LMFDB - Embedded newform 2646.2.t.a.1979.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1979,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("2646.1979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1979.4
Root			$1.62181 - 0.608059i$ of defining polynomial
Character	$\chi$	$=$	2646.1979
Dual form			2646.2.t.a.2285.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.89111 q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.89111 q^{5} +1.00000i q^{8} +(-3.36980 + 1.94556i) q^{10} +3.94462i q^{11} +(2.46687 - 1.42425i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.371058 + 0.642692i) q^{17} +(-1.54563 - 0.892369i) q^{19} +(1.94556 - 3.36980i) q^{20} +(-1.97231 - 3.41614i) q^{22} +6.25311i q^{23} +10.1408 q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.50079 + 1.44383i) q^{29} +(-3.04125 - 1.75587i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.642692 - 0.371058i) q^{34} +(-1.50079 + 2.59944i) q^{37} +1.78474 q^{38} +3.89111i q^{40} +(5.24705 + 9.08816i) q^{41} +(0.471521 - 0.816699i) q^{43} +(3.41614 + 1.97231i) q^{44} +(-3.12656 - 5.41535i) q^{46} +(-1.09263 - 1.89248i) q^{47} +(-8.78217 + 5.07039i) q^{50} -2.84849i q^{52} +15.3490i q^{55} -2.88766 q^{58} +(-0.0105673 + 0.0183031i) q^{59} +(2.13832 - 1.23456i) q^{61} +3.51174 q^{62} -1.00000 q^{64} +(9.59886 - 5.54191i) q^{65} +(-6.72463 + 11.6474i) q^{67} +0.742117 q^{68} -1.94304i q^{71} +(-4.20443 + 2.42743i) q^{73} -3.00158i q^{74} +(-1.54563 + 0.892369i) q^{76} +(-1.81806 - 3.14898i) q^{79} +(-1.94556 - 3.36980i) q^{80} +(-9.08816 - 5.24705i) q^{82} +(4.02998 - 6.98012i) q^{83} +(1.44383 + 2.50079i) q^{85} +0.943042i q^{86} -3.94462 q^{88} +(-4.63323 + 8.02499i) q^{89} +(5.41535 + 3.12656i) q^{92} +(1.89248 + 1.09263i) q^{94} +(-6.01422 - 3.47231i) q^{95} +(16.2983 + 9.40980i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.89111			1.74016			0.870080	−	0.492911i	$-0.164067\pi$
$5$	3.89111			1.74016			0.870080	+	0.492911i	$0.164067\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.36980	+	1.94556i	−1.06563	+	0.615239i
$11$			3.94462i			1.18935i	0.803967	+	0.594674i	$0.202719\pi$
$11$			3.94462i			1.18935i	−0.803967	+	0.594674i	$0.797281\pi$
$12$		0			0
$13$	2.46687	−	1.42425i	0.684186	−	0.395015i	−0.117244	−	0.993103i	$-0.537406\pi$
$13$	2.46687	−	1.42425i	0.684186	−	0.395015i	0.801430	+	0.598088i	$0.204073\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.371058	+	0.642692i	0.0899949	+	0.155876i	0.907509	−	0.420033i	$-0.137982\pi$
$17$	0.371058	+	0.642692i	0.0899949	+	0.155876i	−0.817514	+	0.575909i	$0.804648\pi$
$18$		0			0
$19$	−1.54563	−	0.892369i	−0.354591	−	0.204723i	0.312114	−	0.950045i	$-0.398963\pi$
$19$	−1.54563	−	0.892369i	−0.354591	−	0.204723i	−0.666706	+	0.745321i	$0.732296\pi$
$20$	1.94556	−	3.36980i	0.435040	−	0.753511i
$21$		0			0
$22$	−1.97231	−	3.41614i	−0.420498	−	0.728324i
$23$			6.25311i			1.30386i	0.758278	+	0.651932i	$0.226041\pi$
$23$			6.25311i			1.30386i	−0.758278	+	0.651932i	$0.773959\pi$
$24$		0			0
$25$	10.1408			2.02815
$26$	−1.42425	+	2.46687i	−0.279318	+	0.483793i
$27$		0			0
$28$		0			0
$29$	2.50079	+	1.44383i	0.464385	+	0.268113i	0.713886	−	0.700262i	$-0.246933\pi$
$29$	2.50079	+	1.44383i	0.464385	+	0.268113i	−0.249501	+	0.968374i	$0.580267\pi$
$30$		0			0
$31$	−3.04125	−	1.75587i	−0.546225	−	0.315363i	0.201373	−	0.979515i	$-0.435460\pi$
$31$	−3.04125	−	1.75587i	−0.546225	−	0.315363i	−0.747598	+	0.664152i	$0.768793\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−0.642692	−	0.371058i	−0.110221	−	0.0636360i
$35$		0			0
$36$		0			0
$37$	−1.50079	+	2.59944i	−0.246728	+	0.427346i	−0.962616	−	0.270870i	$-0.912689\pi$
$37$	−1.50079	+	2.59944i	−0.246728	+	0.427346i	0.715888	+	0.698215i	$0.246022\pi$
$38$	1.78474			0.289523
$39$		0			0
$40$			3.89111i			0.615239i
$41$	5.24705	+	9.08816i	0.819452	+	1.41933i	0.906087	+	0.423092i	$0.139055\pi$
$41$	5.24705	+	9.08816i	0.819452	+	1.41933i	−0.0866345	+	0.996240i	$0.527611\pi$
$42$		0			0
$43$	0.471521	−	0.816699i	0.0719063	−	0.124545i	−0.827830	−	0.560978i	$-0.810425\pi$
$43$	0.471521	−	0.816699i	0.0719063	−	0.124545i	0.899737	+	0.436433i	$0.143758\pi$
$44$	3.41614	+	1.97231i	0.515003	+	0.297337i
$45$		0			0
$46$	−3.12656	−	5.41535i	−0.460985	−	0.798450i
$47$	−1.09263	−	1.89248i	−0.159376	−	0.276047i	0.775268	−	0.631633i	$-0.217615\pi$
$47$	−1.09263	−	1.89248i	−0.159376	−	0.276047i	−0.934644	+	0.355585i	$0.884282\pi$
$48$		0			0
$49$		0			0
$50$	−8.78217	+	5.07039i	−1.24199	+	0.717061i
$51$		0			0
$52$		−	2.84849i		−	0.395015i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$			15.3490i			2.06965i
$56$		0			0
$57$		0			0
$58$	−2.88766			−0.379169
$59$	−0.0105673	+	0.0183031i	−0.00137575	+	0.00238286i	−0.866712	−	0.498808i	$-0.833771\pi$
$59$	−0.0105673	+	0.0183031i	−0.00137575	+	0.00238286i	0.865337	+	0.501191i	$0.167105\pi$
$60$		0			0
$61$	2.13832	−	1.23456i	0.273783	−	0.158069i	−0.356822	−	0.934172i	$-0.616140\pi$
$61$	2.13832	−	1.23456i	0.273783	−	0.158069i	0.630606	+	0.776103i	$0.282807\pi$
$62$	3.51174			0.445991
$63$		0			0
$64$	−1.00000			−0.125000
$65$	9.59886	−	5.54191i	1.19059	−	0.687389i
$66$		0			0
$67$	−6.72463	+	11.6474i	−0.821544	+	1.42296i	0.0829874	+	0.996551i	$0.473554\pi$
$67$	−6.72463	+	11.6474i	−0.821544	+	1.42296i	−0.904532	+	0.426406i	$0.859779\pi$
$68$	0.742117			0.0899949
$69$		0			0
$70$		0			0
$71$		−	1.94304i		−	0.230597i	−0.993331	−	0.115298i	$-0.963218\pi$
$71$		−	1.94304i		−	0.230597i	0.993331	−	0.115298i	$-0.0367824\pi$
$72$		0			0
$73$	−4.20443	+	2.42743i	−0.492092	+	0.284109i	−0.725442	−	0.688284i	$-0.758364\pi$
$73$	−4.20443	+	2.42743i	−0.492092	+	0.284109i	0.233350	+	0.972393i	$0.425031\pi$
$74$		−	3.00158i		−	0.348926i
$75$		0			0
$76$	−1.54563	+	0.892369i	−0.177296	+	0.102362i
$77$		0			0
$78$		0			0
$79$	−1.81806	−	3.14898i	−0.204548	−	0.354288i	0.745440	−	0.666572i	$-0.232239\pi$
$79$	−1.81806	−	3.14898i	−0.204548	−	0.354288i	−0.949989	+	0.312284i	$0.898906\pi$
$80$	−1.94556	−	3.36980i	−0.217520	−	0.376756i
$81$		0			0
$82$	−9.08816	−	5.24705i	−1.00362	−	0.579440i
$83$	4.02998	−	6.98012i	0.442347	−	0.766168i	−0.555516	−	0.831506i	$-0.687479\pi$
$83$	4.02998	−	6.98012i	0.442347	−	0.766168i	0.997863	+	0.0653378i	$0.0208125\pi$
$84$		0			0
$85$	1.44383	+	2.50079i	0.156605	+	0.271249i
$86$			0.943042i			0.101691i
$87$		0			0
$88$	−3.94462			−0.420498
$89$	−4.63323	+	8.02499i	−0.491122	+	0.850647i	−0.999948	−	0.0102218i	$-0.996746\pi$
$89$	−4.63323	+	8.02499i	−0.491122	+	0.850647i	0.508826	+	0.860869i	$0.330080\pi$
$90$		0			0
$91$		0			0
$92$	5.41535	+	3.12656i	0.564589	+	0.325966i
$93$		0			0
$94$	1.89248	+	1.09263i	0.195195	+	0.112696i
