LMFDB - Embedded newform 288.2.p.b.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(47,288)]

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([3, 3, 1]))

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

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

chi := DirichletCharacter("288.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.p (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} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.2
Root			$0.867527 - 1.11687i$ of defining polynomial
Character	$\chi$	$=$	288.47
Dual form			288.2.p.b.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.925606 - 1.46399i) q^{3} +(0.895377 + 1.55084i) q^{5} +(2.08793 + 1.20546i) q^{7} +(-1.28651 + 2.71015i) q^{9} +O(q^{10})$	\(q+(-0.925606 - 1.46399i) q^{3} +(0.895377 + 1.55084i) q^{5} +(2.08793 + 1.20546i) q^{7} +(-1.28651 + 2.71015i) q^{9} +(1.36975 + 0.790826i) q^{11} +(5.35491 - 3.09166i) q^{13} +(1.44164 - 2.74629i) q^{15} -3.69943i q^{17} -3.12941 q^{19} +(-0.167814 - 4.17248i) q^{21} +(1.36036 + 2.35622i) q^{23} +(0.896599 - 1.55296i) q^{25} +(5.15842 - 0.625100i) q^{27} +(-2.55291 + 4.42177i) q^{29} +(5.95312 - 3.43703i) q^{31} +(-0.110092 - 2.73729i) q^{33} +4.31738i q^{35} +5.24328i q^{37} +(-9.48268 - 4.97786i) q^{39} +(-5.32220 + 3.07278i) q^{41} +(0.452455 - 0.783675i) q^{43} +(-5.35491 + 0.431438i) q^{45} +(-4.88993 + 8.46960i) q^{47} +(-0.593711 - 1.02834i) q^{49} +(-5.41592 + 3.42422i) q^{51} -7.05913 q^{53} +2.83235i q^{55} +(2.89660 + 4.58141i) q^{57} +(6.10118 - 3.52252i) q^{59} +(-3.05109 - 1.76155i) q^{61} +(-5.95312 + 4.10775i) q^{63} +(9.58933 + 5.53640i) q^{65} +(-1.03786 - 1.79762i) q^{67} +(2.19031 - 4.17248i) q^{69} -3.31507 q^{71} +0.631029 q^{73} +(-3.10340 + 0.124816i) q^{75} +(1.90662 + 3.30237i) q^{77} +(-7.82515 - 4.51785i) q^{79} +(-5.68980 - 6.97325i) q^{81} +(-13.5542 - 7.82551i) q^{83} +(5.73722 - 3.31239i) q^{85} +(8.83640 - 0.355393i) q^{87} +1.16402i q^{89} +14.9075 q^{91} +(-10.5420 - 5.53394i) q^{93} +(-2.80200 - 4.85321i) q^{95} +(-6.72981 + 11.6564i) q^{97} +(-3.90545 + 2.69482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^3 - 6 * q^9	$ 16 q + 6 q^{3} - 6 q^{9} - 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{27} + 12 q^{33} - 36 q^{41} - 8 q^{43} + 10 q^{49} - 18 q^{51} + 18 q^{57} - 12 q^{59} - 6 q^{65} + 16 q^{67} - 4 q^{73} - 78 q^{75} - 6 q^{81} - 54 q^{83} + 36 q^{91} + 8 q^{97} + 6 q^{99}+O(q^{100}) $ 16 * q + 6 * q^3 - 6 * q^9 - 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^27 + 12 * q^33 - 36 * q^41 - 8 * q^43 + 10 * q^49 - 18 * q^51 + 18 * q^57 - 12 * q^59 - 6 * q^65 + 16 * q^67 - 4 * q^73 - 78 * q^75 - 6 * q^81 - 54 * q^83 + 36 * q^91 + 8 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	−0.925606	−	1.46399i	−0.534399	−	0.845232i
$3$	−0.925606	−	1.46399i	−0.534399	−	0.845232i
$4$		0			0
$5$	0.895377	+	1.55084i	0.400425	+	0.693556i	0.993777	−	0.111387i	$-0.0355292\pi$
$5$	0.895377	+	1.55084i	0.400425	+	0.693556i	−0.593352	+	0.804943i	$0.702196\pi$
$6$		0			0
$7$	2.08793	+	1.20546i	0.789162	+	0.455623i	0.839667	−	0.543101i	$-0.182750\pi$
$7$	2.08793	+	1.20546i	0.789162	+	0.455623i	−0.0505056	+	0.998724i	$0.516083\pi$
$8$		0			0
$9$	−1.28651	+	2.71015i	−0.428836	+	0.903382i
$10$		0			0
$11$	1.36975	+	0.790826i	0.412995	+	0.238443i	0.692076	−	0.721825i	$-0.256696\pi$
$11$	1.36975	+	0.790826i	0.412995	+	0.238443i	−0.279081	+	0.960268i	$0.590030\pi$
$12$		0			0
$13$	5.35491	−	3.09166i	1.48519	−	0.857472i	0.485327	−	0.874332i	$-0.338700\pi$
$13$	5.35491	−	3.09166i	1.48519	−	0.857472i	0.999858	+	0.0168604i	$0.00536707\pi$
$14$		0			0
$15$	1.44164	−	2.74629i	0.372230	−	0.709088i
$16$		0			0
$17$		−	3.69943i		−	0.897244i	−0.893722	−	0.448622i	$-0.851915\pi$
$17$		−	3.69943i		−	0.897244i	0.893722	−	0.448622i	$-0.148085\pi$
$18$		0			0
$19$	−3.12941			−0.717936			−0.358968	−	0.933350i	$-0.616871\pi$
$19$	−3.12941			−0.717936			−0.358968	+	0.933350i	$0.616871\pi$
$20$		0			0
$21$	−0.167814	−	4.17248i	−0.0366200	−	0.910509i
$22$		0			0
$23$	1.36036	+	2.35622i	0.283655	+	0.491305i	0.972282	−	0.233811i	$-0.0751196\pi$
$23$	1.36036	+	2.35622i	0.283655	+	0.491305i	−0.688627	+	0.725116i	$0.741786\pi$
$24$		0			0
$25$	0.896599	−	1.55296i	0.179320	−	0.310591i
$26$		0			0
$27$	5.15842	−	0.625100i	0.992738	−	0.120301i
$28$		0			0
$29$	−2.55291	+	4.42177i	−0.474064	+	0.821102i	−0.999559	−	0.0296942i	$-0.990547\pi$
$29$	−2.55291	+	4.42177i	−0.474064	+	0.821102i	0.525495	+	0.850796i	$0.323880\pi$
$30$		0			0
$31$	5.95312	−	3.43703i	1.06921	−	0.617310i	0.141246	−	0.989975i	$-0.454889\pi$
$31$	5.95312	−	3.43703i	1.06921	−	0.617310i	0.927966	+	0.372665i	$0.121556\pi$
$32$		0			0
$33$	−0.110092	−	2.73729i	−0.0191645	−	0.476501i
$34$		0			0
$35$			4.31738i			0.729771i
$36$		0			0
$37$			5.24328i			0.861990i	0.902354	+	0.430995i	$0.141837\pi$
$37$			5.24328i			0.861990i	−0.902354	+	0.430995i	$0.858163\pi$
$38$		0			0
$39$	−9.48268	−	4.97786i	−1.51844	−	0.797095i
$40$		0			0
$41$	−5.32220	+	3.07278i	−0.831189	+	0.479887i	−0.854260	−	0.519847i	$-0.825989\pi$
$41$	−5.32220	+	3.07278i	−0.831189	+	0.479887i	0.0230708	+	0.999734i	$0.492656\pi$
$42$		0			0
$43$	0.452455	−	0.783675i	0.0689987	−	0.119509i	−0.829462	−	0.558563i	$-0.811353\pi$
$43$	0.452455	−	0.783675i	0.0689987	−	0.119509i	0.898461	+	0.439054i	$0.144686\pi$
$44$		0			0
$45$	−5.35491	+	0.431438i	−0.798263	+	0.0643150i
$46$		0			0
$47$	−4.88993	+	8.46960i	−0.713269	+	1.23542i	0.250354	+	0.968154i	$0.419453\pi$
$47$	−4.88993	+	8.46960i	−0.713269	+	1.23542i	−0.963623	+	0.267264i	$0.913880\pi$
$48$		0			0
$49$	−0.593711	−	1.02834i	−0.0848159	−	0.146905i
$50$		0			0
$51$	−5.41592	+	3.42422i	−0.758380	+	0.479486i
$52$		0			0
$53$	−7.05913			−0.969646			−0.484823	−	0.874612i	$-0.661116\pi$
$53$	−7.05913			−0.969646			−0.484823	+	0.874612i	$0.661116\pi$
$54$		0			0
$55$			2.83235i			0.381914i
$56$		0			0
$57$	2.89660	+	4.58141i	0.383664	+	0.606822i
$58$		0			0
$59$	6.10118	−	3.52252i	0.794306	−	0.458593i	−0.0471702	−	0.998887i	$-0.515020\pi$
$59$	6.10118	−	3.52252i	0.794306	−	0.458593i	0.841476	+	0.540294i	$0.181687\pi$
$60$		0			0
$61$	−3.05109	−	1.76155i	−0.390652	−	0.225543i	0.291790	−	0.956482i	$-0.405749\pi$
$61$	−3.05109	−	1.76155i	−0.390652	−	0.225543i	−0.682443	+	0.730939i	$0.739082\pi$
$62$		0			0
$63$	−5.95312	+	4.10775i	−0.750022	+	0.517527i
$64$		0			0
$65$	9.58933	+	5.53640i	1.18941	+	0.686706i
$66$		0			0
$67$	−1.03786	−	1.79762i	−0.126794	−	0.219614i	0.795639	−	0.605772i	$-0.207135\pi$
$67$	−1.03786	−	1.79762i	−0.126794	−	0.219614i	−0.922433	+	0.386158i	$0.873802\pi$
$68$		0			0
$69$	2.19031	−	4.17248i	0.263682	−	0.502307i
$70$		0			0
$71$	−3.31507			−0.393426			−0.196713	−	0.980461i	$-0.563027\pi$
