LMFDB - Embedded newform 975.2.bb.k.874.2

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			874.2
Root			$2.23871 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.874
Dual form			975.2.bb.k.724.2

$q$-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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

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

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	−0.992754	−	0.120165i	$-0.961658\pi$
$2$	−1.95878	+	1.13090i	−1.38507	+	0.799668i	−0.392311	+	0.919832i	$0.628324\pi$
$3$	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	0.692087	−	0.721814i	$-0.256691\pi$
$7$	1.09275	+	0.630901i	0.413022	+	0.238458i	−0.279066	+	0.960272i	$0.590025\pi$
$8$			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	−0.974382	−	0.224899i	$-0.927795\pi$
$11$	−2.26180	−	3.91756i	−0.681959	−	1.18119i	0.292423	−	0.956289i	$-0.405538\pi$
$12$		−	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	0.891144	−	0.453721i	$-0.149904\pi$
$17$	3.89131	+	2.24665i	0.943782	+	0.544893i	0.0526381	+	0.998614i	$0.483237\pi$
$18$			2.26180i			0.533112i
$19$	2.55787	−	4.43037i	0.586817	−	1.01640i	−0.407830	−	0.913058i	$-0.633714\pi$
$19$	2.55787	−	4.43037i	0.586817	−	1.01640i	0.994646	−	0.103338i	$-0.0329524\pi$
$20$		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	−0.687761	−	0.725937i	$-0.741406\pi$
$23$	−1.93253	+	1.11575i	−0.402961	+	0.232650i	0.284800	+	0.958587i	$0.408073\pi$
$24$	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	0.794961	−	0.606660i	$-0.207491\pi$
$29$	−0.688776	−	1.19299i	−0.127902	−	0.221534i	−0.922864	+	0.385127i	$0.874158\pi$
$30$		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	−0.516389	−	0.856354i	$-0.672724\pi$
$37$	−0.200484	+	0.115749i	−0.0329593	+	0.0190291i	0.483430	+	0.875383i	$0.339391\pi$
$38$			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	0.817805	−	0.575496i	$-0.195191\pi$
$41$	−0.573026	−	0.992511i	−0.0894917	−	0.155004i	−0.907296	+	0.420492i	$0.861858\pi$
$42$	−2.47159	+	1.42697i	−0.381375	+	0.220187i
$43$	5.52312	+	3.18878i	0.842268	+	0.486284i	0.858035	−	0.513592i	$-0.171685\pi$
$43$	5.52312	+	3.18878i	0.842268	+	0.486284i	−0.0157664	+	0.999876i	$0.505019\pi$
$44$	−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	$-0.711836\pi$
$47$		−	10.7854i		−	1.57321i	0.617454	−	0.786607i	$-0.288164\pi$
$48$	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	$-0.899442\pi$
$53$		−	4.52360i		−	0.621365i	0.950514	−	0.310682i	$-0.100558\pi$
$54$	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	−0.892480	−	0.451087i	$-0.851036\pi$
$59$	−0.426974	+	0.739540i	−0.0555872	+	0.0962799i	0.836893	+	0.547367i	$0.184370\pi$
$60$		0			0
$61$	−2.31968	+	4.01780i	−0.297004	+	0.514426i	−0.975449	−	0.220225i	$-0.929321\pi$
$61$	−2.31968	+	4.01780i	−0.297004	+	0.514426i	0.678445	+	0.734651i	$0.262654\pi$
$62$	−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	0.396205	−	0.918162i	$-0.370327\pi$
$67$	11.3732	−	6.56633i	1.38946	−	0.802205i	0.993254	+	0.115958i	$0.0369937\pi$
$68$	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	−0.426354	−	0.904557i	$-0.640202\pi$
$71$	4.80453	−	8.32168i	0.570192	−	0.987602i	0.996546	−	0.0830453i	$-0.0264646\pi$
$72$	2.18551	+	1.26180i	0.257564	+	0.148705i
$73$		−	13.7854i		−	1.61346i	−0.590920	−	0.806730i	$-0.701235\pi$