$95$	−6.01422	−	3.47231i	−0.617046	−	0.356251i
$96$		0			0
$97$	16.2983	+	9.40980i	1.65484	+	0.955421i	0.975043	+	0.222018i	$0.0712643\pi$
$97$	16.2983	+	9.40980i	1.65484	+	0.955421i	0.679794	+	0.733403i	$0.262069\pi$
$98$		0			0
$99$		0			0
$100$	5.07039	−	8.78217i	0.507039	−	0.878217i
$101$	8.28158			0.824048			0.412024	−	0.911173i	$-0.364822\pi$
$101$	8.28158			0.824048			0.412024	+	0.911173i	$0.364822\pi$
$102$		0			0
$103$		−	17.0487i		−	1.67986i	−0.542697	−	0.839929i	$-0.682597\pi$
$103$		−	17.0487i		−	1.67986i	0.542697	−	0.839929i	$-0.317403\pi$
$104$	1.42425	+	2.46687i	0.139659	+	0.241896i
$105$		0			0
$106$		0			0
$107$	−12.4161	−	7.16846i	−1.20031	−	0.693001i	−0.239689	−	0.970850i	$-0.577045\pi$
$107$	−12.4161	−	7.16846i	−1.20031	−	0.693001i	−0.960625	+	0.277848i	$0.910379\pi$
$108$		0			0
$109$	−5.63998	−	9.76874i	−0.540212	−	0.935675i	−0.998891	−	0.0470733i	$-0.985011\pi$
$109$	−5.63998	−	9.76874i	−0.540212	−	0.935675i	0.458679	−	0.888602i	$-0.348323\pi$
$110$	−7.67448	−	13.2926i	−0.731733	−	1.26740i
$111$		0			0
$112$		0			0
$113$	8.51501	−	4.91614i	0.801024	−	0.462472i	−0.0428049	−	0.999083i	$-0.513629\pi$
$113$	8.51501	−	4.91614i	0.801024	−	0.462472i	0.843829	+	0.536612i	$0.180296\pi$
$114$		0			0
$115$			24.3316i			2.26893i
$116$	2.50079	−	1.44383i	0.232192	−	0.134056i
$117$		0			0
$118$		−	0.0211346i		−	0.00194560i
$119$		0			0
$120$		0			0
$121$	−4.56002			−0.414548
$122$	−1.23456	+	2.13832i	−0.111772	+	0.193594i
$123$		0			0
$124$	−3.04125	+	1.75587i	−0.273112	+	0.157682i
$125$	20.0033			1.78915
$126$		0			0
$127$	2.94462			0.261293			0.130646	−	0.991429i	$-0.458295\pi$
$127$	2.94462			0.261293			0.130646	+	0.991429i	$0.458295\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−5.54191	+	9.59886i	−0.486057	+	0.841876i
$131$	15.0651			1.31624			0.658122	−	0.752911i	$-0.271351\pi$
$131$	15.0651			1.31624			0.658122	+	0.752911i	$0.271351\pi$
$132$		0			0
$133$		0			0
$134$		−	13.4493i		−	1.16184i
$135$		0			0
$136$	−0.642692	+	0.371058i	−0.0551104	+	0.0318180i
$137$		−	15.7199i		−	1.34305i	−0.740984	−	0.671523i	$-0.765641\pi$
$137$		−	15.7199i		−	1.34305i	0.740984	−	0.671523i	$-0.234359\pi$
$138$		0			0
$139$	2.86373	−	1.65337i	0.242898	−	0.140237i	−0.373610	−	0.927586i	$-0.621880\pi$
$139$	2.86373	−	1.65337i	0.242898	−	0.140237i	0.616508	+	0.787349i	$0.288547\pi$
$140$		0			0
$141$		0			0
$142$	0.971521	+	1.68272i	0.0815282	+	0.141211i
$143$	5.61811	+	9.73085i	0.469810	+	0.813735i
$144$		0			0
$145$	9.73085	+	5.61811i	0.808103	+	0.466559i
$146$	2.42743	−	4.20443i	0.200896	−	0.347961i
$147$		0			0
$148$	1.50079	+	2.59944i	0.123364	+	0.213673i
$149$		−	11.0016i		−	0.901284i	−0.892705	−	0.450642i	$-0.851195\pi$
$149$		−	11.0016i		−	0.901284i	0.892705	−	0.450642i	$-0.148805\pi$
$150$		0			0
$151$	−1.43998			−0.117184			−0.0585918	−	0.998282i	$-0.518661\pi$
$151$	−1.43998			−0.117184			−0.0585918	+	0.998282i	$0.518661\pi$
$152$	0.892369	−	1.54563i	0.0723807	−	0.125367i
$153$		0			0
$154$		0			0
$155$	−11.8339	−	6.83228i	−0.950518	−	0.548782i
$156$		0			0
$157$	−14.3822	−	8.30354i	−1.14782	−	0.662695i	−0.199465	−	0.979905i	$-0.563921\pi$
$157$	−14.3822	−	8.30354i	−1.14782	−	0.662695i	−0.948355	+	0.317210i	$0.897254\pi$
$158$	3.14898	+	1.81806i	0.250519	+	0.144637i
$159$		0			0
$160$	3.36980	+	1.94556i	0.266406	+	0.153810i
$161$		0			0
$162$		0			0
$163$	6.19773	−	10.7348i	0.485444	−	0.840813i	−0.514416	−	0.857541i	$-0.671991\pi$
$163$	6.19773	−	10.7348i	0.485444	−	0.840813i	0.999860	+	0.0167274i	$0.00532476\pi$
$164$	10.4941			0.819452
$165$		0			0
$166$			8.05995i			0.625574i
$167$	5.86087	+	10.1513i	0.453528	+	0.785534i	0.998602	−	0.0528541i	$-0.0168318\pi$
$167$	5.86087	+	10.1513i	0.453528	+	0.785534i	−0.545074	+	0.838388i	$0.683498\pi$
$168$		0			0
$169$	−2.44304	+	4.23147i	−0.187926	+	0.325498i
$170$	−2.50079	−	1.44383i	−0.191802	−	0.110737i
$171$		0			0
$172$	−0.471521	−	0.816699i	−0.0359532	−	0.0622727i
$173$	8.38548	+	14.5241i	0.637536	+	1.10425i	0.985972	+	0.166913i	$0.0533798\pi$
$173$	8.38548	+	14.5241i	0.637536	+	1.10425i	−0.348435	+	0.937333i	$0.613287\pi$
$174$		0			0
$175$		0			0
$176$	3.41614	−	1.97231i	0.257501	−	0.148668i
$177$		0			0
$178$		−	9.26646i		−	0.694551i
$179$	−5.00158	+	2.88766i	−0.373835	+	0.215834i	−0.675133	−	0.737696i	$-0.735914\pi$
$179$	−5.00158	+	2.88766i	−0.373835	+	0.215834i	0.301297	+	0.953530i	$0.402580\pi$
$180$		0			0
$181$		−	5.53310i		−	0.411272i	−0.978629	−	0.205636i	$-0.934074\pi$
$181$		−	5.53310i		−	0.411272i	0.978629	−	0.205636i	$-0.0659263\pi$
$182$		0			0
$183$		0			0
$184$	−6.25311			−0.460985
$185$	−5.83974	+	10.1147i	−0.429346	+	0.743649i
$186$		0			0
$187$	−2.53518	+	1.46368i	−0.185390	+	0.107035i
$188$	−2.18525			−0.159376
$189$		0			0
$190$	6.94462			0.503816
$191$	−5.38124	+	3.10686i	−0.389373	+	0.224805i	−0.681888	−	0.731456i	$-0.738841\pi$
$191$	−5.38124	+	3.10686i	−0.389373	+	0.224805i	0.292515	+	0.956261i	$0.405508\pi$
$192$		0			0
$193$	3.90271	−	6.75970i	0.280923	−	0.486574i	−0.690689	−	0.723152i	$-0.742693\pi$
$193$	3.90271	−	6.75970i	0.280923	−	0.486574i	0.971612	+	0.236578i	$0.0760260\pi$
$194$	−18.8196			−1.35117
$195$		0			0
$196$		0			0
$197$			12.7737i			0.910092i	0.890468	+	0.455046i	$0.150377\pi$
$197$			12.7737i			0.910092i	−0.890468	+	0.455046i	$0.849623\pi$
$198$		0			0
$199$	−1.56925	+	0.906005i	−0.111241	+	0.0642250i	−0.554588	−	0.832125i	$-0.687124\pi$
$199$	−1.56925	+	0.906005i	−0.111241	+	0.0642250i	0.443347	+	0.896350i	$0.353791\pi$
$200$			10.1408i			0.717061i
$201$		0			0
$202$	−7.17206	+	4.14079i	−0.504624	+	0.291345i
$203$		0			0
$204$		0			0
$205$	20.4169	+	35.3631i	1.42598	+	2.46986i
$206$	8.52435	+	14.7646i	0.593919	+	1.02870i
$207$		0			0
$208$	−2.46687	−	1.42425i	−0.171047	−	0.0987537i
$209$	3.52006	−	6.09692i	0.243487	−	0.421732i
$210$		0			0
$211$	−1.88766	−	3.26953i	−0.129952	−	0.225083i	0.793706	−	0.608302i	$-0.208149\pi$
$211$	−1.88766	−	3.26953i	−0.129952	−	0.225083i	−0.923658	+	0.383218i	$0.874816\pi$
$212$		0			0
$213$		0			0
$214$	14.3369			0.980052
$215$	1.83474	−	3.17787i	0.125128	−	0.216729i
$216$		0			0
$217$		0			0
$218$	9.76874	+	5.63998i	0.661622	+	0.381988i
$219$		0			0
$220$	13.2926	+	7.67448i	0.896187	+	0.517414i
$221$	1.83070	+	1.05696i	0.123146	+	0.0710987i
$222$		0			0
$223$	11.0662	+	6.38910i	0.741051	+	0.427846i	0.822451	−	0.568836i	$-0.192606\pi$
$223$	11.0662	+	6.38910i	0.741051	+	0.427846i	−0.0814006	+	0.996681i	$0.525939\pi$
$224$		0			0
$225$		0			0
$226$	−4.91614	+	8.51501i	−0.327017	+	0.566410i
$227$	−19.9822			−1.32627			−0.663133	−	0.748502i	$-0.730773\pi$
$227$	−19.9822			−1.32627			−0.663133	+	0.748502i	$0.730773\pi$
$228$		0			0
