LMFDB - Embedded newform 896.2.ba.f.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(289,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("896.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.ba (of order $12$, degree $4$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	896.289
Dual form			896.2.ba.f.865.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.430984 + 1.60845i) q^{3} +(0.522232 + 1.94900i) q^{5} +(1.89075 + 1.85069i) q^{7} +(0.196696 + 0.113563i) q^{9} +O(q^{10})$	\(q+(-0.430984 + 1.60845i) q^{3} +(0.522232 + 1.94900i) q^{5} +(1.89075 + 1.85069i) q^{7} +(0.196696 + 0.113563i) q^{9} +(6.09856 + 1.63411i) q^{11} +(-1.13388 - 1.13388i) q^{13} -3.35995 q^{15} +(-0.960789 - 1.66414i) q^{17} +(6.09532 - 1.63324i) q^{19} +(-3.79164 + 2.24357i) q^{21} +(0.924606 + 0.533821i) q^{23} +(0.804265 - 0.464342i) q^{25} +(-3.79985 + 3.79985i) q^{27} +(-5.08936 - 5.08936i) q^{29} +(-0.198293 - 0.343454i) q^{31} +(-5.25677 + 9.10499i) q^{33} +(-2.61958 + 4.65156i) q^{35} +(0.0877006 + 0.327303i) q^{37} +(2.31247 - 1.33510i) q^{39} -7.26189i q^{41} +(-1.75565 + 1.75565i) q^{43} +(-0.118612 + 0.442666i) q^{45} +(-1.08118 + 1.87265i) q^{47} +(0.149895 + 6.99839i) q^{49} +(3.09077 - 0.828170i) q^{51} +(0.415727 + 0.111394i) q^{53} +12.7395i q^{55} +10.5079i q^{57} +(-8.67527 - 2.32453i) q^{59} +(-10.1763 + 2.72673i) q^{61} +(0.161735 + 0.578743i) q^{63} +(1.61777 - 2.80206i) q^{65} +(2.10994 - 7.87441i) q^{67} +(-1.25712 + 1.25712i) q^{69} +2.78982i q^{71} +(-2.05730 + 1.18779i) q^{73} +(0.400248 + 1.49375i) q^{75} +(8.50666 + 14.3762i) q^{77} +(5.10829 - 8.84782i) q^{79} +(-4.13352 - 7.15947i) q^{81} +(-1.17951 - 1.17951i) q^{83} +(2.74164 - 2.74164i) q^{85} +(10.3794 - 5.99257i) q^{87} +(-11.0470 - 6.37800i) q^{89} +(-0.0454269 - 4.24233i) q^{91} +(0.637891 - 0.170922i) q^{93} +(6.36634 + 11.0268i) q^{95} -2.21148 q^{97} +(1.01399 + 1.01399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5}+O(q^{10}) $ 48 * q - 4 * q^5	$ 48 q - 4 q^{5} + 4 q^{11} + 24 q^{13} - 40 q^{15} + 8 q^{17} + 4 q^{19} + 8 q^{21} + 24 q^{27} - 24 q^{29} + 28 q^{31} + 16 q^{33} - 28 q^{35} + 24 q^{37} + 40 q^{43} + 28 q^{45} - 20 q^{47} - 24 q^{51} + 16 q^{53} + 20 q^{59} - 8 q^{61} - 16 q^{63} + 8 q^{65} - 48 q^{67} + 40 q^{69} + 4 q^{75} + 20 q^{77} - 36 q^{79} + 8 q^{83} - 64 q^{91} - 8 q^{93} - 4 q^{95} - 48 q^{97} + 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^11 + 24 * q^13 - 40 * q^15 + 8 * q^17 + 4 * q^19 + 8 * q^21 + 24 * q^27 - 24 * q^29 + 28 * q^31 + 16 * q^33 - 28 * q^35 + 24 * q^37 + 40 * q^43 + 28 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 + 20 * q^59 - 8 * q^61 - 16 * q^63 + 8 * q^65 - 48 * q^67 + 40 * q^69 + 4 * q^75 + 20 * q^77 - 36 * q^79 + 8 * q^83 - 64 * q^91 - 8 * q^93 - 4 * q^95 - 48 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.430984	+	1.60845i	−0.248829	+	0.928642i	0.722591	+	0.691275i	$0.242951\pi$
$3$	−0.430984	+	1.60845i	−0.248829	+	0.928642i	−0.971420	+	0.237366i	$0.923716\pi$
$4$		0			0
$5$	0.522232	+	1.94900i	0.233549	+	0.871618i	0.978797	+	0.204831i	$0.0656644\pi$
$5$	0.522232	+	1.94900i	0.233549	+	0.871618i	−0.745248	+	0.666787i	$0.767669\pi$
$6$		0			0
$7$	1.89075	+	1.85069i	0.714638	+	0.699495i
$7$	1.89075	+	1.85069i	0.714638	+	0.699495i
$8$		0			0
$9$	0.196696	+	0.113563i	0.0655654	+	0.0378542i
$10$		0			0
$11$	6.09856	+	1.63411i	1.83879	+	0.492701i	0.998757	−	0.0498403i	$-0.0158712\pi$
$11$	6.09856	+	1.63411i	1.83879	+	0.492701i	0.840029	+	0.542542i	$0.182538\pi$
$12$		0			0
$13$	−1.13388	−	1.13388i	−0.314480	−	0.314480i	0.532162	−	0.846642i	$-0.321380\pi$
$13$	−1.13388	−	1.13388i	−0.314480	−	0.314480i	−0.846642	+	0.532162i	$0.821380\pi$
$14$		0			0
$15$	−3.35995			−0.867535
$16$		0			0
$17$	−0.960789	−	1.66414i	−0.233026	−	0.403612i	0.725671	−	0.688041i	$-0.241529\pi$
$17$	−0.960789	−	1.66414i	−0.233026	−	0.403612i	−0.958697	+	0.284429i	$0.908196\pi$
$18$		0			0
$19$	6.09532	−	1.63324i	1.39836	−	0.374690i	0.520605	−	0.853797i	$-0.325706\pi$
$19$	6.09532	−	1.63324i	1.39836	−	0.374690i	0.877756	+	0.479107i	$0.159040\pi$
$20$		0			0
$21$	−3.79164	+	2.24357i	−0.827403	+	0.489588i
$22$		0			0
$23$	0.924606	+	0.533821i	0.192794	+	0.111309i	0.593290	−	0.804989i	$-0.297829\pi$
$23$	0.924606	+	0.533821i	0.192794	+	0.111309i	−0.400496	+	0.916298i	$0.631162\pi$
$24$		0			0
$25$	0.804265	−	0.464342i	0.160853	−	0.0928685i
$26$		0			0
$27$	−3.79985	+	3.79985i	−0.731281	+	0.731281i
$28$		0			0
$29$	−5.08936	−	5.08936i	−0.945070	−	0.945070i	0.0534979	−	0.998568i	$-0.482963\pi$
$29$	−5.08936	−	5.08936i	−0.945070	−	0.945070i	−0.998568	+	0.0534979i	$0.982963\pi$
$30$		0			0
$31$	−0.198293	−	0.343454i	−0.0356145	−	0.0616861i	0.847669	−	0.530526i	$-0.178006\pi$
$31$	−0.198293	−	0.343454i	−0.0356145	−	0.0616861i	−0.883283	+	0.468840i	$0.844672\pi$
$32$		0			0
$33$	−5.25677	+	9.10499i	−0.915086	+	1.58498i
$34$		0			0
$35$	−2.61958	+	4.65156i	−0.442789	+	0.786257i
$36$		0			0
$37$	0.0877006	+	0.327303i	0.0144179	+	0.0538083i	0.972760	−	0.231814i	$-0.0744662\pi$
$37$	0.0877006	+	0.327303i	0.0144179	+	0.0538083i	−0.958342	+	0.285623i	$0.907800\pi$
$38$		0			0
$39$	2.31247	−	1.33510i	0.370291	−	0.213788i
$40$		0			0
$41$		−	7.26189i		−	1.13412i	−0.823678	−	0.567058i	$-0.808081\pi$
$41$		−	7.26189i		−	1.13412i	0.823678	−	0.567058i	$-0.191919\pi$
$42$		0			0
$43$	−1.75565	+	1.75565i	−0.267734	+	0.267734i	−0.828187	−	0.560452i	$-0.810627\pi$
$43$	−1.75565	+	1.75565i	−0.267734	+	0.267734i	0.560452	+	0.828187i	$0.310627\pi$
$44$		0			0
$45$	−0.118612	+	0.442666i	−0.0176816	+	0.0659888i
$46$		0			0
$47$	−1.08118	+	1.87265i	−0.157706	+	0.273155i	−0.934041	−	0.357166i	$-0.883743\pi$
$47$	−1.08118	+	1.87265i	−0.157706	+	0.273155i	0.776335	+	0.630320i	$0.217076\pi$
$48$		0			0
$49$	0.149895	+	6.99839i	0.0214136	+	0.999771i
$50$		0			0
$51$	3.09077	−	0.828170i	0.432795	−	0.115967i
$52$		0			0
$53$	0.415727	+	0.111394i	0.0571045	+	0.0153011i	0.287258	−	0.957853i	$-0.407256\pi$
$53$	0.415727	+	0.111394i	0.0571045	+	0.0153011i	−0.230154	+	0.973154i	$0.573923\pi$
$54$		0			0
$55$			12.7395i			1.71779i
$56$		0			0
$57$			10.5079i			1.39181i
$58$		0			0
$59$	−8.67527	−	2.32453i	−1.12942	−	0.302628i	−0.354732	−	0.934968i	$-0.615428\pi$
$59$	−8.67527	−	2.32453i	−1.12942	−	0.302628i	−0.774691	+	0.632340i	$0.782095\pi$
$60$		0			0
$61$	−10.1763	+	2.72673i	−1.30294	+	0.349122i	−0.842561	−	0.538601i	$-0.818953\pi$
$61$	−10.1763	+	2.72673i	−1.30294	+	0.349122i	−0.460379	+	0.887722i	$0.652287\pi$
$62$		0			0
$63$	0.161735	+	0.578743i	0.0203767	+	0.0729147i
$64$		0			0
$65$	1.61777	−	2.80206i	0.200660	−	0.347553i
$66$		0			0
$67$	2.10994	−	7.87441i	0.257770	−	0.962012i	−0.708758	−	0.705452i	$-0.750744\pi$
$67$	2.10994	−	7.87441i	0.257770	−	0.962012i	0.966528	−	0.256560i	$-0.0825893\pi$
$68$		0			0
$69$	−1.25712	+	1.25712i	−0.151339	+	0.151339i
$70$		0			0
$71$			2.78982i			0.331090i	0.986202	+	0.165545i	$0.0529384\pi$
$71$			2.78982i			0.331090i	−0.986202	+	0.165545i	$0.947062\pi$
