LMFDB - Embedded newform 54.2.e.b.43.2

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			43.2
Root			$0.500000 + 0.168222i$ of defining polynomial
Character	$\chi$	$=$	54.43
Dual form			54.2.e.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.247510 - 1.71428i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96209 - 0.714144i) q^{5} +(1.29152 - 1.15411i) q^{6} +(-0.696712 + 3.95125i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.87748 - 0.848600i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.247510 - 1.71428i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96209 - 0.714144i) q^{5} +(1.29152 - 1.15411i) q^{6} +(-0.696712 + 3.95125i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.87748 - 0.848600i) q^{9} +(-1.04401 - 1.80828i) q^{10} +(-0.199635 + 0.0726611i) q^{11} +(1.73121 - 0.0539310i) q^{12} +(3.98269 - 3.34187i) q^{13} +(-3.07353 + 2.57900i) q^{14} +(-1.70988 + 3.18681i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.89276 - 3.27836i) q^{17} +(-1.65881 - 2.49967i) q^{18} +(0.636405 - 1.10229i) q^{19} +(0.362580 - 2.05630i) q^{20} +(6.60109 + 2.17233i) q^{21} +(-0.199635 - 0.0726611i) q^{22} +(0.144031 + 0.816841i) q^{23} +(1.36085 + 1.07149i) q^{24} +(-0.490411 - 0.411503i) q^{25} +5.19903 q^{26} +(-2.16694 + 4.72275i) q^{27} -4.01220 q^{28} +(7.05621 + 5.92087i) q^{29} +(-3.35828 + 1.34215i) q^{30} +(0.614003 + 3.48219i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.0751495 + 0.360213i) q^{33} +(0.657349 - 3.72801i) q^{34} +(4.18878 - 7.25517i) q^{35} +(0.336039 - 2.98112i) q^{36} +(-1.77730 - 3.07838i) q^{37} +(1.19605 - 0.435326i) q^{38} +(-4.74313 - 7.65457i) q^{39} +(1.59951 - 1.34215i) q^{40} +(2.09850 - 1.76085i) q^{41} +(3.66038 + 5.90720i) q^{42} +(-6.48062 + 2.35875i) q^{43} +(-0.106223 - 0.183984i) q^{44} +(5.03986 + 3.71997i) q^{45} +(-0.414721 + 0.718318i) q^{46} +(-0.221796 + 1.25787i) q^{47} +(0.353733 + 1.69554i) q^{48} +(-8.54912 - 3.11163i) q^{49} +(-0.111167 - 0.630460i) q^{50} +(-6.08849 + 2.43329i) q^{51} +(3.98269 + 3.34187i) q^{52} -11.2992 q^{53} +(-4.69570 + 2.22496i) q^{54} +0.443592 q^{55} +(-3.07353 - 2.57900i) q^{56} +(-1.73210 - 1.36380i) q^{57} +(1.59951 + 9.07129i) q^{58} +(8.04363 + 2.92764i) q^{59} +(-3.43531 - 1.13052i) q^{60} +(0.492064 - 2.79063i) q^{61} +(-1.76795 + 3.06218i) q^{62} +(5.35781 - 10.7784i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-10.2010 + 3.71285i) q^{65} +(-0.173973 + 0.324244i) q^{66} +(7.47702 - 6.27396i) q^{67} +(2.89988 - 2.43329i) q^{68} +(1.43594 - 0.0447327i) q^{69} +(7.87232 - 2.86529i) q^{70} +(5.86207 + 10.1534i) q^{71} +(2.17365 - 2.06767i) q^{72} +(-0.375162 + 0.649800i) q^{73} +(0.617250 - 3.50060i) q^{74} +(-0.826812 + 0.738848i) q^{75} +(1.19605 + 0.435326i) q^{76} +(-0.148014 - 0.839430i) q^{77} +(1.28681 - 8.91256i) q^{78} +(-1.81383 - 1.52198i) q^{79} +2.08802 q^{80} +(7.55976 + 4.88366i) q^{81} +2.73940 q^{82} +(-8.73328 - 7.32809i) q^{83} +(-0.993061 + 6.87802i) q^{84} +(1.37256 + 7.78415i) q^{85} +(-6.48062 - 2.35875i) q^{86} +(11.8965 - 10.6308i) q^{87} +(0.0368910 - 0.209219i) q^{88} +(-2.69813 + 4.67329i) q^{89} +(1.46961 + 6.08922i) q^{90} +(10.4298 + 18.0649i) q^{91} +(-0.779421 + 0.283686i) q^{92} +(6.12140 - 0.190695i) q^{93} +(-0.978448 + 0.821016i) q^{94} +(-2.03588 + 1.70830i) q^{95} +(-0.818900 + 1.52624i) q^{96} +(11.8055 - 4.29685i) q^{97} +(-4.54889 - 7.87892i) q^{98} +(0.636104 - 0.0396706i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.247510	−	1.71428i	0.142900	−	0.989737i
$3$	0.247510	−	1.71428i	0.142900	−	0.989737i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−1.96209	−	0.714144i	−0.877475	−	0.319375i	−0.136285	−	0.990670i	$-0.543516\pi$
$5$	−1.96209	−	0.714144i	−0.877475	−	0.319375i	−0.741190	+	0.671295i	$0.765738\pi$
$6$	1.29152	−	1.15411i	0.527260	−	0.471165i
$7$	−0.696712	+	3.95125i	−0.263332	+	1.49343i	0.510410	+	0.859931i	$0.329494\pi$
$7$	−0.696712	+	3.95125i	−0.263332	+	1.49343i	−0.773742	+	0.633501i	$0.781617\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.87748	−	0.848600i	−0.959159	−	0.282867i
$10$	−1.04401	−	1.80828i	−0.330144	−	0.571827i
$11$	−0.199635	+	0.0726611i	−0.0601921	+	0.0219081i	−0.371941	−	0.928256i	$-0.621308\pi$
$11$	−0.199635	+	0.0726611i	−0.0601921	+	0.0219081i	0.311749	+	0.950165i	$0.399085\pi$
$12$	1.73121	−	0.0539310i	0.499758	−	0.0155685i
$13$	3.98269	−	3.34187i	1.10460	−	0.926868i	0.106873	−	0.994273i	$-0.465916\pi$
$13$	3.98269	−	3.34187i	1.10460	−	0.926868i	0.997726	+	0.0674046i	$0.0214718\pi$
$14$	−3.07353	+	2.57900i	−0.821435	+	0.689266i
$15$	−1.70988	+	3.18681i	−0.441488	+	0.822831i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.89276	−	3.27836i	−0.459062	−	0.795119i	0.539850	−	0.841762i	$-0.318481\pi$
$17$	−1.89276	−	3.27836i	−0.459062	−	0.795119i	−0.998912	+	0.0466426i	$0.985148\pi$
$18$	−1.65881	−	2.49967i	−0.390984	−	0.589178i
$19$	0.636405	−	1.10229i	0.146001	−	0.252882i	−0.783745	−	0.621083i	$-0.786693\pi$
$19$	0.636405	−	1.10229i	0.146001	−	0.252882i	0.929746	+	0.368201i	$0.120026\pi$
$20$	0.362580	−	2.05630i	0.0810754	−	0.459802i
$21$	6.60109	+	2.17233i	1.44048	+	0.474041i
$22$	−0.199635	−	0.0726611i	−0.0425622	−	0.0154914i
$23$	0.144031	+	0.816841i	0.0300326	+	0.170323i	0.996135	−	0.0878361i	$-0.0279952\pi$
$23$	0.144031	+	0.816841i	0.0300326	+	0.170323i	−0.966102	+	0.258159i	$0.916884\pi$
$24$	1.36085	+	1.07149i	0.277782	+	0.218716i
$25$	−0.490411	−	0.411503i	−0.0980821	−	0.0823007i
$26$	5.19903			1.01961
$27$	−2.16694	+	4.72275i	−0.417028	+	0.908894i
$28$	−4.01220			−0.758235
$29$	7.05621	+	5.92087i	1.31031	+	1.09948i	0.988265	+	0.152752i	$0.0488134\pi$
$29$	7.05621	+	5.92087i	1.31031	+	1.09948i	0.322041	+	0.946726i	$0.395631\pi$
$30$	−3.35828	+	1.34215i	−0.613136	+	0.245042i
$31$	0.614003	+	3.48219i	0.110278	+	0.625419i	0.988980	+	0.148048i	$0.0472991\pi$
$31$	0.614003	+	3.48219i	0.110278	+	0.625419i	−0.878702	+	0.477371i	$0.841590\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.0751495	+	0.360213i	0.0130818	+	0.0627050i
$34$	0.657349	−	3.72801i	0.112734	−	0.639349i
$35$	4.18878	−	7.25517i	0.708032	−	1.22635i
$36$	0.336039	−	2.98112i	0.0560066	−	0.496853i
$37$	−1.77730	−	3.07838i	−0.292187	−	0.506082i	0.682140	−	0.731222i	$-0.261049\pi$
$37$	−1.77730	−	3.07838i	−0.292187	−	0.506082i	−0.974326	+	0.225140i	$0.927716\pi$
$38$	1.19605	−	0.435326i	0.194025	−	0.0706193i
$39$	−4.74313	−	7.65457i	−0.759509	−	1.22571i
$40$	1.59951	−	1.34215i	0.252905	−	0.212213i
$41$	2.09850	−	1.76085i	0.327730	−	0.274998i	−0.464044	−	0.885812i	$-0.653602\pi$
$41$	2.09850	−	1.76085i	0.327730	−	0.274998i	0.791774	+	0.610814i	$0.209158\pi$
$42$	3.66038	+	5.90720i	0.564809	+	0.911500i
$43$	−6.48062	+	2.35875i	−0.988286	+	0.359707i	−0.785056	−	0.619425i	$-0.787366\pi$
$43$	−6.48062	+	2.35875i	−0.988286	+	0.359707i	−0.203229	+	0.979131i	$0.565144\pi$
$44$	−0.106223	−	0.183984i	−0.0160138	−	0.0277367i
$45$	5.03986	+	3.71997i	0.751298	+	0.554540i
$46$	−0.414721	+	0.718318i	−0.0611473	+	0.105910i
$47$	−0.221796	+	1.25787i	−0.0323523	+	0.183479i	−0.996702	−	0.0811536i	$-0.974140\pi$
$47$	−0.221796	+	1.25787i	−0.0323523	+	0.183479i	0.964349	+	0.264633i	$0.0852507\pi$
$48$	0.353733	+	1.69554i	0.0510570	+	0.244731i
$49$	−8.54912	−	3.11163i	−1.22130	−	0.444518i