$73$		−	13.7854i		−	1.61346i	0.590920	−	0.806730i	$-0.298765\pi$
$74$	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	$0.149204\pi$
$83$			8.23150i			0.903524i	−0.892138	+	0.451762i	$0.850796\pi$
$84$	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	0.986423	−	0.164224i	$-0.0525121\pi$
$89$	3.31122	+	5.73521i	0.350989	+	0.607931i	−0.635434	+	0.772155i	$0.719179\pi$
$90$		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	−0.0488041	−	0.998808i	$-0.515541\pi$
$97$	−9.24019	−	5.33483i	−0.938200	−	0.541670i	−0.889395	+	0.457139i	$0.848874\pi$
$98$	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	0.882875	+	0.469609i	$0.155605\pi$
$101$	8.52360	+	14.7633i	0.848130	+	1.46900i	−0.0347444	+	0.999396i	$0.511062\pi$
$102$	−8.80138	+	5.08148i	−0.871466	+	0.503141i
$103$			13.9484i			1.37437i	0.726481	+	0.687187i	$0.241155\pi$
$103$			13.9484i			1.37437i	−0.726481	+	0.687187i	$0.758845\pi$
$104$	−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	0.124446	−	0.992226i	$-0.460285\pi$
$107$	10.8195	−	6.24665i	1.04596	−	0.603886i	0.921516	+	0.388340i	$0.126951\pi$
$108$	−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	0.438653	−	0.898657i	$-0.355456\pi$
$113$	−1.27860	−	0.738198i	−0.120280	−	0.0694438i	−0.558933	+	0.829213i	$0.688789\pi$
$114$	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	−0.990513	−	0.137419i	$-0.956119\pi$
$127$	−15.4026	+	8.89270i	−1.36676	+	0.789100i	−0.376248	+	0.926519i	$0.622786\pi$
$128$	−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	0.999845	−	0.0175898i	$-0.00559931\pi$
$137$	17.3760	+	10.0321i	1.48453	+	0.857096i	0.484689	+	0.874686i	$0.338933\pi$
$138$		−	5.04721i		−	0.429647i
$139$	8.16966	−	14.1503i	0.692941	−	1.20021i	−0.277928	−	0.960602i	$-0.589648\pi$
$139$	8.16966	−	14.1503i	0.692941	−	1.20021i	0.970870	−	0.239608i	$-0.0770188\pi$
$140$		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	−0.924799	−	0.380455i	$-0.875767\pi$
$149$	−1.62245	+	2.81016i	−0.132916	+	0.230218i	0.791883	+	0.610672i	$0.209101\pi$
$150$		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	$-0.950852\pi$
$157$		−	3.85395i		−	0.307578i	0.988104	−	0.153789i	$-0.0491477\pi$
$158$	−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	0.132490	−	0.991184i	$-0.457703\pi$
$163$	−8.42192	−	4.86240i	−0.659656	−	0.380853i	−0.792146	+	0.610332i	$0.791036\pi$
$164$	−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	−0.979002	−	0.203850i	$-0.934654\pi$
$167$	−16.6959	+	9.63935i	−1.29196	+	0.745916i	−0.312962	+	0.949766i	$0.601321\pi$
$168$			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	0.397380	−	0.917654i	$-0.369919\pi$
$173$	−2.61272	−	1.50845i	−0.198641	−	0.114686i	−0.596022	+	0.802968i	$0.703253\pi$
$174$	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	0.749405	−	0.662112i	$-0.230340\pi$
$179$	−2.65847	−	4.60461i	−0.198704	−	0.344165i	−0.948108	+	0.317947i	$0.897006\pi$
$180$		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	−0.991843	−	0.127469i	$-0.959315\pi$
$191$	−5.32813	+	9.22859i	−0.385530	+	0.667757i	0.606313	+	0.795226i	$0.292648\pi$
$192$	11.2992	−	6.52360i	0.815451	−	0.470801i
$193$	−6.91356	+	3.99155i	−0.497649	+	0.287318i	−0.727742	−	0.685851i	$-0.759430\pi$
$193$	−6.91356	+	3.99155i	−0.497649	+	0.287318i	0.230093	+	0.973169i	$0.426097\pi$
