LMFDB - Embedded newform 169.2.g.a.27.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			27.3
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.568511 - 1.49904i) q^{2} +(-1.77394 + 2.57000i) q^{3} +(-0.426895 + 0.378196i) q^{4} +(0.00472042 + 0.0388761i) q^{5} +(4.86104 + 1.19814i) q^{6} +(-3.29128 - 1.72740i) q^{7} +(-2.02954 - 1.06519i) q^{8} +(-2.39421 - 6.31302i) q^{9} +O(q^{10})$	\(q+(-0.568511 - 1.49904i) q^{2} +(-1.77394 + 2.57000i) q^{3} +(-0.426895 + 0.378196i) q^{4} +(0.00472042 + 0.0388761i) q^{5} +(4.86104 + 1.19814i) q^{6} +(-3.29128 - 1.72740i) q^{7} +(-2.02954 - 1.06519i) q^{8} +(-2.39421 - 6.31302i) q^{9} +(0.0555933 - 0.0291776i) q^{10} +(0.680286 - 1.79377i) q^{11} +(-0.214676 - 1.76802i) q^{12} +(-3.41862 - 1.14589i) q^{13} +(-0.718309 + 5.91581i) q^{14} +(-0.108285 - 0.0568326i) q^{15} +(-0.580430 + 4.78027i) q^{16} +(3.52523 + 1.85018i) q^{17} +(-8.10234 + 7.17804i) q^{18} -6.43536 q^{19} +(-0.0167179 - 0.0148108i) q^{20} +(10.2780 - 5.39429i) q^{21} -3.07568 q^{22} -3.92377 q^{23} +(6.33782 - 3.32635i) q^{24} +(4.85322 - 1.19621i) q^{25} +(0.225784 + 5.77609i) q^{26} +(11.3755 + 2.80382i) q^{27} +(2.05833 - 0.507332i) q^{28} +(1.01974 + 2.68884i) q^{29} +(-0.0236329 + 0.194634i) q^{30} +(0.0209135 + 0.00515471i) q^{31} +(3.04483 - 0.750483i) q^{32} +(3.40319 + 4.93037i) q^{33} +(0.769367 - 6.33631i) q^{34} +(0.0516183 - 0.136106i) q^{35} +(3.40964 + 1.78952i) q^{36} +(-9.43808 - 2.32628i) q^{37} +(3.65857 + 9.64687i) q^{38} +(9.00937 - 6.75310i) q^{39} +(0.0318300 - 0.0839289i) q^{40} +(4.85721 - 7.03689i) q^{41} +(-13.9294 - 12.3404i) q^{42} +(-4.79339 + 1.18146i) q^{43} +(0.387985 + 1.02303i) q^{44} +(0.234124 - 0.122878i) q^{45} +(2.23070 + 5.88188i) q^{46} +(8.53161 + 7.55835i) q^{47} +(-11.2556 - 9.97163i) q^{48} +(3.87218 + 5.60982i) q^{49} +(-4.55228 - 6.59511i) q^{50} +(-11.0085 + 5.77772i) q^{51} +(1.89276 - 0.803732i) q^{52} +(-1.29858 - 0.681548i) q^{53} +(-2.26408 - 18.6464i) q^{54} +(0.0729460 + 0.0179796i) q^{55} +(4.83980 + 7.01166i) q^{56} +(11.4160 - 16.5389i) q^{57} +(3.45095 - 3.05727i) q^{58} +(-0.219032 - 1.80389i) q^{59} +(0.0677204 - 0.0166916i) q^{60} +(-0.676767 + 0.355195i) q^{61} +(-0.00416242 - 0.0342806i) q^{62} +(-3.02507 + 24.9137i) q^{63} +(2.61487 + 3.78829i) q^{64} +(0.0284105 - 0.138312i) q^{65} +(5.45608 - 7.90449i) q^{66} +(-2.03540 - 1.80321i) q^{67} +(-2.20463 + 0.543394i) q^{68} +(6.96054 - 10.0841i) q^{69} -0.233375 q^{70} +(-1.18093 + 1.71087i) q^{71} +(-1.86539 + 15.3628i) q^{72} +(2.06682 - 5.44977i) q^{73} +(1.87847 + 15.4706i) q^{74} +(-5.53507 + 14.5948i) q^{75} +(2.74722 - 2.43383i) q^{76} +(-5.33756 + 4.72867i) q^{77} +(-15.2451 - 9.66620i) q^{78} +(-6.77962 - 6.00622i) q^{79} -0.188578 q^{80} +(-12.2241 + 10.8296i) q^{81} +(-13.3100 - 3.28061i) q^{82} +(4.20354 + 6.08988i) q^{83} +(-2.34751 + 6.18988i) q^{84} +(-0.0552874 + 0.145781i) q^{85} +(4.49616 + 6.51381i) q^{86} +(-8.71929 - 2.14911i) q^{87} +(-3.29136 + 2.91589i) q^{88} -4.07667 q^{89} +(-0.317301 - 0.281104i) q^{90} +(9.27222 + 9.67676i) q^{91} +(1.67504 - 1.48395i) q^{92} +(-0.0503469 + 0.0446035i) q^{93} +(6.47995 - 17.0862i) q^{94} +(-0.0303776 - 0.250182i) q^{95} +(-3.47261 + 9.15653i) q^{96} +(0.361319 - 2.97573i) q^{97} +(6.20797 - 8.99380i) q^{98} -12.9528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.568511	−	1.49904i	−0.401998	−	1.05998i	−0.971301	−	0.237854i	$-0.923556\pi$
$2$	−0.568511	−	1.49904i	−0.401998	−	1.05998i	0.569303	−	0.822128i	$-0.307213\pi$
$3$	−1.77394	+	2.57000i	−1.02419	+	1.48379i	−0.155872	+	0.987777i	$0.549819\pi$
$3$	−1.77394	+	2.57000i	−1.02419	+	1.48379i	−0.868315	+	0.496013i	$0.834797\pi$
$4$	−0.426895	+	0.378196i	−0.213447	+	0.189098i
$5$	0.00472042	+	0.0388761i	0.00211104	+	0.0173859i	0.993726	−	0.111839i	$-0.0356741\pi$
$5$	0.00472042	+	0.0388761i	0.00211104	+	0.0173859i	−0.991615	+	0.129225i	$0.958751\pi$
$6$	4.86104	+	1.19814i	1.98451	+	0.489138i
$7$	−3.29128	−	1.72740i	−1.24399	−	0.652895i	−0.291238	−	0.956651i	$-0.594067\pi$
$7$	−3.29128	−	1.72740i	−1.24399	−	0.652895i	−0.952750	+	0.303756i	$0.901759\pi$
$8$	−2.02954	−	1.06519i	−0.717552	−	0.376600i
$9$	−2.39421	−	6.31302i	−0.798071	−	2.10434i
$10$	0.0555933	−	0.0291776i	0.0175801	−	0.00922677i
$11$	0.680286	−	1.79377i	0.205114	−	0.540841i	−0.792501	−	0.609871i	$-0.791221\pi$
$11$	0.680286	−	1.79377i	0.205114	−	0.540841i	0.997615	+	0.0690301i	$0.0219905\pi$
$12$	−0.214676	−	1.76802i	−0.0619717	−	0.510383i
$13$	−3.41862	−	1.14589i	−0.948153	−	0.317813i
$13$	−3.41862	−	1.14589i	−0.948153	−	0.317813i
$14$	−0.718309	+	5.91581i	−0.191976	+	1.58107i
$15$	−0.108285	−	0.0568326i	−0.0279592	−	0.0146741i
$16$	−0.580430	+	4.78027i	−0.145107	+	1.19507i
$17$	3.52523	+	1.85018i	0.854994	+	0.448735i	0.834470	−	0.551054i	$-0.185774\pi$
$17$	3.52523	+	1.85018i	0.854994	+	0.448735i	0.0205243	+	0.999789i	$0.493466\pi$
$18$	−8.10234	+	7.17804i	−1.90974	+	1.69188i
$19$	−6.43536			−1.47637			−0.738187	−	0.674597i	$-0.764318\pi$
$19$	−6.43536			−1.47637			−0.738187	+	0.674597i	$0.764318\pi$
$20$	−0.0167179	−	0.0148108i	−0.00373824	−	0.00331179i
$21$	10.2780	−	5.39429i	2.24284	−	1.17713i
$22$	−3.07568			−0.655737
$23$	−3.92377			−0.818162			−0.409081	−	0.912498i	$-0.634151\pi$
$23$	−3.92377			−0.818162			−0.409081	+	0.912498i	$0.634151\pi$
$24$	6.33782	−	3.32635i	1.29370	−	0.678987i
$25$	4.85322	−	1.19621i	0.970644	−	0.239242i
$26$	0.225784	+	5.77609i	0.0442799	+	1.13279i
$27$	11.3755	+	2.80382i	2.18922	+	0.539595i
$28$	2.05833	−	0.507332i	0.388987	−	0.0958767i
$29$	1.01974	+	2.68884i	0.189362	+	0.499305i	0.995752	−	0.0920785i	$-0.0293511\pi$
$29$	1.01974	+	2.68884i	0.189362	+	0.499305i	−0.806390	+	0.591384i	$0.798582\pi$
$30$	−0.0236329	+	0.194634i	−0.00431475	+	0.0355352i
$31$	0.0209135	+	0.00515471i	0.00375617	+	0.000925812i	0.241193	−	0.970477i	$-0.422461\pi$
$31$	0.0209135	+	0.00515471i	0.00375617	+	0.000925812i	−0.237437	+	0.971403i	$0.576307\pi$
$32$	3.04483	−	0.750483i	0.538255	−	0.132668i
$33$	3.40319	+	4.93037i	0.592420	+	0.858268i
$34$	0.769367	−	6.33631i	0.131945	−	1.08667i
$35$	0.0516183	−	0.136106i	0.00872509	−	0.0230062i
$36$	3.40964	+	1.78952i	0.568273	+	0.298253i
$37$	−9.43808	−	2.32628i	−1.55161	−	0.382438i	−0.631905	−	0.775046i	$-0.717727\pi$
$37$	−9.43808	−	2.32628i	−1.55161	−	0.382438i	−0.919706	+	0.392608i	$0.871573\pi$
$38$	3.65857	+	9.64687i	0.593499	+	1.56493i
$39$	9.00937	−	6.75310i	1.44265	−	1.08136i
$40$	0.0318300	−	0.0839289i	0.00503277	−	0.0132703i
$41$	4.85721	−	7.03689i	0.758570	−	1.09898i	−0.233385	−	0.972384i	$-0.574980\pi$
$41$	4.85721	−	7.03689i	0.758570	−	1.09898i	0.991955	−	0.126593i	$-0.0404043\pi$
$42$	−13.9294	−	12.3404i	−2.14935	−	1.90416i
$43$	−4.79339	+	1.18146i	−0.730985	+	0.180172i	−0.587205	−	0.809438i	$-0.699772\pi$
$43$	−4.79339	+	1.18146i	−0.730985	+	0.180172i	−0.143780	+	0.989610i	$0.545926\pi$
$44$	0.387985	+	1.02303i	0.0584909	+	0.154228i
$45$	0.234124	−	0.122878i	0.0349012	−	0.0183176i
$46$	2.23070	+	5.88188i	0.328899	+	0.867236i
$47$	8.53161	+	7.55835i	1.24446	+	1.10250i	0.990818	+	0.135201i	$0.0431679\pi$
$47$	8.53161	+	7.55835i	1.24446	+	1.10250i	0.253645	+	0.967297i	$0.418371\pi$
$48$	−11.2556	−	9.97163i	−1.62461	−	1.43928i
$49$	3.87218	+	5.60982i	0.553169	+	0.801403i
$50$	−4.55228	−	6.59511i	−0.643789	−	0.932690i
$51$	−11.0085	+	5.77772i	−1.54150	+	0.809043i
