LMFDB - Embedded newform 169.2.h.a.12.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.14
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07618 - 1.43308i) q^{2} +(-1.76851 - 0.928185i) q^{3} +(1.54757 - 4.08062i) q^{4} +(-0.134767 - 0.152121i) q^{5} +(-5.00190 + 0.607340i) q^{6} +(0.524392 + 2.12754i) q^{7} +(-1.42736 - 5.79101i) q^{8} +(0.561902 + 0.814056i) q^{9} +O(q^{10})$	\(q+(2.07618 - 1.43308i) q^{2} +(-1.76851 - 0.928185i) q^{3} +(1.54757 - 4.08062i) q^{4} +(-0.134767 - 0.152121i) q^{5} +(-5.00190 + 0.607340i) q^{6} +(0.524392 + 2.12754i) q^{7} +(-1.42736 - 5.79101i) q^{8} +(0.561902 + 0.814056i) q^{9} +(-0.497802 - 0.122697i) q^{10} +(-0.114284 - 0.0788846i) q^{11} +(-6.52447 + 5.78018i) q^{12} +(3.55731 - 0.587841i) q^{13} +(4.13767 + 3.66565i) q^{14} +(0.0971409 + 0.394116i) q^{15} +(-4.72909 - 4.18961i) q^{16} +(-0.835105 + 0.205835i) q^{17} +(2.33322 + 0.884872i) q^{18} +7.01701i q^{19} +(-0.829309 + 0.314516i) q^{20} +(1.04736 - 4.24931i) q^{21} -0.350322 q^{22} +2.12087 q^{23} +(-2.85084 + 11.5663i) q^{24} +(0.597705 - 4.92254i) q^{25} +(6.54317 - 6.31837i) q^{26} +(0.484104 + 3.98696i) q^{27} +(9.49322 + 1.15269i) q^{28} +(-2.45609 - 3.55826i) q^{29} +(0.766481 + 0.679043i) q^{30} +(5.33322 - 0.647570i) q^{31} +(-3.98079 - 0.483355i) q^{32} +(0.128893 + 0.245585i) q^{33} +(-1.43885 + 1.62412i) q^{34} +(0.252972 - 0.366494i) q^{35} +(4.19144 - 1.03310i) q^{36} +(-10.9608 + 1.33088i) q^{37} +(10.0559 + 14.5686i) q^{38} +(-6.83676 - 2.26224i) q^{39} +(-0.688572 + 0.997569i) q^{40} +(-4.22027 + 8.04105i) q^{41} +(-3.91510 - 10.3233i) q^{42} +(-0.267028 + 2.19917i) q^{43} +(-0.498761 + 0.344270i) q^{44} +(0.0481088 - 0.195185i) q^{45} +(4.40329 - 3.03937i) q^{46} +(-10.5654 + 4.00691i) q^{47} +(4.47471 + 11.7988i) q^{48} +(1.94675 - 1.02173i) q^{49} +(-5.81346 - 11.0766i) q^{50} +(1.66794 + 0.411111i) q^{51} +(3.10645 - 15.4257i) q^{52} +(3.47744 - 0.857112i) q^{53} +(6.71871 + 7.58386i) q^{54} +(0.00340177 + 0.0280161i) q^{55} +(11.5721 - 6.07352i) q^{56} +(6.51309 - 12.4097i) q^{57} +(-10.1986 - 3.86780i) q^{58} +(-5.59291 - 6.31309i) q^{59} +(1.75857 + 0.213529i) q^{60} +(-11.0114 - 2.71407i) q^{61} +(10.1447 - 8.98740i) q^{62} +(-1.43728 + 1.62235i) q^{63} +(2.23112 - 1.17098i) q^{64} +(-0.568831 - 0.461919i) q^{65} +(0.619547 + 0.325164i) q^{66} +(-4.05657 + 1.53845i) q^{67} +(-0.452454 + 3.72629i) q^{68} +(-3.75077 - 1.96856i) q^{69} -1.12343i q^{70} +(-0.556136 + 1.05963i) q^{71} +(3.91217 - 4.41593i) q^{72} +(11.5747 + 7.98947i) q^{73} +(-20.8492 + 18.4708i) q^{74} +(-5.62608 + 8.15078i) q^{75} +(28.6338 + 10.8594i) q^{76} +(0.107901 - 0.284511i) q^{77} +(-17.4363 + 5.10082i) q^{78} +(0.784145 + 2.06762i) q^{79} +1.28401i q^{80} +(3.89677 - 10.2749i) q^{81} +(2.76145 + 22.7426i) q^{82} +(-3.98160 - 7.58630i) q^{83} +(-15.7189 - 10.8500i) q^{84} +(0.143857 + 0.0992971i) q^{85} +(2.59720 + 4.94854i) q^{86} +(1.04089 + 8.57253i) q^{87} +(-0.293698 + 0.774417i) q^{88} -16.2753i q^{89} +(-0.179834 - 0.474182i) q^{90} +(3.11608 + 7.26006i) q^{91} +(3.28220 - 8.65445i) q^{92} +(-10.0329 - 3.80498i) q^{93} +(-16.1933 + 23.4601i) q^{94} +(1.06743 - 0.945664i) q^{95} +(6.59142 + 4.54973i) q^{96} +(-2.46253 + 2.77963i) q^{97} +(2.57757 - 4.91114i) q^{98} -0.137359i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	2.07618	−	1.43308i	1.46808	−	1.01334i	0.477168	−	0.878812i	$-0.341663\pi$
$2$	2.07618	−	1.43308i	1.46808	−	1.01334i	0.990910	−	0.134529i	$-0.0429520\pi$
$3$	−1.76851	−	0.928185i	−1.02105	−	0.535888i	−0.130823	−	0.991406i	$-0.541762\pi$
$3$	−1.76851	−	0.928185i	−1.02105	−	0.535888i	−0.890227	+	0.455518i	$0.849454\pi$
$4$	1.54757	−	4.08062i	0.773787	−	2.04031i
$5$	−0.134767	−	0.152121i	−0.0602697	−	0.0680305i	0.717603	−	0.696453i	$-0.245239\pi$
$5$	−0.134767	−	0.152121i	−0.0602697	−	0.0680305i	−0.777872	+	0.628422i	$0.783701\pi$
$6$	−5.00190	+	0.607340i	−2.04202	+	0.247946i
$7$	0.524392	+	2.12754i	0.198201	+	0.804135i	0.982882	+	0.184235i	$0.0589807\pi$
$7$	0.524392	+	2.12754i	0.198201	+	0.804135i	−0.784681	+	0.619900i	$0.787173\pi$
$8$	−1.42736	−	5.79101i	−0.504647	−	2.04743i
$9$	0.561902	+	0.814056i	0.187301	+	0.271352i
$10$	−0.497802	−	0.122697i	−0.157419	−	0.0388002i
$11$	−0.114284	−	0.0788846i	−0.0344580	−	0.0237846i	0.550711	−	0.834696i	$-0.314357\pi$
$11$	−0.114284	−	0.0788846i	−0.0344580	−	0.0237846i	−0.585169	+	0.810911i	$0.698972\pi$
$12$	−6.52447	+	5.78018i	−1.88345	+	1.66859i
$13$	3.55731	−	0.587841i	0.986620	−	0.163038i
$13$	3.55731	−	0.587841i	0.986620	−	0.163038i
$14$	4.13767	+	3.66565i	1.10584	+	0.979687i
$15$	0.0971409	+	0.394116i	0.0250817	+	0.101760i
$16$	−4.72909	−	4.18961i	−1.18227	−	1.04740i
$17$	−0.835105	+	0.205835i	−0.202543	+	0.0499223i	−0.339282	−	0.940685i	$-0.610184\pi$
$17$	−0.835105	+	0.205835i	−0.202543	+	0.0499223i	0.136739	+	0.990607i	$0.456338\pi$
$18$	2.33322	+	0.884872i	0.549944	+	0.208566i
$19$			7.01701i			1.60981i	0.593401	+	0.804907i	$0.297785\pi$
$19$			7.01701i			1.60981i	−0.593401	+	0.804907i	$0.702215\pi$
$20$	−0.829309	+	0.314516i	−0.185439	+	0.0703278i
$21$	1.04736	−	4.24931i	0.228553	−	0.927275i
$22$	−0.350322			−0.0746889
$23$	2.12087			0.442231			0.221116	−	0.975248i	$-0.429030\pi$
$23$	2.12087			0.442231			0.221116	+	0.975248i	$0.429030\pi$
$24$	−2.85084	+	11.5663i	−0.581925	+	2.36096i
$25$	0.597705	−	4.92254i	0.119541	−	0.984509i
$26$	6.54317	−	6.31837i	1.28322	−	1.23913i
$27$	0.484104	+	3.98696i	0.0931659	+	0.767290i
$28$	9.49322	+	1.15269i	1.79405	+	0.217837i
$29$	−2.45609	−	3.55826i	−0.456085	−	0.660753i	0.525717	−	0.850659i	$-0.323797\pi$
$29$	−2.45609	−	3.55826i	−0.456085	−	0.660753i	−0.981802	+	0.189906i	$0.939182\pi$
$30$	0.766481	+	0.679043i	0.139940	+	0.123976i
$31$	5.33322	−	0.647570i	0.957874	−	0.116307i	0.373357	−	0.927688i	$-0.378207\pi$
$31$	5.33322	−	0.647570i	0.957874	−	0.116307i	0.584518	+	0.811381i	$0.301284\pi$
$32$	−3.98079	−	0.483355i	−0.703711	−	0.0854459i
$33$	0.128893	+	0.245585i	0.0224374	+	0.0427509i
$34$	−1.43885	+	1.62412i	−0.246760	+	0.278535i
$35$	0.252972	−	0.366494i	0.0427601	−	0.0619487i
$36$	4.19144	−	1.03310i	0.698573	−	0.172183i
$37$	−10.9608	+	1.33088i	−1.80194	+	0.218795i	−0.951579	−	0.307405i	$-0.900539\pi$
$37$	−10.9608	+	1.33088i	−1.80194	+	0.218795i	−0.850361	+	0.526200i	$0.823616\pi$
$38$	10.0559	+	14.5686i	1.63129	+	2.36333i
$39$	−6.83676	−	2.26224i	−1.09476	−	0.362248i
$40$	−0.688572	+	0.997569i	−0.108873	+	0.157730i
$41$	−4.22027	+	8.04105i	−0.659096	+	1.25580i	0.294770	+	0.955568i	$0.404757\pi$
$41$	−4.22027	+	8.04105i	−0.659096	+	1.25580i	−0.953866	+	0.300234i	$0.902935\pi$
$42$	−3.91510	−	10.3233i	−0.604112	−	1.59291i
$43$	−0.267028	+	2.19917i	−0.0407214	+	0.335371i	0.958083	+	0.286490i	$0.0924885\pi$
$43$	−0.267028	+	2.19917i	−0.0407214	+	0.335371i	−0.998805	+	0.0488809i	$0.984435\pi$
$44$	−0.498761	+	0.344270i	−0.0751911	+	0.0519007i
$45$	0.0481088	−	0.195185i	0.00717164	−	0.0290965i
$46$	4.40329	−	3.03937i	0.649230	−	0.448131i
$47$	−10.5654	+	4.00691i	−1.54112	+	0.584468i	−0.971416	−	0.237385i	$-0.923710\pi$
$47$	−10.5654	+	4.00691i	−1.54112	+	0.584468i	−0.569700	+	0.821853i	$0.692940\pi$
$48$	4.47471	+	11.7988i	0.645868	+	1.70301i
$49$	1.94675	−	1.02173i	0.278107	−	0.145962i
$50$	−5.81346	−	11.0766i	−0.822147	−	1.56647i
$51$	1.66794	+	0.411111i	0.233559	+	0.0575671i
