LMFDB - Embedded newform 1080.2.m.c.539.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(539,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("1080.539");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.m (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			539.21
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.c.539.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.341092 - 1.37246i) q^{2} +(-1.76731 + 0.936273i) q^{4} +(-2.13531 + 0.663669i) q^{5} +4.39866 q^{7} +(1.88782 + 2.10622i) q^{8} +O(q^{10})$	\(q+(-0.341092 - 1.37246i) q^{2} +(-1.76731 + 0.936273i) q^{4} +(-2.13531 + 0.663669i) q^{5} +4.39866 q^{7} +(1.88782 + 2.10622i) q^{8} +(1.63920 + 2.70426i) q^{10} +0.633050i q^{11} -3.40649 q^{13} +(-1.50035 - 6.03700i) q^{14} +(2.24679 - 3.30937i) q^{16} -5.48913 q^{17} +0.323423 q^{19} +(3.15238 - 3.17214i) q^{20} +(0.868838 - 0.215928i) q^{22} +6.26839i q^{23} +(4.11909 - 2.83428i) q^{25} +(1.16193 + 4.67528i) q^{26} +(-7.77381 + 4.11835i) q^{28} -3.77896 q^{29} +7.86723i q^{31} +(-5.30835 - 1.95483i) q^{32} +(1.87230 + 7.53363i) q^{34} +(-9.39250 + 2.91926i) q^{35} -5.90433 q^{37} +(-0.110317 - 0.443887i) q^{38} +(-5.42890 - 3.24454i) q^{40} -0.877482i q^{41} -2.31397i q^{43} +(-0.592707 - 1.11880i) q^{44} +(8.60314 - 2.13810i) q^{46} +8.67090i q^{47} +12.3482 q^{49} +(-5.29493 - 4.68655i) q^{50} +(6.02033 - 3.18940i) q^{52} +7.09416i q^{53} +(-0.420136 - 1.35176i) q^{55} +(8.30386 + 9.26454i) q^{56} +(1.28897 + 5.18649i) q^{58} -10.5321i q^{59} +14.0673i q^{61} +(10.7975 - 2.68345i) q^{62} +(-0.872299 + 7.95230i) q^{64} +(7.27391 - 2.26078i) q^{65} +5.99382i q^{67} +(9.70101 - 5.13933i) q^{68} +(7.21028 + 11.8951i) q^{70} +10.7806 q^{71} +13.9654i q^{73} +(2.01392 + 8.10348i) q^{74} +(-0.571590 + 0.302812i) q^{76} +2.78457i q^{77} -7.33728i q^{79} +(-2.60125 + 8.55766i) q^{80} +(-1.20431 + 0.299302i) q^{82} -1.90716 q^{83} +(11.7210 - 3.64297i) q^{85} +(-3.17585 + 0.789278i) q^{86} +(-1.33334 + 1.19508i) q^{88} -8.16899i q^{89} -14.9840 q^{91} +(-5.86892 - 11.0782i) q^{92} +(11.9005 - 2.95758i) q^{94} +(-0.690609 + 0.214646i) q^{95} +6.27222i q^{97} +(-4.21188 - 16.9475i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4}+O(q^{10}) $ 48 * q + 4 * q^4	$ 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.341092	−	1.37246i	−0.241188	−	0.970478i
$2$	−0.341092	−	1.37246i	−0.241188	−	0.970478i
$3$		0			0
$3$		0			0
$4$	−1.76731	+	0.936273i	−0.883656	+	0.468136i
$5$	−2.13531	+	0.663669i	−0.954939	+	0.296802i
$5$	−2.13531	+	0.663669i	−0.954939	+	0.296802i
$6$		0			0
$7$	4.39866			1.66254			0.831269	−	0.555871i	$-0.187615\pi$
$7$	4.39866			1.66254			0.831269	+	0.555871i	$0.187615\pi$
$8$	1.88782	+	2.10622i	0.667444	+	0.744660i
$9$		0			0
$10$	1.63920	+	2.70426i	0.518360	+	0.855162i
$11$			0.633050i			0.190872i	0.995436	+	0.0954359i	$0.0304245\pi$
$11$			0.633050i			0.190872i	−0.995436	+	0.0954359i	$0.969576\pi$
$12$		0			0
$13$	−3.40649			−0.944790			−0.472395	−	0.881387i	$-0.656610\pi$
$13$	−3.40649			−0.944790			−0.472395	+	0.881387i	$0.656610\pi$
$14$	−1.50035	−	6.03700i	−0.400985	−	1.61346i
$15$		0			0
$16$	2.24679	−	3.30937i	0.561697	−	0.827343i
$17$	−5.48913			−1.33131			−0.665655	−	0.746260i	$-0.731848\pi$
$17$	−5.48913			−1.33131			−0.665655	+	0.746260i	$0.731848\pi$
$18$		0			0
$19$	0.323423			0.0741984			0.0370992	−	0.999312i	$-0.488188\pi$
$19$	0.323423			0.0741984			0.0370992	+	0.999312i	$0.488188\pi$
$20$	3.15238	−	3.17214i	0.704894	−	0.709313i
$21$		0			0
$22$	0.868838	−	0.215928i	0.185237	−	0.0460361i
$23$			6.26839i			1.30705i	0.756905	+	0.653525i	$0.226710\pi$
$23$			6.26839i			1.30705i	−0.756905	+	0.653525i	$0.773290\pi$
$24$		0			0
$25$	4.11909	−	2.83428i	0.823817	−	0.566856i
$26$	1.16193	+	4.67528i	0.227873	+	0.916899i
$27$		0			0
$28$	−7.77381	+	4.11835i	−1.46911	+	0.778294i
$29$	−3.77896			−0.701736			−0.350868	−	0.936425i	$-0.614113\pi$
$29$	−3.77896			−0.701736			−0.350868	+	0.936425i	$0.614113\pi$
$30$		0			0
$31$			7.86723i			1.41300i	0.707715	+	0.706498i	$0.249726\pi$
$31$			7.86723i			1.41300i	−0.707715	+	0.706498i	$0.750274\pi$
$32$	−5.30835	−	1.95483i	−0.938393	−	0.345569i
$33$		0			0
$34$	1.87230	+	7.53363i	0.321097	+	1.29201i
$35$	−9.39250	+	2.91926i	−1.58762	+	0.493444i
$36$		0			0
$37$	−5.90433			−0.970666			−0.485333	−	0.874329i	$-0.661302\pi$
$37$	−5.90433			−0.970666			−0.485333	+	0.874329i	$0.661302\pi$
$38$	−0.110317	−	0.443887i	−0.0178958	−	0.0720079i
$39$		0			0
$40$	−5.42890	−	3.24454i	−0.858385	−	0.513006i
$41$		−	0.877482i		−	0.137040i	−0.997650	−	0.0685198i	$-0.978172\pi$
$41$		−	0.877482i		−	0.137040i	0.997650	−	0.0685198i	$-0.0218276\pi$
$42$		0			0
$43$		−	2.31397i		−	0.352878i	−0.984312	−	0.176439i	$-0.943542\pi$
$43$		−	2.31397i		−	0.352878i	0.984312	−	0.176439i	$-0.0564578\pi$
$44$	−0.592707	−	1.11880i	−0.0893540	−	0.168665i
$45$		0			0
$46$	8.60314	−	2.13810i	1.26846	−	0.315245i
$47$			8.67090i			1.26478i	0.774650	+	0.632391i	$0.217926\pi$
$47$			8.67090i			1.26478i	−0.774650	+	0.632391i	$0.782074\pi$
$48$		0			0
$49$	12.3482			1.76403
$50$	−5.29493	−	4.68655i	−0.748816	−	0.662778i
$51$		0			0
$52$	6.02033	−	3.18940i	0.834870	−	0.442291i
$53$			7.09416i			0.974457i	0.873274	+	0.487229i	$0.161992\pi$
$53$			7.09416i			0.974457i	−0.873274	+	0.487229i	$0.838008\pi$
$54$		0			0
$55$	−0.420136	−	1.35176i	−0.0566511	−	0.182271i
$56$	8.30386	+	9.26454i	1.10965	+	1.23803i
$57$		0			0
$58$	1.28897	+	5.18649i	0.169251	+	0.681019i
$59$		−	10.5321i		−	1.37117i	−0.727993	−	0.685584i	$-0.759547\pi$
$59$		−	10.5321i		−	1.37117i	0.727993	−	0.685584i	$-0.240453\pi$
$60$		0			0
$61$			14.0673i			1.80113i	0.434717	+	0.900567i	$0.356848\pi$
$61$			14.0673i			1.80113i	−0.434717	+	0.900567i	$0.643152\pi$
$62$	10.7975	−	2.68345i	1.37128	−	0.340798i
$63$		0			0
$64$	−0.872299	+	7.95230i	−0.109037	+	0.994038i
$65$	7.27391	−	2.26078i	0.902217	−	0.280416i
$66$		0			0
$67$			5.99382i			0.732262i	0.930563	+	0.366131i	$0.119318\pi$
$67$			5.99382i			0.732262i	−0.930563	+	0.366131i	$0.880682\pi$
$68$	9.70101	−	5.13933i	1.17642	−	0.623235i
$69$		0			0
$70$	7.21028	+	11.8951i	0.861793	+	1.42174i
$71$	10.7806			1.27942			0.639710	−	0.768617i	$-0.279055\pi$
$71$	10.7806			1.27942			0.639710	+	0.768617i	$0.279055\pi$
$72$		0			0
$73$			13.9654i			1.63453i	0.576264	+	0.817264i	$0.304510\pi$
$73$			13.9654i			1.63453i	−0.576264	+	0.817264i	$0.695490\pi$
$74$	2.01392	+	8.10348i	0.234113	+	0.942010i
$75$		0			0
$76$	−0.571590	+	0.302812i	−0.0655659	+	0.0347350i
$77$			2.78457i			0.317331i
$78$		0			0
$79$		−	7.33728i		−	0.825508i	−0.910843	−	0.412754i	$-0.864567\pi$
$79$		−	7.33728i		−	0.825508i	0.910843	−	0.412754i	$-0.135433\pi$
