LMFDB - Embedded newform 54.2.e.b.7.1

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			7.1
Root			$0.500000 - 1.96356i$ of defining polynomial
Character	$\chi$	$=$	54.7
Dual form			54.2.e.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.14517 + 1.29945i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.617090 + 3.49969i) q^{5} +(0.631669 - 1.61276i) q^{6} +(-0.244752 - 0.205371i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.377165 - 2.97620i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.14517 + 1.29945i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.617090 + 3.49969i) q^{5} +(0.631669 - 1.61276i) q^{6} +(-0.244752 - 0.205371i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.377165 - 2.97620i) q^{9} +(-1.77684 - 3.07758i) q^{10} +(0.773091 - 4.38442i) q^{11} +(-0.0419788 + 1.73154i) q^{12} +(4.39657 + 1.60022i) q^{13} +(0.300233 + 0.109276i) q^{14} +(-5.25437 - 3.20587i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.567354 - 0.982686i) q^{17} +(1.37234 + 2.66771i) q^{18} +(-0.928896 + 1.60890i) q^{19} +(2.72228 + 2.28426i) q^{20} +(0.547153 - 0.0828588i) q^{21} +(0.773091 + 4.38442i) q^{22} +(0.110473 - 0.0926974i) q^{23} +(-0.552775 - 1.64147i) q^{24} +(-7.16859 + 2.60915i) q^{25} -4.67874 q^{26} +(4.29935 + 2.91815i) q^{27} -0.319501 q^{28} +(4.09634 - 1.49095i) q^{29} +(6.03396 + 1.21543i) q^{30} +(0.514546 - 0.431755i) q^{31} +(0.173648 + 0.984808i) q^{32} +(4.81203 + 6.02551i) q^{33} +(0.869237 + 0.729376i) q^{34} +(0.567702 - 0.983289i) q^{35} +(-2.20199 - 2.03746i) q^{36} +(-3.79438 - 6.57207i) q^{37} +(0.322602 - 1.82957i) q^{38} +(-7.11425 + 3.88062i) q^{39} +(-3.33937 - 1.21543i) q^{40} +(-2.04599 - 0.744678i) q^{41} +(-0.485817 + 0.264999i) q^{42} +(-1.23250 + 6.98988i) q^{43} +(-2.22603 - 3.85559i) q^{44} +(10.1830 - 3.15654i) q^{45} +(-0.0721058 + 0.124891i) q^{46} +(-7.91059 - 6.63778i) q^{47} +(1.08086 + 1.35342i) q^{48} +(-1.19781 - 6.79312i) q^{49} +(5.84389 - 4.90360i) q^{50} +(1.92667 + 0.388093i) q^{51} +(4.39657 - 1.60022i) q^{52} +0.805554 q^{53} +(-5.03813 - 1.27170i) q^{54} +15.8212 q^{55} +(0.300233 - 0.109276i) q^{56} +(-1.02694 - 3.04952i) q^{57} +(-3.33937 + 2.80206i) q^{58} +(0.517966 + 2.93753i) q^{59} +(-6.08577 + 0.921605i) q^{60} +(-2.67705 - 2.24631i) q^{61} +(-0.335846 + 0.581702i) q^{62} +(-0.518913 + 0.805889i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.88720 + 16.3741i) q^{65} +(-6.58267 - 4.01631i) q^{66} +(-6.99437 - 2.54574i) q^{67} +(-1.06628 - 0.388093i) q^{68} +(-0.00605383 + 0.249708i) q^{69} +(-0.197161 + 1.11816i) q^{70} +(4.04928 + 7.01356i) q^{71} +(2.76604 + 1.16146i) q^{72} +(-7.30065 + 12.6451i) q^{73} +(5.81333 + 4.87797i) q^{74} +(4.81879 - 12.3032i) q^{75} +(0.322602 + 1.82957i) q^{76} +(-1.08965 + 0.914324i) q^{77} +(5.35796 - 6.07981i) q^{78} +(11.8279 - 4.30501i) q^{79} +3.55368 q^{80} +(-8.71549 + 2.24503i) q^{81} +2.17729 q^{82} +(5.08715 - 1.85157i) q^{83} +(0.365883 - 0.415177i) q^{84} +(3.08899 - 2.59197i) q^{85} +(-1.23250 - 6.98988i) q^{86} +(-2.75360 + 7.03040i) q^{87} +(3.41047 + 2.86173i) q^{88} +(-2.52624 + 4.37558i) q^{89} +(-8.48932 + 6.44898i) q^{90} +(-0.747430 - 1.29459i) q^{91} +(0.0250421 - 0.142021i) q^{92} +(-0.0281968 + 1.16306i) q^{93} +(9.70378 + 3.53189i) q^{94} +(-6.20385 - 2.25802i) q^{95} +(-1.47857 - 0.902126i) q^{96} +(3.24273 - 18.3904i) q^{97} +(3.44896 + 5.97377i) q^{98} +(-13.3405 - 0.647222i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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
$3$	−1.14517	+	1.29945i	−0.661165	+	0.750241i
$3$	−1.14517	+	1.29945i	−0.661165	+	0.750241i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.617090	+	3.49969i	0.275971	+	1.56511i	0.735860	+	0.677134i	$0.236778\pi$
$5$	0.617090	+	3.49969i	0.275971	+	1.56511i	−0.459889	+	0.887977i	$0.652111\pi$
$6$	0.631669	−	1.61276i	0.257878	−	0.658406i
$7$	−0.244752	−	0.205371i	−0.0925075	−	0.0776230i	0.595361	−	0.803458i	$-0.297009\pi$
$7$	−0.244752	−	0.205371i	−0.0925075	−	0.0776230i	−0.687869	+	0.725835i	$0.741453\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.377165	−	2.97620i	−0.125722	−	0.992066i
$10$	−1.77684	−	3.07758i	−0.561886	−	0.973216i
$11$	0.773091	−	4.38442i	0.233096	−	1.32195i	−0.613491	−	0.789702i	$-0.710235\pi$
$11$	0.773091	−	4.38442i	0.233096	−	1.32195i	0.846587	−	0.532250i	$-0.178653\pi$
$12$	−0.0419788	+	1.73154i	−0.0121182	+	0.499853i
$13$	4.39657	+	1.60022i	1.21939	+	0.443822i	0.869951	−	0.493137i	$-0.164150\pi$
$13$	4.39657	+	1.60022i	1.21939	+	0.443822i	0.349439	+	0.936959i	$0.386372\pi$
$14$	0.300233	+	0.109276i	0.0802405	+	0.0292052i
$15$	−5.25437	−	3.20587i	−1.35667	−	0.827751i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.567354	−	0.982686i	−0.137604	−	0.238336i	0.788985	−	0.614412i	$-0.210607\pi$
$17$	−0.567354	−	0.982686i	−0.137604	−	0.238336i	−0.926589	+	0.376075i	$0.877273\pi$
$18$	1.37234	+	2.66771i	0.323463	+	0.628786i
$19$	−0.928896	+	1.60890i	−0.213103	+	0.369106i	−0.952684	−	0.303962i	$-0.901690\pi$
$19$	−0.928896	+	1.60890i	−0.213103	+	0.369106i	0.739581	+	0.673068i	$0.235024\pi$
$20$	2.72228	+	2.28426i	0.608720	+	0.510777i
$21$	0.547153	−	0.0828588i	0.119399	−	0.0180813i
$22$	0.773091	+	4.38442i	0.164824	+	0.934761i
$23$	0.110473	−	0.0926974i	0.0230351	−	0.0193288i	−0.631197	−	0.775622i	$-0.717436\pi$
$23$	0.110473	−	0.0926974i	0.0230351	−	0.0193288i	0.654233	+	0.756293i	$0.272992\pi$
$24$	−0.552775	−	1.64147i	−0.112835	−	0.335065i
$25$	−7.16859	+	2.60915i	−1.43372	+	0.521831i
$26$	−4.67874			−0.917576
$27$	4.29935	+	2.91815i	0.827411	+	0.561598i
$28$	−0.319501			−0.0603800
$29$	4.09634	−	1.49095i	0.760672	−	0.276862i	0.0675824	−	0.997714i	$-0.478471\pi$
$29$	4.09634	−	1.49095i	0.760672	−	0.276862i	0.693089	+	0.720852i	$0.256249\pi$
$30$	6.03396	+	1.21543i	1.10165	+	0.221906i
$31$	0.514546	−	0.431755i	0.0924152	−	0.0775455i	−0.595410	−	0.803422i	$-0.703010\pi$
$31$	0.514546	−	0.431755i	0.0924152	−	0.0775455i	0.687825	+	0.725877i	$0.258566\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	4.81203	+	6.02551i	0.837667	+	1.04891i
$34$	0.869237	+	0.729376i	0.149073	+	0.125087i
$35$	0.567702	−	0.983289i	0.0959592	−	0.166206i
$36$	−2.20199	−	2.03746i	−0.366998	−	0.339577i
$37$	−3.79438	−	6.57207i	−0.623793	−	1.08044i	−0.988773	−	0.149426i	$-0.952258\pi$
$37$	−3.79438	−	6.57207i	−0.623793	−	1.08044i	0.364980	−	0.931015i	$-0.381076\pi$
$38$	0.322602	−	1.82957i	0.0523330	−	0.296795i
$39$	−7.11425	+	3.88062i	−1.13919	+	0.621397i
$40$	−3.33937	−	1.21543i	−0.528000	−	0.192176i
$41$	−2.04599	−	0.744678i	−0.319529	−	0.116299i	0.177276	−	0.984161i	$-0.443271\pi$
$41$	−2.04599	−	0.744678i	−0.319529	−	0.116299i	−0.496805	+	0.867862i	$0.665494\pi$
$42$	−0.485817	+	0.264999i	−0.0749631	+	0.0408903i
$43$	−1.23250	+	6.98988i	−0.187955	+	1.06595i	0.734144	+	0.678994i	$0.237584\pi$
$43$	−1.23250	+	6.98988i	−0.187955	+	1.06595i	−0.922099	+	0.386953i	$0.873528\pi$
$44$	−2.22603	−	3.85559i	−0.335586	−	0.581252i
$45$	10.1830	−	3.15654i	1.51800	−	0.470550i
$46$	−0.0721058	+	0.124891i	−0.0106314	+	0.0184142i
$47$	−7.91059	−	6.63778i	−1.15388	−	0.968219i	−0.154075	−	0.988059i	$-0.549240\pi$
$47$	−7.91059	−	6.63778i	−1.15388	−	0.968219i	−0.999803	+	0.0198400i	$0.993684\pi$
$48$	1.08086	+	1.35342i	0.156008	+	0.195350i