$72$		0			0
$73$	−2.05730	+	1.18779i	−0.240789	+	0.139020i	−0.615539	−	0.788106i	$-0.711062\pi$
$73$	−2.05730	+	1.18779i	−0.240789	+	0.139020i	0.374750	+	0.927126i	$0.377728\pi$
$74$		0			0
$75$	0.400248	+	1.49375i	0.0462167	+	0.172483i
$76$		0			0
$77$	8.50666	+	14.3762i	0.969424	+	1.63832i
$78$		0			0
$79$	5.10829	−	8.84782i	0.574727	−	0.995457i	−0.421344	−	0.906901i	$-0.638441\pi$
$79$	5.10829	−	8.84782i	0.574727	−	0.995457i	0.996071	−	0.0885562i	$-0.0282253\pi$
$80$		0			0
$81$	−4.13352	−	7.15947i	−0.459280	−	0.795496i
$82$		0			0
$83$	−1.17951	−	1.17951i	−0.129468	−	0.129468i	0.639404	−	0.768871i	$-0.279181\pi$
$83$	−1.17951	−	1.17951i	−0.129468	−	0.129468i	−0.768871	+	0.639404i	$0.779181\pi$
$84$		0			0
$85$	2.74164	−	2.74164i	0.297373	−	0.297373i
$86$		0			0
$87$	10.3794	−	5.99257i	1.11279	−	0.642471i
$88$		0			0
$89$	−11.0470	−	6.37800i	−1.17098	−	0.676066i	−0.217070	−	0.976156i	$-0.569650\pi$
$89$	−11.0470	−	6.37800i	−1.17098	−	0.676066i	−0.953911	+	0.300089i	$0.902983\pi$
$90$		0			0
$91$	−0.0454269	−	4.24233i	−0.00476204	−	0.444717i
$92$		0			0
$93$	0.637891	−	0.170922i	0.0661462	−	0.0177238i
$94$		0			0
$95$	6.36634	+	11.0268i	0.653173	+	1.13133i
$96$		0			0
$97$	−2.21148			−0.224542			−0.112271	−	0.993678i	$-0.535813\pi$
$97$	−2.21148			−0.224542			−0.112271	+	0.993678i	$0.535813\pi$
$98$		0			0
$99$	1.01399	+	1.01399i	0.101910	+	0.101910i
$100$		0			0
$101$	6.95024	+	1.86231i	0.691575	+	0.185307i	0.587454	−	0.809258i	$-0.300130\pi$
$101$	6.95024	+	1.86231i	0.691575	+	0.185307i	0.104121	+	0.994565i	$0.466797\pi$
$102$		0			0
$103$	−15.1457	−	8.74438i	−1.49235	−	0.861609i	−0.492390	−	0.870375i	$-0.663877\pi$
$103$	−15.1457	−	8.74438i	−1.49235	−	0.861609i	−0.999962	+	0.00876536i	$0.997210\pi$
$104$		0			0
$105$	−6.35283	−	6.21822i	−0.619973	−	0.606836i
$106$		0			0
$107$	0.779344	+	2.90855i	0.0753420	+	0.281180i	0.993311	−	0.115473i	$-0.0368383\pi$
$107$	0.779344	+	2.90855i	0.0753420	+	0.281180i	−0.917969	+	0.396653i	$0.870172\pi$
$108$		0			0
$109$	1.83957	−	6.86536i	0.176199	−	0.657583i	−0.820146	−	0.572155i	$-0.806108\pi$
$109$	1.83957	−	6.86536i	0.176199	−	0.657583i	0.996344	−	0.0854277i	$-0.0272257\pi$
$110$		0			0
$111$	−0.564250			−0.0535562
$112$		0			0
$113$	−5.96535			−0.561173			−0.280586	−	0.959829i	$-0.590529\pi$
$113$	−5.96535			−0.561173			−0.280586	+	0.959829i	$0.590529\pi$
$114$		0			0
$115$	−0.557557	+	2.08083i	−0.0519925	+	0.194039i
$116$		0			0
$117$	−0.0942631	−	0.351795i	−0.00871463	−	0.0325234i
$118$		0			0
$119$	1.26318	−	4.92459i	0.115796	−	0.451437i
$120$		0			0
$121$	24.9959	+	14.4314i	2.27235	+	1.31194i
$122$		0			0
$123$	11.6804	+	3.12976i	1.05319	+	0.282201i
$124$		0			0
$125$	8.45884	+	8.45884i	0.756582	+	0.756582i
$126$		0			0
$127$	6.41296			0.569058			0.284529	−	0.958667i	$-0.408163\pi$
$127$	6.41296			0.569058			0.284529	+	0.958667i	$0.408163\pi$
$128$		0			0
$129$	−2.06723	−	3.58055i	−0.182009	−	0.315250i
$130$		0			0
$131$	−14.4542	+	3.87298i	−1.26287	+	0.338384i	−0.827294	−	0.561769i	$-0.810121\pi$
$131$	−14.4542	+	3.87298i	−1.26287	+	0.338384i	−0.435573	+	0.900154i	$0.643454\pi$
$132$		0			0
$133$	14.5474	+	8.19250i	1.26142	+	0.710380i
$134$		0			0
$135$	−9.39029	−	5.42149i	−0.808187	−	0.466607i
$136$		0			0
$137$	−1.50928	+	0.871382i	−0.128946	+	0.0744472i	−0.563086	−	0.826399i	$-0.690386\pi$
$137$	−1.50928	+	0.871382i	−0.128946	+	0.0744472i	0.434139	+	0.900846i	$0.357053\pi$
$138$		0			0
$139$	−2.84436	+	2.84436i	−0.241256	+	0.241256i	−0.817370	−	0.576114i	$-0.804569\pi$
$139$	−2.84436	+	2.84436i	−0.241256	+	0.241256i	0.576114	+	0.817370i	$0.304569\pi$
$140$		0			0
$141$	−2.54611	−	2.54611i	−0.214421	−	0.214421i
$142$		0			0
$143$	−5.06214	−	8.76788i	−0.423317	−	0.733207i
$144$		0			0
$145$	7.26132	−	12.5770i	0.603020	−	1.04446i
$146$		0			0
$147$	−11.3212	−	2.77510i	−0.933757	−	0.228886i
$148$		0			0
$149$	−4.76543	−	17.7848i	−0.390399	−	1.45699i	−0.829477	−	0.558541i	$-0.811361\pi$
$149$	−4.76543	−	17.7848i	−0.390399	−	1.45699i	0.439077	−	0.898449i	$-0.355305\pi$
$150$		0			0
$151$	5.52437	−	3.18949i	0.449567	−	0.259557i	−0.258081	−	0.966123i	$-0.583090\pi$
$151$	5.52437	−	3.18949i	0.449567	−	0.259557i	0.707647	+	0.706566i	$0.249757\pi$
$152$		0			0
$153$		−	0.436439i		−	0.0352840i
$154$		0			0
$155$	0.565835	−	0.565835i	0.0454490	−	0.0454490i
$156$		0			0
$157$	4.72065	−	17.6177i	0.376749	−	1.40605i	−0.474024	−	0.880512i	$-0.657199\pi$
$157$	4.72065	−	17.6177i	0.376749	−	1.40605i	0.850773	−	0.525534i	$-0.176134\pi$
$158$		0			0
$159$	−0.358344	+	0.620669i	−0.0284185	+	0.0492223i
$160$		0			0
$161$	0.760264	+	2.72048i	0.0599172	+	0.214404i
$162$		0			0
$163$	11.0968	−	2.97338i	0.869170	−	0.232893i	0.203441	−	0.979087i	$-0.434787\pi$
$163$	11.0968	−	2.97338i	0.869170	−	0.232893i	0.665729	+	0.746194i	$0.268121\pi$
$164$		0			0
$165$	−20.4909	−	5.49051i	−1.59521	−	0.427435i
$166$		0			0
$167$			21.6693i			1.67682i	0.545040	+	0.838410i	$0.316514\pi$
$167$			21.6693i			1.67682i	−0.545040	+	0.838410i	$0.683486\pi$
$168$		0			0
$169$		−	10.4287i		−	0.802204i
$170$		0			0
$171$	1.38440	+	0.370949i	0.105868	+	0.0283672i
$172$		0			0
$173$	12.3596	−	3.31175i	0.939684	−	0.251788i	0.243705	−	0.969849i	$-0.421637\pi$
$173$	12.3596	−	3.31175i	0.939684	−	0.251788i	0.695979	+	0.718062i	$0.254970\pi$
$174$		0			0
$175$	2.38002	+	0.610487i	0.179913	+	0.0461485i
$176$		0			0
$177$	7.47780	−	12.9519i	0.562066	−	0.973527i
$178$		0			0
$179$	0.819762	−	3.05939i	0.0612719	−	0.228670i	−0.928499	−	0.371334i	$-0.878900\pi$
$179$	0.819762	−	3.05939i	0.0612719	−	0.228670i	0.989771	+	0.142665i	$0.0455670\pi$
$180$		0			0
$181$	14.3765	−	14.3765i	1.06860	−	1.06860i	0.0711279	−	0.997467i	$-0.477340\pi$
$181$	14.3765	−	14.3765i	1.06860	−	1.06860i	0.997467	−	0.0711279i	$-0.0226598\pi$
$182$		0			0
$183$		−	17.5433i		−	1.29684i
$184$		0			0
$185$	−0.592113	+	0.341857i	−0.0435330	+	0.0251338i
$186$		0			0
$187$	−3.14006	−	11.7189i	−0.229624	−	0.856969i
$188$		0			0
$189$	−14.2169	+	0.152235i	−1.03413	+	0.0110735i
$190$		0			0
$191$	−6.12089	+	10.6017i	−0.442892	+	0.767111i	−0.997903	−	0.0647319i	$-0.979381\pi$
$191$	−6.12089	+	10.6017i	−0.442892	+	0.767111i	0.555011	+	0.831843i	$0.312714\pi$
$192$		0			0
$193$	1.08900	+	1.88620i	0.0783877	+	0.135771i	0.902554	−	0.430576i	$-0.141689\pi$
$193$	1.08900	+	1.88620i	0.0783877	+	0.135771i	−0.824167	+	0.566347i	$0.808356\pi$
$194$		0			0
$195$	3.80976	+	3.80976i	0.272823	+	0.272823i
$196$		0			0
$197$	−9.97878	+	9.97878i	−0.710959	+	0.710959i	−0.966736	−	0.255777i	$-0.917669\pi$
$197$	−9.97878	+	9.97878i	−0.710959	+	0.710959i	0.255777	+	0.966736i	$0.417669\pi$
$198$		0			0
$199$	9.14271	−	5.27854i	0.648109	−	0.374186i	−0.139622	−	0.990205i	$-0.544589\pi$
$199$	9.14271	−	5.27854i	0.648109	−	0.374186i	0.787731	+	0.616019i	$0.211255\pi$
$200$		0			0
$201$	11.7563	+	6.78749i	0.829224	+	0.478753i
$202$		0			0
$203$	−0.203897	−	19.0415i	−0.0143108	−	1.33645i
$204$		0			0
$205$	14.1534	−	3.79239i	0.988516	−	0.264872i
$206$		0			0
