LMFDB - Embedded newform 162.2.g.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	162.31
Dual form			162.2.g.a.115.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396080 - 0.918216i) q^{2} +(-1.31402 - 1.12843i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.205044 + 3.52046i) q^{5} +(-0.515687 + 1.65350i) q^{6} +(-4.52050 + 1.07138i) q^{7} +(0.939693 + 0.342020i) q^{8} +(0.453287 + 2.96556i) q^{9} +O(q^{10})$	\(q+(-0.396080 - 0.918216i) q^{2} +(-1.31402 - 1.12843i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.205044 + 3.52046i) q^{5} +(-0.515687 + 1.65350i) q^{6} +(-4.52050 + 1.07138i) q^{7} +(0.939693 + 0.342020i) q^{8} +(0.453287 + 2.96556i) q^{9} +(3.31376 - 1.20611i) q^{10} +(2.48308 - 1.63315i) q^{11} +(1.72252 - 0.181406i) q^{12} +(-3.18650 + 0.372448i) q^{13} +(2.77423 + 3.72644i) q^{14} +(4.24203 - 4.39457i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(1.87620 + 1.57432i) q^{17} +(2.54348 - 1.59081i) q^{18} +(-4.02475 + 3.37717i) q^{19} +(-2.41998 - 2.56503i) q^{20} +(7.14899 + 3.69326i) q^{21} +(-2.48308 - 1.63315i) q^{22} +(-2.43351 - 0.576753i) q^{23} +(-0.848827 - 1.50980i) q^{24} +(-7.38542 - 0.863232i) q^{25} +(1.60410 + 2.77838i) q^{26} +(2.75080 - 4.40830i) q^{27} +(2.32286 - 4.02331i) q^{28} +(-1.83677 + 2.46722i) q^{29} +(-5.71535 - 2.15450i) q^{30} +(-0.0198244 - 0.0662182i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-5.10571 - 0.655999i) q^{33} +(0.702441 - 2.34632i) q^{34} +(-2.84485 - 16.1339i) q^{35} +(-2.46813 - 1.70538i) q^{36} +(0.866417 - 4.91369i) q^{37} +(4.69509 + 2.35796i) q^{38} +(4.60740 + 3.10634i) q^{39} +(-1.39675 + 3.23802i) q^{40} +(0.000942526 - 0.00218502i) q^{41} +(0.559639 - 8.02714i) q^{42} +(5.11254 + 2.56761i) q^{43} +(-0.516085 + 2.92686i) q^{44} +(-10.5331 + 0.987713i) q^{45} +(0.434281 + 2.46293i) q^{46} +(-3.22387 + 10.7685i) q^{47} +(-1.05012 + 1.37741i) q^{48} +(13.0316 - 6.54472i) q^{49} +(2.13258 + 7.12332i) q^{50} +(-0.688852 - 4.18585i) q^{51} +(1.91580 - 2.57336i) q^{52} +(-0.606712 + 1.05086i) q^{53} +(-5.13731 - 0.779789i) q^{54} +(5.24030 + 9.07646i) q^{55} +(-4.61431 - 0.539336i) q^{56} +(9.09950 + 0.103995i) q^{57} +(2.99295 + 0.709342i) q^{58} +(3.94550 + 2.59499i) q^{59} +(0.285440 + 6.10128i) q^{60} +(-0.101710 - 0.107806i) q^{61} +(-0.0529505 + 0.0444308i) q^{62} +(-5.22632 - 12.9202i) q^{63} +(0.766044 + 0.642788i) q^{64} +(-0.657819 - 11.2943i) q^{65} +(1.41992 + 4.94797i) q^{66} +(-8.47079 - 11.3782i) q^{67} +(-2.43265 + 0.284336i) q^{68} +(2.54685 + 3.50391i) q^{69} +(-13.6876 + 9.00250i) q^{70} +(9.62559 - 3.50343i) q^{71} +(-0.588330 + 2.94175i) q^{72} +(-2.04347 - 0.743761i) q^{73} +(-4.85500 + 1.15066i) q^{74} +(8.73048 + 9.46824i) q^{75} +(0.305489 - 5.24505i) q^{76} +(-9.47505 + 10.0430i) q^{77} +(1.02739 - 5.46095i) q^{78} +(6.56354 + 15.2160i) q^{79} +3.52643 q^{80} +(-8.58906 + 2.68850i) q^{81} -0.00237964 q^{82} +(-0.212777 - 0.493273i) q^{83} +(-7.59231 + 2.66552i) q^{84} +(-5.92704 + 6.28230i) q^{85} +(0.332651 - 5.71140i) q^{86} +(5.19764 - 1.16929i) q^{87} +(2.89190 - 0.685394i) q^{88} +(14.7565 + 5.37094i) q^{89} +(5.07887 + 9.28043i) q^{90} +(14.0055 - 5.09759i) q^{91} +(2.08949 - 1.37428i) q^{92} +(-0.0486730 + 0.109382i) q^{93} +(11.1647 - 1.30497i) q^{94} +(-11.0639 - 14.8615i) q^{95} +(1.68069 + 0.418672i) q^{96} +(1.03234 + 17.7246i) q^{97} +(-11.1710 - 9.37361i) q^{98} +(5.96875 + 6.62344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$3$	−1.31402	−	1.12843i	−0.758649	−	0.651500i
$3$	−1.31402	−	1.12843i	−0.758649	−	0.651500i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	−0.205044	+	3.52046i	−0.0916983	+	1.57440i	0.568102	+	0.822958i	$0.307678\pi$
$5$	−0.205044	+	3.52046i	−0.0916983	+	1.57440i	−0.659801	+	0.751441i	$0.729359\pi$
$6$	−0.515687	+	1.65350i	−0.210529	+	0.675039i
$7$	−4.52050	+	1.07138i	−1.70859	+	0.404943i	−0.964698	−	0.263360i	$-0.915169\pi$
$7$	−4.52050	+	1.07138i	−1.70859	+	0.404943i	−0.743890	+	0.668302i	$0.767021\pi$
$8$	0.939693	+	0.342020i	0.332232	+	0.120922i
$9$	0.453287	+	2.96556i	0.151096	+	0.988519i
$10$	3.31376	−	1.20611i	1.04790	−	0.381405i
$11$	2.48308	−	1.63315i	0.748677	−	0.492413i	−0.116928	−	0.993140i	$-0.537305\pi$
$11$	2.48308	−	1.63315i	0.748677	−	0.492413i	0.865605	+	0.500728i	$0.166934\pi$
$12$	1.72252	−	0.181406i	0.497250	−	0.0523674i
$13$	−3.18650	+	0.372448i	−0.883776	+	0.103299i	−0.545859	−	0.837877i	$-0.683796\pi$
$13$	−3.18650	+	0.372448i	−0.883776	+	0.103299i	−0.337917	+	0.941176i	$0.609722\pi$
$14$	2.77423	+	3.72644i	0.741445	+	0.995934i
$15$	4.24203	−	4.39457i	1.09529	−	1.13467i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	1.87620	+	1.57432i	0.455046	+	0.381829i	0.841304	−	0.540562i	$-0.181788\pi$
$17$	1.87620	+	1.57432i	0.455046	+	0.381829i	−0.386258	+	0.922391i	$0.626233\pi$
$18$	2.54348	−	1.59081i	0.599505	−	0.374958i
$19$	−4.02475	+	3.37717i	−0.923341	+	0.774775i	−0.974610	−	0.223909i	$-0.928118\pi$
$19$	−4.02475	+	3.37717i	−0.923341	+	0.774775i	0.0512685	+	0.998685i	$0.483674\pi$
$20$	−2.41998	−	2.56503i	−0.541124	−	0.573558i
$21$	7.14899	+	3.69326i	1.56004	+	0.805935i
$22$	−2.48308	−	1.63315i	−0.529395	−	0.348188i
$23$	−2.43351	−	0.576753i	−0.507422	−	0.120261i	−0.0310723	−	0.999517i	$-0.509892\pi$
$23$	−2.43351	−	0.576753i	−0.507422	−	0.120261i	−0.476350	+	0.879256i	$0.658040\pi$
$24$	−0.848827	−	1.50980i	−0.173266	−	0.308186i
$25$	−7.38542	−	0.863232i	−1.47708	−	0.172646i
$26$	1.60410	+	2.77838i	0.314589	+	0.544884i
$27$	2.75080	−	4.40830i	0.529391	−	0.848378i
$28$	2.32286	−	4.02331i	0.438980	−	0.760335i
$29$	−1.83677	+	2.46722i	−0.341081	+	0.458151i	−0.939257	−	0.343213i	$-0.888485\pi$
$29$	−1.83677	+	2.46722i	−0.341081	+	0.458151i	0.598177	+	0.801364i	$0.295892\pi$
$30$	−5.71535	−	2.15450i	−1.04348	−	0.393356i
$31$	−0.0198244	−	0.0662182i	−0.00356057	−	0.0118931i	0.956191	−	0.292744i	$-0.0945685\pi$
$31$	−0.0198244	−	0.0662182i	−0.00356057	−	0.0118931i	−0.959751	+	0.280851i	$0.909383\pi$
$32$	−0.893633	+	0.448799i	−0.157973	+	0.0793372i
$33$	−5.10571	−	0.655999i	−0.888790	−	0.114195i
$34$	0.702441	−	2.34632i	0.120468	−	0.402390i
$35$	−2.84485	−	16.1339i	−0.480867	−	2.72713i
$36$	−2.46813	−	1.70538i	−0.411355	−	0.284230i
$37$	0.866417	−	4.91369i	0.142438	−	0.807806i	−0.826951	−	0.562275i	$-0.809926\pi$
$37$	0.866417	−	4.91369i	0.142438	−	0.807806i	0.969389	−	0.245532i	$-0.0789625\pi$
$38$	4.69509	+	2.35796i	0.761645	+	0.382512i
$39$	4.60740	+	3.10634i	0.737774	+	0.497412i
$40$	−1.39675	+	3.23802i	−0.220845	+	0.511976i
$41$	0.000942526	−	0.00218502i	0.000147198	−	0.000341243i	−0.918142	−	0.396250i	$-0.870311\pi$
$41$	0.000942526	−	0.00218502i	0.000147198	−	0.000341243i	0.918290	+	0.395909i	$0.129570\pi$
$42$	0.559639	−	8.02714i	0.0863542	−	1.23862i
$43$	5.11254	+	2.56761i	0.779655	+	0.391558i	0.793673	−	0.608344i	$-0.208166\pi$
$43$	5.11254	+	2.56761i	0.779655	+	0.391558i	−0.0140182	+	0.999902i	$0.504462\pi$
$44$	−0.516085	+	2.92686i	−0.0778027	+	0.441241i
$45$	−10.5331	+	0.987713i	−1.57018	+	0.147240i
$46$	0.434281	+	2.46293i	0.0640312	+	0.363139i
$47$	−3.22387	+	10.7685i	−0.470250	+	1.57074i	0.313450	+	0.949605i	$0.398515\pi$
$47$	−3.22387	+	10.7685i	−0.470250	+	1.57074i	−0.783700	+	0.621139i	$0.786670\pi$
$48$	−1.05012	+	1.37741i	−0.151572	+	0.198812i
$49$	13.0316	−	6.54472i	1.86166	−	0.934961i
$50$	2.13258	+	7.12332i	0.301593	+	1.00739i
$51$	−0.688852	−	4.18585i	−0.0964586	−	0.586137i
$52$	1.91580	−	2.57336i	0.265674	−	0.356861i
$53$	−0.606712	+	1.05086i	−0.0833384	+	0.144346i	−0.904682	−	0.426088i	$-0.859892\pi$
$53$	−0.606712	+	1.05086i	−0.0833384	+	0.144346i	0.821344	+	0.570434i	$0.193225\pi$
$54$	−5.13731	−	0.779789i	−0.699099	−	0.106116i
$55$	5.24030	+	9.07646i	0.706602	+	1.22387i
$56$	−4.61431	−	0.539336i	−0.616613	−	0.0720717i
$57$	9.09950	+	0.103995i	1.20526	+	0.0137744i
$58$	2.99295	+	0.709342i	0.392993	+	0.0931411i
$59$	3.94550	+	2.59499i	0.513660	+	0.337840i	0.779732	−	0.626114i	$-0.215355\pi$
$59$	3.94550	+	2.59499i	0.513660	+	0.337840i	−0.266072	+	0.963953i	$0.585726\pi$
$60$	0.285440	+	6.10128i	0.0368501	+	0.787672i
$61$	−0.101710	−	0.107806i	−0.0130226	−	0.0138031i	0.720830	−	0.693112i	$-0.243761\pi$
$61$	−0.101710	−	0.107806i	−0.0130226	−	0.0138031i	−0.733852	+	0.679309i	$0.762280\pi$
$62$	−0.0529505	+	0.0444308i	−0.00672472	+	0.00564271i
$63$	−5.22632	−	12.9202i	−0.658454	−	1.62779i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	−0.657819	−	11.2943i	−0.0815924	−	1.40089i
$66$	1.41992	+	4.94797i	0.174780	+	0.609053i
$67$	−8.47079	−	11.3782i	−1.03487	−	1.39007i	−0.917842	−	0.396945i	$-0.870070\pi$
$67$	−8.47079	−	11.3782i	−1.03487	−	1.39007i	−0.117029	−	0.993128i	$-0.537337\pi$
$68$	−2.43265	+	0.284336i	−0.295002	+	0.0344808i
$69$	2.54685	+	3.50391i	0.306605	+	0.421821i
$70$	−13.6876	+	9.00250i	−1.63599	+	1.07600i
$71$	9.62559	−	3.50343i	1.14235	−	0.415780i	0.299587	−	0.954069i	$-0.403151\pi$
$71$	9.62559	−	3.50343i	1.14235	−	0.415780i	0.842760	+	0.538289i	$0.180929\pi$
$72$	−0.588330	+	2.94175i	−0.0693353	+	0.346688i
$73$	−2.04347	−	0.743761i	−0.239170	−	0.0870506i	0.219654	−	0.975578i	$-0.429507\pi$
$73$	−2.04347	−	0.743761i	−0.239170	−	0.0870506i	−0.458824	+	0.888527i	$0.651729\pi$
$74$	−4.85500	+	1.15066i	−0.564383	+	0.133761i
$75$	8.73048	+	9.46824i	1.00811	+	1.09330i
$76$	0.305489	−	5.24505i	0.0350420	−	0.601649i
$77$	−9.47505	+	10.0430i	−1.07978	+	1.14450i
