LMFDB - Embedded newform 880.2.bo.i.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 $ x^12 - x^11 + 5x^10 + 4x^9 + 28x^8 - 81x^7 + 335x^6 - 235x^5 + 782x^4 - 302x^3 + 711x^2 - 43x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-2.19470 + 1.59454i$ of defining polynomial
Character	$\chi$	$=$	880.81
Dual form			880.2.bo.i.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.529284 + 1.62897i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-1.14492 - 3.52372i) q^{7} +(0.0536500 + 0.0389790i) q^{9} +(-2.68927 + 1.94109i) q^{11} +(0.952617 + 0.692117i) q^{13} +(0.529284 + 1.62897i) q^{15} +(4.36891 - 3.17420i) q^{17} +(1.18895 - 3.65921i) q^{19} +6.34602 q^{21} +8.68237 q^{23} +(0.309017 - 0.951057i) q^{25} +(-4.24895 + 3.08704i) q^{27} +(-2.12479 - 6.53944i) q^{29} +(7.08327 + 5.14630i) q^{31} +(-1.73859 - 5.40813i) q^{33} +(-2.99745 - 2.17778i) q^{35} +(0.696735 + 2.14433i) q^{37} +(-1.63164 + 1.18546i) q^{39} +(0.493602 - 1.51915i) q^{41} -4.11979 q^{43} +0.0663151 q^{45} +(3.91833 - 12.0594i) q^{47} +(-5.44260 + 3.95428i) q^{49} +(2.85828 + 8.79688i) q^{51} +(10.0152 + 7.27650i) q^{53} +(-1.03472 + 3.15109i) q^{55} +(5.33145 + 3.87353i) q^{57} +(0.121753 + 0.374716i) q^{59} +(-1.45692 + 1.05851i) q^{61} +(0.0759258 - 0.233676i) q^{63} +1.17750 q^{65} +14.3809 q^{67} +(-4.59544 + 14.1433i) q^{69} +(-5.54603 + 4.02943i) q^{71} +(3.10719 + 9.56296i) q^{73} +(1.38568 + 1.00676i) q^{75} +(9.91887 + 7.25381i) q^{77} +(-0.901110 - 0.654695i) q^{79} +(-2.71832 - 8.36612i) q^{81} +(0.0140132 - 0.0101812i) q^{83} +(1.66878 - 5.13596i) q^{85} +11.7772 q^{87} -8.49434 q^{89} +(1.34815 - 4.14917i) q^{91} +(-12.1322 + 8.81458i) q^{93} +(-1.18895 - 3.65921i) q^{95} +(-8.50719 - 6.18083i) q^{97} +(-0.219941 - 0.000685401i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} + 18 q^{13} - q^{15} + 3 q^{17} - 4 q^{19} - 28 q^{21} + 18 q^{23} - 3 q^{25} - 23 q^{27} + 15 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{35} + 6 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) $ 12 * q + q^3 + 3 * q^5 + q^7 - 10 * q^9 - 4 * q^11 + 18 * q^13 - q^15 + 3 * q^17 - 4 * q^19 - 28 * q^21 + 18 * q^23 - 3 * q^25 - 23 * q^27 + 15 * q^29 + 8 * q^31 + 4 * q^33 - 6 * q^35 + 6 * q^37 + 33 * q^39 + 2 * q^41 + 36 * q^43 - 10 * q^45 + 16 * q^47 - 16 * q^49 + 10 * q^51 + 19 * q^53 - 6 * q^55 + 62 * q^57 - 46 * q^59 + 18 * q^61 + 7 * q^63 + 2 * q^65 + 44 * q^67 - q^69 + 6 * q^71 + 25 * q^73 - 4 * q^75 + 10 * q^77 - 19 * q^79 + 30 * q^81 - 3 * q^85 - 6 * q^87 - 50 * q^89 + 46 * q^91 - 37 * q^93 + 4 * q^95 - 31 * q^97 - 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.529284	+	1.62897i	−0.305582	+	0.940486i	0.673877	+	0.738844i	$0.264628\pi$
$3$	−0.529284	+	1.62897i	−0.305582	+	0.940486i	−0.979459	+	0.201642i	$0.935372\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	−1.14492	−	3.52372i	−0.432741	−	1.33184i	−0.895384	−	0.445295i	$-0.853099\pi$