$52$	3.10645	−	15.4257i	0.430787	−	2.13917i
$53$	3.47744	−	0.857112i	0.477663	−	0.117733i	0.00686874	−	0.999976i	$-0.497814\pi$
$53$	3.47744	−	0.857112i	0.477663	−	0.117733i	0.470794	+	0.882243i	$0.343967\pi$
$54$	6.71871	+	7.58386i	0.914301	+	1.03203i
$55$	0.00340177	+	0.0280161i	0.000458694	+	0.00377768i
$56$	11.5721	−	6.07352i	1.54639	−	0.811608i
$57$	6.51309	−	12.4097i	0.862680	−	1.64370i
$58$	−10.1986	−	3.86780i	−1.33914	−	0.507867i
$59$	−5.59291	−	6.31309i	−0.728135	−	0.821895i	0.261545	−	0.965191i	$-0.415768\pi$
$59$	−5.59291	−	6.31309i	−0.728135	−	0.821895i	−0.989680	+	0.143297i	$0.954230\pi$
$60$	1.75857	+	0.213529i	0.227030	+	0.0275665i
$61$	−11.0114	−	2.71407i	−1.40987	−	0.347501i	−0.540365	−	0.841431i	$-0.681714\pi$
$61$	−11.0114	−	2.71407i	−1.40987	−	0.347501i	−0.869502	+	0.493930i	$0.835560\pi$
$62$	10.1447	−	8.98740i	1.28838	−	1.14140i
$63$	−1.43728	+	1.62235i	−0.181080	+	0.204397i
$64$	2.23112	−	1.17098i	0.278890	−	0.146373i
$65$	−0.568831	−	0.461919i	−0.0705549	−	0.0572940i
$66$	0.619547	+	0.325164i	0.0762610	+	0.0400249i
$67$	−4.05657	+	1.53845i	−0.495589	+	0.187952i	−0.589720	−	0.807608i	$-0.700762\pi$
$67$	−4.05657	+	1.53845i	−0.495589	+	0.187952i	0.0941311	+	0.995560i	$0.469993\pi$
$68$	−0.452454	+	3.72629i	−0.0548681	+	0.451879i
$69$	−3.75077	−	1.96856i	−0.451540	−	0.236986i
$70$		−	1.12343i		−	0.134276i
$71$	−0.556136	+	1.05963i	−0.0660012	+	0.125755i	−0.916221	−	0.400673i	$-0.868776\pi$
$71$	−0.556136	+	1.05963i	−0.0660012	+	0.125755i	0.850220	+	0.526427i	$0.176469\pi$
$72$	3.91217	−	4.41593i	0.461054	−	0.520422i
$73$	11.5747	+	7.98947i	1.35472	+	0.935097i	1.00000		0.000124814i	$3.97296e-5\pi$
$73$	11.5747	+	7.98947i	1.35472	+	0.935097i	0.354722	+	0.934972i	$0.384576\pi$
$74$	−20.8492	+	18.4708i	−2.42367	+	2.14719i
$75$	−5.62608	+	8.15078i	−0.649643	+	0.941171i
$76$	28.6338	+	10.8594i	3.28452	+	1.24565i
$77$	0.107901	−	0.284511i	0.0122964	−	0.0324230i
$78$	−17.4363	+	5.10082i	−1.97427	+	0.577554i
$79$	0.784145	+	2.06762i	0.0882232	+	0.232626i	0.971865	−	0.235538i	$-0.0756851\pi$
$79$	0.784145	+	2.06762i	0.0882232	+	0.232626i	−0.883642	+	0.468163i	$0.844916\pi$
$80$			1.28401i			0.143557i
$81$	3.89677	−	10.2749i	0.432974	−	1.14166i
$82$	2.76145	+	22.7426i	0.304952	+	2.51150i
$83$	−3.98160	−	7.58630i	−0.437037	−	0.832705i	−0.999981	−	0.00620962i	$-0.998023\pi$
$83$	−3.98160	−	7.58630i	−0.437037	−	0.832705i	0.562943	−	0.826495i	$-0.309669\pi$
$84$	−15.7189	−	10.8500i	−1.71508	−	1.18383i
$85$	0.143857	+	0.0992971i	0.0156034	+	0.0107703i
$86$	2.59720	+	4.94854i	0.280063	+	0.533615i
$87$	1.04089	+	8.57253i	0.111596	+	0.919072i
$88$	−0.293698	+	0.774417i	−0.0313083	+	0.0825531i
$89$		−	16.2753i		−	1.72518i	−0.505902	−	0.862591i	$-0.668840\pi$
$89$		−	16.2753i		−	1.72518i	0.505902	−	0.862591i	$-0.331160\pi$
$90$	−0.179834	−	0.474182i	−0.0189561	−	0.0499832i
$91$	3.11608	+	7.26006i	0.326654	+	0.761061i
$92$	3.28220	−	8.65445i	0.342193	−	0.902289i
$93$	−10.0329	−	3.80498i	−1.04036	−	0.394558i
$94$	−16.1933	+	23.4601i	−1.67021	+	2.41972i
$95$	1.06743	−	0.945664i	0.109516	−	0.0970231i
$96$	6.59142	+	4.54973i	0.672734	+	0.464355i
$97$	−2.46253	+	2.77963i	−0.250032	+	0.282228i	−0.860105	−	0.510117i	$-0.829602\pi$
$97$	−2.46253	+	2.77963i	−0.250032	+	0.282228i	0.610072	+	0.792346i	$0.291140\pi$
$98$	2.57757	−	4.91114i	0.260374	−	0.496100i
$99$		−	0.137359i		−	0.0138051i
$100$	−19.1620	−	10.0570i	−1.91620	−	1.00570i
$101$	−0.0304135	+	0.250478i	−0.00302626	+	0.0249235i	−0.994144	−	0.108065i	$-0.965534\pi$
$101$	−0.0304135	+	0.250478i	−0.00302626	+	0.0249235i	0.991118	+	0.132989i	$0.0424575\pi$
$102$	4.05210	−	1.53676i	0.401218	−	0.152162i
$103$	9.22413	+	4.84120i	0.908881	+	0.477017i	0.853290	−	0.521436i	$-0.174604\pi$
$103$	9.22413	+	4.84120i	0.908881	+	0.477017i	0.0555905	+	0.998454i	$0.482296\pi$
$104$	−8.48174	−	19.7614i	−0.831703	−	1.93776i
$105$	−0.787558	+	0.413342i	−0.0768578	+	0.0403381i
$106$	5.99146	−	6.76296i	0.581942	−	0.656877i
$107$	0.557891	−	0.494248i	0.0539333	−	0.0477807i	−0.635726	−	0.771915i	$-0.719299\pi$
$107$	0.557891	−	0.494248i	0.0539333	−	0.0477807i	0.689659	+	0.724134i	$0.257761\pi$
$108$	17.0184	+	4.19467i	1.63760	+	0.403632i
$109$	10.5255	+	1.27802i	1.00816	+	0.122412i	0.607918	−	0.793999i	$-0.292005\pi$
$109$	10.5255	+	1.27802i	1.00816	+	0.122412i	0.400237	+	0.916412i	$0.368928\pi$
$110$	0.0472119	+	0.0532912i	0.00450148	+	0.00508112i
$111$	20.6195	+	7.81995i	1.95712	+	0.742237i
$112$	6.43367	−	12.2583i	0.607924	−	1.15830i
$113$	6.05532	−	3.17808i	0.569636	−	0.298968i	−0.155207	−	0.987882i	$-0.549604\pi$
$113$	6.05532	−	3.17808i	0.569636	−	0.298968i	0.724843	+	0.688914i	$0.241912\pi$
$114$	−4.26172	−	35.0984i	−0.399146	−	3.28727i
$115$	−0.285823	−	0.322628i	−0.0266532	−	0.0300852i
$116$	−18.3209	+	4.51570i	−1.70105	+	0.419272i
$117$	2.47739	+	2.56554i	0.229035	+	0.237184i
$118$	−20.6590	−	5.09199i	−1.90182	−	0.468756i
$119$	−0.875844	−	1.66878i	−0.0802885	−	0.152977i
$120$	2.14368	−	1.12509i	0.195690	−	0.102706i
$121$	−3.89382	−	10.2671i	−0.353983	−	0.933377i
$122$	−26.7511	+	10.1453i	−2.42193	+	0.918517i
$123$	14.9272	−	10.3035i	1.34594	−	0.929034i
$124$	5.61107	−	22.7650i	0.503889	−	2.04436i
$125$	−1.66565	+	1.14972i	−0.148980	+	0.102834i
$126$	−0.659082	+	5.42803i	−0.0587157	+	0.483567i
$127$	0.694532	+	1.83133i	0.0616298	+	0.162504i	0.962294	−	0.272011i	$-0.0876888\pi$
$127$	0.694532	+	1.83133i	0.0616298	+	0.162504i	−0.900664	+	0.434516i	$0.856920\pi$
$128$	6.68118	−	12.7299i	0.590539	−	1.12518i
$129$	2.51348	−	3.64141i	0.221300	−	0.320608i
$130$	−1.84296	−	0.143843i	−0.161638	−	0.0126159i
$131$	−2.94748	−	4.27016i	−0.257523	−	0.373086i	0.672802	−	0.739822i	$-0.265090\pi$
$131$	−2.94748	−	4.27016i	−0.257523	−	0.373086i	−0.930325	+	0.366736i	$0.880475\pi$
$132$	1.20161	−	0.145902i	0.104587	−	0.0126991i
$133$	−14.9290	+	3.67966i	−1.29451	+	0.319067i
$134$	−6.21742	+	9.00749i	−0.537104	+	0.778129i
$135$	0.541258	−	0.610953i	0.0465840	−	0.0525825i
$136$	2.38398	+	4.54230i	0.204425	+	0.389499i
$137$	19.6204	+	2.38235i	1.67628	+	0.203538i	0.902734	−	0.430199i	$-0.141557\pi$
$137$	19.6204	+	2.38235i	1.67628	+	0.203538i	0.773549	+	0.633736i	$0.218480\pi$
$138$	−10.6084	+	1.28809i	−0.903044	+	0.109649i
$139$	3.15612	+	2.79608i	0.267699	+	0.237160i	0.786284	−	0.617866i	$-0.212002\pi$
$139$	3.15612	+	2.79608i	0.267699	+	0.237160i	−0.518585	+	0.855026i	$0.673541\pi$
$140$	−1.10403	−	1.59946i	−0.0933074	−	0.135179i
$141$	22.4041	+	2.72035i	1.88676	+	0.229095i
$142$	0.363897	+	2.99696i	0.0305376	+	0.251499i
$143$	−0.452915	−	0.213436i	−0.0378747	−	0.0178484i
$144$	0.753289	−	6.20389i	0.0627741	−	0.516991i
$145$	−0.210285	+	0.853160i	−0.0174632	+	0.0708511i
$146$	35.4808			2.93641
$147$	−4.39120			−0.362180
$148$	−11.5318	+	46.7864i	−0.947908	+	3.84582i
$149$	1.87008	−	0.709228i	0.153203	−	0.0581023i	−0.276811	−	0.960924i	$-0.589278\pi$
$149$	1.87008	−	0.709228i	0.153203	−	0.0581023i	0.430014	+	0.902822i	$0.358508\pi$
$150$			24.9851i			2.04002i
$151$	0.582865	+	0.221052i	0.0474329	+	0.0179889i	0.378207	−	0.925721i	$-0.376541\pi$
$151$	0.582865	+	0.221052i	0.0474329	+	0.0179889i	−0.330774	+	0.943710i	$0.607310\pi$
$152$	40.6356	−	10.0158i	3.29598	−	0.812387i
$153$	−0.636809	−	0.564163i	−0.0514829	−	0.0456099i
$154$	−0.183706	−	0.745324i	−0.0148034	−	0.0600599i
