LMFDB - Embedded newform 960.2.bf.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(17,960)]

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, 3, 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("960.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bf (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			17.5
Character	$\chi$	$=$	960.17
Dual form			960.2.bf.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59602 - 0.672846i) q^{3} +(1.06348 + 1.96698i) q^{5} +(3.58885 - 3.58885i) q^{7} +(2.09456 + 2.14775i) q^{9} +O(q^{10})$	\(q+(-1.59602 - 0.672846i) q^{3} +(1.06348 + 1.96698i) q^{5} +(3.58885 - 3.58885i) q^{7} +(2.09456 + 2.14775i) q^{9} +(1.75370 + 1.75370i) q^{11} -1.86312 q^{13} +(-0.373870 - 3.85490i) q^{15} +(2.63049 - 2.63049i) q^{17} +(-0.850543 + 0.850543i) q^{19} +(-8.14261 + 3.31313i) q^{21} +(-2.34712 + 2.34712i) q^{23} +(-2.73800 + 4.18370i) q^{25} +(-1.89785 - 4.83716i) q^{27} +(2.25712 + 2.25712i) q^{29} -3.07693 q^{31} +(-1.61897 - 3.97892i) q^{33} +(10.8759 + 3.24250i) q^{35} +9.19181 q^{37} +(2.97357 + 1.25359i) q^{39} +7.89015 q^{41} -1.44191i q^{43} +(-1.99705 + 6.40405i) q^{45} +(3.16802 - 3.16802i) q^{47} -18.7596i q^{49} +(-5.96823 + 2.42840i) q^{51} +7.55812 q^{53} +(-1.58446 + 5.31453i) q^{55} +(1.92977 - 0.785199i) q^{57} +(-3.61161 + 3.61161i) q^{59} +(-2.53592 - 2.53592i) q^{61} +(15.2250 + 0.190899i) q^{63} +(-1.98140 - 3.66471i) q^{65} -1.34890i q^{67} +(5.32531 - 2.16680i) q^{69} +11.4066 q^{71} +(-4.59201 - 4.59201i) q^{73} +(7.18489 - 4.83502i) q^{75} +12.5875 q^{77} -1.73652i q^{79} +(-0.225658 + 8.99717i) q^{81} -0.755155i q^{83} +(7.97160 + 2.37663i) q^{85} +(-2.08372 - 5.12110i) q^{87} +8.15881i q^{89} +(-6.68644 + 6.68644i) q^{91} +(4.91083 + 2.07030i) q^{93} +(-2.57754 - 0.768459i) q^{95} +(1.60445 + 1.60445i) q^{97} +(-0.0932835 + 7.43975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3}+O(q^{10}) $ 88 * q + 4 * q^3	$ 88 q + 4 q^{3} - 8 q^{13} + 4 q^{15} - 8 q^{19} - 4 q^{21} + 4 q^{27} + 16 q^{31} - 4 q^{33} - 8 q^{37} + 24 q^{39} + 8 q^{45} + 4 q^{51} - 12 q^{57} - 24 q^{61} + 32 q^{63} + 12 q^{69} + 36 q^{75} - 8 q^{81} + 16 q^{85} - 12 q^{87} + 8 q^{91} - 16 q^{93} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 8 * q^13 + 4 * q^15 - 8 * q^19 - 4 * q^21 + 4 * q^27 + 16 * q^31 - 4 * q^33 - 8 * q^37 + 24 * q^39 + 8 * q^45 + 4 * q^51 - 12 * q^57 - 24 * q^61 + 32 * q^63 + 12 * q^69 + 36 * q^75 - 8 * q^81 + 16 * q^85 - 12 * q^87 + 8 * q^91 - 16 * q^93 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.59602	−	0.672846i	−0.921462	−	0.388468i
$3$	−1.59602	−	0.672846i	−0.921462	−	0.388468i
$4$		0			0
$5$	1.06348	+	1.96698i	0.475605	+	0.879659i
$5$	1.06348	+	1.96698i	0.475605	+	0.879659i
$6$		0			0
$7$	3.58885	−	3.58885i	1.35646	−	1.35646i	0.478212	−	0.878244i	$-0.341285\pi$
$7$	3.58885	−	3.58885i	1.35646	−	1.35646i	0.878244	−	0.478212i	$-0.158715\pi$
$8$		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	$-0.128024\pi$
$11$	1.75370	+	1.75370i	0.528761	+	0.528761i	−0.391442	+	0.920203i	$0.628024\pi$
$12$		0			0
$13$	−1.86312			−0.516735			−0.258368	−	0.966047i	$-0.583185\pi$
$13$	−1.86312			−0.516735			−0.258368	+	0.966047i	$0.583185\pi$
$14$		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	$-0.794060\pi$
$19$	−0.850543	+	0.850543i	−0.195128	+	0.195128i	0.602780	+	0.797908i	$0.294060\pi$
$20$		0			0
$21$	−8.14261	+	3.31313i	−1.77686	+	0.722984i
$22$		0			0
$23$	−2.34712	+	2.34712i	−0.489409	+	0.489409i	−0.908120	−	0.418710i	$-0.862482\pi$
$23$	−2.34712	+	2.34712i	−0.489409	+	0.489409i	0.418710	+	0.908120i	$0.362482\pi$
$24$		0			0
$25$	−2.73800	+	4.18370i	−0.547600	+	0.836740i
$26$		0			0
$27$	−1.89785	−	4.83716i	−0.365242	−	0.930913i
$28$		0			0
$29$	2.25712	+	2.25712i	0.419137	+	0.419137i	0.884906	−	0.465769i	$-0.154222\pi$
$29$	2.25712	+	2.25712i	0.419137	+	0.419137i	−0.465769	+	0.884906i	$0.654222\pi$
$30$		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
$35$	10.8759	+	3.24250i	1.83836	+	0.548082i
$36$		0			0
$37$	9.19181			1.51112			0.755562	−	0.655077i	$-0.227364\pi$
$37$	9.19181			1.51112			0.755562	+	0.655077i	$0.227364\pi$
$38$		0			0
$39$	2.97357	+	1.25359i	0.476152	+	0.200735i
$40$		0			0
$41$	7.89015			1.23223			0.616117	−	0.787654i	$-0.288705\pi$
$41$	7.89015			1.23223			0.616117	+	0.787654i	$0.288705\pi$
$42$		0			0
$43$		−	1.44191i		−	0.219889i	−0.993938	−	0.109944i	$-0.964933\pi$
$43$		−	1.44191i		−	0.219889i	0.993938	−	0.109944i	$-0.0350673\pi$
$44$		0			0
$45$	−1.99705	+	6.40405i	−0.297702	+	0.954659i
$46$		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
$51$	−5.96823	+	2.42840i	−0.835719	+	0.340044i
$52$		0			0
$53$	7.55812			1.03819			0.519094	−	0.854717i	$-0.326269\pi$
$53$	7.55812			1.03819			0.519094	+	0.854717i	$0.326269\pi$
$54$		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	−0.901976	−	0.431785i	$-0.857884\pi$
$59$	−3.61161	+	3.61161i	−0.470191	+	0.470191i	0.431785	+	0.901976i	$0.357884\pi$
$60$		0			0
$61$	−2.53592	−	2.53592i	−0.324691	−	0.324691i	0.525872	−	0.850563i	$-0.323739\pi$
