LMFDB - Embedded newform 960.2.bb.a.497.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(497,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("960.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bb (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.18
Character	$\chi$	$=$	960.497
Dual form			960.2.bb.a.593.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.672846 + 1.59602i) q^{3} +(-1.96698 + 1.06348i) q^{5} +(-3.58885 + 3.58885i) q^{7} +(-2.09456 - 2.14775i) q^{9} +O(q^{10})$	\(q+(-0.672846 + 1.59602i) q^{3} +(-1.96698 + 1.06348i) q^{5} +(-3.58885 + 3.58885i) q^{7} +(-2.09456 - 2.14775i) q^{9} +(-1.75370 + 1.75370i) q^{11} +1.86312i q^{13} +(-0.373870 - 3.85490i) q^{15} +(2.63049 - 2.63049i) q^{17} +(0.850543 + 0.850543i) q^{19} +(-3.31313 - 8.14261i) q^{21} +(2.34712 - 2.34712i) q^{23} +(2.73800 - 4.18370i) q^{25} +(4.83716 - 1.89785i) q^{27} +(2.25712 - 2.25712i) q^{29} -3.07693 q^{31} +(-1.61897 - 3.97892i) q^{33} +(3.24250 - 10.8759i) q^{35} +9.19181i q^{37} +(-2.97357 - 1.25359i) q^{39} -7.89015 q^{41} +1.44191 q^{43} +(6.40405 + 1.99705i) q^{45} +(3.16802 - 3.16802i) q^{47} -18.7596i q^{49} +(2.42840 + 5.96823i) q^{51} +7.55812i q^{53} +(1.58446 - 5.31453i) q^{55} +(-1.92977 + 0.785199i) q^{57} +(-3.61161 - 3.61161i) q^{59} +(-2.53592 + 2.53592i) q^{61} +(15.2250 + 0.190899i) q^{63} +(-1.98140 - 3.66471i) q^{65} -1.34890 q^{67} +(2.16680 + 5.32531i) q^{69} -11.4066 q^{71} +(4.59201 + 4.59201i) q^{73} +(4.83502 + 7.18489i) q^{75} -12.5875i q^{77} -1.73652i q^{79} +(-0.225658 + 8.99717i) q^{81} -0.755155 q^{83} +(-2.37663 + 7.97160i) q^{85} +(2.08372 + 5.12110i) q^{87} -8.15881i q^{89} +(-6.68644 - 6.68644i) q^{91} +(2.07030 - 4.91083i) q^{93} +(-2.57754 - 0.768459i) q^{95} +(1.60445 + 1.60445i) q^{97} +(7.43975 + 0.0932835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q+O(q^{10}) $ 88 * q	$ 88 q + 4 q^{15} + 8 q^{19} - 4 q^{21} + 16 q^{31} - 4 q^{33} - 24 q^{39} + 40 q^{43} + 8 q^{45} + 4 q^{51} + 12 q^{57} - 24 q^{61} + 32 q^{63} + 8 q^{67} - 12 q^{69} + 24 q^{75} - 8 q^{81} - 24 q^{85} + 12 q^{87} + 8 q^{91} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 88 * q + 4 * q^15 + 8 * q^19 - 4 * q^21 + 16 * q^31 - 4 * q^33 - 24 * q^39 + 40 * q^43 + 8 * q^45 + 4 * q^51 + 12 * q^57 - 24 * q^61 + 32 * q^63 + 8 * q^67 - 12 * q^69 + 24 * q^75 - 8 * q^81 - 24 * q^85 + 12 * q^87 + 8 * q^91 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.672846	+	1.59602i	−0.388468	+	0.921462i
$3$	−0.672846	+	1.59602i	−0.388468	+	0.921462i
$4$		0			0
$5$	−1.96698	+	1.06348i	−0.879659	+	0.475605i
$5$	−1.96698	+	1.06348i	−0.879659	+	0.475605i
$6$		0			0
$7$	−3.58885	+	3.58885i	−1.35646	+	1.35646i	−0.478212	+	0.878244i	$0.658715\pi$
$7$	−3.58885	+	3.58885i	−1.35646	+	1.35646i	−0.878244	+	0.478212i	$0.841285\pi$
$8$		0			0
$9$	−2.09456	−	2.14775i	−0.698186	−	0.715917i
$10$		0			0
$11$	−1.75370	+	1.75370i	−0.528761	+	0.528761i	−0.920203	−	0.391442i	$-0.871976\pi$
$11$	−1.75370	+	1.75370i	−0.528761	+	0.528761i	0.391442	+	0.920203i	$0.371976\pi$
$12$		0			0
$13$			1.86312i			0.516735i	0.966047	+	0.258368i	$0.0831846\pi$
$13$			1.86312i			0.516735i	−0.966047	+	0.258368i	$0.916815\pi$
$14$		0			0
$15$	−0.373870	−	3.85490i	−0.0965329	−	0.995330i
$16$		0			0
$17$	2.63049	−	2.63049i	0.637987	−	0.637987i	−0.312071	−	0.950059i	$-0.601023\pi$
$17$	2.63049	−	2.63049i	0.637987	−	0.637987i	0.950059	+	0.312071i	$0.101023\pi$
$18$		0			0
$19$	0.850543	+	0.850543i	0.195128	+	0.195128i	0.797908	−	0.602780i	$-0.205940\pi$
$19$	0.850543	+	0.850543i	0.195128	+	0.195128i	−0.602780	+	0.797908i	$0.705940\pi$
$20$		0			0
$21$	−3.31313	−	8.14261i	−0.722984	−	1.77686i
$22$		0			0
$23$	2.34712	−	2.34712i	0.489409	−	0.489409i	−0.418710	−	0.908120i	$-0.637518\pi$
$23$	2.34712	−	2.34712i	0.489409	−	0.489409i	0.908120	+	0.418710i	$0.137518\pi$
$24$		0			0
$25$	2.73800	−	4.18370i	0.547600	−	0.836740i
$26$		0			0
$27$	4.83716	−	1.89785i	0.930913	−	0.365242i
$28$		0			0
$29$	2.25712	−	2.25712i	0.419137	−	0.419137i	−0.465769	−	0.884906i	$-0.654222\pi$
$29$	2.25712	−	2.25712i	0.419137	−	0.419137i	0.884906	+	0.465769i	$0.154222\pi$
$30$		0			0
$31$	−3.07693			−0.552632			−0.276316	−	0.961067i	$-0.589114\pi$
$31$	−3.07693			−0.552632			−0.276316	+	0.961067i	$0.589114\pi$
$32$		0			0
$33$	−1.61897	−	3.97892i	−0.281827	−	0.692640i
$34$		0			0
$35$	3.24250	−	10.8759i	0.548082	−	1.83836i
$36$		0			0
$37$			9.19181i			1.51112i	0.655077	+	0.755562i	$0.272636\pi$
$37$			9.19181i			1.51112i	−0.655077	+	0.755562i	$0.727364\pi$
$38$		0			0
$39$	−2.97357	−	1.25359i	−0.476152	−	0.200735i
$40$		0			0
$41$	−7.89015			−1.23223			−0.616117	−	0.787654i	$-0.711295\pi$
$41$	−7.89015			−1.23223			−0.616117	+	0.787654i	$0.711295\pi$
$42$		0			0
$43$	1.44191			0.219889			0.109944	−	0.993938i	$-0.464933\pi$
$43$	1.44191			0.219889			0.109944	+	0.993938i	$0.464933\pi$
$44$		0			0
$45$	6.40405	+	1.99705i	0.954659	+	0.297702i
$46$		0			0
$47$	3.16802	−	3.16802i	0.462104	−	0.462104i	−0.437241	−	0.899344i	$-0.644044\pi$
$47$	3.16802	−	3.16802i	0.462104	−	0.462104i	0.899344	+	0.437241i	$0.144044\pi$
$48$		0			0
$49$		−	18.7596i		−	2.67995i
$50$		0			0
$51$	2.42840	+	5.96823i	0.340044	+	0.835719i
$52$		0			0
$53$			7.55812i			1.03819i	0.854717	+	0.519094i	$0.173731\pi$
$53$			7.55812i			1.03819i	−0.854717	+	0.519094i	$0.826269\pi$
$54$		0			0
$55$	1.58446	−	5.31453i	0.213648	−	0.716611i
$56$		0			0
$57$	−1.92977	+	0.785199i	−0.255604	+	0.104002i
$58$		0			0
$59$	−3.61161	−	3.61161i	−0.470191	−	0.470191i	0.431785	−	0.901976i	$-0.357884\pi$
$59$	−3.61161	−	3.61161i	−0.470191	−	0.470191i	−0.901976	+	0.431785i	$0.857884\pi$
$60$		0			0
$61$	−2.53592	+	2.53592i	−0.324691	+	0.324691i	−0.850563	−	0.525872i	$-0.823739\pi$
$61$	−2.53592	+	2.53592i	−0.324691	+	0.324691i	0.525872	+	0.850563i	$0.323739\pi$
$62$		0			0
$63$	15.2250	+	0.190899i	1.91817	+	0.0240510i
$64$		0			0
$65$	−1.98140	−	3.66471i	−0.245762	−	0.454551i
$66$		0			0
$67$	−1.34890			−0.164794			−0.0823972	−	0.996600i	$-0.526258\pi$
$67$	−1.34890			−0.164794			−0.0823972	+	0.996600i	$0.526258\pi$
$68$		0			0
$69$	2.16680	+	5.32531i	0.260853	+	0.641092i
$70$		0			0
$71$	−11.4066			−1.35371			−0.676856	−	0.736116i	$-0.736658\pi$
$71$	−11.4066			−1.35371			−0.676856	+	0.736116i	$0.736658\pi$
$72$		0			0
$73$	4.59201	+	4.59201i	0.537454	+	0.537454i	0.922780	−	0.385327i	$-0.125911\pi$
$73$	4.59201	+	4.59201i	0.537454	+	0.537454i	−0.385327	+	0.922780i	$0.625911\pi$
$74$		0			0
$75$	4.83502	+	7.18489i	0.558300	+	0.829639i
