LMFDB - Embedded newform 576.2.bb.e.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71513 + 0.241506i) q^{3} +(-1.98415 + 0.531653i) q^{5} +(1.54969 - 0.894715i) q^{7} +(2.88335 - 0.828427i) q^{9} +O(q^{10})$	\(q+(-1.71513 + 0.241506i) q^{3} +(-1.98415 + 0.531653i) q^{5} +(1.54969 - 0.894715i) q^{7} +(2.88335 - 0.828427i) q^{9} +(0.693015 - 2.58637i) q^{11} +(1.24314 + 4.63944i) q^{13} +(3.27469 - 1.39104i) q^{15} -3.58889 q^{17} +(-4.85244 + 4.85244i) q^{19} +(-2.44185 + 1.90881i) q^{21} +(-0.446082 - 0.257545i) q^{23} +(-0.675912 + 0.390238i) q^{25} +(-4.74525 + 2.11721i) q^{27} +(-6.44956 - 1.72815i) q^{29} +(-4.05128 + 7.01703i) q^{31} +(-0.563989 + 4.60332i) q^{33} +(-2.59915 + 2.59915i) q^{35} +(1.25948 + 1.25948i) q^{37} +(-3.25259 - 7.65703i) q^{39} +(-4.07959 - 2.35535i) q^{41} +(1.76222 - 6.57670i) q^{43} +(-5.28058 + 3.17667i) q^{45} +(3.48945 + 6.04391i) q^{47} +(-1.89897 + 3.28911i) q^{49} +(6.15542 - 0.866737i) q^{51} +(5.26302 + 5.26302i) q^{53} +5.50019i q^{55} +(7.15068 - 9.49446i) q^{57} +(-6.76946 + 1.81387i) q^{59} +(5.78773 + 1.55082i) q^{61} +(3.72710 - 3.86359i) q^{63} +(-4.93314 - 8.54446i) q^{65} +(0.453328 + 1.69184i) q^{67} +(0.827288 + 0.333993i) q^{69} +7.58339i q^{71} -12.5473i q^{73} +(1.06503 - 0.832546i) q^{75} +(-1.24010 - 4.62812i) q^{77} +(4.01735 + 6.95825i) q^{79} +(7.62742 - 4.77729i) q^{81} +(-7.99826 - 2.14313i) q^{83} +(7.12091 - 1.90804i) q^{85} +(11.4792 + 1.40641i) q^{87} +16.5414i q^{89} +(6.07746 + 6.07746i) q^{91} +(5.25383 - 13.0135i) q^{93} +(7.04818 - 12.2078i) q^{95} +(-4.15739 - 7.20082i) q^{97} +(-0.144412 - 8.03151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	−1.71513	+	0.241506i	−0.990231	+	0.139433i
$3$	−1.71513	+	0.241506i	−0.990231	+	0.139433i
$4$		0			0
$5$	−1.98415	+	0.531653i	−0.887341	+	0.237762i	−0.673572	−	0.739122i	$-0.735241\pi$
$5$	−1.98415	+	0.531653i	−0.887341	+	0.237762i	−0.213769	+	0.976884i	$0.568574\pi$
$6$		0			0
$7$	1.54969	−	0.894715i	0.585729	−	0.338171i	−0.177678	−	0.984089i	$-0.556859\pi$
$7$	1.54969	−	0.894715i	0.585729	−	0.338171i	0.763407	+	0.645918i	$0.223525\pi$
$8$		0			0
$9$	2.88335	−	0.828427i	0.961117	−	0.276142i
$10$		0			0
$11$	0.693015	−	2.58637i	0.208952	−	0.779819i	−0.779257	−	0.626705i	$-0.784403\pi$
$11$	0.693015	−	2.58637i	0.208952	−	0.779819i	0.988209	−	0.153114i	$-0.0489301\pi$
$12$		0			0
$13$	1.24314	+	4.63944i	0.344784	+	1.28675i	0.892865	+	0.450325i	$0.148692\pi$
$13$	1.24314	+	4.63944i	0.344784	+	1.28675i	−0.548081	+	0.836425i	$0.684641\pi$
$14$		0			0
$15$	3.27469	−	1.39104i	0.845521	−	0.359165i
$16$		0			0
$17$	−3.58889			−0.870434			−0.435217	−	0.900326i	$-0.643328\pi$
$17$	−3.58889			−0.870434			−0.435217	+	0.900326i	$0.643328\pi$
$18$		0			0
$19$	−4.85244	+	4.85244i	−1.11323	+	1.11323i	−0.120514	+	0.992712i	$0.538454\pi$
$19$	−4.85244	+	4.85244i	−1.11323	+	1.11323i	−0.992712	+	0.120514i	$0.961546\pi$
$20$		0			0
$21$	−2.44185	+	1.90881i	−0.532855	+	0.416537i
$22$		0			0
$23$	−0.446082	−	0.257545i	−0.0930145	−	0.0537019i	0.452771	−	0.891627i	$-0.350435\pi$
$23$	−0.446082	−	0.257545i	−0.0930145	−	0.0537019i	−0.545786	+	0.837925i	$0.683769\pi$
$24$		0			0
$25$	−0.675912	+	0.390238i	−0.135182	+	0.0780476i
$26$		0			0
$27$	−4.74525	+	2.11721i	−0.913225	+	0.407457i
$28$		0			0
$29$	−6.44956	−	1.72815i	−1.19765	−	0.320910i	−0.395746	−	0.918360i	$-0.629514\pi$
$29$	−6.44956	−	1.72815i	−1.19765	−	0.320910i	−0.801906	+	0.597450i	$0.796181\pi$
$30$		0			0
$31$	−4.05128	+	7.01703i	−0.727632	+	1.26030i	0.230249	+	0.973132i	$0.426046\pi$
$31$	−4.05128	+	7.01703i	−0.727632	+	1.26030i	−0.957881	+	0.287164i	$0.907287\pi$
$32$		0			0
$33$	−0.563989	+	4.60332i	−0.0981779	+	0.801336i
$34$		0			0
$35$	−2.59915	+	2.59915i	−0.439337	+	0.439337i
$36$		0			0
$37$	1.25948	+	1.25948i	0.207057	+	0.207057i	0.803015	−	0.595959i	$-0.203228\pi$
$37$	1.25948	+	1.25948i	0.207057	+	0.207057i	−0.595959	+	0.803015i	$0.703228\pi$
$38$		0			0
$39$	−3.25259	−	7.65703i	−0.520831	−	1.22611i
$40$		0			0
$41$	−4.07959	−	2.35535i	−0.637126	−	0.367845i	0.146381	−	0.989228i	$-0.453238\pi$
$41$	−4.07959	−	2.35535i	−0.637126	−	0.367845i	−0.783506	+	0.621384i	$0.786571\pi$
$42$		0			0
$43$	1.76222	−	6.57670i	0.268736	−	1.00294i	−0.691187	−	0.722676i	$-0.742912\pi$
$43$	1.76222	−	6.57670i	0.268736	−	1.00294i	0.959924	−	0.280262i	$-0.0904212\pi$
$44$		0			0
$45$	−5.28058	+	3.17667i	−0.787182	+	0.473550i
$46$		0			0
$47$	3.48945	+	6.04391i	0.508989	+	0.881595i	0.999946	+	0.0104109i	$0.00331395\pi$
$47$	3.48945	+	6.04391i	0.508989	+	0.881595i	−0.490957	+	0.871184i	$0.663353\pi$
$48$		0			0
$49$	−1.89897	+	3.28911i	−0.271281	+	0.469873i
$50$		0			0
$51$	6.15542	−	0.866737i	0.861931	−	0.121367i
$52$		0			0
$53$	5.26302	+	5.26302i	0.722932	+	0.722932i	0.969201	−	0.246269i	$-0.0792048\pi$
$53$	5.26302	+	5.26302i	0.722932	+	0.722932i	−0.246269	+	0.969201i	$0.579205\pi$
$54$		0			0
$55$			5.50019i			0.741646i
$56$		0			0
$57$	7.15068	−	9.49446i	0.947131	−	1.25757i
$58$		0			0
$59$	−6.76946	+	1.81387i	−0.881308	+	0.236146i	−0.670972	−	0.741483i	$-0.734123\pi$
$59$	−6.76946	+	1.81387i	−0.881308	+	0.236146i	−0.210337	+	0.977629i	$0.567456\pi$
$60$		0			0
$61$	5.78773	+	1.55082i	0.741042	+	0.198562i	0.609541	−	0.792754i	$-0.291354\pi$
$61$	5.78773	+	1.55082i	0.741042	+	0.198562i	0.131501	+	0.991316i	$0.458020\pi$
$62$		0			0
$63$	3.72710	−	3.86359i	0.469570	−	0.486766i
$64$		0			0
$65$	−4.93314	−	8.54446i	−0.611881	−	1.05981i
$66$		0			0
$67$	0.453328	+	1.69184i	0.0553829	+	0.206692i	0.988073	−	0.153988i	$-0.0492116\pi$
$67$	0.453328	+	1.69184i	0.0553829	+	0.206692i	−0.932690	+	0.360679i	$0.882545\pi$
$68$		0			0
$69$	0.827288	+	0.333993i	0.0995937	+	0.0402080i
$70$		0			0
$71$			7.58339i			0.899983i	0.893033	+	0.449992i	$0.148573\pi$
$71$			7.58339i			0.899983i	−0.893033	+	0.449992i	$0.851427\pi$
$72$		0			0
$73$		−	12.5473i		−	1.46855i	−0.678854	−	0.734273i	$-0.737523\pi$
$73$		−	12.5473i		−	1.46855i	0.678854	−	0.734273i	$-0.262477\pi$
$74$		0			0
$75$	1.06503	−	0.832546i	0.122979	−	0.0961341i
$76$		0			0
$77$	−1.24010	−	4.62812i	−0.141323	−	0.527423i
$78$		0			0
$79$	4.01735	+	6.95825i	0.451987	+	0.782864i	0.998509	−	0.0545802i	$-0.0173821\pi$
$79$	4.01735	+	6.95825i	0.451987	+	0.782864i	−0.546523	+	0.837444i	$0.684049\pi$
$80$		0			0
$81$	7.62742	−	4.77729i	0.847491	−	0.530810i
$82$		0			0
$83$	−7.99826	−	2.14313i	−0.877923	−	0.235239i	−0.208412	−	0.978041i	$-0.566829\pi$
$83$	−7.99826	−	2.14313i	−0.877923	−	0.235239i	−0.669511	+	0.742802i	$0.733496\pi$
$84$		0			0
$85$	7.12091	−	1.90804i	0.772371	−	0.206956i
$86$		0			0
$87$	11.4792	+	1.40641i	1.23070	+	0.150783i
$88$		0			0
$89$			16.5414i			1.75339i	0.481047	+	0.876695i	$0.340257\pi$