$50$	−0.111167	−	0.630460i	−0.0157214	−	0.0891605i
$51$	−6.08849	+	2.43329i	−0.852559	+	0.340728i
$52$	3.98269	+	3.34187i	0.552299	+	0.463434i
$53$	−11.2992			−1.55207			−0.776036	−	0.630689i	$-0.782772\pi$
$53$	−11.2992			−1.55207			−0.776036	+	0.630689i	$0.782772\pi$
$54$	−4.69570	+	2.22496i	−0.639003	+	0.302778i
$55$	0.443592			0.0598140
$56$	−3.07353	−	2.57900i	−0.410717	−	0.344633i
$57$	−1.73210	−	1.36380i	−0.229423	−	0.180640i
$58$	1.59951	+	9.07129i	0.210026	+	1.19112i
$59$	8.04363	+	2.92764i	1.04719	+	0.381147i	0.807602	−	0.589728i	$-0.200765\pi$
$59$	8.04363	+	2.92764i	1.04719	+	0.381147i	0.239589	+	0.970874i	$0.422987\pi$
$60$	−3.43531	−	1.13052i	−0.443497	−	0.145949i
$61$	0.492064	−	2.79063i	0.0630023	−	0.357304i	−0.936967	−	0.349419i	$-0.886379\pi$
$61$	0.492064	−	2.79063i	0.0630023	−	0.357304i	0.999969	−	0.00788485i	$-0.00250985\pi$
$62$	−1.76795	+	3.06218i	−0.224530	+	0.388898i
$63$	5.35781	−	10.7784i	0.675020	−	1.35795i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−10.2010	+	3.71285i	−1.26528	+	0.460523i
$66$	−0.173973	+	0.324244i	−0.0214145	+	0.0399117i
$67$	7.47702	−	6.27396i	0.913463	−	0.766487i	−0.0593114	−	0.998240i	$-0.518890\pi$
$67$	7.47702	−	6.27396i	0.913463	−	0.766487i	0.972775	+	0.231753i	$0.0744460\pi$
$68$	2.89988	−	2.43329i	0.351662	−	0.295079i
$69$	1.43594	−	0.0447327i	0.172867	−	0.00538518i
$70$	7.87232	−	2.86529i	0.940923	−	0.342468i
$71$	5.86207	+	10.1534i	0.695700	+	1.20499i	0.969944	+	0.243327i	$0.0782390\pi$
$71$	5.86207	+	10.1534i	0.695700	+	1.20499i	−0.274244	+	0.961660i	$0.588428\pi$
$72$	2.17365	−	2.06767i	0.256167	−	0.243677i
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	−0.887145	−	0.461491i	$-0.847315\pi$
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	0.843235	+	0.537544i	$0.180648\pi$
$74$	0.617250	−	3.50060i	0.0717539	−	0.406937i
$75$	−0.826812	+	0.738848i	−0.0954720	+	0.0853148i
$76$	1.19605	+	0.435326i	0.137196	+	0.0499354i
$77$	−0.148014	−	0.839430i	−0.0168678	−	0.0956620i
$78$	1.28681	−	8.91256i	0.145703	−	1.00915i
$79$	−1.81383	−	1.52198i	−0.204071	−	0.171236i	0.535024	−	0.844837i	$-0.320302\pi$
$79$	−1.81383	−	1.52198i	−0.204071	−	0.171236i	−0.739096	+	0.673600i	$0.764747\pi$
$80$	2.08802			0.233447
$81$	7.55976	+	4.88366i	0.839973	+	0.542628i
$82$	2.73940			0.302516
$83$	−8.73328	−	7.32809i	−0.958602	−	0.804363i	0.0221230	−	0.999755i	$-0.492957\pi$
$83$	−8.73328	−	7.32809i	−0.958602	−	0.804363i	−0.980725	+	0.195393i	$0.937402\pi$
$84$	−0.993061	+	6.87802i	−0.108352	+	0.750454i
$85$	1.37256	+	7.78415i	0.148875	+	0.844310i
$86$	−6.48062	−	2.35875i	−0.698823	−	0.254351i
$87$	11.8965	−	10.6308i	1.27544	−	1.13974i
$88$	0.0368910	−	0.209219i	0.00393259	−	0.0223028i
$89$	−2.69813	+	4.67329i	−0.286001	+	0.495368i	−0.972851	−	0.231431i	$-0.925659\pi$
$89$	−2.69813	+	4.67329i	−0.286001	+	0.495368i	0.686851	+	0.726799i	$0.258993\pi$
$90$	1.46961	+	6.08922i	0.154910	+	0.641860i
$91$	10.4298	+	18.0649i	1.09334	+	1.89372i
$92$	−0.779421	+	0.283686i	−0.0812602	+	0.0295763i
$93$	6.12140	−	0.190695i	0.634759	−	0.0197741i
$94$	−0.978448	+	0.821016i	−0.100919	+	0.0846813i
$95$	−2.03588	+	1.70830i	−0.208876	+	0.175268i
$96$	−0.818900	+	1.52624i	−0.0835786	+	0.155771i
$97$	11.8055	−	4.29685i	1.19867	−	0.436279i	0.335909	−	0.941895i	$-0.390957\pi$
$97$	11.8055	−	4.29685i	1.19867	−	0.436279i	0.862759	+	0.505615i	$0.168734\pi$
$98$	−4.54889	−	7.87892i	−0.459508	−	0.795891i
$99$	0.636104	−	0.0396706i	0.0639309	−	0.00398705i
$100$	0.320093	−	0.554417i	0.0320093	−	0.0554417i
$101$	−0.502628	+	2.85055i	−0.0500134	+	0.283640i	−0.999549	−	0.0300181i	$-0.990443\pi$
$101$	−0.502628	+	2.85055i	−0.0500134	+	0.283640i	0.949536	+	0.313658i	$0.101555\pi$
$102$	−6.22814	−	2.04960i	−0.616678	−	0.202940i
$103$	−15.6835	−	5.70832i	−1.54534	−	0.562458i	−0.578022	−	0.816021i	$-0.696175\pi$
$103$	−15.6835	−	5.70832i	−1.54534	−	0.562458i	−0.967319	+	0.253564i	$0.918397\pi$
$104$	0.902802	+	5.12004i	0.0885270	+	0.502061i
$105$	−11.4006	−	8.97644i	−1.11258	−	0.876011i
$106$	−8.65573	−	7.26302i	−0.840719	−	0.705447i
$107$	0.321371			0.0310681			0.0155341	−	0.999879i	$-0.495055\pi$
$107$	0.321371			0.0310681			0.0155341	+	0.999879i	$0.495055\pi$
$108$	−5.02729	−	1.31392i	−0.483751	−	0.126432i
$109$	0.568378			0.0544407			0.0272204	−	0.999629i	$-0.491334\pi$
$109$	0.568378			0.0544407			0.0272204	+	0.999629i	$0.491334\pi$
$110$	0.339811	+	0.285136i	0.0323998	+	0.0271866i
$111$	−5.71708	+	2.28485i	−0.542642	+	0.216869i
$112$	−0.696712	−	3.95125i	−0.0658331	−	0.373358i
$113$	1.27781	+	0.465084i	0.120206	+	0.0437514i	0.401423	−	0.915893i	$-0.368516\pi$
$113$	1.27781	+	0.465084i	0.120206	+	0.0437514i	−0.281217	+	0.959644i	$0.590738\pi$
$114$	−0.450235	−	2.15811i	−0.0421684	−	0.202125i
$115$	0.300739	−	1.70558i	0.0280441	−	0.159046i
$116$	−4.60562	+	7.97716i	−0.427621	+	0.740661i
$117$	−14.2960	+	6.23645i	−1.32167	+	0.576560i
$118$	4.27993	+	7.41305i	0.393999	+	0.682427i
$119$	14.2723	−	5.19470i	1.30834	−	0.476198i
$120$	−1.90492	−	3.07420i	−0.173895	−	0.280635i
$121$	−8.39191	+	7.04165i	−0.762901	+	0.640150i
$122$	2.17073	−	1.82146i	0.196528	−	0.164907i
$123$	−2.49918	−	4.03323i	−0.225344	−	0.363664i
$124$	−3.32266	+	1.20935i	−0.298384	+	0.108603i
$125$	5.88840	+	10.1990i	0.526675	+	0.912227i
$126$	11.0325	−	4.81281i	0.982857	−	0.428759i
$127$	−0.902007	+	1.56232i	−0.0800402	+	0.138634i	−0.903267	−	0.429079i	$-0.858838\pi$
$127$	−0.902007	+	1.56232i	−0.0800402	+	0.138634i	0.823227	+	0.567713i	$0.192172\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	2.43953	+	11.6934i	0.214789	+	1.02954i
$130$	−10.2010	−	3.71285i	−0.894685	−	0.325639i
$131$	−1.68689	−	9.56684i	−0.147384	−	0.835859i	−0.965422	−	0.260694i	$-0.916049\pi$
$131$	−1.68689	−	9.56684i	−0.147384	−	0.835859i	0.818037	−	0.575165i	$-0.195062\pi$
$132$	−0.341691	+	0.136558i	−0.0297404	+	0.0118859i
$133$	3.91201	+	3.28257i	0.339215	+	0.284635i
$134$	9.76056			0.843184
$135$	7.62446	−	7.71898i	0.656209	−	0.664344i
$136$	3.78552			0.324606
$137$	−6.94643	−	5.82875i	−0.593474	−	0.497984i	0.295867	−	0.955229i	$-0.404392\pi$
$137$	−6.94643	−	5.82875i	−0.593474	−	0.497984i	−0.889340	+	0.457246i	$0.848836\pi$
$138$	1.12875	+	0.888737i	0.0960853	+	0.0756543i
$139$	−1.74358	−	9.88833i	−0.147888	−	0.838717i	−0.965002	−	0.262241i	$-0.915538\pi$
$139$	−1.74358	−	9.88833i	−0.147888	−	0.838717i	0.817114	−	0.576476i	$-0.195573\pi$
$140$	7.87232	+	2.86529i	0.665333	+	0.242161i
$141$	2.10144	+	0.691555i	0.176973	+	0.0582394i
$142$	−2.03588	+	11.5460i	−0.170847	+	0.968921i
$143$	−0.552258	+	0.956539i	−0.0461822	+	0.0799898i
$144$	2.99418	−	0.186732i	0.249515	−	0.0155610i
$145$	−9.61660	−	16.6564i	−0.798615	−	1.38324i
$146$	−0.705075	+	0.256626i	−0.0583524	+	0.0212385i
$147$	−7.45018	+	13.8854i	−0.614480	+	1.14525i
$148$	2.72298	−	2.28485i	0.223828	−	0.187814i
$149$	12.1360	−	10.1833i	0.994221	−	0.834250i	0.00804728	−	0.999968i	$-0.497438\pi$
$149$	12.1360	−	10.1833i	0.994221	−	0.834250i	0.986173	+	0.165718i	$0.0529940\pi$
$150$	−1.10830	+	0.0345259i	−0.0904920	+	0.00281903i
$151$	−4.98746	+	1.81529i	−0.405874	+	0.147726i	−0.536886	−	0.843655i	$-0.680400\pi$
$151$	−4.98746	+	1.81529i	−0.405874	+	0.147726i	0.131012	+	0.991381i	$0.458177\pi$
$152$	0.636405	+	1.10229i	0.0516192	+	0.0894071i
$153$	2.66436	+	11.0396i	0.215401	+	0.892499i