$194$	24.1327			1.73262
$195$		0			0
$196$	−16.8495			−1.20354
$197$	15.0163	−	8.66966i	1.06987	−	0.617688i	0.141721	−	0.989907i	$-0.454736\pi$
$197$	15.0163	−	8.66966i	1.06987	−	0.617688i	0.928145	+	0.372219i	$0.121403\pi$
$198$	8.86074	−	5.11575i	0.629705	−	0.363560i
$199$	−0.615749	+	1.06651i	−0.0436493	+	0.0756028i	−0.887025	−	0.461722i	$-0.847232\pi$
$199$	−0.615749	+	1.06651i	−0.0436493	+	0.0756028i	0.843375	+	0.537325i	$0.180565\pi$
$200$		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	0.631377	−	0.775476i	$-0.282490\pi$
$211$	−5.16966	−	8.95411i	−0.355894	−	0.616426i	−0.987271	+	0.159050i	$0.949157\pi$
$212$	−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	−0.971301	−	0.237854i	$-0.923556\pi$
$223$	−18.6809	+	10.7854i	−1.25096	+	0.722244i	−0.279663	+	0.960098i	$0.590223\pi$
$224$	−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	0.335245	−	0.942131i	$-0.391181\pi$
$227$	−4.71645	−	2.72305i	−0.313042	−	0.180735i	−0.648287	+	0.761396i	$0.724514\pi$
$228$	−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	$-0.688831\pi$
$233$		−	25.3125i		−	1.65828i	0.559042	−	0.829139i	$-0.311169\pi$
$234$	−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	−0.987629	−	0.156809i	$-0.949879\pi$
$241$	−5.55787	+	9.62652i	−0.358014	+	0.620099i	0.629615	+	0.776907i	$0.283213\pi$
$242$		−	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	−0.986009	−	0.166690i	$-0.946692\pi$
$251$	−5.52360	+	9.56716i	−0.348647	+	0.603874i	0.637363	+	0.770564i	$0.280025\pi$
$252$		−	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	−0.553836	−	0.832626i	$-0.686837\pi$
$257$	−1.75829	+	1.01515i	−0.109679	+	0.0633234i	0.444157	+	0.895949i	$0.353503\pi$
$258$	−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	−0.584221	−	0.811595i	$-0.698600\pi$
$263$	−2.81320	+	1.62420i	−0.173469	+	0.100153i	0.410751	+	0.911747i	$0.365266\pi$
$264$	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	−0.0830032	−	0.996549i	$-0.526451\pi$
$269$	13.4742	−	23.3380i	0.821535	−	1.42294i	0.904539	−	0.426392i	$-0.140216\pi$
$270$		0			0
$271$	9.92476	+	17.1902i	0.602886	+	1.04423i	0.992382	+	0.123201i	$0.0393161\pi$
$271$	9.92476	+	17.1902i	0.602886	+	1.04423i	−0.389495	+	0.921028i	$0.627351\pi$
$272$			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	0.0189376	−	0.999821i	$-0.493972\pi$
$277$	−13.9382	−	8.04721i	−0.837464	−	0.483510i	−0.856401	+	0.516311i	$0.827305\pi$
$278$			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	−0.992523	−	0.122057i	$-0.961051\pi$
$283$	−23.2670	+	13.4332i	−1.38308	+	0.798522i	−0.390557	+	0.920579i	$0.627718\pi$
$284$	−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	0.931887	−	0.362748i	$-0.118161\pi$
$293$	18.5497	+	10.7096i	1.08368	+	0.625664i	0.151795	+	0.988412i	$0.451495\pi$
$294$	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	$-0.928048\pi$
$307$		−	7.85395i		−	0.448248i	0.974561	−	0.224124i	$-0.0719521\pi$
$308$	−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	$-0.928441\pi$
$313$		−	7.88776i		−	0.445842i	0.974836	−	0.222921i	$-0.0715593\pi$
$314$	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	$0.121054\pi$
$317$			13.2181i			0.742403i	−0.928552	+	0.371201i	$0.878946\pi$
$318$	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	−0.326338	−	0.945253i	$-0.605815\pi$
