LMFDB - Embedded newform 1280.2.l.f.321.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(321,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1280.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.l (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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			321.4
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1280.321
Dual form			1280.2.l.f.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07313 + 2.07313i) q^{3} +(0.707107 - 0.707107i) q^{5} +4.34607i q^{7} +5.59575i q^{9} +O(q^{10})$	\(q+(2.07313 + 2.07313i) q^{3} +(0.707107 - 0.707107i) q^{5} +4.34607i q^{7} +5.59575i q^{9} +(2.66390 - 2.66390i) q^{11} +(-0.482362 - 0.482362i) q^{13} +2.93185 q^{15} +0.353113 q^{17} +(5.39595 + 5.39595i) q^{19} +(-9.00997 + 9.00997i) q^{21} -6.62863i q^{23} -1.00000i q^{25} +(-5.38134 + 5.38134i) q^{27} +(-3.42883 - 3.42883i) q^{29} -0.635674 q^{31} +11.0452 q^{33} +(3.07313 + 3.07313i) q^{35} +(-3.13165 + 3.13165i) q^{37} -2.00000i q^{39} -2.33245i q^{41} +(-7.59077 + 7.59077i) q^{43} +(3.95680 + 3.95680i) q^{45} -5.41057 q^{47} -11.8883 q^{49} +(0.732051 + 0.732051i) q^{51} +(-4.49233 + 4.49233i) q^{53} -3.76733i q^{55} +22.3730i q^{57} +(9.46651 - 9.46651i) q^{59} +(6.21682 + 6.21682i) q^{61} -24.3195 q^{63} -0.682163 q^{65} +(0.362741 + 0.362741i) q^{67} +(13.7420 - 13.7420i) q^{69} -7.32780i q^{71} -10.3682i q^{73} +(2.07313 - 2.07313i) q^{75} +(11.5775 + 11.5775i) q^{77} +8.13630 q^{79} -5.52520 q^{81} +(-8.41920 - 8.41920i) q^{83} +(0.249689 - 0.249689i) q^{85} -14.2168i q^{87} +4.55583i q^{89} +(2.09638 - 2.09638i) q^{91} +(-1.31784 - 1.31784i) q^{93} +7.63103 q^{95} +2.17549 q^{97} +(14.9065 + 14.9065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3}+O(q^{10}) $ 8 * q + 4 * q^3	$ 8 q + 4 q^{3} - 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} - 16 q^{21} - 8 q^{27} - 8 q^{29} + 24 q^{33} + 12 q^{35} - 8 q^{37} - 44 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{51} + 16 q^{53} + 16 q^{59} + 8 q^{61} - 48 q^{63} - 8 q^{65} + 12 q^{67} + 40 q^{69} + 4 q^{75} + 16 q^{77} + 96 q^{79} - 16 q^{81} - 28 q^{83} - 16 q^{85} + 8 q^{91} - 8 q^{93} + 8 q^{95} - 24 q^{97} + 56 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 - 16 * q^21 - 8 * q^27 - 8 * q^29 + 24 * q^33 + 12 * q^35 - 8 * q^37 - 44 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^51 + 16 * q^53 + 16 * q^59 + 8 * q^61 - 48 * q^63 - 8 * q^65 + 12 * q^67 + 40 * q^69 + 4 * q^75 + 16 * q^77 + 96 * q^79 - 16 * q^81 - 28 * q^83 - 16 * q^85 + 8 * q^91 - 8 * q^93 + 8 * q^95 - 24 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.07313	+	2.07313i	1.19692	+	1.19692i	0.975083	+	0.221840i	$0.0712064\pi$
$3$	2.07313	+	2.07313i	1.19692	+	1.19692i	0.221840	+	0.975083i	$0.428794\pi$
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			4.34607i			1.64266i	0.570455	+	0.821329i	$0.306767\pi$
$7$			4.34607i			1.64266i	−0.570455	+	0.821329i	$0.693233\pi$
$8$		0			0
$9$			5.59575i			1.86525i
$10$		0			0
$11$	2.66390	−	2.66390i	0.803197	−	0.803197i	−0.180397	−	0.983594i	$-0.557738\pi$
$11$	2.66390	−	2.66390i	0.803197	−	0.803197i	0.983594	+	0.180397i	$0.0577383\pi$
$12$		0			0
$13$	−0.482362	−	0.482362i	−0.133783	−	0.133783i	0.637044	−	0.770827i	$-0.280157\pi$
$13$	−0.482362	−	0.482362i	−0.133783	−	0.133783i	−0.770827	+	0.637044i	$0.780157\pi$
$14$		0			0
$15$	2.93185			0.757001
$16$		0			0
$17$	0.353113			0.0856426			0.0428213	−	0.999083i	$-0.486365\pi$
$17$	0.353113			0.0856426			0.0428213	+	0.999083i	$0.486365\pi$
$18$		0			0
$19$	5.39595	+	5.39595i	1.23792	+	1.23792i	0.960851	+	0.277066i	$0.0893619\pi$
$19$	5.39595	+	5.39595i	1.23792	+	1.23792i	0.277066	+	0.960851i	$0.410638\pi$
$20$		0			0
$21$	−9.00997	+	9.00997i	−1.96614	+	1.96614i
$22$		0			0
$23$		−	6.62863i		−	1.38216i	−0.722776	−	0.691082i	$-0.757134\pi$
$23$		−	6.62863i		−	1.38216i	0.722776	−	0.691082i	$-0.242866\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−5.38134	+	5.38134i	−1.03564	+	1.03564i
$28$		0			0
$29$	−3.42883	−	3.42883i	−0.636717	−	0.636717i	0.313027	−	0.949744i	$-0.398657\pi$
$29$	−3.42883	−	3.42883i	−0.636717	−	0.636717i	−0.949744	+	0.313027i	$0.898657\pi$
$30$		0			0
$31$	−0.635674			−0.114171			−0.0570853	−	0.998369i	$-0.518181\pi$
$31$	−0.635674			−0.114171			−0.0570853	+	0.998369i	$0.518181\pi$
$32$		0			0
$33$	11.0452			1.92273
$34$		0			0
$35$	3.07313	+	3.07313i	0.519454	+	0.519454i
$36$		0			0
$37$	−3.13165	+	3.13165i	−0.514840	+	0.514840i	−0.916006	−	0.401165i	$-0.868605\pi$
$37$	−3.13165	+	3.13165i	−0.514840	+	0.514840i	0.401165	+	0.916006i	$0.368605\pi$
$38$		0			0
$39$		−	2.00000i		−	0.320256i
$40$		0			0
$41$		−	2.33245i		−	0.364267i	−0.983274	−	0.182134i	$-0.941700\pi$
$41$		−	2.33245i		−	0.364267i	0.983274	−	0.182134i	$-0.0583004\pi$
$42$		0			0
$43$	−7.59077	+	7.59077i	−1.15758	+	1.15758i	−0.172587	+	0.984994i	$0.555213\pi$
$43$	−7.59077	+	7.59077i	−1.15758	+	1.15758i	−0.984994	+	0.172587i	$0.944787\pi$
$44$		0			0
$45$	3.95680	+	3.95680i	0.589844	+	0.589844i
$46$		0			0
$47$	−5.41057			−0.789212			−0.394606	−	0.918850i	$-0.629119\pi$
$47$	−5.41057			−0.789212			−0.394606	+	0.918850i	$0.629119\pi$
$48$		0			0
$49$	−11.8883			−1.69833
$50$		0			0
$51$	0.732051	+	0.732051i	0.102508	+	0.102508i
$52$		0			0
$53$	−4.49233	+	4.49233i	−0.617069	+	0.617069i	−0.944779	−	0.327710i	$-0.893723\pi$
$53$	−4.49233	+	4.49233i	−0.617069	+	0.617069i	0.327710	+	0.944779i	$0.393723\pi$
$54$		0			0
$55$		−	3.76733i		−	0.507986i
$56$		0			0
$57$			22.3730i			2.96338i
$58$		0			0
$59$	9.46651	−	9.46651i	1.23243	−	1.23243i	0.269408	−	0.963026i	$-0.413172\pi$
$59$	9.46651	−	9.46651i	1.23243	−	1.23243i	0.963026	−	0.269408i	$-0.0868280\pi$
$60$		0			0
$61$	6.21682	+	6.21682i	0.795982	+	0.795982i	0.982459	−	0.186477i	$-0.0597071\pi$
$61$	6.21682	+	6.21682i	0.795982	+	0.795982i	−0.186477	+	0.982459i	$0.559707\pi$
$62$		0			0
$63$	−24.3195			−3.06397
$64$		0			0
$65$	−0.682163			−0.0846119
$66$		0			0
$67$	0.362741	+	0.362741i	0.0443159	+	0.0443159i	0.728917	−	0.684602i	$-0.240024\pi$
$67$	0.362741	+	0.362741i	0.0443159	+	0.0443159i	−0.684602	+	0.728917i	$0.740024\pi$
$68$		0			0
$69$	13.7420	−	13.7420i	1.65434	−	1.65434i
$70$		0			0
