LMFDB - Embedded newform 169.2.k.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(4,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.k (of order $78$, degree $24$, 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:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	169.127
Dual form			169.2.k.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81837 + 0.113576i) q^{2} +(0.467697 + 1.61468i) q^{3} +(5.93678 - 0.479267i) q^{4} +(1.59753 - 0.605865i) q^{5} +(-1.50153 - 4.49764i) q^{6} +(1.15667 - 2.71481i) q^{7} +(-11.0774 + 1.34504i) q^{8} +(0.147123 - 0.0930351i) q^{9} +O(q^{10})$	\(q+(-2.81837 + 0.113576i) q^{2} +(0.467697 + 1.61468i) q^{3} +(5.93678 - 0.479267i) q^{4} +(1.59753 - 0.605865i) q^{5} +(-1.50153 - 4.49764i) q^{6} +(1.15667 - 2.71481i) q^{7} +(-11.0774 + 1.34504i) q^{8} +(0.147123 - 0.0930351i) q^{9} +(-4.43363 + 1.88899i) q^{10} +(1.00246 - 1.58527i) q^{11} +(3.55048 + 9.36185i) q^{12} +(-1.18730 - 3.40445i) q^{13} +(-2.95159 + 7.78269i) q^{14} +(1.72544 + 2.29614i) q^{15} +(19.3096 - 3.13811i) q^{16} +(-0.139658 - 0.0595025i) q^{17} +(-0.404081 + 0.278917i) q^{18} +(3.60617 + 2.08202i) q^{19} +(9.19385 - 4.36253i) q^{20} +(4.92451 + 0.597944i) q^{21} +(-2.64526 + 4.58172i) q^{22} +(-0.549486 - 0.951737i) q^{23} +(-7.35269 - 17.2574i) q^{24} +(-1.55751 + 1.37983i) q^{25} +(3.73292 + 9.46015i) q^{26} +(3.99388 + 3.53827i) q^{27} +(5.56579 - 16.6716i) q^{28} +(0.145118 + 3.60106i) q^{29} +(-5.12371 - 6.27541i) q^{30} +(-3.40949 + 3.84852i) q^{31} +(-32.1985 + 6.57336i) q^{32} +(3.02854 + 0.877228i) q^{33} +(0.400364 + 0.151838i) q^{34} +(0.203016 - 5.03779i) q^{35} +(0.828850 - 0.622840i) q^{36} +(-3.51635 - 0.717868i) q^{37} +(-10.4000 - 5.45833i) q^{38} +(4.94180 - 3.50937i) q^{39} +(-16.8817 + 8.86018i) q^{40} +(-4.62982 + 1.34104i) q^{41} +(-13.9470 - 1.12592i) q^{42} +(0.658342 + 3.22477i) q^{43} +(5.19163 - 9.89182i) q^{44} +(0.178668 - 0.237764i) q^{45} +(1.65675 + 2.61994i) q^{46} +(7.83635 + 5.40904i) q^{47} +(14.0981 + 29.7110i) q^{48} +(-1.18322 - 1.23186i) q^{49} +(4.23292 - 4.06577i) q^{50} +(0.0307600 - 0.253331i) q^{51} +(-8.68040 - 19.6425i) q^{52} +(-0.943119 - 7.76728i) q^{53} +(-11.6581 - 9.51854i) q^{54} +(0.641010 - 3.13987i) q^{55} +(-9.16140 + 31.6288i) q^{56} +(-1.67520 + 6.79657i) q^{57} +(-0.817990 - 10.1326i) q^{58} +(0.889991 - 5.47633i) q^{59} +(11.3440 + 12.8048i) q^{60} +(-8.26450 - 6.21037i) q^{61} +(9.17210 - 11.2338i) q^{62} +(-0.0823991 - 0.507022i) q^{63} +(52.0117 - 12.8197i) q^{64} +(-3.95940 - 4.71939i) q^{65} +(-8.63518 - 2.12838i) q^{66} +(-1.16823 + 14.4711i) q^{67} +(-0.857634 - 0.286320i) q^{68} +(1.27976 - 1.33237i) q^{69} +14.2214i q^{70} +(-3.77271 - 3.62374i) q^{71} +(-1.50461 + 1.22848i) q^{72} +(-0.450298 - 0.857971i) q^{73} +(9.99190 + 1.62384i) q^{74} +(-2.95643 - 1.86953i) q^{75} +(22.4069 + 10.6322i) q^{76} +(-3.14417 - 4.55512i) q^{77} +(-13.5292 + 10.4520i) q^{78} +(-0.951562 + 1.37858i) q^{79} +(28.9464 - 16.7122i) q^{80} +(-3.62137 + 7.63188i) q^{81} +(12.8962 - 4.30539i) q^{82} +(2.87759 + 11.6748i) q^{83} +(29.5223 + 1.18971i) q^{84} +(-0.259158 - 0.0104437i) q^{85} +(-2.22171 - 9.01382i) q^{86} +(-5.74668 + 1.91853i) q^{87} +(-8.97244 + 18.9090i) q^{88} +(4.63954 - 2.67864i) q^{89} +(-0.476547 + 0.690398i) q^{90} +(-10.6158 - 0.714534i) q^{91} +(-3.71831 - 5.38691i) q^{92} +(-7.80874 - 3.70529i) q^{93} +(-22.7000 - 14.3546i) q^{94} +(7.02241 + 1.14125i) q^{95} +(-25.6730 - 48.9158i) q^{96} +(-6.11236 + 4.99059i) q^{97} +(3.47465 + 3.33745i) q^{98} -0.326493i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{77}{78}\right)$

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 $

$2$	−2.81837	+	0.113576i	−1.99289	+	0.0803106i	−0.999426	−	0.0338657i	$-0.989218\pi$
$2$	−2.81837	+	0.113576i	−1.99289	+	0.0803106i	−0.993461	+	0.114176i	$0.963577\pi$
$3$	0.467697	+	1.61468i	0.270025	+	0.932235i	0.974852	+	0.222855i	$0.0715378\pi$
$3$	0.467697	+	1.61468i	0.270025	+	0.932235i	−0.704826	+	0.709380i	$0.748975\pi$
$4$	5.93678	−	0.479267i	2.96839	−	0.239633i
$5$	1.59753	−	0.605865i	0.714439	−	0.270951i	0.0295140	−	0.999564i	$-0.490604\pi$
$5$	1.59753	−	0.605865i	0.714439	−	0.270951i	0.684925	+	0.728613i	$0.259835\pi$
$6$	−1.50153	−	4.49764i	−0.612998	−	1.83615i
$7$	1.15667	−	2.71481i	0.437181	−	1.02610i	−0.545047	−	0.838406i	$-0.683488\pi$
$7$	1.15667	−	2.71481i	0.437181	−	1.02610i	0.982227	−	0.187695i	$-0.0601016\pi$
$8$	−11.0774	+	1.34504i	−3.91646	+	0.475544i
$9$	0.147123	−	0.0930351i	0.0490411	−	0.0310117i
$10$	−4.43363	+	1.88899i	−1.40204	+	0.597352i
$11$	1.00246	−	1.58527i	0.302253	−	0.477975i	−0.659571	−	0.751642i	$-0.729262\pi$
$11$	1.00246	−	1.58527i	0.302253	−	0.477975i	0.961825	+	0.273667i	$0.0882365\pi$
$12$	3.55048	+	9.36185i	1.02494	+	2.70253i
$13$	−1.18730	−	3.40445i	−0.329299	−	0.944226i
$13$	−1.18730	−	3.40445i	−0.329299	−	0.944226i
$14$	−2.95159	+	7.78269i	−0.788845	+	2.08001i
$15$	1.72544	+	2.29614i	0.445507	+	0.592862i
$16$	19.3096	−	3.13811i	4.82739	−	0.784527i
$17$	−0.139658	−	0.0595025i	−0.0338719	−	0.0144315i	0.374964	−	0.927039i	$-0.377655\pi$
$17$	−0.139658	−	0.0595025i	−0.0338719	−	0.0144315i	−0.408836	+	0.912608i	$0.634065\pi$
$18$	−0.404081	+	0.278917i	−0.0952428	+	0.0657413i
$19$	3.60617	+	2.08202i	0.827313	+	0.477649i	0.852932	−	0.522023i	$-0.174822\pi$
$19$	3.60617	+	2.08202i	0.827313	+	0.477649i	−0.0256190	+	0.999672i	$0.508156\pi$
$20$	9.19385	−	4.36253i	2.05581	−	0.975492i
$21$	4.92451	+	0.597944i	1.07462	+	0.130482i
$22$	−2.64526	+	4.58172i	−0.563970	+	0.976825i
$23$	−0.549486	−	0.951737i	−0.114576	−	0.198451i	0.803034	−	0.595933i	$-0.203218\pi$
$23$	−0.549486	−	0.951737i	−0.114576	−	0.198451i	−0.917610	+	0.397482i	$0.869884\pi$
$24$	−7.35269	−	17.2574i	−1.50086	−	3.52265i
$25$	−1.55751	+	1.37983i	−0.311502	+	0.275966i
$26$	3.73292	+	9.46015i	0.732087	+	1.85529i
$27$	3.99388	+	3.53827i	0.768623	+	0.680941i
$28$	5.56579	−	16.6716i	1.05184	−	3.15063i
$29$	0.145118	+	3.60106i	0.0269477	+	0.668700i	0.955062	+	0.296405i	$0.0957879\pi$
$29$	0.145118	+	3.60106i	0.0269477	+	0.668700i	−0.928115	+	0.372295i	$0.878571\pi$
$30$	−5.12371	−	6.27541i	−0.935458	−	1.14573i
$31$	−3.40949	+	3.84852i	−0.612363	+	0.691215i	−0.970127	−	0.242597i	$-0.922001\pi$
$31$	−3.40949	+	3.84852i	−0.612363	+	0.691215i	0.357764	+	0.933812i	$0.383539\pi$
$32$	−32.1985	+	6.57336i	−5.69194	+	1.16202i
$33$	3.02854	+	0.877228i	0.527202	+	0.152706i
$34$	0.400364	+	0.151838i	0.0686619	+	0.0260400i
$35$	0.203016	−	5.03779i	0.0343159	−	0.851541i
$36$	0.828850	−	0.622840i	0.138142	−	0.103807i
$37$	−3.51635	−	0.717868i	−0.578084	−	0.118017i	−0.0979183	−	0.995194i	$-0.531218\pi$
$37$	−3.51635	−	0.717868i	−0.578084	−	0.118017i	−0.480166	+	0.877178i	$0.659424\pi$
$38$	−10.4000	−	5.45833i	−1.68710	−	0.885459i
$39$	4.94180	−	3.50937i	0.791322	−	0.561949i
$40$	−16.8817	+	8.86018i	−2.66922	+	1.40092i
$41$	−4.62982	+	1.34104i	−0.723056	+	0.209436i	−0.619286	−	0.785165i	$-0.712578\pi$
$41$	−4.62982	+	1.34104i	−0.723056	+	0.209436i	−0.103770	+	0.994601i	$0.533091\pi$
$42$	−13.9470	−	1.12592i	−2.15207	−	0.173733i
$43$	0.658342	+	3.22477i	0.100396	+	0.491773i	0.998633	+	0.0522622i	$0.0166432\pi$
$43$	0.658342	+	3.22477i	0.100396	+	0.491773i	−0.898237	+	0.439511i	$0.855152\pi$
$44$	5.19163	−	9.89182i	0.782667	−	1.49125i
$45$	0.178668	−	0.237764i	0.0266342	−	0.0354437i
$46$	1.65675	+	2.61994i	0.244274	+	0.386289i
