LMFDB - Embedded newform 891.2.k.a.728.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(161,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			728.17
Character	$\chi$	$=$	891.728
Dual form			891.2.k.a.809.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.525662 - 1.61782i) q^{2} +(-0.722987 - 0.525281i) q^{4} +(1.67332 - 0.543696i) q^{5} +(-1.64977 + 2.27071i) q^{7} +(1.52254 - 1.10619i) q^{8} -2.99294i q^{10} +(3.04425 + 1.31627i) q^{11} +(3.13591 + 1.01892i) q^{13} +(2.80638 + 3.86266i) q^{14} +(-1.54159 - 4.74453i) q^{16} +(2.08549 + 6.41848i) q^{17} +(0.847917 + 1.16706i) q^{19} +(-1.49539 - 0.485880i) q^{20} +(3.72973 - 4.23313i) q^{22} -1.74990i q^{23} +(-1.54067 + 1.11937i) q^{25} +(3.29685 - 4.53773i) q^{26} +(2.38552 - 0.775104i) q^{28} +(-4.79604 - 3.48452i) q^{29} +(1.50617 - 4.63551i) q^{31} -4.72221 q^{32} +11.4802 q^{34} +(-1.52602 + 4.69661i) q^{35} +(-2.98102 - 2.16584i) q^{37} +(2.33381 - 0.758300i) q^{38} +(1.94628 - 2.67882i) q^{40} +(2.61178 - 1.89757i) q^{41} -8.71517i q^{43} +(-1.50954 - 2.55073i) q^{44} +(-2.83103 - 0.919856i) q^{46} +(3.45009 + 4.74864i) q^{47} +(-0.271279 - 0.834911i) q^{49} +(1.00106 + 3.08094i) q^{50} +(-1.73200 - 2.38390i) q^{52} +(3.88131 + 1.26111i) q^{53} +(5.80966 + 0.547398i) q^{55} +5.28222i q^{56} +(-8.15843 + 5.92744i) q^{58} +(1.41595 - 1.94889i) q^{59} +(5.42716 - 1.76339i) q^{61} +(-6.70769 - 4.87342i) q^{62} +(0.600895 - 1.84936i) q^{64} +5.80137 q^{65} -14.1912 q^{67} +(1.86372 - 5.73594i) q^{68} +(6.79610 + 4.93766i) q^{70} +(-7.80443 + 2.53581i) q^{71} +(5.29322 - 7.28550i) q^{73} +(-5.07094 + 3.68426i) q^{74} -1.28916i q^{76} +(-8.01117 + 4.74107i) q^{77} +(-13.7531 - 4.46865i) q^{79} +(-5.15916 - 7.10098i) q^{80} +(-1.69701 - 5.22286i) q^{82} +(0.308534 + 0.949571i) q^{83} +(6.97940 + 9.60632i) q^{85} +(-14.0996 - 4.58123i) q^{86} +(6.09104 - 1.36345i) q^{88} -14.0272i q^{89} +(-7.48719 + 5.43976i) q^{91} +(-0.919191 + 1.26516i) q^{92} +(9.49603 - 3.08545i) q^{94} +(2.05337 + 1.49186i) q^{95} +(-3.86008 + 11.8801i) q^{97} -1.49334 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.525662	−	1.61782i	0.371699	−	1.14397i	−0.573980	−	0.818869i	$-0.694601\pi$
$2$	0.525662	−	1.61782i	0.371699	−	1.14397i	0.945679	−	0.325102i	$-0.105399\pi$
$3$		0			0
$3$		0			0
$4$	−0.722987	−	0.525281i	−0.361494	−	0.262641i
$5$	1.67332	−	0.543696i	0.748334	−	0.243148i	0.0900696	−	0.995935i	$-0.471291\pi$
$5$	1.67332	−	0.543696i	0.748334	−	0.243148i	0.658264	+	0.752787i	$0.271291\pi$
$6$		0			0
$7$	−1.64977	+	2.27071i	−0.623554	+	0.858249i	−0.997606	−	0.0691592i	$-0.977968\pi$
$7$	−1.64977	+	2.27071i	−0.623554	+	0.858249i	0.374051	+	0.927408i	$0.377968\pi$
$8$	1.52254	−	1.10619i	0.538300	−	0.391098i
$9$		0			0
$10$		−	2.99294i		−	0.946450i
$11$	3.04425	+	1.31627i	0.917875	+	0.396870i
$11$	3.04425	+	1.31627i	0.917875	+	0.396870i
$12$		0			0
$13$	3.13591	+	1.01892i	0.869744	+	0.282597i	0.709692	−	0.704512i	$-0.248834\pi$
$13$	3.13591	+	1.01892i	0.869744	+	0.282597i	0.160052	+	0.987109i	$0.448834\pi$
$14$	2.80638	+	3.86266i	0.750038	+	1.03234i
$15$		0			0
$16$	−1.54159	−	4.74453i	−0.385398	−	1.18613i
$17$	2.08549	+	6.41848i	0.505805	+	1.55671i	0.799412	+	0.600783i	$0.205144\pi$
$17$	2.08549	+	6.41848i	0.505805	+	1.55671i	−0.293607	+	0.955926i	$0.594856\pi$
$18$		0			0
$19$	0.847917	+	1.16706i	0.194526	+	0.267741i	0.895127	−	0.445811i	$-0.147085\pi$
$19$	0.847917	+	1.16706i	0.194526	+	0.267741i	−0.700601	+	0.713553i	$0.747085\pi$
$20$	−1.49539	−	0.485880i	−0.334378	−	0.108646i
$21$		0			0
$22$	3.72973	−	4.23313i	0.795181	−	0.902507i
$23$		−	1.74990i		−	0.364880i	−0.983217	−	0.182440i	$-0.941600\pi$
$23$		−	1.74990i		−	0.364880i	0.983217	−	0.182440i	$-0.0583995\pi$
$24$		0			0
$25$	−1.54067	+	1.11937i	−0.308135	+	0.223873i
$26$	3.29685	−	4.53773i	0.646566	−	0.889921i
$27$		0			0
$28$	2.38552	−	0.775104i	0.450822	−	0.146481i
$29$	−4.79604	−	3.48452i	−0.890602	−	0.647060i	0.0454332	−	0.998967i	$-0.485533\pi$
$29$	−4.79604	−	3.48452i	−0.890602	−	0.647060i	−0.936035	+	0.351907i	$0.885533\pi$
$30$		0			0
$31$	1.50617	−	4.63551i	0.270516	−	0.832563i	−0.719855	−	0.694124i	$-0.755792\pi$
$31$	1.50617	−	4.63551i	0.270516	−	0.832563i	0.990371	−	0.138438i	$-0.0442083\pi$
$32$	−4.72221			−0.834777
$33$		0			0
$34$	11.4802			1.96884
$35$	−1.52602	+	4.69661i	−0.257945	+	0.793873i
$36$		0			0
$37$	−2.98102	−	2.16584i	−0.490077	−	0.356062i	0.315137	−	0.949046i	$-0.397950\pi$
$37$	−2.98102	−	2.16584i	−0.490077	−	0.356062i	−0.805214	+	0.592985i	$0.797950\pi$
$38$	2.33381	−	0.758300i	0.378593	−	0.123012i
$39$		0			0
$40$	1.94628	−	2.67882i	0.307733	−	0.423559i
$41$	2.61178	−	1.89757i	0.407891	−	0.296350i	−0.364857	−	0.931064i	$-0.618882\pi$
$41$	2.61178	−	1.89757i	0.407891	−	0.296350i	0.772747	+	0.634714i	$0.218882\pi$
$42$		0			0
$43$		−	8.71517i		−	1.32905i	−0.747266	−	0.664526i	$-0.768634\pi$
$43$		−	8.71517i		−	1.32905i	0.747266	−	0.664526i	$-0.231366\pi$
$44$	−1.50954	−	2.55073i	−0.227572	−	0.384537i
$45$		0			0
$46$	−2.83103	−	0.919856i	−0.417412	−	0.135625i
$47$	3.45009	+	4.74864i	0.503248	+	0.692661i	0.982762	−	0.184873i	$-0.0591873\pi$
$47$	3.45009	+	4.74864i	0.503248	+	0.692661i	−0.479515	+	0.877534i	$0.659187\pi$
$48$		0			0
$49$	−0.271279	−	0.834911i	−0.0387541	−	0.119273i
$50$	1.00106	+	3.08094i	0.141571	+	0.435711i
$51$		0			0
$52$	−1.73200	−	2.38390i	−0.240186	−	0.330587i
$53$	3.88131	+	1.26111i	0.533138	+	0.173227i	0.563200	−	0.826321i	$-0.309570\pi$
$53$	3.88131	+	1.26111i	0.533138	+	0.173227i	−0.0300612	+	0.999548i	$0.509570\pi$
$54$		0			0
$55$	5.80966	+	0.547398i	0.783375	+	0.0738112i
$56$			5.28222i			0.705866i
$57$		0			0
$58$	−8.15843	+	5.92744i	−1.07125	+	0.778311i
$59$	1.41595	−	1.94889i	0.184341	−	0.253724i	−0.706838	−	0.707376i	$-0.749879\pi$
$59$	1.41595	−	1.94889i	0.184341	−	0.253724i	0.891179	+	0.453652i	$0.149879\pi$
$60$		0			0
$61$	5.42716	−	1.76339i	0.694877	−	0.225779i	0.0597797	−	0.998212i	$-0.480960\pi$
$61$	5.42716	−	1.76339i	0.694877	−	0.225779i	0.635097	+	0.772433i	$0.280960\pi$
$62$	−6.70769	−	4.87342i	−0.851877	−	0.618925i
$63$		0			0
$64$	0.600895	−	1.84936i	0.0751119	−	0.231171i
$65$	5.80137			0.719572
$66$		0			0
$67$	−14.1912			−1.73373			−0.866865	−	0.498543i	$-0.833869\pi$
$67$	−14.1912			−1.73373			−0.866865	+	0.498543i	$0.833869\pi$
$68$	1.86372	−	5.73594i	0.226009	−	0.695585i
$69$		0			0
$70$	6.79610	+	4.93766i	0.812290	+	0.590163i
$71$	−7.80443	+	2.53581i	−0.926215	+	0.300946i	−0.733014	−	0.680214i	$-0.761887\pi$
$71$	−7.80443	+	2.53581i	−0.926215	+	0.300946i	−0.193201	+	0.981159i	$0.561887\pi$
$72$		0			0
$73$	5.29322	−	7.28550i	0.619525	−	0.852703i	−0.377793	−	0.925890i	$-0.623317\pi$
$73$	5.29322	−	7.28550i	0.619525	−	0.852703i	0.997318	+	0.0731871i	$0.0233170\pi$
$74$	−5.07094	+	3.68426i	−0.589485	+	0.428286i
$75$		0			0
$76$		−	1.28916i		−	0.147877i
$77$	−8.01117	+	4.74107i	−0.912958	+	0.540295i
$78$		0			0
$79$	−13.7531	−	4.46865i	−1.54734	−	0.502763i	−0.593954	−	0.804499i	$-0.702434\pi$
$79$	−13.7531	−	4.46865i	−1.54734	−	0.502763i	−0.953391	+	0.301736i	$0.902434\pi$
$80$	−5.15916	−	7.10098i	−0.576812	−	0.793914i
$81$		0			0
$82$	−1.69701	−	5.22286i	−0.187403	−	0.576768i
$83$	0.308534	+	0.949571i	0.0338660	+	0.104229i	0.966561	−	0.256438i	$-0.0825490\pi$
