LMFDB - Embedded newform 288.2.r.b.241.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(49,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("288.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.r (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:	$2.29969157821$
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} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.5
Root			$-0.722180 + 1.21592i$ of defining polynomial
Character	$\chi$	$=$	288.241
Dual form			288.2.r.b.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.294546 + 1.70682i) q^{3} +(-3.17262 + 1.83171i) q^{5} +(0.191926 - 0.332426i) q^{7} +(-2.82649 + 1.00547i) q^{9} +O(q^{10})$	\(q+(0.294546 + 1.70682i) q^{3} +(-3.17262 + 1.83171i) q^{5} +(0.191926 - 0.332426i) q^{7} +(-2.82649 + 1.00547i) q^{9} +(-1.73849 - 1.00372i) q^{11} +(0.397799 - 0.229669i) q^{13} +(-4.06089 - 4.87557i) q^{15} -4.08495 q^{17} +4.72398i q^{19} +(0.623923 + 0.229669i) q^{21} +(2.97594 + 5.15447i) q^{23} +(4.21034 - 7.29252i) q^{25} +(-2.54870 - 4.52815i) q^{27} +(2.03783 + 1.17654i) q^{29} +(-0.592083 - 1.02552i) q^{31} +(1.20110 - 3.26293i) q^{33} +1.40621i q^{35} +5.74432i q^{37} +(0.509175 + 0.611324i) q^{39} +(4.75281 + 8.23212i) q^{41} +(1.03633 + 0.598327i) q^{43} +(7.12562 - 8.36729i) q^{45} +(-3.27688 + 5.67572i) q^{47} +(3.42633 + 5.93458i) q^{49} +(-1.20321 - 6.97229i) q^{51} -7.63807i q^{53} +7.35407 q^{55} +(-8.06300 + 1.39143i) q^{57} +(0.603703 - 0.348548i) q^{59} +(-4.23774 - 2.44666i) q^{61} +(-0.208231 + 1.13257i) q^{63} +(-0.841376 + 1.45731i) q^{65} +(8.87932 - 5.12648i) q^{67} +(-7.92122 + 6.59762i) q^{69} +3.73792 q^{71} -2.68275 q^{73} +(13.6872 + 5.03832i) q^{75} +(-0.667322 + 0.385279i) q^{77} +(5.35979 - 9.28342i) q^{79} +(6.97804 - 5.68392i) q^{81} +(-5.49039 - 3.16988i) q^{83} +(12.9600 - 7.48246i) q^{85} +(-1.40792 + 3.82477i) q^{87} +7.56802 q^{89} -0.176318i q^{91} +(1.57598 - 1.31264i) q^{93} +(-8.65297 - 14.9874i) q^{95} +(-2.98511 + 5.17036i) q^{97} +(5.92302 + 1.08898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 6 * q^7 + 2 * q^9	$ 16 q - 6 q^{7} + 2 q^{9} + 10 q^{15} - 28 q^{17} + 10 q^{23} + 2 q^{25} + 10 q^{31} - 2 q^{39} - 8 q^{41} - 6 q^{47} + 18 q^{49} + 4 q^{55} + 10 q^{57} - 2 q^{63} - 14 q^{65} - 72 q^{71} - 44 q^{73} + 30 q^{79} + 10 q^{81} - 42 q^{87} + 64 q^{89} - 44 q^{95}+O(q^{100}) $ 16 * q - 6 * q^7 + 2 * q^9 + 10 * q^15 - 28 * q^17 + 10 * q^23 + 2 * q^25 + 10 * q^31 - 2 * q^39 - 8 * q^41 - 6 * q^47 + 18 * q^49 + 4 * q^55 + 10 * q^57 - 2 * q^63 - 14 * q^65 - 72 * q^71 - 44 * q^73 + 30 * q^79 + 10 * q^81 - 42 * q^87 + 64 * q^89 - 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.294546	+	1.70682i	0.170056	+	0.985434i
$3$	0.294546	+	1.70682i	0.170056	+	0.985434i
$4$		0			0
$5$	−3.17262	+	1.83171i	−1.41884	+	0.819167i	−0.996197	−	0.0871306i	$-0.972230\pi$
$5$	−3.17262	+	1.83171i	−1.41884	+	0.819167i	−0.422641	+	0.906297i	$0.638897\pi$
$6$		0			0
$7$	0.191926	−	0.332426i	0.0725413	−	0.125645i	−0.827473	−	0.561505i	$-0.810222\pi$
$7$	0.191926	−	0.332426i	0.0725413	−	0.125645i	0.900014	+	0.435860i	$0.143556\pi$
$8$		0			0
$9$	−2.82649	+	1.00547i	−0.942162	+	0.335158i
$10$		0			0
$11$	−1.73849	−	1.00372i	−0.524173	−	0.302632i	0.214467	−	0.976731i	$-0.431199\pi$
$11$	−1.73849	−	1.00372i	−0.524173	−	0.302632i	−0.738640	+	0.674100i	$0.764532\pi$
$12$		0			0
$13$	0.397799	−	0.229669i	0.110330	−	0.0636988i	−0.443820	−	0.896116i	$-0.646377\pi$
$13$	0.397799	−	0.229669i	0.110330	−	0.0636988i	0.554149	+	0.832417i	$0.313044\pi$
$14$		0			0
$15$	−4.06089	−	4.87557i	−1.04852	−	1.25887i
$16$		0			0
$17$	−4.08495			−0.990747			−0.495373	−	0.868680i	$-0.664969\pi$
$17$	−4.08495			−0.990747			−0.495373	+	0.868680i	$0.664969\pi$
$18$		0			0
$19$			4.72398i			1.08376i	0.840457	+	0.541878i	$0.182286\pi$
$19$			4.72398i			1.08376i	−0.840457	+	0.541878i	$0.817714\pi$
$20$		0			0
$21$	0.623923	+	0.229669i	0.136151	+	0.0501179i
$22$		0			0
$23$	2.97594	+	5.15447i	0.620525	+	1.07478i	0.989388	+	0.145298i	$0.0464140\pi$
$23$	2.97594	+	5.15447i	0.620525	+	1.07478i	−0.368863	+	0.929484i	$0.620253\pi$
$24$		0			0
$25$	4.21034	−	7.29252i	0.842068	−	1.45850i
$26$		0			0
$27$	−2.54870	−	4.52815i	−0.490497	−	0.871443i
$28$		0			0
$29$	2.03783	+	1.17654i	0.378416	+	0.218479i	0.677129	−	0.735864i	$-0.263224\pi$
$29$	2.03783	+	1.17654i	0.378416	+	0.218479i	−0.298713	+	0.954343i	$0.596557\pi$
$30$		0			0
$31$	−0.592083	−	1.02552i	−0.106341	−	0.184188i	0.807944	−	0.589259i	$-0.200580\pi$
$31$	−0.592083	−	1.02552i	−0.106341	−	0.184188i	−0.914285	+	0.405071i	$0.867247\pi$
$32$		0			0
$33$	1.20110	−	3.26293i	0.209085	−	0.568003i
$34$		0			0
$35$			1.40621i			0.237693i
$36$		0			0
$37$			5.74432i			0.944360i	0.881502	+	0.472180i	$0.156533\pi$
$37$			5.74432i			0.944360i	−0.881502	+	0.472180i	$0.843467\pi$
$38$		0			0
$39$	0.509175	+	0.611324i	0.0815332	+	0.0978902i
$40$		0			0
$41$	4.75281	+	8.23212i	0.742265	+	1.28564i	0.951462	+	0.307767i	$0.0995817\pi$
$41$	4.75281	+	8.23212i	0.742265	+	1.28564i	−0.209197	+	0.977874i	$0.567085\pi$
$42$		0			0
$43$	1.03633	+	0.598327i	0.158039	+	0.0912440i	0.576934	−	0.816791i	$-0.304249\pi$
$43$	1.03633	+	0.598327i	0.158039	+	0.0912440i	−0.418895	+	0.908035i	$0.637582\pi$
$44$		0			0
$45$	7.12562	−	8.36729i	1.06222	−	1.24732i
$46$		0			0
$47$	−3.27688	+	5.67572i	−0.477982	+	0.827889i	−0.999681	−	0.0252403i	$-0.991965\pi$
$47$	−3.27688	+	5.67572i	−0.477982	+	0.827889i	0.521699	+	0.853129i	$0.325298\pi$
$48$		0			0
$49$	3.42633	+	5.93458i	0.489476	+	0.847796i
$50$		0			0
$51$	−1.20321	−	6.97229i	−0.168482	−	0.976316i
$52$		0			0
$53$		−	7.63807i		−	1.04917i	−0.851358	−	0.524585i	$-0.824221\pi$
$53$		−	7.63807i		−	1.04917i	0.851358	−	0.524585i	$-0.175779\pi$
$54$		0			0
$55$	7.35407			0.991623
$56$		0			0
$57$	−8.06300	+	1.39143i	−1.06797	+	0.184299i
$58$		0			0
$59$	0.603703	−	0.348548i	0.0785954	−	0.0453771i	−0.460187	−	0.887822i	$-0.652218\pi$
$59$	0.603703	−	0.348548i	0.0785954	−	0.0453771i	0.538783	+	0.842445i	$0.318884\pi$
$60$		0			0
$61$	−4.23774	−	2.44666i	−0.542587	−	0.313263i	0.203540	−	0.979067i	$-0.434755\pi$
$61$	−4.23774	−	2.44666i	−0.542587	−	0.313263i	−0.746127	+	0.665804i	$0.768089\pi$
$62$		0			0
$63$	−0.208231	+	1.13257i	−0.0262346	+	0.142691i
$64$		0			0
$65$	−0.841376	+	1.45731i	−0.104360	+	0.180757i
$66$		0			0
$67$	8.87932	−	5.12648i	1.08478	−	0.626299i	0.152599	−	0.988288i	$-0.451236\pi$
$67$	8.87932	−	5.12648i	1.08478	−	0.626299i	0.932182	+	0.361989i	$0.117902\pi$
$68$		0			0
$69$	−7.92122	+	6.59762i	−0.953603	+	0.794260i
$70$		0			0
$71$	3.73792			0.443610			0.221805	−	0.975091i	$-0.428805\pi$
$71$	3.73792			0.443610			0.221805	+	0.975091i	$0.428805\pi$
$72$		0			0
$73$	−2.68275			−0.313992			−0.156996	−	0.987599i	$-0.550181\pi$