$47$	7.83635	+	5.40904i	1.14305	+	0.788990i	0.980268	−	0.197673i	$-0.0633383\pi$
$47$	7.83635	+	5.40904i	1.14305	+	0.788990i	0.162781	+	0.986662i	$0.447954\pi$
$48$	14.0981	+	29.7110i	2.03488	+	4.28842i
$49$	−1.18322	−	1.23186i	−0.169031	−	0.175980i
$50$	4.23292	−	4.06577i	0.598625	−	0.574987i
$51$	0.0307600	−	0.253331i	0.00430726	−	0.0354735i
$52$	−8.68040	−	19.6425i	−1.20376	−	2.72392i
$53$	−0.943119	−	7.76728i	−0.129547	−	1.06692i	−0.901967	−	0.431806i	$-0.857877\pi$
$53$	−0.943119	−	7.76728i	−0.129547	−	1.06692i	0.772419	−	0.635113i	$-0.219046\pi$
$54$	−11.6581	−	9.51854i	−1.58647	−	1.29531i
$55$	0.641010	−	3.13987i	0.0864337	−	0.423380i
$56$	−9.16140	+	31.6288i	−1.22424	+	4.22658i
$57$	−1.67520	+	6.79657i	−0.221886	+	0.900227i
$58$	−0.817990	−	10.1326i	−0.107407	−	1.33048i
$59$	0.889991	−	5.47633i	0.115867	−	0.712958i	−0.862496	−	0.506063i	$-0.831100\pi$
$59$	0.889991	−	5.47633i	0.115867	−	0.712958i	0.978363	−	0.206895i	$-0.0663357\pi$
$60$	11.3440	+	12.8048i	1.46451	+	1.65309i
$61$	−8.26450	−	6.21037i	−1.05816	−	0.795156i	−0.0787217	−	0.996897i	$-0.525084\pi$
$61$	−8.26450	−	6.21037i	−1.05816	−	0.795156i	−0.979439	+	0.201740i	$0.935340\pi$
$62$	9.17210	−	11.2338i	1.16486	−	1.42669i
$63$	−0.0823991	−	0.507022i	−0.0103813	−	0.0638788i
$64$	52.0117	−	12.8197i	6.50146	−	1.60247i
$65$	−3.95940	−	4.71939i	−0.491103	−	0.585368i
$66$	−8.63518	−	2.12838i	−1.06292	−	0.261986i
$67$	−1.16823	+	14.4711i	−0.142722	+	1.76793i	0.389219	+	0.921145i	$0.372745\pi$
$67$	−1.16823	+	14.4711i	−0.142722	+	1.76793i	−0.531941	+	0.846781i	$0.678537\pi$
$68$	−0.857634	−	0.286320i	−0.104003	−	0.0347214i
$69$	1.27976	−	1.33237i	0.154065	−	0.160398i
$70$			14.2214i			1.69978i
$71$	−3.77271	−	3.62374i	−0.447738	−	0.430058i	0.434636	−	0.900606i	$-0.356877\pi$
$71$	−3.77271	−	3.62374i	−0.447738	−	0.430058i	−0.882375	+	0.470548i	$0.844056\pi$
$72$	−1.50461	+	1.22848i	−0.177320	+	0.144777i
$73$	−0.450298	−	0.857971i	−0.0527034	−	0.100418i	0.857680	−	0.514184i	$-0.171905\pi$
$73$	−0.450298	−	0.857971i	−0.0527034	−	0.100418i	−0.910383	+	0.413767i	$0.864213\pi$
$74$	9.99190	+	1.62384i	1.16153	+	0.188768i
$75$	−2.95643	−	1.86953i	−0.341379	−	0.215875i
$76$	22.4069	+	10.6322i	2.57025	+	1.21960i
$77$	−3.14417	−	4.55512i	−0.358312	−	0.519104i
$78$	−13.5292	+	10.4520i	−1.53188	+	1.18345i
$79$	−0.951562	+	1.37858i	−0.107059	+	0.155102i	−0.872851	−	0.487986i	$-0.837732\pi$
$79$	−0.951562	+	1.37858i	−0.107059	+	0.155102i	0.765792	+	0.643088i	$0.222347\pi$
$80$	28.9464	−	16.7122i	3.23631	−	1.86848i
$81$	−3.62137	+	7.63188i	−0.402375	+	0.847987i
$82$	12.8962	−	4.30539i	1.42415	−	0.475451i
$83$	2.87759	+	11.6748i	0.315856	+	1.28148i	0.887435	+	0.460933i	$0.152485\pi$
$83$	2.87759	+	11.6748i	0.315856	+	1.28148i	−0.571579	+	0.820547i	$0.693669\pi$
$84$	29.5223	+	1.18971i	3.22115	+	0.129808i
$85$	−0.259158	−	0.0104437i	−0.0281097	−	0.00113278i
$86$	−2.22171	−	9.01382i	−0.239573	−	0.971986i
$87$	−5.74668	+	1.91853i	−0.616109	+	0.205687i
$88$	−8.97244	+	18.9090i	−0.956465	+	2.01571i
$89$	4.63954	−	2.67864i	0.491791	−	0.283936i	−0.233526	−	0.972350i	$-0.575026\pi$
$89$	4.63954	−	2.67864i	0.491791	−	0.283936i	0.725317	+	0.688415i	$0.241693\pi$
$90$	−0.476547	+	0.690398i	−0.0502325	+	0.0727743i
$91$	−10.6158	−	0.714534i	−1.11283	−	0.0749036i
$92$	−3.71831	−	5.38691i	−0.387661	−	0.561624i
$93$	−7.80874	−	3.70529i	−0.809728	−	0.384221i
$94$	−22.7000	−	14.3546i	−2.34133	−	1.48057i
$95$	7.02241	+	1.14125i	0.720484	+	0.117090i
$96$	−25.6730	−	48.9158i	−2.62024	−	4.99245i
$97$	−6.11236	+	4.99059i	−0.620616	+	0.506717i	−0.889788	−	0.456375i	$-0.849148\pi$
$97$	−6.11236	+	4.99059i	−0.620616	+	0.506717i	0.269172	+	0.963092i	$0.413250\pi$
$98$	3.47465	+	3.33745i	0.350993	+	0.337133i
$99$		−	0.326493i		−	0.0328138i
$100$	−8.58528	+	8.93823i	−0.858528	+	0.893823i
$101$	−2.68789	−	0.897349i	−0.267455	−	0.0892896i	0.179778	−	0.983707i	$-0.442462\pi$
$101$	−2.68789	−	0.897349i	−0.267455	−	0.0892896i	−0.447233	+	0.894418i	$0.647590\pi$
$102$	−0.0579205	+	0.717474i	−0.00573498	+	0.0710405i
$103$	−5.53449	−	1.36413i	−0.545329	−	0.134412i	−0.0429794	−	0.999076i	$-0.513685\pi$
$103$	−5.53449	−	1.36413i	−0.545329	−	0.134412i	−0.502350	+	0.864664i	$0.667531\pi$
$104$	17.7314	+	36.1156i	1.73871	+	3.54143i
$105$	8.22936	−	2.02835i	0.803103	−	0.197947i
$106$	3.54024	+	21.7839i	0.343858	+	2.11584i
$107$	4.90312	−	6.00523i	0.474002	−	0.580547i	−0.481159	−	0.876633i	$-0.659784\pi$
$107$	4.90312	−	6.00523i	0.474002	−	0.580547i	0.955161	+	0.296086i	$0.0956815\pi$
$108$	25.4066	+	19.0918i	2.44475	+	1.83711i
$109$	−9.48399	−	10.7052i	−0.908401	−	1.02537i	−0.999564	−	0.0295371i	$-0.990597\pi$
$109$	−9.48399	−	10.7052i	−0.908401	−	1.02537i	0.0911624	−	0.995836i	$-0.470942\pi$
$110$	−1.44999	+	8.92212i	−0.138251	+	0.850691i
$111$	−0.485461	−	6.01352i	−0.0460780	−	0.570778i
$112$	13.8154	−	56.0515i	1.30544	−	5.29637i
$113$	1.55132	−	5.35577i	0.145936	−	0.503828i	−0.853927	−	0.520393i	$-0.825786\pi$
$113$	1.55132	−	5.35577i	0.145936	−	0.503828i	0.999863	+	0.0165642i	$0.00527281\pi$
$114$	3.94941	−	19.3455i	0.369896	−	1.81187i
$115$	−1.45445	−	1.18752i	−0.135628	−	0.110737i
$116$	2.58740	+	21.3092i	0.240234	+	1.97851i
$117$	−0.491414	−	0.390414i	−0.0454312	−	0.0360937i
$118$	−1.88634	+	15.5354i	−0.173652	+	1.43015i
$119$	−0.323076	+	0.310318i	−0.0296163	+	0.0284468i
$120$	−22.2018	−	23.1146i	−2.02674	−	2.11006i
$121$	3.20748	+	6.75962i	0.291589	+	0.614511i
$122$	23.9977	+	16.5645i	2.17265	+	1.49967i
$123$	−4.33071	−	6.84847i	−0.390487	−	0.617506i
$124$	−18.3969	+	24.4819i	−1.65209	+	2.19854i
$125$	−5.62223	+	10.7123i	−0.502867	+	0.958134i
$126$	0.289817	+	1.41962i	0.0258189	+	0.126469i
$127$	10.1701	+	0.821011i	0.902446	+	0.0728530i	0.522972	−	0.852350i	$-0.324823\pi$
$127$	10.1701	+	0.821011i	0.902446	+	0.0728530i	0.379474	+	0.925203i	$0.376105\pi$
$128$	−82.0018	+	23.7521i	−7.24800	+	2.09941i
$129$	−4.89907	+	2.57123i	−0.431339	+	0.226384i
$130$	11.6951	+	12.8513i	1.02572	+	1.12713i
$131$	3.59496	+	1.88678i	0.314094	+	0.164849i	0.614402	−	0.788993i	$-0.289397\pi$
$131$	3.59496	+	1.88678i	0.314094	+	0.164849i	−0.300308	+	0.953842i	$0.597090\pi$
$132$	18.4002	+	3.75643i	1.60153	+	0.326956i
$133$	9.82345	−	7.38184i	0.851801	−	0.640087i
$134$	1.64892	−	40.9176i	0.142445	−	3.53474i
$135$	8.52408	+	3.23276i	0.733636	+	0.278231i
$136$	1.62708	+	0.471289i	0.139521	+	0.0404127i
$137$	−2.76910	+	0.565316i	−0.236580	+	0.0482982i	−0.316853	−	0.948475i	$-0.602626\pi$
$137$	−2.76910	+	0.565316i	−0.236580	+	0.0482982i	0.0802725	+	0.996773i	$0.474421\pi$
$138$	−3.45550	+	3.90045i	−0.294152	+	0.332029i
$139$	−2.53539	−	3.10528i	−0.215049	−	0.263387i	0.655804	−	0.754931i	$-0.272330\pi$
$139$	−2.53539	−	3.10528i	−0.215049	−	0.263387i	−0.870852	+	0.491545i	$0.836432\pi$
$140$	−1.20918	−	30.0055i	−0.102194	−	2.53593i
$141$	−5.06882	+	15.1830i	−0.426872	+	1.27864i
$142$	11.0445	+	9.78453i	0.926830	+	0.821099i
$143$	−6.58719	−	1.53064i	−0.550848	−	0.127999i
$144$	2.54893	−	2.25816i	0.212411	−	0.188180i
$145$	2.41359	+	5.66490i	0.200438	+	0.470444i
$146$	1.36655	+	2.36693i	0.113096	+	0.195889i
$147$	1.43567	−	2.48666i	0.118412	−	0.205096i
$148$	−21.2198	−	2.57656i	−1.74426	−	0.211792i
$149$	−3.46824	+	1.64570i	−0.284129	+	0.134821i	−0.565424	−	0.824800i	$-0.691287\pi$
$149$	−3.46824	+	1.64570i	−0.284129	+	0.134821i	0.281295	+	0.959621i	$0.409236\pi$
$150$	8.54464	+	4.93325i	0.697667	+	0.402798i
$151$	5.65159	−	3.90101i	0.459919	−	0.317459i	−0.315478	−	0.948933i	$-0.602165\pi$