$52$	1.89276	−	0.803732i	0.262479	−	0.111458i
$53$	−1.29858	−	0.681548i	−0.178374	−	0.0936179i	0.373173	−	0.927762i	$-0.378270\pi$
$53$	−1.29858	−	0.681548i	−0.178374	−	0.0936179i	−0.551547	+	0.834144i	$0.685962\pi$
$54$	−2.26408	−	18.6464i	−0.308103	−	2.53745i
$55$	0.0729460	+	0.0179796i	0.00983603	+	0.00242436i
$56$	4.83980	+	7.01166i	0.646745	+	0.936972i
$57$	11.4160	−	16.5389i	1.51208	−	2.19063i
$58$	3.45095	−	3.05727i	0.453131	−	0.401439i
$59$	−0.219032	−	1.80389i	−0.0285156	−	0.234847i	0.971482	−	0.237114i	$-0.0762015\pi$
$59$	−0.219032	−	1.80389i	−0.0285156	−	0.234847i	−0.999997	+	0.00226697i	$0.999278\pi$
$60$	0.0677204	−	0.0166916i	0.00874266	−	0.00215487i
$61$	−0.676767	+	0.355195i	−0.0866512	+	0.0454780i	−0.507492	−	0.861656i	$-0.669427\pi$
$61$	−0.676767	+	0.355195i	−0.0866512	+	0.0454780i	0.420841	+	0.907134i	$0.361735\pi$
$62$	−0.00416242	−	0.0342806i	−0.000528628	−	0.00435364i
$63$	−3.02507	+	24.9137i	−0.381123	+	3.13883i
$64$	2.61487	+	3.78829i	0.326859	+	0.473537i
$65$	0.0284105	−	0.138312i	0.00352389	−	0.0171555i
$66$	5.45608	−	7.90449i	0.671597	−	0.972976i
$67$	−2.03540	−	1.80321i	−0.248664	−	0.220297i	0.529579	−	0.848261i	$-0.322350\pi$
$67$	−2.03540	−	1.80321i	−0.248664	−	0.220297i	−0.778242	+	0.627964i	$0.783889\pi$
$68$	−2.20463	+	0.543394i	−0.267351	+	0.0658962i
$69$	6.96054	−	10.0841i	0.837951	−	1.21398i
$70$	−0.233375			−0.0278936
$71$	−1.18093	+	1.71087i	−0.140150	+	0.203043i	−0.886773	−	0.462205i	$-0.847059\pi$
$71$	−1.18093	+	1.71087i	−0.140150	+	0.203043i	0.746623	+	0.665247i	$0.231674\pi$
$72$	−1.86539	+	15.3628i	−0.219838	+	1.81053i
$73$	2.06682	−	5.44977i	0.241903	−	0.637847i	−0.757993	−	0.652263i	$-0.773820\pi$
$73$	2.06682	−	5.44977i	0.241903	−	0.637847i	0.999896	+	0.0144162i	$0.00458896\pi$
$74$	1.87847	+	15.4706i	0.218367	+	1.79842i
$75$	−5.53507	+	14.5948i	−0.639135	+	1.68526i
$76$	2.74722	−	2.43383i	0.315128	−	0.279179i
$77$	−5.33756	+	4.72867i	−0.608272	+	0.538882i
$78$	−15.2451	−	9.66620i	−1.72617	−	1.09448i
$79$	−6.77962	−	6.00622i	−0.762767	−	0.675753i	0.189205	−	0.981938i	$-0.439409\pi$
$79$	−6.77962	−	6.00622i	−0.762767	−	0.675753i	−0.951972	+	0.306185i	$0.900947\pi$
$80$	−0.188578			−0.0210837
$81$	−12.2241	+	10.8296i	−1.35823	+	1.20329i
$82$	−13.3100	−	3.28061i	−1.46984	−	0.362283i
$83$	4.20354	+	6.08988i	0.461398	+	0.668451i	0.982760	−	0.184885i	$-0.0591912\pi$
$83$	4.20354	+	6.08988i	0.461398	+	0.668451i	−0.521362	+	0.853336i	$0.674576\pi$
$84$	−2.34751	+	6.18988i	−0.256134	+	0.675371i
$85$	−0.0552874	+	0.145781i	−0.00599676	+	0.0158122i
$86$	4.49616	+	6.51381i	0.484833	+	0.702402i
$87$	−8.71929	−	2.14911i	−0.934806	−	0.230409i
$88$	−3.29136	+	2.91589i	−0.350861	+	0.310835i
$89$	−4.07667			−0.432126			−0.216063	−	0.976379i	$-0.569322\pi$
$89$	−4.07667			−0.432126			−0.216063	+	0.976379i	$0.569322\pi$
$90$	−0.317301	−	0.281104i	−0.0334465	−	0.0296310i
$91$	9.27222	+	9.67676i	0.971993	+	1.01440i
$92$	1.67504	−	1.48395i	0.174635	−	0.154713i
$93$	−0.0503469	+	0.0446035i	−0.00522073	+	0.00462516i
$94$	6.47995	−	17.0862i	0.668356	−	1.76231i
$95$	−0.0303776	−	0.250182i	−0.00311668	−	0.0256681i
$96$	−3.47261	+	9.15653i	−0.354422	+	0.934535i
$97$	0.361319	−	2.97573i	0.0366864	−	0.302139i	−0.962804	−	0.270202i	$-0.912909\pi$
$97$	0.361319	−	2.97573i	0.0366864	−	0.302139i	0.999490	−	0.0319369i	$-0.0101675\pi$
$98$	6.20797	−	8.99380i	0.627100	−	0.908511i
$99$	−12.9528			−1.30181
$100$	−1.61941	+	2.34612i	−0.161941	+	0.234612i
$101$	1.59216	−	0.392433i	0.158426	−	0.0390485i	−0.159305	−	0.987229i	$-0.550925\pi$
$101$	1.59216	−	0.392433i	0.158426	−	0.0390485i	0.317731	+	0.948181i	$0.397079\pi$
$102$	14.9195	+	13.2175i	1.47725	+	1.30873i
$103$	7.75262	−	11.2316i	0.763889	−	1.10668i	−0.227248	−	0.973837i	$-0.572973\pi$
$103$	7.75262	−	11.2316i	0.763889	−	1.10668i	0.991137	−	0.132847i	$-0.0424118\pi$
$104$	5.71764	+	5.96710i	0.560661	+	0.585122i
$105$	0.258225	+	0.374104i	0.0252002	+	0.0365088i
$106$	−0.283410	+	2.33409i	−0.0275272	+	0.226707i
$107$	−1.82182	−	15.0040i	−0.176122	−	1.45050i	−0.765915	−	0.642942i	$-0.777714\pi$
$107$	−1.82182	−	15.0040i	−0.176122	−	1.45050i	0.589793	−	0.807554i	$-0.299209\pi$
$108$	−5.91656	+	3.10525i	−0.569321	+	0.298803i
$109$	−11.8782	+	2.92772i	−1.13773	+	0.280425i	−0.762803	−	0.646631i	$-0.776178\pi$
$109$	−11.8782	+	2.92772i	−1.13773	+	0.280425i	−0.374925	+	0.927055i	$0.622331\pi$
$110$	−0.0145185	−	0.119570i	−0.00138428	−	0.0114006i
$111$	22.7212	−	20.1292i	2.15660	−	1.91058i
$112$	10.1678	−	14.7306i	0.960766	−	1.39191i
$113$	−9.91833	−	14.3692i	−0.933038	−	1.35174i	−0.936096	−	0.351744i	$-0.885589\pi$
$113$	−9.91833	−	14.3692i	−0.933038	−	1.35174i	0.00305809	−	0.999995i	$-0.499027\pi$
$114$	−31.2826	−	7.71046i	−2.92988	−	0.722150i
$115$	−0.0185218	−	0.152541i	−0.00172717	−	0.0142245i
$116$	−1.45223	−	0.762190i	−0.134836	−	0.0707676i
$117$	0.950862	+	24.3253i	0.0879072	+	2.24888i
$118$	−2.57959	+	1.35387i	−0.237470	+	0.124634i
$119$	−8.40652	−	12.1790i	−0.770625	−	1.11644i
$120$	0.159233	+	0.230688i	0.0145359	+	0.0210589i
$121$	5.47881	+	4.85380i	0.498074	+	0.441255i
$122$	0.917201	+	0.812569i	0.0830395	+	0.0735665i
$123$	9.46839	+	24.9661i	0.853736	+	2.25112i
$124$	−0.0108773	+	0.00570887i	−0.000976814	+	0.000512672i
$125$	0.138848	+	0.366112i	0.0124189	+	0.0327460i
$126$	39.0664	−	9.62901i	3.48031	−	0.857820i
$127$	−6.37889	−	5.65121i	−0.566035	−	0.501464i	0.330876	−	0.943674i	$-0.392656\pi$
$127$	−6.37889	−	5.65121i	−0.566035	−	0.501464i	−0.896911	+	0.442211i	$0.854194\pi$
$128$	7.75508	−	11.2352i	0.685458	−	0.993058i
$129$	5.46684	−	14.4149i	0.481328	−	1.26916i
$130$	−0.223486	+	0.0360432i	−0.0196011	+	0.00316120i
$131$	−4.88926	−	12.8919i	−0.427176	−	1.12637i	−0.959964	−	0.280123i	$-0.909625\pi$
$131$	−4.88926	−	12.8919i	−0.427176	−	1.12637i	0.532788	−	0.846249i	$-0.321144\pi$
$132$	−3.31745	−	0.817679i	−0.288747	−	0.0711698i
$133$	21.1806	+	11.1164i	1.83659	+	0.963917i
$134$	−1.54593	+	4.07629i	−0.133548	+	0.352138i
$135$	−0.0553044	+	0.455472i	−0.00475984	+	0.0392008i
$136$	−5.18382	−	7.51005i	−0.444508	−	0.643982i
$137$	−14.5496	+	3.58615i	−1.24306	+	0.306386i	−0.805386	−	0.592750i	$-0.798042\pi$
$137$	−14.5496	+	3.58615i	−1.24306	+	0.306386i	−0.437669	+	0.899136i	$0.644196\pi$
$138$	−19.0736	−	4.70122i	−1.62365	−	0.400194i
$139$	0.669781	−	5.51615i	0.0568101	−	0.467873i	−0.936346	−	0.351079i	$-0.885815\pi$
$139$	0.669781	−	5.51615i	0.0568101	−	0.467873i	0.993156	−	0.116795i	$-0.0372620\pi$
$140$	0.0294393	+	0.0776250i	0.00248807	+	0.00656051i
$141$	−34.5595	+	8.51816i	−2.91044	+	0.717359i
$142$	3.23603	+	0.797610i	0.271562	+	0.0669339i
$143$	−4.38110	+	5.35266i	−0.366366	+	0.447612i
$144$	31.5676	−	7.78072i	2.63064	−	0.648393i
$145$	−0.0997182	+	0.0523361i	−0.00828114	+	0.00434628i
$146$	−9.34443			−0.773351
$147$	−21.2863			−1.75566
$148$	4.90886	−	2.57637i	0.403506	−	0.211776i
$149$	−2.93801	−	2.60285i	−0.240691	−	0.213233i	0.534150	−	0.845390i	$-0.320632\pi$
$149$	−2.93801	−	2.60285i	−0.240691	−	0.213233i	−0.774841	+	0.632156i	$0.782170\pi$
$150$	25.0249			2.04328
$151$	−7.01963	+	6.21885i	−0.571249	+	0.506083i	−0.898570	−	0.438831i	$-0.855393\pi$
$151$	−7.01963	+	6.21885i	−0.571249	+	0.506083i	0.327321	+	0.944913i	$0.393854\pi$
$152$	13.0608	+	6.85486i	1.05937	+	0.556002i
$153$	3.24010	−	26.6846i	0.261946	−	2.15732i