$207$	0.121244	+	0.210001i	0.00842706	+	0.0145961i
$208$		0			0
$209$	39.8416			2.75590
$210$		0			0
$211$	−5.20378	−	5.20378i	−0.358243	−	0.358243i	0.504922	−	0.863165i	$-0.331521\pi$
$211$	−5.20378	−	5.20378i	−0.358243	−	0.358243i	−0.863165	+	0.504922i	$0.831521\pi$
$212$		0			0
$213$	−4.48730	−	1.20237i	−0.307464	−	0.0823849i
$214$		0			0
$215$	−4.33862	−	2.50490i	−0.295891	−	0.170833i
$216$		0			0
$217$	0.260703	−	1.01636i	0.0176977	−	0.0689953i
$218$		0			0
$219$	−1.02383	−	3.82100i	−0.0691843	−	0.258199i
$220$		0			0
$221$	−0.797507	+	2.97634i	−0.0536461	+	0.200210i
$222$		0			0
$223$	−22.3888			−1.49926			−0.749632	−	0.661855i	$-0.769770\pi$
$223$	−22.3888			−1.49926			−0.749632	+	0.661855i	$0.769770\pi$
$224$		0			0
$225$	0.210928			0.0140619
$226$		0			0
$227$	−4.81647	+	17.9753i	−0.319680	+	1.19306i	0.599872	+	0.800096i	$0.295218\pi$
$227$	−4.81647	+	17.9753i	−0.319680	+	1.19306i	−0.919552	+	0.392967i	$0.871448\pi$
$228$		0			0
$229$	2.17689	+	8.12426i	0.143853	+	0.536866i	0.999804	+	0.0198093i	$0.00630590\pi$
$229$	2.17689	+	8.12426i	0.143853	+	0.536866i	−0.855951	+	0.517057i	$0.827027\pi$
$230$		0			0
$231$	−26.7898	+	7.48664i	−1.76264	+	0.492585i
$232$		0			0
$233$	−14.9278	−	8.61859i	−0.977955	−	0.564623i	−0.0763032	−	0.997085i	$-0.524312\pi$
$233$	−14.9278	−	8.61859i	−0.977955	−	0.564623i	−0.901652	+	0.432462i	$0.857645\pi$
$234$		0			0
$235$	−4.21442	−	1.12925i	−0.274919	−	0.0736642i
$236$		0			0
$237$	12.0297	+	12.0297i	0.781414	+	0.781414i
$238$		0			0
$239$	−0.572679			−0.0370435			−0.0185218	−	0.999828i	$-0.505896\pi$
$239$	−0.572679			−0.0370435			−0.0185218	+	0.999828i	$0.505896\pi$
$240$		0			0
$241$	5.89318	+	10.2073i	0.379613	+	0.657510i	0.991006	−	0.133818i	$-0.0427237\pi$
$241$	5.89318	+	10.2073i	0.379613	+	0.657510i	−0.611393	+	0.791327i	$0.709390\pi$
$242$		0			0
$243$	−2.27490	+	0.609557i	−0.145935	+	0.0391031i
$244$		0			0
$245$	−13.5616	+	3.94693i	−0.866417	+	0.252160i
$246$		0			0
$247$	−8.76321	−	5.05944i	−0.557590	−	0.321925i
$248$		0			0
$249$	2.40553	−	1.38883i	0.152444	−	0.0880137i
$250$		0			0
$251$	5.57539	−	5.57539i	0.351916	−	0.351916i	−0.508906	−	0.860822i	$-0.669950\pi$
$251$	5.57539	−	5.57539i	0.351916	−	0.351916i	0.860822	+	0.508906i	$0.169950\pi$
$252$		0			0
$253$	4.76645	+	4.76645i	0.299664	+	0.299664i
$254$		0			0
$255$	3.22820	+	5.59141i	0.202158	+	0.350148i
$256$		0			0
$257$	−14.5328	+	25.1715i	−0.906528	+	1.57015i	−0.0876753	+	0.996149i	$0.527944\pi$
$257$	−14.5328	+	25.1715i	−0.906528	+	1.57015i	−0.818853	+	0.574004i	$0.805390\pi$
$258$		0			0
$259$	−0.439916	+	0.781156i	−0.0273351	+	0.0485387i
$260$		0			0
$261$	−0.423097	−	1.57902i	−0.0261890	−	0.0977388i
$262$		0			0
$263$	15.3142	−	8.84163i	0.944311	−	0.545198i	0.0530021	−	0.998594i	$-0.483121\pi$
$263$	15.3142	−	8.84163i	0.944311	−	0.545198i	0.891309	+	0.453396i	$0.149788\pi$
$264$		0			0
$265$			0.868424i			0.0533469i
$266$		0			0
$267$	15.0198	−	15.0198i	0.919198	−	0.919198i
$268$		0			0
$269$	3.86566	−	14.4268i	0.235693	−	0.879620i	−0.742142	−	0.670243i	$-0.766190\pi$
$269$	3.86566	−	14.4268i	0.235693	−	0.879620i	0.977835	−	0.209377i	$-0.0671435\pi$
$270$		0			0
$271$	6.93172	−	12.0061i	0.421072	−	0.729319i	−0.574972	−	0.818173i	$-0.694987\pi$
$271$	6.93172	−	12.0061i	0.421072	−	0.729319i	0.996045	+	0.0888543i	$0.0283205\pi$
$272$		0			0
$273$	6.84317	+	1.75531i	0.414168	+	0.106236i
$274$		0			0
$275$	5.66364	−	1.51757i	0.341531	−	0.0915128i
$276$		0			0
$277$	−2.22980	−	0.597472i	−0.133975	−	0.0358986i	0.191208	−	0.981550i	$-0.438759\pi$
$277$	−2.22980	−	0.597472i	−0.133975	−	0.0358986i	−0.325184	+	0.945651i	$0.605426\pi$
$278$		0			0
$279$		−	0.0900747i		−	0.00539263i
$280$		0			0
$281$			0.680351i			0.0405863i	0.999794	+	0.0202932i	$0.00645996\pi$
$281$			0.680351i			0.0405863i	−0.999794	+	0.0202932i	$0.993540\pi$
$282$		0			0
$283$	0.367652	+	0.0985120i	0.0218546	+	0.00585593i	0.269730	−	0.962936i	$-0.413066\pi$
$283$	0.367652	+	0.0985120i	0.0218546	+	0.00585593i	−0.247875	+	0.968792i	$0.579732\pi$
$284$		0			0
$285$	−20.4799	+	5.48759i	−1.21313	+	0.325056i
$286$		0			0
$287$	13.4395	−	13.7304i	0.793309	−	0.810482i
$288$		0			0
$289$	6.65377	−	11.5247i	0.391398	−	0.677921i
$290$		0			0
$291$	0.953115	−	3.55707i	0.0558726	−	0.208519i
$292$		0			0
$293$	−7.49220	+	7.49220i	−0.437699	+	0.437699i	−0.891237	−	0.453538i	$-0.850162\pi$
$293$	−7.49220	+	7.49220i	−0.437699	+	0.437699i	0.453538	+	0.891237i	$0.350162\pi$
$294$		0			0
$295$		−	18.1220i		−	1.05510i
$296$		0			0
$297$	−29.3829	+	16.9643i	−1.70497	+	0.984366i
$298$		0			0
$299$	−0.443101	−	1.65367i	−0.0256252	−	0.0956345i
$300$		0			0
$301$	−6.56867	+	0.0703375i	−0.378612	+	0.00405418i
$302$		0			0
$303$	−5.99089	+	10.3765i	−0.344168	+	0.596116i
$304$		0			0
$305$	−10.6288	−	18.4096i	−0.608602	−	1.05413i
$306$		0			0
$307$	6.27988	+	6.27988i	0.358412	+	0.358412i	0.863227	−	0.504816i	$-0.168439\pi$
$307$	6.27988	+	6.27988i	0.358412	+	0.358412i	−0.504816	+	0.863227i	$0.668439\pi$
$308$		0			0
$309$	20.5925	−	20.5925i	1.17147	−	1.17147i
$310$		0			0
$311$	−8.55685	+	4.94030i	−0.485215	+	0.280139i	−0.722587	−	0.691280i	$-0.757047\pi$
$311$	−8.55685	+	4.94030i	−0.485215	+	0.280139i	0.237372	+	0.971419i	$0.423714\pi$
$312$		0			0
$313$	14.8734	+	8.58714i	0.840692	+	0.485374i	0.857499	−	0.514485i	$-0.172017\pi$
$313$	14.8734	+	8.58714i	0.840692	+	0.485374i	−0.0168075	+	0.999859i	$0.505350\pi$
$314$		0			0
$315$	−1.04350	+	0.617459i	−0.0587948	+	0.0347899i
$316$		0			0
$317$	−20.5214	+	5.49870i	−1.15260	+	0.308838i	−0.784006	−	0.620754i	$-0.786827\pi$
$317$	−20.5214	+	5.49870i	−1.15260	+	0.308838i	−0.368592	+	0.929591i	$0.620160\pi$
$318$		0			0
$319$	−22.7212	−	39.3543i	−1.27214	−	2.20342i
$320$		0			0
$321$	−5.01416			−0.279863
$322$		0			0
$323$	−8.57424	−	8.57424i	−0.477084	−	0.477084i
$324$		0			0
$325$	−1.43844	−	0.385429i	−0.0797904	−	0.0213798i
$326$		0			0
$327$	10.2498	+	5.91773i	0.566815	+	0.327251i
$328$		0			0
$329$	−5.50994	+	1.53980i	−0.303773	+	0.0848921i
$330$		0			0
$331$	6.26326	+	23.3748i	0.344260	+	1.28479i	0.893475	+	0.449113i	$0.148260\pi$
$331$	6.26326	+	23.3748i	0.344260	+	1.28479i	−0.549215	+	0.835681i	$0.685073\pi$
$332$		0			0
$333$	−0.0199190	+	0.0743388i	−0.00109156	+	0.00407374i
$334$		0			0
$335$	16.4491			0.898709
$336$		0			0
$337$	−4.26739			−0.232460			−0.116230	−	0.993222i	$-0.537081\pi$
$337$	−4.26739			−0.232460			−0.116230	+	0.993222i	$0.537081\pi$
$338$		0			0
$339$	2.57097	−	9.59499i	0.139636	−	0.521128i
$340$		0			0
$341$	−0.648063	−	2.41861i	−0.0350946	−	0.130975i
$342$		0			0
$343$	−12.6684	+	13.5096i	−0.684032	+	0.729452i
$344$		0			0
$345$	−3.10663	−	1.79361i	−0.167255	−	0.0965648i
$346$		0			0
$347$	−0.0521865	−	0.0139833i	−0.00280152	−	0.000750664i	0.257418	−	0.966300i	$-0.417128\pi$
$347$	−0.0521865	−	0.0139833i	−0.00280152	−	0.000750664i	−0.260220	+	0.965549i	$0.583795\pi$
$348$		0			0
$349$	15.4928	+	15.4928i	0.829309	+	0.829309i	0.987421	−	0.158112i	$-0.0505407\pi$
