LMFDB - Embedded newform 54.2.e.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	54.43
Dual form			54.2.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.26604 - 0.460802i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.0209445 + 0.118782i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.26604 - 0.460802i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.0209445 + 0.118782i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +(0.673648 + 1.16679i) q^{10} +(-3.49273 + 1.27125i) q^{11} +(0.592396 + 1.62760i) q^{12} +(-4.64543 + 3.89798i) q^{13} +(0.0923963 - 0.0775297i) q^{14} +(-2.29813 - 0.405223i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.58512 + 4.47756i) q^{17} +(-2.81908 - 1.02606i) q^{18} +(2.96064 - 5.12797i) q^{19} +(0.233956 - 1.32683i) q^{20} +0.208911i q^{21} +(3.49273 + 1.27125i) q^{22} +(-0.826352 - 4.68647i) q^{23} +(0.592396 - 1.62760i) q^{24} +(-2.43969 - 2.04715i) q^{25} +6.06418 q^{26} +(4.50000 - 2.59808i) q^{27} -0.120615 q^{28} +(4.55303 + 3.82045i) q^{29} +(1.50000 + 1.78763i) q^{30} +(-0.875515 - 4.96529i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-5.57532 + 3.21891i) q^{33} +(0.897804 - 5.09170i) q^{34} +(0.0812519 - 0.140732i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-0.145430 - 0.251892i) q^{37} +(-5.56418 + 2.02520i) q^{38} +(-6.75150 + 8.04612i) q^{39} +(-1.03209 + 0.866025i) q^{40} +(4.44356 - 3.72859i) q^{41} +(0.134285 - 0.160035i) q^{42} +(-0.426022 + 0.155059i) q^{43} +(-1.85844 - 3.21891i) q^{44} -4.04189 q^{45} +(-2.37939 + 4.12122i) q^{46} +(-0.134285 + 0.761570i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(6.56418 + 2.38917i) q^{49} +(0.553033 + 3.13641i) q^{50} +(5.75624 + 6.86002i) q^{51} +(-4.64543 - 3.89798i) q^{52} -7.29086 q^{53} +(-5.11721 - 0.902302i) q^{54} +5.00774 q^{55} +(0.0923963 + 0.0775297i) q^{56} +(3.50774 - 9.63744i) q^{57} +(-1.03209 - 5.85327i) q^{58} +(1.40033 + 0.509678i) q^{59} -2.33359i q^{60} +(-0.656574 + 3.72362i) q^{61} +(-2.52094 + 4.36640i) q^{62} +(0.0628336 + 0.356347i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(7.67752 - 2.79439i) q^{65} +(6.34002 + 1.11792i) q^{66} +(-5.08512 + 4.26692i) q^{67} +(-3.96064 + 3.32337i) q^{68} +(-2.81908 - 7.74535i) q^{69} +(-0.152704 + 0.0555796i) q^{70} +(-2.87211 - 4.97464i) q^{71} +(0.520945 - 2.95442i) q^{72} +(-5.20961 + 9.02330i) q^{73} +(-0.0505072 + 0.286441i) q^{74} +(-4.77719 - 2.75811i) q^{75} +(5.56418 + 2.02520i) q^{76} +(-0.0778483 - 0.441500i) q^{77} +(10.3439 - 1.82391i) q^{78} +(10.7194 + 8.99465i) q^{79} +1.34730 q^{80} +(6.89440 - 5.78509i) q^{81} -5.80066 q^{82} +(-1.81521 - 1.52314i) q^{83} +(-0.205737 + 0.0362770i) q^{84} +(-1.20961 - 6.86002i) q^{85} +(0.426022 + 0.155059i) q^{86} +(8.91534 + 5.14728i) q^{87} +(-0.645430 + 3.66041i) q^{88} +(1.08512 - 1.87949i) q^{89} +(3.09627 + 2.59808i) q^{90} +(-0.365715 - 0.633436i) q^{91} +(4.47178 - 1.62760i) q^{92} +(-2.98680 - 8.20616i) q^{93} +(0.592396 - 0.497079i) q^{94} +(-6.11128 + 5.12797i) q^{95} +(1.70574 + 0.300767i) q^{96} +(3.21941 - 1.17177i) q^{97} +(-3.49273 - 6.04958i) q^{98} +(-8.54189 + 7.16750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	1.70574	−	0.300767i	0.984808	−	0.173648i
$3$	1.70574	−	0.300767i	0.984808	−	0.173648i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−1.26604	−	0.460802i	−0.566192	−	0.206077i	0.0430339	−	0.999074i	$-0.486298\pi$
$5$	−1.26604	−	0.460802i	−0.566192	−	0.206077i	−0.609226	+	0.792996i	$0.708520\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	−0.0209445	+	0.118782i	−0.00791629	+	0.0448955i	−0.988510	−	0.151155i	$-0.951701\pi$
$7$	−0.0209445	+	0.118782i	−0.00791629	+	0.0448955i	0.980594	+	0.196051i	$0.0628118\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$	0.673648	+	1.16679i	0.213026	+	0.368972i
$11$	−3.49273	+	1.27125i	−1.05310	+	0.383296i	−0.809831	−	0.586664i	$-0.800441\pi$
$11$	−3.49273	+	1.27125i	−1.05310	+	0.383296i	−0.243266	+	0.969960i	$0.578219\pi$
$12$	0.592396	+	1.62760i	0.171010	+	0.469846i
$13$	−4.64543	+	3.89798i	−1.28841	+	1.08110i	−0.296385	+	0.955069i	$0.595781\pi$
$13$	−4.64543	+	3.89798i	−1.28841	+	1.08110i	−0.992026	+	0.126036i	$0.959775\pi$
$14$	0.0923963	−	0.0775297i	0.0246939	−	0.0207207i
$15$	−2.29813	−	0.405223i	−0.593375	−	0.104628i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.58512	+	4.47756i	0.626984	+	1.08597i	0.988154	+	0.153468i	$0.0490443\pi$
$17$	2.58512	+	4.47756i	0.626984	+	1.08597i	−0.361169	+	0.932500i	$0.617622\pi$
$18$	−2.81908	−	1.02606i	−0.664463	−	0.241845i
$19$	2.96064	−	5.12797i	0.679217	−	1.17644i	−0.296000	−	0.955188i	$-0.595653\pi$
$19$	2.96064	−	5.12797i	0.679217	−	1.17644i	0.975217	−	0.221250i	$-0.0710137\pi$
$20$	0.233956	−	1.32683i	0.0523141	−	0.296688i
$21$			0.208911i			0.0455881i
$22$	3.49273	+	1.27125i	0.744652	+	0.271031i
$23$	−0.826352	−	4.68647i	−0.172306	−	0.977197i	−0.941207	−	0.337830i	$-0.890307\pi$
$23$	−0.826352	−	4.68647i	−0.172306	−	0.977197i	0.768901	−	0.639368i	$-0.220804\pi$
$24$	0.592396	−	1.62760i	0.120922	−	0.332232i
$25$	−2.43969	−	2.04715i	−0.487939	−	0.409429i
$26$	6.06418			1.18928
$27$	4.50000	−	2.59808i	0.866025	−	0.500000i
$28$	−0.120615			−0.0227940
$29$	4.55303	+	3.82045i	0.845477	+	0.709440i	0.958789	−	0.284120i	$-0.0917014\pi$
$29$	4.55303	+	3.82045i	0.845477	+	0.709440i	−0.113312	+	0.993559i	$0.536146\pi$
$30$	1.50000	+	1.78763i	0.273861	+	0.326375i
$31$	−0.875515	−	4.96529i	−0.157247	−	0.891793i	−0.956703	−	0.291067i	$-0.905990\pi$
$31$	−0.875515	−	4.96529i	−0.157247	−	0.891793i	0.799455	−	0.600725i	$-0.205121\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−5.57532	+	3.21891i	−0.970539	+	0.560341i
$34$	0.897804	−	5.09170i	0.153972	−	0.873219i
$35$	0.0812519	−	0.140732i	0.0137341	−	0.0237881i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−0.145430	−	0.251892i	−0.0239085	−	0.0414107i	0.853824	−	0.520562i	$-0.174278\pi$
$37$	−0.145430	−	0.251892i	−0.0239085	−	0.0414107i	−0.877732	+	0.479152i	$0.840944\pi$
$38$	−5.56418	+	2.02520i	−0.902629	+	0.328530i
$39$	−6.75150	+	8.04612i	−1.08110	+	1.28841i
$40$	−1.03209	+	0.866025i	−0.163188	+	0.136931i
$41$	4.44356	−	3.72859i	0.693968	−	0.582308i	−0.226082	−	0.974108i	$-0.572592\pi$
$41$	4.44356	−	3.72859i	0.693968	−	0.582308i	0.920050	+	0.391800i	$0.128147\pi$
$42$	0.134285	−	0.160035i	0.0207207	−	0.0246939i
$43$	−0.426022	+	0.155059i	−0.0649678	+	0.0236463i	−0.374300	−	0.927308i	$-0.622117\pi$
$43$	−0.426022	+	0.155059i	−0.0649678	+	0.0236463i	0.309332	+	0.950954i	$0.399895\pi$
$44$	−1.85844	−	3.21891i	−0.280170	−	0.485270i
$45$	−4.04189			−0.602529
$46$	−2.37939	+	4.12122i	−0.350821	+	0.607640i
$47$	−0.134285	+	0.761570i	−0.0195875	+	0.111086i	−0.993034	−	0.117829i	$-0.962407\pi$
$47$	−0.134285	+	0.761570i	−0.0195875	+	0.111086i	0.973446	+	0.228915i	$0.0735178\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	6.56418	+	2.38917i	0.937740	+	0.341309i
$50$	0.553033	+	3.13641i	0.0782107	+	0.443555i
$51$	5.75624	+	6.86002i	0.806035	+	0.960596i
$52$	−4.64543	−	3.89798i	−0.644205	−	0.540552i
$53$	−7.29086			−1.00148			−0.500738	−	0.865599i	$-0.666938\pi$
$53$	−7.29086			−1.00148			−0.500738	+	0.865599i	$0.666938\pi$
