LMFDB - Embedded newform 342.2.bb.b.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(53,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

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

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

chi := DirichletCharacter("342.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bb (of order $18$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.2
Character	$\chi$	$=$	342.143
Dual form			342.2.bb.b.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.530375 + 1.45719i) q^{5} +(1.76968 - 3.06517i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.530375 + 1.45719i) q^{5} +(1.76968 - 3.06517i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.52715 + 0.269279i) q^{10} +(0.499077 - 0.288142i) q^{11} +(2.39646 - 2.85600i) q^{13} +(-3.32591 - 1.21053i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.96930 - 0.347241i) q^{17} +(3.36897 - 2.76587i) q^{19} -1.55071i q^{20} +(-0.370428 - 0.441459i) q^{22} +(-1.24571 - 3.42256i) q^{23} +(1.98811 + 1.66822i) q^{25} +(-3.22875 - 1.86412i) q^{26} +(-0.614603 + 3.48559i) q^{28} +(0.884021 - 5.01353i) q^{29} +(-2.68528 - 1.55035i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.683932 - 1.87909i) q^{34} +(3.52796 + 4.20446i) q^{35} +8.66903i q^{37} +(-3.30887 - 2.83750i) q^{38} +(-1.52715 + 0.269279i) q^{40} +(-8.67839 + 7.28204i) q^{41} +(-6.41658 - 2.33544i) q^{43} +(-0.370428 + 0.441459i) q^{44} +(-3.15425 + 1.82111i) q^{46} +(6.84245 + 1.20651i) q^{47} +(-2.76353 - 4.78657i) q^{49} +(1.29764 - 2.24758i) q^{50} +(-1.27513 + 3.50340i) q^{52} +(3.17228 - 1.15462i) q^{53} +(0.155181 + 0.880075i) q^{55} +3.53936 q^{56} -5.09087 q^{58} +(0.710856 + 4.03147i) q^{59} +(-5.73508 + 2.08740i) q^{61} +(-1.06050 + 2.91370i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(2.89071 + 5.00686i) q^{65} +(12.9550 + 2.28432i) q^{67} +(-1.73178 + 0.999842i) q^{68} +(3.52796 - 4.20446i) q^{70} +(0.352917 + 0.128451i) q^{71} +(-4.40942 + 3.69995i) q^{73} +(8.53732 - 1.50536i) q^{74} +(-2.21981 + 3.75132i) q^{76} -2.03968i q^{77} +(2.45213 + 2.92233i) q^{79} +(0.530375 + 1.45719i) q^{80} +(8.67839 + 7.28204i) q^{82} +(13.7230 + 7.92300i) q^{83} +(-0.538472 + 3.05383i) q^{85} +(-1.18574 + 6.72464i) q^{86} +(0.499077 + 0.288142i) q^{88} +(-13.4021 - 11.2457i) q^{89} +(-4.51315 - 12.3998i) q^{91} +(2.34117 + 2.79010i) q^{92} -6.94801i q^{94} +(2.24359 + 6.37619i) q^{95} +(-5.49864 + 0.969559i) q^{97} +(-4.23397 + 3.55272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} + 36 q^{26} - 12 q^{29} + 12 q^{34} - 48 q^{35} - 12 q^{38} - 12 q^{41} + 12 q^{44} - 36 q^{46} + 60 q^{47} - 36 q^{49} - 24 q^{50} - 48 q^{53} - 60 q^{55} - 24 q^{58} + 24 q^{59} - 60 q^{61} + 24 q^{62} - 12 q^{64} - 24 q^{65} - 48 q^{70} - 36 q^{71} + 24 q^{79} + 12 q^{82} + 72 q^{83} - 36 q^{86} - 120 q^{89} - 24 q^{91} + 12 q^{95}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 + 36 * q^26 - 12 * q^29 + 12 * q^34 - 48 * q^35 - 12 * q^38 - 12 * q^41 + 12 * q^44 - 36 * q^46 + 60 * q^47 - 36 * q^49 - 24 * q^50 - 48 * q^53 - 60 * q^55 - 24 * q^58 + 24 * q^59 - 60 * q^61 + 24 * q^62 - 12 * q^64 - 24 * q^65 - 48 * q^70 - 36 * q^71 + 24 * q^79 + 12 * q^82 + 72 * q^83 - 36 * q^86 - 120 * q^89 - 24 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.530375	+	1.45719i	−0.237191	+	0.651677i	0.762796	+	0.646639i	$0.223826\pi$
$5$	−0.530375	+	1.45719i	−0.237191	+	0.651677i	−0.999987	+	0.00503816i	$0.998396\pi$
$6$		0			0
$7$	1.76968	−	3.06517i	0.668876	−	1.15853i	−0.309343	−	0.950951i	$-0.600109\pi$
$7$	1.76968	−	3.06517i	0.668876	−	1.15853i	0.978219	−	0.207576i	$-0.0665575\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	1.52715	+	0.269279i	0.482929	+	0.0851534i
$11$	0.499077	−	0.288142i	0.150477	−	0.0868781i	−0.422871	−	0.906190i	$-0.638978\pi$
$11$	0.499077	−	0.288142i	0.150477	−	0.0868781i	0.573348	+	0.819312i	$0.305644\pi$
$12$		0			0
$13$	2.39646	−	2.85600i	0.664660	−	0.792111i	−0.323387	−	0.946267i	$-0.604821\pi$
$13$	2.39646	−	2.85600i	0.664660	−	0.792111i	0.988046	+	0.154156i	$0.0492659\pi$
$14$	−3.32591	−	1.21053i	−0.888886	−	0.323528i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.96930	−	0.347241i	0.477626	−	0.0842184i	0.0703480	−	0.997523i	$-0.477589\pi$
$17$	1.96930	−	0.347241i	0.477626	−	0.0842184i	0.407278	+	0.913304i	$0.366478\pi$
$18$		0			0
$19$	3.36897	−	2.76587i	0.772894	−	0.634535i
$19$	3.36897	−	2.76587i	0.772894	−	0.634535i
$20$		−	1.55071i		−	0.346750i
$21$		0			0
$22$	−0.370428	−	0.441459i	−0.0789756	−	0.0941194i
$23$	−1.24571	−	3.42256i	−0.259749	−	0.713654i	−0.999183	−	0.0404245i	$-0.987129\pi$
$23$	−1.24571	−	3.42256i	−0.259749	−	0.713654i	0.739434	−	0.673229i	$-0.235093\pi$
$24$		0			0
$25$	1.98811	+	1.66822i	0.397621	+	0.333644i
$26$	−3.22875	−	1.86412i	−0.633210	−	0.365584i
$27$		0			0
$28$	−0.614603	+	3.48559i	−0.116149	+	0.658714i
$29$	0.884021	−	5.01353i	0.164159	−	0.930989i	−0.785769	−	0.618520i	$-0.787733\pi$
$29$	0.884021	−	5.01353i	0.164159	−	0.930989i	0.949928	−	0.312469i	$-0.101156\pi$
$30$		0			0
$31$	−2.68528	−	1.55035i	−0.482291	−	0.278451i	0.239080	−	0.971000i	$-0.423154\pi$
$31$	−2.68528	−	1.55035i	−0.482291	−	0.278451i	−0.721371	+	0.692549i	$0.756488\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$		0			0
$34$	−0.683932	−	1.87909i	−0.117293	−	0.322261i
$35$	3.52796	+	4.20446i	0.596334	+	0.710683i
$36$		0			0
$37$			8.66903i			1.42518i	0.701581	+	0.712590i	$0.252478\pi$
$37$			8.66903i			1.42518i	−0.701581	+	0.712590i	$0.747522\pi$
$38$	−3.30887	−	2.83750i	−0.536769	−	0.460303i
$39$		0			0
$40$	−1.52715	+	0.269279i	−0.241464	+	0.0425767i
$41$	−8.67839	+	7.28204i	−1.35534	+	1.13726i	−0.377945	+	0.925828i	$0.623369\pi$
$41$	−8.67839	+	7.28204i	−1.35534	+	1.13726i	−0.977392	+	0.211435i	$0.932186\pi$
$42$		0			0
$43$	−6.41658	−	2.33544i	−0.978519	−	0.356152i	−0.197255	−	0.980352i	$-0.563203\pi$
$43$	−6.41658	−	2.33544i	−0.978519	−	0.356152i	−0.781264	+	0.624201i	$0.785425\pi$
$44$	−0.370428	+	0.441459i	−0.0558442	+	0.0665525i
$45$		0			0
$46$	−3.15425	+	1.82111i	−0.465069	+	0.268508i
$47$	6.84245	+	1.20651i	0.998074	+	0.175987i	0.648739	−	0.761011i	$-0.275297\pi$
$47$	6.84245	+	1.20651i	0.998074	+	0.175987i	0.349335	+	0.936998i	$0.386408\pi$
$48$		0			0
$49$	−2.76353	−	4.78657i	−0.394790	−	0.683796i
$50$	1.29764	−	2.24758i	0.183515	−	0.317856i
$51$		0			0
$52$	−1.27513	+	3.50340i	−0.176829	+	0.485834i
$53$	3.17228	−	1.15462i	0.435747	−	0.158599i	−0.114827	−	0.993386i	$-0.536631\pi$
$53$	3.17228	−	1.15462i	0.435747	−	0.158599i	0.550574	+	0.834787i	$0.314409\pi$
$54$		0			0
$55$	0.155181	+	0.880075i	0.0209246	+	0.118669i
$56$	3.53936			0.472967
$57$		0			0
$58$	−5.09087			−0.668464
$59$	0.710856	+	4.03147i	0.0925456	+	0.524852i	0.995472	+	0.0950567i	$0.0303032\pi$
$59$	0.710856	+	4.03147i	0.0925456	+	0.524852i	−0.902926	+	0.429795i	$0.858586\pi$
$60$		0			0
$61$	−5.73508	+	2.08740i	−0.734302	+	0.267264i	−0.681985	−	0.731366i	$-0.738883\pi$
$61$	−5.73508	+	2.08740i	−0.734302	+	0.267264i	−0.0523174	+	0.998631i	$0.516661\pi$
$62$	−1.06050	+	2.91370i	−0.134684	+	0.370041i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.89071	+	5.00686i	0.358549	+	0.621025i
$66$		0			0
$67$	12.9550	+	2.28432i	1.58271	+	0.279074i	0.894712	−	0.446643i	$-0.147380\pi$
$67$	12.9550	+	2.28432i	1.58271	+	0.279074i	0.687994	+	0.725716i	$0.258492\pi$
$68$	−1.73178	+	0.999842i	−0.210009	+	0.121249i
$69$		0			0
$70$	3.52796	−	4.20446i	0.421672	−	0.502529i
$71$	0.352917	+	0.128451i	0.0418835	+	0.0152443i	0.362877	−	0.931837i	$-0.381795\pi$
$71$	0.352917	+	0.128451i	0.0418835	+	0.0152443i	−0.320993	+	0.947081i	$0.604017\pi$
