LMFDB - Embedded newform 54.2.e.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.2
Root			$0.500000 + 1.74095i$ of defining polynomial
Character	$\chi$	$=$	54.25
Dual form			54.2.e.b.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(1.56529 - 0.741539i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.10057 + 2.60168i) q^{5} +(-0.458464 - 1.67027i) q^{6} +(0.144365 - 0.0525446i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.90024 - 2.32144i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(1.56529 - 0.741539i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.10057 + 2.60168i) q^{5} +(-0.458464 - 1.67027i) q^{6} +(0.144365 - 0.0525446i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.90024 - 2.32144i) q^{9} +(2.02375 + 3.50524i) q^{10} +(0.169211 + 0.141985i) q^{11} +(-1.72451 + 0.161460i) q^{12} +(0.103202 + 0.585289i) q^{13} +(-0.0266776 - 0.151296i) q^{14} +(-2.92402 + 6.37157i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.78255 - 4.81952i) q^{17} +(-1.95620 - 2.27448i) q^{18} +(-1.91041 + 3.30893i) q^{19} +(3.80341 - 1.38433i) q^{20} +(0.187009 - 0.189300i) q^{21} +(0.169211 - 0.141985i) q^{22} +(5.50570 + 2.00391i) q^{23} +(-0.140451 + 1.72635i) q^{24} +(1.97651 - 11.2093i) q^{25} +0.594318 q^{26} +(1.25298 - 5.04282i) q^{27} -0.153630 q^{28} +(0.129880 - 0.736585i) q^{29} +(5.76702 + 3.98601i) q^{30} +(-4.77702 - 1.73869i) q^{31} +(0.766044 - 0.642788i) q^{32} +(0.370152 + 0.0967705i) q^{33} +(-5.22949 + 1.90338i) q^{34} +(-0.310909 + 0.538510i) q^{35} +(-2.57962 + 1.53152i) q^{36} +(-1.87388 - 3.24566i) q^{37} +(2.92692 + 2.45598i) q^{38} +(0.595555 + 0.839616i) q^{39} +(-0.702841 - 3.98601i) q^{40} +(0.690156 + 3.91407i) q^{41} +(-0.153950 - 0.217039i) q^{42} +(7.81896 + 6.56088i) q^{43} +(-0.110445 - 0.191296i) q^{44} +(0.147838 + 12.1416i) q^{45} +(2.92952 - 5.07408i) q^{46} +(0.447025 - 0.162704i) q^{47} +(1.67573 + 0.438094i) q^{48} +(-5.34423 + 4.48434i) q^{49} +(-10.6958 - 3.89296i) q^{50} +(-7.92935 - 5.48056i) q^{51} +(0.103202 - 0.585289i) q^{52} +3.29955 q^{53} +(-4.74863 - 2.10962i) q^{54} -0.894051 q^{55} +(-0.0266776 + 0.151296i) q^{56} +(-0.536639 + 6.59606i) q^{57} +(-0.702841 - 0.255813i) q^{58} +(5.57221 - 4.67564i) q^{59} +(4.92689 - 4.98724i) q^{60} +(-3.16654 + 1.15253i) q^{61} +(-2.54180 + 4.40252i) q^{62} +(0.152349 - 0.434982i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.84272 - 1.54623i) q^{65} +(0.159577 - 0.347724i) q^{66} +(1.29509 + 7.34481i) q^{67} +(0.966370 + 5.48056i) q^{68} +(10.1040 - 0.945999i) q^{69} +(0.476340 + 0.399697i) q^{70} +(-1.42889 - 2.47490i) q^{71} +(1.06031 + 2.80638i) q^{72} +(0.638922 - 1.10665i) q^{73} +(-3.52175 + 1.28181i) q^{74} +(-5.21836 - 19.0115i) q^{75} +(2.92692 - 2.45598i) q^{76} +(0.0318887 + 0.0116066i) q^{77} +(0.930277 - 0.440710i) q^{78} +(-0.574268 + 3.25684i) q^{79} -4.04750 q^{80} +(-1.77818 - 8.82259i) q^{81} +3.97445 q^{82} +(-1.43627 + 8.14551i) q^{83} +(-0.240475 + 0.113923i) q^{84} +(21.1664 + 7.70392i) q^{85} +(7.81896 - 6.56088i) q^{86} +(-0.342907 - 1.24928i) q^{87} +(-0.207568 + 0.0755487i) q^{88} +(2.47882 - 4.29345i) q^{89} +(11.9828 + 1.96277i) q^{90} +(0.0456525 + 0.0790725i) q^{91} +(-4.48829 - 3.76612i) q^{92} +(-8.76671 + 0.820795i) q^{93} +(-0.0826070 - 0.468487i) q^{94} +(-2.68543 - 15.2298i) q^{95} +(0.722426 - 1.57420i) q^{96} +(4.33127 + 3.63437i) q^{97} +(3.48820 + 6.04174i) q^{98} +(0.651152 - 0.123008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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
$3$	1.56529	−	0.741539i	0.903718	−	0.428128i
$3$	1.56529	−	0.741539i	0.903718	−	0.428128i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−3.10057	+	2.60168i	−1.38661	+	1.16351i	−0.419925	+	0.907559i	$0.637944\pi$
$5$	−3.10057	+	2.60168i	−1.38661	+	1.16351i	−0.966690	+	0.255949i	$0.917612\pi$
$6$	−0.458464	−	1.67027i	−0.187167	−	0.681886i
$7$	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
$9$	1.90024	−	2.32144i	0.633413	−	0.773814i
$10$	2.02375	+	3.50524i	0.639966	+	1.10845i
$11$	0.169211	+	0.141985i	0.0510191	+	0.0428101i	0.667941	−	0.744215i	$-0.267176\pi$
$11$	0.169211	+	0.141985i	0.0510191	+	0.0428101i	−0.616922	+	0.787025i	$0.711620\pi$
$12$	−1.72451	+	0.161460i	−0.497823	+	0.0466094i
$13$	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
$15$	−2.92402	+	6.37157i	−0.754979	+	1.64513i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.78255	−	4.81952i	−0.674868	−	1.16891i	−0.976507	−	0.215484i	$-0.930867\pi$
$17$	−2.78255	−	4.81952i	−0.674868	−	1.16891i	0.301639	−	0.953422i	$-0.402466\pi$
$18$	−1.95620	−	2.27448i	−0.461081	−	0.536101i
$19$	−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
$21$	0.187009	−	0.189300i	0.0408086	−	0.0413086i
$22$	0.169211	−	0.141985i	0.0360760	−	0.0302713i
$23$	5.50570	+	2.00391i	1.14802	+	0.417844i	0.844803	−	0.535078i	$-0.179718\pi$
$23$	5.50570	+	2.00391i	1.14802	+	0.417844i	0.303215	+	0.952922i	$0.401940\pi$
$24$	−0.140451	+	1.72635i	−0.0286695	+	0.352389i
$25$	1.97651	−	11.2093i	0.395302	−	2.24187i
$26$	0.594318			0.116555
$27$	1.25298	−	5.04282i	0.241136	−	0.970491i
$28$	−0.153630			−0.0290333
$29$	0.129880	−	0.736585i	0.0241181	−	0.136780i	−0.970371	−	0.241619i	$-0.922322\pi$
$29$	0.129880	−	0.736585i	0.0241181	−	0.136780i	0.994489	+	0.104839i	$0.0334327\pi$
$30$	5.76702	+	3.98601i	1.05291	+	0.727743i
$31$	−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
$33$	0.370152	+	0.0967705i	0.0644351	+	0.0168456i
$34$	−5.22949	+	1.90338i	−0.896850	+	0.326427i
$35$	−0.310909	+	0.538510i	−0.0525532	+	0.0910248i
$36$	−2.57962	+	1.53152i	−0.429937	+	0.255254i
$37$	−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
$39$	0.595555	+	0.839616i	0.0953652	+	0.134446i
$40$	−0.702841	−	3.98601i	−0.111129	−	0.630244i
$41$	0.690156	+	3.91407i	0.107784	+	0.611275i	0.990072	+	0.140564i	$0.0448915\pi$
$41$	0.690156	+	3.91407i	0.107784	+	0.611275i	−0.882287	+	0.470711i	$0.843997\pi$
$42$	−0.153950	−	0.217039i	−0.0237550	−	0.0334899i
$43$	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
$45$	0.147838	+	12.1416i	0.0220384	+	1.80996i
