LMFDB - Embedded newform 92.2.e.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 51x^18 - 200x^17 + 633x^16 - 1688x^15 + 3957x^14 - 8161x^13 + 14788x^12 - 23925x^11 + 35080x^10 - 43945x^9 + 57269x^8 - 57348x^7 + 52821x^6 - 34986x^5 + 26231x^4 + 96928x^3 + 49370x^2 + 8165*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.1
Root			$-0.858865 + 1.88065i$ of defining polynomial
Character	$\chi$	$=$	92.9
Dual form			92.2.e.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35392 - 1.56250i) q^{3} +(-0.187926 - 1.30705i) q^{5} +(1.18148 - 2.58708i) q^{7} +(-0.181380 + 1.26153i) q^{9} +O(q^{10})$	\(q+(-1.35392 - 1.56250i) q^{3} +(-0.187926 - 1.30705i) q^{5} +(1.18148 - 2.58708i) q^{7} +(-0.181380 + 1.26153i) q^{9} +(-2.10179 - 0.617142i) q^{11} +(2.61757 + 5.73168i) q^{13} +(-1.78784 + 2.06327i) q^{15} +(2.92674 + 1.88090i) q^{17} +(0.593681 - 0.381536i) q^{19} +(-5.64195 + 1.65663i) q^{21} +(3.67636 + 3.07967i) q^{23} +(3.12440 - 0.917405i) q^{25} +(-3.00113 + 1.92871i) q^{27} +(-7.98898 - 5.13420i) q^{29} +(2.11967 - 2.44622i) q^{31} +(1.88136 + 4.11961i) q^{33} +(-3.60348 - 1.05808i) q^{35} +(0.667311 - 4.64125i) q^{37} +(5.41179 - 11.8502i) q^{39} +(0.422099 + 2.93576i) q^{41} +(7.93911 + 9.16223i) q^{43} +1.68297 q^{45} -7.35564 q^{47} +(-0.713075 - 0.822933i) q^{49} +(-1.02365 - 7.11961i) q^{51} +(4.41466 - 9.66676i) q^{53} +(-0.411656 + 2.86313i) q^{55} +(-1.39995 - 0.411061i) q^{57} +(0.411077 + 0.900134i) q^{59} +(-3.23209 + 3.73003i) q^{61} +(3.04938 + 1.95972i) q^{63} +(6.99970 - 4.49843i) q^{65} +(-2.10066 + 0.616811i) q^{67} +(-0.165486 - 9.91393i) q^{69} +(-8.62902 + 2.53371i) q^{71} +(-7.78596 + 5.00373i) q^{73} +(-5.66362 - 3.63979i) q^{75} +(-4.07983 + 4.70837i) q^{77} +(1.67545 + 3.66873i) q^{79} +(10.7455 + 3.15516i) q^{81} +(-2.38059 + 16.5574i) q^{83} +(1.90842 - 4.17887i) q^{85} +(2.79420 + 19.4341i) q^{87} +(1.78506 + 2.06007i) q^{89} +17.9209 q^{91} -6.69208 q^{93} +(-0.610255 - 0.704272i) q^{95} +(-0.835242 - 5.80923i) q^{97} +(1.15976 - 2.53953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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
$3$	−1.35392	−	1.56250i	−0.781683	−	0.902111i	0.215546	−	0.976494i	$-0.430847\pi$
$3$	−1.35392	−	1.56250i	−0.781683	−	0.902111i	−0.997230	+	0.0743828i	$0.976301\pi$
$4$		0			0
$5$	−0.187926	−	1.30705i	−0.0840429	−	0.584531i	−0.987710	−	0.156296i	$-0.950045\pi$
$5$	−0.187926	−	1.30705i	−0.0840429	−	0.584531i	0.903667	−	0.428235i	$-0.140865\pi$
$6$		0			0
$7$	1.18148	−	2.58708i	0.446558	−	0.977825i	−0.543790	−	0.839221i	$-0.683011\pi$
$7$	1.18148	−	2.58708i	0.446558	−	0.977825i	0.990348	−	0.138604i	$-0.0442615\pi$
$8$		0			0
$9$	−0.181380	+	1.26153i	−0.0604600	+	0.420509i
$10$		0			0
$11$	−2.10179	−	0.617142i	−0.633714	−	0.186075i	−0.0509301	−	0.998702i	$-0.516219\pi$
$11$	−2.10179	−	0.617142i	−0.633714	−	0.186075i	−0.582784	+	0.812627i	$0.698037\pi$
$12$		0			0
$13$	2.61757	+	5.73168i	0.725984	+	1.58968i	0.805324	+	0.592835i	$0.201991\pi$
$13$	2.61757	+	5.73168i	0.725984	+	1.58968i	−0.0793402	+	0.996848i	$0.525281\pi$
$14$		0			0
$15$	−1.78784	+	2.06327i	−0.461617	+	0.532735i
$16$		0			0
$17$	2.92674	+	1.88090i	0.709838	+	0.456185i	0.845089	−	0.534626i	$-0.179548\pi$
$17$	2.92674	+	1.88090i	0.709838	+	0.456185i	−0.135251	+	0.990811i	$0.543184\pi$
$18$		0			0
$19$	0.593681	−	0.381536i	0.136200	−	0.0875303i	−0.470767	−	0.882258i	$-0.656023\pi$
$19$	0.593681	−	0.381536i	0.136200	−	0.0875303i	0.606966	+	0.794727i	$0.292386\pi$
$20$		0			0
$21$	−5.64195	+	1.65663i	−1.23117	+	0.361505i
$22$		0			0
$23$	3.67636	+	3.07967i	0.766574	+	0.642156i
$23$	3.67636	+	3.07967i	0.766574	+	0.642156i
$24$		0			0
$25$	3.12440	−	0.917405i	0.624879	−	0.183481i
$26$		0			0
$27$	−3.00113	+	1.92871i	−0.577568	+	0.371180i
$28$		0			0
$29$	−7.98898	−	5.13420i	−1.48352	−	0.953398i	−0.996808	−	0.0798331i	$-0.974561\pi$
$29$	−7.98898	−	5.13420i	−1.48352	−	0.953398i	−0.486708	−	0.873565i	$-0.661802\pi$
$30$		0			0
$31$	2.11967	−	2.44622i	0.380703	−	0.439355i	−0.532766	−	0.846263i	$-0.678847\pi$
$31$	2.11967	−	2.44622i	0.380703	−	0.439355i	0.913469	+	0.406908i	$0.133393\pi$
$32$		0			0
$33$	1.88136	+	4.11961i	0.327503	+	0.717133i
$34$		0			0
$35$	−3.60348	−	1.05808i	−0.609100	−	0.178848i
$36$		0			0
$37$	0.667311	−	4.64125i	0.109705	−	0.763017i	−0.858492	−	0.512828i	$-0.828598\pi$
$37$	0.667311	−	4.64125i	0.109705	−	0.763017i	0.968197	−	0.250189i	$-0.0804929\pi$
$38$		0			0
$39$	5.41179	−	11.8502i	0.866580	−	1.89755i
$40$		0			0
$41$	0.422099	+	2.93576i	0.0659207	+	0.458489i	0.995869	+	0.0907990i	$0.0289421\pi$
$41$	0.422099	+	2.93576i	0.0659207	+	0.458489i	−0.929948	+	0.367690i	$0.880149\pi$
$42$		0			0
$43$	7.93911	+	9.16223i	1.21070	+	1.39723i	0.893617	+	0.448830i	$0.148159\pi$
$43$	7.93911	+	9.16223i	1.21070	+	1.39723i	0.317086	+	0.948397i	$0.397296\pi$
$44$		0			0
$45$	1.68297			0.250882
$46$		0			0
$47$	−7.35564			−1.07293			−0.536465	−	0.843922i	$-0.680241\pi$
$47$	−7.35564			−1.07293			−0.536465	+	0.843922i	$0.680241\pi$
$48$		0			0
$49$	−0.713075	−	0.822933i	−0.101868	−	0.117562i
$50$		0			0
$51$	−1.02365	−	7.11961i	−0.143339	−	0.996945i
$52$		0			0
$53$	4.41466	−	9.66676i	0.606401	−	1.32783i	−0.318608	−	0.947886i	$-0.603215\pi$
$53$	4.41466	−	9.66676i	0.606401	−	1.32783i	0.925009	−	0.379945i	$-0.124057\pi$
$54$		0			0
$55$	−0.411656	+	2.86313i	−0.0555077	+	0.386064i
$56$		0			0
$57$	−1.39995	−	0.411061i	−0.185427	−	0.0544464i
$58$		0			0
$59$	0.411077	+	0.900134i	0.0535177	+	0.117187i	0.934502	−	0.355959i	$-0.115846\pi$
$59$	0.411077	+	0.900134i	0.0535177	+	0.117187i	−0.880984	+	0.473146i	$0.843118\pi$
$60$		0			0
$61$	−3.23209	+	3.73003i	−0.413826	+	0.477581i	−0.923946	−	0.382522i	$-0.875056\pi$
$61$	−3.23209	+	3.73003i	−0.413826	+	0.477581i	0.510120	+	0.860103i	$0.329601\pi$
$62$		0			0
$63$	3.04938	+	1.95972i	0.384185	+	0.246901i
$64$		0			0
$65$	6.99970	−	4.49843i	0.868206	−	0.557962i
$66$		0			0
$67$	−2.10066	+	0.616811i	−0.256637	+	0.0753554i	−0.407520	−	0.913196i	$-0.633606\pi$
$67$	−2.10066	+	0.616811i	−0.256637	+	0.0753554i	0.150883	+	0.988552i	$0.451788\pi$
$68$		0			0
$69$	−0.165486	−	9.91393i	−0.0199222	−	1.19350i
$70$		0			0
$71$	−8.62902	+	2.53371i	−1.02408	+	0.300696i	−0.750300	−	0.661097i	$-0.770091\pi$
$71$	−8.62902	+	2.53371i	−1.02408	+	0.300696i	−0.273776	+	0.961793i	$0.588273\pi$
$72$		0			0
$73$	−7.78596	+	5.00373i	−0.911278	+	0.585643i	−0.910115	−	0.414356i	$-0.864007\pi$
$73$	−7.78596	+	5.00373i	−0.911278	+	0.585643i	−0.00116337	+	0.999999i	$0.500370\pi$
$74$		0			0
$75$	−5.66362	−	3.63979i	−0.653978	−	0.420286i
$76$		0			0
$77$	−4.07983	+	4.70837i	−0.464939	+	0.536569i
$78$		0			0
$79$	1.67545	+	3.66873i	0.188503	+	0.412764i	0.980162	−	0.198200i	$-0.0635094\pi$
