LMFDB - Embedded newform 169.2.g.a.14.10

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			14.10
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711778 - 1.03119i) q^{2} +(-1.78709 + 0.937940i) q^{3} +(0.152488 + 0.402078i) q^{4} +(-0.453990 - 0.402200i) q^{5} +(-0.304822 + 2.51044i) q^{6} +(4.78395 + 1.17914i) q^{7} +(2.95631 + 0.728665i) q^{8} +(0.609782 - 0.883421i) q^{9} +O(q^{10})$	\(q+(0.711778 - 1.03119i) q^{2} +(-1.78709 + 0.937940i) q^{3} +(0.152488 + 0.402078i) q^{4} +(-0.453990 - 0.402200i) q^{5} +(-0.304822 + 2.51044i) q^{6} +(4.78395 + 1.17914i) q^{7} +(2.95631 + 0.728665i) q^{8} +(0.609782 - 0.883421i) q^{9} +(-0.737885 + 0.181872i) q^{10} +(-1.82902 - 2.64980i) q^{11} +(-0.649635 - 0.575526i) q^{12} +(1.59116 + 3.23546i) q^{13} +(4.62103 - 4.09387i) q^{14} +(1.18856 + 0.292954i) q^{15} +(2.21188 - 1.95955i) q^{16} +(1.50016 + 0.369755i) q^{17} +(-0.476945 - 1.25760i) q^{18} -2.25327 q^{19} +(0.0924877 - 0.243870i) q^{20} +(-9.65534 + 2.37983i) q^{21} -4.03430 q^{22} -8.24595 q^{23} +(-5.96665 + 1.47065i) q^{24} +(-0.558341 - 4.59835i) q^{25} +(4.46892 + 0.662149i) q^{26} +(0.468687 - 3.85998i) q^{27} +(0.255390 + 2.10332i) q^{28} +(1.82087 - 2.63799i) q^{29} +(1.14808 - 1.01711i) q^{30} +(-0.939103 + 7.73421i) q^{31} +(0.287715 + 2.36955i) q^{32} +(5.75399 + 3.01993i) q^{33} +(1.44906 - 1.28376i) q^{34} +(-1.69762 - 2.45942i) q^{35} +(0.448188 + 0.110468i) q^{36} +(1.06272 - 8.75226i) q^{37} +(-1.60383 + 2.32354i) q^{38} +(-5.87822 - 4.28967i) q^{39} +(-1.04907 - 1.51984i) q^{40} +(1.66364 - 0.873146i) q^{41} +(-4.41841 + 11.6504i) q^{42} +(-0.731069 - 6.02089i) q^{43} +(0.786520 - 1.13947i) q^{44} +(-0.632147 + 0.155810i) q^{45} +(-5.86929 + 8.50313i) q^{46} +(0.0810172 - 0.213625i) q^{47} +(-2.11489 + 5.57651i) q^{48} +(15.2976 + 8.02882i) q^{49} +(-5.13919 - 2.69725i) q^{50} +(-3.02773 + 0.746268i) q^{51} +(-1.05828 + 1.13314i) q^{52} +(-6.05988 - 1.49363i) q^{53} +(-3.64677 - 3.23076i) q^{54} +(-0.235391 + 1.93862i) q^{55} +(13.2837 + 6.97180i) q^{56} +(4.02680 - 2.11343i) q^{57} +(-1.42421 - 3.75532i) q^{58} +(-4.59429 - 4.07018i) q^{59} +(0.0634511 + 0.522567i) q^{60} +(-2.22262 + 0.547828i) q^{61} +(7.30699 + 6.47343i) q^{62} +(3.95884 - 3.50723i) q^{63} +(7.88135 + 4.13645i) q^{64} +(0.578935 - 2.10883i) q^{65} +(7.20968 - 3.78393i) q^{66} +(-1.39820 + 3.68676i) q^{67} +(0.0800853 + 0.659562i) q^{68} +(14.7363 - 7.73420i) q^{69} -3.74446 q^{70} +(-3.75267 + 1.96956i) q^{71} +(2.44642 - 2.16734i) q^{72} +(-5.78742 - 8.38452i) q^{73} +(-8.26881 - 7.32552i) q^{74} +(5.31079 + 7.69400i) q^{75} +(-0.343596 - 0.905988i) q^{76} +(-5.62548 - 14.8332i) q^{77} +(-8.60744 + 3.00826i) q^{78} +(0.932193 - 2.45799i) q^{79} -1.79230 q^{80} +(3.92478 + 10.3488i) q^{81} +(0.283765 - 2.33701i) q^{82} +(-0.543969 - 0.285497i) q^{83} +(-2.42920 - 3.51930i) q^{84} +(-0.532340 - 0.771228i) q^{85} +(-6.72904 - 3.53167i) q^{86} +(-0.779797 + 6.42220i) q^{87} +(-3.47635 - 9.16637i) q^{88} +18.0185 q^{89} +(-0.289279 + 0.762765i) q^{90} +(3.79696 + 17.3545i) q^{91} +(-1.25741 - 3.31551i) q^{92} +(-5.57595 - 14.7026i) q^{93} +(-0.162621 - 0.235597i) q^{94} +(1.02296 + 0.906264i) q^{95} +(-2.73667 - 3.96474i) q^{96} +(-6.01270 + 5.32678i) q^{97} +(19.1678 - 10.0600i) q^{98} -3.45619 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	0.711778	−	1.03119i	0.503303	−	0.729160i	−0.486172	−	0.873863i	$-0.661607\pi$
$2$	0.711778	−	1.03119i	0.503303	−	0.729160i	0.989475	+	0.144703i	$0.0462226\pi$
$3$	−1.78709	+	0.937940i	−1.03178	+	0.541520i	−0.893589	−	0.448886i	$-0.851821\pi$
$3$	−1.78709	+	0.937940i	−1.03178	+	0.541520i	−0.138190	+	0.990406i	$0.544129\pi$
$4$	0.152488	+	0.402078i	0.0762440	+	0.201039i
$5$	−0.453990	−	0.402200i	−0.203031	−	0.179869i	0.555480	−	0.831530i	$-0.312534\pi$
$5$	−0.453990	−	0.402200i	−0.203031	−	0.179869i	−0.758511	+	0.651660i	$0.774073\pi$
$6$	−0.304822	+	2.51044i	−0.124443	+	1.02488i
$7$	4.78395	+	1.17914i	1.80816	+	0.445672i	0.991352	−	0.131231i	$-0.0418930\pi$
$7$	4.78395	+	1.17914i	1.80816	+	0.445672i	0.816812	+	0.576903i	$0.195739\pi$
$8$	2.95631	+	0.728665i	1.04521	+	0.257622i
$9$	0.609782	−	0.883421i	0.203261	−	0.294474i
$10$	−0.737885	+	0.181872i	−0.233340	+	0.0575130i
$11$	−1.82902	−	2.64980i	−0.551471	−	0.798944i	0.443795	−	0.896128i	$-0.353632\pi$
$11$	−1.82902	−	2.64980i	−0.551471	−	0.798944i	−0.995266	+	0.0971842i	$0.969016\pi$
$12$	−0.649635	−	0.575526i	−0.187533	−	0.166140i
$13$	1.59116	+	3.23546i	0.441307	+	0.897356i
$13$	1.59116	+	3.23546i	0.441307	+	0.897356i
$14$	4.62103	−	4.09387i	1.23502	−	1.09413i
$15$	1.18856	+	0.292954i	0.306886	+	0.0756405i
$16$	2.21188	−	1.95955i	0.552969	−	0.489888i
$17$	1.50016	+	0.369755i	0.363841	+	0.0896788i	0.416998	−	0.908907i	$-0.363082\pi$
$17$	1.50016	+	0.369755i	0.363841	+	0.0896788i	−0.0531569	+	0.998586i	$0.516928\pi$
$18$	−0.476945	−	1.25760i	−0.112417	−	0.296419i
$19$	−2.25327			−0.516935			−0.258467	−	0.966020i	$-0.583217\pi$
$19$	−2.25327			−0.516935			−0.258467	+	0.966020i	$0.583217\pi$
$20$	0.0924877	−	0.243870i	0.0206809	−	0.0545310i
$21$	−9.65534	+	2.37983i	−2.10697	+	0.519321i
$22$	−4.03430			−0.860116
$23$	−8.24595			−1.71940			−0.859700	−	0.510799i	$-0.829350\pi$
$23$	−8.24595			−1.71940			−0.859700	+	0.510799i	$0.829350\pi$
$24$	−5.96665	+	1.47065i	−1.21794	+	0.300195i
$25$	−0.558341	−	4.59835i	−0.111668	−	0.919671i
$26$	4.46892	+	0.662149i	0.876428	+	0.129858i
$27$	0.468687	−	3.85998i	0.0901989	−	0.742854i
$28$	0.255390	+	2.10332i	0.0482641	+	0.397491i
$29$	1.82087	−	2.63799i	0.338127	−	0.489862i	−0.616628	−	0.787255i	$-0.711502\pi$
$29$	1.82087	−	2.63799i	0.338127	−	0.489862i	0.954755	+	0.297393i	$0.0961170\pi$
$30$	1.14808	−	1.01711i	0.209611	−	0.185699i
$31$	−0.939103	+	7.73421i	−0.168668	+	1.38910i	0.624939	+	0.780674i	$0.285124\pi$
$31$	−0.939103	+	7.73421i	−0.168668	+	1.38910i	−0.793607	+	0.608431i	$0.791799\pi$
$32$	0.287715	+	2.36955i	0.0508613	+	0.418881i
$33$	5.75399	+	3.01993i	1.00164	+	0.525702i
$34$	1.44906	−	1.28376i	0.248513	−	0.220163i
$35$	−1.69762	−	2.45942i	−0.286950	−	0.415719i
$36$	0.448188	+	0.110468i	0.0746981	+	0.0184114i
$37$	1.06272	−	8.75226i	0.174709	−	1.43886i	−0.596670	−	0.802487i	$-0.703510\pi$
$37$	1.06272	−	8.75226i	0.174709	−	1.43886i	0.771380	−	0.636375i	$-0.219567\pi$
$38$	−1.60383	+	2.32354i	−0.260175	+	0.376928i
$39$	−5.87822	−	4.28967i	−0.941268	−	0.686897i
$40$	−1.04907	−	1.51984i	−0.165872	−	0.240307i
$41$	1.66364	−	0.873146i	0.259817	−	0.136363i	−0.329786	−	0.944056i	$-0.606977\pi$
$41$	1.66364	−	0.873146i	0.259817	−	0.136363i	0.589603	+	0.807693i	$0.299284\pi$
$42$	−4.41841	+	11.6504i	−0.681775	+	1.79769i
$43$	−0.731069	−	6.02089i	−0.111487	−	0.918178i	−0.935919	−	0.352216i	$-0.885428\pi$
$43$	−0.731069	−	6.02089i	−0.111487	−	0.918178i	0.824432	−	0.565961i	$-0.191495\pi$
$44$	0.786520	−	1.13947i	0.118572	−	0.171782i
$45$	−0.632147	+	0.155810i	−0.0942350	+	0.0232268i
$46$	−5.86929	+	8.50313i	−0.865379	+	1.25372i
$47$	0.0810172	−	0.213625i	0.0118176	−	0.0311604i	−0.928978	−	0.370136i	$-0.879311\pi$
$47$	0.0810172	−	0.213625i	0.0118176	−	0.0311604i	0.940795	+	0.338975i	$0.110080\pi$
$48$	−2.11489	+	5.57651i	−0.305258	+	0.804900i
$49$	15.2976	+	8.02882i	2.18538	+	1.14697i
$50$	−5.13919	−	2.69725i	−0.726791	−	0.381449i
