LMFDB - Embedded newform 1232.2.q.o.177.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.939795628203.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - 9x^{7} + 10x^{6} - 26x^{5} + 87x^{4} - 48x^{3} - 65x^{2} + 30x + 36 $ x^10 - x^9 + x^8 - 9x^7 + 10x^6 - 26x^5 + 87x^4 - 48x^3 - 65x^2 + 30*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.3
Root			$1.60172 - 0.387640i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.o.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142113 - 0.246147i) q^{3} +(1.10172 - 1.90824i) q^{5} +(-1.07405 + 2.41794i) q^{7} +(1.45961 - 2.52811i) q^{9} +O(q^{10})$	\(q+(-0.142113 - 0.246147i) q^{3} +(1.10172 - 1.90824i) q^{5} +(-1.07405 + 2.41794i) q^{7} +(1.45961 - 2.52811i) q^{9} +(-0.500000 - 0.866025i) q^{11} -5.87258 q^{13} -0.626276 q^{15} +(-2.21616 - 3.83850i) q^{17} +(1.86224 - 3.22550i) q^{19} +(0.747804 - 0.0792469i) q^{21} +(-1.81352 + 3.14112i) q^{23} +(0.0724225 + 0.125440i) q^{25} -1.68240 q^{27} -7.36025 q^{29} +(-1.50436 - 2.60562i) q^{31} +(-0.142113 + 0.246147i) q^{33} +(3.43070 + 4.71343i) q^{35} +(5.19235 - 8.99341i) q^{37} +(0.834571 + 1.44552i) q^{39} +9.67786 q^{41} -9.91468 q^{43} +(-3.21616 - 5.57055i) q^{45} +(-0.216160 + 0.374401i) q^{47} +(-4.69284 - 5.19396i) q^{49} +(-0.629891 + 1.09100i) q^{51} +(4.40738 + 7.63381i) q^{53} -2.20344 q^{55} -1.05860 q^{57} +(-4.64760 - 8.04988i) q^{59} +(-0.548720 + 0.950410i) q^{61} +(4.54514 + 6.24456i) q^{63} +(-6.46995 + 11.2063i) q^{65} +(-0.665816 - 1.15323i) q^{67} +1.03090 q^{69} +1.90348 q^{71} +(-2.12107 - 3.67380i) q^{73} +(0.0205844 - 0.0356532i) q^{75} +(2.63102 - 0.278816i) q^{77} +(0.830600 - 1.43864i) q^{79} +(-4.13973 - 7.17023i) q^{81} -13.7038 q^{83} -9.76636 q^{85} +(1.04599 + 1.81170i) q^{87} +(-2.21142 + 3.83029i) q^{89} +(6.30743 - 14.1995i) q^{91} +(-0.427577 + 0.740586i) q^{93} +(-4.10335 - 7.10720i) q^{95} -10.8479 q^{97} -2.91922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.142113	−	0.246147i	−0.0820490	−	0.142113i	0.822081	−	0.569371i	$-0.192813\pi$
$3$	−0.142113	−	0.246147i	−0.0820490	−	0.142113i	−0.904130	+	0.427258i	$0.859480\pi$
$4$		0			0
$5$	1.10172	−	1.90824i	0.492705	−	0.853389i	−0.507260	−	0.861793i	$-0.669342\pi$
$5$	1.10172	−	1.90824i	0.492705	−	0.853389i	0.999965	+	0.00840370i	$0.00267501\pi$
$6$		0			0
$7$	−1.07405	+	2.41794i	−0.405952	+	0.913894i
$7$	−1.07405	+	2.41794i	−0.405952	+	0.913894i
$8$		0			0
$9$	1.45961	−	2.52811i	0.486536	−	0.842705i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−5.87258			−1.62876			−0.814381	−	0.580331i	$-0.802923\pi$
$13$	−5.87258			−1.62876			−0.814381	+	0.580331i	$0.802923\pi$
$14$		0			0
$15$	−0.626276			−0.161704
$16$		0			0
$17$	−2.21616	−	3.83850i	−0.537498	−	0.930974i	−0.999038	−	0.0438543i	$-0.986036\pi$
$17$	−2.21616	−	3.83850i	−0.537498	−	0.930974i	0.461540	−	0.887119i	$-0.347297\pi$
$18$		0			0
$19$	1.86224	−	3.22550i	0.427228	−	0.739981i	−0.569398	−	0.822062i	$-0.692823\pi$
$19$	1.86224	−	3.22550i	0.427228	−	0.739981i	0.996626	+	0.0820816i	$0.0261568\pi$
$20$		0			0
$21$	0.747804	−	0.0792469i	0.163184	−	0.0172931i
$22$		0			0
$23$	−1.81352	+	3.14112i	−0.378146	+	0.654968i	−0.990793	−	0.135389i	$-0.956772\pi$
$23$	−1.81352	+	3.14112i	−0.378146	+	0.654968i	0.612647	+	0.790357i	$0.290105\pi$
$24$		0			0
$25$	0.0724225	+	0.125440i	0.0144845	+	0.0250879i
$26$		0			0
$27$	−1.68240			−0.323777
$28$		0			0
$29$	−7.36025			−1.36676			−0.683382	−	0.730061i	$-0.739492\pi$
$29$	−7.36025			−1.36676			−0.683382	+	0.730061i	$0.739492\pi$
$30$		0			0
$31$	−1.50436	−	2.60562i	−0.270190	−	0.467984i	0.698720	−	0.715395i	$-0.253753\pi$
$31$	−1.50436	−	2.60562i	−0.270190	−	0.467984i	−0.968910	+	0.247412i	$0.920420\pi$
$32$		0			0
$33$	−0.142113	+	0.246147i	−0.0247387	+	0.0428487i
$34$		0			0
$35$	3.43070	+	4.71343i	0.579893	+	0.796715i
$36$		0			0
$37$	5.19235	−	8.99341i	0.853617	−	1.47851i	−0.0243057	−	0.999705i	$-0.507738\pi$
$37$	5.19235	−	8.99341i	0.853617	−	1.47851i	0.877922	−	0.478803i	$-0.158929\pi$
$38$		0			0
$39$	0.834571	+	1.44552i	0.133638	+	0.231468i
$40$		0			0
$41$	9.67786			1.51143			0.755714	−	0.654902i	$-0.227290\pi$
$41$	9.67786			1.51143			0.755714	+	0.654902i	$0.227290\pi$
$42$		0			0
$43$	−9.91468			−1.51197			−0.755987	−	0.654587i	$-0.772843\pi$
$43$	−9.91468			−1.51197			−0.755987	+	0.654587i	$0.772843\pi$
$44$		0			0
$45$	−3.21616	−	5.57055i	−0.479437	−	0.830409i
$46$		0			0
$47$	−0.216160	+	0.374401i	−0.0315302	+	0.0546120i	−0.881360	−	0.472445i	$-0.843371\pi$
$47$	−0.216160	+	0.374401i	−0.0315302	+	0.0546120i	0.849830	+	0.527057i	$0.176705\pi$
$48$		0			0
$49$	−4.69284	−	5.19396i	−0.670406	−	0.741994i
$50$		0			0
$51$	−0.629891	+	1.09100i	−0.0882023	+	0.152771i
$52$		0			0
$53$	4.40738	+	7.63381i	0.605400	+	1.04858i	0.991988	+	0.126331i	$0.0403202\pi$
$53$	4.40738	+	7.63381i	0.605400	+	1.04858i	−0.386588	+	0.922253i	$0.626346\pi$
$54$		0			0
$55$	−2.20344			−0.297112
$56$		0			0
$57$	−1.05860			−0.140215
$58$		0			0
$59$	−4.64760	−	8.04988i	−0.605066	−	1.04800i	−0.992041	−	0.125915i	$-0.959813\pi$
$59$	−4.64760	−	8.04988i	−0.605066	−	1.04800i	0.386975	−	0.922090i	$-0.373520\pi$
$60$		0			0
$61$	−0.548720	+	0.950410i	−0.0702563	+	0.121688i	−0.899014	−	0.437921i	$-0.855715\pi$
$61$	−0.548720	+	0.950410i	−0.0702563	+	0.121688i	0.828757	+	0.559608i	$0.189048\pi$
$62$		0			0
$63$	4.54514	+	6.24456i	0.572633	+	0.786740i
$64$		0			0
$65$	−6.46995	+	11.2063i	−0.802498	+	1.38997i
$66$		0			0
$67$	−0.665816	−	1.15323i	−0.0813424	−	0.140889i	0.822484	−	0.568788i	$-0.192587\pi$
$67$	−0.665816	−	1.15323i	−0.0813424	−	0.140889i	−0.903827	+	0.427899i	$0.859254\pi$
$68$		0			0
$69$	1.03090			0.124106
$70$		0			0
$71$	1.90348			0.225902			0.112951	−	0.993601i	$-0.463970\pi$
$71$	1.90348			0.225902			0.112951	+	0.993601i	$0.463970\pi$
$72$		0			0
$73$	−2.12107	−	3.67380i	−0.248252	−	0.429985i	0.714789	−	0.699340i	$-0.246523\pi$
$73$	−2.12107	−	3.67380i	−0.248252	−	0.429985i	−0.963041	+	0.269355i	$0.913189\pi$
$74$		0			0
$75$	0.0205844	−	0.0356532i	0.00237688	−	0.00411687i
$76$		0			0
$77$	2.63102	−	0.278816i	0.299832	−	0.0317741i
$78$		0			0
$79$	0.830600	−	1.43864i	0.0934498	−	0.161860i	−0.815511	−	0.578742i	$-0.803544\pi$
$79$	0.830600	−	1.43864i	0.0934498	−	0.161860i	0.908961	+	0.416882i	$0.136877\pi$
$80$		0			0
