LMFDB - Embedded newform 560.2.cc.b.479.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(159,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 5]))

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

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

chi := DirichletCharacter("560.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cc (of order $6$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	560.479
Dual form			560.2.cc.b.159.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686141 + 0.396143i) q^{3} +(-2.18614 + 0.469882i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-1.18614 - 2.05446i) q^{9} +O(q^{10})$	\(q+(0.686141 + 0.396143i) q^{3} +(-2.18614 + 0.469882i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-1.18614 - 2.05446i) q^{9} +(1.50000 + 0.866025i) q^{11} +4.37228 q^{13} +(-1.68614 - 0.543620i) q^{15} +(3.68614 - 6.38458i) q^{17} +(-2.87228 - 4.97494i) q^{19} +(-0.686141 - 1.98072i) q^{21} +(-2.87228 - 4.97494i) q^{23} +(4.55842 - 2.05446i) q^{25} -4.25639i q^{27} -2.74456 q^{29} +(-5.05842 + 8.76144i) q^{31} +(0.686141 + 1.18843i) q^{33} +(5.18614 + 2.84674i) q^{35} +(7.50000 - 4.33013i) q^{37} +(3.00000 + 1.73205i) q^{39} -0.939764i q^{41} +4.00000 q^{43} +(3.55842 + 3.93398i) q^{45} +(-10.2446 + 5.91470i) q^{47} +(1.00000 + 6.92820i) q^{49} +(5.05842 - 2.92048i) q^{51} +(-5.61684 - 3.24289i) q^{53} +(-3.68614 - 1.18843i) q^{55} -4.55134i q^{57} +(-2.31386 + 4.00772i) q^{59} +(-0.941578 + 0.543620i) q^{61} +(-1.18614 + 6.16337i) q^{63} +(-9.55842 + 2.05446i) q^{65} +(4.05842 - 7.02939i) q^{67} -4.55134i q^{69} -10.3923i q^{71} +(-2.31386 + 4.00772i) q^{73} +(3.94158 + 0.396143i) q^{75} +(-1.50000 - 4.33013i) q^{77} +(8.05842 - 4.65253i) q^{79} +(-1.87228 + 3.24289i) q^{81} +8.51278i q^{83} +(-5.05842 + 15.6896i) q^{85} +(-1.88316 - 1.08724i) q^{87} +(-3.68614 + 2.12819i) q^{89} +(-8.74456 - 7.57301i) q^{91} +(-6.94158 + 4.00772i) q^{93} +(8.61684 + 9.52628i) q^{95} +6.00000 q^{97} -4.10891i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} - 3 q^{5} - 8 q^{7} + q^{9}+O(q^{10}) $ 4 * q - 3 * q^3 - 3 * q^5 - 8 * q^7 + q^9	$ 4 q - 3 q^{3} - 3 q^{5} - 8 q^{7} + q^{9} + 6 q^{11} + 6 q^{13} - q^{15} + 9 q^{17} + 3 q^{21} + q^{25} + 12 q^{29} - 3 q^{31} - 3 q^{33} + 15 q^{35} + 30 q^{37} + 12 q^{39} + 16 q^{43} - 3 q^{45} - 18 q^{47} + 4 q^{49} + 3 q^{51} + 12 q^{53} - 9 q^{55} - 15 q^{59} - 21 q^{61} + q^{63} - 21 q^{65} - q^{67} - 15 q^{73} + 33 q^{75} - 6 q^{77} + 15 q^{79} + 4 q^{81} - 3 q^{85} - 42 q^{87} - 9 q^{89} - 12 q^{91} - 45 q^{93} + 24 q^{97}+O(q^{100}) $ 4 * q - 3 * q^3 - 3 * q^5 - 8 * q^7 + q^9 + 6 * q^11 + 6 * q^13 - q^15 + 9 * q^17 + 3 * q^21 + q^25 + 12 * q^29 - 3 * q^31 - 3 * q^33 + 15 * q^35 + 30 * q^37 + 12 * q^39 + 16 * q^43 - 3 * q^45 - 18 * q^47 + 4 * q^49 + 3 * q^51 + 12 * q^53 - 9 * q^55 - 15 * q^59 - 21 * q^61 + q^63 - 21 * q^65 - q^67 - 15 * q^73 + 33 * q^75 - 6 * q^77 + 15 * q^79 + 4 * q^81 - 3 * q^85 - 42 * q^87 - 9 * q^89 - 12 * q^91 - 45 * q^93 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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
$3$	0.686141	+	0.396143i	0.396143	+	0.228714i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	0.686141	+	0.396143i	0.396143	+	0.228714i	−0.288675	+	0.957427i	$0.593215\pi$
$4$		0			0
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$		0			0
$9$	−1.18614	−	2.05446i	−0.395380	−	0.684819i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	4.37228			1.21265			0.606326	−	0.795216i	$-0.292643\pi$
$13$	4.37228			1.21265			0.606326	+	0.795216i	$0.292643\pi$
$14$		0			0
$15$	−1.68614	−	0.543620i	−0.435360	−	0.140362i
$16$		0			0
$17$	3.68614	−	6.38458i	0.894020	−	1.54849i	0.0590081	−	0.998258i	$-0.481206\pi$
$17$	3.68614	−	6.38458i	0.894020	−	1.54849i	0.835012	−	0.550231i	$-0.185460\pi$
$18$		0			0
$19$	−2.87228	−	4.97494i	−0.658947	−	1.14133i	−0.980889	−	0.194570i	$-0.937669\pi$
$19$	−2.87228	−	4.97494i	−0.658947	−	1.14133i	0.321942	−	0.946759i	$-0.395664\pi$
$20$		0			0
$21$	−0.686141	−	1.98072i	−0.149728	−	0.432228i
$22$		0			0
$23$	−2.87228	−	4.97494i	−0.598912	−	1.03735i	−0.992982	−	0.118266i	$-0.962267\pi$
$23$	−2.87228	−	4.97494i	−0.598912	−	1.03735i	0.394070	−	0.919080i	$-0.371067\pi$
$24$		0			0
$25$	4.55842	−	2.05446i	0.911684	−	0.410891i
$26$		0			0
$27$		−	4.25639i		−	0.819142i
$28$		0			0
$29$	−2.74456			−0.509652			−0.254826	−	0.966987i	$-0.582018\pi$
$29$	−2.74456			−0.509652			−0.254826	+	0.966987i	$0.582018\pi$
$30$		0			0
$31$	−5.05842	+	8.76144i	−0.908519	+	1.57360i	−0.0923973	+	0.995722i	$0.529453\pi$
$31$	−5.05842	+	8.76144i	−0.908519	+	1.57360i	−0.816122	+	0.577880i	$0.803880\pi$
$32$		0			0
$33$	0.686141	+	1.18843i	0.119442	+	0.206879i
$34$		0			0
$35$	5.18614	+	2.84674i	0.876618	+	0.481187i
$36$		0			0
$37$	7.50000	−	4.33013i	1.23299	−	0.711868i	0.265340	−	0.964155i	$-0.414516\pi$
$37$	7.50000	−	4.33013i	1.23299	−	0.711868i	0.967653	+	0.252286i	$0.0811825\pi$
$38$		0			0
$39$	3.00000	+	1.73205i	0.480384	+	0.277350i
$40$		0			0
$41$		−	0.939764i		−	0.146766i	−0.997304	−	0.0733832i	$-0.976620\pi$
$41$		−	0.939764i		−	0.146766i	0.997304	−	0.0733832i	$-0.0233796\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	3.55842	+	3.93398i	0.530458	+	0.586444i
$46$		0			0
$47$	−10.2446	+	5.91470i	−1.49432	+	0.862748i	−0.999979	−	0.00651839i	$-0.997925\pi$
$47$	−10.2446	+	5.91470i	−1.49432	+	0.862748i	−0.494344	+	0.869266i	$0.664592\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	5.05842	−	2.92048i	0.708321	−	0.408949i
$52$		0			0
$53$	−5.61684	−	3.24289i	−0.771533	−	0.445445i	0.0618883	−	0.998083i	$-0.480288\pi$
$53$	−5.61684	−	3.24289i	−0.771533	−	0.445445i	−0.833421	+	0.552638i	$0.813621\pi$
$54$		0			0
$55$	−3.68614	−	1.18843i	−0.497039	−	0.160248i
$56$		0			0
$57$		−	4.55134i		−	0.602840i
$58$		0			0
$59$	−2.31386	+	4.00772i	−0.301239	+	0.521761i	−0.976417	−	0.215894i	$-0.930733\pi$
$59$	−2.31386	+	4.00772i	−0.301239	+	0.521761i	0.675178	+	0.737655i	$0.264067\pi$
$60$		0			0
$61$	−0.941578	+	0.543620i	−0.120557	+	0.0696034i	−0.559066	−	0.829123i	$-0.688840\pi$
$61$	−0.941578	+	0.543620i	−0.120557	+	0.0696034i	0.438509	+	0.898727i	$0.355507\pi$
$62$		0			0
$63$	−1.18614	+	6.16337i	−0.149440	+	0.776511i
$64$		0			0
$65$	−9.55842	+	2.05446i	−1.18558	+	0.254824i
$66$		0			0
$67$	4.05842	−	7.02939i	0.495815	−	0.858777i	−0.504173	−	0.863603i	$-0.668203\pi$
$67$	4.05842	−	7.02939i	0.495815	−	0.858777i	0.999988	+	0.00482552i	$0.00153602\pi$
$68$		0			0
$69$		−	4.55134i		−	0.547917i
$70$		0			0