$73$	−2.68275			−0.313992			−0.156996	+	0.987599i	$0.550181\pi$
$74$		0			0
$75$	13.6872	+	5.03832i	1.58046	+	0.581775i
$76$		0			0
$77$	−0.667322	+	0.385279i	−0.0760484	+	0.0439066i
$78$		0			0
$79$	5.35979	−	9.28342i	0.603023	−	1.04447i	−0.389337	−	0.921095i	$-0.627296\pi$
$79$	5.35979	−	9.28342i	0.603023	−	1.04447i	0.992361	−	0.123372i	$-0.0393707\pi$
$80$		0			0
$81$	6.97804	−	5.68392i	0.775338	−	0.631546i
$82$		0			0
$83$	−5.49039	−	3.16988i	−0.602648	−	0.347939i	0.167434	−	0.985883i	$-0.446452\pi$
$83$	−5.49039	−	3.16988i	−0.602648	−	0.347939i	−0.770083	+	0.637944i	$0.779785\pi$
$84$		0			0
$85$	12.9600	−	7.48246i	1.40571	−	0.811586i
$86$		0			0
$87$	−1.40792	+	3.82477i	−0.150945	+	0.410058i
$88$		0			0
$89$	7.56802			0.802208			0.401104	−	0.916032i	$-0.368627\pi$
$89$	7.56802			0.802208			0.401104	+	0.916032i	$0.368627\pi$
$90$		0			0
$91$		−	0.176318i		−	0.0184832i
$92$		0			0
$93$	1.57598	−	1.31264i	0.163422	−	0.136115i
$94$		0			0
$95$	−8.65297	−	14.9874i	−0.887776	−	1.53767i
$96$		0			0
$97$	−2.98511	+	5.17036i	−0.303092	+	0.524971i	−0.976835	−	0.213995i	$-0.931352\pi$
$97$	−2.98511	+	5.17036i	−0.303092	+	0.524971i	0.673743	+	0.738966i	$0.264686\pi$
$98$		0			0
$99$	5.92302	+	1.08898i	0.595286	+	0.109447i
$100$		0			0
$101$	−4.81265	−	2.77859i	−0.478877	−	0.276480i	0.241071	−	0.970507i	$-0.422501\pi$
$101$	−4.81265	−	2.77859i	−0.478877	−	0.276480i	−0.719948	+	0.694028i	$0.755835\pi$
$102$		0			0
$103$	6.14380	+	10.6414i	0.605366	+	1.04853i	0.991993	+	0.126289i	$0.0403067\pi$
$103$	6.14380	+	10.6414i	0.605366	+	1.04853i	−0.386627	+	0.922236i	$0.626360\pi$
$104$		0			0
$105$	−2.40016	+	0.414194i	−0.234231	+	0.0404212i
$106$		0			0
$107$			6.61773i			0.639760i	0.947458	+	0.319880i	$0.103643\pi$
$107$			6.61773i			0.639760i	−0.947458	+	0.319880i	$0.896357\pi$
$108$		0			0
$109$			7.01563i			0.671975i	0.941866	+	0.335988i	$0.109070\pi$
$109$			7.01563i			0.671975i	−0.941866	+	0.335988i	$0.890930\pi$
$110$		0			0
$111$	−9.80453	+	1.69196i	−0.930605	+	0.160594i
$112$		0			0
$113$	−4.09419	−	7.09135i	−0.385149	−	0.667098i	0.606641	−	0.794976i	$-0.292517\pi$
$113$	−4.09419	−	7.09135i	−0.385149	−	0.667098i	−0.991790	+	0.127878i	$0.959183\pi$
$114$		0			0
$115$	−18.8830	−	10.9021i	−1.76085	−	1.01663i
$116$		0			0
$117$	−0.893446	+	1.04913i	−0.0825991	+	0.0969924i
$118$		0			0
$119$	−0.784009	+	1.35794i	−0.0718700	+	0.124483i
$120$		0			0
$121$	−3.48511	−	6.03639i	−0.316828	−	0.548762i
$122$		0			0
$123$	−12.6508	+	10.5369i	−1.14069	+	0.950084i
$124$		0			0
$125$			12.5314i			1.12084i
$126$		0			0
$127$	−21.0113			−1.86445			−0.932224	−	0.361882i	$-0.882134\pi$
$127$	−21.0113			−1.86445			−0.932224	+	0.361882i	$0.882134\pi$
$128$		0			0
$129$	−0.715991	+	1.94507i	−0.0630395	+	0.171254i
$130$		0			0
$131$	5.49039	−	3.16988i	0.479697	−	0.276953i	−0.240593	−	0.970626i	$-0.577342\pi$
$131$	5.49039	−	3.16988i	0.479697	−	0.276953i	0.720290	+	0.693673i	$0.244009\pi$
$132$		0			0
$133$	1.57037	+	0.906655i	0.136169	+	0.0786170i
$134$		0			0
$135$	16.3803	+	9.69762i	1.40979	+	0.834638i
$136$		0			0
$137$	0.483695	−	0.837785i	0.0413249	−	0.0715768i	−0.844623	−	0.535361i	$-0.820175\pi$
$137$	0.483695	−	0.837785i	0.0413249	−	0.0715768i	0.885948	+	0.463784i	$0.153509\pi$
$138$		0			0
$139$	−5.18167	+	2.99164i	−0.439503	+	0.253747i	−0.703387	−	0.710807i	$-0.748330\pi$
$139$	−5.18167	+	2.99164i	−0.439503	+	0.253747i	0.263884	+	0.964554i	$0.414996\pi$
$140$		0			0
$141$	−10.6526	−	3.92129i	−0.897114	−	0.330232i
$142$		0			0
$143$	−0.922090			−0.0771091
$144$		0			0
$145$	−8.62036			−0.715882
$146$		0			0
$147$	−9.12006	+	7.59614i	−0.752210	+	0.626519i
$148$		0			0
$149$	6.43764	−	3.71678i	0.527392	−	0.304490i	−0.212562	−	0.977148i	$-0.568181\pi$
$149$	6.43764	−	3.71678i	0.527392	−	0.304490i	0.739954	+	0.672658i	$0.234847\pi$
$150$		0			0
$151$	0.492870	−	0.853676i	0.0401092	−	0.0694711i	−0.845274	−	0.534333i	$-0.820563\pi$
$151$	0.492870	−	0.853676i	0.0401092	−	0.0694711i	0.885383	+	0.464862i	$0.153896\pi$
$152$		0			0
$153$	11.5461	−	4.10732i	0.933444	−	0.332057i
$154$		0			0
$155$	3.75691	+	2.16905i	0.301762	+	0.174222i
$156$		0			0
$157$	−15.2336	+	8.79510i	−1.21577	+	0.701925i	−0.964010	−	0.265864i	$-0.914343\pi$
$157$	−15.2336	+	8.79510i	−1.21577	+	0.701925i	−0.251760	+	0.967790i	$0.581009\pi$
$158$		0			0
$159$	13.0368	−	2.24976i	1.03389	−	0.178418i
$160$		0			0
$161$	2.28464			0.180055
$162$		0			0
$163$			17.8852i			1.40088i	0.713711	+	0.700440i	$0.247013\pi$
$163$			17.8852i			1.40088i	−0.713711	+	0.700440i	$0.752987\pi$
$164$		0			0
$165$	2.16611	+	12.5521i	0.168631	+	0.977179i
$166$		0			0
$167$	1.04037	+	1.80197i	0.0805062	+	0.139441i	0.903467	−	0.428657i	$-0.141013\pi$
$167$	1.04037	+	1.80197i	0.0805062	+	0.139441i	−0.822961	+	0.568097i	$0.807680\pi$
$168$		0			0
$169$	−6.39450	+	11.0756i	−0.491885	+	0.851970i
$170$		0			0
$171$	−4.74984	−	13.3523i	−0.363229	−	1.02107i
$172$		0			0
$173$	16.4718	+	9.51000i	1.25233	+	0.723032i	0.971571	−	0.236747i	$-0.0760813\pi$
$173$	16.4718	+	9.51000i	1.25233	+	0.723032i	0.280757	+	0.959779i	$0.409415\pi$
$174$		0			0
$175$	−1.61615	−	2.79925i	−0.122169	−	0.211603i
$176$		0			0
$177$	0.772728	+	0.927750i	0.0580818	+	0.0697340i
$178$		0			0
$179$			2.12111i			0.158539i	0.996853	+	0.0792697i	$0.0252588\pi$
$179$			2.12111i			0.158539i	−0.996853	+	0.0792697i	$0.974741\pi$
$180$		0			0
$181$		−	1.66297i		−	0.123608i	−0.998088	−	0.0618039i	$-0.980315\pi$
$181$		−	1.66297i		−	0.123608i	0.998088	−	0.0618039i	$-0.0196853\pi$
$182$		0			0
$183$	2.92781	−	7.95372i	0.216430	−	0.587956i
$184$		0			0
$185$	−10.5219	−	18.2245i	−0.773588	−	1.33989i
$186$		0			0
$187$	7.10164	+	4.10013i	0.519323	+	0.299831i
$188$		0			0
$189$	−1.99444	−	0.0218184i	−0.145074	−	0.00158705i
$190$		0			0
$191$	8.69755	−	15.0646i	0.629333	−	1.09004i	−0.358353	−	0.933586i	$-0.616662\pi$
$191$	8.69755	−	15.0646i	0.629333	−	1.09004i	0.987686	−	0.156450i	$-0.0500052\pi$
$192$		0			0
$193$	−1.41709	−	2.45447i	−0.102004	−	0.176677i	0.810506	−	0.585730i	$-0.199192\pi$
$193$	−1.41709	−	2.45447i	−0.102004	−	0.176677i	−0.912510	+	0.409054i	$0.865859\pi$
$194$		0			0
$195$	−2.73519	−	1.00684i	−0.195871	−	0.0721010i
$196$		0			0
$197$		−	12.5991i		−	0.897646i	−0.893621	−	0.448823i	$-0.851843\pi$
$197$		−	12.5991i		−	0.897646i	0.893621	−	0.448823i	$-0.148157\pi$
$198$		0			0
$199$	−17.2733			−1.22447			−0.612237	−	0.790674i	$-0.709730\pi$
$199$	−17.2733			−1.22447			−0.612237	+	0.790674i	$0.709730\pi$
$200$		0			0
$201$	11.3654	+	13.6454i	0.801650	+	0.962475i
$202$		0			0
$203$	0.782227	−	0.451619i	0.0549016	−	0.0316975i
$204$		0			0
$205$	−30.1577	−	17.4116i	−2.10631	−	1.21608i
$206$		0			0
$207$	−13.5941	−	11.5768i	−0.944857	−	0.804644i