$81$	−4.13973	−	7.17023i	−0.459970	−	0.796692i
$82$		0			0
$83$	−13.7038			−1.50419			−0.752096	−	0.659053i	$-0.770957\pi$
$83$	−13.7038			−1.50419			−0.752096	+	0.659053i	$0.770957\pi$
$84$		0			0
$85$	−9.76636			−1.05931
$86$		0			0
$87$	1.04599	+	1.81170i	0.112142	+	0.194235i
$88$		0			0
$89$	−2.21142	+	3.83029i	−0.234410	+	0.406010i	−0.959101	−	0.283064i	$-0.908649\pi$
$89$	−2.21142	+	3.83029i	−0.234410	+	0.406010i	0.724691	+	0.689074i	$0.241982\pi$
$90$		0			0
$91$	6.30743	−	14.1995i	0.661199	−	1.48852i
$92$		0			0
$93$	−0.427577	+	0.740586i	−0.0443377	+	0.0767952i
$94$		0			0
$95$	−4.10335	−	7.10720i	−0.420994	−	0.729184i
$96$		0			0
$97$	−10.8479			−1.10144			−0.550720	−	0.834690i	$-0.685647\pi$
$97$	−10.8479			−1.10144			−0.550720	+	0.834690i	$0.685647\pi$
$98$		0			0
$99$	−2.91922			−0.293392
$100$		0			0
$101$	−1.33919	−	2.31954i	−0.133254	−	0.230803i	0.791675	−	0.610942i	$-0.209209\pi$
$101$	−1.33919	−	2.31954i	−0.133254	−	0.230803i	−0.924929	+	0.380140i	$0.875876\pi$
$102$		0			0
$103$	3.38992	−	5.87151i	0.334018	−	0.578537i	−0.649277	−	0.760552i	$-0.724929\pi$
$103$	3.38992	−	5.87151i	0.334018	−	0.578537i	0.983296	+	0.182015i	$0.0582619\pi$
$104$		0			0
$105$	0.672650	−	1.51430i	0.0656439	−	0.147780i
$106$		0			0
$107$	−1.12716	+	1.95230i	−0.108967	+	0.188736i	−0.915352	−	0.402655i	$-0.868087\pi$
$107$	−1.12716	+	1.95230i	−0.108967	+	0.188736i	0.806385	+	0.591390i	$0.201421\pi$
$108$		0			0
$109$	−2.66702	−	4.61941i	−0.255454	−	0.442460i	0.709565	−	0.704640i	$-0.248892\pi$
$109$	−2.66702	−	4.61941i	−0.255454	−	0.442460i	−0.965019	+	0.262181i	$0.915558\pi$
$110$		0			0
$111$	−2.95160			−0.280154
$112$		0			0
$113$	18.4118			1.73204			0.866020	−	0.500010i	$-0.166670\pi$
$113$	18.4118			1.73204			0.866020	+	0.500010i	$0.166670\pi$
$114$		0			0
$115$	3.99600	+	6.92127i	0.372628	+	0.645411i
$116$		0			0
$117$	−8.57167	+	14.8466i	−0.792451	+	1.37257i
$118$		0			0
$119$	11.6615	−	1.23580i	1.06901	−	0.113286i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−1.37535	−	2.38217i	−0.124011	−	0.214793i
$124$		0			0
$125$	11.3364			1.01396
$126$		0			0
$127$	−14.4989			−1.28657			−0.643283	−	0.765629i	$-0.722428\pi$
$127$	−14.4989			−1.28657			−0.643283	+	0.765629i	$0.722428\pi$
$128$		0			0
$129$	1.40900	+	2.44047i	0.124056	+	0.214871i
$130$		0			0
$131$	9.17566	−	15.8927i	0.801681	−	1.38855i	−0.116828	−	0.993152i	$-0.537273\pi$
$131$	9.17566	−	15.8927i	0.801681	−	1.38855i	0.918509	−	0.395400i	$-0.129394\pi$
$132$		0			0
$133$	5.79892	+	7.96713i	0.502830	+	0.690838i
$134$		0			0
$135$	−1.85353	+	3.21041i	−0.159526	+	0.276308i
$136$		0			0
$137$	5.77264	+	9.99850i	0.493190	+	0.854229i	0.999969	−	0.00784626i	$-0.00249757\pi$
$137$	5.77264	+	9.99850i	0.493190	+	0.854229i	−0.506780	+	0.862076i	$0.669164\pi$
$138$		0			0
$139$	21.2389			1.80146			0.900728	−	0.434383i	$-0.143034\pi$
$139$	21.2389			1.80146			0.900728	+	0.434383i	$0.143034\pi$
$140$		0			0
$141$	0.122877			0.0103481
$142$		0			0
$143$	2.93629	+	5.08581i	0.245545	+	0.425296i
$144$		0			0
$145$	−8.10894	+	14.0451i	−0.673411	+	1.16638i
$146$		0			0
$147$	−0.611563	+	1.89326i	−0.0504409	+	0.156153i
$148$		0			0
$149$	−0.371638	+	0.643695i	−0.0304457	+	0.0527336i	−0.880847	−	0.473401i	$-0.843026\pi$
$149$	−0.371638	+	0.643695i	−0.0304457	+	0.0527336i	0.850401	+	0.526135i	$0.176359\pi$
$150$		0			0
$151$	0.0446739	+	0.0773775i	0.00363551	+	0.00629689i	0.867837	−	0.496848i	$-0.165509\pi$
$151$	0.0446739	+	0.0773775i	0.00363551	+	0.00629689i	−0.864202	+	0.503145i	$0.832176\pi$
$152$		0			0
$153$	−12.9389			−1.04605
$154$		0			0
$155$	−6.62953			−0.532496
$156$		0			0
$157$	−5.76527	−	9.98573i	−0.460118	−	0.796948i	0.538848	−	0.842403i	$-0.318860\pi$
$157$	−5.76527	−	9.98573i	−0.460118	−	0.796948i	−0.998966	+	0.0454546i	$0.985526\pi$
$158$		0			0
$159$	1.25269	−	2.16973i	0.0993450	−	0.172071i
$160$		0			0
$161$	−5.64721	−	7.75870i	−0.445063	−	0.611471i
$162$		0			0
$163$	8.98854	−	15.5686i	0.704037	−	1.21943i	−0.263002	−	0.964795i	$-0.584712\pi$
$163$	8.98854	−	15.5686i	0.704037	−	1.21943i	0.967038	−	0.254632i	$-0.0819542\pi$
$164$		0			0
$165$	0.313138	+	0.542371i	0.0243777	+	0.0422235i
$166$		0			0
$167$	−4.81399			−0.372517			−0.186259	−	0.982501i	$-0.559636\pi$
$167$	−4.81399			−0.372517			−0.186259	+	0.982501i	$0.559636\pi$
$168$		0			0
$169$	21.4872			1.65286
$170$		0			0
$171$	−5.43629	−	9.41593i	−0.415724	−	0.720054i
$172$		0			0
$173$	−4.00737	+	6.94097i	−0.304675	+	0.527712i	−0.977189	−	0.212372i	$-0.931881\pi$
$173$	−4.00737	+	6.94097i	−0.304675	+	0.527712i	0.672514	+	0.740084i	$0.265214\pi$
$174$		0			0
$175$	−0.381090	+	0.0403852i	−0.0288077	+	0.00305283i
$176$		0			0
$177$	−1.32097	+	2.28798i	−0.0992901	+	0.171975i
$178$		0			0
$179$	−4.39752	−	7.61674i	−0.328686	−	0.569302i	0.653565	−	0.756870i	$-0.273273\pi$
$179$	−4.39752	−	7.61674i	−0.328686	−	0.569302i	−0.982251	+	0.187569i	$0.939939\pi$
$180$		0			0
$181$	17.9321			1.33288			0.666441	−	0.745557i	$-0.267817\pi$
$181$	17.9321			1.33288			0.666441	+	0.745557i	$0.267817\pi$
$182$		0			0
$183$	0.311921			0.0230579
$184$		0			0
$185$	−11.4410	−	19.8165i	−0.841162	−	1.45693i
$186$		0			0
$187$	−2.21616	+	3.83850i	−0.162062	+	0.280699i
$188$		0			0
$189$	1.80697	−	4.06793i	0.131438	−	0.295898i
$190$		0			0
$191$	−12.4930	+	21.6385i	−0.903962	+	1.56571i	−0.0816576	+	0.996660i	$0.526021\pi$
$191$	−12.4930	+	21.6385i	−0.903962	+	1.56571i	−0.822304	+	0.569048i	$0.807312\pi$
$192$		0			0
$193$	8.15554	+	14.1258i	0.587049	+	1.01680i	0.994617	+	0.103623i	$0.0330436\pi$
$193$	8.15554	+	14.1258i	0.587049	+	1.01680i	−0.407568	+	0.913175i	$0.633623\pi$
$194$		0			0
$195$	3.67786			0.263377
$196$		0			0
$197$	8.81454			0.628010			0.314005	−	0.949421i	$-0.398329\pi$
$197$	8.81454			0.628010			0.314005	+	0.949421i	$0.398329\pi$
$198$		0			0
$199$	3.89143	+	6.74016i	0.275856	+	0.477797i	0.970351	−	0.241701i	$-0.0777053\pi$
$199$	3.89143	+	6.74016i	0.275856	+	0.477797i	−0.694494	+	0.719498i	$0.744372\pi$
$200$		0			0
$201$	−0.189242	+	0.327777i	−0.0133481	+	0.0231196i
$202$		0			0
$203$	7.90526	−	17.7966i	0.554840	−	1.24908i
$204$		0			0
$205$	10.6623	−	18.4676i	0.744687	−	1.28984i
$206$		0			0
$207$	5.29407	+	9.16960i	0.367963	+	0.637331i
$208$		0			0
$209$	−3.72449			−0.257628
$210$		0			0
$211$	23.6786			1.63010			0.815051	−	0.579389i	$-0.196709\pi$
