LMFDB - Embedded newform 1344.2.s.d.239.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.6
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.d.911.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29441 - 1.15087i) q^{3} +(0.186466 + 0.186466i) q^{5} -1.00000 q^{7} +(0.350987 + 2.97940i) q^{9} +O(q^{10})$	\(q+(-1.29441 - 1.15087i) q^{3} +(0.186466 + 0.186466i) q^{5} -1.00000 q^{7} +(0.350987 + 2.97940i) q^{9} +(-4.29691 + 4.29691i) q^{11} +(2.73763 + 2.73763i) q^{13} +(-0.0267646 - 0.455961i) q^{15} -4.98546i q^{17} +(3.09905 - 3.09905i) q^{19} +(1.29441 + 1.15087i) q^{21} -3.55879i q^{23} -4.93046i q^{25} +(2.97458 - 4.26050i) q^{27} +(3.75624 - 3.75624i) q^{29} -6.58926i q^{31} +(10.5072 - 0.616763i) q^{33} +(-0.186466 - 0.186466i) q^{35} +(-4.82165 + 4.82165i) q^{37} +(-0.392949 - 6.69427i) q^{39} -10.5690 q^{41} +(5.79966 + 5.79966i) q^{43} +(-0.490108 + 0.621002i) q^{45} -3.22550 q^{47} +1.00000 q^{49} +(-5.73763 + 6.45322i) q^{51} +(-7.95980 - 7.95980i) q^{53} -1.60245 q^{55} +(-7.57805 + 0.444827i) q^{57} +(3.18645 - 3.18645i) q^{59} +(-3.17662 - 3.17662i) q^{61} +(-0.350987 - 2.97940i) q^{63} +1.02095i q^{65} +(-2.39721 + 2.39721i) q^{67} +(-4.09571 + 4.60652i) q^{69} -9.06458i q^{71} +2.32026i q^{73} +(-5.67433 + 6.38203i) q^{75} +(4.29691 - 4.29691i) q^{77} -6.89467i q^{79} +(-8.75362 + 2.09146i) q^{81} +(1.12559 + 1.12559i) q^{83} +(0.929618 - 0.929618i) q^{85} +(-9.18506 + 0.539157i) q^{87} +7.81580 q^{89} +(-2.73763 - 2.73763i) q^{91} +(-7.58340 + 8.52920i) q^{93} +1.15573 q^{95} +12.6744 q^{97} +(-14.3104 - 11.2940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{7}+O(q^{10}) $ 48 * q - 48 * q^7	$ 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) $ 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.29441	−	1.15087i	−0.747327	−	0.664456i
$3$	−1.29441	−	1.15087i	−0.747327	−	0.664456i
$4$		0			0
$5$	0.186466	+	0.186466i	0.0833900	+	0.0833900i	0.747571	−	0.664181i	$-0.231220\pi$
$5$	0.186466	+	0.186466i	0.0833900	+	0.0833900i	−0.664181	+	0.747571i	$0.731220\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$		0			0
$9$	0.350987	+	2.97940i	0.116996	+	0.993132i
$10$		0			0
$11$	−4.29691	+	4.29691i	−1.29557	+	1.29557i	−0.364276	+	0.931291i	$0.618684\pi$
$11$	−4.29691	+	4.29691i	−1.29557	+	1.29557i	−0.931291	+	0.364276i	$0.881316\pi$
$12$		0			0
$13$	2.73763	+	2.73763i	0.759281	+	0.759281i	0.976192	−	0.216910i	$-0.0695979\pi$
$13$	2.73763	+	2.73763i	0.759281	+	0.759281i	−0.216910	+	0.976192i	$0.569598\pi$
$14$		0			0
$15$	−0.0267646	−	0.455961i	−0.00691060	−	0.117729i
$16$		0			0
$17$		−	4.98546i		−	1.20915i	−0.796547	−	0.604576i	$-0.793343\pi$
$17$		−	4.98546i		−	1.20915i	0.796547	−	0.604576i	$-0.206657\pi$
$18$		0			0
$19$	3.09905	−	3.09905i	0.710971	−	0.710971i	−0.255767	−	0.966738i	$-0.582328\pi$
$19$	3.09905	−	3.09905i	0.710971	−	0.710971i	0.966738	+	0.255767i	$0.0823281\pi$
$20$		0			0
$21$	1.29441	+	1.15087i	0.282463	+	0.251141i
$22$		0			0
$23$		−	3.55879i		−	0.742058i	−0.928621	−	0.371029i	$-0.879005\pi$
$23$		−	3.55879i		−	0.742058i	0.928621	−	0.371029i	$-0.120995\pi$
$24$		0			0
$25$		−	4.93046i		−	0.986092i
$26$		0			0
$27$	2.97458	−	4.26050i	0.572459	−	0.819933i
$28$		0			0
$29$	3.75624	−	3.75624i	0.697516	−	0.697516i	−0.266358	−	0.963874i	$-0.585820\pi$
$29$	3.75624	−	3.75624i	0.697516	−	0.697516i	0.963874	+	0.266358i	$0.0858203\pi$
$30$		0			0
$31$		−	6.58926i		−	1.18347i	−0.806134	−	0.591733i	$-0.798444\pi$
$31$		−	6.58926i		−	1.18347i	0.806134	−	0.591733i	$-0.201556\pi$
$32$		0			0
$33$	10.5072	−	0.616763i	1.82906	−	0.107365i
$34$		0			0
$35$	−0.186466	−	0.186466i	−0.0315185	−	0.0315185i
$36$		0			0
$37$	−4.82165	+	4.82165i	−0.792675	+	0.792675i	−0.981928	−	0.189253i	$-0.939393\pi$
$37$	−4.82165	+	4.82165i	−0.792675	+	0.792675i	0.189253	+	0.981928i	$0.439393\pi$
$38$		0			0
$39$	−0.392949	−	6.69427i	−0.0629223	−	1.07194i
$40$		0			0
$41$	−10.5690			−1.65060			−0.825298	−	0.564698i	$-0.808993\pi$
$41$	−10.5690			−1.65060			−0.825298	+	0.564698i	$0.808993\pi$
$42$		0			0
$43$	5.79966	+	5.79966i	0.884439	+	0.884439i	0.993982	−	0.109543i	$-0.0349387\pi$
$43$	5.79966	+	5.79966i	0.884439	+	0.884439i	−0.109543	+	0.993982i	$0.534939\pi$
$44$		0			0
$45$	−0.490108	+	0.621002i	−0.0730610	+	0.0925736i
$46$		0			0
$47$	−3.22550			−0.470487			−0.235244	−	0.971936i	$-0.575589\pi$
$47$	−3.22550			−0.470487			−0.235244	+	0.971936i	$0.575589\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−5.73763	+	6.45322i	−0.803429	+	0.903632i
$52$		0			0
$53$	−7.95980	−	7.95980i	−1.09336	−	1.09336i	−0.995167	−	0.0981957i	$-0.968693\pi$
$53$	−7.95980	−	7.95980i	−1.09336	−	1.09336i	−0.0981957	−	0.995167i	$-0.531307\pi$
$54$		0			0
$55$	−1.60245			−0.216075
$56$		0			0
$57$	−7.57805	+	0.444827i	−1.00374	+	0.0589188i
$58$		0			0
$59$	3.18645	−	3.18645i	0.414840	−	0.414840i	−0.468580	−	0.883421i	$-0.655234\pi$
$59$	3.18645	−	3.18645i	0.414840	−	0.414840i	0.883421	+	0.468580i	$0.155234\pi$
$60$		0			0
$61$	−3.17662	−	3.17662i	−0.406725	−	0.406725i	0.473870	−	0.880595i	$-0.342857\pi$
$61$	−3.17662	−	3.17662i	−0.406725	−	0.406725i	−0.880595	+	0.473870i	$0.842857\pi$
$62$		0			0
$63$	−0.350987	−	2.97940i	−0.0442202	−	0.375369i
$64$		0			0
$65$			1.02095i			0.126633i
$66$		0			0
$67$	−2.39721	+	2.39721i	−0.292865	+	0.292865i	−0.838211	−	0.545346i	$-0.816398\pi$
$67$	−2.39721	+	2.39721i	−0.292865	+	0.292865i	0.545346	+	0.838211i	$0.316398\pi$
$68$		0			0
$69$	−4.09571	+	4.60652i	−0.493065	+	0.554560i
$70$		0			0
$71$		−	9.06458i		−	1.07577i	−0.843019	−	0.537884i	$-0.819224\pi$
$71$		−	9.06458i		−	1.07577i	0.843019	−	0.537884i	$-0.180776\pi$
$72$		0			0
$73$			2.32026i			0.271566i	0.990739	+	0.135783i	$0.0433549\pi$
$73$			2.32026i			0.271566i	−0.990739	+	0.135783i	$0.956645\pi$
$74$		0			0
$75$	−5.67433	+	6.38203i	−0.655215	+	0.736933i
$76$		0			0
$77$	4.29691	−	4.29691i	0.489678	−	0.489678i
$78$		0			0
$79$		−	6.89467i		−	0.775711i	−0.921720	−	0.387855i	$-0.873216\pi$
$79$		−	6.89467i		−	0.775711i	0.921720	−	0.387855i	$-0.126784\pi$
$80$		0			0
$81$	−8.75362	+	2.09146i	−0.972624	+	0.232384i
$82$		0			0
$83$	1.12559	+	1.12559i	0.123550	+	0.123550i	0.766178	−	0.642628i	$-0.222156\pi$
$83$	1.12559	+	1.12559i	0.123550	+	0.123550i	−0.642628	+	0.766178i	$0.722156\pi$
