LMFDB - Embedded newform 666.2.bs.a.557.4

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			557.4
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.a.611.4

$q$-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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

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

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	−0.328951	−	0.944347i	$-0.606695\pi$
$5$	−2.82596	−	1.31777i	−1.26381	−	0.589324i	−0.934857	+	0.355023i	$0.884473\pi$
$6$		0			0
$7$	1.97276	−	0.718026i	0.745634	−	0.271388i	0.0588664	−	0.998266i	$-0.481251\pi$
$7$	1.97276	−	0.718026i	0.745634	−	0.271388i	0.686767	+	0.726877i	$0.259029\pi$
$8$	−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	0.590389	−	0.807119i	$-0.298974\pi$
$11$	−1.33922	−	2.31960i	−0.403791	−	0.699387i	−0.994180	+	0.107732i	$0.965641\pi$
$12$		0			0
$13$	−0.527495	−	0.753341i	−0.146301	−	0.208939i	0.739313	−	0.673362i	$-0.235151\pi$
$13$	−0.527495	−	0.753341i	−0.146301	−	0.208939i	−0.885613	+	0.464423i	$0.846262\pi$
$14$	−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	0.300565	+	0.953761i	$0.402825\pi$
$17$	−2.87989	+	4.11292i	−0.698477	+	0.997528i	−0.999042	+	0.0437671i	$0.986064\pi$
$18$		0			0
$19$	−2.92670	+	0.256053i	−0.671432	+	0.0587427i	−0.417773	−	0.908551i	$-0.637189\pi$
$19$	−2.92670	+	0.256053i	−0.671432	+	0.0587427i	−0.253658	+	0.967294i	$0.581634\pi$
$20$	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	−0.529800	−	0.848123i	$-0.677733\pi$
$23$	−2.70753	+	0.725480i	−0.564558	+	0.151273i	−0.0347586	+	0.999396i	$0.511066\pi$
$24$		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	−0.232404	−	0.972619i	$-0.574659\pi$
$29$	−4.95425	−	1.32749i	−0.919981	−	0.246508i	−0.687577	+	0.726111i	$0.741326\pi$
$30$		0			0
$31$	−1.88370	−	1.88370i	−0.338323	−	0.338323i	0.517413	−	0.855736i	$-0.326895\pi$
$31$	−1.88370	−	1.88370i	−0.338323	−	0.338323i	−0.855736	+	0.517413i	$0.826895\pi$
$32$	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	−0.999962	−	0.00875197i	$-0.997214\pi$
$41$	−0.366974	+	2.08121i	−0.0573117	+	0.325031i	0.942650	+	0.333783i	$0.108325\pi$
$42$		0			0
$43$	−6.00144	+	6.00144i	−0.915211	+	0.915211i	−0.996676	−	0.0814648i	$-0.974040\pi$
$43$	−6.00144	+	6.00144i	−0.915211	+	0.915211i	0.0814648	+	0.996676i	$0.474040\pi$
$44$	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	0.819812	−	0.572632i	$-0.194078\pi$
$47$	5.03071	+	2.90448i	0.733805	+	0.423662i	−0.0860078	+	0.996294i	$0.527411\pi$
$48$		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	−0.676542	−	0.736404i	$-0.736522\pi$
$53$	2.29375	−	6.30203i	0.315071	−	0.865650i	0.991613	−	0.129246i	$-0.0412556\pi$
$54$		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	−0.759071	−	0.651008i	$-0.774346\pi$
$59$	−5.91334	−	12.6812i	−0.769851	−	1.65095i	−0.0107801	−	0.999942i	$-0.503431\pi$
$60$		0			0
$61$	5.22818	−	3.66081i	0.669400	−	0.468719i	−0.188813	−	0.982013i	$-0.560464\pi$
$61$	5.22818	−	3.66081i	0.669400	−	0.468719i	0.858213	+	0.513294i	$0.171575\pi$
$62$	−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	−0.980209	−	0.197963i	$-0.936567\pi$
$67$	−2.91868	−	8.01901i	−0.356574	−	0.979678i	0.623636	−	0.781715i	$-0.285655\pi$
$68$	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	−0.478903	−	0.877868i	$-0.658965\pi$
$71$	3.95008	−	4.70753i	0.468789	−	0.558681i	0.947692	+	0.319187i	$0.103410\pi$
$72$		0			0
$73$		−	9.01662i		−	1.05532i	−0.849457	−	0.527658i	$-0.823070\pi$
$73$		−	9.01662i		−	1.05532i	0.849457	−	0.527658i	$-0.176930\pi$
$74$	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	−0.893383	−	0.449296i	$-0.851675\pi$
$79$	0.222674	−	0.477526i	0.0250528	−	0.0537259i	0.918436	+	0.395570i	$0.129453\pi$
$80$	−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	−0.343364	−	0.939202i	$-0.611566\pi$
$83$	−3.14123	+	0.553883i	−0.344795	+	0.0607966i	−0.00143059	+	0.999999i	$0.500455\pi$
$84$		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	−0.296393	−	0.955066i	$-0.595784\pi$
$89$	2.30861	−	1.07652i	0.244712	−	0.114111i	0.541105	+	0.840955i	$0.318006\pi$
$90$		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	−0.920398	−	0.390982i	$-0.872135\pi$
$97$	−3.13983	−	11.7180i	−0.318801	−	1.18978i	0.601597	−	0.798800i	$-0.294531\pi$
$98$	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	0.0832381	+	0.996530i	$0.473474\pi$
$101$	−8.25498	+	14.2980i	−0.821401	+	1.42271i	−0.904639	+	0.426179i	$0.859860\pi$
$102$		0			0
$103$	−1.49274	+	5.57097i	−0.147084	+	0.548924i	0.852570	+	0.522613i	$0.175043\pi$
