LMFDB - Embedded newform 92.2.e.a.29.2

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			29.2
Root			$-0.250875 + 1.74487i$ of defining polynomial
Character	$\chi$	$=$	92.29
Dual form			92.2.e.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69141 + 0.496642i) q^{3} +(-0.630070 + 0.404921i) q^{5} +(-0.0283674 + 0.197300i) q^{7} +(0.0904475 + 0.0581271i) q^{9} +O(q^{10})$	\(q+(1.69141 + 0.496642i) q^{3} +(-0.630070 + 0.404921i) q^{5} +(-0.0283674 + 0.197300i) q^{7} +(0.0904475 + 0.0581271i) q^{9} +(-1.64271 - 3.59702i) q^{11} +(0.588198 + 4.09101i) q^{13} +(-1.26681 + 0.371968i) q^{15} +(1.78696 - 2.06226i) q^{17} +(-2.52857 - 2.91812i) q^{19} +(-0.145968 + 0.319626i) q^{21} +(-4.78098 - 0.377157i) q^{23} +(-1.84405 + 4.03790i) q^{25} +(-3.33908 - 3.85350i) q^{27} +(-4.13471 + 4.77171i) q^{29} +(5.69528 - 1.67229i) q^{31} +(-0.992052 - 6.89987i) q^{33} +(-0.0620175 - 0.135799i) q^{35} +(6.76233 + 4.34589i) q^{37} +(-1.03688 + 7.21169i) q^{39} +(5.51823 - 3.54635i) q^{41} +(6.37671 + 1.87237i) q^{43} -0.0805251 q^{45} +1.22850 q^{47} +(6.67833 + 1.96093i) q^{49} +(4.04668 - 2.60065i) q^{51} +(0.705887 - 4.90955i) q^{53} +(2.49153 + 1.60121i) q^{55} +(-2.82757 - 6.19152i) q^{57} +(1.64337 + 11.4299i) q^{59} +(-11.9727 + 3.51551i) q^{61} +(-0.0140342 + 0.0161964i) q^{63} +(-2.02714 - 2.33945i) q^{65} +(-0.860140 + 1.88344i) q^{67} +(-7.89927 - 3.01236i) q^{69} +(3.58538 - 7.85089i) q^{71} +(0.122624 + 0.141516i) q^{73} +(-5.12443 + 5.91391i) q^{75} +(0.756292 - 0.222067i) q^{77} +(-0.139435 - 0.969792i) q^{79} +(-3.86792 - 8.46957i) q^{81} +(4.66355 + 2.99708i) q^{83} +(-0.290856 + 2.02295i) q^{85} +(-9.36331 + 6.01743i) q^{87} +(-16.2669 - 4.77638i) q^{89} -0.823841 q^{91} +10.4636 q^{93} +(2.77478 + 0.814749i) q^{95} +(11.6502 - 7.48715i) q^{97} +(0.0605058 - 0.420827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

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
$3$	1.69141	+	0.496642i	0.976535	+	0.286737i	0.730793	−	0.682599i	$-0.239150\pi$
$3$	1.69141	+	0.496642i	0.976535	+	0.286737i	0.245742	+	0.969335i	$0.420969\pi$
$4$		0			0
$5$	−0.630070	+	0.404921i	−0.281776	+	0.181086i	−0.673893	−	0.738829i	$-0.735379\pi$
$5$	−0.630070	+	0.404921i	−0.281776	+	0.181086i	0.392117	+	0.919915i	$0.371743\pi$
$6$		0			0
$7$	−0.0283674	+	0.197300i	−0.0107219	+	0.0745724i	−0.994480	−	0.104928i	$-0.966539\pi$
$7$	−0.0283674	+	0.197300i	−0.0107219	+	0.0745724i	0.983758	+	0.179500i	$0.0574480\pi$
$8$		0			0
$9$	0.0904475	+	0.0581271i	0.0301492	+	0.0193757i
$10$		0			0
$11$	−1.64271	−	3.59702i	−0.495294	−	1.08454i	−0.977970	−	0.208744i	$-0.933062\pi$
$11$	−1.64271	−	3.59702i	−0.495294	−	1.08454i	0.482676	−	0.875799i	$-0.339665\pi$
$12$		0			0
$13$	0.588198	+	4.09101i	0.163137	+	1.13464i	0.892675	+	0.450701i	$0.148826\pi$
$13$	0.588198	+	4.09101i	0.163137	+	1.13464i	−0.729538	+	0.683940i	$0.760265\pi$
$14$		0			0
$15$	−1.26681	+	0.371968i	−0.327088	+	0.0960417i
$16$		0			0
$17$	1.78696	−	2.06226i	0.433401	−	0.500172i	−0.496471	−	0.868053i	$-0.665371\pi$
$17$	1.78696	−	2.06226i	0.433401	−	0.500172i	0.929873	+	0.367881i	$0.119917\pi$
$18$		0			0
$19$	−2.52857	−	2.91812i	−0.580093	−	0.669463i	0.387532	−	0.921856i	$-0.373328\pi$
$19$	−2.52857	−	2.91812i	−0.580093	−	0.669463i	−0.967625	+	0.252394i	$0.918782\pi$
$20$		0			0
$21$	−0.145968	+	0.319626i	−0.0318529	+	0.0697482i
$22$		0			0
$23$	−4.78098	−	0.377157i	−0.996903	−	0.0786426i
$23$	−4.78098	−	0.377157i	−0.996903	−	0.0786426i
$24$		0			0
$25$	−1.84405	+	4.03790i	−0.368810	+	0.807580i
$26$		0			0
$27$	−3.33908	−	3.85350i	−0.642606	−	0.741607i
$28$		0			0
$29$	−4.13471	+	4.77171i	−0.767796	+	0.886084i	−0.996165	−	0.0874909i	$-0.972115\pi$
$29$	−4.13471	+	4.77171i	−0.767796	+	0.886084i	0.228369	+	0.973575i	$0.426661\pi$
$30$		0			0
$31$	5.69528	−	1.67229i	1.02290	−	0.300351i	0.273081	−	0.961991i	$-0.411957\pi$
$31$	5.69528	−	1.67229i	1.02290	−	0.300351i	0.749822	+	0.661640i	$0.230139\pi$
$32$		0			0
$33$	−0.992052	−	6.89987i	−0.172694	−	1.20111i
$34$		0			0
$35$	−0.0620175	−	0.135799i	−0.0104829	−	0.0229543i
$36$		0			0
$37$	6.76233	+	4.34589i	1.11172	+	0.714459i	0.961667	−	0.274219i	$-0.0884192\pi$
$37$	6.76233	+	4.34589i	1.11172	+	0.714459i	0.150053	+	0.988678i	$0.452056\pi$
$38$		0			0
$39$	−1.03688	+	7.21169i	−0.166034	+	1.15479i
$40$		0			0
$41$	5.51823	−	3.54635i	0.861803	−	0.553847i	−0.0334323	−	0.999441i	$-0.510644\pi$
$41$	5.51823	−	3.54635i	0.861803	−	0.553847i	0.895235	+	0.445594i	$0.147007\pi$
$42$		0			0
$43$	6.37671	+	1.87237i	0.972439	+	0.285534i	0.729100	−	0.684407i	$-0.239939\pi$
$43$	6.37671	+	1.87237i	0.972439	+	0.285534i	0.243339	+	0.969941i	$0.421757\pi$
$44$		0			0
$45$	−0.0805251			−0.0120040
$46$		0			0
$47$	1.22850			0.179195			0.0895974	−	0.995978i	$-0.471442\pi$
$47$	1.22850			0.179195			0.0895974	+	0.995978i	$0.471442\pi$
$48$		0			0
$49$	6.67833	+	1.96093i	0.954047	+	0.280133i
$50$		0			0
$51$	4.04668	−	2.60065i	0.566649	−	0.364163i
$52$		0			0
$53$	0.705887	−	4.90955i	0.0969611	−	0.674379i	−0.882137	−	0.470992i	$-0.843896\pi$
$53$	0.705887	−	4.90955i	0.0969611	−	0.674379i	0.979098	−	0.203387i	$-0.0651949\pi$
$54$		0			0
$55$	2.49153	+	1.60121i	0.335958	+	0.215907i
$56$		0			0
$57$	−2.82757	−	6.19152i	−0.374521	−	0.820087i
$58$		0			0
$59$	1.64337	+	11.4299i	0.213949	+	1.48804i	0.759797	+	0.650161i	$0.225298\pi$
$59$	1.64337	+	11.4299i	0.213949	+	1.48804i	−0.545848	+	0.837884i	$0.683792\pi$
$60$		0			0
$61$	−11.9727	+	3.51551i	−1.53295	+	0.450115i	−0.935952	−	0.352128i	$-0.885458\pi$
$61$	−11.9727	+	3.51551i	−1.53295	+	0.450115i	−0.596998	+	0.802243i	$0.703640\pi$
$62$		0			0
$63$	−0.0140342	+	0.0161964i	−0.00176815	+	0.00204055i
$64$		0			0
$65$	−2.02714	−	2.33945i	−0.251436	−	0.290173i
$66$		0			0
$67$	−0.860140	+	1.88344i	−0.105083	+	0.230099i	−0.954868	−	0.297029i	$-0.904004\pi$
$67$	−0.860140	+	1.88344i	−0.105083	+	0.230099i	0.849786	+	0.527129i	$0.176731\pi$
$68$		0			0
$69$	−7.89927	−	3.01236i	−0.950961	−	0.362646i
$70$		0			0
$71$	3.58538	−	7.85089i	0.425506	−	0.931729i	−0.568528	−	0.822664i	$-0.692487\pi$
$71$	3.58538	−	7.85089i	0.425506	−	0.931729i	0.994035	−	0.109065i	$-0.0347857\pi$
$72$		0			0
$73$	0.122624	+	0.141516i	0.0143521	+	0.0165632i	0.762880	−	0.646540i	$-0.223785\pi$
$73$	0.122624	+	0.141516i	0.0143521	+	0.0165632i	−0.748528	+	0.663103i	$0.769239\pi$
$74$		0			0
$75$	−5.12443	+	5.91391i	−0.591718	+	0.682879i
$76$		0			0
$77$	0.756292	−	0.222067i	0.0861874	−	0.0253069i
$78$		0			0
$79$	−0.139435	−	0.969792i	−0.0156877	−	0.109110i	0.980473	−	0.196654i	$-0.0630074\pi$
$79$	−0.139435	−	0.969792i	−0.0156877	−	0.109110i	−0.996161	+	0.0875434i	$0.972098\pi$
$80$		0			0
$81$	−3.86792	−	8.46957i	−0.429769	−	0.941063i
$82$		0			0
$83$	4.66355	+	2.99708i	0.511891	+	0.328972i	0.770957	−	0.636887i	$-0.219778\pi$
