LMFDB - Embedded newform 560.2.x.a.463.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(127,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1, 0]))

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

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

chi := DirichletCharacter("560.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.x (of order $4$, 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.5
Root			$-0.0912546 - 1.41127i$ of defining polynomial
Character	$\chi$	$=$	560.463
Dual form			560.2.x.a.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50252 - 1.50252i) q^{3} +(1.32001 + 1.80487i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.51514i q^{9} +O(q^{10})$	\(q+(1.50252 - 1.50252i) q^{3} +(1.32001 + 1.80487i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.51514i q^{9} -3.96669i q^{11} +(0.195126 + 0.195126i) q^{13} +(4.69521 + 0.728515i) q^{15} +(4.44490 - 4.44490i) q^{17} +4.46207 q^{19} -2.12489 q^{21} +(-0.728515 + 0.728515i) q^{23} +(-1.51514 + 4.76491i) q^{25} +(2.23104 + 2.23104i) q^{27} +5.79518i q^{29} -4.92834i q^{31} +(-5.96004 - 5.96004i) q^{33} +(0.342849 - 2.20963i) q^{35} +(-0.875115 + 0.875115i) q^{37} +0.586363 q^{39} -10.8898 q^{41} +(-0.233133 + 0.233133i) q^{43} +(2.73463 - 2.00000i) q^{45} +(7.88789 + 7.88789i) q^{47} +1.00000i q^{49} -13.3571i q^{51} +(-0.609747 - 0.609747i) q^{53} +(7.15938 - 5.23608i) q^{55} +(6.70436 - 6.70436i) q^{57} -12.3955 q^{59} -7.21949 q^{61} +(-1.07136 + 1.07136i) q^{63} +(-0.0946093 + 0.609747i) q^{65} +(-10.7053 - 10.7053i) q^{67} +2.18922i q^{69} +6.01008i q^{71} +(5.76491 + 5.76491i) q^{73} +(4.88285 + 9.43590i) q^{75} +(-2.80487 + 2.80487i) q^{77} -7.34702 q^{79} +11.2498 q^{81} +(-5.65685 + 5.65685i) q^{83} +(13.8898 + 2.15516i) q^{85} +(8.70739 + 8.70739i) q^{87} +2.71995i q^{89} -0.275950i q^{91} +(-7.40493 - 7.40493i) q^{93} +(5.88999 + 8.05348i) q^{95} +(1.86543 - 1.86543i) q^{97} -6.01008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 20 q^{13} + 4 q^{17} + 8 q^{21} - 20 q^{25} - 24 q^{33} - 44 q^{37} - 32 q^{41} - 36 q^{45} + 28 q^{53} + 8 q^{57} - 16 q^{61} + 36 q^{65} + 4 q^{73} - 16 q^{77} + 68 q^{81} + 68 q^{85} + 8 q^{93} + 12 q^{97}+O(q^{100}) $ 12 * q + 20 * q^13 + 4 * q^17 + 8 * q^21 - 20 * q^25 - 24 * q^33 - 44 * q^37 - 32 * q^41 - 36 * q^45 + 28 * q^53 + 8 * q^57 - 16 * q^61 + 36 * q^65 + 4 * q^73 - 16 * q^77 + 68 * q^81 + 68 * q^85 + 8 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50252	−	1.50252i	0.867481	−	0.867481i	−0.124712	−	0.992193i	$-0.539801\pi$
$3$	1.50252	−	1.50252i	0.867481	−	0.867481i	0.992193	+	0.124712i	$0.0398007\pi$
$4$		0			0
$5$	1.32001	+	1.80487i	0.590327	+	0.807164i
$5$	1.32001	+	1.80487i	0.590327	+	0.807164i
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$		−	1.51514i		−	0.505046i
$10$		0			0
$11$		−	3.96669i		−	1.19600i	−0.801495	−	0.598001i	$-0.795962\pi$
$11$		−	3.96669i		−	1.19600i	0.801495	−	0.598001i	$-0.204038\pi$
$12$		0			0
$13$	0.195126	+	0.195126i	0.0541183	+	0.0541183i	0.733648	−	0.679530i	$-0.237816\pi$
$13$	0.195126	+	0.195126i	0.0541183	+	0.0541183i	−0.679530	+	0.733648i	$0.737816\pi$
$14$		0			0
$15$	4.69521	+	0.728515i	1.21230	+	0.188102i
$16$		0			0
$17$	4.44490	−	4.44490i	1.07805	−	1.07805i	0.0813612	−	0.996685i	$-0.474073\pi$
$17$	4.44490	−	4.44490i	1.07805	−	1.07805i	0.996685	−	0.0813612i	$-0.0259267\pi$
$18$		0			0
$19$	4.46207			1.02367			0.511835	−	0.859084i	$-0.328966\pi$
$19$	4.46207			1.02367			0.511835	+	0.859084i	$0.328966\pi$
$20$		0			0
$21$	−2.12489			−0.463688
$22$		0			0
$23$	−0.728515	+	0.728515i	−0.151906	+	0.151906i	−0.778969	−	0.627063i	$-0.784257\pi$
$23$	−0.728515	+	0.728515i	−0.151906	+	0.151906i	0.627063	+	0.778969i	$0.284257\pi$
$24$		0			0
$25$	−1.51514	+	4.76491i	−0.303028	+	0.952982i
$26$		0			0
$27$	2.23104	+	2.23104i	0.429363	+	0.429363i
$28$		0			0
$29$			5.79518i			1.07614i	0.842901	+	0.538069i	$0.180846\pi$
$29$			5.79518i			1.07614i	−0.842901	+	0.538069i	$0.819154\pi$
$30$		0			0
$31$		−	4.92834i		−	0.885156i	−0.896730	−	0.442578i	$-0.854064\pi$
$31$		−	4.92834i		−	0.885156i	0.896730	−	0.442578i	$-0.145936\pi$
$32$		0			0
$33$	−5.96004	−	5.96004i	−1.03751	−	1.03751i
$34$		0			0
$35$	0.342849	−	2.20963i	0.0579521	−	0.373495i
$36$		0			0
$37$	−0.875115	+	0.875115i	−0.143868	+	0.143868i	−0.775372	−	0.631504i	$-0.782438\pi$
$37$	−0.875115	+	0.875115i	−0.143868	+	0.143868i	0.631504	+	0.775372i	$0.282438\pi$
$38$		0			0
$39$	0.586363			0.0938932
$40$		0			0
$41$	−10.8898			−1.70070			−0.850350	−	0.526217i	$-0.823610\pi$
$41$	−10.8898			−1.70070			−0.850350	+	0.526217i	$0.823610\pi$
$42$		0			0
$43$	−0.233133	+	0.233133i	−0.0355525	+	0.0355525i	−0.724660	−	0.689107i	$-0.758003\pi$
$43$	−0.233133	+	0.233133i	−0.0355525	+	0.0355525i	0.689107	+	0.724660i	$0.258003\pi$
$44$		0			0
$45$	2.73463	−	2.00000i	0.407655	−	0.298142i
$46$		0			0
$47$	7.88789	+	7.88789i	1.15057	+	1.15057i	0.986439	+	0.164128i	$0.0524810\pi$
$47$	7.88789	+	7.88789i	1.15057	+	1.15057i	0.164128	+	0.986439i	$0.447519\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		−	13.3571i		−	1.87037i
$52$		0			0
$53$	−0.609747	−	0.609747i	−0.0837552	−	0.0837552i	0.663988	−	0.747743i	$-0.268863\pi$
$53$	−0.609747	−	0.609747i	−0.0837552	−	0.0837552i	−0.747743	+	0.663988i	$0.768863\pi$
$54$		0			0
$55$	7.15938	−	5.23608i	0.965370	−	0.706033i
$56$		0			0
$57$	6.70436	−	6.70436i	0.888014	−	0.888014i
$58$		0			0
$59$	−12.3955			−1.61375			−0.806875	−	0.590722i	$-0.798843\pi$
$59$	−12.3955			−1.61375			−0.806875	+	0.590722i	$0.798843\pi$
$60$		0			0
$61$	−7.21949			−0.924362			−0.462181	−	0.886786i	$-0.652933\pi$
$61$	−7.21949			−0.924362			−0.462181	+	0.886786i	$0.652933\pi$
$62$		0			0
$63$	−1.07136	+	1.07136i	−0.134979	+	0.134979i
$64$		0			0
$65$	−0.0946093	+	0.609747i	−0.0117348	+	0.0756299i
$66$		0			0
$67$	−10.7053	−	10.7053i	−1.30786	−	1.30786i	−0.922958	−	0.384902i	$-0.874235\pi$
$67$	−10.7053	−	10.7053i	−1.30786	−	1.30786i	−0.384902	−	0.922958i	$-0.625765\pi$
$68$		0			0
$69$			2.18922i			0.263551i
$70$		0			0
$71$			6.01008i			0.713266i	0.934245	+	0.356633i	$0.116075\pi$
$71$			6.01008i			0.713266i	−0.934245	+	0.356633i	$0.883925\pi$
$72$		0			0
