LMFDB - Embedded newform 975.2.bb.k.724.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			724.2
Root			$2.23871 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.724
Dual form			975.2.bb.k.874.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95878 - 1.13090i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.55787 + 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(1.09275 - 0.630901i) q^{7} -2.52360i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.95878 - 1.13090i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.55787 + 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(1.09275 - 0.630901i) q^{7} -2.52360i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.26180 + 3.91756i) q^{11} +3.11575i q^{12} +(-1.04571 - 3.45058i) q^{13} -2.85395 q^{14} +(0.261802 - 0.453455i) q^{16} +(3.89131 - 2.24665i) q^{17} -2.26180i q^{18} +(2.55787 + 4.43037i) q^{19} +1.26180 q^{21} +(8.86074 - 5.11575i) q^{22} +(-1.93253 - 1.11575i) q^{23} +(1.26180 - 2.18551i) q^{24} +(-1.85395 + 7.94151i) q^{26} +1.00000i q^{27} +(3.40474 + 1.96573i) q^{28} +(-0.688776 + 1.19299i) q^{29} +8.87085 q^{31} +(-5.39664 + 3.11575i) q^{32} +(-3.91756 + 2.26180i) q^{33} -10.1630 q^{34} +(-1.55787 + 2.69832i) q^{36} +(-0.200484 - 0.115749i) q^{37} -11.5708i q^{38} +(0.819677 - 3.51114i) q^{39} +(-0.573026 + 0.992511i) q^{41} +(-2.47159 - 1.42697i) q^{42} +(5.52312 - 3.18878i) q^{43} -14.0944 q^{44} +(2.52360 + 4.37101i) q^{46} +10.7854i q^{47} +(0.453455 - 0.261802i) q^{48} +(-2.70393 + 4.68334i) q^{49} +4.49330 q^{51} +(7.68167 - 8.19723i) q^{52} +4.52360i q^{53} +(1.13090 - 1.95878i) q^{54} +(-1.59214 - 2.75768i) q^{56} +5.11575i q^{57} +(2.69832 - 1.55787i) q^{58} +(-0.426974 - 0.739540i) q^{59} +(-2.31968 - 4.01780i) q^{61} +(-17.3760 - 10.0321i) q^{62} +(1.09275 + 0.630901i) q^{63} +13.0472 q^{64} +10.2315 q^{66} +(11.3732 + 6.56633i) q^{67} +(12.1244 + 7.00000i) q^{68} +(-1.11575 - 1.93253i) q^{69} +(4.80453 + 8.32168i) q^{71} +(2.18551 - 1.26180i) q^{72} +13.7854i q^{73} +(0.261802 + 0.453455i) q^{74} +(-7.96970 + 13.8039i) q^{76} +5.70789i q^{77} +(-5.57632 + 5.95058i) q^{78} +8.87085 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.24486 - 1.29607i) q^{82} -8.23150i q^{83} +(1.96573 + 3.40474i) q^{84} -14.4248 q^{86} +(-1.19299 + 0.688776i) q^{87} +(9.88636 + 5.70789i) q^{88} +(3.31122 - 5.73521i) q^{89} +(-3.31968 - 3.11089i) q^{91} -6.95279i q^{92} +(7.68238 + 4.43543i) q^{93} +(12.1972 - 21.1262i) q^{94} -6.23150 q^{96} +(-9.24019 + 5.33483i) q^{97} +(10.5928 - 6.11575i) q^{98} -4.52360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q + 12 * q^4 + 6 * q^9	$ 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) $ 12 * q + 12 * q^4 + 6 * q^9 - 48 * q^14 - 24 * q^16 + 24 * q^19 - 12 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 + 12 * q^31 - 12 * q^36 - 24 * q^39 + 48 * q^44 - 24 * q^46 - 12 * q^49 - 60 * q^56 - 12 * q^59 + 6 * q^61 + 48 * q^64 + 96 * q^66 + 24 * q^71 - 24 * q^74 - 96 * q^76 + 12 * q^79 - 6 * q^81 - 24 * q^84 - 24 * q^86 + 60 * q^89 - 6 * q^91 + 72 * q^94 - 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−1.95878	−	1.13090i	−1.38507	−	0.799668i	−0.392311	−	0.919832i	$-0.628324\pi$
$2$	−1.95878	−	1.13090i	−1.38507	−	0.799668i	−0.992754	+	0.120165i	$0.961658\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	1.55787	+	2.69832i	0.778937	+	1.34916i
$5$		0			0
$5$		0			0
$6$	−1.13090	−	1.95878i	−0.461688	−	0.799668i
$7$	1.09275	−	0.630901i	0.413022	−	0.238458i	−0.279066	−	0.960272i	$-0.590025\pi$
$7$	1.09275	−	0.630901i	0.413022	−	0.238458i	0.692087	+	0.721814i	$0.256691\pi$
$8$		−	2.52360i		−	0.892229i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.26180	+	3.91756i	−0.681959	+	1.18119i	0.292423	+	0.956289i	$0.405538\pi$
$11$	−2.26180	+	3.91756i	−0.681959	+	1.18119i	−0.974382	+	0.224899i	$0.927795\pi$
$12$			3.11575i			0.899439i
$13$	−1.04571	−	3.45058i	−0.290028	−	0.957018i
$13$	−1.04571	−	3.45058i	−0.290028	−	0.957018i
$14$	−2.85395			−0.762749
$15$		0			0
$16$	0.261802	−	0.453455i	0.0654506	−	0.113364i
$17$	3.89131	−	2.24665i	0.943782	−	0.544893i	0.0526381	−	0.998614i	$-0.483237\pi$
$17$	3.89131	−	2.24665i	0.943782	−	0.544893i	0.891144	+	0.453721i	$0.149904\pi$
$18$		−	2.26180i		−	0.533112i
$19$	2.55787	+	4.43037i	0.586817	+	1.01640i	0.994646	+	0.103338i	$0.0329524\pi$
$19$	2.55787	+	4.43037i	0.586817	+	1.01640i	−0.407830	+	0.913058i	$0.633714\pi$
$20$		0			0
$21$	1.26180			0.275348
$22$	8.86074	−	5.11575i	1.88912	−	1.09068i
$23$	−1.93253	−	1.11575i	−0.402961	−	0.232650i	0.284800	−	0.958587i	$-0.408073\pi$
$23$	−1.93253	−	1.11575i	−0.402961	−	0.232650i	−0.687761	+	0.725937i	$0.741406\pi$
$24$	1.26180	−	2.18551i	0.257564	−	0.446114i
$25$		0			0
$26$	−1.85395	+	7.94151i	−0.363589	+	1.55746i
$27$			1.00000i			0.192450i
$28$	3.40474	+	1.96573i	0.643436	+	0.371488i
$29$	−0.688776	+	1.19299i	−0.127902	+	0.221534i	−0.922864	−	0.385127i	$-0.874158\pi$
$29$	−0.688776	+	1.19299i	−0.127902	+	0.221534i	0.794961	+	0.606660i	$0.207491\pi$
$30$		0			0
$31$	8.87085			1.59325			0.796626	−	0.604472i	$-0.206616\pi$
$31$	8.87085			1.59325			0.796626	+	0.604472i	$0.206616\pi$
$32$	−5.39664	+	3.11575i	−0.954000	+	0.550792i
$33$	−3.91756	+	2.26180i	−0.681959	+	0.393729i
$34$	−10.1630			−1.74293
$35$		0			0
$36$	−1.55787	+	2.69832i	−0.259646	+	0.449720i
$37$	−0.200484	−	0.115749i	−0.0329593	−	0.0190291i	0.483430	−	0.875383i	$-0.339391\pi$
$37$	−0.200484	−	0.115749i	−0.0329593	−	0.0190291i	−0.516389	+	0.856354i	$0.672724\pi$
$38$		−	11.5708i		−	1.87703i
$39$	0.819677	−	3.51114i	0.131253	−	0.562233i
$40$		0			0
$41$	−0.573026	+	0.992511i	−0.0894917	+	0.155004i	−0.907296	−	0.420492i	$-0.861858\pi$
$41$	−0.573026	+	0.992511i	−0.0894917	+	0.155004i	0.817805	+	0.575496i	$0.195191\pi$
$42$	−2.47159	−	1.42697i	−0.381375	−	0.220187i
$43$	5.52312	−	3.18878i	0.842268	−	0.486284i	−0.0157664	−	0.999876i	$-0.505019\pi$
$43$	5.52312	−	3.18878i	0.842268	−	0.486284i	0.858035	+	0.513592i	$0.171685\pi$
$44$	−14.0944			−2.12481
$45$		0			0
$46$	2.52360	+	4.37101i	0.372085	+	0.644470i
$47$			10.7854i			1.57321i	0.617454	+	0.786607i	$0.288164\pi$
$47$			10.7854i			1.57321i	−0.617454	+	0.786607i	$0.711836\pi$
$48$	0.453455	−	0.261802i	0.0654506	−	0.0377879i
$49$	−2.70393	+	4.68334i	−0.386275	+	0.669049i
$50$		0			0
$51$	4.49330			0.629188
$52$	7.68167	−	8.19723i	1.06526	−	1.13675i
$53$			4.52360i			0.621365i	0.950514	+	0.310682i	$0.100558\pi$
$53$			4.52360i			0.621365i	−0.950514	+	0.310682i	$0.899442\pi$
$54$	1.13090	−	1.95878i	0.153896	−	0.266556i
$55$		0			0
$56$	−1.59214	−	2.75768i	−0.212759	−	0.368510i
$57$			5.11575i			0.677598i
$58$	2.69832	−	1.55787i	0.354307	−	0.204559i
$59$	−0.426974	−	0.739540i	−0.0555872	−	0.0962799i	0.836893	−	0.547367i	$-0.184370\pi$
$59$	−0.426974	−	0.739540i	−0.0555872	−	0.0962799i	−0.892480	+	0.451087i	$0.851036\pi$
$60$		0			0
$61$	−2.31968	−	4.01780i	−0.297004	−	0.514426i	0.678445	−	0.734651i	$-0.262654\pi$
$61$	−2.31968	−	4.01780i	−0.297004	−	0.514426i	−0.975449	+	0.220225i	$0.929321\pi$
$62$	−17.3760	−	10.0321i	−2.20676	−	1.27407i
$63$	1.09275	+	0.630901i	0.137674	+	0.0794861i
$64$	13.0472			1.63090
$65$		0			0
$66$	10.2315			1.25941
$67$	11.3732	+	6.56633i	1.38946	+	0.802205i	0.993254	−	0.115958i	$-0.0369937\pi$
$67$	11.3732	+	6.56633i	1.38946	+	0.802205i	0.396205	+	0.918162i	$0.370327\pi$
$68$	12.1244	+	7.00000i	1.47029	+	0.848875i
$69$	−1.11575	−	1.93253i	−0.134320	−	0.232650i
$70$		0			0
$71$	4.80453	+	8.32168i	0.570192	+	0.987602i	0.996546	+	0.0830453i	$0.0264646\pi$
$71$	4.80453	+	8.32168i	0.570192	+	0.987602i	−0.426354	+	0.904557i	$0.640202\pi$
$72$	2.18551	−	1.26180i	0.257564	−	0.148705i
$73$			13.7854i			1.61346i	0.590920	+	0.806730i	$0.298765\pi$
