LMFDB - Embedded newform 169.2.k.a.4.1

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			4.1
Character	$\chi$	$=$	169.4
Dual form			169.2.k.a.127.1

$q$-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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{78}\right)$

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	−0.993461	−	0.114176i	$-0.963577\pi$
$2$	−2.81837	−	0.113576i	−1.99289	−	0.0803106i	−0.999426	+	0.0338657i	$0.989218\pi$
$3$	0.467697	−	1.61468i	0.270025	−	0.932235i	−0.704826	−	0.709380i	$-0.748975\pi$
$3$	0.467697	−	1.61468i	0.270025	−	0.932235i	0.974852	−	0.222855i	$-0.0715378\pi$
$4$	5.93678	+	0.479267i	2.96839	+	0.239633i
$5$	1.59753	+	0.605865i	0.714439	+	0.270951i	0.684925	−	0.728613i	$-0.259835\pi$
$5$	1.59753	+	0.605865i	0.714439	+	0.270951i	0.0295140	+	0.999564i	$0.490604\pi$
$6$	−1.50153	+	4.49764i	−0.612998	+	1.83615i
$7$	1.15667	+	2.71481i	0.437181	+	1.02610i	0.982227	+	0.187695i	$0.0601016\pi$
$7$	1.15667	+	2.71481i	0.437181	+	1.02610i	−0.545047	+	0.838406i	$0.683488\pi$
$8$	−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	0.961825	−	0.273667i	$-0.0882365\pi$
$11$	1.00246	+	1.58527i	0.302253	+	0.477975i	−0.659571	+	0.751642i	$0.729262\pi$
$12$	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	−0.408836	−	0.912608i	$-0.634065\pi$
$17$	−0.139658	+	0.0595025i	−0.0338719	+	0.0144315i	0.374964	+	0.927039i	$0.377655\pi$
$18$	−0.404081	−	0.278917i	−0.0952428	−	0.0657413i
$19$	3.60617	−	2.08202i	0.827313	−	0.477649i	−0.0256190	−	0.999672i	$-0.508156\pi$
$19$	3.60617	−	2.08202i	0.827313	−	0.477649i	0.852932	+	0.522023i	$0.174822\pi$
$20$	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	−0.917610	−	0.397482i	$-0.869884\pi$
$23$	−0.549486	+	0.951737i	−0.114576	+	0.198451i	0.803034	+	0.595933i	$0.203218\pi$
$24$	−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	−0.928115	−	0.372295i	$-0.878571\pi$
$29$	0.145118	−	3.60106i	0.0269477	−	0.668700i	0.955062	−	0.296405i	$-0.0957879\pi$
$30$	−5.12371	+	6.27541i	−0.935458	+	1.14573i
$31$	−3.40949	−	3.84852i	−0.612363	−	0.691215i	0.357764	−	0.933812i	$-0.383539\pi$
$31$	−3.40949	−	3.84852i	−0.612363	−	0.691215i	−0.970127	+	0.242597i	$0.922001\pi$
$32$	−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	−0.480166	−	0.877178i	$-0.659424\pi$
$37$	−3.51635	+	0.717868i	−0.578084	+	0.118017i	−0.0979183	+	0.995194i	$0.531218\pi$
$38$	−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	−0.103770	−	0.994601i	$-0.533091\pi$
$41$	−4.62982	−	1.34104i	−0.723056	−	0.209436i	−0.619286	+	0.785165i	$0.712578\pi$
$42$	−13.9470	+	1.12592i	−2.15207	+	0.173733i
$43$	0.658342	−	3.22477i	0.100396	−	0.491773i	−0.898237	−	0.439511i	$-0.855152\pi$
$43$	0.658342	−	3.22477i	0.100396	−	0.491773i	0.998633	−	0.0522622i	$-0.0166432\pi$
$44$	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	0.162781	−	0.986662i	$-0.447954\pi$
$47$	7.83635	−	5.40904i	1.14305	−	0.788990i	0.980268	+	0.197673i	$0.0633383\pi$
$48$	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	0.772419	+	0.635113i	$0.219046\pi$
$53$	−0.943119	+	7.76728i	−0.129547	+	1.06692i	−0.901967	+	0.431806i	$0.857877\pi$
