LMFDB - Embedded newform 54.2.e.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,2,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, 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:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			31.2
Root			$0.500000 - 0.677980i$ of defining polynomial
Character	$\chi$	$=$	54.31
Dual form			54.2.e.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.552775 + 1.64147i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.177398 + 1.00607i) q^{5} +(0.0419788 - 1.73154i) q^{6} +(2.04289 - 1.71418i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.38888 + 1.81473i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.552775 + 1.64147i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.177398 + 1.00607i) q^{5} +(0.0419788 - 1.73154i) q^{6} +(2.04289 - 1.71418i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.38888 + 1.81473i) q^{9} +(0.510796 - 0.884725i) q^{10} +(-0.720058 - 4.08365i) q^{11} +(-0.631669 + 1.61276i) q^{12} +(-3.68356 + 1.34071i) q^{13} +(-2.50597 + 0.912098i) q^{14} +(-1.74950 + 0.264938i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.925795 - 1.60352i) q^{17} +(2.86549 - 0.888246i) q^{18} +(-3.21653 - 5.57120i) q^{19} +(-0.782585 + 0.656667i) q^{20} +(3.94305 + 2.40579i) q^{21} +(-0.720058 + 4.08365i) q^{22} +(6.69746 + 5.61984i) q^{23} +(1.14517 - 1.29945i) q^{24} +(3.71775 + 1.35315i) q^{25} +3.91997 q^{26} +(-4.29935 - 2.91815i) q^{27} +2.66680 q^{28} +(-1.17759 - 0.428609i) q^{29} +(1.73461 + 0.349405i) q^{30} +(-2.56758 - 2.15445i) q^{31} +(0.173648 - 0.984808i) q^{32} +(6.30518 - 3.43930i) q^{33} +(-1.41840 + 1.19018i) q^{34} +(1.36219 + 2.35938i) q^{35} +(-2.99648 - 0.145376i) q^{36} +(-4.58887 + 7.94816i) q^{37} +(1.11709 + 6.33533i) q^{38} +(-4.23692 - 5.30537i) q^{39} +(0.959983 - 0.349405i) q^{40} +(-3.53914 + 1.28814i) q^{41} +(-2.88242 - 3.60930i) q^{42} +(0.536567 + 3.04303i) q^{43} +(2.07332 - 3.59110i) q^{44} +(-1.40197 - 2.72531i) q^{45} +(-4.37146 - 7.57159i) q^{46} +(-2.11809 + 1.77729i) q^{47} +(-1.52055 + 0.829416i) q^{48} +(0.0194152 - 0.110109i) q^{49} +(-3.03074 - 2.54309i) q^{50} +(3.14390 + 0.633281i) q^{51} +(-3.68356 - 1.34071i) q^{52} -0.231576 q^{53} +(3.04200 + 4.21263i) q^{54} +4.23618 q^{55} +(-2.50597 - 0.912098i) q^{56} +(7.36696 - 8.35948i) q^{57} +(0.959983 + 0.805521i) q^{58} +(0.613793 - 3.48099i) q^{59} +(-1.51050 - 0.921605i) q^{60} +(0.405075 - 0.339899i) q^{61} +(1.67587 + 2.90269i) q^{62} +(-1.76942 + 7.80227i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.695393 - 3.94377i) q^{65} +(-7.10124 + 1.07538i) q^{66} +(7.67276 - 2.79266i) q^{67} +(1.73993 - 0.633281i) q^{68} +(-5.52263 + 14.1002i) q^{69} +(-0.473084 - 2.68299i) q^{70} +(-4.03086 + 6.98165i) q^{71} +(2.76604 + 1.16146i) q^{72} +(1.57397 + 2.72620i) q^{73} +(7.03056 - 5.89934i) q^{74} +(-0.166083 + 6.85058i) q^{75} +(1.11709 - 6.33533i) q^{76} +(-8.47113 - 7.10812i) q^{77} +(2.16686 + 6.43453i) q^{78} +(2.43473 + 0.886167i) q^{79} -1.02159 q^{80} +(2.41349 - 8.67036i) q^{81} +3.76627 q^{82} +(7.55488 + 2.74975i) q^{83} +(1.47414 + 4.37748i) q^{84} +(1.44903 + 1.21588i) q^{85} +(0.536567 - 3.04303i) q^{86} +(0.0526065 - 2.16991i) q^{87} +(-3.17652 + 2.66541i) q^{88} +(-6.12693 - 10.6122i) q^{89} +(0.385309 + 3.04046i) q^{90} +(-5.22688 + 9.05322i) q^{91} +(1.51819 + 8.61009i) q^{92} +(2.11719 - 5.40555i) q^{93} +(2.59823 - 0.945677i) q^{94} +(6.17564 - 2.24775i) q^{95} +(1.71253 - 0.259338i) q^{96} +(-1.51264 - 8.57862i) q^{97} +(-0.0559038 + 0.0968282i) q^{98} +(9.13087 + 8.44864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.552775	+	1.64147i	0.319145	+	0.947706i
$3$	0.552775	+	1.64147i	0.319145	+	0.947706i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.177398	+	1.00607i	−0.0793347	+	0.449929i	0.919101	+	0.394021i	$0.128916\pi$
$5$	−0.177398	+	1.00607i	−0.0793347	+	0.449929i	−0.998436	+	0.0559078i	$0.982195\pi$
$6$	0.0419788	−	1.73154i	0.0171378	−	0.706899i
$7$	2.04289	−	1.71418i	0.772138	−	0.647901i	−0.169118	−	0.985596i	$-0.554092\pi$
$7$	2.04289	−	1.71418i	0.772138	−	0.647901i	0.941256	+	0.337695i	$0.109647\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.38888	+	1.81473i	−0.796293	+	0.604911i
$10$	0.510796	−	0.884725i	0.161528	−	0.279775i
$11$	−0.720058	−	4.08365i	−0.217106	−	1.23127i	−0.877215	−	0.480098i	$-0.840601\pi$
$11$	−0.720058	−	4.08365i	−0.217106	−	1.23127i	0.660109	−	0.751169i	$-0.270510\pi$
$12$	−0.631669	+	1.61276i	−0.182347	+	0.465564i
$13$	−3.68356	+	1.34071i	−1.02164	+	0.371845i	−0.797891	−	0.602802i	$-0.794051\pi$
$13$	−3.68356	+	1.34071i	−1.02164	+	0.371845i	−0.223746	+	0.974647i	$0.571829\pi$
$14$	−2.50597	+	0.912098i	−0.669749	+	0.243769i
$15$	−1.74950	+	0.264938i	−0.451720	+	0.0684067i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.925795	−	1.60352i	0.224538	−	0.388912i	−0.731643	−	0.681688i	$-0.761246\pi$
$17$	0.925795	−	1.60352i	0.224538	−	0.388912i	0.956181	+	0.292777i	$0.0945793\pi$
$18$	2.86549	−	0.888246i	0.675402	−	0.209362i
$19$	−3.21653	−	5.57120i	−0.737923	−	1.27812i	−0.953429	−	0.301618i	$-0.902473\pi$
$19$	−3.21653	−	5.57120i	−0.737923	−	1.27812i	0.215505	−	0.976503i	$-0.430860\pi$
$20$	−0.782585	+	0.656667i	−0.174991	+	0.146835i
$21$	3.94305	+	2.40579i	0.860443	+	0.524986i
$22$	−0.720058	+	4.08365i	−0.153517	+	0.870637i
$23$	6.69746	+	5.61984i	1.39652	+	1.17182i	0.962620	+	0.270854i	$0.0873062\pi$
$23$	6.69746	+	5.61984i	1.39652	+	1.17182i	0.433897	+	0.900963i	$0.357138\pi$
$24$	1.14517	−	1.29945i	0.233757	−	0.265250i
$25$	3.71775	+	1.35315i	0.743550	+	0.270630i
$26$	3.91997			0.768769
$27$	−4.29935	−	2.91815i	−0.827411	−	0.561598i
$28$	2.66680			0.503977
$29$	−1.17759	−	0.428609i	−0.218674	−	0.0795907i	0.230360	−	0.973105i	$-0.426010\pi$
$29$	−1.17759	−	0.428609i	−0.218674	−	0.0795907i	−0.449034	+	0.893515i	$0.648232\pi$
$30$	1.73461	+	0.349405i	0.316695	+	0.0637924i
$31$	−2.56758	−	2.15445i	−0.461151	−	0.386952i	0.382403	−	0.923995i	$-0.375096\pi$
$31$	−2.56758	−	2.15445i	−0.461151	−	0.386952i	−0.843554	+	0.537044i	$0.819541\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	6.30518	−	3.43930i	1.09759	−	0.598705i
$34$	−1.41840	+	1.19018i	−0.243254	+	0.204114i
$35$	1.36219	+	2.35938i	0.230252	+	0.398808i
$36$	−2.99648	−	0.145376i	−0.499413	−	0.0242293i
$37$	−4.58887	+	7.94816i	−0.754406	+	1.30667i	0.191263	+	0.981539i	$0.438742\pi$
$37$	−4.58887	+	7.94816i	−0.754406	+	1.30667i	−0.945669	+	0.325131i	$0.894592\pi$
$38$	1.11709	+	6.33533i	0.181216	+	1.02773i
$39$	−4.23692	−	5.30537i	−0.678450	−	0.849539i
$40$	0.959983	−	0.349405i	0.151787	−	0.0552458i
$41$	−3.53914	+	1.28814i	−0.552720	+	0.201174i	−0.603255	−	0.797549i	$-0.706130\pi$
$41$	−3.53914	+	1.28814i	−0.552720	+	0.201174i	0.0505345	+	0.998722i	$0.483908\pi$
$42$	−2.88242	−	3.60930i	−0.444768	−	0.556927i
$43$	0.536567	+	3.04303i	0.0818258	+	0.464057i	0.997997	+	0.0632688i	$0.0201526\pi$
$43$	0.536567	+	3.04303i	0.0818258	+	0.464057i	−0.916171	+	0.400788i	$0.868736\pi$
$44$	2.07332	−	3.59110i	0.312565	−	0.541379i
$45$	−1.40197	−	2.72531i	−0.208993	−	0.406266i
$46$	−4.37146	−	7.57159i	−0.644536	−	1.11637i
$47$	−2.11809	+	1.77729i	−0.308956	+	0.259244i	−0.784060	−	0.620685i	$-0.786855\pi$
$47$	−2.11809	+	1.77729i	−0.308956	+	0.259244i	0.475105	+	0.879929i	$0.342410\pi$