$80$	−2.60125	+	8.55766i	−0.290829	+	0.956775i
$81$		0			0
$82$	−1.20431	+	0.299302i	−0.132994	+	0.0330524i
$83$	−1.90716			−0.209338			−0.104669	−	0.994507i	$-0.533378\pi$
$83$	−1.90716			−0.209338			−0.104669	+	0.994507i	$0.533378\pi$
$84$		0			0
$85$	11.7210	−	3.64297i	1.27132	−	0.395135i
$86$	−3.17585	+	0.789278i	−0.342460	+	0.0851101i
$87$		0			0
$88$	−1.33334	+	1.19508i	−0.142135	+	0.127396i
$89$		−	8.16899i		−	0.865911i	−0.901415	−	0.432956i	$-0.857471\pi$
$89$		−	8.16899i		−	0.865911i	0.901415	−	0.432956i	$-0.142529\pi$
$90$		0			0
$91$	−14.9840			−1.57075
$92$	−5.86892	−	11.0782i	−0.611877	−	1.15498i
$93$		0			0
$94$	11.9005	−	2.95758i	1.22744	−	0.305051i
$95$	−0.690609	+	0.214646i	−0.0708549	+	0.0220222i
$96$		0			0
$97$			6.27222i			0.636847i	0.947949	+	0.318424i	$0.103153\pi$
$97$			6.27222i			0.636847i	−0.947949	+	0.318424i	$0.896847\pi$
$98$	−4.21188	−	16.9475i	−0.425464	−	1.71195i
$99$		0			0
$100$	−4.62606	+	8.86564i	−0.462606	+	0.886564i
$101$	−0.535487			−0.0532830			−0.0266415	−	0.999645i	$-0.508481\pi$
$101$	−0.535487			−0.0532830			−0.0266415	+	0.999645i	$0.508481\pi$
$102$		0			0
$103$	−12.5566			−1.23724			−0.618621	−	0.785689i	$-0.712308\pi$
$103$	−12.5566			−1.23724			−0.618621	+	0.785689i	$0.712308\pi$
$104$	−6.43083	−	7.17481i	−0.630595	−	0.703548i
$105$		0			0
$106$	9.73647	−	2.41976i	0.945690	−	0.235028i
$107$	13.4267			1.29801			0.649003	−	0.760786i	$-0.275186\pi$
$107$	13.4267			1.29801			0.649003	+	0.760786i	$0.275186\pi$
$108$		0			0
$109$			1.43706i			0.137646i	0.997629	+	0.0688228i	$0.0219243\pi$
$109$			1.43706i			0.137646i	−0.997629	+	0.0688228i	$0.978076\pi$
$110$	−1.71193	+	1.03769i	−0.163226	+	0.0989403i
$111$		0			0
$112$	9.88286	−	14.5568i	0.933842	−	1.37549i
$113$	−6.45479			−0.607216			−0.303608	−	0.952797i	$-0.598191\pi$
$113$	−6.45479			−0.607216			−0.303608	+	0.952797i	$0.598191\pi$
$114$		0			0
$115$	−4.16014	−	13.3849i	−0.387935	−	1.24815i
$116$	6.67861	−	3.53814i	0.620093	−	0.328508i
$117$		0			0
$118$	−14.4550	+	3.59243i	−1.33069	+	0.330710i
$119$	−24.1448			−2.21335
$120$		0			0
$121$	10.5992			0.963568
$122$	19.3069	−	4.79825i	1.74796	−	0.434413i
$123$		0			0
$124$	−7.36587	−	13.9039i	−0.661475	−	1.24860i
$125$	−6.91450	+	8.78577i	−0.618451	+	0.785823i
$126$		0			0
$127$	−10.8023			−0.958550			−0.479275	−	0.877665i	$-0.659100\pi$
$127$	−10.8023			−0.958550			−0.479275	+	0.877665i	$0.659100\pi$
$128$	11.2118	−	1.51527i	0.990991	−	0.133932i
$129$		0			0
$130$	−5.58391	−	9.21204i	−0.489742	−	0.807949i
$131$			18.2846i			1.59754i	0.601639	+	0.798768i	$0.294515\pi$
$131$			18.2846i			1.59754i	−0.601639	+	0.798768i	$0.705485\pi$
$132$		0			0
$133$	1.42263			0.123358
$134$	8.22630	−	2.04444i	0.710644	−	0.176613i
$135$		0			0
$136$	−10.3625	−	11.5613i	−0.888575	−	0.991374i
$137$	−14.9351			−1.27599			−0.637997	−	0.770039i	$-0.720237\pi$
$137$	−14.9351			−1.27599			−0.637997	+	0.770039i	$0.720237\pi$
$138$		0			0
$139$	−16.0327			−1.35988			−0.679939	−	0.733269i	$-0.737994\pi$
$139$	−16.0327			−1.35988			−0.679939	+	0.733269i	$0.737994\pi$
$140$	13.8663	−	13.9532i	1.17191	−	1.17926i
$141$		0			0
$142$	−3.67717	−	14.7960i	−0.308581	−	1.24165i
$143$		−	2.15648i		−	0.180334i
$144$		0			0
$145$	8.06925	−	2.50798i	0.670115	−	0.208276i
$146$	19.1670	−	4.76349i	1.58627	−	0.394229i
$147$		0			0
$148$	10.4348	−	5.52806i	0.857735	−	0.454404i
$149$	11.4476			0.937820			0.468910	−	0.883246i	$-0.344647\pi$
$149$	11.4476			0.937820			0.468910	+	0.883246i	$0.344647\pi$
$150$		0			0
$151$		−	12.0407i		−	0.979859i	−0.871762	−	0.489930i	$-0.837023\pi$
$151$		−	12.0407i		−	0.979859i	0.871762	−	0.489930i	$-0.162977\pi$
$152$	0.610564	+	0.681200i	0.0495233	+	0.0552526i
$153$		0			0
$154$	3.82172	−	0.949795i	0.307963	−	0.0765367i
$155$	−5.22124	−	16.7990i	−0.419380	−	1.34933i
$156$		0			0
$157$	4.16913			0.332732			0.166366	−	0.986064i	$-0.446797\pi$
$157$	4.16913			0.332732			0.166366	+	0.986064i	$0.446797\pi$
$158$	−10.0701	+	2.50269i	−0.801138	+	0.199103i
$159$		0			0
$160$	12.6323	+	0.651179i	0.998674	+	0.0514802i
$161$			27.5725i			2.17302i
$162$		0			0
$163$		−	1.77553i		−	0.139070i	−0.997580	−	0.0695350i	$-0.977848\pi$
$163$		−	1.77553i		−	0.139070i	0.997580	−	0.0695350i	$-0.0221516\pi$
$164$	0.821563	+	1.55079i	0.0641533	+	0.121096i
$165$		0			0
$166$	0.650516	+	2.61750i	0.0504898	+	0.203158i
$167$			2.93164i			0.226857i	0.993546	+	0.113429i	$0.0361833\pi$
$167$			2.93164i			0.226857i	−0.993546	+	0.113429i	$0.963817\pi$
$168$		0			0
$169$	−1.39582			−0.107371
$170$	−8.99778	−	14.8440i	−0.690098	−	1.13849i
$171$		0			0
$172$	2.16651	+	4.08952i	0.165195	+	0.311823i
$173$		−	5.27138i		−	0.400775i	−0.979717	−	0.200388i	$-0.935780\pi$
$173$		−	5.27138i		−	0.400775i	0.979717	−	0.200388i	$-0.0642202\pi$
$174$		0			0
$175$	18.1185	−	12.4670i	1.36963	−	0.942419i
$176$	2.09500	+	1.42233i	0.157916	+	0.107212i
$177$		0			0
$178$	−11.2116	+	2.78638i	−0.840348	+	0.208848i
$179$			11.6443i			0.870340i	0.900348	+	0.435170i	$0.143312\pi$
$179$			11.6443i			0.870340i	−0.900348	+	0.435170i	$0.856688\pi$
$180$		0			0
$181$		−	13.6718i		−	1.01622i	−0.861293	−	0.508109i	$-0.830345\pi$
$181$		−	13.6718i		−	1.01622i	0.861293	−	0.508109i	$-0.169655\pi$
$182$	5.11092	+	20.5650i	0.378847	+	1.52438i
$183$		0			0
$184$	−13.2026	+	11.8336i	−0.973308	+	0.872382i
$185$	12.6076	−	3.91852i	0.926927	−	0.288095i
$186$		0			0
$187$		−	3.47489i		−	0.254109i
$188$	−8.11833	−	15.3242i	−0.592090	−	1.11763i
$189$		0			0
$190$	0.530155	+	0.874621i	0.0384615	+	0.0634517i
$191$	−6.04522			−0.437417			−0.218709	−	0.975790i	$-0.570184\pi$
$191$	−6.04522			−0.437417			−0.218709	+	0.975790i	$0.570184\pi$
$192$		0			0
$193$		−	25.9530i		−	1.86814i	−0.357088	−	0.934071i	$-0.616230\pi$
$193$		−	25.9530i		−	1.86814i	0.357088	−	0.934071i	$-0.383770\pi$
$194$	8.60839	−	2.13940i	0.618046	−	0.153600i
$195$		0			0
$196$	−21.8232	+	11.5613i	−1.55880	+	0.825807i
$197$			10.4843i			0.746973i	0.927636	+	0.373487i	$0.121838\pi$
$197$			10.4843i			0.746973i	−0.927636	+	0.373487i	$0.878162\pi$
$198$		0			0
$199$			3.19670i			0.226608i	0.993560	+	0.113304i	$0.0361434\pi$
$199$			3.19670i			0.226608i	−0.993560	+	0.113304i	$0.963857\pi$
$200$	13.7457	+	3.32509i	0.971966	+	0.235120i
$201$		0			0
$202$	0.182650	+	0.734937i	0.0128512	+	0.0517100i
$203$	−16.6224			−1.16666
$204$		0			0
$205$	0.582358	+	1.87370i	0.0406736	+	0.130865i
$206$	4.28297	+	17.2335i	0.298409	+	1.20072i
$207$		0			0
$208$	−7.65366	+	11.2733i	−0.530686	+	0.781666i
$209$			0.204743i			0.0141624i
$210$		0			0
$211$	−17.2016			−1.18421			−0.592105	−	0.805861i	$-0.701703\pi$
$211$	−17.2016			−1.18421			−0.592105	+	0.805861i	$0.701703\pi$
$212$	−6.64207	−	12.5376i	−0.456179	−	0.861085i