$54$	−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	0.978363	+	0.206895i	$0.0663357\pi$
$59$	0.889991	+	5.47633i	0.115867	+	0.712958i	−0.862496	+	0.506063i	$0.831100\pi$
$60$	11.3440	−	12.8048i	1.46451	−	1.65309i
$61$	−8.26450	+	6.21037i	−1.05816	+	0.795156i	−0.979439	−	0.201740i	$-0.935340\pi$
$61$	−8.26450	+	6.21037i	−1.05816	+	0.795156i	−0.0787217	+	0.996897i	$0.525084\pi$
$62$	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	−0.531941	−	0.846781i	$-0.678537\pi$
$67$	−1.16823	−	14.4711i	−0.142722	−	1.76793i	0.389219	−	0.921145i	$-0.372745\pi$
$68$	−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	−0.882375	−	0.470548i	$-0.844056\pi$
$71$	−3.77271	+	3.62374i	−0.447738	+	0.430058i	0.434636	+	0.900606i	$0.356877\pi$
$72$	−1.50461	−	1.22848i	−0.177320	−	0.144777i
$73$	−0.450298	+	0.857971i	−0.0527034	+	0.100418i	−0.910383	−	0.413767i	$-0.864213\pi$
$73$	−0.450298	+	0.857971i	−0.0527034	+	0.100418i	0.857680	+	0.514184i	$0.171905\pi$
$74$	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	0.765792	−	0.643088i	$-0.222347\pi$
$79$	−0.951562	−	1.37858i	−0.107059	−	0.155102i	−0.872851	+	0.487986i	$0.837732\pi$
$80$	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	−0.571579	−	0.820547i	$-0.693669\pi$
$83$	2.87759	−	11.6748i	0.315856	−	1.28148i	0.887435	−	0.460933i	$-0.152485\pi$
$84$	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	0.725317	−	0.688415i	$-0.241693\pi$
$89$	4.63954	+	2.67864i	0.491791	+	0.283936i	−0.233526	+	0.972350i	$0.575026\pi$
$90$	−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	0.269172	−	0.963092i	$-0.413250\pi$
$97$	−6.11236	−	4.99059i	−0.620616	−	0.506717i	−0.889788	+	0.456375i	$0.849148\pi$
$98$	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	−0.447233	−	0.894418i	$-0.647590\pi$
$101$	−2.68789	+	0.897349i	−0.267455	+	0.0892896i	0.179778	+	0.983707i	$0.442462\pi$
$102$	−0.0579205	−	0.717474i	−0.00573498	−	0.0710405i
$103$	−5.53449	+	1.36413i	−0.545329	+	0.134412i	−0.502350	−	0.864664i	$-0.667531\pi$
$103$	−5.53449	+	1.36413i	−0.545329	+	0.134412i	−0.0429794	+	0.999076i	$0.513685\pi$
$104$	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	0.955161	−	0.296086i	$-0.0956815\pi$
$107$	4.90312	+	6.00523i	0.474002	+	0.580547i	−0.481159	+	0.876633i	$0.659784\pi$
$108$	25.4066	−	19.0918i	2.44475	−	1.83711i
$109$	−9.48399	+	10.7052i	−0.908401	+	1.02537i	0.0911624	+	0.995836i	$0.470942\pi$
$109$	−9.48399	+	10.7052i	−0.908401	+	1.02537i	−0.999564	+	0.0295371i	$0.990597\pi$
$110$	−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	0.999863	−	0.0165642i	$-0.00527281\pi$
$113$	1.55132	+	5.35577i	0.145936	+	0.503828i	−0.853927	+	0.520393i	$0.825786\pi$
$114$	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	0.379474	−	0.925203i	$-0.376105\pi$
$127$	10.1701	−	0.821011i	0.902446	−	0.0728530i	0.522972	+	0.852350i	$0.324823\pi$
$128$	−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	−0.300308	−	0.953842i	$-0.597090\pi$
$131$	3.59496	−	1.88678i	0.314094	−	0.164849i	0.614402	+	0.788993i	$0.289397\pi$
$132$	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	0.0802725	−	0.996773i	$-0.474421\pi$
$137$	−2.76910	−	0.565316i	−0.236580	−	0.0482982i	−0.316853	+	0.948475i	$0.602626\pi$
