LMFDB - Embedded newform 539.2.e.n.177.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.e (of order $3$, degree $2$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6927565824.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 23x^{4} + 10x^{2} + 4 $ x^8 + 5x^6 + 23x^4 + 10*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.4
Root			$1.06789 + 1.84964i$ of defining polynomial
Character	$\chi$	$=$	539.177
Dual form			539.2.e.n.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780776 - 1.35234i) q^{2} +(0.599676 + 1.03867i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(1.53610 - 2.66061i) q^{5} +1.87285 q^{6} +2.43845 q^{8} +(0.780776 - 1.35234i) q^{9} +O(q^{10})$	\(q+(0.780776 - 1.35234i) q^{2} +(0.599676 + 1.03867i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(1.53610 - 2.66061i) q^{5} +1.87285 q^{6} +2.43845 q^{8} +(0.780776 - 1.35234i) q^{9} +(-2.39871 - 4.15468i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.262926 - 0.455402i) q^{12} -6.67026 q^{13} +3.68466 q^{15} +(2.34233 - 4.05703i) q^{16} +(2.13578 + 3.69928i) q^{17} +(-1.21922 - 2.11176i) q^{18} +(-1.19935 + 2.07734i) q^{19} -1.34700 q^{20} +1.56155 q^{22} +(0.719224 - 1.24573i) q^{23} +(1.46228 + 2.53274i) q^{24} +(-2.21922 - 3.84381i) q^{25} +(-5.20798 + 9.02049i) q^{26} +5.47091 q^{27} +2.00000 q^{29} +(2.87689 - 4.98293i) q^{30} +(-3.67188 - 6.35989i) q^{31} +(-1.21922 - 2.11176i) q^{32} +(-0.599676 + 1.03867i) q^{33} +6.67026 q^{34} -0.684658 q^{36} +(-4.28078 + 7.41452i) q^{37} +(1.87285 + 3.24388i) q^{38} +(-4.00000 - 6.92820i) q^{39} +(3.74571 - 6.48775i) q^{40} -4.27156 q^{41} +6.24621 q^{43} +(0.219224 - 0.379706i) q^{44} +(-2.39871 - 4.15468i) q^{45} +(-1.12311 - 1.94528i) q^{46} +(2.13578 - 3.69928i) q^{47} +5.61856 q^{48} -6.93087 q^{50} +(-2.56155 + 4.43674i) q^{51} +(1.46228 + 2.53274i) q^{52} +(1.00000 + 1.73205i) q^{53} +(4.27156 - 7.39856i) q^{54} +3.07221 q^{55} -2.87689 q^{57} +(1.56155 - 2.70469i) q^{58} +(2.99838 + 5.19335i) q^{59} +(-0.807764 - 1.39909i) q^{60} +(-4.00863 + 6.94315i) q^{61} -11.4677 q^{62} +5.56155 q^{64} +(-10.2462 + 17.7470i) q^{65} +(0.936426 + 1.62194i) q^{66} +(-3.84233 - 6.65511i) q^{67} +(0.936426 - 1.62194i) q^{68} +1.72521 q^{69} -16.8078 q^{71} +(1.90388 - 3.29762i) q^{72} +(6.40734 + 11.0978i) q^{73} +(6.68466 + 11.5782i) q^{74} +(2.66163 - 4.61008i) q^{75} +1.05171 q^{76} -12.4924 q^{78} +(-6.56155 + 11.3649i) q^{79} +(-7.19612 - 12.4640i) q^{80} +(0.938447 + 1.62544i) q^{81} +(-3.33513 + 5.77662i) q^{82} +8.54312 q^{83} +13.1231 q^{85} +(4.87689 - 8.44703i) q^{86} +(1.19935 + 2.07734i) q^{87} +(1.21922 + 2.11176i) q^{88} +(-6.33351 + 10.9700i) q^{89} -7.49141 q^{90} -0.630683 q^{92} +(4.40388 - 7.62775i) q^{93} +(-3.33513 - 5.77662i) q^{94} +(3.68466 + 6.38202i) q^{95} +(1.46228 - 2.53274i) q^{96} -4.12391 q^{97} +1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 10 q^{4} + 36 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 10 * q^4 + 36 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 10 q^{4} + 36 q^{8} - 2 q^{9} + 4 q^{11} - 20 q^{15} - 6 q^{16} - 18 q^{18} - 4 q^{22} + 14 q^{23} - 26 q^{25} + 16 q^{29} + 56 q^{30} - 18 q^{32} + 44 q^{36} - 26 q^{37} - 32 q^{39} - 16 q^{43} + 10 q^{44} + 24 q^{46} + 60 q^{50} - 4 q^{51} + 8 q^{53} - 56 q^{57} - 4 q^{58} + 76 q^{60} + 28 q^{64} - 16 q^{65} - 6 q^{67} - 52 q^{71} - 26 q^{72} + 4 q^{74} + 32 q^{78} - 36 q^{79} + 24 q^{81} + 72 q^{85} + 72 q^{86} + 18 q^{88} - 104 q^{92} - 6 q^{93} - 20 q^{95} - 4 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 10 * q^4 + 36 * q^8 - 2 * q^9 + 4 * q^11 - 20 * q^15 - 6 * q^16 - 18 * q^18 - 4 * q^22 + 14 * q^23 - 26 * q^25 + 16 * q^29 + 56 * q^30 - 18 * q^32 + 44 * q^36 - 26 * q^37 - 32 * q^39 - 16 * q^43 + 10 * q^44 + 24 * q^46 + 60 * q^50 - 4 * q^51 + 8 * q^53 - 56 * q^57 - 4 * q^58 + 76 * q^60 + 28 * q^64 - 16 * q^65 - 6 * q^67 - 52 * q^71 - 26 * q^72 + 4 * q^74 + 32 * q^78 - 36 * q^79 + 24 * q^81 + 72 * q^85 + 72 * q^86 + 18 * q^88 - 104 * q^92 - 6 * q^93 - 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.780776	−	1.35234i	0.552092	−	0.956252i	−0.446031	−	0.895017i	$-0.647163\pi$
$2$	0.780776	−	1.35234i	0.552092	−	0.956252i	0.998123	−	0.0612344i	$-0.0195037\pi$
$3$	0.599676	+	1.03867i	0.346223	+	0.599676i	0.985575	−	0.169238i	$-0.0541306\pi$
$3$	0.599676	+	1.03867i	0.346223	+	0.599676i	−0.639352	+	0.768914i	$0.720797\pi$
$4$	−0.219224	−	0.379706i	−0.109612	−	0.189853i
$5$	1.53610	−	2.66061i	0.686966	−	1.18986i	−0.285849	−	0.958275i	$-0.592275\pi$
$5$	1.53610	−	2.66061i	0.686966	−	1.18986i	0.972815	−	0.231585i	$-0.0743912\pi$
$6$	1.87285			0.764589
$7$		0			0
$7$		0			0
$8$	2.43845			0.862121
$9$	0.780776	−	1.35234i	0.260259	−	0.450781i
$10$	−2.39871	−	4.15468i	−0.758537	−	1.31383i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.262926	−	0.455402i	0.0759003	−	0.131463i
$13$	−6.67026			−1.85000			−0.924999	−	0.379969i	$-0.875935\pi$
$13$	−6.67026			−1.85000			−0.924999	+	0.379969i	$0.875935\pi$
$14$		0			0
$15$	3.68466			0.951375
$16$	2.34233	−	4.05703i	0.585582	−	1.01426i
$17$	2.13578	+	3.69928i	0.518003	+	0.897207i	0.999781	+	0.0209138i	$0.00665756\pi$
$17$	2.13578	+	3.69928i	0.518003	+	0.897207i	−0.481779	+	0.876293i	$0.660009\pi$
$18$	−1.21922	−	2.11176i	−0.287374	−	0.497746i
$19$	−1.19935	+	2.07734i	−0.275150	+	0.476574i	−0.970173	−	0.242413i	$-0.922061\pi$
$19$	−1.19935	+	2.07734i	−0.275150	+	0.476574i	0.695023	+	0.718988i	$0.255394\pi$
$20$	−1.34700			−0.301198
$21$		0			0
$22$	1.56155			0.332924
$23$	0.719224	−	1.24573i	0.149968	−	0.259753i	−0.781247	−	0.624222i	$-0.785416\pi$
$23$	0.719224	−	1.24573i	0.149968	−	0.259753i	0.931216	+	0.364469i	$0.118749\pi$
$24$	1.46228	+	2.53274i	0.298487	+	0.516994i
$25$	−2.21922	−	3.84381i	−0.443845	−	0.768762i
$26$	−5.20798	+	9.02049i	−1.02137	+	1.76906i
$27$	5.47091			1.05288
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	2.87689	−	4.98293i	0.525247	−	0.909754i
$31$	−3.67188	−	6.35989i	−0.659489	−	1.14227i	−0.980748	−	0.195278i	$-0.937439\pi$
$31$	−3.67188	−	6.35989i	−0.659489	−	1.14227i	0.321259	−	0.946992i	$-0.395894\pi$
$32$	−1.21922	−	2.11176i	−0.215530	−	0.373309i
$33$	−0.599676	+	1.03867i	−0.104390	+	0.180809i
$34$	6.67026			1.14394
$35$		0			0
$36$	−0.684658			−0.114110
$37$	−4.28078	+	7.41452i	−0.703755	+	1.21894i	0.263384	+	0.964691i	$0.415162\pi$
$37$	−4.28078	+	7.41452i	−0.703755	+	1.21894i	−0.967139	+	0.254249i	$0.918172\pi$
$38$	1.87285	+	3.24388i	0.303817	+	0.526226i
$39$	−4.00000	−	6.92820i	−0.640513	−	1.10940i
$40$	3.74571	−	6.48775i	0.592248	−	1.02580i
$41$	−4.27156			−0.667105			−0.333553	−	0.942731i	$-0.608248\pi$
$41$	−4.27156			−0.667105			−0.333553	+	0.942731i	$0.608248\pi$
$42$		0			0
$43$	6.24621			0.952538			0.476269	−	0.879300i	$-0.341989\pi$
$43$	6.24621			0.952538			0.476269	+	0.879300i	$0.341989\pi$
$44$	0.219224	−	0.379706i	0.0330492	−	0.0572429i
$45$	−2.39871	−	4.15468i	−0.357578	−	0.619343i
$46$	−1.12311	−	1.94528i	−0.165593	−	0.286815i
$47$	2.13578	−	3.69928i	0.311535	−	0.539595i	−0.667160	−	0.744915i	$-0.732490\pi$
$47$	2.13578	−	3.69928i	0.311535	−	0.539595i	0.978695	+	0.205320i	$0.0658234\pi$
$48$	5.61856			0.810969
$49$		0			0
$50$	−6.93087			−0.980173
$51$	−2.56155	+	4.43674i	−0.358689	+	0.621268i
$52$	1.46228	+	2.53274i	0.202782	+	0.351228i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	4.27156	−	7.39856i	0.581285	−	1.00682i
$55$	3.07221			0.414256
$56$		0			0
$57$	−2.87689			−0.381054
$58$	1.56155	−	2.70469i	0.205042	−	0.355143i
$59$	2.99838	+	5.19335i	0.390356	+	0.676117i	0.992496	−	0.122274i	$-0.0390186\pi$
$59$	2.99838	+	5.19335i	0.390356	+	0.676117i	−0.602140	+	0.798390i	$0.705685\pi$
$60$	−0.807764	−	1.39909i	−0.104282	−	0.180622i
$61$	−4.00863	+	6.94315i	−0.513253	+	0.888980i	0.486629	+	0.873609i	$0.338226\pi$
$61$	−4.00863	+	6.94315i	−0.513253	+	0.888980i	−0.999882	+	0.0153711i	$0.995107\pi$
$62$	−11.4677			−1.45640
$63$		0			0
$64$	5.56155			0.695194