$49$	−1.19781	−	6.79312i	−0.171116	−	0.970446i
$50$	5.84389	−	4.90360i	0.826450	−	0.693474i
$51$	1.92667	+	0.388093i	0.269788	+	0.0543439i
$52$	4.39657	−	1.60022i	0.609695	−	0.221911i
$53$	0.805554			0.110651			0.0553257	−	0.998468i	$-0.482380\pi$
$53$	0.805554			0.110651			0.0553257	+	0.998468i	$0.482380\pi$
$54$	−5.03813	−	1.27170i	−0.685603	−	0.173056i
$55$	15.8212			2.13333
$56$	0.300233	−	0.109276i	0.0401203	−	0.0146026i
$57$	−1.02694	−	3.04952i	−0.136022	−	0.403919i
$58$	−3.33937	+	2.80206i	−0.438481	+	0.367929i
$59$	0.517966	+	2.93753i	0.0674334	+	0.382434i	0.999782	+	0.0208736i	$0.00664476\pi$
$59$	0.517966	+	2.93753i	0.0674334	+	0.382434i	−0.932349	+	0.361560i	$0.882244\pi$
$60$	−6.08577	+	0.921605i	−0.785670	+	0.118979i
$61$	−2.67705	−	2.24631i	−0.342761	−	0.287611i	0.455114	−	0.890433i	$-0.349598\pi$
$61$	−2.67705	−	2.24631i	−0.342761	−	0.287611i	−0.797876	+	0.602822i	$0.794043\pi$
$62$	−0.335846	+	0.581702i	−0.0426525	+	0.0738763i
$63$	−0.518913	+	0.805889i	−0.0653769	+	0.101532i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.88720	+	16.3741i	−0.358113	+	2.03096i
$66$	−6.58267	−	4.01631i	−0.810271	−	0.494374i
$67$	−6.99437	−	2.54574i	−0.854498	−	0.311012i	−0.122625	−	0.992453i	$-0.539131\pi$
$67$	−6.99437	−	2.54574i	−0.854498	−	0.311012i	−0.731873	+	0.681441i	$0.761353\pi$
$68$	−1.06628	−	0.388093i	−0.129305	−	0.0470632i
$69$	−0.00605383	+	0.249708i	−0.000728795	+	0.0300614i
$70$	−0.197161	+	1.11816i	−0.0235652	+	0.133645i
$71$	4.04928	+	7.01356i	0.480561	+	0.832356i	0.999751	−	0.0223028i	$-0.00709978\pi$
$71$	4.04928	+	7.01356i	0.480561	+	0.832356i	−0.519190	+	0.854659i	$0.673766\pi$
$72$	2.76604	+	1.16146i	0.325981	+	0.136880i
$73$	−7.30065	+	12.6451i	−0.854477	+	1.48000i	0.0226526	+	0.999743i	$0.492789\pi$
$73$	−7.30065	+	12.6451i	−0.854477	+	1.48000i	−0.877129	+	0.480254i	$0.840545\pi$
$74$	5.81333	+	4.87797i	0.675786	+	0.567052i
$75$	4.81879	−	12.3032i	0.556426	−	1.42065i
$76$	0.322602	+	1.82957i	0.0370050	+	0.209866i
$77$	−1.08965	+	0.914324i	−0.124177	+	0.104197i
$78$	5.35796	−	6.07981i	0.606669	−	0.688403i
$79$	11.8279	−	4.30501i	1.33074	−	0.484351i	0.423859	−	0.905728i	$-0.360675\pi$
$79$	11.8279	−	4.30501i	1.33074	−	0.484351i	0.906886	+	0.421377i	$0.138453\pi$
$80$	3.55368			0.397314
$81$	−8.71549	+	2.24503i	−0.968388	+	0.249448i
$82$	2.17729			0.240442
$83$	5.08715	−	1.85157i	0.558387	−	0.203236i	−0.0473820	−	0.998877i	$-0.515088\pi$
$83$	5.08715	−	1.85157i	0.558387	−	0.203236i	0.605769	+	0.795641i	$0.292866\pi$
$84$	0.365883	−	0.415177i	0.0399211	−	0.0452995i
$85$	3.08899	−	2.59197i	0.335048	−	0.281139i
$86$	−1.23250	−	6.98988i	−0.132904	−	0.753738i
$87$	−2.75360	+	7.03040i	−0.295216	+	0.753738i
$88$	3.41047	+	2.86173i	0.363558	+	0.305061i
$89$	−2.52624	+	4.37558i	−0.267781	+	0.463810i	−0.968288	−	0.249835i	$-0.919624\pi$
$89$	−2.52624	+	4.37558i	−0.267781	+	0.463810i	0.700508	+	0.713645i	$0.252957\pi$
$90$	−8.48932	+	6.44898i	−0.894853	+	0.679782i
$91$	−0.747430	−	1.29459i	−0.0783520	−	0.135710i
$92$	0.0250421	−	0.142021i	0.00261082	−	0.0148067i
$93$	−0.0281968	+	1.16306i	−0.00292387	+	0.120604i
$94$	9.70378	+	3.53189i	1.00087	+	0.364286i
$95$	−6.20385	−	2.25802i	−0.636502	−	0.231668i
$96$	−1.47857	−	0.902126i	−0.150906	−	0.0920728i
$97$	3.24273	−	18.3904i	0.329249	−	1.86726i	−0.148708	−	0.988881i	$-0.547511\pi$
$97$	3.24273	−	18.3904i	0.329249	−	1.86726i	0.477957	−	0.878383i	$-0.341377\pi$
$98$	3.44896	+	5.97377i	0.348398	+	0.603442i
$99$	−13.3405	−	0.647222i	−1.34077	−	0.0650483i
$100$	−3.81433	+	6.60661i	−0.381433	+	0.660661i
$101$	−1.85357	−	1.55533i	−0.184438	−	0.154761i	0.545894	−	0.837854i	$-0.316190\pi$
$101$	−1.85357	−	1.55533i	−0.184438	−	0.154761i	−0.730332	+	0.683093i	$0.760634\pi$
$102$	−1.94322	+	0.294273i	−0.192407	+	0.0291374i
$103$	0.346489	+	1.96504i	0.0341406	+	0.193621i	0.997108	−	0.0759967i	$-0.0242138\pi$
$103$	0.346489	+	1.96504i	0.0341406	+	0.193621i	−0.962967	+	0.269618i	$0.913103\pi$
$104$	−3.58412	+	3.00743i	−0.351452	+	0.294903i
$105$	0.627623	+	1.86374i	0.0612498	+	0.181882i
$106$	−0.756973	+	0.275516i	−0.0735238	+	0.0267605i
$107$	8.87072			0.857565			0.428783	−	0.903408i	$-0.358943\pi$
$107$	8.87072			0.857565			0.428783	+	0.903408i	$0.358943\pi$
$108$	5.16924	−	0.528140i	0.497411	−	0.0508203i
$109$	−1.97204			−0.188887			−0.0944434	−	0.995530i	$-0.530107\pi$
$109$	−1.97204			−0.188887			−0.0944434	+	0.995530i	$0.530107\pi$
$110$	−14.8671	+	5.41116i	−1.41752	+	0.515934i
$111$	12.8853	+	2.59551i	1.22302	+	0.246355i
$112$	−0.244752	+	0.205371i	−0.0231269	+	0.0194058i
$113$	−1.67200	−	9.48237i	−0.157288	−	0.892026i	−0.956664	−	0.291195i	$-0.905947\pi$
$113$	−1.67200	−	9.48237i	−0.157288	−	0.892026i	0.799375	−	0.600832i	$-0.205164\pi$
$114$	2.00801	+	2.51438i	0.188067	+	0.235493i
$115$	0.392584	+	0.329417i	0.0366087	+	0.0307183i
$116$	2.17962	−	3.77521i	0.202372	−	0.350519i
$117$	3.10434	−	13.6886i	0.286996	−	1.26551i
$118$	−1.49142	−	2.58322i	−0.137297	−	0.237805i
$119$	−0.0629545	+	0.357033i	−0.00577103	+	0.0327291i
$120$	5.40355	−	2.94748i	0.493274	−	0.269067i
$121$	−8.28884	−	3.01689i	−0.753530	−	0.274263i
$122$	3.28389	+	1.19524i	0.297309	+	0.108212i
$123$	3.31068	−	1.80588i	0.298514	−	0.162831i
$124$	0.116638	−	0.661487i	0.0104744	−	0.0594033i
$125$	−4.67070	−	8.08988i	−0.417760	−	0.723581i
$126$	0.211989	−	0.934766i	0.0188855	−	0.0832756i
$127$	−0.0796049	+	0.137880i	−0.00706379	+	0.0122348i	−0.869536	−	0.493870i	$-0.835582\pi$
$127$	−0.0796049	+	0.137880i	−0.00706379	+	0.0122348i	0.862472	+	0.506105i	$0.168915\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−7.67160	−	9.60619i	−0.675447	−	0.845778i
$130$	−2.88720	−	16.3741i	−0.253224	−	1.43611i
$131$	−7.26657	+	6.09738i	−0.634883	+	0.532730i	−0.902442	−	0.430811i	$-0.858227\pi$
$131$	−7.26657	+	6.09738i	−0.634883	+	0.532730i	0.267559	+	0.963542i	$0.413783\pi$
$132$	7.55935	+	1.52269i	0.657957	+	0.132533i
$133$	0.557770	−	0.203012i	0.0483648	−	0.0176033i
$134$	7.44325			0.642999
$135$	−7.55953	+	16.8472i	−0.650621	+	1.44997i
$136$	1.13471			0.0973004
$137$	−11.0032	+	4.00484i	−0.940067	+	0.342156i	−0.766192	−	0.642611i	$-0.777851\pi$
$137$	−11.0032	+	4.00484i	−0.940067	+	0.342156i	−0.173875	+	0.984768i	$0.555629\pi$
$138$	−0.0797166	−	0.236720i	−0.00678593	−	0.0201509i
$139$	−4.02194	+	3.37481i	−0.341136	+	0.286247i	−0.797219	−	0.603690i	$-0.793696\pi$
$139$	−4.02194	+	3.37481i	−0.341136	+	0.286247i	0.456083	+	0.889937i	$0.349252\pi$
$140$	−0.197161	−	1.11816i	−0.0166631	−	0.0945014i
$141$	17.6845	−	2.67807i	1.48930	−	0.225534i
$142$	−6.20385	−	5.20565i	−0.520616	−	0.436849i
$143$	10.4150	−	18.0393i	0.870946	−	1.50852i
$144$	−2.99648	−	0.145376i	−0.249706	−	0.0121147i
$145$	7.74567	+	13.4159i	0.643243	+	1.11413i
$146$	2.53549	−	14.3795i	0.209839	−	1.19005i
$147$	10.1991	+	6.22279i	0.841204	+	0.513247i
$148$	−7.13111	−	2.59551i	−0.586174	−	0.213350i
$149$	15.3097	+	5.57227i	1.25422	+	0.456499i	0.881825	−	0.471576i	$-0.156315\pi$
$149$	15.3097	+	5.57227i	1.25422	+	0.456499i	0.372394	+	0.928075i	$0.378537\pi$
$150$	−0.320242	+	13.2093i	−0.0261476	+	1.07854i
$151$	−2.71203	+	15.3807i	−0.220702	+	1.25166i	0.650033	+	0.759906i	$0.274755\pi$
$151$	−2.71203	+	15.3807i	−0.220702	+	1.25166i	−0.870734	+	0.491754i	$0.836356\pi$
$152$	−0.928896	−	1.60890i	−0.0753434	−	0.130499i