$103$	−1.49274	+	5.57097i	−0.147084	+	0.548924i	−0.999654	+	0.0263109i	$0.991624\pi$
$104$	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	0.991239	−	0.132083i	$-0.0421666\pi$
$107$	19.4213	+	3.42449i	1.87752	+	0.331058i	0.886285	+	0.463141i	$0.153278\pi$
$108$		0			0
$109$	0.366026	−	4.18369i	0.0350589	−	0.400725i	−0.958308	−	0.285737i	$-0.907762\pi$
$109$	0.366026	−	4.18369i	0.0350589	−	0.400725i	0.993367	−	0.114988i	$-0.0366829\pi$
$110$	8.35167			0.796301
$111$		0			0
$112$	2.09937			0.198372
$113$	0.703066	−	8.03608i	0.0661389	−	0.755971i	−0.888630	−	0.458624i	$-0.848343\pi$
$113$	0.703066	−	8.03608i	0.0661389	−	0.755971i	0.954769	−	0.297347i	$-0.0961019\pi$
$114$		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	0.436188	−	0.899855i	$-0.356328\pi$
$127$	2.16274	+	0.787173i	0.191912	+	0.0698503i	−0.244276	+	0.969706i	$0.578550\pi$
$128$	−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	0.800300	−	0.599600i	$-0.204674\pi$
$131$	5.84384	+	4.09190i	0.510578	+	0.357511i	−0.289721	+	0.957111i	$0.593563\pi$
$132$		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	−0.852022	−	0.523505i	$-0.824624\pi$
$137$	−9.65245	+	5.57285i	−0.824665	+	0.476120i	0.0273576	+	0.999626i	$0.491291\pi$
$138$		0			0
$139$	−19.7613	+	3.48445i	−1.67613	+	0.295547i	−0.929261	−	0.369423i	$-0.879555\pi$
$139$	−19.7613	+	3.48445i	−1.67613	+	0.295547i	−0.746870	+	0.664970i	$0.768444\pi$
$140$	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	$-0.644410\pi$
$149$		−	21.9435i		−	1.79768i	0.438274	−	0.898841i	$-0.355590\pi$
$150$		0			0
$151$	7.27082	−	8.66503i	0.591691	−	0.705150i	−0.384239	−	0.923234i	$-0.625536\pi$
$151$	7.27082	−	8.66503i	0.591691	−	0.705150i	0.975930	+	0.218084i	$0.0699806\pi$
$152$	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	−0.607960	−	0.793968i	$-0.708012\pi$
$157$	−3.86195	−	21.9022i	−0.308217	−	1.74799i	0.299742	−	0.954020i	$-0.403099\pi$
$158$	−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	−0.945344	−	0.326074i	$-0.894274\pi$
$163$	−7.50039	−	16.0846i	−0.587476	−	1.25985i	0.357868	−	0.933772i	$-0.383504\pi$
$164$	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	0.873734	+	0.486403i	$0.161691\pi$
$167$	1.26304	+	14.4366i	0.0977370	+	1.11714i	−0.775997	+	0.630736i	$0.782753\pi$
$168$		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	−0.840839	−	0.541285i	$-0.817938\pi$
$173$	−5.96864	+	5.00828i	−0.453787	+	0.380773i	0.387052	+	0.922058i	$0.373493\pi$
$174$		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	−0.309456	−	0.950914i	$-0.600147\pi$
$179$	8.58212	−	8.58212i	0.641458	−	0.641458i	0.950914	+	0.309456i	$0.100147\pi$
$180$		0			0
$181$	−0.181925	+	1.03175i	−0.0135224	+	0.0766892i	−0.990822	−	0.135172i	$-0.956841\pi$
$181$	−0.181925	+	1.03175i	−0.0135224	+	0.0766892i	0.977300	+	0.211861i	$0.0679524\pi$
$182$	−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	0.980803	+	0.194999i	$0.0624705\pi$
$191$	16.2499	+	16.2499i	1.17580	+	1.17580i	0.194999	+	0.980803i	$0.437530\pi$
$192$		0			0
$193$	10.1485	+	2.71928i	0.730505	+	0.195738i	0.604854	−	0.796336i	$-0.293231\pi$
$193$	10.1485	+	2.71928i	0.730505	+	0.195738i	0.125651	+	0.992075i	$0.459898\pi$
$194$	−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	−0.920755	−	0.390142i	$-0.872426\pi$
$197$	−16.0720	−	19.1539i	−1.14508	−	1.36466i	−0.224328	−	0.974514i	$-0.572019\pi$
$198$		0			0
$199$	−0.892139	+	0.239048i	−0.0632421	+	0.0169457i	−0.290301	−	0.956935i	$-0.593756\pi$
$199$	−0.892139	+	0.239048i	−0.0632421	+	0.0169457i	0.227059	+	0.973881i	$0.427089\pi$
$200$	−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	0.991290	+	0.131695i	$0.0420419\pi$
$211$	8.85635	+	15.3396i	0.609696	+	1.05602i	−0.381594	+	0.924330i	$0.624625\pi$
$212$	−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	0.141281	−	0.989970i	$-0.454878\pi$
$227$	−7.92901	−	3.69736i	−0.526267	−	0.245402i	−0.667547	+	0.744567i	$0.732656\pi$
$228$		0			0
$229$	−20.8633	+	7.59364i	−1.37869	+	0.501802i	−0.921780	−	0.387712i	$-0.873265\pi$
$229$	−20.8633	+	7.59364i	−1.37869	+	0.501802i	−0.456908	+	0.889514i	$0.651043\pi$
$230$	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	0.713134	−	0.701027i	$-0.247275\pi$
$233$	−3.82433	−	6.62394i	−0.250540	−	0.433949i	−0.963675	+	0.267079i	$0.913942\pi$
$234$		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	−0.992922	−	0.118768i	$-0.962105\pi$
$239$	−8.37474	+	11.9604i	−0.541717	+	0.773652i	0.451205	+	0.892420i	$0.350994\pi$
$240$		0			0
