LMFDB - Embedded newform 162.2.e.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, 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("162.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.29357651274$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.2
Root			$0.500000 + 2.42499i$ of defining polynomial
Character	$\chi$	$=$	162.73
Dual form			162.2.e.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(3.10057 - 2.60168i) q^{5} +(0.144365 - 0.0525446i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(3.10057 - 2.60168i) q^{5} +(0.144365 - 0.0525446i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.02375 + 3.50524i) q^{10} +(-0.169211 - 0.141985i) q^{11} +(0.103202 + 0.585289i) q^{13} +(0.0266776 + 0.151296i) q^{14} +(0.766044 + 0.642788i) q^{16} +(2.78255 + 4.81952i) q^{17} +(-1.91041 + 3.30893i) q^{19} +(-3.80341 + 1.38433i) q^{20} +(0.169211 - 0.141985i) q^{22} +(-5.50570 - 2.00391i) q^{23} +(1.97651 - 11.2093i) q^{25} -0.594318 q^{26} -0.153630 q^{28} +(-0.129880 + 0.736585i) q^{29} +(-4.77702 - 1.73869i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.22949 + 1.90338i) q^{34} +(0.310909 - 0.538510i) q^{35} +(-1.87388 - 3.24566i) q^{37} +(-2.92692 - 2.45598i) q^{38} +(-0.702841 - 3.98601i) q^{40} +(-0.690156 - 3.91407i) q^{41} +(7.81896 + 6.56088i) q^{43} +(0.110445 + 0.191296i) q^{44} +(2.92952 - 5.07408i) q^{46} +(-0.447025 + 0.162704i) q^{47} +(-5.34423 + 4.48434i) q^{49} +(10.6958 + 3.89296i) q^{50} +(0.103202 - 0.585289i) q^{52} -3.29955 q^{53} -0.894051 q^{55} +(0.0266776 - 0.151296i) q^{56} +(-0.702841 - 0.255813i) q^{58} +(-5.57221 + 4.67564i) q^{59} +(-3.16654 + 1.15253i) q^{61} +(2.54180 - 4.40252i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.84272 + 1.54623i) q^{65} +(1.29509 + 7.34481i) q^{67} +(-0.966370 - 5.48056i) q^{68} +(0.476340 + 0.399697i) q^{70} +(1.42889 + 2.47490i) q^{71} +(0.638922 - 1.10665i) q^{73} +(3.52175 - 1.28181i) q^{74} +(2.92692 - 2.45598i) q^{76} +(-0.0318887 - 0.0116066i) q^{77} +(-0.574268 + 3.25684i) q^{79} +4.04750 q^{80} +3.97445 q^{82} +(1.43627 - 8.14551i) q^{83} +(21.1664 + 7.70392i) q^{85} +(-7.81896 + 6.56088i) q^{86} +(-0.207568 + 0.0755487i) q^{88} +(-2.47882 + 4.29345i) q^{89} +(0.0456525 + 0.0790725i) q^{91} +(4.48829 + 3.76612i) q^{92} +(-0.0826070 - 0.468487i) q^{94} +(2.68543 + 15.2298i) q^{95} +(4.33127 + 3.63437i) q^{97} +(-3.48820 - 6.04174i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	3.10057	−	2.60168i	1.38661	−	1.16351i	0.419925	−	0.907559i	$-0.362056\pi$
$5$	3.10057	−	2.60168i	1.38661	−	1.16351i	0.966690	−	0.255949i	$-0.0823880\pi$
$6$		0			0
$7$	0.144365	−	0.0525446i	0.0545648	−	0.0198600i	−0.314594	−	0.949226i	$-0.601868\pi$
$7$	0.144365	−	0.0525446i	0.0545648	−	0.0198600i	0.369158	+	0.929366i	$0.379646\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	2.02375	+	3.50524i	0.639966	+	1.10845i
$11$	−0.169211	−	0.141985i	−0.0510191	−	0.0428101i	0.616922	−	0.787025i	$-0.288380\pi$
$11$	−0.169211	−	0.141985i	−0.0510191	−	0.0428101i	−0.667941	+	0.744215i	$0.732824\pi$
$12$		0			0
$13$	0.103202	+	0.585289i	0.0286231	+	0.162330i	0.995769	−	0.0918925i	$-0.0292916\pi$
$13$	0.103202	+	0.585289i	0.0286231	+	0.162330i	−0.967146	+	0.254222i	$0.918180\pi$
$14$	0.0266776	+	0.151296i	0.00712988	+	0.0404356i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	2.78255	+	4.81952i	0.674868	+	1.16891i	0.976507	+	0.215484i	$0.0691328\pi$
$17$	2.78255	+	4.81952i	0.674868	+	1.16891i	−0.301639	+	0.953422i	$0.597534\pi$
$18$		0			0
$19$	−1.91041	+	3.30893i	−0.438278	+	0.759120i	−0.997557	−	0.0698599i	$-0.977745\pi$
$19$	−1.91041	+	3.30893i	−0.438278	+	0.759120i	0.559279	+	0.828980i	$0.311078\pi$
$20$	−3.80341	+	1.38433i	−0.850468	+	0.309545i
$21$		0			0
$22$	0.169211	−	0.141985i	0.0360760	−	0.0302713i
$23$	−5.50570	−	2.00391i	−1.14802	−	0.417844i	−0.303215	−	0.952922i	$-0.598060\pi$
$23$	−5.50570	−	2.00391i	−1.14802	−	0.417844i	−0.844803	+	0.535078i	$0.820282\pi$
$24$		0			0
$25$	1.97651	−	11.2093i	0.395302	−	2.24187i
$26$	−0.594318			−0.116555
$27$		0			0
$28$	−0.153630			−0.0290333
$29$	−0.129880	+	0.736585i	−0.0241181	+	0.136780i	−0.994489	−	0.104839i	$-0.966567\pi$
$29$	−0.129880	+	0.736585i	−0.0241181	+	0.136780i	0.970371	+	0.241619i	$0.0776785\pi$
$30$		0			0
$31$	−4.77702	−	1.73869i	−0.857978	−	0.312278i	−0.124689	−	0.992196i	$-0.539793\pi$
$31$	−4.77702	−	1.73869i	−0.857978	−	0.312278i	−0.733289	+	0.679917i	$0.762016\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$		0			0
$34$	−5.22949	+	1.90338i	−0.896850	+	0.326427i
$35$	0.310909	−	0.538510i	0.0525532	−	0.0910248i
$36$		0			0
$37$	−1.87388	−	3.24566i	−0.308065	−	0.533584i	0.669874	−	0.742474i	$-0.266348\pi$
$37$	−1.87388	−	3.24566i	−0.308065	−	0.533584i	−0.977939	+	0.208891i	$0.933015\pi$
$38$	−2.92692	−	2.45598i	−0.474809	−	0.398412i
$39$		0			0
$40$	−0.702841	−	3.98601i	−0.111129	−	0.630244i
$41$	−0.690156	−	3.91407i	−0.107784	−	0.611275i	−0.990072	−	0.140564i	$-0.955109\pi$
$41$	−0.690156	−	3.91407i	−0.107784	−	0.611275i	0.882287	−	0.470711i	$-0.156003\pi$
$42$		0			0
$43$	7.81896	+	6.56088i	1.19238	+	1.00053i	0.999815	+	0.0192411i	$0.00612500\pi$
$43$	7.81896	+	6.56088i	1.19238	+	1.00053i	0.192565	+	0.981284i	$0.438319\pi$
$44$	0.110445	+	0.191296i	0.0166502	+	0.0288390i
$45$		0			0
$46$	2.92952	−	5.07408i	0.431935	−	0.748133i
$47$	−0.447025	+	0.162704i	−0.0652054	+	0.0237328i	−0.374417	−	0.927260i	$-0.622157\pi$
$47$	−0.447025	+	0.162704i	−0.0652054	+	0.0237328i	0.309212	+	0.950993i	$0.399935\pi$
$48$		0			0
$49$	−5.34423	+	4.48434i	−0.763462	+	0.640620i
$50$	10.6958	+	3.89296i	1.51262	+	0.550548i
$51$		0			0
$52$	0.103202	−	0.585289i	0.0143116	−	0.0811650i
$53$	−3.29955			−0.453228			−0.226614	−	0.973985i	$-0.572766\pi$
$53$	−3.29955			−0.453228			−0.226614	+	0.973985i	$0.572766\pi$
$54$		0			0
$55$	−0.894051			−0.120554
$56$	0.0266776	−	0.151296i	0.00356494	−	0.0202178i
$57$		0			0
$58$	−0.702841	−	0.255813i	−0.0922876	−	0.0335899i
$59$	−5.57221	+	4.67564i	−0.725440	+	0.608716i	−0.928884	−	0.370370i	$-0.879231\pi$
$59$	−5.57221	+	4.67564i	−0.725440	+	0.608716i	0.203444	+	0.979086i	$0.434786\pi$
$60$		0			0
$61$	−3.16654	+	1.15253i	−0.405434	+	0.147566i	−0.536684	−	0.843783i	$-0.680323\pi$
$61$	−3.16654	+	1.15253i	−0.405434	+	0.147566i	0.131250	+	0.991349i	$0.458101\pi$
$62$	2.54180	−	4.40252i	0.322809	−	0.559121i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.84272	+	1.54623i	0.228561	+	0.191786i
$66$		0			0
$67$	1.29509	+	7.34481i	0.158220	+	0.897312i	0.955782	+	0.294075i	$0.0950115\pi$
$67$	1.29509	+	7.34481i	0.158220	+	0.897312i	−0.797562	+	0.603237i	$0.793877\pi$
$68$	−0.966370	−	5.48056i	−0.117190	−	0.664615i
$69$		0			0
$70$	0.476340	+	0.399697i	0.0569335	+	0.0477729i
$71$	1.42889	+	2.47490i	0.169578	+	0.293717i	0.938271	−	0.345900i	$-0.112426\pi$
$71$	1.42889	+	2.47490i	0.169578	+	0.293717i	−0.768694	+	0.639617i	$0.779093\pi$
$72$		0			0
$73$	0.638922	−	1.10665i	0.0747802	−	0.129523i	−0.826210	−	0.563362i	$-0.809508\pi$
$73$	0.638922	−	1.10665i	0.0747802	−	0.129523i	0.900991	+	0.433838i	$0.142841\pi$
$74$	3.52175	−	1.28181i	0.409395	−	0.149008i
$75$		0			0
$76$	2.92692	−	2.45598i	0.335740	−	0.281720i
$77$	−0.0318887	−	0.0116066i	−0.00363406	−	0.00132269i
$78$		0			0
$79$	−0.574268	+	3.25684i	−0.0646102	+	0.366423i	0.935310	+	0.353828i	$0.115120\pi$
$79$	−0.574268	+	3.25684i	−0.0646102	+	0.366423i	−0.999921	+	0.0125947i	$0.995991\pi$
$80$	4.04750			0.452524
$81$		0			0
$82$	3.97445			0.438904
$83$	1.43627	−	8.14551i	0.157651	−	0.894085i	−0.798670	−	0.601769i	$-0.794463\pi$