$46$	2.92952	−	5.07408i	0.431935	−	0.748133i
$47$	0.447025	−	0.162704i	0.0652054	−	0.0237328i	−0.309212	−	0.950993i	$-0.600065\pi$
$47$	0.447025	−	0.162704i	0.0652054	−	0.0237328i	0.374417	+	0.927260i	$0.377843\pi$
$48$	1.67573	+	0.438094i	0.241871	+	0.0632335i
$49$	−5.34423	+	4.48434i	−0.763462	+	0.640620i
$50$	−10.6958	−	3.89296i	−1.51262	−	0.550548i
$51$	−7.92935	−	5.48056i	−1.11033	−	0.767432i
$52$	0.103202	−	0.585289i	0.0143116	−	0.0811650i
$53$	3.29955			0.453228			0.226614	−	0.973985i	$-0.427234\pi$
$53$	3.29955			0.453228			0.226614	+	0.973985i	$0.427234\pi$
$54$	−4.74863	−	2.10962i	−0.646207	−	0.287083i
$55$	−0.894051			−0.120554
$56$	−0.0266776	+	0.151296i	−0.00356494	+	0.0202178i
$57$	−0.536639	+	6.59606i	−0.0710795	+	0.873669i
$58$	−0.702841	−	0.255813i	−0.0922876	−	0.0335899i
$59$	5.57221	−	4.67564i	0.725440	−	0.608716i	−0.203444	−	0.979086i	$-0.565214\pi$
$59$	5.57221	−	4.67564i	0.725440	−	0.608716i	0.928884	+	0.370370i	$0.120769\pi$
$60$	4.92689	−	4.98724i	0.636058	−	0.643850i
$61$	−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
$63$	0.152349	−	0.434982i	0.0191942	−	0.0548026i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.84272	−	1.54623i	−0.228561	−	0.191786i
$66$	0.159577	−	0.347724i	0.0196425	−	0.0428019i
$67$	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
$69$	10.1040	−	0.945999i	1.21638	−	0.113885i
$70$	0.476340	+	0.399697i	0.0569335	+	0.0477729i
$71$	−1.42889	−	2.47490i	−0.169578	−	0.293717i	0.768694	−	0.639617i	$-0.220907\pi$
$71$	−1.42889	−	2.47490i	−0.169578	−	0.293717i	−0.938271	+	0.345900i	$0.887574\pi$
$72$	1.06031	+	2.80638i	0.124958	+	0.330735i
$73$	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
$75$	−5.21836	−	19.0115i	−0.602564	−	2.19526i
$76$	2.92692	−	2.45598i	0.335740	−	0.281720i
$77$	0.0318887	+	0.0116066i	0.00363406	+	0.00132269i
$78$	0.930277	−	0.440710i	0.105333	−	0.0499006i
$79$	−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
$81$	−1.77818	−	8.82259i	−0.197575	−	0.980288i
$82$	3.97445			0.438904
$83$	−1.43627	+	8.14551i	−0.157651	+	0.894085i	0.798670	+	0.601769i	$0.205537\pi$
$83$	−1.43627	+	8.14551i	−0.157651	+	0.894085i	−0.956322	+	0.292316i	$0.905574\pi$
$84$	−0.240475	+	0.113923i	−0.0262380	+	0.0124300i
$85$	21.1664	+	7.70392i	2.29581	+	0.835608i
$86$	7.81896	−	6.56088i	0.843140	−	0.707478i
$87$	−0.342907	−	1.24928i	−0.0367635	−	0.133937i
$88$	−0.207568	+	0.0755487i	−0.0221269	+	0.00805352i
$89$	2.47882	−	4.29345i	0.262755	−	0.455105i	−0.704218	−	0.709984i	$-0.748702\pi$
$89$	2.47882	−	4.29345i	0.262755	−	0.455105i	0.966973	+	0.254879i	$0.0820356\pi$
$90$	11.9828	+	1.96277i	1.26310	+	0.206895i
$91$	0.0456525	+	0.0790725i	0.00478569	+	0.00828905i
$92$	−4.48829	−	3.76612i	−0.467936	−	0.392645i
$93$	−8.76671	+	0.820795i	−0.909065	+	0.0851125i
$94$	−0.0826070	−	0.468487i	−0.00852026	−	0.0483208i
$95$	−2.68543	−	15.2298i	−0.275519	−	1.56255i
$96$	0.722426	−	1.57420i	0.0737323	−	0.160666i
$97$	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
$99$	0.651152	−	0.123008i	0.0654433	−	0.0123628i
$100$	−5.69113	+	9.85733i	−0.569113	+	0.985733i
$101$	−14.8467	+	5.40376i	−1.47730	+	0.537694i	−0.950072	−	0.312029i	$-0.898991\pi$
$101$	−14.8467	+	5.40376i	−1.47730	+	0.537694i	−0.527229	+	0.849723i	$0.676769\pi$
$102$	−6.77421	+	6.85720i	−0.670747	+	0.678964i
$103$	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
$105$	−0.0873351	+	1.07347i	−0.00852303	+	0.104760i
$106$	0.572961	−	3.24943i	0.0556509	−	0.315612i
$107$	1.85236			0.179075			0.0895374	−	0.995983i	$-0.471461\pi$
$107$	1.85236			0.179075			0.0895374	+	0.995983i	$0.471461\pi$
$108$	−2.90216	+	4.31016i	−0.279261	+	0.414745i
$109$	−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
$111$	−5.33995	−	3.69083i	−0.506846	−	0.350318i
$112$	0.144365	+	0.0525446i	0.0136412	+	0.00496500i
$113$	−10.2514	+	8.60195i	−0.964371	+	0.809204i	−0.981659	−	0.190647i	$-0.938941\pi$
$113$	−10.2514	+	8.60195i	−0.964371	+	0.809204i	0.0172875	+	0.999851i	$0.494497\pi$
$114$	6.40266	+	1.67388i	0.599664	+	0.156773i
$115$	−22.2843	+	8.11083i	−2.07802	+	0.756339i
$116$	−0.373974	+	0.647742i	−0.0347226	+	0.0601413i
$117$	1.55482	+	0.872611i	0.143743	+	0.0806729i
$118$	−3.63700	−	6.29947i	−0.334813	−	0.579913i
$119$	−0.654943	−	0.549562i	−0.0600385	−	0.0503783i
$120$	−4.05593	−	5.71806i	−0.370254	−	0.521985i
$121$	−1.90166	−	10.7848i	−0.172878	−	0.980439i
$122$	0.585154	+	3.31857i	0.0529773	+	0.300449i
$123$	3.98273	+	5.61486i	0.359110	+	0.506275i
$124$	3.89426	+	3.26767i	0.349715	+	0.293446i
$125$	12.9161	+	22.3713i	1.15525	+	2.00095i
$126$	−0.401919	−	0.225568i	−0.0358058	−	0.0200952i
$127$	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
$129$	17.1041	+	4.47160i	1.50593	+	0.393702i
$130$	−1.84272	+	1.54623i	−0.161617	+	0.135613i
$131$	6.45330	+	2.34881i	0.563828	+	0.205217i	0.608180	−	0.793799i	$-0.291900\pi$
$131$	6.45330	+	2.34881i	0.563828	+	0.205217i	−0.0443519	+	0.999016i	$0.514122\pi$
$132$	−0.314731	−	0.217534i	−0.0273938	−	0.0189339i
$133$	−0.101930	+	0.578075i	−0.00883847	+	0.0501254i
$134$	7.45812			0.644283
$135$	9.23488	+	18.8954i	0.794812	+	1.62626i
$136$	5.56510			0.477204
$137$	2.60219	−	14.7577i	0.222320	−	1.26084i	−0.645423	−	0.763826i	$-0.723319\pi$
$137$	2.60219	−	14.7577i	0.222320	−	1.26084i	0.867743	−	0.497014i	$-0.165570\pi$
$138$	0.822910	−	10.1147i	0.0700508	−	0.861024i
$139$	−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
$141$	0.579071	−	0.586165i	0.0487666	−	0.0493640i
$142$	−2.68543	+	0.977416i	−0.225356	+	0.0820229i
$143$	−0.0656393	+	0.113691i	−0.00548904	+	0.00950729i
$144$	2.94786	−	0.556877i	0.245655	−	0.0464064i
$145$	1.51366	+	2.62174i	0.125703	+	0.217723i
$146$	−0.978886	−	0.821383i	−0.0810132	−	0.0679781i
$147$	−5.03993	+	10.9822i	−0.415687	+	0.905799i
$148$	0.650793	+	3.69083i	0.0534949	+	0.303384i
$149$	−2.60884	−	14.7955i	−0.213725	−	1.21209i	−0.883106	−	0.469174i	$-0.844552\pi$
$149$	−2.60884	−	14.7955i	−0.213725	−	1.21209i	0.669381	−	0.742919i	$-0.266559\pi$
$150$	−19.6288	+	1.83777i	−1.60269	+	0.150054i
$151$	−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