$71$	−3.31507			−0.393426			−0.196713	+	0.980461i	$0.563027\pi$
$72$		0			0
$73$	0.631029			0.0738563			0.0369282	−	0.999318i	$-0.488243\pi$
$73$	0.631029			0.0738563			0.0369282	+	0.999318i	$0.488243\pi$
$74$		0			0
$75$	−3.10340	+	0.124816i	−0.358350	+	0.0144125i
$76$		0			0
$77$	1.90662	+	3.30237i	0.217280	+	0.376340i
$78$		0			0
$79$	−7.82515	−	4.51785i	−0.880398	−	0.508298i	−0.00960849	−	0.999954i	$-0.503059\pi$
$79$	−7.82515	−	4.51785i	−0.880398	−	0.508298i	−0.870790	+	0.491656i	$0.836392\pi$
$80$		0			0
$81$	−5.68980	−	6.97325i	−0.632200	−	0.774806i
$82$		0			0
$83$	−13.5542	−	7.82551i	−1.48776	−	0.858961i	−0.487861	−	0.872921i	$-0.662223\pi$
$83$	−13.5542	−	7.82551i	−1.48776	−	0.858961i	−0.999903	+	0.0139604i	$0.995556\pi$
$84$		0			0
$85$	5.73722	−	3.31239i	0.622289	−	0.359279i
$86$		0			0
$87$	8.83640	−	0.355393i	0.947361	−	0.0381021i
$88$		0			0
$89$			1.16402i			0.123386i	0.998095	+	0.0616929i	$0.0196499\pi$
$89$			1.16402i			0.123386i	−0.998095	+	0.0616929i	$0.980350\pi$
$90$		0			0
$91$	14.9075			1.56274
$92$		0			0
$93$	−10.5420	−	5.53394i	−1.09316	−	0.573843i
$94$		0			0
$95$	−2.80200	−	4.85321i	−0.287479	−	0.497929i
$96$		0			0
$97$	−6.72981	+	11.6564i	−0.683309	+	1.18353i	0.290656	+	0.956827i	$0.406126\pi$
$97$	−6.72981	+	11.6564i	−0.683309	+	1.18353i	−0.973965	+	0.226698i	$0.927207\pi$
$98$		0			0
$99$	−3.90545	+	2.69482i	−0.392512	+	0.270840i
$100$		0			0
$101$	3.28047	−	5.68195i	0.326419	−	0.565375i	−0.655379	−	0.755300i	$-0.727491\pi$
$101$	3.28047	−	5.68195i	0.326419	−	0.565375i	0.981799	+	0.189925i	$0.0608245\pi$
$102$		0			0
$103$	5.12167	−	2.95700i	0.504653	−	0.291361i	−0.225980	−	0.974132i	$-0.572558\pi$
$103$	5.12167	−	2.95700i	0.504653	−	0.291361i	0.730633	+	0.682771i	$0.239225\pi$
$104$		0			0
$105$	6.32058	−	3.99619i	0.616826	−	0.389989i
$106$		0			0
$107$		−	1.01487i		−	0.0981111i	−0.998796	−	0.0490555i	$-0.984379\pi$
$107$		−	1.01487i		−	0.0981111i	0.998796	−	0.0490555i	$-0.0156211\pi$
$108$		0			0
$109$			4.46314i			0.427491i	0.976889	+	0.213746i	$0.0685664\pi$
$109$			4.46314i			0.427491i	−0.976889	+	0.213746i	$0.931434\pi$
$110$		0			0
$111$	7.67608	−	4.85321i	0.728582	−	0.460646i
$112$		0			0
$113$	7.35628	−	4.24715i	0.692021	−	0.399538i	−0.112348	−	0.993669i	$-0.535837\pi$
$113$	7.35628	−	4.24715i	0.692021	−	0.399538i	0.804369	+	0.594131i	$0.202504\pi$
$114$		0			0
$115$	−2.43607	+	4.21940i	−0.227165	+	0.393462i
$116$		0			0
$117$	1.48972	+	18.4900i	0.137725	+	1.70941i
$118$		0			0
$119$	4.45953	−	7.72414i	0.408805	−	0.708071i
$120$		0			0
$121$	−4.24919	−	7.35981i	−0.386290	−	0.669074i
$122$		0			0
$123$	9.42476	+	4.94745i	0.849802	+	0.446097i
$124$		0			0
$125$	12.1650			1.08807
$126$		0			0
$127$			15.9098i			1.41176i	0.708329	+	0.705882i	$0.249449\pi$
$127$			15.9098i			1.41176i	−0.708329	+	0.705882i	$0.750551\pi$
$128$		0			0
$129$	−1.56608	+	0.0629866i	−0.137886	+	0.00554566i
$130$		0			0
$131$	−1.38769	+	0.801182i	−0.121243	+	0.0699996i	−0.559395	−	0.828901i	$-0.688966\pi$
$131$	−1.38769	+	0.801182i	−0.121243	+	0.0699996i	0.438152	+	0.898901i	$0.355633\pi$
$132$		0			0
$133$	−6.53397	−	3.77239i	−0.566567	−	0.327108i
$134$		0			0
$135$	5.58816	+	7.44017i	0.480952	+	0.640348i
$136$		0			0
$137$	−10.6153	−	6.12877i	−0.906930	−	0.523616i	−0.0274877	−	0.999622i	$-0.508751\pi$
$137$	−10.6153	−	6.12877i	−0.906930	−	0.523616i	−0.879442	+	0.476006i	$0.842084\pi$
$138$		0			0
$139$	0.618940	+	1.07204i	0.0524978	+	0.0909289i	0.891080	−	0.453846i	$-0.149948\pi$
$139$	0.618940	+	1.07204i	0.0524978	+	0.0909289i	−0.838582	+	0.544775i	$0.816615\pi$
$140$		0			0
$141$	16.9255	−	0.680731i	1.42539	−	0.0573279i
$142$		0			0
$143$	9.77985			0.817832
$144$		0			0
$145$	−9.14327			−0.759307
$146$		0			0
$147$	−0.955929	+	1.82102i	−0.0788437	+	0.150195i
$148$		0			0
$149$	−2.96982	−	5.14387i	−0.243297	−	0.421402i	0.718355	−	0.695677i	$-0.244896\pi$
$149$	−2.96982	−	5.14387i	−0.243297	−	0.421402i	−0.961651	+	0.274275i	$0.911562\pi$
$150$		0			0
$151$	−11.9663	−	6.90874i	−0.973803	−	0.562226i	−0.0734098	−	0.997302i	$-0.523388\pi$
$151$	−11.9663	−	6.90874i	−0.973803	−	0.562226i	−0.900394	+	0.435076i	$0.856721\pi$
$152$		0			0
$153$	10.0260	+	4.75935i	0.810555	+	0.384770i
$154$		0			0
$155$	10.6606	+	6.15488i	0.856278	+	0.494372i
$156$		0			0
$157$	−4.98995	+	2.88095i	−0.398241	+	0.229925i	−0.685725	−	0.727861i	$-0.740515\pi$
$157$	−4.98995	+	2.88095i	−0.398241	+	0.229925i	0.287483	+	0.957786i	$0.407181\pi$
$158$		0			0
$159$	6.53397	+	10.3345i	0.518178	+	0.819576i
$160$		0			0
$161$			6.55947i			0.516959i
$162$		0			0
$163$	−11.2888			−0.884209			−0.442104	−	0.896964i	$-0.645768\pi$
$163$	−11.2888			−0.884209			−0.442104	+	0.896964i	$0.645768\pi$
$164$		0			0
$165$	4.14652	−	2.62164i	0.322806	−	0.204094i
$166$		0			0
$167$	0.378448	+	0.655492i	0.0292852	+	0.0507235i	0.880297	−	0.474424i	$-0.157344\pi$
$167$	0.378448	+	0.655492i	0.0292852	+	0.0507235i	−0.851011	+	0.525147i	$0.824010\pi$
$168$		0			0
$169$	12.6167	−	21.8528i	0.970517	−	1.68098i
$170$		0			0
$171$	4.02601	−	8.48116i	0.307876	−	0.648570i
$172$		0			0
$173$	4.62735	−	8.01480i	0.351811	−	0.609354i	−0.634756	−	0.772713i	$-0.718899\pi$
$173$	4.62735	−	8.01480i	0.351811	−	0.609354i	0.986567	+	0.163359i	$0.0522327\pi$
$174$		0			0
$175$	3.74406	−	2.16164i	0.283025	−	0.163404i
$176$		0			0
$177$	−10.8042	−	5.67158i	−0.812094	−	0.426302i
$178$		0			0
$179$			1.56530i			0.116996i	0.998288	+	0.0584980i	$0.0186311\pi$
$179$			1.56530i			0.116996i	−0.998288	+	0.0584980i	$0.981369\pi$
$180$		0			0
$181$			3.68300i			0.273755i	0.990588	+	0.136878i	$0.0437067\pi$
$181$			3.68300i			0.273755i	−0.990588	+	0.136878i	$0.956293\pi$
$182$		0			0
$183$	0.245227	+	6.09726i	0.0181277	+	0.450722i
$184$		0			0
$185$	−8.13148	+	4.69471i	−0.597838	+	0.345162i
$186$		0			0
$187$	2.92561	−	5.06730i	0.213941	−	0.370558i
$188$		0			0
$189$	11.5239	+	4.91312i	0.838242	+	0.357377i
$190$		0			0
$191$	11.8678	−	20.5556i	0.858722	−	1.48735i	−0.0144258	−	0.999896i	$-0.504592\pi$
$191$	11.8678	−	20.5556i	0.858722	−	1.48735i	0.873148	−	0.487455i	$-0.162075\pi$
$192$		0			0
$193$	12.8012	+	22.1723i	0.921451	+	1.59600i	0.797172	+	0.603752i	$0.206328\pi$
$193$	12.8012	+	22.1723i	0.921451	+	1.59600i	0.124279	+	0.992247i	$0.460338\pi$
$194$		0			0
$195$	−0.770728	−	19.1632i	−0.0551929	−	1.37230i
$196$		0			0
$197$	5.76656			0.410850			0.205425	−	0.978673i	$-0.434142\pi$
$197$	5.76656			0.410850			0.205425	+	0.978673i	$0.434142\pi$
$198$		0			0
$199$		−	1.24163i		−	0.0880169i	−0.999031	−	0.0440085i	$-0.985987\pi$
$199$		−	1.24163i		−	0.0880169i	0.999031	−	0.0440085i	$-0.0140129\pi$
$200$		0			0
$201$	−1.67104	+	3.18329i	−0.117866	+	0.224532i
$202$		0			0
$203$	−10.6606	+	6.15488i	−0.748226	+	0.431988i
$204$		0			0
$205$	−9.53076	−	5.50259i	−0.665657	−	0.384317i
