LMFDB - Embedded newform 162.2.e.b.91.2

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			91.2
Root			$0.500000 - 2.42499i$ of defining polynomial
Character	$\chi$	$=$	162.91
Dual form			162.2.e.b.73.2

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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	0.966690	+	0.255949i	$0.0823880\pi$
$5$	3.10057	+	2.60168i	1.38661	+	1.16351i	0.419925	+	0.907559i	$0.362056\pi$
$6$		0			0
$7$	0.144365	+	0.0525446i	0.0545648	+	0.0198600i	0.369158	−	0.929366i	$-0.379646\pi$
$7$	0.144365	+	0.0525446i	0.0545648	+	0.0198600i	−0.314594	+	0.949226i	$0.601868\pi$
$8$	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	−0.667941	−	0.744215i	$-0.732824\pi$
$11$	−0.169211	+	0.141985i	−0.0510191	+	0.0428101i	0.616922	+	0.787025i	$0.288380\pi$
$12$		0			0
$13$	0.103202	−	0.585289i	0.0286231	−	0.162330i	−0.967146	−	0.254222i	$-0.918180\pi$
$13$	0.103202	−	0.585289i	0.0286231	−	0.162330i	0.995769	+	0.0918925i	$0.0292916\pi$
$14$	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	−0.301639	−	0.953422i	$-0.597534\pi$
$17$	2.78255	−	4.81952i	0.674868	−	1.16891i	0.976507	−	0.215484i	$-0.0691328\pi$
$18$		0			0
$19$	−1.91041	−	3.30893i	−0.438278	−	0.759120i	0.559279	−	0.828980i	$-0.311078\pi$
$19$	−1.91041	−	3.30893i	−0.438278	−	0.759120i	−0.997557	+	0.0698599i	$0.977745\pi$
$20$	−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	−0.844803	−	0.535078i	$-0.820282\pi$
$23$	−5.50570	+	2.00391i	−1.14802	+	0.417844i	−0.303215	+	0.952922i	$0.598060\pi$
$24$		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	0.970371	−	0.241619i	$-0.0776785\pi$
$29$	−0.129880	−	0.736585i	−0.0241181	−	0.136780i	−0.994489	+	0.104839i	$0.966567\pi$
$30$		0			0
$31$	−4.77702	+	1.73869i	−0.857978	+	0.312278i	−0.733289	−	0.679917i	$-0.762016\pi$
$31$	−4.77702	+	1.73869i	−0.857978	+	0.312278i	−0.124689	+	0.992196i	$0.539793\pi$
$32$	−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	−0.977939	−	0.208891i	$-0.933015\pi$
$37$	−1.87388	+	3.24566i	−0.308065	+	0.533584i	0.669874	+	0.742474i	$0.266348\pi$
$38$	−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	0.882287	+	0.470711i	$0.156003\pi$
$41$	−0.690156	+	3.91407i	−0.107784	+	0.611275i	−0.990072	+	0.140564i	$0.955109\pi$
$42$		0			0
$43$	7.81896	−	6.56088i	1.19238	−	1.00053i	0.192565	−	0.981284i	$-0.438319\pi$
$43$	7.81896	−	6.56088i	1.19238	−	1.00053i	0.999815	−	0.0192411i	$-0.00612500\pi$
$44$	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	0.309212	−	0.950993i	$-0.399935\pi$
$47$	−0.447025	−	0.162704i	−0.0652054	−	0.0237328i	−0.374417	+	0.927260i	$0.622157\pi$
$48$		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	0.203444	−	0.979086i	$-0.434786\pi$
$59$	−5.57221	−	4.67564i	−0.725440	−	0.608716i	−0.928884	+	0.370370i	$0.879231\pi$
$60$		0			0
$61$	−3.16654	−	1.15253i	−0.405434	−	0.147566i	0.131250	−	0.991349i	$-0.458101\pi$
$61$	−3.16654	−	1.15253i	−0.405434	−	0.147566i	−0.536684	+	0.843783i	$0.680323\pi$
$62$	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	−0.797562	−	0.603237i	$-0.793877\pi$
$67$	1.29509	−	7.34481i	0.158220	−	0.897312i	0.955782	−	0.294075i	$-0.0950115\pi$
$68$	−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	−0.768694	−	0.639617i	$-0.779093\pi$