$154$	10.1229	+	5.31292i	0.815728	+	0.428127i
$155$	−0.000101675	0	0.000837367i	−8.16671e−6	0	6.72589e-5i
$156$	−1.29206	+	6.29017i	−0.103448	+	0.503617i
$157$	1.26511	+	10.4191i	0.100967	+	0.831539i	0.951931	+	0.306314i	$0.0990957\pi$
$157$	1.26511	+	10.4191i	0.100967	+	0.831539i	−0.850964	+	0.525225i	$0.823981\pi$
$158$	−5.14928	+	13.5775i	−0.409654	+	1.08017i
$159$	4.05519	−	2.12833i	0.321598	−	0.168787i
$160$	0.0435488	+	0.114829i	0.00344283	+	0.00907800i
$161$	12.9142	+	6.77791i	1.01778	+	0.534174i
$162$	23.1835	+	12.1676i	1.82146	+	0.955978i
$163$	14.9790	+	3.69198i	1.17324	+	0.289179i	0.777320	−	0.629105i	$-0.216579\pi$
$163$	14.9790	+	3.69198i	1.17324	+	0.289179i	0.395923	+	0.918284i	$0.370425\pi$
$164$	0.587803	+	4.84099i	0.0458997	+	0.378018i
$165$	−0.175609	+	0.155576i	−0.0136712	+	0.0121116i
$166$	6.73921	−	9.76344i	0.523064	−	0.757790i
$167$	2.60498	+	6.86877i	0.201580	+	0.531522i	0.997242	−	0.0742187i	$-0.0236463\pi$
$167$	2.60498	+	6.86877i	0.201580	+	0.531522i	−0.795662	+	0.605740i	$0.792877\pi$
$168$	−26.6055			−2.05266
$169$	10.3739	+	7.83472i	0.797990	+	0.602671i
$170$	0.249963			0.0191713
$171$	15.4076	+	40.6266i	1.17825	+	3.10679i
$172$	1.59945	−	2.31720i	0.121957	−	0.176685i
$173$	−6.29403	+	5.57602i	−0.478526	+	0.423937i	−0.867595	−	0.497272i	$-0.834335\pi$
$173$	−6.29403	+	5.57602i	−0.478526	+	0.423937i	0.389069	+	0.921209i	$0.372797\pi$
$174$	1.73541	+	14.2924i	0.131561	+	1.08350i
$175$	−18.0396	−	4.44637i	−1.36367	−	0.336114i
$176$	8.17983	+	4.29311i	0.616578	+	0.323605i
$177$	5.02456	+	2.63709i	0.377669	+	0.198216i
$178$	2.31763	+	6.11109i	0.173714	+	0.458045i
$179$	16.7482	−	8.79014i	1.25182	−	0.657006i	0.297195	−	0.954817i	$-0.403949\pi$
$179$	16.7482	−	8.79014i	1.25182	−	0.657006i	0.954625	+	0.297811i	$0.0962566\pi$
$180$	−0.0534745	+	0.141001i	−0.00398576	+	0.0105096i
$181$	−0.459591	−	3.78507i	−0.0341611	−	0.281342i	−0.999772	−	0.0213508i	$-0.993203\pi$
$181$	−0.459591	−	3.78507i	−0.0341611	−	0.281342i	0.965611	−	0.259991i	$-0.0837197\pi$
$182$	9.23449	−	19.4008i	0.684506	−	1.43808i
$183$	0.287696	−	2.36939i	0.0212671	−	0.175150i
$184$	7.96345	+	4.17954i	0.587073	+	0.308120i
$185$	0.0458850	−	0.377897i	0.00337353	−	0.0277835i
$186$	0.0954851	+	0.0501145i	0.00700131	+	0.00367457i
$187$	5.71696	−	5.06479i	0.418066	−	0.370374i
$188$	−6.50064			−0.474108
$189$	−32.5968	−	28.8783i	−2.37107	−	2.10058i
$190$	−0.357763	+	0.187768i	−0.0259549	+	0.0136222i
$191$	−17.3024			−1.25196			−0.625980	−	0.779839i	$-0.715301\pi$
$191$	−17.3024			−1.25196			−0.625980	+	0.779839i	$0.715301\pi$
$192$	−14.3746			−1.03739
$193$	23.8475	−	12.5162i	1.71658	−	0.900933i	0.744065	−	0.668107i	$-0.232895\pi$
$193$	23.8475	−	12.5162i	1.71658	−	0.900933i	0.972519	−	0.232825i	$-0.0747971\pi$
$194$	−4.66615	+	1.15010i	−0.335010	+	0.0825725i
$195$	0.305062	+	0.318372i	0.0218460	+	0.0227991i
$196$	−3.77463	−	0.930362i	−0.269616	−	0.0664544i
$197$	7.82984	−	1.92988i	0.557853	−	0.137498i	0.0496984	−	0.998764i	$-0.484174\pi$
$197$	7.82984	−	1.92988i	0.557853	−	0.137498i	0.508155	+	0.861266i	$0.330328\pi$
$198$	7.36383	+	19.4168i	0.523324	+	1.37989i
$199$	−2.96888	+	24.4510i	−0.210459	+	1.73328i	0.378924	+	0.925428i	$0.376294\pi$
$199$	−2.96888	+	24.4510i	−0.210459	+	1.73328i	−0.589382	+	0.807854i	$0.700629\pi$
$200$	−11.1240	−	2.74182i	−0.786586	−	0.193876i
$201$	8.24493	−	2.03219i	0.581552	−	0.143340i
$202$	−1.49343	−	2.16361i	−0.105078	−	0.152231i
$203$	1.28844	−	10.6112i	0.0904306	−	0.744763i
$204$	2.51438	−	6.62986i	0.176041	−	0.464183i
$205$	0.296495	+	0.155613i	0.0207081	+	0.0108685i
$206$	−21.2441	−	5.23620i	−1.48015	−	0.364823i
$207$	9.39433	+	24.7708i	0.652951	+	1.72169i
$208$	7.46194	−	15.6768i	0.517392	−	1.08699i
$209$	−4.37789	+	11.5435i	−0.302825	+	0.798483i
$210$	0.413993	−	0.599773i	0.0285682	−	0.0413882i
$211$	−14.9798	−	13.2710i	−1.03125	−	0.913610i	−0.0349387	−	0.999389i	$-0.511124\pi$
$211$	−14.9798	−	13.2710i	−1.03125	−	0.913610i	−0.996314	+	0.0857791i	$0.972662\pi$
$212$	0.812117	−	0.200169i	0.0557764	−	0.0137477i
$213$	−2.30203	−	6.06996i	−0.157733	−	0.415907i
$214$	−21.4559	+	11.2609i	−1.46670	+	0.769782i
$215$	−0.0685576	−	0.180772i	−0.00467559	−	0.0123285i
$216$	−20.1006	−	17.8075i	−1.36767	−	1.21165i
$217$	−0.0599279	−	0.0530915i	−0.00406817	−	0.00360408i
$218$	11.1417	+	16.1415i	0.754609	+	1.09324i
$219$	10.3395	+	14.9793i	0.698677	+	1.01221i
$220$	−0.0379401	+	0.0199125i	−0.00255792	+	0.00134250i
$221$	−9.93130	−	10.3646i	−0.668051	−	0.697198i
$222$	−43.0917	−	22.6163i	−2.89212	−	1.51790i
$223$	1.40034	+	11.5328i	0.0937736	+	0.772295i	0.961415	+	0.275104i	$0.0887122\pi$
$223$	1.40034	+	11.5328i	0.0937736	+	0.772295i	−0.867641	+	0.497191i	$0.834365\pi$
$224$	−11.3178	−	2.78958i	−0.756201	−	0.186387i
$225$	−19.1714	−	27.7745i	−1.27809	−	1.85163i
$226$	−15.9013	+	23.0370i	−1.05774	+	1.53240i
$227$	4.60510	−	4.07976i	0.305651	−	0.270783i	−0.496328	−	0.868135i	$-0.665319\pi$
$227$	4.60510	−	4.07976i	0.305651	−	0.270783i	0.801979	+	0.597352i	$0.203780\pi$
$228$	1.38152	+	11.3778i	0.0914934	+	0.753516i
$229$	−11.6521	+	2.87198i	−0.769992	+	0.189786i	−0.604694	−	0.796458i	$-0.706705\pi$
$229$	−11.6521	+	2.87198i	−0.769992	+	0.189786i	−0.165298	+	0.986244i	$0.552859\pi$
$230$	−0.218135	+	0.114486i	−0.0143834	+	0.00754899i
$231$	−2.68414	−	22.1059i	−0.176604	−	1.45446i
$232$	0.794505	−	6.54333i	0.0521618	−	0.429591i
$233$	6.82624	+	9.88952i	0.447202	+	0.647884i	0.980148	−	0.198265i	$-0.0635307\pi$
$233$	6.82624	+	9.88952i	0.447202	+	0.647884i	−0.532947	+	0.846149i	$0.678915\pi$
$234$	35.9240	−	15.2546i	2.34843	−	0.997223i
$235$	−0.253567	+	0.367355i	−0.0165409	+	0.0239636i
$236$	0.775729	+	0.687236i	0.0504957	+	0.0447353i
$237$	27.4627	−	6.76894i	1.78389	−	0.439690i
$238$	−13.4775	+	19.5256i	−0.873619	+	1.26566i
$239$	14.8575			0.961050			0.480525	−	0.876981i	$-0.340446\pi$
$239$	14.8575			0.961050			0.480525	+	0.876981i	$0.340446\pi$
$240$	0.334527	−	0.484646i	0.0215936	−	0.0312838i
$241$	1.06219	−	8.74790i	0.0684215	−	0.563502i	−0.917676	−	0.397331i	$-0.869937\pi$
$241$	1.06219	−	8.74790i	0.0684215	−	0.563502i	0.986097	−	0.166171i	$-0.0531403\pi$
$242$	4.16128	−	10.9724i	0.267497	−	0.705332i
$243$	−1.91059	−	15.7352i	−0.122565	−	1.00941i
$244$	0.154575	−	0.407582i	0.00989567	−	0.0260927i
$245$	−0.199810	+	0.177016i	−0.0127654	+	0.0113091i
$246$	32.0423	−	28.3870i	2.04294	−	1.80989i
$247$	22.0000	+	7.37422i	1.39983	+	0.469211i
$248$	−0.0369540	−	0.0327384i	−0.00234658	−	0.00207889i
$249$	−23.1078			−1.46440
$250$	0.469880	−	0.416277i	0.0297178	−	0.0263277i
$251$	28.1320	+	6.93392i	1.77568	+	0.437665i	0.984711	−	0.174194i	$-0.0557319\pi$
$251$	28.1320	+	6.93392i	1.77568	+	0.437665i	0.790967	+	0.611859i	$0.209578\pi$
$252$	−8.13087	−	11.7796i	−0.512197	−	0.742045i
$253$	−2.66928	+	7.03832i	−0.167816	+	0.442495i
$254$	−4.84491	+	12.7750i	−0.303997	+	0.801574i
$255$	−0.276580	−	0.400696i	−0.0173201	−	0.0250926i
$256$	−12.3121	−	3.03466i	−0.769505	−	0.189666i
$257$	−2.44338	+	2.16465i	−0.152414	+	0.135027i	−0.735884	−	0.677108i	$-0.763233\pi$
$257$	−2.44338	+	2.16465i	−0.152414	+	0.135027i	0.583470	+	0.812135i	$0.301695\pi$
$258$	−24.7164			−1.53878
$259$	27.0450	+	23.9598i	1.68049	+	1.48879i
$260$	0.0401806	+	0.0697893i	0.00249190	+	0.00432815i
$261$	14.5332	−	12.8753i	0.899584	−	0.796962i
