LMFDB - Embedded newform 792.2.q.f.265.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(265,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.265"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,1,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 7x^{10} - 2x^{9} + 39x^{8} - 9x^{7} + 67x^{6} - 18x^{5} + 88x^{4} - 16x^{3} + 24x^{2} + 4x + 4 $ x^12 + 7x^10 - 2x^9 + 39x^8 - 9x^7 + 67x^6 - 18x^5 + 88x^4 - 16x^3 + 24x^2 + 4x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			265.6
Root			$1.08357 + 1.87680i$ of defining polynomial
Character	$\chi$	$=$	792.265
Dual form			792.2.q.f.529.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71613 - 0.234283i) q^{3} +(0.848245 - 1.46920i) q^{5} +(-0.951006 - 1.64719i) q^{7} +(2.89022 - 0.804122i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(1.04198 - 1.80476i) q^{13} +(1.11149 - 2.72008i) q^{15} -0.310342 q^{17} -2.59850 q^{19} +(-2.01796 - 2.60399i) q^{21} +(-0.113193 + 0.196056i) q^{23} +(1.06096 + 1.83764i) q^{25} +(4.77161 - 2.05711i) q^{27} +(-2.21016 - 3.82811i) q^{29} +(1.49298 - 2.58592i) q^{31} +(-1.06096 - 1.36907i) q^{33} -3.22674 q^{35} +4.20720 q^{37} +(1.36535 - 3.34132i) q^{39} +(-2.81188 + 4.87031i) q^{41} +(1.01197 + 1.75278i) q^{43} +(1.27020 - 4.92842i) q^{45} +(-0.740187 - 1.28204i) q^{47} +(1.69118 - 2.92920i) q^{49} +(-0.532589 + 0.0727080i) q^{51} +3.56433 q^{53} -1.69649 q^{55} +(-4.45937 + 0.608785i) q^{57} +(-4.93826 + 8.55332i) q^{59} +(4.18696 + 7.25203i) q^{61} +(-4.07316 - 3.99602i) q^{63} +(-1.76770 - 3.06175i) q^{65} +(-3.16867 + 5.48830i) q^{67} +(-0.148322 + 0.362978i) q^{69} +0.355974 q^{71} +11.9857 q^{73} +(2.25128 + 2.90507i) q^{75} +(-0.951006 + 1.64719i) q^{77} +(2.41844 + 4.18886i) q^{79} +(7.70678 - 4.64818i) q^{81} +(-1.45033 - 2.51204i) q^{83} +(-0.263246 + 0.455956i) q^{85} +(-4.68979 - 6.05174i) q^{87} +3.43554 q^{89} -3.96371 q^{91} +(1.95632 - 4.78757i) q^{93} +(-2.20417 + 3.81773i) q^{95} +(8.75068 + 15.1566i) q^{97} +(-2.14150 - 2.10095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{3} - 4 q^{5} - 5 q^{7} + 5 q^{9} - 6 q^{11} - 3 q^{13} - 7 q^{15} + 14 q^{17} + 10 q^{19} + 9 q^{21} - 8 q^{23} + 2 q^{25} - 11 q^{27} - 8 q^{29} - 4 q^{31} - 2 q^{33} + 16 q^{35} + 6 q^{37}+ \cdots - 7 q^{99}+O(q^{100}) $ 12 * q + q^3 - 4 * q^5 - 5 * q^7 + 5 * q^9 - 6 * q^11 - 3 * q^13 - 7 * q^15 + 14 * q^17 + 10 * q^19 + 9 * q^21 - 8 * q^23 + 2 * q^25 - 11 * q^27 - 8 * q^29 - 4 * q^31 - 2 * q^33 + 16 * q^35 + 6 * q^37 + 14 * q^39 - 5 * q^43 + 25 * q^45 - 17 * q^47 - 3 * q^49 - 15 * q^51 + 28 * q^53 + 8 * q^55 + 15 * q^57 - 4 * q^59 - q^61 + 15 * q^63 - 15 * q^65 + 4 * q^67 - 14 * q^69 + 14 * q^71 - 24 * q^73 + 38 * q^75 - 5 * q^77 - q^79 + 5 * q^81 - 22 * q^83 + 3 * q^85 - q^87 + 44 * q^89 + 22 * q^91 + 12 * q^93 - 24 * q^95 + 16 * q^97 - 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.71613	−	0.234283i	0.990810	−	0.135263i
$3$	1.71613	−	0.234283i	0.990810	−	0.135263i
$4$		0			0
$5$	0.848245	−	1.46920i	0.379347	−	0.657048i	−0.611621	−	0.791151i	$-0.709482\pi$
$5$	0.848245	−	1.46920i	0.379347	−	0.657048i	0.990967	+	0.134104i	$0.0428155\pi$
$6$		0			0
$7$	−0.951006	−	1.64719i	−0.359446	−	0.622579i	0.628422	−	0.777873i	$-0.283701\pi$
$7$	−0.951006	−	1.64719i	−0.359446	−	0.622579i	−0.987868	+	0.155293i	$0.950368\pi$
$8$		0			0
$9$	2.89022	−	0.804122i	0.963408	−	0.268041i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	1.04198	−	1.80476i	0.288993	−	0.500550i	−0.684577	−	0.728941i	$-0.740013\pi$
$13$	1.04198	−	1.80476i	0.288993	−	0.500550i	0.973570	+	0.228391i	$0.0733463\pi$
$14$		0			0
$15$	1.11149	−	2.72008i	0.286986	−	0.702321i
$16$		0			0
$17$	−0.310342			−0.0752691			−0.0376345	−	0.999292i	$-0.511982\pi$
$17$	−0.310342			−0.0752691			−0.0376345	+	0.999292i	$0.511982\pi$
$18$		0			0
$19$	−2.59850			−0.596137			−0.298069	−	0.954544i	$-0.596342\pi$
$19$	−2.59850			−0.596137			−0.298069	+	0.954544i	$0.596342\pi$
$20$		0			0
$21$	−2.01796	−	2.60399i	−0.440355	−	0.568238i
$22$		0			0
$23$	−0.113193	+	0.196056i	−0.0236024	+	0.0408806i	−0.877585	−	0.479420i	$-0.840847\pi$
$23$	−0.113193	+	0.196056i	−0.0236024	+	0.0408806i	0.853983	+	0.520301i	$0.174180\pi$
$24$		0			0
$25$	1.06096	+	1.83764i	0.212192	+	0.367528i
$26$		0			0
$27$	4.77161	−	2.05711i	0.918297	−	0.395891i
$28$		0			0
$29$	−2.21016	−	3.82811i	−0.410416	−	0.710862i	0.584519	−	0.811380i	$-0.301283\pi$
$29$	−2.21016	−	3.82811i	−0.410416	−	0.710862i	−0.994935	+	0.100518i	$0.967950\pi$
$30$		0			0
$31$	1.49298	−	2.58592i	0.268148	−	0.464446i	−0.700236	−	0.713912i	$-0.746922\pi$
$31$	1.49298	−	2.58592i	0.268148	−	0.464446i	0.968384	+	0.249466i	$0.0802551\pi$
$32$		0			0
$33$	−1.06096	−	1.36907i	−0.184690	−	0.238325i
$34$		0			0
$35$	−3.22674			−0.545419
$36$		0			0
$37$	4.20720			0.691659			0.345830	−	0.938297i	$-0.387598\pi$
$37$	4.20720			0.691659			0.345830	+	0.938297i	$0.387598\pi$
$38$		0			0
$39$	1.36535	−	3.34132i	0.218631	−	0.535040i
$40$		0			0
$41$	−2.81188	+	4.87031i	−0.439142	+	0.760615i	−0.997623	−	0.0689013i	$-0.978051\pi$
$41$	−2.81188	+	4.87031i	−0.439142	+	0.760615i	0.558482	+	0.829517i	$0.311384\pi$
$42$		0			0
$43$	1.01197	+	1.75278i	0.154324	+	0.267296i	0.932813	−	0.360362i	$-0.117347\pi$
$43$	1.01197	+	1.75278i	0.154324	+	0.267296i	−0.778489	+	0.627658i	$0.784014\pi$
$44$		0			0
$45$	1.27020	−	4.92842i	0.189350	−	0.734685i
$46$		0			0
$47$	−0.740187	−	1.28204i	−0.107967	−	0.187005i	0.806979	−	0.590580i	$-0.201101\pi$
$47$	−0.740187	−	1.28204i	−0.107967	−	0.187005i	−0.914947	+	0.403575i	$0.867768\pi$
$48$		0			0
$49$	1.69118	−	2.92920i	0.241597	−	0.418457i
$50$		0			0
$51$	−0.532589	+	0.0727080i	−0.0745773	+	0.0101812i
$52$		0			0
$53$	3.56433			0.489598			0.244799	−	0.969574i	$-0.421278\pi$
$53$	3.56433			0.489598			0.244799	+	0.969574i	$0.421278\pi$
$54$		0			0
$55$	−1.69649			−0.228755
$56$		0			0
$57$	−4.45937	+	0.608785i	−0.590658	+	0.0806356i
$58$		0			0
$59$	−4.93826	+	8.55332i	−0.642907	+	1.11355i	0.341874	+	0.939746i	$0.388938\pi$
$59$	−4.93826	+	8.55332i	−0.642907	+	1.11355i	−0.984781	+	0.173801i	$0.944395\pi$
$60$		0			0
$61$	4.18696	+	7.25203i	0.536085	+	0.928527i	0.999110	+	0.0421816i	$0.0134308\pi$
$61$	4.18696	+	7.25203i	0.536085	+	0.928527i	−0.463025	+	0.886345i	$0.653236\pi$
$62$		0			0
$63$	−4.07316	−	3.99602i	−0.513170	−	0.503452i
$64$		0			0
$65$	−1.76770	−	3.06175i	−0.219257	−	0.379764i
$66$		0			0
$67$	−3.16867	+	5.48830i	−0.387115	+	0.670503i	−0.992060	−	0.125764i	$-0.959862\pi$
$67$	−3.16867	+	5.48830i	−0.387115	+	0.670503i	0.604945	+	0.796267i	$0.293195\pi$
$68$		0			0