$48$	−1.52055	+	0.829416i	−0.219472	+	0.119716i
$49$	0.0194152	−	0.110109i	0.00277360	−	0.0157298i
$50$	−3.03074	−	2.54309i	−0.428611	−	0.359647i
$51$	3.14390	+	0.633281i	0.440234	+	0.0886771i
$52$	−3.68356	−	1.34071i	−0.510818	−	0.185923i
$53$	−0.231576			−0.0318094			−0.0159047	−	0.999874i	$-0.505063\pi$
$53$	−0.231576			−0.0318094			−0.0159047	+	0.999874i	$0.505063\pi$
$54$	3.04200	+	4.21263i	0.413964	+	0.573266i
$55$	4.23618			0.571207
$56$	−2.50597	−	0.912098i	−0.334874	−	0.121884i
$57$	7.36696	−	8.35948i	0.975778	−	1.10724i
$58$	0.959983	+	0.805521i	0.126052	+	0.105770i
$59$	0.613793	−	3.48099i	0.0799090	−	0.453187i	−0.918430	−	0.395582i	$-0.870543\pi$
$59$	0.613793	−	3.48099i	0.0799090	−	0.453187i	0.998339	−	0.0576042i	$-0.0183462\pi$
$60$	−1.51050	−	0.921605i	−0.195004	−	0.118979i
$61$	0.405075	−	0.339899i	0.0518646	−	0.0435196i	−0.616487	−	0.787365i	$-0.711445\pi$
$61$	0.405075	−	0.339899i	0.0518646	−	0.0435196i	0.668351	+	0.743846i	$0.267000\pi$
$62$	1.67587	+	2.90269i	0.212835	+	0.368642i
$63$	−1.76942	+	7.80227i	−0.222926	+	0.982994i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.695393	−	3.94377i	−0.0862529	−	0.489164i
$66$	−7.10124	+	1.07538i	−0.874102	+	0.132371i
$67$	7.67276	−	2.79266i	0.937377	−	0.341177i	0.172247	−	0.985054i	$-0.444897\pi$
$67$	7.67276	−	2.79266i	0.937377	−	0.341177i	0.765130	+	0.643876i	$0.222675\pi$
$68$	1.73993	−	0.633281i	0.210997	−	0.0767966i
$69$	−5.52263	+	14.1002i	−0.664847	+	1.69747i
$70$	−0.473084	−	2.68299i	−0.0565443	−	0.320679i
$71$	−4.03086	+	6.98165i	−0.478375	+	0.828570i	−0.999693	−	0.0247929i	$-0.992107\pi$
$71$	−4.03086	+	6.98165i	−0.478375	+	0.828570i	0.521318	+	0.853363i	$0.325441\pi$
$72$	2.76604	+	1.16146i	0.325981	+	0.136880i
$73$	1.57397	+	2.72620i	0.184219	+	0.319078i	0.943313	−	0.331904i	$-0.107691\pi$
$73$	1.57397	+	2.72620i	0.184219	+	0.319078i	−0.759094	+	0.650981i	$0.774358\pi$
$74$	7.03056	−	5.89934i	0.817286	−	0.685784i
$75$	−0.166083	+	6.85058i	−0.0191776	+	0.791037i
$76$	1.11709	−	6.33533i	0.128139	−	0.726713i
$77$	−8.47113	−	7.10812i	−0.965374	−	0.810045i
$78$	2.16686	+	6.43453i	0.245349	+	0.728567i
$79$	2.43473	+	0.886167i	0.273928	+	0.0997016i	0.475332	−	0.879807i	$-0.342328\pi$
$79$	2.43473	+	0.886167i	0.273928	+	0.0997016i	−0.201404	+	0.979508i	$0.564550\pi$
$80$	−1.02159			−0.114218
$81$	2.41349	−	8.67036i	0.268165	−	0.963373i
$82$	3.76627			0.415915
$83$	7.55488	+	2.74975i	0.829256	+	0.301824i	0.721553	−	0.692359i	$-0.243428\pi$
$83$	7.55488	+	2.74975i	0.829256	+	0.301824i	0.107702	+	0.994183i	$0.465651\pi$
$84$	1.47414	+	4.37748i	0.160842	+	0.477622i
$85$	1.44903	+	1.21588i	0.157169	+	0.131880i
$86$	0.536567	−	3.04303i	0.0578596	−	0.328138i
$87$	0.0526065	−	2.16991i	0.00564001	−	0.232639i
$88$	−3.17652	+	2.66541i	−0.338618	+	0.284134i
$89$	−6.12693	−	10.6122i	−0.649453	−	1.12489i	−0.983254	−	0.182242i	$-0.941664\pi$
$89$	−6.12693	−	10.6122i	−0.649453	−	1.12489i	0.333800	−	0.942644i	$-0.391669\pi$
$90$	0.385309	+	3.04046i	0.0406151	+	0.320493i
$91$	−5.22688	+	9.05322i	−0.547926	+	0.949035i
$92$	1.51819	+	8.61009i	0.158282	+	0.897664i
$93$	2.11719	−	5.40555i	0.219542	−	0.560529i
$94$	2.59823	−	0.945677i	0.267986	−	0.0975391i
$95$	6.17564	−	2.24775i	0.633607	−	0.230614i
$96$	1.71253	−	0.259338i	0.174784	−	0.0264686i
$97$	−1.51264	−	8.57862i	−0.153586	−	0.871027i	−0.960068	−	0.279768i	$-0.909742\pi$
$97$	−1.51264	−	8.57862i	−0.153586	−	0.871027i	0.806482	−	0.591259i	$-0.201369\pi$
$98$	−0.0559038	+	0.0968282i	−0.00564713	+	0.00978112i
$99$	9.13087	+	8.44864i	0.917687	+	0.849120i
$100$	1.97817	+	3.42630i	0.197817	+	0.342630i
$101$	−4.14121	+	3.47489i	−0.412066	+	0.345764i	−0.825135	−	0.564935i	$-0.808901\pi$
$101$	−4.14121	+	3.47489i	−0.412066	+	0.345764i	0.413069	+	0.910700i	$0.364457\pi$
$102$	−2.73771	−	1.67037i	−0.271073	−	0.165391i
$103$	1.87292	−	10.6218i	0.184544	−	1.04660i	−0.741996	−	0.670405i	$-0.766120\pi$
$103$	1.87292	−	10.6218i	0.184544	−	1.04660i	0.926540	−	0.376197i	$-0.122768\pi$
$104$	3.00287	+	2.51971i	0.294455	+	0.247077i
$105$	−3.11988	+	3.54021i	−0.304469	+	0.345489i
$106$	0.217610	+	0.0792037i	0.0211362	+	0.00769295i
$107$	−14.8511			−1.43571			−0.717856	−	0.696191i	$-0.754876\pi$
$107$	−14.8511			−1.43571			−0.717856	+	0.696191i	$0.754876\pi$
$108$	−1.41775	−	4.99900i	−0.136423	−	0.481029i
$109$	17.6598			1.69150			0.845752	−	0.533576i	$-0.179152\pi$
$109$	17.6598			1.69150			0.845752	+	0.533576i	$0.179152\pi$
$110$	−3.98071	−	1.44886i	−0.379546	−	0.138143i
$111$	−15.5833	−	3.13897i	−1.47910	−	0.297938i
$112$	2.04289	+	1.71418i	0.193035	+	0.161975i
$113$	0.339716	−	1.92663i	0.0319578	−	0.181242i	−0.964651	−	0.263532i	$-0.915112\pi$
$113$	0.339716	−	1.92663i	0.0319578	−	0.181242i	0.996608	+	0.0822905i	$0.0262235\pi$
$114$	−9.78179	+	5.33569i	−0.916149	+	0.499733i
$115$	−6.84208	+	5.74118i	−0.638027	+	0.535368i
$116$	−0.626584	−	1.08528i	−0.0581769	−	0.100765i
$117$	6.36656	−	9.88747i	0.588589	−	0.914097i
$118$	−1.76735	+	3.06113i	−0.162697	+	0.281800i
$119$	−0.857442	−	4.86280i	−0.0786016	−	0.445772i
$120$	1.10419	+	1.38265i	0.100799	+	0.126218i
$121$	−5.82110	+	2.11871i	−0.529191	+	0.192610i
$122$	−0.496899	+	0.180856i	−0.0449871	+	0.0163740i
$123$	−4.07080	−	5.09735i	−0.367051	−	0.459613i
$124$	−0.582023	−	3.30082i	−0.0522672	−	0.296422i
$125$	−4.57487	+	7.92391i	−0.409189	+	0.708736i
$126$	4.33124	−	6.72656i	0.385858	−	0.599249i
$127$	−2.78998	−	4.83239i	−0.247571	−	0.428805i	0.715281	−	0.698837i	$-0.246299\pi$
$127$	−2.78998	−	4.83239i	−0.247571	−	0.428805i	−0.962851	+	0.270032i	$0.912966\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−4.69845	+	2.56287i	−0.413675	+	0.225648i
$130$	−0.695393	+	3.94377i	−0.0609900	+	0.345891i
$131$	1.18532	+	0.994600i	0.103562	+	0.0868986i	0.693098	−	0.720843i	$-0.256245\pi$
$131$	1.18532	+	0.994600i	0.103562	+	0.0868986i	−0.589537	+	0.807742i	$0.700690\pi$
$132$	7.04079	+	1.41824i	0.612822	+	0.123442i
$133$	−16.1211	−	5.86759i	−1.39787	−	0.508785i
$134$	−8.16518			−0.705364
$135$	3.69856	−	3.80779i	0.318321	−	0.327722i
$136$	−1.85159			−0.158773
$137$	18.8496	+	6.86070i	1.61043	+	0.586149i	0.981525	−	0.191332i	$-0.0612807\pi$
$137$	18.8496	+	6.86070i	1.61043	+	0.586149i	0.628906	+	0.777481i	$0.283503\pi$
$138$	10.0121	−	11.3610i	0.852290	−	0.967114i
$139$	2.98779	+	2.50705i	0.253421	+	0.212645i	0.760644	−	0.649170i	$-0.224883\pi$
$139$	2.98779	+	2.50705i	0.253421	+	0.212645i	−0.507223	+	0.861815i	$0.669328\pi$
$140$	−0.473084	+	2.68299i	−0.0399829	+	0.226754i
$141$	−4.08821	−	2.49435i	−0.344289	−	0.210062i
$142$	6.17564	−	5.18197i	0.518248	−	0.434862i
$143$	8.12736	+	14.0770i	0.679644	+	1.17718i
$144$	−2.20199	−	2.03746i	−0.183499	−	0.169788i
$145$	0.640114	−	1.10871i	0.0531586	−	0.0920734i
$146$	−0.546635	−	3.10012i	−0.0452398	−	0.256568i
$147$	0.191473	−	0.0289960i	0.0157925	−	0.00239155i
$148$	−8.62426	+	3.13897i	−0.708910	+	0.258022i
$149$	9.24128	−	3.36355i	0.757075	−	0.275553i	0.0654951	−	0.997853i	$-0.479137\pi$
$149$	9.24128	−	3.36355i	0.757075	−	0.275553i	0.691580	+	0.722300i	$0.256915\pi$
$150$	2.49910	−	6.38064i	0.204051	−	0.520977i
$151$	0.697011	+	3.95294i	0.0567219	+	0.321686i	0.999945	−	0.0104735i	$-0.00333387\pi$
$151$	0.697011	+	3.95294i	0.0567219	+	0.321686i	−0.943223	+	0.332160i	$0.892223\pi$