$71$	1.42889	−	2.47490i	0.169578	−	0.293717i	0.938271	+	0.345900i	$0.112426\pi$
$72$		0			0
$73$	0.638922	+	1.10665i	0.0747802	+	0.129523i	0.900991	−	0.433838i	$-0.142841\pi$
$73$	0.638922	+	1.10665i	0.0747802	+	0.129523i	−0.826210	+	0.563362i	$0.809508\pi$
$74$	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	−0.999921	−	0.0125947i	$-0.995991\pi$
$79$	−0.574268	−	3.25684i	−0.0646102	−	0.366423i	0.935310	−	0.353828i	$-0.115120\pi$
$80$	4.04750			0.452524
$81$		0			0
$82$	3.97445			0.438904
$83$	1.43627	+	8.14551i	0.157651	+	0.894085i	0.956322	+	0.292316i	$0.0944261\pi$
$83$	1.43627	+	8.14551i	0.157651	+	0.894085i	−0.798670	+	0.601769i	$0.794463\pi$
$84$		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	0.704218	−	0.709984i	$-0.251298\pi$
$89$	−2.47882	−	4.29345i	−0.262755	−	0.455105i	−0.966973	+	0.254879i	$0.917964\pi$
$90$		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	−0.395851	−	0.918315i	$-0.629550\pi$
$97$	4.33127	−	3.63437i	0.439774	−	0.369014i	0.835625	+	0.549301i	$0.185106\pi$
$98$	−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	0.950072	−	0.312029i	$-0.101009\pi$
$101$	14.8467	+	5.40376i	1.47730	+	0.537694i	0.527229	+	0.849723i	$0.323231\pi$
$102$		0			0
$103$	8.19426	+	6.87580i	0.807404	+	0.677493i	0.949987	−	0.312290i	$-0.101096\pi$
$103$	8.19426	+	6.87580i	0.807404	+	0.677493i	−0.142582	+	0.989783i	$0.545541\pi$
$104$	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	0.981659	−	0.190647i	$-0.0610586\pi$
$113$	10.2514	+	8.60195i	0.964371	+	0.809204i	−0.0172875	+	0.999851i	$0.505503\pi$
$114$		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	0.900681	+	0.434481i	$0.143068\pi$
$127$	9.31545	+	16.1348i	0.826612	+	1.43173i	−0.0740688	+	0.997253i	$0.523598\pi$
$128$	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	−0.608180	−	0.793799i	$-0.708100\pi$
$131$	−6.45330	+	2.34881i	−0.563828	+	0.205217i	0.0443519	+	0.999016i	$0.485878\pi$
$132$		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	−0.867743	−	0.497014i	$-0.834430\pi$
$137$	−2.60219	−	14.7577i	−0.222320	−	1.26084i	0.645423	−	0.763826i	$-0.276681\pi$
$138$		0			0
$139$	−17.0110	+	6.19150i	−1.44286	+	0.525156i	−0.940586	−	0.339555i	$-0.889724\pi$
$139$	−17.0110	+	6.19150i	−1.44286	+	0.525156i	−0.502269	+	0.864711i	$0.667501\pi$
$140$	−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	−0.669381	−	0.742919i	$-0.733441\pi$
$149$	2.60884	−	14.7955i	0.213725	−	1.21209i	0.883106	−	0.469174i	$-0.155448\pi$
$150$		0			0
$151$	−4.32258	+	3.62708i	−0.351767	+	0.295167i	−0.801499	−	0.597996i	$-0.795964\pi$
$151$	−4.32258	+	3.62708i	−0.351767	+	0.295167i	0.449732	+	0.893163i	$0.351519\pi$
$152$	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	0.836801	−	0.547507i	$-0.184423\pi$
$157$	5.54978	+	4.65682i	0.442921	+	0.371655i	−0.393880	+	0.919162i	$0.628868\pi$
$158$	−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	0.952829	−	0.303507i	$-0.0981576\pi$
$167$	10.5889	+	8.88510i	0.819390	+	0.687550i	−0.133439	+	0.991057i	$0.542602\pi$
$168$		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	−0.521154	−	0.853463i	$-0.674498\pi$
$173$	3.00999	−	2.52568i	0.228845	−	0.192024i	0.749999	+	0.661439i	$0.230054\pi$