$61$	−2.53592	−	2.53592i	−0.324691	−	0.324691i	−0.850563	+	0.525872i	$0.823739\pi$
$62$		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
$67$		−	1.34890i		−	0.164794i	−0.996600	−	0.0823972i	$-0.973742\pi$
$67$		−	1.34890i		−	0.164794i	0.996600	−	0.0823972i	$-0.0262576\pi$
$68$		0			0
$69$	5.32531	−	2.16680i	0.641092	−	0.260853i
$70$		0			0
$71$	11.4066			1.35371			0.676856	−	0.736116i	$-0.263342\pi$
$71$	11.4066			1.35371			0.676856	+	0.736116i	$0.263342\pi$
$72$		0			0
$73$	−4.59201	−	4.59201i	−0.537454	−	0.537454i	0.385327	−	0.922780i	$-0.374089\pi$
$73$	−4.59201	−	4.59201i	−0.537454	−	0.537454i	−0.922780	+	0.385327i	$0.874089\pi$
$74$		0			0
$75$	7.18489	−	4.83502i	0.829639	−	0.558300i
$76$		0			0
$77$	12.5875			1.43448
$78$		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
$83$		−	0.755155i		−	0.0828890i	−0.999141	−	0.0414445i	$-0.986804\pi$
$83$		−	0.755155i		−	0.0828890i	0.999141	−	0.0414445i	$-0.0131960\pi$
$84$		0			0
$85$	7.97160	+	2.37663i	0.864641	+	0.257781i
$86$		0			0
$87$	−2.08372	−	5.12110i	−0.223398	−	0.549040i
$88$		0			0
$89$			8.15881i			0.864832i	0.901674	+	0.432416i	$0.142339\pi$
$89$			8.15881i			0.864832i	−0.901674	+	0.432416i	$0.857661\pi$
$90$		0			0
$91$	−6.68644	+	6.68644i	−0.700929	+	0.700929i
$92$		0			0
$93$	4.91083	+	2.07030i	0.509230	+	0.214680i
$94$		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
$99$	−0.0932835	+	7.43975i	−0.00937535	+	0.747723i
$100$		0			0
$101$	−3.42953	−	3.42953i	−0.341251	−	0.341251i	0.515587	−	0.856837i	$-0.327574\pi$
$101$	−3.42953	−	3.42953i	−0.341251	−	0.341251i	−0.856837	+	0.515587i	$0.827574\pi$
$102$		0			0
$103$	12.9263	+	12.9263i	1.27367	+	1.27367i	0.944147	+	0.329524i	$0.106888\pi$
$103$	12.9263	+	12.9263i	1.27367	+	1.27367i	0.329524	+	0.944147i	$0.393112\pi$
$104$		0			0
$105$	−15.1764	−	12.4929i	−1.48106	−	1.21918i
$106$		0			0
$107$			5.97350i			0.577480i	0.957407	+	0.288740i	$0.0932364\pi$
$107$			5.97350i			0.577480i	−0.957407	+	0.288740i	$0.906764\pi$
$108$		0			0
$109$	0.559509	−	0.559509i	0.0535912	−	0.0535912i	−0.679803	−	0.733395i	$-0.737935\pi$
$109$	0.559509	−	0.559509i	0.0535912	−	0.0535912i	0.733395	+	0.679803i	$0.237935\pi$
$110$		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
$115$	−7.11287	−	2.12061i	−0.663279	−	0.197748i
$116$		0			0
$117$	−3.90240	−	4.00151i	−0.360777	−	0.369939i
$118$		0			0
$119$		−	18.8808i		−	1.73080i
$120$		0			0
$121$		−	4.84905i		−	0.440823i
$122$		0			0
$123$	−12.5928	−	5.30886i	−1.13546	−	0.478683i
$124$		0			0
$125$	−11.1411	−	0.936283i	−0.996487	−	0.0837437i
$126$		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	$-0.629618\pi$
$131$	5.97669	−	5.97669i	0.522186	−	0.522186i	0.918231	+	0.396045i	$0.129618\pi$
$132$		0			0
$133$			6.10494i			0.529365i
$134$		0			0
$135$	7.49626	−	8.87728i	0.645175	−	0.764035i
$136$		0			0
$137$	−8.98602	−	8.98602i	−0.767727	−	0.767727i	0.209979	−	0.977706i	$-0.432661\pi$
$137$	−8.98602	−	8.98602i	−0.767727	−	0.767727i	−0.977706	+	0.209979i	$0.932661\pi$
$138$		0			0
$139$	−12.1554	−	12.1554i	−1.03100	−	1.03100i	−0.999504	−	0.0315006i	$-0.989971\pi$
$139$	−12.1554	−	12.1554i	−1.03100	−	1.03100i	−0.0315006	−	0.999504i	$-0.510029\pi$
$140$		0			0
$141$	−7.18782	+	2.92464i	−0.605324	+	0.246299i
$142$		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
$147$	−12.6223	+	29.9408i	−1.04107	+	2.46947i
$148$		0			0
$149$	−8.45496	+	8.45496i	−0.692657	+	0.692657i	−0.962816	−	0.270159i	$-0.912924\pi$
$149$	−8.45496	+	8.45496i	−0.692657	+	0.692657i	0.270159	+	0.962816i	$0.412924\pi$
$150$		0			0
$151$			2.95291i			0.240305i	0.992755	+	0.120152i	$0.0383383\pi$
$151$			2.95291i			0.240305i	−0.992755	+	0.120152i	$0.961662\pi$
$152$		0			0
$153$	11.1593	+	0.139922i	0.902179	+	0.0113120i
$154$		0			0
$155$	−3.27226	−	6.05224i	−0.262835	−	0.486128i
$156$		0			0
$157$			1.25890i			0.100471i	0.998737	+	0.0502355i	$0.0159972\pi$
$157$			1.25890i			0.100471i	−0.998737	+	0.0502355i	$0.984003\pi$
$158$		0			0
$159$	−12.0629	−	5.08545i	−0.956651	−	0.403302i
$160$		0			0
$161$			16.8469i			1.32773i
$162$		0			0
$163$	−4.52220			−0.354206			−0.177103	−	0.984192i	$-0.556673\pi$
$163$	−4.52220			−0.354206			−0.177103	+	0.984192i	$0.556673\pi$
$164$		0			0
$165$	6.10468	−	7.41600i	0.475249	−	0.577335i
$166$		0			0
$167$	11.2815	+	11.2815i	0.872992	+	0.872992i	0.992797	−	0.119806i	$-0.0382272\pi$
$167$	11.2815	+	11.2815i	0.872992	+	0.872992i	−0.119806	+	0.992797i	$0.538227\pi$
$168$		0			0
$169$	−9.52880			−0.732985
$170$		0			0
$171$	−3.60826	−	0.0452423i	−0.275931	−	0.00345977i
$172$		0			0
$173$		−	18.7329i		−	1.42424i	−0.702060	−	0.712118i	$-0.747736\pi$
$173$		−	18.7329i		−	1.42424i	0.702060	−	0.712118i	$-0.252264\pi$
$174$		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	0.686030	−	0.727574i	$-0.259352\pi$
$179$	−0.555823	−	0.555823i	−0.0415441	−	0.0415441i	−0.727574	+	0.686030i	$0.759352\pi$
$180$		0			0
$181$	−8.29080	+	8.29080i	−0.616251	+	0.616251i	−0.944568	−	0.328317i	$-0.893519\pi$