$7$	−1.14492	−	3.52372i	−0.432741	−	1.33184i	0.462643	−	0.886545i	$-0.346901\pi$
$8$		0			0
$9$	0.0536500	+	0.0389790i	0.0178833	+	0.0129930i
$10$		0			0
$11$	−2.68927	+	1.94109i	−0.810845	+	0.585261i
$11$	−2.68927	+	1.94109i	−0.810845	+	0.585261i
$12$		0			0
$13$	0.952617	+	0.692117i	0.264208	+	0.191959i	0.712000	−	0.702179i	$-0.247789\pi$
$13$	0.952617	+	0.692117i	0.264208	+	0.191959i	−0.447792	+	0.894138i	$0.647789\pi$
$14$		0			0
$15$	0.529284	+	1.62897i	0.136661	+	0.420598i
$16$		0			0
$17$	4.36891	−	3.17420i	1.05962	−	0.769856i	0.0855991	−	0.996330i	$-0.472720\pi$
$17$	4.36891	−	3.17420i	1.05962	−	0.769856i	0.974017	+	0.226473i	$0.0727196\pi$
$18$		0			0
$19$	1.18895	−	3.65921i	0.272764	−	0.839480i	−0.717039	−	0.697033i	$-0.754503\pi$
$19$	1.18895	−	3.65921i	0.272764	−	0.839480i	0.989802	−	0.142447i	$-0.0454971\pi$
$20$		0			0
$21$	6.34602			1.38481
$22$		0			0
$23$	8.68237			1.81040			0.905200	−	0.424986i	$-0.139721\pi$
$23$	8.68237			1.81040			0.905200	+	0.424986i	$0.139721\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−4.24895	+	3.08704i	−0.817710	+	0.594101i
$28$		0			0
$29$	−2.12479	−	6.53944i	−0.394564	−	1.21434i	−0.929301	−	0.369324i	$-0.879589\pi$
$29$	−2.12479	−	6.53944i	−0.394564	−	1.21434i	0.534736	−	0.845019i	$-0.320411\pi$
$30$		0			0
$31$	7.08327	+	5.14630i	1.27219	+	0.924302i	0.999288	−	0.0377385i	$-0.0120154\pi$
$31$	7.08327	+	5.14630i	1.27219	+	0.924302i	0.272905	+	0.962041i	$0.412015\pi$
$32$		0			0
$33$	−1.73859	−	5.40813i	−0.302650	−	0.941434i
$34$		0			0
$35$	−2.99745	−	2.17778i	−0.506662	−	0.368111i
$36$		0			0
$37$	0.696735	+	2.14433i	0.114543	+	0.352526i	0.991851	−	0.127401i	$-0.0406634\pi$
$37$	0.696735	+	2.14433i	0.114543	+	0.352526i	−0.877309	+	0.479926i	$0.840663\pi$
$38$		0			0
$39$	−1.63164	+	1.18546i	−0.261272	+	0.189825i
$40$		0			0
$41$	0.493602	−	1.51915i	0.0770877	−	0.237251i	−0.905086	−	0.425229i	$-0.860193\pi$
$41$	0.493602	−	1.51915i	0.0770877	−	0.237251i	0.982173	+	0.187978i	$0.0601934\pi$
$42$		0			0
$43$	−4.11979			−0.628262			−0.314131	−	0.949380i	$-0.601713\pi$
$43$	−4.11979			−0.628262			−0.314131	+	0.949380i	$0.601713\pi$
$44$		0			0
$45$	0.0663151			0.00988567
$46$		0			0
$47$	3.91833	−	12.0594i	0.571547	−	1.75904i	−0.0761009	−	0.997100i	$-0.524247\pi$
$47$	3.91833	−	12.0594i	0.571547	−	1.75904i	0.647648	−	0.761940i	$-0.275753\pi$
$48$		0			0
$49$	−5.44260	+	3.95428i	−0.777514	+	0.564897i
$50$		0			0
$51$	2.85828	+	8.79688i	0.400239	+	1.23181i
$52$		0			0
$53$	10.0152	+	7.27650i	1.37570	+	0.999504i	0.997268	+	0.0738747i	$0.0235365\pi$
$53$	10.0152	+	7.27650i	1.37570	+	0.999504i	0.378432	+	0.925629i	$0.376464\pi$
$54$		0			0
$55$	−1.03472	+	3.15109i	−0.139521	+	0.424893i
$56$		0			0
$57$	5.33145	+	3.87353i	0.706168	+	0.513061i
$58$		0			0
$59$	0.121753	+	0.374716i	0.0158508	+	0.0487838i	0.958669	−	0.284523i	$-0.0918354\pi$