$211$	23.6786			1.63010			0.815051	+	0.579389i	$0.196709\pi$
$212$		0			0
$213$	−0.270510	−	0.468537i	−0.0185350	−	0.0321036i
$214$		0			0
$215$	−10.9232	+	18.9195i	−0.744956	+	1.29030i
$216$		0			0
$217$	7.91598	−	0.838879i	0.537372	−	0.0569468i
$218$		0			0
$219$	−0.602862	+	1.04419i	−0.0407377	+	0.0705597i
$220$		0			0
$221$	13.0146	+	22.5419i	0.875456	+	1.51633i
$222$		0			0
$223$	21.6588			1.45038			0.725192	−	0.688547i	$-0.241751\pi$
$223$	21.6588			1.45038			0.725192	+	0.688547i	$0.241751\pi$
$224$		0			0
$225$	0.422834			0.0281889
$226$		0			0
$227$	−13.1667	−	22.8053i	−0.873901	−	1.51364i	−0.857929	−	0.513769i	$-0.828249\pi$
$227$	−13.1667	−	22.8053i	−0.873901	−	1.51364i	−0.0159728	−	0.999872i	$-0.505085\pi$
$228$		0			0
$229$	−0.959994	+	1.66276i	−0.0634382	+	0.109878i	−0.896000	−	0.444054i	$-0.853540\pi$
$229$	−0.959994	+	1.66276i	−0.0634382	+	0.109878i	0.832562	+	0.553932i	$0.186873\pi$
$230$		0			0
$231$	−0.442532	−	0.607994i	−0.0291165	−	0.0400031i
$232$		0			0
$233$	−12.6874	+	21.9752i	−0.831180	+	1.43965i	0.0659227	+	0.997825i	$0.479001\pi$
$233$	−12.6874	+	21.9752i	−0.831180	+	1.43965i	−0.897103	+	0.441822i	$0.854332\pi$
$234$		0			0
$235$	0.476297	+	0.824971i	0.0310702	+	0.0538152i
$236$		0			0
$237$	−0.472156			−0.0306699
$238$		0			0
$239$	−12.2895			−0.794940			−0.397470	−	0.917615i	$-0.630112\pi$
$239$	−12.2895			−0.794940			−0.397470	+	0.917615i	$0.630112\pi$
$240$		0			0
$241$	−6.99040	−	12.1077i	−0.450291	−	0.779927i	0.548113	−	0.836405i	$-0.315347\pi$
$241$	−6.99040	−	12.1077i	−0.450291	−	0.779927i	−0.998404	+	0.0564772i	$0.982013\pi$
$242$		0			0
$243$	−3.70021	+	6.40896i	−0.237369	+	0.411135i
$244$		0			0
$245$	−15.0815	+	3.23276i	−0.963522	+	0.206534i
$246$		0			0
$247$	−10.9362	+	18.9420i	−0.695853	+	1.20525i
$248$		0			0
$249$	1.94750	+	3.37316i	0.123417	+	0.213765i
$250$		0			0
$251$	3.66249			0.231174			0.115587	−	0.993297i	$-0.463125\pi$
$251$	3.66249			0.231174			0.115587	+	0.993297i	$0.463125\pi$
$252$		0			0
$253$	3.62705			0.228031
$254$		0			0
$255$	1.38793	+	2.40396i	0.0869154	+	0.150542i
$256$		0			0
$257$	−0.635003	+	1.09986i	−0.0396104	+	0.0686072i	−0.885151	−	0.465304i	$-0.845945\pi$
$257$	−0.635003	+	1.09986i	−0.0396104	+	0.0686072i	0.845541	+	0.533911i	$0.179278\pi$
$258$		0			0
$259$	16.1687	+	22.2141i	1.00467	+	1.38032i
$260$		0			0
$261$	−10.7431	+	18.6076i	−0.664980	+	1.15178i
$262$		0			0
$263$	16.1214	+	27.9231i	0.994090	+	1.72182i	0.591057	+	0.806630i	$0.298711\pi$
$263$	16.1214	+	27.9231i	0.994090	+	1.72182i	0.403033	+	0.915185i	$0.367956\pi$
$264$		0			0
$265$	19.4228			1.19313
$266$		0			0
$267$	1.25708			0.0769323
$268$		0			0
$269$	2.05856	+	3.56553i	0.125513	+	0.217394i	0.921933	−	0.387349i	$-0.126609\pi$
$269$	2.05856	+	3.56553i	0.125513	+	0.217394i	−0.796421	+	0.604743i	$0.793276\pi$
$270$		0			0
$271$	0.944188	−	1.63538i	0.0573553	−	0.0993424i	−0.835922	−	0.548848i	$-0.815067\pi$
$271$	0.944188	−	1.63538i	0.0573553	−	0.0993424i	0.893277	+	0.449506i	$0.148400\pi$
$272$		0			0
$273$	−4.39154	+	0.465384i	−0.265788	+	0.0281663i
$274$		0			0
$275$	0.0724225	−	0.125440i	0.00436724	−	0.00756429i
$276$		0			0
$277$	−0.307929	−	0.533349i	−0.0185017	−	0.0320458i	0.856626	−	0.515937i	$-0.172556\pi$
$277$	−0.307929	−	0.533349i	−0.0185017	−	0.0320458i	−0.875128	+	0.483892i	$0.839223\pi$
$278$		0			0
$279$	−8.78308			−0.525830
$280$		0			0
$281$	18.2539			1.08894			0.544468	−	0.838782i	$-0.316732\pi$
$281$	18.2539			1.08894			0.544468	+	0.838782i	$0.316732\pi$
$282$		0			0
$283$	14.8674	+	25.7510i	0.883773	+	1.53074i	0.847114	+	0.531412i	$0.178338\pi$
$283$	14.8674	+	25.7510i	0.883773	+	1.53074i	0.0366592	+	0.999328i	$0.488328\pi$
$284$		0			0
$285$	−1.16628	+	2.02005i	−0.0690843	+	0.119658i
$286$		0			0
$287$	−10.3945	+	23.4004i	−0.613566	+	1.38128i
$288$		0			0
$289$	−1.32273	+	2.29104i	−0.0778079	+	0.134767i
$290$		0			0
$291$	1.54163	+	2.67018i	0.0903720	+	0.156529i
$292$		0			0
$293$	3.41334			0.199409			0.0997047	−	0.995017i	$-0.468210\pi$
$293$	3.41334			0.199409			0.0997047	+	0.995017i	$0.468210\pi$
$294$		0			0
$295$	−20.4814			−1.19247
$296$		0			0
$297$	0.841198	+	1.45700i	0.0488112	+	0.0845435i
$298$		0			0
$299$	10.6501	−	18.4465i	0.615910	−	1.06679i
$300$		0			0
$301$	10.6488	−	23.9731i	0.613788	−	1.38178i
$302$		0			0
$303$	−0.380632	+	0.659273i	−0.0218667	+	0.0378743i
$304$		0			0
$305$	1.20907	+	2.09417i	0.0692312	+	0.119912i
$306$		0			0
$307$	20.8398			1.18939			0.594694	−	0.803952i	$-0.297273\pi$
$307$	20.8398			1.18939			0.594694	+	0.803952i	$0.297273\pi$
$308$		0			0
$309$	−1.92701			−0.109624
$310$		0			0
$311$	7.40585	+	12.8273i	0.419947	+	0.727370i	0.995934	−	0.0900892i	$-0.0287152\pi$
$311$	7.40585	+	12.8273i	0.419947	+	0.727370i	−0.575986	+	0.817459i	$0.695382\pi$
$312$		0			0
$313$	5.17501	−	8.96339i	0.292509	−	0.506641i	−0.681893	−	0.731452i	$-0.738843\pi$
$313$	5.17501	−	8.96339i	0.292509	−	0.506641i	0.974402	+	0.224811i	$0.0721765\pi$
$314$		0			0
$315$	16.9236	−	1.79344i	0.953535	−	0.101049i
$316$		0			0
$317$	−0.118133	+	0.204613i	−0.00663503	+	0.0114922i	−0.869324	−	0.494243i	$-0.835445\pi$
$317$	−0.118133	+	0.204613i	−0.00663503	+	0.0114922i	0.862689	+	0.505735i	$0.168779\pi$
$318$		0			0
$319$	3.68013	+	6.37416i	0.206047	+	0.356885i
$320$		0			0
$321$	0.640736			0.0357624
$322$		0			0
$323$	−16.5081			−0.918537
$324$		0			0
$325$	−0.425307	−	0.736654i	−0.0235918	−	0.0408622i
$326$		0			0
$327$	−0.758037	+	1.31296i	−0.0419195	+	0.0726067i
$328$		0			0
$329$	−0.673112	−	0.924787i	−0.0371098	−	0.0509852i
$330$		0			0
$331$	−12.1466	+	21.0386i	−0.667640	+	1.15639i	0.310923	+	0.950435i	$0.399362\pi$
$331$	−12.1466	+	21.0386i	−0.667640	+	1.15639i	−0.978562	+	0.205950i	$0.933971\pi$
$332$		0			0
$333$	−15.1576	−	26.2537i	−0.830630	−	1.43869i
$334$		0			0
$335$	−2.93417			−0.160311
$336$		0			0
$337$	2.20721			0.120234			0.0601172	−	0.998191i	$-0.480853\pi$
$337$	2.20721			0.120234			0.0601172	+	0.998191i	$0.480853\pi$
$338$		0			0
$339$	−2.61656	−	4.53202i	−0.142112	−	0.246145i
$340$		0			0
$341$	−1.50436	+	2.60562i	−0.0814655	+	0.141102i
$342$		0			0
$343$	17.5990	−	5.76845i	0.950257	−	0.311467i
$344$		0			0
$345$	1.13577	−	1.96720i	0.0611476	−	0.105911i
$346$		0			0
$347$	−13.2310	−	22.9168i	−0.710278	−	1.23024i	−0.964753	−	0.263158i	$-0.915236\pi$