$262$	−16.5459	+	14.6584i	−1.02221	+	0.905598i
$263$	8.53964	−	22.5172i	0.526577	−	1.38847i	−0.363046	−	0.931771i	$-0.618263\pi$
$263$	8.53964	−	22.5172i	0.526577	−	1.38847i	0.889622	−	0.456697i	$-0.150968\pi$
$264$	−1.65516	−	13.6314i	−0.101868	−	0.838957i
$265$	0.0203661	−	0.0537011i	0.00125108	−	0.00329883i
$266$	4.62258	−	38.0704i	0.283429	−	2.33424i
$267$	7.23177	−	10.4770i	0.442577	−	0.641184i
$268$	1.55087			0.0947343
$269$	−16.3445	+	23.6791i	−0.996544	+	1.44374i	−0.103045	+	0.994677i	$0.532859\pi$
$269$	−16.3445	+	23.6791i	−0.996544	+	1.44374i	−0.893499	+	0.449066i	$0.851757\pi$
$270$	0.714213	−	0.176038i	0.0434656	−	0.0107133i
$271$	−15.8591	−	14.0500i	−0.963375	−	0.853475i	0.0258820	−	0.999665i	$-0.491761\pi$
$271$	−15.8591	−	14.0500i	−0.963375	−	0.853475i	−0.989257	+	0.146190i	$0.953299\pi$
$272$	−10.8905	+	15.7777i	−0.660335	+	0.956661i
$273$	−41.3177	+	6.66358i	−2.50066	+	0.403298i
$274$	13.6474	+	19.7717i	0.824469	+	1.19445i
$275$	1.15585	−	9.51931i	0.0697006	−	0.574036i
$276$	0.842340	+	6.93729i	0.0507029	+	0.417576i
$277$	6.63650	−	3.48310i	0.398749	−	0.209279i	−0.253415	−	0.967358i	$-0.581554\pi$
$277$	6.63650	−	3.48310i	0.398749	−	0.209279i	0.652164	+	0.758078i	$0.273862\pi$
$278$	−8.64970	+	2.13196i	−0.518775	+	0.127866i
$279$	−0.0175295	−	0.144369i	−0.00104946	−	0.00864312i
$280$	−0.249740	+	0.221251i	−0.0149248	+	0.0132223i
$281$	−5.50309	+	7.97260i	−0.328287	+	0.475605i	−0.952022	−	0.306031i	$-0.900999\pi$
$281$	−5.50309	+	7.97260i	−0.328287	+	0.475605i	0.623735	+	0.781636i	$0.285614\pi$
$282$	32.4165	+	46.9635i	1.93038	+	2.79663i
$283$	−17.4904	−	4.31100i	−1.03970	−	0.256262i	−0.317724	−	0.948183i	$-0.602919\pi$
$283$	−17.4904	−	4.31100i	−1.03970	−	0.256262i	−0.721973	+	0.691921i	$0.756765\pi$
$284$	−0.142912	−	1.17698i	−0.00848024	−	0.0698411i
$285$	0.696856	+	0.365738i	0.0412782	+	0.0216645i
$286$	10.5146	+	3.52439i	0.621739	+	0.208402i
$287$	−28.1420	+	14.7700i	−1.66117	+	0.871848i
$288$	−12.0278	−	17.4253i	−0.708744	−	1.02679i
$289$	−0.653032	−	0.946080i	−0.0384136	−	0.0556518i
$290$	0.135145	+	0.119728i	0.00793598	+	0.00703066i
$291$	7.00666	+	6.20736i	0.410738	+	0.363882i
$292$	1.17876	+	3.10814i	0.0689819	+	0.181890i
$293$	−13.5769	+	7.12571i	−0.793171	+	0.416288i	−0.812090	−	0.583533i	$-0.801670\pi$
$293$	−13.5769	+	7.12571i	−0.793171	+	0.416288i	0.0189184	+	0.999821i	$0.493978\pi$
$294$	12.1015	+	31.9090i	0.705773	+	1.86097i
$295$	0.0690945	−	0.0170303i	0.00402284	−	0.000991541i
$296$	16.6771	+	14.7746i	0.969335	+	0.858756i
$297$	12.7680	−	18.4977i	0.740876	−	1.07334i
$298$	−2.23148	+	5.88394i	−0.129266	+	0.340847i
$299$	13.4139	+	4.49621i	0.775743	+	0.260022i
$300$	−3.15679	−	8.32378i	−0.182258	−	0.480574i
$301$	17.8173	+	4.39156i	1.02697	+	0.253125i
$302$	13.3130	+	6.98722i	0.766079	+	0.402069i
$303$	−1.81585	+	4.78801i	−0.104318	+	0.275064i
$304$	3.73528	−	30.7628i	0.214233	−	1.76437i
$305$	−0.0170032	−	0.0246334i	−0.000973602	−	0.00141051i
$306$	−41.8433	+	10.3134i	−2.39202	+	0.589580i
$307$	−10.5780	−	2.60725i	−0.603719	−	0.148803i	−0.0744034	−	0.997228i	$-0.523705\pi$
$307$	−10.5780	−	2.60725i	−0.603719	−	0.148803i	−0.529316	+	0.848425i	$0.677551\pi$
$308$	0.490215	−	4.03729i	0.0279326	−	0.230046i
$309$	15.1125	+	39.8485i	0.859722	+	2.26690i
$310$	0.00131305		0.000323638i	7.45762e−5		1.83814e-5i
$311$	−25.7661	−	6.35078i	−1.46106	−	0.360120i	−0.572892	−	0.819631i	$-0.694178\pi$
$311$	−25.7661	−	6.35078i	−1.46106	−	0.360120i	−0.888172	+	0.459511i	$0.848025\pi$
$312$	−25.4782	+	4.10905i	−1.44242	+	0.232629i
$313$	−18.7422	+	4.61954i	−1.05937	+	0.261112i	−0.730254	−	0.683176i	$-0.760598\pi$
$313$	−18.7422	+	4.61954i	−1.05937	+	0.261112i	−0.329120	+	0.944288i	$0.606752\pi$
$314$	14.8995	−	7.81986i	0.840827	−	0.441300i
$315$	−0.982828			−0.0553761
$316$	5.16571			0.290594
$317$	−1.10622	+	0.580591i	−0.0621317	+	0.0326092i	−0.495503	−	0.868606i	$-0.665016\pi$
$317$	−1.10622	+	0.580591i	−0.0621317	+	0.0326092i	0.433371	+	0.901216i	$0.357324\pi$
$318$	−5.49587	−	4.86892i	−0.308193	−	0.273035i
$319$	5.51687			0.308885
$320$	−0.134931	+	0.119538i	−0.00754287	+	0.00668240i
$321$	41.7922	+	21.9342i	2.33261	+	1.22425i
$322$	2.81848	−	23.2123i	0.157068	−	1.29357i
$323$	−22.6861	−	11.9066i	−1.26229	−	0.662501i
$324$	1.12269	−	9.24617i	0.0623716	−	0.513676i
$325$	−17.9620	−	1.47187i	−0.996354	−	0.0816449i
$326$	−2.98127	−	24.5530i	−0.165118	−	1.35987i
$327$	13.5471	−	35.7207i	0.749154	−	1.97536i
$328$	−17.3535	+	9.10783i	−0.958188	+	0.502896i
$329$	−15.0237	−	39.6141i	−0.828281	−	2.18400i
$330$	0.333051	+	0.174799i	0.0183339	+	0.00962235i
$331$	14.0077	+	7.35179i	0.769931	+	0.404091i	0.803469	−	0.595347i	$-0.202985\pi$
$331$	14.0077	+	7.35179i	0.769931	+	0.404091i	−0.0335383	+	0.999437i	$0.510678\pi$
$332$	−4.09764	−	1.00998i	−0.224887	−	0.0554297i
$333$	7.91093	+	65.1524i	0.433516	+	3.57033i
$334$	8.81561	−	7.80995i	0.482368	−	0.427341i
$335$	0.0604938	−	0.0876404i	0.00330513	−	0.00478831i
$336$	19.8205	+	52.2624i	1.08130	+	2.85115i
$337$	−13.5445			−0.737818			−0.368909	−	0.929465i	$-0.620269\pi$
$337$	−13.5445			−0.737818			−0.368909	+	0.929465i	$0.620269\pi$
$338$	5.84690	−	20.0050i	0.318030	−	1.08813i
$339$	54.5234			2.96130
$340$	−0.0315319	−	0.0831427i	−0.00171005	−	0.00450904i
$341$	0.0234735	−	0.0340072i	0.00127116	−	0.00184159i
$342$	52.1415	−	46.1933i	2.81949	−	2.49785i
$343$	0.0822417	+	0.677321i	0.00444063	+	0.0365719i
$344$	10.9869	+	2.70802i	0.592372	+	0.146007i
$345$	0.424887	+	0.222998i	0.0228751	+	0.0120058i
$346$	11.9369	+	6.26497i	0.641732	+	0.336807i
$347$	−2.86896	−	7.56483i	−0.154014	−	0.406101i	0.835696	−	0.549193i	$-0.185065\pi$
$347$	−2.86896	−	7.56483i	−0.154014	−	0.406101i	−0.989709	+	0.143092i	$0.954296\pi$
$348$	4.53501	−	2.38015i	0.243102	−	0.127590i
$349$	−1.33694	+	3.52523i	−0.0715650	+	0.188701i	−0.966026	−	0.258444i	$-0.916790\pi$
$349$	−1.33694	+	3.52523i	−0.0715650	+	0.188701i	0.894461	+	0.447146i	$0.147559\pi$
$350$	3.59044	+	29.5700i	0.191917	+	1.58058i
$351$	−35.6757	−	22.6203i	−1.90423	−	1.20738i
$352$	0.725163	−	5.97226i	0.0386513	−	0.318322i
$353$	−7.98851	−	4.19269i	−0.425185	−	0.223154i	0.238537	−	0.971133i	$-0.423332\pi$
$353$	−7.98851	−	4.19269i	−0.425185	−	0.223154i	−0.663723	+	0.747979i	$0.731024\pi$
$354$	1.09659	−	9.03123i	0.0582831	−	0.480005i
$355$	−0.0720864	−	0.0378339i	−0.00382595	−	0.00200801i
$356$	1.74031	−	1.54178i	0.0922361	−	0.0817141i
$357$	46.2126			2.44583
$358$	−22.6983	−	20.1089i	−1.19964	−	1.06279i
$359$	−2.60889	+	1.36925i	−0.137692	+	0.0722663i	−0.532162	−	0.846642i	$-0.678620\pi$
$359$	−2.60889	+	1.36925i	−0.137692	+	0.0722663i	0.394470	+	0.918909i	$0.370928\pi$
$360$	−0.606053			−0.0319418
$361$	22.4139			1.17968
$362$	−5.41269	+	2.84080i	−0.284485	+	0.149309i
$363$	−22.1934	+	5.47017i	−1.16485	+	0.287110i
$364$	−7.61798	−	0.624245i	−0.399290	−	0.0327193i
$365$	0.221622	+	0.0546250i	0.0116002	+	0.00285920i
$366$	−3.71537	+	0.915755i	−0.194205	+	0.0478673i
$367$	5.37095	+	14.1620i	0.280361	+	0.739252i	0.999036	+	0.0439055i	$0.0139801\pi$
$367$	5.37095	+	14.1620i	0.280361	+	0.739252i	−0.718674	+	0.695347i	$0.755251\pi$
$368$	2.27747	−	18.7567i	0.118721	−	0.977759i
$369$	−56.0533	−	13.8159i	−2.91802	−	0.719226i
$370$	−0.592569	+	0.146055i	−0.0308062	+	0.00759305i
$371$	3.09669	+	4.48634i	0.160772	+	0.232919i
$372$	0.00462399	−	0.0380820i	0.000239743	−	0.00197446i