$155$	−0.817252	−	0.724022i	−0.0656433	−	0.0581549i
$156$	−19.8117	+	24.3972i	−1.58621	+	1.95334i
$157$	−13.1356	+	11.6372i	−1.04834	+	0.928747i	−0.997550	−	0.0699621i	$-0.977712\pi$
$157$	−13.1356	+	11.6372i	−1.04834	+	0.928747i	−0.0507893	+	0.998709i	$0.516174\pi$
$158$	4.59109	+	3.16900i	0.365248	+	0.252112i
$159$	−6.94544	−	1.71190i	−0.550809	−	0.135762i
$160$	0.462952	+	0.670701i	0.0365995	+	0.0530236i
$161$	1.11217	+	4.51223i	0.0876509	+	0.355614i
$162$	−6.63443	−	26.9169i	−0.521250	−	2.11479i
$163$	−18.7893	+	2.28143i	−1.47169	+	0.178695i	−0.816752	−	0.576988i	$-0.804228\pi$
$163$	−18.7893	+	2.28143i	−1.47169	+	0.178695i	−0.654937	+	0.755684i	$0.727305\pi$
$164$	26.2813	+	29.6655i	2.05222	+	2.31648i
$165$	0.0199880	−	0.0527041i	0.00155607	−	0.00410301i
$166$	−19.1383	−	10.0445i	−1.48542	−	0.779608i
$167$	−12.3722	+	8.53988i	−0.957386	+	0.660836i	−0.940777	−	0.339026i	$-0.889903\pi$
$167$	−12.3722	+	8.53988i	−0.957386	+	0.660836i	−0.0166093	+	0.999862i	$0.505287\pi$
$168$	−26.1027			−2.01387
$169$	12.3089	−	4.18226i	0.946837	−	0.321712i
$170$	0.440972			0.0338210
$171$	−5.71224	+	3.94288i	−0.436826	+	0.301519i
$172$	8.56075	+	4.49303i	0.652751	+	0.342590i
$173$	8.36955	−	22.0687i	0.636325	−	1.67785i	−0.0947054	−	0.995505i	$-0.530191\pi$
$173$	8.36955	−	22.0687i	0.636325	−	1.67785i	0.731030	−	0.682345i	$-0.239040\pi$
$174$	14.4462	+	16.3064i	1.09516	+	1.23618i
$175$	10.7863	−	1.30970i	0.815371	−	0.0990039i
$176$	0.209964	+	0.851858i	0.0158266	+	0.0642112i
$177$	4.03140	+	16.3560i	0.303018	+	1.22939i
$178$	−23.3239	−	33.7905i	−1.74820	−	2.53270i
$179$	−7.93236	−	1.95515i	−0.592893	−	0.146135i	−0.0685579	−	0.997647i	$-0.521840\pi$
$179$	−7.93236	−	1.95515i	−0.592893	−	0.146135i	−0.524335	+	0.851512i	$0.675686\pi$
$180$	−0.722024	−	0.498377i	−0.0538165	−	0.0371469i
$181$	0.172488	−	0.152811i	0.0128210	−	0.0113584i	−0.656688	−	0.754162i	$-0.728043\pi$
$181$	0.172488	−	0.152811i	0.0128210	−	0.0113584i	0.669509	+	0.742804i	$0.266505\pi$
$182$	16.8738	+	10.6076i	1.25077	+	0.786285i
$183$	16.9546	+	15.0205i	1.25332	+	1.11035i
$184$	−3.02723	−	12.2820i	−0.223171	−	0.905438i
$185$	1.67961	+	1.48800i	0.123487	+	0.109400i
$186$	−26.2829	+	6.47816i	−1.92716	+	0.475002i
$187$	0.111676	+	0.0423533i	0.00816659	+	0.00309718i
$188$			49.3142i			3.59661i
$189$	−8.22855	+	3.12068i	−0.598539	+	0.226996i
$190$	0.860967	−	3.49308i	0.0624611	−	0.253415i
$191$	11.7788			0.852281			0.426141	−	0.904657i	$-0.359873\pi$
$191$	11.7788			0.852281			0.426141	+	0.904657i	$0.359873\pi$
$192$	−5.03264			−0.363199
$193$	−5.87862	+	23.8505i	−0.423152	+	1.71680i	0.242165	+	0.970235i	$0.422142\pi$
$193$	−5.87862	+	23.8505i	−0.423152	+	1.71680i	−0.665317	+	0.746561i	$0.731704\pi$
$194$	−1.12922	+	9.30000i	−0.0810736	+	0.667701i
$195$	0.577237	+	1.34489i	0.0413368	+	0.0963095i
$196$	−1.15656	−	9.52515i	−0.0826116	−	0.680368i
$197$	0.149724	+	0.0181798i	0.0106674	+	0.00129526i	0.125869	−	0.992047i	$-0.459828\pi$
$197$	0.149724	+	0.0181798i	0.0106674	+	0.00129526i	−0.115201	+	0.993342i	$0.536751\pi$
$198$	−0.196847	−	0.285182i	−0.0139893	−	0.0202670i
$199$	−2.58713	−	2.29200i	−0.183397	−	0.162475i	0.566429	−	0.824110i	$-0.308324\pi$
$199$	−2.58713	−	2.29200i	−0.183397	−	0.162475i	−0.749826	+	0.661635i	$0.769863\pi$
$200$	−29.3596	+	3.56491i	−2.07604	+	0.252077i
$201$	8.60205	+	1.04448i	0.606742	+	0.0736718i
$202$	0.295811	+	0.563621i	0.0208132	+	0.0396563i
$203$	6.28240	−	7.09136i	0.440938	−	0.497716i
$204$	4.25886	−	6.17002i	0.298180	−	0.431988i
$205$	1.79197	−	0.441680i	0.125156	−	0.0308483i
$206$	26.0887	−	3.16775i	1.81769	−	0.220707i
$207$	1.19172	+	1.72650i	0.0828303	+	0.120000i
$208$	−19.2856	−	12.1238i	−1.33722	−	0.840633i
$209$	0.553535	−	0.801933i	0.0382888	−	0.0554709i
$210$	−1.04276	+	1.98680i	−0.0719570	+	0.137103i
$211$	−5.09512	−	13.4347i	−0.350763	−	0.924885i	−0.988033	−	0.154245i	$-0.950706\pi$
$211$	−5.09512	−	13.4347i	−0.350763	−	0.924885i	0.637270	−	0.770641i	$-0.280064\pi$
$212$	1.88405	−	15.5165i	0.129397	−	1.06568i
$213$	1.96706	−	1.35777i	0.134781	−	0.0930325i
$214$	0.449982	−	1.82565i	0.0307601	−	0.124799i
$215$	0.370527	−	0.255756i	0.0252697	−	0.0174424i
$216$	22.3975	−	8.49426i	1.52396	−	0.577961i
$217$	4.17443	+	11.0071i	0.283379	+	0.747208i
$218$	23.6842	−	12.4304i	1.60410	−	0.841894i
$219$	−13.0543	−	24.8730i	−0.882130	−	1.68076i
$220$	0.119587	+	0.0294756i	0.00806258	+	0.00198725i
$221$	−2.84973	+	1.22313i	−0.191693	+	0.0822764i
$222$	54.0164	−	13.3138i	3.62534	−	0.893566i
$223$	−1.08114	−	1.22035i	−0.0723983	−	0.0817208i	0.711195	−	0.702994i	$-0.248154\pi$
$223$	−1.08114	−	1.22035i	−0.0723983	−	0.0817208i	−0.783594	+	0.621273i	$0.786616\pi$
$224$	−1.05913	−	8.72276i	−0.0707664	−	0.582814i
$225$	4.34308	−	2.27942i	0.289538	−	0.151962i
$226$	8.01746	−	15.2760i	0.533314	−	1.01614i
$227$	14.7334	+	5.58763i	0.977888	+	0.370864i	0.791202	−	0.611555i	$-0.209456\pi$
$227$	14.7334	+	5.58763i	0.977888	+	0.370864i	0.186687	+	0.982420i	$0.440225\pi$
$228$	−40.5596	−	45.7823i	−2.68612	−	3.03201i
$229$	5.97838	+	0.725906i	0.395062	+	0.0479692i	0.315657	−	0.948873i	$-0.397775\pi$
$229$	5.97838	+	0.725906i	0.395062	+	0.0479692i	0.0794048	+	0.996842i	$0.474698\pi$
$230$	−1.05577	−	0.260224i	−0.0696155	−	0.0171587i
$231$	−0.454902	+	0.403008i	−0.0299303	+	0.0265160i
$232$	−17.1002	+	19.3022i	−1.12269	+	1.26725i
$233$	−15.4569	+	8.11243i	−1.01262	+	0.531463i	−0.887563	−	0.460687i	$-0.847603\pi$
$233$	−15.4569	+	8.11243i	−1.01262	+	0.531463i	−0.125055	+	0.992150i	$0.539911\pi$
$234$	8.82013	+	1.77620i	0.576590	+	0.116114i
$235$	2.03340	+	1.06721i	0.132644	+	0.0696171i
$236$	−34.4168	+	13.0526i	−2.24034	+	0.849649i
$237$	0.532367	−	4.38444i	0.0345810	−	0.284800i
$238$	−4.20991	−	2.20953i	−0.272888	−	0.143222i
$239$		−	18.1571i		−	1.17449i	−0.809411	−	0.587243i	$-0.800213\pi$
$239$		−	18.1571i		−	1.17449i	0.809411	−	0.587243i	$-0.199787\pi$
$240$	1.19180	−	2.27079i	0.0769306	−	0.146579i
$241$	11.9483	−	13.4868i	0.769657	−	0.868763i	−0.224746	−	0.974417i	$-0.572155\pi$
$241$	11.9483	−	13.4868i	0.769657	−	0.868763i	0.994403	+	0.105654i	$0.0336937\pi$
$242$	−22.7979	−	15.7362i	−1.46550	−	1.01156i
$243$	−7.40990	+	6.56460i	−0.475346	+	0.421119i
$244$	−28.1161	+	40.7331i	−1.79995	+	2.60767i
$245$	−0.417785	−	0.158445i	−0.0266913	−	0.0101227i
$246$	16.2257	−	42.7837i	1.03451	−	2.72779i
$247$	4.12489	+	24.9617i	0.262460	+	1.58827i
$248$	−11.3625	−	29.9604i	−0.721519	−	1.90249i
$249$			17.1121i			1.08444i
$250$	−1.81055	+	4.77403i	−0.114509	+	0.301936i
$251$	−2.63061	−	21.6650i	−0.166043	−	1.36748i	−0.802721	−	0.596355i	$-0.796615\pi$
$251$	−2.63061	−	21.6650i	−0.166043	−	1.36748i	0.636678	−	0.771129i	$-0.280308\pi$
$252$	4.39591	+	8.37571i	0.276916	+	0.527620i
$253$	−0.242381	−	0.167304i	−0.0152384	−	0.0105183i
$254$	4.06642	+	2.80684i	0.255150	+	0.176117i
$255$	−0.162246	−	0.309133i	−0.0101602	−	0.0193587i
$256$	−3.76427	−	31.0015i	−0.235267	−	1.93759i
$257$	−2.35721	+	6.21544i	−0.147038	+	0.387708i	−0.988219	−	0.153046i	$-0.951092\pi$
$257$	−2.35721	+	6.21544i	−0.147038	+	0.387708i	0.841181	+	0.540754i	$0.181861\pi$
$258$		−	11.1622i		−	0.694930i
$259$	−8.57923	−	22.6216i	−0.533088	−	1.40564i
$260$	−2.76522	+	1.60633i	−0.171492	+	0.0996204i
$261$	1.51654	−	3.99879i	0.0938716	−	0.247519i
$262$	−12.2390	−	4.64163i	−0.756126	−	0.286761i