$83$	0.308534	+	0.949571i	0.0338660	+	0.104229i	−0.932695	+	0.360667i	$0.882549\pi$
$84$		0			0
$85$	6.97940	+	9.60632i	0.757022	+	1.04195i
$86$	−14.0996	−	4.58123i	−1.52040	−	0.494007i
$87$		0			0
$88$	6.09104	−	1.36345i	0.649307	−	0.145344i
$89$		−	14.0272i		−	1.48688i	−0.668800	−	0.743442i	$-0.733192\pi$
$89$		−	14.0272i		−	1.48688i	0.668800	−	0.743442i	$-0.266808\pi$
$90$		0			0
$91$	−7.48719	+	5.43976i	−0.784871	+	0.570242i
$92$	−0.919191	+	1.26516i	−0.0958322	+	0.131902i
$93$		0			0
$94$	9.49603	−	3.08545i	0.979441	−	0.318240i
$95$	2.05337	+	1.49186i	0.210671	+	0.153061i
$96$		0			0
$97$	−3.86008	+	11.8801i	−0.391932	+	1.20624i	0.539393	+	0.842054i	$0.318654\pi$
$97$	−3.86008	+	11.8801i	−0.391932	+	1.20624i	−0.931325	+	0.364188i	$0.881346\pi$
$98$	−1.49334			−0.150850
$99$		0			0
$100$	1.70187			0.170187
$101$	−2.68601	+	8.26668i	−0.267268	+	0.822565i	0.723895	+	0.689910i	$0.242350\pi$
$101$	−2.68601	+	8.26668i	−0.267268	+	0.822565i	−0.991162	+	0.132655i	$0.957650\pi$
$102$		0			0
$103$	−13.0342	−	9.46988i	−1.28430	−	0.933095i	−0.284622	−	0.958640i	$-0.591868\pi$
$103$	−13.0342	−	9.46988i	−1.28430	−	0.933095i	−0.999674	+	0.0255445i	$0.991868\pi$
$104$	5.90167	−	1.91757i	0.578706	−	0.188033i
$105$		0			0
$106$	4.08051	−	5.61634i	0.396334	−	0.545507i
$107$	7.84961	−	5.70308i	0.758851	−	0.551337i	−0.139707	−	0.990193i	$-0.544616\pi$
$107$	7.84961	−	5.70308i	0.758851	−	0.551337i	0.898558	+	0.438856i	$0.144616\pi$
$108$		0			0
$109$			12.3066i			1.17876i	0.807856	+	0.589380i	$0.200628\pi$
$109$			12.3066i			1.17876i	−0.807856	+	0.589380i	$0.799372\pi$
$110$	3.93951	−	9.11124i	0.375617	−	0.868723i
$111$		0			0
$112$	13.3167	+	4.32687i	1.25831	+	0.408851i
$113$	3.97808	+	5.47535i	0.374226	+	0.515078i	0.954043	−	0.299669i	$-0.0968761\pi$
$113$	3.97808	+	5.47535i	0.374226	+	0.515078i	−0.579817	+	0.814746i	$0.696876\pi$
$114$		0			0
$115$	−0.951415	−	2.92815i	−0.0887199	−	0.273052i
$116$	1.63712	+	5.03853i	0.152003	+	0.467816i
$117$		0			0
$118$	−2.40864	−	3.31521i	−0.221734	−	0.305190i
$119$	−18.0151	−	5.85346i	−1.65144	−	0.536586i
$120$		0			0
$121$	7.53488	+	8.01409i	0.684989	+	0.728554i
$122$		−	9.70711i		−	0.878841i
$123$		0			0
$124$	−3.52389	+	2.56025i	−0.316455	+	0.229918i
$125$	−7.14031	+	9.82780i	−0.638649	+	0.879025i
$126$		0			0
$127$	0.223004	−	0.0724583i	0.0197884	−	0.00642964i	−0.299106	−	0.954220i	$-0.596688\pi$
$127$	0.223004	−	0.0724583i	0.0197884	−	0.00642964i	0.318894	+	0.947790i	$0.396688\pi$
$128$	−10.3168	−	7.49558i	−0.911883	−	0.662521i
$129$		0			0
$130$	3.04956	−	9.38557i	0.267464	−	0.823169i
$131$	−6.06671			−0.530051			−0.265025	−	0.964241i	$-0.585380\pi$
$131$	−6.06671			−0.530051			−0.265025	+	0.964241i	$0.585380\pi$
$132$		0			0
$133$	−4.04892			−0.351086
$134$	−7.45977	+	22.9588i	−0.644426	+	1.98334i
$135$		0			0
$136$	10.2753	+	7.46545i	0.881101	+	0.640157i
$137$	15.4116	−	5.00753i	1.31670	−	0.427822i	0.435340	−	0.900266i	$-0.356628\pi$
$137$	15.4116	−	5.00753i	1.31670	−	0.427822i	0.881361	+	0.472444i	$0.156628\pi$
$138$		0			0
$139$	−0.457452	+	0.629629i	−0.0388006	+	0.0534044i	−0.827977	−	0.560763i	$-0.810508\pi$
$139$	−0.457452	+	0.629629i	−0.0388006	+	0.0534044i	0.789176	+	0.614167i	$0.210508\pi$
$140$	3.57034	−	2.59400i	0.301749	−	0.219233i
$141$		0			0
$142$			13.9591i			1.17142i
$143$	8.20530	+	7.22953i	0.686162	+	0.604564i
$144$		0			0
$145$	−9.91985	−	3.22315i	−0.823799	−	0.267668i
$146$	−9.00418	−	12.3932i	−0.745191	−	1.02567i
$147$		0			0
$148$	1.01757	+	3.13175i	0.0836434	+	0.257428i
$149$	3.96515	+	12.2035i	0.324838	+	0.999747i	0.971514	+	0.236983i	$0.0761585\pi$
$149$	3.96515	+	12.2035i	0.324838	+	0.999747i	−0.646676	+	0.762765i	$0.723841\pi$
$150$		0			0
$151$	6.03914	+	8.31217i	0.491458	+	0.676435i	0.980656	−	0.195738i	$-0.0627103\pi$
$151$	6.03914	+	8.31217i	0.491458	+	0.676435i	−0.489198	+	0.872173i	$0.662710\pi$
$152$	2.58198	+	0.838936i	0.209426	+	0.0680467i
$153$		0			0
$154$	3.45904	+	15.4528i	0.278737	+	1.24522i
$155$		−	8.57562i		−	0.688810i
$156$		0			0
$157$	−14.9493	+	10.8613i	−1.19309	+	0.866827i	−0.993587	−	0.113071i	$-0.963931\pi$
$157$	−14.9493	+	10.8613i	−1.19309	+	0.866827i	−0.199498	+	0.979898i	$0.563931\pi$
$158$	−14.4590	+	19.9010i	−1.15029	+	1.58324i
$159$		0			0
$160$	−7.90180	+	2.56745i	−0.624692	+	0.202975i
$161$	3.97353	+	2.88694i	0.313158	+	0.227522i
$162$		0			0
$163$	−2.49626	+	7.68270i	−0.195522	+	0.601756i	0.804448	+	0.594023i	$0.202461\pi$
$163$	−2.49626	+	7.68270i	−0.195522	+	0.601756i	−0.999970	+	0.00773239i	$0.997539\pi$
$164$	−2.88504			−0.225283
$165$		0			0
$166$	1.69842			0.131823
$167$	2.09374	−	6.44386i	0.162018	−	0.498641i	−0.836786	−	0.547530i	$-0.815568\pi$
$167$	2.09374	−	6.44386i	0.162018	−	0.498641i	0.998804	+	0.0488894i	$0.0155682\pi$
$168$		0			0
$169$	−1.72150	−	1.25075i	−0.132423	−	0.0962113i
$170$	19.2101	−	6.24174i	1.47335	−	0.478720i
$171$		0			0
$172$	−4.57791	+	6.30096i	−0.349063	+	0.480444i
$173$	4.04350	−	2.93777i	0.307422	−	0.223355i	−0.423368	−	0.905958i	$-0.639152\pi$
$173$	4.04350	−	2.93777i	0.307422	−	0.223355i	0.730789	+	0.682603i	$0.239152\pi$
$174$		0			0
$175$		−	5.34513i		−	0.404054i
$176$	1.55209	−	16.4727i	0.116993	−	1.24167i
$177$		0			0
$178$	−22.6935	−	7.37358i	−1.70095	−	0.552673i
$179$	−2.07499	−	2.85598i	−0.155092	−	0.213466i	0.724400	−	0.689380i	$-0.242117\pi$
$179$	−2.07499	−	2.85598i	−0.155092	−	0.213466i	−0.879491	+	0.475915i	$0.842117\pi$
$180$		0			0
$181$	−4.32686	−	13.3167i	−0.321613	−	0.989823i	−0.972946	−	0.231031i	$-0.925790\pi$
$181$	−4.32686	−	13.3167i	−0.321613	−	0.989823i	0.651333	−	0.758792i	$-0.274210\pi$
$182$	4.86483	+	14.9724i	0.360605	+	1.10983i
$183$		0			0
$184$	−1.93573	−	2.66430i	−0.142704	−	0.196415i
$185$	−6.16577	−	2.00338i	−0.453317	−	0.147292i
$186$		0			0
$187$	−2.09969	+	22.2845i	−0.153545	+	1.62960i
$188$		−	5.24548i		−	0.382566i
$189$		0			0
$190$	3.49293	−	2.53776i	0.253404	−	0.184109i
$191$	−3.42667	+	4.71641i	−0.247945	+	0.341268i	−0.914790	−	0.403929i	$-0.867644\pi$
$191$	−3.42667	+	4.71641i	−0.247945	+	0.341268i	0.666845	+	0.745196i	$0.267644\pi$
$192$		0			0
$193$	0.117302	−	0.0381136i	0.00844355	−	0.00274347i	−0.304792	−	0.952419i	$-0.598587\pi$
$193$	0.117302	−	0.0381136i	0.00844355	−	0.00274347i	0.313236	+	0.949675i	$0.398587\pi$
$194$	17.1908	+	12.4898i	1.23423	+	0.896718i
$195$		0			0
$196$	−0.242431	+	0.746127i	−0.0173165	+	0.0532948i
$197$	2.67501			0.190586			0.0952932	−	0.995449i	$-0.469621\pi$
$197$	2.67501			0.190586			0.0952932	+	0.995449i	$0.469621\pi$
$198$		0			0
$199$	−23.4261			−1.66063			−0.830314	−	0.557295i	$-0.811839\pi$
$199$	−23.4261			−1.66063			−0.830314	+	0.557295i	$0.811839\pi$
$200$	−1.10751	+	3.40857i	−0.0783128	+	0.241022i
$201$		0			0
$202$	11.9621	+	8.69095i	0.841648	+	0.611493i
$203$	15.8247	−	5.14176i	1.11068	−	0.360881i
$204$		0			0
$205$	3.33865	−	4.59526i	0.233181	−	0.320947i
$206$	−22.1721	+	16.1090i	−1.54481	+	1.12237i
$207$		0			0
$208$		−	16.4492i		−	1.14054i
$209$	1.04511	+	4.66890i	0.0722916	+	0.322954i
$210$		0			0
$211$	−8.87623	−	2.88406i	−0.611065	−	0.198547i	−0.0128957	−	0.999917i	$-0.504105\pi$
$211$	−8.87623	−	2.88406i	−0.611065	−	0.198547i	−0.598169	+	0.801370i	$0.704105\pi$
$212$	−2.14370	−	2.95054i	−0.147230	−	0.202644i
$213$		0			0
