LMFDB - Embedded newform 1248.2.ca.b.49.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1248,2,Mod(49,1248)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1248, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1248.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.21
Character	$\chi$	$=$	1248.49
Dual form			1248.2.ca.b.433.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} -2.09848 q^{5} +(0.271467 + 0.156732i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.72516 - 4.72012i) q^{11} +(3.57644 - 0.457231i) q^{13} +(-1.81734 + 1.04924i) q^{15} +(-2.72851 + 4.72591i) q^{17} +(1.45653 - 2.52278i) q^{19} +0.313463 q^{21} +(-1.87839 - 3.25346i) q^{23} -0.596381 q^{25} -1.00000i q^{27} +(-6.94137 + 4.00760i) q^{29} +0.514113i q^{31} +(-4.72012 - 2.72516i) q^{33} +(-0.569668 - 0.328898i) q^{35} +(-2.45591 - 4.25376i) q^{37} +(2.86867 - 2.18419i) q^{39} +(-0.638588 + 0.368689i) q^{41} +(-7.75984 - 4.48015i) q^{43} +(-1.04924 + 1.81734i) q^{45} -0.233036i q^{47} +(-3.45087 - 5.97708i) q^{49} +5.45701i q^{51} -10.7779i q^{53} +(5.71870 + 9.90507i) q^{55} -2.91306i q^{57} +(3.99560 - 6.92057i) q^{59} +(4.25265 + 2.45527i) q^{61} +(0.271467 - 0.156732i) q^{63} +(-7.50509 + 0.959489i) q^{65} +(-5.53265 - 9.58284i) q^{67} +(-3.25346 - 1.87839i) q^{69} +(-10.2705 - 5.92965i) q^{71} +8.59916i q^{73} +(-0.516481 + 0.298191i) q^{75} -1.70848i q^{77} +4.49154 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.2544 q^{83} +(5.72572 - 9.91724i) q^{85} +(-4.00760 + 6.94137i) q^{87} +(-1.00878 + 0.582419i) q^{89} +(1.04255 + 0.436418i) q^{91} +(0.257056 + 0.445235i) q^{93} +(-3.05650 + 5.29401i) q^{95} +(8.51390 + 4.91550i) q^{97} -5.45032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) $ 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	−2.09848			−0.938469			−0.469234	−	0.883074i	$-0.655470\pi$
$5$	−2.09848			−0.938469			−0.469234	+	0.883074i	$0.655470\pi$
$6$		0			0
$7$	0.271467	+	0.156732i	0.102605	+	0.0592390i	0.550424	−	0.834885i	$-0.314466\pi$
$7$	0.271467	+	0.156732i	0.102605	+	0.0592390i	−0.447819	+	0.894124i	$0.647799\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.72516	−	4.72012i	−0.821667	−	1.42317i	−0.904440	−	0.426601i	$-0.859711\pi$
$11$	−2.72516	−	4.72012i	−0.821667	−	1.42317i	0.0827731	−	0.996568i	$-0.473622\pi$
$12$		0			0
$13$	3.57644	−	0.457231i	0.991927	−	0.126813i
$13$	3.57644	−	0.457231i	0.991927	−	0.126813i
$14$		0			0
$15$	−1.81734	+	1.04924i	−0.469234	+	0.270913i
$16$		0			0
$17$	−2.72851	+	4.72591i	−0.661760	+	1.14620i	0.318393	+	0.947959i	$0.396857\pi$
$17$	−2.72851	+	4.72591i	−0.661760	+	1.14620i	−0.980153	+	0.198243i	$0.936476\pi$
$18$		0			0
$19$	1.45653	−	2.52278i	0.334151	−	0.578766i	−0.649170	−	0.760643i	$-0.724884\pi$
$19$	1.45653	−	2.52278i	0.334151	−	0.578766i	0.983321	+	0.181877i	$0.0582172\pi$
$20$		0			0
$21$	0.313463			0.0684033
$22$		0			0
$23$	−1.87839	−	3.25346i	−0.391671	−	0.678394i	0.600999	−	0.799250i	$-0.294770\pi$
$23$	−1.87839	−	3.25346i	−0.391671	−	0.678394i	−0.992670	+	0.120855i	$0.961436\pi$
$24$		0			0
$25$	−0.596381			−0.119276
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−6.94137	+	4.00760i	−1.28898	+	0.744193i	−0.978472	−	0.206378i	$-0.933832\pi$
$29$	−6.94137	+	4.00760i	−1.28898	+	0.744193i	−0.310508	+	0.950571i	$0.600499\pi$
$30$		0			0
$31$			0.514113i			0.0923374i	0.998934	+	0.0461687i	$0.0147012\pi$
$31$			0.514113i			0.0923374i	−0.998934	+	0.0461687i	$0.985299\pi$
$32$		0			0
$33$	−4.72012	−	2.72516i	−0.821667	−	0.474390i
$34$		0			0
$35$	−0.569668	−	0.328898i	−0.0962915	−	0.0555939i
$36$		0			0
$37$	−2.45591	−	4.25376i	−0.403749	−	0.699313i	0.590426	−	0.807092i	$-0.298960\pi$
$37$	−2.45591	−	4.25376i	−0.403749	−	0.699313i	−0.994175	+	0.107778i	$0.965626\pi$
$38$		0			0
$39$	2.86867	−	2.18419i	0.459356	−	0.349751i
$40$		0			0
$41$	−0.638588	+	0.368689i	−0.0997306	+	0.0575795i	−0.549036	−	0.835799i	$-0.685005\pi$
$41$	−0.638588	+	0.368689i	−0.0997306	+	0.0575795i	0.449305	+	0.893378i	$0.351672\pi$
$42$		0			0
$43$	−7.75984	−	4.48015i	−1.18336	−	0.683216i	−0.226574	−	0.973994i	$-0.572753\pi$
$43$	−7.75984	−	4.48015i	−1.18336	−	0.683216i	−0.956791	+	0.290778i	$0.906086\pi$
$44$		0			0
$45$	−1.04924	+	1.81734i	−0.156411	+	0.270913i
$46$		0			0
$47$		−	0.233036i		−	0.0339917i	−0.999856	−	0.0169959i	$-0.994590\pi$
$47$		−	0.233036i		−	0.0339917i	0.999856	−	0.0169959i	$-0.00541021\pi$
$48$		0			0
$49$	−3.45087	−	5.97708i	−0.492981	−	0.853869i
$50$		0			0
$51$			5.45701i			0.764135i
$52$		0			0
$53$		−	10.7779i		−	1.48045i	−0.672357	−	0.740227i	$-0.734718\pi$
$53$		−	10.7779i		−	1.48045i	0.672357	−	0.740227i	$-0.265282\pi$
$54$		0			0
$55$	5.71870	+	9.90507i	0.771109	+	1.33560i
$56$		0			0
$57$		−	2.91306i		−	0.385844i
$58$		0			0
$59$	3.99560	−	6.92057i	0.520182	−	0.900982i	−0.479542	−	0.877519i	$-0.659197\pi$
$59$	3.99560	−	6.92057i	0.520182	−	0.900982i	0.999725	−	0.0234634i	$-0.00746932\pi$
$60$		0			0
$61$	4.25265	+	2.45527i	0.544496	+	0.314365i	0.746899	−	0.664937i	$-0.231542\pi$
$61$	4.25265	+	2.45527i	0.544496	+	0.314365i	−0.202403	+	0.979302i	$0.564875\pi$
$62$		0			0
$63$	0.271467	−	0.156732i	0.0342016	−	0.0197463i
$64$		0			0
$65$	−7.50509	+	0.959489i	−0.930892	+	0.119010i
$66$		0			0
$67$	−5.53265	−	9.58284i	−0.675921	−	1.17073i	−0.976199	−	0.216878i	$-0.930413\pi$
$67$	−5.53265	−	9.58284i	−0.675921	−	1.17073i	0.300278	−	0.953852i	$-0.402921\pi$
$68$		0			0
$69$	−3.25346	−	1.87839i	−0.391671	−	0.226131i
$70$		0			0
$71$	−10.2705	−	5.92965i	−1.21888	−	0.703720i	−0.254201	−	0.967151i	$-0.581812\pi$
$71$	−10.2705	−	5.92965i	−1.21888	−	0.703720i	−0.964678	+	0.263431i	$0.915146\pi$
$72$		0			0
$73$			8.59916i			1.00646i	0.864154	+	0.503228i	$0.167854\pi$
$73$			8.59916i			1.00646i	−0.864154	+	0.503228i	$0.832146\pi$
$74$		0			0
$75$	−0.516481	+	0.298191i	−0.0596381	+	0.0344321i
$76$		0			0
$77$		−	1.70848i		−	0.194699i
$78$		0			0
$79$	4.49154			0.505337			0.252669	−	0.967553i	$-0.418692\pi$
$79$	4.49154			0.505337			0.252669	+	0.967553i	$0.418692\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.2544			1.34510			0.672550	−	0.740052i	$-0.265199\pi$
$83$	12.2544			1.34510			0.672550	+	0.740052i	$0.265199\pi$
$84$		0			0
$85$	5.72572	−	9.91724i	0.621041	−	1.07568i
$86$		0			0
$87$	−4.00760	+	6.94137i	−0.429660	+	0.744193i
$88$		0			0