$84$		0			0
$85$	0.929618	−	0.929618i	0.100831	−	0.100831i
$86$		0			0
$87$	−9.18506	+	0.539157i	−0.984742	+	0.0578037i
$88$		0			0
$89$	7.81580			0.828474			0.414237	−	0.910169i	$-0.364049\pi$
$89$	7.81580			0.828474			0.414237	+	0.910169i	$0.364049\pi$
$90$		0			0
$91$	−2.73763	−	2.73763i	−0.286981	−	0.286981i
$92$		0			0
$93$	−7.58340	+	8.52920i	−0.786362	+	0.884437i
$94$		0			0
$95$	1.15573			0.118576
$96$		0			0
$97$	12.6744			1.28689			0.643445	−	0.765493i	$-0.277505\pi$
$97$	12.6744			1.28689			0.643445	+	0.765493i	$0.277505\pi$
$98$		0			0
$99$	−14.3104	−	11.2940i	−1.43825	−	1.13509i
$100$		0			0
$101$	1.08794	+	1.08794i	0.108254	+	0.108254i	0.759159	−	0.650905i	$-0.225611\pi$
$101$	1.08794	+	1.08794i	0.108254	+	0.108254i	−0.650905	+	0.759159i	$0.725611\pi$
$102$		0			0
$103$	4.90252			0.483060			0.241530	−	0.970393i	$-0.422351\pi$
$103$	4.90252			0.483060			0.241530	+	0.970393i	$0.422351\pi$
$104$		0			0
$105$	0.0267646	+	0.455961i	0.00261196	+	0.0444972i
$106$		0			0
$107$	3.37243	−	3.37243i	0.326025	−	0.326025i	−0.525048	−	0.851073i	$-0.675953\pi$
$107$	3.37243	−	3.37243i	0.326025	−	0.326025i	0.851073	+	0.525048i	$0.175953\pi$
$108$		0			0
$109$	−12.5591	−	12.5591i	−1.20295	−	1.20295i	−0.973266	−	0.229679i	$-0.926232\pi$
$109$	−12.5591	−	12.5591i	−1.20295	−	1.20295i	−0.229679	−	0.973266i	$-0.573768\pi$
$110$		0			0
$111$	11.7903	−	0.692083i	1.11909	−	0.0656896i
$112$		0			0
$113$		−	4.22031i		−	0.397014i	−0.980100	−	0.198507i	$-0.936391\pi$
$113$		−	4.22031i		−	0.397014i	0.980100	−	0.198507i	$-0.0636092\pi$
$114$		0			0
$115$	0.663592	−	0.663592i	0.0618802	−	0.0618802i
$116$		0			0
$117$	−7.19561	+	9.11735i	−0.665234	+	0.842900i
$118$		0			0
$119$			4.98546i			0.457016i
$120$		0			0
$121$		−	25.9269i		−	2.35699i
$122$		0			0
$123$	13.6806	+	12.1635i	1.23353	+	1.09675i
$124$		0			0
$125$	1.85169	−	1.85169i	0.165620	−	0.165620i
$126$		0			0
$127$		−	12.8142i		−	1.13708i	−0.822657	−	0.568538i	$-0.807509\pi$
$127$		−	12.8142i		−	1.13708i	0.822657	−	0.568538i	$-0.192491\pi$
$128$		0			0
$129$	−0.832462	−	14.1818i	−0.0732942	−	1.24864i
$130$		0			0
$131$	4.94838	+	4.94838i	0.432342	+	0.432342i	0.889424	−	0.457082i	$-0.151106\pi$
$131$	4.94838	+	4.94838i	0.432342	+	0.432342i	−0.457082	+	0.889424i	$0.651106\pi$
$132$		0			0
$133$	−3.09905	+	3.09905i	−0.268722	+	0.268722i
$134$		0			0
$135$	1.34909	−	0.239779i	0.116112	−	0.0206369i
$136$		0			0
$137$	5.07482			0.433571			0.216786	−	0.976219i	$-0.430443\pi$
$137$	5.07482			0.433571			0.216786	+	0.976219i	$0.430443\pi$
$138$		0			0
$139$	−2.63077	−	2.63077i	−0.223139	−	0.223139i	0.586680	−	0.809819i	$-0.300435\pi$
$139$	−2.63077	−	2.63077i	−0.223139	−	0.223139i	−0.809819	+	0.586680i	$0.800435\pi$
$140$		0			0
$141$	4.17511	+	3.71214i	0.351608	+	0.312618i
$142$		0			0
$143$	−23.5267			−1.96740
$144$		0			0
$145$	1.40082			0.116332
$146$		0			0
$147$	−1.29441	−	1.15087i	−0.106761	−	0.0949223i
$148$		0			0
$149$	0.771487	+	0.771487i	0.0632027	+	0.0632027i	0.738002	−	0.674799i	$-0.235770\pi$
$149$	0.771487	+	0.771487i	0.0632027	+	0.0632027i	−0.674799	+	0.738002i	$0.735770\pi$
$150$		0			0
$151$	−4.82092			−0.392321			−0.196160	−	0.980572i	$-0.562847\pi$
$151$	−4.82092			−0.392321			−0.196160	+	0.980572i	$0.562847\pi$
$152$		0			0
$153$	14.8537	−	1.74983i	1.20085	−	0.141465i
$154$		0			0
$155$	1.22867	−	1.22867i	0.0986893	−	0.0986893i
$156$		0			0
$157$	−5.25487	−	5.25487i	−0.419384	−	0.419384i	0.465607	−	0.884991i	$-0.345836\pi$
$157$	−5.25487	−	5.25487i	−0.419384	−	0.419384i	−0.884991	+	0.465607i	$0.845836\pi$
$158$		0			0
$159$	1.14252	+	19.4639i	0.0906079	+	1.54359i
$160$		0			0
$161$			3.55879i			0.280472i
$162$		0			0
$163$	−2.10862	+	2.10862i	−0.165160	+	0.165160i	−0.784848	−	0.619688i	$-0.787259\pi$
$163$	−2.10862	+	2.10862i	−0.165160	+	0.165160i	0.619688	+	0.784848i	$0.287259\pi$
$164$		0			0
$165$	2.07423	+	1.84422i	0.161478	+	0.143572i
$166$		0			0
$167$			17.3053i			1.33913i	0.742755	+	0.669563i	$0.233519\pi$
$167$			17.3053i			1.33913i	−0.742755	+	0.669563i	$0.766481\pi$
$168$		0			0
$169$			1.98921i			0.153017i
$170$		0			0
$171$	10.3210	+	8.14558i	0.789269	+	0.622908i
$172$		0			0
$173$	−1.96496	+	1.96496i	−0.149393	+	0.149393i	−0.777847	−	0.628454i	$-0.783688\pi$
$173$	−1.96496	+	1.96496i	−0.149393	+	0.149393i	0.628454	+	0.777847i	$0.283688\pi$
$174$		0			0
$175$			4.93046i			0.372708i
$176$		0			0
$177$	−7.79176	+	0.457372i	−0.585665	+	0.0343782i
$178$		0			0
$179$	−3.67595	−	3.67595i	−0.274754	−	0.274754i	0.556257	−	0.831010i	$-0.312237\pi$
$179$	−3.67595	−	3.67595i	−0.274754	−	0.274754i	−0.831010	+	0.556257i	$0.812237\pi$
$180$		0			0
$181$	−1.91774	+	1.91774i	−0.142544	+	0.142544i	−0.774778	−	0.632233i	$-0.782138\pi$
$181$	−1.91774	+	1.91774i	−0.142544	+	0.142544i	0.632233	+	0.774778i	$0.282138\pi$
$182$		0			0
$183$	0.455961	+	7.76773i	0.0337056	+	0.574207i
$184$		0			0
$185$	−1.79815			−0.132202
$186$		0			0
$187$	21.4221	+	21.4221i	1.56654	+	1.56654i
$188$		0			0
$189$	−2.97458	+	4.26050i	−0.216369	+	0.309906i
$190$		0			0
$191$	2.62732			0.190106			0.0950531	−	0.995472i	$-0.469698\pi$
$191$	2.62732			0.190106			0.0950531	+	0.995472i	$0.469698\pi$
$192$		0			0
$193$	3.55423			0.255839			0.127920	−	0.991785i	$-0.459170\pi$
$193$	3.55423			0.255839			0.127920	+	0.991785i	$0.459170\pi$
$194$		0			0
$195$	1.17498	−	1.32152i	0.0841421	−	0.0946362i
$196$		0			0
$197$	−16.7933	−	16.7933i	−1.19648	−	1.19648i	−0.975215	−	0.221261i	$-0.928983\pi$
$197$	−16.7933	−	16.7933i	−1.19648	−	1.19648i	−0.221261	−	0.975215i	$-0.571017\pi$
$198$		0			0
$199$	−11.8244			−0.838212			−0.419106	−	0.907937i	$-0.637656\pi$
$199$	−11.8244			−0.838212			−0.419106	+	0.907937i	$0.637656\pi$
$200$		0			0
$201$	5.86184	−	0.344086i	0.413462	−	0.0242700i
$202$		0			0
$203$	−3.75624	+	3.75624i	−0.263636	+	0.263636i
$204$		0			0
$205$	−1.97075	−	1.97075i	−0.137643	−	0.137643i
$206$		0			0
$207$	10.6030	−	1.24909i	0.736962	−	0.0868176i
$208$		0			0
$209$			26.6327i			1.84222i
$210$		0			0
$211$	3.52746	−	3.52746i	0.242840	−	0.242840i	−0.575184	−	0.818024i	$-0.695069\pi$
$211$	3.52746	−	3.52746i	0.242840	−	0.242840i	0.818024	+	0.575184i	$0.195069\pi$
$212$		0			0
$213$	−10.4322	+	11.7333i	−0.714800	+	0.803950i