$138$	−3.45550	−	3.90045i	−0.294152	−	0.332029i
$139$	−2.53539	+	3.10528i	−0.215049	+	0.263387i	−0.870852	−	0.491545i	$-0.836432\pi$
$139$	−2.53539	+	3.10528i	−0.215049	+	0.263387i	0.655804	+	0.754931i	$0.272330\pi$
$140$	−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	0.281295	−	0.959621i	$-0.409236\pi$
$149$	−3.46824	−	1.64570i	−0.284129	−	0.134821i	−0.565424	+	0.824800i	$0.691287\pi$
$150$	8.54464	−	4.93325i	0.697667	−	0.402798i
$151$	5.65159	+	3.90101i	0.459919	+	0.317459i	0.775398	−	0.631473i	$-0.217549\pi$
$151$	5.65159	+	3.90101i	0.459919	+	0.317459i	−0.315478	+	0.948933i	$0.602165\pi$
$152$	−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	−0.928310	−	0.371807i	$-0.878738\pi$
$157$	0.164067	−	0.432608i	0.0130939	−	0.0345259i	0.941404	+	0.337281i	$0.109507\pi$
$158$	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	0.430300	+	0.902686i	$0.358408\pi$
$163$	−5.82159	+	17.4378i	−0.455982	+	1.36583i	−0.886282	+	0.463146i	$0.846720\pi$
$164$	−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	0.364098	−	0.931361i	$-0.381377\pi$
$167$	8.42661	+	0.339581i	0.652071	+	0.0262776i	0.287973	+	0.957638i	$0.407018\pi$
$168$	−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	0.364508	−	0.931200i	$-0.381237\pi$
$173$	7.56191	+	0.610460i	0.574921	+	0.0464124i	0.210413	+	0.977613i	$0.432519\pi$
$174$	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	0.773729	−	0.633517i	$-0.218389\pi$
$179$	11.4099	+	4.86130i	0.852816	+	0.363351i	0.0790871	+	0.996868i	$0.474799\pi$
$180$	0.946760	+	1.49718i	0.0705673	+	0.111593i
$181$	−3.26245	+	8.60237i	−0.242496	+	0.639409i	−0.999909	−	0.0135273i	$-0.995694\pi$
$181$	−3.26245	+	8.60237i	−0.242496	+	0.639409i	0.757413	+	0.652937i	$0.226463\pi$
$182$	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	0.589984	−	0.807415i	$-0.299134\pi$
$191$	−5.58684	−	9.67670i	−0.404250	−	0.700181i	−0.994234	+	0.107234i	$0.965801\pi$
$192$	45.0255	−	77.9864i	3.24943	−	5.62818i
$193$	9.97810	−	23.4195i	0.718239	−	1.68577i	−0.00953651	−	0.999955i	$-0.503036\pi$
$193$	9.97810	−	23.4195i	0.718239	−	1.68577i	0.727776	−	0.685815i	$-0.240554\pi$
$194$	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	0.857527	−	0.514440i	$-0.172000\pi$
$197$	−1.92376	−	5.76238i	−0.137063	−	0.410552i	−0.994589	+	0.103887i	$0.966872\pi$
$198$	0.0370819	−	0.920179i	0.00263530	−	0.0653942i
$199$	−1.15291	+	1.41206i	−0.0817279	+	0.100098i	−0.813850	−	0.581075i	$-0.802632\pi$
$199$	−1.15291	+	1.41206i	−0.0817279	+	0.100098i	0.732122	+	0.681173i	$0.238530\pi$
$200$	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	−0.588031	−	0.808838i	$-0.700097\pi$
$211$	−15.0880	+	1.21803i	−1.03870	+	0.0838526i	−0.450669	+	0.892691i	$0.648815\pi$
$212$	−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	−0.521225	−	0.853419i	$-0.674525\pi$
$223$	3.14625	−	2.56883i	0.210688	−	0.172022i	0.731914	+	0.681397i	$0.238627\pi$
$224$	−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	0.528554	+	0.848900i	$0.322735\pi$
$227$	−1.94853	+	24.1369i	−0.129328	+	1.60202i	−0.657882	+	0.753121i	$0.728548\pi$
$228$	−6.68795	−	41.1526i	−0.442920	−	2.72540i