$72$		0			0
$73$	−4.40942	+	3.69995i	−0.516084	+	0.433046i	−0.863264	−	0.504753i	$-0.831584\pi$
$73$	−4.40942	+	3.69995i	−0.516084	+	0.433046i	0.347180	+	0.937799i	$0.387139\pi$
$74$	8.53732	−	1.50536i	0.992444	−	0.174995i
$75$		0			0
$76$	−2.21981	+	3.75132i	−0.254630	+	0.430306i
$77$		−	2.03968i		−	0.232443i
$78$		0			0
$79$	2.45213	+	2.92233i	0.275886	+	0.328788i	0.886140	−	0.463418i	$-0.153377\pi$
$79$	2.45213	+	2.92233i	0.275886	+	0.328788i	−0.610254	+	0.792206i	$0.708933\pi$
$80$	0.530375	+	1.45719i	0.0592978	+	0.162919i
$81$		0			0
$82$	8.67839	+	7.28204i	0.958368	+	0.804166i
$83$	13.7230	+	7.92300i	1.50630	+	0.869662i	0.999973	+	0.00732024i	$0.00233012\pi$
$83$	13.7230	+	7.92300i	1.50630	+	0.869662i	0.506326	+	0.862342i	$0.331003\pi$
$84$		0			0
$85$	−0.538472	+	3.05383i	−0.0584055	+	0.331234i
$86$	−1.18574	+	6.72464i	−0.127861	+	0.725136i
$87$		0			0
$88$	0.499077	+	0.288142i	0.0532017	+	0.0307160i
$89$	−13.4021	−	11.2457i	−1.42062	−	1.19204i	−0.951007	−	0.309171i	$-0.899948\pi$
$89$	−13.4021	−	11.2457i	−1.42062	−	1.19204i	−0.469614	−	0.882872i	$-0.655607\pi$
$90$		0			0
$91$	−4.51315	−	12.3998i	−0.473107	−	1.29985i
$92$	2.34117	+	2.79010i	0.244084	+	0.290888i
$93$		0			0
$94$		−	6.94801i		−	0.716632i
$95$	2.24359	+	6.37619i	0.230188	+	0.654184i
$96$		0			0
$97$	−5.49864	+	0.969559i	−0.558303	+	0.0984438i	−0.445677	−	0.895194i	$-0.647037\pi$
$97$	−5.49864	+	0.969559i	−0.558303	+	0.0984438i	−0.112625	+	0.993638i	$0.535926\pi$
$98$	−4.23397	+	3.55272i	−0.427696	+	0.358879i
$99$		0			0
$100$	−2.43877	−	0.887640i	−0.243877	−	0.0887640i
$101$	4.20850	−	5.01550i	0.418762	−	0.499061i	−0.514883	−	0.857260i	$-0.672165\pi$
$101$	4.20850	−	5.01550i	0.418762	−	0.499061i	0.933645	+	0.358199i	$0.116609\pi$
$102$		0			0
$103$	−11.2162	+	6.47570i	−1.10517	+	0.638070i	−0.937574	−	0.347786i	$-0.886933\pi$
$103$	−11.2162	+	6.47570i	−1.10517	+	0.638070i	−0.167595	+	0.985856i	$0.553600\pi$
$104$	3.67160	+	0.647402i	0.360030	+	0.0634829i
$105$		0			0
$106$	−1.68794	−	2.92359i	−0.163947	−	0.283964i
$107$	−4.67228	+	8.09263i	−0.451687	+	0.782344i	−0.998491	−	0.0549160i	$-0.982511\pi$
$107$	−4.67228	+	8.09263i	−0.451687	+	0.782344i	0.546804	+	0.837261i	$0.315844\pi$
$108$		0			0
$109$	−2.50977	+	6.89553i	−0.240392	+	0.660472i	0.759557	+	0.650440i	$0.225416\pi$
$109$	−2.50977	+	6.89553i	−0.240392	+	0.660472i	−0.999950	+	0.0100319i	$0.996807\pi$
$110$	0.839758	−	0.305647i	0.0800678	−	0.0291423i
$111$		0			0
$112$	−0.614603	−	3.48559i	−0.0580745	−	0.329357i
$113$	−10.0698			−0.947287			−0.473643	−	0.880717i	$-0.657061\pi$
$113$	−10.0698			−0.947287			−0.473643	+	0.880717i	$0.657061\pi$
$114$		0			0
$115$	5.64803			0.526682
$116$	0.884021	+	5.01353i	0.0820793	+	0.465495i
$117$		0			0
$118$	3.84678	−	1.40011i	0.354125	−	0.128891i
$119$	2.42068	−	6.65076i	0.221903	−	0.609675i
$120$		0			0
$121$	−5.33395	+	9.23867i	−0.484904	+	0.839879i
$122$	3.05157	+	5.28548i	0.276277	+	0.478525i
$123$		0			0
$124$	3.05359	+	0.538431i	0.274221	+	0.0483525i
$125$	−10.2001	+	5.88906i	−0.912329	+	0.526733i
$126$		0			0
$127$	−0.00645359	+	0.00769109i	−0.000572664	+	0.000682474i	−0.766331	−	0.642446i	$-0.777920\pi$
$127$	−0.00645359	+	0.00769109i	−0.000572664	+	0.000682474i	0.765758	+	0.643129i	$0.222364\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$		0			0
$130$	4.42883	−	3.71623i	0.388434	−	0.325935i
$131$	13.2004	−	2.32759i	1.15332	−	0.203362i	0.435898	−	0.899996i	$-0.356431\pi$
$131$	13.2004	−	2.32759i	1.15332	−	0.203362i	0.717427	+	0.696634i	$0.245320\pi$
$132$		0			0
$133$	−2.51589	−	15.2212i	−0.218155	−	1.31984i
$134$		−	13.1549i		−	1.13641i
$135$		0			0
$136$	1.28537	+	1.53185i	0.110220	+	0.131355i
$137$	−7.89275	−	21.6852i	−0.674323	−	1.85269i	−0.494986	−	0.868901i	$-0.664827\pi$
$137$	−7.89275	−	21.6852i	−0.674323	−	1.85269i	−0.179337	−	0.983788i	$-0.557395\pi$
$138$		0			0
$139$	12.7589	+	10.7060i	1.08220	+	0.908073i	0.996102	−	0.0882132i	$-0.0281157\pi$
$139$	12.7589	+	10.7060i	1.08220	+	0.908073i	0.0860981	+	0.996287i	$0.472560\pi$
$140$	−4.75321	−	2.74427i	−0.401719	−	0.231933i
$141$		0			0
$142$	0.0652164	−	0.369860i	0.00547283	−	0.0310380i
$143$	0.373087	−	2.11588i	0.0311991	−	0.176939i
$144$		0			0
$145$	6.83682	+	3.94724i	0.567767	+	0.327801i
$146$	4.40942	+	3.69995i	0.364927	+	0.306210i
$147$		0			0
$148$	−2.96498	−	8.14622i	−0.243720	−	0.669615i
$149$	−0.871018	−	1.03804i	−0.0713566	−	0.0850394i	0.729185	−	0.684316i	$-0.239899\pi$
$149$	−0.871018	−	1.03804i	−0.0713566	−	0.0850394i	−0.800542	+	0.599277i	$0.795455\pi$
$150$		0			0
$151$		−	1.10492i		−	0.0899172i	−0.998989	−	0.0449586i	$-0.985684\pi$
$151$		−	1.10492i		−	0.0899172i	0.998989	−	0.0449586i	$-0.0143156\pi$
$152$	4.07980	+	1.53468i	0.330915	+	0.124479i
$153$		0			0
$154$	−2.00869	+	0.354186i	−0.161865	+	0.0285411i
$155$	3.68337	−	3.09071i	0.295855	−	0.248252i
$156$		0			0
$157$	7.73289	+	2.81454i	0.617151	+	0.224625i	0.631629	−	0.775270i	$-0.282386\pi$
$157$	7.73289	+	2.81454i	0.617151	+	0.224625i	−0.0144780	+	0.999895i	$0.504609\pi$
$158$	2.45213	−	2.92233i	0.195081	−	0.232488i
$159$		0			0
$160$	1.34296	−	0.775357i	0.106170	−	0.0612973i
$161$	−12.6953	−	2.23852i	−1.00053	−	0.176420i
$162$		0			0
$163$	−9.79179	−	16.9599i	−0.766952	−	1.32840i	−0.939208	−	0.343348i	$-0.888439\pi$
$163$	−9.79179	−	16.9599i	−0.766952	−	1.32840i	0.172256	−	0.985052i	$-0.444894\pi$
$164$	5.66442	−	9.81106i	0.442317	−	0.766115i
$165$		0			0
$166$	5.41965	−	14.8904i	0.420647	−	1.15572i
$167$	−16.2370	+	5.90979i	−1.25646	+	0.457313i	−0.882579	−	0.470164i	$-0.844195\pi$
$167$	−16.2370	+	5.90979i	−1.25646	+	0.457313i	−0.373879	+	0.927477i	$0.621973\pi$
$168$		0			0
$169$	−0.156240	−	0.886083i	−0.0120185	−	0.0681602i
$170$	3.10094			0.237831
$171$		0			0
$172$	6.82838			0.520659
$173$	0.845759	+	4.79654i	0.0643019	+	0.364674i	0.999932	+	0.0116912i	$0.00372151\pi$
$173$	0.845759	+	4.79654i	0.0643019	+	0.364674i	−0.935630	+	0.352983i	$0.885167\pi$
$174$		0			0
$175$	8.63169	−	3.14168i	0.652494	−	0.237488i
$176$	0.197101	−	0.541530i	0.0148570	−	0.0408193i
$177$		0			0
$178$	−8.74761	+	15.1513i	−0.655661	+	1.13564i
$179$	−8.55841	−	14.8236i	−0.639686	−	1.10797i	−0.985502	−	0.169666i	$-0.945731\pi$
$179$	−8.55841	−	14.8236i	−0.639686	−	1.10797i	0.345816	−	0.938302i	$-0.387602\pi$
$180$		0			0
$181$	2.14110	+	0.377534i	0.159147	+	0.0280619i	0.252654	−	0.967557i	$-0.418697\pi$
$181$	2.14110	+	0.377534i	0.159147	+	0.0280619i	−0.0935070	+	0.995619i	$0.529808\pi$
$182$	−11.4277	+	6.59778i	−0.847077	+	0.489060i
$183$		0			0
$184$	2.34117	−	2.79010i	0.172593	−	0.205689i
$185$	−12.6325	−	4.59784i	−0.928756	−	0.338040i
$186$		0			0
$187$	0.882779	−	0.740739i	0.0645552	−	0.0541682i
$188$	−6.84245	+	1.20651i	−0.499037	+	0.0879937i
$189$		0			0
$190$	5.88973	−	3.31672i	0.427286	−	0.240620i
$191$		−	22.2447i		−	1.60957i	−0.593568	−	0.804784i	$-0.702281\pi$
$191$		−	22.2447i		−	1.60957i	0.593568	−	0.804784i	$-0.297719\pi$
$192$		0			0
$193$	11.5979	+	13.8218i	0.834834	+	0.994916i	0.999963	+	0.00864433i	$0.00275161\pi$
$193$	11.5979	+	13.8218i	0.834834	+	0.994916i	−0.165129	+	0.986272i	$0.552804\pi$
$194$	1.90966	+	5.24675i	0.137106	+	0.376694i
$195$		0			0
$196$	4.23397	+	3.55272i	0.302426	+	0.253766i
$197$	11.3401	+	6.54723i	0.807951	+	0.466471i	0.846244	−	0.532796i	$-0.178859\pi$
$197$	11.3401	+	6.54723i	0.807951	+	0.466471i	−0.0382927	+	0.999267i	$0.512192\pi$
$198$		0			0
$199$	2.55041	−	14.4641i	0.180794	−	1.02533i	−0.750447	−	0.660930i	$-0.770162\pi$
$199$	2.55041	−	14.4641i	0.180794	−	1.02533i	0.931241	−	0.364403i	$-0.118727\pi$
$200$	−0.450667	+	2.55586i	−0.0318670	+	0.180727i
$201$		0			0