$214$	−5.10031	−	15.6972i	−0.348650	−	1.07304i
$215$	−4.73841	−	14.5833i	−0.323157	−	0.994574i
$216$		0			0
$217$	8.04109	+	11.0676i	0.545865	+	0.751318i
$218$	19.9099	+	6.46912i	1.34847	+	0.438144i
$219$		0			0
$220$	−3.91277	−	3.44747i	−0.263799	−	0.232428i
$221$			22.2527i			1.49688i
$222$		0			0
$223$	−2.77960	+	2.01949i	−0.186136	+	0.135235i	−0.676951	−	0.736028i	$-0.736699\pi$
$223$	−2.77960	+	2.01949i	−0.186136	+	0.135235i	0.490815	+	0.871264i	$0.336699\pi$
$224$	7.79056	−	10.7228i	0.520529	−	0.716447i
$225$		0			0
$226$	10.9493	−	3.55763i	0.728334	−	0.236650i
$227$	19.4288	+	14.1159i	1.28954	+	0.936904i	0.999796	−	0.0202014i	$-0.00643075\pi$
$227$	19.4288	+	14.1159i	1.28954	+	0.936904i	0.289741	+	0.957105i	$0.406431\pi$
$228$		0			0
$229$	−0.582877	+	1.79391i	−0.0385176	+	0.118545i	−0.968467	−	0.249144i	$-0.919851\pi$
$229$	−0.582877	+	1.79391i	−0.0385176	+	0.118545i	0.929949	+	0.367689i	$0.119851\pi$
$230$	−5.23735			−0.345341
$231$		0			0
$232$	−11.1567			−0.732475
$233$	2.04683	−	6.29949i	0.134092	−	0.412693i	−0.861356	−	0.508003i	$-0.830384\pi$
$233$	2.04683	−	6.29949i	0.134092	−	0.412693i	0.995448	+	0.0953094i	$0.0303841\pi$
$234$		0			0
$235$	8.35494	+	6.07022i	0.545017	+	0.395978i
$236$	−2.04743	+	0.665251i	−0.133276	+	0.0433041i
$237$		0			0
$238$	−18.9397	+	26.0682i	−1.22768	+	1.68975i
$239$	17.5417	−	12.7448i	1.13468	−	0.824391i	0.148309	−	0.988941i	$-0.452617\pi$
$239$	17.5417	−	12.7448i	1.13468	−	0.824391i	0.986369	+	0.164550i	$0.0526171\pi$
$240$		0			0
$241$		−	4.85401i		−	0.312674i	−0.987704	−	0.156337i	$-0.950031\pi$
$241$		−	4.85401i		−	0.312674i	0.987704	−	0.156337i	$-0.0499686\pi$
$242$	16.9261	−	7.97738i	1.08805	−	0.512805i
$243$		0			0
$244$	−4.85004	−	1.57587i	−0.310492	−	0.100885i
$245$	−0.907875	−	1.24958i	−0.0580020	−	0.0798329i
$246$		0			0
$247$	1.46985	+	4.52374i	0.0935245	+	0.287839i
$248$	−2.83456	−	8.72388i	−0.179995	−	0.553967i
$249$		0			0
$250$	12.1462	+	16.7178i	0.768194	+	1.05733i
$251$	−8.17445	−	2.65604i	−0.515967	−	0.167648i	0.0394474	−	0.999222i	$-0.487440\pi$
$251$	−8.17445	−	2.65604i	−0.515967	−	0.167648i	−0.555414	+	0.831574i	$0.687440\pi$
$252$		0			0
$253$	2.30334	−	5.32713i	0.144810	−	0.334914i
$254$		−	0.398869i		−	0.0250272i
$255$		0			0
$256$	−14.4033	+	10.4646i	−0.900206	+	0.654038i
$257$	3.12245	−	4.29769i	0.194773	−	0.268082i	−0.700449	−	0.713703i	$-0.747017\pi$
$257$	3.12245	−	4.29769i	0.194773	−	0.268082i	0.895222	+	0.445620i	$0.147017\pi$
$258$		0			0
$259$	9.83599	−	3.19591i	0.611179	−	0.198584i
$260$	−4.19432	−	3.04735i	−0.260121	−	0.188989i
$261$		0			0
$262$	−3.18903	+	9.81484i	−0.197019	+	0.606363i
$263$	−16.1706			−0.997121			−0.498560	−	0.866855i	$-0.666138\pi$
$263$	−16.1706			−0.997121			−0.498560	+	0.866855i	$0.666138\pi$
$264$		0			0
$265$	7.18035			0.441085
$266$	−2.12836	+	6.55043i	−0.130498	+	0.401632i
$267$		0			0
$268$	10.2601	+	7.45436i	0.626732	+	0.455348i
$269$	10.0420	−	3.26285i	0.612274	−	0.198940i	0.0135667	−	0.999908i	$-0.495681\pi$
$269$	10.0420	−	3.26285i	0.612274	−	0.198940i	0.598707	+	0.800968i	$0.295681\pi$
$270$		0			0
$271$	2.99871	−	4.12736i	0.182158	−	0.250719i	−0.708166	−	0.706046i	$-0.750477\pi$
$271$	2.99871	−	4.12736i	0.182158	−	0.250719i	0.890325	+	0.455326i	$0.150477\pi$
$272$	27.2377	−	19.7893i	1.65153	−	1.19990i
$273$		0			0
$274$		−	27.5654i		−	1.66529i
$275$	−6.16358	+	1.37968i	−0.371678	+	0.0831981i
$276$		0			0
$277$	22.9515	+	7.45740i	1.37902	+	0.448071i	0.902348	−	0.431009i	$-0.141842\pi$
$277$	22.9515	+	7.45740i	1.37902	+	0.448071i	0.476674	+	0.879080i	$0.341842\pi$
$278$	0.778161	+	1.07105i	0.0466710	+	0.0642371i
$279$		0			0
$280$	2.87192	+	8.83887i	0.171630	+	0.528224i
$281$	3.58653	+	11.0382i	0.213955	+	0.658485i	0.999226	+	0.0393333i	$0.0125234\pi$
$281$	3.58653	+	11.0382i	0.213955	+	0.658485i	−0.785271	+	0.619152i	$0.787477\pi$
$282$		0			0
$283$	8.68055	+	11.9477i	0.516005	+	0.710220i	0.984917	−	0.173025i	$-0.0553540\pi$
$283$	8.68055	+	11.9477i	0.516005	+	0.710220i	−0.468913	+	0.883245i	$0.655354\pi$
$284$	6.97452	+	2.26616i	0.413861	+	0.134472i
$285$		0			0
$286$	16.0093	−	9.47442i	0.946649	−	0.560234i
$287$			9.06114i			0.534862i
$288$		0			0
$289$	−23.0943	+	16.7790i	−1.35849	+	0.986999i
$290$	−10.4290	+	14.3542i	−0.612410	+	0.842910i
$291$		0			0
$292$	−7.65387	+	2.48689i	−0.447909	+	0.145534i
$293$	−16.6443	−	12.0928i	−0.972370	−	0.706468i	−0.0163792	−	0.999866i	$-0.505214\pi$
$293$	−16.6443	−	12.0928i	−0.972370	−	0.706468i	−0.955990	+	0.293398i	$0.905214\pi$
$294$		0			0
$295$	1.30974	−	4.03098i	0.0762562	−	0.234692i
$296$	−6.93457			−0.403063
$297$		0			0
$298$	21.8273			1.26442
$299$	1.78301	−	5.48753i	0.103114	−	0.317352i
$300$		0			0
$301$	19.7897	+	14.3780i	1.14066	+	0.828736i
$302$	16.6221	−	5.40086i	0.956496	−	0.310785i
$303$		0			0
$304$	4.23000	−	5.82209i	0.242607	−	0.333920i
$305$	8.12265	−	5.90145i	0.465102	−	0.337916i
$306$		0			0
$307$		−	5.48347i		−	0.312958i	−0.987681	−	0.156479i	$-0.949986\pi$
$307$		−	5.48347i		−	0.312958i	0.987681	−	0.156479i	$-0.0500144\pi$
$308$	8.28237	+	0.780382i	0.471932	+	0.0444664i
$309$		0			0
$310$	−13.8738	−	4.50787i	−0.787979	−	0.256030i
$311$	−6.49912	−	8.94527i	−0.368531	−	0.507240i	0.583970	−	0.811775i	$-0.301499\pi$
$311$	−6.49912	−	8.94527i	−0.368531	−	0.507240i	−0.952501	+	0.304536i	$0.901499\pi$
$312$		0			0
$313$	0.408904	+	1.25848i	0.0231126	+	0.0711334i	0.961948	−	0.273234i	$-0.0880934\pi$
$313$	0.408904	+	1.25848i	0.0231126	+	0.0711334i	−0.938835	+	0.344368i	$0.888093\pi$
$314$	9.71337	+	29.8947i	0.548157	+	1.68705i
$315$		0			0
$316$	7.59602	+	10.4550i	0.427309	+	0.588141i
$317$	6.32513	+	2.05516i	0.355255	+	0.115429i	0.481207	−	0.876607i	$-0.340199\pi$
$317$	6.32513	+	2.05516i	0.355255	+	0.115429i	−0.125952	+	0.992036i	$0.540199\pi$
$318$		0			0
$319$	−10.0138	−	16.9206i	−0.560662	−	0.947373i
$320$		−	3.42129i		−	0.191256i
$321$		0			0
$322$	6.75927	−	4.91090i	0.376680	−	0.273674i
$323$	−5.72241	+	7.87622i	−0.318403	+	0.438245i
$324$		0			0
$325$	−5.97195	+	1.94041i	−0.331264	+	0.107634i
$326$	11.1170	+	8.07700i	0.615716	+	0.447344i
$327$		0			0
$328$	1.87747	−	5.77825i	0.103666	−	0.319051i
$329$	−16.4747			−0.908278
$330$		0			0
$331$	−23.5556			−1.29473			−0.647366	−	0.762179i	$-0.724130\pi$
$331$	−23.5556			−1.29473			−0.647366	+	0.762179i	$0.724130\pi$
$332$	0.275725	−	0.848595i	0.0151324	−	0.0465727i
$333$		0			0
$334$	−9.32441	−	6.77458i	−0.510209	−	0.370688i
$335$	−23.7465	+	7.71570i	−1.29741	+	0.421554i
$336$		0			0
$337$	8.87735	−	12.2186i	0.483580	−	0.665591i	−0.495608	−	0.868546i	$-0.665055\pi$
$337$	8.87735	−	12.2186i	0.483580	−	0.665591i	0.979188	+	0.202956i	$0.0650547\pi$
$338$	−2.92841	+	2.12762i	−0.159285	+	0.115727i
$339$		0			0
$340$		−	10.6114i		−	0.575484i
$341$	10.6867	−	12.1291i	0.578719	−	0.656829i
$342$		0			0
$343$	−16.3423	−	5.30993i	−0.882401	−	0.286709i
$344$	−9.64065	−	13.2692i	−0.519789	−	0.715429i
$345$		0			0
$346$	−2.62728	−	8.08593i	−0.141243	−	0.434702i
$347$	6.68288	+	20.5678i	0.358756	+	1.10414i	0.953800	+	0.300444i	$0.0971348\pi$
$347$	6.68288	+	20.5678i	0.358756	+	1.10414i	−0.595044	+	0.803693i	$0.702865\pi$
$348$		0			0
$349$	−11.0228	−	15.1716i	−0.590038	−	0.812118i	0.404712	−	0.914444i	$-0.367372\pi$