$71$		−	7.32780i		−	0.869650i	−0.900515	−	0.434825i	$-0.856810\pi$
$71$		−	7.32780i		−	0.869650i	0.900515	−	0.434825i	$-0.143190\pi$
$72$		0			0
$73$		−	10.3682i		−	1.21351i	−0.794889	−	0.606755i	$-0.792471\pi$
$73$		−	10.3682i		−	1.21351i	0.794889	−	0.606755i	$-0.207529\pi$
$74$		0			0
$75$	2.07313	−	2.07313i	0.239385	−	0.239385i
$76$		0			0
$77$	11.5775	+	11.5775i	1.31938	+	1.31938i
$78$		0			0
$79$	8.13630			0.915405			0.457702	−	0.889105i	$-0.348673\pi$
$79$	8.13630			0.915405			0.457702	+	0.889105i	$0.348673\pi$
$80$		0			0
$81$	−5.52520			−0.613911
$82$		0			0
$83$	−8.41920	−	8.41920i	−0.924127	−	0.924127i	0.0731910	−	0.997318i	$-0.476682\pi$
$83$	−8.41920	−	8.41920i	−0.924127	−	0.924127i	−0.997318	+	0.0731910i	$0.976682\pi$
$84$		0			0
$85$	0.249689	−	0.249689i	0.0270826	−	0.0270826i
$86$		0			0
$87$		−	14.2168i		−	1.52420i
$88$		0			0
$89$			4.55583i			0.482917i	0.970411	+	0.241459i	$0.0776258\pi$
$89$			4.55583i			0.482917i	−0.970411	+	0.241459i	$0.922374\pi$
$90$		0			0
$91$	2.09638	−	2.09638i	0.219760	−	0.219760i
$92$		0			0
$93$	−1.31784	−	1.31784i	−0.136653	−	0.136653i
$94$		0			0
$95$	7.63103			0.782927
$96$		0			0
$97$	2.17549			0.220887			0.110444	−	0.993882i	$-0.464773\pi$
$97$	2.17549			0.220887			0.110444	+	0.993882i	$0.464773\pi$
$98$		0			0
$99$	14.9065	+	14.9065i	1.49816	+	1.49816i
$100$		0			0
$101$	4.03528	−	4.03528i	0.401525	−	0.401525i	−0.477245	−	0.878770i	$-0.658365\pi$
$101$	4.03528	−	4.03528i	0.401525	−	0.401525i	0.878770	+	0.477245i	$0.158365\pi$
$102$		0			0
$103$		−	2.92116i		−	0.287830i	−0.989590	−	0.143915i	$-0.954031\pi$
$103$		−	2.92116i		−	0.287830i	0.989590	−	0.143915i	$-0.0459692\pi$
$104$		0			0
$105$			12.7420i			1.24349i
$106$		0			0
$107$	−2.67958	+	2.67958i	−0.259045	+	0.259045i	−0.824666	−	0.565621i	$-0.808637\pi$
$107$	−2.67958	+	2.67958i	−0.259045	+	0.259045i	0.565621	+	0.824666i	$0.308637\pi$
$108$		0			0
$109$	7.81382	+	7.81382i	0.748428	+	0.748428i	0.974184	−	0.225756i	$-0.0724852\pi$
$109$	7.81382	+	7.81382i	0.748428	+	0.748428i	−0.225756	+	0.974184i	$0.572485\pi$
$110$		0			0
$111$	−12.9847			−1.23245
$112$		0			0
$113$	−14.3923			−1.35391			−0.676957	−	0.736022i	$-0.736702\pi$
$113$	−14.3923			−1.35391			−0.676957	+	0.736022i	$0.736702\pi$
$114$		0			0
$115$	−4.68715	−	4.68715i	−0.437079	−	0.437079i
$116$		0			0
$117$	2.69918	−	2.69918i	0.249539	−	0.249539i
$118$		0			0
$119$			1.53465i			0.140681i
$120$		0			0
$121$		−	3.19275i		−	0.290250i
$122$		0			0
$123$	4.83548	−	4.83548i	0.436000	−	0.436000i
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	20.6534			1.83269			0.916345	−	0.400389i	$-0.131125\pi$
$127$	20.6534			1.83269			0.916345	+	0.400389i	$0.131125\pi$
$128$		0			0
$129$	−31.4733			−2.77107
$130$		0			0
$131$	−2.07812	−	2.07812i	−0.181566	−	0.181566i	0.610472	−	0.792038i	$-0.290980\pi$
$131$	−2.07812	−	2.07812i	−0.181566	−	0.181566i	−0.792038	+	0.610472i	$0.790980\pi$
$132$		0			0
$133$	−23.4512	+	23.4512i	−2.03347	+	2.03347i
$134$		0			0
$135$			7.61037i			0.654996i
$136$		0			0
$137$		−	14.4195i		−	1.23194i	−0.787768	−	0.615972i	$-0.788763\pi$
$137$		−	14.4195i		−	1.23194i	0.787768	−	0.615972i	$-0.211237\pi$
$138$		0			0
$139$	0.987792	−	0.987792i	0.0837834	−	0.0837834i	−0.663973	−	0.747756i	$-0.731131\pi$
$139$	0.987792	−	0.987792i	0.0837834	−	0.0837834i	0.747756	+	0.663973i	$0.231131\pi$
$140$		0			0
$141$	−11.2168	−	11.2168i	−0.944626	−	0.944626i
$142$		0			0
$143$	−2.56993			−0.214908
$144$		0			0
$145$	−4.84909			−0.402695
$146$		0			0
$147$	−24.6460	−	24.6460i	−2.03277	−	2.03277i
$148$		0			0
$149$	1.08176	−	1.08176i	0.0886216	−	0.0886216i	−0.661406	−	0.750028i	$-0.730040\pi$
$149$	1.08176	−	1.08176i	0.0886216	−	0.0886216i	0.750028	+	0.661406i	$0.230040\pi$
$150$		0			0
$151$		−	12.2220i		−	0.994610i	−0.867576	−	0.497305i	$-0.834323\pi$
$151$		−	12.2220i		−	0.994610i	0.867576	−	0.497305i	$-0.165677\pi$
$152$		0			0
$153$			1.97594i			0.159745i
$154$		0			0
$155$	−0.449490	+	0.449490i	−0.0361039	+	0.0361039i
$156$		0			0
$157$	0.285961	+	0.285961i	0.0228222	+	0.0228222i	0.718426	−	0.695604i	$-0.244863\pi$
$157$	0.285961	+	0.285961i	0.0228222	+	0.0228222i	−0.695604	+	0.718426i	$0.744863\pi$
$158$		0			0
$159$	−18.6264			−1.47717
$160$		0			0
$161$	28.8084			2.27042
$162$		0			0
$163$	1.15490	+	1.15490i	0.0904585	+	0.0904585i	0.750888	−	0.660430i	$-0.229626\pi$
$163$	1.15490	+	1.15490i	0.0904585	+	0.0904585i	−0.660430	+	0.750888i	$0.729626\pi$
$164$		0			0
$165$	7.81017	−	7.81017i	0.608021	−	0.608021i
$166$		0			0
$167$			9.52280i			0.736896i	0.929648	+	0.368448i	$0.120111\pi$
$167$			9.52280i			0.736896i	−0.929648	+	0.368448i	$0.879889\pi$
$168$		0			0
$169$		−	12.5347i		−	0.964204i
$170$		0			0
$171$	−30.1944	+	30.1944i	−2.30903	+	2.30903i
$172$		0			0
$173$	−2.73205	−	2.73205i	−0.207714	−	0.207714i	0.595581	−	0.803295i	$-0.296922\pi$
$173$	−2.73205	−	2.73205i	−0.207714	−	0.207714i	−0.803295	+	0.595581i	$0.796922\pi$
$174$		0			0
$175$	4.34607			0.328532
$176$		0			0
$177$	39.2506			2.95026
$178$		0			0
$179$	17.7656	+	17.7656i	1.32786	+	1.32786i	0.907231	+	0.420632i	$0.138192\pi$
$179$	17.7656	+	17.7656i	1.32786	+	1.32786i	0.420632	+	0.907231i	$0.361808\pi$
$180$		0			0
$181$	3.75787	−	3.75787i	0.279321	−	0.279321i	−0.553517	−	0.832838i	$-0.686715\pi$
$181$	3.75787	−	3.75787i	0.279321	−	0.279321i	0.832838	+	0.553517i	$0.186715\pi$
$182$		0			0
$183$			25.7766i			1.90546i
$184$		0			0
$185$			4.42883i			0.325614i
$186$		0			0
$187$	0.940660	−	0.940660i	0.0687879	−	0.0687879i
$188$		0			0
$189$	−23.3877	−	23.3877i	−1.70120	−	1.70120i
$190$		0			0
$191$	−14.4702			−1.04702			−0.523512	−	0.852018i	$-0.675378\pi$
$191$	−14.4702			−1.04702			−0.523512	+	0.852018i	$0.675378\pi$
$192$		0			0
$193$	4.41886			0.318076			0.159038	−	0.987272i	$-0.449161\pi$
$193$	4.41886			0.318076			0.159038	+	0.987272i	$0.449161\pi$
$194$		0			0
$195$	−1.41421	−	1.41421i	−0.101274	−	0.101274i
$196$		0			0
$197$	−9.01826	+	9.01826i	−0.642524	+	0.642524i	−0.951175	−	0.308651i	$-0.900123\pi$
$197$	−9.01826	+	9.01826i	−0.642524	+	0.642524i	0.308651	+	0.951175i	$0.400123\pi$
$198$		0			0
$199$		−	0.585057i		−	0.0414736i	−0.999785	−	0.0207368i	$-0.993399\pi$
$199$		−	0.585057i		−	0.0414736i	0.999785	−	0.0207368i	$-0.00660121\pi$