$202$	−5.67010	−	3.27363i	−0.398947	−	0.230332i
$203$	−13.8029	−	11.5820i	−0.968774	−	0.812898i
$204$		0			0
$205$	−6.00853	−	16.5083i	−0.419654	−	1.15299i
$206$	8.32500	+	9.92135i	0.580030	+	0.691253i
$207$		0			0
$208$		−	3.72824i		−	0.258507i
$209$	0.884410	−	2.35112i	0.0611759	−	0.162631i
$210$		0			0
$211$	−22.7484	+	4.01116i	−1.56607	+	0.276140i	−0.888344	−	0.459179i	$-0.848144\pi$
$211$	−22.7484	+	4.01116i	−1.56607	+	0.276140i	−0.677722	+	0.735318i	$0.737033\pi$
$212$	−2.58607	+	2.16997i	−0.177612	+	0.149034i
$213$		0			0
$214$	8.78102	+	3.19603i	0.600258	+	0.218476i
$215$	6.80639	−	8.11154i	0.464192	−	0.553202i
$216$		0			0
$217$	−9.50418	+	5.48724i	−0.645186	+	0.372498i
$218$	7.22659	+	1.27424i	0.489446	+	0.0863026i
$219$		0			0
$220$	−0.446826	−	0.773925i	−0.0301250	−	0.0521780i
$221$	3.72765	−	6.45647i	0.250749	−	0.434309i
$222$		0			0
$223$	−0.128837	+	0.353978i	−0.00862759	+	0.0237041i	−0.943932	−	0.330141i	$-0.892904\pi$
$223$	−0.128837	+	0.353978i	−0.00862759	+	0.0237041i	0.935304	+	0.353845i	$0.115126\pi$
$224$	−3.32591	+	1.21053i	−0.222222	+	0.0808821i
$225$		0			0
$226$	1.74860	+	9.91681i	0.116315	+	0.659656i
$227$	−0.432769			−0.0287239			−0.0143620	−	0.999897i	$-0.504572\pi$
$227$	−0.432769			−0.0287239			−0.0143620	+	0.999897i	$0.504572\pi$
$228$		0			0
$229$	25.6706			1.69636			0.848182	−	0.529705i	$-0.177697\pi$
$229$	25.6706			1.69636			0.848182	+	0.529705i	$0.177697\pi$
$230$	−0.980771	−	5.56223i	−0.0646701	−	0.366762i
$231$		0			0
$232$	4.78385	−	1.74118i	0.314075	−	0.114314i
$233$	−9.62927	+	26.4562i	−0.630834	+	1.73320i	0.0479339	+	0.998851i	$0.484736\pi$
$233$	−9.62927	+	26.4562i	−0.630834	+	1.73320i	−0.678768	+	0.734353i	$0.737486\pi$
$234$		0			0
$235$	−5.38718	+	9.33088i	−0.351421	+	0.608679i
$236$	−2.04683	−	3.54521i	−0.133237	−	0.230774i
$237$		0			0
$238$	−6.97007	−	1.22901i	−0.451803	−	0.0796650i
$239$	4.97436	−	2.87195i	0.321765	−	0.185771i	−0.330414	−	0.943836i	$-0.607188\pi$
$239$	4.97436	−	2.87195i	0.321765	−	0.185771i	0.652179	+	0.758065i	$0.273855\pi$
$240$		0			0
$241$	4.52174	−	5.38880i	0.291271	−	0.347123i	−0.600488	−	0.799634i	$-0.705027\pi$
$241$	4.52174	−	5.38880i	0.291271	−	0.347123i	0.891759	+	0.452511i	$0.149472\pi$
$242$	10.0245	+	3.64864i	0.644402	+	0.234543i
$243$		0			0
$244$	4.67528	−	3.92303i	0.299304	−	0.251146i
$245$	8.44067	−	1.48832i	0.539255	−	0.0950851i
$246$		0			0
$247$	0.174297	−	16.2501i	0.0110903	−	1.03397i
$248$		−	3.10070i		−	0.196895i
$249$		0			0
$250$	7.57083	+	9.02256i	0.478821	+	0.570637i
$251$	5.68018	+	15.6062i	0.358530	+	0.985052i	0.979540	+	0.201250i	$0.0645003\pi$
$251$	5.68018	+	15.6062i	0.358530	+	0.985052i	−0.621010	+	0.783803i	$0.713277\pi$
$252$		0			0
$253$	−1.60789	−	1.34918i	−0.101087	−	0.0848222i
$254$	0.00869490	+	0.00502000i	0.000545567	+	0.000314983i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.53426	+	20.0438i	−0.220461	+	1.25030i	0.650713	+	0.759324i	$0.274470\pi$
$257$	−3.53426	+	20.0438i	−0.220461	+	1.25030i	−0.871174	+	0.490974i	$0.836641\pi$
$258$		0			0
$259$	26.5721	+	15.3414i	1.65111	+	0.953268i
$260$	−4.42883	−	3.71623i	−0.274664	−	0.230471i
$261$		0			0
$262$	−4.58445	−	12.5957i	−0.283228	−	0.778163i
$263$	19.6592	+	23.4290i	1.21224	+	1.44469i	0.861150	+	0.508352i	$0.169745\pi$
$263$	19.6592	+	23.4290i	1.21224	+	1.44469i	0.351092	+	0.936341i	$0.385811\pi$
$264$		0			0
$265$			5.23502i			0.321584i
$266$	−14.5531	+	5.12079i	−0.892305	+	0.313976i
$267$		0			0
$268$	−12.9550	+	2.28432i	−0.791353	+	0.139537i
$269$	21.4761	−	18.0206i	1.30942	−	1.09874i	0.320990	−	0.947083i	$-0.395984\pi$
$269$	21.4761	−	18.0206i	1.30942	−	1.09874i	0.988434	−	0.151654i	$-0.0484600\pi$
$270$		0			0
$271$	8.64250	+	3.14561i	0.524994	+	0.191082i	0.590902	−	0.806743i	$-0.298772\pi$
$271$	8.64250	+	3.14561i	0.524994	+	0.191082i	−0.0659075	+	0.997826i	$0.520994\pi$
$272$	1.28537	−	1.53185i	0.0779371	−	0.0928818i
$273$		0			0
$274$	−19.9852	+	11.5384i	−1.20735	+	0.697062i
$275$	1.47290	+	0.259712i	0.0888193	+	0.0156612i
$276$		0			0
$277$	−10.8162	−	18.7341i	−0.649880	−	1.12563i	−0.983151	−	0.182794i	$-0.941486\pi$
$277$	−10.8162	−	18.7341i	−0.649880	−	1.12563i	0.333271	−	0.942831i	$-0.391848\pi$
$278$	8.32781	−	14.4242i	0.499469	−	0.865106i
$279$		0			0
$280$	−1.87719	+	5.15753i	−0.112183	+	0.308221i
$281$	−5.52117	+	2.00954i	−0.329365	+	0.119879i	−0.501410	−	0.865210i	$-0.667185\pi$
$281$	−5.52117	+	2.00954i	−0.329365	+	0.119879i	0.172044	+	0.985089i	$0.444963\pi$
$282$		0			0
$283$	1.14593	+	6.49891i	0.0681187	+	0.386320i	0.999738	+	0.0228850i	$0.00728515\pi$
$283$	1.14593	+	6.49891i	0.0681187	+	0.386320i	−0.931619	+	0.363435i	$0.881604\pi$
$284$	−0.375566			−0.0222857
$285$		0			0
$286$	−2.14852			−0.127045
$287$	6.96274	+	39.4876i	0.410997	+	2.33088i
$288$		0			0
$289$	−12.2172	+	4.44670i	−0.718659	+	0.261570i
$290$	2.70007	−	7.41839i	0.158554	−	0.435623i
$291$		0			0
$292$	2.87805	−	4.98492i	0.168425	−	0.291721i
$293$	11.5232	+	19.9588i	0.673195	+	1.16601i	0.976993	+	0.213272i	$0.0684119\pi$
$293$	11.5232	+	19.9588i	0.673195	+	1.16601i	−0.303798	+	0.952736i	$0.598255\pi$
$294$		0			0
$295$	−6.25165	−	1.10233i	−0.363985	−	0.0641804i
$296$	−7.50760	+	4.33451i	−0.436370	+	0.251938i
$297$		0			0
$298$	−0.871018	+	1.03804i	−0.0504567	+	0.0601320i
$299$	−12.7601	−	4.64431i	−0.737937	−	0.268587i
$300$		0			0
$301$	−18.5138	+	15.5349i	−1.06712	+	0.895419i
$302$	−1.08814	+	0.191868i	−0.0626151	+	0.0110407i
$303$		0			0
$304$	0.802912	−	4.28431i	0.0460501	−	0.245722i
$305$		−	9.46424i		−	0.541921i
$306$		0			0
$307$	−17.5810	−	20.9522i	−1.00340	−	1.19581i	−0.980591	−	0.196066i	$-0.937183\pi$
$307$	−17.5810	−	20.9522i	−1.00340	−	1.19581i	−0.0228091	−	0.999740i	$-0.507261\pi$
$308$	0.697610	+	1.91667i	0.0397500	+	0.109212i
$309$		0			0
$310$	−3.68337	−	3.09071i	−0.209201	−	0.175541i
$311$	7.51990	+	4.34161i	0.426414	+	0.246190i	0.697818	−	0.716275i	$-0.254155\pi$
$311$	7.51990	+	4.34161i	0.426414	+	0.246190i	−0.271404	+	0.962466i	$0.587488\pi$
$312$		0			0
$313$	−6.02331	+	34.1599i	−0.340457	+	1.93083i	0.0242467	+	0.999706i	$0.492281\pi$
$313$	−6.02331	+	34.1599i	−0.340457	+	1.93083i	−0.364704	+	0.931123i	$0.618830\pi$
$314$	1.42898	−	8.10415i	0.0806420	−	0.457343i
$315$		0			0
$316$	−3.30374	−	1.90742i	−0.185850	−	0.107301i
$317$	1.15456	+	0.968794i	0.0648468	+	0.0544129i	0.674635	−	0.738152i	$-0.264301\pi$
$317$	1.15456	+	0.968794i	0.0648468	+	0.0544129i	−0.609788	+	0.792564i	$0.708746\pi$
$318$		0			0
$319$	−1.00341	−	2.75686i	−0.0561804	−	0.154354i
$320$	−0.996780	−	1.18792i	−0.0557217	−	0.0664065i
$321$		0			0
$322$			12.8911i			0.718393i
$323$	5.67410	−	6.61669i	0.315715	−	0.368162i
$324$		0			0
$325$	9.52885	−	1.68019i	0.528565	−	0.0932003i
$326$	−15.0019	+	12.5881i	−0.830878	+	0.697190i
$327$		0			0
$328$	−10.6456	−	3.87469i	−0.587806	−	0.213944i
$329$	15.8071	−	18.8382i	0.871474	−	1.03858i
$330$		0			0
$331$	−6.49877	+	3.75207i	−0.357205	+	0.206232i	−0.667854	−	0.744292i	$-0.732787\pi$
$331$	−6.49877	+	3.75207i	−0.357205	+	0.206232i	0.310649	+	0.950525i	$0.399454\pi$
$332$	−15.6053	−	2.75163i	−0.856450	−	0.151015i
$333$		0			0
$334$	8.63954	+	14.9641i	0.472734	+	0.818800i
$335$	−10.1997	+	17.6664i	−0.557270	+	0.965220i
$336$		0			0
$337$	−1.45392	+	3.99461i	−0.0792001	+	0.217601i	−0.972973	−	0.230920i	$-0.925827\pi$
$337$	−1.45392	+	3.99461i	−0.0792001	+	0.217601i	0.893773	+	0.448520i	$0.148049\pi$
$338$	−0.845490	+	0.307733i	−0.0459886	+	0.0167385i
$339$		0			0
$340$	−0.538472	−	3.05383i	−0.0292027	−	0.165617i
$341$	−1.78688			−0.0967651
$342$		0			0
$343$	5.21328			0.281490
$344$	−1.18574	−	6.72464i	−0.0639306	−	0.362568i