$83$	4.66355	+	2.99708i	0.511891	+	0.328972i	−0.259066	+	0.965860i	$0.583415\pi$
$84$		0			0
$85$	−0.290856	+	2.02295i	−0.0315477	+	0.219419i
$86$		0			0
$87$	−9.36331	+	6.01743i	−1.00385	+	0.645137i
$88$		0			0
$89$	−16.2669	−	4.77638i	−1.72428	−	0.506295i	−0.738491	−	0.674263i	$-0.764461\pi$
$89$	−16.2669	−	4.77638i	−1.72428	−	0.506295i	−0.985792	+	0.167968i	$0.946279\pi$
$90$		0			0
$91$	−0.823841			−0.0863620
$92$		0			0
$93$	10.4636			1.08502
$94$		0			0
$95$	2.77478	+	0.814749i	0.284687	+	0.0835915i
$96$		0			0
$97$	11.6502	−	7.48715i	1.18290	−	0.760205i	0.206984	−	0.978344i	$-0.433635\pi$
$97$	11.6502	−	7.48715i	1.18290	−	0.760205i	0.975918	+	0.218139i	$0.0699987\pi$
$98$		0			0
$99$	0.0605058	−	0.420827i	0.00608107	−	0.0422947i
$100$		0			0
$101$	3.17015	+	2.03733i	0.315442	+	0.202722i	0.688775	−	0.724975i	$-0.258149\pi$
$101$	3.17015	+	2.03733i	0.315442	+	0.202722i	−0.373333	+	0.927697i	$0.621785\pi$
$102$		0			0
$103$	−6.65087	−	14.5634i	−0.655330	−	1.43497i	−0.886811	−	0.462133i	$-0.847084\pi$
$103$	−6.65087	−	14.5634i	−0.655330	−	1.43497i	0.231481	−	0.972840i	$-0.425643\pi$
$104$		0			0
$105$	−0.0374532	−	0.260493i	−0.00365506	−	0.0254215i
$106$		0			0
$107$	−11.5338	+	3.38664i	−1.11502	+	0.327399i	−0.786803	−	0.617204i	$-0.788265\pi$
$107$	−11.5338	+	3.38664i	−1.11502	+	0.327399i	−0.328215	+	0.944603i	$0.606447\pi$
$108$		0			0
$109$	−9.05400	+	10.4489i	−0.867216	+	1.00082i	0.132737	+	0.991151i	$0.457623\pi$
$109$	−9.05400	+	10.4489i	−0.867216	+	1.00082i	−0.999953	+	0.00966948i	$0.996922\pi$
$110$		0			0
$111$	9.27951	+	10.7091i	0.880772	+	1.01647i
$112$		0			0
$113$	−0.977799	+	2.14108i	−0.0919836	+	0.201416i	−0.950032	−	0.312153i	$-0.898950\pi$
$113$	−0.977799	+	2.14108i	−0.0919836	+	0.201416i	0.858048	+	0.513569i	$0.171677\pi$
$114$		0			0
$115$	3.16507	−	1.69828i	0.295144	−	0.158366i
$116$		0			0
$117$	−0.184597	+	0.404212i	−0.0170660	+	0.0373694i
$118$		0			0
$119$	0.356192	+	0.411068i	0.0326521	+	0.0376825i
$120$		0			0
$121$	−3.03663	+	3.50445i	−0.276057	+	0.318587i
$122$		0			0
$123$	11.0948	−	3.25774i	1.00039	−	0.293741i
$124$		0			0
$125$	−1.00610	−	6.99757i	−0.0899882	−	0.625881i
$126$		0			0
$127$	−3.81612	−	8.35614i	−0.338626	−	0.741488i	0.661337	−	0.750089i	$-0.269989\pi$
$127$	−3.81612	−	8.35614i	−0.338626	−	0.741488i	−0.999963	+	0.00860123i	$0.997262\pi$
$128$		0			0
$129$	9.85572	+	6.33389i	0.867748	+	0.557668i
$130$		0			0
$131$	−0.783447	+	5.44900i	−0.0684501	+	0.476081i	0.926547	+	0.376179i	$0.122762\pi$
$131$	−0.783447	+	5.44900i	−0.0684501	+	0.476081i	−0.994997	+	0.0999023i	$0.968147\pi$
$132$		0			0
$133$	0.647474	−	0.416106i	0.0561431	−	0.0360810i
$134$		0			0
$135$	3.66422	+	1.07591i	0.315366	+	0.0925997i
$136$		0			0
$137$	19.3075			1.64955			0.824775	−	0.565462i	$-0.191302\pi$
$137$	19.3075			1.64955			0.824775	+	0.565462i	$0.191302\pi$
$138$		0			0
$139$	−16.9937			−1.44138			−0.720692	−	0.693255i	$-0.756176\pi$
$139$	−16.9937			−1.44138			−0.720692	+	0.693255i	$0.756176\pi$
$140$		0			0
$141$	2.07789	+	0.610124i	0.174990	+	0.0513817i
$142$		0			0
$143$	13.7492	−	8.83608i	1.14977	−	0.738910i
$144$		0			0
$145$	0.672989	−	4.68074i	0.0558887	−	0.388714i
$146$		0			0
$147$	10.3219	+	6.63348i	0.851336	+	0.547120i
$148$		0			0
$149$	8.32099	+	18.2204i	0.681682	+	1.49268i	0.860851	+	0.508857i	$0.169932\pi$
$149$	8.32099	+	18.2204i	0.681682	+	1.49268i	−0.179169	+	0.983818i	$0.557341\pi$
$150$		0			0
$151$	0.517361	+	3.59832i	0.0421022	+	0.292827i	0.999984	+	0.00566439i	$0.00180304\pi$
$151$	0.517361	+	3.59832i	0.0421022	+	0.292827i	−0.957882	+	0.287163i	$0.907288\pi$
$152$		0			0
$153$	0.281499	−	0.0826556i	0.0227579	−	0.00668231i
$154$		0			0
$155$	−2.91128	+	3.35980i	−0.233840	+	0.269865i
$156$		0			0
$157$	−2.38983	−	2.75802i	−0.190730	−	0.220114i	0.652328	−	0.757937i	$-0.273792\pi$
$157$	−2.38983	−	2.75802i	−0.190730	−	0.220114i	−0.843058	+	0.537823i	$0.819247\pi$
$158$		0			0
$159$	3.63224	−	7.95349i	0.288055	−	0.630753i
$160$		0			0
$161$	0.210037	−	0.932588i	0.0165532	−	0.0734982i
$162$		0			0
$163$	9.98965	−	21.8743i	0.782450	−	1.71333i	0.0853500	−	0.996351i	$-0.472799\pi$
$163$	9.98965	−	21.8743i	0.782450	−	1.71333i	0.697099	−	0.716974i	$-0.254474\pi$
$164$		0			0
$165$	3.41897	+	3.94570i	0.266166	+	0.307172i
$166$		0			0
$167$	−9.38045	+	10.8256i	−0.725881	+	0.837711i	−0.992001	−	0.126228i	$-0.959713\pi$
$167$	−9.38045	+	10.8256i	−0.725881	+	0.837711i	0.266120	+	0.963940i	$0.414258\pi$
$168$		0			0
$169$	−3.91695	+	1.15012i	−0.301304	+	0.0884708i
$170$		0			0
$171$	−0.0590806	−	0.410915i	−0.00451801	−	0.0314234i
$172$		0			0
$173$	−4.31858	−	9.45638i	−0.328336	−	0.718955i	0.671419	−	0.741078i	$-0.265685\pi$
$173$	−4.31858	−	9.45638i	−0.328336	−	0.718955i	−0.999755	+	0.0221223i	$0.992958\pi$
$174$		0			0
$175$	−0.744367	−	0.478376i	−0.0562688	−	0.0361618i
$176$		0			0
$177$	−2.89696	+	20.1488i	−0.217749	+	1.51447i
$178$		0			0
$179$	−0.273115	+	0.175520i	−0.0204135	+	0.0131190i	−0.550808	−	0.834632i	$-0.685680\pi$
$179$	−0.273115	+	0.175520i	−0.0204135	+	0.0131190i	0.530394	+	0.847751i	$0.322044\pi$
$180$		0			0
$181$	−12.2935	−	3.60971i	−0.913772	−	0.268308i	−0.209144	−	0.977885i	$-0.567068\pi$
$181$	−12.2935	−	3.60971i	−0.913772	−	0.268308i	−0.704628	+	0.709577i	$0.748886\pi$
$182$		0			0
$183$	−21.9967			−1.62604
$184$		0			0
$185$	−6.02048			−0.442635
$186$		0			0
$187$	−10.3534	−	3.04005i	−0.757119	−	0.222310i
$188$		0			0
$189$	0.855017	−	0.549486i	0.0621933	−	0.0399692i
$190$		0			0
$191$	0.147662	−	1.02701i	0.0106844	−	0.0743119i	−0.983782	−	0.179370i	$-0.942594\pi$
$191$	0.147662	−	1.02701i	0.0106844	−	0.0743119i	0.994466	+	0.105059i	$0.0335030\pi$
$192$		0			0
$193$	−10.9520	−	7.03845i	−0.788345	−	0.506639i	0.0834483	−	0.996512i	$-0.473407\pi$
$193$	−10.9520	−	7.03845i	−0.788345	−	0.506639i	−0.871794	+	0.489873i	$0.837043\pi$
$194$		0			0
$195$	−2.26686	−	4.96372i	−0.162333	−	0.355460i
$196$		0			0
$197$	−1.72567	−	12.0023i	−0.122949	−	0.855131i	−0.954186	−	0.299213i	$-0.903276\pi$
$197$	−1.72567	−	12.0023i	−0.122949	−	0.855131i	0.831237	−	0.555918i	$-0.187633\pi$
$198$		0			0
$199$	−0.0473142	+	0.0138927i	−0.00335401	+	0.000984827i	−0.283409	−	0.958999i	$-0.591465\pi$
$199$	−0.0473142	+	0.0138927i	−0.00335401	+	0.000984827i	0.280055	+	0.959984i	$0.409647\pi$
$200$		0			0
$201$	−2.39025	+	2.75849i	−0.168595	+	0.194569i
$202$		0			0
$203$	−0.824166	−	0.951139i	−0.0578451	−	0.0667568i
$204$		0			0
$205$	−2.04088	+	4.46890i	−0.142541	+	0.312121i
$206$		0			0
$207$	−0.410504	−	0.312017i	−0.0285320	−	0.0216867i
$208$		0			0
$209$	−6.34286	+	13.8889i	−0.438745	+	0.960717i
$210$		0			0
$211$	−0.520031	−	0.600147i	−0.0358004	−	0.0413158i	0.737567	−	0.675274i	$-0.235975\pi$
