LMFDB - Embedded newform 668.2.e.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.360076 - 2.70211i) q^{3} +(2.66599 + 1.17892i) q^{5} +(0.359959 - 0.774059i) q^{7} +(-4.27644 + 1.16034i) q^{9} +O(q^{10})$	\(q+(-0.360076 - 2.70211i) q^{3} +(2.66599 + 1.17892i) q^{5} +(0.359959 - 0.774059i) q^{7} +(-4.27644 + 1.16034i) q^{9} +(1.41822 - 1.81840i) q^{11} +(0.212957 - 0.416003i) q^{13} +(2.22562 - 7.62829i) q^{15} +(0.00376620 + 0.000285651i) q^{17} +(2.82122 - 4.24396i) q^{19} +(-2.22121 - 0.693930i) q^{21} +(4.68688 + 1.86388i) q^{23} +(2.35326 + 2.58718i) q^{25} +(1.50992 + 3.59703i) q^{27} +(1.55654 - 0.619007i) q^{29} +(-4.46558 + 1.03195i) q^{31} +(-5.42418 - 3.17744i) q^{33} +(1.87220 - 1.63927i) q^{35} +(-7.73988 - 2.10008i) q^{37} +(-1.20077 - 0.425641i) q^{39} +(-4.78039 + 2.33404i) q^{41} +(-0.447049 + 4.71025i) q^{43} +(-12.7689 - 1.94814i) q^{45} +(-0.117670 - 6.21686i) q^{47} +(4.04118 + 4.79558i) q^{49} +(-0.000584257 - 0.0102795i) q^{51} +(-0.235266 - 1.36787i) q^{53} +(5.92471 - 3.17584i) q^{55} +(-12.4835 - 6.09511i) q^{57} +(4.70272 - 0.356683i) q^{59} +(6.63150 - 6.75821i) q^{61} +(-0.641175 + 3.72789i) q^{63} +(1.05818 - 0.858000i) q^{65} +(1.55333 - 0.686896i) q^{67} +(3.34878 - 13.3356i) q^{69} +(-10.4919 + 1.19652i) q^{71} +(-12.8510 + 9.63743i) q^{73} +(6.14351 - 7.29036i) q^{75} +(-0.897042 - 1.75234i) q^{77} +(3.48394 - 9.26768i) q^{79} +(-2.29420 + 1.34393i) q^{81} +(-1.64790 + 2.28629i) q^{83} +(0.00970387 + 0.00520159i) q^{85} +(-2.23310 - 3.98307i) q^{87} +(4.34168 + 14.8811i) q^{89} +(-0.245355 - 0.314586i) q^{91} +(4.39639 + 11.6949i) q^{93} +(12.5246 - 7.98833i) q^{95} +(8.95939 + 2.07042i) q^{97} +(-3.95500 + 9.42188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.360076	−	2.70211i	−0.207890	−	1.56007i	−0.715583	−	0.698527i	$-0.753839\pi$
$3$	−0.360076	−	2.70211i	−0.207890	−	1.56007i	0.507693	−	0.861538i	$-0.330498\pi$
$4$		0			0
$5$	2.66599	+	1.17892i	1.19227	+	0.527230i	0.902842	−	0.429972i	$-0.141476\pi$
$5$	2.66599	+	1.17892i	1.19227	+	0.527230i	0.289423	+	0.957201i	$0.406537\pi$
$6$		0			0
$7$	0.359959	−	0.774059i	0.136052	−	0.292567i	−0.826848	−	0.562425i	$-0.809868\pi$
$7$	0.359959	−	0.774059i	0.136052	−	0.292567i	0.962900	+	0.269858i	$0.0869769\pi$
$8$		0			0
$9$	−4.27644	+	1.16034i	−1.42548	+	0.386780i
$10$		0			0
$11$	1.41822	−	1.81840i	0.427611	−	0.548267i	−0.525537	−	0.850770i	$-0.676136\pi$
$11$	1.41822	−	1.81840i	0.427611	−	0.548267i	0.953148	+	0.302504i	$0.0978225\pi$
$12$		0			0
$13$	0.212957	−	0.416003i	0.0590636	−	0.115379i	−0.858743	−	0.512407i	$-0.828754\pi$
$13$	0.212957	−	0.416003i	0.0590636	−	0.115379i	0.917806	+	0.397029i	$0.129959\pi$
$14$		0			0
$15$	2.22562	−	7.62829i	0.574653	−	1.96962i
$16$		0			0
$17$	0.00376620		0.000285651i	0.000913437		6.92805e-5i	0.0760855	−	0.997101i	$-0.475758\pi$
$17$	0.00376620		0.000285651i	0.000913437		6.92805e-5i	−0.0751720	+	0.997171i	$0.523951\pi$
$18$		0			0
$19$	2.82122	−	4.24396i	0.647233	−	0.973630i	−0.352058	−	0.935978i	$-0.614518\pi$
$19$	2.82122	−	4.24396i	0.647233	−	0.973630i	0.999291	−	0.0376523i	$-0.0119879\pi$
$20$		0			0
$21$	−2.22121	−	0.693930i	−0.484707	−	0.151428i
$22$		0			0
$23$	4.68688	+	1.86388i	0.977281	+	0.388646i	0.802953	−	0.596042i	$-0.203261\pi$
$23$	4.68688	+	1.86388i	0.977281	+	0.388646i	0.174328	+	0.984688i	$0.444225\pi$
$24$		0			0
$25$	2.35326	+	2.58718i	0.470652	+	0.517437i
$26$		0			0
$27$	1.50992	+	3.59703i	0.290583	+	0.692248i
$28$		0			0
$29$	1.55654	−	0.619007i	0.289043	−	0.114947i	−0.220513	−	0.975384i	$-0.570773\pi$
$29$	1.55654	−	0.619007i	0.289043	−	0.114947i	0.509557	+	0.860437i	$0.329809\pi$
$30$		0			0
$31$	−4.46558	+	1.03195i	−0.802041	+	0.185344i	−0.606221	−	0.795296i	$-0.707315\pi$
$31$	−4.46558	+	1.03195i	−0.802041	+	0.185344i	−0.195820	+	0.980640i	$0.562737\pi$
$32$		0			0
$33$	−5.42418	−	3.17744i	−0.944228	−	0.553121i
$34$		0			0
$35$	1.87220	−	1.63927i	0.316460	−	0.277087i
$36$		0			0
$37$	−7.73988	−	2.10008i	−1.27243	−	0.345251i	−0.439305	−	0.898338i	$-0.644775\pi$
$37$	−7.73988	−	2.10008i	−1.27243	−	0.345251i	−0.833124	+	0.553087i	$0.813450\pi$
$38$		0			0
$39$	−1.20077	−	0.425641i	−0.192277	−	0.0681571i
$40$		0			0
$41$	−4.78039	+	2.33404i	−0.746571	+	0.364516i	−0.772388	−	0.635151i	$-0.780938\pi$
$41$	−4.78039	+	2.33404i	−0.746571	+	0.364516i	0.0258170	+	0.999667i	$0.491781\pi$
$42$		0			0
$43$	−0.447049	+	4.71025i	−0.0681743	+	0.718307i	0.894396	+	0.447276i	$0.147606\pi$
$43$	−0.447049	+	4.71025i	−0.0681743	+	0.718307i	−0.962571	+	0.271031i	$0.912635\pi$
$44$		0			0
$45$	−12.7689	−	1.94814i	−1.90347	−	0.290412i
$46$		0			0
$47$	−0.117670	−	6.21686i	−0.0171639	−	0.906823i	−0.899682	−	0.436545i	$-0.856202\pi$
$47$	−0.117670	−	6.21686i	−0.0171639	−	0.906823i	0.882518	−	0.470278i	$-0.155846\pi$
$48$		0			0
$49$	4.04118	+	4.79558i	0.577312	+	0.685083i
$50$		0			0
$51$	−0.000584257	−	0.0102795i	−8.18124e−5	−	0.00143942i
$52$		0			0
$53$	−0.235266	−	1.36787i	−0.0323163	−	0.187892i	0.964883	−	0.262679i	$-0.0846060\pi$
$53$	−0.235266	−	1.36787i	−0.0323163	−	0.187892i	−0.997200	+	0.0747871i	$0.976172\pi$
$54$		0			0
$55$	5.92471	−	3.17584i	0.798888	−	0.428230i
$56$		0			0
$57$	−12.4835	−	6.09511i	−1.65348	−	0.807317i
$58$		0			0
$59$	4.70272	−	0.356683i	0.612243	−	0.0464361i	0.234145	−	0.972202i	$-0.424771\pi$
$59$	4.70272	−	0.356683i	0.612243	−	0.0464361i	0.378098	+	0.925766i	$0.376578\pi$
$60$		0			0
$61$	6.63150	−	6.75821i	0.849077	−	0.865300i	−0.143155	−	0.989700i	$-0.545725\pi$
$61$	6.63150	−	6.75821i	0.849077	−	0.865300i	0.992232	+	0.124400i	$0.0397006\pi$
$62$		0			0
$63$	−0.641175	+	3.72789i	−0.0807804	+	0.469670i
$64$		0			0
$65$	1.05818	−	0.858000i	0.131251	−	0.106422i
$66$		0			0
$67$	1.55333	−	0.686896i	0.189769	−	0.0839176i	−0.307363	−	0.951592i	$-0.599447\pi$
$67$	1.55333	−	0.686896i	0.189769	−	0.0839176i	0.497132	+	0.867675i	$0.334386\pi$
$68$		0			0
$69$	3.34878	−	13.3356i	0.403145	−	1.60542i
$70$		0			0
$71$	−10.4919	+	1.19652i	−1.24516	+	0.142000i	−0.710883	−	0.703310i	$-0.751704\pi$
$71$	−10.4919	+	1.19652i	−1.24516	+	0.142000i	−0.534275	+	0.845311i	$0.679415\pi$
$72$		0			0
$73$	−12.8510	+	9.63743i	−1.50410	+	1.12798i	−0.547411	+	0.836864i	$0.684386\pi$
$73$	−12.8510	+	9.63743i	−1.50410	+	1.12798i	−0.956689	+	0.291111i	$0.905975\pi$
$74$		0			0
$75$	6.14351	−	7.29036i	0.709391	−	0.841818i
$76$		0			0
$77$	−0.897042	−	1.75234i	−0.102227	−	0.199697i
$78$		0			0
$79$	3.48394	−	9.26768i	0.391973	−	1.04270i	−0.581430	−	0.813597i	$-0.697506\pi$
$79$	3.48394	−	9.26768i	0.391973	−	1.04270i	0.973403	−	0.229099i	$-0.0735779\pi$
$80$		0			0
$81$	−2.29420	+	1.34393i	−0.254911	+	0.149325i
$82$		0			0
$83$	−1.64790	+	2.28629i	−0.180881	+	0.250953i	−0.891914	−	0.452206i	$-0.850637\pi$
$83$	−1.64790	+	2.28629i	−0.180881	+	0.250953i	0.711033	+	0.703159i	$0.248228\pi$