$83$	1.43627	−	8.14551i	0.157651	−	0.894085i	0.956322	−	0.292316i	$-0.0944261\pi$
$84$		0			0
$85$	21.1664	+	7.70392i	2.29581	+	0.835608i
$86$	−7.81896	+	6.56088i	−0.843140	+	0.707478i
$87$		0			0
$88$	−0.207568	+	0.0755487i	−0.0221269	+	0.00805352i
$89$	−2.47882	+	4.29345i	−0.262755	+	0.455105i	−0.966973	−	0.254879i	$-0.917964\pi$
$89$	−2.47882	+	4.29345i	−0.262755	+	0.455105i	0.704218	+	0.709984i	$0.251298\pi$
$90$		0			0
$91$	0.0456525	+	0.0790725i	0.00478569	+	0.00828905i
$92$	4.48829	+	3.76612i	0.467936	+	0.392645i
$93$		0			0
$94$	−0.0826070	−	0.468487i	−0.00852026	−	0.0483208i
$95$	2.68543	+	15.2298i	0.275519	+	1.56255i
$96$		0			0
$97$	4.33127	+	3.63437i	0.439774	+	0.369014i	0.835625	−	0.549301i	$-0.185106\pi$
$97$	4.33127	+	3.63437i	0.439774	+	0.369014i	−0.395851	+	0.918315i	$0.629550\pi$
$98$	−3.48820	−	6.04174i	−0.352361	−	0.610308i
$99$		0			0
$100$	−5.69113	+	9.85733i	−0.569113	+	0.985733i
$101$	14.8467	−	5.40376i	1.47730	−	0.537694i	0.527229	−	0.849723i	$-0.323231\pi$
$101$	14.8467	−	5.40376i	1.47730	−	0.537694i	0.950072	+	0.312029i	$0.101009\pi$
$102$		0			0
$103$	8.19426	−	6.87580i	0.807404	−	0.677493i	−0.142582	−	0.989783i	$-0.545541\pi$
$103$	8.19426	−	6.87580i	0.807404	−	0.677493i	0.949987	+	0.312290i	$0.101096\pi$
$104$	0.558476	+	0.203269i	0.0547631	+	0.0199321i
$105$		0			0
$106$	0.572961	−	3.24943i	0.0556509	−	0.315612i
$107$	−1.85236			−0.179075			−0.0895374	−	0.995983i	$-0.528539\pi$
$107$	−1.85236			−0.179075			−0.0895374	+	0.995983i	$0.528539\pi$
$108$		0			0
$109$	−14.5495			−1.39359			−0.696793	−	0.717273i	$-0.745390\pi$
$109$	−14.5495			−1.39359			−0.696793	+	0.717273i	$0.745390\pi$
$110$	0.155250	−	0.880468i	0.0148025	−	0.0839494i
$111$		0			0
$112$	0.144365	+	0.0525446i	0.0136412	+	0.00496500i
$113$	10.2514	−	8.60195i	0.964371	−	0.809204i	−0.0172875	−	0.999851i	$-0.505503\pi$
$113$	10.2514	−	8.60195i	0.964371	−	0.809204i	0.981659	+	0.190647i	$0.0610586\pi$
$114$		0			0
$115$	−22.2843	+	8.11083i	−2.07802	+	0.756339i
$116$	0.373974	−	0.647742i	0.0347226	−	0.0601413i
$117$		0			0
$118$	−3.63700	−	6.29947i	−0.334813	−	0.579913i
$119$	0.654943	+	0.549562i	0.0600385	+	0.0503783i
$120$		0			0
$121$	−1.90166	−	10.7848i	−0.172878	−	0.980439i
$122$	−0.585154	−	3.31857i	−0.0529773	−	0.300449i
$123$		0			0
$124$	3.89426	+	3.26767i	0.349715	+	0.293446i
$125$	−12.9161	−	22.3713i	−1.15525	−	2.00095i
$126$		0			0
$127$	9.31545	−	16.1348i	0.826612	−	1.43173i	−0.0740688	−	0.997253i	$-0.523598\pi$
$127$	9.31545	−	16.1348i	0.826612	−	1.43173i	0.900681	−	0.434481i	$-0.143068\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$		0			0
$130$	−1.84272	+	1.54623i	−0.161617	+	0.135613i
$131$	−6.45330	−	2.34881i	−0.563828	−	0.205217i	0.0443519	−	0.999016i	$-0.485878\pi$
$131$	−6.45330	−	2.34881i	−0.563828	−	0.205217i	−0.608180	+	0.793799i	$0.708100\pi$
$132$		0			0
$133$	−0.101930	+	0.578075i	−0.00883847	+	0.0501254i
$134$	−7.45812			−0.644283
$135$		0			0
$136$	5.56510			0.477204
$137$	−2.60219	+	14.7577i	−0.222320	+	1.26084i	0.645423	+	0.763826i	$0.276681\pi$
$137$	−2.60219	+	14.7577i	−0.222320	+	1.26084i	−0.867743	+	0.497014i	$0.834430\pi$
$138$		0			0
$139$	−17.0110	−	6.19150i	−1.44286	−	0.525156i	−0.502269	−	0.864711i	$-0.667501\pi$
$139$	−17.0110	−	6.19150i	−1.44286	−	0.525156i	−0.940586	+	0.339555i	$0.889724\pi$
$140$	−0.476340	+	0.399697i	−0.0402581	+	0.0337805i
$141$		0			0
$142$	−2.68543	+	0.977416i	−0.225356	+	0.0820229i
$143$	0.0656393	−	0.113691i	0.00548904	−	0.00950729i
$144$		0			0
$145$	1.51366	+	2.62174i	0.125703	+	0.217723i
$146$	0.978886	+	0.821383i	0.0810132	+	0.0679781i
$147$		0			0
$148$	0.650793	+	3.69083i	0.0534949	+	0.303384i
$149$	2.60884	+	14.7955i	0.213725	+	1.21209i	0.883106	+	0.469174i	$0.155448\pi$
$149$	2.60884	+	14.7955i	0.213725	+	1.21209i	−0.669381	+	0.742919i	$0.733441\pi$
$150$		0			0
$151$	−4.32258	−	3.62708i	−0.351767	−	0.295167i	0.449732	−	0.893163i	$-0.351519\pi$
$151$	−4.32258	−	3.62708i	−0.351767	−	0.295167i	−0.801499	+	0.597996i	$0.795964\pi$
$152$	1.91041	+	3.30893i	0.154955	+	0.268389i
$153$		0			0
$154$	0.0169676	−	0.0293888i	0.00136729	−	0.00236822i
$155$	−19.3350	+	7.03736i	−1.55302	+	0.565254i
$156$		0			0
$157$	5.54978	−	4.65682i	0.442921	−	0.371655i	−0.393880	−	0.919162i	$-0.628868\pi$
$157$	5.54978	−	4.65682i	0.442921	−	0.371655i	0.836801	+	0.547507i	$0.184423\pi$
$158$	−3.10764	−	1.13109i	−0.247230	−	0.0899845i
$159$		0			0
$160$	−0.702841	+	3.98601i	−0.0555645	+	0.315122i
$161$	−0.900125			−0.0709398
$162$		0			0
$163$	14.1079			1.10501			0.552506	−	0.833509i	$-0.313672\pi$
$163$	14.1079			1.10501			0.552506	+	0.833509i	$0.313672\pi$
$164$	−0.690156	+	3.91407i	−0.0538921	+	0.305637i
$165$		0			0
$166$	7.77235	+	2.82890i	0.603251	+	0.219566i
$167$	10.5889	−	8.88510i	0.819390	−	0.687550i	−0.133439	−	0.991057i	$-0.542602\pi$
$167$	10.5889	−	8.88510i	0.819390	−	0.687550i	0.952829	+	0.303507i	$0.0981576\pi$
$168$		0			0
$169$	11.8841	−	4.32546i	0.914161	−	0.332727i
$170$	−11.2624	+	19.5070i	−0.863785	+	1.49612i
$171$		0			0
$172$	−5.10346	−	8.83945i	−0.389135	−	0.674002i
$173$	3.00999	+	2.52568i	0.228845	+	0.192024i	0.749999	−	0.661439i	$-0.230054\pi$
$173$	3.00999	+	2.52568i	0.228845	+	0.192024i	−0.521154	+	0.853463i	$0.674498\pi$
$174$		0			0
$175$	−0.303651	−	1.72209i	−0.0229539	−	0.130178i
$176$	−0.0383571	−	0.217534i	−0.00289127	−	0.0163972i
$177$		0			0
$178$	−3.79778	−	3.18671i	−0.284656	−	0.238854i
$179$	1.42211	+	2.46317i	0.106294	+	0.184106i	0.914266	−	0.405115i	$-0.132768\pi$
$179$	1.42211	+	2.46317i	0.106294	+	0.184106i	−0.807972	+	0.589220i	$0.799435\pi$
$180$		0			0
$181$	−6.46274	+	11.1938i	−0.480372	+	0.832028i	−0.999746	−	0.0225186i	$-0.992832\pi$
$181$	−6.46274	+	11.1938i	−0.480372	+	0.832028i	0.519375	+	0.854547i	$0.326165\pi$
$182$	−0.0857987	+	0.0312282i	−0.00635982	+	0.00231479i
$183$		0			0
$184$	−4.48829	+	3.76612i	−0.330881	+	0.277642i
$185$	−14.2543	−	5.18813i	−1.04800	−	0.381439i
$186$		0			0
$187$	0.213461	−	1.21060i	0.0156098	−	0.0885277i
$188$	0.475715			0.0346951
$189$		0			0
$190$	−15.4648			−1.12193
$191$	3.49774	−	19.8367i	0.253088	−	1.43533i	−0.547846	−	0.836579i	$-0.684552\pi$
$191$	3.49774	−	19.8367i	0.253088	−	1.43533i	0.800934	−	0.598753i	$-0.204337\pi$
$192$		0			0
$193$	−9.03669	−	3.28909i	−0.650476	−	0.236754i	−0.00435663	−	0.999991i	$-0.501387\pi$
$193$	−9.03669	−	3.28909i	−0.650476	−	0.236754i	−0.646119	+	0.763237i	$0.723609\pi$
$194$	−4.33127	+	3.63437i	−0.310967	+	0.260932i
$195$		0			0
$196$	6.55567	−	2.38607i	0.468262	−	0.170433i
$197$	3.77527	−	6.53895i	0.268977	−	0.465881i	−0.699621	−	0.714514i	$-0.746648\pi$
$197$	3.77527	−	6.53895i	0.268977	−	0.465881i	0.968598	+	0.248633i	$0.0799812\pi$
$198$		0			0
$199$	6.07071	+	10.5148i	0.430341	+	0.745372i	0.996903	−	0.0786471i	$-0.0250600\pi$
$199$	6.07071	+	10.5148i	0.430341	+	0.745372i	−0.566562	+	0.824019i	$0.691727\pi$
$200$	−8.71932	−	7.31638i	−0.616549	−	0.517346i
$201$		0			0
$202$	2.74356	+	15.5595i	0.193036	+	1.09476i
$203$	0.0199534	+	0.113162i	0.00140046	+	0.00794238i
$204$		0			0
$205$	−12.3230	−	10.3403i	−0.860678	−	0.722195i
$206$	5.34842	+	9.26374i	0.372642	+	0.645435i
$207$		0			0
$208$	−0.297159	+	0.514694i	−0.0206043	+	0.0356876i
$209$	0.793081	−	0.288658i	0.0548586	−	0.0199669i
$210$		0			0
$211$	−5.53378	+	4.64340i	−0.380961	+	0.319665i	−0.813080	−	0.582152i	$-0.802211\pi$
$211$	−5.53378	+	4.64340i	−0.380961	+	0.319665i	0.432118	+	0.901817i	$0.357766\pi$
$212$	3.10057	+	1.12851i	0.212948	+	0.0775066i
$213$		0			0
$214$	0.321660	−	1.82422i	0.0219882	−	0.124701i
$215$	41.3125			2.81749