$153$	−2.71068	+	2.05919i	−0.219146	+	0.166476i
$154$	0.711218	−	1.23187i	0.0573116	−	0.0992665i
$155$	1.82853	+	1.53432i	0.146871	+	0.123240i
$156$	−2.95541	+	7.54568i	−0.236623	+	0.604138i
$157$	3.06168	+	17.3637i	0.244349	+	1.38577i	0.822000	+	0.569488i	$0.192859\pi$
$157$	3.06168	+	17.3637i	0.244349	+	1.38577i	−0.577651	+	0.816284i	$0.696030\pi$
$158$	−9.64221	+	8.09077i	−0.767093	+	0.643667i
$159$	−0.922498	+	1.04678i	−0.0731588	+	0.0830151i
$160$	−3.33937	+	1.21543i	−0.264000	+	0.0960882i
$161$	−0.0460757			−0.00363128
$162$	7.42204	−	5.09052i	0.583130	−	0.399949i
$163$	−15.8801			−1.24382			−0.621912	−	0.783087i	$-0.713644\pi$
$163$	−15.8801			−1.24382			−0.621912	+	0.783087i	$0.713644\pi$
$164$	−2.04599	+	0.744678i	−0.159765	+	0.0581496i
$165$	−18.1180	+	20.5589i	−1.41048	+	1.60051i
$166$	−4.14708	+	3.47981i	−0.321876	+	0.270086i
$167$	−2.35787	−	13.3721i	−0.182457	−	1.03477i	−0.929179	−	0.369630i	$-0.879484\pi$
$167$	−2.35787	−	13.3721i	−0.182457	−	1.03477i	0.746722	−	0.665137i	$-0.231627\pi$
$168$	−0.201819	+	0.515278i	−0.0155707	+	0.0397546i
$169$	6.81058	+	5.71475i	0.523891	+	0.439596i
$170$	−2.01620	+	3.49215i	−0.154635	+	0.267836i
$171$	5.13874	+	2.15776i	0.392969	+	0.165008i
$172$	3.54885	+	6.14680i	0.270598	+	0.468689i
$173$	1.11906	−	6.34650i	0.0850805	−	0.482516i	−0.912259	−	0.409615i	$-0.865663\pi$
$173$	1.11906	−	6.34650i	0.0850805	−	0.482516i	0.997339	−	0.0729010i	$-0.0232257\pi$
$174$	0.182995	−	7.54820i	0.0138728	−	0.572228i
$175$	2.29037	+	0.833627i	0.173136	+	0.0630163i
$176$	−4.18356	−	1.52269i	−0.315348	−	0.114777i
$177$	−4.41035	−	2.69090i	−0.331502	−	0.202261i
$178$	0.877354	−	4.97572i	0.0657605	−	0.372946i
$179$	6.25613	+	10.8359i	0.467605	+	0.809915i	0.999315	−	0.0370111i	$-0.0117837\pi$
$179$	6.25613	+	10.8359i	0.467605	+	0.809915i	−0.531710	+	0.846927i	$0.678450\pi$
$180$	5.77167	−	8.96358i	0.430195	−	0.668106i
$181$	−0.152251	+	0.263707i	−0.0113168	+	0.0196012i	−0.871628	−	0.490167i	$-0.836936\pi$
$181$	−0.152251	+	0.263707i	−0.0113168	+	0.0196012i	0.860312	+	0.509769i	$0.170269\pi$
$182$	1.14513	+	0.960878i	0.0848827	+	0.0712250i
$183$	5.98466	−	0.906293i	0.442399	−	0.0669951i
$184$	0.0250421	+	0.142021i	0.00184613	+	0.0104699i
$185$	20.6587	−	17.3347i	1.51886	−	1.27448i
$186$	−0.371295	−	1.10257i	−0.0272246	−	0.0808440i
$187$	−4.74712	+	1.72781i	−0.347144	+	0.126350i
$188$	−10.3265			−0.753141
$189$	−0.452971	−	1.59718i	−0.0329488	−	0.116178i
$190$	6.60200			0.478960
$191$	13.5247	−	4.92260i	0.978615	−	0.356187i	0.197313	−	0.980341i	$-0.436778\pi$
$191$	13.5247	−	4.92260i	0.978615	−	0.356187i	0.781301	+	0.624154i	$0.214556\pi$
$192$	1.69795	+	0.342020i	0.122539	+	0.0246832i
$193$	2.33692	−	1.96090i	0.168215	−	0.141149i	−0.554794	−	0.831988i	$-0.687203\pi$
$193$	2.33692	−	1.96090i	0.168215	−	0.141149i	0.723009	+	0.690839i	$0.242759\pi$
$194$	3.24273	+	18.3904i	0.232814	+	1.32036i
$195$	−17.9711	−	22.5030i	−1.28694	−	1.61147i
$196$	−5.28411	−	4.43390i	−0.377437	−	0.316707i
$197$	−11.1321	+	19.2814i	−0.793129	+	1.37374i	0.130891	+	0.991397i	$0.458216\pi$
$197$	−11.1321	+	19.2814i	−0.793129	+	1.37374i	−0.924020	+	0.382343i	$0.875117\pi$
$198$	12.7573	−	3.95452i	0.906622	−	0.281036i
$199$	−12.2817	−	21.2725i	−0.870626	−	1.50797i	−0.861350	−	0.508012i	$-0.830381\pi$
$199$	−12.2817	−	21.2725i	−0.870626	−	1.50797i	−0.00927642	−	0.999957i	$-0.502953\pi$
$200$	1.32470	−	7.51276i	0.0936705	−	0.531232i
$201$	11.3178	−	6.17355i	0.798298	−	0.435449i
$202$	2.27375	+	0.827576i	0.159980	+	0.0582280i
$203$	−1.30878	−	0.476359i	−0.0918587	−	0.0334338i
$204$	1.72538	−	0.941146i	0.120801	−	0.0658934i
$205$	1.34359	−	7.61986i	0.0938402	−	0.532194i
$206$	−0.997676	−	1.72802i	−0.0695114	−	0.120397i
$207$	−0.317552	−	0.293826i	−0.0220714	−	0.0204223i
$208$	2.33937	−	4.05190i	0.162206	−	0.280949i
$209$	6.33595	+	5.31649i	0.438267	+	0.367750i
$210$	−1.22721	−	1.53668i	−0.0846855	−	0.106041i
$211$	−0.524297	−	2.97344i	−0.0360941	−	0.204700i	0.961428	−	0.275058i	$-0.0886970\pi$
$211$	−0.524297	−	2.97344i	−0.0360941	−	0.204700i	−0.997522	+	0.0703579i	$0.977586\pi$
$212$	0.617090	−	0.517800i	0.0423819	−	0.0355627i
$213$	−13.7509	−	2.76987i	−0.942197	−	0.189788i
$214$	−8.33575	+	3.03397i	−0.569820	+	0.207398i
$215$	−25.2230			−1.72019
$216$	−4.67686	+	2.26427i	−0.318220	+	0.154064i
$217$	−0.214606			−0.0145684
$218$	1.85311	−	0.674476i	0.125508	−	0.0456813i
$219$	−8.07124	−	23.9677i	−0.545404	−	1.61959i
$220$	12.1197	−	10.1697i	0.817112	−	0.685638i
$221$	−0.921898	−	5.22835i	−0.0620136	−	0.351697i
$222$	−12.9960	+	1.96806i	−0.872232	+	0.132087i
$223$	7.64543	+	6.41527i	0.511976	+	0.429599i	0.861824	−	0.507208i	$-0.169322\pi$
$223$	7.64543	+	6.41527i	0.511976	+	0.429599i	−0.349848	+	0.936806i	$0.613767\pi$
$224$	0.159750	−	0.276696i	0.0106738	−	0.0184875i
$225$	10.4691	+	20.3510i	0.697940	+	1.35674i
$226$	4.81433	+	8.33866i	0.320244	+	0.554679i
$227$	−3.66786	+	20.8015i	−0.243444	+	1.38064i	0.580633	+	0.814165i	$0.302805\pi$
$227$	−3.66786	+	20.8015i	−0.243444	+	1.38064i	−0.824078	+	0.566477i	$0.808306\pi$
$228$	−2.74688	−	1.67596i	−0.181916	−	0.110993i
$229$	21.8767	+	7.96248i	1.44566	+	0.526176i	0.941374	−	0.337364i	$-0.109535\pi$
$229$	21.8767	+	7.96248i	1.44566	+	0.526176i	0.504281	+	0.863539i	$0.331757\pi$
$230$	−0.481576	−	0.175279i	−0.0317542	−	0.0115576i
$231$	0.0597121	−	2.46301i	0.00392877	−	0.162054i
$232$	−0.756973	+	4.29301i	−0.0496977	+	0.281850i
$233$	−13.3621	−	23.1439i	−0.875383	−	1.51621i	−0.856354	−	0.516390i	$-0.827276\pi$
$233$	−13.3621	−	23.1439i	−0.875383	−	1.51621i	−0.0190296	−	0.999819i	$-0.506058\pi$
$234$	1.76466	+	13.9248i	0.115359	+	0.910295i
$235$	18.3486	−	31.7808i	1.19693	−	2.07315i
$236$	2.28499	+	1.91734i	0.148740	+	0.124808i
$237$	−7.95083	+	20.2998i	−0.516462	+	1.31861i
$238$	−0.0629545	−	0.357033i	−0.00408073	−	0.0231430i
$239$	−18.4309	+	15.4654i	−1.19220	+	1.00037i	−0.192379	+	0.981321i	$0.561620\pi$
$239$	−18.4309	+	15.4654i	−1.19220	+	1.00037i	−0.999818	+	0.0190518i	$0.993935\pi$
$240$	−4.06957	+	4.61785i	−0.262690	+	0.298081i
$241$	1.40157	−	0.510130i	0.0902831	−	0.0328604i	−0.296484	−	0.955038i	$-0.595814\pi$
$241$	1.40157	−	0.510130i	0.0902831	−	0.0328604i	0.386767	+	0.922178i	$0.373592\pi$
$242$	8.82079			0.567022
$243$	7.06341	−	13.8963i	0.453118	−	0.891451i
$244$	−3.49464			−0.223721
$245$	23.0347	−	8.38394i	1.47163	−	0.535630i
$246$	−2.49337	+	2.82929i	−0.158972	+	0.180389i
$247$	−6.65855	+	5.58719i	−0.423674	+	0.355504i
$248$	0.116638	+	0.661487i	0.00740653	+	0.0420045i
$249$	−3.41962	+	8.73088i	−0.216710	+	0.553297i
$250$	7.15592	+	6.00453i	0.452580	+	0.379760i
$251$	−7.28748	+	12.6223i	−0.459982	+	0.796711i	−0.998959	−	0.0456086i	$-0.985477\pi$
$251$	−7.28748	+	12.6223i	−0.459982	+	0.796711i	0.538978	+	0.842320i	$0.318811\pi$
$252$	0.120505	+	0.950897i	0.00759107	+	0.0599009i
$253$	−0.321019	−	0.556021i	−0.0201823	−	0.0349568i
$254$	0.0276465	−	0.156791i	0.00173469	−	0.00983794i
$255$	−0.169275	+	6.98226i	−0.0106004	+	0.437246i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	10.3598	+	3.77064i	0.646224	+	0.235206i	0.644277	−	0.764792i	$-0.277158\pi$
$257$	10.3598	+	3.77064i	0.646224	+	0.235206i	0.00194649	+	0.999998i	$0.499380\pi$
$258$	10.4945	+	6.40303i	0.653357	+	0.398635i
$259$	−0.421030	+	2.38778i	−0.0261616	+	0.148370i