$84$		0			0
$85$	0.00970387	+	0.00520159i	0.00105253	+	0.000564192i
$86$		0			0
$87$	−2.23310	−	3.98307i	−0.239414	−	0.427030i
$88$		0			0
$89$	4.34168	+	14.8811i	0.460218	+	1.57739i	0.777387	+	0.629023i	$0.216545\pi$
$89$	4.34168	+	14.8811i	0.460218	+	1.57739i	−0.317169	+	0.948369i	$0.602732\pi$
$90$		0			0
$91$	−0.245355	−	0.314586i	−0.0257202	−	0.0329775i
$92$		0			0
$93$	4.39639	+	11.6949i	0.455884	+	1.21271i
$94$		0			0
$95$	12.5246	−	7.98833i	1.28500	−	0.819585i
$96$		0			0
$97$	8.95939	+	2.07042i	0.909688	+	0.210220i	0.653960	−	0.756529i	$-0.273106\pi$
$97$	8.95939	+	2.07042i	0.909688	+	0.210220i	0.255728	+	0.966749i	$0.417685\pi$
$98$		0			0
$99$	−3.95500	+	9.42188i	−0.397493	+	0.946935i
$100$		0			0
$101$	0.700273	+	7.37831i	0.0696798	+	0.734169i	0.960216	+	0.279257i	$0.0900883\pi$
$101$	0.700273	+	7.37831i	0.0696798	+	0.734169i	−0.890536	+	0.454912i	$0.849671\pi$
$102$		0			0
$103$	−4.27542	+	2.96031i	−0.421270	+	0.291688i	−0.760897	−	0.648872i	$-0.775241\pi$
$103$	−4.27542	+	2.96031i	−0.421270	+	0.291688i	0.339628	+	0.940560i	$0.389699\pi$
$104$		0			0
$105$	−5.10362	−	4.46864i	−0.498062	−	0.436094i
$106$		0			0
$107$	10.2193	+	7.07586i	0.987937	+	0.684049i	0.949028	−	0.315193i	$-0.102069\pi$
$107$	10.2193	+	7.07586i	0.987937	+	0.684049i	0.0389098	+	0.999243i	$0.487612\pi$
$108$		0			0
$109$	9.35869	+	5.96906i	0.896400	+	0.571732i	0.903664	−	0.428241i	$-0.140867\pi$
$109$	9.35869	+	5.96906i	0.896400	+	0.571732i	−0.00726466	+	0.999974i	$0.502312\pi$
$110$		0			0
$111$	−2.88771	+	21.6702i	−0.274090	+	2.05685i
$112$		0			0
$113$	6.08987	−	9.95891i	0.572887	−	0.936856i	−0.426587	−	0.904446i	$-0.640284\pi$
$113$	6.08987	−	9.95891i	0.572887	−	0.936856i	0.999475	−	0.0324094i	$-0.0103180\pi$
$114$		0			0
$115$	10.2978	+	10.4945i	0.960273	+	0.978620i
$116$		0			0
$117$	−0.427993	+	2.02612i	−0.0395680	+	0.187315i
$118$		0			0
$119$	0.00157679	−	0.00281244i	0.000144544	−	0.000257816i
$120$		0			0
$121$	1.38389	+	5.51098i	0.125808	+	0.500998i
$122$		0			0
$123$	8.02814	+	12.0767i	0.723873	+	1.08892i
$124$		0			0
$125$	−1.38508	−	4.15554i	−0.123886	−	0.371683i
$126$		0			0
$127$	−8.68374	−	0.990312i	−0.770557	−	0.0878760i	−0.280837	−	0.959756i	$-0.590612\pi$
$127$	−8.68374	−	0.990312i	−0.770557	−	0.0878760i	−0.489720	+	0.871880i	$0.662901\pi$
$128$		0			0
$129$	12.8886	−	0.488073i	1.13478	−	0.0429725i
$130$		0			0
$131$	−0.0196468	+	0.345670i	−0.00171655	+	0.0302013i	−0.999133	−	0.0416381i	$-0.986742\pi$
$131$	−0.0196468	+	0.345670i	−0.00171655	+	0.0302013i	0.997416	+	0.0718394i	$0.0228869\pi$
$132$		0			0
$133$	−2.26955	−	3.71144i	−0.196795	−	0.321823i
$134$		0			0
$135$	−0.215200	+	11.3697i	−0.0185215	+	0.978548i
$136$		0			0
$137$	13.0445	−	4.62394i	1.11447	−	0.395050i	0.287773	−	0.957699i	$-0.407085\pi$
$137$	13.0445	−	4.62394i	1.11447	−	0.395050i	0.826696	+	0.562649i	$0.190218\pi$
$138$		0			0
$139$	6.50848	+	6.14906i	0.552042	+	0.521556i	0.911333	−	0.411669i	$-0.135054\pi$
$139$	6.50848	+	6.14906i	0.552042	+	0.521556i	−0.359292	+	0.933225i	$0.616982\pi$
$140$		0			0
$141$	−16.7563	+	2.55650i	−1.41113	+	0.215296i
$142$		0			0
$143$	−0.454438	−	0.977226i	−0.0380020	−	0.0817197i
$144$		0			0
$145$	4.87949	+	0.184779i	0.405219	+	0.0153451i
$146$		0			0
$147$	11.5031	−	12.6465i	0.948756	−	1.04307i
$148$		0			0
$149$	3.77569	+	3.06144i	0.309316	+	0.250803i	0.771858	−	0.635795i	$-0.219328\pi$
$149$	3.77569	+	3.06144i	0.309316	+	0.250803i	−0.462542	+	0.886597i	$0.653063\pi$
$150$		0			0
$151$	12.8517	+	9.63794i	1.04586	+	0.784325i	0.976987	−	0.213301i	$-0.0684214\pi$
$151$	12.8517	+	9.63794i	1.04586	+	0.784325i	0.0688721	+	0.997625i	$0.478060\pi$
$152$		0			0
$153$	−0.0164374	+	0.00314850i	−0.00132888	+	0.000254541i
$154$		0			0
$155$	−13.1218	−	2.51340i	−1.05396	−	0.201882i
$156$		0			0
$157$	1.95548	+	9.25724i	0.156065	+	0.738808i	0.984026	+	0.178024i	$0.0569703\pi$
$157$	1.95548	+	9.25724i	0.156065	+	0.738808i	−0.827962	+	0.560785i	$0.810500\pi$
$158$		0			0
$159$	−3.61144	+	1.12825i	−0.286406	+	0.0894763i
$160$		0			0
$161$	3.12984	−	2.95700i	0.246666	−	0.233044i
$162$		0			0
$163$	−3.38123	+	10.1444i	−0.264838	+	0.794571i	0.729078	+	0.684431i	$0.239949\pi$
$163$	−3.38123	+	10.1444i	−0.264838	+	0.794571i	−0.993916	+	0.110140i	$0.964870\pi$
$164$		0			0
$165$	−10.7148	−	14.8657i	−0.834148	−	1.15729i
$166$		0			0
$167$	−9.73848	−	8.49482i	−0.753586	−	0.657349i
$167$	−9.73848	−	8.49482i	−0.753586	−	0.657349i
$168$		0			0
$169$	7.47364	+	10.3689i	0.574895	+	0.797607i
$170$		0			0
$171$	−7.14037	+	21.4226i	−0.546037	+	1.63823i
$172$		0			0
$173$	2.02587	−	1.91399i	0.154024	−	0.145518i	−0.605874	−	0.795560i	$-0.707177\pi$
$173$	2.02587	−	1.91399i	0.154024	−	0.145518i	0.759898	+	0.650042i	$0.225249\pi$
$174$		0			0
$175$	2.84971	−	0.890282i	0.215418	−	0.0672990i
$176$		0			0
$177$	−2.65714	−	12.5789i	−0.199723	−	0.945485i
$178$		0			0
$179$	−0.653800	−	0.125232i	−0.0488673	−	0.00936029i	0.163633	−	0.986521i	$-0.447679\pi$
$179$	−0.653800	−	0.125232i	−0.0488673	−	0.00936029i	−0.212500	+	0.977161i	$0.568161\pi$
$180$		0			0
$181$	−3.94947	+	0.756500i	−0.293561	+	0.0562302i	−0.332793	−	0.943000i	$-0.607991\pi$
$181$	−3.94947	+	0.756500i	−0.293561	+	0.0562302i	0.0392314	+	0.999230i	$0.487509\pi$
$182$		0			0
$183$	−20.6493	−	15.4856i	−1.52644	−	1.14473i
$184$		0			0
$185$	−18.1586	−	14.7235i	−1.33505	−	1.08249i
$186$		0			0
$187$	0.00586074	−	0.00644332i	0.000428580	−	0.000471182i
$188$		0			0
$189$	3.32782	+	0.126020i	0.242063	+	0.00916660i
$190$		0			0
$191$	−0.476049	−	1.02370i	−0.0344457	−	0.0740722i	0.888772	−	0.458349i	$-0.151559\pi$
$191$	−0.476049	−	1.02370i	−0.0344457	−	0.0740722i	−0.923218	+	0.384277i	$0.874451\pi$
$192$		0			0
$193$	1.66894	−	0.254629i	0.120133	−	0.0183286i	−0.0904793	−	0.995898i	$-0.528840\pi$
$193$	1.66894	−	0.254629i	0.120133	−	0.0183286i	0.210612	+	0.977570i	$0.432454\pi$
$194$		0			0
$195$	−2.69943	−	2.55036i	−0.193311	−	0.182635i
$196$		0			0
$197$	1.99891	−	0.708562i	0.142417	−	0.0504829i	−0.261941	−	0.965084i	$-0.584363\pi$
$197$	1.99891	−	0.708562i	0.142417	−	0.0504829i	0.404358	+	0.914601i	$0.367495\pi$
$198$		0			0
$199$	−0.258661	+	13.6659i	−0.0183360	+	0.968749i	0.865488	+	0.500930i	$0.167008\pi$
$199$	−0.258661	+	13.6659i	−0.0183360	+	0.968749i	−0.883824	+	0.467820i	$0.845040\pi$
$200$		0			0
$201$	−2.41539	−	3.94994i	−0.170368	−	0.278607i
$202$		0			0
$203$	0.0811446	−	1.42768i	0.00569523	−	0.100203i
$204$		0			0
$205$	−15.4961	+	0.586815i	−1.08229	+	0.0409850i
$206$		0			0
$207$	−22.2059	−	2.53241i	−1.54342	−	0.176014i
$208$		0			0
$209$	−3.71606	−	11.1490i	−0.257046	−	0.771191i
$210$		0			0
$211$	3.22627	+	4.85326i	0.222105	+	0.334112i	0.926906	−	0.375293i	$-0.122458\pi$
$211$	3.22627	+	4.85326i	0.222105	+	0.334112i	−0.704801	+	0.709405i	$0.748964\pi$