$51$	−3.02773	+	0.746268i	−0.423967	+	0.104498i
$52$	−1.05828	+	1.13314i	−0.146756	+	0.157138i
$53$	−6.05988	−	1.49363i	−0.832389	−	0.205165i	−0.199980	−	0.979800i	$-0.564088\pi$
$53$	−6.05988	−	1.49363i	−0.832389	−	0.205165i	−0.632409	+	0.774635i	$0.717934\pi$
$54$	−3.64677	−	3.23076i	−0.496263	−	0.439650i
$55$	−0.235391	+	1.93862i	−0.0317401	+	0.261403i
$56$	13.2837	+	6.97180i	1.77510	+	0.931646i
$57$	4.02680	−	2.11343i	0.533363	−	0.279930i
$58$	−1.42421	−	3.75532i	−0.187008	−	0.493098i
$59$	−4.59429	−	4.07018i	−0.598125	−	0.529893i	0.308831	−	0.951117i	$-0.400062\pi$
$59$	−4.59429	−	4.07018i	−0.598125	−	0.529893i	−0.906957	+	0.421224i	$0.861601\pi$
$60$	0.0634511	+	0.522567i	0.00819150	+	0.0674631i
$61$	−2.22262	+	0.547828i	−0.284578	+	0.0701422i	−0.379021	−	0.925388i	$-0.623739\pi$
$61$	−2.22262	+	0.547828i	−0.284578	+	0.0701422i	0.0944430	+	0.995530i	$0.469893\pi$
$62$	7.30699	+	6.47343i	0.927989	+	0.822127i
$63$	3.95884	−	3.50723i	0.498767	−	0.441869i
$64$	7.88135	+	4.13645i	0.985169	+	0.517056i
$65$	0.578935	−	2.10883i	0.0718080	−	0.261568i
$66$	7.20968	−	3.78393i	0.887450	−	0.465770i
$67$	−1.39820	+	3.68676i	−0.170818	+	0.450409i	−0.992899	−	0.118961i	$-0.962044\pi$
$67$	−1.39820	+	3.68676i	−0.170818	+	0.450409i	0.822081	+	0.569370i	$0.192813\pi$
$68$	0.0800853	+	0.659562i	0.00971177	+	0.0799836i
$69$	14.7363	−	7.73420i	1.77404	−	0.931089i
$70$	−3.74446			−0.447548
$71$	−3.75267	+	1.96956i	−0.445360	+	0.233743i	−0.672468	−	0.740127i	$-0.734766\pi$
$71$	−3.75267	+	1.96956i	−0.445360	+	0.233743i	0.227107	+	0.973870i	$0.427073\pi$
$72$	2.44642	−	2.16734i	0.288314	−	0.255424i
$73$	−5.78742	−	8.38452i	−0.677366	−	0.981334i	−0.999401	−	0.0346065i	$-0.988982\pi$
$73$	−5.78742	−	8.38452i	−0.677366	−	0.981334i	0.322035	−	0.946728i	$-0.395633\pi$
$74$	−8.26881	−	7.32552i	−0.961229	−	0.851575i
$75$	5.31079	+	7.69400i	0.613237	+	0.888427i
$76$	−0.343596	−	0.905988i	−0.0394131	−	0.103924i
$77$	−5.62548	−	14.8332i	−0.641083	−	1.69040i
$78$	−8.60744	+	3.00826i	−0.974601	+	0.340618i
$79$	0.932193	−	2.45799i	0.104880	−	0.276546i	−0.872296	−	0.488979i	$-0.837370\pi$
$79$	0.932193	−	2.45799i	0.104880	−	0.276546i	0.977176	+	0.212433i	$0.0681388\pi$
$80$	−1.79230			−0.200386
$81$	3.92478	+	10.3488i	0.436087	+	1.14987i
$82$	0.283765	−	2.33701i	0.0313366	−	0.258080i
$83$	−0.543969	−	0.285497i	−0.0597084	−	0.0313374i	0.434605	−	0.900621i	$-0.356888\pi$
$83$	−0.543969	−	0.285497i	−0.0597084	−	0.0313374i	−0.494313	+	0.869284i	$0.664580\pi$
$84$	−2.42920	−	3.51930i	−0.265047	−	0.383987i
$85$	−0.532340	−	0.771228i	−0.0577404	−	0.0836514i
$86$	−6.72904	−	3.53167i	−0.725611	−	0.380830i
$87$	−0.779797	+	6.42220i	−0.0836030	+	0.688532i
$88$	−3.47635	−	9.16637i	−0.370580	−	0.977139i
$89$	18.0185			1.90995			0.954977	−	0.296679i	$-0.0958791\pi$
$89$	18.0185			1.90995			0.954977	+	0.296679i	$0.0958791\pi$
$90$	−0.289279	+	0.762765i	−0.0304927	+	0.0804025i
$91$	3.79696	+	17.3545i	0.398029	+	1.81925i
$92$	−1.25741	−	3.31551i	−0.131094	−	0.345666i
$93$	−5.57595	−	14.7026i	−0.578200	−	1.52459i
$94$	−0.162621	−	0.235597i	−0.0167731	−	0.0243000i
$95$	1.02296	+	0.906264i	0.104954	+	0.0929807i
$96$	−2.73667	−	3.96474i	−0.279310	−	0.404650i
$97$	−6.01270	+	5.32678i	−0.610497	+	0.540853i	−0.910724	−	0.413015i	$-0.864476\pi$
$97$	−6.01270	+	5.32678i	−0.610497	+	0.540853i	0.300228	+	0.953868i	$0.402937\pi$
$98$	19.1678	−	10.0600i	1.93624	−	1.01622i
$99$	−3.45619			−0.347361
$100$	1.76375	−	0.925690i	0.176375	−	0.0925690i
$101$	0.643619	+	5.30068i	0.0640425	+	0.527438i	0.989060	+	0.147513i	$0.0471269\pi$
$101$	0.643619	+	5.30068i	0.0640425	+	0.527438i	−0.925018	+	0.379924i	$0.875950\pi$
$102$	−1.38553	+	3.65333i	−0.137188	+	0.361734i
$103$	−10.0567	+	5.27817i	−0.990917	+	0.520073i	−0.880619	−	0.473825i	$-0.842873\pi$
$103$	−10.0567	+	5.27817i	−0.990917	+	0.520073i	−0.110298	+	0.993899i	$0.535181\pi$
$104$	2.34638	+	10.7245i	0.230082	+	1.05162i
$105$	5.34060	+	2.80296i	0.521189	+	0.273541i
$106$	−5.85350	+	5.18575i	−0.568542	+	0.503685i
$107$	−5.70612	−	5.05518i	−0.551632	−	0.488703i	0.340645	−	0.940192i	$-0.389355\pi$
$107$	−5.70612	−	5.05518i	−0.551632	−	0.488703i	−0.892277	+	0.451489i	$0.850893\pi$
$108$	1.62348	−	0.400153i	0.156220	−	0.0385047i
$109$	−1.18538	−	9.76245i	−0.113538	−	0.935073i	−0.932486	−	0.361205i	$-0.882365\pi$
$109$	−1.18538	−	9.76245i	−0.113538	−	0.935073i	0.818948	−	0.573868i	$-0.194558\pi$
$110$	1.83153	+	1.62260i	0.174630	+	0.154709i
$111$	6.30991	+	16.6379i	0.598910	+	1.57920i
$112$	12.8921	−	6.76629i	1.21819	−	0.639355i
$113$	18.3548	+	9.63334i	1.72667	+	0.906228i	0.966561	+	0.256436i	$0.0825484\pi$
$113$	18.3548	+	9.63334i	1.72667	+	0.906228i	0.760112	+	0.649792i	$0.225144\pi$
$114$	0.686845	−	5.65668i	0.0643290	−	0.529797i
$115$	3.74358	+	3.31652i	0.349091	+	0.309267i
$116$	1.33834	+	0.329870i	0.124261	+	0.0306277i
$117$	3.82854	+	0.567265i	0.353948	+	0.0524436i
$118$	−7.46724	+	1.84051i	−0.687415	+	0.169433i
$119$	6.74068	+	3.53778i	0.617917	+	0.324308i
$120$	3.30030	+	1.73213i	0.301274	+	0.158121i
$121$	0.224552	−	0.592094i	0.0204138	−	0.0538267i
$122$	−1.01710	+	2.68188i	−0.0920841	+	0.242806i
$123$	−2.15413	+	3.12079i	−0.194231	+	0.281392i
$124$	−3.25295	+	0.801781i	−0.292124	+	0.0720021i
$125$	−3.31870	+	4.80797i	−0.296834	+	0.430038i
$126$	−0.798797	−	6.57868i	−0.0711625	−	0.586076i
$127$	0.207774	−	0.547856i	0.0184370	−	0.0486144i	−0.925482	−	0.378792i	$-0.876339\pi$
$127$	0.207774	−	0.547856i	0.0184370	−	0.0486144i	0.943919	+	0.330178i	$0.107109\pi$
$128$	5.64815	−	2.96438i	0.499231	−	0.262017i
$129$	6.95372	+	10.0742i	0.612241	+	0.886984i
$130$	−1.76253	−	2.09801i	−0.154584	−	0.184008i
$131$	−0.476298	+	0.690037i	−0.0416144	+	0.0602888i	−0.843239	−	0.537539i	$-0.819354\pi$
$131$	−0.476298	+	0.690037i	−0.0416144	+	0.0602888i	0.801624	+	0.597828i	$0.203969\pi$
$132$	−0.336831	+	2.77405i	−0.0293174	+	0.241450i
$133$	−10.7795	−	2.65691i	−0.934703	−	0.230384i
$134$	2.80653	+	4.06597i	0.242448	+	0.351246i
$135$	−1.76527	+	1.56389i	−0.151930	+	0.134598i
$136$	4.16550	+	2.18622i	0.357189	+	0.187467i
$137$	−2.38027	−	19.6033i	−0.203360	−	1.67482i	−0.634797	−	0.772679i	$-0.718916\pi$
$137$	−2.38027	−	19.6033i	−0.203360	−	1.67482i	0.431437	−	0.902143i	$-0.358007\pi$
$138$	2.51355	−	20.7009i	0.213967	−	1.76218i
$139$	−10.1891	+	9.02671i	−0.864224	+	0.765636i	−0.973575	−	0.228367i	$-0.926661\pi$
$139$	−10.1891	+	9.02671i	−0.864224	+	0.765636i	0.109351	+	0.994003i	$0.465123\pi$
$140$	0.730013	−	1.05761i	0.0616974	−	0.0893841i
$141$	0.0555818	+	0.457757i	0.00468083	+	0.0385501i
$142$	−0.640088	+	5.27160i	−0.0537150	+	0.442383i
$143$	5.66306	−	10.1340i	0.473569	−	0.847446i
$144$	−0.382348	−	3.14892i	−0.0318623	−	0.262410i
$145$	−1.88766	+	0.465266i	−0.156761	+	0.0386382i
$146$	−12.7654			−1.05647
$147$	−34.8689			−2.87594
$148$	3.68114	−	0.907319i	0.302588	−	0.0745811i
$149$	−7.09531	+	18.7088i	−0.581270	+	1.53268i	0.245066	+	0.969506i	$0.421190\pi$
$149$	−7.09531	+	18.7088i	−0.581270	+	1.53268i	−0.826336	+	0.563177i	$0.809579\pi$
$150$	11.7141			0.956450
$151$	3.08714	+	8.14011i	0.251228	+	0.662433i	1.00000		0.000394387i	$-0.000125537\pi$
$151$	3.08714	+	8.14011i	0.251228	+	0.662433i	−0.748772	+	0.662827i	$0.769356\pi$
$152$	−6.66136	−	1.64188i	−0.540307	−	0.133174i
$153$	1.24142	−	1.09980i	0.100363	−	0.0889135i