$206$		0			0
$207$	−8.13581	+	0.655492i	−0.565478	+	0.0455598i
$208$		0			0
$209$	−4.28651	−	2.47482i	−0.296504	−	0.171187i
$210$		0			0
$211$	−1.62194	−	2.80928i	−0.111659	−	0.193399i	0.804780	−	0.593573i	$-0.202283\pi$
$211$	−1.62194	−	2.80928i	−0.111659	−	0.193399i	−0.916439	+	0.400174i	$0.868950\pi$
$212$		0			0
$213$	3.06844	+	4.85321i	0.210246	+	0.332536i
$214$		0			0
$215$	1.62047			0.110515
$216$		0			0
$217$	16.5729			1.12504
$218$		0			0
$219$	−0.584084	−	0.923817i	−0.0394687	−	0.0624258i
$220$		0			0
$221$	−11.4374	−	19.8101i	−0.769362	−	1.33257i
$222$		0			0
$223$	−12.1221	−	6.99871i	−0.811758	−	0.468669i	0.0358081	−	0.999359i	$-0.488599\pi$
$223$	−12.1221	−	6.99871i	−0.811758	−	0.468669i	−0.847566	+	0.530690i	$0.821933\pi$
$224$		0			0
$225$	3.05526	+	4.42780i	0.203684	+	0.295187i
$226$		0			0
$227$	8.75366	+	5.05393i	0.581001	+	0.335441i	0.761531	−	0.648128i	$-0.224448\pi$
$227$	8.75366	+	5.05393i	0.581001	+	0.335441i	−0.180530	+	0.983569i	$0.557781\pi$
$228$		0			0
$229$	−9.93043	+	5.73334i	−0.656221	+	0.378869i	−0.790836	−	0.612029i	$-0.790354\pi$
$229$	−9.93043	+	5.73334i	−0.656221	+	0.378869i	0.134615	+	0.990898i	$0.457020\pi$
$230$		0			0
$231$	3.06984	−	5.84796i	0.201981	−	0.384768i
$232$		0			0
$233$		−	6.74860i		−	0.442115i	−0.975261	−	0.221058i	$-0.929049\pi$
$233$		−	6.74860i		−	0.442115i	0.975261	−	0.221058i	$-0.0709509\pi$
$234$		0			0
$235$	−17.5133			−1.14244
$236$		0			0
$237$	0.628934	+	15.6377i	0.0408537	+	1.01578i
$238$		0			0
$239$	0.0677896	+	0.117415i	0.00438494	+	0.00759495i	0.868210	−	0.496198i	$-0.165271\pi$
$239$	0.0677896	+	0.117415i	0.00438494	+	0.00759495i	−0.863825	+	0.503793i	$0.831938\pi$
$240$		0			0
$241$	−9.71742	+	16.8311i	−0.625954	+	1.08418i	0.362401	+	0.932022i	$0.381957\pi$
$241$	−9.71742	+	16.8311i	−0.625954	+	1.08418i	−0.988355	+	0.152163i	$0.951376\pi$
$242$		0			0
$243$	−4.94223	+	14.7843i	−0.317044	+	0.948411i
$244$		0			0
$245$	1.06319	−	1.84150i	0.0679248	−	0.117649i
$246$		0			0
$247$	−16.7577	+	9.67507i	−1.06627	+	0.615610i
$248$		0			0
$249$	1.08940	+	27.0864i	0.0690376	+	1.71653i
$250$		0			0
$251$		−	18.7837i		−	1.18561i	−0.805344	−	0.592807i	$-0.798020\pi$
$251$		−	18.7837i		−	1.18561i	0.805344	−	0.592807i	$-0.201980\pi$
$252$		0			0
$253$			4.30324i			0.270542i
$254$		0			0
$255$	−10.1597	−	5.33325i	−0.636225	−	0.333981i
$256$		0			0
$257$	18.6937	−	10.7928i	1.16608	−	0.673238i	0.213329	−	0.976981i	$-0.431570\pi$
$257$	18.6937	−	10.7928i	1.16608	−	0.673238i	0.952754	+	0.303742i	$0.0982362\pi$
$258$		0			0
$259$	−6.32058	+	10.9476i	−0.392742	+	0.680249i
$260$		0			0
$261$	−8.69931	−	12.6074i	−0.538474	−	0.780379i
$262$		0			0
$263$	−8.56995	+	14.8436i	−0.528446	+	0.915295i	0.471004	+	0.882131i	$0.343892\pi$
$263$	−8.56995	+	14.8436i	−0.528446	+	0.915295i	−0.999450	+	0.0331642i	$0.989442\pi$
$264$		0			0
$265$	−6.32058	−	10.9476i	−0.388270	−	0.672504i
$266$		0			0
$267$	1.70411	−	1.07742i	0.104290	−	0.0659372i
$268$		0			0
$269$	−20.1271			−1.22717			−0.613585	−	0.789629i	$-0.710273\pi$
$269$	−20.1271			−1.22717			−0.613585	+	0.789629i	$0.710273\pi$
$270$		0			0
$271$			6.20336i			0.376827i	0.982090	+	0.188414i	$0.0603345\pi$
$271$			6.20336i			0.376827i	−0.982090	+	0.188414i	$0.939665\pi$
$272$		0			0
$273$	−13.7985	−	21.8244i	−0.835124	−	1.32087i
$274$		0			0
$275$	2.45623	−	1.41811i	0.148116	−	0.0855151i
$276$		0			0
$277$	−10.6060	−	6.12340i	−0.637256	−	0.367920i	0.146301	−	0.989240i	$-0.453263\pi$
$277$	−10.6060	−	6.12340i	−0.637256	−	0.367920i	−0.783557	+	0.621320i	$0.786597\pi$
$278$		0			0
$279$	1.65614	+	20.5556i	0.0991504	+	1.23063i
$280$		0			0
$281$	−15.1623	−	8.75399i	−0.904510	−	0.522219i	−0.0258492	−	0.999666i	$-0.508229\pi$
$281$	−15.1623	−	8.75399i	−0.904510	−	0.522219i	−0.878661	+	0.477447i	$0.841562\pi$
$282$		0			0
$283$	3.79698	+	6.57656i	0.225707	+	0.390936i	0.956531	−	0.291630i	$-0.0941975\pi$
$283$	3.79698	+	6.57656i	0.225707	+	0.390936i	−0.730824	+	0.682565i	$0.760864\pi$
$284$		0			0
$285$	−4.51148	+	8.59425i	−0.267237	+	0.509079i
$286$		0			0
$287$	−14.8165			−0.874590
$288$		0			0
$289$	3.31420			0.194953
$290$		0			0
$291$	23.2939	−	0.936863i	1.36551	−	0.0549199i
$292$		0			0
$293$	12.6164	+	21.8523i	0.737061	+	1.27663i	0.953813	+	0.300400i	$0.0971202\pi$
$293$	12.6164	+	21.8523i	0.737061	+	1.27663i	−0.216753	+	0.976227i	$0.569546\pi$
$294$		0			0
$295$	10.9257	+	6.30797i	0.636120	+	0.367264i
$296$		0			0
$297$	7.56008	+	3.22318i	0.438681	+	0.187028i
$298$		0			0
$299$	14.5692	+	8.41155i	0.842561	+	0.486453i
$300$		0			0
$301$	1.88938	−	1.09084i	0.108902	−	0.0628748i
$302$		0			0
$303$	−11.3547	+	0.456678i	−0.652311	+	0.0262354i
$304$		0			0
$305$		−	6.30900i		−	0.361253i
$306$		0			0
$307$	29.5997			1.68934			0.844671	−	0.535286i	$-0.179796\pi$
$307$	29.5997			1.68934			0.844671	+	0.535286i	$0.179796\pi$
$308$		0			0
$309$	−9.06964	−	4.76103i	−0.515954	−	0.270846i
$310$		0			0
$311$	−10.3607	−	17.9453i	−0.587502	−	1.01758i	−0.994558	−	0.104180i	$-0.966778\pi$
$311$	−10.3607	−	17.9453i	−0.587502	−	1.01758i	0.407057	−	0.913403i	$-0.366555\pi$
$312$		0			0
$313$	1.73680	−	3.00823i	0.0981700	−	0.170035i	−0.812757	−	0.582603i	$-0.802034\pi$
$313$	1.73680	−	3.00823i	0.0981700	−	0.170035i	0.910927	+	0.412567i	$0.135368\pi$
$314$		0			0
$315$	−11.7007	−	5.55434i	−0.659262	−	0.312952i
$316$		0			0
$317$	−7.64385	+	13.2395i	−0.429321	+	0.743606i	−0.996813	−	0.0797728i	$-0.974581\pi$
$317$	−7.64385	+	13.2395i	−0.429321	+	0.743606i	0.567492	+	0.823379i	$0.307914\pi$
$318$		0			0
$319$	−6.99370	+	4.03781i	−0.391572	+	0.226074i
$320$		0			0
$321$	−1.48575	+	0.939368i	−0.0829267	+	0.0524304i
$322$		0			0
$323$			11.5770i			0.644164i
$324$		0			0
$325$		−	11.0879i		−	0.615047i
$326$		0			0
$327$	6.53397	−	4.13111i	0.361329	−	0.228451i
$328$		0			0
$329$	−20.4196	+	11.7893i	−1.12577	+	0.649963i
$330$		0			0
$331$	−3.09986	+	5.36912i	−0.170384	+	0.295114i	−0.938554	−	0.345132i	$-0.887834\pi$
$331$	−3.09986	+	5.36912i	−0.170384	+	0.295114i	0.768170	+	0.640246i	$0.221167\pi$
$332$		0			0
$333$	−14.2101	−	6.74552i	−0.778706	−	0.369652i
$334$		0			0
$335$	1.85854	−	3.21909i	0.101543	−	0.175878i
$336$		0			0
$337$	−9.63097	−	16.6813i	−0.524632	−	0.908690i	−0.999589	−	0.0286803i	$-0.990870\pi$
$337$	−9.63097	−	16.6813i	−0.524632	−	0.908690i	0.474956	−	0.880009i	$-0.342464\pi$
$338$		0			0
$339$	−13.0268	−	6.83830i	−0.707518	−	0.371406i
$340$		0			0
$341$	10.8724			0.588772
$342$		0			0
$343$		−	19.7393i		−	1.06582i
$344$		0			0
$345$	8.43199	−	0.339128i	0.453963	−	0.0182580i
$346$		0			0
$347$	−22.9191	+	13.2323i	−1.23036	+	0.710349i	−0.967105	−	0.254378i	$-0.918129\pi$
$347$	−22.9191	+	13.2323i	−1.23036	+	0.710349i	−0.263255	+	0.964726i	$0.584796\pi$
$348$		0			0