$154$	0.426190	−	0.738183i	0.0343434	−	0.0594845i
$155$	1.28205	−	7.27086i	0.102977	−	0.584010i
$156$	6.71464	−	6.00027i	0.537601	−	0.480406i
$157$	10.8225	+	3.93906i	0.863727	+	0.314371i	0.735624	−	0.677390i	$-0.236889\pi$
$157$	10.8225	+	3.93906i	0.863727	+	0.314371i	0.128103	+	0.991761i	$0.459111\pi$
$158$	−0.411161	−	2.33181i	−0.0327102	−	0.185509i
$159$	−2.79668	+	19.3700i	−0.221791	+	1.53614i
$160$	1.59951	+	1.34215i	0.126453	+	0.106106i
$161$	−3.32789			−0.262275
$162$	2.65195	+	8.60041i	0.208357	+	0.675712i
$163$	7.66336			0.600241			0.300120	−	0.953901i	$-0.402973\pi$
$163$	7.66336			0.600241			0.300120	+	0.953901i	$0.402973\pi$
$164$	2.09850	+	1.76085i	0.163865	+	0.137499i
$165$	0.109794	−	0.760439i	0.00854741	−	0.0592001i
$166$	−1.97967	−	11.2273i	−0.153653	−	0.871407i
$167$	−5.74151	−	2.08974i	−0.444292	−	0.161709i	0.110180	−	0.993912i	$-0.464857\pi$
$167$	−5.74151	−	2.08974i	−0.444292	−	0.161709i	−0.554472	+	0.832203i	$0.687080\pi$
$168$	−5.18184	+	4.63054i	−0.399787	+	0.357254i
$169$	2.43626	−	13.8167i	0.187405	−	1.06283i
$170$	−3.95212	+	6.84527i	−0.303114	+	0.525008i
$171$	−2.76664	+	2.63175i	−0.211570	+	0.201255i
$172$	−3.44827	−	5.97257i	−0.262928	−	0.455404i
$173$	10.6218	−	3.86602i	0.807561	−	0.293928i	0.0949449	−	0.995483i	$-0.469732\pi$
$173$	10.6218	−	3.86602i	0.807561	−	0.293928i	0.712616	+	0.701554i	$0.247510\pi$
$174$	15.9466	−	0.496771i	1.20891	−	0.0376601i
$175$	1.96763	−	1.65104i	0.148739	−	0.124807i
$176$	0.162744	−	0.136558i	0.0122673	−	0.0102935i
$177$	7.00966	−	13.0644i	0.526879	−	0.981979i
$178$	−5.07082	+	1.84563i	−0.380074	+	0.138336i
$179$	−3.46495	−	6.00147i	−0.258982	−	0.448571i	0.706987	−	0.707226i	$-0.250054\pi$
$179$	−3.46495	−	6.00147i	−0.258982	−	0.448571i	−0.965970	+	0.258656i	$0.916721\pi$
$180$	−2.78829	+	5.60926i	−0.207827	+	0.418089i
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	−0.916935	−	0.399036i	$-0.869345\pi$
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	0.804043	+	0.594572i	$0.202678\pi$
$182$	−3.62223	+	20.5427i	−0.268497	+	1.52272i
$183$	−4.66212	−	1.53424i	−0.344634	−	0.113414i
$184$	−0.779421	−	0.283686i	−0.0574597	−	0.0209136i
$185$	1.28883	+	7.30931i	0.0947566	+	0.537391i
$186$	4.81184	+	3.78868i	0.352821	+	0.277799i
$187$	0.616070	+	0.516944i	0.0450515	+	0.0378027i
$188$	−1.27727			−0.0931547
$189$	−17.1510	−	11.8525i	−1.24755	−	0.862144i
$190$	−2.65765			−0.192806
$191$	−3.90467	−	3.27640i	−0.282532	−	0.237072i	0.490498	−	0.871443i	$-0.336815\pi$
$191$	−3.90467	−	3.27640i	−0.282532	−	0.237072i	−0.773029	+	0.634370i	$0.781259\pi$
$192$	−1.60836	+	0.642788i	−0.116073	+	0.0463892i
$193$	3.27644	+	18.5816i	0.235843	+	1.33753i	0.840830	+	0.541299i	$0.182067\pi$
$193$	3.27644	+	18.5816i	0.235843	+	1.33753i	−0.604987	+	0.796235i	$0.706822\pi$
$194$	11.8055	+	4.29685i	0.847586	+	0.308496i
$195$	3.84001	+	18.4063i	0.274989	+	1.31810i
$196$	1.57981	−	8.95957i	0.112844	−	0.639969i
$197$	10.0220	−	17.3586i	0.714036	−	1.23675i	−0.249294	−	0.968428i	$-0.580199\pi$
$197$	10.0220	−	17.3586i	0.714036	−	1.23675i	0.963330	−	0.268319i	$-0.0864682\pi$
$198$	0.512784	+	0.378491i	0.0364420	+	0.0268982i
$199$	−2.75106	−	4.76498i	−0.195018	−	0.337780i	0.751889	−	0.659290i	$-0.229143\pi$
$199$	−2.75106	−	4.76498i	−0.195018	−	0.337780i	−0.946906	+	0.321510i	$0.895810\pi$
$200$	0.601578	−	0.218956i	0.0425380	−	0.0154826i
$201$	−8.90466	−	14.3705i	−0.628087	−	1.01362i
$202$	−2.21733	+	1.86056i	−0.156011	+	0.130909i
$203$	−28.3110	+	23.7557i	−1.98704	+	1.66733i
$204$	−3.45357	−	5.57345i	−0.241799	−	0.390220i
$205$	−5.37495	+	1.95632i	−0.375403	+	0.136635i
$206$	−8.34501	−	14.4540i	−0.581425	−	1.00706i
$207$	0.278725	−	2.47267i	0.0193727	−	0.171862i
$208$	−2.59951	+	4.50249i	−0.180244	+	0.312191i
$209$	−0.0469552	+	0.266296i	−0.00324796	+	0.0184201i
$210$	−2.96342	−	14.2045i	−0.204495	−	0.980205i
$211$	23.6287	+	8.60014i	1.62667	+	0.592058i	0.984636	−	0.174621i	$-0.0558699\pi$
$211$	23.6287	+	8.60014i	1.62667	+	0.592058i	0.642031	+	0.766679i	$0.278092\pi$
$212$	−1.96209	−	11.1276i	−0.134757	−	0.764246i
$213$	18.8566	−	7.53613i	1.29204	−	0.516367i
$214$	0.246185	+	0.206573i	0.0168288	+	0.0141211i
$215$	14.4001			0.982077
$216$	−3.00655	−	4.23800i	−0.204570	−	0.288359i
$217$	−14.1868			−0.963061
$218$	0.435403	+	0.365346i	0.0294892	+	0.0247444i
$219$	1.02108	+	0.803963i	0.0689982	+	0.0543268i
$220$	0.0770290	+	0.436853i	0.00519329	+	0.0294526i
$221$	−18.4941	−	6.73131i	−1.24405	−	0.452797i
$222$	−5.84822	−	1.92457i	−0.392507	−	0.129169i
$223$	−0.651596	+	3.69539i	−0.0436341	+	0.247461i	−0.998821	−	0.0485415i	$-0.984543\pi$
$223$	−0.651596	+	3.69539i	−0.0436341	+	0.247461i	0.955187	+	0.296003i	$0.0956538\pi$
$224$	2.00610	−	3.47467i	0.134038	−	0.232161i
$225$	1.06194	+	1.60025i	0.0707963	+	0.106684i
$226$	0.679907	+	1.17763i	0.0452267	+	0.0783350i
$227$	−17.5983	+	6.40524i	−1.16804	+	0.425131i	−0.851962	−	0.523603i	$-0.824588\pi$
$227$	−17.5983	+	6.40524i	−1.16804	+	0.425131i	−0.316076	+	0.948734i	$0.602365\pi$
$228$	1.04230	−	1.94261i	0.0690282	−	0.128653i
$229$	−3.17397	+	2.66328i	−0.209742	+	0.175994i	−0.741607	−	0.670835i	$-0.765936\pi$
$229$	−3.17397	+	2.66328i	−0.209742	+	0.175994i	0.531865	+	0.846829i	$0.321491\pi$
$230$	1.32670	−	1.11324i	0.0874803	−	0.0734047i
$231$	−1.47565	+	0.0459697i	−0.0970906	+	0.00302459i
$232$	−8.65573	+	3.15043i	−0.568276	+	0.206836i
$233$	0.958556	+	1.66027i	0.0627971	+	0.108768i	0.895715	−	0.444629i	$-0.146665\pi$
$233$	0.958556	+	1.66027i	0.0627971	+	0.108768i	−0.832918	+	0.553397i	$0.813331\pi$
$234$	−14.9601	−	4.41190i	−0.977971	−	0.288415i
$235$	1.33348	−	2.30966i	0.0869869	−	0.150666i
$236$	−1.48640	+	8.42981i	−0.0967566	+	0.548734i
$237$	−3.05803	+	2.73269i	−0.198641	+	0.177507i
$238$	14.2723	+	5.19470i	0.925138	+	0.336723i
$239$	4.20216	+	23.8316i	0.271815	+	1.54154i	0.748900	+	0.662683i	$0.230582\pi$
$239$	4.20216	+	23.8316i	0.271815	+	1.54154i	−0.477085	+	0.878857i	$0.658307\pi$
$240$	0.516805	−	3.57944i	0.0333596	−	0.231052i
$241$	10.1156	+	8.48797i	0.651601	+	0.546758i	0.907556	−	0.419931i	$-0.137946\pi$
$241$	10.1156	+	8.48797i	0.651601	+	0.546758i	−0.255955	+	0.966689i	$0.582390\pi$
$242$	−10.9549			−0.704205
$243$	10.2430	−	11.7507i	0.657092	−	0.753811i
$244$	2.83368			0.181408
$245$	14.5520	+	12.2106i	0.929695	+	0.780107i
$246$	0.678028	−	4.69608i	0.0432295	−	0.299411i
$247$	−1.14909	−	6.51684i	−0.0731151	−	0.414656i
$248$	−3.32266	−	1.20935i	−0.210989	−	0.0767938i
$249$	−14.7239	+	13.1575i	−0.933092	+	0.833821i
$250$	−2.04502	+	11.5979i	−0.129338	+	0.733515i
$251$	4.32994	−	7.49967i	0.273303	−	0.473375i	−0.696402	−	0.717652i	$-0.745217\pi$
$251$	4.32994	−	7.49967i	0.273303	−	0.473375i	0.969706	+	0.244276i	$0.0785504\pi$
$252$	11.5450	+	3.40476i	0.727269	+	0.214480i
$253$	−0.0881062	−	0.152604i	−0.00553919	−	0.00959415i
$254$	−1.69522	+	0.617009i	−0.106368	+	0.0387146i
$255$	13.6839	−	0.426284i	0.856919	−	0.0266949i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	16.7233	−	14.0326i	1.04317	−	0.875326i	0.0508142	−	0.998708i	$-0.483818\pi$
$257$	16.7233	−	14.0326i	1.04317	−	0.875326i	0.992359	+	0.123382i	$0.0393739\pi$
$258$	−5.64757	+	10.5258i	−0.351602	+	0.655305i
$259$	13.4017	−	4.87782i	0.832741	−	0.303093i
$260$	−5.42783	−	9.40127i	−0.336620	−	0.583042i