$69$	−0.148322	+	0.362978i	−0.0178558	+	0.0436974i
$70$		0			0
$71$	0.355974			0.0422464			0.0211232	−	0.999777i	$-0.493276\pi$
$71$	0.355974			0.0422464			0.0211232	+	0.999777i	$0.493276\pi$
$72$		0			0
$73$	11.9857			1.40282			0.701412	−	0.712756i	$-0.252553\pi$
$73$	11.9857			1.40282			0.701412	+	0.712756i	$0.252553\pi$
$74$		0			0
$75$	2.25128	+	2.90507i	0.259955	+	0.335448i
$76$		0			0
$77$	−0.951006	+	1.64719i	−0.108377	+	0.187715i
$78$		0			0
$79$	2.41844	+	4.18886i	0.272096	+	0.471283i	0.969398	−	0.245494i	$-0.0789500\pi$
$79$	2.41844	+	4.18886i	0.272096	+	0.471283i	−0.697303	+	0.716777i	$0.745617\pi$
$80$		0			0
$81$	7.70678	−	4.64818i	0.856308	−	0.516465i
$82$		0			0
$83$	−1.45033	−	2.51204i	−0.159194	−	0.275732i	0.775384	−	0.631490i	$-0.217556\pi$
$83$	−1.45033	−	2.51204i	−0.159194	−	0.275732i	−0.934578	+	0.355758i	$0.884223\pi$
$84$		0			0
$85$	−0.263246	+	0.455956i	−0.0285531	+	0.0494554i
$86$		0			0
$87$	−4.68979	−	6.05174i	−0.502798	−	0.648814i
$88$		0			0
$89$	3.43554			0.364167			0.182083	−	0.983283i	$-0.441716\pi$
$89$	3.43554			0.364167			0.182083	+	0.983283i	$0.441716\pi$
$90$		0			0
$91$	−3.96371			−0.415510
$92$		0			0
$93$	1.95632	−	4.78757i	0.202861	−	0.496448i
$94$		0			0
$95$	−2.20417	+	3.81773i	−0.226143	+	0.391690i
$96$		0			0
$97$	8.75068	+	15.1566i	0.888497	+	1.53892i	0.841653	+	0.540019i	$0.181583\pi$
$97$	8.75068	+	15.1566i	0.888497	+	1.53892i	0.0468441	+	0.998902i	$0.485084\pi$
$98$		0			0
$99$	−2.14150	−	2.10095i	−0.215229	−	0.211153i
$100$		0			0
$101$	−8.01452	−	13.8816i	−0.797474	−	1.38127i	−0.921256	−	0.388957i	$-0.872836\pi$
$101$	−8.01452	−	13.8816i	−0.797474	−	1.38127i	0.123782	−	0.992309i	$-0.460498\pi$
$102$		0			0
$103$	1.06062	−	1.83704i	0.104506	−	0.181009i	−0.809030	−	0.587767i	$-0.800007\pi$
$103$	1.06062	−	1.83704i	0.104506	−	0.181009i	0.913536	+	0.406758i	$0.133341\pi$
$104$		0			0
$105$	−5.53752	+	0.755972i	−0.540407	+	0.0737753i
$106$		0			0
$107$	−20.4972			−1.98154			−0.990771	−	0.135548i	$-0.956721\pi$
$107$	−20.4972			−1.98154			−0.990771	+	0.135548i	$0.956721\pi$
$108$		0			0
$109$	14.7125			1.40920			0.704599	−	0.709606i	$-0.251127\pi$
$109$	14.7125			1.40920			0.704599	+	0.709606i	$0.251127\pi$
$110$		0			0
$111$	7.22011	−	0.985676i	0.685303	−	0.0935562i
$112$		0			0
$113$	−3.69683	+	6.40311i	−0.347769	+	0.602354i	−0.985853	−	0.167613i	$-0.946394\pi$
$113$	−3.69683	+	6.40311i	−0.347769	+	0.602354i	0.638084	+	0.769967i	$0.279727\pi$
$114$		0			0
$115$	0.192031	+	0.332607i	0.0179070	+	0.0310158i
$116$		0			0
$117$	1.56030	−	6.05403i	0.144250	−	0.559695i
$118$		0			0
$119$	0.295137	+	0.511193i	0.0270552	+	0.0468610i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.68452	+	9.01688i	−0.332222	+	0.813025i
$124$		0			0
$125$	12.0823			1.08067
$126$		0			0
$127$	−9.88973			−0.877572			−0.438786	−	0.898592i	$-0.644591\pi$
$127$	−9.88973			−0.877572			−0.438786	+	0.898592i	$0.644591\pi$
$128$		0			0
$129$	2.14732	+	2.77091i	0.189061	+	0.243965i
$130$		0			0
$131$	−4.17119	+	7.22472i	−0.364439	+	0.631227i	−0.988686	−	0.150000i	$-0.952073\pi$
$131$	−4.17119	+	7.22472i	−0.364439	+	0.631227i	0.624247	+	0.781227i	$0.285406\pi$
$132$		0			0
$133$	2.47119	+	4.28023i	0.214279	+	0.371143i
$134$		0			0
$135$	1.02518	−	8.75540i	0.0882337	−	0.753545i
$136$		0			0
$137$	−2.88841	−	5.00287i	−0.246773	−	0.427424i	0.715855	−	0.698249i	$-0.246037\pi$
$137$	−2.88841	−	5.00287i	−0.246773	−	0.427424i	−0.962629	+	0.270825i	$0.912704\pi$
$138$		0			0
$139$	−0.830981	+	1.43930i	−0.0704829	+	0.122080i	−0.899113	−	0.437717i	$-0.855787\pi$
$139$	−0.830981	+	1.43930i	−0.0704829	+	0.122080i	0.828630	+	0.559796i	$0.189121\pi$
$140$		0			0
$141$	−1.57062	−	2.02674i	−0.132270	−	0.170682i
$142$		0			0
$143$	−2.08396			−0.174269
$144$		0			0
$145$	−7.49902			−0.622760
$146$		0			0
$147$	2.21602	−	5.42311i	0.182774	−	0.447291i
$148$		0			0
$149$	2.59665	−	4.49753i	0.212726	−	0.368452i	−0.739841	−	0.672782i	$-0.765099\pi$
$149$	2.59665	−	4.49753i	0.212726	−	0.368452i	0.952567	+	0.304330i	$0.0984326\pi$
$150$		0			0
$151$	−2.08868	−	3.61769i	−0.169974	−	0.294404i	0.768436	−	0.639926i	$-0.221035\pi$
$151$	−2.08868	−	3.61769i	−0.169974	−	0.294404i	−0.938410	+	0.345523i	$0.887702\pi$
$152$		0			0
$153$	−0.896958	+	0.249553i	−0.0725148	+	0.0201752i
$154$		0			0
$155$	−2.53283	−	4.38699i	−0.203442	−	0.352372i
$156$		0			0
$157$	−5.76686	+	9.98850i	−0.460246	+	0.797169i	−0.998973	−	0.0453114i	$-0.985572\pi$
$157$	−5.76686	+	9.98850i	−0.460246	+	0.797169i	0.538727	+	0.842480i	$0.318905\pi$
$158$		0			0
$159$	6.11686	−	0.835063i	0.485099	−	0.0662248i
$160$		0			0
$161$	0.430589			0.0339352
$162$		0			0
$163$	20.5911			1.61282			0.806408	−	0.591359i	$-0.201408\pi$
$163$	20.5911			1.61282			0.806408	+	0.591359i	$0.201408\pi$
$164$		0			0
$165$	−2.91140	+	0.397459i	−0.226652	+	0.0309421i
$166$		0			0
$167$	−9.65241	+	16.7185i	−0.746926	+	1.29371i	0.202364	+	0.979310i	$0.435138\pi$
$167$	−9.65241	+	16.7185i	−0.746926	+	1.29371i	−0.949290	+	0.314403i	$0.898196\pi$
$168$		0			0
$169$	4.32856	+	7.49729i	0.332966	+	0.576715i
$170$		0			0
$171$	−7.51025	+	2.08951i	−0.574323	+	0.159789i
$172$		0			0
$173$	3.71665	+	6.43742i	0.282571	+	0.489428i	0.972017	−	0.234909i	$-0.0754793\pi$
$173$	3.71665	+	6.43742i	0.282571	+	0.489428i	−0.689446	+	0.724337i	$0.742146\pi$
$174$		0			0
$175$	2.01796	−	3.49521i	0.152544	−	0.264213i
$176$		0			0
$177$	−6.47081	+	15.8356i	−0.486376	+	1.19027i
$178$		0			0
$179$	−3.12740			−0.233752			−0.116876	−	0.993146i	$-0.537288\pi$
$179$	−3.12740			−0.233752			−0.116876	+	0.993146i	$0.537288\pi$
$180$		0			0
$181$	−15.8491			−1.17805			−0.589027	−	0.808114i	$-0.700489\pi$
$181$	−15.8491			−1.17805			−0.589027	+	0.808114i	$0.700489\pi$
$182$		0			0
$183$	8.88441	+	11.4645i	0.656754	+	0.847481i
$184$		0			0
$185$	3.56873	−	6.18123i	0.262379	−	0.454453i
$186$		0			0
$187$	0.155171	+	0.268764i	0.0113472	+	0.0196540i
$188$		0			0
$189$	−7.92629	−	5.90343i	−0.576552	−	0.429411i
$190$		0			0
$191$	6.77407	+	11.7330i	0.490155	+	0.848973i	0.999936	−	0.0113314i	$-0.00360697\pi$
$191$	6.77407	+	11.7330i	0.490155	+	0.848973i	−0.509781	+	0.860304i	$0.670274\pi$
$192$		0			0
$193$	−7.81877	+	13.5425i	−0.562807	+	0.974811i	0.434443	+	0.900700i	$0.356945\pi$
$193$	−7.81877	+	13.5425i	−0.562807	+	0.974811i	−0.997250	+	0.0741114i	$0.976388\pi$
$194$		0			0
$195$	−3.75093	−	4.84023i	−0.268610	−	0.346616i
$196$		0			0
$197$	1.36469			0.0972301			0.0486151	−	0.998818i	$-0.484519\pi$
$197$	1.36469			0.0972301			0.0486151	+	0.998818i	$0.484519\pi$
$198$		0			0
$199$	−1.35834			−0.0962903			−0.0481451	−	0.998840i	$-0.515331\pi$