$71$		−	10.3923i		−	1.23334i	−0.787222	−	0.616670i	$-0.788481\pi$
$71$		−	10.3923i		−	1.23334i	0.787222	−	0.616670i	$-0.211519\pi$
$72$		0			0
$73$	−2.31386	+	4.00772i	−0.270817	+	0.469068i	−0.969071	−	0.246781i	$-0.920627\pi$
$73$	−2.31386	+	4.00772i	−0.270817	+	0.469068i	0.698254	+	0.715850i	$0.253960\pi$
$74$		0			0
$75$	3.94158	+	0.396143i	0.455134	+	0.0457427i
$76$		0			0
$77$	−1.50000	−	4.33013i	−0.170941	−	0.493464i
$78$		0			0
$79$	8.05842	−	4.65253i	0.906643	−	0.523451i	0.0272937	−	0.999627i	$-0.491311\pi$
$79$	8.05842	−	4.65253i	0.906643	−	0.523451i	0.879350	+	0.476177i	$0.157978\pi$
$80$		0			0
$81$	−1.87228	+	3.24289i	−0.208031	+	0.360321i
$82$		0			0
$83$			8.51278i			0.934399i	0.884152	+	0.467199i	$0.154737\pi$
$83$			8.51278i			0.934399i	−0.884152	+	0.467199i	$0.845263\pi$
$84$		0			0
$85$	−5.05842	+	15.6896i	−0.548663	+	1.70178i
$86$		0			0
$87$	−1.88316	−	1.08724i	−0.201896	−	0.116564i
$88$		0			0
$89$	−3.68614	+	2.12819i	−0.390730	+	0.225588i	−0.682476	−	0.730908i	$-0.739097\pi$
$89$	−3.68614	+	2.12819i	−0.390730	+	0.225588i	0.291746	+	0.956496i	$0.405764\pi$
$90$		0			0
$91$	−8.74456	−	7.57301i	−0.916679	−	0.793868i
$92$		0			0
$93$	−6.94158	+	4.00772i	−0.719808	+	0.415581i
$94$		0			0
$95$	8.61684	+	9.52628i	0.884070	+	0.977376i
$96$		0			0
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$		−	4.10891i		−	0.412961i
$100$		0			0
$101$	9.43070	+	5.44482i	0.938390	+	0.541780i	0.889455	−	0.457022i	$-0.151084\pi$
$101$	9.43070	+	5.44482i	0.938390	+	0.541780i	0.0489348	+	0.998802i	$0.484417\pi$
$102$		0			0
$103$	8.05842	−	4.65253i	0.794020	−	0.458428i	−0.0473559	−	0.998878i	$-0.515079\pi$
$103$	8.05842	−	4.65253i	0.794020	−	0.458428i	0.841376	+	0.540450i	$0.181746\pi$
$104$		0			0
$105$	2.43070	+	4.00772i	0.237212	+	0.391114i
$106$		0			0
$107$	0.686141	+	1.18843i	0.0663317	+	0.114890i	0.897284	−	0.441454i	$-0.145537\pi$
$107$	0.686141	+	1.18843i	0.0663317	+	0.114890i	−0.830952	+	0.556344i	$0.812204\pi$
$108$		0			0
$109$	6.05842	−	10.4935i	0.580292	−	1.00509i	−0.415153	−	0.909752i	$-0.636272\pi$
$109$	6.05842	−	10.4935i	0.580292	−	1.00509i	0.995444	−	0.0953429i	$-0.0303947\pi$
$110$		0			0
$111$	6.86141			0.651256
$112$		0			0
$113$			6.92820i			0.651751i	0.945413	+	0.325875i	$0.105659\pi$
$113$			6.92820i			0.651751i	−0.945413	+	0.325875i	$0.894341\pi$
$114$		0			0
$115$	8.61684	+	9.52628i	0.803525	+	0.888330i
$116$		0			0
$117$	−5.18614	−	8.98266i	−0.479459	−	0.830447i
$118$		0			0
$119$	−18.4307	+	6.38458i	−1.68954	+	0.585274i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$	0.372281	−	0.644810i	0.0335675	−	0.0581406i
$124$		0			0
$125$	−9.00000	+	6.63325i	−0.804984	+	0.593296i
$126$		0			0
$127$	−15.1168			−1.34140			−0.670701	−	0.741727i	$-0.734007\pi$
$127$	−15.1168			−1.34140			−0.670701	+	0.741727i	$0.734007\pi$
$128$		0			0
$129$	2.74456	+	1.58457i	0.241645	+	0.139514i
$130$		0			0
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$		0			0
$133$	−2.87228	+	14.9248i	−0.249058	+	1.29415i
$134$		0			0
$135$	2.00000	+	9.30506i	0.172133	+	0.800852i
$136$		0			0
$137$	−8.05842	−	4.65253i	−0.688477	−	0.397493i	0.114564	−	0.993416i	$-0.463453\pi$
$137$	−8.05842	−	4.65253i	−0.688477	−	0.397493i	−0.803041	+	0.595923i	$0.796786\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	−9.37228			−0.789288
$142$		0			0
$143$	6.55842	+	3.78651i	0.548443	+	0.316644i
$144$		0			0
$145$	6.00000	−	1.28962i	0.498273	−	0.107097i
$146$		0			0
$147$	−2.05842	+	5.14987i	−0.169776	+	0.424754i
$148$		0			0
$149$	6.43070	+	11.1383i	0.526824	+	0.912485i	0.999511	+	0.0312555i	$0.00995054\pi$
$149$	6.43070	+	11.1383i	0.526824	+	0.912485i	−0.472688	+	0.881230i	$0.656716\pi$
$150$		0			0
$151$	9.94158	+	5.73977i	0.809034	+	0.467096i	0.846620	−	0.532197i	$-0.178634\pi$
$151$	9.94158	+	5.73977i	0.809034	+	0.467096i	−0.0375862	+	0.999293i	$0.511967\pi$
$152$		0			0
$153$	−17.4891			−1.41391
$154$		0			0
$155$	6.94158	−	21.5306i	0.557561	−	1.72938i
$156$		0			0
$157$	4.50000	−	7.79423i	0.359139	−	0.622047i	−0.628678	−	0.777666i	$-0.716404\pi$
$157$	4.50000	−	7.79423i	0.359139	−	0.622047i	0.987817	+	0.155618i	$0.0497370\pi$
$158$		0			0
$159$	−2.56930	−	4.45015i	−0.203758	−	0.352920i
$160$		0			0
$161$	−2.87228	+	14.9248i	−0.226367	+	1.17624i
$162$		0			0
$163$	1.94158	+	3.36291i	0.152076	+	0.263404i	0.931991	−	0.362483i	$-0.118071\pi$
$163$	1.94158	+	3.36291i	0.152076	+	0.263404i	−0.779914	+	0.625886i	$0.784737\pi$
$164$		0			0
$165$	−2.05842	−	2.27567i	−0.160248	−	0.177161i
$166$		0			0
$167$		−	5.69349i		−	0.440575i	−0.975435	−	0.220288i	$-0.929300\pi$
$167$		−	5.69349i		−	0.440575i	0.975435	−	0.220288i	$-0.0706996\pi$
$168$		0			0
$169$	6.11684			0.470526
$170$		0			0
$171$	−6.81386	+	11.8020i	−0.521069	+	0.902518i
$172$		0			0
$173$	5.61684	+	9.72866i	0.427041	+	0.739656i	0.996609	−	0.0822881i	$-0.0262228\pi$
$173$	5.61684	+	9.72866i	0.427041	+	0.739656i	−0.569568	+	0.821944i	$0.692889\pi$
$174$		0			0
$175$	−12.6753	−	3.78651i	−0.958160	−	0.286233i
$176$		0			0
$177$	−3.17527	+	1.83324i	−0.238668	+	0.137795i
$178$		0			0
$179$	15.7337	+	9.08385i	1.17599	+	0.678959i	0.955084	−	0.296336i	$-0.0957648\pi$
$179$	15.7337	+	9.08385i	1.17599	+	0.678959i	0.220907	+	0.975295i	$0.429098\pi$
$180$		0			0
$181$		−	1.28962i		−	0.0958567i	−0.998851	−	0.0479284i	$-0.984738\pi$
$181$		−	1.28962i		−	0.0958567i	0.998851	−	0.0479284i	$-0.0152619\pi$
$182$		0			0
$183$	−0.861407			−0.0636770
$184$		0			0
$185$	−14.3614	+	12.9904i	−1.05587	+	0.955072i
$186$		0			0
$187$	11.0584	−	6.38458i	0.808672	−	0.466887i
$188$		0			0
$189$	−7.37228	+	8.51278i	−0.536255	+	0.619213i
$190$		0			0
$191$	−5.05842	+	2.92048i	−0.366015	+	0.211319i	−0.671716	−	0.740809i	$-0.734442\pi$
$191$	−5.05842	+	2.92048i	−0.366015	+	0.211319i	0.305701	+	0.952127i	$0.401109\pi$
$192$		0			0
$193$	3.94158	+	2.27567i	0.283721	+	0.163806i	0.635107	−	0.772424i	$-0.280956\pi$
$193$	3.94158	+	2.27567i	0.283721	+	0.163806i	−0.351386	+	0.936231i	$0.614289\pi$
$194$		0			0
$195$	−7.37228	−	2.37686i	−0.527940	−	0.170211i
$196$		0			0
$197$		−	9.74749i		−	0.694480i	−0.937776	−	0.347240i	$-0.887119\pi$
$197$		−	9.74749i		−	0.694480i	0.937776	−	0.347240i	$-0.112881\pi$
$198$		0			0
$199$	−3.43070	+	5.94215i	−0.243196	+	0.421228i	−0.961623	−	0.274375i	$-0.911529\pi$
$199$	−3.43070	+	5.94215i	−0.243196	+	0.421228i	0.718427	+	0.695603i	$0.244863\pi$
$200$		0			0
$201$	5.56930	−	3.21543i	0.392828	−	0.226799i
$202$		0			0
$203$	5.48913	+	4.75372i	0.385261	+	0.333646i
$204$		0			0
$205$	0.441578	+	2.05446i	0.0308411	+	0.143489i