$79$	1.67545	+	3.66873i	0.188503	+	0.412764i	−0.791659	+	0.610964i	$0.790782\pi$
$80$		0			0
$81$	10.7455	+	3.15516i	1.19395	+	0.350574i
$82$		0			0
$83$	−2.38059	+	16.5574i	−0.261304	+	1.81741i	0.261780	+	0.965128i	$0.415691\pi$
$83$	−2.38059	+	16.5574i	−0.261304	+	1.81741i	−0.523084	+	0.852281i	$0.675218\pi$
$84$		0			0
$85$	1.90842	−	4.17887i	0.206998	−	0.453262i
$86$		0			0
$87$	2.79420	+	19.4341i	0.299569	+	2.08355i
$88$		0			0
$89$	1.78506	+	2.06007i	0.189216	+	0.218367i	0.842429	−	0.538807i	$-0.181125\pi$
$89$	1.78506	+	2.06007i	0.189216	+	0.218367i	−0.653213	+	0.757174i	$0.726579\pi$
$90$		0			0
$91$	17.9209			1.87863
$92$		0			0
$93$	−6.69208			−0.693936
$94$		0			0
$95$	−0.610255	−	0.704272i	−0.0626109	−	0.0722568i
$96$		0			0
$97$	−0.835242	−	5.80923i	−0.0848059	−	0.589838i	−0.987268	−	0.159068i	$-0.949151\pi$
$97$	−0.835242	−	5.80923i	−0.0848059	−	0.589838i	0.902462	−	0.430770i	$-0.141758\pi$
$98$		0			0
$99$	1.15976	−	2.53953i	0.116561	−	0.255232i
$100$		0			0
$101$	−1.47826	+	10.2815i	−0.147092	+	1.02305i	0.773856	+	0.633362i	$0.218325\pi$
$101$	−1.47826	+	10.2815i	−0.147092	+	1.02305i	−0.920948	+	0.389686i	$0.872584\pi$
$102$		0			0
$103$	−3.97533	−	1.16726i	−0.391701	−	0.115014i	0.0799504	−	0.996799i	$-0.474524\pi$
$103$	−3.97533	−	1.16726i	−0.391701	−	0.115014i	−0.471652	+	0.881785i	$0.656342\pi$
$104$		0			0
$105$	3.22556	+	7.06300i	0.314783	+	0.689278i
$106$		0			0
$107$	10.8930	−	12.5712i	1.05306	−	1.21530i	0.0771790	−	0.997017i	$-0.475409\pi$
$107$	10.8930	−	12.5712i	1.05306	−	1.21530i	0.975885	−	0.218284i	$-0.0700458\pi$
$108$		0			0
$109$	−14.5403	−	9.34447i	−1.39271	−	0.895038i	−0.393006	−	0.919536i	$-0.628565\pi$
$109$	−14.5403	−	9.34447i	−1.39271	−	0.895038i	−0.999700	+	0.0244985i	$0.992201\pi$
$110$		0			0
$111$	−8.15544	+	5.24119i	−0.774081	+	0.497471i
$112$		0			0
$113$	−7.12950	+	2.09341i	−0.670687	+	0.196931i	−0.599309	−	0.800518i	$-0.704558\pi$
$113$	−7.12950	+	2.09341i	−0.670687	+	0.196931i	−0.0713780	+	0.997449i	$0.522740\pi$
$114$		0			0
$115$	3.33441	−	5.38394i	0.310935	−	0.502055i
$116$		0			0
$117$	−7.70544	+	2.26252i	−0.712369	+	0.209170i
$118$		0			0
$119$	8.32393	−	5.34946i	0.763053	−	0.490384i
$120$		0			0
$121$	−5.21712	−	3.35284i	−0.474284	−	0.304804i
$122$		0			0
$123$	4.01565	−	4.63430i	0.362079	−	0.417861i
$124$		0			0
$125$	−4.52901	−	9.91716i	−0.405087	−	0.887017i
$126$		0			0
$127$	−4.09409	−	1.20213i	−0.363292	−	0.106672i	0.0949921	−	0.995478i	$-0.469717\pi$
$127$	−4.09409	−	1.20213i	−0.363292	−	0.106672i	−0.458284	+	0.888806i	$0.651536\pi$
$128$		0			0
$129$	3.56711	−	24.8098i	0.314066	−	2.18438i
$130$		0			0
$131$	−1.79912	+	3.93953i	−0.157190	+	0.344198i	−0.971798	−	0.235813i	$-0.924225\pi$
$131$	−1.79912	+	3.93953i	−0.157190	+	0.344198i	0.814608	+	0.580011i	$0.196952\pi$
$132$		0			0
$133$	−0.285642	−	1.98668i	−0.0247683	−	0.172267i
$134$		0			0
$135$	3.08491	+	3.56018i	0.265507	+	0.306411i
$136$		0			0
$137$	20.4811			1.74982			0.874909	−	0.484288i	$-0.160921\pi$
$137$	20.4811			1.74982			0.874909	+	0.484288i	$0.160921\pi$
$138$		0			0
$139$	2.92438			0.248043			0.124021	−	0.992280i	$-0.460421\pi$
$139$	2.92438			0.248043			0.124021	+	0.992280i	$0.460421\pi$
$140$		0			0
$141$	9.95892	+	11.4932i	0.838692	+	0.967903i
$142$		0			0
$143$	−1.96433	−	13.6622i	−0.164266	−	1.14249i
$144$		0			0
$145$	−5.20934	+	11.4069i	−0.432612	+	0.947288i
$146$		0			0
$147$	−0.320390	+	2.22836i	−0.0264253	+	0.183792i
$148$		0			0
$149$	9.84948	+	2.89207i	0.806901	+	0.236927i	0.659067	−	0.752085i	$-0.270952\pi$
$149$	9.84948	+	2.89207i	0.806901	+	0.236927i	0.147834	+	0.989012i	$0.452770\pi$
$150$		0			0
$151$	−5.29936	−	11.6040i	−0.431256	−	0.944319i	−0.993121	−	0.117090i	$-0.962643\pi$
$151$	−5.29936	−	11.6040i	−0.431256	−	0.944319i	0.561865	−	0.827229i	$-0.310084\pi$
$152$		0			0
$153$	−2.90366	+	3.35100i	−0.234747	+	0.270912i
$154$		0			0
$155$	−3.59568	−	2.31080i	−0.288812	−	0.185608i
$156$		0			0
$157$	5.29594	−	3.40349i	0.422662	−	0.271628i	−0.311973	−	0.950091i	$-0.600990\pi$
$157$	5.29594	−	3.40349i	0.422662	−	0.271628i	0.734635	+	0.678463i	$0.237354\pi$
$158$		0			0
$159$	−21.0814	+	6.19006i	−1.67186	+	0.490904i
$160$		0			0
$161$	12.3109	−	5.87247i	0.970236	−	0.462816i
$162$		0			0
$163$	−6.81317	+	2.00053i	−0.533649	+	0.156693i	−0.537444	−	0.843299i	$-0.680610\pi$
$163$	−6.81317	+	2.00053i	−0.533649	+	0.156693i	0.00379532	+	0.999993i	$0.498792\pi$
$164$		0			0
$165$	5.03099	−	3.23322i	0.391662	−	0.251706i
$166$		0			0
$167$	6.27509	+	4.03276i	0.485581	+	0.312064i	0.760426	−	0.649425i	$-0.224990\pi$
$167$	6.27509	+	4.03276i	0.485581	+	0.312064i	−0.274845	+	0.961489i	$0.588627\pi$
$168$		0			0
$169$	−17.4873	+	20.1814i	−1.34518	+	1.55242i
$170$		0			0
$171$	0.373636	+	0.818148i	0.0285726	+	0.0625653i
$172$		0			0
$173$	5.86329	+	1.72162i	0.445777	+	0.130892i	0.496914	−	0.867800i	$-0.334466\pi$
$173$	5.86329	+	1.72162i	0.445777	+	0.130892i	−0.0511369	+	0.998692i	$0.516284\pi$
$174$		0			0
$175$	1.31801	−	9.16697i	0.0996323	−	0.692958i
$176$		0			0
$177$	0.849897	−	1.86101i	0.0638822	−	0.139882i
$178$		0			0
$179$	−0.920717	−	6.40373i	−0.0688176	−	0.478637i	−0.994863	−	0.101226i	$-0.967723\pi$
$179$	−0.920717	−	6.40373i	−0.0688176	−	0.478637i	0.926046	−	0.377411i	$-0.123186\pi$
$180$		0			0
$181$	1.90566	+	2.19925i	0.141647	+	0.163469i	0.822140	−	0.569285i	$-0.192780\pi$
$181$	1.90566	+	2.19925i	0.141647	+	0.163469i	−0.680493	+	0.732754i	$0.738234\pi$
$182$		0			0
$183$	10.2041			0.754312
$184$		0			0
$185$	−6.19176			−0.455227
$186$		0			0
$187$	−4.99061	−	5.75947i	−0.364950	−	0.421174i
$188$		0			0
$189$	1.44395	+	10.0429i	0.105032	+	0.730514i
$190$		0			0
$191$	−3.20210	+	7.01162i	−0.231696	+	0.507343i	−0.989393	−	0.145263i	$-0.953597\pi$
$191$	−3.20210	+	7.01162i	−0.231696	+	0.507343i	0.757697	+	0.652606i	$0.226324\pi$
$192$		0			0
$193$	−1.81222	+	12.6043i	−0.130446	+	0.907275i	0.814526	+	0.580127i	$0.196997\pi$
$193$	−1.81222	+	12.6043i	−0.130446	+	0.907275i	−0.944973	+	0.327149i	$0.893912\pi$
$194$		0			0
$195$	−16.5058	−	4.84654i	−1.18201	−	0.347068i
$196$		0			0
$197$	4.62887	+	10.1358i	0.329794	+	0.722147i	0.999796	−	0.0202118i	$-0.00643407\pi$
$197$	4.62887	+	10.1358i	0.329794	+	0.722147i	−0.670002	+	0.742359i	$0.733707\pi$
$198$		0			0
$199$	10.9575	−	12.6457i	0.776759	−	0.896428i	−0.220112	−	0.975475i	$-0.570642\pi$
$199$	10.9575	−	12.6457i	0.776759	−	0.896428i	0.996871	+	0.0790471i	$0.0251877\pi$
$200$		0			0
$201$	3.80789	+	2.44718i	0.268588	+	0.172611i
$202$		0			0
$203$	−22.7214	+	14.6022i	−1.59473	+	1.02487i
$204$		0			0
$205$	3.75787	−	1.10341i	0.262461	−	0.0770655i
$206$		0			0
$207$	−4.55191	+	4.07923i	−0.316379	+	0.283526i
$208$		0			0