$349$	−11.0228	−	15.1716i	−0.590038	−	0.812118i	−0.994751	+	0.102326i	$0.967372\pi$
$350$	−8.64745	−	2.80973i	−0.462226	−	0.150186i
$351$		0			0
$352$	−14.3756	−	6.21570i	−0.766221	−	0.331298i
$353$		−	28.7268i		−	1.52897i	−0.644641	−	0.764485i	$-0.722993\pi$
$353$		−	28.7268i		−	1.52897i	0.644641	−	0.764485i	$-0.277007\pi$
$354$		0			0
$355$	−11.6806	+	8.48648i	−0.619944	+	0.450415i
$356$	−7.36824	+	10.1415i	−0.390516	+	0.537499i
$357$		0			0
$358$	−5.71120	+	1.85568i	−0.301846	+	0.0980758i
$359$	0.595876	+	0.432930i	0.0314492	+	0.0228491i	0.603399	−	0.797440i	$-0.293813\pi$
$359$	0.595876	+	0.432930i	0.0314492	+	0.0228491i	−0.571950	+	0.820289i	$0.693813\pi$
$360$		0			0
$361$	5.22826	−	16.0909i	0.275172	−	0.846891i
$362$	−23.8185			−1.25187
$363$		0			0
$364$	8.27055			0.433495
$365$	4.89618	−	15.0689i	0.256278	−	0.788743i
$366$		0			0
$367$	−4.17759	−	3.03520i	−0.218069	−	0.158436i	0.473388	−	0.880854i	$-0.343031\pi$
$367$	−4.17759	−	3.03520i	−0.218069	−	0.158436i	−0.691457	+	0.722418i	$0.743031\pi$
$368$	−8.30246	+	2.69763i	−0.432796	+	0.140624i
$369$		0			0
$370$	−6.48222	+	8.92201i	−0.336995	+	0.463833i
$371$	−9.26689	+	6.73279i	−0.481113	+	0.349549i
$372$		0			0
$373$		−	11.9302i		−	0.617722i	−0.951107	−	0.308861i	$-0.900052\pi$
$373$		−	11.9302i		−	0.617722i	0.951107	−	0.308861i	$-0.0999478\pi$
$374$	34.9486	+	15.1110i	1.80715	+	0.781372i
$375$		0			0
$376$	10.5058	+	3.41355i	0.541797	+	0.176040i
$377$	−11.4895	−	15.8139i	−0.591738	−	0.814458i
$378$		0			0
$379$	2.53286	+	7.79533i	0.130104	+	0.400419i	0.994796	−	0.101883i	$-0.0324866\pi$
$379$	2.53286	+	7.79533i	0.130104	+	0.400419i	−0.864692	+	0.502302i	$0.832487\pi$
$380$	−0.700913	−	2.15719i	−0.0359561	−	0.110661i
$381$		0			0
$382$	5.82903	+	8.02298i	0.298239	+	0.410491i
$383$	−22.1441	−	7.19505i	−1.13151	−	0.367650i	−0.317360	−	0.948305i	$-0.602796\pi$
$383$	−22.1441	−	7.19505i	−1.13151	−	0.367650i	−0.814150	+	0.580655i	$0.802796\pi$
$384$		0			0
$385$	−10.8276	+	12.2890i	−0.551825	+	0.626305i
$386$		−	0.209808i		−	0.0106789i
$387$		0			0
$388$	9.03119	−	6.56154i	0.458489	−	0.333112i
$389$	7.61146	−	10.4763i	0.385917	−	0.531169i	−0.571223	−	0.820795i	$-0.693531\pi$
$389$	7.61146	−	10.4763i	0.385917	−	0.531169i	0.957140	+	0.289626i	$0.0935310\pi$
$390$		0			0
$391$	11.2317	−	3.64940i	0.568012	−	0.184558i
$392$	−1.33661	−	0.971101i	−0.0675088	−	0.0490480i
$393$		0			0
$394$	1.40615	−	4.32768i	0.0708408	−	0.218025i
$395$	−25.4430			−1.28018
$396$		0			0
$397$	10.8950			0.546802			0.273401	−	0.961900i	$-0.411851\pi$
$397$	10.8950			0.546802			0.273401	+	0.961900i	$0.411851\pi$
$398$	−12.3142	+	37.8991i	−0.617254	+	1.89971i
$399$		0			0
$400$	7.68595	+	5.58417i	0.384298	+	0.279209i
$401$	−29.9517	+	9.73188i	−1.49571	+	0.485987i	−0.938765	−	0.344559i	$-0.888028\pi$
$401$	−29.9517	+	9.73188i	−1.49571	+	0.485987i	−0.556950	+	0.830546i	$0.688028\pi$
$402$		0			0
$403$	9.44641	−	13.0019i	0.470559	−	0.647669i
$404$	6.28428	−	4.56579i	0.312654	−	0.227157i
$405$		0			0
$406$		−	28.3044i		−	1.40472i
$407$	−6.22414	−	10.5172i	−0.308519	−	0.521317i
$408$		0			0
$409$	15.9979	+	5.19804i	0.791046	+	0.257026i	0.676549	−	0.736397i	$-0.263475\pi$
$409$	15.9979	+	5.19804i	0.791046	+	0.257026i	0.114497	+	0.993424i	$0.463475\pi$
$410$	−5.67930	−	7.81688i	−0.280480	−	0.386048i
$411$		0			0
$412$	4.44919	+	13.6932i	0.219196	+	0.674616i
$413$	2.08938	+	6.43044i	0.102812	+	0.316421i
$414$		0			0
$415$	1.03256	+	1.42119i	0.0506862	+	0.0697635i
$416$	−14.8084	−	4.81155i	−0.726043	−	0.235906i
$417$		0			0
$418$	8.10281	+	0.763463i	0.396321	+	0.0373422i
$419$		−	10.9051i		−	0.532748i	−0.963870	−	0.266374i	$-0.914174\pi$
$419$		−	10.9051i		−	0.532748i	0.963870	−	0.266374i	$-0.0858257\pi$
$420$		0			0
$421$	−18.9365	+	13.7582i	−0.922909	+	0.670533i	−0.944246	−	0.329239i	$-0.893208\pi$
$421$	−18.9365	+	13.7582i	−0.922909	+	0.670533i	0.0213370	+	0.999772i	$0.493208\pi$
$422$	−9.33179	+	12.8441i	−0.454264	+	0.625241i
$423$		0			0
$424$	7.30449	−	2.37337i	0.354737	−	0.115261i
$425$	−10.3977	−	7.55436i	−0.504362	−	0.366440i
$426$		0			0
$427$	−4.94941	+	15.2327i	−0.239519	+	0.737162i
$428$	−8.67089			−0.419123
$429$		0			0
$430$	−26.0840			−1.25788
$431$	1.11900	−	3.44393i	0.0539004	−	0.165888i	−0.920482	−	0.390784i	$-0.872204\pi$
$431$	1.11900	−	3.44393i	0.0539004	−	0.165888i	0.974383	+	0.224895i	$0.0722040\pi$
$432$		0			0
$433$	3.61240	+	2.62456i	0.173601	+	0.126128i	0.671193	−	0.741283i	$-0.265782\pi$
$433$	3.61240	+	2.62456i	0.173601	+	0.126128i	−0.497592	+	0.867411i	$0.665782\pi$
$434$	22.1323	−	7.19122i	1.06238	−	0.345189i
$435$		0			0
$436$	6.46443	−	8.89753i	0.309590	−	0.426114i
$437$	2.04224	−	1.48377i	0.0976935	−	0.0709785i
$438$		0			0
$439$			1.62672i			0.0776393i	0.999246	+	0.0388196i	$0.0123598\pi$
$439$			1.62672i			0.0776393i	−0.999246	+	0.0388196i	$0.987640\pi$
$440$	9.45099	−	5.59317i	0.450558	−	0.266644i
$441$		0			0
$442$	36.0008	+	11.6974i	1.71239	+	0.556388i
$443$	10.1890	+	14.0239i	0.484093	+	0.666297i	0.979285	−	0.202487i	$-0.0649023\pi$
$443$	10.1890	+	14.0239i	0.484093	+	0.666297i	−0.495192	+	0.868784i	$0.664902\pi$
$444$		0			0
$445$	−7.62656	−	23.4721i	−0.361533	−	1.11269i
$446$	1.80605	+	5.55846i	0.0855190	+	0.263201i
$447$		0			0
$448$	3.20804	+	4.41549i	0.151566	+	0.208612i
$449$	−37.5369	−	12.1965i	−1.77147	−	0.575587i	−0.773192	−	0.634172i	$-0.781341\pi$
$449$	−37.5369	−	12.1965i	−1.77147	−	0.575587i	−0.998282	+	0.0585850i	$0.981341\pi$
$450$		0			0
$451$	10.4486	−	2.33886i	0.492005	−	0.110133i
$452$		−	6.04822i		−	0.284484i
$453$		0			0
$454$	33.0499	−	24.0122i	1.55111	−	1.12695i
$455$	−9.57093	+	13.1732i	−0.448692	+	0.617571i
$456$		0			0
$457$	25.7436	−	8.36460i	1.20423	−	0.391279i	0.362917	−	0.931821i	$-0.381781\pi$
$457$	25.7436	−	8.36460i	1.20423	−	0.391279i	0.841317	+	0.540542i	$0.181781\pi$
$458$	2.59583	+	1.88598i	0.121295	+	0.0881261i
$459$		0			0
$460$	−0.850243	+	2.61678i	−0.0396428	+	0.122008i
$461$	−25.6359			−1.19398			−0.596990	−	0.802248i	$-0.703637\pi$
$461$	−25.6359			−1.19398			−0.596990	+	0.802248i	$0.703637\pi$
$462$		0			0
$463$	−9.64491			−0.448237			−0.224118	−	0.974562i	$-0.571950\pi$
$463$	−9.64491			−0.448237			−0.224118	+	0.974562i	$0.571950\pi$
$464$	−9.13890	+	28.1266i	−0.424263	+	1.30575i
$465$		0			0
$466$	−9.11550	−	6.62280i	−0.422267	−	0.306795i
$467$	−2.74419	+	0.891640i	−0.126986	+	0.0412602i	−0.371820	−	0.928305i	$-0.621266\pi$
$467$	−2.74419	+	0.891640i	−0.126986	+	0.0412602i	0.244835	+	0.969565i	$0.421266\pi$
$468$		0			0
$469$	23.4122	−	32.2241i	1.08107	−	1.48797i
$470$	14.2124	−	10.3259i	0.655569	−	0.476299i
$471$		0			0
$472$		−	4.53359i		−	0.208675i
$473$	11.4715	−	26.5311i	0.527460	−	1.21990i
$474$		0			0
$475$	−2.61273	−	0.848927i	−0.119880	−	0.0389514i
$476$	9.94997	+	13.6950i	0.456056	+	0.627708i
$477$		0			0
$478$	−11.3978	−	35.0787i	−0.521322	−	1.60446i
$479$	0.932416	+	2.86968i	0.0426032	+	0.131119i	0.970096	−	0.242722i	$-0.0780404\pi$
$479$	0.932416	+	2.86968i	0.0426032	+	0.131119i	−0.927493	+	0.373841i	$0.878040\pi$
$480$		0			0
$481$	−7.14139	−	9.82928i	−0.325619	−	0.448177i
$482$	−7.85291	−	2.55157i	−0.357690	−	0.116221i
$483$		0			0
$484$	−1.23797	−	9.75201i	−0.0562714	−	0.443273i
$485$			21.9780i			0.997969i
$486$		0			0