$208$		0			0
$209$	4.74153	−	8.21258i	0.327979	−	0.568076i
$210$		0			0
$211$	15.2192	−	8.78678i	1.04773	−	0.604907i	0.125717	−	0.992066i	$-0.459877\pi$
$211$	15.2192	−	8.78678i	1.04773	−	0.604907i	0.922013	+	0.387159i	$0.126544\pi$
$212$		0			0
$213$	1.10099	+	6.37997i	0.0754386	+	0.437149i
$214$		0			0
$215$	−4.38385			−0.298976
$216$		0			0
$217$	−0.454545			−0.0308565
$218$		0			0
$219$	−0.790193	−	4.57898i	−0.0533963	−	0.309419i
$220$		0			0
$221$	−1.62499	+	0.938188i	−0.109309	+	0.0631094i
$222$		0			0
$223$	−12.3137	+	21.3280i	−0.824587	+	1.42823i	0.0776484	+	0.996981i	$0.475259\pi$
$223$	−12.3137	+	21.3280i	−0.824587	+	1.42823i	−0.902235	+	0.431245i	$0.858074\pi$
$224$		0			0
$225$	−4.56802	+	24.8456i	−0.304535	+	1.65637i
$226$		0			0
$227$	16.9918	+	9.81024i	1.12779	+	0.651128i	0.943378	−	0.331721i	$-0.107629\pi$
$227$	16.9918	+	9.81024i	1.12779	+	0.651128i	0.184410	+	0.982849i	$0.440963\pi$
$228$		0			0
$229$	21.3431	−	12.3224i	1.41039	−	0.814289i	0.414965	−	0.909837i	$-0.363794\pi$
$229$	21.3431	−	12.3224i	1.41039	−	0.814289i	0.995425	+	0.0955486i	$0.0304605\pi$
$230$		0			0
$231$	−0.854159	−	1.02552i	−0.0561995	−	0.0674741i
$232$		0			0
$233$	−20.9222			−1.37066			−0.685330	−	0.728233i	$-0.740342\pi$
$233$	−20.9222			−1.37066			−0.685330	+	0.728233i	$0.740342\pi$
$234$		0			0
$235$		−	24.0092i		−	1.56619i
$236$		0			0
$237$	17.4239	+	6.41381i	1.13180	+	0.416622i
$238$		0			0
$239$	5.14584	+	8.91286i	0.332857	+	0.576525i	0.983071	−	0.183226i	$-0.0586541\pi$
$239$	5.14584	+	8.91286i	0.332857	+	0.576525i	−0.650214	+	0.759751i	$0.725321\pi$
$240$		0			0
$241$	10.2379	−	17.7326i	0.659483	−	1.14226i	−0.321267	−	0.946989i	$-0.604109\pi$
$241$	10.2379	−	17.7326i	0.659483	−	1.14226i	0.980750	−	0.195269i	$-0.0625579\pi$
$242$		0			0
$243$	11.7568	+	10.2361i	0.754199	+	0.656646i
$244$		0			0
$245$	−21.7409	−	12.5521i	−1.38897	−	0.801924i
$246$		0			0
$247$	1.08495	+	1.87919i	0.0690339	+	0.119570i
$248$		0			0
$249$	3.79325	−	10.3048i	0.240387	−	0.653040i
$250$		0			0
$251$		−	28.0987i		−	1.77358i	−0.462177	−	0.886788i	$-0.652932\pi$
$251$		−	28.0987i		−	1.77358i	0.462177	−	0.886788i	$-0.347068\pi$
$252$		0			0
$253$		−	11.9480i		−	0.751163i
$254$		0			0
$255$	16.5885	+	19.9165i	1.03881	+	1.24722i
$256$		0			0
$257$	5.53682	+	9.59006i	0.345378	+	0.598211i	0.985422	−	0.170126i	$-0.0544175\pi$
$257$	5.53682	+	9.59006i	0.345378	+	0.598211i	−0.640045	+	0.768338i	$0.721084\pi$
$258$		0			0
$259$	1.90956	+	1.10248i	0.118654	+	0.0685050i
$260$		0			0
$261$	−6.94290	−	1.27650i	−0.429754	−	0.0790131i
$262$		0			0
$263$	12.7620	−	22.1044i	0.786938	−	1.36302i	−0.140897	−	0.990024i	$-0.544998\pi$
$263$	12.7620	−	22.1044i	0.786938	−	1.36302i	0.927834	−	0.372992i	$-0.121668\pi$
$264$		0			0
$265$	13.9907	+	24.2327i	0.859444	+	1.48860i
$266$		0			0
$267$	2.22913	+	12.9173i	0.136420	+	0.790524i
$268$		0			0
$269$			18.3998i			1.12185i	0.827865	+	0.560927i	$0.189555\pi$
$269$			18.3998i			1.12185i	−0.827865	+	0.560927i	$0.810445\pi$
$270$		0			0
$271$	22.4135			1.36152			0.680760	−	0.732506i	$-0.261650\pi$
$271$	22.4135			1.36152			0.680760	+	0.732506i	$0.261650\pi$
$272$		0			0
$273$	0.300944	−	0.0519337i	0.0182139	−	0.00314317i
$274$		0			0
$275$	−14.6392	+	8.45196i	−0.882779	+	0.509673i
$276$		0			0
$277$	20.2421	+	11.6868i	1.21623	+	0.702190i	0.964109	−	0.265506i	$-0.0855391\pi$
$277$	20.2421	+	11.6868i	1.21623	+	0.702190i	0.252119	+	0.967696i	$0.418872\pi$
$278$		0			0
$279$	2.70465	+	2.30329i	0.161923	+	0.137894i
$280$		0			0
$281$	5.29466	−	9.17062i	0.315853	−	0.547073i	−0.663765	−	0.747941i	$-0.731043\pi$
$281$	5.29466	−	9.17062i	0.315853	−	0.547073i	0.979618	+	0.200867i	$0.0643760\pi$
$282$		0			0
$283$	−7.69029	+	4.43999i	−0.457140	+	0.263930i	−0.710841	−	0.703353i	$-0.751686\pi$
$283$	−7.69029	+	4.43999i	−0.457140	+	0.263930i	0.253701	+	0.967283i	$0.418352\pi$
$284$		0			0
$285$	23.0321	−	19.1836i	1.36430	−	1.13634i
$286$		0			0
$287$	3.64876			0.215379
$288$		0			0
$289$	−0.313160			−0.0184212
$290$		0			0
$291$	−9.70414	−	3.57214i	−0.568867	−	0.209403i
$292$		0			0
$293$	9.82117	−	5.67026i	0.573759	−	0.331260i	−0.184890	−	0.982759i	$-0.559193\pi$
$293$	9.82117	−	5.67026i	0.573759	−	0.331260i	0.758649	+	0.651499i	$0.225860\pi$
$294$		0			0
$295$	−1.27688	+	2.21162i	−0.0743428	+	0.128765i
$296$		0			0
$297$	−0.114103	+	10.4303i	−0.00662095	+	0.605227i
$298$		0			0
$299$	2.36765	+	1.36696i	0.136925	+	0.0790534i
$300$		0			0
$301$	0.397799	−	0.229669i	0.0229287	−	0.0132379i
$302$		0			0
$303$	3.32501	−	9.03277i	0.191017	−	0.518919i
$304$		0			0
$305$	17.9263			1.02646
$306$		0			0
$307$		−	0.628678i		−	0.0358805i	−0.999839	−	0.0179403i	$-0.994289\pi$
$307$		−	0.628678i		−	0.0358805i	0.999839	−	0.0179403i	$-0.00571087\pi$
$308$		0			0
$309$	−16.3533	+	13.6207i	−0.930307	+	0.774857i
$310$		0			0
$311$	9.64443	+	16.7046i	0.546885	+	0.947233i	0.998486	+	0.0550127i	$0.0175199\pi$
$311$	9.64443	+	16.7046i	0.546885	+	0.947233i	−0.451600	+	0.892220i	$0.649147\pi$
$312$		0			0
$313$	−2.86959	+	4.97028i	−0.162199	+	0.280937i	−0.935657	−	0.352911i	$-0.885192\pi$
$313$	−2.86959	+	4.97028i	−0.162199	+	0.280937i	0.773458	+	0.633847i	$0.218525\pi$
$314$		0			0
$315$	−1.41391	−	3.97464i	−0.0796649	−	0.223946i
$316$		0			0
$317$	10.8187	+	6.24618i	0.607639	+	0.350821i	0.772041	−	0.635573i	$-0.219236\pi$
$317$	10.8187	+	6.24618i	0.607639	+	0.350821i	−0.164402	+	0.986393i	$0.552569\pi$
$318$		0			0
$319$	−2.36183	−	4.09081i	−0.132237	−	0.229042i
$320$		0			0
$321$	−11.2953	+	1.94922i	−0.630442	+	0.108795i
$322$		0			0
$323$		−	19.2972i		−	1.07373i
$324$		0			0
$325$		−	3.86794i		−	0.214555i
$326$		0			0
$327$	−11.9744	+	2.06642i	−0.662188	+	0.114273i
$328$		0			0
$329$	1.25784	+	2.17864i	0.0693468	+	0.120112i
$330$		0			0
$331$	−3.00014	−	1.73213i	−0.164902	−	0.0952065i	0.415278	−	0.909695i	$-0.363684\pi$
$331$	−3.00014	−	1.73213i	−0.164902	−	0.0952065i	−0.580180	+	0.814488i	$0.697018\pi$
$332$		0			0
$333$	−5.77576	−	16.2362i	−0.316510	−	0.889740i
$334$		0			0
$335$	−18.7805	+	32.5287i	−1.02609	+	1.77723i
$336$		0			0
$337$	−9.30453	−	16.1159i	−0.506850	−	0.877890i	−0.999969	−	0.00792778i	$-0.997476\pi$
$337$	−9.30453	−	16.1159i	−0.506850	−	0.877890i	0.493119	−	0.869962i	$-0.335857\pi$
$338$		0			0
$339$	10.8977	−	9.07678i	0.591884	−	0.492983i
$340$		0			0
$341$			2.37713i			0.128729i
$342$		0			0
$343$	5.31737			0.287111
$344$		0			0
$345$	13.0461	−	35.4411i	0.702376	−	1.90809i
$346$		0			0
$347$	−0.0408752	+	0.0235993i	−0.00219430	+	0.00126688i	−0.501097	−	0.865391i	$-0.667070\pi$
$347$	−0.0408752	+	0.0235993i	−0.00219430	+	0.00126688i	0.498902	+	0.866658i	$0.333737\pi$
$348$		0			0
$349$	12.8884	+	7.44113i	0.689901	+	0.398314i	0.803575	−	0.595204i	$-0.202929\pi$