$331$	11.9248	−	20.6543i	0.655444	−	1.13526i	0.981782	−	0.190009i	$-0.0608519\pi$
$332$	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	$0.0494694\pi$
$337$			5.68306i			0.309576i	−0.987948	+	0.154788i	$0.950531\pi$
$338$	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	0.907421	−	0.420224i	$-0.138048\pi$
$347$	18.5759	+	10.7248i	0.997206	+	0.575737i	0.0897859	+	0.995961i	$0.471382\pi$
$348$	−3.71707	+	2.14605i	−0.199256	+	0.115041i
$349$	3.43543	+	5.95033i	0.183894	+	0.318514i	0.943203	−	0.332216i	$-0.107796\pi$
$349$	3.43543	+	5.95033i	0.183894	+	0.318514i	−0.759309	+	0.650730i	$0.774463\pi$
$350$		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	−0.596802	+	0.802389i	$0.703562\pi$
$353$	−29.8751	+	17.2484i	−1.59009	+	0.918040i	−0.993290	+	0.115651i	$0.963104\pi$
$354$	−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	−0.646584	−	0.762843i	$-0.723803\pi$
$367$	−5.92409	+	3.42027i	−0.309235	+	0.178537i	0.337349	+	0.941380i	$0.390470\pi$
$368$	−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	0.776740	−	0.629821i	$-0.216872\pi$
$373$	11.9678	+	6.90961i	0.619669	+	0.357766i	−0.157071	+	0.987587i	$0.550205\pi$
$374$	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	0.975161	−	0.221495i	$-0.0710938\pi$
$379$	5.75784	+	9.97286i	0.295760	+	0.512272i	−0.679401	+	0.733767i	$0.737760\pi$
$380$		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	0.911915	−	0.410379i	$-0.134604\pi$
$383$	19.8145	+	11.4399i	1.01247	+	0.584552i	0.100559	+	0.994931i	$0.467937\pi$
$384$	−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	0.325115	−	0.945675i	$-0.394597\pi$
$397$	−6.60123	−	3.81122i	−0.331306	−	0.191280i	−0.656421	+	0.754395i	$0.727930\pi$
$398$		−	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	−0.999713	−	0.0239381i	$-0.992380\pi$
$401$	−10.4248	−	18.0562i	−0.520588	−	0.901684i	0.479126	−	0.877746i	$-0.340954\pi$
$402$			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	−0.995883	−	0.0906466i	$-0.971107\pi$
$409$	−8.48264	+	14.6924i	−0.419439	+	0.726490i	0.576444	+	0.817137i	$0.304440\pi$
$410$		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	0.890520	−	0.454943i	$-0.150341\pi$
$419$	1.04942	+	1.81765i	0.0512676	+	0.0887981i	−0.839253	+	0.543742i	$0.817007\pi$
$420$		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	0.999260	+	0.0384626i	$0.0122461\pi$
$431$	11.0641	+	19.1636i	0.532940	+	0.923079i	−0.466320	+	0.884616i	$0.654421\pi$
$432$	0.453455	−	0.261802i	0.0218169	−	0.0125960i
$433$	−27.1553	−	15.6781i	−1.30500	−	0.753442i	−0.323743	−	0.946145i	$-0.604941\pi$
$433$	−27.1553	−	15.6781i	−1.30500	−	0.753442i	−0.981257	+	0.192703i	$0.938275\pi$
$434$	−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	0.912892	−	0.408200i	$-0.133843\pi$
$439$	2.15672	+	3.73555i	0.102935	+	0.178288i	−0.809958	+	0.586488i	$0.800510\pi$
$440$		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	$-0.996270\pi$
$443$		−	0.493301i		−	0.0234374i	0.999931	−	0.0117187i	$-0.00373027\pi$
$444$	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	0.448174	+	0.893946i	$0.352074\pi$
$449$	−11.6563	+	20.1892i	−0.550093	+	0.952789i	−0.998267	+	0.0588427i	$0.981259\pi$
$450$		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	−0.358782	−	0.933422i	$-0.616808\pi$
$457$	5.77609	−	3.33483i	0.270194	−	0.155997i	0.628976	+	0.777425i	$0.283474\pi$