$214$		0			0
$215$			2.16287i			0.147507i
$216$		0			0
$217$			6.58926i			0.447308i
$218$		0			0
$219$	2.67032	−	3.00336i	0.180443	−	0.202948i
$220$		0			0
$221$	13.6483	−	13.6483i	0.918087	−	0.918087i
$222$		0			0
$223$		−	21.2549i		−	1.42333i	−0.702516	−	0.711667i	$-0.747940\pi$
$223$		−	21.2549i		−	1.42333i	0.702516	−	0.711667i	$-0.252060\pi$
$224$		0			0
$225$	14.6898	−	1.73053i	0.979320	−	0.115368i
$226$		0			0
$227$	12.5784	+	12.5784i	0.834858	+	0.834858i	0.988177	−	0.153319i	$-0.0489962\pi$
$227$	12.5784	+	12.5784i	0.834858	+	0.834858i	−0.153319	+	0.988177i	$0.548996\pi$
$228$		0			0
$229$	17.0628	−	17.0628i	1.12754	−	1.12754i	0.136968	−	0.990575i	$-0.456264\pi$
$229$	17.0628	−	17.0628i	1.12754	−	1.12754i	0.990575	−	0.136968i	$-0.0437357\pi$
$230$		0			0
$231$	−10.5072	+	0.616763i	−0.691320	+	0.0405800i
$232$		0			0
$233$	4.85495			0.318058			0.159029	−	0.987274i	$-0.449164\pi$
$233$	4.85495			0.318058			0.159029	+	0.987274i	$0.449164\pi$
$234$		0			0
$235$	−0.601445	−	0.601445i	−0.0392339	−	0.0392339i
$236$		0			0
$237$	−7.93488	+	8.92451i	−0.515426	+	0.579710i
$238$		0			0
$239$	−4.50251			−0.291243			−0.145622	−	0.989340i	$-0.546518\pi$
$239$	−4.50251			−0.291243			−0.145622	+	0.989340i	$0.546518\pi$
$240$		0			0
$241$	23.4318			1.50937			0.754686	−	0.656086i	$-0.227789\pi$
$241$	23.4318			1.50937			0.754686	+	0.656086i	$0.227789\pi$
$242$		0			0
$243$	13.7378	+	7.36709i	0.881278	+	0.472599i
$244$		0			0
$245$	0.186466	+	0.186466i	0.0119129	+	0.0119129i
$246$		0			0
$247$	16.9681			1.07965
$248$		0			0
$249$	−0.161563	−	2.75239i	−0.0102387	−	0.174425i
$250$		0			0
$251$	1.95980	−	1.95980i	0.123701	−	0.123701i	−0.642546	−	0.766247i	$-0.722122\pi$
$251$	1.95980	−	1.95980i	0.123701	−	0.123701i	0.766247	+	0.642546i	$0.222122\pi$
$252$		0			0
$253$	15.2918	+	15.2918i	0.961386	+	0.961386i
$254$		0			0
$255$	−2.27318	+	0.133434i	−0.142352	+	0.00835596i
$256$		0			0
$257$			26.9134i			1.67881i	0.543506	+	0.839405i	$0.317096\pi$
$257$			26.9134i			1.67881i	−0.543506	+	0.839405i	$0.682904\pi$
$258$		0			0
$259$	4.82165	−	4.82165i	0.299603	−	0.299603i
$260$		0			0
$261$	12.5097	+	9.87294i	0.774332	+	0.611120i
$262$		0			0
$263$			20.0669i			1.23738i	0.785635	+	0.618690i	$0.212336\pi$
$263$			20.0669i			1.23738i	−0.785635	+	0.618690i	$0.787664\pi$
$264$		0			0
$265$		−	2.96846i		−	0.182351i
$266$		0			0
$267$	−10.1168	−	8.99499i	−0.619141	−	0.550485i
$268$		0			0
$269$	−6.39355	+	6.39355i	−0.389822	+	0.389822i	−0.874624	−	0.484802i	$-0.838892\pi$
$269$	−6.39355	+	6.39355i	−0.389822	+	0.389822i	0.484802	+	0.874624i	$0.338892\pi$
$270$		0			0
$271$		−	15.5182i		−	0.942663i	−0.881956	−	0.471331i	$-0.843774\pi$
$271$		−	15.5182i		−	0.942663i	0.881956	−	0.471331i	$-0.156226\pi$
$272$		0			0
$273$	0.392949	+	6.69427i	0.0237824	+	0.405156i
$274$		0			0
$275$	21.1858	+	21.1858i	1.27755	+	1.27755i
$276$		0			0
$277$	−6.16207	+	6.16207i	−0.370243	+	0.370243i	−0.867566	−	0.497323i	$-0.834316\pi$
$277$	−6.16207	+	6.16207i	−0.370243	+	0.370243i	0.497323	+	0.867566i	$0.334316\pi$
$278$		0			0
$279$	19.6320	−	2.31275i	1.17534	−	0.138460i
$280$		0			0
$281$	−9.59320			−0.572282			−0.286141	−	0.958188i	$-0.592373\pi$
$281$	−9.59320			−0.572282			−0.286141	+	0.958188i	$0.592373\pi$
$282$		0			0
$283$	−20.3342	−	20.3342i	−1.20874	−	1.20874i	−0.971434	−	0.237309i	$-0.923735\pi$
$283$	−20.3342	−	20.3342i	−1.20874	−	1.20874i	−0.237309	−	0.971434i	$-0.576265\pi$
$284$		0			0
$285$	−1.49599	−	1.33010i	−0.0886149	−	0.0787884i
$286$		0			0
$287$	10.5690			0.623866
$288$		0			0
$289$	−7.85482			−0.462048
$290$		0			0
$291$	−16.4058	−	14.5866i	−0.961727	−	0.855082i
$292$		0			0
$293$	8.88152	+	8.88152i	0.518864	+	0.518864i	0.917228	−	0.398364i	$-0.130422\pi$
$293$	8.88152	+	8.88152i	0.518864	+	0.518864i	−0.398364	+	0.917228i	$0.630422\pi$
$294$		0			0
$295$	1.18833			0.0691871
$296$		0			0
$297$	5.52546	+	31.0885i	0.320619	+	1.80394i
$298$		0			0
$299$	9.74263	−	9.74263i	0.563431	−	0.563431i
$300$		0			0
$301$	−5.79966	−	5.79966i	−0.334287	−	0.334287i
$302$		0			0
$303$	−0.156158	−	2.66031i	−0.00897107	−	0.152831i
$304$		0			0
$305$		−	1.18466i		−	0.0678335i
$306$		0			0
$307$	−14.8766	+	14.8766i	−0.849051	+	0.849051i	−0.990015	−	0.140964i	$-0.954980\pi$
$307$	−14.8766	+	14.8766i	−0.849051	+	0.849051i	0.140964	+	0.990015i	$0.454980\pi$
$308$		0			0
$309$	−6.34586	−	5.64217i	−0.361004	−	0.320972i
$310$		0			0
$311$		−	32.2860i		−	1.83077i	−0.402577	−	0.915386i	$-0.631885\pi$
$311$		−	32.2860i		−	1.83077i	0.402577	−	0.915386i	$-0.368115\pi$
$312$		0			0
$313$			7.17013i			0.405280i	0.979253	+	0.202640i	$0.0649521\pi$
$313$			7.17013i			0.405280i	−0.979253	+	0.202640i	$0.935048\pi$
$314$		0			0
$315$	0.490108	−	0.621002i	0.0276145	−	0.0349895i
$316$		0			0
$317$	0.591819	−	0.591819i	0.0332399	−	0.0332399i	−0.690291	−	0.723531i	$-0.742518\pi$
$317$	0.591819	−	0.591819i	0.0332399	−	0.0332399i	0.723531	+	0.690291i	$0.242518\pi$
$318$		0			0
$319$			32.2805i			1.80736i
$320$		0			0
$321$	−8.24653	+	0.484066i	−0.460277	+	0.0270179i
$322$		0			0
$323$	−15.4502	−	15.4502i	−0.859672	−	0.859672i
$324$		0			0
$325$	13.4978	−	13.4978i	0.748721	−	0.748721i
$326$		0			0
$327$	1.80269	+	30.7106i	0.0996890	+	1.69830i
$328$		0			0
$329$	3.22550			0.177828
$330$		0			0
$331$	−5.73842	−	5.73842i	−0.315412	−	0.315412i	0.531590	−	0.847002i	$-0.321595\pi$
$331$	−5.73842	−	5.73842i	−0.315412	−	0.315412i	−0.847002	+	0.531590i	$0.821595\pi$
$332$		0			0
$333$	−16.0580	−	12.6733i	−0.879971	−	0.694492i
$334$		0			0
$335$	−0.893993			−0.0488441
$336$		0			0
$337$	−13.4003			−0.729958			−0.364979	−	0.931016i	$-0.618924\pi$
$337$	−13.4003			−0.729958			−0.364979	+	0.931016i	$0.618924\pi$
$338$		0			0
$339$	−4.85704	+	5.46281i	−0.263798	+	0.296699i
$340$		0			0
$341$	28.3135	+	28.3135i	1.53326	+	1.53326i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−1.62267	+	0.0952496i	−0.0873615	+	0.00512807i
$346$		0			0
$347$	10.7294	−	10.7294i	0.575986	−	0.575986i	−0.357809	−	0.933795i	$-0.616476\pi$
$347$	10.7294	−	10.7294i	0.575986	−	0.575986i	0.933795	+	0.357809i	$0.116476\pi$
$348$		0			0
$349$	25.6400	+	25.6400i	1.37248	+	1.37248i	0.856754	+	0.515726i	$0.172478\pi$