$209$	−1.48326	+	0.435524i	−0.102599	+	0.0301258i
$210$		0			0
$211$	−10.6094	+	6.81827i	−0.730384	+	0.469389i	−0.852235	−	0.523159i	$-0.824753\pi$
$211$	−10.6094	+	6.81827i	−0.730384	+	0.469389i	0.121851	+	0.992548i	$0.461117\pi$
$212$		0			0
$213$	15.6419	+	10.0524i	1.07176	+	0.688781i
$214$		0			0
$215$	10.4835	−	12.0987i	0.714972	−	0.825121i
$216$		0			0
$217$	−3.82424	−	8.37392i	−0.259606	−	0.568459i
$218$		0			0
$219$	18.3599	+	5.39095i	1.24065	+	0.364286i
$220$		0			0
$221$	−3.11977	+	21.6985i	−0.209859	+	1.45960i
$222$		0			0
$223$	−0.599423	+	1.31255i	−0.0401404	+	0.0878951i	−0.928640	−	0.370982i	$-0.879021\pi$
$223$	−0.599423	+	1.31255i	−0.0401404	+	0.0878951i	0.888500	+	0.458877i	$0.151748\pi$
$224$		0			0
$225$	0.590628	+	4.10791i	0.0393752	+	0.273860i
$226$		0			0
$227$	2.72038	+	3.13948i	0.180558	+	0.208375i	0.838812	−	0.544421i	$-0.183250\pi$
$227$	2.72038	+	3.13948i	0.180558	+	0.208375i	−0.658255	+	0.752795i	$0.728705\pi$
$228$		0			0
$229$	−23.0257			−1.52158			−0.760790	−	0.648999i	$-0.775188\pi$
$229$	−23.0257			−1.52158			−0.760790	+	0.648999i	$0.775188\pi$
$230$		0			0
$231$	12.8806			0.847480
$232$		0			0
$233$	−4.03788	−	4.65996i	−0.264530	−	0.305284i	0.607909	−	0.794007i	$-0.292009\pi$
$233$	−4.03788	−	4.65996i	−0.264530	−	0.305284i	−0.872439	+	0.488722i	$0.837463\pi$
$234$		0			0
$235$	1.38231	+	9.61421i	0.0901723	+	0.627162i
$236$		0			0
$237$	3.46397	−	7.58504i	0.225009	−	0.492701i
$238$		0			0
$239$	1.18637	−	8.25138i	0.0767399	−	0.533737i	−0.914797	−	0.403913i	$-0.867650\pi$
$239$	1.18637	−	8.25138i	0.0767399	−	0.533737i	0.991537	−	0.129824i	$-0.0414412\pi$
$240$		0			0
$241$	2.73096	+	0.801882i	0.175916	+	0.0516537i	0.368504	−	0.929626i	$-0.379870\pi$
$241$	2.73096	+	0.801882i	0.175916	+	0.0516537i	−0.192588	+	0.981280i	$0.561688\pi$
$242$		0			0
$243$	−5.17264	−	11.3265i	−0.331825	−	0.726595i
$244$		0			0
$245$	−0.941611	+	1.08668i	−0.0601573	+	0.0694252i
$246$		0			0
$247$	3.74085	+	2.40410i	0.238024	+	0.152969i
$248$		0			0
$249$	29.0941	−	18.6976i	1.84376	−	1.18491i
$250$		0			0
$251$	23.5858	−	6.92542i	1.48872	−	0.437129i	0.566590	−	0.824000i	$-0.308262\pi$
$251$	23.5858	−	6.92542i	1.48872	−	0.437129i	0.922134	+	0.386872i	$0.126444\pi$
$252$		0			0
$253$	−5.82635	−	8.74167i	−0.366300	−	0.549584i
$254$		0			0
$255$	−9.11333	+	2.67592i	−0.570699	+	0.167572i
$256$		0			0
$257$	−19.2697	+	12.3839i	−1.20201	+	0.772484i	−0.979303	−	0.202402i	$-0.935125\pi$
$257$	−19.2697	+	12.3839i	−1.20201	+	0.772484i	−0.222706	+	0.974886i	$0.571489\pi$
$258$		0			0
$259$	−11.2189	−	7.20994i	−0.697108	−	0.448004i
$260$		0			0
$261$	7.92598	−	9.14706i	0.490606	−	0.566189i
$262$		0			0
$263$	1.54658	+	3.38654i	0.0953662	+	0.208823i	0.951303	−	0.308258i	$-0.0997459\pi$
$263$	1.54658	+	3.38654i	0.0953662	+	0.208823i	−0.855937	+	0.517081i	$0.827019\pi$
$264$		0			0
$265$	−13.4646	−	3.95356i	−0.827123	−	0.242865i
$266$		0			0
$267$	0.802041	−	5.57832i	0.0490841	−	0.341387i
$268$		0			0
$269$	0.612474	−	1.34113i	0.0373432	−	0.0817702i	−0.890041	−	0.455880i	$-0.849325\pi$
$269$	0.612474	−	1.34113i	0.0373432	−	0.0817702i	0.927384	+	0.374110i	$0.122052\pi$
$270$		0			0
$271$	−0.335160	−	2.33109i	−0.0203595	−	0.141603i	0.977106	−	0.212752i	$-0.0682426\pi$
$271$	−0.335160	−	2.33109i	−0.0203595	−	0.141603i	−0.997466	+	0.0711486i	$0.977334\pi$
$272$		0			0
$273$	−24.2634	−	28.0015i	−1.46849	−	1.69473i
$274$		0			0
$275$	−7.13300			−0.430136
$276$		0			0
$277$	−1.08114			−0.0649592			−0.0324796	−	0.999472i	$-0.510340\pi$
$277$	−1.08114			−0.0649592			−0.0324796	+	0.999472i	$0.510340\pi$
$278$		0			0
$279$	2.70151	+	3.11771i	0.161735	+	0.186652i
$280$		0			0
$281$	−3.83970	−	26.7057i	−0.229057	−	1.59313i	−0.702094	−	0.712085i	$-0.747751\pi$
$281$	−3.83970	−	26.7057i	−0.229057	−	1.59313i	0.473037	−	0.881043i	$-0.343158\pi$
$282$		0			0
$283$	8.19942	−	17.9542i	0.487405	−	1.06727i	−0.492956	−	0.870054i	$-0.664084\pi$
$283$	8.19942	−	17.9542i	0.487405	−	1.06727i	0.980361	−	0.197213i	$-0.0631891\pi$
$284$		0			0
$285$	−0.274192	+	1.90705i	−0.0162418	+	0.112964i
$286$		0			0
$287$	8.09376	+	2.37654i	0.477759	+	0.140283i
$288$		0			0
$289$	−2.03405	−	4.45395i	−0.119650	−	0.261997i
$290$		0			0
$291$	−7.94609	+	9.17028i	−0.465808	+	0.537571i
$292$		0			0
$293$	5.95014	+	3.82392i	0.347611	+	0.223396i	0.702782	−	0.711405i	$-0.251941\pi$
$293$	5.95014	+	3.82392i	0.347611	+	0.223396i	−0.355171	+	0.934801i	$0.615577\pi$
$294$		0			0
$295$	1.09927	−	0.706458i	0.0640020	−	0.0411316i
$296$		0			0
$297$	7.49804	−	2.20162i	0.435080	−	0.127751i
$298$		0			0
$299$	−8.02857	+	29.1330i	−0.464304	+	1.68480i
$300$		0			0
$301$	33.0834	−	9.71415i	1.90689	−	0.559914i
$302$		0			0
$303$	18.0663	−	11.6105i	1.03788	−	0.667006i
$304$		0			0
$305$	5.48273	+	3.52354i	0.313940	+	0.201757i
$306$		0			0
$307$	−5.54223	+	6.39607i	−0.316312	+	0.365043i	−0.891534	−	0.452954i	$-0.850370\pi$
$307$	−5.54223	+	6.39607i	−0.316312	+	0.365043i	0.575222	+	0.817997i	$0.304916\pi$
$308$		0			0
$309$	3.55841	+	7.79184i	0.202431	+	0.443262i
$310$		0			0
$311$	−21.6433	−	6.35504i	−1.22728	−	0.360361i	−0.397056	−	0.917795i	$-0.629968\pi$
$311$	−21.6433	−	6.35504i	−1.22728	−	0.360361i	−0.830222	+	0.557433i	$0.811786\pi$
$312$		0			0
$313$	−2.40527	+	16.7290i	−0.135954	+	0.945579i	0.801630	+	0.597820i	$0.203966\pi$
$313$	−2.40527	+	16.7290i	−0.135954	+	0.945579i	−0.937584	+	0.347759i	$0.886943\pi$
$314$		0			0
$315$	1.98839	−	4.35397i	0.112033	−	0.245319i
$316$		0			0
$317$	−3.58913	−	24.9630i	−0.201586	−	1.40206i	−0.799580	−	0.600559i	$-0.794945\pi$
$317$	−3.58913	−	24.9630i	−0.201586	−	1.40206i	0.597994	−	0.801500i	$-0.295964\pi$
$318$		0			0
$319$	13.6226	+	15.7214i	0.762722	+	0.880228i
$320$		0			0
$321$	−34.3907			−1.91950
$322$		0			0
$323$	2.45518			0.136610
$324$		0			0
$325$	13.4366	+	15.5067i	0.745329	+	0.860155i
$326$		0			0
$327$	5.08556	+	35.3708i	0.281232	+	1.95601i
$328$		0			0
$329$	−8.69055	+	19.0297i	−0.479126	+	1.04914i
$330$		0			0
$331$	1.20796	−	8.40157i	0.0663957	−	0.461792i	−0.929316	−	0.369285i	$-0.879603\pi$
$331$	1.20796	−	8.40157i	0.0663957	−	0.461792i	0.995712	−	0.0925074i	$-0.0294882\pi$
$332$		0			0
$333$	5.73402	+	1.68366i	0.314223	+	0.0922641i
$334$		0			0
$335$	1.20097	+	2.62976i	0.0656161	+	0.143679i
$336$		0			0
$337$	−11.2267	+	12.9563i	−0.611557	+	0.705774i	−0.974081	−	0.226200i	$-0.927370\pi$
$337$	−11.2267	+	12.9563i	−0.611557	+	0.705774i	0.362524	+	0.931974i	$0.381915\pi$
$338$		0			0
$339$	12.9237	+	8.30556i	0.701919	+	0.451096i
$340$		0			0
$341$	−5.96477	+	3.83332i	−0.323010	+	0.207586i
$342$		0			0
$343$	16.1308	−	4.73642i	0.870980	−	0.255743i
$344$		0			0
$345$	−12.9269	+	2.07938i	−0.695962	+	0.111950i
$346$		0			0