$373$	4.18305	−	11.0298i	0.216590	−	0.571101i	−0.782051	−	0.623214i	$-0.785826\pi$
$373$	4.18305	−	11.0298i	0.216590	−	0.571101i	0.998641	+	0.0521133i	$0.0165957\pi$
$374$	−10.8425	−	5.69057i	−0.560651	−	0.294252i
$375$	−1.18722	−	0.292622i	−0.0613076	−	0.0151110i
$376$	−9.26422	−	24.4277i	−0.477766	−	1.25976i
$377$	−0.404991	−	10.3606i	−0.0208581	−	0.533600i
$378$	−24.7580	+	65.2815i	−1.27341	+	3.35772i
$379$	−16.9143	+	24.5046i	−0.868829	+	1.25872i	0.0958783	+	0.995393i	$0.469434\pi$
$379$	−16.9143	+	24.5046i	−0.868829	+	1.25872i	−0.964708	+	0.263323i	$0.915181\pi$
$380$	0.107586	+	0.0953128i	0.00551904	+	0.00488944i
$381$	25.8394	−	6.36884i	1.32379	−	0.326286i
$382$	9.83662	+	25.9370i	0.503285	+	1.32705i
$383$	17.6480	−	9.26239i	0.901772	−	0.473286i	0.0509262	−	0.998702i	$-0.483783\pi$
$383$	17.6480	−	9.26239i	0.901772	−	0.473286i	0.850845	+	0.525416i	$0.176090\pi$
$384$	15.1173	+	39.8611i	0.771452	+	2.03415i
$385$	−0.209028	−	0.185183i	−0.0106530	−	0.00943777i
$386$	−32.3198	−	28.6328i	−1.64503	−	1.45737i
$387$	18.9350	+	27.4321i	0.962521	+	1.39445i
$388$	0.971163	+	1.40697i	0.0493033	+	0.0714282i
$389$	16.8604	−	8.84900i	0.854854	−	0.448662i	0.0204342	−	0.999791i	$-0.493495\pi$
$389$	16.8604	−	8.84900i	0.854854	−	0.448662i	0.834420	+	0.551129i	$0.185803\pi$
$390$	0.303821	−	0.638299i	0.0153846	−	0.0323215i
$391$	−13.8322	−	7.25969i	−0.699523	−	0.367138i
$392$	−1.88325	−	15.5100i	−0.0951185	−	0.783371i
$393$	41.8055	+	10.3041i	2.10881	+	0.519775i
$394$	−7.34432	−	10.6401i	−0.370001	−	0.536040i
$395$	0.201496	−	0.291917i	0.0101384	−	0.0146880i
$396$	5.52950	−	4.89871i	0.277868	−	0.246169i
$397$	1.26140	+	10.3885i	0.0633077	+	0.521386i	0.989521	+	0.144387i	$0.0461209\pi$
$397$	1.26140	+	10.3885i	0.0633077	+	0.521386i	−0.926214	+	0.376999i	$0.876956\pi$
$398$	38.3408	−	9.45016i	1.92185	−	0.473694i
$399$	−66.1424	+	34.7142i	−3.31126	+	1.73788i
$400$	2.90126	+	23.8940i	0.145063	+	1.19470i
$401$	2.02071	−	16.6420i	0.100909	−	0.831063i	−0.851102	−	0.525000i	$-0.824065\pi$
$401$	2.02071	−	16.6420i	0.100909	−	0.831063i	0.952011	−	0.306062i	$-0.0990117\pi$
$402$	−7.73367	−	11.2042i	−0.385720	−	0.558812i
$403$	−0.0655884	−	0.0415865i	−0.00326719	−	0.00207157i
$404$	−0.531269	+	0.769677i	−0.0264316	+	0.0382928i
$405$	−0.478714	−	0.424104i	−0.0237875	−	0.0210739i
$406$	−16.6392	+	4.10118i	−0.825788	+	0.203538i
$407$	−10.5934	+	15.3472i	−0.525095	+	0.760731i
$408$	28.4966			1.41079
$409$	6.62677	−	9.60054i	0.327673	−	0.474716i	−0.624176	−	0.781284i	$-0.714565\pi$
$409$	6.62677	−	9.60054i	0.327673	−	0.474716i	0.951849	+	0.306568i	$0.0991806\pi$
$410$	0.0647089	−	0.532926i	0.00319575	−	0.0263193i
$411$	16.5937	−	43.7541i	0.818509	−	2.15823i
$412$	0.938195	+	7.72673i	0.0462215	+	0.380669i
$413$	−2.39515	+	6.31548i	−0.117857	+	0.310764i
$414$	31.7917	−	28.1650i	1.56248	−	1.38423i
$415$	−0.216909	+	0.192164i	−0.0106476	+	0.00943297i
$416$	−11.2691	−	0.923429i	−0.552512	−	0.0452749i
$417$	12.9883	+	11.5067i	0.636042	+	0.563484i
$418$	19.7931			0.968112
$419$	−3.05362	+	2.70527i	−0.149179	+	0.132161i	−0.734411	−	0.678704i	$-0.762542\pi$
$419$	−3.05362	+	2.70527i	−0.149179	+	0.132161i	0.585232	+	0.810866i	$0.301003\pi$
$420$	−0.251720	−	0.0620434i	−0.0122827	−	0.00302741i
$421$	−9.52303	−	13.7965i	−0.464124	−	0.672400i	0.519118	−	0.854702i	$-0.326260\pi$
$421$	−9.52303	−	13.7965i	−0.464124	−	0.672400i	−0.983243	+	0.182302i	$0.941645\pi$
$422$	−11.3775	+	30.0000i	−0.553848	+	1.46038i
$423$	27.2895	−	71.9565i	1.32686	−	3.49865i
$424$	1.90955	+	2.76646i	0.0927360	+	0.134351i
$425$	19.3219	+	4.76243i	0.937251	+	0.231012i
$426$	−7.79039	+	6.90168i	−0.377446	+	0.334388i
$427$	2.84099			0.137485
$428$	6.45220	+	5.71615i	0.311879	+	0.276300i
$429$	−5.98453	−	20.7547i	−0.288936	−	1.00205i
$430$	−0.232008	+	0.205541i	−0.0111884	+	0.00991207i
$431$	18.2047	−	16.1280i	0.876890	−	0.776857i	−0.0990074	−	0.995087i	$-0.531567\pi$
$431$	18.2047	−	16.1280i	0.876890	−	0.776857i	0.975897	+	0.218230i	$0.0700283\pi$
$432$	−20.0057	+	52.7508i	−0.962526	+	2.53797i
$433$	1.29610	+	10.6743i	0.0622865	+	0.512976i	0.990145	+	0.140044i	$0.0447244\pi$
$433$	1.29610	+	10.6743i	0.0622865	+	0.512976i	−0.927859	+	0.372932i	$0.878353\pi$
$434$	−0.0455166	+	0.120017i	−0.00218487	+	0.00576102i
$435$	0.0423905	−	0.349117i	0.00203247	−	0.0167389i
$436$	3.96350	−	5.74213i	0.189817	−	0.274998i
$437$	25.2509			1.20791
$438$	16.5765	−	24.0152i	0.792055	−	1.14749i
$439$	5.34781	−	1.31812i	0.255237	−	0.0629103i	−0.109621	−	0.993973i	$-0.534964\pi$
$439$	5.34781	−	1.31812i	0.255237	−	0.0629103i	0.364858	+	0.931063i	$0.381118\pi$
$440$	−0.128895	−	0.114191i	−0.00614484	−	0.00544386i
$441$	26.1441	−	37.8763i	1.24496	−	1.80363i
$442$	−9.89089	+	20.7798i	−0.470462	+	0.988394i
$443$	5.70056	+	8.25869i	0.270842	+	0.392382i	0.934678	−	0.355496i	$-0.115688\pi$
$443$	5.70056	+	8.25869i	0.270842	+	0.392382i	−0.663836	+	0.747878i	$0.731073\pi$
$444$	−2.08677	+	17.1861i	−0.0990337	+	0.815616i
$445$	−0.0192436	−	0.158485i	−0.000912233	−	0.00751291i
$446$	16.4921	−	8.65570i	0.780921	−	0.409859i
$447$	11.9012	−	2.93338i	0.562906	−	0.138744i
$448$	−2.06239	−	16.9853i	−0.0974385	−	0.802479i
$449$	−7.14011	+	6.32559i	−0.336963	+	0.298523i	−0.814587	−	0.580041i	$-0.803036\pi$
$449$	−7.14011	+	6.32559i	−0.336963	+	0.298523i	0.477624	+	0.878564i	$0.341498\pi$
$450$	−30.7360	+	44.5287i	−1.44891	+	2.09910i
$451$	−9.31824	−	13.4998i	−0.438779	−	0.635681i
$452$	9.66845	+	2.38306i	0.454766	+	0.112090i
$453$	−3.53002	−	29.0723i	−0.165855	−	1.36594i
$454$	−8.73378	−	4.58384i	−0.409896	−	0.215130i
$455$	−0.332426	+	0.406146i	−0.0155844	+	0.0190404i
$456$	−40.7862	+	21.4062i	−1.90999	+	1.00244i
$457$	8.36900	+	12.1246i	0.391485	+	0.567164i	0.968325	−	0.249693i	$-0.0803297\pi$
$457$	8.36900	+	12.1246i	0.391485	+	0.567164i	−0.576840	+	0.816857i	$0.695714\pi$
$458$	10.9296	+	15.8342i	0.510705	+	0.739884i
$459$	34.9138	+	30.9310i	1.62964	+	1.44373i
$460$	0.0655972	+	0.0581141i	0.00305849	+	0.00270958i
$461$	0.623521	+	1.64409i	0.0290403	+	0.0765729i	0.948752	−	0.316021i	$-0.102347\pi$
$461$	0.623521	+	1.64409i	0.0290403	+	0.0765729i	−0.919712	+	0.392594i	$0.871578\pi$
$462$	−31.6117	+	16.5911i	−1.47071	+	0.771888i
$463$	−9.35213	−	24.6595i	−0.434630	−	1.14603i	−0.956173	−	0.292801i	$-0.905413\pi$
$463$	−9.35213	−	24.6595i	−0.434630	−	1.14603i	0.521543	−	0.853225i	$-0.325357\pi$
$464$	−13.4453	+	3.31396i	−0.624181	+	0.153847i
$465$	−0.00197167	−	0.00174675i	−9.14339e−5	−	8.10034e-5i
$466$	10.9440	−	15.8551i	0.506970	−	0.734473i
$467$	3.13865	−	8.27593i	0.145239	−	0.382965i	−0.842580	−	0.538572i	$-0.818964\pi$
$467$	3.13865	−	8.27593i	0.145239	−	0.382965i	0.987819	+	0.155607i	$0.0497334\pi$
$468$	−9.60565	−	10.0247i	−0.444021	−	0.463394i
$469$	3.58422	+	9.45081i	0.165504	+	0.436398i
$470$	0.694835	+	0.171261i	0.0320503	+	0.00789970i
$471$	−29.0215	−	15.2316i	−1.33724	−	0.701837i
$472$	−1.47695	+	3.89439i	−0.0679820	+	0.179254i
$473$	−1.14160	+	9.40195i	−0.0524910	+	0.432302i
$474$	−25.7597	−	37.3194i	−1.18318	−	1.71414i
$475$	−31.2322	+	7.69805i	−1.43303	+	0.353211i
$476$	8.19473	+	2.01982i	0.375605	+	0.0925783i
$477$	−1.19355	+	9.82975i	−0.0546488	+	0.450073i
$478$	−8.44664	−	22.2719i	−0.386340	−	1.01870i
$479$	−5.95175	+	1.46697i	−0.271942	+	0.0670278i	−0.372929	−	0.927860i	$-0.621646\pi$