$200$		0			0
$201$			1.50402i			0.106086i
$202$		0			0
$203$	14.9019	−	14.9019i	1.04591	−	1.04591i
$204$		0			0
$205$	−1.64929	−	1.64929i	−0.115191	−	0.115191i
$206$		0			0
$207$	37.0922			2.57808
$208$		0			0
$209$	28.7486			1.98858
$210$		0			0
$211$	0.270869	+	0.270869i	0.0186474	+	0.0186474i	0.716369	−	0.697722i	$-0.245803\pi$
$211$	0.270869	+	0.270869i	0.0186474	+	0.0186474i	−0.697722	+	0.716369i	$0.745803\pi$
$212$		0			0
$213$	15.1915	−	15.1915i	1.04090	−	1.04090i
$214$		0			0
$215$			10.7350i			0.732119i
$216$		0			0
$217$		−	2.76268i		−	0.187543i
$218$		0			0
$219$	21.4947	−	21.4947i	1.45248	−	1.45248i
$220$		0			0
$221$	−0.170328	−	0.170328i	−0.0114575	−	0.0114575i
$222$		0			0
$223$	0.964475			0.0645860			0.0322930	−	0.999478i	$-0.489719\pi$
$223$	0.964475			0.0645860			0.0322930	+	0.999478i	$0.489719\pi$
$224$		0			0
$225$	5.59575			0.373050
$226$		0			0
$227$	6.81588	+	6.81588i	0.452386	+	0.452386i	0.896146	−	0.443760i	$-0.146356\pi$
$227$	6.81588	+	6.81588i	0.452386	+	0.452386i	−0.443760	+	0.896146i	$0.646356\pi$
$228$		0			0
$229$	−2.53465	+	2.53465i	−0.167495	+	0.167495i	−0.785877	−	0.618383i	$-0.787788\pi$
$229$	−2.53465	+	2.53465i	−0.167495	+	0.167495i	0.618383	+	0.785877i	$0.287788\pi$
$230$		0			0
$231$			48.0034i			3.15839i
$232$		0			0
$233$		−	10.8233i		−	0.709056i	−0.935045	−	0.354528i	$-0.884642\pi$
$233$		−	10.8233i		−	0.709056i	0.935045	−	0.354528i	$-0.115358\pi$
$234$		0			0
$235$	−3.82585	+	3.82585i	−0.249571	+	0.249571i
$236$		0			0
$237$	16.8676	+	16.8676i	1.09567	+	1.09567i
$238$		0			0
$239$	21.1137			1.36573			0.682865	−	0.730545i	$-0.260734\pi$
$239$	21.1137			1.36573			0.682865	+	0.730545i	$0.260734\pi$
$240$		0			0
$241$	−18.9296			−1.21936			−0.609682	−	0.792646i	$-0.708703\pi$
$241$	−18.9296			−1.21936			−0.609682	+	0.792646i	$0.708703\pi$
$242$		0			0
$243$	4.68955	+	4.68955i	0.300835	+	0.300835i
$244$		0			0
$245$	−8.40629	+	8.40629i	−0.537058	+	0.537058i
$246$		0			0
$247$		−	5.20560i		−	0.331225i
$248$		0			0
$249$		−	34.9082i		−	2.21222i
$250$		0			0
$251$	11.6286	−	11.6286i	0.733992	−	0.733992i	−0.237416	−	0.971408i	$-0.576300\pi$
$251$	11.6286	−	11.6286i	0.733992	−	0.733992i	0.971408	+	0.237416i	$0.0763004\pi$
$252$		0			0
$253$	−17.6580	−	17.6580i	−1.11015	−	1.11015i
$254$		0			0
$255$	1.03528			0.0648315
$256$		0			0
$257$	−6.49258			−0.404996			−0.202498	−	0.979283i	$-0.564906\pi$
$257$	−6.49258			−0.404996			−0.202498	+	0.979283i	$0.564906\pi$
$258$		0			0
$259$	−13.6104	−	13.6104i	−0.845707	−	0.845707i
$260$		0			0
$261$	19.1869	−	19.1869i	1.18764	−	1.18764i
$262$		0			0
$263$		−	2.66102i		−	0.164085i	−0.996629	−	0.0820427i	$-0.973856\pi$
$263$		−	2.66102i		−	0.164085i	0.996629	−	0.0820427i	$-0.0261444\pi$
$264$		0			0
$265$			6.35311i			0.390269i
$266$		0			0
$267$	−9.44485	+	9.44485i	−0.578015	+	0.578015i
$268$		0			0
$269$	−12.2460	−	12.2460i	−0.746654	−	0.746654i	0.227195	−	0.973849i	$-0.427045\pi$
$269$	−12.2460	−	12.2460i	−0.746654	−	0.746654i	−0.973849	+	0.227195i	$0.927045\pi$
$270$		0			0
$271$	25.0280			1.52034			0.760171	−	0.649723i	$-0.225115\pi$
$271$	25.0280			1.52034			0.760171	+	0.649723i	$0.225115\pi$
$272$		0			0
$273$	8.69213			0.526072
$274$		0			0
$275$	−2.66390	−	2.66390i	−0.160639	−	0.160639i
$276$		0			0
$277$	0.318353	−	0.318353i	0.0191280	−	0.0191280i	−0.697478	−	0.716606i	$-0.745695\pi$
$277$	0.318353	−	0.318353i	0.0191280	−	0.0191280i	0.716606	+	0.697478i	$0.245695\pi$
$278$		0			0
$279$		−	3.55708i		−	0.212957i
$280$		0			0
$281$		−	7.90843i		−	0.471777i	−0.971780	−	0.235889i	$-0.924200\pi$
$281$		−	7.90843i		−	0.471777i	0.971780	−	0.235889i	$-0.0758001\pi$
$282$		0			0
$283$	−11.9520	+	11.9520i	−0.710470	+	0.710470i	−0.966634	−	0.256163i	$-0.917542\pi$
$283$	−11.9520	+	11.9520i	−0.710470	+	0.710470i	0.256163	+	0.966634i	$0.417542\pi$
$284$		0			0
$285$	15.8201	+	15.8201i	0.937104	+	0.937104i
$286$		0			0
$287$	10.1370			0.598367
$288$		0			0
$289$	−16.8753			−0.992665
$290$		0			0
$291$	4.51007	+	4.51007i	0.264385	+	0.264385i
$292$		0			0
$293$	17.9043	−	17.9043i	1.04598	−	1.04598i	0.0470899	−	0.998891i	$-0.485005\pi$
$293$	17.9043	−	17.9043i	1.04598	−	1.04598i	0.998891	−	0.0470899i	$-0.0149947\pi$
$294$		0			0
$295$		−	13.3877i		−	0.779460i
$296$		0			0
$297$			28.6707i			1.66364i
$298$		0			0
$299$	−3.19740	+	3.19740i	−0.184910	+	0.184910i
$300$		0			0
$301$	−32.9900	−	32.9900i	−1.90151	−	1.90151i
$302$		0			0
$303$	16.7313			0.961189
$304$		0			0
$305$	8.79191			0.503423
$306$		0			0
$307$	0.955096	+	0.955096i	0.0545102	+	0.0545102i	0.733836	−	0.679326i	$-0.237728\pi$
$307$	0.955096	+	0.955096i	0.0545102	+	0.0545102i	−0.679326	+	0.733836i	$0.737728\pi$
$308$		0			0
$309$	6.05594	−	6.05594i	0.344510	−	0.344510i
$310$		0			0
$311$		−	13.3550i		−	0.757295i	−0.925541	−	0.378647i	$-0.876389\pi$
$311$		−	13.3550i		−	0.757295i	0.925541	−	0.378647i	$-0.123611\pi$
$312$		0			0
$313$		−	21.1069i		−	1.19303i	−0.802602	−	0.596515i	$-0.796552\pi$
$313$		−	21.1069i		−	1.19303i	0.802602	−	0.596515i	$-0.203448\pi$
$314$		0			0
$315$	−17.1965	+	17.1965i	−0.968913	+	0.968913i
$316$		0			0
$317$	21.0966	+	21.0966i	1.18491	+	1.18491i	0.978458	+	0.206448i	$0.0661904\pi$
$317$	21.0966	+	21.0966i	1.18491	+	1.18491i	0.206448	+	0.978458i	$0.433810\pi$
$318$		0			0
$319$	−18.2681			−1.02282
$320$		0			0
$321$	−11.1103			−0.620114
$322$		0			0
$323$	1.90538	+	1.90538i	0.106018	+	0.106018i
$324$		0			0
$325$	−0.482362	+	0.482362i	−0.0267566	+	0.0267566i
$326$		0			0
$327$			32.3981i			1.79162i
$328$		0			0
$329$		−	23.5147i		−	1.29641i
$330$		0			0
$331$	21.7763	−	21.7763i	1.19693	−	1.19693i	0.221854	−	0.975080i	$-0.428789\pi$
$331$	21.7763	−	21.7763i	1.19693	−	1.19693i	0.975080	−	0.221854i	$-0.0712107\pi$
$332$		0			0
$333$	−17.5240	−	17.5240i	−0.960307	−	0.960307i
$334$		0			0
$335$	0.512994			0.0280279
$336$		0			0
$337$	−19.0260			−1.03641			−0.518206	−	0.855256i	$-0.673400\pi$
$337$	−19.0260			−1.03641			−0.518206	+	0.855256i	$0.673400\pi$
$338$		0			0
$339$	−29.8372	−	29.8372i	−1.62053	−	1.62053i
$340$		0			0
$341$	−1.69337	+	1.69337i	−0.0917014	+	0.0917014i
$342$		0			0
$343$		−	21.2448i		−	1.14711i
$344$		0			0
$345$		−	19.4341i		−	1.04630i
$346$		0			0