$154$	−19.2999	−	4.75700i	−1.55523	−	0.383330i
$155$	3.53704	−	3.13355i	0.284102	−	0.251693i
$156$	0.828423	−	3.01762i	0.0663269	−	0.241603i
$157$	7.93276	+	7.02781i	0.633103	+	0.560880i	0.917455	−	0.397840i	$-0.130240\pi$
$157$	7.93276	+	7.02781i	0.633103	+	0.560880i	−0.284352	+	0.958720i	$0.591778\pi$
$158$	−1.87114	−	2.71081i	−0.148860	−	0.215661i
$159$	12.2305	−	3.01455i	0.969943	−	0.239069i
$160$	0.822412	−	1.19147i	0.0650174	−	0.0941940i
$161$	−39.4482	−	9.72312i	−3.10896	−	0.766289i
$162$	13.4651	+	3.31886i	1.05792	+	0.260754i
$163$	−1.48223	+	12.2073i	−0.116097	+	0.956146i	0.811961	+	0.583711i	$0.198400\pi$
$163$	−1.48223	+	12.2073i	−0.116097	+	0.956146i	−0.928058	+	0.372435i	$0.878523\pi$
$164$	0.604758	+	0.535769i	0.0472236	+	0.0418365i
$165$	−1.39764	−	3.68527i	−0.108806	−	0.286898i
$166$	−0.681587	+	0.357724i	−0.0529014	+	0.0277648i
$167$	2.66157	−	3.85595i	0.205959	−	0.298383i	−0.706369	−	0.707844i	$-0.749668\pi$
$167$	2.66157	−	3.85595i	0.205959	−	0.298383i	0.912327	+	0.409461i	$0.134283\pi$
$168$	−30.2783			−2.33602
$169$	−7.93644	+	10.2963i	−0.610496	+	0.792020i
$170$	−1.17419			−0.0900562
$171$	−1.37400	+	1.99058i	−0.105072	+	0.152224i
$172$	2.30939	−	1.21206i	0.176089	−	0.0924187i
$173$	0.356782	+	0.940758i	0.0271257	+	0.0715245i	0.947895	−	0.318583i	$-0.103207\pi$
$173$	0.356782	+	0.940758i	0.0271257	+	0.0715245i	−0.920769	+	0.390108i	$0.872438\pi$
$174$	6.06746	+	5.37530i	0.459973	+	0.407500i
$175$	2.75102	−	22.6567i	0.207957	−	1.71268i
$176$	−9.23799	−	2.27696i	−0.696340	−	0.171632i
$177$	12.0280	+	2.96464i	0.904080	+	0.222836i
$178$	12.8252	−	18.5804i	0.961286	−	1.39266i
$179$	6.99346	−	1.72373i	0.522716	−	0.128838i	0.0308754	−	0.999523i	$-0.490170\pi$
$179$	6.99346	−	1.72373i	0.522716	−	0.128838i	0.491840	+	0.870685i	$0.336324\pi$
$180$	−0.159043	−	0.230413i	−0.0118543	−	0.0171740i
$181$	1.86860	+	1.65543i	0.138892	+	0.123047i	0.729708	−	0.683759i	$-0.239656\pi$
$181$	1.86860	+	1.65543i	0.138892	+	0.123047i	−0.590817	+	0.806806i	$0.701194\pi$
$182$	20.5984	+	8.43717i	1.52685	+	0.625405i
$183$	3.45821	−	3.06371i	0.255638	−	0.226476i
$184$	−24.3776	−	6.00854i	−1.79714	−	0.442955i
$185$	−4.00262	+	3.54601i	−0.294279	+	0.260708i
$186$	−19.1300	−	4.71512i	−1.40268	−	0.345729i
$187$	−1.76404	−	4.65140i	−0.129000	−	0.340144i
$188$	0.0982479			0.00716546
$189$	6.79363	−	17.9133i	0.494164	−	1.30300i
$190$	1.66265	−	0.409806i	0.120621	−	0.0297305i
$191$	1.42233			0.102917			0.0514583	−	0.998675i	$-0.483613\pi$
$191$	1.42233			0.102917			0.0514583	+	0.998675i	$0.483613\pi$
$192$	−17.9645			−1.29647
$193$	−2.80225	+	0.690693i	−0.201710	+	0.0497172i	−0.338876	−	0.940831i	$-0.610047\pi$
$193$	−2.80225	+	0.690693i	−0.201710	+	0.0497172i	0.137166	+	0.990548i	$0.456201\pi$
$194$	1.21321	+	9.99171i	0.0871037	+	0.717363i
$195$	0.943346	+	4.31169i	0.0675544	+	0.308766i
$196$	−0.895504	+	7.37514i	−0.0639646	+	0.526796i
$197$	1.19443	+	9.83702i	0.0850996	+	0.700858i	0.971350	+	0.237652i	$0.0763779\pi$
$197$	1.19443	+	9.83702i	0.0850996	+	0.700858i	−0.886251	+	0.463206i	$0.846699\pi$
$198$	−2.46004	+	3.56399i	−0.174828	+	0.253282i
$199$	1.40139	−	1.24152i	0.0993420	−	0.0880094i	−0.611990	−	0.790866i	$-0.709631\pi$
$199$	1.40139	−	1.24152i	0.0993420	−	0.0880094i	0.711332	+	0.702856i	$0.248092\pi$
$200$	1.70003	−	14.0010i	0.120210	−	0.990021i
$201$	−0.959236	−	7.90002i	−0.0676593	−	0.557224i
$202$	5.92412	+	3.10922i	0.416819	+	0.218764i
$203$	11.8215	−	10.4730i	0.829708	−	0.735057i
$204$	−0.761749	−	1.10358i	−0.0533331	−	0.0772664i
$205$	−1.10646	−	0.272717i	−0.0772783	−	0.0190474i
$206$	−1.71536	+	14.1272i	−0.119515	+	0.984292i
$207$	−5.02823	+	7.28465i	−0.349486	+	0.506318i
$208$	9.85950	+	4.03849i	0.683633	+	0.280019i
$209$	4.12128	+	5.97070i	0.285075	+	0.413002i
$210$	6.69170	−	3.51207i	0.461771	−	0.242356i
$211$	7.67190	−	20.2291i	0.528155	−	1.39263i	−0.359941	−	0.932975i	$-0.617203\pi$
$211$	7.67190	−	20.2291i	0.528155	−	1.39263i	0.888097	−	0.459656i	$-0.152027\pi$
$212$	−0.323505	−	2.66430i	−0.0222184	−	0.182985i
$213$	4.85906	−	7.03956i	0.332937	−	0.482343i
$214$	−9.27434	+	2.28592i	−0.633981	+	0.156262i
$215$	−2.08971	+	3.02746i	−0.142517	+	0.206471i
$216$	4.19822	−	11.0698i	0.285653	−	0.753205i
$217$	−13.6123	+	35.8928i	−0.924065	+	2.43656i
$218$	−10.9107	−	5.72635i	−0.738963	−	0.387838i
$219$	18.2068	+	9.55569i	1.23030	+	0.645714i
$220$	−0.815368	+	0.200970i	−0.0549721	+	0.0135494i
$221$	1.19065	+	5.44203i	0.0800920	+	0.366071i
$222$	21.6480	+	5.33576i	1.45292	+	0.358113i
$223$	−5.70573	−	5.05483i	−0.382084	−	0.338497i	0.450118	−	0.892969i	$-0.351382\pi$
$223$	−5.70573	−	5.05483i	−0.382084	−	0.338497i	−0.832202	+	0.554472i	$0.812920\pi$
$224$	−1.41761	+	11.6751i	−0.0947179	+	0.780072i
$225$	−4.40275	−	2.31074i	−0.293517	−	0.154049i
$226$	22.9983	−	12.0705i	1.52983	−	0.802915i
$227$	−3.95018	−	10.4158i	−0.262183	−	0.691319i	−0.999869	−	0.0161757i	$-0.994851\pi$
$227$	−3.95018	−	10.4158i	−0.262183	−	0.691319i	0.737686	−	0.675144i	$-0.235918\pi$
$228$	1.46380	+	1.29681i	0.0969425	+	0.0858836i
$229$	0.635772	+	5.23605i	0.0420130	+	0.346008i	0.998524	+	0.0543120i	$0.0172966\pi$
$229$	0.635772	+	5.23605i	0.0420130	+	0.346008i	−0.956511	+	0.291696i	$0.905780\pi$
$230$	6.08456	−	1.49971i	0.401204	−	0.0988879i
$231$	23.9659	+	21.2319i	1.57684	+	1.39696i
$232$	7.30528	−	6.47191i	0.479615	−	0.424902i
$233$	−0.784662	−	0.411822i	−0.0514049	−	0.0269794i	0.438825	−	0.898573i	$-0.355395\pi$
$233$	−0.784662	−	0.411822i	−0.0514049	−	0.0269794i	−0.490230	+	0.871593i	$0.663087\pi$
$234$	3.31002	−	3.54418i	0.216383	−	0.231690i
$235$	−0.122701	+	0.0643984i	−0.00800413	+	0.00420089i
$236$	0.935956	−	2.46791i	0.0609255	−	0.160647i
$237$	0.639530	+	5.26700i	0.0415419	+	0.342129i
$238$	8.44599	−	4.43280i	0.547472	−	0.287335i
$239$	3.96777			0.256654			0.128327	−	0.991732i	$-0.459039\pi$
$239$	3.96777			0.256654			0.128327	+	0.991732i	$0.459039\pi$
$240$	3.20301	−	1.68107i	0.206754	−	0.108513i
$241$	3.65869	−	3.24132i	0.235677	−	0.208792i	−0.537015	−	0.843573i	$-0.680448\pi$
$241$	3.65869	−	3.24132i	0.235677	−	0.208792i	0.772692	+	0.634781i	$0.218910\pi$
$242$	−0.450730	−	0.652995i	−0.0289740	−	0.0419761i
$243$	−7.98912	−	7.07775i	−0.512503	−	0.454038i
$244$	−0.559193	−	0.810130i	−0.0357986	−	0.0518633i
$245$	−3.71579	−	9.79772i	−0.237393	−	0.625954i
$246$	1.68486	+	4.44262i	0.107423	+	0.283251i
$247$	−3.58530	−	7.29036i	−0.228127	−	0.463874i
$248$	−8.41193	+	22.1804i	−0.534158	+	1.40846i
$249$	1.23990			0.0785757
$250$	2.59575	+	6.84442i	0.164169	+	0.432879i
$251$	−2.53708	+	20.8948i	−0.160139	+	1.31887i	0.661967	+	0.749533i	$0.269722\pi$
$251$	−2.53708	+	20.8948i	−0.160139	+	1.31887i	−0.822107	+	0.569334i	$0.807201\pi$
$252$	2.01385	+	1.05695i	0.126861	+	0.0665817i
$253$	15.0820	+	21.8501i	0.948200	+	1.37370i
$254$	−0.417054	−	0.604207i	−0.0261683	−	0.0379113i
$255$	1.67471	+	0.878954i	0.104874	+	0.0550423i
$256$	−1.18237	+	9.73770i	−0.0738982	+	0.608606i
$257$	1.92476	+	5.07518i	0.120063	+	0.316581i	0.981552	−	0.191196i	$-0.0612367\pi$
$257$	1.92476	+	5.07518i	0.120063	+	0.316581i	−0.861489	+	0.507777i	$0.830467\pi$
$258$	15.3379			0.954897
$259$	15.4041	−	40.6173i	0.957164	−	2.52384i
$260$	0.936195	−	0.0887948i	0.0580603	−	0.00550682i
$261$	−1.22012	−	3.21719i	−0.0755236	−	0.199139i