$89$	−1.00878	+	0.582419i	−0.106930	+	0.0617363i	−0.552511	−	0.833505i	$-0.686330\pi$
$89$	−1.00878	+	0.582419i	−0.106930	+	0.0617363i	0.445581	+	0.895242i	$0.352997\pi$
$90$		0			0
$91$	1.04255	+	0.436418i	0.109289	+	0.0457491i
$92$		0			0
$93$	0.257056	+	0.445235i	0.0266555	+	0.0461687i
$94$		0			0
$95$	−3.05650	+	5.29401i	−0.313590	+	0.543154i
$96$		0			0
$97$	8.51390	+	4.91550i	0.864455	+	0.499093i	0.865502	−	0.500906i	$-0.167000\pi$
$97$	8.51390	+	4.91550i	0.864455	+	0.499093i	−0.00104649	+	0.999999i	$0.500333\pi$
$98$		0			0
$99$	−5.45032			−0.547778
$100$		0			0
$101$	−12.2472	+	7.07094i	−1.21864	+	0.703584i	−0.964628	−	0.263616i	$-0.915085\pi$
$101$	−12.2472	+	7.07094i	−1.21864	+	0.703584i	−0.254016	+	0.967200i	$0.581752\pi$
$102$		0			0
$103$	−5.06936			−0.499499			−0.249749	−	0.968311i	$-0.580348\pi$
$103$	−5.06936			−0.499499			−0.249749	+	0.968311i	$0.580348\pi$
$104$		0			0
$105$	−0.657796			−0.0641943
$106$		0			0
$107$	−6.30915	+	3.64259i	−0.609929	+	0.352143i	−0.772938	−	0.634482i	$-0.781213\pi$
$107$	−6.30915	+	3.64259i	−0.609929	+	0.352143i	0.163009	+	0.986625i	$0.447880\pi$
$108$		0			0
$109$	−0.947305			−0.0907354			−0.0453677	−	0.998970i	$-0.514446\pi$
$109$	−0.947305			−0.0907354			−0.0453677	+	0.998970i	$0.514446\pi$
$110$		0			0
$111$	−4.25376	−	2.45591i	−0.403749	−	0.233104i
$112$		0			0
$113$	5.86587	−	10.1600i	0.551814	−	0.955770i	−0.446330	−	0.894869i	$-0.647269\pi$
$113$	5.86587	−	10.1600i	0.551814	−	0.955770i	0.998144	−	0.0609016i	$-0.0193976\pi$
$114$		0			0
$115$	3.94176	+	6.82733i	0.367571	+	0.636652i
$116$		0			0
$117$	1.39225	−	3.32591i	0.128713	−	0.307480i
$118$		0			0
$119$	−1.48140	+	0.855287i	−0.135800	+	0.0784040i
$120$		0			0
$121$	−9.35301	+	16.1999i	−0.850273	+	1.47272i
$122$		0			0
$123$	−0.368689	+	0.638588i	−0.0332435	+	0.0575795i
$124$		0			0
$125$	11.7439			1.05041
$126$		0			0
$127$	10.8620	+	18.8135i	0.963845	+	1.66943i	0.712688	+	0.701482i	$0.247478\pi$
$127$	10.8620	+	18.8135i	0.963845	+	1.66943i	0.251157	+	0.967946i	$0.419189\pi$
$128$		0			0
$129$	−8.96029			−0.788910
$130$		0			0
$131$			14.4731i			1.26452i	0.774755	+	0.632261i	$0.217873\pi$
$131$			14.4731i			1.26452i	−0.774755	+	0.632261i	$0.782127\pi$
$132$		0			0
$133$	0.790800	−	0.456568i	0.0685710	−	0.0395895i
$134$		0			0
$135$			2.09848i			0.180608i
$136$		0			0
$137$	15.5779	+	8.99389i	1.33091	+	0.768400i	0.985439	−	0.170030i	$-0.0543866\pi$
$137$	15.5779	+	8.99389i	1.33091	+	0.768400i	0.345469	+	0.938430i	$0.387720\pi$
$138$		0			0
$139$	5.14879	+	2.97266i	0.436715	+	0.252137i	0.702203	−	0.711977i	$-0.252200\pi$
$139$	5.14879	+	2.97266i	0.436715	+	0.252137i	−0.265488	+	0.964114i	$0.585533\pi$
$140$		0			0
$141$	−0.116518	−	0.201815i	−0.00981257	−	0.0169959i
$142$		0			0
$143$	−11.9046	−	15.6352i	−0.995510	−	1.30748i
$144$		0			0
$145$	14.5663	−	8.40987i	1.20967	−	0.698402i
$146$		0			0
$147$	−5.97708	−	3.45087i	−0.492981	−	0.284623i
$148$		0			0
$149$	3.63811	−	6.30138i	0.298045	−	0.516229i	−0.677643	−	0.735391i	$-0.736999\pi$
$149$	3.63811	−	6.30138i	0.298045	−	0.516229i	0.975689	+	0.219161i	$0.0703321\pi$
$150$		0			0
$151$		−	8.17854i		−	0.665560i	−0.943005	−	0.332780i	$-0.892013\pi$
$151$		−	8.17854i		−	0.665560i	0.943005	−	0.332780i	$-0.107987\pi$
$152$		0			0
$153$	2.72851	+	4.72591i	0.220587	+	0.382067i
$154$		0			0
$155$		−	1.07886i		−	0.0866558i
$156$		0			0
$157$		−	19.1531i		−	1.52858i	−0.644871	−	0.764291i	$-0.723089\pi$
$157$		−	19.1531i		−	1.52858i	0.644871	−	0.764291i	$-0.276911\pi$
$158$		0			0
$159$	−5.38894	−	9.33391i	−0.427370	−	0.740227i
$160$		0			0
$161$		−	1.17761i		−	0.0928088i
$162$		0			0
$163$	−0.257211	+	0.445503i	−0.0201463	+	0.0348945i	−0.875923	−	0.482451i	$-0.839747\pi$
$163$	−0.257211	+	0.445503i	−0.0201463	+	0.0348945i	0.855776	+	0.517346i	$0.173080\pi$
$164$		0			0
$165$	9.90507	+	5.71870i	0.771109	+	0.445200i
$166$		0			0
$167$	1.78396	−	1.02997i	0.138047	−	0.0797013i	−0.429386	−	0.903121i	$-0.641270\pi$
$167$	1.78396	−	1.02997i	0.138047	−	0.0797013i	0.567433	+	0.823420i	$0.307937\pi$
$168$		0			0
$169$	12.5819	−	3.27052i	0.967837	−	0.251578i
$170$		0			0
$171$	−1.45653	−	2.52278i	−0.111384	−	0.192922i
$172$		0			0
$173$	−6.69644	−	3.86619i	−0.509121	−	0.293941i	0.223351	−	0.974738i	$-0.428300\pi$
$173$	−6.69644	−	3.86619i	−0.509121	−	0.293941i	−0.732472	+	0.680797i	$0.761634\pi$
$174$		0			0
$175$	−0.161898	−	0.0934718i	−0.0122383	−	0.00706580i
$176$		0			0
$177$		−	7.99119i		−	0.600655i
$178$		0			0
$179$	−14.4554	+	8.34581i	−1.08045	+	0.623795i	−0.931016	−	0.364977i	$-0.881077\pi$
$179$	−14.4554	+	8.34581i	−1.08045	+	0.623795i	−0.149429	+	0.988773i	$0.547743\pi$
$180$		0			0
$181$			2.59200i			0.192662i	0.995349	+	0.0963311i	$0.0307108\pi$
$181$			2.59200i			0.192662i	−0.995349	+	0.0963311i	$0.969289\pi$
$182$		0			0
$183$	4.91054			0.362998
$184$		0			0
$185$	5.15367	+	8.92642i	0.378905	+	0.656284i
$186$		0			0
$187$	29.7425			2.17499
$188$		0			0
$189$	0.156732	−	0.271467i	0.0114005	−	0.0197463i
$190$		0			0
$191$	5.19164	−	8.99218i	0.375654	−	0.650652i	−0.614771	−	0.788706i	$-0.710751\pi$
$191$	5.19164	−	8.99218i	0.375654	−	0.650652i	0.990425	+	0.138054i	$0.0440848\pi$
$192$		0			0
$193$	14.4597	−	8.34834i	1.04084	−	0.600927i	0.120766	−	0.992681i	$-0.461465\pi$
$193$	14.4597	−	8.34834i	1.04084	−	0.600927i	0.920070	+	0.391754i	$0.128132\pi$
$194$		0			0
$195$	−6.01986	+	4.58349i	−0.431091	+	0.328230i
$196$		0			0
$197$	10.8247	+	18.7489i	0.771226	+	1.33580i	0.936891	+	0.349621i	$0.113690\pi$
$197$	10.8247	+	18.7489i	0.771226	+	1.33580i	−0.165665	+	0.986182i	$0.552977\pi$
$198$		0			0
$199$	0.444224	−	0.769419i	0.0314902	−	0.0545427i	−0.849851	−	0.527023i	$-0.823308\pi$
$199$	0.444224	−	0.769419i	0.0314902	−	0.0545427i	0.881341	+	0.472481i	$0.156641\pi$
$200$		0			0
$201$	−9.58284	−	5.53265i	−0.675921	−	0.390243i
$202$		0			0
$203$	−2.51247			−0.176341
$204$		0			0
$205$	1.34006	−	0.773686i	0.0935941	−	0.0540366i
$206$		0			0
$207$	−3.75678			−0.261114
$208$		0			0
$209$	−15.8771			−1.09824
$210$		0			0
$211$	−4.09674	+	2.36525i	−0.282031	+	0.162831i	−0.634342	−	0.773052i	$-0.718729\pi$
$211$	−4.09674	+	2.36525i	−0.282031	+	0.162831i	0.352312	+	0.935883i	$0.385396\pi$
$212$		0			0
$213$	−11.8593			−0.812586
$214$		0			0
$215$	16.2839	+	9.40150i	1.11055	+	0.641177i
$216$		0			0
$217$	−0.0805777	+	0.139565i	−0.00546997	+	0.00947427i