$263$	−5.90404	+	8.55348i	−0.364059	+	0.527430i	−0.961617	−	0.274395i	$-0.911522\pi$
$263$	−5.90404	+	8.55348i	−0.364059	+	0.527430i	0.597558	+	0.801826i	$0.296138\pi$
$264$	1.23821	−	1.09696i	0.0762065	−	0.0675131i
$265$	−0.599029	−	0.413480i	−0.0367981	−	0.0253999i
$266$	−25.7219	+	29.0341i	−1.57711	+	1.78019i
$267$	−15.1065	+	28.7831i	−0.924504	+	1.76150i
$268$			18.9342i			1.15659i
$269$	−22.7850	−	11.9585i	−1.38923	−	0.729123i	−0.406409	−	0.913691i	$-0.633219\pi$
$269$	−22.7850	−	11.9585i	−1.38923	−	0.729123i	−0.982820	+	0.184568i	$0.940911\pi$
$270$	0.248200	−	2.04411i	0.0151050	−	0.124401i
$271$	5.47521	−	2.07647i	0.332595	−	0.126137i	−0.182654	−	0.983177i	$-0.558469\pi$
$271$	5.47521	−	2.07647i	0.332595	−	0.126137i	0.515249	+	0.857041i	$0.327699\pi$
$272$	4.81165	+	2.52535i	0.291749	+	0.153122i
$273$	1.22787	−	15.7318i	0.0743140	−	0.952131i
$274$	44.1495	−	23.1714i	2.66717	−	1.39984i
$275$	−0.456621	+	0.515419i	−0.0275353	+	0.0310809i
$276$	−13.8375	+	12.2590i	−0.832922	+	0.737904i
$277$	16.8435	+	4.15154i	1.01203	+	0.249442i	0.710260	−	0.703940i	$-0.248577\pi$
$277$	16.8435	+	4.15154i	1.01203	+	0.249442i	0.301767	+	0.953382i	$0.402424\pi$
$278$	10.5597	+	1.28218i	0.633327	+	0.0768998i
$279$	3.52391	+	3.97767i	0.210971	+	0.238137i
$280$	−2.48345	−	0.941849i	−0.148415	−	0.0562862i
$281$	0.462882	−	0.881947i	0.0276132	−	0.0526126i	−0.871259	−	0.490824i	$-0.836696\pi$
$281$	0.462882	−	0.881947i	0.0276132	−	0.0526126i	0.898872	+	0.438212i	$0.144388\pi$
$282$	50.4133	−	26.4589i	3.00207	−	1.57561i
$283$	1.75750	+	14.4743i	0.104472	+	0.860406i	0.946885	+	0.321573i	$0.104212\pi$
$283$	1.75750	+	14.4743i	0.104472	+	0.860406i	−0.842412	+	0.538833i	$0.818865\pi$
$284$	3.46328	+	3.90923i	0.205508	+	0.231970i
$285$	−2.76552	+	0.681639i	−0.163815	+	0.0403768i
$286$	−1.24620	+	0.205933i	−0.0736895	+	0.0121771i
$287$	−19.3207	−	4.76214i	−1.14047	−	0.281100i
$288$	−1.84334	−	3.51218i	−0.108620	−	0.206957i
$289$	−14.3977	+	7.55651i	−0.846925	+	0.444500i
$290$	0.786058	+	2.07267i	0.0461589	+	0.121711i
$291$	6.93502	−	2.63011i	0.406538	−	0.154180i
$292$	50.5148	−	34.8678i	2.95615	−	2.04049i
$293$	−0.513385	+	2.08289i	−0.0299923	+	0.121684i	−0.984030	−	0.178004i	$-0.943036\pi$
$293$	−0.513385	+	2.08289i	−0.0299923	+	0.121684i	0.954038	+	0.299687i	$0.0968823\pi$
$294$	−9.11690	+	6.29294i	−0.531709	+	0.367012i
$295$	−0.206611	+	1.70160i	−0.0120294	+	0.0990708i
$296$	23.3521	+	61.5743i	1.35731	+	3.57893i
$297$	0.259184	−	0.493834i	0.0150394	−	0.0286552i
$298$	2.86624	−	4.15246i	0.166037	−	0.240546i
$299$	7.54458	−	1.24673i	0.436314	−	0.0721003i
$300$	24.5535	+	35.5718i	1.41759	+	2.05374i
$301$	−4.81886	+	0.585116i	−0.277755	+	0.0337255i
$302$	1.52691	−	0.376351i	0.0878641	−	0.0216565i
$303$	0.286277	−	0.414743i	0.0164462	−	0.0238264i
$304$	29.3985	−	33.1841i	1.68612	−	1.90324i
$305$	1.07111	+	2.04083i	0.0613316	+	0.116858i
$306$	−2.13062	−	0.258704i	−0.121799	−	0.0147891i
$307$	0.386575	−	0.0469388i	0.0220630	−	0.00267894i	−0.109498	−	0.993987i	$-0.534924\pi$
$307$	0.386575	−	0.0469388i	0.0220630	−	0.00267894i	0.131561	+	0.991308i	$0.458001\pi$
$308$	−0.993995	−	0.880603i	−0.0566381	−	0.0501770i
$309$	−11.8194	−	17.1234i	−0.672384	−	0.974116i
$310$	−2.73434	−	0.332009i	−0.155300	−	0.0188568i
$311$	−3.04278	−	25.0596i	−0.172540	−	1.42100i	−0.779568	−	0.626317i	$-0.784562\pi$
$311$	−3.04278	−	25.0596i	−0.172540	−	1.42100i	0.607028	−	0.794680i	$-0.292362\pi$
$312$	−3.34217	+	42.8208i	−0.189213	+	2.42425i
$313$	−1.30394	+	10.7389i	−0.0737030	+	0.606999i	0.908325	+	0.418265i	$0.137362\pi$
$313$	−1.30394	+	10.7389i	−0.0737030	+	0.606999i	−0.982028	+	0.188734i	$0.939562\pi$
$314$	−10.5949	+	42.9852i	−0.597905	+	2.42580i
$315$	0.440492			0.0248189
$316$	9.65070			0.542894
$317$	−2.92353	+	11.8612i	−0.164202	+	0.666194i	0.829916	+	0.557889i	$0.188388\pi$
$317$	−2.92353	+	11.8612i	−0.164202	+	0.666194i	−0.994118	+	0.108305i	$0.965458\pi$
$318$	−16.8732	+	6.39917i	−0.946204	+	0.358848i
$319$			0.600401i			0.0336160i
$320$	−0.478812	−	0.181589i	−0.0267664	−	0.0101512i
$321$	−1.44539	+	0.356256i	−0.0806737	+	0.0198843i
$322$	8.77544	+	7.77436i	0.489036	+	0.433248i
$323$	−1.44435	−	5.85995i	−0.0803656	−	0.326056i
$324$	−35.8975	−	31.8024i	−1.99431	−	1.76680i
$325$	−0.767449	−	17.8624i	−0.0425704	−	0.990825i
$326$	−35.7403	+	31.6632i	−1.97947	+	1.75366i
$327$	−17.4281	−	12.0298i	−0.963777	−	0.665247i
$328$	52.5897	+	12.9622i	2.90378	+	0.715717i
$329$	−14.0652	−	20.3770i	−0.775442	−	1.12342i
$330$	−0.0340306	−	0.138067i	−0.00187332	−	0.00760036i
$331$	−2.84542	−	11.5443i	−0.156398	−	0.634533i	−0.995843	−	0.0910875i	$-0.970966\pi$
$331$	−2.84542	−	11.5443i	−0.156398	−	0.634533i	0.839445	−	0.543445i	$-0.182880\pi$
$332$	−37.1186	+	4.50702i	−2.03715	+	0.247355i
$333$	−7.24229	−	8.17486i	−0.396875	−	0.447979i
$334$	−13.4484	+	35.4606i	−0.735865	+	1.94032i
$335$	0.780724	+	0.409756i	0.0426555	+	0.0223873i
$336$	−22.7560	+	15.7073i	−1.24144	+	0.856905i
$337$	−8.67012			−0.472292			−0.236146	−	0.971718i	$-0.575884\pi$
$337$	−8.67012			−0.472292			−0.236146	+	0.971718i	$0.575884\pi$
$338$	19.5619	−	26.3227i	1.06403	−	1.43177i
$339$	−13.6587			−0.741840
$340$	0.627822	−	0.433354i	0.0340484	−	0.0235019i
$341$	−0.660586	−	0.346702i	−0.0357727	−	0.0187750i
$342$	−6.20916	+	16.3722i	−0.335753	+	0.885307i
$343$	13.3659	+	15.0870i	0.721693	+	0.814623i
$344$	13.1166	−	1.59264i	0.707199	−	0.0858695i
$345$	0.206023	+	0.835867i	0.0110919	+	0.0450016i
$346$	−14.2495	−	57.8127i	−0.766060	−	3.10803i
$347$	2.04846	+	2.96770i	0.109967	+	0.159315i	0.874103	−	0.485740i	$-0.161450\pi$
$347$	2.04846	+	2.96770i	0.109967	+	0.159315i	−0.764136	+	0.645055i	$0.776835\pi$
$348$	36.5921	+	9.01914i	1.96154	+	0.483477i
$349$	22.6063	+	15.6040i	1.21009	+	0.835264i	0.990117	−	0.140242i	$-0.0447881\pi$
$349$	22.6063	+	15.6040i	1.21009	+	0.835264i	0.219972	+	0.975506i	$0.429403\pi$
$350$	20.5174	−	18.1769i	1.09670	−	0.971594i
$351$	4.06580	+	13.8983i	0.217016	+	0.741834i
$352$	0.416812	+	0.369263i	0.0222161	+	0.0196818i
$353$	−5.48378	−	22.2486i	−0.291872	−	1.18417i	−0.915457	−	0.402417i	$-0.868170\pi$
$353$	−5.48378	−	22.2486i	−0.291872	−	1.18417i	0.623584	−	0.781756i	$-0.285676\pi$
$354$	31.8094	+	28.1806i	1.69065	+	1.49778i
$355$	0.236140	−	0.0582034i	0.0125330	−	0.00308911i
$356$	−66.4135	−	25.1873i	−3.51991	−	1.33492i
$357$			3.76420i			0.199223i
$358$	−19.2709	+	7.30848i	−1.01850	+	0.386265i
$359$	−7.75849	+	31.4774i	−0.409477	+	1.66132i	0.297990	+	0.954569i	$0.403684\pi$
$359$	−7.75849	+	31.4774i	−0.409477	+	1.66132i	−0.707467	+	0.706746i	$0.750162\pi$
$360$	−1.19899			−0.0631922
$361$	−30.2385			−1.59150
$362$	0.139125	−	0.564453i	0.00731225	−	0.0296670i
$363$	−2.64357	+	21.7717i	−0.138751	+	1.14272i
$364$	34.4479	−	1.48004i	1.80556	−	0.0775752i
$365$	−0.344532	−	2.83748i	−0.0180336	−	0.148520i
$366$	56.7263	+	6.88782i	2.96513	+	0.360032i
$367$	−15.3166	−	22.1899i	−0.799520	−	1.15831i	−0.984469	−	0.175557i	$-0.943827\pi$
$367$	−15.3166	−	22.1899i	−0.799520	−	1.15831i	0.184949	−	0.982748i	$-0.440788\pi$
$368$	−10.0298	−	8.88560i	−0.522838	−	0.463194i
$369$	−8.91725	+	1.08275i	−0.464213	+	0.0563657i
$370$	5.61959	+	0.682341i	0.292148	+	0.0354732i
$371$	3.64708	+	6.94893i	0.189347	+	0.360770i
$372$	−31.0534	+	35.0520i	−1.61004	+	1.81736i