$153$	−16.4758	−	2.69871i	−1.33199	−	0.218178i
$154$	0.0169676	−	0.0293888i	0.00136729	−	0.00236822i
$155$	19.3350	−	7.03736i	1.55302	−	0.565254i
$156$	−0.272474	−	0.992673i	−0.0218153	−	0.0794774i
$157$	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
$159$	5.16474	−	2.44675i	0.409591	−	0.194040i
$160$	−0.702841	+	3.98601i	−0.0555645	+	0.315122i
$161$	0.900125			0.0709398
$162$	−8.99733	+	0.219138i	−0.706897	+	0.0172171i
$163$	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
$165$	−1.39945	+	0.662974i	−0.108947	+	0.0516124i
$166$	7.77235	+	2.82890i	0.603251	+	0.219566i
$167$	−10.5889	+	8.88510i	−0.819390	+	0.687550i	−0.952829	−	0.303507i	$-0.901842\pi$
$167$	−10.5889	+	8.88510i	−0.819390	+	0.687550i	0.133439	+	0.991057i	$0.457398\pi$
$168$	0.0704339	+	0.256604i	0.00543409	+	0.0197974i
$169$	11.8841	−	4.32546i	0.914161	−	0.332727i
$170$	11.2624	−	19.5070i	0.863785	−	1.49612i
$171$	4.05124	+	10.7227i	0.309806	+	0.819982i
$172$	−5.10346	−	8.83945i	−0.389135	−	0.674002i
$173$	−3.00999	−	2.52568i	−0.228845	−	0.192024i	0.521154	−	0.853463i	$-0.325502\pi$
$173$	−3.00999	−	2.52568i	−0.228845	−	0.192024i	−0.749999	+	0.661439i	$0.769946\pi$
$174$	−1.28984	+	0.120763i	−0.0977827	+	0.00915504i
$175$	−0.303651	−	1.72209i	−0.0229539	−	0.130178i
$176$	0.0383571	+	0.217534i	0.00289127	+	0.0163972i
$177$	5.25493	−	11.4507i	0.394985	−	0.860689i
$178$	−3.79778	−	3.18671i	−0.284656	−	0.238854i
$179$	−1.42211	−	2.46317i	−0.106294	−	0.184106i	0.807972	−	0.589220i	$-0.200565\pi$
$179$	−1.42211	−	2.46317i	−0.106294	−	0.184106i	−0.914266	+	0.405115i	$0.867232\pi$
$180$	4.01375	−	11.4599i	0.299167	−	0.854173i
$181$	−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
$183$	−4.10190	+	4.15215i	−0.303221	+	0.306936i
$184$	−4.48829	+	3.76612i	−0.330881	+	0.277642i
$185$	14.2543	+	5.18813i	1.04800	+	0.381439i
$186$	−0.713998	+	8.77605i	−0.0523528	+	0.643491i
$187$	0.213461	−	1.21060i	0.0156098	−	0.0885277i
$188$	−0.475715			−0.0346951
$189$	−0.0840866	−	0.793844i	−0.00611640	−	0.0577437i
$190$	−15.4648			−1.12193
$191$	−3.49774	+	19.8367i	−0.253088	+	1.43533i	0.547846	+	0.836579i	$0.315448\pi$
$191$	−3.49774	+	19.8367i	−0.253088	+	1.43533i	−0.800934	+	0.598753i	$0.795663\pi$
$192$	−1.42483	−	0.984808i	−0.102829	−	0.0710724i
$193$	−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
$195$	−4.03097	−	1.05384i	−0.288664	−	0.0754668i
$196$	6.55567	−	2.38607i	0.468262	−	0.170433i
$197$	−3.77527	+	6.53895i	−0.268977	+	0.465881i	−0.968598	−	0.248633i	$-0.920019\pi$
$197$	−3.77527	+	6.53895i	−0.268977	+	0.465881i	0.699621	+	0.714514i	$0.253352\pi$
$198$	−0.00806817	−	0.662620i	−0.000573380	−	0.0470903i
$199$	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
$201$	7.47365	+	10.5364i	0.527151	+	0.743178i
$202$	2.74356	+	15.5595i	0.193036	+	1.09476i
$203$	−0.0199534	−	0.113162i	−0.00140046	−	0.00794238i
$204$	5.57669	+	7.86204i	0.390447	+	0.550453i
$205$	−12.3230	−	10.3403i	−0.860678	−	0.722195i
$206$	−5.34842	−	9.26374i	−0.372642	−	0.645435i
$207$	15.1141	−	8.97325i	1.05050	−	0.623684i
$208$	−0.297159	+	0.514694i	−0.0206043	+	0.0356876i
$209$	−0.793081	+	0.288658i	−0.0548586	+	0.0199669i
$210$	1.04200	+	0.272415i	0.0719048	+	0.0187984i
$211$	−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
$213$	−4.07185	−	2.81436i	−0.278999	−	0.192837i
$214$	0.321660	−	1.82422i	0.0219882	−	0.124701i
$215$	−41.3125			−2.81749
$216$	3.74072	+	3.60652i	0.254524	+	0.245393i
$217$	−0.780993			−0.0530173
$218$	−2.52649	+	14.3284i	−0.171115	+	0.970443i
$219$	0.179475	−	2.20600i	0.0121278	−	0.149068i
$220$	0.840133	+	0.305783i	0.0566418	+	0.0206159i
$221$	2.53365	−	2.12598i	0.170432	−	0.143009i
$222$	−4.56203	+	4.61792i	−0.306183	+	0.309934i
$223$	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
$225$	−22.2660	−	25.8888i	−1.48440	−	1.72592i
$226$	6.69113	+	11.5894i	0.445087	+	0.770914i
$227$	10.9999	+	9.22998i	0.730086	+	0.612615i	0.930155	−	0.367167i	$-0.119672\pi$
$227$	10.9999	+	9.22998i	0.730086	+	0.612615i	−0.200069	+	0.979782i	$0.564117\pi$
$228$	2.76026	−	6.01473i	0.182803	−	0.398335i
$229$	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
$231$	0.0585217	−	0.00547918i	0.00385045	−	0.000360503i
$232$	0.572961	+	0.480772i	0.0376168	+	0.0315642i
$233$	−8.48936	−	14.7040i	−0.556157	−	0.963292i	−0.997813	−	0.0661072i	$-0.978942\pi$
$233$	−8.48936	−	14.7040i	−0.556157	−	0.963292i	0.441656	−	0.897185i	$-0.354391\pi$
$234$	1.12935	−	1.37967i	0.0738277	−	0.0901921i
$235$	−0.962728	+	1.66749i	−0.0628014	+	0.108775i
$236$	−6.83533	+	2.48786i	−0.444942	+	0.161946i
$237$	1.51618	+	5.52372i	0.0984864	+	0.358804i
$238$	−0.654943	+	0.549562i	−0.0424536	+	0.0356228i
$239$	−20.0419	−	7.29464i	−1.29640	−	0.471851i	−0.400577	−	0.916263i	$-0.631190\pi$
$239$	−20.0419	−	7.29464i	−1.29640	−	0.471851i	−0.895823	+	0.444412i	$0.853413\pi$
$240$	−6.33550	+	3.00138i	−0.408954	+	0.193738i
$241$	−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
$243$	−9.32565	−	12.4913i	−0.598241	−	0.801316i
$244$	3.36977			0.215727
$245$	4.90330	−	27.8080i	0.313260	−	1.77659i
$246$	6.22115	−	2.94721i	0.396646	−	0.187907i
$247$	−2.13384	−	0.776653i	−0.135773	−	0.0494172i
$248$	3.89426	−	3.26767i	0.247286	−	0.207497i
$249$	3.79203	+	13.8151i	0.240310	+	0.875496i
$250$	24.2743	−	8.83513i	1.53524	−	0.558783i
$251$	−2.08811	+	3.61672i	−0.131801	+	0.228285i	−0.924371	−	0.381495i	$-0.875409\pi$
$251$	−2.08811	+	3.61672i	−0.131801	+	0.228285i	0.792570	+	0.609781i	$0.208743\pi$
$252$	−0.291934	+	0.356643i	−0.0183901	+	0.0224664i
$253$	0.647101	+	1.12081i	0.0406829	+	0.0704649i
$254$	−14.2721	−	11.9757i	−0.895511	−	0.751423i
$255$	38.8442	−	3.63684i	2.43252	−	0.227748i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.83797	+	16.0949i	0.177028	+	1.00397i	0.935777	+	0.352592i	$0.114699\pi$
$257$	2.83797	+	16.0949i	0.177028	+	1.00397i	−0.758750	+	0.651382i	$0.774189\pi$
$258$	7.37375	−	16.0677i	0.459070	−	1.00033i
$259$	−0.441065	−	0.370098i	−0.0274065	−	0.0229967i
$260$	1.20275	+	2.08323i	0.0745914	+	0.129196i
$261$	−1.46314	−	1.70120i	−0.0905658	−	0.105301i