$78$	1.02739	−	5.46095i	0.116329	−	0.618330i
$79$	6.56354	+	15.2160i	0.738456	+	1.71193i	0.701556	+	0.712615i	$0.252489\pi$
$79$	6.56354	+	15.2160i	0.738456	+	1.71193i	0.0369004	+	0.999319i	$0.488252\pi$
$80$	3.52643			0.394267
$81$	−8.58906	+	2.68850i	−0.954340	+	0.298722i
$82$	−0.00237964			−0.000262787
$83$	−0.212777	−	0.493273i	−0.0233554	−	0.0541438i	0.906139	−	0.422979i	$-0.139016\pi$
$83$	−0.212777	−	0.493273i	−0.0233554	−	0.0541438i	−0.929495	+	0.368836i	$0.879757\pi$
$84$	−7.59231	+	2.66552i	−0.828389	+	0.290832i
$85$	−5.92704	+	6.28230i	−0.642878	+	0.681411i
$86$	0.332651	−	5.71140i	0.0358707	−	0.615876i
$87$	5.19764	−	1.16929i	0.557245	−	0.125361i
$88$	2.89190	−	0.685394i	0.308278	−	0.0730632i
$89$	14.7565	+	5.37094i	1.56419	+	0.569319i	0.971692	−	0.236252i	$-0.0759192\pi$
$89$	14.7565	+	5.37094i	1.56419	+	0.569319i	0.592499	+	0.805571i	$0.298141\pi$
$90$	5.07887	+	9.28043i	0.535360	+	0.978243i
$91$	14.0055	−	5.09759i	1.46818	−	0.534373i
$92$	2.08949	−	1.37428i	0.217845	−	0.143279i
$93$	−0.0486730	+	0.109382i	−0.00504715	+	0.0113424i
$94$	11.1647	−	1.30497i	1.15155	−	0.134597i
$95$	−11.0639	−	14.8615i	−1.13514	−	1.52475i
$96$	1.68069	+	0.418672i	0.171535	+	0.0427306i
$97$	1.03234	+	17.7246i	0.104818	+	1.79966i	0.484758	+	0.874648i	$0.338908\pi$
$97$	1.03234	+	17.7246i	0.104818	+	1.79966i	−0.379940	+	0.925011i	$0.624055\pi$
$98$	−11.1710	−	9.37361i	−1.12844	−	0.946877i
$99$	5.96875	+	6.62344i	0.599881	+	0.665680i
$100$	5.69607	−	4.77957i	0.569607	−	0.477957i
$101$	−5.21098	−	5.52331i	−0.518512	−	0.549590i	0.414213	−	0.910180i	$-0.364057\pi$
$101$	−5.21098	−	5.52331i	−0.518512	−	0.549590i	−0.932725	+	0.360590i	$0.882575\pi$
$102$	−3.57068	+	2.29045i	−0.353550	+	0.226788i
$103$	−8.35048	−	5.49220i	−0.822797	−	0.541162i	0.0668754	−	0.997761i	$-0.478697\pi$
$103$	−8.35048	−	5.49220i	−0.822797	−	0.541162i	−0.889673	+	0.456599i	$0.849067\pi$
$104$	−3.12171	−	0.739860i	−0.306109	−	0.0725492i
$105$	−14.4678	+	24.4105i	−1.41192	+	2.38222i
$106$	1.20522	+	0.140870i	0.117061	+	0.0136825i
$107$	3.12443	+	5.41167i	0.302050	+	0.523166i	0.976600	−	0.215063i	$-0.0689957\pi$
$107$	3.12443	+	5.41167i	0.302050	+	0.523166i	−0.674550	+	0.738229i	$0.735662\pi$
$108$	1.31877	+	5.02602i	0.126899	+	0.483629i
$109$	−3.13613	+	5.43194i	−0.300387	+	0.520286i	−0.976224	−	0.216766i	$-0.930449\pi$
$109$	−3.13613	+	5.43194i	−0.300387	+	0.520286i	0.675836	+	0.737052i	$0.263783\pi$
$110$	6.25858	−	8.40673i	0.596732	−	0.801550i
$111$	−6.68325	+	5.47899i	−0.634346	+	0.520043i
$112$	1.33241	+	4.45055i	0.125901	+	0.420538i
$113$	12.0627	−	6.05813i	1.13477	−	0.569901i	0.220650	−	0.975353i	$-0.429182\pi$
$113$	12.0627	−	6.05813i	1.13477	−	0.569901i	0.914117	+	0.405452i	$0.132886\pi$
$114$	−3.50864	−	8.39650i	−0.328614	−	0.786404i
$115$	2.52941	−	8.44882i	0.235869	−	0.787857i
$116$	−0.534117	−	3.02913i	−0.0495915	−	0.281248i
$117$	−2.54892	−	9.28092i	−0.235647	−	0.858021i
$118$	0.820034	−	4.65064i	0.0754903	−	0.428127i
$119$	−10.1681	−	5.10660i	−0.932105	−	0.468121i
$120$	5.48924	−	2.67869i	0.501096	−	0.244530i
$121$	−0.858357	+	1.98990i	−0.0780325	+	0.180900i
$122$	−0.0587040	+	0.136091i	−0.00531481	+	0.0123211i
$123$	−0.00370414	+	0.00180758i	−0.000333991	+	0.000162984i
$124$	0.0617697	+	0.0310219i	0.00554708	+	0.00278585i
$125$	1.49152	−	8.45882i	0.133405	−	0.756580i
$126$	−9.79345	+	9.91630i	−0.872470	+	0.883414i
$127$	0.696995	+	3.95285i	0.0618483	+	0.350759i	0.999990	+	0.00450709i	$0.00143466\pi$
$127$	0.696995	+	3.95285i	0.0618483	+	0.350759i	−0.938142	+	0.346252i	$0.887454\pi$
$128$	0.286803	−	0.957990i	0.0253501	−	0.0846751i
$129$	−3.82060	−	9.14304i	−0.336385	−	0.805000i
$130$	−10.1101	+	5.07747i	−0.886712	+	0.445324i
$131$	−0.759655	−	2.53742i	−0.0663713	−	0.221696i	0.918369	−	0.395725i	$-0.129507\pi$
$131$	−0.759655	−	2.53742i	−0.0663713	−	0.221696i	−0.984741	+	0.174029i	$0.944321\pi$
$132$	3.98091	−	3.26358i	0.346493	−	0.284059i
$133$	14.5757	−	19.5785i	1.26387	−	1.69767i
$134$	−7.09258	+	12.2847i	−0.612705	+	1.06124i
$135$	14.9552	+	10.5880i	1.28714	+	0.911268i
$136$	1.22461	+	2.12108i	0.105009	+	0.181881i
$137$	1.62951	+	0.190462i	0.139218	+	0.0162723i	0.185417	−	0.982660i	$-0.440637\pi$
$137$	1.62951	+	0.190462i	0.139218	+	0.0162723i	−0.0461982	+	0.998932i	$0.514711\pi$
$138$	2.20859	−	3.72639i	0.188008	−	0.317211i
$139$	−12.5240	−	2.96823i	−1.06227	−	0.251762i	−0.337904	−	0.941180i	$-0.609718\pi$
$139$	−12.5240	−	2.96823i	−1.06227	−	0.251762i	−0.724363	+	0.689418i	$0.757866\pi$
$140$	13.6876	+	9.00250i	1.15682	+	0.760850i
$141$	16.3877	−	10.5121i	1.38009	−	0.885275i
$142$	−7.02940	−	7.45073i	−0.589895	−	0.625252i
$143$	−7.30407	+	6.12885i	−0.610797	+	0.512520i
$144$	2.93418	−	0.624952i	0.244515	−	0.0520794i
$145$	−8.30912	−	6.97218i	−0.690035	−	0.579008i
$146$	0.126442	+	2.17093i	0.0104644	+	0.179668i
$147$	−24.5091	−	6.10539i	−2.02147	−	0.503564i
$148$	2.97952	+	4.00219i	0.244915	+	0.328978i
$149$	−11.6140	+	1.35749i	−0.951460	+	0.111210i	−0.577640	−	0.816292i	$-0.696026\pi$
$149$	−11.6140	+	1.35749i	−0.951460	+	0.111210i	−0.373820	+	0.927501i	$0.621952\pi$
$150$	5.23592	−	11.7666i	0.427511	−	0.960742i
$151$	−5.40823	+	3.55705i	−0.440115	+	0.289468i	−0.750163	−	0.661253i	$-0.770025\pi$
$151$	−5.40823	+	3.55705i	−0.440115	+	0.289468i	0.310048	+	0.950721i	$0.399655\pi$
$152$	−4.93709	+	1.79695i	−0.400451	+	0.145752i
$153$	−3.81828	+	6.27761i	−0.308690	+	0.507515i
$154$	12.9745	+	4.72233i	1.04551	+	0.380536i
$155$	0.237183	−	0.0562135i	0.0190510	−	0.00451518i
$156$	−5.42126	+	1.21960i	−0.434048	+	0.0976462i
$157$	0.897783	−	15.4143i	0.0716509	−	1.23020i	−0.750477	−	0.660896i	$-0.770176\pi$
$157$	0.897783	−	15.4143i	0.0716509	−	1.23020i	0.822128	−	0.569302i	$-0.192787\pi$
$158$	11.3719	−	12.0535i	0.904699	−	0.958925i
$159$	1.98305	−	0.696212i	0.157266	−	0.0552132i
$160$	−1.39675	−	3.23802i	−0.110423	−	0.255988i
$161$	11.6186			0.915674
$162$	5.87058	+	6.82175i	0.461236	+	0.535968i
$163$	−5.05225			−0.395723			−0.197861	−	0.980230i	$-0.563400\pi$
$163$	−5.05225			−0.395723			−0.197861	+	0.980230i	$0.563400\pi$
$164$	0.000942526		0.00218502i	7.35989e−5		0.000170621i
$165$	3.35631	−	17.8399i	0.261289	−	1.38884i
$166$	−0.368655	+	0.390751i	−0.0286132	+	0.0303282i
$167$	−1.30871	+	22.4696i	−0.101271	+	1.73875i	0.440083	+	0.897957i	$0.354949\pi$
$167$	−1.30871	+	22.4696i	−0.101271	+	1.73875i	−0.541353	+	0.840795i	$0.682088\pi$
$168$	5.45469	+	5.91563i	0.420838	+	0.456401i
$169$	−2.63453	+	0.624394i	−0.202656	+	0.0480303i
$170$	8.11609	+	2.95402i	0.622476	+	0.226563i
$171$	−11.8396	−	10.4048i	−0.905393	−	0.795675i
$172$	−5.37605	+	1.95672i	−0.409920	+	0.149199i
$173$	0.477662	−	0.314163i	0.0363159	−	0.0238854i	−0.531221	−	0.847233i	$-0.678267\pi$
$173$	0.477662	−	0.314163i	0.0363159	−	0.0238854i	0.567537	+	0.823348i	$0.307896\pi$
$174$	−3.13234	−	4.30942i	−0.237462	−	0.326696i
$175$	34.3106	−	4.01034i	2.59364	−	0.303153i
$176$	−1.77476	−	2.38392i	−0.133778	−	0.179695i
$177$	−2.25618	−	7.86209i	−0.169585	−	0.590951i
$178$	−0.913082	−	15.6770i	−0.0684384	−	1.17504i
$179$	−17.2919	−	14.5096i	−1.29246	−	1.08450i	−0.991396	−	0.130898i	$-0.958214\pi$
$179$	−17.2919	−	14.5096i	−1.29246	−	1.08450i	−0.301063	−	0.953604i	$-0.597342\pi$
$180$	6.50980	−	8.33929i	0.485212	−	0.621574i
$181$	0.713662	−	0.598833i	0.0530461	−	0.0445109i	−0.615879	−	0.787841i	$-0.711199\pi$
$181$	0.713662	−	0.598833i	0.0530461	−	0.0445109i	0.668925	+	0.743330i	$0.266755\pi$
$182$	−10.2280	−	10.8410i	−0.758150	−	0.803592i
$183$	0.0119968	+	0.256431i	0.000886828	+	0.0189560i
$184$	−2.08949	−	1.37428i	−0.154039	−	0.101313i
$185$	17.1208	+	4.05771i	1.25875	+	0.298329i
$186$	0.119715	+	0.00136818i	0.00877793	+	0.000100320i
$187$	7.22987	+	0.845050i	0.528700	+	0.0617962i
$188$	−5.62035	−	9.73474i	−0.409906	−	0.709979i
$189$	−7.71202	+	22.8749i	−0.560967	+	1.66390i
$190$	−9.26382	+	16.0454i	−0.672068	+	1.16406i
$191$	5.34412	−	7.17840i	0.386687	−	0.519411i	−0.565573	−	0.824698i	$-0.691345\pi$
$191$	5.34412	−	7.17840i	0.386687	−	0.519411i	0.952260	+	0.305287i	$0.0987525\pi$
$192$	−0.281255	−	1.70906i	−0.0202978	−	0.123341i
$193$	4.91322	+	16.4113i	0.353661	+	1.18131i	0.931066	+	0.364852i	$0.118880\pi$
$193$	4.91322	+	16.4113i	0.353661	+	1.18131i	−0.577404	+	0.816458i	$0.695934\pi$
$194$	15.8661	−	7.96826i	1.13912	−	0.572088i
$195$	−11.8805	+	15.5832i	−0.850778	+	1.11594i
$196$	−4.18238	+	13.9701i	−0.298741	+	0.997866i
$197$	0.576101	+	3.26723i	0.0410455	+	0.232781i	0.998428	−	0.0560409i	$-0.0178477\pi$
$197$	0.576101	+	3.26723i	0.0410455	+	0.232781i	−0.957383	+	0.288821i	$0.906737\pi$
$198$	3.71765	−	8.10401i	0.264202	−	0.575927i
$199$	−2.11440	+	11.9914i	−0.149886	+	0.850046i	0.813427	+	0.581667i	$0.197599\pi$
$199$	−2.11440	+	11.9914i	−0.149886	+	0.850046i	−0.963313	+	0.268379i	$0.913512\pi$
$200$	−6.64478	−	3.33713i	−0.469857	−	0.235971i
$201$	−1.70879	+	24.5099i	−0.120529	+	1.72880i
$202$	−3.00763	+	6.97248i	−0.211616	+	0.490582i
$203$	5.65981	−	13.1209i	0.397241	−	0.920908i
$204$	3.51740	+	2.37145i	0.246267	+	0.166035i
$205$	0.00749903	+	0.00376615i	0.000523755	+	0.000263039i
$206$	−1.73557	+	9.84289i	−0.120923	+	0.685787i
$207$	0.607313	−	7.47815i	0.0422112	−	0.519767i
$208$	0.557097	+	3.15945i	0.0386277	+	0.219069i
$209$	−4.47837	+	14.9588i	−0.309775	+	1.03472i
$210$	28.1445	+	3.61610i	1.94216	+	0.249535i