$216$		0			0
$217$	−0.780993			−0.0530173
$218$	2.52649	−	14.3284i	0.171115	−	0.970443i
$219$		0			0
$220$	0.840133	+	0.305783i	0.0566418	+	0.0206159i
$221$	−2.53365	+	2.12598i	−0.170432	+	0.143009i
$222$		0			0
$223$	23.9856	−	8.73004i	1.60619	−	0.584607i	0.625512	−	0.780214i	$-0.284890\pi$
$223$	23.9856	−	8.73004i	1.60619	−	0.584607i	0.980682	+	0.195607i	$0.0626678\pi$
$224$	−0.0768150	+	0.133048i	−0.00513242	+	0.00888961i
$225$		0			0
$226$	6.69113	+	11.5894i	0.445087	+	0.770914i
$227$	−10.9999	−	9.22998i	−0.730086	−	0.612615i	0.200069	−	0.979782i	$-0.435883\pi$
$227$	−10.9999	−	9.22998i	−0.730086	−	0.612615i	−0.930155	+	0.367167i	$0.880328\pi$
$228$		0			0
$229$	0.704853	+	3.99742i	0.0465780	+	0.264157i	0.999200	−	0.0400010i	$-0.0127361\pi$
$229$	0.704853	+	3.99742i	0.0465780	+	0.264157i	−0.952622	+	0.304158i	$0.901625\pi$
$230$	−4.11798	−	23.3542i	−0.271531	−	1.53993i
$231$		0			0
$232$	0.572961	+	0.480772i	0.0376168	+	0.0315642i
$233$	8.48936	+	14.7040i	0.556157	+	0.963292i	0.997813	+	0.0661072i	$0.0210579\pi$
$233$	8.48936	+	14.7040i	0.556157	+	0.963292i	−0.441656	+	0.897185i	$0.645609\pi$
$234$		0			0
$235$	−0.962728	+	1.66749i	−0.0628014	+	0.108775i
$236$	6.83533	−	2.48786i	0.444942	−	0.161946i
$237$		0			0
$238$	−0.654943	+	0.549562i	−0.0424536	+	0.0356228i
$239$	20.0419	+	7.29464i	1.29640	+	0.471851i	0.895823	−	0.444412i	$-0.146587\pi$
$239$	20.0419	+	7.29464i	1.29640	+	0.471851i	0.400577	+	0.916263i	$0.368810\pi$
$240$		0			0
$241$	−1.86745	+	10.5909i	−0.120293	+	0.682217i	0.863699	+	0.504007i	$0.168142\pi$
$241$	−1.86745	+	10.5909i	−0.120293	+	0.682217i	−0.983993	+	0.178210i	$0.942970\pi$
$242$	10.9512			0.703970
$243$		0			0
$244$	3.36977			0.215727
$245$	−4.90330	+	27.8080i	−0.313260	+	1.77659i
$246$		0			0
$247$	−2.13384	−	0.776653i	−0.135773	−	0.0494172i
$248$	−3.89426	+	3.26767i	−0.247286	+	0.207497i
$249$		0			0
$250$	24.2743	−	8.83513i	1.53524	−	0.558783i
$251$	2.08811	−	3.61672i	0.131801	−	0.228285i	−0.792570	−	0.609781i	$-0.791257\pi$
$251$	2.08811	−	3.61672i	0.131801	−	0.228285i	0.924371	+	0.381495i	$0.124591\pi$
$252$		0			0
$253$	0.647101	+	1.12081i	0.0406829	+	0.0704649i
$254$	14.2721	+	11.9757i	0.895511	+	0.751423i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.83797	−	16.0949i	−0.177028	−	1.00397i	−0.935777	−	0.352592i	$-0.885301\pi$
$257$	−2.83797	−	16.0949i	−0.177028	−	1.00397i	0.758750	−	0.651382i	$-0.225811\pi$
$258$		0			0
$259$	−0.441065	−	0.370098i	−0.0274065	−	0.0229967i
$260$	−1.20275	−	2.08323i	−0.0745914	−	0.129196i
$261$		0			0
$262$	3.43373	−	5.94740i	0.212137	−	0.367431i
$263$	−2.51963	+	0.917071i	−0.155367	+	0.0565490i	−0.418533	−	0.908202i	$-0.637456\pi$
$263$	−2.51963	+	0.917071i	−0.155367	+	0.0565490i	0.263166	+	0.964751i	$0.415233\pi$
$264$		0			0
$265$	−10.2305	+	8.58439i	−0.628453	+	0.527335i
$266$	−0.551593	−	0.200763i	−0.0338203	−	0.0123096i
$267$		0			0
$268$	1.29509	−	7.34481i	0.0791101	−	0.448656i
$269$	−22.3509			−1.36276			−0.681380	−	0.731930i	$-0.738620\pi$
$269$	−22.3509			−1.36276			−0.681380	+	0.731930i	$0.738620\pi$
$270$		0			0
$271$	25.4813			1.54788			0.773941	−	0.633258i	$-0.218283\pi$
$271$	25.4813			1.54788			0.773941	+	0.633258i	$0.218283\pi$
$272$	−0.966370	+	5.48056i	−0.0585948	+	0.332308i
$273$		0			0
$274$	−14.0817	−	5.12531i	−0.850705	−	0.309631i
$275$	−1.92601	+	1.61611i	−0.116143	+	0.0974552i
$276$		0			0
$277$	2.41221	−	0.877972i	0.144936	−	0.0527523i	−0.268534	−	0.963270i	$-0.586539\pi$
$277$	2.41221	−	0.877972i	0.144936	−	0.0527523i	0.413469	+	0.910518i	$0.364317\pi$
$278$	9.05137	−	15.6774i	0.542865	−	0.940270i
$279$		0			0
$280$	−0.310909	−	0.538510i	−0.0185804	−	0.0321821i
$281$	−16.2374	−	13.6248i	−0.968642	−	0.812787i	0.0136956	−	0.999906i	$-0.495640\pi$
$281$	−16.2374	−	13.6248i	−0.968642	−	0.812787i	−0.982337	+	0.187119i	$0.940085\pi$
$282$		0			0
$283$	−3.40928	−	19.3350i	−0.202660	−	1.14934i	−0.901079	−	0.433655i	$-0.857224\pi$
$283$	−3.40928	−	19.3350i	−0.202660	−	1.14934i	0.698419	−	0.715689i	$-0.253887\pi$
$284$	−0.496247	−	2.81436i	−0.0294468	−	0.167001i
$285$		0			0
$286$	0.100565	+	0.0843843i	0.00594655	+	0.00498975i
$287$	−0.305297	−	0.528791i	−0.0180211	−	0.0312135i
$288$		0			0
$289$	−6.98519	+	12.0987i	−0.410894	+	0.711689i
$290$	−2.84475	+	1.03540i	−0.167049	+	0.0608010i
$291$		0			0
$292$	−0.978886	+	0.821383i	−0.0572850	+	0.0480678i
$293$	20.1808	+	7.34522i	1.17898	+	0.429112i	0.855840	−	0.517240i	$-0.173041\pi$
$293$	20.1808	+	7.34522i	1.17898	+	0.429112i	0.323136	+	0.946352i	$0.395263\pi$
$294$		0			0
$295$	−5.11247	+	28.9942i	−0.297659	+	1.68811i
$296$	−3.74777			−0.217835
$297$		0			0
$298$	−15.0237			−0.870301
$299$	0.604666	−	3.42923i	0.0349688	−	0.198318i
$300$		0			0
$301$	1.47352	+	0.536318i	0.0849324	+	0.0309129i
$302$	4.32258	−	3.62708i	0.248737	−	0.208715i
$303$		0			0
$304$	−3.59040	+	1.30680i	−0.205923	+	0.0749500i
$305$	−6.81956	+	11.8118i	−0.390487	+	0.676343i
$306$		0			0
$307$	−2.82636	−	4.89540i	−0.161309	−	0.279395i	0.774029	−	0.633150i	$-0.218238\pi$
$307$	−2.82636	−	4.89540i	−0.161309	−	0.279395i	−0.935338	+	0.353754i	$0.884905\pi$
$308$	0.0259959	+	0.0218132i	0.00148126	+	0.00124292i
$309$		0			0
$310$	−3.57296	−	20.2633i	−0.202931	−	1.15088i
$311$	−1.61574	−	9.16334i	−0.0916205	−	0.519605i	−0.995731	−	0.0923061i	$-0.970576\pi$
$311$	−1.61574	−	9.16334i	−0.0916205	−	0.519605i	0.904110	−	0.427299i	$-0.140535\pi$
$312$		0			0
$313$	−2.05976	−	1.72835i	−0.116425	−	0.0976920i	0.582717	−	0.812675i	$-0.301990\pi$
$313$	−2.05976	−	1.72835i	−0.116425	−	0.0976920i	−0.699141	+	0.714983i	$0.746434\pi$
$314$	3.62236	+	6.27412i	0.204422	+	0.354069i
$315$		0			0
$316$	1.65354	−	2.86401i	0.0930189	−	0.161113i
$317$	−26.2511	+	9.55461i	−1.47441	+	0.536641i	−0.949294	−	0.314391i	$-0.898200\pi$
$317$	−26.2511	+	9.55461i	−1.47441	+	0.536641i	−0.525114	+	0.851032i	$0.675977\pi$
$318$		0			0
$319$	0.126561	−	0.106197i	0.00708607	−	0.00594592i
$320$	−3.80341	−	1.38433i	−0.212617	−	0.0773862i
$321$		0			0
$322$	0.156305	−	0.886450i	0.00871054	−	0.0494000i
$323$	−21.2633			−1.18312
$324$		0			0
$325$	6.76468			0.375237
$326$	−2.44980	+	13.8935i	−0.135682	+	0.769491i
$327$		0			0
$328$	−3.73476	−	1.35934i	−0.206218	−	0.0750571i
$329$	−0.0559856	+	0.0469775i	−0.00308659	+	0.00258995i
$330$		0			0
$331$	−0.794144	+	0.289045i	−0.0436501	+	0.0158873i	−0.363753	−	0.931495i	$-0.618505\pi$
$331$	−0.794144	+	0.289045i	−0.0436501	+	0.0158873i	0.320103	+	0.947383i	$0.396283\pi$
$332$	−4.13558	+	7.16304i	−0.226970	+	0.393123i
$333$		0			0
$334$	6.91138	+	11.9709i	0.378174	+	0.655017i
$335$	23.1244	+	19.4037i	1.26342	+	1.06014i
$336$		0			0
$337$	5.09088	+	28.8718i	0.277318	+	1.57275i	0.731501	+	0.681840i	$0.238820\pi$
$337$	5.09088	+	28.8718i	0.277318	+	1.57275i	−0.454183	+	0.890908i	$0.650069\pi$
$338$	2.19609	+	12.4547i	0.119452	+	0.677444i
$339$		0			0
$340$	−17.2550	−	14.4786i	−0.935782	−	0.785214i
$341$	0.561457	+	0.972472i	0.0304046	+	0.0526623i
$342$		0			0
$343$	−1.07360	+	1.85953i	−0.0579688	+	0.100405i
$344$	9.59137	−	3.49097i	0.517132	−	0.188221i
$345$		0			0
$346$	−3.00999	+	2.52568i	−0.161818	+	0.135781i
$347$	−18.9820	−	6.90888i	−1.01901	−	0.370888i	−0.222121	−	0.975019i	$-0.571298\pi$
$347$	−18.9820	−	6.90888i	−1.01901	−	0.370888i	−0.796885	+	0.604131i	$0.793520\pi$
$348$		0			0
$349$	1.66866	−	9.46343i	0.0893212	−	0.506566i	−0.907019	−	0.421090i	$-0.861648\pi$
$349$	1.66866	−	9.46343i	0.0893212	−	0.506566i	0.996340	−	0.0854761i	$-0.0272411\pi$
$350$	1.74866			0.0934697
$351$		0			0
$352$	0.220890			0.0117735