$229$			10.1314i			0.669500i	0.942307	+	0.334750i	$0.108652\pi$
$229$			10.1314i			0.669500i	−0.942307	+	0.334750i	$0.891348\pi$
$230$	−12.1658	−	21.0718i	−0.802188	−	1.38943i
$231$		0			0
$232$	−1.44383	+	2.50079i	−0.0947921	+	0.164185i
$233$	−6.33070	−	3.65503i	−0.414738	−	0.239449i	0.278085	−	0.960556i	$-0.410300\pi$
$233$	−6.33070	−	3.65503i	−0.414738	−	0.239449i	−0.692824	+	0.721107i	$0.743634\pi$
$234$		0			0
$235$	−4.25153	−	7.36387i	−0.277339	−	0.480366i
$236$	0.0105673	+	0.0183031i	0.000687873	+	0.00119143i
$237$		0			0
$238$		0			0
$239$	−7.28317	+	4.20494i	−0.471109	+	0.271995i	−0.716704	−	0.697378i	$-0.754350\pi$
$239$	−7.28317	+	4.20494i	−0.471109	+	0.271995i	0.245595	+	0.969373i	$0.421017\pi$
$240$		0			0
$241$			8.95213i			0.576657i	0.957531	+	0.288329i	$0.0930996\pi$
$241$			8.95213i			0.576657i	−0.957531	+	0.288329i	$0.906900\pi$
$242$	3.94910	−	2.28001i	0.253858	−	0.146565i
$243$		0			0
$244$		−	2.46911i		−	0.158069i
$245$		0			0
$246$		0			0
$247$	−5.08381			−0.323475
$248$	1.75587	−	3.04125i	0.111498	−	0.193120i
$249$		0			0
$250$	−17.3234	+	10.0017i	−1.09563	+	0.632561i
$251$	−12.6432			−0.798033			−0.399017	−	0.916944i	$-0.630648\pi$
$251$	−12.6432			−0.798033			−0.399017	+	0.916944i	$0.630648\pi$
$252$		0			0
$253$	−24.6661			−1.55075
$254$	−2.55012	+	1.47231i	−0.160008	+	0.0923809i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.3066			−1.01718			−0.508588	−	0.861010i	$-0.669832\pi$
$257$	−16.3066			−1.01718			−0.508588	+	0.861010i	$0.669832\pi$
$258$		0			0
$259$		0			0
$260$		−	11.0838i		−	0.687389i
$261$		0			0
$262$	−13.0468	+	7.53255i	−0.806032	+	0.465363i
$263$			23.7215i			1.46273i	0.681985	+	0.731366i	$0.261117\pi$
$263$			23.7215i			1.46273i	−0.681985	+	0.731366i	$0.738883\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	6.72463	+	11.6474i	0.410772	+	0.711478i
$269$	3.64144	+	6.30716i	0.222022	+	0.384554i	0.955422	−	0.295244i	$-0.0954009\pi$
$269$	3.64144	+	6.30716i	0.222022	+	0.384554i	−0.733400	+	0.679798i	$0.762068\pi$
$270$		0			0
$271$	19.6483	+	11.3440i	1.19355	+	0.689097i	0.959110	−	0.283033i	$-0.0913407\pi$
$271$	19.6483	+	11.3440i	1.19355	+	0.689097i	0.234441	+	0.972130i	$0.424674\pi$
$272$	0.371058	−	0.642692i	0.0224987	−	0.0389689i
$273$		0			0
$274$	7.85997	+	13.6139i	0.474838	+	0.822444i
$275$			40.0015i			2.41218i
$276$		0			0
$277$	24.1676			1.45209			0.726046	−	0.687646i	$-0.241356\pi$
$277$	24.1676			1.45209			0.726046	+	0.687646i	$0.241356\pi$
$278$	−1.65337	+	2.86373i	−0.0991628	+	0.171755i
$279$		0			0
$280$		0			0
$281$	4.11229	+	2.37423i	0.245319	+	0.141635i	0.617619	−	0.786478i	$-0.288097\pi$
$281$	4.11229	+	2.37423i	0.245319	+	0.141635i	−0.372300	+	0.928112i	$0.621431\pi$
$282$		0			0
$283$	25.4484	+	14.6926i	1.51275	+	0.873387i	0.999889	+	0.0149153i	$0.00474785\pi$
$283$	25.4484	+	14.6926i	1.51275	+	0.873387i	0.512861	+	0.858471i	$0.328585\pi$
$284$	−1.68272	−	0.971521i	−0.0998513	−	0.0576492i
$285$		0			0
$286$	−9.73085	−	5.61811i	−0.575398	−	0.332206i
$287$		0			0
$288$		0			0
$289$	8.22463	−	14.2455i	0.483802	−	0.837969i
$290$	−11.2362			−0.659814
$291$		0			0
$292$			4.85486i			0.284109i
$293$	−3.31206	−	5.73666i	−0.193493	−	0.335139i	0.752913	−	0.658121i	$-0.228648\pi$
$293$	−3.31206	−	5.73666i	−0.193493	−	0.335139i	−0.946405	+	0.322981i	$0.895315\pi$
$294$		0			0
$295$	−0.0411186	+	0.0712195i	−0.00239402	+	0.00414656i
$296$	−2.59944	−	1.50079i	−0.151090	−	0.0872316i
$297$		0			0
$298$	5.50079	+	9.52765i	0.318652	+	0.551922i
$299$	8.90597	+	15.4256i	0.515046	+	0.892085i
$300$		0			0
$301$		0			0
$302$	1.24706	−	0.719988i	0.0717600	−	0.0414307i
$303$		0			0
$304$			1.78474i			0.102362i
$305$	8.32043	−	4.80380i	0.476426	−	0.275065i
$306$		0			0
$307$			21.7242i			1.23987i	0.784655	+	0.619933i	$0.212840\pi$
$307$			21.7242i			1.23987i	−0.784655	+	0.619933i	$0.787160\pi$
$308$		0			0
$309$		0			0
$310$	13.6646			0.776095
$311$	−3.14900	+	5.45422i	−0.178563	+	0.309281i	−0.941389	−	0.337324i	$-0.890478\pi$
$311$	−3.14900	+	5.45422i	−0.178563	+	0.309281i	0.762825	+	0.646605i	$0.223812\pi$
$312$		0			0
$313$	19.2423	−	11.1095i	1.08764	−	0.627948i	0.154691	−	0.987963i	$-0.450562\pi$
$313$	19.2423	−	11.1095i	1.08764	−	0.627948i	0.932946	+	0.360015i	$0.117229\pi$
$314$	16.6071			0.937192
$315$		0			0
$316$	−3.63613			−0.204548
$317$	13.5632	−	7.83070i	0.761784	−	0.439816i	−0.0681519	−	0.997675i	$-0.521710\pi$
$317$	13.5632	−	7.83070i	0.761784	−	0.439816i	0.829936	+	0.557859i	$0.188377\pi$
$318$		0			0
$319$	−5.69536	+	9.86466i	−0.318879	+	0.552315i
$320$	−3.89111			−0.217520
$321$		0			0
$322$		0			0
$323$		−	1.32448i		−	0.0736963i
$324$		0			0
$325$	25.0159	−	14.4430i	1.38763	−	0.801151i
$326$			12.3955i			0.686521i
$327$		0			0
$328$	−9.08816	+	5.24705i	−0.501810	+	0.289720i
$329$		0			0
$330$		0			0
$331$	−0.636129	−	1.10181i	−0.0349648	−	0.0605608i	0.848013	−	0.529975i	$-0.177799\pi$
$331$	−0.636129	−	1.10181i	−0.0349648	−	0.0605608i	−0.882978	+	0.469414i	$0.844465\pi$
$332$	−4.02998	−	6.98012i	−0.221174	−	0.383084i
$333$		0			0
$334$	−10.1513	−	5.86087i	−0.555456	−	0.320693i
$335$	−26.1663	+	45.3214i	−1.42962	+	2.47617i
$336$		0			0
$337$	−3.78001	−	6.54717i	−0.205910	−	0.356647i	0.744512	−	0.667609i	$-0.232682\pi$
$337$	−3.78001	−	6.54717i	−0.205910	−	0.356647i	−0.950422	+	0.310962i	$0.899349\pi$
$338$		−	4.88608i		−	0.265768i
$339$		0			0
$340$	2.88766			0.156605
$341$	6.92623	−	11.9966i	0.375076	−	0.649651i
$342$		0			0
$343$		0			0
$344$	0.816699	+	0.471521i	0.0440334	+	0.0254227i
$345$		0			0
$346$	−14.5241	−	8.38548i	−0.780820	−	0.450806i
$347$	19.1470	+	11.0545i	1.02787	+	0.593439i	0.916373	−	0.400326i	$-0.131103\pi$
$347$	19.1470	+	11.0545i	1.02787	+	0.593439i	0.111494	+	0.993765i	$0.464436\pi$
$348$		0			0
$349$	−12.7682	−	7.37173i	−0.683467	−	0.394600i	0.117693	−	0.993050i	$-0.462450\pi$
$349$	−12.7682	−	7.37173i	−0.683467	−	0.394600i	−0.801160	+	0.598450i	$0.795783\pi$
$350$		0			0
$351$		0			0
$352$	−1.97231	+	3.41614i	−0.105124	+	0.182081i
$353$	17.2776			0.919595			0.459798	−	0.888024i	$-0.347922\pi$
$353$	17.2776			0.919595			0.459798	+	0.888024i	$0.347922\pi$
$354$		0			0
$355$		−	7.56060i		−	0.401275i
$356$	4.63323	+	8.02499i	0.245561	+	0.425324i
$357$		0			0
$358$	2.88766	−	5.00158i	0.152618	−	0.264342i
$359$	−9.45088	−	5.45647i	−0.498799	−	0.287982i	0.229419	−	0.973328i	$-0.426318\pi$
$359$	−9.45088	−	5.45647i	−0.498799	−	0.287982i	−0.728217	+	0.685346i	$0.759651\pi$
$360$		0			0
$361$	−7.90736	−	13.6959i	−0.416177	−	0.720839i
$362$	2.76655	+	4.79180i	0.145407	+	0.251852i
$363$		0			0
$364$		0			0
$365$	−16.3599	+	9.44541i	−0.856318	+	0.494395i
$366$		0			0
$367$		−	35.7272i		−	1.86494i	−0.361242	−	0.932472i	$-0.617647\pi$