$181$	−8.29080	+	8.29080i	−0.616251	+	0.616251i	0.328317	+	0.944568i	$0.393519\pi$
$182$		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
$187$	9.22619			0.674686
$188$		0			0
$189$	−24.1709	−	10.5487i	−1.75818	−	0.767309i
$190$		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
$195$	0.696564	+	7.18212i	0.0498820	+	0.514322i
$196$		0			0
$197$			13.1631i			0.937832i	0.883243	+	0.468916i	$0.155355\pi$
$197$			13.1631i			0.937832i	−0.883243	+	0.468916i	$0.844645\pi$
$198$		0			0
$199$	−17.4015			−1.23356			−0.616779	−	0.787136i	$-0.711563\pi$
$199$	−17.4015			−1.23356			−0.616779	+	0.787136i	$0.711563\pi$
$200$		0			0
$201$	−0.907602	+	2.15287i	−0.0640173	+	0.151852i
$202$		0			0
$203$	16.2009			1.13708
$204$		0			0
$205$	8.39106	+	15.5198i	0.586057	+	1.08395i
$206$		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	0.176289	−	0.984338i	$-0.443591\pi$
$211$	−11.7376	−	11.7376i	−0.808049	−	0.808049i	−0.984338	+	0.176289i	$0.943591\pi$
$212$		0			0
$213$	−18.2051	−	7.67486i	−1.24739	−	0.525873i
$214$		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
$219$	4.23922	+	10.4186i	0.286460	+	0.704027i
$220$		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
$227$	−28.7764			−1.90996			−0.954978	−	0.296677i	$-0.904121\pi$
$227$	−28.7764			−1.90996			−0.954978	+	0.296677i	$0.904121\pi$
$228$		0			0
$229$	9.08971	+	9.08971i	0.600665	+	0.600665i	0.940489	−	0.339824i	$-0.110368\pi$
$229$	9.08971	+	9.08971i	0.600665	+	0.600665i	−0.339824	+	0.940489i	$0.610368\pi$
$230$		0			0
$231$	−20.0900	−	8.46947i	−1.32182	−	0.557250i
$232$		0			0
$233$	12.4047	−	12.4047i	0.812662	−	0.812662i	−0.172370	−	0.985032i	$-0.555143\pi$
$233$	12.4047	−	12.4047i	0.812662	−	0.812662i	0.985032	+	0.172370i	$0.0551426\pi$
$234$		0			0
$235$	9.60058	+	2.86229i	0.626273	+	0.186715i
$236$		0			0
$237$	−1.16841	+	2.77152i	−0.0758965	+	0.180030i
$238$		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
$243$	6.41386	−	14.2078i	0.411449	−	0.911433i
$244$		0			0
$245$	36.8998	−	19.9506i	2.35744	−	1.27460i
$246$		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	$-0.336874\pi$
$251$	−6.03931	−	6.03931i	−0.381198	−	0.381198i	−0.871534	+	0.490336i	$0.836874\pi$
$252$		0			0
$253$	−8.23232			−0.517561
$254$		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
$261$	−0.120062	+	9.57540i	−0.00743162	+	0.592702i
$262$		0			0
$263$	−9.98311	+	9.98311i	−0.615585	+	0.615585i	−0.944396	−	0.328811i	$-0.893352\pi$
$263$	−9.98311	+	9.98311i	−0.615585	+	0.615585i	0.328811	+	0.944396i	$0.393352\pi$
$264$		0			0
$265$	8.03795	+	14.8667i	0.493767	+	0.913252i
$266$		0			0
$267$	5.48962	−	13.0216i	0.335959	−	0.796910i
$268$		0			0
$269$	15.2141	+	15.2141i	0.927622	+	0.927622i	0.997552	−	0.0699303i	$-0.0222777\pi$
$269$	15.2141	+	15.2141i	0.927622	+	0.927622i	−0.0699303	+	0.997552i	$0.522278\pi$
$270$		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
$275$	−12.1386	+	2.53533i	−0.731986	+	0.152886i
$276$		0			0
$277$	6.36620			0.382508			0.191254	−	0.981541i	$-0.438745\pi$
$277$	6.36620			0.382508			0.191254	+	0.981541i	$0.438745\pi$
$278$		0			0
$279$	−6.44480	−	6.60847i	−0.385840	−	0.395639i
$280$		0			0
$281$	−9.37349			−0.559175			−0.279588	−	0.960120i	$-0.590198\pi$
$281$	−9.37349			−0.559175			−0.279588	+	0.960120i	$0.590198\pi$
$282$		0			0
$283$		−	17.2536i		−	1.02562i	−0.858502	−	0.512810i	$-0.828604\pi$
$283$		−	17.2536i		−	1.02562i	0.858502	−	0.512810i	$-0.171396\pi$
$284$		0			0
$285$	3.59675	+	2.96076i	0.213053	+	0.175380i
$286$		0			0
$287$	28.3166	−	28.3166i	1.67147	−	1.67147i
$288$		0			0
$289$			3.16105i			0.185944i
$290$		0			0
$291$	−1.48119	−	3.64029i	−0.0868288	−	0.213397i
$292$		0			0
$293$	−28.2155			−1.64837			−0.824184	−	0.566322i	$-0.808366\pi$
$293$	−28.2155			−1.64837			−0.824184	+	0.566322i	$0.808366\pi$
$294$		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
$307$		−	4.66927i		−	0.266489i	−0.991083	−	0.133245i	$-0.957460\pi$
$307$		−	4.66927i		−	0.266489i	0.991083	−	0.133245i	$-0.0425396\pi$
$308$		0			0
$309$	−11.9333	−	29.3281i	−0.678860	−	1.66842i
$310$		0			0
$311$	−11.8492			−0.671907			−0.335953	−	0.941879i	$-0.609058\pi$
$311$	−11.8492			−0.671907			−0.335953	+	0.941879i	$0.609058\pi$
$312$		0			0
$313$	−8.99137	−	8.99137i	−0.508222	−	0.508222i	0.405758	−	0.913980i	$-0.367007\pi$
$313$	−8.99137	−	8.99137i	−0.508222	−	0.508222i	−0.913980	+	0.405758i	$0.867007\pi$
$314$		0			0
$315$	15.8161	+	30.1502i	0.891134	+	1.69877i
$316$		0			0
$317$	−12.4217			−0.697669			−0.348835	−	0.937184i	$-0.613423\pi$
$317$	−12.4217			−0.697669			−0.348835	+	0.937184i	$0.613423\pi$
$318$		0			0
$319$			7.91664i			0.443247i
$320$		0			0
$321$	4.01925	−	9.53383i	0.224332	−	0.532126i
$322$		0			0
$323$			4.47469i			0.248978i
$324$		0			0
$325$	5.10121	−	7.79472i	0.282964	−	0.432373i
$326$		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	−0.869224	−	0.494418i	$-0.835381\pi$
$331$	−6.81900	+	6.81900i	−0.374806	+	0.374806i	0.494418	+	0.869224i	$0.335381\pi$
$332$		0			0
$333$	19.2528	+	19.7417i	1.05505	+	1.08184i