$211$	−0.520031	−	0.600147i	−0.0358004	−	0.0413158i	−0.773367	+	0.633958i	$0.781429\pi$
$212$		0			0
$213$	9.96342	−	11.4984i	0.682682	−	0.787857i
$214$		0			0
$215$	−4.77594	+	1.40234i	−0.325716	+	0.0956389i
$216$		0			0
$217$	0.168381	+	1.17112i	0.0114305	+	0.0795006i
$218$		0			0
$219$	0.137125	+	0.300262i	0.00926604	+	0.0202898i
$220$		0			0
$221$	9.48781	+	6.09745i	0.638219	+	0.410159i
$222$		0			0
$223$	0.771523	−	5.36606i	0.0516650	−	0.359338i	−0.947546	−	0.319620i	$-0.896445\pi$
$223$	0.771523	−	5.36606i	0.0516650	−	0.359338i	0.999211	−	0.0397183i	$-0.0126460\pi$
$224$		0			0
$225$	−0.401501	+	0.258029i	−0.0267667	+	0.0172019i
$226$		0			0
$227$	2.71986	+	0.798622i	0.180523	+	0.0530064i	0.370745	−	0.928735i	$-0.379102\pi$
$227$	2.71986	+	0.798622i	0.180523	+	0.0530064i	−0.190222	+	0.981741i	$0.560921\pi$
$228$		0			0
$229$	3.78590			0.250179			0.125090	−	0.992145i	$-0.460078\pi$
$229$	3.78590			0.250179			0.125090	+	0.992145i	$0.460078\pi$
$230$		0			0
$231$	1.38949			0.0914215
$232$		0			0
$233$	14.6483	+	4.30114i	0.959645	+	0.281777i	0.723797	−	0.690013i	$-0.242395\pi$
$233$	14.6483	+	4.30114i	0.959645	+	0.281777i	0.235848	+	0.971790i	$0.424213\pi$
$234$		0			0
$235$	−0.774040	+	0.497445i	−0.0504928	+	0.0324497i
$236$		0			0
$237$	0.245798	−	1.70956i	0.0159663	−	0.111048i
$238$		0			0
$239$	1.02770	+	0.660464i	0.0664765	+	0.0427219i	0.573457	−	0.819236i	$-0.305602\pi$
$239$	1.02770	+	0.660464i	0.0664765	+	0.0427219i	−0.506980	+	0.861958i	$0.669238\pi$
$240$		0			0
$241$	−2.43354	−	5.32871i	−0.156758	−	0.343252i	0.814915	−	0.579580i	$-0.196783\pi$
$241$	−2.43354	−	5.32871i	−0.156758	−	0.343252i	−0.971673	+	0.236328i	$0.924056\pi$
$242$		0			0
$243$	−0.158937	−	1.10543i	−0.0101958	−	0.0709134i
$244$		0			0
$245$	−5.00184	+	1.46867i	−0.319556	+	0.0938300i
$246$		0			0
$247$	10.4508	−	12.0608i	0.664965	−	0.767411i
$248$		0			0
$249$	6.39948	+	7.38540i	0.405551	+	0.468031i
$250$		0			0
$251$	5.54841	−	12.1493i	0.350213	−	0.766859i	−0.649765	−	0.760135i	$-0.725133\pi$
$251$	5.54841	−	12.1493i	0.350213	−	0.766859i	0.999977	−	0.00672333i	$-0.00214012\pi$
$252$		0			0
$253$	6.49710	+	17.8168i	0.408469	+	1.12014i
$254$		0			0
$255$	−1.49664	+	3.27718i	−0.0937230	+	0.205225i
$256$		0			0
$257$	1.91135	+	2.20582i	0.119227	+	0.137595i	0.812225	−	0.583344i	$-0.198256\pi$
$257$	1.91135	+	2.20582i	0.119227	+	0.137595i	−0.692998	+	0.720939i	$0.743711\pi$
$258$		0			0
$259$	−1.04927	+	1.21093i	−0.0651987	+	0.0752433i
$260$		0			0
$261$	−0.651339	+	0.191250i	−0.0403169	+	0.0118381i
$262$		0			0
$263$	3.90184	+	27.1379i	0.240598	+	1.67339i	0.649150	+	0.760660i	$0.275125\pi$
$263$	3.90184	+	27.1379i	0.240598	+	1.67339i	−0.408552	+	0.912735i	$0.633966\pi$
$264$		0			0
$265$	1.54323	+	3.37919i	0.0947996	+	0.207582i
$266$		0			0
$267$	−25.1417	−	16.1576i	−1.53865	−	0.988830i
$268$		0			0
$269$	4.07708	−	28.3567i	0.248584	−	1.72894i	−0.357829	−	0.933787i	$-0.616483\pi$
$269$	4.07708	−	28.3567i	0.248584	−	1.72894i	0.606412	−	0.795150i	$-0.292608\pi$
$270$		0			0
$271$	−4.88049	+	3.13650i	−0.296469	+	0.190529i	−0.680416	−	0.732826i	$-0.738201\pi$
$271$	−4.88049	+	3.13650i	−0.296469	+	0.190529i	0.383947	+	0.923355i	$0.374564\pi$
$272$		0			0
$273$	−1.39345	−	0.409154i	−0.0843355	−	0.0247631i
$274$		0			0
$275$	17.5537			1.05853
$276$		0			0
$277$	22.6782			1.36260			0.681301	−	0.732004i	$-0.261415\pi$
$277$	22.6782			1.36260			0.681301	+	0.732004i	$0.261415\pi$
$278$		0			0
$279$	0.612329	+	0.179796i	0.0366592	+	0.0107641i
$280$		0			0
$281$	−16.2288	+	10.4296i	−0.968130	+	0.622180i	−0.926237	−	0.376943i	$-0.876975\pi$
$281$	−16.2288	+	10.4296i	−0.968130	+	0.622180i	−0.0418936	+	0.999122i	$0.513339\pi$
$282$		0			0
$283$	−2.85865	+	19.8823i	−0.169929	+	1.18188i	0.709098	+	0.705110i	$0.249102\pi$
$283$	−2.85865	+	19.8823i	−0.169929	+	1.18188i	−0.879027	+	0.476772i	$0.841807\pi$
$284$		0			0
$285$	4.28865	+	2.75615i	0.254038	+	0.163260i
$286$		0			0
$287$	0.543157	+	1.18935i	0.0320615	+	0.0702050i
$288$		0			0
$289$	1.35966	+	9.45661i	0.0799797	+	0.556271i
$290$		0			0
$291$	23.4237	−	6.87783i	1.37312	−	0.403186i
$292$		0			0
$293$	5.28180	−	6.09553i	0.308566	−	0.356104i	−0.580193	−	0.814479i	$-0.697023\pi$
$293$	5.28180	−	6.09553i	0.308566	−	0.356104i	0.888759	+	0.458375i	$0.151568\pi$
$294$		0			0
$295$	−5.66364	−	6.53619i	−0.329750	−	0.380552i
$296$		0			0
$297$	−8.37601	+	18.3409i	−0.486026	+	1.06425i
$298$		0			0
$299$	−1.26921	−	19.7809i	−0.0734004	−	1.14396i
$300$		0			0
$301$	−0.550310	+	1.20501i	−0.0317193	+	0.0694556i
$302$		0			0
$303$	4.35020	+	5.02040i	0.249912	+	0.288414i
$304$		0			0
$305$	6.12015	−	7.06303i	0.350439	−	0.404428i
$306$		0			0
$307$	9.54991	−	2.80411i	0.545042	−	0.160039i	0.00239127	−	0.999997i	$-0.499239\pi$
$307$	9.54991	−	2.80411i	0.545042	−	0.160039i	0.542651	+	0.839958i	$0.317421\pi$
$308$		0			0
$309$	−4.01655	−	27.9357i	−0.228494	−	1.58921i
$310$		0			0
$311$	13.2296	+	28.9688i	0.750182	+	1.64267i	0.766038	+	0.642795i	$0.222225\pi$
$311$	13.2296	+	28.9688i	0.750182	+	1.64267i	−0.0158562	+	0.999874i	$0.505047\pi$
$312$		0			0
$313$	−4.04969	−	2.60258i	−0.228902	−	0.147106i	0.421163	−	0.906985i	$-0.361622\pi$
$313$	−4.04969	−	2.60258i	−0.228902	−	0.147106i	−0.650065	+	0.759879i	$0.725258\pi$
$314$		0			0
$315$	0.00228429	−	0.0158876i	0.000128705	−	0.000895165i
$316$		0			0
$317$	12.2911	−	7.89904i	0.690340	−	0.443654i	−0.147867	−	0.989007i	$-0.547241\pi$
$317$	12.2911	−	7.89904i	0.690340	−	0.443654i	0.838207	+	0.545353i	$0.183604\pi$
$318$		0			0
$319$	23.9560	+	7.03413i	1.34128	+	0.393836i
$320$		0			0
$321$	−21.1904			−1.18273
$322$		0			0
$323$	−10.5364			−0.586259
$324$		0			0
$325$	−17.6038	−	5.16893i	−0.976480	−	0.286721i
$326$		0			0
$327$	−20.5034	+	13.1767i	−1.13384	+	0.728674i
$328$		0			0
$329$	−0.0348494	+	0.242383i	−0.00192131	+	0.0133630i
$330$		0			0
$331$	−6.05567	−	3.89174i	−0.332850	−	0.213909i	0.363531	−	0.931582i	$-0.381571\pi$
$331$	−6.05567	−	3.89174i	−0.332850	−	0.213909i	−0.696381	+	0.717673i	$0.745207\pi$
$332$		0			0
$333$	0.359022	+	0.786149i	0.0196743	+	0.0430807i
$334$		0			0
$335$	−0.220698	−	1.53499i	−0.0120580	−	0.0838655i
$336$		0			0
$337$	24.0331	−	7.05674i	1.30916	−	0.384405i	0.448593	−	0.893736i	$-0.351925\pi$
$337$	24.0331	−	7.05674i	1.30916	−	0.384405i	0.860571	+	0.509331i	$0.170107\pi$
$338$		0			0
$339$	−2.71721	+	3.13583i	−0.147579	+	0.170315i
$340$		0			0
$341$	−15.3709	−	17.7390i	−0.832382	−	0.960620i
$342$		0			0
$343$	−1.15597	+	2.53122i	−0.0624164	+	0.136673i
$344$		0			0
$345$	6.19686	−	1.30059i	0.333628	−	0.0700212i
$346$		0			0
$347$	−11.5366	+	25.2617i	−0.619320	+	1.35612i	0.296694	+	0.954973i	$0.404116\pi$
$347$	−11.5366	+	25.2617i	−0.619320	+	1.35612i	−0.916013	+	0.401148i	$0.868611\pi$
$348$		0			0