$152$	−3.21653	+	5.57120i	−0.260895	+	0.451884i
$153$	0.698355	+	5.51070i	0.0564587	+	0.445513i
$154$	5.52913	+	9.57674i	0.445550	+	0.771716i
$155$	2.62302	−	2.20098i	0.210686	−	0.176787i
$156$	0.164555	−	6.78759i	0.0131750	−	0.543442i
$157$	−2.48817	+	14.1111i	−0.198578	+	1.12619i	0.708653	+	0.705557i	$0.249303\pi$
$157$	−2.48817	+	14.1111i	−0.198578	+	1.12619i	−0.907231	+	0.420634i	$0.861808\pi$
$158$	−1.98481	−	1.66545i	−0.157903	−	0.132496i
$159$	−0.128010	−	0.380127i	−0.0101518	−	0.0301460i
$160$	0.959983	+	0.349405i	0.0758933	+	0.0276229i
$161$	23.3156			1.83753
$162$	−5.23337	+	7.32201i	−0.411173	+	0.575271i
$163$	−14.2911			−1.11937			−0.559683	−	0.828707i	$-0.689077\pi$
$163$	−14.2911			−1.11937			−0.559683	+	0.828707i	$0.689077\pi$
$164$	−3.53914	−	1.28814i	−0.276360	−	0.100587i
$165$	2.34166	+	6.95359i	0.182298	+	0.541336i
$166$	−6.15879	−	5.16784i	−0.478015	−	0.401102i
$167$	−1.65921	+	9.40983i	−0.128393	+	0.728154i	0.850841	+	0.525423i	$0.176093\pi$
$167$	−1.65921	+	9.40983i	−0.128393	+	0.728154i	−0.979234	+	0.202731i	$0.935018\pi$
$168$	0.111949	−	4.61767i	0.00863704	−	0.356261i
$169$	1.81256	−	1.52092i	0.139428	−	0.116994i
$170$	−0.945785	−	1.63815i	−0.0725384	−	0.125640i
$171$	17.7941	+	7.47177i	1.36075	+	0.571381i
$172$	−1.54498	+	2.67599i	−0.117804	+	0.204042i
$173$	1.73345	+	9.83089i	0.131792	+	0.747429i	0.977040	+	0.213055i	$0.0683414\pi$
$173$	1.73345	+	9.83089i	0.131792	+	0.747429i	−0.845248	+	0.534374i	$0.820547\pi$
$174$	−0.791588	+	2.02106i	−0.0600102	+	0.153216i
$175$	9.91449	−	3.60858i	0.749465	−	0.272783i
$176$	3.89657	−	1.41824i	0.293715	−	0.106904i
$177$	6.05325	−	0.916681i	0.454990	−	0.0689019i
$178$	2.12786	+	12.0677i	0.159490	+	0.904512i
$179$	11.2541	−	19.4927i	0.841174	−	1.45696i	−0.0477290	−	0.998860i	$-0.515198\pi$
$179$	11.2541	−	19.4927i	0.841174	−	1.45696i	0.888903	−	0.458096i	$-0.151468\pi$
$180$	0.677827	−	2.98888i	0.0505222	−	0.222778i
$181$	−0.248078	−	0.429684i	−0.0184395	−	0.0319382i	0.856658	−	0.515884i	$-0.172536\pi$
$181$	−0.248078	−	0.429684i	−0.0184395	−	0.0319382i	−0.875098	+	0.483946i	$0.839203\pi$
$182$	8.00804	−	6.71954i	0.593595	−	0.498086i
$183$	0.781851	+	0.477034i	0.0577961	+	0.0352633i
$184$	1.51819	−	8.61009i	0.111923	−	0.634744i
$185$	−7.18237	−	6.02672i	−0.528058	−	0.443093i
$186$	−3.83831	+	4.35543i	−0.281439	+	0.319356i
$187$	−7.21486	−	2.62599i	−0.527603	−	0.192032i
$188$	−2.76497			−0.201656
$189$	−13.7853	+	1.40844i	−1.00273	+	0.102449i
$190$	−6.57197			−0.476781
$191$	−6.75481	−	2.45855i	−0.488761	−	0.177894i	0.0858713	−	0.996306i	$-0.472633\pi$
$191$	−6.75481	−	2.45855i	−0.488761	−	0.177894i	−0.574632	+	0.818412i	$0.694855\pi$
$192$	−1.69795	−	0.342020i	−0.122539	−	0.0246832i
$193$	−10.3185	−	8.65825i	−0.742742	−	0.623234i	0.190831	−	0.981623i	$-0.438882\pi$
$193$	−10.3185	−	8.65825i	−0.742742	−	0.623234i	−0.933572	+	0.358389i	$0.883326\pi$
$194$	−1.51264	+	8.57862i	−0.108601	+	0.615909i
$195$	6.08920	−	3.32149i	0.436057	−	0.237857i
$196$	0.0856496	−	0.0718685i	0.00611783	−	0.00513346i
$197$	−2.53340	−	4.38797i	−0.180497	−	0.312630i	0.761553	−	0.648103i	$-0.224437\pi$
$197$	−2.53340	−	4.38797i	−0.180497	−	0.312630i	−0.942050	+	0.335473i	$0.891104\pi$
$198$	−5.69060	−	11.0621i	−0.404414	−	0.786147i
$199$	8.97242	−	15.5407i	0.636038	−	1.10165i	−0.350256	−	0.936654i	$-0.613906\pi$
$199$	8.97242	−	15.5407i	0.636038	−	1.10165i	0.986294	−	0.164996i	$-0.0527611\pi$
$200$	−0.687013	−	3.89624i	−0.0485791	−	0.275506i
$201$	8.82539	+	11.0509i	0.622495	+	0.779473i
$202$	5.07995	−	1.84895i	0.357424	−	0.130092i
$203$	−3.14040	+	1.14301i	−0.220413	+	0.0802238i
$204$	2.00130	+	2.50598i	0.140119	+	0.175454i
$205$	−0.668128	−	3.78914i	−0.0466641	−	0.264645i
$206$	−5.39285	+	9.34070i	−0.375738	+	0.650797i
$207$	−26.1979	−	1.27101i	−1.82088	−	0.0883413i
$208$	−1.95998	−	3.39479i	−0.135900	−	0.235386i
$209$	−20.4347	+	17.1468i	−1.41350	+	1.18607i
$210$	4.14255	−	2.25965i	0.285863	−	0.155930i
$211$	−0.884489	+	5.01618i	−0.0608907	+	0.345328i	0.939108	+	0.343623i	$0.111654\pi$
$211$	−0.884489	+	5.01618i	−0.0608907	+	0.345328i	−0.999999	+	0.00170581i	$0.999457\pi$
$212$	−0.177398	−	0.148854i	−0.0121837	−	0.0102234i
$213$	−13.6884	−	2.75727i	−0.937912	−	0.188925i
$214$	13.9555	+	5.07938i	0.953978	+	0.347220i
$215$	−3.15669			−0.215284
$216$	−0.377513	+	5.18242i	−0.0256865	+	0.352619i
$217$	−8.93840			−0.606778
$218$	−16.5948	−	6.04001i	−1.12394	−	0.409081i
$219$	−3.60494	+	4.09061i	−0.243599	+	0.276418i
$220$	3.24511	+	2.72297i	0.218785	+	0.183582i
$221$	−1.26037	+	7.14790i	−0.0847815	+	0.480820i
$222$	13.5699	+	8.27948i	0.910754	+	0.555682i
$223$	2.92334	−	2.45297i	0.195761	−	0.164263i	−0.539638	−	0.841897i	$-0.681439\pi$
$223$	2.92334	−	2.45297i	0.195761	−	0.164263i	0.735399	+	0.677634i	$0.236995\pi$
$224$	−1.33340	−	2.30951i	−0.0890914	−	0.154311i
$225$	−11.3369	+	3.51421i	−0.755791	+	0.234281i
$226$	−0.978174	+	1.69425i	−0.0650672	+	0.112700i
$227$	−3.53875	−	20.0693i	−0.234875	−	1.33204i	−0.842876	−	0.538108i	$-0.819139\pi$
$227$	−3.53875	−	20.0693i	−0.234875	−	1.33204i	0.608001	−	0.793936i	$-0.291972\pi$
$228$	11.0168	−	1.66834i	0.729605	−	0.110488i
$229$	1.41711	−	0.515787i	0.0936455	−	0.0340842i	−0.294773	−	0.955567i	$-0.595244\pi$
$229$	1.41711	−	0.515787i	0.0936455	−	0.0340842i	0.388418	+	0.921483i	$0.373022\pi$
$230$	8.39305	−	3.05482i	0.553421	−	0.201429i
$231$	6.98517	−	17.8343i	0.459590	−	1.17341i
$232$	0.217610	+	1.23413i	0.0142868	+	0.0810246i
$233$	10.0838	−	17.4656i	0.660610	−	1.14421i	−0.319845	−	0.947470i	$-0.603631\pi$
$233$	10.0838	−	17.4656i	0.660610	−	1.14421i	0.980456	−	0.196741i	$-0.0630357\pi$
$234$	−9.36433	+	7.11369i	−0.612165	+	0.465037i
$235$	−1.41234	−	2.44624i	−0.0921308	−	0.159575i
$236$	2.70773	−	2.27206i	0.176258	−	0.147898i
$237$	−0.108766	+	4.48639i	−0.00706512	+	0.291422i
$238$	−0.857442	+	4.86280i	−0.0555797	+	0.315208i
$239$	−9.68541	−	8.12702i	−0.626497	−	0.525693i	0.273341	−	0.961917i	$-0.411871\pi$
$239$	−9.68541	−	8.12702i	−0.626497	−	0.525693i	−0.899838	+	0.436224i	$0.856316\pi$
$240$	−0.564711	−	1.67692i	−0.0364519	−	0.108245i
$241$	26.1605	+	9.52166i	1.68515	+	0.613344i	0.994001	−	0.109369i	$-0.0348831\pi$
$241$	26.1605	+	9.52166i	1.68515	+	0.613344i	0.691148	+	0.722713i	$0.257105\pi$
$242$	6.19469			0.398210
$243$	15.5663	−	0.831075i	0.998578	−	0.0533135i
$244$	0.528788			0.0338522
$245$	0.107333	+	0.0390661i	0.00685728	+	0.00249584i
$246$	2.08190	+	6.18224i	0.132737	+	0.394165i
$247$	19.3177	+	16.2094i	1.22915	+	1.03138i
$248$	−0.582023	+	3.30082i	−0.0369585	+	0.209602i
$249$	−0.337498	+	13.9211i	−0.0213881	+	0.882216i
$250$	7.00911	−	5.88134i	0.443295	−	0.371969i
$251$	0.336641	+	0.583079i	0.0212486	+	0.0368036i	0.876454	−	0.481485i	$-0.159903\pi$
$251$	0.336641	+	0.583079i	0.0212486	+	0.0368036i	−0.855206	+	0.518289i	$0.826569\pi$
$252$	−6.37066	+	4.83952i	−0.401314	+	0.304861i
$253$	18.1269	−	31.3967i	1.13963	−	1.97389i
$254$	0.968950	+	5.49519i	0.0607973	+	0.344799i
$255$	−1.19485	+	3.05065i	−0.0748242	+	0.191039i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−28.7904	+	10.4789i	−1.79590	+	0.653653i	−0.797141	+	0.603793i	$0.793655\pi$
$257$	−28.7904	+	10.4789i	−1.79590	+	0.653653i	−0.998756	+	0.0498599i	$0.984123\pi$
$258$	5.29165	−	0.801347i	0.329444	−	0.0498897i