$349$	14.8362	+	8.56568i	0.794164	+	0.458511i	0.841426	−	0.540372i	$-0.181716\pi$
$349$	14.8362	+	8.56568i	0.794164	+	0.458511i	−0.0472627	+	0.998882i	$0.515050\pi$
$350$		0			0
$351$	25.6903	−	19.2954i	1.37124	−	1.02991i
$352$		0			0
$353$	26.8134	+	15.4807i	1.42713	+	0.823955i	0.996894	−	0.0787597i	$-0.0250960\pi$
$353$	26.8134	+	15.4807i	1.42713	+	0.823955i	0.430239	+	0.902715i	$0.358429\pi$
$354$		0			0
$355$	−2.96823	−	5.14113i	−0.157538	−	0.272863i
$356$		0			0
$357$	−15.4358	+	0.620816i	−0.816949	+	0.0328570i
$358$		0			0
$359$	6.43781			0.339775			0.169887	−	0.985463i	$-0.445660\pi$
$359$	6.43781			0.339775			0.169887	+	0.985463i	$0.445660\pi$
$360$		0			0
$361$	−9.20680			−0.484569
$362$		0			0
$363$	−6.84158	+	13.0330i	−0.359090	+	0.684057i
$364$		0			0
$365$	0.565009	+	0.978624i	0.0295739	+	0.0512235i
$366$		0			0
$367$	23.8725	+	13.7828i	1.24614	+	0.719457i	0.970337	−	0.241758i	$-0.0777241\pi$
$367$	23.8725	+	13.7828i	1.24614	+	0.719457i	0.275800	+	0.961215i	$0.411057\pi$
$368$		0			0
$369$	−1.48062	−	18.3771i	−0.0770780	−	0.956674i
$370$		0			0
$371$	−14.7389	−	8.50953i	−0.765208	−	0.441793i
$372$		0			0
$373$	23.2547	−	13.4261i	1.20408	−	0.695178i	0.242623	−	0.970121i	$-0.421992\pi$
$373$	23.2547	−	13.4261i	1.20408	−	0.695178i	0.961461	+	0.274942i	$0.0886587\pi$
$374$		0			0
$375$	−11.2599	−	17.8093i	−0.581461	−	0.919669i
$376$		0			0
$377$			31.5709i			1.62599i
$378$		0			0
$379$	−4.63966			−0.238323			−0.119162	−	0.992875i	$-0.538021\pi$
$379$	−4.63966			−0.238323			−0.119162	+	0.992875i	$0.538021\pi$
$380$		0			0
$381$	23.2917	−	14.7262i	1.19327	−	0.754445i
$382$		0			0
$383$	17.7531	+	30.7493i	0.907141	+	1.57122i	0.818017	+	0.575195i	$0.195074\pi$
$383$	17.7531	+	30.7493i	0.907141	+	1.57122i	0.0891248	+	0.996020i	$0.471593\pi$
$384$		0			0
$385$	−3.41430	+	5.91373i	−0.174009	+	0.301392i
$386$		0			0
$387$	1.54179	+	2.23442i	0.0783735	+	0.113582i
$388$		0			0
$389$	−3.19920	+	5.54117i	−0.162206	+	0.280949i	−0.935659	−	0.352904i	$-0.885194\pi$
$389$	−3.19920	+	5.54117i	−0.162206	+	0.280949i	0.773454	+	0.633853i	$0.218527\pi$
$390$		0			0
$391$	8.71666	−	5.03257i	0.440821	−	0.254508i
$392$		0			0
$393$	2.45737	+	1.28998i	0.123958	+	0.0650707i
$394$		0			0
$395$		−	16.1807i		−	0.814141i
$396$		0			0
$397$			3.01894i			0.151516i	0.997126	+	0.0757581i	$0.0241377\pi$
$397$			3.01894i			0.151516i	−0.997126	+	0.0757581i	$0.975862\pi$
$398$		0			0
$399$	0.525158	+	13.0574i	0.0262908	+	0.653687i
$400$		0			0
$401$	25.1191	−	14.5025i	1.25439	−	0.724222i	0.282411	−	0.959294i	$-0.408866\pi$
$401$	25.1191	−	14.5025i	1.25439	−	0.724222i	0.971978	+	0.235072i	$0.0755326\pi$
$402$		0			0
$403$	21.2523	−	36.8100i	1.05865	−	1.83364i
$404$		0			0
$405$	5.71987	−	15.0676i	0.284223	−	0.748717i
$406$		0			0
$407$	−4.14652	+	7.18198i	−0.205535	+	0.355998i
$408$		0			0
$409$	−0.662169	−	1.14691i	−0.0327422	−	0.0567111i	0.849190	−	0.528087i	$-0.177091\pi$
$409$	−0.662169	−	1.14691i	−0.0327422	−	0.0567111i	−0.881932	+	0.471376i	$0.843757\pi$
$410$		0			0
$411$	0.853191	+	21.2135i	0.0420848	+	1.04639i
$412$		0			0
$413$	16.9851			0.835781
$414$		0			0
$415$		−	28.0271i		−	1.37580i
$416$		0			0
$417$	0.996550	−	1.89840i	0.0488013	−	0.0929651i
$418$		0			0
$419$	27.2974	−	15.7602i	1.33357	−	0.769935i	0.347722	−	0.937598i	$-0.386955\pi$
$419$	27.2974	−	15.7602i	1.33357	−	0.769935i	0.985844	+	0.167663i	$0.0536219\pi$
$420$		0			0
$421$	30.9851	+	17.8893i	1.51012	+	0.871869i	0.999930	+	0.0118087i	$0.00375891\pi$
$421$	30.9851	+	17.8893i	1.51012	+	0.871869i	0.510192	+	0.860061i	$0.329574\pi$
$422$		0			0
$423$	−16.6629	−	24.1486i	−0.810180	−	1.17415i
$424$		0			0
$425$	−5.74505	−	3.31691i	−0.278676	−	0.160894i
$426$		0			0
$427$	−4.24697	−	7.35597i	−0.205525	−	0.355980i
$428$		0			0
$429$	−9.05229	−	14.3176i	−0.437049	−	0.691259i
$430$		0			0
$431$	−17.1129			−0.824301			−0.412150	−	0.911116i	$-0.635222\pi$
$431$	−17.1129			−0.824301			−0.412150	+	0.911116i	$0.635222\pi$
$432$		0			0
$433$	−19.1099			−0.918363			−0.459182	−	0.888342i	$-0.651857\pi$
$433$	−19.1099			−0.918363			−0.459182	+	0.888342i	$0.651857\pi$
$434$		0			0
$435$	8.46307	+	13.3856i	0.405773	+	0.641791i
$436$		0			0
$437$	−4.25713	−	7.37356i	−0.203646	−	0.352725i
$438$		0			0
$439$	29.4886	+	17.0253i	1.40742	+	0.812572i	0.995138	−	0.0984868i	$-0.0314002\pi$
$439$	29.4886	+	17.0253i	1.40742	+	0.812572i	0.412277	+	0.911058i	$0.364734\pi$
$440$		0			0
$441$	3.55076	−	0.286080i	0.169084	−	0.0136229i
$442$		0			0
$443$	−17.1586	−	9.90651i	−0.815229	−	0.470673i	0.0335394	−	0.999437i	$-0.489322\pi$
$443$	−17.1586	−	9.90651i	−0.815229	−	0.470673i	−0.848768	+	0.528765i	$0.822655\pi$
$444$		0			0
$445$	−1.80521	+	1.04224i	−0.0855749	+	0.0494067i
$446$		0			0
$447$	−4.78167	+	9.10896i	−0.226165	+	0.430839i
$448$		0			0
$449$			8.73916i			0.412426i	0.978507	+	0.206213i	$0.0661140\pi$
$449$			8.73916i			0.412426i	−0.978507	+	0.206213i	$0.933886\pi$
$450$		0			0
$451$	−9.72012			−0.457703
$452$		0			0
$453$	0.961772	+	23.9133i	0.0451880	+	1.12354i
$454$		0			0
$455$	13.3479	+	23.1192i	0.625758	+	1.08384i
$456$		0			0
$457$	−1.25081	+	2.16647i	−0.0585104	+	0.101343i	−0.893797	−	0.448472i	$-0.851968\pi$
$457$	−1.25081	+	2.16647i	−0.0585104	+	0.101343i	0.835287	+	0.549815i	$0.185302\pi$
$458$		0			0
$459$	−2.31252	−	19.0832i	−0.107939	−	0.890728i
$460$		0			0
$461$	2.63419	−	4.56255i	0.122686	−	0.212499i	−0.798140	−	0.602472i	$-0.794182\pi$
$461$	2.63419	−	4.56255i	0.122686	−	0.212499i	0.920826	+	0.389973i	$0.127516\pi$
$462$		0			0
$463$	15.2227	−	8.78883i	0.707459	−	0.408451i	−0.102661	−	0.994716i	$-0.532736\pi$
$463$	15.2227	−	8.78883i	0.707459	−	0.408451i	0.810119	+	0.586265i	$0.199402\pi$
$464$		0			0
$465$	−0.856827	−	21.3039i	−0.0397344	−	0.987946i
$466$		0			0
$467$		−	2.29842i		−	0.106358i	−0.998585	−	0.0531791i	$-0.983065\pi$
$467$		−	2.29842i		−	0.106358i	0.998585	−	0.0531791i	$-0.0169354\pi$
$468$		0			0
$469$		−	5.00439i		−	0.231081i
$470$		0			0
$471$	8.83640	+	4.63859i	0.407160	+	0.213735i
$472$		0			0
$473$	1.23950	−	0.715626i	0.0569923	−	0.0329045i
$474$		0			0
$475$	−2.80582	+	4.85983i	−0.128740	+	0.222984i
$476$		0			0
$477$	9.08162	−	19.1313i	0.415819	−	0.875961i
$478$		0			0
$479$	−18.0219	+	31.2149i	−0.823442	+	1.42624i	0.0796622	+	0.996822i	$0.474616\pi$
$479$	−18.0219	+	31.2149i	−0.823442	+	1.42624i	−0.903104	+	0.429422i	$0.858717\pi$
$480$		0			0
$481$	16.2104	+	28.0773i	0.739132	+	1.28021i
$482$		0			0
$483$	9.60297	−	6.07149i	0.436950	−	0.276262i
$484$		0			0
$485$	−24.1029			−1.09446
$486$		0			0
$487$		−	2.72292i		−	0.123387i	−0.998095	−	0.0616937i	$-0.980350\pi$
$487$		−	2.72292i		−	0.123387i	0.998095	−	0.0616937i	$-0.0196502\pi$
$488$		0			0
$489$	10.4490	+	16.5267i	0.472520	+	0.747362i