$65$	−10.2462	+	17.7470i	−1.27089	+	2.20124i
$66$	0.936426	+	1.62194i	0.115266	+	0.199647i
$67$	−3.84233	−	6.65511i	−0.469415	−	0.813051i	0.529973	−	0.848014i	$-0.322202\pi$
$67$	−3.84233	−	6.65511i	−0.469415	−	0.813051i	−0.999389	+	0.0349633i	$0.988869\pi$
$68$	0.936426	−	1.62194i	0.113558	−	0.196689i
$69$	1.72521			0.207690
$70$		0			0
$71$	−16.8078			−1.99471			−0.997357	−	0.0726526i	$-0.976854\pi$
$71$	−16.8078			−1.99471			−0.997357	+	0.0726526i	$0.976854\pi$
$72$	1.90388	−	3.29762i	0.224375	−	0.388628i
$73$	6.40734	+	11.0978i	0.749922	+	1.29890i	0.947859	+	0.318689i	$0.103242\pi$
$73$	6.40734	+	11.0978i	0.749922	+	1.29890i	−0.197937	+	0.980215i	$0.563424\pi$
$74$	6.68466	+	11.5782i	0.777076	+	1.34593i
$75$	2.66163	−	4.61008i	0.307339	−	0.532326i
$76$	1.05171			0.120639
$77$		0			0
$78$	−12.4924			−1.41449
$79$	−6.56155	+	11.3649i	−0.738232	+	1.27866i	0.215058	+	0.976601i	$0.431006\pi$
$79$	−6.56155	+	11.3649i	−0.738232	+	1.27866i	−0.953291	+	0.302055i	$0.902327\pi$
$80$	−7.19612	−	12.4640i	−0.804550	−	1.39352i
$81$	0.938447	+	1.62544i	0.104272	+	0.180604i
$82$	−3.33513	+	5.77662i	−0.368304	+	0.637921i
$83$	8.54312			0.937729			0.468864	−	0.883270i	$-0.344663\pi$
$83$	8.54312			0.937729			0.468864	+	0.883270i	$0.344663\pi$
$84$		0			0
$85$	13.1231			1.42340
$86$	4.87689	−	8.44703i	0.525889	−	0.910867i
$87$	1.19935	+	2.07734i	0.128584	+	0.222714i
$88$	1.21922	+	2.11176i	0.129970	+	0.225114i
$89$	−6.33351	+	10.9700i	−0.671351	+	1.16281i	0.306170	+	0.951977i	$0.400952\pi$
$89$	−6.33351	+	10.9700i	−0.671351	+	1.16281i	−0.977521	+	0.210837i	$0.932381\pi$
$90$	−7.49141			−0.789664
$91$		0			0
$92$	−0.630683			−0.0657533
$93$	4.40388	−	7.62775i	0.456661	−	0.790961i
$94$	−3.33513	−	5.77662i	−0.343993	−	0.595813i
$95$	3.68466	+	6.38202i	0.378038	+	0.654781i
$96$	1.46228	−	2.53274i	0.149243	−	0.258497i
$97$	−4.12391			−0.418720			−0.209360	−	0.977839i	$-0.567138\pi$
$97$	−4.12391			−0.418720			−0.209360	+	0.977839i	$0.567138\pi$
$98$		0			0
$99$	1.56155			0.156942
$100$	−0.973012	+	1.68531i	−0.0973012	+	0.168531i
$101$	−7.60669	−	13.1752i	−0.756894	−	1.31098i	−0.944427	−	0.328721i	$-0.893383\pi$
$101$	−7.60669	−	13.1752i	−0.756894	−	1.31098i	0.187533	−	0.982258i	$-0.439951\pi$
$102$	4.00000	+	6.92820i	0.396059	+	0.685994i
$103$	4.53448	−	7.85396i	0.446796	−	0.773873i	−0.551379	−	0.834255i	$-0.685898\pi$
$103$	4.53448	−	7.85396i	0.446796	−	0.773873i	0.998175	+	0.0603812i	$0.0192316\pi$
$104$	−16.2651			−1.59492
$105$		0			0
$106$	3.12311			0.303343
$107$	0.561553	−	0.972638i	0.0542874	−	0.0940285i	−0.837605	−	0.546277i	$-0.816045\pi$
$107$	0.561553	−	0.972638i	0.0542874	−	0.0940285i	0.891892	+	0.452248i	$0.149378\pi$
$108$	−1.19935	−	2.07734i	−0.115408	−	0.199892i
$109$	2.68466	+	4.64996i	0.257144	+	0.445386i	0.965476	−	0.260494i	$-0.0838853\pi$
$109$	2.68466	+	4.64996i	0.257144	+	0.445386i	−0.708332	+	0.705880i	$0.750552\pi$
$110$	2.39871	−	4.15468i	0.228708	−	0.396133i
$111$	−10.2683			−0.974626
$112$		0			0
$113$	−14.8078			−1.39300			−0.696499	−	0.717558i	$-0.745260\pi$
$113$	−14.8078			−1.39300			−0.696499	+	0.717558i	$0.745260\pi$
$114$	−2.24621	+	3.89055i	−0.210377	+	0.364384i
$115$	−2.20960	−	3.82714i	−0.206047	−	0.356883i
$116$	−0.438447	−	0.759413i	−0.0407088	−	0.0705097i
$117$	−5.20798	+	9.02049i	−0.481478	+	0.833945i
$118$	9.36426			0.862050
$119$		0			0
$120$	8.98485			0.820200
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	6.25969	+	10.8421i	0.566726	+	0.981598i
$123$	−2.56155	−	4.43674i	−0.230967	−	0.400047i
$124$	−1.60993	+	2.78847i	−0.144576	+	0.250412i
$125$	1.72521			0.154307
$126$		0			0
$127$	−13.1231			−1.16449			−0.582244	−	0.813014i	$-0.697825\pi$
$127$	−13.1231			−1.16449			−0.582244	+	0.813014i	$0.697825\pi$
$128$	6.78078	−	11.7446i	0.599342	−	1.03809i
$129$	3.74571	+	6.48775i	0.329791	+	0.571215i
$130$	16.0000	+	27.7128i	1.40329	+	2.43057i
$131$	3.07221	−	5.32122i	0.268420	−	0.464917i	−0.700034	−	0.714109i	$-0.746832\pi$
$131$	3.07221	−	5.32122i	0.268420	−	0.464917i	0.968454	+	0.249193i	$0.0801652\pi$
$132$	0.525853			0.0457696
$133$		0			0
$134$	−12.0000			−1.03664
$135$	8.40388	−	14.5560i	0.723291	−	1.25278i
$136$	5.20798	+	9.02049i	0.446581	+	0.773501i
$137$	4.28078	+	7.41452i	0.365731	+	0.633465i	0.988893	−	0.148628i	$-0.0474855\pi$
$137$	4.28078	+	7.41452i	0.365731	+	0.633465i	−0.623162	+	0.782093i	$0.714152\pi$
$138$	1.34700	−	2.33307i	0.114664	−	0.198604i
$139$	2.39871			0.203456			0.101728	−	0.994812i	$-0.467563\pi$
$139$	2.39871			0.203456			0.101728	+	0.994812i	$0.467563\pi$
$140$		0			0
$141$	5.12311			0.431443
$142$	−13.1231	+	22.7299i	−1.10127	+	1.90745i
$143$	−3.33513	−	5.77662i	−0.278898	−	0.483065i
$144$	−3.65767	−	6.33527i	−0.304806	−	0.527939i
$145$	3.07221	−	5.32122i	0.255133	−	0.441903i
$146$	20.0108			1.65610
$147$		0			0
$148$	3.75379			0.308560
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	−4.15628	−	7.19889i	−0.339359	−	0.587787i
$151$	3.68466	+	6.38202i	0.299853	+	0.519361i	0.976102	−	0.217312i	$-0.0697289\pi$
$151$	3.68466	+	6.38202i	0.299853	+	0.519361i	−0.676249	+	0.736673i	$0.736396\pi$
$152$	−2.92456	+	5.06548i	−0.237213	+	0.410865i
$153$	6.67026			0.539259
$154$		0			0
$155$	−22.5616			−1.81219
$156$	−1.75379	+	3.03765i	−0.140415	+	0.243207i
$157$	−3.93481	−	6.81529i	−0.314032	−	0.543919i	0.665199	−	0.746666i	$-0.268347\pi$
$157$	−3.93481	−	6.81529i	−0.314032	−	0.543919i	−0.979231	+	0.202747i	$0.935013\pi$
$158$	10.2462	+	17.7470i	0.815145	+	1.41187i
$159$	−1.19935	+	2.07734i	−0.0951149	+	0.164744i
$160$	−7.49141			−0.592248
$161$		0			0
$162$	2.93087			0.230271
$163$	12.2462	−	21.2111i	0.959197	−	1.66138i	0.234741	−	0.972058i	$-0.424576\pi$
$163$	12.2462	−	21.2111i	0.959197	−	1.66138i	0.724457	−	0.689320i	$-0.242091\pi$
$164$	0.936426	+	1.62194i	0.0731226	+	0.126652i
$165$	1.84233	+	3.19101i	0.143425	+	0.248420i
$166$	6.67026	−	11.5532i	0.517713	−	0.896705i
$167$	23.2306			1.79764			0.898821	−	0.438317i	$-0.144425\pi$
$167$	23.2306			1.79764			0.898821	+	0.438317i	$0.144425\pi$
$168$		0			0
$169$	31.4924			2.42249
$170$	10.2462	−	17.7470i	0.785849	−	1.36113i
$171$	1.87285	+	3.24388i	0.143221	+	0.248065i
$172$	−1.36932	−	2.37173i	−0.104409	−	0.180842i
$173$	−1.46228	+	2.53274i	−0.111175	+	0.192561i	−0.916244	−	0.400620i	$-0.868795\pi$
$173$	−1.46228	+	2.53274i	−0.111175	+	0.192561i	0.805069	+	0.593181i	$0.202128\pi$
$174$	3.74571			0.283961
$175$		0			0
$176$	4.68466			0.353119
$177$	−3.59612	+	6.22866i	−0.270301	+	0.468175i
$178$	9.89012	+	17.1302i	0.741296	+	1.28396i
$179$	−2.40388	−	4.16365i	−0.179675	−	0.311205i	0.762095	−	0.647466i	$-0.224171\pi$
$179$	−2.40388	−	4.16365i	−0.179675	−	0.311205i	−0.941769	+	0.336260i	$0.890838\pi$
$180$	−1.05171	+	1.82161i	−0.0783895	+	0.135775i
$181$	10.2683			0.763238			0.381619	−	0.924320i	$-0.375367\pi$
$181$	10.2683			0.763238			0.381619	+	0.924320i	$0.375367\pi$
$182$		0			0
$183$	−9.61553			−0.710800
$184$	1.75379	−	3.03765i	0.129291	−	0.223939i
$185$	13.1514	+	22.7789i	0.966912	+	1.67474i
$186$	−6.87689	−	11.9111i	−0.504238	−	0.873366i
$187$	−2.13578	+	3.69928i	−0.156184	+	0.270518i
$188$	−1.87285			−0.136592
$189$		0			0
$190$	11.5076			0.834847
$191$	−4.40388	+	7.62775i	−0.318654	+	0.551924i	−0.980207	−	0.197973i	$-0.936564\pi$
$191$	−4.40388	+	7.62775i	−0.318654	+	0.551924i	0.661554	+	0.749898i	$0.269897\pi$
$192$	3.33513	+	5.77662i	0.240692	+	0.416892i
$193$	−3.24621	−	5.62260i	−0.233667	−	0.404724i	0.725217	−	0.688520i	$-0.241739\pi$
$193$	−3.24621	−	5.62260i	−0.233667	−	0.404724i	−0.958885	+	0.283796i	$0.908406\pi$
$194$	−3.21985	+	5.57695i	−0.231172	+	0.400402i
$195$	−24.5776			−1.76004
$196$		0			0
$197$	−4.24621			−0.302530			−0.151265	−	0.988493i	$-0.548335\pi$
$197$	−4.24621			−0.302530			−0.151265	+	0.988493i	$0.548335\pi$
$198$	1.21922	−	2.11176i	0.0866464	−	0.150076i
$199$	−2.66163	−	4.61008i	−0.188678	−	0.326800i	0.756132	−	0.654420i	$-0.227087\pi$