$349$	−17.4688	−	20.1600i	−0.935082	−	1.07914i	−0.996711	−	0.0810427i	$-0.974175\pi$
$349$	−17.4688	−	20.1600i	−0.935082	−	1.07914i	0.0616289	−	0.998099i	$-0.480370\pi$
$350$		0			0
$351$	13.8007	−	15.9268i	0.736625	−	0.850111i
$352$		0			0
$353$	−31.2815	+	9.18507i	−1.66494	+	0.488872i	−0.972559	−	0.232656i	$-0.925258\pi$
$353$	−31.2815	+	9.18507i	−1.66494	+	0.488872i	−0.692385	+	0.721528i	$0.743440\pi$
$354$		0			0
$355$	0.919952	+	6.39840i	0.0488260	+	0.339592i
$356$		0			0
$357$	0.398313	+	0.872184i	0.0210810	+	0.0461609i
$358$		0			0
$359$	−15.5338	−	9.98295i	−0.819841	−	0.526880i	0.0621938	−	0.998064i	$-0.480190\pi$
$359$	−15.5338	−	9.98295i	−0.819841	−	0.526880i	−0.882035	+	0.471184i	$0.843827\pi$
$360$		0			0
$361$	0.582201	−	4.04930i	0.0306422	−	0.213121i
$362$		0			0
$363$	−6.87663	+	4.41934i	−0.360930	+	0.231955i
$364$		0			0
$365$	−0.134565	−	0.0395118i	−0.00704344	−	0.00206814i
$366$		0			0
$367$	−1.97568			−0.103129			−0.0515647	−	0.998670i	$-0.516421\pi$
$367$	−1.97568			−0.103129			−0.0515647	+	0.998670i	$0.516421\pi$
$368$		0			0
$369$	0.705249			0.0367138
$370$		0			0
$371$	0.948631	+	0.278543i	0.0492504	+	0.0144612i
$372$		0			0
$373$	−25.3504	+	16.2917i	−1.31259	+	0.843552i	−0.994523	−	0.104515i	$-0.966671\pi$
$373$	−25.3504	+	16.2917i	−1.31259	+	0.843552i	−0.318070	+	0.948067i	$0.603035\pi$
$374$		0			0
$375$	1.77356	−	12.3354i	0.0915865	−	0.636998i
$376$		0			0
$377$	−21.9531	−	14.1084i	−1.13064	−	0.726620i
$378$		0			0
$379$	14.1117	+	30.9003i	0.724869	+	1.58724i	0.806952	+	0.590617i	$0.201116\pi$
$379$	14.1117	+	30.9003i	0.724869	+	1.58724i	−0.0820824	+	0.996626i	$0.526157\pi$
$380$		0			0
$381$	−2.30461	−	16.0289i	−0.118069	−	0.821185i
$382$		0			0
$383$	−14.1867	+	4.16559i	−0.724907	+	0.212852i	−0.623311	−	0.781974i	$-0.714213\pi$
$383$	−14.1867	+	4.16559i	−0.724907	+	0.212852i	−0.101596	+	0.994826i	$0.532395\pi$
$384$		0			0
$385$	−0.386597	+	0.446157i	−0.0197028	+	0.0227382i
$386$		0			0
$387$	0.467922	+	0.540011i	0.0237858	+	0.0274503i
$388$		0			0
$389$	5.64245	−	12.3552i	0.286084	−	0.626436i	−0.710964	−	0.703229i	$-0.751741\pi$
$389$	5.64245	−	12.3552i	0.286084	−	0.626436i	0.997047	+	0.0767934i	$0.0244682\pi$
$390$		0			0
$391$	−9.32121	+	9.18566i	−0.471394	+	0.464539i
$392$		0			0
$393$	−4.03133	+	8.82738i	−0.203354	+	0.445283i
$394$		0			0
$395$	0.480544	+	0.554577i	0.0241788	+	0.0279038i
$396$		0			0
$397$	8.89835	−	10.2692i	0.446595	−	0.515398i	−0.487159	−	0.873313i	$-0.661967\pi$
$397$	8.89835	−	10.2692i	0.446595	−	0.515398i	0.933754	+	0.357915i	$0.116512\pi$
$398$		0			0
$399$	1.30180	−	0.382242i	0.0651714	−	0.0191361i
$400$		0			0
$401$	0.282371	+	1.96393i	0.0141009	+	0.0980742i	0.995656	−	0.0931030i	$-0.0296786\pi$
$401$	0.282371	+	1.96393i	0.0141009	+	0.0980742i	−0.981556	+	0.191177i	$0.938769\pi$
$402$		0			0
$403$	10.1913	+	22.3158i	0.507664	+	1.11163i
$404$		0			0
$405$	5.86657	+	3.77022i	0.291512	+	0.187344i
$406$		0			0
$407$	4.52374	−	31.4633i	0.224233	−	1.55958i
$408$		0			0
$409$	28.7886	−	18.5013i	1.42350	−	0.914831i	0.423544	−	0.905875i	$-0.360786\pi$
$409$	28.7886	−	18.5013i	1.42350	−	0.914831i	0.999960	−	0.00895532i	$-0.00285061\pi$
$410$		0			0
$411$	32.6568	+	9.58891i	1.61084	+	0.472986i
$412$		0			0
$413$	−2.30173			−0.113261
$414$		0			0
$415$	−4.15194			−0.203811
$416$		0			0
$417$	−28.7432	−	8.43978i	−1.40756	−	0.413298i
$418$		0			0
$419$	−1.36373	+	0.876415i	−0.0666225	+	0.0428157i	−0.573528	−	0.819186i	$-0.694426\pi$
$419$	−1.36373	+	0.876415i	−0.0666225	+	0.0428157i	0.506906	+	0.862002i	$0.330789\pi$
$420$		0			0
$421$	−3.20128	+	22.2654i	−0.156021	+	1.08515i	0.749854	+	0.661604i	$0.230124\pi$
$421$	−3.20128	+	22.2654i	−0.156021	+	1.08515i	−0.905875	+	0.423546i	$0.860785\pi$
$422$		0			0
$423$	0.111115	+	0.0714090i	0.00540258	+	0.00347202i
$424$		0			0
$425$	5.03197	+	11.0185i	0.244086	+	0.534475i
$426$		0			0
$427$	−0.353974	−	2.46194i	−0.0171300	−	0.119142i
$428$		0			0
$429$	27.6439	−	8.11698i	1.33466	−	0.391892i
$430$		0			0
$431$	24.3589	−	28.1117i	1.17333	−	1.35409i	0.250855	−	0.968025i	$-0.419288\pi$
$431$	24.3589	−	28.1117i	1.17333	−	1.35409i	0.922471	−	0.386066i	$-0.126166\pi$
$432$		0			0
$433$	11.0521	+	12.7548i	0.531129	+	0.612955i	0.956382	−	0.292119i	$-0.0943605\pi$
$433$	11.0521	+	12.7548i	0.531129	+	0.612955i	−0.425253	+	0.905074i	$0.639815\pi$
$434$		0			0
$435$	3.46295	−	7.58281i	0.166036	−	0.363568i
$436$		0			0
$437$	10.9884	+	14.9051i	0.525648	+	0.713009i
$438$		0			0
$439$	5.24667	−	11.4886i	0.250410	−	0.548321i	−0.742128	−	0.670258i	$-0.766183\pi$
$439$	5.24667	−	11.4886i	0.250410	−	0.548321i	0.992538	+	0.121937i	$0.0389107\pi$
$440$		0			0
$441$	0.490055	+	0.565553i	0.0233359	+	0.0269311i
$442$		0			0
$443$	−6.76884	+	7.81166i	−0.321598	+	0.371143i	−0.893411	−	0.449240i	$-0.851695\pi$
$443$	−6.76884	+	7.81166i	−0.321598	+	0.371143i	0.571813	+	0.820384i	$0.306240\pi$
$444$		0			0
$445$	12.1833	−	3.57734i	0.577545	−	0.169582i
$446$		0			0
$447$	5.02516	+	34.9507i	0.237682	+	1.65311i
$448$		0			0
$449$	13.2761	+	29.0705i	0.626536	+	1.37192i	0.910669	+	0.413137i	$0.135567\pi$
$449$	13.2761	+	29.0705i	0.626536	+	1.37192i	−0.284133	+	0.958785i	$0.591706\pi$
$450$		0			0
$451$	−21.8211	−	14.0236i	−1.02752	−	0.660345i
$452$		0			0
$453$	−0.912011	+	6.34318i	−0.0428500	+	0.298028i
$454$		0			0
$455$	0.519077	−	0.333591i	0.0243347	−	0.0156390i
$456$		0			0
$457$	15.4562	+	4.53834i	0.723009	+	0.212294i	0.622476	−	0.782639i	$-0.286127\pi$
$457$	15.4562	+	4.53834i	0.723009	+	0.212294i	0.100533	+	0.994934i	$0.467945\pi$
$458$		0			0
$459$	−13.9137			−0.649437
$460$		0			0
$461$	16.7708			0.781095			0.390548	−	0.920583i	$-0.372286\pi$
$461$	16.7708			0.781095			0.390548	+	0.920583i	$0.372286\pi$
$462$		0			0
$463$	4.96682	+	1.45839i	0.230828	+	0.0677771i	0.395101	−	0.918638i	$-0.370710\pi$
$463$	4.96682	+	1.45839i	0.230828	+	0.0677771i	−0.164273	+	0.986415i	$0.552528\pi$
$464$		0			0
$465$	−6.59278	+	4.23692i	−0.305733	+	0.196483i
$466$		0			0
$467$	3.96774	−	27.5962i	0.183605	−	1.27700i	−0.664546	−	0.747247i	$-0.731375\pi$
$467$	3.96774	−	27.5962i	0.183605	−	1.27700i	0.848151	−	0.529754i	$-0.177716\pi$
$468$		0			0
$469$	−0.347203	−	0.223134i	−0.0160324	−	0.0103034i
$470$		0			0
$471$	−2.67244	−	5.85182i	−0.123139	−	0.269638i
$472$		0			0
$473$	−3.74009	−	26.0129i	−0.171970	−	1.19608i
$474$		0			0
$475$	16.4459	−	4.82895i	0.754589	−	0.221567i
$476$		0			0
$477$	0.349224	−	0.403026i	0.0159899	−	0.0184533i
$478$		0			0
$479$	−4.97644	−	5.74312i	−0.227379	−	0.262410i	0.630584	−	0.776121i	$-0.282816\pi$
$479$	−4.97644	−	5.74312i	−0.227379	−	0.262410i	−0.857963	+	0.513712i	$0.828270\pi$
$480$		0			0
$481$	−13.8015	+	30.2210i	−0.629293	+	1.37796i
$482$		0			0
$483$	0.818421	−	1.47307i	0.0372394	−	0.0670271i