$259$	4.25007	+	24.1033i	0.264087	+	1.49771i
$260$	2.00230	−	3.46809i	0.124178	−	0.215082i
$261$	3.59094	−	1.11312i	0.222274	−	0.0689006i
$262$	−0.773661	−	1.34002i	−0.0477969	−	0.0827867i
$263$	−4.54929	+	3.81731i	−0.280521	+	0.235385i	−0.772182	−	0.635402i	$-0.780835\pi$
$263$	−4.54929	+	3.81731i	−0.280521	+	0.235385i	0.491661	+	0.870787i	$0.336390\pi$
$264$	−6.13111	−	3.74080i	−0.377344	−	0.230230i
$265$	0.0410811	−	0.232982i	0.00252359	−	0.0143120i
$266$	13.1420	+	11.0275i	0.805789	+	0.676137i
$267$	14.0328	−	15.9233i	0.858792	−	0.974492i
$268$	7.67276	+	2.79266i	0.468688	+	0.170589i
$269$	15.3624			0.936661			0.468330	−	0.883553i	$-0.344856\pi$
$269$	15.3624			0.936661			0.468330	+	0.883553i	$0.344856\pi$
$270$	−4.77785	+	2.31317i	−0.290771	+	0.140775i
$271$	−14.5939			−0.886516			−0.443258	−	0.896394i	$-0.646177\pi$
$271$	−14.5939			−0.886516			−0.443258	+	0.896394i	$0.646177\pi$
$272$	1.73993	+	0.633281i	0.105498	+	0.0383983i
$273$	−17.7499	−	3.57539i	−1.07427	−	0.216393i
$274$	−15.3663	−	12.8939i	−0.928315	−	0.778949i
$275$	2.84880	−	16.1563i	0.171789	−	0.974264i
$276$	−13.2940	+	7.25152i	−0.800206	+	0.436490i
$277$	4.35786	−	3.65668i	0.261838	−	0.219709i	−0.502412	−	0.864629i	$-0.667554\pi$
$277$	4.35786	−	3.65668i	0.261838	−	0.219709i	0.764250	+	0.644920i	$0.223109\pi$
$278$	−1.95014	−	3.37774i	−0.116962	−	0.202584i
$279$	10.0434	+	0.487262i	0.601282	+	0.0291716i
$280$	1.36219	−	2.35938i	0.0814064	−	0.141000i
$281$	2.37136	+	13.4487i	0.141464	+	0.802281i	0.970139	+	0.242551i	$0.0779841\pi$
$281$	2.37136	+	13.4487i	0.141464	+	0.802281i	−0.828675	+	0.559730i	$0.810905\pi$
$282$	2.98854	+	3.74217i	0.177965	+	0.222843i
$283$	−24.3720	+	8.87068i	−1.44876	+	0.527307i	−0.942246	−	0.334922i	$-0.891290\pi$
$283$	−24.3720	+	8.87068i	−1.44876	+	0.527307i	−0.506519	+	0.862229i	$0.669068\pi$
$284$	−7.57554	+	2.75727i	−0.449525	+	0.163614i
$285$	7.10336	+	8.89465i	0.420767	+	0.526874i
$286$	−2.82260	−	16.0078i	−0.166904	−	0.946559i
$287$	−5.02194	+	8.69825i	−0.296436	+	0.513442i
$288$	1.37234	+	2.66771i	0.0808658	+	0.157196i
$289$	6.78581	+	11.7534i	0.399165	+	0.691374i
$290$	−0.980712	+	0.822915i	−0.0575894	+	0.0483232i
$291$	13.2454	−	7.22501i	0.776461	−	0.423538i
$292$	−0.546635	+	3.10012i	−0.0319894	+	0.181421i
$293$	15.2378	+	12.7860i	0.890199	+	0.746966i	0.968250	−	0.249984i	$-0.0804253\pi$
$293$	15.2378	+	12.7860i	0.890199	+	0.746966i	−0.0780511	+	0.996949i	$0.524870\pi$
$294$	−0.189843	−	0.0382404i	−0.0110719	−	0.00223023i
$295$	3.39325	+	1.23504i	0.197562	+	0.0719068i
$296$	9.17774			0.533446
$297$	−8.82091	+	19.6583i	−0.511841	+	1.14069i
$298$	−9.83436			−0.569689
$299$	−32.2051	−	11.7217i	−1.86247	−	0.677883i
$300$	−4.53070	+	5.14110i	−0.261580	+	0.296821i
$301$	6.31245	+	5.29678i	0.363844	+	0.305301i
$302$	0.697011	−	3.95294i	0.0401085	−	0.227466i
$303$	−7.99310	−	4.87686i	−0.459192	−	0.280168i
$304$	4.92802	−	4.13510i	0.282641	−	0.237164i
$305$	0.270103	+	0.467832i	0.0154661	+	0.0267880i
$306$	1.22853	−	5.41721i	0.0702304	−	0.309681i
$307$	4.75733	−	8.23993i	0.271515	−	0.470278i	−0.697735	−	0.716356i	$-0.745809\pi$
$307$	4.75733	−	8.23993i	0.271515	−	0.470278i	0.969250	+	0.246078i	$0.0791420\pi$
$308$	−1.92025	−	10.8903i	−0.109416	−	0.620531i
$309$	18.4708	−	2.79714i	1.05077	−	0.159124i
$310$	−3.21761	+	1.17111i	−0.182748	+	0.0665148i
$311$	13.5916	−	4.94693i	0.770707	−	0.280514i	0.0734150	−	0.997301i	$-0.476610\pi$
$311$	13.5916	−	4.94693i	0.770707	−	0.280514i	0.697292	+	0.716787i	$0.254388\pi$
$312$	−2.47612	+	6.32196i	−0.140183	+	0.357911i
$313$	−2.32518	−	13.1867i	−0.131427	−	0.745359i	−0.977281	−	0.211946i	$-0.932020\pi$
$313$	−2.32518	−	13.1867i	−0.131427	−	0.745359i	0.845855	−	0.533414i	$-0.179091\pi$
$314$	7.16441	−	12.4091i	0.404311	−	0.700287i
$315$	−7.53576	−	3.16427i	−0.424592	−	0.178286i
$316$	1.29549	+	2.24385i	0.0728770	+	0.126227i
$317$	19.2768	−	16.1751i	1.08269	−	0.908487i	0.0865506	−	0.996247i	$-0.472416\pi$
$317$	19.2768	−	16.1751i	1.08269	−	0.908487i	0.996142	+	0.0877609i	$0.0279711\pi$
$318$	−0.00972129	+	0.400984i	−0.000545143	+	0.0224861i
$319$	−0.902354	+	5.11750i	−0.0505221	+	0.286525i
$320$	−0.782585	−	0.656667i	−0.0437479	−	0.0367088i
$321$	−8.20933	−	24.3777i	−0.458200	−	1.36063i
$322$	−21.9095	−	7.97440i	−1.22097	−	0.444396i
$323$	−11.9114			−0.662768
$324$	7.42204	−	5.09052i	0.412335	−	0.282806i
$325$	−15.5088			−0.860271
$326$	13.4292	+	4.88784i	0.743777	+	0.270713i
$327$	9.76191	+	28.9882i	0.539835	+	1.60305i
$328$	2.88513	+	2.42091i	0.159305	+	0.133672i
$329$	−1.28042	+	7.26160i	−0.0705916	+	0.400345i
$330$	0.177830	−	7.33513i	0.00978921	−	0.403786i
$331$	−16.1905	+	13.5855i	−0.889912	+	0.746725i	−0.968193	−	0.250206i	$-0.919502\pi$
$331$	−16.1905	+	13.5855i	−0.889912	+	0.746725i	0.0782802	+	0.996931i	$0.475057\pi$
$332$	4.01987	+	6.96261i	0.220619	+	0.382123i
$333$	−3.46152	−	27.3148i	−0.189690	−	1.49684i
$334$	4.77749	−	8.27486i	0.261413	−	0.452780i
$335$	1.44848	+	8.21476i	0.0791392	+	0.448820i
$336$	−1.68453	+	4.30090i	−0.0918989	+	0.234633i
$337$	−4.48414	+	1.63209i	−0.244267	+	0.0889058i	−0.461252	−	0.887269i	$-0.652600\pi$
$337$	−4.48414	+	1.63209i	−0.244267	+	0.0889058i	0.216986	+	0.976175i	$0.430378\pi$
$338$	−2.22344	+	0.809266i	−0.120939	+	0.0440183i
$339$	3.35030	−	0.507356i	0.181963	−	0.0275558i
$340$	0.328468	+	1.86283i	0.0178137	+	0.101026i
$341$	−6.94924	+	12.0364i	−0.376322	+	0.651809i
$342$	−14.1655	−	13.1071i	−0.765984	−	0.708752i
$343$	9.18471	+	15.9084i	0.495928	+	0.858972i
$344$	2.36705	−	1.98619i	0.127623	−	0.107088i
$345$	−13.2061	−	8.05751i	−0.710995	−	0.433802i
$346$	1.73345	−	9.83089i	0.0931909	−	0.528512i
$347$	12.0020	+	10.0708i	0.644299	+	0.540631i	0.905335	−	0.424698i	$-0.139620\pi$
$347$	12.0020	+	10.0708i	0.644299	+	0.540631i	−0.261036	+	0.965329i	$0.584064\pi$
$348$	1.43509	−	1.62844i	0.0769291	−	0.0872933i
$349$	−18.6170	−	6.77604i	−0.996547	−	0.362713i	−0.208295	−	0.978066i	$-0.566791\pi$
$349$	−18.6170	−	6.77604i	−0.996547	−	0.362713i	−0.788252	+	0.615353i	$0.789014\pi$
$350$	−10.5508			−0.563963
$351$	19.7493	+	4.98500i	1.05414	+	0.266080i
$352$	−4.14665			−0.221017
$353$	14.8445	+	5.40296i	0.790093	+	0.287570i	0.705375	−	0.708835i	$-0.250779\pi$
$353$	14.8445	+	5.40296i	0.790093	+	0.287570i	0.0847183	+	0.996405i	$0.473001\pi$
$354$	−6.00172	−	1.20894i	−0.318988	−	0.0642542i
$355$	−6.30898	−	5.29387i	−0.334846	−	0.280969i
$356$	2.12786	−	12.0677i	0.112776	−	0.639587i
$357$	7.50819	−	4.09550i	0.397375	−	0.216757i
$358$	−17.2423	+	14.4680i	−0.911286	+	0.764660i
$359$	−2.43474	−	4.21710i	−0.128501	−	0.222570i	0.794595	−	0.607140i	$-0.207683\pi$
$359$	−2.43474	−	4.21710i	−0.128501	−	0.222570i	−0.923096	+	0.384570i	$0.874350\pi$
$360$	−1.65921	+	2.57680i	−0.0874479	+	0.135809i
$361$	−11.1922	+	19.3854i	−0.589062	+	1.02028i
$362$	0.0861567	+	0.488619i	0.00452830	+	0.0256812i
$363$	−6.69557	−	8.38402i	−0.351426	−	0.440047i
$364$	−9.82332	+	3.57539i	−0.514882	+	0.187402i
$365$	−3.02197	+	1.09991i	−0.158177	+	0.0575718i
$366$	−0.571544	−	0.715674i	−0.0298751	−	0.0374089i
$367$	−1.47394	−	8.35914i	−0.0769392	−	0.436344i	−0.998807	−	0.0488385i	$-0.984448\pi$
$367$	−1.47394	−	8.35914i	−0.0769392	−	0.436344i	0.921868	−	0.387505i	$-0.126663\pi$
$368$	−4.37146	+	7.57159i	−0.227878	+	0.394696i