$349$	15.4928	+	15.4928i	0.829309	+	0.829309i	−0.158112	+	0.987421i	$0.550541\pi$
$350$		0			0
$351$	8.61710			0.459947
$352$		0			0
$353$	−8.38161	−	14.5174i	−0.446108	−	0.772682i	0.552020	−	0.833831i	$-0.313857\pi$
$353$	−8.38161	−	14.5174i	−0.446108	−	0.772682i	−0.998129	+	0.0611484i	$0.980524\pi$
$354$		0			0
$355$	−5.43735	+	1.45693i	−0.288584	+	0.0773259i
$356$		0			0
$357$	7.37657	+	4.15420i	0.390410	+	0.219863i
$358$		0			0
$359$	29.8777	+	17.2499i	1.57689	+	0.910415i	0.995291	+	0.0969365i	$0.0309044\pi$
$359$	29.8777	+	17.2499i	1.57689	+	0.910415i	0.581595	+	0.813479i	$0.302429\pi$
$360$		0			0
$361$	18.0310	−	10.4102i	0.948998	−	0.547904i
$362$		0			0
$363$	−33.9851	+	33.9851i	−1.78375	+	1.78375i
$364$		0			0
$365$	−3.38938	−	3.38938i	−0.177408	−	0.177408i
$366$		0			0
$367$	10.2644	+	17.7785i	0.535799	+	0.928032i	0.999124	+	0.0418433i	$0.0133230\pi$
$367$	10.2644	+	17.7785i	0.535799	+	0.928032i	−0.463325	+	0.886189i	$0.653344\pi$
$368$		0			0
$369$	0.824679	−	1.42839i	0.0429311	−	0.0743588i
$370$		0			0
$371$	0.579882	+	0.980000i	0.0301060	+	0.0508791i
$372$		0			0
$373$	4.09353	+	15.2773i	0.211955	+	0.791027i	0.987216	+	0.159386i	$0.0509514\pi$
$373$	4.09353	+	15.2773i	0.211955	+	0.791027i	−0.775261	+	0.631641i	$0.782382\pi$
$374$		0			0
$375$	−17.2513	+	9.96003i	−0.890853	+	0.514334i
$376$		0			0
$377$			11.5414i			0.594412i
$378$		0			0
$379$	−11.2717	+	11.2717i	−0.578987	+	0.578987i	−0.934624	−	0.355637i	$-0.884264\pi$
$379$	−11.2717	+	11.2717i	−0.578987	+	0.578987i	0.355637	+	0.934624i	$0.384264\pi$
$380$		0			0
$381$	−2.76388	+	10.3150i	−0.141598	+	0.528451i
$382$		0			0
$383$	−5.14594	+	8.91303i	−0.262945	+	0.455434i	−0.967023	−	0.254688i	$-0.918027\pi$
$383$	−5.14594	+	8.91303i	−0.262945	+	0.455434i	0.704078	+	0.710123i	$0.251360\pi$
$384$		0			0
$385$	−23.5768	+	24.0872i	−1.20158	+	1.22760i
$386$		0			0
$387$	−0.544707	+	0.145954i	−0.0276890	+	0.00741925i
$388$		0			0
$389$	19.7990	+	5.30513i	1.00385	+	0.268981i	0.723058	−	0.690788i	$-0.242736\pi$
$389$	19.7990	+	5.30513i	1.00385	+	0.268981i	0.280792	+	0.959769i	$0.409403\pi$
$390$		0			0
$391$		−	2.05156i		−	0.103752i
$392$		0			0
$393$		−	24.9181i		−	1.25695i
$394$		0			0
$395$	19.9121	+	5.33543i	1.00189	+	0.268454i
$396$		0			0
$397$	−7.56231	+	2.02632i	−0.379542	+	0.101698i	−0.443546	−	0.896252i	$-0.646280\pi$
$397$	−7.56231	+	2.02632i	−0.379542	+	0.101698i	0.0640041	+	0.997950i	$0.479613\pi$
$398$		0			0
$399$	−19.4469	+	19.8679i	−0.973565	+	0.994640i
$400$		0			0
$401$	−7.09985	+	12.2973i	−0.354549	+	0.614098i	−0.987041	−	0.160470i	$-0.948699\pi$
$401$	−7.09985	+	12.2973i	−0.354549	+	0.614098i	0.632491	+	0.774567i	$0.282032\pi$
$402$		0			0
$403$	−0.164594	+	0.614273i	−0.00819901	+	0.0305991i
$404$		0			0
$405$	11.7951	−	11.7951i	0.586104	−	0.586104i
$406$		0			0
$407$			2.13939i			0.106046i
$408$		0			0
$409$	22.8759	−	13.2074i	1.13114	−	0.653065i	0.186920	−	0.982375i	$-0.440149\pi$
$409$	22.8759	−	13.2074i	1.13114	−	0.653065i	0.944222	+	0.329310i	$0.106816\pi$
$410$		0			0
$411$	−0.751104	−	2.80316i	−0.0370492	−	0.138270i
$412$		0			0
$413$	−12.1008	−	20.4503i	−0.595442	−	1.00630i
$414$		0			0
$415$	1.68288	−	2.91483i	0.0826092	−	0.143083i
$416$		0			0
$417$	−3.34915	−	5.80091i	−0.164009	−	0.284072i
$418$		0			0
$419$	15.6893	+	15.6893i	0.766471	+	0.766471i	0.977483	−	0.211012i	$-0.0676759\pi$
$419$	15.6893	+	15.6893i	0.766471	+	0.766471i	−0.211012	+	0.977483i	$0.567676\pi$
$420$		0			0
$421$	−25.7068	+	25.7068i	−1.25287	+	1.25287i	−0.298444	+	0.954427i	$0.596468\pi$
$421$	−25.7068	+	25.7068i	−1.25287	+	1.25287i	−0.954427	+	0.298444i	$0.903532\pi$
$422$		0			0
$423$	−0.425327	+	0.245563i	−0.0206801	+	0.0119397i
$424$		0			0
$425$	−1.54546	−	0.892270i	−0.0749657	−	0.0432815i
$426$		0			0
$427$	−24.2872	−	13.6776i	−1.17534	−	0.661905i
$428$		0			0
$429$	16.2844	−	4.36340i	0.786220	−	0.210667i
$430$		0			0
$431$	12.3981	+	21.4741i	0.597194	+	1.03437i	0.993233	+	0.116137i	$0.0370510\pi$
$431$	12.3981	+	21.4741i	0.597194	+	1.03437i	−0.396039	+	0.918234i	$0.629616\pi$
$432$		0			0
$433$	5.22863			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$433$	5.22863			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$434$		0			0
$435$	17.1000	+	17.1000i	0.819881	+	0.819881i
$436$		0			0
$437$	6.50762	+	1.74371i	0.311302	+	0.0834131i
$438$		0			0
$439$	19.1771	+	11.0719i	0.915273	+	0.528433i	0.882124	−	0.471017i	$-0.156113\pi$
$439$	19.1771	+	11.0719i	0.915273	+	0.528433i	0.0331491	+	0.999450i	$0.489446\pi$
$440$		0			0
$441$	−0.765272	+	1.39358i	−0.0364415	+	0.0663610i
$442$		0			0
$443$	5.84309	+	21.8067i	0.277614	+	1.03607i	0.954070	+	0.299585i	$0.0968483\pi$
$443$	5.84309	+	21.8067i	0.277614	+	1.03607i	−0.676456	+	0.736483i	$0.736485\pi$
$444$		0			0
$445$	6.66159	−	24.8614i	0.315790	−	1.17854i
$446$		0			0
$447$	30.6599			1.45017
$448$		0			0
$449$	−36.3678			−1.71630			−0.858152	−	0.513396i	$-0.828387\pi$
$449$	−36.3678			−1.71630			−0.858152	+	0.513396i	$0.828387\pi$
$450$		0			0
$451$	11.8667	−	44.2871i	0.558781	−	2.08540i
$452$		0			0
$453$	2.74924	+	10.2603i	0.129171	+	0.482072i
$454$		0			0
$455$	8.24456	−	2.30402i	0.386511	−	0.108014i
$456$		0			0
$457$	−21.5807	−	12.4596i	−1.00950	−	0.582837i	−0.0984570	−	0.995141i	$-0.531391\pi$
$457$	−21.5807	−	12.4596i	−1.00950	−	0.582837i	−0.911046	+	0.412304i	$0.864724\pi$
$458$		0			0
$459$	9.97431	+	2.67261i	0.465561	+	0.124747i
$460$		0			0
$461$	1.60588	+	1.60588i	0.0747933	+	0.0747933i	0.743514	−	0.668721i	$-0.233158\pi$
$461$	1.60588	+	1.60588i	0.0747933	+	0.0747933i	−0.668721	+	0.743514i	$0.733158\pi$
$462$		0			0
$463$	−14.8176			−0.688634			−0.344317	−	0.938853i	$-0.611890\pi$
$463$	−14.8176			−0.688634			−0.344317	+	0.938853i	$0.611890\pi$
$464$		0			0
$465$	0.666254	+	1.15399i	0.0308968	+	0.0535148i
$466$		0			0
$467$	−11.9916	+	3.21315i	−0.554907	+	0.148687i	−0.525365	−	0.850877i	$-0.676071\pi$
$467$	−11.9916	+	3.21315i	−0.554907	+	0.148687i	−0.0295414	+	0.999564i	$0.509405\pi$
$468$		0			0
$469$	18.5625	−	10.9837i	0.857135	−	0.507181i
$470$		0			0
$471$	26.3028	+	15.1859i	1.21197	+	0.699730i
$472$		0			0
$473$	−13.5759	+	7.83804i	−0.624220	+	0.360393i
$474$		0			0
$475$	4.14387	−	4.14387i	0.190134	−	0.190134i
$476$		0			0
$477$	0.0691218	+	0.0691218i	0.00316487	+	0.00316487i
$478$		0			0
$479$	1.02709	+	1.77897i	0.0469288	+	0.0812831i	0.888536	−	0.458808i	$-0.151723\pi$
$479$	1.02709	+	1.77897i	0.0469288	+	0.0812831i	−0.841607	+	0.540091i	$0.818390\pi$
$480$		0			0
$481$	0.271679	−	0.470563i	0.0123875	−	0.0214558i
$482$		0			0
$483$	−4.70344	+	0.0503645i	−0.214014	+	0.00229166i
$484$		0			0
$485$	−1.15491	−	4.31018i	−0.0524417	−	0.195715i
$486$		0			0
$487$	35.4045	−	20.4408i	1.60433	−	0.926261i	0.613724	−	0.789521i	$-0.289671\pi$
$487$	35.4045	−	20.4408i	1.60433	−	0.926261i	0.990607	−	0.136740i	$-0.0436625\pi$
$488$		0			0
$489$			19.1302i			0.865098i
$490$		0			0
$491$	0.278015	−	0.278015i	0.0125466	−	0.0125466i	−0.700806	−	0.713352i	$-0.747176\pi$