$54$	−5.11721	−	0.902302i	−0.696364	−	0.122788i
$55$	5.00774			0.675244
$56$	0.0923963	+	0.0775297i	0.0123470	+	0.0103603i
$57$	3.50774	−	9.63744i	0.464612	−	1.27651i
$58$	−1.03209	−	5.85327i	−0.135520	−	0.768572i
$59$	1.40033	+	0.509678i	0.182307	+	0.0663545i	0.431561	−	0.902084i	$-0.357963\pi$
$59$	1.40033	+	0.509678i	0.182307	+	0.0663545i	−0.249253	+	0.968438i	$0.580185\pi$
$60$		−	2.33359i		−	0.301265i
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	0.913489	+	0.406864i	$0.133378\pi$
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	−0.997554	+	0.0698959i	$0.977733\pi$
$62$	−2.52094	+	4.36640i	−0.320160	+	0.554534i
$63$	0.0628336	+	0.356347i	0.00791629	+	0.0448955i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	7.67752	−	2.79439i	0.952279	−	0.346601i
$66$	6.34002	+	1.11792i	0.780403	+	0.137606i
$67$	−5.08512	+	4.26692i	−0.621247	+	0.521288i	−0.898195	−	0.439597i	$-0.855121\pi$
$67$	−5.08512	+	4.26692i	−0.621247	+	0.521288i	0.276949	+	0.960885i	$0.410677\pi$
$68$	−3.96064	+	3.32337i	−0.480298	+	0.403018i
$69$	−2.81908	−	7.74535i	−0.339377	−	0.932431i
$70$	−0.152704	+	0.0555796i	−0.0182516	+	0.00664303i
$71$	−2.87211	−	4.97464i	−0.340857	−	0.590381i	0.643735	−	0.765248i	$-0.277384\pi$
$71$	−2.87211	−	4.97464i	−0.340857	−	0.590381i	−0.984592	+	0.174867i	$0.944050\pi$
$72$	0.520945	−	2.95442i	0.0613939	−	0.348182i
$73$	−5.20961	+	9.02330i	−0.609738	+	1.05610i	0.381545	+	0.924350i	$0.375392\pi$
$73$	−5.20961	+	9.02330i	−0.609738	+	1.05610i	−0.991283	+	0.131748i	$0.957941\pi$
$74$	−0.0505072	+	0.286441i	−0.00587134	+	0.0332980i
$75$	−4.77719	−	2.75811i	−0.551622	−	0.318479i
$76$	5.56418	+	2.02520i	0.638255	+	0.232306i
$77$	−0.0778483	−	0.441500i	−0.00887164	−	0.0503136i
$78$	10.3439	−	1.82391i	1.17122	−	0.206517i
$79$	10.7194	+	8.99465i	1.20603	+	1.01198i	0.999437	+	0.0335498i	$0.0106812\pi$
$79$	10.7194	+	8.99465i	1.20603	+	1.01198i	0.206591	+	0.978427i	$0.433763\pi$
$80$	1.34730			0.150632
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$	−5.80066			−0.640576
$83$	−1.81521	−	1.52314i	−0.199245	−	0.167186i	0.537706	−	0.843132i	$-0.319291\pi$
$83$	−1.81521	−	1.52314i	−0.199245	−	0.167186i	−0.736951	+	0.675946i	$0.763735\pi$
$84$	−0.205737	+	0.0362770i	−0.0224478	+	0.00395814i
$85$	−1.20961	−	6.86002i	−0.131200	−	0.744074i
$86$	0.426022	+	0.155059i	0.0459391	+	0.0167205i
$87$	8.91534	+	5.14728i	0.955825	+	0.551846i
$88$	−0.645430	+	3.66041i	−0.0688030	+	0.390201i
$89$	1.08512	−	1.87949i	0.115023	−	0.199225i	−0.802766	−	0.596294i	$-0.796639\pi$
$89$	1.08512	−	1.87949i	0.115023	−	0.199225i	0.917789	+	0.397069i	$0.129973\pi$
$90$	3.09627	+	2.59808i	0.326375	+	0.273861i
$91$	−0.365715	−	0.633436i	−0.0383373	−	0.0664022i
$92$	4.47178	−	1.62760i	0.466215	−	0.169689i
$93$	−2.98680	−	8.20616i	−0.309716	−	0.850939i
$94$	0.592396	−	0.497079i	0.0611010	−	0.0512698i
$95$	−6.11128	+	5.12797i	−0.627004	+	0.526119i
$96$	1.70574	+	0.300767i	0.174091	+	0.0306970i
$97$	3.21941	−	1.17177i	0.326881	−	0.118975i	−0.173366	−	0.984857i	$-0.555464\pi$
$97$	3.21941	−	1.17177i	0.326881	−	0.118975i	0.500248	+	0.865882i	$0.333242\pi$
$98$	−3.49273	−	6.04958i	−0.352819	−	0.611100i
$99$	−8.54189	+	7.16750i	−0.858492	+	0.720360i
$100$	1.59240	−	2.75811i	0.159240	−	0.275811i
$101$	1.49660	−	8.48762i	0.148917	−	0.844550i	−0.815221	−	0.579149i	$-0.803385\pi$
$101$	1.49660	−	8.48762i	0.148917	−	0.844550i	0.964138	−	0.265400i	$-0.0855041\pi$
$102$		−	8.95513i		−	0.886690i
$103$	2.05303	+	0.747243i	0.202291	+	0.0736280i	0.441179	−	0.897419i	$-0.354560\pi$
$103$	2.05303	+	0.747243i	0.202291	+	0.0736280i	−0.238887	+	0.971047i	$0.576783\pi$
$104$	1.05303	+	5.97205i	0.103258	+	0.585608i
$105$	0.0962667	−	0.264490i	0.00939466	−	0.0258116i
$106$	5.58512	+	4.68647i	0.542475	+	0.455191i
$107$	−10.2909			−0.994855			−0.497427	−	0.867506i	$-0.665722\pi$
$107$	−10.2909			−0.994855			−0.497427	+	0.867506i	$0.665722\pi$
$108$	3.34002	+	3.98048i	0.321394	+	0.383022i
$109$	−11.0915			−1.06237			−0.531187	−	0.847254i	$-0.678254\pi$
$109$	−11.0915			−1.06237			−0.531187	+	0.847254i	$0.678254\pi$
$110$	−3.83615	−	3.21891i	−0.365763	−	0.306911i
$111$	−0.323826	−	0.385920i	−0.0307362	−	0.0366299i
$112$	−0.0209445	−	0.118782i	−0.00197907	−	0.0112239i
$113$	−5.56670	−	2.02611i	−0.523671	−	0.190601i	0.0666389	−	0.997777i	$-0.478772\pi$
$113$	−5.56670	−	2.02611i	−0.523671	−	0.190601i	−0.590310	+	0.807176i	$0.700995\pi$
$114$	−8.88191	+	5.12797i	−0.831867	+	0.480279i
$115$	−1.11334	+	6.31407i	−0.103820	+	0.588790i
$116$	−2.97178	+	5.14728i	−0.275923	+	0.477913i
$117$	−9.09627	+	15.7552i	−0.840950	+	1.45657i
$118$	−0.745100	−	1.29055i	−0.0685920	−	0.118805i
$119$	−0.586000	+	0.213286i	−0.0537185	+	0.0195519i
$120$	−1.50000	+	1.78763i	−0.136931	+	0.163188i
$121$	2.15657	−	1.80958i	0.196052	−	0.164507i
$122$	2.89646	−	2.43042i	0.262233	−	0.220040i
$123$	6.45811	−	7.69648i	0.582308	−	0.693968i
$124$	4.73783	−	1.72443i	0.425469	−	0.154858i
$125$	5.51367	+	9.54996i	0.493158	+	0.854174i
$126$	0.180922	−	0.313366i	0.0161178	−	0.0279169i
$127$	2.86959	−	4.97027i	0.254634	−	0.441040i	−0.710162	−	0.704039i	$-0.751378\pi$
$127$	2.86959	−	4.97027i	0.254634	−	0.441040i	0.964796	+	0.262999i	$0.0847115\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−0.680045	+	0.392624i	−0.0598746	+	0.0345686i
$130$	−7.67752	−	2.79439i	−0.673363	−	0.245084i
$131$	2.99020	+	16.9583i	0.261255	+	1.48165i	0.779491	+	0.626413i	$0.215478\pi$
$131$	2.99020	+	16.9583i	0.261255	+	1.48165i	−0.518236	+	0.855237i	$0.673411\pi$
$132$	−4.13816	−	4.93166i	−0.360180	−	0.429246i
$133$	0.547104	+	0.459074i	0.0474399	+	0.0398068i
$134$	6.63816			0.573449
$135$	−6.89440	+	1.21567i	−0.593375	+	0.104628i
$136$	5.17024			0.443345
$137$	0.0662372	+	0.0555796i	0.00565902	+	0.00474848i	0.645613	−	0.763665i	$-0.276602\pi$
$137$	0.0662372	+	0.0555796i	0.00565902	+	0.00474848i	−0.639954	+	0.768413i	$0.721046\pi$
$138$	−2.81908	+	7.74535i	−0.239976	+	0.659328i
$139$	−3.18866	−	18.0838i	−0.270459	−	1.53385i	−0.753027	−	0.657990i	$-0.771407\pi$
$139$	−3.18866	−	18.0838i	−0.270459	−	1.53385i	0.482568	−	0.875859i	$-0.339704\pi$
$140$	0.152704	+	0.0555796i	0.0129058	+	0.00469733i
$141$			1.33943i			0.112800i
$142$	−0.997474	+	5.65695i	−0.0837061	+	0.474721i
$143$	11.2699	−	19.5201i	0.942438	−	1.63235i
$144$	−2.29813	+	1.92836i	−0.191511	+	0.160697i
$145$	−4.00387	−	6.93491i	−0.332503	−	0.575913i
$146$	9.79086	−	3.56358i	0.810297	−	0.294924i
$147$	11.9153	+	2.10100i	0.982761	+	0.173287i
$148$	0.222811	−	0.186961i	0.0183150	−	0.0153681i
$149$	−3.75490	+	3.15074i	−0.307613	+	0.258118i	−0.783505	−	0.621386i	$-0.786570\pi$
$149$	−3.75490	+	3.15074i	−0.307613	+	0.258118i	0.475891	+	0.879504i	$0.342126\pi$
$150$	1.88666	+	5.18355i	0.154045	+	0.423235i
$151$	−1.62701	+	0.592184i	−0.132404	+	0.0481912i	−0.407372	−	0.913262i	$-0.633555\pi$
$151$	−1.62701	+	0.592184i	−0.132404	+	0.0481912i	0.274968	+	0.961453i	$0.411333\pi$
$152$	−2.96064	−	5.12797i	−0.240139	−	0.415934i
$153$	11.8819	+	9.97011i	0.960596	+	0.806035i
$154$	−0.224155	+	0.388249i	−0.0180630	+	0.0312860i
$155$	−1.17958	+	6.68972i	−0.0947460	+	0.537331i
$156$	−9.09627	−	5.25173i	−0.728284	−	0.420475i