$174$		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	−0.807972	−	0.589220i	$-0.799435\pi$
$179$	1.42211	−	2.46317i	0.106294	−	0.184106i	0.914266	+	0.405115i	$0.132768\pi$
$180$		0			0
$181$	−6.46274	−	11.1938i	−0.480372	−	0.832028i	0.519375	−	0.854547i	$-0.326165\pi$
$181$	−6.46274	−	11.1938i	−0.480372	−	0.832028i	−0.999746	+	0.0225186i	$0.992832\pi$
$182$	−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	0.800934	+	0.598753i	$0.204337\pi$
$191$	3.49774	+	19.8367i	0.253088	+	1.43533i	−0.547846	+	0.836579i	$0.684552\pi$
$192$		0			0
$193$	−9.03669	+	3.28909i	−0.650476	+	0.236754i	−0.646119	−	0.763237i	$-0.723609\pi$
$193$	−9.03669	+	3.28909i	−0.650476	+	0.236754i	−0.00435663	+	0.999991i	$0.501387\pi$
$194$	−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	0.968598	−	0.248633i	$-0.0799812\pi$
$197$	3.77527	+	6.53895i	0.268977	+	0.465881i	−0.699621	+	0.714514i	$0.746648\pi$
$198$		0			0
$199$	6.07071	−	10.5148i	0.430341	−	0.745372i	−0.566562	−	0.824019i	$-0.691727\pi$
$199$	6.07071	−	10.5148i	0.430341	−	0.745372i	0.996903	+	0.0786471i	$0.0250600\pi$
$200$	−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	0.432118	−	0.901817i	$-0.357766\pi$
$211$	−5.53378	−	4.64340i	−0.380961	−	0.319665i	−0.813080	+	0.582152i	$0.802211\pi$
$212$	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	0.980682	−	0.195607i	$-0.0626678\pi$
$223$	23.9856	+	8.73004i	1.60619	+	0.584607i	0.625512	+	0.780214i	$0.284890\pi$
$224$	−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	−0.930155	−	0.367167i	$-0.880328\pi$
$227$	−10.9999	+	9.22998i	−0.730086	+	0.612615i	0.200069	+	0.979782i	$0.435883\pi$
$228$		0			0
$229$	0.704853	−	3.99742i	0.0465780	−	0.264157i	−0.952622	−	0.304158i	$-0.901625\pi$
$229$	0.704853	−	3.99742i	0.0465780	−	0.264157i	0.999200	+	0.0400010i	$0.0127361\pi$
$230$	−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	−0.441656	−	0.897185i	$-0.645609\pi$
$233$	8.48936	−	14.7040i	0.556157	−	0.963292i	0.997813	−	0.0661072i	$-0.0210579\pi$
$234$		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	0.400577	−	0.916263i	$-0.368810\pi$
$239$	20.0419	−	7.29464i	1.29640	−	0.471851i	0.895823	+	0.444412i	$0.146587\pi$
$240$		0			0
$241$	−1.86745	−	10.5909i	−0.120293	−	0.682217i	−0.983993	−	0.178210i	$-0.942970\pi$
$241$	−1.86745	−	10.5909i	−0.120293	−	0.682217i	0.863699	−	0.504007i	$-0.168142\pi$
$242$	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	0.924371	−	0.381495i	$-0.124591\pi$
$251$	2.08811	+	3.61672i	0.131801	+	0.228285i	−0.792570	+	0.609781i	$0.791257\pi$
$252$		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	0.758750	+	0.651382i	$0.225811\pi$
$257$	−2.83797	+	16.0949i	−0.177028	+	1.00397i	−0.935777	+	0.352592i	$0.885301\pi$
$258$		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	0.263166	−	0.964751i	$-0.415233\pi$
$263$	−2.51963	−	0.917071i	−0.155367	−	0.0565490i	−0.418533	+	0.908202i	$0.637456\pi$
$264$		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	0.413469	−	0.910518i	$-0.364317\pi$
$277$	2.41221	+	0.877972i	0.144936	+	0.0527523i	−0.268534	+	0.963270i	$0.586539\pi$
$278$	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	−0.982337	−	0.187119i	$-0.940085\pi$