$262$	0.372540	+	0.982307i	0.0230156	+	0.0606871i
$263$	10.2576	+	14.8608i	0.632513	+	0.916353i	0.999906	−	0.0137124i	$-0.00436492\pi$
$263$	10.2576	+	14.8608i	0.632513	+	0.916353i	−0.367393	+	0.930066i	$0.619750\pi$
$264$	14.8101	+	13.1206i	0.911496	+	0.807515i
$265$	2.15039	+	3.11538i	0.132097	+	0.191376i
$266$	−10.4124	+	9.22458i	−0.638425	+	0.565595i
$267$	−32.2007	+	16.9002i	−1.97065	+	1.03428i
$268$	−1.69557			−0.103574
$269$	−0.438435	+	0.230108i	−0.0267318	+	0.0140299i	−0.478036	−	0.878340i	$-0.658651\pi$
$269$	−0.438435	+	0.230108i	−0.0267318	+	0.0140299i	0.451304	+	0.892370i	$0.350959\pi$
$270$	0.356187	+	2.93346i	0.0216769	+	0.178525i
$271$	1.21815	−	3.21200i	0.0739974	−	0.195115i	−0.892914	−	0.450227i	$-0.851343\pi$
$271$	1.21815	−	3.21200i	0.0739974	−	0.195115i	0.966912	+	0.255112i	$0.0821123\pi$
$272$	4.04271	−	2.12178i	0.245125	−	0.128652i
$273$	−23.0630	−	27.4528i	−1.39584	−	1.66152i
$274$	−21.9089	−	11.4987i	−1.32357	−	0.694661i
$275$	−11.1635	+	9.88999i	−0.673184	+	0.596389i
$276$	5.35686	+	4.74576i	0.322445	+	0.285661i
$277$	23.3988	−	5.76728i	1.40590	−	0.346522i	0.537865	−	0.843031i	$-0.319231\pi$
$277$	23.3988	−	5.76728i	1.40590	−	0.346522i	0.868032	+	0.496509i	$0.165385\pi$
$278$	2.05590	+	16.9319i	0.123305	+	1.01551i
$279$	6.25992	+	5.54580i	0.374771	+	0.332019i
$280$	−3.22659	−	8.50782i	−0.192826	−	0.508439i
$281$	15.9500	−	8.37120i	0.951497	−	0.499384i	0.0838026	−	0.996482i	$-0.473293\pi$
$281$	15.9500	−	8.37120i	0.951497	−	0.499384i	0.867694	+	0.497098i	$0.165601\pi$
$282$	0.511596	+	0.268506i	0.0304651	+	0.0159893i
$283$	3.53153	−	29.0848i	0.209928	−	1.72891i	−0.383083	−	0.923714i	$-0.625138\pi$
$283$	3.53153	−	29.0848i	0.209928	−	1.72891i	0.593010	−	0.805195i	$-0.297939\pi$
$284$	−1.36415	−	1.20853i	−0.0809475	−	0.0717132i
$285$	−2.67815	−	0.660104i	−0.158640	−	0.0391012i
$286$	−6.41920	−	13.0528i	−0.379575	−	0.771830i
$287$	8.98834	−	2.21543i	0.530565	−	0.130773i
$288$	2.26875	+	1.19073i	0.133687	+	0.0701646i
$289$	−12.9390	−	6.79091i	−0.761118	−	0.399466i
$290$	−0.863817	+	2.27770i	−0.0507251	+	0.133751i
$291$	5.74906	−	15.1590i	0.337016	−	0.888637i
$292$	2.48872	−	3.60553i	0.145641	−	0.210998i
$293$	−21.0768	+	5.19497i	−1.23132	+	0.303493i	−0.800714	−	0.599047i	$-0.795546\pi$
$293$	−21.0768	+	5.19497i	−1.23132	+	0.303493i	−0.430606	+	0.902540i	$0.641700\pi$
$294$	−24.8189	+	35.9564i	−1.44747	+	2.09702i
$295$	0.448733	+	3.69565i	0.0261262	+	0.215169i
$296$	9.51919	−	25.1000i	0.553291	−	1.45891i
$297$	−11.0854	+	5.81808i	−0.643241	+	0.337599i
$298$	14.2420	+	20.6331i	0.825017	+	1.19524i
$299$	−13.1206	−	26.6795i	−0.758784	−	1.54291i
$300$	−2.28376	+	3.30859i	−0.131853	+	0.191022i
$301$	3.60207	−	29.6657i	0.207620	−	1.70990i
$302$	10.5913	+	2.61053i	0.609464	+	0.150219i
$303$	−6.12193	−	8.86914i	−0.351696	−	0.509519i
$304$	−4.98395	+	4.41539i	−0.285849	+	0.253240i
$305$	1.22939	+	0.645232i	0.0703945	+	0.0369459i
$306$	−0.250487	−	2.06295i	−0.0143194	−	0.117931i
$307$	−1.98592	+	16.3556i	−0.113343	+	0.933461i	0.819476	+	0.573114i	$0.194265\pi$
$307$	−1.98592	+	16.3556i	−0.113343	+	0.933461i	−0.932818	+	0.360347i	$0.882658\pi$
$308$	5.10627	−	4.52376i	0.290957	−	0.257765i
$309$	13.0217	−	18.8652i	0.740778	−	1.07320i
$310$	−0.713688	−	5.87775i	−0.0405348	−	0.333834i
$311$	−0.736957	+	6.06938i	−0.0417890	+	0.344163i	0.956786	+	0.290793i	$0.0939193\pi$
$311$	−0.736957	+	6.06938i	−0.0417890	+	0.344163i	−0.998575	+	0.0533697i	$0.983004\pi$
$312$	−14.2521	−	16.9649i	−0.806866	−	0.960446i
$313$	−0.325546	−	2.68111i	−0.0184010	−	0.151546i	0.980612	−	0.195958i	$-0.0627816\pi$
$313$	−0.325546	−	2.68111i	−0.0184010	−	0.151546i	−0.999013	+	0.0444123i	$0.985858\pi$
$314$	12.8934	−	3.17793i	0.727614	−	0.179341i
$315$	−3.20788			−0.180744
$316$	1.13045			0.0635928
$317$	−22.7041	+	5.59605i	−1.27519	+	0.314306i	−0.818079	−	0.575105i	$-0.804961\pi$
$317$	−22.7041	+	5.59605i	−1.27519	+	0.314306i	−0.457109	+	0.889411i	$0.651115\pi$
$318$	5.59684	−	14.7577i	0.313855	−	0.827568i
$319$	−10.3206			−0.577840
$320$	−1.91437	−	5.04779i	−0.107017	−	0.282180i
$321$	14.9388	+	3.68209i	0.833805	+	0.205514i
$322$	−38.1048	+	33.7579i	−2.12350	+	1.88125i
$323$	−3.38025	−	0.833156i	−0.188082	−	0.0463581i
$324$	−3.56254	+	3.15613i	−0.197919	+	0.175341i
$325$	13.9894	−	9.12319i	0.775992	−	0.506064i
$326$	11.5330	+	10.2173i	0.638752	+	0.565885i
$327$	11.2750	+	16.3346i	0.623507	+	0.903306i
$328$	5.55447	−	1.36905i	0.306694	−	0.0755934i
$329$	0.639476	−	0.926441i	0.0352554	−	0.0510763i
$330$	−4.79502	−	1.18187i	−0.263957	−	0.0650596i
$331$	26.0630	+	6.42396i	1.43255	+	0.353093i	0.877843	−	0.478949i	$-0.158982\pi$
$331$	26.0630	+	6.42396i	1.43255	+	0.353093i	0.554712	+	0.832042i	$0.312828\pi$
$332$	0.0318432	−	0.262253i	0.00174762	−	0.0143930i
$333$	−7.08390	−	6.27579i	−0.388196	−	0.343911i
$334$	−2.08177	−	5.48917i	−0.113909	−	0.300354i
$335$	2.11759	−	1.11140i	0.115696	−	0.0607220i
$336$	−16.6930	+	24.1840i	−0.910679	+	1.31935i
$337$	13.2123			0.719719			0.359859	−	0.933007i	$-0.382825\pi$
$337$	13.2123			0.719719			0.359859	+	0.933007i	$0.382825\pi$
$338$	4.96840	+	15.5126i	0.270245	+	0.843775i
$339$	−41.8372			−2.27229
$340$	0.228918	−	0.331645i	0.0124148	−	0.0179860i
$341$	22.2117	−	11.6576i	1.20283	−	0.631295i
$342$	1.07468	+	2.83371i	0.0581122	+	0.153229i
$343$	37.9001	+	33.5765i	2.04641	+	1.81296i
$344$	2.22595	−	18.3323i	0.120015	−	0.988414i
$345$	−9.80083	−	2.41569i	−0.527659	−	0.130056i
$346$	1.22405	+	0.301701i	0.0658052	+	0.0162195i
$347$	−4.89543	+	7.09226i	−0.262801	+	0.380732i	−0.932064	−	0.362292i	$-0.881994\pi$
$347$	−4.89543	+	7.09226i	−0.262801	+	0.380732i	0.669264	+	0.743025i	$0.266610\pi$
$348$	−2.70113	+	0.665770i	−0.144796	+	0.0356890i
$349$	9.69269	+	14.0423i	0.518838	+	0.751666i	0.991575	−	0.129538i	$-0.0413493\pi$
$349$	9.69269	+	14.0423i	0.518838	+	0.751666i	−0.472737	+	0.881204i	$0.656734\pi$
$350$	−21.4052	−	18.9633i	−1.14416	−	1.01363i
$351$	13.2346	−	4.62542i	0.706410	−	0.246887i
$352$	5.75258	−	5.09634i	0.306614	−	0.271636i
$353$	−20.1579	−	4.96848i	−1.07290	−	0.264445i	−0.336976	−	0.941513i	$-0.609404\pi$
$353$	−20.1579	−	4.96848i	−1.07290	−	0.264445i	−0.735920	+	0.677068i	$0.763250\pi$
$354$	11.6184	−	10.2930i	0.617510	−	0.547066i
$355$	2.49583	+	0.615168i	0.132465	+	0.0326497i
$356$	2.74760	+	7.24483i	0.145622	+	0.383975i
$357$	−15.3645			−0.813173
$358$	3.20030	−	8.43849i	0.169141	−	0.445988i
$359$	−35.1334	+	8.65960i	−1.85427	+	0.457036i	−0.998208	−	0.0598386i	$-0.980941\pi$
$359$	−35.1334	+	8.65960i	−1.85427	+	0.457036i	−0.856061	+	0.516875i	$0.827095\pi$
$360$	−1.98236			−0.104479
$361$	−13.9228			−0.732779
$362$	3.03709	−	0.748576i	0.159626	−	0.0393443i
$363$	0.154053	+	1.26874i	0.00808571	+	0.0665918i
$364$	−6.39886	+	4.17302i	−0.335392	+	0.218726i
$365$	−0.744826	+	6.13419i	−0.0389860	+	0.321078i
$366$	−0.697781	−	5.74675i	−0.0364736	−	0.300387i
$367$	10.1164	−	14.6562i	0.528074	−	0.765048i	−0.464645	−	0.885497i	$-0.653818\pi$
$367$	10.1164	−	14.6562i	0.528074	−	0.765048i	0.992719	+	0.120449i	$0.0384335\pi$
$368$	−18.2390	+	16.1584i	−0.950775	+	0.842313i
$369$	0.243102	−	2.00213i	0.0126554	−	0.104226i
$370$	0.807630	+	6.65143i	0.0419867	+	0.345792i
$371$	−27.2290	−	14.2909i	−1.41366	−	0.741946i
$372$	5.06131	−	4.48393i	0.262417	−	0.232481i