$260$	8.31337	+	14.3992i	0.515573	+	0.892999i
$261$	−5.98235	−	11.6292i	−0.370298	−	0.719829i
$262$	4.74292	−	8.21497i	0.293018	−	0.507523i
$263$	−10.0659	−	8.44626i	−0.620688	−	0.520819i	0.277332	−	0.960774i	$-0.410550\pi$
$263$	−10.0659	−	8.44626i	−0.620688	−	0.520819i	−0.898020	+	0.439955i	$0.854994\pi$
$264$	−7.62426	+	1.15459i	−0.469241	+	0.0710599i
$265$	0.497100	+	2.81919i	0.0305366	+	0.173182i
$266$	−0.454698	+	0.381537i	−0.0278793	+	0.0233935i
$267$	−2.79289	−	8.29352i	−0.170922	−	0.507555i
$268$	−6.99437	+	2.54574i	−0.427249	+	0.155506i
$269$	−10.3086			−0.628528			−0.314264	−	0.949336i	$-0.601758\pi$
$269$	−10.3086			−0.628528			−0.314264	+	0.949336i	$0.601758\pi$
$270$	1.34156	−	18.4167i	0.0816448	−	1.12080i
$271$	1.01454			0.0616288			0.0308144	−	0.999525i	$-0.490190\pi$
$271$	1.01454			0.0616288			0.0308144	+	0.999525i	$0.490190\pi$
$272$	−1.06628	+	0.388093i	−0.0646525	+	0.0235316i
$273$	2.53819	+	0.511272i	0.153618	+	0.0309436i
$274$	8.96989	−	7.52663i	0.541891	−	0.454700i
$275$	5.89764	+	33.4472i	0.355641	+	2.01694i
$276$	0.155872	+	0.195179i	0.00938239	+	0.0117484i
$277$	−8.29755	−	6.96247i	−0.498552	−	0.418334i	0.358528	−	0.933519i	$-0.383279\pi$
$277$	−8.29755	−	6.96247i	−0.498552	−	0.418334i	−0.857079	+	0.515185i	$0.827723\pi$
$278$	2.62513	−	4.54686i	0.157445	−	0.272703i
$279$	−1.47906	−	1.36855i	−0.0885488	−	0.0819327i
$280$	0.567702	+	0.983289i	0.0339267	+	0.0587628i
$281$	−1.47197	+	8.34795i	−0.0878103	+	0.497997i	0.908904	+	0.417004i	$0.136920\pi$
$281$	−1.47197	+	8.34795i	−0.0878103	+	0.497997i	−0.996715	+	0.0809924i	$0.974191\pi$
$282$	−15.7020	+	8.56501i	−0.935041	+	0.510039i
$283$	−5.92408	−	2.15619i	−0.352150	−	0.128172i	0.159887	−	0.987135i	$-0.448887\pi$
$283$	−5.92408	−	2.15619i	−0.352150	−	0.128172i	−0.512037	+	0.858963i	$0.671109\pi$
$284$	7.61015	+	2.76987i	0.451580	+	0.164362i
$285$	10.0387	−	5.47581i	0.594639	−	0.324359i
$286$	−3.61709	+	20.5135i	−0.213883	+	1.21299i
$287$	0.347824	+	0.602448i	0.0205314	+	0.0355614i
$288$	2.86549	−	0.888246i	0.168850	−	0.0523404i
$289$	7.85622	−	13.6074i	0.462130	−	0.800434i
$290$	−11.8671	−	9.95764i	−0.696857	−	0.584733i
$291$	20.1840	+	25.2740i	1.18321	+	1.48159i
$292$	2.53549	+	14.3795i	0.148378	+	0.841495i
$293$	−1.86383	+	1.56394i	−0.108886	+	0.0913662i	−0.695605	−	0.718424i	$-0.744864\pi$
$293$	−1.86383	+	1.56394i	−0.108886	+	0.0913662i	0.586719	+	0.809790i	$0.300419\pi$
$294$	−11.7123	−	2.35923i	−0.683075	−	0.137593i
$295$	−9.96083	+	3.62544i	−0.579942	+	0.211082i
$296$	7.58877			0.441088
$297$	16.1182	−	16.5942i	0.935271	−	0.962891i
$298$	−16.2922			−0.943784
$299$	0.634037	−	0.230771i	0.0366673	−	0.0133458i
$300$	−4.21693	−	12.5222i	−0.243465	−	0.722972i
$301$	1.73718	−	1.45767i	0.100129	−	0.0840184i
$302$	−2.71203	−	15.3807i	−0.156060	−	0.885058i
$303$	4.14375	−	0.627512i	0.238052	−	0.0360496i
$304$	1.42315	+	1.19417i	0.0816233	+	0.0684901i
$305$	6.20942	−	10.7550i	0.355550	−	0.615831i
$306$	1.84292	−	2.86212i	0.105353	−	0.163616i
$307$	11.8629	+	20.5471i	0.677050	+	1.17269i	0.975865	+	0.218374i	$0.0700754\pi$
$307$	11.8629	+	20.5471i	0.677050	+	1.17269i	−0.298815	+	0.954311i	$0.596591\pi$
$308$	−0.247003	+	1.40083i	−0.0140743	+	0.0798194i
$309$	−2.95027	−	1.80006i	−0.167835	−	0.102402i
$310$	−2.24303	−	0.816395i	−0.127395	−	0.0463681i
$311$	10.1493	+	3.69403i	0.575511	+	0.209469i	0.613345	−	0.789815i	$-0.289824\pi$
$311$	10.1493	+	3.69403i	0.575511	+	0.209469i	−0.0378338	+	0.999284i	$0.512046\pi$
$312$	0.196408	−	8.10143i	0.0111194	−	0.458653i
$313$	−2.75948	+	15.6498i	−0.155975	+	0.884577i	0.801914	+	0.597439i	$0.203815\pi$
$313$	−2.75948	+	15.6498i	−0.155975	+	0.884577i	−0.957889	+	0.287138i	$0.907296\pi$
$314$	−8.81577	−	15.2694i	−0.497503	−	0.861700i
$315$	−3.14058	−	1.31873i	−0.176952	−	0.0743021i
$316$	6.29350	−	10.9007i	0.354037	−	0.613210i
$317$	−2.47819	−	2.07944i	−0.139189	−	0.116793i	0.570535	−	0.821273i	$-0.306736\pi$
$317$	−2.47819	−	2.07944i	−0.139189	−	0.116793i	−0.709724	+	0.704480i	$0.751180\pi$
$318$	0.508844	−	1.29917i	0.0285346	−	0.0728536i
$319$	−3.37009	−	19.1127i	−0.188689	−	1.07011i
$320$	2.72228	−	2.28426i	0.152180	−	0.127694i
$321$	−10.1585	+	11.5271i	−0.566992	+	0.643380i
$322$	0.0432970	−	0.0157588i	0.00241285	−	0.000878205i
$323$	2.10805			0.117295
$324$	−5.23337	+	7.32201i	−0.290743	+	0.406778i
$325$	−35.6925			−1.97986
$326$	14.9224	−	5.43131i	0.826475	−	0.300812i
$327$	2.25832	−	2.56257i	0.124885	−	0.141711i
$328$	1.66790	−	1.39954i	0.0920946	−	0.0772765i
$329$	0.572924	+	3.24922i	0.0315863	+	0.179135i
$330$	9.99376	−	25.5158i	0.550138	−	1.40460i
$331$	−13.5311	−	11.3540i	−0.743739	−	0.624071i	0.190100	−	0.981765i	$-0.439119\pi$
$331$	−13.5311	−	11.3540i	−0.743739	−	0.624071i	−0.933839	+	0.357693i	$0.883563\pi$
$332$	2.70681	−	4.68834i	0.148556	−	0.257306i
$333$	−18.1287	+	13.7716i	−0.993444	+	0.754678i
$334$	6.78921	+	11.7593i	0.371489	+	0.643438i
$335$	4.59316	−	26.0491i	0.250951	−	1.42321i
$336$	0.0134123	−	0.553229i	0.000731699	−	0.0301811i
$337$	9.90706	+	3.60588i	0.539672	+	0.196425i	0.597452	−	0.801905i	$-0.296180\pi$
$337$	9.90706	+	3.60588i	0.539672	+	0.196425i	−0.0577798	+	0.998329i	$0.518402\pi$
$338$	−8.35441	−	3.04076i	−0.454420	−	0.165395i
$339$	14.2366	+	8.68625i	0.773228	+	0.471773i
$340$	0.700218	−	3.97113i	0.0379746	−	0.215365i
$341$	−1.49520	−	2.58977i	−0.0809699	−	0.140244i
$342$	−5.56683	−	0.270079i	−0.301020	−	0.0146042i
$343$	−2.22020	+	3.84550i	−0.119879	+	0.207637i
$344$	−5.43716	−	4.56232i	−0.293152	−	0.245984i
$345$	−0.877639	+	0.132906i	−0.0472505	+	0.00715543i
$346$	1.11906	+	6.34650i	0.0601610	+	0.341190i
$347$	24.9000	−	20.8936i	1.33670	−	1.12163i	0.354243	−	0.935153i	$-0.384739\pi$
$347$	24.9000	−	20.8936i	1.33670	−	1.12163i	0.982460	−	0.186473i	$-0.0597058\pi$
$348$	2.40968	+	7.15558i	0.129172	+	0.383579i
$349$	18.8599	−	6.86444i	1.00955	−	0.367445i	0.216289	−	0.976329i	$-0.430605\pi$
$349$	18.8599	−	6.86444i	1.00955	−	0.367445i	0.793259	+	0.608884i	$0.208383\pi$
$350$	−2.43736			−0.130282
$351$	14.2327	+	19.7098i	0.759687	+	1.05203i
$352$	4.45206			0.237295
$353$	−10.3705	+	3.77455i	−0.551966	+	0.200899i	−0.602920	−	0.797802i	$-0.705996\pi$
$353$	−10.3705	+	3.77455i	−0.551966	+	0.200899i	0.0509539	+	0.998701i	$0.483774\pi$
$354$	5.06472	+	1.02019i	0.269187	+	0.0542227i
$355$	−22.0465	+	18.4992i	−1.17011	+	0.981837i
$356$	0.877354	+	4.97572i	0.0464997	+	0.263713i
$357$	−0.391854	−	0.490670i	−0.0207391	−	0.0259690i
$358$	−9.58494	−	8.04272i	−0.506580	−	0.425071i
$359$	1.96044	−	3.39557i	0.103468	−	0.179212i	−0.809643	−	0.586922i	$-0.800339\pi$
$359$	1.96044	−	3.39557i	0.103468	−	0.179212i	0.913111	+	0.407711i	$0.133673\pi$
$360$	−2.35787	+	10.3970i	−0.124271	+	0.547972i
$361$	7.77430	+	13.4655i	0.409174	+	0.708710i
$362$	0.0528764	−	0.299877i	0.00277912	−	0.0157612i
$363$	13.4124	−	7.31611i	0.703971	−	0.383996i
$364$	−1.40471	−	0.511272i	−0.0736268	−	0.0267980i
$365$	−48.7591	−	17.7469i	−2.55217	−	0.928914i
$366$	−5.31377	+	2.89851i	−0.277755	+	0.151508i
$367$	5.06206	−	28.7084i	0.264237	−	1.49856i	−0.506961	−	0.861969i	$-0.669231\pi$
$367$	5.06206	−	28.7084i	0.264237	−	1.49856i	0.771198	−	0.636595i	$-0.219658\pi$
$368$	−0.0721058	−	0.124891i	−0.00375878	−	0.00651039i
$369$	−1.44463	+	6.37013i	−0.0752047	+	0.331615i