$490$		0			0
$491$	−13.1715	+	7.60457i	−0.594421	+	0.343189i	−0.766844	−	0.641834i	$-0.778174\pi$
$491$	−13.1715	+	7.60457i	−0.594421	+	0.343189i	0.172422	+	0.985023i	$0.444841\pi$
$492$		0			0
$493$	16.3580	+	9.44432i	0.736729	+	0.425351i
$494$		0			0
$495$	−7.67608	−	3.64384i	−0.345014	−	0.163778i
$496$		0			0
$497$	−6.92161	−	3.99619i	−0.310477	−	0.179254i
$498$		0			0
$499$	19.7305	+	34.1743i	0.883260	+	1.52985i	0.847695	+	0.530483i	$0.177990\pi$
$499$	19.7305	+	34.1743i	0.883260	+	1.52985i	0.0355642	+	0.999367i	$0.488677\pi$
$500$		0			0
$501$	0.609336	−	1.16077i	0.0272231	−	0.0518594i
$502$		0			0
$503$	18.4749			0.823756			0.411878	−	0.911239i	$-0.364873\pi$
$503$	18.4749			0.823756			0.411878	+	0.911239i	$0.364873\pi$
$504$		0			0
$505$	11.7490			0.522826
$506$		0			0
$507$	−43.6703	+	1.75638i	−1.93947	+	0.0780038i
$508$		0			0
$509$	17.0068	+	29.4566i	0.753813	+	1.30564i	0.945962	+	0.324277i	$0.105121\pi$
$509$	17.0068	+	29.4566i	0.753813	+	1.30564i	−0.192149	+	0.981366i	$0.561546\pi$
$510$		0			0
$511$	1.31754	+	0.760683i	0.0582846	+	0.0336506i
$512$		0			0
$513$	−16.1428	+	1.95619i	−0.712722	+	0.0863680i
$514$		0			0
$515$	9.17165	+	5.29525i	0.404151	+	0.233337i
$516$		0			0
$517$	−13.3960	+	7.73416i	−0.589153	+	0.340148i
$518$		0			0
$519$	−16.0167	+	0.644177i	−0.703053	+	0.0282762i
$520$		0			0
$521$		−	12.0788i		−	0.529182i	−0.964361	−	0.264591i	$-0.914763\pi$
$521$		−	12.0788i		−	0.529182i	0.964361	−	0.264591i	$-0.0852369\pi$
$522$		0			0
$523$	−5.27483			−0.230652			−0.115326	−	0.993328i	$-0.536791\pi$
$523$	−5.27483			−0.230652			−0.115326	+	0.993328i	$0.536791\pi$
$524$		0			0
$525$	−6.63013	−	3.48043i	−0.289363	−	0.151899i
$526$		0			0
$527$	−12.7151	−	22.0232i	−0.553877	−	0.959344i
$528$		0			0
$529$	7.79883	−	13.5080i	0.339080	−	0.587303i
$530$		0			0
$531$	1.69733	+	21.0668i	0.0736578	+	0.914223i
$532$		0			0
$533$	−19.0000	+	32.9089i	−0.822980	+	1.42544i
$534$		0			0
$535$	1.57390	−	0.908690i	0.0680455	−	0.0392861i
$536$		0			0
$537$	2.29158	−	1.44885i	0.0988889	−	0.0625226i
$538$		0			0
$539$		−	1.87809i		−	0.0808950i
$540$		0			0
$541$		−	23.6734i		−	1.01780i	−0.860826	−	0.508900i	$-0.830052\pi$
$541$		−	23.6734i		−	1.01780i	0.860826	−	0.508900i	$-0.169948\pi$
$542$		0			0
$543$	5.39186	−	3.40901i	0.231387	−	0.146295i
$544$		0			0
$545$	−6.92161	+	3.99619i	−0.296489	+	0.171178i
$546$		0			0
$547$	−10.5319	+	18.2418i	−0.450312	+	0.779964i	−0.998405	−	0.0564536i	$-0.982021\pi$
$547$	−10.5319	+	18.2418i	−0.450312	+	0.779964i	0.548093	+	0.836417i	$0.315354\pi$
$548$		0			0
$549$	8.69931	−	6.00266i	0.371278	−	0.256187i
$550$		0			0
$551$	7.98910	−	13.8375i	0.340347	−	0.589498i
$552$		0			0
$553$	−10.8922	−	18.8659i	−0.463184	−	0.802259i
$554$		0			0
$555$	14.3995	+	7.55892i	0.611226	+	0.320858i
$556$		0			0
$557$	−9.64427			−0.408641			−0.204321	−	0.978904i	$-0.565498\pi$
$557$	−9.64427			−0.408641			−0.204321	+	0.978904i	$0.565498\pi$
$558$		0			0
$559$		−	5.59535i		−	0.236658i
$560$		0			0
$561$	−10.1264	+	0.407276i	−0.427537	+	0.0171952i
$562$		0			0
$563$	36.8534	−	21.2773i	1.55319	−	0.896733i	0.555307	−	0.831645i	$-0.312601\pi$
$563$	36.8534	−	21.2773i	1.55319	−	0.896733i	0.997880	−	0.0650873i	$-0.0207326\pi$
$564$		0			0
$565$	13.1733	+	7.60561i	0.554205	+	0.319970i
$566$		0			0
$567$	−3.47387	−	21.4185i	−0.145889	−	0.899491i
$568$		0			0
$569$	−8.25996	−	4.76889i	−0.346275	−	0.199922i	0.316768	−	0.948503i	$-0.397402\pi$
$569$	−8.25996	−	4.76889i	−0.346275	−	0.199922i	−0.663044	+	0.748581i	$0.730736\pi$
$570$		0			0
$571$	−13.4455	−	23.2882i	−0.562675	−	0.974582i	−0.997262	−	0.0739518i	$-0.976439\pi$
$571$	−13.4455	−	23.2882i	−0.562675	−	0.974582i	0.434587	−	0.900630i	$-0.356894\pi$
$572$		0			0
$573$	−41.0780	+	1.65212i	−1.71606	+	0.0690185i
$574$		0			0
$575$	4.87880			0.203460
$576$		0			0
$577$	−8.52363			−0.354843			−0.177422	−	0.984135i	$-0.556776\pi$
$577$	−8.52363			−0.354843			−0.177422	+	0.984135i	$0.556776\pi$
$578$		0			0
$579$	20.6111	−	39.2636i	0.856569	−	1.63174i
$580$		0			0
$581$	−18.8667	−	32.6781i	−0.782724	−	1.35572i
$582$		0			0
$583$	−9.66924	−	5.58254i	−0.400459	−	0.231205i
$584$		0			0
$585$	−27.3412	+	18.8659i	−1.13042	+	0.780008i
$586$		0			0
$587$	19.4568	+	11.2334i	0.803067	+	0.463651i	0.844542	−	0.535489i	$-0.179873\pi$
$587$	19.4568	+	11.2334i	0.803067	+	0.463651i	−0.0414756	+	0.999140i	$0.513206\pi$
$588$		0			0
$589$	−18.6297	+	10.7559i	−0.767625	+	0.443189i
$590$		0			0
$591$	−5.33756	−	8.44216i	−0.219558	−	0.347264i
$592$		0			0
$593$		−	28.8424i		−	1.18442i	−0.805785	−	0.592208i	$-0.798257\pi$
$593$		−	28.8424i		−	1.18442i	0.805785	−	0.592208i	$-0.201743\pi$
$594$		0			0
$595$	15.9719			0.654783
$596$		0			0
$597$	−1.81773	+	1.14926i	−0.0743947	+	0.0470361i
$598$		0			0
$599$	−8.40225	−	14.5531i	−0.343307	−	0.594625i	0.641738	−	0.766924i	$-0.278214\pi$
$599$	−8.40225	−	14.5531i	−0.343307	−	0.594625i	−0.985045	+	0.172299i	$0.944880\pi$
$600$		0			0
$601$	14.8802	−	25.7732i	0.606974	−	1.05131i	−0.384762	−	0.923016i	$-0.625716\pi$
$601$	14.8802	−	25.7732i	0.606974	−	1.05131i	0.991736	−	0.128294i	$-0.0409502\pi$
$602$		0			0
$603$	6.20702	−	0.500092i	0.252769	−	0.0203653i
$604$		0			0
$605$	7.60926	−	13.1796i	0.309360	−	0.535828i
$606$		0			0
$607$	−20.9599	+	12.1012i	−0.850737	+	0.491173i	−0.860899	−	0.508775i	$-0.830098\pi$
$607$	−20.9599	+	12.1012i	−0.850737	+	0.491173i	0.0101625	+	0.999948i	$0.496765\pi$
$608$		0			0
$609$	18.8782	+	9.90993i	0.764981	+	0.401571i
$610$		0			0
$611$			60.4720i			2.44643i
$612$		0			0
$613$		−	38.3189i		−	1.54769i	−0.633377	−	0.773843i	$-0.718332\pi$
$613$		−	38.3189i		−	1.54769i	0.633377	−	0.773843i	$-0.281668\pi$
$614$		0			0
$615$	0.766020	+	19.0461i	0.0308889	+	0.768014i
$616$		0			0
$617$	−7.31357	+	4.22249i	−0.294433	+	0.169991i	−0.639939	−	0.768425i	$-0.721041\pi$
$617$	−7.31357	+	4.22249i	−0.294433	+	0.169991i	0.345506	+	0.938417i	$0.387707\pi$
$618$		0			0
$619$	−4.12431	+	7.14352i	−0.165770	+	0.287122i	−0.936929	−	0.349521i	$-0.886344\pi$
$619$	−4.12431	+	7.14352i	−0.165770	+	0.287122i	0.771158	+	0.636643i	$0.219678\pi$
$620$		0			0
$621$	8.49018	+	11.3040i	0.340699	+	0.453613i
$622$		0			0
$623$	−1.40318	+	2.43038i	−0.0562173	+	0.0973713i
$624$		0			0
$625$	6.40923	+	11.1011i	0.256369	+	0.444044i
$626$		0			0
$627$	0.344521	+	8.56609i	0.0137589	+	0.342097i
$628$		0			0
$629$	19.3972			0.773415
$630$		0			0
$631$			34.0954i			1.35732i	0.734454	+	0.678659i	$0.237439\pi$
$631$			34.0954i			1.35732i	−0.734454	+	0.678659i	$0.762561\pi$
$632$		0			0
$633$	−2.61147	+	4.97478i	−0.103797	+	0.197730i
$634$		0			0
$635$	−24.6735	+	14.2452i	−0.979138	+	0.565305i
$636$		0			0
$637$	−6.35854	−	3.67111i	−0.251935	−	0.145455i
$638$		0			0
$639$	4.26486	−	8.98432i	0.168715	−	0.355414i