$373$	−7.42081	+	10.7509i	−0.384235	+	0.556661i	−0.966608	−	0.256261i	$-0.917509\pi$
$373$	−7.42081	+	10.7509i	−0.384235	+	0.556661i	0.582372	+	0.812922i	$0.302125\pi$
$374$	0.292556	−	0.0721085i	0.0151277	−	0.00372864i
$375$	4.01287	−	0.487251i	0.207224	−	0.0251615i
$376$	38.2846	+	55.4648i	1.97438	+	2.86038i
$377$	−10.8288	−	11.2141i	−0.557710	−	0.577553i
$378$	−12.6117	+	18.2713i	−0.648678	+	0.939772i
$379$	7.88178	−	15.0175i	0.404860	−	0.771396i	−0.594608	−	0.804016i	$-0.702693\pi$
$379$	7.88178	−	15.0175i	0.404860	−	0.771396i	0.999468	+	0.0326201i	$0.0103851\pi$
$380$	−2.20696	−	5.81928i	−0.113215	−	0.298523i
$381$	0.471528	−	3.88338i	0.0241571	−	0.198952i
$382$	24.4548	−	16.8799i	1.25122	−	0.863651i
$383$	6.97055	−	28.2806i	0.356179	−	1.44507i	−0.470501	−	0.882400i	$-0.655927\pi$
$383$	6.97055	−	28.2806i	0.356179	−	1.44507i	0.826679	−	0.562674i	$-0.190227\pi$
$384$	−23.6315	+	16.3116i	−1.20594	+	0.832399i
$385$	−0.0578214	+	0.0219288i	−0.00294685	+	0.00111759i
$386$	21.9746	+	57.9423i	1.11848	+	2.94919i
$387$	−1.94029	+	1.01835i	−0.0986307	+	0.0517654i
$388$	7.53164	+	14.3503i	0.382361	+	0.728528i
$389$	22.1810	+	5.46713i	1.12462	+	0.277194i	0.757408	−	0.652942i	$-0.226466\pi$
$389$	22.1810	+	5.46713i	1.12462	+	0.277194i	0.367214	+	0.930137i	$0.380312\pi$
$390$	3.12578	+	1.96500i	0.158280	+	0.0995015i
$391$	−1.77115	+	0.436549i	−0.0895708	+	0.0220772i
$392$	−8.69557	−	9.81527i	−0.439193	−	0.495746i
$393$	1.24914	+	10.2876i	0.0630110	+	0.518942i
$394$	0.336907	−	0.176823i	0.0169731	−	0.00890819i
$395$	0.208851	−	0.397932i	0.0105084	−	0.0200222i
$396$	−0.560510	−	0.212574i	−0.0281667	−	0.0106822i
$397$	−0.875306	−	0.988016i	−0.0439303	−	0.0495871i	0.726135	−	0.687552i	$-0.241315\pi$
$397$	−0.875306	−	0.988016i	−0.0439303	−	0.0495871i	−0.770065	+	0.637965i	$0.779776\pi$
$398$	−8.65595	−	1.05102i	−0.433883	−	0.0526830i
$399$	29.8175	+	7.34934i	1.49274	+	0.367927i
$400$	−23.4501	+	20.7750i	−1.17251	+	1.03875i
$401$	−16.6143	+	18.7536i	−0.829677	+	0.936512i	−0.998795	−	0.0490843i	$-0.984370\pi$
$401$	−16.6143	+	18.7536i	−0.829677	+	0.936512i	0.169118	+	0.985596i	$0.445908\pi$
$402$	19.3562	−	10.1589i	0.965399	−	0.506681i
$403$	18.5912	−	5.43869i	0.926095	−	0.270920i
$404$	0.975038	+	0.511740i	0.0485100	+	0.0254600i
$405$	−2.08819	+	0.791945i	−0.103763	+	0.0393520i
$406$	2.88087	−	23.7261i	0.142975	−	1.17751i
$407$	1.35763	+	0.712538i	0.0672951	+	0.0353192i
$408$		−	10.2459i		−	0.507247i
$409$	10.4795	−	19.9670i	0.518177	−	0.987304i	−0.475990	−	0.879451i	$-0.657910\pi$
$409$	10.4795	−	19.9670i	0.518177	−	0.987304i	0.994167	−	0.107853i	$-0.0343976\pi$
$410$	3.08747	−	3.48504i	0.152479	−	0.172114i
$411$	−32.4876	−	22.4246i	−1.60249	−	1.10612i
$412$	34.0301	−	30.1481i	1.67654	−	1.48529i
$413$	10.4985	−	15.2097i	0.516597	−	0.748419i
$414$	4.94844	+	1.87670i	0.243203	+	0.0922345i
$415$	−0.617445	+	1.62807i	−0.0303092	+	0.0799188i
$416$	−14.4450	+	0.620625i	−0.708226	+	0.0304286i
$417$	−2.98635	−	7.87436i	−0.146242	−	0.385609i
$418$		−	2.45821i		−	0.120235i
$419$	−8.93275	+	23.5537i	−0.436393	+	1.15067i	0.518853	+	0.854863i	$0.326359\pi$
$419$	−8.93275	+	23.5537i	−0.436393	+	1.15067i	−0.955246	+	0.295811i	$0.904410\pi$
$420$	0.467888	+	3.85340i	0.0228306	+	0.188027i
$421$	−0.281705	−	0.536744i	−0.0137295	−	0.0261593i	0.878495	−	0.477752i	$-0.158548\pi$
$421$	−0.281705	−	0.536744i	−0.0137295	−	0.0261593i	−0.892224	+	0.451593i	$0.850856\pi$
$422$	−29.8314	−	20.5911i	−1.45217	−	1.00236i
$423$	−9.19855	−	6.34930i	−0.447249	−	0.308713i
$424$	−9.92709	−	18.9145i	−0.482102	−	0.918568i
$425$	0.514085	+	4.23387i	0.0249368	+	0.205373i
$426$	2.13818	−	5.63792i	0.103595	−	0.273158i
$427$		−	24.8505i		−	1.20260i
$428$	−1.15346	−	3.04142i	−0.0557546	−	0.147013i
$429$	0.602877	+	0.797853i	0.0291072	+	0.0385207i
$430$	0.402759	−	1.06199i	0.0194228	−	0.0512137i
$431$	22.1442	+	8.39820i	1.06665	+	0.404527i	0.824588	−	0.565734i	$-0.191407\pi$
$431$	22.1442	+	8.39820i	1.06665	+	0.404527i	0.242062	+	0.970261i	$0.422176\pi$
$432$	14.4144	−	20.8829i	0.693514	−	1.00473i
$433$	13.2021	−	11.6960i	0.634450	−	0.562074i	−0.283399	−	0.959002i	$-0.591462\pi$
$433$	13.2021	−	11.6960i	0.634450	−	0.562074i	0.917850	+	0.396928i	$0.129924\pi$
$434$	24.4408	+	16.8703i	1.17320	+	0.809800i
$435$	1.16378	−	1.31364i	0.0557991	−	0.0629841i
$436$	21.5040	−	40.9725i	1.02986	−	1.96223i
$437$			14.8822i			0.711910i
$438$	−62.7480	−	32.9327i	−2.99822	−	1.57359i
$439$	−2.42917	+	20.0060i	−0.115938	+	0.954835i	0.812401	+	0.583099i	$0.198160\pi$
$439$	−2.42917	+	20.0060i	−0.115938	+	0.954835i	−0.928339	+	0.371735i	$0.878763\pi$
$440$	0.157386	−	0.0596885i	0.00750307	−	0.00284554i
$441$	1.92563	+	1.01065i	0.0916967	+	0.0481261i
$442$	−4.16370	+	6.62332i	−0.198047	+	0.315039i
$443$	−8.16562	+	4.28565i	−0.387960	+	0.203617i	−0.647414	−	0.762138i	$-0.724150\pi$
$443$	−8.16562	+	4.28565i	−0.387960	+	0.203617i	0.259454	+	0.965755i	$0.416457\pi$
$444$	63.8205	−	72.0385i	3.02879	−	3.41879i
$445$	−2.47582	+	2.19338i	−0.117365	+	0.103976i
$446$	−3.99349	−	0.984308i	−0.189097	−	0.0466083i
$447$	−3.96555	−	0.481505i	−0.187564	−	0.0227744i
$448$	3.66129	+	4.13274i	0.172980	+	0.195254i
$449$	25.8952	+	9.82076i	1.22207	+	0.463470i	0.879444	−	0.476002i	$-0.157914\pi$
$449$	25.8952	+	9.82076i	1.22207	+	0.463470i	0.342626	+	0.939472i	$0.388684\pi$
$450$	5.75039	−	10.9565i	0.271076	−	0.516492i
$451$	1.11663	−	0.586050i	0.0525798	−	0.0275960i
$452$	−3.59746	−	29.6277i	−0.169210	−	1.39357i
$453$	−0.825625	−	0.931938i	−0.0387913	−	0.0437863i
$454$	38.5966	−	9.51320i	1.81143	−	0.446477i
$455$	0.684461	−	1.45244i	0.0320880	−	0.0680914i
$456$	−81.1609	−	20.0044i	−3.80071	−	0.936791i
$457$	8.80406	+	16.7747i	0.411837	+	0.784689i	0.999706	−	0.0242672i	$-0.00772524\pi$
$457$	8.80406	+	16.7747i	0.411837	+	0.784689i	−0.587869	+	0.808956i	$0.700033\pi$
$458$	13.4524	−	7.06038i	0.628591	−	0.329910i
$459$	−1.22493	−	3.22988i	−0.0571750	−	0.150758i
$460$	−1.75886	+	0.667046i	−0.0820070	+	0.0311012i
$461$	−24.2297	+	16.7245i	−1.12849	+	0.778939i	−0.977779	−	0.209639i	$-0.932771\pi$
$461$	−24.2297	+	16.7245i	−1.12849	+	0.778939i	−0.150709	+	0.988578i	$0.548156\pi$
$462$	−0.366913	+	1.48863i	−0.0170703	+	0.0692571i
$463$	16.9569	−	11.7045i	0.788053	−	0.543954i	−0.104698	−	0.994504i	$-0.533388\pi$
$463$	16.9569	−	11.7045i	0.788053	−	0.543954i	0.892751	+	0.450550i	$0.148772\pi$
$464$	−3.29265	+	27.1174i	−0.152857	+	1.25889i
$465$	0.773291	+	2.03900i	0.0358605	+	0.0945564i
$466$	−20.4656	+	38.9939i	−0.948048	+	1.80636i
$467$	−20.7574	+	30.0723i	−0.960538	+	1.39158i	−0.0407481	+	0.999169i	$0.512974\pi$
$467$	−20.7574	+	30.0723i	−0.960538	+	1.39158i	−0.919790	+	0.392410i	$0.871641\pi$
$468$	14.3029	−	6.13894i	0.661154	−	0.283773i
$469$	−5.40036	−	7.82377i	−0.249365	−	0.361268i
$470$	5.75109	−	0.698309i	0.265278	−	0.0322106i
$471$	34.0320	−	8.38813i	1.56811	−	0.386504i
$472$	−28.5761	+	41.3996i	−1.31532	+	1.90557i
$473$	0.203998	−	0.230266i	0.00937984	−	0.0105877i
$474$	−5.17797	−	9.86579i	−0.237832	−	0.453151i
$475$	34.5416	+	4.19410i	1.58488	+	0.192439i
$476$	−8.16510	+	0.991423i	−0.374247	+	0.0454418i
$477$	2.65172	+	2.34922i	0.121414	+	0.107563i
$478$	−26.0206	−	37.6973i	−1.19015	−	1.72424i
$479$	15.5463	+	1.88766i	0.710328	+	0.0862494i	0.467722	−	0.883876i	$-0.345075\pi$