$218$		0			0
$219$	4.29958	+	7.44709i	0.290539	+	0.503228i
$220$		0			0
$221$	−7.59752	+	18.1495i	−0.511064	+	1.22087i
$222$		0			0
$223$	−2.04336	+	1.17974i	−0.136834	+	0.0790009i	−0.566854	−	0.823818i	$-0.691840\pi$
$223$	−2.04336	+	1.17974i	−0.136834	+	0.0790009i	0.430020	+	0.902819i	$0.358506\pi$
$224$		0			0
$225$	−0.298191	+	0.516481i	−0.0198794	+	0.0344321i
$226$		0			0
$227$	−0.473407	+	0.819965i	−0.0314211	+	0.0544230i	−0.881308	−	0.472542i	$-0.843337\pi$
$227$	−0.473407	+	0.819965i	−0.0314211	+	0.0544230i	0.849887	+	0.526965i	$0.176670\pi$
$228$		0			0
$229$	−19.2314			−1.27085			−0.635424	−	0.772164i	$-0.719174\pi$
$229$	−19.2314			−1.27085			−0.635424	+	0.772164i	$0.719174\pi$
$230$		0			0
$231$	−0.854238	−	1.47958i	−0.0562047	−	0.0973494i
$232$		0			0
$233$	−3.40170			−0.222853			−0.111426	−	0.993773i	$-0.535542\pi$
$233$	−3.40170			−0.222853			−0.111426	+	0.993773i	$0.535542\pi$
$234$		0			0
$235$			0.489021i			0.0319002i
$236$		0			0
$237$	3.88979	−	2.24577i	0.252669	−	0.145878i
$238$		0			0
$239$		−	0.682800i		−	0.0441667i	−0.999756	−	0.0220833i	$-0.992970\pi$
$239$		−	0.682800i		−	0.0441667i	0.999756	−	0.0220833i	$-0.00702992\pi$
$240$		0			0
$241$	−5.24788	−	3.02987i	−0.338046	−	0.195171i	0.321362	−	0.946957i	$-0.395859\pi$
$241$	−5.24788	−	3.02987i	−0.338046	−	0.195171i	−0.659408	+	0.751786i	$0.729193\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	7.24158	+	12.5428i	0.462648	+	0.801329i
$246$		0			0
$247$	4.05570	−	9.68856i	0.258058	−	0.616468i
$248$		0			0
$249$	10.6127	−	6.12722i	0.672550	−	0.388297i
$250$		0			0
$251$	14.7400	+	8.51013i	0.930379	+	0.537155i	0.886931	−	0.461901i	$-0.152832\pi$
$251$	14.7400	+	8.51013i	0.930379	+	0.537155i	0.0434477	+	0.999056i	$0.486166\pi$
$252$		0			0
$253$	−10.2378	+	17.7324i	−0.643647	+	1.11483i
$254$		0			0
$255$		−	11.4514i		−	0.717117i
$256$		0			0
$257$	−14.0728	−	24.3749i	−0.877839	−	1.52046i	−0.853708	−	0.520753i	$-0.825651\pi$
$257$	−14.0728	−	24.3749i	−0.877839	−	1.52046i	−0.0241312	−	0.999709i	$-0.507682\pi$
$258$		0			0
$259$		−	1.53967i		−	0.0956706i
$260$		0			0
$261$			8.01520i			0.496129i
$262$		0			0
$263$	−11.1498	−	19.3120i	−0.687526	−	1.19083i	−0.972636	−	0.232335i	$-0.925363\pi$
$263$	−11.1498	−	19.3120i	−0.687526	−	1.19083i	0.285109	−	0.958495i	$-0.407970\pi$
$264$		0			0
$265$			22.6171i			1.38936i
$266$		0			0
$267$	−0.582419	+	1.00878i	−0.0356435	+	0.0617363i
$268$		0			0
$269$	6.77982	+	3.91433i	0.413373	+	0.238661i	0.692238	−	0.721669i	$-0.256625\pi$
$269$	6.77982	+	3.91433i	0.413373	+	0.238661i	−0.278865	+	0.960330i	$0.589958\pi$
$270$		0			0
$271$	14.2139	−	8.20639i	0.863432	−	0.498502i	−0.00172834	−	0.999999i	$-0.500550\pi$
$271$	14.2139	−	8.20639i	0.863432	−	0.498502i	0.865160	+	0.501496i	$0.167217\pi$
$272$		0			0
$273$	1.12108	−	0.143325i	0.0678510	−	0.00867442i
$274$		0			0
$275$	1.62524	+	2.81499i	0.0980054	+	0.169750i
$276$		0			0
$277$	16.1690	+	9.33520i	0.971503	+	0.560898i	0.899694	−	0.436521i	$-0.143789\pi$
$277$	16.1690	+	9.33520i	0.971503	+	0.560898i	0.0718091	+	0.997418i	$0.477123\pi$
$278$		0			0
$279$	0.445235	+	0.257056i	0.0266555	+	0.0153896i
$280$		0			0
$281$		−	13.8036i		−	0.823457i	−0.911307	−	0.411728i	$-0.864925\pi$
$281$		−	13.8036i		−	0.823457i	0.911307	−	0.411728i	$-0.135075\pi$
$282$		0			0
$283$	−6.27773	+	3.62445i	−0.373172	+	0.215451i	−0.674843	−	0.737961i	$-0.735789\pi$
$283$	−6.27773	+	3.62445i	−0.373172	+	0.215451i	0.301671	+	0.953412i	$0.402456\pi$
$284$		0			0
$285$			6.11300i			0.362103i
$286$		0			0
$287$	−0.231141			−0.0136438
$288$		0			0
$289$	−6.38951	−	11.0669i	−0.375853	−	0.650997i
$290$		0			0
$291$	9.83100			0.576303
$292$		0			0
$293$	4.40832	−	7.63543i	0.257537	−	0.446067i	−0.708045	−	0.706168i	$-0.750422\pi$
$293$	4.40832	−	7.63543i	0.257537	−	0.446067i	0.965581	+	0.260101i	$0.0837558\pi$
$294$		0			0
$295$	−8.38468	+	14.5227i	−0.488175	+	0.845544i
$296$		0			0
$297$	−4.72012	+	2.72516i	−0.273889	+	0.158130i
$298$		0			0
$299$	−8.20553	−	10.7770i	−0.474538	−	0.623248i
$300$		0			0
$301$	−1.40436	−	2.43242i	−0.0809460	−	0.140203i
$302$		0			0
$303$	−7.07094	+	12.2472i	−0.406215	+	0.703584i
$304$		0			0
$305$	−8.92411	−	5.15234i	−0.510993	−	0.295022i
$306$		0			0
$307$	−8.62295			−0.492138			−0.246069	−	0.969252i	$-0.579139\pi$
$307$	−8.62295			−0.492138			−0.246069	+	0.969252i	$0.579139\pi$
$308$		0			0
$309$	−4.39019	+	2.53468i	−0.249749	+	0.144193i
$310$		0			0
$311$	30.6497			1.73799			0.868993	−	0.494825i	$-0.164768\pi$
$311$	30.6497			1.73799			0.868993	+	0.494825i	$0.164768\pi$
$312$		0			0
$313$	26.7480			1.51189			0.755944	−	0.654637i	$-0.227178\pi$
$313$	26.7480			1.51189			0.755944	+	0.654637i	$0.227178\pi$
$314$		0			0
$315$	−0.569668	+	0.328898i	−0.0320972	+	0.0185313i
$316$		0			0
$317$	9.28415			0.521450			0.260725	−	0.965413i	$-0.416038\pi$
$317$	9.28415			0.521450			0.260725	+	0.965413i	$0.416038\pi$
$318$		0			0
$319$	37.8327	+	21.8427i	2.11823	+	1.22296i
$320$		0			0
$321$	−3.64259	+	6.30915i	−0.203310	+	0.352143i
$322$		0			0
$323$	7.94831	+	13.7669i	0.442256	+	0.766009i
$324$		0			0
$325$	−2.13292	+	0.272684i	−0.118313	+	0.0151258i
$326$		0			0
$327$	−0.820390	+	0.473653i	−0.0453677	+	0.0261930i
$328$		0			0
$329$	0.0365240	−	0.0632615i	0.00201364	−	0.00348772i
$330$		0			0
$331$	11.3270	−	19.6189i	0.622586	−	1.07835i	−0.366416	−	0.930451i	$-0.619415\pi$
$331$	11.3270	−	19.6189i	0.622586	−	1.07835i	0.989002	−	0.147900i	$-0.0472514\pi$
$332$		0			0
$333$	−4.91181			−0.269166
$334$		0			0
$335$	11.6102	+	20.1094i	0.634331	+	1.09869i
$336$		0			0
$337$	−21.2211			−1.15599			−0.577993	−	0.816042i	$-0.696164\pi$
$337$	−21.2211			−1.15599			−0.577993	+	0.816042i	$0.696164\pi$
$338$		0			0
$339$		−	11.7317i		−	0.637180i
$340$		0			0
$341$	2.42667	−	1.40104i	0.131412	−	0.0758706i
$342$		0			0
$343$		−	4.35768i		−	0.235293i
$344$		0			0
$345$	6.82733	+	3.94176i	0.367571	+	0.212217i
$346$		0			0
$347$	−21.8750	−	12.6295i	−1.17431	−	0.677989i	−0.219619	−	0.975586i	$-0.570482\pi$
$347$	−21.8750	−	12.6295i	−1.17431	−	0.677989i	−0.954692	+	0.297597i	$0.903815\pi$
$348$		0			0
$349$	9.94741	+	17.2294i	0.532473	+	0.922270i	0.999281	+	0.0379114i	$0.0120705\pi$
$349$	9.94741	+	17.2294i	0.532473	+	0.922270i	−0.466808	+	0.884359i	$0.654596\pi$
$350$		0			0
$351$	−0.457231	−	3.57644i	−0.0244052	−	0.190896i