$213$		0			0
$214$	−4.57973	−	18.4276i	−0.313064	−	1.25969i
$215$	1.53571	+	4.94105i	0.104735	+	0.336977i
$216$		0			0
$217$			34.6053i			2.34916i
$218$	1.97231	−	0.490170i	0.133582	−	0.0331985i
$219$		0			0
$220$	2.00812	+	1.99562i	0.135388	+	0.134544i
$221$	18.6987			1.25781
$222$		0			0
$223$	11.8087			0.790766			0.395383	−	0.918516i	$-0.370612\pi$
$223$	11.8087			0.790766			0.395383	+	0.918516i	$0.370612\pi$
$224$	−23.3497	−	8.59865i	−1.56011	−	0.574521i
$225$		0			0
$226$	2.20168	+	8.85897i	0.146453	+	0.589290i
$227$	4.14942			0.275407			0.137703	−	0.990474i	$-0.456028\pi$
$227$	4.14942			0.275407			0.137703	+	0.990474i	$0.456028\pi$
$228$		0			0
$229$			17.7520i			1.17308i	0.809919	+	0.586542i	$0.199511\pi$
$229$			17.7520i			1.17308i	−0.809919	+	0.586542i	$0.800489\pi$
$230$	−16.9514	+	10.2751i	−1.11774	+	0.677522i
$231$		0			0
$232$	−7.13399	−	7.95931i	−0.468369	−	0.522555i
$233$	7.55127			0.494700			0.247350	−	0.968926i	$-0.420440\pi$
$233$	7.55127			0.494700			0.247350	+	0.968926i	$0.420440\pi$
$234$		0			0
$235$	−5.75461	−	18.5151i	−0.375389	−	1.20779i
$236$	9.86096	+	18.6136i	0.641894	+	1.21164i
$237$		0			0
$238$	8.23561	+	33.1379i	0.533835	+	2.14801i
$239$	−1.11479			−0.0721100			−0.0360550	−	0.999350i	$-0.511479\pi$
$239$	−1.11479			−0.0721100			−0.0360550	+	0.999350i	$0.511479\pi$
$240$		0			0
$241$	23.4788			1.51240			0.756201	−	0.654339i	$-0.227053\pi$
$241$	23.4788			1.51240			0.756201	+	0.654339i	$0.227053\pi$
$242$	−3.61532	−	14.5471i	−0.232401	−	0.935122i
$243$		0			0
$244$	−13.1708	−	24.8613i	−0.843176	−	1.59158i
$245$	−26.3673	+	8.19514i	−1.68454	+	0.523568i
$246$		0			0
$247$	−1.10174			−0.0701019
$248$	−16.5701	+	14.8519i	−1.05220	+	0.943096i
$249$		0			0
$250$	14.4166	+	6.49314i	0.911788	+	0.410662i
$251$		−	19.8709i		−	1.25424i	−0.778923	−	0.627119i	$-0.784234\pi$
$251$		−	19.8709i		−	1.25424i	0.778923	−	0.627119i	$-0.215766\pi$
$252$		0			0
$253$	−3.96820			−0.249479
$254$	3.68458	+	14.8258i	0.231191	+	0.930252i
$255$		0			0
$256$	−5.90390	−	14.8709i	−0.368994	−	0.929432i
$257$	−16.1801			−1.00929			−0.504643	−	0.863328i	$-0.668376\pi$
$257$	−16.1801			−1.00929			−0.504643	+	0.863328i	$0.668376\pi$
$258$		0			0
$259$	−25.9711			−1.61377
$260$	−10.7386	+	10.8059i	−0.665977	+	0.670152i
$261$		0			0
$262$	25.0950	−	6.23674i	1.55037	−	0.385307i
$263$		−	12.5368i		−	0.773051i	−0.922279	−	0.386525i	$-0.873675\pi$
$263$		−	12.5368i		−	0.773051i	0.922279	−	0.386525i	$-0.126325\pi$
$264$		0			0
$265$	−4.70817	−	15.1482i	−0.289221	−	0.930548i
$266$	−0.485248	−	1.95251i	−0.0297524	−	0.119716i
$267$		0			0
$268$	−5.61185	−	10.5930i	−0.342798	−	0.647068i
$269$	23.1238			1.40988			0.704941	−	0.709266i	$-0.250973\pi$
$269$	23.1238			1.40988			0.704941	+	0.709266i	$0.250973\pi$
$270$		0			0
$271$		−	10.1608i		−	0.617224i	−0.951188	−	0.308612i	$-0.900136\pi$
$271$		−	10.1608i		−	0.617224i	0.951188	−	0.308612i	$-0.0998645\pi$
$272$	−12.3329	+	18.1656i	−0.747793	+	1.10145i
$273$		0			0
$274$	5.09425	+	20.4979i	0.307755	+	1.23832i
$275$	1.79424	+	2.60759i	0.108197	+	0.157243i
$276$		0			0
$277$	−5.64642			−0.339260			−0.169630	−	0.985508i	$-0.554257\pi$
$277$	−5.64642			−0.339260			−0.169630	+	0.985508i	$0.554257\pi$
$278$	5.46863	+	22.0043i	0.327987	+	1.31973i
$279$		0			0
$280$	−23.8799	−	14.2716i	−1.42710	−	0.852893i
$281$		−	29.4258i		−	1.75540i	−0.479212	−	0.877699i	$-0.659077\pi$
$281$		−	29.4258i		−	1.75540i	0.479212	−	0.877699i	$-0.340923\pi$
$282$		0			0
$283$			2.34373i			0.139320i	0.997571	+	0.0696602i	$0.0221915\pi$
$283$			2.34373i			0.139320i	−0.997571	+	0.0696602i	$0.977809\pi$
$284$	−19.0527	+	10.0936i	−1.13057	+	0.598943i
$285$		0			0
$286$	−2.95969	+	0.735558i	−0.175010	+	0.0434944i
$287$		−	3.85975i		−	0.227834i
$288$		0			0
$289$	13.1306			0.772387
$290$	−6.19447	−	10.2193i	−0.363752	−	0.600098i
$291$		0			0
$292$	−13.0754	−	24.6812i	−0.765182	−	1.44436i
$293$			23.4485i			1.36987i	0.728603	+	0.684937i	$0.240170\pi$
$293$			23.4485i			1.36987i	−0.728603	+	0.684937i	$0.759830\pi$
$294$		0			0
$295$	6.98986	+	22.4894i	0.406965	+	1.30938i
$296$	−11.1463	−	12.4358i	−0.647865	−	0.722816i
$297$		0			0
$298$	−3.90467	−	15.7113i	−0.226191	−	0.910134i
$299$		−	21.3532i		−	1.23489i
$300$		0			0
$301$		−	10.1784i		−	0.586673i
$302$	−16.5254	+	4.10699i	−0.950932	+	0.236331i
$303$		0			0
$304$	0.726663	−	1.07033i	0.0416770	−	0.0613875i
$305$	−9.33604	−	30.0380i	−0.534580	−	1.71997i
$306$		0			0
$307$			1.32995i			0.0759041i	0.999280	+	0.0379520i	$0.0120834\pi$
$307$			1.32995i			0.0759041i	−0.999280	+	0.0379520i	$0.987917\pi$
$308$	−2.60712	−	4.92121i	−0.148554	−	0.280412i
$309$		0			0
$310$	−21.2750	+	12.8960i	−1.20834	+	0.732441i
$311$	32.6861			1.85346			0.926729	−	0.375732i	$-0.122609\pi$
$311$	32.6861			1.85346			0.926729	+	0.375732i	$0.122609\pi$
$312$		0			0
$313$			8.29685i			0.468966i	0.972120	+	0.234483i	$0.0753397\pi$
$313$			8.29685i			0.468966i	−0.972120	+	0.234483i	$0.924660\pi$
$314$	−1.42206	−	5.72197i	−0.0802512	−	0.322910i
$315$		0			0
$316$	6.86969	+	12.9673i	0.386450	+	0.729465i
$317$		−	29.8855i		−	1.67854i	−0.543718	−	0.839268i	$-0.682984\pi$
$317$		−	29.8855i		−	1.67854i	0.543718	−	0.839268i	$-0.317016\pi$
$318$		0			0
$319$		−	2.39227i		−	0.133941i
$320$	−3.41507	−	17.5595i	−0.190908	−	0.981608i
$321$		0			0
$322$	37.8423	−	9.40477i	2.10887	−	0.524107i
$323$	−1.77531			−0.0987811
$324$		0			0
$325$	−14.0316	+	9.65494i	−0.778335	+	0.535560i
$326$	−2.43685	+	0.605618i	−0.134964	+	0.0335421i
$327$		0			0
$328$	1.84817	−	1.65653i	0.102048	−	0.0914663i
$329$			38.1404i			2.10275i
$330$		0			0
$331$	11.6308			0.639289			0.319645	−	0.947538i	$-0.396437\pi$
$331$	11.6308			0.639289			0.319645	+	0.947538i	$0.396437\pi$
$332$	3.37054	−	1.78562i	0.184982	−	0.0979985i
$333$		0			0
$334$	4.02357	−	0.999960i	0.220160	−	0.0547154i
$335$	−3.97791	−	12.7987i	−0.217337	−	0.699265i
$336$		0			0
$337$		−	8.39265i		−	0.457177i	−0.973523	−	0.228588i	$-0.926589\pi$
$337$		−	8.39265i		−	0.457177i	0.973523	−	0.228588i	$-0.0734110\pi$
$338$	0.476104	+	1.91571i	0.0258966	+	0.104201i
$339$		0			0
$340$	−17.3038	+	17.4123i	−0.938433	+	0.944315i
$341$	−4.98035			−0.269701
$342$		0			0
$343$	23.5250			1.27023
$344$	4.87373	−	4.36836i	0.262774	−	0.235526i
$345$		0			0
$346$	−7.23477	+	1.79802i	−0.388944	+	0.0966624i
$347$	14.3801			0.771965			0.385982	−	0.922506i	$-0.373863\pi$
$347$	14.3801			0.771965			0.385982	+	0.922506i	$0.373863\pi$
$348$		0			0
$349$		−	33.6982i		−	1.80382i	−0.431920	−	0.901912i	$-0.642164\pi$
$349$		−	33.6982i		−	1.80382i	0.431920	−	0.901912i	$-0.357836\pi$
$350$	−23.2906	−	20.6145i	−1.24494	−	1.10189i
$351$		0			0
$352$	1.23751	−	3.36045i	0.0659593	−	0.179113i