$487$	20.5362	−	14.9204i	0.930584	−	0.676109i	−0.0155521	−	0.999879i	$-0.504951\pi$
$487$	20.5362	−	14.9204i	0.930584	−	0.676109i	0.946136	+	0.323771i	$0.104951\pi$
$488$	6.31243	−	8.68832i	0.285750	−	0.393302i
$489$		0			0
$490$	−2.49884	+	0.811921i	−0.112886	+	0.0366788i
$491$	0.861485	+	0.625905i	0.0388783	+	0.0282467i	0.607055	−	0.794660i	$-0.292351\pi$
$491$	0.861485	+	0.625905i	0.0388783	+	0.0282467i	−0.568176	+	0.822907i	$0.692351\pi$
$492$		0			0
$493$	12.3633	−	38.0502i	0.556813	−	1.71369i
$494$	8.09125			0.364042
$495$		0			0
$496$	−24.3152			−1.09179
$497$	7.11741	−	21.9051i	0.319259	−	0.982579i
$498$		0			0
$499$	−21.8865	−	15.9014i	−0.979772	−	0.711846i	−0.0221146	−	0.999755i	$-0.507040\pi$
$499$	−21.8865	−	15.9014i	−0.979772	−	0.711846i	−0.957658	+	0.287909i	$0.907040\pi$
$500$	10.3247	−	3.35470i	0.461735	−	0.150027i
$501$		0			0
$502$	−8.59399	+	11.8286i	−0.383568	+	0.527937i
$503$	16.7826	−	12.1933i	0.748299	−	0.543671i	−0.147000	−	0.989136i	$-0.546962\pi$
$503$	16.7826	−	12.1933i	0.748299	−	0.543671i	0.895299	+	0.445466i	$0.146962\pi$
$504$		0			0
$505$			15.2932i			0.680539i
$506$	−7.40757	−	6.52666i	−0.329307	−	0.290145i
$507$		0			0
$508$	−0.199290	−	0.0647532i	−0.00884206	−	0.00287296i
$509$	5.35111	+	7.36517i	0.237184	+	0.326455i	0.910971	−	0.412470i	$-0.135334\pi$
$509$	5.35111	+	7.36517i	0.237184	+	0.326455i	−0.673788	+	0.738925i	$0.735334\pi$
$510$		0			0
$511$	7.81067	+	24.0388i	0.345524	+	1.06341i
$512$	1.47728	+	4.54659i	0.0652870	+	0.200933i
$513$		0			0
$514$	−5.31153	−	7.31069i	−0.234282	−	0.322461i
$515$	−26.9591	−	8.75956i	−1.18796	−	0.385992i
$516$		0			0
$517$	4.25244	+	18.9973i	0.187022	+	0.835500i
$518$		−	17.5928i		−	0.772985i
$519$		0			0
$520$	8.83284	−	6.41743i	0.387346	−	0.281423i
$521$	−14.5125	+	19.9748i	−0.635805	+	0.875110i	−0.998383	−	0.0568430i	$-0.981897\pi$
$521$	−14.5125	+	19.9748i	−0.635805	+	0.875110i	0.362578	+	0.931953i	$0.381897\pi$
$522$		0			0
$523$	−18.0229	+	5.85598i	−0.788085	+	0.256064i	−0.675288	−	0.737554i	$-0.735981\pi$
$523$	−18.0229	+	5.85598i	−0.788085	+	0.256064i	−0.112797	+	0.993618i	$0.535981\pi$
$524$	4.38615	+	3.18673i	0.191610	+	0.139213i
$525$		0			0
$526$	−8.50025	+	26.1611i	−0.370629	+	1.14068i
$527$	32.8940			1.43289
$528$		0			0
$529$	19.9378			0.866863
$530$	3.77443	−	11.6165i	0.163951	−	0.504589i
$531$		0			0
$532$	2.92732	+	2.12682i	0.126915	+	0.0922094i
$533$	10.1237	−	3.28940i	0.438508	−	0.142480i
$534$		0			0
$535$	10.0342	−	13.8109i	0.433817	−	0.597098i
$536$	−21.6067	+	15.6982i	−0.933267	+	0.678058i
$537$		0			0
$538$		−	17.9614i		−	0.774369i
$539$	0.273126	−	2.89875i	0.0117644	−	0.124858i
$540$		0			0
$541$	15.4821	+	5.03045i	0.665628	+	0.216276i	0.622293	−	0.782785i	$-0.286201\pi$
$541$	15.4821	+	5.03045i	0.665628	+	0.216276i	0.0433359	+	0.999061i	$0.486201\pi$
$542$	−5.10103	−	7.02096i	−0.219108	−	0.301576i
$543$		0			0
$544$	−9.84813	−	30.3094i	−0.422235	−	1.29951i
$545$	6.69106	+	20.5930i	0.286614	+	0.882106i
$546$		0			0
$547$	−25.6787	−	35.3437i	−1.09794	−	1.51119i	−0.838086	−	0.545538i	$-0.816325\pi$
$547$	−25.6787	−	35.3437i	−1.09794	−	1.51119i	−0.259855	−	0.965648i	$-0.583675\pi$
$548$	−13.7727	−	4.47503i	−0.588342	−	0.191164i
$549$		0			0
$550$	−1.00788	+	10.6968i	−0.0429760	+	0.456113i
$551$		−	8.55184i		−	0.364321i
$552$		0			0
$553$	32.8365	−	23.8571i	1.39635	−	1.01451i
$554$	24.1294	−	33.2113i	1.02516	−	1.41101i
$555$		0			0
$556$	0.661464	−	0.214923i	0.0280523	−	0.00911476i
$557$	11.8526	+	8.61141i	0.502210	+	0.364877i	0.809861	−	0.586622i	$-0.199543\pi$
$557$	11.8526	+	8.61141i	0.502210	+	0.364877i	−0.307650	+	0.951500i	$0.599543\pi$
$558$		0			0
$559$	8.88004	−	27.3300i	0.375586	−	1.15593i
$560$	24.6357			1.04105
$561$		0			0
$562$	19.7432			0.832815
$563$	−2.85577	+	8.78915i	−0.120356	+	0.370419i	−0.993026	−	0.117892i	$-0.962386\pi$
$563$	−2.85577	+	8.78915i	−0.120356	+	0.370419i	0.872670	+	0.488310i	$0.162386\pi$
$564$		0			0
$565$	9.63354	+	6.99918i	0.405286	+	0.294458i
$566$	23.8923	−	7.76309i	1.00427	−	0.326307i
$567$		0			0
$568$	−9.07748	+	12.4941i	−0.380883	+	0.524240i
$569$	−22.9590	+	16.6807i	−0.962490	+	0.699290i	−0.953728	−	0.300672i	$-0.902789\pi$
$569$	−22.9590	+	16.6807i	−0.962490	+	0.699290i	−0.00876215	+	0.999962i	$0.502789\pi$
$570$		0			0
$571$			16.7686i			0.701744i	0.936423	+	0.350872i	$0.114115\pi$
$571$			16.7686i			0.701744i	−0.936423	+	0.350872i	$0.885885\pi$
$572$	−2.13480	−	9.53695i	−0.0892603	−	0.398760i
$573$		0			0
$574$	14.6593	+	4.76309i	0.611867	+	0.198808i
$575$	1.95878	+	2.69603i	0.0816868	+	0.112432i
$576$		0			0
$577$	11.7263	+	36.0897i	0.488171	+	1.50244i	0.827336	+	0.561708i	$0.189856\pi$
$577$	11.7263	+	36.0897i	0.488171	+	1.50244i	−0.339165	+	0.940727i	$0.610144\pi$
$578$	15.0056	+	46.1824i	0.624150	+	1.92094i
$579$		0			0
$580$	5.47886	+	7.54101i	0.227497	+	0.313123i
$581$	−2.66521	−	0.865980i	−0.110572	−	0.0359269i
$582$		0			0
$583$	10.1557	+	8.94798i	0.420606	+	0.370587i
$584$		−	16.9478i		−	0.701305i
$585$		0			0
$586$	−28.3132	+	20.5707i	−1.16961	+	0.849770i
$587$	8.33959	−	11.4785i	0.344212	−	0.473767i	−0.601454	−	0.798907i	$-0.705412\pi$
$587$	8.33959	−	11.4785i	0.344212	−	0.473767i	0.945666	+	0.325141i	$0.105412\pi$
$588$		0			0
$589$	6.68702	−	2.17274i	0.275534	−	0.0895264i
$590$	−5.83291	−	4.23786i	−0.240137	−	0.174470i
$591$		0			0
$592$	−5.68037	+	17.4824i	−0.233462	+	0.718521i
$593$	14.4106			0.591771			0.295886	−	0.955223i	$-0.404385\pi$
$593$	14.4106			0.591771			0.295886	+	0.955223i	$0.404385\pi$
$594$		0			0
$595$	−33.3276			−1.36630
$596$	3.54350	−	10.9058i	0.145147	−	0.446718i
$597$		0			0
$598$	−7.94058	−	5.76917i	−0.324714	−	0.235919i
$599$	2.78374	−	0.904492i	0.113741	−	0.0369565i	−0.251594	−	0.967833i	$-0.580955\pi$
$599$	2.78374	−	0.904492i	0.113741	−	0.0369565i	0.365334	+	0.930876i	$0.380955\pi$
$600$		0			0
$601$	4.69573	−	6.46312i	0.191543	−	0.263636i	−0.702434	−	0.711749i	$-0.747904\pi$
$601$	4.69573	−	6.46312i	0.191543	−	0.263636i	0.893977	+	0.448112i	$0.147904\pi$
$602$	33.6637	−	24.4581i	1.37203	−	0.996839i
$603$		0			0
$604$		−	9.18184i		−	0.373604i
$605$	16.9655	+	9.31349i	0.689747	+	0.378647i
$606$		0			0
$607$	−24.0417	−	7.81162i	−0.975822	−	0.317064i	−0.222658	−	0.974897i	$-0.571473\pi$
$607$	−24.0417	−	7.81162i	−0.975822	−	0.317064i	−0.753164	+	0.657833i	$0.771473\pi$
$608$	−4.00405	−	5.51110i	−0.162386	−	0.223504i
$609$		0			0
$610$	−5.27772	−	16.2432i	−0.213689	−	0.657666i
$611$	5.98069	+	18.4067i	0.241953	+	0.744654i
$612$		0			0
$613$	−5.81317	−	8.00115i	−0.234792	−	0.323163i	0.675321	−	0.737524i	$-0.264005\pi$
$613$	−5.81317	−	8.00115i	−0.234792	−	0.323163i	−0.910113	+	0.414361i	$0.864005\pi$
$614$	−8.87126	−	2.88245i	−0.358015	−	0.116326i
$615$		0			0
$616$	−6.95282	+	16.0804i	−0.280137	+	0.647897i
$617$		−	21.8907i		−	0.881288i	−0.897682	−	0.440644i	$-0.854750\pi$
$617$		−	21.8907i		−	0.881288i	0.897682	−	0.440644i	$-0.145250\pi$
$618$		0			0
$619$	−19.1050	+	13.8806i	−0.767894	+	0.557908i	−0.901321	−	0.433151i	$-0.857402\pi$
$619$	−19.1050	+	13.8806i	−0.767894	+	0.557908i	0.133427	+	0.991059i	$0.457402\pi$
$620$	−4.50461	+	6.20006i	−0.180909	+	0.249000i
$621$		0			0
$622$	−17.8882	+	5.81222i	−0.717250	+	0.233049i
$623$	31.8518	+	23.1417i	1.27612	+	0.927153i
$624$		0			0
$625$	−3.66230	+	11.2714i	−0.146492	+	0.450856i
