LMFDB - Embedded newform 864.2.y.b.97.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.9
Character	$\chi$	$=$	864.97
Dual form			864.2.y.b.481.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64243 + 0.549936i) q^{3} +(3.46982 + 1.26291i) q^{5} +(0.136240 - 0.772655i) q^{7} +(2.39514 + 1.80646i) q^{9} +O(q^{10})$	\(q+(1.64243 + 0.549936i) q^{3} +(3.46982 + 1.26291i) q^{5} +(0.136240 - 0.772655i) q^{7} +(2.39514 + 1.80646i) q^{9} +(-2.62684 + 0.956091i) q^{11} +(-1.82171 + 1.52860i) q^{13} +(5.00441 + 3.98242i) q^{15} +(1.40662 + 2.43633i) q^{17} +(1.63600 - 2.83364i) q^{19} +(0.648675 - 1.19411i) q^{21} +(0.199921 + 1.13381i) q^{23} +(6.61450 + 5.55023i) q^{25} +(2.94041 + 4.28416i) q^{27} +(-3.27035 - 2.74415i) q^{29} +(-1.17254 - 6.64983i) q^{31} +(-4.84018 + 0.125718i) q^{33} +(1.44852 - 2.50892i) q^{35} +(-4.74640 - 8.22100i) q^{37} +(-3.83267 + 1.50879i) q^{39} +(-4.24300 + 3.56030i) q^{41} +(-7.82509 + 2.84810i) q^{43} +(6.02931 + 9.29295i) q^{45} +(2.04415 - 11.5930i) q^{47} +(5.99941 + 2.18361i) q^{49} +(0.970441 + 4.77505i) q^{51} +14.2600 q^{53} -10.3221 q^{55} +(4.24534 - 3.75436i) q^{57} +(-1.69317 - 0.616264i) q^{59} +(-1.27314 + 7.22031i) q^{61} +(1.72209 - 1.60451i) q^{63} +(-8.25151 + 3.00331i) q^{65} +(-7.76236 + 6.51339i) q^{67} +(-0.295165 + 1.97214i) q^{69} +(-5.54743 - 9.60843i) q^{71} +(4.31723 - 7.47766i) q^{73} +(7.81158 + 12.7534i) q^{75} +(0.380849 + 2.15990i) q^{77} +(-0.504702 - 0.423495i) q^{79} +(2.47340 + 8.65346i) q^{81} +(9.80329 + 8.22594i) q^{83} +(1.80384 + 10.2301i) q^{85} +(-3.86220 - 6.30554i) q^{87} +(4.53244 - 7.85041i) q^{89} +(0.932890 + 1.61581i) q^{91} +(1.73116 - 11.5667i) q^{93} +(9.25529 - 7.76611i) q^{95} +(4.09676 - 1.49110i) q^{97} +(-8.01879 - 2.45531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) $ 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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			0
$2$		0			0
$3$	1.64243	+	0.549936i	0.948256	+	0.317506i
$3$	1.64243	+	0.549936i	0.948256	+	0.317506i
$4$		0			0
$5$	3.46982	+	1.26291i	1.55175	+	0.564792i	0.968828	−	0.247735i	$-0.0796862\pi$
$5$	3.46982	+	1.26291i	1.55175	+	0.564792i	0.582924	+	0.812526i	$0.301908\pi$
$6$		0			0
$7$	0.136240	−	0.772655i	0.0514939	−	0.292036i	−0.948176	−	0.317747i	$-0.897074\pi$
$7$	0.136240	−	0.772655i	0.0514939	−	0.292036i	0.999669	+	0.0257107i	$0.00818487\pi$
$8$		0			0
$9$	2.39514	+	1.80646i	0.798380	+	0.602153i
$10$		0			0
$11$	−2.62684	+	0.956091i	−0.792022	+	0.288272i	−0.706176	−	0.708036i	$-0.749581\pi$
$11$	−2.62684	+	0.956091i	−0.792022	+	0.288272i	−0.0858456	+	0.996308i	$0.527359\pi$
$12$		0			0
$13$	−1.82171	+	1.52860i	−0.505253	+	0.423957i	−0.859455	−	0.511212i	$-0.829197\pi$
$13$	−1.82171	+	1.52860i	−0.505253	+	0.423957i	0.354202	+	0.935169i	$0.384752\pi$
$14$		0			0
$15$	5.00441	+	3.98242i	1.29213	+	1.02826i
$16$		0			0
$17$	1.40662	+	2.43633i	0.341155	+	0.590897i	0.984647	−	0.174555i	$-0.0558487\pi$
$17$	1.40662	+	2.43633i	0.341155	+	0.590897i	−0.643493	+	0.765452i	$0.722515\pi$
$18$		0			0
$19$	1.63600	−	2.83364i	0.375325	−	0.650082i	−0.615050	−	0.788488i	$-0.710864\pi$
$19$	1.63600	−	2.83364i	0.375325	−	0.650082i	0.990376	+	0.138405i	$0.0441977\pi$
$20$		0			0
$21$	0.648675	−	1.19411i	0.141553	−	0.260576i
$22$		0			0
$23$	0.199921	+	1.13381i	0.0416863	+	0.236415i	0.998531	−	0.0541853i	$-0.0172562\pi$
$23$	0.199921	+	1.13381i	0.0416863	+	0.236415i	−0.956845	+	0.290600i	$0.906145\pi$
$24$		0			0
$25$	6.61450	+	5.55023i	1.32290	+	1.11005i
$26$		0			0
$27$	2.94041	+	4.28416i	0.565882	+	0.824486i
$28$		0			0
$29$	−3.27035	−	2.74415i	−0.607288	−	0.509575i	0.286491	−	0.958083i	$-0.407511\pi$
$29$	−3.27035	−	2.74415i	−0.607288	−	0.509575i	−0.893779	+	0.448508i	$0.851956\pi$
$30$		0			0
$31$	−1.17254	−	6.64983i	−0.210595	−	1.19434i	−0.888389	−	0.459092i	$-0.848175\pi$
$31$	−1.17254	−	6.64983i	−0.210595	−	1.19434i	0.677793	−	0.735252i	$-0.262936\pi$
$32$		0			0
$33$	−4.84018	+	0.125718i	−0.842568	+	0.0218847i
$34$		0			0
$35$	1.44852	−	2.50892i	0.244845	−	0.424085i
$36$		0			0
$37$	−4.74640	−	8.22100i	−0.780303	−	1.35152i	−0.931765	−	0.363062i	$-0.881731\pi$
$37$	−4.74640	−	8.22100i	−0.780303	−	1.35152i	0.151462	−	0.988463i	$-0.451602\pi$
$38$		0			0
$39$	−3.83267	+	1.50879i	−0.613718	+	0.241600i
$40$		0			0
$41$	−4.24300	+	3.56030i	−0.662645	+	0.556025i	−0.910878	−	0.412675i	$-0.864594\pi$
$41$	−4.24300	+	3.56030i	−0.662645	+	0.556025i	0.248233	+	0.968700i	$0.420150\pi$
$42$		0			0
$43$	−7.82509	+	2.84810i	−1.19331	+	0.434331i	−0.860886	−	0.508798i	$-0.830090\pi$
$43$	−7.82509	+	2.84810i	−1.19331	+	0.434331i	−0.332428	+	0.943129i	$0.607868\pi$
$44$		0			0
$45$	6.02931	+	9.29295i	0.898797	+	1.38531i
$46$		0			0
$47$	2.04415	−	11.5930i	0.298170	−	1.69101i	−0.355859	−	0.934539i	$-0.615812\pi$
$47$	2.04415	−	11.5930i	0.298170	−	1.69101i	0.654030	−	0.756469i	$-0.273077\pi$
$48$		0			0
$49$	5.99941	+	2.18361i	0.857059	+	0.311944i
$50$		0			0
$51$	0.970441	+	4.77505i	0.135889	+	0.668641i
$52$		0			0
$53$	14.2600			1.95876			0.979380	−	0.202027i	$-0.0647529\pi$
$53$	14.2600			1.95876			0.979380	+	0.202027i	$0.0647529\pi$
$54$		0			0
$55$	−10.3221			−1.39184
$56$		0			0
$57$	4.24534	−	3.75436i	0.562309	−	0.497277i
$58$		0			0
$59$	−1.69317	−	0.616264i	−0.220432	−	0.0802307i	0.229443	−	0.973322i	$-0.426309\pi$
$59$	−1.69317	−	0.616264i	−0.220432	−	0.0802307i	−0.449875	+	0.893091i	$0.648532\pi$
$60$		0			0
$61$	−1.27314	+	7.22031i	−0.163008	+	0.924466i	0.788086	+	0.615565i	$0.211072\pi$
$61$	−1.27314	+	7.22031i	−0.163008	+	0.924466i	−0.951094	+	0.308901i	$0.900039\pi$
$62$		0			0
$63$	1.72209	−	1.60451i	0.216962	−	0.202149i
$64$		0			0
$65$	−8.25151	+	3.00331i	−1.02347	+	0.372514i
$66$		0			0
$67$	−7.76236	+	6.51339i	−0.948323	+	0.795737i	−0.979014	−	0.203791i	$-0.934674\pi$
$67$	−7.76236	+	6.51339i	−0.948323	+	0.795737i	0.0306914	+	0.999529i	$0.490229\pi$
$68$		0			0
$69$	−0.295165	+	1.97214i	−0.0355337	+	0.237418i
$70$		0			0
$71$	−5.54743	−	9.60843i	−0.658359	−	1.14031i	−0.981040	−	0.193803i	$-0.937918\pi$
$71$	−5.54743	−	9.60843i	−0.658359	−	1.14031i	0.322682	−	0.946508i	$-0.395416\pi$
$72$		0			0
$73$	4.31723	−	7.47766i	0.505293	−	0.875194i	−0.494688	−	0.869071i	$-0.664718\pi$
$73$	4.31723	−	7.47766i	0.505293	−	0.875194i	0.999981	−	0.00612295i	$-0.00194901\pi$
$74$		0			0
$75$	7.81158	+	12.7534i	0.902003	+	1.47264i
$76$		0			0
$77$	0.380849	+	2.15990i	0.0434017	+	0.246143i
$78$		0			0
$79$	−0.504702	−	0.423495i	−0.0567834	−	0.0476470i	0.613954	−	0.789342i	$-0.289578\pi$
$79$	−0.504702	−	0.423495i	−0.0567834	−	0.0476470i	−0.670738	+	0.741695i	$0.734022\pi$
$80$		0			0
$81$	2.47340	+	8.65346i	0.274822	+	0.961495i