$76$		0			0
$77$		−	12.5875i		−	1.43448i
$78$		0			0
$79$		−	1.73652i		−	0.195374i	−0.995217	−	0.0976870i	$-0.968856\pi$
$79$		−	1.73652i		−	0.195374i	0.995217	−	0.0976870i	$-0.0311444\pi$
$80$		0			0
$81$	−0.225658	+	8.99717i	−0.0250731	+	0.999686i
$82$		0			0
$83$	−0.755155			−0.0828890			−0.0414445	−	0.999141i	$-0.513196\pi$
$83$	−0.755155			−0.0828890			−0.0414445	+	0.999141i	$0.513196\pi$
$84$		0			0
$85$	−2.37663	+	7.97160i	−0.257781	+	0.864641i
$86$		0			0
$87$	2.08372	+	5.12110i	0.223398	+	0.549040i
$88$		0			0
$89$		−	8.15881i		−	0.864832i	−0.901674	−	0.432416i	$-0.857661\pi$
$89$		−	8.15881i		−	0.864832i	0.901674	−	0.432416i	$-0.142339\pi$
$90$		0			0
$91$	−6.68644	−	6.68644i	−0.700929	−	0.700929i
$92$		0			0
$93$	2.07030	−	4.91083i	0.214680	−	0.509230i
$94$		0			0
$95$	−2.57754	−	0.768459i	−0.264450	−	0.0788422i
$96$		0			0
$97$	1.60445	+	1.60445i	0.162908	+	0.162908i	0.783853	−	0.620946i	$-0.213251\pi$
$97$	1.60445	+	1.60445i	0.162908	+	0.162908i	−0.620946	+	0.783853i	$0.713251\pi$
$98$		0			0
$99$	7.43975	+	0.0932835i	0.747723	+	0.00937535i
$100$		0			0
$101$	3.42953	−	3.42953i	0.341251	−	0.341251i	−0.515587	−	0.856837i	$-0.672426\pi$
$101$	3.42953	−	3.42953i	0.341251	−	0.341251i	0.856837	+	0.515587i	$0.172426\pi$
$102$		0			0
$103$	−12.9263	−	12.9263i	−1.27367	−	1.27367i	−0.944147	−	0.329524i	$-0.893112\pi$
$103$	−12.9263	−	12.9263i	−1.27367	−	1.27367i	−0.329524	−	0.944147i	$-0.606888\pi$
$104$		0			0
$105$	15.1764	+	12.4929i	1.48106	+	1.21918i
$106$		0			0
$107$	−5.97350			−0.577480			−0.288740	−	0.957407i	$-0.593236\pi$
$107$	−5.97350			−0.577480			−0.288740	+	0.957407i	$0.593236\pi$
$108$		0			0
$109$	−0.559509	−	0.559509i	−0.0535912	−	0.0535912i	0.679803	−	0.733395i	$-0.262065\pi$
$109$	−0.559509	−	0.559509i	−0.0535912	−	0.0535912i	−0.733395	+	0.679803i	$0.762065\pi$
$110$		0			0
$111$	−14.6703	−	6.18467i	−1.39244	−	0.587023i
$112$		0			0
$113$	−4.78740	−	4.78740i	−0.450361	−	0.450361i	0.445113	−	0.895474i	$-0.353163\pi$
$113$	−4.78740	−	4.78740i	−0.450361	−	0.450361i	−0.895474	+	0.445113i	$0.853163\pi$
$114$		0			0
$115$	−2.12061	+	7.11287i	−0.197748	+	0.663279i
$116$		0			0
$117$	4.00151	−	3.90240i	0.369939	−	0.360777i
$118$		0			0
$119$			18.8808i			1.73080i
$120$		0			0
$121$			4.84905i			0.440823i
$122$		0			0
$123$	5.30886	−	12.5928i	0.478683	−	1.13546i
$124$		0			0
$125$	−0.936283	+	11.1411i	−0.0837437	+	0.996487i
$126$		0			0
$127$	4.13372	+	4.13372i	0.366808	+	0.366808i	0.866312	−	0.499503i	$-0.166484\pi$
$127$	4.13372	+	4.13372i	0.366808	+	0.366808i	−0.499503	+	0.866312i	$0.666484\pi$
$128$		0			0
$129$	−0.970181	+	2.30131i	−0.0854197	+	0.202619i
$130$		0			0
$131$	−5.97669	−	5.97669i	−0.522186	−	0.522186i	0.396045	−	0.918231i	$-0.370382\pi$
$131$	−5.97669	−	5.97669i	−0.522186	−	0.522186i	−0.918231	+	0.396045i	$0.870382\pi$
$132$		0			0
$133$	−6.10494			−0.529365
$134$		0			0
$135$	−7.49626	+	8.87728i	−0.645175	+	0.764035i
$136$		0			0
$137$	8.98602	+	8.98602i	0.767727	+	0.767727i	0.977706	−	0.209979i	$-0.0673395\pi$
$137$	8.98602	+	8.98602i	0.767727	+	0.767727i	−0.209979	+	0.977706i	$0.567339\pi$
$138$		0			0
$139$	12.1554	−	12.1554i	1.03100	−	1.03100i	0.0315006	−	0.999504i	$-0.489971\pi$
$139$	12.1554	−	12.1554i	1.03100	−	1.03100i	0.999504	−	0.0315006i	$-0.0100286\pi$
$140$		0			0
$141$	2.92464	+	7.18782i	0.246299	+	0.605324i
$142$		0			0
$143$	−3.26735	−	3.26735i	−0.273230	−	0.273230i
$144$		0			0
$145$	−2.03929	+	6.84012i	−0.169354	+	0.568041i
$146$		0			0
$147$	29.9408	+	12.6223i	2.46947	+	1.04107i
$148$		0			0
$149$	−8.45496	−	8.45496i	−0.692657	−	0.692657i	0.270159	−	0.962816i	$-0.412924\pi$
$149$	−8.45496	−	8.45496i	−0.692657	−	0.692657i	−0.962816	+	0.270159i	$0.912924\pi$
$150$		0			0
$151$		−	2.95291i		−	0.240305i	−0.992755	−	0.120152i	$-0.961662\pi$
$151$		−	2.95291i		−	0.240305i	0.992755	−	0.120152i	$-0.0383383\pi$
$152$		0			0
$153$	−11.1593	−	0.139922i	−0.902179	−	0.0113120i
$154$		0			0
$155$	6.05224	−	3.27226i	0.486128	−	0.262835i
$156$		0			0
$157$	1.25890			0.100471			0.0502355	−	0.998737i	$-0.484003\pi$
$157$	1.25890			0.100471			0.0502355	+	0.998737i	$0.484003\pi$
$158$		0			0
$159$	−12.0629	−	5.08545i	−0.956651	−	0.403302i
$160$		0			0
$161$			16.8469i			1.32773i
$162$		0			0
$163$			4.52220i			0.354206i	0.984192	+	0.177103i	$0.0566726\pi$
$163$			4.52220i			0.354206i	−0.984192	+	0.177103i	$0.943327\pi$
$164$		0			0
$165$	7.41600	+	6.10468i	0.577335	+	0.475249i
$166$		0			0
$167$	−11.2815	−	11.2815i	−0.872992	−	0.872992i	0.119806	−	0.992797i	$-0.461773\pi$
$167$	−11.2815	−	11.2815i	−0.872992	−	0.872992i	−0.992797	+	0.119806i	$0.961773\pi$
$168$		0			0
$169$	9.52880			0.732985
$170$		0			0
$171$	0.0452423	−	3.60826i	0.00345977	−	0.275931i
$172$		0			0
$173$	−18.7329			−1.42424			−0.712118	−	0.702060i	$-0.752264\pi$
$173$	−18.7329			−1.42424			−0.712118	+	0.702060i	$0.752264\pi$
$174$		0			0
$175$	5.18840	+	24.8409i	0.392206	+	1.87780i
$176$		0			0
$177$	8.19425	−	3.33414i	0.615917	−	0.250609i
$178$		0			0
$179$	−0.555823	+	0.555823i	−0.0415441	+	0.0415441i	−0.727574	−	0.686030i	$-0.759352\pi$
$179$	−0.555823	+	0.555823i	−0.0415441	+	0.0415441i	0.686030	+	0.727574i	$0.259352\pi$
$180$		0			0
$181$	−8.29080	−	8.29080i	−0.616251	−	0.616251i	0.328317	−	0.944568i	$-0.393519\pi$
$181$	−8.29080	−	8.29080i	−0.616251	−	0.616251i	−0.944568	+	0.328317i	$0.893519\pi$
$182$		0			0
$183$	−2.34109	−	5.75366i	−0.173059	−	0.425323i
$184$		0			0
$185$	−9.77535	−	18.0801i	−0.718698	−	1.32927i
$186$		0			0
$187$			9.22619i			0.674686i
$188$		0			0
$189$	−10.5487	+	24.1709i	−0.767309	+	1.75818i
$190$		0			0
$191$			26.3360i			1.90561i	0.303584	+	0.952805i	$0.401817\pi$
$191$			26.3360i			1.90561i	−0.303584	+	0.952805i	$0.598183\pi$
$192$		0			0
$193$	7.13109	−	7.13109i	0.513307	−	0.513307i	−0.402231	−	0.915538i	$-0.631765\pi$
$193$	7.13109	−	7.13109i	0.513307	−	0.513307i	0.915538	+	0.402231i	$0.131765\pi$
$194$		0			0
$195$	7.18212	−	0.696564i	0.514322	−	0.0498820i
$196$		0			0
$197$	−13.1631			−0.937832			−0.468916	−	0.883243i	$-0.655355\pi$
$197$	−13.1631			−0.937832			−0.468916	+	0.883243i	$0.655355\pi$
$198$		0			0
$199$	17.4015			1.23356			0.616779	−	0.787136i	$-0.288437\pi$
$199$	17.4015			1.23356			0.616779	+	0.787136i	$0.288437\pi$
$200$		0			0
$201$	0.907602	−	2.15287i	0.0640173	−	0.151852i
$202$		0			0
$203$			16.2009i			1.13708i
$204$		0			0
$205$	15.5198	−	8.39106i	1.08395	−	0.586057i
$206$		0			0
$207$	−9.95722	−	0.124849i	−0.692075	−	0.00867761i
$208$		0			0