$89$			16.5414i			1.75339i	−0.481047	+	0.876695i	$0.659743\pi$
$90$		0			0
$91$	6.07746	+	6.07746i	0.637091	+	0.637091i
$92$		0			0
$93$	5.25383	−	13.0135i	0.544797	−	1.34944i
$94$		0			0
$95$	7.04818	−	12.2078i	0.723128	−	1.25249i
$96$		0			0
$97$	−4.15739	−	7.20082i	−0.422119	−	0.731132i	0.574027	−	0.818836i	$-0.305380\pi$
$97$	−4.15739	−	7.20082i	−0.422119	−	0.731132i	−0.996147	+	0.0877040i	$0.972047\pi$
$98$		0			0
$99$	−0.144412	−	8.03151i	−0.0145140	−	0.807197i
$100$		0			0
$101$	1.25971	−	4.70129i	0.125346	−	0.467796i	−0.874506	−	0.485014i	$-0.838814\pi$
$101$	1.25971	−	4.70129i	0.125346	−	0.467796i	0.999852	+	0.0172183i	$0.00548104\pi$
$102$		0			0
$103$	−6.13162	−	3.54009i	−0.604166	−	0.348816i	0.166512	−	0.986039i	$-0.446749\pi$
$103$	−6.13162	−	3.54009i	−0.604166	−	0.348816i	−0.770679	+	0.637224i	$0.780083\pi$
$104$		0			0
$105$	3.83018	−	5.08560i	0.373787	−	0.496303i
$106$		0			0
$107$	−6.68494	−	6.68494i	−0.646258	−	0.646258i	0.305829	−	0.952087i	$-0.401066\pi$
$107$	−6.68494	−	6.68494i	−0.646258	−	0.646258i	−0.952087	+	0.305829i	$0.901066\pi$
$108$		0			0
$109$	−11.6423	+	11.6423i	−1.11513	+	1.11513i	−0.122687	+	0.992445i	$0.539151\pi$
$109$	−11.6423	+	11.6423i	−1.11513	+	1.11513i	−0.992445	+	0.122687i	$0.960849\pi$
$110$		0			0
$111$	−2.46434	−	1.85600i	−0.233905	−	0.176163i
$112$		0			0
$113$	0.346060	−	0.599393i	0.0325545	−	0.0563861i	−0.849289	−	0.527928i	$-0.822969\pi$
$113$	0.346060	−	0.599393i	0.0325545	−	0.0563861i	0.881844	+	0.471542i	$0.156302\pi$
$114$		0			0
$115$	1.02202	+	0.273849i	0.0953039	+	0.0255366i
$116$		0			0
$117$	7.42784	+	12.3473i	0.686704	+	1.14151i
$118$		0			0
$119$	−5.56168	+	3.21104i	−0.509838	+	0.294355i
$120$		0			0
$121$	3.31726	+	1.91522i	0.301569	+	0.174111i
$122$		0			0
$123$	7.56587	+	3.05450i	0.682192	+	0.275415i
$124$		0			0
$125$	8.39615	−	8.39615i	0.750975	−	0.750975i
$126$		0			0
$127$	−5.71585			−0.507200			−0.253600	−	0.967309i	$-0.581615\pi$
$127$	−5.71585			−0.507200			−0.253600	+	0.967309i	$0.581615\pi$
$128$		0			0
$129$	−1.43413	+	11.7055i	−0.126268	+	1.03061i
$130$		0			0
$131$	−2.36823	−	8.83835i	−0.206913	−	0.772210i	−0.988858	−	0.148863i	$-0.952439\pi$
$131$	−2.36823	−	8.83835i	−0.206913	−	0.772210i	0.781945	−	0.623348i	$-0.214228\pi$
$132$		0			0
$133$	−3.17824	+	11.8613i	−0.275588	+	1.02851i
$134$		0			0
$135$	8.28970	−	6.72369i	0.713464	−	0.578683i
$136$		0			0
$137$	0.535518	−	0.309181i	0.0457524	−	0.0264151i	−0.476949	−	0.878931i	$-0.658257\pi$
$137$	0.535518	−	0.309181i	0.0457524	−	0.0264151i	0.522702	+	0.852516i	$0.324924\pi$
$138$		0			0
$139$	18.4588	−	4.94601i	1.56565	−	0.419515i	0.631205	−	0.775616i	$-0.282561\pi$
$139$	18.4588	−	4.94601i	1.56565	−	0.419515i	0.934447	+	0.356101i	$0.115894\pi$
$140$		0			0
$141$	−7.44451	−	9.52338i	−0.626941	−	0.802013i
$142$		0			0
$143$	12.8608			1.07547
$144$		0			0
$145$	13.7157			1.13903
$146$		0			0
$147$	2.46264	−	6.09987i	0.203115	−	0.503109i
$148$		0			0
$149$	−5.06509	+	1.35719i	−0.414948	+	0.111185i	−0.460252	−	0.887788i	$-0.652241\pi$
$149$	−5.06509	+	1.35719i	−0.414948	+	0.111185i	0.0453039	+	0.998973i	$0.485574\pi$
$150$		0			0
$151$	7.80108	−	4.50395i	0.634843	−	0.366527i	−0.147782	−	0.989020i	$-0.547214\pi$
$151$	7.80108	−	4.50395i	0.634843	−	0.366527i	0.782625	+	0.622493i	$0.213880\pi$
$152$		0			0
$153$	−10.3480	+	2.97313i	−0.836588	+	0.240364i
$154$		0			0
$155$	4.30775	−	16.0767i	0.346007	−	1.29132i
$156$		0			0
$157$	2.93223	+	10.9432i	0.234017	+	0.873364i	0.978589	+	0.205822i	$0.0659868\pi$
$157$	2.93223	+	10.9432i	0.234017	+	0.873364i	−0.744572	+	0.667542i	$0.767347\pi$
$158$		0			0
$159$	−10.2978	−	7.75573i	−0.816671	−	0.615069i
$160$		0			0
$161$	−0.921720			−0.0726417
$162$		0			0
$163$	11.9073	−	11.9073i	0.932649	−	0.932649i	−0.0652222	−	0.997871i	$-0.520776\pi$
$163$	11.9073	−	11.9073i	0.932649	−	0.932649i	0.997871	+	0.0652222i	$0.0207756\pi$
$164$		0			0
$165$	−1.32833	−	9.43355i	−0.103410	−	0.734401i
$166$		0			0
$167$	−8.19418	−	4.73091i	−0.634085	−	0.366089i	0.148248	−	0.988950i	$-0.452637\pi$
$167$	−8.19418	−	4.73091i	−0.634085	−	0.366089i	−0.782332	+	0.622861i	$0.785970\pi$
$168$		0			0
$169$	−8.72072	+	5.03491i	−0.670825	+	0.387301i
$170$		0			0
$171$	−9.97139	+	18.0112i	−0.762531	+	1.37735i
$172$		0			0
$173$	23.1112	+	6.19263i	1.75711	+	0.470817i	0.986121	−	0.166030i	$-0.0530948\pi$
$173$	23.1112	+	6.19263i	1.75711	+	0.470817i	0.770991	+	0.636846i	$0.219761\pi$
$174$		0			0
$175$	−0.698304	+	1.20950i	−0.0527868	+	0.0914295i
$176$		0			0
$177$	11.1724	−	4.74589i	0.839773	−	0.356723i
$178$		0			0
$179$	−11.6334	+	11.6334i	−0.869521	+	0.869521i	−0.992419	−	0.122898i	$-0.960781\pi$
$179$	−11.6334	+	11.6334i	−0.869521	+	0.869521i	0.122898	+	0.992419i	$0.460781\pi$
$180$		0			0
$181$	−10.9379	−	10.9379i	−0.813010	−	0.813010i	0.172074	−	0.985084i	$-0.444953\pi$
$181$	−10.9379	−	10.9379i	−0.813010	−	0.813010i	−0.985084	+	0.172074i	$0.944953\pi$
$182$		0			0
$183$	−10.3012	−	1.26209i	−0.761490	−	0.0932961i
$184$		0			0
$185$	−3.16860	−	1.82939i	−0.232960	−	0.134500i
$186$		0			0
$187$	−2.48715	+	9.28218i	−0.181879	+	0.678780i
$188$		0			0
$189$	−5.45939	+	7.52667i	−0.397112	+	0.547485i
$190$		0			0
$191$	−3.34360	−	5.79129i	−0.241934	−	0.419043i	0.719331	−	0.694668i	$-0.244449\pi$
$191$	−3.34360	−	5.79129i	−0.241934	−	0.419043i	−0.961265	+	0.275625i	$0.911115\pi$
$192$		0			0
$193$	−0.468469	+	0.811411i	−0.0337211	+	0.0584067i	−0.882393	−	0.470512i	$-0.844069\pi$
$193$	−0.468469	+	0.811411i	−0.0337211	+	0.0584067i	0.848672	+	0.528919i	$0.177402\pi$
$194$		0			0
$195$	10.5245	+	13.4635i	0.753677	+	0.964140i
$196$		0			0
$197$	−14.7962	−	14.7962i	−1.05419	−	1.05419i	−0.998445	−	0.0557400i	$-0.982248\pi$
$197$	−14.7962	−	14.7962i	−1.05419	−	1.05419i	−0.0557400	−	0.998445i	$-0.517752\pi$
$198$		0			0
$199$			2.36977i			0.167988i	0.996466	+	0.0839942i	$0.0267677\pi$
$199$			2.36977i			0.167988i	−0.996466	+	0.0839942i	$0.973232\pi$
$200$		0			0
$201$	−1.18611	−	2.79225i	−0.0836616	−	0.196950i
$202$		0			0
$203$	−11.5410	+	3.09241i	−0.810022	+	0.217045i
$204$		0			0
$205$	9.34678	+	2.50446i	0.652807	+	0.174919i
$206$		0			0
$207$	−1.49957	−	0.373047i	−0.104227	−	0.0259286i
$208$		0			0
$209$	9.18737	+	15.9130i	0.635504	+	1.10072i
$210$		0			0
$211$	0.521927	+	1.94786i	0.0359309	+	0.134096i	0.981561	−	0.191147i	$-0.0612206\pi$
$211$	0.521927	+	1.94786i	0.0359309	+	0.134096i	−0.945631	+	0.325243i	$0.894554\pi$
$212$		0			0
$213$	−1.83143	−	13.0065i	−0.125488	−	0.891192i
$214$		0			0
$215$			13.9861i			0.953842i
$216$		0			0
$217$			14.4990i			0.984255i
$218$		0			0
$219$	3.03023	+	21.5202i	0.204764	+	1.45420i
$220$		0			0