$484$		0			0
$485$	−4.30875	+	9.43486i	−0.195650	+	0.428415i
$486$		0			0
$487$	13.6781	+	15.7854i	0.619815	+	0.715304i	0.975672	−	0.219236i	$-0.0703565\pi$
$487$	13.6781	+	15.7854i	0.619815	+	0.715304i	−0.355857	+	0.934540i	$0.615811\pi$
$488$		0			0
$489$	27.7603	−	32.0370i	1.25536	−	1.44877i
$490$		0			0
$491$	−37.3013	+	10.9527i	−1.68338	+	0.494286i	−0.976946	−	0.213488i	$-0.931518\pi$
$491$	−37.3013	+	10.9527i	−1.68338	+	0.494286i	−0.706439	+	0.707774i	$0.749699\pi$
$492$		0			0
$493$	2.45195	+	17.0537i	0.110430	+	0.768060i
$494$		0			0
$495$	0.132279	+	0.289651i	0.00594550	+	0.0130188i
$496$		0			0
$497$	1.44727	+	0.930105i	0.0649190	+	0.0417209i
$498$		0			0
$499$	1.71140	−	11.9031i	0.0766128	−	0.532854i	−0.914984	−	0.403489i	$-0.867797\pi$
$499$	1.71140	−	11.9031i	0.0766128	−	0.532854i	0.991597	−	0.129364i	$-0.0412937\pi$
$500$		0			0
$501$	−21.2426	+	13.6518i	−0.949051	+	0.609918i
$502$		0			0
$503$	−39.3913	−	11.5663i	−1.75637	−	0.515717i	−0.764685	−	0.644405i	$-0.777105\pi$
$503$	−39.3913	−	11.5663i	−1.75637	−	0.515717i	−0.991685	+	0.128688i	$0.958923\pi$
$504$		0			0
$505$	−2.82238			−0.125594
$506$		0			0
$507$	−7.19636			−0.319602
$508$		0			0
$509$	−0.131914	−	0.0387334i	−0.00584698	−	0.00171683i	0.278808	−	0.960347i	$-0.410061\pi$
$509$	−0.131914	−	0.0387334i	−0.00584698	−	0.00171683i	−0.284655	+	0.958630i	$0.591879\pi$
$510$		0			0
$511$	−0.0313996	+	0.0201793i	−0.00138904	+	0.000892680i
$512$		0			0
$513$	−2.80190	+	19.4877i	−0.123707	+	0.860401i
$514$		0			0
$515$	10.0875	+	6.48287i	0.444510	+	0.285669i
$516$		0			0
$517$	−2.01806	−	4.41894i	−0.0887542	−	0.194345i
$518$		0			0
$519$	−2.60805	−	18.1394i	−0.114481	−	0.796231i
$520$		0			0
$521$	3.29022	−	0.966095i	0.144147	−	0.0423254i	−0.208863	−	0.977945i	$-0.566976\pi$
$521$	3.29022	−	0.966095i	0.144147	−	0.0423254i	0.353010	+	0.935620i	$0.385158\pi$
$522$		0			0
$523$	1.97888	−	2.28375i	0.0865304	−	0.0998614i	−0.710833	−	0.703361i	$-0.751682\pi$
$523$	1.97888	−	2.28375i	0.0865304	−	0.0998614i	0.797364	+	0.603499i	$0.206227\pi$
$524$		0			0
$525$	−1.02145	−	1.17881i	−0.0445796	−	0.0514476i
$526$		0			0
$527$	6.72855	−	14.7335i	0.293100	−	0.641800i
$528$		0			0
$529$	22.7155	+	3.60636i	0.987631	+	0.156798i
$530$		0			0
$531$	−0.515747	+	1.12933i	−0.0223815	+	0.0490087i
$532$		0			0
$533$	17.7540	+	20.4892i	0.769009	+	0.887484i
$534$		0			0
$535$	5.89580	−	6.80412i	0.254898	−	0.294168i
$536$		0			0
$537$	−0.549119	+	0.161236i	−0.0236962	+	0.00695784i
$538$		0			0
$539$	−3.91700	−	27.2433i	−0.168717	−	1.17345i
$540$		0			0
$541$	−10.6436	−	23.3063i	−0.457606	−	1.00202i	−0.988027	−	0.154283i	$-0.950693\pi$
$541$	−10.6436	−	23.3063i	−0.457606	−	1.00202i	0.530420	−	0.847735i	$-0.322034\pi$
$542$		0			0
$543$	−19.0007	−	12.2110i	−0.815397	−	0.524024i
$544$		0			0
$545$	1.47368	−	10.2497i	0.0631256	−	0.439048i
$546$		0			0
$547$	−15.3761	+	9.88165i	−0.657436	+	0.422509i	−0.826377	−	0.563118i	$-0.809602\pi$
$547$	−15.3761	+	9.88165i	−0.657436	+	0.422509i	0.168940	+	0.985626i	$0.445965\pi$
$548$		0			0
$549$	−1.28725	−	0.377970i	−0.0549385	−	0.0161314i
$550$		0			0
$551$	24.3793			1.03859
$552$		0			0
$553$	0.195295			0.00830480
$554$		0			0
$555$	−10.1831	−	2.99003i	−0.432248	−	0.126920i
$556$		0			0
$557$	−26.7412	+	17.1855i	−1.13306	+	0.728175i	−0.966197	−	0.257805i	$-0.917001\pi$
$557$	−26.7412	+	17.1855i	−1.13306	+	0.728175i	−0.166865	+	0.985980i	$0.553365\pi$
$558$		0			0
$559$	−3.90911	+	27.1885i	−0.165338	+	1.14995i
$560$		0			0
$561$	−16.0021	−	10.2839i	−0.675609	−	0.434187i
$562$		0			0
$563$	15.3961	+	33.7127i	0.648868	+	1.42082i	0.892542	+	0.450965i	$0.148920\pi$
$563$	15.3961	+	33.7127i	0.648868	+	1.42082i	−0.243674	+	0.969857i	$0.578353\pi$
$564$		0			0
$565$	−0.250888	−	1.74496i	−0.0105549	−	0.0734111i
$566$		0			0
$567$	1.78077	−	0.522881i	0.0747853	−	0.0219589i
$568$		0			0
$569$	−23.8546	+	27.5297i	−1.00004	+	1.15411i	−0.0119947	+	0.999928i	$0.503818\pi$
$569$	−23.8546	+	27.5297i	−1.00004	+	1.15411i	−0.988043	+	0.154177i	$0.950727\pi$
$570$		0			0
$571$	7.08281	+	8.17400i	0.296406	+	0.342071i	0.884345	−	0.466835i	$-0.154606\pi$
$571$	7.08281	+	8.17400i	0.296406	+	0.342071i	−0.587938	+	0.808906i	$0.700060\pi$
$572$		0			0
$573$	0.759813	−	1.66376i	0.0317417	−	0.0695045i
$574$		0			0
$575$	10.3393	−	18.6096i	0.431178	−	0.776075i
$576$		0			0
$577$	7.20753	−	15.7823i	0.300053	−	0.657025i	−0.698213	−	0.715890i	$-0.746021\pi$
$577$	7.20753	−	15.7823i	0.300053	−	0.657025i	0.998266	+	0.0588653i	$0.0187482\pi$
$578$		0			0
$579$	−15.0288	−	17.3441i	−0.624575	−	0.720798i
$580$		0			0
$581$	−0.723616	+	0.835098i	−0.0300207	+	0.0346457i
$582$		0			0
$583$	−18.8193	+	5.52586i	−0.779418	+	0.228858i
$584$		0			0
$585$	−0.0473647	−	0.329429i	−0.00195829	−	0.0136202i
$586$		0			0
$587$	−4.34288	−	9.50958i	−0.179250	−	0.392502i	0.798584	−	0.601883i	$-0.205583\pi$
$587$	−4.34288	−	9.50958i	−0.179250	−	0.392502i	−0.977834	+	0.209380i	$0.932855\pi$
$588$		0			0
$589$	−19.2808	−	12.3910i	−0.794452	−	0.510563i
$590$		0			0
$591$	3.04204	−	21.1579i	0.125133	−	0.870319i
$592$		0			0
$593$	4.38117	−	2.81561i	0.179913	−	0.115623i	−0.447584	−	0.894242i	$-0.647716\pi$
$593$	4.38117	−	2.81561i	0.179913	−	0.115623i	0.627498	+	0.778619i	$0.284079\pi$
$594$		0			0
$595$	−0.390876	−	0.114772i	−0.0160244	−	0.00470518i
$596$		0			0
$597$	−0.0869273			−0.00355770
$598$		0			0
$599$	−27.2177			−1.11208			−0.556042	−	0.831154i	$-0.687681\pi$
$599$	−27.2177			−1.11208			−0.556042	+	0.831154i	$0.687681\pi$
$600$		0			0
$601$	−3.92547	−	1.15262i	−0.160123	−	0.0470164i	0.200689	−	0.979655i	$-0.435682\pi$
$601$	−3.92547	−	1.15262i	−0.160123	−	0.0470164i	−0.360812	+	0.932639i	$0.617500\pi$
$602$		0			0
$603$	−0.187277	+	0.120355i	−0.00762649	+	0.00490125i
$604$		0			0
$605$	0.494259	−	3.43765i	0.0200945	−	0.139760i
$606$		0			0
$607$	−8.53923	−	5.48783i	−0.346597	−	0.222744i	0.355747	−	0.934582i	$-0.384227\pi$
$607$	−8.53923	−	5.48783i	−0.346597	−	0.222744i	−0.702343	+	0.711838i	$0.747863\pi$
$608$		0			0
$609$	−0.921626	−	2.01808i	−0.0373462	−	0.0817767i
$610$		0			0
$611$	0.722600	+	5.02579i	0.0292333	+	0.203322i
$612$		0			0
$613$	−3.28162	+	0.963572i	−0.132544	+	0.0389183i	−0.347332	−	0.937742i	$-0.612912\pi$
$613$	−3.28162	+	0.963572i	−0.132544	+	0.0389183i	0.214788	+	0.976661i	$0.431094\pi$
$614$		0			0
$615$	−5.67140	+	6.54515i	−0.228693	+	0.263926i
$616$		0			0
$617$	9.88661	+	11.4098i	0.398020	+	0.459340i	0.919016	−	0.394219i	$-0.128985\pi$
$617$	9.88661	+	11.4098i	0.398020	+	0.459340i	−0.520996	+	0.853559i	$0.674439\pi$
$618$		0			0
$619$	9.50970	−	20.8233i	0.382227	−	0.836961i	−0.616540	−	0.787323i	$-0.711466\pi$
$619$	9.50970	−	20.8233i	0.382227	−	0.836961i	0.998767	−	0.0496373i	$-0.0158065\pi$
$620$		0			0