$73$			13.7854i			1.61346i	−0.590920	+	0.806730i	$0.701235\pi$
$74$	0.261802	+	0.453455i	0.0304339	+	0.0527130i
$75$		0			0
$76$	−7.96970	+	13.8039i	−0.914187	+	1.58342i
$77$			5.70789i			0.650475i
$78$	−5.57632	+	5.95058i	−0.631394	+	0.673770i
$79$	8.87085			0.998049			0.499024	−	0.866588i	$-0.333692\pi$
$79$	8.87085			0.998049			0.499024	+	0.866588i	$0.333692\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.24486	−	1.29607i	0.247904	−	0.143127i
$83$		−	8.23150i		−	0.903524i	−0.892138	−	0.451762i	$-0.850796\pi$
$83$		−	8.23150i		−	0.903524i	0.892138	−	0.451762i	$-0.149204\pi$
$84$	1.96573	+	3.40474i	0.214479	+	0.371488i
$85$		0			0
$86$	−14.4248			−1.55546
$87$	−1.19299	+	0.688776i	−0.127902	+	0.0738445i
$88$	9.88636	+	5.70789i	1.05389	+	0.608464i
$89$	3.31122	−	5.73521i	0.350989	−	0.607931i	−0.635434	−	0.772155i	$-0.719179\pi$
$89$	3.31122	−	5.73521i	0.350989	−	0.607931i	0.986423	+	0.164224i	$0.0525121\pi$
$90$		0			0
$91$	−3.31968	−	3.11089i	−0.347997	−	0.326110i
$92$		−	6.95279i		−	0.724879i
$93$	7.68238	+	4.43543i	0.796626	+	0.459932i
$94$	12.1972	−	21.1262i	1.25805	−	2.17900i
$95$		0			0
$96$	−6.23150			−0.636000
$97$	−9.24019	+	5.33483i	−0.938200	+	0.541670i	−0.889395	−	0.457139i	$-0.848874\pi$
$97$	−9.24019	+	5.33483i	−0.938200	+	0.541670i	−0.0488041	+	0.998808i	$0.515541\pi$
$98$	10.5928	−	6.11575i	1.07003	−	0.617784i
$99$	−4.52360			−0.454639
$100$		0			0
$101$	8.52360	−	14.7633i	0.848130	−	1.46900i	−0.0347444	−	0.999396i	$-0.511062\pi$
$101$	8.52360	−	14.7633i	0.848130	−	1.46900i	0.882875	−	0.469609i	$-0.155605\pi$
$102$	−8.80138	−	5.08148i	−0.871466	−	0.503141i
$103$		−	13.9484i		−	1.37437i	−0.726481	−	0.687187i	$-0.758845\pi$
$103$		−	13.9484i		−	1.37437i	0.726481	−	0.687187i	$-0.241155\pi$
$104$	−8.70789	+	2.63896i	−0.853879	+	0.258771i
$105$		0			0
$106$	5.11575	−	8.86074i	0.496886	−	0.860631i
$107$	10.8195	+	6.24665i	1.04596	+	0.603886i	0.921516	−	0.388340i	$-0.126951\pi$
$107$	10.8195	+	6.24665i	1.04596	+	0.603886i	0.124446	+	0.992226i	$0.460285\pi$
$108$	−2.69832	+	1.55787i	−0.259646	+	0.149907i
$109$	2.27871			0.218261			0.109130	−	0.994027i	$-0.465193\pi$
$109$	2.27871			0.218261			0.109130	+	0.994027i	$0.465193\pi$
$110$		0			0
$111$	−0.115749	−	0.200484i	−0.0109864	−	0.0190291i
$112$		−	0.660685i		−	0.0624289i
$113$	−1.27860	+	0.738198i	−0.120280	+	0.0694438i	−0.558933	−	0.829213i	$-0.688789\pi$
$113$	−1.27860	+	0.738198i	−0.120280	+	0.0694438i	0.438653	+	0.898657i	$0.355456\pi$
$114$	5.78541	−	10.0206i	0.541853	−	0.938517i
$115$		0			0
$116$	−4.29211			−0.398512
$117$	2.46543	−	2.63090i	0.227929	−	0.243227i
$118$			1.93146i			0.177805i
$119$	2.83483	−	4.91007i	0.259868	−	0.450105i
$120$		0			0
$121$	−4.73150	−	8.19520i	−0.430136	−	0.745018i
$122$			10.4933i			0.950019i
$123$	−0.992511	+	0.573026i	−0.0894917	+	0.0516681i
$124$	13.8197	+	23.9364i	1.24104	+	2.14955i
$125$		0			0
$126$	−1.42697	−	2.47159i	−0.127125	−	0.220187i
$127$	−15.4026	−	8.89270i	−1.36676	−	0.789100i	−0.376248	−	0.926519i	$-0.622786\pi$
$127$	−15.4026	−	8.89270i	−1.36676	−	0.789100i	−0.990513	+	0.137419i	$0.956119\pi$
$128$	−14.7633	−	8.52360i	−1.30491	−	0.753387i
$129$	6.37755			0.561512
$130$		0			0
$131$	11.6697			1.01958			0.509791	−	0.860298i	$-0.329723\pi$
$131$	11.6697			1.01958			0.509791	+	0.860298i	$0.329723\pi$
$132$	−12.2061	−	7.04721i	−1.06241	−	0.613381i
$133$	5.59025	+	3.22753i	0.484736	+	0.279863i
$134$	−14.8517	−	25.7240i	−1.28299	−	2.22221i
$135$		0			0
$136$	−5.66966	−	9.82013i	−0.486169	−	0.842070i
$137$	17.3760	−	10.0321i	1.48453	−	0.857096i	0.484689	−	0.874686i	$-0.338933\pi$
$137$	17.3760	−	10.0321i	1.48453	−	0.857096i	0.999845	+	0.0175898i	$0.00559931\pi$
$138$			5.04721i			0.429647i
$139$	8.16966	+	14.1503i	0.692941	+	1.20021i	0.970870	+	0.239608i	$0.0770188\pi$
$139$	8.16966	+	14.1503i	0.692941	+	1.20021i	−0.277928	+	0.960602i	$0.589648\pi$
$140$		0			0
$141$	−5.39270	+	9.34044i	−0.454148	+	0.786607i
$142$		−	21.7338i		−	1.82386i
$143$	15.8830	+	3.70789i	1.32821	+	0.310070i
$144$	0.523604			0.0436337
$145$		0			0
$146$	15.5899	−	27.0026i	1.29023	−	2.23475i
$147$	−4.68334	+	2.70393i	−0.386275	+	0.223016i
$148$		−	0.721292i		−	0.0592899i
$149$	−1.62245	−	2.81016i	−0.132916	−	0.230218i	0.791883	−	0.610672i	$-0.209101\pi$
$149$	−1.62245	−	2.81016i	−0.132916	−	0.230218i	−0.924799	+	0.380455i	$0.875767\pi$
$150$		0			0
$151$	5.69996			0.463856			0.231928	−	0.972733i	$-0.425497\pi$
$151$	5.69996			0.463856			0.231928	+	0.972733i	$0.425497\pi$
$152$	11.1805	−	6.45506i	0.906858	−	0.523575i
$153$	3.89131	+	2.24665i	0.314594	+	0.181631i
$154$	6.45506	−	11.1805i	0.520164	−	0.900950i
$155$		0			0
$156$	10.7511	−	3.25817i	0.860780	−	0.260863i
$157$			3.85395i			0.307578i	0.988104	+	0.153789i	$0.0491477\pi$
$157$			3.85395i			0.307578i	−0.988104	+	0.153789i	$0.950852\pi$
$158$	−17.3760	−	10.0321i	−1.38236	−	0.798108i
$159$	−2.26180	+	3.91756i	−0.179373	+	0.310682i
$160$		0			0
$161$	−2.81571			−0.221909
$162$	1.95878	−	1.13090i	0.153896	−	0.0888520i
$163$	−8.42192	+	4.86240i	−0.659656	+	0.380853i	−0.792146	−	0.610332i	$-0.791036\pi$
$163$	−8.42192	+	4.86240i	−0.659656	+	0.380853i	0.132490	+	0.991184i	$0.457703\pi$
$164$	−3.57081			−0.278834
$165$		0			0
$166$	−9.30901	+	16.1237i	−0.722519	+	1.25144i
$167$	−16.6959	−	9.63935i	−1.29196	−	0.745916i	−0.312962	−	0.949766i	$-0.601321\pi$
$167$	−16.6959	−	9.63935i	−1.29196	−	0.745916i	−0.979002	+	0.203850i	$0.934654\pi$
$168$		−	3.18429i		−	0.245673i
$169$	−10.8130	+	7.21661i	−0.831768	+	0.555124i
$170$		0			0
$171$	−2.55787	+	4.43037i	−0.195606	+	0.338799i
$172$	17.2087	+	9.93543i	1.31215	+	0.757569i
$173$	−2.61272	+	1.50845i	−0.198641	+	0.114686i	−0.596022	−	0.802968i	$-0.703253\pi$
$173$	−2.61272	+	1.50845i	−0.198641	+	0.114686i	0.397380	+	0.917654i	$0.369919\pi$
$174$	3.11575			0.236204
$175$		0			0
$176$	1.18429	+	2.05125i	0.0892692	+	0.154619i
$177$		−	0.853947i		−	0.0641866i
$178$	−12.9719	+	7.48933i	−0.972286	+	0.561349i
$179$	−2.65847	+	4.60461i	−0.198704	+	0.344165i	−0.948108	−	0.317947i	$-0.897006\pi$
$179$	−2.65847	+	4.60461i	−0.198704	+	0.344165i	0.749405	+	0.662112i	$0.230340\pi$
$180$		0			0
$181$	25.8709			1.92297			0.961483	−	0.274866i	$-0.0886333\pi$
$181$	25.8709			1.92297			0.961483	+	0.274866i	$0.0886333\pi$
$182$	2.98440	+	9.84777i	0.221219	+	0.729965i
$183$		−	4.63935i		−	0.342951i
$184$	−2.81571	+	4.87695i	−0.207577	+	0.359534i
$185$		0			0
$186$	−10.0321	−	17.3760i	−0.735586	−	1.27407i
$187$			20.3259i			1.48638i
$188$	−29.1025	+	16.8023i	−2.12251	+	1.22543i
$189$	0.630901	+	1.09275i	0.0458913	+	0.0794861i
$190$		0			0
$191$	−5.32813	−	9.22859i	−0.385530	−	0.667757i	0.606313	−	0.795226i	$-0.292648\pi$
$191$	−5.32813	−	9.22859i	−0.385530	−	0.667757i	−0.991843	+	0.127469i	$0.959315\pi$
$192$	11.2992	+	6.52360i	0.815451	+	0.470801i
$193$	−6.91356	−	3.99155i	−0.497649	−	0.287318i	0.230093	−	0.973169i	$-0.426097\pi$
$193$	−6.91356	−	3.99155i	−0.497649	−	0.287318i	−0.727742	+	0.685851i	$0.759430\pi$
$194$	24.1327			1.73262
$195$		0			0
$196$	−16.8495			−1.20354
$197$	15.0163	+	8.66966i	1.06987	+	0.617688i	0.928145	−	0.372219i	$-0.121403\pi$
$197$	15.0163	+	8.66966i	1.06987	+	0.617688i	0.141721	+	0.989907i	$0.454736\pi$
$198$	8.86074	+	5.11575i	0.629705	+	0.363560i
$199$	−0.615749	−	1.06651i	−0.0436493	−	0.0756028i	0.843375	−	0.537325i	$-0.180565\pi$
$199$	−0.615749	−	1.06651i	−0.0436493	−	0.0756028i	−0.887025	+	0.461722i	$0.847232\pi$
$200$		0			0
$201$	6.56633	+	11.3732i	0.463153	+	0.802205i
$202$	−33.3917	+	19.2787i	−2.34943	+	1.35645i
$203$			1.73820i			0.121998i
$204$	7.00000	+	12.1244i	0.490098	+	0.848875i
$205$		0			0
$206$	−15.7742	+	27.3218i	−1.09904	+	1.90360i
$207$		−	2.23150i		−	0.155100i
$208$	−1.83845	−	0.429187i	−0.127474	−	0.0297587i
$209$	−23.1416			−1.60074