$479$	−5.95175	+	1.46697i	−0.271942	+	0.0670278i	0.100986	+	0.994888i	$0.467800\pi$
$480$	−0.372363	−	0.0917792i	−0.0169960	−	0.00418913i
$481$	29.5995	+	18.7677i	1.34962	+	0.855732i
$482$	−13.7173	+	3.38101i	−0.624806	+	0.154001i
$483$	−40.3283	+	21.1659i	−1.83500	+	0.963084i
$484$	−4.17456			−0.189753
$485$	0.117390			0.00533042
$486$	−22.5014	+	11.8097i	−1.02069	+	0.535697i
$487$	−17.7365	−	15.7132i	−0.803719	−	0.712033i	0.157590	−	0.987505i	$-0.449627\pi$
$487$	−17.7365	−	15.7132i	−0.803719	−	0.712033i	−0.961309	+	0.275472i	$0.911166\pi$
$488$	1.75188			0.0793037
$489$	−36.0602	+	31.9466i	−1.63070	+	1.44467i
$490$	0.378948	+	0.198887i	0.0171191	+	0.00898482i
$491$	−3.52027	+	28.9920i	−0.158868	+	1.30839i	0.667224	+	0.744857i	$0.267482\pi$
$491$	−3.52027	+	28.9920i	−0.158868	+	1.30839i	−0.826092	+	0.563535i	$0.809441\pi$
$492$	−13.4841	−	7.07699i	−0.607909	−	0.319055i
$493$	−1.38002	+	11.3655i	−0.0621530	+	0.511876i
$494$	−1.45300	−	37.1713i	−0.0653737	−	1.67241i
$495$	−0.0611428	−	0.503556i	−0.00274816	−	0.0226332i
$496$	−0.0367797	+	0.0969801i	−0.00165146	+	0.00435453i
$497$	6.84211	−	3.59102i	0.306911	−	0.161079i
$498$	13.1371	+	34.6396i	0.588685	+	1.55224i
$499$	−3.45829	−	1.81505i	−0.154815	−	0.0812529i	0.385537	−	0.922693i	$-0.374016\pi$
$499$	−3.45829	−	1.81505i	−0.154815	−	0.0812529i	−0.540351	+	0.841440i	$0.681709\pi$
$500$	−0.197736	−	0.103780i	−0.00884300	−	0.00464116i
$501$	−22.2738	−	5.49001i	−0.995122	−	0.245276i
$502$	−5.59914	−	46.1131i	−0.249902	−	2.05813i
$503$	16.0883	−	14.2530i	0.717341	−	0.635509i	−0.223364	−	0.974735i	$-0.571704\pi$
$503$	16.0883	−	14.2530i	0.717341	−	0.635509i	0.940705	+	0.339227i	$0.110165\pi$
$504$	32.6772	−	47.3411i	1.45556	−	2.10874i
$505$	0.0227719	+	0.0600447i	0.00101334	+	0.00267195i
$506$	12.0682			0.536499
$507$	−38.5379	+	12.7625i	−1.71153	+	0.566802i
$508$	4.86038			0.215645
$509$	5.07939	+	13.3933i	0.225140	+	0.593646i	0.999222	−	0.0394397i	$-0.0125573\pi$
$509$	5.07939	+	13.3933i	0.225140	+	0.593646i	−0.774082	+	0.633086i	$0.781788\pi$
$510$	−0.443420	+	0.642405i	−0.0196350	+	0.0284462i
$511$	−16.2164	+	14.3665i	−0.717372	+	0.635536i
$512$	−0.840590	−	6.92288i	−0.0371492	−	0.305951i
$513$	−73.2057	−	18.0436i	−3.23211	−	0.796644i
$514$	4.63398	+	2.43210i	0.204396	+	0.107275i
$515$	0.473237	+	0.248374i	0.0208533	+	0.0109447i
$516$	3.11788	+	8.22117i	0.137257	+	0.361917i
$517$	19.3618	−	10.1619i	0.851533	−	0.446919i
$518$	20.5413	−	54.1629i	0.902532	−	2.37978i
$519$	−3.16513	−	26.0672i	−0.138934	−	1.14422i
$520$	−0.204988	+	0.250447i	−0.00898932	+	0.0109828i
$521$	−3.68616	+	30.3583i	−0.161494	+	1.33002i	0.656296	+	0.754504i	$0.272122\pi$
$521$	−3.68616	+	30.3583i	−0.161494	+	1.33002i	−0.817790	+	0.575517i	$0.804801\pi$
$522$	−27.5629	−	14.4661i	−1.20640	−	0.633166i
$523$	0.602059	−	4.95840i	0.0263262	−	0.216816i	−0.973609	−	0.228224i	$-0.926708\pi$
$523$	0.602059	−	4.95840i	0.0263262	−	0.216816i	0.999935	+	0.0114078i	$0.00363131\pi$
$524$	6.96287	+	3.65440i	0.304174	+	0.159643i
$525$	43.4285	−	38.4743i	1.89538	−	1.67916i
$526$	−38.6090			−1.68343
$527$	0.0641876	+	0.0568653i	0.00279606	+	0.00247709i
$528$	−25.5438	+	13.4064i	−1.11165	+	0.583440i
$529$	−7.60405			−0.330611
$530$	−0.0920784			−0.00399963
$531$	−10.8636	+	5.70166i	−0.471441	+	0.247431i
$532$	−13.2461	+	3.26486i	−0.574290	+	0.141550i
$533$	−24.6685	+	18.4906i	−1.06851	+	0.800916i
$534$	−19.8168	−	4.88441i	−0.857558	−	0.211369i
$535$	0.574700	−	0.141651i	0.0248464	−	0.00612410i
$536$	2.21018	+	5.82777i	0.0954652	+	0.251721i
$537$	−7.11971	+	58.6361i	−0.307238	+	2.53033i
$538$	44.7880	+	11.0393i	1.93095	+	0.475936i
$539$	12.6969	−	3.12950i	0.546894	−	0.134797i
$540$	−0.148649	−	0.215355i	−0.00639682	−	0.00926740i
$541$	2.96614	−	24.4284i	0.127525	−	1.05026i	−0.778681	−	0.627420i	$-0.784111\pi$
$541$	2.96614	−	24.4284i	0.127525	−	1.05026i	0.906205	−	0.422838i	$-0.138966\pi$
$542$	−12.0454	+	31.7611i	−0.517393	+	1.36425i
$543$	10.5429	+	5.53335i	0.452440	+	0.237459i
$544$	12.1223	+	2.98787i	0.519738	+	0.128104i
$545$	−0.169889	−	0.447960i	−0.00727723	−	0.0191885i
$546$	33.4785	+	58.1485i	1.43275	+	2.48853i
$547$	13.1155	−	34.5826i	0.560776	−	1.47865i	−0.292026	−	0.956411i	$-0.594329\pi$
$547$	13.1155	−	34.5826i	0.560776	−	1.47865i	0.852802	−	0.522235i	$-0.174902\pi$
$548$	4.85488	−	7.03351i	0.207390	−	0.300457i
$549$	3.86268	+	3.42203i	0.164855	+	0.146049i
$550$	−14.9269	+	3.67916i	−0.636487	+	0.156880i
$551$	−6.56241	−	17.3037i	−0.279568	−	0.737161i
$552$	−24.8681	+	13.0518i	−1.05846	+	0.555522i
$553$	11.9385	+	31.4793i	0.507677	+	1.33863i
$554$	−8.99423	−	7.96820i	−0.382128	−	0.338536i
$555$	0.889798	+	0.788293i	0.0377698	+	0.0334612i
$556$	1.80026	+	2.60812i	0.0763479	+	0.110609i
$557$	11.7132	+	16.9696i	0.496306	+	0.719023i	0.988460	−	0.151485i	$-0.0484056\pi$
$557$	11.7132	+	16.9696i	0.496306	+	0.719023i	−0.492154	+	0.870508i	$0.663790\pi$
$558$	−0.206449	+	0.108353i	−0.00873967	+	0.00458693i
$559$	17.7406	+	1.45373i	0.750347	+	0.0614862i
$560$	0.620665	+	0.325750i	0.0262279	+	0.0137654i
$561$	2.87494	+	23.6772i	0.121380	+	0.999654i
$562$	15.0798	+	3.71684i	0.636103	+	0.156785i
$563$	0.768892	+	1.11393i	0.0324049	+	0.0469467i	0.838852	−	0.544360i	$-0.183228\pi$
$563$	0.768892	+	1.11393i	0.0324049	+	0.0469467i	−0.806447	+	0.591307i	$0.798612\pi$
$564$	11.5318	−	16.7066i	0.485575	−	0.703476i
$565$	0.511800	−	0.453415i	0.0215316	−	0.0190753i
$566$	3.48113	+	28.6697i	0.146323	+	1.20508i
$567$	58.9398	−	14.5274i	2.47524	−	0.610091i
$568$	4.21913	−	2.21437i	0.177031	−	0.0929130i
$569$	1.69319	+	13.9447i	0.0709824	+	0.584593i	0.984192	+	0.177103i	$0.0566726\pi$
$569$	1.69319	+	13.9447i	0.0709824	+	0.584593i	−0.913210	+	0.407489i	$0.866404\pi$
$570$	0.152086	−	1.25254i	0.00637018	−	0.0524632i
$571$	7.11512	+	10.3080i	0.297758	+	0.431378i	0.943096	−	0.332520i	$-0.107899\pi$
$571$	7.11512	+	10.3080i	0.297758	+	0.431378i	−0.645338	+	0.763897i	$0.723283\pi$
$572$	−0.154088	−	3.94194i	−0.00644274	−	0.164821i
$573$	30.6935	−	44.4672i	1.28224	−	1.85765i
$574$	38.1399	+	33.7890i	1.59193	+	1.41033i
$575$	−19.0429	+	4.69365i	−0.794144	+	0.195739i
$576$	17.6550	−	25.5777i	0.735626	−	1.06574i
$577$	−1.34830			−0.0561306			−0.0280653	−	0.999606i	$-0.508935\pi$
$577$	−1.34830			−0.0561306			−0.0280653	+	0.999606i	$0.508935\pi$
$578$	−1.04696	+	1.51678i	−0.0435476	+	0.0630897i
$579$	−10.1377	+	83.4911i	−0.421307	+	3.46977i
$580$	0.0227759	−	0.0600550i	0.000945717	−	0.00249365i
$581$	−3.31539	−	27.3047i	−0.137546	−	1.13279i
$582$	5.32172	−	14.0322i	0.220592	−	0.581654i
$583$	−2.10595	+	1.86570i	−0.0872193	+	0.0772696i
$584$	−9.99972	+	8.85898i	−0.413791	+	0.366587i
$585$	−0.941186	+	0.151791i	−0.0389132	+	0.00627580i
$586$	18.4003	+	16.3013i	0.760111	+	0.673400i
$587$	8.17767			0.337528			0.168764	−	0.985656i	$-0.446022\pi$
$587$	8.17767			0.337528			0.168764	+	0.985656i	$0.446022\pi$
$588$	9.08700	−	8.05038i	0.374742	−	0.331992i
$589$	−0.134586	−	0.0331724i	−0.00554551	−	0.00136684i
$590$	−0.0648100	−	0.0938936i	−0.00266819	−	0.00386554i
$591$	−8.92989	+	23.5462i	−0.367327	+	0.968561i
$592$	16.5984	−	43.7663i	0.682189	−	1.79879i
$593$	−16.3223	−	23.6469i	−0.670275	−	0.971061i	−0.999639	−	0.0268580i	$-0.991450\pi$
$593$	−16.3223	−	23.6469i	−0.670275	−	0.971061i	0.329364	−	0.944203i	$-0.393166\pi$