$262$	3.43373	−	5.94740i	0.212137	−	0.367431i
$263$	2.51963	−	0.917071i	0.155367	−	0.0565490i	−0.263166	−	0.964751i	$-0.584767\pi$
$263$	2.51963	−	0.917071i	0.155367	−	0.0565490i	0.418533	+	0.908202i	$0.362544\pi$
$264$	−0.268882	+	0.272175i	−0.0165485	+	0.0167512i
$265$	−10.2305	+	8.58439i	−0.628453	+	0.527335i
$266$	0.551593	+	0.200763i	0.0338203	+	0.0123096i
$267$	0.696308	−	8.55862i	0.0426133	−	0.523779i
$268$	1.29509	−	7.34481i	0.0791101	−	0.448656i
$269$	22.3509			1.36276			0.681380	−	0.731930i	$-0.261380\pi$
$269$	22.3509			1.36276			0.681380	+	0.731930i	$0.261380\pi$
$270$	20.2120	−	5.81342i	1.23006	−	0.353794i
$271$	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
$273$	0.130095	+	0.0899179i	0.00787369	+	0.00544208i
$274$	−14.0817	−	5.12531i	−0.850705	−	0.309631i
$275$	1.92601	−	1.61611i	0.116143	−	0.0974552i
$276$	−9.81818	−	2.56682i	−0.590985	−	0.154504i
$277$	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
$279$	−13.1138	+	7.78564i	−0.785100	+	0.466114i
$280$	−0.310909	−	0.538510i	−0.0185804	−	0.0321821i
$281$	16.2374	+	13.6248i	0.968642	+	0.812787i	0.982337	−	0.187119i	$-0.0599151\pi$
$281$	16.2374	+	13.6248i	0.968642	+	0.812787i	−0.0136956	+	0.999906i	$0.504360\pi$
$282$	−0.476705	−	0.672060i	−0.0283874	−	0.0400206i
$283$	−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
$285$	−15.4970	−	21.8477i	−0.917961	−	1.29414i
$286$	0.100565	+	0.0843843i	0.00594655	+	0.00498975i
$287$	0.305297	+	0.528791i	0.0180211	+	0.0312135i
$288$	−0.0365258	−	2.99978i	−0.00215230	−	0.176764i
$289$	−6.98519	+	12.0987i	−0.410894	+	0.711689i
$290$	2.84475	−	1.03540i	0.167049	−	0.0608010i
$291$	9.47470	+	2.47702i	0.555417	+	0.145205i
$292$	−0.978886	+	0.821383i	−0.0572850	+	0.0480678i
$293$	−20.1808	−	7.34522i	−1.17898	−	0.429112i	−0.323136	−	0.946352i	$-0.604737\pi$
$293$	−20.1808	−	7.34522i	−1.17898	−	0.429112i	−0.855840	+	0.517240i	$0.826959\pi$
$294$	9.94021	+	6.87041i	0.579725	+	0.400690i
$295$	−5.11247	+	28.9942i	−0.297659	+	1.68811i
$296$	3.74777			0.217835
$297$	0.928024	−	0.675398i	0.0538494	−	0.0391906i
$298$	−15.0237			−0.870301
$299$	−0.604666	+	3.42923i	−0.0349688	+	0.198318i
$300$	−1.59865	+	19.6497i	−0.0922982	+	1.13448i
$301$	1.47352	+	0.536318i	0.0849324	+	0.0309129i
$302$	−4.32258	+	3.62708i	−0.248737	+	0.208715i
$303$	−19.2322	+	19.4678i	−1.10486	+	1.11840i
$304$	−3.59040	+	1.30680i	−0.205923	+	0.0749500i
$305$	6.81956	−	11.8118i	0.390487	−	0.676343i
$306$	−5.51870	+	15.7568i	−0.315483	+	0.900758i
$307$	−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
$309$	7.72768	−	16.8390i	0.439613	−	0.957935i
$310$	−3.57296	−	20.2633i	−0.202931	−	1.15088i
$311$	1.61574	+	9.16334i	0.0916205	+	0.519605i	0.995731	+	0.0923061i	$0.0294238\pi$
$311$	1.61574	+	9.16334i	0.0916205	+	0.519605i	−0.904110	+	0.427299i	$0.859465\pi$
$312$	−1.02491	+	0.0959583i	−0.0580239	+	0.00543257i
$313$	−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
$315$	0.659318	+	1.74505i	0.0371484	+	0.0983227i
$316$	1.65354	−	2.86401i	0.0930189	−	0.161113i
$317$	26.2511	−	9.55461i	1.47441	−	0.536641i	0.525114	−	0.851032i	$-0.324023\pi$
$317$	26.2511	−	9.55461i	1.47441	−	0.536641i	0.949294	+	0.314391i	$0.101800\pi$
$318$	−1.51273	−	5.51115i	−0.0848295	−	0.309050i
$319$	0.126561	−	0.106197i	0.00708607	−	0.00594592i
$320$	3.80341	+	1.38433i	0.212617	+	0.0773862i
$321$	2.89948	−	1.37360i	0.161833	−	0.0766669i
$322$	0.156305	−	0.886450i	0.00871054	−	0.0494000i
$323$	21.2633			1.18312
$324$	−1.34656	+	8.89870i	−0.0748089	+	0.494372i
$325$	6.76468			0.375237
$326$	2.44980	−	13.8935i	0.135682	−	0.769491i
$327$	−22.7741	+	10.7890i	−1.25941	+	0.596633i
$328$	−3.73476	−	1.35934i	−0.206218	−	0.0750571i
$329$	0.0559856	−	0.0469775i	0.00308659	−	0.00258995i
$330$	0.409891	+	1.49331i	0.0225637	+	0.0822039i
$331$	−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
$333$	−11.0954	−	1.81742i	−0.608026	−	0.0995942i
$334$	6.91138	+	11.9709i	0.378174	+	0.655017i
$335$	−23.1244	−	19.4037i	−1.26342	−	1.06014i
$336$	0.264936	−	0.0248050i	0.0144535	−	0.00135323i
$337$	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
$339$	−9.66770	+	21.0663i	−0.525077	+	1.14417i
$340$	−17.2550	−	14.4786i	−0.935782	−	0.785214i
$341$	−0.561457	−	0.972472i	−0.0304046	−	0.0526623i
$342$	11.2632	−	2.12773i	0.609047	−	0.115054i
$343$	−1.07360	+	1.85953i	−0.0579688	+	0.100405i
$344$	−9.59137	+	3.49097i	−0.517132	+	0.188221i
$345$	−28.8668	+	29.2205i	−1.55414	+	1.57318i
$346$	−3.00999	+	2.52568i	−0.161818	+	0.135781i
$347$	18.9820	+	6.90888i	1.01901	+	0.370888i	0.796885	−	0.604131i	$-0.206480\pi$
$347$	18.9820	+	6.90888i	1.01901	+	0.370888i	0.222121	+	0.975019i	$0.428702\pi$
$348$	−0.105050	+	1.29122i	−0.00563128	+	0.0692165i
$349$	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
$351$	3.08082	+	0.212924i	0.164442	+	0.0113650i
$352$	0.220890			0.0117735
$353$	−1.70637	+	9.67729i	−0.0908208	+	0.515070i	0.905127	+	0.425141i	$0.139775\pi$
$353$	−1.70637	+	9.67729i	−0.0908208	+	0.515070i	−0.995948	+	0.0899297i	$0.971336\pi$
$354$	−10.3642	−	7.16349i	−0.550854	−	0.380735i
$355$	10.8693	+	3.95609i	0.576881	+	0.209968i
$356$	−3.79778	+	3.18671i	−0.201282	+	0.168896i
$357$	−1.43269	−	0.374556i	−0.0758262	−	0.0198236i
$358$	−2.67269	+	0.972781i	−0.141256	+	0.0514131i
$359$	−5.94469	+	10.2965i	−0.313749	+	0.543429i	−0.979171	−	0.203039i	$-0.934918\pi$
$359$	−5.94469	+	10.2965i	−0.313749	+	0.543429i	0.665422	+	0.746467i	$0.268252\pi$
$360$	−10.5889	−	5.94277i	−0.558082	−	0.313211i
$361$	2.20067	+	3.81167i	0.115825	+	0.200614i
$362$	9.90149	+	8.30834i	0.520411	+	0.436676i
$363$	−10.9740	−	15.4712i	−0.575986	−	0.812027i
$364$	−0.0158550	−	0.0899179i	−0.000831026	−	0.00471298i
$365$	0.898122	+	5.09350i	0.0470098	+	0.266606i
$366$	3.37678	+	4.76060i	0.176507	+	0.248840i
$367$	−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
$369$	10.3977	+	5.83551i	0.541285	+	0.303785i
$370$	7.58455	−	13.1368i	0.394302	−	0.682951i
$371$	0.476340	−	0.173374i	0.0247303	−	0.00900111i
$372$	8.51874	+	2.22710i	0.441676	+	0.115470i
$373$	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