$353$	1.70637	−	9.67729i	0.0908208	−	0.515070i	−0.905127	−	0.425141i	$-0.860225\pi$
$353$	1.70637	−	9.67729i	0.0908208	−	0.515070i	0.995948	−	0.0899297i	$-0.0286642\pi$
$354$		0			0
$355$	10.8693	+	3.95609i	0.576881	+	0.209968i
$356$	3.79778	−	3.18671i	0.201282	−	0.168896i
$357$		0			0
$358$	−2.67269	+	0.972781i	−0.141256	+	0.0514131i
$359$	5.94469	−	10.2965i	0.313749	−	0.543429i	−0.665422	−	0.746467i	$-0.731748\pi$
$359$	5.94469	−	10.2965i	0.313749	−	0.543429i	0.979171	+	0.203039i	$0.0650817\pi$
$360$		0			0
$361$	2.20067	+	3.81167i	0.115825	+	0.200614i
$362$	−9.90149	−	8.30834i	−0.520411	−	0.436676i
$363$		0			0
$364$	−0.0158550	−	0.0899179i	−0.000831026	−	0.00471298i
$365$	−0.898122	−	5.09350i	−0.0470098	−	0.266606i
$366$		0			0
$367$	−27.7867	−	23.3158i	−1.45045	−	1.21708i	−0.932248	−	0.361821i	$-0.882155\pi$
$367$	−27.7867	−	23.3158i	−1.45045	−	1.21708i	−0.518207	−	0.855255i	$-0.673400\pi$
$368$	−2.92952	−	5.07408i	−0.152712	−	0.264505i
$369$		0			0
$370$	7.58455	−	13.1368i	0.394302	−	0.682951i
$371$	−0.476340	+	0.173374i	−0.0247303	+	0.00900111i
$372$		0			0
$373$	10.8389	−	9.09489i	0.561215	−	0.470916i	−0.317502	−	0.948258i	$-0.602844\pi$
$373$	10.8389	−	9.09489i	0.561215	−	0.470916i	0.878718	+	0.477342i	$0.158400\pi$
$374$	1.15514	+	0.420436i	0.0597308	+	0.0217403i
$375$		0			0
$376$	−0.0826070	+	0.468487i	−0.00426013	+	0.0241604i
$377$	−0.444519			−0.0228939
$378$		0			0
$379$	−29.5237			−1.51653			−0.758265	−	0.651946i	$-0.773953\pi$
$379$	−29.5237			−1.51653			−0.758265	+	0.651946i	$0.773953\pi$
$380$	2.68543	−	15.2298i	0.137760	−	0.781273i
$381$		0			0
$382$	18.9279	+	6.88921i	0.968438	+	0.352483i
$383$	−18.9404	+	15.8929i	−0.967811	+	0.812090i	−0.982206	−	0.187807i	$-0.939862\pi$
$383$	−18.9404	+	15.8929i	−0.967811	+	0.812090i	0.0143953	+	0.999896i	$0.495418\pi$
$384$		0			0
$385$	−0.129070	+	0.0469775i	−0.00657800	+	0.00239420i
$386$	4.80832	−	8.32826i	0.244737	−	0.423897i
$387$		0			0
$388$	−2.82704	−	4.89657i	−0.143521	−	0.248586i
$389$	−11.1425	−	9.34969i	−0.564948	−	0.474048i	0.315017	−	0.949086i	$-0.397990\pi$
$389$	−11.1425	−	9.34969i	−0.564948	−	0.474048i	−0.879965	+	0.475038i	$0.842434\pi$
$390$		0			0
$391$	−5.66201	−	32.1108i	−0.286340	−	1.62391i
$392$	1.21144	+	6.87041i	0.0611869	+	0.347008i
$393$		0			0
$394$	5.78404	+	4.85339i	0.291396	+	0.244510i
$395$	6.69270	+	11.5921i	0.336746	+	0.583262i
$396$		0			0
$397$	−2.10870	+	3.65238i	−0.105833	+	0.183308i	−0.914078	−	0.405538i	$-0.867084\pi$
$397$	−2.10870	+	3.65238i	−0.105833	+	0.183308i	0.808245	+	0.588846i	$0.200418\pi$
$398$	−11.4092	+	4.15261i	−0.571891	+	0.208151i
$399$		0			0
$400$	8.71932	−	7.31638i	0.435966	−	0.365819i
$401$	−15.2143	−	5.53755i	−0.759765	−	0.276532i	−0.0670561	−	0.997749i	$-0.521361\pi$
$401$	−15.2143	−	5.53755i	−0.759765	−	0.276532i	−0.692709	+	0.721217i	$0.743583\pi$
$402$		0			0
$403$	0.524638	−	2.97537i	0.0261341	−	0.148214i
$404$	−15.7995			−0.786056
$405$		0			0
$406$	−0.114907			−0.00570275
$407$	−0.143753	+	0.815266i	−0.00712559	+	0.0404112i
$408$		0			0
$409$	−3.70550	−	1.34869i	−0.183225	−	0.0666885i	0.248778	−	0.968560i	$-0.419971\pi$
$409$	−3.70550	−	1.34869i	−0.183225	−	0.0666885i	−0.432003	+	0.901872i	$0.642193\pi$
$410$	12.3230	−	10.3403i	0.608591	−	0.510669i
$411$		0			0
$412$	−10.0517	+	3.65854i	−0.495214	+	0.180243i
$413$	−0.558753	+	0.967788i	−0.0274944	+	0.0476217i
$414$		0			0
$415$	−16.7388	−	28.9924i	−0.821674	−	1.42318i
$416$	−0.455274	−	0.382020i	−0.0223216	−	0.0187301i
$417$		0			0
$418$	0.146555	+	0.831157i	0.00716826	+	0.0406532i
$419$	5.98994	+	33.9707i	0.292628	+	1.65957i	0.676690	+	0.736268i	$0.263414\pi$
$419$	5.98994	+	33.9707i	0.292628	+	1.65957i	−0.384062	+	0.923307i	$0.625475\pi$
$420$		0			0
$421$	−8.80184	−	7.38562i	−0.428976	−	0.359953i	0.402589	−	0.915381i	$-0.368110\pi$
$421$	−8.80184	−	7.38562i	−0.428976	−	0.359953i	−0.831565	+	0.555427i	$0.812555\pi$
$422$	−3.61192	−	6.25603i	−0.175826	−	0.304539i
$423$		0			0
$424$	−1.64978	+	2.85750i	−0.0801202	+	0.138772i
$425$	59.5234	−	21.6647i	2.88731	−	1.05089i
$426$		0			0
$427$	−0.396579	+	0.332769i	−0.0191918	+	0.0161038i
$428$	1.74065	+	0.633546i	0.0841376	+	0.0306236i
$429$		0			0
$430$	−7.17384	+	40.6849i	−0.345954	+	1.96200i
$431$	−24.6371			−1.18673			−0.593364	−	0.804934i	$-0.702201\pi$
$431$	−24.6371			−1.18673			−0.593364	+	0.804934i	$0.702201\pi$
$432$		0			0
$433$	12.8011			0.615181			0.307590	−	0.951519i	$-0.400477\pi$
$433$	12.8011			0.615181			0.307590	+	0.951519i	$0.400477\pi$
$434$	0.135618	−	0.769128i	0.00650988	−	0.0369193i
$435$		0			0
$436$	13.6720	+	4.97621i	0.654771	+	0.238317i
$437$	17.1489	−	14.3897i	0.820345	−	0.688351i
$438$		0			0
$439$	34.1541	−	12.4311i	1.63009	−	0.593303i	0.644822	−	0.764333i	$-0.276932\pi$
$439$	34.1541	−	12.4311i	1.63009	−	0.593303i	0.985266	+	0.171029i	$0.0547093\pi$
$440$	−0.447025	+	0.774271i	−0.0213111	+	0.0369119i
$441$		0			0
$442$	−1.65372	−	2.86433i	−0.0786595	−	0.136242i
$443$	29.5753	+	24.8166i	1.40516	+	1.17907i	0.958752	+	0.284245i	$0.0917428\pi$
$443$	29.5753	+	24.8166i	1.40516	+	1.17907i	0.446412	+	0.894828i	$0.352702\pi$
$444$		0			0
$445$	3.48444	+	19.7612i	0.165178	+	0.936772i
$446$	4.43236	+	25.1372i	0.209878	+	1.19028i
$447$		0			0
$448$	−0.117687	−	0.0987515i	−0.00556021	−	0.00466557i
$449$	−7.76357	−	13.4469i	−0.366385	−	0.634598i	0.622612	−	0.782531i	$-0.286072\pi$
$449$	−7.76357	−	13.4469i	−0.366385	−	0.634598i	−0.988997	+	0.147932i	$0.952738\pi$
$450$		0			0
$451$	−0.438957	+	0.760296i	−0.0206697	+	0.0358010i
$452$	−12.5752	+	4.57700i	−0.591488	+	0.215284i
$453$		0			0
$454$	10.9999	−	9.22998i	0.516249	−	0.433184i
$455$	0.347270	+	0.126396i	0.0162803	+	0.00592554i
$456$		0			0
$457$	−6.26933	+	35.5551i	−0.293267	+	1.66320i	0.380897	+	0.924618i	$0.375615\pi$
$457$	−6.26933	+	35.5551i	−0.293267	+	1.66320i	−0.674164	+	0.738582i	$0.735496\pi$
$458$	−4.05908			−0.189669
$459$		0			0
$460$	23.7145			1.10569
$461$	−1.72646	+	9.79122i	−0.0804091	+	0.456023i	0.917844	+	0.396941i	$0.129928\pi$
$461$	−1.72646	+	9.79122i	−0.0804091	+	0.456023i	−0.998253	+	0.0590816i	$0.981183\pi$
$462$		0			0
$463$	18.0852	+	6.58248i	0.840492	+	0.305914i	0.726158	−	0.687528i	$-0.241304\pi$
$463$	18.0852	+	6.58248i	0.840492	+	0.305914i	0.114334	+	0.993442i	$0.463527\pi$
$464$	−0.572961	+	0.480772i	−0.0265991	+	0.0223193i
$465$		0			0
$466$	−15.9548	+	5.80707i	−0.739091	+	0.269007i
$467$	15.7918	−	27.3521i	0.730756	−	1.26571i	−0.225805	−	0.974173i	$-0.572501\pi$
$467$	15.7918	−	27.3521i	0.730756	−	1.26571i	0.956561	−	0.291534i	$-0.0941655\pi$
$468$		0			0
$469$	0.572895	+	0.992284i	0.0264539	+	0.0458194i
$470$	−1.47498	−	1.23766i	−0.0680359	−	0.0570889i
$471$		0			0
$472$	1.26312	+	7.16349i	0.0581397	+	0.329727i
$473$	−0.391508	−	2.22035i	−0.0180015	−	0.102092i
$474$		0			0
$475$	33.3149	+	27.9545i	1.52859	+	1.28264i
$476$	−0.427484	−	0.740423i	−0.0195937	−	0.0339372i
$477$		0			0
$478$	−10.6640	+	18.4707i	−0.487762	+	0.844829i
$479$	10.6027	−	3.85905i	0.484448	−	0.176325i	−0.0882381	−	0.996099i	$-0.528124\pi$
$479$	10.6027	−	3.85905i	0.484448	−	0.176325i	0.572686	+	0.819775i	$0.305901\pi$
$480$		0			0
$481$	1.70626	−	1.43172i	0.0777988	−	0.0652809i
$482$	−10.1057	−	3.67817i	−0.460301	−	0.167536i
$483$		0			0
$484$	−1.90166	+	10.7848i	−0.0864390	+	0.490220i
$485$	22.8849			1.03915
$486$		0			0
$487$	−29.3219			−1.32870			−0.664352	−	0.747420i	$-0.731292\pi$
$487$	−29.3219			−1.32870			−0.664352	+	0.747420i	$0.731292\pi$
$488$	−0.585154	+	3.31857i	−0.0264887	+	0.150225i
$489$		0			0
$490$	−26.5341	−	9.65761i	−1.19869	−	0.436287i
