LMFDB - Embedded newform 2548.2.bb.g.1733.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(569,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2548.569"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,-8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1733.6
Character	$\chi$	$=$	2548.1733
Dual form			2548.2.bb.g.569.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.307410 - 0.532450i) q^{3} +(-2.46799 + 1.42489i) q^{5} +(1.31100 - 2.27072i) q^{9} +(1.56065 - 0.901040i) q^{11} +(3.01398 + 1.97887i) q^{13} +(1.51737 + 0.876054i) q^{15} -1.61378 q^{17} +(-4.64909 - 2.68415i) q^{19} +1.15172 q^{23} +(1.56065 - 2.70312i) q^{25} -3.45652 q^{27} +(-1.88686 + 3.26813i) q^{29} +(-0.325340 - 0.187835i) q^{31} +(-0.959517 - 0.553978i) q^{33} -2.27086i q^{37} +(0.127123 - 2.21312i) q^{39} +(5.59731 + 3.23161i) q^{41} +(-0.235139 - 0.407272i) q^{43} +7.47213i q^{45} +(-1.24641 + 0.719614i) q^{47} +(0.496093 + 0.859258i) q^{51} +(6.06542 - 10.5056i) q^{53} +(-2.56777 + 4.44751i) q^{55} +3.30054i q^{57} +7.12856i q^{59} +(2.80721 - 4.86224i) q^{61} +(-10.2581 - 0.589234i) q^{65} +(1.40482 - 0.811071i) q^{67} +(-0.354050 - 0.613233i) q^{69} +(8.79759 - 5.07929i) q^{71} +(-4.86733 - 2.81016i) q^{73} -1.91903 q^{75} +(-7.18620 - 12.4469i) q^{79} +(-2.87043 - 4.97172i) q^{81} -2.93485i q^{83} +(3.98279 - 2.29947i) q^{85} +2.32016 q^{87} -12.9042i q^{89} +0.230970i q^{93} +15.2985 q^{95} +(10.4934 - 6.05837i) q^{97} -4.72505i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 12 q^{15} - 32 q^{23} + 24 q^{29} - 28 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} + 32 q^{65} - 24 q^{71} + 24 q^{79} + 4 q^{81} + 12 q^{85} + 40 q^{95}+O(q^{100}) $ 24 * q - 8 * q^9 - 12 * q^15 - 32 * q^23 + 24 * q^29 - 28 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 + 32 * q^65 - 24 * q^71 + 24 * q^79 + 4 * q^81 + 12 * q^85 + 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.307410	−	0.532450i	−0.177483	−	0.307410i	0.763535	−	0.645767i	$-0.223462\pi$
$3$	−0.307410	−	0.532450i	−0.177483	−	0.307410i	−0.941018	+	0.338357i	$0.890129\pi$
$4$		0			0
$5$	−2.46799	+	1.42489i	−1.10372	+	0.637232i	−0.937195	−	0.348805i	$-0.886587\pi$
$5$	−2.46799	+	1.42489i	−1.10372	+	0.637232i	−0.166523	+	0.986038i	$0.553254\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.31100	−	2.27072i	0.436999	−	0.756905i
$10$		0			0
$11$	1.56065	−	0.901040i	0.470553	−	0.271674i	−0.245918	−	0.969291i	$-0.579090\pi$
$11$	1.56065	−	0.901040i	0.470553	−	0.271674i	0.716471	+	0.697617i	$0.245756\pi$
$12$		0			0
$13$	3.01398	+	1.97887i	0.835927	+	0.548840i
$13$	3.01398	+	1.97887i	0.835927	+	0.548840i
$14$		0			0
$15$	1.51737	+	0.876054i	0.391783	+	0.226196i
$16$		0			0
$17$	−1.61378			−0.391399			−0.195700	−	0.980664i	$-0.562698\pi$
$17$	−1.61378			−0.391399			−0.195700	+	0.980664i	$0.562698\pi$
$18$		0			0
$19$	−4.64909	−	2.68415i	−1.06657	−	0.615787i	−0.139331	−	0.990246i	$-0.544495\pi$
$19$	−4.64909	−	2.68415i	−1.06657	−	0.615787i	−0.927243	+	0.374459i	$0.877828\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.15172			0.240150			0.120075	−	0.992765i	$-0.461687\pi$
$23$	1.15172			0.240150			0.120075	+	0.992765i	$0.461687\pi$
$24$		0			0
$25$	1.56065	−	2.70312i	0.312129	−	0.540624i
$26$		0			0
$27$	−3.45652			−0.665207
$28$		0			0
$29$	−1.88686	+	3.26813i	−0.350381	+	0.606877i	−0.986316	−	0.164865i	$-0.947281\pi$
$29$	−1.88686	+	3.26813i	−0.350381	+	0.606877i	0.635936	+	0.771742i	$0.280614\pi$
$30$		0			0
$31$	−0.325340	−	0.187835i	−0.0584328	−	0.0337362i	0.470499	−	0.882401i	$-0.344074\pi$
$31$	−0.325340	−	0.187835i	−0.0584328	−	0.0337362i	−0.528932	+	0.848664i	$0.677407\pi$
$32$		0			0
$33$	−0.959517	−	0.553978i	−0.167031	−	0.0964351i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	2.27086i		−	0.373327i	−0.982424	−	0.186664i	$-0.940233\pi$
$37$		−	2.27086i		−	0.373327i	0.982424	−	0.186664i	$-0.0597675\pi$
$38$		0			0
$39$	0.127123	−	2.21312i	0.0203559	−	0.354383i
$40$		0			0
$41$	5.59731	+	3.23161i	0.874153	+	0.504692i	0.868726	−	0.495293i	$-0.164939\pi$
$41$	5.59731	+	3.23161i	0.874153	+	0.504692i	0.00542662	+	0.999985i	$0.498273\pi$
$42$		0			0
$43$	−0.235139	−	0.407272i	−0.0358583	−	0.0621084i	0.847539	−	0.530733i	$-0.178083\pi$
$43$	−0.235139	−	0.407272i	−0.0358583	−	0.0621084i	−0.883398	+	0.468624i	$0.844750\pi$
$44$		0			0
$45$			7.47213i			1.11388i
$46$		0			0
$47$	−1.24641	+	0.719614i	−0.181807	+	0.104966i	−0.588141	−	0.808758i	$-0.700140\pi$
$47$	−1.24641	+	0.719614i	−0.181807	+	0.104966i	0.406334	+	0.913724i	$0.366807\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.496093	+	0.859258i	0.0694669	+	0.120320i
$52$		0			0
$53$	6.06542	−	10.5056i	0.833150	−	1.44306i	−0.0623786	−	0.998053i	$-0.519869\pi$
$53$	6.06542	−	10.5056i	0.833150	−	1.44306i	0.895528	−	0.445005i	$-0.146798\pi$
$54$		0			0
$55$	−2.56777	+	4.44751i	−0.346238	+	0.599703i
$56$		0			0
$57$			3.30054i			0.437168i
$58$		0			0
$59$			7.12856i			0.928060i	0.885819	+	0.464030i	$0.153597\pi$
$59$			7.12856i			0.928060i	−0.885819	+	0.464030i	$0.846403\pi$
$60$		0			0
$61$	2.80721	−	4.86224i	0.359427	−	0.622546i	−0.628438	−	0.777860i	$-0.716306\pi$
$61$	2.80721	−	4.86224i	0.359427	−	0.622546i	0.987865	+	0.155314i	$0.0496388\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.2581	−	0.589234i	−1.27237	−	0.0730854i
$66$		0			0
$67$	1.40482	−	0.811071i	0.171626	−	0.0990881i	−0.411727	−	0.911307i	$-0.635074\pi$
$67$	1.40482	−	0.811071i	0.171626	−	0.0990881i	0.583352	+	0.812219i	$0.301741\pi$
$68$		0			0
$69$	−0.354050	−	0.613233i	−0.0426226	−	0.0738245i
$70$		0			0
$71$	8.79759	−	5.07929i	1.04408	−	0.602801i	0.123095	−	0.992395i	$-0.460718\pi$
$71$	8.79759	−	5.07929i	1.04408	−	0.602801i	0.920987	+	0.389594i	$0.127385\pi$
$72$		0			0
$73$	−4.86733	−	2.81016i	−0.569678	−	0.328904i	0.187343	−	0.982295i	$-0.440013\pi$
$73$	−4.86733	−	2.81016i	−0.569678	−	0.328904i	−0.757021	+	0.653391i	$0.773346\pi$
$74$		0			0
$75$	−1.91903			−0.221591
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.18620	−	12.4469i	−0.808510	−	1.40038i	−0.913896	−	0.405949i	$-0.866941\pi$
$79$	−7.18620	−	12.4469i	−0.808510	−	1.40038i	0.105385	−	0.994431i	$-0.466392\pi$