$621$	14.5107	+	19.6829i	0.582294	+	0.789846i
$622$		0			0
$623$	1.40383	−	3.07396i	0.0562432	−	0.123155i
$624$		0			0
$625$	−11.0674	−	12.7725i	−0.442697	−	0.510900i
$626$		0			0
$627$	−17.6262	+	20.3417i	−0.703922	+	0.812369i
$628$		0			0
$629$	21.0464	−	6.17977i	0.839174	−	0.246404i
$630$		0			0
$631$	4.41104	+	30.6795i	0.175601	+	1.22133i	0.866796	+	0.498662i	$0.166175\pi$
$631$	4.41104	+	30.6795i	0.175601	+	1.22133i	−0.691196	+	0.722668i	$0.742916\pi$
$632$		0			0
$633$	−0.581525	−	1.27336i	−0.0231136	−	0.0506116i
$634$		0			0
$635$	5.78800	+	3.71972i	0.229690	+	0.147613i
$636$		0			0
$637$	−4.09402	+	28.4745i	−0.162211	+	1.12820i
$638$		0			0
$639$	0.780638	−	0.501685i	0.0308815	−	0.0198464i
$640$		0			0
$641$	−27.7622	−	8.15172i	−1.09654	−	0.321974i	−0.317064	−	0.948404i	$-0.602697\pi$
$641$	−27.7622	−	8.15172i	−1.09654	−	0.321974i	−0.779477	+	0.626431i	$0.784515\pi$
$642$		0			0
$643$	−9.38054			−0.369933			−0.184966	−	0.982745i	$-0.559218\pi$
$643$	−9.38054			−0.369933			−0.184966	+	0.982745i	$0.559218\pi$
$644$		0			0
$645$	−8.77452			−0.345496
$646$		0			0
$647$	3.69096	+	1.08376i	0.145106	+	0.0426071i	0.353479	−	0.935442i	$-0.384999\pi$
$647$	3.69096	+	1.08376i	0.145106	+	0.0426071i	−0.208373	+	0.978049i	$0.566817\pi$
$648$		0			0
$649$	38.4140	−	24.6872i	1.50788	−	0.969057i
$650$		0			0
$651$	−0.296825	+	2.06446i	−0.0116335	+	0.0809126i
$652$		0			0
$653$	12.9455	+	8.31956i	0.506596	+	0.325569i	0.768850	−	0.639429i	$-0.220829\pi$
$653$	12.9455	+	8.31956i	0.506596	+	0.325569i	−0.262254	+	0.964999i	$0.584466\pi$
$654$		0			0
$655$	−1.71279	−	3.75048i	−0.0669242	−	0.146543i
$656$		0			0
$657$	0.00286515	+	0.0199276i	0.000111780	+	0.000777448i
$658$		0			0
$659$	47.3276	−	13.8966i	1.84362	−	0.541336i	0.843632	−	0.536923i	$-0.180413\pi$
$659$	47.3276	−	13.8966i	1.84362	−	0.541336i	0.999990	−	0.00441364i	$-0.00140491\pi$
$660$		0			0
$661$	−9.56387	+	11.0373i	−0.371991	+	0.429301i	−0.910621	−	0.413241i	$-0.864397\pi$
$661$	−9.56387	+	11.0373i	−0.371991	+	0.429301i	0.538630	+	0.842542i	$0.318942\pi$
$662$		0			0
$663$	13.0195	+	15.0253i	0.505636	+	0.583535i
$664$		0			0
$665$	−0.239463	+	0.524352i	−0.00928599	+	0.0203335i
$666$		0			0
$667$	21.5676	−	21.2540i	0.835102	−	0.822958i
$668$		0			0
$669$	3.96997	−	8.69303i	0.153488	−	0.336092i
$670$		0			0
$671$	32.3130	+	37.2912i	1.24743	+	1.43961i
$672$		0			0
$673$	28.2862	−	32.6440i	1.09035	−	1.25833i	0.126479	−	0.991969i	$-0.459632\pi$
$673$	28.2862	−	32.6440i	1.09035	−	1.25833i	0.963873	−	0.266363i	$-0.0858221\pi$
$674$		0			0
$675$	21.7175	−	6.37683i	0.835907	−	0.245444i
$676$		0			0
$677$	2.07110	+	14.4048i	0.0795988	+	0.553622i	0.990127	+	0.140175i	$0.0447664\pi$
$677$	2.07110	+	14.4048i	0.0795988	+	0.553622i	−0.910528	+	0.413448i	$0.864325\pi$
$678$		0			0
$679$	1.14673	+	2.51098i	0.0440073	+	0.0963626i
$680$		0			0
$681$	4.20376	+	2.70159i	0.161088	+	0.103525i
$682$		0			0
$683$	0.994794	−	6.91895i	0.0380647	−	0.264746i	−0.961898	−	0.273410i	$-0.911849\pi$
$683$	0.994794	−	6.91895i	0.0380647	−	0.264746i	0.999962	+	0.00866340i	$0.00275768\pi$
$684$		0			0
$685$	−12.1651	+	7.81801i	−0.464803	+	0.298711i
$686$		0			0
$687$	6.40350	+	1.88024i	0.244309	+	0.0717355i
$688$		0			0
$689$	20.5002			0.780996
$690$		0			0
$691$	−22.5417			−0.857526			−0.428763	−	0.903417i	$-0.641050\pi$
$691$	−22.5417			−0.857526			−0.428763	+	0.903417i	$0.641050\pi$
$692$		0			0
$693$	0.0813128	+	0.0238756i	0.00308882	+	0.000906959i
$694$		0			0
$695$	10.7072	−	6.88110i	0.406147	−	0.261015i
$696$		0			0
$697$	2.54735	−	17.7172i	0.0964878	−	0.671088i
$698$		0			0
$699$	22.6402	+	14.5500i	0.856331	+	0.550331i
$700$		0			0
$701$	19.7188	+	43.1781i	0.744768	+	1.63082i	0.775548	+	0.631289i	$0.217474\pi$
$701$	19.7188	+	43.1781i	0.744768	+	1.63082i	−0.0307792	+	0.999526i	$0.509799\pi$
$702$		0			0
$703$	−4.41718	−	30.7221i	−0.166597	−	1.15871i
$704$		0			0
$705$	−1.55627	+	0.456962i	−0.0586125	+	0.0172102i
$706$		0			0
$707$	−0.491895	+	0.567677i	−0.0184996	+	0.0213497i
$708$		0			0
$709$	−4.65401	−	5.37101i	−0.174785	−	0.201713i	0.661597	−	0.749859i	$-0.269879\pi$
$709$	−4.65401	−	5.37101i	−0.174785	−	0.201713i	−0.836382	+	0.548147i	$0.815333\pi$
$710$		0			0
$711$	0.0437596	−	0.0958202i	0.00164111	−	0.00359354i
$712$		0			0
$713$	−27.8597	+	5.84715i	−1.04336	+	0.218977i
$714$		0			0
$715$	−5.08505	+	11.1347i	−0.190170	+	0.416414i
$716$		0			0
$717$	1.41025	+	1.62752i	0.0526667	+	0.0607807i
$718$		0			0
$719$	−20.8656	+	24.0801i	−0.778154	+	0.898037i	−0.996975	−	0.0777277i	$-0.975234\pi$
$719$	−20.8656	+	24.0801i	−0.778154	+	0.898037i	0.218821	+	0.975765i	$0.429779\pi$
$720$		0			0
$721$	3.06202	−	0.899091i	0.114036	−	0.0334839i
$722$		0			0
$723$	−1.46965	−	10.2216i	−0.0546568	−	0.380146i
$724$		0			0
$725$	−11.6431	−	25.4948i	−0.432413	−	0.946853i
$726$		0			0
$727$	30.6547	+	19.7006i	1.13692	+	0.730655i	0.966993	−	0.254802i	$-0.0820103\pi$
$727$	30.6547	+	19.7006i	1.13692	+	0.730655i	0.169928	+	0.985457i	$0.445647\pi$
$728$		0			0
$729$	−3.69510	+	25.7000i	−0.136855	+	0.951851i
$730$		0			0
$731$	15.2562	−	9.80459i	0.564272	−	0.362636i
$732$		0			0
$733$	1.19047	+	0.349555i	0.0439712	+	0.0129111i	0.303644	−	0.952786i	$-0.401797\pi$
$733$	1.19047	+	0.349555i	0.0439712	+	0.0129111i	−0.259673	+	0.965697i	$0.583615\pi$
$734$		0			0
$735$	−9.18955			−0.338962
$736$		0			0
$737$	8.18775			0.301600
$738$		0			0
$739$	−32.7209	−	9.60774i	−1.20366	−	0.353426i	−0.382408	−	0.923993i	$-0.624905\pi$
$739$	−32.7209	−	9.60774i	−1.20366	−	0.353426i	−0.821251	+	0.570567i	$0.806723\pi$
$740$		0			0
$741$	23.6664	−	15.2095i	0.869407	−	0.558734i
$742$		0			0
$743$	4.57221	−	31.8004i	0.167738	−	1.16664i	−0.715807	−	0.698298i	$-0.753941\pi$
$743$	4.57221	−	31.8004i	0.167738	−	1.16664i	0.883545	−	0.468346i	$-0.155150\pi$
$744$		0			0
$745$	−12.6206	−	8.11080i	−0.462385	−	0.297157i
$746$		0			0
$747$	0.247595	+	0.542157i	0.00905901	+	0.0198365i
$748$		0			0
$749$	−0.340998	−	2.37170i	−0.0124598	−	0.0866599i
$750$		0			0
$751$	−50.6689	+	14.8777i	−1.84894	+	0.542897i	−0.849042	+	0.528325i	$0.822820\pi$
$751$	−50.6689	+	14.8777i	−1.84894	+	0.542897i	−0.999894	+	0.0145711i	$0.995362\pi$
$752$		0			0
$753$	15.4185	−	17.7939i	0.561881	−	0.648446i
$754$		0			0
$755$	−1.78301	−	2.05770i	−0.0648904	−	0.0748875i
$756$		0			0
$757$	1.09081	−	2.38854i	0.0396461	−	0.0868129i	−0.888773	−	0.458348i	$-0.848441\pi$
$757$	1.09081	−	2.38854i	0.0396461	−	0.0868129i	0.928419	+	0.371535i	$0.121169\pi$
$758$		0			0
$759$	2.14064	+	33.3623i	0.0777005	+	1.21097i
$760$		0			0
$761$	0.934686	−	2.04668i	0.0338823	−	0.0741920i	−0.891934	−	0.452165i	$-0.850652\pi$
$761$	0.934686	−	2.04668i	0.0338823	−	0.0741920i	0.925816	+	0.377973i	$0.123379\pi$
$762$		0			0
$763$	−1.80472	−	2.08276i	−0.0653354	−	0.0754010i