$347$	−13.2310	−	22.9168i	−0.710278	−	1.23024i	0.254475	−	0.967079i	$-0.418097\pi$
$348$		0			0
$349$	20.8494			1.11604			0.558021	−	0.829827i	$-0.311561\pi$
$349$	20.8494			1.11604			0.558021	+	0.829827i	$0.311561\pi$
$350$		0			0
$351$	9.88001			0.527356
$352$		0			0
$353$	−10.9141	−	18.9037i	−0.580898	−	1.00614i	−0.995373	−	0.0960842i	$-0.969368\pi$
$353$	−10.9141	−	18.9037i	−0.580898	−	1.00614i	0.414475	−	0.910061i	$-0.363965\pi$
$354$		0			0
$355$	2.09711	−	3.63230i	0.111303	−	0.192782i
$356$		0			0
$357$	−1.96144	−	2.69482i	−0.103811	−	0.142625i
$358$		0			0
$359$	13.0013	−	22.5188i	0.686180	−	1.18850i	−0.286884	−	0.957965i	$-0.592620\pi$
$359$	13.0013	−	22.5188i	0.686180	−	1.18850i	0.973064	−	0.230534i	$-0.0740471\pi$
$360$		0			0
$361$	2.56410	+	4.44114i	0.134952	+	0.233744i
$362$		0			0
$363$	0.284226			0.0149180
$364$		0			0
$365$	−9.34729			−0.489260
$366$		0			0
$367$	−13.6239	−	23.5972i	−0.711160	−	1.23176i	−0.964422	−	0.264367i	$-0.914837\pi$
$367$	−13.6239	−	23.5972i	−0.711160	−	1.23176i	0.253262	−	0.967398i	$-0.418496\pi$
$368$		0			0
$369$	14.1259	−	24.4667i	0.735364	−	1.27369i
$370$		0			0
$371$	−23.1918	+	2.45770i	−1.20406	+	0.127597i
$372$		0			0
$373$	−3.72789	+	6.45689i	−0.193023	+	0.334325i	−0.946251	−	0.323435i	$-0.895162\pi$
$373$	−3.72789	+	6.45689i	−0.193023	+	0.334325i	0.753228	+	0.657760i	$0.228496\pi$
$374$		0			0
$375$	−1.61105	−	2.79041i	−0.0831940	−	0.144096i
$376$		0			0
$377$	43.2237			2.22613
$378$		0			0
$379$	−10.6623			−0.547688			−0.273844	−	0.961774i	$-0.588295\pi$
$379$	−10.6623			−0.547688			−0.273844	+	0.961774i	$0.588295\pi$
$380$		0			0
$381$	2.06048	+	3.56885i	0.105561	+	0.182838i
$382$		0			0
$383$	6.00899	−	10.4079i	0.307045	−	0.531818i	−0.670669	−	0.741756i	$-0.733993\pi$
$383$	6.00899	−	10.4079i	0.307045	−	0.531818i	0.977715	+	0.209939i	$0.0673264\pi$
$384$		0			0
$385$	2.36660	−	5.32778i	0.120613	−	0.271529i
$386$		0			0
$387$	−14.4715	+	25.0654i	−0.735630	+	1.27415i
$388$		0			0
$389$	−5.63094	−	9.75307i	−0.285500	−	0.494501i	0.687230	−	0.726440i	$-0.258826\pi$
$389$	−5.63094	−	9.75307i	−0.285500	−	0.494501i	−0.972730	+	0.231939i	$0.925493\pi$
$390$		0			0
$391$	16.0762			0.813011
$392$		0			0
$393$	−5.21592			−0.263108
$394$		0			0
$395$	−1.83018	−	3.16996i	−0.0920863	−	0.159498i
$396$		0			0
$397$	0.621735	−	1.07688i	0.0312040	−	0.0540469i	−0.850002	−	0.526780i	$-0.823399\pi$
$397$	0.621735	−	1.07688i	0.0312040	−	0.0540469i	0.881206	+	0.472733i	$0.156733\pi$
$398$		0			0
$399$	1.13698	−	2.55962i	0.0569203	−	0.128141i
$400$		0			0
$401$	−1.17897	+	2.04203i	−0.0588747	+	0.101974i	−0.893961	−	0.448146i	$-0.852085\pi$
$401$	−1.17897	+	2.04203i	−0.0588747	+	0.101974i	0.835086	+	0.550120i	$0.185418\pi$
$402$		0			0
$403$	8.83446	+	15.3017i	0.440076	+	0.762234i
$404$		0			0
$405$	−18.2433			−0.906518
$406$		0			0
$407$	−10.3847			−0.514750
$408$		0			0
$409$	−6.03004	−	10.4443i	−0.298166	−	0.516439i	0.677550	−	0.735477i	$-0.263042\pi$
$409$	−6.03004	−	10.4443i	−0.298166	−	0.516439i	−0.975716	+	0.219037i	$0.929708\pi$
$410$		0			0
$411$	1.64073	−	2.84183i	0.0809314	−	0.140177i
$412$		0			0
$413$	24.4558	−	2.59165i	1.20339	−	0.127527i
$414$		0			0
$415$	−15.0978	+	26.1502i	−0.741122	+	1.28366i
$416$		0			0
$417$	−3.01832	−	5.22788i	−0.147808	−	0.256010i
$418$		0			0
$419$	7.58141			0.370376			0.185188	−	0.982703i	$-0.440711\pi$
$419$	7.58141			0.370376			0.185188	+	0.982703i	$0.440711\pi$
$420$		0			0
$421$	−38.9271			−1.89719			−0.948596	−	0.316490i	$-0.897496\pi$
$421$	−38.9271			−1.89719			−0.948596	+	0.316490i	$0.897496\pi$
$422$		0			0
$423$	0.631019	+	1.09296i	0.0306812	+	0.0531414i
$424$		0			0
$425$	0.321000	−	0.555988i	0.0155708	−	0.0269694i
$426$		0			0
$427$	−1.70868	−	2.34756i	−0.0826889	−	0.113606i
$428$		0			0
$429$	0.834571	−	1.44552i	0.0402934	−	0.0697903i
$430$		0			0
$431$	4.24167	+	7.34679i	0.204314	+	0.353882i	0.949914	−	0.312512i	$-0.101170\pi$
$431$	4.24167	+	7.34679i	0.204314	+	0.353882i	−0.745600	+	0.666394i	$0.767837\pi$
$432$		0			0
$433$	8.22833			0.395428			0.197714	−	0.980260i	$-0.436648\pi$
$433$	8.22833			0.395428			0.197714	+	0.980260i	$0.436648\pi$
$434$		0			0
$435$	4.60954			0.221011
$436$		0			0
$437$	6.75445	+	11.6990i	0.323109	+	0.559641i
$438$		0			0
$439$	12.9978	−	22.5128i	0.620351	−	1.07448i	−0.369070	−	0.929402i	$-0.620324\pi$
$439$	12.9978	−	22.5128i	0.620351	−	1.07448i	0.989420	−	0.145077i	$-0.0463430\pi$
$440$		0			0
$441$	−19.9806	+	4.28291i	−0.951459	+	0.203948i
$442$		0			0
$443$	−3.57221	+	6.18725i	−0.169721	+	0.293965i	−0.938322	−	0.345764i	$-0.887620\pi$
$443$	−3.57221	+	6.18725i	−0.169721	+	0.293965i	0.768601	+	0.639729i	$0.220953\pi$
$444$		0			0
$445$	4.87273	+	8.43981i	0.230989	+	0.400085i
$446$		0			0
$447$	0.211258			0.00999217
$448$		0			0
$449$	−29.7330			−1.40319			−0.701594	−	0.712577i	$-0.747528\pi$
$449$	−29.7330			−1.40319			−0.701594	+	0.712577i	$0.747528\pi$
$450$		0			0
$451$	−4.83893	−	8.38127i	−0.227856	−	0.394659i
$452$		0			0
$453$	0.0126975	−	0.0219927i	0.000596580	−	0.00103331i
$454$		0			0
$455$	−20.1470	−	27.6800i	−0.944508	−	1.29766i
$456$		0			0
$457$	17.5662	−	30.4255i	0.821712	−	1.42325i	−0.0826952	−	0.996575i	$-0.526353\pi$
$457$	17.5662	−	30.4255i	0.821712	−	1.42325i	0.904407	−	0.426671i	$-0.140314\pi$
$458$		0			0
$459$	3.72846	+	6.45788i	0.174030	+	0.301428i
$460$		0			0
$461$	14.8047			0.689523			0.344762	−	0.938690i	$-0.387960\pi$
$461$	14.8047			0.689523			0.344762	+	0.938690i	$0.387960\pi$
$462$		0			0
$463$	22.6097			1.05076			0.525382	−	0.850867i	$-0.323922\pi$
$463$	22.6097			1.05076			0.525382	+	0.850867i	$0.323922\pi$
$464$		0			0
$465$	0.942142	+	1.63184i	0.0436908	+	0.0756747i
$466$		0			0
$467$	6.44211	−	11.1581i	0.298105	−	0.516334i	−0.677597	−	0.735433i	$-0.736979\pi$
$467$	6.44211	−	11.1581i	0.298105	−	0.516334i	0.975702	+	0.219100i	$0.0703120\pi$
$468$		0			0
$469$	3.50355	−	0.371281i	0.161779	−	0.0171442i
$470$		0			0
$471$	−1.63864	+	2.83821i	−0.0755045	+	0.130778i
$472$		0			0
$473$	4.95734	+	8.58636i	0.227939	+	0.394801i
$474$		0			0
$475$	0.539474			0.0247527
$476$		0			0
$477$	25.7322			1.17820
$478$		0			0
$479$	−0.299847	−	0.519351i	−0.0137004	−	0.0237297i	0.859094	−	0.511818i	$-0.171028\pi$
$479$	−0.299847	−	0.519351i	−0.0137004	−	0.0237297i	−0.872794	+	0.488088i	$0.837694\pi$