$211$	−0.418441	+	0.210149i	−0.0288067	+	0.0144673i	−0.463144	−	0.886283i	$-0.653279\pi$
$211$	−0.418441	+	0.210149i	−0.0288067	+	0.0144673i	0.434338	+	0.900750i	$0.356983\pi$
$212$	−0.348014	−	1.16245i	−0.0239017	−	0.0798373i
$213$	−16.6016	−	6.25824i	−1.13752	−	0.428808i
$214$	3.73156	−	5.01236i	0.255084	−	0.342638i
$215$	−10.0875	+	17.4720i	−0.687961	+	1.19158i
$216$	4.09263	−	3.20162i	0.278468	−	0.217843i
$217$	0.160561	+	0.278100i	0.0108996	+	0.0188786i
$218$	6.22986	+	0.728166i	0.421939	+	0.0493176i
$219$	1.84587	+	3.28323i	0.124732	+	0.221860i
$220$	−10.1981	−	2.41699i	−0.687555	−	0.162954i
$221$	−6.56488	−	4.31779i	−0.441601	−	0.290446i
$222$	7.67800	+	3.96655i	0.515314	+	0.266217i
$223$	7.98105	+	8.45942i	0.534451	+	0.566485i	0.937185	−	0.348832i	$-0.113422\pi$
$223$	7.98105	+	8.45942i	0.534451	+	0.566485i	−0.402734	+	0.915317i	$0.631940\pi$
$224$	3.55883	−	2.98621i	0.237784	−	0.199525i
$225$	−0.787754	−	22.2932i	−0.0525170	−	1.48621i
$226$	−10.3405	−	8.67670i	−0.687839	−	0.577165i
$227$	1.33134	+	22.8582i	0.0883639	+	1.51715i	0.693169	+	0.720775i	$0.256214\pi$
$227$	1.33134	+	22.8582i	0.0883639	+	1.51715i	−0.604805	+	0.796374i	$0.706749\pi$
$228$	−6.32010	+	6.54737i	−0.418559	+	0.433610i
$229$	2.06512	+	2.77394i	0.136467	+	0.183307i	0.865103	−	0.501594i	$-0.167253\pi$
$229$	2.06512	+	2.77394i	0.136467	+	0.183307i	−0.728636	+	0.684901i	$0.759845\pi$
$230$	−8.75969	+	1.02386i	−0.577597	+	0.0675114i
$231$	23.7832	−	2.50470i	1.56482	−	0.164797i
$232$	−2.56984	+	1.69021i	−0.168718	+	0.110968i
$233$	7.00030	−	2.54790i	0.458605	−	0.166918i	−0.102379	−	0.994745i	$-0.532645\pi$
$233$	7.00030	−	2.54790i	0.458605	−	0.166918i	0.560983	+	0.827827i	$0.310423\pi$
$234$	−7.51232	+	6.01644i	−0.491095	+	0.393307i
$235$	−37.2490	−	13.5575i	−2.42986	−	0.884395i
$236$	−4.59510	+	1.08906i	−0.299115	+	0.0708916i
$237$	8.54559	−	27.4006i	0.555096	−	1.77986i
$238$	−0.661592	+	11.3591i	−0.0428847	+	0.736301i
$239$	−6.53242	+	6.92396i	−0.422547	+	0.447874i	−0.903317	−	0.428973i	$-0.858876\pi$
$239$	−6.53242	+	6.92396i	−0.422547	+	0.447874i	0.480770	+	0.876847i	$0.340357\pi$
$240$	−4.63379	−	3.97933i	−0.299110	−	0.256865i
$241$	−10.9673	−	25.4250i	−0.706463	−	1.63777i	−0.768625	−	0.639700i	$-0.779059\pi$
$241$	−10.9673	−	25.4250i	−0.706463	−	1.63777i	0.0621616	−	0.998066i	$-0.480201\pi$
$242$	2.16713			0.139309
$243$	14.3200	+	6.15942i	0.918626	+	0.395127i
$244$	0.148213			0.00948834
$245$	20.3684	+	47.2193i	1.30129	+	3.01673i
$246$	0.00312689	+	0.00268526i	0.000199363	+	0.000171206i
$247$	11.5670	−	12.2604i	0.735994	−	0.780108i
$248$	0.00401909	−	0.0690051i	0.000255212	−	0.00438183i
$249$	−0.277032	+	0.888275i	−0.0175562	+	0.0562921i
$250$	−8.35779	+	1.98083i	−0.528593	+	0.125279i
$251$	−5.11035	−	1.86001i	−0.322562	−	0.117403i	0.175664	−	0.984450i	$-0.443793\pi$
$251$	−5.11035	−	1.86001i	−0.322562	−	0.117403i	−0.498226	+	0.867047i	$0.666015\pi$
$252$	12.9843	+	5.06486i	0.817934	+	0.319056i
$253$	−6.98453	+	2.54216i	−0.439114	+	0.159824i
$254$	3.35351	−	2.20564i	0.210418	−	0.138394i
$255$	14.8774	−	1.56680i	0.931658	−	0.0981166i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	−1.42785	−	1.91793i	−0.0890666	−	0.119637i	0.755356	−	0.655314i	$-0.227464\pi$
$257$	−1.42785	−	1.91793i	−0.0890666	−	0.119637i	−0.844423	+	0.535677i	$0.820056\pi$
$258$	−6.88203	+	7.12951i	−0.428456	+	0.443864i
$259$	1.34779	+	23.1406i	0.0837474	+	1.43789i
$260$	8.66661	+	7.27215i	0.537480	+	0.451000i
$261$	−8.14926	−	4.32870i	−0.504427	−	0.267940i
$262$	−2.02902	+	1.70255i	−0.125353	+	0.105184i
$263$	0.126323	+	0.133895i	0.00778944	+	0.00825632i	0.731257	−	0.682102i	$-0.238934\pi$
$263$	0.126323	+	0.133895i	0.00778944	+	0.00825632i	−0.723467	+	0.690359i	$0.757453\pi$
$264$	−4.57343	−	2.36269i	−0.281475	−	0.145414i
$265$	−3.57510	−	2.35138i	−0.219617	−	0.144444i
$266$	−23.7504	−	5.62895i	−1.45623	−	0.345133i
$267$	−13.3296	−	23.7093i	−0.815760	−	1.45098i
$268$	14.0892	+	1.64680i	0.860637	+	0.100594i
$269$	14.1563	+	24.5194i	0.863125	+	1.49498i	0.868897	+	0.494992i	$0.164829\pi$
$269$	14.1563	+	24.5194i	0.863125	+	1.49498i	−0.00577268	+	0.999983i	$0.501838\pi$
$270$	3.79859	−	17.9258i	0.231175	−	1.09093i
$271$	2.89178	−	5.00871i	0.175663	−	0.304258i	−0.764727	−	0.644354i	$-0.777126\pi$
$271$	2.89178	−	5.00871i	0.175663	−	0.304258i	0.940391	+	0.340096i	$0.110460\pi$
$272$	1.46257	−	1.96457i	0.0886811	−	0.119119i
$273$	−24.1558	−	9.10594i	−1.46198	−	0.551116i
$274$	−0.470530	−	1.57168i	−0.0284258	−	0.0949487i
$275$	−19.7484	+	9.91801i	−1.19087	+	0.598079i
$276$	−4.29641	−	0.552018i	−0.258613	−	0.0332276i
$277$	5.46348	−	18.2493i	0.328269	−	1.09649i	−0.621466	−	0.783441i	$-0.713463\pi$
$277$	5.46348	−	18.2493i	0.328269	−	1.09649i	0.949735	−	0.313054i	$-0.101352\pi$
$278$	2.23501	+	12.6754i	0.134047	+	0.760217i
$279$	0.187388	−	0.0888063i	0.0112186	−	0.00531669i
$280$	2.84485	−	16.1339i	0.170012	−	0.964186i
$281$	3.46068	+	1.73802i	0.206447	+	0.103681i	0.549018	−	0.835810i	$-0.315002\pi$
$281$	3.46068	+	1.73802i	0.206447	+	0.103681i	−0.342572	+	0.939492i	$0.611298\pi$
$282$	−16.1432	−	10.8838i	−0.961313	−	0.648123i
$283$	−4.68034	+	10.8503i	−0.278218	+	0.644981i	−0.998830	−	0.0483573i	$-0.984601\pi$
$283$	−4.68034	+	10.8503i	−0.278218	+	0.644981i	0.720613	+	0.693338i	$0.243861\pi$
$284$	−4.05718	+	9.40560i	−0.240749	+	0.558119i
$285$	−2.23190	+	32.0131i	−0.132207	+	1.89629i
$286$	8.52060	+	4.27921i	0.503834	+	0.253035i
$287$	−0.00191970	+	0.0108872i	−0.000113317	+	0.000642650i
$288$	−1.73601	−	2.44668i	−0.102295	−	0.144172i
$289$	−1.91037	−	10.8342i	−0.112375	−	0.637308i
$290$	−3.11089	+	10.3911i	−0.182678	+	0.610187i
$291$	18.6445	−	24.4554i	1.09296	−	1.43360i
$292$	1.94330	−	0.975964i	0.113723	−	0.0571140i
$293$	−2.64395	−	8.83139i	−0.154461	−	0.515935i	0.845373	−	0.534177i	$-0.179378\pi$
$293$	−2.64395	−	8.83139i	−0.154461	−	0.515935i	−0.999834	+	0.0182415i	$0.994193\pi$
$294$	4.10147	+	24.9228i	0.239203	+	1.45353i
$295$	−9.94458	+	13.3579i	−0.578996	+	0.777726i
$296$	2.49475	−	4.32103i	0.145004	−	0.251155i
$297$	−0.368950	−	15.4386i	−0.0214087	−	0.895840i
$298$	5.84656	+	10.1265i	0.338682	+	0.586614i
$299$	7.96919	+	0.931465i	0.460870	+	0.0538680i
$300$	−12.8782	−	0.147179i	−0.743521	−	0.00849741i
$301$	−25.8621	−	6.12943i	−1.49067	−	0.353295i
$302$	5.40823	+	3.55705i	0.311208	+	0.204685i
$303$	0.614641	+	13.1380i	0.0353102	+	0.754756i
$304$	3.60547	+	3.82158i	0.206788	+	0.219183i
$305$	0.400382	−	0.335960i	0.0229258	−	0.0192370i
$306$	7.27655	+	1.01957i	0.415973	+	0.0582852i
$307$	0.177740	+	0.149142i	0.0101442	+	0.00851197i	0.647846	−	0.761772i	$-0.275670\pi$
$307$	0.177740	+	0.149142i	0.0101442	+	0.00851197i	−0.637701	+	0.770284i	$0.720115\pi$
$308$	−0.802815	−	13.7838i	−0.0457446	−	0.785405i
$309$	4.77512	+	16.6398i	0.271647	+	0.946604i
$310$	−0.145560	−	0.195521i	−0.00826724	−	0.0111048i
$311$	18.0894	−	2.11435i	1.02576	−	0.119894i	0.413461	−	0.910522i	$-0.364320\pi$
$311$	18.0894	−	2.11435i	1.02576	−	0.119894i	0.612296	+	0.790628i	$0.290246\pi$
$312$	3.26711	+	4.49483i	0.184964	+	0.254470i
$313$	22.7927	−	14.9910i	1.28832	−	0.847340i	0.294211	−	0.955740i	$-0.404943\pi$
$313$	22.7927	−	14.9910i	1.28832	−	0.847340i	0.994107	+	0.108400i	$0.0345727\pi$
$314$	−14.5093	+	5.28095i	−0.818807	+	0.298021i
$315$	46.5565	−	15.7499i	2.62316	−	0.887404i
$316$	−15.5719	−	5.66771i	−0.875987	−	0.318833i
$317$	13.0246	−	3.08690i	0.731537	−	0.173377i	0.152066	−	0.988370i	$-0.451407\pi$
$317$	13.0246	−	3.08690i	0.731537	−	0.173377i	0.579471	+	0.814993i	$0.303259\pi$
$318$	−1.42472	−	1.54511i	−0.0798943	−	0.0866457i
$319$	−0.531531	+	9.12603i	−0.0297600	+	0.510959i
$320$	−2.41998	+	2.56503i	−0.135281	+	0.143390i
$321$	2.00114	−	10.6367i	0.111693	−	0.593685i
$322$	−4.60189	−	10.6684i	−0.256453	−	0.594526i
$323$	−12.8680			−0.715995
$324$	3.93863	−	8.09242i	0.218813	−	0.449579i
$325$	23.8551			1.32325
$326$	2.00109	+	4.63906i	0.110830	+	0.256934i
$327$	10.2505	−	3.59876i	0.566854	−	0.199012i
$328$	0.00163301	−	0.00173089i	9.01677e−5	−	9.55722e-5i
$329$	3.03639	−	52.1329i	0.167402	−	2.87418i
$330$	−17.7103	+	3.98422i	−0.974920	+	0.219324i
$331$	2.88099	−	0.682806i	0.158353	−	0.0375304i	−0.150674	−	0.988583i	$-0.548145\pi$
$331$	2.88099	−	0.682806i	0.158353	−	0.0375304i	0.309028	+	0.951053i	$0.399996\pi$
$332$	0.504811	+	0.183736i	0.0277051	+	0.0100838i
$333$	14.9646	+	0.342093i	0.820054	+	0.0187466i
$334$	21.1503	−	7.69809i	1.15729	−	0.421221i
$335$	41.7936	−	27.4881i	2.28343	−	1.50183i
$336$	3.27133	−	7.35164i	0.178466	−	0.401065i
$337$	4.66280	−	0.545003i	0.253999	−	0.0296882i	0.0118593	−	0.999930i	$-0.496225\pi$
$337$	4.66280	−	0.545003i	0.253999	−	0.0296882i	0.242139	+	0.970241i	$0.422151\pi$
$338$	1.61681	+	2.17175i	0.0879429	+	0.118128i
$339$	−22.6868	−	5.65147i	−1.23218	−	0.306946i
$340$	−0.502195	−	8.62235i	−0.0272353	−	0.467613i
$341$	−0.157370	−	0.132049i	−0.00852205	−	0.00715085i
$342$	−4.86445	+	14.9924i	−0.263039	+	0.810696i
$343$	−26.9857	+	22.6437i	−1.45709	+	1.22264i
$344$	3.92604	+	4.16136i	0.211678	+	0.224366i
$345$	−12.8576	+	8.24764i	−0.692230	+	0.444038i
$346$	−0.477662	−	0.314163i	−0.0256792	−	0.0168895i
$347$	9.36289	+	2.21905i	0.502626	+	0.119125i	0.474105	−	0.880469i	$-0.342772\pi$
$347$	9.36289	+	2.21905i	0.502626	+	0.119125i	0.0285217	+	0.999593i	$0.490920\pi$
$348$	−2.71632	+	4.58304i	−0.145610	+	0.245677i