$458$	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	0.297440	+	0.954740i	$0.403867\pi$
$461$	−14.5596	+	25.2180i	−0.678110	+	1.17452i	−0.975550	+	0.219780i	$0.929466\pi$
$462$	11.1805	+	6.45506i	0.520164	+	0.300317i
$463$			1.79334i			0.0833436i	0.999131	+	0.0416718i	$0.0132684\pi$
$463$			1.79334i			0.0833436i	−0.999131	+	0.0416718i	$0.986732\pi$
$464$	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	$0.127231\pi$
$467$			16.8192i			0.778301i	−0.921174	+	0.389150i	$0.872769\pi$
$468$	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	0.917571	+	0.397571i	$0.130147\pi$
$479$	17.5765	+	30.4434i	0.803092	+	1.39100i	−0.114479	+	0.993426i	$0.536520\pi$
$480$		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	0.659614	−	0.751605i	$-0.270720\pi$
$487$	7.47030	+	4.31298i	0.338511	+	0.195440i	−0.321102	+	0.947045i	$0.604053\pi$
$488$	−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	0.999616	+	0.0277143i	$0.00882287\pi$
$491$	11.6068	+	20.1036i	0.523809	+	0.907264i	−0.475807	+	0.879550i	$0.657844\pi$
$492$	−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	0.124906	−	0.992169i	$-0.460137\pi$
$503$	−15.0688	−	8.69996i	−0.671883	−	0.387912i	−0.796790	+	0.604256i	$0.793470\pi$
$504$	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	−0.999967	−	0.00808731i	$-0.997426\pi$
$509$	−11.4382	−	19.8115i	−0.506987	−	0.878128i	0.492980	−	0.870041i	$-0.335908\pi$
$510$		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	0.0886892	−	0.996059i	$-0.471732\pi$
$523$	22.7696	−	13.1461i	0.995646	−	0.574837i	0.906957	+	0.421223i	$0.138399\pi$
$524$	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	$0.0834230\pi$
$547$			12.1193i			0.518182i	−0.965853	+	0.259091i	$0.916577\pi$
$548$	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	0.400829	−	0.916153i	$-0.368722\pi$
$557$	32.9150	−	19.0035i	1.39466	−	0.805204i	0.993826	+	0.110948i	$0.0353889\pi$
$558$			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	0.755591	−	0.655044i	$-0.227350\pi$
$563$	13.4322	+	7.75510i	0.566101	+	0.326839i	−0.189490	+	0.981883i	$0.560683\pi$
$564$	−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	0.994122	−	0.108265i	$-0.0345293\pi$
$569$	9.62024	+	16.6627i	0.403301	+	0.698538i	−0.590821	+	0.806803i	$0.701196\pi$
$570$		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	$0.189865\pi$
$577$			26.9866i			1.12347i	−0.827318	+	0.561733i	$0.810135\pi$
$578$	−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	−0.936963	−	0.349427i	$-0.886376\pi$
$587$	−26.7195	+	15.4265i	−1.10283	+	0.636720i	−0.165869	+	0.986148i	$0.553043\pi$
$588$	−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	$-0.971912\pi$
$593$		−	4.29211i		−	0.176256i	0.996109	−	0.0881278i	$-0.0280884\pi$
$594$	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	0.839054	−	0.544048i	$-0.183109\pi$
$601$	−1.26577	−	2.19238i	−0.0516318	−	0.0894289i	−0.890686	+	0.454619i	$0.849776\pi$
$602$	−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	0.285242	−	0.958456i	$-0.407926\pi$
$607$	−9.90877	−	5.72083i	−0.402185	−	0.232201i	−0.687426	+	0.726254i	$0.741260\pi$
$608$	−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	−0.368892	−	0.929472i	$-0.620263\pi$
$613$	6.22955	−	3.59663i	0.251609	−	0.145267i	0.620501	+	0.784206i	$0.286929\pi$