$80$		0			0
$81$	−2.87043	−	4.97172i	−0.318936	−	0.552414i
$82$		0			0
$83$		−	2.93485i		−	0.322141i	−0.986943	−	0.161071i	$-0.948505\pi$
$83$		−	2.93485i		−	0.322141i	0.986943	−	0.161071i	$-0.0514947\pi$
$84$		0			0
$85$	3.98279	−	2.29947i	0.431995	−	0.249412i
$86$		0			0
$87$	2.32016			0.248747
$88$		0			0
$89$		−	12.9042i		−	1.36784i	−0.729556	−	0.683921i	$-0.760273\pi$
$89$		−	12.9042i		−	1.36784i	0.729556	−	0.683921i	$-0.239727\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$			0.230970i			0.0239504i
$94$		0			0
$95$	15.2985			1.56960
$96$		0			0
$97$	10.4934	−	6.05837i	1.06544	−	0.615135i	0.138511	−	0.990361i	$-0.455768\pi$
$97$	10.4934	−	6.05837i	1.06544	−	0.615135i	0.926933	+	0.375226i	$0.122435\pi$
$98$		0			0
$99$		−	4.72505i		−	0.474885i
$100$		0			0
$101$	2.03122	+	3.51818i	0.202114	+	0.350072i	0.949209	−	0.314645i	$-0.101885\pi$
$101$	2.03122	+	3.51818i	0.202114	+	0.350072i	−0.747095	+	0.664717i	$0.768552\pi$
$102$		0			0
$103$	−9.58973	−	16.6099i	−0.944904	−	1.63662i	−0.755944	−	0.654637i	$-0.772822\pi$
$103$	−9.58973	−	16.6099i	−0.944904	−	1.63662i	−0.188960	−	0.981985i	$-0.560512\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.18162			−0.887621			−0.443810	−	0.896121i	$-0.646374\pi$
$107$	−9.18162			−0.887621			−0.443810	+	0.896121i	$0.646374\pi$
$108$		0			0
$109$	−4.38060	−	2.52914i	−0.419586	−	0.242248i	0.275314	−	0.961354i	$-0.411218\pi$
$109$	−4.38060	−	2.52914i	−0.419586	−	0.242248i	−0.694900	+	0.719106i	$0.744551\pi$
$110$		0			0
$111$	−1.20912	+	0.698086i	−0.114765	+	0.0662594i
$112$		0			0
$113$	−2.21934	−	3.84401i	−0.208778	−	0.361614i	0.742552	−	0.669788i	$-0.233615\pi$
$113$	−2.21934	−	3.84401i	−0.208778	−	0.361614i	−0.951330	+	0.308175i	$0.900282\pi$
$114$		0			0
$115$	−2.84243	+	1.64108i	−0.265058	+	0.153031i
$116$		0			0
$117$	8.44477	−	4.24959i	0.780720	−	0.392875i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.87625	+	6.71387i	−0.352387	+	0.610352i
$122$		0			0
$123$		−	3.97372i		−	0.358298i
$124$		0			0
$125$		−	5.35392i		−	0.478869i
$126$		0			0
$127$	8.68065	−	15.0353i	0.770283	−	1.33417i	−0.167125	−	0.985936i	$-0.553448\pi$
$127$	8.68065	−	15.0353i	0.770283	−	1.33417i	0.937408	−	0.348234i	$-0.113218\pi$
$128$		0			0
$129$	−0.144568	+	0.250399i	−0.0127285	+	0.0220464i
$130$		0			0
$131$	2.62997	+	4.55524i	0.229781	+	0.397993i	0.957743	−	0.287625i	$-0.0928655\pi$
$131$	2.62997	+	4.55524i	0.229781	+	0.397993i	−0.727962	+	0.685618i	$0.759532\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	8.53065	−	4.92517i	0.734201	−	0.423891i
$136$		0			0
$137$		−	18.2216i		−	1.55678i	−0.627782	−	0.778389i	$-0.716037\pi$
$137$		−	18.2216i		−	1.55678i	0.627782	−	0.778389i	$-0.283963\pi$
$138$		0			0
$139$	−10.0434	−	17.3956i	−0.851868	−	1.47548i	−0.879520	−	0.475861i	$-0.842137\pi$
$139$	−10.0434	−	17.3956i	−0.851868	−	1.47548i	0.0276525	−	0.999618i	$-0.491197\pi$
$140$		0			0
$141$	0.766317	+	0.442433i	0.0645355	+	0.0372596i
$142$		0			0
$143$	6.48680	+	0.372605i	0.542453	+	0.0311588i
$144$		0			0
$145$		−	10.7543i		−	0.893095i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.9068	+	7.45173i	1.05736	+	0.610469i	0.924702	−	0.380692i	$-0.124314\pi$
$149$	12.9068	+	7.45173i	1.05736	+	0.610469i	0.132662	+	0.991161i	$0.457648\pi$
$150$		0			0
$151$	6.02529	+	3.47870i	0.490331	+	0.283093i	0.724712	−	0.689052i	$-0.241973\pi$
$151$	6.02529	+	3.47870i	0.490331	+	0.283093i	−0.234381	+	0.972145i	$0.575306\pi$
$152$		0			0
$153$	−2.11566	+	3.66444i	−0.171041	+	0.296252i
$154$		0			0
$155$	1.07058			0.0859911
$156$		0			0
$157$	−3.10683	+	5.38118i	−0.247952	+	0.429465i	−0.962957	−	0.269654i	$-0.913091\pi$
$157$	−3.10683	+	5.38118i	−0.247952	+	0.429465i	0.715006	+	0.699119i	$0.246424\pi$
$158$		0			0
$159$	−7.45829			−0.591481
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.94888	−	4.58929i	−0.622605	−	0.359461i	0.155278	−	0.987871i	$-0.450373\pi$
$163$	−7.94888	−	4.58929i	−0.622605	−	0.359461i	−0.777882	+	0.628410i	$0.783706\pi$
$164$		0			0
$165$	3.15744			0.245806
$166$		0			0
$167$	−0.810372	−	0.467869i	−0.0627085	−	0.0362048i	0.468318	−	0.883560i	$-0.344860\pi$
$167$	−0.810372	−	0.467869i	−0.0627085	−	0.0362048i	−0.531026	+	0.847355i	$0.678194\pi$
$168$		0			0
$169$	5.16813	+	11.9286i	0.397549	+	0.917581i
$170$		0			0
$171$	−12.1899	+	7.03784i	−0.932184	+	0.538197i
$172$		0			0
$173$	1.73303	−	3.00170i	0.131760	−	0.228215i	−0.792595	−	0.609748i	$-0.791270\pi$
$173$	1.73303	−	3.00170i	0.131760	−	0.228215i	0.924355	+	0.381533i	$0.124604\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.79560	−	2.19139i	0.285295	−	0.164715i
$178$		0			0
$179$	−1.28051	−	2.21792i	−0.0957102	−	0.165775i	0.814195	−	0.580592i	$-0.197179\pi$
$179$	−1.28051	−	2.21792i	−0.0957102	−	0.165775i	−0.909905	+	0.414817i	$0.863846\pi$
$180$		0			0
$181$	12.9745			0.964389			0.482194	−	0.876064i	$-0.339840\pi$
$181$	12.9745			0.964389			0.482194	+	0.876064i	$0.339840\pi$
$182$		0			0
$183$	−3.45187			−0.255169
$184$		0			0
$185$	3.23574	+	5.60446i	0.237896	+	0.412048i
$186$		0			0
$187$	−2.51854	+	1.45408i	−0.184174	+	0.106333i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.9853	−	22.4912i	0.939583	−	1.62741i	0.173334	−	0.984863i	$-0.444546\pi$
$191$	12.9853	−	22.4912i	0.939583	−	1.62741i	0.766250	−	0.642543i	$-0.222121\pi$
$192$		0			0
$193$	−5.94916	+	3.43475i	−0.428230	+	0.247239i	−0.698592	−	0.715520i	$-0.746190\pi$
$193$	−5.94916	+	3.43475i	−0.428230	+	0.247239i	0.270362	+	0.962759i	$0.412857\pi$
$194$		0			0
$195$	2.83972	+	5.64309i	0.203357	+	0.404110i
$196$		0			0
$197$	12.9358	+	7.46849i	0.921638	+	0.532108i	0.884157	−	0.467189i	$-0.154733\pi$
$197$	12.9358	+	7.46849i	0.921638	+	0.532108i	0.0374808	+	0.999297i	$0.488067\pi$
$198$		0			0
$199$	−5.39791			−0.382648			−0.191324	−	0.981527i	$-0.561278\pi$
$199$	−5.39791			−0.382648			−0.191324	+	0.981527i	$0.561278\pi$
$200$		0			0
$201$	−0.863709	−	0.498663i	−0.0609214	−	0.0351730i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−18.4188			−1.28642
$206$		0			0
$207$	1.50990	−	2.61522i	0.104945	−	0.181771i
$208$		0			0
$209$	−9.67411			−0.669172
$210$		0			0