$199$	−1.35834			−0.0962903			−0.0481451	+	0.998840i	$0.515331\pi$
$200$		0			0
$201$	−4.15205	+	10.1610i	−0.292863	+	0.716703i
$202$		0			0
$203$	−4.20375	+	7.28111i	−0.295045	+	0.511033i
$204$		0			0
$205$	4.77032	+	8.26244i	0.333174	+	0.577074i
$206$		0			0
$207$	−0.169500	+	0.657668i	−0.0117811	+	0.0457111i
$208$		0			0
$209$	1.29925	+	2.25037i	0.0898710	+	0.155661i
$210$		0			0
$211$	−7.27874	+	12.6072i	−0.501089	+	0.867912i	0.498910	+	0.866654i	$0.333734\pi$
$211$	−7.27874	+	12.6072i	−0.501089	+	0.867912i	−0.999999	+	0.00125834i	$0.999599\pi$
$212$		0			0
$213$	0.610899	−	0.0833988i	0.0418581	−	0.00571439i
$214$		0			0
$215$	3.43358			0.234169
$216$		0			0
$217$	−5.67935			−0.385539
$218$		0			0
$219$	20.5691	−	2.80805i	1.38993	−	0.189751i
$220$		0			0
$221$	−0.323370	+	0.560093i	−0.0217522	+	0.0376759i
$222$		0			0
$223$	−10.6003	−	18.3602i	−0.709846	−	1.22949i	−0.964914	−	0.262566i	$-0.915431\pi$
$223$	−10.6003	−	18.3602i	−0.709846	−	1.22949i	0.255068	−	0.966923i	$-0.417902\pi$
$224$		0			0
$225$	4.54410	+	4.45804i	0.302940	+	0.297203i
$226$		0			0
$227$	−5.99988	−	10.3921i	−0.398226	−	0.689748i	0.595281	−	0.803518i	$-0.297041\pi$
$227$	−5.99988	−	10.3921i	−0.398226	−	0.689748i	−0.993507	+	0.113770i	$0.963707\pi$
$228$		0			0
$229$	4.05812	−	7.02888i	0.268168	−	0.464481i	−0.700221	−	0.713927i	$-0.746915\pi$
$229$	4.05812	−	7.02888i	0.268168	−	0.464481i	0.968389	+	0.249445i	$0.0802483\pi$
$230$		0			0
$231$	−1.24614	+	3.04960i	−0.0819902	+	0.200649i
$232$		0			0
$233$	−27.6506			−1.81145			−0.905726	−	0.423863i	$-0.860674\pi$
$233$	−27.6506			−1.81145			−0.905726	+	0.423863i	$0.860674\pi$
$234$		0			0
$235$	−2.51144			−0.163828
$236$		0			0
$237$	5.13174	+	6.62204i	0.333342	+	0.430147i
$238$		0			0
$239$	−3.61477	+	6.26097i	−0.233820	+	0.404988i	−0.958929	−	0.283646i	$-0.908456\pi$
$239$	−3.61477	+	6.26097i	−0.233820	+	0.404988i	0.725109	+	0.688634i	$0.241789\pi$
$240$		0			0
$241$	2.60924	+	4.51933i	0.168076	+	0.291116i	0.937743	−	0.347329i	$-0.112911\pi$
$241$	2.60924	+	4.51933i	0.168076	+	0.291116i	−0.769668	+	0.638445i	$0.779578\pi$
$242$		0			0
$243$	12.1369	−	9.78247i	0.778580	−	0.627546i
$244$		0			0
$245$	−2.86906	−	4.96936i	−0.183298	−	0.317481i
$246$		0			0
$247$	−2.70758	+	4.68967i	−0.172279	+	0.298396i
$248$		0			0
$249$	−3.07748	−	3.97120i	−0.195027	−	0.251665i
$250$		0			0
$251$	12.0710			0.761918			0.380959	−	0.924592i	$-0.375594\pi$
$251$	12.0710			0.761918			0.380959	+	0.924592i	$0.375594\pi$
$252$		0			0
$253$	0.226386			0.0142328
$254$		0			0
$255$	−0.344943	+	0.844155i	−0.0216011	+	0.0528630i
$256$		0			0
$257$	−9.52708	+	16.5014i	−0.594283	+	1.02933i	0.399365	+	0.916792i	$0.369231\pi$
$257$	−9.52708	+	16.5014i	−0.594283	+	1.02933i	−0.993648	+	0.112536i	$0.964103\pi$
$258$		0			0
$259$	−4.00107	−	6.93006i	−0.248614	−	0.430613i
$260$		0			0
$261$	−9.46612	−	9.28685i	−0.585938	−	0.574841i
$262$		0			0
$263$	10.9085	+	18.8941i	0.672649	+	1.16506i	0.977150	+	0.212551i	$0.0681770\pi$
$263$	10.9085	+	18.8941i	0.672649	+	1.16506i	−0.304501	+	0.952512i	$0.598490\pi$
$264$		0			0
$265$	3.02342	−	5.23673i	0.185727	−	0.321689i
$266$		0			0
$267$	5.89584	−	0.804889i	0.360820	−	0.0492584i
$268$		0			0
$269$	11.0157			0.671640			0.335820	−	0.941926i	$-0.390987\pi$
$269$	11.0157			0.671640			0.335820	+	0.941926i	$0.390987\pi$
$270$		0			0
$271$	14.7950			0.898733			0.449367	−	0.893347i	$-0.351650\pi$
$271$	14.7950			0.898733			0.449367	+	0.893347i	$0.351650\pi$
$272$		0			0
$273$	−6.80225	+	0.928630i	−0.411691	+	0.0562033i
$274$		0			0
$275$	1.06096	−	1.83764i	0.0639784	−	0.110814i
$276$		0			0
$277$	−4.89355	−	8.47588i	−0.294025	−	0.509266i	0.680733	−	0.732532i	$-0.261662\pi$
$277$	−4.89355	−	8.47588i	−0.294025	−	0.509266i	−0.974758	+	0.223266i	$0.928328\pi$
$278$		0			0
$279$	2.23566	−	8.67444i	0.133845	−	0.519325i
$280$		0			0
$281$	−7.82471	−	13.5528i	−0.466783	−	0.808492i	0.532497	−	0.846432i	$-0.321254\pi$
$281$	−7.82471	−	13.5528i	−0.466783	−	0.808492i	−0.999280	+	0.0379400i	$0.987920\pi$
$282$		0			0
$283$	3.37490	−	5.84549i	0.200617	−	0.347478i	−0.748111	−	0.663574i	$-0.769039\pi$
$283$	3.37490	−	5.84549i	0.200617	−	0.347478i	0.948727	+	0.316096i	$0.102372\pi$
$284$		0			0
$285$	−2.88821	+	7.06812i	−0.171083	+	0.418680i
$286$		0			0
$287$	10.6964			0.631391
$288$		0			0
$289$	−16.9037			−0.994335
$290$		0			0
$291$	18.5683	+	23.9606i	1.08849	+	1.40460i
$292$		0			0
$293$	2.00685	−	3.47597i	0.117241	−	0.203068i	−0.801432	−	0.598086i	$-0.795928\pi$
$293$	2.00685	−	3.47597i	0.117241	−	0.203068i	0.918674	+	0.395018i	$0.129262\pi$
$294$		0			0
$295$	8.37771	+	14.5106i	0.487769	+	0.844840i
$296$		0			0
$297$	−4.16732	−	3.10378i	−0.241812	−	0.180100i
$298$		0			0
$299$	0.235890	+	0.408573i	0.0136418	+	0.0236284i
$300$		0			0
$301$	1.92477	−	3.33381i	0.110942	−	0.192157i
$302$		0			0
$303$	−17.0062	−	21.9449i	−0.976980	−	1.26070i
$304$		0			0
$305$	14.2063			0.813449
$306$		0			0
$307$	25.0796			1.43137			0.715683	−	0.698425i	$-0.246116\pi$
$307$	25.0796			1.43137			0.715683	+	0.698425i	$0.246116\pi$
$308$		0			0
$309$	1.38977	−	3.40109i	0.0790613	−	0.193481i
$310$		0			0
$311$	−12.0638	+	20.8951i	−0.684076	+	1.18485i	0.289650	+	0.957133i	$0.406461\pi$
$311$	−12.0638	+	20.8951i	−0.684076	+	1.18485i	−0.973726	+	0.227722i	$0.926872\pi$
$312$		0			0
$313$	0.192171	+	0.332850i	0.0108622	+	0.0188138i	0.871405	−	0.490564i	$-0.163209\pi$
$313$	0.192171	+	0.332850i	0.0108622	+	0.0188138i	−0.860543	+	0.509377i	$0.829876\pi$
$314$		0			0
$315$	−9.32601	+	2.59470i	−0.525461	+	0.146195i
$316$		0			0
$317$	−16.5927	−	28.7395i	−0.931942	−	1.61417i	−0.779999	−	0.625781i	$-0.784780\pi$
$317$	−16.5927	−	28.7395i	−0.931942	−	1.61417i	−0.151943	−	0.988389i	$-0.548553\pi$
$318$		0			0
$319$	−2.21016	+	3.82811i	−0.123745	+	0.214333i
$320$		0			0
$321$	−35.1760	+	4.80216i	−1.96333	+	0.268030i
$322$		0			0
$323$	0.806425			0.0448707
$324$		0			0
$325$	4.42199			0.245288
$326$		0			0
$327$	25.2485	−	3.44688i	1.39625	−	0.190613i
$328$		0			0
$329$	−1.40784	+	2.43846i	−0.0776170	+	0.134437i
$330$		0			0
$331$	−14.6522	−	25.3783i	−0.805356	−	1.39492i	−0.916050	−	0.401063i	$-0.868641\pi$
$331$	−14.6522	−	25.3783i	−0.805356	−	1.39492i	0.110694	−	0.993854i	$-0.464693\pi$
$332$		0			0
$333$	12.1597	−	3.38310i	0.666350	−	0.185393i
$334$		0			0
$335$	5.37562	+	9.31085i	0.293702	+	0.508706i
$336$		0			0
$337$	−1.29202	+	2.23785i	−0.0703810	+	0.121903i	−0.899068	−	0.437808i	$-0.855755\pi$
$337$	−1.29202	+	2.23785i	−0.0703810	+	0.121903i	0.828687	+	0.559712i	$0.189088\pi$
$338$		0			0