$479$	15.5463	+	1.88766i	0.710328	+	0.0862494i	0.242606	+	0.970125i	$0.421998\pi$
$480$	−0.196199	−	1.61585i	−0.00895523	−	0.0737529i
$481$	−38.2085	+	11.1775i	−1.74216	+	0.509651i
$482$	5.47903	−	45.1239i	0.249563	−	2.05534i
$483$	2.22131	−	9.01222i	0.101073	−	0.410070i
$484$	−47.9223			−2.17829
$485$	0.754708			0.0342695
$486$	−5.97666	+	24.2482i	−0.271107	+	1.09992i
$487$	24.3392	−	9.23065i	1.10292	−	0.418281i	0.265093	−	0.964223i	$-0.414597\pi$
$487$	24.3392	−	9.23065i	1.10292	−	0.418281i	0.837823	+	0.545942i	$0.183828\pi$
$488$			67.6411i			3.06197i
$489$	35.3466	+	13.4052i	1.59843	+	0.606204i
$490$	−1.09446	+	0.269760i	−0.0494426	+	0.0121865i
$491$	7.36326	+	6.52328i	0.332299	+	0.294392i	0.812729	−	0.582642i	$-0.197981\pi$
$491$	7.36326	+	6.52328i	0.332299	+	0.294392i	−0.480430	+	0.877033i	$0.659519\pi$
$492$	−18.9437	−	76.8575i	−0.854047	−	3.46501i
$493$	2.78351	+	2.46598i	0.125363	+	0.111062i
$494$	44.3361	+	45.9135i	1.99477	+	2.06575i
$495$	−0.0208952	+	0.0185115i	−0.000939168	+	0.000832031i
$496$	−27.9343	−	19.2817i	−1.25429	−	0.865773i
$497$	−2.54604	−	0.627541i	−0.114205	−	0.0281491i
$498$	24.5230	+	35.5277i	1.09890	+	1.59204i
$499$	−3.03604	−	12.3177i	−0.135912	−	0.551417i	−0.998930	−	0.0462438i	$-0.985275\pi$
$499$	−3.03604	−	12.3177i	−0.135912	−	0.551417i	0.863018	−	0.505173i	$-0.168571\pi$
$500$	2.11384	+	8.57617i	0.0945336	+	0.383538i
$501$	29.8069	−	3.61921i	1.33167	−	0.161694i
$502$	−36.5093	−	41.2105i	−1.62949	−	1.83932i
$503$	−6.59014	+	17.3768i	−0.293840	+	0.774792i	0.704068	+	0.710133i	$0.251365\pi$
$503$	−6.59014	+	17.3768i	−0.293840	+	0.774792i	−0.997907	+	0.0646587i	$0.979404\pi$
$504$	11.4466	+	6.00763i	0.509871	+	0.267601i
$505$	0.0422017	−	0.0291297i	0.00187795	−	0.00129625i
$506$	−0.742986			−0.0330298
$507$	−25.6503	−	4.02856i	−1.13917	−	0.178915i
$508$	8.54781			0.379248
$509$	−10.9580	+	7.56375i	−0.485704	+	0.335257i	−0.785621	−	0.618708i	$-0.787656\pi$
$509$	−10.9580	+	7.56375i	−0.485704	+	0.335257i	0.299917	+	0.953965i	$0.403041\pi$
$510$	−0.779863	−	0.409304i	−0.0345329	−	0.0181243i
$511$	−10.9282	+	28.8154i	−0.483436	+	1.27472i
$512$	−33.1759	−	37.4479i	−1.46618	−	1.65498i
$513$	−27.9765	+	3.39697i	−1.23519	+	0.149980i
$514$	4.01325	+	16.2824i	0.177017	+	0.718186i
$515$	−0.506664	−	2.05562i	−0.0223263	−	0.0905813i
$516$	−10.9694	−	15.8919i	−0.482901	−	0.699603i
$517$	1.52354	+	0.375518i	0.0670050	+	0.0165153i
$518$	−50.2305	−	34.6716i	−2.20700	−	1.52338i
$519$	−35.2854	+	31.2602i	−1.54886	+	1.37217i
$520$	−1.86305	+	3.95343i	−0.0817003	+	0.173369i
$521$	9.91920	+	8.78765i	0.434568	+	0.384994i	0.851852	−	0.523782i	$-0.175479\pi$
$521$	9.91920	+	8.78765i	0.434568	+	0.384994i	−0.417284	+	0.908776i	$0.637018\pi$
$522$	−2.58198	−	10.4755i	−0.113010	−	0.458501i
$523$	1.70795	+	1.51311i	0.0746833	+	0.0661637i	0.699639	−	0.714497i	$-0.253344\pi$
$523$	1.70795	+	1.51311i	0.0746833	+	0.0661637i	−0.624955	+	0.780661i	$0.714883\pi$
$524$	−21.9864	+	5.41915i	−0.960478	+	0.236737i
$525$	−20.2914	−	7.69551i	−0.885589	−	0.335859i
$526$			26.2195i			1.14322i
$527$	−4.32051	+	1.63855i	−0.188204	+	0.0713764i
$528$	0.419358	−	1.70140i	0.0182502	−	0.0740441i
$529$	−18.5019			−0.804431
$530$	−1.83624			−0.0797612
$531$	1.99654	−	8.10028i	0.0866425	−	0.351522i
$532$	−8.08841	+	66.6141i	−0.350677	+	2.88809i
$533$	−10.2859	+	31.0854i	−0.445534	+	1.34646i
$534$	9.88467	+	81.4076i	0.427752	+	3.52285i
$535$	−0.150371	−	0.0182583i	−0.00650109	−	0.000789376i
$536$	14.6994	+	21.2957i	0.634916	+	0.919835i
$537$	12.2137	+	10.8204i	0.527061	+	0.466935i
$538$	−64.4432	+	7.82483i	−2.77835	+	0.337352i
$539$	−0.303082	−	0.0368008i	−0.0130546	−	0.00158512i
$540$	−1.65543	−	3.15416i	−0.0712385	−	0.135734i
$541$	4.12854	−	4.66016i	0.177500	−	0.200356i	−0.653027	−	0.757335i	$-0.726501\pi$
$541$	4.12854	−	4.66016i	0.177500	−	0.200356i	0.830527	+	0.556979i	$0.188040\pi$
$542$	8.39175	−	12.1575i	0.360456	−	0.522211i
$543$	−0.446884	+	0.110147i	−0.0191776	+	0.00472686i
$544$	3.42387	−	0.415733i	0.146797	−	0.0178244i
$545$	−1.22407	−	1.77338i	−0.0524335	−	0.0759630i
$546$	−19.9956	−	34.4216i	−0.855734	−	1.47311i
$547$	2.76298	−	4.00287i	0.118137	−	0.171150i	−0.759454	−	0.650561i	$-0.774534\pi$
$547$	2.76298	−	4.00287i	0.118137	−	0.171150i	0.877591	+	0.479410i	$0.159149\pi$
$548$	40.0855	−	76.3765i	1.71237	−	3.26264i
$549$	−3.97793	−	10.4889i	−0.169774	−	0.447657i
$550$	−0.209389	+	1.72447i	−0.00892838	+	0.0735318i
$551$	24.9684	−	17.2344i	1.06369	−	0.734212i
$552$	−6.04625	+	24.5306i	−0.257345	+	1.04409i
$553$	−3.98775	+	2.75254i	−0.169576	+	0.117050i
$554$	40.9195	−	15.5187i	1.73850	−	0.659327i
$555$	−1.58926	−	4.19053i	−0.0674603	−	0.177878i
$556$	16.2941	−	8.55179i	0.691023	−	0.362677i
$557$	6.81654	+	12.9878i	0.288826	+	0.550312i	0.986031	−	0.166559i	$-0.0532657\pi$
$557$	6.81654	+	12.9878i	0.288826	+	0.550312i	−0.697205	+	0.716872i	$0.745573\pi$
$558$	13.0166	+	3.20829i	0.551035	+	0.135818i
$559$	0.342862	+	7.98011i	0.0145015	+	0.337523i
$560$	−2.73179	+	0.673327i	−0.115439	+	0.0284532i
$561$	−0.158189	−	0.178559i	−0.00667875	−	0.00753875i
$562$	−0.302878	−	2.49442i	−0.0127761	−	0.105221i
$563$	−31.6498	+	16.6111i	−1.33388	+	0.700075i	−0.972623	−	0.232390i	$-0.925345\pi$
$563$	−31.6498	+	16.6111i	−1.33388	+	0.700075i	−0.361259	+	0.932465i	$0.617653\pi$
$564$	45.7727	−	87.2126i	1.92738	−	3.67231i
$565$	−1.29951	−	0.492839i	−0.0546708	−	0.0207339i
$566$	24.3917	+	27.5325i	1.02526	+	1.15728i
$567$	23.9038	+	2.90244i	1.00386	+	0.121891i
$568$	6.93012	+	1.70812i	0.290781	+	0.0716712i
$569$	33.6582	−	29.8186i	1.41102	−	1.25006i	0.483995	−	0.875071i	$-0.339185\pi$
$569$	33.6582	−	29.8186i	1.41102	−	1.25006i	0.927030	−	0.374988i	$-0.122353\pi$
$570$	−4.76486	+	5.37841i	−0.199578	+	0.225277i
$571$	34.3662	−	18.0368i	1.43818	−	0.754815i	0.447923	−	0.894072i	$-0.352164\pi$
$571$	34.3662	−	18.0368i	1.43818	−	0.754815i	0.990256	+	0.139257i	$0.0444715\pi$
$572$	−1.57187	+	1.51787i	−0.0657233	+	0.0634652i
$573$	−20.8308	−	10.9329i	−0.870221	−	0.456727i
$574$	−46.9378	+	17.8012i	−1.95915	+	0.743006i
$575$	1.26765	−	10.4401i	0.0528648	−	0.435381i
$576$	2.20691	+	1.15828i	0.0919547	+	0.0482615i
$577$		−	6.71871i		−	0.279704i	−0.990172	−	0.139852i	$-0.955337\pi$
$577$		−	6.71871i		−	0.279704i	0.990172	−	0.139852i	$-0.0446626\pi$
$578$	−19.0631	+	36.3217i	−0.792921	+	1.51078i
$579$	32.5341	−	36.7234i	1.35207	−	1.52617i
$580$	3.15599	+	2.17842i	0.131045	+	0.0904541i
$581$	14.0523	−	12.4492i	0.582986	−	0.516480i
$582$	10.6292	−	15.3990i	0.440593	−	0.638309i
$583$	−0.465029	−	0.176362i	−0.0192595	−	0.00730418i
$584$	29.7458	−	78.4333i	1.23089	−	3.24559i
$585$	0.0564002	−	0.722614i	0.00233186	−	0.0298764i
$586$	1.91907	+	5.06016i	0.0792759	+	0.209033i
$587$		−	44.0921i		−	1.81987i	−0.414745	−	0.909937i	$-0.636129\pi$
$587$		−	44.0921i		−	1.81987i	0.414745	−	0.909937i	$-0.363871\pi$
$588$	−6.79571	+	17.9188i	−0.280250	+	0.738960i
$589$	4.54401	+	37.4233i	0.187233	+	1.54200i
$590$	2.00956	+	3.82890i	0.0827324	+	0.157633i
$591$	−0.247915	−	0.171123i	−0.0101979	−	0.00703907i
$592$	57.4103	+	39.6275i	2.35955	+	1.62868i
$593$	10.0084	+	19.0694i	0.410995	+	0.783086i	0.999681	−	0.0252764i	$-0.00804657\pi$
$593$	10.0084	+	19.0694i	0.410995	+	0.783086i	−0.588685	+	0.808362i	$0.700354\pi$
$594$	−0.169592	−	1.39672i	−0.00695846	−	0.0573080i