$206$		0			0
$207$	−6.81386	+	11.8020i	−0.473596	+	0.820292i
$208$		0			0
$209$		−	9.94987i		−	0.688247i
$210$		0			0
$211$		−	7.57301i		−	0.521348i	−0.965427	−	0.260674i	$-0.916055\pi$
$211$		−	7.57301i		−	0.521348i	0.965427	−	0.260674i	$-0.0839447\pi$
$212$		0			0
$213$	4.11684	−	7.13058i	0.282082	−	0.488579i
$214$		0			0
$215$	−8.74456	+	1.87953i	−0.596374	+	0.128183i
$216$		0			0
$217$	25.2921	−	8.76144i	1.71694	−	0.594766i
$218$		0			0
$219$	−3.17527	+	1.83324i	−0.214565	+	0.123879i
$220$		0			0
$221$	16.1168	−	27.9152i	1.08414	−	1.87778i
$222$		0			0
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$		0			0
$225$	−9.62772	−	6.92820i	−0.641848	−	0.461880i
$226$		0			0
$227$	−5.31386	−	3.06796i	−0.352693	−	0.203628i	0.313178	−	0.949695i	$-0.398606\pi$
$227$	−5.31386	−	3.06796i	−0.352693	−	0.203628i	−0.665871	+	0.746067i	$0.731940\pi$
$228$		0			0
$229$	−6.94158	+	4.00772i	−0.458712	+	0.264838i	−0.711503	−	0.702683i	$-0.751985\pi$
$229$	−6.94158	+	4.00772i	−0.458712	+	0.264838i	0.252790	+	0.967521i	$0.418652\pi$
$230$		0			0
$231$	0.686141	−	3.56529i	0.0451447	−	0.234579i
$232$		0			0
$233$	18.1753	−	10.4935i	1.19070	−	0.687452i	0.232236	−	0.972660i	$-0.425396\pi$
$233$	18.1753	−	10.4935i	1.19070	−	0.687452i	0.958466	+	0.285208i	$0.0920626\pi$
$234$		0			0
$235$	19.6168	−	17.7441i	1.27966	−	1.15750i
$236$		0			0
$237$	7.37228			0.478881
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	13.5000	+	7.79423i	0.869611	+	0.502070i	0.867219	−	0.497927i	$-0.165905\pi$
$241$	13.5000	+	7.79423i	0.869611	+	0.502070i	0.00239235	+	0.999997i	$0.499238\pi$
$242$		0			0
$243$	−13.6277	+	7.86797i	−0.874219	+	0.504730i
$244$		0			0
$245$	−5.44158	−	14.6761i	−0.347650	−	0.937625i
$246$		0			0
$247$	−12.5584	−	21.7518i	−0.799073	−	1.38404i
$248$		0			0
$249$	−3.37228	+	5.84096i	−0.213710	+	0.370156i
$250$		0			0
$251$	−3.86141			−0.243730			−0.121865	−	0.992547i	$-0.538887\pi$
$251$	−3.86141			−0.243730			−0.121865	+	0.992547i	$0.538887\pi$
$252$		0			0
$253$		−	9.94987i		−	0.625543i
$254$		0			0
$255$	−9.68614	+	8.76144i	−0.606570	+	0.548663i
$256$		0			0
$257$	−5.05842	−	8.76144i	−0.315536	−	0.546524i	0.664016	−	0.747719i	$-0.268851\pi$
$257$	−5.05842	−	8.76144i	−0.315536	−	0.546524i	−0.979551	+	0.201195i	$0.935518\pi$
$258$		0			0
$259$	−22.5000	−	4.33013i	−1.39808	−	0.269061i
$260$		0			0
$261$	3.25544	+	5.63858i	0.201507	+	0.349020i
$262$		0			0
$263$	9.68614	−	16.7769i	0.597273	−	1.03451i	−0.395949	−	0.918273i	$-0.629584\pi$
$263$	9.68614	−	16.7769i	0.597273	−	1.03451i	0.993222	−	0.116235i	$-0.0370824\pi$
$264$		0			0
$265$	13.8030	+	4.45015i	0.847911	+	0.273371i
$266$		0			0
$267$	−3.37228			−0.206380
$268$		0			0
$269$	1.19702	+	0.691097i	0.0729833	+	0.0421369i	0.536048	−	0.844188i	$-0.319917\pi$
$269$	1.19702	+	0.691097i	0.0729833	+	0.0421369i	−0.463064	+	0.886325i	$0.653250\pi$
$270$		0			0
$271$	0.686141	+	1.18843i	0.0416801	+	0.0721920i	0.886113	−	0.463469i	$-0.153396\pi$
$271$	0.686141	+	1.18843i	0.0416801	+	0.0721920i	−0.844433	+	0.535662i	$0.820062\pi$
$272$		0			0
$273$	−3.00000	−	8.66025i	−0.181568	−	0.524142i
$274$		0			0
$275$	8.61684	+	0.866025i	0.519615	+	0.0522233i
$276$		0			0
$277$	17.0584	+	9.84868i	1.02494	+	0.591750i	0.915531	−	0.402247i	$-0.131771\pi$
$277$	17.0584	+	9.84868i	1.02494	+	0.591750i	0.109410	+	0.993997i	$0.465104\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	−25.1168			−1.49835			−0.749173	−	0.662375i	$-0.769549\pi$
$281$	−25.1168			−1.49835			−0.749173	+	0.662375i	$0.769549\pi$
$282$		0			0
$283$	−6.94158	−	4.00772i	−0.412634	−	0.238234i	0.279287	−	0.960208i	$-0.409902\pi$
$283$	−6.94158	−	4.00772i	−0.412634	−	0.238234i	−0.691921	+	0.721973i	$0.743235\pi$
$284$		0			0
$285$	2.13859	+	9.94987i	0.126679	+	0.589380i
$286$		0			0
$287$	−1.62772	+	1.87953i	−0.0960812	+	0.110945i
$288$		0			0
$289$	−18.6753	−	32.3465i	−1.09855	−	1.90274i
$290$		0			0
$291$	4.11684	+	2.37686i	0.241334	+	0.139334i
$292$		0			0
$293$	2.13859			0.124938			0.0624690	−	0.998047i	$-0.480103\pi$
$293$	2.13859			0.124938			0.0624690	+	0.998047i	$0.480103\pi$
$294$		0			0
$295$	3.17527	−	9.84868i	0.184871	−	0.573413i
$296$		0			0
$297$	3.68614	−	6.38458i	0.213892	−	0.370471i
$298$		0			0
$299$	−12.5584	−	21.7518i	−0.726272	−	1.25794i
$300$		0			0
$301$	−8.00000	−	6.92820i	−0.461112	−	0.399335i
$302$		0			0
$303$	4.31386	+	7.47182i	0.247825	+	0.429245i
$304$		0			0
$305$	1.80298	−	1.63086i	0.103239	−	0.0933828i
$306$		0			0
$307$			12.9715i			0.740325i	0.928967	+	0.370163i	$0.120698\pi$
$307$			12.9715i			0.740325i	−0.928967	+	0.370163i	$0.879302\pi$
$308$		0			0
$309$	7.37228			0.419394
$310$		0			0
$311$	−0.686141	+	1.18843i	−0.0389075	+	0.0673897i	−0.884823	−	0.465927i	$-0.845721\pi$
$311$	−0.686141	+	1.18843i	−0.0389075	+	0.0673897i	0.845916	+	0.533316i	$0.179054\pi$
$312$		0			0
$313$	6.43070	+	11.1383i	0.363485	+	0.629574i	0.988532	−	0.151013i	$-0.0482535\pi$
$313$	6.43070	+	11.1383i	0.363485	+	0.629574i	−0.625047	+	0.780587i	$0.714920\pi$
$314$		0			0
$315$	−0.302985	−	14.0313i	−0.0170713	−	0.790576i
$316$		0			0
$317$	−0.941578	+	0.543620i	−0.0528843	+	0.0305328i	−0.526209	−	0.850355i	$-0.676387\pi$
$317$	−0.941578	+	0.543620i	−0.0528843	+	0.0305328i	0.473325	+	0.880888i	$0.343054\pi$
$318$		0			0
$319$	−4.11684	−	2.37686i	−0.230499	−	0.133079i
$320$		0			0
$321$			1.08724i			0.0606839i
$322$		0			0
$323$	−42.3505			−2.35645
$324$		0			0
$325$	19.9307	−	8.98266i	1.10556	−	0.498268i
$326$		0			0
$327$	8.31386	−	4.80001i	0.459757	−	0.265441i
$328$		0			0
$329$	30.7337	+	5.91470i	1.69440	+	0.326088i
$330$		0			0
$331$	10.5000	−	6.06218i	0.577132	−	0.333207i	−0.182861	−	0.983139i	$-0.558536\pi$
$331$	10.5000	−	6.06218i	0.577132	−	0.333207i	0.759993	+	0.649931i	$0.225202\pi$
$332$		0			0
$333$	−17.7921	−	10.2723i	−0.975002	−	0.562917i
$334$		0			0
$335$	−5.56930	+	17.2742i	−0.304283	+	0.943792i
$336$		0			0
$337$			6.92820i			0.377403i	0.982034	+	0.188702i	$0.0604279\pi$
$337$			6.92820i			0.377403i	−0.982034	+	0.188702i	$0.939572\pi$
$338$		0			0
$339$	−2.74456	+	4.75372i	−0.149064	+	0.258187i
$340$		0			0
$341$	−15.1753	+	8.76144i	−0.821787	+	0.474459i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	2.13859	+	9.94987i	0.115138	+	0.535683i
$346$		0			0
$347$	6.43070	−	11.1383i	0.345218	−	0.597936i	−0.640175	−	0.768229i	$-0.721138\pi$
$347$	6.43070	−	11.1383i	0.345218	−	0.597936i	0.985393	+	0.170293i	$0.0544716\pi$
$348$		0			0
$349$		−	8.21782i		−	0.439890i	−0.975512	−	0.219945i	$-0.929412\pi$