$212$		0			0
$213$	7.01100	+	27.9194i	0.480386	+	1.91301i
$214$		0			0
$215$	−6.74484	+	12.0304i	−0.459995	+	0.820469i
$216$		0			0
$217$	−0.808637	+	3.82808i	−0.0548939	+	0.259867i
$218$		0			0
$219$	30.6688	+	31.2547i	2.07240	+	2.11200i
$220$		0			0
$221$	0.000920870	−	0.00150592i	6.19444e−5	−	0.000101299i
$222$		0			0
$223$	2.35123	−	17.6443i	0.157450	−	1.18155i	−0.717226	−	0.696841i	$-0.754588\pi$
$223$	2.35123	−	17.6443i	0.157450	−	1.18155i	0.874676	−	0.484709i	$-0.161074\pi$
$224$		0			0
$225$	−13.0656	−	8.33336i	−0.871040	−	0.555557i
$226$		0			0
$227$	−21.9251	−	15.1810i	−1.45522	−	1.00760i	−0.992651	−	0.121012i	$-0.961386\pi$
$227$	−21.9251	−	15.1810i	−1.45522	−	1.00760i	−0.462567	−	0.886584i	$-0.653072\pi$
$228$		0			0
$229$	−7.36394	−	6.44774i	−0.486623	−	0.426079i	0.380042	−	0.924969i	$-0.375910\pi$
$229$	−7.36394	−	6.44774i	−0.486623	−	0.426079i	−0.866665	+	0.498891i	$0.833741\pi$
$230$		0			0
$231$	−4.41201	+	3.05488i	−0.290289	+	0.200997i
$232$		0			0
$233$	−1.74697	−	18.4067i	−0.114448	−	1.20586i	−0.849403	−	0.527745i	$-0.823038\pi$
$233$	−1.74697	−	18.4067i	−0.114448	−	1.20586i	0.734955	−	0.678116i	$-0.237203\pi$
$234$		0			0
$235$	7.01549	−	16.7128i	0.457640	−	1.09022i
$236$		0			0
$237$	−26.2968	−	6.07692i	−1.70816	−	0.394738i
$238$		0			0
$239$	4.84805	−	3.09213i	0.313595	−	0.200014i	−0.371564	−	0.928407i	$-0.621179\pi$
$239$	4.84805	−	3.09213i	0.313595	−	0.200014i	0.685159	+	0.728394i	$0.259733\pi$
$240$		0			0
$241$	8.64612	+	22.9997i	0.556946	+	1.48154i	0.850696	+	0.525658i	$0.176181\pi$
$241$	8.64612	+	22.9997i	0.556946	+	1.48154i	−0.293750	+	0.955882i	$0.594903\pi$
$242$		0			0
$243$	11.6550	+	14.9436i	0.747669	+	0.958634i
$244$		0			0
$245$	5.12012	+	17.5492i	0.327113	+	1.12118i
$246$		0			0
$247$	−1.16470	−	2.07742i	−0.0741082	−	0.132183i
$248$		0			0
$249$	6.77119	+	3.62958i	0.429106	+	0.230015i
$250$		0			0
$251$	−2.53316	+	3.51449i	−0.159892	+	0.221833i	−0.883563	−	0.468311i	$-0.844863\pi$
$251$	−2.53316	+	3.51449i	−0.159892	+	0.221833i	0.723672	+	0.690144i	$0.242453\pi$
$252$		0			0
$253$	10.0363	−	5.87919i	0.630977	−	0.369622i
$254$		0			0
$255$	0.0105612	−	0.0280939i	0.000661365	−	0.00175931i
$256$		0			0
$257$	−8.20254	−	16.0233i	−0.511660	−	0.999509i	−0.992447	−	0.122672i	$-0.960854\pi$
$257$	−8.20254	−	16.0233i	−0.511660	−	0.999509i	0.480787	−	0.876837i	$-0.340351\pi$
$258$		0			0
$259$	−4.41163	+	5.23518i	−0.274125	+	0.325298i
$260$		0			0
$261$	−5.93822	+	4.45327i	−0.367566	+	0.275650i
$262$		0			0
$263$	−9.87494	+	1.12616i	−0.608915	+	0.0694419i	−0.412314	−	0.911042i	$-0.635279\pi$
$263$	−9.87494	+	1.12616i	−0.608915	+	0.0694419i	−0.196601	+	0.980484i	$0.562990\pi$
$264$		0			0
$265$	0.985401	−	3.92409i	0.0605327	−	0.241055i
$266$		0			0
$267$	38.6470	−	17.0900i	2.36516	−	1.04589i
$268$		0			0
$269$	−8.78453	+	7.12275i	−0.535602	+	0.434282i	−0.858996	−	0.511983i	$-0.828911\pi$
$269$	−8.78453	+	7.12275i	−0.535602	+	0.434282i	0.323394	+	0.946265i	$0.395176\pi$
$270$		0			0
$271$	1.48628	−	8.64148i	0.0902852	−	0.524933i	−0.904794	−	0.425850i	$-0.859975\pi$
$271$	1.48628	−	8.64148i	0.0902852	−	0.524933i	0.995079	−	0.0990832i	$-0.0315910\pi$
$272$		0			0
$273$	−0.761699	+	0.776253i	−0.0461001	+	0.0469809i
$274$		0			0
$275$	8.04197	−	0.609951i	0.484949	−	0.0367814i
$276$		0			0
$277$	13.0611	+	6.37711i	0.784764	+	0.383164i	0.787093	−	0.616834i	$-0.211585\pi$
$277$	13.0611	+	6.37711i	0.784764	+	0.383164i	−0.00232964	+	0.999997i	$0.500742\pi$
$278$		0			0
$279$	17.8994	−	9.59465i	1.07161	−	0.574417i
$280$		0			0
$281$	−3.35769	−	19.5222i	−0.200303	−	1.16459i	−0.895260	−	0.445543i	$-0.853011\pi$
$281$	−3.35769	−	19.5222i	−0.200303	−	1.16459i	0.694957	−	0.719051i	$-0.255423\pi$
$282$		0			0
$283$	1.19226	+	20.9769i	0.0708725	+	1.24695i	0.815219	+	0.579153i	$0.196616\pi$
$283$	1.19226	+	20.9769i	0.0708725	+	1.24695i	−0.744347	+	0.667793i	$0.767239\pi$
$284$		0			0
$285$	−26.0952	−	30.9666i	−1.54575	−	1.83430i
$286$		0			0
$287$	0.0859397	+	4.54046i	0.00507286	+	0.268015i
$288$		0			0
$289$	−16.8055	−	2.56401i	−0.988560	−	0.150824i
$290$		0			0
$291$	2.36845	−	24.9548i	0.138841	−	1.46288i
$292$		0			0
$293$	−27.8816	+	13.6133i	−1.62886	+	0.795296i	−0.629020	+	0.777389i	$0.716543\pi$
$293$	−27.8816	+	13.6133i	−1.62886	+	0.795296i	−0.999840	+	0.0179065i	$0.994300\pi$
$294$		0			0
$295$	12.9579	+	4.59323i	0.754438	+	0.267428i
$296$		0			0
$297$	8.68222	+	2.35577i	0.503793	+	0.136696i
$298$		0			0
$299$	1.77348	−	1.55283i	0.102563	−	0.0898025i
$300$		0			0
$301$	3.48510	+	2.04154i	0.200878	+	0.117673i
$302$		0			0
$303$	19.6849	−	4.54897i	1.13087	−	0.261332i
$304$		0			0
$305$	25.6469	−	10.1993i	1.46854	−	0.584008i
$306$		0			0
$307$	−7.85568	−	18.7144i	−0.448347	−	1.06808i	−0.975832	−	0.218520i	$-0.929877\pi$
$307$	−7.85568	−	18.7144i	−0.448347	−	1.06808i	0.527485	−	0.849564i	$-0.323135\pi$
$308$		0			0
$309$	9.53856	+	10.4867i	0.542630	+	0.596569i
$310$		0			0
$311$	20.1904	+	8.02933i	1.14489	+	0.455302i	0.863529	−	0.504299i	$-0.168249\pi$
$311$	20.1904	+	8.02933i	1.14489	+	0.455302i	0.281364	+	0.959601i	$0.409213\pi$
$312$		0			0
$313$	17.1322	+	5.35230i	0.968370	+	0.302530i	0.741169	−	0.671318i	$-0.234272\pi$
$313$	17.1322	+	5.35230i	0.968370	+	0.302530i	0.227201	+	0.973848i	$0.427043\pi$
$314$		0			0
$315$	−6.10426	+	9.18262i	−0.343936	+	0.517382i
$316$		0			0
$317$	−4.81593	−	0.365269i	−0.270489	−	0.0205155i	−0.0603149	−	0.998179i	$-0.519210\pi$
$317$	−4.81593	−	0.365269i	−0.270489	−	0.0205155i	−0.210175	+	0.977664i	$0.567403\pi$
$318$		0			0
$319$	1.08193	−	3.70830i	0.0605764	−	0.207625i
$320$		0			0
$321$	15.4400	−	30.1616i	0.861780	−	1.68345i
$322$		0			0
$323$	0.0118376	−	0.0151777i	0.000658660	−	0.000844510i
$324$		0			0
$325$	1.57742	−	0.428006i	0.0874995	−	0.0237415i
$326$		0			0
$327$	12.7592	−	27.4375i	0.705587	−	1.51730i
$328$		0			0
$329$	−4.85458	−	2.14674i	−0.267641	−	0.118353i
$330$		0			0
$331$	4.42474	+	33.2045i	0.243206	+	1.82508i	0.508668	+	0.860963i	$0.330138\pi$
$331$	4.42474	+	33.2045i	0.243206	+	1.82508i	−0.265462	+	0.964121i	$0.585525\pi$
$332$		0			0
$333$	35.5360			1.94736
$334$		0			0
$335$	4.95095			0.270499
$336$		0			0
$337$	0.678789	+	5.09382i	0.0369760	+	0.277478i	0.999968	+	0.00794965i	$0.00253048\pi$
$337$	0.678789	+	5.09382i	0.0369760	+	0.277478i	−0.962992	+	0.269528i	$0.913132\pi$
$338$		0			0
$339$	−29.1029	−	12.8696i	−1.58065	−	0.698978i
$340$		0			0
$341$	−4.45670	+	9.58372i	−0.241344	+	0.518987i
$342$		0			0
$343$	10.9338	−	2.96671i	0.590371	−	0.160187i
$344$		0			0
$345$	24.6494	−	31.6046i	1.32708	−	1.70153i
$346$		0			0
$347$	−6.56407	+	12.8227i	−0.352378	+	0.688357i	−0.997103	−	0.0760574i	$-0.975767\pi$
$347$	−6.56407	+	12.8227i	−0.352378	+	0.688357i	0.644726	+	0.764414i	$0.276972\pi$
$348$		0			0