$349$	25.6400	+	25.6400i	1.37248	+	1.37248i	0.515726	+	0.856754i	$0.327522\pi$
$350$		0			0
$351$	19.8070	−	3.52035i	1.05722	−	0.187903i
$352$		0			0
$353$		−	9.84311i		−	0.523896i	−0.965082	−	0.261948i	$-0.915635\pi$
$353$		−	9.84311i		−	0.523896i	0.965082	−	0.261948i	$-0.0843649\pi$
$354$		0			0
$355$	1.69023	−	1.69023i	0.0897082	−	0.0897082i
$356$		0			0
$357$	5.73763	−	6.45322i	0.303667	−	0.341541i
$358$		0			0
$359$			18.0480i			0.952539i	0.879299	+	0.476270i	$0.158011\pi$
$359$			18.0480i			0.952539i	−0.879299	+	0.476270i	$0.841989\pi$
$360$		0			0
$361$		−	0.208240i		−	0.0109600i
$362$		0			0
$363$	−29.8385	+	33.5600i	−1.56612	+	1.76144i
$364$		0			0
$365$	−0.432648	+	0.432648i	−0.0226458	+	0.0226458i
$366$		0			0
$367$		−	4.70285i		−	0.245487i	−0.992438	−	0.122743i	$-0.960831\pi$
$367$		−	4.70285i		−	0.245487i	0.992438	−	0.122743i	$-0.0391692\pi$
$368$		0			0
$369$	−3.70957	−	31.4891i	−0.193112	−	1.63926i
$370$		0			0
$371$	7.95980	+	7.95980i	0.413252	+	0.413252i
$372$		0			0
$373$	−13.1792	+	13.1792i	−0.682391	+	0.682391i	−0.960538	−	0.278148i	$-0.910280\pi$
$373$	−13.1792	+	13.1792i	−0.682391	+	0.682391i	0.278148	+	0.960538i	$0.410280\pi$
$374$		0			0
$375$	−4.52790	+	0.265785i	−0.233820	+	0.0137251i
$376$		0			0
$377$	20.5664			1.05922
$378$		0			0
$379$	−8.13513	−	8.13513i	−0.417874	−	0.417874i	0.466597	−	0.884470i	$-0.345480\pi$
$379$	−8.13513	−	8.13513i	−0.417874	−	0.417874i	−0.884470	+	0.466597i	$0.845480\pi$
$380$		0			0
$381$	−14.7475	+	16.5868i	−0.755537	+	0.849767i
$382$		0			0
$383$	16.4573			0.840931			0.420465	−	0.907309i	$-0.361867\pi$
$383$	16.4573			0.840931			0.420465	+	0.907309i	$0.361867\pi$
$384$		0			0
$385$	1.60245			0.0816686
$386$		0			0
$387$	−15.2439	+	19.3151i	−0.774890	+	0.981841i
$388$		0			0
$389$	10.5195	+	10.5195i	0.533359	+	0.533359i	0.921570	−	0.388212i	$-0.126907\pi$
$389$	10.5195	+	10.5195i	0.533359	+	0.533359i	−0.388212	+	0.921570i	$0.626907\pi$
$390$		0			0
$391$	−17.7422			−0.897261
$392$		0			0
$393$	−0.710273	−	12.1002i	−0.0358285	−	0.610373i
$394$		0			0
$395$	1.28562	−	1.28562i	0.0646865	−	0.0646865i
$396$		0			0
$397$	−11.7420	−	11.7420i	−0.589315	−	0.589315i	0.348131	−	0.937446i	$-0.386816\pi$
$397$	−11.7420	−	11.7420i	−0.589315	−	0.589315i	−0.937446	+	0.348131i	$0.886816\pi$
$398$		0			0
$399$	7.57805	−	0.444827i	0.379377	−	0.0222692i
$400$		0			0
$401$			4.47320i			0.223381i	0.993743	+	0.111691i	$0.0356265\pi$
$401$			4.47320i			0.223381i	−0.993743	+	0.111691i	$0.964373\pi$
$402$		0			0
$403$	18.0390	−	18.0390i	0.898584	−	0.898584i
$404$		0			0
$405$	−2.02223	−	1.24226i	−0.100486	−	0.0617286i
$406$		0			0
$407$		−	41.4364i		−	2.05393i
$408$		0			0
$409$		−	0.161698i		−	0.00799545i	−0.999992	−	0.00399772i	$-0.998727\pi$
$409$		−	0.161698i		−	0.00799545i	0.999992	−	0.00399772i	$-0.00127252\pi$
$410$		0			0
$411$	−6.56889	−	5.84047i	−0.324019	−	0.288089i
$412$		0			0
$413$	−3.18645	+	3.18645i	−0.156795	+	0.156795i
$414$		0			0
$415$			0.419768i			0.0206056i
$416$		0			0
$417$	0.377612	+	6.43298i	0.0184917	+	0.315024i
$418$		0			0
$419$	2.77435	+	2.77435i	0.135536	+	0.135536i	0.771620	−	0.636084i	$-0.219447\pi$
$419$	2.77435	+	2.77435i	0.135536	+	0.135536i	−0.636084	+	0.771620i	$0.719447\pi$
$420$		0			0
$421$	−5.72980	+	5.72980i	−0.279253	+	0.279253i	−0.832811	−	0.553558i	$-0.813270\pi$
$421$	−5.72980	+	5.72980i	−0.279253	+	0.279253i	0.553558	+	0.832811i	$0.313270\pi$
$422$		0			0
$423$	−1.13211	−	9.61004i	−0.0550450	−	0.467256i
$424$		0			0
$425$	−24.5806			−1.19234
$426$		0			0
$427$	3.17662	+	3.17662i	0.153727	+	0.153727i
$428$		0			0
$429$	30.4531	+	27.0762i	1.47029	+	1.30725i
$430$		0			0
$431$	−20.1681			−0.971462			−0.485731	−	0.874108i	$-0.661447\pi$
$431$	−20.1681			−0.971462			−0.485731	+	0.874108i	$0.661447\pi$
$432$		0			0
$433$	−29.7401			−1.42922			−0.714610	−	0.699523i	$-0.753396\pi$
$433$	−29.7401			−1.42922			−0.714610	+	0.699523i	$0.753396\pi$
$434$		0			0
$435$	−1.81323	−	1.61216i	−0.0869379	−	0.0772974i
$436$		0			0
$437$	−11.0289	−	11.0289i	−0.527582	−	0.527582i
$438$		0			0
$439$	−24.0542			−1.14805			−0.574023	−	0.818839i	$-0.694618\pi$
$439$	−24.0542			−1.14805			−0.574023	+	0.818839i	$0.694618\pi$
$440$		0			0
$441$	0.350987	+	2.97940i	0.0167137	+	0.141876i
$442$		0			0
$443$	−9.65299	+	9.65299i	−0.458628	+	0.458628i	−0.898205	−	0.439577i	$-0.855128\pi$
$443$	−9.65299	+	9.65299i	−0.458628	+	0.458628i	0.439577	+	0.898205i	$0.355128\pi$
$444$		0			0
$445$	1.45738	+	1.45738i	0.0690864	+	0.0690864i
$446$		0			0
$447$	−0.110737	−	1.88650i	−0.00523766	−	0.0892285i
$448$		0			0
$449$			14.9336i			0.704760i	0.935857	+	0.352380i	$0.114628\pi$
$449$			14.9336i			0.704760i	−0.935857	+	0.352380i	$0.885372\pi$
$450$		0			0
$451$	45.4139	−	45.4139i	2.13846	−	2.13846i
$452$		0			0
$453$	6.24023	+	5.54826i	0.293192	+	0.260680i
$454$		0			0
$455$		−	1.02095i		−	0.0478628i
$456$		0			0
$457$		−	10.4103i		−	0.486975i	−0.969904	−	0.243487i	$-0.921709\pi$
$457$		−	10.4103i		−	0.486975i	0.969904	−	0.243487i	$-0.0782914\pi$
$458$		0			0
$459$	−21.2405	−	14.8297i	−0.991424	−	0.692190i
$460$		0			0
$461$	18.7575	−	18.7575i	0.873623	−	0.873623i	−0.119242	−	0.992865i	$-0.538046\pi$
$461$	18.7575	−	18.7575i	0.873623	−	0.873623i	0.992865	+	0.119242i	$0.0380464\pi$
$462$		0			0
$463$			25.5530i			1.18755i	0.804631	+	0.593775i	$0.202363\pi$
$463$			25.5530i			1.18755i	−0.804631	+	0.593775i	$0.797637\pi$
$464$		0			0
$465$	−3.00445	+	0.176359i	−0.139328	+	0.00817846i
$466$		0			0
$467$	13.5596	+	13.5596i	0.627463	+	0.627463i	0.947429	−	0.319966i	$-0.103671\pi$
$467$	13.5596	+	13.5596i	0.627463	+	0.627463i	−0.319966	+	0.947429i	$0.603671\pi$
$468$		0			0
$469$	2.39721	−	2.39721i	0.110693	−	0.110693i
$470$		0			0
$471$	0.754265	+	12.8496i	0.0347547	+	0.592080i
$472$		0			0
$473$	−49.8412			−2.29170
$474$		0			0
$475$	−15.2798	−	15.2798i	−0.701083	−	0.701083i
$476$		0			0
$477$	20.9216	−	26.5092i	0.957935	−	1.21377i
$478$		0			0
$479$	−5.16716			−0.236094			−0.118047	−	0.993008i	$-0.537663\pi$
$479$	−5.16716			−0.236094			−0.118047	+	0.993008i	$0.537663\pi$
$480$		0			0
$481$	−26.3998			−1.20373
$482$		0			0
$483$	4.09571	−	4.60652i	0.186361	−	0.209604i
$484$		0			0
$485$	2.36334	+	2.36334i	0.107314	+	0.107314i
$486$		0			0