$614$	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	−0.0170827	−	0.999854i	$-0.505438\pi$
$617$	−22.1450	−	12.7854i	−0.891523	−	0.514721i	−0.874440	+	0.485133i	$0.838771\pi$
$618$	−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	−0.0189080	−	0.999821i	$-0.506019\pi$
$631$	21.5129	−	37.2615i	0.856417	−	1.48336i	0.875325	−	0.483536i	$-0.160648\pi$
$632$			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	−0.792319	−	0.610107i	$-0.791127\pi$
$641$	3.34725	−	5.79760i	0.132208	−	0.228992i	0.924528	+	0.381115i	$0.124460\pi$
$642$			28.2574i			1.11523i
$643$	7.08477	+	4.09039i	0.279396	+	0.161309i	0.633150	−	0.774029i	$-0.281762\pi$
$643$	7.08477	+	4.09039i	0.279396	+	0.161309i	−0.353754	+	0.935338i	$0.615095\pi$
$644$	−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	−0.679560	−	0.733620i	$-0.737829\pi$
$647$	−9.76765	+	5.63935i	−0.384006	+	0.221706i	0.295554	+	0.955326i	$0.404496\pi$
$648$	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	−0.884735	−	0.466094i	$-0.845661\pi$
$653$	−23.5978	+	13.6242i	−0.923454	+	0.533156i	−0.0387184	+	0.999250i	$0.512328\pi$
$654$	−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	−0.792711	−	0.609597i	$-0.791331\pi$
$659$	3.37755	−	5.85009i	0.131571	−	0.227887i	0.924282	+	0.381710i	$0.124665\pi$
$660$		0			0
$661$	13.2551	+	22.9585i	0.515564	+	0.892983i	0.999837	+	0.0180657i	$0.00575081\pi$
$661$	13.2551	+	22.9585i	0.515564	+	0.892983i	−0.484273	+	0.874917i	$0.660916\pi$
$662$			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	−0.488647	−	0.872481i	$-0.662510\pi$
$673$	0.586811	−	0.338795i	0.0226199	−	0.0130596i	0.511267	+	0.859422i	$0.329176\pi$
$674$	−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	$-0.935560\pi$
$677$		−	10.4630i		−	0.402126i	0.979578	−	0.201063i	$-0.0644395\pi$
$678$	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	0.156025	−	0.987753i	$-0.450132\pi$
$683$	−16.2394	−	9.37580i	−0.621382	−	0.358755i	−0.777407	+	0.628998i	$0.783465\pi$
$684$	−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	−0.899096	−	0.437752i	$-0.855775\pi$
$691$	−21.7827	−	37.7287i	−0.828652	−	1.43527i	0.0704440	−	0.997516i	$-0.477558\pi$
$692$	−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	−0.0543307	−	0.998523i	$-0.517303\pi$
$709$	22.3023	−	38.6287i	0.837581	−	1.45073i	0.891912	−	0.452210i	$-0.149364\pi$
$710$		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	−0.961306	−	0.275484i	$-0.911162\pi$
$719$	−6.49109	+	11.2429i	−0.242077	+	0.419289i	0.719229	+	0.694773i	$0.244495\pi$
$720$		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	$0.104566\pi$
$727$			17.3980i			0.645255i	−0.946526	+	0.322627i	$0.895434\pi$
$728$	−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	$-0.678806\pi$
$733$		−	45.8272i		−	1.69266i	0.532655	−	0.846332i	$-0.321194\pi$
$734$	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	0.981142	−	0.193290i	$-0.0619159\pi$
$739$	8.78541	+	15.2168i	0.323176	+	0.559758i	−0.657965	+	0.753048i	$0.728583\pi$
$740$		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	0.0669167	−	0.997759i	$-0.478684\pi$
$743$	26.2893	−	15.1781i	0.964459	−	0.556831i	0.897543	+	0.440928i	$0.145350\pi$
$744$	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	0.829242	−	0.558889i	$-0.188772\pi$
$751$	−1.90162	−	3.29369i	−0.0693909	−	0.120189i	−0.898633	+	0.438700i	$0.855439\pi$