$370$	−13.4840	+	23.3550i	−0.701001	+	1.21417i
$371$	−0.197161	−	0.165438i	−0.0102361	−	0.00858909i
$372$	0.726002	+	0.909082i	0.0376415	+	0.0471337i
$373$	1.08909	+	6.17653i	0.0563909	+	0.319809i	0.999935	−	0.0114395i	$-0.00364140\pi$
$373$	1.08909	+	6.17653i	0.0563909	+	0.319809i	−0.943544	+	0.331248i	$0.892530\pi$
$374$	3.86989	−	3.24722i	0.200107	−	0.167910i
$375$	15.8612	+	3.19494i	0.819068	+	0.164986i
$376$	9.70378	−	3.53189i	0.500434	−	0.182143i
$377$	20.3957			1.05043
$378$	0.971923	+	1.34594i	0.0499903	+	0.0692276i
$379$	−26.9562			−1.38465			−0.692324	−	0.721587i	$-0.743413\pi$
$379$	−26.9562			−1.38465			−0.692324	+	0.721587i	$0.743413\pi$
$380$	−6.20385	+	2.25802i	−0.318251	+	0.115834i
$381$	−0.0880072	−	0.261339i	−0.00450874	−	0.0133888i
$382$	−11.0255	+	9.25146i	−0.564111	+	0.473346i
$383$	−0.565446	−	3.20680i	−0.0288929	−	0.163860i	0.966947	−	0.254976i	$-0.0820676\pi$
$383$	−0.565446	−	3.20680i	−0.0288929	−	0.163860i	−0.995840	+	0.0911163i	$0.970957\pi$
$384$	−1.71253	+	0.259338i	−0.0873920	+	0.0132343i
$385$	−3.87226	−	3.24922i	−0.197349	−	0.165595i
$386$	−1.52531	+	2.64192i	−0.0776364	+	0.134470i
$387$	21.2681	+	1.03184i	1.08112	+	0.0524512i
$388$	−9.33706	−	16.1723i	−0.474018	−	0.821022i
$389$	0.241315	−	1.36857i	0.0122352	−	0.0693891i	−0.978079	−	0.208235i	$-0.933228\pi$
$389$	0.241315	−	1.36857i	0.0122352	−	0.0693891i	0.990314	+	0.138846i	$0.0443392\pi$
$390$	24.5838	+	14.9994i	1.24485	+	0.759525i
$391$	−0.153770	−	0.0559675i	−0.00777646	−	0.00283040i
$392$	6.48192	+	2.35923i	0.327387	+	0.119159i
$393$	0.398204	−	16.4251i	0.0200867	−	0.828538i
$394$	3.86614	−	21.9260i	0.194773	−	1.10461i
$395$	22.3651	+	38.7375i	1.12531	+	1.94909i
$396$	−10.6354	+	8.07929i	−0.534450	+	0.406000i
$397$	−1.07010	+	1.85347i	−0.0537069	+	0.0930230i	−0.891629	−	0.452767i	$-0.850437\pi$
$397$	−1.07010	+	1.85347i	−0.0537069	+	0.0930230i	0.837922	+	0.545790i	$0.183770\pi$
$398$	18.8167	+	15.7890i	0.943193	+	0.791433i
$399$	−0.374938	+	0.957280i	−0.0187704	+	0.0479239i
$400$	1.32470	+	7.51276i	0.0662351	+	0.375638i
$401$	−6.55222	+	5.49796i	−0.327202	+	0.274555i	−0.791559	−	0.611093i	$-0.790730\pi$
$401$	−6.55222	+	5.49796i	−0.327202	+	0.274555i	0.464357	+	0.885648i	$0.346286\pi$
$402$	−8.52379	+	9.67216i	−0.425128	+	0.482404i
$403$	2.95314	−	1.07486i	0.147107	−	0.0535424i
$404$	−2.41967			−0.120383
$405$	−13.2352	−	29.1162i	−0.657661	−	1.44679i
$406$	1.39278			0.0691225
$407$	−31.7481	+	11.5554i	−1.57369	+	0.572778i
$408$	−1.29944	+	1.47450i	−0.0643316	+	0.0729987i
$409$	20.8915	−	17.5300i	1.03302	−	0.866804i	0.0418096	−	0.999126i	$-0.486688\pi$
$409$	20.8915	−	17.5300i	1.03302	−	0.866804i	0.991207	+	0.132322i	$0.0422433\pi$
$410$	1.34359	+	7.61986i	0.0663550	+	0.376318i
$411$	7.39644	−	18.8844i	0.364840	−	0.931498i
$412$	1.52853	+	1.28259i	0.0753052	+	0.0631885i
$413$	0.476511	−	0.825342i	0.0234476	−	0.0406124i
$414$	0.398896	+	0.167497i	0.0196047	+	0.00823201i
$415$	9.61916	+	16.6609i	0.472186	+	0.817850i
$416$	−0.812454	+	4.60766i	−0.0398338	+	0.225909i
$417$	0.220400	−	9.09106i	0.0107930	−	0.445191i
$418$	−7.77219	−	2.82885i	−0.380150	−	0.138363i
$419$	−15.0495	−	5.47757i	−0.735216	−	0.267597i	−0.0528448	−	0.998603i	$-0.516829\pi$
$419$	−15.0495	−	5.47757i	−0.735216	−	0.267597i	−0.682371	+	0.731006i	$0.739051\pi$
$420$	1.67877	+	1.02428i	0.0819158	+	0.0499796i
$421$	−3.15120	+	17.8713i	−0.153580	+	0.870995i	0.806493	+	0.591244i	$0.201363\pi$
$421$	−3.15120	+	17.8713i	−0.153580	+	0.870995i	−0.960073	+	0.279751i	$0.909748\pi$
$422$	1.50965	+	2.61480i	0.0734888	+	0.127286i
$423$	−16.7717	+	26.0470i	−0.815469	+	1.26645i
$424$	−0.402777	+	0.697630i	−0.0195606	+	0.0338799i
$425$	6.63111	+	5.56416i	0.321656	+	0.269901i
$426$	13.8690	−	2.10026i	0.671954	−	0.101758i
$427$	0.193885	+	1.09958i	0.00938276	+	0.0532123i
$428$	6.79537	−	5.70199i	0.328467	−	0.275616i
$429$	11.5143	+	34.1919i	0.555916	+	1.65080i
$430$	23.7019	−	8.62677i	1.14301	−	0.416020i
$431$	2.13698			0.102935			0.0514673	−	0.998675i	$-0.483610\pi$
$431$	2.13698			0.102935			0.0514673	+	0.998675i	$0.483610\pi$
$432$	3.62039	−	3.72730i	0.174186	−	0.179330i
$433$	25.1733			1.20975			0.604876	−	0.796320i	$-0.293223\pi$
$433$	25.1733			1.20975			0.604876	+	0.796320i	$0.293223\pi$
$434$	0.201664	−	0.0733996i	0.00968017	−	0.00352329i
$435$	−26.3035	−	5.29835i	−1.26115	−	0.254036i
$436$	−1.51067	+	1.26760i	−0.0723478	+	0.0607071i
$437$	0.0465230	+	0.263845i	0.00222550	+	0.0126214i
$438$	15.7819	+	19.7617i	0.754089	+	0.944252i
$439$	19.8037	+	16.6173i	0.945179	+	0.793099i	0.978479	−	0.206346i	$-0.0661573\pi$
$439$	19.8037	+	16.6173i	0.945179	+	0.793099i	−0.0333002	+	0.999445i	$0.510602\pi$
$440$	−7.91059	+	13.7015i	−0.377123	+	0.653196i
$441$	−19.7659	+	6.12705i	−0.941233	+	0.291764i
$442$	2.65450	+	4.59773i	0.126262	+	0.218692i
$443$	2.42041	−	13.7268i	0.114997	−	0.652181i	−0.871755	−	0.489943i	$-0.837018\pi$
$443$	2.42041	−	13.7268i	0.114997	−	0.652181i	0.986752	−	0.162238i	$-0.0518713\pi$
$444$	11.5391	−	6.29425i	0.547621	−	0.298712i
$445$	−16.8721	−	6.14094i	−0.799814	−	0.291108i
$446$	−9.37850	−	3.41350i	−0.444085	−	0.161634i
$447$	−24.7731	+	13.5131i	−1.17173	+	0.639145i
$448$	−0.0554807	+	0.314647i	−0.00262122	+	0.0148657i
$449$	−14.5769	−	25.2479i	−0.687927	−	1.19152i	−0.972507	−	0.232872i	$-0.925188\pi$
$449$	−14.5769	−	25.2479i	−0.687927	−	1.19152i	0.284581	−	0.958652i	$-0.408146\pi$
$450$	−16.7982	−	15.5431i	−0.791875	−	0.732708i
$451$	−4.84672	+	8.39476i	−0.228223	+	0.395294i
$452$	−7.37598	−	6.18918i	−0.346937	−	0.291114i
$453$	−16.8807	−	21.1376i	−0.793126	−	0.993133i
$454$	−3.66786	−	20.8015i	−0.172141	−	0.976261i
$455$	4.06943	−	3.41465i	0.190778	−	0.160081i
$456$	3.15443	+	0.635402i	0.147720	+	0.0297554i
$457$	−22.3630	+	8.13945i	−1.04609	+	0.380747i	−0.807188	−	0.590295i	$-0.799011\pi$
$457$	−22.3630	+	8.13945i	−1.04609	+	0.380747i	−0.238907	+	0.971042i	$0.576789\pi$
$458$	−23.2807			−1.08784
$459$	0.428367	−	5.88054i	0.0199945	−	0.274480i
$460$	0.512482			0.0238946
$461$	−28.9550	+	10.5388i	−1.34857	+	0.490839i	−0.912501	−	0.409074i	$-0.865852\pi$
$461$	−28.9550	+	10.5388i	−1.34857	+	0.490839i	−0.436069	+	0.899913i	$0.643630\pi$
$462$	0.786287	+	2.33489i	0.0365814	+	0.108629i
$463$	27.6849	−	23.2304i	1.28663	−	1.07961i	0.294334	−	0.955703i	$-0.404902\pi$
$463$	27.6849	−	23.2304i	1.28663	−	1.07961i	0.992294	−	0.123907i	$-0.0395424\pi$
$464$	−0.756973	−	4.29301i	−0.0351416	−	0.199298i
$465$	−4.08776	+	0.619035i	−0.189565	+	0.0287070i
$466$	20.4720	+	17.1780i	0.948347	+	0.795758i
$467$	18.4877	−	32.0217i	0.855509	−	1.48179i	−0.0206626	−	0.999787i	$-0.506578\pi$
$467$	18.4877	−	32.0217i	0.855509	−	1.48179i	0.876172	−	0.481999i	$-0.160089\pi$
$468$	−6.42081	−	12.4815i	−0.296802	−	0.576959i
$469$	1.18906	+	2.05952i	0.0549058	+	0.0950996i
$470$	−6.37241	+	36.1397i	−0.293937	+	1.66700i
$471$	−26.0695	−	15.9059i	−1.20122	−	0.732904i
$472$	−2.80296	−	1.02019i	−0.129017	−	0.0469582i
$473$	29.6937	+	10.8076i	1.36532	+	0.496935i
$474$	0.528387	−	21.7949i	0.0242696	−	1.00107i
$475$	2.46102	−	13.9571i	0.112919	−	0.640398i
$476$	0.181270	+	0.313969i	0.00830850	+	0.0143908i
$477$	−0.303827	−	2.39749i	−0.0139113	−	0.109773i
$478$	12.0299	−	20.8365i	0.550236	−	0.953037i
$479$	29.4015	+	24.6708i	1.34339	+	1.12724i	0.980741	+	0.195311i	$0.0625715\pi$