$349$	12.8884	+	7.44113i	0.689901	+	0.398314i	−0.113674	+	0.993518i	$0.536262\pi$
$350$		0			0
$351$	−2.05384	−	1.21594i	−0.109626	−	0.0649019i
$352$		0			0
$353$	−9.25423	+	16.0288i	−0.492553	+	0.853127i	−0.999963	−	0.00857792i	$-0.997270\pi$
$353$	−9.25423	+	16.0288i	−0.492553	+	0.853127i	0.507410	+	0.861705i	$0.330603\pi$
$354$		0			0
$355$	−11.8590	+	6.84680i	−0.629411	+	0.363390i
$356$		0			0
$357$	−2.54870	−	0.938188i	−0.134891	−	0.0496542i
$358$		0			0
$359$	−31.3426			−1.65420			−0.827101	−	0.562054i	$-0.810011\pi$
$359$	−31.3426			−1.65420			−0.827101	+	0.562054i	$0.810011\pi$
$360$		0			0
$361$	−3.31599			−0.174526
$362$		0			0
$363$	9.27652	−	7.72646i	0.486891	−	0.405534i
$364$		0			0
$365$	8.51135	−	4.91403i	0.445504	−	0.257212i
$366$		0			0
$367$	10.2308	−	17.7203i	0.534043	−	0.924990i	−0.465166	−	0.885224i	$-0.654005\pi$
$367$	10.2308	−	17.7203i	0.534043	−	0.924990i	0.999209	−	0.0397663i	$-0.0126613\pi$
$368$		0			0
$369$	−21.7109	−	18.4891i	−1.13023	−	0.962505i
$370$		0			0
$371$	−2.53909	−	1.46594i	−0.131823	−	0.0761081i
$372$		0			0
$373$	−20.6021	+	11.8946i	−1.06674	+	0.615880i	−0.927288	−	0.374349i	$-0.877866\pi$
$373$	−20.6021	+	11.8946i	−1.06674	+	0.615880i	−0.139448	+	0.990229i	$0.544533\pi$
$374$		0			0
$375$	−21.3889	+	3.69107i	−1.10452	+	0.190606i
$376$		0			0
$377$	1.08086			0.0556673
$378$		0			0
$379$			24.0988i			1.23787i	0.785441	+	0.618937i	$0.212436\pi$
$379$			24.0988i			1.23787i	−0.785441	+	0.618937i	$0.787564\pi$
$380$		0			0
$381$	−6.18878	−	35.8625i	−0.317061	−	1.83729i
$382$		0			0
$383$	−9.39161	−	16.2667i	−0.479889	−	0.831192i	0.519845	−	0.854261i	$-0.325990\pi$
$383$	−9.39161	−	16.2667i	−0.479889	−	0.831192i	−0.999734	+	0.0230686i	$0.992656\pi$
$384$		0			0
$385$	1.41144	−	2.44468i	0.0719336	−	0.124593i
$386$		0			0
$387$	−3.53078	−	0.649157i	−0.179480	−	0.0329985i
$388$		0			0
$389$	−15.0467	−	8.68720i	−0.762897	−	0.440459i	0.0674382	−	0.997723i	$-0.478517\pi$
$389$	−15.0467	−	8.68720i	−0.762897	−	0.440459i	−0.830335	+	0.557265i	$0.811851\pi$
$390$		0			0
$391$	−12.1566	−	21.0558i	−0.614783	−	1.06484i
$392$		0			0
$393$	7.02759	+	8.43744i	0.354495	+	0.425613i
$394$		0			0
$395$			39.2703i			1.97591i
$396$		0			0
$397$			26.2401i			1.31696i	0.752600	+	0.658478i	$0.228799\pi$
$397$			26.2401i			1.31696i	−0.752600	+	0.658478i	$0.771201\pi$
$398$		0			0
$399$	−1.08495	+	2.94740i	−0.0543156	+	0.147555i
$400$		0			0
$401$	10.8194	+	18.7398i	0.540296	+	0.935820i	0.998887	+	0.0471725i	$0.0150210\pi$
$401$	10.8194	+	18.7398i	0.540296	+	0.935820i	−0.458591	+	0.888648i	$0.651646\pi$
$402$		0			0
$403$	−0.471060	−	0.271967i	−0.0234652	−	0.0135476i
$404$		0			0
$405$	−11.7274	+	30.8147i	−0.582737	+	1.53119i
$406$		0			0
$407$	5.76566	−	9.98642i	0.285793	−	0.495008i
$408$		0			0
$409$	−6.00563	−	10.4021i	−0.296959	−	0.514348i	0.678480	−	0.734619i	$-0.262639\pi$
$409$	−6.00563	−	10.4021i	−0.296959	−	0.514348i	−0.975439	+	0.220271i	$0.929306\pi$
$410$		0			0
$411$	1.57242	+	0.578816i	0.0775618	+	0.0285509i
$412$		0			0
$413$		−	0.267582i		−	0.0131668i
$414$		0			0
$415$	23.2252			1.14008
$416$		0			0
$417$	−6.63243	−	7.96301i	−0.324791	−	0.389950i
$418$		0			0
$419$	−1.38092	+	0.797277i	−0.0674625	+	0.0389495i	−0.533352	−	0.845893i	$-0.679068\pi$
$419$	−1.38092	+	0.797277i	−0.0674625	+	0.0389495i	0.465889	+	0.884843i	$0.345734\pi$
$420$		0			0
$421$	15.6612	+	9.04197i	0.763278	+	0.440679i	0.830471	−	0.557061i	$-0.188071\pi$
$421$	15.6612	+	9.04197i	0.763278	+	0.440679i	−0.0671934	+	0.997740i	$0.521404\pi$
$422$		0			0
$423$	3.55526	−	19.3372i	0.172863	−	0.940205i
$424$		0			0
$425$	−17.1990	+	29.7896i	−0.834276	+	1.44501i
$426$		0			0
$427$	−1.62667	+	0.939156i	−0.0787199	+	0.0454489i
$428$		0			0
$429$	−0.271598	−	1.57384i	−0.0131129	−	0.0759859i
$430$		0			0
$431$	34.7451			1.67361			0.836806	−	0.547499i	$-0.184420\pi$
$431$	34.7451			1.67361			0.836806	+	0.547499i	$0.184420\pi$
$432$		0			0
$433$	12.7197			0.611270			0.305635	−	0.952149i	$-0.401131\pi$
$433$	12.7197			0.611270			0.305635	+	0.952149i	$0.401131\pi$
$434$		0			0
$435$	−2.53909	−	14.7134i	−0.121740	−	0.705455i
$436$		0			0
$437$	−24.3496	+	14.0583i	−1.16480	+	0.672498i
$438$		0			0
$439$	7.45900	−	12.9194i	0.355999	−	0.616608i	−0.631290	−	0.775547i	$-0.717474\pi$
$439$	7.45900	−	12.9194i	0.355999	−	0.616608i	0.987288	+	0.158939i	$0.0508074\pi$
$440$		0			0
$441$	−15.6515	−	13.3289i	−0.745311	−	0.634710i
$442$		0			0
$443$	−3.48405	−	2.01152i	−0.165532	−	0.0955702i	0.414945	−	0.909846i	$-0.363801\pi$
$443$	−3.48405	−	2.01152i	−0.165532	−	0.0955702i	−0.580478	+	0.814276i	$0.697134\pi$
$444$		0			0
$445$	−24.0104	+	13.8624i	−1.13820	+	0.657142i
$446$		0			0
$447$	8.24006	+	9.89315i	0.389741	+	0.467930i
$448$		0			0
$449$	10.9179			0.515246			0.257623	−	0.966245i	$-0.417061\pi$
$449$	10.9179			0.515246			0.257623	+	0.966245i	$0.417061\pi$
$450$		0			0
$451$		−	19.0819i		−	0.898531i
$452$		0			0
$453$	1.60225	+	0.589795i	0.0752801	+	0.0277110i
$454$		0			0
$455$	0.322964	+	0.559390i	0.0151408	+	0.0262246i
$456$		0			0
$457$	−0.815204	+	1.41197i	−0.0381336	+	0.0660494i	−0.884462	−	0.466612i	$-0.845475\pi$
$457$	−0.815204	+	1.41197i	−0.0381336	+	0.0660494i	0.846329	+	0.532661i	$0.178808\pi$
$458$		0			0
$459$	10.4113	+	18.4973i	0.485958	+	0.863379i
$460$		0			0
$461$	−10.1812	−	5.87811i	−0.474185	−	0.273771i	0.243805	−	0.969824i	$-0.421604\pi$
$461$	−10.1812	−	5.87811i	−0.474185	−	0.273771i	−0.717990	+	0.696054i	$0.754938\pi$
$462$		0			0
$463$	10.6473	+	18.4416i	0.494820	+	0.857053i	0.999982	−	0.00597113i	$-0.00190068\pi$
$463$	10.6473	+	18.4416i	0.494820	+	0.857053i	−0.505162	+	0.863024i	$0.668567\pi$
$464$		0			0
$465$	−2.59560	+	7.05126i	−0.120368	+	0.326994i
$466$		0			0
$467$			18.9230i			0.875650i	0.899060	+	0.437825i	$0.144251\pi$
$467$			18.9230i			0.875650i	−0.899060	+	0.437825i	$0.855749\pi$
$468$		0			0
$469$		−	3.93562i		−	0.181730i
$470$		0			0
$471$	−19.4987	−	23.4104i	−0.898451	−	1.07870i
$472$		0			0
$473$	−1.20110	−	2.08037i	−0.0552267	−	0.0956554i
$474$		0			0
$475$	34.4497	+	19.8896i	1.58066	+	0.912595i
$476$		0			0
$477$	7.67988	+	21.5889i	0.351638	+	0.988487i
$478$		0			0
$479$	−14.9759	+	25.9391i	−0.684268	+	1.18519i	0.289398	+	0.957209i	$0.406545\pi$
$479$	−14.9759	+	25.9391i	−0.684268	+	1.18519i	−0.973666	+	0.227978i	$0.926789\pi$
$480$		0			0
$481$	1.31929	+	2.28508i	0.0601546	+	0.104191i
$482$		0			0
$483$	0.672931	+	3.89947i	0.0306194	+	0.177432i
$484$		0			0
$485$		−	21.8714i		−	0.993131i
$486$		0			0
$487$	17.3370			0.785614			0.392807	−	0.919621i	$-0.371504\pi$
$487$	17.3370			0.785614			0.392807	+	0.919621i	$0.371504\pi$
$488$		0			0
$489$	−30.5269	+	5.26802i	−1.38048	+	0.238228i
$490$		0			0