$752$	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	−0.552673	−	0.833398i	$-0.686392\pi$
$757$	−2.95129	+	1.70393i	−0.107266	+	0.0619303i	0.445407	+	0.895328i	$0.353059\pi$
$758$	−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	−0.924183	−	0.381949i	$-0.875253\pi$
$761$	−3.62245	+	6.27426i	−0.131314	+	0.227442i	0.792870	+	0.609391i	$0.208586\pi$
$762$		−	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	0.997311	+	0.0732873i	$0.0233490\pi$
$769$	15.5882	+	26.9995i	0.562124	+	0.973627i	−0.435187	+	0.900340i	$0.643318\pi$
$770$		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	0.771466	−	0.636271i	$-0.219524\pi$
$773$	16.8533	+	9.73026i	0.606172	+	0.349973i	−0.165294	+	0.986244i	$0.552857\pi$
$774$	−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	0.260923	−	0.965359i	$-0.415973\pi$
$787$	−12.4737	−	7.20171i	−0.444641	−	0.256713i	−0.705564	+	0.708646i	$0.749306\pi$
$788$		−	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	0.816220	−	0.577741i	$-0.196066\pi$
$797$	20.4392	+	11.8006i	0.723992	+	0.417997i	−0.0922279	+	0.995738i	$0.529399\pi$
$798$			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	0.999424	−	0.0339280i	$-0.0108017\pi$
$809$	13.3776	+	23.1706i	0.470330	+	0.814635i	−0.529095	+	0.848563i	$0.677468\pi$
$810$		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	0.694131	−	0.719849i	$-0.255789\pi$
$821$	−7.91806	−	13.7145i	−0.276342	−	0.478639i	−0.970473	+	0.241210i	$0.922456\pi$
$822$	−39.3012	+	22.6905i	−1.37079	+	0.791423i
$823$	6.42226	+	3.70789i	0.223866	+	0.129249i	0.607739	−	0.794137i	$-0.292077\pi$
$823$	6.42226	+	3.70789i	0.223866	+	0.129249i	−0.383873	+	0.923386i	$0.625410\pi$
$824$	−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	$-0.906783\pi$
$827$		−	16.6036i		−	0.577363i	0.957425	−	0.288682i	$-0.0932169\pi$
$828$	6.02129	+	3.47640i	0.209254	+	0.120813i
$829$	−14.6421	−	25.3608i	−0.508541	−	0.880818i	−0.999951	−	0.00989015i	$-0.996852\pi$
$829$	−14.6421	−	25.3608i	−0.508541	−	0.880818i	0.491410	−	0.870928i	$-0.336482\pi$
$830$		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	0.479057	+	0.877784i	$0.340979\pi$
$839$	−15.0810	+	26.1211i	−0.520655	+	0.901800i	−0.999712	+	0.0240164i	$0.992355\pi$
$840$		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	$0.0136641\pi$
$853$			2.50670i			0.0858277i	−0.999079	+	0.0429139i	$0.986336\pi$
$854$	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	$-0.862976\pi$
$857$		−	24.4327i		−	0.834605i	0.908768	−	0.417302i	$-0.137024\pi$
$858$	−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	$0.0175888\pi$
$863$			3.24490i			0.110458i	−0.998474	+	0.0552288i	$0.982411\pi$
$864$	−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	0.195995	−	0.980605i	$-0.437206\pi$
$877$	−16.4429	−	9.49330i	−0.555237	−	0.320566i	−0.751231	+	0.660039i	$0.770540\pi$
$878$	−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	0.982132	−	0.188191i	$-0.0602623\pi$
$881$	9.73820	+	16.8671i	0.328088	+	0.568265i	−0.654044	+	0.756456i	$0.726929\pi$
$882$	10.5928	−	6.11575i	0.356678	−	0.205928i
$883$			50.5664i			1.70169i	0.525413	+	0.850847i	$0.323911\pi$
$883$			50.5664i			1.70169i	−0.525413	+	0.850847i	$0.676089\pi$
$884$	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	−0.670951	−	0.741502i	$-0.734114\pi$