$349$	9.33586	+	1.09121i	0.499737	+	0.0584109i	0.362228	−	0.932090i	$-0.382016\pi$
$349$	9.33586	+	1.09121i	0.499737	+	0.0584109i	0.137509	+	0.990500i	$0.456090\pi$
$350$	−17.2721	−	29.9161i	−0.923232	−	1.59909i
$351$	−7.12355	+	15.0716i	−0.380227	+	0.804461i
$352$	−1.48601	+	2.57384i	−0.0792044	+	0.137186i
$353$	−14.8837	+	19.9923i	−0.792180	+	1.06408i	0.204188	+	0.978932i	$0.434545\pi$
$353$	−14.8837	+	19.9923i	−0.792180	+	1.06408i	−0.996368	+	0.0851507i	$0.972863\pi$
$354$	−6.32547	+	5.18568i	−0.336195	+	0.275616i
$355$	10.3600	+	34.6049i	0.549853	+	1.83664i
$356$	−14.0332	+	7.04776i	−0.743760	+	0.373530i
$357$	7.59859	+	18.1841i	0.402160	+	0.962406i
$358$	−6.47401	+	21.6247i	−0.342162	+	1.14290i
$359$	−4.06017	−	23.0264i	−0.214288	−	1.21529i	−0.882138	−	0.470991i	$-0.843897\pi$
$359$	−4.06017	−	23.0264i	−0.214288	−	1.21529i	0.667850	−	0.744295i	$-0.267215\pi$
$360$	−10.2357	−	2.67438i	−0.539467	−	0.140952i
$361$	1.49405	−	8.47318i	0.0786342	−	0.445957i
$362$	−0.832525	−	0.418110i	−0.0437566	−	0.0219754i
$363$	3.37336	−	1.64616i	0.177055	−	0.0864011i
$364$	−5.90332	+	13.6854i	−0.309418	+	0.717312i
$365$	3.03738	−	7.04144i	0.158984	−	0.368566i
$366$	0.230708	−	0.112583i	0.0120593	−	0.00588480i
$367$	−12.0487	−	6.05106i	−0.628935	−	0.315863i	0.105626	−	0.994406i	$-0.466315\pi$
$367$	−12.0487	−	6.05106i	−0.628935	−	0.315863i	−0.734561	+	0.678543i	$0.762612\pi$
$368$	−0.434281	+	2.46293i	−0.0226385	+	0.128389i
$369$	0.00690704	+	0.00180467i	0.000359566	+	9.39475e-5i
$370$	−3.05536	−	17.3278i	−0.158840	−	0.900829i
$371$	1.61678	−	5.40041i	0.0839389	−	0.280375i
$372$	−0.0461604	−	0.110466i	−0.00239331	−	0.00572740i
$373$	19.2110	−	9.64813i	0.994708	−	0.499561i	0.124486	−	0.992221i	$-0.460272\pi$
$373$	19.2110	−	9.64813i	0.994708	−	0.499561i	0.870222	+	0.492660i	$0.163975\pi$
$374$	−2.08767	−	6.97329i	−0.107951	−	0.360580i
$375$	−11.5051	+	9.43197i	−0.594120	+	0.487065i
$376$	−6.71248	+	9.01643i	−0.346170	+	0.464987i
$377$	4.93397	−	8.54589i	0.254112	−	0.440136i
$378$	24.0586	−	1.97896i	1.23744	−	0.101787i
$379$	−5.31897	−	9.21272i	−0.273217	−	0.473226i	0.696467	−	0.717589i	$-0.254754\pi$
$379$	−5.31897	−	9.21272i	−0.273217	−	0.473226i	−0.969684	+	0.244363i	$0.921421\pi$
$380$	18.4024	+	2.15093i	0.944022	+	0.110340i
$381$	3.54466	−	5.98063i	0.181598	−	0.306397i
$382$	−8.70802	−	2.06384i	−0.445541	−	0.105595i
$383$	−7.31747	−	4.81277i	−0.373905	−	0.245921i	0.348623	−	0.937263i	$-0.386649\pi$
$383$	−7.31747	−	4.81277i	−0.373905	−	0.245921i	−0.722528	+	0.691342i	$0.757020\pi$
$384$	−1.45789	+	0.935178i	−0.0743976	+	0.0477231i
$385$	−33.4131	−	35.4158i	−1.70289	−	1.80496i
$386$	13.1231	−	11.0116i	0.667947	−	0.560474i
$387$	−5.29696	+	16.3254i	−0.269259	+	0.829867i
$388$	−13.6008	−	11.4125i	−0.690478	−	0.579380i
$389$	−1.90200	−	32.6560i	−0.0964350	−	1.65573i	−0.606127	−	0.795368i	$-0.707278\pi$
$389$	−1.90200	−	32.6560i	−0.0964350	−	1.65573i	0.509692	−	0.860357i	$-0.329760\pi$
$390$	19.0144	+	4.73663i	0.962831	+	0.239849i
$391$	−3.65777	−	4.91324i	−0.184981	−	0.248473i
$392$	14.4841	−	1.69295i	0.731560	−	0.0855071i
$393$	−1.86511	+	4.19144i	−0.0940822	+	0.211430i
$394$	2.77184	−	1.82307i	0.139643	−	0.0918449i
$395$	−54.9132	+	19.9868i	−2.76298	+	1.00564i
$396$	−8.91371	−	0.203769i	−0.447931	−	0.0102398i
$397$	17.1234	+	6.23242i	0.859400	+	0.312796i	0.733867	−	0.679293i	$-0.237714\pi$
$397$	17.1234	+	6.23242i	0.859400	+	0.312796i	0.125533	+	0.992089i	$0.459936\pi$
$398$	11.8481	−	2.80806i	0.593894	−	0.140755i
$399$	−41.2457	+	9.27889i	−2.06487	+	0.464526i
$400$	−0.432347	+	7.42312i	−0.0216174	+	0.371156i
$401$	−1.52550	+	1.61693i	−0.0761797	+	0.0807458i	−0.764342	−	0.644811i	$-0.776936\pi$
$401$	−1.52550	+	1.61693i	−0.0761797	+	0.0807458i	0.688162	+	0.725557i	$0.258418\pi$
$402$	23.1822	−	8.13884i	1.15622	−	0.405929i
$403$	0.0878333	+	0.203621i	0.00437529	+	0.0101431i
$404$	7.59350			0.377791
$405$	−7.70363	−	30.7887i	−0.382796	−	1.52990i
$406$	−14.2896			−0.709180
$407$	−5.87341	−	13.6161i	−0.291134	−	0.674925i
$408$	0.784337	−	4.16902i	0.0388305	−	0.206397i
$409$	−7.25912	+	7.69422i	−0.358940	+	0.380454i	−0.881529	−	0.472131i	$-0.843485\pi$
$409$	−7.25912	+	7.69422i	−0.358940	+	0.380454i	0.522588	+	0.852585i	$0.324967\pi$
$410$	0.000487929	−	0.00837742i	2.40971e−5	−	0.000413731i
$411$	−1.92628	−	2.08906i	−0.0950165	−	0.103046i
$412$	9.72533	−	2.30494i	0.479132	−	0.113556i
$413$	−20.6158	−	7.50355i	−1.01444	−	0.369226i
$414$	−7.10710	+	2.40430i	−0.349295	+	0.118165i
$415$	1.78018	−	0.647932i	0.0873856	−	0.0318057i
$416$	2.68040	−	1.76293i	0.131418	−	0.0864348i
$417$	13.1073	+	18.0327i	0.641865	+	0.883066i
$418$	15.5092	−	1.81277i	0.758580	−	0.0886653i
$419$	−5.04072	−	6.77086i	−0.246255	−	0.330778i	0.661760	−	0.749716i	$-0.269810\pi$
$419$	−5.04072	−	6.77086i	−0.246255	−	0.330778i	−0.908015	+	0.418938i	$0.862402\pi$
$420$	−7.82710	−	27.2750i	−0.381924	−	1.33088i
$421$	−0.0721923	−	1.23949i	−0.00351844	−	0.0604092i	0.996092	−	0.0883228i	$-0.0281507\pi$
$421$	−0.0721923	−	1.23949i	−0.00351844	−	0.0604092i	−0.999610	+	0.0279136i	$0.991114\pi$
$422$	0.358698	+	0.300984i	0.0174612	+	0.0146517i
$423$	−33.3959	−	4.67936i	−1.62376	−	0.227518i
$424$	−0.929537	+	0.779974i	−0.0451423	+	0.0378789i
$425$	−12.4975	−	13.2466i	−0.606220	−	0.642556i
$426$	0.829127	+	17.7226i	0.0401713	+	0.858663i
$427$	0.575279	+	0.378367i	0.0278397	+	0.0183105i
$428$	−6.08042	−	1.44109i	−0.293908	−	0.0696575i
$429$	16.5137	+	0.188728i	0.797287	+	0.00911188i
$430$	20.0386	+	2.34217i	0.966345	+	0.112950i
$431$	14.6183	+	25.3197i	0.704140	+	1.21961i	0.967001	+	0.254772i	$0.0820006\pi$
$431$	14.6183	+	25.3197i	0.704140	+	1.21961i	−0.262861	+	0.964834i	$0.584666\pi$
$432$	−4.56079	−	2.48982i	−0.219431	−	0.119792i
$433$	10.4993	−	18.1853i	0.504564	−	0.873931i	−0.495422	−	0.868653i	$-0.664986\pi$
$433$	10.4993	−	18.1853i	0.504564	−	0.873931i	0.999986	−	0.00527848i	$-0.00168020\pi$
$434$	0.191761	−	0.257579i	0.00920480	−	0.0123642i
$435$	3.05071	+	18.5378i	0.146271	+	0.888822i
$436$	−1.79891	−	6.00877i	−0.0861520	−	0.287768i
$437$	11.7421	−	5.89709i	0.561699	−	0.282096i
$438$	2.28360	−	2.99533i	0.109115	−	0.143122i
$439$	5.83254	−	19.4820i	0.278372	−	0.929827i	−0.698429	−	0.715679i	$-0.746117\pi$
$439$	5.83254	−	19.4820i	0.278372	−	0.929827i	0.976801	−	0.214148i	$-0.0686974\pi$
$440$	1.81994	+	10.3214i	0.0867621	+	0.492052i
$441$	25.3158	+	35.6794i	1.20552	+	1.69902i
$442$	−1.36445	+	7.73816i	−0.0649001	+	0.368067i
$443$	−6.86038	−	3.44541i	−0.325946	−	0.163696i	0.278300	−	0.960494i	$-0.410229\pi$
$443$	−6.86038	−	3.44541i	−0.325946	−	0.163696i	−0.604246	+	0.796798i	$0.706526\pi$
$444$	0.601051	−	8.62113i	0.0285246	−	0.409141i
$445$	−21.9339	+	50.8486i	−1.03977	+	2.41045i
$446$	4.60644	−	10.6789i	0.218121	−	0.505662i
$447$	16.7929	+	11.3219i	0.794277	+	0.535507i
$448$	−4.15157	−	2.08500i	−0.196143	−	0.0985068i
$449$	0.579342	−	3.28561i	0.0273409	−	0.155058i	−0.968081	−	0.250638i	$-0.919360\pi$
$449$	0.579342	−	3.28561i	0.0273409	−	0.155058i	0.995422	+	0.0955804i	$0.0304707\pi$
$450$	−20.1579	+	9.55321i	−0.950255	+	0.450342i
$451$	−0.00122809	−	0.00696487i	−5.78287e−5	−	0.000327963i
$452$	−3.87143	+	12.9315i	−0.182097	+	0.608245i
$453$	11.1204	+	1.42879i	0.522481	+	0.0671302i
$454$	20.4614	−	10.2761i	0.960302	−	0.482282i
$455$	15.0741	+	50.3512i	0.706687	+	2.36050i
$456$	8.51516	+	3.20993i	0.398759	+	0.150319i
$457$	−20.4969	+	27.5321i	−0.958803	+	1.28790i	−0.00114161	+	0.999999i	$0.500363\pi$
$457$	−20.4969	+	27.5321i	−0.958803	+	1.28790i	−0.957661	+	0.287897i	$0.907044\pi$
$458$	1.72913	−	2.99493i	0.0807967	−	0.139944i
$459$	12.1011	−	3.94023i	0.564833	−	0.183914i
$460$	4.40966	+	7.63776i	0.205602	+	0.356112i
$461$	−16.3981	−	1.91666i	−0.763735	−	0.0892678i	−0.274698	−	0.961531i	$-0.588578\pi$
$461$	−16.3981	−	1.91666i	−0.763735	−	0.0892678i	−0.489037	+	0.872263i	$0.662652\pi$
$462$	−11.7199	−	20.8460i	−0.545259	−	0.969845i
$463$	17.2695	+	4.09295i	0.802582	+	0.190215i	0.611382	−	0.791336i	$-0.290614\pi$
$463$	17.2695	+	4.09295i	0.802582	+	0.190215i	0.191200	+	0.981551i	$0.438762\pi$
$464$	2.56984	+	1.69021i	0.119302	+	0.0784661i
$465$	−0.375096	−	0.193780i	−0.0173947	−	0.00898631i
$466$	−5.11220	−	5.41861i	−0.236818	−	0.251012i
$467$	19.0368	−	15.9738i	0.880920	−	0.739179i	−0.0854484	−	0.996343i	$-0.527232\pi$
$467$	19.0368	−	15.9738i	0.880920	−	0.739179i	0.966368	+	0.257163i	$0.0827878\pi$
$468$	8.49987	+	4.51494i	0.392907	+	0.208703i
$469$	50.4826	+	42.3599i	2.33107	+	1.95600i
$470$	2.30483	+	39.5725i	0.106314	+	1.82534i
$471$	−18.5737	+	19.2416i	−0.855832	+	0.886608i
$472$	2.82001	+	3.78794i	0.129802	+	0.174354i
$473$	16.8882	−	1.97394i	0.776518	−	0.0907619i
$474$	−28.5444	+	3.00612i	−1.31109	+	0.138076i
$475$	32.6398	−	21.4675i	1.49762	−	0.984997i
$476$	10.6922	−	3.89163i	0.490074	−	0.178372i
$477$	−3.39139	−	1.32290i	−0.155281	−	0.0605714i
$478$	8.94505	+	3.25573i	0.409137	+	0.148914i
$479$	16.3637	−	3.87826i	0.747676	−	0.177202i	0.160921	−	0.986967i	$-0.448554\pi$
$479$	16.3637	−	3.87826i	0.747676	−	0.177202i	0.586754	+	0.809765i	$0.300405\pi$
$480$	−1.81853	+	5.83095i	−0.0830044	+	0.266145i
$481$	−0.930739	+	15.9802i	−0.0424381	+	0.728633i
$482$	−19.0017	+	20.1406i	−0.865504	+	0.917380i
$483$	−15.2670	−	13.1108i	−0.694675	−	0.596561i
$484$	−0.858357	−	1.98990i	−0.0390162	−	0.0904498i
$485$	−62.6104			−2.84299
$486$	−0.0161667	−	15.5884i	−0.000733338	−	0.707106i