$82$		0			0
$83$	9.80329	+	8.22594i	1.07605	+	0.902914i	0.995587	−	0.0938438i	$-0.0299154\pi$
$83$	9.80329	+	8.22594i	1.07605	+	0.902914i	0.0804638	+	0.996758i	$0.474360\pi$
$84$		0			0
$85$	1.80384	+	10.2301i	0.195654	+	1.10961i
$86$		0			0
$87$	−3.86220	−	6.30554i	−0.414072	−	0.676025i
$88$		0			0
$89$	4.53244	−	7.85041i	0.480437	−	0.832142i	−0.519311	−	0.854585i	$-0.673811\pi$
$89$	4.53244	−	7.85041i	0.480437	−	0.832142i	0.999748	+	0.0224438i	$0.00714467\pi$
$90$		0			0
$91$	0.932890	+	1.61581i	0.0977935	+	0.169383i
$92$		0			0
$93$	1.73116	−	11.5667i	0.179513	−	1.19941i
$94$		0			0
$95$	9.25529	−	7.76611i	0.949573	−	0.796786i
$96$		0			0
$97$	4.09676	−	1.49110i	0.415962	−	0.151398i	−0.125557	−	0.992086i	$-0.540072\pi$
$97$	4.09676	−	1.49110i	0.415962	−	0.151398i	0.541519	+	0.840689i	$0.317849\pi$
$98$		0			0
$99$	−8.01879	−	2.45531i	−0.805919	−	0.246768i
$100$		0			0
$101$	−0.172914	+	0.980644i	−0.0172056	+	0.0975777i	−0.992201	−	0.124646i	$-0.960220\pi$
$101$	−0.172914	+	0.980644i	−0.0172056	+	0.0975777i	0.974996	+	0.222224i	$0.0713316\pi$
$102$		0			0
$103$	−5.12606	−	1.86573i	−0.505086	−	0.183836i	0.0768942	−	0.997039i	$-0.475500\pi$
$103$	−5.12606	−	1.86573i	−0.505086	−	0.183836i	−0.581980	+	0.813203i	$0.697722\pi$
$104$		0			0
$105$	3.75884	−	3.32412i	0.366825	−	0.324401i
$106$		0			0
$107$	17.4135			1.68342			0.841711	−	0.539928i	$-0.181549\pi$
$107$	17.4135			1.68342			0.841711	+	0.539928i	$0.181549\pi$
$108$		0			0
$109$	−8.95114			−0.857364			−0.428682	−	0.903455i	$-0.641022\pi$
$109$	−8.95114			−0.857364			−0.428682	+	0.903455i	$0.641022\pi$
$110$		0			0
$111$	−3.27459	−	16.1126i	−0.310811	−	1.52934i
$112$		0			0
$113$	−0.693703	−	0.252487i	−0.0652581	−	0.0237520i	0.309185	−	0.951002i	$-0.399944\pi$
$113$	−0.693703	−	0.252487i	−0.0652581	−	0.0237520i	−0.374443	+	0.927250i	$0.622166\pi$
$114$		0			0
$115$	−0.738209	+	4.18659i	−0.0688383	+	0.390401i
$116$		0			0
$117$	−7.12462	+	0.370357i	−0.658671	+	0.0342395i
$118$		0			0
$119$	2.07408	−	0.754904i	0.190131	−	0.0692020i
$120$		0			0
$121$	−2.44032	+	2.04767i	−0.221847	+	0.186152i
$122$		0			0
$123$	−8.92675	+	3.51416i	−0.804898	+	0.316861i
$124$		0			0
$125$	6.71044	+	11.6228i	0.600200	+	1.03958i
$126$		0			0
$127$	−8.39687	+	14.5438i	−0.745102	+	1.29055i	0.205046	+	0.978752i	$0.434266\pi$
$127$	−8.39687	+	14.5438i	−0.745102	+	1.29055i	−0.950147	+	0.311801i	$0.899068\pi$
$128$		0			0
$129$	−14.4184	+	0.374501i	−1.26947	+	0.0329730i
$130$		0			0
$131$	−2.80858	−	15.9283i	−0.245387	−	1.39166i	−0.819592	−	0.572947i	$-0.805800\pi$
$131$	−2.80858	−	15.9283i	−0.245387	−	1.39166i	0.574205	−	0.818711i	$-0.305311\pi$
$132$		0			0
$133$	−1.96654	−	1.65012i	−0.170521	−	0.143084i
$134$		0			0
$135$	4.79219	+	18.5787i	0.412446	+	1.59900i
$136$		0			0
$137$	−14.7541	−	12.3802i	−1.26053	−	1.05771i	−0.995625	−	0.0934368i	$-0.970215\pi$
$137$	−14.7541	−	12.3802i	−1.26053	−	1.05771i	−0.264906	−	0.964274i	$-0.585341\pi$
$138$		0			0
$139$	2.45669	+	13.9326i	0.208374	+	1.18174i	0.892042	+	0.451952i	$0.149272\pi$
$139$	2.45669	+	13.9326i	0.208374	+	1.18174i	−0.683669	+	0.729793i	$0.739617\pi$
$140$		0			0
$141$	9.73276	−	17.9165i	0.819647	−	1.50884i
$142$		0			0
$143$	3.32387	−	5.75711i	0.277956	−	0.481434i
$144$		0			0
$145$	−7.88191	−	13.6519i	−0.654557	−	1.13373i
$146$		0			0
$147$	8.65276	+	6.88571i	0.713668	+	0.567924i
$148$		0			0
$149$	4.00955	−	3.36441i	0.328475	−	0.275623i	−0.463603	−	0.886043i	$-0.653444\pi$
$149$	4.00955	−	3.36441i	0.328475	−	0.275623i	0.792078	+	0.610420i	$0.208999\pi$
$150$		0			0
$151$	−2.08707	+	0.759631i	−0.169843	+	0.0618179i	−0.425542	−	0.904939i	$-0.639917\pi$
$151$	−2.08707	+	0.759631i	−0.169843	+	0.0618179i	0.255699	+	0.966756i	$0.417694\pi$
$152$		0			0
$153$	−1.03209	+	8.37636i	−0.0834397	+	0.677188i
$154$		0			0
$155$	4.32963	−	24.5546i	0.347764	−	1.97227i
$156$		0			0
$157$	−5.74887	−	2.09242i	−0.458809	−	0.166993i	0.102267	−	0.994757i	$-0.467390\pi$
$157$	−5.74887	−	2.09242i	−0.458809	−	0.166993i	−0.561076	+	0.827764i	$0.689613\pi$
$158$		0			0
$159$	23.4210	+	7.84208i	1.85741	+	0.621917i
$160$		0			0
$161$	0.903278			0.0711883
$162$		0			0
$163$	−10.0142			−0.784369			−0.392184	−	0.919887i	$-0.628280\pi$
$163$	−10.0142			−0.784369			−0.392184	+	0.919887i	$0.628280\pi$
$164$		0			0
$165$	−16.9534	−	5.67651i	−1.31982	−	0.441916i
$166$		0			0
$167$	14.1784	+	5.16052i	1.09716	+	0.399333i	0.826268	−	0.563277i	$-0.190460\pi$
$167$	14.1784	+	5.16052i	1.09716	+	0.399333i	0.270890	+	0.962610i	$0.412682\pi$
$168$		0			0
$169$	−1.27540	+	7.23316i	−0.0981077	+	0.556397i
$170$		0			0
$171$	9.03733	−	3.83160i	0.691102	−	0.293010i
$172$		0			0
$173$	−18.2705	+	6.64991i	−1.38908	+	0.505583i	−0.924918	−	0.380168i	$-0.875866\pi$
$173$	−18.2705	+	6.64991i	−1.38908	+	0.505583i	−0.464161	+	0.885751i	$0.653644\pi$
$174$		0			0
$175$	5.18957	−	4.35457i	0.392295	−	0.329174i
$176$		0			0
$177$	−2.44201	−	1.94330i	−0.183552	−	0.146068i
$178$		0			0
$179$	5.76902	+	9.99223i	0.431197	+	0.746855i	0.996977	−	0.0777016i	$-0.0247581\pi$
$179$	5.76902	+	9.99223i	0.431197	+	0.746855i	−0.565780	+	0.824556i	$0.691425\pi$
$180$		0			0
$181$	1.11311	−	1.92797i	0.0827372	−	0.143305i	−0.821688	−	0.569938i	$-0.806967\pi$
$181$	1.11311	−	1.92797i	0.0827372	−	0.143305i	0.904425	+	0.426633i	$0.140300\pi$
$182$		0			0
$183$	−6.06174	+	11.1587i	−0.448097	+	0.824875i
$184$		0			0
$185$	−6.08676	−	34.5197i	−0.447507	−	2.53794i
$186$		0			0
$187$	−6.02431	−	5.05500i	−0.440541	−	0.369658i
$188$		0			0
$189$	3.71078	−	1.68825i	0.269919	−	0.122802i
$190$		0			0
$191$	13.0184	+	10.9237i	0.941979	+	0.790415i	0.977929	−	0.208939i	$-0.0670010\pi$
$191$	13.0184	+	10.9237i	0.941979	+	0.790415i	−0.0359493	+	0.999354i	$0.511445\pi$
$192$		0			0
$193$	−3.89009	−	22.0618i	−0.280015	−	1.58804i	−0.722567	−	0.691301i	$-0.757038\pi$
$193$	−3.89009	−	22.0618i	−0.280015	−	1.58804i	0.442552	−	0.896743i	$-0.354073\pi$
$194$		0			0
$195$	−15.2041	+	0.394910i	−1.08879	+	0.0282801i
$196$		0			0
$197$	−3.55722	+	6.16128i	−0.253441	+	0.438973i	−0.964471	−	0.264189i	$-0.914896\pi$
$197$	−3.55722	+	6.16128i	−0.253441	+	0.438973i	0.711030	+	0.703162i	$0.248229\pi$
$198$		0			0
$199$	−1.05224	−	1.82253i	−0.0745912	−	0.129196i	0.826317	−	0.563205i	$-0.190432\pi$
$199$	−1.05224	−	1.82253i	−0.0745912	−	0.129196i	−0.900908	+	0.434009i	$0.857099\pi$
$200$		0			0
$201$	−16.3311	+	6.42898i	−1.15190	+	0.453465i
$202$		0			0
$203$	−2.56583	+	2.15299i	−0.180086	+	0.151110i
$204$		0			0
$205$	−19.2188	+	6.99507i	−1.34230	+	0.488557i
$206$		0			0
$207$	−1.56934	+	3.07677i	−0.109077	+	0.213851i
$208$		0			0
$209$	−1.58830	+	9.00769i	−0.109865	+	0.623075i