$339$	−4.84412	+	11.8547i	−0.263096	+	0.643858i
$340$		0			0
$341$	−2.98597			−0.161699
$342$		0			0
$343$	−19.7474			−1.06626
$344$		0			0
$345$	0.407475	+	0.525809i	0.0219377	+	0.0283086i
$346$		0			0
$347$	3.52683	−	6.10865i	0.189330	−	0.327929i	−0.755697	−	0.654921i	$-0.772702\pi$
$347$	3.52683	−	6.10865i	0.189330	−	0.327929i	0.945027	+	0.326992i	$0.106035\pi$
$348$		0			0
$349$	−3.28361	−	5.68738i	−0.175768	−	0.304439i	0.764659	−	0.644435i	$-0.222907\pi$
$349$	−3.28361	−	5.68738i	−0.175768	−	0.304439i	−0.940427	+	0.339997i	$0.889574\pi$
$350$		0			0
$351$	1.25933	−	10.7551i	0.0672179	−	0.574063i
$352$		0			0
$353$	4.84281	+	8.38799i	0.257757	+	0.446447i	0.965641	−	0.259881i	$-0.0836834\pi$
$353$	4.84281	+	8.38799i	0.257757	+	0.446447i	−0.707884	+	0.706329i	$0.750350\pi$
$354$		0			0
$355$	0.301953	−	0.522998i	0.0160260	−	0.0277579i
$356$		0			0
$357$	0.626259	+	0.808129i	0.0331451	+	0.0427707i
$358$		0			0
$359$	37.5152			1.97998			0.989990	−	0.141141i	$-0.0450771\pi$
$359$	37.5152			1.97998			0.989990	+	0.141141i	$0.0450771\pi$
$360$		0			0
$361$	−12.2478			−0.644621
$362$		0			0
$363$	−0.655171	+	1.60336i	−0.0343876	+	0.0841544i
$364$		0			0
$365$	10.1668	−	17.6095i	0.532156	−	0.921722i
$366$		0			0
$367$	−15.5496	−	26.9327i	−0.811684	−	1.40588i	−0.911685	−	0.410890i	$-0.865218\pi$
$367$	−15.5496	−	26.9327i	−0.811684	−	1.40588i	0.100001	−	0.994987i	$-0.468115\pi$
$368$		0			0
$369$	−4.21062	+	16.3374i	−0.219196	+	0.850490i
$370$		0			0
$371$	−3.38970	−	5.87113i	−0.175984	−	0.304814i
$372$		0			0
$373$	10.3862	−	17.9894i	0.537776	−	0.931455i	−0.461248	−	0.887271i	$-0.652598\pi$
$373$	10.3862	−	17.9894i	0.537776	−	0.931455i	0.999023	−	0.0441835i	$-0.0140686\pi$
$374$		0			0
$375$	20.7348	−	2.83067i	1.07074	−	0.146175i
$376$		0			0
$377$	−9.21175			−0.474429
$378$		0			0
$379$	18.8314			0.967303			0.483652	−	0.875261i	$-0.339310\pi$
$379$	18.8314			0.967303			0.483652	+	0.875261i	$0.339310\pi$
$380$		0			0
$381$	−16.9721	+	2.31700i	−0.869507	+	0.118703i
$382$		0			0
$383$	9.49828	−	16.4515i	0.485339	−	0.840632i	−0.514519	−	0.857479i	$-0.672029\pi$
$383$	9.49828	−	16.4515i	0.485339	−	0.840632i	0.999858	+	0.0168467i	$0.00536272\pi$
$384$		0			0
$385$	1.61337	+	2.79444i	0.0822250	+	0.142418i
$386$		0			0
$387$	4.33426	+	4.25218i	0.220323	+	0.216150i
$388$		0			0
$389$	−1.61402	−	2.79557i	−0.0818343	−	0.141741i	0.822204	−	0.569194i	$-0.192744\pi$
$389$	−1.61402	−	2.79557i	−0.0818343	−	0.141741i	−0.904038	+	0.427452i	$0.859411\pi$
$390$		0			0
$391$	0.0351286	−	0.0608446i	0.00177653	−	0.00307704i
$392$		0			0
$393$	−5.46569	+	13.3758i	−0.275708	+	0.674721i
$394$		0			0
$395$	8.20571			0.412874
$396$		0			0
$397$	36.5699			1.83539			0.917694	−	0.397288i	$-0.130048\pi$
$397$	36.5699			1.83539			0.917694	+	0.397288i	$0.130048\pi$
$398$		0			0
$399$	5.24368	+	6.76648i	0.262512	+	0.338748i
$400$		0			0
$401$	6.69868	−	11.6025i	0.334516	−	0.579399i	−0.648876	−	0.760894i	$-0.724760\pi$
$401$	6.69868	−	11.6025i	0.334516	−	0.579399i	0.983392	+	0.181496i	$0.0580938\pi$
$402$		0			0
$403$	−3.11131	−	5.38895i	−0.154986	−	0.268443i
$404$		0			0
$405$	−0.291894	−	15.2656i	−0.0145043	−	0.758555i
$406$		0			0
$407$	−2.10360	−	3.64354i	−0.104272	−	0.180604i
$408$		0			0
$409$	7.44699	−	12.8986i	0.368230	−	0.637793i	−0.621059	−	0.783764i	$-0.713297\pi$
$409$	7.44699	−	12.8986i	0.368230	−	0.637793i	0.989289	+	0.145971i	$0.0466306\pi$
$410$		0			0
$411$	−6.12898	−	7.90888i	−0.302320	−	0.390116i
$412$		0			0
$413$	18.7853			0.924362
$414$		0			0
$415$	−4.92093			−0.241559
$416$		0			0
$417$	−1.08887	+	2.66472i	−0.0533222	+	0.130492i
$418$		0			0
$419$	18.5771	−	32.1765i	0.907551	−	1.57193i	0.0900963	−	0.995933i	$-0.471283\pi$
$419$	18.5771	−	32.1765i	0.907551	−	1.57193i	0.817455	−	0.575992i	$-0.195384\pi$
$420$		0			0
$421$	−16.7812	−	29.0660i	−0.817868	−	1.41659i	−0.907250	−	0.420591i	$-0.861823\pi$
$421$	−16.7812	−	29.0660i	−0.817868	−	1.41659i	0.0893828	−	0.995997i	$-0.471511\pi$
$422$		0			0
$423$	−3.17022	−	3.11019i	−0.154142	−	0.151222i
$424$		0			0
$425$	−0.329261	−	0.570297i	−0.0159715	−	0.0276635i
$426$		0			0
$427$	7.96365	−	13.7934i	0.385388	−	0.667511i
$428$		0			0
$429$	−3.57634	+	0.488236i	−0.172668	+	0.0235722i
$430$		0			0
$431$	11.9350			0.574890			0.287445	−	0.957797i	$-0.407194\pi$
$431$	11.9350			0.574890			0.287445	+	0.957797i	$0.407194\pi$
$432$		0			0
$433$	−18.0875			−0.869230			−0.434615	−	0.900616i	$-0.643116\pi$
$433$	−18.0875			−0.869230			−0.434615	+	0.900616i	$0.643116\pi$
$434$		0			0
$435$	−12.8693	+	1.75690i	−0.617037	+	0.0842367i
$436$		0			0
$437$	0.294133	−	0.509453i	0.0140703	−	0.0243704i
$438$		0			0
$439$	−5.99501	−	10.3837i	−0.286126	−	0.495585i	0.686755	−	0.726889i	$-0.259034\pi$
$439$	−5.99501	−	10.3837i	−0.286126	−	0.495585i	−0.972882	+	0.231303i	$0.925701\pi$
$440$		0			0
$441$	2.53244	−	9.82596i	0.120592	−	0.467903i
$442$		0			0
$443$	−9.30925	−	16.1241i	−0.442296	−	0.766079i	0.555564	−	0.831474i	$-0.312502\pi$
$443$	−9.30925	−	16.1241i	−0.442296	−	0.766079i	−0.997859	+	0.0653954i	$0.979169\pi$
$444$		0			0
$445$	2.91418	−	5.04751i	0.138145	−	0.239275i
$446$		0			0
$447$	3.40250	−	8.32670i	0.160933	−	0.393839i
$448$		0			0
$449$	33.1000			1.56208			0.781042	−	0.624478i	$-0.214688\pi$
$449$	33.1000			1.56208			0.781042	+	0.624478i	$0.214688\pi$
$450$		0			0
$451$	5.62376			0.264812
$452$		0			0
$453$	−4.43201	−	5.71910i	−0.208234	−	0.268707i
$454$		0			0
$455$	−3.36220	+	5.82349i	−0.157622	+	0.273010i
$456$		0			0
$457$	17.0222	+	29.4833i	0.796266	+	1.37917i	0.922032	+	0.387113i	$0.126528\pi$
$457$	17.0222	+	29.4833i	0.796266	+	1.37917i	−0.125767	+	0.992060i	$0.540139\pi$
$458$		0			0
$459$	−1.48083	+	0.638408i	−0.0691194	+	0.0297984i
$460$		0			0
$461$	−9.08371	−	15.7335i	−0.423071	−	0.732780i	0.573167	−	0.819438i	$-0.305714\pi$
$461$	−9.08371	−	15.7335i	−0.423071	−	0.732780i	−0.996238	+	0.0866584i	$0.972381\pi$
$462$		0			0
$463$	−8.69997	+	15.0688i	−0.404322	+	0.700306i	−0.994242	−	0.107155i	$-0.965826\pi$
$463$	−8.69997	+	15.0688i	−0.404322	+	0.700306i	0.589920	+	0.807461i	$0.299159\pi$
$464$		0			0
$465$	−5.37447	−	6.93526i	−0.249235	−	0.321615i
$466$		0			0
$467$	23.2774			1.07715			0.538575	−	0.842578i	$-0.318963\pi$
$467$	23.2774			1.07715			0.538575	+	0.842578i	$0.318963\pi$
$468$		0			0
$469$	12.0537			0.556589
$470$		0			0
$471$	−7.55656	+	18.4927i	−0.348188	+	0.852097i
$472$		0			0
$473$	1.01197	−	1.75278i	0.0465303	−	0.0805929i
$474$		0			0
$475$	−2.75691	−	4.77511i	−0.126496	−	0.219097i
$476$		0			0
$477$	10.3017	−	2.86616i	0.471683	−	0.131232i
$478$		0			0