$157$	5.46451	+	1.98892i	0.436115	+	0.158733i	0.550742	−	0.834676i	$-0.314345\pi$
$157$	5.46451	+	1.98892i	0.436115	+	0.158733i	−0.114627	+	0.993409i	$0.536567\pi$
$158$	−2.42989	−	13.7806i	−0.193312	−	1.09633i
$159$	−12.4363	+	2.19285i	−0.986262	+	0.173905i
$160$	−1.03209	−	0.866025i	−0.0815938	−	0.0684653i
$161$	0.573978			0.0452358
$162$	−9.00000			−0.707107
$163$	−2.70914			−0.212196			−0.106098	−	0.994356i	$-0.533836\pi$
$163$	−2.70914			−0.212196			−0.106098	+	0.994356i	$0.533836\pi$
$164$	4.44356	+	3.72859i	0.346984	+	0.291154i
$165$	8.54189	−	1.50617i	0.664985	−	0.117255i
$166$	0.411474	+	2.33359i	0.0319366	+	0.181121i
$167$	23.1202	+	8.41507i	1.78910	+	0.651177i	0.999284	+	0.0378268i	$0.0120435\pi$
$167$	23.1202	+	8.41507i	1.78910	+	0.651177i	0.789811	+	0.613351i	$0.210179\pi$
$168$	0.180922	+	0.104455i	0.0139584	+	0.00805891i
$169$	4.12836	−	23.4131i	0.317566	−	1.80101i
$170$	−3.48293	+	6.03260i	−0.267128	+	0.462680i
$171$	3.08466	−	17.4940i	0.235890	−	1.33780i
$172$	−0.226682	−	0.392624i	−0.0172843	−	0.0299373i
$173$	10.0753	−	3.66712i	0.766013	−	0.278806i	0.0706849	−	0.997499i	$-0.477482\pi$
$173$	10.0753	−	3.66712i	0.766013	−	0.278806i	0.695328	+	0.718693i	$0.255259\pi$
$174$	−3.52094	−	9.67372i	−0.266922	−	0.733362i
$175$	0.294263	−	0.246916i	0.0222442	−	0.0186651i
$176$	2.84730	−	2.38917i	0.214623	−	0.180090i
$177$	2.54189	+	0.448204i	0.191060	+	0.0336890i
$178$	−2.03936	+	0.742267i	−0.152857	+	0.0556353i
$179$	6.92262	+	11.9903i	0.517421	+	0.896199i	0.999795	+	0.0202340i	$0.00644112\pi$
$179$	6.92262	+	11.9903i	0.517421	+	0.896199i	−0.482374	+	0.875965i	$0.660226\pi$
$180$	−0.701867	−	3.98048i	−0.0523141	−	0.296688i
$181$	−1.75490	+	3.03958i	−0.130441	+	0.225930i	−0.923847	−	0.382763i	$-0.874973\pi$
$181$	−1.75490	+	3.03958i	−0.130441	+	0.225930i	0.793406	+	0.608693i	$0.208306\pi$
$182$	−0.127011	+	0.720317i	−0.00941471	+	0.0533935i
$183$			6.54899i			0.484115i
$184$	−4.47178	−	1.62760i	−0.329664	−	0.119988i
$185$	0.0680482	+	0.385920i	0.00500300	+	0.0283734i
$186$	−2.98680	+	8.20616i	−0.219003	+	0.601704i
$187$	−14.7212	−	12.3526i	−1.07652	−	0.903309i
$188$	−0.773318			−0.0564000
$189$	0.214355	+	0.588936i	0.0155920	+	0.0428388i
$190$	7.97771			0.578764
$191$	−16.7704	−	14.0720i	−1.21346	−	1.01822i	−0.999140	−	0.0414526i	$-0.986801\pi$
$191$	−16.7704	−	14.0720i	−1.21346	−	1.01822i	−0.214322	−	0.976763i	$-0.568754\pi$
$192$	−1.11334	−	1.32683i	−0.0803485	−	0.0957556i
$193$	4.44743	+	25.2226i	0.320133	+	1.81557i	0.541873	+	0.840460i	$0.317715\pi$
$193$	4.44743	+	25.2226i	0.320133	+	1.81557i	−0.221740	+	0.975106i	$0.571174\pi$
$194$	−3.21941	−	1.17177i	−0.231140	−	0.0841281i
$195$	12.2554	−	7.07564i	0.877625	−	0.506697i
$196$	−1.21301	+	6.87933i	−0.0866436	+	0.491381i
$197$	−6.84255	+	11.8516i	−0.487511	+	0.844395i	−0.999897	−	0.0143611i	$-0.995429\pi$
$197$	−6.84255	+	11.8516i	−0.487511	+	0.844395i	0.512385	+	0.858756i	$0.328762\pi$
$198$	11.1506			0.792442
$199$	6.19981	+	10.7384i	0.439493	+	0.761224i	0.997650	−	0.0685113i	$-0.0218249\pi$
$199$	6.19981	+	10.7384i	0.439493	+	0.761224i	−0.558158	+	0.829735i	$0.688492\pi$
$200$	−2.99273	+	1.08926i	−0.211618	+	0.0770225i
$201$	−7.39053	+	8.80769i	−0.521288	+	0.621247i
$202$	−6.60220	+	5.53990i	−0.464529	+	0.389786i
$203$	−0.549163	+	0.460802i	−0.0385437	+	0.0323420i
$204$	−5.75624	+	6.86002i	−0.403018	+	0.480298i
$205$	−7.34389	+	2.67296i	−0.512920	+	0.186688i
$206$	−1.09240	−	1.89209i	−0.0761109	−	0.131828i
$207$	−7.13816	−	12.3636i	−0.496136	−	0.859333i
$208$	3.03209	−	5.25173i	0.210238	−	0.364142i
$209$	−3.82177	+	21.6743i	−0.264357	+	1.49924i
$210$	−0.243756	+	0.140732i	−0.0168207	+	0.00971146i
$211$	−13.9474	−	5.07645i	−0.960181	−	0.349477i	−0.186077	−	0.982535i	$-0.559577\pi$
$211$	−13.9474	−	5.07645i	−0.960181	−	0.349477i	−0.774104	+	0.633058i	$0.781799\pi$
$212$	−1.26604	−	7.18009i	−0.0869523	−	0.493131i
$213$	−6.39528	−	7.62159i	−0.438197	−	0.522223i
$214$	7.88326	+	6.61484i	0.538888	+	0.452181i
$215$	0.610815			0.0416572
$216$		−	5.19615i		−	0.353553i
$217$	0.608126			0.0412823
$218$	8.49660	+	7.12949i	0.575462	+	0.482870i
$219$	−6.17230	+	16.9583i	−0.417086	+	1.14593i
$220$	0.869585	+	4.93166i	0.0586274	+	0.332493i
$221$	−29.4624	−	10.7235i	−1.98186	−	0.721338i
$222$			0.503783i			0.0338117i
$223$	−1.16890	+	6.62916i	−0.0782754	+	0.443922i	0.920331	+	0.391141i	$0.127920\pi$
$223$	−1.16890	+	6.62916i	−0.0782754	+	0.443922i	−0.998606	+	0.0527806i	$0.983192\pi$
$224$	−0.0603074	+	0.104455i	−0.00402946	+	0.00697922i
$225$	−8.97818	−	3.26779i	−0.598545	−	0.217853i
$226$	2.96198	+	5.13030i	0.197028	+	0.341263i
$227$	−13.6211	+	4.95767i	−0.904063	+	0.329052i	−0.751880	−	0.659300i	$-0.770853\pi$
$227$	−13.6211	+	4.95767i	−0.904063	+	0.329052i	−0.152183	+	0.988352i	$0.548630\pi$
$228$	10.1001	+	1.78093i	0.668898	+	0.117945i
$229$	19.7540	−	16.5756i	1.30538	−	1.09535i	0.316194	−	0.948694i	$-0.397595\pi$
$229$	19.7540	−	16.5756i	1.30538	−	1.09535i	0.989188	−	0.146652i	$-0.0468496\pi$
$230$	4.91147	−	4.12122i	0.323853	−	0.271745i
$231$	−0.265578	−	0.729669i	−0.0174737	−	0.0480087i
$232$	5.58512	−	2.03282i	0.366681	−	0.133461i
$233$	−5.19846	−	9.00400i	−0.340563	−	0.589872i	0.643975	−	0.765047i	$-0.277284\pi$
$233$	−5.19846	−	9.00400i	−0.340563	−	0.589872i	−0.984537	+	0.175175i	$0.943951\pi$
$234$	17.0954	−	6.22221i	1.11756	−	0.406759i
$235$	0.520945	−	0.902302i	0.0339827	−	0.0588597i
$236$	−0.258770	+	1.46756i	−0.0168445	+	0.0955300i
$237$	20.9898	+	12.1185i	1.36343	+	0.787179i
$238$	0.586000	+	0.213286i	0.0379847	+	0.0138253i
$239$	−3.97906	−	22.5663i	−0.257384	−	1.45970i	−0.789879	−	0.613263i	$-0.789857\pi$
$239$	−3.97906	−	22.5663i	−0.257384	−	1.45970i	0.532495	−	0.846433i	$-0.321254\pi$
$240$	2.29813	−	0.405223i	0.148344	−	0.0261570i
$241$	−9.25150	−	7.76293i	−0.595941	−	0.500054i	0.294197	−	0.955745i	$-0.404948\pi$
$241$	−9.25150	−	7.76293i	−0.595941	−	0.500054i	−0.890138	+	0.455691i	$0.849392\pi$
$242$	−2.81521			−0.180968
$243$	10.0201	−	11.9415i	0.642788	−	0.766044i
$244$	−3.78106			−0.242058
$245$	−7.20961	−	6.04958i	−0.460605	−	0.386493i
$246$	−9.89440	+	1.74465i	−0.630844	+	0.111235i
$247$	6.23530	+	35.3621i	0.396743	+	2.25004i
$248$	−4.73783	−	1.72443i	−0.300852	−	0.109501i
$249$	−3.55438	−	2.05212i	−0.225250	−	0.130048i
$250$	1.91488	−	10.8598i	0.121107	−	0.686835i
$251$	7.02347	−	12.1650i	0.443318	−	0.767849i	−0.554616	−	0.832107i	$-0.687135\pi$
$251$	7.02347	−	12.1650i	0.443318	−	0.767849i	0.997933	+	0.0642581i	$0.0204681\pi$
$252$	−0.340022	+	0.123758i	−0.0214194	+	0.00779602i
$253$	8.84389	+	15.3181i	0.556011	+	0.963039i
$254$	−5.39306	+	1.96291i	−0.338390	+	0.123164i
$255$	−4.12654	−	11.3376i	−0.258414	−	0.709987i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	13.8983	−	11.6620i	0.866950	−	0.727458i	−0.0965034	−	0.995333i	$-0.530766\pi$
$257$	13.8983	−	11.6620i	0.866950	−	0.727458i	0.963454	+	0.267875i	$0.0863214\pi$
$258$	0.773318	+	0.136357i	0.0481447	+	0.00848921i
$259$	0.0329662	−	0.0119987i	0.00204842	−	0.000745565i
$260$	4.08512	+	7.07564i	0.253349	+	0.438813i
$261$	16.7554	+	6.09845i	1.03713	+	0.377485i
$262$	8.60994	−	14.9128i	0.531924	−	0.921319i