$347$	−1.92463	+	1.92463i	−0.103319	+	0.103319i	−0.756877	−	0.653557i	$-0.773276\pi$
$347$	−1.92463	+	1.92463i	−0.103319	+	0.103319i	0.653557	+	0.756877i	$0.273276\pi$
$348$		0			0
$349$	−16.2621	−	16.2621i	−0.870488	−	0.870488i	0.122037	−	0.992526i	$-0.461057\pi$
$349$	−16.2621	−	16.2621i	−0.870488	−	0.870488i	−0.992526	+	0.122037i	$0.961057\pi$
$350$		0			0
$351$	5.19151			0.277102
$352$		0			0
$353$	−22.9058			−1.21915			−0.609576	−	0.792728i	$-0.708660\pi$
$353$	−22.9058			−1.21915			−0.609576	+	0.792728i	$0.708660\pi$
$354$		0			0
$355$	−5.18154	−	5.18154i	−0.275008	−	0.275008i
$356$		0			0
$357$	−3.18154	+	3.18154i	−0.168385	+	0.168385i
$358$		0			0
$359$			21.5687i			1.13835i	0.822216	+	0.569176i	$0.192738\pi$
$359$			21.5687i			1.13835i	−0.822216	+	0.569176i	$0.807262\pi$
$360$		0			0
$361$			39.2326i			2.06487i
$362$		0			0
$363$	6.61900	−	6.61900i	0.347407	−	0.347407i
$364$		0			0
$365$	−7.33145	−	7.33145i	−0.383746	−	0.383746i
$366$		0			0
$367$	4.32097			0.225553			0.112776	−	0.993620i	$-0.464026\pi$
$367$	4.32097			0.225553			0.112776	+	0.993620i	$0.464026\pi$
$368$		0			0
$369$	13.0518			0.679450
$370$		0			0
$371$	−19.5240	−	19.5240i	−1.01363	−	1.01363i
$372$		0			0
$373$	20.0458	−	20.0458i	1.03793	−	1.03793i	0.0386784	−	0.999252i	$-0.487685\pi$
$373$	20.0458	−	20.0458i	1.03793	−	1.03793i	0.999252	−	0.0386784i	$-0.0123148\pi$
$374$		0			0
$375$		−	2.93185i		−	0.151400i
$376$		0			0
$377$			3.30787i			0.170364i
$378$		0			0
$379$	−12.5103	+	12.5103i	−0.642613	+	0.642613i	−0.951197	−	0.308584i	$-0.900145\pi$
$379$	−12.5103	+	12.5103i	−0.642613	+	0.642613i	0.308584	+	0.951197i	$0.400145\pi$
$380$		0			0
$381$	42.8172	+	42.8172i	2.19359	+	2.19359i
$382$		0			0
$383$	−12.0645			−0.616469			−0.308234	−	0.951310i	$-0.599738\pi$
$383$	−12.0645			−0.616469			−0.308234	+	0.951310i	$0.599738\pi$
$384$		0			0
$385$	16.3730			0.834448
$386$		0			0
$387$	−42.4761	−	42.4761i	−2.15918	−	2.15918i
$388$		0			0
$389$	−23.9228	+	23.9228i	−1.21294	+	1.21294i	−0.242879	+	0.970057i	$0.578092\pi$
$389$	−23.9228	+	23.9228i	−1.21294	+	1.21294i	−0.970057	+	0.242879i	$0.921908\pi$
$390$		0			0
$391$		−	2.34066i		−	0.118372i
$392$		0			0
$393$		−	8.61642i		−	0.434641i
$394$		0			0
$395$	5.75323	−	5.75323i	0.289476	−	0.289476i
$396$		0			0
$397$	7.11804	+	7.11804i	0.357244	+	0.357244i	0.862796	−	0.505552i	$-0.168711\pi$
$397$	7.11804	+	7.11804i	0.357244	+	0.357244i	−0.505552	+	0.862796i	$0.668711\pi$
$398$		0			0
$399$	−97.2347			−4.86783
$400$		0			0
$401$	−30.9895			−1.54754			−0.773770	−	0.633467i	$-0.781631\pi$
$401$	−30.9895			−1.54754			−0.773770	+	0.633467i	$0.781631\pi$
$402$		0			0
$403$	0.306625	+	0.306625i	0.0152741	+	0.0152741i
$404$		0			0
$405$	−3.90691	+	3.90691i	−0.194136	+	0.194136i
$406$		0			0
$407$			16.6848i			0.827036i
$408$		0			0
$409$			0.344554i			0.0170371i	0.999964	+	0.00851855i	$0.00271157\pi$
$409$			0.344554i			0.0170371i	−0.999964	+	0.00851855i	$0.997288\pi$
$410$		0			0
$411$	29.8936	−	29.8936i	1.47454	−	1.47454i
$412$		0			0
$413$	41.1421	+	41.1421i	2.02447	+	2.02447i
$414$		0			0
$415$	−11.9065			−0.584469
$416$		0			0
$417$	4.09565			0.200565
$418$		0			0
$419$	13.6799	+	13.6799i	0.668308	+	0.668308i	0.957324	−	0.289016i	$-0.0933282\pi$
$419$	13.6799	+	13.6799i	0.668308	+	0.668308i	−0.289016	+	0.957324i	$0.593328\pi$
$420$		0			0
$421$	−20.4728	+	20.4728i	−0.997784	+	0.997784i	−0.999998	−	0.00221312i	$-0.999296\pi$
$421$	−20.4728	+	20.4728i	−0.997784	+	0.997784i	0.00221312	+	0.999998i	$0.499296\pi$
$422$		0			0
$423$		−	30.2762i		−	1.47208i
$424$		0			0
$425$		−	0.353113i		−	0.0171285i
$426$		0			0
$427$	−27.0187	+	27.0187i	−1.30753	+	1.30753i
$428$		0			0
$429$	−5.32780	−	5.32780i	−0.257229	−	0.257229i
$430$		0			0
$431$	−0.928203			−0.0447100			−0.0223550	−	0.999750i	$-0.507116\pi$
$431$	−0.928203			−0.0447100			−0.0223550	+	0.999750i	$0.507116\pi$
$432$		0			0
$433$	4.01926			0.193153			0.0965766	−	0.995326i	$-0.469211\pi$
$433$	4.01926			0.193153			0.0965766	+	0.995326i	$0.469211\pi$
$434$		0			0
$435$	−10.0528	−	10.0528i	−0.481995	−	0.481995i
$436$		0			0
$437$	35.7678	−	35.7678i	1.71100	−	1.71100i
$438$		0			0
$439$		−	37.4578i		−	1.78776i	−0.448301	−	0.893882i	$-0.647971\pi$
$439$		−	37.4578i		−	1.78776i	0.448301	−	0.893882i	$-0.352029\pi$
$440$		0			0
$441$		−	66.5239i		−	3.16781i
$442$		0			0
$443$	10.3505	−	10.3505i	0.491769	−	0.491769i	−0.417094	−	0.908863i	$-0.636952\pi$
$443$	10.3505	−	10.3505i	0.491769	−	0.491769i	0.908863	+	0.417094i	$0.136952\pi$
$444$		0			0
$445$	3.22146	+	3.22146i	0.152712	+	0.152712i
$446$		0			0
$447$	4.48528			0.212147
$448$		0			0
$449$	9.78623			0.461841			0.230920	−	0.972973i	$-0.425826\pi$
$449$	9.78623			0.461841			0.230920	+	0.972973i	$0.425826\pi$
$450$		0			0
$451$	−6.21342	−	6.21342i	−0.292578	−	0.292578i
$452$		0			0
$453$	25.3378	−	25.3378i	1.19047	−	1.19047i
$454$		0			0
$455$		−	2.96472i		−	0.138988i
$456$		0			0
$457$		−	0.907307i		−	0.0424420i	−0.999775	−	0.0212210i	$-0.993245\pi$
$457$		−	0.907307i		−	0.0424420i	0.999775	−	0.0212210i	$-0.00675537\pi$
$458$		0			0
$459$	−1.90022	+	1.90022i	−0.0886949	+	0.0886949i
$460$		0			0
$461$	8.03528	+	8.03528i	0.374240	+	0.374240i	0.869019	−	0.494779i	$-0.164751\pi$
$461$	8.03528	+	8.03528i	0.374240	+	0.374240i	−0.494779	+	0.869019i	$0.664751\pi$
$462$		0			0
$463$	39.0533			1.81496			0.907481	−	0.420093i	$-0.138003\pi$
$463$	39.0533			1.81496			0.907481	+	0.420093i	$0.138003\pi$
$464$		0			0
$465$	−1.86370			−0.0864272
$466$		0			0
$467$	−9.82296	−	9.82296i	−0.454553	−	0.454553i	0.442310	−	0.896862i	$-0.354159\pi$
$467$	−9.82296	−	9.82296i	−0.454553	−	0.454553i	−0.896862	+	0.442310i	$0.854159\pi$
$468$		0			0
$469$	−1.57650	+	1.57650i	−0.0727959	+	0.0727959i
$470$		0			0
$471$			1.18567i			0.0546328i
$472$		0			0
$473$			40.4421i			1.85953i
$474$		0			0
$475$	5.39595	−	5.39595i	0.247583	−	0.247583i
$476$		0			0
$477$	−25.1380	−	25.1380i	−1.15099	−	1.15099i
$478$		0			0
$479$	−31.0479			−1.41862			−0.709308	−	0.704899i	$-0.750992\pi$
$479$	−31.0479			−1.41862			−0.709308	+	0.704899i	$0.750992\pi$
$480$		0			0
$481$	3.02118			0.137754
$482$		0			0
$483$	59.7237	+	59.7237i	2.71752	+	2.71752i
$484$		0			0