$375$	36.8066	+	25.4398i	1.90069	+	1.31370i
$376$	−0.0826070	+	0.468487i	−0.00426013	+	0.0241604i
$377$	0.444519			0.0228939
$378$	−0.796385	−	0.0550405i	−0.0409616	−	0.00283098i
$379$	−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
$381$	2.61673	−	32.1634i	0.134059	−	1.64778i
$382$	18.9279	+	6.88921i	0.968438	+	0.352483i
$383$	18.9404	−	15.8929i	0.967811	−	0.812090i	−0.0143953	−	0.999896i	$-0.504582\pi$
$383$	18.9404	−	15.8929i	0.967811	−	0.812090i	0.982206	+	0.187807i	$0.0601379\pi$
$384$	−1.21727	+	1.23218i	−0.0621184	+	0.0628793i
$385$	−0.129070	+	0.0469775i	−0.00657800	+	0.00239420i
$386$	−4.80832	+	8.32826i	−0.244737	+	0.423897i
$387$	30.0886	−	5.68400i	1.52949	−	0.288934i
$388$	−2.82704	−	4.89657i	−0.143521	−	0.248586i
$389$	11.1425	+	9.34969i	0.564948	+	0.474048i	0.879965	−	0.475038i	$-0.157566\pi$
$389$	11.1425	+	9.34969i	0.564948	+	0.474048i	−0.315017	+	0.949086i	$0.602010\pi$
$390$	−1.73780	+	3.78674i	−0.0879968	+	0.191749i
$391$	−5.66201	−	32.1108i	−0.286340	−	1.62391i
$392$	−1.21144	−	6.87041i	−0.0611869	−	0.347008i
$393$	11.8430	−	1.10882i	0.597400	−	0.0559324i
$394$	5.78404	+	4.85339i	0.291396	+	0.244510i
$395$	−6.69270	−	11.5921i	−0.336746	−	0.583262i
$396$	−0.653954	−	0.107117i	−0.0328624	−	0.00538284i
$397$	−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
$399$	0.269115	+	0.980438i	0.0134726	+	0.0490833i
$400$	8.71932	−	7.31638i	0.435966	−	0.365819i
$401$	15.2143	+	5.53755i	0.759765	+	0.276532i	0.692709	−	0.721217i	$-0.256417\pi$
$401$	15.2143	+	5.53755i	0.759765	+	0.276532i	0.0670561	+	0.997749i	$0.478639\pi$
$402$	11.6741	−	5.53049i	0.582250	−	0.275836i
$403$	0.524638	−	2.97537i	0.0261341	−	0.148214i
$404$	15.7995			0.786056
$405$	28.4669	+	22.7288i	1.41453	+	1.12940i
$406$	−0.114907			−0.00570275
$407$	0.143753	−	0.815266i	0.00712559	−	0.0404112i
$408$	8.71098	−	4.12674i	0.431258	−	0.204304i
$409$	−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
$411$	−6.87028	−	25.0297i	−0.338886	−	1.23463i
$412$	−10.0517	+	3.65854i	−0.495214	+	0.180243i
$413$	0.558753	−	0.967788i	0.0274944	−	0.0476217i
$414$	−6.21239	−	16.4427i	−0.305322	−	0.808114i
$415$	−16.7388	−	28.9924i	−0.821674	−	1.42318i
$416$	0.455274	+	0.382020i	0.0223216	+	0.0187301i
$417$	−31.2183	+	2.92286i	−1.52877	+	0.143133i
$418$	0.146555	+	0.831157i	0.00716826	+	0.0406532i
$419$	−5.98994	−	33.9707i	−0.292628	−	1.65957i	−0.676690	−	0.736268i	$-0.736586\pi$
$419$	−5.98994	−	33.9707i	−0.292628	−	1.65957i	0.384062	−	0.923307i	$-0.374525\pi$
$420$	0.449217	−	0.978864i	0.0219196	−	0.0477637i
$421$	−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
$423$	0.471748	−	1.34692i	0.0229372	−	0.0654895i
$424$	−1.64978	+	2.85750i	−0.0801202	+	0.138772i
$425$	−59.5234	+	21.6647i	−2.88731	+	1.05089i
$426$	−3.47867	+	3.52129i	−0.168542	+	0.170607i
$427$	−0.396579	+	0.332769i	−0.0191918	+	0.0161038i
$428$	−1.74065	−	0.633546i	−0.0841376	−	0.0306236i
$429$	−0.0184382	+	0.226632i	−0.000890207	+	0.0109419i
$430$	−7.17384	+	40.6849i	−0.345954	+	1.96200i
$431$	24.6371			1.18673			0.593364	−	0.804934i	$-0.297799\pi$
$431$	24.6371			1.18673			0.593364	+	0.804934i	$0.297799\pi$
$432$	4.20130	−	3.05763i	0.202135	−	0.147110i
$433$	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
$435$	4.31343	+	2.98133i	0.206813	+	0.142944i
$436$	13.6720	+	4.97621i	0.654771	+	0.238317i
$437$	−17.1489	+	14.3897i	−0.820345	+	0.688351i
$438$	−2.14132	−	0.559817i	−0.102316	−	0.0267491i
$439$	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
$441$	0.254818	+	20.9276i	0.0121342	+	0.996554i
$442$	−1.65372	−	2.86433i	−0.0786595	−	0.136242i
$443$	−29.5753	−	24.8166i	−1.40516	−	1.17907i	−0.958752	−	0.284245i	$-0.908257\pi$
$443$	−29.5753	−	24.8166i	−1.40516	−	1.17907i	−0.446412	−	0.894828i	$-0.647298\pi$
$444$	3.75557	+	5.29462i	0.178232	+	0.251271i
$445$	3.48444	+	19.7612i	0.165178	+	0.936772i
$446$	−4.43236	−	25.1372i	−0.209878	−	1.19028i
$447$	−15.0550	−	21.2246i	−0.712077	−	1.00389i
$448$	−0.117687	−	0.0987515i	−0.00556021	−	0.00466557i
$449$	7.76357	+	13.4469i	0.366385	+	0.634598i	0.988997	−	0.147932i	$-0.0472618\pi$
$449$	7.76357	+	13.4469i	0.366385	+	0.634598i	−0.622612	+	0.782531i	$0.713928\pi$
$450$	−29.3619	+	17.4322i	−1.38413	+	0.821760i
$451$	−0.438957	+	0.760296i	−0.0206697	+	0.0358010i
$452$	12.5752	−	4.57700i	0.591488	−	0.215284i
$453$	−9.45569	−	2.47205i	−0.444267	−	0.116147i
$454$	10.9999	−	9.22998i	0.516249	−	0.433184i
$455$	−0.347270	−	0.126396i	−0.0162803	−	0.00592554i
$456$	−5.44404	−	3.76277i	−0.254940	−	0.176208i
$457$	−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
$459$	−27.7905	+	7.99316i	−1.29715	+	0.373089i
$460$	23.7145			1.10569
$461$	1.72646	−	9.79122i	0.0804091	−	0.456023i	−0.917844	−	0.396941i	$-0.870072\pi$
$461$	1.72646	−	9.79122i	0.0804091	−	0.456023i	0.998253	−	0.0590816i	$-0.0188172\pi$
$462$	0.00476625	−	0.0585841i	0.000221746	−	0.00272558i
$463$	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
$465$	25.0463	−	25.3531i	1.16149	−	1.17572i
$466$	−15.9548	+	5.80707i	−0.739091	+	0.269007i
$467$	−15.7918	+	27.3521i	−0.730756	+	1.26571i	0.225805	+	0.974173i	$0.427499\pi$
$467$	−15.7918	+	27.3521i	−0.730756	+	1.26571i	−0.956561	+	0.291534i	$0.905835\pi$
$468$	−1.16260	−	1.35177i	−0.0537414	−	0.0624854i
$469$	0.572895	+	0.992284i	0.0264539	+	0.0458194i
$470$	1.47498	+	1.23766i	0.0680359	+	0.0570889i
$471$	5.23378	−	11.4046i	0.241160	−	0.525498i
$472$	1.26312	+	7.16349i	0.0581397	+	0.329727i
$473$	0.391508	+	2.22035i	0.0180015	+	0.102092i
$474$	5.70309	−	0.533960i	0.261952	−	0.0245256i
$475$	33.3149	+	27.9545i	1.52859	+	1.28264i
$476$	0.427484	+	0.740423i	0.0195937	+	0.0339372i
$477$	6.26994	−	7.65972i	0.287081	−	0.350714i
$478$	−10.6640	+	18.4707i	−0.487762	+	0.844829i
$479$	−10.6027	+	3.85905i	−0.484448	+	0.176325i	−0.572686	−	0.819775i	$-0.694099\pi$
$479$	−10.6027	+	3.85905i	−0.484448	+	0.176325i	0.0882381	+	0.996099i	$0.471876\pi$
$480$	1.85563	+	6.76043i	0.0846978	+	0.308570i
$481$	1.70626	−	1.43172i	0.0777988	−	0.0652809i
$482$	10.1057	+	3.67817i	0.460301	+	0.167536i
$483$	1.40895	−	0.667478i	0.0641096	−	0.0303713i