$595$	−0.135821	+	0.358131i	−0.00556813	+	0.0146820i
$596$		−	8.72868i		−	0.357541i
$597$	2.44796	+	6.45475i	0.100188	+	0.264175i
$598$	13.8772	−	13.4004i	0.567481	−	0.547984i
$599$	−6.30549	+	16.6262i	−0.257635	+	0.679329i	0.742322	+	0.670044i	$0.233725\pi$
$599$	−6.30549	+	16.6262i	−0.257635	+	0.679329i	−0.999957	+	0.00928474i	$0.997045\pi$
$600$	55.2317	+	20.9466i	2.25482	+	0.855142i
$601$	23.0087	−	33.3339i	0.938544	−	1.35972i	0.00548829	−	0.999985i	$-0.498253\pi$
$601$	23.0087	−	33.3339i	0.938544	−	1.35972i	0.933056	−	0.359731i	$-0.117132\pi$
$602$	−9.16628	+	8.12062i	−0.373590	+	0.330972i
$603$	−3.53178	−	2.43782i	−0.143825	−	0.0992755i
$604$	1.80405	−	2.03636i	0.0734059	−	0.0828582i
$605$	−1.03709	+	1.97601i	−0.0421636	+	0.0803361i
$606$		−	1.27134i		−	0.0516445i
$607$	−14.8031	−	7.76928i	−0.600840	−	0.315345i	0.136738	−	0.990607i	$-0.456338\pi$
$607$	−14.8031	−	7.76928i	−0.600840	−	0.315345i	−0.737578	+	0.675262i	$0.764031\pi$
$608$	3.39171	−	27.9333i	0.137552	−	1.13284i
$609$	−17.6926	+	6.70991i	−0.716939	+	0.271899i
$610$	5.14849	+	2.70214i	0.208456	+	0.109406i
$611$	−35.2288	+	20.4646i	−1.42520	+	0.827907i
$612$	−3.28764	+	1.72549i	−0.132895	+	0.0697488i
$613$	16.5128	−	18.6390i	0.666944	−	0.752824i	−0.313507	−	0.949586i	$-0.601504\pi$
$613$	16.5128	−	18.6390i	0.666944	−	0.752824i	0.980451	+	0.196762i	$0.0630425\pi$
$614$	0.735331	−	0.651447i	0.0296756	−	0.0262903i
$615$	−3.57907	−	0.882161i	−0.144322	−	0.0355722i
$616$	−1.80162	−	0.218756i	−0.0725892	−	0.00881392i
$617$	−8.16703	−	9.21867i	−0.328792	−	0.371130i	0.560748	−	0.827986i	$-0.310514\pi$
$617$	−8.16703	−	9.21867i	−0.328792	−	0.371130i	−0.889540	+	0.456857i	$0.848975\pi$
$618$	−49.0784	−	18.6130i	−1.97422	−	0.748724i
$619$	−0.448273	+	0.854112i	−0.0180176	+	0.0343297i	−0.894298	−	0.447471i	$-0.852325\pi$
$619$	−0.448273	+	0.854112i	−0.0180176	+	0.0343297i	0.876281	+	0.481801i	$0.160017\pi$
$620$	−4.21922	+	2.21442i	−0.169448	+	0.0889331i
$621$	1.02672	+	8.45580i	0.0412009	+	0.339320i
$622$	−42.2297	−	47.6675i	−1.69326	−	1.91129i
$623$	34.6264	−	8.53465i	1.38728	−	0.341934i
$624$	22.8537	+	39.3417i	0.914882	+	1.57493i
$625$	−23.6737	−	5.83503i	−0.946946	−	0.233401i
$626$	12.6825	+	24.1645i	0.506895	+	0.965808i
$627$	−1.72327	+	0.904444i	−0.0688209	+	0.0361200i
$628$	27.1585	+	71.6110i	1.08374	+	2.85759i
$629$	8.87945	−	3.36753i	0.354047	−	0.134272i
$630$	0.914539	−	0.631261i	0.0364361	−	0.0251500i
$631$	−2.65784	+	10.7833i	−0.105807	+	0.429275i	−0.999824	−	0.0187574i	$-0.994029\pi$
$631$	−2.65784	+	10.7833i	−0.105807	+	0.429275i	0.894017	+	0.448033i	$0.147875\pi$
$632$	10.8544	−	7.49223i	0.431763	−	0.298025i
$633$	−3.45915	+	28.4887i	−0.137489	+	1.13232i
$634$	10.9283	+	28.8157i	0.434020	+	1.14442i
$635$	0.184983	−	0.352456i	0.00734084	−	0.0139868i
$636$	−17.7342	+	25.6924i	−0.703206	+	1.01877i
$637$	6.32457	−	4.77900i	0.250589	−	0.189351i
$638$	0.860423	+	1.24654i	0.0340645	+	0.0493509i
$639$	−1.17509	+	0.142682i	−0.0464859	+	0.00564441i
$640$	−2.83689	+	0.699231i	−0.112138	+	0.0276395i
$641$	13.5292	−	19.6004i	0.534370	−	0.774168i	−0.459085	−	0.888392i	$-0.651823\pi$
$641$	13.5292	−	19.6004i	0.534370	−	0.774168i	0.993455	+	0.114224i	$0.0364382\pi$
$642$	−2.49034	+	2.81101i	−0.0982857	+	0.110942i
$643$	6.02448	+	11.4787i	0.237582	+	0.452675i	0.974831	−	0.222947i	$-0.0715676\pi$
$643$	6.02448	+	11.4787i	0.237582	+	0.452675i	−0.737248	+	0.675622i	$0.763875\pi$
$644$	20.1339	+	2.44469i	0.793385	+	0.0963344i
$645$	−0.892669	+	0.108390i	−0.0351488	+	0.00426784i
$646$	−11.3965	−	10.0964i	−0.448389	−	0.397238i
$647$	0.796259	+	1.15358i	0.0313042	+	0.0453519i	0.838323	−	0.545173i	$-0.183536\pi$
$647$	0.796259	+	1.15358i	0.0313042	+	0.0453519i	−0.807019	+	0.590525i	$0.798921\pi$
$648$	−65.0643	−	7.90023i	−2.55597	−	0.310350i
$649$	0.141175	+	1.16268i	0.00554160	+	0.0456392i
$650$	−27.1916	−	35.9856i	−1.06654	−	1.41147i
$651$	2.83408	−	23.3407i	0.111076	−	0.914795i
$652$	−19.7682	+	80.2025i	−0.774181	+	3.14097i
$653$	29.7550			1.16440			0.582201	−	0.813045i	$-0.302192\pi$
$653$	29.7550			1.16440			0.582201	+	0.813045i	$0.302192\pi$
$654$	−53.4234			−2.08902
$655$	−0.252357	+	1.02385i	−0.00986039	+	0.0400052i
$656$	53.6469	−	20.3456i	2.09456	−	0.794362i
$657$			13.9118i			0.542751i
$658$	−58.4038	−	22.1497i	−2.27682	−	0.863484i
$659$	9.25036	−	2.28001i	0.360343	−	0.0888166i	−0.0549878	−	0.998487i	$-0.517512\pi$
$659$	9.25036	−	2.28001i	0.360343	−	0.0888166i	0.415331	+	0.909670i	$0.363666\pi$
$660$	−0.184132	−	0.163127i	−0.00716735	−	0.00634971i
$661$	6.68995	+	27.1422i	0.260209	+	1.05571i	0.945026	+	0.326995i	$0.106036\pi$
$661$	6.68995	+	27.1422i	0.260209	+	1.05571i	−0.684817	+	0.728715i	$0.740118\pi$
$662$	−22.4515	−	19.8903i	−0.872603	−	0.773059i
$663$	6.17506	+	0.481965i	0.239819	+	0.0187180i
$664$	−38.2492	+	33.8858i	−1.48436	+	1.31503i
$665$	2.57169	+	1.77511i	0.0997259	+	0.0688358i
$666$	−26.7515	−	6.59365i	−1.03660	−	0.255499i
$667$	−5.20905	−	7.54661i	−0.201695	−	0.292206i
$668$	15.7012	+	63.7022i	0.607497	+	2.46471i
$669$	0.779289	+	3.16170i	0.0301290	+	0.122238i
$670$	2.20813	−	0.268116i	0.0853076	−	0.0103582i
$671$	1.04433	+	1.17881i	0.0403159	+	0.0455073i
$672$	−6.22324	+	16.4093i	−0.240067	+	0.633004i
$673$	5.57326	+	2.92507i	0.214834	+	0.112753i	0.568708	−	0.822540i	$-0.307444\pi$
$673$	5.57326	+	2.92507i	0.214834	+	0.112753i	−0.353874	+	0.935293i	$0.615136\pi$
$674$	−18.0007	+	12.4250i	−0.693361	+	0.478592i
$675$	19.9153			0.766541
$676$	1.98271	−	56.7002i	0.0762582	−	2.18078i
$677$	39.6810			1.52506			0.762532	−	0.646950i	$-0.223956\pi$
$677$	39.6810			1.52506			0.762532	+	0.646950i	$0.223956\pi$
$678$	−28.3579	+	19.5740i	−1.08908	+	0.751737i
$679$	−7.20510	−	3.78153i	−0.276506	−	0.145122i
$680$	0.369696	−	0.974807i	0.0141772	−	0.0373822i
$681$	−20.8697	−	23.5571i	−0.799730	−	0.902709i
$682$	−1.86834	+	0.226858i	−0.0715426	+	0.00868684i
$683$	−12.4248	−	50.4095i	−0.475423	−	1.92887i	−0.349950	−	0.936769i	$-0.613801\pi$
$683$	−12.4248	−	50.4095i	−0.475423	−	1.92887i	−0.125473	−	0.992097i	$-0.540045\pi$
$684$	7.24926	+	29.4114i	0.277182	+	1.12457i
$685$	−2.28178	−	3.30573i	−0.0871824	−	0.126306i
$686$	49.3710	+	12.1688i	1.88499	+	0.464609i
$687$	−9.89904	−	6.83281i	−0.377672	−	0.260688i
$688$	10.4765	−	9.28135i	0.399412	−	0.353848i
$689$	11.8665	−	5.09319i	0.452077	−	0.194035i
$690$	1.62560	+	1.44016i	0.0618857	+	0.0548260i
$691$	−0.761891	−	3.09111i	−0.0289837	−	0.117591i	0.954668	−	0.297672i	$-0.0962102\pi$
$691$	−0.761891	−	3.09111i	−0.0289837	−	0.117591i	−0.983652	+	0.180081i	$0.942364\pi$
$692$	−77.1014	−	68.3059i	−2.93095	−	2.59660i
$693$	0.292237	−	0.0720300i	0.0111012	−	0.00273619i
$694$	8.50591	+	3.22587i	0.322880	+	0.122452i
$695$		−	0.856932i		−	0.0325053i
$696$	48.1579	−	18.2639i	1.82542	−	0.692291i
$697$	1.86924	−	7.58381i	0.0708025	−	0.287257i
$698$	69.2965			2.62291
$699$	34.8656			1.31874
$700$	11.3483	−	46.0418i	0.428925	−	1.74022i
$701$	−2.67469	+	22.0281i	−0.101022	+	0.831989i	0.850832	+	0.525438i	$0.176098\pi$
$701$	−2.67469	+	22.0281i	−0.101022	+	0.831989i	−0.951854	+	0.306552i	$0.900825\pi$
$702$	28.3586	+	23.0286i	1.07033	+	0.869158i
$703$	−9.33879	−	76.9119i	−0.352219	−	2.90079i
$704$	−0.347353	−	0.0421763i	−0.0130914	−	0.00158958i
$705$	−2.60551	−	3.77474i	−0.0981294	−	0.142165i
$706$	−43.2693	−	38.3333i	−1.62846	−	1.44269i