$73$	5.76491	+	5.76491i	0.674732	+	0.674732i	0.958803	−	0.284072i	$-0.0916853\pi$
$73$	5.76491	+	5.76491i	0.674732	+	0.674732i	−0.284072	+	0.958803i	$0.591685\pi$
$74$		0			0
$75$	4.88285	+	9.43590i	0.563823	+	1.08956i
$76$		0			0
$77$	−2.80487	+	2.80487i	−0.319645	+	0.319645i
$78$		0			0
$79$	−7.34702			−0.826604			−0.413302	−	0.910594i	$-0.635625\pi$
$79$	−7.34702			−0.826604			−0.413302	+	0.910594i	$0.635625\pi$
$80$		0			0
$81$	11.2498			1.24997
$82$		0			0
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	−0.945767	−	0.324846i	$-0.894687\pi$
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	0.324846	+	0.945767i	$0.394687\pi$
$84$		0			0
$85$	13.8898	+	2.15516i	1.50656	+	0.233760i
$86$		0			0
$87$	8.70739	+	8.70739i	0.933530	+	0.933530i
$88$		0			0
$89$			2.71995i			0.288314i	0.989555	+	0.144157i	$0.0460471\pi$
$89$			2.71995i			0.288314i	−0.989555	+	0.144157i	$0.953953\pi$
$90$		0			0
$91$		−	0.275950i		−	0.0289274i
$92$		0			0
$93$	−7.40493	−	7.40493i	−0.767856	−	0.767856i
$94$		0			0
$95$	5.88999	+	8.05348i	0.604300	+	0.826269i
$96$		0			0
$97$	1.86543	−	1.86543i	0.189405	−	0.189405i	−0.606034	−	0.795439i	$-0.707240\pi$
$97$	1.86543	−	1.86543i	0.189405	−	0.189405i	0.795439	+	0.606034i	$0.207240\pi$
$98$		0			0
$99$	−6.01008			−0.604036
$100$		0			0
$101$	7.60975			0.757198			0.378599	−	0.925561i	$-0.376406\pi$
$101$	7.60975			0.757198			0.378599	+	0.925561i	$0.376406\pi$
$102$		0			0
$103$	−9.43590	+	9.43590i	−0.929747	+	0.929747i	−0.997689	−	0.0679422i	$-0.978357\pi$
$103$	−9.43590	+	9.43590i	−0.929747	+	0.929747i	0.0679422	+	0.997689i	$0.478357\pi$
$104$		0			0
$105$	−2.80487	−	3.83515i	−0.273728	−	0.374272i
$106$		0			0
$107$	0.233133	+	0.233133i	0.0225379	+	0.0225379i	0.718286	−	0.695748i	$-0.244927\pi$
$107$	0.233133	+	0.233133i	0.0225379	+	0.0225379i	−0.695748	+	0.718286i	$0.744927\pi$
$108$		0			0
$109$		−	9.73463i		−	0.932409i	−0.884677	−	0.466204i	$-0.845621\pi$
$109$		−	9.73463i		−	0.932409i	0.884677	−	0.466204i	$-0.154379\pi$
$110$		0			0
$111$			2.62976i			0.249605i
$112$		0			0
$113$	10.6547	+	10.6547i	1.00231	+	1.00231i	0.999997	+	0.00231284i	$0.000736200\pi$
$113$	10.6547	+	10.6547i	1.00231	+	1.00231i	0.00231284	+	0.999997i	$0.499264\pi$
$114$		0			0
$115$	−2.27653	−	0.353229i	−0.212287	−	0.0329388i
$116$		0			0
$117$	0.295643	−	0.295643i	0.0273322	−	0.0273322i
$118$		0			0
$119$	−6.28603			−0.576240
$120$		0			0
$121$	−4.73463			−0.430421
$122$		0			0
$123$	−16.3621	+	16.3621i	−1.47532	+	1.47532i
$124$		0			0
$125$	−10.6001	+	3.55510i	−0.948098	+	0.317978i
$126$		0			0
$127$	4.69521	+	4.69521i	0.416632	+	0.416632i	0.884041	−	0.467409i	$-0.154812\pi$
$127$	4.69521	+	4.69521i	0.416632	+	0.416632i	−0.467409	+	0.884041i	$0.654812\pi$
$128$		0			0
$129$			0.700576i			0.0616822i
$130$		0			0
$131$		−	9.39041i		−	0.820444i	−0.911986	−	0.410222i	$-0.865451\pi$
$131$		−	9.39041i		−	0.820444i	0.911986	−	0.410222i	$-0.134549\pi$
$132$		0			0
$133$	−3.15516	−	3.15516i	−0.273587	−	0.273587i
$134$		0			0
$135$	−1.08174	+	6.97173i	−0.0931017	+	0.600031i
$136$		0			0
$137$	−3.51514	+	3.51514i	−0.300319	+	0.300319i	−0.841138	−	0.540820i	$-0.818114\pi$
$137$	−3.51514	+	3.51514i	−0.300319	+	0.300319i	0.540820	+	0.841138i	$0.318114\pi$
$138$		0			0
$139$	−19.9535			−1.69244			−0.846219	−	0.532835i	$-0.821126\pi$
$139$	−19.9535			−1.69244			−0.846219	+	0.532835i	$0.821126\pi$
$140$		0			0
$141$	23.7034			1.99619
$142$		0			0
$143$	0.774006	−	0.774006i	0.0647256	−	0.0647256i
$144$		0			0
$145$	−10.4596	+	7.64971i	−0.868621	+	0.635274i
$146$		0			0
$147$	1.50252	+	1.50252i	0.123926	+	0.123926i
$148$		0			0
$149$			6.24977i			0.512001i	0.966677	+	0.256001i	$0.0824049\pi$
$149$			6.24977i			0.512001i	−0.966677	+	0.256001i	$0.917595\pi$
$150$		0			0
$151$		−	18.9009i		−	1.53813i	−0.639168	−	0.769067i	$-0.720721\pi$
$151$		−	18.9009i		−	1.53813i	0.639168	−	0.769067i	$-0.279279\pi$
$152$		0			0
$153$	−6.73463	−	6.73463i	−0.544463	−	0.544463i
$154$		0			0
$155$	8.89503	−	6.50547i	0.714466	−	0.522532i
$156$		0			0
$157$	−12.0752	+	12.0752i	−0.963708	+	0.963708i	−0.999364	−	0.0356557i	$-0.988648\pi$
$157$	−12.0752	+	12.0752i	−0.963708	+	0.963708i	0.0356557	+	0.999364i	$0.488648\pi$
$158$		0			0
$159$	−1.83232			−0.145312
$160$		0			0
$161$	1.03028			0.0811971
$162$		0			0
$163$	−7.20487	+	7.20487i	−0.564329	+	0.564329i	−0.930534	−	0.366205i	$-0.880657\pi$
$163$	−7.20487	+	7.20487i	−0.564329	+	0.564329i	0.366205	+	0.930534i	$0.380657\pi$
$164$		0			0
$165$	2.88979	−	18.6244i	0.224970	−	1.44991i
$166$		0			0
$167$	7.97887	+	7.97887i	0.617424	+	0.617424i	0.944870	−	0.327446i	$-0.106188\pi$
$167$	7.97887	+	7.97887i	0.617424	+	0.617424i	−0.327446	+	0.944870i	$0.606188\pi$
$168$		0			0
$169$		−	12.9239i		−	0.994142i
$170$		0			0
$171$		−	6.76066i		−	0.517000i
$172$		0			0
$173$	−9.80487	−	9.80487i	−0.745451	−	0.745451i	0.228170	−	0.973621i	$-0.426726\pi$
$173$	−9.80487	−	9.80487i	−0.745451	−	0.745451i	−0.973621	+	0.228170i	$0.926726\pi$
$174$		0			0
$175$	4.44066	−	2.29793i	0.335683	−	0.173708i
$176$		0			0
$177$	−18.6244	+	18.6244i	−1.39990	+	1.39990i
$178$		0			0
$179$	25.4974			1.90576			0.952881	−	0.303344i	$-0.0981030\pi$
$179$	25.4974			1.90576			0.952881	+	0.303344i	$0.0981030\pi$
$180$		0			0
$181$	−3.35998			−0.249745			−0.124873	−	0.992173i	$-0.539852\pi$
$181$	−3.35998			−0.249745			−0.124873	+	0.992173i	$0.539852\pi$
$182$		0			0
$183$	−10.8474	+	10.8474i	−0.801866	+	0.801866i
$184$		0			0
$185$	−2.73463	−	0.424310i	−0.201054	−	0.0311959i
$186$		0			0
$187$	−17.6315	−	17.6315i	−1.28935	−	1.28935i
$188$		0			0
$189$		−	3.15516i		−	0.229504i
$190$		0			0
$191$			12.8908i			0.932748i	0.884588	+	0.466374i	$0.154440\pi$
$191$			12.8908i			0.932748i	−0.884588	+	0.466374i	$0.845560\pi$
$192$		0			0
$193$	19.2342	+	19.2342i	1.38451	+	1.38451i	0.836425	+	0.548081i	$0.184641\pi$
$193$	19.2342	+	19.2342i	1.38451	+	1.38451i	0.548081	+	0.836425i	$0.315359\pi$
$194$		0			0
$195$	0.774006	+	1.05831i	0.0554277	+	0.0757872i
$196$		0			0
$197$	13.5795	−	13.5795i	0.967497	−	0.967497i	−0.0319909	−	0.999488i	$-0.510185\pi$
$197$	13.5795	−	13.5795i	0.967497	−	0.967497i	0.999488	+	0.0319909i	$0.0101848\pi$
$198$		0			0
$199$	−15.4915			−1.09816			−0.549081	−	0.835769i	$-0.685022\pi$