$209$	−2.98320			−0.206352
$210$		0			0
$211$	−11.7376	+	11.7376i	−0.808049	+	0.808049i	−0.984338	−	0.176289i	$-0.943591\pi$
$211$	−11.7376	+	11.7376i	−0.808049	+	0.808049i	0.176289	+	0.984338i	$0.443591\pi$
$212$		0			0
$213$	7.67486	−	18.2051i	0.525873	−	1.24739i
$214$		0			0
$215$	−2.83620	+	1.53345i	−0.193427	+	0.104580i
$216$		0			0
$217$	11.0426	−	11.0426i	0.749622	−	0.749622i
$218$		0			0
$219$	−10.4186	+	4.23922i	−0.704027	+	0.286460i
$220$		0			0
$221$	4.90091	+	4.90091i	0.329671	+	0.329671i
$222$		0			0
$223$	6.61949	−	6.61949i	0.443274	−	0.443274i	−0.449837	−	0.893111i	$-0.648518\pi$
$223$	6.61949	−	6.61949i	0.443274	−	0.443274i	0.893111	+	0.449837i	$0.148518\pi$
$224$		0			0
$225$	−14.7204	+	2.88246i	−0.981363	+	0.192164i
$226$		0			0
$227$			28.7764i			1.90996i	0.296677	+	0.954978i	$0.404121\pi$
$227$			28.7764i			1.90996i	−0.296677	+	0.954978i	$0.595879\pi$
$228$		0			0
$229$	−9.08971	+	9.08971i	−0.600665	+	0.600665i	−0.940489	−	0.339824i	$-0.889632\pi$
$229$	−9.08971	+	9.08971i	−0.600665	+	0.600665i	0.339824	+	0.940489i	$0.389632\pi$
$230$		0			0
$231$	20.0900	+	8.46947i	1.32182	+	0.557250i
$232$		0			0
$233$	−12.4047	+	12.4047i	−0.812662	+	0.812662i	−0.985032	−	0.172370i	$-0.944857\pi$
$233$	−12.4047	+	12.4047i	−0.812662	+	0.812662i	0.172370	+	0.985032i	$0.444857\pi$
$234$		0			0
$235$	−2.86229	+	9.60058i	−0.186715	+	0.626273i
$236$		0			0
$237$	2.77152	+	1.16841i	0.180030	+	0.0758965i
$238$		0			0
$239$	−17.8479			−1.15448			−0.577242	−	0.816573i	$-0.695871\pi$
$239$	−17.8479			−1.15448			−0.577242	+	0.816573i	$0.695871\pi$
$240$		0			0
$241$	−15.1589			−0.976472			−0.488236	−	0.872712i	$-0.662359\pi$
$241$	−15.1589			−0.976472			−0.488236	+	0.872712i	$0.662359\pi$
$242$		0			0
$243$	−14.2078	−	6.41386i	−0.911433	−	0.411449i
$244$		0			0
$245$	19.9506	+	36.8998i	1.27460	+	2.35744i
$246$		0			0
$247$	−1.58466	+	1.58466i	−0.100829	+	0.100829i
$248$		0			0
$249$	0.508102	−	1.20524i	0.0321997	−	0.0763791i
$250$		0			0
$251$	6.03931	−	6.03931i	0.381198	−	0.381198i	−0.490336	−	0.871534i	$-0.663126\pi$
$251$	6.03931	−	6.03931i	0.381198	−	0.381198i	0.871534	+	0.490336i	$0.163126\pi$
$252$		0			0
$253$			8.23232i			0.517561i
$254$		0			0
$255$	−11.1237	−	9.15680i	−0.696595	−	0.573421i
$256$		0			0
$257$	−8.85518	+	8.85518i	−0.552371	+	0.552371i	−0.927125	−	0.374753i	$-0.877727\pi$
$257$	−8.85518	+	8.85518i	−0.552371	+	0.552371i	0.374753	+	0.927125i	$0.377727\pi$
$258$		0			0
$259$	−32.9880	−	32.9880i	−2.04978	−	2.04978i
$260$		0			0
$261$	−9.57540	−	0.120062i	−0.592702	−	0.00743162i
$262$		0			0
$263$	9.98311	−	9.98311i	0.615585	−	0.615585i	−0.328811	−	0.944396i	$-0.606648\pi$
$263$	9.98311	−	9.98311i	0.615585	−	0.615585i	0.944396	+	0.328811i	$0.106648\pi$
$264$		0			0
$265$	−8.03795	−	14.8667i	−0.493767	−	0.913252i
$266$		0			0
$267$	13.0216	+	5.48962i	0.796910	+	0.335959i
$268$		0			0
$269$	15.2141	−	15.2141i	0.927622	−	0.927622i	−0.0699303	−	0.997552i	$-0.522278\pi$
$269$	15.2141	−	15.2141i	0.927622	−	0.927622i	0.997552	+	0.0699303i	$0.0222777\pi$
$270$		0			0
$271$	22.8247			1.38650			0.693251	−	0.720697i	$-0.256178\pi$
$271$	22.8247			1.38650			0.693251	+	0.720697i	$0.256178\pi$
$272$		0			0
$273$	15.1706	−	6.17274i	0.918168	−	0.373592i
$274$		0			0
$275$	2.53533	+	12.1386i	0.152886	+	0.731986i
$276$		0			0
$277$			6.36620i			0.382508i	0.981541	+	0.191254i	$0.0612554\pi$
$277$			6.36620i			0.382508i	−0.981541	+	0.191254i	$0.938745\pi$
$278$		0			0
$279$	6.44480	+	6.60847i	0.385840	+	0.395639i
$280$		0			0
$281$	9.37349			0.559175			0.279588	−	0.960120i	$-0.409802\pi$
$281$	9.37349			0.559175			0.279588	+	0.960120i	$0.409802\pi$
$282$		0			0
$283$	17.2536			1.02562			0.512810	−	0.858502i	$-0.328604\pi$
$283$	17.2536			1.02562			0.512810	+	0.858502i	$0.328604\pi$
$284$		0			0
$285$	2.96076	−	3.59675i	0.175380	−	0.213053i
$286$		0			0
$287$	28.3166	−	28.3166i	1.67147	−	1.67147i
$288$		0			0
$289$			3.16105i			0.185944i
$290$		0			0
$291$	−3.64029	+	1.48119i	−0.213397	+	0.0868288i
$292$		0			0
$293$		−	28.2155i		−	1.64837i	−0.566322	−	0.824184i	$-0.691634\pi$
$293$		−	28.2155i		−	1.64837i	0.566322	−	0.824184i	$-0.308366\pi$
$294$		0			0
$295$	10.9448	+	3.26306i	0.637233	+	0.189983i
$296$		0			0
$297$	−5.15468	+	11.8112i	−0.299105	+	0.685356i
$298$		0			0
$299$	4.37296	+	4.37296i	0.252895	+	0.252895i
$300$		0			0
$301$	−5.17478	+	5.17478i	−0.298270	+	0.298270i
$302$		0			0
$303$	3.16605	+	7.78114i	0.181885	+	0.447015i
$304$		0			0
$305$	2.29118	−	7.68501i	0.131193	−	0.440042i
$306$		0			0
$307$	−4.66927			−0.266489			−0.133245	−	0.991083i	$-0.542540\pi$
$307$	−4.66927			−0.266489			−0.133245	+	0.991083i	$0.542540\pi$
$308$		0			0
$309$	29.3281	−	11.9333i	1.66842	−	0.678860i
$310$		0			0
$311$	11.8492			0.671907			0.335953	−	0.941879i	$-0.390942\pi$
$311$	11.8492			0.671907			0.335953	+	0.941879i	$0.390942\pi$
$312$		0			0
$313$	8.99137	+	8.99137i	0.508222	+	0.508222i	0.913980	−	0.405758i	$-0.132993\pi$
$313$	8.99137	+	8.99137i	0.508222	+	0.508222i	−0.405758	+	0.913980i	$0.632993\pi$
$314$		0			0
$315$	−30.1502	+	15.8161i	−1.69877	+	0.891134i
$316$		0			0
$317$			12.4217i			0.697669i	0.937184	+	0.348835i	$0.113423\pi$
$317$			12.4217i			0.697669i	−0.937184	+	0.348835i	$0.886577\pi$
$318$		0			0
$319$			7.91664i			0.443247i
$320$		0			0
$321$	4.01925	−	9.53383i	0.224332	−	0.532126i
$322$		0			0
$323$	4.47469			0.248978
$324$		0			0
$325$	7.79472	+	5.10121i	0.432373	+	0.282964i
$326$		0			0
$327$	1.26945	−	0.516524i	0.0702007	−	0.0285638i
$328$		0			0
$329$			22.7391i			1.25365i
$330$		0			0
$331$	−6.81900	−	6.81900i	−0.374806	−	0.374806i	0.494418	−	0.869224i	$-0.335381\pi$
$331$	−6.81900	−	6.81900i	−0.374806	−	0.374806i	−0.869224	+	0.494418i	$0.835381\pi$
$332$		0			0
$333$	19.7417	−	19.2528i	1.08184	−	1.05505i
$334$		0			0
$335$	2.65326	−	1.43453i	0.144963	−	0.0783770i
$336$		0			0
$337$	−6.86691	−	6.86691i	−0.374064	−	0.374064i	0.494891	−	0.868955i	$-0.335208\pi$
$337$	−6.86691	−	6.86691i	−0.374064	−	0.374064i	−0.868955	+	0.494891i	$0.835208\pi$
$338$		0			0
$339$	10.8620	−	4.41960i	0.589941	−	0.240040i
$340$		0			0
$341$	5.39601	−	5.39601i	0.292211	−	0.292211i
$342$		0			0
$343$	42.2036	+	42.2036i	2.27878	+	2.27878i
$344$		0			0
$345$	−9.92544	−	8.17040i	−0.534368	−	0.439880i
$346$		0			0
$347$	−22.0820			−1.18543			−0.592713	−	0.805414i	$-0.701943\pi$
$347$	−22.0820			−1.18543			−0.592713	+	0.805414i	$0.701943\pi$
$348$		0			0
$349$	−20.0088	−	20.0088i	−1.07105	−	1.07105i	−0.997275	−	0.0737742i	$-0.976496\pi$