$261$	−15.2796	−	23.0251i	−0.945786	−	1.42522i
$262$	4.85721	−	8.41294i	0.300080	−	0.519753i
$263$	−0.987629	+	5.60112i	−0.0608998	+	0.345380i	0.939099	+	0.343648i	$0.111663\pi$
$263$	−0.987629	+	5.60112i	−0.0608998	+	0.345380i	−0.999998	+	0.00173240i	$0.999449\pi$
$264$	−0.349528	−	0.115025i	−0.0215120	−	0.00707931i
$265$	22.1702	+	8.06929i	1.36190	+	0.495692i
$266$	0.886782	+	5.02919i	0.0543721	+	0.308359i
$267$	7.34349	+	5.78201i	0.449414	+	0.353854i
$268$	7.47702	+	6.27396i	0.456732	+	0.383243i
$269$	−22.7662			−1.38808			−0.694041	−	0.719936i	$-0.744171\pi$
$269$	−22.7662			−1.38808			−0.694041	+	0.719936i	$0.744171\pi$
$270$	10.8023	−	1.01217i	0.657409	−	0.0615987i
$271$	−19.8340			−1.20483			−0.602414	−	0.798184i	$-0.705794\pi$
$271$	−19.8340			−1.20483			−0.602414	+	0.798184i	$0.705794\pi$
$272$	2.89988	+	2.43329i	0.175831	+	0.147540i
$273$	33.5497	−	13.4083i	2.03052	−	0.811505i
$274$	−1.57463	−	8.93016i	−0.0951268	−	0.539491i
$275$	0.127803	+	0.0465166i	0.00770683	+	0.00280506i
$276$	0.293401	+	1.40636i	0.0176607	+	0.0846527i
$277$	−4.19132	+	23.7701i	−0.251832	+	1.42821i	0.552244	+	0.833683i	$0.313772\pi$
$277$	−4.19132	+	23.7701i	−0.251832	+	1.42821i	−0.804076	+	0.594527i	$0.797339\pi$
$278$	5.02044	−	8.69565i	0.301106	−	0.521530i
$279$	1.18820	−	10.5410i	0.0711358	−	0.631070i
$280$	4.18878	+	7.25517i	0.250327	+	0.433579i
$281$	22.2287	−	8.09058i	1.32605	−	0.482644i	0.420660	−	0.907219i	$-0.361799\pi$
$281$	22.2287	−	8.09058i	1.32605	−	0.482644i	0.905393	+	0.424575i	$0.139576\pi$
$282$	1.16527	+	1.88054i	0.0693909	+	0.111984i
$283$	−8.90462	+	7.47186i	−0.529325	+	0.444156i	−0.867868	−	0.496795i	$-0.834510\pi$
$283$	−8.90462	+	7.47186i	−0.529325	+	0.444156i	0.338543	+	0.940951i	$0.390066\pi$
$284$	−8.98121	+	7.53613i	−0.532937	+	0.447187i
$285$	2.42460	+	3.91287i	0.143621	+	0.231779i
$286$	−1.03791	+	0.377767i	−0.0613727	+	0.0223378i
$287$	5.49551	+	9.51850i	0.324390	+	0.561859i
$288$	2.41371	+	1.78158i	0.142229	+	0.104981i
$289$	1.33491	−	2.31213i	0.0785239	−	0.136007i
$290$	3.33981	−	18.9410i	0.196120	−	1.11225i
$291$	−4.44401	−	21.3014i	−0.260512	−	1.24871i
$292$	−0.705075	−	0.256626i	−0.0412614	−	0.0150179i
$293$	−1.85993	−	10.5482i	−0.108658	−	0.616232i	−0.989696	−	0.143186i	$-0.954265\pi$
$293$	−1.85993	−	10.5482i	−0.108658	−	0.616232i	0.881037	−	0.473046i	$-0.156846\pi$
$294$	−14.6325	+	5.84795i	−0.853386	+	0.341059i
$295$	−13.6916	−	11.4886i	−0.797156	−	0.668893i
$296$	3.55460			0.206607
$297$	0.0894359	−	1.10028i	0.00518959	−	0.0638445i
$298$	15.8424			0.917728
$299$	3.30341	+	2.77189i	0.191041	+	0.160302i
$300$	−0.871197	−	0.685951i	−0.0502986	−	0.0396034i
$301$	−4.80490	−	27.2499i	−0.276950	−	1.57066i
$302$	−4.98746	−	1.81529i	−0.286996	−	0.104458i
$303$	4.76222	+	1.56718i	0.273582	+	0.0900323i
$304$	−0.221021	+	1.25347i	−0.0126764	+	0.0718916i
$305$	−2.95839	+	5.12408i	−0.169397	+	0.293404i
$306$	−5.05510	+	10.1694i	−0.288981	+	0.581349i
$307$	−12.3938	−	21.4667i	−0.707351	−	1.22517i	−0.965836	−	0.259153i	$-0.916557\pi$
$307$	−12.3938	−	21.4667i	−0.707351	−	1.22517i	0.258485	−	0.966015i	$-0.416777\pi$
$308$	0.800975	−	0.291531i	0.0456398	−	0.0166115i
$309$	−13.6675	+	25.4730i	−0.777514	+	1.44911i
$310$	5.65573	−	4.74572i	0.321224	−	0.269539i
$311$	−16.6871	+	14.0022i	−0.946241	+	0.793990i	−0.978660	−	0.205484i	$-0.934123\pi$
$311$	−16.6871	+	14.0022i	−0.946241	+	0.793990i	0.0324195	+	0.999474i	$0.489679\pi$
$312$	9.00061	−	0.280389i	0.509559	−	0.0158739i
$313$	8.83542	−	3.21583i	0.499408	−	0.181770i	−0.0800199	−	0.996793i	$-0.525498\pi$
$313$	8.83542	−	3.21583i	0.499408	−	0.181770i	0.579428	+	0.815024i	$0.303276\pi$
$314$	5.75852	+	9.97404i	0.324972	+	0.562868i
$315$	−18.2098	+	17.3220i	−1.02601	+	0.975984i
$316$	1.18389	−	2.05056i	0.0665990	−	0.115353i
$317$	−2.51892	+	14.2855i	−0.141477	+	0.802353i	0.828652	+	0.559763i	$0.189108\pi$
$317$	−2.51892	+	14.2855i	−0.141477	+	0.802353i	−0.970129	+	0.242590i	$0.922003\pi$
$318$	−14.5932	+	13.0406i	−0.818345	+	0.731282i
$319$	−1.83888	−	0.669298i	−0.102958	−	0.0374735i
$320$	0.362580	+	2.05630i	0.0202689	+	0.114950i
$321$	0.0795426	−	0.550919i	0.00443963	−	0.0307493i
$322$	−2.54931	−	2.13913i	−0.142068	−	0.119209i
$323$	−4.81825			−0.268095
$324$	−3.49672	+	8.29294i	−0.194262	+	0.460719i
$325$	−3.32834			−0.184623
$326$	5.87047	+	4.92591i	0.325135	+	0.272821i
$327$	0.140679	−	0.974356i	0.00777957	−	0.0538820i
$328$	0.475691	+	2.69778i	0.0262656	+	0.148960i
$329$	−4.81563	−	1.75274i	−0.265494	−	0.0966319i
$330$	0.572908	−	0.511956i	0.0315375	−	0.0281823i
$331$	0.140089	−	0.794483i	0.00769998	−	0.0436688i	−0.980716	−	0.195440i	$-0.937387\pi$
$331$	0.140089	−	0.794483i	0.00769998	−	0.0436688i	0.988416	+	0.151771i	$0.0484977\pi$
$332$	5.70024	−	9.87311i	0.312842	−	0.541857i
$333$	2.50183	+	10.3662i	0.137100	+	0.568063i
$334$	−3.05500	−	5.29141i	−0.167162	−	0.289533i
$335$	−19.1511	+	6.97044i	−1.04634	+	0.380836i
$336$	−6.94597	+	0.216382i	−0.378934	+	0.0118046i
$337$	−20.4272	+	17.1404i	−1.11274	+	0.933700i	−0.998215	−	0.0597207i	$-0.980979\pi$
$337$	−20.4272	+	17.1404i	−1.11274	+	0.933700i	−0.114525	+	0.993420i	$0.536535\pi$
$338$	10.7475	−	9.01824i	0.584588	−	0.490527i
$339$	1.11355	−	2.07540i	0.0604798	−	0.112720i
$340$	−7.42755	+	2.70341i	−0.402816	+	0.146613i
$341$	−0.375596	−	0.650551i	−0.0203396	−	0.0352293i
$342$	−3.81102	+	0.237674i	−0.206077	+	0.0128519i
$343$	4.20838	−	7.28912i	0.227231	−	0.393576i
$344$	1.19757	−	6.79176i	0.0645687	−	0.366187i
$345$	−2.84939	−	0.937698i	−0.153406	−	0.0504839i
$346$	10.6218	+	3.86602i	0.571032	+	0.207839i
$347$	−5.05391	−	28.6621i	−0.271308	−	1.53866i	−0.750450	−	0.660927i	$-0.770163\pi$
$347$	−5.05391	−	28.6621i	−0.271308	−	1.53866i	0.479142	−	0.877737i	$-0.340948\pi$
$348$	12.5351	+	9.86972i	0.671953	+	0.529072i
$349$	−22.6355	−	18.9934i	−1.21165	−	1.01669i	−0.999219	−	0.0395179i	$-0.987418\pi$
$349$	−22.6355	−	18.9934i	−1.21165	−	1.01669i	−0.212430	−	0.977176i	$-0.568138\pi$
$350$	2.56856			0.137295
$351$	7.15259	+	26.0509i	0.381777	+	1.39049i
$352$	0.212447			0.0113235
$353$	4.78974	+	4.01907i	0.254932	+	0.213913i	0.761293	−	0.648408i	$-0.224565\pi$
$353$	4.78974	+	4.01907i	0.254932	+	0.213913i	−0.506361	+	0.862322i	$0.669010\pi$
$354$	13.7673	−	5.50217i	0.731725	−	0.292437i
$355$	−4.25094	−	24.1083i	−0.225617	−	1.27954i
$356$	−5.07082	−	1.84563i	−0.268753	−	0.0978180i
$357$	−5.37261	−	25.7524i	−0.284348	−	1.36296i
$358$	1.20336	−	6.82462i	0.0635998	−	0.360692i
$359$	1.29314	−	2.23979i	0.0682495	−	0.118212i	−0.829881	−	0.557940i	$-0.811592\pi$
$359$	1.29314	−	2.23979i	0.0682495	−	0.118212i	0.898131	+	0.439728i	$0.144925\pi$
$360$	−5.74151	+	2.50466i	−0.302604	+	0.132007i
$361$	8.68998	+	15.0515i	0.457367	+	0.792183i
$362$	−2.85444	+	1.03893i	−0.150026	+	0.0546050i
$363$	9.99425	+	16.1289i	0.524562	+	0.846549i
$364$	−15.9794	+	13.4083i	−0.837546	+	0.702784i
$365$	1.20015	−	1.00705i	0.0628190	−	0.0527114i
$366$	−2.58520	−	4.17205i	−0.135131	−	0.218076i
$367$	−17.5546	+	6.38935i	−0.916342	+	0.333521i	−0.756782	−	0.653667i	$-0.773230\pi$
$367$	−17.5546	+	6.38935i	−0.916342	+	0.333521i	−0.159560	+	0.987188i	$0.551007\pi$
$368$	−0.414721	−	0.718318i	−0.0216188	−	0.0374449i
$369$	−7.53264	+	3.28602i	−0.392134	+	0.171063i
$370$	−3.71104	+	6.42770i	−0.192928	+	0.334160i