$479$	−15.9737	−	27.6672i	−0.729855	−	1.26415i	−0.956944	−	0.290272i	$-0.906254\pi$
$479$	−15.9737	−	27.6672i	−0.729855	−	1.26415i	0.227089	−	0.973874i	$-0.427079\pi$
$480$		0			0
$481$	4.38381	−	7.59298i	0.199884	−	0.346210i
$482$		0			0
$483$	0.738949	−	0.100880i	0.0336233	−	0.00459019i
$484$		0			0
$485$	29.6909			1.34819
$486$		0			0
$487$	−29.7548			−1.34832			−0.674159	−	0.738586i	$-0.735494\pi$
$487$	−29.7548			−1.34832			−0.674159	+	0.738586i	$0.735494\pi$
$488$		0			0
$489$	35.3370	−	4.82414i	1.59799	−	0.218155i
$490$		0			0
$491$	0.884768	−	1.53246i	0.0399290	−	0.0691591i	−0.845370	−	0.534181i	$-0.820620\pi$
$491$	0.884768	−	1.53246i	0.0399290	−	0.0691591i	0.885299	+	0.465022i	$0.153953\pi$
$492$		0			0
$493$	0.685906	+	1.18802i	0.0308916	+	0.0535059i
$494$		0			0
$495$	−4.90323	+	1.36418i	−0.220384	+	0.0613155i
$496$		0			0
$497$	−0.338534	−	0.586357i	−0.0151853	−	0.0263017i
$498$		0			0
$499$	7.94578	−	13.7625i	0.355702	−	0.616094i	−0.631536	−	0.775347i	$-0.717575\pi$
$499$	7.94578	−	13.7625i	0.355702	−	0.616094i	0.987238	+	0.159253i	$0.0509085\pi$
$500$		0			0
$501$	−12.6480	+	30.9525i	−0.565069	+	1.38286i
$502$		0			0
$503$	14.5272			0.647735			0.323867	−	0.946102i	$-0.395017\pi$
$503$	14.5272			0.647735			0.323867	+	0.946102i	$0.395017\pi$
$504$		0			0
$505$	−27.1931			−1.21008
$506$		0			0
$507$	9.18488	+	11.8522i	0.407915	+	0.526376i
$508$		0			0
$509$	−14.9830	+	25.9514i	−0.664112	+	1.15028i	0.315413	+	0.948954i	$0.397857\pi$
$509$	−14.9830	+	25.9514i	−0.664112	+	1.15028i	−0.979525	+	0.201321i	$0.935476\pi$
$510$		0			0
$511$	−11.3985	−	19.7428i	−0.504240	−	0.873369i
$512$		0			0
$513$	−12.3990	+	5.34541i	−0.547431	+	0.236005i
$514$		0			0
$515$	−1.79932	−	3.11652i	−0.0792877	−	0.137330i
$516$		0			0
$517$	−0.740187	+	1.28204i	−0.0325534	+	0.0563841i
$518$		0			0
$519$	7.88644	+	10.1767i	0.346176	+	0.446708i
$520$		0			0
$521$	−11.3725			−0.498237			−0.249118	−	0.968473i	$-0.580141\pi$
$521$	−11.3725			−0.498237			−0.249118	+	0.968473i	$0.580141\pi$
$522$		0			0
$523$	13.1069			0.573124			0.286562	−	0.958062i	$-0.407488\pi$
$523$	13.1069			0.573124			0.286562	+	0.958062i	$0.407488\pi$
$524$		0			0
$525$	2.64422	−	6.47102i	0.115403	−	0.282419i
$526$		0			0
$527$	−0.463336	+	0.802522i	−0.0201832	+	0.0349584i
$528$		0			0
$529$	11.4744	+	19.8742i	0.498886	+	0.864096i
$530$		0			0
$531$	−7.39476	+	28.6920i	−0.320905	+	1.24512i
$532$		0			0
$533$	5.85983	+	10.1495i	0.253817	+	0.439625i
$534$		0			0
$535$	−17.3867	+	30.1146i	−0.751691	+	1.30197i
$536$		0			0
$537$	−5.36702	+	0.732696i	−0.231604	+	0.0316182i
$538$		0			0
$539$	−3.38235			−0.145688
$540$		0			0
$541$	−25.4013			−1.09209			−0.546043	−	0.837757i	$-0.683866\pi$
$541$	−25.4013			−1.09209			−0.546043	+	0.837757i	$0.683866\pi$
$542$		0			0
$543$	−27.1991	+	3.71317i	−1.16723	+	0.159348i
$544$		0			0
$545$	12.4798	−	21.6156i	0.534574	−	0.925910i
$546$		0			0
$547$	2.20859	+	3.82539i	0.0944325	+	0.163562i	0.909372	−	0.415985i	$-0.136563\pi$
$547$	2.20859	+	3.82539i	0.0944325	+	0.163562i	−0.814939	+	0.579547i	$0.803230\pi$
$548$		0			0
$549$	17.9328	+	17.5931i	0.765352	+	0.750857i
$550$		0			0
$551$	5.74310	+	9.94734i	0.244664	+	0.423771i
$552$		0			0
$553$	4.59990	−	7.96726i	0.195608	−	0.338802i
$554$		0			0
$555$	4.67626	−	11.4439i	0.198496	−	0.485767i
$556$		0			0
$557$	−4.65681			−0.197315			−0.0986577	−	0.995121i	$-0.531455\pi$
$557$	−4.65681			−0.197315			−0.0986577	+	0.995121i	$0.531455\pi$
$558$		0			0
$559$	4.21779			0.178394
$560$		0			0
$561$	0.329261	+	0.424881i	0.0139014	+	0.0179385i
$562$		0			0
$563$	2.92737	−	5.07036i	0.123374	−	0.213690i	−0.797722	−	0.603025i	$-0.793962\pi$
$563$	2.92737	−	5.07036i	0.123374	−	0.213690i	0.921096	+	0.389335i	$0.127295\pi$
$564$		0			0
$565$	6.27164	+	10.8628i	0.263850	+	0.457002i
$566$		0			0
$567$	−14.9856	−	8.27408i	−0.629337	−	0.347479i
$568$		0			0
$569$	15.6601	+	27.1240i	0.656504	+	1.13710i	0.981515	+	0.191388i	$0.0612987\pi$
$569$	15.6601	+	27.1240i	0.656504	+	1.13710i	−0.325011	+	0.945710i	$0.605368\pi$
$570$		0			0
$571$	−2.97698	+	5.15628i	−0.124583	+	0.215784i	−0.921570	−	0.388213i	$-0.873093\pi$
$571$	−2.97698	+	5.15628i	−0.124583	+	0.215784i	0.796987	+	0.603996i	$0.206426\pi$
$572$		0			0
$573$	14.3741	+	18.5484i	0.600485	+	0.774870i
$574$		0			0
$575$	−0.480374			−0.0200330
$576$		0			0
$577$	−15.4452			−0.642993			−0.321497	−	0.946911i	$-0.604186\pi$
$577$	−15.4452			−0.642993			−0.321497	+	0.946911i	$0.604186\pi$
$578$		0			0
$579$	−10.2453	+	25.0725i	−0.425779	+	1.04198i
$580$		0			0
$581$	−2.75854	+	4.77793i	−0.114443	+	0.198222i
$582$		0			0
$583$	−1.78217	−	3.08680i	−0.0738097	−	0.127842i
$584$		0			0
$585$	−7.57109	−	7.42770i	−0.313026	−	0.307098i
$586$		0			0
$587$	−20.0341	−	34.7001i	−0.826896	−	1.43223i	−0.900462	−	0.434935i	$-0.856771\pi$
$587$	−20.0341	−	34.7001i	−0.826896	−	1.43223i	0.0735662	−	0.997290i	$-0.476562\pi$
$588$		0			0
$589$	−3.87952	+	6.71953i	−0.159853	+	0.276873i
$590$		0			0
$591$	2.34199	−	0.319724i	0.0963365	−	0.0131517i
$592$		0			0
$593$	20.1031			0.825537			0.412769	−	0.910836i	$-0.364562\pi$
$593$	20.1031			0.825537			0.412769	+	0.910836i	$0.364562\pi$
$594$		0			0
$595$	1.00139			0.0410532
$596$		0			0
$597$	−2.33109	+	0.318237i	−0.0954053	+	0.0130246i
$598$		0			0
$599$	−12.1189	+	20.9906i	−0.495166	+	0.857652i	−0.999984	−	0.00557313i	$-0.998226\pi$
$599$	−12.1189	+	20.9906i	−0.495166	+	0.857652i	0.504819	+	0.863225i	$0.331559\pi$
$600$		0			0
$601$	−14.0758	−	24.3800i	−0.574164	−	0.994481i	−0.996132	−	0.0878702i	$-0.971994\pi$
$601$	−14.0758	−	24.3800i	−0.574164	−	0.994481i	0.421968	−	0.906611i	$-0.361339\pi$
$602$		0			0
$603$	−4.74491	+	18.4104i	−0.193228	+	0.749730i
$604$		0			0
$605$	0.848245	+	1.46920i	0.0344861	+	0.0597316i
$606$		0			0
$607$	−13.7737	+	23.8567i	−0.559056	+	0.968313i	0.438520	+	0.898722i	$0.355503\pi$
$607$	−13.7737	+	23.8567i	−0.559056	+	0.968313i	−0.997576	+	0.0695916i	$0.977830\pi$
$608$		0			0
$609$	−5.50835	+	13.4802i	−0.223210	+	0.546246i
$610$		0			0
$611$	−3.08504			−0.124807
$612$		0			0
$613$	−34.2328			−1.38265			−0.691325	−	0.722544i	$-0.742973\pi$
$613$	−34.2328			−1.38265			−0.691325	+	0.722544i	$0.742973\pi$
$614$		0			0
$615$	10.1223	+	13.0618i	0.408169	+	0.526704i
$616$		0			0
$617$	0.106873	−	0.185109i	0.00430253	−	0.00745221i	−0.863866	−	0.503721i	$-0.831964\pi$
$617$	0.106873	−	0.185109i	0.00430253	−	0.00745221i	0.868169	+	0.496269i	$0.165297\pi$
$618$		0			0
$619$	−15.2272	−	26.3743i	−0.612032	−	1.06007i	−0.990897	−	0.134619i	$-0.957019\pi$
$619$	−15.2272	−	26.3743i	−0.612032	−	1.06007i	0.378865	−	0.925452i	$-0.376314\pi$