$887$	−10.8488	+	6.26356i	−0.364267	+	0.210310i	0.306684	+	0.951811i	$0.400781\pi$
$888$	−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	−0.0393265	−	0.999226i	$-0.512521\pi$
$907$	24.2849	−	14.0209i	0.806366	−	0.465555i	0.845692	+	0.533671i	$0.179188\pi$
$908$	−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	0.249619	+	0.968344i	$0.419695\pi$
$919$	−21.6389	+	37.4797i	−0.713801	+	1.23634i	−0.963420	+	0.267996i	$0.913639\pi$
$920$		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	−0.730714	−	0.682684i	$-0.760813\pi$
$929$	6.88425	−	11.9239i	0.225865	−	0.391210i	0.956579	+	0.291475i	$0.0941459\pi$
$930$		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	$-0.785593\pi$
$937$		−	38.1888i		−	1.24757i	0.781594	−	0.623787i	$-0.214407\pi$
$938$	−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	−0.392705	−	0.919665i	$-0.628461\pi$
$947$	6.38228	−	3.68481i	0.207396	−	0.119740i	0.600101	+	0.799924i	$0.295127\pi$
$948$		−	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	0.788971	−	0.614430i	$-0.210614\pi$
$953$	20.1075	+	11.6091i	0.651345	+	0.376054i	−0.137627	+	0.990484i	$0.543947\pi$
$954$	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	$-0.961294\pi$
$967$		−	7.54402i		−	0.242599i	0.992616	−	0.121300i	$-0.0387062\pi$
$968$	−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	−0.509196	−	0.860650i	$-0.670057\pi$
$971$	15.2921	−	26.4867i	0.490747	−	0.849999i	0.999943	+	0.0106517i	$0.00339059\pi$
$972$	−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	−0.904856	−	0.425717i	$-0.860022\pi$
$977$	−30.9007	+	17.8405i	−0.988602	+	0.570770i	−0.0837460	+	0.996487i	$0.526688\pi$
$978$	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	$-0.933596\pi$
$983$		−	12.9866i		−	0.414208i	0.978319	−	0.207104i	$-0.0664039\pi$
$984$	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	0.988174	−	0.153336i	$-0.0490018\pi$
$991$	11.3736	+	19.6996i	0.361294	+	0.625779i	−0.626880	+	0.779116i	$0.715668\pi$
$992$	−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	0.677713	−	0.735326i	$-0.262971\pi$
$997$	11.9910	+	6.92301i	0.379759	+	0.219254i	−0.297955	+	0.954580i	$0.596304\pi$
$998$	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.874.2		12
5.2	odd	4		975.2.i.l.601.1		6
5.3	odd	4		195.2.i.d.16.3	✓	6
5.4	even	2	inner	975.2.bb.k.874.5		12
13.9	even	3	inner	975.2.bb.k.724.5		12
15.8	even	4		585.2.j.f.406.1		6
65.3	odd	12		2535.2.a.bb.1.1		3
65.9	even	6	inner	975.2.bb.k.724.2		12
65.22	odd	12		975.2.i.l.451.1		6
65.23	odd	12		2535.2.a.ba.1.3		3
65.48	odd	12		195.2.i.d.61.3	yes	6
195.23	even	12		7605.2.a.bw.1.1		3
195.68	even	12		7605.2.a.bv.1.3		3
195.113	even	12		585.2.j.f.451.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.3	✓	6	5.3	odd	4
195.2.i.d.61.3	yes	6	65.48	odd	12
585.2.j.f.406.1		6	15.8	even	4
585.2.j.f.451.1		6	195.113	even	12
975.2.i.l.451.1		6	65.22	odd	12
975.2.i.l.601.1		6	5.2	odd	4
975.2.bb.k.724.2		12	65.9	even	6	inner
975.2.bb.k.724.5		12	13.9	even	3	inner
975.2.bb.k.874.2		12	1.1	even	1	trivial
975.2.bb.k.874.5		12	5.4	even	2	inner
2535.2.a.ba.1.3		3	65.23	odd	12
2535.2.a.bb.1.1		3	65.3	odd	12
7605.2.a.bv.1.3		3	195.68	even	12
7605.2.a.bw.1.1		3	195.23	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

L-functions

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