$263$	0.742107	−	4.20870i	0.0457603	−	0.259519i	−0.953342	−	0.301894i	$-0.902381\pi$
$263$	0.742107	−	4.20870i	0.0457603	−	0.259519i	0.999102	+	0.0423745i	$0.0134923\pi$
$264$			6.43783i			0.396221i
$265$	9.23055	+	3.35965i	0.567028	+	0.206381i
$266$	−0.124018	−	0.703343i	−0.00760405	−	0.0431247i
$267$	1.28564	−	3.53228i	0.0786802	−	0.216172i
$268$	−5.08512	−	4.26692i	−0.310623	−	0.260644i
$269$	13.0615			0.796373			0.398187	−	0.917304i	$-0.369640\pi$
$269$	13.0615			0.796373			0.398187	+	0.917304i	$0.369640\pi$
$270$	6.06283	+	3.50038i	0.368972	+	0.213026i
$271$	8.48751			0.515580			0.257790	−	0.966201i	$-0.417006\pi$
$271$	8.48751			0.515580			0.257790	+	0.966201i	$0.417006\pi$
$272$	−3.96064	−	3.32337i	−0.240149	−	0.201509i
$273$	−0.814330	−	0.970481i	−0.0492855	−	0.0587362i
$274$	−0.0150147	−	0.0851529i	−0.000907074	−	0.00514427i
$275$	11.1236	+	4.04866i	0.670779	+	0.244144i
$276$	7.13816	−	4.12122i	0.429666	−	0.248068i
$277$	1.14842	−	6.51303i	0.0690020	−	0.391330i	−0.930673	−	0.365851i	$-0.880778\pi$
$277$	1.14842	−	6.51303i	0.0690020	−	0.391330i	0.999675	−	0.0254787i	$-0.00811100\pi$
$278$	−9.18139	+	15.9026i	−0.550663	+	0.953776i
$279$	−7.56283	−	13.0992i	−0.452775	−	0.784229i
$280$	−0.0812519	−	0.140732i	−0.00485573	−	0.00841037i
$281$	−27.9320	+	10.1664i	−1.66628	+	0.606478i	−0.991332	−	0.131384i	$-0.958058\pi$
$281$	−27.9320	+	10.1664i	−1.66628	+	0.606478i	−0.674952	+	0.737861i	$0.735836\pi$
$282$	0.860967	−	1.02606i	0.0512698	−	0.0611010i
$283$	−2.15657	+	1.80958i	−0.128195	+	0.107568i	−0.704631	−	0.709574i	$-0.748887\pi$
$283$	−2.15657	+	1.80958i	−0.128195	+	0.107568i	0.576436	+	0.817142i	$0.304443\pi$
$284$	4.40033	−	3.69232i	0.261112	−	0.219099i
$285$	−8.88191	+	10.5850i	−0.526119	+	0.627004i
$286$	−21.1805	+	7.70908i	−1.25243	+	0.455847i
$287$	0.349823	+	0.605910i	0.0206494	+	0.0357658i
$288$	3.00000			0.176777
$289$	−4.86571	+	8.42767i	−0.286219	+	0.495745i
$290$	−1.39053	+	7.88609i	−0.0816547	+	0.463087i
$291$	5.13903	−	2.96702i	0.301255	−	0.173930i
$292$	−9.79086	−	3.56358i	−0.572967	−	0.208543i
$293$	1.70796	+	9.68631i	0.0997800	+	0.565881i	0.993177	+	0.116613i	$0.0372038\pi$
$293$	1.70796	+	9.68631i	0.0997800	+	0.565881i	−0.893397	+	0.449267i	$0.851685\pi$
$294$	−7.77719	−	9.26849i	−0.453575	−	0.540549i
$295$	−1.53802	−	1.29055i	−0.0895469	−	0.0751388i
$296$	−0.290859			−0.0169059
$297$	−12.4145	+	14.7950i	−0.720360	+	0.858492i
$298$	4.90167			0.283946
$299$	22.1065	+	18.5496i	1.27845	+	1.07275i
$300$	1.88666	−	5.18355i	0.108926	−	0.299273i
$301$	−0.00949548	−	0.0538515i	−0.000547310	−	0.00310395i
$302$	1.62701	+	0.592184i	0.0936240	+	0.0340763i
$303$		−	14.9278i		−	0.857578i
$304$	−1.02822	+	5.83132i	−0.0589724	+	0.334449i
$305$	2.54710	−	4.41171i	0.145847	−	0.252614i
$306$	−2.69341	−	15.2751i	−0.153972	−	0.873219i
$307$	−6.78106	−	11.7451i	−0.387015	−	0.670330i	0.605031	−	0.796202i	$-0.293161\pi$
$307$	−6.78106	−	11.7451i	−0.387015	−	0.670330i	−0.992047	+	0.125871i	$0.959827\pi$
$308$	0.421274	−	0.153331i	0.0240043	−	0.00873686i
$309$	3.72668	+	0.657115i	0.212004	+	0.0373819i
$310$	5.20368	−	4.36640i	0.295549	−	0.247995i
$311$	−8.10220	+	6.79855i	−0.459433	+	0.385510i	−0.842922	−	0.538035i	$-0.819167\pi$
$311$	−8.10220	+	6.79855i	−0.459433	+	0.385510i	0.383489	+	0.923545i	$0.374722\pi$
$312$	3.59240	+	9.87003i	0.203379	+	0.558780i
$313$	10.0544	−	3.65949i	0.568307	−	0.206847i	−0.0418547	−	0.999124i	$-0.513327\pi$
$313$	10.0544	−	3.65949i	0.568307	−	0.206847i	0.610162	+	0.792277i	$0.291104\pi$
$314$	−2.90760	−	5.03612i	−0.164086	−	0.284205i
$315$	0.0846555	−	0.480105i	0.00476980	−	0.0270509i
$316$	−6.99660	+	12.1185i	−0.393589	+	0.681717i
$317$	5.06717	−	28.7374i	0.284601	−	1.61405i	−0.422108	−	0.906546i	$-0.638710\pi$
$317$	5.06717	−	28.7374i	0.284601	−	1.61405i	0.706708	−	0.707505i	$-0.250179\pi$
$318$	10.9363	+	6.31407i	0.613277	+	0.354075i
$319$	−20.7592	−	7.55574i	−1.16229	−	0.423040i
$320$	0.233956	+	1.32683i	0.0130785	+	0.0741719i
$321$	−17.5535	+	3.09516i	−0.979741	+	0.172755i
$322$	−0.439693	−	0.368946i	−0.0245031	−	0.0205606i
$323$	30.6144			1.70343
$324$	6.89440	+	5.78509i	0.383022	+	0.321394i
$325$	19.3131			1.07130
$326$	2.07532	+	1.74140i	0.114941	+	0.0964473i
$327$	−18.9192	+	3.33597i	−1.04623	+	0.184479i
$328$	−1.00727	−	5.71253i	−0.0556174	−	0.315422i
$329$	−0.0876485	−	0.0319015i	−0.00483222	−	0.00175878i
$330$	−7.51161	−	4.33683i	−0.413501	−	0.238735i
$331$	−1.26739	+	7.18772i	−0.0696620	+	0.395073i	0.929962	+	0.367655i	$0.119839\pi$
$331$	−1.26739	+	7.18772i	−0.0696620	+	0.395073i	−0.999624	+	0.0274173i	$0.991272\pi$
$332$	1.18479	−	2.05212i	0.0650239	−	0.112625i
$333$	−0.668434	−	0.560882i	−0.0366299	−	0.0307362i
$334$	−12.3020	−	21.3077i	−0.673136	−	1.16591i
$335$	8.40420	−	3.05888i	0.459171	−	0.167124i
$336$	−0.0714517	−	0.196312i	−0.00389801	−	0.0107097i
$337$	−1.24376	+	1.04363i	−0.0677517	+	0.0568504i	−0.676035	−	0.736870i	$-0.736303\pi$
$337$	−1.24376	+	1.04363i	−0.0677517	+	0.0568504i	0.608283	+	0.793720i	$0.291859\pi$
$338$	−18.2121	+	15.2818i	−0.990609	+	0.831220i
$339$	−10.1047	−	1.78174i	−0.548813	−	0.0967706i
$340$	6.54576	−	2.38246i	0.354994	−	0.129207i
$341$	9.37005	+	16.2294i	0.507417	+	0.878872i
$342$	−13.6079	+	11.4184i	−0.735830	+	0.617434i
$343$	−0.843426	+	1.46086i	−0.0455407	+	0.0788788i
$344$	−0.0787257	+	0.446476i	−0.00424460	+	0.0240724i
$345$			11.1050i			0.597873i
$346$	−10.0753	−	3.66712i	−0.541653	−	0.197145i
$347$	−0.949655	−	5.38576i	−0.0509801	−	0.289123i	0.948650	−	0.316329i	$-0.102450\pi$
$347$	−0.949655	−	5.38576i	−0.0509801	−	0.289123i	−0.999630	+	0.0272057i	$0.991339\pi$
$348$	−3.52094	+	9.67372i	−0.188742	+	0.518566i
$349$	2.37346	+	1.99157i	0.127048	+	0.106606i	0.704098	−	0.710103i	$-0.251352\pi$
$349$	2.37346	+	1.99157i	0.127048	+	0.106606i	−0.577050	+	0.816709i	$0.695796\pi$
$350$	−0.384133			−0.0205328
$351$	−10.7772	+	29.6101i	−0.575244	+	1.58047i
$352$	−3.71688			−0.198110
$353$	0.233956	+	0.196312i	0.0124522	+	0.0104486i	0.648992	−	0.760795i	$-0.275191\pi$
$353$	0.233956	+	0.196312i	0.0124522	+	0.0104486i	−0.636540	+	0.771243i	$0.719635\pi$
$354$	−1.65910	−	1.97724i	−0.0881802	−	0.105089i
$355$	1.34389	+	7.62159i	0.0713264	+	0.404512i
$356$	2.03936	+	0.742267i	0.108086	+	0.0393401i
$357$	−0.935412	+	0.540060i	−0.0495072	+	0.0285830i
$358$	2.40420	−	13.6349i	0.127066	−	0.720627i
$359$	−5.28493	+	9.15377i	−0.278928	+	0.483117i	−0.971119	−	0.238597i	$-0.923312\pi$
$359$	−5.28493	+	9.15377i	−0.278928	+	0.483117i	0.692191	+	0.721715i	$0.256646\pi$
$360$	−2.02094	+	3.50038i	−0.106513	+	0.184486i
$361$	−8.03074	−	13.9097i	−0.422671	−	0.732087i
$362$	3.29813	−	1.20042i	0.173346	−	0.0630928i
$363$	3.13429	−	3.73530i	0.164507	−	0.196052i
$364$	0.560307	−	0.470154i	0.0293681	−	0.0246428i
$365$	10.7536	−	9.02330i	0.562867	−	0.472301i
$366$	4.20961	−	5.01681i	0.220040	−	0.262233i
$367$	−2.51842	+	0.916629i	−0.131460	+	0.0478477i	−0.406913	−	0.913467i	$-0.633395\pi$
$367$	−2.51842	+	0.916629i	−0.131460	+	0.0478477i	0.275452	+	0.961315i	$0.411172\pi$
$368$	2.37939	+	4.12122i	0.124034	+	0.214833i
$369$	8.70099	−	15.0706i	0.452955	−	0.784542i
$370$	0.195937	−	0.339373i	0.0101863	−	0.0176431i