$211$	−4.46899	+	7.74051i	−0.307658	+	0.532879i	−0.977850	−	0.209309i	$-0.932879\pi$
$211$	−4.46899	+	7.74051i	−0.307658	+	0.532879i	0.670192	+	0.742188i	$0.266212\pi$
$212$		0			0
$213$	−5.40894	−	3.12285i	−0.370614	−	0.213974i
$214$		0			0
$215$	1.16064	+	0.670096i	0.0791550	+	0.0457001i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			3.45548i			0.233500i
$220$		0			0
$221$	−4.86390	−	3.19347i	−0.327181	−	0.214816i
$222$		0			0
$223$	12.8537	+	7.42106i	0.860744	+	0.496951i	0.864262	−	0.503043i	$-0.167786\pi$
$223$	12.8537	+	7.42106i	0.860744	+	0.496951i	−0.00351707	+	0.999994i	$0.501120\pi$
$224$		0			0
$225$	−4.09201	−	7.08757i	−0.272801	−	0.472505i
$226$		0			0
$227$			22.6321i			1.50214i	0.660221	+	0.751072i	$0.270463\pi$
$227$			22.6321i			1.50214i	−0.660221	+	0.751072i	$0.729537\pi$
$228$		0			0
$229$	−14.2649	+	8.23585i	−0.942651	+	0.544240i	−0.890790	−	0.454414i	$-0.849849\pi$
$229$	−14.2649	+	8.23585i	−0.942651	+	0.544240i	−0.0518610	+	0.998654i	$0.516515\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.12721	+	12.3447i	0.466919	+	0.808728i	0.999286	−	0.0377862i	$-0.0120306\pi$
$233$	7.12721	+	12.3447i	0.466919	+	0.808728i	−0.532367	+	0.846514i	$0.678697\pi$
$234$		0			0
$235$	2.05075	−	3.55200i	0.133776	−	0.231707i
$236$		0			0
$237$	−4.41822	+	7.65258i	−0.286994	+	0.497089i
$238$		0			0
$239$			25.1730i			1.62831i	0.580650	+	0.814154i	$0.302799\pi$
$239$			25.1730i			1.62831i	−0.580650	+	0.814154i	$0.697201\pi$
$240$		0			0
$241$		−	13.9466i		−	0.898381i	−0.893436	−	0.449191i	$-0.851712\pi$
$241$		−	13.9466i		−	0.898381i	0.893436	−	0.449191i	$-0.148288\pi$
$242$		0			0
$243$	−6.94957	+	12.0370i	−0.445815	+	0.772175i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.70066	−	17.2899i	−0.553610	−	1.10013i
$248$		0			0
$249$	−1.56266	+	0.902202i	−0.0990296	+	0.0571748i
$250$		0			0
$251$	−9.08534	−	15.7363i	−0.573462	−	0.993265i	−0.996207	−	0.0870160i	$-0.972267\pi$
$251$	−9.08534	−	15.7363i	−0.573462	−	0.993265i	0.422745	−	0.906248i	$-0.361066\pi$
$252$		0			0
$253$	1.79743	−	1.03774i	0.113003	−	0.0652424i
$254$		0			0
$255$	−2.44870	−	1.41376i	−0.153344	−	0.0885330i
$256$		0			0
$257$	−5.05703			−0.315449			−0.157724	−	0.987483i	$-0.550416\pi$
$257$	−5.05703			−0.315449			−0.157724	+	0.987483i	$0.550416\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.94733	+	8.56903i	0.306232	+	0.530410i
$262$		0			0
$263$	−2.60888	−	4.51872i	−0.160871	−	0.278636i	0.774311	−	0.632806i	$-0.218097\pi$
$263$	−2.60888	−	4.51872i	−0.160871	−	0.278636i	−0.935181	+	0.354170i	$0.884764\pi$
$264$		0			0
$265$			34.5703i			2.12364i
$266$		0			0
$267$	−6.87084	+	3.96688i	−0.420488	+	0.242769i
$268$		0			0
$269$	4.20548			0.256413			0.128206	−	0.991748i	$-0.459078\pi$
$269$	4.20548			0.256413			0.128206	+	0.991748i	$0.459078\pi$
$270$		0			0
$271$		−	9.64024i		−	0.585603i	−0.956173	−	0.292801i	$-0.905413\pi$
$271$		−	9.64024i		−	0.585603i	0.956173	−	0.292801i	$-0.0945875\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	5.62482i		−	0.339189i
$276$		0			0
$277$	−4.95633			−0.297797			−0.148898	−	0.988852i	$-0.547573\pi$
$277$	−4.95633			−0.297797			−0.148898	+	0.988852i	$0.547573\pi$
$278$		0			0
$279$	−0.853040	+	0.492503i	−0.0510702	+	0.0294854i
$280$		0			0
$281$			9.93319i			0.592564i	0.955100	+	0.296282i	$0.0957469\pi$
$281$			9.93319i			0.592564i	−0.955100	+	0.296282i	$0.904253\pi$
$282$		0			0
$283$	−12.8921	−	22.3298i	−0.766356	−	1.32737i	−0.939527	−	0.342476i	$-0.888734\pi$
$283$	−12.8921	−	22.3298i	−0.766356	−	1.32737i	0.173170	−	0.984892i	$-0.444599\pi$
$284$		0			0
$285$	−4.70292	−	8.14570i	−0.278577	−	0.482510i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−14.3957			−0.846806
$290$		0			0
$291$	−6.45156	−	3.72481i	−0.378197	−	0.218352i
$292$		0			0
$293$	−8.82379	+	5.09442i	−0.515492	+	0.297619i	−0.735088	−	0.677972i	$-0.762859\pi$
$293$	−8.82379	+	5.09442i	−0.515492	+	0.297619i	0.219597	+	0.975591i	$0.429526\pi$
$294$		0			0
$295$	−10.1575	−	17.5932i	−0.591390	−	1.02432i
$296$		0			0
$297$	−5.39440	+	3.11446i	−0.313015	+	0.180719i
$298$		0			0
$299$	3.47125	+	2.27910i	0.200748	+	0.131804i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.24884	−	2.16305i	0.0717438	−	0.124264i
$304$		0			0
$305$			15.9999i			0.916154i
$306$		0			0
$307$		−	30.2516i		−	1.72655i	−0.504734	−	0.863275i	$-0.668409\pi$
$307$		−	30.2516i		−	1.72655i	0.504734	−	0.863275i	$-0.331591\pi$
$308$		0			0
$309$	−5.89596	+	10.2121i	−0.335409	+	0.580946i
$310$		0			0
$311$	10.3599	−	17.9440i	0.587459	−	1.01751i	−0.407105	−	0.913381i	$-0.633462\pi$
$311$	10.3599	−	17.9440i	0.587459	−	1.01751i	0.994564	−	0.104127i	$-0.0332049\pi$
$312$		0			0
$313$	5.68142	+	9.84051i	0.321133	+	0.556218i	0.980722	−	0.195408i	$-0.0626031\pi$
$313$	5.68142	+	9.84051i	0.321133	+	0.556218i	−0.659589	+	0.751626i	$0.729270\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.6218	+	7.86454i	−0.765076	+	0.441717i	−0.831115	−	0.556100i	$-0.812297\pi$
$317$	−13.6218	+	7.86454i	−0.765076	+	0.441717i	0.0660394	+	0.997817i	$0.478964\pi$
$318$		0			0
$319$			6.80053i			0.380757i
$320$		0			0
$321$	2.82252	+	4.88875i	0.157538	+	0.272864i
$322$		0			0
$323$	7.50261	+	4.33163i	0.417456	+	0.241019i
$324$		0			0
$325$	10.0529	−	5.05882i	0.557634	−	0.280613i
$326$		0			0
$327$			3.10994i			0.171980i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	30.1029	+	17.3799i	1.65461	+	0.955288i	0.975142	+	0.221579i	$0.0711211\pi$
$331$	30.1029	+	17.3799i	1.65461	+	0.955288i	0.679464	+	0.733709i	$0.262212\pi$
$332$		0			0
$333$	−5.15648	−	2.97709i	−0.282573	−	0.163144i
$334$		0			0
$335$	−2.31138	+	4.00343i	−0.126284	+	0.218731i
$336$		0			0
$337$	15.4211			0.840042			0.420021	−	0.907514i	$-0.362023\pi$
$337$	15.4211			0.840042			0.420021	+	0.907514i	$0.362023\pi$
$338$		0			0
$339$	−1.36449	+	2.36337i	−0.0741091	+	0.128361i
$340$		0			0
$341$	−0.676988			−0.0366609
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.74758	+	1.00897i	0.0940867	+	0.0543210i
$346$		0			0
$347$	18.3491			0.985030			0.492515	−	0.870304i	$-0.336078\pi$
$347$	18.3491			0.985030			0.492515	+	0.870304i	$0.336078\pi$
$348$		0			0
$349$	10.9773	+	6.33774i	0.587600	+	0.339251i	0.764148	−	0.645041i	$-0.223160\pi$
