LMFDB - Embedded newform 169.2.h.a.25.4

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			25.4
Character	$\chi$	$=$	169.25
Dual form			169.2.h.a.142.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52590 - 0.578696i) q^{2} +(-1.45490 - 2.10779i) q^{3} +(0.496446 + 0.439813i) q^{4} +(-3.46589 - 0.420835i) q^{5} +(1.00026 + 4.05821i) q^{6} +(0.131788 + 0.251102i) q^{7} +(1.01380 + 1.93163i) q^{8} +(-1.26222 + 3.32819i) q^{9} +O(q^{10})$	\(q+(-1.52590 - 0.578696i) q^{2} +(-1.45490 - 2.10779i) q^{3} +(0.496446 + 0.439813i) q^{4} +(-3.46589 - 0.420835i) q^{5} +(1.00026 + 4.05821i) q^{6} +(0.131788 + 0.251102i) q^{7} +(1.01380 + 1.93163i) q^{8} +(-1.26222 + 3.32819i) q^{9} +(5.04505 + 2.64785i) q^{10} +(3.17160 - 1.20283i) q^{11} +(0.204752 - 1.68629i) q^{12} +(1.72059 - 3.16853i) q^{13} +(-0.0557837 - 0.459420i) q^{14} +(4.15549 + 7.91763i) q^{15} +(-0.589014 - 4.85097i) q^{16} +(-5.24407 + 2.75230i) q^{17} +(3.85202 - 4.34804i) q^{18} +6.15812i q^{19} +(-1.53554 - 1.73326i) q^{20} +(0.337530 - 0.643110i) q^{21} -5.53561 q^{22} -7.85938 q^{23} +(2.59649 - 4.94720i) q^{24} +(6.98058 + 1.72056i) q^{25} +(-4.45905 + 3.83915i) q^{26} +(1.39133 - 0.342933i) q^{27} +(-0.0450120 + 0.182621i) q^{28} +(-0.328405 + 0.865932i) q^{29} +(-1.75895 - 14.4862i) q^{30} +(0.800199 + 3.24653i) q^{31} +(-0.864321 + 3.50669i) q^{32} +(-7.14968 - 4.93507i) q^{33} +(9.59464 - 1.16500i) q^{34} +(-0.351092 - 0.925752i) q^{35} +(-2.09040 + 1.09713i) q^{36} +(0.0881308 + 0.357561i) q^{37} +(3.56367 - 9.39664i) q^{38} +(-9.18187 + 0.983259i) q^{39} +(-2.70082 - 7.12147i) q^{40} +(-3.32971 + 2.29833i) q^{41} +(-0.887201 + 0.785991i) q^{42} +(-6.05675 - 1.49286i) q^{43} +(2.10355 + 0.797771i) q^{44} +(5.77533 - 11.0040i) q^{45} +(11.9926 + 4.54819i) q^{46} +(1.12029 + 1.26455i) q^{47} +(-9.36785 + 8.29919i) q^{48} +(3.93077 - 5.69470i) q^{49} +(-9.65596 - 6.66503i) q^{50} +(13.4309 + 7.04906i) q^{51} +(2.24774 - 0.816266i) q^{52} +(10.3302 - 5.42170i) q^{53} +(-2.32149 - 0.281879i) q^{54} +(-11.4986 + 2.83416i) q^{55} +(-0.351429 + 0.509133i) q^{56} +(12.9800 - 8.95945i) q^{57} +(1.00222 - 1.13128i) q^{58} +(-2.79572 - 0.339462i) q^{59} +(-1.41930 + 5.75832i) q^{60} +(-4.14978 - 2.17797i) q^{61} +(0.657736 - 5.41694i) q^{62} +(-1.00206 + 0.121672i) q^{63} +(-2.20364 + 3.19252i) q^{64} +(-7.29680 + 10.2577i) q^{65} +(8.05376 + 11.6679i) q^{66} +(2.12514 + 2.39879i) q^{67} +(-3.81389 - 0.940040i) q^{68} +(11.4346 + 16.5659i) q^{69} +1.61578i q^{70} +(-0.877468 + 0.605673i) q^{71} +(-7.70848 + 0.935979i) q^{72} +(-8.56965 + 3.25004i) q^{73} +(0.0724405 - 0.596601i) q^{74} +(-6.52948 - 17.2168i) q^{75} +(-2.70842 + 3.05717i) q^{76} +(0.720013 + 0.637876i) q^{77} +(14.5796 + 3.81316i) q^{78} +(-10.9025 + 9.65876i) q^{79} +17.0608i q^{80} +(5.24590 + 4.64746i) q^{81} +(6.41083 - 1.58013i) q^{82} +(-6.54622 - 4.51853i) q^{83} +(0.450413 - 0.170819i) q^{84} +(19.3336 - 7.33228i) q^{85} +(8.37806 + 5.78296i) q^{86} +(2.30300 - 0.567638i) q^{87} +(5.53879 + 4.90694i) q^{88} +4.56708i q^{89} +(-15.1805 + 13.4487i) q^{90} +(1.02238 + 0.0144676i) q^{91} +(-3.90176 - 3.45666i) q^{92} +(5.67879 - 6.41003i) q^{93} +(-0.977660 - 2.57788i) q^{94} +(2.59155 - 21.3434i) q^{95} +(8.64885 - 3.28008i) q^{96} +(-6.77197 + 0.822265i) q^{97} +(-9.29344 + 6.41480i) q^{98} +12.0739i 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−1.52590	−	0.578696i	−1.07897	−	0.409200i	−0.249859	−	0.968282i	$-0.580384\pi$
$2$	−1.52590	−	0.578696i	−1.07897	−	0.409200i	−0.829112	+	0.559083i	$0.811153\pi$
$3$	−1.45490	−	2.10779i	−0.839987	−	1.21693i	−0.974134	−	0.225970i	$-0.927445\pi$
$3$	−1.45490	−	2.10779i	−0.839987	−	1.21693i	0.134147	−	0.990961i	$-0.457171\pi$
$4$	0.496446	+	0.439813i	0.248223	+	0.219906i
$5$	−3.46589	−	0.420835i	−1.54999	−	0.188203i	−0.699671	−	0.714465i	$-0.746670\pi$
$5$	−3.46589	−	0.420835i	−1.54999	−	0.188203i	−0.850322	+	0.526262i	$0.823593\pi$
$6$	1.00026	+	4.05821i	0.408354	+	1.65676i
$7$	0.131788	+	0.251102i	0.0498113	+	0.0949076i	0.909089	−	0.416602i	$-0.136779\pi$
$7$	0.131788	+	0.251102i	0.0498113	+	0.0949076i	−0.859278	+	0.511509i	$0.829087\pi$
$8$	1.01380	+	1.93163i	0.358432	+	0.682935i
$9$	−1.26222	+	3.32819i	−0.420739	+	1.10940i
$10$	5.04505	+	2.64785i	1.59538	+	0.837323i
$11$	3.17160	−	1.20283i	0.956274	−	0.362667i	0.173403	−	0.984851i	$-0.444524\pi$
$11$	3.17160	−	1.20283i	0.956274	−	0.362667i	0.782871	+	0.622184i	$0.213754\pi$
$12$	0.204752	−	1.68629i	0.0591069	−	0.486789i
$13$	1.72059	−	3.16853i	0.477205	−	0.878792i
$13$	1.72059	−	3.16853i	0.477205	−	0.878792i
$14$	−0.0557837	−	0.459420i	−0.0149088	−	0.122785i
$15$	4.15549	+	7.91763i	1.07294	+	2.04432i
$16$	−0.589014	−	4.85097i	−0.147254	−	1.21274i
$17$	−5.24407	+	2.75230i	−1.27187	+	0.667531i	−0.959307	−	0.282365i	$-0.908881\pi$
$17$	−5.24407	+	2.75230i	−1.27187	+	0.667531i	−0.312566	+	0.949896i	$0.601189\pi$
$18$	3.85202	−	4.34804i	0.907931	−	1.02484i
$19$			6.15812i			1.41277i	0.707829	+	0.706384i	$0.249675\pi$
$19$			6.15812i			1.41277i	−0.707829	+	0.706384i	$0.750325\pi$
$20$	−1.53554	−	1.73326i	−0.343357	−	0.387570i
$21$	0.337530	−	0.643110i	0.0736551	−	0.140338i
$22$	−5.53561			−1.18020
$23$	−7.85938			−1.63879			−0.819397	−	0.573226i	$-0.805692\pi$
$23$	−7.85938			−1.63879			−0.819397	+	0.573226i	$0.805692\pi$
$24$	2.59649	−	4.94720i	0.530007	−	1.00984i
$25$	6.98058	+	1.72056i	1.39612	+	0.344112i
$26$	−4.45905	+	3.83915i	−0.874492	+	0.752918i
$27$	1.39133	−	0.342933i	0.267763	−	0.0659975i
$28$	−0.0450120	+	0.182621i	−0.00850646	+	0.0345121i
$29$	−0.328405	+	0.865932i	−0.0609833	+	0.160800i	−0.962045	−	0.272892i	$-0.912020\pi$
$29$	−0.328405	+	0.865932i	−0.0609833	+	0.160800i	0.901062	+	0.433691i	$0.142789\pi$
$30$	−1.75895	−	14.4862i	−0.321139	−	2.64481i
$31$	0.800199	+	3.24653i	0.143720	+	0.583095i	0.997996	+	0.0632753i	$0.0201546\pi$
$31$	0.800199	+	3.24653i	0.143720	+	0.583095i	−0.854276	+	0.519819i	$0.825999\pi$
$32$	−0.864321	+	3.50669i	−0.152792	+	0.619901i
$33$	−7.14968	−	4.93507i	−1.24460	−	0.859085i
$34$	9.59464	−	1.16500i	1.64547	−	0.199796i
$35$	−0.351092	−	0.925752i	−0.0593453	−	0.156481i
$36$	−2.09040	+	1.09713i	−0.348401	+	0.182855i
$37$	0.0881308	+	0.357561i	0.0144886	+	0.0587826i	0.977741	−	0.209815i	$-0.0672861\pi$
$37$	0.0881308	+	0.357561i	0.0144886	+	0.0587826i	−0.963253	+	0.268597i	$0.913440\pi$
$38$	3.56367	−	9.39664i	0.578104	−	1.52434i
$39$	−9.18187	+	0.983259i	−1.47028	+	0.157447i
$40$	−2.70082	−	7.12147i	−0.427037	−	1.12600i
$41$	−3.32971	+	2.29833i	−0.520014	+	0.358939i	−0.798976	−	0.601362i	$-0.794625\pi$
$41$	−3.32971	+	2.29833i	−0.520014	+	0.358939i	0.278963	+	0.960302i	$0.410009\pi$
$42$	−0.887201	+	0.785991i	−0.136898	+	0.121281i
$43$	−6.05675	−	1.49286i	−0.923646	−	0.227658i	−0.251312	−	0.967906i	$-0.580862\pi$
$43$	−6.05675	−	1.49286i	−0.923646	−	0.227658i	−0.672334	+	0.740248i	$0.734708\pi$
$44$	2.10355	+	0.797771i	0.317122	+	0.120269i
$45$	5.77533	−	11.0040i	0.860935	−	1.64037i
$46$	11.9926	+	4.54819i	1.76821	+	0.670594i
$47$	1.12029	+	1.26455i	0.163411	+	0.184453i	0.824513	−	0.565843i	$-0.191449\pi$
$47$	1.12029	+	1.26455i	0.163411	+	0.184453i	−0.661101	+	0.750296i	$0.729911\pi$
$48$	−9.36785	+	8.29919i	−1.35213	+	1.19789i
$49$	3.93077	−	5.69470i	0.561538	−	0.813529i
$50$	−9.65596	−	6.66503i	−1.36556	−	0.942577i