$367$		−	35.7272i		−	1.86494i	0.361242	−	0.932472i	$-0.382353\pi$
$368$	5.41535	−	3.12656i	0.282295	−	0.162983i
$369$		0			0
$370$		−	11.6795i		−	0.607187i
$371$		0			0
$372$		0			0
$373$	−32.0600			−1.66001			−0.830003	−	0.557760i	$-0.811661\pi$
$373$	−32.0600			−1.66001			−0.830003	+	0.557760i	$0.811661\pi$
$374$	1.46368	−	2.53518i	0.0756853	−	0.131091i
$375$		0			0
$376$	1.89248	−	1.09263i	0.0975974	−	0.0563479i
$377$	8.22549			0.423634
$378$		0			0
$379$	34.8891			1.79214			0.896068	−	0.443918i	$-0.146412\pi$
$379$	34.8891			1.79214			0.896068	+	0.443918i	$0.146412\pi$
$380$	−6.01422	+	3.47231i	−0.308523	+	0.178126i
$381$		0			0
$382$	3.10686	−	5.38124i	0.158961	−	0.275328i
$383$	−17.5342			−0.895957			−0.447978	−	0.894044i	$-0.647856\pi$
$383$	−17.5342			−0.895957			−0.447978	+	0.894044i	$0.647856\pi$
$384$		0			0
$385$		0			0
$386$			7.80542i			0.397286i
$387$		0			0
$388$	16.2983	−	9.40980i	0.827418	−	0.477710i
$389$		−	7.62171i		−	0.386436i	−0.981156	−	0.193218i	$-0.938108\pi$
$389$		−	7.62171i		−	0.386436i	0.981156	−	0.193218i	$-0.0618925\pi$
$390$		0			0
$391$	−4.01882	+	2.32027i	−0.203241	+	0.117341i
$392$		0			0
$393$		0			0
$394$	−6.38687	−	11.0624i	−0.321766	−	0.557315i
$395$	−7.07430	−	12.2530i	−0.355947	−	0.616517i
$396$		0			0
$397$	−32.6032	−	18.8234i	−1.63631	−	0.944722i	−0.982090	−	0.188414i	$-0.939665\pi$
$397$	−32.6032	−	18.8234i	−1.63631	−	0.944722i	−0.654216	−	0.756307i	$-0.727001\pi$
$398$	0.906005	−	1.56925i	0.0454139	−	0.0786592i
$399$		0			0
$400$	−5.07039	−	8.78217i	−0.253519	−	0.439108i
$401$		−	21.4415i		−	1.07074i	−0.844619	−	0.535368i	$-0.820173\pi$
$401$		−	21.4415i		−	1.07074i	0.844619	−	0.535368i	$-0.179827\pi$
$402$		0			0
$403$	−10.0032			−0.498293
$404$	4.14079	−	7.17206i	0.206012	−	0.356823i
$405$		0			0
$406$		0			0
$407$	−10.2538	−	5.92004i	−0.508262	−	0.293445i
$408$		0			0
$409$	25.6086	+	14.7851i	1.26627	+	0.731079i	0.974279	−	0.225344i	$-0.0723506\pi$
$409$	25.6086	+	14.7851i	1.26627	+	0.731079i	0.291986	+	0.956423i	$0.405684\pi$
$410$	−35.3631	−	20.4169i	−1.74646	−	1.00832i
$411$		0			0
$412$	−14.7646	−	8.52435i	−0.727400	−	0.419964i
$413$		0			0
$414$		0			0
$415$	15.6811	−	27.1605i	0.769755	−	1.33325i
$416$	2.84849			0.139659
$417$		0			0
$418$			7.04011i			0.344343i
$419$	−3.56481	−	6.17443i	−0.174152	−	0.301641i	0.765715	−	0.643180i	$-0.222385\pi$
$419$	−3.56481	−	6.17443i	−0.174152	−	0.301641i	−0.939868	+	0.341539i	$0.889052\pi$
$420$		0			0
$421$	−2.31007	+	4.00115i	−0.112586	+	0.195004i	−0.916812	−	0.399319i	$-0.869247\pi$
$421$	−2.31007	+	4.00115i	−0.112586	+	0.195004i	0.804226	+	0.594323i	$0.202580\pi$
$422$	3.26953	+	1.88766i	0.159158	+	0.0918899i
$423$		0			0
$424$		0			0
$425$	3.76282	+	6.51739i	0.182524	+	0.316140i
$426$		0			0
$427$		0			0
$428$	−12.4161	+	7.16846i	−0.600157	+	0.346501i
$429$		0			0
$430$			3.66949i			0.176958i
$431$	−3.47078	+	2.00385i	−0.167181	+	0.0965223i	−0.581256	−	0.813721i	$-0.697439\pi$
$431$	−3.47078	+	2.00385i	−0.167181	+	0.0965223i	0.414075	+	0.910243i	$0.364105\pi$
$432$		0			0
$433$		−	29.4125i		−	1.41348i	−0.707475	−	0.706738i	$-0.750166\pi$
$433$		−	29.4125i		−	1.41348i	0.707475	−	0.706738i	$-0.249834\pi$
$434$		0			0
$435$		0			0
$436$	−11.2800			−0.540212
$437$	5.58008	−	9.66498i	0.266931	−	0.462339i
$438$		0			0
$439$	−18.5130	+	10.6885i	−0.883575	+	0.510133i	−0.871836	−	0.489799i	$-0.837070\pi$
$439$	−18.5130	+	10.6885i	−0.883575	+	0.510133i	−0.0117398	+	0.999931i	$0.503737\pi$
$440$	−15.3490			−0.731733
$441$		0			0
$442$	−2.11392			−0.100549
$443$	5.05227	−	2.91693i	0.240041	−	0.138587i	−0.375155	−	0.926962i	$-0.622410\pi$
$443$	5.05227	−	2.91693i	0.240041	−	0.138587i	0.615195	+	0.788375i	$0.289077\pi$
$444$		0			0
$445$	−18.0284	+	31.2262i	−0.854630	+	1.48026i
$446$	−12.7782			−0.605065
$447$		0			0
$448$		0			0
$449$		−	22.5823i		−	1.06573i	−0.846202	−	0.532863i	$-0.821116\pi$
$449$		−	22.5823i		−	1.06573i	0.846202	−	0.532863i	$-0.178884\pi$
$450$		0			0
$451$	−35.8493	+	20.6976i	−1.68808	+	0.974613i
$452$		−	9.83228i		−	0.462472i
$453$		0			0
$454$	17.3051	−	9.99110i	0.812168	−	0.468906i
$455$		0			0
$456$		0			0
$457$	−19.9311	−	34.5218i	−0.932340	−	1.61486i	−0.779310	−	0.626638i	$-0.784430\pi$
$457$	−19.9311	−	34.5218i	−0.932340	−	1.61486i	−0.153029	−	0.988222i	$-0.548903\pi$
$458$	−5.06568	−	8.77402i	−0.236704	−	0.409983i
$459$		0			0
$460$	21.0718	+	12.1658i	0.982476	+	0.567233i
$461$	−3.68254	+	6.37834i	−0.171513	+	0.297069i	−0.938949	−	0.344056i	$-0.888199\pi$
$461$	−3.68254	+	6.37834i	−0.171513	+	0.297069i	0.767436	+	0.641125i	$0.221532\pi$
$462$		0			0
$463$	−14.3457	−	24.8475i	−0.666702	−	1.15476i	−0.978821	−	0.204718i	$-0.934372\pi$
$463$	−14.3457	−	24.8475i	−0.666702	−	1.15476i	0.312119	−	0.950043i	$-0.398961\pi$
$464$		−	2.88766i		−	0.134056i
$465$		0			0
$466$	7.31007			0.338632
$467$	6.83519	−	11.8389i	0.316295	−	0.547839i	−0.663417	−	0.748250i	$-0.730894\pi$
$467$	6.83519	−	11.8389i	0.316295	−	0.547839i	0.979712	+	0.200411i	$0.0642278\pi$
$468$		0			0
$469$		0			0
$470$	7.36387	+	4.25153i	0.339670	+	0.196109i
$471$		0			0
$472$	−0.0183031	−	0.0105673i	−0.000842469	−	0.000486400i
$473$	3.22157	+	1.85997i	0.148128	+	0.0855216i
$474$		0			0
$475$	−15.6739	−	9.04931i	−0.719166	−	0.415211i
$476$		0			0
$477$		0			0
$478$	4.20494	−	7.28317i	0.192329	−	0.333124i
$479$	−10.4107			−0.475679			−0.237839	−	0.971304i	$-0.576439\pi$
$479$	−10.4107			−0.475679			−0.237839	+	0.971304i	$0.576439\pi$
$480$		0			0
$481$			8.54997i			0.389845i
$482$	−4.47607	−	7.75277i	−0.203879	−	0.353129i
$483$		0			0
$484$	−2.28001	+	3.94910i	−0.103637	+	0.179504i
$485$	63.4184	+	36.6146i	2.87968	+	1.66258i
$486$		0			0
$487$	−1.16925	−	2.02520i	−0.0529838	−	0.0917707i	0.838317	−	0.545183i	$-0.183540\pi$
$487$	−1.16925	−	2.02520i	−0.0529838	−	0.0917707i	−0.891301	+	0.453412i	$0.850207\pi$
$488$	1.23456	+	2.13832i	0.0558858	+	0.0967970i
$489$		0			0
$490$		0			0
$491$	29.3448	−	16.9422i	1.32431	−	0.764591i	0.339898	−	0.940462i	$-0.389608\pi$
$491$	29.3448	−	16.9422i	1.32431	−	0.764591i	0.984413	+	0.175871i	$0.0562742\pi$
$492$		0			0
$493$			2.14298i			0.0965151i
$494$	4.40271	−	2.54191i	0.198087	−	0.114366i
$495$		0			0
$496$			3.51174i			0.157682i
$497$		0			0
$498$		0			0
$499$	−16.6045			−0.743317			−0.371659	−	0.928369i	$-0.621211\pi$
$499$	−16.6045			−0.743317			−0.371659	+	0.928369i	$0.621211\pi$
$500$	10.0017	−	17.3234i	0.447288	−	0.774726i
$501$		0			0
$502$	10.9494	−	6.32161i	0.488694	−	0.282147i
$503$	−35.3661			−1.57690			−0.788449	−	0.615100i	$-0.789115\pi$
$503$	−35.3661			−1.57690			−0.788449	+	0.615100i	$0.789115\pi$
$504$		0			0
$505$	32.2246			1.43398
$506$	21.3615	−	12.3331i	0.949635	−	0.548272i