$221$	−4.46148	−	16.6505i	−0.300111	−	1.12003i
$222$		0			0
$223$	−5.55008	−	9.61302i	−0.371661	−	0.643735i	0.618160	−	0.786052i	$-0.287878\pi$
$223$	−5.55008	−	9.61302i	−0.371661	−	0.643735i	−0.989821	+	0.142317i	$0.954545\pi$
$224$		0			0
$225$	−1.62561	+	1.68514i	−0.108374	+	0.112342i
$226$		0			0
$227$	16.7860	+	4.49779i	1.11412	+	0.298529i	0.768504	−	0.639845i	$-0.221002\pi$
$227$	16.7860	+	4.49779i	1.11412	+	0.298529i	0.345621	+	0.938374i	$0.387668\pi$
$228$		0			0
$229$	15.4674	−	4.14447i	1.02211	−	0.273874i	0.291430	−	0.956592i	$-0.405869\pi$
$229$	15.4674	−	4.14447i	1.02211	−	0.273874i	0.730682	+	0.682718i	$0.239202\pi$
$230$		0			0
$231$	3.24465	+	7.63835i	0.213483	+	0.502566i
$232$		0			0
$233$			25.2041i			1.65118i	0.564273	+	0.825588i	$0.309156\pi$
$233$			25.2041i			1.65118i	−0.564273	+	0.825588i	$0.690844\pi$
$234$		0			0
$235$	−10.1369	−	10.1369i	−0.661257	−	0.661257i
$236$		0			0
$237$	−8.57073	−	10.9641i	−0.556729	−	0.712195i
$238$		0			0
$239$	−4.14085	+	7.17217i	−0.267850	+	0.463929i	−0.968306	−	0.249766i	$-0.919646\pi$
$239$	−4.14085	+	7.17217i	−0.267850	+	0.463929i	0.700457	+	0.713695i	$0.252980\pi$
$240$		0			0
$241$	−6.40038	−	11.0858i	−0.412285	−	0.714098i	0.582854	−	0.812577i	$-0.301936\pi$
$241$	−6.40038	−	11.0858i	−0.412285	−	0.714098i	−0.995139	+	0.0984784i	$0.968602\pi$
$242$		0			0
$243$	−11.9283	+	10.0357i	−0.765199	+	0.643793i
$244$		0			0
$245$	2.01918	−	7.53570i	0.129001	−	0.481438i
$246$		0			0
$247$	−28.5449	−	16.4804i	−1.81627	−	1.04862i
$248$		0			0
$249$	14.2356	+	1.74412i	0.902147	+	0.110529i
$250$		0			0
$251$	13.9414	+	13.9414i	0.879976	+	0.879976i	0.993532	−	0.113556i	$-0.0362241\pi$
$251$	13.9414	+	13.9414i	0.879976	+	0.879976i	−0.113556	+	0.993532i	$0.536224\pi$
$252$		0			0
$253$	−0.975248	+	0.975248i	−0.0613133	+	0.0613133i
$254$		0			0
$255$	−11.7525	+	4.99228i	−0.735970	+	0.312629i
$256$		0			0
$257$	−3.51445	+	6.08720i	−0.219225	+	0.379709i	−0.954571	−	0.297983i	$-0.903686\pi$
$257$	−3.51445	+	6.08720i	−0.219225	+	0.379709i	0.735346	+	0.677692i	$0.237020\pi$
$258$		0			0
$259$	3.07867	+	0.824928i	0.191299	+	0.0512585i
$260$		0			0
$261$	−20.0280	+	0.360117i	−1.23970	+	0.0222907i
$262$		0			0
$263$	15.1779	−	8.76296i	0.935909	−	0.540348i	0.0472338	−	0.998884i	$-0.484959\pi$
$263$	15.1779	−	8.76296i	0.935909	−	0.540348i	0.888676	+	0.458536i	$0.151626\pi$
$264$		0			0
$265$	−13.2408	−	7.64455i	−0.813373	−	0.469601i
$266$		0			0
$267$	−3.99485	−	28.3707i	−0.244481	−	1.73626i
$268$		0			0
$269$	−0.311911	+	0.311911i	−0.0190176	+	0.0190176i	−0.716552	−	0.697534i	$-0.754281\pi$
$269$	−0.311911	+	0.311911i	−0.0190176	+	0.0190176i	0.697534	+	0.716552i	$0.254281\pi$
$270$		0			0
$271$	−7.46993			−0.453766			−0.226883	−	0.973922i	$-0.572853\pi$
$271$	−7.46993			−0.453766			−0.226883	+	0.973922i	$0.572853\pi$
$272$		0			0
$273$	−11.8914	−	8.95590i	−0.719699	−	0.542036i
$274$		0			0
$275$	0.540881	+	2.01860i	0.0326164	+	0.121726i
$276$		0			0
$277$	2.71916	−	10.1481i	0.163379	−	0.609737i	−0.834863	−	0.550458i	$-0.814453\pi$
$277$	2.71916	−	10.1481i	0.163379	−	0.609737i	0.998241	−	0.0592792i	$-0.0188802\pi$
$278$		0			0
$279$	−5.86817	+	23.5887i	−0.351318	+	1.41222i
$280$		0			0
$281$	5.76358	−	3.32761i	0.343826	−	0.198508i	−0.318136	−	0.948045i	$-0.603057\pi$
$281$	5.76358	−	3.32761i	0.343826	−	0.198508i	0.661963	+	0.749537i	$0.269724\pi$
$282$		0			0
$283$	10.6365	−	2.85005i	0.632275	−	0.169418i	0.0715734	−	0.997435i	$-0.477198\pi$
$283$	10.6365	−	2.85005i	0.632275	−	0.169418i	0.560702	+	0.828018i	$0.310531\pi$
$284$		0			0
$285$	−9.14030	+	22.6402i	−0.541424	+	1.34109i
$286$		0			0
$287$	−8.42949			−0.497577
$288$		0			0
$289$	−4.11987			−0.242345
$290$		0			0
$291$	8.86951	+	11.3463i	0.519940	+	0.665133i
$292$		0			0
$293$	−2.75926	+	0.739342i	−0.161198	+	0.0431928i	−0.338515	−	0.940961i	$-0.609925\pi$
$293$	−2.75926	+	0.739342i	−0.161198	+	0.0431928i	0.177318	+	0.984154i	$0.443258\pi$
$294$		0			0
$295$	12.4673	−	7.19800i	0.725874	−	0.419084i
$296$		0			0
$297$	2.18734	+	13.7402i	0.126922	+	0.797288i
$298$		0			0
$299$	0.640328	−	2.38974i	0.0370311	−	0.138202i
$300$		0			0
$301$	−3.15337	−	11.7685i	−0.181757	−	0.678328i
$302$		0			0
$303$	−1.02518	+	8.36756i	−0.0588948	+	0.480704i
$304$		0			0
$305$	−12.3082			−0.704768
$306$		0			0
$307$	8.15691	−	8.15691i	0.465540	−	0.465540i	−0.434926	−	0.900466i	$-0.643226\pi$
$307$	8.15691	−	8.15691i	0.465540	−	0.465540i	0.900466	+	0.434926i	$0.143226\pi$
$308$		0			0
$309$	11.3715	+	4.59090i	0.646901	+	0.261167i
$310$		0			0
$311$	8.33416	+	4.81173i	0.472587	+	0.272848i	0.717322	−	0.696742i	$-0.245368\pi$
$311$	8.33416	+	4.81173i	0.472587	+	0.272848i	−0.244735	+	0.969590i	$0.578701\pi$
$312$		0			0
$313$	−22.2531	+	12.8478i	−1.25782	+	0.726202i	−0.972650	−	0.232276i	$-0.925383\pi$
$313$	−22.2531	+	12.8478i	−1.25782	+	0.726202i	−0.285168	+	0.958477i	$0.592049\pi$
$314$		0			0
$315$	−5.34106	+	9.64747i	−0.300934	+	0.543573i
$316$		0			0
$317$	15.6062	+	4.18167i	0.876532	+	0.234866i	0.668910	−	0.743343i	$-0.266761\pi$
$317$	15.6062	+	4.18167i	0.876532	+	0.234866i	0.207622	+	0.978209i	$0.433428\pi$
$318$		0			0
$319$	−8.93928	+	15.4833i	−0.500503	+	0.866897i
$320$		0			0
$321$	13.0800	+	9.85110i	0.730055	+	0.549835i
$322$		0			0
$323$	17.4149	−	17.4149i	0.968989	−	0.968989i
$324$		0			0
$325$	−2.65074	−	2.65074i	−0.147036	−	0.147036i
$326$		0			0
$327$	17.1564	−	22.7798i	0.948752	−	1.25973i
$328$		0			0
$329$	10.8152	+	6.24413i	0.596259	+	0.344250i
$330$		0			0
$331$	−5.25422	+	19.6090i	−0.288798	+	1.07781i	0.657221	+	0.753698i	$0.271732\pi$
$331$	−5.25422	+	19.6090i	−0.288798	+	1.07781i	−0.946019	+	0.324111i	$0.894935\pi$
$332$		0			0
$333$	4.67489	+	2.58813i	0.256183	+	0.141828i
$334$		0			0
$335$	−1.79895	−	3.11587i	−0.0982870	−	0.170238i
$336$		0			0
$337$	1.04249	−	1.80564i	0.0567879	−	0.0983595i	−0.836234	−	0.548373i	$-0.815247\pi$
$337$	1.04249	−	1.80564i	0.0567879	−	0.0983595i	0.893022	+	0.450013i	$0.148581\pi$
$338$		0			0
$339$	−0.448781	+	1.11161i	−0.0243744	+	0.0603745i
$340$		0			0
$341$	15.3410	+	15.3410i	0.830762	+	0.830762i
$342$		0			0
$343$			19.3222i			1.04330i
$344$		0			0
$345$	−1.81903	−	0.222864i	−0.0979335	−	0.0119986i
$346$		0			0
$347$	−8.16281	+	2.18722i	−0.438203	+	0.117416i	−0.471174	−	0.882040i	$-0.656170\pi$
$347$	−8.16281	+	2.18722i	−0.438203	+	0.117416i	0.0329715	+	0.999456i	$0.489503\pi$
$348$		0			0
$349$	−1.50715	−	0.403839i	−0.0806758	−	0.0216170i	0.218255	−	0.975892i	$-0.429963\pi$
$349$	−1.50715	−	0.403839i	−0.0806758	−	0.0216170i	−0.298931	+	0.954275i	$0.596630\pi$
$350$		0			0
$351$	−15.7217	−	19.3834i	−0.839160	−	1.03461i
$352$		0			0