$51$	13.4309	+	7.04906i	1.88070	+	0.987066i
$52$	2.24774	−	0.816266i	0.311705	−	0.113196i
$53$	10.3302	−	5.42170i	1.41896	−	0.744727i	0.431427	−	0.902148i	$-0.358010\pi$
$53$	10.3302	−	5.42170i	1.41896	−	0.744727i	0.987532	+	0.157421i	$0.0503178\pi$
$54$	−2.32149	−	0.281879i	−0.315914	−	0.0383589i
$55$	−11.4986	+	2.83416i	−1.55047	+	0.382157i
$56$	−0.351429	+	0.509133i	−0.0469617	+	0.0680358i
$57$	12.9800	−	8.95945i	1.71924	−	1.18671i
$58$	1.00222	−	1.13128i	0.131598	−	0.148544i
$59$	−2.79572	−	0.339462i	−0.363971	−	0.0441941i	−0.0634917	−	0.997982i	$-0.520224\pi$
$59$	−2.79572	−	0.339462i	−0.363971	−	0.0441941i	−0.300480	+	0.953788i	$0.597147\pi$
$60$	−1.41930	+	5.75832i	−0.183231	+	0.743395i
$61$	−4.14978	−	2.17797i	−0.531324	−	0.278861i	0.177651	−	0.984094i	$-0.443150\pi$
$61$	−4.14978	−	2.17797i	−0.531324	−	0.278861i	−0.708976	+	0.705233i	$0.750842\pi$
$62$	0.657736	−	5.41694i	0.0835325	−	0.687952i
$63$	−1.00206	+	0.121672i	−0.126248	+	0.0153293i
$64$	−2.20364	+	3.19252i	−0.275455	+	0.399065i
$65$	−7.29680	+	10.2577i	−0.905057	+	1.27231i
$66$	8.05376	+	11.6679i	0.991349	+	1.43622i
$67$	2.12514	+	2.39879i	0.259628	+	0.293059i	0.863842	−	0.503763i	$-0.168051\pi$
$67$	2.12514	+	2.39879i	0.259628	+	0.293059i	−0.604214	+	0.796822i	$0.706513\pi$
$68$	−3.81389	−	0.940040i	−0.462502	−	0.113997i
$69$	11.4346	+	16.5659i	1.37657	+	1.99430i
$70$			1.61578i			0.193122i
$71$	−0.877468	+	0.605673i	−0.104136	+	0.0718801i	−0.618995	−	0.785395i	$-0.712460\pi$
$71$	−0.877468	+	0.605673i	−0.104136	+	0.0718801i	0.514859	+	0.857275i	$0.327844\pi$
$72$	−7.70848	+	0.935979i	−0.908453	+	0.110306i
$73$	−8.56965	+	3.25004i	−1.00300	+	0.380388i	−0.800785	−	0.598952i	$-0.795584\pi$
$73$	−8.56965	+	3.25004i	−1.00300	+	0.380388i	−0.202217	+	0.979341i	$0.564815\pi$
$74$	0.0724405	−	0.596601i	0.00842103	−	0.0693535i
$75$	−6.52948	−	17.2168i	−0.753960	−	1.98803i
$76$	−2.70842	+	3.05717i	−0.310677	+	0.350682i
$77$	0.720013	+	0.637876i	0.0820531	+	0.0726927i
$78$	14.5796	+	3.81316i	1.65081	+	0.431755i
$79$	−10.9025	+	9.65876i	−1.22663	+	1.08670i	−0.233175	+	0.972435i	$0.574912\pi$
$79$	−10.9025	+	9.65876i	−1.22663	+	1.08670i	−0.993451	+	0.114261i	$0.963550\pi$
$80$			17.0608i			1.90746i
$81$	5.24590	+	4.64746i	0.582877	+	0.516384i
$82$	6.41083	−	1.58013i	0.707957	−	0.174496i
$83$	−6.54622	−	4.51853i	−0.718542	−	0.495973i	0.151807	−	0.988410i	$-0.451491\pi$
$83$	−6.54622	−	4.51853i	−0.718542	−	0.495973i	−0.870348	+	0.492437i	$0.836106\pi$
$84$	0.450413	−	0.170819i	0.0491441	−	0.0186379i
$85$	19.3336	−	7.33228i	2.09703	−	0.795297i
$86$	8.37806	+	5.78296i	0.903429	+	0.623592i
$87$	2.30300	−	0.567638i	0.246907	−	0.0608572i
$88$	5.53879	+	4.90694i	0.590437	+	0.523082i
$89$			4.56708i			0.484110i	0.970263	+	0.242055i	$0.0778214\pi$
$89$			4.56708i			0.484110i	−0.970263	+	0.242055i	$0.922179\pi$
$90$	−15.1805	+	13.4487i	−1.60016	+	1.41762i
$91$	1.02238	+	0.0144676i	0.107174	+	0.00151662i
$92$	−3.90176	−	3.45666i	−0.406786	−	0.360381i
$93$	5.67879	−	6.41003i	0.588864	−	0.664690i
$94$	−0.977660	−	2.57788i	−0.100838	−	0.265888i
$95$	2.59155	−	21.3434i	0.265888	−	2.18978i
$96$	8.64885	−	3.28008i	0.882720	−	0.334771i
$97$	−6.77197	+	0.822265i	−0.687589	+	0.0834884i	−0.456872	−	0.889532i	$-0.651030\pi$
$97$	−6.77197	+	0.822265i	−0.687589	+	0.0834884i	−0.230717	+	0.973021i	$0.574107\pi$
$98$	−9.29344	+	6.41480i	−0.938779	+	0.647993i
$99$			12.0739i			1.21348i
$100$	2.70876	+	3.92431i	0.270876	+	0.392431i
$101$	−14.1879	−	3.49700i	−1.41175	−	0.347964i	−0.541550	−	0.840669i	$-0.682162\pi$
$101$	−14.1879	−	3.49700i	−1.41175	−	0.347964i	−0.870197	+	0.492705i	$0.836008\pi$
$102$	−16.4148	−	18.5285i	−1.62531	−	1.83460i
$103$	−8.79920	−	12.7478i	−0.867011	−	1.25608i	−0.965358	−	0.260930i	$-0.915971\pi$
$103$	−8.79920	−	12.7478i	−0.867011	−	1.25608i	0.0983467	−	0.995152i	$-0.468645\pi$
$104$	7.86476	+	0.111294i	0.771203	+	0.0109133i
$105$	−1.44049	+	2.08690i	−0.140577	+	0.203661i
$106$	−18.9003	+	2.29491i	−1.83576	+	0.222901i
$107$	−1.02135	+	8.41159i	−0.0987378	+	0.813179i	0.856256	+	0.516552i	$0.172785\pi$
$107$	−1.02135	+	8.41159i	−0.0987378	+	0.813179i	−0.954994	+	0.296627i	$0.904138\pi$
$108$	0.841549	+	0.441679i	0.0809781	+	0.0425006i
$109$	2.86021	−	11.6043i	0.273959	−	1.11149i	−0.659182	−	0.751983i	$-0.729097\pi$
$109$	2.86021	−	11.6043i	0.273959	−	1.11149i	0.933141	−	0.359511i	$-0.117056\pi$
$110$	19.1858	+	2.32958i	1.82929	+	0.222117i
$111$	0.625440	−	0.705976i	0.0593642	−	0.0670083i
$112$	1.14046	−	0.787204i	0.107763	−	0.0743838i
$113$	8.11531	−	11.7571i	0.763424	−	1.10601i	−0.227786	−	0.973711i	$-0.573149\pi$
$113$	8.11531	−	11.7571i	0.763424	−	1.10601i	0.991210	−	0.132299i	$-0.0422360\pi$
$114$	−24.9909	+	6.15971i	−2.34061	+	0.576909i
$115$	27.2398	+	3.30750i	2.54012	+	0.308426i
$116$	−0.543883	+	0.285452i	−0.0504983	+	0.0265036i
$117$	8.37372	+	9.72582i	0.774151	+	0.899153i
$118$	4.06953	+	2.13585i	0.374630	+	0.196621i
$119$	−1.38221	−	0.954074i	−0.126707	−	0.0874598i
$120$	−11.0811	+	16.0538i	−1.01156	+	1.46550i
$121$	0.378646	−	0.335451i	0.0344224	−	0.0304956i
$122$	5.07174	+	5.72481i	0.459174	+	0.518300i
$123$	9.68880	+	3.67448i	0.873610	+	0.331316i
$124$	−1.03061	+	1.96367i	−0.0925517	+	0.176342i
$125$	−7.14754	−	2.71071i	−0.639296	−	0.242453i
$126$	1.59945	+	0.394229i	0.142490	+	0.0351207i
$127$	−7.46403	+	6.61255i	−0.662325	+	0.586769i	−0.925854	−	0.377883i	$-0.876652\pi$
$127$	−7.46403	+	6.61255i	−0.662325	+	0.586769i	0.263528	+	0.964652i	$0.415114\pi$
$128$	11.1547	−	7.69950i	0.985941	−	0.680546i
$129$	5.66535	+	14.9383i	0.498806	+	1.31524i
$130$	17.0702	−	11.4295i	1.49716	−	1.00244i
$131$	−0.466992	+	1.23136i	−0.0408013	+	0.107584i	−0.953868	−	0.300226i	$-0.902938\pi$
$131$	−0.466992	+	1.23136i	−0.0408013	+	0.107584i	0.913067	+	0.407810i	$0.133707\pi$
$132$	−1.37892	−	5.59451i	−0.120020	−	0.486940i
$133$	−1.54631	+	0.811568i	−0.134082	+	0.0703719i
$134$	−1.85458	−	4.89011i	−0.160211	−	0.422442i
$135$	−4.96653	+	0.603046i	−0.427451	+	0.0519020i
$136$	−10.6329	−	7.33933i	−0.911760	−	0.629342i
$137$	1.50598	−	6.10999i	0.128664	−	0.522011i	−0.870871	−	0.491512i	$-0.836444\pi$
$137$	1.50598	−	6.10999i	0.128664	−	0.522011i	0.999535	−	0.0304989i	$-0.00970960\pi$
$138$	−7.86141	−	31.8950i	−0.669208	−	2.71508i
$139$	0.239299	+	1.97081i	0.0202971	+	0.167162i	0.999333	−	0.0365279i	$-0.0116298\pi$
$139$	0.239299	+	1.97081i	0.0202971	+	0.167162i	−0.979036	+	0.203689i	$0.934707\pi$
$140$	0.232860	−	0.614001i	0.0196802	−	0.0518925i
$141$	1.03549	−	4.20113i	0.0872037	−	0.353799i
$142$	1.68943	−	0.416406i	0.141773	−	0.0349440i
$143$	1.64582	−	12.1189i	0.137631	−	1.01343i
$144$	16.8884	+	4.16262i	1.40737	+	0.346885i
$145$	1.50263	−	2.86302i	0.124787	−	0.237761i
$146$	14.9572			1.23786
$147$	−17.7221			−1.46169
$148$	−0.113508	+	0.216271i	−0.00933026	+	0.0177773i
$149$	−1.82208	−	2.05671i	−0.149271	−	0.168492i	0.669119	−	0.743155i	$-0.266672\pi$
$149$	−1.82208	−	2.05671i	−0.149271	−	0.168492i	−0.818390	+	0.574663i	$0.805133\pi$
$150$			30.0497i			2.45354i
$151$	−5.41180	+	6.10866i	−0.440406	+	0.497116i	−0.926239	−	0.376936i	$-0.876978\pi$
$151$	−5.41180	+	6.10866i	−0.440406	+	0.497116i	0.485833	+	0.874051i	$0.338516\pi$
$152$	−11.8952	+	6.24309i	−0.964829	+	0.506381i
$153$	−2.54103	−	20.9273i	−0.205430	−	1.69187i