$352$		0			0
$353$	20.5991	−	11.8929i	1.09638	−	0.632995i	0.161111	−	0.986936i	$-0.448492\pi$
$353$	20.5991	−	11.8929i	1.09638	−	0.632995i	0.935267	+	0.353942i	$0.115159\pi$
$354$		0			0
$355$	21.5524	+	12.4433i	1.14388	+	0.660419i
$356$		0			0
$357$	−0.855287	+	1.48140i	−0.0452666	+	0.0784040i
$358$		0			0
$359$			25.3258i			1.33664i	0.743872	+	0.668322i	$0.232987\pi$
$359$			25.3258i			1.33664i	−0.743872	+	0.668322i	$0.767013\pi$
$360$		0			0
$361$	5.25704	+	9.10546i	0.276686	+	0.479235i
$362$		0			0
$363$			18.7060i			0.981811i
$364$		0			0
$365$		−	18.0452i		−	0.944527i
$366$		0			0
$367$	0.556637	+	0.964124i	0.0290562	+	0.0503269i	0.880188	−	0.474625i	$-0.157416\pi$
$367$	0.556637	+	0.964124i	0.0290562	+	0.0503269i	−0.851132	+	0.524952i	$0.824083\pi$
$368$		0			0
$369$			0.737378i			0.0383863i
$370$		0			0
$371$	1.68923	−	2.92584i	0.0877006	−	0.151902i
$372$		0			0
$373$	24.0473	+	13.8837i	1.24512	+	0.718873i	0.970133	−	0.242574i	$-0.0779917\pi$
$373$	24.0473	+	13.8837i	1.24512	+	0.718873i	0.274991	+	0.961447i	$0.411325\pi$
$374$		0			0
$375$	10.1705	−	5.87195i	0.525203	−	0.303226i
$376$		0			0
$377$	−22.9930	+	17.5068i	−1.18420	+	0.901644i
$378$		0			0
$379$	−3.19771	−	5.53859i	−0.164255	−	0.284498i	0.772135	−	0.635458i	$-0.219189\pi$
$379$	−3.19771	−	5.53859i	−0.164255	−	0.284498i	−0.936391	+	0.350960i	$0.885855\pi$
$380$		0			0
$381$	18.8135	+	10.8620i	0.963845	+	0.556476i
$382$		0			0
$383$	−9.47584	−	5.47088i	−0.484193	−	0.279549i	0.237969	−	0.971273i	$-0.423518\pi$
$383$	−9.47584	−	5.47088i	−0.484193	−	0.279549i	−0.722162	+	0.691724i	$0.756852\pi$
$384$		0			0
$385$			3.58520i			0.182719i
$386$		0			0
$387$	−7.75984	+	4.48015i	−0.394455	+	0.227739i
$388$		0			0
$389$			0.805661i			0.0408486i	0.999791	+	0.0204243i	$0.00650172\pi$
$389$			0.805661i			0.0408486i	−0.999791	+	0.0204243i	$0.993498\pi$
$390$		0			0
$391$	20.5008			1.03677
$392$		0			0
$393$	7.23656	+	12.5341i	0.365036	+	0.632261i
$394$		0			0
$395$	−9.42540			−0.474243
$396$		0			0
$397$	−6.62359	+	11.4724i	−0.332429	+	0.575783i	−0.982987	−	0.183673i	$-0.941201\pi$
$397$	−6.62359	+	11.4724i	−0.332429	+	0.575783i	0.650559	+	0.759456i	$0.274535\pi$
$398$		0			0
$399$	0.456568	−	0.790800i	0.0228570	−	0.0395895i
$400$		0			0
$401$	21.7142	−	12.5367i	1.08435	−	0.626052i	0.152286	−	0.988336i	$-0.451337\pi$
$401$	21.7142	−	12.5367i	1.08435	−	0.626052i	0.932067	+	0.362285i	$0.118003\pi$
$402$		0			0
$403$	0.235068	+	1.83870i	0.0117096	+	0.0915919i
$404$		0			0
$405$	1.04924	+	1.81734i	0.0521372	+	0.0903042i
$406$		0			0
$407$	−13.3855	+	23.1843i	−0.663494	+	1.14920i
$408$		0			0
$409$	4.26820	+	2.46425i	0.211049	+	0.121849i	0.601799	−	0.798648i	$-0.294451\pi$
$409$	4.26820	+	2.46425i	0.211049	+	0.121849i	−0.390750	+	0.920497i	$0.627784\pi$
$410$		0			0
$411$	17.9878			0.887272
$412$		0			0
$413$	2.16935	−	1.25247i	0.106746	−	0.0616301i
$414$		0			0
$415$	−25.7157			−1.26233
$416$		0			0
$417$	5.94531			0.291143
$418$		0			0
$419$	25.2117	−	14.5560i	1.23167	−	0.711106i	0.264294	−	0.964442i	$-0.414861\pi$
$419$	25.2117	−	14.5560i	1.23167	−	0.711106i	0.967378	+	0.253336i	$0.0815279\pi$
$420$		0			0
$421$	3.56321			0.173660			0.0868301	−	0.996223i	$-0.472326\pi$
$421$	3.56321			0.173660			0.0868301	+	0.996223i	$0.472326\pi$
$422$		0			0
$423$	−0.201815	−	0.116518i	−0.00981257	−	0.00566529i
$424$		0			0
$425$	1.62723	−	2.81845i	0.0789323	−	0.136715i
$426$		0			0
$427$	0.769637	+	1.33305i	0.0372453	+	0.0645108i
$428$		0			0
$429$	−18.1273	−	7.58820i	−0.875192	−	0.366362i
$430$		0			0
$431$	−27.3090	+	15.7668i	−1.31543	+	0.759462i	−0.982989	−	0.183663i	$-0.941205\pi$
$431$	−27.3090	+	15.7668i	−1.31543	+	0.759462i	−0.332438	+	0.943125i	$0.607871\pi$
$432$		0			0
$433$	−15.9464	+	27.6200i	−0.766337	+	1.32733i	0.173200	+	0.984887i	$0.444589\pi$
$433$	−15.9464	+	27.6200i	−0.766337	+	1.32733i	−0.939537	+	0.342448i	$0.888744\pi$
$434$		0			0
$435$	8.40987	−	14.5663i	0.403223	−	0.698402i
$436$		0			0
$437$	−10.9437			−0.523509
$438$		0			0
$439$	−19.6769	−	34.0814i	−0.939127	−	1.62662i	−0.767104	−	0.641523i	$-0.778303\pi$
$439$	−19.6769	−	34.0814i	−0.939127	−	1.62662i	−0.172024	−	0.985093i	$-0.555031\pi$
$440$		0			0
$441$	−6.90174			−0.328654
$442$		0			0
$443$			6.10659i			0.290133i	0.989422	+	0.145066i	$0.0463396\pi$
$443$			6.10659i			0.290133i	−0.989422	+	0.145066i	$0.953660\pi$
$444$		0			0
$445$	2.11690	−	1.22220i	0.100351	−	0.0579376i
$446$		0			0
$447$		−	7.27621i		−	0.344153i
$448$		0			0
$449$	−16.1559	−	9.32761i	−0.762444	−	0.440197i	0.0677286	−	0.997704i	$-0.478425\pi$
$449$	−16.1559	−	9.32761i	−0.762444	−	0.440197i	−0.830172	+	0.557507i	$0.811758\pi$
$450$		0			0
$451$	3.48051	+	2.00947i	0.163891	+	0.0946224i
$452$		0			0
$453$	−4.08927	−	7.08282i	−0.192131	−	0.332780i
$454$		0			0
$455$	−2.18777	−	0.915815i	−0.102564	−	0.0429341i
$456$		0			0
$457$	−4.04431	+	2.33498i	−0.189185	+	0.109226i	−0.591601	−	0.806231i	$-0.701504\pi$
$457$	−4.04431	+	2.33498i	−0.189185	+	0.109226i	0.402416	+	0.915457i	$0.368171\pi$
$458$		0			0
$459$	4.72591	+	2.72851i	0.220587	+	0.127356i
$460$		0			0
$461$	−8.90866	+	15.4303i	−0.414918	+	0.718658i	−0.995420	−	0.0956002i	$-0.969523\pi$
$461$	−8.90866	+	15.4303i	−0.414918	+	0.718658i	0.580502	+	0.814259i	$0.302856\pi$
$462$		0			0
$463$		−	24.9171i		−	1.15800i	−0.815329	−	0.578998i	$-0.803444\pi$
$463$		−	24.9171i		−	1.15800i	0.815329	−	0.578998i	$-0.196556\pi$
$464$		0			0
$465$	−0.539428	−	0.934316i	−0.0250154	−	0.0433279i
$466$		0			0
$467$		−	2.76721i		−	0.128051i	−0.997948	−	0.0640257i	$-0.979606\pi$
$467$		−	2.76721i		−	0.128051i	0.997948	−	0.0640257i	$-0.0203939\pi$
$468$		0			0
$469$		−	3.46857i		−	0.160163i
$470$		0			0
$471$	−9.57654	−	16.5871i	−0.441264	−	0.764291i
$472$		0			0
$473$			48.8365i			2.24550i
$474$		0			0
$475$	−0.868647	+	1.50454i	−0.0398563	+	0.0690331i
$476$		0			0
$477$	−9.33391	−	5.38894i	−0.427370	−	0.246742i
$478$		0			0
$479$	22.9569	−	13.2542i	1.04893	−	0.605599i	0.126579	−	0.991956i	$-0.459600\pi$
$479$	22.9569	−	13.2542i	1.04893	−	0.605599i	0.922349	+	0.386357i	$0.126267\pi$
$480$		0			0
$481$	−10.7284	−	14.0904i	−0.489171	−	0.642467i
$482$		0			0
$483$	−0.588806	−	1.01984i	−0.0267916	−	0.0464044i
$484$		0			0
$485$	−17.8662	−	10.3151i	−0.811264	−	0.468384i
$486$		0			0