$485$	1.53830	−	1.53830i	0.0698507	−	0.0698507i
$486$		0			0
$487$		−	11.5809i		−	0.524780i	−0.964962	−	0.262390i	$-0.915489\pi$
$487$		−	11.5809i		−	0.524780i	0.964962	−	0.262390i	$-0.0845108\pi$
$488$		0			0
$489$			4.78851i			0.216544i
$490$		0			0
$491$	−5.53542	+	5.53542i	−0.249810	+	0.249810i	−0.820893	−	0.571083i	$-0.806524\pi$
$491$	−5.53542	+	5.53542i	−0.249810	+	0.249810i	0.571083	+	0.820893i	$0.306524\pi$
$492$		0			0
$493$	−1.21076	−	1.21076i	−0.0545301	−	0.0545301i
$494$		0			0
$495$	21.0810			0.947522
$496$		0			0
$497$	31.8471			1.42854
$498$		0			0
$499$	−5.01702	−	5.01702i	−0.224592	−	0.224592i	0.585837	−	0.810429i	$-0.300766\pi$
$499$	−5.01702	−	5.01702i	−0.224592	−	0.224592i	−0.810429	+	0.585837i	$0.800766\pi$
$500$		0			0
$501$	−19.7420	+	19.7420i	−0.882008	+	0.882008i
$502$		0			0
$503$			30.2548i			1.34899i	0.738277	+	0.674497i	$0.235640\pi$
$503$			30.2548i			1.34899i	−0.738277	+	0.674497i	$0.764360\pi$
$504$		0			0
$505$		−	5.70674i		−	0.253947i
$506$		0			0
$507$	25.9860	−	25.9860i	1.15408	−	1.15408i
$508$		0			0
$509$	15.2127	+	15.2127i	0.674291	+	0.674291i	0.958702	−	0.284412i	$-0.0917983\pi$
$509$	15.2127	+	15.2127i	0.674291	+	0.674291i	−0.284412	+	0.958702i	$0.591798\pi$
$510$		0			0
$511$	45.0611			1.99338
$512$		0			0
$513$	−58.0749			−2.56407
$514$		0			0
$515$	−2.06557	−	2.06557i	−0.0910198	−	0.0910198i
$516$		0			0
$517$	−14.4132	+	14.4132i	−0.633893	+	0.633893i
$518$		0			0
$519$		−	11.3278i		−	0.497235i
$520$		0			0
$521$			13.2742i			0.581552i	0.956791	+	0.290776i	$0.0939134\pi$
$521$			13.2742i			0.581552i	−0.956791	+	0.290776i	$0.906087\pi$
$522$		0			0
$523$	11.4474	−	11.4474i	0.500561	−	0.500561i	−0.411051	−	0.911612i	$-0.634838\pi$
$523$	11.4474	−	11.4474i	0.500561	−	0.500561i	0.911612	+	0.411051i	$0.134838\pi$
$524$		0			0
$525$	9.00997	+	9.00997i	0.393227	+	0.393227i
$526$		0			0
$527$	−0.224465			−0.00977786
$528$		0			0
$529$	−20.9387			−0.910378
$530$		0			0
$531$	52.9722	+	52.9722i	2.29880	+	2.29880i
$532$		0			0
$533$	−1.12508	+	1.12508i	−0.0487328	+	0.0487328i
$534$		0			0
$535$			3.78950i			0.163834i
$536$		0			0
$537$			73.6609i			3.17870i
$538$		0			0
$539$	−31.6692	+	31.6692i	−1.36409	+	1.36409i
$540$		0			0
$541$	−23.1762	−	23.1762i	−0.996421	−	0.996421i	0.00357236	−	0.999994i	$-0.498863\pi$
$541$	−23.1762	−	23.1762i	−0.996421	−	0.996421i	−0.999994	+	0.00357236i	$0.998863\pi$
$542$		0			0
$543$	15.5811			0.668651
$544$		0			0
$545$	11.0504			0.473347
$546$		0			0
$547$	1.63701	+	1.63701i	0.0699935	+	0.0699935i	0.741237	−	0.671243i	$-0.234239\pi$
$547$	1.63701	+	1.63701i	0.0699935	+	0.0699935i	−0.671243	+	0.741237i	$0.734239\pi$
$548$		0			0
$549$	−34.7878	+	34.7878i	−1.48471	+	1.48471i
$550$		0			0
$551$		−	37.0036i		−	1.57640i
$552$		0			0
$553$			35.3609i			1.50370i
$554$		0			0
$555$	−9.18154	+	9.18154i	−0.389735	+	0.389735i
$556$		0			0
$557$	−5.83823	−	5.83823i	−0.247374	−	0.247374i	0.572518	−	0.819892i	$-0.305967\pi$
$557$	−5.83823	−	5.83823i	−0.247374	−	0.247374i	−0.819892	+	0.572518i	$0.805967\pi$
$558$		0			0
$559$	7.32300			0.309730
$560$		0			0
$561$	3.90022			0.164668
$562$		0			0
$563$	−13.7207	−	13.7207i	−0.578258	−	0.578258i	0.356165	−	0.934423i	$-0.384084\pi$
$563$	−13.7207	−	13.7207i	−0.578258	−	0.578258i	−0.934423	+	0.356165i	$0.884084\pi$
$564$		0			0
$565$	−10.1769	+	10.1769i	−0.428145	+	0.428145i
$566$		0			0
$567$		−	24.0129i		−	1.00845i
$568$		0			0
$569$		−	7.05861i		−	0.295912i	−0.988994	−	0.147956i	$-0.952731\pi$
$569$		−	7.05861i		−	0.295912i	0.988994	−	0.147956i	$-0.0472695\pi$
$570$		0			0
$571$	−18.8002	+	18.8002i	−0.786764	+	0.786764i	−0.980962	−	0.194198i	$-0.937789\pi$
$571$	−18.8002	+	18.8002i	−0.786764	+	0.786764i	0.194198	+	0.980962i	$0.437789\pi$
$572$		0			0
$573$	−29.9985	−	29.9985i	−1.25321	−	1.25321i
$574$		0			0
$575$	−6.62863			−0.276433
$576$		0			0
$577$	−30.6181			−1.27465			−0.637325	−	0.770595i	$-0.719959\pi$
$577$	−30.6181			−1.27465			−0.637325	+	0.770595i	$0.719959\pi$
$578$		0			0
$579$	9.16088	+	9.16088i	0.380713	+	0.380713i
$580$		0			0
$581$	36.5904	−	36.5904i	1.51802	−	1.51802i
$582$		0			0
$583$			23.9343i			0.991256i
$584$		0			0
$585$		−	3.81722i		−	0.157822i
$586$		0			0
$587$	−22.0103	+	22.0103i	−0.908463	+	0.908463i	−0.996148	−	0.0876856i	$-0.972053\pi$
$587$	−22.0103	+	22.0103i	−0.908463	+	0.908463i	0.0876856	+	0.996148i	$0.472053\pi$
$588$		0			0
$589$	−3.43007	−	3.43007i	−0.141334	−	0.141334i
$590$		0			0
$591$	−37.3921			−1.53811
$592$		0			0
$593$	−15.6014			−0.640674			−0.320337	−	0.947304i	$-0.603796\pi$
$593$	−15.6014			−0.640674			−0.320337	+	0.947304i	$0.603796\pi$
$594$		0			0
$595$	1.08516	+	1.08516i	0.0444874	+	0.0444874i
$596$		0			0
$597$	1.21290	−	1.21290i	0.0496408	−	0.0496408i
$598$		0			0
$599$			47.5264i			1.94188i	0.239331	+	0.970938i	$0.423072\pi$
$599$			47.5264i			1.94188i	−0.239331	+	0.970938i	$0.576928\pi$
$600$		0			0
$601$			4.35238i			0.177537i	0.996052	+	0.0887687i	$0.0282932\pi$
$601$			4.35238i			0.177537i	−0.996052	+	0.0887687i	$0.971707\pi$
$602$		0			0
$603$	−2.02981	+	2.02981i	−0.0826603	+	0.0826603i
$604$		0			0
$605$	−2.25762	−	2.25762i	−0.0917852	−	0.0917852i
$606$		0			0
$607$	−7.08152			−0.287430			−0.143715	−	0.989619i	$-0.545905\pi$
$607$	−7.08152			−0.287430			−0.143715	+	0.989619i	$0.545905\pi$
$608$		0			0
$609$	61.7872			2.50374
$610$		0			0
$611$	2.60985	+	2.60985i	0.105583	+	0.105583i
$612$		0			0
$613$	−0.0708010	+	0.0708010i	−0.00285963	+	0.00285963i	−0.708535	−	0.705676i	$-0.750644\pi$
$613$	−0.0708010	+	0.0708010i	−0.00285963	+	0.00285963i	0.705676	+	0.708535i	$0.250644\pi$
$614$		0			0
$615$		−	6.83839i		−	0.275751i
$616$		0			0
$617$			4.13217i			0.166355i	0.996535	+	0.0831774i	$0.0265068\pi$
$617$			4.13217i			0.166355i	−0.996535	+	0.0831774i	$0.973493\pi$
$618$		0			0
$619$	−4.43123	+	4.43123i	−0.178106	+	0.178106i	−0.790530	−	0.612424i	$-0.790195\pi$
$619$	−4.43123	+	4.43123i	−0.178106	+	0.178106i	0.612424	+	0.790530i	$0.290195\pi$
$620$		0			0
$621$	35.6709	+	35.6709i	1.43142	+	1.43142i
$622$		0			0
$623$	−19.8000			−0.793268
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	59.5996	+	59.5996i	2.38018	+	2.38018i
$628$		0			0
$629$	−1.10583	+	1.10583i	−0.0440923	+	0.0440923i