$349$	10.9773	+	6.33774i	0.587600	+	0.339251i	−0.176548	+	0.984292i	$0.556493\pi$
$350$		0			0
$351$	−10.4179	−	6.84001i	−0.556065	−	0.365092i
$352$		0			0
$353$	10.2825	−	5.93658i	0.547280	−	0.315972i	−0.200744	−	0.979644i	$-0.564336\pi$
$353$	10.2825	−	5.93658i	0.547280	−	0.315972i	0.748024	+	0.663671i	$0.231003\pi$
$354$		0			0
$355$	−14.4749	+	25.0713i	−0.768248	+	1.33064i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.12250	−	3.53483i	0.323133	−	0.186561i	−0.329655	−	0.944101i	$-0.606932\pi$
$359$	6.12250	−	3.53483i	0.323133	−	0.186561i	0.652788	+	0.757540i	$0.273599\pi$
$360$		0			0
$361$	4.90935	+	8.50324i	0.258387	+	0.447539i
$362$		0			0
$363$	4.76640			0.250171
$364$		0			0
$365$	16.0167			0.838352
$366$		0			0
$367$	−13.8085	−	23.9169i	−0.720795	−	1.24845i	−0.960681	−	0.277653i	$-0.910443\pi$
$367$	−13.8085	−	23.9169i	−0.720795	−	1.24845i	0.239886	−	0.970801i	$-0.422890\pi$
$368$		0			0
$369$	14.6761	−	8.47326i	0.764008	−	0.441100i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	14.3110	−	24.7874i	0.740996	−	1.28344i	−0.211046	−	0.977476i	$-0.567687\pi$
$373$	14.3110	−	24.7874i	0.740996	−	1.28344i	0.952042	−	0.305967i	$-0.0989797\pi$
$374$		0			0
$375$	−2.85069	+	1.64585i	−0.147209	+	0.0849912i
$376$		0			0
$377$	−12.1542	+	6.11623i	−0.625971	+	0.315002i
$378$		0			0
$379$	−27.8128	−	16.0577i	−1.42865	−	0.824830i	−0.431634	−	0.902049i	$-0.642063\pi$
$379$	−27.8128	−	16.0577i	−1.42865	−	0.824830i	−0.997014	+	0.0772189i	$0.975396\pi$
$380$		0			0
$381$	−10.6741			−0.546850
$382$		0			0
$383$	19.1914	+	11.0801i	0.980633	+	0.566169i	0.902461	−	0.430771i	$-0.141758\pi$
$383$	19.1914	+	11.0801i	0.980633	+	0.566169i	0.0781720	+	0.996940i	$0.475092\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.23307			−0.0626802
$388$		0			0
$389$	−7.95497	+	13.7784i	−0.403333	+	0.698593i	−0.994126	−	0.108230i	$-0.965482\pi$
$389$	−7.95497	+	13.7784i	−0.403333	+	0.698593i	0.590793	+	0.806823i	$0.298815\pi$
$390$		0			0
$391$	−1.85862			−0.0939945
$392$		0			0
$393$	1.61696	−	2.80065i	0.0815648	−	0.141274i
$394$		0			0
$395$	35.4709	+	20.4791i	1.78474	+	1.03042i
$396$		0			0
$397$	26.1161	+	15.0781i	1.31073	+	0.756750i	0.982217	−	0.187750i	$-0.0601195\pi$
$397$	26.1161	+	15.0781i	1.31073	+	0.756750i	0.328512	+	0.944500i	$0.393453\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			34.5516i			1.72542i	0.505695	+	0.862712i	$0.331236\pi$
$401$			34.5516i			1.72542i	−0.505695	+	0.862712i	$0.668764\pi$
$402$		0			0
$403$	−0.608866	−	1.20994i	−0.0303298	−	0.0602713i
$404$		0			0
$405$	14.1684	+	8.18010i	0.704031	+	0.406473i
$406$		0			0
$407$	−2.04614	−	3.54401i	−0.101423	−	0.175670i
$408$		0			0
$409$			28.3007i			1.39938i	0.714446	+	0.699690i	$0.246679\pi$
$409$			28.3007i			1.39938i	−0.714446	+	0.699690i	$0.753321\pi$
$410$		0			0
$411$	−9.70210	+	5.60151i	−0.478569	+	0.276302i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.18185	+	7.24317i	0.205279	+	0.355553i
$416$		0			0
$417$	−6.17487	+	10.6952i	−0.302385	+	0.523746i
$418$		0			0
$419$	6.75416	−	11.6985i	0.329962	−	0.571511i	−0.652542	−	0.757753i	$-0.726297\pi$
$419$	6.75416	−	11.6985i	0.329962	−	0.571511i	0.982504	+	0.186241i	$0.0596307\pi$
$420$		0			0
$421$		−	1.45597i		−	0.0709594i	−0.999370	−	0.0354797i	$-0.988704\pi$
$421$		−	1.45597i		−	0.0709594i	0.999370	−	0.0354797i	$-0.0112959\pi$
$422$		0			0
$423$			3.77365i			0.183481i
$424$		0			0
$425$	−2.51854	+	4.36224i	−0.122167	+	0.211600i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.79571	−	3.56844i	−0.0866979	−	0.172286i
$430$		0			0
$431$	−31.8357	+	18.3804i	−1.53347	+	0.885352i	−0.534276	+	0.845310i	$0.679416\pi$
$431$	−31.8357	+	18.3804i	−1.53347	+	0.885352i	−0.999198	+	0.0400414i	$0.987251\pi$
$432$		0			0
$433$	−7.33480	−	12.7043i	−0.352488	−	0.610527i	0.634197	−	0.773172i	$-0.281331\pi$
$433$	−7.33480	−	12.7043i	−0.352488	−	0.610527i	−0.986685	+	0.162644i	$0.947998\pi$
$434$		0			0
$435$	−5.72612	+	3.30598i	−0.274546	+	0.158509i
$436$		0			0
$437$	−5.35444	−	3.09139i	−0.256138	−	0.147881i
$438$		0			0
$439$	16.4785			0.786476			0.393238	−	0.919437i	$-0.371355\pi$
$439$	16.4785			0.786476			0.393238	+	0.919437i	$0.371355\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.02121	+	15.6252i	0.428610	+	0.742375i	0.996750	−	0.0805572i	$-0.0256700\pi$
$443$	9.02121	+	15.6252i	0.428610	+	0.742375i	−0.568140	+	0.822932i	$0.692337\pi$
$444$		0			0
$445$	18.3871	+	31.8474i	0.871633	+	1.50971i
$446$		0			0
$447$		−	9.16294i		−	0.433392i
$448$		0			0
$449$	−5.28375	+	3.05058i	−0.249356	+	0.143966i	−0.619469	−	0.785021i	$-0.712652\pi$
$449$	−5.28375	+	3.05058i	−0.249356	+	0.143966i	0.370113	+	0.928987i	$0.379319\pi$
$450$		0			0
$451$	11.6472			0.548446
$452$		0			0
$453$		−	4.27755i		−	0.200977i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	1.42654i		−	0.0667306i	−0.999443	−	0.0333653i	$-0.989378\pi$
$457$		−	1.42654i		−	0.0667306i	0.999443	−	0.0333653i	$-0.0106225\pi$
$458$		0			0
$459$	5.57806			0.260362
$460$		0			0
$461$	3.67565	−	2.12213i	0.171192	−	0.0988377i	−0.411956	−	0.911204i	$-0.635154\pi$
$461$	3.67565	−	2.12213i	0.171192	−	0.0988377i	0.583148	+	0.812366i	$0.301821\pi$
$462$		0			0
$463$		−	31.0675i		−	1.44383i	−0.691982	−	0.721915i	$-0.743262\pi$
$463$		−	31.0675i		−	1.44383i	0.691982	−	0.721915i	$-0.256738\pi$
$464$		0			0
$465$	−0.329107	−	0.570031i	−0.0152620	−	0.0264345i
$466$		0			0
$467$	7.90146	+	13.6857i	0.365636	+	0.633300i	0.988878	−	0.148729i	$-0.0475182\pi$
$467$	7.90146	+	13.6857i	0.365636	+	0.633300i	−0.623242	+	0.782029i	$0.714185\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.82028			0.176029
$472$		0			0
$473$	−0.733937	−	0.423739i	−0.0337465	−	0.0194835i
$474$		0			0
$475$	−14.5112	+	8.37803i	−0.665818	+	0.384410i
$476$		0			0
$477$	−15.9035	−	27.5457i	−0.728172	−	1.26123i
$478$		0			0
$479$	31.4478	−	18.1564i	1.43689	−	0.829586i	0.439253	−	0.898363i	$-0.355243\pi$
$479$	31.4478	−	18.1564i	1.43689	−	0.829586i	0.997632	+	0.0687771i	$0.0219097\pi$
$480$		0			0
$481$	4.49374	−	6.84433i	0.204897	−	0.312074i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.2651	+	29.9040i	−0.783967	+	1.35787i
