089i	−0.153517	+	0.0943272i
$889$	−2.06047	−	4.80222i	−0.0691060	−	0.161061i
$890$		−	14.6195i		−	0.490046i
$891$	−2.89181	+	4.33168i	−0.0968792	+	0.145117i
$892$	5.98101	+	3.45314i	0.200259	+	0.115620i
$893$	−20.7827	−	3.66454i	−0.695465	−	0.122629i
$894$	14.6498	−	27.0583i	0.489961	−	0.904966i
$895$	7.57348	+	9.02572i	0.253154	+	0.301697i
$896$	12.5442	−	11.7890i	0.419071	−	0.393844i
$897$	−49.3681	−	39.1732i	−1.64835	−	1.30795i
$898$	0.452957	−	2.56885i	0.0151154	−	0.0857235i
$899$	−0.571342	−	0.989594i	−0.0190553	−	0.0330048i
$900$	−11.1168	+	0.609175i	−0.370559	+	0.0203058i
$901$	18.8777	+	10.8990i	0.628906	+	0.363099i
$902$	−0.130940	+	0.742597i	−0.00435982	+	0.0247258i
$903$	12.6729	+	12.7658i	0.421729	+	0.424820i
$904$	−54.5596	−	19.8581i	−1.81463	−	0.660470i
$905$	−7.89488	+	1.39208i	−0.262435	+	0.0462743i
$906$	4.36863	−	0.894231i	0.145138	−	0.0297088i
$907$	31.0373	+	26.0433i	1.03058	+	0.864755i	0.990919	−	0.134458i	$-0.0429294\pi$
$907$	31.0373	+	26.0433i	1.03058	+	0.864755i	0.0396558	+	0.999213i	$0.487374\pi$
$908$	−10.6607	+	18.4649i	−0.353788	+	0.612779i
$909$	33.5964	−	14.3554i	1.11432	−	0.476139i
$910$	14.8715	−	9.73999i	0.492986	−	0.322878i
$911$	−32.6169	+	38.8713i	−1.08064	+	1.28786i	−0.125380	+	0.992109i	$0.540015\pi$
$911$	−32.6169	+	38.8713i	−1.08064	+	1.28786i	−0.955264	+	0.295753i	$0.904429\pi$
$912$	0.292657	+	0.740365i	0.00969085	+	0.0245159i
$913$	2.37528	−	6.52604i	0.0786104	−	0.215980i
$914$	−21.6084	+	3.81015i	−0.714743	+	0.126028i
$915$	27.6712	−	17.0023i	0.914780	−	0.562079i
$916$	5.65994	+	15.5505i	0.187010	+	0.513805i
$917$	4.93792	−	3.23406i	0.163064	−	0.106798i
$918$	−6.18658	+	8.73919i	−0.204188	+	0.288436i
$919$	27.9766	+	48.4569i	0.922864	+	1.59845i	0.794962	+	0.606660i	$0.207491\pi$
$919$	27.9766	+	48.4569i	0.922864	+	1.59845i	0.127902	+	0.991787i	$0.459176\pi$
$920$	−4.60225	+	26.1007i	−0.151732	+	0.860513i
$921$	−25.7327	+	15.8112i	−0.847921	+	0.520997i
$922$	−11.5280	+	31.6730i	−0.379655	+	1.04309i
$923$	14.8462	+	84.1968i	0.488667	+	2.77137i
$924$	−2.90311	+	1.34086i	−0.0955053	+	0.0441110i
$925$	2.55817	+	2.14656i	0.0841121	+	0.0705785i
$926$			9.62647i			0.316345i
$927$	26.3608	+	28.1338i	0.865803	+	0.924035i
$928$	3.67269			0.120562
$929$	−21.4697	+	7.81435i	−0.704399	+	0.256380i	−0.669288	−	0.743003i	$-0.733401\pi$
$929$	−21.4697	+	7.81435i	−0.704399	+	0.256380i	−0.0351113	+	0.999383i	$0.511179\pi$
$930$	−0.746965	−	3.64919i	−0.0244940	−	0.119662i
$931$	−22.9871	+	6.78512i	−0.753373	+	0.222373i
$932$	−3.77205	+	10.3636i	−0.123558	+	0.339472i
$933$	1.95615	−	1.73481i	0.0640414	−	0.0567953i
$934$	−16.6330	+	19.8224i	−0.544247	+	0.648609i
$935$		−	1.85531i		−	0.0606751i
$936$	−34.0110	+	31.8677i	−1.11169	+	1.04163i