$630$		0			0
$631$		−	14.7165i		−	0.585856i	−0.956134	−	0.292928i	$-0.905370\pi$
$631$		−	14.7165i		−	0.585856i	0.956134	−	0.292928i	$-0.0946297\pi$
$632$		0			0
$633$			1.12309i			0.0446389i
$634$		0			0
$635$	14.6041	−	14.6041i	0.579548	−	0.579548i
$636$		0			0
$637$	5.73445	+	5.73445i	0.227207	+	0.227207i
$638$		0			0
$639$	41.0046			1.62212
$640$		0			0
$641$	40.5416			1.60130			0.800649	−	0.599134i	$-0.204488\pi$
$641$	40.5416			1.60130			0.800649	+	0.599134i	$0.204488\pi$
$642$		0			0
$643$	23.5941	+	23.5941i	0.930461	+	0.930461i	0.997735	−	0.0672733i	$-0.0214299\pi$
$643$	23.5941	+	23.5941i	0.930461	+	0.930461i	−0.0672733	+	0.997735i	$0.521430\pi$
$644$		0			0
$645$	−22.2550	+	22.2550i	−0.876290	+	0.876290i
$646$		0			0
$647$		−	43.4154i		−	1.70683i	−0.521228	−	0.853417i	$-0.674526\pi$
$647$		−	43.4154i		−	1.70683i	0.521228	−	0.853417i	$-0.325474\pi$
$648$		0			0
$649$		−	50.4357i		−	1.97977i
$650$		0			0
$651$	5.72741	−	5.72741i	0.224475	−	0.224475i
$652$		0			0
$653$	4.42178	+	4.42178i	0.173038	+	0.173038i	0.788313	−	0.615275i	$-0.210955\pi$
$653$	4.42178	+	4.42178i	0.173038	+	0.173038i	−0.615275	+	0.788313i	$0.710955\pi$
$654$		0			0
$655$	−2.93890			−0.114832
$656$		0			0
$657$	58.0181			2.26350
$658$		0			0
$659$	7.84544	+	7.84544i	0.305615	+	0.305615i	0.843206	−	0.537591i	$-0.180665\pi$
$659$	7.84544	+	7.84544i	0.305615	+	0.305615i	−0.537591	+	0.843206i	$0.680665\pi$
$660$		0			0
$661$	−10.6763	+	10.6763i	−0.415259	+	0.415259i	−0.883566	−	0.468307i	$-0.844864\pi$
$661$	−10.6763	+	10.6763i	−0.415259	+	0.415259i	0.468307	+	0.883566i	$0.344864\pi$
$662$		0			0
$663$		−	0.706227i		−	0.0274276i
$664$		0			0
$665$			33.1650i			1.28608i
$666$		0			0
$667$	−22.7284	+	22.7284i	−0.880047	+	0.880047i
$668$		0			0
$669$	1.99948	+	1.99948i	0.0773045	+	0.0773045i
$670$		0			0
$671$	33.1220			1.27866
$672$		0			0
$673$	11.8323			0.456103			0.228052	−	0.973649i	$-0.426764\pi$
$673$	11.8323			0.456103			0.228052	+	0.973649i	$0.426764\pi$
$674$		0			0
$675$	5.38134	+	5.38134i	0.207128	+	0.207128i
$676$		0			0
$677$	−20.3003	+	20.3003i	−0.780202	+	0.780202i	−0.979865	−	0.199663i	$-0.936015\pi$
$677$	−20.3003	+	20.3003i	−0.780202	+	0.780202i	0.199663	+	0.979865i	$0.436015\pi$
$678$		0			0
$679$			9.45481i			0.362842i
$680$		0			0
$681$			28.2604i			1.08294i
$682$		0			0
$683$	23.9889	−	23.9889i	0.917910	−	0.917910i	−0.0789669	−	0.996877i	$-0.525162\pi$
$683$	23.9889	−	23.9889i	0.917910	−	0.917910i	0.996877	+	0.0789669i	$0.0251622\pi$
$684$		0			0
$685$	−10.1962	−	10.1962i	−0.389575	−	0.389575i
$686$		0			0
$687$	−10.5093			−0.400957
$688$		0			0
$689$	4.33386			0.165107
$690$		0			0
$691$	18.8287	+	18.8287i	0.716277	+	0.716277i	0.967841	−	0.251564i	$-0.0809447\pi$
$691$	18.8287	+	18.8287i	0.716277	+	0.716277i	−0.251564	+	0.967841i	$0.580945\pi$
$692$		0			0
$693$	−64.7848	+	64.7848i	−2.46097	+	2.46097i
$694$		0			0
$695$		−	1.39695i		−	0.0529893i
$696$		0			0
$697$		−	0.823619i		−	0.0311968i
$698$		0			0
$699$	22.4381	−	22.4381i	0.848686	−	0.848686i
$700$		0			0
$701$	−20.8934	−	20.8934i	−0.789134	−	0.789134i	0.192218	−	0.981352i	$-0.438432\pi$
$701$	−20.8934	−	20.8934i	−0.789134	−	0.789134i	−0.981352	+	0.192218i	$0.938432\pi$
$702$		0			0
$703$	−33.7965			−1.27466
$704$		0			0
$705$	−15.8630			−0.597434
$706$		0			0
$707$	17.5376	+	17.5376i	0.659568	+	0.659568i
$708$		0			0
$709$	−0.105829	+	0.105829i	−0.00397447	+	0.00397447i	−0.709091	−	0.705117i	$-0.750895\pi$
$709$	−0.105829	+	0.105829i	−0.00397447	+	0.00397447i	0.705117	+	0.709091i	$0.250895\pi$
$710$		0			0
$711$			45.5287i			1.70746i
$712$		0			0
$713$			4.21365i			0.157802i
$714$		0			0
$715$	−1.81722	+	1.81722i	−0.0679600	+	0.0679600i
$716$		0			0
$717$	43.7714	+	43.7714i	1.63467	+	1.63467i
$718$		0			0
$719$	−32.4142			−1.20885			−0.604423	−	0.796663i	$-0.706596\pi$
$719$	−32.4142			−1.20885			−0.604423	+	0.796663i	$0.706596\pi$
$720$		0			0
$721$	12.6955			0.472806
$722$		0			0
$723$	−39.2436	−	39.2436i	−1.45948	−	1.45948i
$724$		0			0
$725$	−3.42883	+	3.42883i	−0.127343	+	0.127343i
$726$		0			0
$727$			49.3403i			1.82993i	0.403531	+	0.914966i	$0.367783\pi$
$727$			49.3403i			1.82993i	−0.403531	+	0.914966i	$0.632217\pi$
$728$		0			0
$729$			36.0197i			1.33406i
$730$		0			0
$731$	−2.68040	+	2.68040i	−0.0991383	+	0.0991383i
$732$		0			0
$733$	1.20220	+	1.20220i	0.0444044	+	0.0444044i	0.728960	−	0.684556i	$-0.240004\pi$
$733$	1.20220	+	1.20220i	0.0444044	+	0.0444044i	−0.684556	+	0.728960i	$0.740004\pi$
$734$		0			0
$735$	−34.8547			−1.28563
$736$		0			0
$737$	1.93262			0.0711888
$738$		0			0
$739$	−7.85274	−	7.85274i	−0.288868	−	0.288868i	0.547765	−	0.836632i	$-0.315479\pi$
$739$	−7.85274	−	7.85274i	−0.288868	−	0.288868i	−0.836632	+	0.547765i	$0.815479\pi$
$740$		0			0
$741$	10.7919	−	10.7919i	0.396451	−	0.396451i
$742$		0			0
$743$			39.8689i			1.46265i	0.682029	+	0.731325i	$0.261098\pi$
$743$			39.8689i			1.46265i	−0.682029	+	0.731325i	$0.738902\pi$
$744$		0			0
$745$		−	1.52985i		−	0.0560492i
$746$		0			0
$747$	47.1118	−	47.1118i	1.72373	−	1.72373i
$748$		0			0
$749$	−11.6456	−	11.6456i	−0.425523	−	0.425523i
$750$		0			0
$751$	−41.4417			−1.51223			−0.756115	−	0.654438i	$-0.772905\pi$
$751$	−41.4417			−1.51223			−0.756115	+	0.654438i	$0.772905\pi$
$752$		0			0
$753$	48.2154			1.75707
$754$		0			0
$755$	−8.64224	−	8.64224i	−0.314523	−	0.314523i
$756$		0			0
$757$	−17.2655	+	17.2655i	−0.627524	+	0.627524i	−0.947444	−	0.319921i	$-0.896344\pi$
$757$	−17.2655	+	17.2655i	−0.627524	+	0.627524i	0.319921	+	0.947444i	$0.396344\pi$
$758$		0			0
$759$		−	73.2148i		−	2.65753i
$760$		0			0
$761$			34.9189i			1.26581i	0.774230	+	0.632905i	$0.218138\pi$
$761$			34.9189i			1.26581i	−0.774230	+	0.632905i	$0.781862\pi$
$762$		0			0
$763$	−33.9594	+	33.9594i	−1.22941	+	1.22941i
$764$		0			0
$765$	1.39720	+	1.39720i	0.0505158	+	0.0505158i
$766$		0			0
$767$	−9.13256			−0.329758
$768$		0			0
$769$	−20.8099			−0.750422			−0.375211	−	0.926939i	$-0.622430\pi$
$769$	−20.8099			−0.750422			−0.375211	+	0.926939i	$0.622430\pi$
$770$		0			0
$771$	−13.4600	−	13.4600i	−0.484749	−	0.484749i
$772$		0			0
$773$	−24.0620	+	24.0620i	−0.865452	+	0.865452i	−0.991965	−	0.126513i	$-0.959621\pi$