$154$	−0.729529	−	1.39000i	−0.0587871	−	0.112009i
$155$	−1.40715	−	11.5889i	−0.113025	−	0.930842i
$156$	−4.99075	−	3.55017i	−0.399580	−	0.284241i
$157$	−0.279690	+	2.30346i	−0.0223217	+	0.183836i	−0.999605	−	0.0281009i	$-0.991054\pi$
$157$	−0.279690	+	2.30346i	−0.0223217	+	0.183836i	0.977283	+	0.211937i	$0.0679771\pi$
$158$	22.2255	−	8.42904i	1.76817	−	0.670578i
$159$	−26.4572	−	13.8858i	−2.09819	−	1.10121i
$160$	4.47138	−	11.7901i	0.353494	−	0.932086i
$161$	−1.03578	−	1.97350i	−0.0816305	−	0.155534i
$162$	−5.31522	−	10.1273i	−0.417603	−	0.795677i
$163$	3.95081	+	16.0291i	0.309452	+	1.25549i	0.895443	+	0.445177i	$0.146859\pi$
$163$	3.95081	+	16.0291i	0.309452	+	1.25549i	−0.585991	+	0.810318i	$0.699295\pi$
$164$	−2.66386	−	0.323451i	−0.208012	−	0.0252573i
$165$	22.7031	+	20.1132i	1.76744	+	1.56581i
$166$	7.37400	+	10.6831i	0.572333	+	0.829168i
$167$	−9.84628	−	3.73420i	−0.761928	−	0.288961i	−0.0571276	−	0.998367i	$-0.518194\pi$
$167$	−9.84628	−	3.73420i	−0.761928	−	0.288961i	−0.704800	+	0.709406i	$0.748963\pi$
$168$	1.58444			0.122242
$169$	−7.07915	−	10.9035i	−0.544550	−	0.838728i
$170$	−33.7442			−2.58807
$171$	−20.4954	−	7.77288i	−1.56732	−	0.594407i
$172$	−2.35027	−	3.40496i	−0.179207	−	0.259626i
$173$	−2.28685	−	2.02597i	−0.173866	−	0.154032i	0.571702	−	0.820461i	$-0.306283\pi$
$173$	−2.28685	−	2.02597i	−0.173866	−	0.154032i	−0.745568	+	0.666430i	$0.767822\pi$
$174$	−3.84262	−	0.466579i	−0.291309	−	0.0353713i
$175$	0.487924	+	1.97959i	0.0368836	+	0.149643i
$176$	−7.70301	−	14.6769i	−0.580636	−	1.10631i
$177$	3.35198	+	6.38666i	0.251950	+	0.480051i
$178$	2.64295	−	6.96889i	0.198098	−	0.522340i
$179$	21.0811	+	11.0642i	1.57568	+	0.826979i	0.999956	+	0.00933213i	$0.00297055\pi$
$179$	21.0811	+	11.0642i	1.57568	+	0.826979i	0.575720	+	0.817647i	$0.304722\pi$
$180$	7.70682	−	2.92281i	0.574433	−	0.217854i
$181$	2.83259	−	23.3285i	0.210545	−	1.73399i	−0.378244	−	0.925706i	$-0.623472\pi$
$181$	2.83259	−	23.3285i	0.210545	−	1.73399i	0.588788	−	0.808287i	$-0.299605\pi$
$182$	−1.55167	−	0.613721i	−0.115017	−	0.0454920i
$183$	1.44681	+	11.9156i	0.106951	+	0.880825i
$184$	−7.96783	−	15.1814i	−0.587396	−	1.11919i
$185$	−0.154977	−	1.27635i	−0.0113942	−	0.0938394i
$186$	−12.3747	+	6.49475i	−0.907357	+	0.476218i
$187$	−13.3216	+	15.0369i	−0.974168	+	1.09961i
$188$			1.12050i			0.0817208i
$189$	0.269473	+	0.304172i	0.0196013	+	0.0221253i
$190$	−16.3057	+	31.0680i	−1.18294	+	2.25391i
$191$	5.98448			0.433022			0.216511	−	0.976280i	$-0.430532\pi$
$191$	5.98448			0.433022			0.216511	+	0.976280i	$0.430532\pi$
$192$	9.93523			0.717014
$193$	−6.49469	+	12.3746i	−0.467498	+	0.890743i	0.531546	+	0.847029i	$0.321611\pi$
$193$	−6.49469	+	12.3746i	−0.467498	+	0.890743i	−0.999044	+	0.0437136i	$0.986081\pi$
$194$	10.8092	+	2.66422i	0.776052	+	0.191280i
$195$	32.2371	+	0.456186i	2.30855	+	0.0326682i
$196$	4.45602	−	1.09831i	0.318287	−	0.0784507i
$197$	−0.579622	+	2.35162i	−0.0412963	+	0.167546i	−0.987969	−	0.154650i	$-0.950575\pi$
$197$	−0.579622	+	2.35162i	−0.0412963	+	0.167546i	0.946673	+	0.322196i	$0.104421\pi$
$198$	6.98714	−	18.4236i	0.496554	−	1.30931i
$199$	−1.12764	−	9.28692i	−0.0799360	−	0.658332i	−0.976515	−	0.215449i	$-0.930879\pi$
$199$	−1.12764	−	9.28692i	−0.0799360	−	0.658332i	0.896579	−	0.442884i	$-0.146044\pi$
$200$	3.75342	+	15.2282i	0.265407	+	1.07680i
$201$	1.96427	−	7.96935i	0.138549	−	0.562115i
$202$	19.6255	+	13.5465i	1.38085	+	0.953129i
$203$	−0.260717	+	0.0316568i	−0.0182988	+	0.00222187i
$204$	3.56743	+	9.40654i	0.249770	+	0.658589i
$205$	12.5076	−	6.56451i	0.873571	−	0.458486i
$206$	6.04954	+	24.5439i	0.421491	+	1.71006i
$207$	9.92025	−	26.1575i	0.689505	−	1.81807i
$208$	−16.3839	−	6.48021i	−1.13602	−	0.449322i
$209$	7.40717	+	19.5311i	0.512365	+	1.35099i
$210$	3.40571	−	2.35079i	0.235017	−	0.162220i
$211$	0.350252	−	0.310296i	0.0241123	−	0.0213616i	−0.650980	−	0.759094i	$-0.725642\pi$
$211$	0.350252	−	0.310296i	0.0241123	−	0.0213616i	0.675093	+	0.737733i	$0.264104\pi$
$212$	7.51291	+	1.85176i	0.515988	+	0.127180i
$213$	2.55326	+	0.968323i	0.174946	+	0.0663484i
$214$	6.42623	−	12.2442i	0.439288	−	0.836993i
$215$	20.3638	+	7.72297i	1.38880	+	0.526702i
$216$	2.07295	+	2.33988i	0.141047	+	0.159209i
$217$	−0.709754	+	0.628787i	−0.0481812	+	0.0426848i
$218$	−11.0798	+	16.0518i	−0.750416	+	1.08717i
$219$	19.3184	+	13.3345i	1.30542	+	0.901063i
$220$	−6.95494	−	3.65023i	−0.468902	−	0.246099i
$221$	−0.302145	+	21.3516i	−0.0203245	+	1.43626i
$222$	−1.36290	+	0.715306i	−0.0914720	+	0.0480082i
$223$	4.02681	+	0.488944i	0.269655	+	0.0327421i	0.254247	−	0.967139i	$-0.418172\pi$
$223$	4.02681	+	0.488944i	0.269655	+	0.0327421i	0.0154079	+	0.999881i	$0.495095\pi$
$224$	−0.994443	+	0.245108i	−0.0664440	+	0.0163770i
$225$	−14.5374	+	21.0610i	−0.969158	+	1.40407i
$226$	−19.1869	+	13.2437i	−1.27629	+	0.880960i
$227$	−16.3352	+	18.4386i	−1.08420	+	1.22381i	−0.111011	+	0.993819i	$0.535409\pi$
$227$	−16.3352	+	18.4386i	−1.08420	+	1.22381i	−0.973192	+	0.229993i	$0.926130\pi$
$228$	10.3843	+	1.26089i	0.687720	+	0.0835043i
$229$	0.900746	−	3.65447i	0.0595230	−	0.241494i	−0.933643	−	0.358205i	$-0.883389\pi$
$229$	0.900746	−	3.65447i	0.0595230	−	0.241494i	0.993166	+	0.116711i	$0.0372351\pi$
$230$	−39.6510	−	20.8104i	−2.61451	−	1.37220i
$231$	0.296959	−	2.44568i	0.0195385	−	0.160914i
$232$	−2.00560	+	0.243524i	−0.131674	+	0.0159881i
$233$	3.62008	−	5.24460i	0.237160	−	0.343585i	−0.686274	−	0.727343i	$-0.740755\pi$
$233$	3.62008	−	5.24460i	0.237160	−	0.343585i	0.923434	+	0.383758i	$0.125370\pi$
$234$	−7.14913	−	19.6864i	−0.467353	−	1.28694i
$235$	−3.35064	−	4.85425i	−0.218572	−	0.316656i
$236$	−1.23862	−	1.39812i	−0.0806275	−	0.0910096i
$237$	36.2207	+	8.92759i	2.35278	+	0.579909i
$238$	1.55700	+	2.25570i	0.100925	+	0.146215i
$239$		−	18.9309i		−	1.22454i	−0.790649	−	0.612270i	$-0.790257\pi$
$239$		−	18.9309i		−	1.22454i	0.790649	−	0.612270i	$-0.209743\pi$
$240$	35.9605	−	24.8218i	2.32124	−	1.60224i
$241$	−23.5770	+	2.86276i	−1.51873	+	0.184407i	−0.837001	−	0.547201i	$-0.815693\pi$
$241$	−23.5770	+	2.86276i	−1.51873	+	0.184407i	−0.681726	+	0.731608i	$0.738770\pi$
$242$	−0.771899	+	0.292743i	−0.0496195	+	0.0188182i
$243$	2.68177	−	22.0864i	0.172036	−	1.41684i
$244$	−1.10224	−	2.90637i	−0.0705637	−	0.186061i
$245$	−16.0201	+	18.0830i	−1.02349	+	1.15528i
$246$	−12.6577	−	11.2137i	−0.807025	−	0.714962i
$247$	19.5122	+	10.5956i	1.24153	+	0.674181i
$248$	−5.45987	+	4.83702i	−0.346702	+	0.307151i
$249$			20.3721i			1.29103i
$250$	9.33773	+	8.27250i	0.590570	+	0.523199i
$251$	6.49939	−	1.60196i	0.410238	−	0.101115i	−0.0287954	−	0.999585i	$-0.509167\pi$
$251$	6.49939	−	1.60196i	0.410238	−	0.101115i	0.439033	+	0.898471i	$0.355321\pi$
$252$	−0.550982	−	0.380315i	−0.0347086	−	0.0239576i
$253$	−24.9268	+	9.45350i	−1.56714	+	0.594337i
$254$	15.2160	−	5.77066i	0.954736	−	0.362083i
$255$	−43.5834	−	30.0834i	−2.72930	−	1.88390i
$256$	−13.9435	+	3.43677i	−0.871471	+	0.214798i
$257$	12.6077	+	11.1694i	0.786446	+	0.696730i	0.957469	−	0.288537i	$-0.0931688\pi$
$257$	12.6077	+	11.1694i	0.786446	+	0.696730i	−0.171023	+	0.985267i	$0.554707\pi$
$258$		−	26.0728i		−	1.62322i
$259$	−0.0781695	+	0.0692521i	−0.00485722	+	0.00430312i
$260$	−8.13393	+	1.88316i	−0.504445	+	0.116789i
$261$	−2.46747	−	2.18599i	−0.152733	−	0.135309i