$210$		0			0
$211$	−16.6641	−	6.06522i	−1.14720	−	0.417547i	−0.302692	−	0.953088i	$-0.597885\pi$
$211$	−16.6641	−	6.06522i	−1.14720	−	0.417547i	−0.844509	+	0.535541i	$0.820108\pi$
$212$		0			0
$213$	−3.82723	−	18.8319i	−0.262238	−	1.29034i
$214$		0			0
$215$	−30.7486			−2.09703
$216$		0			0
$217$	−5.29777			−0.359636
$218$		0			0
$219$	11.2030	−	9.90732i	0.757026	−	0.669474i
$220$		0			0
$221$	−6.28663	−	2.28815i	−0.422884	−	0.153917i
$222$		0			0
$223$	2.85695	−	16.2026i	0.191315	−	1.08500i	−0.726254	−	0.687427i	$-0.758740\pi$
$223$	2.85695	−	16.2026i	0.191315	−	1.08500i	0.917569	−	0.397577i	$-0.130149\pi$
$224$		0			0
$225$	5.81640	+	25.2424i	0.387760	+	1.68283i
$226$		0			0
$227$	−26.6238	+	9.69027i	−1.76708	+	0.643166i	−0.767086	+	0.641545i	$0.778294\pi$
$227$	−26.6238	+	9.69027i	−1.76708	+	0.643166i	−0.999999	+	0.00162118i	$0.999484\pi$
$228$		0			0
$229$	21.7100	−	18.2169i	1.43464	−	1.20381i	0.491734	−	0.870746i	$-0.336363\pi$
$229$	21.7100	−	18.2169i	1.43464	−	1.20381i	0.942906	−	0.333060i	$-0.108081\pi$
$230$		0			0
$231$	−0.562290	+	3.75692i	−0.0369960	+	0.247187i
$232$		0			0
$233$	−0.199672	−	0.345842i	−0.0130809	−	0.0226569i	0.859411	−	0.511286i	$-0.170831\pi$
$233$	−0.199672	−	0.345842i	−0.0130809	−	0.0226569i	−0.872492	+	0.488629i	$0.837497\pi$
$234$		0			0
$235$	21.7338	−	37.6440i	1.41775	−	2.45562i
$236$		0			0
$237$	−0.596042	−	0.973115i	−0.0387171	−	0.0632106i
$238$		0			0
$239$	−0.462767	−	2.62448i	−0.0299339	−	0.169764i	0.966176	−	0.257884i	$-0.0830252\pi$
$239$	−0.462767	−	2.62448i	−0.0299339	−	0.169764i	−0.996110	+	0.0881201i	$0.971914\pi$
$240$		0			0
$241$	−10.4298	−	8.75168i	−0.671845	−	0.563745i	0.241766	−	0.970335i	$-0.422274\pi$
$241$	−10.4298	−	8.75168i	−0.671845	−	0.563745i	−0.913611	+	0.406589i	$0.866718\pi$
$242$		0			0
$243$	−0.696462	+	15.5729i	−0.0446781	+	0.999001i
$244$		0			0
$245$	18.0592	+	15.1535i	1.15376	+	0.968120i
$246$		0			0
$247$	1.35117	+	7.66288i	0.0859731	+	0.487578i
$248$		0			0
$249$	11.5775	+	18.9017i	0.733692	+	1.19785i
$250$		0			0
$251$	1.07612	−	1.86390i	0.0679242	−	0.117648i	−0.830063	−	0.557669i	$-0.811696\pi$
$251$	1.07612	−	1.86390i	0.0679242	−	0.117648i	0.897987	+	0.440021i	$0.145029\pi$
$252$		0			0
$253$	−1.60918	−	2.78718i	−0.101168	−	0.175229i
$254$		0			0
$255$	−2.66321	+	17.7942i	−0.166777	+	1.11431i
$256$		0			0
$257$	16.9755	−	14.2441i	1.05890	−	0.888523i	0.0648994	−	0.997892i	$-0.479327\pi$
$257$	16.9755	−	14.2441i	1.05890	−	0.888523i	0.994001	+	0.109369i	$0.0348829\pi$
$258$		0			0
$259$	−6.99865	+	2.54730i	−0.434875	+	0.158282i
$260$		0			0
$261$	−2.87575	−	12.4804i	−0.178004	−	0.772515i
$262$		0			0
$263$	1.18018	−	6.69313i	0.0727730	−	0.412716i	−0.926558	−	0.376151i	$-0.877247\pi$
$263$	1.18018	−	6.69313i	0.0727730	−	0.412716i	0.999331	−	0.0365650i	$-0.0116416\pi$
$264$		0			0
$265$	49.4796	+	18.0091i	3.03951	+	1.10629i
$266$		0			0
$267$	11.7614	−	10.4012i	0.719787	−	0.636542i
$268$		0			0
$269$	−4.37982			−0.267042			−0.133521	−	0.991046i	$-0.542628\pi$
$269$	−4.37982			−0.267042			−0.133521	+	0.991046i	$0.542628\pi$
$270$		0			0
$271$	−18.1524			−1.10268			−0.551341	−	0.834280i	$-0.685884\pi$
$271$	−18.1524			−1.10268			−0.551341	+	0.834280i	$0.685884\pi$
$272$		0			0
$273$	0.643612	+	3.16689i	0.0389532	+	0.191669i
$274$		0			0
$275$	−22.6818	−	8.25549i	−1.36776	−	0.497825i
$276$		0			0
$277$	−4.04143	+	22.9201i	−0.242826	+	1.37713i	0.582662	+	0.812714i	$0.302011\pi$
$277$	−4.04143	+	22.9201i	−0.242826	+	1.37713i	−0.825488	+	0.564420i	$0.809100\pi$
$278$		0			0
$279$	9.20424	−	18.0454i	0.551044	−	1.08035i
$280$		0			0
$281$	1.60746	−	0.585066i	0.0958928	−	0.0349021i	−0.293628	−	0.955920i	$-0.594863\pi$
$281$	1.60746	−	0.585066i	0.0958928	−	0.0349021i	0.389521	+	0.921018i	$0.372641\pi$
$282$		0			0
$283$	5.74480	−	4.82046i	0.341493	−	0.286547i	−0.455870	−	0.890046i	$-0.650672\pi$
$283$	5.74480	−	4.82046i	0.341493	−	0.286547i	0.797363	+	0.603499i	$0.206227\pi$
$284$		0			0
$285$	19.4720	−	7.66546i	1.15342	−	0.454063i
$286$		0			0
$287$	2.17282	+	3.76343i	0.128257	+	0.222148i
$288$		0			0
$289$	4.54286	−	7.86846i	0.267227	−	0.462851i
$290$		0			0
$291$	7.54863	−	0.196067i	0.442509	−	0.0114936i
$292$		0			0
$293$	−3.43831	−	19.4996i	−0.200868	−	1.13918i	−0.903810	−	0.427934i	$-0.859242\pi$
$293$	−3.43831	−	19.4996i	−0.200868	−	1.13918i	0.702942	−	0.711248i	$-0.251870\pi$
$294$		0			0
$295$	−5.09672	−	4.27665i	−0.296742	−	0.248996i
$296$		0			0
$297$	−11.8200	−	8.44249i	−0.685868	−	0.489883i
$298$		0			0
$299$	−2.09733	−	1.75987i	−0.121292	−	0.101776i
$300$		0			0
$301$	1.13451	+	6.43412i	0.0653920	+	0.370856i
$302$		0			0
$303$	−0.823290	+	1.51555i	−0.0472968	+	0.0870659i
$304$		0			0
$305$	−13.5362	+	23.4454i	−0.775079	+	1.34248i
$306$		0			0
$307$	15.1634	+	26.2638i	0.865422	+	1.49895i	0.866628	+	0.498955i	$0.166283\pi$
$307$	15.1634	+	26.2638i	0.865422	+	1.49895i	−0.00120595	+	0.999999i	$0.500384\pi$
$308$		0			0
$309$	−7.39316	−	5.88334i	−0.420582	−	0.334692i
$310$		0			0
$311$	−4.51159	+	3.78567i	−0.255829	+	0.214666i	−0.761677	−	0.647956i	$-0.775624\pi$
$311$	−4.51159	+	3.78567i	−0.255829	+	0.214666i	0.505849	+	0.862622i	$0.331179\pi$
$312$		0			0
$313$	−30.3326	+	11.0402i	−1.71450	+	0.624027i	−0.997341	−	0.0728818i	$-0.976780\pi$
$313$	−30.3326	+	11.0402i	−1.71450	+	0.624027i	−0.717160	+	0.696909i	$0.754558\pi$
$314$		0			0
$315$	8.00168	−	3.39251i	0.450844	−	0.191146i
$316$		0			0
$317$	−2.15961	+	12.2478i	−0.121296	+	0.687902i	0.862144	+	0.506664i	$0.169122\pi$
$317$	−2.15961	+	12.2478i	−0.121296	+	0.687902i	−0.983439	+	0.181238i	$0.941990\pi$
$318$		0			0
$319$	11.2143	+	4.08168i	0.627882	+	0.228530i
$320$		0			0
$321$	28.6004	+	9.57629i	1.59632	+	0.534496i
$322$		0			0
$323$	9.20493			0.512176
$324$		0			0
$325$	−20.5338			−1.13901
$326$		0			0
$327$	−14.7016	−	4.92255i	−0.813001	−	0.272218i
$328$		0			0
$329$	−8.67887	−	3.15885i	−0.478482	−	0.174153i
$330$		0			0
$331$	−2.30816	+	13.0902i	−0.126868	+	0.719503i	0.853313	+	0.521399i	$0.174590\pi$
$331$	−2.30816	+	13.0902i	−0.126868	+	0.719503i	−0.980181	+	0.198104i	$0.936522\pi$
$332$		0			0
$333$	3.48262	−	28.2646i	0.190847	−	1.54889i
$334$		0			0
$335$	−35.1599	+	12.7971i	−1.92099	+	0.699182i
$336$		0			0
$337$	12.7465	−	10.6956i	0.694347	−	0.582626i	−0.225812	−	0.974171i	$-0.572504\pi$
$337$	12.7465	−	10.6956i	0.694347	−	0.582626i	0.920159	+	0.391545i	$0.128059\pi$
$338$		0			0
$339$	−1.00051	−	0.796185i	−0.0543400	−	0.0432428i
$340$		0			0
$341$	9.43793	+	16.3470i	0.511092	+	0.885238i
$342$		0			0
$343$	5.25055	−	9.09422i	0.283503	−	0.491042i
$344$		0			0
$345$	−3.51481	+	6.47020i	−0.189231	+	0.348344i
$346$		0			0