$210$		0			0
$211$	−5.16966	+	8.95411i	−0.355894	+	0.616426i	−0.987271	−	0.159050i	$-0.949157\pi$
$211$	−5.16966	+	8.95411i	−0.355894	+	0.616426i	0.631377	+	0.775476i	$0.282490\pi$
$212$	−12.2061	+	7.04721i	−0.838320	+	0.484004i
$213$			9.60905i			0.658401i
$214$	−14.1287	−	24.4716i	−0.965817	−	1.67284i
$215$		0			0
$216$	2.52360			0.171710
$217$	9.69365	−	5.59663i	0.658048	−	0.379924i
$218$	−4.46348	−	2.57699i	−0.302305	−	0.174536i
$219$	−6.89270	+	11.9385i	−0.465766	+	0.806730i
$220$		0			0
$221$	−11.8214	−	11.0779i	−0.795195	−	0.745182i
$222$			0.523604i			0.0351420i
$223$	−18.6809	−	10.7854i	−1.25096	−	0.722244i	−0.279663	−	0.960098i	$-0.590223\pi$
$223$	−18.6809	−	10.7854i	−1.25096	−	0.722244i	−0.971301	+	0.237854i	$0.923556\pi$
$224$	−3.93146	+	6.80949i	−0.262682	+	0.454978i
$225$		0			0
$226$	3.33931			0.222128
$227$	−4.71645	+	2.72305i	−0.313042	+	0.180735i	−0.648287	−	0.761396i	$-0.724514\pi$
$227$	−4.71645	+	2.72305i	−0.313042	+	0.180735i	0.335245	+	0.942131i	$0.391181\pi$
$228$	−13.8039	+	7.96970i	−0.914187	+	0.527806i
$229$	−21.9315			−1.44927			−0.724636	−	0.689132i	$-0.757992\pi$
$229$	−21.9315			−1.44927			−0.724636	+	0.689132i	$0.757992\pi$
$230$		0			0
$231$	−2.85395	+	4.94318i	−0.187776	+	0.325237i
$232$	3.01065	+	1.73820i	0.197659	+	0.114118i
$233$			25.3125i			1.65828i	0.559042	+	0.829139i	$0.311169\pi$
$233$			25.3125i			1.65828i	−0.559042	+	0.829139i	$0.688831\pi$
$234$	−7.80453	+	2.36519i	−0.510198	+	0.154617i
$235$		0			0
$236$	1.33034	−	2.30422i	0.0865979	−	0.149992i
$237$	7.68238	+	4.43543i	0.499024	+	0.288112i
$238$	−11.1056	+	6.41182i	−0.719869	+	0.415617i
$239$	−22.5236			−1.45693			−0.728465	−	0.685083i	$-0.759766\pi$
$239$	−22.5236			−1.45693			−0.728465	+	0.685083i	$0.759766\pi$
$240$		0			0
$241$	−5.55787	−	9.62652i	−0.358014	−	0.620099i	0.629615	−	0.776907i	$-0.283213\pi$
$241$	−5.55787	−	9.62652i	−0.358014	−	0.620099i	−0.987629	+	0.156809i	$0.949879\pi$
$242$			21.4034i			1.37586i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	7.22753	−	12.5185i	0.462695	−	0.801412i
$245$		0			0
$246$	2.59214			0.165269
$247$	12.6125	−	13.4590i	0.802516	−	0.856378i
$248$		−	22.3865i		−	1.42155i
$249$	4.11575	−	7.12869i	0.260825	−	0.451762i
$250$		0			0
$251$	−5.52360	−	9.56716i	−0.348647	−	0.603874i	0.637363	−	0.770564i	$-0.280025\pi$
$251$	−5.52360	−	9.56716i	−0.348647	−	0.603874i	−0.986009	+	0.166690i	$0.946692\pi$
$252$			3.93146i			0.247659i
$253$	8.74202	−	5.04721i	0.549606	−	0.317315i
$254$	20.1135	+	34.8377i	1.26204	+	2.18591i
$255$		0			0
$256$	6.23150	+	10.7933i	0.389469	+	0.674580i
$257$	−1.75829	−	1.01515i	−0.109679	−	0.0633234i	0.444157	−	0.895949i	$-0.353503\pi$
$257$	−1.75829	−	1.01515i	−0.109679	−	0.0633234i	−0.553836	+	0.832626i	$0.686837\pi$
$258$	−12.4922	−	7.21238i	−0.777731	−	0.449023i
$259$	−0.292106			−0.0181506
$260$		0			0
$261$	−1.37755			−0.0852683
$262$	−22.8583	−	13.1972i	−1.41219	−	0.815328i
$263$	−2.81320	−	1.62420i	−0.173469	−	0.100153i	0.410751	−	0.911747i	$-0.365266\pi$
$263$	−2.81320	−	1.62420i	−0.173469	−	0.100153i	−0.584221	+	0.811595i	$0.698600\pi$
$264$	5.70789	+	9.88636i	0.351297	+	0.608464i
$265$		0			0
$266$	−7.30004	−	12.6440i	−0.447594	−	0.775256i
$267$	5.73521	−	3.31122i	0.350989	−	0.202644i
$268$			40.9181i			2.49947i
$269$	13.4742	+	23.3380i	0.821535	+	1.42294i	0.904539	+	0.426392i	$0.140216\pi$
$269$	13.4742	+	23.3380i	0.821535	+	1.42294i	−0.0830032	+	0.996549i	$0.526451\pi$
$270$		0			0
$271$	9.92476	−	17.1902i	0.602886	−	1.04423i	−0.389495	−	0.921028i	$-0.627351\pi$
$271$	9.92476	−	17.1902i	0.602886	−	1.04423i	0.992382	−	0.123201i	$-0.0393161\pi$
$272$		−	2.35271i		−	0.142654i
$273$	−1.31948	−	4.35395i	−0.0798586	−	0.263513i
$274$	−45.3811			−2.74157
$275$		0			0
$276$	3.47640	−	6.02129i	0.209254	−	0.362439i
$277$	−13.9382	+	8.04721i	−0.837464	+	0.483510i	−0.856401	−	0.516311i	$-0.827305\pi$
$277$	−13.9382	+	8.04721i	−0.837464	+	0.483510i	0.0189376	+	0.999821i	$0.493972\pi$
$278$		−	36.9563i		−	2.21649i
$279$	4.43543	+	7.68238i	0.265542	+	0.459932i
$280$		0			0
$281$	−5.37755			−0.320798			−0.160399	−	0.987052i	$-0.551278\pi$
$281$	−5.37755			−0.320798			−0.160399	+	0.987052i	$0.551278\pi$
$282$	21.1262	−	12.1972i	1.25805	−	0.726334i
$283$	−23.2670	−	13.4332i	−1.38308	−	0.798522i	−0.390557	−	0.920579i	$-0.627718\pi$
$283$	−23.2670	−	13.4332i	−1.38308	−	0.798522i	−0.992523	+	0.122057i	$0.961051\pi$
$284$	−14.9697	+	25.9283i	−0.888288	+	1.53856i
$285$		0			0
$286$	−26.9181	−	25.2251i	−1.59170	−	1.49159i
$287$			1.44609i			0.0853601i
$288$	−5.39664	−	3.11575i	−0.318000	−	0.183597i
$289$	1.59488	−	2.76241i	0.0938163	−	0.162495i
$290$		0			0
$291$	−10.6697			−0.625466
$292$	−37.1974	+	21.4759i	−2.17681	+	1.25678i
$293$	18.5497	−	10.7096i	1.08368	−	0.625664i	0.151795	−	0.988412i	$-0.451495\pi$
$293$	18.5497	−	10.7096i	1.08368	−	0.625664i	0.931887	+	0.362748i	$0.118161\pi$
$294$	12.2315			0.713355
$295$		0			0
$296$	−0.292106	+	0.505942i	−0.0169783	+	0.0294073i
$297$	−3.91756	−	2.26180i	−0.227320	−	0.131243i
$298$			7.33931i			0.425155i
$299$	−1.82911	+	7.83511i	−0.105780	+	0.453116i
$300$		0			0
$301$	4.02360	−	6.96909i	0.231917	−	0.401692i
$302$	−11.1650	−	6.44609i	−0.642471	−	0.370931i
$303$	14.7633	−	8.52360i	0.848130	−	0.489668i
$304$	2.67863			0.153630
$305$		0			0
$306$	−5.08148	−	8.80138i	−0.290489	−	0.503141i
$307$			7.85395i			0.448248i	0.974561	+	0.224124i	$0.0719521\pi$
$307$			7.85395i			0.448248i	−0.974561	+	0.224124i	$0.928048\pi$
$308$	−15.4017	+	8.89218i	−0.877594	+	0.506679i
$309$	6.97418	−	12.0796i	0.396747	−	0.687187i
$310$		0			0
$311$	−27.8744			−1.58061			−0.790305	−	0.612714i	$-0.790078\pi$
$311$	−27.8744			−1.58061			−0.790305	+	0.612714i	$0.790078\pi$
$312$	−8.86074	−	2.06854i	−0.501641	−	0.117108i
$313$			7.88776i			0.445842i	0.974836	+	0.222921i	$0.0715593\pi$
$313$			7.88776i			0.445842i	−0.974836	+	0.222921i	$0.928441\pi$
$314$	4.35843	−	7.54903i	0.245961	−	0.426016i
$315$		0			0
$316$	13.8197	+	23.9364i	0.777418	+	1.34653i
$317$		−	13.2181i		−	0.742403i	−0.928552	−	0.371201i	$-0.878946\pi$
$317$		−	13.2181i		−	0.742403i	0.928552	−	0.371201i	$-0.121054\pi$
$318$	8.86074	−	5.11575i	0.496886	−	0.286877i
$319$	−3.11575	−	5.39664i	−0.174448	−	0.302154i
$320$		0			0
$321$	6.24665	+	10.8195i	0.348654	+	0.603886i
$322$	5.51535	+	3.18429i	0.307359	+	0.177454i
$323$	19.9070	+	11.4933i	1.10765	+	0.639504i
$324$	−3.11575			−0.173097
$325$		0			0
$326$	21.9956			1.21822
$327$	1.97342	+	1.13935i	0.109130	+	0.0630064i
$328$	2.50470	+	1.44609i	0.138299	+	0.0798471i
$329$	6.80453	+	11.7858i	0.375146	+	0.649771i
$330$		0			0
$331$	11.9248	+	20.6543i	0.655444	+	1.13526i	0.981782	+	0.190009i	$0.0608519\pi$
$331$	11.9248	+	20.6543i	0.655444	+	1.13526i	−0.326338	+	0.945253i	$0.605815\pi$
$332$	22.2112	−	12.8236i	1.21900	−	0.703789i
$333$		−	0.231499i		−	0.0126861i
$334$	21.8023	+	37.7627i	1.19297	+	2.06628i
$335$		0			0
$336$	0.330343	−	0.572170i	0.0180217	−	0.0312144i
$337$		−	5.68306i		−	0.309576i	−0.987948	−	0.154788i	$-0.950531\pi$
$337$		−	5.68306i		−	0.309576i	0.987948	−	0.154788i	$-0.0494694\pi$
$338$	29.3415	−	1.90734i	1.59597	−	0.103745i
$339$	−1.47640			−0.0801868
$340$		0			0
$341$	−20.0641	+	34.7521i	−1.08653	+	1.88193i
$342$	10.0206	−	5.78541i	0.541853	−	0.312839i
$343$			15.6563i			0.845359i
$344$	−8.04721	−	13.9382i	−0.433876	−	0.751496i
$345$		0			0
$346$	6.82364			0.366841
$347$	18.5759	−	10.7248i	0.997206	−	0.575737i	0.0897859	−	0.995961i	$-0.471382\pi$
$347$	18.5759	−	10.7248i	0.997206	−	0.575737i	0.907421	+	0.420224i	$0.138048\pi$
$348$	−3.71707	−	2.14605i	−0.199256	−	0.115041i
$349$	3.43543	−	5.95033i	0.183894	−	0.318514i	−0.759309	−	0.650730i	$-0.774463\pi$
$349$	3.43543	−	5.95033i	0.183894	−	0.318514i	0.943203	+	0.332216i	$0.107796\pi$