$371$	7.87232	−	44.6462i	0.408711	−	2.31791i
$372$	1.25077	+	5.99528i	0.0648493	+	0.310841i
$373$	−12.7104	−	4.62621i	−0.658120	−	0.239536i	−0.00869564	−	0.999962i	$-0.502768\pi$
$373$	−12.7104	−	4.62621i	−0.658120	−	0.239536i	−0.649425	+	0.760426i	$0.724990\pi$
$374$	0.139652	+	0.792004i	0.00722122	+	0.0409536i
$375$	18.9413	−	7.56998i	0.978127	−	0.390912i
$376$	−0.978448	−	0.821016i	−0.0504596	−	0.0423406i
$377$	47.8894			2.46643
$378$	−5.51981	−	20.1040i	−0.283908	−	1.03404i
$379$	30.2178			1.55218			0.776092	−	0.630620i	$-0.217199\pi$
$379$	30.2178			1.55218			0.776092	+	0.630620i	$0.217199\pi$
$380$	−2.03588	−	1.70830i	−0.104438	−	0.0876341i
$381$	2.45499	+	1.93298i	0.125773	+	0.0990295i
$382$	−0.885116	−	5.01974i	−0.0452865	−	0.256832i
$383$	36.2619	+	13.1982i	1.85289	+	0.674398i	0.983670	+	0.179980i	$0.0576031\pi$
$383$	36.2619	+	13.1982i	1.85289	+	0.674398i	0.869224	+	0.494419i	$0.164619\pi$
$384$	−1.64525	−	0.541430i	−0.0839589	−	0.0276298i
$385$	−0.309056	+	1.75274i	−0.0157510	+	0.0893281i
$386$	−9.43413	+	16.3404i	−0.480185	+	0.831704i
$387$	20.6495	−	1.28780i	1.04967	−	0.0654627i
$388$	6.28158	+	10.8800i	0.318899	+	0.552349i
$389$	5.28688	−	1.92427i	0.268056	−	0.0975642i	−0.204496	−	0.978867i	$-0.565555\pi$
$389$	5.28688	−	1.92427i	0.268056	−	0.0975642i	0.472551	+	0.881303i	$0.343333\pi$
$390$	−8.88970	+	16.5683i	−0.450147	+	0.838969i
$391$	2.40528	−	2.01827i	0.121640	−	0.102068i
$392$	6.96931	−	5.84795i	0.352003	−	0.295366i
$393$	−16.8177	+	0.523909i	−0.848342	+	0.0264277i
$394$	18.8352	−	6.85544i	0.948901	−	0.345372i
$395$	2.47198	+	4.28160i	0.124379	+	0.215431i
$396$	0.149526	+	0.619552i	0.00751398	+	0.0311337i
$397$	−3.85809	+	6.68240i	−0.193632	+	0.335380i	−0.946451	−	0.322847i	$-0.895360\pi$
$397$	−3.85809	+	6.68240i	−0.193632	+	0.335380i	0.752819	+	0.658227i	$0.228693\pi$
$398$	0.955433	−	5.41853i	0.0478915	−	0.271606i
$399$	6.59549	−	5.89380i	0.330187	−	0.295059i
$400$	0.601578	+	0.218956i	0.0300789	+	0.0109478i
$401$	6.31721	+	35.8267i	0.315466	+	1.78910i	0.569593	+	0.821927i	$0.307101\pi$
$401$	6.31721	+	35.8267i	0.315466	+	1.78910i	−0.254126	+	0.967171i	$0.581788\pi$
$402$	2.41583	−	16.7323i	0.120491	−	0.834530i
$403$	14.0824	+	11.8165i	0.701494	+	0.588623i
$404$	−2.89452			−0.144008
$405$	−11.3453	−	14.9809i	−0.563753	−	0.744409i
$406$	−36.9574			−1.83416
$407$	0.578489	+	0.485410i	0.0286746	+	0.0240609i
$408$	0.936955	−	6.48943i	0.0463862	−	0.321275i
$409$	1.01891	+	5.77853i	0.0503819	+	0.285730i	0.999581	−	0.0289462i	$-0.00921516\pi$
$409$	1.01891	+	5.77853i	0.0503819	+	0.285730i	−0.949199	+	0.314676i	$0.898104\pi$
$410$	−5.37495	−	1.95632i	−0.265450	−	0.0966159i
$411$	−11.7114	+	10.4654i	−0.577680	+	0.516221i
$412$	2.89819	−	16.4365i	0.142784	−	0.809766i
$413$	−17.1719	+	29.7427i	−0.844976	+	1.46354i
$414$	1.80292	−	1.71501i	0.0886085	−	0.0842882i
$415$	11.9022	+	20.6152i	0.584256	+	1.01196i
$416$	−4.88549	+	1.77817i	−0.239531	+	0.0871821i
$417$	−17.3829	+	0.541514i	−0.851243	+	0.0265181i
$418$	−0.207142	+	0.173812i	−0.0101316	+	0.00850145i
$419$	16.1908	−	13.5857i	0.790972	−	0.663704i	−0.155014	−	0.987912i	$-0.549542\pi$
$419$	16.1908	−	13.5857i	0.790972	−	0.663704i	0.945986	+	0.324208i	$0.105098\pi$
$420$	6.86038	−	12.7861i	0.334752	−	0.623900i
$421$	−6.99405	+	2.54563i	−0.340869	+	0.124066i	−0.506782	−	0.862074i	$-0.669165\pi$
$421$	−6.99405	+	2.54563i	−0.340869	+	0.124066i	0.165913	+	0.986140i	$0.446943\pi$
$422$	12.5726	+	21.7763i	0.612023	+	1.06005i
$423$	1.70564	−	3.43127i	0.0829311	−	0.166834i
$424$	5.64962	−	9.78544i	0.274370	−	0.475223i
$425$	−0.420826	+	2.38662i	−0.0204130	+	0.115768i
$426$	19.2892	+	6.34781i	0.934563	+	0.307552i
$427$	10.6837	+	3.88853i	0.517018	+	0.188179i
$428$	0.0558055	+	0.316489i	0.00269746	+	0.0152981i
$429$	1.50308	+	1.18348i	0.0725695	+	0.0571387i
$430$	11.0311	+	9.25619i	0.531967	+	0.446373i
$431$	−13.0502			−0.628607			−0.314303	−	0.949323i	$-0.601771\pi$
$431$	−13.0502			−0.628607			−0.314303	+	0.949323i	$0.601771\pi$
$432$	0.420980	−	5.17907i	0.0202544	−	0.249178i
$433$	0.143533			0.00689775			0.00344887	−	0.999994i	$-0.498902\pi$
$433$	0.143533			0.00689775			0.00344887	+	0.999994i	$0.498902\pi$
$434$	−10.8677	−	9.11908i	−0.521666	−	0.437730i
$435$	−30.9339	+	12.3629i	−1.48317	+	0.592754i
$436$	0.0986977	+	0.559743i	0.00472676	+	0.0268068i
$437$	0.992054	+	0.361078i	0.0474564	+	0.0172727i
$438$	0.265415	+	1.27221i	0.0126820	+	0.0607885i
$439$	2.35406	−	13.3506i	0.112353	−	0.637187i	−0.875673	−	0.482904i	$-0.839582\pi$
$439$	2.35406	−	13.3506i	0.112353	−	0.637187i	0.988027	−	0.154283i	$-0.0493069\pi$
$440$	−0.221796	+	0.384162i	−0.0105737	+	0.0183142i
$441$	21.9594	+	16.2084i	1.04569	+	0.771830i
$442$	−9.84052	−	17.0443i	−0.468066	−	0.810714i
$443$	−11.5406	+	4.20044i	−0.548311	+	0.199569i	−0.601296	−	0.799026i	$-0.705349\pi$
$443$	−11.5406	+	4.20044i	−0.548311	+	0.199569i	0.0529847	+	0.998595i	$0.483127\pi$
$444$	−3.24290	−	5.23347i	−0.153901	−	0.248369i
$445$	8.63138	−	7.24258i	0.409166	−	0.343331i
$446$	−2.87450	+	2.41199i	−0.136112	+	0.114211i
$447$	−14.4532	−	23.3249i	−0.683614	−	1.10323i
$448$	3.77024	−	1.37225i	0.178127	−	0.0648329i
$449$	−20.3323	−	35.2165i	−0.959540	−	1.66197i	−0.723620	−	0.690199i	$-0.757523\pi$
$449$	−20.3323	−	35.2165i	−0.959540	−	1.66197i	−0.235920	−	0.971772i	$-0.575810\pi$
$450$	−0.215128	+	1.90847i	−0.0101412	+	0.0899662i
$451$	−0.290988	+	0.504006i	−0.0137021	+	0.0237327i
$452$	−0.236129	+	1.33916i	−0.0111066	+	0.0629886i
$453$	1.87746	+	8.99919i	0.0882106	+	0.422819i
$454$	−17.5983	−	6.40524i	−0.825928	−	0.300613i
$455$	−7.56327	−	42.8934i	−0.354571	−	2.01087i
$456$	2.04714	−	0.818146i	0.0958660	−	0.0383132i
$457$	24.9661	+	20.9491i	1.16787	+	0.979956i	0.999983	−	0.00585037i	$-0.00186224\pi$
$457$	24.9661	+	20.9491i	1.16787	+	0.979956i	0.167884	+	0.985807i	$0.446307\pi$
$458$	−4.14333			−0.193605
$459$	19.5844	−	1.83504i	0.914120	−	0.0856523i
$460$	1.73189			0.0807498
$461$	−20.9287	−	17.5612i	−0.974745	−	0.817909i	0.00854291	−	0.999964i	$-0.497281\pi$
$461$	−20.9287	−	17.5612i	−0.974745	−	0.817909i	−0.983288	+	0.182055i	$0.941725\pi$
$462$	−1.15996	−	0.913314i	−0.0539663	−	0.0424912i
$463$	−0.590262	−	3.34754i	−0.0274318	−	0.155574i	0.968015	−	0.250892i	$-0.0807240\pi$
$463$	−0.590262	−	3.34754i	−0.0274318	−	0.155574i	−0.995447	+	0.0953189i	$0.969613\pi$
$464$	−8.65573	−	3.15043i	−0.401832	−	0.146255i
$465$	−12.1469	−	3.99740i	−0.563301	−	0.185375i
$466$	−0.332903	+	1.88799i	−0.0154214	+	0.0874593i
$467$	−16.4988	+	28.5767i	−0.763473	+	1.32237i	0.177577	+	0.984107i	$0.443174\pi$
$467$	−16.4988	+	28.5767i	−0.763473	+	1.32237i	−0.941050	+	0.338267i	$0.890159\pi$
$468$	−8.62418	−	12.9959i	−0.398653	−	0.600734i
$469$	19.5807	+	33.9147i	0.904152	+	1.56604i
$470$	2.50613	−	0.912157i	0.115599	−	0.0420747i
$471$	9.43130	−	17.5777i	0.434571	−	0.809939i
$472$	−6.55723	+	5.50217i	−0.301821	+	0.253258i
$473$	1.12237	−	0.941778i	0.0516065	−	0.0433030i
$474$	−4.09913	+	0.127697i	−0.188279	+	0.00586531i
$475$	−0.765694	+	0.278690i	−0.0351324	+	0.0127872i
$476$	7.59415	+	13.1534i	0.348077	+	0.602887i
$477$	32.5133	+	9.58855i	1.48868	+	0.439029i
$478$	−12.0996	+	20.9572i	−0.553424	+	0.958559i
$479$	−4.00142	+	22.6932i	−0.182830	+	1.03688i	0.745883	+	0.666077i	$0.232028\pi$