$151$	5.65159	−	3.90101i	0.459919	−	0.317459i	0.775398	+	0.631473i	$0.217549\pi$
$152$	−42.7475	−	18.2130i	−3.46728	−	1.47727i
$153$	−0.0260827	+	0.00423885i	−0.00210866	+	0.000342691i
$154$	9.37879	+	12.4809i	0.755764	+	1.00574i
$155$	−3.11510	+	8.21384i	−0.250211	+	0.659752i
$156$	27.6565	−	23.2028i	2.21429	−	1.85771i
$157$	0.164067	+	0.432608i	0.0130939	+	0.0345259i	0.941404	−	0.337281i	$-0.109507\pi$
$157$	0.164067	+	0.432608i	0.0130939	+	0.0345259i	−0.928310	+	0.371807i	$0.878738\pi$
$158$	2.52528	−	3.99341i	0.200900	−	0.317699i
$159$	12.1006	−	5.15557i	0.959638	−	0.408863i
$160$	−47.4556	+	30.0091i	−3.75169	+	2.37243i
$161$	−3.21936	+	0.390901i	−0.253721	+	0.0308073i
$162$	9.33956	−	21.9208i	0.733785	−	1.72226i
$163$	−5.82159	−	17.4378i	−0.455982	−	1.36583i	−0.886282	−	0.463146i	$-0.846720\pi$
$163$	−5.82159	−	17.4378i	−0.455982	−	1.36583i	0.430300	−	0.902686i	$-0.358408\pi$
$164$	−26.8435	+	10.1804i	−2.09613	+	0.794956i
$165$	5.36968	−	0.433486i	0.418029	−	0.0337468i
$166$	−9.43609	−	32.5772i	−0.732383	−	2.52848i
$167$	8.42661	−	0.339581i	0.652071	−	0.0262776i	0.287973	−	0.957638i	$-0.407018\pi$
$167$	8.42661	−	0.339581i	0.652071	−	0.0262776i	0.364098	+	0.931361i	$0.381377\pi$
$168$	−55.3552			−4.27074
$169$	−10.1806	+	8.08424i	−0.783125	+	0.621865i
$170$	0.731589			0.0561103
$171$	0.724253	−	0.0291864i	0.0553850	−	0.00223194i
$172$	5.45396	+	18.8293i	0.415861	+	1.43572i
$173$	7.56191	−	0.610460i	0.574921	−	0.0464124i	0.210413	−	0.977613i	$-0.432519\pi$
$173$	7.56191	−	0.610460i	0.574921	−	0.0464124i	0.364508	+	0.931200i	$0.381237\pi$
$174$	15.9784	−	6.05980i	1.21132	−	0.459392i
$175$	1.94445	+	5.82435i	0.146987	+	0.440279i
$176$	14.3823	−	33.7566i	1.08411	−	2.54450i
$177$	9.25877	−	1.12422i	0.695932	−	0.0845014i
$178$	−12.7717	+	8.07634i	−0.957280	+	0.605347i
$179$	11.4099	−	4.86130i	0.852816	−	0.363351i	0.0790871	−	0.996868i	$-0.474799\pi$
$179$	11.4099	−	4.86130i	0.852816	−	0.363351i	0.773729	+	0.633517i	$0.218389\pi$
$180$	0.946760	−	1.49718i	0.0705673	−	0.111593i
$181$	−3.26245	−	8.60237i	−0.242496	−	0.639409i	0.757413	−	0.652937i	$-0.226463\pi$
$181$	−3.26245	−	8.60237i	−0.242496	−	0.639409i	−0.999909	+	0.0135273i	$0.995694\pi$
$182$	30.0003	+	0.808122i	2.22377	+	0.0599020i
$183$	6.16247	−	16.2491i	0.455543	−	1.20117i
$184$	7.36701	+	9.80372i	0.543104	+	0.722740i
$185$	−6.05242	+	0.983614i	−0.444983	+	0.0723167i
$186$	22.4287	+	9.55599i	1.64455	+	0.700679i
$187$	−0.234328	+	0.161745i	−0.0171358	+	0.0118280i
$188$	49.1151	+	28.3566i	3.58208	+	2.06812i
$189$	14.2253	−	6.75000i	1.03474	−	0.490991i
$190$	−19.9214	−	2.41889i	−1.44525	−	0.175485i
$191$	−5.58684	+	9.67670i	−0.404250	+	0.700181i	−0.994234	−	0.107234i	$-0.965801\pi$
$191$	−5.58684	+	9.67670i	−0.404250	+	0.700181i	0.589984	+	0.807415i	$0.299134\pi$
$192$	45.0255	+	77.9864i	3.24943	+	5.62818i
$193$	9.97810	+	23.4195i	0.718239	+	1.68577i	0.727776	+	0.685815i	$0.240554\pi$
$193$	9.97810	+	23.4195i	0.718239	+	1.68577i	−0.00953651	+	0.999955i	$0.503036\pi$
$194$	16.6601	−	14.7595i	1.19612	−	1.05967i
$195$	5.76850	−	8.60040i	0.413091	−	0.615888i
$196$	−7.61490	−	6.74621i	−0.543921	−	0.481872i
$197$	−1.92376	+	5.76238i	−0.137063	+	0.410552i	−0.994589	−	0.103887i	$-0.966872\pi$
$197$	−1.92376	+	5.76238i	−0.137063	+	0.410552i	0.857527	+	0.514440i	$0.172000\pi$
$198$	0.0370819	+	0.920179i	0.00263530	+	0.0653942i
$199$	−1.15291	−	1.41206i	−0.0817279	−	0.100098i	0.732122	−	0.681173i	$-0.238530\pi$
$199$	−1.15291	−	1.41206i	−0.0817279	−	0.100098i	−0.813850	+	0.581075i	$0.802632\pi$
$200$	15.3972	−	17.3799i	1.08875	−	1.22894i
$201$	−23.9126	+	4.88178i	−1.68666	+	0.344334i
$202$	7.67738	+	2.22378i	0.540178	+	0.156465i
$203$	9.94404	+	3.77128i	0.697935	+	0.264692i
$204$	0.0612021	−	1.51871i	0.00428500	−	0.106331i
$205$	−6.58381	+	4.94741i	−0.459833	+	0.345542i
$206$	15.7532	+	3.21603i	1.09757	+	0.224071i
$207$	−0.169387	−	0.0889012i	−0.0117732	−	0.00617906i
$208$	−33.6098	−	62.0126i	−2.33042	−	4.29980i
$209$	6.91561	−	3.62959i	0.478363	−	0.251064i
$210$	−22.9630	+	6.65131i	−1.58460	+	0.458984i
$211$	−15.0880	−	1.21803i	−1.03870	−	0.0838526i	−0.450669	−	0.892691i	$-0.648815\pi$
$211$	−15.0880	−	1.21803i	−1.03870	−	0.0838526i	−0.588031	+	0.808838i	$0.700097\pi$
$212$	−9.32169	−	45.6607i	−0.640216	−	3.13599i
$213$	4.08668	−	7.78652i	0.280015	−	0.533524i
$214$	−13.1367	+	17.4818i	−0.898009	+	1.19503i
$215$	3.00550	+	4.75282i	0.204974	+	0.324140i
$216$	−49.0011	−	33.8230i	−3.33410	−	2.30136i
$217$	6.50433	+	13.7076i	0.441543	+	0.930532i
$218$	27.9452	+	29.0941i	1.89269	+	1.97050i
$219$	1.17474	−	1.12836i	0.0793818	−	0.0762473i
$220$	2.30070	−	18.9480i	0.155113	−	1.27747i
$221$	−0.0367577	+	0.546105i	−0.00247259	+	0.0367350i
$222$	2.05120	+	16.8932i	0.137668	+	1.13380i
$223$	3.14625	+	2.56883i	0.210688	+	0.172022i	0.731914	−	0.681397i	$-0.238627\pi$
$223$	3.14625	+	2.56883i	0.210688	+	0.172022i	−0.521225	+	0.853419i	$0.674525\pi$
$224$	−19.3976	+	95.0158i	−1.29606	+	6.34851i
$225$	−0.100773	+	0.347908i	−0.00671819	+	0.0231939i
$226$	−3.76389	+	15.2707i	−0.250370	+	1.01579i
$227$	−1.94853	−	24.1369i	−0.129328	−	1.60202i	−0.657882	−	0.753121i	$-0.728548\pi$
$227$	−1.94853	−	24.1369i	−0.129328	−	1.60202i	0.528554	−	0.848900i	$-0.322735\pi$
$228$	−6.68795	+	41.1526i	−0.442920	+	2.72540i
$229$	4.94193	+	5.57828i	0.326572	+	0.368623i	0.888750	−	0.458393i	$-0.151575\pi$
$229$	4.94193	+	5.57828i	0.326572	+	0.368623i	−0.562178	+	0.827016i	$0.690036\pi$
$230$	4.23404	+	3.18168i	0.279184	+	0.209793i
$231$	5.88453	−	7.20724i	0.387174	−	0.474202i
$232$	−6.45111	−	39.6953i	−0.423536	−	2.60612i
$233$	−13.2946	+	3.27682i	−0.870957	+	0.214672i	−0.649373	−	0.760470i	$-0.724969\pi$
$233$	−13.2946	+	3.27682i	−0.870957	+	0.214672i	−0.221584	+	0.975141i	$0.571123\pi$
$234$	1.42933	+	1.04452i	0.0934380	+	0.0682821i
$235$	15.7960	+	3.89336i	1.03042	+	0.253975i
$236$	2.65906	−	32.9383i	0.173090	−	2.14410i
$237$	−2.67100	−	0.891711i	−0.173500	−	0.0579229i
$238$	0.875301	−	0.911285i	0.0567373	−	0.0590698i
$239$			26.2250i			1.69635i	0.529714	+	0.848177i	$0.322299\pi$
$239$			26.2250i			1.69635i	−0.529714	+	0.848177i	$0.677701\pi$
$240$	40.5230	+	38.9229i	2.61575	+	2.51246i
$241$	−3.13218	+	2.55734i	−0.201761	+	0.164733i	−0.727940	−	0.685641i	$-0.759522\pi$
$241$	−3.13218	+	2.55734i	−0.201761	+	0.164733i	0.526178	+	0.850374i	$0.323624\pi$
$242$	−9.80759	−	18.6868i	−0.630456	−	1.20123i
$243$	1.78328	+	0.289810i	0.114397	+	0.0185914i
$244$	−52.0410	−	32.9087i	−3.33158	−	2.10676i
$245$	−2.63657	−	1.25107i	−0.168445	−	0.0799279i
$246$	12.9834	+	18.8096i	0.827788	+	1.19926i
$247$	2.80654	−	14.7490i	0.178576	−	0.938459i
$248$	32.5920	−	47.2176i	2.06959	−	2.99832i
$249$	−17.5053	+	10.1067i	−1.10935	+	0.640485i
$250$	14.6288	−	30.8296i	0.925209	−	1.94984i
$251$	−26.8377	+	8.95974i	−1.69398	+	0.565534i	−0.989544	−	0.144233i	$-0.953928\pi$
$251$	−26.8377	+	8.95974i	−1.69398	+	0.565534i	−0.704437	+	0.709767i	$0.748800\pi$
$252$	−0.732185	−	2.97059i	−0.0461233	−	0.187130i
$253$	−2.05959	−	0.0829988i	−0.129486	−	0.00521809i
$254$	−28.7562	−	1.15883i	−1.80432	−	0.0727118i
$255$	−0.104344	−	0.423342i	−0.00653430	−	0.0265107i
$256$	126.791	−	42.3289i	7.92441	−	2.64556i
$257$	−0.409954	+	0.863960i	−0.0255722	+	0.0538923i	−0.915835	−	0.401556i	$-0.868470\pi$
$257$	−0.409954	+	0.863960i	−0.0255722	+	0.0538923i	0.890262	+	0.455448i	$0.150521\pi$
$258$	13.5153	−	7.80309i	0.841429	−	0.485799i