$199$	−15.4915			−1.09816			−0.549081	+	0.835769i	$0.685022\pi$
$200$		0			0
$201$	−32.1698			−2.26909
$202$		0			0
$203$	4.09781	−	4.09781i	0.287610	−	0.287610i
$204$		0			0
$205$	−14.3747	−	19.6547i	−1.00397	−	1.37274i
$206$		0			0
$207$	1.10380	+	1.10380i	0.0767195	+	0.0767195i
$208$		0			0
$209$		−	17.6997i		−	1.22431i
$210$		0			0
$211$		−	16.7374i		−	1.15225i	−0.817361	−	0.576126i	$-0.804564\pi$
$211$		−	16.7374i		−	1.15225i	0.817361	−	0.576126i	$-0.195436\pi$
$212$		0			0
$213$	9.03028	+	9.03028i	0.618744	+	0.618744i
$214$		0			0
$215$	−0.728515	−	0.113038i	−0.0496843	−	0.00770910i
$216$		0			0
$217$	−3.48486	+	3.48486i	−0.236568	+	0.236568i
$218$		0			0
$219$	17.3238			1.17063
$220$		0			0
$221$	1.73463			0.116684
$222$		0			0
$223$	16.9030	−	16.9030i	1.13191	−	1.13191i	0.142050	−	0.989859i	$-0.454631\pi$
$223$	16.9030	−	16.9030i	1.13191	−	1.13191i	0.989859	−	0.142050i	$-0.0453694\pi$
$224$		0			0
$225$	7.21949	+	2.29564i	0.481300	+	0.153043i
$226$		0			0
$227$	10.4267	+	10.4267i	0.692042	+	0.692042i	0.962681	−	0.270639i	$-0.0872349\pi$
$227$	10.4267	+	10.4267i	0.692042	+	0.692042i	−0.270639	+	0.962681i	$0.587235\pi$
$228$		0			0
$229$			7.54920i			0.498865i	0.968392	+	0.249432i	$0.0802440\pi$
$229$			7.54920i			0.498865i	−0.968392	+	0.249432i	$0.919756\pi$
$230$		0			0
$231$			8.42876i			0.554572i
$232$		0			0
$233$	14.9844	+	14.9844i	0.981661	+	0.981661i	0.999835	−	0.0181739i	$-0.00578526\pi$
$233$	14.9844	+	14.9844i	0.981661	+	0.981661i	−0.0181739	+	0.999835i	$0.505785\pi$
$234$		0			0
$235$	−3.82454	+	24.6488i	−0.249485	+	1.60791i
$236$		0			0
$237$	−11.0390	+	11.0390i	−0.717063	+	0.717063i
$238$		0			0
$239$	−15.2804			−0.988407			−0.494203	−	0.869346i	$-0.664540\pi$
$239$	−15.2804			−0.988407			−0.494203	+	0.869346i	$0.664540\pi$
$240$		0			0
$241$	20.7493			1.33658			0.668290	−	0.743901i	$-0.267026\pi$
$241$	20.7493			1.33658			0.668290	+	0.743901i	$0.267026\pi$
$242$		0			0
$243$	10.2099	−	10.2099i	0.654966	−	0.654966i
$244$		0			0
$245$	−1.80487	+	1.32001i	−0.115309	+	0.0843325i
$246$		0			0
$247$	0.870668	+	0.870668i	0.0553993	+	0.0553993i
$248$		0			0
$249$			16.9991i			1.07727i
$250$		0			0
$251$		−	0.466267i		−	0.0294305i	−0.999892	−	0.0147153i	$-0.995316\pi$
$251$		−	0.466267i		−	0.0294305i	0.999892	−	0.0147153i	$-0.00468418\pi$
$252$		0			0
$253$	2.88979	+	2.88979i	0.181680	+	0.181680i
$254$		0			0
$255$	24.1079	−	17.6315i	1.50969	−	1.10413i
$256$		0			0
$257$	7.26537	−	7.26537i	0.453201	−	0.453201i	−0.443214	−	0.896416i	$-0.646162\pi$
$257$	7.26537	−	7.26537i	0.453201	−	0.453201i	0.896416	+	0.443214i	$0.146162\pi$
$258$		0			0
$259$	1.23760			0.0769007
$260$		0			0
$261$	8.78051			0.543500
$262$		0			0
$263$	5.07049	−	5.07049i	0.312660	−	0.312660i	−0.533279	−	0.845939i	$-0.679041\pi$
$263$	5.07049	−	5.07049i	0.312660	−	0.312660i	0.845939	+	0.533279i	$0.179041\pi$
$264$		0			0
$265$	0.295643	−	1.90539i	0.0181612	−	0.117047i
$266$		0			0
$267$	4.08679	+	4.08679i	0.250107	+	0.250107i
$268$		0			0
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$		−	26.4299i		−	1.60550i	−0.596314	−	0.802751i	$-0.703369\pi$
$271$		−	26.4299i		−	1.60550i	0.596314	−	0.802751i	$-0.296631\pi$
$272$		0			0
$273$	−0.414621	−	0.414621i	−0.0250940	−	0.0250940i
$274$		0			0
$275$	18.9009	+	6.01008i	1.13977	+	0.362422i
$276$		0			0
$277$	2.40493	−	2.40493i	0.144498	−	0.144498i	−0.631157	−	0.775655i	$-0.717420\pi$
$277$	2.40493	−	2.40493i	0.144498	−	0.144498i	0.775655	+	0.631157i	$0.217420\pi$
$278$		0			0
$279$	−7.46711			−0.447044
$280$		0			0
$281$	19.3250			1.15283			0.576417	−	0.817156i	$-0.304451\pi$
$281$	19.3250			1.15283			0.576417	+	0.817156i	$0.304451\pi$
$282$		0			0
$283$	−6.80615	+	6.80615i	−0.404583	+	0.404583i	−0.879845	−	0.475261i	$-0.842354\pi$
$283$	−6.80615	+	6.80615i	−0.404583	+	0.404583i	0.475261	+	0.879845i	$0.342354\pi$
$284$		0			0
$285$	20.9503	+	3.25069i	1.24099	+	0.192554i
$286$		0			0
$287$	7.70025	+	7.70025i	0.454531	+	0.454531i
$288$		0			0
$289$		−	22.5142i		−	1.32437i
$290$		0			0
$291$		−	5.60568i		−	0.328611i
$292$		0			0
$293$	−5.53573	−	5.53573i	−0.323401	−	0.323401i	0.526670	−	0.850070i	$-0.323441\pi$
$293$	−5.53573	−	5.53573i	−0.323401	−	0.323401i	−0.850070	+	0.526670i	$0.823441\pi$
$294$		0			0
$295$	−16.3621	−	22.3722i	−0.952641	−	1.30256i
$296$		0			0
$297$	8.84983	−	8.84983i	0.513519	−	0.513519i
$298$		0			0
$299$	−0.284305			−0.0164418
$300$		0			0
$301$	0.329700			0.0190036
$302$		0			0
$303$	11.4338	−	11.4338i	0.656855	−	0.656855i
$304$		0			0
$305$	−9.52982	−	13.0303i	−0.545676	−	0.746111i
$306$		0			0
$307$	−2.34407	−	2.34407i	−0.133783	−	0.133783i	0.637044	−	0.770827i	$-0.280157\pi$
$307$	−2.34407	−	2.34407i	−0.133783	−	0.133783i	−0.770827	+	0.637044i	$0.780157\pi$
$308$		0			0
$309$			28.3553i			1.61308i
$310$		0			0
$311$			31.6425i			1.79428i	0.441742	+	0.897142i	$0.354361\pi$
$311$			31.6425i			1.79428i	−0.441742	+	0.897142i	$0.645639\pi$
$312$		0			0
$313$	−5.86543	−	5.86543i	−0.331533	−	0.331533i	0.521635	−	0.853169i	$-0.325322\pi$
$313$	−5.86543	−	5.86543i	−0.331533	−	0.331533i	−0.853169	+	0.521635i	$0.825322\pi$
$314$		0			0
$315$	−3.34789	−	0.519464i	−0.188632	−	0.0292685i
$316$		0			0
$317$	−6.93945	+	6.93945i	−0.389758	+	0.389758i	−0.874601	−	0.484843i	$-0.838877\pi$
$317$	−6.93945	+	6.93945i	−0.389758	+	0.389758i	0.484843	+	0.874601i	$0.338877\pi$
$318$		0			0
$319$	22.9877			1.28706
$320$		0			0
$321$	0.700576			0.0391023
$322$		0			0
$323$	19.8335	−	19.8335i	1.10356	−	1.10356i
$324$		0			0
$325$	−1.22540	+	0.634116i	−0.0679731	+	0.0351744i
$326$		0			0
$327$	−14.6265	−	14.6265i	−0.808847	−	0.808847i
$328$		0			0
$329$		−	11.1552i		−	0.615004i
$330$		0			0
$331$		−	20.9443i		−	1.15120i	−0.817730	−	0.575602i	$-0.804768\pi$
$331$		−	20.9443i		−	1.15120i	0.817730	−	0.575602i	$-0.195232\pi$
$332$		0			0
$333$	1.32592	+	1.32592i	0.0726599	+	0.0726599i
$334$		0			0
$335$	5.19059	−	33.4528i	0.283592	−	1.82772i
$336$		0			0
$337$	10.0946	−	10.0946i	0.549888	−	0.549888i	−0.376520	−	0.926408i	$-0.622879\pi$
$337$	10.0946	−	10.0946i	0.549888	−	0.549888i	0.926408	+	0.376520i	$0.122879\pi$
$338$		0			0
$339$	32.0178			1.73897
$340$		0			0
$341$	−19.5492			−1.05865