$349$	−8.56481	+	29.3558i	−0.458464	+	1.57138i	0.322353	+	0.946619i	$0.395526\pi$
$349$	−8.56481	+	29.3558i	−0.458464	+	1.57138i	−0.780817	+	0.624760i	$0.785197\pi$
$350$		0			0
$351$	1.81792	+	0.137882i	0.0970335	+	0.00735960i
$352$		0			0
$353$	7.79623	−	11.7278i	0.414951	−	0.624210i	−0.564610	−	0.825358i	$-0.690973\pi$
$353$	7.79623	−	11.7278i	0.414951	−	0.624210i	0.979561	+	0.201148i	$0.0644672\pi$
$354$		0			0
$355$	−29.3818	−	9.17921i	−1.55943	−	0.487182i
$356$		0			0
$357$	−0.00816729	−	0.00324797i	−0.000432259	−	0.000171901i
$358$		0			0
$359$	−8.85868	−	9.73926i	−0.467543	−	0.514018i	0.459906	−	0.887967i	$-0.347883\pi$
$359$	−8.85868	−	9.73926i	−0.467543	−	0.514018i	−0.927449	+	0.373949i	$0.878003\pi$
$360$		0			0
$361$	−2.69792	−	6.42718i	−0.141996	−	0.338272i
$362$		0			0
$363$	14.3930	−	5.72380i	0.755435	−	0.300422i
$364$		0			0
$365$	−45.6224	+	10.5429i	−2.38799	+	0.551839i
$366$		0			0
$367$	−6.58858	−	3.85954i	−0.343921	−	0.201466i	0.323353	−	0.946278i	$-0.395190\pi$
$367$	−6.58858	−	3.85954i	−0.343921	−	0.201466i	−0.667274	+	0.744812i	$0.732539\pi$
$368$		0			0
$369$	17.7348	−	15.5283i	0.923236	−	0.808369i
$370$		0			0
$371$	−1.14350	−	0.310269i	−0.0593676	−	0.0161084i
$372$		0			0
$373$	29.3753	+	10.4128i	1.52100	+	0.539153i	0.957866	−	0.287215i	$-0.0927294\pi$
$373$	29.3753	+	10.4128i	1.52100	+	0.539153i	0.563130	+	0.826368i	$0.309597\pi$
$374$		0			0
$375$	−10.7300	+	5.23896i	−0.554095	+	0.270539i
$376$		0			0
$377$	0.0739679	−	0.779350i	0.00380954	−	0.0401386i
$378$		0			0
$379$	−1.74850	−	0.266767i	−0.0898142	−	0.0137029i	0.105761	−	0.994392i	$-0.466272\pi$
$379$	−1.74850	−	0.266767i	−0.0898142	−	0.0137029i	−0.195576	+	0.980689i	$0.562658\pi$
$380$		0			0
$381$	0.450873	+	23.8210i	0.0230989	+	1.22039i
$382$		0			0
$383$	−20.3609	−	24.1618i	−1.04039	−	1.23461i	−0.971513	−	0.236986i	$-0.923840\pi$
$383$	−20.3609	−	24.1618i	−1.04039	−	1.23461i	−0.0688808	−	0.997625i	$-0.521943\pi$
$384$		0			0
$385$	−0.325633	−	5.72925i	−0.0165958	−	0.291990i
$386$		0			0
$387$	−3.55371	−	20.6619i	−0.180645	−	1.05030i
$388$		0			0
$389$	6.81756	−	3.65444i	0.345664	−	0.185287i	−0.290435	−	0.956895i	$-0.593800\pi$
$389$	6.81756	−	3.65444i	0.345664	−	0.185287i	0.636099	+	0.771607i	$0.280547\pi$
$390$		0			0
$391$	0.0171193	+	0.00835855i	0.000865759	+	0.000422710i
$392$		0			0
$393$	0.941114	−	0.0713797i	0.0474729	−	0.00360063i
$394$		0			0
$395$	20.2140	−	20.6002i	1.01708	−	1.03651i
$396$		0			0
$397$	−3.96560	+	23.0567i	−0.199028	+	1.15718i	0.698296	+	0.715809i	$0.253942\pi$
$397$	−3.96560	+	23.0567i	−0.199028	+	1.15718i	−0.897324	+	0.441372i	$0.854492\pi$
$398$		0			0
$399$	−9.21153	+	7.46898i	−0.461153	+	0.373917i
$400$		0			0
$401$	−30.8579	+	13.6456i	−1.54097	+	0.681431i	−0.988378	−	0.152019i	$-0.951422\pi$
$401$	−30.8579	+	13.6456i	−1.54097	+	0.681431i	−0.552595	+	0.833450i	$0.686362\pi$
$402$		0			0
$403$	−0.521682	+	2.07746i	−0.0259868	+	0.103485i
$404$		0			0
$405$	−7.70069	+	0.878203i	−0.382650	+	0.0436383i
$406$		0			0
$407$	−14.7957	+	11.0958i	−0.733394	+	0.549997i
$408$		0			0
$409$	−2.51598	+	2.98565i	−0.124407	+	0.147631i	−0.823324	−	0.567572i	$-0.807883\pi$
$409$	−2.51598	+	2.98565i	−0.124407	+	0.147631i	0.698917	+	0.715203i	$0.253666\pi$
$410$		0			0
$411$	−17.1914	−	33.5828i	−0.847990	−	1.65652i
$412$		0			0
$413$	1.41670	−	3.76858i	0.0697111	−	0.185440i
$414$		0			0
$415$	−7.08864	+	4.15247i	−0.347968	+	0.203837i
$416$		0			0
$417$	14.2719	−	19.8008i	0.698898	−	0.969648i
$418$		0			0
$419$	−26.4994	−	14.2046i	−1.29458	−	0.693939i	−0.326649	−	0.945146i	$-0.605920\pi$
$419$	−26.4994	−	14.2046i	−1.29458	−	0.693939i	−0.967933	+	0.251207i	$0.919173\pi$
$420$		0			0
$421$	−11.5432	−	20.5890i	−0.562580	−	1.00345i	−0.994817	−	0.101685i	$-0.967577\pi$
$421$	−11.5432	−	20.5890i	−0.562580	−	1.00345i	0.432237	−	0.901760i	$-0.357725\pi$
$422$		0			0
$423$	7.71688	+	26.4495i	0.375207	+	1.28602i
$424$		0			0
$425$	0.00812382	+	0.0104161i	0.000394063	+	0.000505253i
$426$		0			0
$427$	−2.84418	−	7.56586i	−0.137640	−	0.366138i
$428$		0			0
$429$	−2.47694	+	1.57982i	−0.119588	+	0.0762743i
$430$		0			0
$431$	13.4428	+	3.10648i	0.647515	+	0.149634i	0.536120	−	0.844142i	$-0.319890\pi$
$431$	13.4428	+	3.10648i	0.647515	+	0.149634i	0.111396	+	0.993776i	$0.464468\pi$
$432$		0			0
$433$	6.22588	−	14.8317i	0.299197	−	0.712768i	−0.700803	−	0.713355i	$-0.747175\pi$
$433$	6.22588	−	14.8317i	0.299197	−	0.712768i	1.00000		0.000586982i	$0.000186842\pi$
$434$		0			0
$435$	−1.25769	−	13.2515i	−0.0603017	−	0.635359i
$436$		0			0
$437$	21.1329	−	14.6325i	1.01093	−	0.699967i
$438$		0			0
$439$	−13.3010	−	11.6461i	−0.634821	−	0.555838i	0.279846	−	0.960045i	$-0.409716\pi$
$439$	−13.3010	−	11.6461i	−0.634821	−	0.555838i	−0.914668	+	0.404206i	$0.867548\pi$
$440$		0			0
$441$	−22.8464	−	15.8189i	−1.08792	−	0.753280i
$442$		0			0
$443$	7.50010	+	4.78363i	0.356340	+	0.227277i	0.703769	−	0.710429i	$-0.251499\pi$
$443$	7.50010	+	4.78363i	0.356340	+	0.227277i	−0.347428	+	0.937707i	$0.612945\pi$
$444$		0			0
$445$	−5.96876	+	44.7913i	−0.282946	+	2.12331i
$446$		0			0
$447$	6.91281	−	11.3047i	0.326965	−	0.534693i
$448$		0			0
$449$	8.34740	+	8.50689i	0.393938	+	0.401465i	0.881928	−	0.471385i	$-0.156246\pi$
$449$	8.34740	+	8.50689i	0.393938	+	0.401465i	−0.487990	+	0.872849i	$0.662270\pi$
$450$		0			0
$451$	−2.53546	+	12.0028i	−0.119390	+	0.565191i
$452$		0			0
$453$	21.4152	−	38.1972i	1.00617	−	1.79466i
$454$		0			0
$455$	−0.283242	−	1.12794i	−0.0132786	−	0.0528784i
$456$		0			0
$457$	−5.92303	−	8.91000i	−0.277068	−	0.416792i	0.667752	−	0.744384i	$-0.267257\pi$
$457$	−5.92303	−	8.91000i	−0.277068	−	0.416792i	−0.944819	+	0.327592i	$0.893763\pi$
$458$		0			0
$459$	0.00465915	+	0.0139784i	0.000217470	+	0.000652457i
$460$		0			0
$461$	16.8222	+	1.91844i	0.783489	+	0.0893507i	0.495873	−	0.868395i	$-0.334848\pi$
$461$	16.8222	+	1.91844i	0.783489	+	0.0893507i	0.287616	+	0.957746i	$0.407137\pi$
$462$		0			0
$463$	−30.1352	+	1.14118i	−1.40050	+	0.0530351i	−0.727248	−	0.686375i	$-0.759201\pi$
$463$	−30.1352	+	1.14118i	−1.40050	+	0.0530351i	−0.673256	+	0.739410i	$0.735105\pi$
$464$		0			0
$465$	−2.06667	+	36.3615i	−0.0958396	+	1.68622i
$466$		0			0
$467$	−18.4871	−	30.2323i	−0.855479	−	1.39898i	−0.916154	−	0.400827i	$-0.868723\pi$
$467$	−18.4871	−	30.2323i	−0.855479	−	1.39898i	0.0606748	−	0.998158i	$-0.480675\pi$
$468$		0			0
$469$	0.0274378	−	1.44962i	0.00126696	−	0.0669374i
$470$		0			0
$471$	24.3100	−	8.61725i	1.12014	−	0.397062i
$472$		0			0
$473$	7.93109	+	7.49311i	0.364672	+	0.344533i
$474$		0			0
$475$	17.6190	−	2.68812i	0.808414	−	0.123339i
$476$		0			0
$477$	2.59330	+	5.57665i	0.118739	+	0.255337i
$478$		0			0
$479$	13.0908	+	0.495729i	0.598133	+	0.0226504i	0.335173	−	0.942156i	$-0.391205\pi$
$479$	13.0908	+	0.495729i	0.598133	+	0.0226504i	0.262959	+	0.964807i	$0.415302\pi$