$371$	0.152704	−	0.866025i	0.00792798	−	0.0449618i
$372$	7.56283	−	4.36640i	0.392115	−	0.226388i
$373$	−22.9008	−	8.33521i	−1.18576	−	0.431581i	−0.327526	−	0.944842i	$-0.606215\pi$
$373$	−22.9008	−	8.33521i	−1.18576	−	0.431581i	−0.858232	+	0.513261i	$0.828437\pi$
$374$	3.33703	+	18.9252i	0.172554	+	0.978601i
$375$	12.2772	+	14.6314i	0.633991	+	0.755561i
$376$	0.592396	+	0.497079i	0.0305505	+	0.0256349i
$377$	−36.0428			−1.85630
$378$	0.214355	−	0.588936i	0.0110252	−	0.0302916i
$379$	−4.08647			−0.209908			−0.104954	−	0.994477i	$-0.533469\pi$
$379$	−4.08647			−0.209908			−0.104954	+	0.994477i	$0.533469\pi$
$380$	−6.11128	−	5.12797i	−0.313502	−	0.263060i
$381$	3.39986	−	9.34105i	0.174180	−	0.478556i
$382$	3.80154	+	21.5596i	0.194504	+	1.10308i
$383$	15.4017	+	5.60575i	0.786989	+	0.286440i	0.704084	−	0.710117i	$-0.251358\pi$
$383$	15.4017	+	5.60575i	0.786989	+	0.286440i	0.0829050	+	0.996557i	$0.473580\pi$
$384$			1.73205i			0.0883883i
$385$	−0.104885	+	0.594831i	−0.00534542	+	0.0303154i
$386$	12.8059	−	22.1804i	0.651802	−	1.12895i
$387$	−1.04189	+	0.874249i	−0.0529622	+	0.0444406i
$388$	1.71301	+	2.96702i	0.0869650	+	0.150628i
$389$	26.2263	−	9.54558i	1.32972	−	0.483980i	0.423163	−	0.906054i	$-0.360920\pi$
$389$	26.2263	−	9.54558i	1.32972	−	0.483980i	0.906562	+	0.422073i	$0.138698\pi$
$390$	−13.9363	−	2.45734i	−0.705691	−	0.124432i
$391$	18.8478	−	15.8152i	0.953172	−	0.799807i
$392$	5.35117	−	4.49016i	0.270275	−	0.226787i
$393$	10.2010	+	28.0270i	0.514572	+	1.41377i
$394$	12.8598	−	4.68058i	0.647867	−	0.235804i
$395$	−9.42649	−	16.3272i	−0.474298	−	0.821508i
$396$	−8.54189	−	7.16750i	−0.429246	−	0.360180i
$397$	16.2469	−	28.1405i	0.815409	−	1.41233i	−0.0936247	−	0.995608i	$-0.529845\pi$
$397$	16.2469	−	28.1405i	0.815409	−	1.41233i	0.909034	−	0.416722i	$-0.136821\pi$
$398$	2.15317	−	12.2112i	0.107929	−	0.612094i
$399$	1.07129	+	0.618509i	0.0536316	+	0.0309642i
$400$	2.99273	+	1.08926i	0.149636	+	0.0544632i
$401$	2.67096	+	15.1478i	0.133381	+	0.756443i	0.975973	+	0.217891i	$0.0699176\pi$
$401$	2.67096	+	15.1478i	0.133381	+	0.756443i	−0.842592	+	0.538553i	$0.818971\pi$
$402$	11.3229	−	1.99654i	0.564737	−	0.0995784i
$403$	23.4217	+	19.6532i	1.16672	+	0.978994i
$404$	8.61856			0.428789
$405$	−11.3944	+	4.14722i	−0.566192	+	0.206077i
$406$	0.716881			0.0355782
$407$	0.828163	+	0.694911i	0.0410505	+	0.0344455i
$408$	8.81908	−	1.55504i	0.436609	−	0.0769860i
$409$	−1.65822	−	9.40425i	−0.0819938	−	0.465010i	−0.997965	−	0.0637658i	$-0.979689\pi$
$409$	−1.65822	−	9.40425i	−0.0819938	−	0.465010i	0.915971	−	0.401244i	$-0.131422\pi$
$410$	7.34389	+	2.67296i	0.362689	+	0.132008i
$411$	0.129700	+	0.0748822i	0.00639762	+	0.00369366i
$412$	−0.379385	+	2.15160i	−0.0186910	+	0.106002i
$413$	−0.0898700	+	0.155659i	−0.00442222	+	0.00765950i
$414$	−2.47906	+	14.0594i	−0.121839	+	0.690983i
$415$	1.59627	+	2.76481i	0.0783576	+	0.135719i
$416$	−5.69846	+	2.07407i	−0.279390	+	0.101690i
$417$	−10.8780	−	29.8872i	−0.532700	−	1.46358i
$418$	16.8596	−	14.1469i	0.824631	−	0.691948i
$419$	−26.0239	+	21.8367i	−1.27135	+	1.06679i	−0.276977	+	0.960876i	$0.589333\pi$
$419$	−26.0239	+	21.8367i	−1.27135	+	1.06679i	−0.994375	+	0.105915i	$0.966223\pi$
$420$	0.277189	+	0.0488759i	0.0135254	+	0.00238490i
$421$	11.8229	−	4.30320i	0.576215	−	0.209725i	−0.0374406	−	0.999299i	$-0.511920\pi$
$421$	11.8229	−	4.30320i	0.576215	−	0.209725i	0.613656	+	0.789574i	$0.289698\pi$
$422$	7.42127	+	12.8540i	0.361262	+	0.625724i
$423$	0.402856	+	2.28471i	0.0195875	+	0.111086i
$424$	−3.64543	+	6.31407i	−0.177038	+	0.306638i
$425$	2.85932	−	16.2160i	0.138697	−	0.786591i
$426$			9.94929i			0.482044i
$427$	−0.428548	−	0.155979i	−0.0207389	−	0.00754834i
$428$	−1.78699	−	10.1345i	−0.0863774	−	0.489870i
$429$	13.3525	−	36.6857i	0.644665	−	1.77120i
$430$	−0.467911	−	0.392624i	−0.0225647	−	0.0189340i
$431$	−7.77601			−0.374557			−0.187279	−	0.982307i	$-0.559967\pi$
$431$	−7.77601			−0.374557			−0.187279	+	0.982307i	$0.559967\pi$
$432$	−3.34002	+	3.98048i	−0.160697	+	0.191511i
$433$	−40.6536			−1.95369			−0.976845	−	0.213950i	$-0.931367\pi$
$433$	−40.6536			−1.95369			−0.976845	+	0.213950i	$0.931367\pi$
$434$	−0.465852	−	0.390896i	−0.0223616	−	0.0187636i
$435$	−8.91534	−	10.6249i	−0.427458	−	0.509425i
$436$	−1.92602	−	10.9230i	−0.0922397	−	0.523117i
$437$	−26.4786	−	9.63744i	−1.26665	−	0.461021i
$438$	15.6288	−	9.02330i	0.746774	−	0.431150i
$439$	−3.07280	+	17.4267i	−0.146657	+	0.831731i	0.819366	+	0.573271i	$0.194326\pi$
$439$	−3.07280	+	17.4267i	−0.146657	+	0.831731i	−0.966022	+	0.258459i	$0.916785\pi$
$440$	2.50387	−	4.33683i	0.119367	−	0.206750i
$441$	20.9564			0.997922
$442$	15.6766	+	27.1527i	0.745662	+	1.29152i
$443$	−13.5086	+	4.91673i	−0.641814	+	0.233601i	−0.642365	−	0.766399i	$-0.722047\pi$
$443$	−13.5086	+	4.91673i	−0.641814	+	0.233601i	0.000551343		1.00000i	$0.499825\pi$
$444$	0.323826	−	0.385920i	0.0153681	−	0.0183150i
$445$	−2.23989	+	1.87949i	−0.106181	+	0.0890962i
$446$	5.15657	−	4.32688i	0.244171	−	0.204884i
$447$	−5.45723	+	6.50368i	−0.258118	+	0.307613i
$448$	0.113341	−	0.0412527i	0.00535485	−	0.00194901i
$449$	−13.9859	−	24.2243i	−0.660036	−	1.14322i	−0.980606	−	0.195991i	$-0.937208\pi$
$449$	−13.9859	−	24.2243i	−0.660036	−	1.14322i	0.320569	−	0.947225i	$-0.396126\pi$
$450$	4.77719	+	8.27433i	0.225199	+	0.390056i
$451$	−10.7802	+	18.6718i	−0.507619	+	0.879222i
$452$	1.02869	−	5.83396i	0.0483853	−	0.274407i
$453$	−2.59714	+	1.49946i	−0.122024	+	0.0704509i
$454$	13.6211	+	4.95767i	0.639269	+	0.232675i
$455$	0.171122	+	0.970481i	0.00802232	+	0.0454968i
$456$	−6.59240	−	7.85651i	−0.308717	−	0.367915i
$457$	6.53280	+	5.48167i	0.305592	+	0.256422i	0.782667	−	0.622440i	$-0.213859\pi$
$457$	6.53280	+	5.48167i	0.305592	+	0.256422i	−0.477075	+	0.878862i	$0.658303\pi$
$458$	−25.7870			−1.20495
$459$	23.2661	+	13.4327i	1.08597	+	0.626984i
$460$	−6.41147			−0.298937
$461$	16.6361	+	13.9593i	0.774820	+	0.650151i	0.941938	−	0.335785i	$-0.109002\pi$
$461$	16.6361	+	13.9593i	0.774820	+	0.650151i	−0.167118	+	0.985937i	$0.553446\pi$
$462$	−0.265578	+	0.729669i	−0.0123558	+	0.0339473i
$463$	−3.43882	−	19.5025i	−0.159815	−	0.906358i	−0.954250	−	0.299009i	$-0.903344\pi$
$463$	−3.43882	−	19.5025i	−0.159815	−	0.906358i	0.794435	−	0.607349i	$-0.207767\pi$
$464$	−5.58512	−	2.03282i	−0.259283	−	0.0943712i
$465$			11.7657i			0.545620i
$466$	−1.80541	+	10.2390i	−0.0836339	+	0.474311i
$467$	−18.4927	+	32.0303i	−0.855741	+	1.48219i	0.0202143	+	0.999796i	$0.493565\pi$
$467$	−18.4927	+	32.0303i	−0.855741	+	1.48219i	−0.875956	+	0.482392i	$0.839768\pi$
$468$	−17.0954	−	6.22221i	−0.790235	−	0.287622i
$469$	−0.400330	−	0.693392i	−0.0184855	−	0.0320178i
$470$	−0.979055	+	0.356347i	−0.0451605	+	0.0164371i
$471$	9.91921	+	1.74903i	0.457053	+	0.0805908i
$472$	1.14156	−	0.957882i	0.0525445	−	0.0440901i
$473$	1.29086	−	1.08316i	0.0593538	−	0.0498037i
$474$	−8.28952	−	22.7753i	−0.380750	−	1.04610i
$475$	−17.7208	+	6.44983i	−0.813084	+	0.295938i
$476$	−0.311804	−	0.540060i	−0.0142915	−	0.0247536i
$477$	−20.5535	+	7.48086i	−0.941080	+	0.342525i
$478$	−11.4572	+	19.8445i	−0.524042	+	0.907667i
$479$	−1.97131	+	11.1799i	−0.0900717	+	0.510822i	0.906075	+	0.423117i	$0.139064\pi$