$345$		0			0
$346$	4.57680	−	1.66582i	0.246051	−	0.0895551i
$347$	2.65506	−	7.29471i	0.142531	−	0.391601i	−0.847802	−	0.530313i	$-0.822074\pi$
$347$	2.65506	−	7.29471i	0.142531	−	0.391601i	0.990333	+	0.138713i	$0.0442965\pi$
$348$		0			0
$349$	−5.83748	+	10.1108i	−0.312473	+	0.541220i	−0.978897	−	0.204353i	$-0.934491\pi$
$349$	−5.83748	+	10.1108i	−0.312473	+	0.541220i	0.666424	+	0.745573i	$0.267824\pi$
$350$	−4.59283	−	7.95501i	−0.245497	−	0.425213i
$351$		0			0
$352$	−0.567529	−	0.100071i	−0.0302494	−	0.00533378i
$353$	3.76329	−	2.17273i	0.200299	−	0.115643i	−0.396496	−	0.918037i	$-0.629774\pi$
$353$	3.76329	−	2.17273i	0.200299	−	0.115643i	0.596795	+	0.802394i	$0.296440\pi$
$354$		0			0
$355$	−0.374357	+	0.446141i	−0.0198688	+	0.0236787i
$356$	16.4401	+	5.98372i	0.871325	+	0.317136i
$357$		0			0
$358$	−13.1122	+	11.0025i	−0.693004	+	0.581499i
$359$	−6.85547	+	1.20881i	−0.361818	+	0.0637983i	−0.351602	−	0.936150i	$-0.614363\pi$
$359$	−6.85547	+	1.20881i	−0.361818	+	0.0637983i	−0.0102160	+	0.999948i	$0.503252\pi$
$360$		0			0
$361$	3.69990	−	18.6363i	0.194732	−	0.980857i
$362$		−	2.17413i		−	0.114270i
$363$		0			0
$364$	8.48195	+	10.1084i	0.444575	+	0.529824i
$365$	−3.05289	−	8.38775i	−0.159796	−	0.439035i
$366$		0			0
$367$	24.0516	+	20.1817i	1.25548	+	1.05348i	0.996148	+	0.0876885i	$0.0279480\pi$
$367$	24.0516	+	20.1817i	1.25548	+	1.05348i	0.259336	+	0.965787i	$0.416496\pi$
$368$	−3.15425	−	1.82111i	−0.164427	−	0.0949318i
$369$		0			0
$370$	−2.33438	+	13.2389i	−0.121359	+	0.688260i
$371$	2.07482	−	11.7669i	0.107719	−	0.610907i
$372$		0			0
$373$	−9.04765	−	5.22366i	−0.468469	−	0.270471i	0.247129	−	0.968982i	$-0.420513\pi$
$373$	−9.04765	−	5.22366i	−0.468469	−	0.270471i	−0.715599	+	0.698512i	$0.753846\pi$
$374$	−0.882779	−	0.740739i	−0.0456474	−	0.0383027i
$375$		0			0
$376$	2.37636	+	6.52899i	0.122551	+	0.336707i
$377$	−12.2001	−	14.5395i	−0.628337	−	0.748823i
$378$		0			0
$379$		−	18.3582i		−	0.942996i	−0.881867	−	0.471498i	$-0.843713\pi$
$379$		−	18.3582i		−	0.942996i	0.881867	−	0.471498i	$-0.156287\pi$
$380$	−4.28908	−	5.22431i	−0.220025	−	0.268001i
$381$		0			0
$382$	−21.9067	+	3.86274i	−1.12084	+	0.197635i
$383$	0.873288	−	0.732776i	0.0446230	−	0.0374431i	−0.620203	−	0.784441i	$-0.712950\pi$
$383$	0.873288	−	0.732776i	0.0446230	−	0.0374431i	0.664826	+	0.746998i	$0.268506\pi$
$384$		0			0
$385$	2.97220	+	1.08179i	0.151478	+	0.0551333i
$386$	11.5979	−	13.8218i	0.590317	−	0.703512i
$387$		0			0
$388$	4.83543	−	2.79173i	0.245482	−	0.141729i
$389$	30.4393	+	5.36727i	1.54333	+	0.272131i	0.879555	−	0.475798i	$-0.157841\pi$
$389$	30.4393	+	5.36727i	1.54333	+	0.272131i	0.663779	+	0.747929i	$0.268952\pi$
$390$		0			0
$391$	−3.64164	−	6.30750i	−0.184166	−	0.318984i
$392$	2.76353	−	4.78657i	0.139579	−	0.241758i
$393$		0			0
$394$	4.47857	−	12.3048i	0.225627	−	0.619905i
$395$	−5.55895	+	2.02329i	−0.279701	+	0.101803i
$396$		0			0
$397$	−2.02518	−	11.4854i	−0.101641	−	0.576434i	−0.992509	−	0.122172i	$-0.961014\pi$
$397$	−2.02518	−	11.4854i	−0.101641	−	0.576434i	0.890868	−	0.454262i	$-0.150097\pi$
$398$	−14.6872			−0.736205
$399$		0			0
$400$	2.59529			0.129764
$401$	5.71466	+	32.4094i	0.285376	+	1.61845i	0.703938	+	0.710261i	$0.251423\pi$
$401$	5.71466	+	32.4094i	0.285376	+	1.61845i	−0.418562	+	0.908188i	$0.637466\pi$
$402$		0			0
$403$	−10.8630	+	3.95380i	−0.541123	+	0.196953i
$404$	−2.23930	+	6.15242i	−0.111409	+	0.306094i
$405$		0			0
$406$	−9.00921	+	15.6044i	−0.447120	+	0.774434i
$407$	2.49791	+	4.32651i	0.123817	+	0.214457i
$408$		0			0
$409$	17.4389	+	3.07496i	0.862300	+	0.152047i	0.587272	−	0.809389i	$-0.300202\pi$
$409$	17.4389	+	3.07496i	0.862300	+	0.152047i	0.275028	+	0.961436i	$0.411313\pi$
$410$	−15.2141	+	8.78389i	−0.751373	+	0.433805i
$411$		0			0
$412$	8.32500	−	9.92135i	0.410143	−	0.488790i
$413$	13.6151	+	4.95550i	0.669957	+	0.243844i
$414$		0			0
$415$	−18.8237	+	15.7950i	−0.924020	+	0.775345i
$416$	−3.67160	+	0.647402i	−0.180015	+	0.0317415i
$417$		0			0
$418$	−2.46898	−	0.462705i	−0.120762	−	0.0226317i
$419$			1.62962i			0.0796123i	0.999207	+	0.0398061i	$0.0126740\pi$
$419$			1.62962i			0.0796123i	−0.999207	+	0.0398061i	$0.987326\pi$
$420$		0			0
$421$	−19.5930	−	23.3500i	−0.954905	−	1.13801i	−0.990343	−	0.138640i	$-0.955727\pi$
$421$	−19.5930	−	23.3500i	−0.954905	−	1.13801i	0.0354379	−	0.999372i	$-0.488717\pi$
$422$	7.90044	+	21.7063i	0.384587	+	1.05665i
$423$		0			0
$424$	2.58607	+	2.16997i	0.125591	+	0.105383i
$425$	4.49446	+	2.59488i	0.218013	+	0.125870i
$426$		0			0
$427$	−3.75101	+	21.2731i	−0.181524	+	1.02948i
$428$	1.62267	−	9.20260i	0.0784346	−	0.444825i
$429$		0			0
$430$	−9.17022	−	5.29443i	−0.442227	−	0.255320i
$431$	−21.5860	−	18.1128i	−1.03976	−	0.872464i	−0.0477823	−	0.998858i	$-0.515215\pi$
$431$	−21.5860	−	18.1128i	−1.03976	−	0.872464i	−0.991980	+	0.126393i	$0.959660\pi$
$432$		0			0
$433$	−6.89361	−	18.9400i	−0.331286	−	0.910200i	−0.987778	−	0.155868i	$-0.950183\pi$
$433$	−6.89361	−	18.9400i	−0.331286	−	0.910200i	0.656492	−	0.754333i	$-0.272040\pi$
$434$	7.05426	+	8.40694i	0.338615	+	0.403546i
$435$		0			0
$436$		−	7.33807i		−	0.351430i
$437$	−13.6631	−	8.08503i	−0.653596	−	0.386759i
$438$		0			0
$439$	0.803801	−	0.141732i	0.0383633	−	0.00676449i	−0.154434	−	0.988003i	$-0.549355\pi$
$439$	0.803801	−	0.141732i	0.0383633	−	0.00676449i	0.192797	+	0.981239i	$0.438244\pi$
$440$	−0.684577	+	0.574428i	−0.0326359	+	0.0273848i
$441$		0			0
$442$	−7.00568	−	2.54986i	−0.333226	−	0.121284i
$443$	−17.0274	+	20.2924i	−0.808995	+	0.964122i	−0.999847	−	0.0174963i	$-0.994430\pi$
$443$	−17.0274	+	20.2924i	−0.808995	+	0.964122i	0.190852	+	0.981619i	$0.438875\pi$
$444$		0			0
$445$	23.4953	−	13.5650i	1.11379	−	0.643044i
$446$	0.370972	+	0.0654124i	0.0175661	+	0.00309737i
$447$		0			0
$448$	1.76968	+	3.06517i	0.0836095	+	0.144816i
$449$	4.03239	−	6.98431i	0.190300	−	0.329610i	−0.755049	−	0.655668i	$-0.772387\pi$
$449$	4.03239	−	6.98431i	0.190300	−	0.329610i	0.945350	+	0.326058i	$0.105720\pi$
$450$		0			0
$451$	−2.23292	+	6.13490i	−0.105144	+	0.288881i
$452$	9.46251	−	3.44407i	0.445079	−	0.161996i
$453$		0			0
$454$	0.0751496	+	0.426195i	0.00352695	+	0.0200023i
$455$	20.4625			0.959299
$456$		0			0
$457$	−3.96913			−0.185668			−0.0928340	−	0.995682i	$-0.529593\pi$
$457$	−3.96913			−0.185668			−0.0928340	+	0.995682i	$0.529593\pi$
$458$	−4.45766	−	25.2807i	−0.208293	−	1.18129i
$459$		0			0
$460$	−5.30742	+	1.93174i	−0.247460	+	0.0900679i
$461$	−5.17707	+	14.2239i	−0.241120	+	0.662472i	0.758818	+	0.651303i	$0.225777\pi$
$461$	−5.17707	+	14.2239i	−0.241120	+	0.662472i	−0.999938	+	0.0111687i	$0.996445\pi$
$462$		0			0
$463$	13.7571	−	23.8280i	0.639347	−	1.10738i	−0.346229	−	0.938150i	$-0.612538\pi$
$463$	13.7571	−	23.8280i	0.639347	−	1.10738i	0.985576	−	0.169232i	$-0.0541287\pi$
$464$	−2.54544	−	4.40882i	−0.118169	−	0.204675i
$465$		0			0
$466$	27.7264	+	4.88891i	1.28440	+	0.226474i
$467$	2.56552	−	1.48120i	0.118718	−	0.0685420i	−0.439465	−	0.898260i	$-0.644832\pi$
$467$	2.56552	−	1.48120i	0.118718	−	0.0685420i	0.558183	+	0.829718i	$0.311499\pi$
$468$		0			0
$469$	29.9280	−	35.6669i	1.38195	−	1.64694i
$470$	10.1246	+	3.68505i	0.467013	+	0.169979i
$471$		0			0
$472$	−3.13592	+	2.63135i	−0.144343	+	0.121118i
$473$	−3.87530	+	0.683320i	−0.178187	+	0.0314191i
$474$		0			0
$475$	11.3119	+	0.121331i	0.519028	+	0.00556706i
$476$			7.07760i			0.324401i
$477$		0			0
$478$	−3.69211	−	4.40008i	−0.168873	−	0.201255i
$479$	−7.48040	−	20.5522i	−0.341788	−	0.939055i	−0.984876	−	0.173262i	$-0.944569\pi$
$479$	−7.48040	−	20.5522i	−0.341788	−	0.939055i	0.643088	−	0.765793i	$-0.277653\pi$
$480$		0			0