$640$		0			0
$641$	20.9715	+	12.1079i	0.828324	+	0.478233i	0.853279	−	0.521455i	$-0.174611\pi$
$641$	20.9715	+	12.1079i	0.828324	+	0.478233i	−0.0249544	+	0.999689i	$0.507944\pi$
$642$		0			0
$643$	−11.3299	−	19.6240i	−0.446808	−	0.773895i	0.551368	−	0.834262i	$-0.314106\pi$
$643$	−11.3299	−	19.6240i	−0.446808	−	0.773895i	−0.998176	+	0.0603676i	$0.980773\pi$
$644$		0			0
$645$	−1.49992	−	2.37235i	−0.0590592	−	0.0934110i
$646$		0			0
$647$	−38.6020			−1.51760			−0.758800	−	0.651323i	$-0.774214\pi$
$647$	−38.6020			−1.51760			−0.758800	+	0.651323i	$0.774214\pi$
$648$		0			0
$649$	11.1428			0.437393
$650$		0			0
$651$	−15.3400	−	24.2625i	−0.601221	−	0.950921i
$652$		0			0
$653$	13.1416	+	22.7619i	0.514271	+	0.890743i	0.999863	+	0.0165576i	$0.00527069\pi$
$653$	13.1416	+	22.7619i	0.514271	+	0.890743i	−0.485592	+	0.874185i	$0.661396\pi$
$654$		0			0
$655$	−2.48501	−	1.43472i	−0.0970973	−	0.0560592i
$656$		0			0
$657$	−0.811823	+	1.71018i	−0.0316722	+	0.0667205i
$658$		0			0
$659$	−33.1862	−	19.1601i	−1.29275	−	0.746370i	−0.313610	−	0.949552i	$-0.601538\pi$
$659$	−33.1862	−	19.1601i	−1.29275	−	0.746370i	−0.979141	+	0.203182i	$0.934872\pi$
$660$		0			0
$661$	−38.7145	+	22.3518i	−1.50582	+	0.869385i	−0.505842	+	0.862626i	$0.668818\pi$
$661$	−38.7145	+	22.3518i	−1.50582	+	0.869385i	−0.999977	+	0.00675901i	$0.997849\pi$
$662$		0			0
$663$	−18.4152	+	35.0805i	−0.715189	+	1.36242i
$664$		0			0
$665$		−	13.5109i		−	0.523928i
$666$		0			0
$667$	−13.8915			−0.537882
$668$		0			0
$669$	0.974297	+	24.2247i	0.0376685	+	0.936580i
$670$		0			0
$671$	−2.78616	−	4.82576i	−0.107558	−	0.186297i
$672$		0			0
$673$	−12.8138	+	22.1942i	−0.493937	+	0.855524i	−0.999976	−	0.00698696i	$-0.997776\pi$
$673$	−12.8138	+	22.1942i	−0.493937	+	0.855524i	0.506039	+	0.862511i	$0.331109\pi$
$674$		0			0
$675$	3.65428	−	8.57125i	0.140653	−	0.329908i
$676$		0			0
$677$	11.1613	−	19.3320i	0.428964	−	0.742988i	−0.567817	−	0.823155i	$-0.692212\pi$
$677$	11.1613	−	19.3320i	0.428964	−	0.742988i	0.996781	+	0.0801666i	$0.0255452\pi$
$678$		0			0
$679$	−28.1027	+	16.2251i	−1.07848	+	0.622662i
$680$		0			0
$681$	−0.703562	−	17.4932i	−0.0269605	−	0.670340i
$682$		0			0
$683$			20.5229i			0.785288i	0.919691	+	0.392644i	$0.128440\pi$
$683$			20.5229i			0.785288i	−0.919691	+	0.392644i	$0.871560\pi$
$684$		0			0
$685$		−	21.9502i		−	0.838676i
$686$		0			0
$687$	17.5852	+	9.23119i	0.670917	+	0.352192i
$688$		0			0
$689$	−37.8010	+	21.8244i	−1.44010	+	0.831444i
$690$		0			0
$691$	5.97960	−	10.3570i	0.227475	−	0.393998i	−0.729584	−	0.683891i	$-0.760286\pi$
$691$	5.97960	−	10.3570i	0.227475	−	0.393998i	0.957059	+	0.289893i	$0.0936198\pi$
$692$		0			0
$693$	−11.4028	+	0.918709i	−0.433156	+	0.0348989i
$694$		0			0
$695$	−1.10837	+	1.91975i	−0.0420429	+	0.0728204i
$696$		0			0
$697$	11.3675	+	19.6891i	0.430576	+	0.745779i
$698$		0			0
$699$	−9.87985	+	6.24654i	−0.373690	+	0.236266i
$700$		0			0
$701$	−41.9171			−1.58319			−0.791593	−	0.611049i	$-0.790748\pi$
$701$	−41.9171			−1.58319			−0.791593	+	0.611049i	$0.790748\pi$
$702$		0			0
$703$		−	16.4084i		−	0.618853i
$704$		0			0
$705$	16.2104	+	25.6392i	0.610520	+	0.965630i
$706$		0			0
$707$	13.6988	−	7.90899i	0.515195	−	0.297448i
$708$		0			0
$709$	−4.41486	−	2.54892i	−0.165803	−	0.0957266i	0.414802	−	0.909912i	$-0.363851\pi$
$709$	−4.41486	−	2.54892i	−0.165803	−	0.0957266i	−0.580606	+	0.814185i	$0.697184\pi$
$710$		0			0
$711$	22.3112	−	15.3951i	0.836734	−	0.577360i
$712$		0			0
$713$	16.1968	+	9.35122i	0.606575	+	0.350206i
$714$		0			0
$715$	8.75666	+	15.1670i	0.327480	+	0.567213i
$716$		0			0
$717$	0.109147	−	0.207923i	0.00407619	−	0.00776503i
$718$		0			0
$719$	35.1676			1.31153			0.655765	−	0.754965i	$-0.272346\pi$
$719$	35.1676			1.31153			0.655765	+	0.754965i	$0.272346\pi$
$720$		0			0
$721$	14.2582			0.531003
$722$		0			0
$723$	33.6350	−	1.35277i	1.25090	−	0.0503101i
$724$		0			0
$725$	4.57787	+	7.92911i	0.170018	+	0.294480i
$726$		0			0
$727$	−19.9209	−	11.5013i	−0.738826	−	0.426561i	0.0828164	−	0.996565i	$-0.473609\pi$
$727$	−19.9209	−	11.5013i	−0.738826	−	0.426561i	−0.821642	+	0.570003i	$0.806942\pi$
$728$		0			0
$729$	26.2185	−	6.44905i	0.971056	−	0.238854i
$730$		0			0
$731$	−2.89915	−	1.67383i	−0.107229	−	0.0619087i
$732$		0			0
$733$	7.38177	−	4.26187i	0.272652	−	0.157416i	−0.357440	−	0.933936i	$-0.616350\pi$
$733$	7.38177	−	4.26187i	0.272652	−	0.157416i	0.630092	+	0.776520i	$0.283017\pi$
$734$		0			0
$735$	−3.68003	+	0.148008i	−0.135740	+	0.00545935i
$736$		0			0
$737$		−	3.28305i		−	0.120933i
$738$		0			0
$739$	−32.3956			−1.19169			−0.595846	−	0.803099i	$-0.703183\pi$
$739$	−32.3956			−1.19169			−0.595846	+	0.803099i	$0.703183\pi$
$740$		0			0
$741$	29.6752	+	15.5777i	1.09015	+	0.572263i
$742$		0			0
$743$	−2.22350	−	3.85122i	−0.0815725	−	0.141288i	0.822353	−	0.568978i	$-0.192661\pi$
$743$	−2.22350	−	3.85122i	−0.0815725	−	0.141288i	−0.903926	+	0.427690i	$0.859328\pi$
$744$		0			0
$745$	5.31821	−	9.21141i	0.194844	−	0.337480i
$746$		0			0
$747$	38.6458	−	26.6662i	1.41398	−	0.975666i
$748$		0			0
$749$	1.22339	−	2.11897i	0.0447016	−	0.0774255i
$750$		0			0
$751$	−32.3801	+	18.6946i	−1.18157	+	0.682177i	−0.956376	−	0.292138i	$-0.905633\pi$
$751$	−32.3801	+	18.6946i	−1.18157	+	0.682177i	−0.225189	+	0.974315i	$0.572300\pi$
$752$		0			0
$753$	−27.4990	+	17.3863i	−1.00212	+	0.633591i
$754$		0			0
$755$		−	24.7437i		−	0.900517i
$756$		0			0
$757$			46.7837i			1.70038i	0.526474	+	0.850191i	$0.323514\pi$
$757$			46.7837i			1.70038i	−0.526474	+	0.850191i	$0.676486\pi$
$758$		0			0
$759$	6.29988	−	3.98310i	0.228671	−	0.144577i
$760$		0			0
$761$	5.83226	−	3.36726i	0.211419	−	0.122063i	−0.390552	−	0.920581i	$-0.627716\pi$
$761$	5.83226	−	3.36726i	0.211419	−	0.122063i	0.601971	+	0.798518i	$0.294382\pi$
$762$		0			0
$763$	−5.38016	+	9.31870i	−0.194775	+	0.337360i
$764$		0			0
$765$	1.59608	+	19.8101i	0.0577063	+	0.716237i
$766$		0			0
$767$	21.7809	−	37.7255i	0.786461	−	1.36219i
$768$		0			0
$769$	−8.91160	−	15.4353i	−0.321361	−	0.556613i	0.659408	−	0.751785i	$-0.270807\pi$
$769$	−8.91160	−	15.4353i	−0.321361	−	0.556613i	−0.980769	+	0.195172i	$0.937473\pi$
$770$		0			0
$771$	−33.1036	−	17.3774i	−1.19220	−	0.625833i
$772$		0			0
$773$	18.9682			0.682237			0.341119	−	0.940020i	$-0.389194\pi$
$773$	18.9682			0.682237			0.341119	+	0.940020i	$0.389194\pi$
$774$		0			0
$775$		−	12.3266i		−	0.442783i
$776$		0			0
$777$	21.8775	−	0.879894i	0.784850	−	0.0315660i
$778$		0			0
$779$	16.6554	−	9.61597i	0.596740	−	0.344528i
$780$		0			0
$781$	−4.54081	−	2.62164i	−0.162483	−	0.0938096i
$782$		0			0
$783$	−10.4049	+	24.4052i	−0.371842	+	0.872169i
$784$		0			0
$785$	−8.93578	−	5.15907i	−0.318932	−	0.184135i
$786$		0			0
$787$	1.03810	+	1.79804i	0.0370041	+	0.0640931i	0.883934	−	0.467611i	$-0.154885\pi$