$199$	−2.66163	−	4.61008i	−0.188678	−	0.326800i	−0.944810	+	0.327619i	$0.893754\pi$
$200$	−5.41146	−	9.37292i	−0.382648	−	0.662766i
$201$	4.60831	−	7.98182i	0.325045	−	0.562994i
$202$	−23.7565			−1.67150
$203$		0			0
$204$	2.24621			0.157266
$205$	−6.56155	+	11.3649i	−0.458279	+	0.793762i
$206$	−7.08084	−	12.2644i	−0.493345	−	0.854499i
$207$	−1.12311	−	1.94528i	−0.0780612	−	0.135206i
$208$	−15.6240	+	27.0615i	−1.08333	+	1.87638i
$209$	−2.39871			−0.165922
$210$		0			0
$211$	−3.36932			−0.231953			−0.115977	−	0.993252i	$-0.537000\pi$
$211$	−3.36932			−0.231953			−0.115977	+	0.993252i	$0.537000\pi$
$212$	0.438447	−	0.759413i	0.0301127	−	0.0521567i
$213$	−10.0792	−	17.4577i	−0.690617	−	1.19618i
$214$	−0.876894	−	1.51883i	−0.0599433	−	0.103825i
$215$	9.59482	−	16.6187i	0.654361	−	1.13339i
$216$	13.3405			0.907708
$217$		0			0
$218$	8.38447			0.567868
$219$	−7.68466	+	13.3102i	−0.519281	+	0.899421i
$220$	−0.673500	−	1.16654i	−0.0454074	−	0.0786478i
$221$	−14.2462	−	24.6752i	−0.958304	−	1.65983i
$222$	−8.01726	+	13.8863i	−0.538084	+	0.931988i
$223$	−19.6326			−1.31470			−0.657348	−	0.753587i	$-0.728322\pi$
$223$	−19.6326			−1.31470			−0.657348	+	0.753587i	$0.728322\pi$
$224$		0			0
$225$	−6.93087			−0.462058
$226$	−11.5616	+	20.0252i	−0.769063	+	1.33206i
$227$	−4.79741	−	8.30936i	−0.318415	−	0.551512i	0.661742	−	0.749731i	$-0.269817\pi$
$227$	−4.79741	−	8.30936i	−0.318415	−	0.551512i	−0.980158	+	0.198220i	$0.936484\pi$
$228$	0.630683	+	1.09238i	0.0417680	+	0.0723443i
$229$	0.336750	−	0.583268i	0.0222531	−	0.0385434i	−0.854684	−	0.519148i	$-0.826249\pi$
$229$	0.336750	−	0.583268i	0.0222531	−	0.0385434i	0.876937	+	0.480604i	$0.159583\pi$
$230$	−6.90082			−0.455027
$231$		0			0
$232$	4.87689			0.320184
$233$	2.12311	−	3.67733i	0.139089	−	0.240910i	−0.788063	−	0.615595i	$-0.788916\pi$
$233$	2.12311	−	3.67733i	0.139089	−	0.240910i	0.927152	+	0.374685i	$0.122249\pi$
$234$	8.13254	+	14.0860i	0.531641	+	0.920829i
$235$	−6.56155	−	11.3649i	−0.428029	−	0.741367i
$236$	1.31463	−	2.27701i	0.0855753	−	0.148221i
$237$	−15.7392			−1.02237
$238$		0			0
$239$	10.2462			0.662772			0.331386	−	0.943495i	$-0.392484\pi$
$239$	10.2462			0.662772			0.331386	+	0.943495i	$0.392484\pi$
$240$	8.63068	−	14.9488i	0.557108	−	0.964940i
$241$	−9.47954	−	16.4191i	−0.610631	−	1.05764i	−0.991134	−	0.132864i	$-0.957583\pi$
$241$	−9.47954	−	16.4191i	−0.610631	−	1.05764i	0.380503	−	0.924780i	$-0.375751\pi$
$242$	0.780776	+	1.35234i	0.0501902	+	0.0869320i
$243$	7.08084	−	12.2644i	0.454236	−	0.786760i
$244$	3.51515			0.225034
$245$		0			0
$246$	−8.00000			−0.510061
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$	−8.95369	−	15.5082i	−0.568560	−	0.984775i
$249$	5.12311	+	8.87348i	0.324664	+	0.562334i
$250$	1.34700	−	2.33307i	0.0851918	−	0.147556i
$251$	27.8804			1.75980			0.879898	−	0.475163i	$-0.157611\pi$
$251$	27.8804			1.75980			0.879898	+	0.475163i	$0.157611\pi$
$252$		0			0
$253$	1.43845			0.0904344
$254$	−10.2462	+	17.7470i	−0.642904	+	1.11354i
$255$	7.86962	+	13.6306i	0.492815	+	0.853580i
$256$	−5.02699	−	8.70700i	−0.314187	−	0.544187i
$257$	3.74571	−	6.48775i	0.233651	−	0.404695i	−0.725229	−	0.688508i	$-0.758266\pi$
$257$	3.74571	−	6.48775i	0.233651	−	0.404695i	0.958880	+	0.283813i	$0.0915994\pi$
$258$	11.6982			0.728300
$259$		0			0
$260$	8.98485			0.557216
$261$	1.56155	−	2.70469i	0.0966577	−	0.167416i
$262$	−4.79741	−	8.30936i	−0.296385	−	0.513354i
$263$	−11.6847	−	20.2384i	−0.720507	−	1.24795i	−0.960797	−	0.277253i	$-0.910576\pi$
$263$	−11.6847	−	20.2384i	−0.720507	−	1.24795i	0.240290	−	0.970701i	$-0.422757\pi$
$264$	−1.46228	+	2.53274i	−0.0899971	+	0.155879i
$265$	6.14441			0.377448
$266$		0			0
$267$	−15.1922			−0.929750
$268$	−1.68466	+	2.91791i	−0.102907	+	0.178240i
$269$	−8.01726	−	13.8863i	−0.488821	−	0.846663i	0.511096	−	0.859524i	$-0.329240\pi$
$269$	−8.01726	−	13.8863i	−0.488821	−	0.846663i	−0.999917	+	0.0128604i	$0.995906\pi$
$270$	−13.1231	−	22.7299i	−0.798647	−	1.38330i
$271$	−6.67026	+	11.5532i	−0.405190	+	0.701809i	−0.994344	−	0.106212i	$-0.966128\pi$
$271$	−6.67026	+	11.5532i	−0.405190	+	0.701809i	0.589154	+	0.808021i	$0.299461\pi$
$272$	20.0108			1.21333
$273$		0			0
$274$	13.3693			0.807670
$275$	2.21922	−	3.84381i	0.133824	−	0.231790i
$276$	−0.378206	−	0.655072i	−0.0227653	−	0.0394307i
$277$	−11.8078	−	20.4516i	−0.709460	−	1.22882i	−0.965058	−	0.262037i	$-0.915606\pi$
$277$	−11.8078	−	20.4516i	−0.709460	−	1.22882i	0.255598	−	0.966783i	$-0.417728\pi$
$278$	1.87285	−	3.24388i	0.112326	−	0.194555i
$279$	−11.4677			−0.686552
$280$		0			0
$281$	−11.6155			−0.692924			−0.346462	−	0.938064i	$-0.612617\pi$
$281$	−11.6155			−0.692924			−0.346462	+	0.938064i	$0.612617\pi$
$282$	4.00000	−	6.92820i	0.238197	−	0.412568i
$283$	4.79741	+	8.30936i	0.285176	+	0.493940i	0.972652	−	0.232267i	$-0.0746144\pi$
$283$	4.79741	+	8.30936i	0.285176	+	0.493940i	−0.687475	+	0.726208i	$0.741281\pi$
$284$	3.68466	+	6.38202i	0.218644	+	0.378703i
$285$	−4.41921	+	7.65429i	−0.261771	+	0.453401i
$286$	−10.4160			−0.615909
$287$		0			0
$288$	−3.80776			−0.224375
$289$	−0.623106	+	1.07925i	−0.0366533	+	0.0634853i
$290$	−4.79741	−	8.30936i	−0.281714	−	0.487942i
$291$	−2.47301	−	4.28338i	−0.144971	−	0.251096i
$292$	2.80928	−	4.86581i	0.164401	−	0.284750i
$293$	−13.8664			−0.810083			−0.405041	−	0.914298i	$-0.632743\pi$
$293$	−13.8664			−0.810083			−0.405041	+	0.914298i	$0.632743\pi$
$294$		0			0
$295$	18.4233			1.07265
$296$	−10.4384	+	18.0799i	−0.606722	+	1.05087i
$297$	2.73546	+	4.73795i	0.158727	+	0.274924i
$298$	4.68466	+	8.11407i	0.271375	+	0.470035i
$299$	−4.79741	+	8.30936i	−0.277441	+	0.480543i
$300$	−2.33397			−0.134752
$301$		0			0
$302$	11.5076			0.662187
$303$	9.12311	−	15.8017i	0.524109	−	0.907783i
$304$	5.61856	+	9.73163i	0.322246	+	0.558147i
$305$	12.3153	+	21.3308i	0.705174	+	1.22140i
$306$	5.20798	−	9.02049i	0.297721	−	0.515667i
$307$	4.79741			0.273803			0.136901	−	0.990585i	$-0.456286\pi$
$307$	4.79741			0.273803			0.136901	+	0.990585i	$0.456286\pi$
$308$		0			0
$309$	10.8769			0.618765
$310$	−17.6155	+	30.5110i	−1.00049	+	1.73291i
$311$	15.4763	+	26.8058i	0.877581	+	1.52001i	0.853988	+	0.520293i	$0.174177\pi$
$311$	15.4763	+	26.8058i	0.877581	+	1.52001i	0.0235931	+	0.999722i	$0.492489\pi$
$312$	−9.75379	−	16.8941i	−0.552200	−	0.956438i
$313$	12.4779	−	21.6124i	0.705294	−	1.22161i	−0.261291	−	0.965260i	$-0.584148\pi$
$313$	12.4779	−	21.6124i	0.705294	−	1.22161i	0.966585	−	0.256345i	$-0.0825184\pi$
$314$	−12.2888			−0.693498
$315$		0			0
$316$	5.75379			0.323676
$317$	9.40388	−	16.2880i	0.528175	−	0.914825i	−0.471286	−	0.881981i	$-0.656210\pi$
$317$	9.40388	−	16.2880i	0.528175	−	0.914825i	0.999460	−	0.0328448i	$-0.0104567\pi$
$318$	1.87285	+	3.24388i	0.105024	+	0.181908i
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$	8.54312	−	14.7971i	0.477575	−	0.827184i
$321$	1.34700			0.0751822
$322$		0			0
$323$	−10.2462			−0.570114
$324$	0.411460	−	0.712669i	0.0228589	−	0.0395927i
$325$	14.8028	+	25.6392i	0.821112	+	1.42221i
$326$	−19.1231	−	33.1222i	−1.05913	−	1.83447i
$327$	−3.21985	+	5.57695i	−0.178058	+	0.308406i
$328$	−10.4160			−0.575126
$329$		0			0
$330$	5.75379			0.316736
$331$	6.40388	−	11.0918i	0.351989	−	0.609663i	−0.634609	−	0.772834i	$-0.718839\pi$
$331$	6.40388	−	11.0918i	0.351989	−	0.609663i	0.986598	+	0.163170i	$0.0521720\pi$
$332$	−1.87285	−	3.24388i	−0.102786	−	0.178031i
$333$	6.68466	+	11.5782i	0.366317	+	0.634480i
$334$	18.1379	−	31.4158i	0.992464	−	1.71900i
$335$	−23.6089			−1.28989
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	24.5885	−	42.5886i	1.33744	−	2.31651i
$339$	−8.87987	−	15.3804i	−0.482288	−	0.835348i
$340$	−2.87689	−	4.98293i	−0.156022	−	0.270237i
$341$	3.67188	−	6.35989i	0.198844	−	0.344407i
$342$	5.84912			0.316284
$343$		0			0
$344$	15.2311			0.821204
$345$	2.65009	−	4.59010i	0.142676	−	0.247122i
$346$	2.28343	+	3.95501i	0.122758	+	0.212623i
$347$	0.561553	+	0.972638i	0.0301457	+	0.0522139i	0.880705	−	0.473666i	$-0.157070\pi$