$349$	−20.0088	−	20.0088i	−1.07105	−	1.07105i	−0.0737742	−	0.997275i	$-0.523504\pi$
$350$		0			0
$351$	3.53592	+	9.01220i	0.188733	+	0.481036i
$352$		0			0
$353$	8.38668	+	8.38668i	0.446378	+	0.446378i	0.894149	−	0.447770i	$-0.147782\pi$
$353$	8.38668	+	8.38668i	0.446378	+	0.446378i	−0.447770	+	0.894149i	$0.647782\pi$
$354$		0			0
$355$	22.4365	−	12.1307i	1.19080	−	0.643832i
$356$		0			0
$357$	−30.1342	−	12.7039i	−1.59487	−	0.672361i
$358$		0			0
$359$		−	5.32243i		−	0.280907i	−0.990087	−	0.140454i	$-0.955144\pi$
$359$		−	5.32243i		−	0.280907i	0.990087	−	0.140454i	$-0.0448561\pi$
$360$		0			0
$361$		−	17.5532i		−	0.923850i
$362$		0			0
$363$	−7.73918	−	3.26266i	−0.406202	−	0.171245i
$364$		0			0
$365$	−13.9159	−	4.14884i	−0.728391	−	0.217160i
$366$		0			0
$367$	−8.73756	−	8.73756i	−0.456097	−	0.456097i	0.441275	−	0.897372i	$-0.354526\pi$
$367$	−8.73756	−	8.73756i	−0.456097	−	0.456097i	−0.897372	+	0.441275i	$0.854526\pi$
$368$		0			0
$369$	16.5264	+	16.9461i	0.860329	+	0.882177i
$370$		0			0
$371$	−27.1249	−	27.1249i	−1.40826	−	1.40826i
$372$		0			0
$373$	20.2482			1.04841			0.524205	−	0.851592i	$-0.324362\pi$
$373$	20.2482			1.04841			0.524205	+	0.851592i	$0.324362\pi$
$374$		0			0
$375$	−17.1514	−	8.99054i	−0.885694	−	0.464270i
$376$		0			0
$377$	4.20528	+	4.20528i	0.216583	+	0.216583i
$378$		0			0
$379$	−18.8709	+	18.8709i	−0.969332	+	0.969332i	−0.999544	−	0.0302112i	$-0.990382\pi$
$379$	−18.8709	+	18.8709i	−0.969332	+	0.969332i	0.0302112	+	0.999544i	$0.490382\pi$
$380$		0			0
$381$	−9.37886	+	3.81614i	−0.480493	+	0.195507i
$382$		0			0
$383$	−16.3590	−	16.3590i	−0.835906	−	0.835906i	0.152411	−	0.988317i	$-0.451296\pi$
$383$	−16.3590	−	16.3590i	−0.835906	−	0.835906i	−0.988317	+	0.152411i	$0.951296\pi$
$384$		0			0
$385$	13.3867	+	24.7594i	0.682247	+	1.26186i
$386$		0			0
$387$	−3.02016	−	3.09686i	−0.153523	−	0.157422i
$388$		0			0
$389$	−6.57439	−	6.57439i	−0.333335	−	0.333335i	0.520517	−	0.853851i	$-0.325739\pi$
$389$	−6.57439	−	6.57439i	−0.333335	−	0.333335i	−0.853851	+	0.520517i	$0.825739\pi$
$390$		0			0
$391$		−	12.3482i		−	0.624474i
$392$		0			0
$393$	13.5603	−	5.51753i	0.684027	−	0.278322i
$394$		0			0
$395$	1.84677	+	3.41570i	0.0929208	+	0.171863i
$396$		0			0
$397$	−32.0317			−1.60762			−0.803812	−	0.594883i	$-0.797198\pi$
$397$	−32.0317			−1.60762			−0.803812	+	0.594883i	$0.797198\pi$
$398$		0			0
$399$	4.10768	−	9.74360i	0.205641	−	0.487790i
$400$		0			0
$401$		−	13.7490i		−	0.686591i	−0.939227	−	0.343295i	$-0.888457\pi$
$401$		−	13.7490i		−	0.686591i	0.939227	−	0.343295i	$-0.111543\pi$
$402$		0			0
$403$		−	5.73267i		−	0.285565i
$404$		0			0
$405$	−9.12449	−	17.9372i	−0.453400	−	0.891307i
$406$		0			0
$407$	−16.1197	−	16.1197i	−0.799024	−	0.799024i
$408$		0			0
$409$	−26.0398			−1.28759			−0.643793	−	0.765200i	$-0.722640\pi$
$409$	−26.0398			−1.28759			−0.643793	+	0.765200i	$0.722640\pi$
$410$		0			0
$411$	−20.3881	+	8.29566i	−1.00567	+	0.409195i
$412$		0			0
$413$	25.9230			1.27559
$414$		0			0
$415$	1.48537	−	0.803095i	0.0729140	−	0.0394224i
$416$		0			0
$417$	11.2215	+	27.5789i	0.549520	+	1.35054i
$418$		0			0
$419$	6.26684	−	6.26684i	0.306155	−	0.306155i	−0.537261	−	0.843416i	$-0.680541\pi$
$419$	6.26684	−	6.26684i	0.306155	−	0.306155i	0.843416	+	0.537261i	$0.180541\pi$
$420$		0			0
$421$	5.48981	+	5.48981i	0.267557	+	0.267557i	0.828115	−	0.560558i	$-0.189413\pi$
$421$	5.48981	+	5.48981i	0.267557	+	0.267557i	−0.560558	+	0.828115i	$0.689413\pi$
$422$		0			0
$423$	−13.4397	−	0.168515i	−0.653462	−	0.00819346i
$424$		0			0
$425$	−3.80290	−	18.2075i	−0.184468	−	0.883192i
$426$		0			0
$427$		−	18.2020i		−	0.880859i
$428$		0			0
$429$	7.41318	−	3.01633i	0.357912	−	0.145630i
$430$		0			0
$431$			25.7055i			1.23819i	0.785316	+	0.619095i	$0.212500\pi$
$431$			25.7055i			1.23819i	−0.785316	+	0.619095i	$0.787500\pi$
$432$		0			0
$433$	−16.3977	+	16.3977i	−0.788023	+	0.788023i	−0.981170	−	0.193147i	$-0.938131\pi$
$433$	−16.3977	+	16.3977i	−0.788023	+	0.788023i	0.193147	+	0.981170i	$0.438131\pi$
$434$		0			0
$435$	−9.54484	−	7.85710i	−0.457640	−	0.376719i
$436$		0			0
$437$	3.99266			0.190995
$438$		0			0
$439$	−17.1043			−0.816342			−0.408171	−	0.912906i	$-0.633833\pi$
$439$	−17.1043			−0.816342			−0.408171	+	0.912906i	$0.633833\pi$
$440$		0			0
$441$	−40.2910	+	39.2932i	−1.91862	+	1.87110i
$442$		0			0
$443$		−	20.7177i		−	0.984328i	−0.870502	−	0.492164i	$-0.836206\pi$
$443$		−	20.7177i		−	0.984328i	0.870502	−	0.492164i	$-0.163794\pi$
$444$		0			0
$445$	8.67677	+	16.0482i	0.411318	+	0.760757i
$446$		0			0
$447$	19.1832	−	7.80540i	0.907332	−	0.369183i
$448$		0			0
$449$	−9.19887			−0.434121			−0.217061	−	0.976158i	$-0.569647\pi$
$449$	−9.19887			−0.434121			−0.217061	+	0.976158i	$0.569647\pi$
$450$		0			0
$451$	13.8370	−	13.8370i	0.651558	−	0.651558i
$452$		0			0
$453$	4.71291	+	1.98685i	0.221432	+	0.0933506i
$454$		0			0
$455$	20.2630	+	6.04115i	0.949944	+	0.283213i
$456$		0			0
$457$	14.7004	−	14.7004i	0.687654	−	0.687654i	−0.274059	−	0.961713i	$-0.588366\pi$
$457$	14.7004	−	14.7004i	0.687654	−	0.687654i	0.961713	+	0.274059i	$0.0883662\pi$
$458$		0			0
$459$	7.73183	−	17.7164i	0.360891	−	0.826930i
$460$		0			0
$461$	−9.02405	−	9.02405i	−0.420292	−	0.420292i	0.465012	−	0.885304i	$-0.346050\pi$
$461$	−9.02405	−	9.02405i	−0.420292	−	0.420292i	−0.885304	+	0.465012i	$0.846050\pi$
$462$		0			0
$463$	−9.23314	+	9.23314i	−0.429100	+	0.429100i	−0.888322	−	0.459222i	$-0.848128\pi$
$463$	−9.23314	+	9.23314i	−0.429100	+	0.429100i	0.459222	+	0.888322i	$0.348128\pi$
$464$		0			0
$465$	1.15037	+	11.8612i	0.0533472	+	0.550051i
$466$		0			0
$467$		−	12.0452i		−	0.557385i	−0.960380	−	0.278693i	$-0.910099\pi$
$467$		−	12.0452i		−	0.557385i	0.960380	−	0.278693i	$-0.0899011\pi$
$468$		0			0
$469$	4.84100	−	4.84100i	0.223536	−	0.223536i
$470$		0			0
$471$	−0.847043	+	2.00922i	−0.0390297	+	0.0925802i
$472$		0			0
$473$	−2.52868	+	2.52868i	−0.116269	+	0.116269i
$474$		0			0
$475$	5.88720	−	1.22963i	0.270123	−	0.0564193i
$476$		0			0
$477$	16.2330	−	15.8309i	0.743256	−	0.724848i
$478$		0			0
$479$	14.5523			0.664913			0.332456	−	0.943119i	$-0.392123\pi$
$479$	14.5523			0.664913			0.332456	+	0.943119i	$0.392123\pi$
$480$		0			0
$481$	−17.1254			−0.780851
$482$		0			0
$483$	−26.8881	−	11.3354i	−1.22345	−	0.515778i
$484$		0			0
$485$	−4.86223	−	1.44961i	−0.220783	−	0.0658235i
$486$		0			0
$487$	8.60134	−	8.60134i	0.389764	−	0.389764i	−0.484839	−	0.874603i	$-0.661122\pi$
$487$	8.60134	−	8.60134i	0.389764	−	0.389764i	0.874603	+	0.484839i	$0.161122\pi$