$353$	−8.13441	−	14.0892i	−0.432951	−	0.749893i	0.564175	−	0.825655i	$-0.309194\pi$
$353$	−8.13441	−	14.0892i	−0.432951	−	0.749893i	−0.997126	+	0.0757623i	$0.975861\pi$
$354$		0			0
$355$	−4.03173	−	15.0466i	−0.213982	−	0.798592i
$356$		0			0
$357$	8.76352	−	6.85052i	0.463815	−	0.362568i
$358$		0			0
$359$			3.08148i			0.162634i	0.996688	+	0.0813172i	$0.0259127\pi$
$359$			3.08148i			0.162634i	−0.996688	+	0.0813172i	$0.974087\pi$
$360$		0			0
$361$		−	28.0923i		−	1.47854i
$362$		0			0
$363$	−6.15208	−	2.48372i	−0.322900	−	0.130362i
$364$		0			0
$365$	6.67079	+	24.8957i	0.349165	+	1.30310i
$366$		0			0
$367$	1.38231	+	2.39424i	0.0721562	+	0.124978i	0.899846	−	0.436208i	$-0.143679\pi$
$367$	1.38231	+	2.39424i	0.0721562	+	0.124978i	−0.827690	+	0.561186i	$0.810345\pi$
$368$		0			0
$369$	−13.7141	−	3.41167i	−0.713930	−	0.177604i
$370$		0			0
$371$	12.8650	+	3.44716i	0.667916	+	0.178968i
$372$		0			0
$373$	−22.6202	+	6.06106i	−1.17123	+	0.313830i	−0.791442	−	0.611244i	$-0.790669\pi$
$373$	−22.6202	+	6.06106i	−1.17123	+	0.313830i	−0.379787	+	0.925074i	$0.624003\pi$
$374$		0			0
$375$	−12.3728	+	16.4282i	−0.638928	+	0.848350i
$376$		0			0
$377$		−	32.0707i		−	1.65172i
$378$		0			0
$379$	−4.70551	−	4.70551i	−0.241706	−	0.241706i	0.575850	−	0.817555i	$-0.304671\pi$
$379$	−4.70551	−	4.70551i	−0.241706	−	0.241706i	−0.817555	+	0.575850i	$0.804671\pi$
$380$		0			0
$381$	9.80344	−	1.38041i	0.502245	−	0.0707206i
$382$		0			0
$383$	−18.3311	+	31.7505i	−0.936678	+	1.62237i	−0.165063	+	0.986283i	$0.552783\pi$
$383$	−18.3311	+	31.7505i	−0.936678	+	1.62237i	−0.771614	+	0.636091i	$0.780550\pi$
$384$		0			0
$385$	4.92111	+	8.52361i	0.250803	+	0.434403i
$386$		0			0
$387$	−0.367216	−	20.4228i	−0.0186666	−	1.03815i
$388$		0			0
$389$	−0.757647	+	2.82758i	−0.0384142	+	0.143364i	−0.982469	−	0.186423i	$-0.940310\pi$
$389$	−0.757647	+	2.82758i	−0.0384142	+	0.143364i	0.944055	+	0.329787i	$0.106977\pi$
$390$		0			0
$391$	1.60094	+	0.924302i	0.0809630	+	0.0467440i
$392$		0			0
$393$	6.19634	+	14.5870i	0.312564	+	0.735817i
$394$		0			0
$395$	−11.6704	−	11.6704i	−0.587202	−	0.587202i
$396$		0			0
$397$	13.3392	−	13.3392i	0.669474	−	0.669474i	−0.288120	−	0.957594i	$-0.593030\pi$
$397$	13.3392	−	13.3392i	0.669474	−	0.669474i	0.957594	+	0.288120i	$0.0930302\pi$
$398$		0			0
$399$	2.58651	−	21.1113i	0.129488	−	1.05689i
$400$		0			0
$401$	−4.84547	+	8.39261i	−0.241971	+	0.419107i	−0.961276	−	0.275588i	$-0.911127\pi$
$401$	−4.84547	+	8.39261i	−0.241971	+	0.419107i	0.719304	+	0.694695i	$0.244461\pi$
$402$		0			0
$403$	−37.5914	−	10.0726i	−1.87256	−	0.501751i
$404$		0			0
$405$	−12.5941	+	13.5340i	−0.625807	+	0.672511i
$406$		0			0
$407$	4.13030	−	2.38463i	0.204731	−	0.118202i
$408$		0			0
$409$	−6.19403	−	3.57613i	−0.306275	−	0.176828i	0.338983	−	0.940792i	$-0.389917\pi$
$409$	−6.19403	−	3.57613i	−0.306275	−	0.176828i	−0.645258	+	0.763964i	$0.723250\pi$
$410$		0			0
$411$	−0.843814	+	0.659617i	−0.0416223	+	0.0325365i
$412$		0			0
$413$	−8.86768	+	8.86768i	−0.436350	+	0.436350i
$414$		0			0
$415$	17.0092			0.834948
$416$		0			0
$417$	−30.4647	+	12.9410i	−1.49186	+	0.633721i
$418$		0			0
$419$	4.80711	+	17.9404i	0.234843	+	0.876445i	0.978220	+	0.207572i	$0.0665562\pi$
$419$	4.80711	+	17.9404i	0.234843	+	0.876445i	−0.743377	+	0.668873i	$0.766777\pi$
$420$		0			0
$421$	−0.527873	+	1.97005i	−0.0257270	+	0.0960144i	−0.977596	−	0.210492i	$-0.932493\pi$
$421$	−0.527873	+	1.97005i	−0.0257270	+	0.0960144i	0.951869	+	0.306506i	$0.0991601\pi$
$422$		0			0
$423$	15.0683	+	14.5359i	0.732644	+	0.706762i
$424$		0			0
$425$	2.42577	−	1.40052i	0.117667	−	0.0679353i
$426$		0			0
$427$	10.3567	−	2.77508i	0.501198	−	0.134295i
$428$		0			0
$429$	−22.0580	+	3.10596i	−1.06497	+	0.149957i
$430$		0			0
$431$	19.8202			0.954707			0.477354	−	0.878711i	$-0.341596\pi$
$431$	19.8202			0.954707			0.477354	+	0.878711i	$0.341596\pi$
$432$		0			0
$433$	23.7342			1.14060			0.570298	−	0.821438i	$-0.306828\pi$
$433$	23.7342			1.14060			0.570298	+	0.821438i	$0.306828\pi$
$434$		0			0
$435$	−23.5242	+	3.31242i	−1.12790	+	0.158818i
$436$		0			0
$437$	3.41431	−	0.914861i	0.163329	−	0.0437637i
$438$		0			0
$439$	−19.0949	+	11.0245i	−0.911350	+	0.526168i	−0.880865	−	0.473367i	$-0.843039\pi$
$439$	−19.0949	+	11.0245i	−0.911350	+	0.526168i	−0.0304850	+	0.999535i	$0.509705\pi$
$440$		0			0
$441$	−2.75060	+	11.0568i	−0.130981	+	0.526515i
$442$		0			0
$443$	−2.60232	+	9.71199i	−0.123640	+	0.461431i	−0.999788	−	0.0206123i	$-0.993438\pi$
$443$	−2.60232	+	9.71199i	−0.123640	+	0.461431i	0.876148	+	0.482043i	$0.160105\pi$
$444$		0			0
$445$	−8.79430	−	32.8208i	−0.416890	−	1.55585i
$446$		0			0
$447$	8.35953	−	3.55100i	0.395392	−	0.167957i
$448$		0			0
$449$	24.6980			1.16557			0.582786	−	0.812626i	$-0.301963\pi$
$449$	24.6980			1.16557			0.582786	+	0.812626i	$0.301963\pi$
$450$		0			0
$451$	−8.91903	+	8.91903i	−0.419981	+	0.419981i
$452$		0			0
$453$	−12.2921	+	9.60887i	−0.577535	+	0.451464i
$454$		0			0
$455$	−15.2897	−	8.82752i	−0.716793	−	0.413841i
$456$		0			0
$457$	27.1171	−	15.6561i	1.26849	−	0.732360i	0.293784	−	0.955872i	$-0.405085\pi$
$457$	27.1171	−	15.6561i	1.26849	−	0.732360i	0.974701	+	0.223511i	$0.0717520\pi$
$458$		0			0
$459$	17.0302	−	7.59842i	0.794902	−	0.354664i
$460$		0			0
$461$	−11.8344	−	3.17103i	−0.551185	−	0.147689i	−0.0275314	−	0.999621i	$-0.508765\pi$
$461$	−11.8344	−	3.17103i	−0.551185	−	0.147689i	−0.523653	+	0.851931i	$0.675431\pi$
$462$		0			0
$463$	12.7250	−	22.0403i	0.591379	−	1.02430i	−0.402668	−	0.915346i	$-0.631917\pi$
$463$	12.7250	−	22.0403i	0.591379	−	1.02430i	0.994047	−	0.108953i	$-0.0347497\pi$
$464$		0			0
$465$	−3.50574	+	28.6141i	−0.162575	+	1.32695i
$466$		0			0
$467$	6.28473	−	6.28473i	0.290822	−	0.290822i	−0.546583	−	0.837405i	$-0.684072\pi$
$467$	6.28473	−	6.28473i	0.290822	−	0.290822i	0.837405	+	0.546583i	$0.184072\pi$
$468$		0			0
$469$	2.21624	+	2.21624i	0.102336	+	0.102336i
$470$		0			0
$471$	−7.67200	−	18.0609i	−0.353507	−	0.832203i
$472$		0			0
$473$	−15.7885	−	9.11550i	−0.725956	−	0.419131i
$474$		0			0
$475$	1.38622	−	5.17343i	0.0636040	−	0.237373i
$476$		0			0
$477$	19.5352	+	10.8151i	0.894454	+	0.495190i
$478$		0			0
$479$	1.61178	+	2.79169i	0.0736442	+	0.127555i	0.900496	−	0.434865i	$-0.143204\pi$
$479$	1.61178	+	2.79169i	0.0736442	+	0.127555i	−0.826852	+	0.562420i	$0.809870\pi$
$480$		0			0
$481$	−4.27757	+	7.40897i	−0.195040	+	0.337820i
$482$		0			0
$483$	1.58087	−	0.222600i	0.0719321	−	0.0101287i
$484$		0			0
$485$	12.0772	+	12.0772i	0.548399	+	0.548399i
$486$		0			0
$487$		−	11.2953i		−	0.511838i	−0.966698	−	0.255919i	$-0.917622\pi$
$487$		−	11.2953i		−	0.511838i	0.966698	−	0.255919i	$-0.0823780\pi$
$488$		0			0
$489$	−17.5468	+	23.2982i	−0.793496	+	1.05358i