$347$	4.64888	+	26.3651i	0.249565	+	1.41535i	0.809648	+	0.586916i	$0.199658\pi$
$347$	4.64888	+	26.3651i	0.249565	+	1.41535i	−0.560083	+	0.828436i	$0.689231\pi$
$348$		0			0
$349$	−1.16438	−	0.977030i	−0.0623278	−	0.0522992i	0.611092	−	0.791560i	$-0.290731\pi$
$349$	−1.16438	−	0.977030i	−0.0623278	−	0.0522992i	−0.673419	+	0.739261i	$0.735175\pi$
$350$		0			0
$351$	−11.9053	−	3.30980i	−0.635460	−	0.176664i
$352$		0			0
$353$	−8.76553	−	7.35516i	−0.466542	−	0.391475i	0.378989	−	0.925401i	$-0.376272\pi$
$353$	−8.76553	−	7.35516i	−0.466542	−	0.391475i	−0.845531	+	0.533926i	$0.820716\pi$
$354$		0			0
$355$	−7.11400	−	40.3455i	−0.377572	−	2.14132i
$356$		0			0
$357$	3.82168	−	0.0992637i	0.202265	−	0.00525359i
$358$		0			0
$359$	−1.09908	+	1.90366i	−0.0580073	+	0.100472i	−0.893571	−	0.448922i	$-0.851808\pi$
$359$	−1.09908	+	1.90366i	−0.0580073	+	0.100472i	0.835564	+	0.549394i	$0.185141\pi$
$360$		0			0
$361$	4.14698	+	7.18278i	0.218262	+	0.378041i
$362$		0			0
$363$	−5.13413	+	2.02113i	−0.269472	+	0.106082i
$364$		0			0
$365$	24.4236	−	20.4939i	1.27839	−	1.07270i
$366$		0			0
$367$	25.2409	−	9.18693i	1.31756	−	0.479554i	0.414886	−	0.909873i	$-0.363821\pi$
$367$	25.2409	−	9.18693i	1.31756	−	0.479554i	0.902677	+	0.430320i	$0.141599\pi$
$368$		0			0
$369$	−16.5941	+	0.862607i	−0.863855	+	0.0449055i
$370$		0			0
$371$	1.94278	−	11.0181i	0.100864	−	0.572029i
$372$		0			0
$373$	0.827349	+	0.301130i	0.0428385	+	0.0155919i	0.363351	−	0.931653i	$-0.381633\pi$
$373$	0.827349	+	0.301130i	0.0428385	+	0.0155919i	−0.320512	+	0.947244i	$0.603855\pi$
$374$		0			0
$375$	4.62961	+	22.7800i	0.239072	+	1.17635i
$376$		0			0
$377$	10.1523			0.522872
$378$		0			0
$379$	0.359229			0.0184524			0.00922619	−	0.999957i	$-0.497063\pi$
$379$	0.359229			0.0184524			0.00922619	+	0.999957i	$0.497063\pi$
$380$		0			0
$381$	−21.7894	+	19.2694i	−1.11631	+	0.987202i
$382$		0			0
$383$	9.66660	+	3.51836i	0.493940	+	0.179780i	0.576967	−	0.816768i	$-0.304236\pi$
$383$	9.66660	+	3.51836i	0.493940	+	0.179780i	−0.0830262	+	0.996547i	$0.526459\pi$
$384$		0			0
$385$	−1.40629	+	7.97545i	−0.0716710	+	0.406466i
$386$		0			0
$387$	−23.8872	−	7.31411i	−1.21425	−	0.371797i
$388$		0			0
$389$	−8.86628	+	3.22706i	−0.449538	+	0.163619i	−0.556861	−	0.830606i	$-0.687994\pi$
$389$	−8.86628	+	3.22706i	−0.449538	+	0.163619i	0.107323	+	0.994224i	$0.465772\pi$
$390$		0			0
$391$	−2.48112	+	2.08190i	−0.125475	+	0.105286i
$392$		0			0
$393$	4.14663	−	27.7056i	0.209170	−	1.39756i
$394$		0			0
$395$	−1.21639	−	2.10685i	−0.0612032	−	0.106007i
$396$		0			0
$397$	−5.15730	+	8.93271i	−0.258837	+	0.448320i	−0.965931	−	0.258801i	$-0.916673\pi$
$397$	−5.15730	+	8.93271i	−0.258837	+	0.448320i	0.707093	+	0.707120i	$0.250006\pi$
$398$		0			0
$399$	−2.32244	−	3.79168i	−0.116267	−	0.189821i
$400$		0			0
$401$	−0.293768	−	1.66604i	−0.0146701	−	0.0831982i	0.976594	−	0.215092i	$-0.0690052\pi$
$401$	−0.293768	−	1.66604i	−0.0146701	−	0.0831982i	−0.991264	+	0.131894i	$0.957894\pi$
$402$		0			0
$403$	12.3010	+	10.3217i	0.612755	+	0.514162i
$404$		0			0
$405$	−2.34629	+	33.1496i	−0.116588	+	1.64722i
$406$		0			0
$407$	20.3281	+	17.0573i	1.00762	+	0.845497i
$408$		0			0
$409$	−1.33335	−	7.56178i	−0.0659297	−	0.373906i	−0.999864	−	0.0164625i	$-0.994760\pi$
$409$	−1.33335	−	7.56178i	−0.0659297	−	0.373906i	0.933935	−	0.357444i	$-0.116352\pi$
$410$		0			0
$411$	−17.4243	−	28.4474i	−0.859477	−	1.40321i
$412$		0			0
$413$	−0.706837	+	1.22428i	−0.0347812	+	0.0602428i
$414$		0			0
$415$	23.6270	+	40.9232i	1.15981	+	2.00884i
$416$		0			0
$417$	−3.62709	+	24.2343i	−0.177619	+	1.18676i
$418$		0			0
$419$	−6.04653	+	5.07364i	−0.295392	+	0.247864i	−0.778423	−	0.627740i	$-0.783980\pi$
$419$	−6.04653	+	5.07364i	−0.295392	+	0.247864i	0.483031	+	0.875603i	$0.339536\pi$
$420$		0			0
$421$	−14.8809	+	5.41621i	−0.725251	+	0.263970i	−0.678153	−	0.734920i	$-0.737219\pi$
$421$	−14.8809	+	5.41621i	−0.725251	+	0.263970i	−0.0470978	+	0.998890i	$0.514997\pi$
$422$		0			0
$423$	25.8383	−	24.0741i	1.25630	−	1.17052i
$424$		0			0
$425$	−4.21812	+	23.9222i	−0.204609	+	1.16040i
$426$		0			0
$427$	5.40536	+	1.96739i	0.261584	+	0.0952087i
$428$		0			0
$429$	8.62526	−	7.62773i	0.416431	−	0.368270i
$430$		0			0
$431$	20.9171			1.00754			0.503770	−	0.863838i	$-0.331946\pi$
$431$	20.9171			1.00754			0.503770	+	0.863838i	$0.331946\pi$
$432$		0			0
$433$	9.36489			0.450048			0.225024	−	0.974353i	$-0.427754\pi$
$433$	9.36489			0.450048			0.225024	+	0.974353i	$0.427754\pi$
$434$		0			0
$435$	−5.43782	−	26.7567i	−0.260723	−	1.28289i
$436$		0			0
$437$	3.53987	+	1.28841i	0.169335	+	0.0616329i
$438$		0			0
$439$	−3.92216	+	22.2437i	−0.187195	+	1.06163i	0.735909	+	0.677081i	$0.236755\pi$
$439$	−3.92216	+	22.2437i	−0.187195	+	1.06163i	−0.923103	+	0.384552i	$0.874356\pi$
$440$		0			0
$441$	10.4248	+	16.0678i	0.496421	+	0.765131i
$442$		0			0
$443$	38.4509	−	13.9950i	1.82686	−	0.664922i	0.833132	−	0.553075i	$-0.186546\pi$
$443$	38.4509	−	13.9950i	1.82686	−	0.664922i	0.993725	−	0.111847i	$-0.0356767\pi$
$444$		0			0
$445$	25.6411	−	21.5155i	1.21551	−	1.01993i
$446$		0			0
$447$	8.43560	−	3.32081i	0.398990	−	0.157069i
$448$		0			0
$449$	8.21768	+	14.2334i	0.387816	+	0.671718i	0.992156	−	0.125010i	$-0.0398962\pi$
$449$	8.21768	+	14.2334i	0.387816	+	0.671718i	−0.604339	+	0.796727i	$0.706563\pi$
$450$		0			0
$451$	7.74170	−	13.4090i	0.364542	−	0.631406i
$452$		0			0
$453$	−3.84561	+	0.0998852i	−0.180682	+	0.00469302i
$454$		0			0
$455$	1.19633	+	6.78475i	0.0560850	+	0.318074i
$456$		0			0
$457$	19.9037	+	16.7012i	0.931056	+	0.781249i	0.976007	−	0.217741i	$-0.0698687\pi$
$457$	19.9037	+	16.7012i	0.931056	+	0.781249i	−0.0449508	+	0.998989i	$0.514313\pi$
$458$		0			0
$459$	−6.30159	+	13.1900i	−0.294133	+	0.615655i
$460$		0			0
$461$	13.6701	+	11.4705i	0.636678	+	0.534236i	0.902996	−	0.429649i	$-0.141363\pi$
$461$	13.6701	+	11.4705i	0.636678	+	0.534236i	−0.266318	+	0.963885i	$0.585807\pi$
$462$		0			0
$463$	4.05701	+	23.0084i	0.188545	+	1.06929i	0.921315	+	0.388816i	$0.127116\pi$
$463$	4.05701	+	23.0084i	0.188545	+	1.06929i	−0.732770	+	0.680476i	$0.761773\pi$
$464$		0			0
$465$	20.6145	−	37.9481i	0.955976	−	1.75980i
$466$		0			0
$467$	−5.34976	+	9.26605i	−0.247557	+	0.428782i	−0.962847	−	0.270046i	$-0.912961\pi$
$467$	−5.34976	+	9.26605i	−0.247557	+	0.428782i	0.715290	+	0.698827i	$0.246294\pi$
$468$		0			0
$469$	3.97506	+	6.88501i	0.183551	+	0.317920i
$470$		0			0
$471$	−8.29141	−	6.59815i	−0.382048	−	0.304027i
$472$		0			0
$473$	17.8322	−	14.9630i	0.819925	−	0.687999i
$474$		0			0
$475$	26.5487	−	9.66294i	1.21814	−	0.443366i
$476$		0			0
$477$	34.1547	+	25.7601i	1.56384	+	1.17947i
$478$		0			0