$241$	−26.4890	+	2.31749i	−1.70631	+	0.149283i	−0.898152	−	0.439684i	$-0.855090\pi$
$241$	−26.4890	+	2.31749i	−1.70631	+	0.149283i	−0.808157	+	0.588967i	$0.799535\pi$
$242$	−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	0.838664	−	0.544650i	$-0.183337\pi$
$251$	20.4793	+	5.48741i	1.29264	+	0.346363i	0.453979	+	0.891012i	$0.350004\pi$
$252$		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	−0.221899	−	0.975070i	$-0.571226\pi$
$257$	−9.77498	−	0.855200i	−0.609747	−	0.0533459i	−0.387847	+	0.921724i	$0.626781\pi$
$258$		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	0.831813	+	0.555057i	$0.187303\pi$
$263$	−2.26517	+	12.8464i	−0.139676	+	0.792142i	−0.971489	+	0.237086i	$0.923808\pi$
$264$		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	0.168879	−	0.985637i	$-0.445985\pi$
$269$	−9.84514	−	5.68409i	−0.600269	−	0.346565i	−0.769147	+	0.639072i	$0.779319\pi$
$270$		0			0
$271$	−18.5306	+	15.5490i	−1.12566	+	0.944537i	−0.998876	−	0.0473935i	$-0.984909\pi$
$271$	−18.5306	+	15.5490i	−1.12566	+	0.944537i	−0.126780	+	0.991931i	$0.540464\pi$
$272$	−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	0.995231	−	0.0975459i	$-0.0310993\pi$
$277$	−0.0302720	−	0.346010i	−0.00181887	−	0.0207898i	−0.997050	+	0.0767561i	$0.975544\pi$
$278$	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	0.917750	−	0.397158i	$-0.130004\pi$
$281$	0.395455	+	0.848057i	0.0235909	+	0.0505908i	−0.894159	+	0.447749i	$0.852226\pi$
$282$		0			0
$283$	−8.50619	+	5.95610i	−0.505641	+	0.354053i	−0.798395	−	0.602134i	$-0.794317\pi$
$283$	−8.50619	+	5.95610i	−0.505641	+	0.354053i	0.292754	+	0.956188i	$0.405428\pi$
$284$	−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	−0.343303	−	0.939225i	$-0.611546\pi$
$293$	10.9767	−	13.0815i	0.641266	−	0.764231i	0.984570	+	0.174993i	$0.0559903\pi$
$294$		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	0.0121515	−	0.999926i	$-0.496132\pi$
$307$	15.4922	−	8.94445i	0.884189	−	0.510487i	0.872037	+	0.489440i	$0.162799\pi$
$308$	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	−0.658752	−	0.752360i	$-0.728915\pi$
$311$	−8.92073	+	4.15980i	−0.505848	+	0.235881i	0.152904	+	0.988241i	$0.451138\pi$
$312$		0			0
$313$	−4.60506	−	3.22450i	−0.260293	−	0.182259i	0.436144	−	0.899877i	$-0.356344\pi$
$313$	−4.60506	−	3.22450i	−0.260293	−	0.182259i	−0.696437	+	0.717618i	$0.745233\pi$
$314$	−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	0.994545	−	0.104309i	$-0.0332630\pi$
$317$	30.0782	+	10.9476i	1.68936	+	0.614878i	0.694817	+	0.719186i	$0.255485\pi$
$318$		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	−0.947004	−	0.321223i	$-0.895906\pi$
$331$	0.753073	−	8.60767i	0.0413926	−	0.473120i	0.988396	−	0.151897i	$-0.0485383\pi$
$332$	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	0.979060	−	0.203570i	$-0.0652544\pi$
$337$	33.5843	+	5.92181i	1.82945	+	0.322582i	0.850391	+	0.526151i	$0.176366\pi$
$338$	−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	0.949870	−	0.312644i	$-0.101215\pi$
$347$	−0.541394	−	2.02051i	−0.0290635	−	0.108467i	−0.978934	+	0.204177i	$0.934548\pi$
$348$		0			0
$349$	2.20609	+	0.802950i	0.118089	+	0.0429809i	0.400389	−	0.916345i	$-0.368875\pi$
$349$	2.20609	+	0.802950i	0.118089	+	0.0429809i	−0.282300	+	0.959326i	$0.591097\pi$
$350$	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	−0.0818985	−	0.996641i	$-0.526098\pi$
$353$	−19.6609	−	13.7667i	−1.04645	−	0.732729i	−0.964547	+	0.263912i	$0.914987\pi$
$354$		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	−0.608430	−	0.793608i	$-0.708200\pi$
$359$	−4.26996	+	2.46526i	−0.225360	+	0.130111i	0.383070	+	0.923719i	$0.374867\pi$
$360$		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	0.912224	−	0.409691i	$-0.134363\pi$
$367$	12.7810	+	10.7245i	0.667164	+	0.559817i	−0.245061	+	0.969508i	$0.578808\pi$
$368$	−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	−0.649593	−	0.760283i	$-0.725061\pi$
$373$	4.09324	−	4.87814i	0.211940	−	0.252580i	0.861533	+	0.507702i	$0.169505\pi$
$374$	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	0.999999	+	0.00122683i	$0.000390514\pi$
$379$	1.18223	+	6.70474i	0.0607269	+	0.344400i	−0.939272	+	0.343173i	$0.888498\pi$
$380$	−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	−0.102397	−	0.994744i	$-0.532651\pi$
$383$	15.6041	−	10.9261i	0.797335	−	0.558300i	0.899731	+	0.436444i	$0.143762\pi$
$384$		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	0.999999	+	0.00135294i	$0.000430655\pi$
$389$	0.304271	+	3.47784i	0.0154272	+	0.176333i	−0.984572	+	0.174980i	$0.944014\pi$