$773$	−24.0620	+	24.0620i	−0.865452	+	0.865452i	0.126513	+	0.991965i	$0.459621\pi$
$774$		0			0
$775$			0.635674i			0.0228341i
$776$		0			0
$777$		−	56.4322i		−	2.02449i
$778$		0			0
$779$	12.5858	−	12.5858i	0.450933	−	0.450933i
$780$		0			0
$781$	−19.5206	−	19.5206i	−0.698500	−	0.698500i
$782$		0			0
$783$	36.9034			1.31882
$784$		0			0
$785$	0.404410			0.0144340
$786$		0			0
$787$	8.62124	+	8.62124i	0.307314	+	0.307314i	0.843867	−	0.536553i	$-0.180274\pi$
$787$	8.62124	+	8.62124i	0.307314	+	0.307314i	−0.536553	+	0.843867i	$0.680274\pi$
$788$		0			0
$789$	5.51664	−	5.51664i	0.196398	−	0.196398i
$790$		0			0
$791$		−	62.5499i		−	2.22402i
$792$		0			0
$793$		−	5.99751i		−	0.212978i
$794$		0			0
$795$	−13.1708	+	13.1708i	−0.467122	+	0.467122i
$796$		0			0
$797$	−18.5264	−	18.5264i	−0.656237	−	0.656237i	0.298250	−	0.954488i	$-0.403597\pi$
$797$	−18.5264	−	18.5264i	−0.656237	−	0.656237i	−0.954488	+	0.298250i	$0.903597\pi$
$798$		0			0
$799$	−1.91054			−0.0675902
$800$		0			0
$801$	−25.4933			−0.900762
$802$		0			0
$803$	−27.6200	−	27.6200i	−0.974688	−	0.974688i
$804$		0			0
$805$	20.3706	−	20.3706i	0.717971	−	0.717971i
$806$		0			0
$807$		−	50.7753i		−	1.78738i
$808$		0			0
$809$			29.0318i			1.02070i	0.859965	+	0.510352i	$0.170485\pi$
$809$			29.0318i			1.02070i	−0.859965	+	0.510352i	$0.829515\pi$
$810$		0			0
$811$	−33.1891	+	33.1891i	−1.16543	+	1.16543i	−0.182156	+	0.983270i	$0.558307\pi$
$811$	−33.1891	+	33.1891i	−1.16543	+	1.16543i	−0.983270	+	0.182156i	$0.941693\pi$
$812$		0			0
$813$	51.8863	+	51.8863i	1.81973	+	1.81973i
$814$		0			0
$815$	1.63327			0.0572110
$816$		0			0
$817$	−81.9189			−2.86598
$818$		0			0
$819$	11.7308	+	11.7308i	0.409908	+	0.409908i
$820$		0			0
$821$	24.4470	−	24.4470i	0.853206	−	0.853206i	−0.137320	−	0.990527i	$-0.543849\pi$
$821$	24.4470	−	24.4470i	0.853206	−	0.853206i	0.990527	+	0.137320i	$0.0438490\pi$
$822$		0			0
$823$		−	7.59713i		−	0.264819i	−0.991195	−	0.132410i	$-0.957729\pi$
$823$		−	7.59713i		−	0.264819i	0.991195	−	0.132410i	$-0.0422714\pi$
$824$		0			0
$825$		−	11.0452i		−	0.384546i
$826$		0			0
$827$	7.74184	−	7.74184i	0.269210	−	0.269210i	−0.559572	−	0.828782i	$-0.689034\pi$
$827$	7.74184	−	7.74184i	0.269210	−	0.269210i	0.828782	+	0.559572i	$0.189034\pi$
$828$		0			0
$829$	15.8512	+	15.8512i	0.550537	+	0.550537i	0.926596	−	0.376059i	$-0.122721\pi$
$829$	15.8512	+	15.8512i	0.550537	+	0.550537i	−0.376059	+	0.926596i	$0.622721\pi$
$830$		0			0
$831$	1.31997			0.0457894
$832$		0			0
$833$	−4.19791			−0.145449
$834$		0			0
$835$	6.73363	+	6.73363i	0.233027	+	0.233027i
$836$		0			0
$837$	3.42078	−	3.42078i	0.118240	−	0.118240i
$838$		0			0
$839$			0.821130i			0.0283486i	0.999900	+	0.0141743i	$0.00451197\pi$
$839$			0.821130i			0.0283486i	−0.999900	+	0.0141743i	$0.995488\pi$
$840$		0			0
$841$		−	5.48631i		−	0.189183i
$842$		0			0
$843$	16.3952	−	16.3952i	0.564682	−	0.564682i
$844$		0			0
$845$	−8.86334	−	8.86334i	−0.304908	−	0.304908i
$846$		0			0
$847$	13.8759			0.476782
$848$		0			0
$849$	−49.5560			−1.70076
$850$		0			0
$851$	20.7586	+	20.7586i	0.711594	+	0.711594i
$852$		0			0
$853$	13.1521	−	13.1521i	0.450318	−	0.450318i	−0.445142	−	0.895460i	$-0.646847\pi$
$853$	13.1521	−	13.1521i	0.450318	−	0.450318i	0.895460	+	0.445142i	$0.146847\pi$
$854$		0			0
$855$			42.7014i			1.46036i
$856$		0			0
$857$		−	28.1630i		−	0.962031i	−0.876712	−	0.481015i	$-0.840268\pi$
$857$		−	28.1630i		−	0.962031i	0.876712	−	0.481015i	$-0.159732\pi$
$858$		0			0
$859$	−29.0528	+	29.0528i	−0.991269	+	0.991269i	−0.999962	−	0.00869321i	$-0.997233\pi$
$859$	−29.0528	+	29.0528i	−0.991269	+	0.991269i	0.00869321	+	0.999962i	$0.497233\pi$
$860$		0			0
$861$	21.0153	+	21.0153i	0.716199	+	0.716199i
$862$		0			0
$863$	−40.4434			−1.37671			−0.688355	−	0.725374i	$-0.741667\pi$
$863$	−40.4434			−1.37671			−0.688355	+	0.725374i	$0.741667\pi$
$864$		0			0
$865$	−3.86370			−0.131370
$866$		0			0
$867$	−34.9848	−	34.9848i	−1.18814	−	1.18814i
$868$		0			0
$869$	21.6743	−	21.6743i	0.735250	−	0.735250i
$870$		0			0
$871$		−	0.349945i		−	0.0118574i
$872$		0			0
$873$			12.1735i			0.412010i
$874$		0			0
$875$	3.07313	−	3.07313i	0.103891	−	0.103891i
$876$		0			0
$877$	4.94990	+	4.94990i	0.167146	+	0.167146i	0.785724	−	0.618578i	$-0.212291\pi$
$877$	4.94990	+	4.94990i	0.167146	+	0.167146i	−0.618578	+	0.785724i	$0.712291\pi$
$878$		0			0
$879$	74.2360			2.50392
$880$		0			0
$881$	−13.6262			−0.459079			−0.229540	−	0.973299i	$-0.573722\pi$
$881$	−13.6262			−0.459079			−0.229540	+	0.973299i	$0.573722\pi$
$882$		0			0
$883$	18.9205	+	18.9205i	0.636724	+	0.636724i	0.949746	−	0.313022i	$-0.101341\pi$
$883$	18.9205	+	18.9205i	0.636724	+	0.636724i	−0.313022	+	0.949746i	$0.601341\pi$
$884$		0			0
$885$	27.7544	−	27.7544i	0.932954	−	0.932954i
$886$		0			0
$887$			9.21197i			0.309308i	0.987969	+	0.154654i	$0.0494262\pi$
$887$			9.21197i			0.309308i	−0.987969	+	0.154654i	$0.950574\pi$
$888$		0			0
$889$			89.7609i			3.01048i
$890$		0			0
$891$	−14.7186	+	14.7186i	−0.493092	+	0.493092i
$892$		0			0
$893$	−29.1952	−	29.1952i	−0.976979	−	0.976979i
$894$		0			0
$895$	25.1244			0.839815
$896$		0			0
$897$	−13.2573			−0.442647
$898$		0			0
$899$	2.17962	+	2.17962i	0.0726943	+	0.0726943i
$900$		0			0
$901$	−1.58630	+	1.58630i	−0.0528474	+	0.0528474i
$902$		0			0
$903$		−	136.785i		−	4.55193i
$904$		0			0
$905$		−	5.31444i		−	0.176658i
$906$		0			0
$907$	−14.8561	+	14.8561i	−0.493289	+	0.493289i	−0.909341	−	0.416052i	$-0.863413\pi$
$907$	−14.8561	+	14.8561i	−0.493289	+	0.493289i	0.416052	+	0.909341i	$0.363413\pi$
$908$		0			0
$909$	22.5804	+	22.5804i	0.748945	+	0.748945i
$910$		0			0
$911$	−37.0308			−1.22689			−0.613443	−	0.789739i	$-0.710216\pi$
$911$	−37.0308			−1.22689			−0.613443	+	0.789739i	$0.710216\pi$
$912$		0			0
$913$	−44.8558			−1.48451
$914$		0			0
$915$	18.2268	+	18.2268i	0.602559	+	0.602559i
$916$		0			0
$917$	9.03163	−	9.03163i	0.298251	−	0.298251i
$918$		0			0
$919$			11.8760i			0.391754i	0.980629	+	0.195877i	$0.0627553\pi$
$919$			11.8760i			0.391754i	−0.980629	+	0.195877i	$0.937245\pi$
$920$		0			0
$921$			3.96008i			0.130489i
$922$		0			0
$923$	−3.53465	+	3.53465i	−0.116345	+	0.116345i
$924$		0			0
$925$	3.13165	+	3.13165i	0.102968	+	0.102968i
$926$		0			0
$927$	16.3461			0.536875