$481$	24.7587	+	20.7750i	1.12890	+	0.947259i
$482$	−6.09212	−	3.51729i	−0.277489	−	0.160208i
$483$		0			0
$484$	1.85246	−	10.5058i	0.0842028	−	0.477538i
$485$	1.50351	−	8.52682i	0.0682708	−	0.387183i
$486$		0			0
$487$	14.4911	+	8.36646i	0.656656	+	0.379120i	0.791002	−	0.611814i	$-0.209560\pi$
$487$	14.4911	+	8.36646i	0.656656	+	0.379120i	−0.134346	+	0.990935i	$0.542893\pi$
$488$	−4.67528	−	3.92303i	−0.211640	−	0.177587i
$489$		0			0
$490$	−2.93141	−	8.05399i	−0.132428	−	0.363842i
$491$	−15.4021	−	18.3555i	−0.695087	−	0.828373i	0.296874	−	0.954917i	$-0.404056\pi$
$491$	−15.4021	−	18.3555i	−0.695087	−	0.828373i	−0.991961	+	0.126544i	$0.959612\pi$
$492$		0			0
$493$		−	10.1801i		−	0.458490i
$494$	−16.0335	+	2.65015i	−0.721380	+	0.119236i
$495$		0			0
$496$	−3.05359	+	0.538431i	−0.137110	+	0.0241762i
$497$	1.01827	−	0.854434i	0.0456758	−	0.0383266i
$498$		0			0
$499$	10.6551	+	3.87814i	0.476988	+	0.173609i	0.569315	−	0.822119i	$-0.307208\pi$
$499$	10.6551	+	3.87814i	0.476988	+	0.173609i	−0.0923275	+	0.995729i	$0.529431\pi$
$500$	7.57083	−	9.02256i	0.338578	−	0.403501i
$501$		0			0
$502$	14.3827	−	8.30387i	0.641932	−	0.370620i
$503$	0.0351994	+	0.00620660i	0.00156946	+	0.000276739i	0.174433	−	0.984669i	$-0.444191\pi$
$503$	0.0351994	+	0.00620660i	0.00156946	+	0.000276739i	−0.172863	+	0.984946i	$0.555302\pi$
$504$		0			0
$505$	5.07647	+	8.79270i	0.225900	+	0.391270i
$506$	−1.04948	+	1.81774i	−0.0466549	+	0.0808086i
$507$		0			0
$508$	0.00343389	−	0.00943452i	0.000152354	−	0.000418589i
$509$	−6.36298	+	2.31594i	−0.282034	+	0.102652i	−0.479164	−	0.877725i	$-0.659060\pi$
$509$	−6.36298	+	2.31594i	−0.282034	+	0.102652i	0.197130	+	0.980377i	$0.436838\pi$
$510$		0			0
$511$	3.53771	+	20.0634i	0.156499	+	0.887551i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	20.3530			0.897733
$515$	−3.48753	−	19.7788i	−0.153679	−	0.871558i
$516$		0			0
$517$	3.76255	−	1.36946i	0.165477	−	0.0602287i
$518$	10.4941	−	28.8324i	0.461086	−	1.26682i
$519$		0			0
$520$	−2.89071	+	5.00686i	−0.126766	+	0.219566i
$521$	10.7305	+	18.5858i	0.470114	+	0.814261i	0.999416	−	0.0341725i	$-0.0108796\pi$
$521$	10.7305	+	18.5858i	0.470114	+	0.814261i	−0.529302	+	0.848433i	$0.677546\pi$
$522$		0			0
$523$	6.39826	+	1.12818i	0.279776	+	0.0493321i	0.311775	−	0.950156i	$-0.399076\pi$
$523$	6.39826	+	1.12818i	0.279776	+	0.0493321i	−0.0319993	+	0.999488i	$0.510187\pi$
$524$	−11.6082	+	6.70202i	−0.507108	+	0.292779i
$525$		0			0
$526$	19.6592	−	23.4290i	0.857184	−	1.02155i
$527$	−5.82648	−	2.12067i	−0.253806	−	0.0923777i
$528$		0			0
$529$	7.45688	−	6.25707i	0.324212	−	0.272046i
$530$	5.15548	−	0.909051i	0.223940	−	0.0394866i
$531$		0			0
$532$	7.57011	+	13.4427i	0.328206	+	0.582817i
$533$			42.2366i			1.82947i
$534$		0			0
$535$	−9.31448	−	11.1006i	−0.402700	−	0.479919i
$536$	4.49923	+	12.3615i	0.194337	+	0.533937i
$537$		0			0
$538$	−21.4761	−	18.0206i	−0.925902	−	0.776924i
$539$	−2.75842	−	1.59258i	−0.118814	−	0.0685971i
$540$		0			0
$541$	3.78965	−	21.4922i	0.162930	−	0.924020i	−0.788244	−	0.615363i	$-0.789009\pi$
$541$	3.78965	−	21.4922i	0.162930	−	0.924020i	0.951173	−	0.308657i	$-0.0998796\pi$
$542$	1.59707	−	9.05743i	0.0686000	−	0.389050i
$543$		0			0
$544$	−1.73178	−	0.999842i	−0.0742493	−	0.0428679i
$545$	−8.71701	−	7.31444i	−0.373396	−	0.313316i
$546$		0			0
$547$	3.35401	+	9.21508i	0.143407	+	0.394008i	0.990514	−	0.137415i	$-0.0438795\pi$
$547$	3.35401	+	9.21508i	0.143407	+	0.394008i	−0.847106	+	0.531424i	$0.821657\pi$
$548$	14.8335	+	17.6779i	0.633657	+	0.755163i
$549$		0			0
$550$		−	1.49562i		−	0.0637736i
$551$	−10.8885	−	19.3355i	−0.463868	−	0.823721i
$552$		0			0
$553$	13.2969	−	2.34461i	0.565443	−	0.0997029i
$554$	−16.5713	+	13.9050i	−0.704048	+	0.590766i
$555$		0			0
$556$	−15.6512	−	5.69656i	−0.663757	−	0.241588i
$557$	17.4858	−	20.8387i	0.740896	−	0.882966i	−0.255584	−	0.966787i	$-0.582268\pi$
$557$	17.4858	−	20.8387i	0.740896	−	0.882966i	0.996481	+	0.0838208i	$0.0267123\pi$
$558$		0			0
$559$	−22.0471	+	12.7289i	−0.932493	+	0.538375i
$560$	5.40515	+	0.953073i	0.228409	+	0.0402747i
$561$		0			0
$562$	2.93775	+	5.08833i	0.123922	+	0.214638i
$563$	−11.9866	+	20.7614i	−0.505175	+	0.874989i	0.494807	+	0.869003i	$0.335239\pi$
$563$	−11.9866	+	20.7614i	−0.505175	+	0.874989i	−0.999982	+	0.00598625i	$0.998095\pi$
$564$		0			0
$565$	5.34077	−	14.6736i	0.224688	−	0.617325i
$566$	6.20119	−	2.25705i	0.260656	−	0.0948709i
$567$		0			0
$568$	0.0652164	+	0.369860i	0.00273642	+	0.0155190i
$569$	−38.1220			−1.59816			−0.799079	−	0.601226i	$-0.794679\pi$
$569$	−38.1220			−1.59816			−0.799079	+	0.601226i	$0.794679\pi$
$570$		0			0
$571$	−11.1214			−0.465415			−0.232708	−	0.972547i	$-0.574759\pi$
$571$	−11.1214			−0.465415			−0.232708	+	0.972547i	$0.574759\pi$
$572$	0.373087	+	2.11588i	0.0155996	+	0.0884695i
$573$		0			0
$574$	37.6787	−	13.7139i	1.57268	−	0.572408i
$575$	3.23298	−	8.88253i	0.134824	−	0.370427i
$576$		0			0
$577$	−7.36873	+	12.7630i	−0.306764	+	0.531331i	−0.977653	−	0.210227i	$-0.932580\pi$
$577$	−7.36873	+	12.7630i	−0.306764	+	0.531331i	0.670888	+	0.741558i	$0.265913\pi$
$578$	6.50063	+	11.2594i	0.270391	+	0.468330i
$579$		0			0
$580$	−7.77455	−	1.37086i	−0.322821	−	0.0569220i
$581$	48.5708	−	28.0423i	2.01505	−	1.16339i
$582$		0			0
$583$	1.25052	−	1.49031i	0.0517912	−	0.0617224i
$584$	−5.40896	−	1.96870i	−0.223824	−	0.0814654i
$585$		0			0
$586$	17.6546	−	14.8140i	0.729306	−	0.611961i
$587$	−21.0886	+	3.71848i	−0.870418	+	0.153478i	−0.590981	−	0.806686i	$-0.701259\pi$
$587$	−21.0886	+	3.71848i	−0.870418	+	0.153478i	−0.279438	+	0.960164i	$0.590148\pi$
$588$		0			0
$589$	−13.3347	+	2.20407i	−0.549447	+	0.0908172i
$590$			6.34809i			0.261347i
$591$		0			0
$592$	5.57234	+	6.64086i	0.229022	+	0.272938i
$593$	1.31486	+	3.61253i	0.0539946	+	0.148349i	0.963758	−	0.266778i	$-0.0859592\pi$
$593$	1.31486	+	3.61253i	0.0539946	+	0.148349i	−0.909763	+	0.415127i	$0.863737\pi$
$594$		0			0
$595$	8.40759	+	7.05480i	0.344677	+	0.289219i
$596$	1.17352	+	0.677532i	0.0480692	+	0.0277528i
$597$		0			0
$598$	−2.35798	+	13.3727i	−0.0964248	+	0.546852i
$599$	6.25829	−	35.4925i	0.255707	−	1.45019i	−0.538545	−	0.842597i	$-0.681026\pi$
$599$	6.25829	−	35.4925i	0.255707	−	1.45019i	0.794252	−	0.607589i	$-0.207863\pi$
$600$		0			0
$601$	−0.398046	−	0.229812i	−0.0162366	−	0.00937422i	0.491860	−	0.870674i	$-0.336317\pi$
$601$	−0.398046	−	0.229812i	−0.0162366	−	0.00937422i	−0.508096	+	0.861300i	$0.669651\pi$
$602$	18.5138	+	15.5349i	0.754567	+	0.633157i
$603$		0			0
$604$	0.377905	+	1.03829i	0.0153767	+	0.0422473i
$605$	−10.6335	−	12.6726i	−0.432315	−	0.515213i
$606$		0			0
$607$			0.979677i			0.0397639i	0.999802	+	0.0198819i	$0.00632903\pi$
$607$			0.979677i			0.0397639i	−0.999802	+	0.0198819i	$0.993671\pi$
$608$	−4.35865	−	0.0467506i	−0.176767	−	0.00189599i
$609$		0			0
$610$	−9.32045	+	1.64345i	−0.377374	+	0.0665412i
$611$	19.8435	−	16.6507i	0.802781	−	0.673613i
$612$		0			0
$613$	−30.9806	−	11.2760i	−1.25129	−	0.455433i	−0.370454	−	0.928851i	$-0.620798\pi$
$613$	−30.9806	−	11.2760i	−1.25129	−	0.455433i	−0.880838	+	0.473417i	$0.843020\pi$
$614$	−17.5810	+	20.9522i	−0.709511	+	0.845562i
$615$		0			0
$616$	1.76641	−	1.01984i	0.0711707	−	0.0410904i
$617$	17.9043	+	3.15702i	0.720802	+	0.127097i	0.522003	−	0.852944i	$-0.325185\pi$
$617$	17.9043	+	3.15702i	0.720802	+	0.127097i	0.198799	+	0.980040i	$0.436296\pi$
$618$		0			0
$619$	−9.97935	−	17.2847i	−0.401104	−	0.694732i	0.592756	−	0.805382i	$-0.298040\pi$
$619$	−9.97935	−	17.2847i	−0.401104	−	0.694732i	−0.993859	+	0.110650i	$0.964707\pi$
$620$	−2.40415	+	4.16411i	−0.0965529	+	0.167234i
$621$		0			0
$622$	2.96984	−	8.15956i	0.119080	−	0.327169i