$491$	7.76464	−	6.51531i	0.350413	−	0.294032i	−0.450543	−	0.892755i	$-0.648769\pi$
$491$	7.76464	−	6.51531i	0.350413	−	0.294032i	0.800956	+	0.598723i	$0.204325\pi$
$492$		0			0
$493$	−3.91138	+	1.42363i	−0.176160	+	0.0641169i
$494$	1.13539	−	1.96655i	0.0510836	−	0.0884794i
$495$		0			0
$496$	−2.54180	−	4.40252i	−0.114130	−	0.197679i
$497$	0.336324	+	0.282209i	0.0150862	+	0.0126588i
$498$		0			0
$499$	3.87086	+	21.9527i	0.173284	+	0.982740i	0.940106	+	0.340881i	$0.110725\pi$
$499$	3.87086	+	21.9527i	0.173284	+	0.982740i	−0.766823	+	0.641859i	$0.778164\pi$
$500$	4.48571	+	25.4398i	0.200607	+	1.13770i
$501$		0			0
$502$	3.19918	+	2.68443i	0.142786	+	0.119812i
$503$	−7.31535	−	12.6706i	−0.326175	−	0.564952i	0.655574	−	0.755131i	$-0.272427\pi$
$503$	−7.31535	−	12.6706i	−0.326175	−	0.564952i	−0.981750	+	0.190179i	$0.939093\pi$
$504$		0			0
$505$	31.9743	−	55.3811i	1.42284	−	2.46443i
$506$	−1.21615	+	0.442643i	−0.0540646	+	0.0196779i
$507$		0			0
$508$	−14.2721	+	11.9757i	−0.633222	+	0.531336i
$509$	6.70321	+	2.43977i	0.297115	+	0.108141i	0.486276	−	0.873805i	$-0.338355\pi$
$509$	6.70321	+	2.43977i	0.297115	+	0.108141i	−0.189162	+	0.981946i	$0.560577\pi$
$510$		0			0
$511$	0.0340898	−	0.193333i	0.00150804	−	0.00855254i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	16.3432			0.720868
$515$	7.51818	−	42.6377i	0.331291	−	1.87884i
$516$		0			0
$517$	0.0987433	+	0.0359396i	0.00434273	+	0.00158062i
$518$	0.441065	−	0.370098i	0.0193793	−	0.0162612i
$519$		0			0
$520$	2.26043	−	0.822730i	0.0991265	−	0.0360791i
$521$	−4.12053	+	7.13696i	−0.180524	+	0.312676i	−0.942059	−	0.335447i	$-0.891113\pi$
$521$	−4.12053	+	7.13696i	−0.180524	+	0.312676i	0.761535	+	0.648123i	$0.224446\pi$
$522$		0			0
$523$	11.2705	+	19.5211i	0.492826	+	0.853599i	0.999966	−	0.00826425i	$-0.00263062\pi$
$523$	11.2705	+	19.5211i	0.492826	+	0.853599i	−0.507140	+	0.861864i	$0.669297\pi$
$524$	5.26078	+	4.41432i	0.229818	+	0.192840i
$525$		0			0
$526$	−0.465609	−	2.64060i	−0.0203015	−	0.115136i
$527$	−4.91264	−	27.8610i	−0.213998	−	1.21364i
$528$		0			0
$529$	8.67807	+	7.28176i	0.377307	+	0.316598i
$530$	−6.67747	−	11.5657i	−0.290051	−	0.502383i
$531$		0			0
$532$	0.293496	−	0.508350i	0.0127247	−	0.0220398i
$533$	2.21963	−	0.807881i	0.0961430	−	0.0349932i
$534$		0			0
$535$	−5.74337	+	4.81926i	−0.248308	+	0.208355i
$536$	7.00834	+	2.55083i	0.302714	+	0.110179i
$537$		0			0
$538$	3.88120	−	22.0114i	0.167330	−	0.948977i
$539$	1.54101			0.0663762
$540$		0			0
$541$	−31.4683			−1.35293			−0.676464	−	0.736476i	$-0.736488\pi$
$541$	−31.4683			−1.35293			−0.676464	+	0.736476i	$0.736488\pi$
$542$	−4.42479	+	25.0942i	−0.190061	+	1.07789i
$543$		0			0
$544$	−5.22949	−	1.90338i	−0.224212	−	0.0816066i
$545$	−45.1115	+	37.8531i	−1.93237	+	1.62145i
$546$		0			0
$547$	−28.3635	+	10.3235i	−1.21274	+	0.441400i	−0.867652	−	0.497171i	$-0.834372\pi$
$547$	−28.3635	+	10.3235i	−1.21274	+	0.441400i	−0.345085	+	0.938571i	$0.612150\pi$
$548$	7.49271	−	12.9777i	0.320073	−	0.554382i
$549$		0			0
$550$	−1.25711	−	2.17738i	−0.0536034	−	0.0928439i
$551$	−2.18918	−	1.83694i	−0.0932623	−	0.0782563i
$552$		0			0
$553$	0.0882249	+	0.500348i	0.00375170	+	0.0212770i
$554$	0.445758	+	2.52802i	0.0189385	+	0.107405i
$555$		0			0
$556$	13.8675	+	11.6362i	0.588113	+	0.493486i
$557$	16.4210	+	28.4420i	0.695779	+	1.20512i	0.969917	+	0.243434i	$0.0782741\pi$
$557$	16.4210	+	28.4420i	0.695779	+	1.20512i	−0.274138	+	0.961690i	$0.588393\pi$
$558$		0			0
$559$	−3.03308	+	5.25345i	−0.128286	+	0.222197i
$560$	0.584317	−	0.212674i	0.0246919	−	0.00898712i
$561$		0			0
$562$	16.2374	−	13.6248i	0.684933	−	0.574727i
$563$	17.5885	+	6.40168i	0.741266	+	0.269799i	0.684926	−	0.728613i	$-0.259835\pi$
$563$	17.5885	+	6.40168i	0.741266	+	0.269799i	0.0563401	+	0.998412i	$0.482057\pi$
$564$		0			0
$565$	9.40560	−	53.3418i	0.395697	−	2.24411i
$566$	19.6332			0.825246
$567$		0			0
$568$	2.85777			0.119910
$569$	1.38771	−	7.87008i	0.0581757	−	0.329931i	−0.941805	−	0.336160i	$-0.890872\pi$
$569$	1.38771	−	7.87008i	0.0581757	−	0.329931i	0.999981	+	0.00622922i	$0.00198284\pi$
$570$		0			0
$571$	26.7013	+	9.71847i	1.11741	+	0.406705i	0.833708	−	0.552206i	$-0.186214\pi$
$571$	26.7013	+	9.71847i	1.11741	+	0.406705i	0.283706	+	0.958911i	$0.408436\pi$
$572$	−0.100565	+	0.0843843i	−0.00420485	+	0.00352828i
$573$		0			0
$574$	0.573771	−	0.208836i	0.0239488	−	0.00871663i
$575$	−33.3446	+	57.7545i	−1.39057	+	2.40853i
$576$		0			0
$577$	−23.5780	−	40.8383i	−0.981564	−	1.70012i	−0.656307	−	0.754494i	$-0.727883\pi$
$577$	−23.5780	−	40.8383i	−0.981564	−	1.70012i	−0.325257	−	0.945626i	$-0.605451\pi$
$578$	−10.7019	−	8.97999i	−0.445142	−	0.373518i
$579$		0			0
$580$	−0.525688	−	2.98133i	−0.0218280	−	0.123793i
$581$	−0.220655	−	1.25139i	−0.00915429	−	0.0519166i
$582$		0			0
$583$	0.558322	+	0.468487i	0.0231233	+	0.0194028i
$584$	−0.638922	−	1.10665i	−0.0264388	−	0.0457933i
$585$		0			0
$586$	−10.7380	+	18.5988i	−0.443582	+	0.768307i
$587$	−16.5971	+	6.04086i	−0.685036	+	0.249333i	−0.661008	−	0.750378i	$-0.729871\pi$
$587$	−16.5971	+	6.04086i	−0.685036	+	0.249333i	−0.0240279	+	0.999711i	$0.507649\pi$
$588$		0			0
$589$	14.8793	−	12.4852i	0.613090	−	0.514443i
$590$	−27.6660	−	10.0696i	−1.13899	−	0.414559i
$591$		0			0
$592$	0.650793	−	3.69083i	0.0267474	−	0.151692i
$593$	−4.89941			−0.201195			−0.100597	−	0.994927i	$-0.532075\pi$
$593$	−4.89941			−0.201195			−0.100597	+	0.994927i	$0.532075\pi$
$594$		0			0
$595$	3.46048			0.141866
$596$	2.60884	−	14.7955i	0.106862	−	0.606046i
$597$		0			0
$598$	3.27214	+	1.19096i	0.133808	+	0.0487020i
$599$	−13.8351	+	11.6090i	−0.565288	+	0.474333i	−0.880078	−	0.474828i	$-0.842510\pi$
$599$	−13.8351	+	11.6090i	−0.565288	+	0.474333i	0.314791	+	0.949161i	$0.398066\pi$
$600$		0			0
$601$	−3.04117	+	1.10690i	−0.124052	+	0.0451513i	−0.403300	−	0.915068i	$-0.632137\pi$
$601$	−3.04117	+	1.10690i	−0.124052	+	0.0451513i	0.279248	+	0.960219i	$0.409915\pi$
$602$	−0.784045	+	1.35801i	−0.0319553	+	0.0553482i
$603$		0			0
$604$	2.82136	+	4.88675i	0.114800	+	0.198839i
$605$	−33.9549	−	28.4916i	−1.38046	−	1.15835i
$606$		0			0
$607$	4.71790	+	26.7566i	0.191494	+	1.08602i	0.917324	+	0.398141i	$0.130345\pi$
$607$	4.71790	+	26.7566i	0.191494	+	1.08602i	−0.725830	+	0.687874i	$0.758544\pi$
$608$	−0.663478	−	3.76277i	−0.0269076	−	0.152601i
$609$		0			0
$610$	−10.4482	−	8.76706i	−0.423034	−	0.354968i
$611$	−0.141363	−	0.244848i	−0.00571893	−	0.00990547i
$612$		0			0
$613$	−13.6622	+	23.6636i	−0.551810	+	0.955763i	0.446334	+	0.894866i	$0.352729\pi$
$613$	−13.6622	+	23.6636i	−0.551810	+	0.955763i	−0.998144	+	0.0608964i	$0.980604\pi$
$614$	5.31182	−	1.93335i	0.214368	−	0.0780235i
$615$		0			0
$616$	−0.0259959	+	0.0218132i	−0.00104741	+	0.000878878i
$617$	25.0923	+	9.13284i	1.01018	+	0.367674i	0.793501	−	0.608569i	$-0.208256\pi$
$617$	25.0923	+	9.13284i	1.01018	+	0.367674i	0.216676	+	0.976244i	$0.430478\pi$
$618$		0			0
$619$	6.92886	−	39.2955i	0.278494	−	1.57942i	−0.449145	−	0.893459i	$-0.648271\pi$
$619$	6.92886	−	39.2955i	0.278494	−	1.57942i	0.727639	−	0.685960i	$-0.240618\pi$
$620$	20.5759			0.826347
$621$		0			0
$622$	9.30470			0.373085
$623$	−0.132258	+	0.750073i	−0.00529881	+	0.0300510i
$624$		0			0
$625$	−44.7712	−	16.2954i	−1.79085	−	0.651816i
$626$	2.05976	−	1.72835i	0.0823247	−	0.0690786i
$627$		0			0
$628$	−6.80782	+	2.47784i	−0.271661	+	0.0988767i
$629$	10.4284	−	18.0624i	0.415806	−	0.720197i
$630$		0			0
$631$	4.36875	+	7.56690i	0.173917	+	0.301234i	0.939786	−	0.341763i	$-0.111024\pi$
$631$	4.36875	+	7.56690i	0.173917	+	0.301234i	−0.765869	+	0.642997i	$0.777691\pi$