$491$	0.278015	−	0.278015i	0.0125466	−	0.0125466i	0.713352	+	0.700806i	$0.247176\pi$
$492$		0			0
$493$	−3.57958	+	13.3592i	−0.161216	+	0.601667i
$494$		0			0
$495$	−1.44673	+	2.50580i	−0.0650255	+	0.112628i
$496$		0			0
$497$	−5.16309	+	5.27486i	−0.231596	+	0.236610i
$498$		0			0
$499$	−11.9067	+	3.19039i	−0.533018	+	0.142822i	−0.515281	−	0.857021i	$-0.672313\pi$
$499$	−11.9067	+	3.19039i	−0.533018	+	0.142822i	−0.0177363	+	0.999843i	$0.505646\pi$
$500$		0			0
$501$	−34.8541	−	9.33912i	−1.55717	−	0.417241i
$502$		0			0
$503$			0.367839i			0.0164011i	0.999966	+	0.00820057i	$0.00261035\pi$
$503$			0.367839i			0.0164011i	−0.999966	+	0.00820057i	$0.997390\pi$
$504$		0			0
$505$			14.5186i			0.646068i
$506$		0			0
$507$	16.7740	+	4.49459i	0.744960	+	0.199612i
$508$		0			0
$509$	−7.83060	+	2.09820i	−0.347085	+	0.0930012i	−0.428150	−	0.903708i	$-0.640835\pi$
$509$	−7.83060	+	2.09820i	−0.347085	+	0.0930012i	0.0810649	+	0.996709i	$0.474168\pi$
$510$		0			0
$511$	−6.08808	−	1.56162i	−0.269321	−	0.0690822i
$512$		0			0
$513$	−16.9552	+	29.3673i	−0.748591	+	1.29660i
$514$		0			0
$515$	9.13319	−	34.0855i	0.402457	−	1.50199i
$516$		0			0
$517$	−9.65374	+	9.65374i	−0.424571	+	0.424571i
$518$		0			0
$519$			21.3072i			0.935282i
$520$		0			0
$521$	11.5215	−	6.65193i	0.504766	−	0.291427i	−0.225914	−	0.974147i	$-0.572537\pi$
$521$	11.5215	−	6.65193i	0.504766	−	0.291427i	0.730679	+	0.682721i	$0.239203\pi$
$522$		0			0
$523$	−7.35616	−	27.4536i	−0.321663	−	1.20046i	−0.917625	−	0.397448i	$-0.869896\pi$
$523$	−7.35616	−	27.4536i	−0.321663	−	1.20046i	0.595962	−	0.803013i	$-0.296771\pi$
$524$		0			0
$525$	−2.00769	+	3.56504i	−0.0876229	+	0.155591i
$526$		0			0
$527$	−0.381036	+	0.659973i	−0.0165982	+	0.0287489i
$528$		0			0
$529$	−10.9301	−	18.9314i	−0.475220	−	0.823106i
$530$		0			0
$531$	−1.44241	−	1.44241i	−0.0625954	−	0.0625954i
$532$		0			0
$533$	−8.23408	+	8.23408i	−0.356657	+	0.356657i
$534$		0			0
$535$	−5.26176	+	3.03788i	−0.227486	+	0.131339i
$536$		0			0
$537$	4.56759	+	2.63710i	0.197106	+	0.113799i
$538$		0			0
$539$	−10.5220	+	42.9251i	−0.453213	+	1.84892i
$540$		0			0
$541$	−17.7572	+	4.75802i	−0.763441	+	0.204563i	−0.619472	−	0.785019i	$-0.712653\pi$
$541$	−17.7572	+	4.75802i	−0.763441	+	0.204563i	−0.143969	+	0.989582i	$0.545987\pi$
$542$		0			0
$543$	16.9279	+	29.3199i	0.726445	+	1.25824i
$544$		0			0
$545$	14.3413			0.614312
$546$		0			0
$547$	22.9801	+	22.9801i	0.982558	+	0.982558i	0.999850	−	0.0172930i	$-0.00550479\pi$
$547$	22.9801	+	22.9801i	0.982558	+	0.982558i	−0.0172930	+	0.999850i	$0.505505\pi$
$548$		0			0
$549$	−2.31129	−	0.619309i	−0.0986436	−	0.0264315i
$550$		0			0
$551$	−39.3334	−	22.7091i	−1.67566	−	0.967442i
$552$		0			0
$553$	26.0331	−	7.27518i	1.10704	−	0.309372i
$554$		0			0
$555$	−0.294670	−	1.09972i	−0.0125080	−	0.0466806i
$556$		0			0
$557$	1.20665	−	4.50327i	0.0511273	−	0.190810i	−0.935639	−	0.352958i	$-0.885176\pi$
$557$	1.20665	−	4.50327i	0.0511273	−	0.190810i	0.986766	+	0.162149i	$0.0518424\pi$
$558$		0			0
$559$	3.98138			0.168394
$560$		0			0
$561$	20.2026			0.852954
$562$		0			0
$563$	−1.08332	+	4.04301i	−0.0456566	+	0.170393i	−0.984990	−	0.172614i	$-0.944779\pi$
$563$	−1.08332	+	4.04301i	−0.0456566	+	0.170393i	0.939333	+	0.343007i	$0.111445\pi$
$564$		0			0
$565$	−3.11530	−	11.6264i	−0.131061	−	0.489128i
$566$		0			0
$567$	5.43448	−	21.1866i	0.228227	−	0.889755i
$568$		0			0
$569$	−3.88173	−	2.24111i	−0.162730	−	0.0939524i	0.416423	−	0.909171i	$-0.363283\pi$
$569$	−3.88173	−	2.24111i	−0.162730	−	0.0939524i	−0.579154	+	0.815218i	$0.696617\pi$
$570$		0			0
$571$	−0.470896	−	0.126176i	−0.0197064	−	0.00528031i	0.248952	−	0.968516i	$-0.419914\pi$
$571$	−0.470896	−	0.126176i	−0.0197064	−	0.00528031i	−0.268659	+	0.963235i	$0.586580\pi$
$572$		0			0
$573$	−14.4143	−	14.4143i	−0.602167	−	0.602167i
$574$		0			0
$575$	0.991504			0.0413486
$576$		0			0
$577$	5.31982	+	9.21420i	0.221467	+	0.383592i	0.955254	−	0.295788i	$-0.0955821\pi$
$577$	5.31982	+	9.21420i	0.221467	+	0.383592i	−0.733787	+	0.679380i	$0.762249\pi$
$578$		0			0
$579$	−3.50320	+	0.938680i	−0.145588	+	0.0390102i
$580$		0			0
$581$	−0.0472550	−	4.41305i	−0.00196047	−	0.183084i
$582$		0			0
$583$	2.35331	+	1.35868i	0.0974641	+	0.0562709i
$584$		0			0
$585$	0.636420	−	0.367437i	0.0263127	−	0.0151917i
$586$		0			0
$587$	13.2861	−	13.2861i	0.548376	−	0.548376i	−0.377595	−	0.925971i	$-0.623249\pi$
$587$	13.2861	−	13.2861i	0.548376	−	0.548376i	0.925971	+	0.377595i	$0.123249\pi$
$588$		0			0
$589$	−1.76960	−	1.76960i	−0.0729151	−	0.0729151i
$590$		0			0
$591$	−11.7497	−	20.3511i	−0.483319	−	0.837133i
$592$		0			0
$593$	0.198497	−	0.343806i	0.00815128	−	0.0141184i	−0.861921	−	0.507043i	$-0.830739\pi$
$593$	0.198497	−	0.343806i	0.00815128	−	0.0141184i	0.870072	+	0.492924i	$0.164072\pi$
$594$		0			0
$595$	10.2577	−	0.109840i	0.420524	−	0.00450298i
$596$		0			0
$597$	4.54994	+	16.9806i	0.186217	+	0.694970i
$598$		0			0
$599$	−11.9718	+	6.91190i	−0.489153	+	0.282412i	−0.724223	−	0.689566i	$-0.757801\pi$
$599$	−11.9718	+	6.91190i	−0.489153	+	0.282412i	0.235070	+	0.971978i	$0.424468\pi$
$600$		0			0
$601$		−	8.73396i		−	0.356266i	−0.984006	−	0.178133i	$-0.942994\pi$
$601$		−	8.73396i		−	0.356266i	0.984006	−	0.178133i	$-0.0570057\pi$
$602$		0			0
$603$	1.30926	−	1.30926i	0.0533170	−	0.0533170i
$604$		0			0
$605$	−15.0731	+	56.2535i	−0.612807	+	2.28703i
$606$		0			0
$607$	14.3937	−	24.9305i	0.584220	−	1.01190i	−0.410752	−	0.911747i	$-0.634734\pi$
$607$	14.3937	−	24.9305i	0.584220	−	1.01190i	0.994972	−	0.100152i	$-0.0319330\pi$
$608$		0			0
$609$	30.7153	+	7.87864i	1.24465	+	0.319259i
$610$		0			0
$611$	3.34928	−	0.897436i	0.135497	−	0.0363064i
$612$		0			0
$613$	34.0918	+	9.13486i	1.37695	+	0.368954i	0.870014	−	0.493028i	$-0.164110\pi$
$613$	34.0918	+	9.13486i	1.37695	+	0.368954i	0.506940	+	0.861981i	$0.330777\pi$
$614$		0			0
$615$			24.3996i			0.983886i
$616$		0			0
$617$			33.4612i			1.34710i	0.739143	+	0.673548i	$0.235231\pi$
$617$			33.4612i			1.34710i	−0.739143	+	0.673548i	$0.764769\pi$
$618$		0			0
$619$	−9.00777	−	2.41362i	−0.362053	−	0.0970118i	0.0732067	−	0.997317i	$-0.476677\pi$
$619$	−9.00777	−	2.41362i	−0.362053	−	0.0970118i	−0.435260	+	0.900305i	$0.643343\pi$
$620$		0			0
$621$	−5.54180	+	1.48492i	−0.222385	+	0.0595878i
$622$		0			0
$623$	−9.08349	−	32.5038i	−0.363922	−	1.30224i
$624$		0			0
$625$	−9.74706	+	16.8824i	−0.389882	+	0.675296i
$626$		0			0
$627$	−17.1711	+	64.0834i	−0.685747	+	2.55924i
$628$		0			0
$629$	0.460415	−	0.460415i	0.0183580	−	0.0183580i
$630$		0			0
$631$			22.2587i			0.886105i	0.896496	+	0.443053i	$0.146104\pi$
$631$			22.2587i			0.886105i	−0.896496	+	0.443053i	$0.853896\pi$
$632$		0			0
$633$	10.6128	−	6.12730i	0.421821	−	0.243538i
$634$		0			0
$635$	3.34905	+	12.4988i	0.132903	+	0.496001i
$636$		0			0
$637$	7.76534	−	8.10527i	0.307674	−	0.321142i
$638$		0			0
$639$	−0.316819	+	0.548747i	−0.0125332	+	0.0217081i
$640$		0			0
$641$	4.13758	+	7.16649i	0.163424	+	0.283059i	0.936095	−	0.351748i	$-0.114413\pi$