$487$	8.11050			0.367522			0.183761	−	0.982971i	$-0.441173\pi$
$487$	8.11050			0.367522			0.183761	+	0.982971i	$0.441173\pi$
$488$		0			0
$489$	5.15617	−	0.302664i	0.233170	−	0.0136869i
$490$		0			0
$491$	−5.58977	+	5.58977i	−0.252263	+	0.252263i	−0.821898	−	0.569635i	$-0.807085\pi$
$491$	−5.58977	+	5.58977i	−0.252263	+	0.252263i	0.569635	+	0.821898i	$0.307085\pi$
$492$		0			0
$493$	−18.7266	−	18.7266i	−0.843403	−	0.843403i
$494$		0			0
$495$	−0.562440	−	4.77434i	−0.0252798	−	0.214591i
$496$		0			0
$497$			9.06458i			0.406602i
$498$		0			0
$499$	−22.1413	+	22.1413i	−0.991181	+	0.991181i	−0.999961	−	0.00878026i	$-0.997205\pi$
$499$	−22.1413	+	22.1413i	−0.991181	+	0.991181i	0.00878026	+	0.999961i	$0.497205\pi$
$500$		0			0
$501$	19.9162	−	22.4002i	0.889791	−	1.00077i
$502$		0			0
$503$		−	5.43465i		−	0.242319i	−0.992633	−	0.121160i	$-0.961339\pi$
$503$		−	5.43465i		−	0.242319i	0.992633	−	0.121160i	$-0.0386613\pi$
$504$		0			0
$505$			0.405726i			0.0180545i
$506$		0			0
$507$	2.28933	−	2.57486i	0.101673	−	0.114353i
$508$		0			0
$509$	−14.4527	+	14.4527i	−0.640604	+	0.640604i	−0.950704	−	0.310100i	$-0.899637\pi$
$509$	−14.4527	+	14.4527i	−0.640604	+	0.640604i	0.310100	+	0.950704i	$0.399637\pi$
$510$		0			0
$511$		−	2.32026i		−	0.102642i
$512$		0			0
$513$	−3.98511	−	22.4219i	−0.175947	−	0.989951i
$514$		0			0
$515$	0.914152	+	0.914152i	0.0402823	+	0.0402823i
$516$		0			0
$517$	13.8597	−	13.8597i	0.609548	−	0.609548i
$518$		0			0
$519$	4.80489	−	0.282044i	0.210911	−	0.0123804i
$520$		0			0
$521$	6.52150			0.285712			0.142856	−	0.989743i	$-0.454371\pi$
$521$	6.52150			0.285712			0.142856	+	0.989743i	$0.454371\pi$
$522$		0			0
$523$	−15.5234	−	15.5234i	−0.678791	−	0.678791i	0.280935	−	0.959727i	$-0.409355\pi$
$523$	−15.5234	−	15.5234i	−0.678791	−	0.678791i	−0.959727	+	0.280935i	$0.909355\pi$
$524$		0			0
$525$	5.67433	−	6.38203i	0.247648	−	0.278535i
$526$		0			0
$527$	−32.8505			−1.43099
$528$		0			0
$529$	10.3350			0.449349
$530$		0			0
$531$	10.6121	+	8.37530i	0.460526	+	0.363457i
$532$		0			0
$533$	−28.9339	−	28.9339i	−1.25327	−	1.25327i
$534$		0			0
$535$	1.25768			0.0543744
$536$		0			0
$537$	0.527633	+	8.98873i	0.0227690	+	0.387892i
$538$		0			0
$539$	−4.29691	+	4.29691i	−0.185081	+	0.185081i
$540$		0			0
$541$	24.2270	+	24.2270i	1.04160	+	1.04160i	0.999096	+	0.0425030i	$0.0135332\pi$
$541$	24.2270	+	24.2270i	1.04160	+	1.04160i	0.0425030	+	0.999096i	$0.486467\pi$
$542$		0			0
$543$	4.68941	−	0.275266i	0.201242	−	0.0118128i
$544$		0			0
$545$		−	4.68369i		−	0.200627i
$546$		0			0
$547$	−24.8683	+	24.8683i	−1.06329	+	1.06329i	−0.0654358	+	0.997857i	$0.520844\pi$
$547$	−24.8683	+	24.8683i	−1.06329	+	1.06329i	−0.997857	+	0.0654358i	$0.979156\pi$
$548$		0			0
$549$	8.34947	−	10.5794i	0.356346	−	0.451517i
$550$		0			0
$551$		−	23.2816i		−	0.991828i
$552$		0			0
$553$			6.89467i			0.293191i
$554$		0			0
$555$	2.32754	+	2.06944i	0.0987984	+	0.0878427i
$556$		0			0
$557$	16.3675	−	16.3675i	0.693514	−	0.693514i	−0.269490	−	0.963003i	$-0.586855\pi$
$557$	16.3675	−	16.3675i	0.693514	−	0.693514i	0.963003	+	0.269490i	$0.0868550\pi$
$558$		0			0
$559$			31.7546i			1.34308i
$560$		0			0
$561$	−3.07485	−	52.3830i	−0.129820	−	2.21161i
$562$		0			0
$563$	−0.736871	−	0.736871i	−0.0310554	−	0.0310554i	0.691409	−	0.722464i	$-0.256990\pi$
$563$	−0.736871	−	0.736871i	−0.0310554	−	0.0310554i	−0.722464	+	0.691409i	$0.756990\pi$
$564$		0			0
$565$	0.786944	−	0.786944i	0.0331070	−	0.0331070i
$566$		0			0
$567$	8.75362	−	2.09146i	0.367617	−	0.0878330i
$568$		0			0
$569$	26.3718			1.10556			0.552781	−	0.833326i	$-0.313567\pi$
$569$	26.3718			1.10556			0.552781	+	0.833326i	$0.313567\pi$
$570$		0			0
$571$	19.5755	+	19.5755i	0.819211	+	0.819211i	0.985994	−	0.166783i	$-0.0533378\pi$
$571$	19.5755	+	19.5755i	0.819211	+	0.819211i	−0.166783	+	0.985994i	$0.553338\pi$
$572$		0			0
$573$	−3.40083	−	3.02371i	−0.142072	−	0.126317i
$574$		0			0
$575$	−17.5465			−0.731738
$576$		0			0
$577$	2.45494			0.102200			0.0511002	−	0.998694i	$-0.483727\pi$
$577$	2.45494			0.102200			0.0511002	+	0.998694i	$0.483727\pi$
$578$		0			0
$579$	−4.60063	−	4.09047i	−0.191196	−	0.169994i
$580$		0			0
$581$	−1.12559	−	1.12559i	−0.0466974	−	0.0466974i
$582$		0			0
$583$	68.4051			2.83305
$584$		0			0
$585$	−3.04181	+	0.358339i	−0.125763	+	0.0148155i
$586$		0			0
$587$	17.7714	−	17.7714i	0.733505	−	0.733505i	−0.237807	−	0.971312i	$-0.576429\pi$
$587$	17.7714	−	17.7714i	0.733505	−	0.733505i	0.971312	+	0.237807i	$0.0764286\pi$
$588$		0			0
$589$	−20.4205	−	20.4205i	−0.841411	−	0.841411i
$590$		0			0
$591$	2.41046	+	41.0644i	0.0991529	+	1.68916i
$592$		0			0
$593$			41.1462i			1.68967i	0.535025	+	0.844836i	$0.320302\pi$
$593$			41.1462i			1.68967i	−0.535025	+	0.844836i	$0.679698\pi$
$594$		0			0
$595$	−0.929618	+	0.929618i	−0.0381106	+	0.0381106i
$596$		0			0
$597$	15.3056	+	13.6084i	0.626418	+	0.556955i
$598$		0			0
$599$		−	29.4373i		−	1.20278i	−0.798957	−	0.601388i	$-0.794615\pi$
$599$		−	29.4373i		−	1.20278i	0.798957	−	0.601388i	$-0.205385\pi$
$600$		0			0
$601$			5.56552i			0.227022i	0.993537	+	0.113511i	$0.0362097\pi$
$601$			5.56552i			0.227022i	−0.993537	+	0.113511i	$0.963790\pi$
$602$		0			0
$603$	−7.98362	−	6.30084i	−0.325118	−	0.256590i
$604$		0			0
$605$	4.83447	−	4.83447i	0.196549	−	0.196549i
$606$		0			0
$607$			24.2531i			0.984402i	0.870482	+	0.492201i	$0.163808\pi$
$607$			24.2531i			0.984402i	−0.870482	+	0.492201i	$0.836192\pi$
$608$		0			0
$609$	9.18506	−	0.539157i	0.372197	−	0.0218478i
$610$		0			0
$611$	−8.83022	−	8.83022i	−0.357232	−	0.357232i
$612$		0			0
$613$	8.76284	−	8.76284i	0.353928	−	0.353928i	−0.507641	−	0.861569i	$-0.669482\pi$
$613$	8.76284	−	8.76284i	0.353928	−	0.353928i	0.861569	+	0.507641i	$0.169482\pi$
$614$		0			0
$615$	0.282874	+	4.81904i	0.0114066	+	0.194322i
$616$		0			0
$617$	−12.0201			−0.483910			−0.241955	−	0.970287i	$-0.577789\pi$
$617$	−12.0201			−0.483910			−0.241955	+	0.970287i	$0.577789\pi$
$618$		0			0
$619$	23.3157	+	23.3157i	0.937136	+	0.937136i	0.998138	−	0.0610020i	$-0.0194296\pi$
$619$	23.3157	+	23.3157i	0.937136	+	0.937136i	−0.0610020	+	0.998138i	$0.519430\pi$
$620$		0			0
$621$	−15.1622	−	10.5859i	−0.608438	−	0.424798i
$622$		0			0
$623$	−7.81580			−0.313134
$624$		0			0