$347$	0.561553	+	0.972638i	0.0301457	+	0.0522139i	−0.850559	+	0.525880i	$0.823736\pi$
$348$	0.525853	−	0.910804i	0.0281887	−	0.0488242i
$349$	22.4095			1.19955			0.599776	−	0.800168i	$-0.295256\pi$
$349$	22.4095			1.19955			0.599776	+	0.800168i	$0.295256\pi$
$350$		0			0
$351$	−36.4924			−1.94782
$352$	1.21922	−	2.11176i	0.0649848	−	0.112557i
$353$	−4.60831	−	7.98182i	−0.245276	−	0.424830i	0.716934	−	0.697142i	$-0.245545\pi$
$353$	−4.60831	−	7.98182i	−0.245276	−	0.424830i	−0.962209	+	0.272312i	$0.912212\pi$
$354$	5.61553	+	9.72638i	0.298462	+	0.516951i
$355$	−25.8185	+	44.7189i	−1.37030	+	2.37343i
$356$	5.55382			0.294352
$357$		0			0
$358$	−7.50758			−0.396788
$359$	−5.12311	+	8.87348i	−0.270387	+	0.468324i	−0.968961	−	0.247214i	$-0.920485\pi$
$359$	−5.12311	+	8.87348i	−0.270387	+	0.468324i	0.698574	+	0.715538i	$0.253818\pi$
$360$	−5.84912	−	10.1310i	−0.308276	−	0.533949i
$361$	6.62311	+	11.4716i	0.348585	+	0.603766i
$362$	8.01726	−	13.8863i	0.421378	−	0.729848i
$363$	−1.19935			−0.0629497
$364$		0			0
$365$	39.3693			2.06068
$366$	−7.50758	+	13.0035i	−0.392427	+	0.679704i
$367$	−1.12553	−	1.94947i	−0.0587522	−	0.101762i	0.835153	−	0.550017i	$-0.185379\pi$
$367$	−1.12553	−	1.94947i	−0.0587522	−	0.101762i	−0.893906	+	0.448255i	$0.852045\pi$
$368$	−3.36932	−	5.83583i	−0.175638	−	0.304214i
$369$	−3.33513	+	5.77662i	−0.173620	+	0.300719i
$370$	41.0733			2.13530
$371$		0			0
$372$	−3.86174			−0.200222
$373$	8.68466	−	15.0423i	0.449675	−	0.778859i	−0.548690	−	0.836026i	$-0.684873\pi$
$373$	8.68466	−	15.0423i	0.449675	−	0.778859i	0.998365	+	0.0571666i	$0.0182066\pi$
$374$	3.33513	+	5.77662i	0.172456	+	0.298702i
$375$	1.03457	+	1.79192i	0.0534247	+	0.0925343i
$376$	5.20798	−	9.02049i	0.268581	−	0.465196i
$377$	−13.3405			−0.687072
$378$		0			0
$379$	16.3153			0.838063			0.419031	−	0.907972i	$-0.362370\pi$
$379$	16.3153			0.838063			0.419031	+	0.907972i	$0.362370\pi$
$380$	1.61553	−	2.79818i	0.0828748	−	0.143543i
$381$	−7.86962	−	13.6306i	−0.403173	−	0.698316i
$382$	6.87689	+	11.9111i	0.351853	+	0.609426i
$383$	−12.2150	+	21.1570i	−0.624157	+	1.08107i	0.364546	+	0.931185i	$0.381224\pi$
$383$	−12.2150	+	21.1570i	−0.624157	+	1.08107i	−0.988703	+	0.149887i	$0.952109\pi$
$384$	16.2651			0.830024
$385$		0			0
$386$	−10.1383			−0.516024
$387$	4.87689	−	8.44703i	0.247906	−	0.429387i
$388$	0.904059	+	1.56588i	0.0458966	+	0.0794953i
$389$	−2.52699	−	4.37687i	−0.128123	−	0.221916i	0.794826	−	0.606837i	$-0.207562\pi$
$389$	−2.52699	−	4.37687i	−0.128123	−	0.221916i	−0.922950	+	0.384921i	$0.874229\pi$
$390$	−19.1896	+	33.2374i	−0.971705	+	1.68304i
$391$	6.14441			0.310736
$392$		0			0
$393$	7.36932			0.371733
$394$	−3.31534	+	5.74234i	−0.167024	+	0.289295i
$395$	20.1584	+	34.9154i	1.01428	+	1.75679i
$396$	−0.342329	−	0.592932i	−0.0172027	−	0.0297959i
$397$	−14.6875	+	25.4395i	−0.737146	+	1.27677i	0.216630	+	0.976254i	$0.430494\pi$
$397$	−14.6875	+	25.4395i	−0.737146	+	1.27677i	−0.953775	+	0.300520i	$0.902840\pi$
$398$	−8.31256			−0.416671
$399$		0			0
$400$	−20.7926			−1.03963
$401$	−9.24621	+	16.0149i	−0.461734	+	0.799746i	−0.999047	−	0.0436361i	$-0.986106\pi$
$401$	−9.24621	+	16.0149i	−0.461734	+	0.799746i	0.537314	+	0.843382i	$0.319439\pi$
$402$	−7.19612	−	12.4640i	−0.358910	−	0.621650i
$403$	24.4924	+	42.4221i	1.22005	+	2.11320i
$404$	−3.33513	+	5.77662i	−0.165929	+	0.287397i
$405$	5.76621			0.286525
$406$		0			0
$407$	−8.56155			−0.424380
$408$	−6.24621	+	10.8188i	−0.309234	+	0.535608i
$409$	−5.88148	−	10.1870i	−0.290821	−	0.503716i	0.683183	−	0.730247i	$-0.260595\pi$
$409$	−5.88148	−	10.1870i	−0.290821	−	0.503716i	−0.974004	+	0.226531i	$0.927262\pi$
$410$	10.2462	+	17.7470i	0.506024	+	0.876460i
$411$	−5.13416	+	8.89263i	−0.253249	+	0.438641i
$412$	−3.97626			−0.195896
$413$		0			0
$414$	−3.50758			−0.172388
$415$	13.1231	−	22.7299i	0.644188	−	1.11577i
$416$	8.13254	+	14.0860i	0.398731	+	0.690622i
$417$	1.43845	+	2.49146i	0.0704411	+	0.122007i
$418$	−1.87285	+	3.24388i	−0.0916042	+	0.158663i
$419$	0.525853			0.0256896			0.0128448	−	0.999918i	$-0.495911\pi$
$419$	0.525853			0.0256896			0.0128448	+	0.999918i	$0.495911\pi$
$420$		0			0
$421$	3.75379			0.182948			0.0914742	−	0.995807i	$-0.470842\pi$
$421$	3.75379			0.182948			0.0914742	+	0.995807i	$0.470842\pi$
$422$	−2.63068	+	4.55648i	−0.128060	+	0.221806i
$423$	−3.33513	−	5.77662i	−0.162160	−	0.280869i
$424$	2.43845	+	4.22351i	0.118421	+	0.205112i
$425$	9.47954	−	16.4191i	0.459825	−	0.796441i
$426$	−31.4785			−1.52514
$427$		0			0
$428$	−0.492423			−0.0238021
$429$	4.00000	−	6.92820i	0.193122	−	0.334497i
$430$	−14.9828	−	25.9510i	−0.722536	−	1.25147i
$431$	−6.24621	−	10.8188i	−0.300869	−	0.521121i	0.675464	−	0.737393i	$-0.263943\pi$
$431$	−6.24621	−	10.8188i	−0.300869	−	0.521121i	−0.976333	+	0.216272i	$0.930610\pi$
$432$	12.8147	−	22.1957i	0.616546	−	1.06789i
$433$	27.3546			1.31458			0.657288	−	0.753639i	$-0.271704\pi$
$433$	27.3546			1.31458			0.657288	+	0.753639i	$0.271704\pi$
$434$		0			0
$435$	7.36932			0.353332
$436$	1.17708	−	2.03876i	0.0563720	−	0.0976391i
$437$	1.72521	+	2.98814i	0.0825278	+	0.142942i
$438$	12.0000	+	20.7846i	0.573382	+	0.993127i
$439$	11.0895	−	19.2075i	0.529272	−	0.916725i	−0.470146	−	0.882589i	$-0.655799\pi$
$439$	11.0895	−	19.2075i	0.529272	−	0.916725i	0.999417	−	0.0341363i	$-0.0108680\pi$
$440$	7.49141			0.357139
$441$		0			0
$442$	−44.4924			−2.11629
$443$	11.8423	−	20.5115i	0.562646	−	0.974532i	−0.434618	−	0.900615i	$-0.643117\pi$
$443$	11.8423	−	20.5115i	0.562646	−	0.974532i	0.997264	−	0.0739168i	$-0.0235499\pi$
$444$	2.25106	+	3.89895i	0.106831	+	0.185036i
$445$	19.4579	+	33.7020i	0.922391	+	1.59763i
$446$	−15.3287	+	26.5500i	−0.725833	+	1.25718i
$447$	−7.19612			−0.340365
$448$		0			0
$449$	18.1771			0.857829			0.428915	−	0.903345i	$-0.358896\pi$
$449$	18.1771			0.857829			0.428915	+	0.903345i	$0.358896\pi$
$450$	−5.41146	+	9.37292i	−0.255099	+	0.441844i
$451$	−2.13578	−	3.69928i	−0.100570	−	0.174192i
$452$	3.24621	+	5.62260i	0.152689	+	0.264465i
$453$	−4.41921	+	7.65429i	−0.207632	+	0.359630i
$454$	−14.9828			−0.703179
$455$		0			0
$456$	−7.01515			−0.328515
$457$	−18.9309	+	32.7892i	−0.885549	+	1.53382i	−0.0404653	+	0.999181i	$0.512884\pi$
$457$	−18.9309	+	32.7892i	−0.885549	+	1.53382i	−0.845083	+	0.534634i	$0.820449\pi$
$458$	−0.525853	−	0.910804i	−0.0245715	−	0.0425591i
$459$	11.6847	+	20.2384i	0.545393	+	0.944649i
$460$	−0.968794	+	1.67800i	−0.0451703	+	0.0782372i
$461$	−21.3578			−0.994732			−0.497366	−	0.867541i	$-0.665699\pi$
$461$	−21.3578			−0.994732			−0.497366	+	0.867541i	$0.665699\pi$
$462$		0			0
$463$	21.9309			1.01921			0.509607	−	0.860407i	$-0.329791\pi$
$463$	21.9309			1.01921			0.509607	+	0.860407i	$0.329791\pi$
$464$	4.68466	−	8.11407i	0.217480	−	0.376686i
$465$	−13.5296	−	23.4340i	−0.627422	−	1.08673i
$466$	−3.31534	−	5.74234i	−0.153580	−	0.266009i
$467$	4.19773	−	7.27069i	0.194248	−	0.336447i	−0.752406	−	0.658700i	$-0.771107\pi$
$467$	4.19773	−	7.27069i	0.194248	−	0.336447i	0.946654	+	0.322253i	$0.104440\pi$
$468$	4.56685			0.211103
$469$		0			0
$470$	−20.4924			−0.945245
$471$	4.71922	−	8.17394i	0.217450	−	0.376635i
$472$	7.31140	+	12.6637i	0.336534	+	0.582894i
$473$	3.12311	+	5.40938i	0.143601	+	0.248723i
$474$	−12.2888	+	21.2849i	−0.564444	+	0.977646i
$475$	10.6465			0.488496
$476$		0			0
$477$	3.12311			0.142997
$478$	8.00000	−	13.8564i	0.365911	−	0.633777i
$479$	−5.32326	−	9.22016i	−0.243226	−	0.421280i	0.718405	−	0.695625i	$-0.244872\pi$
$479$	−5.32326	−	9.22016i	−0.243226	−	0.421280i	−0.961631	+	0.274345i	$0.911539\pi$
$480$	−4.49242	−	7.78110i	−0.205050	−	0.355157i
$481$	28.5539	−	49.4568i	1.30195	−	2.25504i
$482$	−29.6056			−1.34850
$483$		0			0
$484$	0.438447			0.0199294
$485$	−6.33475	+	10.9721i	−0.287646	+	0.498218i
$486$	−11.0571	−	19.1515i	−0.501560	−	0.868728i
$487$	−7.28078	−	12.6107i	−0.329923	−	0.571444i	0.652573	−	0.757726i	$-0.273690\pi$
$487$	−7.28078	−	12.6107i	−0.329923	−	0.571444i	−0.982496	+	0.186282i	$0.940356\pi$