$334$		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
$339$	4.41960	+	10.8620i	0.240040	+	0.589941i
$340$		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
$347$			22.0820i			1.18543i	0.805414	+	0.592713i	$0.201943\pi$
$347$			22.0820i			1.18543i	−0.805414	+	0.592713i	$0.798057\pi$
$348$		0			0
$349$	20.0088	−	20.0088i	1.07105	−	1.07105i	0.0737742	−	0.997275i	$-0.476496\pi$
$349$	20.0088	−	20.0088i	1.07105	−	1.07105i	0.997275	−	0.0737742i	$-0.0235044\pi$
$350$		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
$355$	12.1307	+	22.4365i	0.643832	+	1.19080i
$356$		0			0
$357$	−12.7039	+	30.1342i	−0.672361	+	1.59487i
$358$		0			0
$359$			5.32243i			0.280907i	0.990087	+	0.140454i	$0.0448561\pi$
$359$			5.32243i			0.280907i	−0.990087	+	0.140454i	$0.955144\pi$
$360$		0			0
$361$			17.5532i			0.923850i
$362$		0			0
$363$	−3.26266	+	7.73918i	−0.171245	+	0.406202i
$364$		0			0
$365$	4.14884	−	13.9159i	0.217160	−	0.728391i
$366$		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
$373$		−	20.2482i		−	1.04841i	−0.851592	−	0.524205i	$-0.824362\pi$
$373$		−	20.2482i		−	1.04841i	0.851592	−	0.524205i	$-0.175638\pi$
$374$		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	$-0.00961800\pi$
$379$	18.8709	+	18.8709i	0.969332	+	0.969332i	−0.0302112	+	0.999544i	$0.509618\pi$
$380$		0			0
$381$	−3.81614	−	9.37886i	−0.195507	−	0.480493i
$382$		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
$387$	3.09686	−	3.02016i	0.157422	−	0.153523i
$388$		0			0
$389$	−6.57439	+	6.57439i	−0.333335	+	0.333335i	−0.853851	−	0.520517i	$-0.825739\pi$
$389$	−6.57439	+	6.57439i	−0.333335	+	0.333335i	0.520517	+	0.853851i	$0.325739\pi$
$390$		0			0
$391$			12.3482i			0.624474i
$392$		0			0
$393$	−13.5603	+	5.51753i	−0.684027	+	0.278322i
$394$		0			0
$395$	3.41570	−	1.84677i	0.171863	−	0.0929208i
$396$		0			0
$397$		−	32.0317i		−	1.60762i	−0.594883	−	0.803812i	$-0.702802\pi$
$397$		−	32.0317i		−	1.60762i	0.594883	−	0.803812i	$-0.297198\pi$
$398$		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
$403$	5.73267			0.285565
$404$		0			0
$405$	−17.9372	+	9.12449i	−0.891307	+	0.453400i
$406$		0			0
$407$	16.1197	+	16.1197i	0.799024	+	0.799024i
$408$		0			0
$409$	26.0398			1.28759			0.643793	−	0.765200i	$-0.277360\pi$
$409$	26.0398			1.28759			0.643793	+	0.765200i	$0.277360\pi$
$410$		0			0
$411$	8.29566	+	20.3881i	0.409195	+	1.00567i
$412$		0			0
$413$			25.9230i			1.27559i
$414$		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	0.843416	−	0.537261i	$-0.180541\pi$
$419$	6.26684	+	6.26684i	0.306155	+	0.306155i	−0.537261	+	0.843416i	$0.680541\pi$
$420$		0			0
$421$	5.48981	−	5.48981i	0.267557	−	0.267557i	−0.560558	−	0.828115i	$-0.689413\pi$
$421$	5.48981	−	5.48981i	0.267557	−	0.267557i	0.828115	+	0.560558i	$0.189413\pi$
$422$		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
$427$	−18.2020			−0.880859
$428$		0			0
$429$	3.01633	+	7.41318i	0.145630	+	0.357912i
$430$		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
$435$	7.85710	−	9.54484i	0.376719	−	0.457640i
$436$		0			0
$437$		−	3.99266i		−	0.190995i
$438$		0			0
$439$	17.1043			0.816342			0.408171	−	0.912906i	$-0.366167\pi$
$439$	17.1043			0.816342			0.408171	+	0.912906i	$0.366167\pi$
$440$		0			0
$441$	40.2910	−	39.2932i	1.91862	−	1.87110i
$442$		0			0
$443$	−20.7177			−0.984328			−0.492164	−	0.870502i	$-0.663794\pi$
$443$	−20.7177			−0.984328			−0.492164	+	0.870502i	$0.663794\pi$
$444$		0			0
$445$	−16.0482	+	8.67677i	−0.760757	+	0.411318i
$446$		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
$453$	1.98685	−	4.71291i	0.0933506	−	0.221432i
$454$		0			0
$455$	−20.2630	−	6.04115i	−0.949944	−	0.283213i
$456$		0			0
$457$	−14.7004	+	14.7004i	−0.687654	+	0.687654i	−0.961713	−	0.274059i	$-0.911634\pi$
$457$	−14.7004	+	14.7004i	−0.687654	+	0.687654i	0.274059	+	0.961713i	$0.411634\pi$
$458$		0			0
$459$	−17.7164	−	7.73183i	−0.826930	−	0.360891i
$460$		0			0
$461$	9.02405	−	9.02405i	0.420292	−	0.420292i	−0.465012	−	0.885304i	$-0.653950\pi$
$461$	9.02405	−	9.02405i	0.420292	−	0.420292i	0.885304	+	0.465012i	$0.153950\pi$
$462$		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
$467$	12.0452			0.557385			0.278693	−	0.960380i	$-0.410099\pi$
$467$	12.0452			0.557385			0.278693	+	0.960380i	$0.410099\pi$
$468$		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
$475$	−1.22963	−	5.88720i	−0.0564193	−	0.270123i
$476$		0			0
$477$	15.8309	+	16.2330i	0.724848	+	0.743256i
$478$		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
$483$	11.3354	−	26.8881i	0.515778	−	1.22345i
$484$		0			0
$485$	−1.44961	+	4.86223i	−0.0658235	+	0.220783i
$486$		0			0
$487$	−8.60134	+	8.60134i	−0.389764	+	0.389764i	−0.874603	−	0.484839i	$-0.838878\pi$
$487$	−8.60134	+	8.60134i	−0.389764	+	0.389764i	0.484839	+	0.874603i	$0.338878\pi$
$488$		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	$-0.425928\pi$
$491$	−16.4513	−	16.4513i	−0.742438	−	0.742438i	−0.973047	+	0.230609i	$0.925928\pi$
$492$		0			0
$493$	11.8747			0.534808
$494$		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	$-0.706682\pi$