$707$	−0.548851	+	0.0666425i	−0.0206417	+	0.00250635i
$708$	72.9816	+	8.86157i	2.74282	+	0.333038i
$709$	−2.94598	−	5.61309i	−0.110638	−	0.210804i	0.823841	−	0.566821i	$-0.191827\pi$
$709$	−2.94598	−	5.61309i	−0.110638	−	0.210804i	−0.934479	+	0.356017i	$0.884135\pi$
$710$	0.406859	−	0.459249i	0.0152691	−	0.0172353i
$711$	−1.24255	+	1.80014i	−0.0465991	+	0.0675105i
$712$	−94.2507	+	23.2307i	−3.53219	+	0.870607i
$713$	11.3110	−	1.37341i	0.423602	−	0.0514346i
$714$	5.39440	+	7.81514i	0.201881	+	0.292474i
$715$	0.0285701	+	0.0976621i	0.00106846	+	0.00365235i
$716$	−20.2542	+	29.3432i	−0.756933	+	1.09661i
$717$	−16.8532	+	32.1110i	−0.629392	+	1.19921i
$718$	29.0017	+	76.4712i	1.08233	+	2.85388i
$719$	−5.12729	+	42.2271i	−0.191216	+	1.57480i	0.508933	+	0.860806i	$0.330040\pi$
$719$	−5.12729	+	42.2271i	−0.191216	+	1.57480i	−0.700149	+	0.713997i	$0.746883\pi$
$720$	−1.04526	+	0.721491i	−0.0389545	+	0.0268884i
$721$	−5.46279	+	22.1634i	−0.203445	+	0.825408i
$722$	−62.7804	+	43.3342i	−2.33644	+	1.61273i
$723$	−33.6489	+	12.7614i	−1.25142	+	0.474600i
$724$	−0.356626	−	0.940346i	−0.0132539	−	0.0349477i
$725$	−18.9837	+	9.96343i	−0.705038	+	0.370032i
$726$	25.7121	+	48.9904i	0.954266	+	1.81820i
$727$	25.4873	+	6.28206i	0.945273	+	0.232989i	0.681684	−	0.731646i	$-0.261248\pi$
$727$	25.4873	+	6.28206i	0.945273	+	0.232989i	0.263588	+	0.964635i	$0.415094\pi$
$728$	37.5953	−	28.4079i	1.39338	−	1.05287i
$729$	−12.8115	+	3.15775i	−0.474500	+	0.116954i
$730$	−4.78164	−	5.39736i	−0.176977	−	0.199765i
$731$	−0.229670	−	1.89151i	−0.00849467	−	0.0699599i
$732$	87.5314	−	45.9400i	3.23525	−	1.69799i
$733$	−1.85983	+	3.54361i	−0.0686944	+	0.130886i	−0.917382	−	0.398009i	$-0.869701\pi$
$733$	−1.85983	+	3.54361i	−0.0686944	+	0.130886i	0.848687	+	0.528895i	$0.177394\pi$
$734$	−63.5999	−	24.1203i	−2.34752	−	0.890295i
$735$	0.591790	+	0.667993i	0.0218285	+	0.0246393i
$736$	−8.44272	−	1.02513i	−0.311203	−	0.0377869i
$737$	0.584962	+	0.144180i	0.0215474	+	0.00531095i
$738$	−16.9621	+	15.0271i	−0.624384	+	0.553156i
$739$	−30.6085	+	34.5499i	−1.12595	+	1.27094i	−0.167441	+	0.985882i	$0.553550\pi$
$739$	−30.6085	+	34.5499i	−1.12595	+	1.27094i	−0.958511	+	0.285055i	$0.907988\pi$
$740$	8.67129	−	4.55104i	0.318763	−	0.167300i
$741$	15.8742	−	47.9736i	0.583152	−	1.76236i
$742$	17.5304	+	9.20064i	0.643559	+	0.337766i
$743$	23.0228	−	8.73141i	0.844626	−	0.320324i	0.105938	−	0.994373i	$-0.466215\pi$
$743$	23.0228	−	8.73141i	0.844626	−	0.320324i	0.738687	+	0.674048i	$0.235446\pi$
$744$	−7.71415	+	63.5318i	−0.282815	+	2.32919i
$745$	−0.359914	−	0.188898i	−0.0131862	−	0.00692067i
$746$			32.9554i			1.20658i
$747$	3.93841	−	7.50401i	0.144099	−	0.274557i
$748$	0.345655	−	0.390164i	0.0126384	−	0.0142658i
$749$	1.34409	+	0.927755i	0.0491118	+	0.0338994i
$750$	7.63315	−	6.76238i	0.278723	−	0.246927i
$751$	21.2790	−	30.8279i	0.776481	−	1.12493i	−0.212540	−	0.977152i	$-0.568174\pi$
$751$	21.2790	−	30.8279i	0.776481	−	1.12493i	0.989021	−	0.147775i	$-0.0472110\pi$
$752$	66.7519	+	25.3157i	2.43419	+	0.923167i
$753$	−15.4569	+	40.7565i	−0.563281	+	1.48525i
$754$	−38.5531	−	7.76384i	−1.40402	−	0.282742i
$755$	−0.0449246	−	0.118456i	−0.00163497	−	0.00431107i
$756$			38.4071i			1.39685i
$757$	−0.572631	+	1.50990i	−0.0208126	+	0.0548783i	−0.945020	−	0.327013i	$-0.893958\pi$
$757$	−0.572631	+	1.50990i	−0.0208126	+	0.0548783i	0.924207	+	0.381891i	$0.124727\pi$
$758$	−5.15729	−	42.4741i	−0.187321	−	1.54273i
$759$	0.273365	+	0.520853i	0.00992251	+	0.0189058i
$760$	−6.99996	−	4.83172i	−0.253915	−	0.175265i
$761$	−9.65171	−	6.66209i	−0.349874	−	0.241501i	0.380146	−	0.924927i	$-0.375874\pi$
$761$	−9.65171	−	6.66209i	−0.349874	−	0.241501i	−0.730020	+	0.683426i	$0.760489\pi$
$762$	−4.58622	−	8.73832i	−0.166141	−	0.316556i
$763$	2.80042	+	23.0635i	0.101382	+	0.834955i
$764$	18.2285	−	48.0646i	0.659485	−	1.73892i
$765$			0.172903i			0.00625131i
$766$	−26.0563	−	68.7049i	−0.941454	−	2.48241i
$767$	−23.6068	−

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.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07618 - 1.43308i) q^{2} +(-1.76851 - 0.928185i) q^{3} +(1.54757 - 4.08062i) q^{4} +(-0.134767 - 0.152121i) q^{5} +(-5.00190 + 0.607340i) q^{6} +(0.524392 + 2.12754i) q^{7} +(-1.42736 - 5.79101i) q^{8} +(0.561902 + 0.814056i) q^{9} +O(q^{10})\)	\(q+(2.07618 - 1.43308i) q^{2} +(-1.76851 - 0.928185i) q^{3} +(1.54757 - 4.08062i) q^{4} +(-0.134767 - 0.152121i) q^{5} +(-5.00190 + 0.607340i) q^{6} +(0.524392 + 2.12754i) q^{7} +(-1.42736 - 5.79101i) q^{8} +(0.561902 + 0.814056i) q^{9} +(-0.497802 - 0.122697i) q^{10} +(-0.114284 - 0.0788846i) q^{11} +(-6.52447 + 5.78018i) q^{12} +(3.55731 - 0.587841i) q^{13} +(4.13767 + 3.66565i) q^{14} +(0.0971409 + 0.394116i) q^{15} +(-4.72909 - 4.18961i) q^{16} +(-0.835105 + 0.205835i) q^{17} +(2.33322 + 0.884872i) q^{18} +7.01701i q^{19} +(-0.829309 + 0.314516i) q^{20} +(1.04736 - 4.24931i) q^{21} -0.350322 q^{22} +2.12087 q^{23} +(-2.85084 + 11.5663i) q^{24} +(0.597705 - 4.92254i) q^{25} +(6.54317 - 6.31837i) q^{26} +(0.484104 + 3.98696i) q^{27} +(9.49322 + 1.15269i) q^{28} +(-2.45609 - 3.55826i) q^{29} +(0.766481 + 0.679043i) q^{30} +(5.33322 - 0.647570i) q^{31} +(-3.98079 - 0.483355i) q^{32} +(0.128893 + 0.245585i) q^{33} +(-1.43885 + 1.62412i) q^{34} +(0.252972 - 0.366494i) q^{35} +(4.19144 - 1.03310i) q^{36} +(-10.9608 + 1.33088i) q^{37} +(10.0559 + 14.5686i) q^{38} +(-6.83676 - 2.26224i) q^{39} +(-0.688572 + 0.997569i) q^{40} +(-4.22027 + 8.04105i) q^{41} +(-3.91510 - 10.3233i) q^{42} +(-0.267028 + 2.19917i) q^{43} +(-0.498761 + 0.344270i) q^{44} +(0.0481088 - 0.195185i) q^{45} +(4.40329 - 3.03937i) q^{46} +(-10.5654 + 4.00691i) q^{47} +(4.47471 + 11.7988i) q^{48} +(1.94675 - 1.02173i) q^{49} +(-5.81346 - 11.0766i) q^{50} +(1.66794 + 0.411111i) q^{51} +(3.10645 - 15.4257i) q^{52} +(3.47744 - 0.857112i) q^{53} +(6.71871 + 7.58386i) q^{54} +(0.00340177 + 0.0280161i) q^{55} +(11.5721 - 6.07352i) q^{56} +(6.51309 - 12.4097i) q^{57} +(-10.1986 - 3.86780i) q^{58} +(-5.59291 - 6.31309i) q^{59} +(1.75857 + 0.213529i) q^{60} +(-11.0114 - 2.71407i) q^{61} +(10.1447 - 8.98740i) q^{62} +(-1.43728 + 1.62235i) q^{63} +(2.23112 - 1.17098i) q^{64} +(-0.568831 - 0.461919i) q^{65} +(0.619547 + 0.325164i) q^{66} +(-4.05657 + 1.53845i) q^{67} +(-0.452454 + 3.72629i) q^{68} +(-3.75077 - 1.96856i) q^{69} -1.12343i q^{70} +(-0.556136 + 1.05963i) q^{71} +(3.91217 - 4.41593i) q^{72} +(11.5747 + 7.98947i) q^{73} +(-20.8492 + 18.4708i) q^{74} +(-5.62608 + 8.15078i) q^{75} +(28.6338 + 10.8594i) q^{76} +(0.107901 - 0.284511i) q^{77} +(-17.4363 + 5.10082i) q^{78} +(0.784145 + 2.06762i) q^{79} +1.28401i q^{80} +(3.89677 - 10.2749i) q^{81} +(2.76145 + 22.7426i) q^{82} +(-3.98160 - 7.58630i) q^{83} +(-15.7189 - 10.8500i) q^{84} +(0.143857 + 0.0992971i) q^{85} +(2.59720 + 4.94854i) q^{86} +(1.04089 + 8.57253i) q^{87} +(-0.293698 + 0.774417i) q^{88} -16.2753i q^{89} +(-0.179834 - 0.474182i) q^{90} +(3.11608 + 7.26006i) q^{91} +(3.28220 - 8.65445i) q^{92} +(-10.0329 - 3.80498i) q^{93} +(-16.1933 + 23.4601i) q^{94} +(1.06743 - 0.945664i) q^{95} +(6.59142 + 4.54973i) q^{96} +(-2.46253 + 2.77963i) q^{97} +(2.57757 - 4.91114i) q^{98} -0.137359i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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