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	−3.95126	+	2.88979i	−0.212729	+	0.155581i
$346$		0			0
$347$	4.57511	+	4.57511i	0.245605	+	0.245605i	0.819164	−	0.573559i	$-0.194438\pi$
$347$	4.57511	+	4.57511i	0.245605	+	0.245605i	−0.573559	+	0.819164i	$0.694438\pi$
$348$		0			0
$349$			21.2001i			1.13482i	0.823437	+	0.567408i	$0.192054\pi$
$349$			21.2001i			1.13482i	−0.823437	+	0.567408i	$0.807946\pi$
$350$		0			0
$351$			0.870668i			0.0464728i
$352$		0			0
$353$	−10.8351	−	10.8351i	−0.576697	−	0.576697i	0.357295	−	0.933992i	$-0.383699\pi$
$353$	−10.8351	−	10.8351i	−0.576697	−	0.576697i	−0.933992	+	0.357295i	$0.883699\pi$
$354$		0			0
$355$	−10.8474	+	7.93338i	−0.575722	+	0.421060i
$356$		0			0
$357$	−9.44490	+	9.44490i	−0.499877	+	0.499877i
$358$		0			0
$359$	3.62052			0.191084			0.0955419	−	0.995425i	$-0.469542\pi$
$359$	3.62052			0.191084			0.0955419	+	0.995425i	$0.469542\pi$
$360$		0			0
$361$	0.910088			0.0478994
$362$		0			0
$363$	−7.11388	+	7.11388i	−0.373382	+	0.373382i
$364$		0			0
$365$	−2.79518	+	18.0147i	−0.146307	+	0.942931i
$366$		0			0
$367$	−11.3592	−	11.3592i	−0.592945	−	0.592945i	0.345481	−	0.938426i	$-0.387716\pi$
$367$	−11.3592	−	11.3592i	−0.592945	−	0.592945i	−0.938426	+	0.345481i	$0.887716\pi$
$368$		0			0
$369$			16.4995i			0.858932i
$370$		0			0
$371$			0.862313i			0.0447691i
$372$		0			0
$373$	−4.67408	−	4.67408i	−0.242015	−	0.242015i	0.575668	−	0.817683i	$-0.304742\pi$
$373$	−4.67408	−	4.67408i	−0.242015	−	0.242015i	−0.817683	+	0.575668i	$0.804742\pi$
$374$		0			0
$375$	−10.5852	+	21.2684i	−0.546617	+	1.09830i
$376$		0			0
$377$	−1.13079	+	1.13079i	−0.0582388	+	0.0582388i
$378$		0			0
$379$	7.22692			0.371222			0.185611	−	0.982623i	$-0.440574\pi$
$379$	7.22692			0.371222			0.185611	+	0.982623i	$0.440574\pi$
$380$		0			0
$381$	14.1093			0.722841
$382$		0			0
$383$	−9.74364	+	9.74364i	−0.497877	+	0.497877i	−0.910776	−	0.412900i	$-0.864516\pi$
$383$	−9.74364	+	9.74364i	−0.497877	+	0.497877i	0.412900	+	0.910776i	$0.364516\pi$
$384$		0			0
$385$	−8.76491	−	1.35998i	−0.446701	−	0.0693108i
$386$		0			0
$387$	0.353229	+	0.353229i	0.0179557	+	0.0179557i
$388$		0			0
$389$		−	28.4234i		−	1.44112i	−0.693391	−	0.720562i	$-0.743884\pi$
$389$		−	28.4234i		−	1.44112i	0.693391	−	0.720562i	$-0.256116\pi$
$390$		0			0
$391$			6.47635i			0.327523i
$392$		0			0
$393$	−14.1093	−	14.1093i	−0.711719	−	0.711719i
$394$		0			0
$395$	−9.69815	−	13.2604i	−0.487967	−	0.667205i
$396$		0			0
$397$	20.6341	−	20.6341i	1.03560	−	1.03560i	0.0362540	−	0.999343i	$-0.488457\pi$
$397$	20.6341	−	20.6341i	1.03560	−	1.03560i	0.999343	−	0.0362540i	$-0.0115425\pi$
$398$		0			0
$399$	−9.48139			−0.474663
$400$		0			0
$401$	−6.10551			−0.304895			−0.152447	−	0.988312i	$-0.548715\pi$
$401$	−6.10551			−0.304895			−0.152447	+	0.988312i	$0.548715\pi$
$402$		0			0
$403$	0.961649	−	0.961649i	0.0479031	−	0.0479031i
$404$		0			0
$405$	14.8498	+	20.3044i	0.737894	+	1.00893i
$406$		0			0
$407$	3.47131	+	3.47131i	0.172066	+	0.172066i
$408$		0			0
$409$		−	14.9503i		−	0.739247i	−0.929182	−	0.369624i	$-0.879487\pi$
$409$		−	14.9503i		−	0.739247i	0.929182	−	0.369624i	$-0.120513\pi$
$410$		0			0
$411$			10.5631i			0.521041i
$412$		0			0
$413$	8.76491	+	8.76491i	0.431293	+	0.431293i
$414$		0			0
$415$	−17.6770	−	2.74279i	−0.867731	−	0.134638i
$416$		0			0
$417$	−29.9806	+	29.9806i	−1.46816	+	1.46816i
$418$		0			0
$419$	−14.5589			−0.711251			−0.355625	−	0.934629i	$-0.615732\pi$
$419$	−14.5589			−0.711251			−0.355625	+	0.934629i	$0.615732\pi$
$420$		0			0
$421$	−40.8548			−1.99114			−0.995571	−	0.0940121i	$-0.970031\pi$
$421$	−40.8548			−1.99114			−0.995571	+	0.0940121i	$0.970031\pi$
$422$		0			0
$423$	11.9512	−	11.9512i	0.581089	−	0.581089i
$424$		0			0
$425$	14.4449	+	27.9142i	0.700680	+	1.35404i
$426$		0			0
$427$	5.10495	+	5.10495i	0.247046	+	0.247046i
$428$		0			0
$429$		−	2.32592i		−	0.112296i
$430$		0			0
$431$		−	4.20688i		−	0.202638i	−0.994854	−	0.101319i	$-0.967694\pi$
$431$		−	4.20688i		−	0.202638i	0.994854	−	0.101319i	$-0.0323063\pi$
$432$		0			0
$433$	−20.0946	−	20.0946i	−0.965685	−	0.965685i	0.0337452	−	0.999430i	$-0.489257\pi$
$433$	−20.0946	−	20.0946i	−0.965685	−	0.965685i	−0.999430	+	0.0337452i	$0.989257\pi$
$434$		0			0
$435$	−4.22188	+	27.2096i	−0.202424	+	1.30460i
$436$		0			0
$437$	−3.25069	+	3.25069i	−0.155501	+	0.155501i
$438$		0			0
$439$	10.8474			0.517720			0.258860	−	0.965915i	$-0.416653\pi$
$439$	10.8474			0.517720			0.258860	+	0.965915i	$0.416653\pi$
$440$		0			0
$441$	1.51514			0.0721494
$442$		0			0
$443$	−19.2541	+	19.2541i	−0.914792	+	0.914792i	−0.996644	−	0.0818523i	$-0.973916\pi$
$443$	−19.2541	+	19.2541i	−0.914792	+	0.914792i	0.0818523	+	0.996644i	$0.473916\pi$
$444$		0			0
$445$	−4.90917	+	3.59037i	−0.232717	+	0.170200i
$446$		0			0
$447$	9.39041	+	9.39041i	0.444151	+	0.444151i
$448$		0			0
$449$			3.92385i			0.185178i	0.995704	+	0.0925890i	$0.0295143\pi$
$449$			3.92385i			0.185178i	−0.995704	+	0.0925890i	$0.970486\pi$
$450$		0			0
$451$			43.1964i			2.03404i
$452$		0			0
$453$	−28.3990	−	28.3990i	−1.33430	−	1.33430i
$454$		0			0
$455$	0.498055	−	0.364258i	0.0233492	−	0.0170767i
$456$		0			0
$457$	24.6997	−	24.6997i	1.15540	−	1.15540i	0.169948	−	0.985453i	$-0.445640\pi$
$457$	24.6997	−	24.6997i	1.15540	−	1.15540i	0.985453	−	0.169948i	$-0.0543601\pi$
$458$		0			0
$459$	19.8335			0.925746
$460$		0			0
$461$	−26.5895			−1.23839			−0.619197	−	0.785236i	$-0.712542\pi$
$461$	−26.5895			−1.23839			−0.619197	+	0.785236i	$0.712542\pi$
$462$		0			0
$463$	12.6577	−	12.6577i	0.588253	−	0.588253i	−0.348905	−	0.937158i	$-0.613446\pi$
$463$	12.6577	−	12.6577i	0.588253	−	0.588253i	0.937158	+	0.348905i	$0.113446\pi$
$464$		0			0
$465$	3.59037	−	23.1396i	0.166499	−	1.07307i
$466$		0			0
$467$	−4.97383	−	4.97383i	−0.230161	−	0.230161i	0.582599	−	0.812760i	$-0.302036\pi$
$467$	−4.97383	−	4.97383i	−0.230161	−	0.230161i	−0.812760	+	0.582599i	$0.802036\pi$
$468$		0			0
$469$			15.1396i			0.699080i
$470$		0			0
$471$			36.2866i			1.67200i
$472$		0			0
$473$	0.924768	+	0.924768i	0.0425209	+	0.0425209i
$474$		0			0
$475$	−6.76066	+	21.2614i	−0.310200	+	0.975538i
$476$		0			0
$477$	−0.923851	+	0.923851i	−0.0423003	+	0.0423003i
$478$		0			0
