LMFDB - Embedded newform 666.2.bs.a.611.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			611.4
Character	$\chi$	$=$	666.611
Dual form			666.2.bs.a.557.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 + 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-2.82596 + 1.31777i) q^{5} +(1.97276 + 0.718026i) q^{7} +(-0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-2.82596 + 1.31777i) q^{5} +(1.97276 + 0.718026i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-1.55905 - 2.70036i) q^{10} +(-1.33922 + 2.31960i) q^{11} +(-0.527495 + 0.753341i) q^{13} +(-0.543357 + 2.02783i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-2.87989 - 4.11292i) q^{17} +(-2.92670 - 0.256053i) q^{19} +(2.55420 - 1.78847i) q^{20} +(-2.42750 - 1.13196i) q^{22} +(-2.70753 - 0.725480i) q^{23} +(3.03561 - 3.61770i) q^{25} +(-0.796448 - 0.459830i) q^{26} +(-2.06747 - 0.364552i) q^{28} +(-4.95425 + 1.32749i) q^{29} +(-1.88370 + 1.88370i) q^{31} +(0.422618 + 0.906308i) q^{32} +(3.84627 - 3.22740i) q^{34} +(-6.52114 + 0.570526i) q^{35} +(-1.40496 - 5.91828i) q^{37} -2.93788i q^{38} +(2.00428 + 2.38861i) q^{40} +(-0.366974 - 2.08121i) q^{41} +(-6.00144 - 6.00144i) q^{43} +(0.916083 - 2.51692i) q^{44} +(0.486742 - 2.76045i) q^{46} +(5.03071 - 2.90448i) q^{47} +(-1.98609 - 1.66652i) q^{49} +(3.86850 + 2.70876i) q^{50} +(0.388665 - 0.833494i) q^{52} +(2.29375 + 6.30203i) q^{53} +(0.727896 - 8.31989i) q^{55} +(0.182972 - 2.09138i) q^{56} +(-1.75423 - 4.81970i) q^{58} +(-5.91334 + 12.6812i) q^{59} +(5.22818 + 3.66081i) q^{61} +(-2.04071 - 1.71236i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(0.497952 - 2.82403i) q^{65} +(-2.91868 + 8.01901i) q^{67} +(3.55034 + 3.55034i) q^{68} +(-1.13671 - 6.44660i) q^{70} +(3.95008 + 4.70753i) q^{71} +9.01662i q^{73} +(5.77331 - 1.91543i) q^{74} +(2.92670 - 0.256053i) q^{76} +(-4.30750 + 3.61442i) q^{77} +(0.222674 + 0.477526i) q^{79} +(-2.20483 + 2.20483i) q^{80} +(2.04131 - 0.546967i) q^{82} +(-3.14123 - 0.553883i) q^{83} +(13.5583 + 7.82791i) q^{85} +(5.45554 - 6.50167i) q^{86} +(2.58718 + 0.693233i) q^{88} +(2.30861 + 1.07652i) q^{89} +(-1.58154 + 1.10741i) q^{91} +(2.79237 + 0.244301i) q^{92} +(3.33189 + 4.75842i) q^{94} +(8.60817 - 3.13312i) q^{95} +(-3.13983 + 11.7180i) q^{97} +(1.48708 - 2.12378i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{35}{36}\right)$

Coefficient data

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

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

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

$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$3$		0			0
$3$		0			0
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$	−2.82596	+	1.31777i	−1.26381	+	0.589324i	−0.934857	−	0.355023i	$-0.884473\pi$
$5$	−2.82596	+	1.31777i	−1.26381	+	0.589324i	−0.328951	+	0.944347i	$0.606695\pi$
$6$		0			0
$7$	1.97276	+	0.718026i	0.745634	+	0.271388i	0.686767	−	0.726877i	$-0.259029\pi$
$7$	1.97276	+	0.718026i	0.745634	+	0.271388i	0.0588664	+	0.998266i	$0.481251\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$		0			0
$10$	−1.55905	−	2.70036i	−0.493015	−	0.853928i
$11$	−1.33922	+	2.31960i	−0.403791	+	0.699387i	−0.994180	−	0.107732i	$-0.965641\pi$
$11$	−1.33922	+	2.31960i	−0.403791	+	0.699387i	0.590389	+	0.807119i	$0.298974\pi$
$12$		0			0
$13$	−0.527495	+	0.753341i	−0.146301	+	0.208939i	−0.885613	−	0.464423i	$-0.846262\pi$
$13$	−0.527495	+	0.753341i	−0.146301	+	0.208939i	0.739313	+	0.673362i	$0.235151\pi$
$14$	−0.543357	+	2.02783i	−0.145218	+	0.541962i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−2.87989	−	4.11292i	−0.698477	−	0.997528i	−0.999042	−	0.0437671i	$-0.986064\pi$
$17$	−2.87989	−	4.11292i	−0.698477	−	0.997528i	0.300565	−	0.953761i	$-0.402825\pi$
$18$		0			0
$19$	−2.92670	−	0.256053i	−0.671432	−	0.0587427i	−0.253658	−	0.967294i	$-0.581634\pi$
$19$	−2.92670	−	0.256053i	−0.671432	−	0.0587427i	−0.417773	+	0.908551i	$0.637189\pi$
$20$	2.55420	−	1.78847i	0.571137	−	0.399914i
$21$		0			0
$22$	−2.42750	−	1.13196i	−0.517544	−	0.241335i
$23$	−2.70753	−	0.725480i	−0.564558	−	0.151273i	−0.0347586	−	0.999396i	$-0.511066\pi$
$23$	−2.70753	−	0.725480i	−0.564558	−	0.151273i	−0.529800	+	0.848123i	$0.677733\pi$
$24$		0			0
$25$	3.03561	−	3.61770i	0.607122	−	0.723540i
$26$	−0.796448	−	0.459830i	−0.156196	−	0.0901800i
$27$		0			0
$28$	−2.06747	−	0.364552i	−0.390716	−	0.0688938i
$29$	−4.95425	+	1.32749i	−0.919981	+	0.246508i	−0.687577	−	0.726111i	$-0.741326\pi$
$29$	−4.95425	+	1.32749i	−0.919981	+	0.246508i	−0.232404	+	0.972619i	$0.574659\pi$
$30$		0			0
$31$	−1.88370	+	1.88370i	−0.338323	+	0.338323i	−0.855736	−	0.517413i	$-0.826895\pi$
$31$	−1.88370	+	1.88370i	−0.338323	+	0.338323i	0.517413	+	0.855736i	$0.326895\pi$
$32$	0.422618	+	0.906308i	0.0747091	+	0.160214i
$33$		0			0
$34$	3.84627	−	3.22740i	0.659629	−	0.553494i
$35$	−6.52114	+	0.570526i	−1.10227	+	0.0964365i
$36$		0			0
$37$	−1.40496	−	5.91828i	−0.230974	−	0.972960i
$37$	−1.40496	−	5.91828i	−0.230974	−	0.972960i
$38$		−	2.93788i		−	0.476587i
$39$		0			0
$40$	2.00428	+	2.38861i	0.316904	+	0.377672i
$41$	−0.366974	−	2.08121i	−0.0573117	−	0.325031i	0.942650	−	0.333783i	$-0.108325\pi$
$41$	−0.366974	−	2.08121i	−0.0573117	−	0.325031i	−0.999962	+	0.00875197i	$0.997214\pi$
$42$		0			0
$43$	−6.00144	−	6.00144i	−0.915211	−	0.915211i	0.0814648	−	0.996676i	$-0.474040\pi$
$43$	−6.00144	−	6.00144i	−0.915211	−	0.915211i	−0.996676	+	0.0814648i	$0.974040\pi$
$44$	0.916083	−	2.51692i	0.138105	−	0.379439i
$45$		0			0
$46$	0.486742	−	2.76045i	0.0717662	−	0.407007i
$47$	5.03071	−	2.90448i	0.733805	−	0.423662i	−0.0860078	−	0.996294i	$-0.527411\pi$
$47$	5.03071	−	2.90448i	0.733805	−	0.423662i	0.819812	+	0.572632i	$0.194078\pi$
$48$		0			0
$49$	−1.98609	−	1.66652i	−0.283727	−	0.238075i
$50$	3.86850	+	2.70876i	0.547089	+	0.383076i
$51$		0			0
$52$	0.388665	−	0.833494i	0.0538981	−	0.115585i
$53$	2.29375	+	6.30203i	0.315071	+	0.865650i	0.991613	+	0.129246i	$0.0412556\pi$
$53$	2.29375	+	6.30203i	0.315071	+	0.865650i	−0.676542	+	0.736404i	$0.736522\pi$
$54$		0			0
$55$	0.727896	−	8.31989i	0.0981495	−	1.12185i