$487$	−24.5221	−	14.1578i	−1.11120	−	0.641552i	−0.172060	−	0.985086i	$-0.555042\pi$
$487$	−24.5221	−	14.1578i	−1.11120	−	0.641552i	−0.939140	+	0.343534i	$0.888376\pi$
$488$		0			0
$489$			0.514423i			0.0232630i
$490$		0			0
$491$	−20.6604	+	11.9283i	−0.932391	+	0.538316i	−0.887567	−	0.460679i	$-0.847606\pi$
$491$	−20.6604	+	11.9283i	−0.932391	+	0.538316i	−0.0448241	+	0.998995i	$0.514273\pi$
$492$		0			0
$493$		−	43.7391i		−	1.96991i
$494$		0			0
$495$	11.4374			0.514073
$496$		0			0
$497$	−1.85873	−	3.21941i	−0.0833753	−	0.144410i
$498$		0			0
$499$	−23.3984			−1.04746			−0.523728	−	0.851886i	$-0.675459\pi$
$499$	−23.3984			−1.04746			−0.523728	+	0.851886i	$0.675459\pi$
$500$		0			0
$501$	1.02997	−	1.78396i	0.0460156	−	0.0797013i
$502$		0			0
$503$	−1.35256	+	2.34271i	−0.0603079	+	0.104456i	−0.894603	−	0.446862i	$-0.852542\pi$
$503$	−1.35256	+	2.34271i	−0.0603079	+	0.104456i	0.834295	+	0.551318i	$0.185875\pi$
$504$		0			0
$505$	25.7005	−	14.8382i	1.14366	−	0.660292i
$506$		0			0
$507$	9.26097	−	9.12329i	0.411294	−	0.405180i
$508$		0			0
$509$	−10.5171	−	18.2162i	−0.466162	−	0.807417i	0.533091	−	0.846058i	$-0.321030\pi$
$509$	−10.5171	−	18.2162i	−0.466162	−	0.807417i	−0.999253	+	0.0386411i	$0.987697\pi$
$510$		0			0
$511$	−1.34776	+	2.33439i	−0.0596214	+	0.103267i
$512$		0			0
$513$	−2.52278	−	1.45653i	−0.111384	−	0.0643074i
$514$		0			0
$515$	10.6379			0.468764
$516$		0			0
$517$	−1.09996	+	0.635060i	−0.0483760	+	0.0279299i
$518$		0			0
$519$	−7.73238			−0.339414
$520$		0			0
$521$	16.7402			0.733400			0.366700	−	0.930339i	$-0.380488\pi$
$521$	16.7402			0.733400			0.366700	+	0.930339i	$0.380488\pi$
$522$		0			0
$523$	−32.5186	+	18.7746i	−1.42194	+	0.820956i	−0.996464	−	0.0840153i	$-0.973226\pi$
$523$	−32.5186	+	18.7746i	−1.42194	+	0.820956i	−0.425473	+	0.904971i	$0.639892\pi$
$524$		0			0
$525$	−0.186944			−0.00815889
$526$		0			0
$527$	−2.42965	−	1.40276i	−0.105837	−	0.0611052i
$528$		0			0
$529$	4.44331	−	7.69604i	0.193187	−	0.334610i
$530$		0			0
$531$	−3.99560	−	6.92057i	−0.173394	−	0.300327i
$532$		0			0
$533$	−2.11530	+	1.61058i	−0.0916237	+	0.0697618i
$534$		0			0
$535$	13.2396	−	7.64391i	0.572399	−	0.330475i
$536$		0			0
$537$	−8.34581	+	14.4554i	−0.360148	+	0.623795i
$538$		0			0
$539$	−18.8084	+	32.5770i	−0.810133	+	1.40319i
$540$		0			0
$541$	13.4046			0.576307			0.288153	−	0.957584i	$-0.406959\pi$
$541$	13.4046			0.576307			0.288153	+	0.957584i	$0.406959\pi$
$542$		0			0
$543$	1.29600	+	2.24474i	0.0556168	+	0.0963311i
$544$		0			0
$545$	1.98790			0.0851523
$546$		0			0
$547$		−	34.8445i		−	1.48984i	−0.667153	−	0.744921i	$-0.732487\pi$
$547$		−	34.8445i		−	1.48984i	0.667153	−	0.744921i	$-0.267513\pi$
$548$		0			0
$549$	4.25265	−	2.45527i	0.181499	−	0.104788i
$550$		0			0
$551$			23.3488i			0.994691i
$552$		0			0
$553$	1.21930	+	0.703966i	0.0518501	+	0.0299357i
$554$		0			0
$555$	8.92642	+	5.15367i	0.378905	+	0.218761i
$556$		0			0
$557$	−14.7015	−	25.4638i	−0.622924	−	1.07894i	−0.988938	−	0.148326i	$-0.952611\pi$
$557$	−14.7015	−	25.4638i	−0.622924	−	1.07894i	0.366015	−	0.930609i	$-0.380722\pi$
$558$		0			0
$559$	−29.8011	−	12.4750i	−1.26045	−	0.527634i
$560$		0			0
$561$	25.7578	−	14.8712i	1.08749	−	0.627864i
$562$		0			0
$563$	17.5567	+	10.1363i	0.739925	+	0.427196i	0.822042	−	0.569427i	$-0.192835\pi$
$563$	17.5567	+	10.1363i	0.739925	+	0.427196i	−0.0821172	+	0.996623i	$0.526168\pi$
$564$		0			0
$565$	−12.3094	+	21.3205i	−0.517860	+	0.896961i
$566$		0			0
$567$		−	0.313463i		−	0.0131642i
$568$		0			0
$569$	−10.7365	−	18.5961i	−0.450097	−	0.779590i	0.548295	−	0.836285i	$-0.315277\pi$
$569$	−10.7365	−	18.5961i	−0.450097	−	0.779590i	−0.998392	+	0.0566947i	$0.981944\pi$
$570$		0			0
$571$			4.71314i			0.197239i	0.995125	+	0.0986193i	$0.0314426\pi$
$571$			4.71314i			0.197239i	−0.995125	+	0.0986193i	$0.968557\pi$
$572$		0			0
$573$		−	10.3833i		−	0.433768i
$574$		0			0
$575$	1.12024	+	1.94031i	0.0467171	+	0.0809164i
$576$		0			0
$577$		−	18.2969i		−	0.761711i	−0.924634	−	0.380856i	$-0.875629\pi$
$577$		−	18.2969i		−	0.761711i	0.924634	−	0.380856i	$-0.124371\pi$
$578$		0			0
$579$	8.34834	−	14.4597i	0.346945	−	0.600927i
$580$		0			0
$581$	3.32668	+	1.92066i	0.138014	+	0.0796823i
$582$		0			0
$583$	−50.8728	+	29.3714i	−2.10694	+	1.21644i
$584$		0			0
$585$	−2.92160	+	6.97935i	−0.120793	+	0.288560i
$586$		0			0
$587$	−18.7244	−	32.4316i	−0.772839	−	1.33860i	−0.936001	−	0.351997i	$-0.885503\pi$
$587$	−18.7244	−	32.4316i	−0.772839	−	1.33860i	0.163162	−	0.986599i	$-0.447831\pi$
$588$		0			0
$589$	1.29700	+	0.748821i	0.0534418	+	0.0308546i
$590$		0			0
$591$	18.7489	+	10.8247i	0.771226	+	0.445268i
$592$		0			0
$593$		−	25.0123i		−	1.02713i	−0.858050	−	0.513566i	$-0.828324\pi$
$593$		−	25.0123i		−	1.02713i	0.858050	−	0.513566i	$-0.171676\pi$
$594$		0			0
$595$	3.10869	−	1.79480i	0.127444	−	0.0735797i
$596$		0			0
$597$		−	0.888449i		−	0.0363618i
$598$		0			0
$599$	26.3523			1.07673			0.538364	−	0.842713i	$-0.319043\pi$
$599$	26.3523			1.07673			0.538364	+	0.842713i	$0.319043\pi$
$600$		0			0
$601$	8.59419	+	14.8856i	0.350564	+	0.607195i	0.986348	−	0.164672i	$-0.0526564\pi$
$601$	8.59419	+	14.8856i	0.350564	+	0.607195i	−0.635784	+	0.771867i	$0.719323\pi$
$602$		0			0
$603$	−11.0653			−0.450614
$604$		0			0
$605$	19.6271	−	33.9951i	0.797955	−	1.38210i
$606$		0			0
$607$	−13.4030	+	23.2148i	−0.544013	+	0.942258i	0.454656	+	0.890667i	$0.349762\pi$
$607$	−13.4030	+	23.2148i	−0.544013	+	0.942258i	−0.998668	+	0.0515904i	$0.983571\pi$
$608$		0			0
$609$	−2.17586	+	1.25624i	−0.0881705	+	0.0509052i
$610$		0			0
$611$	−0.106551	−	0.833439i	−0.00431059	−	0.0337173i
$612$		0			0
$613$	−9.86389	−	17.0848i	−0.398399	−	0.690047i	0.595130	−	0.803630i	$-0.297101\pi$
$613$	−9.86389	−	17.0848i	−0.398399	−	0.690047i	−0.993529	+	0.113583i	$0.963767\pi$
$614$		0			0
$615$	0.773686	−	1.34006i	0.0311980	−	0.0540366i
$616$		0			0
$617$	15.7585	+	9.09819i	0.634414	+	0.366279i	0.782460	−	0.622701i	$-0.213965\pi$
$617$	15.7585	+	9.09819i	0.634414	+	0.366279i	−0.148045	+	0.988981i	$0.547298\pi$
$618$		0			0
$619$	−19.8662			−0.798490			−0.399245	−	0.916844i	$-0.630728\pi$
$619$	−19.8662			−0.798490			−0.399245	+	0.916844i	$0.630728\pi$
$620$		0			0
$621$	−3.25346	+	1.87839i	−0.130557	+	0.0753771i
$622$		0			0
$623$	−0.365134			−0.0146288
$624$		0			0
$625$	−21.6624			−0.866497
$626$		0			0
$627$	−13.7500	+	7.93856i	−0.549121	+	0.317035i