$479$	−7.31754	+	41.4998i	−0.334347	+	1.89617i	0.0992413	+	0.995063i	$0.468358\pi$
$479$	−7.31754	+	41.4998i	−0.334347	+	1.89617i	−0.433588	+	0.901111i	$0.642753\pi$
$480$		0			0
$481$	21.2132	+	7.72098i	0.967239	+	0.352046i
$482$		0			0
$483$	1.48357	+	0.496745i	0.0675048	+	0.0226027i
$484$		0			0
$485$	16.0981			0.730979
$486$		0			0
$487$	−13.2206			−0.599081			−0.299540	−	0.954084i	$-0.596833\pi$
$487$	−13.2206			−0.599081			−0.299540	+	0.954084i	$0.596833\pi$
$488$		0			0
$489$	−16.4475	−	5.50714i	−0.743783	−	0.249042i
$490$		0			0
$491$	4.06541	+	1.47969i	0.183470	+	0.0667775i	0.432121	−	0.901815i	$-0.357765\pi$
$491$	4.06541	+	1.47969i	0.183470	+	0.0667775i	−0.248652	+	0.968593i	$0.579987\pi$
$492$		0			0
$493$	2.08553	−	11.8276i	0.0939274	−	0.532689i
$494$		0			0
$495$	−24.7230	−	18.6465i	−1.11121	−	0.838099i
$496$		0			0
$497$	−8.17979	+	2.97720i	−0.366914	+	0.133546i
$498$		0			0
$499$	−17.4218	+	14.6186i	−0.779908	+	0.654421i	−0.943226	−	0.332153i	$-0.892225\pi$
$499$	−17.4218	+	14.6186i	−0.779908	+	0.654421i	0.163317	+	0.986574i	$0.447781\pi$
$500$		0			0
$501$	20.4491	+	16.2730i	0.913597	+	0.727024i
$502$		0			0
$503$	−2.95861	−	5.12446i	−0.131918	−	0.228488i	0.792498	−	0.609874i	$-0.208780\pi$
$503$	−2.95861	−	5.12446i	−0.131918	−	0.228488i	−0.924416	+	0.381386i	$0.875447\pi$
$504$		0			0
$505$	−1.83845	+	3.18429i	−0.0818099	+	0.141699i
$506$		0			0
$507$	−6.07253	+	11.1786i	−0.269690	+	0.496457i
$508$		0			0
$509$	1.40592	+	7.97339i	0.0623165	+	0.353414i	0.999983	+	0.00587734i	$0.00187083\pi$
$509$	1.40592	+	7.97339i	0.0623165	+	0.353414i	−0.937666	+	0.347537i	$0.887018\pi$
$510$		0			0
$511$	−5.18947	−	4.35448i	−0.229569	−	0.192631i
$512$		0			0
$513$	16.9503	−	1.32317i	0.748374	−	0.0584195i
$514$		0			0
$515$	−15.4303	−	12.9475i	−0.679939	−	0.570537i
$516$		0			0
$517$	5.71427	+	32.4073i	0.251314	+	1.42527i
$518$		0			0
$519$	−33.6650	+	0.874408i	−1.47773	+	0.0383823i
$520$		0			0
$521$	−1.21522	+	2.10482i	−0.0532398	+	0.0922140i	−0.891417	−	0.453184i	$-0.850288\pi$
$521$	−1.21522	+	2.10482i	−0.0532398	+	0.0922140i	0.838177	+	0.545398i	$0.183621\pi$
$522$		0			0
$523$	−8.49730	−	14.7178i	−0.371561	−	0.643563i	0.618245	−	0.785986i	$-0.287844\pi$
$523$	−8.49730	−	14.7178i	−0.371561	−	0.643563i	−0.989806	+	0.142423i	$0.954511\pi$
$524$		0			0
$525$	10.9182	−	4.29813i	0.476511	−	0.187586i
$526$		0			0
$527$	14.5519	−	12.2105i	0.633889	−	0.531896i
$528$		0			0
$529$	20.3674	−	7.41312i	0.885538	−	0.322310i
$530$		0			0
$531$	−2.94213	−	4.53468i	−0.127677	−	0.196789i
$532$		0			0
$533$	2.28726	−	12.9717i	0.0990722	−	0.561866i
$534$		0			0
$535$	60.4216	+	21.9917i	2.61225	+	0.950783i
$536$		0			0
$537$	3.98011	+	19.5841i	0.171755	+	0.845117i
$538$		0			0
$539$	−17.8472			−0.768734
$540$		0			0
$541$	4.67548			0.201015			0.100507	−	0.994936i	$-0.467953\pi$
$541$	4.67548			0.201015			0.100507	+	0.994936i	$0.467953\pi$
$542$		0			0
$543$	2.88847	−	2.55441i	0.123956	−	0.109620i
$544$		0			0
$545$	−31.0589	−	11.3045i	−1.33042	−	0.484232i
$546$		0			0
$547$	−2.32170	+	13.1670i	−0.0992686	+	0.562980i	0.894087	+	0.447894i	$0.147826\pi$
$547$	−2.32170	+	13.1670i	−0.0992686	+	0.562980i	−0.993355	+	0.115087i	$0.963285\pi$
$548$		0			0
$549$	−16.0926	+	14.9938i	−0.686813	+	0.639920i
$550$		0			0
$551$	−13.1262	+	4.77756i	−0.559196	+	0.203531i
$552$		0			0
$553$	−0.395977	+	0.332264i	−0.0168386	+	0.0141293i
$554$		0			0
$555$	8.98657	−	60.0435i	0.381459	−	2.54870i
$556$		0			0
$557$	13.7017	+	23.7321i	0.580561	+	1.00556i	0.995413	+	0.0956725i	$0.0305002\pi$
$557$	13.7017	+	23.7321i	0.580561	+	1.00556i	−0.414852	+	0.909889i	$0.636167\pi$
$558$		0			0
$559$	9.90147	−	17.1498i	0.418787	−	0.725361i
$560$		0			0
$561$	−7.11457	−	11.6155i	−0.300378	−	0.490405i
$562$		0			0
$563$	1.25534	+	7.11937i	0.0529061	+	0.300046i	0.999767	−	0.0215986i	$-0.00687560\pi$
$563$	1.25534	+	7.11937i	0.0529061	+	0.300046i	−0.946861	+	0.321644i	$0.895764\pi$
$564$		0			0
$565$	−2.08816	−	1.75217i	−0.0878495	−	0.0737145i
$566$		0			0
$567$	7.02311	−	0.732140i	0.294943	−	0.0307470i
$568$		0			0
$569$	−10.9664	−	9.20193i	−0.459737	−	0.385765i	0.383297	−	0.923625i	$-0.374788\pi$
$569$	−10.9664	−	9.20193i	−0.459737	−	0.385765i	−0.843034	+	0.537860i	$0.819233\pi$
$570$		0			0
$571$	1.60526	+	9.10386i	0.0671779	+	0.380985i	0.999797	+	0.0201238i	$0.00640604\pi$
$571$	1.60526	+	9.10386i	0.0671779	+	0.380985i	−0.932620	+	0.360861i	$0.882483\pi$
$572$		0			0
$573$	15.3745	+	25.1008i	0.642277	+	1.04860i
$574$		0			0
$575$	−4.97051	+	8.60917i	−0.207284	+	0.359027i
$576$		0			0
$577$	−11.4500	−	19.8320i	−0.476671	−	0.825618i	0.522972	−	0.852350i	$-0.324823\pi$
$577$	−11.4500	−	19.8320i	−0.476671	−	0.825618i	−0.999643	+	0.0267323i	$0.991490\pi$
$578$		0			0
$579$	5.74338	−	38.3742i	0.238687	−	1.59478i
$580$		0			0
$581$	7.69141	−	6.45386i	0.319094	−	0.267751i
$582$		0			0
$583$	−37.4587	+	13.6338i	−1.55138	+	0.564656i
$584$		0			0
$585$	−25.1889	−	7.71269i	−1.04143	−	0.318881i
$586$		0			0
$587$	1.80298	−	10.2252i	0.0744171	−	0.422040i	−0.924725	−	0.380635i	$-0.875705\pi$
$587$	1.80298	−	10.2252i	0.0744171	−	0.422040i	0.999142	−	0.0414052i	$-0.0131834\pi$
$588$		0			0
$589$	−20.7615	−	7.55658i	−0.855464	−	0.311363i
$590$		0			0
$591$	−9.23078	+	8.16322i	−0.379704	+	0.335790i
$592$		0			0
$593$	8.03385			0.329911			0.164955	−	0.986301i	$-0.447252\pi$
$593$	8.03385			0.329911			0.164955	+	0.986301i	$0.447252\pi$
$594$		0			0
$595$	8.15008			0.334121
$596$		0			0
$597$	−0.725951	−	3.57204i	−0.0297112	−	0.146194i
$598$		0			0
$599$	−3.56554	−	1.29775i	−0.145684	−	0.0530247i	0.268149	−	0.963377i	$-0.413588\pi$
$599$	−3.56554	−	1.29775i	−0.145684	−	0.0530247i	−0.413833	+	0.910353i	$0.635810\pi$
$600$		0			0
$601$	−1.65470	+	9.38427i	−0.0674966	+	0.382792i	0.932282	+	0.361733i	$0.117815\pi$
$601$	−1.65470	+	9.38427i	−0.0674966	+	0.382792i	−0.999778	+	0.0210590i	$0.993296\pi$
$602$		0			0
$603$	−30.3581	+	1.57810i	−1.23628	+	0.0642651i
$604$		0			0
$605$	−11.0535	+	4.02314i	−0.449388	+	0.163564i
$606$		0			0
$607$	24.9254	−	20.9149i	1.01169	−	0.848911i	0.0231313	−	0.999732i	$-0.492636\pi$
$607$	24.9254	−	20.9149i	1.01169	−	0.848911i	0.988561	+	0.150822i	$0.0481920\pi$
$608$		0			0
$609$	−5.39820	+	2.12509i	−0.218746	+	0.0861128i
$610$		0			0
$611$	13.9971	+	24.2438i	0.566264	+	0.980798i
$612$		0			0
$613$	7.36210	−	12.7515i	0.297353	−	0.515030i	−0.678177	−	0.734899i	$-0.737230\pi$
$613$	7.36210	−	12.7515i	0.297353	−	0.515030i	0.975529	+	0.219869i	$0.0705630\pi$
$614$		0			0
$615$	−35.4123	+	0.919794i	−1.42796	+	0.0370897i
$616$		0			0
$617$	3.24374	+	18.3962i	0.130588	+	0.740603i	0.977831	+	0.209396i	$0.0671499\pi$