$484$	−1.90166	+	10.7848i	−0.0864390	+	0.490220i
$485$	−22.8849			−1.03915
$486$	−13.9209	+	7.01489i	−0.631465	+	0.318202i
$487$	−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
$489$	22.0828	−	10.4615i	0.998620	−	0.473087i
$490$	−26.5341	−	9.65761i	−1.19869	−	0.436287i
$491$	−7.76464	+	6.51531i	−0.350413	+	0.294032i	−0.800956	−	0.598723i	$-0.795675\pi$
$491$	−7.76464	+	6.51531i	−0.350413	+	0.294032i	0.450543	+	0.892755i	$0.351231\pi$
$492$	−1.82214	−	6.63841i	−0.0821486	−	0.299283i
$493$	−3.91138	+	1.42363i	−0.176160	+	0.0641169i
$494$	−1.13539	+	1.96655i	−0.0510836	+	0.0884794i
$495$	−1.69891	+	2.07549i	−0.0763604	+	0.0932862i
$496$	−2.54180	−	4.40252i	−0.114130	−	0.197679i
$497$	−0.336324	−	0.282209i	−0.0150862	−	0.0126588i
$498$	14.2637	−	1.33546i	0.639171	−	0.0598433i
$499$	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
$501$	−9.98593	+	21.7598i	−0.446139	+	0.972155i
$502$	3.19918	+	2.68443i	0.142786	+	0.119812i
$503$	7.31535	+	12.6706i	0.326175	+	0.564952i	0.981750	−	0.190179i	$-0.0609067\pi$
$503$	7.31535	+	12.6706i	0.326175	+	0.564952i	−0.655574	+	0.755131i	$0.727573\pi$
$504$	0.300531	+	0.349429i	0.0133867	+	0.0155648i
$505$	31.9743	−	55.3811i	1.42284	−	2.46443i
$506$	1.21615	−	0.442643i	0.0540646	−	0.0196779i
$507$	15.3945	−	15.5831i	0.683694	−	0.692069i
$508$	−14.2721	+	11.9757i	−0.633222	+	0.531336i
$509$	−6.70321	−	2.43977i	−0.297115	−	0.108141i	0.189162	−	0.981946i	$-0.439423\pi$
$509$	−6.70321	−	2.43977i	−0.297115	−	0.108141i	−0.486276	+	0.873805i	$0.661645\pi$
$510$	3.16363	−	38.8856i	0.140088	−	1.72188i
$511$	0.0340898	−	0.193333i	0.00150804	−	0.00855254i
$512$	1.00000			0.0441942
$513$	14.2926	+	13.7799i	0.631035	+	0.608396i
$514$	16.3432			0.720868
$515$	−7.51818	+	42.6377i	−0.331291	+	1.87884i
$516$	−14.5432	−	10.0519i	−0.640228	−	0.442508i
$517$	0.0987433	+	0.0359396i	0.00434273	+	0.00158062i
$518$	−0.441065	+	0.370098i	−0.0193793	+	0.0162612i
$519$	−6.58438	−	1.72139i	−0.289022	−	0.0755605i
$520$	2.26043	−	0.822730i	0.0991265	−	0.0360791i
$521$	4.12053	−	7.13696i	0.180524	−	0.312676i	−0.761535	−	0.648123i	$-0.775554\pi$
$521$	4.12053	−	7.13696i	0.180524	−	0.312676i	0.942059	+	0.335447i	$0.108887\pi$
$522$	−1.92942	+	1.14550i	−0.0844485	+	0.0501371i
$523$	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
$525$	−1.75230	−	2.47040i	−0.0764766	−	0.107817i
$526$	−0.465609	−	2.64060i	−0.0203015	−	0.115136i
$527$	4.91264	+	27.8610i	0.213998	+	1.21364i
$528$	0.221350	+	0.312059i	0.00963301	+	0.0135806i
$529$	8.67807	+	7.28176i	0.377307	+	0.316598i
$530$	6.67747	+	11.5657i	0.290051	+	0.502383i
$531$	−0.265689	−	21.8204i	−0.0115299	−	0.946924i
$532$	0.293496	−	0.508350i	0.0127247	−	0.0220398i
$533$	−2.21963	+	0.807881i	−0.0961430	+	0.0349932i
$534$	−8.30768	−	2.17192i	−0.359509	−	0.0939881i
$535$	−5.74337	+	4.81926i	−0.248308	+	0.208355i
$536$	−7.00834	−	2.55083i	−0.302714	−	0.110179i
$537$	−4.05254	−	2.80101i	−0.174880	−	0.120873i
$538$	3.88120	−	22.0114i	0.167330	−	0.948977i
$539$	−1.54101			−0.0663762
$540$	−2.21533	−	20.9144i	−0.0953324	−	0.900014i
$541$	−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
$543$	−1.81540	+	22.3139i	−0.0779062	+	0.957579i
$544$	−5.22949	−	1.90338i	−0.224212	−	0.0816066i
$545$	45.1115	−	37.8531i	1.93237	−	1.62145i
$546$	0.111143	−	0.112504i	0.00475646	−	0.00481473i
$547$	−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
$549$	−3.34167	+	9.54102i	−0.142619	+	0.407201i
$550$	−1.25711	−	2.17738i	−0.0536034	−	0.0928439i
$551$	2.18918	+	1.83694i	0.0932623	+	0.0782563i
$552$	−4.23273	+	9.22330i	−0.180157	+	0.392570i
$553$	0.0882249	+	0.500348i	0.00375170	+	0.0212770i
$554$	−0.445758	−	2.52802i	−0.0189385	−	0.107405i
$555$	26.1592	−	2.44919i	1.11040	−	0.103963i
$556$	13.8675	+	11.6362i	0.588113	+	0.493486i
$557$	−16.4210	−	28.4420i	−0.695779	−	1.20512i	−0.969917	−	0.243434i	$-0.921726\pi$
$557$	−16.4210	−	28.4420i	−0.695779	−	1.20512i	0.274138	−	0.961690i	$-0.411607\pi$
$558$	5.39018	+	14.2665i	0.228184	+	0.603949i
$559$	−3.03308	+	5.25345i	−0.128286	+	0.222197i
$560$	−0.584317	+	0.212674i	−0.0246919	+	0.00898712i
$561$	−0.563578	−	2.05322i	−0.0237943	−	0.0866871i
$562$	16.2374	−	13.6248i	0.684933	−	0.574727i
$563$	−17.5885	−	6.40168i	−0.741266	−	0.269799i	−0.0563401	−	0.998412i	$-0.517943\pi$
$563$	−17.5885	−	6.40168i	−0.741266	−	0.269799i	−0.684926	+	0.728613i	$0.740165\pi$
$564$	−0.744629	+	0.352761i	−0.0313545	+	0.0148539i
$565$	9.40560	−	53.3418i	0.395697	−	2.24411i
$566$	−19.6332			−0.825246
$567$	−0.720286	−	1.18024i	−0.0302492	−	0.0495654i
$568$	2.85777			0.119910
$569$	−1.38771	+	7.87008i	−0.0581757	+	0.329931i	−0.999981	−	0.00622922i	$-0.998017\pi$
$569$	−1.38771	+	7.87008i	−0.0581757	+	0.329931i	0.941805	+	0.336160i	$0.109128\pi$
$570$	−24.2068	+	11.4677i	−1.01391	+	0.480330i
$571$	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
$573$	9.23471	+	33.6438i	0.385786	+	1.40549i
$574$	0.573771	−	0.208836i	0.0239488	−	0.00871663i
$575$	33.3446	−	57.7545i	1.39057	−	2.40853i
$576$	−2.96055	−	0.484935i	−0.123356	−	0.0202056i
$577$	−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
$579$	−16.5840	+	1.55270i	−0.689207	+	0.0645280i
$580$	−0.525688	−	2.98133i	−0.0218280	−	0.123793i
$581$	0.220655	+	1.25139i	0.00915429	+	0.0519166i
$582$	4.08465	−	8.90063i	0.169314	−	0.368943i
$583$	0.558322	+	0.468487i	0.0231233	+	0.0194028i
$584$	0.638922	+	1.10665i	0.0264388	+	0.0457933i
$585$	−7.09109	+	1.33957i	−0.293180	+	0.0553843i
$586$	−10.7380	+	18.5988i	−0.443582	+	0.768307i
$587$	16.5971	−	6.04086i	0.685036	−	0.249333i	0.0240279	−	0.999711i	$-0.492351\pi$
$587$	16.5971	−	6.04086i	0.685036	−	0.249333i	0.661008	+	0.750378i	$0.270129\pi$
$588$	8.49213	−	8.59616i	0.350210	−	0.354500i
$589$	14.8793	−	12.4852i	0.613090	−	0.514443i
$590$	27.6660	+	10.0696i	1.13899	+	0.414559i
$591$	−1.06048	+	13.0348i	−0.0436224	+	0.536182i
$592$	0.650793	−	3.69083i	0.0267474	−	0.151692i
$593$	4.89941			0.201195			0.100597	−	0.994927i	$-0.467925\pi$
$593$	4.89941			0.201195			0.100597	+	0.994927i	$0.467925\pi$
$594$	−0.503987	−	1.03121i	−0.0206789	−	0.0423109i