$488$	−9.77484	+	16.9305i	−0.442486	+	0.766408i
$489$	29.3751			1.32839
$490$		0			0
$491$	−19.3693			−0.874125			−0.437063	−	0.899431i	$-0.643981\pi$
$491$	−19.3693			−0.874125			−0.437063	+	0.899431i	$0.643981\pi$
$492$	−1.12311	+	1.94528i	−0.0506335	+	0.0876998i
$493$	4.27156	+	7.39856i	0.192381	+	0.333214i
$494$	−12.4924	−	21.6375i	−0.562061	−	0.973518i
$495$	2.39871	−	4.15468i	0.107814	−	0.186739i
$496$	−34.4030			−1.54474
$497$		0			0
$498$	16.0000			0.716977
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	−0.699903	−	0.714238i	$-0.746773\pi$
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	0.968500	+	0.249015i	$0.0801067\pi$
$500$	−0.378206	−	0.655072i	−0.0169139	−	0.0292957i
$501$	13.9309	+	24.1290i	0.622385	+	1.07800i
$502$	21.7684	−	37.7039i	0.971570	−	1.68281i
$503$	16.0345			0.714944			0.357472	−	0.933924i	$-0.383639\pi$
$503$	16.0345			0.714944			0.357472	+	0.933924i	$0.383639\pi$
$504$		0			0
$505$	−46.7386			−2.07984
$506$	1.12311	−	1.94528i	0.0499281	−	0.0864781i
$507$	18.8853	+	32.7102i	0.838724	+	1.45271i
$508$	2.87689	+	4.98293i	0.127642	+	0.221082i
$509$	5.80766	−	10.0592i	0.257420	−	0.445865i	−0.708130	−	0.706082i	$-0.750461\pi$
$509$	5.80766	−	10.0592i	0.257420	−	0.445865i	0.965550	+	0.260217i	$0.0837943\pi$
$510$	24.5776			1.08832
$511$		0			0
$512$	11.4233			0.504843
$513$	−6.56155	+	11.3649i	−0.289700	+	0.501774i
$514$	−5.84912	−	10.1310i	−0.257993	−	0.446858i
$515$	−13.9309	−	24.1290i	−0.613867	−	1.06325i
$516$	1.64229	−	2.84454i	0.0722980	−	0.125224i
$517$	4.27156			0.187863
$518$		0			0
$519$	−3.50758			−0.153966
$520$	−24.9848	+	43.2750i	−1.09566	+	1.89774i
$521$	2.73546	+	4.73795i	0.119842	+	0.207573i	0.919705	−	0.392610i	$-0.128428\pi$
$521$	2.73546	+	4.73795i	0.119842	+	0.207573i	−0.799863	+	0.600183i	$0.795094\pi$
$522$	−2.43845	−	4.22351i	−0.106728	−	0.184858i
$523$	6.14441	−	10.6424i	0.268676	−	0.465361i	−0.699844	−	0.714296i	$-0.746747\pi$
$523$	6.14441	−	10.6424i	0.268676	−	0.465361i	0.968520	+	0.248935i	$0.0800805\pi$
$524$	−2.69400			−0.117688
$525$		0			0
$526$	−36.4924			−1.59115
$527$	15.6847	−	27.1666i	0.683234	−	1.18340i
$528$	2.80928	+	4.86581i	0.122258	+	0.211757i
$529$	10.4654	+	18.1267i	0.455019	+	0.788116i
$530$	4.79741	−	8.30936i	0.208386	−	0.360936i
$531$	9.36426			0.406374
$532$		0			0
$533$	28.4924			1.23414
$534$	−11.8617	+	20.5451i	−0.513308	+	0.889075i
$535$	−1.72521	−	2.98814i	−0.0745871	−	0.129189i
$536$	−9.36932	−	16.2281i	−0.404693	−	0.700949i
$537$	2.88310	−	4.99368i	0.124415	−	0.215493i
$538$	−25.0388			−1.07950
$539$		0			0
$540$	−7.36932			−0.317125
$541$	−16.4384	+	28.4722i	−0.706744	+	1.22412i	0.259314	+	0.965793i	$0.416503\pi$
$541$	−16.4384	+	28.4722i	−0.706744	+	1.22412i	−0.966058	+	0.258324i	$0.916830\pi$
$542$	10.4160	+	18.0410i	0.447404	+	0.774927i
$543$	6.15767	+	10.6654i	0.264251	+	0.457696i
$544$	5.20798	−	9.02049i	0.223291	−	0.386751i
$545$	16.4956			0.706596
$546$		0			0
$547$	1.75379			0.0749866			0.0374933	−	0.999297i	$-0.488063\pi$
$547$	1.75379			0.0749866			0.0374933	+	0.999297i	$0.488063\pi$
$548$	1.87689	−	3.25088i	0.0801770	−	0.138871i
$549$	6.25969	+	10.8421i	0.267157	+	0.462730i
$550$	−3.46543	−	6.00231i	−0.147767	−	0.255939i
$551$	−2.39871	+	4.15468i	−0.102188	+	0.176995i
$552$	4.20682			0.179054
$553$		0			0
$554$	−36.8769			−1.56675
$555$	−15.7732	+	27.3200i	−0.669535	+	1.15967i
$556$	−0.525853	−	0.910804i	−0.0223011	−	0.0386267i
$557$	−4.12311	−	7.14143i	−0.174702	−	0.302592i	0.765356	−	0.643607i	$-0.222563\pi$
$557$	−4.12311	−	7.14143i	−0.174702	−	0.302592i	−0.940058	+	0.341015i	$0.889229\pi$
$558$	−8.95369	+	15.5082i	−0.379040	+	0.656516i
$559$	−41.6639			−1.76219
$560$		0			0
$561$	−5.12311			−0.216298
$562$	−9.06913	+	15.7082i	−0.382558	+	0.662610i
$563$	−9.06897	−	15.7079i	−0.382212	−	0.662010i	0.609167	−	0.793042i	$-0.291504\pi$
$563$	−9.06897	−	15.7079i	−0.382212	−	0.662010i	−0.991378	+	0.131033i	$0.958171\pi$
$564$	−1.12311	−	1.94528i	−0.0472913	−	0.0819109i
$565$	−22.7462	+	39.3977i	−0.956942	+	1.65747i
$566$	14.9828			0.629775
$567$		0			0
$568$	−40.9848			−1.71969
$569$	−16.1231	+	27.9260i	−0.675916	+	1.17072i	0.300285	+	0.953850i	$0.402918\pi$
$569$	−16.1231	+	27.9260i	−0.675916	+	1.17072i	−0.976200	+	0.216871i	$0.930415\pi$
$570$	6.90082	+	11.9526i	0.289044	+	0.500638i
$571$	−4.87689	−	8.44703i	−0.204092	−	0.353497i	0.745751	−	0.666224i	$-0.232091\pi$
$571$	−4.87689	−	8.44703i	−0.204092	−	0.353497i	−0.949843	+	0.312727i	$0.898757\pi$
$572$	−1.46228	+	2.53274i	−0.0611410	+	0.105899i
$573$	−10.5636			−0.441301
$574$		0			0
$575$	−6.38447			−0.266251
$576$	4.34233	−	7.52113i	0.180930	−	0.313381i
$577$	11.9521	+	20.7016i	0.497571	+	0.861819i	0.999996	−	0.00280217i	$-0.000891961\pi$
$577$	11.9521	+	20.7016i	0.497571	+	0.861819i	−0.502425	+	0.864621i	$0.667559\pi$
$578$	0.973012	+	1.68531i	0.0404720	+	0.0700995i
$579$	3.89335	−	6.74348i	0.161802	−	0.280250i
$580$	−2.69400			−0.111862
$581$		0			0
$582$	−7.72348			−0.320148
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	15.6240	+	27.0615i	0.646524	+	1.11981i
$585$	16.0000	+	27.7128i	0.661519	+	1.14578i
$586$	−10.8265	+	18.7521i	−0.447240	+	0.774643i
$587$	−14.9181			−0.615735			−0.307868	−	0.951429i	$-0.599615\pi$
$587$	−14.9181			−0.615735			−0.307868	+	0.951429i	$0.599615\pi$
$588$		0			0
$589$	17.6155			0.725835
$590$	14.3845	−	24.9146i	0.592199	−	1.02572i
$591$	−2.54635	−	4.41041i	−0.104743	−	0.181420i
$592$	20.0540	+	34.7345i	0.824213	+	1.42758i
$593$	−3.48278	+	6.03235i	−0.143021	+	0.247719i	−0.928633	−	0.371000i	$-0.879015\pi$
$593$	−3.48278	+	6.03235i	−0.143021	+	0.247719i	0.785612	+	0.618719i	$0.212348\pi$
$594$	8.54312			0.350528
$595$		0			0
$596$	2.63068			0.107757
$597$	3.19224	−	5.52911i	0.130650	−	0.226292i
$598$	7.49141	+	12.9755i	0.306347	+	0.530608i
$599$	16.0000	+	27.7128i	0.653742	+	1.13231i	0.982208	+	0.187799i	$0.0601353\pi$
$599$	16.0000	+	27.7128i	0.653742	+	1.13231i	−0.328465	+	0.944516i	$0.606531\pi$
$600$	6.49025	−	11.2414i	0.264963	−	0.458930i
$601$	−7.72197			−0.314986			−0.157493	−	0.987520i	$-0.550341\pi$
$601$	−7.72197			−0.314986			−0.157493	+	0.987520i	$0.550341\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	1.61553	−	2.79818i	0.0657349	−	0.113856i
$605$	1.53610	+	2.66061i	0.0624515	+	0.108169i
$606$	−14.2462	−	24.6752i	−0.578713	−	1.00236i
$607$	22.5571	−	39.0701i	0.915566	−	1.58581i	0.109496	−	0.993987i	$-0.465076\pi$
$607$	22.5571	−	39.0701i	0.915566	−	1.58581i	0.806070	−	0.591820i	$-0.201590\pi$
$608$	5.84912			0.237213
$609$		0			0
$610$	38.4621			1.55729
$611$	−14.2462	+	24.6752i	−0.576340	+	0.998250i
$612$	−1.46228	−	2.53274i	−0.0591091	−	0.102380i
$613$	−16.6847	−	28.8987i	−0.673887	−	1.16721i	−0.976793	−	0.214186i	$-0.931290\pi$
$613$	−16.6847	−	28.8987i	−0.673887	−	1.16721i	0.302906	−	0.953020i	$-0.402043\pi$
$614$	3.74571	−	6.48775i	0.151164	−	0.261824i
$615$	−15.7392			−0.634667
$616$		0			0
$617$	12.7386			0.512838			0.256419	−	0.966566i	$-0.417457\pi$
$617$	12.7386			0.512838			0.256419	+	0.966566i	$0.417457\pi$
$618$	8.49242	−	14.7093i	0.341615	−	0.591695i
$619$	−10.1945	−	17.6574i	−0.409752	−	0.709710i	0.585110	−	0.810954i	$-0.301051\pi$
$619$	−10.1945	−	17.6574i	−0.409752	−	0.709710i	−0.994862	+	0.101243i	$0.967718\pi$
$620$	4.94602	+	8.56677i	0.198637	+	0.344050i
$621$	3.93481	−	6.81529i	0.157898	−	0.273488i
$622$	48.3341			1.93802
$623$		0			0
$624$	−37.4773			−1.50029
$625$	13.7462	−	23.8091i	0.549848	−	0.952365i
$626$	−19.4849	−	33.7489i	−0.778775	−	1.34888i
$627$	−1.43845	−	2.49146i	−0.0574460	−	0.0994995i
$628$	−1.72521	+	2.98814i	−0.0688432	+	0.119240i
$629$	−36.5712			−1.45819
$630$		0			0
$631$	−0.807764			−0.0321566			−0.0160783	−	0.999871i	$-0.505118\pi$
$631$	−0.807764			−0.0321566			−0.0160783	+	0.999871i	$0.505118\pi$
$632$	−16.0000	+	27.7128i	−0.636446	+	1.10236i
$633$	−2.02050	−	3.49961i	−0.0803077	−	0.139097i
$634$	−14.6847	−	25.4346i	−0.583202	−	1.01014i
$635$	−20.1584	+	34.9154i	−0.799963	+	1.38558i