$617$	3.24374	+	18.3962i	0.130588	+	0.740603i	−0.847243	+	0.531206i	$0.821739\pi$
$618$		0			0
$619$	32.6479	+	27.3949i	1.31223	+	1.10109i	0.987891	+	0.155152i	$0.0495867\pi$
$619$	32.6479	+	27.3949i	1.31223	+	1.10109i	0.324340	+	0.945940i	$0.394858\pi$
$620$		0			0
$621$	−4.26955	+	4.19035i	−0.171331	+	0.168153i
$622$		0			0
$623$	−5.44816	−	4.57155i	−0.218276	−	0.183155i
$624$		0			0
$625$	1.10850	+	6.28660i	0.0443399	+	0.251464i
$626$		0			0
$627$	−7.56232	+	13.9210i	−0.302010	+	0.555952i
$628$		0			0
$629$	13.3527	−	23.1276i	0.532408	−	0.922158i
$630$		0			0
$631$	12.1590	+	21.0600i	0.484041	+	0.838384i	0.999832	−	0.0183305i	$-0.00583511\pi$
$631$	12.1590	+	21.0600i	0.484041	+	0.838384i	−0.515791	+	0.856715i	$0.672502\pi$
$632$		0			0
$633$	−24.0340	−	19.1259i	−0.955267	−	0.760185i
$634$		0			0
$635$	−47.5032	+	39.8599i	−1.88511	+	1.58179i
$636$		0			0
$637$	−14.2671	+	5.19279i	−0.565282	+	0.205746i
$638$		0			0
$639$	4.07037	−	33.0348i	0.161021	−	1.30683i
$640$		0			0
$641$	−3.28469	+	18.6284i	−0.129738	+	0.735778i	0.848643	+	0.528966i	$0.177420\pi$
$641$	−3.28469	+	18.6284i	−0.129738	+	0.735778i	−0.978381	+	0.206812i	$0.933691\pi$
$642$		0			0
$643$	−21.0384	−	7.65736i	−0.829675	−	0.301977i	−0.107949	−	0.994156i	$-0.534428\pi$
$643$	−21.0384	−	7.65736i	−0.829675	−	0.301977i	−0.721725	+	0.692180i	$0.756651\pi$
$644$		0			0
$645$	−50.5023	−	16.9097i	−1.98853	−	0.665820i
$646$		0			0
$647$	−30.4106			−1.19557			−0.597783	−	0.801658i	$-0.703951\pi$
$647$	−30.4106			−1.19557			−0.597783	+	0.801658i	$0.703951\pi$
$648$		0			0
$649$	5.03689			0.197715
$650$		0			0
$651$	−8.70121	−	2.91344i	−0.341027	−	0.114187i
$652$		0			0
$653$	1.13344	+	0.412538i	0.0443549	+	0.0161439i	0.364102	−	0.931359i	$-0.381376\pi$
$653$	1.13344	+	0.412538i	0.0443549	+	0.0161439i	−0.319747	+	0.947503i	$0.603598\pi$
$654$		0			0
$655$	10.3707	−	58.8152i	0.405217	−	2.29810i
$656$		0			0
$657$	23.8485	−	10.1111i	0.930417	−	0.394473i
$658$		0			0
$659$	16.7806	−	6.10765i	0.653680	−	0.237920i	0.00617474	−	0.999981i	$-0.498035\pi$
$659$	16.7806	−	6.10765i	0.653680	−	0.237920i	0.647505	+	0.762061i	$0.275812\pi$
$660$		0			0
$661$	−11.1710	+	9.37360i	−0.434503	+	0.364591i	−0.833647	−	0.552297i	$-0.813751\pi$
$661$	−11.1710	+	9.37360i	−0.434503	+	0.364591i	0.399145	+	0.916888i	$0.369307\pi$
$662$		0			0
$663$	−9.06700	−	7.21536i	−0.352133	−	0.280221i
$664$		0			0
$665$	−4.73959	−	8.20920i	−0.183793	−	0.318339i
$666$		0			0
$667$	2.45752	−	4.25655i	0.0951555	−	0.164814i
$668$		0			0
$669$	13.6027	−	25.0404i	0.525911	−	0.968118i
$670$		0			0
$671$	−3.55895	−	20.1838i	−0.137392	−	0.779188i
$672$		0			0
$673$	−18.1409	−	15.2220i	−0.699281	−	0.586766i	0.222288	−	0.974981i	$-0.428647\pi$
$673$	−18.1409	−	15.2220i	−0.699281	−	0.586766i	−0.921569	+	0.388215i	$0.873092\pi$
$674$		0			0
$675$	−4.32869	+	44.6575i	−0.166611	+	1.71887i
$676$		0			0
$677$	−16.6750	−	13.9919i	−0.640871	−	0.537754i	0.263415	−	0.964683i	$-0.415151\pi$
$677$	−16.6750	−	13.9919i	−0.640871	−	0.537754i	−0.904285	+	0.426928i	$0.859596\pi$
$678$		0			0
$679$	−0.593962	−	3.36853i	−0.0227942	−	0.129272i
$680$		0			0
$681$	−49.0567	+	1.27419i	−1.87986	+	0.0488271i
$682$		0			0
$683$	−15.6951	+	27.1847i	−0.600557	+	1.04020i	0.392180	+	0.919889i	$0.371721\pi$
$683$	−15.6951	+	27.1847i	−0.600557	+	1.04020i	−0.992737	+	0.120307i	$0.961612\pi$
$684$		0			0
$685$	−35.5592	−	61.5903i	−1.35865	−	2.35324i
$686$		0			0
$687$	45.6753	−	17.9808i	1.74262	−	0.686010i
$688$		0			0
$689$	−25.9776	+	21.7978i	−0.989669	+	0.830431i
$690$		0			0
$691$	32.0483	−	11.6646i	1.21918	−	0.443744i	0.349298	−	0.937012i	$-0.386420\pi$
$691$	32.0483	−	11.6646i	1.21918	−	0.443744i	0.869877	+	0.493268i	$0.164198\pi$
$692$		0			0
$693$	−2.98959	+	5.86125i	−0.113565	+	0.222651i
$694$		0			0
$695$	−9.07134	+	51.4461i	−0.344096	+	1.95146i
$696$		0			0
$697$	−14.6423	−	5.32937i	−0.554618	−	0.201864i
$698$		0			0
$699$	−0.137756	−	0.677828i	−0.00521041	−	0.0256378i
$700$		0			0
$701$	3.60207			0.136048			0.0680242	−	0.997684i	$-0.478331\pi$
$701$	3.60207			0.136048			0.0680242	+	0.997684i	$0.478331\pi$
$702$		0			0
$703$	−31.0605			−1.17147
$704$		0			0
$705$	56.3979	−	49.8753i	2.12407	−	1.87841i
$706$		0			0
$707$	0.734142	+	0.267206i	0.0276103	+	0.0100493i
$708$		0			0
$709$	−7.48149	+	42.4296i	−0.280973	+	1.59348i	0.438351	+	0.898804i	$0.355563\pi$
$709$	−7.48149	+	42.4296i	−0.280973	+	1.59348i	−0.719324	+	0.694675i	$0.755548\pi$
$710$		0			0
$711$	−0.443805	−	1.92606i	−0.0166440	−	0.0722327i
$712$		0			0
$713$	7.30520	−	2.65888i	0.273582	−	0.0995757i
$714$		0			0
$715$	18.8040	−	15.7784i	0.703228	−	0.590079i
$716$		0			0
$717$	0.683235	−	4.56502i	0.0255159	−	0.170484i
$718$		0			0
$719$	−7.11515	−	12.3238i	−0.265350	−	0.459600i	0.702305	−	0.711876i	$-0.252154\pi$
$719$	−7.11515	−	12.3238i	−0.265350	−	0.459600i	−0.967655	+	0.252276i	$0.918821\pi$
$720$		0			0
$721$	−2.13994	+	3.70649i	−0.0796957	+	0.138037i
$722$		0			0
$723$	−12.3174	−	20.1098i	−0.458089	−	0.747890i
$724$		0			0
$725$	−6.40108	−	36.3023i	−0.237730	−	1.34823i
$726$		0			0
$727$	−34.8085	−	29.2078i	−1.29097	−	1.08326i	−0.991630	−	0.129111i	$-0.958788\pi$
$727$	−34.8085	−	29.2078i	−1.29097	−	1.08326i	−0.299344	−	0.954145i	$-0.596768\pi$
$728$		0			0
$729$	−9.70798	+	25.1943i	−0.359555	+	0.933124i
$730$		0			0
$731$	−17.9458	−	15.0583i	−0.663750	−	0.556952i
$732$		0			0
$733$	−1.66078	−	9.41876i	−0.0613424	−	0.347890i	−0.999995	−	0.00302696i	$-0.999036\pi$
$733$	−1.66078	−	9.41876i	−0.0613424	−	0.347890i	0.938653	−	0.344863i	$-0.112075\pi$
$734$		0			0
$735$	21.3275	+	34.8199i	0.786677	+	1.28435i
$736$		0			0
$737$	14.1631	−	24.5312i	0.521703	−	0.903617i
$738$		0			0
$739$	16.9999	+	29.4446i	0.625350	+	1.08314i	0.988473	+	0.151397i	$0.0483771\pi$
$739$	16.9999	+	29.4446i	0.625350	+	1.08314i	−0.363123	+	0.931741i	$0.618290\pi$
$740$		0			0
$741$	−1.99489	+	13.3288i	−0.0732841	+	0.489646i
$742$		0			0
$743$	10.3002	−	8.64291i	0.377878	−	0.317078i	−0.433990	−	0.900917i	$-0.642895\pi$
$743$	10.3002	−	8.64291i	0.377878	−	0.317078i	0.811869	+	0.583840i	$0.198450\pi$
$744$		0			0
$745$	18.1614	−	6.61020i	0.665381	−	0.242179i
$746$		0			0
$747$	8.62043	+	37.4115i	0.315405	+	1.36882i
$748$		0			0
$749$	2.37241	−	13.4546i	0.0866859	−	0.491620i
$750$		0			0
$751$	−11.2741	−	4.10342i	−0.411396	−	0.149736i	0.128027	−	0.991771i	$-0.459135\pi$
$751$	−11.2741	−	4.10342i	−0.411396	−	0.149736i	−0.539423	+	0.842035i	$0.681358\pi$
$752$		0			0
$753$	2.79248	−	2.46952i	0.101763	−	0.0899943i
$754$		0			0
$755$	−8.20111			−0.298469
$756$		0			0
$757$	16.8149			0.611149			0.305574	−	0.952168i	$-0.401152\pi$
$757$	16.8149			0.611149			0.305574	+	0.952168i	$0.401152\pi$