$595$	3.46048			0.141866
$596$	−2.60884	+	14.7955i	−0.106862	+	0.606046i
$597$	17.2995	+	11.9570i	0.708021	+	0.489366i
$598$	3.27214	+	1.19096i	0.133808	+	0.0487020i
$599$	13.8351	−	11.6090i	0.565288	−	0.474333i	−0.314791	−	0.949161i	$-0.601934\pi$
$599$	13.8351	−	11.6090i	0.565288	−	0.474333i	0.880078	+	0.474828i	$0.157490\pi$
$600$	19.0736	+	4.98651i	0.778677	+	0.203573i
$601$	−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
$603$	19.5115	+	10.9504i	0.794571	+	0.445936i
$604$	2.82136	+	4.88675i	0.114800	+	0.198839i
$605$	33.9549	+	28.4916i	1.38046	+	1.15835i
$606$	15.8324	+	22.3206i	0.643148	+	0.906713i
$607$	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
$609$	−0.115147	−	0.162334i	−0.00466597	−	0.00657810i
$610$	−10.4482	−	8.76706i	−0.423034	−	0.354968i
$611$	0.141363	+	0.244848i	0.00571893	+	0.00990547i
$612$	14.5591	+	8.17100i	0.588518	+	0.330293i
$613$	−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
$615$	−26.9568	−	7.04744i	−1.08700	−	0.284180i
$616$	−0.0259959	+	0.0218132i	−0.00104741	+	0.000878878i
$617$	−25.0923	−	9.13284i	−1.01018	−	0.367674i	−0.216676	−	0.976244i	$-0.569522\pi$
$617$	−25.0923	−	9.13284i	−1.01018	−	0.367674i	−0.793501	+	0.608569i	$0.791744\pi$
$618$	−15.2412	−	10.5343i	−0.613092	−	0.423753i
$619$	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
$621$	17.0039	−	25.2534i	0.682343	−	1.01338i
$622$	9.30470			0.373085
$623$	0.132258	−	0.750073i	0.00529881	−	0.0300510i
$624$	−0.0834727	+	1.02600i	−0.00334158	+	0.0410728i
$625$	−44.7712	−	16.2954i	−1.79085	−	0.651816i
$626$	−2.05976	+	1.72835i	−0.0823247	+	0.0690786i
$627$	−1.02735	+	1.03993i	−0.0410283	+	0.0415309i
$628$	−6.80782	+	2.47784i	−0.271661	+	0.0988767i
$629$	−10.4284	+	18.0624i	−0.415806	+	0.720197i
$630$	1.83303	−	0.346276i	0.0730298	−	0.0137960i
$631$	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
$633$	−5.21869	+	11.3718i	−0.207424	+	0.451987i
$634$	−4.85100	−	27.5114i	−0.192658	−	1.09262i
$635$	13.0946	+	74.2629i	0.519642	+	2.94703i
$636$	−5.69011	+	0.532744i	−0.225627	+	0.0211247i
$637$	−3.17617	−	2.66512i	−0.125845	−	0.105596i
$638$	−0.0826070	−	0.143079i	−0.00327044	−	0.00566457i
$639$	−8.46057	−	1.38583i	−0.334695	−	0.0548228i
$640$	2.02375	−	3.50524i	0.0799958	−	0.138557i
$641$	−17.0222	+	6.19556i	−0.672335	+	0.244710i	−0.655553	−	0.755149i	$-0.727564\pi$
$641$	−17.0222	+	6.19556i	−0.672335	+	0.244710i	−0.0167821	+	0.999859i	$0.505342\pi$
$642$	−0.849243	−	3.09395i	−0.0335169	−	0.122109i
$643$	−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
$645$	−64.6659	+	30.6349i	−2.54622	+	1.20625i
$646$	3.69233	−	20.9402i	0.145273	−	0.823882i
$647$	−11.1390			−0.437918			−0.218959	−	0.975734i	$-0.570266\pi$
$647$	−11.1390			−0.437918			−0.218959	+	0.975734i	$0.570266\pi$
$648$	8.52968	+	2.87135i	0.335077	+	0.112797i
$649$	1.60675			0.0630705
$650$	1.17467	−	6.66191i	0.0460745	−	0.261302i
$651$	−1.22248	+	0.579137i	−0.0479127	+	0.0226982i
$652$	−13.2570	−	4.82517i	−0.519186	−	0.188968i
$653$	1.15447	−	0.968718i	0.0451780	−	0.0379089i	−0.619919	−	0.784666i	$-0.712835\pi$
$653$	1.15447	−	0.968718i	0.0451780	−	0.0379089i	0.665097	+	0.746757i	$0.268390\pi$
$654$	6.67041	+	24.3016i	0.260834	+	0.950266i
$655$	−26.1197	+	9.50681i	−1.02058	+	0.371462i
$656$	−1.98722	+	3.44197i	−0.0775881	+	0.134386i
$657$	−1.35491	−	3.58611i	−0.0528600	−	0.139908i
$658$	−0.0365420	−	0.0632926i	−0.00142456	−	0.00246740i
$659$	−6.06158	−	5.08627i	−0.236126	−	0.198133i	0.517045	−	0.855958i	$-0.327032\pi$
$659$	−6.06158	−	5.08627i	−0.236126	−	0.198133i	−0.753171	+	0.657825i	$0.771477\pi$
$660$	1.54180	−	0.144353i	0.0600144	−	0.00561893i
$661$	−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
$663$	2.38938	−	5.20657i	0.0927959	−	0.202206i
$664$	−6.33608	−	5.31660i	−0.245888	−	0.206324i
$665$	−1.18793	−	2.05755i	−0.0460658	−	0.0797883i
$666$	−3.71652	+	10.6113i	−0.144012	+	0.411179i
$667$	2.19113	−	3.79515i	0.0848409	−	0.146949i
$668$	12.9892	−	4.72767i	0.502565	−	0.182919i
$669$	31.0707	−	31.4513i	1.20126	−	1.21598i
$670$	−23.1244	+	19.4037i	−0.893373	+	0.749629i
$671$	−0.699457	−	0.254581i	−0.0270022	−	0.00982801i
$672$	0.0215775	−	0.265219i	0.000832371	−	0.0102310i
$673$	−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
$675$	−54.0502	−	24.0122i	−2.08039	−	0.924232i
$676$	−12.6468			−0.486415
$677$	7.00672	−	39.7371i	0.269290	−	1.52722i	−0.487245	−	0.873266i	$-0.661998\pi$
$677$	7.00672	−	39.7371i	0.269290	−	1.52722i	0.756535	−	0.653954i	$-0.226891\pi$
$678$	19.0675	+	13.1790i	0.732283	+	0.506135i
$679$	0.816250	+	0.297091i	0.0313248	+	0.0114013i
$680$	−17.2550	+	14.4786i	−0.661698	+	0.555230i
$681$	24.0623	+	6.29073i	0.922070	+	0.241061i
$682$	−1.05519	+	0.384059i	−0.0404055	+	0.0147064i
$683$	12.5504	−	21.7380i	0.480229	−	0.831780i	−0.519514	−	0.854462i	$-0.673887\pi$
$683$	12.5504	−	21.7380i	0.480229	−	0.831780i	0.999743	+	0.0226815i	$0.00722037\pi$
$684$	−0.139558	−	11.4616i	−0.00533615	−	0.438246i
$685$	30.3267	+	52.5274i	1.15872	+	2.00697i
$686$	1.64485	+	1.38019i	0.0628005	+	0.0526959i
$687$	4.06754	+	5.73443i	0.155186	+	0.218782i
$688$	1.77241	+	10.0519i	0.0675726	+	0.383223i
$689$	0.340521	+	1.93119i	0.0129728	+	0.0735725i
$690$	23.7639	+	33.5024i	0.904675	+	1.27541i
$691$	−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
$693$	0.0875402	−	0.0519726i	0.00332538	−	0.00197428i
$694$	10.1001	−	17.4939i	0.383395	−	0.664059i
$695$	68.8521	−	25.0601i	2.61171	−	0.950584i
$696$	1.25336	+	0.327672i	0.0475085	+	0.0124204i
$697$	16.9435	−	14.2173i	0.641782	−	0.538519i
$698$	−9.02990	−	3.28661i	−0.341787	−	0.124400i
$699$	−24.1919	−	16.7208i	−0.915021	−	0.632438i
$700$	−0.303651	+	1.72209i	−0.0114769	+	0.0650889i
$701$	−24.5608			−0.927648			−0.463824	−	0.885927i	$-0.653523\pi$
$701$	−24.5608			−0.927648			−0.463824	+	0.885927i	$0.653523\pi$
$702$	0.744667	−	2.99704i	0.0281057	−	0.113116i
$703$	14.3195			0.540072
$704$	0.0383571	−	0.217534i	0.00144564	−	0.00819862i
$705$	−0.270433	+	3.32400i	−0.0101851	+	0.125189i
$706$	9.23396	+	3.36089i	0.347525	+	0.126489i
$707$	−1.85941	+	1.56023i	−0.0699302	+	0.0586784i