$487$	−8.26367			−0.374463			−0.187231	−	0.982316i	$-0.559951\pi$
$487$	−8.26367			−0.374463			−0.187231	+	0.982316i	$0.559951\pi$
$488$	−0.0587040	−	0.136091i	−0.00265741	−	0.00616056i
$489$	6.63875	+	5.70111i	0.300215	+	0.257813i
$490$	35.2900	−	37.4052i	1.59424	−	1.68979i
$491$	−0.917071	+	15.7455i	−0.0413868	+	0.710584i	0.912252	+	0.409630i	$0.134342\pi$
$491$	−0.917071	+	15.7455i	−0.0413868	+	0.710584i	−0.953639	+	0.300954i	$0.902695\pi$
$492$	0.00122715	−	0.00393473i	5.53242e−5	−	0.000177391i
$493$	−7.33036	+	1.73733i	−0.330143	+	0.0782453i
$494$	−15.8391	−	5.76497i	−0.712636	−	0.259378i
$495$	−24.5414	+	19.6546i	−1.10305	+	0.883411i
$496$	−0.0649534	+	0.0236411i	−0.00291650	+	0.00106152i
$497$	−39.7590	+	26.1499i	−1.78343	+	1.17298i
$498$	0.925355	−	0.0974528i	0.0414661	−	0.00436696i
$499$	27.4911	−	3.21324i	1.23067	−	0.143845i	0.524204	−	0.851593i	$-0.324363\pi$
$499$	27.4911	−	3.21324i	1.23067	−	0.143845i	0.706465	+	0.707748i	$0.250289\pi$
$500$	5.12918	+	6.88969i	0.229384	+	0.308116i
$501$	27.0751	−	28.0487i	1.20963	−	1.25312i
$502$	0.316210	+	5.42912i	0.0141132	+	0.242313i
$503$	7.36897	+	6.18330i	0.328566	+	0.275700i	0.792115	−	0.610371i	$-0.208980\pi$
$503$	7.36897	+	6.18330i	0.328566	+	0.275700i	−0.463549	+	0.886071i	$0.653424\pi$
$504$	−0.492178	−	13.9285i	−0.0219234	−	0.620424i
$505$	20.5131	−	17.2125i	0.912821	−	0.765948i
$506$	5.10068	+	5.40641i	0.226753	+	0.240344i
$507$	4.16640	+	2.15242i	0.185036	+	0.0955921i
$508$	−3.35351	−	2.20564i	−0.148788	−	0.0978593i
$509$	−18.3567	−	4.35063i	−0.813648	−	0.192838i	−0.197332	−	0.980337i	$-0.563228\pi$
$509$	−18.3567	−	4.35063i	−0.813648	−	0.192838i	−0.616317	+	0.787499i	$0.711376\pi$
$510$	−7.33129	−	13.0401i	−0.324635	−	0.577424i
$511$	10.0343	+	1.17285i	0.443893	+	0.0518836i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	3.81629	+	27.0322i	0.168493	+	1.19350i
$514$	−1.19553	+	2.07072i	−0.0527327	+	0.0913357i
$515$	21.0473	−	28.2714i	0.927454	−	1.24579i
$516$	9.27226	+	3.49533i	0.408188	+	0.153874i
$517$	9.58139	+	32.0041i	0.421389	+	1.40754i
$518$	20.7142	−	10.4031i	0.910131	−	0.457085i
$519$	−0.982167	−	0.126192i	−0.0431123	−	0.00553922i
$520$	3.24474	−	10.8382i	0.142291	−	0.475285i
$521$	2.41495	+	13.6959i	0.105801	+	0.600027i	0.990897	+	0.134619i	$0.0429811\pi$
$521$	2.41495	+	13.6959i	0.105801	+	0.600027i	−0.885096	+	0.465408i	$0.845908\pi$
$522$	−0.746928	+	9.19729i	−0.0326921	+	0.402555i
$523$	−3.32812	+	18.8747i	−0.145529	+	0.825333i	0.821413	+	0.570334i	$0.193186\pi$
$523$	−3.32812	+	18.8747i	−0.145529	+	0.825333i	−0.966941	+	0.254999i	$0.917925\pi$
$524$	2.36696	+	1.18873i	0.103401	+	0.0519300i
$525$	−49.6102	−	33.4475i	−2.16516	−	1.45977i
$526$	0.0729104	−	0.169025i	0.00317904	−	0.00736985i
$527$	0.0670541	−	0.155449i	0.00292092	−	0.00677146i
$528$	−0.358019	+	5.13521i	−0.0155808	+	0.223482i
$529$	−14.9642	−	7.51531i	−0.650618	−	0.326753i
$530$	−0.743050	+	4.21405i	−0.0322760	+	0.183047i
$531$	−5.90716	+	12.8769i	−0.256349	+	0.558809i
$532$	4.23847	+	24.0375i	0.183761	+	1.04216i
$533$	−0.00218955	+	0.00731361i	−9.48400e−5	+	0.000316788i
$534$	−16.4906	+	21.6302i	−0.713619	+	0.936032i
$535$	−19.6922	+	9.88981i	−0.851369	+	0.427574i
$536$	−4.06835	−	13.5892i	−0.175726	−	0.586965i
$537$	6.34877	+	38.5787i	0.273970	+	1.66479i
$538$	16.9071	−	22.7102i	0.728917	−	0.979106i
$539$	21.6701	−	37.5337i	0.933396	−	1.61669i
$540$	−17.9643	+	3.61212i	−0.773061	+	0.155441i
$541$	−8.69771	−	15.0649i	−0.373944	−	0.647690i	0.616224	−	0.787571i	$-0.288661\pi$
$541$	−8.69771	−	15.0649i	−0.373944	−	0.647690i	−0.990168	+	0.139881i	$0.955328\pi$
$542$	−5.74446	−	0.671431i	−0.246746	−	0.0288404i
$543$	−1.61351	−	0.0184401i	−0.0692422	−	0.000791342i
$544$	−2.38319	−	0.564827i	−0.102178	−	0.0242167i
$545$	−18.4799	−	12.1544i	−0.791592	−	0.520638i
$546$	1.20641	+	25.7869i	0.0516294	+	1.10358i
$547$	−6.13961	−	6.50761i	−0.262511	−	0.278245i	0.582689	−	0.812695i	$-0.302000\pi$
$547$	−6.13961	−	6.50761i	−0.262511	−	0.278245i	−0.845200	+	0.534450i	$0.820519\pi$
$548$	−1.25678	+	1.05456i	−0.0536868	+	0.0450486i
$549$	0.273601	−	0.350493i	0.0116770	−	0.0149587i
$550$	16.9288	+	14.2050i	0.721847	+	0.605702i
$551$	−0.939642	−	16.1330i	−0.0400301	−	0.687290i
$552$	1.19485	+	4.16368i	0.0508562	+	0.177218i
$553$	−45.9725	−	61.7519i	−1.95495	−	2.62596i
$554$	−18.9208	+	2.21152i	−0.803867	+	0.0939586i
$555$	−17.9182	−	24.6516i	−0.760586	−	1.04640i
$556$	10.7535	−	7.07267i	0.456049	−	0.299948i
$557$	23.3027	−	8.48147i	0.987365	−	0.359372i	0.202666	−	0.979248i	$-0.435039\pi$
$557$	23.3027	−	8.48147i	0.987365	−	0.359372i	0.784700	+	0.619876i	$0.212817\pi$
$558$	−0.155764	−	0.136888i	−0.00659401	−	0.00579493i
$559$	−17.2474	−	6.27754i	−0.729488	−	0.265512i
$560$	−15.9412	+	3.77814i	−0.673639	+	0.159655i
$561$	−8.54660	−	9.26882i	−0.360838	−	0.391330i
$562$	0.225171	−	3.86604i	0.00949828	−	0.163079i
$563$	8.35655	−	8.85743i	0.352187	−	0.373296i	−0.526925	−	0.849912i	$-0.676655\pi$
$563$	8.35655	−	8.85743i	0.352187	−	0.373296i	0.879112	+	0.476616i	$0.158137\pi$
$564$	−3.59973	+	19.1338i	−0.151576	+	0.805678i
$565$	18.8540	+	43.7086i	0.793196	+	1.83883i
$566$	11.8167			0.496692
$567$	35.9464	−	21.3555i	1.50961	−	0.896846i
$568$	10.2433			0.429801
$569$	−6.04088	−	14.0043i	−0.253247	−	0.587092i	0.743406	−	0.668840i	$-0.233209\pi$
$569$	−6.04088	−	14.0043i	−0.253247	−	0.587092i	−0.996653	+	0.0817480i	$0.973950\pi$
$570$	30.2790	−	10.6304i	1.26825	−	0.445258i
$571$	−9.55204	+	10.1246i	−0.399740	+	0.423700i	−0.895709	−	0.444640i	$-0.853332\pi$
$571$	−9.55204	+	10.1246i	−0.399740	+	0.423700i	0.495969	+	0.868340i	$0.334813\pi$
$572$	0.554399	−	9.51866i	0.0231806	−	0.397995i
$573$	−15.1226	+	3.40208i	−0.631755	+	0.142124i
$574$	0.0107571	−	0.00254949i	0.000448995	−	0.000106414i
$575$	17.4746	+	6.36024i	0.728742	+	0.265241i
$576$	−1.55899	+	2.56312i	−0.0649577	+	0.106797i
$577$	−36.3064	+	13.2145i	−1.51146	+	0.550125i	−0.958997	−	0.283415i	$-0.908533\pi$
$577$	−36.3064	+	13.2145i	−1.51146	+	0.550125i	−0.552459	+	0.833540i	$0.686311\pi$
$578$	−9.19151	+	6.04535i	−0.382316	+	0.251453i
$579$	12.0629	−	27.1090i	0.501319	−	1.12661i
$580$	10.7734	−	1.25924i	0.447343	−	0.0522869i
$581$	1.49034	+	2.00188i	0.0618298	+	0.0830518i
$582$	−29.8400	−	7.43337i	−1.23691	−	0.308123i
$583$	0.209689	+	3.60021i	0.00868441	+	0.149106i
$584$	−1.66585	−	1.39781i	−0.0689333	−	0.0578419i
$585$	33.1958	−	7.07037i	1.37248	−	0.292324i
$586$	−7.06191	+	5.92565i	−0.291725	+	0.244786i
$587$	15.6512	+	16.5893i	0.645993	+	0.684713i	0.964763	−	0.263119i	$-0.0847513\pi$
$587$	15.6512	+	16.5893i	0.645993	+	0.684713i	−0.318770	+	0.947832i	$0.603270\pi$
$588$	21.2600	−	13.6375i	0.876749	−	0.562399i
$589$	0.303418	+	0.199561i	0.0125021	+	0.00822278i
$590$	16.2043	+	3.84048i	0.667119	+	0.158110i
$591$	2.92984	−	4.94329i	0.120517	−	0.203340i
$592$	−4.95576	−	0.579245i	−0.203680	−	0.0238068i
$593$	1.39786	+	2.42116i	0.0574031	+	0.0994251i	0.893299	−	0.449463i	$-0.148385\pi$
$593$	1.39786	+	2.42116i	0.0574031	+	0.0994251i	−0.835896	+	0.548888i	$0.815051\pi$
$594$	−14.0299	+	6.45371i	−0.575652	+	0.264799i
$595$	20.0625	−	34.7492i	0.822481	−	1.42458i
$596$	6.98264	−	9.37932i	0.286020	−	0.384192i
$597$	16.3098	−	13.3709i	0.667516	−	0.547235i
$598$	−2.30115	−	7.68637i	−0.0941010	−	0.314319i
$599$	−10.0578	+	5.05124i	−0.410952	+	0.206388i	−0.642250	−	0.766495i	$-0.721999\pi$
$599$	−10.0578	+	5.05124i	−0.410952	+	0.206388i	0.231298	+	0.972883i	$0.425703\pi$
$600$	4.96564	+	11.8832i	0.202721	+	0.485131i
$601$	−13.9497	+	46.5954i	−0.569022	+	1.90067i	−0.163632	+	0.986521i	$0.552321\pi$
$601$	−13.9497	+	46.5954i	−0.569022	+	1.90067i	−0.405390	+	0.914144i	$0.632864\pi$
$602$	4.61531	+	26.1748i	0.188106	+	1.06680i
$603$	29.9031	−	30.2782i	1.21775	−	1.23302i
$604$	1.12405	−	6.37479i	0.0457369	−	0.259387i
$605$	−6.82935	−	3.42983i	−0.277653	−	0.139442i
$606$	11.8200	−	5.76805i	0.480156	−	0.234311i
$607$	13.7621	−	31.9040i	0.558585	−	1.29495i	−0.371784	−	0.928319i	$-0.621254\pi$
$607$	13.7621	−	31.9040i	0.558585	−	1.29495i	0.930368	−	0.366626i	$-0.119487\pi$
$608$	2.08098	−	4.82425i	0.0843949	−	0.195649i
$609$	−22.2432	+	10.8544i	−0.901338	+	0.439843i
$610$	−0.467067	−	0.234570i	−0.0189110	−	0.00949746i
$611$	6.26216	−	35.5145i	0.253340	−	1.43676i
$612$	−1.94590	−	7.08528i	−0.0786585	−	0.286405i
$613$	−0.862381	−	4.89080i	−0.0348312	−	0.197538i	0.962427	−	0.271542i	$-0.0875334\pi$
$613$	−0.862381	−	4.89080i	−0.0348312	−	0.197538i	−0.997258	+	0.0740038i	$0.976422\pi$
$614$	0.0665451	−	0.222276i	0.00268554	−	0.00897033i
$615$	−0.00560401	−	0.0134109i	−0.000225976	−	0.000540781i
$616$	−12.3385	+	6.19664i	−0.497133	+	0.249670i
$617$	0.381205	+	1.27331i	0.0153467	+	0.0512616i	0.965320	−	0.261070i	$-0.0840753\pi$
$617$	0.381205	+	1.27331i	0.0153467	+	0.0512616i	−0.949973	+	0.312331i	$0.898890\pi$
$618$	13.3876	−	10.9753i	0.538528	−	0.441490i
$619$	−15.1038	+	20.2880i	−0.607074	+	0.815442i	−0.994309	−	0.106539i	$-0.966023\pi$
$619$	−15.1038	+	20.2880i	−0.607074	+	0.815442i	0.387234	+	0.921981i	$0.373430\pi$
$620$	−0.121877	+	0.211097i	−0.00489469	+	0.00847786i
$621$	−9.23660	+	9.14111i	−0.370652	+	0.366820i
$622$	−9.10628	−	15.7725i	−0.365129	−	0.632422i
$623$	−72.4612	−	8.46950i	−2.90310	−	0.339323i
$624$	2.83319	−	4.78022i	0.113418	−	0.191362i
$625$	−6.70320	−	1.58869i	−0.268128	−	0.0635475i