$262$	1.42516	−	1.60867i	0.0880468	−	0.0993843i
$263$	−4.89012	−	12.8942i	−0.301538	−	0.795090i	−0.997063	−	0.0765881i	$-0.975597\pi$
$263$	−4.89012	−	12.8942i	−0.301538	−	0.795090i	0.695525	−	0.718502i	$-0.255172\pi$
$264$	2.28440	−	18.8137i	0.140595	−	1.15790i
$265$	−38.0849	+	14.4437i	−2.33954	+	0.887269i
$266$	2.82916	−	0.343523i	0.173467	−	0.0210627i
$267$	9.62644	−	6.64465i	0.589128	−	0.406646i
$268$			2.12554i			0.129838i
$269$	−7.79679	−	11.2956i	−0.475379	−	0.688705i	0.509789	−	0.860300i	$-0.329723\pi$
$269$	−7.79679	−	11.2956i	−0.475379	−	0.688705i	−0.985168	+	0.171595i	$0.945108\pi$
$270$	7.92739	+	1.95393i	0.482446	+	0.118912i
$271$	−12.3655	−	13.9578i	−0.751152	−	0.847876i	0.241307	−	0.970449i	$-0.422424\pi$
$271$	−12.3655	−	13.9578i	−0.751152	−	0.847876i	−0.992459	+	0.122573i	$0.960885\pi$
$272$	16.4401	+	23.8177i	0.996830	+	1.44416i
$273$	−1.45696	−	2.17600i	−0.0881794	−	0.131698i
$274$	−5.83378	+	8.45169i	−0.352432	+	0.510586i
$275$	24.2092	−	2.93953i	1.45987	−	0.177260i
$276$	−1.60923	+	13.2532i	−0.0968640	+	0.797747i
$277$	−3.66752	−	1.92486i	−0.220360	−	0.115654i	0.350932	−	0.936401i	$-0.385865\pi$
$277$	−3.66752	−	1.92486i	−0.220360	−	0.115654i	−0.571291	+	0.820747i	$0.693557\pi$
$278$	0.775352	−	3.14572i	0.0465025	−	0.188668i
$279$	−11.8151	−	1.43462i	−0.707353	−	0.0858882i
$280$	1.43228	−	1.61671i	0.0855949	−	0.0966167i
$281$	23.0601	−	15.9172i	1.37565	−	0.949542i	0.375911	−	0.926656i	$-0.377330\pi$
$281$	23.0601	−	15.9172i	1.37565	−	0.949542i	0.999738	−	0.0228864i	$-0.00728559\pi$
$282$	−4.01122	+	5.81126i	−0.238865	+	0.346055i
$283$	12.2647	−	3.02297i	0.729060	−	0.179697i	0.142721	−	0.989763i	$-0.454415\pi$
$283$	12.2647	−	3.02297i	0.729060	−	0.179697i	0.586339	+	0.810066i	$0.300569\pi$
$284$	−0.701998	−	0.0852380i	−0.0416559	−	0.00505795i
$285$	−48.7577	+	25.5900i	−2.88816	+	1.51582i
$286$	−9.52450	+	17.5397i	−0.563196	+	1.03715i
$287$	−1.01593	−	0.533203i	−0.0599686	−	0.0314740i
$288$	−10.5800	−	7.30283i	−0.623431	−	0.430323i
$289$	10.2680	−	14.8758i	0.604000	−	0.875044i
$290$	−3.94968	+	3.49911i	−0.231933	+	0.205475i
$291$	11.5857	+	13.0775i	0.679166	+	0.766620i
$292$	−5.68378	−	2.15557i	−0.332618	−	0.126145i
$293$	6.31230	−	12.0271i	0.368768	−	0.702630i	−0.628395	−	0.777894i	$-0.716288\pi$
$293$	6.31230	−	12.0271i	0.368768	−	0.702630i	0.997164	+	0.0752647i	$0.0239802\pi$
$294$	27.0421	+	10.2557i	1.57713	+	0.598125i
$295$	9.54679	+	2.35307i	0.555836	+	0.137001i
$296$	−0.601329	+	0.532731i	−0.0349515	+	0.0309643i
$297$	4.00027	−	2.76119i	0.232119	−	0.160220i
$298$	1.59010	+	4.19275i	0.0921120	+	0.242879i
$299$	−13.5228	+	24.9027i	−0.782042	+	1.44016i
$300$	4.33065	−	11.4190i	0.250030	−	0.659275i
$301$	−0.423351	−	1.71760i	−0.0244015	−	0.0990009i
$302$	11.7929	−	6.18939i	0.678605	−	0.356159i
$303$	13.2710	+	34.9928i	0.762400	+	2.01028i
$304$	29.8728	−	3.62722i	1.71332	−	0.208035i
$305$	13.4661	+	9.29498i	0.771067	+	0.532229i
$306$	−8.23318	+	33.4033i	−0.470659	+	1.90954i
$307$	−0.0191960	−	0.0778814i	−0.00109558	−	0.00444492i	0.970391	−	0.241537i	$-0.0776517\pi$
$307$	−0.0191960	−	0.0778814i	−0.00109558	−	0.00444492i	−0.971487	+	0.237093i	$0.923806\pi$
$308$	0.0769016	+	0.633342i	0.00438188	+	0.0360880i
$309$	−14.0678	+	37.0937i	−0.800288	+	2.11019i
$310$	−4.55928	+	18.4977i	−0.258950	+	1.05060i
$311$	17.8831	−	4.40778i	1.01406	−	0.249942i	0.302934	−	0.953011i	$-0.402034\pi$
$311$	17.8831	−	4.40778i	1.01406	−	0.249942i	0.711122	+	0.703069i	$0.248188\pi$
$312$	−11.2079	−	16.7392i	−0.634520	−	0.947669i
$313$	−2.32514	−	0.573095i	−0.131425	−	0.0323932i	0.173055	−	0.984912i	$-0.444636\pi$
$313$	−2.32514	−	0.573095i	−0.131425	−	0.0323932i	−0.304479	+	0.952519i	$0.598482\pi$
$314$	1.75978	−	3.35298i	0.0993101	−	0.189220i
$315$	3.52424			0.198568
$316$	−9.66054			−0.543448
$317$	6.00869	−	11.4486i	0.337482	−	0.643018i	−0.656283	−	0.754515i	$-0.727872\pi$
$317$	6.00869	−	11.4486i	0.337482	−	0.643018i	0.993765	+	0.111497i	$0.0355646\pi$
$318$	32.3352	+	36.4989i	1.81327	+	2.04676i
$319$			3.14141i			0.175885i
$320$	8.98109	−	10.1376i	0.502058	−	0.566707i
$321$	19.2158	−	10.0852i	1.07252	−	0.562903i
$322$	0.438426	+	3.61076i	0.0244325	+	0.201220i
$323$	−16.9490	−	32.2936i	−0.943066	−	1.79686i
$324$	0.560292	+	4.61442i	0.0311274	+	0.256357i
$325$	17.4624	−	19.1578i	0.968637	−	1.06268i
$326$	3.24743	−	26.7450i	0.179859	−	1.48127i
$327$	−28.6208	+	10.8544i	−1.58273	+	0.600252i
$328$	−7.81519	−	4.10173i	−0.431522	−	0.226480i
$329$	−0.169889	+	0.447960i	−0.00936628	+	0.0246969i
$330$	−23.0032	−	43.8289i	−1.26628	−	2.41270i
$331$	−9.62062	−	18.3306i	−0.528797	−	1.00754i	−0.992580	−	0.121590i	$-0.961201\pi$
$331$	−9.62062	−	18.3306i	−0.528797	−	1.00754i	0.463783	−	0.885949i	$-0.346492\pi$
$332$	−1.26254	−	5.12232i	−0.0692908	−	0.281124i
$333$	−1.30127	−	0.158003i	−0.0713092	−	0.00865851i
$334$	12.8634	+	11.3960i	0.703855	+	0.623561i
$335$	−6.35602	−	9.20828i	−0.347266	−	0.503102i
$336$	−3.31852	−	1.25855i	−0.181040	−	0.0686594i
$337$	−10.9815			−0.598201			−0.299101	−	0.954222i	$-0.596687\pi$
$337$	−10.9815			−0.598201			−0.299101	+	0.954222i	$0.596687\pi$
$338$	4.49225	+	20.7342i	0.244346	+	1.12779i
$339$	−36.5883			−1.98721
$340$	12.8229	+	4.86310i	0.695421	+	0.263738i
$341$	6.44294	+	9.33421i	0.348905	+	0.505476i
$342$	26.7757	+	23.7212i	1.44786	+	1.28270i
$343$	3.91860	+	0.475804i	0.211584	+	0.0256910i
$344$	−3.25668	−	13.2129i	−0.175588	−	0.712390i
$345$	−32.6596	−	62.2277i	−1.75833	−	3.35023i
$346$	2.31707	+	4.41480i	0.124566	+	0.237341i
$347$	−3.35106	+	8.83601i	−0.179894	+	0.474342i	−0.994384	−	0.105837i	$-0.966248\pi$
$347$	−3.35106	+	8.83601i	−0.179894	+	0.474342i	0.814489	+	0.580178i	$0.197017\pi$
$348$	1.39297	+	0.731086i	0.0746709	+	0.0391903i
$349$	28.4068	−	10.7733i	1.52058	−	0.576681i	0.553883	−	0.832595i	$-0.313146\pi$
$349$	28.4068	−	10.7733i	1.52058	−	0.576681i	0.966700	+	0.255914i	$0.0823763\pi$
$350$	0.401057	−	3.30300i	0.0214374	−	0.176553i
$351$	1.30732	−	4.99853i	0.0697796	−	0.266802i
$352$	1.47667	+	12.1615i	0.0787066	+	0.648207i
$353$	14.3893	+	27.4166i	0.765868	+	1.45924i	0.884619	+	0.466315i	$0.154419\pi$
$353$	14.3893	+	27.4166i	0.765868	+	1.45924i	−0.118751	+	0.992924i	$0.537889\pi$
$354$	−1.41883	−	11.6851i	−0.0754102	−	0.621059i
$355$	3.29610	−	1.72993i	0.174939	−	0.0918149i
$356$	−2.00866	+	2.26731i	−0.106459	+	0.120167i
$357$			4.30150i			0.227659i
$358$	−25.7648	−	29.0824i	−1.36171	−	1.53705i
$359$	−3.92571	+	7.47981i	−0.207191	+	0.394769i	−0.966771	−	0.255645i	$-0.917712\pi$
$359$	−3.92571	+	7.47981i	−0.207191	+	0.394769i	0.759580	+	0.650414i	$0.225405\pi$
$360$	27.1106			1.42886
$361$	−18.9224			−0.995915
$362$	−17.8223	+	33.9576i	−0.936721	+	1.78477i
$363$	−1.25795	−	0.310058i	−0.0660254	−	0.0162738i
$364$	0.501192	+	0.456837i	0.0262696	+	0.0239448i
$365$	31.0692	−	7.65787i	1.62624	−	0.400831i
$366$	4.68781	−	19.0192i	0.245036	−	0.994149i
$367$	−7.28741	+	19.2153i	−0.380400	+	1.00303i	0.598937	+	0.800796i	$0.295590\pi$
$367$	−7.28741	+	19.2153i	−0.380400	+	1.00303i	−0.979337	+	0.202236i	$0.935179\pi$
$368$	4.62929	+	38.1256i	0.241318	+	1.98743i
$369$	−3.44648	−	13.9829i	−0.179417	−	0.727922i
$370$	−0.502141	+	2.03727i	−0.0261051	+	0.105913i
$371$	2.72279	+	1.87941i	0.141360	+	0.0975741i