$480$		0			0
$481$	−2.52190	+	2.77259i	−0.114989	+	0.126419i
$482$		0			0
$483$	−9.11712	−	7.39243i	−0.414843	−	0.336367i
$484$		0			0
$485$	21.4447	+	16.0821i	0.973756	+	0.730252i
$486$		0			0
$487$	−37.7632	+	7.23334i	−1.71121	+	0.327774i	−0.947975	−	0.318344i	$-0.896873\pi$
$487$	−37.7632	+	7.23334i	−1.71121	+	0.327774i	−0.763237	+	0.646118i	$0.776391\pi$
$488$		0			0
$489$	28.6288	+	5.48370i	1.29464	+	0.247982i
$490$		0			0
$491$	4.66933	+	22.1046i	0.210724	+	0.997566i	0.947086	+	0.320979i	$0.104012\pi$
$491$	4.66933	+	22.1046i	0.210724	+	0.997566i	−0.736362	+	0.676587i	$0.763458\pi$
$492$		0			0
$493$	0.00603908	−	0.00188668i	0.000271986	−	8.49716e-5i
$494$		0			0
$495$	−21.6516	+	20.4560i	−0.973169	+	0.919427i
$496$		0			0
$497$	−2.85048	+	8.55204i	−0.127861	+	0.383611i
$498$		0			0
$499$	−10.6315	−	14.7501i	−0.475931	−	0.660304i	0.503050	−	0.864257i	$-0.332211\pi$
$499$	−10.6315	−	14.7501i	−0.475931	−	0.660304i	−0.978981	+	0.203954i	$0.934621\pi$
$500$		0			0
$501$	−19.4474	+	29.3732i	−0.868845	+	1.31230i
$502$		0			0
$503$	−25.1806	−	34.9355i	−1.12275	−	1.55770i	−0.788311	−	0.615277i	$-0.789044\pi$
$503$	−25.1806	−	34.9355i	−1.12275	−	1.55770i	−0.334438	−	0.942418i	$-0.608546\pi$
$504$		0			0
$505$	−6.83153	+	20.4960i	−0.303999	+	0.912062i
$506$		0			0
$507$	25.3268	−	23.9282i	1.12480	−	1.06269i
$508$		0			0
$509$	20.8270	−	6.50660i	0.923142	−	0.288400i	0.200557	−	0.979682i	$-0.435725\pi$
$509$	20.8270	−	6.50660i	0.923142	−	0.288400i	0.722585	+	0.691282i	$0.242954\pi$
$510$		0			0
$511$	2.83409	+	13.4165i	0.125373	+	0.593513i
$512$		0			0
$513$	19.5254	+	3.74000i	0.862069	+	0.165125i
$514$		0			0
$515$	−14.8882	+	2.85175i	−0.656051	+	0.125663i
$516$		0			0
$517$	−11.4716	−	8.60294i	−0.504520	−	0.378357i
$518$		0			0
$519$	−5.90129	−	4.78494i	−0.259038	−	0.210035i
$520$		0			0
$521$	−23.9180	+	26.2955i	−1.04787	+	1.15203i	−0.0597675	+	0.998212i	$0.519036\pi$
$521$	−23.9180	+	26.2955i	−1.04787	+	1.15203i	−0.988099	+	0.153816i	$0.950844\pi$
$522$		0			0
$523$	−30.2973	−	1.14732i	−1.32481	−	0.0501686i	−0.634071	−	0.773275i	$-0.718617\pi$
$523$	−30.2973	−	1.14732i	−1.32481	−	0.0501686i	−0.690737	+	0.723106i	$0.742714\pi$
$524$		0			0
$525$	−3.43176	−	7.37967i	−0.149774	−	0.322075i
$526$		0			0
$527$	−0.0171130	+	0.00261093i	−0.000745455	+	0.000113734i
$528$		0			0
$529$	1.77423	+	1.67625i	0.0771405	+	0.0728806i
$530$		0			0
$531$	−19.6971	+	6.98209i	−0.854779	+	0.302997i
$532$		0			0
$533$	−0.0470483	+	2.48571i	−0.00203789	+	0.107668i
$534$		0			0
$535$	18.9026	+	30.9119i	0.817232	+	1.33644i
$536$		0			0
$537$	−0.102973	+	1.81174i	−0.00444363	+	0.0781821i
$538$		0			0
$539$	14.4516	−	0.547260i	0.622473	−	0.0235722i
$540$		0			0
$541$	−30.3669	−	3.46310i	−1.30557	−	0.148890i	−0.567367	−	0.823465i	$-0.692038\pi$
$541$	−30.3669	−	3.46310i	−1.30557	−	0.148890i	−0.738206	+	0.674575i	$0.764327\pi$
$542$		0			0
$543$	3.46626	+	10.3995i	0.148751	+	0.446285i
$544$		0			0
$545$	17.9131	+	26.9466i	0.767312	+	1.15427i
$546$		0			0
$547$	8.41781	+	33.5217i	0.359920	+	1.43328i	0.833494	+	0.552529i	$0.186337\pi$
$547$	8.41781	+	33.5217i	0.359920	+	1.43328i	−0.473574	+	0.880754i	$0.657036\pi$
$548$		0			0
$549$	−20.5174	+	36.5959i	−0.875663	+	1.56187i
$550$		0			0
$551$	1.76432	−	8.35227i	0.0751625	−	0.355819i
$552$		0			0
$553$	−5.91966	−	6.03276i	−0.251729	−	0.256539i
$554$		0			0
$555$	−33.2461	+	54.3681i	−1.41122	+	2.30780i
$556$		0			0
$557$	−3.91899	+	29.4092i	−0.166053	+	1.24611i	0.687919	+	0.725787i	$0.258524\pi$
$557$	−3.91899	+	29.4092i	−0.166053	+	1.24611i	−0.853972	+	0.520319i	$0.825813\pi$
$558$		0			0
$559$	1.86428	+	1.18906i	0.0788506	+	0.0502917i
$560$		0			0
$561$	−0.0195209	−	0.0135163i	−0.000824172	−	0.000570658i
$562$		0			0
$563$	−2.53019	−	2.21539i	−0.106635	−	0.0933674i	0.603779	−	0.797152i	$-0.293661\pi$
$563$	−2.53019	−	2.21539i	−0.106635	−	0.0933674i	−0.710414	+	0.703784i	$0.751492\pi$
$564$		0			0
$565$	27.9763	−	19.3708i	1.17697	−	0.814937i
$566$		0			0
$567$	0.214459	+	2.25961i	0.00900642	+	0.0948945i
$568$		0			0
$569$	−0.599848	+	1.42900i	−0.0251469	+	0.0599068i	−0.934145	−	0.356893i	$-0.883836\pi$
$569$	−0.599848	+	1.42900i	−0.0251469	+	0.0599068i	0.908998	+	0.416799i	$0.136848\pi$
$570$		0			0
$571$	14.4824	+	3.34674i	0.606071	+	0.140057i	0.517024	−	0.855971i	$-0.327040\pi$
$571$	14.4824	+	3.34674i	0.606071	+	0.140057i	0.0890466	+	0.996027i	$0.471618\pi$
$572$		0			0
$573$	−2.59473	+	1.65495i	−0.108397	+	0.0691364i
$574$		0			0
$575$	6.20725	+	16.5120i	0.258860	+	0.688598i
$576$		0			0
$577$	16.5578	+	21.2298i	0.689310	+	0.883808i	0.997723	−	0.0674446i	$-0.0214846\pi$
$577$	16.5578	+	21.2298i	0.689310	+	0.883808i	−0.308413	+	0.951253i	$0.599798\pi$
$578$		0			0
$579$	−1.28898	−	4.41796i	−0.0535681	−	0.183604i
$580$		0			0
$581$	1.17655	+	2.09855i	0.0488114	+	0.0870623i
$582$		0			0
$583$	−2.82100	−	1.51215i	−0.116834	−	0.0626267i
$584$		0			0
$585$	−3.52966	+	4.89703i	−0.145933	+	0.202467i
$586$		0			0
$587$	24.0997	−	14.1174i	0.994700	−	0.582688i	0.0843104	−	0.996440i	$-0.473131\pi$
$587$	24.0997	−	14.1174i	0.994700	−	0.582688i	0.910390	+	0.413752i	$0.135782\pi$
$588$		0			0
$589$	−8.21884	+	21.8631i	−0.338651	+	0.900852i
$590$		0			0
$591$	−2.63437	−	5.14615i	−0.108364	−	0.211684i
$592$		0			0
$593$	−3.21278	+	3.81253i	−0.131933	+	0.156562i	−0.826640	−	0.562731i	$-0.809751\pi$
$593$	−3.21278	+	3.81253i	−0.131933	+	0.156562i	0.694707	+	0.719293i	$0.255534\pi$
$594$		0			0
$595$	0.00751934	−	0.00563901i	0.000308263	−	0.000231177i
$596$		0			0
$597$	37.0199	−	4.22183i	1.51512	−	0.172788i
$598$		0			0
$599$	−0.0298905	+	0.119031i	−0.00122129	+	0.00486347i	−0.970495	−	0.241121i	$-0.922485\pi$
$599$	−0.0298905	+	0.119031i	−0.00122129	+	0.00486347i	0.969274	+	0.245985i	$0.0791113\pi$
$600$		0			0
$601$	23.9324	−	10.5831i	0.976224	−	0.431695i	0.146098	−	0.989270i	$-0.453329\pi$
$601$	23.9324	−	10.5831i	0.976224	−	0.431695i	0.830126	+	0.557576i	$0.188268\pi$
$602$		0			0
$603$	−5.84569	+	4.73986i	−0.238055	+	0.193022i
$604$		0			0
$605$	−2.80757	+	16.3237i	−0.114144	+	0.663652i
$606$		0			0
$607$	23.5263	−	23.9758i	0.954901	−	0.973146i	−0.0447646	−	0.998998i	$-0.514254\pi$
$607$	23.5263	−	23.9758i	0.954901	−	0.973146i	0.999666	+	0.0258514i	$0.00822967\pi$
$608$		0			0
$609$	−3.88696	+	0.294810i	−0.157507	+	0.0119463i
$610$		0			0
$611$	−2.61130	−	1.27497i	−0.105642	−	0.0515799i
$612$		0			0
$613$	40.6368	−	21.7827i	1.64130	−	0.879793i	0.648344	−	0.761347i	$-0.275462\pi$
$613$	40.6368	−	21.7827i	1.64130	−	0.879793i	0.992960	−	0.118446i	$-0.0377913\pi$
$614$		0			0
$615$	7.16542	+	41.6609i	0.288937	+	1.67993i
$616$		0			0
$617$	−2.52189	−	44.3708i	−0.101528	−	1.78630i	−0.496929	−	0.867791i	$-0.665539\pi$
$617$	−2.52189	−	44.3708i	−0.101528	−	1.78630i	0.395401	−	0.918508i	$-0.370606\pi$