$479$	−35.6383			−1.62836			−0.814179	−	0.580614i	$-0.802812\pi$
$479$	−35.6383			−1.62836			−0.814179	+	0.580614i	$0.802812\pi$
$480$		0			0
$481$	−0.341516			−0.0155718
$482$		0			0
$483$	1.54801	−	1.54801i	0.0704370	−	0.0704370i
$484$		0			0
$485$	5.82924	+	0.904474i	0.264692	+	0.0410701i
$486$		0			0
$487$	−16.1290	−	16.1290i	−0.730875	−	0.730875i	0.239918	−	0.970793i	$-0.422879\pi$
$487$	−16.1290	−	16.1290i	−0.730875	−	0.730875i	−0.970793	+	0.239918i	$0.922879\pi$
$488$		0			0
$489$			21.6509i			0.979089i
$490$		0			0
$491$			25.8435i			1.16630i	0.812364	+	0.583151i	$0.198180\pi$
$491$			25.8435i			1.16630i	−0.812364	+	0.583151i	$0.801820\pi$
$492$		0			0
$493$	25.7590	+	25.7590i	1.16013	+	1.16013i
$494$		0			0
$495$	−7.93338	−	10.8474i	−0.356579	−	0.487556i
$496$		0			0
$497$	4.24977	−	4.24977i	0.190628	−	0.190628i
$498$		0			0
$499$	13.1169			0.587194			0.293597	−	0.955929i	$-0.405148\pi$
$499$	13.1169			0.587194			0.293597	+	0.955929i	$0.405148\pi$
$500$		0			0
$501$	23.9768			1.07121
$502$		0			0
$503$	9.81119	−	9.81119i	0.437459	−	0.437459i	−0.453697	−	0.891156i	$-0.649895\pi$
$503$	9.81119	−	9.81119i	0.437459	−	0.437459i	0.891156	+	0.453697i	$0.149895\pi$
$504$		0			0
$505$	10.0450	+	13.7346i	0.446995	+	0.611183i
$506$		0			0
$507$	−19.4184	−	19.4184i	−0.862400	−	0.862400i
$508$		0			0
$509$		−	11.9688i		−	0.530508i	−0.964179	−	0.265254i	$-0.914544\pi$
$509$		−	11.9688i		−	0.530508i	0.964179	−	0.265254i	$-0.0854558\pi$
$510$		0			0
$511$		−	8.15281i		−	0.360659i
$512$		0			0
$513$	9.95504	+	9.95504i	0.439526	+	0.439526i
$514$		0			0
$515$	−29.4861	−	4.57511i	−1.29931	−	0.201603i
$516$		0			0
$517$	31.2888	−	31.2888i	1.37608	−	1.37608i
$518$		0			0
$519$	−29.4641			−1.29333
$520$		0			0
$521$	−14.5483			−0.637372			−0.318686	−	0.947860i	$-0.603241\pi$
$521$	−14.5483			−0.637372			−0.318686	+	0.947860i	$0.603241\pi$
$522$		0			0
$523$	−5.28157	+	5.28157i	−0.230947	+	0.230947i	−0.813088	−	0.582141i	$-0.802215\pi$
$523$	−5.28157	+	5.28157i	−0.230947	+	0.230947i	0.582141	+	0.813088i	$0.302215\pi$
$524$		0			0
$525$	3.21949	−	10.1249i	0.140510	−	0.441886i
$526$		0			0
$527$	−21.9060	−	21.9060i	−0.954239	−	0.954239i
$528$		0			0
$529$			21.9385i			0.953849i
$530$		0			0
$531$			18.7808i			0.815018i
$532$		0			0
$533$	−2.12489	−	2.12489i	−0.0920390	−	0.0920390i
$534$		0			0
$535$	−0.113038	+	0.728515i	−0.00488704	+	0.0314965i
$536$		0			0
$537$	38.3103	−	38.3103i	1.65321	−	1.65321i
$538$		0			0
$539$	3.96669			0.170857
$540$		0			0
$541$	24.4158			1.04972			0.524859	−	0.851189i	$-0.324118\pi$
$541$	24.4158			1.04972			0.524859	+	0.851189i	$0.324118\pi$
$542$		0			0
$543$	−5.04843	+	5.04843i	−0.216649	+	0.216649i
$544$		0			0
$545$	17.5698	−	12.8498i	0.752607	−	0.550426i
$546$		0			0
$547$	−6.64762	−	6.64762i	−0.284232	−	0.284232i	0.550562	−	0.834794i	$-0.314413\pi$
$547$	−6.64762	−	6.64762i	−0.284232	−	0.284232i	−0.834794	+	0.550562i	$0.814413\pi$
$548$		0			0
$549$			10.9385i			0.466845i
$550$		0			0
$551$			25.8585i			1.10161i
$552$		0			0
$553$	5.19513	+	5.19513i	0.220919	+	0.220919i
$554$		0			0
$555$	−4.74638	+	3.47131i	−0.201472	+	0.147349i
$556$		0			0
$557$	4.07523	−	4.07523i	0.172673	−	0.172673i	−0.615480	−	0.788153i	$-0.711038\pi$
$557$	4.07523	−	4.07523i	0.172673	−	0.172673i	0.788153	+	0.615480i	$0.211038\pi$
$558$		0			0
$559$	−0.0909809			−0.00384808
$560$		0			0
$561$	−52.9835			−2.23696
$562$		0			0
$563$	3.73356	−	3.73356i	0.157351	−	0.157351i	−0.624041	−	0.781392i	$-0.714510\pi$
$563$	3.73356	−	3.73356i	0.157351	−	0.157351i	0.781392	+	0.624041i	$0.214510\pi$
$564$		0			0
$565$	−5.16606	+	33.2947i	−0.217338	+	1.40072i
$566$		0			0
$567$	−7.95479	−	7.95479i	−0.334070	−	0.334070i
$568$		0			0
$569$			17.3094i			0.725648i	0.931858	+	0.362824i	$0.118187\pi$
$569$			17.3094i			0.725648i	−0.931858	+	0.362824i	$0.881813\pi$
$570$		0			0
$571$			3.09602i			0.129565i	0.997899	+	0.0647823i	$0.0206353\pi$
$571$			3.09602i			0.129565i	−0.997899	+	0.0647823i	$0.979365\pi$
$572$		0			0
$573$	19.3687	+	19.3687i	0.809141	+	0.809141i
$574$		0			0
$575$	−2.36751	−	4.57511i	−0.0987319	−	0.190795i
$576$		0			0
$577$	−13.6644	+	13.6644i	−0.568856	+	0.568856i	−0.931808	−	0.362952i	$-0.881769\pi$
$577$	−13.6644	+	13.6644i	−0.568856	+	0.568856i	0.362952	+	0.931808i	$0.381769\pi$
$578$		0			0
$579$	57.7995			2.40207
$580$		0			0
$581$	8.00000			0.331896
$582$		0			0
$583$	−2.41868	+	2.41868i	−0.100171	+	0.100171i
$584$		0			0
$585$	0.923851	+	0.143346i	0.0381966	+	0.00592664i
$586$		0			0
$587$	19.6003	+	19.6003i	0.808992	+	0.808992i	0.984481	−	0.175490i	$-0.0561508\pi$
$587$	19.6003	+	19.6003i	0.808992	+	0.808992i	−0.175490	+	0.984481i	$0.556151\pi$
$588$		0			0
$589$		−	21.9906i		−	0.906107i
$590$		0			0
$591$		−	40.8069i		−	1.67857i
$592$		0			0
$593$	12.6753	+	12.6753i	0.520512	+	0.520512i	0.917726	−	0.397214i	$-0.130023\pi$
$593$	12.6753	+	12.6753i	0.520512	+	0.520512i	−0.397214	+	0.917726i	$0.630023\pi$
$594$		0			0
$595$	−8.29764	−	11.3455i	−0.340170	−	0.465120i
$596$		0			0
$597$	−23.2763	+	23.2763i	−0.952634	+	0.952634i
$598$		0			0
$599$	−33.1287			−1.35360			−0.676801	−	0.736166i	$-0.736634\pi$
$599$	−33.1287			−1.35360			−0.676801	+	0.736166i	$0.736634\pi$
$600$		0			0
$601$	24.5407			1.00104			0.500518	−	0.865726i	$-0.333143\pi$
$601$	24.5407			1.00104			0.500518	+	0.865726i	$0.333143\pi$
$602$		0			0
$603$	−16.2200	+	16.2200i	−0.660529	+	0.660529i
$604$		0			0
$605$	−6.24977	−	8.54541i	−0.254089	−	0.347420i
$606$		0			0
$607$	26.2934	+	26.2934i	1.06722	+	1.06722i	0.997572	+	0.0696455i	$0.0221868\pi$
$607$	26.2934	+	26.2934i	1.06722	+	1.06722i	0.0696455	+	0.997572i	$0.477813\pi$
$608$		0			0
$609$		−	12.3141i		−	0.498993i
$610$		0			0
$611$			3.07827i			0.124533i
$612$		0			0
$613$	−16.5904	−	16.5904i	−0.670079	−	0.670079i	0.287655	−	0.957734i	$-0.407124\pi$
$613$	−16.5904	−	16.5904i	−0.670079	−	0.670079i	−0.957734	+	0.287655i	$0.907124\pi$
$614$		0			0
$615$	−51.1298	−	7.93338i	−2.06175	−	0.319905i
$616$		0			0
$617$	12.4655	−	12.4655i	0.501842	−	0.501842i	−0.410168	−	0.912010i	$-0.634530\pi$
$617$	12.4655	−	12.4655i	0.501842	−	0.501842i	0.912010	+	0.410168i	$0.134530\pi$
$618$		0			0
$619$	−0.990764			−0.0398222			−0.0199111	−	0.999802i	$-0.506338\pi$