$259$	−6.01613	+	8.71587i	−0.373824	+	0.541578i
$260$	−25.7679	−	26.1204i	−1.59806	−	1.61992i
$261$	0.356375	+	0.516299i	0.0220591	+	0.0319581i
$262$	−10.3462	−	4.90935i	−0.639192	−	0.303300i
$263$	−3.31086	−	2.09366i	−0.204156	−	0.129101i	0.428475	−	0.903553i	$-0.359051\pi$
$263$	−3.31086	−	2.09366i	−0.204156	−	0.129101i	−0.632632	+	0.774453i	$0.718025\pi$
$264$	−34.7284	−	5.64391i	−2.13738	−	0.347359i
$265$	−6.21259	−	11.8371i	−0.381636	−	0.727147i
$266$	−26.8477	+	21.9205i	−1.64614	+	1.34403i
$267$	6.49505	+	6.23858i	0.397491	+	0.381795i
$268$			86.4717i			5.28210i
$269$	−1.45975	+	1.51976i	−0.0890024	+	0.0926614i	−0.764214	−	0.644963i	$-0.776873\pi$
$269$	−1.45975	+	1.51976i	−0.0890024	+	0.0926614i	0.675212	+	0.737624i	$0.264052\pi$
$270$	−24.3912	−	8.14297i	−1.48440	−	0.495565i
$271$	−0.0270782	+	0.335423i	−0.00164488	+	0.0203755i	−0.997528	−	0.0702746i	$-0.977612\pi$
$271$	−0.0270782	+	0.335423i	−0.00164488	+	0.0203755i	0.995883	+	0.0906501i	$0.0288945\pi$
$272$	−2.88345	−	0.710706i	−0.174835	−	0.0430929i
$273$	−3.81122	−	17.4752i	−0.230665	−	1.05765i
$274$	7.74013	−	1.90777i	0.467598	−	0.115253i
$275$	0.626059	+	3.85229i	0.0377527	+	0.232302i
$276$	6.95908	−	8.52333i	0.418887	−	0.513044i
$277$	−11.7199	−	8.80696i	−0.704183	−	0.529159i	0.187250	−	0.982312i	$-0.440043\pi$
$277$	−11.7199	−	8.80696i	−0.704183	−	0.529159i	−0.891433	+	0.453153i	$0.850299\pi$
$278$	7.49834	+	8.46387i	0.449720	+	0.507629i
$279$	−0.143568	+	0.883410i	−0.00859519	+	0.0528884i
$280$	4.52714	+	56.0787i	0.270549	+	3.35135i
$281$	−4.44158	+	18.0202i	−0.264962	+	1.07499i	0.676113	+	0.736798i	$0.263663\pi$
$281$	−4.44158	+	18.0202i	−0.264962	+	1.07499i	−0.941076	+	0.338196i	$0.890183\pi$
$282$	12.5614	−	43.3669i	0.748019	−	2.58246i
$283$	−4.26357	+	20.8844i	−0.253443	+	1.24145i	0.631363	+	0.775487i	$0.282496\pi$
$283$	−4.26357	+	20.8844i	−0.253443	+	1.24145i	−0.884806	+	0.465959i	$0.845710\pi$
$284$	−24.1345	−	19.7052i	−1.43212	−	1.16929i
$285$	1.44161	+	11.8727i	0.0853934	+	0.703278i
$286$	18.7390	+	3.56576i	1.10806	+	0.210848i
$287$	−1.71450	+	14.1202i	−0.101204	+	0.833490i
$288$	−4.12559	+	3.96268i	−0.243103	+	0.233503i
$289$	−11.7604	−	12.2438i	−0.691785	−	0.720225i
$290$	−7.44577	−	15.6916i	−0.437231	−	0.921445i
$291$	−10.9169	−	7.53541i	−0.639962	−	0.441734i
$292$	−3.08452	−	4.87777i	−0.180508	−	0.285450i
$293$	18.4958	−	24.6134i	1.08054	−	1.43793i	0.190700	−	0.981648i	$-0.438924\pi$
$293$	18.4958	−	24.6134i	1.08054	−	1.43793i	0.889835	−	0.456283i	$-0.150819\pi$
$294$	−3.76382	+	7.17137i	−0.219511	+	0.418243i
$295$	−1.89613	−	9.28785i	−0.110397	−	0.540759i
$296$	39.9176	+	3.22249i	2.32017	+	0.187303i
$297$	9.61281	−	2.78438i	0.557792	−	0.161566i
$298$	9.58786	−	5.03209i	0.555410	−	0.291501i
$299$	−2.58774	+	3.00070i	−0.149653	+	0.173535i
$300$	−18.4477	−	9.68209i	−1.06508	−	0.558996i
$301$	9.51612	+	1.94273i	0.548500	+	0.111977i
$302$	−15.4852	+	11.6364i	−0.891072	+	0.669597i
$303$	0.191812	−	4.75977i	0.0110193	−	0.273441i
$304$	76.1672	+	28.8864i	4.36849	+	1.65675i
$305$	−16.9655	−	4.91411i	−0.971440	−	0.281381i
$306$	0.0730292	−	0.0149090i	0.00417480	−	0.000852292i
$307$	−3.84631	+	4.34159i	−0.219520	+	0.247787i	−0.847946	−	0.530082i	$-0.822161\pi$
$307$	−3.84631	+	4.34159i	−0.219520	+	0.247787i	0.628426	+	0.777869i	$0.283700\pi$
$308$	−20.8494	−	25.5359i	−1.18800	−	1.45504i
$309$	−0.385836	−	9.57442i	−0.0219494	−	0.544670i
$310$	7.84660	−	23.5034i	0.445657	−	1.33490i
$311$	−5.13393	−	4.54826i	−0.291118	−	0.257908i	0.504904	−	0.863175i	$-0.331528\pi$
$311$	−5.13393	−	4.54826i	−0.291118	−	0.257908i	−0.796022	+	0.605267i	$0.793066\pi$
$312$	−50.0222	+	45.5217i	−2.83195	+	2.57716i
$313$	19.6958	−	17.4489i	1.11327	−	0.986271i	0.113296	−	0.993561i	$-0.463859\pi$
$313$	19.6958	−	17.4489i	1.11327	−	0.986271i	0.999973	+	0.00729028i	$0.00232059\pi$
$314$	−0.511534	−	1.20062i	−0.0288676	−	0.0677546i
$315$	−0.438823	−	0.760063i	−0.0247249	−	0.0428247i
$316$	−4.98851	+	8.64036i	−0.280626	+	0.486058i
$317$	−18.3180	−	2.22421i	−1.02884	−	0.124924i	−0.411332	−	0.911486i	$-0.634936\pi$
$317$	−18.3180	−	2.22421i	−1.02884	−	0.124924i	−0.617512	+	0.786562i	$0.711859\pi$
$318$	−33.5183	+	15.9046i	−1.87961	+	0.891888i
$319$	5.85411	+	3.37987i	0.327767	+	0.189237i
$320$	75.3234	−	51.9920i	4.21071	−	2.90644i
$321$	11.9897	+	5.10833i	0.669199	+	0.285119i
$322$	9.02894	−	1.46735i	0.503163	−	0.0817719i
$323$	−0.379743	−	0.505347i	−0.0211295	−	0.0281182i
$324$	−17.8416	+	47.0444i	−0.991200	+	2.61358i
$325$	6.54681	+	3.66419i	0.363152	+	0.203253i
$326$	18.3879	+	48.4849i	1.01841	+	2.68533i
$327$	12.8498	−	20.3204i	0.710598	−	1.12372i
$328$	49.4827	−	21.0826i	2.73223	−	1.16409i
$329$	23.7486	−	15.0177i	1.30930	−	0.827952i
$330$	−15.0845	+	1.83159i	−0.830375	+	0.100826i
$331$	8.54018	−	20.0445i	0.469411	−	1.10175i	−0.502112	−	0.864802i	$-0.667444\pi$
$331$	8.54018	−	20.0445i	0.469411	−	1.10175i	0.971523	−	0.236945i	$-0.0761461\pi$
$332$	22.6790	+	67.9318i	1.24467	+	3.72824i
$333$	−0.584124	+	0.221529i	−0.0320098	+	0.0121397i
$334$	−23.7107	+	1.91413i	−1.29739	+	0.104736i
$335$	6.90125	+	23.8259i	0.377056	+	1.30175i
$336$	96.9666	−	3.90762i	5.28996	−	0.213178i
$337$	15.9897			0.871014			0.435507	−	0.900185i	$-0.356569\pi$
$337$	15.9897			0.871014			0.435507	+	0.900185i	$0.356569\pi$
$338$	27.7746	−	23.9406i	1.51074	−	1.30220i
$339$	9.37339			0.509093
$340$	−1.54357	+	0.0622038i	−0.0837119	+	0.00337347i
$341$	2.68304	+	9.26294i	0.145295	+	0.501617i
$342$	−2.03790	+	0.164516i	−0.110197	+	0.00889601i
$343$	14.6014	−	5.53758i	0.788401	−	0.299001i
$344$	−11.6302	−	34.8367i	−0.627058	−	1.87827i
$345$	1.23722	−	2.90387i	0.0666098	−	0.156339i
$346$	−21.2429	+	2.57936i	−1.14203	+	0.138667i
$347$	−25.4819	+	16.1138i	−1.36794	+	0.865032i	−0.997950	−	0.0640044i	$-0.979613\pi$
$347$	−25.4819	+	16.1138i	−1.36794	+	0.865032i	−0.369989	+	0.929036i	$0.620638\pi$
$348$	−33.1973	+	14.1441i	−1.77956	+	0.758201i
$349$	−4.79331	+	7.58001i	−0.256580	+	0.405749i	−0.948770	−	0.315966i	$-0.897671\pi$
$349$	−4.79331	+	7.58001i	−0.256580	+	0.405749i	0.692191	+	0.721715i	$0.256646\pi$
$350$	−6.14169	−	16.1943i	−0.328287	−	0.865622i
$351$	7.30393	−	17.7980i	0.389855	−	0.949987i
$352$	−21.8572	+	57.6326i	−1.16499	+	3.07183i
$353$	−9.32455	−	12.4087i	−0.496296	−	0.660450i	0.479905	−	0.877321i	$-0.340671\pi$
$353$	−9.32455	−	12.4087i	−0.496296	−	0.660450i	−0.976200	+	0.216871i	$0.930415\pi$
$354$	−25.9669	+	4.22004i	−1.38013	+	0.224292i
$355$	−8.22253	−	3.50329i	−0.436406	−	0.185935i
$356$	26.2602	−	18.1261i	1.39179	−	0.960681i
$357$	−0.652166	−	0.376528i	−0.0345163	−	0.0199280i
$358$	−31.6052	+	14.9968i	−1.67038	+	0.792608i
$359$	12.5590	+	1.52494i	0.662841	+	0.0804834i	0.445041	−	0.895510i	$-0.353189\pi$
$359$	12.5590	+	1.52494i	0.662841	+	0.0804834i	0.217799	+	0.975994i	$0.430112\pi$
$360$	−1.65938	+	2.87412i	−0.0874568	+	0.151480i
$361$	−0.830349	−	1.43821i	−0.0437026	−	0.0756951i
$362$	10.1718	+	23.8741i	0.534618	+	1.25480i
$363$	−9.41449	+	8.34051i	−0.494132	+	0.437763i
$364$	−63.3659	+	0.845743i	−3.32127	+	0.0443290i
$365$	−1.23918	−	1.09782i	−0.0648617	−	0.0574624i
$366$	−15.5226	+	46.4958i	−0.811378	+	2.43037i
$367$	−0.172026	−	4.26878i	−0.00897969	−	0.222829i	−0.997448	−	0.0713995i	$-0.977253\pi$
$367$	−0.172026	−	4.26878i	−0.00897969	−	0.222829i	0.988468	−	0.151429i	$-0.0483876\pi$
$368$	−13.5970	−	16.6533i	−0.708792	−	0.868112i