$488$		0			0
$489$	−7.21752	−	3.04274i	−0.326388	−	0.137598i
$490$		0			0
$491$	16.4513	−	16.4513i	0.742438	−	0.742438i	−0.230609	−	0.973047i	$-0.574072\pi$
$491$	16.4513	−	16.4513i	0.742438	−	0.742438i	0.973047	+	0.230609i	$0.0740718\pi$
$492$		0			0
$493$		−	11.8747i		−	0.534808i
$494$		0			0
$495$	−14.7330	+	7.72857i	−0.662200	+	0.347373i
$496$		0			0
$497$	40.9364	−	40.9364i	1.83625	−	1.83625i
$498$		0			0
$499$	−4.28594	−	4.28594i	−0.191865	−	0.191865i	0.604637	−	0.796501i	$-0.293318\pi$
$499$	−4.28594	−	4.28594i	−0.191865	−	0.191865i	−0.796501	+	0.604637i	$0.793318\pi$
$500$		0			0
$501$	25.5963	−	10.4148i	1.14356	−	0.465300i
$502$		0			0
$503$	7.60889	−	7.60889i	0.339264	−	0.339264i	−0.516827	−	0.856090i	$-0.672887\pi$
$503$	7.60889	−	7.60889i	0.339264	−	0.339264i	0.856090	+	0.516827i	$0.172887\pi$
$504$		0			0
$505$	−3.09855	+	10.3931i	−0.137884	+	0.462485i
$506$		0			0
$507$	−6.41141	+	15.2082i	−0.284741	+	0.675418i
$508$		0			0
$509$	−24.7598	+	24.7598i	−1.09746	+	1.09746i	−0.102754	+	0.994707i	$0.532765\pi$
$509$	−24.7598	+	24.7598i	−1.09746	+	1.09746i	−0.994707	+	0.102754i	$0.967235\pi$
$510$		0			0
$511$	−32.9600			−1.45807
$512$		0			0
$513$	5.72842	+	2.50001i	0.252916	+	0.110378i
$514$		0			0
$515$	39.1728	+	11.6789i	1.72616	+	0.514632i
$516$		0			0
$517$			11.1115i			0.488685i
$518$		0			0
$519$	12.6043	−	29.8981i	0.553269	−	1.31238i
$520$		0			0
$521$	16.6628			0.730011			0.365005	−	0.931005i	$-0.381067\pi$
$521$	16.6628			0.730011			0.365005	+	0.931005i	$0.381067\pi$
$522$		0			0
$523$	−33.6498			−1.47140			−0.735702	−	0.677305i	$-0.763148\pi$
$523$	−33.6498			−1.47140			−0.735702	+	0.677305i	$0.763148\pi$
$524$		0			0
$525$	−43.1376	−	8.43333i	−1.88268	−	0.368060i
$526$		0			0
$527$	−8.09382	+	8.09382i	−0.352572	+	0.352572i
$528$		0			0
$529$			11.9820i			0.520957i
$530$		0			0
$531$	−0.192110	+	15.3215i	−0.00833685	+	0.664898i
$532$		0			0
$533$		−	14.7003i		−	0.636739i
$534$		0			0
$535$	11.7497	−	6.35273i	0.507986	−	0.274652i
$536$		0			0
$537$	−0.513121	−	1.26109i	−0.0221428	−	0.0544199i
$538$		0			0
$539$	32.8988	+	32.8988i	1.41705	+	1.41705i
$540$		0			0
$541$	10.3993	−	10.3993i	0.447100	−	0.447100i	−0.447289	−	0.894389i	$-0.647611\pi$
$541$	10.3993	−	10.3993i	0.447100	−	0.447100i	0.894389	+	0.447289i	$0.147611\pi$
$542$		0			0
$543$	18.8107	−	7.65386i	0.807245	−	0.328458i
$544$		0			0
$545$	1.69557	+	0.505512i	0.0726302	+	0.0216538i
$546$		0			0
$547$	−31.1709			−1.33277			−0.666387	−	0.745606i	$-0.732160\pi$
$547$	−31.1709			−1.33277			−0.666387	+	0.745606i	$0.732160\pi$
$548$		0			0
$549$	10.7581	+	0.134891i	0.459146	+	0.00575702i
$550$		0			0
$551$	3.83956			0.163571
$552$		0			0
$553$	6.23211	+	6.23211i	0.265016	+	0.265016i
$554$		0			0
$555$	35.4335	−	3.43655i	1.50407	−	0.145873i
$556$		0			0
$557$			7.16851i			0.303739i	0.988401	+	0.151870i	$0.0485294\pi$
$557$			7.16851i			0.303739i	−0.988401	+	0.151870i	$0.951471\pi$
$558$		0			0
$559$			2.68644i			0.113624i
$560$		0			0
$561$	−14.7252	−	6.20780i	−0.621698	−	0.262094i
$562$		0			0
$563$	−27.1779			−1.14541			−0.572706	−	0.819761i	$-0.694106\pi$
$563$	−27.1779			−1.14541			−0.572706	+	0.819761i	$0.694106\pi$
$564$		0			0
$565$	14.5080	+	4.32538i	0.610358	+	0.181970i
$566$		0			0
$567$	−31.4796	−	33.0993i	−1.32202	−	1.39004i
$568$		0			0
$569$		−	38.2814i		−	1.60484i	−0.596760	−	0.802420i	$-0.703545\pi$
$569$		−	38.2814i		−	1.60484i	0.596760	−	0.802420i	$-0.296455\pi$
$570$		0			0
$571$	18.9686	+	18.9686i	0.793812	+	0.793812i	0.982112	−	0.188300i	$-0.0602977\pi$
$571$	18.9686	+	18.9686i	0.793812	+	0.793812i	−0.188300	+	0.982112i	$0.560298\pi$
$572$		0			0
$573$	−42.0328	−	17.7201i	−1.75595	−	0.740268i
$574$		0			0
$575$	−3.39324	−	16.2461i	−0.141508	−	0.677509i
$576$		0			0
$577$	−24.0744	−	24.0744i	−1.00223	−	1.00223i	−0.999998	−	0.00223126i	$-0.999290\pi$
$577$	−24.0744	−	24.0744i	−1.00223	−	1.00223i	−0.00223126	−	0.999998i	$-0.500710\pi$
$578$		0			0
$579$	6.58324	+	16.1795i	0.273590	+	0.672397i
$580$		0			0
$581$	2.71013	−	2.71013i	0.112435	−	0.112435i
$582$		0			0
$583$	−13.2547	−	13.2547i	−0.548954	−	0.548954i
$584$		0			0
$585$	−3.72073	+	11.9315i	−0.153833	+	0.493306i
$586$		0			0
$587$	−5.91999			−0.244344			−0.122172	−	0.992509i	$-0.538986\pi$
$587$	−5.91999			−0.244344			−0.122172	+	0.992509i	$0.538986\pi$
$588$		0			0
$589$	−2.61706	−	2.61706i	−0.107834	−	0.107834i
$590$		0			0
$591$	8.85674	−	21.0086i	0.364317	−	0.864177i
$592$		0			0
$593$	29.2667	+	29.2667i	1.20184	+	1.20184i	0.973607	+	0.228232i	$0.0732944\pi$
$593$	29.2667	+	29.2667i	1.20184	+	1.20184i	0.228232	+	0.973607i	$0.426706\pi$
$594$		0			0
$595$	−20.0795	−	37.1382i	−0.823179	−	1.52252i
$596$		0			0
$597$	−11.7085	+	27.7731i	−0.479198	+	1.13668i
$598$		0			0
$599$		−	15.8668i		−	0.648301i	−0.946006	−	0.324150i	$-0.894922\pi$
$599$		−	15.8668i		−	0.648301i	0.946006	−	0.324150i	$-0.105078\pi$
$600$		0			0
$601$			1.04285i			0.0425388i	0.999774	+	0.0212694i	$0.00677077\pi$
$601$			1.04285i			0.0425388i	−0.999774	+	0.0212694i	$0.993229\pi$
$602$		0			0
$603$	2.82535	+	2.89710i	0.115057	+	0.117979i
$604$		0			0
$605$	−5.15689	−	9.53798i	−0.209658	−	0.387774i
$606$		0			0
$607$	−0.178537	−	0.178537i	−0.00724658	−	0.00724658i	0.703474	−	0.710721i	$-0.251631\pi$
$607$	−0.178537	−	0.178537i	−0.00724658	−	0.00724658i	−0.710721	+	0.703474i	$0.751631\pi$
$608$		0			0
$609$	−25.8570	−	10.9007i	−1.04778	−	0.441720i
$610$		0			0
$611$	5.90239	+	5.90239i	0.238785	+	0.238785i
$612$		0			0
$613$	−20.6148			−0.832626			−0.416313	−	0.909221i	$-0.636678\pi$
$613$	−20.6148			−0.832626			−0.416313	+	0.909221i	$0.636678\pi$
$614$		0			0
$615$	2.94989	+	30.4157i	0.118951	+	1.22648i
$616$		0			0
$617$	24.9684	+	24.9684i	1.00519	+	1.00519i	0.999986	+	0.00520238i	$0.00165598\pi$
$617$	24.9684	+	24.9684i	1.00519	+	1.00519i	0.00520238	+	0.999986i	$0.498344\pi$
$618$		0			0
$619$	6.37593	−	6.37593i	0.256270	−	0.256270i	−0.567265	−	0.823535i	$-0.691999\pi$
$619$	6.37593	−	6.37593i	0.256270	−	0.256270i	0.823535	+	0.567265i	$0.191999\pi$
$620$		0			0
$621$	6.89894	−	15.8079i	0.276845	−	0.634350i
$622$		0			0
$623$	29.2807	+	29.2807i	1.17311	+	1.17311i
$624$		0			0
$625$	−10.0067	−	22.9100i	−0.400268	−	0.916398i
$626$		0			0
$627$	2.00723	−	4.76124i	0.0801611	−	0.190146i
$628$		0			0
$629$	24.1790	+	24.1790i	0.964078	+	0.964078i
$630$		0			0
$631$		−	13.0451i		−	0.519318i	−0.965700	−	0.259659i	$-0.916390\pi$
$631$		−	13.0451i		−	0.519318i	0.965700	−	0.259659i	$-0.0836101\pi$