$369$	6.11694	−	9.49980i	0.318435	−	0.494540i
$370$	4.68796	+	8.11978i	0.243715	+	0.422127i
$371$	−0.473084	+	0.396964i	−0.0245613	+	0.0206094i
$372$	5.09648	−	2.77999i	0.264240	−	0.144136i
$373$	0.783900	−	4.44572i	0.0405888	−	0.230190i	−0.957765	−	0.287553i	$-0.907158\pi$
$373$	0.783900	−	4.44572i	0.0405888	−	0.230190i	0.998353	+	0.0573629i	$0.0182692\pi$
$374$	5.88161	+	4.93525i	0.304131	+	0.255196i
$375$	−15.5358	−	3.12940i	−0.802264	−	0.161601i
$376$	2.59823	+	0.945677i	0.133993	+	0.0487695i
$377$	4.91238			0.253000
$378$	13.4357	+	3.39135i	0.691057	+	0.174432i
$379$	11.1018			0.570262			0.285131	−	0.958489i	$-0.407963\pi$
$379$	11.1018			0.570262			0.285131	+	0.958489i	$0.407963\pi$
$380$	6.17564	+	2.24775i	0.316803	+	0.115307i
$381$	6.39001	−	7.25091i	0.327370	−	0.371475i
$382$	5.50657	+	4.62056i	0.281741	+	0.236408i
$383$	−3.82767	+	21.7078i	−0.195585	+	1.10922i	0.715999	+	0.698101i	$0.245971\pi$
$383$	−3.82767	+	21.7078i	−0.195585	+	1.10922i	−0.911584	+	0.411114i	$0.865140\pi$
$384$	1.47857	+	0.902126i	0.0754530	+	0.0460364i
$385$	8.65404	−	7.26160i	0.441051	−	0.370085i
$386$	6.73492	+	11.6652i	0.342798	+	0.593744i
$387$	−6.80407	−	6.29569i	−0.345870	−	0.320028i
$388$	4.35548	−	7.54391i	0.221116	−	0.382984i
$389$	−2.95836	−	16.7777i	−0.149995	−	0.850663i	−0.963220	−	0.268714i	$-0.913401\pi$
$389$	−2.95836	−	16.7777i	−0.149995	−	0.850663i	0.813225	−	0.581949i	$-0.197710\pi$
$390$	−6.85799	+	1.03855i	−0.347268	+	0.0525889i
$391$	15.2120	−	5.53672i	0.769305	−	0.280004i
$392$	−0.105065	+	0.0382404i	−0.00530657	+	0.00193143i
$393$	−0.977396	+	2.49546i	−0.0493031	+	0.125879i
$394$	0.879840	+	4.98982i	0.0443257	+	0.251383i
$395$	−1.32346	+	2.29231i	−0.0665907	+	0.115338i
$396$	1.56397	+	12.3412i	0.0785925	+	0.620171i
$397$	7.80452	+	13.5178i	0.391698	+	0.678441i	0.992674	−	0.120827i	$-0.0385545\pi$
$397$	7.80452	+	13.5178i	0.391698	+	0.678441i	−0.600976	+	0.799267i	$0.705221\pi$
$398$	−13.7465	+	11.5347i	−0.689052	+	0.578183i
$399$	0.720175	−	29.7058i	0.0360538	−	1.48715i
$400$	−0.687013	+	3.89624i	−0.0343506	+	0.194812i
$401$	−2.82242	−	2.36829i	−0.140945	−	0.118267i	0.569589	−	0.821929i	$-0.307102\pi$
$401$	−2.82242	−	2.36829i	−0.140945	−	0.118267i	−0.710534	+	0.703663i	$0.751547\pi$
$402$	−4.51351	−	13.4029i	−0.225113	−	0.668478i
$403$	12.3463	+	4.49370i	0.615015	+	0.223847i
$404$	−5.40597			−0.268957
$405$	8.29486	+	3.96625i	0.412175	+	0.197084i
$406$	3.34195			0.165858
$407$	35.7618	+	13.0162i	1.77264	+	0.645190i
$408$	−1.02351	−	3.03934i	−0.0506714	−	0.150470i
$409$	−10.3077	−	8.64918i	−0.509682	−	0.427674i	0.351335	−	0.936250i	$-0.385728\pi$
$409$	−10.3077	−	8.64918i	−0.509682	−	0.427674i	−0.861017	+	0.508576i	$0.830172\pi$
$410$	−0.668128	+	3.78914i	−0.0329965	+	0.187132i
$411$	−0.842067	+	34.7336i	−0.0415361	+	1.71328i
$412$	8.26233	−	6.93292i	0.407056	−	0.341560i
$413$	−4.71316	−	8.16342i	−0.231919	−	0.401696i
$414$	24.1833	+	10.1546i	1.18854	+	0.499070i
$415$	−4.10667	+	7.11296i	−0.201588	+	0.349161i
$416$	0.680695	+	3.86041i	0.0333738	+	0.189272i
$417$	−2.46369	+	6.29022i	−0.120647	+	0.308033i
$418$	25.0669	−	9.12361i	1.22606	−	0.446251i
$419$	−1.29440	+	0.471124i	−0.0632357	+	0.0230159i	−0.373444	−	0.927653i	$-0.621823\pi$
$419$	−1.29440	+	0.471124i	−0.0632357	+	0.0230159i	0.310209	+	0.950668i	$0.399601\pi$
$420$	−4.66557	+	0.706536i	−0.227657	+	0.0344754i
$421$	−1.39368	−	7.90398i	−0.0679240	−	0.385216i	−0.999751	−	0.0223134i	$-0.992897\pi$
$421$	−1.39368	−	7.90398i	−0.0679240	−	0.385216i	0.931827	−	0.362903i	$-0.118214\pi$
$422$	2.54678	−	4.41116i	0.123975	−	0.214732i
$423$	1.83456	−	8.08950i	0.0891993	−	0.393325i
$424$	0.115788	+	0.200551i	0.00562317	+	0.00973961i
$425$	5.61168	−	4.70876i	0.272207	−	0.228409i
$426$	11.9198	+	7.27268i	0.577517	+	0.352363i
$427$	0.244874	−	1.38875i	0.0118503	−	0.0672062i
$428$	−11.3766	−	9.54612i	−0.549910	−	0.461429i
$429$	−18.6144	+	21.1223i	−0.898714	+	1.01979i
$430$	2.96632	+	1.07965i	0.143049	+	0.0520654i
$431$	−34.6923			−1.67107			−0.835534	−	0.549438i	$-0.814842\pi$
$431$	−34.6923			−1.67107			−0.835534	+	0.549438i	$0.814842\pi$
$432$	2.12724	−	4.74077i	0.102347	−	0.228090i
$433$	0.605990			0.0291220			0.0145610	−	0.999894i	$-0.495365\pi$
$433$	0.605990			0.0291220			0.0145610	+	0.999894i	$0.495365\pi$
$434$	8.39935	+	3.05711i	0.403182	+	0.146746i
$435$	2.17376	+	0.437864i	0.104224	+	0.0209940i
$436$	13.5282	+	11.3515i	0.647884	+	0.543639i
$437$	9.76663	−	55.3893i	0.467201	−	2.64963i
$438$	4.78660	−	2.61096i	0.228713	−	0.124756i
$439$	−0.853735	+	0.716369i	−0.0407466	+	0.0341904i	−0.662934	−	0.748678i	$-0.730689\pi$
$439$	−0.853735	+	0.716369i	−0.0407466	+	0.0341904i	0.622187	+	0.782869i	$0.286244\pi$
$440$	−2.11809	−	3.66864i	−0.100976	−	0.174896i
$441$	0.153438	+	0.298270i	0.00730656	+	0.0142033i
$442$	3.62908	−	6.28576i	0.172618	−	0.298983i
$443$	1.06252	+	6.02583i	0.0504817	+	0.286296i	0.999589	−	0.0286559i	$-0.00912271\pi$
$443$	1.06252	+	6.02583i	0.0504817	+	0.286296i	−0.949108	+	0.314952i	$0.898012\pi$
$444$	−9.91982	−	12.4214i	−0.470774	−	0.589491i
$445$	11.7635	−	4.28156i	0.557643	−	0.202966i
$446$	−3.58600	+	1.30520i	−0.169802	+	0.0618029i
$447$	10.6295	+	13.3100i	0.502759	+	0.629543i
$448$	0.463084	+	2.62628i	0.0218787	+	0.124080i
$449$	−18.1443	+	31.4269i	−0.856283	+	1.48313i	0.0191664	+	0.999816i	$0.493899\pi$
$449$	−18.1443	+	31.4269i	−0.856283	+	1.48313i	−0.875450	+	0.483310i	$0.839435\pi$
$450$	11.8551	+	0.575158i	0.558855	+	0.0271132i
$451$	7.80870	+	13.5251i	0.367697	+	0.636870i
$452$	1.49865	−	1.25752i	0.0704906	−	0.0591486i
$453$	−6.10337	+	3.32922i	−0.286761	+	0.156420i
$454$	−3.53875	+	20.0693i	−0.166082	+	0.941897i
$455$	−8.18096	−	6.86464i	−0.383529	−	0.321819i
$456$	−10.9230	−	2.20024i	−0.511516	−	0.103036i
$457$	−19.4942	−	7.09531i	−0.911900	−	0.331905i	−0.156889	−	0.987616i	$-0.550146\pi$
$457$	−19.4942	−	7.09531i	−0.911900	−	0.331905i	−0.755011	+	0.655712i	$0.772369\pi$
$458$	−1.50806			−0.0704670
$459$	−8.65963	+	4.19251i	−0.404197	+	0.195689i
$460$	−8.93170			−0.416443
$461$	−38.8668	−	14.1464i	−1.81021	−	0.658861i	−0.997045	−	0.0768243i	$-0.975522\pi$
$461$	−38.8668	−	14.1464i	−1.81021	−	0.658861i	−0.813162	−	0.582037i	$-0.802256\pi$
$462$	−12.6636	+	14.3697i	−0.589165	+	0.668540i
$463$	−18.1032	−	15.1904i	−0.841328	−	0.705958i	0.116534	−	0.993187i	$-0.462822\pi$
$463$	−18.1032	−	15.1904i	−0.841328	−	0.705958i	−0.957862	+	0.287229i	$0.907266\pi$
$464$	0.217610	−	1.23413i	0.0101023	−	0.0572931i
$465$	5.06279	+	3.08898i	0.234781	+	0.143248i
$466$	−15.4492	+	12.9635i	−0.715672	+	0.600520i
$467$	10.5877	+	18.3384i	0.489939	+	0.848599i	0.999933	−	0.0115789i	$-0.00368576\pi$
$467$	10.5877	+	18.3384i	0.489939	+	0.848599i	−0.509994	+	0.860178i	$0.670352\pi$
$468$	11.2326	−	3.48190i	0.519228	−	0.160951i
$469$	10.8874	−	18.8576i	0.502735	−	0.870763i
$470$	0.490500	+	2.78176i	0.0226251	+	0.128313i
$471$	−24.5385	+	3.71601i	−1.13067	+	0.171225i
$472$	−3.32153	+	1.20894i	−0.152886	+	0.0556458i
$473$	12.0403	−	4.38231i	0.553613	−	0.201499i
$474$	1.63664	−	4.17863i	0.0751735	−	0.191931i
$475$	−4.41960	−	25.0648i	−0.202785	−	1.15005i
$476$	2.46891	−	4.27627i	0.113162	−	0.196003i
$477$	0.553208	−	0.420249i	0.0253296	−	0.0192419i
$478$	6.32170	+	10.9495i	0.289148	+	0.500819i