$625$	−23.9618			−0.958470
$626$		0			0
$627$	30.6508	−	34.4736i	1.22408	−	1.37674i
$628$		0			0
$629$	24.0382	+	24.0382i	0.958464	+	0.958464i
$630$		0			0
$631$	37.5507			1.49487			0.747436	−	0.664334i	$-0.231285\pi$
$631$	37.5507			1.49487			0.747436	+	0.664334i	$0.231285\pi$
$632$		0			0
$633$	−8.62563	+	0.506319i	−0.342838	+	0.0201244i
$634$		0			0
$635$	2.38941	−	2.38941i	0.0948207	−	0.0948207i
$636$		0			0
$637$	2.73763	+	2.73763i	0.108469	+	0.108469i
$638$		0			0
$639$	27.0070	−	3.18155i	1.06838	−	0.125860i
$640$		0			0
$641$			0.680137i			0.0268638i	0.999910	+	0.0134319i	$0.00427563\pi$
$641$			0.680137i			0.0268638i	−0.999910	+	0.0134319i	$0.995724\pi$
$642$		0			0
$643$	−6.40677	+	6.40677i	−0.252658	+	0.252658i	−0.822060	−	0.569401i	$-0.807175\pi$
$643$	−6.40677	+	6.40677i	−0.252658	+	0.252658i	0.569401	+	0.822060i	$0.307175\pi$
$644$		0			0
$645$	2.48919	−	2.79964i	0.0980118	−	0.110236i
$646$		0			0
$647$			30.0799i			1.18256i	0.806466	+	0.591281i	$0.201378\pi$
$647$			30.0799i			1.18256i	−0.806466	+	0.591281i	$0.798622\pi$
$648$		0			0
$649$			27.3838i			1.07491i
$650$		0			0
$651$	7.58340	−	8.52920i	0.297217	−	0.334286i
$652$		0			0
$653$	−4.68675	+	4.68675i	−0.183407	+	0.183407i	−0.792838	−	0.609432i	$-0.791398\pi$
$653$	−4.68675	+	4.68675i	−0.183407	+	0.183407i	0.609432	+	0.792838i	$0.291398\pi$
$654$		0			0
$655$			1.84541i			0.0721060i
$656$		0			0
$657$	−6.91297	+	0.814380i	−0.269701	+	0.0317720i
$658$		0			0
$659$	−21.0024	−	21.0024i	−0.818136	−	0.818136i	0.167702	−	0.985838i	$-0.446365\pi$
$659$	−21.0024	−	21.0024i	−0.818136	−	0.818136i	−0.985838	+	0.167702i	$0.946365\pi$
$660$		0			0
$661$	6.30679	−	6.30679i	0.245306	−	0.245306i	−0.573735	−	0.819041i	$-0.694506\pi$
$661$	6.30679	−	6.30679i	0.245306	−	0.245306i	0.819041	+	0.573735i	$0.194506\pi$
$662$		0			0
$663$	−33.3740	+	1.95903i	−1.29614	+	0.0760826i
$664$		0			0
$665$	−1.15573			−0.0448174
$666$		0			0
$667$	−13.3677	−	13.3677i	−0.517598	−	0.517598i
$668$		0			0
$669$	−24.4617	+	27.5126i	−0.945744	+	1.06370i
$670$		0			0
$671$	27.2993			1.05388
$672$		0			0
$673$	−17.2127			−0.663502			−0.331751	−	0.943367i	$-0.607639\pi$
$673$	−17.2127			−0.663502			−0.331751	+	0.943367i	$0.607639\pi$
$674$		0			0
$675$	−21.0062	−	14.6661i	−0.808530	−	0.564497i
$676$		0			0
$677$	−32.3963	−	32.3963i	−1.24509	−	1.24509i	−0.957861	−	0.287231i	$-0.907265\pi$
$677$	−32.3963	−	32.3963i	−1.24509	−	1.24509i	−0.287231	−	0.957861i	$-0.592735\pi$
$678$		0			0
$679$	−12.6744			−0.486398
$680$		0			0
$681$	−1.80546	−	30.7577i	−0.0691853	−	1.17864i
$682$		0			0
$683$	−4.46231	+	4.46231i	−0.170746	+	0.170746i	−0.787307	−	0.616561i	$-0.788525\pi$
$683$	−4.46231	+	4.46231i	−0.170746	+	0.170746i	0.616561	+	0.787307i	$0.288525\pi$
$684$		0			0
$685$	0.946280	+	0.946280i	0.0361555	+	0.0361555i
$686$		0			0
$687$	−41.7234	+	2.44914i	−1.59185	+	0.0934404i
$688$		0			0
$689$		−	43.5820i		−	1.66034i
$690$		0			0
$691$	23.7096	−	23.7096i	0.901957	−	0.901957i	−0.0936479	−	0.995605i	$-0.529853\pi$
$691$	23.7096	−	23.7096i	0.901957	−	0.901957i	0.995605	+	0.0936479i	$0.0298528\pi$
$692$		0			0
$693$	14.3104	+	11.2940i	0.543606	+	0.429025i
$694$		0			0
$695$		−	0.981098i		−	0.0372152i
$696$		0			0
$697$			52.6912i			1.99582i
$698$		0			0
$699$	−6.28429	−	5.58743i	−0.237694	−	0.211336i
$700$		0			0
$701$	6.57459	−	6.57459i	0.248319	−	0.248319i	−0.571962	−	0.820280i	$-0.693817\pi$
$701$	6.57459	−	6.57459i	0.248319	−	0.248319i	0.820280	+	0.571962i	$0.193817\pi$
$702$		0			0
$703$			29.8851i			1.12714i
$704$		0			0
$705$	0.0863293	+	1.47070i	0.00325135	+	0.0553898i
$706$		0			0
$707$	−1.08794	−	1.08794i	−0.0409160	−	0.0409160i
$708$		0			0
$709$	34.7204	−	34.7204i	1.30395	−	1.30395i	0.378250	−	0.925704i	$-0.376526\pi$
$709$	34.7204	−	34.7204i	1.30395	−	1.30395i	0.925704	−	0.378250i	$-0.123474\pi$
$710$		0			0
$711$	20.5419	−	2.41994i	0.770383	−	0.0907547i
$712$		0			0
$713$	−23.4498			−0.878201
$714$		0			0
$715$	−4.38692	−	4.38692i	−0.164062	−	0.164062i
$716$		0			0
$717$	5.82809	+	5.18181i	0.217654	+	0.193518i
$718$		0			0
$719$	−15.1919			−0.566562			−0.283281	−	0.959037i	$-0.591423\pi$
$719$	−15.1919			−0.566562			−0.283281	+	0.959037i	$0.591423\pi$
$720$		0			0
$721$	−4.90252			−0.182579
$722$		0			0
$723$	−30.3303	−	26.9670i	−1.12799	−	1.00291i
$724$		0			0
$725$	−18.5200	−	18.5200i	−0.687815	−	0.687815i
$726$		0			0
$727$	50.4025			1.86933			0.934663	−	0.355536i	$-0.115702\pi$
$727$	50.4025			1.86933			0.934663	+	0.355536i	$0.115702\pi$
$728$		0			0
$729$	−9.30369	−	25.3464i	−0.344581	−	0.938757i
$730$		0			0
$731$	28.9140	−	28.9140i	1.06942	−	1.06942i
$732$		0			0
$733$	−17.7495	−	17.7495i	−0.655592	−	0.655592i	0.298742	−	0.954334i	$-0.403433\pi$
$733$	−17.7495	−	17.7495i	−0.655592	−	0.655592i	−0.954334	+	0.298742i	$0.903433\pi$
$734$		0			0
$735$	−0.0267646	−	0.455961i	−0.000987228	−	0.0168184i
$736$		0			0
$737$		−	20.6012i		−	0.758853i
$738$		0			0
$739$	−32.8936	+	32.8936i	−1.21001	+	1.21001i	−0.238988	+	0.971022i	$0.576816\pi$
$739$	−32.8936	+	32.8936i	−1.21001	+	1.21001i	−0.971022	+	0.238988i	$0.923184\pi$
$740$		0			0
$741$	−21.9637	−	19.5281i	−0.806855	−	0.717383i
$742$		0			0
$743$			0.740043i			0.0271495i	0.999908	+	0.0135748i	$0.00432112\pi$
$743$			0.740043i			0.0271495i	−0.999908	+	0.0135748i	$0.995679\pi$
$744$		0			0
$745$			0.287712i			0.0105409i
$746$		0			0
$747$	−2.95852	+	3.74865i	−0.108246	+	0.137156i
$748$		0			0
$749$	−3.37243	+	3.37243i	−0.123226	+	0.123226i
$750$		0			0
$751$		−	44.9022i		−	1.63851i	−0.573433	−	0.819253i	$-0.694389\pi$
$751$		−	44.9022i		−	1.63851i	0.573433	−	0.819253i	$-0.305611\pi$
$752$		0			0
$753$	−4.79225	+	0.281302i	−0.174639	+	0.0102512i
$754$		0			0
$755$	−0.898935	−	0.898935i	−0.0327156	−	0.0327156i
$756$		0			0
$757$	−10.1054	+	10.1054i	−0.367289	+	0.367289i	−0.866488	−	0.499199i	$-0.833628\pi$
$757$	−10.1054	+	10.1054i	−0.367289	+	0.367289i	0.499199	+	0.866488i	$0.333628\pi$
$758$		0			0
$759$	−2.19493	−	37.3927i	−0.0796709	−	1.35727i
$760$		0			0
$761$	44.5291			1.61418			0.807089	−	0.590430i	$-0.201042\pi$
$761$	44.5291			1.61418			0.807089	+	0.590430i	$0.201042\pi$
$762$		0			0
$763$	12.5591	+	12.5591i	0.454671	+	0.454671i
$764$		0			0
$765$	3.09598	+	2.44342i	0.111936	+	0.0883419i