$349$		−	8.21782i		−	0.439890i	0.975512	−	0.219945i	$-0.0705878\pi$
$350$		0			0
$351$		−	18.6101i		−	0.993335i
$352$		0			0
$353$	5.31386	−	9.20387i	0.282828	−	0.489873i	−0.689252	−	0.724522i	$-0.742061\pi$
$353$	5.31386	−	9.20387i	0.282828	−	0.489873i	0.972080	+	0.234649i	$0.0753940\pi$
$354$		0			0
$355$	4.88316	+	22.7190i	0.259171	+	1.20580i
$356$		0			0
$357$	−15.1753	−	2.92048i	−0.803160	−	0.154568i
$358$		0			0
$359$	9.17527	−	5.29734i	0.484252	−	0.279583i	−0.237935	−	0.971281i	$-0.576470\pi$
$359$	9.17527	−	5.29734i	0.484252	−	0.279583i	0.722187	+	0.691698i	$0.243137\pi$
$360$		0			0
$361$	−7.00000	+	12.1244i	−0.368421	+	0.638124i
$362$		0			0
$363$		−	6.33830i		−	0.332674i
$364$		0			0
$365$	3.17527	−	9.84868i	0.166201	−	0.515504i
$366$		0			0
$367$	14.6168	+	8.43904i	0.762993	+	0.440514i	0.830369	−	0.557213i	$-0.188129\pi$
$367$	14.6168	+	8.43904i	0.762993	+	0.440514i	−0.0673763	+	0.997728i	$0.521463\pi$
$368$		0			0
$369$	−1.93070	+	1.11469i	−0.100508	+	0.0580286i
$370$		0			0
$371$	5.61684	+	16.2144i	0.291612	+	0.841811i
$372$		0			0
$373$	13.2921	−	7.67420i	0.688239	−	0.397355i	−0.114713	−	0.993399i	$-0.536595\pi$
$373$	13.2921	−	7.67420i	0.688239	−	0.397355i	0.802952	+	0.596044i	$0.203261\pi$
$374$		0			0
$375$	−8.80298	+	0.986051i	−0.454584	+	0.0509194i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$			35.2858i			1.81251i	0.422730	+	0.906256i	$0.361072\pi$
$379$			35.2858i			1.81251i	−0.422730	+	0.906256i	$0.638928\pi$
$380$		0			0
$381$	−10.3723	−	5.98844i	−0.531388	−	0.306797i
$382$		0			0
$383$	19.2446	−	11.1109i	0.983351	−	0.567738i	0.0800710	−	0.996789i	$-0.474485\pi$
$383$	19.2446	−	11.1109i	0.983351	−	0.567738i	0.903280	+	0.429051i	$0.141152\pi$
$384$		0			0
$385$	5.31386	+	8.76144i	0.270819	+	0.446525i
$386$		0			0
$387$	−4.74456	−	8.21782i	−0.241180	−	0.417735i
$388$		0			0
$389$	−5.05842	+	8.76144i	−0.256472	+	0.444223i	−0.965294	−	0.261164i	$-0.915894\pi$
$389$	−5.05842	+	8.76144i	−0.256472	+	0.444223i	0.708822	+	0.705387i	$0.249227\pi$
$390$		0			0
$391$	−42.3505			−2.14176
$392$		0			0
$393$			2.37686i			0.119897i
$394$		0			0
$395$	−15.4307	+	13.9576i	−0.776403	+	0.702283i
$396$		0			0
$397$	8.05842	+	13.9576i	0.404441	+	0.700512i	0.994256	−	0.107026i	$-0.0341329\pi$
$397$	8.05842	+	13.9576i	0.404441	+	0.700512i	−0.589816	+	0.807538i	$0.700800\pi$
$398$		0			0
$399$	−7.88316	+	9.10268i	−0.394651	+	0.455704i
$400$		0			0
$401$	−3.12772	−	5.41737i	−0.156191	−	0.270530i	0.777301	−	0.629129i	$-0.216588\pi$
$401$	−3.12772	−	5.41737i	−0.156191	−	0.270530i	−0.933492	+	0.358598i	$0.883255\pi$
$402$		0			0
$403$	−22.1168	+	38.3075i	−1.10172	+	1.90823i
$404$		0			0
$405$	2.56930	−	7.96916i	0.127669	−	0.395991i
$406$		0			0
$407$	15.0000			0.743522
$408$		0			0
$409$	−0.941578	−	0.543620i	−0.0465580	−	0.0268803i	0.476540	−	0.879153i	$-0.341891\pi$
$409$	−0.941578	−	0.543620i	−0.0465580	−	0.0268803i	−0.523098	+	0.852272i	$0.675224\pi$
$410$		0			0
$411$	−3.68614	−	6.38458i	−0.181824	−	0.314928i
$412$		0			0
$413$	11.5693	−	4.00772i	0.569288	−	0.197207i
$414$		0			0
$415$	−4.00000	−	18.6101i	−0.196352	−	0.913535i
$416$		0			0
$417$	8.23369	+	4.75372i	0.403205	+	0.232791i
$418$		0			0
$419$	25.6277			1.25200			0.625998	−	0.779825i	$-0.284692\pi$
$419$	25.6277			1.25200			0.625998	+	0.779825i	$0.284692\pi$
$420$		0			0
$421$	16.2337			0.791182			0.395591	−	0.918427i	$-0.370540\pi$
$421$	16.2337			0.791182			0.395591	+	0.918427i	$0.370540\pi$
$422$		0			0
$423$	24.3030	+	14.0313i	1.18165	+	0.682227i
$424$		0			0
$425$	3.68614	−	36.6766i	0.178804	−	1.77908i
$426$		0			0
$427$	2.82473	+	0.543620i	0.136698	+	0.0263076i
$428$		0			0
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	12.1753	+	7.02939i	0.586462	+	0.338594i	0.763697	−	0.645575i	$-0.223382\pi$
$431$	12.1753	+	7.02939i	0.586462	+	0.338594i	−0.177235	+	0.984169i	$0.556715\pi$
$432$		0			0
$433$	−0.510875			−0.0245511			−0.0122755	−	0.999925i	$-0.503908\pi$
$433$	−0.510875			−0.0245511			−0.0122755	+	0.999925i	$0.503908\pi$
$434$		0			0
$435$	4.62772	+	1.49200i	0.221882	+	0.0715359i
$436$		0			0
$437$	−16.5000	+	28.5788i	−0.789302	+	1.36711i
$438$		0			0
$439$	−10.8030	−	18.7113i	−0.515598	−	0.893042i	−0.999836	−	0.0181060i	$-0.994236\pi$
$439$	−10.8030	−	18.7113i	−0.515598	−	0.893042i	0.484238	−	0.874936i	$-0.339097\pi$
$440$		0			0
$441$	13.0475	−	10.2723i	0.621312	−	0.489156i
$442$		0			0
$443$	−9.68614	−	16.7769i	−0.460202	−	0.797094i	0.538768	−	0.842454i	$-0.318890\pi$
$443$	−9.68614	−	16.7769i	−0.460202	−	0.797094i	−0.998971	+	0.0453600i	$0.985557\pi$
$444$		0			0
$445$	7.05842	−	6.38458i	0.334601	−	0.302658i
$446$		0			0
$447$			10.1899i			0.481967i
$448$		0			0
$449$	2.13859			0.100926			0.0504632	−	0.998726i	$-0.483930\pi$
$449$	2.13859			0.100926			0.0504632	+	0.998726i	$0.483930\pi$
$450$		0			0
$451$	0.813859	−	1.40965i	0.0383231	−	0.0663776i
$452$		0			0
$453$	4.54755	+	7.87658i	0.213662	+	0.370074i
$454$		0			0
$455$	22.6753	+	12.4468i	1.06303	+	0.583513i
$456$		0			0
$457$	−28.2921	+	16.3345i	−1.32345	+	0.764094i	−0.984277	−	0.176631i	$-0.943480\pi$
$457$	−28.2921	+	16.3345i	−1.32345	+	0.764094i	−0.339172	+	0.940724i	$0.610147\pi$
$458$		0			0
$459$	−27.1753	−	15.6896i	−1.26843	−	0.732330i
$460$		0			0
$461$			28.4125i			1.32330i	0.749811	+	0.661652i	$0.230144\pi$
$461$			28.4125i			1.32330i	−0.749811	+	0.661652i	$0.769856\pi$
$462$		0			0
$463$	37.3505			1.73583			0.867913	−	0.496716i	$-0.165461\pi$
$463$	37.3505			1.73583			0.867913	+	0.496716i	$0.165461\pi$
$464$		0			0
$465$	13.2921	−	12.0232i	0.616407	−	0.557561i
$466$		0			0
$467$	−20.9198	+	12.0781i	−0.968054	+	0.558906i	−0.898642	−	0.438682i	$-0.855446\pi$
$467$	−20.9198	+	12.0781i	−0.968054	+	0.558906i	−0.0694117	+	0.997588i	$0.522112\pi$
$468$		0			0
$469$	−20.2921	+	7.02939i	−0.937003	+	0.324587i
$470$		0			0
$471$	6.17527	−	3.56529i	0.284541	−	0.164280i
$472$		0			0
$473$	6.00000	+	3.46410i	0.275880	+	0.159280i
$474$		0			0
$475$	−23.3139	−	16.7769i	−1.06971	−	0.769776i
$476$		0			0
$477$			15.3861i			0.704480i
$478$		0			0
$479$	16.8030	−	29.1036i	0.767748	−	1.32978i	−0.171033	−	0.985265i	$-0.554711\pi$
$479$	16.8030	−	29.1036i	0.767748	−	1.32978i	0.938781	−	0.344513i	$-0.111956\pi$
$480$		0			0
$481$	32.7921	−	18.9325i	1.49519	−	0.863249i
$482$		0			0
$483$	−7.88316	+	9.10268i	−0.358696	+	0.414186i
$484$		0			0
$485$	−13.1168	+	2.81929i	−0.595605	+	0.128017i
$486$		0			0
$487$	4.94158	−	8.55906i	0.223924	−	0.387848i	−0.732072	−	0.681227i	$-0.761447\pi$