$479$	10.2101	−	8.56728i	0.466511	−	0.391449i	−0.379009	−	0.925393i	$-0.623735\pi$
$479$	10.2101	−	8.56728i	0.466511	−	0.391449i	0.845520	+	0.533944i	$0.179291\pi$
$480$	−0.0428852	+	1.76893i	−0.00195743	+	0.0807403i
$481$	6.24724	−	35.4299i	0.284850	−	1.61546i
$482$	−21.3263	−	17.8949i	−0.971385	−	0.815089i
$483$	12.8883	+	38.2719i	0.586437	+	1.74143i
$484$	−5.82110	−	2.11871i	−0.264596	−	0.0963049i
$485$	8.89905			0.404085
$486$	−14.9118	−	4.54303i	−0.676412	−	0.206076i
$487$	−18.3872			−0.833202			−0.416601	−	0.909090i	$-0.636779\pi$
$487$	−18.3872			−0.833202			−0.416601	+	0.909090i	$0.636779\pi$
$488$	−0.496899	−	0.180856i	−0.0224935	−	0.00818698i
$489$	−7.89976	−	23.4585i	−0.357240	−	1.06083i
$490$	−0.0874990	−	0.0734203i	−0.00395280	−	0.00331679i
$491$	3.35081	−	19.0034i	0.151220	−	0.857610i	−0.810941	−	0.585128i	$-0.801044\pi$
$491$	3.35081	−	19.0034i	0.151220	−	0.857610i	0.962161	−	0.272482i	$-0.0878446\pi$
$492$	0.158103	−	6.52145i	0.00712785	−	0.294010i
$493$	−1.77749	+	1.49150i	−0.0800543	+	0.0671736i
$494$	−12.6087	−	21.8389i	−0.567292	−	0.982579i
$495$	−10.1197	+	7.68754i	−0.454848	+	0.345529i
$496$	1.67587	−	2.90269i	0.0752487	−	0.130335i
$497$	3.73326	+	21.1724i	0.167459	+	0.949710i
$498$	5.07845	−	12.9662i	0.227571	−	0.581028i
$499$	15.3641	−	5.59206i	0.687790	−	0.250335i	0.0256013	−	0.999672i	$-0.491850\pi$
$499$	15.3641	−	5.59206i	0.687790	−	0.250335i	0.662189	+	0.749337i	$0.269628\pi$
$500$	−8.59794	+	3.12940i	−0.384512	+	0.139951i
$501$	−16.3632	+	2.47797i	−0.731052	+	0.110708i
$502$	−0.116914	−	0.663053i	−0.00521814	−	0.0295935i
$503$	19.9756	−	34.5988i	0.890670	−	1.54269i	0.0515962	−	0.998668i	$-0.483569\pi$
$503$	19.9756	−	34.5988i	0.890670	−	1.54269i	0.839074	−	0.544018i	$-0.183098\pi$
$504$	7.64167	−	2.36877i	0.340387	−	0.105514i
$505$	−2.76135	−	4.78280i	−0.122878	−	0.212832i
$506$	−27.7720	+	23.3035i	−1.23462	+	1.03597i
$507$	3.49850	+	2.13455i	0.155374	+	0.0947987i
$508$	0.968950	−	5.49519i	0.0429902	−	0.243810i
$509$	24.7041	+	20.7292i	1.09499	+	0.918805i	0.997078	−	0.0763905i	$-0.0243396\pi$
$509$	24.7041	+	20.7292i	1.09499	+	0.918805i	0.0979108	+	0.995195i	$0.468784\pi$
$510$	2.16617	−	2.45801i	0.0959197	−	0.108843i
$511$	7.88865	+	2.87123i	0.348973	+	0.127016i
$512$	1.00000			0.0441942
$513$	−2.42857	+	33.3389i	−0.107224	+	1.47195i
$514$	30.6381			1.35139
$515$	10.3541	+	3.76858i	0.456256	+	0.166064i
$516$	−5.24660	−	1.05683i	−0.230969	−	0.0465244i
$517$	8.78298	+	7.36980i	0.386275	+	0.324123i
$518$	4.25007	−	24.1033i	0.186737	−	1.05904i
$519$	−15.1790	+	8.27969i	−0.666282	+	0.363438i
$520$	−3.06771	+	2.57411i	−0.134528	+	0.112882i
$521$	−18.6915	−	32.3746i	−0.818890	−	1.41836i	−0.906501	−	0.422204i	$-0.861257\pi$
$521$	−18.6915	−	32.3746i	−0.818890	−	1.41836i	0.0876112	−	0.996155i	$-0.472077\pi$
$522$	−3.75509	−	0.182181i	−0.164356	−	0.00797383i
$523$	−14.5920	+	25.2740i	−0.638062	+	1.10516i	0.347795	+	0.937570i	$0.386930\pi$
$523$	−14.5920	+	25.2740i	−0.638062	+	1.10516i	−0.985858	+	0.167586i	$0.946403\pi$
$524$	0.268690	+	1.52382i	0.0117378	+	0.0665682i
$525$	11.4039	+	14.2797i	0.497706	+	0.623215i
$526$	5.58053	−	2.03115i	0.243323	−	0.0885622i
$527$	−5.83177	+	2.12259i	−0.254036	+	0.0924615i
$528$	4.48193	+	5.61216i	0.195051	+	0.244238i
$529$	9.27951	+	52.6267i	0.403457	+	2.28812i
$530$	−0.118288	+	0.204881i	−0.00513812	+	0.00889948i
$531$	4.85080	+	9.42954i	0.210507	+	0.409207i
$532$	−8.57784	−	14.8573i	−0.371897	−	0.644144i
$533$	11.3096	−	9.48989i	0.489874	−	0.411053i
$534$	−18.6326	+	10.1636i	−0.806311	+	0.439820i
$535$	2.63456	−	14.9413i	0.113902	−	0.645969i
$536$	−6.25489	−	5.24848i	−0.270170	−	0.226700i
$537$	38.2179	+	7.69828i	1.64922	+	0.332206i
$538$	−14.4359	−	5.25424i	−0.622377	−	0.226527i
$539$	−0.463627			−0.0199698
$540$	5.28086	−	0.539544i	0.227252	−	0.0232183i
$541$	12.6132			0.542283			0.271142	−	0.962539i	$-0.412599\pi$
$541$	12.6132			0.542283			0.271142	+	0.962539i	$0.412599\pi$
$542$	13.7138	+	4.99141i	0.589057	+	0.214399i
$543$	0.568185	−	0.644733i	0.0243831	−	0.0276682i
$544$	−1.41840	−	1.19018i	−0.0608134	−	0.0510285i
$545$	−3.13281	+	17.7671i	−0.134195	+	0.761057i
$546$	15.4566	+	9.43060i	0.661482	+	0.403592i
$547$	22.3688	−	18.7696i	0.956419	−	0.802531i	−0.0239476	−	0.999713i	$-0.507623\pi$
$547$	22.3688	−	18.7696i	0.956419	−	0.802531i	0.980367	+	0.197182i	$0.0631790\pi$
$548$	10.0297	+	17.3719i	0.428446	+	0.742091i
$549$	−0.350851	+	1.54708i	−0.0149740	+	0.0660278i
$550$	−8.20279	+	14.2077i	−0.349768	+	0.605816i
$551$	1.39990	+	7.93924i	0.0596379	+	0.338223i
$552$	14.9725	−	2.26737i	0.637270	−	0.0965057i
$553$	6.49292	−	2.36323i	0.276107	−	0.100495i
$554$	−5.34571	+	1.94568i	−0.227117	+	0.0826639i
$555$	5.92248	−	15.1211i	0.251395	−	0.641855i
$556$	0.677277	+	3.84103i	0.0287229	+	0.162896i
$557$	−21.6137	+	37.4361i	−0.915804	+	1.58622i	−0.110083	+	0.993922i	$0.535112\pi$
$557$	−21.6137	+	37.4361i	−0.915804	+	1.58622i	−0.805720	+	0.592296i	$0.798222\pi$
$558$	−9.27105	−	3.89292i	−0.392475	−	0.164800i
$559$	−6.05629	−	10.4898i	−0.256154	−	0.443671i
$560$	−2.08700	+	1.75120i	−0.0881917	+	0.0740016i
$561$	0.322308	−	13.2946i	0.0136079	−	0.561298i
$562$	2.37136	−	13.4487i	0.100030	−	0.567298i
$563$	−5.18375	−	4.34968i	−0.218469	−	0.183317i	0.526984	−	0.849875i	$-0.323323\pi$
$563$	−5.18375	−	4.34968i	−0.218469	−	0.183317i	−0.745454	+	0.666558i	$0.767767\pi$
$564$	−1.52841	−	4.53863i	−0.0643576	−	0.191111i
$565$	1.87806	+	0.683558i	0.0790106	+	0.0287575i
$566$	25.9361			1.09018
$567$	−9.93211	−	21.8497i	−0.417109	−	0.917601i
$568$	8.06172			0.338262
$569$	1.78951	+	0.651329i	0.0750203	+	0.0273051i	0.379258	−	0.925291i	$-0.376179\pi$
$569$	1.78951	+	0.651329i	0.0750203	+	0.0273051i	−0.304237	+	0.952596i	$0.598402\pi$
$570$	−3.63282	−	10.7877i	−0.152162	−	0.451848i
$571$	−8.59231	−	7.20980i	−0.359577	−	0.301721i	0.445045	−	0.895508i	$-0.353188\pi$
$571$	−8.59231	−	7.20980i	−0.359577	−	0.301721i	−0.804622	+	0.593787i	$0.797632\pi$
$572$	−2.82260	+	16.0078i	−0.118019	+	0.669319i
$573$	0.301757	−	12.4469i	0.0126061	−	0.519976i
$574$	7.69406	−	6.45608i	0.321144	−	0.269472i
$575$	17.2950	+	29.9558i	0.721252	+	1.24924i
$576$	−0.377165	−	2.97620i	−0.0157152	−	0.124008i
$577$	−19.6634	+	34.0581i	−0.818600	+	1.41786i	0.0881143	+	0.996110i	$0.471916\pi$
$577$	−19.6634	+	34.0581i	−0.818600	+	1.41786i	−0.906714	+	0.421746i	$0.861417\pi$
$578$	−2.35669	−	13.3654i	−0.0980252	−	0.555929i
$579$	8.50849	−	21.7236i	0.353601	−	0.902803i
$580$	1.20302	−	0.437864i	0.0499527	−	0.0181813i
$581$	20.1473	−	7.33303i	0.835852	−	0.304225i
$582$	−14.9177	+	2.25908i	−0.618360	+	0.0936420i
$583$	0.166748	+	0.945677i	0.00690601	+	0.0391659i
$584$	1.57397	−	2.72620i	0.0651314	−	0.112811i
$585$	8.81810	+	8.15924i	0.364583	+	0.337343i
$586$	−9.94574	−	17.2265i	−0.410855	−	0.711621i
$587$	5.98030	−	5.01807i	0.246834	−	0.207118i	−0.510974	−	0.859596i	$-0.670715\pi$
$587$	5.98030	−	5.01807i	0.246834	−	0.207118i	0.757807	+	0.652478i	$0.226271\pi$
$588$	0.165315	+	0.100864i	0.00681749	+	0.00415958i
$589$	−3.74419	+	21.2344i	−0.154277	+	0.874947i
$590$	−2.76620	−	2.32112i	−0.113883	−	0.0955589i
$591$	5.80235	−	6.58407i	0.238677	−	0.270832i
$592$	−8.62426	−	3.13897i	−0.354455	−	0.129011i
$593$	−12.2602			−0.503465			−0.251733	−	0.967797i	$-0.581000\pi$