$626$	2.25094			0.0899655
$627$		0			0
$628$	16.5134			0.658957
$629$	7.68449	−	23.6504i	0.306401	−	0.943005i
$630$		0			0
$631$	14.6739	+	10.6612i	0.584159	+	0.424416i	0.840221	−	0.542244i	$-0.182425\pi$
$631$	14.6739	+	10.6612i	0.584159	+	0.424416i	−0.256062	+	0.966660i	$0.582425\pi$
$632$	−25.8829	+	8.40986i	−1.02957	+	0.334526i
$633$		0			0
$634$	6.64976	−	9.15261i	0.264096	−	0.363496i
$635$	0.333763	−	0.242493i	0.0132450	−	0.00962303i
$636$		0			0
$637$		−	2.89461i		−	0.114689i
$638$	−32.6384	+	7.30593i	−1.29217	+	0.289244i
$639$		0			0
$640$	−21.3386	−	6.93334i	−0.843483	−	0.274064i
$641$	14.1228	+	19.4383i	0.557815	+	0.767767i	0.991047	−	0.133516i	$-0.0426268\pi$
$641$	14.1228	+	19.4383i	0.557815	+	0.767767i	−0.433232	+	0.901283i	$0.642627\pi$
$642$		0			0
$643$	12.8162	+	39.4443i	0.505423	+	1.55553i	0.800058	+	0.599923i	$0.204802\pi$
$643$	12.8162	+	39.4443i	0.505423	+	1.55553i	−0.294634	+	0.955610i	$0.595198\pi$
$644$	−1.35636	−	4.17444i	−0.0534479	−	0.164496i
$645$		0			0
$646$	9.73426	+	13.3981i	0.382989	+	0.527139i
$647$	31.8320	+	10.3428i	1.25144	+	0.406619i	0.858438	−	0.512917i	$-0.171435\pi$
$647$	31.8320	+	10.3428i	1.25144	+	0.406619i	0.393006	+	0.919536i	$0.371435\pi$
$648$		0			0
$649$	6.87577	−	4.06913i	0.269898	−	0.159727i
$650$			10.6815i			0.418965i
$651$		0			0
$652$	5.84034	−	4.24326i	0.228725	−	0.166179i
$653$	0.936845	−	1.28946i	0.0366616	−	0.0504603i	−0.790293	−	0.612730i	$-0.790072\pi$
$653$	0.936845	−	1.28946i	0.0366616	−	0.0504603i	0.826954	+	0.562269i	$0.190072\pi$
$654$		0			0
$655$	−10.1516	+	3.29845i	−0.396655	+	0.128881i
$656$	−13.0293	−	9.46637i	−0.508710	−	0.369600i
$657$		0			0
$658$	−8.66010	+	26.6530i	−0.337606	+	1.03904i
$659$	30.8533			1.20187			0.600936	−	0.799297i	$-0.294795\pi$
$659$	30.8533			1.20187			0.600936	+	0.799297i	$0.294795\pi$
$660$		0			0
$661$	−42.5461			−1.65485			−0.827425	−	0.561576i	$-0.810195\pi$
$661$	−42.5461			−1.65485			−0.827425	+	0.561576i	$0.810195\pi$
$662$	−12.3823	+	38.1087i	−0.481250	+	1.48114i
$663$		0			0
$664$	1.52016	+	1.10446i	0.0589938	+	0.0428615i
$665$	−6.77516	+	2.20138i	−0.262729	+	0.0853660i
$666$		0			0
$667$	−6.09758	+	8.39260i	−0.236099	+	0.324963i
$668$	−4.89858	+	3.55903i	−0.189532	+	0.137703i
$669$		0			0
$670$			42.4734i			1.64089i
$671$	18.8427	+	1.77540i	0.727415	+	0.0685385i
$672$		0			0
$673$	27.3162	+	8.87556i	1.05296	+	0.342128i	0.783830	−	0.620976i	$-0.213263\pi$
$673$	27.3162	+	8.87556i	1.05296	+	0.342128i	0.269131	+	0.963104i	$0.413263\pi$
$674$	−15.1010	−	20.7848i	−0.581671	−	0.800601i
$675$		0			0
$676$	0.587633	+	1.80855i	0.0226013	+	0.0695595i
$677$	−1.53435	−	4.72225i	−0.0589699	−	0.181491i	0.917232	−	0.398352i	$-0.130418\pi$
$677$	−1.53435	−	4.72225i	−0.0589699	−	0.181491i	−0.976202	+	0.216862i	$0.930418\pi$
$678$		0			0
$679$	−20.6081	−	28.3646i	−0.790865	−	1.08853i
$680$	21.2529	+	6.90548i	0.815011	+	0.264813i
$681$		0			0
$682$	−14.0051	−	23.6650i	−0.536284	−	0.906180i
$683$		−	3.46565i		−	0.132610i	−0.997799	−	0.0663048i	$-0.978879\pi$
$683$		−	3.46565i		−	0.132610i	0.997799	−	0.0663048i	$-0.0211210\pi$
$684$		0			0
$685$	23.0660	−	16.7584i	0.881307	−	0.640307i
$686$	−17.1810	+	23.6477i	−0.655975	+	0.902872i
$687$		0			0
$688$	−41.3494	+	13.4352i	−1.57643	+	0.512213i
$689$	10.8864	+	7.90946i	0.414740	+	0.301327i
$690$		0			0
$691$	1.69452	−	5.21519i	0.0644625	−	0.198395i	−0.913638	−	0.406529i	$-0.866739\pi$
$691$	1.69452	−	5.21519i	0.0644625	−	0.198395i	0.978100	+	0.208134i	$0.0667390\pi$
$692$	−4.46656			−0.169793
$693$		0			0
$694$	36.7879			1.39645
$695$	−0.423139	+	1.30229i	−0.0160506	+	0.0493986i
$696$		0			0
$697$	17.6263	+	12.8063i	0.667644	+	0.485072i
$698$	−30.3392	+	9.85781i	−1.14836	+	0.373124i
$699$		0			0
$700$	−2.80769	+	3.86446i	−0.106121	+	0.146063i
$701$	−15.0478	+	10.9329i	−0.568347	+	0.412928i	−0.834504	−	0.551001i	$-0.814246\pi$
$701$	−15.0478	+	10.9329i	−0.568347	+	0.412928i	0.266157	+	0.963930i	$0.414246\pi$
$702$		0			0
$703$		−	5.31547i		−	0.200477i
$704$	4.26353	−	4.83898i	0.160688	−	0.182376i
$705$		0			0
$706$	−46.4747	−	15.1005i	−1.74910	−	0.568317i
$707$	−14.3400	−	19.7373i	−0.539310	−	0.742296i
$708$		0			0
$709$	1.58230	+	4.86982i	0.0594245	+	0.182890i	0.976362	−	0.216140i	$-0.0693469\pi$
$709$	1.58230	+	4.86982i	0.0594245	+	0.182890i	−0.916938	+	0.399030i	$0.869347\pi$
$710$	7.58953	+	23.3582i	0.284830	+	0.876617i
$711$		0			0
$712$	−15.5168	−	21.3571i	−0.581518	−	0.800390i
$713$	−8.11170	−	2.63565i	−0.303785	−	0.0987059i
$714$		0			0
$715$	17.6608	+	7.63616i	0.660477	+	0.285576i
$716$			3.15479i			0.117900i
$717$		0			0
$718$	1.01363	−	0.736446i	0.0378284	−	0.0274839i
$719$	8.72981	−	12.0156i	0.325567	−	0.448104i	−0.614590	−	0.788847i	$-0.710678\pi$
$719$	8.72981	−	12.0156i	0.325567	−	0.448104i	0.940157	+	0.340742i	$0.110678\pi$
$720$		0			0
$721$	43.0068	−	13.9737i	1.60166	−	0.520410i
$722$	−23.2839	−	16.9168i	−0.866539	−	0.629577i
$723$		0			0
$724$	−3.86675	+	11.9006i	−0.143707	+	0.442283i
$725$	11.2896			0.419285
$726$		0			0
$727$	44.2120			1.63973			0.819866	−	0.572556i	$-0.194048\pi$
$727$	44.2120			1.63973			0.819866	+	0.572556i	$0.194048\pi$
$728$	−5.38215	+	16.5645i	−0.199476	+	0.613923i
$729$		0			0
$730$	−21.8050	−	15.8423i	−0.807041	−	0.586349i
$731$	55.9381	−	18.1754i	2.06895	−	0.672241i
$732$		0			0
$733$	14.0367	−	19.3199i	0.518459	−	0.713597i	−0.466858	−	0.884332i	$-0.654614\pi$
$733$	14.0367	−	19.3199i	0.518459	−	0.713597i	0.985317	+	0.170735i	$0.0546141\pi$
$734$	−7.10640	+	5.16310i	−0.262302	+	0.190574i
$735$		0			0
$736$			8.26341i			0.304593i
$737$	−43.2015	−	18.6794i	−1.59135	−	0.688065i
$738$		0			0
$739$	22.8689	+	7.43057i	0.841248	+	0.273338i	0.697776	−	0.716316i	$-0.254173\pi$
$739$	22.8689	+	7.43057i	0.841248	+	0.273338i	0.143472	+	0.989654i	$0.454173\pi$
$740$	3.40544	+	4.68718i	0.125186	+	0.172304i
$741$		0			0
$742$	6.02119	+	18.5313i	0.221045	+	0.680306i
$743$	2.13407	+	6.56799i	0.0782914	+	0.240956i	0.982540	−	0.186049i	$-0.0595685\pi$
$743$	2.13407	+	6.56799i	0.0782914	+	0.240956i	−0.904249	+	0.427006i	$0.859568\pi$
$744$		0			0
$745$	13.2700	+	18.2645i	0.486174	+	0.669161i
$746$	−19.3009	−	6.27124i	−0.706656	−	0.229607i
$747$		0			0
$748$	13.2237	−	15.0085i	0.483505	−	0.548764i
$749$			27.2330i			0.995072i
$750$		0			0
$751$	12.8262	−	9.31876i	0.468033	−	0.340046i	−0.328641	−	0.944455i	$-0.606591\pi$
$751$	12.8262	−	9.31876i	0.468033	−	0.340046i	0.796674	+	0.604409i	$0.206591\pi$
$752$	17.2114	−	23.6895i	0.627637	−	0.863868i
$753$		0			0
$754$	−31.6236	+	10.2751i	−1.15166	+	0.374199i
$755$	14.6247	+	10.6255i	0.532249	+	0.386701i
$756$		0			0
$757$	−7.92506	+	24.3908i	−0.288041	+	0.886499i	0.697429	+	0.716653i	$0.254327\pi$
$757$	−7.92506	+	24.3908i	−0.288041	+	0.886499i	−0.985471	+	0.169846i	$0.945673\pi$
$758$	13.9429			0.506428
$759$		0			0
$760$	4.77662			0.173266
$761$	−1.33599	+	4.11176i	−0.0484297	+	0.149051i	−0.972347	−	0.233541i	$-0.924969\pi$
$761$	−1.33599	+	4.11176i	−0.0484297	+	0.149051i	0.923917	+	0.382592i	$0.124969\pi$
$762$		0			0
$763$	−27.9448	−	20.3031i	−1.01167	−	0.735021i
$764$	4.95488	−	1.60994i	0.179261	−	0.0582455i
$765$		0			0
$766$	−23.2806	+	32.0430i	−0.841162	+	1.15776i
$767$	6.42605	−	4.66880i	0.232031	−	0.168581i
$768$		0			0