$623$	−58.1875	+	21.1785i	−2.33123	+	0.848499i
$624$		0			0
$625$	−0.918260	−	5.20771i	−0.0367304	−	0.208308i
$626$	34.6868			1.38636
$627$		0			0
$628$	−8.22917			−0.328379
$629$	3.01024	+	17.0719i	0.120026	+	0.680703i
$630$		0			0
$631$	−27.5304	+	10.0202i	−1.09597	+	0.398899i	−0.825828	−	0.563922i	$-0.809292\pi$
$631$	−27.5304	+	10.0202i	−1.09597	+	0.398899i	−0.270139	+	0.962821i	$0.587070\pi$
$632$	−1.30475	+	3.58477i	−0.0519002	+	0.142595i
$633$		0			0
$634$	0.753588	−	1.30525i	0.0299288	−	0.0518382i
$635$	−0.00778459	−	0.0134833i	−0.000308922	−	0.000535069i
$636$		0			0
$637$	−20.2931	−	3.57822i	−0.804043	−	0.141774i
$638$	−2.54074	+	1.46689i	−0.100589	+	0.0580749i
$639$		0			0
$640$	−0.996780	+	1.18792i	−0.0394012	+	0.0469565i
$641$	−44.2424	−	16.1029i	−1.74747	−	0.636027i	−0.747857	−	0.663860i	$-0.768917\pi$
$641$	−44.2424	−	16.1029i	−1.74747	−	0.636027i	−0.999613	+	0.0278331i	$0.991139\pi$
$642$		0			0
$643$	−18.3085	+	15.3627i	−0.722018	+	0.605845i	−0.927943	−	0.372723i	$-0.878424\pi$
$643$	−18.3085	+	15.3627i	−0.722018	+	0.605845i	0.205925	+	0.978568i	$0.433980\pi$
$644$	12.6953	−	2.23852i	0.500263	−	0.0882099i
$645$		0			0
$646$	−7.50146	−	4.43892i	−0.295141	−	0.174647i
$647$		−	17.5533i		−	0.690093i	−0.938586	−	0.345047i	$-0.887863\pi$
$647$		−	17.5533i		−	0.690093i	0.938586	−	0.345047i	$-0.112137\pi$
$648$		0			0
$649$	1.51641	+	1.80718i	0.0595242	+	0.0709381i
$650$	−3.30933	−	9.09232i	−0.129803	−	0.356630i
$651$		0			0
$652$	15.0019	+	12.5881i	0.587520	+	0.492987i
$653$	13.3682	+	7.71813i	0.523138	+	0.302034i	0.738218	−	0.674563i	$-0.235668\pi$
$653$	13.3682	+	7.71813i	0.523138	+	0.302034i	−0.215080	+	0.976597i	$0.569001\pi$
$654$		0			0
$655$	−3.60942	+	20.4700i	−0.141032	+	0.799831i
$656$	−1.96723	+	11.1567i	−0.0768075	+	0.435597i
$657$		0			0
$658$	−21.2968	−	12.2957i	−0.830238	−	0.479338i
$659$	18.6411	+	15.6418i	0.726156	+	0.609317i	0.929081	−	0.369877i	$-0.120600\pi$
$659$	18.6411	+	15.6418i	0.726156	+	0.609317i	−0.202925	+	0.979194i	$0.565045\pi$
$660$		0			0
$661$	14.8420	+	40.7782i	0.577289	+	1.58609i	0.792732	+	0.609571i	$0.208658\pi$
$661$	14.8420	+	40.7782i	0.577289	+	1.58609i	−0.215443	+	0.976516i	$0.569120\pi$
$662$	4.82357	+	5.74850i	0.187473	+	0.223422i
$663$		0			0
$664$			15.8460i			0.614944i
$665$	23.5146	+	4.40681i	0.911856	+	0.170889i
$666$		0			0
$667$	−18.2604	+	3.21979i	−0.707044	+	0.124671i
$668$	13.2365	−	11.1068i	0.512137	−	0.429734i
$669$		0			0
$670$	19.1692	+	6.97701i	0.740570	+	0.269546i
$671$	−2.26078	+	2.69429i	−0.0872764	+	0.104012i
$672$		0			0
$673$	−3.12877	+	1.80639i	−0.120605	+	0.0696314i	−0.559089	−	0.829108i	$-0.688849\pi$
$673$	−3.12877	+	1.80639i	−0.120605	+	0.0696314i	0.438484	+	0.898739i	$0.355516\pi$
$674$	4.18640	+	0.738175i	0.161254	+	0.0284334i
$675$		0			0
$676$	0.449876	+	0.779208i	0.0173029	+	0.0299695i
$677$	2.68656	−	4.65326i	0.103253	−	0.178839i	−0.809770	−	0.586747i	$-0.800408\pi$
$677$	2.68656	−	4.65326i	0.103253	−	0.178839i	0.913023	+	0.407908i	$0.133742\pi$
$678$		0			0
$679$	−6.75897	+	18.5701i	−0.259385	+	0.712655i
$680$	−2.91393	+	1.06058i	−0.111744	+	0.0406715i
$681$		0			0
$682$	0.310289	+	1.75974i	0.0118816	+	0.0673838i
$683$	1.68803			0.0645906			0.0322953	−	0.999478i	$-0.489718\pi$
$683$	1.68803			0.0645906			0.0322953	+	0.999478i	$0.489718\pi$
$684$		0			0
$685$	35.7856			1.36730
$686$	−0.905276	−	5.13408i	−0.0345636	−	0.196020i
$687$		0			0
$688$	−6.41658	+	2.33544i	−0.244630	+	0.0890379i
$689$	4.30469	−	11.8270i	0.163995	−	0.450574i
$690$		0			0
$691$	12.5447	−	21.7281i	0.477223	−	0.826575i	−0.522436	−	0.852678i	$-0.674977\pi$
$691$	12.5447	−	21.7281i	0.477223	−	0.826575i	0.999659	+	0.0261037i	$0.00831002\pi$
$692$	−2.43527	−	4.21801i	−0.0925749	−	0.160345i
$693$		0			0
$694$	−7.64494	−	1.34801i	−0.290198	−	0.0511697i
$695$	−22.3678	+	12.9141i	−0.848459	+	0.489858i
$696$		0			0
$697$	−14.5618	+	17.3540i	−0.551566	+	0.657331i
$698$	10.9709	+	3.99307i	0.415254	+	0.151140i
$699$		0			0
$700$	−7.03662	+	5.90442i	−0.265959	+	0.223166i
$701$	−15.4959	+	2.73234i	−0.585270	+	0.103199i	−0.458440	−	0.888725i	$-0.651592\pi$
$701$	−15.4959	+	2.73234i	−0.585270	+	0.103199i	−0.126831	+	0.991924i	$0.540480\pi$
$702$		0			0
$703$	23.9774	+	29.2057i	0.904325	+	1.10151i
$704$			0.576284i			0.0217195i
$705$		0			0
$706$	−2.79321	−	3.32882i	−0.105124	−	0.125282i
$707$	−7.92568	−	21.7756i	−0.298076	−	0.818957i
$708$		0			0
$709$	−21.4768	−	18.0212i	−0.806579	−	0.676800i	0.143209	−	0.989692i	$-0.454258\pi$
$709$	−21.4768	−	18.0212i	−0.806579	−	0.676800i	−0.949789	+	0.312892i	$0.898702\pi$
$710$	0.504369	+	0.291198i	0.0189286	+	0.0109285i
$711$		0			0
$712$	3.03801	−	17.2294i	0.113854	−	0.645700i
$713$	−1.96108	+	11.1218i	−0.0734430	+	0.416516i
$714$		0			0
$715$	2.88538	+	1.66587i	0.107907	+	0.0623001i
$716$	13.1122	+	11.0025i	0.490028	+	0.411182i
$717$		0			0
$718$	2.38088	+	6.54142i	0.0888537	+	0.244124i
$719$	−19.6909	−	23.4667i	−0.734346	−	0.875159i	0.261594	−	0.965178i	$-0.415752\pi$
$719$	−19.6909	−	23.4667i	−0.734346	−	0.875159i	−0.995940	+	0.0900186i	$0.971307\pi$
$720$		0			0
$721$			45.8396i			1.70716i
$722$	−18.9956	−	0.407539i	−0.706944	−	0.0151670i
$723$		0			0
$724$	−2.14110	+	0.377534i	−0.0795734	+	0.0140309i
$725$	10.1212	−	8.49269i	0.375892	−	0.315410i
$726$		0			0
$727$	−25.4071	−	9.24742i	−0.942296	−	0.342968i	−0.175224	−	0.984529i	$-0.556065\pi$
$727$	−25.4071	−	9.24742i	−0.942296	−	0.342968i	−0.767072	+	0.641561i	$0.778287\pi$
$728$	8.48195	−	10.1084i	0.314362	−	0.374642i
$729$		0			0
$730$	−7.73019	+	4.46303i	−0.286107	+	0.165184i
$731$	−13.4471	−	2.37109i	−0.497361	−	0.0876981i
$732$		0			0
$733$	−17.4637	−	30.2481i	−0.645038	−	1.11724i	−0.984293	−	0.176544i	$-0.943508\pi$
$733$	−17.4637	−	30.2481i	−0.645038	−	1.11724i	0.339254	−	0.940695i	$-0.389825\pi$
$734$	15.6986	−	27.1907i	0.579445	−	1.00363i
$735$		0			0
$736$	−1.24571	+	3.42256i	−0.0459175	+	0.126157i
$737$	7.12375	−	2.59283i	0.262407	−	0.0955082i
$738$		0			0
$739$	4.76826	+	27.0421i	0.175403	+	0.994761i	0.937678	+	0.347507i	$0.112972\pi$
$739$	4.76826	+	27.0421i	0.175403	+	0.994761i	−0.762274	+	0.647254i	$0.775917\pi$
$740$	13.4432			0.494181
$741$		0			0
$742$	−11.9484			−0.438641
$743$	−0.202960	−	1.15104i	−0.00744588	−	0.0422277i	0.980858	−	0.194722i	$-0.0623805\pi$
$743$	−0.202960	−	1.15104i	−0.00744588	−	0.0422277i	−0.988304	+	0.152494i	$0.951269\pi$
$744$		0			0
$745$	1.97459	−	0.718692i	0.0723434	−	0.0263308i
$746$	−3.57319	+	9.81727i	−0.130824	+	0.359436i
$747$		0			0
$748$	−0.576193	+	0.997995i	−0.0210677	+	0.0364903i
$749$	16.5369	+	28.6427i	0.604245	+	1.04658i
$750$		0			0
$751$	−47.2002	−	8.32266i	−1.72236	−	0.303698i	−0.776944	−	0.629570i	$-0.783231\pi$
$751$	−47.2002	−	8.32266i	−1.72236	−	0.303698i	−0.945414	+	0.325872i	$0.894342\pi$
$752$	6.01715	−	3.47400i	0.219423	−	0.126684i
$753$		0			0
$754$	−12.2001	+	14.5395i	−0.444301	+	0.529498i
$755$	1.61008	+	0.586023i	0.0585970	+	0.0213276i
$756$		0			0
$757$	−5.30834	+	4.45422i	−0.192935	+	0.161892i	−0.734138	−	0.679000i	$-0.762413\pi$
$757$	−5.30834	+	4.45422i	−0.192935	+	0.161892i	0.541203	+	0.840892i	$0.317969\pi$
$758$	−18.0793	+	3.18786i	−0.656669	+	0.115788i
$759$		0			0
$760$	−4.40015	+	5.13111i	−0.159610	+	0.186125i
$761$			5.31790i			0.192774i	0.995344	+	0.0963868i	$0.0307286\pi$
$761$			5.31790i			0.192774i	−0.995344	+	0.0963868i	$0.969271\pi$
$762$		0			0
$763$	16.6945	+	19.8958i	0.604382	+	0.720275i
$764$	7.60812	+	20.9031i	0.275252	+	0.756249i
$765$		0			0
$766$	−0.873288	−	0.732776i	−0.0315532	−	0.0264763i
$767$	13.2174	+	7.63106i	0.477252	+	0.275542i
$768$		0			0