$620$		0			0
$621$	−0.136804	+	1.16836i	−0.00548977	+	0.0468845i
$622$		0			0
$623$	−3.26722	−	5.65899i	−0.130898	−	0.226723i
$624$		0			0
$625$	4.94391	−	8.56311i	0.197757	−	0.342524i
$626$		0			0
$627$	2.75691	+	3.55754i	0.110100	+	0.142074i
$628$		0			0
$629$	−1.30567			−0.0520605
$630$		0			0
$631$	−27.6272			−1.09982			−0.549910	−	0.835224i	$-0.685338\pi$
$631$	−27.6272			−1.09982			−0.549910	+	0.835224i	$0.685338\pi$
$632$		0			0
$633$	−9.53765	+	23.3408i	−0.379087	+	0.927715i
$634$		0			0
$635$	−8.38891	+	14.5300i	−0.332904	+	0.576606i
$636$		0			0
$637$	−3.52434	−	6.10433i	−0.139639	−	0.241862i
$638$		0			0
$639$	1.02884	−	0.286247i	0.0407005	−	0.0113237i
$640$		0			0
$641$	11.6370	+	20.1559i	0.459634	+	0.796110i	0.998941	−	0.0459993i	$-0.0146472\pi$
$641$	11.6370	+	20.1559i	0.459634	+	0.796110i	−0.539307	+	0.842109i	$0.681314\pi$
$642$		0			0
$643$	7.21107	−	12.4899i	0.284377	−	0.492555i	−0.688081	−	0.725634i	$-0.741547\pi$
$643$	7.21107	−	12.4899i	0.284377	−	0.492555i	0.972458	+	0.233079i	$0.0748800\pi$
$644$		0			0
$645$	5.89249	−	0.804431i	0.232016	−	0.0316744i
$646$		0			0
$647$	0.518760			0.0203946			0.0101973	−	0.999948i	$-0.496754\pi$
$647$	0.518760			0.0203946			0.0101973	+	0.999948i	$0.496754\pi$
$648$		0			0
$649$	9.87652			0.387687
$650$		0			0
$651$	−9.74651	+	1.33058i	−0.381996	+	0.0521494i
$652$		0			0
$653$	−14.3977	+	24.9375i	−0.563424	+	0.975880i	0.433770	+	0.901024i	$0.357183\pi$
$653$	−14.3977	+	24.9375i	−0.563424	+	0.975880i	−0.997194	+	0.0748561i	$0.976150\pi$
$654$		0			0
$655$	7.07639	+	12.2567i	0.276497	+	0.478907i
$656$		0			0
$657$	34.6414	−	9.63799i	1.35149	−	0.376014i
$658$		0			0
$659$	15.0559	+	26.0776i	0.586494	+	1.01584i	0.994687	+	0.102942i	$0.0328257\pi$
$659$	15.0559	+	26.0776i	0.586494	+	1.01584i	−0.408193	+	0.912896i	$0.633841\pi$
$660$		0			0
$661$	24.1247	−	41.7853i	0.938344	−	1.62526i	0.169784	−	0.985481i	$-0.445693\pi$
$661$	24.1247	−	41.7853i	0.938344	−	1.62526i	0.768560	−	0.639778i	$-0.220974\pi$
$662$		0			0
$663$	−0.423725	+	1.03695i	−0.0164561	+	0.0402720i
$664$		0			0
$665$	8.38470			0.325145
$666$		0			0
$667$	1.00070			0.0387472
$668$		0			0
$669$	−22.4929	−	29.0251i	−0.869627	−	1.12217i
$670$		0			0
$671$	4.18696	−	7.25203i	0.161636	−	0.279961i
$672$		0			0
$673$	−1.29571	−	2.24423i	−0.0499458	−	0.0865087i	0.839972	−	0.542630i	$-0.182572\pi$
$673$	−1.29571	−	2.24423i	−0.0499458	−	0.0865087i	−0.889917	+	0.456122i	$0.849238\pi$
$674$		0			0
$675$	8.84273	+	6.58599i	0.340357	+	0.253495i
$676$		0			0
$677$	−6.00135	−	10.3946i	−0.230651	−	0.399499i	0.727349	−	0.686268i	$-0.240752\pi$
$677$	−6.00135	−	10.3946i	−0.230651	−	0.399499i	−0.958000	+	0.286769i	$0.907419\pi$
$678$		0			0
$679$	16.6439	−	28.8281i	0.638734	−	1.10632i
$680$		0			0
$681$	−12.7313	−	16.4285i	−0.487864	−	0.629543i
$682$		0			0
$683$	−10.4104			−0.398341			−0.199171	−	0.979965i	$-0.563825\pi$
$683$	−10.4104			−0.398341			−0.199171	+	0.979965i	$0.563825\pi$
$684$		0			0
$685$	−9.80030			−0.374450
$686$		0			0
$687$	5.31753	−	13.0132i	0.202876	−	0.496486i
$688$		0			0
$689$	3.71395	−	6.43276i	0.141490	−	0.245069i
$690$		0			0
$691$	23.0332	+	39.8948i	0.876226	+	1.51767i	0.855451	+	0.517884i	$0.173280\pi$
$691$	23.0332	+	39.8948i	0.876226	+	1.51767i	0.0207750	+	0.999784i	$0.493387\pi$
$692$		0			0
$693$	−1.42408	+	5.52547i	−0.0540962	+	0.209895i
$694$		0			0
$695$	1.40975	+	2.44176i	0.0534749	+	0.0926212i
$696$		0			0
$697$	0.872645	−	1.51146i	0.0330538	−	0.0572508i
$698$		0			0
$699$	−47.4521	+	6.47808i	−1.79480	+	0.245023i
$700$		0			0
$701$	−18.3855			−0.694410			−0.347205	−	0.937789i	$-0.612869\pi$
$701$	−18.3855			−0.694410			−0.347205	+	0.937789i	$0.612869\pi$
$702$		0			0
$703$	−10.9324			−0.412324
$704$		0			0
$705$	−4.30996	+	0.588388i	−0.162323	+	0.0221600i
$706$		0			0
$707$	−15.2437	+	26.4029i	−0.573299	+	0.992982i
$708$		0			0
$709$	−11.3938	−	19.7347i	−0.427904	−	0.741152i	0.568782	−	0.822488i	$-0.307415\pi$
$709$	−11.3938	−	19.7347i	−0.427904	−	0.741152i	−0.996687	+	0.0813360i	$0.974081\pi$
$710$		0			0
$711$	10.3582	+	10.1620i	0.388462	+	0.381105i
$712$		0			0
$713$	0.337991	+	0.585418i	0.0126579	+	0.0219241i
$714$		0			0
$715$	−1.76770	+	3.06175i	−0.0661084	+	0.114503i
$716$		0			0
$717$	−4.73659	+	11.5915i	−0.176891	+	0.432894i
$718$		0			0
$719$	8.21384			0.306325			0.153162	−	0.988201i	$-0.451054\pi$
$719$	8.21384			0.306325			0.153162	+	0.988201i	$0.451054\pi$
$720$		0			0
$721$	−4.03461			−0.150257
$722$		0			0
$723$	5.53660	+	7.14447i	0.205908	+	0.265706i
$724$		0			0
$725$	4.68979	−	8.12295i	0.174174	−	0.301679i
$726$		0			0
$727$	12.9220	+	22.3816i	0.479252	+	0.830088i	0.999717	−	0.0237945i	$-0.00757475\pi$
$727$	12.9220	+	22.3816i	0.479252	+	0.830088i	−0.520465	+	0.853883i	$0.674241\pi$
$728$		0			0
$729$	18.5366	−	19.6315i	0.686540	−	0.727092i
$730$		0			0
$731$	−0.314056	−	0.543961i	−0.0116158	−	0.0201191i
$732$		0			0
$733$	−17.1099	+	29.6352i	−0.631968	+	1.09460i	0.355181	+	0.934798i	$0.384419\pi$
$733$	−17.1099	+	29.6352i	−0.631968	+	1.09460i	−0.987149	+	0.159803i	$0.948914\pi$
$734$		0			0
$735$	−6.08793	−	7.85591i	−0.224557	−	0.289770i
$736$		0			0
$737$	6.33735			0.233439
$738$		0			0
$739$	38.8028			1.42738			0.713692	−	0.700460i	$-0.247022\pi$
$739$	38.8028			1.42738			0.713692	+	0.700460i	$0.247022\pi$
$740$		0			0
$741$	−3.54786	+	8.68243i	−0.130334	+	0.318957i
$742$		0			0
$743$	−0.675496	+	1.16999i	−0.0247816	+	0.0429229i	−0.878150	−	0.478385i	$-0.841222\pi$
$743$	−0.675496	+	1.16999i	−0.0247816	+	0.0429229i	0.853369	+	0.521308i	$0.174556\pi$
$744$		0			0
$745$	−4.40519	−	7.63001i	−0.161394	−	0.279542i
$746$		0			0
$747$	−6.21175	−	6.09411i	−0.227276	−	0.222972i
$748$		0			0
$749$	19.4930	+	33.7628i	0.712258	+	1.23367i
$750$		0			0
$751$	−9.26715	+	16.0512i	−0.338163	+	0.585715i	−0.984087	−	0.177686i	$-0.943139\pi$
$751$	−9.26715	+	16.0512i	−0.338163	+	0.585715i	0.645924	+	0.763402i	$0.276472\pi$
$752$		0			0
$753$	20.7155	−	2.82804i	0.754915	−	0.103060i
$754$		0			0
$755$	−7.08683			−0.257916
$756$		0			0
$757$	−17.5676			−0.638504			−0.319252	−	0.947670i	$-0.603432\pi$
$757$	−17.5676			−0.638504			−0.319252	+	0.947670i	$0.603432\pi$
$758$		0			0
$759$	0.388509	−	0.0530385i	0.0141020	−	0.00192518i
$760$		0			0
$761$	−5.90148	+	10.2217i	−0.213928	+	0.370535i	−0.952941	−	0.303157i	$-0.901959\pi$
$761$	−5.90148	+	10.2217i	−0.213928	+	0.370535i	0.739012	+	0.673692i	$0.235293\pi$
$762$		0			0
$763$	−13.9916	−	24.2342i	−0.506531	−	0.877338i
$764$		0			0
$765$	−0.394196	+	1.52950i	−0.0142522	+	0.0552990i
$766$		0			0