$632$		0			0
$633$	−10.8358	−	26.6310i	−0.430686	−	1.05849i
$634$		0			0
$635$	−12.5271	−	3.73479i	−0.497122	−	0.148210i
$636$		0			0
$637$	34.9514			1.38482
$638$		0			0
$639$	23.8917	+	24.4985i	0.945142	+	0.969144i
$640$		0			0
$641$			44.3272i			1.75082i	0.483381	+	0.875410i	$0.339409\pi$
$641$			44.3272i			1.75082i	−0.483381	+	0.875410i	$0.660591\pi$
$642$		0			0
$643$			34.8590i			1.37470i	0.726324	+	0.687352i	$0.241227\pi$
$643$			34.8590i			1.37470i	−0.726324	+	0.687352i	$0.758773\pi$
$644$		0			0
$645$	−0.539086	−	5.55840i	−0.0212265	−	0.218862i
$646$		0			0
$647$	19.9549	+	19.9549i	0.784510	+	0.784510i	0.980588	−	0.196078i	$-0.0628207\pi$
$647$	19.9549	+	19.9549i	0.784510	+	0.784510i	−0.196078	+	0.980588i	$0.562821\pi$
$648$		0			0
$649$	12.6674			0.497238
$650$		0			0
$651$	10.1943	+	25.0542i	0.399544	+	0.981952i
$652$		0			0
$653$	35.3830			1.38464			0.692321	−	0.721590i	$-0.256588\pi$
$653$	35.3830			1.38464			0.692321	+	0.721590i	$0.256588\pi$
$654$		0			0
$655$	18.1121	+	5.39990i	0.707700	+	0.210991i
$656$		0			0
$657$	0.244259	−	19.4807i	0.00952947	−	0.760014i
$658$		0			0
$659$	11.6897	−	11.6897i	0.455365	−	0.455365i	−0.441766	−	0.897130i	$-0.645648\pi$
$659$	11.6897	−	11.6897i	0.455365	−	0.455365i	0.897130	+	0.441766i	$0.145648\pi$
$660$		0			0
$661$	−7.75765	−	7.75765i	−0.301738	−	0.301738i	0.539956	−	0.841693i	$-0.318441\pi$
$661$	−7.75765	−	7.75765i	−0.301738	−	0.301738i	−0.841693	+	0.539956i	$0.818441\pi$
$662$		0			0
$663$	−11.1195	+	4.52439i	−0.431845	+	0.175713i
$664$		0			0
$665$	12.0083	−	6.49251i	0.465661	−	0.251769i
$666$		0			0
$667$		−	10.5955i		−	0.410259i
$668$		0			0
$669$	6.11094	+	15.0187i	0.236263	+	0.580658i
$670$		0			0
$671$		−	8.89449i		−	0.343368i
$672$		0			0
$673$	−3.87832	+	3.87832i	−0.149498	+	0.149498i	−0.777894	−	0.628396i	$-0.783712\pi$
$673$	−3.87832	+	3.87832i	−0.149498	+	0.149498i	0.628396	+	0.777894i	$0.283712\pi$
$674$		0			0
$675$	5.30412	−	25.4336i	0.204156	−	0.978938i
$676$		0			0
$677$	−38.9780			−1.49805			−0.749023	−	0.662544i	$-0.769477\pi$
$677$	−38.9780			−1.49805			−0.749023	+	0.662544i	$0.769477\pi$
$678$		0			0
$679$	−11.5163			−0.441954
$680$		0			0
$681$	−45.9277	−	19.3621i	−1.75995	−	0.741956i
$682$		0			0
$683$			6.39734i			0.244787i	0.992482	+	0.122394i	$0.0390570\pi$
$683$			6.39734i			0.244787i	−0.992482	+	0.122394i	$0.960943\pi$
$684$		0			0
$685$	−27.2318	−	8.11880i	−1.04047	−	0.310203i
$686$		0			0
$687$	−8.39138	−	20.6233i	−0.320151	−	0.786829i
$688$		0			0
$689$	−14.0817			−0.536468
$690$		0			0
$691$	−22.9727	+	22.9727i	−0.873922	+	0.873922i	−0.992897	−	0.118976i	$-0.962039\pi$
$691$	−22.9727	+	22.9727i	−0.873922	+	0.873922i	0.118976	+	0.992897i	$0.462039\pi$
$692$		0			0
$693$	−27.0349	+	26.3653i	−1.02697	+	1.00154i
$694$		0			0
$695$	−10.9823	+	36.8364i	−0.416582	+	1.39728i
$696$		0			0
$697$	−20.7550	+	20.7550i	−0.786150	+	0.786150i
$698$		0			0
$699$	−11.4517	−	28.1447i	−0.433144	−	1.06453i
$700$		0			0
$701$	0.909621	+	0.909621i	0.0343559	+	0.0343559i	0.724076	−	0.689720i	$-0.242266\pi$
$701$	0.909621	+	0.909621i	0.0343559	+	0.0343559i	−0.689720	+	0.724076i	$0.742266\pi$
$702$		0			0
$703$	−7.81803	+	7.81803i	−0.294863	+	0.294863i
$704$		0			0
$705$	−13.3968	−	11.0280i	−0.504554	−	0.415337i
$706$		0			0
$707$			24.6161i			0.925784i
$708$		0			0
$709$	28.4965	−	28.4965i	1.07021	−	1.07021i	0.0728671	−	0.997342i	$-0.476785\pi$
$709$	28.4965	−	28.4965i	1.07021	−	1.07021i	0.997342	−	0.0728671i	$-0.0232149\pi$
$710$		0			0
$711$	−3.72962	+	3.63725i	−0.139872	+	0.136407i
$712$		0			0
$713$	−7.22193	+	7.22193i	−0.270463	+	0.270463i
$714$		0			0
$715$	9.90158	+	2.95203i	0.370298	+	0.110400i
$716$		0			0
$717$	12.0089	−	28.4856i	0.448480	−	1.06381i
$718$		0			0
$719$	−16.8451			−0.628217			−0.314108	−	0.949387i	$-0.601706\pi$
$719$	−16.8451			−0.628217			−0.314108	+	0.949387i	$0.601706\pi$
$720$		0			0
$721$	92.7814			3.45536
$722$		0			0
$723$	10.1996	−	24.1939i	0.379328	−	0.899782i
$724$		0			0
$725$	−3.26312	−	15.6231i	−0.121189	−	0.580228i
$726$		0			0
$727$	−10.7957	+	10.7957i	−0.400390	+	0.400390i	−0.878370	−	0.477981i	$-0.841369\pi$
$727$	−10.7957	+	10.7957i	−0.400390	+	0.400390i	0.477981	+	0.878370i	$0.341369\pi$
$728$		0			0
$729$	19.7963	−	18.3604i	0.733197	−	0.680016i
$730$		0			0
$731$	3.79292	−	3.79292i	0.140286	−	0.140286i
$732$		0			0
$733$			1.22075i			0.0450894i	0.999746	+	0.0225447i	$0.00717681\pi$
$733$			1.22075i			0.0450894i	−0.999746	+	0.0225447i	$0.992823\pi$
$734$		0			0
$735$	−72.3165	+	7.01367i	−2.66743	+	0.258703i
$736$		0			0
$737$	2.36557	−	2.36557i	0.0871369	−	0.0871369i
$738$		0			0
$739$	23.9011	+	23.9011i	0.879217	+	0.879217i	0.993454	−	0.114236i	$-0.0364421\pi$
$739$	23.9011	+	23.9011i	0.879217	+	0.879217i	−0.114236	+	0.993454i	$0.536442\pi$
$740$		0			0
$741$	−1.46292	−	3.59538i	−0.0537416	−	0.132080i
$742$		0			0
$743$	−21.4093	+	21.4093i	−0.785429	+	0.785429i	−0.980741	−	0.195312i	$-0.937428\pi$
$743$	−21.4093	+	21.4093i	−0.785429	+	0.785429i	0.195312	+	0.980741i	$0.437428\pi$
$744$		0			0
$745$	25.6224	+	7.63899i	0.938733	+	0.279871i
$746$		0			0
$747$	1.58171	+	1.62188i	0.0578719	+	0.0593416i
$748$		0			0
$749$	21.4380	−	21.4380i	0.783327	−	0.783327i
$750$		0			0
$751$	29.1166			1.06248			0.531240	−	0.847222i	$-0.321726\pi$
$751$	29.1166			1.06248			0.531240	+	0.847222i	$0.321726\pi$
$752$		0			0
$753$	5.57533	+	13.7024i	0.203176	+	0.499343i
$754$		0			0
$755$	3.14038	+	5.80831i	0.114290	+	0.211386i
$756$		0			0
$757$		−	9.67244i		−	0.351551i	−0.984430	−	0.175775i	$-0.943757\pi$
$757$		−	9.67244i		−	0.351551i	0.984430	−	0.175775i	$-0.0562433\pi$
$758$		0			0
$759$	−13.1389	−	5.53908i	−0.476913	−	0.201056i
$760$		0			0
$761$	1.97234			0.0714972			0.0357486	−	0.999361i	$-0.488618\pi$
$761$	1.97234			0.0714972			0.0357486	+	0.999361i	$0.488618\pi$
$762$		0			0
$763$	4.01598			0.145388
$764$		0			0
$765$	22.0990	−	11.5926i	0.798990	−	0.419130i
$766$		0			0
$767$	6.72884	−	6.72884i	0.242964	−	0.242964i
$768$		0			0
$769$			24.3132i			0.876756i	0.898791	+	0.438378i	$0.144447\pi$
$769$			24.3132i			0.876756i	−0.898791	+	0.438378i	$0.855553\pi$
$770$		0			0
$771$	−8.17488	−	20.0912i	−0.294411	−	0.723568i
$772$		0			0
$773$		−	2.61533i		−	0.0940670i	−0.998893	−	0.0470335i	$-0.985023\pi$
$773$		−	2.61533i		−	0.0940670i	0.998893	−	0.0470335i	$-0.0149767\pi$
$774$		0			0
$775$	−8.42463	+	12.8729i	−0.302621	+	0.462410i
$776$		0			0
$777$	74.8453	−	30.4537i	2.68506	−	1.09252i
$778$		0			0
$779$	−6.71091	−	6.71091i	−0.240443	−	0.240443i