$769$	5.69185	−	32.2801i	0.205254	−	1.16405i	−0.691787	−	0.722102i	$-0.743176\pi$
$769$	5.69185	−	32.2801i	0.205254	−	1.16405i	0.897040	−	0.441949i	$-0.145713\pi$
$770$	0.549241	−	3.11490i	0.0197933	−	0.112253i
$771$		0			0
$772$	−15.6258	−	9.02155i	−0.562384	−	0.324693i
$773$	19.1085	+	16.0339i	0.687285	+	0.576701i	0.918125	−	0.396291i	$-0.129703\pi$
$773$	19.1085	+	16.0339i	0.687285	+	0.576701i	−0.230840	+	0.972992i	$0.574147\pi$
$774$		0			0
$775$	−2.75230	−	7.56190i	−0.0988657	−	0.271631i
$776$	−3.58898	−	4.27719i	−0.128837	−	0.153542i
$777$		0			0
$778$		−	30.9089i		−	1.10814i
$779$	−9.09605	+	48.5363i	−0.325900	+	1.73899i
$780$		0			0
$781$	0.213145	−	0.0375831i	0.00762691	−	0.00134483i
$782$	−5.57931	+	4.68160i	−0.199516	+	0.167414i
$783$		0			0
$784$	−5.19373	−	1.89036i	−0.185490	−	0.0675130i
$785$	−8.20266	+	9.77555i	−0.292766	+	0.348904i
$786$		0			0
$787$	6.59273	−	3.80631i	0.235005	−	0.135680i	−0.377874	−	0.925857i	$-0.623345\pi$
$787$	6.59273	−	3.80631i	0.235005	−	0.135680i	0.612879	+	0.790177i	$0.290011\pi$
$788$	−12.8955	−	2.27383i	−0.459384	−	0.0810018i
$789$		0			0
$790$	2.95786	+	5.12316i	0.105236	+	0.182274i
$791$	−17.8203	+	30.8657i	−0.633617	+	1.09746i
$792$		0			0
$793$	−7.78232	+	21.3818i	−0.276358	+	0.759288i
$794$	−10.9592	+	3.98883i	−0.388928	+	0.141558i
$795$		0			0
$796$	2.55041	+	14.4641i	0.0903970	+	0.512667i
$797$	33.2435			1.17754			0.588772	−	0.808299i	$-0.299611\pi$
$797$	33.2435			1.17754			0.588772	+	0.808299i	$0.299611\pi$
$798$		0			0
$799$	13.8938			0.491528
$800$	−0.450667	−	2.55586i	−0.0159335	−	0.0903633i
$801$		0			0
$802$	30.9247	−	11.2557i	1.09199	−	0.397452i
$803$	−1.13453	+	3.11710i	−0.0400367	+	0.110000i
$804$		0			0
$805$	9.99521	−	17.3122i	0.352285	−	0.610175i
$806$	5.78007	+	10.0114i	0.203594	+	0.352636i
$807$		0			0
$808$	6.44780	+	1.13692i	0.226833	+	0.0399968i
$809$	−2.45508	+	1.41744i	−0.0863159	+	0.0498345i	−0.542537	−	0.840032i	$-0.682536\pi$
$809$	−2.45508	+	1.41744i	−0.0863159	+	0.0498345i	0.456221	+	0.889867i	$0.349203\pi$
$810$		0			0
$811$	−12.8996	+	15.3731i	−0.452965	+	0.539822i	−0.943401	−	0.331655i	$-0.892393\pi$
$811$	−12.8996	+	15.3731i	−0.452965	+	0.539822i	0.490436	+	0.871477i	$0.336838\pi$
$812$	16.9318	+	6.16266i	0.594189	+	0.216267i
$813$		0			0
$814$	3.82702	−	3.21125i	0.134137	−	0.112554i
$815$	29.9072	−	5.27344i	1.04760	−	0.184721i
$816$		0			0
$817$	−28.0768	+	9.87939i	−0.982282	+	0.345636i
$818$		−	17.7080i		−	0.619145i
$819$		0			0
$820$	11.2924	+	13.4577i	0.394346	+	0.469963i
$821$	6.74215	+	18.5239i	0.235303	+	0.646488i	0.999998	+	0.00209636i	$0.000667294\pi$
$821$	6.74215	+	18.5239i	0.235303	+	0.646488i	−0.764695	+	0.644392i	$0.777110\pi$
$822$		0			0
$823$	−28.1155	−	23.5917i	−0.980046	−	0.822356i	0.00405064	−	0.999992i	$-0.498711\pi$
$823$	−28.1155	−	23.5917i	−0.980046	−	0.822356i	−0.984096	+	0.177636i	$0.943155\pi$
$824$	−11.2162	−	6.47570i	−0.390736	−	0.225592i
$825$		0			0
$826$	2.51597	−	14.2688i	0.0875420	−	0.496475i
$827$	2.25472	−	12.7872i	0.0784043	−	0.444653i	−0.920182	−	0.391492i	$-0.871959\pi$
$827$	2.25472	−	12.7872i	0.0784043	−	0.444653i	0.998586	−	0.0531613i	$-0.0169298\pi$
$828$		0			0
$829$	18.6792	+	10.7844i	0.648755	+	0.374559i	0.787979	−	0.615702i	$-0.211127\pi$
$829$	18.6792	+	10.7844i	0.648755	+	0.374559i	−0.139224	+	0.990261i	$0.544461\pi$
$830$	18.8237	+	15.7950i	0.653381	+	0.548251i
$831$		0			0
$832$	1.27513	+	3.50340i	0.0442073	+	0.121458i
$833$	−7.10432	−	8.46660i	−0.246150	−	0.293350i
$834$		0			0
$835$		−	26.7949i		−	0.927276i
$836$	−0.0269416	+	2.51182i	−0.000931796	+	0.0868731i
$837$		0			0
$838$	1.60487	−	0.282981i	0.0554392	−	0.00977542i
$839$	24.1233	−	20.2418i	0.832827	−	0.698825i	−0.123111	−	0.992393i	$-0.539287\pi$
$839$	24.1233	−	20.2418i	0.832827	−	0.698825i	0.955938	+	0.293568i	$0.0948426\pi$
$840$		0			0
$841$	2.89709	+	1.05446i	0.0998998	+	0.0363606i
$842$	−19.5930	+	23.3500i	−0.675220	+	0.804696i
$843$		0			0
$844$	20.0046	−	11.5497i	0.688587	−	0.397556i
$845$	1.37406	+	0.242284i	0.0472691	+	0.00833482i
$846$		0			0
$847$	18.8788	+	32.6990i	0.648682	+	1.12355i
$848$	1.68794	−	2.92359i	0.0579640	−	0.100397i
$849$		0			0
$850$	1.77500	−	4.87677i	0.0608820	−	0.167272i
$851$	29.6703	−	10.7991i	1.01708	−	0.370188i
$852$		0			0
$853$	6.07931	+	34.4775i	0.208151	+	1.18049i	0.892403	+	0.451239i	$0.149018\pi$
$853$	6.07931	+	34.4775i	0.208151	+	1.18049i	−0.684252	+	0.729246i	$0.739871\pi$
$854$	21.6012			0.739179
$855$		0			0
$856$	−9.34457			−0.319391
$857$	−6.62955	−	37.5980i	−0.226461	−	1.28432i	−0.859872	−	0.510509i	$-0.829457\pi$
$857$	−6.62955	−	37.5980i	−0.226461	−	1.28432i	0.633411	−	0.773815i	$-0.281654\pi$
$858$		0			0
$859$	12.4417	−	4.52842i	0.424506	−	0.154508i	−0.120928	−	0.992661i	$-0.538587\pi$
$859$	12.4417	−	4.52842i	0.424506	−	0.154508i	0.545434	+	0.838154i	$0.316365\pi$
$860$	−3.62160	+	9.95027i	−0.123496	+	0.339301i
$861$		0			0
$862$	−14.0893	+	24.4034i	−0.479883	+	0.831181i
$863$	2.44932	+	4.24234i	0.0833757	+	0.144411i	0.904698	−	0.426054i	$-0.140097\pi$
$863$	2.44932	+	4.24234i	0.0833757	+	0.144411i	−0.821322	+	0.570465i	$0.806763\pi$
$864$		0			0
$865$	−7.43806	−	1.31153i	−0.252902	−	0.0445934i
$866$	−17.4552	+	10.0778i	−0.593153	+	0.342457i
$867$		0			0
$868$	7.05426	−	8.40694i	0.239437	−	0.285350i
$869$	2.06585	+	0.751907i	0.0700791	+	0.0255067i
$870$		0			0
$871$	37.5702	−	31.5252i	1.27302	−	1.06819i
$872$	−7.22659	+	1.27424i	−0.244723	+	0.0431513i
$873$		0			0
$874$	−5.58962	+	14.8595i	−0.189072	+	0.502630i
$875$			41.6870i			1.40928i
$876$		0			0
$877$	−6.73441	−	8.02576i	−0.227405	−	0.271011i	0.640262	−	0.768157i	$-0.278826\pi$
$877$	−6.73441	−	8.02576i	−0.227405	−	0.271011i	−0.867667	+	0.497146i	$0.834381\pi$
$878$	−0.279157	−	0.766978i	−0.00942110	−	0.0258843i
$879$		0			0
$880$	0.684577	+	0.574428i	0.0230771	+	0.0193640i
$881$	6.64613	+	3.83715i	0.223914	+	0.129277i	0.607761	−	0.794120i	$-0.292068\pi$
$881$	6.64613	+	3.83715i	0.223914	+	0.129277i	−0.383847	+	0.923397i	$0.625401\pi$
$882$		0			0
$883$	2.71371	−	15.3902i	0.0913236	−	0.517922i	−0.904489	−	0.426498i	$-0.859747\pi$
$883$	2.71371	−	15.3902i	0.0913236	−	0.517922i	0.995812	−	0.0914237i	$-0.0291418\pi$
$884$	−1.29460	+	7.34203i	−0.0435420	+	0.246939i
$885$		0			0
$886$	22.9409	+	13.2449i	0.770715	+	0.444973i
$887$	10.0691	+	8.44899i	0.338088	+	0.283689i	0.795986	−	0.605316i	$-0.206953\pi$
$887$	10.0691	+	8.44899i	0.338088	+	0.283689i	−0.457898	+	0.889005i	$0.651397\pi$
$888$		0			0
$889$	0.0121538	+	0.0333922i	0.000407624	+	0.00111994i
$890$	−17.4389	−	20.7828i	−0.584552	−	0.696642i
$891$		0			0
$892$		−	0.376695i		−	0.0126127i
$893$	26.3891	−	14.8607i	0.883076	−	0.497293i
$894$		0			0
$895$	26.1400	−	4.60919i	0.873765	−	0.154068i
$896$	2.71131	−	2.27506i	0.0905784	−	0.0760043i
$897$		0			0
$898$	−7.57842	−	2.75832i	−0.252895	−	0.0920463i
$899$	−10.1466	+	12.0922i	−0.338407	+	0.403298i
$900$		0			0
$901$	5.84626	−	3.37534i	0.194767	−	0.112449i
$902$	6.42944	+	1.13368i	0.214077	+	0.0377476i
$903$		0			0
$904$	−5.03490	−	8.72070i	−0.167458	−	0.290046i
$905$	−1.68573	+	2.91976i	−0.0560354	+	0.0970562i
$906$		0			0
$907$	8.24601	−	22.6557i	0.273804	−	0.752271i	−0.724228	−	0.689561i	$-0.757803\pi$
$907$	8.24601	−	22.6557i	0.273804	−	0.752271i	0.998032	−	0.0627099i	$-0.0199743\pi$
$908$	0.406670	−	0.148016i	0.0134958	−	0.00491208i
$909$		0			0
$910$	−3.55328	−	20.1517i	−0.117790	−	0.668021i
$911$	−21.5734			−0.714757			−0.357379	−	0.933960i	$-0.616329\pi$
$911$	−21.5734			−0.714757			−0.357379	+	0.933960i	$0.616329\pi$
$912$		0			0
$913$	9.13180			0.302218
$914$	0.689232	+	3.90883i	0.0227978	+	0.129293i