$390$		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	0.991420	−	0.130716i	$-0.0417275\pi$
$397$	27.3753	+	15.8051i	1.37393	+	0.793237i	0.382507	+	0.923953i	$0.375061\pi$
$398$	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	−0.415752	−	0.909478i	$-0.636482\pi$
$401$	9.88686	−	9.88686i	0.493726	−	0.493726i	0.909478	+	0.415752i	$0.136482\pi$
$402$		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	−0.839618	−	0.543177i	$-0.817221\pi$
$409$	−35.6100	−	3.11547i	−1.76080	−	0.154050i	−0.921184	+	0.389127i	$0.872777\pi$
$410$	−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	0.665571	−	0.746335i	$-0.268188\pi$
$419$	−3.78686	−	4.51301i	−0.185000	−	0.220475i	−0.850571	+	0.525860i	$0.823744\pi$
$420$		0			0
$421$	10.7741	−	2.88690i	0.525096	−	0.140699i	0.0134732	−	0.999909i	$-0.495711\pi$
$421$	10.7741	−	2.88690i	0.525096	−	0.140699i	0.511623	+	0.859210i	$0.329045\pi$
$422$	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	0.873810	−	0.486267i	$-0.161642\pi$
$431$	2.44990	+	3.49882i	0.118007	+	0.168532i	−0.755803	+	0.654800i	$0.772753\pi$
$432$		0			0
$433$	10.9074	+	18.8921i	0.524174	+	0.907896i	0.999604	+	0.0281424i	$0.00895918\pi$
$433$	10.9074	+	18.8921i	0.524174	+	0.907896i	−0.475430	+	0.879754i	$0.657707\pi$
$434$	−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	0.600806	−	0.799395i	$-0.294847\pi$
$439$	7.84924	+	3.66016i	0.374624	+	0.174690i	−0.226182	+	0.974085i	$0.572624\pi$
$440$	−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	0.224376	−	0.974503i	$-0.427966\pi$
$449$	−8.00777	−	3.73409i	−0.377910	−	0.176222i	−0.602286	+	0.798280i	$0.705743\pi$
$450$		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	0.564991	−	0.825097i	$-0.308880\pi$
$457$	−8.62766	−	12.3216i	−0.403585	−	0.576379i	−0.968576	+	0.248718i	$0.919991\pi$
$458$	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	−0.855188	−	0.518318i	$-0.826558\pi$
$461$	−1.62400	+	2.31931i	−0.0756372	+	0.108021i	0.779551	+	0.626339i	$0.215447\pi$
$462$		0			0
$463$	−36.1930	+	3.16648i	−1.68203	+	0.147159i	−0.887729	−	0.460366i	$-0.847718\pi$
$463$	−36.1930	+	3.16648i	−1.68203	+	0.147159i	−0.794301	+	0.607524i	$0.792163\pi$
$464$	−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	−0.946241	−	0.323462i	$-0.895153\pi$
$467$	−34.6623	+	9.28773i	−1.60398	+	0.429785i	−0.657738	+	0.753247i	$0.728487\pi$
$468$		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	0.665388	−	0.746497i	$-0.268266\pi$
$479$	26.0672	+	2.28058i	1.19104	+	0.104203i	0.525652	+	0.850700i	$0.323821\pi$
$480$		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	−0.691309	−	0.722559i	$-0.742966\pi$
$487$	0.689631	−	0.689631i	0.0312502	−	0.0312502i	0.722559	+	0.691309i	$0.242966\pi$
$488$	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	−0.962157	−	0.272497i	$-0.912150\pi$
$491$	−37.2091	−	21.4827i	−1.67922	−	0.969501i	−0.717068	−	0.697003i	$-0.754516\pi$
$492$		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	−0.979612	−	0.200899i	$-0.935614\pi$
$499$	−1.11174	−	12.7072i	−0.0497682	−	0.568854i	0.929844	−	0.367955i	$-0.119942\pi$
$500$	−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	0.774196	−	0.632946i	$-0.218155\pi$
$503$	−4.67196	−	10.0191i	−0.208313	−	0.446728i	−0.982508	+	0.186219i	$0.940377\pi$
$504$		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	0.948424	+	0.317005i	$0.102677\pi$
$509$	3.73654	+	21.1910i	0.165619	+	0.939273i	−0.782805	+	0.622268i	$0.786212\pi$
$510$		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	0.650423	−	0.759572i	$-0.274592\pi$
$521$	0.350028	+	0.293708i	0.0153350	+	0.0128676i	−0.635088	+	0.772440i	$0.719036\pi$
$522$		0			0
$523$	−7.60898	+	16.3175i	−0.332717	+	0.713515i	−0.999496	−	0.0317411i	$-0.989895\pi$
$523$	−7.60898	+	16.3175i	−0.332717	+	0.713515i	0.666779	+	0.745256i	$0.267673\pi$
$524$	−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	0.837947	+	0.545752i	$0.183756\pi$
$541$	8.95812	+	33.4321i	0.385139	+	1.43736i	−0.452807	+	0.891608i	$0.649577\pi$
$542$	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	−0.608132	−	0.793836i	$-0.708081\pi$
$547$	7.37760	−	27.5336i	0.315444	−	1.17725i	0.923576	−	0.383416i	$-0.125252\pi$
$548$	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	0.887732	+	0.460360i	$0.152280\pi$
$557$	−1.56837	+	17.9266i	−0.0664540	+	0.759573i	−0.954186	+	0.299213i	$0.903276\pi$
$558$		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	−0.809379	−	0.587286i	$-0.800196\pi$