$628$		0			0
$629$	26.8038			1.06874
$630$		0			0
$631$	33.7151	+	19.4654i	1.34218	+	0.774905i	0.987126	−	0.159942i	$-0.0511308\pi$
$631$	33.7151	+	19.4654i	1.34218	+	0.774905i	0.355049	+	0.934848i	$0.384464\pi$
$632$		0			0
$633$	−2.36525	+	4.09674i	−0.0940103	+	0.162831i
$634$		0			0
$635$	−22.7936	−	39.4797i	−0.904538	−	1.56671i
$636$		0			0
$637$	−15.0747	−	19.7988i	−0.597283	−	0.784459i
$638$		0			0
$639$	−10.2705	+	5.92965i	−0.406293	+	0.234573i
$640$		0			0
$641$	−1.88863	+	3.27121i	−0.0745965	+	0.129205i	−0.900911	−	0.434004i	$-0.857100\pi$
$641$	−1.88863	+	3.27121i	−0.0745965	+	0.129205i	0.826314	+	0.563209i	$0.190434\pi$
$642$		0			0
$643$	−21.6147	+	37.4378i	−0.852402	+	1.47640i	0.0266315	+	0.999645i	$0.491522\pi$
$643$	−21.6147	+	37.4378i	−0.852402	+	1.47640i	−0.879034	+	0.476759i	$0.841811\pi$
$644$		0			0
$645$	18.8030			0.740367
$646$		0			0
$647$	−13.3101	−	23.0538i	−0.523274	−	0.906337i	−0.999633	−	0.0270860i	$-0.991377\pi$
$647$	−13.3101	−	23.0538i	−0.523274	−	0.906337i	0.476359	−	0.879251i	$-0.341956\pi$
$648$		0			0
$649$	−43.5546			−1.70967
$650$		0			0
$651$			0.161155i			0.00631618i
$652$		0			0
$653$	12.5518	−	7.24678i	0.491189	−	0.283588i	−0.233878	−	0.972266i	$-0.575142\pi$
$653$	12.5518	−	7.24678i	0.491189	−	0.283588i	0.725068	+	0.688678i	$0.241808\pi$
$654$		0			0
$655$		−	30.3716i		−	1.18671i
$656$		0			0
$657$	7.44709	+	4.29958i	0.290539	+	0.167743i
$658$		0			0
$659$	9.60769	+	5.54700i	0.374263	+	0.216081i	0.675319	−	0.737526i	$-0.264006\pi$
$659$	9.60769	+	5.54700i	0.374263	+	0.216081i	−0.301056	+	0.953606i	$0.597339\pi$
$660$		0			0
$661$	−10.4124	−	18.0348i	−0.404996	−	0.701474i	0.589325	−	0.807896i	$-0.299394\pi$
$661$	−10.4124	−	18.0348i	−0.404996	−	0.701474i	−0.994321	+	0.106422i	$0.966060\pi$
$662$		0			0
$663$	2.49511	+	19.5167i	0.0969022	+	0.757966i
$664$		0			0
$665$	−1.65948	+	0.958100i	−0.0643518	+	0.0371535i
$666$		0			0
$667$	26.0772	+	15.0557i	1.00971	+	0.582958i
$668$		0			0
$669$	−1.17974	+	2.04336i	−0.0456112	+	0.0790009i
$670$		0			0
$671$		−	26.7640i		−	1.03321i
$672$		0			0
$673$	−25.1355	−	43.5359i	−0.968901	−	1.67819i	−0.698748	−	0.715368i	$-0.746259\pi$
$673$	−25.1355	−	43.5359i	−0.968901	−	1.67819i	−0.270153	−	0.962817i	$-0.587074\pi$
$674$		0			0
$675$			0.596381i			0.0229547i
$676$		0			0
$677$		−	1.15925i		−	0.0445537i	−0.999752	−	0.0222769i	$-0.992908\pi$
$677$		−	1.15925i		−	0.0445537i	0.999752	−	0.0222769i	$-0.00709153\pi$
$678$		0			0
$679$	1.54083	+	2.66879i	0.0591316	+	0.102419i
$680$		0			0
$681$			0.946814i			0.0362820i
$682$		0			0
$683$	2.05391	−	3.55747i	0.0785906	−	0.136123i	−0.824051	−	0.566515i	$-0.808291\pi$
$683$	2.05391	−	3.55747i	0.0785906	−	0.136123i	0.902642	+	0.430392i	$0.141625\pi$
$684$		0			0
$685$	−32.6899	−	18.8735i	−1.24902	−	0.721119i
$686$		0			0
$687$	−16.6549	+	9.61570i	−0.635424	+	0.366862i
$688$		0			0
$689$	−4.92797	−	38.5464i	−0.187741	−	1.46850i
$690$		0			0
$691$	−22.0592	−	38.2077i	−0.839173	−	1.45349i	−0.890587	−	0.454812i	$-0.849706\pi$
$691$	−22.0592	−	38.2077i	−0.839173	−	1.45349i	0.0514148	−	0.998677i	$-0.483627\pi$
$692$		0			0
$693$	−1.47958	−	0.854238i	−0.0562047	−	0.0324498i
$694$		0			0
$695$	−10.8046	−	6.23806i	−0.409843	−	0.236623i
$696$		0			0
$697$		−	4.02388i		−	0.152415i
$698$		0			0
$699$	−2.94596	+	1.70085i	−0.111426	+	0.0643320i
$700$		0			0
$701$			42.5841i			1.60838i	0.594373	+	0.804189i	$0.297400\pi$
$701$			42.5841i			1.60838i	−0.594373	+	0.804189i	$0.702600\pi$
$702$		0			0
$703$	−14.3084			−0.539652
$704$		0			0
$705$	0.244510	+	0.423504i	0.00920879	+	0.0159501i
$706$		0			0
$707$	−4.43296			−0.166718
$708$		0			0
$709$	15.1238	−	26.1952i	0.567985	−	0.983780i	−0.428780	−	0.903409i	$-0.641056\pi$
$709$	15.1238	−	26.1952i	0.567985	−	0.983780i	0.996765	−	0.0803705i	$-0.0256104\pi$
$710$		0			0
$711$	2.24577	−	3.88979i	0.0842229	−	0.145878i
$712$		0			0
$713$	1.67265	−	0.965704i	0.0626412	−	0.0361659i
$714$		0			0
$715$	24.9815	+	32.8102i	0.934255	+	1.22703i
$716$		0			0
$717$	−0.341400	−	0.591322i	−0.0127498	−	0.0220833i
$718$		0			0
$719$	−18.6668	+	32.3318i	−0.696152	+	1.20577i	0.273638	+	0.961833i	$0.411773\pi$
$719$	−18.6668	+	32.3318i	−0.696152	+	1.20577i	−0.969791	+	0.243939i	$0.921560\pi$
$720$		0			0
$721$	−1.37616	−	0.794529i	−0.0512510	−	0.0295898i
$722$		0			0
$723$	−6.05974			−0.225364
$724$		0			0
$725$	4.13970	−	2.39006i	0.153745	−	0.0887646i
$726$		0			0
$727$	−13.6532			−0.506371			−0.253185	−	0.967418i	$-0.581478\pi$
$727$	−13.6532			−0.506371			−0.253185	+	0.967418i	$0.581478\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	42.3456	−	24.4482i	1.56621	−	0.904251i
$732$		0			0
$733$	−6.99689			−0.258436			−0.129218	−	0.991616i	$-0.541247\pi$
$733$	−6.99689			−0.258436			−0.129218	+	0.991616i	$0.541247\pi$
$734$		0			0
$735$	12.5428	+	7.24158i	0.462648	+	0.267110i
$736$		0			0
$737$	−30.1547	+	52.2295i	−1.11076	+	1.92390i
$738$		0			0
$739$	−19.7960	−	34.2878i	−0.728209	−	1.26130i	−0.957639	−	0.287970i	$-0.907020\pi$
$739$	−19.7960	−	34.2878i	−0.728209	−	1.26130i	0.229430	−	0.973325i	$-0.426314\pi$
$740$		0			0
$741$	−1.33194	−	10.4184i	−0.0489300	−	0.382729i
$742$		0			0
$743$	30.3873	−	17.5441i	1.11480	−	0.643631i	0.174733	−	0.984616i	$-0.444094\pi$
$743$	30.3873	−	17.5441i	1.11480	−	0.643631i	0.940069	+	0.340984i	$0.110760\pi$
$744$		0			0
$745$	−7.63449	+	13.2233i	−0.279706	+	0.484465i
$746$		0			0
$747$	6.12722	−	10.6127i	0.224183	−	0.388297i
$748$		0			0
$749$	−2.28364			−0.0834423
$750$		0			0
$751$	7.32809	+	12.6926i	0.267406	+	0.463160i	0.968191	−	0.250212i	$-0.0805002\pi$
$751$	7.32809	+	12.6926i	0.267406	+	0.463160i	−0.700785	+	0.713372i	$0.747167\pi$
$752$		0			0
$753$	17.0203			0.620253
$754$		0			0
$755$			17.1625i			0.624607i
$756$		0			0
$757$	−45.4728	+	26.2537i	−1.65274	+	0.954208i	−0.676797	+	0.736170i	$0.736632\pi$
$757$	−45.4728	+	26.2537i	−1.65274	+	0.954208i	−0.975940	+	0.218038i	$0.930034\pi$
$758$		0			0
$759$			20.4756i			0.743219i
$760$		0			0
$761$	26.9115	+	15.5373i	0.975540	+	0.563228i	0.900921	−	0.433984i	$-0.142893\pi$
$761$	26.9115	+	15.5373i	0.975540	+	0.563228i	0.0746191	+	0.997212i	$0.476226\pi$
$762$		0			0
$763$	−0.257162	−	0.148473i	−0.00930989	−	0.00537507i
$764$		0			0
$765$	−5.72572	−	9.91724i	−0.207014	−	0.358558i
$766$		0			0