$486$		0			0
$487$		−	22.6136i		−	1.02472i	−0.858771	−	0.512359i	$-0.828772\pi$
$487$		−	22.6136i		−	1.02472i	0.858771	−	0.512359i	$-0.171228\pi$
$488$		0			0
$489$			5.64318i			0.255193i
$490$		0			0
$491$	0.687916	−	1.19151i	0.0310452	−	0.0537719i	−0.850085	−	0.526645i	$-0.823450\pi$
$491$	0.687916	−	1.19151i	0.0310452	−	0.0537719i	0.881131	+	0.472873i	$0.156783\pi$
$492$		0			0
$493$	3.04497	−	5.27405i	0.137139	−	0.237531i
$494$		0			0
$495$	6.73269	+	11.6614i	0.302612	+	0.524139i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.621513	+	0.358831i	−0.0278227	+	0.0160635i	−0.513847	−	0.857882i	$-0.671780\pi$
$499$	−0.621513	+	0.358831i	−0.0278227	+	0.0160635i	0.486024	+	0.873945i	$0.338447\pi$
$500$		0			0
$501$			0.575310i			0.0257030i
$502$		0			0
$503$	−16.5915	−	28.7373i	−0.739777	−	1.28133i	−0.952596	−	0.304239i	$-0.901598\pi$
$503$	−16.5915	−	28.7373i	−0.739777	−	1.28133i	0.212819	−	0.977092i	$-0.431736\pi$
$504$		0			0
$505$	−10.0261	−	5.78855i	−0.446154	−	0.257587i
$506$		0			0
$507$	4.76262	−	6.41873i	0.211515	−	0.285066i
$508$		0			0
$509$		−	12.5066i		−	0.554345i	−0.960820	−	0.277172i	$-0.910603\pi$
$509$		−	12.5066i		−	0.554345i	0.960820	−	0.277172i	$-0.0893973\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	16.0697	+	9.27782i	0.709493	+	0.409626i
$514$		0			0
$515$	47.3347	+	27.3287i	2.08582	+	1.20425i
$516$		0			0
$517$	−1.29680	+	2.24613i	−0.0570332	+	0.0987845i
$518$		0			0
$519$	−2.13101			−0.0935410
$520$		0			0
$521$	−4.87558	+	8.44474i	−0.213603	+	0.369971i	−0.952839	−	0.303475i	$-0.901853\pi$
$521$	−4.87558	+	8.44474i	−0.213603	+	0.369971i	0.739237	+	0.673446i	$0.235187\pi$
$522$		0			0
$523$	17.5641			0.768023			0.384012	−	0.923328i	$-0.374542\pi$
$523$	17.5641			0.768023			0.384012	+	0.923328i	$0.374542\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.525027	+	0.303125i	0.0228706	+	0.0132043i
$528$		0			0
$529$	−21.6735			−0.942328
$530$		0			0
$531$	16.1869	+	9.34553i	0.702453	+	0.405562i
$532$		0			0
$533$	10.4752	+	20.8163i	0.453733	+	0.901656i
$534$		0			0
$535$	22.6601	−	13.0828i	0.979683	−	0.565620i
$536$		0			0
$537$	−0.787286	+	1.36362i	−0.0339739	+	0.0588446i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.9883	+	11.5402i	−0.859363	+	0.496153i	−0.863799	−	0.503837i	$-0.831921\pi$
$541$	−19.9883	+	11.5402i	−0.859363	+	0.496153i	0.00443624	+	0.999990i	$0.498588\pi$
$542$		0			0
$543$	−3.98850	−	6.90829i	−0.171163	−	0.296463i
$544$		0			0
$545$	14.4150			0.617472
$546$		0			0
$547$	−40.2760			−1.72208			−0.861039	−	0.508538i	$-0.830186\pi$
$547$	−40.2760			−1.72208			−0.861039	+	0.508538i	$0.830186\pi$
$548$		0			0
$549$	−7.36050	−	12.7488i	−0.314139	−	0.544104i
$550$		0			0
$551$	17.5443	−	10.1292i	0.747414	−	0.431519i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.98940	−	3.44574i	0.0844452	−	0.146263i
$556$		0			0
$557$	−21.2364	+	12.2609i	−0.899817	+	0.519510i	−0.877141	−	0.480233i	$-0.840552\pi$
$557$	−21.2364	+	12.2609i	−0.899817	+	0.519510i	−0.0226763	+	0.999743i	$0.507219\pi$
$558$		0			0
$559$	0.0972365	−	1.69282i	0.00411266	−	0.0715986i
$560$		0			0
$561$	1.54845	+	0.893999i	0.0653757	+	0.0377447i
$562$		0			0
$563$	−12.0368			−0.507292			−0.253646	−	0.967297i	$-0.581630\pi$
$563$	−12.0368			−0.507292			−0.253646	+	0.967297i	$0.581630\pi$
$564$		0			0
$565$	10.9546	+	6.32464i	0.460864	+	0.266080i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.4426			−0.815075			−0.407538	−	0.913188i	$-0.633612\pi$
$569$	−19.4426			−0.815075			−0.407538	+	0.913188i	$0.633612\pi$
$570$		0			0
$571$	−17.7418	+	30.7297i	−0.742470	+	1.28600i	0.208897	+	0.977938i	$0.433013\pi$
$571$	−17.7418	+	30.7297i	−0.742470	+	1.28600i	−0.951367	+	0.308059i	$0.900321\pi$
$572$		0			0
$573$	−15.9673			−0.667042
$574$		0			0
$575$	1.79743	−	3.11323i	0.0749578	−	0.129831i
$576$		0			0
$577$	4.82701	+	2.78687i	0.200951	+	0.116019i	0.597099	−	0.802168i	$-0.296320\pi$
$577$	4.82701	+	2.78687i	0.200951	+	0.116019i	−0.396148	+	0.918187i	$0.629653\pi$
$578$		0			0
$579$	3.65767	+	2.11176i	0.152007	+	0.0877616i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		−	21.8607i		−	0.905379i
$584$		0			0
$585$	−14.7864	+	22.5208i	−0.611342	+	0.931123i
$586$		0			0
$587$	−8.01798	−	4.62918i	−0.330938	−	0.191067i	0.325320	−	0.945604i	$-0.394528\pi$
$587$	−8.01798	−	4.62918i	−0.330938	−	0.191067i	−0.656257	+	0.754537i	$0.727861\pi$
$588$		0			0
$589$	1.00836	+	1.74652i	0.0415486	+	0.0719643i
$590$		0			0
$591$		−	9.18356i		−	0.377761i
$592$		0			0
$593$	−4.45422	+	2.57164i	−0.182913	+	0.105605i	−0.588660	−	0.808380i	$-0.700344\pi$
$593$	−4.45422	+	2.57164i	−0.182913	+	0.105605i	0.405748	+	0.913985i	$0.367011\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.65937	+	2.87412i	0.0679136	+	0.117630i
$598$		0			0
$599$	8.02624	−	13.9018i	0.327943	−	0.568014i	−0.654160	−	0.756356i	$-0.726978\pi$
$599$	8.02624	−	13.9018i	0.327943	−	0.568014i	0.982104	+	0.188342i	$0.0603112\pi$
$600$		0			0
$601$	2.32115	−	4.02035i	0.0946816	−	0.163993i	−0.814794	−	0.579750i	$-0.803150\pi$
$601$	2.32115	−	4.02035i	0.0946816	−	0.163993i	0.909476	+	0.415757i	$0.136483\pi$
$602$		0			0
$603$		−	4.25325i		−	0.173206i
$604$		0			0
$605$		−	22.0930i		−	0.898209i
$606$		0			0
$607$	−4.37417	+	7.57629i	−0.177542	+	0.307512i	−0.941038	−	0.338301i	$-0.890148\pi$
$607$	−4.37417	+	7.57629i	−0.177542	+	0.307512i	0.763496	+	0.645813i	$0.223481\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.18067	−	0.297580i	−0.209587	−	0.0120388i
$612$		0			0
$613$	−40.2324	+	23.2282i	−1.62497	+	0.938179i	−0.639411	+	0.768865i	$0.720822\pi$
$613$	−40.2324	+	23.2282i	−1.62497	+	0.938179i	−0.985562	+	0.169313i	$0.945845\pi$
$614$		0			0
$615$	5.66212	+	9.80709i	0.228319	+	0.395460i
$616$		0			0
$617$	−29.0761	+	16.7871i	−1.17056	+	0.675822i	−0.953812	−	0.300406i	$-0.902878\pi$
$617$	−29.0761	+	16.7871i	−1.17056	+	0.675822i	−0.216747	+	0.976228i	$0.569545\pi$
$618$		0			0
$619$	−2.10330	−	1.21434i	−0.0845387	−	0.0488085i	0.457135	−	0.889397i	$-0.348876\pi$
$619$	−2.10330	−	1.21434i	−0.0845387	−	0.0488085i	−0.541673	+	0.840589i	$0.682209\pi$
$620$		0			0
$621$	−3.98094			−0.159749