$563$	4.39452	−	16.4006i	0.185207	−	0.691201i	0.994586	−	0.103915i	$-0.0331370\pi$
$564$		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	0.964503	−	0.264072i	$-0.0850658\pi$
$569$	−0.0672038	−	0.250808i	−0.00281733	−	0.0105144i	−0.967320	+	0.253558i	$0.918399\pi$
$570$		0			0
$571$	−43.2375	−	15.7372i	−1.80943	−	0.658579i	−0.997161	−	0.0752988i	$-0.976009\pi$
$571$	−43.2375	−	15.7372i	−1.80943	−	0.658579i	−0.812271	−	0.583280i	$-0.801769\pi$
$572$	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	0.579985	−	0.814627i	$-0.303058\pi$
$577$	37.8768	−	17.6623i	1.57683	−	0.735289i	0.996848	+	0.0793374i	$0.0252804\pi$
$578$	−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	0.511146	+	0.859494i	$0.329221\pi$
$587$	−11.5283	+	24.7225i	−0.475823	+	1.02041i	−0.986969	+	0.160912i	$0.948557\pi$
$588$		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	$-0.942833\pi$
$593$		−	8.69991i		−	0.357263i	0.983916	−	0.178631i	$-0.0571669\pi$
$594$		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	−0.927997	−	0.372589i	$-0.878470\pi$
$599$	−11.1752	−	30.7035i	−0.456605	−	1.25451i	0.471391	−	0.881924i	$-0.343752\pi$
$600$		0			0
$601$	−5.74854	−	32.6016i	−0.234488	−	1.32985i	−0.843690	−	0.536831i	$-0.819621\pi$
$601$	−5.74854	−	32.6016i	−0.234488	−	1.32985i	0.609202	−	0.793015i	$-0.291490\pi$
$602$	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	0.974598	+	0.223962i	$0.0718990\pi$
$607$	12.8041	+	27.4585i	0.519703	+	1.11451i	−0.454895	+	0.890545i	$0.650323\pi$
$608$	−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	−0.109574	−	0.993979i	$-0.534949\pi$
$613$	15.1841	−	41.7181i	0.613282	−	1.68498i	0.722856	−	0.690999i	$-0.242829\pi$
$614$	−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	0.117448	−	0.993079i	$-0.462529\pi$
$617$	27.7168	−	23.2571i	1.11583	−	0.936296i	0.998387	+	0.0567827i	$0.0180842\pi$
$618$		0			0
$619$	26.5570	+	15.3327i	1.06742	+	0.616274i	0.927475	−	0.373886i	$-0.121975\pi$
$619$	26.5570	+	15.3327i	1.06742	+	0.616274i	0.139943	+	0.990160i	$0.455308\pi$
$620$	−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	0.121568	−	0.992583i	$-0.461208\pi$
$631$	1.73147	+	0.151484i	0.0689289	+	0.00603049i	−0.0526391	+	0.998614i	$0.516763\pi$
$632$	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	0.628453	−	0.777847i	$-0.283688\pi$
$641$	−6.24611	−	7.44382i	−0.246706	−	0.294013i	−0.875160	+	0.483834i	$0.839244\pi$
$642$		0			0
$643$	32.9105	−	8.81835i	1.29786	−	0.347762i	0.457222	−	0.889352i	$-0.348844\pi$
$643$	32.9105	−	8.81835i	1.29786	−	0.347762i	0.840642	+	0.541591i	$0.182178\pi$
$644$	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	0.555415	−	0.831573i	$-0.312559\pi$
$647$	31.7137	−	2.77459i	1.24679	−	0.109080i	0.691378	+	0.722493i	$0.257004\pi$
$648$		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	0.868381	−	0.495897i	$-0.165161\pi$
$653$	2.69304	+	3.84606i	0.105387	+	0.150508i	−0.762995	+	0.646405i	$0.776272\pi$
$654$		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	−0.810626	−	0.585564i	$-0.800873\pi$
$659$	−27.0882	+	9.85932i	−1.05521	+	0.384064i	−0.244582	+	0.969629i	$0.578651\pi$
$660$		0			0
$661$	−27.7552	−	12.9425i	−1.07955	−	0.503403i	−0.200288	−	0.979737i	$-0.564188\pi$
$661$	−27.7552	−	12.9425i	−1.07955	−	0.503403i	−0.879265	+	0.476334i	$0.841965\pi$
$662$	−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	−0.0596314	−	0.998220i	$-0.518993\pi$
$673$	13.9137	−	5.06416i	0.536332	−	0.195209i	0.595963	+	0.803012i	$0.296770\pi$
$674$	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	−0.989673	−	0.143345i	$-0.954214\pi$
$677$	−16.1053	−	27.8952i	−0.618977	−	1.07210i	0.370696	−	0.928754i	$-0.379119\pi$
$678$		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	−0.910036	−	0.414528i	$-0.863947\pi$
$683$	−5.46876	+	7.81020i	−0.209256	+	0.298849i	0.700780	+	0.713377i	$0.252835\pi$
$684$		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	0.999926	+	0.0121863i	$0.00387911\pi$
$691$	22.0361	+	26.2616i	0.838292	+	0.999037i	−0.161634	+	0.986851i	$0.551676\pi$
$692$	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	0.912894	−	0.408196i	$-0.133842\pi$
$701$	46.0964	+	4.03291i	1.74104	+	0.152321i	0.828143	+	0.560517i	$0.189397\pi$
$702$		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	−0.887177	−	0.461428i	$-0.847337\pi$
$709$	−11.3364	+	11.3364i	−0.425749	+	0.425749i	0.461428	+	0.887177i	$0.347337\pi$
$710$	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	−0.999833	−	0.0182729i	$-0.994183\pi$
$719$	−5.95733	+	16.3676i	−0.222171	+	0.610409i	0.777662	+	0.628682i	$0.216405\pi$