$487$	4.94158	−	8.55906i	0.223924	−	0.387848i	0.955996	+	0.293379i	$0.0947798\pi$
$488$		0			0
$489$			3.07657i			0.139127i
$490$		0			0
$491$		−	10.3923i		−	0.468998i	−0.972116	−	0.234499i	$-0.924655\pi$
$491$		−	10.3923i		−	0.468998i	0.972116	−	0.234499i	$-0.0753450\pi$
$492$		0			0
$493$	−10.1168	+	17.5229i	−0.455640	+	0.789191i
$494$		0			0
$495$	1.93070	+	8.98266i	0.0867787	+	0.403741i
$496$		0			0
$497$	−18.0000	+	20.7846i	−0.807410	+	0.932317i
$498$		0			0
$499$	16.2921	−	9.40625i	0.729335	−	0.421082i	−0.0888438	−	0.996046i	$-0.528317\pi$
$499$	16.2921	−	9.40625i	0.729335	−	0.421082i	0.818179	+	0.574964i	$0.194984\pi$
$500$		0			0
$501$	2.25544	−	3.90653i	0.100766	−	0.174531i
$502$		0			0
$503$		−	14.1514i		−	0.630978i	−0.948929	−	0.315489i	$-0.897831\pi$
$503$		−	14.1514i		−	0.630978i	0.948929	−	0.315489i	$-0.102169\pi$
$504$		0			0
$505$	−23.1753	−	7.47182i	−1.03129	−	0.332492i
$506$		0			0
$507$	4.19702	+	2.42315i	0.186396	+	0.107616i
$508$		0			0
$509$	−36.4307	+	21.0333i	−1.61476	+	0.932284i	−0.626517	+	0.779408i	$0.715520\pi$
$509$	−36.4307	+	21.0333i	−1.61476	+	0.932284i	−0.988245	+	0.152876i	$0.951147\pi$
$510$		0			0
$511$	11.5693	−	4.00772i	0.511796	−	0.177291i
$512$		0			0
$513$	−21.1753	+	12.2255i	−0.934911	+	0.539771i
$514$		0			0
$515$	−15.4307	+	13.9576i	−0.679958	+	0.615045i
$516$		0			0
$517$	−20.4891			−0.901111
$518$		0			0
$519$			8.90030i			0.390680i
$520$		0			0
$521$	−14.3614	−	8.29156i	−0.629185	−	0.363260i	0.151252	−	0.988495i	$-0.451670\pi$
$521$	−14.3614	−	8.29156i	−0.629185	−	0.363260i	−0.780436	+	0.625235i	$0.785003\pi$
$522$		0			0
$523$	−15.9416	+	9.20387i	−0.697077	+	0.402457i	−0.806258	−	0.591565i	$-0.798510\pi$
$523$	−15.9416	+	9.20387i	−0.697077	+	0.402457i	0.109181	+	0.994022i	$0.465177\pi$
$524$		0			0
$525$	−7.19702	−	7.61930i	−0.314104	−	0.332534i
$526$		0			0
$527$	37.2921	+	64.5918i	1.62447	+	2.81366i
$528$		0			0
$529$	−5.00000	+	8.66025i	−0.217391	+	0.376533i
$530$		0			0
$531$	10.9783			0.476415
$532$		0			0
$533$		−	4.10891i		−	0.177977i
$534$		0			0
$535$	−2.05842	−	2.27567i	−0.0889933	−	0.0983858i
$536$		0			0
$537$	7.19702	+	12.4656i	0.310574	+	0.537930i
$538$		0			0
$539$	−4.50000	+	11.2583i	−0.193829	+	0.484931i
$540$		0			0
$541$	11.1753	+	19.3561i	0.480462	+	0.832185i	0.999749	−	0.0224152i	$-0.00713559\pi$
$541$	11.1753	+	19.3561i	0.480462	+	0.832185i	−0.519287	+	0.854600i	$0.673802\pi$
$542$		0			0
$543$	0.510875	−	0.884861i	0.0219237	−	0.0379730i
$544$		0			0
$545$	−8.31386	+	25.7870i	−0.356127	+	1.10459i
$546$		0			0
$547$	36.4674			1.55923			0.779616	−	0.626258i	$-0.215414\pi$
$547$	36.4674			1.55923			0.779616	+	0.626258i	$0.215414\pi$
$548$		0			0
$549$	2.23369	+	1.28962i	0.0953315	+	0.0550397i
$550$		0			0
$551$	7.88316	+	13.6540i	0.335834	+	0.581681i
$552$		0			0
$553$	−24.1753	−	4.65253i	−1.02804	−	0.197846i
$554$		0			0
$555$	−15.0000	+	3.22405i	−0.636715	+	0.136853i
$556$		0			0
$557$	−30.7337	−	17.7441i	−1.30223	−	0.751842i	−0.321442	−	0.946929i	$-0.604168\pi$
$557$	−30.7337	−	17.7441i	−1.30223	−	0.751842i	−0.980786	+	0.195087i	$0.937501\pi$
$558$		0			0
$559$	17.4891			0.739711
$560$		0			0
$561$	10.1168			0.427133
$562$		0			0
$563$	−16.8030	−	9.70121i	−0.708161	−	0.408857i	0.102219	−	0.994762i	$-0.467406\pi$
$563$	−16.8030	−	9.70121i	−0.708161	−	0.408857i	−0.810380	+	0.585905i	$0.800739\pi$
$564$		0			0
$565$	−3.25544	−	15.1460i	−0.136957	−	0.637198i
$566$		0			0
$567$	9.36141	−	3.24289i	0.393142	−	0.136188i
$568$		0			0
$569$	−0.383156	−	0.663646i	−0.0160627	−	0.0278215i	0.857882	−	0.513846i	$-0.171780\pi$
$569$	−0.383156	−	0.663646i	−0.0160627	−	0.0278215i	−0.873945	+	0.486025i	$0.838446\pi$
$570$		0			0
$571$	12.1753	+	7.02939i	0.509519	+	0.294171i	0.732636	−	0.680621i	$-0.238290\pi$
$571$	12.1753	+	7.02939i	0.509519	+	0.294171i	−0.223117	+	0.974792i	$0.571623\pi$
$572$		0			0
$573$	−4.62772			−0.193326
$574$		0			0
$575$	−23.3139	−	16.7769i	−0.972255	−	0.699645i
$576$		0			0
$577$	−12.6861	+	21.9730i	−0.528131	+	0.914750i	0.471331	+	0.881956i	$0.343774\pi$
$577$	−12.6861	+	21.9730i	−0.528131	+	0.914750i	−0.999462	+	0.0327933i	$0.989560\pi$
$578$		0			0
$579$	1.80298	+	3.12286i	0.0749295	+	0.129782i
$580$		0			0
$581$	14.7446	−	17.0256i	0.611708	−	0.706339i
$582$		0			0
$583$	−5.61684	−	9.72866i	−0.232626	−	0.402920i
$584$		0			0
$585$	15.5584	+	17.2005i	0.643262	+	0.711152i
$586$		0			0
$587$			6.63325i			0.273784i	0.990586	+	0.136892i	$0.0437113\pi$
$587$			6.63325i			0.273784i	−0.990586	+	0.136892i	$0.956289\pi$
$588$		0			0
$589$	58.1168			2.39466
$590$		0			0
$591$	3.86141	−	6.68815i	0.158837	−	0.275114i
$592$		0			0
$593$	−10.5475	−	18.2689i	−0.433136	−	0.750213i	0.564006	−	0.825771i	$-0.309260\pi$
$593$	−10.5475	−	18.2689i	−0.433136	−	0.750213i	−0.997141	+	0.0755577i	$0.975926\pi$
$594$		0			0
$595$	37.2921	−	22.6179i	1.52883	−	0.927241i
$596$		0			0
$597$	−4.70789	+	2.71810i	−0.192681	+	0.111244i
$598$		0			0
$599$	−27.1753	−	15.6896i	−1.11035	−	0.641062i	−0.171431	−	0.985196i	$-0.554839\pi$
$599$	−27.1753	−	15.6896i	−1.11035	−	0.641062i	−0.938920	+	0.344135i	$0.888172\pi$
$600$		0			0
$601$			9.50744i			0.387817i	0.981020	+	0.193908i	$0.0621164\pi$
$601$			9.50744i			0.387817i	−0.981020	+	0.193908i	$0.937884\pi$
$602$		0			0
$603$	−19.2554			−0.784142
$604$		0			0
$605$	12.0000	+	13.2665i	0.487869	+	0.539360i
$606$		0			0
$607$	−6.38316	+	3.68532i	−0.259084	+	0.149582i	−0.623917	−	0.781491i	$-0.714460\pi$
$607$	−6.38316	+	3.68532i	−0.259084	+	0.149582i	0.364832	+	0.931073i	$0.381126\pi$
$608$		0			0
$609$	1.88316	+	5.43620i	0.0763093	+	0.220286i
$610$		0			0
$611$	−44.7921	+	25.8607i	−1.81209	+	1.04621i
$612$		0			0
$613$	−4.50000	−	2.59808i	−0.181753	−	0.104935i	0.406363	−	0.913712i	$-0.366797\pi$
$613$	−4.50000	−	2.59808i	−0.181753	−	0.104935i	−0.588116	+	0.808776i	$0.700130\pi$
$614$		0			0
$615$	−0.510875	+	1.58457i	−0.0206005	+	0.0638962i
$616$		0			0
$617$			45.4381i			1.82927i	0.404283	+	0.914634i	$0.367521\pi$
$617$			45.4381i			1.82927i	−0.404283	+	0.914634i	$0.632479\pi$
$618$		0			0
$619$	21.9891	−	38.0863i	0.883818	−	1.53082i	0.0367546	−	0.999324i	$-0.488298\pi$
$619$	21.9891	−	38.0863i	0.883818	−	1.53082i	0.847063	−	0.531493i	$-0.178369\pi$
$620$		0			0
$621$	−21.1753	+	12.2255i	−0.849734	+	0.490594i
$622$		0			0
$623$	11.0584	+	2.12819i	0.443046	+	0.0852643i
$624$		0			0
$625$	16.5584	−	18.7302i	0.662337	−	0.749206i
$626$		0			0
$627$	3.94158	−	6.82701i	0.157411	−	0.272645i
$628$		0			0
$629$		−	63.8458i		−	2.54570i
$630$		0			0
$631$			28.1176i			1.11934i	0.828715	+	0.559671i	$0.189073\pi$