$769$			39.9506i			1.44066i	0.693634	+	0.720328i	$0.256009\pi$
$769$			39.9506i			1.44066i	−0.693634	+	0.720328i	$0.743991\pi$
$770$	14.1897	+	23.9769i	0.511363	+	0.864069i
$771$		0			0
$772$	−0.104828	−	0.0340606i	−0.00377284	−	0.00122587i
$773$	30.2857	+	41.6846i	1.08930	+	1.49929i	0.848852	+	0.528630i	$0.177294\pi$
$773$	30.2857	+	41.6846i	1.08930	+	1.49929i	0.240447	+	0.970662i	$0.422706\pi$
$774$		0			0
$775$	2.86832	+	8.82777i	0.103033	+	0.317103i
$776$	7.26454	+	22.3580i	0.260782	+	0.802604i
$777$		0			0
$778$	−12.9477	−	17.8210i	−0.464197	−	0.638912i
$779$	4.42914	+	1.43911i	0.158690	+	0.0515616i
$780$		0			0
$781$	−27.0964	−	2.55308i	−0.969586	−	0.0913564i
$782$		−	20.0892i		−	0.718389i
$783$		0			0
$784$	−3.54306	+	2.57418i	−0.126538	+	0.0919350i
$785$	−19.1098	+	26.3024i	−0.682058	+	0.938772i
$786$		0			0
$787$	−11.7642	+	3.82244i	−0.419350	+	0.136255i	−0.511089	−	0.859528i	$-0.670758\pi$
$787$	−11.7642	+	3.82244i	−0.419350	+	0.136255i	0.0917385	+	0.995783i	$0.470758\pi$
$788$	−1.93400	−	1.40513i	−0.0688958	−	0.0500557i
$789$		0			0
$790$	−13.3744	+	41.1622i	−0.475840	+	1.46448i
$791$	−18.9959			−0.675415
$792$		0			0
$793$	18.8158			0.668169
$794$	5.72706	−	17.6261i	0.203246	−	0.625526i
$795$		0			0
$796$	16.9367	+	12.3053i	0.600307	+	0.436148i
$797$	41.9299	−	13.6239i	1.48523	−	0.482582i	0.549563	−	0.835453i	$-0.314794\pi$
$797$	41.9299	−	13.6239i	1.48523	−	0.482582i	0.935672	+	0.352871i	$0.114794\pi$
$798$		0			0
$799$	−23.2839	+	32.0476i	−0.823726	+	1.13376i
$800$	7.27540	−	5.28588i	0.257224	−	0.186884i
$801$		0			0
$802$			53.5721i			1.89170i
$803$	25.7035	−	15.2115i	0.907058	−	0.536804i
$804$		0			0
$805$	8.21862	+	2.67039i	0.289668	+	0.0941189i
$806$	−16.0691	−	22.1172i	−0.566009	−	0.779044i
$807$		0			0
$808$	5.05497	+	15.5576i	0.177833	+	0.547315i
$809$	4.87082	+	14.9908i	0.171249	+	0.527050i	0.999442	−	0.0333924i	$-0.0106311\pi$
$809$	4.87082	+	14.9908i	0.171249	+	0.527050i	−0.828193	+	0.560442i	$0.810631\pi$
$810$		0			0
$811$	−1.85940	−	2.55924i	−0.0652923	−	0.0898672i	0.775122	−	0.631812i	$-0.217688\pi$
$811$	−1.85940	−	2.55924i	−0.0652923	−	0.0898672i	−0.840414	+	0.541944i	$0.817688\pi$
$812$	−14.1419	−	4.59499i	−0.496285	−	0.161253i
$813$		0			0
$814$	−20.2867	+	4.54106i	−0.711048	+	0.159164i
$815$			14.2129i			0.497855i
$816$		0			0
$817$	10.1711	−	7.38974i	0.355842	−	0.258534i
$818$	16.8190	−	23.1493i	0.588062	−	0.809398i
$819$		0			0
$820$	−4.82760	+	1.56858i	−0.168587	+	0.0547773i
$821$	−39.7796	−	28.9016i	−1.38832	−	1.00867i	−0.996047	−	0.0888230i	$-0.971689\pi$
$821$	−39.7796	−	28.9016i	−1.38832	−	1.00867i	−0.392271	−	0.919850i	$-0.628311\pi$
$822$		0			0
$823$	13.0339	−	40.1143i	0.454334	−	1.39830i	−0.417581	−	0.908640i	$-0.637122\pi$
$823$	13.0339	−	40.1143i	0.454334	−	1.39830i	0.871915	−	0.489657i	$-0.162878\pi$
$824$	−30.3206			−1.05627
$825$		0			0
$826$	11.5016			0.400192
$827$	4.11309	−	12.6588i	0.143026	−	0.440189i	−0.853726	−	0.520723i	$-0.825663\pi$
$827$	4.11309	−	12.6588i	0.143026	−	0.440189i	0.996752	+	0.0805340i	$0.0256626\pi$
$828$		0			0
$829$	−37.7524	−	27.4288i	−1.31120	−	0.952640i	−0.999997	−	0.00229533i	$-0.999269\pi$
$829$	−37.7524	−	27.4288i	−1.31120	−	0.952640i	−0.311199	−	0.950345i	$-0.600731\pi$
$830$	2.84201	−	0.923424i	0.0986475	−	0.0320525i
$831$		0			0
$832$	3.76870	−	5.18717i	0.130656	−	0.179833i
$833$	4.79310	−	3.48239i	0.166071	−	0.120658i
$834$		0			0
$835$		−	11.9210i		−	0.412544i
$836$	1.69688	−	3.92453i	0.0586879	−	0.135733i
$837$		0			0
$838$	−17.6425	−	5.73238i	−0.609449	−	0.198022i
$839$	−8.27668	−	11.3919i	−0.285743	−	0.393291i	0.641883	−	0.766803i	$-0.278154\pi$
$839$	−8.27668	−	11.3919i	−0.285743	−	0.393291i	−0.927625	+	0.373512i	$0.878154\pi$
$840$		0			0
$841$	1.89856	+	5.84318i	0.0654677	+	0.201489i
$842$	12.3041	+	37.8680i	0.424026	+	1.30502i
$843$		0			0
$844$	4.90246	+	6.74766i	0.168750	+	0.232264i
$845$	−3.56066	−	1.15693i	−0.122491	−	0.0397996i
$846$		0			0
$847$	−30.6285	+	3.88814i	−1.05241	+	0.133598i
$848$		−	20.3591i		−	0.699134i
$849$		0			0
$850$	−17.6873	+	12.8505i	−0.606668	+	0.440770i
$851$	−3.79001	+	5.21650i	−0.129920	+	0.178819i
$852$		0			0
$853$	−2.58409	+	0.839622i	−0.0884776	+	0.0287481i	−0.352921	−	0.935653i	$-0.614812\pi$
$853$	−2.58409	+	0.839622i	−0.0884776	+	0.0287481i	0.264444	+	0.964401i	$0.414812\pi$
$854$	22.0421	+	16.0145i	0.754264	+	0.548005i
$855$		0			0
$856$	5.64267	−	17.3664i	0.192863	−	0.593570i
$857$	−34.3028			−1.17176			−0.585881	−	0.810397i	$-0.699251\pi$
$857$	−34.3028			−1.17176			−0.585881	+	0.810397i	$0.699251\pi$
$858$		0			0
$859$	53.4273			1.82292			0.911458	−	0.411394i	$-0.134958\pi$
$859$	53.4273			1.82292			0.911458	+	0.411394i	$0.134958\pi$
$860$	−4.23453	+	13.0325i	−0.144396	+	0.444406i
$861$		0			0
$862$	−4.98345	−	3.62069i	−0.169737	−	0.123321i
$863$	51.3521	−	16.6853i	1.74804	−	0.567974i	0.752191	−	0.658945i	$-0.228997\pi$
$863$	51.3521	−	16.6853i	1.74804	−	0.567974i	0.995854	+	0.0909712i	$0.0289971\pi$
$864$		0			0
$865$	5.16883	−	7.11429i	0.175746	−	0.241893i
$866$	6.14496	−	4.46458i	0.208814	−	0.151712i
$867$		0			0
$868$		−	12.2256i		−	0.414963i
$869$	−35.9859	−	31.7065i	−1.22074	−	1.07557i
$870$		0			0
$871$	−44.5023	−	14.4597i	−1.50790	−	0.489947i
$872$	13.6135	+	18.7374i	0.461011	+	0.634527i
$873$		0			0
$874$	−1.32695	−	4.08393i	−0.0448848	−	0.138141i
$875$	−10.5362	−	32.4272i	−0.356190	−	1.09624i
$876$		0			0
$877$	−5.73684	−	7.89608i	−0.193719	−	0.266632i	0.701097	−	0.713065i	$-0.252694\pi$
$877$	−5.73684	−	7.89608i	−0.193719	−	0.266632i	−0.894817	+	0.446434i	$0.852694\pi$
$878$	2.63175	+	0.855106i	0.0888171	+	0.0288584i
$879$		0			0
$880$	−6.35898	−	28.4080i	−0.214361	−	0.957633i
$881$		−	1.83055i		−	0.0616727i	−0.999524	−	0.0308364i	$-0.990183\pi$
$881$		−	1.83055i		−	0.0616727i	0.999524	−	0.0308364i	$-0.00981708\pi$
$882$		0			0
$883$	1.61899	−	1.17627i	0.0544835	−	0.0395846i	−0.560210	−	0.828351i	$-0.689280\pi$
$883$	1.61899	−	1.17627i	0.0544835	−	0.0395846i	0.614694	+	0.788766i	$0.289280\pi$
$884$	11.6889	−	16.0884i	0.393141	−	0.541112i
$885$		0			0
$886$	28.0441	−	9.11209i	0.942161	−	0.306127i
$887$	−11.1751	−	8.11915i	−0.375222	−	0.272614i	0.384151	−	0.923270i	$-0.374494\pi$
$887$	−11.1751	−	8.11915i	−0.375222	−	0.272614i	−0.759373	+	0.650656i	$0.774494\pi$
$888$		0			0
$889$	−0.203373	+	0.625917i	−0.00682091	+	0.0209926i
$890$	−41.9827			−1.40726
$891$		0			0
$892$	3.07041			0.102805
$893$	−2.61655	+	8.05291i	−0.0875595	+	0.269481i
$894$		0			0
$895$	−5.02491	−	3.65081i	−0.167964	−	0.122033i
$896$	34.0406	−	11.0605i	1.13722	−	0.369504i
$897$		0			0
$898$	−39.4634	+	54.3167i	−1.31691	+	1.81257i
$899$	−23.3762	+	16.9838i	−0.779640	+	0.566442i
$900$		0			0
$901$			27.5421i			0.917561i
$902$	1.70857	−	18.1334i	0.0568890	−	0.603776i
$903$		0			0
$904$	12.1136	+	3.93594i	0.402892	+	0.130907i
$905$	−14.4805	−	19.9307i	−0.481348	−	0.662518i
$906$		0			0
$907$	0.431231	+	1.32719i	0.0143188	+	0.0440687i	0.957961	−	0.286900i	$-0.0926246\pi$
$907$	0.431231	+	1.32719i	0.0143188	+	0.0440687i	−0.943642	+	0.330968i	$0.892625\pi$
$908$	−6.63200	−	20.4112i	−0.220091	−	0.677369i
$909$		0			0
$910$	16.2809	+	22.4087i	0.539706	+	0.742841i
$911$	−28.6848	−	9.32027i	−0.950371	−	0.308794i	−0.207505	−	0.978234i	$-0.566534\pi$