$499$	4.28594	−	4.28594i	0.191865	−	0.191865i	0.796501	+	0.604637i	$0.206682\pi$
$500$		0			0
$501$	−10.4148	−	25.5963i	−0.465300	−	1.14356i
$502$		0			0
$503$	−7.60889	+	7.60889i	−0.339264	+	0.339264i	−0.856090	−	0.516827i	$-0.827113\pi$
$503$	−7.60889	+	7.60889i	−0.339264	+	0.339264i	0.516827	+	0.856090i	$0.327113\pi$
$504$		0			0
$505$	3.09855	−	10.3931i	0.137884	−	0.462485i
$506$		0			0
$507$	15.2082	+	6.41141i	0.675418	+	0.284741i
$508$		0			0
$509$	−24.7598	−	24.7598i	−1.09746	−	1.09746i	−0.994707	−	0.102754i	$-0.967235\pi$
$509$	−24.7598	−	24.7598i	−1.09746	−	1.09746i	−0.102754	−	0.994707i	$-0.532765\pi$
$510$		0			0
$511$	−32.9600			−1.45807
$512$		0			0
$513$	5.72842	+	2.50001i	0.252916	+	0.110378i
$514$		0			0
$515$	−11.6789	+	39.1728i	−0.514632	+	1.72616i
$516$		0			0
$517$	11.1115			0.488685
$518$		0			0
$519$	−12.6043	+	29.8981i	−0.553269	+	1.31238i
$520$		0			0
$521$	−16.6628			−0.730011			−0.365005	−	0.931005i	$-0.618933\pi$
$521$	−16.6628			−0.730011			−0.365005	+	0.931005i	$0.618933\pi$
$522$		0			0
$523$			33.6498i			1.47140i	0.677305	+	0.735702i	$0.263148\pi$
$523$			33.6498i			1.47140i	−0.677305	+	0.735702i	$0.736852\pi$
$524$		0			0
$525$	8.43333	−	43.1376i	0.368060	−	1.88268i
$526$		0			0
$527$	−8.09382	+	8.09382i	−0.352572	+	0.352572i
$528$		0			0
$529$			11.9820i			0.520957i
$530$		0			0
$531$	−15.3215	−	0.192110i	−0.664898	−	0.00833685i
$532$		0			0
$533$	−14.7003			−0.636739
$534$		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	0.894389	−	0.447289i	$-0.147611\pi$
$541$	10.3993	+	10.3993i	0.447100	+	0.447100i	−0.447289	+	0.894389i	$0.647611\pi$
$542$		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
$547$		−	31.1709i		−	1.33277i	−0.745606	−	0.666387i	$-0.767840\pi$
$547$		−	31.1709i		−	1.33277i	0.745606	−	0.666387i	$-0.232160\pi$
$548$		0			0
$549$	0.134891	−	10.7581i	0.00575702	−	0.459146i
$550$		0			0
$551$	−3.83956			−0.163571
$552$		0			0
$553$	−6.23211	−	6.23211i	−0.265016	−	0.265016i
$554$		0			0
$555$	−3.43655	−	35.4335i	−0.145873	−	1.50407i
$556$		0			0
$557$	−7.16851			−0.303739			−0.151870	−	0.988401i	$-0.548529\pi$
$557$	−7.16851			−0.303739			−0.151870	+	0.988401i	$0.548529\pi$
$558$		0			0
$559$			2.68644i			0.113624i
$560$		0			0
$561$	−14.7252	−	6.20780i	−0.621698	−	0.262094i
$562$		0			0
$563$		−	27.1779i		−	1.14541i	−0.819761	−	0.572706i	$-0.805894\pi$
$563$		−	27.1779i		−	1.14541i	0.819761	−	0.572706i	$-0.194106\pi$
$564$		0			0
$565$	4.32538	−	14.5080i	0.181970	−	0.610358i
$566$		0			0
$567$	31.4796	+	33.0993i	1.32202	+	1.39004i
$568$		0			0
$569$			38.2814i			1.60484i	0.596760	+	0.802420i	$0.296455\pi$
$569$			38.2814i			1.60484i	−0.596760	+	0.802420i	$0.703545\pi$
$570$		0			0
$571$	18.9686	−	18.9686i	0.793812	−	0.793812i	−0.188300	−	0.982112i	$-0.560298\pi$
$571$	18.9686	−	18.9686i	0.793812	−	0.793812i	0.982112	+	0.188300i	$0.0602977\pi$
$572$		0			0
$573$	17.7201	−	42.0328i	0.740268	−	1.75595i
$574$		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
$579$	−16.1795	+	6.58324i	−0.672397	+	0.273590i
$580$		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
$587$			5.91999i			0.244344i	0.992509	+	0.122172i	$0.0389860\pi$
$587$			5.91999i			0.244344i	−0.992509	+	0.122172i	$0.961014\pi$
$588$		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
$595$	37.1382	−	20.0795i	1.52252	−	0.823179i
$596$		0			0
$597$	27.7731	+	11.7085i	1.13668	+	0.479198i
$598$		0			0
$599$			15.8668i			0.648301i	0.946006	+	0.324150i	$0.105078\pi$
$599$			15.8668i			0.648301i	−0.946006	+	0.324150i	$0.894922\pi$
$600$		0			0
$601$		−	1.04285i		−	0.0425388i	−0.999774	−	0.0212694i	$-0.993229\pi$
$601$		−	1.04285i		−	0.0425388i	0.999774	−	0.0212694i	$-0.00677077\pi$
$602$		0			0
$603$	2.89710	−	2.82535i	0.117979	−	0.115057i
$604$		0			0
$605$	9.53798	−	5.15689i	0.387774	−	0.209658i
$606$		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
$613$			20.6148i			0.832626i	0.909221	+	0.416313i	$0.136678\pi$
$613$			20.6148i			0.832626i	−0.909221	+	0.416313i	$0.863322\pi$
$614$		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	$-0.998344\pi$
$617$	−24.9684	−	24.9684i	−1.00519	−	1.00519i	−0.00520238	−	0.999986i	$-0.501656\pi$
$618$		0			0
$619$	−6.37593	−	6.37593i	−0.256270	−	0.256270i	0.567265	−	0.823535i	$-0.308001\pi$
$619$	−6.37593	−	6.37593i	−0.256270	−	0.256270i	−0.823535	+	0.567265i	$0.808001\pi$
$620$		0			0
$621$	15.8079	+	6.89894i	0.634350	+	0.276845i
$622$		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
$627$	4.76124	+	2.00723i	0.190146	+	0.0801611i
$628$		0			0
$629$	24.1790	−	24.1790i	0.964078	−	0.964078i
$630$		0			0
$631$			13.0451i			0.519318i	0.965700	+	0.259659i	$0.0836101\pi$
$631$			13.0451i			0.519318i	−0.965700	+	0.259659i	$0.916390\pi$
$632$		0			0
$633$	10.8358	+	26.6310i	0.430686	+	1.05849i
$634$		0			0
$635$	−3.73479	+	12.5271i	−0.148210	+	0.497122i
$636$		0			0
$637$			34.9514i			1.38482i
$638$		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
$643$	−34.8590			−1.37470			−0.687352	−	0.726324i	$-0.741227\pi$