$56$	0.182972	−	2.09138i	0.0244507	−	0.279472i
$57$		0			0
$58$	−1.75423	−	4.81970i	−0.230341	−	0.632857i
$59$	−5.91334	+	12.6812i	−0.769851	+	1.65095i	−0.0107801	+	0.999942i	$0.503431\pi$
$59$	−5.91334	+	12.6812i	−0.769851	+	1.65095i	−0.759071	+	0.651008i	$0.774346\pi$
$60$		0			0
$61$	5.22818	+	3.66081i	0.669400	+	0.468719i	0.858213	−	0.513294i	$-0.171575\pi$
$61$	5.22818	+	3.66081i	0.669400	+	0.468719i	−0.188813	+	0.982013i	$0.560464\pi$
$62$	−2.04071	−	1.71236i	−0.259170	−	0.217470i
$63$		0			0
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	0.497952	−	2.82403i	0.0617634	−	0.350278i
$66$		0			0
$67$	−2.91868	+	8.01901i	−0.356574	+	0.979678i	0.623636	+	0.781715i	$0.285655\pi$
$67$	−2.91868	+	8.01901i	−0.356574	+	0.979678i	−0.980209	+	0.197963i	$0.936567\pi$
$68$	3.55034	+	3.55034i	0.430542	+	0.430542i
$69$		0			0
$70$	−1.13671	−	6.44660i	−0.135863	−	0.770516i
$71$	3.95008	+	4.70753i	0.468789	+	0.558681i	0.947692	−	0.319187i	$-0.103410\pi$
$71$	3.95008	+	4.70753i	0.468789	+	0.558681i	−0.478903	+	0.877868i	$0.658965\pi$
$72$		0			0
$73$			9.01662i			1.05532i	0.849457	+	0.527658i	$0.176930\pi$
$73$			9.01662i			1.05532i	−0.849457	+	0.527658i	$0.823070\pi$
$74$	5.77331	−	1.91543i	0.671134	−	0.222664i
$75$		0			0
$76$	2.92670	−	0.256053i	0.335716	−	0.0293713i
$77$	−4.30750	+	3.61442i	−0.490886	+	0.411902i
$78$		0			0
$79$	0.222674	+	0.477526i	0.0250528	+	0.0537259i	0.918436	−	0.395570i	$-0.129453\pi$
$79$	0.222674	+	0.477526i	0.0250528	+	0.0537259i	−0.893383	+	0.449296i	$0.851675\pi$
$80$	−2.20483	+	2.20483i	−0.246508	+	0.246508i
$81$		0			0
$82$	2.04131	−	0.546967i	0.225425	−	0.0604024i
$83$	−3.14123	−	0.553883i	−0.344795	−	0.0607966i	−0.00143059	−	0.999999i	$-0.500455\pi$
$83$	−3.14123	−	0.553883i	−0.344795	−	0.0607966i	−0.343364	+	0.939202i	$0.611566\pi$
$84$		0			0
$85$	13.5583	+	7.82791i	1.47061	+	0.849056i
$86$	5.45554	−	6.50167i	0.588287	−	0.701093i
$87$		0			0
$88$	2.58718	+	0.693233i	0.275794	+	0.0738989i
$89$	2.30861	+	1.07652i	0.244712	+	0.114111i	0.541105	−	0.840955i	$-0.318006\pi$
$89$	2.30861	+	1.07652i	0.244712	+	0.114111i	−0.296393	+	0.955066i	$0.595784\pi$
$90$		0			0
$91$	−1.58154	+	1.10741i	−0.165790	+	0.116088i
$92$	2.79237	+	0.244301i	0.291125	+	0.0254701i
$93$		0			0
$94$	3.33189	+	4.75842i	0.343658	+	0.490794i
$95$	8.60817	−	3.13312i	0.883179	−	0.321451i
$96$		0			0
$97$	−3.13983	+	11.7180i	−0.318801	+	1.18978i	0.601597	+	0.798800i	$0.294531\pi$
$97$	−3.13983	+	11.7180i	−0.318801	+	1.18978i	−0.920398	+	0.390982i	$0.872135\pi$
$98$	1.48708	−	2.12378i	0.150218	−	0.214534i
$99$		0			0
$100$	−2.36129	+	4.08987i	−0.236129	+	0.408987i
$101$	−8.25498	−	14.2980i	−0.821401	−	1.42271i	−0.904639	−	0.426179i	$-0.859860\pi$
$101$	−8.25498	−	14.2980i	−0.821401	−	1.42271i	0.0832381	−	0.996530i	$-0.473474\pi$
$102$		0			0
$103$	−1.49274	−	5.57097i	−0.147084	−	0.548924i	−0.999654	−	0.0263109i	$-0.991624\pi$
$103$	−1.49274	−	5.57097i	−0.147084	−	0.548924i	0.852570	−	0.522613i	$-0.175043\pi$
$104$	0.864197	+	0.314542i	0.0847415	+	0.0308434i
$105$		0			0
$106$	−6.07813	+	2.83428i	−0.590360	+	0.275290i
$107$	19.4213	−	3.42449i	1.87752	−	0.331058i	0.886285	−	0.463141i	$-0.153278\pi$
$107$	19.4213	−	3.42449i	1.87752	−	0.331058i	0.991239	+	0.132083i	$0.0421666\pi$
$108$		0			0
$109$	0.366026	+	4.18369i	0.0350589	+	0.400725i	0.993367	+	0.114988i	$0.0366829\pi$
$109$	0.366026	+	4.18369i	0.0350589	+	0.400725i	−0.958308	+	0.285737i	$0.907762\pi$
$110$	8.35167			0.796301
$111$		0			0
$112$	2.09937			0.198372
$113$	0.703066	+	8.03608i	0.0661389	+	0.755971i	0.954769	+	0.297347i	$0.0961019\pi$
$113$	0.703066	+	8.03608i	0.0661389	+	0.755971i	−0.888630	+	0.458624i	$0.848343\pi$
$114$		0			0
$115$	8.60738	−	1.51771i	0.802642	−	0.141527i
$116$	4.64847	−	2.16762i	0.431599	−	0.201258i
$117$		0			0
$118$	−13.1483	−	4.78560i	−1.21040	−	0.440550i
$119$	−2.72816	−	10.1816i	−0.250090	−	0.933349i
$120$		0			0
$121$	1.91296	+	3.31335i	0.173906	+	0.301213i
$122$	−3.19121	+	5.52735i	−0.288919	+	0.500422i
$123$		0			0
$124$	1.52798	−	2.18219i	0.137217	−	0.195966i
$125$	0.223892	−	0.835578i	0.0200256	−	0.0747364i
$126$		0			0
$127$	2.16274	−	0.787173i	0.191912	−	0.0698503i	−0.244276	−	0.969706i	$-0.578550\pi$
$127$	2.16274	−	0.787173i	0.191912	−	0.0698503i	0.436188	+	0.899855i	$0.356328\pi$
$128$	−0.573576	−	0.819152i	−0.0506975	−	0.0724035i
$129$		0			0
$130$	2.85668	+	0.249927i	0.250547	+	0.0219201i
$131$	5.84384	−	4.09190i	0.510578	−	0.357511i	−0.289721	−	0.957111i	$-0.593563\pi$
$131$	5.84384	−	4.09190i	0.510578	−	0.357511i	0.800300	+	0.599600i	$0.204674\pi$
$132$		0			0
$133$	−5.58983	−	2.60658i	−0.484700	−	0.226019i
$134$	−8.24288	−	2.20867i	−0.712076	−	0.190800i
$135$		0			0
$136$	−3.22740	+	3.84627i	−0.276747	+	0.329815i
$137$	−9.65245	−	5.57285i	−0.824665	−	0.476120i	0.0273576	−	0.999626i	$-0.491291\pi$
$137$	−9.65245	−	5.57285i	−0.824665	−	0.476120i	−0.852022	+	0.523505i	$0.824624\pi$
$138$		0			0
$139$	−19.7613	−	3.48445i	−1.67613	−	0.295547i	−0.746870	−	0.664970i	$-0.768444\pi$
$139$	−19.7613	−	3.48445i	−1.67613	−	0.295547i	−0.929261	+	0.369423i	$0.879555\pi$
$140$	6.32300	−	1.69424i	0.534391	−	0.143190i
$141$		0			0
$142$	−4.34534	+	4.34534i	−0.364653	+	0.364653i
$143$	−1.04102	−	2.23247i	−0.0870543	−	0.186689i
$144$		0			0
$145$	12.2512	−	10.2800i	1.01741	−	0.853705i
$146$	−8.98231	+	0.785850i	−0.743381	+	0.0650374i
$147$		0			0
$148$	2.41132	+	5.58440i	0.198209	+	0.459035i
$149$			21.9435i			1.79768i	0.438274	+	0.898841i	$0.355590\pi$
$149$			21.9435i			1.79768i	−0.438274	+	0.898841i	$0.644410\pi$
$150$		0			0
$151$	7.27082	+	8.66503i	0.591691	+	0.705150i	0.975930	−	0.218084i	$-0.0699806\pi$
$151$	7.27082	+	8.66503i	0.591691	+	0.705150i	−0.384239	+	0.923234i	$0.625536\pi$
$152$	0.510158	+	2.89325i	0.0413793	+	0.234674i
$153$		0			0
$154$	−3.97609	−	3.97609i	−0.320403	−	0.320403i
$155$	2.84099	−	7.80555i	0.228194	−	0.626957i
$156$		0			0
$157$	−3.86195	+	21.9022i	−0.308217	+	1.74799i	0.299742	+	0.954020i	$0.403099\pi$
$157$	−3.86195	+	21.9022i	−0.308217	+	1.74799i	−0.607960	+	0.793968i	$0.708012\pi$