$619$	−0.990764			−0.0398222			−0.0199111	+	0.999802i	$0.506338\pi$
$620$		0			0
$621$	−3.25069			−0.130446
$622$		0			0
$623$	1.92330	−	1.92330i	0.0770553	−	0.0770553i
$624$		0			0
$625$	−20.4087	−	14.4390i	−0.816349	−	0.577560i
$626$		0			0
$627$	−26.5941	−	26.5941i	−1.06207	−	1.06207i
$628$		0			0
$629$			7.77959i			0.310193i
$630$		0			0
$631$			34.7677i			1.38408i	0.721859	+	0.692040i	$0.243288\pi$
$631$			34.7677i			1.38408i	−0.721859	+	0.692040i	$0.756712\pi$
$632$		0			0
$633$	−25.1483	−	25.1483i	−0.999557	−	0.999557i
$634$		0			0
$635$	−2.27653	+	14.6720i	−0.0903412	+	0.582240i
$636$		0			0
$637$	−0.195126	+	0.195126i	−0.00773119	+	0.00773119i
$638$		0			0
$639$	9.10611			0.360232
$640$		0			0
$641$	20.8780			0.824631			0.412315	−	0.911041i	$-0.364720\pi$
$641$	20.8780			0.824631			0.412315	+	0.911041i	$0.364720\pi$
$642$		0			0
$643$	11.7345	−	11.7345i	0.462763	−	0.462763i	−0.436797	−	0.899560i	$-0.643887\pi$
$643$	11.7345	−	11.7345i	0.462763	−	0.462763i	0.899560	+	0.436797i	$0.143887\pi$
$644$		0			0
$645$	−1.26445	+	0.924768i	−0.0497877	+	0.0364127i
$646$		0			0
$647$	19.5093	+	19.5093i	0.766991	+	0.766991i	0.977576	−	0.210584i	$-0.0675367\pi$
$647$	19.5093	+	19.5093i	0.766991	+	0.766991i	−0.210584	+	0.977576i	$0.567537\pi$
$648$		0			0
$649$			49.1689i			1.93005i
$650$		0			0
$651$			10.4722i			0.410436i
$652$		0			0
$653$	18.7796	+	18.7796i	0.734902	+	0.734902i	0.971587	−	0.236684i	$-0.0760608\pi$
$653$	18.7796	+	18.7796i	0.734902	+	0.734902i	−0.236684	+	0.971587i	$0.576061\pi$
$654$		0			0
$655$	16.9485	−	12.3955i	0.662233	−	0.484330i
$656$		0			0
$657$	8.73463	−	8.73463i	0.340770	−	0.340770i
$658$		0			0
$659$	17.4439			0.679517			0.339759	−	0.940513i	$-0.389655\pi$
$659$	17.4439			0.679517			0.339759	+	0.940513i	$0.389655\pi$
$660$		0			0
$661$	−42.6188			−1.65768			−0.828840	−	0.559486i	$-0.810999\pi$
$661$	−42.6188			−1.65768			−0.828840	+	0.559486i	$0.810999\pi$
$662$		0			0
$663$	2.60632	−	2.60632i	0.101221	−	0.101221i
$664$		0			0
$665$	1.52982	−	9.85952i	0.0593238	−	0.382336i
$666$		0			0
$667$	−4.22188	−	4.22188i	−0.163472	−	0.163472i
$668$		0			0
$669$		−	50.7943i		−	1.96382i
$670$		0			0
$671$			28.6375i			1.10554i
$672$		0			0
$673$	−13.9541	−	13.9541i	−0.537892	−	0.537892i	0.385017	−	0.922909i	$-0.374195\pi$
$673$	−13.9541	−	13.9541i	−0.537892	−	0.537892i	−0.922909	+	0.385017i	$0.874195\pi$
$674$		0			0
$675$	−14.0110	+	7.25036i	−0.539284	+	0.279066i
$676$		0			0
$677$	33.9142	−	33.9142i	1.30343	−	1.30343i	0.377361	−	0.926066i	$-0.376832\pi$
$677$	33.9142	−	33.9142i	1.30343	−	1.30343i	0.926066	−	0.377361i	$-0.123168\pi$
$678$		0			0
$679$	−2.63811			−0.101241
$680$		0			0
$681$	31.3326			1.20067
$682$		0			0
$683$	9.74364	−	9.74364i	0.372830	−	0.372830i	−0.495677	−	0.868507i	$-0.665080\pi$
$683$	9.74364	−	9.74364i	0.372830	−	0.372830i	0.868507	+	0.495677i	$0.165080\pi$
$684$		0			0
$685$	−10.9844	−	1.70436i	−0.419692	−	0.0651201i
$686$		0			0
$687$	11.3428	+	11.3428i	0.432756	+	0.432756i
$688$		0			0
$689$		−	0.237956i		−	0.00906538i
$690$		0			0
$691$			42.1147i			1.60212i	0.598585	+	0.801059i	$0.295730\pi$
$691$			42.1147i			1.60212i	−0.598585	+	0.801059i	$0.704270\pi$
$692$		0			0
$693$	4.24977	+	4.24977i	0.161435	+	0.161435i
$694$		0			0
$695$	−26.3389	−	36.0136i	−0.999092	−	1.36607i
$696$		0			0
$697$	−48.4040	+	48.4040i	−1.83343	+	1.83343i
$698$		0			0
$699$	45.0288			1.70314
$700$		0			0
$701$	−32.4839			−1.22690			−0.613451	−	0.789733i	$-0.710219\pi$
$701$	−32.4839			−1.22690			−0.613451	+	0.789733i	$0.710219\pi$
$702$		0			0
$703$	−3.90482	+	3.90482i	−0.147273	+	0.147273i
$704$		0			0
$705$	31.2888	+	42.7817i	1.17841	+	1.61125i
$706$		0			0
$707$	−5.38090	−	5.38090i	−0.202370	−	0.202370i
$708$		0			0
$709$		−	48.6126i		−	1.82568i	−0.408312	−	0.912842i	$-0.633882\pi$
$709$		−	48.6126i		−	1.82568i	0.408312	−	0.912842i	$-0.366118\pi$
$710$		0			0
$711$			11.1317i			0.417473i
$712$		0			0
$713$	3.59037	+	3.59037i	0.134460	+	0.134460i
$714$		0			0
$715$	2.41868	+	0.375286i	0.0904535	+	0.0140349i
$716$		0			0
$717$	−22.9591	+	22.9591i	−0.857424	+	0.857424i
$718$		0			0
$719$	−26.8962			−1.00306			−0.501529	−	0.865141i	$-0.667229\pi$
$719$	−26.8962			−1.00306			−0.501529	+	0.865141i	$0.667229\pi$
$720$		0			0
$721$	13.3444			0.496971
$722$		0			0
$723$	31.1763	−	31.1763i	1.15946	−	1.15946i
$724$		0			0
$725$	−27.6135	−	8.78051i	−1.02554	−	0.326100i
$726$		0			0
$727$	−19.6003	−	19.6003i	−0.726936	−	0.726936i	0.243073	−	0.970008i	$-0.421845\pi$
$727$	−19.6003	−	19.6003i	−0.726936	−	0.726936i	−0.970008	+	0.243073i	$0.921845\pi$
$728$		0			0
$729$			3.06811i			0.113634i
$730$		0			0
$731$			2.07251i			0.0766545i
$732$		0			0
$733$	−0.805790	−	0.805790i	−0.0297625	−	0.0297625i	0.692069	−	0.721831i	$-0.256699\pi$
$733$	−0.805790	−	0.805790i	−0.0297625	−	0.0297625i	−0.721831	+	0.692069i	$0.756699\pi$
$734$		0			0
$735$	−0.728515	+	4.69521i	−0.0268717	+	0.173185i
$736$		0			0
$737$	−42.4646	+	42.4646i	−1.56420	+	1.56420i
$738$		0			0
$739$	22.2230			0.817487			0.408743	−	0.912649i	$-0.365967\pi$
$739$	22.2230			0.817487			0.408743	+	0.912649i	$0.365967\pi$
$740$		0			0
$741$	2.61639			0.0961156
$742$		0			0
$743$	32.8664	−	32.8664i	1.20575	−	1.20575i	0.233363	−	0.972390i	$-0.425027\pi$
$743$	32.8664	−	32.8664i	1.20575	−	1.20575i	0.972390	−	0.233363i	$-0.0749730\pi$
$744$		0			0
$745$	−11.2800	+	8.24977i	−0.413269	+	0.302248i
$746$		0			0
$747$	8.57092	+	8.57092i	0.313593	+	0.313593i
$748$		0			0
$749$		−	0.329700i		−	0.0120470i
$750$		0			0
$751$		−	11.6599i		−	0.425475i	−0.977109	−	0.212738i	$-0.931762\pi$
$751$		−	11.6599i		−	0.425475i	0.977109	−	0.212738i	$-0.0682379\pi$
$752$		0			0
$753$	−0.700576	−	0.700576i	−0.0255304	−	0.0255304i
$754$		0			0
$755$	34.1138	−	24.9494i	1.24153	−	0.908003i
$756$		0			0
$757$	−10.6741	+	10.6741i	−0.387956	+	0.387956i	−0.873958	−	0.486002i	$-0.838455\pi$
$757$	−10.6741	+	10.6741i	−0.387956	+	0.387956i	0.486002	+	0.873958i	$0.338455\pi$
$758$		0			0
$759$	8.68395			0.315208
$760$		0			0
$761$	−8.71995			−0.316098			−0.158049	−	0.987431i	$-0.550520\pi$
$761$	−8.71995			−0.316098			−0.158049	+	0.987431i	$0.550520\pi$
$762$		0			0