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.4320	+	26.7290i	0.617280	+	1.06916i
$626$		0			0
$627$	2.97392	+	5.15098i	0.118767	+	0.205710i
$628$		0			0
$629$			3.66467i			0.146120i
$630$		0			0
$631$	13.2815	−	7.66809i	0.528729	−	0.305262i	−0.211770	−	0.977320i	$-0.567923\pi$
$631$	13.2815	−	7.66809i	0.528729	−	0.305262i	0.740499	+	0.672058i	$0.234589\pi$
$632$		0			0
$633$	5.49525			0.218416
$634$		0			0
$635$			49.4760i			1.96340i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		−	26.6358i		−	1.05369i
$640$		0			0
$641$	33.0247			1.30440			0.652199	−	0.758047i	$-0.273846\pi$
$641$	33.0247			1.30440			0.652199	+	0.758047i	$0.273846\pi$
$642$		0			0
$643$	−14.5972	+	8.42772i	−0.575659	+	0.332357i	−0.759406	−	0.650617i	$-0.774510\pi$
$643$	−14.5972	+	8.42772i	−0.575659	+	0.332357i	0.183747	+	0.982973i	$0.441177\pi$
$644$		0			0
$645$		−	0.823977i		−	0.0324441i
$646$		0			0
$647$	−22.7037	−	39.3240i	−0.892576	−	1.54599i	−0.836776	−	0.547545i	$-0.815562\pi$
$647$	−22.7037	−	39.3240i	−0.892576	−	1.54599i	−0.0557999	−	0.998442i	$-0.517771\pi$
$648$		0			0
$649$	6.42312	+	11.1252i	0.252130	+	0.436701i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−40.3950			−1.58078			−0.790389	−	0.612605i	$-0.790121\pi$
$653$	−40.3950			−1.58078			−0.790389	+	0.612605i	$0.790121\pi$
$654$		0			0
$655$	−12.9815	−	7.49485i	−0.507228	−	0.292848i
$656$		0			0
$657$	−12.7621	+	7.36822i	−0.497898	+	0.287461i
$658$		0			0
$659$	18.2656	+	31.6369i	0.711526	+	1.23240i	0.964284	+	0.264870i	$0.0853292\pi$
$659$	18.2656	+	31.6369i	0.711526	+	1.23240i	−0.252758	+	0.967530i	$0.581338\pi$
$660$		0			0
$661$	−17.4301	+	10.0633i	−0.677951	+	0.391415i	−0.799083	−	0.601221i	$-0.794681\pi$
$661$	−17.4301	+	10.0633i	−0.677951	+	0.391415i	0.121131	+	0.992636i	$0.461348\pi$
$662$		0			0
$663$	−0.205148	+	3.57149i	−0.00796730	+	0.138705i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.17313	+	3.76397i	−0.0841439	+	0.145741i
$668$		0			0
$669$		−	9.12524i		−	0.352802i
$670$		0			0
$671$		−	10.1176i		−	0.390587i
$672$		0			0
$673$	−7.89716	+	13.6783i	−0.304413	+	0.527259i	−0.977131	−	0.212641i	$-0.931794\pi$
$673$	−7.89716	+	13.6783i	−0.304413	+	0.527259i	0.672717	+	0.739900i	$0.265127\pi$
$674$		0			0
$675$	−5.39440	+	9.34338i	−0.207631	+	0.359627i
$676$		0			0
$677$	12.8720	+	22.2949i	0.494710	+	0.856862i	0.999981	−	0.00609819i	$-0.00194113\pi$
$677$	12.8720	+	22.2949i	0.494710	+	0.856862i	−0.505272	+	0.862960i	$0.668608\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	12.0504	−	6.95733i	0.461774	−	0.266605i
$682$		0			0
$683$			6.51147i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$683$			6.51147i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$684$		0			0
$685$	25.9639	+	44.9708i	0.992029	+	1.71824i
$686$		0			0
$687$	8.77035	+	5.06357i	0.334610	+	0.193187i
$688$		0			0
$689$	39.0703	−	19.6610i	1.48846	−	0.749025i
$690$		0			0
$691$		−	1.11468i		−	0.0424044i	−0.999775	−	0.0212022i	$-0.993251\pi$
$691$		−	1.11468i		−	0.0424044i	0.999775	−	0.0212022i	$-0.00674937\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	49.5739	+	28.6215i	1.88044	+	1.08568i
$696$		0			0
$697$	−9.03283	−	5.21511i	−0.342143	−	0.197536i
$698$		0			0
$699$	4.38195	−	7.58977i	0.165741	−	0.287071i
$700$		0			0
$701$	29.3444			1.10832			0.554161	−	0.832410i	$-0.313039\pi$
$701$	29.3444			1.10832			0.554161	+	0.832410i	$0.313039\pi$
$702$		0			0
$703$	−6.09534	+	10.5574i	−0.229890	+	0.398181i
$704$		0			0
$705$	−2.52168			−0.0949720
$706$		0			0
$707$		0			0
$708$		0			0
$709$	34.9489	+	20.1778i	1.31253	+	0.757792i	0.982515	−	0.186183i	$-0.0596117\pi$
$709$	34.9489	+	20.1778i	1.31253	+	0.757792i	0.330018	+	0.943975i	$0.392945\pi$
$710$		0			0
$711$	−37.6844			−1.41327
$712$		0			0
$713$	−0.374700	−	0.216333i	−0.0140326	−	0.00810174i
$714$		0			0
$715$	−16.5403	+	8.32342i	−0.618571	+	0.311278i
$716$		0			0
$717$	13.4034	−	7.73844i	0.500558	−	0.288997i
$718$		0			0
$719$	−15.0163	+	26.0090i	−0.560013	+	0.969972i	0.437481	+	0.899228i	$0.355871\pi$
$719$	−15.0163	+	26.0090i	−0.560013	+	0.969972i	−0.997494	+	0.0707441i	$0.977463\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−7.42588	+	4.28734i	−0.276172	+	0.159448i
$724$		0			0
$725$	5.88944	+	10.2008i	0.218728	+	0.378848i
$726$		0			0
$727$	−30.7097			−1.13896			−0.569479	−	0.822006i	$-0.692855\pi$
$727$	−30.7097			−1.13896			−0.569479	+	0.822006i	$0.692855\pi$
$728$		0			0
$729$	−8.67707			−0.321373
$730$		0			0
$731$	0.379462	+	0.657248i	0.0140349	+	0.0243092i
$732$		0			0
$733$	10.0877	−	5.82412i	0.372597	−	0.215119i	−0.301996	−	0.953309i	$-0.597653\pi$
$733$	10.0877	−	5.82412i	0.372597	−	0.215119i	0.674592	+	0.738190i	$0.264319\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.46161	−	2.53159i	0.0538393	−	0.0932523i
$738$		0			0
$739$	11.8399	−	6.83578i	0.435539	−	0.251458i	−0.266165	−	0.963928i	$-0.585757\pi$
$739$	11.8399	−	6.83578i	0.435539	−	0.251458i	0.701703	+	0.712469i	$0.252423\pi$
$740$		0			0
$741$	−6.53135	+	9.94777i	−0.239935	+	0.365440i
$742$		0			0
$743$	3.73344	+	2.15550i	0.136966	+	0.0790776i	0.566917	−	0.823775i	$-0.308136\pi$
$743$	3.73344	+	2.15550i	0.136966	+	0.0790776i	−0.429951	+	0.902852i	$0.641469\pi$
$744$		0			0
$745$	−42.4717			−1.55604
$746$		0			0
$747$	−6.66421	−	3.84758i	−0.243831	−	0.140776i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	42.7764			1.56093			0.780466	−	0.625198i	$-0.214982\pi$
$751$	42.7764			1.56093			0.780466	+	0.625198i	$0.214982\pi$
$752$		0			0
$753$	−5.58585	+	9.67498i	−0.203560	+	0.352576i
$754$		0			0
$755$	−19.8271			−0.721583
$756$		0			0
$757$	−8.90718	+	15.4277i	−0.323737	+	0.560729i	−0.981256	−	0.192709i	$-0.938273\pi$
$757$	−8.90718	+	15.4277i	−0.323737	+	0.560729i	0.657519	+	0.753438i	$0.271606\pi$
$758$		0			0
$759$	−1.10509	−	0.638026i	−0.0401124	−	0.0231589i
$760$		0			0
$761$	−18.5610	−	10.7162i	−0.672837	−	0.388463i	0.124314	−	0.992243i	$-0.460327\pi$
$761$	−18.5610	−	10.7162i	−0.672837	−	0.388463i	−0.797151	+	0.603780i	$0.793660\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		−	12.0584i		−	0.435972i
$766$		0			0
$767$	−14.1065	+	21.4853i	−0.509357	+	0.775791i
$768$		0			0