$636$	1.05171			0.0417028
$637$		0			0
$638$	3.12311			0.123645
$639$	−13.1231	+	22.7299i	−0.519142	+	0.899180i
$640$	−20.8319	−	36.0820i	−0.823455	−	1.42627i
$641$	3.96543	+	6.86833i	0.156625	+	0.271283i	0.933650	−	0.358188i	$-0.116605\pi$
$641$	3.96543	+	6.86833i	0.156625	+	0.271283i	−0.777024	+	0.629471i	$0.783272\pi$
$642$	1.05171	−	1.82161i	0.0415075	−	0.0718931i
$643$	−23.3783			−0.921950			−0.460975	−	0.887413i	$-0.652500\pi$
$643$	−23.3783			−0.921950			−0.460975	+	0.887413i	$0.652500\pi$
$644$		0			0
$645$	23.0152			0.906221
$646$	−8.00000	+	13.8564i	−0.314756	+	0.545173i
$647$	−20.7581	−	35.9541i	−0.816086	−	1.41350i	−0.908546	−	0.417786i	$-0.862806\pi$
$647$	−20.7581	−	35.9541i	−0.816086	−	1.41350i	0.0924599	−	0.995716i	$-0.470527\pi$
$648$	2.28835	+	3.96355i	0.0898950	+	0.155703i
$649$	−2.99838	+	5.19335i	−0.117697	+	0.203857i
$650$	46.2307			1.81332
$651$		0			0
$652$	−10.7386			−0.420557
$653$	5.15767	−	8.93335i	0.201835	−	0.349589i	−0.747285	−	0.664504i	$-0.768643\pi$
$653$	5.15767	−	8.93335i	0.201835	−	0.349589i	0.949120	+	0.314915i	$0.101976\pi$
$654$	5.02797	+	8.70870i	0.196609	+	0.340537i
$655$	−9.43845	−	16.3479i	−0.368791	−	0.638764i
$656$	−10.0054	+	17.3299i	−0.390645	+	0.676617i
$657$	20.0108			0.780695
$658$		0			0
$659$	−19.3693			−0.754521			−0.377261	−	0.926107i	$-0.623134\pi$
$659$	−19.3693			−0.754521			−0.377261	+	0.926107i	$0.623134\pi$
$660$	0.807764	−	1.39909i	0.0314422	−	0.0544594i
$661$	3.26131	+	5.64875i	0.126850	+	0.219711i	0.922455	−	0.386105i	$-0.126180\pi$
$661$	3.26131	+	5.64875i	0.126850	+	0.219711i	−0.795604	+	0.605816i	$0.792847\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$	17.0862	−	29.5942i	0.663574	−	1.14934i
$664$	20.8319			0.808436
$665$		0			0
$666$	20.8769			0.808963
$667$	1.43845	−	2.49146i	0.0556969	−	0.0964699i
$668$	−5.09271	−	8.82082i	−0.197043	−	0.341288i
$669$	−11.7732	−	20.3918i	−0.455178	−	0.788392i
$670$	−18.4332	+	31.9273i	−0.712138	+	1.23346i
$671$	−8.01726			−0.309503
$672$		0			0
$673$	15.6155			0.601934			0.300967	−	0.953634i	$-0.402691\pi$
$673$	15.6155			0.601934			0.300967	+	0.953634i	$0.402691\pi$
$674$	10.9309	−	18.9328i	0.421041	−	0.729265i
$675$	−12.1412	−	21.0291i	−0.467314	−	0.809412i
$676$	−6.90388	−	11.9579i	−0.265534	−	0.459918i
$677$	−10.6789	+	18.4964i	−0.410423	+	0.710874i	−0.994936	−	0.100511i	$-0.967952\pi$
$677$	−10.6789	+	18.4964i	−0.410423	+	0.710874i	0.584513	+	0.811385i	$0.301286\pi$
$678$	−27.7328			−1.06507
$679$		0			0
$680$	32.0000			1.22714
$681$	5.75379	−	9.96585i	0.220486	−	0.381892i
$682$	−5.73384	−	9.93130i	−0.219560	−	0.380289i
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	0.901750	−	0.432259i	$-0.142283\pi$
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	−0.825222	+	0.564809i	$0.808950\pi$
$684$	0.821147	−	1.42227i	0.0313973	−	0.0543818i
$685$	26.3029			1.00498
$686$		0			0
$687$	0.807764			0.0308181
$688$	14.6307	−	25.3411i	0.557790	−	0.966120i
$689$	−6.67026	−	11.5532i	−0.254117	−	0.440143i
$690$	−4.13826	−	7.16768i	−0.157541	−	0.272869i
$691$	−12.7409	+	22.0678i	−0.484685	+	0.839499i	−0.999845	−	0.0175950i	$-0.994399\pi$
$691$	−12.7409	+	22.0678i	−0.484685	+	0.839499i	0.515160	+	0.857094i	$0.327732\pi$
$692$	1.28226			0.0487444
$693$		0			0
$694$	1.75379			0.0665729
$695$	3.68466	−	6.38202i	0.139767	−	0.242084i
$696$	2.92456	+	5.06548i	0.110855	+	0.192007i
$697$	−9.12311	−	15.8017i	−0.345562	−	0.598531i
$698$	17.4968	−	30.3054i	0.662264	−	1.14707i
$699$	5.09271			0.192624
$700$		0			0
$701$	10.6307			0.401515			0.200758	−	0.979641i	$-0.435660\pi$
$701$	10.6307			0.401515			0.200758	+	0.979641i	$0.435660\pi$
$702$	−28.4924	+	49.3503i	−1.07538	+	1.86261i
$703$	−10.2683	−	17.7853i	−0.387277	−	0.670784i
$704$	2.78078	+	4.81645i	0.104804	+	0.181527i
$705$	7.86962	−	13.6306i	0.296387	−	0.513357i
$706$	−14.3922			−0.541659
$707$		0			0
$708$	3.15342			0.118513
$709$	−4.59612	+	7.96071i	−0.172611	+	0.298971i	−0.939332	−	0.343010i	$-0.888554\pi$
$709$	−4.59612	+	7.96071i	−0.172611	+	0.298971i	0.766721	+	0.641980i	$0.221887\pi$
$710$	40.3169	+	69.8309i	1.51307	+	2.62071i
$711$	10.2462	+	17.7470i	0.384263	+	0.665563i
$712$	−15.4439	+	26.7497i	−0.578786	+	1.00249i
$713$	−10.5636			−0.395611
$714$		0			0
$715$	−20.4924			−0.766373
$716$	−1.05398	+	1.82554i	−0.0393889	+	0.0682236i
$717$	6.14441	+	10.6424i	0.229467	+	0.397449i
$718$	8.00000	+	13.8564i	0.298557	+	0.517116i
$719$	−1.27318	+	2.20521i	−0.0474815	+	0.0822403i	−0.888789	−	0.458316i	$-0.848453\pi$
$719$	−1.27318	+	2.20521i	−0.0474815	+	0.0822403i	0.841308	+	0.540556i	$0.181786\pi$
$720$	−22.4742			−0.837565
$721$		0			0
$722$	20.6847			0.769803
$723$	11.3693	−	19.6922i	0.422829	−	0.732362i
$724$	−2.25106	−	3.89895i	−0.0836599	−	0.144903i
$725$	−4.43845	−	7.68762i	−0.164840	−	0.285511i
$726$	−0.936426	+	1.62194i	−0.0347540	+	0.0601958i
$727$	27.1240			1.00597			0.502987	−	0.864294i	$-0.332234\pi$
$727$	27.1240			1.00597			0.502987	+	0.864294i	$0.332234\pi$
$728$		0			0
$729$	22.6155			0.837612
$730$	30.7386	−	53.2409i	1.13769	−	1.97053i
$731$	13.3405	+	23.1065i	0.493417	+	0.854624i
$732$	2.10795	+	3.65108i	0.0779121	+	0.134948i
$733$	−3.33513	+	5.77662i	−0.123186	+	0.213364i	−0.921022	−	0.389510i	$-0.872644\pi$
$733$	−3.33513	+	5.77662i	−0.123186	+	0.213364i	0.797836	+	0.602874i	$0.205978\pi$
$734$	−3.51515			−0.129746
$735$		0			0
$736$	−3.50758			−0.129291
$737$	3.84233	−	6.65511i	0.141534	−	0.245144i
$738$	5.20798	+	9.02049i	0.191709	+	0.332049i
$739$	−9.68466	−	16.7743i	−0.356256	−	0.617053i	0.631076	−	0.775721i	$-0.282614\pi$
$739$	−9.68466	−	16.7743i	−0.356256	−	0.617053i	−0.987332	+	0.158668i	$0.949280\pi$
$740$	5.76621	−	9.98736i	0.211970	−	0.367143i
$741$	19.1896			0.704949
$742$		0			0
$743$	29.7538			1.09156			0.545780	−	0.837928i	$-0.316233\pi$
$743$	29.7538			1.09156			0.545780	+	0.837928i	$0.316233\pi$
$744$	10.7386	−	18.5999i	0.393697	−	0.681904i
$745$	9.21662	+	15.9636i	0.337671	+	0.584863i
$746$	−13.5616	−	23.4893i	−0.496524	−	0.860004i
$747$	6.67026	−	11.5532i	0.244052	−	0.422711i
$748$	1.87285			0.0684783
$749$		0			0
$750$	3.23106			0.117981
$751$	−12.0885	+	20.9380i	−0.441117	+	0.764037i	−0.997773	−	0.0667062i	$-0.978751\pi$
$751$	−12.0885	+	20.9380i	−0.441117	+	0.764037i	0.556656	+	0.830743i	$0.312084\pi$
$752$	−10.0054	−	17.3299i	−0.364859	−	0.631955i
$753$	16.7192	+	28.9585i	0.609282	+	1.05531i
$754$	−10.4160	+	18.0410i	−0.379327	+	0.657014i
$755$	22.6401			0.823956
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	12.7386	−	22.0640i	0.462688	−	0.801399i
$759$	0.862603	+	1.49407i	0.0313105	+	0.0542314i
$760$	8.98485	+	15.5622i	0.325915	+	0.564501i
$761$	−4.15628	+	7.19889i	−0.150665	+	0.260959i	−0.931472	−	0.363813i	$-0.881475\pi$
$761$	−4.15628	+	7.19889i	−0.150665	+	0.260959i	0.780807	+	0.624772i	$0.214808\pi$
$762$	−24.5776			−0.890354
$763$		0			0
$764$	3.86174			0.139713
$765$	10.2462	−	17.7470i	0.370453	−	0.641643i
$766$	19.0744	+	33.0378i	0.689185	+	1.19370i
$767$	−20.0000	−	34.6410i	−0.722158	−	1.25081i
$768$	6.02913	−	10.4428i	0.217558	−	0.376821i
$769$	−11.4677			−0.413535			−0.206767	−	0.978390i	$-0.566294\pi$
$769$	−11.4677			−0.413535			−0.206767	+	0.978390i	$0.566294\pi$
$770$		0			0
$771$	8.98485			0.323581
$772$	−1.42329	+	2.46521i	−0.0512254	+	0.0887250i
$773$	16.2651	+	28.1720i	0.585015	+	1.01327i	0.994874	+	0.101126i	$0.0322445\pi$
$773$	16.2651	+	28.1720i	0.585015	+	1.01327i	−0.409859	+	0.912149i	$0.634422\pi$
$774$	−7.61553	−	13.1905i	−0.273735	−	0.474122i
$775$	−16.2975	+	28.2280i	−0.585422	+	1.01398i
$776$	−10.0559			−0.360987
$777$		0			0
$778$	−7.89205			−0.282944
$779$	5.12311	−	8.87348i	0.183554	−	0.317925i
$780$	5.38800	+	9.33229i	0.192921	+	0.334150i
$781$	−8.40388	−	14.5560i	−0.300715	−	0.520853i
$782$	4.79741	−	8.30936i	0.171555	−	0.297142i
$783$	10.9418			0.391029
$784$		0			0
$785$	−24.1771			−0.862917
$786$	5.75379	−	9.96585i	0.205231	−	0.355470i