$490$		0			0
$491$	27.3357	−	7.32459i	1.23364	−	0.330554i	0.417647	−	0.908609i	$-0.362855\pi$
$491$	27.3357	−	7.32459i	1.23364	−	0.330554i	0.815998	+	0.578055i	$0.196188\pi$
$492$		0			0
$493$	23.1468	+	6.20215i	1.04248	+	0.279331i
$494$		0			0
$495$	4.55651	+	15.8590i	0.204800	+	0.712808i
$496$		0			0
$497$	6.78498	+	11.7519i	0.304348	+	0.527146i
$498$		0			0
$499$	4.52377	+	16.8830i	0.202512	+	0.755785i	0.990194	+	0.139702i	$0.0446145\pi$
$499$	4.52377	+	16.8830i	0.202512	+	0.755785i	−0.787682	+	0.616082i	$0.788719\pi$
$500$		0			0
$501$	15.1966	+	6.13520i	0.678936	+	0.274100i
$502$		0			0
$503$		−	14.1184i		−	0.629509i	−0.949173	−	0.314754i	$-0.898078\pi$
$503$		−	14.1184i		−	0.629509i	0.949173	−	0.314754i	$-0.101922\pi$
$504$		0			0
$505$			9.99782i			0.444897i
$506$		0			0
$507$	13.7412	−	10.7416i	0.610269	−	0.477053i
$508$		0			0
$509$	−7.88327	−	29.4208i	−0.349420	−	1.30405i	−0.887363	−	0.461072i	$-0.847465\pi$
$509$	−7.88327	−	29.4208i	−0.349420	−	1.30405i	0.537943	−	0.842981i	$-0.319202\pi$
$510$		0			0
$511$	−11.2262	−	19.4444i	−0.496619	−	0.860170i
$512$		0			0
$513$	12.7524	−	33.2997i	0.563034	−	1.47022i
$514$		0			0
$515$	14.0482	+	3.76420i	0.619037	+	0.165870i
$516$		0			0
$517$	18.0500	−	4.83648i	0.793838	−	0.212708i
$518$		0			0
$519$	−41.1343	−	5.03969i	−1.80559	−	0.221218i
$520$		0			0
$521$		−	8.75761i		−	0.383678i	−0.981426	−	0.191839i	$-0.938555\pi$
$521$		−	8.75761i		−	0.383678i	0.981426	−	0.191839i	$-0.0614451\pi$
$522$		0			0
$523$	−21.3424	−	21.3424i	−0.933236	−	0.933236i	0.0646706	−	0.997907i	$-0.479400\pi$
$523$	−21.3424	−	21.3424i	−0.933236	−	0.933236i	−0.997907	+	0.0646706i	$0.979400\pi$
$524$		0			0
$525$	0.905583	−	2.24309i	0.0395229	−	0.0978966i
$526$		0			0
$527$	14.5396	−	25.1834i	0.633356	−	1.09700i
$528$		0			0
$529$	−11.3673	−	19.6888i	−0.494232	−	0.856035i
$530$		0			0
$531$	−18.0161	+	10.8380i	−0.781830	+	0.470330i
$532$		0			0
$533$	5.85605	−	21.8551i	0.253654	−	0.946648i
$534$		0			0
$535$	16.8180	+	9.70989i	0.727107	+	0.419795i
$536$		0			0
$537$	17.1433	−	22.7623i	0.739787	−	0.982268i
$538$		0			0
$539$	7.19083	+	7.19083i	0.309731	+	0.309731i
$540$		0			0
$541$	−25.1121	+	25.1121i	−1.07965	+	1.07965i	−0.0831121	+	0.996540i	$0.526486\pi$
$541$	−25.1121	+	25.1121i	−1.07965	+	1.07965i	−0.996540	+	0.0831121i	$0.973514\pi$
$542$		0			0
$543$	21.4016	+	16.1184i	0.918429	+	0.691707i
$544$		0			0
$545$	16.9105	−	29.2898i	0.724366	−	1.25464i
$546$		0			0
$547$	5.32802	+	1.42764i	0.227810	+	0.0610414i	0.370918	−	0.928666i	$-0.379043\pi$
$547$	5.32802	+	1.42764i	0.227810	+	0.0610414i	−0.143108	+	0.989707i	$0.545710\pi$
$548$		0			0
$549$	17.9728	−	0.323163i	0.767060	−	0.0137923i
$550$		0			0
$551$	39.6818	−	22.9103i	1.69050	−	0.976013i
$552$		0			0
$553$	12.4513	+	7.18876i	0.529483	+	0.305697i
$554$		0			0
$555$	5.87637	+	2.37241i	0.249438	+	0.100703i
$556$		0			0
$557$	−15.4160	+	15.4160i	−0.653197	+	0.653197i	−0.953761	−	0.300565i	$-0.902825\pi$
$557$	−15.4160	+	15.4160i	−0.653197	+	0.653197i	0.300565	+	0.953761i	$0.402825\pi$
$558$		0			0
$559$	32.7029			1.38319
$560$		0			0
$561$	2.02410	−	16.5208i	0.0854574	−	0.697510i
$562$		0			0
$563$	−4.27894	−	15.9692i	−0.180336	−	0.673022i	−0.995581	−	0.0939062i	$-0.970065\pi$
$563$	−4.27894	−	15.9692i	−0.180336	−	0.673022i	0.815245	−	0.579116i	$-0.196602\pi$
$564$		0			0
$565$	−0.367967	+	1.37327i	−0.0154805	+	0.0577740i
$566$		0			0
$567$	7.54583	−	14.2277i	0.316895	−	0.597507i
$568$		0			0
$569$	9.85656	−	5.69069i	0.413208	−	0.238566i	−0.278959	−	0.960303i	$-0.589989\pi$
$569$	9.85656	−	5.69069i	0.413208	−	0.238566i	0.692167	+	0.721737i	$0.256656\pi$
$570$		0			0
$571$	−11.8982	+	3.18813i	−0.497926	+	0.133419i	−0.499037	−	0.866580i	$-0.666313\pi$
$571$	−11.8982	+	3.18813i	−0.497926	+	0.133419i	0.00111115	+	0.999999i	$0.499646\pi$
$572$		0			0
$573$	7.13334	+	9.12532i	0.298000	+	0.381216i
$574$		0			0
$575$	0.402016			0.0167652
$576$		0			0
$577$	21.7471			0.905342			0.452671	−	0.891678i	$-0.350471\pi$
$577$	21.7471			0.905342			0.452671	+	0.891678i	$0.350471\pi$
$578$		0			0
$579$	0.607525	−	1.50481i	0.0252479	−	0.0625380i
$580$		0			0
$581$	−14.3123	+	3.83498i	−0.593775	+	0.159102i
$582$		0			0
$583$	17.2595	−	9.96475i	0.714814	−	0.412698i
$584$		0			0
$585$	−21.3024	−	20.5499i	−0.880748	−	0.849634i
$586$		0			0
$587$	−4.07718	+	15.2163i	−0.168283	+	0.628042i	0.829315	+	0.558781i	$0.188731\pi$
$587$	−4.07718	+	15.2163i	−0.168283	+	0.628042i	−0.997599	+	0.0692610i	$0.977936\pi$
$588$		0			0
$589$	−14.3911	−	53.7083i	−0.592975	−	2.21301i
$590$		0			0
$591$	28.9508	+	21.8041i	1.19088	+	0.896899i
$592$		0			0
$593$	10.1125			0.415270			0.207635	−	0.978206i	$-0.433423\pi$
$593$	10.1125			0.415270			0.207635	+	0.978206i	$0.433423\pi$
$594$		0			0
$595$	9.32807	−	9.32807i	0.382414	−	0.382414i
$596$		0			0
$597$	−0.572312	−	4.06446i	−0.0234232	−	0.166347i
$598$		0			0
$599$	4.23917	+	2.44748i	0.173208	+	0.100002i	0.584097	−	0.811684i	$-0.301449\pi$
$599$	4.23917	+	2.44748i	0.173208	+	0.100002i	−0.410890	+	0.911685i	$0.634782\pi$
$600$		0			0
$601$	25.8322	−	14.9142i	1.05372	−	0.608364i	0.130030	−	0.991510i	$-0.458493\pi$
$601$	25.8322	−	14.9142i	1.05372	−	0.608364i	0.923688	+	0.383146i	$0.125159\pi$
$602$		0			0
$603$	2.70867	+	4.50263i	0.110306	+	0.183361i
$604$		0			0
$605$	−7.60019	−	2.03647i	−0.308992	−	0.0827941i
$606$		0			0
$607$	8.48425	−	14.6952i	0.344365	−	0.596458i	−0.640873	−	0.767647i	$-0.721428\pi$
$607$	8.48425	−	14.6952i	0.344365	−	0.596458i	0.985238	+	0.171189i	$0.0547609\pi$
$608$		0			0
$609$	19.0476	−	8.09112i	0.771846	−	0.327869i
$610$		0			0
$611$	−23.7025	+	23.7025i	−0.958901	+	0.958901i
$612$		0			0
$613$	30.2781	+	30.2781i	1.22292	+	1.22292i	0.966589	+	0.256332i	$0.0825140\pi$
$613$	30.2781	+	30.2781i	1.22292	+	1.22292i	0.256332	+	0.966589i	$0.417486\pi$
$614$		0			0
$615$	−16.6358	−	2.03818i	−0.670820	−	0.0821874i
$616$		0			0
$617$	14.9377	+	8.62428i	0.601368	+	0.347200i	0.769580	−	0.638551i	$-0.220466\pi$
$617$	14.9377	+	8.62428i	0.601368	+	0.347200i	−0.168211	+	0.985751i	$0.553799\pi$
$618$		0			0
$619$	−4.48369	+	16.7334i	−0.180215	+	0.672570i	0.815390	+	0.578912i	$0.196523\pi$
$619$	−4.48369	+	16.7334i	−0.180215	+	0.672570i	−0.995604	+	0.0936580i	$0.970144\pi$
$620$		0			0
$621$	2.66205	+	0.277671i	0.106824	+	0.0111426i
$622$		0			0
$623$	14.7999	+	25.6341i	0.592945	+	1.02701i
$624$		0			0
$625$	−10.2442	+	17.7435i	−0.409770	+	0.709742i
$626$		0			0
$627$	−19.6006	−	25.0741i	−0.782773	−	1.00136i
$628$		0			0
$629$	−4.52012	−	4.52012i	−0.180229	−	0.180229i
$630$		0			0
$631$			11.6246i			0.462766i	0.972863	+	0.231383i	$0.0743251\pi$
$631$			11.6246i			0.462766i	−0.972863	+	0.231383i	$0.925675\pi$