$479$	−1.97131	+	11.1799i	−0.0900717	+	0.510822i	−0.996147	+	0.0877044i	$0.972047\pi$
$480$	−2.02094	−	1.16679i	−0.0922431	−	0.0532566i
$481$	1.65745	+	0.603263i	0.0755733	+	0.0275064i
$482$	2.09714	+	11.8935i	0.0955223	+	0.541734i
$483$	0.979055	−	0.172634i	0.0445486	−	0.00785511i
$484$	2.15657	+	1.80958i	0.0980261	+	0.0822537i
$485$	−4.61587			−0.209596
$486$	−15.3516	+	2.70691i	−0.696364	+	0.122788i
$487$	1.13785			0.0515610			0.0257805	−	0.999668i	$-0.491793\pi$
$487$	1.13785			0.0515610			0.0257805	+	0.999668i	$0.491793\pi$
$488$	2.89646	+	2.43042i	0.131117	+	0.110020i
$489$	−4.62108	+	0.814821i	−0.208973	+	0.0368475i
$490$	1.63429	+	9.26849i	0.0738295	+	0.418708i
$491$	14.3880	+	5.23680i	0.649322	+	0.236334i	0.645619	−	0.763659i	$-0.276599\pi$
$491$	14.3880	+	5.23680i	0.649322	+	0.236334i	0.00370223	+	0.999993i	$0.498822\pi$
$492$	8.70099	+	5.02352i	0.392271	+	0.226478i
$493$	−5.33615	+	30.2628i	−0.240328	+	1.36297i
$494$	17.9538	−	31.0969i	0.807781	−	1.39912i
$495$	14.1172	−	5.13824i	0.634521	−	0.230947i
$496$	2.52094	+	4.36640i	0.113194	+	0.196057i
$497$	0.651055	−	0.236965i	0.0292038	−	0.0106293i
$498$	1.40373	+	3.85673i	0.0629028	+	0.172824i
$499$	1.77584	−	1.49011i	0.0794977	−	0.0667065i	−0.602173	−	0.798366i	$-0.705698\pi$
$499$	1.77584	−	1.49011i	0.0794977	−	0.0667065i	0.681671	+	0.731659i	$0.261254\pi$
$500$	−8.44743	+	7.08824i	−0.377781	+	0.316996i
$501$	41.9680	+	7.40008i	1.87499	+	0.330611i
$502$	−13.1998	+	4.80434i	−0.589136	+	0.214428i
$503$	−4.02869	−	6.97789i	−0.179630	−	0.311129i	0.762124	−	0.647431i	$-0.224157\pi$
$503$	−4.02869	−	6.97789i	−0.179630	−	0.311129i	−0.941754	+	0.336303i	$0.890823\pi$
$504$	0.340022	+	0.123758i	0.0151458	+	0.00551262i
$505$	−5.80587	+	10.0561i	−0.258358	+	0.447489i
$506$	3.07145	−	17.4191i	0.136543	−	0.774372i
$507$		−	41.1782i		−	1.82879i
$508$	5.39306	+	1.96291i	0.239278	+	0.0870901i
$509$	1.24944	+	7.08591i	0.0553803	+	0.314077i	0.999896	−	0.0143875i	$-0.00457984\pi$
$509$	1.24944	+	7.08591i	0.0553803	+	0.314077i	−0.944516	+	0.328465i	$0.893469\pi$
$510$	−4.12654	+	11.3376i	−0.182726	+	0.502037i
$511$	−0.962697	−	0.807798i	−0.0425872	−	0.0357349i
$512$	−1.00000			−0.0441942
$513$		−	30.7678i		−	1.35843i
$514$	−18.1429			−0.800249
$515$	−2.25490	−	1.89209i	−0.0993628	−	0.0833753i
$516$	−0.504748	−	0.601535i	−0.0222203	−	0.0264811i
$517$	−0.499123	−	2.83067i	−0.0219514	−	0.124493i
$518$	−0.0329662	−	0.0119987i	−0.00144845	−	0.000527194i
$519$	16.0829	−	9.28547i	0.705961	−	0.407587i
$520$	1.41875	−	8.04612i	0.0622162	−	0.352846i
$521$	−4.84343	+	8.38906i	−0.212194	+	0.367531i	−0.952401	−	0.304848i	$-0.901394\pi$
$521$	−4.84343	+	8.38906i	−0.212194	+	0.367531i	0.740207	+	0.672379i	$0.234728\pi$
$522$	−8.91534	−	15.4418i	−0.390214	−	0.675871i
$523$	−7.29339	−	12.6325i	−0.318917	−	0.552381i	0.661345	−	0.750082i	$-0.269986\pi$
$523$	−7.29339	−	12.6325i	−0.318917	−	0.552381i	−0.980262	+	0.197701i	$0.936653\pi$
$524$	−16.1814	+	5.88954i	−0.706887	+	0.257286i
$525$	0.427671	−	0.509678i	0.0186651	−	0.0222442i
$526$	−3.27379	+	2.74703i	−0.142744	+	0.119776i
$527$	19.9691	−	16.7561i	0.869867	−	0.729905i
$528$	4.13816	−	4.93166i	0.180090	−	0.214623i
$529$	0.332748	−	0.121111i	0.0144673	−	0.00526568i
$530$	−4.91147	−	8.50692i	−0.213341	−	0.369517i
$531$	4.47060			0.194007
$532$	−0.357097	+	0.618509i	−0.0154821	+	0.0268158i
$533$	−6.10829	+	34.6418i	−0.264579	+	1.50050i
$534$	−3.25537	+	1.87949i	−0.140874	+	0.0813334i
$535$	13.0287	+	4.74205i	0.563279	+	0.205017i
$536$	1.15270	+	6.53731i	0.0497892	+	0.282369i
$537$	15.4145	+	18.3702i	0.665183	+	0.792735i
$538$	−10.0057	−	8.39576i	−0.431376	−	0.361967i
$539$	−25.9641			−1.11835
$540$	−2.39440	−	6.57856i	−0.103039	−	0.283096i
$541$	23.9786			1.03092			0.515461	−	0.856913i	$-0.327621\pi$
$541$	23.9786			1.03092			0.515461	+	0.856913i	$0.327621\pi$
$542$	−6.50181	−	5.45567i	−0.279277	−	0.234341i
$543$	−2.07919	+	5.71253i	−0.0892267	+	0.245148i
$544$	0.897804	+	5.09170i	0.0384930	+	0.218305i
$545$	14.0424	+	5.11100i	0.601508	+	0.218931i
$546$			1.26687i			0.0542171i
$547$	6.94269	−	39.3739i	0.296848	−	1.68351i	−0.362748	−	0.931887i	$-0.618161\pi$
$547$	6.94269	−	39.3739i	0.296848	−	1.68351i	0.659596	−	0.751620i	$-0.270727\pi$
$548$	−0.0432332	+	0.0748822i	−0.00184683	+	0.00319881i
$549$	1.96972	+	11.1708i	0.0840657	+	0.476760i
$550$	−5.91875	−	10.2516i	−0.252376	−	0.437129i
$551$	33.0710	−	12.0369i	1.40887	−	0.512788i
$552$	−8.11721	−	1.43128i	−0.345491	−	0.0609195i
$553$	−1.29292	+	1.08489i	−0.0549805	+	0.0461341i
$554$	−5.06624	+	4.25108i	−0.215244	+	0.180611i
$555$	0.232145	+	0.637812i	0.00985399	+	0.0270736i
$556$	17.2554	−	6.28044i	0.731791	−	0.266350i
$557$	−1.17958	−	2.04309i	−0.0499803	−	0.0865685i	0.839953	−	0.542659i	$-0.182583\pi$
$557$	−1.17958	−	2.04309i	−0.0499803	−	0.0865685i	−0.889933	+	0.456091i	$0.849249\pi$
$558$	−2.62654	+	14.8959i	−0.111190	+	0.630593i
$559$	1.37464	−	2.38094i	0.0581410	−	0.100703i
$560$	−0.0282185	+	0.160035i	−0.00119245	+	0.00676271i
$561$	−28.8258	−	16.6426i	−1.21703	−	0.702650i
$562$	27.9320	+	10.1664i	1.17824	+	0.428845i
$563$	−7.55825	−	42.8650i	−0.318542	−	1.80654i	−0.551632	−	0.834087i	$-0.685995\pi$
$563$	−7.55825	−	42.8650i	−0.318542	−	1.80654i	0.233090	−	0.972455i	$-0.425116\pi$
$564$	−1.31908	+	0.232589i	−0.0555432	+	0.00979376i
$565$	6.11406	+	5.13030i	0.257220	+	0.215833i
$566$	2.81521			0.118332
$567$	0.542766	+	0.940099i	0.0227940	+	0.0394804i
$568$	−5.74422			−0.241022
$569$	11.2187	+	9.41360i	0.470312	+	0.394639i	0.846908	−	0.531739i	$-0.178461\pi$
$569$	11.2187	+	9.41360i	0.470312	+	0.394639i	−0.376596	+	0.926377i	$0.622906\pi$
$570$	13.6079	−	2.39944i	0.569971	−	0.100501i
$571$	−2.57145	−	14.5834i	−0.107612	−	0.610297i	−0.990145	−	0.140047i	$-0.955275\pi$
$571$	−2.57145	−	14.5834i	−0.107612	−	0.610297i	0.882533	−	0.470251i	$-0.155836\pi$
$572$	21.1805	+	7.70908i	0.885602	+	0.322333i
$573$	−32.8383	−	18.9592i	−1.37184	−	0.792031i
$574$	0.121492	−	0.689016i	0.00507098	−	0.0287590i
$575$	−7.57785	+	13.1252i	−0.316018	+	0.547359i
$576$	−2.29813	−	1.92836i	−0.0957556	−	0.0803485i
$577$	16.0706	+	27.8351i	0.669027	+	1.15879i	0.978177	+	0.207775i	$0.0666222\pi$
$577$	16.0706	+	27.8351i	0.669027	+	1.15879i	−0.309150	+	0.951013i	$0.600044\pi$
$578$	9.14455	−	3.32834i	0.380363	−	0.138441i
$579$	15.1723	+	41.6856i	0.630539	+	1.73239i
$580$	6.13429	−	5.14728i	0.254712	−	0.213729i
$581$	0.218941	−	0.183713i	0.00908320	−	0.00762171i
$582$	−5.84389	−	1.03044i	−0.242237	−	0.0427129i
$583$	25.4650	−	9.26849i	1.05465	−	0.383862i
$584$	5.20961	+	9.02330i	0.215575	+	0.373387i
$585$	18.7763	−	15.7552i	0.776305	−	0.651397i
$586$	4.91787	−	8.51800i	0.203155	−	0.351875i
$587$	4.75918	−	26.9907i	0.196432	−	1.11402i	−0.713932	−	0.700215i	$-0.753087\pi$
$587$	4.75918	−	26.9907i	0.196432	−	1.11402i	0.910364	−	0.413808i	$-0.135802\pi$
$588$			12.0992i			0.498961i
$589$	−28.0540	−	10.2108i	−1.15594	−	0.420729i
$590$	0.348641	+	1.97724i	0.0143533	+	0.0814016i
$591$	−8.10700	+	22.2738i	−0.333477	+	0.916222i
$592$	0.222811	+	0.186961i	0.00915748	+	0.00768404i
$593$	36.2377			1.48810			0.744052	−	0.668121i	$-0.232901\pi$