$480$		0			0
$481$	−30.4925	+	52.8145i	−1.39034	+	2.40814i
$482$		0			0
$483$	−1.10724	+	2.49266i	−0.0503810	+	0.113420i
$484$		0			0
$485$	−11.9514	+	20.7004i	−0.542684	+	0.939956i
$486$		0			0
$487$	−5.39192	−	9.33907i	−0.244331	−	0.423194i	0.717612	−	0.696443i	$-0.245235\pi$
$487$	−5.39192	−	9.33907i	−0.244331	−	0.423194i	−0.961943	+	0.273249i	$0.911902\pi$
$488$		0			0
$489$	−5.10955			−0.231062
$490$		0			0
$491$	−0.735741			−0.0332035			−0.0166018	−	0.999862i	$-0.505285\pi$
$491$	−0.735741			−0.0332035			−0.0166018	+	0.999862i	$0.505285\pi$
$492$		0			0
$493$	16.3115	+	28.2523i	0.734633	+	1.27242i
$494$		0			0
$495$	−3.21616	+	5.57055i	−0.144556	+	0.250378i
$496$		0			0
$497$	−2.04443	+	4.60251i	−0.0917053	+	0.206451i
$498$		0			0
$499$	5.27079	−	9.12927i	0.235953	−	0.408682i	−0.723596	−	0.690223i	$-0.757512\pi$
$499$	5.27079	−	9.12927i	0.235953	−	0.408682i	0.959549	+	0.281541i	$0.0908456\pi$
$500$		0			0
$501$	0.684130	+	1.18495i	0.0305647	+	0.0529396i
$502$		0			0
$503$	−12.4458			−0.554931			−0.277465	−	0.960736i	$-0.589494\pi$
$503$	−12.4458			−0.554931			−0.277465	+	0.960736i	$0.589494\pi$
$504$		0			0
$505$	−5.90164			−0.262619
$506$		0			0
$507$	−3.05362	−	5.28902i	−0.135616	−	0.234893i
$508$		0			0
$509$	0.188636	−	0.326727i	0.00836114	−	0.0144819i	−0.861815	−	0.507223i	$-0.830672\pi$
$509$	0.188636	−	0.326727i	0.00836114	−	0.0144819i	0.870176	+	0.492742i	$0.164005\pi$
$510$		0			0
$511$	11.1611	−	1.18278i	0.493740	−	0.0523229i
$512$		0			0
$513$	−3.13303	+	5.42657i	−0.138327	+	0.239589i
$514$		0			0
$515$	−7.46948	−	12.9375i	−0.329145	−	0.570096i
$516$		0			0
$517$	0.432321			0.0190135
$518$		0			0
$519$	2.27800			0.0999930
$520$		0			0
$521$	−5.25617	−	9.10395i	−0.230277	−	0.398851i	0.727613	−	0.685988i	$-0.240630\pi$
$521$	−5.25617	−	9.10395i	−0.230277	−	0.398851i	−0.957890	+	0.287137i	$0.907296\pi$
$522$		0			0
$523$	−1.80896	+	3.13321i	−0.0791003	+	0.137006i	−0.902862	−	0.429930i	$-0.858538\pi$
$523$	−1.80896	+	3.13321i	−0.0791003	+	0.137006i	0.823762	+	0.566936i	$0.191871\pi$
$524$		0			0
$525$	0.0640986	+	0.0880649i	0.00279749	+	0.00384347i
$526$		0			0
$527$	−6.66779	+	11.5490i	−0.290454	+	0.503080i
$528$		0			0
$529$	4.92226	+	8.52560i	0.214011	+	0.370678i
$530$		0			0
$531$	−27.1347			−1.17754
$532$		0			0
$533$	−56.8340			−2.46175
$534$		0			0
$535$	2.48363	+	4.30177i	0.107377	+	0.185982i
$536$		0			0
$537$	−1.24989	+	2.16487i	−0.0539368	+	0.0934212i
$538$		0			0
$539$	−2.15168	+	6.66110i	−0.0926794	+	0.286914i
$540$		0			0
$541$	−14.9035	+	25.8136i	−0.640750	+	1.10981i	0.344515	+	0.938781i	$0.388043\pi$
$541$	−14.9035	+	25.8136i	−0.640750	+	1.10981i	−0.985266	+	0.171031i	$0.945290\pi$
$542$		0			0
$543$	−2.54839	−	4.41393i	−0.109362	−	0.189420i
$544$		0			0
$545$	−11.7532			−0.503454
$546$		0			0
$547$	−11.5996			−0.495964			−0.247982	−	0.968765i	$-0.579767\pi$
$547$	−11.5996			−0.495964			−0.247982	+	0.968765i	$0.579767\pi$
$548$		0			0
$549$	1.60183	+	2.77445i	0.0683645	+	0.118411i
$550$		0			0
$551$	−13.7066	+	23.7405i	−0.583920	+	1.01138i
$552$		0			0
$553$	2.58644	+	3.55351i	0.109987	+	0.151111i
$554$		0			0
$555$	−3.25184	+	5.63235i	−0.138033	+	0.239080i
$556$		0			0
$557$	−3.57298	−	6.18858i	−0.151392	−	0.262219i	0.780347	−	0.625346i	$-0.215042\pi$
$557$	−3.57298	−	6.18858i	−0.151392	−	0.262219i	−0.931739	+	0.363128i	$0.881709\pi$
$558$		0			0
$559$	58.2248			2.46264
$560$		0			0
$561$	1.25978			0.0531880
$562$		0			0
$563$	−5.45326	−	9.44532i	−0.229827	−	0.398073i	0.727929	−	0.685652i	$-0.240483\pi$
$563$	−5.45326	−	9.44532i	−0.229827	−	0.398073i	−0.957757	+	0.287579i	$0.907150\pi$
$564$		0			0
$565$	20.2847	−	35.1341i	0.853384	−	1.47810i
$566$		0			0
$567$	21.7834	−	2.30845i	0.914818	−	0.0969458i
$568$		0			0
$569$	−7.77153	+	13.4607i	−0.325799	+	0.564301i	−0.981674	−	0.190569i	$-0.938967\pi$
$569$	−7.77153	+	13.4607i	−0.325799	+	0.564301i	0.655874	+	0.754870i	$0.272300\pi$
$570$		0			0
$571$	−16.1766	−	28.0188i	−0.676971	−	1.17255i	−0.975889	−	0.218269i	$-0.929959\pi$
$571$	−16.1766	−	28.0188i	−0.676971	−	1.17255i	0.298917	−	0.954279i	$-0.403374\pi$
$572$		0			0
$573$	7.10168			0.296677
$574$		0			0
$575$	−0.525360			−0.0219090
$576$		0			0
$577$	−5.15511	−	8.92891i	−0.214610	−	0.371715i	0.738542	−	0.674208i	$-0.235515\pi$
$577$	−5.15511	−	8.92891i	−0.214610	−	0.371715i	−0.953152	+	0.302492i	$0.902181\pi$
$578$		0			0
$579$	2.31802	−	4.01492i	0.0963335	−	0.166855i
$580$		0			0
$581$	14.7186	−	33.1350i	0.610630	−	1.37467i
$582$		0			0
$583$	4.40738	−	7.63381i	0.182535	−	0.316160i
$584$		0			0
$585$	18.8872	+	32.7135i	0.780888	+	1.35254i
$586$		0			0
$587$	1.27807			0.0527516			0.0263758	−	0.999652i	$-0.491603\pi$
$587$	1.27807			0.0527516			0.0263758	+	0.999652i	$0.491603\pi$
$588$		0			0
$589$	−11.2059			−0.461732
$590$		0			0
$591$	−1.25266	−	2.16967i	−0.0515276	−	0.0892484i
$592$		0			0
$593$	−17.0181	+	29.4762i	−0.698850	+	1.21044i	0.270015	+	0.962856i	$0.412971\pi$
$593$	−17.0181	+	29.4762i	−0.698850	+	1.21044i	−0.968865	+	0.247588i	$0.920362\pi$
$594$		0			0
$595$	10.4895	−	23.6144i	0.430029	−	0.968098i
$596$		0			0
$597$	1.10605	−	1.91573i	0.0452675	−	0.0784056i
$598$		0			0
$599$	−6.35705	−	11.0107i	−0.259742	−	0.449887i	0.706431	−	0.707782i	$-0.250304\pi$
$599$	−6.35705	−	11.0107i	−0.259742	−	0.449887i	−0.966173	+	0.257896i	$0.916971\pi$
$600$		0			0
$601$	−25.1176			−1.02457			−0.512284	−	0.858816i	$-0.671200\pi$
$601$	−25.1176			−1.02457			−0.512284	+	0.858816i	$0.671200\pi$
$602$		0			0
$603$	−3.88732			−0.158304
$604$		0			0
$605$	1.10172	+	1.90824i	0.0447913	+	0.0775808i
$606$		0			0
$607$	−17.0654	+	29.5582i	−0.692664	+	1.19973i	0.278297	+	0.960495i	$0.410230\pi$
$607$	−17.0654	+	29.5582i	−0.692664	+	1.19973i	−0.970962	+	0.239235i	$0.923103\pi$
$608$		0			0
$609$	−5.50403	+	0.583277i	−0.223034	+	0.0236356i
$610$		0			0
$611$	1.26942	−	2.19870i	0.0513553	−	0.0889499i
$612$		0			0
$613$	−15.1536	−	26.2467i	−0.612046	−	1.06010i	−0.990895	−	0.134637i	$-0.957013\pi$
$613$	−15.1536	−	26.2467i	−0.612046	−	1.06010i	0.378849	−	0.925459i	$-0.376320\pi$
$614$		0			0
$615$	−6.06100			−0.244403
$616$		0			0
$617$	21.7228			0.874528			0.437264	−	0.899333i	$-0.355948\pi$
$617$	21.7228			0.874528			0.437264	+	0.899333i	$0.355948\pi$
$618$		0			0
$619$	−22.5203	−	39.0063i	−0.905168	−	1.56780i	−0.820692	−	0.571371i	$-0.806412\pi$