$491$	−31.1204	+	17.9674i	−1.40444	+	0.810856i	−0.994845	−	0.101409i	$-0.967665\pi$
$491$	−31.1204	+	17.9674i	−1.40444	+	0.810856i	−0.409599	+	0.912265i	$0.634332\pi$
$492$		0			0
$493$	−8.32446	−	4.80613i	−0.374915	−	0.216457i
$494$		0			0
$495$	−20.7862	+	7.39433i	−0.934269	+	0.332350i
$496$		0			0
$497$	0.717405	−	1.24258i	0.0321800	−	0.0557374i
$498$		0			0
$499$	−10.4956	+	6.05962i	−0.469846	+	0.271266i	−0.716175	−	0.697920i	$-0.754109\pi$
$499$	−10.4956	+	6.05962i	−0.469846	+	0.271266i	0.246329	+	0.969186i	$0.420776\pi$
$500$		0			0
$501$	−2.76921	+	2.30649i	−0.123719	+	0.103046i
$502$		0			0
$503$	−32.3442			−1.44215			−0.721077	−	0.692855i	$-0.756353\pi$
$503$	−32.3442			−1.44215			−0.721077	+	0.692855i	$0.756353\pi$
$504$		0			0
$505$	20.3583			0.905932
$506$		0			0
$507$	−20.7876	−	7.65201i	−0.923208	−	0.339838i
$508$		0			0
$509$	2.90310	−	1.67610i	0.128677	−	0.0742919i	−0.434280	−	0.900778i	$-0.642997\pi$
$509$	2.90310	−	1.67610i	0.128677	−	0.0742919i	0.562957	+	0.826486i	$0.309664\pi$
$510$		0			0
$511$	−0.514890	+	0.891816i	−0.0227774	+	0.0394516i
$512$		0			0
$513$	21.3909	−	12.0400i	0.944431	−	0.531578i
$514$		0			0
$515$	−38.9838	−	22.5073i	−1.71783	−	0.991792i
$516$		0			0
$517$	11.3936	−	6.57811i	0.501091	−	0.289305i
$518$		0			0
$519$	−11.3802	+	30.9156i	−0.499535	+	1.35704i
$520$		0			0
$521$	21.5651			0.944786			0.472393	−	0.881388i	$-0.343390\pi$
$521$	21.5651			0.944786			0.472393	+	0.881388i	$0.343390\pi$
$522$		0			0
$523$		−	24.9549i		−	1.09120i	−0.838046	−	0.545600i	$-0.816302\pi$
$523$		−	24.9549i		−	1.09120i	0.838046	−	0.545600i	$-0.183698\pi$
$524$		0			0
$525$	4.30179	−	3.58298i	0.187746	−	0.156374i
$526$		0			0
$527$	2.41863	+	4.18919i	0.105357	+	0.182484i
$528$		0			0
$529$	−6.21238	+	10.7602i	−0.270104	+	0.467833i
$530$		0			0
$531$	−1.35590	+	1.59217i	−0.0588411	+	0.0690944i
$532$		0			0
$533$	3.78133	+	2.18315i	0.163787	+	0.0945627i
$534$		0			0
$535$	−12.1218	−	20.9955i	−0.524070	−	0.907716i
$536$		0			0
$537$	−3.62036	+	0.624764i	−0.156230	+	0.0269606i
$538$		0			0
$539$		−	13.7562i		−	0.592523i
$540$		0			0
$541$		−	41.9065i		−	1.80170i	−0.434131	−	0.900850i	$-0.642945\pi$
$541$		−	41.9065i		−	1.80170i	0.434131	−	0.900850i	$-0.357055\pi$
$542$		0			0
$543$	2.83840	−	0.489821i	0.121807	−	0.0210202i
$544$		0			0
$545$	−12.8506	−	22.2579i	−0.550460	−	0.953424i
$546$		0			0
$547$	25.7251	+	14.8524i	1.09993	+	0.635043i	0.936202	−	0.351462i	$-0.114316\pi$
$547$	25.7251	+	14.8524i	1.09993	+	0.635043i	0.163726	+	0.986506i	$0.447649\pi$
$548$		0			0
$549$	14.4380	+	2.65451i	0.616197	+	0.113292i
$550$		0			0
$551$	−5.55797	+	9.62669i	−0.236778	+	0.410111i
$552$		0			0
$553$	−2.05737	−	3.56346i	−0.0874881	−	0.151534i
$554$		0			0
$555$	28.0068	−	23.3270i	1.18882	−	0.990177i
$556$		0			0
$557$			21.9632i			0.930609i	0.885151	+	0.465305i	$0.154055\pi$
$557$			21.9632i			0.930609i	−0.885151	+	0.465305i	$0.845945\pi$
$558$		0			0
$559$	0.549669			0.0232485
$560$		0			0
$561$	−4.90644	+	13.3289i	−0.207150	+	0.562747i
$562$		0			0
$563$	23.8394	−	13.7637i	1.00471	−	0.580069i	0.0950710	−	0.995470i	$-0.469692\pi$
$563$	23.8394	−	13.7637i	1.00471	−	0.580069i	0.909638	+	0.415401i	$0.136359\pi$
$564$		0			0
$565$	25.9786	+	14.9988i	1.09293	+	0.631002i
$566$		0			0
$567$	−0.550212	−	3.41057i	−0.0231067	−	0.143231i
$568$		0			0
$569$	8.83572	−	15.3039i	0.370413	−	0.641574i	−0.619216	−	0.785221i	$-0.712550\pi$
$569$	8.83572	−	15.3039i	0.370413	−	0.641574i	0.989629	+	0.143647i	$0.0458829\pi$
$570$		0			0
$571$	−3.92630	+	2.26685i	−0.164311	+	0.0948648i	−0.579900	−	0.814687i	$-0.696909\pi$
$571$	−3.92630	+	2.26685i	−0.164311	+	0.0948648i	0.415590	+	0.909552i	$0.363575\pi$
$572$		0			0
$573$	28.2744	+	10.4080i	1.18118	+	0.434799i
$574$		0			0
$575$	50.1188			2.09010
$576$		0			0
$577$	23.3909			0.973776			0.486888	−	0.873464i	$-0.338132\pi$
$577$	23.3909			0.973776			0.486888	+	0.873464i	$0.338132\pi$
$578$		0			0
$579$	3.77195	−	3.14168i	0.156757	−	0.130564i
$580$		0			0
$581$	−2.10750	+	1.21676i	−0.0874337	+	0.0504799i
$582$		0			0
$583$	−7.66645	+	13.2787i	−0.317512	+	0.549947i
$584$		0			0
$585$	0.912853	−	4.96504i	0.0377418	−	0.205279i
$586$		0			0
$587$	−7.18259	−	4.14687i	−0.296457	−	0.171160i	0.344393	−	0.938826i	$-0.388085\pi$
$587$	−7.18259	−	4.14687i	−0.296457	−	0.171160i	−0.640850	+	0.767666i	$0.721418\pi$
$588$		0			0
$589$	4.84453	−	2.79699i	0.199615	−	0.115248i
$590$		0			0
$591$	21.5044	−	3.71100i	0.884572	−	0.152650i
$592$		0			0
$593$	−43.5169			−1.78702			−0.893512	−	0.449039i	$-0.851766\pi$
$593$	−43.5169			−1.78702			−0.893512	+	0.449039i	$0.851766\pi$
$594$		0			0
$595$		−	5.74432i		−	0.235494i
$596$		0			0
$597$	−5.08779	−	29.4825i	−0.208229	−	1.20664i
$598$		0			0
$599$	−0.527649	−	0.913915i	−0.0215592	−	0.0373416i	0.855045	−	0.518555i	$-0.173530\pi$
$599$	−0.527649	−	0.913915i	−0.0215592	−	0.0373416i	−0.876604	+	0.481213i	$0.840196\pi$
$600$		0			0
$601$	17.9922	−	31.1633i	0.733915	−	1.27118i	−0.221282	−	0.975210i	$-0.571024\pi$
$601$	17.9922	−	31.1633i	0.733915	−	1.27118i	0.955198	−	0.295969i	$-0.0956424\pi$
$602$		0			0
$603$	−19.9427	+	23.4178i	−0.812131	+	0.953648i
$604$		0			0
$605$	22.1138	+	12.7674i	0.899056	+	0.519070i
$606$		0			0
$607$	9.81512	+	17.0003i	0.398383	+	0.690020i	0.993527	−	0.113599i	$-0.0362381\pi$
$607$	9.81512	+	17.0003i	0.398383	+	0.690020i	−0.595143	+	0.803620i	$0.702905\pi$
$608$		0			0
$609$	1.00124	+	1.20210i	0.0405721	+	0.0487116i
$610$		0			0
$611$			3.01039i			0.121787i
$612$		0			0
$613$		−	0.0630655i		−	0.00254719i	−0.999999	−	0.00127360i	$-0.999595\pi$
$613$		−	0.0630655i		−	0.00254719i	0.999999	−	0.00127360i	$-0.000405399\pi$
$614$		0			0
$615$	20.8356	−	56.6024i	0.840174	−	2.28243i
$616$		0			0
$617$	15.0926	+	26.1412i	0.607606	+	1.05240i	0.991634	+	0.129083i	$0.0412034\pi$
$617$	15.0926	+	26.1412i	0.607606	+	1.05240i	−0.384028	+	0.923322i	$0.625463\pi$
$618$		0			0
$619$	−38.2663	−	22.0930i	−1.53805	−	0.887994i	−0.998953	−	0.0457517i	$-0.985432\pi$
$619$	−38.2663	−	22.0930i	−1.53805	−	0.887994i	−0.539099	−	0.842243i	$-0.681235\pi$
$620$		0			0
$621$	15.7555	−	26.6127i	0.632245	−	1.06793i
$622$		0			0
$623$	1.45250	−	2.51580i	0.0581932	−	0.100794i
$624$		0			0
$625$	−1.90220	−	3.29471i	−0.0760881	−	0.131788i
$626$		0			0
$627$	15.4140	+	5.67398i	0.615576	+	0.226597i
$628$		0			0
$629$		−	23.4653i		−	0.935621i
$630$		0			0
$631$	−19.6743			−0.783221			−0.391610	−	0.920131i	$-0.628082\pi$
$631$	−19.6743			−0.783221			−0.391610	+	0.920131i	$0.628082\pi$
$632$		0			0
$633$	19.4802	+	23.3883i	0.774269	+	0.929601i
$634$		0			0
$635$	66.6607	−	38.4866i	2.64535	−	1.52729i
$636$		0			0
$637$	2.72598	+	1.57384i	0.108007	+	0.0623580i
$638$		0			0
$639$	−10.5652	+	3.75839i	−0.417952	+	0.148679i