$787$	−13.4882	−	23.3622i	−0.480802	−	0.832773i	0.518956	−	0.854801i	$-0.326321\pi$
$787$	−13.4882	−	23.3622i	−0.480802	−	0.832773i	−0.999757	+	0.0220284i	$0.992988\pi$
$788$	0.930870	+	1.61231i	0.0331609	+	0.0574363i
$789$	14.0140	−	24.2730i	0.498913	−	0.864142i
$790$	62.9569			2.23991
$791$		0			0
$792$	3.80776			0.135303
$793$	26.7386	−	46.3127i	0.949517	−	1.64461i
$794$	22.9354	+	39.7252i	0.813945	+	1.40979i
$795$	3.68466	+	6.38202i	0.130681	+	0.226347i
$796$	−1.16699	+	2.02128i	−0.0413627	+	0.0716423i
$797$	23.6089			0.836268			0.418134	−	0.908385i	$-0.362684\pi$
$797$	23.6089			0.836268			0.418134	+	0.908385i	$0.362684\pi$
$798$		0			0
$799$	18.2462			0.645505
$800$	−5.41146	+	9.37292i	−0.191324	+	0.331383i
$801$	9.89012	+	17.1302i	0.349450	+	0.605265i
$802$	14.4384	+	25.0081i	0.509839	+	0.883068i
$803$	−6.40734	+	11.0978i	−0.226110	+	0.391634i
$804$	−4.04100			−0.142515
$805$		0			0
$806$	76.4924			2.69433
$807$	9.61553	−	16.6546i	0.338483	−	0.586269i
$808$	−18.5485	−	32.1270i	−0.652534	−	1.13022i
$809$	19.0000	+	32.9090i	0.668004	+	1.15702i	0.978461	+	0.206430i	$0.0661846\pi$
$809$	19.0000	+	32.9090i	0.668004	+	1.15702i	−0.310457	+	0.950587i	$0.600482\pi$
$810$	4.50212	−	7.79790i	0.158188	−	0.273990i
$811$	−10.9418			−0.384219			−0.192110	−	0.981373i	$-0.561533\pi$
$811$	−10.9418			−0.384219			−0.192110	+	0.981373i	$0.561533\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$	−6.68466	+	11.5782i	−0.234297	+	0.405815i
$815$	−37.6229	−	65.1647i	−1.31787	−	2.28262i
$816$	12.0000	+	20.7846i	0.420084	+	0.727607i
$817$	−7.49141	+	12.9755i	−0.262091	+	0.453955i
$818$	−18.3685			−0.642239
$819$		0			0
$820$	5.75379			0.200931
$821$	−10.3693	+	17.9602i	−0.361892	+	0.626815i	−0.988272	−	0.152703i	$-0.951202\pi$
$821$	−10.3693	+	17.9602i	−0.361892	+	0.626815i	0.626381	+	0.779517i	$0.284536\pi$
$822$	8.01726	+	13.8863i	0.279634	+	0.484341i
$823$	−4.71922	−	8.17394i	−0.164502	−	0.284925i	0.771976	−	0.635651i	$-0.219268\pi$
$823$	−4.71922	−	8.17394i	−0.164502	−	0.284925i	−0.936478	+	0.350726i	$0.885935\pi$
$824$	11.0571	−	19.1515i	0.385192	−	0.667173i
$825$	5.32326			0.185332
$826$		0			0
$827$	39.2311			1.36420			0.682099	−	0.731260i	$-0.261067\pi$
$827$	39.2311			1.36420			0.682099	+	0.731260i	$0.261067\pi$
$828$	−0.492423	+	0.852901i	−0.0171129	+	0.0296404i
$829$	16.2236	+	28.1002i	0.563470	+	0.975959i	0.997190	+	0.0749111i	$0.0238673\pi$
$829$	16.2236	+	28.1002i	0.563470	+	0.975959i	−0.433720	+	0.901048i	$0.642799\pi$
$830$	−20.4924	−	35.4939i	−0.711302	−	1.23201i
$831$	14.1617	−	24.5287i	0.491263	−	0.850893i
$832$	−37.0970			−1.28611
$833$		0			0
$834$	4.49242			0.155560
$835$	35.6847	−	61.8076i	1.23492	−	2.13894i
$836$	0.525853	+	0.910804i	0.0181870	+	0.0315008i
$837$	−20.0885	−	34.7944i	−0.694362	−	1.20267i
$838$	0.410574	−	0.711134i	0.0141830	−	0.0245657i
$839$	−7.04847			−0.243340			−0.121670	−	0.992571i	$-0.538825\pi$
$839$	−7.04847			−0.243340			−0.121670	+	0.992571i	$0.538825\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	2.93087	−	5.07642i	0.101004	−	0.174945i
$843$	−6.96556	−	12.0647i	−0.239907	−	0.415530i
$844$	0.738634	+	1.27935i	0.0254248	+	0.0440371i
$845$	48.3756	−	83.7890i	1.66417	−	2.88243i
$846$	−10.4160			−0.358108
$847$		0			0
$848$	9.36932			0.321744
$849$	−5.75379	+	9.96585i	−0.197470	+	0.342027i
$850$	−14.8028	−	25.6392i	−0.507732	−	0.879418i
$851$	6.15767	+	10.6654i	0.211082	+	0.365605i
$852$	−4.41921	+	7.65429i	−0.151399	+	0.262232i
$853$	−32.5949			−1.11603			−0.558014	−	0.829831i	$-0.688437\pi$
$853$	−32.5949			−1.11603			−0.558014	+	0.829831i	$0.688437\pi$
$854$		0			0
$855$	11.5076			0.393551
$856$	1.36932	−	2.37173i	0.0468023	−	0.0810639i
$857$	−16.1498	−	27.9723i	−0.551667	−	0.955515i	−0.998155	−	0.0607253i	$-0.980659\pi$
$857$	−16.1498	−	27.9723i	−0.551667	−	0.955515i	0.446488	−	0.894790i	$-0.352675\pi$
$858$	−6.24621	−	10.8188i	−0.213242	−	0.369346i
$859$	15.1396	−	26.2225i	0.516555	−	0.894700i	−0.483260	−	0.875477i	$-0.660547\pi$
$859$	15.1396	−	26.2225i	0.516555	−	0.894700i	0.999815	−	0.0192228i	$-0.00611918\pi$
$860$	−8.41365			−0.286903
$861$		0			0
$862$	−19.5076			−0.664431
$863$	−19.3693	+	33.5486i	−0.659339	+	1.14201i	0.321448	+	0.946927i	$0.395831\pi$
$863$	−19.3693	+	33.5486i	−0.659339	+	1.14201i	−0.980787	+	0.195082i	$0.937503\pi$
$864$	−6.67026	−	11.5532i	−0.226927	−	0.393049i
$865$	4.49242	+	7.78110i	0.152747	+	0.264565i
$866$	21.3578	−	36.9928i	0.725767	−	1.25707i
$867$	−1.49465			−0.0507609
$868$		0			0
$869$	−13.1231			−0.445171
$870$	5.75379	−	9.96585i	0.195072	−	0.337874i
$871$	25.6294	+	44.3913i	0.868417	+	1.50414i
$872$	6.54640	+	11.3387i	0.221689	+	0.383977i
$873$	−3.21985	+	5.57695i	−0.108976	+	0.188751i
$874$	5.38800			0.182252
$875$		0			0
$876$	6.73863			0.227677
$877$	1.24621	−	2.15850i	0.0420816	−	0.0728874i	−0.844217	−	0.536001i	$-0.819934\pi$
$877$	1.24621	−	2.15850i	0.0420816	−	0.0728874i	0.886299	+	0.463113i	$0.153268\pi$
$878$	−17.3168	−	29.9936i	−0.584413	−	1.01223i
$879$	−8.31534	−	14.4026i	−0.280470	−	0.485787i
$880$	7.19612	−	12.4640i	0.242581	−	0.420163i
$881$	−8.16491			−0.275083			−0.137541	−	0.990496i	$-0.543920\pi$
$881$	−8.16491			−0.275083			−0.137541	+	0.990496i	$0.543920\pi$
$882$		0			0
$883$	−48.4924			−1.63190			−0.815950	−	0.578123i	$-0.803786\pi$
$883$	−48.4924			−1.63190			−0.815950	+	0.578123i	$0.803786\pi$
$884$	−6.24621	+	10.8188i	−0.210083	+	0.363874i
$885$	11.0480	+	19.1357i	0.371375	+	0.643240i
$886$	−18.4924	−	32.0298i	−0.621265	−	1.07606i
$887$	−22.0313	+	38.1593i	−0.739738	+	1.28126i	0.212875	+	0.977080i	$0.431717\pi$
$887$	−22.0313	+	38.1593i	−0.739738	+	1.28126i	−0.952613	+	0.304185i	$0.901616\pi$
$888$	−25.0388			−0.840246
$889$		0			0
$890$	60.7689			2.03698
$891$	−0.938447	+	1.62544i	−0.0314392	+	0.0544542i
$892$	4.30393	+	7.45462i	0.144106	+	0.249599i
$893$	5.12311	+	8.87348i	0.171438	+	0.296940i
$894$	−5.61856	+	9.73163i	−0.187913	+	0.325474i
$895$	−14.7704			−0.493721
$896$		0			0
$897$	−11.5076			−0.384227
$898$	14.1922	−	24.5817i	0.473601	−	0.820301i
$899$	−7.34376	−	12.7198i	−0.244928	−	0.424228i
$900$	1.51941	+	2.63170i	0.0506470	+	0.0877232i
$901$	−4.27156	+	7.39856i	−0.142306	+	0.246482i
$902$	−6.67026			−0.222095
$903$		0			0
$904$	−36.1080			−1.20093
$905$	15.7732	−	27.3200i	0.524319	−	0.908147i
$906$	6.90082	+	11.9526i	0.229264	+	0.397098i
$907$	−11.1231	−	19.2658i	−0.369337	−	0.639710i	0.620125	−	0.784503i	$-0.287082\pi$
$907$	−11.1231	−	19.2658i	−0.369337	−	0.639710i	−0.989462	+	0.144793i	$0.953748\pi$
$908$	−2.10341	+	3.64322i	−0.0698042	+	0.120904i
$909$	−23.7565			−0.787953
$910$		0			0
$911$	−36.4924			−1.20905			−0.604524	−	0.796587i	$-0.706637\pi$
$911$	−36.4924			−1.20905			−0.604524	+	0.796587i	$0.706637\pi$
$912$	−6.73863	+	11.6717i	−0.223138	+	0.386487i
$913$	4.27156	+	7.39856i	0.141368	+	0.244856i
$914$	29.5616	+	51.2021i	0.977809	+	1.69362i
$915$	−14.7704	+	25.5832i	−0.488296	+	0.845753i
$916$	−0.295294			−0.00975679
$917$		0			0
$918$	36.4924			1.20443
$919$	18.8769	−	32.6957i	0.622691	−	1.07853i	−0.366291	−	0.930500i	$-0.619373\pi$
$919$	18.8769	−	32.6957i	0.622691	−	1.07853i	0.988982	−	0.148033i	$-0.0472941\pi$
$920$	−5.38800	−	9.33229i	−0.177637	−	0.307676i
$921$	2.87689	+	4.98293i	0.0947969	+	0.164193i
$922$	−16.6757	+	28.8831i	−0.549184	+	0.951214i
$923$	112.112			3.69022
$924$		0			0
$925$	38.0000			1.24943
$926$	17.1231	−	29.6581i	0.562700	−	0.974625i
$927$	−7.08084	−	12.2644i	−0.232565	−	0.402815i
$928$	−2.43845	−	4.22351i	−0.0800460	−	0.138644i
$929$	−26.1552	+	45.3021i	−0.858124	+	1.48632i	0.0155915	+	0.999878i	$0.495037\pi$
$929$	−26.1552	+	45.3021i	−0.858124	+	1.48632i	−0.873716	+	0.486437i	$0.838296\pi$
$930$	−42.2545			−1.38558
$931$		0			0
$932$	−1.86174			−0.0609833
$933$	−18.5616	+	32.1496i	−0.607678	+	1.05253i
$934$	−6.55498	−	11.3536i	−0.214486	−	0.371500i
$935$	6.56155	+	11.3649i	0.214586	+	0.371673i
$936$	−12.6994	+	21.9960i	−0.415093	+	0.718962i
$937$	−21.0625			−0.688082			−0.344041	−	0.938955i	$-0.611796\pi$