$373$	−8.58672	−	12.4400i	−0.444604	−	0.644119i	0.535049	−	0.844821i	$-0.320293\pi$
$373$	−8.58672	−	12.4400i	−0.444604	−	0.644119i	−0.979652	+	0.200702i	$0.935678\pi$
$374$	−6.05208	−	1.49170i	−0.312945	−	0.0771341i
$375$	1.42125	−	11.7050i	0.0733930	−	0.604446i
$376$	0.395173	−	0.572507i	0.0203795	−	0.0295248i
$377$	11.4324	+	1.69391i	0.588799	+	0.0872409i
$378$	−13.6365	−	19.7558i	−0.701384	−	1.01613i
$379$	10.5223	−	5.52253i	0.540494	−	0.283673i	−0.172303	−	0.985044i	$-0.555121\pi$
$379$	10.5223	−	5.52253i	0.540494	−	0.283673i	0.712796	+	0.701371i	$0.247428\pi$
$380$	−0.208399	+	0.549504i	−0.0106907	+	0.0281890i
$381$	0.142543	+	1.17395i	0.00730272	+	0.0601433i
$382$	1.01239	−	1.46670i	0.0517982	−	0.0750427i
$383$	−13.6082	+	3.35412i	−0.695347	+	0.171388i	−0.571120	−	0.820866i	$-0.693491\pi$
$383$	−13.6082	+	3.35412i	−0.695347	+	0.171388i	−0.124226	+	0.992254i	$0.539645\pi$
$384$	−7.31338	+	10.5953i	−0.373209	+	0.540687i
$385$	−3.41199	+	8.99669i	−0.173891	+	0.458514i
$386$	−1.28235	+	3.38127i	−0.0652697	+	0.172102i
$387$	−5.76478	−	3.02559i	−0.293040	−	0.153799i
$388$	−3.05864	−	1.60530i	−0.155279	−	0.0814968i
$389$	7.71708	−	1.90209i	0.391271	−	0.0964397i	−0.0387718	−	0.999248i	$-0.512345\pi$
$389$	7.71708	−	1.90209i	0.391271	−	0.0964397i	0.430043	+	0.902808i	$0.358498\pi$
$390$	5.11762	+	2.09620i	0.259141	+	0.106145i
$391$	−12.3702	−	3.04898i	−0.625588	−	0.154194i
$392$	39.3743	+	34.8826i	1.98870	+	1.76184i
$393$	0.203977	−	1.67990i	0.0102893	−	0.0847398i
$394$	10.9940	+	5.77009i	0.553869	+	0.290693i
$395$	−1.41181	+	0.740976i	−0.0710359	+	0.0372825i
$396$	−0.527028	−	1.38966i	−0.0264841	−	0.0698329i
$397$	20.3351	+	18.0153i	1.02059	+	0.904164i	0.995428	−	0.0955198i	$-0.0304513\pi$
$397$	20.3351	+	18.0153i	1.02059	+	0.904164i	0.0251622	+	0.999683i	$0.491990\pi$
$398$	−0.282766	−	2.32879i	−0.0141738	−	0.116732i
$399$	21.7560	−	5.36238i	1.08916	−	0.268455i
$400$	−10.2457	−	9.07690i	−0.512285	−	0.453845i
$401$	−3.39309	+	3.00601i	−0.169443	+	0.150113i	−0.743583	−	0.668644i	$-0.766875\pi$
$401$	−3.39309	+	3.00601i	−0.169443	+	0.150113i	0.574140	+	0.818757i	$0.305337\pi$
$402$	−8.82917	−	4.63391i	−0.440359	−	0.231118i
$403$	−26.5180	+	9.26790i	−1.32096	+	0.461667i
$404$	−2.03314	+	1.06707i	−0.101153	+	0.0530890i
$405$	2.38048	−	6.27680i	0.118287	−	0.311897i
$406$	−2.38529	−	19.6446i	−0.118380	−	0.974947i
$407$	−25.1354	+	13.1921i	−1.24592	+	0.653908i
$408$	−9.49468			−0.470057
$409$	−14.6523	+	7.69010i	−0.724508	+	0.380251i	−0.786306	−	0.617838i	$-0.788009\pi$
$409$	−14.6523	+	7.69010i	−0.724508	+	0.380251i	0.0617979	+	0.998089i	$0.480317\pi$
$410$	−1.06877	+	0.946851i	−0.0527830	+	0.0467617i
$411$	22.6405	+	32.8004i	1.11677	+	1.61792i
$412$	−3.65576	−	3.23872i	−0.180106	−	0.159560i
$413$	−17.1795	−	24.8889i	−0.845350	−	1.22470i
$414$	3.93286	+	10.3701i	0.193290	+	0.509663i
$415$	0.132130	+	0.348397i	0.00648599	+	0.0171022i
$416$	−7.20878	+	4.70121i	−0.353440	+	0.230496i
$417$	9.74229	−	25.6883i	0.477082	−	1.25796i
$418$	9.09035			0.444624
$419$	−6.24800	−	16.4746i	−0.305235	−	0.804838i	−0.996605	−	0.0823366i	$-0.973762\pi$
$419$	−6.24800	−	16.4746i	−0.305235	−	0.804838i	0.691370	−	0.722501i	$-0.257008\pi$
$420$	−0.312631	+	2.57475i	−0.0152549	+	0.125635i
$421$	24.6315	+	12.9276i	1.20046	+	0.630052i	0.941884	−	0.335938i	$-0.109053\pi$
$421$	24.6315	+	12.9276i	1.20046	+	0.630052i	0.258580	+	0.965990i	$0.416746\pi$
$422$	−15.3994	−	22.3098i	−0.749629	−	1.08603i
$423$	−0.139318	−	0.201837i	−0.00677387	−	0.00981364i
$424$	−16.8265	−	8.83125i	−0.817169	−	0.428884i
$425$	0.862666	−	7.10469i	0.0418455	−	0.344628i
$426$	−3.80054	−	10.0212i	−0.184137	−	0.485529i
$427$	−11.2789			−0.545824
$428$	1.16246	−	3.06516i	0.0561897	−	0.148160i
$429$	−0.615363	+	23.4220i	−0.0297100	+	1.13082i
$430$	1.63448	+	4.30976i	0.0788215	+	0.207835i
$431$	0.317628	+	0.837517i	0.0152996	+	0.0403418i	0.942448	−	0.334351i	$-0.108517\pi$
$431$	0.317628	+	0.837517i	0.0152996	+	0.0403418i	−0.927149	+	0.374693i	$0.877748\pi$
$432$	−6.52716	−	9.45623i	−0.314038	−	0.454963i
$433$	4.99347	+	4.42383i	0.239971	+	0.212596i	0.774533	−	0.632534i	$-0.217985\pi$
$433$	4.99347	+	4.42383i	0.239971	+	0.212596i	−0.534562	+	0.845129i	$0.679523\pi$
$434$	27.3232	+	39.5846i	1.31156	+	1.90012i
$435$	2.93703	−	2.60198i	0.140820	−	0.124756i
$436$	3.74451	−	1.96527i	0.179329	−	0.0941193i
$437$	18.5803			0.888817
$438$	22.8129	−	11.9732i	1.09004	−	0.572100i
$439$	1.41918	+	11.6880i	0.0677335	+	0.557836i	0.986587	+	0.163237i	$0.0521934\pi$
$439$	1.41918	+	11.6880i	0.0677335	+	0.557836i	−0.918853	+	0.394599i	$0.870883\pi$
$440$	−2.10849	+	5.55963i	−0.100518	+	0.265045i
$441$	16.4211	−	8.61844i	0.781955	−	0.410402i
$442$	6.45924	+	2.64573i	0.307235	+	0.125845i
$443$	16.3415	+	8.57669i	0.776409	+	0.407491i	0.805883	−	0.592075i	$-0.201691\pi$
$443$	16.3415	+	8.57669i	0.776409	+	0.407491i	−0.0294740	+	0.999566i	$0.509383\pi$
$444$	−5.72753	+	5.07415i	−0.271817	+	0.240808i
$445$	−8.18021	−	7.24704i	−0.387779	−	0.343542i
$446$	−9.27370	+	2.28576i	−0.439122	+	0.108234i
$447$	−4.86773	−	40.0893i	−0.230236	−	1.89616i
$448$	32.8266	+	29.0818i	1.55091	+	1.37399i
$449$	9.80065	+	25.8422i	0.462521	+	1.21957i	0.940075	+	0.340967i	$0.110754\pi$
$449$	9.80065	+	25.8422i	0.462521	+	1.21957i	−0.477554	+	0.878602i	$0.658476\pi$
$450$	−5.51659	+	2.89533i	−0.260055	+	0.136487i
$451$	−5.35650	−	2.81131i	−0.252228	−	0.132379i
$452$	−1.07447	+	8.84902i	−0.0505386	+	0.416223i
$453$	−13.1519	−	11.6516i	−0.617932	−	0.547440i
$454$	−13.5523	−	3.34034i	−0.636040	−	0.156770i
$455$	5.25620	−	9.40591i	0.246414	−	0.440956i
$456$	13.4445	−	3.31376i	0.629594	−	0.155181i
$457$	−18.2340	−	9.56992i	−0.852949	−	0.447662i	−0.0192062	−	0.999816i	$-0.506114\pi$
$457$	−18.2340	−	9.56992i	−0.852949	−	0.447662i	−0.833742	+	0.552154i	$0.813806\pi$
$458$	5.85189	+	3.07131i	0.273441	+	0.143513i
$459$	2.13035	−	5.61728i	0.0994363	−	0.262192i
$460$	−0.762649	+	2.01094i	−0.0355587	+	0.0937606i
$461$	−8.99781	+	13.0356i	−0.419070	+	0.607127i	−0.974487	−	0.224445i	$-0.927943\pi$
$461$	−8.99781	+	13.0356i	−0.419070	+	0.607127i	0.555417	+	0.831572i	$0.312559\pi$
$462$	38.9525	−	9.60093i	1.81224	−	0.446676i
$463$	5.14668	−	7.45625i	0.239186	−	0.346521i	−0.684946	−	0.728594i	$-0.740174\pi$
$463$	5.14668	−	7.45625i	0.239186	−	0.346521i	0.924132	+	0.382073i	$0.124790\pi$
$464$	−1.14173	−	9.40300i	−0.0530035	−	0.436523i
$465$	−3.38195	+	8.91748i	−0.156834	+	0.413538i
$466$	−0.983172	+	0.516008i	−0.0455446	+	0.0239036i
$467$	9.89714	+	14.3385i	0.457985	+	0.663506i	0.982147	−	0.188112i	$-0.0602369\pi$
$467$	9.89714	+	14.3385i	0.457985	+	0.663506i	−0.524163	+	0.851618i	$0.675622\pi$
$468$	0.355721	+	1.62587i	0.0164432	+	0.0751558i
$469$	−11.0361	+	15.9886i	−0.509602	+	0.738285i
$470$	−0.0209289	+	0.172365i	−0.000965380	+	0.00795062i
$471$	−20.7682	−	5.11891i	−0.956950	−	0.235867i
$472$	−10.6163	−	15.3804i	−0.488657	−	0.707941i
$473$	−14.6170	+	12.9495i	−0.672091	+	0.595420i
$474$	5.88648	+	3.08946i	0.270375	+	0.141904i
$475$	1.25809	+	10.3613i	0.0577252	+	0.475410i
$476$	−0.394590	+	3.24974i	−0.0180860	+	0.148952i
$477$	−5.01471	+	4.44264i	−0.229608	+	0.203415i
$478$	2.82417	−	4.09152i	0.129175	−	0.187142i
$479$	4.28664	+	35.3037i	0.195862	+	1.61307i	0.676702	+	0.736257i	$0.263409\pi$