$369$	−0.556390	+	0.628034i	−0.0289645	+	0.0326942i
$370$	16.9462	−	3.45960i	0.880993	−	0.179856i
$371$	−22.1776	−	6.42381i	−1.15140	−	0.333507i
$372$	−48.1346	−	18.2550i	−2.49566	−	0.946480i
$373$	−1.10448	+	27.4074i	−0.0571878	+	1.41910i	0.674909	+	0.737901i	$0.264183\pi$
$373$	−1.10448	+	27.4074i	−0.0571878	+	1.41910i	−0.732097	+	0.681200i	$0.761458\pi$
$374$	0.642053	−	0.482472i	0.0331998	−	0.0249480i
$375$	−19.9264	−	4.06800i	−1.02899	−	0.210070i
$376$	−94.0819	−	49.3780i	−4.85190	−	2.54648i
$377$	12.0873	−	4.76960i	0.622530	−	0.245647i
$378$	−39.3256	+	20.6397i	−2.02269	+	1.06159i
$379$	22.5409	−	6.52905i	1.15785	−	0.335375i	0.356920	−	0.934135i	$-0.383827\pi$
$379$	22.5409	−	6.52905i	1.15785	−	0.335375i	0.800929	+	0.598760i	$0.204340\pi$
$380$	42.2375	+	3.40976i	2.16674	+	0.174917i
$381$	3.43084	+	16.8054i	0.175767	+	0.860964i
$382$	14.6467	−	27.9070i	0.749392	−	1.42785i
$383$	4.67963	−	6.22745i	0.239118	−	0.318208i	−0.663892	−	0.747829i	$-0.731096\pi$
$383$	4.67963	−	6.22745i	0.239118	−	0.318208i	0.903009	+	0.429621i	$0.141353\pi$
$384$	−76.7040	−	121.298i	−3.91429	−	6.18995i
$385$	−7.78271	−	5.37202i	−0.396644	−	0.273783i
$386$	−30.7818	−	64.8714i	−1.56675	−	3.30187i
$387$	0.396875	+	0.413190i	0.0201743	+	0.0210036i
$388$	−33.8959	+	32.5575i	−1.72080	+	1.65286i
$389$	1.98265	−	16.3286i	0.100524	−	0.827893i	−0.852023	−	0.523504i	$-0.824625\pi$
$389$	1.98265	−	16.3286i	0.100524	−	0.827893i	0.952548	−	0.304389i	$-0.0984523\pi$
$390$	−15.2809	+	24.8943i	−0.773781	+	1.26057i
$391$	0.0201091	+	0.165613i	0.00101696	+	0.00837541i
$392$	14.7639	+	12.0544i	0.745690	+	0.608837i
$393$	−1.36519	+	6.68716i	−0.0688649	+	0.337322i
$394$	4.76741	−	16.4590i	0.240178	−	0.829192i
$395$	−0.684923	+	2.77884i	−0.0344622	+	0.139819i
$396$	−0.156477	−	1.93832i	−0.00786329	−	0.0974043i
$397$	4.24193	−	26.1016i	0.212896	−	1.31000i	−0.631957	−	0.775004i	$-0.717748\pi$
$397$	4.24193	−	26.1016i	0.212896	−	1.31000i	0.844853	−	0.534999i	$-0.179688\pi$
$398$	3.40971	+	3.84877i	0.170913	+	0.192921i
$399$	16.5137	+	12.4092i	0.826719	+	0.621239i
$400$	−25.7447	+	31.5316i	−1.28724	+	1.57658i
$401$	0.596776	+	3.67211i	0.0298016	+	0.183377i	0.997683	−	0.0680295i	$-0.0216712\pi$
$401$	0.596776	+	3.67211i	0.0298016	+	0.183377i	−0.967882	+	0.251406i	$0.919107\pi$
$402$	66.8399	−	16.4746i	3.33367	−	0.821676i
$403$	17.1502	+	7.03810i	0.854313	+	0.350593i
$404$	−16.3875	−	4.03915i	−0.815308	−	0.200955i
$405$	−1.16138	+	14.3863i	−0.0577094	+	0.714859i
$406$	−28.4543	−	9.49943i	−1.41216	−	0.471449i
$407$	−4.66301	+	4.85471i	−0.231137	+	0.240639i
$408$			2.84763i			0.140979i
$409$	−16.7510	−	16.0896i	−0.828284	−	0.795578i	0.152983	−	0.988229i	$-0.451112\pi$
$409$	−16.7510	−	16.0896i	−0.828284	−	0.795578i	−0.981267	+	0.192651i	$0.938292\pi$
$410$	17.9937	−	14.6914i	0.888644	−	0.725556i
$411$	−2.20790	−	4.20681i	−0.108908	−	0.207507i
$412$	−33.5108	−	5.44604i	−1.65096	−	0.268307i
$413$	−13.8378	−	8.75047i	−0.680912	−	0.430583i
$414$	0.487492	+	0.231318i	0.0239589	+	0.0113687i
$415$	11.6704	+	16.9075i	0.572879	+	0.829958i
$416$	60.6081	+	101.814i	2.97155	+	4.99182i
$417$	3.82824	−	5.54617i	0.187470	−	0.271597i
$418$	−19.0785	+	11.0150i	−0.933159	+	0.538760i
$419$	−1.81090	+	3.81640i	−0.0884685	+	0.186443i	−0.942862	−	0.333183i	$-0.891877\pi$
$419$	−1.81090	+	3.81640i	−0.0884685	+	0.186443i	0.854394	+	0.519626i	$0.173929\pi$
$420$	47.8838	−	15.9860i	2.33649	−	0.780035i
$421$	4.75317	+	19.2844i	0.231655	+	0.939862i	0.965470	+	0.260513i	$0.0838917\pi$
$421$	4.75317	+	19.2844i	0.231655	+	0.939862i	−0.733815	+	0.679349i	$0.762262\pi$
$422$	42.6619	+	1.71921i	2.07675	+	0.0836900i
$423$	1.65614	+	0.0667401i	0.0805243	+	0.00324502i
$424$	20.8947	+	84.7729i	1.01473	+	4.11694i
$425$	0.299621	−	0.100028i	0.0145338	−	0.00485208i
$426$	−10.6334	+	22.4094i	−0.515190	+	1.08574i
$427$	−26.4193	+	15.2532i	−1.27852	+	0.738152i
$428$	26.2306	−	38.0016i	1.26791	−	1.83688i
$429$	−0.609316	−	11.3521i	−0.0294181	−	0.548083i
$430$	−9.01042	−	13.0538i	−0.434521	−	0.629512i
$431$	17.1860	+	8.15487i	0.827822	+	0.392806i	0.794966	−	0.606654i	$-0.207489\pi$
$431$	17.1860	+	8.15487i	0.827822	+	0.392806i	0.0328558	+	0.999460i	$0.489540\pi$
$432$	88.2236	+	55.7892i	4.24466	+	2.68416i
$433$	30.8839	+	5.01912i	1.48419	+	0.241204i	0.847862	−	0.530218i	$-0.177890\pi$
$433$	30.8839	+	5.01912i	1.48419	+	0.241204i	0.636325	+	0.771421i	$0.280454\pi$
$434$	−19.8885	−	37.8943i	−0.954677	−	1.81898i
$435$	−8.01816	+	6.54663i	−0.384441	+	0.313887i
$436$	−61.4350	−	59.0091i	−2.94220	−	2.82603i
$437$		−	4.57617i		−	0.218908i
$438$	−3.18271	+	3.31355i	−0.152076	+	0.158327i
$439$	24.8936	+	8.31069i	1.18811	+	0.396648i	0.840925	−	0.541151i	$-0.182011\pi$
$439$	24.8936	+	8.31069i	1.18811	+	0.396648i	0.347180	+	0.937799i	$0.387139\pi$
$440$	−2.87747	+	35.6439i	−0.137178	+	1.69926i
$441$	−0.288685	−	0.0711545i	−0.0137469	−	0.00338831i
$442$	0.0415721	−	1.54330i	0.00197738	−	0.0734073i
$443$	−32.8361	+	8.09338i	−1.56009	+	0.384528i	−0.922547	−	0.385885i	$-0.873896\pi$
$443$	−32.8361	+	8.09338i	−1.56009	+	0.384528i	−0.637545	+	0.770413i	$0.720050\pi$
$444$	−5.76416	−	35.4683i	−0.273555	−	1.68325i
$445$	5.78894	−	7.09016i	0.274422	−	0.336106i
$446$	−9.15903	−	6.88257i	−0.433693	−	0.325899i
$447$	−4.27936	−	4.83040i	−0.202407	−	0.228470i
$448$	25.3573	−	156.030i	1.19802	−	7.37172i
$449$	−0.220233	−	2.72807i	−0.0103934	−	0.128746i	0.989480	−	0.144671i	$-0.0462125\pi$
$449$	−0.220233	−	2.72807i	−0.0103934	−	0.128746i	−0.999873	+	0.0159257i	$0.994930\pi$
$450$	0.244501	−	0.991979i	0.0115259	−	0.0467624i
$451$	−2.51530	+	8.68384i	−0.118441	+	0.408906i
$452$	6.64299	−	32.5395i	0.312460	−	1.53053i
$453$	8.94211	+	7.30100i	0.420137	+	0.343031i
$454$	8.23305	+	67.8053i	0.386396	+	3.18226i
$455$	−17.3920	+	5.29022i	−0.815347	+	0.248009i
$456$	9.41526	−	77.5417i	0.440910	−	3.63122i
$457$	22.3989	−	21.5144i	1.04778	−	1.00640i	0.0478041	−	0.998857i	$-0.484778\pi$
$457$	22.3989	−	21.5144i	1.04778	−	1.00640i	0.999972	−	0.00754546i	$-0.00240182\pi$
$458$	−14.5617	−	15.1604i	−0.680425	−	0.708398i
$459$	−0.347240	−	0.731792i	−0.0162078	−	0.0341571i
$460$	−9.20387	−	6.35298i	−0.429133	−	0.296209i
$461$	12.0054	+	18.9850i	0.559146	+	0.884218i	0.999910	−	0.0134047i	$-0.00426698\pi$
$461$	12.0054	+	18.9850i	0.559146	+	0.884218i	−0.440765	+	0.897623i	$0.645293\pi$
$462$	−15.7662	+	20.9810i	−0.733510	+	0.976125i
$463$	−0.244576	+	0.466002i	−0.0113664	+	0.0216569i	−0.891073	−	0.453860i	$-0.850047\pi$
$463$	−0.244576	+	0.466002i	−0.0113664	+	0.0216569i	0.879707	+	0.475517i	$0.157739\pi$
$464$	14.1027	+	69.0795i	0.654700	+	3.20693i
$465$	−14.7196	−	1.18829i	−0.682607	−	0.0551057i
$466$	37.0969	−	10.7452i	1.71848	−	0.497763i
$467$	−9.65797	+	5.06890i	−0.446918	+	0.234561i	−0.673140	−	0.739515i	$-0.735055\pi$
$467$	−9.65797	+	5.06890i	−0.446918	+	0.234561i	0.226222	+	0.974076i	$0.427362\pi$
$468$	−3.10453	−	2.08228i	−0.143507	−	0.0962535i
$469$	37.9350	+	19.9098i	1.75168	+	0.919350i
$470$	−44.9611	−	9.17887i	−2.07390	−	0.423390i
$471$	−0.621790	+	0.467245i	−0.0286506	+	0.0215295i
$472$	−2.49290	+	61.8607i	−0.114745	+	2.84737i
$473$	5.77208	+	2.18906i	0.265401	+	0.100653i
$474$	7.62914	+	2.20981i	0.350418	+	0.101500i
$475$	−8.48949	+	1.73314i	−0.389524	+	0.0795220i
$476$	−1.76930	+	1.99713i	−0.0810959	+	0.0915384i
$477$	−0.861385	−	1.05500i	−0.0394401	−	0.0483053i
$478$	−2.97854	−	73.9116i	−0.136235	−	3.38064i
$479$	2.94693	−	8.82713i	0.134649	−	0.403322i	−0.859527	−	0.511090i	$-0.829242\pi$