$350$		0			0
$351$	3.45058	−	1.04571i	0.184178	−	0.0558159i
$352$		−	28.1888i		−	1.50247i
$353$	−29.8751	−	17.2484i	−1.59009	−	0.918040i	−0.993290	−	0.115651i	$-0.963104\pi$
$353$	−29.8751	−	17.2484i	−1.59009	−	0.918040i	−0.596802	−	0.802389i	$-0.703562\pi$
$354$	−0.965730	+	1.67269i	−0.0513280	+	0.0889026i
$355$		0			0
$356$	20.6339			1.09359
$357$	4.91007	−	2.83483i	0.259868	−	0.150035i
$358$	10.4147	−	6.01294i	0.550435	−	0.317794i
$359$	8.15945			0.430639			0.215320	−	0.976544i	$-0.430921\pi$
$359$	8.15945			0.430639			0.215320	+	0.976544i	$0.430921\pi$
$360$		0			0
$361$	−3.58545	+	6.21017i	−0.188708	+	0.326851i
$362$	−50.6753	−	29.2574i	−2.66343	−	1.53773i
$363$		−	9.46300i		−	0.496679i
$364$	3.22253	−	13.8039i	0.168906	−	0.723522i
$365$		0			0
$366$	−5.24665	+	9.08747i	−0.274247	+	0.475009i
$367$	−5.92409	−	3.42027i	−0.309235	−	0.178537i	0.337349	−	0.941380i	$-0.390470\pi$
$367$	−5.92409	−	3.42027i	−0.309235	−	0.178537i	−0.646584	+	0.762843i	$0.723803\pi$
$368$	−1.01188	+	0.584211i	−0.0527481	+	0.0304541i
$369$	−1.14605			−0.0596611
$370$		0			0
$371$	2.85395	+	4.94318i	0.148170	+	0.256637i
$372$			27.6394i			1.43303i
$373$	11.9678	−	6.90961i	0.619669	−	0.357766i	−0.157071	−	0.987587i	$-0.550205\pi$
$373$	11.9678	−	6.90961i	0.619669	−	0.357766i	0.776740	+	0.629821i	$0.216872\pi$
$374$	22.9866	−	39.8140i	1.18861	−	2.05873i
$375$		0			0
$376$	27.2181			1.40367
$377$	4.83678	+	1.12915i	0.249107	+	0.0581540i
$378$		−	2.85395i		−	0.146791i
$379$	5.75784	−	9.97286i	0.295760	−	0.512272i	−0.679401	−	0.733767i	$-0.737760\pi$
$379$	5.75784	−	9.97286i	0.295760	−	0.512272i	0.975161	+	0.221495i	$0.0710938\pi$
$380$		0			0
$381$	−8.89270	−	15.4026i	−0.455587	−	0.789100i
$382$			24.1024i			1.23318i
$383$	19.8145	−	11.4399i	1.01247	−	0.584552i	0.100559	−	0.994931i	$-0.467937\pi$
$383$	19.8145	−	11.4399i	1.01247	−	0.584552i	0.911915	+	0.410379i	$0.134604\pi$
$384$	−8.52360	−	14.7633i	−0.434968	−	0.753387i
$385$		0			0
$386$	9.02809	+	15.6371i	0.459518	+	0.795908i
$387$	5.52312	+	3.18878i	0.280756	+	0.162095i
$388$	−28.7901	−	16.6220i	−1.46160	−	0.843854i
$389$	4.35271			0.220691			0.110346	−	0.993893i	$-0.464804\pi$
$389$	4.35271			0.220691			0.110346	+	0.993893i	$0.464804\pi$
$390$		0			0
$391$	−10.0268			−0.507077
$392$	11.8189	+	6.82364i	0.596944	+	0.344646i
$393$	10.1062	+	5.83483i	0.509791	+	0.294328i
$394$	−19.6091	−	33.9639i	−0.987890	−	1.71108i
$395$		0			0
$396$	−7.04721	−	12.2061i	−0.354136	−	0.613381i
$397$	−6.60123	+	3.81122i	−0.331306	+	0.191280i	−0.656421	−	0.754395i	$-0.727930\pi$
$397$	−6.60123	+	3.81122i	−0.331306	+	0.191280i	0.325115	+	0.945675i	$0.394597\pi$
$398$			2.78541i			0.139620i
$399$	3.22753	+	5.59025i	0.161579	+	0.279863i
$400$		0			0
$401$	−10.4248	+	18.0562i	−0.520588	+	0.901684i	0.479126	+	0.877746i	$0.340954\pi$
$401$	−10.4248	+	18.0562i	−0.520588	+	0.901684i	−0.999713	+	0.0239381i	$0.992380\pi$
$402$		−	29.7035i		−	1.48147i
$403$	−9.27635	−	30.6096i	−0.462088	−	1.52477i
$404$	53.1148			2.64256
$405$		0			0
$406$	1.96573	−	3.40474i	0.0975575	−	0.168975i
$407$	0.906910	−	0.523604i	0.0449538	−	0.0259541i
$408$		−	11.3393i		−	0.561380i
$409$	−8.48264	−	14.6924i	−0.419439	−	0.726490i	0.576444	−	0.817137i	$-0.304440\pi$
$409$	−8.48264	−	14.6924i	−0.419439	−	0.726490i	−0.995883	+	0.0906466i	$0.971107\pi$
$410$		0			0
$411$	20.0641			0.989690
$412$	37.6371	−	21.7298i	1.85425	−	1.07055i
$413$	−0.933153	−	0.538756i	−0.0459175	−	0.0265105i
$414$	−2.52360	+	4.37101i	−0.124028	+	0.214823i
$415$		0			0
$416$	16.3945	+	15.3633i	0.803804	+	0.753250i
$417$			16.3393i			0.800140i
$418$	45.3293	+	26.1709i	2.21713	+	1.28006i
$419$	1.04942	−	1.81765i	0.0512676	−	0.0887981i	−0.839253	−	0.543742i	$-0.817007\pi$
$419$	1.04942	−	1.81765i	0.0512676	−	0.0887981i	0.890520	+	0.454943i	$0.150341\pi$
$420$		0			0
$421$	−39.6598			−1.93290			−0.966449	−	0.256857i	$-0.917313\pi$
$421$	−39.6598			−1.93290			−0.966449	+	0.256857i	$0.917313\pi$
$422$	20.2524	−	11.6927i	0.985873	−	0.569194i
$423$	−9.34044	+	5.39270i	−0.454148	+	0.262202i
$424$	11.4158			0.554400
$425$		0			0
$426$	10.8669	−	18.8220i	0.526502	−	0.911929i
$427$	−5.06967	−	2.92697i	−0.245338	−	0.141646i
$428$			38.9260i			1.88156i
$429$	11.9012	+	11.1526i	0.574593	+	0.538455i
$430$		0			0
$431$	11.0641	−	19.1636i	0.532940	−	0.923079i	−0.466320	−	0.884616i	$-0.654421\pi$
$431$	11.0641	−	19.1636i	0.532940	−	0.923079i	0.999260	−	0.0384626i	$-0.0122461\pi$
$432$	0.453455	+	0.261802i	0.0218169	+	0.0125960i
$433$	−27.1553	+	15.6781i	−1.30500	+	0.753442i	−0.981257	−	0.192703i	$-0.938275\pi$
$433$	−27.1553	+	15.6781i	−1.30500	+	0.753442i	−0.323743	+	0.946145i	$0.604941\pi$
$434$	−25.3169			−1.21525
$435$		0			0
$436$	3.54994	+	6.14868i	0.170011	+	0.294468i
$437$		−	11.4158i		−	0.546091i
$438$	27.0026	−	15.5899i	1.29023	−	0.744916i
$439$	2.15672	−	3.73555i	0.102935	−	0.178288i	−0.809958	−	0.586488i	$-0.800510\pi$
$439$	2.15672	−	3.73555i	0.102935	−	0.178288i	0.912892	+	0.408200i	$0.133843\pi$
$440$		0			0
$441$	−5.40786			−0.257517
$442$	10.6275	+	35.0681i	0.505499	+	1.66802i
$443$			0.493301i			0.0234374i	0.999931	+	0.0117187i	$0.00373027\pi$
$443$			0.493301i			0.0234374i	−0.999931	+	0.0117187i	$0.996270\pi$
$444$	0.360646	−	0.624657i	0.0171155	−	0.0296449i
$445$		0			0
$446$	24.3945	+	42.2524i	1.15511	+	2.00071i
$447$		−	3.24490i		−	0.153478i
$448$	14.2574	−	8.23150i	0.673598	−	0.388902i
$449$	−11.6563	−	20.1892i	−0.550093	−	0.952789i	−0.998267	−	0.0588427i	$-0.981259\pi$
$449$	−11.6563	−	20.1892i	−0.550093	−	0.952789i	0.448174	−	0.893946i	$-0.352074\pi$
$450$		0			0
$451$	−2.59214	−	4.48973i	−0.122059	−	0.211413i
$452$	−3.98378	−	2.30004i	−0.187381	−	0.108185i
$453$	4.93631	+	2.84998i	0.231928	+	0.133904i
$454$	12.3180			0.578112
$455$		0			0
$456$	12.9101			0.604572
$457$	5.77609	+	3.33483i	0.270194	+	0.155997i	0.628976	−	0.777425i	$-0.283474\pi$
$457$	5.77609	+	3.33483i	0.270194	+	0.155997i	−0.358782	+	0.933422i	$0.616808\pi$
$458$	42.9589	+	24.8023i	2.00734	+	1.15894i
$459$	2.24665	+	3.89131i	0.104865	+	0.181631i
$460$		0			0
$461$	−14.5596	−	25.2180i	−0.678110	−	1.17452i	−0.975550	−	0.219780i	$-0.929466\pi$
$461$	−14.5596	−	25.2180i	−0.678110	−	1.17452i	0.297440	−	0.954740i	$-0.403867\pi$
$462$	11.1805	−	6.45506i	0.520164	−	0.300317i
$463$		−	1.79334i		−	0.0833436i	−0.999131	−	0.0416718i	$-0.986732\pi$
$463$		−	1.79334i		−	0.0833436i	0.999131	−	0.0416718i	$-0.0132684\pi$
$464$	0.360646	+	0.624657i	0.0167426	+	0.0289990i
$465$		0			0
$466$	28.6260	−	49.5816i	1.32607	−	2.29682i
$467$		−	16.8192i		−	0.778301i	−0.921174	−	0.389150i	$-0.872769\pi$
$467$		−	16.8192i		−	0.778301i	0.921174	−	0.389150i	$-0.127231\pi$
$468$	10.9398	+	2.55391i	0.505694	+	0.118054i
$469$	16.5708			0.765169
$470$		0			0
$471$	−1.92697	+	3.33762i	−0.0887903	+	0.153789i
$472$	−1.86631	+	1.07751i	−0.0859037	+	0.0495965i
$473$			28.8495i			1.32650i
$474$	−10.0321	−	17.3760i	−0.460788	−	0.798108i
$475$		0			0
$476$	17.6652			0.809685
$477$	−3.91756	+	2.26180i	−0.179373	+	0.103561i
$478$	44.1187	+	25.4720i	2.01794	+	1.16506i
$479$	17.5765	−	30.4434i	0.803092	−	1.39100i	−0.114479	−	0.993426i	$-0.536520\pi$
$479$	17.5765	−	30.4434i	0.803092	−	1.39100i	0.917571	−	0.397571i	$-0.130147\pi$
$480$		0			0
$481$	−0.189754	+	0.812826i	−0.00865205	+	0.0370617i
$482$			25.1416i			1.14517i
$483$	−2.43848	−	1.40786i	−0.110955	−	0.0640596i
$484$	14.7422	−	25.5342i	0.670098	−	1.16064i
$485$		0			0
$486$	2.26180			0.102597
$487$	7.47030	−	4.31298i	0.338511	−	0.195440i	−0.321102	−	0.947045i	$-0.604053\pi$
$487$	7.47030	−	4.31298i	0.338511	−	0.195440i	0.659614	+	0.751605i	$0.270720\pi$
$488$	−10.1393	+	5.85395i	−0.458986	+	0.264996i
$489$	−9.72480			−0.439771
$490$		0			0