$479$	4.28664	+	35.3037i	0.195862	+	1.61307i	−0.480840	+	0.876808i	$0.659668\pi$
$480$	−0.352202	+	2.90064i	−0.0160757	+	0.132396i
$481$	30.0085	−	10.4878i	1.36827	−	0.478204i
$482$	−0.738234	−	6.07990i	−0.0336256	−	0.276932i
$483$	79.6174	−	19.6239i	3.62272	−	0.892920i
$484$	0.272309			0.0123777
$485$	4.87214			0.221232
$486$	−12.9850	+	3.20051i	−0.589010	+	0.145178i
$487$	6.82054	−	17.9843i	0.309068	−	0.814945i	−0.687025	−	0.726634i	$-0.741084\pi$
$487$	6.82054	−	17.9843i	0.309068	−	0.814945i	0.996093	−	0.0883115i	$-0.0281471\pi$
$488$	−6.96995			−0.315515
$489$	−8.80079	−	23.2058i	−0.397985	−	1.04940i
$490$	−12.7481	−	3.14213i	−0.575901	−	0.141947i
$491$	−20.0189	+	17.7352i	−0.903439	+	0.800377i	−0.980474	−	0.196651i	$-0.936993\pi$
$491$	−20.0189	+	17.7352i	−0.903439	+	0.800377i	0.0770342	+	0.997028i	$0.475455\pi$
$492$	−1.58328	−	0.390243i	−0.0713797	−	0.0175935i
$493$	3.70700	−	3.28412i	0.166955	−	0.147909i
$494$	−10.0697	−	1.49200i	−0.453056	−	0.0671282i
$495$	1.56908	+	1.39008i	0.0705248	+	0.0624795i
$496$	13.0784	+	18.9473i	0.587238	+	0.850761i
$497$	−20.2750	+	4.99734i	−0.909458	+	0.224161i
$498$	0.882536	−	1.27857i	0.0395474	−	0.0572943i
$499$	−22.8936	−	5.64275i	−1.02486	−	0.252604i	−0.309155	−	0.951012i	$-0.600046\pi$
$499$	−22.8936	−	5.64275i	−1.02486	−	0.252604i	−0.715701	+	0.698407i	$0.753892\pi$
$500$	−2.43924	−	0.601219i	−0.109086	−	0.0268873i
$501$	−1.13983	+	9.38735i	−0.0509239	+	0.419396i
$502$	19.7406	+	17.4887i	0.881067	+	0.780557i
$503$	−10.4118	−	27.4536i	−0.464238	−	1.22409i	−0.938981	−	0.343970i	$-0.888228\pi$
$503$	−10.4118	−	27.4536i	−0.464238	−	1.22409i	0.474743	−	0.880125i	$-0.342541\pi$
$504$	14.2592	−	7.48379i	0.635154	−	0.333355i
$505$	1.83974	−	2.66532i	0.0818673	−	0.118605i
$506$	33.2666			1.47888
$507$	4.52591	−	25.8443i	0.201003	−	1.14778i
$508$	0.251964			0.0111791
$509$	−9.63164	+	13.9538i	−0.426915	+	0.618493i	−0.976130	−	0.217188i	$-0.930312\pi$
$509$	−9.63164	+	13.9538i	−0.426915	+	0.618493i	0.549215	+	0.835681i	$0.314927\pi$
$510$	2.09839	−	1.10132i	0.0929182	−	0.0487672i
$511$	−17.8002	−	46.9353i	−0.787436	−	2.07630i
$512$	18.7490	+	16.6102i	0.828598	+	0.734074i
$513$	−1.05608	+	8.69757i	−0.0466269	+	0.384007i
$514$	6.60347	+	1.62761i	0.291266	+	0.0717907i
$515$	6.68853	+	1.64857i	0.294732	+	0.0726449i
$516$	−2.99025	+	4.33213i	−0.131639	+	0.190711i
$517$	−0.714245	+	0.176046i	−0.0314125	+	0.00774248i
$518$	−30.9198	−	44.7950i	−1.35854	−	1.96818i
$519$	−1.51998	−	1.34658i	−0.0667196	−	0.0591084i
$520$	3.24814	−	5.81252i	0.142441	−	0.254896i
$521$	31.4013	−	27.8191i	1.37571	−	1.21878i	0.426366	−	0.904551i	$-0.359794\pi$
$521$	31.4013	−	27.8191i	1.37571	−	1.21878i	0.949348	−	0.314226i	$-0.101745\pi$
$522$	−4.18599	−	1.03175i	−0.183216	−	0.0451586i
$523$	−0.437333	+	0.387443i	−0.0191232	+	0.0169417i	−0.672630	−	0.739979i	$-0.734835\pi$
$523$	−0.437333	+	0.387443i	−0.0191232	+	0.0169417i	0.653507	+	0.756921i	$0.273297\pi$
$524$	−0.350078	−	0.0862865i	−0.0152932	−	0.00376944i
$525$	16.3343	+	43.0699i	0.712885	+	1.87972i
$526$	22.6254			0.986515
$527$	−4.26856	+	11.2553i	−0.185942	+	0.490287i
$528$	18.6448	−	4.59553i	0.811411	−	0.199995i
$529$	44.9957			1.95634
$530$	4.74314			0.206029
$531$	−6.39720	+	1.57677i	−0.277615	+	0.0684259i
$532$	−0.575461	−	4.73935i	−0.0249494	−	0.205477i
$533$	5.47215	+	3.99334i	0.237025	+	0.172971i
$534$	−5.49243	+	45.2342i	−0.237681	+	1.95748i
$535$	0.557328	+	4.59001i	0.0240954	+	0.198443i
$536$	−6.81994	+	9.88039i	−0.294577	+	0.426768i
$537$	−10.8812	+	9.63992i	−0.469559	+	0.415993i
$538$	−0.0747832	+	0.615895i	−0.00322413	+	0.0265531i
$539$	−6.70499	−	55.2206i	−0.288804	−	2.37852i
$540$	−0.897987	−	0.471300i	−0.0386432	−	0.0202815i
$541$	−29.2388	+	25.9033i	−1.25708	+	1.11367i	−0.268447	+	0.963295i	$0.586510\pi$
$541$	−29.2388	+	25.9033i	−1.25708	+	1.11367i	−0.988629	+	0.150377i	$0.951951\pi$
$542$	−2.44513	−	3.54238i	−0.105027	−	0.152158i
$543$	−4.89206	−	1.20578i	−0.209938	−	0.0517452i
$544$	−0.444535	+	3.66107i	−0.0190593	+	0.156967i
$545$	−3.38831	+	4.90882i	−0.145139	+	0.210271i
$546$	−44.7248	+	4.24199i	−1.91404	+	0.181540i
$547$	−1.28683	−	1.86429i	−0.0550207	−	0.0797113i	0.794508	−	0.607254i	$-0.207729\pi$
$547$	−1.28683	−	1.86429i	−0.0550207	−	0.0797113i	−0.849529	+	0.527543i	$0.823114\pi$
$548$	7.51908	−	3.94632i	0.321199	−	0.168578i
$549$	−0.871353	+	2.29757i	−0.0371884	+	0.0980579i
$550$	2.25252	+	18.5511i	0.0960476	+	0.791023i
$551$	−4.10291	+	5.94409i	−0.174790	+	0.253227i
$552$	49.2007	−	12.1269i	2.09412	−	0.516155i
$553$	7.35788	−	10.6597i	0.312889	−	0.453298i
$554$	10.7076	−	28.2336i	0.454922	−	1.19953i
$555$	3.82712	−	10.0913i	0.162452	−	0.428351i
$556$	−5.18315	−	2.72033i	−0.219814	−	0.115368i
$557$	−17.0695	−	8.95879i	−0.723260	−	0.379596i	0.0625685	−	0.998041i	$-0.480071\pi$
$557$	−17.0695	−	8.95879i	−0.723260	−	0.379596i	−0.785828	+	0.618445i	$0.787763\pi$
$558$	10.1744	−	2.50777i	0.430718	−	0.106163i
$559$	18.3171	−	11.9455i	0.774732	−	0.505242i
$560$	−8.57429	−	2.11337i	−0.362330	−	0.0893063i
$561$	7.51524	+	6.65792i	0.317294	+	0.281098i
$562$	2.72057	−	22.4059i	0.114760	−	0.945135i
$563$	11.4985	+	6.03488i	0.484604	+	0.254340i	0.689287	−	0.724488i	$-0.257924\pi$
$563$	11.4985	+	6.03488i	0.484604	+	0.254340i	−0.204683	+	0.978828i	$0.565616\pi$
$564$	−0.175578	+	0.0921506i	−0.00739318	+	0.00388024i
$565$	−4.45837	−	11.7557i	−0.187565	−	0.494568i
$566$	−27.4782	−	24.3436i	−1.15499	−	1.02324i
$567$	6.57330	+	54.1360i	0.276053	+	2.27350i
$568$	−12.5292	+	3.08818i	−0.525714	+	0.129577i
$569$	19.9049	+	17.6342i	0.834459	+	0.739266i	0.967777	−	0.251807i	$-0.0810249\pi$
$569$	19.9049	+	17.6342i	0.834459	+	0.739266i	−0.133319	+	0.991073i	$0.542563\pi$
$570$	−2.58694	+	2.29183i	−0.108355	+	0.0959941i
$571$	13.9323	+	7.31225i	0.583050	+	0.306008i	0.730339	−	0.683085i	$-0.239362\pi$
$571$	13.9323	+	7.31225i	0.583050	+	0.306008i	−0.147289	+	0.989094i	$0.547055\pi$
$572$	4.93819	+	0.731680i	0.206476	+	0.0305931i
$573$	−2.54185	+	1.33406i	−0.106187	+	0.0557313i
$574$	4.11318	−	10.8456i	0.171681	−	0.452685i
$575$	4.60406	+	37.9178i	0.192002	+	1.58128i
$576$	8.46013	−	4.44022i	0.352506	−	0.185009i
$577$	−35.2462			−1.46732			−0.733660	−	0.679516i	$-0.762190\pi$
$577$	−35.2462			−1.46732			−0.733660	+	0.679516i	$0.762190\pi$
$578$	−16.2124	+	8.50893i	−0.674348	+	0.353925i
$579$	4.36006	−	3.86268i	0.181198	−	0.160527i
$580$	−0.474918	−	0.688037i	−0.0197199	−	0.0285692i
$581$	−2.26568	−	2.00722i	−0.0939963	−	0.0832735i
$582$	−11.5397	−	16.7182i	−0.478338	−	0.692992i
$583$	7.12586	+	18.7893i	0.295123	+	0.778175i
$584$	−10.9999	−	29.0044i	−0.455179	−	1.20021i
$585$	−1.50996	−	1.79737i	−0.0624293	−	0.0743121i
$586$	−9.64502	+	25.4318i	−0.398432	+	1.05058i
$587$	−15.9028			−0.656378			−0.328189	−	0.944612i	$-0.606438\pi$
$587$	−15.9028			−0.656378			−0.328189	+	0.944612i	$0.606438\pi$
$588$	−5.31708	−	14.0200i	−0.219273	−	0.578175i
$589$	2.11605	−	17.4272i	0.0871903	−	0.718076i
$590$	4.13031	+	2.16775i	0.170042	+	0.0892449i
$591$	−11.3611	−	16.4594i	−0.467333	−	0.677048i
$592$	−14.7999	−	21.4414i	−0.608272	−	0.881234i
$593$	4.42204	+	2.32087i	0.181592	+	0.0953066i	0.553069	−	0.833135i	$-0.313456\pi$
$593$	4.42204	+	2.32087i	0.181592	+	0.0953066i	−0.371478	+	0.928442i	$0.621149\pi$
$594$	−1.89082	+	15.5723i	−0.0775815	+	0.638941i