$479$	−4.00142	+	22.6932i	−0.182830	+	1.03688i	−0.928712	+	0.370801i	$0.879083\pi$
$480$	2.69671	−	2.40981i	0.123088	−	0.109992i
$481$	−17.3660	−	6.32070i	−0.791820	−	0.288199i
$482$	2.29301	+	13.0043i	0.104444	+	0.592331i
$483$	−0.823686	+	5.70492i	−0.0374790	+	0.259583i
$484$	−8.39191	−	7.04165i	−0.381451	−	0.320075i
$485$	−26.2321			−1.19114
$486$	15.3999	−	2.41749i	0.698552	−	0.109660i
$487$	26.9315			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$487$	26.9315			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$488$	2.17073	+	1.82146i	0.0982641	+	0.0824534i
$489$	1.89676	−	13.1371i	0.0857743	−	0.594080i
$490$	3.29868	+	18.7077i	0.149019	+	0.845129i
$491$	0.233037	+	0.0848187i	0.0105168	+	0.00382781i	0.347273	−	0.937764i	$-0.387108\pi$
$491$	0.233037	+	0.0848187i	0.0105168	+	0.00382781i	−0.336756	+	0.941592i	$0.609330\pi$
$492$	3.53798	−	3.16158i	0.159504	−	0.142535i
$493$	6.05500	−	34.3396i	0.272703	−	1.54658i
$494$	3.30869	−	5.73081i	0.148865	−	0.257841i
$495$	−1.27643	−	0.376433i	−0.0573711	−	0.0169194i
$496$	−1.76795	−	3.06218i	−0.0793834	−	0.137496i
$497$	−44.2028	+	16.0885i	−1.98277	+	0.721668i
$498$	−19.7367	+	0.614840i	−0.884420	+	0.0275516i
$499$	−20.4674	+	17.1742i	−0.916247	+	0.768822i	−0.973297	−	0.229549i	$-0.926275\pi$
$499$	−20.4674	+	17.1742i	−0.916247	+	0.768822i	0.0570505	+	0.998371i	$0.481830\pi$
$500$	−9.02155	+	7.56998i	−0.403456	+	0.338540i
$501$	−5.00347	+	9.32530i	−0.223539	+	0.416624i
$502$	8.13762	−	2.96185i	0.363200	−	0.132194i
$503$	−13.0871	−	22.6676i	−0.583527	−	1.01070i	−0.995057	−	0.0993022i	$-0.968339\pi$
$503$	−13.0871	−	22.6676i	−0.583527	−	1.01070i	0.411530	−	0.911396i	$-0.364994\pi$
$504$	6.65547	+	10.0292i	0.296458	+	0.446736i
$505$	3.02190	−	5.23409i	0.134473	−	0.232914i
$506$	0.0305989	−	0.173535i	0.00136029	−	0.00771458i
$507$	−23.0827	−	7.59621i	−1.02514	−	0.337359i
$508$	−1.69522	−	0.617009i	−0.0752132	−	0.0273754i
$509$	0.947739	+	5.37490i	0.0420078	+	0.238238i	0.998581	−	0.0532542i	$-0.0169594\pi$
$509$	0.947739	+	5.37490i	0.0420078	+	0.238238i	−0.956573	+	0.291492i	$0.905848\pi$
$510$	10.7565	+	8.46929i	0.476305	+	0.375026i
$511$	−2.30614	−	1.93508i	−0.102018	−	0.0856031i
$512$	1.00000			0.0441942
$513$	3.82677	+	5.39417i	0.168956	+	0.238158i
$514$	21.8308			0.962914
$515$	26.6959	+	22.4005i	1.17636	+	0.987086i
$516$	−11.0921	+	4.43301i	−0.488303	+	0.195152i
$517$	−0.0471199	−	0.267230i	−0.00207233	−	0.0117528i
$518$	13.4017	+	4.87782i	0.588837	+	0.214319i
$519$	−3.99842	−	19.1656i	−0.175511	−	0.841275i
$520$	1.88506	−	10.6907i	0.0826656	−	0.468820i
$521$	13.0596	−	22.6199i	0.572151	−	0.990995i	−0.424194	−	0.905572i	$-0.639442\pi$
$521$	13.0596	−	22.6199i	0.572151	−	0.990995i	0.996345	−	0.0854234i	$-0.0272243\pi$
$522$	3.09534	−	27.4598i	0.135479	−	1.20188i
$523$	−3.70382	−	6.41521i	−0.161957	−	0.280518i	0.773614	−	0.633658i	$-0.218447\pi$
$523$	−3.70382	−	6.41521i	−0.161957	−	0.280518i	−0.935570	+	0.353140i	$0.885114\pi$
$524$	9.12858	−	3.32253i	0.398784	−	0.145145i
$525$	−2.34332	−	3.78170i	−0.102271	−	0.165047i
$526$	−4.35690	+	3.65587i	−0.189970	+	0.159404i
$527$	10.2537	−	8.60387i	0.446658	−	0.374791i
$528$	−0.193818	−	0.312787i	−0.00843483	−	0.0136123i
$529$	20.9664	−	7.63116i	0.911585	−	0.331790i
$530$	11.7965	+	20.4322i	0.512408	+	0.887516i
$531$	−20.6610	−	15.2501i	−0.896610	−	0.661796i
$532$	−2.55339	+	4.42259i	−0.110703	+	0.191744i
$533$	2.47313	−	14.0258i	0.107123	−	0.607526i
$534$	1.90883	+	9.14958i	0.0826033	+	0.395941i
$535$	−0.630560	−	0.229505i	−0.0272615	−	0.00992238i
$536$	1.69490	+	9.61227i	0.0732086	+	0.415187i
$537$	−11.1458	+	4.45445i	−0.480976	+	0.192224i
$538$	−17.4399	−	14.6339i	−0.751889	−	0.630910i
$539$	1.93280			0.0832514
$540$	8.92568	+	6.16824i	0.384100	+	0.265439i
$541$	11.3209			0.486725			0.243362	−	0.969935i	$-0.421750\pi$
$541$	11.3209			0.486725			0.243362	+	0.969935i	$0.421750\pi$
$542$	−15.1937	−	12.7490i	−0.652625	−	0.547617i
$543$	4.13376	+	3.25479i	0.177397	+	0.139676i
$544$	0.657349	+	3.72801i	0.0281836	+	0.159837i
$545$	−1.11521	−	0.405903i	−0.0477704	−	0.0173870i
$546$	34.3192	+	11.2940i	1.46873	+	0.483339i
$547$	−1.84721	+	10.4761i	−0.0789811	+	0.447924i	0.919513	+	0.393060i	$0.128584\pi$
$547$	−1.84721	+	10.4761i	−0.0789811	+	0.447924i	−0.998494	+	0.0548639i	$0.982528\pi$
$548$	4.53396	−	7.85305i	0.193681	−	0.335466i
$549$	−3.78403	+	7.61241i	−0.161499	+	0.324890i
$550$	0.0680027	+	0.117784i	0.00289964	+	0.00502233i
$551$	11.0171	−	4.00989i	0.469344	−	0.170827i
$552$	−0.679230	+	1.26593i	−0.0289100	+	0.0538814i
$553$	7.27744	−	6.10650i	0.309468	−	0.259675i
$554$	−18.4899	+	15.5149i	−0.785560	+	0.659163i
$555$	12.8492	−	0.400280i	0.545417	−	0.0169909i
$556$	9.43533	−	3.43418i	0.400147	−	0.145642i
$557$	5.92385	+	10.2604i	0.251001	+	0.434747i	0.963802	−	0.266620i	$-0.0859068\pi$
$557$	5.92385	+	10.2604i	0.251001	+	0.434747i	−0.712800	+	0.701367i	$0.752573\pi$
$558$	7.68581	−	7.31108i	0.325366	−	0.309503i
$559$	−17.9276	+	31.0516i	−0.758258	+	1.31334i
$560$	−1.45475	+	8.25028i	−0.0614743	+	0.348638i
$561$	1.03867	−	0.928164i	0.0438526	−	0.0391871i
$562$	22.2287	+	8.09058i	0.937661	+	0.341281i
$563$	1.04327	+	5.91667i	0.0439686	+	0.249358i	0.998868	−	0.0475719i	$-0.0151483\pi$
$563$	1.04327	+	5.91667i	0.0439686	+	0.249358i	−0.954899	+	0.296930i	$0.904037\pi$
$564$	−0.316138	+	2.18960i	−0.0133118	+	0.0921987i
$565$	−2.17504	−	1.82508i	−0.0915047	−	0.0767815i
$566$	−11.6242			−0.488600
$567$	−24.5635	+	26.4680i	−1.03157	+	1.11155i
$568$	−11.7241			−0.491934
$569$	−22.3596	−	18.7619i	−0.937363	−	0.786541i	0.0397618	−	0.999209i	$-0.487340\pi$
$569$	−22.3596	−	18.7619i	−0.937363	−	0.786541i	−0.977124	+	0.212669i	$0.931785\pi$
$570$	−0.657794	+	4.55594i	−0.0275520	+	0.190827i
$571$	3.78797	+	21.4826i	0.158522	+	0.899021i	0.955495	+	0.295007i	$0.0953219\pi$
$571$	3.78797	+	21.4826i	0.158522	+	0.899021i	−0.796974	+	0.604014i	$0.793567\pi$
$572$	−1.03791	−	0.377767i	−0.0433970	−	0.0157952i
$573$	−6.58310	+	5.88273i	−0.275013	+	0.245755i
$574$	−1.90857	+	10.8240i	−0.0796622	+	0.451787i
$575$	0.265499	−	0.459857i	0.0110721	−	0.0191774i
$576$	0.703829	+	2.91627i	0.0293262	+	0.121511i
$577$	−20.0399	−	34.7102i	−0.834273	−	1.44500i	−0.894621	−	0.446826i	$-0.852554\pi$
$577$	−20.0399	−	34.7102i	−0.834273	−	1.44500i	0.0603476	−	0.998177i	$-0.480779\pi$
$578$	2.50880	−	0.913130i	0.104353	−	0.0379812i
$579$	32.6649	−	1.01758i	1.35751	−	0.0422894i
$580$	14.7335	−	12.3629i	0.611775	−	0.513340i
$581$	35.0397	−	29.4018i	1.45369	−	1.21979i
$582$	10.2880	−	19.1744i	0.426450	−	0.794803i
$583$	2.25572	−	0.821016i	0.0934224	−	0.0340030i
$584$	−0.375162	−	0.649800i	−0.0155243	−	0.0268889i
$585$	32.5038	−	2.02710i	1.34387	−	0.0838102i
$586$	5.35546	−	9.27593i	0.221232	−	0.383185i
$587$	−4.66518	+	26.4576i	−0.192553	+	1.09202i	0.723309	+	0.690525i	$0.242620\pi$
$587$	−4.66518	+	26.4576i	−0.192553	+	1.09202i	−0.915861	+	0.401495i	$0.868491\pi$
$588$	−14.9682	−	4.92582i	−0.617276	−	0.203137i
$589$	4.22912	+	1.53927i	0.174258	+	0.0634246i
$590$	−3.10363	−	17.6016i	−0.127775	−	0.724646i
$591$	−27.2768	−	21.4768i	−1.12202	−	0.883439i
$592$	2.72298	+	2.28485i	0.111914	+	0.0939070i
$593$	30.4609			1.25088			0.625440	−	0.780272i	$-0.284919\pi$
$593$	30.4609			1.25088			0.625440	+	0.780272i	$0.284919\pi$