$158$	−0.456302	+	0.263446i	−0.0363014	+	0.0209586i
$159$		0			0
$160$	−2.38861	−	2.00428i	−0.188836	−	0.158452i
$161$	−4.82039	−	3.37527i	−0.379900	−	0.266009i
$162$		0			0
$163$	−7.50039	+	16.0846i	−0.587476	+	1.25985i	0.357868	+	0.933772i	$0.383504\pi$
$163$	−7.50039	+	16.0846i	−0.587476	+	1.25985i	−0.945344	+	0.326074i	$0.894274\pi$
$164$	0.722798	+	1.98587i	0.0564410	+	0.155070i
$165$		0			0
$166$	0.278000	−	3.17755i	0.0215770	−	0.246626i
$167$	1.26304	−	14.4366i	0.0977370	−	1.11714i	−0.775997	−	0.630736i	$-0.782753\pi$
$167$	1.26304	−	14.4366i	0.0977370	−	1.11714i	0.873734	−	0.486403i	$-0.161691\pi$
$168$		0			0
$169$	4.15699	+	11.4212i	0.319768	+	0.878557i
$170$	−6.61643	+	14.1890i	−0.507457	+	1.08825i
$171$		0			0
$172$	6.95241	+	4.86813i	0.530116	+	0.371191i
$173$	−5.96864	−	5.00828i	−0.453787	−	0.380773i	0.387052	−	0.922058i	$-0.373493\pi$
$173$	−5.96864	−	5.00828i	−0.453787	−	0.380773i	−0.840839	+	0.541285i	$0.817938\pi$
$174$		0			0
$175$	8.58614	−	4.95721i	0.649051	−	0.374730i
$176$	−0.465107	+	2.63775i	−0.0350588	+	0.198828i
$177$		0			0
$178$	−0.871218	+	2.39365i	−0.0653005	+	0.179412i
$179$	8.58212	+	8.58212i	0.641458	+	0.641458i	0.950914	−	0.309456i	$-0.100147\pi$
$179$	8.58212	+	8.58212i	0.641458	+	0.641458i	−0.309456	+	0.950914i	$0.600147\pi$
$180$		0			0
$181$	−0.181925	−	1.03175i	−0.0135224	−	0.0766892i	0.977300	−	0.211861i	$-0.0679524\pi$
$181$	−0.181925	−	1.03175i	−0.0135224	−	0.0766892i	−0.990822	+	0.135172i	$0.956841\pi$
$182$	−1.24103	−	1.47900i	−0.0919914	−	0.109631i
$183$		0			0
$184$			2.80304i			0.206643i
$185$	11.7693	+	14.8734i	0.865296	+	1.09352i
$186$		0			0
$187$	13.3972	−	1.17210i	0.979697	−	0.0857124i
$188$	−4.44992	+	3.73393i	−0.324544	+	0.272325i
$189$		0			0
$190$	3.87145	+	8.30234i	0.280864	+	0.602315i
$191$	16.2499	−	16.2499i	1.17580	−	1.17580i	0.194999	−	0.980803i	$-0.437530\pi$
$191$	16.2499	−	16.2499i	1.17580	−	1.17580i	0.980803	−	0.194999i	$-0.0624705\pi$
$192$		0			0
$193$	10.1485	−	2.71928i	0.730505	−	0.195738i	0.125651	−	0.992075i	$-0.459898\pi$
$193$	10.1485	−	2.71928i	0.730505	−	0.195738i	0.604854	+	0.796336i	$0.293231\pi$
$194$	−11.9471	−	2.10659i	−0.857749	−	0.151244i
$195$		0			0
$196$	2.24530	+	1.29633i	0.160379	+	0.0925947i
$197$	−16.0720	+	19.1539i	−1.14508	+	1.36466i	−0.224328	+	0.974514i	$0.572019\pi$
$197$	−16.0720	+	19.1539i	−1.14508	+	1.36466i	−0.920755	+	0.390142i	$0.872426\pi$
$198$		0			0
$199$	−0.892139	−	0.239048i	−0.0632421	−	0.0169457i	0.227059	−	0.973881i	$-0.427089\pi$
$199$	−0.892139	−	0.239048i	−0.0632421	−	0.0169457i	−0.290301	+	0.956935i	$0.593756\pi$
$200$	−4.28010	−	1.99584i	−0.302649	−	0.141128i
$201$		0			0
$202$	13.5242	−	9.46972i	0.951557	−	0.666287i
$203$	−10.7267	−	0.938466i	−0.752868	−	0.0658674i
$204$		0			0
$205$	3.77961	+	5.39784i	0.263979	+	0.377002i
$206$	5.41967	−	1.97260i	0.377606	−	0.137437i
$207$		0			0
$208$	−0.238025	+	0.888323i	−0.0165041	+	0.0615941i
$209$	4.51345	−	6.44588i	0.312202	−	0.445871i
$210$		0			0
$211$	8.85635	−	15.3396i	0.609696	−	1.05602i	−0.381594	−	0.924330i	$-0.624625\pi$
$211$	8.85635	−	15.3396i	0.609696	−	1.05602i	0.991290	−	0.131695i	$-0.0420419\pi$
$212$	−3.35324	−	5.80798i	−0.230301	−	0.398894i
$213$		0			0
$214$	5.10413	+	19.0489i	0.348911	+	1.30215i
$215$	24.8684	+	9.05134i	1.69601	+	0.617296i
$216$		0			0
$217$	−5.06864	+	2.36355i	−0.344082	+	0.160448i
$218$	−4.13587	+	0.729266i	−0.280117	+	0.0493921i
$219$		0			0
$220$	0.727896	+	8.31989i	0.0490748	+	0.560927i
$221$	4.61756			0.310610
$222$		0			0
$223$	8.46993			0.567188			0.283594	−	0.958944i	$-0.408473\pi$
$223$	8.46993			0.567188			0.283594	+	0.958944i	$0.408473\pi$
$224$	0.182972	+	2.09138i	0.0122253	+	0.139736i
$225$		0			0
$226$	−7.94423	+	1.40078i	−0.528442	+	0.0931786i
$227$	−7.92901	+	3.69736i	−0.526267	+	0.245402i	−0.667547	−	0.744567i	$-0.732656\pi$
$227$	−7.92901	+	3.69736i	−0.526267	+	0.245402i	0.141281	+	0.989970i	$0.454878\pi$
$228$		0			0
$229$	−20.8633	−	7.59364i	−1.37869	−	0.501802i	−0.456908	−	0.889514i	$-0.651043\pi$
$229$	−20.8633	−	7.59364i	−1.37869	−	0.501802i	−0.921780	+	0.387712i	$0.873265\pi$
$230$	2.26212	+	8.44235i	0.149160	+	0.556672i
$231$		0			0
$232$	2.56451	+	4.44186i	0.168368	+	0.291622i
$233$	−3.82433	+	6.62394i	−0.250540	+	0.433949i	−0.963675	−	0.267079i	$-0.913942\pi$
$233$	−3.82433	+	6.62394i	−0.250540	+	0.433949i	0.713134	+	0.701027i	$0.247275\pi$
$234$		0			0
$235$	−10.3892	+	14.8373i	−0.677714	+	0.967876i
$236$	3.62143	−	13.5154i	0.235735	−	0.879776i
$237$		0			0
$238$	9.90512	−	3.60517i	0.642054	−	0.233688i
$239$	−8.37474	−	11.9604i	−0.541717	−	0.773652i	0.451205	−	0.892420i	$-0.350994\pi$
$239$	−8.37474	−	11.9604i	−0.541717	−	0.773652i	−0.992922	+	0.118768i	$0.962105\pi$
$240$		0			0
$241$	−26.4890	−	2.31749i	−1.70631	−	0.149283i	−0.808157	−	0.588967i	$-0.799535\pi$
$241$	−26.4890	−	2.31749i	−1.70631	−	0.149283i	−0.898152	+	0.439684i	$0.855090\pi$
$242$	−3.13401	+	2.19446i	−0.201462	+	0.141065i
$243$		0			0
$244$	−5.78445	−	2.69733i	−0.370311	−	0.172679i
$245$	7.80869	+	2.09233i	0.498879	+	0.133674i
$246$		0			0
$247$	1.73672	−	2.06974i	0.110505	−	0.131694i
$248$	2.30706	+	1.33198i	0.146498	+	0.0845808i
$249$		0			0
$250$	0.851912	+	0.150215i	0.0538796	+	0.00950044i
$251$	20.4793	−	5.48741i	1.29264	−	0.346363i	0.453979	−	0.891012i	$-0.350004\pi$
$251$	20.4793	−	5.48741i	1.29264	−	0.346363i	0.838664	+	0.544650i	$0.183337\pi$
$252$		0			0
$253$	5.30881	−	5.30881i	0.333762	−	0.333762i
$254$	0.972672	+	2.08590i	0.0610309	+	0.130881i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−9.77498	+	0.855200i	−0.609747	+	0.0533459i	−0.387847	−	0.921724i	$-0.626781\pi$
$257$	−9.77498	+	0.855200i	−0.609747	+	0.0533459i	−0.221899	+	0.975070i	$0.571226\pi$
$258$		0			0
$259$	1.47783	−	12.6842i	0.0918278	−	0.788155i
$260$			2.86759i			0.177841i
$261$		0			0
$262$	4.58565	+	5.46497i	0.283303	+	0.337627i
$263$	−2.26517	−	12.8464i	−0.139676	−	0.792142i	−0.971489	−	0.237086i	$-0.923808\pi$
$263$	−2.26517	−	12.8464i	−0.139676	−	0.792142i	0.831813	−	0.555057i	$-0.187303\pi$
$264$		0			0