$928$		0			0
$929$	4.07018			0.133538			0.0667691	−	0.997768i	$-0.478731\pi$
$929$	4.07018			0.133538			0.0667691	+	0.997768i	$0.478731\pi$
$930$		0			0
$931$	−64.1486	−	64.1486i	−2.10239	−	2.10239i
$932$		0			0
$933$	27.6868	−	27.6868i	0.906424	−	0.906424i
$934$		0			0
$935$		−	1.33029i		−	0.0435053i
$936$		0			0
$937$		−	51.6936i		−	1.68875i	−0.535749	−	0.844377i	$-0.679971\pi$
$937$		−	51.6936i		−	1.68875i	0.535749	−	0.844377i	$-0.320029\pi$
$938$		0			0
$939$	43.7573	−	43.7573i	1.42797	−	1.42797i
$940$		0			0
$941$	−9.45357	−	9.45357i	−0.308178	−	0.308178i	0.536025	−	0.844202i	$-0.319925\pi$
$941$	−9.45357	−	9.45357i	−0.308178	−	0.308178i	−0.844202	+	0.536025i	$0.819925\pi$
$942$		0			0
$943$	−15.4609			−0.503477
$944$		0			0
$945$	−33.0751			−1.07593
$946$		0			0
$947$	−5.12742	−	5.12742i	−0.166619	−	0.166619i	0.618873	−	0.785491i	$-0.287590\pi$
$947$	−5.12742	−	5.12742i	−0.166619	−	0.166619i	−0.785491	+	0.618873i	$0.787590\pi$
$948$		0			0
$949$	−5.00124	+	5.00124i	−0.162347	+	0.162347i
$950$		0			0
$951$			87.4723i			2.83648i
$952$		0			0
$953$		−	18.4127i		−	0.596447i	−0.954496	−	0.298224i	$-0.903606\pi$
$953$		−	18.4127i		−	0.596447i	0.954496	−	0.298224i	$-0.0963941\pi$
$954$		0			0
$955$	−10.2319	+	10.2319i	−0.331098	+	0.331098i
$956$		0			0
$957$	−37.8722	−	37.8722i	−1.22423	−	1.22423i
$958$		0			0
$959$	62.6682			2.02366
$960$		0			0
$961$	−30.5959			−0.986965
$962$		0			0
$963$	−14.9943	−	14.9943i	−0.483184	−	0.483184i
$964$		0			0
$965$	3.12460	−	3.12460i	0.100585	−	0.100585i
$966$		0			0
$967$			45.4253i			1.46078i	0.683030	+	0.730390i	$0.260662\pi$
$967$			45.4253i			1.46078i	−0.683030	+	0.730390i	$0.739338\pi$
$968$		0			0
$969$			7.90022i			0.253792i
$970$		0			0
$971$	−17.3485	+	17.3485i	−0.556740	+	0.556740i	−0.928378	−	0.371638i	$-0.878796\pi$
$971$	−17.3485	+	17.3485i	−0.556740	+	0.556740i	0.371638	+	0.928378i	$0.378796\pi$
$972$		0			0
$973$	4.29301	+	4.29301i	0.137628	+	0.137628i
$974$		0			0
$975$	−2.00000			−0.0640513
$976$		0			0
$977$	−6.98733			−0.223544			−0.111772	−	0.993734i	$-0.535653\pi$
$977$	−6.98733			−0.223544			−0.111772	+	0.993734i	$0.535653\pi$
$978$		0			0
$979$	12.1363	+	12.1363i	0.387878	+	0.387878i
$980$		0			0
$981$	−43.7242	+	43.7242i	−1.39601	+	1.39601i
$982$		0			0
$983$			29.1408i			0.929447i	0.885456	+	0.464723i	$0.153846\pi$
$983$			29.1408i			0.929447i	−0.885456	+	0.464723i	$0.846154\pi$
$984$		0			0
$985$			12.7537i			0.406368i
$986$		0			0
$987$	48.7490	−	48.7490i	1.55170	−	1.55170i
$988$		0			0
$989$	50.3164	+	50.3164i	1.59997	+	1.59997i
$990$		0			0
$991$	−47.6299			−1.51302			−0.756508	−	0.653985i	$-0.773096\pi$
$991$	−47.6299			−1.51302			−0.756508	+	0.653985i	$0.773096\pi$
$992$		0			0
$993$	90.2903			2.86528
$994$		0			0
$995$	−0.413698	−	0.413698i	−0.0131151	−	0.0131151i
$996$		0			0
$997$	31.6347	−	31.6347i	1.00188	−	1.00188i	0.00188210	−	0.999998i	$-0.499401\pi$
$997$	31.6347	−	31.6347i	1.00188	−	1.00188i	0.999998	−	0.00188210i	$-0.000599091\pi$
$998$		0			0
$999$		−	33.7050i		−	1.06638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.l.f.321.4	yes	8
4.3	odd	2		1280.2.l.a.321.1	✓	8
8.3	odd	2		1280.2.l.g.321.4	yes	8
8.5	even	2		1280.2.l.d.321.1	yes	8
16.3	odd	4		1280.2.l.g.961.4	yes	8
16.5	even	4	inner	1280.2.l.f.961.4	yes	8
16.11	odd	4		1280.2.l.a.961.1	yes	8
16.13	even	4		1280.2.l.d.961.1	yes	8
32.5	even	8		5120.2.a.b.1.1		4
32.11	odd	8		5120.2.a.a.1.1		4
32.21	even	8		5120.2.a.q.1.4		4
32.27	odd	8		5120.2.a.r.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.l.a.321.1	✓	8	4.3	odd	2
1280.2.l.a.961.1	yes	8	16.11	odd	4
1280.2.l.d.321.1	yes	8	8.5	even	2
1280.2.l.d.961.1	yes	8	16.13	even	4
1280.2.l.f.321.4	yes	8	1.1	even	1	trivial
1280.2.l.f.961.4	yes	8	16.5	even	4	inner
1280.2.l.g.321.4	yes	8	8.3	odd	2
1280.2.l.g.961.4	yes	8	16.3	odd	4
5120.2.a.a.1.1		4	32.11	odd	8
5120.2.a.b.1.1		4	32.5	even	8
5120.2.a.q.1.4		4	32.21	even	8
5120.2.a.r.1.4		4	32.27	odd	8

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07313 + 2.07313i) q^{3} +(0.707107 - 0.707107i) q^{5} +4.34607i q^{7} +5.59575i q^{9} +O(q^{10})\)	\(q+(2.07313 + 2.07313i) q^{3} +(0.707107 - 0.707107i) q^{5} +4.34607i q^{7} +5.59575i q^{9} +(2.66390 - 2.66390i) q^{11} +(-0.482362 - 0.482362i) q^{13} +2.93185 q^{15} +0.353113 q^{17} +(5.39595 + 5.39595i) q^{19} +(-9.00997 + 9.00997i) q^{21} -6.62863i q^{23} -1.00000i q^{25} +(-5.38134 + 5.38134i) q^{27} +(-3.42883 - 3.42883i) q^{29} -0.635674 q^{31} +11.0452 q^{33} +(3.07313 + 3.07313i) q^{35} +(-3.13165 + 3.13165i) q^{37} -2.00000i q^{39} -2.33245i q^{41} +(-7.59077 + 7.59077i) q^{43} +(3.95680 + 3.95680i) q^{45} -5.41057 q^{47} -11.8883 q^{49} +(0.732051 + 0.732051i) q^{51} +(-4.49233 + 4.49233i) q^{53} -3.76733i q^{55} +22.3730i q^{57} +(9.46651 - 9.46651i) q^{59} +(6.21682 + 6.21682i) q^{61} -24.3195 q^{63} -0.682163 q^{65} +(0.362741 + 0.362741i) q^{67} +(13.7420 - 13.7420i) q^{69} -7.32780i q^{71} -10.3682i q^{73} +(2.07313 - 2.07313i) q^{75} +(11.5775 + 11.5775i) q^{77} +8.13630 q^{79} -5.52520 q^{81} +(-8.41920 - 8.41920i) q^{83} +(0.249689 - 0.249689i) q^{85} -14.2168i q^{87} +4.55583i q^{89} +(2.09638 - 2.09638i) q^{91} +(-1.31784 - 1.31784i) q^{93} +7.63103 q^{95} +2.17549 q^{97} +(14.9065 + 14.9065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3}+O(q^{10}) \) 8 * q + 4 * q^3	\( 8 q + 4 q^{3} - 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} - 16 q^{21} - 8 q^{27} - 8 q^{29} + 24 q^{33} + 12 q^{35} - 8 q^{37} - 44 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{51} + 16 q^{53} + 16 q^{59} + 8 q^{61} - 48 q^{63} - 8 q^{65} + 12 q^{67} + 40 q^{69} + 4 q^{75} + 16 q^{77} + 96 q^{79} - 16 q^{81} - 28 q^{83} - 16 q^{85} + 8 q^{91} - 8 q^{93} + 8 q^{95} - 24 q^{97} + 56 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 - 16 * q^21 - 8 * q^27 - 8 * q^29 + 24 * q^33 + 12 * q^35 - 8 * q^37 - 44 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^51 + 16 * q^53 + 16 * q^59 + 8 * q^61 - 48 * q^63 - 8 * q^65 + 12 * q^67 + 40 * q^69 + 4 * q^75 + 16 * q^77 + 96 * q^79 - 16 * q^81 - 28 * q^83 - 16 * q^85 + 8 * q^91 - 8 * q^93 + 8 * q^95 - 24 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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