$507$		0			0
$508$	1.47231	−	2.55012i	0.0653232	−	0.113143i
$509$	37.0582			1.64257			0.821287	−	0.570515i	$-0.193256\pi$
$509$	37.0582			1.64257			0.821287	+	0.570515i	$0.193256\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.1219	−	8.15329i	0.622891	−	0.359626i
$515$		−	66.3384i		−	2.92322i
$516$		0			0
$517$	7.46513	−	4.30999i	0.328316	−	0.189553i
$518$		0			0
$519$		0			0
$520$	5.54191	+	9.59886i	0.243029	+	0.420938i
$521$	−0.891547	−	1.54420i	−0.0390594	−	0.0676528i	0.845835	−	0.533445i	$-0.179103\pi$
$521$	−0.891547	−	1.54420i	−0.0390594	−	0.0676528i	−0.884894	+	0.465792i	$0.845769\pi$
$522$		0			0
$523$	20.8312	+	12.0269i	0.910886	+	0.525901i	0.880716	−	0.473644i	$-0.157062\pi$
$523$	20.8312	+	12.0269i	0.910886	+	0.525901i	0.0301702	+	0.999545i	$0.490395\pi$
$524$	7.53255	−	13.0468i	0.329061	−	0.569950i
$525$		0			0
$526$	−11.8608	−	20.5434i	−0.517154	−	0.895737i
$527$		−	2.60612i		−	0.113524i
$528$		0			0
$529$	−16.1014			−0.700060
$530$		0			0
$531$		0			0
$532$		0			0
$533$	25.8876	+	14.9462i	1.12132	+	0.647392i
$534$		0			0
$535$	−48.3126	−	27.8933i	−2.08874	−	1.20593i
$536$	−11.6474	−	6.72463i	−0.503091	−	0.290460i
$537$		0			0
$538$	−6.30716	−	3.64144i	−0.271921	−	0.156994i
$539$		0			0
$540$		0			0
$541$	−15.0016	+	25.9835i	−0.644968	+	1.11712i	0.339341	+	0.940664i	$0.389796\pi$
$541$	−15.0016	+	25.9835i	−0.644968	+	1.11712i	−0.984309	+	0.176454i	$0.943537\pi$
$542$	−22.6879			−0.974530
$543$		0			0
$544$			0.742117i			0.0318180i
$545$	−21.9458	−	38.0113i	−0.940056	−	1.62822i
$546$		0			0
$547$	−10.7816	+	18.6743i	−0.460987	+	0.798454i	−0.999010	−	0.0444765i	$-0.985838\pi$
$547$	−10.7816	+	18.6743i	−0.460987	+	0.798454i	0.538023	+	0.842930i	$0.319171\pi$
$548$	−13.6139	−	7.85997i	−0.581556	−	0.335761i
$549$		0			0
$550$	−20.0007	−	34.6423i	−0.852835	−	1.47715i
$551$	−2.57686	−	4.46325i	−0.109778	−	0.190141i
$552$		0			0
$553$		0			0
$554$	−20.9298	+	12.0838i	−0.889221	+	0.513392i
$555$		0			0
$556$		−	3.30675i		−	0.140237i
$557$	−31.9976	+	18.4738i	−1.35578	+	0.782762i	−0.989052	−	0.147565i	$-0.952856\pi$
$557$	−31.9976	+	18.4738i	−1.35578	+	0.782762i	−0.366731	+	0.930327i	$0.619523\pi$
$558$		0			0
$559$		−	2.68625i		−	0.113616i
$560$		0			0
$561$		0			0
$562$	−4.74847			−0.200302
$563$	7.58422	−	13.1363i	0.319637	−	0.553627i	−0.660776	−	0.750584i	$-0.729772\pi$
$563$	7.58422	−	13.1363i	0.319637	−	0.553627i	0.980412	+	0.196957i	$0.0631058\pi$
$564$		0			0
$565$	33.1329	−	19.1293i	1.39391	−	0.804774i
$566$	−29.3853			−1.23516
$567$		0			0
$568$	1.94304			0.0815282
$569$	−31.8084	+	18.3646i	−1.33348	+	0.769885i	−0.985831	−	0.167740i	$-0.946353\pi$
$569$	−31.8084	+	18.3646i	−1.33348	+	0.769885i	−0.347648	+	0.937625i	$0.613020\pi$
$570$		0			0
$571$	−5.61387	+	9.72351i	−0.234933	+	0.406916i	−0.959253	−	0.282548i	$-0.908820\pi$
$571$	−5.61387	+	9.72351i	−0.234933	+	0.406916i	0.724320	+	0.689464i	$0.242154\pi$
$572$	11.2362			0.469810
$573$		0			0
$574$		0			0
$575$			63.4114i			2.64444i
$576$		0			0
$577$	31.6545	−	18.2757i	1.31780	−	0.760829i	0.334422	−	0.942424i	$-0.391459\pi$
$577$	31.6545	−	18.2757i	1.31780	−	0.760829i	0.983374	+	0.181594i	$0.0581257\pi$
$578$			16.4493i			0.684199i
$579$		0			0
$580$	9.73085	−	5.61811i	0.404052	−	0.233279i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−2.42743	−	4.20443i	−0.100448	−	0.173981i
$585$		0			0
$586$	5.73666	+	3.31206i	0.236979	+	0.136820i
$587$	4.99738	−	8.65571i	0.206264	−	0.357259i	−0.744271	−	0.667878i	$-0.767203\pi$
$587$	4.99738	−	8.65571i	0.206264	−	0.357259i	0.950535	+	0.310619i	$0.100536\pi$
$588$		0			0
$589$	3.13376	+	5.42784i	0.129124	+	0.223650i
$590$		−	0.0822372i		−	0.00338565i
$591$		0			0
$592$	3.00158			0.123364
$593$	−3.89111	+	6.73961i	−0.159789	+	0.276763i	−0.934792	−	0.355194i	$-0.884415\pi$
$593$	−3.89111	+	6.73961i	−0.159789	+	0.276763i	0.775004	+	0.631957i	$0.217748\pi$
$594$		0			0
$595$		0			0
$596$	−9.52765	−	5.50079i	−0.390268	−	0.225321i
$597$		0			0
$598$	−15.4256	−	8.90597i	−0.630800	−	0.364192i
$599$	21.6614	+	12.5062i	0.885061	+	0.510990i	0.872324	−	0.488929i	$-0.162612\pi$
$599$	21.6614	+	12.5062i	0.885061	+	0.510990i	0.0127373	+	0.999919i	$0.495945\pi$
$600$		0			0
$601$	−25.9925	−	15.0068i	−1.06026	−	0.612139i	−0.134753	−	0.990879i	$-0.543024\pi$
$601$	−25.9925	−	15.0068i	−1.06026	−	0.612139i	−0.925503	+	0.378740i	$0.876357\pi$
$602$		0			0
$603$		0			0
$604$	−0.719988	+	1.24706i	−0.0292959	+	0.0507420i
$605$	−17.7436			−0.721379
$606$		0			0
$607$		−	4.58280i		−	0.186010i	−0.995666	−	0.0930050i	$-0.970353\pi$
$607$		−	4.58280i		−	0.186010i	0.995666	−	0.0930050i	$-0.0296473\pi$
$608$	−0.892369	−	1.54563i	−0.0361903	−	0.0626835i
$609$		0			0
$610$	−4.80380	+	8.32043i	−0.194500	+	0.336884i
$611$	−5.39073	−	3.11234i	−0.218085	−	0.125912i
$612$		0			0
$613$	−15.2761	−	26.4590i	−0.616996	−	1.06867i	−0.990031	−	0.140852i	$-0.955016\pi$
$613$	−15.2761	−	26.4590i	−0.616996	−	1.06867i	0.373034	−	0.927818i	$-0.378317\pi$
$614$	−10.8621	−	18.8137i	−0.438359	−	0.759259i
$615$		0			0
$616$		0			0
$617$	28.2484	−	16.3092i	1.13724	−	0.656585i	0.191493	−	0.981494i	$-0.438667\pi$
$617$	28.2484	−	16.3092i	1.13724	−	0.656585i	0.945745	+	0.324909i	$0.105334\pi$
$618$		0			0
$619$		−	20.0045i		−	0.804049i	−0.915629	−	0.402024i	$-0.868307\pi$
$619$		−	20.0045i		−	0.804049i	0.915629	−	0.402024i	$-0.131693\pi$
$620$	−11.8339	+	6.83228i	−0.475259	+	0.274391i
$621$		0			0
$622$		−	6.29800i		−	0.252527i
$623$		0			0
$624$		0			0
$625$	27.1314			1.08526
$626$	−11.1095	+	19.2423i	−0.444026	+	0.769076i
$627$		0			0
$628$	−14.3822	+	8.30354i	−0.573910	+	0.331347i
$629$	−2.22752			−0.0888171
$630$		0			0
$631$	6.09634			0.242692			0.121346	−	0.992610i	$-0.461279\pi$
$631$	6.09634			0.242692			0.121346	+	0.992610i	$0.461279\pi$
$632$	3.14898	−	1.81806i	0.125260	−	0.0723187i
$633$		0			0
$634$	−7.83070	+	13.5632i	−0.310997	+	0.538663i
$635$	11.4579			0.454691
$636$		0			0
$637$		0			0
$638$		−	11.3907i		−	0.450963i
$639$		0			0
$640$	3.36980	−	1.94556i	0.133203	−	0.0769049i
$641$			33.4415i			1.32086i	0.750888	+	0.660429i	$0.229626\pi$
$641$			33.4415i			1.32086i	−0.750888	+	0.660429i	$0.770374\pi$
$642$		0			0
$643$	16.6022	−	9.58527i	0.654726	−	0.378006i	−0.135539	−	0.990772i	$-0.543276\pi$
$643$	16.6022	−	9.58527i	0.654726	−	0.378006i	0.790264	+	0.612766i	$0.209943\pi$
$644$		0			0
$645$		0			0
$646$	0.662242	+	1.14704i	0.0260556	+	0.0451296i
$647$	−22.3025	−	38.6290i	−0.876800	−	1.51866i	−0.854832	−	0.518904i	$-0.826340\pi$
$647$	−22.3025	−	38.6290i	−0.876800	−	1.51866i	−0.0219681	−	0.999759i	$-0.506993\pi$
$648$		0			0
$649$	−0.0721988	−	0.0416840i	−0.00283405	−	0.00163624i