$353$	26.3609			1.40305			0.701525	−	0.712645i	$-0.252503\pi$
$353$	26.3609			1.40305			0.701525	+	0.712645i	$0.252503\pi$
$354$		0			0
$355$	−23.0199	+	7.15474i	−1.22177	+	0.379734i
$356$	7.64840	+	14.4372i	0.405365	+	0.765168i
$357$		0			0
$358$	15.9814	−	3.97179i	0.844646	−	0.209916i
$359$	−28.3508			−1.49630			−0.748149	−	0.663531i	$-0.769057\pi$
$359$	−28.3508			−1.49630			−0.748149	+	0.663531i	$0.769057\pi$
$360$		0			0
$361$	−18.8954			−0.994495
$362$	−18.7641	+	4.66335i	−0.986218	+	0.245100i
$363$		0			0
$364$	26.4814	−	14.0291i	1.38800	−	0.735325i
$365$	−9.26841	−	29.8205i	−0.485131	−	1.56087i
$366$		0			0
$367$	−18.2123			−0.950675			−0.475337	−	0.879804i	$-0.657674\pi$
$367$	−18.2123			−0.950675			−0.475337	+	0.879804i	$0.657674\pi$
$368$	20.7444	+	14.0837i	1.08138	+	0.734165i
$369$		0			0
$370$	−9.67837	−	15.9668i	−0.503154	−	0.830077i
$371$			31.2048i			1.62007i
$372$		0			0
$373$	−7.21739			−0.373702			−0.186851	−	0.982388i	$-0.559828\pi$
$373$	−7.21739			−0.373702			−0.186851	+	0.982388i	$0.559828\pi$
$374$	−4.76917	+	1.18526i	−0.246608	+	0.0612883i
$375$		0			0
$376$	−18.2628	+	16.3691i	−0.941832	+	0.844170i
$377$	12.8730			0.662993
$378$		0			0
$379$	6.54353			0.336118			0.168059	−	0.985777i	$-0.446250\pi$
$379$	6.54353			0.336118			0.168059	+	0.985777i	$0.446250\pi$
$380$	1.01955	−	1.02594i	0.0523020	−	0.0526298i
$381$		0			0
$382$	2.06198	+	8.29685i	0.105500	+	0.424504i
$383$			15.3236i			0.782999i	0.920178	+	0.391500i	$0.128044\pi$
$383$			15.3236i			0.782999i	−0.920178	+	0.391500i	$0.871956\pi$
$384$		0			0
$385$	−1.84803	−	5.94592i	−0.0941846	−	0.303032i
$386$	−35.6196	+	8.85238i	−1.81299	+	0.450574i
$387$		0			0
$388$	−5.87251	−	11.0850i	−0.298131	−	0.562754i
$389$	−0.599067			−0.0303739			−0.0151869	−	0.999885i	$-0.504834\pi$
$389$	−0.599067			−0.0303739			−0.0151869	+	0.999885i	$0.504834\pi$
$390$		0			0
$391$		−	34.4080i		−	1.74009i
$392$	23.3112	+	26.0080i	1.17739	+	1.31360i
$393$		0			0
$394$	14.3893	−	3.57610i	0.724921	−	0.180161i
$395$	4.86953	+	15.6674i	0.245012	+	0.788310i
$396$		0			0
$397$	−12.8269			−0.643763			−0.321881	−	0.946780i	$-0.604315\pi$
$397$	−12.8269			−0.643763			−0.321881	+	0.946780i	$0.604315\pi$
$398$	4.38736	−	1.09037i	0.219918	−	0.0546553i
$399$		0			0
$400$	−0.124972	−	19.9996i	−0.00624860	−	0.999980i
$401$			5.19431i			0.259391i	0.991554	+	0.129696i	$0.0414000\pi$
$401$			5.19431i			0.259391i	−0.991554	+	0.129696i	$0.958600\pi$
$402$		0			0
$403$		−	26.7996i		−	1.33499i
$404$	0.946373	−	0.501362i	0.0470838	−	0.0249437i
$405$		0			0
$406$	5.66976	+	22.8136i	0.281385	+	1.13222i
$407$		−	3.73774i		−	0.185273i
$408$		0			0
$409$	8.10266			0.400651			0.200325	−	0.979729i	$-0.435800\pi$
$409$	8.10266			0.400651			0.200325	+	0.979729i	$0.435800\pi$
$410$	2.37294	−	1.43837i	0.117191	−	0.0710359i
$411$		0			0
$412$	22.1915	−	11.7564i	1.09330	−	0.579198i
$413$		−	46.3273i		−	2.27962i
$414$		0			0
$415$	4.07237	−	1.26572i	0.199905	−	0.0621318i
$416$	18.0829	+	6.65912i	0.886585	+	0.326490i
$417$		0			0
$418$	0.281002	−	0.0698362i	0.0137443	−	0.00341580i
$419$			3.51505i			0.171721i	0.996307	+	0.0858607i	$0.0273640\pi$
$419$			3.51505i			0.171721i	−0.996307	+	0.0858607i	$0.972636\pi$
$420$		0			0
$421$		−	5.14007i		−	0.250512i	−0.992124	−	0.125256i	$-0.960025\pi$
$421$		−	5.14007i		−	0.250512i	0.992124	−	0.125256i	$-0.0399751\pi$
$422$	5.86734	+	23.6086i	0.285618	+	1.14925i
$423$		0			0
$424$	−14.9418	+	13.3925i	−0.725640	+	0.650396i
$425$	−22.6102	+	15.5577i	−1.09676	+	0.754661i
$426$		0			0
$427$			61.8773i			2.99445i
$428$	−23.7291	+	12.5710i	−1.14699	+	0.607644i
$429$		0			0
$430$	6.25759	−	3.79306i	0.301768	−	0.182918i
$431$	33.9083			1.63330			0.816652	−	0.577130i	$-0.195828\pi$
$431$	33.9083			1.63330			0.816652	+	0.577130i	$0.195828\pi$
$432$		0			0
$433$			6.97168i			0.335038i	0.985869	+	0.167519i	$0.0535755\pi$
$433$			6.97168i			0.335038i	−0.985869	+	0.167519i	$0.946425\pi$
$434$	47.4945	−	11.8036i	2.27981	−	0.566590i
$435$		0			0
$436$	−1.34548	−	2.53974i	−0.0644369	−	0.121631i
$437$			2.02734i			0.0969810i
$438$		0			0
$439$			1.99992i			0.0954509i	0.998860	+	0.0477255i	$0.0151973\pi$
$439$			1.99992i			0.0954509i	−0.998860	+	0.0477255i	$0.984803\pi$
$440$	2.05395	−	3.43677i	0.0979184	−	0.163841i
$441$		0			0
$442$	−6.37797	−	25.6633i	−0.303369	−	1.22068i
$443$	30.0436			1.42741			0.713707	−	0.700445i	$-0.247015\pi$
$443$	30.0436			1.42741			0.713707	+	0.700445i	$0.247015\pi$
$444$		0			0
$445$	5.42151	+	17.4433i	0.257004	+	0.826893i
$446$	−4.02784	−	16.2070i	−0.190724	−	0.767422i
$447$		0			0
$448$	−3.83695	+	34.9795i	−0.181279	+	1.65263i
$449$		−	10.1557i		−	0.479275i	−0.970862	−	0.239638i	$-0.922971\pi$
$449$		−	10.1557i		−	0.479275i	0.970862	−	0.239638i	$-0.0770286\pi$
$450$		0			0
$451$	0.555490			0.0261570
$452$	11.4076	−	6.04344i	0.536570	−	0.284260i
$453$		0			0
$454$	−1.41534	−	5.69493i	−0.0664250	−	0.267276i
$455$	31.9955	−	9.94442i	1.49997	−	0.466202i
$456$		0			0
$457$			37.9896i			1.77708i	0.458800	+	0.888540i	$0.348280\pi$
$457$			37.9896i			1.77708i	−0.458800	+	0.888540i	$0.651720\pi$
$458$	24.3640	−	6.05506i	1.13845	−	0.282934i
$459$		0			0
$460$	19.8842	+	19.7604i	0.927107	+	0.921331i
$461$	−20.5143			−0.955445			−0.477722	−	0.878511i	$-0.658538\pi$
$461$	−20.5143			−0.955445			−0.477722	+	0.878511i	$0.658538\pi$
$462$		0			0
$463$	0.0629776			0.00292682			0.00146341	−	0.999999i	$-0.499534\pi$
$463$	0.0629776			0.00292682			0.00146341	+	0.999999i	$0.499534\pi$
$464$	−8.49052	+	12.5060i	−0.394163	+	0.580576i
$465$		0			0
$466$	−2.57568	−	10.3638i	−0.119316	−	0.480095i
$467$	−21.9620			−1.01628			−0.508140	−	0.861274i	$-0.669667\pi$
$467$	−21.9620			−1.01628			−0.508140	+	0.861274i	$0.669667\pi$
$468$		0			0
$469$			26.3648i			1.21741i
$470$	−23.4484	+	14.2133i	−1.08159	+	0.655612i
$471$		0			0
$472$	22.1830	−	19.8828i	1.02105	−	0.915178i
$473$	1.46486			0.0673544
$474$		0			0
$475$	1.33221	−	0.916671i	0.0611259	−	0.0420598i
$476$	42.6715	−	22.6062i	1.95584	−	1.03615i
$477$		0			0
$478$	0.380247	+	1.53001i	0.0173921	+	0.0699812i
$479$	−7.64777			−0.349436			−0.174718	−	0.984619i	$-0.555901\pi$
$479$	−7.64777			−0.349436			−0.174718	+	0.984619i	$0.555901\pi$
$480$		0			0
$481$	20.1130			0.917076
$482$	−8.00843	−	32.2238i	−0.364774	−	1.46775i
$483$		0			0
$484$	−18.7322	+	9.92379i	−0.851463	+	0.451081i
$485$	−4.16268	−	13.3931i	−0.189017	−	0.608150i
$486$		0			0
$487$	−2.23404			−0.101234			−0.0506171	−	0.998718i	$-0.516119\pi$
$487$	−2.23404			−0.101234			−0.0506171	+	0.998718i	$0.516119\pi$
$488$	−29.6288	+	26.5565i	−1.34123	+	1.20216i
$489$		0			0
$490$	20.2412	+	33.3928i	0.914404	+	1.50853i