$640$		0			0
$641$	−0.994371	+	1.72230i	−0.0392753	+	0.0680268i	−0.884995	−	0.465601i	$-0.845838\pi$
$641$	−0.994371	+	1.72230i	−0.0392753	+	0.0680268i	0.845720	+	0.533628i	$0.179172\pi$
$642$		0			0
$643$	−12.9370	+	7.46917i	−0.510185	+	0.294555i	−0.732910	−	0.680326i	$-0.761838\pi$
$643$	−12.9370	+	7.46917i	−0.510185	+	0.294555i	0.222725	+	0.974881i	$0.428505\pi$
$644$		0			0
$645$	−1.29124	−	7.48246i	−0.0508427	−	0.294621i
$646$		0			0
$647$	8.81283			0.346468			0.173234	−	0.984881i	$-0.444578\pi$
$647$	8.81283			0.346468			0.173234	+	0.984881i	$0.444578\pi$
$648$		0			0
$649$	−1.39937			−0.0549302
$650$		0			0
$651$	−0.133884	−	0.775827i	−0.00524734	−	0.0304071i
$652$		0			0
$653$	−18.1802	+	10.4964i	−0.711447	+	0.410754i	−0.811597	−	0.584218i	$-0.801401\pi$
$653$	−18.1802	+	10.4964i	−0.711447	+	0.410754i	0.100150	+	0.994972i	$0.468068\pi$
$654$		0			0
$655$	−11.6126	+	20.1136i	−0.453742	+	0.785904i
$656$		0			0
$657$	7.58276	−	2.69744i	0.295832	−	0.105237i
$658$		0			0
$659$	40.6209	+	23.4525i	1.58237	+	0.913580i	0.994513	+	0.104612i	$0.0333601\pi$
$659$	40.6209	+	23.4525i	1.58237	+	0.913580i	0.587853	+	0.808968i	$0.299973\pi$
$660$		0			0
$661$	0.736985	−	0.425498i	0.0286654	−	0.0165500i	−0.485599	−	0.874182i	$-0.661398\pi$
$661$	0.736985	−	0.425498i	0.0286654	−	0.0165500i	0.514264	+	0.857632i	$0.328065\pi$
$662$		0			0
$663$	−2.07995	−	2.49723i	−0.0807787	−	0.0969843i
$664$		0			0
$665$	−6.64293			−0.257602
$666$		0			0
$667$			14.0053i			0.542287i
$668$		0			0
$669$	−40.0300	−	14.7352i	−1.54765	−	0.569698i
$670$		0			0
$671$	4.91150	+	8.50697i	0.189606	+	0.328408i
$672$		0			0
$673$	−22.4873	+	38.9491i	−0.866820	+	1.50138i	−0.00159139	+	0.999999i	$0.500507\pi$
$673$	−22.4873	+	38.9491i	−0.866820	+	1.50138i	−0.865229	+	0.501378i	$0.832827\pi$
$674$		0			0
$675$	−43.7525	−	0.478635i	−1.68403	−	0.0184227i
$676$		0			0
$677$	7.29713	+	4.21300i	0.280451	+	0.161919i	0.633628	−	0.773638i	$-0.281565\pi$
$677$	7.29713	+	4.21300i	0.280451	+	0.161919i	−0.353176	+	0.935557i	$0.614898\pi$
$678$		0			0
$679$	1.14584	+	1.98466i	0.0439733	+	0.0761641i
$680$		0			0
$681$	−11.7395	+	31.8916i	−0.449857	+	1.22209i
$682$		0			0
$683$		−	23.3602i		−	0.893853i	−0.894571	−	0.446926i	$-0.852519\pi$
$683$		−	23.3602i		−	0.893853i	0.894571	−	0.446926i	$-0.147481\pi$
$684$		0			0
$685$			3.54396i			0.135408i
$686$		0			0
$687$	27.3187	+	32.7993i	1.04227	+	1.25137i
$688$		0			0
$689$	−1.75423	−	3.03841i	−0.0668308	−	0.115754i
$690$		0			0
$691$	25.9304	+	14.9709i	0.986439	+	0.569521i	0.904208	−	0.427092i	$-0.140462\pi$
$691$	25.9304	+	14.9709i	0.986439	+	0.569521i	0.0822311	+	0.996613i	$0.473795\pi$
$692$		0			0
$693$	1.49879	−	1.75996i	0.0569343	−	0.0668553i
$694$		0			0
$695$	10.9596	−	18.9826i	0.415722	−	0.720052i
$696$		0			0
$697$	−19.4150	−	33.6278i	−0.735396	−	1.27374i
$698$		0			0
$699$	−6.16255	−	35.7105i	−0.233089	−	1.35070i
$700$		0			0
$701$		−	0.718775i		−	0.0271478i	−0.999908	−	0.0135739i	$-0.995679\pi$
$701$		−	0.718775i		−	0.0271478i	0.999908	−	0.0135739i	$-0.00432083\pi$
$702$		0			0
$703$	−27.1360			−1.02346
$704$		0			0
$705$	40.9794	−	7.07181i	1.54337	−	0.266340i
$706$		0			0
$707$	−1.84735	+	1.06657i	−0.0694767	+	0.0401124i
$708$		0			0
$709$	−10.9918	−	6.34613i	−0.412807	−	0.238334i	0.279188	−	0.960236i	$-0.409935\pi$
$709$	−10.9918	−	6.34613i	−0.412807	−	0.238334i	−0.691995	+	0.721902i	$0.743268\pi$
$710$		0			0
$711$	−5.81512	+	31.6286i	−0.218084	+	1.18616i
$712$		0			0
$713$	3.52400	−	6.10375i	0.131975	−	0.228587i
$714$		0			0
$715$	2.92544	−	1.68900i	0.109405	−	0.0631652i
$716$		0			0
$717$	−13.6970	+	11.4083i	−0.511523	+	0.426050i
$718$		0			0
$719$	−7.74226			−0.288738			−0.144369	−	0.989524i	$-0.546115\pi$
$719$	−7.74226			−0.288738			−0.144369	+	0.989524i	$0.546115\pi$
$720$		0			0
$721$	4.71662			0.175656
$722$		0			0
$723$	33.2819	+	12.2513i	1.23777	+	0.455629i
$724$		0			0
$725$	17.1599	−	9.90730i	0.637304	−	0.367948i
$726$		0			0
$727$	−9.91355	+	17.1708i	−0.367673	+	0.636828i	−0.989201	−	0.146563i	$-0.953179\pi$
$727$	−9.91355	+	17.1708i	−0.367673	+	0.636828i	0.621528	+	0.783392i	$0.286512\pi$
$728$		0			0
$729$	−14.0083	+	23.0818i	−0.518826	+	0.854880i
$730$		0			0
$731$	−4.23337	−	2.44414i	−0.156577	−	0.0903997i
$732$		0			0
$733$	−32.7535	+	18.9102i	−1.20978	+	0.698466i	−0.962711	−	0.270532i	$-0.912800\pi$
$733$	−32.7535	+	18.9102i	−1.20978	+	0.698466i	−0.247068	+	0.968998i	$0.579467\pi$
$734$		0			0
$735$	15.0205	−	40.8050i	0.554040	−	1.50511i
$736$		0			0
$737$	−20.5821			−0.758152
$738$		0			0
$739$		−	6.61431i		−	0.243311i	−0.992572	−	0.121656i	$-0.961180\pi$
$739$		−	6.61431i		−	0.243311i	0.992572	−	0.121656i	$-0.0388204\pi$
$740$		0			0
$741$	−2.88788	+	2.40533i	−0.106089	+	0.0883620i
$742$		0			0
$743$	3.30245	+	5.72000i	0.121155	+	0.209847i	0.920223	−	0.391394i	$-0.128007\pi$
$743$	3.30245	+	5.72000i	0.121155	+	0.209847i	−0.799068	+	0.601240i	$0.794674\pi$
$744$		0			0
$745$	−13.6161	+	23.5838i	−0.498856	+	0.864044i
$746$		0			0
$747$	18.7057	+	3.43917i	0.684407	+	0.125833i
$748$		0			0
$749$	2.19990	+	1.27012i	0.0803828	+	0.0464090i
$750$		0			0
$751$	−12.8675	−	22.2871i	−0.469540	−	0.813268i	0.529853	−	0.848089i	$-0.322247\pi$
$751$	−12.8675	−	22.2871i	−0.469540	−	0.813268i	−0.999394	+	0.0348217i	$0.988914\pi$
$752$		0			0
$753$	47.9595	−	8.27636i	1.74774	−	0.301607i
$754$		0			0
$755$			3.61118i			0.131424i
$756$		0			0
$757$		−	48.0424i		−	1.74613i	−0.487602	−	0.873066i	$-0.662128\pi$
$757$		−	48.0424i		−	1.74613i	0.487602	−	0.873066i	$-0.337872\pi$
$758$		0			0
$759$	20.3931	−	3.51922i	0.740221	−	0.127740i
$760$		0			0
$761$	−1.20688	−	2.09038i	−0.0437493	−	0.0757761i	0.843322	−	0.537409i	$-0.180597\pi$
$761$	−1.20688	−	2.09038i	−0.0437493	−	0.0757761i	−0.887071	+	0.461633i	$0.847264\pi$
$762$		0			0
$763$	2.33218	+	1.34648i	0.0844305	+	0.0487459i
$764$		0			0
$765$	−29.1078	+	34.1800i	−1.05240	+	1.23578i
$766$		0			0
$767$	0.160101	−	0.277304i	0.00578093	−	0.0100129i
$768$		0			0
$769$	16.8464	+	29.1788i	0.607496	+	1.05221i	0.991652	+	0.128945i	$0.0411592\pi$
$769$	16.8464	+	29.1788i	0.607496	+	1.05221i	−0.384156	+	0.923268i	$0.625507\pi$
$770$		0			0
$771$	−14.7377	+	12.2751i	−0.530765	+	0.442076i
$772$		0			0
$773$			18.8545i			0.678149i	0.940759	+	0.339075i	$0.110114\pi$
$773$			18.8545i			0.678149i	−0.940759	+	0.339075i	$0.889886\pi$
$774$		0			0
$775$	−9.97148			−0.358186
$776$		0			0
$777$	−1.31929	+	3.58401i	−0.0473294	+	0.128576i
$778$		0			0
$779$	−38.8884	+	22.4522i	−1.39332	+	0.804434i
$780$		0			0
$781$	−6.49833	−	3.75181i	−0.232529	−	0.134250i
$782$		0			0
$783$	0.133751	−	12.2263i	0.00477986	−	0.436931i
$784$		0			0
$785$	32.2202	−	55.8070i	1.14999	−	1.99184i
$786$		0			0