$479$	29.4015	+	24.6708i	1.34339	+	1.12724i	0.362647	+	0.931926i	$0.381873\pi$
$480$	2.24475	−	5.73123i	0.102458	−	0.261594i
$481$	−6.16553	−	34.9664i	−0.281124	−	1.59433i
$482$	−1.14257	+	0.958731i	−0.0520427	+	0.0436690i
$483$	0.0527646	−	0.0598733i	0.00240087	−	0.00272433i
$484$	−8.28884	+	3.01689i	−0.376765	+	0.137131i
$485$	66.3619			3.01334
$486$	−1.88461	+	15.4741i	−0.0854876	+	0.701920i
$487$	34.3088			1.55468			0.777339	−	0.629082i	$-0.216569\pi$
$487$	34.3088			1.55468			0.777339	+	0.629082i	$0.216569\pi$
$488$	3.28389	−	1.19524i	0.148655	−	0.0541059i
$489$	18.1854	−	20.6354i	0.822373	−	0.933167i
$490$	−18.7781	+	15.7567i	−0.848306	+	0.711813i
$491$	−3.02281	−	17.1432i	−0.136417	−	0.773661i	−0.973862	−	0.227139i	$-0.927063\pi$
$491$	−3.02281	−	17.1432i	−0.136417	−	0.773661i	0.837445	−	0.546522i	$-0.184048\pi$
$492$	1.37533	−	3.51145i	0.0620046	−	0.158308i
$493$	−3.78921	−	3.17952i	−0.170657	−	0.143199i
$494$	4.34606	−	7.52760i	0.195539	−	0.338683i
$495$	−5.96720	−	47.0870i	−0.268206	−	2.11640i
$496$	−0.335846	−	0.581702i	−0.0150799	−	0.0261192i
$497$	0.449314	−	2.54819i	0.0201545	−	0.114302i
$498$	0.227258	−	9.37392i	0.0101837	−	0.420056i
$499$	−24.6982	−	8.98939i	−1.10564	−	0.402421i	−0.276248	−	0.961086i	$-0.589091\pi$
$499$	−24.6982	−	8.98939i	−1.10564	−	0.402421i	−0.829393	+	0.558666i	$0.811313\pi$
$500$	−8.77804	−	3.19494i	−0.392566	−	0.142882i
$501$	20.0766	+	12.2494i	0.896958	+	0.547265i
$502$	2.53091	−	14.3535i	0.112960	−	0.640629i
$503$	9.08930	+	15.7431i	0.405272	+	0.701952i	0.994353	−	0.106122i	$-0.0338435\pi$
$503$	9.08930	+	15.7431i	0.405272	+	0.701952i	−0.589081	+	0.808074i	$0.700510\pi$
$504$	−0.438463	−	0.852336i	−0.0195307	−	0.0379661i
$505$	4.29937	−	7.44672i	0.191319	−	0.331375i
$506$	0.491830	+	0.412694i	0.0218645	+	0.0183465i
$507$	−15.2253	+	2.30567i	−0.676181	+	0.102398i
$508$	0.0276465	+	0.156791i	0.00122661	+	0.00695647i
$509$	−18.8746	+	15.8376i	−0.836600	+	0.701991i	−0.956796	−	0.290759i	$-0.906092\pi$
$509$	−18.8746	+	15.8376i	−0.836600	+	0.701991i	0.120196	+	0.992750i	$0.461648\pi$
$510$	−2.22901	−	6.61907i	−0.0987020	−	0.293097i
$511$	4.38379	−	1.59557i	0.193927	−	0.0705838i
$512$	1.00000			0.0441942
$513$	−8.68864	+	4.20655i	−0.383613	+	0.185724i
$514$	−11.0246			−0.486275
$515$	−6.66321	+	2.42521i	−0.293616	+	0.106868i
$516$	−12.0515	−	2.42756i	−0.530539	−	0.106867i
$517$	−35.2184	+	29.5517i	−1.54890	+	1.29968i
$518$	−0.421030	−	2.38778i	−0.0184990	−	0.104913i
$519$	6.96548	+	8.72200i	0.305750	+	0.382853i
$520$	−12.7368	−	10.6875i	−0.558547	−	0.468676i
$521$	−15.0065	+	25.9921i	−0.657449	+	1.13873i	0.323825	+	0.946117i	$0.395031\pi$
$521$	−15.0065	+	25.9921i	−0.657449	+	1.13873i	−0.981274	+	0.192618i	$0.938302\pi$
$522$	9.59898	+	8.88178i	0.420136	+	0.388745i
$523$	13.6719	+	23.6804i	0.597829	+	1.03547i	0.993141	+	0.116924i	$0.0373033\pi$
$523$	13.6719	+	23.6804i	0.597829	+	1.03547i	−0.395312	+	0.918547i	$0.629363\pi$
$524$	−1.64720	+	9.34172i	−0.0719582	+	0.408095i
$525$	−3.70613	+	2.02159i	−0.161749	+	0.0882293i
$526$	12.3476	+	4.49416i	0.538381	+	0.195955i
$527$	−0.716210	−	0.260679i	−0.0311986	−	0.0113554i
$528$	6.76957	−	3.69261i	0.294608	−	0.160700i
$529$	−3.99030	+	22.6301i	−0.173491	+	0.983917i
$530$	−1.43134	−	2.47916i	−0.0621735	−	0.107688i
$531$	8.54731	−	2.64950i	0.370922	−	0.114979i
$532$	0.296783	−	0.514044i	0.0128672	−	0.0222866i
$533$	−7.80368	−	6.54807i	−0.338015	−	0.283628i
$534$	5.46100	+	6.83814i	0.236321	+	0.295915i
$535$	5.47404	+	31.0448i	0.236663	+	1.34218i
$536$	5.70186	−	4.78443i	0.246283	−	0.206656i
$537$	−21.2451	−	4.27944i	−0.916795	−	0.184672i
$538$	9.68695	−	3.52576i	0.417634	−	0.152006i
$539$	−30.7099			−1.32277
$540$	5.03822	+	17.7649i	0.216810	+	0.764478i
$541$	8.65632			0.372164			0.186082	−	0.982534i	$-0.440421\pi$
$541$	8.65632			0.372164			0.186082	+	0.982534i	$0.440421\pi$
$542$	−0.953353	+	0.346992i	−0.0409500	+	0.0149046i
$543$	−0.168322	−	0.499834i	−0.00722337	−	0.0214499i
$544$	0.869237	−	0.729376i	0.0372682	−	0.0312718i
$545$	−1.21692	−	6.90152i	−0.0521273	−	0.295629i
$546$	−2.55999	+	0.387674i	−0.109557	+	0.0165909i
$547$	21.1005	+	17.7055i	0.902194	+	0.757031i	0.970618	−	0.240625i	$-0.0773525\pi$
$547$	21.1005	+	17.7055i	0.902194	+	0.757031i	−0.0684237	+	0.997656i	$0.521797\pi$
$548$	−5.85468	+	10.1406i	−0.250100	+	0.433185i
$549$	−5.67577	+	8.81466i	−0.242236	+	0.376200i
$550$	−16.9816	−	29.4130i	−0.724097	−	1.25417i
$551$	−1.40630	+	7.97552i	−0.0599104	+	0.339769i
$552$	−0.213227	−	0.130097i	−0.00907554	−	0.00553730i
$553$	−3.77903	−	1.37545i	−0.160701	−	0.0584903i
$554$	10.1785	+	3.70465i	0.432441	+	0.157396i
$555$	−1.13209	+	46.6963i	−0.0480544	+	1.98215i
$556$	−0.911699	+	5.17050i	−0.0386647	+	0.219278i
$557$	13.0903	+	22.6730i	0.554653	+	0.960687i	0.997930	+	0.0643022i	$0.0204822\pi$
$557$	13.0903	+	22.6730i	0.554653	+	0.960687i	−0.443278	+	0.896384i	$0.646184\pi$
$558$	1.85793	+	0.780146i	0.0786524	+	0.0330262i
$559$	−16.6042	+	28.7592i	−0.702281	+	1.21639i
$560$	−0.869770	−	0.729824i	−0.0367545	−	0.0308407i
$561$	3.19106	−	8.14731i	0.134727	−	0.343980i
$562$	−1.47197	−	8.34795i	−0.0620912	−	0.352137i
$563$	−3.04293	+	2.55332i	−0.128244	+	0.107610i	−0.704654	−	0.709551i	$-0.748898\pi$
$563$	−3.04293	+	2.55332i	−0.128244	+	0.107610i	0.576410	+	0.817161i	$0.304453\pi$
$564$	11.8257	−	13.4189i	0.497950	−	0.565037i
$565$	32.1536	−	11.7030i	1.35271	−	0.492347i
$566$	6.30428			0.264988
$567$	2.59420	+	1.24043i	0.108946	+	0.0520934i
$568$	−8.09856			−0.339808
$569$	38.0492	−	13.8488i	1.59511	−	0.580571i	0.616688	−	0.787207i	$-0.288474\pi$
$569$	38.0492	−	13.8488i	1.59511	−	0.580571i	0.978418	+	0.206636i	$0.0662516\pi$
$570$	−7.56043	+	8.57900i	−0.316671	+	0.359335i
$571$	29.3406	−	24.6197i	1.22787	−	1.03030i	0.229493	−	0.973310i	$-0.426293\pi$
$571$	29.3406	−	24.6197i	1.22787	−	1.03030i	0.998375	−	0.0569933i	$-0.0181514\pi$
$572$	−3.61709	−	20.5135i	−0.151238	−	0.857714i
$573$	−9.09143	+	23.2120i	−0.379800	+	0.969694i
$574$	−0.532897	−	0.447153i	−0.0222427	−	0.0186638i
$575$	−0.550070	+	0.952749i	−0.0229395	+	0.0397324i
$576$	−2.38888	+	1.81473i	−0.0995366	+	0.0756139i
$577$	−4.13928	−	7.16944i	−0.172320	−	0.298468i	0.766910	−	0.641754i	$-0.221793\pi$
$577$	−4.13928	−	7.16944i	−0.172320	−	0.298468i	−0.939231	+	0.343287i	$0.888460\pi$
$578$	−2.72844	+	15.4737i	−0.113488	+	0.643622i
$579$	−0.128062	+	5.28229i	−0.00532206	+	0.219524i
$580$	14.5571	+	5.29835i	0.604450	+	0.220002i
$581$	−1.62535	−	0.591578i	−0.0674308	−	0.0245428i
$582$	−27.6110	−	16.8464i	−1.14451	−	0.698306i
$583$	0.622767	−	3.53189i	0.0257924	−	0.146276i
$584$	−7.30065	−	12.6451i	−0.302103	−	0.523258i
$585$	49.8216	+	2.41713i	2.05987	+	0.0999360i
$586$	1.21653	−	2.10709i	0.0502543	−	0.0870430i
$587$	−10.6808	−	8.96228i	−0.440845	−	0.369913i	0.395181	−	0.918603i	$-0.370682\pi$
$587$	−10.6808	−	8.96228i	−0.440845	−	0.369913i	−0.836025	+	0.548691i	$0.815126\pi$
$588$	11.8129	−	1.78889i	0.487154	−	0.0737727i
$589$	0.216689	+	1.22891i	0.00892853	+	0.0506362i
$590$	8.12014	−	6.81361i	0.334301	−	0.280512i
$591$	−12.3071	−	36.5461i	−0.506246	−	1.50331i
$592$	−7.13111	+	2.59551i	−0.293087	+	0.106675i
$593$	−41.2342			−1.69329			−0.846644	−	0.532160i	$-0.821380\pi$
$593$	−41.2342			−1.69329			−0.846644	+	0.532160i	$0.821380\pi$