$347$	11.5044	−	3.37799i	0.617588	−	0.181340i	0.0420504	−	0.999115i	$-0.486611\pi$
$347$	11.5044	−	3.37799i	0.617588	−	0.181340i	0.575538	+	0.817775i	$0.304793\pi$
$348$		0			0
$349$	17.9303	−	11.5231i	0.959785	−	0.616817i	0.0358466	−	0.999357i	$-0.488587\pi$
$349$	17.9303	−	11.5231i	0.959785	−	0.616817i	0.923939	+	0.382541i	$0.124951\pi$
$350$		0			0
$351$	−18.9104	−	12.1530i	−1.00936	−	0.648678i
$352$		0			0
$353$	10.2911	−	11.8766i	0.547742	−	0.632128i	−0.412613	−	0.910906i	$-0.635384\pi$
$353$	10.2911	−	11.8766i	0.547742	−	0.632128i	0.960356	+	0.278778i	$0.0899294\pi$
$354$		0			0
$355$	4.93331	+	10.8024i	0.261833	+	0.573334i
$356$		0			0
$357$	−19.6284	−	5.76343i	−1.03885	−	0.305033i
$358$		0			0
$359$	−0.667121	+	4.63993i	−0.0352093	+	0.244886i	−0.999824	−	0.0187788i	$-0.994022\pi$
$359$	−0.667121	+	4.63993i	−0.0352093	+	0.244886i	0.964614	+	0.263665i	$0.0849313\pi$
$360$		0			0
$361$	−7.68600	+	16.8300i	−0.404526	+	0.885789i
$362$		0			0
$363$	1.82472	+	12.6912i	0.0957731	+	0.666116i
$364$		0			0
$365$	8.00332	+	9.23633i	0.418913	+	0.483451i
$366$		0			0
$367$	−29.6072			−1.54548			−0.772741	−	0.634721i	$-0.781115\pi$
$367$	−29.6072			−1.54548			−0.772741	+	0.634721i	$0.781115\pi$
$368$		0			0
$369$	−3.78010			−0.196784
$370$		0			0
$371$	−19.7929	−	22.8422i	−1.02759	−	1.18591i
$372$		0			0
$373$	1.61777	+	11.2518i	0.0837648	+	0.582597i	0.987870	+	0.155286i	$0.0496299\pi$
$373$	1.61777	+	11.2518i	0.0837648	+	0.582597i	−0.904105	+	0.427311i	$0.859461\pi$
$374$		0			0
$375$	−9.36367	+	20.5036i	−0.483538	+	1.05880i
$376$		0			0
$377$	8.51591	−	59.2294i	0.438592	−	3.05047i
$378$		0			0
$379$	2.06375	+	0.605973i	0.106008	+	0.0311267i	0.334306	−	0.942464i	$-0.391498\pi$
$379$	2.06375	+	0.605973i	0.106008	+	0.0311267i	−0.228298	+	0.973591i	$0.573316\pi$
$380$		0			0
$381$	3.66471	+	8.02461i	0.187749	+	0.411113i
$382$		0			0
$383$	−3.80724	+	4.39379i	−0.194541	+	0.224512i	−0.844636	−	0.535340i	$-0.820183\pi$
$383$	−3.80724	+	4.39379i	−0.194541	+	0.224512i	0.650096	+	0.759852i	$0.274729\pi$
$384$		0			0
$385$	6.92079	+	4.44772i	0.352716	+	0.226677i
$386$		0			0
$387$	−12.9984	+	8.35356i	−0.660745	+	0.424635i
$388$		0			0
$389$	−18.1567	+	5.33130i	−0.920583	+	0.270308i	−0.707489	−	0.706724i	$-0.750172\pi$
$389$	−18.1567	+	5.33130i	−0.920583	+	0.270308i	−0.213094	+	0.977032i	$0.568354\pi$
$390$		0			0
$391$	4.96718	+	15.9283i	0.251201	+	0.805526i
$392$		0			0
$393$	8.59138	−	2.52266i	0.433378	−	0.127251i
$394$		0			0
$395$	4.48035	−	2.87935i	0.225431	−	0.144876i
$396$		0			0
$397$	11.6632	+	7.49547i	0.585358	+	0.376187i	0.799545	−	0.600606i	$-0.205074\pi$
$397$	11.6632	+	7.49547i	0.585358	+	0.376187i	−0.214187	+	0.976793i	$0.568710\pi$
$398$		0			0
$399$	−2.71746	+	3.13611i	−0.136043	+	0.157002i
$400$		0			0
$401$	9.29237	+	20.3474i	0.464039	+	1.01610i	0.986548	+	0.163470i	$0.0522686\pi$
$401$	9.29237	+	20.3474i	0.464039	+	1.01610i	−0.522510	+	0.852633i	$0.675004\pi$
$402$		0			0
$403$	19.5694	+	5.74608i	0.974819	+	0.286233i
$404$		0			0
$405$	2.10461	−	14.6379i	0.104579	−	0.727362i
$406$		0			0
$407$	−4.26686	+	9.34312i	−0.211500	+	0.463121i
$408$		0			0
$409$	−2.32755	−	16.1885i	−0.115090	−	0.800469i	−0.962840	−	0.270073i	$-0.912952\pi$
$409$	−2.32755	−	16.1885i	−0.115090	−	0.800469i	0.847750	−	0.530396i	$-0.177957\pi$
$410$		0			0
$411$	−27.7297	−	32.0017i	−1.36780	−	1.57853i
$412$		0			0
$413$	2.81440			0.138488
$414$		0			0
$415$	22.0887			1.08429
$416$		0			0
$417$	−3.95937	−	4.56935i	−0.193891	−	0.223762i
$418$		0			0
$419$	2.98038	+	20.7290i	0.145601	+	1.01268i	0.923310	+	0.384055i	$0.125473\pi$
$419$	2.98038	+	20.7290i	0.145601	+	1.01268i	−0.777709	+	0.628624i	$0.783618\pi$
$420$		0			0
$421$	9.41808	−	20.6227i	0.459009	−	1.00509i	−0.528703	−	0.848807i	$-0.677321\pi$
$421$	9.41808	−	20.6227i	0.459009	−	1.00509i	0.987712	−	0.156283i	$-0.0499512\pi$
$422$		0			0
$423$	1.33417	−	9.27934i	0.0648694	−	0.451177i
$424$		0			0
$425$	10.8698	+	3.19167i	0.527264	+	0.154819i
$426$		0			0
$427$	5.83124	+	12.7686i	0.282194	+	0.617918i
$428$		0			0
$429$	−18.6877	+	21.5668i	−0.902251	+	1.04125i
$430$		0			0
$431$	−16.4212	−	10.5533i	−0.790981	−	0.508333i	0.0816802	−	0.996659i	$-0.473971\pi$
$431$	−16.4212	−	10.5533i	−0.790981	−	0.508333i	−0.872661	+	0.488326i	$0.837608\pi$
$432$		0			0
$433$	15.6946	−	10.0863i	0.754234	−	0.484717i	−0.106158	−	0.994349i	$-0.533855\pi$
$433$	15.6946	−	10.0863i	0.754234	−	0.484717i	0.860392	+	0.509632i	$0.170219\pi$
$434$		0			0
$435$	24.8762	−	7.30432i	1.19272	−	0.350216i
$436$		0			0
$437$	3.35759	+	0.425681i	0.160615	+	0.0203631i
$438$		0			0
$439$	32.5006	−	9.54303i	1.55117	−	0.455464i	0.609718	−	0.792618i	$-0.291283\pi$
$439$	32.5006	−	9.54303i	1.55117	−	0.455464i	0.941449	+	0.337154i	$0.109464\pi$
$440$		0			0
$441$	1.16749	−	0.750300i	0.0555947	−	0.0357286i
$442$		0			0
$443$	31.5264	+	20.2608i	1.49786	+	0.962618i	0.995171	+	0.0981527i	$0.0312933\pi$
$443$	31.5264	+	20.2608i	1.49786	+	0.962618i	0.502692	+	0.864466i	$0.332343\pi$
$444$		0			0
$445$	2.35716	−	2.72031i	0.111740	−	0.128955i
$446$		0			0
$447$	−8.81650	−	19.3054i	−0.417006	−	0.913116i
$448$		0			0
$449$	−20.3111	−	5.96386i	−0.958538	−	0.281452i	−0.235201	−	0.971947i	$-0.575575\pi$
$449$	−20.3111	−	5.96386i	−0.958538	−	0.281452i	−0.723337	+	0.690495i	$0.757393\pi$
$450$		0			0
$451$	0.924618	−	6.43086i	0.0435385	−	0.302817i
$452$		0			0
$453$	−10.9564	+	23.9911i	−0.514775	+	1.12720i
$454$		0			0
$455$	−3.36781	−	23.4236i	−0.157885	−	1.09812i
$456$		0			0
$457$	−20.7872	−	23.9897i	−0.972383	−	1.12219i	−0.992482	−	0.122392i	$-0.960943\pi$
$457$	−20.7872	−	23.9897i	−0.972383	−	1.12219i	0.0200983	−	0.999798i	$-0.493602\pi$
$458$		0			0
$459$	−12.4112			−0.579306
$460$		0			0
$461$	−20.3236			−0.946566			−0.473283	−	0.880911i	$-0.656931\pi$
$461$	−20.3236			−0.946566			−0.473283	+	0.880911i	$0.656931\pi$
$462$		0			0
$463$	−19.9823	−	23.0608i	−0.928658	−	1.07173i	−0.997252	−	0.0740837i	$-0.976397\pi$
$463$	−19.9823	−	23.0608i	−0.928658	−	1.07173i	0.0685941	−	0.997645i	$-0.478149\pi$
$464$		0			0
$465$	1.25761	+	8.74689i	0.0583204	+	0.405628i
$466$		0			0
$467$	8.76014	−	19.1820i	0.405371	−	0.887639i	−0.591326	−	0.806432i	$-0.701395\pi$
$467$	8.76014	−	19.1820i	0.405371	−	0.887639i	0.996697	−	0.0812063i	$-0.0258773\pi$
$468$		0			0
$469$	−0.886155	+	6.16334i	−0.0409188	+	0.284597i
$470$		0			0
$471$	−12.4882	−	3.66687i	−0.575426	−	0.168960i
$472$		0			0
$473$	−11.0320	−	24.1567i	−0.507251	−	1.11072i
$474$		0			0
$475$	1.50487	−	1.73672i	0.0690483	−	0.0796860i
$476$		0			0
$477$	11.3941	+	7.32257i	0.521702	+	0.335278i
$478$		0			0
$479$	−14.0877	+	9.05360i	−0.643682	+	0.413669i	−0.821353	−	0.570421i	$-0.806780\pi$
$479$	−14.0877	+	9.05360i	−0.643682	+	0.413669i	0.177671	+	0.984090i	$0.443144\pi$