$767$	11.1257	−	26.5779i	0.401726	−	0.959674i
$768$		0			0
$769$	−27.8593	+	16.0846i	−1.00463	+	0.580024i	−0.909615	−	0.415451i	$-0.863624\pi$
$769$	−27.8593	+	16.0846i	−1.00463	+	0.580024i	−0.0950162	+	0.995476i	$0.530290\pi$
$770$		0			0
$771$	−24.3749	−	14.0728i	−0.877839	−	0.506820i
$772$		0			0
$773$	17.6492	−	30.5694i	0.634799	−	1.09950i	−0.351759	−	0.936091i	$-0.614416\pi$
$773$	17.6492	−	30.5694i	0.634799	−	1.09950i	0.986558	−	0.163413i	$-0.0522504\pi$
$774$		0			0
$775$		−	0.306607i		−	0.0110137i
$776$		0			0
$777$	−0.769836	−	1.33340i	−0.0276177	−	0.0478353i
$778$		0			0
$779$			2.14802i			0.0769610i
$780$		0			0
$781$			64.6370i			2.31289i
$782$		0			0
$783$	4.00760	+	6.94137i	0.143220	+	0.248064i
$784$		0			0
$785$			40.1924i			1.43453i
$786$		0			0
$787$	3.48371	−	6.03397i	0.124181	−	0.215088i	−0.797232	−	0.603674i	$-0.793703\pi$
$787$	3.48371	−	6.03397i	0.124181	−	0.215088i	0.921412	+	0.388586i	$0.127036\pi$
$788$		0			0
$789$	−19.3120	−	11.1498i	−0.687526	−	0.396943i
$790$		0			0
$791$	3.18478	−	1.83873i	0.113238	−	0.0653778i
$792$		0			0
$793$	16.3320	+	6.83669i	0.579966	+	0.242778i
$794$		0			0
$795$	11.3086	+	19.5870i	0.401074	+	0.694680i
$796$		0			0
$797$	2.66536	+	1.53885i	0.0944119	+	0.0545088i	0.546463	−	0.837484i	$-0.315974\pi$
$797$	2.66536	+	1.53885i	0.0944119	+	0.0545088i	−0.452051	+	0.891992i	$0.649307\pi$
$798$		0			0
$799$	1.10131	+	0.635840i	0.0389614	+	0.0224944i
$800$		0			0
$801$			1.16484i			0.0411576i
$802$		0			0
$803$	40.5891	−	23.4341i	1.43236	−	0.826972i
$804$		0			0
$805$			2.47119i			0.0870981i
$806$		0			0
$807$	7.82866			0.275582
$808$		0			0
$809$	6.93330	+	12.0088i	0.243762	+	0.422208i	0.961783	−	0.273814i	$-0.0882852\pi$
$809$	6.93330	+	12.0088i	0.243762	+	0.422208i	−0.718021	+	0.696021i	$0.754952\pi$
$810$		0			0
$811$	19.9532			0.700652			0.350326	−	0.936628i	$-0.386071\pi$
$811$	19.9532			0.700652			0.350326	+	0.936628i	$0.386071\pi$
$812$		0			0
$813$	8.20639	−	14.2139i	0.287811	−	0.498502i
$814$		0			0
$815$	0.539753	−	0.934879i	0.0189067	−	0.0327474i
$816$		0			0
$817$	−22.6049	+	13.0509i	−0.790845	+	0.456594i
$818$		0			0
$819$	0.899224	−	0.684664i	0.0314214	−	0.0239241i
$820$		0			0
$821$	8.72499	+	15.1121i	0.304504	+	0.527417i	0.977151	−	0.212547i	$-0.0681759\pi$
$821$	8.72499	+	15.1121i	0.304504	+	0.527417i	−0.672647	+	0.739964i	$0.734843\pi$
$822$		0			0
$823$	2.90032	−	5.02351i	0.101099	−	0.175108i	−0.811039	−	0.584992i	$-0.801097\pi$
$823$	2.90032	−	5.02351i	0.101099	−	0.175108i	0.912138	+	0.409884i	$0.134431\pi$
$824$		0			0
$825$	2.81499	+	1.62524i	0.0980054	+	0.0565834i
$826$		0			0
$827$	27.9904			0.973322			0.486661	−	0.873591i	$-0.338215\pi$
$827$	27.9904			0.973322			0.486661	+	0.873591i	$0.338215\pi$
$828$		0			0
$829$	45.7334	−	26.4042i	1.58839	−	0.917056i	0.594814	−	0.803864i	$-0.297226\pi$
$829$	45.7334	−	26.4042i	1.58839	−	0.917056i	0.993573	−	0.113192i	$-0.0361075\pi$
$830$		0			0
$831$	18.6704			0.647669
$832$		0			0
$833$	37.6629			1.30494
$834$		0			0
$835$	−3.74360	+	2.16137i	−0.129552	+	0.0747972i
$836$		0			0
$837$	0.514113			0.0177703
$838$		0			0
$839$	−6.36083	−	3.67243i	−0.219600	−	0.126786i	0.386165	−	0.922430i	$-0.373800\pi$
$839$	−6.36083	−	3.67243i	−0.219600	−	0.126786i	−0.605765	+	0.795644i	$0.707133\pi$
$840$		0			0
$841$	17.6218	−	30.5218i	0.607647	−	1.05247i
$842$		0			0
$843$	−6.90182	−	11.9543i	−0.237711	−	0.411728i
$844$		0			0
$845$	−26.4028	+	6.86312i	−0.908285	+	0.236098i
$846$		0			0
$847$	−5.07807	+	2.93182i	−0.174484	+	0.100739i
$848$		0			0
$849$	−3.62445	+	6.27773i	−0.124391	+	0.215451i
$850$		0			0
$851$	−9.22630	+	15.9804i	−0.316273	+	0.547801i
$852$		0			0
$853$	−43.2083			−1.47942			−0.739712	−	0.672923i	$-0.765038\pi$
$853$	−43.2083			−1.47942			−0.739712	+	0.672923i	$0.765038\pi$
$854$		0			0
$855$	3.05650	+	5.29401i	0.104530	+	0.181051i
$856$		0			0
$857$	−18.4720			−0.630992			−0.315496	−	0.948927i	$-0.602171\pi$
$857$	−18.4720			−0.630992			−0.315496	+	0.948927i	$0.602171\pi$
$858$		0			0
$859$		−	8.98716i		−	0.306638i	−0.988177	−	0.153319i	$-0.951004\pi$
$859$		−	8.98716i		−	0.306638i	0.988177	−	0.153319i	$-0.0489962\pi$
$860$		0			0
$861$	−0.200174	+	0.115570i	−0.00682190	+	0.00393863i
$862$		0			0
$863$			42.4027i			1.44340i	0.692204	+	0.721702i	$0.256640\pi$
$863$			42.4027i			1.44340i	−0.692204	+	0.721702i	$0.743360\pi$
$864$		0			0
$865$	14.0523	+	8.11313i	0.477794	+	0.275855i
$866$		0			0
$867$	−11.0669	−	6.38951i	−0.375853	−	0.216999i
$868$		0			0
$869$	−12.2402	−	21.2006i	−0.415219	−	0.719181i
$870$		0			0
$871$	−24.1688	−	31.7428i	−0.818928	−	1.07556i
$872$		0			0
$873$	8.51390	−	4.91550i	0.288152	−	0.166364i
$874$		0			0
$875$	3.18808	+	1.84064i	0.107777	+	0.0622250i
$876$		0			0
$877$	−7.22623	+	12.5162i	−0.244012	+	0.422642i	−0.961854	−	0.273565i	$-0.911797\pi$
$877$	−7.22623	+	12.5162i	−0.244012	+	0.422642i	0.717841	+	0.696207i	$0.245130\pi$
$878$		0			0
$879$		−	8.81664i		−	0.297378i
$880$		0			0
$881$	3.42746	+	5.93653i	0.115474	+	0.200007i	0.917969	−	0.396652i	$-0.129828\pi$
$881$	3.42746	+	5.93653i	0.115474	+	0.200007i	−0.802495	+	0.596659i	$0.796495\pi$
$882$		0			0
$883$		−	15.1989i		−	0.511484i	−0.966745	−	0.255742i	$-0.917680\pi$
$883$		−	15.1989i		−	0.511484i	0.966745	−	0.255742i	$-0.0823197\pi$
$884$		0			0
$885$			16.7694i			0.563696i
$886$		0			0
$887$	12.6270	+	21.8707i	0.423974	+	0.734345i	0.996324	−	0.0856646i	$-0.0273014\pi$
$887$	12.6270	+	21.8707i	0.423974	+	0.734345i	−0.572350	+	0.820010i	$0.693968\pi$
$888$		0			0
$889$			6.80966i			0.228389i
$890$		0			0
$891$	−2.72516	+	4.72012i	−0.0912963	+	0.158130i
$892$		0			0
$893$	−0.587899	−	0.339423i	−0.0196733	−	0.0113584i
$894$		0			0
$895$	30.3343	−	17.5135i	1.01396	−	0.585412i
$896$		0			0
$897$	−12.4947	−	5.23037i	−0.417185	−	0.174637i
$898$		0			0
$899$	−2.06036	−	3.56865i	−0.0687169	−	0.119021i
$900$		0			0
$901$	50.9353	+	29.4075i	1.69690	+	0.979706i
$902$		0			0
$903$	−2.43242	−	1.40436i	−0.0809460	−	0.0467342i
$904$		0			0
$905$		−	5.43927i		−	0.180807i
$906$		0			0
$907$	0.992046	−	0.572758i	0.0329404	−	0.0190181i	−0.483439	−	0.875378i	$-0.660613\pi$
$907$	0.992046	−	0.572758i	0.0329404	−	0.0190181i	0.516380	+	0.856360i	$0.327279\pi$
$908$		0			0
$909$			14.1419i			0.469056i
$910$		0			0
$911$	33.9691			1.12545			0.562724	−	0.826645i	$-0.309754\pi$