$764$		0			0
$765$	−0.143895	+	0.166064i	−0.00520254	+	0.00600405i
$766$		0			0
$767$	−45.7931	+	13.4461i	−1.65349	+	0.485510i
$768$		0			0
$769$	−4.78019	−	33.2470i	−0.172378	−	1.19892i	−0.873841	−	0.486211i	$-0.838379\pi$
$769$	−4.78019	−	33.2470i	−0.172378	−	1.19892i	0.701463	−	0.712706i	$-0.252531\pi$
$770$		0			0
$771$	2.13738	+	4.68020i	0.0769757	+	0.168553i
$772$		0			0
$773$	−0.00440295	−	0.00282961i	−0.000158363	−	0.000101774i	0.540562	−	0.841304i	$-0.318212\pi$
$773$	−0.00440295	−	0.00282961i	−0.000158363	−	0.000101774i	−0.540720	+	0.841203i	$0.681848\pi$
$774$		0			0
$775$	−3.74985	+	26.0808i	−0.134699	+	0.936849i
$776$		0			0
$777$	−2.37615	+	1.52706i	−0.0852438	+	0.0547828i
$778$		0			0
$779$	−24.3019	−	7.13568i	−0.870705	−	0.255662i
$780$		0			0
$781$	−34.1295			−1.22125
$782$		0			0
$783$	32.1939			1.15052
$784$		0			0
$785$	2.62254	+	0.770048i	0.0936025	+	0.0274842i
$786$		0			0
$787$	−19.2968	+	12.4013i	−0.687858	+	0.442060i	−0.837324	−	0.546707i	$-0.815881\pi$
$787$	−19.2968	+	12.4013i	−0.687858	+	0.442060i	0.149466	+	0.988767i	$0.452245\pi$
$788$		0			0
$789$	−6.87822	+	47.8391i	−0.244871	+	1.70312i
$790$		0			0
$791$	−0.394698	−	0.253657i	−0.0140338	−	0.00901899i
$792$		0			0
$793$	−21.4243	−	46.9127i	−0.760799	−	1.66592i
$794$		0			0
$795$	0.931974	+	6.48202i	0.0330537	+	0.229894i
$796$		0			0
$797$	−21.3480	+	6.26833i	−0.756184	+	0.222036i	−0.637029	−	0.770840i	$-0.719837\pi$
$797$	−21.3480	+	6.26833i	−0.756184	+	0.222036i	−0.119155	+	0.992876i	$0.538019\pi$
$798$		0			0
$799$	2.19528	−	2.53348i	0.0776633	−	0.0896282i
$800$		0			0
$801$	−1.19366	−	1.37756i	−0.0421759	−	0.0486736i
$802$		0			0
$803$	0.307601	−	0.673552i	0.0108550	−	0.0237691i
$804$		0			0
$805$	0.245287	+	0.672644i	0.00864522	+	0.0237076i
$806$		0			0
$807$	20.9791	−	45.9379i	0.738500	−	1.61709i
$808$		0			0
$809$	−6.53840	−	7.54571i	−0.229878	−	0.265293i	0.629079	−	0.777342i	$-0.283432\pi$
$809$	−6.53840	−	7.54571i	−0.229878	−	0.265293i	−0.858957	+	0.512048i	$0.828887\pi$
$810$		0			0
$811$	−0.915373	+	1.05640i	−0.0321431	+	0.0370951i	−0.771593	−	0.636116i	$-0.780540\pi$
$811$	−0.915373	+	1.05640i	−0.0321431	+	0.0370951i	0.739450	+	0.673211i	$0.235085\pi$
$812$		0			0
$813$	−9.81262	+	2.88125i	−0.344144	+	0.101050i
$814$		0			0
$815$	2.56319	+	17.8273i	0.0897845	+	0.624465i
$816$		0			0
$817$	−10.6601	−	23.3424i	−0.372950	−	0.816648i
$818$		0			0
$819$	−0.0745144	−	0.0478875i	−0.00260374	−	0.00167332i
$820$		0			0
$821$	2.18608	−	15.2045i	0.0762947	−	0.530641i	−0.915452	−	0.402427i	$-0.868167\pi$
$821$	2.18608	−	15.2045i	0.0762947	−	0.530641i	0.991747	−	0.128214i	$-0.0409243\pi$
$822$		0			0
$823$	−10.0399	+	6.45226i	−0.349970	+	0.224912i	−0.703801	−	0.710398i	$-0.748515\pi$
$823$	−10.0399	+	6.45226i	−0.349970	+	0.224912i	0.353831	+	0.935309i	$0.384879\pi$
$824$		0			0
$825$	29.6904	+	8.71789i	1.03369	+	0.303518i
$826$		0			0
$827$	36.6154			1.27324			0.636621	−	0.771177i	$-0.280332\pi$
$827$	36.6154			1.27324			0.636621	+	0.771177i	$0.280332\pi$
$828$		0			0
$829$	−28.4161			−0.986933			−0.493467	−	0.869765i	$-0.664270\pi$
$829$	−28.4161			−0.986933			−0.493467	+	0.869765i	$0.664270\pi$
$830$		0			0
$831$	38.3581	+	11.2630i	1.33063	+	0.390708i
$832$		0			0
$833$	15.9779	−	10.2683i	0.553600	−	0.355777i
$834$		0			0
$835$	1.52682	−	10.6192i	0.0528377	−	0.367494i
$836$		0			0
$837$	−25.4611	−	16.3629i	−0.880066	−	0.565584i
$838$		0			0
$839$	−4.79384	−	10.4970i	−0.165502	−	0.362398i	0.808651	−	0.588289i	$-0.200198\pi$
$839$	−4.79384	−	10.4970i	−0.165502	−	0.362398i	−0.974153	+	0.225891i	$0.927471\pi$
$840$		0			0
$841$	−1.54625	−	10.7544i	−0.0533189	−	0.370841i
$842$		0			0
$843$	−32.6294	+	9.58084i	−1.12381	+	0.329982i
$844$		0			0
$845$	2.00224	−	2.31071i	0.0688793	−	0.0794910i
$846$		0			0
$847$	−0.605287	−	0.698539i	−0.0207979	−	0.0240021i
$848$		0			0
$849$	−14.7095	+	32.2094i	−0.504830	+	1.10542i
$850$		0			0
$851$	−30.6915	−	23.3280i	−1.05209	−	0.799675i
$852$		0			0
$853$	2.95257	−	6.46524i	0.101094	−	0.221365i	−0.852326	−	0.523011i	$-0.824809\pi$
$853$	2.95257	−	6.46524i	0.101094	−	0.221365i	0.953420	+	0.301646i	$0.0975359\pi$
$854$		0			0
$855$	0.203613	+	0.234982i	0.00696342	+	0.00803621i
$856$		0			0
$857$	−27.3112	+	31.5188i	−0.932932	+	1.07666i	0.0639652	+	0.997952i	$0.479625\pi$
$857$	−27.3112	+	31.5188i	−0.932932	+	1.07666i	−0.996898	+	0.0787093i	$0.974920\pi$
$858$		0			0
$859$	47.3563	−	13.9051i	1.61578	−	0.474435i	0.655898	−	0.754849i	$-0.272290\pi$
$859$	47.3563	−	13.9051i	1.61578	−	0.474435i	0.959879	+	0.280415i	$0.0904719\pi$
$860$		0			0
$861$	0.328020	+	2.28143i	0.0111789	+	0.0777508i
$862$		0			0
$863$	9.42020	+	20.6274i	0.320667	+	0.702163i	0.999483	−	0.0321451i	$-0.0102339\pi$
$863$	9.42020	+	20.6274i	0.320667	+	0.702163i	−0.678816	+	0.734308i	$0.737507\pi$
$864$		0			0
$865$	6.55010	+	4.20949i	0.222710	+	0.143127i
$866$		0			0
$867$	−2.39682	+	16.6703i	−0.0814003	+	0.566151i
$868$		0			0
$869$	−3.25932	+	2.09463i	−0.110565	+	0.0710556i
$870$		0			0
$871$	−8.21111	−	2.41100i	−0.278223	−	0.0816936i
$872$		0			0
$873$	1.48894			0.0503930
$874$		0			0
$875$	1.40916			0.0476383
$876$		0			0
$877$	14.2666	+	4.18907i	0.481751	+	0.141455i	0.513585	−	0.858038i	$-0.328317\pi$
$877$	14.2666	+	4.18907i	0.481751	+	0.141455i	−0.0318350	+	0.999493i	$0.510135\pi$
$878$		0			0
$879$	11.9610	−	7.68686i	0.403434	−	0.259271i
$880$		0			0
$881$	5.39621	−	37.5314i	0.181803	−	1.26447i	−0.670694	−	0.741734i	$-0.734004\pi$
$881$	5.39621	−	37.5314i	0.181803	−	1.26447i	0.852497	−	0.522732i	$-0.175087\pi$
$882$		0			0
$883$	25.1987	+	16.1942i	0.848003	+	0.544978i	0.890951	−	0.454099i	$-0.150039\pi$
$883$	25.1987	+	16.1942i	0.848003	+	0.544978i	−0.0429485	+	0.999077i	$0.513675\pi$
$884$		0			0
$885$	−6.33338	−	13.8682i	−0.212894	−	0.466174i
$886$		0			0
$887$	3.99431	+	27.7810i	0.134116	+	0.932795i	0.940110	+	0.340872i	$0.110722\pi$
$887$	3.99431	+	27.7810i	0.134116	+	0.932795i	−0.805994	+	0.591924i	$0.798369\pi$
$888$		0			0
$889$	1.75692	−	0.515878i	0.0589252	−	0.0173020i
$890$		0			0
$891$	−24.1114	+	27.8260i	−0.807762	+	0.932207i
$892$		0			0
$893$	−3.10634	−	3.58490i	−0.103950	−	0.119964i
$894$		0			0
$895$	0.101009	−	0.221180i	0.00337637	−	0.00739323i
$896$		0			0
$897$	7.67726	−	34.0878i	0.256336	−	1.13816i
$898$		0			0
$899$	−15.5687	+	34.0906i	−0.519244	+	1.13699i
$900$		0			0
$901$	−8.86339	−	10.2289i	−0.295282	−	0.340774i
$902$		0			0
$903$	−1.52926	+	1.76486i	−0.0508905	+	0.0587307i
$904$		0			0
$905$	9.20744	−	2.70355i	0.306066	−	0.0898690i
$906$		0			0
$907$	−3.27443	−	22.7742i	−0.108726	−	0.756204i	−0.969123	−	0.246579i	$-0.920693\pi$
$907$	−3.27443	−	22.7742i	−0.108726	−	0.756204i	0.860397	−	0.509624i	$-0.170216\pi$
$908$		0			0