$769$	9.01602	+	5.20540i	0.325126	+	0.187712i	0.653675	−	0.756775i	$-0.273226\pi$
$769$	9.01602	+	5.20540i	0.325126	+	0.187712i	−0.328549	+	0.944487i	$0.606560\pi$
$770$		0			0
$771$	1.55458	+	2.69262i	0.0559869	+	0.0969722i
$772$		0			0
$773$			35.2064i			1.26628i	0.774035	+	0.633142i	$0.218235\pi$
$773$			35.2064i			1.26628i	−0.774035	+	0.633142i	$0.781765\pi$
$774$		0			0
$775$	−1.01548	+	0.586289i	−0.0364772	+	0.0210601i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−17.3483	−	30.0481i	−0.621566	−	1.07658i
$780$		0			0
$781$	9.15329	−	15.8540i	0.327530	−	0.567299i
$782$		0			0
$783$	6.52196	−	11.2964i	0.233076	−	0.403699i
$784$		0			0
$785$		−	17.7076i		−	0.632011i
$786$		0			0
$787$			41.0150i			1.46203i	0.682363	+	0.731014i	$0.260952\pi$
$787$			41.0150i			1.46203i	−0.682363	+	0.731014i	$0.739048\pi$
$788$		0			0
$789$	−1.60399	+	2.77820i	−0.0571037	+	0.0989065i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	18.0826	−	9.09956i	0.642133	−	0.323135i
$794$		0			0
$795$	18.4070	−	10.6273i	0.652828	−	0.376910i
$796$		0			0
$797$	−12.1708	−	21.0805i	−0.431113	−	0.746710i	0.565856	−	0.824504i	$-0.308546\pi$
$797$	−12.1708	−	21.0805i	−0.431113	−	0.746710i	−0.996969	+	0.0777940i	$0.975212\pi$
$798$		0			0
$799$	2.01143	−	1.16130i	0.0711592	−	0.0410838i
$800$		0			0
$801$	−29.3017	−	16.9174i	−1.03533	−	0.597746i
$802$		0			0
$803$	−10.1282			−0.357418
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.29281	−	2.23921i	−0.0455090	−	0.0788239i
$808$		0			0
$809$	−6.50727	−	11.2709i	−0.228784	−	0.396265i	0.728664	−	0.684871i	$-0.240141\pi$
$809$	−6.50727	−	11.2709i	−0.228784	−	0.396265i	−0.957448	+	0.288606i	$0.906808\pi$
$810$		0			0
$811$		−	14.5520i		−	0.510988i	−0.966811	−	0.255494i	$-0.917762\pi$
$811$		−	14.5520i		−	0.510988i	0.966811	−	0.255494i	$-0.0822382\pi$
$812$		0			0
$813$	−5.13294	+	2.96351i	−0.180020	+	0.103935i
$814$		0			0
$815$	26.1570			0.916240
$816$		0			0
$817$			2.52459i			0.0883243i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			9.55275i			0.333393i	0.986008	+	0.166697i	$0.0533101\pi$
$821$			9.55275i			0.333393i	−0.986008	+	0.166697i	$0.946690\pi$
$822$		0			0
$823$	−10.6328			−0.370635			−0.185317	−	0.982679i	$-0.559331\pi$
$823$	−10.6328			−0.370635			−0.185317	+	0.982679i	$0.559331\pi$
$824$		0			0
$825$	−2.99494	+	1.72913i	−0.104270	+	0.0602005i
$826$		0			0
$827$			44.7329i			1.55552i	0.628564	+	0.777758i	$0.283643\pi$
$827$			44.7329i			1.55552i	−0.628564	+	0.777758i	$0.716357\pi$
$828$		0			0
$829$	−11.1854	−	19.3737i	−0.388484	−	0.672875i	0.603761	−	0.797165i	$-0.293668\pi$
$829$	−11.1854	−	19.3737i	−0.388484	−	0.672875i	−0.992246	+	0.124290i	$0.960335\pi$
$830$		0			0
$831$	1.52363	+	2.63900i	0.0528540	+	0.0915458i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.66665			0.0922833
$836$		0			0
$837$	1.12454	+	0.649255i	0.0388699	+	0.0224415i
$838$		0			0
$839$	−4.05352	+	2.34030i	−0.139943	+	0.0807961i	−0.568337	−	0.822796i	$-0.692413\pi$
$839$	−4.05352	+	2.34030i	−0.139943	+	0.0807961i	0.428394	+	0.903592i	$0.359080\pi$
$840$		0			0
$841$	7.37954	+	12.7817i	0.254467	+	0.440750i
$842$		0			0
$843$	5.28893	−	3.05356i	0.182160	−	0.105170i
$844$		0			0
$845$	−29.7518	−	22.0755i	−1.02349	−	0.759420i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7.92633	+	13.7288i	−0.272031	+	0.471171i
$850$		0			0
$851$		−	2.61539i		−	0.0896545i
$852$		0			0
$853$			10.1857i			0.348753i	0.984679	+	0.174376i	$0.0557910\pi$
$853$			10.1857i			0.348753i	−0.984679	+	0.174376i	$0.944209\pi$
$854$		0			0
$855$	20.0563	−	34.7386i	0.685913	−	1.18804i
$856$		0			0
$857$	24.4300	−	42.3140i	0.834513	−	1.44542i	−0.0599127	−	0.998204i	$-0.519082\pi$
$857$	24.4300	−	42.3140i	0.834513	−	1.44542i	0.894426	−	0.447216i	$-0.147584\pi$
$858$		0			0
$859$	−2.48320	−	4.30102i	−0.0847256	−	0.146749i	0.820549	−	0.571577i	$-0.193668\pi$
$859$	−2.48320	−	4.30102i	−0.0847256	−	0.146749i	−0.905274	+	0.424828i	$0.860335\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.6926	−	14.8336i	0.874586	−	0.504943i	0.00571676	−	0.999984i	$-0.498180\pi$
$863$	25.6926	−	14.8336i	0.874586	−	0.504943i	0.868870	+	0.495041i	$0.164847\pi$
$864$		0			0
$865$			9.87756i			0.335847i
$866$		0			0
$867$	4.42539	+	7.66500i	0.150294	+	0.260317i
$868$		0			0
$869$	−22.4302	−	12.9501i	−0.760893	−	0.439302i
$870$		0			0
$871$	5.83909	+	0.335401i	0.197850	+	0.0113646i
$872$		0			0
$873$		−	31.7701i		−	1.07525i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.70755	+	3.87261i	0.226498	+	0.130769i	0.608955	−	0.793204i	$-0.291589\pi$
$877$	6.70755	+	3.87261i	0.226498	+	0.130769i	−0.382458	+	0.923973i	$0.624922\pi$
$878$		0			0
$879$	5.42505	+	3.13215i	0.182982	+	0.105645i
$880$		0			0
$881$	26.5762	−	46.0313i	0.895375	−	1.55083i	0.0620348	−	0.998074i	$-0.480241\pi$
$881$	26.5762	−	46.0313i	0.895375	−	1.55083i	0.833340	−	0.552761i	$-0.186426\pi$
$882$		0			0
$883$	−19.7373			−0.664214			−0.332107	−	0.943242i	$-0.607760\pi$
$883$	−19.7373			−0.664214			−0.332107	+	0.943242i	$0.607760\pi$
$884$		0			0
$885$	−6.24501	+	10.8167i	−0.209924	+	0.363598i
$886$		0			0
$887$	−40.9680			−1.37557			−0.687785	−	0.725915i	$-0.741417\pi$
$887$	−40.9680			−1.37557			−0.687785	+	0.725915i	$0.741417\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−8.95944	−	5.17274i	−0.300153	−	0.173293i
$892$		0			0
$893$	7.72621			0.258548
$894$		0			0
$895$	6.32059	+	3.64920i	0.211274	+	0.121979i
$896$		0			0
$897$	0.146410	−	2.54889i	0.00488847	−	0.0851049i
$898$		0			0
$899$	1.22774	−	0.708836i	0.0409474	−	0.0236410i
$900$		0			0
$901$	−9.78826	+	16.9538i	−0.326094	+	0.564812i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−32.0210	+	18.4873i	−1.06441	+	0.614539i
$906$		0			0
$907$	−2.35224	−	4.07421i	−0.0781050	−	0.135282i	0.824327	−	0.566113i	$-0.191554\pi$
$907$	−2.35224	−	4.07421i	−0.0781050	−	0.135282i	−0.902432	+	0.430832i	$0.858220\pi$
$908$		0			0
$909$	10.6517			0.353295
$910$		0			0
$911$	7.33499			0.243019			0.121509	−	0.992590i	$-0.461227\pi$
$911$	7.33499			0.243019			0.121509	+	0.992590i	$0.461227\pi$
$912$		0			0
$913$	−2.64442	−	4.58026i	−0.0875174	−	0.151585i
$914$		0			0