$720$		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	−0.563796	−	0.825914i	$-0.690660\pi$
$727$	0.525227	−	0.367768i	0.0194796	−	0.0136398i	0.583276	+	0.812274i	$0.301771\pi$
$728$	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	0.778313	−	0.627876i	$-0.216076\pi$
$733$	−5.99689	−	16.4763i	−0.221500	−	0.608567i	−0.999814	+	0.0193090i	$0.993853\pi$
$734$	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	$0.266316\pi$
$739$			40.3640i			1.48482i	−0.669949	+	0.742408i	$0.733684\pi$
$740$	−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	0.528407	−	0.848991i	$-0.322789\pi$
$743$	−5.88578	−	4.93876i	−0.215928	−	0.181185i	−0.744336	+	0.667805i	$0.767234\pi$
$744$		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	−0.451134	−	0.892456i	$-0.648980\pi$
$751$	2.63599	−	1.52189i	0.0961885	−	0.0555345i	0.547323	+	0.836922i	$0.315647\pi$
$752$	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	0.112426	−	0.993660i	$-0.464138\pi$
$757$	−21.5392	−	15.0819i	−0.782857	−	0.548162i	−0.895283	+	0.445498i	$0.853027\pi$
$758$	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	0.405436	−	0.914123i	$-0.367120\pi$
$761$	3.54295	+	1.28953i	0.128432	+	0.0467453i	−0.277005	+	0.960869i	$0.589342\pi$
$762$		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	−0.838495	−	0.544909i	$-0.816564\pi$
$769$	4.44019	−	16.5710i	0.160117	−	0.597566i	0.998613	−	0.0526572i	$-0.0167691\pi$
$770$	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	0.683746	−	0.729720i	$-0.260350\pi$
$773$	29.9348	+	5.27830i	1.07668	+	0.189847i	0.392932	+	0.919567i	$0.371461\pi$
$774$		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
$785$	−17.9483	+	66.9840i	−0.640603	+	2.39076i
$786$		0			0
$787$	14.1074	−	24.4347i	0.502873	−	0.871002i	−0.497122	−	0.867681i	$-0.665610\pi$
$787$	14.1074	−	24.4347i	0.502873	−	0.871002i	0.999994	−	0.00332059i	$-0.00105698\pi$
$788$	12.5018	+	21.6537i	0.445358	+	0.771383i
$789$		0			0
$790$	0.942331	+	1.34579i	0.0335266	+	0.0478810i
$791$	−4.38314	−	16.3581i	−0.155846	−	0.581627i
$792$		0			0
$793$	−5.51568	−	2.00754i	−0.195867	−	0.0712899i
$794$	18.1309	−	25.8936i	0.643442	−	0.918930i
$795$		0			0
$796$	0.920096	−	0.0804980i	0.0326119	−	0.00285317i
$797$	17.2016	+	12.0447i	0.609311	+	0.426644i	0.837087	−	0.547069i	$-0.184257\pi$
$797$	17.2016	+	12.0447i	0.609311	+	0.426644i	−0.227776	+	0.973713i	$0.573145\pi$
$798$		0			0
$799$	−26.4338	+	12.3263i	−0.935161	+	0.436073i
$800$	4.56165	−	1.22229i	0.161279	−	0.0432145i
$801$		0			0
$802$	−8.98754	−	10.7109i	−0.317361	−	0.378216i
$803$	−20.9150	+	12.0753i	−0.738073	+	0.426127i
$804$		0			0
$805$	18.0701	−	3.18624i	0.636886	−	0.112300i
$806$	2.36645	+	0.634089i	0.0833548	+	0.0223348i
$807$		0			0
$808$	−11.6743	−	11.6743i	−0.410700	−	0.410700i
$809$	2.40882	−	5.16574i	0.0846898	−	0.181618i	−0.859402	−	0.511300i	$-0.829164\pi$
$809$	2.40882	−	5.16574i	0.0846898	−	0.181618i	0.944092	+	0.329683i	$0.106942\pi$
$810$		0			0
$811$	28.5738	+	23.9763i	1.00336	+	0.841920i	0.987447	−	0.157953i	$-0.0504895\pi$
$811$	28.5738	+	23.9763i	1.00336	+	0.841920i	0.0159147	+	0.999873i	$0.494934\pi$
$812$	10.7267	+	0.938466i	0.376434	+	0.0329337i
$813$		0			0
$814$	−3.28872	−	15.9570i	−0.115270	−	0.559292i
$815$			55.3383i			1.93842i
$816$		0			0
$817$	16.0277	−	19.1011i	0.560740	−	0.668264i
$818$	−6.20724	+	35.2030i	−0.217031	+	1.23084i
$819$		0			0
$820$	−4.65951	+	4.65951i	−0.162717	+	0.162717i
$821$	−8.81959	−	24.2316i	−0.307806	−	0.845690i	−0.993084	−	0.117408i	$-0.962541\pi$
$821$	−8.81959	−	24.2316i	−0.307806	−	0.845690i	0.685278	−	0.728282i	$-0.259681\pi$
$822$		0			0
$823$	2.49692	+	14.1607i	0.0870370	+	0.493611i	0.996898	+	0.0786991i	$0.0250766\pi$
$823$	2.49692	+	14.1607i	0.0870370	+	0.493611i	−0.909861	+	0.414912i	$0.863812\pi$
$824$	−4.99479	−	2.88374i	−0.174002	−	0.100460i
$825$		0			0
$826$	−22.5023	+	18.8817i	−0.782955	+	0.656977i
$827$	20.5519	−	14.3906i	0.714658	−	0.500409i	−0.158798	−	0.987311i	$-0.550762\pi$
$827$	20.5519	−	14.3906i	0.714658	−	0.500409i	0.873457	+	0.486902i	$0.161873\pi$
$828$		0			0
$829$	5.56812	+	11.9409i	0.193389	+	0.414724i	0.978961	−	0.204046i	$-0.0654092\pi$
$829$	5.56812	+	11.9409i	0.193389	+	0.414724i	−0.785572	+	0.618770i	$0.787631\pi$
$830$	3.40166	−	9.34597i	0.118073	−	0.324403i
$831$		0			0
$832$	0.0801536	+	0.916160i	0.00277883	+	0.0317621i
$833$	−1.13455	−	12.9680i	−0.0393100	−	0.449315i
$834$		0			0
$835$	15.4548	−	42.4617i	0.534836	−	1.46945i
$836$	−3.32557	−	7.13170i	−0.115017	−	0.246655i