$780$		0			0
$781$	20.0037	−	20.0037i	0.715790	−	0.715790i
$782$		0			0
$783$	6.63439	−	15.2017i	0.237094	−	0.543266i
$784$		0			0
$785$	−2.47622	+	1.33882i	−0.0883801	+	0.0477844i
$786$		0			0
$787$	32.2329			1.14898			0.574490	−	0.818511i	$-0.305200\pi$
$787$	32.2329			1.14898			0.574490	+	0.818511i	$0.305200\pi$
$788$		0			0
$789$	9.21615	+	22.6503i	0.328104	+	0.806373i
$790$		0			0
$791$	34.3625			1.22179
$792$		0			0
$793$	−4.72471	−	4.72471i	−0.167779	−	0.167779i
$794$		0			0
$795$	29.1358	−	2.82576i	1.03334	−	0.100219i
$796$		0			0
$797$			45.8714i			1.62485i	0.583066	+	0.812425i	$0.301853\pi$
$797$			45.8714i			1.62485i	−0.583066	+	0.812425i	$0.698147\pi$
$798$		0			0
$799$		−	16.6669i		−	0.589633i
$800$		0			0
$801$	−17.5231	+	17.0891i	−0.619148	+	0.603813i
$802$		0			0
$803$	−16.1060			−0.568369
$804$		0			0
$805$	−17.9165	−	33.1376i	−0.631472	−	1.16795i
$806$		0			0
$807$	14.0453	+	34.5188i	0.494417	+	1.21512i
$808$		0			0
$809$			13.9119i			0.489115i	0.969635	+	0.244558i	$0.0786428\pi$
$809$			13.9119i			0.489115i	−0.969635	+	0.244558i	$0.921357\pi$
$810$		0			0
$811$	−14.7468	−	14.7468i	−0.517830	−	0.517830i	0.399084	−	0.916914i	$-0.369328\pi$
$811$	−14.7468	−	14.7468i	−0.517830	−	0.517830i	−0.916914	+	0.399084i	$0.869328\pi$
$812$		0			0
$813$	−15.3575	+	36.4287i	−0.538611	+	1.27761i
$814$		0			0
$815$	−4.80929	−	8.89506i	−0.168462	−	0.311581i
$816$		0			0
$817$	1.22640	+	1.22640i	0.0429064	+	0.0429064i
$818$		0			0
$819$	−0.355667	+	28.3659i	−0.0124280	+	0.991185i
$820$		0			0
$821$	14.3064	−	14.3064i	0.499298	−	0.499298i	−0.411922	−	0.911219i	$-0.635142\pi$
$821$	14.3064	−	14.3064i	0.499298	−	0.499298i	0.911219	+	0.411922i	$0.135142\pi$
$822$		0			0
$823$	−5.19550	−	5.19550i	−0.181104	−	0.181104i	0.610733	−	0.791837i	$-0.290875\pi$
$823$	−5.19550	−	5.19550i	−0.181104	−	0.181104i	−0.791837	+	0.610733i	$0.790875\pi$
$824$		0			0
$825$	−21.0793	−	4.12097i	−0.733888	−	0.143474i
$826$		0			0
$827$	30.8268			1.07195			0.535977	−	0.844233i	$-0.319943\pi$
$827$	30.8268			1.07195			0.535977	+	0.844233i	$0.319943\pi$
$828$		0			0
$829$	8.85151	+	8.85151i	0.307426	+	0.307426i	0.843910	−	0.536484i	$-0.180248\pi$
$829$	8.85151	+	8.85151i	0.307426	+	0.307426i	−0.536484	+	0.843910i	$0.680248\pi$
$830$		0			0
$831$	−10.1606	−	4.28347i	−0.352467	−	0.148592i
$832$		0			0
$833$	−49.3470	−	49.3470i	−1.70977	−	1.70977i
$834$		0			0
$835$	34.1883	+	10.1928i	1.18313	+	0.352736i
$836$		0			0
$837$	−14.8836	+	5.83955i	−0.514452	+	0.201844i
$838$		0			0
$839$			3.85793i			0.133190i	0.997780	+	0.0665952i	$0.0212136\pi$
$839$			3.85793i			0.133190i	−0.997780	+	0.0665952i	$0.978786\pi$
$840$		0			0
$841$			18.8108i			0.648649i
$842$		0			0
$843$	−6.30691	+	14.9603i	−0.217222	+	0.515259i
$844$		0			0
$845$	−18.7429	+	10.1337i	−0.644777	+	0.348611i
$846$		0			0
$847$	−17.4025	−	17.4025i	−0.597957	−	0.597957i
$848$		0			0
$849$	−11.6090	+	27.5371i	−0.398420	+	0.945071i
$850$		0			0
$851$	21.5743	+	21.5743i	0.739558	+	0.739558i
$852$		0			0
$853$	−24.8147			−0.849638			−0.424819	−	0.905278i	$-0.639662\pi$
$853$	−24.8147			−0.849638			−0.424819	+	0.905278i	$0.639662\pi$
$854$		0			0
$855$	3.74834	+	7.14549i	0.128191	+	0.244371i
$856$		0			0
$857$	−1.55141	−	1.55141i	−0.0529951	−	0.0529951i	0.680113	−	0.733108i	$-0.261931\pi$
$857$	−1.55141	−	1.55141i	−0.0529951	−	0.0529951i	−0.733108	+	0.680113i	$0.761931\pi$
$858$		0			0
$859$	5.93140	−	5.93140i	0.202377	−	0.202377i	−0.598641	−	0.801018i	$-0.704292\pi$
$859$	5.93140	−	5.93140i	0.202377	−	0.202377i	0.801018	+	0.598641i	$0.204292\pi$
$860$		0			0
$861$	26.1411	+	64.2464i	0.890886	+	2.18951i
$862$		0			0
$863$	8.09682	+	8.09682i	0.275619	+	0.275619i	0.831357	−	0.555738i	$-0.187564\pi$
$863$	8.09682	+	8.09682i	0.275619	+	0.275619i	−0.555738	+	0.831357i	$0.687564\pi$
$864$		0			0
$865$	36.8472	−	19.9221i	1.25284	−	0.677373i
$866$		0			0
$867$	−5.04510	−	2.12690i	−0.171341	−	0.0722333i
$868$		0			0
$869$	3.04534	+	3.04534i	0.103306	+	0.103306i
$870$		0			0
$871$		−	2.51316i		−	0.0851551i
$872$		0			0
$873$	0.0853446	−	6.80658i	0.00288848	−	0.230368i
$874$		0			0
$875$	−36.6234	−	43.3438i	−1.23810	−	1.46529i
$876$		0			0
$877$	−33.9586			−1.14670			−0.573351	−	0.819310i	$-0.694357\pi$
$877$	−33.9586			−1.14670			−0.573351	+	0.819310i	$0.694357\pi$
$878$		0			0
$879$	45.0325	+	18.9847i	1.51891	+	0.640337i
$880$		0			0
$881$		−	47.8788i		−	1.61308i	−0.591180	−	0.806539i	$-0.701338\pi$
$881$		−	47.8788i		−	1.61308i	0.591180	−	0.806539i	$-0.298662\pi$
$882$		0			0
$883$			38.5302i			1.29664i	0.761367	+	0.648322i	$0.224529\pi$
$883$			38.5302i			1.29664i	−0.761367	+	0.648322i	$0.775471\pi$
$884$		0			0
$885$	−12.5721	+	15.2726i	−0.422606	+	0.513384i
$886$		0			0
$887$	35.8564	+	35.8564i	1.20394	+	1.20394i	0.972958	+	0.230981i	$0.0741935\pi$
$887$	35.8564	+	35.8564i	1.20394	+	1.20394i	0.230981	+	0.972958i	$0.425807\pi$
$888$		0			0
$889$	−29.6706			−0.995119
$890$		0			0
$891$	−15.3826	−	16.1741i	−0.515337	−	0.541853i
$892$		0			0
$893$	5.38908			0.180339
$894$		0			0
$895$	0.502182	−	1.68440i	0.0167861	−	0.0563033i
$896$		0			0
$897$	−9.92167	+	4.03701i	−0.331275	+	0.134792i
$898$		0			0
$899$	−6.94500	+	6.94500i	−0.231629	+	0.231629i
$900$		0			0
$901$	19.8816	+	19.8816i	0.662351	+	0.662351i
$902$		0			0
$903$	−4.77723	−	11.7409i	−0.158976	−	0.390712i
$904$		0			0
$905$	25.1250	+	7.49068i	0.835182	+	0.248999i
$906$		0			0
$907$			52.5256i			1.74408i	0.489430	+	0.872042i	$0.337205\pi$
$907$			52.5256i			1.74408i	−0.489430	+	0.872042i	$0.662795\pi$
$908$		0			0
$909$	−14.5491	−	0.182425i	−0.482564	−	0.00605064i
$910$		0			0
$911$			6.13423i			0.203236i	0.994823	+	0.101618i	$0.0324020\pi$
$911$			6.13423i			0.203236i	−0.994823	+	0.101618i	$0.967598\pi$
$912$		0			0
$913$	1.32432	−	1.32432i	0.0438285	−	0.0438285i
$914$		0			0
$915$	10.7238	+	8.82760i	0.354518	+	0.291831i
$916$		0			0
$917$	42.8989			1.41665
$918$		0			0
$919$	−38.1249			−1.25762			−0.628812	−	0.777557i	$-0.716458\pi$
$919$	−38.1249			−1.25762			−0.628812	+	0.777557i	$0.716458\pi$
$920$		0			0
$921$	3.14170	−	7.45224i	0.103522	−	0.245560i
$922$		0			0
$923$		−	21.2518i		−	0.699510i
$924$		0			0
$925$	38.4558	+	25.1672i	1.26442	+	0.827492i
$926$		0			0
$927$	−0.687583	+	54.8375i	−0.0225832	+	1.80110i
$928$		0			0
$929$	−40.7400			−1.33664			−0.668318	−	0.743876i	$-0.732985\pi$
$929$	−40.7400			−1.33664			−0.668318	+	0.743876i	$0.732985\pi$
$930$		0			0
$931$	15.9559	−	15.9559i	0.522933	−	0.522933i
$932$		0			0