$593$	−12.2602			−0.503465			−0.251733	+	0.967797i	$0.581000\pi$
$594$	15.0125	−	15.4558i	0.615969	−	0.634160i
$595$	5.04444			0.206802
$596$	9.24128	+	3.36355i	0.378537	+	0.137776i
$597$	30.4694	+	6.13750i	1.24703	+	0.251191i
$598$	26.2538	+	22.0296i	1.07360	+	0.900856i
$599$	−3.40179	+	19.2925i	−0.138993	+	0.788271i	0.833002	+	0.553270i	$0.186620\pi$
$599$	−3.40179	+	19.2925i	−0.138993	+	0.788271i	−0.971995	+	0.235001i	$0.924491\pi$
$600$	6.01582	−	3.28146i	0.245595	−	0.133965i
$601$	−3.14380	+	2.63796i	−0.128238	+	0.107605i	−0.704651	−	0.709554i	$-0.748896\pi$
$601$	−3.14380	+	2.63796i	−0.128238	+	0.107605i	0.576413	+	0.817159i	$0.304452\pi$
$602$	−4.12016	−	7.13633i	−0.167925	−	0.290855i
$603$	−13.2614	+	20.5953i	−0.540045	+	0.838707i
$604$	−2.00696	+	3.47616i	−0.0816622	+	0.141443i
$605$	−1.09892	−	6.23230i	−0.0446776	−	0.253379i
$606$	5.84307	+	7.31655i	0.237359	+	0.297215i
$607$	−15.2753	+	5.55976i	−0.620006	+	0.225664i	−0.632876	−	0.774253i	$-0.718126\pi$
$607$	−15.2753	+	5.55976i	−0.620006	+	0.225664i	0.0128694	+	0.999917i	$0.495903\pi$
$608$	−6.04511	+	2.20024i	−0.245161	+	0.0892315i
$609$	−3.61216	−	4.52306i	−0.146372	−	0.183284i
$610$	−0.0938059	−	0.531999i	−0.00379809	−	0.0215400i
$611$	5.41930	−	9.38650i	0.219241	−	0.379737i
$612$	−3.00724	+	4.67033i	−0.121560	+	0.188787i
$613$	−8.52562	−	14.7668i	−0.344347	−	0.596426i	0.640888	−	0.767634i	$-0.278566\pi$
$613$	−8.52562	−	14.7668i	−0.344347	−	0.596426i	−0.985235	+	0.171208i	$0.945233\pi$
$614$	−7.28865	+	6.11590i	−0.294146	+	0.246818i
$615$	5.85045	−	3.19126i	0.235913	−	0.128684i
$616$	−1.92025	+	10.8903i	−0.0773690	+	0.438781i
$617$	−21.2848	−	17.8601i	−0.856895	−	0.719020i	0.104402	−	0.994535i	$-0.466707\pi$
$617$	−21.2848	−	17.8601i	−0.856895	−	0.719020i	−0.961297	+	0.275515i	$0.911152\pi$
$618$	−18.3136	−	3.68893i	−0.736679	−	0.148391i
$619$	−7.09199	−	2.58127i	−0.285051	−	0.103750i	0.195538	−	0.980696i	$-0.437355\pi$
$619$	−7.09199	−	2.58127i	−0.285051	−	0.103750i	−0.480589	+	0.876946i	$0.659577\pi$
$620$	3.42411			0.137516
$621$	−12.3952	−	43.7058i	−0.497404	−	1.75385i
$622$	−14.4638			−0.579947
$623$	−30.7078	−	11.1767i	−1.23028	−	0.447786i
$624$	4.48903	−	5.09382i	0.179705	−	0.203916i
$625$	7.99324	+	6.70713i	0.319730	+	0.268285i
$626$	−2.32518	+	13.1867i	−0.0929329	+	0.527048i
$627$	−39.4418	−	24.0648i	−1.57516	−	0.961056i
$628$	−10.9765	+	9.21039i	−0.438011	+	0.367534i
$629$	8.49671	+	14.7167i	0.338786	+	0.586794i
$630$	5.99905	+	5.55082i	0.239008	+	0.221150i
$631$	12.3054	−	21.3136i	0.489872	−	0.848483i	−0.510060	−	0.860139i	$-0.670377\pi$
$631$	12.3054	−	21.3136i	0.489872	−	0.848483i	0.999932	+	0.0116559i	$0.00371028\pi$
$632$	−0.449919	−	2.55162i	−0.0178968	−	0.101498i
$633$	−8.72286	+	1.32096i	−0.346703	+	0.0525033i
$634$	−23.6465	+	8.60661i	−0.939122	+	0.341812i
$635$	5.35667	−	1.94967i	0.212573	−	0.0773702i
$636$	0.146280	−	0.373477i	0.00580036	−	0.0148093i
$637$	0.0761068	+	0.431623i	0.00301546	+	0.0171015i
$638$	2.59823	−	4.50026i	0.102865	−	0.178167i
$639$	−3.04060	−	23.9933i	−0.120284	−	0.949159i
$640$	0.510796	+	0.884725i	0.0201910	+	0.0349718i
$641$	23.1248	−	19.4040i	0.913373	−	0.766411i	−0.0593849	−	0.998235i	$-0.518914\pi$
$641$	23.1248	−	19.4040i	0.913373	−	0.766411i	0.972758	+	0.231824i	$0.0744695\pi$
$642$	−0.623432	+	25.7153i	−0.0246049	+	1.01490i
$643$	−2.06856	+	11.7314i	−0.0815762	+	0.462641i	0.916467	+	0.400111i	$0.131028\pi$
$643$	−2.06856	+	11.7314i	−0.0815762	+	0.462641i	−0.998043	+	0.0625308i	$0.980083\pi$
$644$	17.8608	+	14.9870i	0.703813	+	0.590569i
$645$	−1.74494	−	5.18163i	−0.0687069	−	0.204026i
$646$	11.1931	+	4.07394i	0.440385	+	0.160287i
$647$	20.4896			0.805528			0.402764	−	0.915304i	$-0.368049\pi$
$647$	20.4896			0.805528			0.402764	+	0.915304i	$0.368049\pi$
$648$	−8.71549	+	2.24503i	−0.342377	+	0.0881933i
$649$	−14.6571			−0.575343
$650$	14.5735	+	5.30431i	0.571618	+	0.208052i
$651$	−4.94093	−	14.6722i	−0.193650	−	0.575047i
$652$	−10.9476	−	9.18614i	−0.428742	−	0.359757i
$653$	−8.53662	+	48.4136i	−0.334064	+	1.89457i	0.102222	+	0.994762i	$0.467405\pi$
$653$	−8.53662	+	48.4136i	−0.334064	+	1.89457i	−0.436286	+	0.899808i	$0.643706\pi$
$654$	0.741338	−	30.5787i	0.0289886	−	1.19572i
$655$	−1.21091	+	1.01608i	−0.0473142	+	0.0397014i
$656$	−1.88313	−	3.26169i	−0.0735241	−	0.127347i
$657$	−8.70735	−	3.65622i	−0.339706	−	0.142643i
$658$	3.68681	−	6.38574i	0.143727	−	0.248942i
$659$	4.93483	+	27.9868i	0.192234	+	1.09021i	0.916303	+	0.400485i	$0.131158\pi$
$659$	4.93483	+	27.9868i	0.192234	+	1.09021i	−0.724070	+	0.689727i	$0.757731\pi$
$660$	−2.67587	+	6.83195i	−0.104158	+	0.265933i
$661$	−40.5404	+	14.7555i	−1.57684	+	0.573923i	−0.974514	−	0.224328i	$-0.927981\pi$
$661$	−40.5404	+	14.7555i	−1.57684	+	0.573923i	−0.602326	+	0.798251i	$0.705759\pi$
$662$	19.8606	−	7.22868i	0.771905	−	0.280951i
$663$	−12.4298	+	1.88232i	−0.482733	+	0.0731032i
$664$	−1.39609	−	7.91759i	−0.0541786	−	0.307262i
$665$	8.76306	−	15.1781i	0.339817	−	0.588580i
$666$	−6.08943	+	26.8514i	−0.235961	+	1.04047i
$667$	−5.47817	−	9.48848i	−0.212116	−	0.367395i
$668$	−7.31955	+	6.14183i	−0.283202	+	0.237634i
$669$	5.64244	+	3.44264i	0.218149	+	0.133100i
$670$	1.44848	−	8.21476i	0.0559598	−	0.317364i
$671$	−1.67971	−	1.40944i	−0.0648443	−	0.0544108i
$672$	3.05394	−	3.46538i	0.117808	−	0.133680i
$673$	33.9219	+	12.3466i	1.30759	+	0.475926i	0.899463	−	0.436997i	$-0.143958\pi$
$673$	33.9219	+	12.3466i	1.30759	+	0.475926i	0.408132	+	0.912923i	$0.366180\pi$
$674$	4.77192			0.183808
$675$	−12.0352	−	16.6666i	−0.463236	−	0.641498i
$676$	2.36613			0.0910052
$677$	−40.5216	−	14.7487i	−1.55737	−	0.566837i	−0.587239	−	0.809413i	$-0.699785\pi$
$677$	−40.5216	−	14.7487i	−1.55737	−	0.566837i	−0.970132	+	0.242576i	$0.922008\pi$
$678$	−3.32177	−	0.669111i	−0.127572	−	0.0256970i
$679$	−17.7955	−	14.9322i	−0.682928	−	0.573045i
$680$	0.328468	−	1.86283i	0.0125962	−	0.0714364i
$681$	30.9871	−	16.9026i	1.18743	−	0.647708i
$682$	10.6468	−	8.93377i	0.407689	−	0.342092i
$683$	−0.0895535	−	0.155111i	−0.00342667	−	0.00593517i	0.864307	−	0.502965i	$-0.167757\pi$
$683$	−0.0895535	−	0.155111i	−0.00342667	−	0.00593517i	−0.867734	+	0.497029i	$0.834424\pi$
$684$	8.82834	+	17.1616i	0.337560	+	0.656189i
$685$	−10.2462	+	17.7470i	−0.391489	+	0.678078i
$686$	−3.18982	−	18.0903i	−0.121788	−	0.690692i
$687$	1.63000	+	2.04104i	0.0621882	+	0.0778706i
$688$	−2.90362	+	1.05683i	−0.110700	+	0.0402913i
$689$	0.853026	−	0.310476i	0.0324977	−	0.0118282i
$690$	9.65388	+	12.0884i	0.367517	+	0.460196i
$691$	−5.97830	−	33.9046i	−0.227425	−	1.28979i	−0.857994	−	0.513660i	$-0.828289\pi$
$691$	−5.97830	−	33.9046i	−0.227425	−	1.28979i	0.630568	−	0.776134i	$-0.282822\pi$
$692$	−4.99127	+	8.64514i	−0.189740	+	0.328639i
$693$	33.1358	+	1.60761i	1.25873	+	0.0610680i
$694$	−7.83372	−	13.5684i	−0.297364	−	0.515050i
$695$	−3.05230	+	2.56119i	−0.115780	+	0.0971514i
$696$	−1.90550	+	1.03940i	−0.0722280	+	0.0393983i
$697$	−1.21095	+	6.86764i	−0.0458680	+	0.260130i
$698$	15.1767	+	12.7348i	0.574448	+	0.482019i
$699$	34.2434	+	6.89771i	1.29521	+	0.260895i
$700$	9.91449	+	3.60858i	0.374732	+	0.136391i
$701$	−17.3215			−0.654224			−0.327112	−	0.944985i	$-0.606076\pi$
$701$	−17.3215			−0.654224			−0.327112	+	0.944985i	$0.606076\pi$