$763$	−6.88342	+	6.88342i	−0.249197	+	0.249197i
$764$		0			0
$765$	3.26537	−	21.0450i	0.118060	−	0.760882i
$766$		0			0
$767$	−2.41868	−	2.41868i	−0.0873334	−	0.0873334i
$768$		0			0
$769$		−	23.6391i		−	0.852448i	−0.904618	−	0.426224i	$-0.859844\pi$
$769$		−	23.6391i		−	0.852448i	0.904618	−	0.426224i	$-0.140156\pi$
$770$		0			0
$771$		−	21.8327i		−	0.786287i
$772$		0			0
$773$	−3.22540	−	3.22540i	−0.116010	−	0.116010i	0.646719	−	0.762728i	$-0.276141\pi$
$773$	−3.22540	−	3.22540i	−0.116010	−	0.116010i	−0.762728	+	0.646719i	$0.776141\pi$
$774$		0			0
$775$	23.4831	+	7.46711i	0.843537	+	0.268227i
$776$		0			0
$777$	1.85952	−	1.85952i	0.0667098	−	0.0667098i
$778$		0			0
$779$	−48.5910			−1.74095
$780$		0			0
$781$	23.8401			0.853067
$782$		0			0
$783$	−12.9293	+	12.9293i	−0.462054	+	0.462054i
$784$		0			0
$785$	−37.7337	−	5.85482i	−1.34677	−	0.208968i
$786$		0			0
$787$	−10.5176	−	10.5176i	−0.374914	−	0.374914i	0.494350	−	0.869263i	$-0.335406\pi$
$787$	−10.5176	−	10.5176i	−0.374914	−	0.374914i	−0.869263	+	0.494350i	$0.835406\pi$
$788$		0			0
$789$		−	15.2370i		−	0.542453i
$790$		0			0
$791$		−	15.0680i		−	0.535757i
$792$		0			0
$793$	−1.40871	−	1.40871i	−0.0500249	−	0.0500249i
$794$		0			0
$795$	−2.41868	−	3.30710i	−0.0857817	−	0.117291i
$796$		0			0
$797$	0.604756	−	0.604756i	0.0214216	−	0.0214216i	−0.696315	−	0.717736i	$-0.745178\pi$
$797$	0.604756	−	0.604756i	0.0214216	−	0.0214216i	0.717736	+	0.696315i	$0.245178\pi$
$798$		0			0
$799$	70.1217			2.48073
$800$		0			0
$801$	4.12110			0.145612
$802$		0			0
$803$	22.8676	−	22.8676i	0.806980	−	0.806980i
$804$		0			0
$805$	1.35998	+	1.85952i	0.0479329	+	0.0655394i
$806$		0			0
$807$	−9.01513	−	9.01513i	−0.317347	−	0.317347i
$808$		0			0
$809$		−	2.29473i		−	0.0806783i	−0.999186	−	0.0403391i	$-0.987156\pi$
$809$		−	2.29473i		−	0.0806783i	0.999186	−	0.0403391i	$-0.0128438\pi$
$810$		0			0
$811$		−	30.3347i		−	1.06520i	−0.846368	−	0.532598i	$-0.821216\pi$
$811$		−	30.3347i		−	1.06520i	0.846368	−	0.532598i	$-0.178784\pi$
$812$		0			0
$813$	−39.7115	−	39.7115i	−1.39274	−	1.39274i
$814$		0			0
$815$	−22.5144	−	3.49337i	−0.788644	−	0.122367i
$816$		0			0
$817$	−1.04026	+	1.04026i	−0.0363940	+	0.0363940i
$818$		0			0
$819$	−0.418103			−0.0146097
$820$		0			0
$821$	36.8936			1.28759			0.643797	−	0.765196i	$-0.277358\pi$
$821$	36.8936			1.28759			0.643797	+	0.765196i	$0.277358\pi$
$822$		0			0
$823$	11.6378	−	11.6378i	0.405669	−	0.405669i	−0.474556	−	0.880225i	$-0.657391\pi$
$823$	11.6378	−	11.6378i	0.405669	−	0.405669i	0.880225	+	0.474556i	$0.157391\pi$
$824$		0			0
$825$	37.4293	−	19.3687i	1.30312	−	0.674333i
$826$		0			0
$827$	−4.29080	−	4.29080i	−0.149206	−	0.149206i	0.628557	−	0.777763i	$-0.283646\pi$
$827$	−4.29080	−	4.29080i	−0.149206	−	0.149206i	−0.777763	+	0.628557i	$0.783646\pi$
$828$		0			0
$829$			30.4196i			1.05652i	0.849084	+	0.528258i	$0.177155\pi$
$829$			30.4196i			1.05652i	−0.849084	+	0.528258i	$0.822845\pi$
$830$		0			0
$831$		−	7.22692i		−	0.250699i
$832$		0			0
$833$	4.44490	+	4.44490i	0.154007	+	0.154007i
$834$		0			0
$835$	−3.86865	+	24.9331i	−0.133880	+	0.862844i
$836$		0			0
$837$	10.9953	−	10.9953i	0.380053	−	0.380053i
$838$		0			0
$839$	6.25028			0.215783			0.107892	−	0.994163i	$-0.465590\pi$
$839$	6.25028			0.215783			0.107892	+	0.994163i	$0.465590\pi$
$840$		0			0
$841$	−4.58417			−0.158075
$842$		0			0
$843$	29.0362	−	29.0362i	1.00006	−	1.00006i
$844$		0			0
$845$	23.3259	−	17.0596i	0.802436	−	0.586869i
$846$		0			0
$847$	3.34789	+	3.34789i	0.115035	+	0.115035i
$848$		0			0
$849$			20.4528i			0.701937i
$850$		0			0
$851$		−	1.27507i		−	0.0437088i
$852$		0			0
$853$	31.3553	+	31.3553i	1.07358	+	1.07358i	0.997068	+	0.0765159i	$0.0243796\pi$
$853$	31.3553	+	31.3553i	1.07358	+	1.07358i	0.0765159	+	0.997068i	$0.475620\pi$
$854$		0			0
$855$	12.2021	−	8.92414i	0.417304	−	0.305199i
$856$		0			0
$857$	−28.1433	+	28.1433i	−0.961358	+	0.961358i	−0.999281	−	0.0379223i	$-0.987926\pi$
$857$	−28.1433	+	28.1433i	−0.961358	+	0.961358i	0.0379223	+	0.999281i	$0.487926\pi$
$858$		0			0
$859$	0.932534			0.0318176			0.0159088	−	0.999873i	$-0.494936\pi$
$859$	0.932534			0.0318176			0.0159088	+	0.999873i	$0.494936\pi$
$860$		0			0
$861$	23.1396			0.788594
$862$		0			0
$863$	38.5922	−	38.5922i	1.31369	−	1.31369i	0.395023	−	0.918671i	$-0.370737\pi$
$863$	38.5922	−	38.5922i	1.31369	−	1.31369i	0.918671	−	0.395023i	$-0.129263\pi$
$864$		0			0
$865$	4.75401	−	30.6391i	0.161641	−	1.04176i
$866$		0			0
$867$	−33.8281	−	33.8281i	−1.14886	−	1.14886i
$868$		0			0
$869$			29.1433i			0.988620i
$870$		0			0
$871$		−	4.17777i		−	0.141558i
$872$		0			0
$873$	−2.82638	−	2.82638i	−0.0956584	−	0.0956584i
$874$		0			0
$875$	10.0092	+	4.98154i	0.338373	+	0.168407i
$876$		0			0
$877$	1.80986	−	1.80986i	0.0611148	−	0.0611148i	−0.675889	−	0.737004i	$-0.736240\pi$
$877$	1.80986	−	1.80986i	0.0611148	−	0.0611148i	0.737004	+	0.675889i	$0.236240\pi$
$878$		0			0
$879$	−16.6351			−0.561088
$880$		0			0
$881$	36.0587			1.21485			0.607425	−	0.794377i	$-0.292203\pi$
$881$	36.0587			1.21485			0.607425	+	0.794377i	$0.292203\pi$
$882$		0			0
$883$	−23.9714	+	23.9714i	−0.806702	+	0.806702i	−0.984133	−	0.177431i	$-0.943221\pi$
$883$	−23.9714	+	23.9714i	−0.806702	+	0.806702i	0.177431	+	0.984133i	$0.443221\pi$
$884$		0			0
$885$	−58.1992	−	9.03028i	−1.95634	−	0.303549i
$886$		0			0
$887$	13.5902	+	13.5902i	0.456315	+	0.456315i	0.897444	−	0.441129i	$-0.145422\pi$
$887$	13.5902	+	13.5902i	0.456315	+	0.456315i	−0.441129	+	0.897444i	$0.645422\pi$
$888$		0			0
$889$		−	6.64002i		−	0.222699i
$890$		0			0
$891$		−	44.6244i		−	1.49497i
$892$		0			0
$893$	35.1963	+	35.1963i	1.17780	+	1.17780i
$894$		0			0
$895$	33.6568	+	46.0195i	1.12502	+	1.53826i
$896$		0			0
$897$	−0.427174	+	0.427174i	−0.0142629	+	0.0142629i
$898$		0			0
$899$	28.5606			0.952551
$900$		0			0
$901$	−5.42053			−0.180584
$902$		0			0
$903$	0.495382	−	0.495382i	0.0164853	−	0.0164853i
$904$		0			0
$905$	−4.43521	−	6.06433i	−0.147431	−	0.201585i
$906$		0			0
$907$	14.2057	+	14.2057i	0.471693	+	0.471693i	0.902462	−	0.430769i	$-0.141758\pi$
$907$	14.2057	+	14.2057i	0.471693	+	0.471693i	−0.430769	+	0.902462i	$0.641758\pi$
$908$		0			0
$909$		−	11.5298i		−	0.382420i
$910$		0			0