$631$			28.1176i			1.11934i	−0.828715	+	0.559671i	$0.810927\pi$
$632$		0			0
$633$	3.00000	−	5.19615i	0.119239	−	0.206529i
$634$		0			0
$635$	33.0475	−	7.10313i	1.31145	−	0.281879i
$636$		0			0
$637$	4.37228	+	30.2921i	0.173236	+	1.20021i
$638$		0			0
$639$	−21.3505	+	12.3267i	−0.844614	+	0.487638i
$640$		0			0
$641$	−17.8723	+	30.9557i	−0.705913	+	1.22268i	0.260448	+	0.965488i	$0.416130\pi$
$641$	−17.8723	+	30.9557i	−0.705913	+	1.22268i	−0.966361	+	0.257189i	$0.917204\pi$
$642$		0			0
$643$			40.6844i			1.60443i	0.597032	+	0.802217i	$0.296346\pi$
$643$			40.6844i			1.60443i	−0.597032	+	0.802217i	$0.703654\pi$
$644$		0			0
$645$	−6.74456	−	2.17448i	−0.265567	−	0.0856201i
$646$		0			0
$647$	3.63859	+	2.10074i	0.143048	+	0.0825887i	0.569816	−	0.821772i	$-0.307015\pi$
$647$	3.63859	+	2.10074i	0.143048	+	0.0825887i	−0.426768	+	0.904361i	$0.640348\pi$
$648$		0			0
$649$	−6.94158	+	4.00772i	−0.272481	+	0.157317i
$650$		0			0
$651$	20.8247	+	4.00772i	0.816186	+	0.157075i
$652$		0			0
$653$	26.6168	−	15.3672i	1.04160	−	0.601367i	0.121312	−	0.992614i	$-0.461290\pi$
$653$	26.6168	−	15.3672i	1.04160	−	0.601367i	0.920285	+	0.391248i	$0.127956\pi$
$654$		0			0
$655$	−4.50000	−	4.97494i	−0.175830	−	0.194387i
$656$		0			0
$657$	10.9783			0.428302
$658$		0			0
$659$			40.6844i			1.58484i	0.609977	+	0.792419i	$0.291178\pi$
$659$			40.6844i			1.58484i	−0.609977	+	0.792419i	$0.708822\pi$
$660$		0			0
$661$	−21.1753	−	12.2255i	−0.823622	−	0.475519i	0.0280416	−	0.999607i	$-0.491073\pi$
$661$	−21.1753	−	12.2255i	−0.823622	−	0.475519i	−0.851664	+	0.524088i	$0.824406\pi$
$662$		0			0
$663$	22.1168	−	12.7692i	0.858947	−	0.495913i
$664$		0			0
$665$	−0.733688	−	33.9774i	−0.0284512	−	1.31759i
$666$		0			0
$667$	7.88316	+	13.6540i	0.305237	+	0.528686i
$668$		0			0
$669$	4.11684	−	7.13058i	0.159166	−	0.275684i
$670$		0			0
$671$	−1.88316			−0.0726984
$672$		0			0
$673$		−	15.1460i		−	0.583836i	−0.956443	−	0.291918i	$-0.905706\pi$
$673$		−	15.1460i		−	0.583836i	0.956443	−	0.291918i	$-0.0942935\pi$
$674$		0			0
$675$	−8.74456	−	19.4024i	−0.336578	−	0.746799i
$676$		0			0
$677$	11.6168	+	20.1210i	0.446472	+	0.773311i	0.998153	−	0.0607432i	$-0.0193471\pi$
$677$	11.6168	+	20.1210i	0.446472	+	0.773311i	−0.551682	+	0.834055i	$0.686014\pi$
$678$		0			0
$679$	−12.0000	−	10.3923i	−0.460518	−	0.398820i
$680$		0			0
$681$	−2.43070	−	4.21010i	−0.0931448	−	0.161331i
$682$		0			0
$683$	5.31386	−	9.20387i	0.203329	−	0.352176i	−0.746270	−	0.665643i	$-0.768157\pi$
$683$	5.31386	−	9.20387i	0.203329	−	0.352176i	0.949599	+	0.313467i	$0.101491\pi$
$684$		0			0
$685$	19.8030	+	6.38458i	0.756633	+	0.243942i
$686$		0			0
$687$	−6.35053			−0.242288
$688$		0			0
$689$	−24.5584	−	14.1788i	−0.935601	−	0.540170i
$690$		0			0
$691$	8.31386	+	14.4000i	0.316274	+	0.547803i	0.979708	−	0.200433i	$-0.0642347\pi$
$691$	8.31386	+	14.4000i	0.316274	+	0.547803i	−0.663433	+	0.748235i	$0.730901\pi$
$692$		0			0
$693$	−7.11684	+	8.21782i	−0.270347	+	0.312169i
$694$		0			0
$695$	−26.2337	+	5.63858i	−0.995101	+	0.213884i
$696$		0			0
$697$	−6.00000	−	3.46410i	−0.227266	−	0.131212i
$698$		0			0
$699$	16.6277			0.628918
$700$		0			0
$701$	9.25544			0.349573			0.174787	−	0.984606i	$-0.444076\pi$
$701$	9.25544			0.349573			0.174787	+	0.984606i	$0.444076\pi$
$702$		0			0
$703$	−43.0842	−	24.8747i	−1.62495	−	0.938167i
$704$		0			0
$705$	20.4891	−	4.40387i	0.771665	−	0.165859i
$706$		0			0
$707$	−9.43070	−	27.2241i	−0.354678	−	1.02387i
$708$		0			0
$709$	17.1753	+	29.7484i	0.645031	+	1.11723i	0.984294	+	0.176535i	$0.0564887\pi$
$709$	17.1753	+	29.7484i	0.645031	+	1.11723i	−0.339264	+	0.940691i	$0.610178\pi$
$710$		0			0
$711$	−19.1168	−	11.0371i	−0.716938	−	0.413924i
$712$		0			0
$713$	58.1168			2.17649
$714$		0			0
$715$	−16.1168	−	5.19615i	−0.602736	−	0.194325i
$716$		0			0
$717$	−4.11684	+	7.13058i	−0.153746	+	0.266296i
$718$		0			0
$719$	−11.3139	−	19.5962i	−0.421936	−	0.730814i	0.574193	−	0.818720i	$-0.305316\pi$
$719$	−11.3139	−	19.5962i	−0.421936	−	0.730814i	−0.996129	+	0.0879058i	$0.971983\pi$
$720$		0			0
$721$	−24.1753	−	4.65253i	−0.900334	−	0.173269i
$722$		0			0
$723$	6.17527	+	10.6959i	0.229661	+	0.397784i
$724$		0			0
$725$	−12.5109	+	5.63858i	−0.464642	+	0.209412i
$726$		0			0
$727$		−	36.5754i		−	1.35651i	−0.734827	−	0.678254i	$-0.762737\pi$
$727$		−	36.5754i		−	1.35651i	0.734827	−	0.678254i	$-0.237263\pi$
$728$		0			0
$729$	−1.23369			−0.0456921
$730$		0			0
$731$	14.7446	−	25.5383i	0.545347	−	0.944569i
$732$		0			0
$733$	−18.9891	−	32.8901i	−0.701379	−	1.21482i	−0.967982	−	0.251018i	$-0.919235\pi$
$733$	−18.9891	−	32.8901i	−0.701379	−	1.21482i	0.266603	−	0.963806i	$-0.414099\pi$
$734$		0			0
$735$	2.08017	−	12.2255i	0.0767283	−	0.450946i
$736$		0			0
$737$	12.1753	−	7.02939i	0.448482	−	0.258931i
$738$		0			0
$739$	−17.6168	−	10.1711i	−0.648046	−	0.374150i	0.139661	−	0.990199i	$-0.455399\pi$
$739$	−17.6168	−	10.1711i	−0.648046	−	0.374150i	−0.787707	+	0.616050i	$0.788732\pi$
$740$		0			0
$741$		−	19.8997i		−	0.731036i
$742$		0			0
$743$	27.8614			1.02214			0.511068	−	0.859540i	$-0.329250\pi$
$743$	27.8614			1.02214			0.511068	+	0.859540i	$0.329250\pi$
$744$		0			0
$745$	−19.2921	−	21.3282i	−0.706808	−	0.781406i
$746$		0			0
$747$	17.4891	−	10.0974i	0.639894	−	0.369443i
$748$		0			0
$749$	0.686141	−	3.56529i	0.0250710	−	0.130273i
$750$		0			0
$751$	6.94158	−	4.00772i	0.253302	−	0.146244i	−0.367973	−	0.929836i	$-0.619948\pi$
$751$	6.94158	−	4.00772i	0.253302	−	0.146244i	0.621275	+	0.783592i	$0.286615\pi$
$752$		0			0
$753$	−2.64947	−	1.52967i	−0.0965520	−	0.0557443i
$754$		0			0
$755$	−24.4307	−	7.87658i	−0.889124	−	0.286658i
$756$		0			0
$757$		−	16.4356i		−	0.597364i	−0.954353	−	0.298682i	$-0.903453\pi$
$757$		−	16.4356i		−	0.597364i	0.954353	−	0.298682i	$-0.0965469\pi$
$758$		0			0
$759$	3.94158	−	6.82701i	0.143070	−	0.247805i
$760$		0			0
$761$	46.3397	−	26.7542i	1.67981	−	0.969839i	0.718033	−	0.696009i	$-0.245042\pi$
$761$	46.3397	−	26.7542i	1.67981	−	0.969839i	0.961778	−	0.273831i	$-0.0882908\pi$
$762$		0			0
$763$	−30.2921	+	10.4935i	−1.09665	+	0.379890i
$764$		0			0
$765$	38.2337	−	8.21782i	1.38234	−	0.297116i
$766$		0			0
$767$	−10.1168	+	17.5229i	−0.365298	+	0.632715i
$768$		0			0
$769$			27.4728i			0.990693i	0.868695	+	0.495347i	$0.164959\pi$
$769$			27.4728i			0.990693i	−0.868695	+	0.495347i	$0.835041\pi$
$770$		0			0
$771$		−	8.01544i		−	0.288669i
$772$		0			0
$773$	20.8723	−	36.1519i	0.750724	−	1.30029i	−0.196749	−	0.980454i	$-0.563038\pi$