$766$		0			0
$767$	17.4466			0.629961
$768$		0			0
$769$	−4.48904			−0.161879			−0.0809395	−	0.996719i	$-0.525792\pi$
$769$	−4.48904			−0.161879			−0.0809395	+	0.996719i	$0.525792\pi$
$770$		0			0
$771$	30.9739	−	34.8369i	1.11550	−	1.25462i
$772$		0			0
$773$	−2.39104	−	2.39104i	−0.0859997	−	0.0859997i	0.662798	−	0.748798i	$-0.269369\pi$
$773$	−2.39104	−	2.39104i	−0.0859997	−	0.0859997i	−0.748798	+	0.662798i	$0.769369\pi$
$774$		0			0
$775$	−32.4881			−1.16701
$776$		0			0
$777$	−11.7903	+	0.692083i	−0.422974	+	0.0248283i
$778$		0			0
$779$	−32.7538	+	32.7538i	−1.17353	+	1.17353i
$780$		0			0
$781$	38.9497	+	38.9497i	1.39373	+	1.39373i
$782$		0			0
$783$	−4.83020	−	27.1767i	−0.172617	−	0.971216i
$784$		0			0
$785$		−	1.95971i		−	0.0699449i
$786$		0			0
$787$	−12.4954	+	12.4954i	−0.445412	+	0.445412i	−0.893826	−	0.448414i	$-0.851989\pi$
$787$	−12.4954	+	12.4954i	−0.445412	+	0.445412i	0.448414	+	0.893826i	$0.351989\pi$
$788$		0			0
$789$	23.0945	−	25.9748i	0.822185	−	0.924727i
$790$		0			0
$791$			4.22031i			0.150057i
$792$		0			0
$793$		−	17.3928i		−	0.617637i
$794$		0			0
$795$	−3.41632	+	3.84240i	−0.121164	+	0.136276i
$796$		0			0
$797$	−12.7544	+	12.7544i	−0.451785	+	0.451785i	−0.895947	−	0.444162i	$-0.853502\pi$
$797$	−12.7544	+	12.7544i	−0.451785	+	0.451785i	0.444162	+	0.895947i	$0.353502\pi$
$798$		0			0
$799$			16.0806i			0.568891i
$800$		0			0
$801$	2.74324	+	23.2864i	0.0969278	+	0.822784i
$802$		0			0
$803$	−9.96994	−	9.96994i	−0.351831	−	0.351831i
$804$		0			0
$805$	−0.663592	+	0.663592i	−0.0233885	+	0.0233885i
$806$		0			0
$807$	15.6340	−	0.917708i	0.550344	−	0.0323048i
$808$		0			0
$809$	40.5344			1.42511			0.712557	−	0.701614i	$-0.247537\pi$
$809$	40.5344			1.42511			0.712557	+	0.701614i	$0.247537\pi$
$810$		0			0
$811$	0.808442	+	0.808442i	0.0283882	+	0.0283882i	0.721158	−	0.692770i	$-0.243610\pi$
$811$	0.808442	+	0.808442i	0.0283882	+	0.0283882i	−0.692770	+	0.721158i	$0.743610\pi$
$812$		0			0
$813$	−17.8595	+	20.0869i	−0.626358	+	0.704478i
$814$		0			0
$815$	−0.786371			−0.0275454
$816$		0			0
$817$	35.9469			1.25762
$818$		0			0
$819$	7.19561	−	9.11735i	0.251435	−	0.318586i
$820$		0			0
$821$	−36.4630	−	36.4630i	−1.27257	−	1.27257i	−0.944736	−	0.327831i	$-0.893682\pi$
$821$	−36.4630	−	36.4630i	−1.27257	−	1.27257i	−0.327831	−	0.944736i	$-0.606318\pi$
$822$		0			0
$823$	−49.3421			−1.71996			−0.859979	−	0.510329i	$-0.829524\pi$
$823$	−49.3421			−1.71996			−0.859979	+	0.510329i	$0.829524\pi$
$824$		0			0
$825$	−3.04093	−	51.8051i	−0.105872	−	1.80362i
$826$		0			0
$827$	26.4919	−	26.4919i	0.921213	−	0.921213i	−0.0759022	−	0.997115i	$-0.524184\pi$
$827$	26.4919	−	26.4919i	0.921213	−	0.921213i	0.997115	+	0.0759022i	$0.0241837\pi$
$828$		0			0
$829$	−20.8538	−	20.8538i	−0.724283	−	0.724283i	0.245192	−	0.969475i	$-0.421149\pi$
$829$	−20.8538	−	20.8538i	−0.724283	−	0.724283i	−0.969475	+	0.245192i	$0.921149\pi$
$830$		0			0
$831$	15.0680	−	0.884481i	0.522702	−	0.0306823i
$832$		0			0
$833$		−	4.98546i		−	0.172736i
$834$		0			0
$835$	−3.22685	+	3.22685i	−0.111670	+	0.111670i
$836$		0			0
$837$	−28.0735	−	19.6003i	−0.970364	−	0.677486i
$838$		0			0
$839$			33.7299i			1.16449i	0.813015	+	0.582243i	$0.197825\pi$
$839$			33.7299i			1.16449i	−0.813015	+	0.582243i	$0.802175\pi$
$840$		0			0
$841$			0.781332i			0.0269425i
$842$		0			0
$843$	12.4175	+	11.0405i	0.427682	+	0.380256i
$844$		0			0
$845$	−0.370920	+	0.370920i	−0.0127600	+	0.0127600i
$846$		0			0
$847$			25.9269i			0.890858i
$848$		0			0
$849$	2.91870	+	49.7228i	0.100170	+	1.70648i
$850$		0			0
$851$	17.1592	+	17.1592i	0.588211	+	0.588211i
$852$		0			0
$853$	−22.1012	+	22.1012i	−0.756732	+	0.756732i	−0.975726	−	0.218994i	$-0.929722\pi$
$853$	−22.1012	+	22.1012i	−0.756732	+	0.756732i	0.218994	+	0.975726i	$0.429722\pi$
$854$		0			0
$855$	0.405647	+	3.44339i	0.0138728	+	0.117761i
$856$		0			0
$857$	−52.0113			−1.77667			−0.888336	−	0.459194i	$-0.848138\pi$
$857$	−52.0113			−1.77667			−0.888336	+	0.459194i	$0.848138\pi$
$858$		0			0
$859$	−24.7863	−	24.7863i	−0.845697	−	0.845697i	0.143896	−	0.989593i	$-0.454037\pi$
$859$	−24.7863	−	24.7863i	−0.845697	−	0.845697i	−0.989593	+	0.143896i	$0.954037\pi$
$860$		0			0
$861$	−13.6806	−	12.1635i	−0.466232	−	0.414532i
$862$		0			0
$863$	3.25607			0.110838			0.0554190	−	0.998463i	$-0.482351\pi$
$863$	3.25607			0.110838			0.0554190	+	0.998463i	$0.482351\pi$
$864$		0			0
$865$	−0.732797			−0.0249158
$866$		0			0
$867$	10.1674	+	9.03990i	0.345301	+	0.307011i
$868$		0			0
$869$	29.6258	+	29.6258i	1.00499	+	1.00499i
$870$		0			0
$871$	−13.1253			−0.444734
$872$		0			0
$873$	4.44854	+	37.7620i	0.150560	+	1.27805i
$874$		0			0
$875$	−1.85169	+	1.85169i	−0.0625986	+	0.0625986i
$876$		0			0
$877$	36.6022	+	36.6022i	1.23597	+	1.23597i	0.961634	+	0.274335i	$0.0884578\pi$
$877$	36.6022	+	36.6022i	1.23597	+	1.23597i	0.274335	+	0.961634i	$0.411542\pi$
$878$		0			0
$879$	−1.27482	−	21.7178i	−0.0429987	−	0.732523i
$880$		0			0
$881$		−	17.7444i		−	0.597824i	−0.954281	−	0.298912i	$-0.903376\pi$
$881$		−	17.7444i		−	0.597824i	0.954281	−	0.298912i	$-0.0966237\pi$
$882$		0			0
$883$	−0.699892	+	0.699892i	−0.0235533	+	0.0235533i	−0.718785	−	0.695232i	$-0.755302\pi$
$883$	−0.699892	+	0.699892i	−0.0235533	+	0.0235533i	0.695232	+	0.718785i	$0.255302\pi$
$884$		0			0
$885$	−1.53818	−	1.36761i	−0.0517054	−	0.0459718i
$886$		0			0
$887$		−	24.7549i		−	0.831190i	−0.909550	−	0.415595i	$-0.863573\pi$
$887$		−	24.7549i		−	0.831190i	0.909550	−	0.415595i	$-0.136427\pi$
$888$		0			0
$889$			12.8142i			0.429774i
$890$		0			0
$891$	28.6267	−	46.6003i	0.959030	−	1.56117i
$892$		0			0
$893$	−9.99599	+	9.99599i	−0.334503	+	0.334503i
$894$		0			0
$895$		−	1.37088i		−	0.0458234i
$896$		0			0
$897$	−23.8235	+	1.39842i	−0.795443	+	0.0466920i
$898$		0			0
$899$	−24.7509	−	24.7509i	−0.825487	−	0.825487i
$900$		0			0
$901$	−39.6833	+	39.6833i	−1.32204	+	1.32204i
$902$		0			0
$903$	0.832462	+	14.1818i	0.0277026	+	0.471940i
$904$		0			0
$905$	−0.715185			−0.0237736
$906$		0			0
$907$	−15.9366	−	15.9366i	−0.529167	−	0.529167i	0.391157	−	0.920324i	$-0.372075\pi$
$907$	−15.9366	−	15.9366i	−0.529167	−	0.529167i	−0.920324	+	0.391157i	$0.872075\pi$
$908$		0			0
$909$	−2.85954	+	3.62324i	−0.0948450	+	0.120175i