$594$	0.775756	−	0.785373i	0.0318297	−	0.0322242i
$595$	−31.7134			−1.30012
$596$	12.1360	+	10.1833i	0.497110	+	0.417125i
$597$	−8.84940	+	3.53670i	−0.362182	+	0.144747i
$598$	0.748822	+	4.24678i	0.0306216	+	0.173664i
$599$	27.4285	+	9.98317i	1.12070	+	0.407901i	0.834908	−	0.550390i	$-0.185521\pi$
$599$	27.4285	+	9.98317i	1.12070	+	0.407901i	0.285792	+	0.958292i	$0.407743\pi$
$600$	−0.226455	−	1.08546i	−0.00924499	−	0.0443139i
$601$	−4.03243	+	22.8690i	−0.164486	+	0.932847i	0.785106	+	0.619361i	$0.212608\pi$
$601$	−4.03243	+	22.8690i	−0.164486	+	0.932847i	−0.949593	+	0.313487i	$0.898503\pi$
$602$	13.8352	−	23.9632i	0.563879	−	0.976667i
$603$	−26.8390	+	11.7082i	−1.09297	+	0.476794i
$604$	−2.65377	−	4.59647i	−0.107981	−	0.187028i
$605$	21.4945	−	7.82335i	0.873875	−	0.318064i
$606$	2.64070	+	4.26162i	0.107271	+	0.173117i
$607$	32.6881	−	27.4286i	1.32677	−	1.11329i	0.341950	−	0.939718i	$-0.388913\pi$
$607$	32.6881	−	27.4286i	1.32677	−	1.11329i	0.984821	−	0.173574i	$-0.0555317\pi$
$608$	−0.975029	+	0.818146i	−0.0395426	+	0.0331802i
$609$	33.7166	+	54.4126i	1.36627	+	2.20491i
$610$	−5.55995	+	2.02366i	−0.225116	+	0.0819354i
$611$	3.32029	+	5.75091i	0.134325	+	0.232657i
$612$	−10.4092	+	4.54089i	−0.420768	+	0.183555i
$613$	6.80411	−	11.7851i	0.274815	−	0.475994i	−0.695273	−	0.718746i	$-0.744717\pi$
$613$	6.80411	−	11.7851i	0.274815	−	0.475994i	0.970089	+	0.242752i	$0.0780500\pi$
$614$	4.30432	−	24.4110i	0.173708	−	0.985148i
$615$	2.02332	+	9.69835i	0.0815882	+	0.391075i
$616$	0.800975	+	0.291531i	0.0322722	+	0.0117461i
$617$	4.88447	+	27.7012i	0.196641	+	1.11521i	0.910062	+	0.414472i	$0.136034\pi$
$617$	4.88447	+	27.7012i	0.196641	+	1.11521i	−0.713421	+	0.700736i	$0.752855\pi$
$618$	−26.8436	+	10.7281i	−1.07981	+	0.431549i
$619$	−14.9355	−	12.5323i	−0.600307	−	0.503717i	0.291237	−	0.956651i	$-0.405933\pi$
$619$	−14.9355	−	12.5323i	−0.600307	−	0.503717i	−0.891544	+	0.452934i	$0.850377\pi$
$620$	7.38303			0.296510
$621$	−4.16984	−	1.08982i	−0.167330	−	0.0437330i
$622$	−21.7835			−0.873439
$623$	−16.5855	−	13.9169i	−0.664485	−	0.557569i
$624$	7.07510	+	5.57069i	0.283231	+	0.223006i
$625$	−3.71420	−	21.0643i	−0.148568	−	0.842571i
$626$	8.83542	+	3.21583i	0.353135	+	0.128530i
$627$	0.444883	+	0.146405i	0.0177669	+	0.00584686i
$628$	−1.99991	+	11.3421i	−0.0798052	+	0.452598i
$629$	−6.72802	+	11.6533i	−0.268264	+	0.464646i
$630$	−25.0839	+	1.56436i	−0.999367	+	0.0623255i
$631$	−6.27471	−	10.8681i	−0.249792	−	0.432653i	0.713676	−	0.700476i	$-0.247029\pi$
$631$	−6.27471	−	10.8681i	−0.249792	−	0.432653i	−0.963468	+	0.267823i	$0.913696\pi$
$632$	2.22499	−	0.809829i	0.0885052	−	0.0322133i
$633$	20.5913	−	38.3775i	0.818433	−	1.52537i
$634$	−11.1121	+	9.32419i	−0.441319	+	0.370311i
$635$	2.88555	−	2.42126i	0.114509	−	0.0960848i
$636$	−19.5614	+	0.609380i	−0.775659	+	0.0241635i
$637$	−44.4471	+	16.1774i	−1.76106	+	0.640973i
$638$	−0.978448	−	1.69472i	−0.0387371	−	0.0670947i
$639$	−8.25180	−	34.1908i	−0.326436	−	1.35257i
$640$	−1.04401	+	1.80828i	−0.0412681	+	0.0714784i
$641$	−2.42288	+	13.7409i	−0.0956981	+	0.542731i	0.898833	+	0.438291i	$0.144416\pi$
$641$	−2.42288	+	13.7409i	−0.0956981	+	0.542731i	−0.994531	+	0.104440i	$0.966695\pi$
$642$	0.415057	−	0.370899i	0.0163810	−	0.0146382i
$643$	−38.5754	−	14.0403i	−1.52127	−	0.553695i	−0.559802	−	0.828627i	$-0.689123\pi$
$643$	−38.5754	−	14.0403i	−1.52127	−	0.553695i	−0.961464	+	0.274931i	$0.911345\pi$
$644$	−0.577882	−	3.27733i	−0.0227718	−	0.129145i
$645$	3.56416	−	24.6857i	0.140339	−	0.971998i
$646$	−3.69099	−	3.09711i	−0.145220	−	0.121854i
$647$	0.303995			0.0119513			0.00597563	−	0.999982i	$-0.498098\pi$
$647$	0.303995			0.0119513			0.00597563	+	0.999982i	$0.498098\pi$
$648$	−8.00925	+	4.10511i	−0.314633	+	0.161264i
$649$	−1.81851			−0.0713829
$650$	−2.54966	−	2.13942i	−0.100006	−	0.0839149i
$651$	−3.51137	+	24.3200i	−0.137621	+	0.953177i
$652$	1.33073	+	7.54693i	0.0521153	+	0.295561i
$653$	−44.2755	−	16.1150i	−1.73263	−	0.630627i	−0.733820	−	0.679344i	$-0.762265\pi$
$653$	−44.2755	−	16.1150i	−1.73263	−	0.630627i	−0.998813	+	0.0487170i	$0.984487\pi$
$654$	0.734070	−	0.655973i	0.0287044	−	0.0256506i
$655$	−3.52226	+	19.9757i	−0.137626	+	0.780516i
$656$	−1.36970	+	2.37239i	−0.0534777	+	0.0926261i
$657$	1.63094	−	1.55142i	0.0636291	−	0.0605268i
$658$	−2.56234	−	4.43811i	−0.0998905	−	0.173015i
$659$	40.3746	−	14.6952i	1.57277	−	0.572442i	0.599156	−	0.800633i	$-0.295503\pi$
$659$	40.3746	−	14.6952i	1.57277	−	0.572442i	0.973617	+	0.228190i	$0.0732809\pi$
$660$	0.767952	−	0.0239234i	0.0298925	−	0.000931217i
$661$	21.0863	−	17.6935i	0.820161	−	0.688197i	−0.132849	−	0.991136i	$-0.542412\pi$
$661$	21.0863	−	17.6935i	0.820161	−	0.688197i	0.953010	+	0.302939i	$0.0979680\pi$
$662$	0.617998	−	0.518562i	0.0240192	−	0.0201545i
$663$	−16.1168	+	30.0380i	−0.625925	+	1.16658i
$664$	10.7130	−	3.89920i	0.415743	−	0.151318i
$665$	−5.33151	−	9.23445i	−0.206747	−	0.358097i
$666$	−4.74673	+	9.54910i	−0.183932	+	0.370020i
$667$	−3.82009	+	6.61659i	−0.147915	+	0.256196i
$668$	1.06099	−	6.01717i	0.0410509	−	0.232811i
$669$	6.17363	+	2.03166i	0.238686	+	0.0785485i
$670$	−19.1511	−	6.97044i	−0.739873	−	0.269292i
$671$	0.104537	+	0.592861i	0.00403562	+	0.0228871i
$672$	−5.46001	−	4.29903i	−0.210625	−	0.165839i
$673$	−25.7719	−	21.6252i	−0.993433	−	0.833589i	−0.00737169	−	0.999973i	$-0.502347\pi$
$673$	−25.7719	−	21.6252i	−0.993433	−	0.833589i	−0.986061	+	0.166384i	$0.946791\pi$
$674$	−26.6658			−1.02713
$675$	3.00612	−	1.42439i	0.115706	−	0.0548246i
$676$	14.0299			0.539611
$677$	26.1138	+	21.9120i	1.00363	+	0.842148i	0.987484	−	0.157721i	$-0.0504147\pi$
$677$	26.1138	+	21.9120i	1.00363	+	0.842148i	0.0161497	+	0.999870i	$0.494859\pi$
$678$	2.18707	−	0.874072i	0.0839940	−	0.0335685i
$679$	8.75290	+	49.6402i	0.335906	+	1.90502i
$680$	−7.42755	−	2.70341i	−0.284834	−	0.103671i
$681$	6.62461	+	31.7536i	0.253855	+	1.21680i
$682$	0.130443	−	0.739779i	0.00499492	−	0.0283276i
$683$	8.22650	−	14.2487i	0.314778	−	0.545212i	−0.664612	−	0.747189i	$-0.731403\pi$
$683$	8.22650	−	14.2487i	0.314778	−	0.545212i	0.979390	+	0.201976i	$0.0647365\pi$
$684$	−3.07219	−	2.26761i	−0.117468	−	0.0867042i
$685$	9.46699	+	16.3973i	0.361715	+	0.626509i
$686$	7.90916	−	2.87870i	0.301973	−	0.109909i
$687$	3.78000	+	6.10025i	0.144216	+	0.232739i
$688$	5.28305	−	4.43301i	0.201414	−	0.169007i
$689$	−45.0014	+	37.7606i	−1.71442	+	1.43857i
$690$	−1.58002	−	2.54987i	−0.0601504	−	0.0970720i
$691$	13.4086	−	4.88033i	0.510087	−	0.185657i	−0.0741383	−	0.997248i	$-0.523621\pi$
$691$	13.4086	−	4.88033i	0.510087	−	0.185657i	0.584225	+	0.811591i	$0.301398\pi$
$692$	5.65174	+	9.78911i	0.214847	+	0.372126i
$693$	−0.286433	+	2.54105i	−0.0108807	+	0.0965264i
$694$	14.5521	−	25.2051i	0.552392	−	0.956771i
$695$	−3.64062	+	20.6470i	−0.138097	+	0.783185i
$696$	3.25832	+	15.6181i	0.123506	+	0.592001i
$697$	−9.74465	−	3.54676i	−0.369105	−	0.134343i
$698$	−5.13104	−	29.0996i	−0.194213	−	1.10144i
$699$	3.08341	−	1.23230i	0.116625	−	0.0466097i
$700$	1.96763	+	1.65104i	0.0743694	+	0.0624033i
$701$	15.8891			0.600123			0.300062	−	0.953920i	$-0.402993\pi$
$701$	15.8891			0.600123			0.300062	+	0.953920i	$0.402993\pi$
$702$	−11.2660	+	24.5537i	−0.425207	+	0.926720i
$703$	−4.52433			−0.170638