$480$		0			0
$481$	28.3489	−	8.32399i	1.29260	−	0.379541i
$482$		0			0
$483$	−25.8437	−	11.2850i	−1.17593	−	0.513485i
$484$		0			0
$485$	−7.43601	+	2.18341i	−0.337652	+	0.0991435i
$486$		0			0
$487$	7.88893	−	5.06991i	0.357481	−	0.229739i	−0.349556	−	0.936915i	$-0.613668\pi$
$487$	7.88893	−	5.06991i	0.357481	−	0.229739i	0.707037	+	0.707176i	$0.250031\pi$
$488$		0			0
$489$	12.3503	+	7.93705i	0.558499	+	0.358926i
$490$		0			0
$491$	11.4898	−	13.2599i	0.518527	−	0.598412i	−0.434734	−	0.900559i	$-0.643158\pi$
$491$	11.4898	−	13.2599i	0.518527	−	0.598412i	0.953262	+	0.302146i	$0.0977032\pi$
$492$		0			0
$493$	−13.7247	−	30.0529i	−0.618130	−	1.35352i
$494$		0			0
$495$	−3.53725	−	1.03863i	−0.158987	−	0.0466829i
$496$		0			0
$497$	−3.64011	+	25.3175i	−0.163281	+	1.13565i
$498$		0			0
$499$	−6.30353	+	13.8028i	−0.282185	+	0.617898i	−0.996651	−	0.0817715i	$-0.973942\pi$
$499$	−6.30353	+	13.8028i	−0.282185	+	0.617898i	0.714466	+	0.699670i	$0.246669\pi$
$500$		0			0
$501$	−2.19475	−	15.2648i	−0.0980544	−	0.681983i
$502$		0			0
$503$	3.98297	+	4.59659i	0.177592	+	0.204952i	0.837566	−	0.546337i	$-0.183978\pi$
$503$	3.98297	+	4.59659i	0.177592	+	0.204952i	−0.659974	+	0.751289i	$0.729433\pi$
$504$		0			0
$505$	13.7163			0.610365
$506$		0			0
$507$	55.2099			2.45196
$508$		0			0
$509$	11.5897	+	13.3753i	0.513706	+	0.592848i	0.952044	−	0.305962i	$-0.0989781\pi$
$509$	11.5897	+	13.3753i	0.513706	+	0.592848i	−0.438338	+	0.898810i	$0.644433\pi$
$510$		0			0
$511$	3.74611	+	26.0548i	0.165718	+	1.15259i
$512$		0			0
$513$	−1.04584	+	2.29008i	−0.0461751	+	0.101109i
$514$		0			0
$515$	−0.778606	+	5.41533i	−0.0343095	+	0.238628i
$516$		0			0
$517$	15.4600	+	4.53948i	0.679932	+	0.199646i
$518$		0			0
$519$	−5.24837	−	11.4923i	−0.230378	−	0.504457i
$520$		0			0
$521$	−8.30617	+	9.58583i	−0.363900	+	0.419963i	−0.907943	−	0.419095i	$-0.862348\pi$
$521$	−8.30617	+	9.58583i	−0.363900	+	0.419963i	0.544043	+	0.839058i	$0.316893\pi$
$522$		0			0
$523$	−28.1383	−	18.0834i	−1.23040	−	0.790732i	−0.246449	−	0.969156i	$-0.579264\pi$
$523$	−28.1383	−	18.0834i	−1.23040	−	0.790732i	−0.983954	+	0.178424i	$0.942900\pi$
$524$		0			0
$525$	−16.1079	+	10.3519i	−0.703006	+	0.451794i
$526$		0			0
$527$	10.8048	−	3.17258i	0.470665	−	0.138200i
$528$		0			0
$529$	4.03124	+	22.6440i	0.175271	+	0.984520i
$530$		0			0
$531$	−1.21010	+	0.355319i	−0.0525140	+	0.0154195i
$532$		0			0
$533$	−15.7220	+	10.1039i	−0.680994	+	0.437648i
$534$		0			0
$535$	−18.4782	−	11.8752i	−0.798884	−	0.513412i
$536$		0			0
$537$	−8.75927	+	10.1087i	−0.377990	+	0.436224i
$538$		0			0
$539$	0.990870	+	2.16970i	0.0426798	+	0.0934557i
$540$		0			0
$541$	29.5688	+	8.68217i	1.27126	+	0.373276i	0.846674	−	0.532112i	$-0.178601\pi$
$541$	29.5688	+	8.68217i	1.27126	+	0.373276i	0.424586	+	0.905388i	$0.360420\pi$
$542$		0			0
$543$	0.856229	−	5.95521i	0.0367443	−	0.255562i
$544$		0			0
$545$	−9.48121	+	20.7610i	−0.406130	+	0.889302i
$546$		0			0
$547$	4.56986	+	31.7841i	0.195393	+	1.35899i	0.817442	+	0.576011i	$0.195391\pi$
$547$	4.56986	+	31.7841i	0.195393	+	1.35899i	−0.622049	+	0.782979i	$0.713699\pi$
$548$		0			0
$549$	−4.11929	−	4.75392i	−0.175807	−	0.202892i
$550$		0			0
$551$	−6.70179			−0.285506
$552$		0			0
$553$	11.4708			0.487789
$554$		0			0
$555$	8.38312	+	9.67464i	0.355844	+	0.410665i
$556$		0			0
$557$	−2.71619	−	18.8915i	−0.115089	−	0.800460i	−0.962841	−	0.270068i	$-0.912954\pi$
$557$	−2.71619	−	18.8915i	−0.115089	−	0.800460i	0.847753	−	0.530392i	$-0.177955\pi$
$558$		0			0
$559$	−31.7338	+	69.4873i	−1.34220	+	2.93900i
$560$		0			0
$561$	−2.24232	+	15.5957i	−0.0946708	+	0.658450i
$562$		0			0
$563$	−28.7422	−	8.43947i	−1.21134	−	0.355681i	−0.387161	−	0.922012i	$-0.626544\pi$
$563$	−28.7422	−	8.43947i	−1.21134	−	0.355681i	−0.824178	+	0.566331i	$0.808363\pi$
$564$		0			0
$565$	4.07601	+	8.92522i	0.171479	+	0.375487i
$566$		0			0
$567$	20.8583	−	24.0717i	0.875966	−	1.01092i
$568$		0			0
$569$	21.3203	+	13.7017i	0.893793	+	0.574406i	0.904944	−	0.425532i	$-0.139913\pi$
$569$	21.3203	+	13.7017i	0.893793	+	0.574406i	−0.0111501	+	0.999938i	$0.503549\pi$
$570$		0			0
$571$	12.5920	−	8.09242i	0.526961	−	0.338657i	−0.249959	−	0.968256i	$-0.580417\pi$
$571$	12.5920	−	8.09242i	0.526961	−	0.338657i	0.776920	+	0.629599i	$0.216781\pi$
$572$		0			0
$573$	15.2910	−	4.48985i	0.638792	−	0.187566i
$574$		0			0
$575$	14.3117	+	6.24940i	0.596840	+	0.260618i
$576$		0			0
$577$	−42.3288	+	12.4289i	−1.76217	+	0.517420i	−0.992631	−	0.121177i	$-0.961333\pi$
$577$	−42.3288	+	12.4289i	−1.76217	+	0.517420i	−0.769541	+	0.638597i	$0.779515\pi$
$578$		0			0
$579$	22.1478	−	14.2335i	0.920431	−	0.591525i
$580$		0			0
$581$	40.0227	+	25.7210i	1.66042	+	1.06709i
$582$		0			0
$583$	−15.2445	+	17.5931i	−0.631361	+	0.728630i
$584$		0			0
$585$	4.40529	+	9.64623i	0.182136	+	0.398822i
$586$		0			0
$587$	−11.1740	−	3.28099i	−0.461202	−	0.135421i	0.0428740	−	0.999080i	$-0.486349\pi$
$587$	−11.1740	−	3.28099i	−0.461202	−	0.135421i	−0.504076	+	0.863659i	$0.668167\pi$
$588$		0			0
$589$	0.325084	−	2.26101i	0.0133948	−	0.0931632i
$590$		0			0
$591$	9.57013	−	20.9557i	0.393663	−	0.862001i
$592$		0			0
$593$	−4.44568	−	30.9204i	−0.182562	−	1.26975i	−0.850677	−	0.525689i	$-0.823807\pi$
$593$	−4.44568	−	30.9204i	−0.182562	−	1.26975i	0.668114	−	0.744059i	$-0.267102\pi$
$594$		0			0
$595$	−8.55631	−	9.87450i	−0.350774	−	0.404815i
$596$		0			0
$597$	−34.5944			−1.41586
$598$		0			0
$599$	−35.8848			−1.46621			−0.733106	−	0.680114i	$-0.761930\pi$
$599$	−35.8848			−1.46621			−0.733106	+	0.680114i	$0.761930\pi$
$600$		0			0
$601$	13.5964	+	15.6911i	0.554609	+	0.640053i	0.961951	−	0.273223i	$-0.0880897\pi$
$601$	13.5964	+	15.6911i	0.554609	+	0.640053i	−0.407342	+	0.913276i	$0.633544\pi$
$602$		0			0
$603$	−0.397104	−	2.76192i	−0.0161713	−	0.112474i
$604$		0			0
$605$	−3.40190	+	7.44913i	−0.138307	+	0.302850i
$606$		0			0
$607$	1.95612	−	13.6051i	0.0793966	−	0.552215i	−0.910834	−	0.412773i	$-0.864560\pi$
$607$	1.95612	−	13.6051i	0.0793966	−	0.552215i	0.990230	−	0.139442i	$-0.0445308\pi$
$608$		0			0
$609$	53.5789	+	15.7322i	2.17112	+	0.637500i
$610$		0			0
$611$	−19.2539	−	42.1602i	−0.778930	−	1.70562i
$612$		0			0
$613$	23.9872	−	27.6827i	0.968834	−	1.11809i	−0.0241334	−	0.999709i	$-0.507683\pi$
$613$	23.9872	−	27.6827i	0.968834	−	1.11809i	0.992968	−	0.118386i	$-0.0377719\pi$
$614$		0			0
$615$	−6.81192	−	4.37775i	−0.274683	−	0.176528i
$616$		0			0
$617$	−19.4764	+	12.5167i	−0.784091	+	0.503905i	−0.870389	−	0.492365i	$-0.836133\pi$
$617$	−19.4764	+	12.5167i	−0.784091	+	0.503905i	0.0862980	+	0.996269i	$0.472496\pi$
$618$		0			0
$619$	−30.2781	+	8.89045i	−1.21698	+	0.357337i	−0.826321	−	0.563199i	$-0.809570\pi$