$281$	−16.2374	+	13.6248i	−0.968642	+	0.812787i	0.0136956	+	0.999906i	$0.495640\pi$
$282$		0			0
$283$	−3.40928	+	19.3350i	−0.202660	+	1.14934i	0.698419	+	0.715689i	$0.253887\pi$
$283$	−3.40928	+	19.3350i	−0.202660	+	1.14934i	−0.901079	+	0.433655i	$0.857224\pi$
$284$	−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	0.323136	−	0.946352i	$-0.395263\pi$
$293$	20.1808	−	7.34522i	1.17898	−	0.429112i	0.855840	+	0.517240i	$0.173041\pi$
$294$		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	−0.935338	−	0.353754i	$-0.884905\pi$
$307$	−2.82636	+	4.89540i	−0.161309	+	0.279395i	0.774029	+	0.633150i	$0.218238\pi$
$308$	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	0.904110	+	0.427299i	$0.140535\pi$
$311$	−1.61574	+	9.16334i	−0.0916205	+	0.519605i	−0.995731	+	0.0923061i	$0.970576\pi$
$312$		0			0
$313$	−2.05976	+	1.72835i	−0.116425	+	0.0976920i	−0.699141	−	0.714983i	$-0.746434\pi$
$313$	−2.05976	+	1.72835i	−0.116425	+	0.0976920i	0.582717	+	0.812675i	$0.301990\pi$
$314$	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	−0.525114	−	0.851032i	$-0.675977\pi$
$317$	−26.2511	−	9.55461i	−1.47441	−	0.536641i	−0.949294	+	0.314391i	$0.898200\pi$
$318$		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	0.320103	−	0.947383i	$-0.396283\pi$
$331$	−0.794144	−	0.289045i	−0.0436501	−	0.0158873i	−0.363753	+	0.931495i	$0.618505\pi$
$332$	−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	−0.454183	−	0.890908i	$-0.650069\pi$
$337$	5.09088	−	28.8718i	0.277318	−	1.57275i	0.731501	−	0.681840i	$-0.238820\pi$
$338$	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	−0.796885	−	0.604131i	$-0.793520\pi$
$347$	−18.9820	+	6.90888i	−1.01901	+	0.370888i	−0.222121	+	0.975019i	$0.571298\pi$
$348$		0			0
$349$	1.66866	+	9.46343i	0.0893212	+	0.506566i	0.996340	+	0.0854761i	$0.0272411\pi$
$349$	1.66866	+	9.46343i	0.0893212	+	0.506566i	−0.907019	+	0.421090i	$0.861648\pi$
$350$	1.74866			0.0934697
$351$		0			0
$352$	0.220890			0.0117735
$353$	1.70637	+	9.67729i	0.0908208	+	0.515070i	0.995948	+	0.0899297i	$0.0286642\pi$
$353$	1.70637	+	9.67729i	0.0908208	+	0.515070i	−0.905127	+	0.425141i	$0.860225\pi$
$354$		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	0.979171	−	0.203039i	$-0.0650817\pi$
$359$	5.94469	+	10.2965i	0.313749	+	0.543429i	−0.665422	+	0.746467i	$0.731748\pi$
$360$		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	−0.518207	+	0.855255i	$0.673400\pi$
$367$	−27.7867	+	23.3158i	−1.45045	+	1.21708i	−0.932248	+	0.361821i	$0.882155\pi$
$368$	−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	0.878718	−	0.477342i	$-0.158400\pi$
$373$	10.8389	+	9.09489i	0.561215	+	0.470916i	−0.317502	+	0.948258i	$0.602844\pi$
$374$	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	0.0143953	−	0.999896i	$-0.495418\pi$
$383$	−18.9404	−	15.8929i	−0.967811	−	0.812090i	−0.982206	+	0.187807i	$0.939862\pi$
$384$		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	−0.879965	−	0.475038i	$-0.842434\pi$
$389$	−11.1425	+	9.34969i	−0.564948	+	0.474048i	0.315017	+	0.949086i	$0.397990\pi$
$390$		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	0.808245	−	0.588846i	$-0.200418\pi$