$641$	4.13758	+	7.16649i	0.163424	+	0.283059i	−0.772670	+	0.634808i	$0.781079\pi$
$642$		0			0
$643$	−4.19175	−	4.19175i	−0.165307	−	0.165307i	0.619606	−	0.784913i	$-0.287292\pi$
$643$	−4.19175	−	4.19175i	−0.165307	−	0.165307i	−0.784913	+	0.619606i	$0.787292\pi$
$644$		0			0
$645$	5.89890	−	5.89890i	0.232269	−	0.232269i
$646$		0			0
$647$	−18.2428	+	10.5325i	−0.717199	+	0.414075i	−0.813721	−	0.581256i	$-0.802561\pi$
$647$	−18.2428	+	10.5325i	−0.717199	+	0.414075i	0.0965221	+	0.995331i	$0.469228\pi$
$648$		0			0
$649$	−49.1081	−	28.3526i	−1.92766	−	1.11294i
$650$		0			0
$651$	1.52242	+	0.857366i	0.0596683	+	0.0336028i
$652$		0			0
$653$	16.5394	−	4.43173i	0.647239	−	0.173427i	0.0797585	−	0.996814i	$-0.474585\pi$
$653$	16.5394	−	4.43173i	0.647239	−	0.173427i	0.567480	+	0.823387i	$0.307918\pi$
$654$		0			0
$655$	−15.0969	−	26.1485i	−0.589883	−	1.02171i
$656$		0			0
$657$	−0.539552			−0.0210499
$658$		0			0
$659$	−19.9513	−	19.9513i	−0.777192	−	0.777192i	0.202161	−	0.979352i	$-0.435204\pi$
$659$	−19.9513	−	19.9513i	−0.777192	−	0.777192i	−0.979352	+	0.202161i	$0.935204\pi$
$660$		0			0
$661$	−20.7436	−	5.55822i	−0.806831	−	0.216190i	−0.168250	−	0.985744i	$-0.553812\pi$
$661$	−20.7436	−	5.55822i	−0.806831	−	0.216190i	−0.638581	+	0.769555i	$0.720478\pi$
$662$		0			0
$663$	−4.44359	−	2.56551i	−0.172575	−	0.0996361i
$664$		0			0
$665$	−8.37005	+	32.6311i	−0.324577	+	1.26538i
$666$		0			0
$667$	−1.98884	−	7.42246i	−0.0770083	−	0.287399i
$668$		0			0
$669$	9.64922	−	36.0114i	0.373060	−	1.39228i
$670$		0			0
$671$	−66.5165			−2.56784
$672$		0			0
$673$	21.0339			0.810796			0.405398	−	0.914140i	$-0.367133\pi$
$673$	21.0339			0.810796			0.405398	+	0.914140i	$0.367133\pi$
$674$		0			0
$675$	−1.29165	+	4.82051i	−0.0497157	+	0.185542i
$676$		0			0
$677$	1.61314	+	6.02033i	0.0619982	+	0.231380i	0.989972	−	0.141266i	$-0.0451172\pi$
$677$	1.61314	+	6.02033i	0.0619982	+	0.231380i	−0.927974	+	0.372646i	$0.878451\pi$
$678$		0			0
$679$	−4.18137	−	4.09277i	−0.160466	−	0.157066i
$680$		0			0
$681$	−26.8367	−	15.4942i	−1.02838	−	0.593737i
$682$		0			0
$683$	−21.5713	−	5.78001i	−0.825402	−	0.221166i	−0.178695	−	0.983904i	$-0.557188\pi$
$683$	−21.5713	−	5.78001i	−0.825402	−	0.221166i	−0.646707	+	0.762739i	$0.723854\pi$
$684$		0			0
$685$	−2.48651	−	2.48651i	−0.0950048	−	0.0950048i
$686$		0			0
$687$	−14.0057			−0.534351
$688$		0			0
$689$	−0.345076	−	0.597689i	−0.0131463	−	0.0227701i
$690$		0			0
$691$	37.1120	−	9.94413i	1.41181	−	0.378292i	0.529237	−	0.848474i	$-0.322478\pi$
$691$	37.1120	−	9.94413i	1.41181	−	0.378292i	0.882570	+	0.470182i	$0.155812\pi$
$692$		0			0
$693$	0.0406240	+	3.79379i	0.00154318	+	0.144114i
$694$		0			0
$695$	−7.02907	−	4.05824i	−0.266628	−	0.153938i
$696$		0			0
$697$	−12.0848	+	6.97715i	−0.457743	+	0.264278i
$698$		0			0
$699$	20.2963	−	20.2963i	0.767676	−	0.767676i
$700$		0			0
$701$	−1.40129	−	1.40129i	−0.0529259	−	0.0529259i	0.680148	−	0.733074i	$-0.261915\pi$
$701$	−1.40129	−	1.40129i	−0.0529259	−	0.0529259i	−0.733074	+	0.680148i	$0.761915\pi$
$702$		0			0
$703$	1.06913	+	1.85178i	0.0403229	+	0.0698413i
$704$		0			0
$705$	3.63270	−	6.29202i	0.136815	−	0.236971i
$706$		0			0
$707$	9.69463	+	16.3839i	0.364604	+	0.616181i
$708$		0			0
$709$	−2.25622	−	8.42034i	−0.0847342	−	0.316232i	0.910530	−	0.413444i	$-0.135674\pi$
$709$	−2.25622	−	8.42034i	−0.0847342	−	0.316232i	−0.995264	+	0.0972117i	$0.969008\pi$
$710$		0			0
$711$	2.00956	−	1.16022i	0.0753645	−	0.0435117i
$712$		0			0
$713$		−	0.423412i		−	0.0158569i
$714$		0			0
$715$	14.4450	−	14.4450i	0.540211	−	0.540211i
$716$		0			0
$717$	0.246816	−	0.921129i	0.00921750	−	0.0344002i
$718$		0			0
$719$	−13.3330	+	23.0934i	−0.497236	+	0.861239i	−0.999995	−	0.00318810i	$-0.998985\pi$
$719$	−13.3330	+	23.0934i	−0.497236	+	0.861239i	0.502758	+	0.864427i	$0.332319\pi$
$720$		0			0
$721$	−12.4537	−	44.5635i	−0.463799	−	1.65963i
$722$		0			0
$723$	−18.9578	+	5.07974i	−0.705050	+	0.188917i
$724$		0			0
$725$	−6.45640	−	1.72999i	−0.239785	−	0.0642501i
$726$		0			0
$727$		−	37.7224i		−	1.39905i	−0.714610	−	0.699523i	$-0.753396\pi$
$727$		−	37.7224i		−	1.39905i	0.714610	−	0.699523i	$-0.246604\pi$
$728$		0			0
$729$		−	28.7229i		−	1.06381i
$730$		0			0
$731$	4.60846	+	1.23483i	0.170450	+	0.0456719i
$732$		0			0
$733$	21.9463	−	5.88050i	0.810606	−	0.217201i	0.170371	−	0.985380i	$-0.445504\pi$
$733$	21.9463	−	5.88050i	0.810606	−	0.217201i	0.640235	+	0.768179i	$0.278837\pi$
$734$		0			0
$735$	−0.503639	−	23.5142i	−0.0185770	−	0.867336i
$736$		0			0
$737$	25.7352	−	44.5747i	0.947969	−	1.64193i
$738$		0			0
$739$	6.78727	−	25.3304i	0.249674	−	0.931795i	−0.721303	−	0.692620i	$-0.756456\pi$
$739$	6.78727	−	25.3304i	0.249674	−	0.931795i	0.970977	−	0.239175i	$-0.0768769\pi$
$740$		0			0
$741$	11.9147	−	11.9147i	0.437697	−	0.437697i
$742$		0			0
$743$		−	20.7110i		−	0.759812i	−0.925025	−	0.379906i	$-0.875956\pi$
$743$		−	20.7110i		−	0.759812i	0.925025	−	0.379906i	$-0.124044\pi$
$744$		0			0
$745$	32.1739	−	18.5756i	1.17876	−	0.680558i
$746$		0			0
$747$	−0.0980566	−	0.365952i	−0.00358770	−	0.0133895i
$748$		0			0
$749$	−3.90928	+	6.94168i	−0.142842	+	0.253643i
$750$		0			0
$751$	7.73865	−	13.4037i	0.282387	−	0.489109i	−0.689585	−	0.724205i	$-0.742207\pi$
$751$	7.73865	−	13.4037i	0.282387	−	0.489109i	0.971972	+	0.235096i	$0.0755403\pi$
$752$		0			0
$753$	6.56486	+	11.3707i	0.239237	+	0.414370i
$754$		0			0
$755$	9.10132	+	9.10132i	0.331231	+	0.331231i
$756$		0			0
$757$	−18.4631	+	18.4631i	−0.671051	+	0.671051i	−0.957958	−	0.286907i	$-0.907373\pi$
$757$	−18.4631	+	18.4631i	−0.671051	+	0.671051i	0.286907	+	0.957958i	$0.407373\pi$
$758$		0			0
$759$	−9.72088	+	5.61235i	−0.352846	+	0.203715i
$760$		0			0
$761$	11.1420	+	6.43283i	0.403897	+	0.233190i	0.688164	−	0.725555i	$-0.258417\pi$
$761$	11.1420	+	6.43283i	0.403897	+	0.233190i	−0.284267	+	0.958745i	$0.591750\pi$
$762$		0			0
$763$	16.1838	−	9.57624i	0.585894	−	0.346683i
$764$		0			0
$765$	0.850618	−	0.227923i	0.0307542	−	0.00824056i
$766$		0			0
$767$	7.20094	+	12.4724i	0.260011	+	0.450352i
$768$		0			0
$769$	−16.5676			−0.597443			−0.298722	−	0.954340i	$-0.596560\pi$
$769$	−16.5676			−0.597443			−0.298722	+	0.954340i	$0.596560\pi$
$770$		0			0
$771$	−34.2238	−	34.2238i	−1.23254	−	1.23254i
$772$		0			0
$773$	−47.3250	−	12.6807i	−1.70216	−	0.456093i	−0.728679	−	0.684856i	$-0.759865\pi$
$773$	−47.3250	−	12.6807i	−1.70216	−	0.456093i	−0.973482	+	0.228763i	$0.926532\pi$
$774$		0			0
$775$	−0.318960	−	0.184152i	−0.0114574	−	0.00661492i
$776$		0			0
$777$	−1.06686	−	1.04425i	−0.0382733	−	0.0374623i
$778$		0			0
$779$	−11.8604	−	44.2635i	−0.424942	−	1.58591i
$780$		0			0
$781$	−4.55886	+	17.0139i	−0.163129	+	0.608805i
$782$		0			0
$783$	38.6776			1.38222
$784$		0			0
$785$	36.8021			1.31352
$786$		0			0
$787$	−1.35582	+	5.05999i	−0.0483298	+	0.180369i	−0.985871	−	0.167504i	$-0.946429\pi$
$787$	−1.35582	+	5.05999i	−0.0483298	+	0.180369i	0.937542	+	0.347873i	$0.113096\pi$
$788$		0			0
$789$	7.62121	+	28.4427i	0.271322	+	1.01259i