$704$	0.162744	+	0.136558i	0.00613363	+	0.00514673i
$705$	−3.62935	−	2.85762i	−0.136689	−	0.107624i
$706$	1.08575	+	6.15757i	0.0408626	+	0.231743i
$707$	−10.9130	−	3.97202i	−0.410427	−	0.149383i
$708$	14.0831	+	4.63457i	0.529276	+	0.174178i
$709$	−1.43117	+	8.11659i	−0.0537488	+	0.304825i	−0.999817	−	0.0191436i	$-0.993906\pi$
$709$	−1.43117	+	8.11659i	−0.0537488	+	0.304825i	0.946068	+	0.323968i	$0.105017\pi$
$710$	12.2401	−	21.2005i	0.459363	−	0.795640i
$711$	3.92769	+	5.91868i	0.147300	+	0.221968i
$712$	−2.69813	−	4.67329i	−0.101117	−	0.175139i
$713$	−2.75596	+	1.00309i	−0.103211	+	0.0375659i
$714$	12.4377	−	23.1810i	0.465469	−	0.867525i
$715$	1.76669	−	1.48243i	0.0660704	−	0.0554397i
$716$	5.30861	−	4.45445i	0.198392	−	0.166471i
$717$	41.8940	−	1.30509i	1.56456	−	0.0487395i
$718$	2.43032	−	0.884563i	0.0906986	−	0.0330116i
$719$	−10.9348	−	18.9397i	−0.407801	−	0.706331i	0.586842	−	0.809701i	$-0.300371\pi$
$719$	−10.9348	−	18.9397i	−0.407801	−	0.706331i	−0.994643	+	0.103370i	$0.967037\pi$
$720$	−6.00822	−	1.77189i	−0.223913	−	0.0660345i
$721$	33.4819	−	57.9923i	1.24693	−	2.15975i
$722$	−3.01800	+	17.1159i	−0.112318	+	0.636988i
$723$	17.0544	−	15.2400i	0.634261	−	0.566782i
$724$	−2.85444	−	1.03893i	−0.106084	−	0.0386116i
$725$	−1.02399	−	5.80731i	−0.0380299	−	0.215678i
$726$	−2.71144	+	18.7797i	−0.100631	+	0.696978i
$727$	37.2742	+	31.2768i	1.38242	+	1.15999i	0.968305	+	0.249769i	$0.0803548\pi$
$727$	37.2742	+	31.2768i	1.38242	+	1.15999i	0.414119	+	0.910223i	$0.364090\pi$
$728$	−20.8596			−0.773107
$729$	−17.6088	−	20.4678i	−0.652176	−	0.758067i
$730$	1.56669			0.0579858
$731$	19.9991	+	16.7812i	0.739694	+	0.620677i
$732$	0.701364	−	4.85771i	0.0259232	−	0.179546i
$733$	−4.54580	−	25.7805i	−0.167903	−	0.952226i	−0.946020	−	0.324107i	$-0.894936\pi$
$733$	−4.54580	−	25.7805i	−0.167903	−	0.952226i	0.778117	−	0.628119i	$-0.216175\pi$
$734$	−17.5546	−	6.38935i	−0.647951	−	0.235835i
$735$	24.5341	−	21.9239i	0.904954	−	0.808677i
$736$	0.144031	−	0.816841i	0.00530906	−	0.0301092i
$737$	−1.03680	+	1.79579i	−0.0381910	+	0.0661487i
$738$	−7.88255	−	2.32465i	−0.290161	−	0.0855716i
$739$	−1.28655	−	2.22838i	−0.0473267	−	0.0819722i	0.841392	−	0.540426i	$-0.181737\pi$
$739$	−1.28655	−	2.22838i	−0.0473267	−	0.0819722i	−0.888718	+	0.458454i	$0.848404\pi$
$740$	−6.97447	+	2.53850i	−0.256386	+	0.0933170i
$741$	−11.4561	+	0.356882i	−0.420849	+	0.0131104i
$742$	34.7285	−	29.1407i	1.27493	−	1.06979i
$743$	−37.5339	+	31.4947i	−1.37699	+	1.15543i	−0.406673	+	0.913574i	$0.633311\pi$
$743$	−37.5339	+	31.4947i	−1.37699	+	1.15543i	−0.970313	+	0.241854i	$0.922245\pi$
$744$	−2.89555	+	5.39663i	−0.106156	+	0.197850i
$745$	−31.0843	+	11.3138i	−1.13884	+	0.414505i
$746$	−6.76307	−	11.7140i	−0.247614	−	0.428879i
$747$	18.9112	+	28.4975i	0.691925	+	1.04267i
$748$	−0.402111	+	0.696477i	−0.0147026	+	0.0254657i
$749$	−0.223903	+	1.26982i	−0.00818124	+	0.0463981i
$750$	19.3758	+	6.37632i	0.707504	+	0.232830i
$751$	−7.99761	−	2.91089i	−0.291837	−	0.106220i	0.191953	−	0.981404i	$-0.438518\pi$
$751$	−7.99761	−	2.91089i	−0.291837	−	0.106220i	−0.483790	+	0.875184i	$0.660740\pi$
$752$	−0.221796	−	1.25787i	−0.00808808	−	0.0458698i
$753$	−11.7848	−	9.27895i	−0.429462	−	0.338144i
$754$	36.6854	+	30.7827i	1.33601	+	1.12104i
$755$	11.0822			0.403324
$756$	8.69420	−	18.9486i	0.316205	−	0.689156i
$757$	17.3242			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$757$	17.3242			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$758$	23.1482	+	19.4236i	0.840779	+	0.705497i
$759$	−0.283413	+	0.113267i	−0.0102872	+	0.00411134i
$760$	−0.461496	−	2.61727i	−0.0167402	−	0.0949384i
$761$	−9.81674	−	3.57300i	−0.355856	−	0.129521i	0.157905	−	0.987454i	$-0.449526\pi$
$761$	−9.81674	−	3.57300i	−0.355856	−	0.129521i	−0.513761	+	0.857933i	$0.671748\pi$
$762$	0.638140	+	3.05879i	0.0231174	+	0.110808i
$763$	−0.395996	+	2.24580i	−0.0143360	+	0.0813035i

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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.247510 - 1.71428i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96209 - 0.714144i) q^{5} +(1.29152 - 1.15411i) q^{6} +(-0.696712 + 3.95125i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.87748 - 0.848600i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.247510 - 1.71428i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96209 - 0.714144i) q^{5} +(1.29152 - 1.15411i) q^{6} +(-0.696712 + 3.95125i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.87748 - 0.848600i) q^{9} +(-1.04401 - 1.80828i) q^{10} +(-0.199635 + 0.0726611i) q^{11} +(1.73121 - 0.0539310i) q^{12} +(3.98269 - 3.34187i) q^{13} +(-3.07353 + 2.57900i) q^{14} +(-1.70988 + 3.18681i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.89276 - 3.27836i) q^{17} +(-1.65881 - 2.49967i) q^{18} +(0.636405 - 1.10229i) q^{19} +(0.362580 - 2.05630i) q^{20} +(6.60109 + 2.17233i) q^{21} +(-0.199635 - 0.0726611i) q^{22} +(0.144031 + 0.816841i) q^{23} +(1.36085 + 1.07149i) q^{24} +(-0.490411 - 0.411503i) q^{25} +5.19903 q^{26} +(-2.16694 + 4.72275i) q^{27} -4.01220 q^{28} +(7.05621 + 5.92087i) q^{29} +(-3.35828 + 1.34215i) q^{30} +(0.614003 + 3.48219i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.0751495 + 0.360213i) q^{33} +(0.657349 - 3.72801i) q^{34} +(4.18878 - 7.25517i) q^{35} +(0.336039 - 2.98112i) q^{36} +(-1.77730 - 3.07838i) q^{37} +(1.19605 - 0.435326i) q^{38} +(-4.74313 - 7.65457i) q^{39} +(1.59951 - 1.34215i) q^{40} +(2.09850 - 1.76085i) q^{41} +(3.66038 + 5.90720i) q^{42} +(-6.48062 + 2.35875i) q^{43} +(-0.106223 - 0.183984i) q^{44} +(5.03986 + 3.71997i) q^{45} +(-0.414721 + 0.718318i) q^{46} +(-0.221796 + 1.25787i) q^{47} +(0.353733 + 1.69554i) q^{48} +(-8.54912 - 3.11163i) q^{49} +(-0.111167 - 0.630460i) q^{50} +(-6.08849 + 2.43329i) q^{51} +(3.98269 + 3.34187i) q^{52} -11.2992 q^{53} +(-4.69570 + 2.22496i) q^{54} +0.443592 q^{55} +(-3.07353 - 2.57900i) q^{56} +(-1.73210 - 1.36380i) q^{57} +(1.59951 + 9.07129i) q^{58} +(8.04363 + 2.92764i) q^{59} +(-3.43531 - 1.13052i) q^{60} +(0.492064 - 2.79063i) q^{61} +(-1.76795 + 3.06218i) q^{62} +(5.35781 - 10.7784i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-10.2010 + 3.71285i) q^{65} +(-0.173973 + 0.324244i) q^{66} +(7.47702 - 6.27396i) q^{67} +(2.89988 - 2.43329i) q^{68} +(1.43594 - 0.0447327i) q^{69} +(7.87232 - 2.86529i) q^{70} +(5.86207 + 10.1534i) q^{71} +(2.17365 - 2.06767i) q^{72} +(-0.375162 + 0.649800i) q^{73} +(0.617250 - 3.50060i) q^{74} +(-0.826812 + 0.738848i) q^{75} +(1.19605 + 0.435326i) q^{76} +(-0.148014 - 0.839430i) q^{77} +(1.28681 - 8.91256i) q^{78} +(-1.81383 - 1.52198i) q^{79} +2.08802 q^{80} +(7.55976 + 4.88366i) q^{81} +2.73940 q^{82} +(-8.73328 - 7.32809i) q^{83} +(-0.993061 + 6.87802i) q^{84} +(1.37256 + 7.78415i) q^{85} +(-6.48062 - 2.35875i) q^{86} +(11.8965 - 10.6308i) q^{87} +(0.0368910 - 0.209219i) q^{88} +(-2.69813 + 4.67329i) q^{89} +(1.46961 + 6.08922i) q^{90} +(10.4298 + 18.0649i) q^{91} +(-0.779421 + 0.283686i) q^{92} +(6.12140 - 0.190695i) q^{93} +(-0.978448 + 0.821016i) q^{94} +(-2.03588 + 1.70830i) q^{95} +(-0.818900 + 1.52624i) q^{96} +(11.8055 - 4.29685i) q^{97} +(-4.54889 - 7.87892i) q^{98} +(0.636104 - 0.0396706i) 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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