$909$	0.168308	+	0.368543i	0.00558243	+	0.0122238i
$910$		0			0
$911$	−1.52588	−	0.980622i	−0.0505546	−	0.0324894i	0.515119	−	0.857118i	$-0.327748\pi$
$911$	−1.52588	−	0.980622i	−0.0505546	−	0.0324894i	−0.565674	+	0.824629i	$0.691384\pi$
$912$		0			0
$913$	3.11973	−	21.6982i	0.103248	−	0.718106i
$914$		0			0
$915$	13.8595	−	8.90694i	0.458180	−	0.294454i
$916$		0			0
$917$	−1.05286	−	0.309148i	−0.0347686	−	0.0102090i
$918$		0			0
$919$	−20.8392			−0.687421			−0.343711	−	0.939076i	$-0.611684\pi$
$919$	−20.8392			−0.687421			−0.343711	+	0.939076i	$0.611684\pi$
$920$		0			0
$921$	17.5454			0.578142
$922$		0			0
$923$	34.2269	+	10.0499i	1.12659	+	0.330798i
$924$		0			0
$925$	−30.0183	+	19.2916i	−0.986997	+	0.634304i
$926$		0			0
$927$	0.244972	−	1.70382i	0.00804593	−	0.0559607i
$928$		0			0
$929$	42.6229	+	27.3921i	1.39841	+	0.898705i	0.999830	−	0.0184284i	$-0.00586627\pi$
$929$	42.6229	+	27.3921i	1.39841	+	0.898705i	0.398581	+	0.917133i	$0.369503\pi$
$930$		0			0
$931$	−11.1643	−	24.4465i	−0.365897	−	0.801202i
$932$		0			0
$933$	7.98953	+	55.5684i	0.261566	+	1.81923i
$934$		0			0
$935$	7.75438	−	2.27689i	0.253595	−	0.0744623i
$936$		0			0
$937$	−9.51089	+	10.9762i	−0.310707	+	0.358575i	−0.889529	−	0.456879i	$-0.848967\pi$
$937$	−9.51089	+	10.9762i	−0.310707	+	0.358575i	0.578822	+	0.815454i	$0.303513\pi$
$938$		0			0
$939$	−5.55713	−	6.41327i	−0.181350	−	0.209289i
$940$		0			0
$941$	5.76599	−	12.6258i	0.187966	−	0.411588i	−0.792064	−	0.610438i	$-0.790993\pi$
$941$	5.76599	−	12.6258i	0.187966	−	0.411588i	0.980030	+	0.198850i	$0.0637207\pi$
$942$		0			0
$943$	−27.7201	+	14.8738i	−0.902690	+	0.484357i
$944$		0			0
$945$	−0.316222	+	0.692429i	−0.0102867	+	0.0225247i
$946$		0			0
$947$	−8.95280	−	10.3321i	−0.290927	−	0.335748i	0.591405	−	0.806374i	$-0.298573\pi$
$947$	−8.95280	−	10.3321i	−0.290927	−	0.335748i	−0.882332	+	0.470627i	$0.844028\pi$
$948$		0			0
$949$	−0.506815	+	0.584896i	−0.0164519	+	0.0189865i
$950$		0			0
$951$	24.7123	−	7.25620i	0.801353	−	0.235298i
$952$		0			0
$953$	−2.15742	−	15.0052i	−0.0698856	−	0.486065i	−0.994464	−	0.105074i	$-0.966492\pi$
$953$	−2.15742	−	15.0052i	−0.0698856	−	0.486065i	0.924579	−	0.380991i	$-0.124417\pi$
$954$		0			0
$955$	0.322821	+	0.706880i	0.0104462	+	0.0228741i
$956$		0			0
$957$	37.0260	+	23.7952i	1.19688	+	0.769189i
$958$		0			0
$959$	−0.547704	+	3.80936i	−0.0176863	+	0.123011i
$960$		0			0
$961$	3.56083	−	2.28840i	0.114865	−	0.0738195i
$962$		0			0
$963$	−1.24006	−	0.364115i	−0.0399605	−	0.0117334i
$964$		0			0
$965$	9.75057			0.313882
$966$		0			0
$967$	60.8825			1.95785			0.978925	−	0.204220i	$-0.0654658\pi$
$967$	60.8825			1.95785			0.978925	+	0.204220i	$0.0654658\pi$
$968$		0			0
$969$	−17.8213	−	5.23281i	−0.572503	−	0.168102i
$970$		0			0
$971$	24.2246	−	15.5682i	0.777404	−	0.499607i	−0.0907672	−	0.995872i	$-0.528932\pi$
$971$	24.2246	−	15.5682i	0.777404	−	0.499607i	0.868171	+	0.496265i	$0.165296\pi$
$972$		0			0
$973$	0.482067	−	3.35285i	0.0154544	−	0.107487i
$974$		0			0
$975$	−27.2080	−	17.4855i	−0.871354	−	0.559985i
$976$		0			0
$977$	0.990600	+	2.16911i	0.0316921	+	0.0693960i	0.924816	−	0.380415i	$-0.124219\pi$
$977$	0.990600	+	2.16911i	0.0316921	+	0.0693960i	−0.893124	+	0.449811i	$0.851491\pi$
$978$		0			0
$979$	9.54090	+	66.3584i	0.304929	+	2.12083i
$980$		0			0
$981$	−1.42627	+	0.418792i	−0.0455374	+	0.0133710i
$982$		0			0
$983$	28.3870	−	32.7603i	0.905403	−	1.04489i	−0.0933826	−	0.995630i	$-0.529768\pi$
$983$	28.3870	−	32.7603i	0.905403	−	1.04489i	0.998786	−	0.0492609i	$-0.0156866\pi$
$984$		0			0
$985$	5.94730	+	6.86354i	0.189497	+	0.218691i
$986$		0			0
$987$	−0.179322	+	0.392660i	−0.00570788	+	0.0124985i
$988$		0			0
$989$	−29.7807	−	11.3568i	−0.946972	−	0.361125i
$990$		0			0
$991$	−2.73170	+	5.98159i	−0.0867754	+	0.190012i	−0.948045	−	0.318137i	$-0.896943\pi$
$991$	−2.73170	+	5.98159i	−0.0867754	+	0.190012i	0.861269	+	0.508149i	$0.169670\pi$
$992$		0			0
$993$	−8.30980	−	9.59002i	−0.263704	−	0.304330i
$994$		0			0
$995$	0.0241858	−	0.0279119i	0.000766741	−	0.000884867i
$996$		0			0
$997$	28.4706	−	8.35971i	0.901672	−	0.264755i	0.202141	−	0.979357i	$-0.435210\pi$
$997$	28.4706	−	8.35971i	0.901672	−	0.264755i	0.699532	+	0.714602i	$0.253392\pi$
$998$		0			0
$999$	−5.83307	−	40.5699i	−0.184550	−	1.28358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.29.2	✓	20
3.2	odd	2		828.2.q.a.397.2		20
4.3	odd	2		368.2.m.d.305.1		20
23.2	even	11		2116.2.a.j.1.3		10
23.4	even	11	inner	92.2.e.a.73.2	yes	20
23.21	odd	22		2116.2.a.i.1.3		10
69.50	odd	22		828.2.q.a.73.2		20
92.27	odd	22		368.2.m.d.257.1		20
92.67	even	22		8464.2.a.cd.1.8		10
92.71	odd	22		8464.2.a.ce.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.29.2	✓	20	1.1	even	1	trivial
92.2.e.a.73.2	yes	20	23.4	even	11	inner
368.2.m.d.257.1		20	92.27	odd	22
368.2.m.d.305.1		20	4.3	odd	2
828.2.q.a.73.2		20	69.50	odd	22
828.2.q.a.397.2		20	3.2	odd	2
2116.2.a.i.1.3		10	23.21	odd	22
2116.2.a.j.1.3		10	23.2	even	11
8464.2.a.cd.1.8		10	92.67	even	22
8464.2.a.ce.1.8		10	92.71	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)

\(f(q)\)	\(=\)	\(q+(1.69141 + 0.496642i) q^{3} +(-0.630070 + 0.404921i) q^{5} +(-0.0283674 + 0.197300i) q^{7} +(0.0904475 + 0.0581271i) q^{9} +O(q^{10})\)	\(q+(1.69141 + 0.496642i) q^{3} +(-0.630070 + 0.404921i) q^{5} +(-0.0283674 + 0.197300i) q^{7} +(0.0904475 + 0.0581271i) q^{9} +(-1.64271 - 3.59702i) q^{11} +(0.588198 + 4.09101i) q^{13} +(-1.26681 + 0.371968i) q^{15} +(1.78696 - 2.06226i) q^{17} +(-2.52857 - 2.91812i) q^{19} +(-0.145968 + 0.319626i) q^{21} +(-4.78098 - 0.377157i) q^{23} +(-1.84405 + 4.03790i) q^{25} +(-3.33908 - 3.85350i) q^{27} +(-4.13471 + 4.77171i) q^{29} +(5.69528 - 1.67229i) q^{31} +(-0.992052 - 6.89987i) q^{33} +(-0.0620175 - 0.135799i) q^{35} +(6.76233 + 4.34589i) q^{37} +(-1.03688 + 7.21169i) q^{39} +(5.51823 - 3.54635i) q^{41} +(6.37671 + 1.87237i) q^{43} -0.0805251 q^{45} +1.22850 q^{47} +(6.67833 + 1.96093i) q^{49} +(4.04668 - 2.60065i) q^{51} +(0.705887 - 4.90955i) q^{53} +(2.49153 + 1.60121i) q^{55} +(-2.82757 - 6.19152i) q^{57} +(1.64337 + 11.4299i) q^{59} +(-11.9727 + 3.51551i) q^{61} +(-0.0140342 + 0.0161964i) q^{63} +(-2.02714 - 2.33945i) q^{65} +(-0.860140 + 1.88344i) q^{67} +(-7.89927 - 3.01236i) q^{69} +(3.58538 - 7.85089i) q^{71} +(0.122624 + 0.141516i) q^{73} +(-5.12443 + 5.91391i) q^{75} +(0.756292 - 0.222067i) q^{77} +(-0.139435 - 0.969792i) q^{79} +(-3.86792 - 8.46957i) q^{81} +(4.66355 + 2.99708i) q^{83} +(-0.290856 + 2.02295i) q^{85} +(-9.36331 + 6.01743i) q^{87} +(-16.2669 - 4.77638i) q^{89} -0.823841 q^{91} +10.4636 q^{93} +(2.77478 + 0.814749i) q^{95} +(11.6502 - 7.48715i) q^{97} +(0.0605058 - 0.420827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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