$937$	−34.1439	−	19.7130i	−1.11543	−	0.643995i	−0.175201	−	0.984533i	$-0.556057\pi$
$937$	−34.1439	−	19.7130i	−1.11543	−	0.643995i	−0.940231	+	0.340538i	$0.889391\pi$
$938$	−15.5570	−	11.6286i	−0.507954	−	0.379687i
$939$	18.5402	+	46.9031i	0.605038	+	1.53063i
$940$	−7.89383	+	6.62371i	−0.257468	+	0.216042i
$941$	−2.36221	−	13.3968i	−0.0770059	−	0.436722i	−0.998797	−	0.0490354i	$-0.984385\pi$
$941$	−2.36221	−	13.3968i	−0.0770059	−	0.436722i	0.921791	−	0.387687i	$-0.126726\pi$
$942$	−6.56391	−	10.6827i	−0.213864	−	0.348062i
$943$	6.28859	−	7.49445i	0.204785	−	0.244053i
$944$	0.680098			0.0221353
$945$	2.62886	+	18.8790i	0.0855170	+	0.614134i
$946$	−2.02431			−0.0658159
$947$	3.05054	−	3.63549i	0.0991292	−	0.118138i	−0.714199	−	0.699943i	$-0.753209\pi$
$947$	3.05054	−	3.63549i	0.0991292	−	0.118138i	0.813328	+	0.581805i	$0.197653\pi$
$948$	−2.66599	+	4.92413i	−0.0865875	+	0.159928i
$949$	2.25854	+	12.8088i	0.0733155	+	0.415793i
$950$	7.19365	−	6.03619i	0.233393	−	0.195840i
$951$	−52.0884	−	7.72122i	−1.68908	−	0.250378i
$952$	−16.0619	+	6.89163i	−0.520570	+	0.223359i
$953$	25.1568	+	14.5243i	0.814909	+	0.470488i	0.848658	−	0.528942i	$-0.177411\pi$
$953$	25.1568	+	14.5243i	0.814909	+	0.470488i	−0.0337488	+	0.999430i	$0.510745\pi$
$954$	23.1755	−	9.90266i	0.750334	−	0.320610i
$955$			32.9775i			1.06713i
$956$	−1.95692	+	2.33217i	−0.0632913	+	0.0754277i
$957$	−0.624294	−	0.208059i	−0.0201805	−	0.00672559i
$958$	−4.15692	+	11.4210i	−0.134304	+	0.368997i
$959$	−2.57095	+	2.41618i	−0.0830202	+	0.0780226i
$960$	11.9695	+	3.98910i	0.386315	+	0.128748i
$961$	−26.2838	+	9.56651i	−0.847864	+	0.308597i
$962$	5.25842			0.169538
$963$	−26.0379	+	16.9976i	−0.839059	+	0.547739i
$964$			8.67358i			0.279357i
$965$	20.0971	+	16.8634i	0.646947	+	0.542853i
$966$	−27.2114	−	2.48084i	−0.875512	−	0.0798197i
$967$	−0.574034	−	3.25551i	−0.0184597	−	0.104690i	0.974186	−	0.225748i	$-0.0724825\pi$
$967$	−0.574034	−	3.25551i	−0.0184597	−	0.104690i	−0.992645	+	0.121058i	$0.961371\pi$
$968$	−10.4211	+	28.6316i	−0.334946	+	0.920256i
$969$	0.375301	+	13.7079i	0.0120564	+	0.440362i
$970$	−3.99854	+	22.6768i	−0.128385	+	0.728109i
$971$	7.79202	+	13.4962i	0.250058	+	0.433113i	0.963541	−	0.267559i	$-0.0862171\pi$
$971$	7.79202	+	13.4962i	0.250058	+	0.433113i	−0.713484	+	0.700672i	$0.752884\pi$
$972$	−5.75917	−	17.8933i	−0.184725	−	0.573928i
$973$	40.2639	−	2.26698i	1.29080	−	0.0726760i
$974$	−9.80616	−	26.9422i	−0.314209	−	0.863283i
$975$	25.4917	+	13.8016i	0.816389	+	0.442004i
$976$	1.78787	−	0.315250i	0.0572284	−	0.0100909i
$977$	−10.4385	+	28.6796i	−0.333958	+	0.917542i	0.653113	+	0.757260i	$0.273463\pi$
$977$	−10.4385	+	28.6796i	−0.333958	+	0.917542i	−0.987071	+	0.160282i	$0.948760\pi$