$626$	−22.7927	−	14.9910i	−0.910979	−	0.599160i
$627$	22.7646	−	14.6026i	0.909132	−	0.583172i
$628$	10.5959	+	11.2310i	0.422822	+	0.448165i
$629$	9.36131	−	7.85507i	0.373260	−	0.313202i
$630$	−32.9019	−	36.5108i	−1.31084	−	1.45462i
$631$	−34.5526	−	28.9931i	−1.37552	−	1.15420i	−0.970837	−	0.239740i	$-0.922938\pi$
$631$	−34.5526	−	28.9931i	−1.37552	−	1.15420i	−0.404681	−	0.914458i	$-0.632618\pi$
$632$	0.963533	+	16.5432i	0.0383273	+	0.658054i
$633$	0.786978	+	0.196042i	0.0312796	+	0.00779198i
$634$	−7.99323	−	10.7368i	−0.317452	−	0.426412i
$635$	−14.0588	+	1.64324i	−0.557906	+	0.0652098i
$636$	−0.854446	+	1.92019i	−0.0338810	+	0.0761404i
$637$	−39.0877	+	25.7084i	−1.54871	+	1.01860i
$638$	8.59019	−	3.12657i	0.340089	−	0.123782i
$639$	14.7528	+	26.9572i	0.583611	+	1.06641i
$640$	3.31376	+	1.20611i	0.130988	+	0.0476757i
$641$	46.9302	−	11.1227i	1.85363	−	0.439319i	0.856578	−	0.516018i	$-0.172586\pi$
$641$	46.9302	−	11.1227i	1.85363	−	0.439319i	0.997054	+	0.0766993i	$0.0244382\pi$
$642$	−10.5594	+	2.37552i	−0.416748	+	0.0937542i
$643$	−0.488608	+	8.38908i	−0.0192688	+	0.330833i	0.974874	+	0.222758i	$0.0715058\pi$
$643$	−0.488608	+	8.38908i	−0.0192688	+	0.330833i	−0.994143	+	0.108075i	$0.965531\pi$
$644$	−7.97317	+	8.45106i	−0.314187	+	0.333019i
$645$	32.9711	−	11.5755i	1.29824	−	0.455787i
$646$	5.09676	+	11.8156i	0.200529	+	0.464879i
$647$	6.93096			0.272484			0.136242	−	0.990676i	$-0.456497\pi$
$647$	6.93096			0.272484			0.136242	+	0.990676i	$0.456497\pi$
$648$	−8.99060	−	0.411269i	−0.353184	−	0.0161562i
$649$	14.0350			0.550922
$650$	−9.44854	−	21.9042i	−0.370602	−	0.859152i
$651$	0.102836	−	0.546610i	0.00403047	−	0.0214233i
$652$	3.46706	−	3.67487i	0.135781	−	0.143919i
$653$	−1.61928	+	27.8020i	−0.0633674	+	1.08798i	0.805393	+	0.592742i	$0.201955\pi$
$653$	−1.61928	+	27.8020i	−0.0633674	+	1.08798i	−0.868760	+	0.495234i	$0.835082\pi$
$654$	−7.36446	−	7.98679i	−0.287973	−	0.312308i
$655$	9.08867	−	2.15405i	0.355124	−	0.0841658i
$656$	−0.00223613		0.000813884i	−8.73061e−5		3.17768e-5i
$657$	1.27939	−	6.39715i	0.0499137	−	0.249577i
$658$	−49.0719	+	17.8607i	−1.91302	+	0.696283i
$659$	−16.7287	+	11.0026i	−0.651656	+	0.428601i	−0.831828	−	0.555034i	$-0.812705\pi$
$659$	−16.7287	+	11.0026i	−0.651656	+	0.428601i	0.180171	+	0.983635i	$0.442335\pi$
$660$	10.6731	+	14.6838i	0.415449	+	0.571567i
$661$	31.7358	−	3.70938i	1.23438	−	0.144278i	0.526231	−	0.850342i	$-0.323605\pi$
$661$	31.7358	−	3.70938i	1.23438	−	0.144278i	0.708149	+	0.706063i	$0.249531\pi$
$662$	−1.76806	−	2.37492i	−0.0687178	−	0.0923040i
$663$	3.75404	+	13.0817i	0.145795	+	0.508049i
$664$	−0.0312359	−	0.536300i	−0.00121219	−	0.0208125i
$665$	65.9368	+	55.3275i	2.55692	+	2.14551i
$666$	−5.61305	−	13.8762i	−0.217501	−	0.537692i
$667$	5.89279	−	4.94463i	0.228170	−	0.191457i
$668$	−15.4457	−	16.3715i	−0.597613	−	0.633433i
$669$	−0.941376	−	20.1219i	−0.0363957	−	0.777958i
$670$	−41.7936	−	27.4881i	−1.61463	−	1.06196i
$671$	−0.428617	−	0.101584i	−0.0165466	−	0.00392161i
$672$	−8.04610	−	0.0919557i	−0.310385	−	0.00354727i
$673$	−1.30483	−	0.152512i	−0.0502973	−	0.00587891i	0.0909070	−	0.995859i	$-0.471023\pi$
$673$	−1.30483	−	0.152512i	−0.0502973	−	0.00587891i	−0.141204	+	0.989980i	$0.545097\pi$
$674$	−2.34727	−	4.06559i	−0.0904134	−	0.156601i
$675$	−24.1212	+	30.1826i	−0.928425	+	1.16173i
$676$	1.35375	−	2.34477i	0.0520674	−	0.0901835i
$677$	−23.9889	+	32.2226i	−0.921967	+	1.23842i	0.0489016	+	0.998804i	$0.484428\pi$
$677$	−23.9889	+	32.2226i	−0.921967	+	1.23842i	−0.970869	+	0.239613i	$0.922979\pi$
$678$	3.79653	+	23.0699i	0.145805	+	0.885992i
$679$	−23.6564	−	79.0179i	−0.907850	−	3.03243i
$680$	−7.71827	+	3.87626i	−0.295982	+	0.148648i
$681$	24.0445	−	31.5384i	0.921385	−	1.20855i
$682$	−0.0589184	+	0.196801i	−0.00225610	+	0.00753591i
$683$	8.35039	+	47.3574i	0.319519	+	1.81208i	0.545682	+	0.837992i	$0.316271\pi$
$683$	8.35039	+	47.3574i	0.319519	+	1.81208i	−0.226163	+	0.974090i	$0.572618\pi$
$684$	15.6930	−	1.47157i	0.600036	−	0.0562669i
$685$	−1.00464	+	5.69758i	−0.0383852	+	0.217693i
$686$	31.4803	+	15.8100i	1.20192	+	0.603629i
$687$	0.416593	−	5.97536i	0.0158940	−	0.227974i
$688$	2.26600	−	5.25318i	0.0863905	−	0.200276i
$689$	1.54190	−	3.57452i	0.0587417	−	0.136178i
$690$	12.6658	+	8.53934i	0.482177	+	0.325087i
$691$	27.6648	+	13.8938i	1.05242	+	0.528545i	0.888951	−	0.458003i	$-0.151435\pi$
$691$	27.6648	+	13.8938i	1.05242	+	0.528545i	0.163470	+	0.986548i	$0.447731\pi$
$692$	−0.0992774	+	0.563030i	−0.00377396	+	0.0214032i
$693$	−34.0779	−	23.5464i	−1.29451	−	0.894455i
$694$	−1.67089	−	9.47608i	−0.0634260	−	0.359707i
$695$	13.0175	−	43.4815i	0.493782	−	1.64935i
$696$	5.28411	+	0.678920i	0.200293	+	0.0257344i
$697$	0.00520830	−	0.00261571i	0.000197278	−	9.90769e-5i
$698$	−2.69578	−	9.00454i	−0.102037	−	0.340827i
$699$	−12.0736	−	4.55137i	−0.456667	−	0.172148i
$700$	−20.6284	+	27.7087i	−0.779679	+	1.04729i
$701$	3.02553	−	5.24037i	0.114273	−	0.197926i	−0.803216	−	0.595688i	$-0.796880\pi$
$701$	3.02553	−	5.24037i	0.114273	−	0.197926i	0.917489	+	0.397762i	$0.130213\pi$
$702$	16.6605	+	0.571416i	0.628808	+	0.0215667i
$703$	13.1073	+	22.7024i	0.494350	+	0.856239i
$704$	2.95192	+	0.345030i	0.111255	+	0.0130038i
$705$	33.6471	+	59.8477i	1.26722	+	2.25400i
$706$	24.2524	+	5.74792i	0.912750	+	0.216326i
$707$	29.4738	+	19.3852i	1.10848	+	0.729055i
$708$	7.26697	+	3.75421i	0.273109	+	0.141092i
$709$	8.30149	+	8.79907i	0.311769	+	0.330456i	0.864243	−	0.503074i	$-0.167798\pi$
$709$	8.30149	+	8.79907i	0.311769	+	0.330456i	−0.552474	+	0.833530i	$0.686316\pi$
$710$	27.6714	−	23.2190i	1.03849	−	0.871395i
$711$	−42.1487	+	26.3618i	−1.58070	+	0.988644i
$712$	12.0296	+	10.0941i	0.450830	+	0.378291i
$713$	0.0100514	+	0.172576i	0.000376429	+	0.00646304i
$714$	13.6873	−	14.1795i	0.512235	−	0.530655i
$715$	−20.0787	−	26.9704i	−0.750901	−	1.00864i
$716$	22.4204	−	2.62057i	0.837889	−	0.0979351i
$717$	16.3969	−	1.72682i	0.612354	−	0.0644894i
$718$	−19.5350	+	12.8484i	−0.729041	+	0.479498i
$719$	10.4059	−	3.78744i	0.388075	−	0.141248i	−0.140612	−	0.990065i	$-0.544907\pi$
$719$	10.4059	−	3.78744i	0.388075	−	0.141248i	0.528687	+	0.848817i	$0.322685\pi$
$720$	1.59849	+	10.4578i	0.0595720	+	0.389740i
$721$	43.6325	+	15.8809i	1.62496	+	0.591437i
$722$	−8.37198	+	1.98419i	−0.311573	+	0.0738441i
$723$	−14.2791	+	45.7847i	−0.531047	+	1.70275i
$724$	−0.0541688	+	0.930043i	−0.00201317	+	0.0345648i
$725$	15.6951	−	16.6359i	0.582903	−	0.617841i
$726$	−2.84765	−	2.44546i	−0.105686	−	0.0907595i
$727$	−12.8513	−	29.7927i	−0.476629	−	1.10495i	−0.971726	−	0.236112i	$-0.924127\pi$
$727$	−12.8513	−	29.7927i	−0.476629	−	1.10495i	0.495097	−	0.868838i	$-0.335133\pi$
$728$	14.9044			0.552393
$729$	−11.8662	−	24.2527i	−0.439489	−	0.898248i
$730$	−7.66861			−0.283828
$731$	5.54992	+	12.8662i	0.205271	+	0.475872i
$732$	−0.194754	−	0.167248i	−0.00719832	−	0.00618165i
$733$	7.15338	−	7.58214i	0.264216	−	0.280053i	−0.581660	−	0.813432i	$-0.697597\pi$
$733$	7.15338	−	7.58214i	0.264216	−	0.280053i	0.845876	+	0.533379i	$0.179078\pi$
$734$	−0.783954	+	13.4600i	−0.0289363	+	0.496817i
$735$	26.5192	−	85.0313i	0.978177	−	3.13643i
$736$	2.43351	−	0.576753i	0.0897004	−	0.0212594i
$737$	−39.6160	−	14.4191i	−1.45927	−	0.531133i
$738$	−0.00107866	−	0.00705695i	−3.97060e−5	−	0.000259770i
$739$	28.5387	−	10.3872i	1.04981	−	0.382101i	0.241221	−	0.970470i	$-0.422452\pi$
$739$	28.5387	−	10.3872i	1.04981	−	0.382101i	0.808592	+	0.588369i	$0.200230\pi$
$740$	−14.7005	+	9.66866i	−0.540401	+	0.355427i
$741$	−29.0343	+	3.05771i	−1.06660	+	0.112328i
$742$	−5.59912	+	0.654443i	−0.205550	+	0.0240254i
$743$	29.4004	+	39.4916i	1.07860	+	1.44881i	0.883742	+	0.467974i	$0.155016\pi$
$743$	29.4004	+	39.4916i	1.07860	+	1.44881i	0.194854	+	0.980832i	$0.437577\pi$
$744$	−0.0831486	+	0.0861387i	−0.00304838	+	0.00315800i
$745$	−2.39760	−	41.1652i	−0.0878412	−	1.50817i
$746$	−16.4682	−	13.8184i	−0.602942	−	0.505929i
$747$	1.36638	−	0.854598i	0.0499933	−	0.0312681i
$748$	−5.57610	+	4.67891i	−0.203883	+	0.171078i
$749$	−19.9219	−	21.1160i	−0.727931	−	0.771562i
$750$	13.2175	+	6.82834i	0.482635	+	0.249336i
$751$	19.6448	+	12.9206i	0.716851	+	0.471480i	0.854799	−	0.518959i	$-0.173680\pi$
$751$	19.6448	+	12.9206i	0.716851	+	0.471480i	−0.137948	+	0.990439i	$0.544051\pi$
$752$	10.9377	+	2.59229i	0.398857	+	0.0945309i
$753$	4.61619	+	8.21077i	0.168223	+	0.299217i
$754$	−9.80122	−	1.14560i	−0.356939	−	0.0417202i
$755$	−11.4135	−	19.7688i	−0.415381	−	0.719460i
$756$	−11.3463	−	21.3072i	−0.412659	−	0.774935i
$757$	−18.5372	+	32.1074i	−0.673746	+	1.16696i	0.303088	+	0.952963i	$0.401982\pi$
$757$	−18.5372	+	32.1074i	−0.673746	+	1.16696i	−0.976834	+	0.214000i	$0.931351\pi$
$758$	−6.35254	+	8.53294i	−0.230735	+	0.309930i
$759$	12.0464	+	4.54111i	0.437258	+	0.164832i
$760$	−5.31379	−	17.7493i	−0.192751	−	0.643834i
$761$	−16.1051	+	8.08826i	−0.583808	+	0.293199i	−0.716085	−	0.698014i	$-0.754068\pi$
$761$	−16.1051	+	8.08826i	−0.583808	+	0.293199i	0.132277	+	0.991213i	$0.457771\pi$
$762$	−6.89548	−	0.885955i	−0.249797	−	0.0320948i
$763$	8.35722	−	27.9151i	0.302552	−	1.01059i
$764$	1.55402	+	8.81329i	0.0562225	+	0.318854i
$765$	−21.3172	−	14.7293i	−0.770724	−	0.532539i
$766$	−1.52087	+	8.62526i	−0.0549511	+	0.311643i
$767$	−13.5388	−	6.79945i	−0.488859	−	0.245514i
$768$	1.43614	+	0.968253i	0.0518221	+	0.0349388i
$769$	−13.9352	+	32.3055i	−0.502518	+	1.16497i	0.458553	+	0.888667i	$0.348368\pi$