$933$	−7.97269	+	18.9116i	−0.261014	+	0.619137i
$934$		0			0
$935$	−9.81191	−	18.1477i	−0.320884	−	0.593494i
$936$		0			0
$937$	−40.7663	+	40.7663i	−1.33178	+	1.33178i	−0.427998	+	0.903780i	$0.640781\pi$
$937$	−40.7663	+	40.7663i	−1.33178	+	1.33178i	−0.903780	+	0.427998i	$0.859219\pi$
$938$		0			0
$939$	−20.4002	+	8.30060i	−0.665735	+	0.270880i
$940$		0			0
$941$	−18.7094	−	18.7094i	−0.609909	−	0.609909i	0.333013	−	0.942922i	$-0.391935\pi$
$941$	−18.7094	−	18.7094i	−0.609909	−	0.609909i	−0.942922	+	0.333013i	$0.891935\pi$
$942$		0			0
$943$	−18.5192	+	18.5192i	−0.603067	+	0.603067i
$944$		0			0
$945$	−4.95628	−	58.7621i	−0.161228	−	1.91153i
$946$		0			0
$947$		−	9.81050i		−	0.318799i	−0.987214	−	0.159399i	$-0.949044\pi$
$947$		−	9.81050i		−	0.318799i	0.987214	−	0.159399i	$-0.0509557\pi$
$948$		0			0
$949$	−8.55544	+	8.55544i	−0.277721	+	0.277721i
$950$		0			0
$951$	−19.8252	−	8.35785i	−0.642876	−	0.271022i
$952$		0			0
$953$	−35.8210	+	35.8210i	−1.16035	+	1.16035i	−0.175957	+	0.984398i	$0.556302\pi$
$953$	−35.8210	+	35.8210i	−1.16035	+	1.16035i	−0.984398	+	0.175957i	$0.943698\pi$
$954$		0			0
$955$	−28.0080	−	51.8024i	−0.906317	−	1.67629i
$956$		0			0
$957$	−12.6351	−	5.32668i	−0.408435	−	0.172187i
$958$		0			0
$959$	−64.4989			−2.08278
$960$		0			0
$961$	−21.5325			−0.694598
$962$		0			0
$963$	12.5118	+	12.8296i	0.403189	+	0.413428i
$964$		0			0
$965$	−6.44289	+	21.6105i	−0.207404	+	0.695667i
$966$		0			0
$967$	3.81689	−	3.81689i	0.122743	−	0.122743i	−0.643067	−	0.765810i	$-0.722338\pi$
$967$	3.81689	−	3.81689i	0.122743	−	0.122743i	0.765810	+	0.643067i	$0.222338\pi$
$968$		0			0
$969$	−3.01077	+	7.14169i	−0.0967200	+	0.229424i
$970$		0			0
$971$	−26.4895	+	26.4895i	−0.850088	+	0.850088i	−0.990144	−	0.140056i	$-0.955272\pi$
$971$	−26.4895	+	26.4895i	−0.850088	+	0.850088i	0.140056	+	0.990144i	$0.455272\pi$
$972$		0			0
$973$			87.2475i			2.79703i
$974$		0			0
$975$	−13.3863	+	9.00820i	−0.428704	+	0.288493i
$976$		0			0
$977$	−43.2079	+	43.2079i	−1.38234	+	1.38234i	−0.541905	+	0.840440i	$0.682297\pi$
$977$	−43.2079	+	43.2079i	−1.38234	+	1.38234i	−0.840440	+	0.541905i	$0.817703\pi$
$978$		0			0
$979$	14.3081	+	14.3081i	0.457290	+	0.457290i
$980$		0			0
$981$	−0.0297616	+	2.37361i	−0.000950214	+	0.0757835i
$982$		0			0
$983$	31.9826	−	31.9826i	1.02009	−	1.02009i	0.0202915	−	0.999794i	$-0.493541\pi$
$983$	31.9826	−	31.9826i	1.02009	−	1.02009i	0.999794	−	0.0202915i	$-0.00645942\pi$
$984$		0			0
$985$	25.8915	−	13.9988i	0.824973	−	0.446038i
$986$		0			0
$987$	−36.2921	−	15.2999i	−1.15519	−	0.487001i
$988$		0			0
$989$	3.38434	−	3.38434i	0.107616	−	0.107616i
$990$		0			0
$991$	44.9665			1.42841			0.714204	−	0.699938i	$-0.246789\pi$
$991$	44.9665			1.42841			0.714204	+	0.699938i	$0.246789\pi$
$992$		0			0
$993$	15.4714	−	6.29513i	0.490970	−	0.199770i
$994$		0			0
$995$	−34.2283	+	18.5062i	−1.08511	+	0.586687i
$996$		0			0
$997$			39.2793i			1.24399i	0.783023	+	0.621993i	$0.213677\pi$
$997$			39.2793i			1.24399i	−0.783023	+	0.621993i	$0.786323\pi$
$998$		0			0
$999$	17.4447	+	44.4623i	0.551925	+	1.40673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bb.a.497.18		88
3.2	odd	2	inner	960.2.bb.a.497.27		88
4.3	odd	2		240.2.bb.a.197.21	yes	88
5.3	odd	4		960.2.bf.a.113.5		88
12.11	even	2		240.2.bb.a.197.24	yes	88
15.8	even	4		960.2.bf.a.113.6		88
16.3	odd	4		240.2.bf.a.77.2	yes	88
16.13	even	4		960.2.bf.a.17.5		88
20.3	even	4		240.2.bf.a.53.43	yes	88
48.29	odd	4		960.2.bf.a.17.6		88
48.35	even	4		240.2.bf.a.77.43	yes	88
60.23	odd	4		240.2.bf.a.53.2	yes	88
80.3	even	4		240.2.bb.a.173.24	yes	88
80.13	odd	4	inner	960.2.bb.a.593.27		88
240.83	odd	4		240.2.bb.a.173.21	✓	88
240.173	even	4	inner	960.2.bb.a.593.18		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.21	✓	88	240.83	odd	4
240.2.bb.a.173.24	yes	88	80.3	even	4
240.2.bb.a.197.21	yes	88	4.3	odd	2
240.2.bb.a.197.24	yes	88	12.11	even	2
240.2.bf.a.53.2	yes	88	60.23	odd	4
240.2.bf.a.53.43	yes	88	20.3	even	4
240.2.bf.a.77.2	yes	88	16.3	odd	4
240.2.bf.a.77.43	yes	88	48.35	even	4
960.2.bb.a.497.18		88	1.1	even	1	trivial
960.2.bb.a.497.27		88	3.2	odd	2	inner
960.2.bb.a.593.18		88	240.173	even	4	inner
960.2.bb.a.593.27		88	80.13	odd	4	inner
960.2.bf.a.17.5		88	16.13	even	4
960.2.bf.a.17.6		88	48.29	odd	4
960.2.bf.a.113.5		88	5.3	odd	4
960.2.bf.a.113.6		88	15.8	even	4

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.672846 + 1.59602i) q^{3} +(-1.96698 + 1.06348i) q^{5} +(-3.58885 + 3.58885i) q^{7} +(-2.09456 - 2.14775i) q^{9} +O(q^{10})\)	\(q+(-0.672846 + 1.59602i) q^{3} +(-1.96698 + 1.06348i) q^{5} +(-3.58885 + 3.58885i) q^{7} +(-2.09456 - 2.14775i) q^{9} +(-1.75370 + 1.75370i) q^{11} +1.86312i q^{13} +(-0.373870 - 3.85490i) q^{15} +(2.63049 - 2.63049i) q^{17} +(0.850543 + 0.850543i) q^{19} +(-3.31313 - 8.14261i) q^{21} +(2.34712 - 2.34712i) q^{23} +(2.73800 - 4.18370i) q^{25} +(4.83716 - 1.89785i) q^{27} +(2.25712 - 2.25712i) q^{29} -3.07693 q^{31} +(-1.61897 - 3.97892i) q^{33} +(3.24250 - 10.8759i) q^{35} +9.19181i q^{37} +(-2.97357 - 1.25359i) q^{39} -7.89015 q^{41} +1.44191 q^{43} +(6.40405 + 1.99705i) q^{45} +(3.16802 - 3.16802i) q^{47} -18.7596i q^{49} +(2.42840 + 5.96823i) q^{51} +7.55812i q^{53} +(1.58446 - 5.31453i) q^{55} +(-1.92977 + 0.785199i) q^{57} +(-3.61161 - 3.61161i) q^{59} +(-2.53592 + 2.53592i) q^{61} +(15.2250 + 0.190899i) q^{63} +(-1.98140 - 3.66471i) q^{65} -1.34890 q^{67} +(2.16680 + 5.32531i) q^{69} -11.4066 q^{71} +(4.59201 + 4.59201i) q^{73} +(4.83502 + 7.18489i) q^{75} -12.5875i q^{77} -1.73652i q^{79} +(-0.225658 + 8.99717i) q^{81} -0.755155 q^{83} +(-2.37663 + 7.97160i) q^{85} +(2.08372 + 5.12110i) q^{87} -8.15881i q^{89} +(-6.68644 - 6.68644i) q^{91} +(2.07030 - 4.91083i) q^{93} +(-2.57754 - 0.768459i) q^{95} +(1.60445 + 1.60445i) q^{97} +(7.43975 + 0.0932835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q+O(q^{10}) \) 88 * q	\( 88 q + 4 q^{15} + 8 q^{19} - 4 q^{21} + 16 q^{31} - 4 q^{33} - 24 q^{39} + 40 q^{43} + 8 q^{45} + 4 q^{51} + 12 q^{57} - 24 q^{61} + 32 q^{63} + 8 q^{67} - 12 q^{69} + 24 q^{75} - 8 q^{81} - 24 q^{85} + 12 q^{87} + 8 q^{91} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 88 * q + 4 * q^15 + 8 * q^19 - 4 * q^21 + 16 * q^31 - 4 * q^33 - 24 * q^39 + 40 * q^43 + 8 * q^45 + 4 * q^51 + 12 * q^57 - 24 * q^61 + 32 * q^63 + 8 * q^67 - 12 * q^69 + 24 * q^75 - 8 * q^81 - 24 * q^85 + 12 * q^87 + 8 * q^91 - 8 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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