$593$	36.2377			1.48810			0.744052	+	0.668121i	$0.232901\pi$
$594$	19.0201	−	3.35375i	0.780403	−	0.137606i
$595$	0.840185			0.0344442
$596$	−3.75490	−	3.15074i	−0.153807	−	0.129059i
$597$	13.8050	+	16.4522i	0.565001	+	0.673342i
$598$	−5.01114	−	28.4196i	−0.204921	−	1.16216i
$599$	−43.2438	−	15.7395i	−1.76689	−	0.643097i	−0.999999	−	0.00132449i	$-0.999578\pi$
$599$	−43.2438	−	15.7395i	−1.76689	−	0.643097i	−0.766895	−	0.641772i	$-0.778199\pi$
$600$	−4.77719	+	2.75811i	−0.195028	+	0.112599i
$601$	0.294673	−	1.67118i	0.0120200	−	0.0681687i	−0.978208	−	0.207628i	$-0.933425\pi$
$601$	0.294673	−	1.67118i	0.0120200	−	0.0681687i	0.990228	+	0.139460i	$0.0445366\pi$
$602$	−0.0273411	+	0.0473563i	−0.00111434	+	0.00193010i
$603$	−9.95723	+	17.2464i	−0.405490	+	0.702329i
$604$	−0.865715	−	1.49946i	−0.0352254	−	0.0610122i
$605$	−3.56418	+	1.29725i	−0.144904	+	0.0527409i
$606$	−9.59539	+	11.4353i	−0.389786	+	0.464529i
$607$	−10.7779	+	9.04374i	−0.437462	+	0.367074i	−0.834758	−	0.550616i	$-0.814393\pi$
$607$	−10.7779	+	9.04374i	−0.437462	+	0.367074i	0.397297	+	0.917690i	$0.369948\pi$
$608$	4.53596	−	3.80612i	0.183957	−	0.154359i
$609$	−0.798133	+	0.951178i	−0.0323420	+	0.0385437i
$610$	−4.78699	+	1.74232i	−0.193820	+	0.0705445i
$611$	−2.34477	−	4.06126i	−0.0948592	−	0.164301i
$612$	−7.75537	+	13.4327i	−0.313492	+	0.542984i
$613$	12.8314	−	22.2246i	0.518256	−	0.897645i	−0.481520	−	0.876435i	$-0.659915\pi$
$613$	12.8314	−	22.2246i	0.518256	−	0.897645i	0.999775	−	0.0212096i	$-0.00675172\pi$
$614$	−2.35504	+	13.3561i	−0.0950416	+	0.539007i
$615$	−11.7228	+	6.76817i	−0.472709	+	0.272919i
$616$	−0.421274	−	0.153331i	−0.0169736	−	0.00617789i
$617$	5.46822	+	31.0118i	0.220142	+	1.24849i	0.871757	+	0.489938i	$0.162981\pi$
$617$	5.46822	+	31.0118i	0.220142	+	1.24849i	−0.651615	+	0.758550i	$0.725908\pi$
$618$	−2.43242	−	2.89884i	−0.0978462	−	0.116609i
$619$	−2.42674	−	2.03627i	−0.0975388	−	0.0818448i	0.592714	−	0.805413i	$-0.298056\pi$
$619$	−2.42674	−	2.03627i	−0.0975388	−	0.0818448i	−0.690253	+	0.723568i	$0.742501\pi$
$620$	−6.79292			−0.272810
$621$	−15.8944	−	18.9422i	−0.637820	−	0.760125i
$622$	10.5767			0.424086
$623$	0.200522	+	0.168258i	0.00803376	+	0.00674113i
$624$	3.59240	−	9.87003i	0.143811	−	0.395117i
$625$	0.185259	+	1.05066i	0.00741037	+	0.0420263i
$626$	−10.0544	−	3.65949i	−0.401854	−	0.146263i
$627$			38.1201i			1.52237i
$628$	−1.00980	+	5.72686i	−0.0402954	+	0.228527i
$629$	0.751907	−	1.30234i	0.0299805	−	0.0519277i
$630$	−0.373455	+	0.313366i	−0.0148788	+	0.0124848i
$631$	−11.2961	−	19.5654i	−0.449690	−	0.778885i	0.548676	−	0.836035i	$-0.315132\pi$
$631$	−11.2961	−	19.5654i	−0.449690	−	0.778885i	−0.998366	+	0.0571498i	$0.981799\pi$
$632$	13.1493	−	4.78595i	0.523051	−	0.190375i
$633$	−25.3175	−	4.46416i	−1.00628	−	0.177434i
$634$	−22.3537	+	18.7570i	−0.887779	+	0.744935i
$635$	−5.92333	+	4.97027i	−0.235060	+	0.197239i
$636$	−4.31908	−	11.8666i	−0.171263	−	0.470540i
$637$	−39.8063	+	14.4883i	−1.57718	+	0.574048i
$638$	11.0458	+	19.1318i	0.437306	+	0.757436i
$639$	−13.2010	−	11.0769i	−0.522223	−	0.438197i
$640$	0.673648	−	1.16679i	0.0266283	−	0.0461215i
$641$	−3.04323	+	17.2590i	−0.120200	+	0.681691i	0.863843	+	0.503761i	$0.168051\pi$
$641$	−3.04323	+	17.2590i	−0.120200	+	0.681691i	−0.984043	+	0.177929i	$0.943060\pi$
$642$	15.4363	+	8.91215i	0.609222	+	0.351734i
$643$	26.4923	+	9.64241i	1.04475	+	0.380260i	0.806681	−	0.590987i	$-0.201262\pi$
$643$	26.4923	+	9.64241i	1.04475	+	0.380260i	0.238074	+	0.971247i	$0.423484\pi$
$644$	0.0996702	+	0.565258i	0.00392756	+	0.0222743i
$645$	1.04189	−	0.183713i	0.0410243	−	0.00723370i
$646$	−23.4520	−	19.6786i	−0.922707	−	0.774243i
$647$	32.3492			1.27178			0.635888	−	0.771781i	$-0.280634\pi$
$647$	32.3492			1.27178			0.635888	+	0.771781i	$0.280634\pi$
$648$	−1.56283	−	8.86327i	−0.0613939	−	0.348182i
$649$	−5.53890			−0.217421
$650$	−14.7947	−	12.4143i	−0.580297	−	0.486927i
$651$	1.03730	−	0.182905i	0.0406551	−	0.00716860i
$652$	−0.470437	−	2.66798i	−0.0184237	−	0.104486i
$653$	25.9329	+	9.43880i	1.01483	+	0.369369i	0.795287	−	0.606234i	$-0.207320\pi$
$653$	25.9329	+	9.43880i	1.01483	+	0.369369i	0.219546	+	0.975602i	$0.429543\pi$
$654$	16.6373	+	9.60554i	0.650569	+	0.375606i
$655$	4.02869	−	22.8478i	0.157414	−	0.892738i
$656$	−2.90033	+	5.02352i	−0.113239	+	0.196135i
$657$	−5.42783	+	30.7828i	−0.211760	+	1.20095i
$658$	0.0466368	+	0.0807773i	0.00181809	+	0.00314903i
$659$	4.90508	−	1.78530i	0.191075	−	0.0695455i	−0.244711	−	0.969596i	$-0.578693\pi$
$659$	4.90508	−	1.78530i	0.191075	−	0.0695455i	0.435785	+	0.900051i	$0.356471\pi$
$660$	2.96657	+	8.15058i	0.115473	+	0.317261i
$661$	−36.7294	+	30.8196i	−1.42861	+	1.19875i	−0.482080	+	0.876127i	$0.660119\pi$
$661$	−36.7294	+	30.8196i	−1.42861	+	1.19875i	−0.946529	+	0.322618i	$0.895437\pi$
$662$	5.59105	−	4.69145i	0.217302	−	0.182338i
$663$	−53.4805	−	9.43005i	−2.07701	−	0.366233i
$664$	−2.22668	+	0.810446i	−0.0864120	+	0.0314514i
$665$	−0.481115	−	0.833315i	−0.0186568	−	0.0323146i
$666$	0.151522	+	0.859322i	0.00587134	+	0.0332980i
$667$	14.1420	−	24.4947i	0.547581	−	0.948439i
$668$	−4.27244	+	24.2302i	−0.165306	+	0.937495i
$669$			11.6592i			0.450770i
$670$	−8.40420	−	3.05888i	−0.324683	−	0.118175i
$671$	−2.44041	−	13.8402i	−0.0942109	−	0.534297i
$672$	−0.0714517	+	0.196312i	−0.00275631	+	0.00757290i
$673$	−8.51960	−	7.14879i	−0.328406	−	0.275566i	0.463644	−	0.886022i	$-0.346542\pi$
$673$	−8.51960	−	7.14879i	−0.328406	−	0.275566i	−0.792050	+	0.610456i	$0.790986\pi$
$674$	1.62361			0.0625390
$675$	−16.2973	−	2.87365i	−0.627282	−	0.110607i
$676$	23.7743			0.914394
$677$	−36.9550	−	31.0089i	−1.42030	−	1.19177i	−0.951181	−	0.308633i	$-0.900128\pi$
$677$	−36.9550	−	31.0089i	−1.42030	−	1.19177i	−0.469115	−	0.883137i	$-0.655427\pi$
$678$	6.59539	+	7.86008i	0.253294	+	0.301865i
$679$	0.0717564	+	0.406951i	0.00275376	+	0.0156173i
$680$	−6.54576	−	2.38246i	−0.251018	−	0.0913632i
$681$	−21.7429	+	12.5533i	−0.833189	+	0.481042i
$682$	3.25418	−	18.4554i	0.124609	−	0.706694i
$683$	−6.60401	+	11.4385i	−0.252695	+	0.437681i	−0.964267	−	0.264932i	$-0.914650\pi$
$683$	−6.60401	+	11.4385i	−0.252695	+	0.437681i	0.711572	+	0.702614i	$0.247984\pi$
$684$	17.7638			0.679217
$685$	−0.0582480	−	0.100888i	−0.00222554	−	0.00385475i
$686$	1.58512	−	0.576937i	0.0605203	−	0.0220276i
$687$	28.7098	−	34.2150i	1.09535	−	1.30538i
$688$	0.347296	−	0.291416i	0.0132405	−	0.0111101i
$689$	33.8692	−	28.4196i	1.29031	−	1.08270i
$690$	7.13816	−	8.50692i	0.271745	−	0.323853i
$691$	9.37211	−	3.41117i	0.356532	−	0.129767i	−0.157543	−	0.987512i	$-0.550357\pi$
$691$	9.37211	−	3.41117i	0.356532	−	0.129767i	0.514075	+	0.857745i	$0.328135\pi$
$692$	5.36097	+	9.28547i	0.203793	+	0.352980i
$693$	−0.672466	−	1.16475i	−0.0255449	−	0.0442450i
$694$	−2.73442	+	4.73616i	−0.103797	+	0.179782i
$695$	−4.29607	+	24.3642i	−0.162959	+	0.924189i
$696$	8.91534	−	5.14728i	0.337935	−	0.195107i
$697$	28.1822	+	10.2575i	1.06748	+	0.388529i
$698$	−0.538019	−	3.05126i	−0.0203643	−	0.115492i
$699$	−11.5753	−	13.7949i	−0.437819	−	0.521772i
$700$	0.294263	+	0.246916i	0.0111221	+	0.00933254i
$701$	46.7588			1.76605			0.883027	−	0.469322i	$-0.155502\pi$