$397$	−2.10870	−	3.65238i	−0.105833	−	0.183308i	−0.914078	+	0.405538i	$0.867084\pi$
$398$	−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	−0.692709	−	0.721217i	$-0.743583\pi$
$401$	−15.2143	+	5.53755i	−0.759765	+	0.276532i	−0.0670561	+	0.997749i	$0.521361\pi$
$402$		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	−0.432003	−	0.901872i	$-0.642193\pi$
$409$	−3.70550	+	1.34869i	−0.183225	+	0.0666885i	0.248778	+	0.968560i	$0.419971\pi$
$410$	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	−0.384062	−	0.923307i	$-0.625475\pi$
$419$	5.98994	−	33.9707i	0.292628	−	1.65957i	0.676690	−	0.736268i	$-0.263414\pi$
$420$		0			0
$421$	−8.80184	+	7.38562i	−0.428976	+	0.359953i	−0.831565	−	0.555427i	$-0.812555\pi$
$421$	−8.80184	+	7.38562i	−0.428976	+	0.359953i	0.402589	+	0.915381i	$0.368110\pi$
$422$	−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	0.985266	−	0.171029i	$-0.0547093\pi$
$439$	34.1541	+	12.4311i	1.63009	+	0.593303i	0.644822	+	0.764333i	$0.276932\pi$
$440$	−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	0.446412	−	0.894828i	$-0.352702\pi$
$443$	29.5753	−	24.8166i	1.40516	−	1.17907i	0.958752	−	0.284245i	$-0.0917428\pi$
$444$		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	−0.988997	−	0.147932i	$-0.952738\pi$
$449$	−7.76357	+	13.4469i	−0.366385	+	0.634598i	0.622612	+	0.782531i	$0.286072\pi$
$450$		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	−0.674164	−	0.738582i	$-0.735496\pi$
$457$	−6.26933	−	35.5551i	−0.293267	−	1.66320i	0.380897	−	0.924618i	$-0.375615\pi$
$458$	−4.05908			−0.189669
$459$		0			0
$460$	23.7145			1.10569
$461$	−1.72646	−	9.79122i	−0.0804091	−	0.456023i	−0.998253	−	0.0590816i	$-0.981183\pi$
$461$	−1.72646	−	9.79122i	−0.0804091	−	0.456023i	0.917844	−	0.396941i	$-0.129928\pi$
$462$		0			0
$463$	18.0852	−	6.58248i	0.840492	−	0.305914i	0.114334	−	0.993442i	$-0.463527\pi$
$463$	18.0852	−	6.58248i	0.840492	−	0.305914i	0.726158	+	0.687528i	$0.241304\pi$
$464$	−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	0.956561	+	0.291534i	$0.0941655\pi$
$467$	15.7918	+	27.3521i	0.730756	+	1.26571i	−0.225805	+	0.974173i	$0.572501\pi$
$468$		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	0.572686	−	0.819775i	$-0.305901\pi$
$479$	10.6027	+	3.85905i	0.484448	+	0.176325i	−0.0882381	+	0.996099i	$0.528124\pi$
$480$		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	0.800956	−	0.598723i	$-0.204325\pi$
$491$	7.76464	+	6.51531i	0.350413	+	0.294032i	−0.450543	+	0.892755i	$0.648769\pi$
$492$		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	−0.766823	−	0.641859i	$-0.778164\pi$
$499$	3.87086	−	21.9527i	0.173284	−	0.982740i	0.940106	−	0.340881i	$-0.110725\pi$
$500$	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	−0.981750	−	0.190179i	$-0.939093\pi$
$503$	−7.31535	+	12.6706i	−0.326175	+	0.564952i	0.655574	+	0.755131i	$0.272427\pi$
$504$		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	−0.189162	−	0.981946i	$-0.560577\pi$
$509$	6.70321	−	2.43977i	0.297115	−	0.108141i	0.486276	+	0.873805i	$0.338355\pi$
$510$		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	0.761535	−	0.648123i	$-0.224446\pi$
$521$	−4.12053	−	7.13696i	−0.180524	−	0.312676i	−0.942059	+	0.335447i	$0.891113\pi$
$522$		0			0