$650$	−14.4430	+	25.0159i	−0.566500	+	0.981206i
$651$		0			0
$652$	−6.19773	−	10.7348i	−0.242722	−	0.420407i
$653$			0.652123i			0.0255195i	0.999919	+	0.0127598i	$0.00406167\pi$
$653$			0.652123i			0.0255195i	−0.999919	+	0.0127598i	$0.995938\pi$
$654$		0			0
$655$	58.6200			2.29047
$656$	5.24705	−	9.08816i	0.204863	−	0.354833i
$657$		0			0
$658$		0			0
$659$	−26.2738	−	15.1692i	−1.02348	−	0.590908i	−0.108372	−	0.994110i	$-0.534564\pi$
$659$	−26.2738	−	15.1692i	−1.02348	−	0.590908i	−0.915111	+	0.403202i	$0.867897\pi$
$660$		0			0
$661$	11.1004	+	6.40881i	0.431755	+	0.249274i	0.700094	−	0.714051i	$-0.253141\pi$
$661$	11.1004	+	6.40881i	0.431755	+	0.249274i	−0.268339	+	0.963325i	$0.586475\pi$
$662$	1.10181	+	0.636129i	0.0428230	+	0.0247239i
$663$		0			0
$664$	6.98012	+	4.02998i	0.270881	+	0.156393i
$665$		0			0
$666$		0			0
$667$	−9.02843	+	15.6377i	−0.349582	+	0.605494i
$668$	11.7217			0.453528
$669$		0			0
$670$		−	52.3326i		−	2.02179i
$671$	4.86986	+	8.43484i	0.187999	+	0.325623i
$672$		0			0
$673$	11.2246	−	19.4416i	0.432678	−	0.749420i	−0.564425	−	0.825484i	$-0.690902\pi$
$673$	11.2246	−	19.4416i	0.432678	−	0.749420i	0.997103	+	0.0760644i	$0.0242355\pi$
$674$	6.54717	+	3.78001i	0.252188	+	0.145601i
$675$		0			0
$676$	2.44304	+	4.23147i	0.0939632	+	0.162749i
$677$	−25.5903	−	44.3237i	−0.983516	−	1.70350i	−0.648353	−	0.761340i	$-0.724542\pi$
$677$	−25.5903	−	44.3237i	−0.983516	−	1.70350i	−0.335163	−	0.942160i	$-0.608791\pi$
$678$		0			0
$679$		0			0
$680$	−2.50079	+	1.44383i	−0.0959009	+	0.0553684i
$681$		0			0
$682$			13.8525i			0.530438i
$683$	−12.6107	+	7.28080i	−0.482536	+	0.278592i	−0.721473	−	0.692443i	$-0.756534\pi$
$683$	−12.6107	+	7.28080i	−0.482536	+	0.278592i	0.238937	+	0.971035i	$0.423201\pi$
$684$		0			0
$685$		−	61.1681i		−	2.33711i
$686$		0			0
$687$		0			0
$688$	−0.943042			−0.0359532
$689$		0			0
$690$		0			0
$691$	21.1757	−	12.2258i	0.805560	−	0.465090i	−0.0398517	−	0.999206i	$-0.512689\pi$
$691$	21.1757	−	12.2258i	0.805560	−	0.465090i	0.845412	+	0.534115i	$0.179355\pi$
$692$	16.7710			0.637536
$693$		0			0
$694$	−22.1091			−0.839250
$695$	11.1431	−	6.43347i	0.422682	−	0.244035i
$696$		0			0
$697$	−3.89393	+	6.74448i	−0.147493	+	0.255465i
$698$	14.7435			0.558048
$699$		0			0
$700$		0			0
$701$		−	2.21697i		−	0.0837337i	−0.999123	−	0.0418669i	$-0.986669\pi$
$701$		−	2.21697i		−	0.0837337i	0.999123	−	0.0418669i	$-0.0133305\pi$
$702$		0			0
$703$	4.63932	−	2.67851i	0.174975	−	0.101022i
$704$		−	3.94462i		−	0.148668i
$705$		0			0
$706$	−14.9629	+	8.63881i	−0.563135	+	0.325126i
$707$		0			0
$708$		0			0
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	0.998857	−	0.0477959i	$-0.0152197\pi$
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	−0.540821	+	0.841138i	$0.681886\pi$
$710$	3.78030	+	6.54767i	0.141872	+	0.245730i
$711$		0			0
$712$	−8.02499	−	4.63323i	−0.300749	−	0.173638i
$713$	10.9796	−	19.0173i	0.411190	−	0.712203i
$714$		0			0
$715$	21.8607	+	37.8639i	0.817544	+	1.41603i
$716$			5.77532i			0.215834i
$717$		0			0
$718$	10.9129			0.407267
$719$	−1.11376	+	1.92909i	−0.0415363	+	0.0719429i	−0.886046	−	0.463597i	$-0.846559\pi$
$719$	−1.11376	+	1.92909i	−0.0415363	+	0.0719429i	0.844510	+	0.535540i	$0.179892\pi$
$720$		0			0
$721$		0			0
$722$	13.6959	+	7.90736i	0.509710	+	0.294281i
$723$		0			0
$724$	−4.79180	−	2.76655i	−0.178086	−	0.102818i
$725$	25.3599	+	14.6416i	0.941844	+	0.543774i
$726$		0			0
$727$	10.4880	+	6.05523i	0.388977	+	0.224576i	0.681717	−	0.731616i	$-0.261234\pi$
$727$	10.4880	+	6.05523i	0.388977	+	0.224576i	−0.292740	+	0.956192i	$0.594567\pi$
$728$		0			0
$729$		0			0
$730$	9.44541	−	16.3599i	0.349590	−	0.605508i
$731$	0.699848			0.0258848
$732$		0			0
$733$			15.6661i			0.578641i	0.957232	+	0.289321i	$0.0934293\pi$
$733$			15.6661i			0.578641i	−0.957232	+	0.289321i	$0.906571\pi$
$734$	17.8636	+	30.9407i	0.659357	+	1.14204i
$735$		0			0
$736$	−3.12656	+	5.41535i	−0.115246	+	0.199613i
$737$	−45.9446	−	26.5261i	−1.69239	−	0.977102i
$738$		0			0
$739$	4.05227	+	7.01874i	0.149065	+	0.258188i	0.930882	−	0.365319i	$-0.119040\pi$
$739$	4.05227	+	7.01874i	0.149065	+	0.258188i	−0.781817	+	0.623508i	$0.785707\pi$
$740$	5.83974	+	10.1147i	0.214673	+	0.371825i
$741$		0			0
$742$		0			0
$743$	10.5429	−	6.08697i	0.386783	−	0.223309i	−0.293982	−	0.955811i	$-0.594981\pi$
$743$	10.5429	−	6.08697i	0.386783	−	0.223309i	0.680765	+	0.732502i	$0.261647\pi$
$744$		0			0
$745$		−	42.8084i		−	1.56838i
$746$	27.7648	−	16.0300i	1.01654	−	0.586900i
$747$		0			0
$748$			2.92737i			0.107035i
$749$		0			0
$750$		0			0
$751$	34.6123			1.26302			0.631511	−	0.775367i	$-0.282435\pi$
$751$	34.6123			1.26302			0.631511	+	0.775367i	$0.282435\pi$
$752$	−1.09263	+	1.89248i	−0.0398440	+	0.0690118i
$753$		0			0
$754$	−7.12348	+	4.11274i	−0.259422	+	0.149777i
$755$	−5.60311			−0.203918
$756$		0			0
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$	−30.2149	+	17.4446i	−1.09745	+	0.633615i
$759$		0			0
$760$	3.47231	−	6.01422i	0.125954	−	0.218159i
$761$	10.2252			0.370665			0.185332	−	0.982676i	$-0.440664\pi$
$761$	10.2252			0.370665			0.185332	+	0.982676i	$0.440664\pi$
$762$		0			0
$763$		0			0
$764$			6.21372i			0.224805i
$765$		0			0
$766$	15.1851	−	8.76711i	0.548659	−	0.316769i
$767$			0.0602018i			0.00217376i
$768$		0			0
$769$	−26.6746	+	15.4006i	−0.961910	+	0.555359i	−0.896760	−	0.442517i	$-0.854086\pi$
$769$	−26.6746	+	15.4006i	−0.961910	+	0.555359i	−0.0651494	+	0.997876i	$0.520752\pi$
$770$		0			0
$771$		0			0
$772$	−3.90271	−	6.75970i	−0.140462	−	0.243287i
$773$	−17.8916	−	30.9892i	−0.643518	−	1.11461i	−0.984642	−	0.174587i	$-0.944141\pi$
$773$	−17.8916	−	30.9892i	−0.643518	−	1.11461i	0.341124	−	0.940018i	$-0.389192\pi$
$774$		0			0
$775$	−30.8406	−	17.8059i	−1.10783	−	0.639605i
$776$	−9.40980	+	16.2983i	−0.337792	+	0.585073i
$777$		0			0
$778$	3.81086	+	6.60060i	0.136626	+	0.236643i
$779$		−	18.7292i		−	0.671044i
$780$		0			0
$781$	7.66456			0.274260
$782$	2.32027	−	4.01882i	0.0829727	−	0.143713i
$783$		0			0
$784$		0			0
$785$	−55.9626	−	32.3100i	−1.99739	−	1.15319i
$786$		0			0
$787$	−13.2859	−	7.67064i	−0.473592	−	0.273429i	0.244150	−	0.969737i	$-0.421491\pi$
$787$	−13.2859	−	7.67064i	−0.473592	−	0.273429i	−0.717742	+	0.696309i	$0.754824\pi$
$788$	11.0624	+	6.38687i	0.394081	+	0.227523i
$789$		0			0
$790$	12.2530	+	7.07430i	0.435944	+	0.251692i
$791$		0			0
$792$		0			0
$793$	3.51663	−	6.09098i	0.124879	−	0.216297i
$794$	37.6469			1.33604
$795$		0			0
$796$			1.81201i			0.0642250i
$797$	17.5200	+	30.3455i	0.620590	+	1.07489i	0.989376	+	0.145379i	$0.0464402\pi$
$797$	17.5200	+	30.3455i	0.620590	+	1.07489i	−0.368786	+	0.929514i	$0.620226\pi$
$798$		0			0