$491$			22.4276i			1.01214i	0.862491	+	0.506072i	$0.168903\pi$
$491$			22.4276i			1.01214i	−0.862491	+	0.506072i	$0.831097\pi$
$492$		0			0
$493$	20.7432			0.934228
$494$	0.375794	+	1.51210i	0.0169078	+	0.0680324i
$495$		0			0
$496$	26.0356	+	17.6760i	1.16903	+	0.793675i
$497$	47.4201			2.12708
$498$		0			0
$499$	20.1585			0.902420			0.451210	−	0.892418i	$-0.350993\pi$
$499$	20.1585			0.902420			0.451210	+	0.892418i	$0.350993\pi$
$500$	3.99420	−	22.0011i	0.178626	−	0.983917i
$501$		0			0
$502$	−27.2721	+	6.77780i	−1.21721	+	0.302508i
$503$		−	17.3479i		−	0.773506i	−0.922183	−	0.386753i	$-0.873597\pi$
$503$		−	17.3479i		−	0.773506i	0.922183	−	0.386753i	$-0.126403\pi$
$504$		0			0
$505$	1.14343	−	0.355386i	0.0508820	−	0.0158145i
$506$	1.35352	+	5.44621i	0.0601714	+	0.242114i
$507$		0			0
$508$	19.0911	−	10.1139i	0.847029	−	0.448732i
$509$	28.4216			1.25976			0.629882	−	0.776691i	$-0.283103\pi$
$509$	28.4216			1.25976			0.629882	+	0.776691i	$0.283103\pi$
$510$		0			0
$511$			61.4291i			2.71746i
$512$	−18.3960	+	13.1752i	−0.812997	+	0.582269i
$513$		0			0
$514$	5.51890	+	22.2066i	0.243428	+	0.979490i
$515$	26.8123	−	8.33345i	1.18149	−	0.367216i
$516$		0			0
$517$	−5.48911			−0.241411
$518$	8.85855	+	35.6445i	0.389222	+	1.56613i
$519$		0			0
$520$	18.4935	+	11.0525i	0.810994	+	0.484684i
$521$			32.7743i			1.43587i	0.696111	+	0.717934i	$0.254912\pi$
$521$			32.7743i			1.43587i	−0.696111	+	0.717934i	$0.745088\pi$
$522$		0			0
$523$		−	43.3032i		−	1.89351i	−0.321948	−	0.946757i	$-0.604338\pi$
$523$		−	43.3032i		−	1.89351i	0.321948	−	0.946757i	$-0.395662\pi$
$524$	−17.1194	−	32.3147i	−0.747865	−	1.41167i
$525$		0			0
$526$	−17.2063	+	4.27619i	−0.750229	+	0.186451i
$527$		−	43.1843i		−	1.88114i
$528$		0			0
$529$	−16.2927			−0.708378
$530$	−19.1845	+	11.6287i	−0.833319	+	0.505120i
$531$		0			0
$532$	−2.51423	+	1.33197i	−0.109006	+	0.0577482i
$533$			2.98913i			0.129474i
$534$		0			0
$535$	−28.6701	+	8.91088i	−1.23952	+	0.385251i
$536$	−12.6243	+	11.3152i	−0.545286	+	0.488744i
$537$		0			0
$538$	−7.88734	−	31.7366i	−0.340047	−	1.36826i
$539$			7.81704i			0.336704i
$540$		0			0
$541$			8.86985i			0.381345i	0.981654	+	0.190672i	$0.0610668\pi$
$541$			8.86985i			0.381345i	−0.981654	+	0.190672i	$0.938933\pi$
$542$	−13.9453	+	3.46576i	−0.599003	+	0.148867i
$543$		0			0
$544$	29.1383	+	10.7303i	1.24929	+	0.460059i
$545$	−0.953734	−	3.06857i	−0.0408535	−	0.131443i
$546$		0			0
$547$			19.1126i			0.817197i	0.912714	+	0.408598i	$0.133982\pi$
$547$			19.1126i			0.817197i	−0.912714	+	0.408598i	$0.866018\pi$
$548$	26.3950	−	13.9834i	1.12754	−	0.597339i
$549$		0			0
$550$	2.96682	−	3.35195i	0.126506	−	0.142928i
$551$	−1.22220			−0.0520676
$552$		0			0
$553$		−	32.2742i		−	1.37244i
$554$	1.92595	+	7.74950i	0.0818257	+	0.329245i
$555$		0			0
$556$	28.3348	−	15.0110i	1.20166	−	0.636608i
$557$		−	18.4103i		−	0.780070i	−0.920800	−	0.390035i	$-0.872463\pi$
$557$		−	18.4103i		−	0.780070i	0.920800	−	0.390035i	$-0.127537\pi$
$558$		0			0
$559$			7.88253i			0.333396i
$560$	−11.4420	+	37.6422i	−0.483514	+	1.59067i
$561$		0			0
$562$	−40.3859	+	10.0369i	−1.70358	+	0.423382i
$563$	−1.23305			−0.0519669			−0.0259835	−	0.999662i	$-0.508272\pi$
$563$	−1.23305			−0.0519669			−0.0259835	+	0.999662i	$0.508272\pi$
$564$		0			0
$565$	13.7830	−	4.28385i	0.579854	−	0.180223i
$566$	3.21668	−	0.799428i	0.135207	−	0.0336025i
$567$		0			0
$568$	20.3518	+	22.7062i	0.853941	+	0.952733i
$569$		−	13.3647i		−	0.560279i	−0.959959	−	0.280140i	$-0.909619\pi$
$569$		−	13.3647i		−	0.560279i	0.959959	−	0.280140i	$-0.0903808\pi$
$570$		0			0
$571$	20.7664			0.869045			0.434522	−	0.900661i	$-0.356917\pi$
$571$	20.7664			0.869045			0.434522	+	0.900661i	$0.356917\pi$
$572$	2.01905	+	3.81117i	0.0844208	+	0.159353i
$573$		0			0
$574$	−5.29736	+	1.31653i	−0.221108	+	0.0549509i
$575$	17.7664	+	25.8200i	0.740908	+	1.07677i
$576$		0			0
$577$			8.90816i			0.370852i	0.982658	+	0.185426i	$0.0593664\pi$
$577$			8.90816i			0.370852i	−0.982658	+	0.185426i	$0.940634\pi$
$578$	−4.47874	−	18.0212i	−0.186291	−	0.749585i
$579$		0			0
$580$	−11.9127	+	11.9874i	−0.494649	+	0.497750i
$581$	−8.38894			−0.348032
$582$		0			0
$583$	−4.49096			−0.185996
$584$	−29.4142	+	26.3641i	−1.21717	+	1.09096i
$585$		0			0
$586$	32.1821	−	7.99808i	1.32943	−	0.330398i
$587$	−33.0278			−1.36320			−0.681601	−	0.731724i	$-0.738716\pi$
$587$	−33.0278			−1.36320			−0.681601	+	0.731724i	$0.738716\pi$
$588$		0			0
$589$			2.54445i			0.104842i
$590$	28.4817	−	17.2643i	1.17257	−	0.710759i
$591$		0			0
$592$	−13.2658	+	19.5396i	−0.545220	+	0.803074i
$593$	0.685529			0.0281513			0.0140757	−	0.999901i	$-0.495519\pi$
$593$	0.685529			0.0281513			0.0140757	+	0.999901i	$0.495519\pi$
$594$		0			0
$595$	51.5567	−	16.0242i	2.11362	−	0.656928i
$596$	−20.2314	+	10.7180i	−0.828710	+	0.439028i
$597$		0			0
$598$	−29.3065	+	7.28341i	−1.19843	+	0.297841i
$599$	−23.7808			−0.971656			−0.485828	−	0.874055i	$-0.661482\pi$
$599$	−23.7808			−0.971656			−0.485828	+	0.874055i	$0.661482\pi$
$600$		0			0
$601$	2.43712			0.0994123			0.0497062	−	0.998764i	$-0.484172\pi$
$601$	2.43712			0.0994123			0.0497062	+	0.998764i	$0.484172\pi$
$602$	−13.9695	+	3.47177i	−0.569353	+	0.141499i
$603$		0			0
$604$	11.2734	+	21.2797i	0.458708	+	0.865859i
$605$	−22.6327	+	7.03440i	−0.920149	+	0.285989i
$606$		0			0
$607$	−28.3537			−1.15084			−0.575420	−	0.817858i	$-0.695161\pi$
$607$	−28.3537			−1.15084			−0.575420	+	0.817858i	$0.695161\pi$
$608$	−1.71685	−	0.632238i	−0.0696273	−	0.0256407i
$609$		0			0
$610$	−38.0417	+	23.0591i	−1.54026	+	0.933636i
$611$		−	29.5373i		−	1.19495i
$612$		0			0
$613$	39.2558			1.58553			0.792763	−	0.609530i	$-0.208642\pi$
$613$	39.2558			1.58553			0.792763	+	0.609530i	$0.208642\pi$
$614$	1.82530	−	0.453634i	0.0736633	−	0.0183072i
$615$		0			0
$616$	−5.86491	+	5.25676i	−0.236304	+	0.211801i
$617$	40.7603			1.64095			0.820473	−	0.571685i	$-0.193710\pi$
$617$	40.7603			1.64095			0.820473	+	0.571685i	$0.193710\pi$
$618$		0			0
$619$	11.3834			0.457538			0.228769	−	0.973481i	$-0.426530\pi$
$619$	11.3834			0.457538			0.228769	+	0.973481i	$0.426530\pi$
$620$	24.9560	+	24.8005i	1.00226	+	0.996013i
$621$		0			0
$622$	−11.1490	−	44.8604i	−0.447032	−	1.79874i
$623$		−	35.9326i		−	1.43961i
$624$		0			0
$625$	8.93374	−	23.3493i	0.357350	−	0.933971i
$626$	11.3871	−	2.82999i	0.455121	−	0.113109i
$627$		0			0
$628$	−7.36815	+	3.90344i	−0.294021	+	0.155764i
$629$	32.4096			1.29226
$630$		0			0
$631$		−	20.7246i		−	0.825035i	−0.910950	−	0.412517i	$-0.864650\pi$
$631$		−	20.7246i		−	0.825035i	0.910950	−	0.412517i	$-0.135350\pi$
$632$	15.4539	−	13.8514i	0.614723	−	0.550980i
$633$		0			0
$634$	−41.0167	+	10.1937i	−1.62898	+	0.404843i