$790$		0			0
$791$	−11.2790	−	11.0400i	−0.401035	−	0.392537i
$792$		0			0
$793$	14.6304	+	8.44687i	0.519541	+	0.299957i
$794$		0			0
$795$	−1.39682	−	0.374277i	−0.0495401	−	0.0132742i
$796$		0			0
$797$	−20.4204	−	20.4204i	−0.723329	−	0.723329i	0.245953	−	0.969282i	$-0.420899\pi$
$797$	−20.4204	−	20.4204i	−0.723329	−	0.723329i	−0.969282	+	0.245953i	$0.920899\pi$
$798$		0			0
$799$	4.15514			0.146998
$800$		0			0
$801$	−1.44860	−	2.50906i	−0.0511839	−	0.0886532i
$802$		0			0
$803$	−14.4876	+	3.88193i	−0.511255	+	0.136990i
$804$		0			0
$805$	−4.90518	+	2.90248i	−0.172885	+	0.102299i
$806$		0			0
$807$	21.5389	+	12.4355i	0.758205	+	0.437750i
$808$		0			0
$809$	33.6734	−	19.4413i	1.18389	−	0.683521i	0.226981	−	0.973899i	$-0.427114\pi$
$809$	33.6734	−	19.4413i	1.18389	−	0.683521i	0.956912	+	0.290378i	$0.0937810\pi$
$810$		0			0
$811$	−12.4718	+	12.4718i	−0.437945	+	0.437945i	−0.891320	−	0.453375i	$-0.850220\pi$
$811$	−12.4718	+	12.4718i	−0.437945	+	0.437945i	0.453375	+	0.891320i	$0.350220\pi$
$812$		0			0
$813$	16.3238	+	16.3238i	0.572501	+	0.572501i
$814$		0			0
$815$	11.5902	+	20.0749i	0.405988	+	0.703192i
$816$		0			0
$817$	−7.83387	+	13.5687i	−0.274072	+	0.474707i
$818$		0			0
$819$	0.472835	−	0.839609i	0.0165222	−	0.0293383i
$820$		0			0
$821$	−4.95650	−	18.4979i	−0.172983	−	0.645581i	−0.996886	−	0.0788511i	$-0.974875\pi$
$821$	−4.95650	−	18.4979i	−0.172983	−	0.645581i	0.823903	−	0.566730i	$-0.191792\pi$
$822$		0			0
$823$	−8.96748	+	5.17738i	−0.312587	+	0.180472i	−0.648083	−	0.761569i	$-0.724429\pi$
$823$	−8.96748	+	5.17738i	−0.312587	+	0.180472i	0.335497	+	0.942041i	$0.391096\pi$
$824$		0			0
$825$			9.76376i			0.339931i
$826$		0			0
$827$	9.65786	−	9.65786i	0.335837	−	0.335837i	−0.518961	−	0.854798i	$-0.673681\pi$
$827$	9.65786	−	9.65786i	0.335837	−	0.335837i	0.854798	+	0.518961i	$0.173681\pi$
$828$		0			0
$829$	6.88583	−	25.6983i	0.239155	−	0.892538i	−0.737077	−	0.675809i	$-0.763795\pi$
$829$	6.88583	−	25.6983i	0.239155	−	0.892538i	0.976232	−	0.216729i	$-0.0695388\pi$
$830$		0			0
$831$	1.92201	−	3.32902i	0.0666739	−	0.115483i
$832$		0			0
$833$	11.5023	−	6.97343i	0.398530	−	0.241615i
$834$		0			0
$835$	−42.2334	+	11.3164i	−1.46155	+	0.391620i
$836$		0			0
$837$	2.05855	+	0.551588i	0.0711540	+	0.0190657i
$838$		0			0
$839$		−	46.4429i		−	1.60339i	−0.597736	−	0.801693i	$-0.703933\pi$
$839$		−	46.4429i		−	1.60339i	0.597736	−	0.801693i	$-0.296067\pi$
$840$		0			0
$841$			22.8031i			0.786315i
$842$		0			0
$843$	−1.09431	−	0.293220i	−0.0376902	−	0.0100990i
$844$		0			0
$845$	20.3254	−	5.44618i	0.699216	−	0.187354i
$846$		0			0
$847$	20.5531	+	73.5459i	0.706211	+	2.52707i
$848$		0			0
$849$	−0.316904	+	0.548894i	−0.0108761	+	0.0188380i
$850$		0			0
$851$	−0.0936330	+	0.349443i	−0.00320970	+	0.0119788i
$852$		0			0
$853$	31.3013	−	31.3013i	1.07174	−	1.07174i	0.0745177	−	0.997220i	$-0.476258\pi$
$853$	31.3013	−	31.3013i	1.07174	−	1.07174i	0.997220	−	0.0745177i	$-0.0237417\pi$
$854$		0			0
$855$			2.89191i			0.0989014i
$856$		0			0
$857$	−22.8393	+	13.1863i	−0.780175	+	0.450434i	−0.836492	−	0.547979i	$-0.815398\pi$
$857$	−22.8393	+	13.1863i	−0.780175	+	0.450434i	0.0563171	+	0.998413i	$0.482064\pi$
$858$		0			0
$859$	−0.782055	−	2.91867i	−0.0266834	−	0.0995837i	0.951300	−	0.308267i	$-0.0997490\pi$
$859$	−0.782055	−	2.91867i	−0.0266834	−	0.0995837i	−0.977983	+	0.208683i	$0.933082\pi$
$860$		0			0
$861$	16.2926	+	27.5344i	0.555250	+	0.938371i
$862$		0			0
$863$	−3.50456	+	6.07008i	−0.119297	+	0.206628i	−0.919489	−	0.393115i	$-0.871397\pi$
$863$	−3.50456	+	6.07008i	−0.119297	+	0.206628i	0.800192	+	0.599743i	$0.204731\pi$
$864$		0			0
$865$	12.9092	+	22.3594i	0.438925	+	0.760241i
$866$		0			0
$867$	15.6692	+	15.6692i	0.532155	+	0.532155i
$868$		0			0
$869$	45.6115	−	45.6115i	1.54726	−	1.54726i
$870$		0			0
$871$	−11.3210	+	6.53619i	−0.383598	+	0.221470i
$872$		0			0
$873$	−0.434991	−	0.251142i	−0.0147222	−	0.00849987i
$874$		0			0
$875$	0.338890	+	31.6483i	0.0114566	+	1.06991i
$876$		0			0
$877$	39.6594	−	10.6267i	1.33920	−	0.358838i	0.483063	−	0.875585i	$-0.339524\pi$
$877$	39.6594	−	10.6267i	1.33920	−	0.358838i	0.856138	+	0.516748i	$0.172857\pi$
$878$		0			0
$879$	−8.82185	−	15.2799i	−0.297554	−	0.515378i
$880$		0			0
$881$	−13.6166			−0.458755			−0.229377	−	0.973338i	$-0.573669\pi$
$881$	−13.6166			−0.458755			−0.229377	+	0.973338i	$0.573669\pi$
$882$		0			0
$883$	−35.2238	−	35.2238i	−1.18537	−	1.18537i	−0.978332	−	0.207042i	$-0.933616\pi$
$883$	−35.2238	−	35.2238i	−1.18537	−	1.18537i	−0.207042	−	0.978332i	$-0.566384\pi$
$884$		0			0
$885$	29.1484	+	7.81030i	0.979814	+	0.262540i
$886$		0			0
$887$	5.44911	+	3.14604i	0.182963	+	0.105634i	0.588684	−	0.808363i	$-0.299646\pi$
$887$	5.44911	+	3.14604i	0.182963	+	0.105634i	−0.405721	+	0.913997i	$0.632980\pi$
$888$		0			0
$889$	12.1253	+	11.8684i	0.406670	+	0.398053i
$890$		0			0
$891$	−13.5092	−	50.4171i	−0.452576	−	1.68904i
$892$		0			0
$893$	−3.53163	+	13.1802i	−0.118182	+	0.441060i
$894$		0			0
$895$	6.39085			0.213623
$896$		0			0
$897$	2.85083			0.0951864
$898$		0			0
$899$	−0.738774	+	2.75714i	−0.0246395	+	0.0919559i
$900$		0			0
$901$	−0.214052	−	0.798852i	−0.00713110	−	0.0266136i
$902$		0			0
$903$	2.71786	−	10.5957i	0.0904447	−	0.352604i
$904$		0			0
$905$	35.5276	+	20.5118i	1.18098	+	0.681837i
$906$		0			0
$907$	43.3049	+	11.6035i	1.43792	+	0.385289i	0.891804	−	0.452423i	$-0.149440\pi$
$907$	43.3049	+	11.6035i	1.43792	+	0.385289i	0.546113	+	0.837711i	$0.316107\pi$
$908$		0			0
$909$	1.15560	+	1.15560i	0.0383288	+	0.0383288i
$910$		0			0
$911$	42.8973			1.42125			0.710625	−	0.703571i	$-0.248412\pi$
$911$	42.8973			1.42125			0.710625	+	0.703571i	$0.248412\pi$
$912$		0			0
$913$	−5.26585	−	9.12073i	−0.174274	−	0.301852i
$914$		0			0
$915$	34.1918	−	9.16166i	1.13035	−	0.302875i
$916$		0			0
$917$	−34.4970	−	19.4273i	−1.13919	−	0.641547i
$918$		0			0
$919$	−26.2242	−	15.1405i	−0.865056	−	0.499440i	0.000646343	−	1.00000i	$-0.499794\pi$
$919$	−26.2242	−	15.1405i	−0.865056	−	0.499440i	−0.865702	+	0.500560i	$0.833128\pi$
$920$		0			0
$921$	−12.8074	+	7.39438i	−0.422019	+	0.243653i
$922$		0			0
$923$	3.16330	−	3.16330i	0.104121	−	0.104121i
$924$		0			0
$925$	0.222515	+	0.222515i	0.00731626	+	0.00731626i
$926$		0			0
$927$	−1.98607	−	3.43997i	−0.0652311	−	0.112984i
$928$		0			0
$929$	6.93334	−	12.0089i	0.227475	−	0.393999i	−0.729584	−	0.683891i	$-0.760286\pi$
$929$	6.93334	−	12.0089i	0.227475	−	0.393999i	0.957059	+	0.289892i	$0.0936195\pi$
$930$		0			0
$931$	12.3437	+	42.4126i	0.404548	+	1.39002i
$932$		0			0
$933$	−4.25838	−	15.8925i	−0.139413	−	0.520297i
$934$		0			0
$935$	21.2002	−	12.2399i	0.693321	−	0.400289i
$936$		0			0
$937$			46.7544i			1.52740i	0.645572	+	0.763699i	$0.276619\pi$
$937$			46.7544i			1.52740i	−0.645572	+	0.763699i	$0.723381\pi$
$938$		0			0
$939$	−20.2222	+	20.2222i	−0.659927	+	0.659927i
$940$		0			0
$941$	2.15540	−	8.04407i	0.0702641	−	0.262229i	−0.921854	−	0.387538i	$-0.873326\pi$