$229$	4.94193	−	5.57828i	0.326572	−	0.368623i	−0.562178	−	0.827016i	$-0.690036\pi$
$229$	4.94193	−	5.57828i	0.326572	−	0.368623i	0.888750	+	0.458393i	$0.151575\pi$
$230$	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	−0.221584	−	0.975141i	$-0.571123\pi$
$233$	−13.2946	−	3.27682i	−0.870957	−	0.214672i	−0.649373	+	0.760470i	$0.724969\pi$
$234$	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	$-0.677701\pi$
$239$		−	26.2250i		−	1.69635i	0.529714	−	0.848177i	$-0.322299\pi$
$240$	40.5230	−	38.9229i	2.61575	−	2.51246i
$241$	−3.13218	−	2.55734i	−0.201761	−	0.164733i	0.526178	−	0.850374i	$-0.323624\pi$
$241$	−3.13218	−	2.55734i	−0.201761	−	0.164733i	−0.727940	+	0.685641i	$0.759522\pi$
$242$	−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	−0.704437	−	0.709767i	$-0.748800\pi$
$251$	−26.8377	−	8.95974i	−1.69398	−	0.565534i	−0.989544	+	0.144233i	$0.953928\pi$
$252$	−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	0.890262	−	0.455448i	$-0.150521\pi$
$257$	−0.409954	−	0.863960i	−0.0255722	−	0.0538923i	−0.915835	+	0.401556i	$0.868470\pi$
$258$	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	−0.632632	−	0.774453i	$-0.718025\pi$
$263$	−3.31086	+	2.09366i	−0.204156	+	0.129101i	0.428475	+	0.903553i	$0.359051\pi$
$264$	−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	0.675212	−	0.737624i	$-0.264052\pi$
$269$	−1.45975	−	1.51976i	−0.0890024	−	0.0926614i	−0.764214	+	0.644963i	$0.776873\pi$
$270$	−24.3912	+	8.14297i	−1.48440	+	0.495565i
$271$	−0.0270782	−	0.335423i	−0.00164488	−	0.0203755i	0.995883	−	0.0906501i	$-0.0288945\pi$
$271$	−0.0270782	−	0.335423i	−0.00164488	−	0.0203755i	−0.997528	+	0.0702746i	$0.977612\pi$
$272$	−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	−0.891433	−	0.453153i	$-0.850299\pi$
$277$	−11.7199	+	8.80696i	−0.704183	+	0.529159i	0.187250	+	0.982312i	$0.440043\pi$
$278$	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	−0.941076	−	0.338196i	$-0.890183\pi$
$281$	−4.44158	−	18.0202i	−0.264962	−	1.07499i	0.676113	−	0.736798i	$-0.263663\pi$
$282$	12.5614	+	43.3669i	0.748019	+	2.58246i
$283$	−4.26357	−	20.8844i	−0.253443	−	1.24145i	−0.884806	−	0.465959i	$-0.845710\pi$
$283$	−4.26357	−	20.8844i	−0.253443	−	1.24145i	0.631363	−	0.775487i	$-0.282496\pi$
$284$	−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	0.889835	+	0.456283i	$0.150819\pi$
$293$	18.4958	+	24.6134i	1.08054	+	1.43793i	0.190700	+	0.981648i	$0.438924\pi$
$294$	−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	0.628426	−	0.777869i	$-0.283700\pi$
$307$	−3.84631	−	4.34159i	−0.219520	−	0.247787i	−0.847946	+	0.530082i	$0.822161\pi$
$308$	−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	−0.796022	−	0.605267i	$-0.793066\pi$
$311$	−5.13393	+	4.54826i	−0.291118	+	0.257908i	0.504904	+	0.863175i	$0.331528\pi$
$312$	−50.0222	−	45.5217i	−2.83195	−	2.57716i
$313$	19.6958	+	17.4489i	1.11327	+	0.986271i	0.999973	−	0.00729028i	$-0.00232059\pi$
$313$	19.6958	+	17.4489i	1.11327	+	0.986271i	0.113296	+	0.993561i	$0.463859\pi$
$314$	−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	−0.617512	−	0.786562i	$-0.711859\pi$
$317$	−18.3180	+	2.22421i	−1.02884	+	0.124924i	−0.411332	+	0.911486i	$0.634936\pi$