$265$	−14.7867	−	14.7867i	−0.908337	−	0.908337i
$266$	2.10948	−	5.79574i	0.129340	−	0.355360i
$267$		0			0
$268$	1.48185	−	8.40401i	0.0905186	−	0.513357i
$269$	−9.84514	+	5.68409i	−0.600269	+	0.346565i	−0.769147	−	0.639072i	$-0.779319\pi$
$269$	−9.84514	+	5.68409i	−0.600269	+	0.346565i	0.168879	+	0.985637i	$0.445985\pi$
$270$		0			0
$271$	−18.5306	−	15.5490i	−1.12566	−	0.944537i	−0.126780	−	0.991931i	$-0.540464\pi$
$271$	−18.5306	−	15.5490i	−1.12566	−	0.944537i	−0.998876	+	0.0473935i	$0.984909\pi$
$272$	−4.11292	−	2.87989i	−0.249382	−	0.174619i
$273$		0			0
$274$	4.71037	−	10.1014i	0.284564	−	0.610250i
$275$	4.32626	+	11.8863i	0.260884	+	0.716772i
$276$		0			0
$277$	−0.0302720	+	0.346010i	−0.00181887	+	0.0207898i	−0.997050	−	0.0767561i	$-0.975544\pi$
$277$	−0.0302720	+	0.346010i	−0.00181887	+	0.0207898i	0.995231	+	0.0975459i	$0.0310993\pi$
$278$	1.74888	−	19.9898i	0.104891	−	1.19891i
$279$		0			0
$280$	2.23888	+	6.15127i	0.133799	+	0.367609i
$281$	0.395455	−	0.848057i	0.0235909	−	0.0505908i	−0.894159	−	0.447749i	$-0.852226\pi$
$281$	0.395455	−	0.848057i	0.0235909	−	0.0505908i	0.917750	+	0.397158i	$0.130004\pi$
$282$		0			0
$283$	−8.50619	−	5.95610i	−0.505641	−	0.354053i	0.292754	−	0.956188i	$-0.405428\pi$
$283$	−8.50619	−	5.95610i	−0.505641	−	0.354053i	−0.798395	+	0.602134i	$0.794317\pi$
$284$	−4.70753	−	3.95008i	−0.279340	−	0.234394i
$285$		0			0
$286$	2.13324	−	1.23163i	0.126141	−	0.0728278i
$287$	0.770414	−	4.36923i	0.0454761	−	0.257908i
$288$		0			0
$289$	−2.80794	+	7.71475i	−0.165173	+	0.453809i
$290$	11.3086	+	11.3086i	0.664065	+	0.664065i
$291$		0			0
$292$	−1.56572	−	8.87964i	−0.0916268	−	0.519641i
$293$	10.9767	+	13.0815i	0.641266	+	0.764231i	0.984570	−	0.174993i	$-0.0559903\pi$
$293$	10.9767	+	13.0815i	0.641266	+	0.764231i	−0.343303	+	0.939225i	$0.611546\pi$
$294$		0			0
$295$		−	43.6290i		−	2.54018i
$296$	−5.35299	+	2.88885i	−0.311136	+	0.167911i
$297$		0			0
$298$	−21.8600	+	1.91250i	−1.26632	+	0.110788i
$299$	1.97474	−	1.65700i	0.114202	−	0.0958270i
$300$		0			0
$301$	−7.53022	−	16.1486i	−0.434035	−	0.930790i
$302$	−7.99836	+	7.99836i	−0.460254	+	0.460254i
$303$		0			0
$304$	−2.83778	+	0.760380i	−0.162758	+	0.0436108i
$305$	−19.5987	−	3.45579i	−1.12222	−	0.197878i
$306$		0			0
$307$	15.4922	+	8.94445i	0.884189	+	0.510487i	0.872037	−	0.489440i	$-0.162799\pi$
$307$	15.4922	+	8.94445i	0.884189	+	0.510487i	0.0121515	+	0.999926i	$0.496132\pi$
$308$	3.61442	−	4.30750i	0.205951	−	0.245443i
$309$		0			0
$310$	8.02346	+	2.14988i	0.455702	+	0.122105i
$311$	−8.92073	−	4.15980i	−0.505848	−	0.235881i	0.152904	−	0.988241i	$-0.451138\pi$
$311$	−8.92073	−	4.15980i	−0.505848	−	0.235881i	−0.658752	+	0.752360i	$0.728915\pi$
$312$		0			0
$313$	−4.60506	+	3.22450i	−0.260293	+	0.182259i	−0.696437	−	0.717618i	$-0.745233\pi$
$313$	−4.60506	+	3.22450i	−0.260293	+	0.182259i	0.436144	+	0.899877i	$0.356344\pi$
$314$	−22.1555	−	1.93835i	−1.25031	−	0.109388i
$315$		0			0
$316$	−0.302213	−	0.431605i	−0.0170008	−	0.0242797i
$317$	30.0782	−	10.9476i	1.68936	−	0.614878i	0.694817	−	0.719186i	$-0.255485\pi$
$317$	30.0782	−	10.9476i	1.68936	−	0.614878i	0.994545	+	0.104309i	$0.0332630\pi$
$318$		0			0
$319$	3.55560	−	13.2697i	0.199076	−	0.742960i
$320$	1.78847	−	2.55420i	0.0999786	−	0.142784i
$321$		0			0
$322$	2.94230	−	5.09622i	0.163968	−	0.284001i
$323$	7.37547	+	12.7747i	0.410382	+	0.710803i
$324$		0			0
$325$	1.12409	+	4.19517i	0.0623534	+	0.232706i
$326$	−16.6771	−	6.06998i	−0.923661	−	0.336185i
$327$		0			0
$328$	−1.91532	+	0.893127i	−0.105756	+	0.0493147i
$329$	12.0099	−	2.11767i	0.662126	−	0.116751i
$330$		0			0
$331$	0.753073	+	8.60767i	0.0413926	+	0.473120i	0.988396	+	0.151897i	$0.0485383\pi$
$331$	0.753073	+	8.60767i	0.0413926	+	0.473120i	−0.947004	+	0.321223i	$0.895906\pi$
$332$	3.18969			0.175057
$333$		0			0
$334$	14.4918			0.792954
$335$	−2.31911	−	26.5076i	−0.126707	−	1.44826i
$336$		0			0
$337$	33.5843	−	5.92181i	1.82945	−	0.322582i	0.850391	−	0.526151i	$-0.176366\pi$
$337$	33.5843	−	5.92181i	1.82945	−	0.322582i	0.979060	+	0.203570i	$0.0652544\pi$
$338$	−11.0155	+	5.13660i	−0.599163	+	0.279394i
$339$		0			0
$340$	−14.7117	−	5.35461i	−0.797852	−	0.290394i
$341$	−1.84674	−	6.89214i	−0.100007	−	0.373230i
$342$		0			0
$343$	−10.0693	−	17.4405i	−0.543689	−	0.941696i
$344$	−4.24366	+	7.35024i	−0.228803	+	0.396298i
$345$		0			0
$346$	4.46902	−	6.38243i	0.240256	−	0.343121i
$347$	−0.541394	+	2.02051i	−0.0290635	+	0.108467i	−0.978934	−	0.204177i	$-0.934548\pi$
$347$	−0.541394	+	2.02051i	−0.0290635	+	0.108467i	0.949870	+	0.312644i	$0.101215\pi$
$348$		0			0
$349$	2.20609	−	0.802950i	0.118089	−	0.0429809i	−0.282300	−	0.959326i	$-0.591097\pi$
$349$	2.20609	−	0.802950i	0.118089	−	0.0429809i	0.400389	+	0.916345i	$0.368875\pi$
$350$	5.68668	+	8.12141i	0.303966	+	0.434108i
$351$		0			0
$352$	−2.66825	−	0.233442i	−0.142218	−	0.0124425i
$353$	−19.6609	+	13.7667i	−1.04645	+	0.732729i	−0.964547	−	0.263912i	$-0.914987\pi$
$353$	−19.6609	+	13.7667i	−1.04645	+	0.732729i	−0.0818985	+	0.996641i	$0.526098\pi$
$354$		0			0
$355$	−17.3662	−	8.09800i	−0.921703	−	0.429797i
$356$	−2.46047	−	0.659282i	−0.130405	−	0.0349419i
$357$		0			0
$358$	−7.80148	+	9.29744i	−0.412321	+	0.491385i
$359$	−4.26996	−	2.46526i	−0.225360	−	0.130111i	0.383070	−	0.923719i	$-0.374867\pi$
$359$	−4.26996	−	2.46526i	−0.225360	−	0.130111i	−0.608430	+	0.793608i	$0.708200\pi$
$360$		0			0
$361$	−10.2113	−	1.80053i	−0.537438	−	0.0947648i
$362$	1.01197	−	0.271156i	0.0531878	−	0.0142516i
$363$		0			0
$364$	1.36521	−	1.36521i	0.0715566	−	0.0715566i
$365$	−11.8818	−	25.4806i	−0.621922	−	1.33372i
$366$		0			0
$367$	12.7810	−	10.7245i	0.667164	−	0.559817i	−0.245061	−	0.969508i	$-0.578808\pi$
$367$	12.7810	−	10.7245i	0.667164	−	0.559817i	0.912224	+	0.409691i	$0.134363\pi$
$368$	−2.79237	+	0.244301i	−0.145562	+	0.0127351i
$369$		0			0
$370$	−13.7911	+	13.0208i	−0.716964	+	0.676920i
$371$			14.0794i			0.730964i
$372$		0			0
$373$	4.09324	+	4.87814i	0.211940	+	0.252580i	0.861533	−	0.507702i	$-0.169505\pi$
$373$	4.09324	+	4.87814i	0.211940	+	0.252580i	−0.649593	+	0.760283i	$0.725061\pi$