$787$	−14.8124	+	8.55193i	−0.528004	+	0.304843i	−0.740203	−	0.672383i	$-0.765271\pi$
$787$	−14.8124	+	8.55193i	−0.528004	+	0.304843i	0.212199	+	0.977226i	$0.431937\pi$
$788$		0			0
$789$	41.4873	+	15.2717i	1.47699	+	0.543687i
$790$		0			0
$791$	−3.14313			−0.111757
$792$		0			0
$793$	−2.24769			−0.0798178
$794$		0			0
$795$	−37.2400	+	31.0173i	−1.32077	+	1.10007i
$796$		0			0
$797$	−3.11800	+	1.80018i	−0.110445	+	0.0637656i	−0.554205	−	0.832380i	$-0.686978\pi$
$797$	−3.11800	+	1.80018i	−0.110445	+	0.0637656i	0.443760	+	0.896146i	$0.353644\pi$
$798$		0			0
$799$	13.3859	−	23.1851i	0.473559	−	0.820228i
$800$		0			0
$801$	−21.3909	+	7.60945i	−0.755810	+	0.268867i
$802$		0			0
$803$	4.66393	+	2.69272i	0.164586	+	0.0950240i
$804$		0			0
$805$	−7.24829	+	4.18480i	−0.255469	+	0.147495i
$806$		0			0
$807$	−31.4052	+	5.41958i	−1.10551	+	0.190778i
$808$		0			0
$809$	13.5918			0.477864			0.238932	−	0.971036i	$-0.423203\pi$
$809$	13.5918			0.477864			0.238932	+	0.971036i	$0.423203\pi$
$810$		0			0
$811$		−	10.0627i		−	0.353349i	−0.984269	−	0.176674i	$-0.943466\pi$
$811$		−	10.0627i		−	0.353349i	0.984269	−	0.176674i	$-0.0565339\pi$
$812$		0			0
$813$	6.60179	+	38.2558i	0.231535	+	1.34169i
$814$		0			0
$815$	−32.7606	−	56.7430i	−1.14755	−	1.98762i
$816$		0			0
$817$	−2.82649	+	4.89562i	−0.0988862	+	0.171276i
$818$		0			0
$819$	0.177283	+	0.498361i	0.00619478	+	0.0174141i
$820$		0			0
$821$	33.4098	+	19.2891i	1.16601	+	0.673196i	0.952737	−	0.303797i	$-0.0982544\pi$
$821$	33.4098	+	19.2891i	1.16601	+	0.673196i	0.213273	+	0.976993i	$0.431588\pi$
$822$		0			0
$823$	16.1120	+	27.9068i	0.561628	+	0.972768i	0.997355	+	0.0726892i	$0.0231581\pi$
$823$	16.1120	+	27.9068i	0.561628	+	0.972768i	−0.435727	+	0.900079i	$0.643509\pi$
$824$		0			0
$825$	−18.7379	−	22.4971i	−0.652371	−	0.783248i
$826$		0			0
$827$			27.7190i			0.963886i	0.876203	+	0.481943i	$0.160069\pi$
$827$			27.7190i			0.963886i	−0.876203	+	0.481943i	$0.839931\pi$
$828$		0			0
$829$			10.3137i			0.358208i	0.983830	+	0.179104i	$0.0573199\pi$
$829$			10.3137i			0.358208i	−0.983830	+	0.179104i	$0.942680\pi$
$830$		0			0
$831$	−13.9850	+	37.9919i	−0.485135	+	1.31793i
$832$		0			0
$833$	−13.9964	−	24.2425i	−0.484946	−	0.839951i
$834$		0			0
$835$	−6.60139	−	3.81131i	−0.228451	−	0.131896i
$836$		0			0
$837$	−3.13466	+	5.29477i	−0.108350	+	0.183014i
$838$		0			0
$839$	19.1961	−	33.2487i	0.662724	−	1.14787i	−0.317173	−	0.948368i	$-0.602733\pi$
$839$	19.1961	−	33.2487i	0.662724	−	1.14787i	0.979897	−	0.199504i	$-0.0639332\pi$
$840$		0			0
$841$	−11.7315	−	20.3195i	−0.404534	−	0.700673i
$842$		0			0
$843$	17.2121	+	6.33588i	0.592818	+	0.218219i
$844$		0			0
$845$		−	46.8516i		−	1.61174i
$846$		0			0
$847$	−2.67553			−0.0919325
$848$		0			0
$849$	−9.84342	−	11.8182i	−0.337825	−	0.405599i
$850$		0			0
$851$	−29.6089	+	17.0947i	−1.01498	+	0.585999i
$852$		0			0
$853$	−24.4212	−	14.0996i	−0.836166	−	0.482761i	0.0197931	−	0.999804i	$-0.493699\pi$
$853$	−24.4212	−	14.0996i	−0.836166	−	0.482761i	−0.855959	+	0.517043i	$0.827033\pi$
$854$		0			0
$855$	39.5269	+	33.6613i	1.35179	+	1.15119i
$856$		0			0
$857$	15.7011	−	27.1951i	0.536339	−	0.928966i	−0.462759	−	0.886484i	$-0.653140\pi$
$857$	15.7011	−	27.1951i	0.536339	−	0.928966i	0.999097	−	0.0424814i	$-0.0135263\pi$
$858$		0			0
$859$	41.6368	−	24.0390i	1.42063	−	0.820201i	0.424278	−	0.905532i	$-0.360528\pi$
$859$	41.6368	−	24.0390i	1.42063	−	0.820201i	0.996353	+	0.0853309i	$0.0271947\pi$
$860$		0			0
$861$	1.07473	+	6.22778i	0.0366266	+	0.212242i
$862$		0			0
$863$	−37.6968			−1.28321			−0.641607	−	0.767034i	$-0.721732\pi$
$863$	−37.6968			−1.28321			−0.641607	+	0.767034i	$0.721732\pi$
$864$		0			0
$865$	−69.6783			−2.36913
$866$		0			0
$867$	−0.0922398	−	0.534508i	−0.00313263	−	0.0181528i
$868$		0			0
$869$	−18.6358	+	10.7594i	−0.632177	+	0.364988i
$870$		0			0
$871$	2.35479	−	4.07861i	0.0797890	−	0.138199i
$872$		0			0
$873$	3.23870	−	17.6154i	0.109614	−	0.596191i
$874$		0			0
$875$	4.16576	+	2.40510i	0.140828	+	0.0813072i
$876$		0			0
$877$	21.6823	−	12.5183i	0.732158	−	0.422711i	−0.0870533	−	0.996204i	$-0.527745\pi$
$877$	21.6823	−	12.5183i	0.732158	−	0.422711i	0.819211	+	0.573492i	$0.194412\pi$
$878$		0			0
$879$	12.5709	+	15.0928i	0.424006	+	0.509069i
$880$		0			0
$881$	−21.0382			−0.708795			−0.354398	−	0.935095i	$-0.615314\pi$
$881$	−21.0382			−0.708795			−0.354398	+	0.935095i	$0.615314\pi$
$882$		0			0
$883$		−	55.5904i		−	1.87077i	−0.353636	−	0.935383i	$-0.615055\pi$
$883$		−	55.5904i		−	1.87077i	0.353636	−	0.935383i	$-0.384945\pi$
$884$		0			0
$885$	−4.15094	−	1.52798i	−0.139532	−	0.0513626i
$886$		0			0
$887$	−0.695385	−	1.20444i	−0.0233487	−	0.0404412i	0.854115	−	0.520084i	$-0.174099\pi$
$887$	−0.695385	−	1.20444i	−0.0233487	−	0.0404412i	−0.877464	+	0.479643i	$0.840766\pi$
$888$		0			0
$889$	−4.03261	+	6.98468i	−0.135249	+	0.234259i
$890$		0			0
$891$	−17.8363	+	2.87744i	−0.597538	+	0.0963980i
$892$		0			0
$893$	−26.8120	−	15.4799i	−0.897229	−	0.518015i
$894$		0			0
$895$	−3.88527	−	6.72948i	−0.129870	−	0.224942i
$896$		0			0
$897$	−1.63578	+	4.44379i	−0.0546171	+	0.148374i
$898$		0			0
$899$		−	2.78645i		−	0.0929332i
$900$		0			0
$901$			31.2011i			1.03946i
$902$		0			0
$903$	0.509175	+	0.611324i	0.0169443	+	0.0203436i
$904$		0			0
$905$	3.04608	+	5.27597i	0.101255	+	0.175379i
$906$		0			0
$907$	−37.3197	−	21.5465i	−1.23918	−	0.715440i	−0.270252	−	0.962789i	$-0.587107\pi$
$907$	−37.3197	−	21.5465i	−1.23918	−	0.715440i	−0.968926	+	0.247349i	$0.920441\pi$
$908$		0			0
$909$	16.3967	+	3.01464i	0.543844	+	0.0999892i
$910$		0			0
$911$	3.96463	−	6.86694i	0.131354	−	0.227512i	−0.792845	−	0.609424i	$-0.791401\pi$
$911$	3.96463	−	6.86694i	0.131354	−	0.227512i	0.924199	+	0.381912i	$0.124734\pi$
$912$		0			0
$913$	6.36331	+	11.0216i	0.210595	+	0.364761i
$914$		0			0
$915$	5.28012	+	30.5970i	0.174555	+	1.01151i
$916$		0			0
$917$		−	2.43353i		−	0.0803622i
$918$		0			0
$919$	−1.66862			−0.0550426			−0.0275213	−	0.999621i	$-0.508761\pi$
$919$	−1.66862			−0.0550426			−0.0275213	+	0.999621i	$0.508761\pi$
$920$		0			0
$921$	1.07304	−	0.185174i	0.0353579	−	0.00610170i
$922$		0			0
$923$	1.48694	−	0.858486i	0.0489433	−	0.0282574i
$924$		0			0
$925$	41.8905	+	24.1855i	1.37735	+	0.795215i
$926$		0			0
$927$	−28.0650	−	23.9002i	−0.921775	−	0.784987i
$928$		0			0
$929$	−23.3838	+	40.5020i	−0.767199	+	1.32883i	0.171878	+	0.985118i	$0.445017\pi$
$929$	−23.3838	+	40.5020i	−0.767199	+	1.32883i	−0.939076	+	0.343709i	$0.888317\pi$
$930$		0			0
$931$	−28.0348	+	16.1859i	−0.918804	+	0.530472i
$932$		0			0
$933$	−25.6711	+	21.3816i	−0.840435	+	0.700002i
$934$		0			0
$935$	−30.0410			−0.982447
$936$		0			0
$937$	−9.30185			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$937$	−9.30185			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$938$		0			0