$594$	−34.9875	−	8.62364i	−1.43555	−	0.353832i
$595$	0.433788	−	0.384303i	0.0177836	−	0.0157549i
$596$	2.23861			0.0916969
$597$	−57.5723	−	51.0046i	−2.35628	−	2.08748i
$598$	−0.885924	−	22.6640i	−0.0362281	−	0.926802i
$599$	−6.93469	+	6.14360i	−0.283344	+	0.251020i	−0.792808	−	0.609471i	$-0.791382\pi$
$599$	−6.93469	+	6.14360i	−0.283344	+	0.251020i	0.509465	+	0.860492i	$0.329843\pi$
$600$	26.7798	−	23.7249i	1.09328	−	0.968563i
$601$	−10.5609	+	27.8467i	−0.430786	+	1.13589i	0.527368	+	0.849637i	$0.323179\pi$
$601$	−10.5609	+	27.8467i	−0.430786	+	1.13589i	−0.958154	+	0.286253i	$0.907590\pi$
$602$	−3.54618	−	29.2054i	−0.144532	−	1.19032i
$603$	−6.51050	+	17.1668i	−0.265128	+	0.699086i
$604$	0.644701	−	5.30959i	0.0262325	−	0.216044i
$605$	−0.162835	+	0.235907i	−0.00662018	+	0.00959098i
$606$	8.20975			0.333498
$607$	16.6149	−	24.0709i	0.674379	−	0.977006i	−0.325130	−	0.945669i	$-0.605408\pi$
$607$	16.6149	−	24.0709i	0.674379	−	0.977006i	0.999509	−	0.0313371i	$-0.00997654\pi$
$608$	−19.5946	+	4.82963i	−0.794665	+	0.195867i
$609$	24.9853	+	22.1350i	1.01245	+	0.896956i
$610$	−0.0272600	+	0.0394929i	−0.00110372	+	0.00159902i
$611$	−20.5053	−	35.6154i	−0.829554	−	1.44084i
$612$	8.70882	+	12.6169i	0.352033	+	0.510008i
$613$	−2.10030	+	17.2975i	−0.0848302	+	0.698639i	0.886803	+	0.462147i	$0.152921\pi$
$613$	−2.10030	+	17.2975i	−0.0848302	+	0.698639i	−0.971633	+	0.236492i	$0.924002\pi$
$614$	2.10535	+	17.3391i	0.0849650	+	0.699750i
$615$	−0.925891	+	0.485945i	−0.0373355	+	0.0195952i
$616$	15.8697	−	3.91153i	0.639409	−	0.157600i
$617$	4.09804	+	33.7504i	0.164981	+	1.35874i	0.806319	+	0.591482i	$0.201457\pi$
$617$	4.09804	+	33.7504i	0.164981	+	1.35874i	−0.641338	+	0.767259i	$0.721620\pi$
$618$	51.1428	−	45.3086i	2.05727	−	1.82258i
$619$	−10.0760	+	14.5976i	−0.404988	+	0.586727i	−0.971416	−	0.237385i	$-0.923710\pi$
$619$	−10.0760	+	14.5976i	−0.404988	+	0.586727i	0.566427	+	0.824112i	$0.308325\pi$
$620$	−0.000273284	0	0.000395921i	−1.09754e−5	0	1.59006e-5i
$621$	−44.6350	−	11.0015i	−1.79114	−	0.441476i
$622$	5.12825	+	42.2350i	0.205624	+	1.69347i
$623$	13.4175	+	7.04202i	0.537559	+	0.282133i
$624$	27.0523	+	46.9869i	1.08296	+	1.88098i
$625$	22.1160	−	11.6074i	0.884641	−	0.464296i
$626$	17.5800	+	25.4691i	0.702640	+	1.01795i
$627$	−21.9008	−	31.7287i	−0.874633	−	1.26712i
$628$	−4.48055	−	3.96942i	−0.178793	−	0.158397i
$629$	−28.9674	−	25.6628i	−1.15500	−	1.02324i
$630$	0.558748	+	1.47330i	0.0222611	+	0.0586976i
$631$	−21.5676	+	11.3196i	−0.858594	+	0.450625i	−0.835747	−	0.549114i	$-0.814965\pi$
$631$	−21.5676	+	11.3196i	−0.858594	+	0.450625i	−0.0228467	+	0.999739i	$0.507273\pi$
$632$	7.36179	+	19.4114i	0.292836	+	0.772146i
$633$	60.6797	−	14.9562i	2.41180	−	0.594456i
$634$	1.49923	+	1.32820i	0.0595420	+	0.0527496i
$635$	0.189586	−	0.274663i	0.00752349	−	0.0108997i
$636$	−0.926215	+	2.44223i	−0.0367268	+	0.0968407i
$637$	−6.80925	−	23.6149i	−0.269792	−	0.935657i
$638$	−3.13640	−	8.27001i	−0.124171	−	0.327413i
$639$	13.6281	+	3.35903i	0.539121	+	0.132881i
$640$	0.473387	+	0.248453i	0.0187123	+	0.00982096i
$641$	6.42381	−	16.9382i	0.253725	−	0.669018i	−0.746269	−	0.665644i	$-0.768157\pi$
$641$	6.42381	−	16.9382i	0.253725	−	0.669018i	0.999994	−	0.00337388i	$-0.00107394\pi$
$642$	9.12098	−	75.1181i	0.359977	−	2.96467i
$643$	−17.9492	−	26.0039i	−0.707848	−	1.02549i	−0.997657	−	0.0684101i	$-0.978207\pi$
$643$	−17.9492	−	26.0039i	−0.707848	−	1.02549i	0.289810	−	0.957084i	$-0.406408\pi$
$644$	−8.07639	+	1.99065i	−0.318254	+	0.0784427i
$645$	0.586200	+	0.144485i	0.0230816	+	0.00568911i
$646$	−4.95116	+	40.7765i	−0.194801	+	1.60433i
$647$	5.04736	+	13.3088i	0.198432	+	0.523222i	0.996888	−	0.0788309i	$-0.0251187\pi$
$647$	5.04736	+	13.3088i	0.198432	+	0.523222i	−0.798456	+	0.602053i	$0.794349\pi$
$648$	36.3447	−	8.95817i	1.42776	−	0.351910i
$649$	−3.38477	−	0.834271i	−0.132864	−	0.0327480i
$650$	8.00521	+	27.7626i	0.313990	+	1.08894i
$651$	0.242754	−	0.0598334i	0.00951427	−	0.00234506i
$652$	−7.79074	+	4.08890i	−0.305109	+	0.160134i
$653$	−18.3202			−0.716925			−0.358462	−	0.933544i	$-0.616699\pi$
$653$	−18.3202			−0.716925			−0.358462	+	0.933544i	$0.616699\pi$
$654$	−61.2484			−2.39500
$655$	0.478109	−	0.250931i	0.0186812	−	0.00980468i
$656$	30.8190	+	27.3032i	1.20328	+	1.06601i
$657$	−39.3529			−1.53530
$658$	−50.8421	+	45.0421i	−1.98203	+	1.75593i
$659$	−2.58290	−	1.35561i	−0.100615	−	0.0528070i	0.413665	−	0.910429i	$-0.364249\pi$
$659$	−2.58290	−	1.35561i	−0.100615	−	0.0528070i	−0.514280	+	0.857622i	$0.671941\pi$
$660$	0.0161284	−	0.132830i	0.000627798	−	0.00517038i
$661$	8.78984	+	4.61326i	0.341885	+	0.179435i	0.626923	−	0.779081i	$-0.284314\pi$
$661$	8.78984	+	4.61326i	0.341885	+	0.179435i	−0.285038	+	0.958516i	$0.592006\pi$
$662$	3.05712	−	25.1776i	0.118818	−	0.978556i
$663$	44.2546	−	7.13724i	1.71871	−	0.277187i
$664$	−2.04441	−	16.8372i	−0.0793384	−	0.653411i
$665$	−0.332183	+	0.875894i	−0.0128815	+	0.0339657i
$666$	93.1686	−	48.8987i	3.61021	−	1.89478i
$667$	−4.00123	−	10.5504i	−0.154928	−	0.408513i
$668$	−3.70980	−	1.94705i	−0.143536	−	0.0753337i
$669$	−32.1235	−	16.8597i	−1.24197	−	0.651834i
$670$	−0.165768	−	0.0408581i	−0.00640417	−	0.00157849i
$671$	0.176741	+	1.45560i	0.00682303	+	0.0561927i
$672$	27.2463	−	24.1381i	1.05105	−	0.931149i
$673$	10.9511	−	15.8654i	0.422135	−	0.611568i	−0.553000	−	0.833181i	$-0.686517\pi$
$673$	10.9511	−	15.8654i	0.422135	−	0.611568i	0.975135	+	0.221614i	$0.0711324\pi$
$674$	7.70022	+	20.3038i	0.296601	+	0.782074i
$675$	58.5620			2.25405
$676$	−7.39161	+	0.578752i	−0.284293	+	0.0222597i
$677$	−44.5338			−1.71157			−0.855786	−	0.517330i	$-0.826926\pi$
$677$	−44.5338			−1.71157			−0.855786	+	0.517330i	$0.826926\pi$
$678$	−30.9971	−	81.7327i	−1.19044	−	3.13893i
$679$	−6.32947	+	9.16982i	−0.242903	+	0.351905i
$680$	0.267492	−	0.236977i	0.0102579	−	0.00908767i
$681$	2.31581	+	19.0724i	0.0887419	+	0.730855i
$682$	−0.0643231	−	0.0158542i	−0.00246306	−	0.000607089i
$683$	18.8907	+	9.91462i	0.722833	+	0.379372i	0.785665	−	0.618652i	$-0.212321\pi$
$683$	18.8907	+	9.91462i	0.722833	+	0.379372i	−0.0628318	+	0.998024i	$0.520013\pi$
$684$	−21.9422	−	11.5162i	−0.838983	−	0.440332i
$685$	−0.208096	−	0.548704i	−0.00795094	−	0.0209649i
$686$	0.968576	−	0.508348i	0.0369804	−	0.0194088i
$687$	13.2892	−	35.0406i	0.507013	−	1.33688i
$688$	−2.86549	−	23.5995i	−0.109246	−	0.899721i
$689$	3.65837	+	3.81799i	0.139373	+	0.145454i
$690$	0.0927299	−	0.763699i	0.00353017	−	0.0290735i
$691$	−30.5451	−	16.0313i	−1.16199	−	0.609860i	−0.230302	−	0.973119i	$-0.573972\pi$
$691$	−30.5451	−	16.0313i	−1.16199	−	0.609860i	−0.931688	+	0.363260i	$0.881664\pi$
$692$	0.578060	−	4.76075i	0.0219745	−	0.180977i
$693$	42.6314	+	22.3747i	1.61943	+	0.849945i
$694$	−9.70894	+	8.60137i	−0.368546	+	0.326504i
$695$	0.217608			0.00825435
$696$	15.4070	+	13.6494i	0.583999	+	0.517378i
$697$	30.1423	−	15.8199i	1.14172	−	0.599222i
$698$	6.04453			0.228789
$699$	−37.5254			−1.41934
$700$	9.38264	−	4.92439i	0.354630	−	0.186124i
$701$	32.9144	−	8.11267i	1.24316	−	0.306411i	0.437732	−	0.899105i	$-0.355782\pi$
$701$	32.9144	−	8.11267i	1.24316	−	0.306411i	0.805428	+	0.592694i	$0.201936\pi$
$702$	−13.6267	+	66.3393i	−0.514307	+	2.50381i
$703$	60.7375	+	14.9704i	2.29076	+	0.564621i
$704$	8.57418	−	2.11334i	0.323151	−	0.0796497i
$705$	−0.494289	−	1.30333i	−0.0186160	−	0.0490863i