$318$	−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	0.971523	+	0.236945i	$0.0761461\pi$
$331$	8.54018	+	20.0445i	0.469411	+	1.10175i	−0.502112	+	0.864802i	$0.667444\pi$
$332$	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	−0.369989	−	0.929036i	$-0.620638\pi$
$347$	−25.4819	−	16.1138i	−1.36794	−	0.865032i	−0.997950	+	0.0640044i	$0.979613\pi$
$348$	−33.1973	−	14.1441i	−1.77956	−	0.758201i
$349$	−4.79331	−	7.58001i	−0.256580	−	0.405749i	0.692191	−	0.721715i	$-0.256646\pi$
$349$	−4.79331	−	7.58001i	−0.256580	−	0.405749i	−0.948770	+	0.315966i	$0.897671\pi$
$350$	−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	−0.976200	−	0.216871i	$-0.930415\pi$
$353$	−9.32455	+	12.4087i	−0.496296	+	0.660450i	0.479905	+	0.877321i	$0.340671\pi$
$354$	−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	0.217799	−	0.975994i	$-0.430112\pi$
$359$	12.5590	−	1.52494i	0.662841	−	0.0804834i	0.445041	+	0.895510i	$0.353189\pi$
$360$	−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	0.988468	+	0.151429i	$0.0483876\pi$
$367$	−0.172026	+	4.26878i	−0.00897969	+	0.222829i	−0.997448	+	0.0713995i	$0.977253\pi$
$368$	−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	−0.732097	−	0.681200i	$-0.761458\pi$
$373$	−1.10448	−	27.4074i	−0.0571878	−	1.41910i	0.674909	−	0.737901i	$-0.264183\pi$
$374$	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	0.800929	−	0.598760i	$-0.204340\pi$
$379$	22.5409	+	6.52905i	1.15785	+	0.335375i	0.356920	+	0.934135i	$0.383827\pi$
$380$	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	0.903009	−	0.429621i	$-0.141353\pi$
$383$	4.67963	+	6.22745i	0.239118	+	0.318208i	−0.663892	+	0.747829i	$0.731096\pi$
$384$	−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	0.952548	+	0.304389i	$0.0984523\pi$
$389$	1.98265	+	16.3286i	0.100524	+	0.827893i	−0.852023	+	0.523504i	$0.824625\pi$
$390$	−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	0.844853	+	0.534999i	$0.179688\pi$
$397$	4.24193	+	26.1016i	0.212896	+	1.31000i	−0.631957	+	0.775004i	$0.717748\pi$
$398$	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	−0.967882	−	0.251406i	$-0.919107\pi$
$401$	0.596776	−	3.67211i	0.0298016	−	0.183377i	0.997683	+	0.0680295i	$0.0216712\pi$
$402$	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	−0.981267	−	0.192651i	$-0.938292\pi$
$409$	−16.7510	+	16.0896i	−0.828284	+	0.795578i	0.152983	+	0.988229i	$0.451112\pi$
$410$	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	0.854394	−	0.519626i	$-0.173929\pi$
$419$	−1.81090	−	3.81640i	−0.0884685	−	0.186443i	−0.942862	+	0.333183i	$0.891877\pi$
$420$	47.8838	+	15.9860i	2.33649	+	0.780035i
$421$	4.75317	−	19.2844i	0.231655	−	0.939862i	−0.733815	−	0.679349i	$-0.762262\pi$
$421$	4.75317	−	19.2844i	0.231655	−	0.939862i	0.965470	−	0.260513i	$-0.0838917\pi$
$422$	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	0.0328558	−	0.999460i	$-0.489540\pi$
$431$	17.1860	−	8.15487i	0.827822	−	0.392806i	0.794966	+	0.606654i	$0.207489\pi$
$432$	88.2236	−	55.7892i	4.24466	−	2.68416i
$433$	30.8839	−	5.01912i	1.48419	−	0.241204i	0.636325	−	0.771421i	$-0.280454\pi$