$911$	33.9691			1.12545			0.562724	+	0.826645i	$0.309754\pi$
$912$		0			0
$913$	−33.3953	−	57.8424i	−1.10522	−	1.91430i
$914$		0			0
$915$	−10.3047			−0.340662
$916$		0			0
$917$	−2.26839	+	3.92897i	−0.0749090	+	0.129746i
$918$		0			0
$919$	−1.69625	+	2.93799i	−0.0559542	+	0.0969155i	−0.892646	−	0.450759i	$-0.851153\pi$
$919$	−1.69625	+	2.93799i	−0.0559542	+	0.0969155i	0.836692	+	0.547674i	$0.184487\pi$
$920$		0			0
$921$	−7.46770	+	4.31148i	−0.246069	+	0.142068i
$922$		0			0
$923$	−39.4429	−	16.5111i	−1.29828	−	0.543469i
$924$		0			0
$925$	1.46466	+	2.53686i	0.0481576	+	0.0834115i
$926$		0			0
$927$	−2.53468	+	4.39019i	−0.0832498	+	0.144193i
$928$		0			0
$929$	13.6753	+	7.89543i	0.448672	+	0.259041i	0.707269	−	0.706944i	$-0.249927\pi$
$929$	13.6753	+	7.89543i	0.448672	+	0.259041i	−0.258597	+	0.965985i	$0.583260\pi$
$930$		0			0
$931$	−20.1052			−0.658921
$932$		0			0
$933$	26.5434	−	15.3249i	0.868993	−	0.501713i
$934$		0			0
$935$	−62.4140			−2.04116
$936$		0			0
$937$	−4.68424			−0.153027			−0.0765137	−	0.997069i	$-0.524379\pi$
$937$	−4.68424			−0.153027			−0.0765137	+	0.997069i	$0.524379\pi$
$938$		0			0
$939$	23.1645	−	13.3740i	0.755944	−	0.436444i
$940$		0			0
$941$	33.4301			1.08979			0.544895	−	0.838504i	$-0.316569\pi$
$941$	33.4301			1.08979			0.544895	+	0.838504i	$0.316569\pi$
$942$		0			0
$943$	2.39903	+	1.38508i	0.0781232	+	0.0451045i
$944$		0			0
$945$	−0.328898	+	0.569668i	−0.0106991	+	0.0185313i
$946$		0			0
$947$	−11.7967	−	20.4324i	−0.383340	−	0.663965i	0.608197	−	0.793786i	$-0.291893\pi$
$947$	−11.7967	−	20.4324i	−0.383340	−	0.663965i	−0.991537	+	0.129821i	$0.958560\pi$
$948$		0			0
$949$	3.93180	+	30.7544i	0.127632	+	0.998330i
$950$		0			0
$951$	8.04031	−	4.64207i	0.260725	−	0.150530i
$952$		0			0
$953$	−15.0985	+	26.1513i	−0.489087	+	0.847124i	−0.999921	−	0.0125557i	$-0.996003\pi$
$953$	−15.0985	+	26.1513i	−0.489087	+	0.847124i	0.510834	+	0.859679i	$0.329337\pi$
$954$		0			0
$955$	−10.8946	+	18.8699i	−0.352539	+	0.610616i
$956$		0			0
$957$	43.6855			1.41215
$958$		0			0
$959$	2.81925	+	4.88309i	0.0910384	+	0.157683i
$960$		0			0
$961$	30.7357			0.991474
$962$		0			0
$963$			7.28518i			0.234762i
$964$		0			0
$965$	−30.3435	+	17.5188i	−0.976792	+	0.563951i
$966$		0			0
$967$			21.6042i			0.694745i	0.937727	+	0.347373i	$0.112926\pi$
$967$			21.6042i			0.694745i	−0.937727	+	0.347373i	$0.887074\pi$
$968$		0			0
$969$	13.7669	+	7.94831i	0.442256	+	0.255336i
$970$		0			0
$971$	19.0345	+	10.9895i	0.610845	+	0.352671i	0.773296	−	0.634045i	$-0.218607\pi$
$971$	19.0345	+	10.9895i	0.610845	+	0.352671i	−0.162451	+	0.986717i	$0.551940\pi$
$972$		0			0
$973$	0.931818	+	1.61396i	0.0298727	+	0.0517411i
$974$		0			0
$975$	−1.71082	+	1.30261i	−0.0547902	+	0.0417170i
$976$		0			0
$977$	4.65434	−	2.68718i	0.148906	−	0.0859707i	−0.423696	−	0.905804i	$-0.639268\pi$
$977$	4.65434	−	2.68718i	0.148906	−	0.0859707i	0.572602	+	0.819834i	$0.305934\pi$
$978$		0			0
$979$	5.49818	+	3.17437i	0.175722	+	0.101453i
$980$		0			0
$981$	−0.473653	+	0.820390i	−0.0151226	+	0.0261930i
$982$		0			0
$983$		−	31.6005i		−	1.00790i	−0.863733	−	0.503949i	$-0.831880\pi$
$983$		−	31.6005i		−	1.00790i	0.863733	−	0.503949i	$-0.168120\pi$
$984$		0			0
$985$	−22.7154	−	39.3442i	−0.723772	−	1.25361i
$986$		0			0
$987$		−	0.0730481i		−	0.00232515i
$988$		0			0
$989$			33.6618i			1.07038i
$990$		0			0
$991$	−12.6021	−	21.8275i	−0.400320	−	0.693374i	0.593445	−	0.804875i	$-0.297768\pi$
$991$	−12.6021	−	21.8275i	−0.400320	−	0.693374i	−0.993764	+	0.111501i	$0.964434\pi$
$992$		0			0
$993$		−	22.6539i		−	0.718901i
$994$		0			0
$995$	−0.932196	+	1.61461i	−0.0295526	+	0.0511866i
$996$		0			0
$997$	−12.3839	−	7.14987i	−0.392203	−	0.226439i	0.290911	−	0.956750i	$-0.406042\pi$
$997$	−12.3839	−	7.14987i	−0.392203	−	0.226439i	−0.683114	+	0.730312i	$0.739375\pi$
$998$		0			0
$999$	−4.25376	+	2.45591i	−0.134583	+	0.0777015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.ca.b.49.21		48
4.3	odd	2		312.2.bk.b.205.14	✓	48
8.3	odd	2		312.2.bk.b.205.21	yes	48
8.5	even	2	inner	1248.2.ca.b.49.4		48
12.11	even	2		936.2.dg.e.829.11		48
13.4	even	6	inner	1248.2.ca.b.433.4		48
24.11	even	2		936.2.dg.e.829.4		48
52.43	odd	6		312.2.bk.b.277.21	yes	48
104.43	odd	6		312.2.bk.b.277.14	yes	48
104.69	even	6	inner	1248.2.ca.b.433.21		48
156.95	even	6		936.2.dg.e.901.4		48
312.251	even	6		936.2.dg.e.901.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.14	✓	48	4.3	odd	2
312.2.bk.b.205.21	yes	48	8.3	odd	2
312.2.bk.b.277.14	yes	48	104.43	odd	6
312.2.bk.b.277.21	yes	48	52.43	odd	6
936.2.dg.e.829.4		48	24.11	even	2
936.2.dg.e.829.11		48	12.11	even	2
936.2.dg.e.901.4		48	156.95	even	6
936.2.dg.e.901.11		48	312.251	even	6
1248.2.ca.b.49.4		48	8.5	even	2	inner
1248.2.ca.b.49.21		48	1.1	even	1	trivial
1248.2.ca.b.433.4		48	13.4	even	6	inner
1248.2.ca.b.433.21		48	104.69	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} -2.09848 q^{5} +(0.271467 + 0.156732i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.72516 - 4.72012i) q^{11} +(3.57644 - 0.457231i) q^{13} +(-1.81734 + 1.04924i) q^{15} +(-2.72851 + 4.72591i) q^{17} +(1.45653 - 2.52278i) q^{19} +0.313463 q^{21} +(-1.87839 - 3.25346i) q^{23} -0.596381 q^{25} -1.00000i q^{27} +(-6.94137 + 4.00760i) q^{29} +0.514113i q^{31} +(-4.72012 - 2.72516i) q^{33} +(-0.569668 - 0.328898i) q^{35} +(-2.45591 - 4.25376i) q^{37} +(2.86867 - 2.18419i) q^{39} +(-0.638588 + 0.368689i) q^{41} +(-7.75984 - 4.48015i) q^{43} +(-1.04924 + 1.81734i) q^{45} -0.233036i q^{47} +(-3.45087 - 5.97708i) q^{49} +5.45701i q^{51} -10.7779i q^{53} +(5.71870 + 9.90507i) q^{55} -2.91306i q^{57} +(3.99560 - 6.92057i) q^{59} +(4.25265 + 2.45527i) q^{61} +(0.271467 - 0.156732i) q^{63} +(-7.50509 + 0.959489i) q^{65} +(-5.53265 - 9.58284i) q^{67} +(-3.25346 - 1.87839i) q^{69} +(-10.2705 - 5.92965i) q^{71} +8.59916i q^{73} +(-0.516481 + 0.298191i) q^{75} -1.70848i q^{77} +4.49154 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.2544 q^{83} +(5.72572 - 9.91724i) q^{85} +(-4.00760 + 6.94137i) q^{87} +(-1.00878 + 0.582419i) q^{89} +(1.04255 + 0.436418i) q^{91} +(0.257056 + 0.445235i) q^{93} +(-3.05650 + 5.29401i) q^{95} +(8.51390 + 4.91550i) q^{97} -5.45032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) \) 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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