$595$	−1.63731	−	4.31722i	−0.0671230	−	0.176989i
$596$	−8.60433			−0.352447
$597$	−1.33994	+	3.53314i	−0.0548403	+	0.144602i
$598$	−36.8505	−	5.46005i	−1.50693	−	0.223278i
$599$	12.1314	+	31.9878i	0.495674	+	1.30699i	0.916569	+	0.399876i	$0.130947\pi$
$599$	12.1314	+	31.9878i	0.495674	+	1.30699i	−0.420895	+	0.907109i	$0.638284\pi$
$600$	10.0940	+	26.6157i	0.412085	+	1.08658i
$601$	−14.4800	−	20.9779i	−0.590653	−	0.855708i	0.407698	−	0.913117i	$-0.366332\pi$
$601$	−14.4800	−	20.9779i	−0.590653	−	0.855708i	−0.998351	+	0.0574087i	$0.981716\pi$
$602$	−28.0271	−	24.8298i	−1.14230	−	1.01199i
$603$	2.40436	+	3.48332i	0.0979132	+	0.141852i
$604$	−2.80221	+	2.48254i	−0.114020	+	0.101013i
$605$	−0.340085	+	0.178490i	−0.0138264	+	0.00725666i
$606$	−13.5032			−0.548531
$607$	39.5596	−	20.7625i	1.60567	−	0.842723i	0.606822	−	0.794838i	$-0.292444\pi$
$607$	39.5596	−	20.7625i	1.60567	−	0.842723i	0.998853	−	0.0478848i	$-0.0152480\pi$
$608$	−0.648299	−	5.33922i	−0.0262920	−	0.216534i
$609$	−11.3032	+	29.8040i	−0.458028	+	1.20772i
$610$	1.54041	−	0.808467i	0.0623692	−	0.0327339i
$611$	0.820086	−	0.0777824i	0.0331771	−	0.00314674i
$612$	0.631506	+	0.331440i	0.0255271	+	0.0133977i
$613$	−24.2776	+	21.5081i	−0.980565	+	0.868705i	−0.991351	−	0.131237i	$-0.958105\pi$
$613$	−24.2776	+	21.5081i	−0.980565	+	0.868705i	0.0107861	+	0.999942i	$0.496567\pi$
$614$	15.4521	+	13.6894i	0.623597	+	0.552459i
$615$	2.23313	−	0.550418i	0.0900487	−	0.0221950i
$616$	−5.82226	−	47.9506i	−0.234585	−	1.93198i
$617$	−36.0473	−	31.9351i	−1.45121	−	1.28566i	−0.888397	−	0.459076i	$-0.848181\pi$
$617$	−36.0473	−	31.9351i	−1.45121	−	1.28566i	−0.562813	−	0.826584i	$-0.690281\pi$
$618$	−10.1850	−	26.8556i	−0.409701	−	1.08029i
$619$	−38.9793	+	20.4579i	−1.56671	+	0.822273i	−0.999999	−	0.00164299i	$-0.999477\pi$
$619$	−38.9793	+	20.4579i	−1.56671	+	0.822273i	−0.566712	+	0.823916i	$0.691785\pi$
$620$	1.79929	+	0.944338i	0.0722611	+	0.0379255i
$621$	−3.86477	+	31.8293i	−0.155088	+	1.27726i
$622$	5.73413	+	5.08000i	0.229918	+	0.203689i
$623$	86.1995	+	21.2463i	3.45351	+	0.851214i
$624$	−21.4077	+	2.03045i	−0.856995	+	0.0812830i
$625$	−19.0472	+	4.69471i	−0.761888	+	0.187789i
$626$	−2.99645	−	1.57266i	−0.119762	−	0.0628561i
$627$	−12.9653	−	6.80470i	−0.517783	−	0.271753i
$628$	−1.61607	+	4.26124i	−0.0644884	+	0.170042i
$629$	4.83043	−	12.7368i	0.192602	−	0.507849i
$630$	−2.28330	+	3.30793i	−0.0909689	+	0.131791i
$631$	16.7250	−	4.12233i	0.665810	−	0.164108i	0.108096	−	0.994140i	$-0.465525\pi$
$631$	16.7250	−	4.12233i	0.665810	−	0.164108i	0.557714	+	0.830033i	$0.311678\pi$
$632$	4.54691	−	6.58733i	0.180866	−	0.262030i
$633$	5.26330	+	43.3472i	0.209197	+	1.72289i
$634$	−10.3897	+	27.3953i	−0.412627	+	1.08801i
$635$	−0.314675	+	0.165154i	−0.0124875	+	0.00655395i
$636$	3.07709	+	4.45793i	0.122015	+	0.176769i
$637$	−1.63601	+	62.2701i	−0.0648212	+	2.46723i
$638$	−7.34594	+	10.6424i	−0.290829	+	0.421338i
$639$	−0.548365	+	4.51619i	−0.0216930	+	0.178658i
$640$	−3.75648	−	0.925889i	−0.148488	−	0.0365990i
$641$	−5.44136	−	7.88317i	−0.214921	−	0.311367i	0.700664	−	0.713491i	$-0.252887\pi$
$641$	−5.44136	−	7.88317i	−0.214921	−	0.311367i	−0.915585	+	0.402125i	$0.868272\pi$
$642$	14.4301	−	12.7839i	0.569510	−	0.504541i
$643$	10.6127	+	5.56997i	0.418523	+	0.219658i	0.660820	−	0.750544i	$-0.270209\pi$
$643$	10.6127	+	5.56997i	0.418523	+	0.219658i	−0.242297	+	0.970202i	$0.577901\pi$
$644$	−2.10593	−	17.3439i	−0.0829854	−	0.683446i
$645$	0.894926	−	7.37038i	0.0352377	−	0.290208i
$646$	−3.26513	+	2.89265i	−0.128465	+	0.113810i
$647$	15.2476	−	22.0899i	0.599444	−	0.868445i	−0.399387	−	0.916782i	$-0.630777\pi$
$647$	15.2476	−	22.0899i	0.599444	−	0.868445i	0.998831	+	0.0483378i	$0.0153924\pi$
$648$	4.06207	+	33.4541i	0.159573	+	1.31420i
$649$	−2.38210	+	19.6184i	−0.0935057	+	0.770089i
$650$	0.549613	−	20.9194i	0.0215576	−	0.820526i
$651$	−9.33872	−	76.9113i	−0.366013	−	3.01439i
$652$	−5.13429	+	1.26549i	−0.201074	+	0.0495603i
$653$	18.5406			0.725548			0.362774	−	0.931877i	$-0.381830\pi$
$653$	18.5406			0.725548			0.362774	+	0.931877i	$0.381830\pi$
$654$	24.8693			0.972468
$655$	0.493768	−	0.121703i	0.0192931	−	0.00475532i
$656$	1.96879	−	5.19128i	0.0768685	−	0.202686i
$657$	−10.9361			−0.426659
$658$	−0.500170	−	1.31884i	−0.0194987	−	0.0514137i
$659$	22.8272	+	5.62641i	0.889223	+	0.219174i	0.657362	−	0.753575i	$-0.271672\pi$
$659$	22.8272	+	5.62641i	0.889223	+	0.219174i	0.231861	+	0.972749i	$0.425518\pi$
$660$	1.26864	−	1.12392i	0.0493818	−	0.0437485i
$661$	21.4451	+	5.28575i	0.834118	+	0.205592i	0.633172	−	0.774011i	$-0.281752\pi$
$661$	21.4451	+	5.28575i	0.834118	+	0.205592i	0.200946	+	0.979602i	$0.435599\pi$
$662$	25.1754	−	22.3035i	0.978471	−	0.866849i
$663$	−7.23211	−	8.60867i	−0.280872	−	0.334333i
$664$	−1.40011	−	1.24039i	−0.0543348	−	0.0481365i
$665$	3.82518	+	5.54174i	0.148334	+	0.214899i
$666$	−11.5137	+	2.83787i	−0.446147	+	0.109965i
$667$	−15.0148	+	21.7527i	−0.581376	+	0.842269i
$668$	1.95625	+	0.482172i	0.0756896	+	0.0186558i
$669$	14.9378	+	3.68184i	0.577529	+	0.142348i
$670$	0.361194	−	2.97470i	0.0139541	−	0.114923i
$671$	5.51687	+	4.88752i	0.212976	+	0.188680i
$672$	−8.41710	−	22.1941i	−0.324697	−	0.856154i
$673$	−3.24327	+	1.70220i	−0.125019	+	0.0656150i	−0.526073	−	0.850439i	$-0.676336\pi$
$673$	−3.24327	+	1.70220i	−0.125019	+	0.0656150i	0.401054	+	0.916054i	$0.368644\pi$
$674$	9.40421	−	13.6243i	0.362237	−	0.524790i
$675$	−18.0113			−0.693254
$676$	−5.35011	−	1.62101i	−0.205773	−	0.0623466i
$677$	−38.9883			−1.49844			−0.749221	−	0.662321i	$-0.769572\pi$
$677$	−38.9883			−1.49844			−0.749221	+	0.662321i	$0.769572\pi$
$678$	−29.7788	+	43.1421i	−1.14365	+	1.65686i
$679$	−35.0455	+	18.3933i	−1.34492	+	0.705869i
$680$	−1.01180	−	2.66789i	−0.0388006	−	0.102309i
$681$	16.8287	+	14.9089i	0.644878	+	0.571312i
$682$	3.78862	−	31.2021i	0.145074	−	1.19479i
$683$	36.5257	+	9.00278i	1.39762	+	0.344482i	0.864957	−	0.501847i	$-0.167346\pi$
$683$	36.5257	+	9.00278i	1.39762	+	0.344482i	0.532661	+	0.846329i	$0.321192\pi$
$684$	−1.00989	−	0.248915i	−0.0386140	−	0.00951750i
$685$	−6.80383	+	9.85705i	−0.259961	+	0.376618i
$686$	61.6002	−	15.1831i	2.35191	−	0.579693i
$687$	−6.04729	−	8.76101i	−0.230718	−	0.334253i
$688$	−13.4153	−	11.8849i	−0.511453	−	0.453108i
$689$	−4.80965	−	21.9831i	−0.183233	−	0.837490i
$690$	−9.46705	+	8.38707i	−0.360404	+	0.319290i
$691$	−10.4696	−	2.58052i	−0.398281	−	0.0981675i	0.0350874	−	0.999384i	$-0.488829\pi$
$691$	−10.4696	−	2.58052i	−0.398281	−	0.0981675i	−0.433369	+	0.901217i	$0.642675\pi$
$692$	−0.323853	+	0.286908i	−0.0123110	+	0.0109066i
$693$	−16.5343	−	4.07533i	−0.628085	−	0.154809i
$694$	3.82899	+	10.0962i	0.145347	+	0.383248i
$695$	8.25628			0.313178
$696$	−6.98496	+	18.4178i	−0.264764	+	0.698126i
$697$	2.81857	−	0.694715i	0.106761	−	0.0263142i
$698$	21.3793			0.809218
$699$	1.78853			0.0676484
$700$	9.52924	−	2.34875i	0.360171	−	0.0887743i
$701$	1.53806	+	12.6671i	0.0580918	+	0.478429i	0.992502	+	0.122230i	$0.0390045\pi$
$701$	1.53806	+	12.6671i	0.0580918	+	0.478429i	−0.934410	+	0.356199i	$0.884072\pi$
$702$	4.65041	−	16.9396i	0.175518	−	0.639345i
$703$	−2.39458	+	19.7212i	−0.0903134	+	0.743798i
$704$	−3.45441	−	28.4496i	−0.130193	−	1.07224i
$705$	0.158876	−	0.230172i	0.00598363	−	0.00866879i
$706$	−19.4714	+	17.2501i	−0.732815	+	0.649218i