$479$	2.94693	−	8.82713i	0.134649	−	0.403322i	0.994176	+	0.107768i	$0.0343702\pi$
$480$	−70.6499	−	62.5904i	−3.22471	−	2.85685i
$481$	1.73103	+	12.8236i	0.0789280	+	0.584705i
$482$	8.53717	−	7.56327i	0.388857	−	0.344498i
$483$	−2.13686	−	5.01541i	−0.0972307	−	0.228209i
$484$	22.2818	+	38.5932i	1.01281	+	1.75423i
$485$	−6.74108	+	11.6759i	−0.306097	+	0.530175i
$486$	−5.05884	−	0.614255i	−0.229474	−	0.0278632i
$487$	21.8525	−	10.3691i	0.990232	−	0.469871i	0.136532	−	0.990636i	$-0.456404\pi$
$487$	21.8525	−	10.3691i	0.990232	−	0.469871i	0.853700	+	0.520765i	$0.174353\pi$
$488$	99.9026	+	57.6788i	4.52238	+	2.61100i
$489$	25.4337	−	17.5556i	1.15015	−	0.793891i
$490$	7.57293	+	3.22652i	0.342110	+	0.145759i
$491$	−9.36729	+	1.52233i	−0.422740	+	0.0687019i	−0.368060	−	0.929802i	$-0.619978\pi$
$491$	−9.36729	+	1.52233i	−0.422740	+	0.0687019i	−0.0546797	+	0.998504i	$0.517414\pi$
$492$	−28.9927	−	38.5823i	−1.30709	−	1.73942i
$493$	0.194005	−	0.511550i	0.00873756	−	0.0230391i
$494$	−6.23471	+	41.8870i	−0.280513	+	1.88458i
$495$	−0.197811	−	0.521585i	−0.00889094	−	0.0234435i
$496$	−53.7587	+	85.0126i	−2.41384	+	3.81718i
$497$	−14.2015	+	6.05070i	−0.637026	+	0.271411i
$498$	48.1884	−	30.4725i	2.15937	−	1.36551i
$499$	−34.3345	+	4.16896i	−1.53702	+	0.186628i	−0.844810	−	0.535066i	$-0.820287\pi$
$499$	−34.3345	+	4.16896i	−1.53702	+	0.186628i	−0.692212	+	0.721695i	$0.743364\pi$
$500$	−28.2439	+	66.2909i	−1.26311	+	2.96462i
$501$	4.48942	+	13.4475i	0.200573	+	0.600788i
$502$	74.6209	−	28.3000i	3.33049	−	1.26309i
$503$	−7.52904	+	0.607807i	−0.335703	+	0.0271008i	−0.247169	−	0.968972i	$-0.579500\pi$
$503$	−7.52904	+	0.607807i	−0.335703	+	0.0271008i	−0.0885343	+	0.996073i	$0.528218\pi$
$504$	1.59474	+	5.50567i	0.0710352	+	0.245242i
$505$	−4.83767	+	0.194951i	−0.215273	+	0.00867522i
$506$	5.81412			0.258469
$507$	−17.8149	−	12.6575i	−0.791188	−	0.562137i
$508$	60.7709			2.69627
$509$	35.7484	−	1.44061i	1.58452	−	0.0638540i	0.767725	−	0.640780i	$-0.221389\pi$
$509$	35.7484	−	1.44061i	1.58452	−	0.0638540i	0.816797	+	0.576926i	$0.195748\pi$
$510$	0.342162	+	1.18128i	0.0151512	+	0.0523080i
$511$	−2.85007	+	0.230082i	−0.126080	+	0.0101782i
$512$	−192.886	+	73.1519i	−8.52442	+	3.23289i
$513$	7.03586	+	21.0750i	0.310641	+	0.930483i
$514$	1.05728	−	2.48152i	0.0466344	−	0.109455i
$515$	−9.66802	+	1.17391i	−0.426024	+	0.0517286i
$516$	−27.8524	+	17.6128i	−1.22613	+	0.775360i
$517$	16.4304	−	7.00034i	0.722608	−	0.307875i
$518$	15.9658	−	25.2478i	0.701495	−	1.10933i
$519$	4.52238	+	11.9245i	0.198511	+	0.523429i
$520$	50.2077	+	46.9531i	2.20175	+	2.05903i
$521$	7.06975	−	18.6414i	0.309731	−	0.816695i	−0.686269	−	0.727348i	$-0.740753\pi$
$521$	7.06975	−	18.6414i	0.309731	−	0.816695i	0.996001	−	0.0893470i	$-0.0284780\pi$
$522$	−1.06304	−	1.41464i	−0.0465278	−	0.0619173i
$523$	−1.62919	+	0.264770i	−0.0712397	+	0.0115776i	−0.195927	−	0.980619i	$-0.562771\pi$
$523$	−1.62919	+	0.264770i	−0.0712397	+	0.0115776i	0.124687	+	0.992196i	$0.460207\pi$
$524$	22.2468	+	9.47847i	0.971856	+	0.414069i
$525$	−8.49504	+	5.86370i	−0.370754	+	0.255913i
$526$	9.56900	+	5.52467i	0.417228	+	0.240887i
$527$	0.705158	−	0.334602i	0.0307172	−	0.0145755i
$528$	61.2326	+	7.43499i	2.66481	+	0.323566i
$529$	10.8961	−	18.8727i	0.473745	−	0.820550i
$530$	18.8538	+	32.6557i	0.818956	+	1.41847i
$531$	−0.378553	−	0.888496i	−0.0164278	−	0.0385575i
$532$	54.7818	−	48.5324i	2.37509	−	2.10415i
$533$	10.0625	+	14.1698i	0.435856	+	0.613761i
$534$	−19.0140	−	16.8449i	−0.822816	−	0.728951i
$535$	4.19454	−	12.5642i	0.181346	−	0.543197i
$536$	−6.52329	−	161.874i	−0.281763	−	6.99188i
$537$	13.1858	+	16.1497i	0.569010	+	0.696911i
$538$	3.94150	−	4.44903i	0.169930	−	0.191811i
$539$	−3.13896	+	0.640823i	−0.135204	+	0.0276022i
$540$	52.1550	+	15.1069i	2.24439	+	0.650096i
$541$	−28.4879	−	10.8040i	−1.22479	−	0.464502i	−0.344433	−	0.938811i	$-0.611929\pi$
$541$	−28.4879	−	10.8040i	−1.22479	−	0.464502i	−0.880359	+	0.474309i	$0.842698\pi$
$542$	0.0382201	−	0.948421i	0.00164169	−	0.0407382i
$543$	12.3642	−	9.29112i	0.530600	−	0.398720i
$544$	4.88789	+	0.997870i	0.209567	+	0.0427833i
$545$	−21.6369	−	11.3559i	−0.926824	−	0.486435i
$546$	12.7262	+	48.8187i	0.544631	+	2.08925i
$547$	−15.9153	+	8.35301i	−0.680491	+	0.357149i	−0.769289	−	0.638901i	$-0.779390\pi$
$547$	−15.9153	+	8.35301i	−0.680491	+	0.357149i	0.0887987	+	0.996050i	$0.471697\pi$
$548$	−16.1686	+	4.68329i	−0.690688	+	0.200060i
$549$	−1.79368	−	0.144801i	−0.0765525	−	0.00617996i
$550$	−2.20199	−	10.7861i	−0.0938933	−	0.459920i
$551$	−6.97418	+	13.2882i	−0.297110	+	0.566096i
$552$	−12.3843	+	16.4805i	−0.527112	+	0.701458i
$553$	2.64192	+	4.17787i	0.112346	+	0.177661i
$554$	34.0313	+	23.4901i	1.44585	+	0.998000i
$555$	−4.41892	−	9.31268i	−0.187573	−	0.395301i
$556$	−16.5403	−	17.2203i	−0.701465	−	0.730302i
$557$	14.4951	−	13.9227i	0.614177	−	0.589925i	−0.319700	−	0.947519i	$-0.603582\pi$
$557$	14.4951	−	13.9227i	0.614177	−	0.589925i	0.933877	+	0.357594i	$0.116403\pi$
$558$	0.304293	−	2.50608i	0.0128818	−	0.106091i
$559$	10.1969	−	6.07008i	0.431285	−	0.256737i
$560$	−11.8890	−	97.9145i	−0.502401	−	4.13764i
$561$	−0.370762	−	0.302717i	−0.0156536	−	0.0127807i
$562$	10.4713	−	51.2919i	0.441706	−	2.16362i
$563$	3.89397	−	13.4435i	0.164111	−	0.566578i	−0.835737	−	0.549131i	$-0.814959\pi$
$563$	3.89397	−	13.4435i	0.164111	−	0.566578i	0.999848	−	0.0174472i	$-0.00555390\pi$
$564$	−22.8158	+	92.5674i	−0.960719	+	3.89779i
$565$	−0.766590	−	9.49592i	−0.0322507	−	0.399496i
$566$	9.64434	−	59.3440i	0.405382	−	2.49442i
$567$	16.5304	+	18.6589i	0.694210	+	0.783601i
$568$	46.6660	+	35.0672i	1.95806	+	1.47139i
$569$	3.30413	−	4.04682i	0.138516	−	0.169652i	−0.700688	−	0.713468i	$-0.747124\pi$
$569$	3.30413	−	4.04682i	0.138516	−	0.169652i	0.839204	+	0.543816i	$0.183021\pi$
$570$	−5.41144	−	33.2979i	−0.226660	−	1.39470i
$571$	−2.30854	+	0.569003i	−0.0966093	+	0.0238120i	−0.287324	−	0.957833i	$-0.592766\pi$
$571$	−2.30854	+	0.569003i	−0.0966093	+	0.0238120i	0.190715	+	0.981646i	$0.438919\pi$
$572$	−39.8403	−	5.93007i	−1.66581	−	0.247949i
$573$	−18.2377	−	4.49519i	−0.761891	−	0.187789i
$574$	3.22838	−	39.9907i	0.134750	−	1.66918i
$575$	2.16907	+	0.724141i	0.0904564	+	0.0301988i
$576$	6.45944	−	6.72499i	0.269143	−	0.280208i
$577$		−	25.9347i		−	1.07968i	−0.841769	−	0.539838i	$-0.818486\pi$
$577$		−	25.9347i		−	1.07968i	0.841769	−	0.539838i	$-0.181514\pi$
$578$	34.5356	+	33.1719i	1.43649	+	1.37977i
$579$	−33.1482	+	27.0646i	−1.37759	+	1.12477i
$580$	17.0439	+	32.4745i	0.707711	+	1.34843i
$581$	35.0234	+	5.69185i	1.45301	+	0.236138i
$582$	31.6238	+	19.9977i	1.31085	+	0.828930i
$583$	−13.2586	−	6.29130i	−0.549117	−	0.260559i
$584$	6.14215	+	8.89843i	0.254164	+	0.368220i
$585$	−1.02159	−	0.325969i	−0.0422375	−	0.0134771i
$586$	−49.3324	+	71.4703i	−2.03790	+	2.95241i
$587$	−27.2103	+	15.7099i	−1.12309	+	0.648416i	−0.942188	−	0.335085i	$-0.891235\pi$
$587$	−27.2103	+	15.7099i	−1.12309	+	0.648416i	−0.180902	+	0.983501i	$0.557902\pi$
$588$	7.33150	−	15.4508i	0.302346	−	0.637180i
$589$	−20.3079	+	6.77978i	−0.836774	+	0.279356i
$590$	6.39887	+	25.9612i	0.263437	+	1.06881i
$591$	−10.2041	−	0.411212i	−0.419742	−	0.0169150i
$592$	−70.1519	−	2.82702i	−2.88322	−	0.116190i
$593$	−7.42771	−	30.1354i	−0.305020	−	1.23751i	−0.900753	−	0.434331i	$-0.856985\pi$
$593$	−7.42771	−	30.1354i	−0.305020	−	1.23751i	0.595734	−	0.803182i	$-0.296861\pi$