$643$	−34.8590			−1.37470			−0.687352	+	0.726324i	$0.741227\pi$
$644$		0			0
$645$	−5.55840	+	0.539086i	−0.218862	+	0.0212265i
$646$		0			0
$647$	−19.9549	−	19.9549i	−0.784510	−	0.784510i	0.196078	−	0.980588i	$-0.437179\pi$
$647$	−19.9549	−	19.9549i	−0.784510	−	0.784510i	−0.980588	+	0.196078i	$0.937179\pi$
$648$		0			0
$649$	−12.6674			−0.497238
$650$		0			0
$651$	25.0542	−	10.1943i	0.981952	−	0.399544i
$652$		0			0
$653$			35.3830i			1.38464i	0.721590	+	0.692321i	$0.243412\pi$
$653$			35.3830i			1.38464i	−0.721590	+	0.692321i	$0.756588\pi$
$654$		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	0.897130	−	0.441766i	$-0.145648\pi$
$659$	11.6897	+	11.6897i	0.455365	+	0.455365i	−0.441766	+	0.897130i	$0.645648\pi$
$660$		0			0
$661$	−7.75765	+	7.75765i	−0.301738	+	0.301738i	−0.841693	−	0.539956i	$-0.818441\pi$
$661$	−7.75765	+	7.75765i	−0.301738	+	0.301738i	0.539956	+	0.841693i	$0.318441\pi$
$662$		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
$667$	−10.5955			−0.410259
$668$		0			0
$669$	−15.0187	+	6.11094i	−0.580658	+	0.236263i
$670$		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
$675$	25.4336	+	5.30412i	0.978938	+	0.204156i
$676$		0			0
$677$			38.9780i			1.49805i	0.662544	+	0.749023i	$0.269477\pi$
$677$			38.9780i			1.49805i	−0.662544	+	0.749023i	$0.730523\pi$
$678$		0			0
$679$	11.5163			0.441954
$680$		0			0
$681$	45.9277	+	19.3621i	1.75995	+	0.741956i
$682$		0			0
$683$	6.39734			0.244787			0.122394	−	0.992482i	$-0.460943\pi$
$683$	6.39734			0.244787			0.122394	+	0.992482i	$0.460943\pi$
$684$		0			0
$685$	8.11880	−	27.2318i	0.310203	−	1.04047i
$686$		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	0.118976	−	0.992897i	$-0.462039\pi$
$691$	−22.9727	−	22.9727i	−0.873922	−	0.873922i	−0.992897	+	0.118976i	$0.962039\pi$
$692$		0			0
$693$	26.3653	+	27.0349i	1.00154	+	1.02697i
$694$		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
$699$	−28.1447	+	11.4517i	−1.06453	+	0.433144i
$700$		0			0
$701$	−0.909621	+	0.909621i	−0.0343559	+	0.0343559i	−0.724076	−	0.689720i	$-0.757734\pi$
$701$	−0.909621	+	0.909621i	−0.0343559	+	0.0343559i	0.689720	+	0.724076i	$0.257734\pi$
$702$		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
$707$	−24.6161			−0.925784
$708$		0			0
$709$	−28.4965	−	28.4965i	−1.07021	−	1.07021i	−0.997342	−	0.0728671i	$-0.976785\pi$
$709$	−28.4965	−	28.4965i	−1.07021	−	1.07021i	−0.0728671	−	0.997342i	$-0.523215\pi$
$710$		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
$715$	2.95203	−	9.90158i	0.110400	−	0.370298i
$716$		0			0
$717$	28.4856	+	12.0089i	1.06381	+	0.448480i
$718$		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
$723$	24.1939	+	10.1996i	0.899782	+	0.379328i
$724$		0			0
$725$	−15.6231	+	3.26312i	−0.580228	+	0.121189i
$726$		0			0
$727$	10.7957	−	10.7957i	0.400390	−	0.400390i	−0.477981	−	0.878370i	$-0.658631\pi$
$727$	10.7957	−	10.7957i	0.400390	−	0.400390i	0.878370	+	0.477981i	$0.158631\pi$
$728$		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
$733$	−1.22075			−0.0450894			−0.0225447	−	0.999746i	$-0.507177\pi$
$733$	−1.22075			−0.0450894			−0.0225447	+	0.999746i	$0.507177\pi$
$734$		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	$-0.963558\pi$
$739$	−23.9011	+	23.9011i	−0.879217	+	0.879217i	0.114236	+	0.993454i	$0.463558\pi$
$740$		0			0
$741$	−3.59538	+	1.46292i	−0.132080	+	0.0537416i
$742$		0			0
$743$	21.4093	−	21.4093i	0.785429	−	0.785429i	−0.195312	−	0.980741i	$-0.562572\pi$
$743$	21.4093	−	21.4093i	0.785429	−	0.785429i	0.980741	+	0.195312i	$0.0625719\pi$
$744$		0			0
$745$	−25.6224	−	7.63899i	−0.938733	−	0.279871i
$746$		0			0
$747$	1.62188	−	1.58171i	0.0593416	−	0.0578719i
$748$		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
$755$	−5.80831	+	3.14038i	−0.211386	+	0.114290i
$756$		0			0
$757$	−9.67244			−0.351551			−0.175775	−	0.984430i	$-0.556243\pi$
$757$	−9.67244			−0.351551			−0.175775	+	0.984430i	$0.556243\pi$
$758$		0			0
$759$	13.1389	+	5.53908i	0.476913	+	0.201056i
$760$		0			0
$761$	−1.97234			−0.0714972			−0.0357486	−	0.999361i	$-0.511382\pi$
$761$	−1.97234			−0.0714972			−0.0357486	+	0.999361i	$0.511382\pi$
$762$		0			0
$763$		−	4.01598i		−	0.145388i
$764$		0			0
$765$	11.5926	+	22.0990i	0.419130	+	0.798990i
$766$		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
$771$	20.0912	−	8.17488i	0.723568	−	0.294411i
$772$		0			0
$773$	−2.61533			−0.0940670			−0.0470335	−	0.998893i	$-0.514977\pi$
$773$	−2.61533			−0.0940670			−0.0470335	+	0.998893i	$0.514977\pi$
$774$		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
$787$			32.2329i			1.14898i	0.818511	+	0.574490i	$0.194800\pi$
$787$			32.2329i			1.14898i	−0.818511	+	0.574490i	$0.805200\pi$
$788$		0			0
$789$	22.6503	−	9.21615i	0.806373	−	0.328104i
$790$		0			0
$791$	−34.3625			−1.22179
$792$		0			0
$793$	4.72471	+	4.72471i	0.167779	+	0.167779i
$794$		0			0
$795$	−2.82576	−	29.1358i	−0.100219	−	1.03334i
$796$		0			0
$797$	−45.8714			−1.62485			−0.812425	−	0.583066i	$-0.801853\pi$
$797$	−45.8714			−1.62485			−0.812425	+	0.583066i	$0.801853\pi$