$632$		0			0
$633$	−1.36559	−	3.21478i	−0.0542774	−	0.127776i
$634$		0			0
$635$	11.3411	−	3.03885i	0.450059	−	0.120593i
$636$		0			0
$637$	−17.6203	−	4.72135i	−0.698142	−	0.187067i
$638$		0			0
$639$	6.28229	+	21.8656i	0.248524	+	0.864989i
$640$		0			0
$641$	−3.04338	−	5.27129i	−0.120206	−	0.208203i	0.799643	−	0.600476i	$-0.205022\pi$
$641$	−3.04338	−	5.27129i	−0.120206	−	0.208203i	−0.919849	+	0.392273i	$0.871689\pi$
$642$		0			0
$643$	8.34195	+	31.1326i	0.328974	+	1.22775i	0.910256	+	0.414046i	$0.135885\pi$
$643$	8.34195	+	31.1326i	0.328974	+	1.22775i	−0.581282	+	0.813702i	$0.697449\pi$
$644$		0			0
$645$	−3.37771	−	23.9880i	−0.132997	−	0.944525i
$646$		0			0
$647$		−	13.1882i		−	0.518482i	−0.965813	−	0.259241i	$-0.916528\pi$
$647$		−	13.1882i		−	0.518482i	0.965813	−	0.259241i	$-0.0834724\pi$
$648$		0			0
$649$			18.7653i			0.736604i
$650$		0			0
$651$	−3.50158	−	24.8677i	−0.137238	−	0.974641i
$652$		0			0
$653$	4.09053	+	15.2661i	0.160075	+	0.597407i	0.998617	+	0.0525710i	$0.0167416\pi$
$653$	4.09053	+	15.2661i	0.160075	+	0.597407i	−0.838542	+	0.544836i	$0.816592\pi$
$654$		0			0
$655$	9.39787	+	16.2776i	0.367205	+	0.636018i
$656$		0			0
$657$	−10.3945	−	36.1782i	−0.405528	−	1.41144i
$658$		0			0
$659$	−34.5804	−	9.26579i	−1.34706	−	0.360944i	−0.488012	−	0.872837i	$-0.662278\pi$
$659$	−34.5804	−	9.26579i	−1.34706	−	0.360944i	−0.859049	+	0.511893i	$0.828944\pi$
$660$		0			0
$661$	−24.5781	+	6.58569i	−0.955978	+	0.256153i	−0.702897	−	0.711292i	$-0.748111\pi$
$661$	−24.5781	+	6.58569i	−0.955978	+	0.256153i	−0.253081	+	0.967445i	$0.581444\pi$
$662$		0			0
$663$	11.6732	+	27.4802i	0.453349	+	1.06724i
$664$		0			0
$665$		−	25.2244i		−	0.978162i
$666$		0			0
$667$	2.43195	+	2.43195i	0.0941656	+	0.0941656i
$668$		0			0
$669$	11.8407	+	15.1472i	0.457788	+	0.585625i
$670$		0			0
$671$	8.02196	−	13.8944i	0.309684	−	0.536389i
$672$		0			0
$673$	−16.8241	−	29.1402i	−0.648522	−	1.12327i	−0.983476	−	0.181039i	$-0.942054\pi$
$673$	−16.8241	−	29.1402i	−0.648522	−	1.12327i	0.334954	−	0.942235i	$-0.391279\pi$
$674$		0			0
$675$	2.38116	−	3.28282i	0.0916509	−	0.126356i
$676$		0			0
$677$	−9.52351	+	35.5422i	−0.366018	+	1.36600i	0.500017	+	0.866015i	$0.333327\pi$
$677$	−9.52351	+	35.5422i	−0.366018	+	1.36600i	−0.866035	+	0.499983i	$0.833340\pi$
$678$		0			0
$679$	−12.8854	−	7.43937i	−0.494495	−	0.285497i
$680$		0			0
$681$	−29.8764	−	3.66039i	−1.14487	−	0.140267i
$682$		0			0
$683$	0.339146	+	0.339146i	0.0129771	+	0.0129771i	0.713566	−	0.700588i	$-0.247079\pi$
$683$	0.339146	+	0.339146i	0.0129771	+	0.0129771i	−0.700588	+	0.713566i	$0.747079\pi$
$684$		0			0
$685$	−0.898173	+	0.898173i	−0.0343174	+	0.0343174i
$686$		0			0
$687$	−25.5277	+	10.8438i	−0.973941	+	0.413715i
$688$		0			0
$689$	−17.8749	+	30.9602i	−0.680978	+	1.17949i
$690$		0			0
$691$	−17.3154	−	4.63964i	−0.658707	−	0.176500i	−0.0860448	−	0.996291i	$-0.527423\pi$
$691$	−17.3154	−	4.63964i	−0.658707	−	0.176500i	−0.572663	+	0.819791i	$0.694089\pi$
$692$		0			0
$693$	−7.40971	−	12.3172i	−0.281472	−	0.467890i
$694$		0			0
$695$	−33.9955	+	19.6273i	−1.28952	+	0.744506i
$696$		0			0
$697$	14.6412	+	8.45311i	0.554576	+	0.320184i
$698$		0			0
$699$	−6.08693	−	43.2284i	−0.230229	−	1.63505i
$700$		0			0
$701$	−14.5424	+	14.5424i	−0.549258	+	0.549258i	−0.926226	−	0.376968i	$-0.876967\pi$
$701$	−14.5424	+	14.5424i	−0.549258	+	0.549258i	0.376968	+	0.926226i	$0.376967\pi$
$702$		0			0
$703$	−12.2231			−0.461001
$704$		0			0
$705$	19.8342	+	14.9380i	0.746998	+	0.562596i
$706$		0			0
$707$	−2.25416	−	8.41264i	−0.0847764	−	0.316390i
$708$		0			0
$709$	−8.65273	+	32.2924i	−0.324960	+	1.21277i	0.589392	+	0.807847i	$0.299367\pi$
$709$	−8.65273	+	32.2924i	−0.324960	+	1.21277i	−0.914352	+	0.404920i	$0.867299\pi$
$710$		0			0
$711$	17.3478	+	16.7350i	0.650594	+	0.627611i
$712$		0			0
$713$	3.61441	−	2.08678i	0.135361	−	0.0781505i
$714$		0			0
$715$	−25.5178	+	6.83748i	−0.954313	+	0.255707i
$716$		0			0
$717$	5.36999	−	13.3012i	0.200546	−	0.496744i
$718$		0			0
$719$	−38.7103			−1.44365			−0.721826	−	0.692075i	$-0.756697\pi$
$719$	−38.7103			−1.44365			−0.721826	+	0.692075i	$0.756697\pi$
$720$		0			0
$721$	−12.6695			−0.471837
$722$		0			0
$723$	13.6548	+	17.4678i	0.507826	+	0.649636i
$724$		0			0
$725$	5.03373	−	1.34878i	0.186948	−	0.0500925i
$726$		0			0
$727$	24.4245	−	14.1015i	0.905853	−	0.522994i	0.0267585	−	0.999642i	$-0.491481\pi$
$727$	24.4245	−	14.1015i	0.905853	−	0.522994i	0.879095	+	0.476647i	$0.158148\pi$
$728$		0			0
$729$	18.0349	−	20.0934i	0.667958	−	0.744199i
$730$		0			0
$731$	−6.32442	+	23.6031i	−0.233917	+	0.872990i
$732$		0			0
$733$	1.95090	+	7.28085i	0.0720580	+	0.268924i	0.992550	−	0.121837i	$-0.0388785\pi$
$733$	1.95090	+	7.28085i	0.0720580	+	0.268924i	−0.920492	+	0.390761i	$0.872212\pi$
$734$		0			0
$735$	−1.64325	+	13.4123i	−0.0606123	+	0.494722i
$736$		0			0
$737$	4.68989			0.172754
$738$		0			0
$739$	16.1043	−	16.1043i	0.592407	−	0.592407i	−0.345874	−	0.938281i	$-0.612417\pi$
$739$	16.1043	−	16.1043i	0.592407	−	0.592407i	0.938281	+	0.345874i	$0.112417\pi$
$740$		0			0
$741$	52.9383	+	21.3723i	1.94474	+	0.785130i
$742$		0			0
$743$	−5.50307	−	3.17720i	−0.201888	−	0.116560i	0.395648	−	0.918402i	$-0.370520\pi$
$743$	−5.50307	−	3.17720i	−0.201888	−	0.116560i	−0.597536	+	0.801842i	$0.703853\pi$
$744$		0			0
$745$	9.32837	−	5.38574i	0.341765	−	0.197318i
$746$		0			0
$747$	−24.8372	+	0.446590i	−0.908746	+	0.0163399i
$748$		0			0
$749$	−16.3407	−	4.37848i	−0.597077	−	0.159986i
$750$		0			0
$751$	−7.20371	+	12.4772i	−0.262867	+	0.455299i	−0.967003	−	0.254767i	$-0.918001\pi$
$751$	−7.20371	+	12.4772i	−0.262867	+	0.455299i	0.704136	+	0.710066i	$0.251335\pi$
$752$		0			0
$753$	−27.2783	−	20.5445i	−0.994077	−	0.748682i
$754$		0			0
$755$	−13.0840	+	13.0840i	−0.476176	+	0.476176i
$756$		0			0
$757$	−29.7018	−	29.7018i	−1.07953	−	1.07953i	−0.996551	−	0.0829799i	$-0.973556\pi$
$757$	−29.7018	−	29.7018i	−1.07953	−	1.07953i	−0.0829799	−	0.996551i	$-0.526444\pi$
$758$		0			0
$759$	1.43715	−	1.90821i	0.0521653	−	0.0692635i
$760$		0			0
$761$	−21.6542	−	12.5021i	−0.784965	−	0.453200i	0.0532222	−	0.998583i	$-0.483051\pi$
$761$	−21.6542	−	12.5021i	−0.784965	−	0.453200i	−0.838187	+	0.545383i	$0.816384\pi$
$762$		0			0
$763$	−7.62545	+	28.4586i	−0.276060	+	1.03027i
$764$		0			0
$765$	18.9514	−	11.4007i	0.685190	−	0.412194i
$766$		0			0
$767$	−16.8307	−	29.1516i	−0.607721	−	1.05260i
$768$		0			0
$769$	−26.1481	+	45.2899i	−0.942926	+	1.63320i	−0.183076	+	0.983099i	$0.558605\pi$
$769$	−26.1481	+	45.2899i	−0.942926	+	1.63320i	−0.759851	+	0.650097i	$0.774728\pi$
$770$		0			0
$771$	4.55764	−	11.2891i	0.164140	−	0.406567i
$772$		0			0