$594$	−26.7762	+	8.93921i	−1.09864	+	0.366780i
$595$	−0.328114	+	0.691485i	−0.0134513	+	0.0283481i
$596$	−19.8014	+	11.4324i	−0.811099	+	0.468288i
$597$	1.74081	−	2.52200i	0.0712467	−	0.103219i
$598$	6.95240	−	8.75098i	0.284305	−	0.357854i
$599$	−17.3969	−	25.2038i	−0.710819	−	1.02980i	−0.997423	−	0.0717500i	$-0.977142\pi$
$599$	−17.3969	−	25.2038i	−0.710819	−	1.02980i	0.286604	−	0.958049i	$-0.407474\pi$
$600$	35.2642	+	16.7331i	1.43966	+	0.683125i
$601$	2.35731	+	1.49067i	0.0961568	+	0.0608059i	0.581679	−	0.813419i	$-0.302396\pi$
$601$	2.35731	+	1.49067i	0.0961568	+	0.0608059i	−0.485522	+	0.874224i	$0.661370\pi$
$602$	−27.0406	−	4.39452i	−1.10209	−	0.179107i
$603$	1.17445	+	2.23772i	0.0478272	+	0.0911271i
$604$	31.6826	−	25.8680i	1.28915	−	1.05256i
$605$	9.21948	+	8.85543i	0.374825	+	0.360024i
$606$			13.4366i			0.545823i
$607$	11.9867	−	12.4795i	0.486525	−	0.506526i	−0.432008	−	0.901870i	$-0.642195\pi$
$607$	11.9867	−	12.4795i	0.486525	−	0.506526i	0.918533	+	0.395343i	$0.129374\pi$
$608$	−129.799	−	43.3333i	−5.26405	−	1.75740i
$609$	−1.43860	+	17.8202i	−0.0582950	+	0.722113i
$610$	48.3731	+	11.9229i	1.95857	+	0.482744i
$611$	9.11071	−	33.1007i	0.368580	−	1.33911i
$612$	−0.152816	+	0.0376657i	−0.00617721	+	0.00152255i
$613$	−2.37667	−	14.6242i	−0.0959928	−	0.590667i	−0.989828	−	0.142271i	$-0.954560\pi$
$613$	−2.37667	−	14.6242i	−0.0959928	−	0.590667i	0.893835	−	0.448396i	$-0.148005\pi$
$614$	10.3472	−	12.6730i	0.417579	−	0.511442i
$615$	−11.0677	−	8.31684i	−0.446293	−	0.335367i
$616$	40.9561	+	46.2299i	1.65017	+	1.86266i
$617$	−0.641616	+	3.94802i	−0.0258305	+	0.158941i	−0.996761	−	0.0804198i	$-0.974374\pi$
$617$	−0.641616	+	3.94802i	−0.0258305	+	0.158941i	0.970931	+	0.239361i	$0.0769380\pi$
$618$	2.17486	+	26.9404i	0.0874855	+	1.08370i
$619$	10.1598	−	41.2201i	0.408358	−	1.65678i	−0.302281	−	0.953219i	$-0.597748\pi$
$619$	10.1598	−	41.2201i	0.408358	−	1.65678i	0.710639	−	0.703556i	$-0.248406\pi$
$620$	−14.5570	+	50.2567i	−0.584625	+	2.01836i
$621$	1.17292	−	5.74536i	0.0470678	−	0.230553i
$622$	14.9859	+	12.2356i	0.600879	+	0.490602i
$623$	−1.90557	−	15.6938i	−0.0763450	−	0.628758i
$624$	84.4112	−	83.2722i	3.37915	−	3.33356i
$625$	−1.23745	+	10.1913i	−0.0494980	+	0.407653i
$626$	−53.5281	+	51.4144i	−2.13941	+	2.05493i
$627$	9.09504	+	9.46894i	0.363221	+	0.378153i
$628$	1.18136	+	2.48967i	0.0471415	+	0.0993486i
$629$	0.448370	+	0.309487i	0.0178777	+	0.0123401i
$630$	1.32309	+	2.09230i	0.0527131	+	0.0833591i
$631$	−7.62442	+	10.1463i	−0.303523	+	0.403916i	−0.925274	−	0.379299i	$-0.876165\pi$
$631$	−7.62442	+	10.1463i	−0.303523	+	0.403916i	0.621751	+	0.783215i	$0.286422\pi$
$632$	8.68662	−	16.5510i	0.345535	−	0.658362i
$633$	−5.08989	−	24.9319i	−0.202305	−	0.990955i
$634$	51.8796	+	4.18815i	2.06040	+	0.166333i
$635$	16.7444	−	4.85008i	0.664483	−	0.192470i
$636$	69.3676	−	36.4069i	2.75060	−	1.44363i
$637$	−2.78897	+	5.49081i	−0.110503	+	0.217554i
$638$	−16.8829	−	8.86083i	−0.668401	−	0.350804i
$639$	−0.892188	−	0.182141i	−0.0352944	−	0.00720540i
$640$	−116.610	+	87.6268i	−4.60942	+	3.46375i
$641$	−1.53924	+	38.1958i	−0.0607963	+	1.50865i	0.624870	+	0.780729i	$0.285152\pi$
$641$	−1.53924	+	38.1958i	−0.0607963	+	1.50865i	−0.685666	+	0.727916i	$0.740489\pi$
$642$	−34.3716	−	13.0354i	−1.35654	−	0.514467i
$643$	0.178161	+	0.0516048i	0.00702597	+	0.00203510i	0.281729	−	0.959494i	$-0.409092\pi$
$643$	0.178161	+	0.0516048i	0.00702597	+	0.00203510i	−0.274703	+	0.961529i	$0.588579\pi$
$644$	−18.9253	+	3.86362i	−0.745761	+	0.152248i
$645$	−6.26861	+	7.07580i	−0.246826	+	0.278609i
$646$	1.12765	+	1.38112i	0.0443669	+	0.0543395i
$647$	0.444061	+	11.0193i	0.0174578	+	0.433212i	0.984157	+	0.177298i	$0.0567355\pi$
$647$	0.444061	+	11.0193i	0.0174578	+	0.433212i	−0.966699	+	0.255914i	$0.917623\pi$
$648$	29.8503	−	89.4125i	1.17263	−	3.51246i
$649$	−7.78926	−	6.90068i	−0.305755	−	0.270876i
$650$	−18.8675	−	9.58347i	−0.740044	−	0.375894i
$651$	−19.0913	+	16.9134i	−0.748247	+	0.662889i
$652$	−42.9188	−	100.734i	−1.68083	−	3.94506i
$653$	19.9813	+	34.6087i	0.781930	+	1.35434i	0.930816	+	0.365487i	$0.119098\pi$
$653$	19.9813	+	34.6087i	0.781930	+	1.35434i	−0.148887	+	0.988854i	$0.547569\pi$
$654$	−33.9077	+	58.7298i	−1.32589	+	2.29652i
$655$	6.88622	+	0.836138i	0.269067	+	0.0326706i
$656$	−85.1914	+	40.4238i	−3.32617	+	1.57829i
$657$	−0.146071	−	0.0843339i	−0.00569876	−	0.00329018i
$658$	−65.2266	+	45.0227i	−2.54280	+	1.75517i
$659$	26.1445	+	11.1391i	1.01845	+	0.433920i	0.835668	−	0.549235i	$-0.185081\pi$
$659$	26.1445	+	11.1391i	1.01845	+	0.433920i	0.182778	+	0.983154i	$0.441491\pi$
$660$	31.6709	−	5.14702i	1.23279	−	0.200348i
$661$	−14.2396	−	18.9495i	−0.553858	−	0.737051i	0.432506	−	0.901631i	$-0.357629\pi$
$661$	−14.2396	−	18.9495i	−0.553858	−	0.737051i	−0.986364	+	0.164580i	$0.947373\pi$
$662$	−21.7928	+	57.4628i	−0.847000	+	2.23336i
$663$	−0.898976	+	0.196060i	−0.0349133	+	0.00761434i
$664$	−47.5794	−	125.457i	−1.84644	−	4.86866i
$665$	11.2209	−	17.7444i	0.435128	−	0.688100i
$666$	1.62111	−	0.690692i	0.0628169	−	0.0267638i
$667$	3.34752	−	2.11685i	0.129617	−	0.0819646i
$668$	49.8642	−	6.05461i	1.92930	−	0.234260i
$669$	−2.67634	+	6.28161i	−0.103473	+	0.242861i
$670$	−22.1563	−	66.3663i	−0.855973	−	2.56395i
$671$	−18.1299	+	6.87577i	−0.699898	+	0.265436i
$672$	−162.492	+	13.1177i	−6.26828	+	0.506028i
$673$	6.47682	+	22.3606i	0.249663	+	0.861937i	0.983238	+	0.182328i	$0.0583634\pi$
$673$	6.47682	+	22.3606i	0.249663	+	0.861937i	−0.733574	+	0.679609i	$0.762149\pi$
$674$	−45.0648	+	1.81605i	−1.73583	+	0.0699517i
$675$	−11.1027			−0.427344
$676$	−56.5656	+	52.8736i	−2.17560	+	2.03360i
$677$	−46.3183			−1.78016			−0.890078	−	0.455809i	$-0.849350\pi$
$677$	−46.3183			−1.78016			−0.890078	+	0.455809i	$0.849350\pi$
$678$	−26.4177	+	1.06460i	−1.01456	+	0.0408855i
$679$	6.47849	+	22.3663i	0.248622	+	0.858341i
$680$	2.88485	−	0.232889i	0.110629	−	0.00893090i
$681$	38.0620	−	14.4350i	1.45854	−	0.553151i
$682$	−8.61386	−	25.8017i	−0.329842	−	0.987996i
$683$	−2.67011	+	6.26697i	−0.102169	+	0.239799i	−0.963217	−	0.268724i	$-0.913398\pi$
$683$	−2.67011	+	6.26697i	−0.102169	+	0.239799i	0.861048	+	0.508523i	$0.169808\pi$
$684$	4.28575	−	0.520384i	0.163870	−	0.0198974i
$685$	−4.08123	+	2.58081i	−0.155936	+	0.0986077i
$686$	−40.5232	+	17.2653i	−1.54718	+	0.659193i
$687$	−6.69581	+	10.5886i	−0.255461	+	0.403979i
$688$	22.8320	+	60.2030i	0.870461	+	2.29522i
$689$	−25.3236	+	12.4329i	−0.964752	+	0.473657i
$690$	−3.15713	+	8.32468i	−0.120190	+	0.316915i
$691$	3.24660	+	4.32045i	0.123507	+	0.164357i	0.856961	−	0.515381i	$-0.172350\pi$
$691$	3.24660	+	4.32045i	0.123507	+	0.164357i	−0.733454	+	0.679739i	$0.762093\pi$
$692$	44.6008	−	7.24834i	1.69547	−	0.275541i
$693$	−0.886367	−	0.377646i	−0.0336703	−	0.0143456i
$694$	69.9871	−	48.3086i	2.65668	−	1.83377i
$695$	−5.93175	−	3.42470i	−0.225004	−	0.129906i
$696$	61.0780	−	28.9819i	2.31515	−	1.09855i
$697$	0.726385	+	0.0881990i	0.0275138	+	0.00334078i
$698$	12.6484	−	21.9077i	0.478749	−	0.829217i
$699$	−11.5089	−	19.9339i	−0.435305	−	0.753970i
$700$	14.3352	+	33.6460i	0.541820	+	1.27170i
$701$	28.5942	−	25.3322i	1.07999	−	0.956786i	0.0807859	−	0.996731i	$-0.474257\pi$
$701$	28.5942	−	25.3322i	1.07999	−	0.956786i	0.999202	+	0.0399458i	$0.0127185\pi$
$702$	−18.5637	+	50.9908i	−0.700643	+	1.92453i
$703$	−11.1859	−	9.90988i	−0.421886	−	0.373758i
$704$	31.8170	−	95.3036i	1.19915	−	3.59189i