$787$	1.03810	+	1.79804i	0.0370041	+	0.0640931i	−0.846930	+	0.531704i	$0.821552\pi$
$788$		0			0
$789$	29.6632	−	1.19303i	1.05604	−	0.0424730i
$790$		0			0
$791$	20.4792			0.728155
$792$		0			0
$793$	−21.7844			−0.773588
$794$		0			0
$795$	−10.1767	+	19.3864i	−0.360931	+	0.687564i
$796$		0			0
$797$	−17.7593	−	30.7601i	−0.629068	−	1.08958i	−0.987739	−	0.156113i	$-0.950103\pi$
$797$	−17.7593	−	30.7601i	−0.629068	−	1.08958i	0.358671	−	0.933464i	$-0.383230\pi$
$798$		0			0
$799$	31.3327	+	18.0900i	1.10847	+	0.639977i
$800$		0			0
$801$	−3.15466	−	1.49752i	−0.111464	−	0.0529122i
$802$		0			0
$803$	0.864352	+	0.499034i	0.0305023	+	0.0176105i
$804$		0			0
$805$	−10.1727	+	5.87320i	−0.358540	+	0.207003i
$806$		0			0
$807$	18.6297	+	29.4657i	0.655798	+	1.03724i
$808$		0			0
$809$		−	41.7225i		−	1.46688i	−0.679752	−	0.733442i	$-0.737913\pi$
$809$		−	41.7225i		−	1.46688i	0.679752	−	0.733442i	$-0.262087\pi$
$810$		0			0
$811$	3.03064			0.106420			0.0532102	−	0.998583i	$-0.483055\pi$
$811$	3.03064			0.106420			0.0532102	+	0.998583i	$0.483055\pi$
$812$		0			0
$813$	9.08162	−	5.74186i	0.318506	−	0.201376i
$814$		0			0
$815$	−10.1078	−	17.5071i	−0.354059	−	0.613248i
$816$		0			0
$817$	−1.41592	+	2.45244i	−0.0495366	+	0.0858000i
$818$		0			0
$819$	−19.1787	+	40.4016i	−0.670157	+	1.41175i
$820$		0			0
$821$	25.9259	−	44.9049i	0.904819	−	1.56719i	0.0836589	−	0.996494i	$-0.473339\pi$
$821$	25.9259	−	44.9049i	0.904819	−	1.56719i	0.821160	−	0.570698i	$-0.193327\pi$
$822$		0			0
$823$	28.3812	−	16.3859i	0.989307	−	0.571177i	0.0842401	−	0.996445i	$-0.473154\pi$
$823$	28.3812	−	16.3859i	0.989307	−	0.571177i	0.905067	+	0.425269i	$0.139820\pi$
$824$		0			0
$825$	−4.34959	−	2.28328i	−0.151433	−	0.0794937i
$826$		0			0
$827$		−	52.8295i		−	1.83706i	−0.395350	−	0.918531i	$-0.629377\pi$
$827$		−	52.8295i		−	1.83706i	0.395350	−	0.918531i	$-0.370623\pi$
$828$		0			0
$829$			0.0144624i			0.000502300i	1.00000		0.000251150i	$7.99435e-5\pi$
$829$			0.0144624i			0.000502300i	−1.00000		0.000251150i	$0.999920\pi$
$830$		0			0
$831$	0.852444	+	21.1950i	0.0295710	+	0.735245i
$832$		0			0
$833$	−3.80427	+	2.19639i	−0.131810	+	0.0761006i
$834$		0			0
$835$	−0.677708	+	1.17382i	−0.0234531	+	0.0406219i
$836$		0			0
$837$	28.5602	−	21.4509i	0.987184	−	0.741453i
$838$		0			0
$839$	16.6802	−	28.8909i	0.575864	−	0.997425i	−0.420083	−	0.907486i	$-0.637999\pi$
$839$	16.6802	−	28.8909i	0.575864	−	0.997425i	0.995947	−	0.0899399i	$-0.0286675\pi$
$840$		0			0
$841$	1.46530	+	2.53797i	0.0505275	+	0.0875162i
$842$		0			0
$843$	1.21865	+	30.3002i	0.0419725	+	1.04359i
$844$		0			0
$845$	45.1869			1.55448
$846$		0			0
$847$		−	20.4890i		−	0.704010i
$848$		0			0
$849$	6.11348	−	11.6460i	0.209814	−	0.399690i
$850$		0			0
$851$	−12.3543	+	7.13276i	−0.423500	+	0.244508i
$852$		0			0
$853$	−32.7219	−	18.8920i	−1.12038	−	0.646850i	−0.178880	−	0.983871i	$-0.557247\pi$
$853$	−32.7219	−	18.8920i	−1.12038	−	0.646850i	−0.941497	+	0.337021i	$0.890581\pi$
$854$		0			0
$855$	16.7577	−	1.35015i	0.573101	−	0.0461741i
$856$		0			0
$857$	9.00665	+	5.19999i	0.307661	+	0.177628i	0.645879	−	0.763439i	$-0.276491\pi$
$857$	9.00665	+	5.19999i	0.307661	+	0.177628i	−0.338218	+	0.941068i	$0.609824\pi$
$858$		0			0
$859$	10.3547	+	17.9348i	0.353297	+	0.611929i	0.986825	−	0.161791i	$-0.0517271\pi$
$859$	10.3547	+	17.9348i	0.353297	+	0.611929i	−0.633528	+	0.773720i	$0.718394\pi$
$860$		0			0
$861$	13.7142	+	21.6911i	0.467380	+	0.739232i
$862$		0			0
$863$	4.67705			0.159209			0.0796043	−	0.996827i	$-0.474634\pi$
$863$	4.67705			0.159209			0.0796043	+	0.996827i	$0.474634\pi$
$864$		0			0
$865$	16.5729			0.563495
$866$		0			0
$867$	−3.06764	−	4.85194i	−0.104183	−	0.164780i
$868$		0			0
$869$	−7.14567	−	12.3767i	−0.242400	−	0.419849i
$870$		0			0
$871$	−11.1152	−	6.41739i	−0.376626	−	0.217445i
$872$		0			0
$873$	−22.9325	−	33.2348i	−0.776149	−	1.12483i
$874$		0			0
$875$	25.3995	+	14.6644i	0.858660	+	0.495748i
$876$		0			0
$877$	9.04467	−	5.22194i	0.305417	−	0.176333i	−0.339457	−	0.940622i	$-0.610243\pi$
$877$	9.04467	−	5.22194i	0.305417	−	0.176333i	0.644874	+	0.764289i	$0.276910\pi$
$878$		0			0
$879$	20.3136	−	38.6969i	0.685162	−	1.30522i
$880$		0			0
$881$			29.7734i			1.00309i	0.865131	+	0.501546i	$0.167235\pi$
$881$			29.7734i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$882$		0			0
$883$	52.9294			1.78122			0.890608	−	0.454772i	$-0.150279\pi$
$883$	52.9294			1.78122			0.890608	+	0.454772i	$0.150279\pi$
$884$		0			0
$885$	−0.878137	−	21.8338i	−0.0295183	−	0.733935i
$886$		0			0
$887$	22.4416	+	38.8700i	0.753515	+	1.30513i	0.946109	+	0.323848i	$0.104977\pi$
$887$	22.4416	+	38.8700i	0.753515	+	1.30513i	−0.192594	+	0.981278i	$0.561690\pi$
$888$		0			0
$889$	−19.1787	+	33.2184i	−0.643232	+	1.11411i
$890$		0			0
$891$	−2.27898	−	14.0512i	−0.0763486	−	0.470734i
$892$		0			0
$893$	15.3026	−	26.5048i	0.512081	−	0.886951i
$894$		0			0
$895$	−2.42753	+	1.40153i	−0.0811434	+	0.0468481i
$896$		0			0
$897$	−1.17098	−	29.1149i	−0.0390979	−	0.972119i
$898$		0			0
$899$			35.0978i			1.17058i
$900$		0			0
$901$			26.1148i			0.870009i
$902$		0			0
$903$	−3.34579	−	1.75635i	−0.111341	−	0.0584475i
$904$		0			0
$905$	−5.71174	+	3.29768i	−0.189865	+	0.109618i
$906$		0			0
$907$	8.19627	−	14.1964i	0.272153	−	0.471382i	−0.697260	−	0.716818i	$-0.745598\pi$
$907$	8.19627	−	14.1964i	0.272153	−	0.471382i	0.969413	+	0.245436i	$0.0789311\pi$
$908$		0			0
$909$	11.1786	+	16.2004i	0.370769	+	0.537335i
$910$		0			0
$911$	−13.4518	+	23.2991i	−0.445677	+	0.771935i	−0.998099	−	0.0616295i	$-0.980370\pi$
$911$	−13.4518	+	23.2991i	−0.445677	+	0.771935i	0.552422	+	0.833564i	$0.313704\pi$
$912$		0			0
$913$	−12.3772	−	21.4380i	−0.409626	−	0.709493i
$914$		0			0
$915$	−9.23629	+	5.83965i	−0.305342	+	0.193053i
$916$		0			0
$917$	−3.86319			−0.127574
$918$		0			0
$919$		−	22.2518i		−	0.734020i	−0.930217	−	0.367010i	$-0.880381\pi$
$919$		−	22.2518i		−	0.734020i	0.930217	−	0.367010i	$-0.119619\pi$
$920$		0			0
$921$	−27.3976	−	43.3335i	−0.902782	−	1.42789i
$922$		0			0
$923$	−17.7519	+	10.2491i	−0.584310	+	0.337352i
$924$		0			0
$925$	8.14257	+	4.70112i	0.267726	+	0.154572i
$926$		0			0
$927$	1.42483	+	17.6847i	0.0467976	+	0.580841i
$928$		0			0
$929$	−8.55489	−	4.93917i	−0.280677	−	0.162049i	0.353053	−	0.935603i	$-0.385144\pi$
$929$	−8.55489	−	4.93917i	−0.280677	−	0.162049i	−0.633730	+	0.773555i	$0.718477\pi$
$930$		0			0
$931$	1.85796	+	3.21809i	0.0608923	+	0.105469i
$932$		0			0
$933$	−16.6817	+	31.7782i	−0.546134	+	1.04037i
$934$		0			0
$935$	10.4781			0.342670
$936$		0			0
$937$	−2.11802			−0.0691926			−0.0345963	−	0.999401i	$-0.511015\pi$
$937$	−2.11802			−0.0691926			−0.0345963	+	0.999401i	$0.511015\pi$
$938$		0			0