$773$	0.679496	+	0.679496i	0.0244398	+	0.0244398i	0.719221	−	0.694781i	$-0.244499\pi$
$773$	0.679496	+	0.679496i	0.0244398	+	0.0244398i	−0.694781	+	0.719221i	$0.744499\pi$
$774$		0			0
$775$		−	6.32386i		−	0.227160i
$776$		0			0
$777$	−5.47955	−	0.671343i	−0.196578	−	0.0240843i
$778$		0			0
$779$	31.2252	−	8.36677i	1.11876	−	0.299771i
$780$		0			0
$781$	19.6134	+	5.25540i	0.701824	+	0.188053i
$782$		0			0
$783$	34.2637	−	5.45452i	1.22448	−	0.194929i
$784$		0			0
$785$	−11.6360	−	20.1541i	−0.415306	−	0.719331i
$786$		0			0
$787$	7.58525	+	28.3085i	0.270385	+	1.00909i	0.958871	+	0.283841i	$0.0916087\pi$
$787$	7.58525	+	28.3085i	0.270385	+	1.00909i	−0.688487	+	0.725249i	$0.741725\pi$
$788$		0			0
$789$	−23.9158	+	18.6952i	−0.851425	+	0.665566i
$790$		0			0
$791$		−	1.23850i		−	0.0440360i
$792$		0			0
$793$			28.7797i			1.02200i
$794$		0			0
$795$	24.5558	+	9.91370i	0.870906	+	0.351603i
$796$		0			0
$797$	5.63071	+	21.0141i	0.199450	+	0.744357i	0.991070	+	0.133343i	$0.0425713\pi$
$797$	5.63071	+	21.0141i	0.199450	+	0.744357i	−0.791620	+	0.611014i	$0.790762\pi$
$798$		0			0
$799$	−12.5233	−	21.6909i	−0.443041	−	0.767370i
$800$		0			0
$801$	13.7034	+	47.6948i	0.484185	+	1.68521i
$802$		0			0
$803$	−32.4518	−	8.69544i	−1.14520	−	0.306855i
$804$		0			0
$805$	1.82883	−	0.490035i	0.0644579	−	0.0172714i
$806$		0			0
$807$	0.459640	−	0.610297i	0.0161801	−	0.0214835i
$808$		0			0
$809$		−	12.5804i		−	0.442303i	−0.975240	−	0.221151i	$-0.929019\pi$
$809$		−	12.5804i		−	0.442303i	0.975240	−	0.221151i	$-0.0709815\pi$
$810$		0			0
$811$	−30.5378	−	30.5378i	−1.07233	−	1.07233i	−0.997172	−	0.0751549i	$-0.976055\pi$
$811$	−30.5378	−	30.5378i	−1.07233	−	1.07233i	−0.0751549	−	0.997172i	$-0.523945\pi$
$812$		0			0
$813$	12.8119	−	1.80403i	0.449333	−	0.0632701i
$814$		0			0
$815$	−17.2953	+	29.9564i	−0.605829	+	1.04933i
$816$		0			0
$817$	23.3620	+	40.4641i	0.817331	+	1.41566i
$818$		0			0
$819$	22.5582	+	12.4887i	0.788246	+	0.436391i
$820$		0			0
$821$	−4.88097	+	18.2160i	−0.170347	+	0.635744i	0.826951	+	0.562275i	$0.190074\pi$
$821$	−4.88097	+	18.2160i	−0.170347	+	0.635744i	−0.997298	+	0.0734689i	$0.976593\pi$
$822$		0			0
$823$	11.5958	+	6.69486i	0.404206	+	0.233368i	0.688297	−	0.725429i	$-0.258359\pi$
$823$	11.5958	+	6.69486i	0.404206	+	0.233368i	−0.284091	+	0.958797i	$0.591692\pi$
$824$		0			0
$825$	−1.41518	−	3.33153i	−0.0492704	−	0.115989i
$826$		0			0
$827$	7.23348	+	7.23348i	0.251533	+	0.251533i	0.821599	−	0.570066i	$-0.193082\pi$
$827$	7.23348	+	7.23348i	0.251533	+	0.251533i	−0.570066	+	0.821599i	$0.693082\pi$
$828$		0			0
$829$	−25.9641	+	25.9641i	−0.901769	+	0.901769i	−0.995589	−	0.0938197i	$-0.970092\pi$
$829$	−25.9641	+	25.9641i	−0.901769	+	0.901769i	0.0938197	+	0.995589i	$0.470092\pi$
$830$		0			0
$831$	−2.21291	+	18.0619i	−0.0767650	+	0.626561i
$832$		0			0
$833$	6.81519	−	11.8043i	0.236132	−	0.408993i
$834$		0			0
$835$	18.7737	+	5.03040i	0.649691	+	0.174084i
$836$		0			0
$837$	4.36787	−	41.8750i	0.150976	−	1.44741i
$838$		0			0
$839$	−41.1955	+	23.7842i	−1.42223	+	0.821123i	−0.996489	−	0.0837230i	$-0.973319\pi$
$839$	−41.1955	+	23.7842i	−1.42223	+	0.821123i	−0.425738	+	0.904846i	$0.639986\pi$
$840$		0			0
$841$	13.4955	+	7.79166i	0.465364	+	0.268678i
$842$		0			0
$843$	−9.08166	+	7.09922i	−0.312789	+	0.244510i
$844$		0			0
$845$	14.6264	−	14.6264i	0.503165	−	0.503165i
$846$		0			0
$847$	6.85431			0.235517
$848$		0			0
$849$	−17.5547	+	7.45698i	−0.602477	+	0.255923i
$850$		0			0
$851$	−0.237457	−	0.886202i	−0.00813992	−	0.0303786i
$852$		0			0
$853$	0.0729011	−	0.272071i	0.00249609	−	0.00931552i	−0.964667	−	0.263474i	$-0.915132\pi$
$853$	0.0729011	−	0.272071i	0.00249609	−	0.00931552i	0.967163	+	0.254158i	$0.0817984\pi$
$854$		0			0
$855$	10.2091	−	41.0383i	0.349143	−	1.40348i
$856$		0			0
$857$	−24.7820	+	14.3079i	−0.846538	+	0.488749i	−0.859481	−	0.511167i	$-0.829213\pi$
$857$	−24.7820	+	14.3079i	−0.846538	+	0.488749i	0.0129433	+	0.999916i	$0.495880\pi$
$858$		0			0
$859$	−1.05613	+	0.282990i	−0.0360347	+	0.00965548i	−0.276791	−	0.960930i	$-0.589271\pi$
$859$	−1.05613	+	0.282990i	−0.0360347	+	0.00965548i	0.240757	+	0.970586i	$0.422604\pi$
$860$		0			0
$861$	14.4577	−	2.03577i	0.492716	−	0.0693788i
$862$		0			0
$863$	−30.2887			−1.03104			−0.515520	−	0.856878i	$-0.672401\pi$
$863$	−30.2887			−1.03104			−0.515520	+	0.856878i	$0.672401\pi$
$864$		0			0
$865$	−49.1485			−1.67110
$866$		0			0
$867$	7.06611	−	0.994970i	0.239978	−	0.0337910i
$868$		0			0
$869$	20.7807	−	5.56816i	0.704935	−	0.188887i
$870$		0			0
$871$	−7.28567	+	4.20638i	−0.246865	+	0.142528i
$872$		0			0
$873$	−17.9526	−	17.3184i	−0.607603	−	0.586138i
$874$		0			0
$875$	5.49929	−	20.5236i	0.185910	−	0.693825i
$876$		0			0
$877$	6.25984	+	23.3620i	0.211380	+	0.788880i	0.987410	+	0.158184i	$0.0505639\pi$
$877$	6.25984	+	23.3620i	0.211380	+	0.788880i	−0.776030	+	0.630696i	$0.782769\pi$
$878$		0			0
$879$	4.55394	−	1.93444i	0.153601	−	0.0652472i
$880$		0			0
$881$	−10.3324			−0.348108			−0.174054	−	0.984736i	$-0.555687\pi$
$881$	−10.3324			−0.348108			−0.174054	+	0.984736i	$0.555687\pi$
$882$		0			0
$883$	−13.2455	+	13.2455i	−0.445745	+	0.445745i	−0.893937	−	0.448192i	$-0.852068\pi$
$883$	−13.2455	+	13.2455i	−0.445745	+	0.445745i	0.448192	+	0.893937i	$0.352068\pi$
$884$		0			0
$885$	−19.6447	+	15.3564i	−0.660349	+	0.516201i
$886$		0			0
$887$	4.21020	+	2.43076i	0.141365	+	0.0816170i	0.569014	−	0.822328i	$-0.307325\pi$
$887$	4.21020	+	2.43076i	0.141365	+	0.0816170i	−0.427650	+	0.903945i	$0.640658\pi$
$888$		0			0
$889$	−8.85782	+	5.11406i	−0.297082	+	0.171520i
$890$		0			0
$891$	−7.06991	−	23.0380i	−0.236851	−	0.771803i
$892$		0			0
$893$	−46.2601	−	12.3953i	−1.54803	−	0.414794i
$894$		0			0
$895$	16.8975	−	29.2674i	0.564822	−	0.978301i
$896$		0			0
$897$	−0.521112	+	4.25335i	−0.0173994	+	0.142015i
$898$		0			0
$899$	38.2555	−	38.2555i	1.27589	−	1.27589i
$900$		0			0
$901$	−18.8884	−	18.8884i	−0.629264	−	0.629264i
$902$		0			0
$903$	8.25062	+	19.4230i	0.274563	+	0.646358i
$904$		0			0
$905$	27.5177	+	15.8874i	0.914720	+	0.528114i
$906$		0			0
$907$	−0.989509	+	3.69290i	−0.0328561	+	0.122621i	−0.980406	−	0.196987i	$-0.936884\pi$
$907$	−0.989509	+	3.69290i	−0.0328561	+	0.122621i	0.947550	+	0.319608i	$0.103551\pi$
$908$		0			0
$909$	−0.262501	−	14.5990i	−0.00870661	−	0.484220i
$910$		0			0
$911$	−24.1877	−	41.8944i	−0.801376	−	1.38802i	−0.918711	−	0.394931i	$-0.870769\pi$
$911$	−24.1877	−	41.8944i	−0.801376	−	1.38802i	0.117335	−	0.993092i	$-0.462565\pi$
$912$		0			0
$913$	−11.0858	+	19.2012i	−0.366887	+	0.635467i
$914$		0			0
$915$	21.1102	−	2.97251i	0.697883	−	0.0982681i
$916$		0			0
$917$	−11.5778	−	11.5778i	−0.382334	−	0.382334i