$618$		0			0
$619$	−29.3939	−	34.8811i	−1.18144	−	1.40199i	−0.896268	−	0.443513i	$-0.853732\pi$
$619$	−29.3939	−	34.8811i	−1.18144	−	1.40199i	−0.285173	−	0.958476i	$-0.592051\pi$
$620$		0			0
$621$	0.372363	+	19.6731i	0.0149424	+	0.789455i
$622$		0			0
$623$	13.0817	+	1.99586i	0.524106	+	0.0799626i
$624$		0			0
$625$	2.85868	−	30.1200i	0.114347	−	1.20480i
$626$		0			0
$627$	−28.7877	+	14.0557i	−1.14967	+	0.561331i
$628$		0			0
$629$	−0.0285500	−	0.0101202i	−0.00113836	−	0.000403520i
$630$		0			0
$631$	−22.9586	−	6.22943i	−0.913969	−	0.247990i	−0.226337	−	0.974049i	$-0.572675\pi$
$631$	−22.9586	−	6.22943i	−0.913969	−	0.247990i	−0.687632	+	0.726060i	$0.741350\pi$
$632$		0			0
$633$	11.9524	−	10.4653i	0.475064	−	0.415957i
$634$		0			0
$635$	−21.9832	−	12.8776i	−0.872377	−	0.511032i
$636$		0			0
$637$	2.85557	−	0.659894i	0.113142	−	0.0261459i
$638$		0			0
$639$	43.4796	−	17.2910i	1.72003	−	0.684021i
$640$		0			0
$641$	−3.22495	−	7.68270i	−0.127378	−	0.303448i	0.845801	−	0.533498i	$-0.179123\pi$
$641$	−3.22495	−	7.68270i	−0.127378	−	0.303448i	−0.973179	+	0.230050i	$0.926111\pi$
$642$		0			0
$643$	−6.94902	−	7.63978i	−0.274043	−	0.301284i	0.587237	−	0.809415i	$-0.300216\pi$
$643$	−6.94902	−	7.63978i	−0.274043	−	0.301284i	−0.861279	+	0.508132i	$0.830336\pi$
$644$		0			0
$645$	34.9362	+	13.8935i	1.37561	+	0.547054i
$646$		0			0
$647$	41.6009	+	12.9966i	1.63550	+	0.510948i	0.971551	−	0.236831i	$-0.0761088\pi$
$647$	41.6009	+	12.9966i	1.63550	+	0.510948i	0.663947	+	0.747779i	$0.268880\pi$
$648$		0			0
$649$	6.02093	−	9.05727i	0.236342	−	0.355529i
$650$		0			0
$651$	10.6351	+	0.806628i	0.416821	+	0.0316142i
$652$		0			0
$653$	−5.44088	+	18.6486i	−0.212918	+	0.729775i	0.781466	+	0.623948i	$0.214472\pi$
$653$	−5.44088	+	18.6486i	−0.212918	+	0.729775i	−0.994384	+	0.105828i	$0.966251\pi$
$654$		0			0
$655$	−0.459896	+	0.898389i	−0.0179696	+	0.0351030i
$656$		0			0
$657$	43.7740	−	56.1255i	1.70779	−	2.18966i
$658$		0			0
$659$	42.0411	−	11.4071i	1.63769	−	0.444358i	0.680246	−	0.732984i	$-0.261873\pi$
$659$	42.0411	−	11.4071i	1.63769	−	0.444358i	0.957442	+	0.288625i	$0.0931981\pi$
$660$		0			0
$661$	16.9460	−	36.4408i	0.659122	−	1.41738i	−0.236086	−	0.971732i	$-0.575865\pi$
$661$	16.9460	−	36.4408i	0.659122	−	1.41738i	0.895208	−	0.445649i	$-0.147027\pi$
$662$		0			0
$663$	−0.00440075	−	0.00194605i	−0.000170911	−	7.55783e-5i
$664$		0			0
$665$	−1.67508	−	12.5703i	−0.0649569	−	0.487454i
$666$		0			0
$667$	8.44909			0.327150
$668$		0			0
$669$	−48.5235			−1.87603
$670$		0			0
$671$	−2.88413	−	21.6434i	−0.111341	−	0.835532i
$672$		0			0
$673$	5.70712	+	2.52374i	0.219993	+	0.0972829i	0.511491	−	0.859289i	$-0.329093\pi$
$673$	5.70712	+	2.52374i	0.219993	+	0.0972829i	−0.291498	+	0.956572i	$0.594154\pi$
$674$		0			0
$675$	−5.75294	+	12.3712i	−0.221431	+	0.476167i
$676$		0			0
$677$	−40.8690	+	11.0891i	−1.57072	+	0.426188i	−0.937558	−	0.347830i	$-0.886919\pi$
$677$	−40.8690	+	11.0891i	−1.57072	+	0.426188i	−0.633164	+	0.774018i	$0.718244\pi$
$678$		0			0
$679$	4.82765	−	6.18983i	0.185268	−	0.237544i
$680$		0			0
$681$	−33.1260	+	64.7103i	−1.26939	+	2.47970i
$682$		0			0
$683$	−9.64220	+	33.0485i	−0.368948	+	1.26457i	0.537864	+	0.843032i	$0.319232\pi$
$683$	−9.64220	+	33.0485i	−0.368948	+	1.26457i	−0.906812	+	0.421535i	$0.861491\pi$
$684$		0			0
$685$	40.2278	+	3.05111i	1.53702	+	0.116577i
$686$		0			0
$687$	−14.7709	+	22.2199i	−0.563546	+	0.847741i
$688$		0			0
$689$	−0.619142	−	0.193427i	−0.0235874	−	0.00736898i
$690$		0			0
$691$	16.2203	+	6.45050i	0.617050	+	0.245389i	0.657093	−	0.753809i	$-0.271786\pi$
$691$	16.2203	+	6.45050i	0.617050	+	0.245389i	−0.0400435	+	0.999198i	$0.512750\pi$
$692$		0			0
$693$	5.86945	+	6.45290i	0.222962	+	0.245125i
$694$		0			0
$695$	10.1022	+	24.0663i	0.383200	+	0.912886i
$696$		0			0
$697$	−0.0186706	+	0.00742494i	−0.000707200	+	0.000281240i
$698$		0			0
$699$	−49.1078	+	11.3483i	−1.85743	+	0.429232i
$700$		0			0
$701$	7.90465	+	4.63048i	0.298555	+	0.174891i	0.647109	−	0.762398i	$-0.275978\pi$
$701$	7.90465	+	4.63048i	0.298555	+	0.174891i	−0.348554	+	0.937289i	$0.613327\pi$
$702$		0			0
$703$	−30.7486	+	26.9229i	−1.15970	+	1.01542i
$704$		0			0
$705$	−47.6860	−	12.9388i	−1.79596	−	0.487302i
$706$		0			0
$707$	5.96332	+	2.11384i	0.224274	+	0.0794991i
$708$		0			0
$709$	6.78755	−	3.31404i	0.254912	−	0.124462i	−0.306857	−	0.951755i	$-0.599277\pi$
$709$	6.78755	−	3.31404i	0.254912	−	0.124462i	0.561769	+	0.827294i	$0.310121\pi$
$710$		0			0
$711$	−4.14521	+	43.6752i	−0.155457	+	1.63795i
$712$		0			0
$713$	−22.8530	−	3.48668i	−0.855853	−	0.130577i
$714$		0			0
$715$	−0.0594517	−	3.14102i	−0.00222337	−	0.117467i
$716$		0			0
$717$	−10.1010	−	11.9866i	−0.377227	−	0.447647i
$718$		0			0
$719$	0.645672	+	11.3601i	0.0240795	+	0.423660i	0.987697	+	0.156377i	$0.0499814\pi$
$719$	0.645672	+	11.3601i	0.0240795	+	0.423660i	−0.963618	+	0.267283i	$0.913874\pi$
$720$		0			0
$721$	0.752476	+	4.37502i	0.0280237	+	0.162934i
$722$		0			0
$723$	59.0345	−	31.6444i	2.19552	−	1.17687i
$724$		0			0
$725$	5.26444	+	2.57038i	0.195516	+	0.0954616i
$726$		0			0
$727$	−20.5371	+	1.55766i	−0.761678	+	0.0577702i	−0.450735	−	0.892658i	$-0.648838\pi$
$727$	−20.5371	+	1.55766i	−0.761678	+	0.0577702i	−0.310944	+	0.950428i	$0.600645\pi$
$728$		0			0
$729$	30.5960	−	31.1806i	1.13318	−	1.15484i
$730$		0			0
$731$	−0.00302916	+	0.0176120i	−0.000112038	+	0.000651405i
$732$		0			0
$733$	−28.7655	+	23.3239i	−1.06248	+	0.861487i	−0.990718	−	0.135935i	$-0.956596\pi$
$733$	−28.7655	+	23.3239i	−1.06248	+	0.861487i	−0.0717592	+	0.997422i	$0.522861\pi$
$734$		0			0
$735$	45.5762	−	20.1542i	1.68110	−	0.743399i
$736$		0			0
$737$	0.953922	−	3.79874i	0.0351382	−	0.139928i
$738$		0			0
$739$	−2.44802	+	0.279178i	−0.0900520	+	0.0102697i	−0.158217	−	0.987404i	$-0.550575\pi$
$739$	−2.44802	+	0.279178i	−0.0900520	+	0.0102697i	0.0681653	+	0.997674i	$0.478285\pi$
$740$		0			0
$741$	−5.19404	+	3.89518i	−0.190808	+	0.143093i
$742$		0			0
$743$	25.1879	−	29.8899i	0.924053	−	1.09655i	−0.0710261	−	0.997474i	$-0.522627\pi$
$743$	25.1879	−	29.8899i	0.924053	−	1.09655i	0.995080	−	0.0990785i	$-0.0315895\pi$
$744$		0			0
$745$	6.45673	+	12.6130i	0.236556	+	0.462104i
$746$		0			0
$747$	4.39429	−	11.6893i	0.160779	−	0.427690i
$748$		0			0
$749$	9.15567	−	5.36332i	0.334541	−	0.195972i
$750$		0			0
$751$	−24.2979	+	33.7108i	−0.886643	+	1.23012i	0.0856418	+	0.996326i	$0.472706\pi$
$751$	−24.2979	+	33.7108i	−0.886643	+	1.23012i	−0.972285	+	0.233798i	$0.924884\pi$
$752$		0			0
$753$	10.4087	+	5.57939i	0.379313	+	0.203324i
$754$		0			0
$755$	22.9001	+	40.8458i	0.833421	+	1.48653i
$756$		0			0
$757$	−5.71345	−	19.5828i	−0.207659	−	0.711749i	−0.995405	−	0.0957493i	$-0.969475\pi$
$757$	−5.71345	−	19.5828i	−0.207659	−	0.711749i	0.787747	−	0.615999i	$-0.211248\pi$