$433$	30.8839	−	5.01912i	1.48419	−	0.241204i	0.847862	+	0.530218i	$0.177890\pi$
$434$	−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	0.347180	−	0.937799i	$-0.387139\pi$
$439$	24.8936	−	8.31069i	1.18811	−	0.396648i	0.840925	+	0.541151i	$0.182011\pi$
$440$	−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	−0.637545	−	0.770413i	$-0.720050\pi$
$443$	−32.8361	−	8.09338i	−1.56009	−	0.384528i	−0.922547	+	0.385885i	$0.873896\pi$
$444$	−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	−0.999873	−	0.0159257i	$-0.994930\pi$
$449$	−0.220233	+	2.72807i	−0.0103934	+	0.128746i	0.989480	+	0.144671i	$0.0462125\pi$
$450$	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	0.999972	+	0.00754546i	$0.00240182\pi$
$457$	22.3989	+	21.5144i	1.04778	+	1.00640i	0.0478041	+	0.998857i	$0.484778\pi$
$458$	−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	−0.440765	−	0.897623i	$-0.645293\pi$
$461$	12.0054	−	18.9850i	0.559146	−	0.884218i	0.999910	+	0.0134047i	$0.00426698\pi$
$462$	−15.7662	−	20.9810i	−0.733510	−	0.976125i
$463$	−0.244576	−	0.466002i	−0.0113664	−	0.0216569i	0.879707	−	0.475517i	$-0.157739\pi$
$463$	−0.244576	−	0.466002i	−0.0113664	−	0.0216569i	−0.891073	+	0.453860i	$0.850047\pi$
$464$	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	0.226222	−	0.974076i	$-0.427362\pi$
$467$	−9.65797	−	5.06890i	−0.446918	−	0.234561i	−0.673140	+	0.739515i	$0.735055\pi$
$468$	−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	0.994176	−	0.107768i	$-0.0343702\pi$
$479$	2.94693	+	8.82713i	0.134649	+	0.403322i	−0.859527	+	0.511090i	$0.829242\pi$
$480$	−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	0.853700	−	0.520765i	$-0.174353\pi$
$487$	21.8525	+	10.3691i	0.990232	+	0.469871i	0.136532	+	0.990636i	$0.456404\pi$
$488$	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	−0.0546797	−	0.998504i	$-0.517414\pi$
$491$	−9.36729	−	1.52233i	−0.422740	−	0.0687019i	−0.368060	+	0.929802i	$0.619978\pi$
$492$	−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	−0.692212	−	0.721695i	$-0.743364\pi$
$499$	−34.3345	−	4.16896i	−1.53702	−	0.186628i	−0.844810	+	0.535066i	$0.820287\pi$
$500$	−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	−0.0885343	−	0.996073i	$-0.528218\pi$
$503$	−7.52904	−	0.607807i	−0.335703	−	0.0271008i	−0.247169	+	0.968972i	$0.579500\pi$
$504$	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	0.816797	−	0.576926i	$-0.195748\pi$
$509$	35.7484	+	1.44061i	1.58452	+	0.0638540i	0.767725	+	0.640780i	$0.221389\pi$
$510$	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	0.996001	+	0.0893470i	$0.0284780\pi$
$521$	7.06975	+	18.6414i	0.309731	+	0.816695i	−0.686269	+	0.727348i	$0.740753\pi$
$522$	−1.06304	+	1.41464i	−0.0465278	+	0.0619173i
$523$	−1.62919	−	0.264770i	−0.0712397	−	0.0115776i	0.124687	−	0.992196i	$-0.460207\pi$
$523$	−1.62919	−	0.264770i	−0.0712397	−	0.0115776i	−0.195927	+	0.980619i	$0.562771\pi$
$524$	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	−0.880359	−	0.474309i	$-0.842698\pi$
$541$	−28.4879	+	10.8040i	−1.22479	+	0.464502i	−0.344433	+	0.938811i	$0.611929\pi$
$542$	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	0.0887987	−	0.996050i	$-0.471697\pi$