$59$	0.121753	+	0.374716i	0.0158508	+	0.0487838i	−0.942818	+	0.333307i	$0.891835\pi$
$60$		0			0
$61$	−1.45692	+	1.05851i	−0.186539	+	0.135529i	−0.677136	−	0.735858i	$-0.736779\pi$
$61$	−1.45692	+	1.05851i	−0.186539	+	0.135529i	0.490596	+	0.871387i	$0.336779\pi$
$62$		0			0
$63$	0.0759258	−	0.233676i	0.00956575	−	0.0294404i
$64$		0			0
$65$	1.17750			0.146051
$66$		0			0
$67$	14.3809			1.75691			0.878455	−	0.477826i	$-0.158575\pi$
$67$	14.3809			1.75691			0.878455	+	0.477826i	$0.158575\pi$
$68$		0			0
$69$	−4.59544	+	14.1433i	−0.553227	+	1.70266i
$70$		0			0
$71$	−5.54603	+	4.02943i	−0.658192	+	0.478205i	−0.866052	−	0.499954i	$-0.833350\pi$
$71$	−5.54603	+	4.02943i	−0.658192	+	0.478205i	0.207860	+	0.978159i	$0.433350\pi$
$72$		0			0
$73$	3.10719	+	9.56296i	0.363670	+	1.11926i	0.950810	+	0.309775i	$0.100254\pi$
$73$	3.10719	+	9.56296i	0.363670	+	1.11926i	−0.587140	+	0.809485i	$0.699746\pi$
$74$		0			0
$75$	1.38568	+	1.00676i	0.160005	+	0.116250i
$76$		0			0
$77$	9.91887	+	7.25381i	1.13036	+	0.826649i
$78$		0			0
$79$	−0.901110	−	0.654695i	−0.101383	−	0.0736589i	0.535939	−	0.844257i	$-0.319958\pi$
$79$	−0.901110	−	0.654695i	−0.101383	−	0.0736589i	−0.637322	+	0.770598i	$0.719958\pi$
$80$		0			0
$81$	−2.71832	−	8.36612i	−0.302035	−	0.929569i
$82$		0			0
$83$	0.0140132	−	0.0101812i	0.00153814	−	0.00111753i	−0.587016	−	0.809575i	$-0.699697\pi$
$83$	0.0140132	−	0.0101812i	0.00153814	−	0.00111753i	0.588554	+	0.808458i	$0.299697\pi$
$84$		0			0
$85$	1.66878	−	5.13596i	0.181004	−	0.557073i
$86$		0			0
$87$	11.7772			1.26265
$88$		0			0
$89$	−8.49434			−0.900399			−0.450199	−	0.892928i	$-0.648647\pi$
$89$	−8.49434			−0.900399			−0.450199	+	0.892928i	$0.648647\pi$
$90$		0			0
$91$	1.34815	−	4.14917i	0.141324	−	0.434951i
$92$		0			0
$93$	−12.1322	+	8.81458i	−1.25805	+	0.914029i
$94$		0			0
$95$	−1.18895	−	3.65921i	−0.121984	−	0.375427i
$96$		0			0
$97$	−8.50719	−	6.18083i	−0.863774	−	0.627569i	0.0651351	−	0.997876i	$-0.479252\pi$
$97$	−8.50719	−	6.18083i	−0.863774	−	0.627569i	−0.928909	+	0.370308i	$0.879252\pi$
$98$		0			0
$99$	−0.219941		0.000685401i	−0.0221049		6.88853e-5i
$100$		0			0
$101$	−5.80762	−	4.21949i	−0.577880	−	0.419855i	0.260079	−	0.965587i	$-0.416251\pi$
$101$	−5.80762	−	4.21949i	−0.577880	−	0.419855i	−0.837959	+	0.545733i	$0.816251\pi$
$102$		0			0
$103$	1.15886	+	3.56662i	0.114186	+	0.351429i	0.991776	−	0.127982i	$-0.0408501\pi$
$103$	1.15886	+	3.56662i	0.114186	+	0.351429i	−0.877590	+	0.479412i	$0.840850\pi$
$104$		0			0
$105$	5.13404	−	3.73010i	0.501031	−	0.364020i
$106$		0			0
$107$	1.96265	−	6.04042i	0.189737	−	0.583950i	−0.810261	−	0.586069i	$-0.800675\pi$
$107$	1.96265	−	6.04042i	0.189737	−	0.583950i	0.999998	+	0.00211949i	$0.000674656\pi$
$108$		0			0
$109$	1.32407			0.126823			0.0634115	−	0.997987i	$-0.479802\pi$
$109$	1.32407			0.126823			0.0634115	+	0.997987i	$0.479802\pi$
$110$		0			0
$111$	−3.86182			−0.366548
$112$		0			0