$758$		0			0
$759$	−1.11019	−	5.46270i	−0.0402974	−	0.198283i
$760$		0			0
$761$	31.2258	+	11.3653i	1.13194	+	0.411991i	0.838994	−	0.544140i	$-0.183144\pi$
$761$	31.2258	+	11.3653i	1.13194	+	0.411991i	0.292941	+	0.956131i	$0.405366\pi$
$762$		0			0
$763$	−1.21950	+	6.91615i	−0.0441490	+	0.250381i
$764$		0			0
$765$	−14.1598	+	27.7610i	−0.511948	+	1.00370i
$766$		0			0
$767$	4.02649	−	1.46552i	0.145388	−	0.0529170i
$768$		0			0
$769$	−35.6617	+	29.9237i	−1.28599	+	1.07908i	−0.293605	+	0.955927i	$0.594855\pi$
$769$	−35.6617	+	29.9237i	−1.28599	+	1.07908i	−0.992388	+	0.123150i	$0.960701\pi$
$770$		0			0
$771$	35.7143	−	14.0595i	1.28622	−	0.506341i
$772$		0			0
$773$	−22.5024	−	38.9753i	−0.809355	−	1.40184i	−0.913312	−	0.407261i	$-0.866484\pi$
$773$	−22.5024	−	38.9753i	−0.809355	−	1.40184i	0.103957	−	0.994582i	$-0.466850\pi$
$774$		0			0
$775$	29.1523	−	50.4932i	1.04718	−	1.81377i
$776$		0			0
$777$	−12.8956	+	0.334949i	−0.462628	+	0.0120162i
$778$		0			0
$779$	3.14705	+	17.8478i	0.112755	+	0.639464i
$780$		0			0
$781$	23.7587	+	19.9360i	0.850155	+	0.713365i
$782$		0			0
$783$	2.14019	−	22.0796i	0.0764842	−	0.789060i
$784$		0			0
$785$	−17.3050	−	14.5206i	−0.617642	−	0.518264i
$786$		0			0
$787$	−3.55273	−	20.1485i	−0.126641	−	0.718217i	−0.980320	−	0.197417i	$-0.936745\pi$
$787$	−3.55273	−	20.1485i	−0.126641	−	0.718217i	0.853679	−	0.520800i	$-0.174366\pi$
$788$		0			0
$789$	5.61916	−	10.3440i	0.200047	−	0.368255i
$790$		0			0
$791$	−0.289596	+	0.501595i	−0.0102968	+	0.0178347i
$792$		0			0
$793$	−8.71768	−	15.0995i	−0.309574	−	0.536198i
$794$		0			0
$795$	71.3629	+	56.7893i	2.53098	+	2.01411i
$796$		0			0
$797$	−40.1990	+	33.7309i	−1.42392	+	1.19481i	−0.474721	+	0.880137i	$0.657451\pi$
$797$	−40.1990	+	33.7309i	−1.42392	+	1.19481i	−0.949200	+	0.314674i	$0.898105\pi$
$798$		0			0
$799$	31.1197	−	11.3266i	1.10093	−	0.400707i
$800$		0			0
$801$	25.0373	−	10.6152i	0.884649	−	0.375069i
$802$		0			0
$803$	−4.19134	+	23.7703i	−0.147909	+	0.838835i
$804$		0			0
$805$	3.13422	+	1.14076i	0.110467	+	0.0402066i
$806$		0			0
$807$	−7.19354	−	2.40862i	−0.253225	−	0.0847875i
$808$		0			0
$809$	33.6516			1.18313			0.591563	−	0.806259i	$-0.298511\pi$
$809$	33.6516			1.18313			0.591563	+	0.806259i	$0.298511\pi$
$810$		0			0
$811$	−47.6175			−1.67208			−0.836039	−	0.548671i	$-0.815134\pi$
$811$	−47.6175			−1.67208			−0.836039	+	0.548671i	$0.815134\pi$
$812$		0			0
$813$	−29.8141	−	9.98268i	−1.04563	−	0.350108i
$814$		0			0
$815$	−34.7473	−	12.6470i	−1.21715	−	0.443005i
$816$		0			0
$817$	−4.73138	+	26.8330i	−0.165530	+	0.938768i
$818$		0			0
$819$	−0.684499	+	5.55533i	−0.0239183	+	0.194119i
$820$		0			0
$821$	−47.4282	+	17.2625i	−1.65526	+	0.602464i	−0.989607	−	0.143799i	$-0.954068\pi$
$821$	−47.4282	+	17.2625i	−1.65526	+	0.602464i	−0.665650	+	0.746264i	$0.731846\pi$
$822$		0			0
$823$	−4.05054	+	3.39881i	−0.141193	+	0.118475i	−0.710649	−	0.703547i	$-0.751598\pi$
$823$	−4.05054	+	3.39881i	−0.141193	+	0.118475i	0.569456	+	0.822022i	$0.307154\pi$
$824$		0			0
$825$	−32.7132	−	26.0326i	−1.13893	−	0.906337i
$826$		0			0
$827$	0.311009	+	0.538684i	0.0108148	+	0.0187319i	0.871382	−	0.490605i	$-0.163224\pi$
$827$	0.311009	+	0.538684i	0.0108148	+	0.0187319i	−0.860567	+	0.509337i	$0.829891\pi$
$828$		0			0
$829$	21.3297	−	36.9441i	0.740810	−	1.28312i	−0.211316	−	0.977418i	$-0.567775\pi$
$829$	21.3297	−	36.9441i	0.740810	−	1.28312i	0.952127	−	0.305703i	$-0.0988916\pi$
$830$		0			0
$831$	−19.2423	+	35.4221i	−0.667509	+	1.22878i
$832$		0			0
$833$	3.11888	+	17.6881i	0.108063	+	0.612855i
$834$		0			0
$835$	42.6793	+	35.8122i	1.47698	+	1.23933i
$836$		0			0
$837$	25.0411	−	24.5766i	0.865548	−	0.849491i
$838$		0			0
$839$	−9.61657	−	8.06926i	−0.332001	−	0.278582i	0.461514	−	0.887133i	$-0.347307\pi$
$839$	−9.61657	−	8.06926i	−0.332001	−	0.278582i	−0.793515	+	0.608551i	$0.791751\pi$
$840$		0			0
$841$	−1.87097	−	10.6108i	−0.0645163	−	0.365890i
$842$		0			0
$843$	2.96188	−	0.0769314i	0.102013	−	0.00264966i
$844$		0			0
$845$	−13.5603	+	23.4871i	−0.466487	+	0.807979i
$846$		0			0
$847$	1.24967	+	2.16450i	0.0429393	+	0.0743730i
$848$		0			0
$849$	12.0864	−	4.75799i	0.414803	−	0.163294i
$850$		0			0
$851$	8.37212	−	7.02504i	0.286993	−	0.240815i
$852$		0			0
$853$	51.7672	−	18.8417i	1.77248	−	0.645129i	0.772528	−	0.634981i	$-0.218992\pi$
$853$	51.7672	−	18.8417i	1.77248	−	0.645129i	0.999949	−	0.0101474i	$-0.00323007\pi$
$854$		0			0
$855$	36.1969	−	1.88161i	1.23791	−	0.0643498i
$856$		0			0
$857$	3.33870	−	18.9347i	0.114048	−	0.646798i	−0.873169	−	0.487417i	$-0.837939\pi$
$857$	3.33870	−	18.9347i	0.114048	−	0.646798i	0.987217	−	0.159381i	$-0.0509498\pi$
$858$		0			0
$859$	−6.37079	−	2.31878i	−0.217369	−	0.0791157i	0.231041	−	0.972944i	$-0.425787\pi$
$859$	−6.37079	−	2.31878i	−0.217369	−	0.0791157i	−0.448409	+	0.893828i	$0.648009\pi$
$860$		0			0
$861$	1.49905	+	7.37607i	0.0510875	+	0.251376i
$862$		0			0
$863$	36.6749			1.24843			0.624215	−	0.781253i	$-0.285419\pi$
$863$	36.6749			1.24843			0.624215	+	0.781253i	$0.285419\pi$
$864$		0			0
$865$	−71.7936			−2.44105
$866$		0			0
$867$	11.7885	−	10.4251i	0.400357	−	0.354055i
$868$		0			0
$869$	1.73067	+	0.629913i	0.0587090	+	0.0213683i
$870$		0			0
$871$	4.18443	−	23.7311i	0.141784	−	0.804097i
$872$		0			0
$873$	12.5059	+	3.82924i	0.423261	+	0.129600i
$874$		0			0
$875$	9.89466	−	3.60136i	0.334501	−	0.121748i
$876$		0			0
$877$	7.38624	−	6.19779i	0.249416	−	0.209285i	−0.509505	−	0.860468i	$-0.670171\pi$
$877$	7.38624	−	6.19779i	0.249416	−	0.209285i	0.758921	+	0.651183i	$0.225727\pi$
$878$		0			0
$879$	5.07637	−	33.9176i	0.171222	−	1.14401i
$880$		0			0
$881$	13.3896	+	23.1914i	0.451106	+	0.781339i	0.998455	−	0.0555658i	$-0.0176963\pi$
$881$	13.3896	+	23.1914i	0.451106	+	0.781339i	−0.547349	+	0.836905i	$0.684363\pi$
$882$		0			0
$883$	25.4219	−	44.0320i	0.855514	−	1.48179i	−0.0206538	−	0.999787i	$-0.506575\pi$
$883$	25.4219	−	44.0320i	0.855514	−	1.48179i	0.876168	−	0.482007i	$-0.160092\pi$
$884$		0			0
$885$	−6.01910	−	9.82696i	−0.202330	−	0.330330i
$886$		0			0
$887$	−0.729816	−	4.13899i	−0.0245048	−	0.138974i	0.970101	−	0.242702i	$-0.0780338\pi$
$887$	−0.729816	−	4.13899i	−0.0245048	−	0.138974i	−0.994606	+	0.103728i	$0.966923\pi$
$888$		0			0
$889$	10.0934	+	8.46933i	0.338520	+	0.284052i
$890$		0			0
$891$	−14.7707	−	20.3664i	−0.494838	−	0.682301i
$892$		0			0
$893$	−29.5061	−	24.7585i	−0.987384	−	0.828513i
$894$		0			0
$895$	7.39816	+	41.9571i	0.247293	+	1.40247i
$896$		0			0
$897$	−2.47690	−	4.04386i	−0.0827014	−	0.135021i
$898$		0			0
$899$	−14.4135	+	24.9649i	−0.480716	+	0.832625i
$900$		0			0
$901$	20.0583	+	34.7421i	0.668240	+	1.15743i