$619$	−22.5203	−	39.0063i	−0.905168	−	1.56780i	−0.0844756	−	0.996426i	$-0.526922\pi$
$620$		0			0
$621$	3.05107	−	5.28460i	0.122435	−	0.212064i
$622$		0			0
$623$	−6.88623	−	9.46098i	−0.275891	−	0.379046i
$624$		0			0
$625$	12.1274	−	21.0053i	0.485096	−	0.840211i
$626$		0			0
$627$	0.529298	+	0.916772i	0.0211381	+	0.0366123i
$628$		0			0
$629$	−46.0283			−1.83527
$630$		0			0
$631$	4.91973			0.195851			0.0979257	−	0.995194i	$-0.468779\pi$
$631$	4.91973			0.195851			0.0979257	+	0.995194i	$0.468779\pi$
$632$		0			0
$633$	−3.36504	−	5.82842i	−0.133748	−	0.231659i
$634$		0			0
$635$	−15.9737	+	27.6672i	−0.633897	+	1.09794i
$636$		0			0
$637$	27.5591	+	30.5020i	1.09193	+	1.20853i
$638$		0			0
$639$	2.77834	−	4.81223i	0.109909	−	0.190369i
$640$		0			0
$641$	−12.0421	−	20.8575i	−0.475634	−	0.823821i	0.523977	−	0.851732i	$-0.324448\pi$
$641$	−12.0421	−	20.8575i	−0.475634	−	0.823821i	−0.999610	+	0.0279110i	$0.991114\pi$
$642$		0			0
$643$	−38.6763			−1.52524			−0.762622	−	0.646845i	$-0.776088\pi$
$643$	−38.6763			−1.52524			−0.762622	+	0.646845i	$0.776088\pi$
$644$		0			0
$645$	6.20932			0.244492
$646$		0			0
$647$	−13.3596	−	23.1395i	−0.525219	−	0.909706i	−0.999569	−	0.0293695i	$-0.990650\pi$
$647$	−13.3596	−	23.1395i	−0.525219	−	0.909706i	0.474350	−	0.880337i	$-0.342683\pi$
$648$		0			0
$649$	−4.64760	+	8.04988i	−0.182434	+	0.315985i
$650$		0			0
$651$	−1.33145	−	1.82928i	−0.0521837	−	0.0716951i
$652$		0			0
$653$	−4.26723	+	7.39105i	−0.166989	+	0.289234i	−0.937360	−	0.348362i	$-0.886738\pi$
$653$	−4.26723	+	7.39105i	−0.166989	+	0.289234i	0.770371	+	0.637596i	$0.220071\pi$
$654$		0			0
$655$	−20.2180	−	35.0187i	−0.789984	−	1.36829i
$656$		0			0
$657$	−12.3837			−0.483134
$658$		0			0
$659$	−1.14909			−0.0447621			−0.0223811	−	0.999750i	$-0.507125\pi$
$659$	−1.14909			−0.0447621			−0.0223811	+	0.999750i	$0.507125\pi$
$660$		0			0
$661$	10.2596	+	17.7702i	0.399053	+	0.691180i	0.993609	−	0.112874i	$-0.0360056\pi$
$661$	10.2596	+	17.7702i	0.399053	+	0.691180i	−0.594556	+	0.804054i	$0.702672\pi$
$662$		0			0
$663$	3.69908	−	6.40700i	0.143661	−	0.248827i
$664$		0			0
$665$	21.5920	−	2.28816i	0.837300	−	0.0887310i
$666$		0			0
$667$	13.3480	−	23.1194i	0.516836	−	0.895187i
$668$		0			0
$669$	−3.07800	−	5.33126i	−0.119003	−	0.206118i
$670$		0			0
$671$	1.09744			0.0423662
$672$		0			0
$673$	31.1385			1.20030			0.600151	−	0.799887i	$-0.295107\pi$
$673$	31.1385			1.20030			0.600151	+	0.799887i	$0.295107\pi$
$674$		0			0
$675$	−0.121843	−	0.211039i	−0.00468975	−	0.00812289i
$676$		0			0
$677$	13.9840	−	24.2211i	0.537450	−	0.930891i	−0.461590	−	0.887093i	$-0.652721\pi$
$677$	13.9840	−	24.2211i	0.537450	−	0.930891i	0.999040	−	0.0437975i	$-0.0139456\pi$
$678$		0			0
$679$	11.6512	−	26.2296i	0.447131	−	1.00660i
$680$		0			0
$681$	−3.74231	+	6.48186i	−0.143405	+	0.248386i
$682$		0			0
$683$	11.9451	+	20.6895i	0.457067	+	0.791663i	0.998804	−	0.0488849i	$-0.0155668\pi$
$683$	11.9451	+	20.6895i	0.457067	+	0.791663i	−0.541738	+	0.840548i	$0.682233\pi$
$684$		0			0
$685$	25.4393			0.971987
$686$		0			0
$687$	0.545711			0.0208202
$688$		0			0
$689$	−25.8827	−	44.8302i	−0.986052	−	1.70789i
$690$		0			0
$691$	−4.49476	+	7.78515i	−0.170989	+	0.296161i	−0.938766	−	0.344556i	$-0.888030\pi$
$691$	−4.49476	+	7.78515i	−0.170989	+	0.296161i	0.767777	+	0.640717i	$0.221363\pi$
$692$		0			0
$693$	3.13538	−	7.05848i	0.119103	−	0.268130i
$694$		0			0
$695$	23.3993	−	40.5288i	0.887586	−	1.53734i
$696$		0			0
$697$	−21.4477	−	37.1485i	−0.812389	−	1.40710i
$698$		0			0
$699$	7.21219			0.272790
$700$		0			0
$701$	−22.2863			−0.841742			−0.420871	−	0.907121i	$-0.638275\pi$
$701$	−22.2863			−0.841742			−0.420871	+	0.907121i	$0.638275\pi$
$702$		0			0
$703$	−19.3388	−	33.4958i	−0.729378	−	1.26332i
$704$		0			0
$705$	0.135376	−	0.234478i	0.00509856	−	0.00883096i
$706$		0			0
$707$	7.04685	−	0.746774i	0.265024	−	0.0280853i
$708$		0			0
$709$	−10.5219	+	18.2244i	−0.395158	+	0.684433i	−0.993121	−	0.117090i	$-0.962643\pi$
$709$	−10.5219	+	18.2244i	−0.395158	+	0.684433i	0.597964	+	0.801523i	$0.295977\pi$
$710$		0			0
$711$	−2.42470	−	4.19971i	−0.0909334	−	0.157501i
$712$		0			0
$713$	10.9128			0.408686
$714$		0			0
$715$	12.9399			0.483925
$716$		0			0
$717$	1.74649	+	3.02502i	0.0652240	+	0.112971i
$718$		0			0
$719$	22.4960	−	38.9642i	0.838959	−	1.45312i	−0.0518065	−	0.998657i	$-0.516498\pi$
$719$	22.4960	−	38.9642i	0.838959	−	1.45312i	0.890766	−	0.454463i	$-0.150169\pi$
$720$		0			0
$721$	10.5560	+	14.5029i	0.393126	+	0.540116i
$722$		0			0
$723$	−1.98685	+	3.44133i	−0.0738919	+	0.127985i
$724$		0			0
$725$	−0.533048	−	0.923266i	−0.0197969	−	0.0342892i
$726$		0			0
$727$	−30.4214			−1.12827			−0.564133	−	0.825684i	$-0.690789\pi$
$727$	−30.4214			−1.12827			−0.564133	+	0.825684i	$0.690789\pi$
$728$		0			0
$729$	−22.7350			−0.842037
$730$		0			0
$731$	21.9725	+	38.0575i	0.812683	+	1.40761i
$732$		0			0
$733$	21.9634	−	38.0417i	0.811237	−	1.40510i	−0.100762	−	0.994911i	$-0.532128\pi$
$733$	21.9634	−	38.0417i	0.811237	−	1.40510i	0.911999	−	0.410193i	$-0.134539\pi$
$734$		0			0
$735$	2.93901	+	3.25285i	0.108407	+	0.119983i
$736$		0			0
$737$	−0.665816	+	1.15323i	−0.0245256	+	0.0424797i
$738$		0			0
$739$	18.4797	+	32.0078i	0.679787	+	1.17743i	0.975045	+	0.222008i	$0.0712612\pi$
$739$	18.4797	+	32.0078i	0.679787	+	1.17743i	−0.295258	+	0.955418i	$0.595405\pi$
$740$		0			0
$741$	6.21670			0.228376
$742$		0			0
$743$	−18.3644			−0.673725			−0.336863	−	0.941554i	$-0.609366\pi$
$743$	−18.3644			−0.673725			−0.336863	+	0.941554i	$0.609366\pi$
$744$		0			0
$745$	0.818882	+	1.41835i	0.0300015	+	0.0519641i
$746$		0			0
$747$	−20.0022	+	34.6449i	−0.731844	+	1.26759i
$748$		0			0
$749$	−3.50991	−	4.82226i	−0.128249	−	0.176201i
$750$		0			0
$751$	0.688064	−	1.19176i	0.0251078	−	0.0434880i	−0.853198	−	0.521586i	$-0.825340\pi$
$751$	0.688064	−	1.19176i	0.0251078	−	0.0434880i	0.878306	+	0.478098i	$0.158674\pi$
$752$		0			0
$753$	−0.520488	−	0.901511i	−0.0189676	−	0.0328529i
$754$		0			0
$755$	0.196873			0.00716493
$756$		0			0
$757$	4.65489			0.169185			0.0845925	−	0.996416i	$-0.473041\pi$
$757$	4.65489			0.169185			0.0845925	+	0.996416i	$0.473041\pi$
$758$		0			0
$759$	−0.515451	−	0.892787i	−0.0187097	−	0.0324061i
$760$		0			0
$761$	18.4222	−	31.9083i	0.667806	−	1.15667i	−0.310711	−	0.950505i	$-0.600567\pi$