$491$	11.6068	−	20.1036i	0.523809	−	0.907264i	−0.475807	−	0.879550i	$-0.657844\pi$
$491$	11.6068	−	20.1036i	0.523809	−	0.907264i	0.999616	−	0.0277143i	$-0.00882287\pi$
$492$	−3.09242	−	1.78541i	−0.139417	−	0.0804924i
$493$			6.18975i			0.278773i
$494$	−39.9260	+	12.0997i	−1.79636	+	0.544392i
$495$		0			0
$496$	2.32241	−	4.02253i	0.104279	−	0.180617i
$497$	10.5003	+	6.06236i	0.471004	+	0.271934i
$498$	−16.1237	+	9.30901i	−0.722519	+	0.417147i
$499$	−29.0393			−1.29998			−0.649988	−	0.759944i	$-0.725226\pi$
$499$	−29.0393			−1.29998			−0.649988	+	0.759944i	$0.725226\pi$
$500$		0			0
$501$	−9.63935	−	16.6959i	−0.430655	−	0.745916i
$502$			24.9866i			1.11521i
$503$	−15.0688	+	8.69996i	−0.671883	+	0.387912i	−0.796790	−	0.604256i	$-0.793470\pi$
$503$	−15.0688	+	8.69996i	−0.671883	+	0.387912i	0.124906	+	0.992169i	$0.460137\pi$
$504$	1.59214	−	2.75768i	0.0709198	−	0.122837i
$505$		0			0
$506$	−22.8316			−1.01499
$507$	−12.9726	+	0.843281i	−0.576134	+	0.0374514i
$508$		−	55.4149i		−	2.45864i
$509$	−11.4382	+	19.8115i	−0.506987	+	0.878128i	0.492980	+	0.870041i	$0.335908\pi$
$509$	−11.4382	+	19.8115i	−0.506987	+	0.878128i	−0.999967	+	0.00808731i	$0.997426\pi$
$510$		0			0
$511$	8.69723	+	15.0640i	0.384743	+	0.666394i
$512$			5.90558i			0.260992i
$513$	−4.43037	+	2.55787i	−0.195606	+	0.112933i
$514$	2.29607	+	3.97691i	0.101275	+	0.175414i
$515$		0			0
$516$	9.93543	+	17.2087i	0.437383	+	0.757569i
$517$	−42.2524	−	24.3945i	−1.85826	−	1.07287i
$518$	0.572170	+	0.330343i	0.0251397	+	0.0145144i
$519$	−3.01691			−0.132427
$520$		0			0
$521$	−26.3642			−1.15503			−0.577517	−	0.816378i	$-0.695978\pi$
$521$	−26.3642			−1.15503			−0.577517	+	0.816378i	$0.695978\pi$
$522$	2.69832	+	1.55787i	0.118102	+	0.0681863i
$523$	22.7696	+	13.1461i	0.995646	+	0.574837i	0.906957	−	0.421223i	$-0.138399\pi$
$523$	22.7696	+	13.1461i	0.995646	+	0.574837i	0.0886892	+	0.996059i	$0.471732\pi$
$524$	18.1799	+	31.4884i	0.794191	+	1.37558i
$525$		0			0
$526$	3.67362	+	6.36290i	0.160178	+	0.277436i
$527$	34.5193	−	19.9297i	1.50368	−	0.868152i
$528$			2.36858i			0.103079i
$529$	−9.01021	−	15.6061i	−0.391748	−	0.678528i
$530$		0			0
$531$	0.426974	−	0.739540i	0.0185291	−	0.0320933i
$532$			20.1124i			0.871981i
$533$	4.02396	+	0.939393i	0.174297	+	0.0406896i
$534$	−14.9787			−0.648190
$535$		0			0
$536$	16.5708	−	28.7015i	0.715750	−	1.23972i
$537$	−4.60461	+	2.65847i	−0.198704	+	0.114722i
$538$		−	60.9519i		−	2.62782i
$539$	−12.2315	−	21.1856i	−0.526848	−	0.912527i
$540$		0			0
$541$	−0.107816			−0.00463537			−0.00231768	−	0.999997i	$-0.500738\pi$
$541$	−0.107816			−0.00463537			−0.00231768	+	0.999997i	$0.500738\pi$
$542$	−38.8808	+	22.4478i	−1.67007	+	0.964218i
$543$	22.4048	+	12.9354i	0.961483	+	0.555112i
$544$	−14.0000	+	24.2487i	−0.600245	+	1.03965i
$545$		0			0
$546$	−2.33931	+	10.0206i	−0.100113	+	0.428843i
$547$		−	12.1193i		−	0.518182i	−0.965853	−	0.259091i	$-0.916577\pi$
$547$		−	12.1193i		−	0.518182i	0.965853	−	0.259091i	$-0.0834230\pi$
$548$	54.1394	+	31.2574i	2.31272	+	1.33525i
$549$	2.31968	−	4.01780i	0.0990014	−	0.171475i
$550$		0			0
$551$	−7.04721			−0.300221
$552$	−4.87695	+	2.81571i	−0.207577	+	0.119845i
$553$	9.69365	−	5.59663i	0.412216	−	0.237993i
$554$	36.4024			1.54659
$555$		0			0
$556$	−25.4546	+	44.0887i	−1.07952	+	1.86978i
$557$	32.9150	+	19.0035i	1.39466	+	0.805204i	0.993826	−	0.110948i	$-0.0353889\pi$
$557$	32.9150	+	19.0035i	1.39466	+	0.805204i	0.400829	+	0.916153i	$0.368722\pi$
$558$		−	20.0641i		−	0.849382i
$559$	−16.7787	−	15.7234i	−0.709664	−	0.665030i
$560$		0			0
$561$	−10.1630	+	17.6028i	−0.429080	+	0.743189i
$562$	10.5334	+	6.08148i	0.444326	+	0.256532i
$563$	13.4322	−	7.75510i	0.566101	−	0.326839i	−0.189490	−	0.981883i	$-0.560683\pi$
$563$	13.4322	−	7.75510i	0.566101	−	0.326839i	0.755591	+	0.655044i	$0.227350\pi$
$564$	−33.6046			−1.41501
$565$		0			0
$566$	30.3833	+	52.6254i	1.27710	+	2.21201i
$567$			1.26180i			0.0529907i
$568$	21.0006	−	12.1247i	0.881167	−	0.508742i
$569$	9.62024	−	16.6627i	0.403301	−	0.698538i	−0.590821	−	0.806803i	$-0.701196\pi$
$569$	9.62024	−	16.6627i	0.403301	−	0.698538i	0.994122	+	0.108265i	$0.0345293\pi$
$570$		0			0
$571$	27.7338			1.16062			0.580311	−	0.814395i	$-0.302931\pi$
$571$	27.7338			1.16062			0.580311	+	0.814395i	$0.302931\pi$
$572$	14.7387	+	48.6339i	0.616255	+	2.03349i
$573$		−	10.6563i		−	0.445172i
$574$	1.63539	−	2.83257i	0.0682597	−	0.118229i
$575$		0			0
$576$	6.52360	+	11.2992i	0.271817	+	0.470801i
$577$		−	26.9866i		−	1.12347i	−0.827318	−	0.561733i	$-0.810135\pi$
$577$		−	26.9866i		−	1.12347i	0.827318	−	0.561733i	$-0.189865\pi$
$578$	−6.24802	+	3.60730i	−0.259883	+	0.150044i
$579$	−3.99155	−	6.91356i	−0.165883	−	0.287318i
$580$		0			0
$581$	−5.19326	−	8.99499i	−0.215453	−	0.373175i
$582$	20.8995	+	12.0663i	0.866312	+	0.500165i
$583$	−17.7215	−	10.2315i	−0.733949	−	0.423745i
$584$	34.7889			1.43958
$585$		0			0
$586$	−48.4462			−2.00129
$587$	−26.7195	−	15.4265i	−1.10283	−	0.636720i	−0.165869	−	0.986148i	$-0.553043\pi$
$587$	−26.7195	−	15.4265i	−1.10283	−	0.636720i	−0.936963	+	0.349427i	$0.886376\pi$
$588$	−14.5921	−	8.42476i	−0.601769	−	0.347431i
$589$	22.6905	+	39.3012i	0.934947	+	1.61938i
$590$		0			0
$591$	8.66966	+	15.0163i	0.356622	+	0.617688i
$592$	−0.104974	+	0.0606069i	−0.00431441	+	0.00249093i
$593$			4.29211i			0.176256i	0.996109	+	0.0881278i	$0.0280884\pi$
$593$			4.29211i			0.176256i	−0.996109	+	0.0881278i	$0.971912\pi$
$594$	5.11575	+	8.86074i	0.209902	+	0.363560i
$595$		0			0
$596$	5.05514	−	8.75576i	0.207067	−	0.358650i
$597$		−	1.23150i		−	0.0504019i
$598$	12.4436	−	13.2787i	0.508855	−	0.543007i
$599$	24.0224			0.981527			0.490764	−	0.871293i	$-0.336718\pi$
$599$	24.0224			0.981527			0.490764	+	0.871293i	$0.336718\pi$
$600$		0			0
$601$	−1.26577	+	2.19238i	−0.0516318	+	0.0894289i	−0.890686	−	0.454619i	$-0.849776\pi$
$601$	−1.26577	+	2.19238i	−0.0516318	+	0.0894289i	0.839054	+	0.544048i	$0.183109\pi$
$602$	−15.7627	+	9.10060i	−0.642440	+	0.370913i
$603$			13.1327i			0.534803i
$604$	8.87982	+	15.3803i	0.361315	+	0.625816i
$605$		0			0
$606$	−38.5574			−1.56629
$607$	−9.90877	+	5.72083i	−0.402185	+	0.232201i	−0.687426	−	0.726254i	$-0.741260\pi$
$607$	−9.90877	+	5.72083i	−0.402185	+	0.232201i	0.285242	+	0.958456i	$0.407926\pi$
$608$	−27.6078	−	15.9394i	−1.11965	−	0.646428i
$609$	−0.869099	+	1.50532i	−0.0352177	+	0.0609988i
$610$		0			0
$611$	37.2159	−	11.2784i	1.50559	−	0.456276i
$612$			14.0000i			0.565916i
$613$	6.22955	+	3.59663i	0.251609	+	0.145267i	0.620501	−	0.784206i	$-0.286929\pi$
$613$	6.22955	+	3.59663i	0.251609	+	0.145267i	−0.368892	+	0.929472i	$0.620263\pi$
$614$	8.88204	−	15.3841i	0.358450	−	0.620853i
$615$		0			0
$616$	14.4045			0.580373
$617$	−22.1450	+	12.7854i	−0.891523	+	0.514721i	−0.874440	−	0.485133i	$-0.838771\pi$
$617$	−22.1450	+	12.7854i	−0.891523	+	0.514721i	−0.0170827	+	0.999854i	$0.505438\pi$
$618$	−27.3218	+	15.7742i	−1.09904	+	0.634532i
$619$	−5.98660			−0.240622			−0.120311	−	0.992736i	$-0.538389\pi$
$619$	−5.98660			−0.240622			−0.120311	+	0.992736i	$0.538389\pi$
$620$		0			0
$621$	1.11575	−	1.93253i	0.0447735	−	0.0775499i
$622$	54.5997	+	31.5231i	2.18925	+	1.26396i
$623$		−	8.35622i		−	0.334785i
$624$	−1.37755	−	1.29091i	−0.0551462	−	0.0516778i
$625$		0			0
$626$	8.92027	−	15.4504i	0.356526	−	0.617521i
$627$	−20.0412	−	11.5708i	−0.800370	−	0.462094i
$628$	−10.3992	+	6.00397i	−0.414972	+	0.239584i
$629$	−1.04019			−0.0414752
$630$		0			0
$631$	21.5129	+	37.2615i	0.856417	+	1.48336i	0.875325	+	0.483536i	$0.160648\pi$
$631$	21.5129	+	37.2615i	0.856417	+	1.48336i	−0.0189080	+	0.999821i	$0.506019\pi$
$632$		−	22.3865i		−	0.890488i
$633$	−8.95411	+	5.16966i	−0.355894	+	0.205475i
$634$	−14.9484	+	25.8913i	−0.593675	+	1.02828i
$635$		0			0
$636$	−14.0944			−0.558880