$705$	1.10121	+	27.3264i	0.0414741	+	1.02917i
$706$	27.6893	+	33.9133i	1.04210	+	1.27634i
$707$	−5.54513	+	6.25916i	−0.208546	+	0.235400i
$708$	54.4285	−	11.1117i	2.04555	−	0.417602i
$709$	5.05870	+	1.46527i	0.189984	+	0.0550294i	0.371845	−	0.928295i	$-0.378725\pi$
$709$	5.05870	+	1.46527i	0.189984	+	0.0550294i	−0.181862	+	0.983324i	$0.558212\pi$
$710$	23.5720	+	8.93968i	0.884641	+	0.335500i
$711$	−0.0117410	+	0.291349i	−0.000440321	+	0.0109265i
$712$	−47.7913	+	35.9128i	−1.79106	+	1.34589i
$713$	5.53625	+	1.13023i	0.207334	+	0.0423276i
$714$	1.88081	+	0.987125i	0.0703875	+	0.0369422i
$715$	−11.4506	+	1.54569i	−0.428229	+	0.0578057i
$716$	65.4082	−	34.3289i	2.44442	−	1.28293i
$717$	−42.3449	+	12.2654i	−1.58140	+	0.458058i
$718$	−35.5692	−	2.87144i	−1.32743	−	0.107161i
$719$	5.09301	+	24.9472i	0.189937	+	0.930374i	0.957286	+	0.289144i	$0.0933705\pi$
$719$	5.09301	+	24.9472i	0.189937	+	0.930374i	−0.767349	+	0.641230i	$0.778424\pi$
$720$	2.70387	−	5.15179i	0.100767	−	0.191996i
$721$	−10.1049	+	13.4472i	−0.376327	+	0.500801i
$722$	2.50358	+	3.95909i	0.0931734	+	0.147342i
$723$	−5.59420	−	3.86140i	−0.208050	−	0.143607i
$724$	−23.4913	−	49.5068i	−0.873047	−	1.83991i
$725$	−5.19488	−	5.40844i	−0.192933	−	0.200865i
$726$	25.5862	−	24.5759i	0.949593	−	0.912097i
$727$	−0.0399584	+	0.329087i	−0.00148197	+	0.0122052i	−0.993431	−	0.114432i	$-0.963495\pi$
$727$	−0.0399584	+	0.329087i	−0.00148197	+	0.0122052i	0.991949	+	0.126637i	$0.0404183\pi$
$728$	118.556	−	6.36345i	4.39399	−	0.235845i
$729$	3.42078	+	28.1726i	0.126695	+	1.04343i
$730$	3.61715	+	2.95331i	0.133877	+	0.109307i
$731$	0.0999396	−	0.489537i	0.00369640	−	0.0181062i
$732$	28.7976	−	99.4208i	1.06439	−	3.67470i
$733$	−0.984522	+	3.99436i	−0.0363642	+	0.147535i	−0.986318	−	0.164856i	$-0.947284\pi$
$733$	−0.984522	+	3.99436i	−0.0363642	+	0.147535i	0.949953	+	0.312392i	$0.101130\pi$
$734$	0.969666	+	12.0115i	0.0357910	+	0.443351i
$735$	0.786957	−	4.84234i	0.0290274	−	0.178612i
$736$	23.9487	+	27.0325i	0.882761	+	0.996432i
$737$	21.7694	+	16.3587i	0.801887	+	0.602579i
$738$	1.49678	−	1.83322i	0.0550973	−	0.0674819i
$739$	−5.21809	−	32.1082i	−0.191951	−	1.18112i	−0.886866	−	0.462028i	$-0.847122\pi$
$739$	−5.21809	−	32.1082i	−0.191951	−	1.18112i	0.694915	−	0.719092i	$-0.255442\pi$
$740$	−35.4605	+	8.74023i	−1.30355	+	0.321297i
$741$	25.1276	−	2.36643i	0.923085	−	0.0869332i
$742$	63.2341	+	15.5858i	2.32140	+	0.572173i
$743$	−1.34210	+	16.6249i	−0.0492370	+	0.609910i	0.924343	+	0.381563i	$0.124614\pi$
$743$	−1.34210	+	16.6249i	−0.0492370	+	0.609910i	−0.973580	+	0.228347i	$0.926668\pi$
$744$	91.4845	+	30.5420i	3.35398	+	1.11972i
$745$	−4.54356	+	4.73035i	−0.166463	+	0.173306i
$746$		−	77.3696i		−	2.83270i
$747$	1.50953	+	1.44992i	0.0552308	+	0.0530499i
$748$	−1.31364	+	1.07255i	−0.0480314	+	0.0392164i
$749$	−10.6317	−	20.2571i	−0.388475	−	0.740178i
$750$	56.6218	+	9.20195i	2.06754	+	0.336008i
$751$	−16.8983	−	10.6858i	−0.616627	−	0.389931i	0.189323	−	0.981915i	$-0.439371\pi$
$751$	−16.8983	−	10.6858i	−0.616627	−	0.389931i	−0.805950	+	0.591984i	$0.798345\pi$
$752$	168.291	+	79.8548i	6.13692	+	2.91201i
$753$	−27.0190	−	39.1438i	−0.984628	−	1.42648i
$754$	−33.5249	+	14.8153i	−1.22090	+	0.539542i
$755$	6.66512	−	9.65609i	0.242569	−	0.351421i
$756$	81.2177	−	46.8910i	2.95386	−	1.70541i
$757$	1.92709	−	4.06125i	0.0700412	−	0.147609i	−0.865410	−	0.501064i	$-0.832942\pi$
$757$	1.92709	−	4.06125i	0.0700412	−	0.147609i	0.935451	+	0.353455i	$0.114993\pi$
$758$	−62.7870	+	20.9614i	−2.28053	+	0.761352i
$759$	−0.829251	−	3.36440i	−0.0300999	−	0.122120i
$760$	−79.3252	−	3.19670i	−2.87743	−	0.115956i
$761$	10.9331	+	0.440590i	0.396326	+	0.0159714i	0.237629	−	0.971356i	$-0.423630\pi$
$761$	10.9331	+	0.440590i	0.396326	+	0.0159714i	0.158697	+	0.987327i	$0.449271\pi$
$762$	−11.5781	−	46.9740i	−0.419429	−	1.70169i
$763$	−40.0324	+	13.3648i	−1.44927	+	0.483838i
$764$	−28.5302	+	60.1260i	−1.03218	+	2.17528i
$765$	−0.0390998	+	0.0225743i	−0.00141366	+	0.000816176i
$766$	−12.4816	+	18.0827i	−0.450979	+	0.653356i

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.k (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81837 + 0.113576i) q^{2} +(0.467697 + 1.61468i) q^{3} +(5.93678 - 0.479267i) q^{4} +(1.59753 - 0.605865i) q^{5} +(-1.50153 - 4.49764i) q^{6} +(1.15667 - 2.71481i) q^{7} +(-11.0774 + 1.34504i) q^{8} +(0.147123 - 0.0930351i) q^{9} +O(q^{10})\)	\(q+(-2.81837 + 0.113576i) q^{2} +(0.467697 + 1.61468i) q^{3} +(5.93678 - 0.479267i) q^{4} +(1.59753 - 0.605865i) q^{5} +(-1.50153 - 4.49764i) q^{6} +(1.15667 - 2.71481i) q^{7} +(-11.0774 + 1.34504i) q^{8} +(0.147123 - 0.0930351i) q^{9} +(-4.43363 + 1.88899i) q^{10} +(1.00246 - 1.58527i) q^{11} +(3.55048 + 9.36185i) q^{12} +(-1.18730 - 3.40445i) q^{13} +(-2.95159 + 7.78269i) q^{14} +(1.72544 + 2.29614i) q^{15} +(19.3096 - 3.13811i) q^{16} +(-0.139658 - 0.0595025i) q^{17} +(-0.404081 + 0.278917i) q^{18} +(3.60617 + 2.08202i) q^{19} +(9.19385 - 4.36253i) q^{20} +(4.92451 + 0.597944i) q^{21} +(-2.64526 + 4.58172i) q^{22} +(-0.549486 - 0.951737i) q^{23} +(-7.35269 - 17.2574i) q^{24} +(-1.55751 + 1.37983i) q^{25} +(3.73292 + 9.46015i) q^{26} +(3.99388 + 3.53827i) q^{27} +(5.56579 - 16.6716i) q^{28} +(0.145118 + 3.60106i) q^{29} +(-5.12371 - 6.27541i) q^{30} +(-3.40949 + 3.84852i) q^{31} +(-32.1985 + 6.57336i) q^{32} +(3.02854 + 0.877228i) q^{33} +(0.400364 + 0.151838i) q^{34} +(0.203016 - 5.03779i) q^{35} +(0.828850 - 0.622840i) q^{36} +(-3.51635 - 0.717868i) q^{37} +(-10.4000 - 5.45833i) q^{38} +(4.94180 - 3.50937i) q^{39} +(-16.8817 + 8.86018i) q^{40} +(-4.62982 + 1.34104i) q^{41} +(-13.9470 - 1.12592i) q^{42} +(0.658342 + 3.22477i) q^{43} +(5.19163 - 9.89182i) q^{44} +(0.178668 - 0.237764i) q^{45} +(1.65675 + 2.61994i) q^{46} +(7.83635 + 5.40904i) q^{47} +(14.0981 + 29.7110i) q^{48} +(-1.18322 - 1.23186i) q^{49} +(4.23292 - 4.06577i) q^{50} +(0.0307600 - 0.253331i) q^{51} +(-8.68040 - 19.6425i) q^{52} +(-0.943119 - 7.76728i) q^{53} +(-11.6581 - 9.51854i) q^{54} +(0.641010 - 3.13987i) q^{55} +(-9.16140 + 31.6288i) q^{56} +(-1.67520 + 6.79657i) q^{57} +(-0.817990 - 10.1326i) q^{58} +(0.889991 - 5.47633i) q^{59} +(11.3440 + 12.8048i) q^{60} +(-8.26450 - 6.21037i) q^{61} +(9.17210 - 11.2338i) q^{62} +(-0.0823991 - 0.507022i) q^{63} +(52.0117 - 12.8197i) q^{64} +(-3.95940 - 4.71939i) q^{65} +(-8.63518 - 2.12838i) q^{66} +(-1.16823 + 14.4711i) q^{67} +(-0.857634 - 0.286320i) q^{68} +(1.27976 - 1.33237i) q^{69} +14.2214i q^{70} +(-3.77271 - 3.62374i) q^{71} +(-1.50461 + 1.22848i) q^{72} +(-0.450298 - 0.857971i) q^{73} +(9.99190 + 1.62384i) q^{74} +(-2.95643 - 1.86953i) q^{75} +(22.4069 + 10.6322i) q^{76} +(-3.14417 - 4.55512i) q^{77} +(-13.5292 + 10.4520i) q^{78} +(-0.951562 + 1.37858i) q^{79} +(28.9464 - 16.7122i) q^{80} +(-3.62137 + 7.63188i) q^{81} +(12.8962 - 4.30539i) q^{82} +(2.87759 + 11.6748i) q^{83} +(29.5223 + 1.18971i) q^{84} +(-0.259158 - 0.0104437i) q^{85} +(-2.22171 - 9.01382i) q^{86} +(-5.74668 + 1.91853i) q^{87} +(-8.97244 + 18.9090i) q^{88} +(4.63954 - 2.67864i) q^{89} +(-0.476547 + 0.690398i) q^{90} +(-10.6158 - 0.714534i) q^{91} +(-3.71831 - 5.38691i) q^{92} +(-7.80874 - 3.70529i) q^{93} +(-22.7000 - 14.3546i) q^{94} +(7.02241 + 1.14125i) q^{95} +(-25.6730 - 48.9158i) q^{96} +(-6.11236 + 4.99059i) q^{97} +(3.47465 + 3.33745i) q^{98} -0.326493i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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