$767$	10.2911	+	17.8247i	0.371591	+	0.643614i
$768$		0			0
$769$	4.87237	−	8.43919i	0.175702	−	0.304325i	−0.764702	−	0.644384i	$-0.777114\pi$
$769$	4.87237	−	8.43919i	0.175702	−	0.304325i	0.940404	+	0.340059i	$0.110447\pi$
$770$		0			0
$771$	−12.4837	+	30.5506i	−0.449591	+	1.10025i
$772$		0			0
$773$	−31.8568			−1.14581			−0.572905	−	0.819622i	$-0.694184\pi$
$773$	−31.8568			−1.14581			−0.572905	+	0.819622i	$0.694184\pi$
$774$		0			0
$775$	6.33599			0.227596
$776$		0			0
$777$	−8.48996	−	10.9555i	−0.304576	−	0.393027i
$778$		0			0
$779$	7.30667	−	12.6555i	0.261789	−	0.453431i
$780$		0			0
$781$	−0.177987	−	0.308283i	−0.00636888	−	0.0110312i
$782$		0			0
$783$	−18.4209	−	13.7197i	−0.658308	−	0.490302i
$784$		0			0
$785$	9.78342	+	16.9454i	0.349185	+	0.604807i
$786$		0			0
$787$	3.02390	−	5.23755i	0.107790	−	0.186699i	−0.807084	−	0.590436i	$-0.798956\pi$
$787$	3.02390	−	5.23755i	0.107790	−	0.186699i	0.914875	+	0.403738i	$0.132289\pi$
$788$		0			0
$789$	23.1471	+	29.8692i	0.824058	+	1.06337i
$790$		0			0
$791$	14.0628			0.500017
$792$		0			0
$793$	17.4509			0.619699
$794$		0			0
$795$	3.96172	−	9.69525i	0.140508	−	0.343855i
$796$		0			0
$797$	−10.8921	+	18.8657i	−0.385819	+	0.668258i	−0.991882	−	0.127158i	$-0.959414\pi$
$797$	−10.8921	+	18.8657i	−0.385819	+	0.668258i	0.606063	+	0.795416i	$0.292748\pi$
$798$		0			0
$799$	0.229711	+	0.397872i	0.00812660	+	0.0140757i
$800$		0			0
$801$	9.92948	−	2.76259i	0.350841	−	0.0976115i
$802$		0			0
$803$	−5.99286	−	10.3799i	−0.211484	−	0.366300i
$804$		0			0
$805$	0.365245	−	0.632623i	0.0128732	−	0.0222970i
$806$		0			0
$807$	18.9044	−	2.58080i	0.665467	−	0.0908483i
$808$		0			0
$809$	−1.07452			−0.0377779			−0.0188890	−	0.999822i	$-0.506013\pi$
$809$	−1.07452			−0.0377779			−0.0188890	+	0.999822i	$0.506013\pi$
$810$		0			0
$811$	6.38538			0.224221			0.112110	−	0.993696i	$-0.464239\pi$
$811$	6.38538			0.224221			0.112110	+	0.993696i	$0.464239\pi$
$812$		0			0
$813$	25.3902	−	3.46622i	0.890474	−	0.121566i
$814$		0			0
$815$	17.4663	−	30.2525i	0.611816	−	1.05970i
$816$		0			0
$817$	−2.62960	−	4.55460i	−0.0919980	−	0.159345i
$818$		0			0
$819$	−11.4560	+	3.18731i	−0.400305	+	0.111373i
$820$		0			0
$821$	−0.291474	−	0.504848i	−0.0101725	−	0.0176193i	0.860894	−	0.508784i	$-0.169905\pi$
$821$	−0.291474	−	0.504848i	−0.0101725	−	0.0176193i	−0.871067	+	0.491164i	$0.836571\pi$
$822$		0			0
$823$	−12.4989	+	21.6488i	−0.435685	+	0.754628i	−0.997351	−	0.0727357i	$-0.976827\pi$
$823$	−12.4989	+	21.6488i	−0.435685	+	0.754628i	0.561667	+	0.827364i	$0.310160\pi$
$824$		0			0
$825$	1.39022	−	3.40220i	0.0484013	−	0.118449i
$826$		0			0
$827$	9.64913			0.335533			0.167767	−	0.985827i	$-0.446345\pi$
$827$	9.64913			0.335533			0.167767	+	0.985827i	$0.446345\pi$
$828$		0			0
$829$	−8.07397			−0.280421			−0.140210	−	0.990122i	$-0.544778\pi$
$829$	−8.07397			−0.280421			−0.140210	+	0.990122i	$0.544778\pi$
$830$		0			0
$831$	−10.3837	−	13.3993i	−0.360208	−	0.464815i
$832$		0			0
$833$	−0.524843	+	0.909055i	−0.0181847	+	0.0314969i
$834$		0			0
$835$	16.3752	+	28.3627i	0.566688	+	0.981532i
$836$		0			0
$837$	1.80441	−	15.4103i	0.0623695	−	0.532657i
$838$		0			0
$839$	20.4457	+	35.4130i	0.705864	+	1.22259i	0.966379	+	0.257123i	$0.0827744\pi$
$839$	20.4457	+	35.4130i	0.705864	+	1.22259i	−0.260515	+	0.965470i	$0.583892\pi$
$840$		0			0
$841$	4.73039	−	8.19328i	0.163117	−	0.282527i
$842$		0			0
$843$	−16.6034	−	21.4252i	−0.571853	−	0.737923i
$844$		0			0
$845$	14.6867			0.505239
$846$		0			0
$847$	1.90201			0.0653539
$848$		0			0
$849$	4.42227	−	10.8223i	0.151772	−	0.371421i
$850$		0			0
$851$	−0.476226	+	0.824848i	−0.0163248	+	0.0282754i
$852$		0			0
$853$	11.5669	+	20.0345i	0.396043	+	0.685967i	0.993234	−	0.116132i	$-0.0370497\pi$
$853$	11.5669	+	20.0345i	0.396043	+	0.685967i	−0.597191	+	0.802099i	$0.703716\pi$
$854$		0			0
$855$	−3.30061	+	12.8065i	−0.112878	+	0.437973i
$856$		0			0
$857$	−18.0922	−	31.3367i	−0.618019	−	1.07044i	−0.989847	−	0.142138i	$-0.954602\pi$
$857$	−18.0922	−	31.3367i	−0.618019	−	1.07044i	0.371828	−	0.928302i	$-0.378731\pi$
$858$		0			0
$859$	2.36582	−	4.09773i	0.0807208	−	0.139813i	−0.822839	−	0.568275i	$-0.807611\pi$
$859$	2.36582	−	4.09773i	0.0807208	−	0.139813i	0.903560	+	0.428462i	$0.140944\pi$
$860$		0			0
$861$	18.3565	−	2.50600i	0.625589	−	0.0854042i
$862$		0			0
$863$	−51.6542			−1.75833			−0.879164	−	0.476519i	$-0.841898\pi$
$863$	−51.6542			−1.75833			−0.879164	+	0.476519i	$0.841898\pi$
$864$		0			0
$865$	12.6105			0.428770
$866$		0			0
$867$	−29.0090	+	3.96025i	−0.985196	+	0.134497i
$868$		0			0
$869$	2.41844	−	4.18886i	0.0820399	−	0.142097i
$870$		0			0
$871$	6.60338	+	11.4374i	0.223747	+	0.387541i
$872$		0			0
$873$	37.4792	+	36.7694i	1.26848	+	1.24446i
$874$		0			0
$875$	−11.4903	−	19.9018i	−0.388443	−	0.672804i
$876$		0			0
$877$	−7.62276	+	13.2030i	−0.257402	+	0.445834i	−0.965545	−	0.260235i	$-0.916200\pi$
$877$	−7.62276	+	13.2030i	−0.257402	+	0.445834i	0.708143	+	0.706069i	$0.249533\pi$
$878$		0			0
$879$	2.62966	−	6.43539i	0.0886962	−	0.217060i
$880$		0			0
$881$	−29.7320			−1.00170			−0.500849	−	0.865535i	$-0.666979\pi$
$881$	−29.7320			−1.00170			−0.500849	+	0.865535i	$0.666979\pi$
$882$		0			0
$883$	−41.5017			−1.39664			−0.698322	−	0.715783i	$-0.746070\pi$
$883$	−41.5017			−1.39664			−0.698322	+	0.715783i	$0.746070\pi$
$884$		0			0
$885$	17.7768	+	22.9394i	0.597562	+	0.771099i
$886$		0			0
$887$	8.27111	−	14.3260i	0.277717	−	0.481020i	−0.693100	−	0.720841i	$-0.743756\pi$
$887$	8.27111	−	14.3260i	0.277717	−	0.481020i	0.970817	+	0.239822i	$0.0770890\pi$
$888$		0			0
$889$	9.40519	+	16.2903i	0.315440	+	0.546358i
$890$		0			0
$891$	−7.87883	−	4.35017i	−0.263951	−	0.145736i
$892$		0			0
$893$	1.92338	+	3.33139i	0.0643634	+	0.111481i
$894$		0			0
$895$	−2.65280	+	4.59478i	−0.0886732	+	0.153587i
$896$		0			0
$897$	0.500540	+	0.645900i	0.0167125	+	0.0215660i
$898$		0			0
$899$	−13.1989			−0.440209
$900$		0			0
$901$	−1.10616			−0.0368516
$902$		0			0
$903$	2.52211	−	6.17220i	0.0839307	−	0.205398i
$904$		0			0
$905$	−13.4439	+	23.2855i	−0.446890	+	0.774037i
$906$		0			0
$907$	−15.3512	−	26.5891i	−0.509729	−	0.882877i	−0.999936	−	0.0112711i	$-0.996412\pi$
$907$	−15.3512	−	26.5891i	−0.509729	−	0.882877i	0.490207	−	0.871606i	$-0.336921\pi$
$908$		0			0
$909$	−34.3262	−	33.6761i	−1.13853	−	1.11697i
$910$		0			0
$911$	−1.03736	−	1.79676i	−0.0343693	−	0.0595294i	0.848329	−	0.529469i	$-0.177609\pi$
$911$	−1.03736	−	1.79676i	−0.0343693	−	0.0595294i	−0.882698	+	0.469940i	$0.844276\pi$
$912$		0			0
$913$	−1.45033	+	2.51204i	−0.0479988	+	0.0831363i
$914$		0			0