$915$	8.51917	−	4.91854i	0.281635	−	0.162602i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.13488	+	5.42976i	−0.103410	+	0.179111i	−0.913087	−	0.407764i	$-0.866309\pi$
$919$	−3.13488	+	5.42976i	−0.103410	+	0.179111i	0.809677	+	0.586875i	$0.199642\pi$
$920$		0			0
$921$	−16.1075	+	9.29965i	−0.530759	+	0.306434i
$922$		0			0
$923$	36.5670	+	2.10043i	1.20362	+	0.0691365i
$924$		0			0
$925$	−6.13841	−	3.54401i	−0.201830	−	0.116526i
$926$		0			0
$927$	−50.2884			−1.65169
$928$		0			0
$929$	39.7459	+	22.9473i	1.30402	+	0.752877i	0.981091	−	0.193546i	$-0.0619988\pi$
$929$	39.7459	+	22.9473i	1.30402	+	0.752877i	0.322930	+	0.946423i	$0.395332\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−12.7390			−0.417057
$934$		0			0
$935$	4.14382	−	7.17731i	0.135518	−	0.234723i
$936$		0			0
$937$	−19.9322			−0.651155			−0.325578	−	0.945515i	$-0.605559\pi$
$937$	−19.9322			−0.651155			−0.325578	+	0.945515i	$0.605559\pi$
$938$		0			0
$939$	3.49305	−	6.05014i	0.113991	−	0.197439i
$940$		0			0
$941$	42.4552	+	24.5115i	1.38400	+	0.799052i	0.992630	−	0.121182i	$-0.0386684\pi$
$941$	42.4552	+	24.5115i	1.38400	+	0.799052i	0.391369	+	0.920234i	$0.372002\pi$
$942$		0			0
$943$	6.44652	+	3.72190i	0.209928	+	0.121202i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	36.2684i		−	1.17856i	−0.807928	−	0.589282i	$-0.799411\pi$
$947$		−	36.2684i		−	1.17856i	0.807928	−	0.589282i	$-0.200589\pi$
$948$		0			0
$949$	−9.10910	−	18.1016i	−0.295694	−	0.587602i
$950$		0			0
$951$	8.37495	+	4.83528i	0.271576	+	0.156795i
$952$		0			0
$953$	26.4115	+	45.7461i	0.855554	+	1.48186i	0.876130	+	0.482074i	$0.160116\pi$
$953$	26.4115	+	45.7461i	0.855554	+	1.48186i	−0.0205766	+	0.999788i	$0.506550\pi$
$954$		0			0
$955$			74.0107i			2.39493i
$956$		0			0
$957$	3.62094	−	2.09055i	0.117049	−	0.0675780i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.4294	−	26.7246i	−0.497724	−	0.862083i
$962$		0			0
$963$	−12.0371	+	20.8488i	−0.387890	+	0.671845i
$964$		0			0
$965$	9.78832	−	16.9539i	0.315097	−	0.545764i
$966$		0			0
$967$		−	21.0424i		−	0.676679i	−0.941024	−	0.338340i	$-0.890135\pi$
$967$		−	21.0424i		−	0.676679i	0.941024	−	0.338340i	$-0.109865\pi$
$968$		0			0
$969$		−	5.32635i		−	0.171107i
$970$		0			0
$971$	22.3678	−	38.7421i	0.717816	−	1.24329i	−0.244048	−	0.969763i	$-0.578475\pi$
$971$	22.3678	−	38.7421i	0.717816	−	1.24329i	0.961864	−	0.273530i	$-0.0881912\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.78393	−	3.79752i	−0.185234	−	0.121618i
$976$		0			0
$977$	28.6223	−	16.5251i	0.915709	−	0.528685i	0.0334455	−	0.999441i	$-0.489352\pi$
$977$	28.6223	−	16.5251i	0.915709	−	0.528685i	0.882264	+	0.470756i	$0.156019\pi$
$978$		0			0
$979$	−11.6272	−	20.1389i	−0.371607	−	0.643642i
$980$		0			0
$981$	−11.4859	+	6.63140i	−0.366717	+	0.211724i
$982$		0			0
$983$	−21.4966	−	12.4111i	−0.685635	−	0.395852i	0.116340	−	0.993209i	$-0.462884\pi$
$983$	−21.4966	−	12.4111i	−0.685635	−	0.395852i	−0.801975	+	0.597358i	$0.796217\pi$
$984$		0			0
$985$	−42.5672			−1.35631
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.270814	−	0.469063i	−0.00861137	−	0.0149153i
$990$		0			0
$991$	3.37733	+	5.84970i	0.107284	+	0.185822i	0.914669	−	0.404203i	$-0.132451\pi$
$991$	3.37733	+	5.84970i	0.107284	+	0.185822i	−0.807385	+	0.590025i	$0.799118\pi$
$992$		0			0
$993$		−	21.3711i		−	0.678191i
$994$		0			0
$995$	13.3220	−	7.69145i	0.422335	−	0.243835i
$996$		0			0
$997$	−23.0076			−0.728659			−0.364330	−	0.931270i	$-0.618702\pi$
$997$	−23.0076			−0.728659			−0.364330	+	0.931270i	$0.618702\pi$
$998$		0			0
$999$			7.84927i			0.248340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bb.g.1733.6		24
7.2	even	3		2548.2.bq.g.1941.7		24
7.3	odd	6		2548.2.u.f.589.7	yes	24
7.4	even	3		2548.2.u.f.589.6	✓	24
7.5	odd	6		2548.2.bq.g.1941.6		24
7.6	odd	2	inner	2548.2.bb.g.1733.7		24
13.10	even	6		2548.2.bq.g.361.7		24
91.10	odd	6		2548.2.u.f.1765.7	yes	24
91.23	even	6	inner	2548.2.bb.g.569.6		24
91.62	odd	6		2548.2.bq.g.361.6		24
91.75	odd	6	inner	2548.2.bb.g.569.7		24
91.88	even	6		2548.2.u.f.1765.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.u.f.589.6	✓	24	7.4	even	3
2548.2.u.f.589.7	yes	24	7.3	odd	6
2548.2.u.f.1765.6	yes	24	91.88	even	6
2548.2.u.f.1765.7	yes	24	91.10	odd	6
2548.2.bb.g.569.6		24	91.23	even	6	inner
2548.2.bb.g.569.7		24	91.75	odd	6	inner
2548.2.bb.g.1733.6		24	1.1	even	1	trivial
2548.2.bb.g.1733.7		24	7.6	odd	2	inner
2548.2.bq.g.361.6		24	91.62	odd	6
2548.2.bq.g.361.7		24	13.10	even	6
2548.2.bq.g.1941.6		24	7.5	odd	6
2548.2.bq.g.1941.7		24	7.2	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.307410 - 0.532450i) q^{3} +(-2.46799 + 1.42489i) q^{5} +(1.31100 - 2.27072i) q^{9} +(1.56065 - 0.901040i) q^{11} +(3.01398 + 1.97887i) q^{13} +(1.51737 + 0.876054i) q^{15} -1.61378 q^{17} +(-4.64909 - 2.68415i) q^{19} +1.15172 q^{23} +(1.56065 - 2.70312i) q^{25} -3.45652 q^{27} +(-1.88686 + 3.26813i) q^{29} +(-0.325340 - 0.187835i) q^{31} +(-0.959517 - 0.553978i) q^{33} -2.27086i q^{37} +(0.127123 - 2.21312i) q^{39} +(5.59731 + 3.23161i) q^{41} +(-0.235139 - 0.407272i) q^{43} +7.47213i q^{45} +(-1.24641 + 0.719614i) q^{47} +(0.496093 + 0.859258i) q^{51} +(6.06542 - 10.5056i) q^{53} +(-2.56777 + 4.44751i) q^{55} +3.30054i q^{57} +7.12856i q^{59} +(2.80721 - 4.86224i) q^{61} +(-10.2581 - 0.589234i) q^{65} +(1.40482 - 0.811071i) q^{67} +(-0.354050 - 0.613233i) q^{69} +(8.79759 - 5.07929i) q^{71} +(-4.86733 - 2.81016i) q^{73} -1.91903 q^{75} +(-7.18620 - 12.4469i) q^{79} +(-2.87043 - 4.97172i) q^{81} -2.93485i q^{83} +(3.98279 - 2.29947i) q^{85} +2.32016 q^{87} -12.9042i q^{89} +0.230970i q^{93} +15.2985 q^{95} +(10.4934 - 6.05837i) q^{97} -4.72505i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 12 q^{15} - 32 q^{23} + 24 q^{29} - 28 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} + 32 q^{65} - 24 q^{71} + 24 q^{79} + 4 q^{81} + 12 q^{85} + 40 q^{95}+O(q^{100}) \) 24 * q - 8 * q^9 - 12 * q^15 - 32 * q^23 + 24 * q^29 - 28 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 + 32 * q^65 - 24 * q^71 + 24 * q^79 + 4 * q^81 + 12 * q^85 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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