$761$	18.4222	−	31.9083i	0.667806	−	1.15667i	0.978516	−	0.206169i	$-0.0660997\pi$
$762$		0			0
$763$	14.0340	−	1.48722i	0.508063	−	0.0538409i
$764$		0			0
$765$	−14.2551	+	24.6905i	−0.515393	+	0.892686i
$766$		0			0
$767$	27.2934	+	47.2736i	0.985508	+	1.70695i
$768$		0			0
$769$	−16.1968			−0.584070			−0.292035	−	0.956408i	$-0.594332\pi$
$769$	−16.1968			−0.584070			−0.292035	+	0.956408i	$0.594332\pi$
$770$		0			0
$771$	0.360969			0.0130000
$772$		0			0
$773$	−4.27051	−	7.39675i	−0.153600	−	0.266043i	0.778949	−	0.627088i	$-0.215753\pi$
$773$	−4.27051	−	7.39675i	−0.153600	−	0.266043i	−0.932548	+	0.361045i	$0.882420\pi$
$774$		0			0
$775$	0.217899	−	0.377412i	0.00782715	−	0.0135570i
$776$		0			0
$777$	3.17016	−	7.13679i	0.113729	−	0.256031i
$778$		0			0
$779$	18.0225	−	31.2159i	0.645724	−	1.11843i
$780$		0			0
$781$	−0.951742	−	1.64847i	−0.0340560	−	0.0589868i
$782$		0			0
$783$	12.3829			0.442527
$784$		0			0
$785$	−25.4069			−0.906810
$786$		0			0
$787$	−6.22853	−	10.7881i	−0.222023	−	0.384556i	0.733399	−	0.679798i	$-0.237933\pi$
$787$	−6.22853	−	10.7881i	−0.222023	−	0.384556i	−0.955422	+	0.295243i	$0.904599\pi$
$788$		0			0
$789$	4.58213	−	7.93649i	0.163128	−	0.282546i
$790$		0			0
$791$	−19.7752	+	44.5187i	−0.703124	+	1.58290i
$792$		0			0
$793$	3.22240	−	5.58136i	0.114431	−	0.198200i
$794$		0			0
$795$	−2.76023	−	4.78087i	−0.0978954	−	0.169560i
$796$		0			0
$797$	−18.4835			−0.654720			−0.327360	−	0.944900i	$-0.606159\pi$
$797$	−18.4835			−0.654720			−0.327360	+	0.944900i	$0.606159\pi$
$798$		0			0
$799$	1.91619			0.0677898
$800$		0			0
$801$	6.45560	+	11.1814i	0.228098	+	0.395076i
$802$		0			0
$803$	−2.12107	+	3.67380i	−0.0748508	+	0.129645i
$804$		0			0
$805$	−21.0271	+	2.22830i	−0.741107	+	0.0785372i
$806$		0			0
$807$	0.585097	−	1.01342i	0.0205964	−	0.0356740i
$808$		0			0
$809$	9.04795	+	15.6715i	0.318109	+	0.550981i	0.980093	−	0.198537i	$-0.0636189\pi$
$809$	9.04795	+	15.6715i	0.318109	+	0.550981i	−0.661985	+	0.749517i	$0.730286\pi$
$810$		0			0
$811$	37.9204			1.33157			0.665783	−	0.746145i	$-0.268098\pi$
$811$	37.9204			1.33157			0.665783	+	0.746145i	$0.268098\pi$
$812$		0			0
$813$	−0.536726			−0.0188238
$814$		0			0
$815$	−19.8057	−	34.3045i	−0.693764	−	1.20163i
$816$		0			0
$817$	−18.4635	+	31.9798i	−0.645958	+	1.11883i
$818$		0			0
$819$	−26.6917	−	36.6717i	−0.932683	−	1.28141i
$820$		0			0
$821$	−15.0584	+	26.0819i	−0.525542	+	0.910266i	0.474015	+	0.880517i	$0.342804\pi$
$821$	−15.0584	+	26.0819i	−0.525542	+	0.910266i	−0.999557	+	0.0297492i	$0.990529\pi$
$822$		0			0
$823$	−13.7776	−	23.8635i	−0.480256	−	0.831829i	0.519487	−	0.854478i	$-0.326123\pi$
$823$	−13.7776	−	23.8635i	−0.480256	−	0.831829i	−0.999743	+	0.0226498i	$0.992790\pi$
$824$		0			0
$825$	−0.0411687			−0.00143331
$826$		0			0
$827$	−1.04974			−0.0365031			−0.0182515	−	0.999833i	$-0.505810\pi$
$827$	−1.04974			−0.0365031			−0.0182515	+	0.999833i	$0.505810\pi$
$828$		0			0
$829$	−12.0816	−	20.9260i	−0.419613	−	0.726790i	0.576288	−	0.817247i	$-0.304501\pi$
$829$	−12.0816	−	20.9260i	−0.419613	−	0.726790i	−0.995900	+	0.0904565i	$0.971167\pi$
$830$		0			0
$831$	−0.0875215	+	0.151592i	−0.00303609	+	0.00525865i
$832$		0			0
$833$	−9.53693	+	29.5241i	−0.330435	+	1.02295i
$834$		0			0
$835$	−5.30367	+	9.18622i	−0.183541	+	0.317902i
$836$		0			0
$837$	2.53092	+	4.38369i	0.0874815	+	0.151522i
$838$		0			0
$839$	−25.0064			−0.863316			−0.431658	−	0.902037i	$-0.642071\pi$
$839$	−25.0064			−0.863316			−0.431658	+	0.902037i	$0.642071\pi$
$840$		0			0
$841$	25.1733			0.868044
$842$		0			0
$843$	−2.59411	−	4.49314i	−0.0893460	−	0.154752i
$844$		0			0
$845$	23.6729	−	41.0027i	0.814373	−	1.41054i
$846$		0			0
$847$	−1.55697	−	2.13912i	−0.0534982	−	0.0735011i
$848$		0			0
$849$	4.22569	−	7.31911i	0.145025	−	0.251191i
$850$		0			0
$851$	18.8329	+	32.6195i	0.645583	+	1.11818i
$852$		0			0
$853$	−32.6681			−1.11853			−0.559267	−	0.828988i	$-0.688917\pi$
$853$	−32.6681			−1.11853			−0.559267	+	0.828988i	$0.688917\pi$
$854$		0			0
$855$	−23.9571			−0.819316
$856$		0			0
$857$	−3.58233	−	6.20478i	−0.122370	−	0.211951i	0.798332	−	0.602218i	$-0.205716\pi$
$857$	−3.58233	−	6.20478i	−0.122370	−	0.211951i	−0.920702	+	0.390267i	$0.872383\pi$
$858$		0			0
$859$	−28.1428	+	48.7448i	−0.960221	+	1.66315i	−0.238279	+	0.971197i	$0.576583\pi$
$859$	−28.1428	+	48.7448i	−0.960221	+	1.66315i	−0.721942	+	0.691954i	$0.756750\pi$
$860$		0			0
$861$	7.23714	−	0.766940i	0.246641	−	0.0261372i
$862$		0			0
$863$	−9.60852	+	16.6424i	−0.327078	+	0.566515i	−0.981931	−	0.189241i	$-0.939397\pi$
$863$	−9.60852	+	16.6424i	−0.327078	+	0.566515i	0.654853	+	0.755756i	$0.272731\pi$
$864$		0			0
$865$	8.83000	+	15.2940i	0.300229	+	0.520012i
$866$		0			0
$867$	0.751911			0.0255362
$868$		0			0
$869$	−1.66120			−0.0563524
$870$		0			0
$871$	3.91006	+	6.77242i	0.132487	+	0.229475i
$872$		0			0
$873$	−15.8337	+	27.4248i	−0.535890	+	0.928188i
$874$		0			0
$875$	−12.1758	+	27.4106i	−0.411617	+	0.926648i
$876$		0			0
$877$	17.5677	−	30.4281i	0.593219	−	1.02748i	−0.400577	−	0.916263i	$-0.631190\pi$
$877$	17.5677	−	30.4281i	0.593219	−	1.02748i	0.993796	−	0.111222i	$-0.0354763\pi$
$878$		0			0
$879$	−0.485080	−	0.840183i	−0.0163613	−	0.0283387i
$880$		0			0
$881$	−19.9196			−0.671109			−0.335554	−	0.942021i	$-0.608924\pi$
$881$	−19.9196			−0.671109			−0.335554	+	0.942021i	$0.608924\pi$
$882$		0			0
$883$	45.4988			1.53116			0.765578	−	0.643344i	$-0.222453\pi$
$883$	45.4988			1.53116			0.765578	+	0.643344i	$0.222453\pi$
$884$		0			0
$885$	2.91068	+	5.04144i	0.0978413	+	0.169466i
$886$		0			0
$887$	−17.1108	+	29.6368i	−0.574524	+	0.995105i	0.421569	+	0.906796i	$0.361479\pi$
$887$	−17.1108	+	29.6368i	−0.574524	+	0.995105i	−0.996093	+	0.0883085i	$0.971854\pi$
$888$		0			0
$889$	15.5725	−	35.0573i	0.522284	−	1.17579i
$890$		0			0
$891$	−4.13973	+	7.17023i	−0.138686	+	0.240212i
$892$		0			0
$893$	0.805087	+	1.39445i	0.0269412	+	0.0466636i
$894$		0			0
$895$	−19.3794			−0.647781
$896$		0			0
$897$	−6.05406			−0.202139
$898$		0			0
$899$	11.0724	+	19.1780i	0.369287	+	0.639623i
$900$		0			0
$901$	19.5349	−	33.8355i	0.650803	−	1.12722i
$902$		0			0
$903$	−7.41424	+	0.785707i	−0.246730	+	0.0261467i
$904$		0			0
$905$	19.7562	−	34.2187i	0.656717	−	1.13747i
$906$		0			0