$798$		0			0
$799$		−	16.6669i		−	0.589633i
$800$		0			0
$801$	−17.5231	+	17.0891i	−0.619148	+	0.603813i
$802$		0			0
$803$		−	16.1060i		−	0.568369i
$804$		0			0
$805$	−33.1376	+	17.9165i	−1.16795	+	0.631472i
$806$		0			0
$807$	−14.0453	−	34.5188i	−0.494417	−	1.21512i
$808$		0			0
$809$		−	13.9119i		−	0.489115i	−0.969635	−	0.244558i	$-0.921357\pi$
$809$		−	13.9119i		−	0.489115i	0.969635	−	0.244558i	$-0.0786428\pi$
$810$		0			0
$811$	−14.7468	+	14.7468i	−0.517830	+	0.517830i	−0.916914	−	0.399084i	$-0.869328\pi$
$811$	−14.7468	+	14.7468i	−0.517830	+	0.517830i	0.399084	+	0.916914i	$0.369328\pi$
$812$		0			0
$813$	−36.4287	−	15.3575i	−1.27761	−	0.538611i
$814$		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
$819$	−28.3659	−	0.355667i	−0.991185	−	0.0124280i
$820$		0			0
$821$	−14.3064	−	14.3064i	−0.499298	−	0.499298i	0.411922	−	0.911219i	$-0.364858\pi$
$821$	−14.3064	−	14.3064i	−0.499298	−	0.499298i	−0.911219	+	0.411922i	$0.864858\pi$
$822$		0			0
$823$	5.19550	+	5.19550i	0.181104	+	0.181104i	0.791837	−	0.610733i	$-0.209125\pi$
$823$	5.19550	+	5.19550i	0.181104	+	0.181104i	−0.610733	+	0.791837i	$0.709125\pi$
$824$		0			0
$825$	21.0793	+	4.12097i	0.733888	+	0.143474i
$826$		0			0
$827$		−	30.8268i		−	1.07195i	−0.844233	−	0.535977i	$-0.819943\pi$
$827$		−	30.8268i		−	1.07195i	0.844233	−	0.535977i	$-0.180057\pi$
$828$		0			0
$829$	−8.85151	+	8.85151i	−0.307426	+	0.307426i	−0.843910	−	0.536484i	$-0.819752\pi$
$829$	−8.85151	+	8.85151i	−0.307426	+	0.307426i	0.536484	+	0.843910i	$0.319752\pi$
$830$		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
$835$	−10.1928	+	34.1883i	−0.352736	+	1.18313i
$836$		0			0
$837$	5.83955	+	14.8836i	0.201844	+	0.514452i
$838$		0			0
$839$		−	3.85793i		−	0.133190i	−0.997780	−	0.0665952i	$-0.978786\pi$
$839$		−	3.85793i		−	0.133190i	0.997780	−	0.0665952i	$-0.0212136\pi$
$840$		0			0
$841$		−	18.8108i		−	0.648649i
$842$		0			0
$843$	14.9603	+	6.30691i	0.515259	+	0.217222i
$844$		0			0
$845$	−10.1337	−	18.7429i	−0.348611	−	0.644777i
$846$		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
$853$			24.8147i			0.849638i	0.905278	+	0.424819i	$0.139662\pi$
$853$			24.8147i			0.849638i	−0.905278	+	0.424819i	$0.860338\pi$
$854$		0			0
$855$	−3.74834	−	7.14549i	−0.128191	−	0.244371i
$856$		0			0
$857$	1.55141	+	1.55141i	0.0529951	+	0.0529951i	0.733108	−	0.680113i	$-0.238069\pi$
$857$	1.55141	+	1.55141i	0.0529951	+	0.0529951i	−0.680113	+	0.733108i	$0.738069\pi$
$858$		0			0
$859$	−5.93140	−	5.93140i	−0.202377	−	0.202377i	0.598641	−	0.801018i	$-0.295708\pi$
$859$	−5.93140	−	5.93140i	−0.202377	−	0.202377i	−0.801018	+	0.598641i	$0.795708\pi$
$860$		0			0
$861$	−64.2464	+	26.1411i	−2.18951	+	0.890886i
$862$		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
$867$	2.12690	−	5.04510i	0.0722333	−	0.171341i
$868$		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
$875$	−43.3438	+	36.6234i	−1.46529	+	1.23810i
$876$		0			0
$877$		−	33.9586i		−	1.14670i	−0.819310	−	0.573351i	$-0.805643\pi$
$877$		−	33.9586i		−	1.14670i	0.819310	−	0.573351i	$-0.194357\pi$
$878$		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
$883$	−38.5302			−1.29664			−0.648322	−	0.761367i	$-0.724529\pi$
$883$	−38.5302			−1.29664			−0.648322	+	0.761367i	$0.724529\pi$
$884$		0			0
$885$	15.2726	+	12.5721i	0.513384	+	0.422606i
$886$		0			0
$887$	−35.8564	−	35.8564i	−1.20394	−	1.20394i	−0.972958	−	0.230981i	$-0.925807\pi$
$887$	−35.8564	−	35.8564i	−1.20394	−	1.20394i	−0.230981	−	0.972958i	$-0.574193\pi$
$888$		0			0
$889$	29.6706			0.995119
$890$		0			0
$891$	−16.1741	+	15.3826i	−0.541853	+	0.515337i
$892$		0			0
$893$			5.38908i			0.180339i
$894$		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
$907$	52.5256			1.74408			0.872042	−	0.489430i	$-0.162795\pi$
$907$	52.5256			1.74408			0.872042	+	0.489430i	$0.162795\pi$
$908$		0			0
$909$	0.182425	−	14.5491i	0.00605064	−	0.482564i
$910$		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
$915$	−8.82760	+	10.7238i	−0.291831	+	0.354518i
$916$		0			0
$917$		−	42.8989i		−	1.41665i
$918$		0			0
$919$	38.1249			1.25762			0.628812	−	0.777557i	$-0.283542\pi$
$919$	38.1249			1.25762			0.628812	+	0.777557i	$0.283542\pi$
$920$		0			0
$921$	−3.14170	+	7.45224i	−0.103522	+	0.245560i
$922$		0			0
$923$	−21.2518			−0.699510
$924$		0			0
$925$	−25.1672	+	38.4558i	−0.827492	+	1.26442i
$926$		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
$933$	18.9116	+	7.97269i	0.619137	+	0.261014i
$934$		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	$-0.359219\pi$
$937$	40.7663	−	40.7663i	1.33178	−	1.33178i	0.903780	−	0.427998i	$-0.140781\pi$
$938$		0			0
$939$	8.30060	+	20.4002i	0.270880	+	0.665735i
$940$		0			0
$941$	18.7094	−	18.7094i	0.609909	−	0.609909i	−0.333013	−	0.942922i	$-0.608065\pi$
$941$	18.7094	−	18.7094i	0.609909	−	0.609909i	0.942922	+	0.333013i	$0.108065\pi$
$942$		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
$947$	9.81050			0.318799			0.159399	−	0.987214i	$-0.449044\pi$
$947$	9.81050			0.318799			0.159399	+	0.987214i	$0.449044\pi$