$619$	−30.2781	+	8.89045i	−1.21698	+	0.357337i	−0.390657	+	0.920536i	$0.627752\pi$
$620$		0			0
$621$	−16.9730	−	2.15187i	−0.681104	−	0.0863515i
$622$		0			0
$623$	7.43858	−	2.18416i	0.298021	−	0.0875067i
$624$		0			0
$625$	1.58575	−	1.01910i	0.0634298	−	0.0407639i
$626$		0			0
$627$	2.68871	+	1.72793i	0.107377	+	0.0690069i
$628$		0			0
$629$	10.6828	−	12.3286i	0.425950	−	0.491572i
$630$		0			0
$631$	−4.48162	−	9.81337i	−0.178410	−	0.390664i	0.799207	−	0.601056i	$-0.205253\pi$
$631$	−4.48162	−	9.81337i	−0.178410	−	0.390664i	−0.977617	+	0.210392i	$0.932526\pi$
$632$		0			0
$633$	25.0178	+	7.34590i	0.994370	+	0.291973i
$634$		0			0
$635$	−0.801866	+	5.57710i	−0.0318211	+	0.221320i
$636$		0			0
$637$	2.85026	−	6.24121i	0.112932	−	0.247286i
$638$		0			0
$639$	−1.63121	−	11.3453i	−0.0645296	−	0.448813i
$640$		0			0
$641$	−8.12516	−	9.37693i	−0.320924	−	0.370366i	0.572248	−	0.820080i	$-0.306071\pi$
$641$	−8.12516	−	9.37693i	−0.320924	−	0.370366i	−0.893173	+	0.449714i	$0.851526\pi$
$642$		0			0
$643$	−33.9930			−1.34055			−0.670277	−	0.742111i	$-0.733825\pi$
$643$	−33.9930			−1.34055			−0.670277	+	0.742111i	$0.733825\pi$
$644$		0			0
$645$	−33.0980			−1.30323
$646$		0			0
$647$	31.8716	+	36.7817i	1.25300	+	1.44604i	0.846500	+	0.532389i	$0.178706\pi$
$647$	31.8716	+	36.7817i	1.25300	+	1.44604i	0.406501	+	0.913650i	$0.366749\pi$
$648$		0			0
$649$	−0.308489	−	2.14559i	−0.0121093	−	0.0842217i
$650$		0			0
$651$	−7.90656	+	17.3130i	−0.309883	+	0.678548i
$652$		0			0
$653$	−1.32303	+	9.20184i	−0.0517740	+	0.360096i	0.947421	+	0.319989i	$0.103679\pi$
$653$	−1.32303	+	9.20184i	−0.0517740	+	0.360096i	−0.999195	+	0.0401073i	$0.987230\pi$
$654$		0			0
$655$	5.48727	+	1.61121i	0.214405	+	0.0629551i
$656$		0			0
$657$	−4.90012	−	10.7298i	−0.191172	−	0.418608i
$658$		0			0
$659$	23.6057	−	27.2425i	0.919549	−	1.06122i	−0.0783816	−	0.996923i	$-0.524975\pi$
$659$	23.6057	−	27.2425i	0.919549	−	1.06122i	0.997931	−	0.0642932i	$-0.0204793\pi$
$660$		0			0
$661$	−6.29318	−	4.04438i	−0.244776	−	0.157308i	0.412501	−	0.910957i	$-0.364655\pi$
$661$	−6.29318	−	4.04438i	−0.244776	−	0.157308i	−0.657277	+	0.753649i	$0.728292\pi$
$662$		0			0
$663$	38.1279	−	24.5033i	1.48076	−	0.951629i
$664$		0			0
$665$	−2.54302	+	0.746697i	−0.0986139	+	0.0289557i
$666$		0			0
$667$	−13.5587	−	43.4786i	−0.524994	−	1.68350i
$668$		0			0
$669$	2.86244	−	0.840487i	0.110668	−	0.0324951i
$670$		0			0
$671$	9.09514	−	5.84509i	0.351114	−	0.225647i
$672$		0			0
$673$	−5.53671	−	3.55822i	−0.213424	−	0.137159i	0.429561	−	0.903038i	$-0.358668\pi$
$673$	−5.53671	−	3.55822i	−0.213424	−	0.137159i	−0.642986	+	0.765878i	$0.722305\pi$
$674$		0			0
$675$	−7.60731	+	8.77930i	−0.292805	+	0.337916i
$676$		0			0
$677$	−7.42862	−	16.2664i	−0.285505	−	0.625169i	0.711485	−	0.702702i	$-0.248023\pi$
$677$	−7.42862	−	16.2664i	−0.285505	−	0.625169i	−0.996990	+	0.0775327i	$0.975296\pi$
$678$		0			0
$679$	−16.0158	−	4.70266i	−0.614630	−	0.180472i
$680$		0			0
$681$	1.22229	−	8.50119i	0.0468381	−	0.325766i
$682$		0			0
$683$	−6.50779	+	14.2501i	−0.249014	+	0.545264i	−0.992321	−	0.123686i	$-0.960529\pi$
$683$	−6.50779	+	14.2501i	−0.249014	+	0.545264i	0.743308	+	0.668950i	$0.233256\pi$
$684$		0			0
$685$	−3.84892	−	26.7698i	−0.147060	−	1.02282i
$686$		0			0
$687$	31.1748	+	35.9777i	1.18939	+	1.37263i
$688$		0			0
$689$	66.9625			2.55107
$690$		0			0
$691$	32.1536			1.22318			0.611590	−	0.791175i	$-0.290530\pi$
$691$	32.1536			1.22318			0.611590	+	0.791175i	$0.290530\pi$
$692$		0			0
$693$	−5.19973	−	6.00081i	−0.197522	−	0.227952i
$694$		0			0
$695$	−0.549566	−	3.82232i	−0.0208462	−	0.144989i
$696$		0			0
$697$	−4.28650	+	9.38612i	−0.162363	+	0.355525i
$698$		0			0
$699$	−1.81425	+	12.6184i	−0.0686212	+	0.477271i
$700$		0			0
$701$	−21.5801	−	6.33648i	−0.815067	−	0.239325i	−0.152477	−	0.988307i	$-0.548725\pi$
$701$	−21.5801	−	6.33648i	−0.815067	−	0.239325i	−0.662591	+	0.748982i	$0.730543\pi$
$702$		0			0
$703$	−1.37463	−	3.01003i	−0.0518453	−	0.113525i
$704$		0			0
$705$	13.1507	−	15.1767i	0.495283	−	0.571587i
$706$		0			0
$707$	24.8526	+	15.9718i	0.934676	+	0.600680i
$708$		0			0
$709$	−6.25399	+	4.01919i	−0.234873	+	0.150944i	−0.652784	−	0.757544i	$-0.726399\pi$
$709$	−6.25399	+	4.01919i	−0.234873	+	0.150944i	0.417910	+	0.908488i	$0.362763\pi$
$710$		0			0
$711$	−4.93209	+	1.44819i	−0.184968	+	0.0543114i
$712$		0			0
$713$	15.3262	−	2.46532i	0.573972	−	0.0923271i
$714$		0			0
$715$	−17.4881	+	5.13497i	−0.654017	+	0.192037i
$716$		0			0
$717$	−14.4990	+	9.31797i	−0.541477	+	0.347986i
$718$		0			0
$719$	17.3714	+	11.1639i	0.647843	+	0.416344i	0.822878	−	0.568219i	$-0.192367\pi$
$719$	17.3714	+	11.1639i	0.647843	+	0.416344i	−0.175034	+	0.984562i	$0.556004\pi$
$720$		0			0
$721$	−7.71659	+	8.90542i	−0.287381	+	0.331655i
$722$		0			0
$723$	−2.44454	−	5.35281i	−0.0909136	−	0.199073i
$724$		0			0
$725$	−29.6709	−	8.71216i	−1.10195	−	0.323561i
$726$		0			0
$727$	3.98390	−	27.7086i	0.147755	−	1.02766i	−0.772129	−	0.635465i	$-0.780808\pi$
$727$	3.98390	−	27.7086i	0.147755	−	1.02766i	0.919884	−	0.392191i	$-0.128283\pi$
$728$		0			0
$729$	3.26253	−	7.14393i	0.120834	−	0.264590i
$730$		0			0
$731$	6.00247	+	41.7481i	0.222009	+	1.54411i
$732$		0			0
$733$	−12.7945	−	14.7657i	−0.472577	−	0.545383i	0.468549	−	0.883437i	$-0.344777\pi$
$733$	−12.7945	−	14.7657i	−0.472577	−	0.545383i	−0.941127	+	0.338054i	$0.890231\pi$
$734$		0			0
$735$	2.97280			0.109653
$736$		0			0
$737$	4.79582			0.176656
$738$		0			0
$739$	−4.05408	−	4.67866i	−0.149132	−	0.172107i	0.676268	−	0.736655i	$-0.263596\pi$
$739$	−4.05408	−	4.67866i	−0.149132	−	0.172107i	−0.825400	+	0.564548i	$0.809050\pi$
$740$		0			0
$741$	−1.30839	−	9.10002i	−0.0480647	−	0.334298i
$742$		0			0
$743$	12.9762	−	28.4139i	0.476051	−	1.04241i	−0.507479	−	0.861664i	$-0.669423\pi$
$743$	12.9762	−	28.4139i	0.476051	−	1.04241i	0.983530	−	0.180743i	$-0.0578501\pi$
$744$		0			0
$745$	1.92911	−	13.4173i	0.0706772	−	0.491571i
$746$		0			0
$747$	−20.4558	−	6.00636i	−0.748438	−	0.219761i
$748$		0			0
$749$	−19.6528	−	43.0337i	−0.718098	−	1.57242i
$750$		0			0
$751$	0.434256	−	0.501158i	0.0158462	−	0.0182875i	−0.747771	−	0.663957i	$-0.768876\pi$
$751$	0.434256	−	0.501158i	0.0158462	−	0.0182875i	0.763617	+	0.645669i	$0.223421\pi$
$752$		0			0
$753$	−42.7542	−	27.4764i	−1.55805	−	1.00130i
$754$		0			0
$755$	−14.1711	+	9.10723i	−0.515740	+	0.331446i
$756$		0			0
$757$	3.88243	−	1.13998i	0.141109	−	0.0414334i	−0.210415	−	0.977612i	$-0.567482\pi$
$757$	3.88243	−	1.13998i	0.141109	−	0.0414334i	0.351524	+	0.936179i	$0.385663\pi$
$758$		0			0
$759$	−5.77049	+	20.9392i	−0.209455	+	0.760044i
$760$		0			0
$761$	−10.3668	+	3.04396i	−0.375796	+	0.110344i	−0.464175	−	0.885743i	$-0.653649\pi$