$706$	−1.74346	+	14.3587i	−0.0656160	+	0.540396i
$707$	−5.91814	−	1.45869i	−0.222575	−	0.0548597i
$708$	−3.14230	+	0.774507i	−0.118095	+	0.0291077i
$709$	−2.02339	−	2.93139i	−0.0759900	−	0.110091i	0.783146	−	0.621838i	$-0.213614\pi$
$709$	−2.02339	−	2.93139i	−0.0759900	−	0.110091i	−0.859136	+	0.511747i	$0.828998\pi$
$710$	−0.0157326	+	0.129569i	−0.000590433	+	0.00486265i
$711$	−21.6855	+	57.1801i	−0.813271	+	2.14442i
$712$	8.27377	+	4.34241i	0.310073	+	0.162739i
$713$	−0.0820595	−	0.0202259i	−0.00307315	−	0.000757464i
$714$	−26.2724	−	69.2745i	−0.983219	−	2.59253i
$715$	−0.228772	−	0.145053i	−0.00855557	−	0.00542469i
$716$	−3.82533	+	10.0866i	−0.142959	+	0.376953i
$717$	−26.3563	+	38.1837i	−0.984295	+	1.42600i
$718$	3.53574	+	3.13240i	0.131953	+	0.116900i
$719$	4.94832	−	1.21965i	0.184541	−	0.0454853i	−0.145962	−	0.989290i	$-0.546628\pi$
$719$	4.94832	−	1.21965i	0.184541	−	0.0454853i	0.330503	+	0.943805i	$0.392782\pi$
$720$	0.451497	+	1.19050i	0.0168263	+	0.0443673i
$721$	−44.9175	+	23.5745i	−1.67282	+	0.877962i
$722$	−12.7425	−	33.5993i	−0.474228	−	1.25044i
$723$	20.5978	+	18.2481i	0.766042	+	0.678654i
$724$	1.62770	+	1.44201i	0.0604928	+	0.0535920i
$725$	8.16546	+	11.8297i	0.303258	+	0.439344i
$726$	20.8172	+	30.1589i	0.772598	+	1.11930i
$727$	27.8842	−	14.6348i	1.03417	−	0.542773i	0.139834	−	0.990175i	$-0.455343\pi$
$727$	27.8842	−	14.6348i	1.03417	−	0.542773i	0.894333	+	0.447402i	$0.147651\pi$
$728$	−8.51081	−	29.5160i	−0.315432	−	1.09394i
$729$	0.447070	+	0.234641i	0.0165582	+	0.00869039i
$730$	−0.0441096	−	0.363275i	−0.00163257	−	0.0134454i
$731$	−19.0837	−	4.70372i	−0.705837	−	0.173973i
$732$	0.773277	+	1.12029i	0.0285811	+	0.0414069i
$733$	13.0617	−	18.9232i	0.482446	−	0.698943i	−0.503876	−	0.863776i	$-0.668093\pi$
$733$	13.0617	−	18.9232i	0.482446	−	0.698943i	0.986322	+	0.164833i	$0.0527085\pi$
$734$	18.1760	−	16.1025i	0.670889	−	0.594356i
$735$	−0.100480	−	0.827528i	−0.00370626	−	0.0305238i
$736$	−11.9472	+	2.94472i	−0.440380	+	0.108544i
$737$	−4.61919	+	2.42434i	−0.170150	+	0.0893016i
$738$	11.1563	+	91.8806i	0.410670	+	3.38217i
$739$	0.350804	−	2.88913i	0.0129045	−	0.106278i	−0.984833	−	0.173503i	$-0.944491\pi$
$739$	0.350804	−	2.88913i	0.0129045	−	0.106278i	0.997738	+	0.0672247i	$0.0214144\pi$
$740$	0.123331	+	0.178676i	0.00453374	+	0.00656826i
$741$	−57.9786	+	43.4586i	−2.12990	+	1.59649i
$742$	4.96469	−	7.19260i	0.182260	−	0.264049i
$743$	−33.5872	−	29.7557i	−1.23220	−	1.09163i	−0.992685	−	0.120737i	$-0.961474\pi$
$743$	−33.5872	−	29.7557i	−1.23220	−	1.09163i	−0.239511	−	0.970894i	$-0.576987\pi$
$744$	0.149692	−	0.0368958i	0.00548798	−	0.00135267i
$745$	0.0873200	−	0.126505i	0.00319916	−	0.00463478i
$746$	−18.9122			−0.692425
$747$	28.3814	−	41.1175i	1.03842	−	1.50441i
$748$	−0.525061	+	4.32426i	−0.0191981	+	0.158111i
$749$	−19.9218	+	52.5296i	−0.727928	+	1.91939i
$750$	0.236292	+	1.94604i	0.00862818	+	0.0710595i
$751$	14.9297	−	39.3664i	0.544792	−	1.43650i	−0.326247	−	0.945285i	$-0.605784\pi$
$751$	14.9297	−	39.3664i	0.544792	−	1.43650i	0.871039	−	0.491214i	$-0.163447\pi$
$752$	−41.0829	+	36.3963i	−1.49814	+	1.32724i
$753$	−67.7248	+	59.9990i	−2.46803	+	2.18648i
$754$	−15.3008	+	6.49723i	−0.557221	+	0.236615i
$755$	−0.274900	−	0.243541i	−0.0100047	−	0.00886335i
$756$	24.8371			0.903315
$757$	35.1875	−	31.1734i	1.27891	−	1.13302i	0.294780	−	0.955565i	$-0.404754\pi$
$757$	35.1875	−	31.1734i	1.27891	−	1.13302i	0.984130	−	0.177450i	$-0.0567850\pi$
$758$	46.3493	+	11.4241i	1.68348	+	0.414941i
$759$	−13.3533	−	19.3456i	−0.484695	−	0.702202i
$760$	−0.204838	+	0.540113i	−0.00743025	+	0.0195920i
$761$	2.06509	−	5.44520i	0.0748596	−	0.197388i	−0.892363	−	0.451318i	$-0.850954\pi$
$761$	2.06509	−	5.44520i	0.0748596	−	0.197388i	0.967223	+	0.253930i	$0.0817232\pi$
$762$	−24.2371	−	35.1135i	−0.878018	−	1.27203i
$763$	44.1519	+	10.8825i	1.59841	+	0.393972i
$764$	7.38632	−	6.54371i	0.267228	−	0.236743i
$765$	1.05269			0.0380600
$766$	−23.9178	−	21.1893i	−0.864185	−	0.765601i
$767$	−1.31828	+	6.41781i	−0.04

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.568511 - 1.49904i) q^{2} +(-1.77394 + 2.57000i) q^{3} +(-0.426895 + 0.378196i) q^{4} +(0.00472042 + 0.0388761i) q^{5} +(4.86104 + 1.19814i) q^{6} +(-3.29128 - 1.72740i) q^{7} +(-2.02954 - 1.06519i) q^{8} +(-2.39421 - 6.31302i) q^{9} +O(q^{10})\)	\(q+(-0.568511 - 1.49904i) q^{2} +(-1.77394 + 2.57000i) q^{3} +(-0.426895 + 0.378196i) q^{4} +(0.00472042 + 0.0388761i) q^{5} +(4.86104 + 1.19814i) q^{6} +(-3.29128 - 1.72740i) q^{7} +(-2.02954 - 1.06519i) q^{8} +(-2.39421 - 6.31302i) q^{9} +(0.0555933 - 0.0291776i) q^{10} +(0.680286 - 1.79377i) q^{11} +(-0.214676 - 1.76802i) q^{12} +(-3.41862 - 1.14589i) q^{13} +(-0.718309 + 5.91581i) q^{14} +(-0.108285 - 0.0568326i) q^{15} +(-0.580430 + 4.78027i) q^{16} +(3.52523 + 1.85018i) q^{17} +(-8.10234 + 7.17804i) q^{18} -6.43536 q^{19} +(-0.0167179 - 0.0148108i) q^{20} +(10.2780 - 5.39429i) q^{21} -3.07568 q^{22} -3.92377 q^{23} +(6.33782 - 3.32635i) q^{24} +(4.85322 - 1.19621i) q^{25} +(0.225784 + 5.77609i) q^{26} +(11.3755 + 2.80382i) q^{27} +(2.05833 - 0.507332i) q^{28} +(1.01974 + 2.68884i) q^{29} +(-0.0236329 + 0.194634i) q^{30} +(0.0209135 + 0.00515471i) q^{31} +(3.04483 - 0.750483i) q^{32} +(3.40319 + 4.93037i) q^{33} +(0.769367 - 6.33631i) q^{34} +(0.0516183 - 0.136106i) q^{35} +(3.40964 + 1.78952i) q^{36} +(-9.43808 - 2.32628i) q^{37} +(3.65857 + 9.64687i) q^{38} +(9.00937 - 6.75310i) q^{39} +(0.0318300 - 0.0839289i) q^{40} +(4.85721 - 7.03689i) q^{41} +(-13.9294 - 12.3404i) q^{42} +(-4.79339 + 1.18146i) q^{43} +(0.387985 + 1.02303i) q^{44} +(0.234124 - 0.122878i) q^{45} +(2.23070 + 5.88188i) q^{46} +(8.53161 + 7.55835i) q^{47} +(-11.2556 - 9.97163i) q^{48} +(3.87218 + 5.60982i) q^{49} +(-4.55228 - 6.59511i) q^{50} +(-11.0085 + 5.77772i) q^{51} +(1.89276 - 0.803732i) q^{52} +(-1.29858 - 0.681548i) q^{53} +(-2.26408 - 18.6464i) q^{54} +(0.0729460 + 0.0179796i) q^{55} +(4.83980 + 7.01166i) q^{56} +(11.4160 - 16.5389i) q^{57} +(3.45095 - 3.05727i) q^{58} +(-0.219032 - 1.80389i) q^{59} +(0.0677204 - 0.0166916i) q^{60} +(-0.676767 + 0.355195i) q^{61} +(-0.00416242 - 0.0342806i) q^{62} +(-3.02507 + 24.9137i) q^{63} +(2.61487 + 3.78829i) q^{64} +(0.0284105 - 0.138312i) q^{65} +(5.45608 - 7.90449i) q^{66} +(-2.03540 - 1.80321i) q^{67} +(-2.20463 + 0.543394i) q^{68} +(6.96054 - 10.0841i) q^{69} -0.233375 q^{70} +(-1.18093 + 1.71087i) q^{71} +(-1.86539 + 15.3628i) q^{72} +(2.06682 - 5.44977i) q^{73} +(1.87847 + 15.4706i) q^{74} +(-5.53507 + 14.5948i) q^{75} +(2.74722 - 2.43383i) q^{76} +(-5.33756 + 4.72867i) q^{77} +(-15.2451 - 9.66620i) q^{78} +(-6.77962 - 6.00622i) q^{79} -0.188578 q^{80} +(-12.2241 + 10.8296i) q^{81} +(-13.3100 - 3.28061i) q^{82} +(4.20354 + 6.08988i) q^{83} +(-2.34751 + 6.18988i) q^{84} +(-0.0552874 + 0.145781i) q^{85} +(4.49616 + 6.51381i) q^{86} +(-8.71929 - 2.14911i) q^{87} +(-3.29136 + 2.91589i) q^{88} -4.07667 q^{89} +(-0.317301 - 0.281104i) q^{90} +(9.27222 + 9.67676i) q^{91} +(1.67504 - 1.48395i) q^{92} +(-0.0503469 + 0.0446035i) q^{93} +(6.47995 - 17.0862i) q^{94} +(-0.0303776 - 0.250182i) q^{95} +(-3.47261 + 9.15653i) q^{96} +(0.361319 - 2.97573i) q^{97} +(6.20797 - 8.99380i) q^{98} -12.9528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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