$948$		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	$-0.443698\pi$
$953$	35.8210	−	35.8210i	1.16035	−	1.16035i	0.984398	−	0.175957i	$-0.0563020\pi$
$954$		0			0
$955$	−51.8024	+	28.0080i	−1.67629	+	0.906317i
$956$		0			0
$957$	5.32668	−	12.6351i	0.172187	−	0.408435i
$958$		0			0
$959$	−64.4989			−2.08278
$960$		0			0
$961$	−21.5325			−0.694598
$962$		0			0
$963$	−12.8296	+	12.5118i	−0.413428	+	0.403189i
$964$		0			0
$965$	21.6105	+	6.44289i	0.695667	+	0.207404i
$966$		0			0
$967$	−3.81689	+	3.81689i	−0.122743	+	0.122743i	−0.765810	−	0.643067i	$-0.777662\pi$
$967$	−3.81689	+	3.81689i	−0.122743	+	0.122743i	0.643067	+	0.765810i	$0.277662\pi$
$968$		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	$-0.0447283\pi$
$971$	26.4895	+	26.4895i	0.850088	+	0.850088i	−0.140056	+	0.990144i	$0.544728\pi$
$972$		0			0
$973$	−87.2475			−2.79703
$974$		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
$981$	2.37361	+	0.0297616i	0.0757835	+	0.000950214i
$982$		0			0
$983$	−31.9826	+	31.9826i	−1.02009	+	1.02009i	−0.0202915	+	0.999794i	$0.506459\pi$
$983$	−31.9826	+	31.9826i	−1.02009	+	1.02009i	−0.999794	+	0.0202915i	$0.993541\pi$
$984$		0			0
$985$	−25.8915	+	13.9988i	−0.824973	+	0.446038i
$986$		0			0
$987$	−15.2999	+	36.2921i	−0.487001	+	1.15519i
$988$		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
$995$	−18.5062	−	34.2283i	−0.586687	−	1.08511i
$996$		0			0
$997$	39.2793			1.24399			0.621993	−	0.783023i	$-0.286323\pi$
$997$	39.2793			1.24399			0.621993	+	0.783023i	$0.286323\pi$
$998$		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.bf.a.17.5		88
3.2	odd	2	inner	960.2.bf.a.17.6		88
4.3	odd	2		240.2.bf.a.77.2	yes	88
5.3	odd	4		960.2.bb.a.593.27		88
12.11	even	2		240.2.bf.a.77.43	yes	88
15.8	even	4		960.2.bb.a.593.18		88
16.5	even	4		960.2.bb.a.497.18		88
16.11	odd	4		240.2.bb.a.197.21	yes	88
20.3	even	4		240.2.bb.a.173.24	yes	88
48.5	odd	4		960.2.bb.a.497.27		88
48.11	even	4		240.2.bb.a.197.24	yes	88
60.23	odd	4		240.2.bb.a.173.21	✓	88
80.43	even	4		240.2.bf.a.53.43	yes	88
80.53	odd	4	inner	960.2.bf.a.113.5		88
240.53	even	4	inner	960.2.bf.a.113.6		88
240.203	odd	4		240.2.bf.a.53.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.21	✓	88	60.23	odd	4
240.2.bb.a.173.24	yes	88	20.3	even	4
240.2.bb.a.197.21	yes	88	16.11	odd	4
240.2.bb.a.197.24	yes	88	48.11	even	4
240.2.bf.a.53.2	yes	88	240.203	odd	4
240.2.bf.a.53.43	yes	88	80.43	even	4
240.2.bf.a.77.2	yes	88	4.3	odd	2
240.2.bf.a.77.43	yes	88	12.11	even	2
960.2.bb.a.497.18		88	16.5	even	4
960.2.bb.a.497.27		88	48.5	odd	4
960.2.bb.a.593.18		88	15.8	even	4
960.2.bb.a.593.27		88	5.3	odd	4
960.2.bf.a.17.5		88	1.1	even	1	trivial
960.2.bf.a.17.6		88	3.2	odd	2	inner
960.2.bf.a.113.5		88	80.53	odd	4	inner
960.2.bf.a.113.6		88	240.53	even	4	inner

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.bf (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59602 - 0.672846i) q^{3} +(1.06348 + 1.96698i) q^{5} +(3.58885 - 3.58885i) q^{7} +(2.09456 + 2.14775i) q^{9} +O(q^{10})\)	\(q+(-1.59602 - 0.672846i) q^{3} +(1.06348 + 1.96698i) q^{5} +(3.58885 - 3.58885i) q^{7} +(2.09456 + 2.14775i) q^{9} +(1.75370 + 1.75370i) q^{11} -1.86312 q^{13} +(-0.373870 - 3.85490i) q^{15} +(2.63049 - 2.63049i) q^{17} +(-0.850543 + 0.850543i) q^{19} +(-8.14261 + 3.31313i) q^{21} +(-2.34712 + 2.34712i) q^{23} +(-2.73800 + 4.18370i) q^{25} +(-1.89785 - 4.83716i) q^{27} +(2.25712 + 2.25712i) q^{29} -3.07693 q^{31} +(-1.61897 - 3.97892i) q^{33} +(10.8759 + 3.24250i) q^{35} +9.19181 q^{37} +(2.97357 + 1.25359i) q^{39} +7.89015 q^{41} -1.44191i q^{43} +(-1.99705 + 6.40405i) q^{45} +(3.16802 - 3.16802i) q^{47} -18.7596i q^{49} +(-5.96823 + 2.42840i) q^{51} +7.55812 q^{53} +(-1.58446 + 5.31453i) q^{55} +(1.92977 - 0.785199i) q^{57} +(-3.61161 + 3.61161i) q^{59} +(-2.53592 - 2.53592i) q^{61} +(15.2250 + 0.190899i) q^{63} +(-1.98140 - 3.66471i) q^{65} -1.34890i q^{67} +(5.32531 - 2.16680i) q^{69} +11.4066 q^{71} +(-4.59201 - 4.59201i) q^{73} +(7.18489 - 4.83502i) q^{75} +12.5875 q^{77} -1.73652i q^{79} +(-0.225658 + 8.99717i) q^{81} -0.755155i q^{83} +(7.97160 + 2.37663i) q^{85} +(-2.08372 - 5.12110i) q^{87} +8.15881i q^{89} +(-6.68644 + 6.68644i) q^{91} +(4.91083 + 2.07030i) q^{93} +(-2.57754 - 0.768459i) q^{95} +(1.60445 + 1.60445i) q^{97} +(-0.0932835 + 7.43975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3}+O(q^{10}) \) 88 * q + 4 * q^3	\( 88 q + 4 q^{3} - 8 q^{13} + 4 q^{15} - 8 q^{19} - 4 q^{21} + 4 q^{27} + 16 q^{31} - 4 q^{33} - 8 q^{37} + 24 q^{39} + 8 q^{45} + 4 q^{51} - 12 q^{57} - 24 q^{61} + 32 q^{63} + 12 q^{69} + 36 q^{75} - 8 q^{81} + 16 q^{85} - 12 q^{87} + 8 q^{91} - 16 q^{93} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 8 * q^13 + 4 * q^15 - 8 * q^19 - 4 * q^21 + 4 * q^27 + 16 * q^31 - 4 * q^33 - 8 * q^37 + 24 * q^39 + 8 * q^45 + 4 * q^51 - 12 * q^57 - 24 * q^61 + 32 * q^63 + 12 * q^69 + 36 * q^75 - 8 * q^81 + 16 * q^85 - 12 * q^87 + 8 * q^91 - 16 * q^93 - 8 * q^97 - 32 * q^99

Introduction

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