$372$	5.63843	−	0.684629i	0.292339	−	0.0354964i
$373$	−11.8381	−	31.2145i	−0.612954	−	1.61623i	−0.776804	−	0.629742i	$-0.783161\pi$
$373$	−11.8381	−	31.2145i	−0.612954	−	1.61623i	0.163850	−	0.986485i	$-0.447609\pi$
$374$	29.0291	−	15.2356i	1.50106	−	0.787816i
$375$	4.68537	+	19.0093i	0.241952	+	0.981636i
$376$	−1.30689	+	3.44599i	−0.0673978	+	0.177713i
$377$	2.17868	+	2.53047i	0.112208	+	0.130326i
$378$	−0.235164	−	0.620078i	−0.0120956	−	0.0318933i
$379$	−16.1186	+	11.1259i	−0.827958	+	0.571498i	−0.904942	−	0.425534i	$-0.860086\pi$
$379$	−16.1186	+	11.1259i	−0.827958	+	0.571498i	0.0769847	+	0.997032i	$0.475471\pi$
$380$	10.6736	−	9.45602i	0.547546	−	0.485084i
$381$	24.7973	+	6.11198i	1.27040	+	0.313126i
$382$	−9.13169	−	3.46319i	−0.467218	−	0.177192i
$383$	−3.50290	+	6.67421i	−0.178990	+	0.341036i	−0.958377	−	0.285506i	$-0.907838\pi$
$383$	−3.50290	+	6.67421i	−0.178990	+	0.341036i	0.779387	+	0.626543i	$0.215531\pi$
$384$	−32.4578	−	12.3096i	−1.65636	−	0.628173i
$385$	−2.22705	−	2.51382i	−0.113501	−	0.128116i
$386$	17.0713	−	15.1239i	0.868908	−	0.769786i
$387$	12.6134	−	18.2737i	0.641178	−	0.928906i
$388$	−3.72356	−	2.57019i	−0.189035	−	0.130481i
$389$	−30.9760	−	16.2574i	−1.57054	−	0.824285i	−0.999995	−	0.00302042i	$-0.999039\pi$
$389$	−30.9760	−	16.2574i	−1.57054	−	0.824285i	−0.570548	−	0.821264i	$-0.693269\pi$
$390$	−48.9265	−	19.3516i	−2.47749	−	0.979906i
$391$	41.2151	−	21.6314i	2.08434	−	1.09395i
$392$	14.9851	+	1.81952i	0.756861	+	0.0918995i
$393$	3.27487	−	0.807182i	0.165195	−	0.0407169i
$394$	2.24531	−	3.25290i	0.113117	−	0.163879i
$395$	41.8516	−	28.8881i	2.10578	−	1.45352i
$396$	−5.31027	+	5.99406i	−0.266851	+	0.301213i
$397$	17.0072	+	2.06505i	0.853567	+	0.103642i	0.535612	−	0.844464i	$-0.320081\pi$
$397$	17.0072	+	2.06505i	0.853567	+	0.103642i	0.317955	+	0.948106i	$0.397004\pi$
$398$	−3.65365	+	14.8234i	−0.183141	+	0.743031i
$399$	3.96035	+	2.07855i	0.198265	+	0.104058i
$400$	4.23472	−	34.8760i	0.211736	−	1.74380i
$401$	−39.1398	+	4.75243i	−1.95455	+	0.237325i	−0.998447	−	0.0557158i	$-0.982256\pi$
$401$	−39.1398	+	4.75243i	−1.95455	+	0.237325i	−0.956100	+	0.293041i	$0.905333\pi$
$402$	−7.60910	+	11.0237i	−0.379507	+	0.549811i
$403$	11.6636	+	3.05050i	0.581003	+	0.151956i
$404$	−5.50549	−	7.97608i	−0.273908	−	0.396825i
$405$	−16.2259	−	18.3152i	−0.806271	−	0.910092i
$406$	0.416147	+	0.102571i	0.0206530	+	0.00509051i
$407$	0.709601	+	1.02803i	0.0351736	+	0.0509578i
$408$			33.0898i			1.63819i
$409$	−0.142311	+	0.0982305i	−0.00703685	+	0.00485718i	−0.571578	−	0.820548i	$-0.693669\pi$
$409$	−0.142311	+	0.0982305i	−0.00703685	+	0.00485718i	0.564541	+	0.825405i	$0.309053\pi$
$410$	−22.8842	+	2.77864i	−1.13017	+	0.137227i
$411$	−15.0696	+	5.71514i	−0.743328	+	0.281907i
$412$	1.23834	−	10.1986i	0.0610084	−	0.502450i
$413$	−0.283204	−	0.746747i	−0.0139355	−	0.0367450i
$414$	−30.2745	+	34.1729i	−1.48791	+	1.67950i
$415$	20.7869	+	18.4156i	1.02039	+	0.903987i
$416$	9.62390	+	8.77219i	0.471850	+	0.430092i
$417$	3.80588	−	3.37172i	0.186375	−	0.165114i
$418$		−	34.0889i		−	1.66734i
$419$	−10.3046	−	9.12906i	−0.503411	−	0.445984i	0.372799	−	0.927912i	$-0.378398\pi$
$419$	−10.3046	−	9.12906i	−0.503411	−	0.445984i	−0.876211	+	0.481928i	$0.839937\pi$
$420$	−1.63297	+	0.402491i	−0.0796808	+	0.0196396i
$421$	−0.748453	−	0.516620i	−0.0364774	−	0.0251785i	0.549687	−	0.835371i	$-0.314747\pi$
$421$	−0.748453	−	0.516620i	−0.0364774	−	0.0251785i	−0.586164	+	0.810192i	$0.699363\pi$
$422$	−0.714014	+	0.270790i	−0.0347577	+	0.0131818i
$423$	−5.62272	+	2.13242i	−0.273386	+	0.103682i
$424$	20.9454	+	14.4576i	1.01720	+	0.702123i
$425$	−41.3422	+	10.1899i	−2.00539	+	0.494284i
$426$	−3.33564	−	2.95512i	−0.161612	−	0.143176i
$427$		−	1.32905i		−	0.0643171i
$428$	−4.20657	+	3.72670i	−0.203332	+	0.180137i
$429$	−27.9386	+	14.1627i	−1.34889	+	0.683784i
$430$	−26.6038	−	23.5689i	−1.28295	−	1.13659i
$431$	−22.3509	+	25.2289i	−1.07660	+	1.21523i	−0.101187	+	0.994867i	$0.532264\pi$
$431$	−22.3509	+	25.2289i	−1.07660	+	1.21523i	−0.975417	+	0.220367i	$0.929274\pi$
$432$	−2.48307	−	6.54733i	−0.119467	−	0.315008i
$433$	−3.61256	+	29.7521i	−0.173609	+	1.42980i	0.601957	+	0.798529i	$0.294388\pi$
$433$	−3.61256	+	29.7521i	−0.173609	+	1.42980i	−0.775565	+	0.631267i	$0.782535\pi$
$434$	1.44689	−	0.548731i	0.0694527	−	0.0263400i
$435$	−8.22082	+	0.998188i	−0.394158	+	0.0478595i
$436$	6.52368	−	4.50297i	0.312427	−	0.215653i
$437$		−	48.3990i		−	2.31524i
$438$	−21.7612	−	31.5265i	−1.03979	−	1.50640i
$439$	37.3593	+	9.20824i	1.78306	+	0.439485i	0.986321	−	0.164837i	$-0.0527097\pi$
$439$	37.3593	+	9.20824i	1.78306	+	0.439485i	0.796740	+	0.604322i	$0.206556\pi$
$440$	−17.1318	−	19.3378i	−0.816728	−	0.921895i
$441$	13.9916	+	20.2703i	0.666266	+	0.965253i
$442$	12.8171	−	32.4054i	0.609647	−	1.54137i
$443$	−5.44942	+	7.89485i	−0.258910	+	0.375096i	−0.930784	−	0.365570i	$-0.880874\pi$
$443$	−5.44942	+	7.89485i	−0.258910	+	0.375096i	0.671874	+	0.740665i	$0.265490\pi$
$444$	0.620995	−	0.0754024i	0.0294711	−	0.00357844i
$445$	1.92199	−	15.8290i	0.0911110	−	0.750367i
$446$	−5.86154	−	3.07638i	−0.277552	−	0.145671i
$447$	−1.68415	+	6.83286i	−0.0796575	+	0.323183i
$448$	−1.09206	−	0.132600i	−0.0515951	−	0.00626478i
$449$	3.92994	−	4.43598i	0.185465	−	0.209347i	−0.648423	−	0.761280i	$-0.724571\pi$
$449$	3.92994	−	4.43598i	0.185465	−	0.209347i	0.833888	+	0.551933i	$0.186110\pi$
$450$	34.3704	−	23.7242i	1.62024	−	1.11837i
$451$	−7.79602	+	11.2945i	−0.367100	+	0.531836i
$452$	9.19971	−	2.26753i	0.432718	−	0.106655i
$453$	20.7494	+	2.51943i	0.974891	+	0.118373i
$454$	35.5961	−	18.6823i	1.67061	−	0.876802i
$455$	−3.53736	−	0.480395i	−0.165834	−	0.0225213i
$456$	30.4655	+	15.9895i	1.42668	+	0.748777i
$457$	10.4070	+	7.18345i	0.486820	+	0.336028i	0.786060	−	0.618150i	$-0.212118\pi$
$457$	10.4070	+	7.18345i	0.486820	+	0.336028i	−0.299240	+	0.954178i	$0.596733\pi$
$458$	−3.48927	+	5.05508i	−0.163043	+	0.236208i
$459$	−6.35240	+	5.62773i	−0.296505	+	0.262680i
$460$	12.0684	+	13.6224i	0.562691	+	0.635147i
$461$	−14.2004	−	5.38550i	−0.661379	−	0.250828i	0.000997050	−	1.00000i	$-0.499683\pi$
$461$	−14.2004	−	5.38550i	−0.661379	−	0.250828i	−0.662376	+	0.749172i	$0.730452\pi$
$462$	−1.86843	+	3.56000i	−0.0869274	+	0.165626i
$463$	8.62303	+	3.27028i	0.400746	+	0.151983i	0.546740	−	0.837303i	$-0.315869\pi$
$463$	8.62303	+	3.27028i	0.400746	+	0.151983i	−0.145994	+	0.989286i	$0.546638\pi$
$464$	4.39405	+	1.08303i	0.203988	+	0.0502786i
$465$	−22.3796	+	19.8266i	−1.03783	+	0.919438i
$466$	−8.55889	+	5.90778i	−0.396483	+	0.273673i
$467$	−1.86972	−	4.93005i	−0.0865203	−	0.228135i	0.884772	−	0.466024i	$-0.154314\pi$
$467$	−1.86972	−	4.93005i	−0.0865203	−	0.228135i	−0.971292	+	0.237889i	$0.923545\pi$
$468$	−0.120442	+	8.51122i	−0.00556743	+	0.393431i
$469$	−0.322271	+	0.849760i	−0.0148811	+	0.0392383i
$470$	2.30360	+	9.34608i	0.106257	+	0.431102i
$471$	5.26212	−	2.76177i	0.242466	−	0.127256i
$472$	−2.17858	−	5.74444i	−0.100277	−	0.264409i
$473$	−21.0053	+	2.55050i	−0.965823	+	0.117272i
$474$	−50.1026	−	34.5833i	−2.30129	−	1.58846i
$475$	−10.5954	+	42.9872i	−0.486151	+	1.97239i
$476$	−0.266581	−	1.08156i	−0.0122187	−	0.0495733i
$477$	5.00552	+	41.2242i	0.229187	+	1.88753i
$478$	−10.9552	+	28.8866i	−0.501081	+	1.32124i
$479$	−5.96736	+	24.2105i	−0.272656	+	1.10621i	0.661672	+	0.749793i	$0.269847\pi$