$523$	11.2705	−	19.5211i	0.492826	−	0.853599i	−0.507140	−	0.861864i	$-0.669297\pi$
$523$	11.2705	−	19.5211i	0.492826	−	0.853599i	0.999966	+	0.00826425i	$0.00263062\pi$
$524$	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	−0.345085	−	0.938571i	$-0.612150\pi$
$547$	−28.3635	−	10.3235i	−1.21274	−	0.441400i	−0.867652	+	0.497171i	$0.834372\pi$
$548$	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	−0.274138	−	0.961690i	$-0.588393\pi$
$557$	16.4210	−	28.4420i	0.695779	−	1.20512i	0.969917	−	0.243434i	$-0.0782741\pi$
$558$		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	0.0563401	−	0.998412i	$-0.482057\pi$
$563$	17.5885	−	6.40168i	0.741266	−	0.269799i	0.684926	+	0.728613i	$0.259835\pi$
$564$		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	0.999981	−	0.00622922i	$-0.00198284\pi$
$569$	1.38771	+	7.87008i	0.0581757	+	0.329931i	−0.941805	+	0.336160i	$0.890872\pi$
$570$		0			0
$571$	26.7013	−	9.71847i	1.11741	−	0.406705i	0.283706	−	0.958911i	$-0.408436\pi$
$571$	26.7013	−	9.71847i	1.11741	−	0.406705i	0.833708	+	0.552206i	$0.186214\pi$
$572$	−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	−0.325257	+	0.945626i	$0.605451\pi$
$577$	−23.5780	+	40.8383i	−0.981564	+	1.70012i	−0.656307	+	0.754494i	$0.727883\pi$
$578$	−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	−0.0240279	−	0.999711i	$-0.507649\pi$
$587$	−16.5971	−	6.04086i	−0.685036	−	0.249333i	−0.661008	+	0.750378i	$0.729871\pi$
$588$		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	0.314791	−	0.949161i	$-0.398066\pi$
$599$	−13.8351	−	11.6090i	−0.565288	−	0.474333i	−0.880078	+	0.474828i	$0.842510\pi$
$600$		0			0
$601$	−3.04117	−	1.10690i	−0.124052	−	0.0451513i	0.279248	−	0.960219i	$-0.409915\pi$
$601$	−3.04117	−	1.10690i	−0.124052	−	0.0451513i	−0.403300	+	0.915068i	$0.632137\pi$
$602$	−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	−0.725830	−	0.687874i	$-0.758544\pi$
$607$	4.71790	−	26.7566i	0.191494	−	1.08602i	0.917324	−	0.398141i	$-0.130345\pi$
$608$	−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	−0.998144	−	0.0608964i	$-0.980604\pi$
$613$	−13.6622	−	23.6636i	−0.551810	−	0.955763i	0.446334	−	0.894866i	$-0.352729\pi$
$614$	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	0.216676	−	0.976244i	$-0.430478\pi$
$617$	25.0923	−	9.13284i	1.01018	−	0.367674i	0.793501	+	0.608569i	$0.208256\pi$
$618$		0			0
$619$	6.92886	+	39.2955i	0.278494	+	1.57942i	0.727639	+	0.685960i	$0.240618\pi$
$619$	6.92886	+	39.2955i	0.278494	+	1.57942i	−0.449145	+	0.893459i	$0.648271\pi$
$620$	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	−0.765869	−	0.642997i	$-0.777691\pi$
$631$	4.36875	−	7.56690i	0.173917	−	0.301234i	0.939786	+	0.341763i	$0.111024\pi$
$632$	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	0.655553	−	0.755149i	$-0.272436\pi$
$641$	17.0222	+	6.19556i	0.672335	+	0.244710i	0.0167821	+	0.999859i	$0.494658\pi$
$642$		0			0
$643$	−24.5762	−	20.6219i	−0.969191	−	0.813247i	0.0132331	−	0.999912i	$-0.495788\pi$
$643$	−24.5762	−	20.6219i	−0.969191	−	0.813247i	−0.982424	+	0.186665i	$0.940232\pi$
$644$	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	0.619919	−	0.784666i	$-0.287165\pi$