$758$		0			0
$759$	−19.5001	−	25.0023i	−0.707808	−	0.907525i
$760$		0			0
$761$	6.56857	+	17.4732i	0.238110	+	0.633401i	0.999896	−	0.0144278i	$-0.00459267\pi$
$761$	6.56857	+	17.4732i	0.238110	+	0.633401i	−0.761786	+	0.647829i	$0.775677\pi$
$762$		0			0
$763$	7.98915	−	5.09556i	0.289227	−	0.184472i
$764$		0			0
$765$	−0.0475337	−	0.0109845i	−0.00171858	−	0.000397147i
$766$		0			0
$767$	0.853097	−	2.03231i	0.0308035	−	0.0733824i
$768$		0			0
$769$	0.177905	+	1.87447i	0.00641543	+	0.0675951i	0.998160	−	0.0606331i	$-0.0193120\pi$
$769$	0.177905	+	1.87447i	0.00641543	+	0.0675951i	−0.991745	+	0.128228i	$0.959071\pi$
$770$		0			0
$771$	−40.3434	+	27.9338i	−1.45293	+	1.00601i
$772$		0			0
$773$	0.0574883	+	0.0503358i	0.00206771	+	0.00181045i	0.659786	−	0.751454i	$-0.270647\pi$
$773$	0.0574883	+	0.0503358i	0.00206771	+	0.00181045i	−0.657718	+	0.753264i	$0.728478\pi$
$774$		0			0
$775$	−13.1785	−	9.12482i	−0.473386	−	0.327773i
$776$		0			0
$777$	15.7346	+	10.0357i	0.564474	+	0.360027i
$778$		0			0
$779$	−3.58097	+	26.8726i	−0.128302	+	0.962811i
$780$		0			0
$781$	−12.7041	+	20.7753i	−0.454589	+	0.743400i
$782$		0			0
$783$	4.57684	+	4.66429i	0.163563	+	0.166688i
$784$		0			0
$785$	−5.70027	+	26.9850i	−0.203451	+	0.963137i
$786$		0			0
$787$	26.1774	−	46.6913i	0.933124	−	1.66437i	0.205185	−	0.978723i	$-0.434220\pi$
$787$	26.1774	−	46.6913i	0.933124	−	1.66437i	0.727939	−	0.685642i	$-0.240478\pi$
$788$		0			0
$789$	6.59874	+	26.2777i	0.234921	+	0.935511i
$790$		0			0
$791$	−5.51668	−	8.29873i	−0.196151	−	0.295069i
$792$		0			0
$793$	−1.39921	−	4.19794i	−0.0496875	−	0.149073i
$794$		0			0
$795$	−10.9582	−	1.24969i	−0.388646	−	0.0443220i
$796$		0			0
$797$	42.0434	−	1.59213i	1.48926	−	0.0563960i	0.719392	−	0.694605i	$-0.244421\pi$
$797$	42.0434	−	1.59213i	1.48926	−	0.0563960i	0.769863	+	0.638209i	$0.220324\pi$
$798$		0			0
$799$	0.00133269	−	0.0234476i	4.71470e−5	−	0.000829515i
$800$		0			0
$801$	−35.8341	−	58.6003i	−1.26613	−	2.07054i
$802$		0			0
$803$	−0.701005	+	37.0363i	−0.0247379	+	1.30698i
$804$		0			0
$805$	11.8302	−	4.19348i	0.416959	−	0.147801i
$806$		0			0
$807$	22.4096	+	21.1721i	0.788854	+	0.745292i
$808$		0			0
$809$	35.5927	−	5.43036i	1.25137	−	0.190921i	0.508916	−	0.860816i	$-0.330047\pi$
$809$	35.5927	−	5.43036i	1.25137	−	0.190921i	0.742456	+	0.669895i	$0.233661\pi$
$810$		0			0
$811$	−1.69171	−	3.63786i	−0.0594039	−	0.127743i	0.874797	−	0.484489i	$-0.160994\pi$
$811$	−1.69171	−	3.63786i	−0.0594039	−	0.127743i	−0.934201	+	0.356746i	$0.883886\pi$
$812$		0			0
$813$	−23.8854	−	0.904508i	−0.837699	−	0.0317225i
$814$		0			0
$815$	−20.9738	+	23.0586i	−0.734679	+	0.807709i
$816$		0			0
$817$	18.7289	+	15.1859i	0.655241	+	0.531288i
$818$		0			0
$819$	1.41427	+	1.06061i	0.0494187	+	0.0370608i
$820$		0			0
$821$	−30.9024	+	5.91920i	−1.07850	+	0.206581i	−0.696483	−	0.717573i	$-0.745253\pi$
$821$	−30.9024	+	5.91920i	−1.07850	+	0.206581i	−0.382018	+	0.924155i	$0.624771\pi$
$822$		0			0
$823$	−13.7577	−	2.63521i	−0.479563	−	0.0918578i	−0.0573492	−	0.998354i	$-0.518265\pi$
$823$	−13.7577	−	2.63521i	−0.479563	−	0.0918578i	−0.422214	+	0.906496i	$0.638747\pi$
$824$		0			0
$825$	−4.54388	−	21.5107i	−0.158198	−	0.748906i
$826$		0			0
$827$	−0.745480	+	0.232896i	−0.0259229	+	0.00809860i	−0.311132	−	0.950367i	$-0.600708\pi$
$827$	−0.745480	+	0.232896i	−0.0259229	+	0.00809860i	0.285209	+	0.958465i	$0.407937\pi$
$828$		0			0
$829$	7.45087	−	7.03941i	0.258779	−	0.244489i	−0.546394	−	0.837528i	$-0.684000\pi$
$829$	7.45087	−	7.03941i	0.258779	−	0.244489i	0.805173	+	0.593039i	$0.202072\pi$
$830$		0			0
$831$	12.5287	−	37.5887i	0.434616	−	1.30394i
$832$		0			0
$833$	0.0138500	+	0.0192155i	0.000479875	+	0.000665776i
$834$		0			0
$835$	−15.9479	−	34.1280i	−0.551900	−	1.18105i
$836$		0			0
$837$	−10.4546	−	14.5046i	−0.361364	−	0.501354i
$838$		0			0
$839$	11.2853	−	33.8584i	0.389613	−	1.16892i	−0.552467	−	0.833535i	$-0.686313\pi$
$839$	11.2853	−	33.8584i	0.389613	−	1.16892i	0.942080	−	0.335388i	$-0.108867\pi$
$840$		0			0
$841$	−19.0402	+	17.9888i	−0.656559	+	0.620302i
$842$		0			0
$843$	−51.5420	+	16.1023i	−1.77520	+	0.554593i
$844$		0			0
$845$	7.70051	+	36.4541i	0.264905	+	1.25406i
$846$		0			0
$847$	4.76397	+	0.912513i	0.163692	+	0.0313543i
$848$		0			0
$849$	56.2526	−	10.7749i	1.93058	−	0.369793i
$850$		0			0
$851$	−32.3616	−	24.2690i	−1.10934	−	0.831931i
$852$		0			0
$853$	2.49772	+	2.02523i	0.0855204	+	0.0693424i	0.671616	−	0.740900i	$-0.265601\pi$
$853$	2.49772	+	2.02523i	0.0855204	+	0.0693424i	−0.586095	+	0.810242i	$0.699336\pi$
$854$		0			0
$855$	−44.2917	+	48.6944i	−1.51474	+	1.66531i
$856$		0			0
$857$	−14.4456	−	0.547034i	−0.493452	−	0.0186863i	−0.210056	−	0.977689i	$-0.567365\pi$
$857$	−14.4456	−	0.547034i	−0.493452	−	0.0186863i	−0.283396	+	0.959003i	$0.591461\pi$
$858$		0			0
$859$	−24.1987	−	52.0372i	−0.825651	−	1.77548i	−0.597520	−	0.801854i	$-0.703847\pi$
$859$	−24.1987	−	52.0372i	−0.825651	−	1.77548i	−0.228131	−	0.973630i	$-0.573261\pi$
$860$		0			0
$861$	12.2379	−	1.86713i	0.417066	−	0.0636316i
$862$		0			0
$863$	−12.1862	−	11.5133i	−0.414824	−	0.391917i	0.450788	−	0.892631i	$-0.351143\pi$
$863$	−12.1862	−	11.5133i	−0.414824	−	0.391917i	−0.865613	+	0.500714i	$0.833071\pi$
$864$		0			0
$865$	7.65738	−	2.71434i	0.260359	−	0.0922903i
$866$		0			0
$867$	−0.876981	+	46.3336i	−0.0297838	+	1.57357i
$868$		0			0
$869$	−11.9113	−	19.4788i	−0.404063	−	0.660774i
$870$		0			0
$871$	0.0450415	−	0.792470i	0.00152617	−	0.0268518i
$872$		0			0
$873$	−40.7167	+	1.54188i	−1.37805	+	0.0521849i
$874$		0			0
$875$	−3.71521	−	0.423690i	−0.125597	−	0.0143233i
$876$		0			0
$877$	−10.4674	−	31.4044i	−0.353459	−	1.06045i	−0.963415	−	0.268016i	$-0.913632\pi$
$877$	−10.4674	−	31.4044i	−0.353459	−	1.06045i	0.609956	−	0.792435i	$-0.291187\pi$
$878$		0			0
$879$	46.8241	+	70.4373i	1.57934	+	2.37579i
$880$		0			0
$881$	−1.32533	−	5.27778i	−0.0446516	−	0.177813i	0.943478	−	0.331435i	$-0.107533\pi$
$881$	−1.32533	−	5.27778i	−0.0446516	−	0.177813i	−0.988130	+	0.153622i	$0.950906\pi$
$882$		0			0
$883$	−4.48670	+	8.00270i	−0.150990	+	0.269312i	−0.937303	−	0.348515i	$-0.886686\pi$
$883$	−4.48670	+	8.00270i	−0.150990	+	0.269312i	0.786314	+	0.617828i	$0.211987\pi$
$884$		0			0
$885$	7.74560	−	36.6676i	0.260365	−	1.23257i
$886$		0			0
$887$	23.3627	+	23.8091i	0.784442	+	0.799430i	0.983567	−	0.180544i	$-0.0577859\pi$
$887$	23.3627	+	23.8091i	0.784442	+	0.799430i	−0.199125	+	0.979974i	$0.563810\pi$
$888$		0			0
$889$	−3.89235	+	6.36525i	−0.130545	+	0.213484i
$890$		0			0
$891$	−0.809905	+	6.07775i	−0.0271328	+	0.203612i
$892$		0			0
$893$	−26.7161	−	17.0398i	−0.894019	−	0.570214i
$894$		0			0
$895$	−1.59538	−	1.10465i	−0.0533278	−	0.0369243i
$896$		0			0
$897$	−4.83451	−	4.23301i	−0.161420	−	0.141336i
$898$		0			0