$637$	18.9878	+	4.43269i	0.752322	+	0.175630i
$638$			14.0944i			0.558003i
$639$	−4.80453	+	8.32168i	−0.190064	+	0.329201i
$640$		0			0
$641$	3.34725	+	5.79760i	0.132208	+	0.228992i	0.924528	−	0.381115i	$-0.124460\pi$
$641$	3.34725	+	5.79760i	0.132208	+	0.228992i	−0.792319	+	0.610107i	$0.791127\pi$
$642$		−	28.2574i		−	1.11523i
$643$	7.08477	−	4.09039i	0.279396	−	0.161309i	−0.353754	−	0.935338i	$-0.615095\pi$
$643$	7.08477	−	4.09039i	0.279396	−	0.161309i	0.633150	+	0.774029i	$0.281762\pi$
$644$	−4.38652	−	7.59768i	−0.172853	−	0.299391i
$645$		0			0
$646$	−25.9956	−	45.0257i	−1.02278	−	1.77151i
$647$	−9.76765	−	5.63935i	−0.384006	−	0.221706i	0.295554	−	0.955326i	$-0.404496\pi$
$647$	−9.76765	−	5.63935i	−0.384006	−	0.221706i	−0.679560	+	0.733620i	$0.737829\pi$
$648$	2.18551	+	1.26180i	0.0858548	+	0.0495683i
$649$	3.86292			0.151633
$650$		0			0
$651$	11.1933			0.438699
$652$	−26.2406	−	15.1500i	−1.02766	−	0.593321i
$653$	−23.5978	−	13.6242i	−0.923454	−	0.533156i	−0.0387184	−	0.999250i	$-0.512328\pi$
$653$	−23.5978	−	13.6242i	−0.923454	−	0.533156i	−0.884735	+	0.466094i	$0.845661\pi$
$654$	−2.57699	−	4.46348i	−0.100768	−	0.174536i
$655$		0			0
$656$	0.300039	+	0.519683i	0.0117146	+	0.0202902i
$657$	−11.9385	+	6.89270i	−0.465766	+	0.268910i
$658$		−	30.7810i		−	1.19997i
$659$	3.37755	+	5.85009i	0.131571	+	0.227887i	0.924282	−	0.381710i	$-0.124665\pi$
$659$	3.37755	+	5.85009i	0.131571	+	0.227887i	−0.792711	+	0.609597i	$0.791331\pi$
$660$		0			0
$661$	13.2551	−	22.9585i	0.515564	−	0.892983i	−0.484273	−	0.874917i	$-0.660916\pi$
$661$	13.2551	−	22.9585i	0.515564	−	0.892983i	0.999837	−	0.0180657i	$-0.00575081\pi$
$662$		−	53.9429i		−	2.09655i
$663$	−4.69869	−	15.5045i	−0.182482	−	0.602144i
$664$	−20.7730			−0.806151
$665$		0			0
$666$	−0.261802	+	0.453455i	−0.0101446	+	0.0175710i
$667$	2.66217	−	1.53700i	0.103079	−	0.0595130i
$668$		−	60.0676i		−	2.32409i
$669$	−10.7854	−	18.6809i	−0.416988	−	0.722244i
$670$		0			0
$671$	20.9866			0.810179
$672$	−6.80949	+	3.93146i	−0.262682	+	0.151659i
$673$	0.586811	+	0.338795i	0.0226199	+	0.0130596i	0.511267	−	0.859422i	$-0.329176\pi$
$673$	0.586811	+	0.338795i	0.0226199	+	0.0130596i	−0.488647	+	0.872481i	$0.662510\pi$
$674$	−6.42697	+	11.1318i	−0.247558	+	0.428783i
$675$		0			0
$676$	−36.3180	−	17.9343i	−1.39685	−	0.689780i
$677$			10.4630i			0.402126i	0.979578	+	0.201063i	$0.0644395\pi$
$677$			10.4630i			0.402126i	−0.979578	+	0.201063i	$0.935560\pi$
$678$	2.89193	+	1.66966i	0.111064	+	0.0641228i
$679$	−6.73150	+	11.6593i	−0.258331	+	0.447443i
$680$		0			0
$681$	−5.44609			−0.208695
$682$	78.6023	−	45.3811i	3.00984	−	1.73773i
$683$	−16.2394	+	9.37580i	−0.621382	+	0.358755i	−0.777407	−	0.628998i	$-0.783465\pi$
$683$	−16.2394	+	9.37580i	−0.621382	+	0.358755i	0.156025	+	0.987753i	$0.450132\pi$
$684$	−15.9394			−0.609458
$685$		0			0
$686$	17.7057	−	30.6671i	0.676006	−	1.17088i
$687$	−18.9932	−	10.9657i	−0.724636	−	0.418369i
$688$		−	3.33931i		−	0.127310i
$689$	15.6091	−	4.73038i	0.594657	−	0.180213i
$690$		0			0
$691$	−21.7827	+	37.7287i	−0.828652	+	1.43527i	0.0704440	+	0.997516i	$0.477558\pi$
$691$	−21.7827	+	37.7287i	−0.828652	+	1.43527i	−0.899096	+	0.437752i	$0.855775\pi$
$692$	−8.14057	−	4.69996i	−0.309458	−	0.178666i
$693$	−4.94318	+	2.85395i	−0.187776	+	0.108412i
$694$	−48.5148			−1.84159
$695$		0			0
$696$	1.73820	+	3.01065i	0.0658862	+	0.114118i
$697$			5.14956i			0.195054i
$698$	−13.4585	+	7.77026i	−0.509411	+	0.294108i
$699$	−12.6563	+	21.9213i	−0.478704	+	0.829139i
$700$		0			0
$701$	−19.0810			−0.720680			−0.360340	−	0.932821i	$-0.617339\pi$
$701$	−19.0810			−0.720680			−0.360340	+	0.932821i	$0.617339\pi$
$702$	−7.94151	−	1.85395i	−0.299733	−	0.0699727i
$703$		−	1.18429i		−	0.0446663i
$704$	−29.5102	+	51.1132i	−1.11221	+	1.92640i
$705$		0			0
$706$	39.0125	+	67.5716i	1.46825	+	2.54309i
$707$		−	21.5102i		−	0.808975i
$708$	2.30422	−	1.33034i	0.0865979	−	0.0499973i
$709$	22.3023	+	38.6287i	0.837581	+	1.45073i	0.891912	+	0.452210i	$0.149364\pi$
$709$	22.3023	+	38.6287i	0.837581	+	1.45073i	−0.0543307	+	0.998523i	$0.517303\pi$
$710$		0			0
$711$	4.43543	+	7.68238i	0.166341	+	0.288112i
$712$	−14.4734	−	8.35622i	−0.542414	−	0.313163i
$713$	−17.1432	−	9.89765i	−0.642019	−	0.370670i
$714$	−12.8236			−0.479913
$715$		0			0
$716$	−16.5663			−0.619110
$717$	−19.5060	−	11.2618i	−0.728465	−	0.420580i
$718$	−15.9826	−	9.22753i	−0.596464	−	0.344368i
$719$	−6.49109	−	11.2429i	−0.242077	−	0.419289i	0.719229	−	0.694773i	$-0.244495\pi$
$719$	−6.49109	−	11.2429i	−0.242077	−	0.419289i	−0.961306	+	0.275484i	$0.911162\pi$
$720$		0			0
$721$	−8.80004	−	15.2421i	−0.327731	−	0.567646i
$722$	14.0462	−	8.10957i	0.522745	−	0.301807i
$723$		−	11.1157i		−	0.413399i
$724$	40.3035	+	69.8078i	1.49787	+	2.59439i
$725$		0			0
$726$	−10.7017	+	18.5359i	−0.397178	+	0.687932i
$727$		−	17.3980i		−	0.645255i	−0.946526	−	0.322627i	$-0.895434\pi$
$727$		−	17.3980i		−	0.645255i	0.946526	−	0.322627i	$-0.104566\pi$
$728$	−7.85065	+	8.37755i	−0.290965	+	0.310493i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	14.3281	−	24.8170i	0.529945	−	0.917892i
$732$	12.5185	−	7.22753i	0.462695	−	0.267137i
$733$			45.8272i			1.69266i	0.532655	+	0.846332i	$0.321194\pi$
$733$			45.8272i			1.69266i	−0.532655	+	0.846332i	$0.678806\pi$
$734$	7.73598	+	13.3991i	0.285540	+	0.494570i
$735$		0			0
$736$	13.9056			0.512567
$737$	−51.4479	+	29.7035i	−1.89511	+	1.09414i
$738$	2.24486	+	1.29607i	0.0826346	+	0.0477091i
$739$	8.78541	−	15.2168i	0.323176	−	0.559758i	−0.657965	−	0.753048i	$-0.728583\pi$
$739$	8.78541	−	15.2168i	0.323176	−	0.559758i	0.981142	+	0.193290i	$0.0619159\pi$
$740$		0			0
$741$	17.6523	−	5.34959i	0.648473	−	0.196522i
$742$		−	12.9101i		−	0.473946i
$743$	26.2893	+	15.1781i	0.964459	+	0.556831i	0.897543	−	0.440928i	$-0.145350\pi$
$743$	26.2893	+	15.1781i	0.964459	+	0.556831i	0.0669167	+	0.997759i	$0.478684\pi$
$744$	11.1933	−	19.3873i	0.410365	−	0.710773i
$745$		0			0
$746$	−31.2563			−1.14438
$747$	7.12869	−	4.11575i	0.260825	−	0.150587i
$748$	−54.8458	+	31.6652i	−2.00536	+	1.15780i
$749$	15.7641			0.576007
$750$		0			0
$751$	−1.90162	+	3.29369i	−0.0693909	+	0.120189i	−0.898633	−	0.438700i	$-0.855439\pi$
$751$	−1.90162	+	3.29369i	−0.0693909	+	0.120189i	0.829242	+	0.558889i	$0.188772\pi$
$752$	4.89069	+	2.82364i	0.178345	+	0.102968i
$753$		−	11.0472i		−	0.402583i
$754$	−8.19723	−	7.68167i	−0.298525	−	0.279750i
$755$		0			0
$756$	−1.96573	+	3.40474i	−0.0714929	+	0.123829i
$757$	−2.95129	−	1.70393i	−0.107266	−	0.0619303i	0.445407	−	0.895328i	$-0.353059\pi$
$757$	−2.95129	−	1.70393i	−0.107266	−	0.0619303i	−0.552673	+	0.833398i	$0.686392\pi$
$758$	−22.5566	+	13.0231i	−0.819294	+	0.473020i
$759$	10.0944			0.366404
$760$		0			0
$761$	−3.62245	−	6.27426i	−0.131314	−	0.227442i	0.792870	−	0.609391i	$-0.208586\pi$
$761$	−3.62245	−	6.27426i	−0.131314	−	0.227442i	−0.924183	+	0.381949i	$0.875253\pi$
$762$			40.2271i			1.45727i
$763$	2.49006	−	1.43764i	0.0901464	−	0.0520460i
$764$	16.6011	−	28.7540i	0.600607	−	1.04028i
$765$		0			0
$766$	−51.7496			−1.86979
$767$	−2.10535	+	2.24665i	−0.0760198	+	0.0811218i
$768$			12.4630i			0.449720i
$769$	15.5882	−	26.9995i	0.562124	−	0.973627i	−0.435187	−	0.900340i	$-0.643318\pi$
$769$	15.5882	−	26.9995i	0.562124	−	0.973627i	0.997311	−	0.0732873i	$-0.0233490\pi$
$770$		0			0
$771$	−1.01515	−	1.75829i	−0.0365598	−	0.0633234i
$772$		−	24.8733i		−	0.895210i
$773$	16.8533	−	9.73026i	0.606172	−	0.349973i	−0.165294	−	0.986244i	$-0.552857\pi$
$773$	16.8533	−	9.73026i	0.606172	−	0.349973i	0.771466	+	0.636271i	$0.219524\pi$
$774$	−7.21238	−	12.4922i	−0.259244	−	0.449023i
$775$		0			0
$776$	13.4630	+	23.3186i	0.483293	+	0.837089i
$777$	−0.252971	−	0.146053i	−0.00907528	−	0.00523962i
$778$	−8.52600	−	4.92249i	−0.305672	−	0.176480i