$915$	24.3798	−	3.32829i	0.805973	−	0.110030i
$916$		0			0
$917$	15.8673			0.523985
$918$		0			0
$919$	51.3954			1.69538			0.847688	−	0.530495i	$-0.177994\pi$
$919$	51.3954			1.69538			0.847688	+	0.530495i	$0.177994\pi$
$920$		0			0
$921$	43.0398	−	5.87572i	1.41821	−	0.193611i
$922$		0			0
$923$	0.370917	−	0.642448i	0.0122089	−	0.0211464i
$924$		0			0
$925$	4.46368	+	7.73131i	0.146765	+	0.254204i
$926$		0			0
$927$	1.58821	−	6.16232i	0.0521637	−	0.202397i
$928$		0			0
$929$	12.9604	+	22.4481i	0.425218	+	0.736500i	0.996441	−	0.0842954i	$-0.0268639\pi$
$929$	12.9604	+	22.4481i	0.425218	+	0.736500i	−0.571222	+	0.820795i	$0.693531\pi$
$930$		0			0
$931$	−4.39452	+	7.61154i	−0.144025	+	0.249458i
$932$		0			0
$933$	−15.8077	+	38.6852i	−0.517522	+	1.26650i
$934$		0			0
$935$	0.526492			0.0172181
$936$		0			0
$937$	−26.1718			−0.854994			−0.427497	−	0.904017i	$-0.640605\pi$
$937$	−26.1718			−0.854994			−0.427497	+	0.904017i	$0.640605\pi$
$938$		0			0
$939$	0.407772	+	0.526192i	0.0133071	+	0.0171716i
$940$		0			0
$941$	26.6558	−	46.1692i	0.868954	−	1.50507i	0.00588670	−	0.999983i	$-0.498126\pi$
$941$	26.6558	−	46.1692i	0.868954	−	1.50507i	0.863067	−	0.505089i	$-0.168540\pi$
$942$		0			0
$943$	−0.636571	−	1.10257i	−0.0207296	−	0.0359047i
$944$		0			0
$945$	−15.3968	+	6.63777i	−0.500857	+	0.215927i
$946$		0			0
$947$	−9.79973	−	16.9736i	−0.318448	−	0.551569i	0.661716	−	0.749754i	$-0.269828\pi$
$947$	−9.79973	−	16.9736i	−0.318448	−	0.551569i	−0.980164	+	0.198186i	$0.936495\pi$
$948$		0			0
$949$	12.4889	−	21.6313i	0.405406	−	0.702183i
$950$		0			0
$951$	−35.2085	−	45.4334i	−1.14171	−	1.47328i
$952$		0			0
$953$	−22.3925			−0.725366			−0.362683	−	0.931913i	$-0.618139\pi$
$953$	−22.3925			−0.725366			−0.362683	+	0.931913i	$0.618139\pi$
$954$		0			0
$955$	22.9843			0.743754
$956$		0			0
$957$	−2.89607	+	7.08734i	−0.0936165	+	0.229101i
$958$		0			0
$959$	−5.49378	+	9.51551i	−0.177404	+	0.307272i
$960$		0			0
$961$	11.0420	+	19.1253i	0.356193	+	0.616945i
$962$		0			0
$963$	−59.2416	+	16.4823i	−1.90903	+	0.531134i
$964$		0			0
$965$	13.2645	+	22.9747i	0.426998	+	0.739582i
$966$		0			0
$967$	−14.4070	+	24.9536i	−0.463297	+	0.802453i	−0.999123	−	0.0418750i	$-0.986667\pi$
$967$	−14.4070	+	24.9536i	−0.463297	+	0.802453i	0.535826	+	0.844328i	$0.320000\pi$
$968$		0			0
$969$	1.38393	−	0.188932i	0.0444583	−	0.00606936i
$970$		0			0
$971$	−8.45080			−0.271199			−0.135599	−	0.990764i	$-0.543296\pi$
$971$	−8.45080			−0.271199			−0.135599	+	0.990764i	$0.543296\pi$
$972$		0			0
$973$	3.16107			0.101339
$974$		0			0
$975$	7.58873	−	1.03600i	0.243034	−	0.0331785i
$976$		0			0
$977$	18.1286	−	31.3996i	0.579985	−	1.00456i	−0.415495	−	0.909595i	$-0.636392\pi$
$977$	18.1286	−	31.3996i	0.579985	−	1.00456i	0.995480	−	0.0949684i	$-0.0302750\pi$
$978$		0			0
$979$	−1.71777	−	2.97527i	−0.0549002	−	0.0950899i
$980$		0			0
$981$	42.5223	−	11.8306i	1.35763	−	0.377722i
$982$		0			0
$983$	−15.7602	−	27.2974i	−0.502672	−	0.870653i	−0.999995	−	0.00308781i	$-0.999017\pi$
$983$	−15.7602	−	27.2974i	−0.502672	−	0.870653i	0.497323	−	0.867565i	$-0.334316\pi$
$984$		0			0
$985$	1.15759	−	2.00501i	0.0368839	−	0.0638848i
$986$		0			0
$987$	−1.84476	+	4.51455i	−0.0587193	+	0.143700i
$988$		0			0
$989$	−0.458191			−0.0145696
$990$		0			0
$991$	−35.9833			−1.14305			−0.571524	−	0.820586i	$-0.693647\pi$
$991$	−35.9833			−1.14305			−0.571524	+	0.820586i	$0.693647\pi$
$992$		0			0
$993$	−31.0908	−	40.1198i	−0.986636	−	1.27316i
$994$		0			0
$995$	−1.15221	+	1.99568i	−0.0365274	+	0.0632673i
$996$		0			0
$997$	−2.42083	−	4.19300i	−0.0766684	−	0.132794i	0.825142	−	0.564925i	$-0.191095\pi$
$997$	−2.42083	−	4.19300i	−0.0766684	−	0.132794i	−0.901811	+	0.432132i	$0.857762\pi$
$998$		0			0
$999$	20.0751	−	8.65467i	0.635149	−	0.273822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.q.f.265.6	✓	12
3.2	odd	2		2376.2.q.f.793.2		12
9.2	odd	6		2376.2.q.f.1585.2		12
9.4	even	3		7128.2.a.ba.1.2		6
9.5	odd	6		7128.2.a.w.1.5		6
9.7	even	3	inner	792.2.q.f.529.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.q.f.265.6	✓	12	1.1	even	1	trivial
792.2.q.f.529.6	yes	12	9.7	even	3	inner
2376.2.q.f.793.2		12	3.2	odd	2
2376.2.q.f.1585.2		12	9.2	odd	6
7128.2.a.w.1.5		6	9.5	odd	6
7128.2.a.ba.1.2		6	9.4	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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71613 - 0.234283i) q^{3} +(0.848245 - 1.46920i) q^{5} +(-0.951006 - 1.64719i) q^{7} +(2.89022 - 0.804122i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(1.04198 - 1.80476i) q^{13} +(1.11149 - 2.72008i) q^{15} -0.310342 q^{17} -2.59850 q^{19} +(-2.01796 - 2.60399i) q^{21} +(-0.113193 + 0.196056i) q^{23} +(1.06096 + 1.83764i) q^{25} +(4.77161 - 2.05711i) q^{27} +(-2.21016 - 3.82811i) q^{29} +(1.49298 - 2.58592i) q^{31} +(-1.06096 - 1.36907i) q^{33} -3.22674 q^{35} +4.20720 q^{37} +(1.36535 - 3.34132i) q^{39} +(-2.81188 + 4.87031i) q^{41} +(1.01197 + 1.75278i) q^{43} +(1.27020 - 4.92842i) q^{45} +(-0.740187 - 1.28204i) q^{47} +(1.69118 - 2.92920i) q^{49} +(-0.532589 + 0.0727080i) q^{51} +3.56433 q^{53} -1.69649 q^{55} +(-4.45937 + 0.608785i) q^{57} +(-4.93826 + 8.55332i) q^{59} +(4.18696 + 7.25203i) q^{61} +(-4.07316 - 3.99602i) q^{63} +(-1.76770 - 3.06175i) q^{65} +(-3.16867 + 5.48830i) q^{67} +(-0.148322 + 0.362978i) q^{69} +0.355974 q^{71} +11.9857 q^{73} +(2.25128 + 2.90507i) q^{75} +(-0.951006 + 1.64719i) q^{77} +(2.41844 + 4.18886i) q^{79} +(7.70678 - 4.64818i) q^{81} +(-1.45033 - 2.51204i) q^{83} +(-0.263246 + 0.455956i) q^{85} +(-4.68979 - 6.05174i) q^{87} +3.43554 q^{89} -3.96371 q^{91} +(1.95632 - 4.78757i) q^{93} +(-2.20417 + 3.81773i) q^{95} +(8.75068 + 15.1566i) q^{97} +(-2.14150 - 2.10095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{3} - 4 q^{5} - 5 q^{7} + 5 q^{9} - 6 q^{11} - 3 q^{13} - 7 q^{15} + 14 q^{17} + 10 q^{19} + 9 q^{21} - 8 q^{23} + 2 q^{25} - 11 q^{27} - 8 q^{29} - 4 q^{31} - 2 q^{33} + 16 q^{35} + 6 q^{37}+ \cdots - 7 q^{99}+O(q^{100}) \) 12 * q + q^3 - 4 * q^5 - 5 * q^7 + 5 * q^9 - 6 * q^11 - 3 * q^13 - 7 * q^15 + 14 * q^17 + 10 * q^19 + 9 * q^21 - 8 * q^23 + 2 * q^25 - 11 * q^27 - 8 * q^29 - 4 * q^31 - 2 * q^33 + 16 * q^35 + 6 * q^37 + 14 * q^39 - 5 * q^43 + 25 * q^45 - 17 * q^47 - 3 * q^49 - 15 * q^51 + 28 * q^53 + 8 * q^55 + 15 * q^57 - 4 * q^59 - q^61 + 15 * q^63 - 15 * q^65 + 4 * q^67 - 14 * q^69 + 14 * q^71 - 24 * q^73 + 38 * q^75 - 5 * q^77 - q^79 + 5 * q^81 - 22 * q^83 + 3 * q^85 - q^87 + 44 * q^89 + 22 * q^91 + 12 * q^93 - 24 * q^95 + 16 * q^97 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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