$547$	−15.9153	−	8.35301i	−0.680491	−	0.357149i	−0.769289	+	0.638901i	$0.779390\pi$
$548$	−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	0.933877	−	0.357594i	$-0.116403\pi$
$557$	14.4951	+	13.9227i	0.614177	+	0.589925i	−0.319700	+	0.947519i	$0.603582\pi$
$558$	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	0.999848	+	0.0174472i	$0.00555390\pi$
$563$	3.89397	+	13.4435i	0.164111	+	0.566578i	−0.835737	+	0.549131i	$0.814959\pi$
$564$	−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	0.839204	−	0.543816i	$-0.183021\pi$
$569$	3.30413	+	4.04682i	0.138516	+	0.169652i	−0.700688	+	0.713468i	$0.747124\pi$
$570$	−5.41144	+	33.2979i	−0.226660	+	1.39470i
$571$	−2.30854	−	0.569003i	−0.0966093	−	0.0238120i	0.190715	−	0.981646i	$-0.438919\pi$
$571$	−2.30854	−	0.569003i	−0.0966093	−	0.0238120i	−0.287324	+	0.957833i	$0.592766\pi$
$572$	−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	$0.181514\pi$
$577$			25.9347i			1.07968i	−0.841769	+	0.539838i	$0.818486\pi$
$578$	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	−0.180902	−	0.983501i	$-0.557902\pi$
$587$	−27.2103	−	15.7099i	−1.12309	−	0.648416i	−0.942188	+	0.335085i	$0.891235\pi$
$588$	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	0.595734	+	0.803182i	$0.296861\pi$
$593$	−7.42771	+	30.1354i	−0.305020	+	1.23751i	−0.900753	+	0.434331i	$0.856985\pi$
$594$	−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	0.286604	+	0.958049i	$0.407474\pi$
$599$	−17.3969	+	25.2038i	−0.710819	+	1.02980i	−0.997423	+	0.0717500i	$0.977142\pi$
$600$	35.2642	−	16.7331i	1.43966	−	0.683125i
$601$	2.35731	−	1.49067i	0.0961568	−	0.0608059i	−0.485522	−	0.874224i	$-0.661370\pi$
$601$	2.35731	−	1.49067i	0.0961568	−	0.0608059i	0.581679	+	0.813419i	$0.302396\pi$
$602$	−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	0.918533	−	0.395343i	$-0.129374\pi$
$607$	11.9867	+	12.4795i	0.486525	+	0.506526i	−0.432008	+	0.901870i	$0.642195\pi$
$608$	−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	0.893835	+	0.448396i	$0.148005\pi$
$613$	−2.37667	+	14.6242i	−0.0959928	+	0.590667i	−0.989828	+	0.142271i	$0.954560\pi$
$614$	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	0.970931	−	0.239361i	$-0.0769380\pi$
$617$	−0.641616	−	3.94802i	−0.0258305	−	0.158941i	−0.996761	+	0.0804198i	$0.974374\pi$
$618$	2.17486	−	26.9404i	0.0874855	−	1.08370i
$619$	10.1598	+	41.2201i	0.408358	+	1.65678i	0.710639	+	0.703556i	$0.248406\pi$
$619$	10.1598	+	41.2201i	0.408358	+	1.65678i	−0.302281	+	0.953219i	$0.597748\pi$
$620$	−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	0.621751	−	0.783215i	$-0.286422\pi$
$631$	−7.62442	−	10.1463i	−0.303523	−	0.403916i	−0.925274	+	0.379299i	$0.876165\pi$
$632$	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	−0.685666	−	0.727916i	$-0.740489\pi$
$641$	−1.53924	−	38.1958i	−0.0607963	−	1.50865i	0.624870	−	0.780729i	$-0.285152\pi$
$642$	−34.3716	+	13.0354i	−1.35654	+	0.514467i
$643$	0.178161	−	0.0516048i	0.00702597	−	0.00203510i	−0.274703	−	0.961529i	$-0.588579\pi$
$643$	0.178161	−	0.0516048i	0.00702597	−	0.00203510i	0.281729	+	0.959494i	$0.409092\pi$
$644$	−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	−0.966699	−	0.255914i	$-0.917623\pi$