$779$	−5.86292			−0.210061
$780$		0			0
$781$	−43.4675			−1.55539
$782$	19.6403	+	11.3393i	0.702335	+	0.405493i
$783$	−1.19299	−	0.688776i	−0.0426342	−	0.0246148i
$784$	1.41579	+	2.45222i	0.0505639	+	0.0875792i
$785$		0			0
$786$	−13.1972	−	22.8583i	−0.470730	−	0.815328i
$787$	−12.4737	+	7.20171i	−0.444641	+	0.256713i	−0.705564	−	0.708646i	$-0.749306\pi$
$787$	−12.4737	+	7.20171i	−0.444641	+	0.256713i	0.260923	+	0.965359i	$0.415973\pi$
$788$			54.0250i			1.92456i
$789$	−1.62420	−	2.81320i	−0.0578231	−	0.100153i
$790$		0			0
$791$	−0.931460	+	1.61334i	−0.0331189	+	0.0573636i
$792$			11.4158i			0.405642i
$793$	−11.4380	+	12.2057i	−0.406176	+	0.433436i
$794$	17.2405			0.611841
$795$		0			0
$796$	1.91852	−	3.32298i	0.0680002	−	0.117780i
$797$	20.4392	−	11.8006i	0.723992	−	0.417997i	−0.0922279	−	0.995738i	$-0.529399\pi$
$797$	20.4392	−	11.8006i	0.723992	−	0.417997i	0.816220	+	0.577741i	$0.196066\pi$
$798$		−	14.6001i		−	0.516837i
$799$	24.2310	+	41.9694i	0.857233	+	1.48477i
$800$		0			0
$801$	6.62245			0.233993
$802$	40.8396	−	23.5787i	1.44210	−	0.832595i
$803$	−54.0051	−	31.1799i	−1.90580	−	1.10031i
$804$	−20.4590	+	35.4361i	−0.721534	+	1.24973i
$805$		0			0
$806$	−16.4461	+	70.4480i	−0.579289	+	2.48142i
$807$			26.9484i			0.948627i
$808$	−37.2568	−	21.5102i	−1.31069	−	0.756726i
$809$	13.3776	−	23.1706i	0.470330	−	0.814635i	−0.529095	−	0.848563i	$-0.677468\pi$
$809$	13.3776	−	23.1706i	0.470330	−	0.814635i	0.999424	+	0.0339280i	$0.0108017\pi$
$810$		0			0
$811$	−3.58421			−0.125859			−0.0629293	−	0.998018i	$-0.520044\pi$
$811$	−3.58421			−0.125859			−0.0629293	+	0.998018i	$0.520044\pi$
$812$	−4.69021	+	2.70789i	−0.164594	+	0.0950285i
$813$	17.1902	−	9.92476i	0.602886	−	0.348077i
$814$	−2.36858			−0.0830187
$815$		0			0
$816$	1.17636	−	2.03751i	0.0411807	−	0.0713271i
$817$	28.2549	+	16.3130i	0.988514	+	0.570719i
$818$			38.3721i			1.34165i
$819$	1.03427	−	4.43037i	0.0361403	−	0.154810i
$820$		0			0
$821$	−7.91806	+	13.7145i	−0.276342	+	0.478639i	−0.970473	−	0.241210i	$-0.922456\pi$
$821$	−7.91806	+	13.7145i	−0.276342	+	0.478639i	0.694131	+	0.719849i	$0.255789\pi$
$822$	−39.3012	−	22.6905i	−1.37079	−	0.791423i
$823$	6.42226	−	3.70789i	0.223866	−	0.129249i	−0.383873	−	0.923386i	$-0.625410\pi$
$823$	6.42226	−	3.70789i	0.223866	−	0.129249i	0.607739	+	0.794137i	$0.292077\pi$
$824$	−35.2002			−1.22626
$825$		0			0
$826$	1.21856	+	2.11061i	0.0423991	+	0.0734374i
$827$			16.6036i			0.577363i	0.957425	+	0.288682i	$0.0932169\pi$
$827$			16.6036i			0.577363i	−0.957425	+	0.288682i	$0.906783\pi$
$828$	6.02129	−	3.47640i	0.209254	−	0.120813i
$829$	−14.6421	+	25.3608i	−0.508541	+	0.880818i	0.491410	+	0.870928i	$0.336482\pi$
$829$	−14.6421	+	25.3608i	−0.508541	+	0.880818i	−0.999951	+	0.00989015i	$0.996852\pi$
$830$		0			0
$831$	−16.0944			−0.558309
$832$	−13.6436	−	45.0204i	−0.473007	−	1.56080i
$833$			24.2991i			0.841915i
$834$	18.4781	−	32.0051i	0.639846	−	1.10825i
$835$		0			0
$836$	−36.0518	−	62.4435i	−1.24688	−	2.15965i
$837$			8.87085i			0.306622i
$838$	−4.11117	+	2.37358i	−0.142018	+	0.0819941i
$839$	−15.0810	−	26.1211i	−0.520655	−	0.901800i	−0.999712	−	0.0240164i	$-0.992355\pi$
$839$	−15.0810	−	26.1211i	−0.520655	−	0.901800i	0.479057	−	0.877784i	$-0.340979\pi$
$840$		0			0
$841$	13.5512	+	23.4713i	0.467282	+	0.809356i
$842$	77.6847	+	44.8513i	2.67719	+	1.54568i
$843$	−4.65710	−	2.68878i	−0.160399	−	0.0926064i
$844$	−32.2147			−1.10888
$845$		0			0
$846$	24.3945			0.838699
$847$	−10.3407	−	5.97022i	−0.355311	−	0.205139i
$848$	2.05125	+	1.18429i	0.0704402	+	0.0406687i
$849$	−13.4332	−	23.2670i	−0.461027	−	0.798522i
$850$		0			0
$851$	0.258295	+	0.447379i	0.00885423	+	0.0153360i
$852$	−25.9283	+	14.9697i	−0.888288	+	0.512853i
$853$		−	2.50670i		−	0.0858277i	−0.999079	−	0.0429139i	$-0.986336\pi$
$853$		−	2.50670i		−	0.0858277i	0.999079	−	0.0429139i	$-0.0136641\pi$
$854$	6.62024	+	11.4666i	0.226540	+	0.392378i
$855$		0			0
$856$	15.7641	−	27.3042i	0.538805	−	0.933238i
$857$			24.4327i			0.834605i	0.908768	+	0.417302i	$0.137024\pi$
$857$			24.4327i			0.834605i	−0.908768	+	0.417302i	$0.862976\pi$
$858$	−10.6992	−	35.3046i	−0.365264	−	1.20528i
$859$	7.10235			0.242329			0.121165	−	0.992632i	$-0.461337\pi$
$859$	7.10235			0.242329			0.121165	+	0.992632i	$0.461337\pi$
$860$		0			0
$861$	−0.723046	+	1.25235i	−0.0246413	+	0.0426801i
$862$	−43.3443	+	25.0248i	−1.47631	+	0.852349i
$863$		−	3.24490i		−	0.110458i	−0.998474	−	0.0552288i	$-0.982411\pi$
$863$		−	3.24490i		−	0.110458i	0.998474	−	0.0552288i	$-0.0175888\pi$
$864$	−3.11575	−	5.39664i	−0.106000	−	0.183597i
$865$		0			0
$866$	70.9216			2.41001
$867$	2.76241	−	1.59488i	0.0938163	−	0.0541649i
$868$	30.2030	+	17.4377i	1.02516	+	0.591874i
$869$	−20.0641	+	34.7521i	−0.680628	+	1.17888i
$870$		0			0
$871$	10.7645	−	46.1106i	0.364742	−	1.56240i
$872$		−	5.75056i		−	0.194738i
$873$	−9.24019	−	5.33483i	−0.312733	−	0.180557i
$874$	−12.9101	+	22.3610i	−0.436692	+	0.756372i
$875$		0			0
$876$	−42.9519			−1.45121
$877$	−16.4429	+	9.49330i	−0.555237	+	0.320566i	−0.751231	−	0.660039i	$-0.770540\pi$
$877$	−16.4429	+	9.49330i	−0.555237	+	0.320566i	0.195995	+	0.980605i	$0.437206\pi$
$878$	−8.44907	+	4.87807i	−0.285142	+	0.164627i
$879$	21.4193			0.722455
$880$		0			0
$881$	9.73820	−	16.8671i	0.328088	−	0.568265i	−0.654044	−	0.756456i	$-0.726929\pi$
$881$	9.73820	−	16.8671i	0.328088	−	0.568265i	0.982132	+	0.188191i	$0.0602623\pi$
$882$	10.5928	+	6.11575i	0.356678	+	0.205928i
$883$		−	50.5664i		−	1.70169i	−0.525413	−	0.850847i	$-0.676089\pi$
$883$		−	50.5664i		−	1.70169i	0.525413	−	0.850847i	$-0.323911\pi$
$884$	11.4755	−	49.1560i	0.385962	−	1.65330i
$885$		0			0
$886$	0.557875	−	0.966267i	0.0187422	−	0.0324624i
$887$	−10.8488	−	6.26356i	−0.364267	−	0.210310i	0.306684	−	0.951811i	$-0.400781\pi$
$887$	−10.8488	−	6.26356i	−0.364267	−	0.210310i	−0.670951	+	0.741502i	$0.734114\pi$
$888$	−0.505942	+	0.292106i	−0.0169783	+	0.00980243i
$889$	−22.4417			−0.752669
$890$		0			0
$891$	−2.26180	−	3.91756i	−0.0757732	−	0.131243i
$892$		−	67.2092i		−	2.25033i
$893$	−47.7833	+	27.5877i	−1.59901	+	0.923188i
$894$	−3.66966	+	6.35603i	−0.122732	+	0.212578i
$895$		0			0
$896$	−21.5102			−0.718606
$897$	−5.50161	+	5.87085i	−0.183693	+	0.196022i
$898$			52.7283i			1.75957i
$899$	−6.11003	+	10.5829i	−0.203781	+	0.352959i
$900$		0			0
$901$	10.1630	+	17.6028i	0.338577	+	0.586433i
$902$			11.7258i			0.390428i
$903$	6.96909	−	4.02360i	0.231917	−	0.133897i
$904$	1.86292	+	3.22667i	0.0619598	+	0.107317i
$905$		0			0
$906$	−6.44609	−	11.1650i	−0.214157	−	0.370931i
$907$	24.2849	+	14.0209i	0.806366	+	0.465555i	0.845692	−	0.533671i	$-0.179188\pi$
$907$	24.2849	+	14.0209i	0.806366	+	0.465555i	−0.0393265	+	0.999226i	$0.512521\pi$
$908$	−14.6953	−	8.48433i	−0.487680	−	0.281562i
$909$	17.0472			0.565420
$910$		0			0
$911$	16.1977			0.536653			0.268327	−	0.963328i	$-0.413529\pi$
$911$	16.1977			0.536653			0.268327	+	0.963328i	$0.413529\pi$
$912$	2.31976	+	1.33931i	0.0768150	+	0.0443491i
$913$	32.2474	+	18.6180i	1.06723	+	0.616167i
$914$	−7.54272	−	13.0644i	−0.249491	−	0.432131i
$915$		0			0
$916$	−34.1665	−	59.1781i	−1.12889	−	1.95530i
$917$	12.7521	−	7.36240i	0.421110	−	0.243128i
$918$		−	10.1630i		−	0.335428i
$919$	−21.6389	−	37.4797i	−0.713801	−	1.23634i	−0.963420	−	0.267996i	$-0.913639\pi$
$919$	−21.6389	−	37.4797i	−0.713801	−	1.23634i	0.249619	−	0.968344i	$-0.419695\pi$
$920$		0			0
$921$	−3.92697	+	6.80172i	−0.129398	+	0.224124i
$922$			65.8620i			2.16905i
$923$	23.6905	−	25.2805i	0.779781	−	0.832117i
$924$	−17.7844			−0.585063
$925$		0			0
$926$	−2.02809	+	3.51276i	−0.0666472	+	0.115436i
$927$	12.0796	−	6.97418i	0.396747	−	0.229062i
$928$		−	8.58421i		−	0.281791i
$929$	6.88425	+	11.9239i	0.225865	+	0.391210i	0.956579	−	0.291475i	$-0.0941459\pi$