$939$	−6.01161	+	0.241782i	−0.196181	+	0.00789026i
$940$		0			0
$941$	−3.56180	−	6.16922i	−0.116111	−	0.201111i	0.802112	−	0.597173i	$-0.203710\pi$
$941$	−3.56180	−	6.16922i	−0.116111	−	0.201111i	−0.918223	+	0.396063i	$0.870376\pi$
$942$		0			0
$943$	−14.4803	−	8.36018i	−0.471542	−	0.272245i
$944$		0			0
$945$	2.69879	+	22.2708i	0.0877918	+	0.724471i
$946$		0			0
$947$	−44.5581	−	25.7256i	−1.44794	−	0.835970i	−0.449584	−	0.893238i	$-0.648428\pi$
$947$	−44.5581	−	25.7256i	−1.44794	−	0.835970i	−0.998359	+	0.0572679i	$0.981761\pi$
$948$		0			0
$949$	3.37910	−	1.95093i	0.109690	−	0.0633297i
$950$		0			0
$951$	26.4577	−	1.06411i	0.857949	−	0.0345060i
$952$		0			0
$953$			45.3652i			1.46952i	0.678326	+	0.734761i	$0.262706\pi$
$953$			45.3652i			1.46952i	−0.678326	+	0.734761i	$0.737294\pi$
$954$		0			0
$955$	42.5046			1.37542
$956$		0			0
$957$	12.3847	+	6.50125i	0.400341	+	0.210156i
$958$		0			0
$959$	−14.7760	−	25.5928i	−0.477143	−	0.826436i
$960$		0			0
$961$	8.12641	−	14.0754i	0.262142	−	0.454044i
$962$		0			0
$963$	2.75044	+	1.30564i	0.0886318	+	0.0420735i
$964$		0			0
$965$	−22.9238	+	39.7052i	−0.737944	+	1.27816i
$966$		0			0
$967$	−2.55341	+	1.47421i	−0.0821121	+	0.0474075i	−0.540494	−	0.841348i	$-0.681763\pi$
$967$	−2.55341	+	1.47421i	−0.0821121	+	0.0474075i	0.458382	+	0.888755i	$0.348429\pi$
$968$		0			0
$969$	16.9486	−	10.7158i	0.544468	−	0.344240i
$970$		0			0
$971$		−	21.8052i		−	0.699763i	−0.936794	−	0.349882i	$-0.886222\pi$
$971$		−	21.8052i		−	0.699763i	0.936794	−	0.349882i	$-0.113778\pi$
$972$		0			0
$973$			2.98444i			0.0956768i
$974$		0			0
$975$	−16.2325	+	10.2630i	−0.519858	+	0.328680i
$976$		0			0
$977$	26.7110	−	15.4216i	0.854560	−	0.493381i	−0.00762657	−	0.999971i	$-0.502428\pi$
$977$	26.7110	−	15.4216i	0.854560	−	0.493381i	0.862187	+	0.506590i	$0.169094\pi$
$978$		0			0
$979$	−0.920536	+	1.59441i	−0.0294204	+	0.0509577i
$980$		0			0
$981$	−12.0958	−	5.74186i	−0.386188	−	0.183324i
$982$		0			0
$983$	−6.49316	+	11.2465i	−0.207100	+	0.358707i	−0.950800	−	0.309806i	$-0.899736\pi$
$983$	−6.49316	+	11.2465i	−0.207100	+	0.358707i	0.743700	+	0.668513i	$0.233069\pi$
$984$		0			0
$985$	5.16324	+	8.94300i	0.164515	+	0.284948i
$986$		0			0
$987$	36.1598	+	18.9818i	1.15098	+	0.604197i
$988$		0			0
$989$	2.46201			0.0782873
$990$		0			0
$991$			47.5865i			1.51163i	0.654783	+	0.755817i	$0.272760\pi$
$991$			47.5865i			1.51163i	−0.654783	+	0.755817i	$0.727240\pi$
$992$		0			0
$993$	10.7296	−	0.431535i	0.340493	−	0.0136943i
$994$		0			0
$995$	1.92557	−	1.11173i	0.0610447	−	0.0352442i
$996$		0			0
$997$	7.41748	+	4.28248i	0.234914	+	0.135628i	0.612837	−	0.790209i	$-0.290028\pi$
$997$	7.41748	+	4.28248i	0.234914	+	0.135628i	−0.377923	+	0.925837i	$0.623362\pi$
$998$		0			0
$999$	3.27757	+	27.0470i	0.103698	+	0.855729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.p.b.47.2		16
3.2	odd	2		864.2.p.b.143.3		16
4.3	odd	2		72.2.l.b.11.3	✓	16
8.3	odd	2	inner	288.2.p.b.47.1		16
8.5	even	2		72.2.l.b.11.7	yes	16
9.2	odd	6		2592.2.f.b.1295.11		16
9.4	even	3		864.2.p.b.719.6		16
9.5	odd	6	inner	288.2.p.b.239.1		16
9.7	even	3		2592.2.f.b.1295.5		16
12.11	even	2		216.2.l.b.35.6		16
24.5	odd	2		216.2.l.b.35.2		16
24.11	even	2		864.2.p.b.143.6		16
36.7	odd	6		648.2.f.b.323.16		16
36.11	even	6		648.2.f.b.323.1		16
36.23	even	6		72.2.l.b.59.7	yes	16
36.31	odd	6		216.2.l.b.179.2		16
72.5	odd	6		72.2.l.b.59.3	yes	16
72.11	even	6		2592.2.f.b.1295.6		16
72.13	even	6		216.2.l.b.179.6		16
72.29	odd	6		648.2.f.b.323.15		16
72.43	odd	6		2592.2.f.b.1295.12		16
72.59	even	6	inner	288.2.p.b.239.2		16
72.61	even	6		648.2.f.b.323.2		16
72.67	odd	6		864.2.p.b.719.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.3	✓	16	4.3	odd	2
72.2.l.b.11.7	yes	16	8.5	even	2
72.2.l.b.59.3	yes	16	72.5	odd	6
72.2.l.b.59.7	yes	16	36.23	even	6
216.2.l.b.35.2		16	24.5	odd	2
216.2.l.b.35.6		16	12.11	even	2
216.2.l.b.179.2		16	36.31	odd	6
216.2.l.b.179.6		16	72.13	even	6
288.2.p.b.47.1		16	8.3	odd	2	inner
288.2.p.b.47.2		16	1.1	even	1	trivial
288.2.p.b.239.1		16	9.5	odd	6	inner
288.2.p.b.239.2		16	72.59	even	6	inner
648.2.f.b.323.1		16	36.11	even	6
648.2.f.b.323.2		16	72.61	even	6
648.2.f.b.323.15		16	72.29	odd	6
648.2.f.b.323.16		16	36.7	odd	6
864.2.p.b.143.3		16	3.2	odd	2
864.2.p.b.143.6		16	24.11	even	2
864.2.p.b.719.3		16	72.67	odd	6
864.2.p.b.719.6		16	9.4	even	3
2592.2.f.b.1295.5		16	9.7	even	3
2592.2.f.b.1295.6		16	72.11	even	6
2592.2.f.b.1295.11		16	9.2	odd	6
2592.2.f.b.1295.12		16	72.43	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.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.925606 - 1.46399i) q^{3} +(0.895377 + 1.55084i) q^{5} +(2.08793 + 1.20546i) q^{7} +(-1.28651 + 2.71015i) q^{9} +O(q^{10})\)	\(q+(-0.925606 - 1.46399i) q^{3} +(0.895377 + 1.55084i) q^{5} +(2.08793 + 1.20546i) q^{7} +(-1.28651 + 2.71015i) q^{9} +(1.36975 + 0.790826i) q^{11} +(5.35491 - 3.09166i) q^{13} +(1.44164 - 2.74629i) q^{15} -3.69943i q^{17} -3.12941 q^{19} +(-0.167814 - 4.17248i) q^{21} +(1.36036 + 2.35622i) q^{23} +(0.896599 - 1.55296i) q^{25} +(5.15842 - 0.625100i) q^{27} +(-2.55291 + 4.42177i) q^{29} +(5.95312 - 3.43703i) q^{31} +(-0.110092 - 2.73729i) q^{33} +4.31738i q^{35} +5.24328i q^{37} +(-9.48268 - 4.97786i) q^{39} +(-5.32220 + 3.07278i) q^{41} +(0.452455 - 0.783675i) q^{43} +(-5.35491 + 0.431438i) q^{45} +(-4.88993 + 8.46960i) q^{47} +(-0.593711 - 1.02834i) q^{49} +(-5.41592 + 3.42422i) q^{51} -7.05913 q^{53} +2.83235i q^{55} +(2.89660 + 4.58141i) q^{57} +(6.10118 - 3.52252i) q^{59} +(-3.05109 - 1.76155i) q^{61} +(-5.95312 + 4.10775i) q^{63} +(9.58933 + 5.53640i) q^{65} +(-1.03786 - 1.79762i) q^{67} +(2.19031 - 4.17248i) q^{69} -3.31507 q^{71} +0.631029 q^{73} +(-3.10340 + 0.124816i) q^{75} +(1.90662 + 3.30237i) q^{77} +(-7.82515 - 4.51785i) q^{79} +(-5.68980 - 6.97325i) q^{81} +(-13.5542 - 7.82551i) q^{83} +(5.73722 - 3.31239i) q^{85} +(8.83640 - 0.355393i) q^{87} +1.16402i q^{89} +14.9075 q^{91} +(-10.5420 - 5.53394i) q^{93} +(-2.80200 - 4.85321i) q^{95} +(-6.72981 + 11.6564i) q^{97} +(-3.90545 + 2.69482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^3 - 6 * q^9	\( 16 q + 6 q^{3} - 6 q^{9} - 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{27} + 12 q^{33} - 36 q^{41} - 8 q^{43} + 10 q^{49} - 18 q^{51} + 18 q^{57} - 12 q^{59} - 6 q^{65} + 16 q^{67} - 4 q^{73} - 78 q^{75} - 6 q^{81} - 54 q^{83} + 36 q^{91} + 8 q^{97} + 6 q^{99}+O(q^{100}) \) 16 * q + 6 * q^3 - 6 * q^9 - 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^27 + 12 * q^33 - 36 * q^41 - 8 * q^43 + 10 * q^49 - 18 * q^51 + 18 * q^57 - 12 * q^59 - 6 * q^65 + 16 * q^67 - 4 * q^73 - 78 * q^75 - 6 * q^81 - 54 * q^83 + 36 * q^91 + 8 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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