$702$	−16.8533	−	11.4390i	−0.636087	−	0.431739i
$703$	59.0410			2.22677
$704$	3.89657	+	1.41824i	0.146858	+	0.0534518i
$705$	3.23474	−	3.67054i	0.121827	−	0.138240i
$706$	−12.1013	−	10.1542i	−0.455440	−	0.382160i
$707$	−2.50342	+	14.1976i	−0.0941508	+	0.533956i
$708$	5.22629	+	3.18874i	0.196416	+	0.119840i
$709$	−28.0038	+	23.4980i	−1.05171	+	0.882485i	−0.993272	−	0.115806i	$-0.963055\pi$
$709$	−28.0038	+	23.4980i	−1.05171	+	0.882485i	−0.0584333	+	0.998291i	$0.518611\pi$
$710$	4.11790	+	7.13241i	0.154542	+	0.267674i
$711$	−7.42442	+	2.30143i	−0.278438	+	0.0863103i
$712$	−6.12693	+	10.6122i	−0.229616	+	0.397707i
$713$	−5.08858	−	28.8588i	−0.190569	−	1.08077i
$714$	−8.45613	+	1.28056i	−0.316463	+	0.0479239i
$715$	−15.6043	+	5.67948i	−0.583566	+	0.212401i
$716$	21.1509	−	7.69828i	0.790445	−	0.287698i
$717$	7.98645	−	20.3908i	0.298259	−	0.761507i
$718$	0.845577	+	4.79551i	0.0315567	+	0.178967i
$719$	22.8804	−	39.6301i	0.853296	−	1.47795i	−0.0249200	−	0.999689i	$-0.507933\pi$
$719$	22.8804	−	39.6301i	0.853296	−	1.47795i	0.878216	−	0.478263i	$-0.158734\pi$
$720$	2.44046	−	1.85392i	0.0909506	−	0.0690914i
$721$	−14.3816	−	24.9097i	−0.535601	−	0.927687i
$722$	17.1474	−	14.3884i	0.638160	−	0.535480i
$723$	−1.16867	+	48.2052i	−0.0434632	+	1.79277i
$724$	0.0861567	−	0.488619i	0.00320199	−	0.0181594i
$725$	−3.79803	−	3.18692i	−0.141055	−	0.118359i
$726$	3.42427	+	10.1684i	0.127087	+	0.377386i
$727$	−8.24873	−	3.00229i	−0.305928	−	0.111349i	0.184494	−	0.982834i	$-0.440935\pi$
$727$	−8.24873	−	3.00229i	−0.305928	−	0.111349i	−0.490423	+	0.871485i	$0.663158\pi$
$728$	10.4538			0.387442
$729$	9.96884	+	25.0923i	0.369216	+	0.929343i
$730$	3.21592			0.119026
$731$	5.37632	+	1.95682i	0.198850	+	0.0723756i
$732$	0.292301	+	0.867993i	0.0108038	+	0.0320819i
$733$	25.4717	+	21.3733i	0.940820	+	0.789441i	0.977728	−	0.209877i	$-0.0673065\pi$
$733$	25.4717	+	21.3733i	0.940820	+	0.789441i	−0.0369082	+	0.999319i	$0.511751\pi$
$734$	−1.47394	+	8.35914i	−0.0544042	+	0.308542i
$735$	−0.00479489	+	0.197780i	−0.000176862	+	0.00729522i
$736$	6.69746	−	5.61984i	0.246872	−	0.207150i
$737$	−16.9291	−	29.3220i	−0.623590	−	1.08009i
$738$	−8.99716	+	6.83477i	−0.331190	+	0.251591i
$739$	1.03598	−	1.79437i	0.0381091	−	0.0660069i	−0.846342	−	0.532640i	$-0.821200\pi$
$739$	1.03598	−	1.79437i	0.0381091	−	0.0660069i	0.884451	+	0.466633i	$0.154533\pi$
$740$	−1.62811	−	9.23347i	−0.0598505	−	0.339429i
$741$	−15.9291	+	40.6696i	−0.585169	+	1.49404i
$742$	0.580323	−	0.211220i	0.0213043	−	0.00775414i
$743$	−3.31599	+	1.20692i	−0.121652	+	0.0442777i	−0.402129	−	0.915583i	$-0.631730\pi$
$743$	−3.31599	+	1.20692i	−0.121652	+	0.0442777i	0.280477	+	0.959861i	$0.409507\pi$
$744$	−5.73993	+	0.869233i	−0.210436	+	0.0318676i
$745$	1.74459	+	9.89408i	0.0639169	+	0.362491i
$746$	−2.25715	+	3.90950i	−0.0826401	+	0.143137i
$747$	−23.0378	+	7.14126i	−0.842908	+	0.261285i
$748$	−3.83895	−	6.64925i	−0.140366	−	0.243121i
$749$	−30.3391	+	25.4576i	−1.10857	+	0.930199i
$750$	13.5285	+	8.25422i	0.493992	+	0.301401i
$751$	−6.65211	+	37.7260i	−0.242739	+	1.37664i	0.582946	+	0.812511i	$0.301900\pi$
$751$	−6.65211	+	37.7260i	−0.242739	+	1.37664i	−0.825685	+	0.564131i	$0.809211\pi$
$752$	−2.11809	−	1.77729i	−0.0772389	−	0.0648111i
$753$	−0.771023	+	0.874899i	−0.0280976	+	0.0318831i
$754$	−4.61613	−	1.68013i	−0.168109	−	0.0611868i
$755$	−4.10060			−0.149236
$756$	−11.4655	−	7.78210i	−0.416996	−	0.283032i
$757$	12.3900			0.450322			0.225161	−	0.974322i	$-0.427709\pi$
$757$	12.3900			0.450322			0.225161	+	0.974322i	$0.427709\pi$
$758$	−10.4323	−	3.79705i	−0.378918	−	0.137915i
$759$	61.5570	+	12.3995i	2.23438	+	0.450074i
$760$	−5.03442	−	4.22438i	−0.182618	−	0.153234i
$761$	−1.41032	+	7.99834i	−0.0511241	+	0.289939i	−0.999641	−	0.0267867i	$-0.991473\pi$
$761$	−1.41032	+	7.99834i	−0.0511241	+	0.289939i	0.948517	+	0.316726i	$0.102584\pi$
$762$	−8.48460	+	4.62811i	−0.307365	+	0.167659i
$763$	36.0770	−	30.2722i	1.30607	−

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.552775 + 1.64147i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.177398 + 1.00607i) q^{5} +(0.0419788 - 1.73154i) q^{6} +(2.04289 - 1.71418i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.38888 + 1.81473i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.552775 + 1.64147i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.177398 + 1.00607i) q^{5} +(0.0419788 - 1.73154i) q^{6} +(2.04289 - 1.71418i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.38888 + 1.81473i) q^{9} +(0.510796 - 0.884725i) q^{10} +(-0.720058 - 4.08365i) q^{11} +(-0.631669 + 1.61276i) q^{12} +(-3.68356 + 1.34071i) q^{13} +(-2.50597 + 0.912098i) q^{14} +(-1.74950 + 0.264938i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.925795 - 1.60352i) q^{17} +(2.86549 - 0.888246i) q^{18} +(-3.21653 - 5.57120i) q^{19} +(-0.782585 + 0.656667i) q^{20} +(3.94305 + 2.40579i) q^{21} +(-0.720058 + 4.08365i) q^{22} +(6.69746 + 5.61984i) q^{23} +(1.14517 - 1.29945i) q^{24} +(3.71775 + 1.35315i) q^{25} +3.91997 q^{26} +(-4.29935 - 2.91815i) q^{27} +2.66680 q^{28} +(-1.17759 - 0.428609i) q^{29} +(1.73461 + 0.349405i) q^{30} +(-2.56758 - 2.15445i) q^{31} +(0.173648 - 0.984808i) q^{32} +(6.30518 - 3.43930i) q^{33} +(-1.41840 + 1.19018i) q^{34} +(1.36219 + 2.35938i) q^{35} +(-2.99648 - 0.145376i) q^{36} +(-4.58887 + 7.94816i) q^{37} +(1.11709 + 6.33533i) q^{38} +(-4.23692 - 5.30537i) q^{39} +(0.959983 - 0.349405i) q^{40} +(-3.53914 + 1.28814i) q^{41} +(-2.88242 - 3.60930i) q^{42} +(0.536567 + 3.04303i) q^{43} +(2.07332 - 3.59110i) q^{44} +(-1.40197 - 2.72531i) q^{45} +(-4.37146 - 7.57159i) q^{46} +(-2.11809 + 1.77729i) q^{47} +(-1.52055 + 0.829416i) q^{48} +(0.0194152 - 0.110109i) q^{49} +(-3.03074 - 2.54309i) q^{50} +(3.14390 + 0.633281i) q^{51} +(-3.68356 - 1.34071i) q^{52} -0.231576 q^{53} +(3.04200 + 4.21263i) q^{54} +4.23618 q^{55} +(-2.50597 - 0.912098i) q^{56} +(7.36696 - 8.35948i) q^{57} +(0.959983 + 0.805521i) q^{58} +(0.613793 - 3.48099i) q^{59} +(-1.51050 - 0.921605i) q^{60} +(0.405075 - 0.339899i) q^{61} +(1.67587 + 2.90269i) q^{62} +(-1.76942 + 7.80227i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.695393 - 3.94377i) q^{65} +(-7.10124 + 1.07538i) q^{66} +(7.67276 - 2.79266i) q^{67} +(1.73993 - 0.633281i) q^{68} +(-5.52263 + 14.1002i) q^{69} +(-0.473084 - 2.68299i) q^{70} +(-4.03086 + 6.98165i) q^{71} +(2.76604 + 1.16146i) q^{72} +(1.57397 + 2.72620i) q^{73} +(7.03056 - 5.89934i) q^{74} +(-0.166083 + 6.85058i) q^{75} +(1.11709 - 6.33533i) q^{76} +(-8.47113 - 7.10812i) q^{77} +(2.16686 + 6.43453i) q^{78} +(2.43473 + 0.886167i) q^{79} -1.02159 q^{80} +(2.41349 - 8.67036i) q^{81} +3.76627 q^{82} +(7.55488 + 2.74975i) q^{83} +(1.47414 + 4.37748i) q^{84} +(1.44903 + 1.21588i) q^{85} +(0.536567 - 3.04303i) q^{86} +(0.0526065 - 2.16991i) q^{87} +(-3.17652 + 2.66541i) q^{88} +(-6.12693 - 10.6122i) q^{89} +(0.385309 + 3.04046i) q^{90} +(-5.22688 + 9.05322i) q^{91} +(1.51819 + 8.61009i) q^{92} +(2.11719 - 5.40555i) q^{93} +(2.59823 - 0.945677i) q^{94} +(6.17564 - 2.24775i) q^{95} +(1.71253 - 0.259338i) q^{96} +(-1.51264 - 8.57862i) q^{97} +(-0.0559038 + 0.0968282i) q^{98} +(9.13087 + 8.44864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Introduction

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