$479$	−5.96736	+	24.2105i	−0.272656	+	1.10621i	−0.934328	+	0.356415i	$0.883999\pi$
$480$	−31.3563	+	7.72864i	−1.43121	+	0.352763i
$481$	1.28458	+	0.335970i	0.0585717	+	0.0153189i
$482$	37.6327	+	9.27562i	1.71412	+	0.422493i
$483$	−2.65278	+	5.05445i	−0.120706	+	0.229985i
$484$	0.335513			0.0152506
$485$	23.8169			1.08147
$486$	−16.8734	+	32.1496i	−0.765394	+	1.45834i
$487$	11.5509	+	13.0383i	0.523422	+	0.590822i	0.949462	−	0.313883i	$-0.101630\pi$
$487$	11.5509	+	13.0383i	0.523422	+	0.590822i	−0.426039	+	0.904705i	$0.640091\pi$
$488$		−	10.2239i		−	0.462813i
$489$	28.0379	−	31.6482i	1.26792	−	1.43118i
$490$	34.9096	−	18.3220i	1.57706	−	0.827703i
$491$	−0.927102	−	7.63537i	−0.0418395	−	0.344579i	−0.998563	−	0.0535822i	$-0.982936\pi$
$491$	−0.927102	−	7.63537i	−0.0418395	−	0.344579i	0.956724	−	0.290997i	$-0.0939870\pi$
$492$	3.19388	+	6.08544i	0.143991	+	0.274353i
$493$	−0.661128	−	5.44488i	−0.0297757	−	0.245225i
$494$	−23.6419	−	27.4594i	−1.06370	−	1.23545i
$495$	5.08114	−	41.8470i	0.228380	−	1.88088i
$496$	15.2775	−	5.79399i	0.685980	−	0.260158i
$497$	−0.267726	−	0.140513i	−0.0120091	−	0.00630288i
$498$	11.7892	−	31.0856i	0.528288	−	1.39298i
$499$	17.0790	+	32.5413i	0.764560	+	1.45675i	0.885772	+	0.464121i	$0.153630\pi$
$499$	17.0790	+	32.5413i	0.764560	+	1.45675i	−0.121211	+	0.992627i	$0.538678\pi$
$500$	−2.35617	−	4.48930i	−0.105371	−	0.200768i
$501$	6.45446	+	26.1868i	0.288364	+	1.16994i
$502$	−10.8444	−	1.31675i	−0.484011	−	0.0587696i
$503$	27.5117	+	24.3732i	1.22668	+	1.08675i	0.993443	+	0.114329i	$0.0364717\pi$
$503$	27.5117	+	24.3732i	1.22668	+	1.08675i	0.233242	+	0.972419i	$0.425067\pi$
$504$	−1.25091	−	1.81226i	−0.0557201	−	0.0807246i
$505$	47.7020	+	18.0910i	2.12271	+	0.805037i
$506$	43.5064			1.93410
$507$	−12.6827	+	30.7848i	−0.563260	+	1.36720i
$508$	−6.61377			−0.293439
$509$	−18.8546	−	7.15061i	−0.835716	−	0.316945i	−0.100634	−	0.994924i	$-0.532087\pi$
$509$	−18.8546	−	7.15061i	−0.835716	−	0.316945i	−0.735082	+	0.677978i	$0.762856\pi$
$510$	49.0945	+	71.1257i	2.17394	+	3.14950i
$511$	−1.94547	−	1.72354i	−0.0860626	−	0.0762448i
$512$	−3.64496	−	0.442578i	−0.161086	−	0.0195594i
$513$	2.11182	+	8.56800i	0.0932392	+	0.378287i
$514$	−12.7743	−	24.3394i	−0.563450	−	1.07356i
$515$	25.1323	+	47.8856i	1.10746	+	2.11009i
$516$	−3.75751	+	9.90775i	−0.165415	+	0.436164i
$517$	5.07416	+	2.66313i	0.223161	+	0.117124i
$518$	0.159354	−	0.0604351i	0.00700163	−	0.00265537i
$519$	−0.943178	+	7.76777i	−0.0414009	+	0.340967i
$520$	−27.2116	−	3.69550i	−1.19331	−	0.162058i
$521$	−3.99686	−	32.9171i	−0.175106	−	1.44213i	−0.769857	−	0.638216i	$-0.779673\pi$
$521$	−3.99686	−	32.9171i	−0.175106	−	1.44213i	0.594751	−	0.803910i	$-0.297251\pi$
$522$	2.50008	+	4.76351i	0.109426	+	0.208493i
$523$	1.92350	+	15.8415i	0.0841089	+	0.692699i	0.972384	+	0.233387i	$0.0749810\pi$
$523$	1.92350	+	15.8415i	0.0841089	+	0.692699i	−0.888275	+	0.459312i	$0.848096\pi$
$524$	−0.773403	+	0.405913i	−0.0337862	+	0.0177324i
$525$	3.46267	−	3.90854i	0.151123	−	0.170583i
$526$			22.5051i			0.981268i
$527$	−13.1317	−	14.8227i	−0.572027	−	0.645685i
$528$	−19.7286	+	37.5897i	−0.858576	+	1.63588i
$529$	38.7699			1.68565
$530$	66.4721			2.88736
$531$	4.65860	−	8.87621i	0.202166	−	0.385195i
$532$	−1.12460	−	0.277189i	−0.0487576	−	0.0120177i
$533$	1.55327	+	14.5048i	0.0672797	+	0.628272i
$534$	−18.5342	+	4.56826i	−0.802052	+	0.197688i
$535$	7.07979	−	28.7238i	0.306086	−	1.24184i
$536$	−2.47911	+	6.53689i	−0.107081	+	0.282350i
$537$	−7.34990	−	60.5319i	−0.317172	−	2.61214i
$538$	5.36037	+	21.7479i	0.231102	+	0.937617i
$539$	5.61708	−	22.7894i	0.241945	−	0.981608i
$540$	−2.73084	−	1.88496i	−0.117517	−	0.0811160i
$541$	−33.1322	+	4.02298i	−1.42447	+	0.172962i	−0.796199	−	0.605035i	$-0.793159\pi$
$541$	−33.1322	+	4.02298i	−1.42447	+	0.172962i	−0.628268	+	0.777997i	$0.716236\pi$
$542$	10.7912	+	28.4540i	0.463521	+	1.22220i
$543$	−53.2926	+	27.9701i	−2.28701	+	1.20031i
$544$	−5.11889	−	20.7682i	−0.219471	−	0.890428i
$545$	−14.7967	+	39.0157i	−0.633821	+	1.67125i
$546$	0.963928	+	4.16349i	0.0412523	+	0.178181i
$547$	−15.7957	−	41.6500i	−0.675377	−	1.78082i	−0.623034	−	0.782195i	$-0.714100\pi$
$547$	−15.7957	−	41.6500i	−0.675377	−	1.78082i	−0.0523431	−	0.998629i	$-0.516669\pi$
$548$	3.43488	−	2.37093i	0.146731	−	0.101281i
$549$	12.4866	−	11.0622i	0.532916	−	0.472123i
$550$	−38.6418	−	9.52434i	−1.64769	−	0.406119i
$551$	−5.33251	−	2.02236i	−0.227173	−	0.0861552i
$552$	−20.4068	+	38.8820i	−0.868572	+	1.65493i
$553$	−3.86215	−	1.46472i	−0.164236	−	0.0622863i
$554$	4.48234	+	5.05951i	0.190436	+	0.214958i
$555$	−2.46481	+	2.18363i	−0.104625	+	0.0926899i
$556$	−0.747986	+	1.08365i	−0.0317217	+	0.0459568i
$557$	−7.42352	−	5.12409i	−0.314545	−	0.217115i	0.400323	−	0.916374i	$-0.368898\pi$
$557$	−7.42352	−	5.12409i	−0.314545	−	0.217115i	−0.714868	+	0.699259i	$0.753513\pi$
$558$	17.1984	+	9.02643i	0.728068	+	0.382119i
$559$	−15.1513	+	16.6224i	−0.640833	+	0.703053i
$560$	−4.28400	+	2.24842i	−0.181032	+	0.0950129i
$561$	51.0762	+	6.20177i	2.15644	+	0.261839i
$562$	−44.3985	+	10.9432i	−1.87284	+	0.461613i
$563$	−4.26768	+	6.18281i	−0.179861	+	0.260574i	−0.902536	−	0.430614i	$-0.858297\pi$
$563$	−4.26768	+	6.18281i	−0.179861	+	0.260574i	0.722675	+	0.691188i	$0.242912\pi$
$564$	2.36177	−	1.63021i	0.0994486	−	0.0686444i
$565$	−33.0745	+	37.3334i	−1.39146	+	1.57063i
$566$	−20.4640	−	2.48478i	−0.860167	−	0.104443i
$567$	−0.475637	+	1.92973i	−0.0199749	+	0.0810412i
$568$	−2.05951	−	1.08092i	−0.0864153	−	0.0453542i
$569$	0.399552	−	3.29061i	0.0167501	−	0.137950i	−0.981935	−	0.189220i	$-0.939404\pi$
$569$	0.399552	−	3.29061i	0.0167501	−	0.137950i	0.998685	+	0.0512706i	$0.0163271\pi$
$570$	89.2080	−	10.8318i	3.73651	−	0.453695i
$571$	5.59256	−	8.10222i	0.234041	−	0.339067i	−0.688312	−	0.725415i	$-0.741648\pi$
$571$	5.59256	−	8.10222i	0.234041	−	0.339067i	0.922353	+	0.386347i	$0.126263\pi$
$572$	6.14710	−	5.29252i	0.257023	−	0.221291i
$573$	−8.70683	−	12.6140i	−0.363733	−	0.526958i
$574$	1.24165	+	1.40153i	0.0518253	+	0.0584986i
$575$	−54.8631	−	13.5225i	−2.28795	−	0.563929i
$576$	−7.84386	−	11.3638i	−0.326827	−	0.473491i
$577$			7.52437i			0.313244i	0.987659	+	0.156622i	$0.0500604\pi$
$577$			7.52437i			0.313244i	−0.987659	+	0.156622i	$0.949940\pi$
$578$	−24.2764	+	16.7568i	−1.00977	+	0.696991i
$579$	35.5321	−	4.31438i	1.47667	−	0.179300i
$580$	2.00517	−	0.760460i	0.0832601	−	0.0315764i
$581$	0.271895	−	2.23926i	0.0112801	−	0.0929001i
$582$	−10.1106	−	26.6596i	−0.419099	−	1.10507i
$583$	26.2418	−	29.6209i	1.08683	−	1.22677i
$584$	−14.9658	−	13.2585i	−0.619288	−	0.548642i
$585$	−24.9294	−	37.2326i	−1.03071	−	1.53938i
$586$	−16.5919	+	14.6992i	−0.685406	+	0.607217i
$587$		−	28.1651i		−	1.16250i	−0.813726	−	0.581248i	$-0.802565\pi$
$587$		−	28.1651i		−	1.16250i	0.813726	−	0.581248i	$-0.197435\pi$
$588$	−8.79806	−	7.79441i	−0.362826	−	0.321436i
$589$	−19.9925	+	4.92772i	−0.823778	+	0.203043i
$590$	−13.2057	−	9.11523i	−0.543670	−	0.375268i
$591$	5.80000	−	2.19965i	0.238580	−	0.0904815i
$592$	1.68260	−	0.638128i	0.0691546	−	0.0262269i
$593$	25.4983	+	17.6002i	1.04709	+	0.722754i	0.961842	−	0.273606i	$-0.0882163\pi$
$593$	25.4983	+	17.6002i	1.04709	+	0.722754i	0.0852481	+	0.996360i	$0.472832\pi$