$769$	−13.9352	+	32.3055i	−0.502518	+	1.16497i	−0.961071	+	0.276301i	$0.910891\pi$
$770$	−19.2851	+	44.7079i	−0.694987	+	1.61116i
$771$	−0.288036	+	4.13142i	−0.0103734	+	0.148789i
$772$	−15.3088	−	7.68836i	−0.550976	−	0.276710i
$773$	−0.640993	+	3.63525i	−0.0230549	+	0.130751i	−0.994163	−	0.107890i	$-0.965591\pi$
$773$	−0.640993	+	3.63525i	−0.0230549	+	0.130751i	0.971108	+	0.238641i	$0.0767018\pi$
$774$	17.0883	−	1.60241i	0.614225	−	0.0575974i
$775$	0.0892500	+	0.506162i	0.00320596	+	0.0181819i
$776$	−5.09208	+	17.0087i	−0.182795	+	0.610578i
$777$	24.3416	−	31.9281i	0.873248	−	1.14541i
$778$	−29.2319	+	14.6808i	−1.04802	+	0.526333i
$779$	0.00358575	+	0.0119772i	0.000128473	+	0.000429129i
$780$	−3.18197	−	19.3354i	−0.113933	−	0.692319i
$781$	18.1795	−	24.4193i	0.650514	−	0.873792i
$782$	−3.06264	+	5.30465i	−0.109520	+	0.189694i
$783$	5.82363	+	14.8839i	0.208120	+	0.531906i
$784$	−7.29137	−	12.6290i	−0.260406	−	0.451037i
$785$	54.0815	+	6.32122i	1.93025	+	0.225614i
$786$	4.58738	+	0.0524273i	0.163626	+	0.00187002i
$787$	−25.2893	−	5.99367i	−0.901466	−	0.213651i	−0.246351	−	0.969181i	$-0.579232\pi$
$787$	−25.2893	−	5.99367i	−0.901466	−	0.213651i	−0.655115	+	0.755529i	$0.727380\pi$
$788$	−2.77184	−	1.82307i	−0.0987428	−	0.0649442i
$789$	−0.0149000	−	0.318488i	−0.000530454	−	0.0113385i
$790$	40.1022	+	42.5058i	1.42677	+	1.51229i
$791$	−48.0390	+	40.3095i	−1.70807	+	1.43324i
$792$	3.34344	+	8.26542i	0.118804	+	0.293699i
$793$	0.364250	+	0.305642i	0.0129349	+	0.0108537i
$794$	−1.05954	−	18.1915i	−0.0376016	−	0.645594i
$795$	2.04438	+	7.12401i	0.0725065	+	0.252663i
$796$	−7.27122	−	9.76694i	−0.257721	−	0.346180i
$797$	6.76016	−	0.790149i	0.239457	−	0.0279885i	0.00448214	−	0.999990i	$-0.498573\pi$
$797$	6.76016	−	0.790149i	0.239457	−	0.0279885i	0.234975	+	0.972001i	$0.424499\pi$
$798$	24.8566	+	34.1973i	0.879914	+	1.21057i
$799$	−23.0017	+	15.1285i	−0.813741	+	0.535206i
$800$	6.98727	−	2.54316i	0.247037	−	0.0899142i
$801$	−9.23888	+	46.1960i	−0.326440	+	1.63225i
$802$	2.08891	+	0.760302i	0.0737620	+	0.0268472i
$803$	−6.28877	+	1.49047i	−0.221926	+	0.0525974i
$804$	−16.6552	−	18.0627i	−0.587384	−	0.637021i
$805$	−2.38232	+	40.9028i	−0.0839657	+	1.44164i
$806$	0.152179	−	0.161300i	0.00536026	−	0.00568155i
$807$	9.06685	−	48.1934i	0.319168	−	1.69649i
$808$	−3.00763	−	6.97248i	−0.105808	−	0.245291i
$809$	11.7219			0.412119			0.206060	−	0.978539i	$-0.433936\pi$
$809$	11.7219			0.412119			0.206060	+	0.978539i	$0.433936\pi$
$810$	−25.2195	+	19.2684i	−0.886121	+	0.677022i
$811$	−6.94120			−0.243738			−0.121869	−	0.992546i	$-0.538889\pi$
$811$	−6.94120			−0.243738			−0.121869	+	0.992546i	$0.538889\pi$
$812$	5.65981	+	13.1209i	0.198621	+	0.460454i
$813$	−9.45184	+	3.31836i	−0.331491	+	0.116380i
$814$	−10.1762	+	10.7861i	−0.356675	+	0.378053i
$815$	1.03593	−	17.7863i	0.0362871	−	0.623025i
$816$	−4.13872	+	0.931073i	−0.144884	+	0.0325941i
$817$	−29.2480	+	6.93190i	−1.02326	+	0.242516i
$818$	9.94014	+	3.61792i	0.347549	+	0.126497i
$819$	21.4657	+	39.2235i	0.750074	+	1.37058i
$820$	−0.00788554	+	0.00287010i	−0.000275375	+	0.000100228i
$821$	−22.2683	+	14.6461i	−0.777169	+	0.511152i	−0.875042	−	0.484047i	$-0.839166\pi$
$821$	−22.2683	+	14.6461i	−0.777169	+	0.511152i	0.0978734	+	0.995199i	$0.468796\pi$
$822$	−1.15525	+	2.59618i	−0.0402939	+	0.0905521i
$823$	−30.3610	+	3.54869i	−1.05832	+	0.123700i	−0.627404	−	0.778694i	$-0.715883\pi$
$823$	−30.3610	+	3.54869i	−1.05832	+	0.123700i	−0.430913	+	0.902393i	$0.641808\pi$
$824$	−5.96844	−	8.01701i	−0.207921	−	0.279286i
$825$	37.1415	+	9.25224i	1.29310	+	0.322122i
$826$	1.27563	+	21.9018i	0.0443850	+	0.762061i
$827$	−2.57030	−	2.15673i	−0.0893780	−	0.0749970i	0.597004	−	0.802238i	$-0.296358\pi$
$827$	−2.57030	−	2.15673i	−0.0893780	−	0.0749970i	−0.686382	+	0.727241i	$0.740802\pi$
$828$	5.02265	+	5.57356i	0.174549	+	0.193695i
$829$	1.55265	−	1.30282i	0.0539256	−	0.0452490i	−0.615427	−	0.788194i	$-0.711016\pi$
$829$	1.55265	−	1.30282i	0.0539256	−	0.0452490i	0.669352	+	0.742945i	$0.266572\pi$
$830$	−1.30003	−	1.37796i	−0.0451249	−	0.0478296i
$831$	−27.7722	+	17.8148i	−0.963407	+	0.617987i
$832$	−2.68040	−	1.76293i	−0.0929263	−	0.0611186i
$833$	34.7535	+	8.23672i	1.20414	+	0.285386i
$834$	11.3664	−	19.1777i	0.393587	−	0.664069i
$835$	−78.8352	−	9.21451i	−2.72820	−	0.318881i
$836$	−7.80739	−	13.5228i	−0.270024	−	0.467696i
$837$	−0.346443	−	0.0947609i	−0.0119748	−	0.00327541i
$838$	−4.22058	+	7.31027i	−0.145798	+	0.252529i
$839$	−4.54085	+	6.09942i	−0.156768	+	0.210575i	−0.873567	−	0.486704i	$-0.838199\pi$
$839$	−4.54085	+	6.09942i	−0.156768	+	0.210575i	0.716799	+	0.697280i	$0.245606\pi$
$840$	−21.9442	+	17.9901i	−0.757147	+	0.620716i
$841$	5.60388	+	18.7183i	0.193237	+	0.645457i
$842$	−1.10953	+	0.557227i	−0.0382369	+	0.0192033i
$843$	−2.58616	−	6.18892i	−0.0890720	−	0.213158i
$844$	0.134295	−	0.448576i	0.00462262	−	0.0154406i
$845$	−1.65796	−	9.40278i	−0.0570357	−	0.323465i
$846$	8.93077	+	32.5180i	0.307046	+	1.11799i
$847$	1.74827	−	9.91494i	0.0600713	−	0.340681i
$848$	1.08436	+	0.544584i	0.0372369	+	0.0187011i
$849$	18.3938	−	8.97599i	0.631274	−	0.308055i
$850$	−7.21324	+	16.7222i	−0.247412	+	0.573566i
$851$	−4.94242	+	11.4578i	−0.169424	+	0.392769i
$852$	15.9448	−	7.78088i	0.546259	−	0.266569i
$853$	−6.89665	−	3.46363i	−0.236137	−	0.118592i	0.326796	−	0.945095i	$-0.394031\pi$
$853$	−6.89665	−	3.46363i	−0.236137	−	0.118592i	−0.562933	+	0.826502i	$0.690327\pi$
$854$	0.119566	−	0.678094i	0.00409148	−	0.0232039i
$855$	39.0574	−	39.5473i	1.33573	−	1.35249i
$856$	1.08510	+	6.15393i	0.0370881	+	0.210337i
$857$	−2.74566	+	9.17113i	−0.0937899	+	0.313280i	−0.991992	−	0.126303i	$-0.959689\pi$
$857$	−2.74566	+	9.17113i	−0.0937899	+	0.313280i	0.898202	+	0.439583i	$0.144874\pi$
$858$	−6.36743	−	15.2379i	−0.217381	−	0.520212i
$859$	33.8635	−	17.0069i	1.15541	−	0.580267i	0.235295	−	0.971924i	$-0.424394\pi$
$859$	33.8635	−	17.0069i	1.15541	−	0.580267i	0.920111	+	0.391657i	$0.128098\pi$
$860$	−5.78625	−	19.3274i	−0.197309	−	0.659059i
$861$	0.0148080	−	0.0121397i	0.000504654	−	0.000413720i
$862$	17.4589	−	23.4514i	0.594653	−	0.798758i
$863$	13.8598	−	24.0058i	0.471792	−	0.817168i	−0.527687	−	0.849439i	$-0.676941\pi$
$863$	13.8598	−	24.0058i	0.471792	−	0.817168i	0.999479	+	0.0322706i	$0.0102738\pi$
$864$	−0.479762	+	5.17396i	−0.0163218	+	0.176022i
$865$	1.00806	+	1.74601i	0.0342750	+	0.0593660i
$866$	−20.8566	−	2.43779i	−0.708737	−	0.0828395i
$867$	−9.71543	+	16.3921i	−0.329953	+	0.556705i
$868$	−0.312466	−	0.0740558i	−0.0106058	−	0.00251362i
$869$	41.1478	+	27.0633i	1.39584	+	0.918061i
$870$	15.8134	−	10.1437i	0.536125	−	0.343903i
$871$	31.2300	+	33.1018i	1.05819	+	1.12161i
$872$	−4.80484	+	4.03174i	−0.162712	+	0.136532i
$873$	−52.0953	+	11.0958i	−1.76316	+	0.375536i
$874$	−10.0656	−	8.44604i	−0.340474	−	0.285692i
$875$	2.32019	+	39.8361i	0.0784366	+	1.34670i
$876$	−3.65484	−	0.910450i	−0.123486	−	0.0307613i
$877$	−5.60001	−	7.52212i	−0.189099	−	0.254004i	0.697456	−	0.716628i	$-0.254315\pi$
$877$	−5.60001	−	7.52212i	−0.189099	−	0.254004i	−0.886555	+	0.462624i	$0.846908\pi$
$878$	−20.1989	+	2.36091i	−0.681679	+	0.0796768i
$879$	−6.49142	+	14.5881i	−0.218950	+	0.492045i
$880$	8.75641	−	5.75918i	0.295179	−	0.194142i
$881$	−39.8524	+	14.5051i	−1.34266	+	0.488689i	−0.910650	−	0.413179i	$-0.864419\pi$
$881$	−39.8524	+	14.5051i	−1.34266	+	0.488689i	−0.432012	+	0.901868i	$0.642196\pi$
$882$	22.7343	−	37.3773i	0.765503	−	1.25856i
$883$	47.0238	+	17.1153i	1.58248	+	0.575975i	0.975741	−	0.218929i	$-0.0702562\pi$
$883$	47.0238	+	17.1153i	1.58248	+	0.575975i	0.606736	+	0.794903i	$0.292478\pi$
$884$	7.64573	−	1.81207i	0.257154	−	0.0609466i
$885$	28.1408	−	6.33074i	0.945943	−	0.212805i
$886$	−0.446375	+	7.66397i	−0.0149963	+	0.257476i
$887$	36.6058	−	38.7998i	1.22910	−	1.30277i	0.290870	−	0.956763i	$-0.406055\pi$
$887$	36.6058	−	38.7998i	1.22910	−	1.30277i	0.938231	−	0.346009i	$-0.112463\pi$
$888$	−8.15413	+	2.86276i	−0.273635	+	0.0960680i
$889$	−7.38576	−	17.1221i	−0.247710	−	0.574257i
$890$	55.3776			1.85626
$891$	−16.9366	+	20.7030i	−0.567398	+	0.693576i
$892$	−11.6301			−0.389404
$893$	−23.3917	−	54.2280i	−0.782773	−	1.81467i
$894$	3.74461	−	19.9039i	0.125239	−	0.665685i
$895$	54.6263	−	57.9005i	1.82595	−	1.93540i
$896$	−0.270125	+	4.63786i	−0.00902424	+	0.154940i
$897$	−9.42057	−	10.2166i	−0.314544	−	0.341124i
$898$	−3.24637	+	0.769404i	−0.108333	+	0.0256753i
$899$	0.199788	+	0.0727167i	0.00666329	+	0.00242524i
$900$	16.7561	+	14.7255i	0.558535	+	0.490851i
$901$	−2.79270	+	1.01646i	−0.0930384	+	0.0338632i
$902$	−0.00590883	+	0.00388630i	−0.000196743	+	0.000129400i
$903$	27.0666	+	37.2378i	0.900721	+	1.23920i
$904$	13.4073	−	1.56709i	0.445919	−	0.0521205i
$905$	1.96184	+	2.63521i	0.0652137	+	0.0875972i
$906$	−3.09263	−	10.7768i	−0.102746	−	0.358036i
$907$	−2.76003	−	47.3878i	−0.0916452	−	1.57349i	−0.660358	−	0.750951i	$-0.729595\pi$
$907$	−2.76003	−	47.3878i	−0.0916452	−	1.57349i	0.568713	−	0.822536i	$-0.307442\pi$
$908$	−17.5400	−	14.7178i	−0.582087	−	0.488429i
$909$	14.0176	−	17.9571i	0.464936	−	0.595599i
$910$	40.2627	−	33.7844i	1.33469	−	1.11994i
$911$	20.0830	+	21.2868i	0.665380	+	0.705262i	0.968869	−	0.247573i	$-0.0796330\pi$
$911$	20.0830	+	21.2868i	0.665380	+	0.705262i	−0.303489	+	0.952835i	$0.598152\pi$
$912$	−0.425270	−	9.09015i	−0.0140821	−	0.301005i