$707$	−3.17119	+	26.1171i	−0.119265	+	0.982236i
$708$	0.642111	+	5.28826i	0.0241320	+	0.198745i
$709$	−14.7557	−	7.74437i	−0.554160	−	0.290846i	0.164304	−	0.986410i	$-0.447462\pi$
$709$	−14.7557	−	7.74437i	−0.554160	−	0.290846i	−0.718464	+	0.695564i	$0.755155\pi$
$710$	2.41083	−	2.13581i	0.0904769	−	0.0801556i
$711$	−1.60301	−	2.32236i	−0.0601175	−	0.0870952i
$712$	53.2682	+	13.1294i	1.99631	+	0.492047i
$713$	7.74380	−	63.7759i	0.290008	−	2.38843i
$714$	−10.9361	+	15.8437i	−0.409273	+	0.592934i
$715$	−6.64686	+	2.32304i	−0.248579	+	0.0868769i
$716$	1.75949	+	2.54907i	0.0657553	+	0.0952631i
$717$	−7.09078	+	3.72153i	−0.264810	+	0.138983i
$718$	−16.0775	+	42.3929i	−0.600007	+	1.58209i
$719$	4.09088	+	33.6914i	0.152564	+	1.25648i	0.844909	+	0.534910i	$0.179655\pi$
$719$	4.09088	+	33.6914i	0.152564	+	1.25648i	−0.692345	+	0.721567i	$0.743422\pi$
$720$	−1.09291	+	1.58336i	−0.0407305	+	0.0590083i
$721$	−54.3345	+	13.3923i	−2.02352	+	0.498754i
$722$	−9.90994	+	14.3570i	−0.368810	+	0.534313i
$723$	−3.49827	+	9.22418i	−0.130102	+	0.343051i
$724$	−0.380674	+	1.00376i	−0.0141476	+	0.0373043i
$725$	−13.1471	−	6.90012i	−0.488270	−	0.256264i
$726$	1.41797	+	0.744206i	0.0526257	+	0.0276201i
$727$	−5.17994	+	1.27674i	−0.192113	+	0.0473517i	−0.334198	−	0.942503i	$-0.608466\pi$
$727$	−5.17994	+	1.27674i	−0.192113	+	0.0473517i	0.142085	+	0.989854i	$0.454619\pi$
$728$	−1.42063	+	54.0720i	−0.0526519	+	2.00404i
$729$	−11.3235	−	2.79098i	−0.419387	−	0.103370i
$730$	5.79536	+	5.13424i	0.214496	+	0.190027i
$731$	1.12954	−	9.30259i	0.0417775	−	0.344069i
$732$	1.75918	+	0.923291i	0.0650213	+	0.0341258i
$733$	25.9333	−	13.6109i	0.957870	−	0.502729i	0.0880597	−	0.996115i	$-0.471933\pi$
$733$	25.9333	−	13.6109i	0.957870	−	0.502729i	0.869810	+	0.493386i	$0.164241\pi$
$734$	−7.91265	−	20.8639i	−0.292061	−	0.770102i
$735$	15.8301	+	14.0243i	0.583903	+	0.517293i
$736$	−2.37248	−	19.5392i	−0.0874509	−	0.720223i
$737$	12.3265	−	3.03821i	0.454053	−	0.111914i
$738$	−1.89153	−	1.67575i	−0.0696283	−	0.0616853i
$739$	10.3402	−	9.16059i	0.380369	−	0.336978i	−0.451176	−	0.892435i	$-0.648995\pi$
$739$	10.3402	−	9.16059i	0.380369	−	0.336978i	0.831545	+	0.555457i	$0.187457\pi$
$740$	−2.03612	−	1.06864i	−0.0748494	−	0.0392840i
$741$	13.2452	+	9.66577i	0.486574	+	0.355081i
$742$	−34.1176	+	17.9063i	−1.25250	+	0.657361i
$743$	6.37358	−	16.8058i	0.233824	−	0.616543i	−0.765825	−	0.643049i	$-0.777669\pi$
$743$	6.37358	−	16.8058i	0.233824	−	0.616543i	0.999649	+	0.0265063i	$0.00843820\pi$
$744$	−5.77099	−	47.5284i	−0.211575	−	1.74248i
$745$	10.7459	−	5.63987i	0.393698	−	0.206629i
$746$	−18.9398			−0.693437
$747$	−0.583917	+	0.306463i	−0.0213644	+	0.0112129i
$748$	1.60123	−	1.41856i	0.0585467	−	0.0518678i
$749$	−21.3371	−	30.9121i	−0.779639	−	1.12950i
$750$	−11.0585	−	9.79697i	−0.403799	−	0.357735i
$751$	−26.3818	−	38.2206i	−0.962685	−	1.39469i	−0.918392	−	0.395671i	$-0.870512\pi$
$751$	−26.3818	−	38.2206i	−0.962685	−	1.39469i	−0.0442922	−	0.999019i	$-0.514103\pi$
$752$	−0.239409	−	0.631269i	−0.00873034	−	0.0230200i
$753$	−15.0640	−	39.7206i	−0.548964	−	1.44750i
$754$	9.88408	−	10.5833i	0.359957	−	0.385420i
$755$	1.87243	−	4.93718i	0.0681445	−	0.179682i
$756$	8.23850			0.299631
$757$	3.80209	+	10.0253i	0.138189	+	0.364375i	0.986190	−	0.165621i	$-0.0529627\pi$
$757$	3.80209	+	10.0253i	0.138189	+	0.364375i	−0.848000	+	0.529996i	$0.822193\pi$
$758$	1.79477	−	14.7813i	0.0651891	−	0.536880i
$759$	−47.4471	−	24.9022i	−1.72222	−	0.903891i
$760$	2.36383	+	3.42459i	0.0857450	+	0.124223i
$761$	−5.72839	−	8.29900i	−0.207654	−	0.300839i	0.705294	−	0.708915i	$-0.250815\pi$
$761$	−5.72839	−	8.29900i	−0.207654	−	0.300839i	−0.912948	+	0.408076i	$0.866200\pi$
$762$	1.31202	+	0.688603i	0.0475296	+	0.0249455i
$763$	5.84050	−	48.1008i	0.211440	−	1.74137i
$764$	0.216889	+	0.571889i	0.00784676	+	0.0206902i
$765$	−1.00593			−0.0363695
$766$	−6.22729	+	16.4200i	−0.225001	+	0.593279i
$767$	5.85870	−	21.3409i	0.211545	−

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)

\(f(q)\)	\(=\)	\(q+(0.711778 - 1.03119i) q^{2} +(-1.78709 + 0.937940i) q^{3} +(0.152488 + 0.402078i) q^{4} +(-0.453990 - 0.402200i) q^{5} +(-0.304822 + 2.51044i) q^{6} +(4.78395 + 1.17914i) q^{7} +(2.95631 + 0.728665i) q^{8} +(0.609782 - 0.883421i) q^{9} +O(q^{10})\)	\(q+(0.711778 - 1.03119i) q^{2} +(-1.78709 + 0.937940i) q^{3} +(0.152488 + 0.402078i) q^{4} +(-0.453990 - 0.402200i) q^{5} +(-0.304822 + 2.51044i) q^{6} +(4.78395 + 1.17914i) q^{7} +(2.95631 + 0.728665i) q^{8} +(0.609782 - 0.883421i) q^{9} +(-0.737885 + 0.181872i) q^{10} +(-1.82902 - 2.64980i) q^{11} +(-0.649635 - 0.575526i) q^{12} +(1.59116 + 3.23546i) q^{13} +(4.62103 - 4.09387i) q^{14} +(1.18856 + 0.292954i) q^{15} +(2.21188 - 1.95955i) q^{16} +(1.50016 + 0.369755i) q^{17} +(-0.476945 - 1.25760i) q^{18} -2.25327 q^{19} +(0.0924877 - 0.243870i) q^{20} +(-9.65534 + 2.37983i) q^{21} -4.03430 q^{22} -8.24595 q^{23} +(-5.96665 + 1.47065i) q^{24} +(-0.558341 - 4.59835i) q^{25} +(4.46892 + 0.662149i) q^{26} +(0.468687 - 3.85998i) q^{27} +(0.255390 + 2.10332i) q^{28} +(1.82087 - 2.63799i) q^{29} +(1.14808 - 1.01711i) q^{30} +(-0.939103 + 7.73421i) q^{31} +(0.287715 + 2.36955i) q^{32} +(5.75399 + 3.01993i) q^{33} +(1.44906 - 1.28376i) q^{34} +(-1.69762 - 2.45942i) q^{35} +(0.448188 + 0.110468i) q^{36} +(1.06272 - 8.75226i) q^{37} +(-1.60383 + 2.32354i) q^{38} +(-5.87822 - 4.28967i) q^{39} +(-1.04907 - 1.51984i) q^{40} +(1.66364 - 0.873146i) q^{41} +(-4.41841 + 11.6504i) q^{42} +(-0.731069 - 6.02089i) q^{43} +(0.786520 - 1.13947i) q^{44} +(-0.632147 + 0.155810i) q^{45} +(-5.86929 + 8.50313i) q^{46} +(0.0810172 - 0.213625i) q^{47} +(-2.11489 + 5.57651i) q^{48} +(15.2976 + 8.02882i) q^{49} +(-5.13919 - 2.69725i) q^{50} +(-3.02773 + 0.746268i) q^{51} +(-1.05828 + 1.13314i) q^{52} +(-6.05988 - 1.49363i) q^{53} +(-3.64677 - 3.23076i) q^{54} +(-0.235391 + 1.93862i) q^{55} +(13.2837 + 6.97180i) q^{56} +(4.02680 - 2.11343i) q^{57} +(-1.42421 - 3.75532i) q^{58} +(-4.59429 - 4.07018i) q^{59} +(0.0634511 + 0.522567i) q^{60} +(-2.22262 + 0.547828i) q^{61} +(7.30699 + 6.47343i) q^{62} +(3.95884 - 3.50723i) q^{63} +(7.88135 + 4.13645i) q^{64} +(0.578935 - 2.10883i) q^{65} +(7.20968 - 3.78393i) q^{66} +(-1.39820 + 3.68676i) q^{67} +(0.0800853 + 0.659562i) q^{68} +(14.7363 - 7.73420i) q^{69} -3.74446 q^{70} +(-3.75267 + 1.96956i) q^{71} +(2.44642 - 2.16734i) q^{72} +(-5.78742 - 8.38452i) q^{73} +(-8.26881 - 7.32552i) q^{74} +(5.31079 + 7.69400i) q^{75} +(-0.343596 - 0.905988i) q^{76} +(-5.62548 - 14.8332i) q^{77} +(-8.60744 + 3.00826i) q^{78} +(0.932193 - 2.45799i) q^{79} -1.79230 q^{80} +(3.92478 + 10.3488i) q^{81} +(0.283765 - 2.33701i) q^{82} +(-0.543969 - 0.285497i) q^{83} +(-2.42920 - 3.51930i) q^{84} +(-0.532340 - 0.771228i) q^{85} +(-6.72904 - 3.53167i) q^{86} +(-0.779797 + 6.42220i) q^{87} +(-3.47635 - 9.16637i) q^{88} +18.0185 q^{89} +(-0.289279 + 0.762765i) q^{90} +(3.79696 + 17.3545i) q^{91} +(-1.25741 - 3.31551i) q^{92} +(-5.57595 - 14.7026i) q^{93} +(-0.162621 - 0.235597i) q^{94} +(1.02296 + 0.906264i) q^{95} +(-2.73667 - 3.96474i) q^{96} +(-6.01270 + 5.32678i) q^{97} +(19.1678 - 10.0600i) q^{98} -3.45619 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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