$915$		0			0
$916$	−24.1225	+	8.77988i	−0.797030	+	0.290095i
$917$	16.2260	−	44.5806i	0.535830	−	1.47218i
$918$		0			0
$919$	−1.60875	+	2.78644i	−0.0530678	+	0.0919160i	−0.891339	−	0.453337i	$-0.850233\pi$
$919$	−1.60875	+	2.78644i	−0.0530678	+	0.0919160i	0.838271	+	0.545253i	$0.183567\pi$
$920$	2.82402	+	4.89134i	0.0931051	+	0.161263i
$921$		0			0
$922$	14.9068	+	2.62847i	0.490928	+	0.0865639i
$923$	1.21261	−	0.700100i	0.0399135	−	0.0230441i
$924$		0			0
$925$	−14.4618	+	17.2349i	−0.475502	+	0.566681i
$926$	−25.8549	−	9.41042i	−0.849645	−	0.309246i
$927$		0			0
$928$	−3.89983	+	3.27235i	−0.128018	+	0.107420i
$929$	1.24190	−	0.218981i	0.0407455	−	0.00718453i	−0.153238	−	0.988189i	$-0.548970\pi$
$929$	1.24190	−	0.218981i	0.0407455	−	0.00718453i	0.193984	+	0.981005i	$0.437859\pi$
$930$		0			0
$931$	−22.5493	−	8.48224i	−0.739023	−	0.277994i
$932$		−	28.1541i		−	0.922218i
$933$		0			0
$934$	−1.90420	−	2.26934i	−0.0623073	−	0.0742550i
$935$	0.611197	+	1.67925i	0.0199883	+	0.0549173i
$936$		0			0
$937$	−31.7335	−	26.6276i	−1.03669	−	0.869885i	−0.0450568	−	0.998984i	$-0.514347\pi$
$937$	−31.7335	−	26.6276i	−1.03669	−	0.869885i	−0.991632	+	0.129100i	$0.958791\pi$
$938$	−40.3219	−	23.2799i	−1.31656	−	0.760115i
$939$		0			0
$940$	1.87095	−	10.6107i	0.0610236	−	0.346082i
$941$	−4.71260	+	26.7265i	−0.153626	+	0.871259i	0.806404	+	0.591365i	$0.201411\pi$
$941$	−4.71260	+	26.7265i	−0.153626	+	0.871259i	−0.960031	+	0.279894i	$0.909701\pi$
$942$		0			0
$943$	35.7340	+	20.6310i	1.16366	+	0.671839i
$944$	3.13592	+	2.63135i	0.102066	+	0.0856432i
$945$		0			0
$946$	1.34588	+	3.69777i	0.0437583	+	0.120225i
$947$	4.56874	+	5.44481i	0.148464	+	0.176933i	0.835151	−	0.550021i	$-0.185380\pi$
$947$	4.56874	+	5.44481i	0.148464	+	0.176933i	−0.686687	+	0.726953i	$0.740936\pi$
$948$		0			0
$949$			21.4601i			0.696624i
$950$	−1.84481	−	11.1612i	−0.0598536	−	0.362116i
$951$		0			0
$952$	6.97007	−	1.22901i	0.225901	−	0.0398325i
$953$	−26.6324	+	22.3472i	−0.862707	+	0.723897i	−0.962550	−	0.271106i	$-0.912611\pi$
$953$	−26.6324	+	22.3472i	−0.862707	+	0.723897i	0.0998422	+	0.995003i	$0.468166\pi$
$954$		0			0
$955$	32.4148	+	11.7980i	1.04892	+	0.381775i
$956$	−3.69211	+	4.40008i	−0.119411	+	0.142309i
$957$		0			0
$958$	−18.9410	+	10.9356i	−0.611957	+	0.353314i
$959$	−80.4364	−	14.1831i	−2.59743	−	0.457997i
$960$		0			0
$961$	−10.6928	−	18.5205i	−0.344930	−	0.597437i
$962$	16.1601	−	27.9901i	0.521022	−	0.902437i
$963$		0			0
$964$	−2.40597	+	6.61034i	−0.0774910	+	0.212905i
$965$	−26.2923	+	9.56962i	−0.846379	+	0.308057i
$966$		0			0
$967$	−8.38706	−	47.5654i	−0.269710	−	1.52960i	−0.755280	−	0.655402i	$-0.772499\pi$
$967$	−8.38706	−	47.5654i	−0.269710	−	1.52960i	0.485571	−	0.874197i	$-0.338612\pi$
$968$	−10.6679			−0.342879
$969$		0			0
$970$	−8.65836			−0.278003
$971$	−1.64748	−	9.34334i	−0.0528702	−	0.299842i	0.946894	−	0.321545i	$-0.104202\pi$
$971$	−1.64748	−	9.34334i	−0.0528702	−	0.299842i	−0.999764	+	0.0217032i	$0.993091\pi$
$972$		0			0
$973$	55.3951	−	20.1622i	1.77588	−	0.646369i
$974$	5.72299	−	15.7238i	0.183377	−	0.503823i
$975$		0			0
$976$	−3.05157	+	5.28548i	−0.0976785	+	0.169184i
$977$	−21.6651	−	37.5251i	−0.693128	−	1.20053i	−0.970808	−	0.239859i	$-0.922899\pi$
$977$	−21.6651	−	37.5251i	−0.693128	−	1.20053i	0.277679	−	0.960674i	$-0.410435\pi$
$978$		0			0
$979$	−9.92904	−	1.75076i	−0.317334	−	0.0559545i
$980$	−7.42260	+	4.28544i	−0.237106	+	0.136893i
$981$		0			0
$982$	−15.4021	+	18.3555i	−0.491501	+	0.585748i
$983$	48.0596	+	17.4922i	1.53286	+	0.557916i	0.964320	−	0.264739i	$-0.0852857\pi$
$983$	48.0596	+	17.4922i	1.53286	+	0.557916i	0.568541	+	0.822655i	$0.307508\pi$
$984$		0			0
$985$	−15.5551	+	13.0523i	−0.495627	+	0.415881i
$986$	−10.0255	+	1.76776i	−0.319276	+	0.0562970i
$987$		0			0
$988$	5.39407	+	15.3297i	0.171608	+	0.487702i
$989$			24.8704i			0.790833i
$990$		0			0
$991$	−23.2423	−	27.6991i	−0.738316	−	0.879890i	0.257956	−	0.966157i	$-0.416951\pi$
$991$	−23.2423	−	27.6991i	−0.738316	−	0.879890i	−0.996272	+	0.0862662i	$0.972506\pi$
$992$	1.06050	+	2.91370i	0.0336709	+	0.0925102i
$993$		0			0
$994$	−1.01827	−	0.854434i	−0.0322977	−	0.0271010i
$995$	19.7243	+	11.3879i	0.625304	+	0.361019i
$996$		0			0
$997$	4.18902	−	23.7571i	0.132668	−	0.752395i	−0.843788	−	0.536677i	$-0.819679\pi$
$997$	4.18902	−	23.7571i	0.132668	−	0.752395i	0.976456	−	0.215719i	$-0.0692094\pi$
$998$	1.96898	−	11.1667i	0.0623270	−	0.353474i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bb.b.143.2	yes	24
3.2	odd	2		342.2.bb.a.143.3	✓	24
19.2	odd	18		342.2.bb.a.287.3	yes	24
57.2	even	18	inner	342.2.bb.b.287.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.bb.a.143.3	✓	24	3.2	odd	2
342.2.bb.a.287.3	yes	24	19.2	odd	18
342.2.bb.b.143.2	yes	24	1.1	even	1	trivial
342.2.bb.b.287.2	yes	24	57.2	even	18	inner

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.530375 + 1.45719i) q^{5} +(1.76968 - 3.06517i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.530375 + 1.45719i) q^{5} +(1.76968 - 3.06517i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.52715 + 0.269279i) q^{10} +(0.499077 - 0.288142i) q^{11} +(2.39646 - 2.85600i) q^{13} +(-3.32591 - 1.21053i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.96930 - 0.347241i) q^{17} +(3.36897 - 2.76587i) q^{19} -1.55071i q^{20} +(-0.370428 - 0.441459i) q^{22} +(-1.24571 - 3.42256i) q^{23} +(1.98811 + 1.66822i) q^{25} +(-3.22875 - 1.86412i) q^{26} +(-0.614603 + 3.48559i) q^{28} +(0.884021 - 5.01353i) q^{29} +(-2.68528 - 1.55035i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.683932 - 1.87909i) q^{34} +(3.52796 + 4.20446i) q^{35} +8.66903i q^{37} +(-3.30887 - 2.83750i) q^{38} +(-1.52715 + 0.269279i) q^{40} +(-8.67839 + 7.28204i) q^{41} +(-6.41658 - 2.33544i) q^{43} +(-0.370428 + 0.441459i) q^{44} +(-3.15425 + 1.82111i) q^{46} +(6.84245 + 1.20651i) q^{47} +(-2.76353 - 4.78657i) q^{49} +(1.29764 - 2.24758i) q^{50} +(-1.27513 + 3.50340i) q^{52} +(3.17228 - 1.15462i) q^{53} +(0.155181 + 0.880075i) q^{55} +3.53936 q^{56} -5.09087 q^{58} +(0.710856 + 4.03147i) q^{59} +(-5.73508 + 2.08740i) q^{61} +(-1.06050 + 2.91370i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(2.89071 + 5.00686i) q^{65} +(12.9550 + 2.28432i) q^{67} +(-1.73178 + 0.999842i) q^{68} +(3.52796 - 4.20446i) q^{70} +(0.352917 + 0.128451i) q^{71} +(-4.40942 + 3.69995i) q^{73} +(8.53732 - 1.50536i) q^{74} +(-2.21981 + 3.75132i) q^{76} -2.03968i q^{77} +(2.45213 + 2.92233i) q^{79} +(0.530375 + 1.45719i) q^{80} +(8.67839 + 7.28204i) q^{82} +(13.7230 + 7.92300i) q^{83} +(-0.538472 + 3.05383i) q^{85} +(-1.18574 + 6.72464i) q^{86} +(0.499077 + 0.288142i) q^{88} +(-13.4021 - 11.2457i) q^{89} +(-4.51315 - 12.3998i) q^{91} +(2.34117 + 2.79010i) q^{92} -6.94801i q^{94} +(2.24359 + 6.37619i) q^{95} +(-5.49864 + 0.969559i) q^{97} +(-4.23397 + 3.55272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} + 36 q^{26} - 12 q^{29} + 12 q^{34} - 48 q^{35} - 12 q^{38} - 12 q^{41} + 12 q^{44} - 36 q^{46} + 60 q^{47} - 36 q^{49} - 24 q^{50} - 48 q^{53} - 60 q^{55} - 24 q^{58} + 24 q^{59} - 60 q^{61} + 24 q^{62} - 12 q^{64} - 24 q^{65} - 48 q^{70} - 36 q^{71} + 24 q^{79} + 12 q^{82} + 72 q^{83} - 36 q^{86} - 120 q^{89} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 + 36 * q^26 - 12 * q^29 + 12 * q^34 - 48 * q^35 - 12 * q^38 - 12 * q^41 + 12 * q^44 - 36 * q^46 + 60 * q^47 - 36 * q^49 - 24 * q^50 - 48 * q^53 - 60 * q^55 - 24 * q^58 + 24 * q^59 - 60 * q^61 + 24 * q^62 - 12 * q^64 - 24 * q^65 - 48 * q^70 - 36 * q^71 + 24 * q^79 + 12 * q^82 + 72 * q^83 - 36 * q^86 - 120 * q^89 - 24 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more