$594$	−7.70188	+	1.89834i	−0.316012	+	0.0778900i
$595$	4.38910	+	3.88840i	0.179935	+	0.159409i
$596$		−	1.82242i		−	0.0746491i
$597$	−17.9343	+	15.8884i	−0.734000	+	0.650267i
$598$	35.0454	−	30.1733i	1.43311	−	1.23388i
$599$	−5.35973	−	4.74831i	−0.218993	−	0.194011i	0.546493	−	0.837464i	$-0.315963\pi$
$599$	−5.35973	−	4.74831i	−0.218993	−	0.194011i	−0.765485	+	0.643453i	$0.777501\pi$
$600$	26.6370	−	30.0670i	1.08745	−	1.22748i
$601$	2.47018	+	6.51334i	0.100761	+	0.265685i	0.975912	−	0.218165i	$-0.0700072\pi$
$601$	2.47018	+	6.51334i	0.100761	+	0.265685i	−0.875151	+	0.483850i	$0.839238\pi$
$602$	−0.347980	+	2.86587i	−0.0141826	+	0.116804i
$603$	−10.6660	+	4.04509i	−0.434354	+	0.164729i
$604$	−5.37333	+	0.652441i	−0.218638	+	0.0265474i
$605$	−1.45352	+	1.00329i	−0.0590938	+	0.0407895i
$606$		−	61.0752i		−	2.48101i
$607$	−6.40415	−	9.27801i	−0.259936	−	0.376583i	0.671187	−	0.741289i	$-0.265785\pi$
$607$	−6.40415	−	9.27801i	−0.259936	−	0.376583i	−0.931123	+	0.364706i	$0.881170\pi$
$608$	−21.5946	−	5.32259i	−0.875776	−	0.215859i
$609$	0.446043	+	0.503479i	0.0180746	+	0.0204020i
$610$	−15.1689	−	21.9759i	−0.614171	−	0.889780i
$611$	5.93432	−	1.37391i	0.240077	−	0.0555825i
$612$	7.94260	−	11.5068i	0.321060	−	0.465136i
$613$	32.3681	−	3.93020i	1.30733	−	0.158739i	0.562950	−	0.826491i	$-0.309666\pi$
$613$	32.3681	−	3.93020i	1.30733	−	0.158739i	0.744384	+	0.667752i	$0.232743\pi$
$614$	−0.0157785	+	0.129947i	−0.000636768	+	0.00524425i
$615$	−32.0340	−	16.8127i	−1.29173	−	0.677954i
$616$	−0.502193	+	2.03748i	−0.0202339	+	0.0820924i
$617$	23.6755	+	2.87473i	0.953141	+	0.115732i	0.582309	−	0.812968i	$-0.302149\pi$
$617$	23.6755	+	2.87473i	0.953141	+	0.115732i	0.370832	+	0.928700i	$0.379073\pi$
$618$	42.9319	−	48.4601i	1.72697	−	1.94935i
$619$	−0.666403	+	0.459985i	−0.0267850	+	0.0184883i	−0.581382	−	0.813631i	$-0.697488\pi$
$619$	−0.666403	+	0.459985i	−0.0267850	+	0.0184883i	0.554597	+	0.832119i	$0.312872\pi$
$620$	4.39837	−	6.37213i	0.176643	−	0.255911i
$621$	−10.9350	+	2.69524i	−0.438808	+	0.108156i
$622$	−29.8385	−	3.62304i	−1.19641	−	0.145271i
$623$	−1.14680	+	0.601888i	−0.0459457	+	0.0241141i
$624$	10.1780	+	43.9618i	0.407446	+	1.75988i
$625$	−8.19809	−	4.30269i	−0.327923	−	0.172107i
$626$	3.21627	+	2.22003i	0.128548	+	0.0887302i
$627$	30.3907	−	44.0285i	1.21369	−	1.75833i
$628$	−1.15194	+	1.02053i	−0.0459674	+	0.0407236i
$629$	−1.44628	−	1.63251i	−0.0576669	−	0.0650924i
$630$	−5.37762	−	2.03946i	−0.214249	−	0.0812541i
$631$	−8.92606	+	17.0072i	−0.355341	+	0.677046i	−0.995860	−	0.0908964i	$-0.971027\pi$
$631$	−8.92606	+	17.0072i	−0.355341	+	0.677046i	0.640519	+	0.767942i	$0.278719\pi$
$632$	−29.7101	−	11.2676i	−1.18180	−	0.448199i
$633$	−1.16362	−	0.286806i	−0.0462497	−	0.0113995i
$634$	−15.7939	+	13.9922i	−0.627255	+	0.555700i
$635$	28.6523	−	19.7773i	1.13703	−	0.784836i
$636$	−7.02740	−	18.5297i	−0.278655	−	0.734752i
$637$	−11.2806	−	22.2530i	−0.446953	−	0.881696i
$638$	1.81792	−	4.79346i	0.0719721	−	0.189775i
$639$	−0.908240	−	3.68488i	−0.0359294	−	0.145771i
$640$	−41.9010	+	21.9914i	−1.65628	+	0.869285i
$641$	10.7201	+	28.2666i	0.423418	+	1.11646i	0.961798	+	0.273760i	$0.0882673\pi$
$641$	10.7201	+	28.2666i	0.423418	+	1.11646i	−0.538380	+	0.842702i	$0.680963\pi$
$642$	−35.1576	+	4.26890i	−1.38756	+	0.168480i
$643$	−2.69124	−	1.85763i	−0.106132	−	0.0732578i	0.513816	−	0.857900i	$-0.328231\pi$
$643$	−2.69124	−	1.85763i	−0.106132	−	0.0732578i	−0.619949	+	0.784642i	$0.712847\pi$
$644$	0.353766	−	1.43529i	0.0139403	−	0.0565582i
$645$	−13.3489	−	54.1587i	−0.525613	−	2.13250i
$646$	7.17421	+	59.0849i	0.282265	+	2.32466i
$647$	12.6448	−	33.3415i	0.497117	−	1.31079i	−0.418310	−	0.908305i	$-0.637377\pi$
$647$	12.6448	−	33.3415i	0.497117	−	1.31079i	0.915427	−	0.402485i	$-0.131854\pi$
$648$	−3.65890	+	14.8447i	−0.143735	+	0.583156i
$649$	−9.27522	+	2.28614i	−0.364084	+	0.0897387i
$650$	−37.7323	+	19.1274i	−1.47998	+	0.750239i
$651$	2.35797	+	0.581187i	0.0924161	+	0.0227785i
$652$	−5.08843	+	9.69519i	−0.199278	+	0.379693i
$653$	21.1172			0.826380			0.413190	−	0.910645i	$-0.364415\pi$
$653$	21.1172			0.826380			0.413190	+	0.910645i	$0.364415\pi$
$654$	49.9538			1.95335
$655$	2.13674	−	4.07122i	0.0834894	−	0.159076i
$656$	13.1104	+	14.7986i	0.511875	+	0.577787i
$657$		−	32.6237i		−	1.27277i
$658$	0.518465	−	0.585227i	0.0202119	−	0.0228145i
$659$	7.40928	−	3.88869i	0.288624	−	0.151482i	−0.314197	−	0.949358i	$-0.601735\pi$
$659$	7.40928	−	3.88869i	0.288624	−	0.151482i	0.602822	+	0.797876i	$0.294043\pi$
$660$	2.42483	+	19.9703i	0.0943864	+	0.777342i
$661$	5.39333	+	10.2761i	0.209776	+	0.399695i	0.967497	−	0.252884i	$-0.0813792\pi$
$661$	5.39333	+	10.2761i	0.209776	+	0.399695i	−0.757720	+	0.652579i	$0.773687\pi$
$662$	4.07224	+	33.5379i	0.158272	+	1.30349i
$663$	45.4441	−	30.4275i	1.76490	−	1.18171i
$664$	2.09159	−	17.2258i	0.0811694	−	0.668490i
$665$	5.70089	−	2.16206i	0.221071	−	0.0838412i
$666$	1.89417	+	0.994136i	0.0733975	+	0.0385220i
$667$	2.58106	−	6.80569i	0.0999390	−	0.263517i
$668$	−3.24580	−	6.18435i	−0.125584	−	0.239280i
$669$	−4.82802	−	9.19903i	−0.186662	−	0.355655i
$670$	4.36982	+	17.7291i	0.168821	+	0.684934i
$671$	−15.7812	−	1.91618i	−0.609225	−	0.0739733i
$672$	1.96345	+	1.73947i	0.0757418	+	0.0671014i
$673$	12.2999	+	17.8195i	0.474126	+	0.686890i	0.984959	−	0.172790i	$-0.0552782\pi$
$673$	12.2999	+	17.8195i	0.474126	+	0.686890i	−0.510833	+	0.859680i	$0.670663\pi$
$674$	16.7566	+	6.35495i	0.645442	+	0.244784i
$675$	10.3024			0.396538
$676$	1.28107	−	8.52648i	0.0492719	−	0.327942i
$677$	−29.4125			−1.13042			−0.565208	−	0.824948i	$-0.691204\pi$
$677$	−29.4125			−1.13042			−0.565208	+	0.824948i	$0.691204\pi$
$678$	55.8300	+	21.1735i	2.14414	+	0.813164i
$679$	−1.09894	−	1.59209i	−0.0421734	−	0.0610987i
$680$	33.7637	+	29.9120i	1.29478	+	1.14707i
$681$	62.6307	+	7.60474i	2.40001	+	0.291414i
$682$	−4.42959	−	17.9715i	−0.169618	−	0.688166i
$683$	−12.4366	−	23.6960i	−0.475875	−	0.906703i	−0.998532	−	0.0541606i	$-0.982752\pi$
$683$	−12.4366	−	23.6960i	−0.475875	−	0.906703i	0.522658	−	0.852543i	$-0.324941\pi$
$684$	−6.75625	−	12.8730i	−0.258332	−	0.492210i
$685$	−7.79085	+	20.5428i	−0.297673	+	0.784899i
$686$	−5.70403	−	2.99370i	−0.217781	−	0.114300i
$687$	−9.01334	+	3.41831i	−0.343880	+	0.130417i
$688$	−3.67428	+	30.2604i	−0.140081	+	1.15367i
$689$	0.595189	−	42.0600i	0.0226749	−	1.60236i
$690$	13.8242	+	113.853i	0.526280	+	4.33431i
$691$	−9.82793	−	18.7256i	−0.373872	−	0.712354i	0.623725	−	0.781644i	$-0.285619\pi$
$691$	−9.82793	−	18.7256i	−0.373872	−	0.712354i	−0.997597	+	0.0692907i	$0.977926\pi$
$692$	−0.244248	−	2.01157i	−0.00928493	−	0.0764683i
$693$	−3.03179	+	1.59121i	−0.115168	+	0.0604449i
$694$	10.2267	−	11.5436i	0.388201	−	0.438188i
$695$		−	6.93130i		−	0.262919i
$696$	3.43124	+	3.87307i	0.130061	+	0.146808i
$697$	11.1355	−	21.2170i	0.421788	−	0.803650i
$698$	−49.5803			−1.87664
$699$	−16.3214			−0.617330
$700$	−0.628420	+	1.19735i	−0.0237520	+	0.0452557i
$701$	−42.8776	−	10.5684i	−1.61946	−	0.399162i	−0.677674	−	0.735363i	$-0.737012\pi$
$701$	−42.8776	−	10.5684i	−1.61946	−	0.399162i	−0.941790	+	0.336201i	$0.890858\pi$
$702$	−4.88746	+	6.87069i	−0.184465	+	0.259318i
$703$	−2.20190	+	0.542720i	−0.0830462	+	0.0204691i
$704$	−3.14900	+	12.7760i	−0.118683	+	0.481514i
$705$	−5.35687	+	14.1249i	−0.201751	+	0.531974i