$761$	−10.3668	+	3.04396i	−0.375796	+	0.110344i	0.0883798	+	0.996087i	$0.471831\pi$
$762$		0			0
$763$	−41.3540	+	26.5766i	−1.49711	+	0.962137i
$764$		0			0
$765$	4.92560	+	3.16549i	0.178085	+	0.114449i
$766$		0			0
$767$	−4.08326	+	4.71233i	−0.147438	+	0.170152i
$768$		0			0
$769$	9.26855	+	20.2953i	0.334233	+	0.731867i	0.999897	−	0.0143843i	$-0.00457883\pi$
$769$	9.26855	+	20.2953i	0.334233	+	0.731867i	−0.665664	+	0.746252i	$0.731852\pi$
$770$		0			0
$771$	45.4393	+	13.3422i	1.63646	+	0.480507i
$772$		0			0
$773$	−3.24693	+	22.5829i	−0.116784	+	0.812249i	0.844276	+	0.535909i	$0.180031\pi$
$773$	−3.24693	+	22.5829i	−0.116784	+	0.812249i	−0.961060	+	0.276340i	$0.910878\pi$
$774$		0			0
$775$	4.37850	−	9.58757i	0.157280	−	0.344396i
$776$		0			0
$777$	3.92388	+	27.2912i	0.140768	+	0.979065i
$778$		0			0
$779$	1.37069	+	1.58186i	0.0491101	+	0.0566761i
$780$		0			0
$781$	19.7001			0.704924
$782$		0			0
$783$	33.8783			1.21071
$784$		0			0
$785$	−5.44378	−	6.28246i	−0.194297	−	0.224231i
$786$		0			0
$787$	0.881877	+	6.13359i	0.0314355	+	0.218639i	0.999484	−	0.0321248i	$-0.0102274\pi$
$787$	0.881877	+	6.13359i	0.0314355	+	0.218639i	−0.968048	+	0.250764i	$0.919318\pi$
$788$		0			0
$789$	3.19753	−	7.00162i	0.113835	−	0.249264i
$790$		0			0
$791$	−3.00754	+	20.9179i	−0.106936	+	0.743756i
$792$		0			0
$793$	−29.8396	−	8.76168i	−1.05963	−	0.311137i
$794$		0			0
$795$	12.0525	+	26.3912i	0.427457	+	0.936000i
$796$		0			0
$797$	−11.2959	+	13.0361i	−0.400121	+	0.461764i	−0.919679	−	0.392671i	$-0.871551\pi$
$797$	−11.2959	+	13.0361i	−0.400121	+	0.461764i	0.519558	+	0.854435i	$0.326097\pi$
$798$		0			0
$799$	−21.5280	−	13.8352i	−0.761607	−	0.489455i
$800$		0			0
$801$	−2.92261	+	1.87824i	−0.103265	+	0.0663645i
$802$		0			0
$803$	19.4525	−	5.71177i	0.686464	−	0.201564i
$804$		0			0
$805$	−9.98916	−	14.9874i	−0.352072	−	0.528237i
$806$		0			0
$807$	−2.92476	+	0.858786i	−0.102956	+	0.0302307i
$808$		0			0
$809$	10.5324	−	6.76877i	0.370300	−	0.237977i	−0.342234	−	0.939615i	$-0.611184\pi$
$809$	10.5324	−	6.76877i	0.370300	−	0.237977i	0.712534	+	0.701637i	$0.247547\pi$
$810$		0			0
$811$	2.97916	+	1.91459i	0.104612	+	0.0672304i	0.591901	−	0.806011i	$-0.298378\pi$
$811$	2.97916	+	1.91459i	0.104612	+	0.0672304i	−0.487289	+	0.873241i	$0.662014\pi$
$812$		0			0
$813$	−3.18855	+	3.67978i	−0.111827	+	0.129056i
$814$		0			0
$815$	3.89516	+	8.52922i	0.136442	+	0.298765i
$816$		0			0
$817$	8.20902	+	2.41039i	0.287197	+	0.0843288i
$818$		0			0
$819$	−3.25050	+	22.6077i	−0.113582	+	0.789979i
$820$		0			0
$821$	−9.79769	+	21.4540i	−0.341942	+	0.748748i	−0.999991	−	0.00422671i	$-0.998655\pi$
$821$	−9.79769	+	21.4540i	−0.341942	+	0.748748i	0.658049	+	0.752975i	$0.271382\pi$
$822$		0			0
$823$	3.62518	+	25.2137i	0.126366	+	0.878895i	0.950106	+	0.311927i	$0.100974\pi$
$823$	3.62518	+	25.2137i	0.126366	+	0.878895i	−0.823740	+	0.566968i	$0.808116\pi$
$824$		0			0
$825$	9.65748	+	11.1453i	0.336230	+	0.388031i
$826$		0			0
$827$	31.1814			1.08428			0.542142	−	0.840287i	$-0.317613\pi$
$827$	31.1814			1.08428			0.542142	+	0.840287i	$0.317613\pi$
$828$		0			0
$829$	−42.3841			−1.47206			−0.736031	−	0.676948i	$-0.763302\pi$
$829$	−42.3841			−1.47206			−0.736031	+	0.676948i	$0.763302\pi$
$830$		0			0
$831$	1.46377	+	1.68928i	0.0507775	+	0.0586004i
$832$		0			0
$833$	−0.539130	−	3.74973i	−0.0186797	−	0.129920i
$834$		0			0
$835$	4.09177	−	8.95973i	0.141602	−	0.310064i
$836$		0			0
$837$	−1.64334	+	11.4297i	−0.0568020	+	0.395067i
$838$		0			0
$839$	34.5340	+	10.1401i	1.19225	+	0.350075i	0.816883	−	0.576803i	$-0.195700\pi$
$839$	34.5340	+	10.1401i	1.19225	+	0.350075i	0.375362	+	0.926878i	$0.377518\pi$
$840$		0			0
$841$	25.4167	+	55.6548i	0.876437	+	1.91913i
$842$		0			0
$843$	−36.5290	+	42.1568i	−1.25813	+	1.45196i
$844$		0			0
$845$	29.6645	+	19.0642i	1.02049	+	0.655829i
$846$		0			0
$847$	−14.8380	+	9.53581i	−0.509840	+	0.327654i
$848$		0			0
$849$	−39.1548	+	11.4969i	−1.34379	+	0.394572i
$850$		0			0
$851$	16.7468	−	15.0078i	0.574073	−	0.514461i
$852$		0			0
$853$	30.0318	−	8.81814i	1.02827	−	0.301927i	0.276263	−	0.961082i	$-0.410904\pi$
$853$	30.0318	−	8.81814i	1.02827	−	0.301927i	0.752007	+	0.659155i	$0.229086\pi$
$854$		0			0
$855$	0.999146	−	0.642112i	0.0341701	−	0.0219598i
$856$		0			0
$857$	−6.23116	−	4.00452i	−0.212852	−	0.136792i	0.429871	−	0.902890i	$-0.358559\pi$
$857$	−6.23116	−	4.00452i	−0.212852	−	0.136792i	−0.642723	+	0.766098i	$0.722195\pi$
$858$		0			0
$859$	29.8196	−	34.4136i	1.01743	−	1.17418i	0.0328124	−	0.999462i	$-0.489554\pi$
$859$	29.8196	−	34.4136i	1.01743	−	1.17418i	0.984619	−	0.174717i	$-0.0559009\pi$
$860$		0			0
$861$	−7.24491	−	15.8641i	−0.246906	−	0.540649i
$862$		0			0
$863$	12.8373	+	3.76938i	0.436987	+	0.128311i	0.492824	−	0.870129i	$-0.335965\pi$
$863$	12.8373	+	3.76938i	0.436987	+	0.128311i	−0.0558369	+	0.998440i	$0.517783\pi$
$864$		0			0
$865$	1.14838	−	7.98716i	0.0390461	−	0.271571i
$866$		0			0
$867$	−4.20537	+	9.20848i	−0.142822	+	0.312736i
$868$		0			0
$869$	−1.25733	−	8.74489i	−0.0426519	−	0.296650i
$870$		0			0
$871$	−9.03400	−	10.4258i	−0.306105	−	0.353264i
$872$		0			0
$873$	7.48000			0.253160
$874$		0			0
$875$	−31.0074			−1.04824
$876$		0			0
$877$	−12.3172	−	14.2149i	−0.415924	−	0.480002i	0.508667	−	0.860963i	$-0.330138\pi$
$877$	−12.3172	−	14.2149i	−0.415924	−	0.480002i	−0.924591	+	0.380962i	$0.875593\pi$
$878$		0			0
$879$	−2.08110	−	14.4744i	−0.0701937	−	0.488208i
$880$		0			0
$881$	10.9146	−	23.8997i	0.367724	−	0.805202i	−0.631824	−	0.775112i	$-0.717693\pi$
$881$	10.9146	−	23.8997i	0.367724	−	0.805202i	0.999547	−	0.0300902i	$-0.00957945\pi$
$882$		0			0
$883$	−5.77832	+	40.1891i	−0.194456	+	1.35247i	0.625581	+	0.780159i	$0.284862\pi$
$883$	−5.77832	+	40.1891i	−0.194456	+	1.35247i	−0.820037	+	0.572311i	$0.806047\pi$
$884$		0			0
$885$	−2.59216	−	0.761127i	−0.0871345	−	0.0255850i
$886$		0			0
$887$	6.80705	+	14.9054i	0.228558	+	0.500473i	0.988815	−	0.149150i	$-0.0476539\pi$
$887$	6.80705	+	14.9054i	0.228558	+	0.500473i	−0.760256	+	0.649623i	$0.774927\pi$
$888$		0			0
$889$	−7.94711	+	9.17145i	−0.266537	+	0.307601i
$890$		0			0
$891$	−20.6376	−	13.2630i	−0.691387	−	0.444327i
$892$		0			0
$893$	−4.36691	+	2.80644i	−0.146133	+	0.0939140i
$894$		0			0
$895$	−8.19698	+	2.40685i	−0.273995	+	0.0804521i
$896$		0			0
$897$	56.3903	−	26.8989i	1.88282	−	0.898130i
$898$		0			0
$899$	−29.4934	+	8.66004i	−0.983659	+	0.288828i
$900$		0			0
$901$	31.1028	−	19.9885i	1.03618	−	0.665914i
$902$		0			0
$903$	−59.9704	−	38.5407i	−1.99569	−	1.28255i
$904$		0			0
$905$	2.51641	−	2.90410i	0.0836485	−	0.0965355i
$906$		0			0
$907$	−5.76775	−	12.6296i	−0.191515	−	0.419360i	0.789378	−	0.613908i	$-0.210403\pi$
$907$	−5.76775	−	12.6296i	−0.191515	−	0.419360i	−0.980893	+	0.194548i	$0.937676\pi$