$594$	−9.47058	+	21.1061i	−0.388583	+	0.865996i
$595$	−1.28835			−0.0528173
$596$	15.3097	−	5.57227i	0.627110	−	0.228249i
$597$	41.7073	+	8.40117i	1.70697	+	0.343837i
$598$	−0.516872	+	0.433707i	−0.0211365	+	0.0177356i
$599$	−0.544602	−	3.08859i	−0.0222518	−	0.126196i	0.971658	−	0.236390i	$-0.0759641\pi$
$599$	−0.544602	−	3.08859i	−0.0222518	−	0.126196i	−0.993910	+	0.110193i	$0.964853\pi$
$600$	8.24548	+	10.3248i	0.336620	+	0.421507i
$601$	−26.6855	−	22.3918i	−1.08853	−	0.913382i	−0.0919256	−	0.995766i	$-0.529302\pi$
$601$	−26.6855	−	22.3918i	−1.08853	−	0.913382i	−0.996601	+	0.0823839i	$0.973747\pi$
$602$	−1.13386	+	1.96391i	−0.0462128	+	0.0800429i
$603$	−4.93859	+	21.7768i	−0.201115	+	0.886819i
$604$	7.80897	+	13.5255i	0.317742	+	0.550346i
$605$	5.44323	−	30.8701i	0.221299	−	1.25505i
$606$	−3.67923	+	2.00691i	−0.149458	+	0.0815253i
$607$	0.726574	+	0.264451i	0.0294907	+	0.0107338i	0.356723	−	0.934210i	$-0.383894\pi$
$607$	0.726574	+	0.264451i	0.0294907	+	0.0107338i	−0.327233	+	0.944944i	$0.606116\pi$
$608$	−1.74575	−	0.635402i	−0.0707997	−	0.0257690i
$609$	2.11779	−	1.15519i	0.0858172	−	0.0468108i
$610$	−2.15651	+	12.2302i	−0.0873145	+	0.495185i
$611$	−24.1576	−	41.8422i	−0.977312	−	1.69275i
$612$	−0.752879	+	3.31983i	−0.0304333	+	0.134196i
$613$	−6.99919	+	12.1230i	−0.282695	+	0.489642i	−0.972048	−	0.234784i	$-0.924562\pi$
$613$	−6.99919	+	12.1230i	−0.282695	+	0.489642i	0.689353	+	0.724426i	$0.257895\pi$
$614$	−18.1750	−	15.2506i	−0.733483	−	0.615465i
$615$	8.36302	+	10.4720i	0.337230	+	0.422271i
$616$	−0.247003	−	1.40083i	−0.00995205	−	0.0564409i
$617$	8.97302	−	7.52926i	0.361240	−	0.303117i	−0.444045	−	0.896005i	$-0.646457\pi$
$617$	8.97302	−	7.52926i	0.361240	−	0.303117i	0.805285	+	0.592888i	$0.202012\pi$
$618$	3.38800	+	0.682450i	0.136285	+	0.0274522i
$619$	−45.1425	+	16.4305i	−1.81443	+	0.660398i	−0.818073	+	0.575114i	$0.804958\pi$
$619$	−45.1425	+	16.4305i	−1.81443	+	0.660398i	−0.996357	+	0.0852845i	$0.972820\pi$
$620$	2.38698			0.0958634
$621$	0.745465	−	0.0761639i	0.0299145	−	0.00305635i
$622$	−10.8006			−0.433065
$623$	1.51692	−	0.552114i	0.0607741	−	0.0221200i
$624$	2.58629	+	7.68003i	0.103534	+	0.307447i
$625$	−3.78956	+	3.17982i	−0.151583	+	0.127193i
$626$	−2.75948	−	15.6498i	−0.110291	−	0.625490i
$627$	−14.1643	+	2.14498i	−0.565667	+	0.0856624i
$628$	13.5065	+	11.3333i	0.538970	+	0.452249i
$629$	−4.30552	+	7.45738i	−0.171672	+	0.297345i
$630$	3.40221	+	0.165061i	0.135547	+	0.00657617i
$631$	−19.7725	−	34.2469i	−0.787130	−	1.36335i	−0.927719	−	0.373280i	$-0.878233\pi$
$631$	−19.7725	−	34.2469i	−0.787130	−	1.36335i	0.140589	−	0.990068i	$-0.455100\pi$
$632$	−2.18571	+	12.3958i	−0.0869429	+	0.493078i
$633$	4.46426	+	2.72379i	0.177438	+	0.108261i
$634$	3.03994	+	1.10645i	0.120732	+	0.0439427i
$635$	−0.531660	−	0.193508i	−0.0210983	−	0.00767915i
$636$	−0.0338162	+	1.39485i	−0.00134090	+	0.0553094i
$637$	5.60424	−	31.7832i	0.222048	−	1.25930i
$638$	9.70378	+	16.8074i	0.384176	+	0.665413i
$639$	19.3465	−	14.6967i	0.765335	−	0.581393i
$640$	−1.77684	+	3.07758i	−0.0702358	+	0.121652i
$641$	0.506596	+	0.425085i	0.0200093	+	0.0167898i	0.652737	−	0.757584i	$-0.273620\pi$
$641$	0.506596	+	0.425085i	0.0200093	+	0.0167898i	−0.632728	+	0.774374i	$0.718065\pi$
$642$	5.60336	−	14.3063i	0.221147	−	0.564626i
$643$	0.314901	+	1.78589i	0.0124185	+	0.0704288i	0.990387	−	0.138323i	$-0.0441711\pi$
$643$	0.314901	+	1.78589i	0.0124185	+	0.0704288i	−0.977969	+	0.208752i	$0.933060\pi$
$644$	−0.0352961	+	0.0296169i	−0.00139086	+	0.00116707i
$645$	28.8847	−	32.7761i	1.13733	−	1.29056i
$646$	−1.98092	+	0.720997i	−0.0779383	+	0.0283672i
$647$	4.13765			0.162668			0.0813339	−	0.996687i	$-0.474082\pi$
$647$	4.13765			0.162668			0.0813339	+	0.996687i	$0.474082\pi$
$648$	2.41349	−	8.67036i	0.0948108	−	0.340604i
$649$	13.2798			0.521278
$650$	33.5399	−	12.2075i	1.31554	−	0.478819i
$651$	0.245761	−	0.278871i	0.00963213	−	0.0109298i
$652$	−12.1648	+	10.2075i	−0.476412	+	0.399757i
$653$	4.66662	+	26.4657i	0.182619	+	1.03568i	0.928976	+	0.370139i	$0.120690\pi$
$653$	4.66662	+	26.4657i	0.182619	+	1.03568i	−0.746357	+	0.665545i	$0.768199\pi$
$654$	−1.24567	+	3.18042i	−0.0487097	+	0.124364i
$655$	−25.8231	−	21.6681i	−1.00899	−	0.846644i
$656$	−1.08865	+	1.88559i	−0.0425045	+	0.0736200i
$657$	40.3879	+	16.9589i	1.57568	+	0.661629i
$658$	−1.64967	−	2.85731i	−0.0643108	−	0.111390i
$659$	2.51054	−	14.2380i	0.0977969	−	0.554634i	−0.896058	−	0.443938i	$-0.853581\pi$
$659$	2.51054	−	14.2380i	0.0977969	−	0.554634i	0.993854	−	0.110696i	$-0.0353078\pi$
$660$	−0.664154	+	27.3950i	−0.0258522	+	1.06635i
$661$	−20.9378	−	7.62074i	−0.814387	−	0.296413i	−0.0989522	−	0.995092i	$-0.531549\pi$
$661$	−20.9378	−	7.62074i	−0.814387	−	0.296413i	−0.715435	+	0.698680i	$0.753771\pi$
$662$	16.5984	+	6.04133i	0.645116	+	0.234803i
$663$	7.84973	+	4.78939i	0.304858	+	0.186004i
$664$	−0.940067	+	5.33138i	−0.0364817	+	0.206898i
$665$	1.05467	+	1.82675i	0.0408985	+	0.0708382i
$666$	12.3252	−	19.1414i	0.477592	−	0.741715i
$667$	0.314326	−	0.544429i	0.0121708	−	0.0210804i
$668$	−10.4017	−	8.72804i	−0.402453	−	0.337698i
$669$	−17.0917	+	2.58830i	−0.660803	+	0.100069i
$670$	4.59316	+	26.0491i	0.177449	+	1.00636i
$671$	−11.9184	+	10.0007i	−0.460104	+	0.386073i
$672$	0.176612	+	0.524453i	0.00681296	+	0.0202312i
$673$	−23.4002	+	8.51699i	−0.902012	+	0.328306i	−0.751059	−	0.660235i	$-0.770457\pi$
$673$	−23.4002	+	8.51699i	−0.902012	+	0.328306i	−0.150954	+	0.988541i	$0.548234\pi$
$674$	−10.5429			−0.406096
$675$	−38.4342	−	9.70132i	−1.47933	−	0.373404i
$676$	8.89058			0.341945
$677$	−7.50239	+	2.73065i	−0.288340	+	0.104947i	−0.482141	−	0.876094i	$-0.660141\pi$
$677$	−7.50239	+	2.73065i	−0.288340	+	0.104947i	0.193801	+	0.981041i	$0.437918\pi$
$678$	−16.3489	−	3.29319i	−0.627877	−	0.126474i
$679$	−4.57053	+	3.83513i	−0.175401	+	0.147179i
$680$	0.700218	+	3.97113i	0.0268521	+	0.152286i
$681$	−22.8302	−	28.5875i	−0.874857	−	1.09547i
$682$	2.29079	+	1.92220i	0.0877187	+	0.0736048i
$683$	17.5306	−	30.3639i	0.670789	−	1.16184i	−0.306891	−	0.951745i	$-0.599289\pi$
$683$	17.5306	−	30.3639i	0.670789	−	1.16184i	0.977681	−	0.210097i	$-0.0673779\pi$
$684$	5.32348	−	1.65018i	0.203548	−	0.0630961i
$685$	−20.8057	−	36.0365i	−0.794944	−	1.37688i
$686$	0.771067	−	4.37294i	0.0294395	−	0.166960i
$687$	−35.3995	+	19.3094i	−1.35058	+	0.736701i
$688$	6.66967	+	2.42756i	0.254279	+	0.0925498i
$689$	3.54168	+	1.28907i	0.134927	+	0.0491095i
$690$	0.779254	−	0.425061i	0.0296657	−	0.0161818i
$691$	−0.344177	+	1.95193i	−0.0130931	+	0.0742548i	−0.990654	−	0.136397i	$-0.956448\pi$
$691$	−0.344177	+	1.95193i	−0.0130931	+	0.0742548i	0.977561	+	0.210652i	$0.0675587\pi$
$692$	−3.22220	−	5.58102i	−0.122490	−	0.212159i
$693$	3.13219	+	2.89816i	0.118982	+	0.110092i
$694$	−16.2523	+	28.1499i	−0.616930	+	1.06855i
$695$	−14.2927	−	11.9930i	−0.542152	−	0.454920i
$696$	−4.71171	−	5.89988i	−0.178597	−	0.223635i
$697$	0.429014	+	2.43306i	0.0162501	+	0.0921587i
$698$	−15.3747	+	12.9009i	−0.581942	+	0.488308i
$699$	45.3764	+	9.14025i	1.71629	+	0.345716i
$700$	2.29037	−	0.833627i	0.0865679	−	0.0315081i
$701$	42.8694			1.61916			0.809578	−	0.587013i	$-0.199696\pi$
$701$	42.8694			1.61916			0.809578	+	0.587013i	$0.199696\pi$
$702$	−20.1155	−	13.6532i	−0.759212	−	0.515308i
$703$	14.0984			0.531730