$706$	−6.09076	−	50.1619i	−0.229229	−	1.88787i
$707$	−0.991695	−	4.02346i	−0.0372965	−	0.151318i
$708$	−1.14486	+	4.64487i	−0.0430264	+	0.174565i
$709$	−8.90160	−	6.14433i	−0.334307	−	0.230755i	0.389071	−	0.921208i	$-0.372796\pi$
$709$	−8.90160	−	6.14433i	−0.334307	−	0.230755i	−0.723378	+	0.690453i	$0.757411\pi$
$710$	−6.03060	+	0.732247i	−0.226324	+	0.0274808i
$711$	−18.3849	−	48.4771i	−0.689489	−	1.81803i
$712$	−8.82192	+	4.63010i	−0.330615	+	0.173520i
$713$	−6.28907	−	25.5157i	−0.235527	−	0.955572i
$714$	2.48926	−	6.56363i	0.0931581	−	0.245638i
$715$	−10.8043	+	41.3101i	−0.404058	+	1.54491i
$716$	5.59945	+	14.7645i	0.209261	+	0.551776i
$717$	−39.9023	+	27.5426i	−1.49018	+	1.02860i
$718$	10.3188	−	9.14162i	0.385092	−	0.341162i
$719$	5.84984	+	1.44186i	0.218162	+	0.0537722i	0.346882	−	0.937909i	$-0.387241\pi$
$719$	5.84984	+	1.44186i	0.218162	+	0.0537722i	−0.128719	+	0.991681i	$0.541087\pi$
$720$	−56.7816	−	21.5344i	−2.11613	−	0.802541i
$721$	2.04137	−	3.88951i	0.0760247	−	0.144853i
$722$	28.8736	+	10.9503i	1.07456	+	0.407528i
$723$	40.3363	+	45.5302i	1.50012	+	1.69329i
$724$	11.6664	−	10.3355i	0.433578	−	0.384117i
$725$	−3.78235	+	5.47967i	−0.140473	+	0.203510i
$726$	1.74008	+	1.20109i	0.0645803	+	0.0445765i
$727$	−1.06332	−	0.558071i	−0.0394362	−	0.0206977i	0.444890	−	0.895585i	$-0.353243\pi$
$727$	−1.06332	−	0.558071i	−0.0394362	−	0.0206977i	−0.484326	+	0.874888i	$0.660935\pi$
$728$	1.00854	+	1.98952i	0.0373789	+	0.0737366i
$729$	−31.8382	+	16.7100i	−1.17919	+	0.618887i
$730$	−51.8399	−	6.29451i	−1.91868	−	0.232970i
$731$	35.8708	−	8.84136i	1.32673	−	0.327009i
$732$	−4.52236	+	6.55177i	−0.167151	+	0.242160i
$733$	−12.9638	+	8.94830i	−0.478831	+	0.330513i	−0.782911	−	0.622133i	$-0.786266\pi$
$733$	−12.9638	+	8.94830i	−0.478831	+	0.330513i	0.304081	+	0.952646i	$0.401651\pi$
$734$	22.2397	−	25.1034i	0.820881	−	0.926583i
$735$	61.4229	+	7.45809i	2.26562	+	0.275096i
$736$	6.79303	−	27.5604i	0.250394	−	1.01589i
$737$	9.62545	+	5.05183i	0.354558	+	0.186086i
$738$	−2.83289	+	23.3309i	−0.104280	+	0.858824i
$739$	16.5014	−	2.00364i	0.607016	−	0.0737050i	0.188743	−	0.982027i	$-0.439559\pi$
$739$	16.5014	−	2.00364i	0.607016	−	0.0737050i	0.418273	+	0.908322i	$0.362636\pi$
$740$	0.484419	−	0.701802i	0.0178076	−	0.0257988i
$741$	−6.05502	−	56.5430i	−0.222437	−	2.07716i
$742$	−3.06709	−	4.44345i	−0.112597	−	0.163124i
$743$	14.6194	+	16.5019i	0.536334	+	0.605396i	0.952741	−	0.303782i	$-0.0982495\pi$
$743$	14.6194	+	16.5019i	0.536334	+	0.605396i	−0.416408	+	0.909178i	$0.636711\pi$
$744$	18.1390	+	4.47086i	0.665007	+	0.163910i
$745$	5.44960	+	7.89511i	0.199658	+	0.289255i
$746$			54.4808i			1.99468i
$747$	23.3013	−	16.0837i	0.852550	−	0.588473i
$748$	−13.2269	+	1.60603i	−0.483622	+	0.0587223i
$749$	−2.24677	+	0.852086i	−0.0820951	+	0.0311346i
$750$	3.85122	−	31.7176i	0.140627	−	1.15816i
$751$	−13.1273	−	34.6139i	−0.479022	−	1.26308i	−0.929014	−	0.370045i	$-0.879342\pi$
$751$	−13.1273	−	34.6139i	−0.479022	−	1.26308i	0.449991	−	0.893033i	$-0.351427\pi$
$752$	5.47442	−	6.17934i	0.199631	−	0.225337i
$753$	−12.8326	−	11.3687i	−0.467644	−	0.414297i
$754$	−1.86007	−	5.12203i	−0.0677396	−	0.186533i
$755$	21.3274	−	18.8945i	0.776185	−	0.687640i
$756$			0.269523i			0.00980244i
$757$	7.96363	+	7.05516i	0.289443	+	0.256424i	0.795331	−	0.606175i	$-0.207297\pi$
$757$	7.96363	+	7.05516i	0.289443	+	0.256424i	−0.505888	+	0.862599i	$0.668835\pi$
$758$	31.0338	−	7.64915i	1.12720	−	0.277830i
$759$	56.1920	+	38.7866i	2.03964	+	1.40786i
$760$	43.8548	−	16.6319i	1.59078	−	0.603304i
$761$	−12.2857	+	4.65934i	−0.445355	+	0.168901i	−0.567079	−	0.823663i	$-0.691927\pi$
$761$	−12.2857	+	4.65934i	−0.445355	+	0.168901i	0.121725	+	0.992564i	$0.461158\pi$
$762$	−34.3011	−	23.6763i	−1.24260	−	0.857702i
$763$	3.29081	−	0.811112i	0.119135	−	0.0293642i
$764$	2.97097	+	2.63205i	0.107486	+	0.0952243i
$765$			73.6010i			2.66105i
$766$	9.20739	−	8.15704i	0.332677	−	0.294726i
$767$	−5.88587	+

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)

\(f(q)\)	\(=\)	\(q+(-1.52590 - 0.578696i) q^{2} +(-1.45490 - 2.10779i) q^{3} +(0.496446 + 0.439813i) q^{4} +(-3.46589 - 0.420835i) q^{5} +(1.00026 + 4.05821i) q^{6} +(0.131788 + 0.251102i) q^{7} +(1.01380 + 1.93163i) q^{8} +(-1.26222 + 3.32819i) q^{9} +O(q^{10})\)	\(q+(-1.52590 - 0.578696i) q^{2} +(-1.45490 - 2.10779i) q^{3} +(0.496446 + 0.439813i) q^{4} +(-3.46589 - 0.420835i) q^{5} +(1.00026 + 4.05821i) q^{6} +(0.131788 + 0.251102i) q^{7} +(1.01380 + 1.93163i) q^{8} +(-1.26222 + 3.32819i) q^{9} +(5.04505 + 2.64785i) q^{10} +(3.17160 - 1.20283i) q^{11} +(0.204752 - 1.68629i) q^{12} +(1.72059 - 3.16853i) q^{13} +(-0.0557837 - 0.459420i) q^{14} +(4.15549 + 7.91763i) q^{15} +(-0.589014 - 4.85097i) q^{16} +(-5.24407 + 2.75230i) q^{17} +(3.85202 - 4.34804i) q^{18} +6.15812i q^{19} +(-1.53554 - 1.73326i) q^{20} +(0.337530 - 0.643110i) q^{21} -5.53561 q^{22} -7.85938 q^{23} +(2.59649 - 4.94720i) q^{24} +(6.98058 + 1.72056i) q^{25} +(-4.45905 + 3.83915i) q^{26} +(1.39133 - 0.342933i) q^{27} +(-0.0450120 + 0.182621i) q^{28} +(-0.328405 + 0.865932i) q^{29} +(-1.75895 - 14.4862i) q^{30} +(0.800199 + 3.24653i) q^{31} +(-0.864321 + 3.50669i) q^{32} +(-7.14968 - 4.93507i) q^{33} +(9.59464 - 1.16500i) q^{34} +(-0.351092 - 0.925752i) q^{35} +(-2.09040 + 1.09713i) q^{36} +(0.0881308 + 0.357561i) q^{37} +(3.56367 - 9.39664i) q^{38} +(-9.18187 + 0.983259i) q^{39} +(-2.70082 - 7.12147i) q^{40} +(-3.32971 + 2.29833i) q^{41} +(-0.887201 + 0.785991i) q^{42} +(-6.05675 - 1.49286i) q^{43} +(2.10355 + 0.797771i) q^{44} +(5.77533 - 11.0040i) q^{45} +(11.9926 + 4.54819i) q^{46} +(1.12029 + 1.26455i) q^{47} +(-9.36785 + 8.29919i) q^{48} +(3.93077 - 5.69470i) q^{49} +(-9.65596 - 6.66503i) q^{50} +(13.4309 + 7.04906i) q^{51} +(2.24774 - 0.816266i) q^{52} +(10.3302 - 5.42170i) q^{53} +(-2.32149 - 0.281879i) q^{54} +(-11.4986 + 2.83416i) q^{55} +(-0.351429 + 0.509133i) q^{56} +(12.9800 - 8.95945i) q^{57} +(1.00222 - 1.13128i) q^{58} +(-2.79572 - 0.339462i) q^{59} +(-1.41930 + 5.75832i) q^{60} +(-4.14978 - 2.17797i) q^{61} +(0.657736 - 5.41694i) q^{62} +(-1.00206 + 0.121672i) q^{63} +(-2.20364 + 3.19252i) q^{64} +(-7.29680 + 10.2577i) q^{65} +(8.05376 + 11.6679i) q^{66} +(2.12514 + 2.39879i) q^{67} +(-3.81389 - 0.940040i) q^{68} +(11.4346 + 16.5659i) q^{69} +1.61578i q^{70} +(-0.877468 + 0.605673i) q^{71} +(-7.70848 + 0.935979i) q^{72} +(-8.56965 + 3.25004i) q^{73} +(0.0724405 - 0.596601i) q^{74} +(-6.52948 - 17.2168i) q^{75} +(-2.70842 + 3.05717i) q^{76} +(0.720013 + 0.637876i) q^{77} +(14.5796 + 3.81316i) q^{78} +(-10.9025 + 9.65876i) q^{79} +17.0608i q^{80} +(5.24590 + 4.64746i) q^{81} +(6.41083 - 1.58013i) q^{82} +(-6.54622 - 4.51853i) q^{83} +(0.450413 - 0.170819i) q^{84} +(19.3336 - 7.33228i) q^{85} +(8.37806 + 5.78296i) q^{86} +(2.30300 - 0.567638i) q^{87} +(5.53879 + 4.90694i) q^{88} +4.56708i q^{89} +(-15.1805 + 13.4487i) q^{90} +(1.02238 + 0.0144676i) q^{91} +(-3.90176 - 3.45666i) q^{92} +(5.67879 - 6.41003i) q^{93} +(-0.977660 - 2.57788i) q^{94} +(2.59155 - 21.3434i) q^{95} +(8.64885 - 3.28008i) q^{96} +(-6.77197 + 0.822265i) q^{97} +(-9.29344 + 6.41480i) q^{98} +12.0739i 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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