$635$	23.0663	−	7.16916i	0.915357	−	0.284500i
$636$		0			0
$637$	−42.0641			−1.66664
$638$	−3.28331	+	0.815985i	−0.129987	+	0.0323051i
$639$		0			0
$640$	−22.9350	+	10.6765i	−0.906584	+	0.422025i
$641$			1.64857i			0.0651148i	0.999470	+	0.0325574i	$0.0103652\pi$
$641$			1.64857i			0.0651148i	−0.999470	+	0.0325574i	$0.989635\pi$
$642$		0			0
$643$			32.4116i			1.27819i	0.769128	+	0.639095i	$0.220691\pi$
$643$			32.4116i			1.27819i	−0.769128	+	0.639095i	$0.779309\pi$
$644$	−25.8154	−	48.7293i	−1.01727	−	1.92020i
$645$		0			0
$646$	0.605545	+	2.43655i	0.0238249	+	0.0958649i
$647$			3.92161i			0.154174i	0.997024	+	0.0770871i	$0.0245620\pi$
$647$			3.92161i			0.154174i	−0.997024	+	0.0770871i	$0.975438\pi$
$648$		0			0
$649$	6.66737			0.261717
$650$	18.0371	+	15.9647i	0.707474	+	0.626186i
$651$		0			0
$652$	1.66238	+	3.13791i	0.0651038	+	0.122890i
$653$		−	16.8499i		−	0.659387i	−0.944088	−	0.329693i	$-0.893055\pi$
$653$		−	16.8499i		−	0.659387i	0.944088	−	0.329693i	$-0.106945\pi$
$654$		0			0
$655$	−12.1350	−	39.0433i	−0.474152	−	1.52555i
$656$	−2.90392	−	1.97152i	−0.113379	−	0.0769747i
$657$		0			0
$658$	52.3463	−	13.0094i	2.04067	−	0.507158i
$659$		−	31.2375i		−	1.21684i	−0.793615	−	0.608420i	$-0.791804\pi$
$659$		−	31.2375i		−	1.21684i	0.793615	−	0.608420i	$-0.208196\pi$
$660$		0			0
$661$			37.8548i			1.47238i	0.676774	+	0.736191i	$0.263377\pi$
$661$			37.8548i			1.47238i	−0.676774	+	0.736191i	$0.736623\pi$
$662$	−3.96719	−	15.9629i	−0.154189	−	0.620416i
$663$		0			0
$664$	−3.60036	−	4.01689i	−0.139721	−	0.155885i
$665$	−3.03775	+	0.944155i	−0.117799	+	0.0366128i
$666$		0			0
$667$		−	23.6880i		−	0.917203i
$668$	−2.74482	−	5.18113i	−0.106200	−	0.200464i
$669$		0			0
$670$	−16.2089	+	9.82506i	−0.626203	+	0.379575i
$671$	−8.90531			−0.343786
$672$		0			0
$673$			6.36802i			0.245469i	0.992440	+	0.122735i	$0.0391664\pi$
$673$			6.36802i			0.245469i	−0.992440	+	0.122735i	$0.960834\pi$
$674$	−11.5186	+	2.86267i	−0.443680	+	0.110266i
$675$		0			0
$676$	2.46685	−	1.30687i	0.0948790	−	0.0502642i
$677$			16.6484i			0.639851i	0.947443	+	0.319926i	$0.103658\pi$
$677$			16.6484i			0.639851i	−0.947443	+	0.319926i	$0.896342\pi$
$678$		0			0
$679$			27.5894i			1.05878i
$680$	29.8000	+	17.8097i	1.14278	+	0.682971i
$681$		0			0
$682$	1.69876	+	6.83535i	0.0650488	+	0.261739i
$683$	29.5071			1.12906			0.564529	−	0.825413i	$-0.309058\pi$
$683$	29.5071			1.12906			0.564529	+	0.825413i	$0.309058\pi$
$684$		0			0
$685$	31.8911	−	9.91199i	1.21850	−	0.378718i
$686$	−8.02420	−	32.2872i	−0.306365	−	1.23273i
$687$		0			0
$688$	−7.65781	−	5.19901i	−0.291951	−	0.198210i
$689$		−	24.1662i		−	0.920658i
$690$		0			0
$691$	31.8365			1.21112			0.605559	−	0.795800i	$-0.292949\pi$
$691$	31.8365			1.21112			0.605559	+	0.795800i	$0.292949\pi$
$692$	4.93545	+	9.31617i	0.187618	+	0.354148i
$693$		0			0
$694$	−4.90494	−	19.7362i	−0.186189	−	0.749175i
$695$	34.2348	−	10.6404i	1.29860	−	0.403614i
$696$		0			0
$697$			4.81662i			0.182442i
$698$	−46.2496	+	11.4942i	−1.75057	+	0.435061i
$699$		0			0
$700$	−20.3485	+	38.9970i	−0.769099	+	1.47395i
$701$	4.54314			0.171592			0.0857960	−	0.996313i	$-0.472657\pi$
$701$	4.54314			0.171592			0.0857960	+	0.996313i	$0.472657\pi$
$702$		0			0
$703$	−1.90960			−0.0720218
$704$	−5.03420	−	0.552209i	−0.189734	−	0.0208122i
$705$		0			0
$706$	−8.99150	−	36.1794i	−0.338400	−	1.36163i
$707$	−2.35543			−0.0885849
$708$		0			0
$709$			7.01898i			0.263603i	0.991276	+	0.131802i	$0.0420762\pi$
$709$			7.01898i			0.263603i	−0.991276	+	0.131802i	$0.957924\pi$
$710$	17.6715	+	29.1535i	0.663200	+	1.09411i
$711$		0			0
$712$	17.2057	−	15.4216i	0.644810	−	0.577947i
$713$	−49.3149			−1.84686
$714$		0			0
$715$	1.43119	+	4.60475i	0.0535234	+	0.172208i
$716$	−10.9023	−	20.5792i	−0.407438	−	0.769081i
$717$		0			0
$718$	9.67023	+	38.9104i	0.360890	+	1.45213i
$719$	−32.6924			−1.21922			−0.609610	−	0.792702i	$-0.708674\pi$
$719$	−32.6924			−1.21922			−0.609610	+	0.792702i	$0.708674\pi$
$720$		0			0
$721$	−55.2324			−2.05696
$722$	6.44507	+	25.9332i	0.239861	+	0.965135i
$723$		0			0
$724$	12.8006	+	24.1624i	0.475729	+	0.897988i
$725$	−15.5659	+	10.7106i	−0.578102	+	0.397783i
$726$		0			0
$727$	−15.4300			−0.572268			−0.286134	−	0.958190i	$-0.592370\pi$
$727$	−15.4300			−0.572268			−0.286134	+	0.958190i	$0.592370\pi$
$728$	−28.2870	−	31.5596i	−1.04839	−	1.16967i
$729$		0			0
$730$	−37.7661	+	22.8921i	−1.39779	+	0.847274i
$731$			12.7017i			0.469790i
$732$		0			0
$733$	50.2010			1.85421			0.927107	−	0.374796i	$-0.122287\pi$
$733$	50.2010			1.85421			0.927107	+	0.374796i	$0.122287\pi$
$734$	6.21207	+	24.9957i	0.229292	+	0.922609i
$735$		0			0
$736$	12.2537	−	33.2748i	0.451676	−	1.22653i
$737$	−3.79439			−0.139768
$738$		0			0
$739$	36.6261			1.34731			0.673657	−	0.739044i	$-0.264723\pi$
$739$	36.6261			1.34731			0.673657	+	0.739044i	$0.264723\pi$
$740$	−18.6127	+	18.7294i	−0.684217	+	0.688505i
$741$		0			0
$742$	42.8274	−	10.6437i	1.57225	−	0.390743i
$743$			35.5474i			1.30411i	0.758172	+	0.652055i	$0.226093\pi$
$743$			35.5474i			1.30411i	−0.758172	+	0.652055i	$0.773907\pi$
$744$		0			0
$745$	−24.4441	+	7.59739i	−0.895561	+	0.278347i
$746$	2.46179	+	9.90561i	0.0901327	+	0.362670i
$747$		0			0
$748$	3.25345	+	6.14122i	0.118958	+	0.224545i
$749$	59.0594			2.15798
$750$		0			0
$751$			41.1833i			1.50280i	0.659848	+	0.751399i	$0.270621\pi$
$751$			41.1833i			1.50280i	−0.659848	+	0.751399i	$0.729379\pi$
$752$	28.6952	+	19.4817i	1.04641	+	0.710423i
$753$		0			0
$754$	−4.39088	−	17.6677i	−0.159906	−	0.643420i
$755$	7.99105	+	25.7106i	0.290824	+	0.935706i
$756$		0			0
$757$	−5.89555			−0.214278			−0.107139	−	0.994244i	$-0.534169\pi$
$757$	−5.89555			−0.214278			−0.107139	+	0.994244i	$0.534169\pi$
$758$	−2.23194	−	8.98075i	−0.0810679	−	0.326196i
$759$		0			0
$760$	−1.75583	−	1.04936i	−0.0636908	−	0.0380642i
$761$		−	41.5797i		−	1.50726i	−0.657297	−	0.753632i	$-0.728300\pi$
$761$		−	41.5797i		−	1.50726i	0.657297	−	0.753632i	$-0.271700\pi$
$762$		0			0
$763$			6.32115i			0.228841i
$764$	10.6838	−	5.65998i	0.386526	−	0.204771i
$765$		0			0
$766$	21.0311	−	5.22676i	0.759884	−	0.188850i
$767$			35.8777i			1.29547i
$768$		0			0
$769$	−26.0235			−0.938432			−0.469216	−	0.883083i	$-0.655463\pi$
$769$	−26.0235			−0.938432			−0.469216	+	0.883083i	$0.655463\pi$
$770$	−7.53021	+	4.56447i	−0.271370	+	0.164492i
$771$		0			0
$772$	24.2991	+	45.8671i	0.874545	+	1.65079i
$773$			10.4488i			0.375819i	0.982186	+	0.187909i	$0.0601711\pi$
$773$			10.4488i			0.375819i	−0.982186	+	0.187909i	$0.939829\pi$
$774$		0			0
$775$	22.2979	+	32.4058i	0.800965	+	1.16405i
$776$	−13.2107	+	11.8408i	−0.474235	+	0.425060i
$777$		0			0
$778$	0.204337	+	0.822197i	0.00732583	+	0.0294772i