$708$	−8.85440	+	8.96287i	−0.332769	+	0.336845i
$709$	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
$711$	6.46931	+	7.52190i	0.242618	+	0.282093i
$712$	2.47882	+	4.29345i	0.0928979	+	0.160904i
$713$	−22.8167	−	19.1454i	−0.854490	−	0.717003i
$714$	−0.617651	+	1.34589i	−0.0231150	+	0.0503686i
$715$	−0.0922680	−	0.523278i	−0.00345063	−	0.0195695i
$716$	0.493894	+	2.80101i	0.0184577	+	0.104679i
$717$	−36.7805	+	3.44362i	−1.37359	+	0.128605i
$718$	9.10779	+	7.64235i	0.339900	+	0.285210i
$719$	18.3086	+	31.7114i	0.682796	+	1.18264i	0.974124	+	0.226014i	$0.0725695\pi$
$719$	18.3086	+	31.7114i	0.682796	+	1.18264i	−0.291328	+	0.956623i	$0.594097\pi$
$720$	−7.69122	+	9.39603i	−0.286635	+	0.350170i
$721$	0.821678	−	1.42319i	0.0306009	−	0.0530023i
$722$	4.13591	−	1.50535i	0.153923	−	0.0560232i
$723$	4.93043	+	17.9625i	0.183365	+	0.668033i
$724$	9.90149	−	8.30834i	0.367986	−	0.308777i
$725$	−7.99992	−	2.91173i	−0.297110	−	0.108139i
$726$	−17.1418	+	8.12075i	−0.636191	+	0.301389i
$727$	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
$729$	−23.8601	−	12.6371i	−0.883707	−	0.468040i
$730$	5.17208			0.191427
$731$	9.86367	−	55.9396i	0.364821	−	2.06900i
$732$	5.27465	−	2.49881i	0.194957	−	0.0923588i
$733$	−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
$735$	−12.9456	−	47.1634i	−0.477507	−	1.73965i
$736$	5.50570	−	2.00391i	0.202943	−	0.0738652i
$737$	−0.823710	+	1.42671i	−0.0303418	+	0.0525535i
$738$	7.55241	−	9.22645i	0.278008	−	0.339630i
$739$	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
$741$	−3.91598	+	0.366639i	−0.143857	+	0.0134688i
$742$	−0.0880241	−	0.499209i	−0.00323147	−	0.0183266i
$743$	−2.01338	−	11.4184i	−0.0738636	−	0.418901i	−0.999209	−	0.0397752i	$-0.987336\pi$
$743$	−2.01338	−	11.4184i	−0.0738636	−	0.418901i	0.925345	−	0.379126i	$-0.123775\pi$
$744$	3.67253	−	8.00259i	0.134641	−	0.293389i
$745$	46.5820	+	39.0870i	1.70663	+	1.43204i
$746$	−7.07457	−	12.2535i	−0.259018	−	0.448633i
$747$	16.1801	+	18.8126i	0.591997	+	0.688318i
$748$	−0.614637	+	1.06458i	−0.0224734	+	0.0389250i
$749$	0.267417	−	0.0973316i	0.00977119	−	0.00355642i
$750$	31.4447	−	31.8299i	1.14820	−	1.16226i
$751$	−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
$753$	−0.586556	+	7.20962i	−0.0213753	+	0.262733i
$754$	0.0771899	−	0.437766i	0.00281109	−	0.0159425i
$755$	22.8390			0.831194
$756$	−0.192495	+	0.774729i	−0.00700098	+	0.0281766i
$757$	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
$759$	1.84402	+	1.27454i	0.0669338	+	0.0462629i
$760$	14.5321	+	5.28926i	0.527136	+	0.191862i
$761$	3.01606	−	2.53078i	0.109332	−	0.0917406i	−0.586483	−	0.809962i	$-0.699488\pi$
$761$	3.01606	−	2.53078i	0.109332	−	0.0917406i	0.695815	+	0.718221i	$0.255043\pi$
$762$	−31.2204	−	8.16209i	−1.13099	−	0.295681i
$763$	−2.10043

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(1.56529 - 0.741539i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.10057 + 2.60168i) q^{5} +(-0.458464 - 1.67027i) q^{6} +(0.144365 - 0.0525446i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.90024 - 2.32144i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(1.56529 - 0.741539i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.10057 + 2.60168i) q^{5} +(-0.458464 - 1.67027i) q^{6} +(0.144365 - 0.0525446i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.90024 - 2.32144i) q^{9} +(2.02375 + 3.50524i) q^{10} +(0.169211 + 0.141985i) q^{11} +(-1.72451 + 0.161460i) q^{12} +(0.103202 + 0.585289i) q^{13} +(-0.0266776 - 0.151296i) q^{14} +(-2.92402 + 6.37157i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.78255 - 4.81952i) q^{17} +(-1.95620 - 2.27448i) q^{18} +(-1.91041 + 3.30893i) q^{19} +(3.80341 - 1.38433i) q^{20} +(0.187009 - 0.189300i) q^{21} +(0.169211 - 0.141985i) q^{22} +(5.50570 + 2.00391i) q^{23} +(-0.140451 + 1.72635i) q^{24} +(1.97651 - 11.2093i) q^{25} +0.594318 q^{26} +(1.25298 - 5.04282i) q^{27} -0.153630 q^{28} +(0.129880 - 0.736585i) q^{29} +(5.76702 + 3.98601i) q^{30} +(-4.77702 - 1.73869i) q^{31} +(0.766044 - 0.642788i) q^{32} +(0.370152 + 0.0967705i) q^{33} +(-5.22949 + 1.90338i) q^{34} +(-0.310909 + 0.538510i) q^{35} +(-2.57962 + 1.53152i) q^{36} +(-1.87388 - 3.24566i) q^{37} +(2.92692 + 2.45598i) q^{38} +(0.595555 + 0.839616i) q^{39} +(-0.702841 - 3.98601i) q^{40} +(0.690156 + 3.91407i) q^{41} +(-0.153950 - 0.217039i) q^{42} +(7.81896 + 6.56088i) q^{43} +(-0.110445 - 0.191296i) q^{44} +(0.147838 + 12.1416i) q^{45} +(2.92952 - 5.07408i) q^{46} +(0.447025 - 0.162704i) q^{47} +(1.67573 + 0.438094i) q^{48} +(-5.34423 + 4.48434i) q^{49} +(-10.6958 - 3.89296i) q^{50} +(-7.92935 - 5.48056i) q^{51} +(0.103202 - 0.585289i) q^{52} +3.29955 q^{53} +(-4.74863 - 2.10962i) q^{54} -0.894051 q^{55} +(-0.0266776 + 0.151296i) q^{56} +(-0.536639 + 6.59606i) q^{57} +(-0.702841 - 0.255813i) q^{58} +(5.57221 - 4.67564i) q^{59} +(4.92689 - 4.98724i) q^{60} +(-3.16654 + 1.15253i) q^{61} +(-2.54180 + 4.40252i) q^{62} +(0.152349 - 0.434982i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.84272 - 1.54623i) q^{65} +(0.159577 - 0.347724i) q^{66} +(1.29509 + 7.34481i) q^{67} +(0.966370 + 5.48056i) q^{68} +(10.1040 - 0.945999i) q^{69} +(0.476340 + 0.399697i) q^{70} +(-1.42889 - 2.47490i) q^{71} +(1.06031 + 2.80638i) q^{72} +(0.638922 - 1.10665i) q^{73} +(-3.52175 + 1.28181i) q^{74} +(-5.21836 - 19.0115i) q^{75} +(2.92692 - 2.45598i) q^{76} +(0.0318887 + 0.0116066i) q^{77} +(0.930277 - 0.440710i) q^{78} +(-0.574268 + 3.25684i) q^{79} -4.04750 q^{80} +(-1.77818 - 8.82259i) q^{81} +3.97445 q^{82} +(-1.43627 + 8.14551i) q^{83} +(-0.240475 + 0.113923i) q^{84} +(21.1664 + 7.70392i) q^{85} +(7.81896 - 6.56088i) q^{86} +(-0.342907 - 1.24928i) q^{87} +(-0.207568 + 0.0755487i) q^{88} +(2.47882 - 4.29345i) q^{89} +(11.9828 + 1.96277i) q^{90} +(0.0456525 + 0.0790725i) q^{91} +(-4.48829 - 3.76612i) q^{92} +(-8.76671 + 0.820795i) q^{93} +(-0.0826070 - 0.468487i) q^{94} +(-2.68543 - 15.2298i) q^{95} +(0.722426 - 1.57420i) q^{96} +(4.33127 + 3.63437i) q^{97} +(3.48820 + 6.04174i) q^{98} +(0.651152 - 0.123008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more