$773$	20.8723	−	36.1519i	0.750724	−	1.30029i	0.947472	−	0.319838i	$-0.103628\pi$
$774$		0			0
$775$	−5.05842	+	50.3307i	−0.181704	+	1.80793i
$776$		0			0
$777$	−13.7228	−	11.8843i	−0.492303	−	0.426347i
$778$		0			0
$779$	−4.67527	+	2.69927i	−0.167509	+	0.0967112i
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$			11.6819i			0.417478i
$784$		0			0
$785$	−6.17527	+	19.1537i	−0.220405	+	0.683627i
$786$		0			0
$787$	8.82473	+	5.09496i	0.314568	+	0.181616i	0.648969	−	0.760815i	$-0.275201\pi$
$787$	8.82473	+	5.09496i	0.314568	+	0.181616i	−0.334401	+	0.942431i	$0.608534\pi$
$788$		0			0
$789$	13.2921	−	7.67420i	0.473212	−	0.273209i
$790$		0			0
$791$	12.0000	−	13.8564i	0.426671	−	0.492677i
$792$		0			0
$793$	−4.11684	+	2.37686i	−0.146193	+	0.0844048i
$794$		0			0
$795$	7.70789	+	8.52139i	0.273371	+	0.302223i
$796$		0			0
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$			87.2097i			3.08526i
$800$		0			0
$801$	8.74456	+	5.04868i	0.308974	+	0.178386i
$802$		0			0
$803$	−6.94158	+	4.00772i	−0.244963	+	0.141429i
$804$		0			0
$805$	−0.733688	−	33.9774i	−0.0258591	−	1.19754i
$806$		0			0
$807$	0.547547	+	0.948380i	0.0192746	+	0.0333845i
$808$		0			0
$809$	−17.8723	+	30.9557i	−0.628356	+	1.08834i	0.359526	+	0.933135i	$0.382939\pi$
$809$	−17.8723	+	30.9557i	−0.628356	+	1.08834i	−0.987882	+	0.155209i	$0.950395\pi$
$810$		0			0
$811$	−46.3723			−1.62835			−0.814176	−	0.580619i	$-0.802811\pi$
$811$	−46.3723			−1.62835			−0.814176	+	0.580619i	$0.802811\pi$
$812$		0			0
$813$			1.08724i			0.0381312i
$814$		0			0
$815$	−5.82473	−	6.43949i	−0.204032	−	0.225565i
$816$		0			0
$817$	−11.4891	−	19.8997i	−0.401954	−	0.696204i
$818$		0			0
$819$	−5.18614	+	26.9480i	−0.181218	+	0.941639i
$820$		0			0
$821$	20.0584	+	34.7422i	0.700044	+	1.21251i	0.968451	+	0.249206i	$0.0801695\pi$
$821$	20.0584	+	34.7422i	0.700044	+	1.21251i	−0.268407	+	0.963306i	$0.586497\pi$
$822$		0			0
$823$	7.17527	−	12.4279i	0.250114	−	0.433210i	−0.713443	−	0.700713i	$-0.752865\pi$
$823$	7.17527	−	12.4279i	0.250114	−	0.433210i	0.963557	+	0.267503i	$0.0861985\pi$
$824$		0			0
$825$	5.56930	+	4.00772i	0.193898	+	0.139531i
$826$		0			0
$827$	19.7228			0.685829			0.342915	−	0.939367i	$-0.388586\pi$
$827$	19.7228			0.685829			0.342915	+	0.939367i	$0.388586\pi$
$828$		0			0
$829$	−41.4090	−	23.9075i	−1.43819	−	0.830341i	−0.440468	−	0.897768i	$-0.645188\pi$
$829$	−41.4090	−	23.9075i	−1.43819	−	0.830341i	−0.997724	+	0.0674274i	$0.978521\pi$
$830$		0			0
$831$	7.80298	+	13.5152i	0.270683	+	0.468836i
$832$		0			0
$833$	47.9198	+	19.1537i	1.66032	+	0.663638i
$834$		0			0
$835$	2.67527	+	12.4468i	0.0925814	+	0.430738i
$836$		0			0
$837$	37.2921	+	21.5306i	1.28900	+	0.744207i
$838$		0			0
$839$	44.7446			1.54475			0.772377	−	0.635164i	$-0.219068\pi$
$839$	44.7446			1.54475			0.772377	+	0.635164i	$0.219068\pi$
$840$		0			0
$841$	−21.4674			−0.740254
$842$		0			0
$843$	−17.2337	−	9.94987i	−0.593560	−	0.342692i
$844$		0			0
$845$	−13.3723	+	2.87419i	−0.460020	+	0.0988753i
$846$		0			0
$847$	−4.00000	+	20.7846i	−0.137442	+	0.714168i
$848$		0			0
$849$	−3.17527	−	5.49972i	−0.108975	−	0.188750i
$850$		0			0
$851$	−43.0842	−	24.8747i	−1.47691	−	0.852693i
$852$		0			0
$853$	−37.1168			−1.27086			−0.635428	−	0.772160i	$-0.719176\pi$
$853$	−37.1168			−1.27086			−0.635428	+	0.772160i	$0.719176\pi$
$854$		0			0
$855$	9.35053	−	29.0024i	0.319781	−	0.991862i
$856$		0			0
$857$	−0.686141	+	1.18843i	−0.0234381	+	0.0405960i	−0.877507	−	0.479565i	$-0.840795\pi$
$857$	−0.686141	+	1.18843i	−0.0234381	+	0.0405960i	0.854068	+	0.520161i	$0.174128\pi$
$858$		0			0
$859$	4.54755	+	7.87658i	0.155160	+	0.268746i	0.933117	−	0.359572i	$-0.117077\pi$
$859$	4.54755	+	7.87658i	0.155160	+	0.268746i	−0.777957	+	0.628317i	$0.783744\pi$
$860$		0			0
$861$	−1.86141	+	0.644810i	−0.0634366	+	0.0219751i
$862$		0			0
$863$	−18.1277	−	31.3981i	−0.617075	−	1.06880i	−0.990017	−	0.140950i	$-0.954984\pi$
$863$	−18.1277	−	31.3981i	−0.617075	−	1.06880i	0.372942	−	0.927855i	$-0.378349\pi$
$864$		0			0
$865$	−16.8505	−	18.6290i	−0.572935	−	0.633404i
$866$		0			0
$867$		−	29.5923i		−	1.00501i
$868$		0			0
$869$	16.1168			0.546726
$870$		0			0
$871$	17.7446	−	30.7345i	0.601252	−	1.04140i
$872$		0			0
$873$	−7.11684	−	12.3267i	−0.240869	−	0.417197i
$874$		0			0
$875$	29.4891	+	2.32196i	0.996914	+	0.0784965i
$876$		0			0
$877$	1.50000	−	0.866025i	0.0506514	−	0.0292436i	−0.474460	−	0.880277i	$-0.657357\pi$
$877$	1.50000	−	0.866025i	0.0506514	−	0.0292436i	0.525112	+	0.851033i	$0.324023\pi$
$878$		0			0
$879$	1.46738	+	0.847190i	0.0494934	+	0.0285750i
$880$		0			0
$881$		−	8.56768i		−	0.288652i	−0.989530	−	0.144326i	$-0.953899\pi$
$881$		−	8.56768i		−	0.288652i	0.989530	−	0.144326i	$-0.0461015\pi$
$882$		0			0
$883$	24.4674			0.823393			0.411696	−	0.911321i	$-0.364936\pi$
$883$	24.4674			0.823393			0.411696	+	0.911321i	$0.364936\pi$
$884$		0			0
$885$	6.08017	−	5.49972i	0.204383	−	0.184871i
$886$		0			0
$887$	5.31386	−	3.06796i	0.178422	−	0.103012i	−0.408129	−	0.912924i	$-0.633819\pi$
$887$	5.31386	−	3.06796i	0.178422	−	0.103012i	0.586551	+	0.809912i	$0.300485\pi$
$888$		0			0
$889$	30.2337	+	26.1831i	1.01401	+	0.878154i
$890$		0			0
$891$	−5.61684	+	3.24289i	−0.188171	+	0.108641i
$892$		0			0
$893$	58.8505	+	33.9774i	1.96936	+	1.13701i
$894$		0			0
$895$	−38.6644	−	12.4656i	−1.29241	−	0.416679i
$896$		0			0
$897$		−	19.8997i		−	0.664433i
$898$		0			0
$899$	13.8832	−	24.0463i	0.463029	−	0.801990i
$900$		0			0
$901$	−41.4090	+	23.9075i	−1.37953	+	0.796473i
$902$		0			0
$903$	−2.74456	−	7.92287i	−0.0913333	−	0.263657i
$904$		0			0
$905$	0.605969	+	2.81929i	0.0201431	+	0.0937164i
$906$		0			0
$907$	−22.1753	+	38.4087i	−0.736318	+	1.27534i	0.217825	+	0.975988i	$0.430104\pi$
$907$	−22.1753	+	38.4087i	−0.736318	+	1.27534i	−0.954143	+	0.299352i	$0.903230\pi$
$908$		0			0
$909$		−	25.8333i		−	0.856836i
$910$		0			0
$911$		−	26.8280i		−	0.888850i	−0.895816	−	0.444425i	$-0.853408\pi$
$911$		−	26.8280i		−	0.888850i	0.895816	−	0.444425i	$-0.146592\pi$
$912$		0			0
$913$	−7.37228	+	12.7692i	−0.243987	+	0.422598i
$914$		0			0
$915$	1.88316	−	0.404759i	0.0622552	−	0.0133809i
$916$		0			0
$917$	1.50000	−	7.79423i	0.0495344	−	0.257388i
$918$		0			0
$919$	−7.29211	+	4.21010i	−0.240545	+	0.138878i	−0.615427	−	0.788194i	$-0.711016\pi$
$919$	−7.29211	+	4.21010i	−0.240545	+	0.138878i	0.374882	+	0.927072i	$0.377683\pi$
$920$		0			0
$921$	−5.13859	+	8.90030i	−0.169322	+	0.293275i
$922$		0			0
$923$		−	45.4381i		−	1.49561i
$924$		0			0
$925$	25.2921	−	35.1470i	0.831599	−	1.15563i
$926$		0			0