$937$	−21.0625			−0.688082			−0.344041	+	0.938955i	$0.611796\pi$
$938$		0			0
$939$	29.9309			0.976757
$940$	−2.87689	+	4.98293i	−0.0938339	+	0.162525i
$941$	−23.4936	−	40.6921i	−0.765869	−	1.32652i	−0.939786	−	0.341763i	$-0.888976\pi$
$941$	−23.4936	−	40.6921i	−0.765869	−	1.32652i	0.173918	−	0.984760i	$-0.444357\pi$
$942$	−7.36932	−	12.7640i	−0.240105	−	0.415875i
$943$	−3.07221	+	5.32122i	−0.100045	+	0.173283i
$944$	28.0928			0.914342
$945$		0			0
$946$	9.75379			0.317123
$947$	−19.5270	+	33.8217i	−0.634542	+	1.09906i	0.352070	+	0.935974i	$0.385478\pi$
$947$	−19.5270	+	33.8217i	−0.634542	+	1.09906i	−0.986612	+	0.163085i	$0.947855\pi$
$948$	3.45041	+	5.97629i	0.112064	+	0.194101i
$949$	−42.7386	−	74.0255i	−1.38735	−	2.40297i
$950$	8.31256	−	14.3978i	0.269695	−	0.467125i
$951$	22.5571			0.731466
$952$		0			0
$953$	2.63068			0.0852162			0.0426081	−	0.999092i	$-0.486433\pi$
$953$	2.63068			0.0852162			0.0426081	+	0.999092i	$0.486433\pi$
$954$	2.43845	−	4.22351i	0.0789476	−	0.136741i
$955$	13.5296	+	23.4340i	0.437809	+	0.758307i
$956$	−2.24621	−	3.89055i	−0.0726477	−	0.125829i
$957$	−1.19935	+	2.07734i	−0.0387696	+	0.0671509i
$958$	−16.6251			−0.537133
$959$		0			0
$960$	20.4924			0.661390
$961$	−11.4654	+	19.8587i	−0.369853	+	0.640604i
$962$	−44.5884	−	77.2294i	−1.43759	−	2.48998i
$963$	−0.876894	−	1.51883i	−0.0282575	−	0.0489435i
$964$	−4.15628	+	7.19889i	−0.133865	+	0.231861i
$965$	−19.9461			−0.642086
$966$		0			0
$967$	−13.1231			−0.422011			−0.211005	−	0.977485i	$-0.567674\pi$
$967$	−13.1231			−0.422011			−0.211005	+	0.977485i	$0.567674\pi$
$968$	−1.21922	+	2.11176i	−0.0391873	+	0.0678744i
$969$	−6.14441	−	10.6424i	−0.197387	−	0.341884i
$970$	9.89205	+	17.1335i	0.317615	+	0.550125i
$971$	−10.4898	+	18.1689i	−0.336633	+	0.583066i	−0.983797	−	0.179285i	$-0.942622\pi$
$971$	−10.4898	+	18.1689i	−0.336633	+	0.583066i	0.647164	+	0.762351i	$0.275955\pi$
$972$	−6.20915			−0.199158
$973$		0			0
$974$	−22.7386			−0.728593
$975$	−17.7538	+	30.7505i	−0.568576	+	0.984803i
$976$	18.7791	+	32.5263i	0.601103	+	1.04114i
$977$	−19.8963	−	34.4614i	−0.636539	−	1.10252i	−0.986187	−	0.165637i	$-0.947032\pi$
$977$	−19.8963	−	34.4614i	−0.636539	−	1.10252i	0.349648	−	0.936881i	$-0.386301\pi$
$978$	22.9354	−	39.7252i	0.733392	−	1.27027i
$979$	−12.6670			−0.404840
$980$		0			0
$981$	8.38447			0.267696
$982$	−15.1231	+	26.1940i	−0.482598	+	0.835884i
$983$	24.5038	+	42.4419i	0.781551	+	1.35369i	0.931038	+	0.364922i	$0.118904\pi$
$983$	24.5038	+	42.4419i	0.781551	+	1.35369i	−0.149488	+	0.988764i	$0.547762\pi$
$984$	−6.24621	−	10.8188i	−0.199122	−	0.344889i
$985$	−6.52262	+	11.2975i	−0.207828	+	0.359968i
$986$	13.3405			0.424849
$987$		0			0
$988$	−7.01515			−0.223182
$989$	4.49242	−	7.78110i	0.142851	−	0.247425i
$990$	−3.74571	−	6.48775i	−0.119046	−	0.206194i
$991$	14.2462	+	24.6752i	0.452546	+	0.783832i	0.998543	−	0.0539544i	$-0.0171826\pi$
$991$	14.2462	+	24.6752i	0.452546	+	0.783832i	−0.545998	+	0.837787i	$0.683849\pi$
$992$	−8.95369	+	15.5082i	−0.284280	+	0.492387i
$993$	15.3610			0.487467
$994$		0			0
$995$	−16.3542			−0.518462
$996$	2.24621	−	3.89055i	0.0711739	−	0.123277i
$997$	8.13254	+	14.0860i	0.257560	+	0.446107i	0.965588	−	0.260077i	$-0.0837481\pi$
$997$	8.13254	+	14.0860i	0.257560	+	0.446107i	−0.708028	+	0.706185i	$0.750415\pi$
$998$	−9.36932	−	16.2281i	−0.296581	−	0.513693i
$999$	−23.4197	+	40.5642i	−0.740968	+	1.28339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.e.n.177.4		8
7.2	even	3		539.2.a.k.1.1	✓	4
7.3	odd	6	inner	539.2.e.n.67.3		8
7.4	even	3	inner	539.2.e.n.67.4		8
7.5	odd	6		539.2.a.k.1.2	yes	4
7.6	odd	2	inner	539.2.e.n.177.3		8
21.2	odd	6		4851.2.a.bv.1.4		4
21.5	even	6		4851.2.a.bv.1.3		4
28.19	even	6		8624.2.a.cu.1.2		4
28.23	odd	6		8624.2.a.cu.1.3		4
77.54	even	6		5929.2.a.ba.1.4		4
77.65	odd	6		5929.2.a.ba.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.a.k.1.1	✓	4	7.2	even	3
539.2.a.k.1.2	yes	4	7.5	odd	6
539.2.e.n.67.3		8	7.3	odd	6	inner
539.2.e.n.67.4		8	7.4	even	3	inner
539.2.e.n.177.3		8	7.6	odd	2	inner
539.2.e.n.177.4		8	1.1	even	1	trivial
4851.2.a.bv.1.3		4	21.5	even	6
4851.2.a.bv.1.4		4	21.2	odd	6
5929.2.a.ba.1.3		4	77.65	odd	6
5929.2.a.ba.1.4		4	77.54	even	6
8624.2.a.cu.1.2		4	28.19	even	6
8624.2.a.cu.1.3		4	28.23	odd	6

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.780776 - 1.35234i) q^{2} +(0.599676 + 1.03867i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(1.53610 - 2.66061i) q^{5} +1.87285 q^{6} +2.43845 q^{8} +(0.780776 - 1.35234i) q^{9} +O(q^{10})\)	\(q+(0.780776 - 1.35234i) q^{2} +(0.599676 + 1.03867i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(1.53610 - 2.66061i) q^{5} +1.87285 q^{6} +2.43845 q^{8} +(0.780776 - 1.35234i) q^{9} +(-2.39871 - 4.15468i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.262926 - 0.455402i) q^{12} -6.67026 q^{13} +3.68466 q^{15} +(2.34233 - 4.05703i) q^{16} +(2.13578 + 3.69928i) q^{17} +(-1.21922 - 2.11176i) q^{18} +(-1.19935 + 2.07734i) q^{19} -1.34700 q^{20} +1.56155 q^{22} +(0.719224 - 1.24573i) q^{23} +(1.46228 + 2.53274i) q^{24} +(-2.21922 - 3.84381i) q^{25} +(-5.20798 + 9.02049i) q^{26} +5.47091 q^{27} +2.00000 q^{29} +(2.87689 - 4.98293i) q^{30} +(-3.67188 - 6.35989i) q^{31} +(-1.21922 - 2.11176i) q^{32} +(-0.599676 + 1.03867i) q^{33} +6.67026 q^{34} -0.684658 q^{36} +(-4.28078 + 7.41452i) q^{37} +(1.87285 + 3.24388i) q^{38} +(-4.00000 - 6.92820i) q^{39} +(3.74571 - 6.48775i) q^{40} -4.27156 q^{41} +6.24621 q^{43} +(0.219224 - 0.379706i) q^{44} +(-2.39871 - 4.15468i) q^{45} +(-1.12311 - 1.94528i) q^{46} +(2.13578 - 3.69928i) q^{47} +5.61856 q^{48} -6.93087 q^{50} +(-2.56155 + 4.43674i) q^{51} +(1.46228 + 2.53274i) q^{52} +(1.00000 + 1.73205i) q^{53} +(4.27156 - 7.39856i) q^{54} +3.07221 q^{55} -2.87689 q^{57} +(1.56155 - 2.70469i) q^{58} +(2.99838 + 5.19335i) q^{59} +(-0.807764 - 1.39909i) q^{60} +(-4.00863 + 6.94315i) q^{61} -11.4677 q^{62} +5.56155 q^{64} +(-10.2462 + 17.7470i) q^{65} +(0.936426 + 1.62194i) q^{66} +(-3.84233 - 6.65511i) q^{67} +(0.936426 - 1.62194i) q^{68} +1.72521 q^{69} -16.8078 q^{71} +(1.90388 - 3.29762i) q^{72} +(6.40734 + 11.0978i) q^{73} +(6.68466 + 11.5782i) q^{74} +(2.66163 - 4.61008i) q^{75} +1.05171 q^{76} -12.4924 q^{78} +(-6.56155 + 11.3649i) q^{79} +(-7.19612 - 12.4640i) q^{80} +(0.938447 + 1.62544i) q^{81} +(-3.33513 + 5.77662i) q^{82} +8.54312 q^{83} +13.1231 q^{85} +(4.87689 - 8.44703i) q^{86} +(1.19935 + 2.07734i) q^{87} +(1.21922 + 2.11176i) q^{88} +(-6.33351 + 10.9700i) q^{89} -7.49141 q^{90} -0.630683 q^{92} +(4.40388 - 7.62775i) q^{93} +(-3.33513 - 5.77662i) q^{94} +(3.68466 + 6.38202i) q^{95} +(1.46228 - 2.53274i) q^{96} -4.12391 q^{97} +1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 10 q^{4} + 36 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 10 * q^4 + 36 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 10 q^{4} + 36 q^{8} - 2 q^{9} + 4 q^{11} - 20 q^{15} - 6 q^{16} - 18 q^{18} - 4 q^{22} + 14 q^{23} - 26 q^{25} + 16 q^{29} + 56 q^{30} - 18 q^{32} + 44 q^{36} - 26 q^{37} - 32 q^{39} - 16 q^{43} + 10 q^{44} + 24 q^{46} + 60 q^{50} - 4 q^{51} + 8 q^{53} - 56 q^{57} - 4 q^{58} + 76 q^{60} + 28 q^{64} - 16 q^{65} - 6 q^{67} - 52 q^{71} - 26 q^{72} + 4 q^{74} + 32 q^{78} - 36 q^{79} + 24 q^{81} + 72 q^{85} + 72 q^{86} + 18 q^{88} - 104 q^{92} - 6 q^{93} - 20 q^{95} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 10 * q^4 + 36 * q^8 - 2 * q^9 + 4 * q^11 - 20 * q^15 - 6 * q^16 - 18 * q^18 - 4 * q^22 + 14 * q^23 - 26 * q^25 + 16 * q^29 + 56 * q^30 - 18 * q^32 + 44 * q^36 - 26 * q^37 - 32 * q^39 - 16 * q^43 + 10 * q^44 + 24 * q^46 + 60 * q^50 - 4 * q^51 + 8 * q^53 - 56 * q^57 - 4 * q^58 + 76 * q^60 + 28 * q^64 - 16 * q^65 - 6 * q^67 - 52 * q^71 - 26 * q^72 + 4 * q^74 + 32 * q^78 - 36 * q^79 + 24 * q^81 + 72 * q^85 + 72 * q^86 + 18 * q^88 - 104 * q^92 - 6 * q^93 - 20 * q^95 - 4 * q^99

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