$647$	0.444061	−	11.0193i	0.0174578	−	0.433212i	0.984157	−	0.177298i	$-0.0567355\pi$
$648$	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	−0.148887	−	0.988854i	$-0.547569\pi$
$653$	19.9813	−	34.6087i	0.781930	−	1.35434i	0.930816	−	0.365487i	$-0.119098\pi$
$654$	−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	0.182778	−	0.983154i	$-0.441491\pi$
$659$	26.1445	−	11.1391i	1.01845	−	0.433920i	0.835668	+	0.549235i	$0.185081\pi$
$660$	31.6709	+	5.14702i	1.23279	+	0.200348i
$661$	−14.2396	+	18.9495i	−0.553858	+	0.737051i	−0.986364	−	0.164580i	$-0.947373\pi$
$661$	−14.2396	+	18.9495i	−0.553858	+	0.737051i	0.432506	+	0.901631i	$0.357629\pi$
$662$	−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	−0.733574	−	0.679609i	$-0.762149\pi$
$673$	6.47682	−	22.3606i	0.249663	−	0.861937i	0.983238	−	0.182328i	$-0.0583634\pi$
$674$	−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	0.861048	−	0.508523i	$-0.169808\pi$
$683$	−2.67011	−	6.26697i	−0.102169	−	0.239799i	−0.963217	+	0.268724i	$0.913398\pi$
$684$	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	−0.733454	−	0.679739i	$-0.762093\pi$
$691$	3.24660	−	4.32045i	0.123507	−	0.164357i	0.856961	+	0.515381i	$0.172350\pi$
$692$	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	0.999202	−	0.0399458i	$-0.0127185\pi$
$701$	28.5942	+	25.3322i	1.07999	+	0.956786i	0.0807859	+	0.996731i	$0.474257\pi$
$702$	−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	−0.181862	−	0.983324i	$-0.558212\pi$
$709$	5.05870	−	1.46527i	0.189984	−	0.0550294i	0.371845	+	0.928295i	$0.378725\pi$
$710$	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	−0.767349	−	0.641230i	$-0.778424\pi$
$719$	5.09301	−	24.9472i	0.189937	−	0.930374i	0.957286	−	0.289144i	$-0.0933705\pi$
$720$	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	0.991949	−	0.126637i	$-0.0404183\pi$
$727$	−0.0399584	−	0.329087i	−0.00148197	−	0.0122052i	−0.993431	+	0.114432i	$0.963495\pi$
$728$	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	0.949953	−	0.312392i	$-0.101130\pi$
$733$	−0.984522	−	3.99436i	−0.0363642	−	0.147535i	−0.986318	+	0.164856i	$0.947284\pi$
$734$	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	0.694915	+	0.719092i	$0.255442\pi$
$739$	−5.21809	+	32.1082i	−0.191951	+	1.18112i	−0.886866	+	0.462028i	$0.847122\pi$
$740$	−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	−0.973580	−	0.228347i	$-0.926668\pi$
$743$	−1.34210	−	16.6249i	−0.0492370	−	0.609910i	0.924343	−	0.381563i	$-0.124614\pi$
$744$	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	−0.805950	−	0.591984i	$-0.798345\pi$
$751$	−16.8983	+	10.6858i	−0.616627	+	0.389931i	0.189323	+	0.981915i	$0.439371\pi$
$752$	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	0.935451	−	0.353455i	$-0.114993\pi$
$757$	1.92709	+	4.06125i	0.0700412	+	0.147609i	−0.865410	+	0.501064i	$0.832942\pi$
$758$	−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	0.158697	−	0.987327i	$-0.449271\pi$
$761$	10.9331	−	0.440590i	0.396326	−	0.0159714i	0.237629	+	0.971356i	$0.423630\pi$
$762$	−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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