$632$	2.53337	+	2.12575i	0.100772	+	0.0845578i
$633$		0			0
$634$	−4.85100	−	27.5114i	−0.192658	−	1.09262i
$635$	−13.0946	−	74.2629i	−0.519642	−	2.94703i
$636$		0			0
$637$	−3.17617	−	2.66512i	−0.125845	−	0.105596i
$638$	0.0826070	+	0.143079i	0.00327044	+	0.00566457i
$639$		0			0
$640$	2.02375	−	3.50524i	0.0799958	−	0.138557i
$641$	17.0222	−	6.19556i	0.672335	−	0.244710i	0.0167821	−	0.999859i	$-0.494658\pi$
$641$	17.0222	−	6.19556i	0.672335	−	0.244710i	0.655553	+	0.755149i	$0.272436\pi$
$642$		0			0
$643$	−24.5762	+	20.6219i	−0.969191	+	0.813247i	−0.982424	−	0.186665i	$-0.940232\pi$
$643$	−24.5762	+	20.6219i	−0.969191	+	0.813247i	0.0132331	+	0.999912i	$0.495788\pi$
$644$	0.845841	+	0.307861i	0.0333308	+	0.0121314i
$645$		0			0
$646$	3.69233	−	20.9402i	0.145273	−	0.823882i
$647$	11.1390			0.437918			0.218959	−	0.975734i	$-0.429734\pi$
$647$	11.1390			0.437918			0.218959	+	0.975734i	$0.429734\pi$
$648$		0			0
$649$	1.60675			0.0630705
$650$	−1.17467	+	6.66191i	−0.0460745	+	0.261302i
$651$		0			0
$652$	−13.2570	−	4.82517i	−0.519186	−	0.188968i
$653$	−1.15447	+	0.968718i	−0.0451780	+	0.0379089i	−0.665097	−	0.746757i	$-0.731610\pi$
$653$	−1.15447	+	0.968718i	−0.0451780	+	0.0379089i	0.619919	+	0.784666i	$0.287165\pi$
$654$		0			0
$655$	−26.1197	+	9.50681i	−1.02058	+	0.371462i
$656$	1.98722	−	3.44197i	0.0775881	−	0.134386i
$657$		0			0
$658$	−0.0365420	−	0.0632926i	−0.00142456	−	0.00246740i
$659$	6.06158	+	5.08627i	0.236126	+	0.198133i	0.753171	−	0.657825i	$-0.228523\pi$
$659$	6.06158	+	5.08627i	0.236126	+	0.198133i	−0.517045	+	0.855958i	$0.672968\pi$
$660$		0			0
$661$	−5.26138	−	29.8388i	−0.204644	−	1.16059i	−0.897999	−	0.439998i	$-0.854979\pi$
$661$	−5.26138	−	29.8388i	−0.204644	−	1.16059i	0.693355	−	0.720597i	$-0.256132\pi$
$662$	−0.146752	−	0.832272i	−0.00570368	−	0.0323472i
$663$		0			0
$664$	−6.33608	−	5.31660i	−0.245888	−	0.206324i
$665$	1.18793	+	2.05755i	0.0460658	+	0.0797883i
$666$		0			0
$667$	2.19113	−	3.79515i	0.0848409	−	0.146949i
$668$	−12.9892	+	4.72767i	−0.502565	+	0.182919i
$669$		0			0
$670$	−23.1244	+	19.4037i	−0.893373	+	0.749629i
$671$	0.699457	+	0.254581i	0.0270022	+	0.00982801i
$672$		0			0
$673$	−3.85949	+	21.8883i	−0.148772	+	0.843731i	0.815488	+	0.578774i	$0.196469\pi$
$673$	−3.85949	+	21.8883i	−0.148772	+	0.843731i	−0.964260	+	0.264956i	$0.914642\pi$
$674$	−29.3172			−1.12926
$675$		0			0
$676$	−12.6468			−0.486415
$677$	−7.00672	+	39.7371i	−0.269290	+	1.52722i	0.487245	+	0.873266i	$0.338002\pi$
$677$	−7.00672	+	39.7371i	−0.269290	+	1.52722i	−0.756535	+	0.653954i	$0.773109\pi$
$678$		0			0
$679$	0.816250	+	0.297091i	0.0313248	+	0.0114013i
$680$	17.2550	−	14.4786i	0.661698	−	0.555230i
$681$		0			0
$682$	−1.05519	+	0.384059i	−0.0404055	+	0.0147064i
$683$	−12.5504	+	21.7380i	−0.480229	+	0.831780i	−0.999743	−	0.0226815i	$-0.992780\pi$
$683$	−12.5504	+	21.7380i	−0.480229	+	0.831780i	0.519514	+	0.854462i	$0.326113\pi$
$684$		0			0
$685$	30.3267	+	52.5274i	1.15872	+	2.00697i
$686$	−1.64485	−	1.38019i	−0.0628005	−	0.0526959i
$687$		0			0
$688$	1.77241	+	10.0519i	0.0675726	+	0.383223i
$689$	−0.340521	−	1.93119i	−0.0129728	−	0.0735725i
$690$		0			0
$691$	−2.21137	−	1.85556i	−0.0841245	−	0.0705889i	0.599756	−	0.800183i	$-0.295264\pi$
$691$	−2.21137	−	1.85556i	−0.0841245	−	0.0705889i	−0.683880	+	0.729594i	$0.739709\pi$
$692$	−1.96463	−	3.40284i	−0.0746840	−	0.129356i
$693$		0			0
$694$	10.1001	−	17.4939i	0.383395	−	0.664059i
$695$	−68.8521	+	25.0601i	−2.61171	+	0.950584i
$696$		0			0
$697$	16.9435	−	14.2173i	0.641782	−	0.538519i
$698$	9.02990	+	3.28661i	0.341787	+	0.124400i
$699$		0			0
$700$	−0.303651	+	1.72209i	−0.0114769	+	0.0650889i
$701$	24.5608			0.927648			0.463824	−	0.885927i	$-0.346477\pi$
$701$	24.5608			0.927648			0.463824	+	0.885927i	$0.346477\pi$
$702$		0			0
$703$	14.3195			0.540072
$704$	−0.0383571	+	0.217534i	−0.00144564	+	0.00819862i
$705$		0			0
$706$	9.23396	+	3.36089i	0.347525	+	0.126489i
$707$	1.85941	−	1.56023i	0.0699302	−	0.0586784i
$708$		0			0
$709$	20.9978	−	7.64257i	0.788588	−	0.287023i	0.0838392	−	0.996479i	$-0.473282\pi$
$709$	20.9978	−	7.64257i	0.788588	−	0.287023i	0.704749	+	0.709457i	$0.251060\pi$
$710$	−5.78342	+	10.0172i	−0.217048	+	0.375938i
$711$		0			0
$712$	2.47882	+	4.29345i	0.0928979	+	0.160904i
$713$	22.8167	+	19.1454i	0.854490	+	0.717003i
$714$		0			0
$715$	−0.0922680	−	0.523278i	−0.00345063	−	0.0195695i
$716$	−0.493894	−	2.80101i	−0.0184577	−	0.104679i
$717$		0			0
$718$	9.10779	+	7.64235i	0.339900	+	0.285210i
$719$	−18.3086	−	31.7114i	−0.682796	−	1.18264i	−0.974124	−	0.226014i	$-0.927430\pi$
$719$	−18.3086	−	31.7114i	−0.682796	−	1.18264i	0.291328	−	0.956623i	$-0.405903\pi$
$720$		0			0
$721$	0.821678	−	1.42319i	0.0306009	−	0.0530023i
$722$	−4.13591	+	1.50535i	−0.153923	+	0.0560232i
$723$		0			0
$724$	9.90149	−	8.30834i	0.367986	−	0.308777i
$725$	7.99992	+	2.91173i	0.297110	+	0.108139i
$726$		0			0
$727$	2.38849	−	13.5458i	0.0885842	−	0.502386i	−0.907941	−	0.419097i	$-0.862347\pi$
$727$	2.38849	−	13.5458i	0.0885842	−	0.502386i	0.996525	−	0.0832885i	$-0.0265423\pi$
$728$	0.0913051			0.00338399
$729$		0			0
$730$	5.17208			0.191427
$731$	−9.86367	+	55.9396i	−0.364821	+	2.06900i
$732$		0			0
$733$	−30.6892	−	11.1699i	−1.13353	−	0.412571i	−0.293957	−	0.955819i	$-0.594972\pi$
$733$	−30.6892	−	11.1699i	−1.13353	−	0.412571i	−0.839573	+	0.543247i	$0.817195\pi$
$734$	27.7867	−	23.3158i	1.02563	−	0.860603i
$735$		0			0
$736$	5.50570	−	2.00391i	0.202943	−	0.0738652i
$737$	0.823710	−	1.42671i	0.0303418	−	0.0525535i
$738$		0			0
$739$	14.0540	+	24.3423i	0.516986	+	0.895445i	0.999805	+	0.0197257i	$0.00627929\pi$
$739$	14.0540	+	24.3423i	0.516986	+	0.895445i	−0.482820	+	0.875720i	$0.660387\pi$
$740$	11.6202	+	9.75050i	0.427167	+	0.358436i
$741$		0			0
$742$	−0.0880241	−	0.499209i	−0.00323147	−	0.0183266i
$743$	2.01338	+	11.4184i	0.0738636	+	0.418901i	0.999209	+	0.0397752i	$0.0126642\pi$
$743$	2.01338	+	11.4184i	0.0738636	+	0.418901i	−0.925345	+	0.379126i	$0.876225\pi$
$744$		0			0
$745$	46.5820	+	39.0870i	1.70663	+	1.43204i
$746$	7.07457	+	12.2535i	0.259018	+	0.448633i
$747$		0			0
$748$	−0.614637	+	1.06458i	−0.0224734	+	0.0389250i
$749$	−0.267417	+	0.0973316i	−0.00977119	+	0.00355642i
$750$		0			0
$751$	−31.0515	+	26.0553i	−1.13309	+	0.950772i	−0.999191	−	0.0402230i	$-0.987193\pi$
$751$	−31.0515	+	26.0553i	−1.13309	+	0.950772i	−0.133896	+	0.990995i	$0.542749\pi$
$752$	−0.447025	−	0.162704i	−0.0163013	−	0.00593320i
$753$		0			0
$754$	0.0771899	−	0.437766i	0.00281109	−	0.0159425i
$755$	−22.8390			−0.831194
$756$		0			0
$757$	51.1841			1.86032			0.930158	−	0.367159i	$-0.119669\pi$
$757$	51.1841			1.86032			0.930158	+	0.367159i	$0.119669\pi$
$758$	5.12674	−	29.0752i	0.186211	−	1.05606i
$759$		0			0
$760$	14.5321	+	5.28926i	0.527136	+	0.191862i
$761$	−3.01606	+	2.53078i	−0.109332	+	0.0917406i	−0.695815	−	0.718221i	$-0.744957\pi$
$761$	−3.01606	+	2.53078i	−0.109332	+	0.0917406i	0.586483	+	0.809962i	$0.300512\pi$
$762$		0			0
$763$	−2.10043	+	0.764495i	−0.0760408	+	0.0276766i
$764$	−10.0714	+	17.4441i	−0.364369	+	0.631105i
$765$		0			0
$766$	−12.3625	−	21.4125i	−0.446675	−	0.773664i
$767$	−3.31166	−	2.77882i	−0.119577	−	0.100337i
$768$		0			0
$769$	−7.45807	−	42.2968i	−0.268945	−	1.52526i	−0.757562	−	0.652763i	$-0.773610\pi$
$769$	−7.45807	−	42.2968i	−0.268945	−	1.52526i	0.488617	−	0.872498i	$-0.337501\pi$
$770$	−0.0238511	−	0.135266i	−0.000859534	−	0.00487466i
$771$		0			0
$772$	7.36678	+	6.18146i	0.265136	+	0.222476i
$773$	−10.6680	−	18.4775i	−0.383702	−	0.664591i	0.607886	−	0.794024i	$-0.292018\pi$