$837$		0			0
$838$	−4.82588	+	3.37912i	−0.166707	+	0.116730i
$839$	14.3198	−	12.0158i	0.494375	−	0.414830i	−0.361216	−	0.932482i	$-0.617638\pi$
$839$	14.3198	−	12.0158i	0.494375	−	0.414830i	0.855591	+	0.517652i	$0.173194\pi$
$840$		0			0
$841$	−2.33238	−	1.34660i	−0.0804269	−	0.0464345i
$842$	−1.93690	−	10.9847i	−0.0667498	−	0.378557i
$843$		0			0
$844$	−6.05810	−	16.6445i	−0.208528	−	0.572927i
$845$	−26.7980	+	26.7980i	−0.921880	+	0.921880i
$846$		0			0
$847$	1.39475	−	7.91000i	0.0479241	−	0.271791i
$848$	4.31084	−	5.13746i	0.148035	−	0.176421i
$849$		0			0
$850$			23.7118i			0.813306i
$851$	−0.489620	−	17.0432i	−0.0167840	−	0.584233i
$852$		0			0
$853$	−42.3155	−	3.70213i	−1.44886	−	0.126758i	−0.664601	−	0.747198i	$-0.731399\pi$
$853$	−42.3155	−	3.70213i	−1.44886	−	0.126758i	−0.784254	+	0.620440i	$0.786954\pi$
$854$	−10.2643	−	8.61276i	−0.351237	−	0.294722i
$855$		0			0
$856$	−8.33439	+	17.8732i	−0.284864	+	0.610892i
$857$	−22.1846	−	22.1846i	−0.757812	−	0.757812i	0.218112	−	0.975924i	$-0.430010\pi$
$857$	−22.1846	−	22.1846i	−0.757812	−	0.757812i	−0.975924	+	0.218112i	$0.930010\pi$
$858$		0			0
$859$	−1.91030	−	0.511864i	−0.0651787	−	0.0174646i	0.226082	−	0.974108i	$-0.427408\pi$
$859$	−1.91030	−	0.511864i	−0.0651787	−	0.0174646i	−0.291261	+	0.956644i	$0.594075\pi$
$860$	−26.0623	+	4.59549i	−0.888717	+	0.156705i
$861$		0			0
$862$	3.69903	−	2.13563i	0.125989	−	0.0727400i
$863$	11.2705	+	13.4316i	0.383651	+	0.457218i	0.922963	−	0.384888i	$-0.125760\pi$
$863$	11.2705	+	13.4316i	0.383651	+	0.457218i	−0.539312	+	0.842106i	$0.681316\pi$
$864$		0			0
$865$	23.4669	−	6.28793i	0.797898	−	0.213796i
$866$	19.7708	−	9.21929i	0.671840	−	0.313284i
$867$		0			0
$868$	4.58121	+	3.20780i	0.155497	+	0.108880i
$869$	−1.40588	+	0.122999i	−0.0476913	+	0.00417245i
$870$		0			0
$871$	−4.50146	+	6.42875i	−0.152526	+	0.217830i
$872$	3.94640	+	1.43637i	0.133642	+	0.0486417i
$873$		0			0
$874$	−2.13137	−	7.95439i	−0.0720948	−	0.269061i
$875$	1.04165	+	1.48764i	0.0352143	+	0.0502913i
$876$		0			0
$877$	24.7178	+	42.8125i	0.834661	+	1.44567i	0.894306	+	0.447455i	$0.147670\pi$
$877$	24.7178	+	42.8125i	0.834661	+	1.44567i	−0.0596455	+	0.998220i	$0.518997\pi$
$878$	4.33034	−	7.50037i	0.146142	−	0.253125i
$879$		0			0
$880$	−2.16157	+	8.06710i	−0.0728666	+	0.271942i
$881$	−15.6147	+	5.68329i	−0.526073	+	0.191475i	−0.591384	−	0.806390i	$-0.701418\pi$
$881$	−15.6147	+	5.68329i	−0.526073	+	0.191475i	0.0653111	+	0.997865i	$0.479196\pi$
$882$		0			0
$883$	13.8652	+	6.46546i	0.466602	+	0.217580i	0.641677	−	0.766975i	$-0.278239\pi$
$883$	13.8652	+	6.46546i	0.466602	+	0.217580i	−0.175075	+	0.984555i	$0.556017\pi$
$884$	−4.54740	−	0.801830i	−0.152946	−	0.0269685i
$885$		0			0
$886$	−1.15502	+	13.2020i	−0.0388038	+	0.443530i
$887$	−46.3541			−1.55642			−0.778209	−	0.628005i	$-0.783872\pi$
$887$	−46.3541			−1.55642			−0.778209	+	0.628005i	$0.783872\pi$
$888$		0			0
$889$	4.83178			0.162053
$890$	−0.692248	+	7.91243i	−0.0232042	+	0.265225i
$891$		0			0
$892$	−8.34125	−	1.47079i	−0.279286	−	0.0492456i
$893$	−15.4671	−	7.21243i	−0.517587	−	0.241355i
$894$		0			0
$895$	−35.5620	+	12.9435i	−1.18871	+	0.432653i
$896$	−0.543357	+	2.02783i	−0.0181523	+	0.0677452i
$897$		0			0
$898$	−4.41780	+	7.65185i	−0.147424	+	0.255346i
$899$	6.83174	+	11.8329i	0.227851	+	0.394650i
$900$		0			0
$901$	19.3139	+	27.5832i	0.643441	+	0.918929i
$902$	−1.46502	−	5.46754i	−0.0487799	−	0.182049i
$903$		0			0
$904$	7.58029	+	2.75900i	0.252117	+	0.0917630i
$905$	1.87372	−	2.67595i	0.0622845	−	0.0889514i
$906$		0			0
$907$	48.1942	−	4.21645i	1.60026	−	0.140005i	0.748211	−	0.663461i	$-0.230913\pi$
$907$	48.1942	−	4.21645i	1.60026	−	0.140005i	0.852053	+	0.523456i	$0.175358\pi$
$908$	7.16651	+	5.01804i	0.237829	+	0.166530i
$909$		0			0
$910$	5.45609	−	2.54422i	0.180868	−	0.0843400i
$911$	46.1555	−	12.3673i	1.52920	−	0.409748i	0.606442	−	0.795128i	$-0.292596\pi$
$911$	46.1555	−	12.3673i	1.52920	−	0.409748i	0.922758	+	0.385380i	$0.125930\pi$
$912$		0			0
$913$	5.49160	+	6.54463i	0.181745	+	0.216596i
$914$	−13.0266	+	7.52093i	−0.430883	+	0.248770i
$915$		0			0
$916$	21.8650	−	3.85539i	0.722440	−	0.127386i
$917$	14.4666	+	3.87631i	0.477729	+	0.128007i
$918$		0			0
$919$	−33.2710	−	33.2710i	−1.09751	−	1.09751i	−0.994701	−	0.102808i	$-0.967217\pi$
$919$	−33.2710	−	33.2710i	−1.09751	−	1.09751i	−0.102808	−	0.994701i	$-0.532783\pi$
$920$	−3.69375	+	7.92128i	−0.121779	+	0.261157i
$921$		0			0
$922$	2.16895	+	1.81996i	0.0714304	+	0.0599372i
$923$	−5.63002	−	0.492563i	−0.185314	−	0.0162129i