$913$	−1.33393	−	0.877341i	−0.0441467	−	0.0290358i
$914$	33.3988	+	7.91566i	1.10473	+	0.261827i
$915$	−0.905217	−	0.0103454i	−0.0299255	−	0.000342007i
$916$	−3.43487	−	0.401478i	−0.113491	−	0.0132652i
$917$	6.15256	+	10.6565i	0.203175	+	0.351910i
$918$	−8.41100	−	9.55082i	−0.277604	−	0.315224i
$919$	−26.6486	+	46.1567i	−0.879055	+	1.52257i	−0.0266755	+	0.999644i	$0.508492\pi$
$919$	−26.6486	+	46.1567i	−0.879055	+	1.52257i	−0.852379	+	0.522924i	$0.824841\pi$
$920$	5.26654	−	7.07419i	0.173633	−	0.233229i
$921$	−0.0652577	−	0.396543i	−0.00215031	−	0.0130665i
$922$	4.73504	+	15.8161i	0.155940	+	0.520877i
$923$	−29.3671	+	14.7487i	−0.966629	+	0.485459i
$924$	−14.4991	+	19.0181i	−0.476987	+	0.625649i
$925$	−10.6405	+	35.5418i	−0.349858	+	1.16861i
$926$	−3.08189	−	17.4783i	−0.101277	−	0.574372i
$927$	12.5023	−	27.2534i	0.410628	−	0.895118i
$928$	0.534117	−	3.02913i	0.0175333	−	0.0994360i
$929$	−37.3823	−	18.7741i	−1.22648	−	0.615959i	−0.286788	−	0.957994i	$-0.592587\pi$
$929$	−37.3823	−	18.7741i	−1.22648	−	0.615959i	−0.939687	+	0.342035i	$0.888884\pi$
$930$	−0.0293634	+	0.421172i	−0.000962864	+	0.0138108i
$931$	−30.3464	+	70.3509i	−0.994563	+	2.30566i
$932$	−2.95062	+	6.84031i	−0.0966508	+	0.224062i
$933$	−26.1557	−	17.6344i	−0.856300	−	0.577323i
$934$	−22.2075	−	11.1530i	−0.726652	−	0.364938i
$935$	−4.45741	+	25.2792i	−0.145773	+	0.826719i
$936$	0.779063	−	9.59299i	0.0254645	−	0.313557i
$937$	−5.61320	−	31.8340i	−0.183375	−	1.03997i	−0.928025	−	0.372517i	$-0.878495\pi$
$937$	−5.61320	−	31.8340i	−0.183375	−	1.03997i	0.744650	−	0.667455i	$-0.232616\pi$
$938$	18.9004	−	63.1318i	0.617121	−	2.06133i
$939$	−46.8663	−	6.02154i	−1.52942	−	0.196506i
$940$	35.4232	−	17.7902i	1.15538	−	0.580252i
$941$	−15.2448	−	50.9210i	−0.496965	−	1.65998i	−0.726877	−	0.686767i	$-0.759029\pi$
$941$	−15.2448	−	50.9210i	−0.496965	−	1.65998i	0.229912	−	0.973211i	$-0.426156\pi$
$942$	25.0247	+	9.43347i	0.815347	+	0.307359i
$943$	−0.00355386	+	0.00477367i	−0.000115730	+	0.000155452i
$944$	2.36119	−	4.08971i	0.0768503	−	0.133109i
$945$	−78.9487	−	31.8402i	−2.56820	−	1.03576i
$946$	−8.50156	−	14.7251i	−0.276410	−	0.478755i
$947$	37.7826	+	4.41616i	1.22777	+	0.143506i	0.705149	−	0.709059i	$-0.250880\pi$
$947$	37.7826	+	4.41616i	1.22777	+	0.143506i	0.522622	+	0.852565i	$0.324954\pi$
$948$	14.0661	+	25.0193i	0.456847	+	0.812588i
$949$	6.78852	+	1.60891i	0.220365	+	0.0522274i
$950$	−32.6398	−	21.4675i	−1.05897	−	0.696498i
$951$	−20.5980	−	10.6412i	−0.667935	−	0.345063i
$952$	−7.80830	−	8.27631i	−0.253068	−	0.268237i
$953$	−17.2675	+	14.4892i	−0.559350	+	0.469350i	−0.878092	−	0.478491i	$-0.841184\pi$
$953$	−17.2675	+	14.4892i	−0.559350	+	0.469350i	0.318743	+	0.947841i	$0.396739\pi$
$954$	0.128553	+	3.63800i	0.00416206	+	0.117785i
$955$	24.1755	+	20.2857i	0.782301	+	0.656428i
$956$	−0.553488	−	9.50302i	−0.0179011	−	0.307349i
$957$	10.9965	−	11.3920i	0.355467	−	0.368250i
$958$	−10.0424	−	13.4893i	−0.324455	−	0.435819i
$959$	−7.57025	+	0.884836i	−0.244456	+	0.0285728i
$960$	6.07436	−	0.639715i	0.196049	−	0.0206467i
$961$	25.8961	−	17.0322i	0.835359	−	0.549424i
$962$	15.0419	−	5.47480i	0.484970	−	0.176515i
$963$	−14.6324	+	11.7187i	−0.471521	+	0.377630i
$964$	26.0196	+	9.47037i	0.838036	+	0.305020i
$965$	−58.7827	+	13.9318i	−1.89228	+	0.448479i
$966$	−5.99157	+	19.2114i	−0.192775	+	0.618116i
$967$	0.157315	−	2.70099i	0.00505891	−	0.0868580i	−0.994834	−	0.101519i	$-0.967630\pi$
$967$	0.157315	−	2.70099i	0.00505891	−	0.0868580i	0.999893	+	0.0146608i	$0.00466683\pi$
$968$	−1.48718	+	1.57631i	−0.0477996	+	0.0506647i
$969$	16.9088	+	14.5207i	0.543189	+	0.466471i
$970$	24.7987	+	57.4899i	0.796239	+	1.84589i
$971$	12.7810			0.410160			0.205080	−	0.978745i	$-0.434254\pi$
$971$	12.7810			0.410160			0.205080	+	0.978745i	$0.434254\pi$
$972$	−14.3072	+	6.18911i	−0.458902	+	0.198516i
$973$	59.7946			1.91693
$974$	3.27307	+	7.58784i	0.104876	+	0.243130i
$975$	−31.3461	−	26.9189i	−1.00388	−	0.862094i
$976$	−0.101710	+	0.107806i	−0.00325565	+	0.00345079i
$977$	−2.96672	+	50.9366i	−0.0949137	+	1.62960i	0.529359	+	0.848398i	$0.322433\pi$
$977$	−2.96672	+	50.9366i	−0.0949137	+	1.62960i	−0.624272	+	0.781207i	$0.714604\pi$
$978$	2.60538	−	8.35390i	0.0833109	−	0.267128i
$979$	45.4133	−	10.7631i	1.45141	−	0.343991i
$980$	−48.3237	−	17.5884i	−1.54364	−	0.561840i
$981$	−17.5303	−	6.83815i	−0.559700	−	0.218325i
$982$	14.8210	−	5.39440i	0.472957	−	0.172142i
$983$	36.6137	−	24.0812i	1.16780	−	0.768071i	0.190863	−	0.981617i	$-0.438871\pi$
$983$	36.6137	−	24.0812i	1.16780	−	0.768071i	0.976933	+	0.213545i	$0.0685011\pi$
$984$	−0.00409898		0.000431680i	−0.000130671		1.37615e-5i
$985$	−11.6203	+	1.35822i	−0.370253	+	0.0432764i
$986$	4.49865	+	6.04273i	0.143266	+	0.192440i
$987$	−62.8182	+	65.0772i	−1.99953	+	2.07143i
$988$	0.980069	+	16.8271i	0.0311801	+	0.535342i
$989$	−10.9605	−	9.19699i	−0.348525	−	0.292447i
$990$	27.7676	+	14.7495i	0.882511	+	0.468770i
$991$	42.9785	−	36.0632i	1.36526	−	1.14559i	0.390935	−	0.920418i	$-0.372152\pi$
$991$	42.9785	−	36.0632i	1.36526	−	1.14559i	0.974320	−	0.225167i	$-0.0722929\pi$
$992$	0.0474344	+	0.0502775i	0.00150604	+	0.00159631i
$993$	−4.55617	−	2.35377i	−0.144586	−	0.0746948i
$994$	39.7590	+	26.1499i	1.26108	+	0.829424i
$995$	−41.7816	−	9.90243i	−1.32457	−	0.313928i
$996$	−0.455997	−	0.811077i	−0.0144488	−	0.0256999i
$997$	−42.9856	−	5.02430i	−1.36137	−	0.159121i	−0.596141	−	0.802880i	$-0.703300\pi$
$997$	−42.9856	−	5.02430i	−1.36137	−	0.159121i	−0.765228	+	0.643759i	$0.777374\pi$
$998$	−13.8391	−	23.9700i	−0.438069	−	0.758758i
$999$	−19.2777	−	17.3360i	−0.609919	−	0.548487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.31.2	✓	72
3.2	odd	2		486.2.g.a.145.4		72
81.34	even	27	inner	162.2.g.a.115.2	yes	72
81.47	odd	54		486.2.g.a.181.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.31.2	✓	72	1.1	even	1	trivial
162.2.g.a.115.2	yes	72	81.34	even	27	inner
486.2.g.a.145.4		72	3.2	odd	2
486.2.g.a.181.4		72	81.47	odd	54

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396080 - 0.918216i) q^{2} +(-1.31402 - 1.12843i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.205044 + 3.52046i) q^{5} +(-0.515687 + 1.65350i) q^{6} +(-4.52050 + 1.07138i) q^{7} +(0.939693 + 0.342020i) q^{8} +(0.453287 + 2.96556i) q^{9} +O(q^{10})\)	\(q+(-0.396080 - 0.918216i) q^{2} +(-1.31402 - 1.12843i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.205044 + 3.52046i) q^{5} +(-0.515687 + 1.65350i) q^{6} +(-4.52050 + 1.07138i) q^{7} +(0.939693 + 0.342020i) q^{8} +(0.453287 + 2.96556i) q^{9} +(3.31376 - 1.20611i) q^{10} +(2.48308 - 1.63315i) q^{11} +(1.72252 - 0.181406i) q^{12} +(-3.18650 + 0.372448i) q^{13} +(2.77423 + 3.72644i) q^{14} +(4.24203 - 4.39457i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(1.87620 + 1.57432i) q^{17} +(2.54348 - 1.59081i) q^{18} +(-4.02475 + 3.37717i) q^{19} +(-2.41998 - 2.56503i) q^{20} +(7.14899 + 3.69326i) q^{21} +(-2.48308 - 1.63315i) q^{22} +(-2.43351 - 0.576753i) q^{23} +(-0.848827 - 1.50980i) q^{24} +(-7.38542 - 0.863232i) q^{25} +(1.60410 + 2.77838i) q^{26} +(2.75080 - 4.40830i) q^{27} +(2.32286 - 4.02331i) q^{28} +(-1.83677 + 2.46722i) q^{29} +(-5.71535 - 2.15450i) q^{30} +(-0.0198244 - 0.0662182i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-5.10571 - 0.655999i) q^{33} +(0.702441 - 2.34632i) q^{34} +(-2.84485 - 16.1339i) q^{35} +(-2.46813 - 1.70538i) q^{36} +(0.866417 - 4.91369i) q^{37} +(4.69509 + 2.35796i) q^{38} +(4.60740 + 3.10634i) q^{39} +(-1.39675 + 3.23802i) q^{40} +(0.000942526 - 0.00218502i) q^{41} +(0.559639 - 8.02714i) q^{42} +(5.11254 + 2.56761i) q^{43} +(-0.516085 + 2.92686i) q^{44} +(-10.5331 + 0.987713i) q^{45} +(0.434281 + 2.46293i) q^{46} +(-3.22387 + 10.7685i) q^{47} +(-1.05012 + 1.37741i) q^{48} +(13.0316 - 6.54472i) q^{49} +(2.13258 + 7.12332i) q^{50} +(-0.688852 - 4.18585i) q^{51} +(1.91580 - 2.57336i) q^{52} +(-0.606712 + 1.05086i) q^{53} +(-5.13731 - 0.779789i) q^{54} +(5.24030 + 9.07646i) q^{55} +(-4.61431 - 0.539336i) q^{56} +(9.09950 + 0.103995i) q^{57} +(2.99295 + 0.709342i) q^{58} +(3.94550 + 2.59499i) q^{59} +(0.285440 + 6.10128i) q^{60} +(-0.101710 - 0.107806i) q^{61} +(-0.0529505 + 0.0444308i) q^{62} +(-5.22632 - 12.9202i) q^{63} +(0.766044 + 0.642788i) q^{64} +(-0.657819 - 11.2943i) q^{65} +(1.41992 + 4.94797i) q^{66} +(-8.47079 - 11.3782i) q^{67} +(-2.43265 + 0.284336i) q^{68} +(2.54685 + 3.50391i) q^{69} +(-13.6876 + 9.00250i) q^{70} +(9.62559 - 3.50343i) q^{71} +(-0.588330 + 2.94175i) q^{72} +(-2.04347 - 0.743761i) q^{73} +(-4.85500 + 1.15066i) q^{74} +(8.73048 + 9.46824i) q^{75} +(0.305489 - 5.24505i) q^{76} +(-9.47505 + 10.0430i) q^{77} +(1.02739 - 5.46095i) q^{78} +(6.56354 + 15.2160i) q^{79} +3.52643 q^{80} +(-8.58906 + 2.68850i) q^{81} -0.00237964 q^{82} +(-0.212777 - 0.493273i) q^{83} +(-7.59231 + 2.66552i) q^{84} +(-5.92704 + 6.28230i) q^{85} +(0.332651 - 5.71140i) q^{86} +(5.19764 - 1.16929i) q^{87} +(2.89190 - 0.685394i) q^{88} +(14.7565 + 5.37094i) q^{89} +(5.07887 + 9.28043i) q^{90} +(14.0055 - 5.09759i) q^{91} +(2.08949 - 1.37428i) q^{92} +(-0.0486730 + 0.109382i) q^{93} +(11.1647 - 1.30497i) q^{94} +(-11.0639 - 14.8615i) q^{95} +(1.68069 + 0.418672i) q^{96} +(1.03234 + 17.7246i) q^{97} +(-11.1710 - 9.37361i) q^{98} +(5.96875 + 6.62344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

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