$773$	−10.6680	−	18.4775i	−0.383702	−	0.664591i	−0.991588	+	0.129433i	$0.958684\pi$
$774$		0			0
$775$	−28.9314	+	50.1107i	−1.03925	+	1.80003i
$776$	5.31309	−	1.93381i	0.190729	−	0.0694196i
$777$		0			0
$778$	11.1425	−	9.34969i	0.399479	−	0.335203i
$779$	14.2698	+	5.19380i	0.511270	+	0.186087i
$780$		0			0
$781$	0.109616	−	0.621662i	0.00392236	−	0.0222448i
$782$	32.6062			1.16600
$783$		0			0
$784$	−6.97640			−0.249157
$785$	5.09189	−	28.8776i	0.181737	−	1.03068i
$786$		0			0
$787$	6.97310	+	2.53800i	0.248564	+	0.0904699i	0.463298	−	0.886203i	$-0.346666\pi$
$787$	6.97310	+	2.53800i	0.248564	+	0.0904699i	−0.214734	+	0.976673i	$0.568888\pi$
$788$	−5.78404	+	4.85339i	−0.206048	+	0.172895i
$789$		0			0
$790$	−12.5782	+	4.57808i	−0.447511	+	0.162881i
$791$	1.02796	−	1.78048i	0.0365500	−	0.0633065i
$792$		0			0
$793$	−1.00136	−	1.73440i	−0.0355592	−	0.0615903i
$794$	−3.23072	−	2.71090i	−0.114654	−	0.0962061i
$795$		0			0
$796$	−2.10833	−	11.9570i	−0.0747279	−	0.423803i
$797$	−2.06082	−	11.6875i	−0.0729980	−	0.413992i	−0.999307	−	0.0372272i	$-0.988147\pi$
$797$	−2.06082	−	11.6875i	−0.0729980	−	0.413992i	0.926309	−	0.376765i	$-0.122964\pi$
$798$		0			0
$799$	−2.02803	−	1.70172i	−0.0717464	−	0.0602024i
$800$	5.69113	+	9.85733i	0.201212	+	0.348509i
$801$		0			0
$802$	8.09535	−	14.0216i	0.285857	−	0.495118i
$803$	−0.265240	+	0.0965395i	−0.00936012	+	0.00340681i
$804$		0			0
$805$	−2.79090	+	2.34184i	−0.0983662	+	0.0825391i
$806$	2.83907	+	1.03334i	0.100002	+	0.0363977i
$807$		0			0
$808$	2.74356	−	15.5595i	0.0965181	−	0.547381i
$809$	46.8455			1.64700			0.823500	−	0.567316i	$-0.192018\pi$
$809$	46.8455			1.64700			0.823500	+	0.567316i	$0.192018\pi$
$810$		0			0
$811$	−1.66252			−0.0583791			−0.0291895	−	0.999574i	$-0.509293\pi$
$811$	−1.66252			−0.0583791			−0.0291895	+	0.999574i	$0.509293\pi$
$812$	0.0199534	−	0.113162i	0.000700228	−	0.00397119i
$813$		0			0
$814$	−0.777918	−	0.283139i	−0.0272660	−	0.00992402i
$815$	43.7423	−	36.7042i	1.53223	−	1.28569i
$816$		0			0
$817$	−36.6469	+	13.3384i	−1.28211	+	0.466651i
$818$	1.97165	−	3.41500i	0.0689373	−	0.119403i
$819$		0			0
$820$	8.04329	+	13.9314i	0.280884	+	0.486505i
$821$	−6.93192	−	5.81657i	−0.241926	−	0.203000i	0.513761	−	0.857934i	$-0.328252\pi$
$821$	−6.93192	−	5.81657i	−0.241926	−	0.203000i	−0.755686	+	0.654934i	$0.772696\pi$
$822$		0			0
$823$	2.04514	+	11.5986i	0.0712892	+	0.404301i	0.999481	+	0.0322000i	$0.0102514\pi$
$823$	2.04514	+	11.5986i	0.0712892	+	0.404301i	−0.928192	+	0.372101i	$0.878638\pi$
$824$	−1.85749	−	10.5343i	−0.0647087	−	0.366981i
$825$		0			0
$826$	−0.856059	−	0.718318i	−0.0297861	−	0.0249935i
$827$	16.9625	+	29.3798i	0.589843	+	1.02164i	0.994253	+	0.107060i	$0.0341436\pi$
$827$	16.9625	+	29.3798i	0.589843	+	1.02164i	−0.404410	+	0.914578i	$0.632523\pi$
$828$		0			0
$829$	−7.37389	+	12.7719i	−0.256106	+	0.443588i	−0.965195	−	0.261530i	$-0.915773\pi$
$829$	−7.37389	+	12.7719i	−0.256106	+	0.443588i	0.709090	+	0.705118i	$0.249106\pi$
$830$	31.4586	−	11.4500i	1.09194	−	0.397435i
$831$		0			0
$832$	0.455274	−	0.382020i	0.0157838	−	0.0132442i
$833$	−36.4830	−	13.2787i	−1.26406	−	0.460080i
$834$		0			0
$835$	9.71521	−	55.0977i	0.336209	−	1.90673i
$836$	−0.843979			−0.0291896
$837$		0			0
$838$	−34.4947			−1.19160
$839$	4.77160	−	27.0611i	0.164734	−	0.934252i	−0.784605	−	0.619996i	$-0.787134\pi$
$839$	4.77160	−	27.0611i	0.164734	−	0.934252i	0.949338	−	0.314256i	$-0.101755\pi$
$840$		0			0
$841$	26.7254	+	9.72725i	0.921565	+	0.335422i
$842$	8.80184	−	7.38562i	0.303332	−	0.254525i
$843$		0			0
$844$	6.78819	−	2.47070i	0.233659	−	0.0850450i
$845$	25.5939	−	44.3300i	0.880458	−	1.52500i
$846$		0			0
$847$	−0.841217	−	1.45703i	−0.0289046	−	0.0500642i
$848$	−2.52760	−	2.12091i	−0.0867983	−	0.0728324i
$849$		0			0
$850$	10.9995	+	62.3811i	0.377279	+	2.13966i
$851$	3.81303	+	21.6247i	0.130709	+	0.741287i
$852$		0			0
$853$	4.59134	+	3.85259i	0.157205	+	0.131910i	0.717997	−	0.696046i	$-0.245059\pi$
$853$	4.59134	+	3.85259i	0.157205	+	0.131910i	−0.560793	+	0.827956i	$0.689503\pi$
$854$	−0.258849	−	0.448339i	−0.00885762	−	0.0153418i
$855$		0			0
$856$	−0.926182	+	1.60419i	−0.0316562	+	0.0548302i
$857$	17.8493	−	6.49663i	0.609722	−	0.221921i	−0.0186598	−	0.999826i	$-0.505940\pi$
$857$	17.8493	−	6.49663i	0.609722	−	0.221921i	0.628381	+	0.777905i	$0.283718\pi$
$858$		0			0
$859$	13.8575	−	11.6278i	0.472812	−	0.396737i	−0.375007	−	0.927022i	$-0.622360\pi$
$859$	13.8575	−	11.6278i	0.472812	−	0.396737i	0.847819	+	0.530285i	$0.177915\pi$
$860$	−38.8211	−	14.1297i	−1.32379	−	0.481819i
$861$		0			0
$862$	4.27819	−	24.2628i	0.145716	−	0.826396i
$863$	8.17235			0.278190			0.139095	−	0.990279i	$-0.455581\pi$
$863$	8.17235			0.278190			0.139095	+	0.990279i	$0.455581\pi$
$864$		0			0
$865$	15.9037			0.540741
$866$	−2.22288	+	12.6066i	−0.0755367	+	0.428390i
$867$		0			0
$868$	0.733894	+	0.267115i	0.0249100	+	0.00906649i
$869$	0.559595	−	0.469556i	0.0189830	−	0.0159286i
$870$		0			0
$871$	−4.16518	+	1.51600i	−0.141132	+	0.0513678i
$872$	−7.27473	+	12.6002i	−0.246353	+	0.426697i
$873$		0			0
$874$	11.1932	+	19.3871i	0.378615	+	0.655780i
$875$	−3.04013	−	2.55097i	−0.102775	−	0.0862385i
$876$		0			0
$877$	3.12176	+	17.7044i	0.105414	+	0.597835i	0.991054	+	0.133462i	$0.0426093\pi$
$877$	3.12176	+	17.7044i	0.105414	+	0.597835i	−0.885639	+	0.464373i	$0.846280\pi$
$878$	6.31143	+	35.7939i	0.213000	+	1.20799i
$879$		0			0
$880$	−0.684883	−	0.574685i	−0.0230874	−	0.0193726i
$881$	13.9064	+	24.0865i	0.468518	+	0.811496i	0.999353	−	0.0359788i	$-0.0114549\pi$
$881$	13.9064	+	24.0865i	0.468518	+	0.811496i	−0.530835	+	0.847475i	$0.678122\pi$
$882$		0			0
$883$	5.86589	−	10.1600i	0.197403	−	0.341912i	−0.750283	−	0.661117i	$-0.770083\pi$
$883$	5.86589	−	10.1600i	0.197403	−	0.341912i	0.947686	+	0.319205i	$0.103416\pi$
$884$	3.10798	−	1.13121i	0.104533	−	0.0380468i
$885$		0			0
$886$	−29.5753	+	24.8166i	−0.993601	+	0.833730i
$887$	−18.0700	−	6.57694i	−0.606731	−	0.220832i	0.0203412	−	0.999793i	$-0.493525\pi$
$887$	−18.0700	−	6.57694i	−0.606731	−	0.220832i	−0.627072	+	0.778961i	$0.715747\pi$
$888$		0			0
$889$	0.497027	−	2.81878i	0.0166698	−	0.0945389i
$890$	−20.0661			−0.672617
$891$		0			0
$892$	−25.5249			−0.854638
$893$	0.315626	−	1.79001i	0.0105620	−	0.0599003i
$894$		0			0
$895$	10.8177	+	3.93733i	0.361597	+	0.131610i
$896$	0.117687	−	0.0987515i	0.00393166	−	0.00329906i
$897$		0			0
$898$	14.5907	−	5.31059i	0.486899	−	0.177217i
$899$	1.90113	−	3.29286i	0.0634063	−	0.109823i
$900$		0			0
$901$	−9.18118	−	15.9023i	−0.305869	−	0.529781i
$902$	−0.672522	−	0.564313i	−0.0223925	−	0.0187896i
$903$		0			0
$904$	−2.32381	−	13.1790i	−0.0772886	−	0.438325i
$905$	9.08456	+	51.5211i	0.301981	+	1.71262i
$906$		0			0
$907$	0.795661	+	0.667639i	0.0264195	+	0.0221686i	0.655902	−	0.754846i	$-0.272289\pi$
$907$	0.795661	+	0.667639i	0.0264195	+	0.0221686i	−0.629482	+	0.777015i	$0.716733\pi$
$908$	7.17965	+	12.4355i	0.238265	+	0.412687i
$909$		0			0
$910$	−0.184779	+	0.320046i	−0.00612535	+	0.0106094i
$911$	8.97004	−	3.26483i	0.297191	−	0.108169i	−0.189121	−	0.981954i	$-0.560564\pi$
$911$	8.97004	−	3.26483i	0.297191	−	0.108169i	0.486312	+	0.873785i	$0.338342\pi$
$912$		0			0
$913$	−1.39957	+	1.17438i	−0.0463191	+	0.0388664i
$914$	−33.9263	−	12.3482i	−1.12218	−	0.408441i
$915$		0			0
$916$	0.704853	−	3.99742i	0.0232890	−	0.132078i
$917$	−1.05505			−0.0348408
$918$		0			0
$919$	2.76185			0.0911049			0.0455525	−	0.998962i	$-0.485495\pi$
$919$	2.76185			0.0911049			0.0455525	+	0.998962i	$0.485495\pi$
$920$	−4.11798	+	23.3542i	−0.135766	+	0.769966i
$921$		0			0