$924$		0			0
$925$	−25.6755	+	12.8829i	−0.844205	+	0.423586i
$926$			36.3312i			1.19392i
$927$		0			0
$928$	−3.29687	+	3.92905i	−0.108225	+	0.128978i
$929$	1.27383	−	7.22425i	0.0417930	−	0.237020i	−0.956755	−	0.290896i	$-0.906047\pi$
$929$	1.27383	−	7.22425i	0.0417930	−	0.237020i	0.998548	+	0.0538762i	$0.0171576\pi$
$930$		0			0
$931$	5.38596	−	5.38596i	0.176518	−	0.176518i
$932$	2.61600	+	7.18740i	0.0856899	+	0.235431i
$933$		0			0
$934$	6.23137	+	35.3399i	0.203897	+	1.15636i
$935$	−36.3153	−	20.9666i	−1.18764	−	0.685682i
$936$		0			0
$937$	−15.3008	+	12.8389i	−0.499856	+	0.419429i	−0.857543	−	0.514413i	$-0.828010\pi$
$937$	−15.3008	+	12.8389i	−0.499856	+	0.419429i	0.357687	+	0.933842i	$0.383566\pi$
$938$	−14.6753	+	10.2758i	−0.479167	+	0.335516i
$939$		0			0
$940$	7.65486	+	16.4159i	0.249674	+	0.535428i
$941$	−11.9782	+	32.9099i	−0.390479	+	1.07283i	0.576304	+	0.817235i	$0.304494\pi$
$941$	−11.9782	+	32.9099i	−0.390479	+	1.07283i	−0.966783	+	0.255597i	$0.917728\pi$
$942$		0			0
$943$	−0.516286	−	5.90117i	−0.0168126	−	0.192169i
$944$	−1.21950	−	13.9389i	−0.0396912	−	0.453673i
$945$		0			0
$946$	7.77509	−	21.3619i	0.252790	−	0.694535i
$947$	−11.8786	−	25.4738i	−0.386004	−	0.827788i	−0.999281	−	0.0379202i	$-0.987927\pi$
$947$	−11.8786	−	25.4738i	−0.386004	−	0.827788i	0.613277	−	0.789868i	$-0.289851\pi$
$948$		0			0
$949$	−6.79259	+	4.75622i	−0.220497	+	0.154393i
$950$	−10.6284	+	8.91826i	−0.344830	+	0.289347i
$951$		0			0
$952$	−9.12861	−	5.27040i	−0.295860	−	0.170815i
$953$	−8.04858	−	45.6458i	−0.260719	−	1.47861i	−0.780954	−	0.624588i	$-0.785267\pi$
$953$	−8.04858	−	45.6458i	−0.260719	−	1.47861i	0.520235	−	0.854023i	$-0.325844\pi$
$954$		0			0
$955$	−24.5080	−	67.3353i	−0.793061	−	2.17892i
$956$	10.3244	−	10.3244i	0.333915	−	0.333915i
$957$		0			0
$958$	4.54381	−	25.7692i	0.146804	−	0.832566i
$959$	−15.0405	+	17.9246i	−0.485684	+	0.578816i
$960$		0			0
$961$		−	23.9033i		−	0.771075i
$962$	−1.60242	−	5.35965i	−0.0516642	−	0.172802i
$963$		0			0
$964$	26.4890	+	2.31749i	0.853155	+	0.0746414i
$965$	−25.0959	−	21.0579i	−0.807865	−	0.677879i
$966$		0			0
$967$	−11.3390	+	24.3166i	−0.364638	+	0.781968i	0.635315	+	0.772253i	$0.280870\pi$
$967$	−11.3390	+	24.3166i	−0.364638	+	0.781968i	−0.999953	+	0.00971516i	$0.996908\pi$
$968$	2.70534	+	2.70534i	0.0869528	+	0.0869528i
$969$		0			0
$970$	36.5379	+	9.79031i	1.17316	+	0.314348i
$971$	−37.4251	+	6.59905i	−1.20103	+	0.211773i	−0.738142	−	0.674645i	$-0.764297\pi$
$971$	−37.4251	+	6.59905i	−1.20103	+	0.211773i	−0.462885	+	0.886418i	$0.653186\pi$
$972$		0			0
$973$	−36.4824	+	21.0631i	−1.16957	+	0.675253i
$974$	−0.626902	−	0.747112i	−0.0200872	−	0.0239390i
$975$		0			0
$976$	6.16495	−	1.65189i	0.197335	−	0.0528758i
$977$	29.6850	−	13.8424i	0.949708	−	0.442856i	0.114888	−	0.993378i	$-0.463349\pi$
$977$	29.6850	−	13.8424i	0.949708	−	0.442856i	0.834821	+	0.550522i	$0.185571\pi$
$978$		0			0
$979$	−5.58885	−	3.91336i	−0.178620	−	0.125071i
$980$	−8.05339	+	0.704581i	−0.257256	+	0.0225070i
$981$		0			0
$982$	−24.6439	+	35.1952i	−0.786420	+	1.12312i
$983$	−36.4512	−	13.2672i	−1.16261	−	0.423157i	−0.312583	−	0.949890i	$-0.601194\pi$
$983$	−36.4512	−	13.2672i	−1.16261	−	0.423157i	−0.850030	+	0.526734i	$0.823417\pi$
$984$		0			0
$985$	20.1785	+	75.3072i	0.642941	+	2.39949i
$986$	−14.7710	−	21.0952i	−0.470405	−	0.671808i
$987$		0			0
$988$	−1.35093	−	2.33987i	−0.0429787	−	0.0744412i
$989$	11.8951	−	20.6030i	0.378243	−	0.655137i
$990$		0			0
$991$	−2.84466	+	10.6164i	−0.0903635	+	0.337241i	−0.996276	−	0.0862243i	$-0.972520\pi$
$991$	−2.84466	+	10.6164i	−0.0903635	+	0.337241i	0.905912	+	0.423465i	$0.139187\pi$
$992$	−2.50330	+	0.911127i	−0.0794799	+	0.0289283i
$993$		0			0
$994$	−11.6924	−	5.45225i	−0.370860	−	0.172935i
$995$	2.83616	+	0.500092i	0.0899124	+	0.0158540i
$996$		0			0
$997$	2.89369	−	33.0750i	0.0916441	−	1.04750i	−0.801581	−	0.597886i	$-0.796007\pi$
$997$	2.89369	−	33.0750i	0.0916441	−	1.04750i	0.893225	−	0.449610i	$-0.148437\pi$
$998$	−12.7558			−0.403777
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.557.4	yes	72
3.2	odd	2	inner	666.2.bs.a.557.3	✓	72
37.19	odd	36	inner	666.2.bs.a.611.3	yes	72
111.56	even	36	inner	666.2.bs.a.611.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.557.3	✓	72	3.2	odd	2	inner
666.2.bs.a.557.4	yes	72	1.1	even	1	trivial
666.2.bs.a.611.3	yes	72	37.19	odd	36	inner
666.2.bs.a.611.4	yes	72	111.56	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
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