$374$	2.33528	+	13.2440i	0.120754	+	0.684832i
$375$		0			0
$376$	−4.10756	−	4.10756i	−0.211831	−	0.211831i
$377$	1.61329	−	4.43248i	0.0830887	−	0.228284i
$378$		0			0
$379$	1.18223	−	6.70474i	0.0607269	−	0.344400i	−0.939272	−	0.343173i	$-0.888498\pi$
$379$	1.18223	−	6.70474i	0.0607269	−	0.344400i	0.999999	−	0.00122683i	$-0.000390514\pi$
$380$	−7.93333	+	4.58031i	−0.406971	+	0.234965i
$381$		0			0
$382$	17.6044	+	14.7718i	0.900717	+	0.755791i
$383$	15.6041	+	10.9261i	0.797335	+	0.558300i	0.899731	−	0.436444i	$-0.143762\pi$
$383$	15.6041	+	10.9261i	0.797335	+	0.558300i	−0.102397	+	0.994744i	$0.532651\pi$
$384$		0			0
$385$	7.40987	−	15.8905i	0.377642	−	0.809856i
$386$	3.59343	+	9.87288i	0.182901	+	0.502516i
$387$		0			0
$388$	1.05732	−	12.0852i	0.0536772	−	0.613533i
$389$	0.304271	−	3.47784i	0.0154272	−	0.176333i	−0.984572	−	0.174980i	$-0.944014\pi$
$389$	0.304271	−	3.47784i	0.0154272	−	0.176333i	0.999999	−	0.00135294i	$-0.000430655\pi$
$390$		0			0
$391$	4.81355	+	13.2251i	0.243432	+	0.668824i
$392$	−1.09570	+	2.34974i	−0.0553413	+	0.118680i
$393$		0			0
$394$	−20.4817	−	14.3415i	−1.03186	−	0.722513i
$395$	−1.25854	−	1.05604i	−0.0633239	−	0.0531351i
$396$		0			0
$397$	27.3753	−	15.8051i	1.37393	−	0.793237i	0.382507	−	0.923953i	$-0.375061\pi$
$397$	27.3753	−	15.8051i	1.37393	−	0.793237i	0.991420	+	0.130716i	$0.0417275\pi$
$398$	0.160383	−	0.909579i	0.00803929	−	0.0455931i
$399$		0			0
$400$	1.61521	−	4.43776i	0.0807607	−	0.221888i
$401$	9.88686	+	9.88686i	0.493726	+	0.493726i	0.909478	−	0.415752i	$-0.136482\pi$
$401$	9.88686	+	9.88686i	0.493726	+	0.493726i	−0.415752	+	0.909478i	$0.636482\pi$
$402$		0			0
$403$	−0.425427	−	2.41271i	−0.0211920	−	0.120186i
$404$	10.6124	+	12.6474i	0.527986	+	0.629230i
$405$		0			0
$406$		−	10.7677i		−	0.534392i
$407$	15.6096	+	4.66695i	0.773740	+	0.231332i
$408$		0			0
$409$	−35.6100	+	3.11547i	−1.76080	+	0.154050i	−0.921184	−	0.389127i	$-0.872777\pi$
$409$	−35.6100	+	3.11547i	−1.76080	+	0.154050i	−0.839618	+	0.543177i	$0.817221\pi$
$410$	−5.04789	+	4.23568i	−0.249297	+	0.209185i
$411$		0			0
$412$	2.43745	+	5.22712i	0.120084	+	0.257522i
$413$	−20.7710	+	20.7710i	−1.02208	+	1.02208i
$414$		0			0
$415$	9.60688	−	2.57416i	0.471583	−	0.126360i
$416$	−0.905688	−	0.159697i	−0.0444050	−	0.00782980i
$417$		0			0
$418$	6.81472	+	3.93448i	0.333319	+	0.192442i
$419$	−3.78686	+	4.51301i	−0.185000	+	0.220475i	−0.850571	−	0.525860i	$-0.823744\pi$
$419$	−3.78686	+	4.51301i	−0.185000	+	0.220475i	0.665571	+	0.746335i	$0.268188\pi$
$420$		0			0
$421$	10.7741	+	2.88690i	0.525096	+	0.140699i	0.511623	−	0.859210i	$-0.329045\pi$
$421$	10.7741	+	2.88690i	0.525096	+	0.140699i	0.0134732	+	0.999909i	$0.495711\pi$
$422$	16.0532	+	7.48571i	0.781455	+	0.364399i
$423$		0			0
$424$	5.49363	−	3.84668i	0.266794	−	0.186811i
$425$	−23.6215	−	2.06662i	−1.14581	−	0.100246i
$426$		0			0
$427$	7.68539	+	10.9759i	0.371922	+	0.531160i
$428$	−18.5315	+	6.74493i	−0.895756	+	0.326028i
$429$		0			0
$430$	−6.84948	+	25.5626i	−0.330311	+	1.23274i
$431$	2.44990	−	3.49882i	0.118007	−	0.168532i	−0.755803	−	0.654800i	$-0.772753\pi$
$431$	2.44990	−	3.49882i	0.118007	−	0.168532i	0.873810	+	0.486267i	$0.161642\pi$
$432$		0			0
$433$	10.9074	−	18.8921i	0.524174	−	0.907896i	−0.475430	−	0.879754i	$-0.657707\pi$
$433$	10.9074	−	18.8921i	0.524174	−	0.907896i	0.999604	−	0.0281424i	$-0.00895918\pi$
$434$	−2.79632	−	4.84336i	−0.134227	−	0.232489i
$435$		0			0
$436$	−1.08696	−	4.05657i	−0.0520557	−	0.194275i
$437$	7.73836	+	2.81653i	0.370176	+	0.134733i
$438$		0			0
$439$	7.84924	−	3.66016i	0.374624	−	0.174690i	−0.226182	−	0.974085i	$-0.572624\pi$
$439$	7.84924	−	3.66016i	0.374624	−	0.174690i	0.600806	+	0.799395i	$0.294847\pi$
$440$	−8.22479	+	1.45025i	−0.392102	+	0.0691381i
$441$		0			0
$442$	0.402447	+	4.59998i	0.0191424	+	0.218799i
$443$	−13.2524			−0.629642			−0.314821	−	0.949151i	$-0.601944\pi$
$443$	−13.2524			−0.629642			−0.314821	+	0.949151i	$0.601944\pi$
$444$		0			0
$445$	−7.94265			−0.376518
$446$	0.738203	+	8.43770i	0.0349549	+	0.399536i
$447$		0			0
$448$	−2.06747	+	0.364552i	−0.0976790	+	0.0172234i
$449$	−8.00777	+	3.73409i	−0.377910	+	0.176222i	−0.602286	−	0.798280i	$-0.705743\pi$
$449$	−8.00777	+	3.73409i	−0.377910	+	0.176222i	0.224376	+	0.974503i	$0.427966\pi$
$450$		0			0
$451$	5.31905	+	1.93598i	0.250464	+	0.0911615i
$452$	−2.08784	−	7.79191i	−0.0982036	−	0.366501i
$453$		0			0
$454$	−4.37435	−	7.57659i	−0.205298	−	0.355587i
$455$	3.01007	−	5.21359i	0.141114	−	0.244417i
$456$		0			0
$457$	−8.62766	+	12.3216i	−0.403585	+	0.576379i	−0.968576	−	0.248718i	$-0.919991\pi$
$457$	−8.62766	+	12.3216i	−0.403585	+	0.576379i	0.564991	+	0.825097i	$0.308880\pi$
$458$	5.74638	−	21.4458i	0.268511	−	1.00210i
$459$		0			0
$460$	−8.21307	+	2.98931i	−0.382936	+	0.139377i
$461$	−1.62400	−	2.31931i	−0.0756372	−	0.108021i	0.779551	−	0.626339i	$-0.215447\pi$
$461$	−1.62400	−	2.31931i	−0.0756372	−	0.108021i	−0.855188	+	0.518318i	$0.826558\pi$
$462$		0			0
$463$	−36.1930	−	3.16648i	−1.68203	−	0.147159i	−0.794301	−	0.607524i	$-0.792163\pi$
$463$	−36.1930	−	3.16648i	−1.68203	−	0.147159i	−0.887729	+	0.460366i	$0.847718\pi$
$464$	−4.20144	+	2.94188i	−0.195047	+	0.136573i
$465$		0			0
$466$	−6.93205	−	3.23247i	−0.321121	−	0.149741i
$467$	−34.6623	−	9.28773i	−1.60398	−	0.429785i	−0.657738	−	0.753247i	$-0.728487\pi$
$467$	−34.6623	−	9.28773i	−1.60398	−	0.429785i	−0.946241	+	0.323462i	$0.895153\pi$
$468$		0			0
$469$	−11.5157	+	13.7239i	−0.531747	+	0.633711i
$470$	−15.6863	−	9.05648i	−0.723554	−	0.417744i
$471$		0			0
$472$	13.7796	+	2.42971i	0.634256	+	0.111836i
$473$	21.9582	−	5.88369i	1.00964	−	0.270532i
$474$		0			0
$475$	−9.81065	+	9.81065i	−0.450144	+	0.450144i
$476$	4.45474	+	9.55322i	0.204183	+	0.437871i
$477$		0			0
$478$	11.1849	−	9.38529i	0.511588	−	0.429273i
$479$	26.0672	−	2.28058i	1.19104	−	0.104203i	0.525652	−	0.850700i	$-0.323821\pi$
$479$	26.0672	−	2.28058i	1.19104	−	0.104203i	0.665388	+	0.746497i	$0.268266\pi$
$480$		0			0
$481$	5.19959	+	2.06345i	0.237081	+	0.0940852i
$482$		−	26.5902i		−	1.21115i
$483$		0			0