$799$	0.810856	−	1.40444i	0.0286860	−	0.0496857i
$800$	8.78217	+	5.07039i	0.310496	+	0.179265i
$801$		0			0
$802$	10.7207	+	18.5689i	0.378562	+	0.655689i
$803$	−9.57529	−	16.5849i	−0.337905	−	0.585268i
$804$		0			0
$805$		0			0
$806$	8.66299	−	5.00158i	0.305141	−	0.176173i
$807$		0			0
$808$			8.28158i			0.291345i
$809$	23.6360	−	13.6462i	0.830997	−	0.479777i	−0.0231967	−	0.999731i	$-0.507384\pi$
$809$	23.6360	−	13.6462i	0.830997	−	0.479777i	0.854194	+	0.519954i	$0.174051\pi$
$810$		0			0
$811$			27.7628i			0.974883i	0.873156	+	0.487442i	$0.162070\pi$
$811$			27.7628i			0.974883i	−0.873156	+	0.487442i	$0.837930\pi$
$812$		0			0
$813$		0			0
$814$	11.8401			0.414995
$815$	24.1161	−	41.7703i	0.844749	−	1.46315i
$816$		0			0
$817$	−1.45759	+	0.841542i	−0.0509947	+	0.0294418i
$818$	−29.5703			−1.03390
$819$		0			0
$820$	40.8338			1.42598
$821$	−38.4968	+	22.2262i	−1.34355	+	0.775698i	−0.987326	−	0.158703i	$-0.949269\pi$
$821$	−38.4968	+	22.2262i	−1.34355	+	0.775698i	−0.356223	+	0.934401i	$0.615936\pi$
$822$		0			0
$823$	25.5577	−	44.2672i	0.890884	−	1.54306i	0.0520663	−	0.998644i	$-0.483419\pi$
$823$	25.5577	−	44.2672i	0.890884	−	1.54306i	0.838818	−	0.544413i	$-0.183247\pi$
$824$	17.0487			0.593919
$825$		0			0
$826$		0			0
$827$		−	14.5414i		−	0.505653i	−0.967512	−	0.252826i	$-0.918640\pi$
$827$		−	14.5414i		−	0.505653i	0.967512	−	0.252826i	$-0.0813601\pi$
$828$		0			0
$829$	−24.2211	+	13.9841i	−0.841234	+	0.485686i	−0.857683	−	0.514178i	$-0.828097\pi$
$829$	−24.2211	+	13.9841i	−0.841234	+	0.485686i	0.0164497	+	0.999865i	$0.494764\pi$
$830$			31.3622i			1.08860i
$831$		0			0
$832$	−2.46687	+	1.42425i	−0.0855233	+	0.0493769i
$833$		0			0
$834$		0			0
$835$	22.8053	+	39.5000i	0.789211	+	1.36695i
$836$	−3.52006	−	6.09692i	−0.121744	−	0.210866i
$837$		0			0
$838$	6.17443	+	3.56481i	0.213292	+	0.123144i
$839$	0.499354	−	0.864906i	0.0172396	−	0.0298599i	−0.857277	−	0.514856i	$-0.827846\pi$
$839$	0.499354	−	0.864906i	0.0172396	−	0.0298599i	0.874517	+	0.484996i	$0.161179\pi$
$840$		0			0
$841$	−10.3307	−	17.8933i	−0.356231	−	0.617011i
$842$		−	4.62014i		−	0.159220i
$843$		0			0
$844$	−3.77532			−0.129952
$845$	−9.50616	+	16.4651i	−0.327022	+	0.566418i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−6.51739	−	3.76282i	−0.223545	−	0.129064i
$851$	−16.2546	−	9.38460i	−0.557200	−	0.321700i
$852$		0			0
$853$	8.48739	+	4.90020i	0.290603	+	0.167780i	0.638214	−	0.769859i	$-0.279674\pi$
$853$	8.48739	+	4.90020i	0.290603	+	0.167780i	−0.347611	+	0.937639i	$0.613007\pi$
$854$		0			0
$855$		0			0
$856$	7.16846	−	12.4161i	0.245013	−	0.424375i
$857$	7.70003			0.263028			0.131514	−	0.991314i	$-0.458016\pi$
$857$	7.70003			0.263028			0.131514	+	0.991314i	$0.458016\pi$
$858$		0			0
$859$		−	18.9396i		−	0.646210i	−0.946363	−	0.323105i	$-0.895273\pi$
$859$		−	18.9396i		−	0.646210i	0.946363	−	0.323105i	$-0.104727\pi$
$860$	−1.83474	−	3.17787i	−0.0625642	−	0.108364i
$861$		0			0
$862$	2.00385	−	3.47078i	0.0682515	−	0.118215i
$863$	−15.1156	−	8.72700i	−0.514541	−	0.297070i	0.220157	−	0.975464i	$-0.429343\pi$
$863$	−15.1156	−	8.72700i	−0.514541	−	0.297070i	−0.734698	+	0.678394i	$0.762676\pi$
$864$		0			0
$865$	32.6289	+	56.5149i	1.10942	+	1.92156i
$866$	14.7063	+	25.4720i	0.499740	+	0.865574i
$867$		0			0
$868$		0			0
$869$	12.4215	−	7.17157i	0.421371	−	0.243279i
$870$		0			0
$871$			38.3101i			1.29809i
$872$	9.76874	−	5.63998i	0.330811	−	0.190994i
$873$		0			0
$874$			11.1602i			0.377498i
$875$		0			0
$876$		0			0
$877$	0.392305			0.0132472			0.00662360	−	0.999978i	$-0.497892\pi$
$877$	0.392305			0.0132472			0.00662360	+	0.999978i	$0.497892\pi$
$878$	10.6885	−	18.5130i	0.360718	−	0.624782i
$879$		0			0
$880$	13.2926	−	7.67448i	0.448093	−	0.258707i
$881$	−37.0259			−1.24744			−0.623718	−	0.781650i	$-0.714378\pi$
$881$	−37.0259			−1.24744			−0.623718	+	0.781650i	$0.714378\pi$
$882$		0			0
$883$	−29.9586			−1.00819			−0.504094	−	0.863649i	$-0.668174\pi$
$883$	−29.9586			−1.00819			−0.504094	+	0.863649i	$0.668174\pi$
$884$	1.83070	−	1.05696i	0.0615732	−	0.0355493i
$885$		0			0
$886$	−2.91693	+	5.05227i	−0.0979962	+	0.169734i
$887$	−28.9859			−0.973252			−0.486626	−	0.873610i	$-0.661773\pi$
$887$	−28.9859			−0.973252			−0.486626	+	0.873610i	$0.661773\pi$
$888$		0			0
$889$		0			0
$890$		−	36.0569i		−	1.20863i
$891$		0			0
$892$	11.0662	−	6.38910i	0.370525	−	0.213923i
$893$			3.90010i			0.130512i
$894$		0			0
$895$	−19.4617	+	11.2362i	−0.650533	+	0.375586i
$896$		0			0
$897$		0			0
$898$	11.2912	+	19.5569i	0.376791	+	0.652621i
$899$	−5.07035	−	8.78211i	−0.169106	−	0.292900i
$900$		0			0
$901$		0			0
$902$	20.6976	−	35.8493i	0.689156	−	1.19365i
$903$		0			0
$904$	4.91614	+	8.51501i	0.163508	+	0.283205i
$905$		−	21.5299i		−	0.715679i
$906$		0			0
$907$	−3.89546			−0.129347			−0.0646733	−	0.997906i	$-0.520601\pi$
$907$	−3.89546			−0.129347			−0.0646733	+	0.997906i	$0.520601\pi$
$908$	−9.99110	+	17.3051i	−0.331566	+	0.574290i
$909$		0			0
$910$		0			0
$911$	−1.32768	−	0.766538i	−0.0439881	−	0.0253966i	0.477845	−	0.878444i	$-0.341418\pi$
$911$	−1.32768	−	0.766538i	−0.0439881	−	0.0253966i	−0.521833	+	0.853048i	$0.674752\pi$
$912$		0			0
$913$	27.5339	+	15.8967i	0.911240	+	0.526105i
$914$	34.5218	+	19.9311i	1.14188	+	0.659264i
$915$		0			0
$916$	8.77402	+	5.06568i	0.289902	+	0.167375i
$917$		0			0
$918$		0			0
$919$	−14.1266	+	24.4679i	−0.465992	+	0.807122i	−0.999246	−	0.0388335i	$-0.987636\pi$
$919$	−14.1266	+	24.4679i	−0.465992	+	0.807122i	0.533254	+	0.845955i	$0.320969\pi$
$920$	−24.3316			−0.802188
$921$		0			0
$922$		−	7.36507i		−	0.242556i
$923$	−2.76737	−	4.79323i	−0.0910892	−	0.157771i
$924$		0			0
$925$	−15.2192	+	26.3603i	−0.500403	+	0.866723i
$926$	24.8475	+	14.3457i	0.816539	+	0.471429i
$927$		0			0
$928$	1.44383	+	2.50079i	0.0473961	+	0.0820924i
$929$	−1.64363	−	2.84685i	−0.0539257	−	0.0934021i	0.837802	−	0.545974i	$-0.183840\pi$
$929$	−1.64363	−	2.84685i	−0.0539257	−	0.0934021i	−0.891728	+	0.452571i	$0.850507\pi$
$930$		0			0
$931$		0			0
$932$	−6.33070	+	3.65503i	−0.207369	+	0.119725i
$933$		0			0
$934$			13.6704i			0.447308i
$935$	−9.86466	+	5.69536i	−0.322609	+	0.186258i
$936$		0			0
$937$		−	35.5084i		−	1.16001i	−0.814613	−	0.580005i	$-0.803051\pi$
$937$		−	35.5084i		−	1.16001i	0.814613	−	0.580005i	$-0.196949\pi$
$938$		0			0
$939$		0			0
$940$	−8.50307			−0.277339
$941$	−6.24941	+	10.8243i	−0.203725	+	0.352862i	−0.949726	−	0.313083i	$-0.898638\pi$
$941$	−6.24941	+	10.8243i	−0.203725	+	0.352862i	0.746001	+	0.665945i	$0.231972\pi$
$942$		0			0
$943$	−56.8293	+	32.8104i	−1.85062	+	1.06845i
$944$	0.0211346			0.000687873
$945$		0			0
$946$	−3.71994			−0.120946
$947$	31.2769	−	18.0577i	1.01636	−	0.586796i	0.103313	−	0.994649i	$-0.467056\pi$