$902$		0			0
$903$	−1.67500	+	11.1915i	−0.0557406	+	0.372429i
$904$		0			0
$905$	6.29717	−	5.28395i	0.209325	−	0.175645i
$906$		0			0
$907$	−52.7545	+	19.2011i	−1.75169	+	0.637561i	−0.999765	−	0.0216920i	$-0.993095\pi$
$907$	−52.7545	+	19.2011i	−1.75169	+	0.637561i	−0.751921	+	0.659253i	$0.770872\pi$
$908$		0			0
$909$	−2.18565	+	2.03642i	−0.0724934	+	0.0675438i
$910$		0			0
$911$	−4.45180	+	25.2474i	−0.147495	+	0.836484i	0.817835	+	0.575452i	$0.195174\pi$
$911$	−4.45180	+	25.2474i	−0.147495	+	0.836484i	−0.965330	+	0.261032i	$0.915937\pi$
$912$		0			0
$913$	−33.6164	−	12.2354i	−1.11254	−	0.404932i
$914$		0			0
$915$	−35.1256	+	31.0633i	−1.16122	+	1.02692i
$916$		0			0
$917$	−12.6897			−0.419051
$918$		0			0
$919$	−3.84634			−0.126879			−0.0634395	−	0.997986i	$-0.520207\pi$
$919$	−3.84634			−0.126879			−0.0634395	+	0.997986i	$0.520207\pi$
$920$		0			0
$921$	10.4614	+	51.4753i	0.344715	+	1.69617i
$922$		0			0
$923$	24.7933	+	9.02402i	0.816081	+	0.297029i
$924$		0			0
$925$	14.2334	−	80.7215i	0.467990	−	2.65411i
$926$		0			0
$927$	−8.90727	−	13.7287i	−0.292553	−	0.450910i
$928$		0			0
$929$	18.7501	−	6.82448i	0.615171	−	0.223904i	−0.0155933	−	0.999878i	$-0.504964\pi$
$929$	18.7501	−	6.82448i	0.615171	−	0.223904i	0.630764	+	0.775974i	$0.282741\pi$
$930$		0			0
$931$	16.0026	−	13.4278i	0.524465	−	0.440078i
$932$		0			0
$933$	−9.49184	+	3.73661i	−0.310749	+	0.122331i
$934$		0			0
$935$	−14.5193	−	25.1481i	−0.474831	−	0.822432i
$936$		0			0
$937$	3.28368	−	5.68751i	0.107273	−	0.185803i	−0.807391	−	0.590016i	$-0.799121\pi$
$937$	3.28368	−	5.68751i	0.107273	−	0.185803i	0.914665	+	0.404213i	$0.132455\pi$
$938$		0			0
$939$	−55.8905	+	1.45169i	−1.82392	+	0.0473741i
$940$		0			0
$941$	4.92322	+	27.9209i	0.160492	+	0.910197i	0.953591	+	0.301104i	$0.0973551\pi$
$941$	4.92322	+	27.9209i	0.160492	+	0.910197i	−0.793099	+	0.609093i	$0.791534\pi$
$942$		0			0
$943$	−4.88495	−	4.09896i	−0.159076	−	0.133480i
$944$		0			0
$945$	15.0079	−	1.17154i	0.488205	−	0.0381103i
$946$		0			0
$947$	−5.71400	−	4.79461i	−0.185680	−	0.155804i	0.545210	−	0.838300i	$-0.316450\pi$
$947$	−5.71400	−	4.79461i	−0.185680	−	0.155804i	−0.730889	+	0.682496i	$0.760895\pi$
$948$		0			0
$949$	3.56559	+	20.2215i	0.115744	+	0.656417i
$950$		0			0
$951$	−10.2825	+	18.9284i	−0.333432	+	0.613796i
$952$		0			0
$953$	12.6442	−	21.9004i	0.409586	−	0.709423i	−0.585258	−	0.810847i	$-0.699007\pi$
$953$	12.6442	−	21.9004i	0.409586	−	0.709423i	0.994843	+	0.101424i	$0.0323399\pi$
$954$		0			0
$955$	31.3759	+	54.3446i	1.01530	+	1.75855i
$956$		0			0
$957$	16.1741	+	12.8710i	0.522833	+	0.416061i
$958$		0			0
$959$	−11.5757	+	9.71319i	−0.373800	+	0.313655i
$960$		0			0
$961$	−13.7149	+	4.99181i	−0.442416	+	0.161026i
$962$		0			0
$963$	41.7077	+	31.4567i	1.34401	+	1.01368i
$964$		0			0
$965$	14.3642	−	81.4634i	0.462400	−	2.62240i
$966$		0			0
$967$	0.111711	+	0.0406595i	0.00359239	+	0.00130752i	0.343816	−	0.939037i	$-0.388280\pi$
$967$	0.111711	+	0.0406595i	0.00359239	+	0.00130752i	−0.340223	+	0.940345i	$0.610503\pi$
$968$		0			0
$969$	15.1184	+	5.06212i	0.485674	+	0.162619i
$970$		0			0
$971$	32.6738			1.04855			0.524276	−	0.851548i	$-0.324336\pi$
$971$	32.6738			1.04855			0.524276	+	0.851548i	$0.324336\pi$
$972$		0			0
$973$	11.0998			0.355842
$974$		0			0
$975$	−33.7253	−	11.2923i	−1.08007	−	0.361642i
$976$		0			0
$977$	20.5424	+	7.47681i	0.657209	+	0.239204i	0.649031	−	0.760762i	$-0.275175\pi$
$977$	20.5424	+	7.47681i	0.657209	+	0.239204i	0.00817808	+	0.999967i	$0.497397\pi$
$978$		0			0
$979$	−4.40027	+	24.9552i	−0.140633	+	0.797571i
$980$		0			0
$981$	−21.4393	−	16.1699i	−0.684503	−	0.516265i
$982$		0			0
$983$	40.1717	−	14.6213i	1.28128	−	0.466348i	0.390424	−	0.920635i	$-0.372328\pi$
$983$	40.1717	−	14.6213i	1.28128	−	0.466348i	0.890855	+	0.454287i	$0.150106\pi$
$984$		0			0
$985$	−20.1241	+	16.8861i	−0.641206	+	0.538036i
$986$		0			0
$987$	−12.5173	−	9.96101i	−0.398429	−	0.317062i
$988$		0			0
$989$	−4.79359	−	8.30274i	−0.152427	−	0.264012i
$990$		0			0
$991$	−6.96954	+	12.0716i	−0.221395	+	0.383467i	−0.955232	−	0.295859i	$-0.904394\pi$
$991$	−6.96954	+	12.0716i	−0.221395	+	0.383467i	0.733837	+	0.679326i	$0.237728\pi$
$992$		0			0
$993$	−10.9898	+	20.2304i	−0.348749	+	0.641992i
$994$		0			0
$995$	−1.34939	−	7.65274i	−0.0427784	−	0.242608i
$996$		0			0
$997$	8.13312	+	6.82450i	0.257578	+	0.216134i	0.762427	−	0.647074i	$-0.224007\pi$
$997$	8.13312	+	6.82450i	0.257578	+	0.216134i	−0.504849	+	0.863208i	$0.668452\pi$
$998$		0			0
$999$	21.2637	−	44.5074i	0.672754	−	1.40815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.b.97.9	✓	54
4.3	odd	2		864.2.y.c.97.1	yes	54
27.22	even	9	inner	864.2.y.b.481.9	yes	54
108.103	odd	18		864.2.y.c.481.1	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.97.9	✓	54	1.1	even	1	trivial
864.2.y.b.481.9	yes	54	27.22	even	9	inner
864.2.y.c.97.1	yes	54	4.3	odd	2
864.2.y.c.481.1	yes	54	108.103	odd	18

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64243 + 0.549936i) q^{3} +(3.46982 + 1.26291i) q^{5} +(0.136240 - 0.772655i) q^{7} +(2.39514 + 1.80646i) q^{9} +O(q^{10})\)	\(q+(1.64243 + 0.549936i) q^{3} +(3.46982 + 1.26291i) q^{5} +(0.136240 - 0.772655i) q^{7} +(2.39514 + 1.80646i) q^{9} +(-2.62684 + 0.956091i) q^{11} +(-1.82171 + 1.52860i) q^{13} +(5.00441 + 3.98242i) q^{15} +(1.40662 + 2.43633i) q^{17} +(1.63600 - 2.83364i) q^{19} +(0.648675 - 1.19411i) q^{21} +(0.199921 + 1.13381i) q^{23} +(6.61450 + 5.55023i) q^{25} +(2.94041 + 4.28416i) q^{27} +(-3.27035 - 2.74415i) q^{29} +(-1.17254 - 6.64983i) q^{31} +(-4.84018 + 0.125718i) q^{33} +(1.44852 - 2.50892i) q^{35} +(-4.74640 - 8.22100i) q^{37} +(-3.83267 + 1.50879i) q^{39} +(-4.24300 + 3.56030i) q^{41} +(-7.82509 + 2.84810i) q^{43} +(6.02931 + 9.29295i) q^{45} +(2.04415 - 11.5930i) q^{47} +(5.99941 + 2.18361i) q^{49} +(0.970441 + 4.77505i) q^{51} +14.2600 q^{53} -10.3221 q^{55} +(4.24534 - 3.75436i) q^{57} +(-1.69317 - 0.616264i) q^{59} +(-1.27314 + 7.22031i) q^{61} +(1.72209 - 1.60451i) q^{63} +(-8.25151 + 3.00331i) q^{65} +(-7.76236 + 6.51339i) q^{67} +(-0.295165 + 1.97214i) q^{69} +(-5.54743 - 9.60843i) q^{71} +(4.31723 - 7.47766i) q^{73} +(7.81158 + 12.7534i) q^{75} +(0.380849 + 2.15990i) q^{77} +(-0.504702 - 0.423495i) q^{79} +(2.47340 + 8.65346i) q^{81} +(9.80329 + 8.22594i) q^{83} +(1.80384 + 10.2301i) q^{85} +(-3.86220 - 6.30554i) q^{87} +(4.53244 - 7.85041i) q^{89} +(0.932890 + 1.61581i) q^{91} +(1.73116 - 11.5667i) q^{93} +(9.25529 - 7.76611i) q^{95} +(4.09676 - 1.49110i) q^{97} +(-8.01879 - 2.45531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) \) 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more