$911$			12.9527i			0.429142i	0.976708	+	0.214571i	$0.0688354\pi$
$911$			12.9527i			0.429142i	−0.976708	+	0.214571i	$0.931165\pi$
$912$		0			0
$913$	22.4390	+	22.4390i	0.742622	+	0.742622i
$914$		0			0
$915$	−33.8970	−	5.25951i	−1.12060	−	0.173874i
$916$		0			0
$917$	−6.64002	+	6.64002i	−0.219273	+	0.219273i
$918$		0			0
$919$	43.1673			1.42396			0.711979	−	0.702200i	$-0.247799\pi$
$919$	43.1673			1.42396			0.711979	+	0.702200i	$0.247799\pi$
$920$		0			0
$921$	−7.04404			−0.232109
$922$		0			0
$923$	−1.17273	+	1.17273i	−0.0386007	+	0.0386007i
$924$		0			0
$925$	−2.84392	−	5.49576i	−0.0935076	−	0.180699i
$926$		0			0
$927$	14.2967	+	14.2967i	0.469565	+	0.469565i
$928$		0			0
$929$			0.761128i			0.0249718i	0.999922	+	0.0124859i	$0.00397449\pi$
$929$			0.761128i			0.0249718i	−0.999922	+	0.0124859i	$0.996026\pi$
$930$		0			0
$931$			4.46207i			0.146239i
$932$		0			0
$933$	47.5436	+	47.5436i	1.55651	+	1.55651i
$934$		0			0
$935$	8.54886	−	55.0965i	0.279578	−	1.80185i
$936$		0			0
$937$	10.0546	−	10.0546i	0.328471	−	0.328471i	−0.523534	−	0.852005i	$-0.675387\pi$
$937$	10.0546	−	10.0546i	0.328471	−	0.328471i	0.852005	+	0.523534i	$0.175387\pi$
$938$		0			0
$939$	−17.6258			−0.575198
$940$		0			0
$941$	47.3700			1.54422			0.772108	−	0.635491i	$-0.219202\pi$
$941$	47.3700			1.54422			0.772108	+	0.635491i	$0.219202\pi$
$942$		0			0
$943$	7.93338	−	7.93338i	0.258346	−	0.258346i
$944$		0			0
$945$	5.69467	−	4.16485i	0.185248	−	0.135483i
$946$		0			0
$947$	31.4094	+	31.4094i	1.02067	+	1.02067i	0.999782	+	0.0208868i	$0.00664896\pi$
$947$	31.4094	+	31.4094i	1.02067	+	1.02067i	0.0208868	+	0.999782i	$0.493351\pi$
$948$		0			0
$949$			2.24977i			0.0730307i
$950$		0			0
$951$			20.8533i			0.676216i
$952$		0			0
$953$	−20.7602	−	20.7602i	−0.672489	−	0.672489i	0.285800	−	0.958289i	$-0.407741\pi$
$953$	−20.7602	−	20.7602i	−0.672489	−	0.672489i	−0.958289	+	0.285800i	$0.907741\pi$
$954$		0			0
$955$	−23.2663	+	17.0161i	−0.752881	+	0.550627i
$956$		0			0
$957$	34.5395	−	34.5395i	1.11650	−	1.11650i
$958$		0			0
$959$	4.97116			0.160527
$960$		0			0
$961$	6.71147			0.216499
$962$		0			0
$963$	0.353229	−	0.353229i	0.0113827	−	0.0113827i
$964$		0			0
$965$	−9.32592	+	60.1046i	−0.300212	+	1.93484i
$966$		0			0
$967$	−19.4802	−	19.4802i	−0.626442	−	0.626442i	0.320729	−	0.947171i	$-0.396072\pi$
$967$	−19.4802	−	19.4802i	−0.626442	−	0.626442i	−0.947171	+	0.320729i	$0.896072\pi$
$968$		0			0
$969$		−	59.6004i		−	1.91464i
$970$		0			0
$971$		−	27.7377i		−	0.890146i	−0.895494	−	0.445073i	$-0.853178\pi$
$971$		−	27.7377i		−	0.890146i	0.895494	−	0.445073i	$-0.146822\pi$
$972$		0			0
$973$	14.1093	+	14.1093i	0.452323	+	0.452323i
$974$		0			0
$975$	−0.888420	+	2.79396i	−0.0284522	+	0.0894785i
$976$		0			0
$977$	−9.43899	+	9.43899i	−0.301980	+	0.301980i	−0.841788	−	0.539808i	$-0.818497\pi$
$977$	−9.43899	+	9.43899i	−0.301980	+	0.301980i	0.539808	+	0.841788i	$0.318497\pi$
$978$		0			0
$979$	10.7892			0.344825
$980$		0			0
$981$	−14.7493			−0.470909
$982$		0			0
$983$	−10.9839	+	10.9839i	−0.350332	+	0.350332i	−0.860233	−	0.509901i	$-0.829682\pi$
$983$	−10.9839	+	10.9839i	−0.350332	+	0.350332i	0.509901	+	0.860233i	$0.329682\pi$
$984$		0			0
$985$	42.4343	+	6.58417i	1.35207	+	0.209789i
$986$		0			0
$987$	−16.7609	−	16.7609i	−0.533504	−	0.533504i
$988$		0			0
$989$		−	0.339682i		−	0.0108013i
$990$		0			0
$991$			33.9552i			1.07862i	0.842106	+	0.539312i	$0.181316\pi$
$991$			33.9552i			1.07862i	−0.842106	+	0.539312i	$0.818684\pi$
$992$		0			0
$993$	−31.4693	−	31.4693i	−0.998647	−	0.998647i
$994$		0			0
$995$	−20.4489	−	27.9602i	−0.648275	−	0.886397i
$996$		0			0
$997$	−17.2136	+	17.2136i	−0.545160	+	0.545160i	−0.925037	−	0.379877i	$-0.875966\pi$
$997$	−17.2136	+	17.2136i	−0.545160	+	0.545160i	0.379877	+	0.925037i	$0.375966\pi$
$998$		0			0
$999$	−3.90482			−0.123543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.x.a.463.5	yes	12
4.3	odd	2	inner	560.2.x.a.463.2	yes	12
5.2	odd	4	inner	560.2.x.a.127.2	✓	12
20.7	even	4	inner	560.2.x.a.127.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.x.a.127.2	✓	12	5.2	odd	4	inner
560.2.x.a.127.5	yes	12	20.7	even	4	inner
560.2.x.a.463.2	yes	12	4.3	odd	2	inner
560.2.x.a.463.5	yes	12	1.1	even	1	trivial

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.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50252 - 1.50252i) q^{3} +(1.32001 + 1.80487i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.51514i q^{9} +O(q^{10})\)	\(q+(1.50252 - 1.50252i) q^{3} +(1.32001 + 1.80487i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.51514i q^{9} -3.96669i q^{11} +(0.195126 + 0.195126i) q^{13} +(4.69521 + 0.728515i) q^{15} +(4.44490 - 4.44490i) q^{17} +4.46207 q^{19} -2.12489 q^{21} +(-0.728515 + 0.728515i) q^{23} +(-1.51514 + 4.76491i) q^{25} +(2.23104 + 2.23104i) q^{27} +5.79518i q^{29} -4.92834i q^{31} +(-5.96004 - 5.96004i) q^{33} +(0.342849 - 2.20963i) q^{35} +(-0.875115 + 0.875115i) q^{37} +0.586363 q^{39} -10.8898 q^{41} +(-0.233133 + 0.233133i) q^{43} +(2.73463 - 2.00000i) q^{45} +(7.88789 + 7.88789i) q^{47} +1.00000i q^{49} -13.3571i q^{51} +(-0.609747 - 0.609747i) q^{53} +(7.15938 - 5.23608i) q^{55} +(6.70436 - 6.70436i) q^{57} -12.3955 q^{59} -7.21949 q^{61} +(-1.07136 + 1.07136i) q^{63} +(-0.0946093 + 0.609747i) q^{65} +(-10.7053 - 10.7053i) q^{67} +2.18922i q^{69} +6.01008i q^{71} +(5.76491 + 5.76491i) q^{73} +(4.88285 + 9.43590i) q^{75} +(-2.80487 + 2.80487i) q^{77} -7.34702 q^{79} +11.2498 q^{81} +(-5.65685 + 5.65685i) q^{83} +(13.8898 + 2.15516i) q^{85} +(8.70739 + 8.70739i) q^{87} +2.71995i q^{89} -0.275950i q^{91} +(-7.40493 - 7.40493i) q^{93} +(5.88999 + 8.05348i) q^{95} +(1.86543 - 1.86543i) q^{97} -6.01008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 20 q^{13} + 4 q^{17} + 8 q^{21} - 20 q^{25} - 24 q^{33} - 44 q^{37} - 32 q^{41} - 36 q^{45} + 28 q^{53} + 8 q^{57} - 16 q^{61} + 36 q^{65} + 4 q^{73} - 16 q^{77} + 68 q^{81} + 68 q^{85} + 8 q^{93} + 12 q^{97}+O(q^{100}) \) 12 * q + 20 * q^13 + 4 * q^17 + 8 * q^21 - 20 * q^25 - 24 * q^33 - 44 * q^37 - 32 * q^41 - 36 * q^45 + 28 * q^53 + 8 * q^57 - 16 * q^61 + 36 * q^65 + 4 * q^73 - 16 * q^77 + 68 * q^81 + 68 * q^85 + 8 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more