$701$	46.7588			1.76605			0.883027	+	0.469322i	$0.155502\pi$
$702$	27.2888	−	15.7552i	1.02995	−	0.594642i
$703$	−1.72226			−0.0649562
$704$	2.84730	+	2.38917i	0.107312	+	0.0900451i
$705$	0.617211	−	1.69577i	0.0232455	−	0.0638665i
$706$	−0.0530334	−	0.300767i	−0.00199594	−	0.0113195i
$707$	0.976834	+	0.355538i	0.0367376	+	0.0133714i
$708$			2.58110i			0.0970037i
$709$	−6.56907	+	37.2550i	−0.246707	+	1.39914i	0.569789	+	0.821791i	$0.307025\pi$
$709$	−6.56907	+	37.2550i	−0.246707	+	1.39914i	−0.816496	+	0.577351i	$0.804086\pi$
$710$	3.86959	−	6.70232i	0.145223	−	0.251534i
$711$	39.4479	+	14.3579i	1.47941	+	0.538462i
$712$	−1.08512	−	1.87949i	−0.0406667	−	0.0704368i
$713$	−22.5462	+	8.20616i	−0.844363	+	0.307323i
$714$	1.06371	+	0.187561i	0.0398084	+	0.00701929i
$715$	−23.2631	+	19.5201i	−0.869991	+	0.730009i
$716$	−10.6061	+	8.89955i	−0.396367	+	0.332592i
$717$	−13.5744	−	37.2955i	−0.506947	−	1.39283i
$718$	9.93242	−	3.61510i	0.370675	−	0.134915i
$719$	−1.65048	−	2.85872i	−0.0615526	−	0.106612i	0.833607	−	0.552358i	$-0.186272\pi$
$719$	−1.65048	−	2.85872i	−0.0615526	−	0.106612i	−0.895160	+	0.445746i	$0.852939\pi$
$720$	3.79813	−	1.38241i	0.141548	−	0.0515193i
$721$	−0.131759	+	0.228213i	−0.00490697	+	0.00849911i
$722$	−2.78905	+	15.8175i	−0.103798	+	0.588666i
$723$	−18.1155	−	10.4590i	−0.673721	−	0.388973i
$724$	−3.29813	−	1.20042i	−0.122574	−	0.0446133i
$725$	−3.28699	−	18.6414i	−0.122076	−	0.692326i
$726$	−4.80200	+	0.846723i	−0.178219	+	0.0314248i
$727$	−16.0548	−	13.4716i	−0.595441	−	0.499635i	0.294535	−	0.955641i	$-0.404835\pi$
$727$	−16.0548	−	13.4716i	−0.595441	−	0.499635i	−0.889977	+	0.456006i	$0.849280\pi$
$728$	−0.731429			−0.0271086
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−14.0378			−0.519561
$731$	−1.79561	−	1.50669i	−0.0664129	−	0.0557271i
$732$	−6.44949	+	1.13722i	−0.238380	+	0.0420328i
$733$	−3.11943	−	17.6912i	−0.115219	−	0.653439i	−0.986642	−	0.162906i	$-0.947913\pi$
$733$	−3.11943	−	17.6912i	−0.115219	−	0.653439i	0.871423	−	0.490533i	$-0.163198\pi$
$734$	2.51842	+	0.916629i	0.0929565	+	0.0338334i
$735$	−14.1172	−	8.15058i	−0.520721	−	0.300639i
$736$	0.826352	−	4.68647i	0.0304597	−	0.172746i
$737$	12.3366	−	21.3677i	0.454425	−	0.787088i
$738$	−16.3525	+	5.95183i	−0.601944	+	0.219090i
$739$	19.6630	+	34.0573i	0.723314	+	1.25282i	0.959664	+	0.281149i	$0.0907154\pi$
$739$	19.6630	+	34.0573i	0.723314	+	1.25282i	−0.236350	+	0.971668i	$0.575951\pi$
$740$	−0.368241	+	0.134029i	−0.0135368	+	0.00492699i
$741$	21.2716	+	58.4431i	0.781430	+	2.14696i
$742$	−0.673648	+	0.565258i	−0.0247304	+	0.0207513i
$743$	−35.7957	+	30.0361i	−1.31322	+	1.10192i	−0.325519	+	0.945535i	$0.605539\pi$
$743$	−35.7957	+	30.0361i	−1.31322	+	1.10192i	−0.987696	+	0.156383i	$0.950017\pi$
$744$	−8.60014	−	1.51644i	−0.315296	−	0.0555952i
$745$	6.20574	−	2.25870i	0.227361	−	0.0827525i
$746$	12.1853	+	21.1055i	0.446134	+	0.772727i
$747$	−6.68004	−	2.43134i	−0.244410	−	0.0889580i
$748$	9.60859	−	16.6426i	0.351325	−	0.608513i
$749$	0.215537	−	1.22237i	0.00787556	−	0.0446645i
$750$		−	19.0999i		−	0.697430i
$751$	31.3184	+	11.3990i	1.14282	+	0.415954i	0.842932	−	0.538020i	$-0.180827\pi$
$751$	31.3184	+	11.3990i	1.14282	+	0.415954i	0.299891	+	0.953973i	$0.403050\pi$
$752$	−0.134285	−	0.761570i	−0.00489688	−	0.0277716i
$753$	8.32136	−	22.8627i	0.303247	−	0.833164i
$754$	27.6104	+	23.1679i	1.00551	+	0.843724i
$755$	2.33275			0.0848974
$756$	−0.542766	+	0.313366i	−0.0197402	+	0.0113970i
$757$	32.3354			1.17525			0.587626	−	0.809133i	$-0.300063\pi$
$757$	32.3354			1.17525			0.587626	+	0.809133i	$0.300063\pi$
$758$	3.13041	+	2.62673i	0.113702	+	0.0954071i
$759$	19.6925	+	23.4686i	0.714794	+	0.851858i
$760$	1.38532	+	7.85651i	0.0502507	+	0.284986i
$761$	−1.81521	−	0.660681i	−0.0658012	−	0.0239497i	0.308910	−	0.951091i	$-0.400036\pi$
$761$	−1.81521	−	0.660681i	−0.0658012	−	0.0239497i	−0.374711	+	0.927142i	$0.622258\pi$
$762$	−8.60876	+	4.97027i	−0.311862	+	0.180054i
$763$	0.232307	−	1.31748i	0.00841007	−	0.0476959i
$764$	10.9461	−	18.9592i	0.396016	−	0.685919i
$765$	&m

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.26604 - 0.460802i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.0209445 + 0.118782i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.26604 - 0.460802i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.0209445 + 0.118782i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +(0.673648 + 1.16679i) q^{10} +(-3.49273 + 1.27125i) q^{11} +(0.592396 + 1.62760i) q^{12} +(-4.64543 + 3.89798i) q^{13} +(0.0923963 - 0.0775297i) q^{14} +(-2.29813 - 0.405223i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.58512 + 4.47756i) q^{17} +(-2.81908 - 1.02606i) q^{18} +(2.96064 - 5.12797i) q^{19} +(0.233956 - 1.32683i) q^{20} +0.208911i q^{21} +(3.49273 + 1.27125i) q^{22} +(-0.826352 - 4.68647i) q^{23} +(0.592396 - 1.62760i) q^{24} +(-2.43969 - 2.04715i) q^{25} +6.06418 q^{26} +(4.50000 - 2.59808i) q^{27} -0.120615 q^{28} +(4.55303 + 3.82045i) q^{29} +(1.50000 + 1.78763i) q^{30} +(-0.875515 - 4.96529i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-5.57532 + 3.21891i) q^{33} +(0.897804 - 5.09170i) q^{34} +(0.0812519 - 0.140732i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-0.145430 - 0.251892i) q^{37} +(-5.56418 + 2.02520i) q^{38} +(-6.75150 + 8.04612i) q^{39} +(-1.03209 + 0.866025i) q^{40} +(4.44356 - 3.72859i) q^{41} +(0.134285 - 0.160035i) q^{42} +(-0.426022 + 0.155059i) q^{43} +(-1.85844 - 3.21891i) q^{44} -4.04189 q^{45} +(-2.37939 + 4.12122i) q^{46} +(-0.134285 + 0.761570i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(6.56418 + 2.38917i) q^{49} +(0.553033 + 3.13641i) q^{50} +(5.75624 + 6.86002i) q^{51} +(-4.64543 - 3.89798i) q^{52} -7.29086 q^{53} +(-5.11721 - 0.902302i) q^{54} +5.00774 q^{55} +(0.0923963 + 0.0775297i) q^{56} +(3.50774 - 9.63744i) q^{57} +(-1.03209 - 5.85327i) q^{58} +(1.40033 + 0.509678i) q^{59} -2.33359i q^{60} +(-0.656574 + 3.72362i) q^{61} +(-2.52094 + 4.36640i) q^{62} +(0.0628336 + 0.356347i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(7.67752 - 2.79439i) q^{65} +(6.34002 + 1.11792i) q^{66} +(-5.08512 + 4.26692i) q^{67} +(-3.96064 + 3.32337i) q^{68} +(-2.81908 - 7.74535i) q^{69} +(-0.152704 + 0.0555796i) q^{70} +(-2.87211 - 4.97464i) q^{71} +(0.520945 - 2.95442i) q^{72} +(-5.20961 + 9.02330i) q^{73} +(-0.0505072 + 0.286441i) q^{74} +(-4.77719 - 2.75811i) q^{75} +(5.56418 + 2.02520i) q^{76} +(-0.0778483 - 0.441500i) q^{77} +(10.3439 - 1.82391i) q^{78} +(10.7194 + 8.99465i) q^{79} +1.34730 q^{80} +(6.89440 - 5.78509i) q^{81} -5.80066 q^{82} +(-1.81521 - 1.52314i) q^{83} +(-0.205737 + 0.0362770i) q^{84} +(-1.20961 - 6.86002i) q^{85} +(0.426022 + 0.155059i) q^{86} +(8.91534 + 5.14728i) q^{87} +(-0.645430 + 3.66041i) q^{88} +(1.08512 - 1.87949i) q^{89} +(3.09627 + 2.59808i) q^{90} +(-0.365715 - 0.633436i) q^{91} +(4.47178 - 1.62760i) q^{92} +(-2.98680 - 8.20616i) q^{93} +(0.592396 - 0.497079i) q^{94} +(-6.11128 + 5.12797i) q^{95} +(1.70574 + 0.300767i) q^{96} +(3.21941 - 1.17177i) q^{97} +(-3.49273 - 6.04958i) q^{98} +(-8.54189 + 7.16750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more