$484$	−2.45926	−	2.93083i	−0.111784	−	0.133219i
$485$	−6.56856	−	37.2522i	−0.298263	−	1.69153i
$486$		0			0
$487$	0.689631	+	0.689631i	0.0312502	+	0.0312502i	0.722559	−	0.691309i	$-0.242966\pi$
$487$	0.689631	+	0.689631i	0.0312502	+	0.0312502i	−0.691309	+	0.722559i	$0.742966\pi$
$488$	2.18292	−	5.99752i	0.0988161	−	0.271495i
$489$		0			0
$490$	−1.40380	+	7.96134i	−0.0634172	+	0.359657i
$491$	−37.2091	+	21.4827i	−1.67922	+	0.969501i	−0.717068	+	0.697003i	$0.754516\pi$
$491$	−37.2091	+	21.4827i	−1.67922	+	0.969501i	−0.962157	+	0.272497i	$0.912150\pi$
$492$		0			0
$493$	19.7276	+	16.5534i	0.888484	+	0.745527i
$494$	2.21323	+	1.54972i	0.0995778	+	0.0697251i
$495$		0			0
$496$	−1.12584	+	2.41437i	−0.0505516	+	0.108408i
$497$	4.41245	+	12.1231i	0.197925	+	0.543795i
$498$		0			0
$499$	−1.11174	+	12.7072i	−0.0497682	+	0.568854i	0.929844	+	0.367955i	$0.119942\pi$
$499$	−1.11174	+	12.7072i	−0.0497682	+	0.568854i	−0.979612	+	0.200899i	$0.935614\pi$
$500$	−0.0753944	+	0.861762i	−0.00337174	+	0.0385392i
$501$		0			0
$502$	7.25142	+	19.9231i	0.323647	+	0.889212i
$503$	−4.67196	+	10.0191i	−0.208313	+	0.446728i	−0.982508	−	0.186219i	$-0.940377\pi$
$503$	−4.67196	+	10.0191i	−0.208313	+	0.446728i	0.774196	+	0.632946i	$0.218155\pi$
$504$		0			0
$505$	42.1697	+	29.5276i	1.87653	+	1.31396i
$506$	5.75130	+	4.82591i	0.255676	+	0.214538i
$507$		0			0
$508$	−1.99319	+	1.15077i	−0.0884336	+	0.0510571i
$509$	3.73654	−	21.1910i	0.165619	−	0.939273i	−0.782805	−	0.622268i	$-0.786212\pi$
$509$	3.73654	−	21.1910i	0.165619	−	0.939273i	0.948424	−	0.317005i	$-0.102677\pi$
$510$		0			0
$511$	−6.47417	+	17.7876i	−0.286400	+	0.786879i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−1.70389	−	9.66325i	−0.0751554	−	0.426228i
$515$	11.5597	+	13.7763i	0.509379	+	0.607054i
$516$		0			0
$517$			15.5590i			0.684284i
$518$	12.7647	+	0.366707i	0.560848	+	0.0161122i
$519$		0			0
$520$	−2.85668	+	0.249927i	−0.125274	+	0.0109600i
$521$	0.350028	−	0.293708i	0.0153350	−	0.0128676i	−0.635088	−	0.772440i	$-0.719036\pi$
$521$	0.350028	−	0.293708i	0.0153350	−	0.0128676i	0.650423	+	0.759572i	$0.274592\pi$
$522$		0			0
$523$	−7.60898	−	16.3175i	−0.332717	−	0.713515i	0.666779	−	0.745256i	$-0.267673\pi$
$523$	−7.60898	−	16.3175i	−0.332717	−	0.713515i	−0.999496	+	0.0317411i	$0.989895\pi$
$524$	−5.04451	+	5.04451i	−0.220370	+	0.220370i
$525$		0			0
$526$	12.6001	−	3.37618i	0.549390	−	0.147209i
$527$	13.1724	+	2.32265i	0.573798	+	0.101176i
$528$		0			0
$529$	−13.1142	−	7.57149i	−0.570183	−	0.329195i
$530$	13.4416	−	16.0191i	0.583868	−	0.695827i
$531$		0			0
$532$	5.95754	+	1.59632i	0.258292	+	0.0692092i
$533$	1.76144	+	0.821373i	0.0762964	+	0.0355776i
$534$		0			0
$535$	−50.3710	+	35.2702i	−2.17773	+	1.52486i
$536$	8.50118	+	0.743757i	0.367195	+	0.0321254i
$537$		0			0
$538$	−6.52052	−	9.31227i	−0.281120	−	0.401481i
$539$	6.52549	−	2.37508i	0.281073	−	0.102302i
$540$		0			0
$541$	8.95812	−	33.4321i	0.385139	−	1.43736i	−0.452807	−	0.891608i	$-0.649577\pi$
$541$	8.95812	−	33.4321i	0.385139	−	1.43736i	0.837947	−	0.545752i	$-0.183756\pi$
$542$	13.8748	−	19.8153i	0.595975	−	0.851140i
$543$		0			0
$544$	2.51047	−	4.34826i	0.107636	−	0.186430i
$545$	−6.54751	−	11.3406i	−0.280465	−	0.485779i
$546$		0			0
$547$	7.37760	+	27.5336i	0.315444	+	1.17725i	0.923576	+	0.383416i	$0.125252\pi$
$547$	7.37760	+	27.5336i	0.315444	+	1.17725i	−0.608132	+	0.793836i	$0.708081\pi$
$548$	10.4735	+	3.81205i	0.447407	+	0.162843i
$549$		0			0
$550$	−11.4640	+	5.34576i	−0.488828	+	0.227944i
$551$	14.8395	−	2.61661i	0.632185	−	0.111471i
$552$		0			0
$553$	0.0964065	+	1.10193i	0.00409962	+	0.0468589i
$554$	−0.347332			−0.0147567
$555$		0			0
$556$	20.0662			0.850994
$557$	−1.56837	−	17.9266i	−0.0664540	−	0.759573i	−0.954186	−	0.299213i	$-0.903276\pi$
$557$	−1.56837	−	17.9266i	−0.0664540	−	0.759573i	0.887732	−	0.460360i	$-0.152280\pi$
$558$		0			0
$559$	7.68686	−	1.35540i	0.325120	−	0.0573274i
$560$	−5.93274	+	2.76648i	−0.250704	+	0.116905i
$561$		0			0
$562$	0.879296	+	0.320037i	0.0370908	+	0.0135000i
$563$	4.39452	+	16.4006i	0.185207	+	0.691201i	0.994586	+	0.103915i	$0.0331370\pi$
$563$	4.39452	+	16.4006i	0.185207	+	0.691201i	−0.809379	+	0.587286i	$0.800196\pi$
$564$		0			0
$565$	−12.5765	−	21.7832i	−0.529099	−	0.916426i
$566$	5.19207	−	8.99293i	0.218239	−	0.378001i
$567$		0			0
$568$	3.52477	−	5.03389i	0.147896	−	0.211217i
$569$	−0.0672038	+	0.250808i	−0.00281733	+	0.0105144i	−0.967320	−	0.253558i	$-0.918399\pi$
$569$	−0.0672038	+	0.250808i	−0.00281733	+	0.0105144i	0.964503	+	0.264072i	$0.0850658\pi$
$570$		0			0
$571$	−43.2375	+	15.7372i	−1.80943	+	0.658579i	−0.812271	+	0.583280i	$0.801769\pi$
$571$	−43.2375	+	15.7372i	−1.80943	+	0.658579i	−0.997161	+	0.0752988i	$0.976009\pi$
$572$	1.41287	+	2.01778i	0.0590749	+	0.0843677i
$573$		0			0
$574$	4.41975	+	0.386678i	0.184477	+	0.0161396i
$575$	−10.8436	+	7.59274i	−0.452208	+	0.316639i
$576$		0			0
$577$	37.8768	+	17.6623i	1.57683	+	0.735289i	0.996848	−	0.0793374i	$-0.0252804\pi$
$577$	37.8768	+	17.6623i	1.57683	+	0.735289i	0.579985	+	0.814627i	$0.303058\pi$
$578$	−7.93012	−	2.12487i	−0.329849	−	0.0883829i
$579$		0			0
$580$	−10.2800	+	12.2512i	−0.426853	+	0.508703i
$581$	−5.79919	−	3.34817i	−0.240591	−	0.138905i
$582$		0			0
$583$	−17.6900	−	3.11923i	−0.732647	−	0.129185i
$584$	8.70939	−	2.33367i	0.360397	−	0.0965681i
$585$		0			0
$586$	−12.0751	+	12.0751i	−0.498817	+	0.498817i
$587$	−11.5283	−	24.7225i	−0.475823	−	1.02041i	−0.986969	−	0.160912i	$-0.948557\pi$
$587$	−11.5283	−	24.7225i	−0.475823	−	1.02041i	0.511146	−	0.859494i	$-0.329221\pi$
$588$		0			0
$589$	5.99537	−	5.03071i	0.247035	−	0.207287i
$590$	43.4629	−	3.80251i	1.78934	−	0.156547i
$591$		0			0
$592$	−3.34441	−	5.08084i	−0.137454	−	0.208821i
$593$			8.69991i			0.357263i	0.983916	+	0.178631i	$0.0571669\pi$
$593$			8.69991i			0.357263i	−0.983916	+	0.178631i	$0.942833\pi$
$594$		0			0
$595$	21.1267	+	25.1778i	0.866111	+	1.03219i
$596$	−3.81045	−	21.6101i	−0.156082	−	0.885186i
$597$		0			0
$598$	1.82281	+	1.82281i	0.0745402	+	0.0745402i
$599$	−11.1752	+	30.7035i	−0.456605	+	1.25451i	0.471391	+	0.881924i	$0.343752\pi$