$779$		−	0.283798i		−	0.0101681i
$780$		0			0
$781$			6.82465i			0.244205i
$782$	−47.2238	+	11.7363i	−1.68872	+	0.419689i
$783$		0			0
$784$	27.7438	−	40.8649i	0.990851	−	1.45946i
$785$	−8.90237	+	2.76692i	−0.317739	+	0.0987556i
$786$		0			0
$787$			35.5171i			1.26605i	0.774132	+	0.633024i	$0.218187\pi$
$787$			35.5171i			1.26605i	−0.774132	+	0.633024i	$0.781813\pi$
$788$	−9.81613	−	18.5290i	−0.349685	−	0.660067i
$789$		0			0
$790$	19.8419	−	12.0273i	0.705944	−	0.427910i
$791$	−28.3924			−1.00952
$792$		0			0
$793$		−	47.9202i		−	1.70169i
$794$	4.37515	+	17.6044i	0.155268	+	0.624758i
$795$		0			0
$796$	−2.99298	−	5.64957i	−0.106083	−	0.200244i
$797$			20.0999i			0.711977i	0.934490	+	0.355988i	$0.115856\pi$
$797$			20.0999i			0.711977i	−0.934490	+	0.355988i	$0.884144\pi$
$798$		0			0
$799$		−	47.5957i		−	1.68382i
$800$	−27.4061	+	6.99323i	−0.968952	+	0.247248i
$801$		0			0
$802$	7.12899	−	1.77174i	0.251734	−	0.0625622i
$803$	−8.84080			−0.311985
$804$		0			0
$805$	−18.2990	−	58.8758i	−0.644956	−	2.07510i
$806$	−36.7815	+	9.14115i	−1.29557	+	0.321983i
$807$		0			0
$808$	−1.01090	−	1.12785i	−0.0355634	−	0.0396777i
$809$			32.5036i			1.14276i	0.820684	+	0.571382i	$0.193593\pi$
$809$			32.5036i			1.14276i	−0.820684	+	0.571382i	$0.806407\pi$
$810$		0			0
$811$	−35.5091			−1.24689			−0.623447	−	0.781866i	$-0.714268\pi$
$811$	−35.5091			−1.24689			−0.623447	+	0.781866i	$0.714268\pi$
$812$	29.3769	−	15.5631i	1.03093	−	0.546157i
$813$		0			0
$814$	−5.12991	+	1.27491i	−0.179803	+	0.0446856i
$815$	1.17836	+	3.79130i	0.0412763	+	0.132803i
$816$		0			0
$817$		−	0.748393i		−	0.0261830i
$818$	−2.76375	−	11.1206i	−0.0966324	−	0.388823i
$819$		0			0
$820$	−2.78350	−	2.76616i	−0.0972040	−	0.0965985i
$821$	−12.6596			−0.441821			−0.220911	−	0.975294i	$-0.570903\pi$
$821$	−12.6596			−0.441821			−0.220911	+	0.975294i	$0.570903\pi$
$822$		0			0
$823$	27.2106			0.948500			0.474250	−	0.880390i	$-0.342719\pi$
$823$	27.2106			0.948500			0.474250	+	0.880390i	$0.342719\pi$
$824$	−23.7046	−	26.4470i	−0.825790	−	0.921325i
$825$		0			0
$826$	−63.5826	+	15.8019i	−2.21232	+	0.549818i
$827$	−37.0039			−1.28675			−0.643376	−	0.765551i	$-0.722467\pi$
$827$	−37.0039			−1.28675			−0.643376	+	0.765551i	$0.722467\pi$
$828$		0			0
$829$		−	33.1179i		−	1.15023i	−0.818072	−	0.575116i	$-0.804957\pi$
$829$		−	33.1179i		−	1.15023i	0.818072	−	0.575116i	$-0.195043\pi$
$830$	−3.12621	−	5.15745i	−0.108512	−	0.179018i
$831$		0			0
$832$	2.97148	−	27.0894i	0.103018	−	0.939157i
$833$	−67.7810			−2.34847
$834$		0			0
$835$	−1.94564	−	6.25996i	−0.0673317	−	0.216635i
$836$	−0.191695	−	0.361845i	−0.00662992	−	0.0125147i
$837$		0			0
$838$	4.82427	−	1.19895i	0.166652	−	0.0414172i
$839$	−29.0655			−1.00345			−0.501726	−	0.865026i	$-0.667302\pi$
$839$	−29.0655			−1.00345			−0.501726	+	0.865026i	$0.667302\pi$
$840$		0			0
$841$	−14.7194			−0.507567
$842$	−7.05455	+	1.75324i	−0.243116	+	0.0604205i
$843$		0			0
$844$	30.4007	−	16.1054i	1.04643	−	0.554372i
$845$	2.98051	−	0.926364i	0.102533	−	0.0318679i
$846$		0			0
$847$	46.6225			1.60197
$848$	23.4772	+	15.9391i	0.806211	+	0.547350i
$849$		0			0
$850$	29.0646	+	25.7251i	0.996907	+	0.882363i
$851$		−	37.0106i		−	1.26871i
$852$		0			0
$853$	−43.9301			−1.50414			−0.752069	−	0.659084i	$-0.770944\pi$
$853$	−43.9301			−1.50414			−0.752069	+	0.659084i	$0.770944\pi$
$854$	84.9244	−	21.1059i	2.90605	−	0.722228i
$855$		0			0
$856$	25.3471	+	28.2795i	0.866346	+	0.966574i
$857$	−8.72872			−0.298167			−0.149084	−	0.988825i	$-0.547632\pi$
$857$	−8.72872			−0.298167			−0.149084	+	0.988825i	$0.547632\pi$
$858$		0			0
$859$	7.59497			0.259137			0.129569	−	0.991570i	$-0.458641\pi$
$859$	7.59497			0.259137			0.129569	+	0.991570i	$0.458641\pi$
$860$	−7.34026	−	7.29453i	−0.250301	−	0.248742i
$861$		0			0
$862$	−11.5658	−	46.5379i	−0.393934	−	1.58509i
$863$			11.9244i			0.405910i	0.979188	+	0.202955i	$0.0650546\pi$
$863$			11.9244i			0.405910i	−0.979188	+	0.202955i	$0.934945\pi$
$864$		0			0
$865$	3.49845	+	11.2560i	0.118951	+	0.382716i
$866$	9.56838	−	2.37798i	0.325147	−	0.0808072i
$867$		0			0
$868$	−32.4000	−	61.1584i	−1.09973	−	2.07585i
$869$	4.64486			0.157566
$870$		0			0
$871$		−	20.4179i		−	0.691834i
$872$	−3.02676	+	2.71291i	−0.102499	+	0.0918707i
$873$		0			0
$874$	2.78245	−	0.691510i	0.0941179	−	0.0233907i
$875$	−30.4145	+	38.6456i	−1.02820	+	1.30646i
$876$		0			0
$877$	−22.3668			−0.755272			−0.377636	−	0.925954i	$-0.623263\pi$
$877$	−22.3668			−0.755272			−0.377636	+	0.925954i	$0.623263\pi$
$878$	2.74482	−	0.682156i	0.0926331	−	0.0230217i
$879$		0			0
$880$	−5.41742	−	1.64672i	−0.182621	−	0.0555110i
$881$		−	18.7665i		−	0.632259i	−0.948716	−	0.316130i	$-0.897617\pi$
$881$		−	18.7665i		−	0.632259i	0.948716	−	0.316130i	$-0.102383\pi$
$882$		0			0
$883$		−	22.0307i		−	0.741393i	−0.928754	−	0.370697i	$-0.879119\pi$
$883$		−	22.0307i		−	0.741393i	0.928754	−	0.370697i	$-0.120881\pi$
$884$	−33.0464	+	17.5071i	−1.11147	+	0.588826i
$885$		0			0
$886$	−10.2476	−	41.2337i	−0.344276	−	1.38527i
$887$		−	39.7930i		−	1.33612i	−0.744108	−	0.668059i	$-0.767125\pi$
$887$		−	39.7930i		−	1.33612i	0.744108	−	0.668059i	$-0.232875\pi$
$888$		0			0
$889$	−47.5157			−1.59363
$890$	22.0911	−	13.3906i	0.740495	−	0.448854i
$891$		0			0
$892$	−20.8696	+	11.0561i	−0.698766	+	0.370186i
$893$			2.80437i			0.0938447i
$894$		0			0
$895$	−7.72800	−	24.8643i	−0.258318	−	0.831121i
$896$	49.3168	−	6.66515i	1.64756	−	0.222667i
$897$		0			0
$898$	−13.9383	+	3.46401i	−0.465126	+	0.115596i
$899$		−	29.7300i		−	0.991550i
$900$		0			0
$901$		−	38.9408i		−	1.29731i
$902$	−0.189473	−	0.762390i	−0.00630877	−	0.0253848i
$903$		0			0
$904$	−12.1855	−	13.5952i	−0.405282	−	0.452169i
$905$	9.07357	+	29.1936i	0.301616	+	0.970427i
$906$		0			0
$907$			24.7832i			0.822914i	0.911429	+	0.411457i	$0.134980\pi$
$907$			24.7832i			0.822914i	−0.911429	+	0.411457i	$0.865020\pi$
$908$	−7.33333	+	3.88499i	−0.243365	+	0.128928i
$909$		0			0
$910$	−24.5618	−	40.5206i	−0.814214	−	1.34325i
$911$	26.0401			0.862747			0.431374	−	0.902173i	$-0.358029\pi$
$911$	26.0401			0.862747			0.431374	+	0.902173i	$0.358029\pi$
$912$		0			0
$913$		−	1.20733i		−	0.0399566i
$914$	52.1394	−	12.9580i	1.72462	−	0.428611i
$915$		0			0
$916$	−16.6207	−	31.3733i	−0.549163	−	1.03660i
$917$			80.4279i			2.65596i
$918$		0			0
$919$			31.9640i			1.05439i	0.849743	+	0.527197i	$0.176757\pi$
$919$			31.9640i			1.05439i	−0.849743	+	0.527197i	$0.823243\pi$
$920$	20.3380	−	34.0305i	0.670525	−	1.12195i
$921$		0			0
$922$	6.99725	+	28.1551i	0.230442	+	0.927239i
$923$	−36.7240			−1.20878
$924$		0			0
$925$	−24.3204	+	16.7345i	−0.799651	+	0.550227i
$926$	−0.0214812	−	0.0864345i	−0.000705915	−	0.00284041i