$978$	−1.58373	−	0.234761i	−0.0506421	−	0.00750683i
$979$	4.40127	−	5.24524i	0.140665	−	0.167638i
$980$	−4.67698	+	10.7282i	−0.149401	+	0.342698i
$981$	22.8432	−	45.0977i	0.729328	−	1.43986i
$982$	10.9657	−	18.9931i	0.349929	−	0.606095i
$983$	−14.4341	−	12.1117i	−0.460377	−	0.386303i	0.382892	−	0.923793i	$-0.374928\pi$
$983$	−14.4341	−	12.1117i	−0.460377	−	0.386303i	−0.843270	+	0.537490i	$0.819372\pi$
$984$	−4.80069	−	5.41318i	−0.153040	−	0.172566i
$985$	14.5404	−	2.56386i	0.463295	−	0.0816915i
$986$	−1.27126	−	0.462701i	−0.0404852	−	0.0147354i
$987$	−19.8988	−	20.0446i	−0.633385	−	0.638027i
$988$	−3.89881	+	22.1113i	−0.124038	+	0.703453i
$989$	22.7453	+	13.1320i	0.723258	+	0.417573i
$990$	−1.71620	−	1.28685i	−0.0545445	−	0.0408988i
$991$	9.66991	+	16.7488i	0.307175	+	0.532042i	0.977743	−	0.209805i	$-0.0672831\pi$
$991$	9.66991	+	16.7488i	0.307175	+	0.532042i	−0.670568	+	0.741848i	$0.733950\pi$
$992$	−1.69077	+	9.58881i	−0.0536819	+	0.304445i
$993$	7.18799	−	48.4912i	0.228104	−	1.53882i
$994$	25.3855	+	27.0116i	0.805181	+	0.856755i
$995$	−8.93652	−	10.6501i	−0.283307	−	0.337632i
$996$	13.1218	+	21.3557i	0.415781	+	0.676682i
$997$	9.92283	+	1.74966i	0.314259	+	0.0554124i	0.328553	−	0.944485i	$-0.393439\pi$
$997$	9.92283	+	1.74966i	0.314259	+	0.0554124i	−0.0142940	+	0.999898i	$0.504550\pi$
$998$	−20.2121	−	11.6694i	−0.639801	−	0.369390i
$999$	−2.40910	+	5.09761i	−0.0762207	+	0.161281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.14	✓	132
3.2	odd	2		567.2.ba.a.143.9		132
7.5	odd	6		189.2.bd.a.47.9	yes	132
21.5	even	6		567.2.bd.a.467.14		132
27.4	even	9		567.2.bd.a.17.14		132
27.23	odd	18		189.2.bd.a.185.9	yes	132
189.131	even	18	inner	189.2.ba.a.131.14	yes	132
189.166	odd	18		567.2.ba.a.341.9		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.14	✓	132	1.1	even	1	trivial
189.2.ba.a.131.14	yes	132	189.131	even	18	inner
189.2.bd.a.47.9	yes	132	7.5	odd	6
189.2.bd.a.185.9	yes	132	27.23	odd	18
567.2.ba.a.143.9		132	3.2	odd	2
567.2.ba.a.341.9		132	189.166	odd	18
567.2.bd.a.17.14		132	27.4	even	9
567.2.bd.a.467.14		132	21.5	even	6

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.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.572822 - 0.682663i) q^{2} +(-1.73140 + 0.0474030i) q^{3} +(0.209393 + 1.18753i) q^{4} +(-1.06212 + 0.891222i) q^{5} +(-0.959425 + 1.20912i) q^{6} +(-1.58403 + 2.11916i) q^{7} +(2.47415 + 1.42845i) q^{8} +(2.99551 - 0.164147i) q^{9} +O(q^{10})\)	\(q+(0.572822 - 0.682663i) q^{2} +(-1.73140 + 0.0474030i) q^{3} +(0.209393 + 1.18753i) q^{4} +(-1.06212 + 0.891222i) q^{5} +(-0.959425 + 1.20912i) q^{6} +(-1.58403 + 2.11916i) q^{7} +(2.47415 + 1.42845i) q^{8} +(2.99551 - 0.164147i) q^{9} +1.23558i q^{10} +(-0.371978 + 