$599$	−11.1752	+	30.7035i	−0.456605	+	1.25451i	−0.927997	+	0.372589i	$0.878470\pi$
$600$		0			0
$601$	−5.74854	+	32.6016i	−0.234488	+	1.32985i	0.609202	+	0.793015i	$0.291490\pi$
$601$	−5.74854	+	32.6016i	−0.234488	+	1.32985i	−0.843690	+	0.536831i	$0.819621\pi$
$602$	15.4309	−	8.90901i	0.628915	−	0.363104i
$603$		0			0
$604$	−8.66503	−	7.27082i	−0.352575	−	0.295845i
$605$	−9.77218	−	6.84255i	−0.397296	−	0.278189i
$606$		0			0
$607$	12.8041	−	27.4585i	0.519703	−	1.11451i	−0.454895	−	0.890545i	$-0.650323\pi$
$607$	12.8041	−	27.4585i	0.519703	−	1.11451i	0.974598	−	0.223962i	$-0.0718990\pi$
$608$	−1.00481	−	2.76071i	−0.0407506	−	0.111961i
$609$		0			0
$610$	1.73449	−	19.8253i	0.0702276	−	0.802705i
$611$	−0.465609	+	5.32194i	−0.0188365	+	0.215303i
$612$		0			0
$613$	15.1841	+	41.7181i	0.613282	+	1.68498i	0.722856	+	0.690999i	$0.242829\pi$
$613$	15.1841	+	41.7181i	0.613282	+	1.68498i	−0.109574	+	0.993979i	$0.534949\pi$
$614$	−7.56017	+	16.2128i	−0.305104	+	0.654297i
$615$		0			0
$616$	4.60613	+	3.22525i	0.185586	+	0.129949i
$617$	27.7168	+	23.2571i	1.11583	+	0.936296i	0.998387	−	0.0567827i	$-0.0180842\pi$
$617$	27.7168	+	23.2571i	1.11583	+	0.936296i	0.117448	+	0.993079i	$0.462529\pi$
$618$		0			0
$619$	26.5570	−	15.3327i	1.06742	−	0.616274i	0.139943	−	0.990160i	$-0.455308\pi$
$619$	26.5570	−	15.3327i	1.06742	−	0.616274i	0.927475	+	0.373886i	$0.121975\pi$
$620$	−1.44241	+	8.18030i	−0.0579285	+	0.328529i
$621$		0			0
$622$	3.36648	−	9.24933i	0.134984	−	0.370864i
$623$	3.78137	+	3.78137i	0.151497	+	0.151497i
$624$		0			0
$625$	4.56871	+	25.9105i	0.182749	+	1.03642i
$626$	−3.61358	−	4.30650i	−0.144428	−	0.172122i
$627$		0			0
$628$		−	22.2401i		−	0.887477i
$629$	−20.2953	+	22.8225i	−0.809225	+	0.909994i
$630$		0			0
$631$	1.73147	−	0.151484i	0.0689289	−	0.00603049i	−0.0526391	−	0.998614i	$-0.516763\pi$
$631$	1.73147	−	0.151484i	0.0689289	−	0.00603049i	0.121568	+	0.992583i	$0.461208\pi$
$632$	0.403623	−	0.338680i	0.0160553	−	0.0134720i
$633$		0			0
$634$	13.5274	+	29.0096i	0.537242	+	1.15212i
$635$	−5.07451	+	5.07451i	−0.201376	+	0.201376i
$636$		0			0
$637$	2.30311	−	0.617117i	0.0912526	−	0.0244511i
$638$	13.5291	+	2.38554i	0.535622	+	0.0944445i
$639$		0			0
$640$	2.70036	+	1.55905i	0.106741	+	0.0616269i
$641$	−6.24611	+	7.44382i	−0.246706	+	0.294013i	−0.875160	−	0.483834i	$-0.839244\pi$
$641$	−6.24611	+	7.44382i	−0.246706	+	0.294013i	0.628453	+	0.777847i	$0.283688\pi$
$642$		0			0
$643$	32.9105	+	8.81835i	1.29786	+	0.347762i	0.840642	−	0.541591i	$-0.182178\pi$
$643$	32.9105	+	8.81835i	1.29786	+	0.347762i	0.457222	+	0.889352i	$0.348844\pi$
$644$	5.33327	+	2.48694i	0.210160	+	0.0979993i
$645$		0			0
$646$	−12.0833	+	8.46079i	−0.475410	+	0.332885i
$647$	31.7137	+	2.77459i	1.24679	+	0.109080i	0.691378	−	0.722493i	$-0.257004\pi$
$647$	31.7137	+	2.77459i	1.24679	+	0.109080i	0.555415	+	0.831573i	$0.312559\pi$
$648$		0			0
$649$	−21.4960	−	30.6995i	−0.843794	−	1.20506i
$650$	−4.08123	+	1.48545i	−0.160079	+	0.0582640i
$651$		0			0
$652$	4.59337	−	17.1427i	0.179890	−	0.671360i
$653$	2.69304	−	3.84606i	0.105387	−	0.150508i	−0.762995	−	0.646405i	$-0.776272\pi$
$653$	2.69304	−	3.84606i	0.105387	−	0.150508i	0.868381	+	0.495897i	$0.165161\pi$
$654$		0			0
$655$	−11.1223	+	19.2644i	−0.434584	+	0.752721i
$656$	−1.05666	−	1.83019i	−0.0412556	−	0.0714568i
$657$		0			0
$658$	3.15634	+	11.7796i	0.123047	+	0.459217i
$659$	−27.0882	−	9.85932i	−1.05521	−	0.384064i	−0.244582	−	0.969629i	$-0.578651\pi$
$659$	−27.0882	−	9.85932i	−1.05521	−	0.384064i	−0.810626	+	0.585564i	$0.800873\pi$
$660$		0			0
$661$	−27.7552	+	12.9425i	−1.07955	+	0.503403i	−0.879265	−	0.476334i	$-0.841965\pi$
$661$	−27.7552	+	12.9425i	−1.07955	+	0.503403i	−0.200288	+	0.979737i	$0.564188\pi$
$662$	−8.50928	+	1.50041i	−0.330722	+	0.0583153i
$663$		0			0
$664$	0.278000	+	3.17755i	0.0107885	+	0.123313i
$665$	19.2315			0.745766
$666$		0			0
$667$	14.3768			0.556673
$668$	1.26304	+	14.4366i	0.0488685	+	0.558570i
$669$		0			0
$670$	26.2046	−	4.62057i	1.01237	−	0.178508i
$671$	−15.4933	+	7.22466i	−0.598113	+	0.278905i
$672$		0			0
$673$	13.9137	+	5.06416i	0.536332	+	0.195209i	0.595963	−	0.803012i	$-0.296770\pi$
$673$	13.9137	+	5.06416i	0.536332	+	0.195209i	−0.0596314	+	0.998220i	$0.518993\pi$
$674$	8.82634	+	32.9403i	0.339978	+	1.26881i
$675$		0			0
$676$	−6.07711	−	10.5259i	−0.233735	−	0.404841i
$677$	−16.1053	+	27.8952i	−0.618977	+	1.07210i	0.370696	+	0.928754i	$0.379119\pi$
$677$	−16.1053	+	27.8952i	−0.618977	+	1.07210i	−0.989673	+	0.143345i	$0.954214\pi$
$678$		0			0
$679$	−14.6080	+	20.8623i	−0.560602	+	0.800622i
$680$	4.05202	−	15.1224i	0.155388	−	0.579916i
$681$		0			0
$682$	6.70496	−	2.44041i	0.256746	−	0.0934480i
$683$	−5.46876	−	7.81020i	−0.209256	−	0.298849i	0.700780	−	0.713377i	$-0.252835\pi$
$683$	−5.46876	−	7.81020i	−0.209256	−	0.298849i	−0.910036	+	0.414528i	$0.863947\pi$
$684$		0			0
$685$	34.6212	+	3.02896i	1.32281	+	0.115731i
$686$	16.4965	−	11.5510i	0.629839	−	0.441018i
$687$		0			0
$688$	−7.69213	−	3.58690i	−0.293260	−	0.136749i
$689$	−5.95752	−	1.59631i	−0.226963	−	0.0608146i
$690$		0			0
$691$	22.0361	−	26.2616i	0.838292	−	0.999037i	−0.161634	−	0.986851i	$-0.551676\pi$
$691$	22.0361	−	26.2616i	0.838292	−	0.999037i	0.999926	−	0.0121863i	$-0.00387911\pi$
$692$	6.74764	+	3.89575i	0.256507	+	0.148094i
$693$		0			0
$694$	−2.06001	−	0.363234i	−0.0781967	−	0.0137882i
$695$	60.4364	−	16.1939i	2.29248	−	0.614269i
$696$		0			0
$697$	−7.50301	+	7.50301i	−0.284197	+	0.284197i
$698$	0.992168	+	2.12771i	0.0375541	+	0.0805350i
$699$		0			0
$700$	−7.59488	+	6.37286i	−0.287060	+	0.240872i
$701$	46.0964	−	4.03291i	1.74104	−	0.152321i	0.828143	−	0.560517i	$-0.189397\pi$
$701$	46.0964	−	4.03291i	1.74104	−	0.152321i	0.912894	+	0.408196i	$0.133842\pi$
$702$		0			0
$703$	2.59651	+	17.6808i	0.0979293	+	0.666844i
$704$		−	2.67845i		−	0.100948i
$705$		0			0
$706$	−15.4279	−	18.3863i	−0.580637	−	0.691976i
$707$	−6.01873	−	34.1339i	−0.226358	−	1.28374i
$708$		0			0
$709$	−11.3364	−	11.3364i	−0.425749	−	0.425749i	0.461428	−	0.887177i	$-0.347337\pi$