$918$		0			0
$919$			44.5150i			1.46841i	0.678926	+	0.734206i	$0.262446\pi$
$919$			44.5150i			1.46841i	−0.678926	+	0.734206i	$0.737554\pi$
$920$		0			0
$921$	−12.0202	+	15.9601i	−0.396080	+	0.525904i
$922$		0			0
$923$	−35.1827	+	9.42718i	−1.15805	+	0.310299i
$924$		0			0
$925$	−1.34279	−	0.359800i	−0.0441507	−	0.0118301i
$926$		0			0
$927$	−20.6123	−	5.12773i	−0.676997	−	0.168417i
$928$		0			0
$929$	26.5718	+	46.0236i	0.871791	+	1.50999i	0.860142	+	0.510054i	$0.170375\pi$
$929$	26.5718	+	46.0236i	0.871791	+	1.50999i	0.0116490	+	0.999932i	$0.496292\pi$
$930$		0			0
$931$	−6.74558	−	25.1748i	−0.221077	−	0.825072i
$932$		0			0
$933$	−15.4562	−	6.24000i	−0.506014	−	0.204288i
$934$		0			0
$935$		−	19.7396i		−	0.645553i
$936$		0			0
$937$		−	2.96531i		−	0.0968724i	−0.998826	−	0.0484362i	$-0.984576\pi$
$937$		−	2.96531i		−	0.0968724i	0.998826	−	0.0484362i	$-0.0154238\pi$
$938$		0			0
$939$	35.0641	−	27.4099i	1.14427	−	0.894489i
$940$		0			0
$941$	12.2347	+	45.6603i	0.398838	+	1.48848i	0.815143	+	0.579260i	$0.196658\pi$
$941$	12.2347	+	45.6603i	0.398838	+	1.48848i	−0.416305	+	0.909225i	$0.636675\pi$
$942$		0			0
$943$	1.21322	+	2.10136i	0.0395079	+	0.0684298i
$944$		0			0
$945$	6.83069	−	17.8366i	0.222203	−	0.580224i
$946$		0			0
$947$	31.0213	+	8.31213i	1.00806	+	0.270108i	0.724817	−	0.688942i	$-0.241924\pi$
$947$	31.0213	+	8.31213i	1.00806	+	0.270108i	0.283239	+	0.959049i	$0.408591\pi$
$948$		0			0
$949$	58.2123	−	15.5979i	1.88965	−	0.506331i
$950$		0			0
$951$	−27.7766	−	3.40313i	−0.900718	−	0.110354i
$952$		0			0
$953$			14.4065i			0.466671i	0.972396	+	0.233336i	$0.0749641\pi$
$953$			14.4065i			0.466671i	−0.972396	+	0.233336i	$0.925036\pi$
$954$		0			0
$955$	9.71317	+	9.71317i	0.314311	+	0.314311i
$956$		0			0
$957$	11.5927	−	28.7147i	0.374740	−	0.928216i
$958$		0			0
$959$	0.553259	−	0.958272i	0.0178656	−	0.0309442i
$960$		0			0
$961$	−17.3258	−	30.0092i	−0.558897	−	0.968038i
$962$		0			0
$963$	−24.8130	−	13.7370i	−0.799588	−	0.442670i
$964$		0			0
$965$	0.498125	−	1.85903i	0.0160352	−	0.0598442i
$966$		0			0
$967$	46.2878	+	26.7243i	1.48852	+	0.859395i	0.999914	−	0.0131113i	$-0.00417357\pi$
$967$	46.2878	+	26.7243i	1.48852	+	0.859395i	0.488602	+	0.872507i	$0.337507\pi$
$968$		0			0
$969$	−25.6630	+	34.0746i	−0.824414	+	1.09463i
$970$		0			0
$971$	18.6508	+	18.6508i	0.598532	+	0.598532i	0.939922	−	0.341389i	$-0.110898\pi$
$971$	18.6508	+	18.6508i	0.598532	+	0.598532i	−0.341389	+	0.939922i	$0.610898\pi$
$972$		0			0
$973$	24.1801	−	24.1801i	0.775180	−	0.775180i
$974$		0			0
$975$	5.18653	+	3.90620i	0.166102	+	0.125098i
$976$		0			0
$977$	1.32572	−	2.29622i	0.0424136	−	0.0734624i	−0.844039	−	0.536281i	$-0.819829\pi$
$977$	1.32572	−	2.29622i	0.0424136	−	0.0734624i	0.886453	+	0.462819i	$0.153162\pi$
$978$		0			0
$979$	42.7822	+	11.4635i	1.36733	+	0.366374i
$980$		0			0
$981$	−23.9241	+	43.2137i	−0.763837	+	1.37971i
$982$		0			0
$983$	−23.4130	+	13.5175i	−0.746760	+	0.431142i	−0.824522	−	0.565830i	$-0.808556\pi$
$983$	−23.4130	+	13.5175i	−0.746760	+	0.431142i	0.0777621	+	0.996972i	$0.475223\pi$
$984$		0			0
$985$	37.2244	+	21.4915i	1.18607	+	0.684776i
$986$		0			0
$987$	−20.0574	−	8.09759i	−0.638434	−	0.257749i
$988$		0			0
$989$	−2.47989	+	2.47989i	−0.0788560	+	0.0788560i
$990$		0			0
$991$	−5.32341			−0.169104			−0.0845519	−	0.996419i	$-0.526946\pi$
$991$	−5.32341			−0.169104			−0.0845519	+	0.996419i	$0.526946\pi$
$992$		0			0
$993$	4.27599	−	34.9010i	0.135695	−	1.10755i
$994$		0			0
$995$	−1.25989	−	4.70199i	−0.0399413	−	0.149063i
$996$		0			0
$997$	1.57391	−	5.87389i	0.0498461	−	0.186028i	−0.936514	−	0.350630i	$-0.885967\pi$
$997$	1.57391	−	5.87389i	0.0498461	−	0.186028i	0.986360	+	0.164602i	$0.0526340\pi$
$998$		0			0
$999$	−8.64310	−	3.30996i	−0.273456	−	0.104723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.49.1		72
3.2	odd	2		1728.2.bc.e.1009.14		72
4.3	odd	2		144.2.x.e.85.15	yes	72
9.2	odd	6		1728.2.bc.e.1585.5		72
9.7	even	3	inner	576.2.bb.e.241.10		72
12.11	even	2		432.2.y.e.37.4		72
16.3	odd	4		144.2.x.e.13.2	✓	72
16.13	even	4	inner	576.2.bb.e.337.10		72
36.7	odd	6		144.2.x.e.133.2	yes	72
36.11	even	6		432.2.y.e.181.17		72
48.29	odd	4		1728.2.bc.e.145.5		72
48.35	even	4		432.2.y.e.253.17		72
144.29	odd	12		1728.2.bc.e.721.14		72
144.61	even	12	inner	576.2.bb.e.529.1		72
144.83	even	12		432.2.y.e.397.4		72
144.115	odd	12		144.2.x.e.61.15	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.2	✓	72	16.3	odd	4
144.2.x.e.61.15	yes	72	144.115	odd	12
144.2.x.e.85.15	yes	72	4.3	odd	2
144.2.x.e.133.2	yes	72	36.7	odd	6
432.2.y.e.37.4		72	12.11	even	2
432.2.y.e.181.17		72	36.11	even	6
432.2.y.e.253.17		72	48.35	even	4
432.2.y.e.397.4		72	144.83	even	12
576.2.bb.e.49.1		72	1.1	even	1	trivial
576.2.bb.e.241.10		72	9.7	even	3	inner
576.2.bb.e.337.10		72	16.13	even	4	inner
576.2.bb.e.529.1		72	144.61	even	12	inner
1728.2.bc.e.145.5		72	48.29	odd	4
1728.2.bc.e.721.14		72	144.29	odd	12
1728.2.bc.e.1009.14		72	3.2	odd	2
1728.2.bc.e.1585.5		72	9.2	odd	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71513 + 0.241506i) q^{3} +(-1.98415 + 0.531653i) q^{5} +(1.54969 - 0.894715i) q^{7} +(2.88335 - 0.828427i) q^{9} +O(q^{10})\)	\(q+(-1.71513 + 0.241506i) q^{3} +(-1.98415 + 0.531653i) q^{5} +(1.54969 - 0.894715i) q^{7} +(2.88335 - 0.828427i) q^{9} +(0.693015 - 2.58637i) q^{11} +(1.24314 + 4.63944i) q^{13} +(3.27469 - 1.39104i) q^{15} -3.58889 q^{17} +(-4.85244 + 4.85244i) q^{19} +(-2.44185 + 1.90881i) q^{21} +(-0.446082 - 0.257545i) q^{23} +(-0.675912 + 0.390238i) q^{25} +(-4.74525 + 2.11721i) q^{27} +(-6.44956 - 1.72815i) q^{29} +(-4.05128 + 7.01703i) q^{31} +(-0.563989 + 4.60332i) q^{33} +(-2.59915 + 2.59915i) q^{35} +(1.25948 + 1.25948i) q^{37} +(-3.25259 - 7.65703i) q^{39} +(-4.07959 - 2.35535i) q^{41} +(1.76222 - 6.57670i) q^{43} +(-5.28058 + 3.17667i) q^{45} +(3.48945 + 6.04391i) q^{47} +(-1.89897 + 3.28911i) q^{49} +(6.15542 - 0.866737i) q^{51} +(5.26302 + 5.26302i) q^{53} +5.50019i q^{55} +(7.15068 - 9.49446i) q^{57} +(-6.76946 + 1.81387i) q^{59} +(5.78773 + 1.55082i) q^{61} +(3.72710 - 3.86359i) q^{63} +(-4.93314 - 8.54446i) q^{65} +(0.453328 + 1.69184i) q^{67} +(0.827288 + 0.333993i) q^{69} +7.58339i q^{71} -12.5473i q^{73} +(1.06503 - 0.832546i) q^{75} +(-1.24010 - 4.62812i) q^{77} +(4.01735 + 6.95825i) q^{79} +(7.62742 - 4.77729i) q^{81} +(-7.99826 - 2.14313i) q^{83} +(7.12091 - 1.90804i) q^{85} +(11.4792 + 1.40641i) q^{87} +16.5414i q^{89} +(6.07746 + 6.07746i) q^{91} +(5.25383 - 13.0135i) q^{93} +(7.04818 - 12.2078i) q^{95} +(-4.15739 - 7.20082i) q^{97} +(-0.144412 - 8.03151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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