$927$		0			0
$928$	20.0601	+	7.38724i	0.658504	+	0.242498i
$929$			55.1162i			1.80830i	0.427211	+	0.904152i	$0.359496\pi$
$929$			55.1162i			1.80830i	−0.427211	+	0.904152i	$0.640504\pi$
$930$		0			0
$931$	3.99370			0.130888
$932$	−13.3454	+	7.07004i	−0.437145	+	0.231587i
$933$		0			0
$934$	7.49106	+	30.1421i	0.245115	+	0.986278i
$935$	2.30618	+	7.41997i	0.0754202	+	0.242659i
$936$		0			0
$937$			17.0794i			0.557960i	0.960297	+	0.278980i	$0.0899964\pi$
$937$			17.0794i			0.557960i	−0.960297	+	0.278980i	$0.910004\pi$
$938$	36.1847	−	8.99282i	1.18147	−	0.293626i
$939$		0			0
$940$	27.5053	+	27.3340i	0.897125	+	0.891537i
$941$	−46.5090			−1.51615			−0.758075	−	0.652168i	$-0.773860\pi$
$941$	−46.5090			−1.51615			−0.758075	+	0.652168i	$0.773860\pi$
$942$		0			0
$943$	5.50040			0.179118
$944$	−34.8548	−	23.6635i	−1.13443	−	0.770181i
$945$		0			0
$946$	−0.499653	−	2.01047i	−0.0162451	−	0.0653660i
$947$	−2.59658			−0.0843776			−0.0421888	−	0.999110i	$-0.513433\pi$
$947$	−2.59658			−0.0843776			−0.0421888	+	0.999110i	$0.513433\pi$
$948$		0			0
$949$		−	47.5730i		−	1.54429i
$950$	−1.71250	−	1.51574i	−0.0555610	−	0.0491770i
$951$		0			0
$952$	−45.5810	−	50.8543i	−1.47729	−	1.64820i
$953$	34.8096			1.12759			0.563797	−	0.825914i	$-0.309340\pi$
$953$	34.8096			1.12759			0.563797	+	0.825914i	$0.309340\pi$
$954$		0			0
$955$	12.9084	−	4.01203i	0.417707	−	0.129826i
$956$	1.97019	−	1.04375i	0.0637204	−	0.0337573i
$957$		0			0
$958$	2.60859	+	10.4963i	0.0842798	+	0.339120i
$959$	−65.6946			−2.12139
$960$		0			0
$961$	−30.8933			−0.996559
$962$	−6.86040	−	27.6044i	−0.221188	−	0.890002i
$963$		0			0
$964$	−41.4944	+	21.9826i	−1.33644	+	0.708011i
$965$	17.2242	+	55.4178i	0.554468	+	1.78396i
$966$		0			0
$967$	−6.55004			−0.210635			−0.105318	−	0.994439i	$-0.533586\pi$
$967$	−6.55004			−0.210635			−0.105318	+	0.994439i	$0.533586\pi$
$968$	20.0094	+	22.3243i	0.643128	+	0.717531i
$969$		0			0
$970$	−16.9617	+	10.2814i	−0.544608	+	0.330116i
$971$			27.4146i			0.879778i	0.898052	+	0.439889i	$0.144982\pi$
$971$			27.4146i			0.879778i	−0.898052	+	0.439889i	$0.855018\pi$
$972$		0			0
$973$	−70.5225			−2.26085
$974$	0.762014	+	3.06614i	0.0244165	+	0.0982455i
$975$		0			0
$976$	46.5540	+	31.6062i	1.49016	+	1.01169i
$977$	14.1922			0.454048			0.227024	−	0.973889i	$-0.427100\pi$
$977$	14.1922			0.454048			0.227024	+	0.973889i	$0.427100\pi$
$978$		0			0
$979$	5.17138			0.165278
$980$	38.9263	−	39.1703i	1.24346	−	1.25125i
$981$		0			0
$982$	30.7811	−	7.64988i	0.982264	−	0.244118i
$983$			6.12231i			0.195272i	0.995222	+	0.0976358i	$0.0311280\pi$
$983$			6.12231i			0.195272i	−0.995222	+	0.0976358i	$0.968872\pi$
$984$		0			0
$985$	−6.95809	−	22.3871i	−0.221703	−	0.713314i
$986$	−7.07535	−	28.4693i	−0.225325	−	0.906648i
$987$		0			0
$988$	1.94712	−	1.03153i	0.0619460	−	0.0328173i
$989$	14.5049			0.461229
$990$		0			0
$991$			36.8386i			1.17022i	0.810955	+	0.585109i	$0.198948\pi$
$991$			36.8386i			1.17022i	−0.810955	+	0.585109i	$0.801052\pi$
$992$	15.3791	−	41.7621i	0.488288	−	1.32595i
$993$		0			0
$994$	−16.1746	−	65.0824i	−0.513028	−	2.06429i
$995$	−2.12155	−	6.82594i	−0.0672577	−	0.216397i
$996$		0			0
$997$	20.2385			0.640960			0.320480	−	0.947255i	$-0.396156\pi$
$997$	20.2385			0.640960			0.320480	+	0.947255i	$0.396156\pi$
$998$	−6.87591	−	27.6668i	−0.217653	−	0.875779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.m.c.539.21	✓	48
3.2	odd	2	inner	1080.2.m.c.539.28	yes	48
4.3	odd	2		4320.2.m.c.2159.7		48
5.4	even	2	inner	1080.2.m.c.539.27	yes	48
8.3	odd	2	inner	1080.2.m.c.539.24	yes	48
8.5	even	2		4320.2.m.c.2159.42		48
12.11	even	2		4320.2.m.c.2159.41		48
15.14	odd	2	inner	1080.2.m.c.539.22	yes	48
20.19	odd	2		4320.2.m.c.2159.6		48
24.5	odd	2		4320.2.m.c.2159.8		48
24.11	even	2	inner	1080.2.m.c.539.25	yes	48
40.19	odd	2	inner	1080.2.m.c.539.26	yes	48
40.29	even	2		4320.2.m.c.2159.43		48
60.59	even	2		4320.2.m.c.2159.44		48
120.29	odd	2		4320.2.m.c.2159.5		48
120.59	even	2	inner	1080.2.m.c.539.23	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.m.c.539.21	✓	48	1.1	even	1	trivial
1080.2.m.c.539.22	yes	48	15.14	odd	2	inner
1080.2.m.c.539.23	yes	48	120.59	even	2	inner
1080.2.m.c.539.24	yes	48	8.3	odd	2	inner
1080.2.m.c.539.25	yes	48	24.11	even	2	inner
1080.2.m.c.539.26	yes	48	40.19	odd	2	inner
1080.2.m.c.539.27	yes	48	5.4	even	2	inner
1080.2.m.c.539.28	yes	48	3.2	odd	2	inner
4320.2.m.c.2159.5		48	120.29	odd	2
4320.2.m.c.2159.6		48	20.19	odd	2
4320.2.m.c.2159.7		48	4.3	odd	2
4320.2.m.c.2159.8		48	24.5	odd	2
4320.2.m.c.2159.41		48	12.11	even	2
4320.2.m.c.2159.42		48	8.5	even	2
4320.2.m.c.2159.43		48	40.29	even	2
4320.2.m.c.2159.44		48	60.59	even	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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.341092 - 1.37246i) q^{2} +(-1.76731 + 0.936273i) q^{4} +(-2.13531 + 0.663669i) q^{5} +4.39866 q^{7} +(1.88782 + 2.10622i) q^{8} +O(q^{10})\)	\(q+(-0.341092 - 1.37246i) q^{2} +(-1.76731 + 0.936273i) q^{4} +(-2.13531 + 0.663669i) q^{5} +4.39866 q^{7} +(1.88782 + 2.10622i) q^{8} +(1.63920 + 2.70426i) q^{10} +0.633050i q^{11} -3.40649 q^{13} +(-1.50035 - 6.03700i) q^{14} +(2.24679 - 3.30937i) q^{16} -5.48913 q^{17} +0.323423 q^{19} +(3.15238 - 3.17214i) q^{20} +(0.868838 - 0.215928i) q^{22} +6.26839i q^{23} +(4.11909 - 2.83428i) q^{25} +(1.16193 + 4.67528i) q^{26} +(-7.77381 + 4.11835i) q^{28} -3.77896 q^{29} +7.86723i q^{31} +(-5.30835 - 1.95483i) q^{32} +(1.87230 + 7.53363i) q^{34} +(-9.39250 + 2.91926i) q^{35} -5.90433 q^{37} +(-0.110317 - 0.443887i) q^{38} +(-5.42890 - 3.24454i) q^{40} -0.877482i q^{41} -2.31397i q^{43} +(-0.592707 - 1.11880i) q^{44} +(8.60314 - 2.13810i) q^{46} +8.67090i q^{47} +12.3482 q^{49} +(-5.29493 - 4.68655i) q^{50} +(6.02033 - 3.18940i) q^{52} +7.09416i q^{53} +(-0.420136 - 1.35176i) q^{55} +(8.30386 + 9.26454i) q^{56} +(1.28897 + 5.18649i) q^{58} -10.5321i q^{59} +14.0673i q^{61} +(10.7975 - 2.68345i) q^{62} +(-0.872299 + 7.95230i) q^{64} +(7.27391 - 2.26078i) q^{65} +5.99382i q^{67} +(9.70101 - 5.13933i) q^{68} +(7.21028 + 11.8951i) q^{70} +10.7806 q^{71} +13.9654i q^{73} +(2.01392 + 8.10348i) q^{74} +(-0.571590 + 0.302812i) q^{76} +2.78457i q^{77} -7.33728i q^{79} +(-2.60125 + 8.55766i) q^{80} +(-1.20431 + 0.299302i) q^{82} -1.90716 q^{83} +(11.7210 - 3.64297i) q^{85} +(-3.17585 + 0.789278i) q^{86} +(-1.33334 + 1.19508i) q^{88} -8.16899i q^{89} -14.9840 q^{91} +(-5.86892 - 11.0782i) q^{92} +(11.9005 - 2.95758i) q^{94} +(-0.690609 + 0.214646i) q^{95} +6.27222i q^{97} +(-4.21188 - 16.9475i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4}+O(q^{10}) \) 48 * q + 4 * q^4	\( 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more