$709$	−11.3364	−	11.3364i	−0.425749	−	0.425749i	−0.887177	+	0.461428i	$0.847337\pi$
$710$	6.55362	−	18.0059i	0.245953	−	0.675750i
$711$		0			0
$712$	0.442329	−	2.50857i	0.0165770	−	0.0940127i
$713$	6.46676	−	3.73359i	0.242182	−	0.139824i
$714$		0			0
$715$	5.88375	+	4.93705i	0.220040	+	0.184635i
$716$	−9.94200	−	6.96147i	−0.371550	−	0.260162i
$717$		0			0
$718$	2.08373	−	4.46857i	0.0777641	−	0.166766i
$719$	−5.95733	−	16.3676i	−0.222171	−	0.610409i	0.777662	−	0.628682i	$-0.216405\pi$
$719$	−5.95733	−	16.3676i	−0.222171	−	0.610409i	−0.999833	+	0.0182729i	$0.994183\pi$
$720$		0			0
$721$	1.05529	−	12.0620i	0.0393010	−	0.449213i
$722$	0.903705	−	10.3294i	0.0336324	−	0.384420i
$723$		0			0
$724$	0.358322	+	0.984483i	0.0133169	+	0.0365880i
$725$	−10.2367	+	21.9527i	−0.380182	+	0.815303i
$726$		0			0
$727$	0.525227	+	0.367768i	0.0194796	+	0.0136398i	0.583276	−	0.812274i	$-0.301771\pi$
$727$	0.525227	+	0.367768i	0.0194796	+	0.0136398i	−0.563796	+	0.825914i	$0.690660\pi$
$728$	1.47900	+	1.24103i	0.0548156	+	0.0459957i
$729$		0			0
$730$	24.3481	−	14.0574i	0.901163	−	0.520287i
$731$	−7.39990	+	41.9669i	−0.273695	+	1.55220i
$732$		0			0
$733$	−5.99689	+	16.4763i	−0.221500	+	0.608567i	−0.999814	−	0.0193090i	$-0.993853\pi$
$733$	−5.99689	+	16.4763i	−0.221500	+	0.608567i	0.778313	+	0.627876i	$0.216076\pi$
$734$	11.7977	+	11.7977i	0.435460	+	0.435460i
$735$		0			0
$736$	−0.486742	−	2.76045i	−0.0179416	−	0.101752i
$737$	−14.6922	−	17.5094i	−0.541193	−	0.644968i
$738$		0			0
$739$		−	40.3640i		−	1.48482i	−0.669949	−	0.742408i	$-0.733684\pi$
$739$		−	40.3640i		−	1.48482i	0.669949	−	0.742408i	$-0.266316\pi$
$740$	−14.1732	−	12.6038i	−0.521018	−	0.463323i
$741$		0			0
$742$	−14.0258	+	1.22710i	−0.514903	+	0.0450482i
$743$	−5.88578	+	4.93876i	−0.215928	+	0.181185i	−0.744336	−	0.667805i	$-0.767234\pi$
$743$	−5.88578	+	4.93876i	−0.215928	+	0.181185i	0.528407	+	0.848991i	$0.322789\pi$
$744$		0			0
$745$	−28.9165	−	62.0115i	−1.05942	−	2.27193i
$746$	−4.50283	+	4.50283i	−0.164860	+	0.164860i
$747$		0			0
$748$	−12.9901	+	3.48068i	−0.474965	+	0.127266i
$749$	40.7724	+	7.18927i	1.48979	+	0.262690i
$750$		0			0
$751$	2.63599	+	1.52189i	0.0961885	+	0.0555345i	0.547323	−	0.836922i	$-0.315647\pi$
$751$	2.63599	+	1.52189i	0.0961885	+	0.0555345i	−0.451134	+	0.892456i	$0.648980\pi$
$752$	3.73393	−	4.44992i	0.136162	−	0.162272i
$753$		0			0
$754$	4.55622	+	1.22084i	0.165928	+	0.0444602i
$755$	−31.9656	−	14.9058i	−1.16335	−	0.542477i
$756$		0			0
$757$	−21.5392	+	15.0819i	−0.782857	+	0.548162i	−0.895283	−	0.445498i	$-0.853027\pi$
$757$	−21.5392	+	15.0819i	−0.782857	+	0.548162i	0.112426	+	0.993660i	$0.464138\pi$
$758$	6.78227	+	0.593372i	0.246343	+	0.0215522i
$759$		0			0
$760$	−5.25432	−	7.50394i	−0.190594	−	0.272197i
$761$	3.54295	−	1.28953i	0.128432	−	0.0467453i	−0.277005	−	0.960869i	$-0.589342\pi$
$761$	3.54295	−	1.28953i	0.128432	−	0.0467453i	0.405436	+	0.914123i	$0.367120\pi$
$762$		0			0
$763$	−2.28192	+	8.51624i	−0.0826111	+	0.308309i
$764$	−13.1813	+	18.8248i	−0.476882	+	0.681058i
$765$		0			0
$766$	−9.52457	+	16.4970i	−0.344137	+	0.596062i
$767$	−6.43400	−	11.1440i	−0.232318	−	0.402387i
$768$		0			0
$769$	4.44019	+	16.5710i	0.160117	+	0.597566i	0.998613	+	0.0526572i	$0.0167691\pi$
$769$	4.44019	+	16.5710i	0.160117	+	0.597566i	−0.838495	+	0.544909i	$0.816564\pi$
$770$	16.4759	+	5.99672i	0.593749	+	0.216107i
$771$		0			0
$772$	−9.52212	+	4.44024i	−0.342709	+	0.159808i
$773$	29.9348	−	5.27830i	1.07668	−	0.189847i	0.392932	−	0.919567i	$-0.371461\pi$
$773$	29.9348	−	5.27830i	1.07668	−	0.189847i	0.683746	+	0.729720i	$0.260350\pi$
$774$		0			0
$775$	1.09648	+	12.5329i	0.0393868	+	0.450193i
$776$	12.1314			0.435490
$777$		0			0
$778$	3.49112			0.125163
$779$	0.541122	+	6.18506i	0.0193877	+	0.221603i
$780$		0			0
$781$	−16.2096	+	2.85820i	−0.580027	+	0.102274i
$782$	−12.7553	+	5.94788i	−0.456128	+	0.212696i
$783$		0			0
$784$	−2.43630	−	0.886739i	−0.0870105	−	0.0316692i

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-2.82596 + 1.31777i) q^{5} +(1.97276 + 0.718026i) q^{7} +(-0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-2.82596 + 1.31777i) q^{5} +(1.97276 + 0.718026i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-1.55905 - 2.70036i) q^{10} +(-1.33922 + 2.31960i) q^{11} +(-0.527495 + 0.753341i) q^{13} +(-0.543357 + 2.02783i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-2.87989 - 4.11292i) q^{17} +(-2.92670 - 0.256053i) q^{19} +(2.55420 - 1.78847i) q^{20} +(-2.42750 - 1.13196i) q^{22} +(-2.70753 - 0.725480i) q^{23} +(3.03561 - 3.61770i) q^{25} +(-0.796448 - 0.459830i) q^{26} +(-2.06747 - 0.364552i) q^{28} +(-4.95425 + 1.32749i) q^{29} +(-1.88370 + 1.88370i) q^{31} +(0.422618 + 0.906308i) q^{32} +(3.84627 - 3.22740i) q^{34} +(-6.52114 + 0.570526i) q^{35} +(-1.40496 - 5.91828i) q^{37} -2.93788i q^{38} +(2.00428 + 2.38861i) q^{40} +(-0.366974 - 2.08121i) q^{41} +(-6.00144 - 6.00144i) q^{43} +(0.916083 - 2.51692i) q^{44} +(0.486742 - 2.76045i) q^{46} +(5.03071 - 2.90448i) q^{47} +(-1.98609 - 1.66652i) q^{49} +(3.86850 + 2.70876i) q^{50} +(0.388665 - 0.833494i) q^{52} +(2.29375 + 6.30203i) q^{53} +(0.727896 - 8.31989i) q^{55} +(0.182972 - 2.09138i) q^{56} +(-1.75423 - 4.81970i) q^{58} +(-5.91334 + 12.6812i) q^{59} +(5.22818 + 3.66081i) q^{61} +(-2.04071 - 1.71236i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(0.497952 - 2.82403i) q^{65} +(-2.91868 + 8.01901i) q^{67} +(3.55034 + 3.55034i) q^{68} +(-1.13671 - 6.44660i) q^{70} +(3.95008 + 4.70753i) q^{71} +9.01662i q^{73} +(5.77331 - 1.91543i) q^{74} +(2.92670 - 0.256053i) q^{76} +(-4.30750 + 3.61442i) q^{77} +(0.222674 + 0.477526i) q^{79} +(-2.20483 + 2.20483i) q^{80} +(2.04131 - 0.546967i) q^{82} +(-3.14123 - 0.553883i) q^{83} +(13.5583 + 7.82791i) q^{85} +(5.45554 - 6.50167i) q^{86} +(2.58718 + 0.693233i) q^{88} +(2.30861 + 1.07652i) q^{89} +(-1.58154 + 1.10741i) q^{91} +(2.79237 + 0.244301i) q^{92} +(3.33189 + 4.75842i) q^{94} +(8.60817 - 3.13312i) q^{95} +(-3.13983 + 11.7180i) q^{97} +(1.48708 - 2.12378i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more