$907$	17.3426	+	30.0383i	0.575852	+	0.997406i	0.995948	+	0.0899260i	$0.0286631\pi$
$907$	17.3426	+	30.0383i	0.575852	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$908$		0			0
$909$	−7.81875			−0.259331
$910$		0			0
$911$	−6.40419			−0.212180			−0.106090	−	0.994357i	$-0.533833\pi$
$911$	−6.40419			−0.212180			−0.106090	+	0.994357i	$0.533833\pi$
$912$		0			0
$913$	6.85192	+	11.8679i	0.226766	+	0.392769i
$914$		0			0
$915$	0.343650	−	0.595219i	0.0113607	−	0.0196773i
$916$		0			0
$917$	28.5725	+	39.2557i	0.943546	+	1.29634i
$918$		0			0
$919$	8.19567	−	14.1953i	0.270350	−	0.468260i	−0.698601	−	0.715511i	$-0.746194\pi$
$919$	8.19567	−	14.1953i	0.270350	−	0.468260i	0.968952	+	0.247251i	$0.0795272\pi$
$920$		0			0
$921$	−2.96160	−	5.12964i	−0.0975881	−	0.169028i
$922$		0			0
$923$	−11.1784			−0.367941
$924$		0			0
$925$	1.50417			0.0494569
$926$		0			0
$927$	−9.89590	−	17.1402i	−0.325024	−	0.562958i
$928$		0			0
$929$	2.98671	−	5.17313i	0.0979908	−	0.169725i	−0.812862	−	0.582456i	$-0.802092\pi$
$929$	2.98671	−	5.17313i	0.0979908	−	0.169725i	0.910853	+	0.412731i	$0.135425\pi$
$930$		0			0
$931$	−25.4923	+	5.46435i	−0.835478	+	0.179087i
$932$		0			0
$933$	2.10494	−	3.64586i	0.0689125	−	0.119360i
$934$		0			0
$935$	4.88318	+	8.45792i	0.159697	+	0.276603i
$936$		0			0
$937$	38.4716			1.25681			0.628406	−	0.777885i	$-0.283708\pi$
$937$	38.4716			1.25681			0.628406	+	0.777885i	$0.283708\pi$
$938$		0			0
$939$	−2.94175			−0.0960003
$940$		0			0
$941$	−5.21799	−	9.03783i	−0.170102	−	0.294625i	0.768354	−	0.640026i	$-0.221076\pi$
$941$	−5.21799	−	9.03783i	−0.170102	−	0.294625i	−0.938455	+	0.345401i	$0.887743\pi$
$942$		0			0
$943$	−17.5510	+	30.3993i	−0.571540	+	0.989936i
$944$		0			0
$945$	−5.77179	−	7.92985i	−0.187756	−	0.257958i
$946$		0			0
$947$	−8.52273	+	14.7618i	−0.276951	+	0.479694i	−0.970626	−	0.240595i	$-0.922657\pi$
$947$	−8.52273	+	14.7618i	−0.276951	+	0.479694i	0.693674	+	0.720289i	$0.255991\pi$
$948$		0			0
$949$	12.4561	+	21.5747i	0.404343	+	0.700343i
$950$		0			0
$951$	0.0671532			0.00217759
$952$		0			0
$953$	21.9077			0.709659			0.354829	−	0.934931i	$-0.384539\pi$
$953$	21.9077			0.709659			0.354829	+	0.934931i	$0.384539\pi$
$954$		0			0
$955$	27.5276	+	47.6792i	0.890772	+	1.54286i
$956$		0			0
$957$	1.04599	−	1.81170i	0.0338120	−	0.0585641i
$958$		0			0
$959$	−30.3758	+	3.21901i	−0.980887	+	0.103947i
$960$		0			0
$961$	10.9738	−	19.0072i	0.353994	−	0.613136i
$962$		0			0
$963$	3.29042	+	5.69917i	0.106032	+	0.183653i
$964$		0			0
$965$	35.9405			1.15697
$966$		0			0
$967$	36.8964			1.18651			0.593254	−	0.805016i	$-0.297843\pi$
$967$	36.8964			1.18651			0.593254	+	0.805016i	$0.297843\pi$
$968$		0			0
$969$	2.34602	+	4.06343i	0.0753650	+	0.130536i
$970$		0			0
$971$	−2.05166	+	3.55357i	−0.0658408	+	0.114040i	−0.897067	−	0.441895i	$-0.854306\pi$
$971$	−2.05166	+	3.55357i	−0.0658408	+	0.114040i	0.831226	+	0.555935i	$0.187640\pi$
$972$		0			0
$973$	−22.8115	+	51.3542i	−0.731304	+	1.64634i
$974$		0			0
$975$	−0.120883	+	0.209376i	−0.00387137	+	0.00670541i
$976$		0			0
$977$	21.3043	+	36.9001i	0.681584	+	1.18054i	0.974497	+	0.224399i	$0.0720420\pi$
$977$	21.3043	+	36.9001i	0.681584	+	1.18054i	−0.292913	+	0.956139i	$0.594625\pi$
$978$		0			0
$979$	4.42283			0.141354
$980$		0			0
$981$	−15.5712			−0.497151
$982$		0			0
$983$	30.5280	+	52.8760i	0.973691	+	1.68648i	0.684188	+	0.729306i	$0.260157\pi$
$983$	30.5280	+	52.8760i	0.973691	+	1.68648i	0.289503	+	0.957177i	$0.406510\pi$
$984$		0			0
$985$	9.71116	−	16.8202i	0.309423	−	0.535937i
$986$		0			0
$987$	−0.131976	+	0.297109i	−0.00420083	+	0.00945707i
$988$		0			0
$989$	17.9805	−	31.1431i	0.571747	−	0.990294i
$990$		0			0
$991$	7.42970	+	12.8686i	0.236012	+	0.408785i	0.959566	−	0.281482i	$-0.0908261\pi$
$991$	7.42970	+	12.8686i	0.236012	+	0.408785i	−0.723554	+	0.690268i	$0.757493\pi$
$992$		0			0
$993$	6.90478			0.219117
$994$		0			0
$995$	17.1491			0.543663
$996$		0			0
$997$	−7.68546	−	13.3116i	−0.243401	−	0.421583i	0.718280	−	0.695754i	$-0.244930\pi$
$997$	−7.68546	−	13.3116i	−0.243401	−	0.421583i	−0.961681	+	0.274172i	$0.911596\pi$
$998$		0			0
$999$	−8.73558	+	15.1305i	−0.276382	+	0.478707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.o.177.3		10
4.3	odd	2		616.2.q.f.177.3	✓	10
7.2	even	3		8624.2.a.dc.1.3		5
7.4	even	3	inner	1232.2.q.o.529.3		10
7.5	odd	6		8624.2.a.db.1.3		5
28.11	odd	6		616.2.q.f.529.3	yes	10
28.19	even	6		4312.2.a.bg.1.3		5
28.23	odd	6		4312.2.a.bf.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.f.177.3	✓	10	4.3	odd	2
616.2.q.f.529.3	yes	10	28.11	odd	6
1232.2.q.o.177.3		10	1.1	even	1	trivial
1232.2.q.o.529.3		10	7.4	even	3	inner
4312.2.a.bf.1.3		5	28.23	odd	6
4312.2.a.bg.1.3		5	28.19	even	6
8624.2.a.db.1.3		5	7.5	odd	6
8624.2.a.dc.1.3		5	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.142113 - 0.246147i) q^{3} +(1.10172 - 1.90824i) q^{5} +(-1.07405 + 2.41794i) q^{7} +(1.45961 - 2.52811i) q^{9} +O(q^{10})\)	\(q+(-0.142113 - 0.246147i) q^{3} +(1.10172 - 1.90824i) q^{5} +(-1.07405 + 2.41794i) q^{7} +(1.45961 - 2.52811i) q^{9} +(-0.500000 - 0.866025i) q^{11} -5.87258 q^{13} -0.626276 q^{15} +(-2.21616 - 3.83850i) q^{17} +(1.86224 - 3.22550i) q^{19} +(0.747804 - 0.0792469i) q^{21} +(-1.81352 + 3.14112i) q^{23} +(0.0724225 + 0.125440i) q^{25} -1.68240 q^{27} -7.36025 q^{29} +(-1.50436 - 2.60562i) q^{31} +(-0.142113 + 0.246147i) q^{33} +(3.43070 + 4.71343i) q^{35} +(5.19235 - 8.99341i) q^{37} +(0.834571 + 1.44552i) q^{39} +9.67786 q^{41} -9.91468 q^{43} +(-3.21616 - 5.57055i) q^{45} +(-0.216160 + 0.374401i) q^{47} +(-4.69284 - 5.19396i) q^{49} +(-0.629891 + 1.09100i) q^{51} +(4.40738 + 7.63381i) q^{53} -2.20344 q^{55} -1.05860 q^{57} +(-4.64760 - 8.04988i) q^{59} +(-0.548720 + 0.950410i) q^{61} +(4.54514 + 6.24456i) q^{63} +(-6.46995 + 11.2063i) q^{65} +(-0.665816 - 1.15323i) q^{67} +1.03090 q^{69} +1.90348 q^{71} +(-2.12107 - 3.67380i) q^{73} +(0.0205844 - 0.0356532i) q^{75} +(2.63102 - 0.278816i) q^{77} +(0.830600 - 1.43864i) q^{79} +(-4.13973 - 7.17023i) q^{81} -13.7038 q^{83} -9.76636 q^{85} +(1.04599 + 1.81170i) q^{87} +(-2.21142 + 3.83029i) q^{89} +(6.30743 - 14.1995i) q^{91} +(-0.427577 + 0.740586i) q^{93} +(-4.10335 - 7.10720i) q^{95} -10.8479 q^{97} -2.91922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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