$908$		0			0
$909$	−12.7023	−	3.72972i	−0.421307	−	0.123707i
$910$		0			0
$911$	1.50267	−	10.4513i	0.0497857	−	0.346267i	−0.949669	−	0.313254i	$-0.898581\pi$
$911$	1.50267	−	10.4513i	0.0497857	−	0.346267i	0.999455	−	0.0330126i	$-0.0105101\pi$
$912$		0			0
$913$	15.2218	−	33.3310i	0.503767	−	1.10310i
$914$		0			0
$915$	−1.91762	−	13.3374i	−0.0633946	−	0.440919i
$916$		0			0
$917$	8.06626	+	9.30896i	0.266371	+	0.307409i
$918$		0			0
$919$	1.88119			0.0620548			0.0310274	−	0.999519i	$-0.490122\pi$
$919$	1.88119			0.0620548			0.0310274	+	0.999519i	$0.490122\pi$
$920$		0			0
$921$	17.4976			0.576565
$922$		0			0
$923$	−37.1095	−	42.8266i	−1.22147	−	1.40966i
$924$		0			0
$925$	−2.17296	−	15.1133i	−0.0714466	−	0.496922i
$926$		0			0
$927$	2.19358	−	4.80327i	0.0720466	−	0.157760i
$928$		0			0
$929$	5.59610	−	38.9217i	0.183602	−	1.27698i	−0.664557	−	0.747238i	$-0.731380\pi$
$929$	5.59610	−	38.9217i	0.183602	−	1.27698i	0.848159	−	0.529742i	$-0.177711\pi$
$930$		0			0
$931$	−0.737318	−	0.216496i	−0.0241646	−	0.00709537i
$932$		0			0
$933$	19.3734	+	42.4218i	0.634257	+	1.38883i
$934$		0			0
$935$	−6.59007	+	7.60534i	−0.215518	+	0.248721i
$936$		0			0
$937$	12.0578	+	7.74905i	0.393910	+	0.253151i	0.722570	−	0.691298i	$-0.242961\pi$
$937$	12.0578	+	7.74905i	0.393910	+	0.253151i	−0.328660	+	0.944448i	$0.606597\pi$
$938$		0			0
$939$	29.3956	−	18.8914i	0.959290	−	0.616498i
$940$		0			0
$941$	−39.3592	+	11.5569i	−1.28307	+	0.376745i	−0.851034	−	0.525110i	$-0.824024\pi$
$941$	−39.3592	+	11.5569i	−1.28307	+	0.376745i	−0.432040	+	0.901854i	$0.642206\pi$
$942$		0			0
$943$	−7.48940	+	12.0928i	−0.243888	+	0.393797i
$944$		0			0
$945$	12.8552	−	3.77464i	0.418181	−	0.122789i
$946$		0			0
$947$	11.4653	−	7.36827i	0.372571	−	0.239437i	−0.340934	−	0.940087i	$-0.610743\pi$
$947$	11.4653	−	7.36827i	0.372571	−	0.239437i	0.713504	+	0.700651i	$0.247107\pi$
$948$		0			0
$949$	−49.0601	−	31.5290i	−1.59256	−	1.02348i
$950$		0			0
$951$	−34.1453	+	39.4058i	−1.10724	+	1.27782i
$952$		0			0
$953$	15.1899	+	33.2613i	0.492050	+	1.07744i	0.978972	+	0.203994i	$0.0653923\pi$
$953$	15.1899	+	33.2613i	0.492050	+	1.07744i	−0.486922	+	0.873445i	$0.661880\pi$
$954$		0			0
$955$	9.76631	+	2.86765i	0.316030	+	0.0927949i
$956$		0			0
$957$	6.12076	−	42.5708i	0.197856	−	1.37612i
$958$		0			0
$959$	24.1980	−	52.9863i	0.781395	−	1.71102i
$960$		0			0
$961$	2.92073	+	20.3141i	0.0942170	+	0.655294i
$962$		0			0
$963$	13.8831	+	16.0219i	0.447376	+	0.516300i
$964$		0			0
$965$	16.8150			0.541294
$966$		0			0
$967$	−44.8598			−1.44259			−0.721296	−	0.692627i	$-0.756453\pi$
$967$	−44.8598			−1.44259			−0.721296	+	0.692627i	$0.756453\pi$
$968$		0			0
$969$	−3.32411	−	3.83622i	−0.106786	−	0.123237i
$970$		0			0
$971$	−2.65511	−	18.4667i	−0.0852067	−	0.592625i	−0.987032	−	0.160524i	$-0.948681\pi$
$971$	−2.65511	−	18.4667i	−0.0852067	−	0.592625i	0.901825	−	0.432101i	$-0.142228\pi$
$972$		0			0
$973$	3.45510	−	7.56562i	0.110765	−	0.242543i
$974$		0			0
$975$	6.03717	−	41.9894i	0.193344	−	1.34474i
$976$		0			0
$977$	−2.76611	−	0.812204i	−0.0884958	−	0.0259847i	0.237185	−	0.971465i	$-0.423775\pi$
$977$	−2.76611	−	0.812204i	−0.0884958	−	0.0259847i	−0.325681	+	0.945480i	$0.605593\pi$
$978$		0			0
$979$	−2.48047	−	5.43147i	−0.0792762	−	0.173591i
$980$		0			0
$981$	14.4256	−	16.6480i	0.460574	−	0.531531i
$982$		0			0
$983$	35.1644	+	22.5988i	1.12157	+	0.720790i	0.963784	−	0.266683i	$-0.0859278\pi$
$983$	35.1644	+	22.5988i	1.12157	+	0.720790i	0.157787	+	0.987473i	$0.449564\pi$
$984$		0			0
$985$	12.3782	−	7.95496i	0.394401	−	0.253466i
$986$		0			0
$987$	41.5002	−	12.1855i	1.32096	−	0.387870i
$988$		0			0
$989$	0.970382	+	58.1335i	0.0308563	+	1.84854i
$990$		0			0
$991$	−4.48733	+	1.31760i	−0.142545	+	0.0418549i	−0.352227	−	0.935915i	$-0.614575\pi$
$991$	−4.48733	+	1.31760i	−0.142545	+	0.0418549i	0.209682	+	0.977770i	$0.432757\pi$
$992$		0			0
$993$	−14.7629	+	9.48757i	−0.468488	+	0.301079i
$994$		0			0
$995$	−18.5877	−	11.9456i	−0.589271	−	0.378702i
$996$		0			0
$997$	0.874652	−	1.00940i	0.0277005	−	0.0319681i	−0.741730	−	0.670698i	$-0.765995\pi$
$997$	0.874652	−	1.00940i	0.0277005	−	0.0319681i	0.769431	+	0.638730i	$0.220540\pi$
$998$		0			0
$999$	6.94893	+	15.2160i	0.219855	+	0.481414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.9.1	✓	20
3.2	odd	2		828.2.q.a.469.1		20
4.3	odd	2		368.2.m.d.193.2		20
23.8	even	11		2116.2.a.j.1.8		10
23.15	odd	22		2116.2.a.i.1.8		10
23.18	even	11	inner	92.2.e.a.41.1	yes	20
69.41	odd	22		828.2.q.a.685.1		20
92.15	even	22		8464.2.a.cd.1.3		10
92.31	odd	22		8464.2.a.ce.1.3		10
92.87	odd	22		368.2.m.d.225.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.9.1	✓	20	1.1	even	1	trivial
92.2.e.a.41.1	yes	20	23.18	even	11	inner
368.2.m.d.193.2		20	4.3	odd	2
368.2.m.d.225.2		20	92.87	odd	22
828.2.q.a.469.1		20	3.2	odd	2
828.2.q.a.685.1		20	69.41	odd	22
2116.2.a.i.1.8		10	23.15	odd	22
2116.2.a.j.1.8		10	23.8	even	11
8464.2.a.cd.1.3		10	92.15	even	22
8464.2.a.ce.1.3		10	92.31	odd	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35392 - 1.56250i) q^{3} +(-0.187926 - 1.30705i) q^{5} +(1.18148 - 2.58708i) q^{7} +(-0.181380 + 1.26153i) q^{9} +O(q^{10})\)	\(q+(-1.35392 - 1.56250i) q^{3} +(-0.187926 - 1.30705i) q^{5} +(1.18148 - 2.58708i) q^{7} +(-0.181380 + 1.26153i) q^{9} +(-2.10179 - 0.617142i) q^{11} +(2.61757 + 5.73168i) q^{13} +(-1.78784 + 2.06327i) q^{15} +(2.92674 + 1.88090i) q^{17} +(0.593681 - 0.381536i) q^{19} +(-5.64195 + 1.65663i) q^{21} +(3.67636 + 3.07967i) q^{23} +(3.12440 - 0.917405i) q^{25} +(-3.00113 + 1.92871i) q^{27} +(-7.98898 - 5.13420i) q^{29} +(2.11967 - 2.44622i) q^{31} +(1.88136 + 4.11961i) q^{33} +(-3.60348 - 1.05808i) q^{35} +(0.667311 - 4.64125i) q^{37} +(5.41179 - 11.8502i) q^{39} +(0.422099 + 2.93576i) q^{41} +(7.93911 + 9.16223i) q^{43} +1.68297 q^{45} -7.35564 q^{47} +(-0.713075 - 0.822933i) q^{49} +(-1.02365 - 7.11961i) q^{51} +(4.41466 - 9.66676i) q^{53} +(-0.411656 + 2.86313i) q^{55} +(-1.39995 - 0.411061i) q^{57} +(0.411077 + 0.900134i) q^{59} +(-3.23209 + 3.73003i) q^{61} +(3.04938 + 1.95972i) q^{63} +(6.99970 - 4.49843i) q^{65} +(-2.10066 + 0.616811i) q^{67} +(-0.165486 - 9.91393i) q^{69} +(-8.62902 + 2.53371i) q^{71} +(-7.78596 + 5.00373i) q^{73} +(-5.66362 - 3.63979i) q^{75} +(-4.07983 + 4.70837i) q^{77} +(1.67545 + 3.66873i) q^{79} +(10.7455 + 3.15516i) q^{81} +(-2.38059 + 16.5574i) q^{83} +(1.90842 - 4.17887i) q^{85} +(2.79420 + 19.4341i) q^{87} +(1.78506 + 2.06007i) q^{89} +17.9209 q^{91} -6.69208 q^{93} +(-0.610255 - 0.704272i) q^{95} +(-0.835242 - 5.80923i) q^{97} +(1.15976 - 2.53953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Introduction

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