$929$	6.88425	+	11.9239i	0.225865	+	0.391210i	−0.730714	+	0.682684i	$0.760813\pi$
$930$		0			0
$931$	−27.6652			−0.906691
$932$	−68.3012	+	39.4337i	−2.23728	+	1.29169i
$933$	−24.1399	−	13.9372i	−0.790305	−	0.456283i
$934$	−19.0209	+	32.9451i	−0.622382	+	1.07800i
$935$		0			0
$936$	−6.63935	−	6.22178i	−0.217014	−	0.203365i
$937$			38.1888i			1.24757i	0.781594	+	0.623787i	$0.214407\pi$
$937$			38.1888i			1.24757i	−0.781594	+	0.623787i	$0.785593\pi$
$938$	−32.4585	−	18.7400i	−1.05981	−	0.611881i
$939$	−3.94388	+	6.83100i	−0.128704	+	0.222921i
$940$		0			0
$941$	−13.9618			−0.455140			−0.227570	−	0.973762i	$-0.573078\pi$
$941$	−13.9618			−0.455140			−0.227570	+	0.973762i	$0.573078\pi$
$942$	7.54903	−	4.35843i	0.245961	−	0.142005i
$943$	2.21479	−	1.27871i	0.0721234	−	0.0416405i
$944$	−0.447131			−0.0145529
$945$		0			0
$946$	32.6260	−	56.5098i	1.06076	−	1.83729i
$947$	6.38228	+	3.68481i	0.207396	+	0.119740i	0.600101	−	0.799924i	$-0.295127\pi$
$947$	6.38228	+	3.68481i	0.207396	+	0.119740i	−0.392705	+	0.919665i	$0.628461\pi$
$948$			27.6394i			0.897684i
$949$	47.5676	−	14.4155i	1.54411	−	0.467948i
$950$		0			0
$951$	6.60905	−	11.4472i	0.214313	−	0.371201i
$952$	−12.3911	−	7.15399i	−0.401597	−	0.231862i
$953$	20.1075	−	11.6091i	0.651345	−	0.376054i	−0.137627	−	0.990484i	$-0.543947\pi$
$953$	20.1075	−	11.6091i	0.651345	−	0.376054i	0.788971	+	0.614430i	$0.210614\pi$
$954$	10.2315			0.331257
$955$		0			0
$956$	−35.0890	−	60.7759i	−1.13486	−	1.96563i
$957$		−	6.23150i		−	0.201436i
$958$	−68.8571	+	39.7546i	−2.22467	+	1.28441i
$959$	12.6585	−	21.9251i	0.408763	−	0.707999i
$960$		0			0
$961$	47.6920			1.53845
$962$	1.29091	−	1.37755i	0.0416207	−	0.0444140i
$963$			12.4933i			0.402591i
$964$	17.3169	−	29.9938i	0.557741	−	0.966036i
$965$		0			0
$966$	3.18429	+	5.51535i	0.102453	+	0.177454i
$967$			7.54402i			0.242599i	0.992616	+	0.121300i	$0.0387062\pi$
$967$			7.54402i			0.242599i	−0.992616	+	0.121300i	$0.961294\pi$
$968$	−20.6814	+	11.9404i	−0.664726	+	0.383780i
$969$	11.4933	+	19.9070i	0.369218	+	0.639504i
$970$		0			0
$971$	15.2921	+	26.4867i	0.490747	+	0.849999i	0.999943	−	0.0106517i	$-0.00339059\pi$
$971$	15.2921	+	26.4867i	0.490747	+	0.849999i	−0.509196	+	0.860650i	$0.670057\pi$
$972$	−2.69832	−	1.55787i	−0.0865486	−	0.0499689i
$973$	17.8548	+	10.3085i	0.572400	+	0.330475i
$974$	−19.5102			−0.625147
$975$		0			0
$976$	−2.42919			−0.0777564
$977$	−30.9007	−	17.8405i	−0.988602	−	0.570770i	−0.0837460	−	0.996487i	$-0.526688\pi$
$977$	−30.9007	−	17.8405i	−0.988602	−	0.570770i	−0.904856	+	0.425717i	$0.860022\pi$
$978$	19.0487	+	10.9978i	0.609111	+	0.351670i
$979$	14.9787	+	25.9438i	0.478720	+	0.829168i
$980$		0			0
$981$	1.13935	+	1.97342i	0.0363768	+	0.0630064i
$982$	−45.4704	+	26.2524i	−1.45102	+	0.837747i
$983$			12.9866i			0.414208i	0.978319	+	0.207104i	$0.0664039\pi$
$983$			12.9866i			0.414208i	−0.978319	+	0.207104i	$0.933596\pi$
$984$	1.44609	+	2.50470i	0.0460997	+	0.0798471i
$985$		0			0
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$			13.6091i			0.433181i
$988$	55.9655	+	13.0652i	1.78050	+	0.415658i
$989$	−14.2315			−0.452535
$990$		0			0
$991$	11.3736	−	19.6996i	0.361294	−	0.625779i	−0.626880	−	0.779116i	$-0.715668\pi$
$991$	11.3736	−	19.6996i	0.361294	−	0.625779i	0.988174	+	0.153336i	$0.0490018\pi$
$992$	−47.8728	+	27.6394i	−1.51996	+	0.877550i
$993$			23.8495i			0.756842i
$994$	−13.7119	−	23.7496i	−0.434914	−	0.753293i
$995$		0			0
$996$	25.6473			0.812665
$997$	11.9910	−	6.92301i	0.379759	−	0.219254i	−0.297955	−	0.954580i	$-0.596304\pi$
$997$	11.9910	−	6.92301i	0.379759	−	0.219254i	0.677713	+	0.735326i	$0.262971\pi$
$998$	56.8815	+	32.8405i	1.80055	+	1.03955i
$999$	0.115749	−	0.200484i	0.00366215	−	0.00634303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.k.724.2		12
5.2	odd	4		195.2.i.d.61.3	yes	6
5.3	odd	4		975.2.i.l.451.1		6
5.4	even	2	inner	975.2.bb.k.724.5		12
13.3	even	3	inner	975.2.bb.k.874.5		12
15.2	even	4		585.2.j.f.451.1		6
65.3	odd	12		975.2.i.l.601.1		6
65.17	odd	12		2535.2.a.ba.1.3		3
65.22	odd	12		2535.2.a.bb.1.1		3
65.29	even	6	inner	975.2.bb.k.874.2		12
65.42	odd	12		195.2.i.d.16.3	✓	6
195.17	even	12		7605.2.a.bw.1.1		3
195.107	even	12		585.2.j.f.406.1		6
195.152	even	12		7605.2.a.bv.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.3	✓	6	65.42	odd	12
195.2.i.d.61.3	yes	6	5.2	odd	4
585.2.j.f.406.1		6	195.107	even	12
585.2.j.f.451.1		6	15.2	even	4
975.2.i.l.451.1		6	5.3	odd	4
975.2.i.l.601.1		6	65.3	odd	12
975.2.bb.k.724.2		12	1.1	even	1	trivial
975.2.bb.k.724.5		12	5.4	even	2	inner
975.2.bb.k.874.2		12	65.29	even	6	inner
975.2.bb.k.874.5		12	13.3	even	3	inner
2535.2.a.ba.1.3		3	65.17	odd	12
2535.2.a.bb.1.1		3	65.22	odd	12
7605.2.a.bv.1.3		3	195.152	even	12
7605.2.a.bw.1.1		3	195.17	even	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.95878 - 1.13090i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.55787 + 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(1.09275 - 0.630901i) q^{7} -2.52360i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.95878 - 1.13090i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.55787 + 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(1.09275 - 0.630901i) q^{7} -2.52360i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.26180 + 3.91756i) q^{11} +3.11575i q^{12} +(-1.04571 - 3.45058i) q^{13} -2.85395 q^{14} +(0.261802 - 0.453455i) q^{16} +(3.89131 - 2.24665i) q^{17} -2.26180i q^{18} +(2.55787 + 4.43037i) q^{19} +1.26180 q^{21} +(8.86074 - 5.11575i) q^{22} +(-1.93253 - 1.11575i) q^{23} +(1.26180 - 2.18551i) q^{24} +(-1.85395 + 7.94151i) q^{26} +1.00000i q^{27} +(3.40474 + 1.96573i) q^{28} +(-0.688776 + 1.19299i) q^{29} +8.87085 q^{31} +(-5.39664 + 3.11575i) q^{32} +(-3.91756 + 2.26180i) q^{33} -10.1630 q^{34} +(-1.55787 + 2.69832i) q^{36} +(-0.200484 - 0.115749i) q^{37} -11.5708i q^{38} +(0.819677 - 3.51114i) q^{39} +(-0.573026 + 0.992511i) q^{41} +(-2.47159 - 1.42697i) q^{42} +(5.52312 - 3.18878i) q^{43} -14.0944 q^{44} +(2.52360 + 4.37101i) q^{46} +10.7854i q^{47} +(0.453455 - 0.261802i) q^{48} +(-2.70393 + 4.68334i) q^{49} +4.49330 q^{51} +(7.68167 - 8.19723i) q^{52} +4.52360i q^{53} +(1.13090 - 1.95878i) q^{54} +(-1.59214 - 2.75768i) q^{56} +5.11575i q^{57} +(2.69832 - 1.55787i) q^{58} +(-0.426974 - 0.739540i) q^{59} +(-2.31968 - 4.01780i) q^{61} +(-17.3760 - 10.0321i) q^{62} +(1.09275 + 0.630901i) q^{63} +13.0472 q^{64} +10.2315 q^{66} +(11.3732 + 6.56633i) q^{67} +(12.1244 + 7.00000i) q^{68} +(-1.11575 - 1.93253i) q^{69} +(4.80453 + 8.32168i) q^{71} +(2.18551 - 1.26180i) q^{72} +13.7854i q^{73} +(0.261802 + 0.453455i) q^{74} +(-7.96970 + 13.8039i) q^{76} +5.70789i q^{77} +(-5.57632 + 5.95058i) q^{78} +8.87085 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.24486 - 1.29607i) q^{82} -8.23150i q^{83} +(1.96573 + 3.40474i) q^{84} -14.4248 q^{86} +(-1.19299 + 0.688776i) q^{87} +(9.88636 + 5.70789i) q^{88} +(3.31122 - 5.73521i) q^{89} +(-3.31968 - 3.11089i) q^{91} -6.95279i q^{92} +(7.68238 + 4.43543i) q^{93} +(12.1972 - 21.1262i) q^{94} -6.23150 q^{96} +(-9.24019 + 5.33483i) q^{97} +(10.5928 - 6.11575i) q^{98} -4.52360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q + 12 * q^4 + 6 * q^9	\( 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) \) 12 * q + 12 * q^4 + 6 * q^9 - 48 * q^14 - 24 * q^16 + 24 * q^19 - 12 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 + 12 * q^31 - 12 * q^36 - 24 * q^39 + 48 * q^44 - 24 * q^46 - 12 * q^49 - 60 * q^56 - 12 * q^59 + 6 * q^61 + 48 * q^64 + 96 * q^66 + 24 * q^71 - 24 * q^74 - 96 * q^76 + 12 * q^79 - 6 * q^81 - 24 * q^84 - 24 * q^86 + 60 * q^89 - 6 * q^91 + 72 * q^94 - 48 * q^96

Introduction

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