$704$	−4.18356	+	1.52269i	−0.157674	+	0.0573886i
$705$	20.2853	+	60.2376i	0.763990	+	2.26868i
$706$	8.45411	−	7.09384i	0.318174	−	0.266980i
$707$	0.134245	+	0.761342i	0.00504881	+	0.0286332i
$708$	−5.10820	+	0.773566i	−0.191978	+	0.0290724i
$709$	26.9016	+	22.5731i	1.01031	+	0.847752i	0.988379	−	0.152008i	$-0.0485738\pi$
$709$	26.9016	+	22.5731i	1.01031	+	0.847752i	0.0219320	+	0.999759i	$0.493018\pi$
$710$	14.3898	−	24.9239i	0.540041	−	0.935379i
$711$	−17.2736	−	33.5785i	−0.647812	−	1.25929i
$712$	−2.52624	−	4.37558i	−0.0946748	−	0.163982i
$713$	0.0168206	−	0.0953942i	0.000629935	−	0.00357254i
$714$	0.536041	+	0.327057i	0.0200608	+	0.0122398i
$715$	69.5590	+	25.3174i	2.60136	+	0.946818i
$716$	11.7577	+	4.27944i	0.439405	+	0.159930i
$717$	1.01000	−	41.6607i	0.0377193	−	1.55585i
$718$	−0.680852	+	3.86130i	−0.0254092	+	0.144103i
$719$	−7.52422	−	13.0323i	−0.280606	−	0.486024i	0.690928	−	0.722924i	$-0.257202\pi$
$719$	−7.52422	−	13.0323i	−0.280606	−	0.486024i	−0.971534	+	0.236899i	$0.923869\pi$
$720$	−1.34032	−	10.5765i	−0.0499509	−	0.394161i
$721$	0.318758	−	0.552105i	0.0118712	−	0.0205615i
$722$	−11.9109	−	9.99445i	−0.443279	−	0.371955i
$723$	−0.942147	+	2.40546i	−0.0350388	+	0.0894601i
$724$	0.0528764	+	0.299877i	0.00196513	+	0.0111448i
$725$	−25.4749	+	21.3760i	−0.946113	+	0.793883i
$726$	−10.1013	+	11.4622i	−0.374895	+	0.425403i
$727$	−13.7436	+	5.00226i	−0.509721	+	0.185523i	−0.584061	−	0.811710i	$-0.698537\pi$
$727$	−13.7436	+	5.00226i	−0.509721	+	0.185523i	0.0743399	+	0.997233i	$0.476315\pi$
$728$	1.49486			0.0554032
$729$	9.96884	+	25.0923i	0.369216	+	0.929343i
$730$	51.8884			1.92048
$731$	7.56813	−	2.75457i	0.279917	−	0.101882i
$732$	4.00196	−	4.54113i	0.147917	−	0.167845i
$733$	11.5481	−	9.69000i	0.426539	−	0.357908i	−0.404105	−	0.914713i	$-0.632417\pi$
$733$	11.5481	−	9.69000i	0.426539	−	0.357908i	0.830644	+	0.556804i	$0.187973\pi$
$734$	5.06206	+	28.7084i	0.186844	+	1.05964i
$735$	−15.4841	+	39.5336i	−0.571140	+	1.45822i
$736$	0.110473	+	0.0926974i	0.00407207	+	0.00341687i
$737$	−16.5689	+	28.6981i	−0.610322	+	1.05711i
$738$	−0.821199	−	6.48005i	−0.0302288	−	0.238534i
$739$	−23.9031	−	41.4014i	−0.879290	−	1.52297i	−0.852122	−	0.523343i	$-0.824685\pi$
$739$	−23.9031	−	41.4014i	−0.879290	−	1.52297i	−0.0271676	−	0.999631i	$-0.508649\pi$
$740$	4.68296	−	26.5584i	0.172149	−	0.976305i
$741$	0.364885	−	15.0508i	0.0134044	−	0.552904i
$742$	0.241854	+	0.0880275i	0.00887873	+	0.00323159i
$743$	43.7125	+	15.9101i	1.60366	+	0.583683i	0.980171	−	0.198152i	$-0.0634940\pi$
$743$	43.7125	+	15.9101i	1.60366	+	0.583683i	0.623485	+	0.781835i	$0.285716\pi$
$744$	−0.993143	−	0.605951i	−0.0364104	−	0.0222152i
$745$	−10.0538	+	57.0178i	−0.368342	+	2.08897i
$746$	−3.13591	−	5.43155i	−0.114814	−	0.198863i
$747$	−7.42933	−	14.4420i	−0.271825	−	0.528405i
$748$	−2.52589	+	4.37497i	−0.0923558	+	0.159965i
$749$	−2.17113	−	1.82179i	−0.0793312	−	0.0665668i
$750$	−15.9974	+	2.42258i	−0.584142	+	0.0884601i
$751$	0.306626	+	1.73897i	0.0111890	+	0.0634557i	0.989891	−	0.141830i	$-0.0452987\pi$
$751$	0.306626	+	1.73897i	0.0111890	+	0.0634557i	−0.978702	+	0.205286i	$0.934188\pi$
$752$	−7.91059	+	6.63778i	−0.288470	+	0.242055i
$753$	−8.05667	−	23.9244i	−0.293601	−	0.871854i
$754$	−19.1657	+	6.97575i	−0.697974	+	0.254042i
$755$	−55.5012			−2.01989
$756$	−1.37365	−	0.932350i	−0.0499590	−	0.0339093i
$757$	3.34143			0.121446			0.0607232	−	0.998155i	$-0.480659\pi$
$757$	3.34143			0.121446			0.0607232	+	0.998155i	$0.480659\pi$
$758$	25.3306	−	9.21957i	0.920048	−	0.334870i
$759$	1.09015	+	0.219590i	0.0395698	+	0.00797061i
$760$	5.05743	−	4.24369i	0.183452	−	0.153935i
$761$	8.29207	+	47.0267i	0.300587	+	1.70472i	0.643581	+	0.765378i	$0.277448\pi$
$761$	8.29207	+	47.0267i	0.300587	+	1.70472i	−0.342994	+	0.939338i	$0.611441\pi$
$762$	0.172083	+	0.215478i	0.00623390	+	0.00780594i
$763$	0.482660	+	0.404999i	0.0174735	+

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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.14517 + 1.29945i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.617090 + 3.49969i) q^{5} +(0.631669 - 1.61276i) q^{6} +(-0.244752 - 0.205371i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.377165 - 2.97620i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.14517 + 1.29945i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.617090 + 3.49969i) q^{5} +(0.631669 - 1.61276i) q^{6} +(-0.244752 - 0.205371i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.377165 - 2.97620i) q^{9} +(-1.77684 - 3.07758i) q^{10} +(0.773091 - 4.38442i) q^{11} +(-0.0419788 + 1.73154i) q^{12} +(4.39657 + 1.60022i) q^{13} +(0.300233 + 0.109276i) q^{14} +(-5.25437 - 3.20587i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.567354 - 0.982686i) q^{17} +(1.37234 + 2.66771i) q^{18} +(-0.928896 + 1.60890i) q^{19} +(2.72228 + 2.28426i) q^{20} +(0.547153 - 0.0828588i) q^{21} +(0.773091 + 4.38442i) q^{22} +(0.110473 - 0.0926974i) q^{23} +(-0.552775 - 1.64147i) q^{24} +(-7.16859 + 2.60915i) q^{25} -4.67874 q^{26} +(4.29935 + 2.91815i) q^{27} -0.319501 q^{28} +(4.09634 - 1.49095i) q^{29} +(6.03396 + 1.21543i) q^{30} +(0.514546 - 0.431755i) q^{31} +(0.173648 + 0.984808i) q^{32} +(4.81203 + 6.02551i) q^{33} +(0.869237 + 0.729376i) q^{34} +(0.567702 - 0.983289i) q^{35} +(-2.20199 - 2.03746i) q^{36} +(-3.79438 - 6.57207i) q^{37} +(0.322602 - 1.82957i) q^{38} +(-7.11425 + 3.88062i) q^{39} +(-3.33937 - 1.21543i) q^{40} +(-2.04599 - 0.744678i) q^{41} +(-0.485817 + 0.264999i) q^{42} +(-1.23250 + 6.98988i) q^{43} +(-2.22603 - 3.85559i) q^{44} +(10.1830 - 3.15654i) q^{45} +(-0.0721058 + 0.124891i) q^{46} +(-7.91059 - 6.63778i) q^{47} +(1.08086 + 1.35342i) q^{48} +(-1.19781 - 6.79312i) q^{49} +(5.84389 - 4.90360i) q^{50} +(1.92667 + 0.388093i) q^{51} +(4.39657 - 1.60022i) q^{52} +0.805554 q^{53} +(-5.03813 - 1.27170i) q^{54} +15.8212 q^{55} +(0.300233 - 0.109276i) q^{56} +(-1.02694 - 3.04952i) q^{57} +(-3.33937 + 2.80206i) q^{58} +(0.517966 + 2.93753i) q^{59} +(-6.08577 + 0.921605i) q^{60} +(-2.67705 - 2.24631i) q^{61} +(-0.335846 + 0.581702i) q^{62} +(-0.518913 + 0.805889i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.88720 + 16.3741i) q^{65} +(-6.58267 - 4.01631i) q^{66} +(-6.99437 - 2.54574i) q^{67} +(-1.06628 - 0.388093i) q^{68} +(-0.00605383 + 0.249708i) q^{69} +(-0.197161 + 1.11816i) q^{70} +(4.04928 + 7.01356i) q^{71} +(2.76604 + 1.16146i) q^{72} +(-7.30065 + 12.6451i) q^{73} +(5.81333 + 4.87797i) q^{74} +(4.81879 - 12.3032i) q^{75} +(0.322602 + 1.82957i) q^{76} +(-1.08965 + 0.914324i) q^{77} +(5.35796 - 6.07981i) q^{78} +(11.8279 - 4.30501i) q^{79} +3.55368 q^{80} +(-8.71549 + 2.24503i) q^{81} +2.17729 q^{82} +(5.08715 - 1.85157i) q^{83} +(0.365883 - 0.415177i) q^{84} +(3.08899 - 2.59197i) q^{85} +(-1.23250 - 6.98988i) q^{86} +(-2.75360 + 7.03040i) q^{87} +(3.41047 + 2.86173i) q^{88} +(-2.52624 + 4.37558i) q^{89} +(-8.48932 + 6.44898i) q^{90} +(-0.747430 - 1.29459i) q^{91} +(0.0250421 - 0.142021i) q^{92} +(-0.0281968 + 1.16306i) q^{93} +(9.70378 + 3.53189i) q^{94} +(-6.20385 - 2.25802i) q^{95} +(-1.47857 - 0.902126i) q^{96} +(3.24273 - 18.3904i) q^{97} +(3.44896 + 5.97377i) q^{98} +(-13.3405 - 0.647222i) 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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