$910$		0			0
$911$	5.23938			0.173588			0.0867942	−	0.996226i	$-0.472338\pi$
$911$	5.23938			0.173588			0.0867942	+	0.996226i	$0.472338\pi$
$912$		0			0
$913$	−9.67313			−0.320134
$914$		0			0
$915$	−1.36339	+	1.53344i	−0.0450724	+	0.0506938i
$916$		0			0
$917$	−4.94838	−	4.94838i	−0.163410	−	0.163410i
$918$		0			0
$919$	−5.00713			−0.165170			−0.0825850	−	0.996584i	$-0.526318\pi$
$919$	−5.00713			−0.165170			−0.0825850	+	0.996584i	$0.526318\pi$
$920$		0			0
$921$	36.3774	−	2.13533i	1.19868	−	0.0703615i
$922$		0			0
$923$	24.8154	−	24.8154i	0.816810	−	0.816810i
$924$		0			0
$925$	23.7730	+	23.7730i	0.781651	+	0.781651i
$926$		0			0
$927$	1.72072	+	14.6066i	0.0565159	+	0.479742i
$928$		0			0
$929$		−	26.2486i		−	0.861188i	−0.902546	−	0.430594i	$-0.858304\pi$
$929$		−	26.2486i		−	0.861188i	0.902546	−	0.430594i	$-0.141696\pi$
$930$		0			0
$931$	3.09905	−	3.09905i	0.101567	−	0.101567i
$932$		0			0
$933$	−37.1571	+	41.7913i	−1.21647	+	1.36819i
$934$		0			0
$935$			7.98897i			0.261267i
$936$		0			0
$937$		−	27.9322i		−	0.912506i	−0.889850	−	0.456253i	$-0.849191\pi$
$937$		−	27.9322i		−	0.912506i	0.889850	−	0.456253i	$-0.150809\pi$
$938$		0			0
$939$	8.25190	−	9.28108i	0.269291	−	0.302876i
$940$		0			0
$941$	32.6760	−	32.6760i	1.06521	−	1.06521i	0.0674877	−	0.997720i	$-0.478502\pi$
$941$	32.6760	−	32.6760i	1.06521	−	1.06521i	0.997720	−	0.0674877i	$-0.0214984\pi$
$942$		0			0
$943$			37.6127i			1.22484i
$944$		0			0
$945$	−1.34909	+	0.239779i	−0.0438861	+	0.00780000i
$946$		0			0
$947$	35.4193	+	35.4193i	1.15097	+	1.15097i	0.986358	+	0.164616i	$0.0526384\pi$
$947$	35.4193	+	35.4193i	1.15097	+	1.15097i	0.164616	+	0.986358i	$0.447362\pi$
$948$		0			0
$949$	−6.35200	+	6.35200i	−0.206195	+	0.206195i
$950$		0			0
$951$	−1.44716	+	0.0849476i	−0.0469275	+	0.00275462i
$952$		0			0
$953$	24.4557			0.792197			0.396098	−	0.918208i	$-0.370364\pi$
$953$	24.4557			0.792197			0.396098	+	0.918208i	$0.370364\pi$
$954$		0			0
$955$	0.489905	+	0.489905i	0.0158530	+	0.0158530i
$956$		0			0
$957$	37.1507	−	41.7841i	1.20091	−	1.35069i
$958$		0			0
$959$	−5.07482			−0.163874
$960$		0			0
$961$	−12.4184			−0.400594
$962$		0			0
$963$	11.2315	+	8.86412i	0.361929	+	0.285642i
$964$		0			0
$965$	0.662743	+	0.662743i	0.0213344	+	0.0213344i
$966$		0			0
$967$	−55.4167			−1.78208			−0.891041	−	0.453923i	$-0.850024\pi$
$967$	−55.4167			−1.78208			−0.891041	+	0.453923i	$0.850024\pi$
$968$		0			0
$969$	2.21767	+	37.7801i	0.0712417	+	1.21367i
$970$		0			0
$971$	−22.9588	+	22.9588i	−0.736782	+	0.736782i	−0.971954	−	0.235172i	$-0.924435\pi$
$971$	−22.9588	+	22.9588i	−0.736782	+	0.736782i	0.235172	+	0.971954i	$0.424435\pi$
$972$		0			0
$973$	2.63077	+	2.63077i	0.0843387	+	0.0843387i
$974$		0			0
$975$	−33.0058	+	1.93742i	−1.05703	+	0.0620472i
$976$		0			0
$977$		−	28.4090i		−	0.908883i	−0.890777	−	0.454442i	$-0.849839\pi$
$977$		−	28.4090i		−	0.908883i	0.890777	−	0.454442i	$-0.150161\pi$
$978$		0			0
$979$	−33.5838	+	33.5838i	−1.07334	+	1.07334i
$980$		0			0
$981$	33.0105	−	41.8267i	1.05394	−	1.33542i
$982$		0			0
$983$			57.7405i			1.84164i	0.389992	+	0.920818i	$0.372478\pi$
$983$			57.7405i			1.84164i	−0.389992	+	0.920818i	$0.627522\pi$
$984$		0			0
$985$		−	6.26276i		−	0.199548i
$986$		0			0
$987$	−4.17511	−	3.71214i	−0.132895	−	0.118159i
$988$		0			0
$989$	20.6397	−	20.6397i	0.656305	−	0.656305i
$990$		0			0
$991$		−	24.5422i		−	0.779609i	−0.920898	−	0.389804i	$-0.872543\pi$
$991$		−	24.5422i		−	0.779609i	0.920898	−	0.389804i	$-0.127457\pi$
$992$		0			0
$993$	0.823673	+	14.0321i	0.0261385	+	0.445294i
$994$		0			0
$995$	−2.20485	−	2.20485i	−0.0698985	−	0.0698985i
$996$		0			0
$997$	24.9091	−	24.9091i	0.788878	−	0.788878i	−0.192432	−	0.981310i	$-0.561637\pi$
$997$	24.9091	−	24.9091i	0.788878	−	0.788878i	0.981310	+	0.192432i	$0.0616375\pi$
$998$		0			0
$999$	6.20023	+	34.8851i	0.196167	+	1.10371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.d.239.6		48
3.2	odd	2	inner	1344.2.s.d.239.19		48
4.3	odd	2		336.2.s.d.323.13	yes	48
12.11	even	2		336.2.s.d.323.12	yes	48
16.5	even	4		336.2.s.d.155.12	✓	48
16.11	odd	4	inner	1344.2.s.d.911.19		48
48.5	odd	4		336.2.s.d.155.13	yes	48
48.11	even	4	inner	1344.2.s.d.911.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.12	✓	48	16.5	even	4
336.2.s.d.155.13	yes	48	48.5	odd	4
336.2.s.d.323.12	yes	48	12.11	even	2
336.2.s.d.323.13	yes	48	4.3	odd	2
1344.2.s.d.239.6		48	1.1	even	1	trivial
1344.2.s.d.239.19		48	3.2	odd	2	inner
1344.2.s.d.911.6		48	48.11	even	4	inner
1344.2.s.d.911.19		48	16.11	odd	4	inner

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29441 - 1.15087i) q^{3} +(0.186466 + 0.186466i) q^{5} -1.00000 q^{7} +(0.350987 + 2.97940i) q^{9} +O(q^{10})\)	\(q+(-1.29441 - 1.15087i) q^{3} +(0.186466 + 0.186466i) q^{5} -1.00000 q^{7} +(0.350987 + 2.97940i) q^{9} +(-4.29691 + 4.29691i) q^{11} +(2.73763 + 2.73763i) q^{13} +(-0.0267646 - 0.455961i) q^{15} -4.98546i q^{17} +(3.09905 - 3.09905i) q^{19} +(1.29441 + 1.15087i) q^{21} -3.55879i q^{23} -4.93046i q^{25} +(2.97458 - 4.26050i) q^{27} +(3.75624 - 3.75624i) q^{29} -6.58926i q^{31} +(10.5072 - 0.616763i) q^{33} +(-0.186466 - 0.186466i) q^{35} +(-4.82165 + 4.82165i) q^{37} +(-0.392949 - 6.69427i) q^{39} -10.5690 q^{41} +(5.79966 + 5.79966i) q^{43} +(-0.490108 + 0.621002i) q^{45} -3.22550 q^{47} +1.00000 q^{49} +(-5.73763 + 6.45322i) q^{51} +(-7.95980 - 7.95980i) q^{53} -1.60245 q^{55} +(-7.57805 + 0.444827i) q^{57} +(3.18645 - 3.18645i) q^{59} +(-3.17662 - 3.17662i) q^{61} +(-0.350987 - 2.97940i) q^{63} +1.02095i q^{65} +(-2.39721 + 2.39721i) q^{67} +(-4.09571 + 4.60652i) q^{69} -9.06458i q^{71} +2.32026i q^{73} +(-5.67433 + 6.38203i) q^{75} +(4.29691 - 4.29691i) q^{77} -6.89467i q^{79} +(-8.75362 + 2.09146i) q^{81} +(1.12559 + 1.12559i) q^{83} +(0.929618 - 0.929618i) q^{85} +(-9.18506 + 0.539157i) q^{87} +7.81580 q^{89} +(-2.73763 - 2.73763i) q^{91} +(-7.58340 + 8.52920i) q^{93} +1.15573 q^{95} +12.6744 q^{97} +(-14.3104 - 11.2940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{7}+O(q^{10}) \) 48 * q - 48 * q^7	\( 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) \) 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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