$922$	−9.34268	−	3.40046i	−0.307685	−	0.111988i
$923$	−1.30107	+	1.09173i	−0.0428252	+	0.0359346i
$924$		0			0
$925$	−40.0855	+	14.5899i	−1.31800	+	0.479714i
$926$	−9.62295	+	16.6674i	−0.316230	+	0.547726i
$927$		0			0
$928$	−0.373974	−	0.647742i	−0.0122763	−	0.0212632i
$929$	−41.9258	−	35.1799i	−1.37554	−	1.15421i	−0.970830	−	0.239769i	$-0.922928\pi$
$929$	−41.9258	−	35.1799i	−1.37554	−	1.15421i	−0.404710	−	0.914445i	$-0.632627\pi$
$930$		0			0
$931$	−4.62869	−	26.2506i	−0.151699	−	0.860329i
$932$	−2.94833	−	16.7208i	−0.0965756	−	0.547707i
$933$		0			0
$934$	24.1944	+	20.3015i	0.791665	+	0.664285i
$935$	−2.48774	−	4.30890i	−0.0813579	−	0.140916i
$936$		0			0
$937$	18.8239	−	32.6039i	0.614950	−	1.06512i	−0.375443	−	0.926845i	$-0.622510\pi$
$937$	18.8239	−	32.6039i	0.614950	−	1.06512i	0.990393	−	0.138279i	$-0.0441571\pi$
$938$	−1.07669	+	0.391884i	−0.0351552	+	0.0127955i
$939$		0			0
$940$	1.47498	−	1.23766i	0.0481087	−	0.0403680i
$941$	39.3948	+	14.3386i	1.28424	+	0.467423i	0.891831	−	0.452369i	$-0.149421\pi$
$941$	39.3948	+	14.3386i	1.28424	+	0.467423i	0.392405	+	0.919793i	$0.371643\pi$
$942$		0			0
$943$	−4.04365	+	22.9327i	−0.131680	+	0.746792i
$944$	−7.27400			−0.236749
$945$		0			0
$946$	2.25460			0.0733035
$947$	1.77265	−	10.0532i	0.0576035	−	0.326686i	−0.942365	−	0.334586i	$-0.891404\pi$
$947$	1.77265	−	10.0532i	0.0576035	−	0.326686i	0.999969	+	0.00790013i	$0.00251471\pi$
$948$		0			0
$949$	0.713646	+	0.259746i	0.0231659	+	0.00843171i
$950$	−33.3149	+	27.9545i	−1.08088	+	0.906965i
$951$		0			0
$952$	0.803406	−	0.292416i	0.0260386	−	0.00947726i
$953$	−9.51525	+	16.4809i	−0.308229	+	0.533869i	−0.977975	−	0.208722i	$-0.933070\pi$
$953$	−9.51525	+	16.4809i	−0.308229	+	0.533869i	0.669746	+	0.742590i	$0.266403\pi$
$954$		0			0
$955$	−40.7638	−	70.6050i	−1.31909	−	2.28472i
$956$	−16.3383	−	13.7094i	−0.528417	−	0.443395i
$957$		0			0
$958$	1.95929	+	11.1117i	0.0633019	+	0.359003i
$959$	0.399774	+	2.26723i	0.0129094	+	0.0732128i
$960$		0			0
$961$	−3.95052	−	3.31488i	−0.127436	−	0.106932i
$962$	1.11368	+	1.92895i	0.0359066	+	0.0621920i
$963$		0			0
$964$	5.37712	−	9.31344i	0.173185	−	0.299966i
$965$	−36.5760	+	13.3126i	−1.17742	+	0.428547i
$966$		0			0
$967$	31.3774	−	26.3288i	1.00903	−	0.846676i	0.0208191	−	0.999783i	$-0.493373\pi$
$967$	31.3774	−	26.3288i	1.00903	−	0.846676i	0.988210	+	0.153108i	$0.0489281\pi$
$968$	−10.2908	−	3.74553i	−0.330758	−	0.120386i
$969$		0			0
$970$	−3.97391	+	22.5372i	−0.127595	+	0.723625i
$971$	−45.2142			−1.45099			−0.725497	−	0.688225i	$-0.758390\pi$
$971$	−45.2142			−1.45099			−0.725497	+	0.688225i	$0.758390\pi$
$972$		0			0
$973$	−2.78113			−0.0891588
$974$	5.09170	−	28.8765i	0.163149	−	0.925261i
$975$		0			0
$976$	−3.16654	−	1.15253i	−0.101359	−	0.0368915i
$977$	−27.0072	+	22.6617i	−0.864036	+	0.725013i	−0.962834	−	0.270095i	$-0.912945\pi$
$977$	−27.0072	+	22.6617i	−0.864036	+	0.725013i	0.0987973	+	0.995108i	$0.468500\pi$
$978$		0			0
$979$	1.02905	−	0.374544i	0.0328886	−	0.0119705i
$980$	14.1185	−	24.4539i	0.450999	−	0.781152i
$981$		0			0
$982$	5.06801	+	8.77805i	0.161727	+	0.280119i
$983$	30.5200	+	25.6093i	0.973437	+	0.816810i	0.983086	−	0.183143i	$-0.0586272\pi$
$983$	30.5200	+	25.6093i	0.973437	+	0.816810i	−0.00964963	+	0.999953i	$0.503072\pi$
$984$		0			0
$985$	−5.30683	−	30.0965i	−0.169090	−	0.958954i
$986$	−0.722795	−	4.09917i	−0.0230185	−	0.130544i
$987$		0			0
$988$	1.73952	+	1.45963i	0.0553415	+	0.0464370i
$989$	−29.9014	−	51.7908i	−0.950810	−	1.64685i
$990$		0			0
$991$	12.6850	−	21.9711i	0.402953	−	0.697935i	−0.591128	−	0.806578i	$-0.701317\pi$
$991$	12.6850	−	21.9711i	0.402953	−	0.697935i	0.994081	+	0.108643i	$0.0346505\pi$
$992$	4.77702	−	1.73869i	0.151671	−	0.0552036i
$993$		0			0
$994$	−0.336324	+	0.282209i	−0.0106676	+	0.00895114i
$995$	46.1787	+	16.8077i	1.46396	+	0.532839i
$996$		0			0
$997$	−4.67785	+	26.5294i	−0.148149	+	0.840194i	0.816636	+	0.577153i	$0.195836\pi$
$997$	−4.67785	+	26.5294i	−0.148149	+	0.840194i	−0.964785	+	0.263041i	$0.915275\pi$
$998$	−22.2914			−0.705622
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.b.73.2		12
3.2	odd	2		54.2.e.b.25.2	yes	12
9.2	odd	6		486.2.e.f.55.1		12
9.4	even	3		486.2.e.e.379.1		12
9.5	odd	6		486.2.e.h.379.2		12
9.7	even	3		486.2.e.g.55.2		12
12.11	even	2		432.2.u.b.241.1		12
27.2	odd	18		1458.2.c.f.487.6		12
27.4	even	9		486.2.e.e.109.1		12
27.5	odd	18		486.2.e.f.433.1		12
27.7	even	9		1458.2.c.g.973.1		12
27.11	odd	18		1458.2.a.g.1.1		6
27.13	even	9	inner	162.2.e.b.91.2		12
27.14	odd	18		54.2.e.b.13.2	✓	12
27.16	even	9		1458.2.a.f.1.6		6
27.20	odd	18		1458.2.c.f.973.6		12
27.22	even	9		486.2.e.g.433.2		12
27.23	odd	18		486.2.e.h.109.2		12
27.25	even	9		1458.2.c.g.487.1		12
108.95	even	18		432.2.u.b.337.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.2	✓	12	27.14	odd	18
54.2.e.b.25.2	yes	12	3.2	odd	2
162.2.e.b.73.2		12	1.1	even	1	trivial
162.2.e.b.91.2		12	27.13	even	9	inner
432.2.u.b.241.1		12	12.11	even	2
432.2.u.b.337.1		12	108.95	even	18
486.2.e.e.109.1		12	27.4	even	9
486.2.e.e.379.1		12	9.4	even	3
486.2.e.f.55.1		12	9.2	odd	6
486.2.e.f.433.1		12	27.5	odd	18
486.2.e.g.55.2		12	9.7	even	3
486.2.e.g.433.2		12	27.22	even	9
486.2.e.h.109.2		12	27.23	odd	18
486.2.e.h.379.2		12	9.5	odd	6
1458.2.a.f.1.6		6	27.16	even	9
1458.2.a.g.1.1		6	27.11	odd	18
1458.2.c.f.487.6		12	27.2	odd	18
1458.2.c.f.973.6		12	27.20	odd	18
1458.2.c.g.487.1		12	27.25	even	9
1458.2.c.g.973.1		12	27.7	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(3.10057 - 2.60168i) q^{5} +(0.144365 - 0.0525446i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(3.10057 - 2.60168i) q^{5} +(0.144365 - 0.0525446i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.02375 + 3.50524i) q^{10} +(-0.169211 - 0.141985i) q^{11} +(0.103202 + 0.585289i) q^{13} +(0.0266776 + 0.151296i) q^{14} +(0.766044 + 0.642788i) q^{16} +(2.78255 + 4.81952i) q^{17} +(-1.91041 + 3.30893i) q^{19} +(-3.80341 + 1.38433i) q^{20} +(0.169211 - 0.141985i) q^{22} +(-5.50570 - 2.00391i) q^{23} +(1.97651 - 11.2093i) q^{25} -0.594318 q^{26} -0.153630 q^{28} +(-0.129880 + 0.736585i) q^{29} +(-4.77702 - 1.73869i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.22949 + 1.90338i) q^{34} +(0.310909 - 0.538510i) q^{35} +(-1.87388 - 3.24566i) q^{37} +(-2.92692 - 2.45598i) q^{38} +(-0.702841 - 3.98601i) q^{40} +(-0.690156 - 3.91407i) q^{41} +(7.81896 + 6.56088i) q^{43} +(0.110445 + 0.191296i) q^{44} +(2.92952 - 5.07408i) q^{46} +(-0.447025 + 0.162704i) q^{47} +(-5.34423 + 4.48434i) q^{49} +(10.6958 + 3.89296i) q^{50} +(0.103202 - 0.585289i) q^{52} -3.29955 q^{53} -0.894051 q^{55} +(0.0266776 - 0.151296i) q^{56} +(-0.702841 - 0.255813i) q^{58} +(-5.57221 + 4.67564i) q^{59} +(-3.16654 + 1.15253i) q^{61} +(2.54180 - 4.40252i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.84272 + 1.54623i) q^{65} +(1.29509 + 7.34481i) q^{67} +(-0.966370 - 5.48056i) q^{68} +(0.476340 + 0.399697i) q^{70} +(1.42889 + 2.47490i) q^{71} +(0.638922 - 1.10665i) q^{73} +(3.52175 - 1.28181i) q^{74} +(2.92692 - 2.45598i) q^{76} +(-0.0318887 - 0.0116066i) q^{77} +(-0.574268 + 3.25684i) q^{79} +4.04750 q^{80} +3.97445 q^{82} +(1.43627 - 8.14551i) q^{83} +(21.1664 + 7.70392i) q^{85} +(-7.81896 + 6.56088i) q^{86} +(-0.207568 + 0.0755487i) q^{88} +(-2.47882 + 4.29345i) q^{89} +(0.0456525 + 0.0790725i) q^{91} +(4.48829 + 3.76612i) q^{92} +(-0.0826070 - 0.468487i) q^{94} +(2.68543 + 15.2298i) q^{95} +(4.33127 + 3.63437i) q^{97} +(-3.48820 - 6.04174i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Introduction

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