$947$	31.2769	−	18.0577i	1.01636	−	0.586796i	0.913048	+	0.407852i	$0.133722\pi$
$948$		0			0
$949$	−6.91452	+	11.9763i	−0.224455	+	0.388767i
$950$	18.0986			0.587197
$951$		0			0
$952$		0			0
$953$			45.2925i			1.46717i	0.679599	+	0.733584i	$0.262154\pi$
$953$			45.2925i			1.46717i	−0.679599	+	0.733584i	$0.737846\pi$
$954$		0			0
$955$	−20.9390	+	12.0892i	−0.677571	+	0.391196i
$956$			8.40988i			0.271995i
$957$		0			0
$958$	9.01596	−	5.20537i	0.291293	−	0.168178i
$959$		0			0
$960$		0			0
$961$	−9.33386	−	16.1667i	−0.301092	−	0.521507i
$962$	−4.27499	−	7.40449i	−0.137831	−	0.238730i
$963$		0			0
$964$	7.75277	+	4.47607i	0.249700	+	0.144164i
$965$	15.1859	−	26.3028i	0.488851	−	0.846716i
$966$		0			0
$967$	12.0000	+	20.7845i	0.385893	+	0.668385i	0.991893	−	0.127079i	$-0.0405602\pi$
$967$	12.0000	+	20.7845i	0.385893	+	0.668385i	−0.606000	+	0.795465i	$0.707227\pi$
$968$		−	4.56002i		−	0.146565i
$969$		0			0
$970$	−73.2292			−2.35125
$971$	−16.6813	+	28.8928i	−0.535328	+	0.927215i	0.463819	+	0.885930i	$0.346479\pi$
$971$	−16.6813	+	28.8928i	−0.535328	+	0.927215i	−0.999147	+	0.0412855i	$0.986855\pi$
$972$		0			0
$973$		0			0
$974$	2.02520	+	1.16925i	0.0648917	+	0.0374652i
$975$		0			0
$976$	−2.13832	−	1.23456i	−0.0684458	−	0.0395172i
$977$	−29.8846	−	17.2539i	−0.956091	−	0.552000i	−0.0611236	−	0.998130i	$-0.519468\pi$
$977$	−29.8846	−	17.2539i	−0.956091	−	0.552000i	−0.894968	+	0.446131i	$0.852802\pi$
$978$		0			0
$979$	−31.6555	−	18.2763i	−1.01172	−	0.584114i
$980$		0			0
$981$		0			0
$982$	−16.9422	+	29.3448i	−0.540648	+	0.936429i
$983$	−2.41302			−0.0769633			−0.0384817	−	0.999259i	$-0.512252\pi$
$983$	−2.41302			−0.0769633			−0.0384817	+	0.999259i	$0.512252\pi$
$984$		0			0
$985$			49.7041i			1.58370i
$986$	−1.07149	−	1.85588i	−0.0341232	−	0.0591032i
$987$		0			0
$988$	−2.54191	+	4.40271i	−0.0808688	+	0.140069i
$989$	5.10691	+	2.94847i	0.162390	+	0.0937560i
$990$		0			0
$991$	−24.2991	−	42.0873i	−0.771887	−	1.33695i	−0.936528	−	0.350594i	$-0.885980\pi$
$991$	−24.2991	−	42.0873i	−0.771887	−	1.33695i	0.164641	−	0.986354i	$-0.447353\pi$
$992$	−1.75587	−	3.04125i	−0.0557488	−	0.0965598i
$993$		0			0
$994$		0			0
$995$	−6.10612	+	3.52537i	−0.193577	+	0.111762i
$996$		0			0
$997$		−	44.8542i		−	1.42055i	−0.703926	−	0.710274i	$-0.748571\pi$
$997$		−	44.8542i		−	1.42055i	0.703926	−	0.710274i	$-0.251429\pi$
$998$	14.3799	−	8.30223i	0.455187	−	0.262802i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.t.a.1979.4		16
3.2	odd	2		882.2.t.b.803.7		16
7.2	even	3		378.2.m.a.251.5		16
7.3	odd	6		2646.2.l.b.521.4		16
7.4	even	3		2646.2.l.b.521.1		16
7.5	odd	6		378.2.m.a.251.8		16
7.6	odd	2	inner	2646.2.t.a.1979.1		16
9.4	even	3		882.2.l.a.509.1		16
9.5	odd	6		2646.2.l.b.1097.8		16
21.2	odd	6		126.2.m.a.83.1	yes	16
21.5	even	6		126.2.m.a.83.4	yes	16
21.11	odd	6		882.2.l.a.227.8		16
21.17	even	6		882.2.l.a.227.5		16
21.20	even	2		882.2.t.b.803.6		16
28.19	even	6		3024.2.cc.b.2897.8		16
28.23	odd	6		3024.2.cc.b.2897.1		16
63.2	odd	6		1134.2.d.a.1133.9		16
63.4	even	3		882.2.t.b.815.6		16
63.5	even	6		378.2.m.a.125.5		16
63.13	odd	6		882.2.l.a.509.4		16
63.16	even	3		1134.2.d.a.1133.8		16
63.23	odd	6		378.2.m.a.125.8		16
63.31	odd	6		882.2.t.b.815.7		16
63.32	odd	6	inner	2646.2.t.a.2285.1		16
63.40	odd	6		126.2.m.a.41.1	✓	16
63.41	even	6		2646.2.l.b.1097.5		16
63.47	even	6		1134.2.d.a.1133.16		16
63.58	even	3		126.2.m.a.41.4	yes	16
63.59	even	6	inner	2646.2.t.a.2285.4		16
63.61	odd	6		1134.2.d.a.1133.1		16
84.23	even	6		1008.2.cc.b.209.7		16
84.47	odd	6		1008.2.cc.b.209.2		16
252.23	even	6		3024.2.cc.b.881.8		16
252.103	even	6		1008.2.cc.b.545.7		16
252.131	odd	6		3024.2.cc.b.881.1		16
252.247	odd	6		1008.2.cc.b.545.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	63.40	odd	6
126.2.m.a.41.4	yes	16	63.58	even	3
126.2.m.a.83.1	yes	16	21.2	odd	6
126.2.m.a.83.4	yes	16	21.5	even	6
378.2.m.a.125.5		16	63.5	even	6
378.2.m.a.125.8		16	63.23	odd	6
378.2.m.a.251.5		16	7.2	even	3
378.2.m.a.251.8		16	7.5	odd	6
882.2.l.a.227.5		16	21.17	even	6
882.2.l.a.227.8		16	21.11	odd	6
882.2.l.a.509.1		16	9.4	even	3
882.2.l.a.509.4		16	63.13	odd	6
882.2.t.b.803.6		16	21.20	even	2
882.2.t.b.803.7		16	3.2	odd	2
882.2.t.b.815.6		16	63.4	even	3
882.2.t.b.815.7		16	63.31	odd	6
1008.2.cc.b.209.2		16	84.47	odd	6
1008.2.cc.b.209.7		16	84.23	even	6
1008.2.cc.b.545.2		16	252.247	odd	6
1008.2.cc.b.545.7		16	252.103	even	6
1134.2.d.a.1133.1		16	63.61	odd	6
1134.2.d.a.1133.8		16	63.16	even	3
1134.2.d.a.1133.9		16	63.2	odd	6
1134.2.d.a.1133.16		16	63.47	even	6
2646.2.l.b.521.1		16	7.4	even	3
2646.2.l.b.521.4		16	7.3	odd	6
2646.2.l.b.1097.5		16	63.41	even	6
2646.2.l.b.1097.8		16	9.5	odd	6
2646.2.t.a.1979.1		16	7.6	odd	2	inner
2646.2.t.a.1979.4		16	1.1	even	1	trivial
2646.2.t.a.2285.1		16	63.32	odd	6	inner
2646.2.t.a.2285.4		16	63.59	even	6	inner
3024.2.cc.b.881.1		16	252.131	odd	6
3024.2.cc.b.881.8		16	252.23	even	6
3024.2.cc.b.2897.1		16	28.23	odd	6
3024.2.cc.b.2897.8		16	28.19	even	6

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.89111 q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.89111 q^{5} +1.00000i q^{8} +(-3.36980 + 1.94556i) q^{10} +3.94462i q^{11} +(2.46687 - 1.42425i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.371058 + 0.642692i) q^{17} +(-1.54563 - 0.892369i) q^{19} +(1.94556 - 3.36980i) q^{20} +(-1.97231 - 3.41614i) q^{22} +6.25311i q^{23} +10.1408 q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.50079 + 1.44383i) q^{29} +(-3.04125 - 1.75587i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.642692 - 0.371058i) q^{34} +(-1.50079 + 2.59944i) q^{37} +1.78474 q^{38} +3.89111i q^{40} +(5.24705 + 9.08816i) q^{41} +(0.471521 - 0.816699i) q^{43} +(3.41614 + 1.97231i) q^{44} +(-3.12656 - 5.41535i) q^{46} +(-1.09263 - 1.89248i) q^{47} +(-8.78217 + 5.07039i) q^{50} -2.84849i q^{52} +15.3490i q^{55} -2.88766 q^{58} +(-0.0105673 + 0.0183031i) q^{59} +(2.13832 - 1.23456i) q^{61} +3.51174 q^{62} -1.00000 q^{64} +(9.59886 - 5.54191i) q^{65} +(-6.72463 + 11.6474i) q^{67} +0.742117 q^{68} -1.94304i q^{71} +(-4.20443 + 2.42743i) q^{73} -3.00158i q^{74} +(-1.54563 + 0.892369i) q^{76} +(-1.81806 - 3.14898i) q^{79} +(-1.94556 - 3.36980i) q^{80} +(-9.08816 - 5.24705i) q^{82} +(4.02998 - 6.98012i) q^{83} +(1.44383 + 2.50079i) q^{85} +0.943042i q^{86} -3.94462 q^{88} +(-4.63323 + 8.02499i) q^{89} +(5.41535 + 3.12656i) q^{92} +(1.89248 + 1.09263i) q^{94} +(-6.01422 - 3.47231i) q^{95} +(16.2983 + 9.40980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Introduction

L-functions

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Database

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