$939$	−9.32861	−	3.43391i	−0.304428	−	0.112061i
$940$		0			0
$941$	5.42009	−	3.12929i	0.176690	−	0.102012i	−0.409047	−	0.912513i	$-0.634139\pi$
$941$	5.42009	−	3.12929i	0.176690	−	0.102012i	0.585736	+	0.810502i	$0.300805\pi$
$942$		0			0
$943$	−28.2881	+	48.9965i	−0.921188	+	1.59555i
$944$		0			0
$945$	6.36755	−	3.58401i	0.207136	−	0.116588i
$946$		0			0
$947$	−38.4243	−	22.1843i	−1.24862	−	0.720893i	−0.277789	−	0.960642i	$-0.589601\pi$
$947$	−38.4243	−	22.1843i	−1.24862	−	0.720893i	−0.970835	+	0.239749i	$0.922935\pi$
$948$		0			0
$949$	−1.06720	+	0.616146i	−0.0346426	+	0.0200009i
$950$		0			0
$951$	−7.47452	+	20.3054i	−0.242378	+	0.658448i
$952$		0			0
$953$	6.11599			0.198116			0.0990582	−	0.995082i	$-0.468417\pi$
$953$	6.11599			0.198116			0.0990582	+	0.995082i	$0.468417\pi$
$954$		0			0
$955$			63.7257i			2.06211i
$956$		0			0
$957$	6.28662	−	5.23616i	0.203218	−	0.169261i
$958$		0			0
$959$	−0.185668	−	0.321586i	−0.00599552	−	0.0103845i
$960$		0			0
$961$	14.7989	−	25.6324i	0.477383	−	0.826852i
$962$		0			0
$963$	−6.65396	−	18.7049i	−0.214421	−	0.602758i
$964$		0			0
$965$	8.99178	+	5.19141i	0.289456	+	0.167117i
$966$		0			0
$967$	−16.9985	−	29.4423i	−0.546635	−	0.946799i	−0.998502	−	0.0547141i	$-0.982575\pi$
$967$	−16.9985	−	29.4423i	−0.546635	−	0.946799i	0.451867	−	0.892085i	$-0.350758\pi$
$968$		0			0
$969$	32.9370	−	5.68392i	1.05809	−	0.182594i
$970$		0			0
$971$			42.4798i			1.36324i	0.731706	+	0.681621i	$0.238725\pi$
$971$			42.4798i			1.36324i	−0.731706	+	0.681621i	$0.761275\pi$
$972$		0			0
$973$			2.29669i			0.0736286i
$974$		0			0
$975$	6.60189	−	1.13929i	0.211430	−	0.0364863i
$976$		0			0
$977$	7.66569	+	13.2774i	0.245247	+	0.424781i	0.962201	−	0.272340i	$-0.0877975\pi$
$977$	7.66569	+	13.2774i	0.245247	+	0.424781i	−0.716954	+	0.697121i	$0.754464\pi$
$978$		0			0
$979$	−13.1569	−	7.59614i	−0.420496	−	0.242774i
$980$		0			0
$981$	−7.05404	−	19.8296i	−0.225218	−	0.633110i
$982$		0			0
$983$	14.8653	−	25.7474i	0.474129	−	0.821216i	−0.525432	−	0.850836i	$-0.676096\pi$
$983$	14.8653	−	25.7474i	0.474129	−	0.821216i	0.999561	+	0.0296198i	$0.00942964\pi$
$984$		0			0
$985$	23.0779	+	39.9720i	0.735322	+	1.27361i
$986$		0			0
$987$	−3.34806	+	2.78861i	−0.106570	+	0.0887626i
$988$		0			0
$989$			7.12233i			0.226477i
$990$		0			0
$991$	49.5495			1.57399			0.786996	−	0.616958i	$-0.211635\pi$
$991$	49.5495			1.57399			0.786996	+	0.616958i	$0.211635\pi$
$992$		0			0
$993$	2.07276	−	5.63089i	0.0657771	−	0.178691i
$994$		0			0
$995$	54.8017	−	31.6398i	1.73733	−	1.00305i
$996$		0			0
$997$	−34.4541	−	19.8921i	−1.09117	−	0.629988i	−0.157284	−	0.987553i	$-0.550274\pi$
$997$	−34.4541	−	19.8921i	−1.09117	−	0.629988i	−0.933888	+	0.357565i	$0.883607\pi$
$998$		0			0
$999$	26.0111	−	14.6405i	0.822956	−	0.463205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.r.b.241.5		16
3.2	odd	2		864.2.r.b.721.8		16
4.3	odd	2		72.2.n.b.61.8	yes	16
8.3	odd	2		72.2.n.b.61.3	yes	16
8.5	even	2	inner	288.2.r.b.241.4		16
9.2	odd	6		2592.2.d.k.1297.8		8
9.4	even	3	inner	288.2.r.b.49.4		16
9.5	odd	6		864.2.r.b.145.1		16
9.7	even	3		2592.2.d.j.1297.1		8
12.11	even	2		216.2.n.b.181.1		16
24.5	odd	2		864.2.r.b.721.1		16
24.11	even	2		216.2.n.b.181.6		16
36.7	odd	6		648.2.d.j.325.3		8
36.11	even	6		648.2.d.k.325.6		8
36.23	even	6		216.2.n.b.37.6		16
36.31	odd	6		72.2.n.b.13.3	✓	16
72.5	odd	6		864.2.r.b.145.8		16
72.11	even	6		648.2.d.k.325.5		8
72.13	even	6	inner	288.2.r.b.49.5		16
72.29	odd	6		2592.2.d.k.1297.1		8
72.43	odd	6		648.2.d.j.325.4		8
72.59	even	6		216.2.n.b.37.1		16
72.61	even	6		2592.2.d.j.1297.8		8
72.67	odd	6		72.2.n.b.13.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.3	✓	16	36.31	odd	6
72.2.n.b.13.8	yes	16	72.67	odd	6
72.2.n.b.61.3	yes	16	8.3	odd	2
72.2.n.b.61.8	yes	16	4.3	odd	2
216.2.n.b.37.1		16	72.59	even	6
216.2.n.b.37.6		16	36.23	even	6
216.2.n.b.181.1		16	12.11	even	2
216.2.n.b.181.6		16	24.11	even	2
288.2.r.b.49.4		16	9.4	even	3	inner
288.2.r.b.49.5		16	72.13	even	6	inner
288.2.r.b.241.4		16	8.5	even	2	inner
288.2.r.b.241.5		16	1.1	even	1	trivial
648.2.d.j.325.3		8	36.7	odd	6
648.2.d.j.325.4		8	72.43	odd	6
648.2.d.k.325.5		8	72.11	even	6
648.2.d.k.325.6		8	36.11	even	6
864.2.r.b.145.1		16	9.5	odd	6
864.2.r.b.145.8		16	72.5	odd	6
864.2.r.b.721.1		16	24.5	odd	2
864.2.r.b.721.8		16	3.2	odd	2
2592.2.d.j.1297.1		8	9.7	even	3
2592.2.d.j.1297.8		8	72.61	even	6
2592.2.d.k.1297.1		8	72.29	odd	6
2592.2.d.k.1297.8		8	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.294546 + 1.70682i) q^{3} +(-3.17262 + 1.83171i) q^{5} +(0.191926 - 0.332426i) q^{7} +(-2.82649 + 1.00547i) q^{9} +O(q^{10})\)	\(q+(0.294546 + 1.70682i) q^{3} +(-3.17262 + 1.83171i) q^{5} +(0.191926 - 0.332426i) q^{7} +(-2.82649 + 1.00547i) q^{9} +(-1.73849 - 1.00372i) q^{11} +(0.397799 - 0.229669i) q^{13} +(-4.06089 - 4.87557i) q^{15} -4.08495 q^{17} +4.72398i q^{19} +(0.623923 + 0.229669i) q^{21} +(2.97594 + 5.15447i) q^{23} +(4.21034 - 7.29252i) q^{25} +(-2.54870 - 4.52815i) q^{27} +(2.03783 + 1.17654i) q^{29} +(-0.592083 - 1.02552i) q^{31} +(1.20110 - 3.26293i) q^{33} +1.40621i q^{35} +5.74432i q^{37} +(0.509175 + 0.611324i) q^{39} +(4.75281 + 8.23212i) q^{41} +(1.03633 + 0.598327i) q^{43} +(7.12562 - 8.36729i) q^{45} +(-3.27688 + 5.67572i) q^{47} +(3.42633 + 5.93458i) q^{49} +(-1.20321 - 6.97229i) q^{51} -7.63807i q^{53} +7.35407 q^{55} +(-8.06300 + 1.39143i) q^{57} +(0.603703 - 0.348548i) q^{59} +(-4.23774 - 2.44666i) q^{61} +(-0.208231 + 1.13257i) q^{63} +(-0.841376 + 1.45731i) q^{65} +(8.87932 - 5.12648i) q^{67} +(-7.92122 + 6.59762i) q^{69} +3.73792 q^{71} -2.68275 q^{73} +(13.6872 + 5.03832i) q^{75} +(-0.667322 + 0.385279i) q^{77} +(5.35979 - 9.28342i) q^{79} +(6.97804 - 5.68392i) q^{81} +(-5.49039 - 3.16988i) q^{83} +(12.9600 - 7.48246i) q^{85} +(-1.40792 + 3.82477i) q^{87} +7.56802 q^{89} -0.176318i q^{91} +(1.57598 - 1.31264i) q^{93} +(-8.65297 - 14.9874i) q^{95} +(-2.98511 + 5.17036i) q^{97} +(5.92302 + 1.08898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 6 * q^7 + 2 * q^9	\( 16 q - 6 q^{7} + 2 q^{9} + 10 q^{15} - 28 q^{17} + 10 q^{23} + 2 q^{25} + 10 q^{31} - 2 q^{39} - 8 q^{41} - 6 q^{47} + 18 q^{49} + 4 q^{55} + 10 q^{57} - 2 q^{63} - 14 q^{65} - 72 q^{71} - 44 q^{73} + 30 q^{79} + 10 q^{81} - 42 q^{87} + 64 q^{89} - 44 q^{95}+O(q^{100}) \) 16 * q - 6 * q^7 + 2 * q^9 + 10 * q^15 - 28 * q^17 + 10 * q^23 + 2 * q^25 + 10 * q^31 - 2 * q^39 - 8 * q^41 - 6 * q^47 + 18 * q^49 + 4 * q^55 + 10 * q^57 - 2 * q^63 - 14 * q^65 - 72 * q^71 - 44 * q^73 + 30 * q^79 + 10 * q^81 - 42 * q^87 + 64 * q^89 - 44 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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