$653$	−1.15447	−	0.968718i	−0.0451780	−	0.0379089i	−0.665097	+	0.746757i	$0.731610\pi$
$654$		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	−0.517045	−	0.855958i	$-0.672968\pi$
$659$	6.06158	−	5.08627i	0.236126	−	0.198133i	0.753171	+	0.657825i	$0.228523\pi$
$660$		0			0
$661$	−5.26138	+	29.8388i	−0.204644	+	1.16059i	0.693355	+	0.720597i	$0.256132\pi$
$661$	−5.26138	+	29.8388i	−0.204644	+	1.16059i	−0.897999	+	0.439998i	$0.854979\pi$
$662$	−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	−0.964260	−	0.264956i	$-0.914642\pi$
$673$	−3.85949	−	21.8883i	−0.148772	−	0.843731i	0.815488	−	0.578774i	$-0.196469\pi$
$674$	−29.3172			−1.12926
$675$		0			0
$676$	−12.6468			−0.486415
$677$	−7.00672	−	39.7371i	−0.269290	−	1.52722i	−0.756535	−	0.653954i	$-0.773109\pi$
$677$	−7.00672	−	39.7371i	−0.269290	−	1.52722i	0.487245	−	0.873266i	$-0.338002\pi$
$678$		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	0.519514	−	0.854462i	$-0.326113\pi$
$683$	−12.5504	−	21.7380i	−0.480229	−	0.831780i	−0.999743	+	0.0226815i	$0.992780\pi$
$684$		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	−0.683880	−	0.729594i	$-0.739709\pi$
$691$	−2.21137	+	1.85556i	−0.0841245	+	0.0705889i	0.599756	+	0.800183i	$0.295264\pi$
$692$	−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	0.704749	−	0.709457i	$-0.251060\pi$
$709$	20.9978	+	7.64257i	0.788588	+	0.287023i	0.0838392	+	0.996479i	$0.473282\pi$
$710$	−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	0.291328	+	0.956623i	$0.405903\pi$
$719$	−18.3086	+	31.7114i	−0.682796	+	1.18264i	−0.974124	+	0.226014i	$0.927430\pi$
$720$		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	0.996525	+	0.0832885i	$0.0265423\pi$
$727$	2.38849	+	13.5458i	0.0885842	+	0.502386i	−0.907941	+	0.419097i	$0.862347\pi$
$728$	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	−0.839573	−	0.543247i	$-0.817195\pi$
$733$	−30.6892	+	11.1699i	−1.13353	+	0.412571i	−0.293957	+	0.955819i	$0.594972\pi$
$734$	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	−0.482820	−	0.875720i	$-0.660387\pi$
$739$	14.0540	−	24.3423i	0.516986	−	0.895445i	0.999805	−	0.0197257i	$-0.00627929\pi$
$740$	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	−0.925345	−	0.379126i	$-0.876225\pi$
$743$	2.01338	−	11.4184i	0.0738636	−	0.418901i	0.999209	−	0.0397752i	$-0.0126642\pi$
$744$		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	−0.133896	−	0.990995i	$-0.542749\pi$
$751$	−31.0515	−	26.0553i	−1.13309	−	0.950772i	−0.999191	+	0.0402230i	$0.987193\pi$
$752$	−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	0.586483	−	0.809962i	$-0.300512\pi$
$761$	−3.01606	−	2.53078i	−0.109332	−	0.0917406i	−0.695815	+	0.718221i	$0.744957\pi$
$762$		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	0.488617	+	0.872498i	$0.337501\pi$
$769$	−7.45807	+	42.2968i	−0.268945	+	1.52526i	−0.757562	+	0.652763i	$0.773610\pi$
$770$	−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	−0.991588	−	0.129433i	$-0.958684\pi$
$773$	−10.6680	+	18.4775i	−0.383702	+	0.664591i	0.607886	+	0.794024i	$0.292018\pi$
$774$		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

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

L-functions

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