$911$	−28.6848	−	9.32027i	−0.950371	−	0.308794i	−0.742866	+	0.669440i	$0.766534\pi$
$912$		0			0
$913$	−0.310635	+	3.29684i	−0.0102805	+	0.109110i
$914$		−	46.0454i		−	1.52305i
$915$		0			0
$916$	1.36372	−	0.990801i	0.0450586	−	0.0327370i
$917$	10.0087	−	13.7758i	0.330515	−	0.454915i
$918$		0			0
$919$	−42.6708	+	13.8646i	−1.40758	+	0.457351i	−0.911634	−	0.411002i	$-0.865179\pi$
$919$	−42.6708	+	13.8646i	−1.40758	+	0.457351i	−0.495947	+	0.868353i	$0.665179\pi$
$920$	−4.68767	−	3.40579i	−0.154548	−	0.112286i
$921$		0			0
$922$	−13.4758	+	41.4742i	−0.443801	+	1.36588i
$923$	−27.0577			−0.890616
$924$		0			0
$925$	7.01715			0.230722
$926$	−5.06996	+	15.6037i	−0.166609	+	0.512770i
$927$		0			0
$928$	22.6479	+	16.4547i	0.743454	+	0.540151i
$929$	16.4880	−	5.35728i	0.540954	−	0.175767i	−0.0257798	−	0.999668i	$-0.508207\pi$
$929$	16.4880	−	5.35728i	0.540954	−	0.175767i	0.566734	+	0.823901i	$0.308207\pi$
$930$		0			0
$931$	0.744367	−	1.02453i	0.0243956	−	0.0335777i
$932$	−4.78883	+	3.47929i	−0.156863	+	0.113968i
$933$		0			0
$934$			4.90830i			0.160604i
$935$	8.60253	+	38.4308i	0.281333	+	1.25682i
$936$		0			0
$937$	34.1168	+	11.0852i	1.11455	+	0.362138i	0.807684	−	0.589616i	$-0.200721\pi$
$937$	34.1168	+	11.0852i	1.11455	+	0.362138i	0.306862	+	0.951754i	$0.400721\pi$
$938$	−39.8259	−	54.8157i	−1.30036	−	1.78980i
$939$		0			0
$940$	−2.85195	−	8.77739i	−0.0930202	−	0.286287i
$941$	6.35673	+	19.5640i	0.207223	+	0.637768i	0.999615	+	0.0277550i	$0.00883583\pi$
$941$	6.35673	+	19.5640i	0.207223	+	0.637768i	−0.792391	+	0.610013i	$0.791164\pi$
$942$		0			0
$943$	−3.32055	−	4.57035i	−0.108132	−	0.148831i
$944$	−11.4294	−	3.71363i	−0.371995	−	0.120868i
$945$		0			0
$946$	−36.8925	−	32.5052i	−1.19948	−	1.05684i
$947$			53.5814i			1.74116i	0.492024	+	0.870581i	$0.336257\pi$
$947$			53.5814i			1.74116i	−0.492024	+	0.870581i	$0.663743\pi$
$948$		0			0
$949$	24.0224	−	17.4533i	0.779799	−	0.566557i
$950$	−2.74682	+	3.78068i	−0.0891187	+	0.122661i
$951$		0			0
$952$	−33.9038	+	11.0160i	−1.09883	+	0.357031i
$953$	12.6652	+	9.20183i	0.410267	+	0.298076i	0.773710	−	0.633540i	$-0.218399\pi$
$953$	12.6652	+	9.20183i	0.410267	+	0.298076i	−0.363443	+	0.931616i	$0.618399\pi$
$954$		0			0
$955$	−3.16964	+	9.75516i	−0.102567	+	0.315669i
$956$	−19.3770			−0.626697
$957$		0			0
$958$	5.13276			0.165832
$959$	−14.0549	+	43.2565i	−0.453857	+	1.39683i
$960$		0			0
$961$	5.86009	+	4.25761i	0.189035	+	0.137342i
$962$	−19.6560	+	6.38661i	−0.633734	+	0.205913i
$963$		0			0
$964$	−2.54972	+	3.50939i	−0.0821209	+	0.113030i
$965$	0.175561	−	0.127553i	0.00565152	−	0.00410607i
$966$		0			0
$967$			51.0560i			1.64185i	0.571037	+	0.820924i	$0.306541\pi$
$967$			51.0560i			1.64185i	−0.571037	+	0.820924i	$0.693459\pi$
$968$	20.3373	+	3.86677i	0.653665	+	0.124283i
$969$		0			0
$970$	35.5564	+	11.5530i	1.14165	+	0.370944i
$971$	−9.08431	−	12.5035i	−0.291529	−	0.401256i	0.637981	−	0.770052i	$-0.279770\pi$
$971$	−9.08431	−	12.5035i	−0.291529	−	0.401256i	−0.929510	+	0.368797i	$0.879770\pi$
$972$		0			0
$973$	−0.675016	−	2.07749i	−0.0216400	−	0.0666011i
$974$	−13.3435	−	41.0669i	−0.427552	−	1.31587i
$975$		0			0
$976$	−16.7329	−	23.0309i	−0.535608	−	0.737201i
$977$	35.3203	+	11.4762i	1.13000	+	0.367158i	0.813574	−	0.581461i	$-0.197519\pi$
$977$	35.3203	+	11.4762i	1.13000	+	0.367158i	0.316421	+	0.948619i	$0.397519\pi$
$978$		0			0
$979$	18.4636	−	42.7024i	0.590099	−	1.36477i
$980$			1.38032i			0.0440928i
$981$		0			0
$982$	1.46545	−	1.06471i	0.0467644	−	0.0339764i
$983$	−10.9843	+	15.1186i	−0.350346	+	0.482210i	−0.947427	−	0.319971i	$-0.896327\pi$
$983$	−10.9843	+	15.1186i	−0.350346	+	0.482210i	0.597082	+	0.802180i	$0.296327\pi$
$984$		0			0
$985$	4.47616	−	1.45439i	0.142622	−	0.0463408i
$986$	−55.0595	−	40.0030i	−1.75345	−	1.27396i
$987$		0			0
$988$	1.31355	−	4.04269i	0.0417896	−	0.128615i
$989$	−15.2507			−0.484944
$990$		0			0
$991$	−25.4516			−0.808496			−0.404248	−	0.914649i	$-0.632467\pi$
$991$	−25.4516			−0.808496			−0.404248	+	0.914649i	$0.632467\pi$
$992$	−7.11245	+	21.8899i	−0.225821	+	0.695005i
$993$		0			0
$994$	−31.6972	−	23.0294i	−1.00537	−	0.730447i
$995$	−39.1994	+	12.7367i	−1.24270	+	0.403779i
$996$		0			0
$997$	−25.3176	+	34.8466i	−0.801815	+	1.10360i	0.190720	+	0.981644i	$0.438918\pi$
$997$	−25.3176	+	34.8466i	−0.801815	+	1.10360i	−0.992535	+	0.121959i	$0.961082\pi$
$998$	−37.2305	+	27.0496i	−1.17851	+	0.856239i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.728.17		80
3.2	odd	2	inner	891.2.k.a.728.4		80
9.2	odd	6		99.2.p.a.68.9	yes	80
9.4	even	3		99.2.p.a.2.9	✓	80
9.5	odd	6		297.2.t.a.35.2		80
9.7	even	3		297.2.t.a.233.2		80
11.6	odd	10	inner	891.2.k.a.809.4		80
33.17	even	10	inner	891.2.k.a.809.17		80
99.50	even	30		297.2.t.a.116.2		80
99.61	odd	30		297.2.t.a.17.2		80
99.83	even	30		99.2.p.a.50.9	yes	80
99.94	odd	30		99.2.p.a.83.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.9	✓	80	9.4	even	3
99.2.p.a.50.9	yes	80	99.83	even	30
99.2.p.a.68.9	yes	80	9.2	odd	6
99.2.p.a.83.9	yes	80	99.94	odd	30
297.2.t.a.17.2		80	99.61	odd	30
297.2.t.a.35.2		80	9.5	odd	6
297.2.t.a.116.2		80	99.50	even	30
297.2.t.a.233.2		80	9.7	even	3
891.2.k.a.728.4		80	3.2	odd	2	inner
891.2.k.a.728.17		80	1.1	even	1	trivial
891.2.k.a.809.4		80	11.6	odd	10	inner
891.2.k.a.809.17		80	33.17	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.525662 - 1.61782i) q^{2} +(-0.722987 - 0.525281i) q^{4} +(1.67332 - 0.543696i) q^{5} +(-1.64977 + 2.27071i) q^{7} +(1.52254 - 1.10619i) q^{8} -2.99294i q^{10} +(3.04425 + 1.31627i) q^{11} +(3.13591 + 1.01892i) q^{13} +(2.80638 + 3.86266i) q^{14} +(-1.54159 - 4.74453i) q^{16} +(2.08549 + 6.41848i) q^{17} +(0.847917 + 1.16706i) q^{19} +(-1.49539 - 0.485880i) q^{20} +(3.72973 - 4.23313i) q^{22} -1.74990i q^{23} +(-1.54067 + 1.11937i) q^{25} +(3.29685 - 4.53773i) q^{26} +(2.38552 - 0.775104i) q^{28} +(-4.79604 - 3.48452i) q^{29} +(1.50617 - 4.63551i) q^{31} -4.72221 q^{32} +11.4802 q^{34} +(-1.52602 + 4.69661i) q^{35} +(-2.98102 - 2.16584i) q^{37} +(2.33381 - 0.758300i) q^{38} +(1.94628 - 2.67882i) q^{40} +(2.61178 - 1.89757i) q^{41} -8.71517i q^{43} +(-1.50954 - 2.55073i) q^{44} +(-2.83103 - 0.919856i) q^{46} +(3.45009 + 4.74864i) q^{47} +(-0.271279 - 0.834911i) q^{49} +(1.00106 + 3.08094i) q^{50} +(-1.73200 - 2.38390i) q^{52} +(3.88131 + 1.26111i) q^{53} +(5.80966 + 0.547398i) q^{55} +5.28222i q^{56} +(-8.15843 + 5.92744i) q^{58} +(1.41595 - 1.94889i) q^{59} +(5.42716 - 1.76339i) q^{61} +(-6.70769 - 4.87342i) q^{62} +(0.600895 - 1.84936i) q^{64} +5.80137 q^{65} -14.1912 q^{67} +(1.86372 - 5.73594i) q^{68} +(6.79610 + 4.93766i) q^{70} +(-7.80443 + 2.53581i) q^{71} +(5.29322 - 7.28550i) q^{73} +(-5.07094 + 3.68426i) q^{74} -1.28916i q^{76} +(-8.01117 + 4.74107i) q^{77} +(-13.7531 - 4.46865i) q^{79} +(-5.15916 - 7.10098i) q^{80} +(-1.69701 - 5.22286i) q^{82} +(0.308534 + 0.949571i) q^{83} +(6.97940 + 9.60632i) q^{85} +(-14.0996 - 4.58123i) q^{86} +(6.09104 - 1.36345i) q^{88} -14.0272i q^{89} +(-7.48719 + 5.43976i) q^{91} +(-0.919191 + 1.26516i) q^{92} +(9.49603 - 3.08545i) q^{94} +(2.05337 + 1.49186i) q^{95} +(-3.86008 + 11.8801i) q^{97} -1.49334 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Introduction

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