$941$	2.15540	−	8.04407i	0.0702641	−	0.262229i	0.992118	+	0.125309i	$0.0399922\pi$
$942$		0			0
$943$	3.87655	−	6.71439i	0.126238	−	0.218651i
$944$		0			0
$945$	−7.72123	−	27.6292i	−0.251172	−	0.898778i
$946$		0			0
$947$	7.09044	−	1.89988i	0.230408	−	0.0617378i	−0.141767	−	0.989900i	$-0.545278\pi$
$947$	7.09044	−	1.89988i	0.230408	−	0.0617378i	0.372176	+	0.928162i	$0.378612\pi$
$948$		0			0
$949$	3.67953	+	0.985926i	0.119442	+	0.0320045i
$950$		0			0
$951$		−	35.3776i		−	1.14720i
$952$		0			0
$953$		−	41.3553i		−	1.33963i	−0.742528	−	0.669815i	$-0.766373\pi$
$953$		−	41.3553i		−	1.33963i	0.742528	−	0.669815i	$-0.233627\pi$
$954$		0			0
$955$	−23.8592	−	6.39305i	−0.772065	−	0.206874i
$956$		0			0
$957$	73.0921	−	19.5850i	2.36273	−	0.633093i
$958$		0			0
$959$	−4.46633	−	1.14564i	−0.144225	−	0.0369945i
$960$		0			0
$961$	15.4214	−	26.7106i	0.497463	−	0.861632i
$962$		0			0
$963$	−0.177009	+	0.660606i	−0.00570403	+	0.0212877i
$964$		0			0
$965$	−3.10748	+	3.10748i	−0.100033	+	0.100033i
$966$		0			0
$967$			40.5984i			1.30556i	0.757549	+	0.652778i	$0.226397\pi$
$967$			40.5984i			1.30556i	−0.757549	+	0.652778i	$0.773603\pi$
$968$		0			0
$969$	17.4866	−	10.0959i	0.561752	−	0.324328i
$970$		0			0
$971$	8.41714	+	31.4132i	0.270119	+	1.00810i	0.959042	+	0.283263i	$0.0914169\pi$
$971$	8.41714	+	31.4132i	0.270119	+	1.00810i	−0.688924	+	0.724834i	$0.741916\pi$
$972$		0			0
$973$	−10.6420	+	0.113955i	−0.341168	+	0.00365323i
$974$		0			0
$975$	1.23989	−	2.14755i	0.0397083	−	0.0687768i
$976$		0			0
$977$	8.34286	+	14.4503i	0.266912	+	0.462305i	0.968063	−	0.250708i	$-0.0806635\pi$
$977$	8.34286	+	14.4503i	0.266912	+	0.462305i	−0.701151	+	0.713013i	$0.747330\pi$
$978$		0			0
$979$	−56.9486	−	56.9486i	−1.82009	−	1.82009i
$980$		0			0
$981$	1.14148	−	1.14148i	0.0364448	−	0.0364448i
$982$		0			0
$983$	10.1999	−	5.88892i	0.325326	−	0.187827i	−0.328438	−	0.944526i	$-0.606522\pi$
$983$	10.1999	−	5.88892i	0.325326	−	0.187827i	0.653764	+	0.756698i	$0.273189\pi$
$984$		0			0
$985$	−24.6599	−	14.2374i	−0.785728	−	0.453640i
$986$		0			0
$987$	−0.102006	−	9.52612i	−0.00324688	−	0.303220i
$988$		0			0
$989$	−2.56049	+	0.686082i	−0.0814189	+	0.0218161i
$990$		0			0
$991$	15.8872	+	27.5175i	0.504675	+	0.874122i	0.999985	+	0.00540613i	$0.00172083\pi$
$991$	15.8872	+	27.5175i	0.504675	+	0.874122i	−0.495311	+	0.868716i	$0.664946\pi$
$992$		0			0
$993$	−40.2967			−1.27878
$994$		0			0
$995$	15.0625	+	15.0625i	0.477513	+	0.477513i
$996$		0			0
$997$	−1.15492	−	0.309461i	−0.0365768	−	0.00980073i	0.240484	−	0.970653i	$-0.422694\pi$
$997$	−1.15492	−	0.309461i	−0.0365768	−	0.00980073i	−0.277061	+	0.960852i	$0.589360\pi$
$998$		0			0
$999$	−1.57695	−	0.910453i	−0.0498925	−	0.0288055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.ba.f.289.4		48
4.3	odd	2		896.2.ba.e.289.9		48
7.4	even	3	inner	896.2.ba.f.417.9		48
8.3	odd	2		448.2.ba.c.401.4		48
8.5	even	2		112.2.w.c.93.10	yes	48
16.3	odd	4		448.2.ba.c.177.9		48
16.5	even	4	inner	896.2.ba.f.737.9		48
16.11	odd	4		896.2.ba.e.737.4		48
16.13	even	4		112.2.w.c.37.2	✓	48
28.11	odd	6		896.2.ba.e.417.4		48
56.5	odd	6		784.2.m.k.589.6		24
56.11	odd	6		448.2.ba.c.81.9		48
56.13	odd	2		784.2.x.o.765.10		48
56.37	even	6		784.2.m.j.589.6		24
56.45	odd	6		784.2.x.o.557.2		48
56.53	even	6		112.2.w.c.109.2	yes	48
112.11	odd	12		896.2.ba.e.865.9		48
112.13	odd	4		784.2.x.o.373.2		48
112.45	odd	12		784.2.x.o.165.10		48
112.53	even	12	inner	896.2.ba.f.865.4		48
112.61	odd	12		784.2.m.k.197.6		24
112.67	odd	12		448.2.ba.c.305.4		48
112.93	even	12		784.2.m.j.197.6		24
112.109	even	12		112.2.w.c.53.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.2	✓	48	16.13	even	4
112.2.w.c.53.10	yes	48	112.109	even	12
112.2.w.c.93.10	yes	48	8.5	even	2
112.2.w.c.109.2	yes	48	56.53	even	6
448.2.ba.c.81.9		48	56.11	odd	6
448.2.ba.c.177.9		48	16.3	odd	4
448.2.ba.c.305.4		48	112.67	odd	12
448.2.ba.c.401.4		48	8.3	odd	2
784.2.m.j.197.6		24	112.93	even	12
784.2.m.j.589.6		24	56.37	even	6
784.2.m.k.197.6		24	112.61	odd	12
784.2.m.k.589.6		24	56.5	odd	6
784.2.x.o.165.10		48	112.45	odd	12
784.2.x.o.373.2		48	112.13	odd	4
784.2.x.o.557.2		48	56.45	odd	6
784.2.x.o.765.10		48	56.13	odd	2
896.2.ba.e.289.9		48	4.3	odd	2
896.2.ba.e.417.4		48	28.11	odd	6
896.2.ba.e.737.4		48	16.11	odd	4
896.2.ba.e.865.9		48	112.11	odd	12
896.2.ba.f.289.4		48	1.1	even	1	trivial
896.2.ba.f.417.9		48	7.4	even	3	inner
896.2.ba.f.737.9		48	16.5	even	4	inner
896.2.ba.f.865.4		48	112.53	even	12	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.430984 + 1.60845i) q^{3} +(0.522232 + 1.94900i) q^{5} +(1.89075 + 1.85069i) q^{7} +(0.196696 + 0.113563i) q^{9} +O(q^{10})\)	\(q+(-0.430984 + 1.60845i) q^{3} +(0.522232 + 1.94900i) q^{5} +(1.89075 + 1.85069i) q^{7} +(0.196696 + 0.113563i) q^{9} +(6.09856 + 1.63411i) q^{11} +(-1.13388 - 1.13388i) q^{13} -3.35995 q^{15} +(-0.960789 - 1.66414i) q^{17} +(6.09532 - 1.63324i) q^{19} +(-3.79164 + 2.24357i) q^{21} +(0.924606 + 0.533821i) q^{23} +(0.804265 - 0.464342i) q^{25} +(-3.79985 + 3.79985i) q^{27} +(-5.08936 - 5.08936i) q^{29} +(-0.198293 - 0.343454i) q^{31} +(-5.25677 + 9.10499i) q^{33} +(-2.61958 + 4.65156i) q^{35} +(0.0877006 + 0.327303i) q^{37} +(2.31247 - 1.33510i) q^{39} -7.26189i q^{41} +(-1.75565 + 1.75565i) q^{43} +(-0.118612 + 0.442666i) q^{45} +(-1.08118 + 1.87265i) q^{47} +(0.149895 + 6.99839i) q^{49} +(3.09077 - 0.828170i) q^{51} +(0.415727 + 0.111394i) q^{53} +12.7395i q^{55} +10.5079i q^{57} +(-8.67527 - 2.32453i) q^{59} +(-10.1763 + 2.72673i) q^{61} +(0.161735 + 0.578743i) q^{63} +(1.61777 - 2.80206i) q^{65} +(2.10994 - 7.87441i) q^{67} +(-1.25712 + 1.25712i) q^{69} +2.78982i q^{71} +(-2.05730 + 1.18779i) q^{73} +(0.400248 + 1.49375i) q^{75} +(8.50666 + 14.3762i) q^{77} +(5.10829 - 8.84782i) q^{79} +(-4.13352 - 7.15947i) q^{81} +(-1.17951 - 1.17951i) q^{83} +(2.74164 - 2.74164i) q^{85} +(10.3794 - 5.99257i) q^{87} +(-11.0470 - 6.37800i) q^{89} +(-0.0454269 - 4.24233i) q^{91} +(0.637891 - 0.170922i) q^{93} +(6.36634 + 11.0268i) q^{95} -2.21148 q^{97} +(1.01399 + 1.01399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5}+O(q^{10}) \) 48 * q - 4 * q^5	\( 48 q - 4 q^{5} + 4 q^{11} + 24 q^{13} - 40 q^{15} + 8 q^{17} + 4 q^{19} + 8 q^{21} + 24 q^{27} - 24 q^{29} + 28 q^{31} + 16 q^{33} - 28 q^{35} + 24 q^{37} + 40 q^{43} + 28 q^{45} - 20 q^{47} - 24 q^{51} + 16 q^{53} + 20 q^{59} - 8 q^{61} - 16 q^{63} + 8 q^{65} - 48 q^{67} + 40 q^{69} + 4 q^{75} + 20 q^{77} - 36 q^{79} + 8 q^{83} - 64 q^{91} - 8 q^{93} - 4 q^{95} - 48 q^{97} + 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^11 + 24 * q^13 - 40 * q^15 + 8 * q^17 + 4 * q^19 + 8 * q^21 + 24 * q^27 - 24 * q^29 + 28 * q^31 + 16 * q^33 - 28 * q^35 + 24 * q^37 + 40 * q^43 + 28 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 + 20 * q^59 - 8 * q^61 - 16 * q^63 + 8 * q^65 - 48 * q^67 + 40 * q^69 + 4 * q^75 + 20 * q^77 - 36 * q^79 + 8 * q^83 - 64 * q^91 - 8 * q^93 - 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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