0.443306i) q^{11} +(-0.418836 - 2.04616i) q^{12} +(-1.85992 + 5.11010i) q^{13} +(0.539301 + 2.29526i) q^{14} +(1.79671 - 1.59341i) q^{15} +(0.126145 - 0.0459131i) q^{16} +2.31232 q^{17} +(1.60383 - 2.13895i) q^{18} -3.42394i q^{19} +(-1.28075 - 1.07468i) q^{20} +(2.64215 - 3.74420i) q^{21} +(0.0895514 + 0.507871i) q^{22} +(2.28843 - 6.28742i) q^{23} +(-4.35146 - 2.35594i) q^{24} +(-0.534425 + 3.03087i) q^{25} +(2.42307 + 4.19688i) q^{26} +(-5.17864 + 0.426201i) q^{27} +(-2.84824 - 1.43735i) q^{28} +(-0.224543 - 0.616928i) q^{29} +(-0.0585702 - 2.13929i) q^{30} +(1.71407 - 0.302237i) q^{31} +(-1.91332 + 5.25680i) q^{32} +(0.623030 - 0.785175i) q^{33} +(1.32455 - 1.57853i) q^{34} +(-0.206211 - 3.66252i) q^{35} +(0.822168 + 3.52287i) q^{36} +(0.542537 - 0.939702i) q^{37} +(-2.33740 - 1.96131i) q^{38} +(2.97804 - 8.93580i) q^{39} +(-3.90090 + 0.687834i) q^{40} +(1.37400 + 0.500093i) q^{41} +(-1.04255 - 3.94846i) q^{42} +(-0.681623 + 3.86568i) q^{43} +(-0.604328 - 0.348909i) q^{44} +(-3.03529 + 2.84401i) q^{45} +(-2.98132 - 5.16380i) q^{46} +(1.07027 - 6.06980i) q^{47} +(-0.216232 + 0.0854738i) q^{48} +(-1.98167 - 6.71364i) q^{49} +(1.76293 + 2.10098i) q^{50} +(-4.00355 + 0.109611i) q^{51} +(-6.45784 - 1.13869i) q^{52} +(8.16395 + 4.71346i) q^{53} +(-2.67549 + 3.77940i) q^{54} -0.802359i q^{55} +(-6.94625 + 2.98040i) q^{56} +(0.162305 + 5.92822i) q^{57} +(-0.549777 - 0.200103i) q^{58} +(4.76072 + 1.73276i) q^{59} +(2.26844 + 1.79999i) q^{60} +(13.3184 + 2.34839i) q^{61} +(0.775532 - 1.34326i) q^{62} +(-4.39713 + 6.60797i) q^{63} +(2.62687 + 4.54987i) q^{64} +(-2.57878 - 7.08513i) q^{65} +(-0.179124 - 0.875085i) q^{66} +(-6.31050 + 5.29514i) q^{67} +(0.484183 + 2.74594i) q^{68} +(-3.66415 + 10.9945i) q^{69} +(-2.61839 - 1.95720i) q^{70} +(13.6154 - 7.86086i) q^{71} +(7.64580 + 3.87280i) q^{72} +(2.07131 - 1.19587i) q^{73} +(-0.330722 - 0.908652i) q^{74} +(0.781631 - 5.27299i) q^{75} +(4.06603 - 0.716950i) q^{76} +(-0.350210 - 1.49049i) q^{77} +(-4.39425 - 7.15162i) q^{78} +(-2.05377 - 1.72332i) q^{79} +(-0.0930623 + 0.161189i) q^{80} +(8.94611 - 0.983409i) q^{81} +(1.12845 - 0.651511i) q^{82} +(-11.2771 + 4.10455i) q^{83} +(4.99959 + 2.35361i) q^{84} +(-2.45595 + 2.06079i) q^{85} +(2.24850 + 2.67966i) q^{86} +(0.418019 + 1.05751i) q^{87} +(-1.55357 + 0.565453i) q^{88} -11.8321 q^{89} +(0.202817 + 3.70119i) q^{90} +(-7.88293 - 12.0361i) q^{91} +(7.94566 + 1.40103i) q^{92} +(-2.95342 + 0.604546i) q^{93} +(-3.53055 - 4.20755i) q^{94} +(3.05150 + 3.63663i) q^{95} +(3.06354 - 9.19233i) q^{96} +(18.3532 + 3.23616i) q^{97} +(-5.71830 - 2.49291i) q^{98} +(-1.04150 + 1.38899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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