$927$	−19.1168	−	11.0371i	−0.627880	−	0.362506i
$928$		0			0
$929$	33.2228	−	19.1812i	1.09001	−	0.629315i	0.156427	−	0.987689i	$-0.450002\pi$
$929$	33.2228	−	19.1812i	1.09001	−	0.629315i	0.933578	+	0.358375i	$0.116669\pi$
$930$		0			0
$931$	31.5951	−	24.8747i	1.03549	−	0.815235i
$932$		0			0
$933$	−0.941578	+	0.543620i	−0.0308259	+	0.0177973i
$934$		0			0
$935$	−21.1753	+	19.1537i	−0.692505	+	0.626395i
$936$		0			0
$937$	14.7446			0.481684			0.240842	−	0.970564i	$-0.422576\pi$
$937$	14.7446			0.481684			0.240842	+	0.970564i	$0.422576\pi$
$938$		0			0
$939$			10.1899i			0.332536i
$940$		0			0
$941$	−10.1970	−	5.88725i	−0.332413	−	0.191919i	0.324499	−	0.945886i	$-0.394804\pi$
$941$	−10.1970	−	5.88725i	−0.332413	−	0.191919i	−0.656912	+	0.753967i	$0.728138\pi$
$942$		0			0
$943$	−4.67527	+	2.69927i	−0.152248	+	0.0879002i
$944$		0			0
$945$	12.1168	−	22.0742i	0.394161	−	0.718075i
$946$		0			0
$947$	−22.8030	−	39.4959i	−0.740997	−	1.28345i	−0.952042	−	0.305969i	$-0.901020\pi$
$947$	−22.8030	−	39.4959i	−0.740997	−	1.28345i	0.211044	−	0.977477i	$-0.432314\pi$
$948$		0			0
$949$	−10.1168	+	17.5229i	−0.328407	+	0.568817i
$950$		0			0
$951$	−0.861407			−0.0279330
$952$		0			0
$953$		−	26.4232i		−	0.855931i	−0.903795	−	0.427966i	$-0.859230\pi$
$953$		−	26.4232i		−	0.855931i	0.903795	−	0.427966i	$-0.140770\pi$
$954$		0			0
$955$	9.68614	−	8.76144i	0.313436	−	0.283514i
$956$		0			0
$957$	−1.88316	−	3.26172i	−0.0608738	−	0.105436i
$958$		0			0
$959$	8.05842	+	23.2627i	0.260220	+	0.751190i
$960$		0			0
$961$	−35.6753	−	61.7914i	−1.15082	−	1.99327i
$962$		0			0
$963$	1.62772	−	2.81929i	0.0524525	−	0.0908504i
$964$		0			0
$965$	−9.68614	−	3.12286i	−0.311808	−	0.100528i
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$	−29.0584	−	16.7769i	−0.933491	−	0.538951i
$970$		0			0
$971$	18.9891	+	32.8901i	0.609390	+	1.05549i	0.991341	+	0.131312i	$0.0419190\pi$
$971$	18.9891	+	32.8901i	0.609390	+	1.05549i	−0.381951	+	0.924183i	$0.624748\pi$
$972$		0			0
$973$	−24.0000	−	20.7846i	−0.769405	−	0.666324i
$974$		0			0
$975$	17.2337	+	1.73205i	0.551920	+	0.0554700i
$976$		0			0
$977$	30.1753	+	17.4217i	0.965392	+	0.557369i	0.897828	−	0.440345i	$-0.145144\pi$
$977$	30.1753	+	17.4217i	0.965392	+	0.557369i	0.0675639	+	0.997715i	$0.478477\pi$
$978$		0			0
$979$	−7.37228			−0.235619
$980$		0			0
$981$	−28.7446			−0.917743
$982$		0			0
$983$	5.36141	+	3.09541i	0.171002	+	0.0987282i	0.583058	−	0.812430i	$-0.301856\pi$
$983$	5.36141	+	3.09541i	0.171002	+	0.0987282i	−0.412056	+	0.911158i	$0.635189\pi$
$984$		0			0
$985$	4.58017	+	21.3094i	0.145936	+	0.678974i
$986$		0			0
$987$	18.7446	+	16.2333i	0.596646	+	0.516711i
$988$		0			0
$989$	−11.4891	−	19.8997i	−0.365333	−	0.632775i
$990$		0			0
$991$	−34.2921	−	19.7986i	−1.08932	−	0.628922i	−0.155928	−	0.987768i	$-0.549837\pi$
$991$	−34.2921	−	19.7986i	−1.08932	−	0.628922i	−0.933397	+	0.358846i	$0.883170\pi$
$992$		0			0
$993$	9.60597			0.304836
$994$		0			0
$995$	4.70789	−	14.6024i	0.149250	−	0.462927i
$996$		0			0
$997$	8.05842	−	13.9576i	0.255213	−	0.442042i	−0.709741	−	0.704463i	$-0.751188\pi$
$997$	8.05842	−	13.9576i	0.255213	−	0.442042i	0.964953	+	0.262422i	$0.0845211\pi$
$998$		0			0
$999$	−18.4307	−	31.9229i	−0.583122	−	1.01000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cc.b.479.2	yes	4
4.3	odd	2		560.2.cc.d.479.1	yes	4
5.4	even	2		560.2.cc.c.479.1	yes	4
7.5	odd	6		560.2.cc.a.159.2	✓	4
20.19	odd	2		560.2.cc.a.479.2	yes	4
28.19	even	6		560.2.cc.c.159.1	yes	4
35.19	odd	6		560.2.cc.d.159.1	yes	4
140.19	even	6	inner	560.2.cc.b.159.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cc.a.159.2	✓	4	7.5	odd	6
560.2.cc.a.479.2	yes	4	20.19	odd	2
560.2.cc.b.159.2	yes	4	140.19	even	6	inner
560.2.cc.b.479.2	yes	4	1.1	even	1	trivial
560.2.cc.c.159.1	yes	4	28.19	even	6
560.2.cc.c.479.1	yes	4	5.4	even	2
560.2.cc.d.159.1	yes	4	35.19	odd	6
560.2.cc.d.479.1	yes	4	4.3	odd	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.686141 + 0.396143i) q^{3} +(-2.18614 + 0.469882i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-1.18614 - 2.05446i) q^{9} +O(q^{10})\)	\(q+(0.686141 + 0.396143i) q^{3} +(-2.18614 + 0.469882i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-1.18614 - 2.05446i) q^{9} +(1.50000 + 0.866025i) q^{11} +4.37228 q^{13} +(-1.68614 - 0.543620i) q^{15} +(3.68614 - 6.38458i) q^{17} +(-2.87228 - 4.97494i) q^{19} +(-0.686141 - 1.98072i) q^{21} +(-2.87228 - 4.97494i) q^{23} +(4.55842 - 2.05446i) q^{25} -4.25639i q^{27} -2.74456 q^{29} +(-5.05842 + 8.76144i) q^{31} +(0.686141 + 1.18843i) q^{33} +(5.18614 + 2.84674i) q^{35} +(7.50000 - 4.33013i) q^{37} +(3.00000 + 1.73205i) q^{39} -0.939764i q^{41} +4.00000 q^{43} +(3.55842 + 3.93398i) q^{45} +(-10.2446 + 5.91470i) q^{47} +(1.00000 + 6.92820i) q^{49} +(5.05842 - 2.92048i) q^{51} +(-5.61684 - 3.24289i) q^{53} +(-3.68614 - 1.18843i) q^{55} -4.55134i q^{57} +(-2.31386 + 4.00772i) q^{59} +(-0.941578 + 0.543620i) q^{61} +(-1.18614 + 6.16337i) q^{63} +(-9.55842 + 2.05446i) q^{65} +(4.05842 - 7.02939i) q^{67} -4.55134i q^{69} -10.3923i q^{71} +(-2.31386 + 4.00772i) q^{73} +(3.94158 + 0.396143i) q^{75} +(-1.50000 - 4.33013i) q^{77} +(8.05842 - 4.65253i) q^{79} +(-1.87228 + 3.24289i) q^{81} +8.51278i q^{83} +(-5.05842 + 15.6896i) q^{85} +(-1.88316 - 1.08724i) q^{87} +(-3.68614 + 2.12819i) q^{89} +(-8.74456 - 7.57301i) q^{91} +(-6.94158 + 4.00772i) q^{93} +(8.61684 + 9.52628i) q^{95} +6.00000 q^{97} -4.10891i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} - 3 q^{5} - 8 q^{7} + q^{9}+O(q^{10}) \) 4 * q - 3 * q^3 - 3 * q^5 - 8 * q^7 + q^9	\( 4 q - 3 q^{3} - 3 q^{5} - 8 q^{7} + q^{9} + 6 q^{11} + 6 q^{13} - q^{15} + 9 q^{17} + 3 q^{21} + q^{25} + 12 q^{29} - 3 q^{31} - 3 q^{33} + 15 q^{35} + 30 q^{37} + 12 q^{39} + 16 q^{43} - 3 q^{45} - 18 q^{47} + 4 q^{49} + 3 q^{51} + 12 q^{53} - 9 q^{55} - 15 q^{59} - 21 q^{61} + q^{63} - 21 q^{65} - q^{67} - 15 q^{73} + 33 q^{75} - 6 q^{77} + 15 q^{79} + 4 q^{81} - 3 q^{85} - 42 q^{87} - 9 q^{89} - 12 q^{91} - 45 q^{93} + 24 q^{97}+O(q^{100}) \) 4 * q - 3 * q^3 - 3 * q^5 - 8 * q^7 + q^9 + 6 * q^11 + 6 * q^13 - q^15 + 9 * q^17 + 3 * q^21 + q^25 + 12 * q^29 - 3 * q^31 - 3 * q^33 + 15 * q^35 + 30 * q^37 + 12 * q^39 + 16 * q^43 - 3 * q^45 - 18 * q^47 + 4 * q^49 + 3 * q^51 + 12 * q^53 - 9 * q^55 - 15 * q^59 - 21 * q^61 + q^63 - 21 * q^65 - q^67 - 15 * q^73 + 33 * q^75 - 6 * q^77 + 15 * q^79 + 4 * q^81 - 3 * q^85 - 42 * q^87 - 9 * q^89 - 12 * q^91 - 45 * q^93 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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