$899$	−6.31209	+	4.37050i	−0.210520	+	0.145764i
$900$		0			0
$901$	−0.000495323	−	0.00521889i	−1.65016e−5	−	0.000173866i
$902$		0			0
$903$	4.26158	−	10.1522i	0.141816	−	0.337845i
$904$		0			0
$905$	−11.4211	−	2.63929i	−0.379649	−	0.0877330i
$906$		0			0
$907$	−18.5510	+	11.8320i	−0.615977	+	0.392876i	−0.808568	−	0.588403i	$-0.799757\pi$
$907$	−18.5510	+	11.8320i	−0.615977	+	0.392876i	0.192591	+	0.981279i	$0.438311\pi$
$908$		0			0
$909$	−11.5560	−	30.7404i	−0.383289	−	1.01959i
$910$		0			0
$911$	−18.4596	−	23.6682i	−0.611593	−	0.784162i	0.378345	−	0.925665i	$-0.376493\pi$
$911$	−18.4596	−	23.6682i	−0.611593	−	0.784162i	−0.989938	+	0.141502i	$0.954807\pi$
$912$		0			0
$913$	1.82029	+	6.23901i	0.0602426	+	0.206481i
$914$		0			0
$915$	−36.7944	−	65.6283i	−1.21639	−	2.16960i
$916$		0			0
$917$	0.260497	+	0.139635i	0.00860237	+	0.00461115i
$918$		0			0
$919$	12.4180	−	17.2287i	0.409633	−	0.568322i	−0.555023	−	0.831835i	$-0.687291\pi$
$919$	12.4180	−	17.2287i	0.409633	−	0.568322i	0.964656	+	0.263512i	$0.0848810\pi$
$920$		0			0
$921$	−47.7396	+	27.9655i	−1.57307	+	0.921495i
$922$		0			0
$923$	−1.73657	+	4.61947i	−0.0571597	+	0.152052i
$924$		0			0
$925$	−12.7807	−	24.9665i	−0.420225	−	0.820895i
$926$		0			0
$927$	14.8486	−	17.6205i	0.487693	−	0.578734i
$928$		0			0
$929$	6.51041	−	4.88238i	0.213600	−	0.160186i	−0.487796	−	0.872958i	$-0.662199\pi$
$929$	6.51041	−	4.88238i	0.213600	−	0.160186i	0.701396	+	0.712772i	$0.252561\pi$
$930$		0			0
$931$	31.7533	−	3.62121i	1.04067	−	0.118680i
$932$		0			0
$933$	14.4261	−	57.4479i	0.472288	−	1.88076i
$934$		0			0
$935$	0.0232208	−	0.0102684i	0.000759402	−	0.000335814i
$936$		0			0
$937$	25.8896	−	20.9920i	0.845776	−	0.685780i	−0.105399	−	0.994430i	$-0.533612\pi$
$937$	25.8896	−	20.9920i	0.845776	−	0.685780i	0.951176	+	0.308650i	$0.0998771\pi$
$938$		0			0
$939$	8.29361	−	48.2204i	0.270652	−	1.57361i
$940$		0			0
$941$	−18.8691	+	19.2296i	−0.615115	+	0.626868i	−0.948823	−	0.315808i	$-0.897724\pi$
$941$	−18.8691	+	19.2296i	−0.615115	+	0.626868i	0.333708	+	0.942677i	$0.391700\pi$
$942$		0			0
$943$	−26.7554	+	2.02929i	−0.871277	+	0.0660829i
$944$		0			0
$945$	8.72335	+	4.25921i	0.283771	+	0.138552i
$946$		0			0
$947$	8.15573	−	4.37174i	0.265026	−	0.142062i	−0.334556	−	0.942376i	$-0.608586\pi$
$947$	8.15573	−	4.37174i	0.265026	−	0.142062i	0.599582	+	0.800313i	$0.295333\pi$
$948$		0			0
$949$	1.27248	+	7.39843i	0.0413066	+	0.240163i
$950$		0			0
$951$	0.747104	+	13.1447i	0.0242265	+	0.426246i
$952$		0			0
$953$	−16.0419	−	19.0365i	−0.519648	−	0.616654i	0.439953	−	0.898021i	$-0.354995\pi$
$953$	−16.0419	−	19.0365i	−0.519648	−	0.616654i	−0.959600	+	0.281367i	$0.909212\pi$
$954$		0			0
$955$	−0.0622789	−	3.29039i	−0.00201530	−	0.106475i
$956$		0			0
$957$	−10.4098	−	1.58822i	−0.336502	−	0.0513400i
$958$		0			0
$959$	1.11630	−	11.7617i	0.0360471	−	0.379804i
$960$		0			0
$961$	−8.98043	+	4.38473i	−0.289691	+	0.141443i
$962$		0			0
$963$	−51.9127	−	18.4017i	−1.67286	−	0.592985i
$964$		0			0
$965$	4.74954	+	1.28871i	0.152893	+	0.0414849i
$966$		0			0
$967$	15.2557	−	13.3577i	0.490592	−	0.429553i	−0.377461	−	0.926025i	$-0.623203\pi$
$967$	15.2557	−	13.3577i	0.490592	−	0.429553i	0.868053	+	0.496472i	$0.165371\pi$
$968$		0			0
$969$	−0.0452743	−	0.0265213i	−0.00145442	−	0.000851988i
$970$		0			0
$971$	40.8377	−	9.43718i	1.31054	−	0.302853i	0.488644	−	0.872484i	$-0.337492\pi$
$971$	40.8377	−	9.43718i	1.31054	−	0.302853i	0.821901	+	0.569630i	$0.192914\pi$
$972$		0			0
$973$	7.10252	−	2.82453i	0.227696	−	0.0905504i
$974$		0			0
$975$	−1.72451	−	4.10825i	−0.0552286	−	0.131569i
$976$		0			0
$977$	8.59944	+	9.45426i	0.275121	+	0.302468i	0.861695	−	0.507427i	$-0.169403\pi$
$977$	8.59944	+	9.45426i	0.275121	+	0.302468i	−0.586574	+	0.809895i	$0.699524\pi$
$978$		0			0
$979$	33.2172	+	13.2098i	1.06163	+	0.422188i
$980$		0			0
$981$	−46.9480	−	14.6671i	−1.49894	−	0.468284i
$982$		0			0
$983$	17.0511	−	25.6499i	0.543845	−	0.818104i	−0.453475	−	0.891269i	$-0.649816\pi$
$983$	17.0511	−	25.6499i	0.543845	−	0.818104i	0.997320	+	0.0731646i	$0.0233098\pi$
$984$		0			0
$985$	6.16441	+	0.467546i	0.196415	+	0.0148972i
$986$		0			0
$987$	−4.05270	+	13.8906i	−0.128999	+	0.442143i
$988$		0			0
$989$	−10.8746	+	21.2431i	−0.345792	+	0.675492i
$990$		0			0
$991$	−9.55085	+	12.2457i	−0.303393	+	0.388999i	−0.915861	−	0.401497i	$-0.868490\pi$
$991$	−9.55085	+	12.2457i	−0.303393	+	0.388999i	0.612468	+	0.790496i	$0.290177\pi$
$992$		0			0
$993$	88.1290	−	23.9123i	2.79669	−	0.758834i
$994$		0			0
$995$	−16.8006	+	36.1281i	−0.532615	+	1.14534i
$996$		0			0
$997$	6.23699	+	2.75805i	0.197527	+	0.0873483i	0.500829	−	0.865546i	$-0.333029\pi$
$997$	6.23699	+	2.75805i	0.197527	+	0.0873483i	−0.303301	+	0.952895i	$0.598089\pi$
$998$		0			0
$999$	−4.13251	−	31.0115i	−0.130747	−	0.981161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.2	✓	1148
167.130	even	83	inner	668.2.e.a.297.2	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.2	✓	1148	1.1	even	1	trivial
668.2.e.a.297.2	yes	1148	167.130	even	83	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.360076 - 2.70211i) q^{3} +(2.66599 + 1.17892i) q^{5} +(0.359959 - 0.774059i) q^{7} +(-4.27644 + 1.16034i) q^{9} +O(q^{10})\)	\(q+(-0.360076 - 2.70211i) q^{3} +(2.66599 + 1.17892i) q^{5} +(0.359959 - 0.774059i) q^{7} +(-4.27644 + 1.16034i) q^{9} +(1.41822 - 1.81840i) q^{11} +(0.212957 - 0.416003i) q^{13} +(2.22562 - 7.62829i) q^{15} +(0.00376620 + 0.000285651i) q^{17} +(2.82122 - 4.24396i) q^{19} +(-2.22121 - 0.693930i) q^{21} +(4.68688 + 1.86388i) q^{23} +(2.35326 + 2.58718i) q^{25} +(1.50992 + 3.59703i) q^{27} +(1.55654 - 0.619007i) q^{29} +(-4.46558 + 1.03195i) q^{31} +(-5.42418 - 3.17744i) q^{33} +(1.87220 - 1.63927i) q^{35} +(-7.73988 - 2.10008i) q^{37} +(-1.20077 - 0.425641i) q^{39} +(-4.78039 + 2.33404i) q^{41} +(-0.447049 + 4.71025i) q^{43} +(-12.7689 - 1.94814i) q^{45} +(-0.117670 - 6.21686i) q^{47} +(4.04118 + 4.79558i) q^{49} +(-0.000584257 - 0.0102795i) q^{51} +(-0.235266 - 1.36787i) q^{53} +(5.92471 - 3.17584i) q^{55} +(-12.4835 - 6.09511i) q^{57} +(4.70272 - 0.356683i) q^{59} +(6.63150 - 6.75821i) q^{61} +(-0.641175 + 3.72789i) q^{63} +(1.05818 - 0.858000i) q^{65} +(1.55333 - 0.686896i) q^{67} +(3.34878 - 13.3356i) q^{69} +(-10.4919 + 1.19652i) q^{71} +(-12.8510 + 9.63743i) q^{73} +(6.14351 - 7.29036i) q^{75} +(-0.897042 - 1.75234i) q^{77} +(3.48394 - 9.26768i) q^{79} +(-2.29420 + 1.34393i) q^{81} +(-1.64790 + 2.28629i) q^{83} +(0.00970387 + 0.00520159i) q^{85} +(-2.23310 - 3.98307i) q^{87} +(4.34168 + 14.8811i) q^{89} +(-0.245355 - 0.314586i) q^{91} +(4.39639 + 11.6949i) q^{93} +(12.5246 - 7.98833i) q^{95} +(8.95939 + 2.07042i) q^{97} +(-3.95500 + 9.42188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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