$113$	1.64758	−	5.07074i	0.154992	−	0.477015i	−0.843168	−	0.537649i	$-0.819312\pi$
$113$	1.64758	−	5.07074i	0.154992	−	0.477015i	0.998160	+	0.0606344i	$0.0193124\pi$
$114$		0			0
$115$	7.02419	−	5.10337i	0.655009	−	0.475892i
$116$		0			0
$117$	0.0241299	+	0.0742642i	0.00223081	+	0.00686572i
$118$		0			0
$119$	−16.1870	−	11.7606i	−1.48386	−	1.07809i
$120$		0			0
$121$	3.46432	−	10.4402i	0.314938	−	0.949112i
$122$		0			0
$123$	2.21339	+	1.60813i	0.199575	+	0.145000i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	11.8445	−	8.60553i	1.05103	−	0.763617i	0.0786209	−	0.996905i	$-0.474948\pi$
$127$	11.8445	−	8.60553i	1.05103	−	0.763617i	0.972408	+	0.233288i	$0.0749484\pi$
$128$		0			0
$129$	2.18054	−	6.71101i	0.191986	−	0.590871i
$130$		0			0
$131$	−5.93922			−0.518912			−0.259456	−	0.965755i	$-0.583543\pi$
$131$	−5.93922			−0.518912			−0.259456	+	0.965755i	$0.583543\pi$
$132$		0			0
$133$	−14.2553			−1.23609
$134$		0			0
$135$	−1.62295	+	4.99493i	−0.139682	+	0.429896i
$136$		0			0
$137$	−11.9490	+	8.68146i	−1.02087	+	0.741707i	−0.966461	−	0.256812i	$-0.917328\pi$
$137$	−11.9490	+	8.68146i	−1.02087	+	0.741707i	−0.0544107	+	0.998519i	$0.517328\pi$
$138$		0			0
$139$	−0.399410	−	1.22926i	−0.0338775	−	0.104264i	0.932688	−	0.360684i	$-0.117457\pi$
$139$	−0.399410	−	1.22926i	−0.0338775	−	0.104264i	−0.966565	+	0.256420i	$0.917457\pi$
$140$		0			0
$141$	17.5704	+	12.7657i	1.47970	+	1.07506i
$142$		0			0
$143$	−3.90530	−	0.0121701i	−0.326578	−	0.00101771i
$144$		0			0
$145$	−5.56278	−	4.04160i	−0.461964	−	0.335636i
$146$		0			0
$147$	−3.56072	−	10.9588i	−0.293683	−	0.903864i
$148$		0			0
$149$	−19.3404	+	14.0516i	−1.58443	+	1.15115i	−0.673036	+	0.739610i	$0.735010\pi$
$149$	−19.3404	+	14.0516i	−1.58443	+	1.15115i	−0.911390	+	0.411543i	$0.864990\pi$
$150$		0			0
$151$	−2.55881	+	7.87521i	−0.208233	+	0.640875i	0.791332	+	0.611387i	$0.209388\pi$
$151$	−2.55881	+	7.87521i	−0.208233	+	0.640875i	−0.999565	+	0.0294888i	$0.990612\pi$
$152$		0			0
$153$	0.358119			0.0289522
$154$		0			0
$155$	8.75541			0.703251
$156$		0			0
$157$	−2.46115	+	7.57463i	−0.196421	+	0.604521i	0.803536	+	0.595256i	$0.202949\pi$
$157$	−2.46115	+	7.57463i	−0.196421	+	0.604521i	−0.999957	+	0.00926547i	$0.997051\pi$
$158$		0			0
$159$	−17.1541	+	12.4632i	−1.36041	+	0.988395i
$160$		0			0
$161$	−9.94066	−	30.5942i	−0.783434	−	2.41116i
$162$		0			0
$163$	−3.30709	−	2.40274i	−0.259031	−	0.188197i	0.450689	−	0.892681i	$-0.351178\pi$
$163$	−3.30709	−	2.40274i	−0.259031	−	0.188197i	−0.709720	+	0.704484i	$0.751178\pi$
$164$		0			0
$165$	−4.58537	−	3.35335i	−0.356970	−	0.261058i
$166$		0			0
$167$	−3.22174	−	2.34073i	−0.249306	−	0.181131i	0.456113	−	0.889922i	$-0.349241\pi$
$167$	−3.22174	−	2.34073i	−0.249306	−	0.181131i	−0.705419	+	0.708790i	$0.749241\pi$
$168$		0			0
$169$	−3.58877	−	11.0451i	−0.276059	−	0.849622i
$170$		0			0
$171$	0.206420	−	0.149973i	0.0157853	−	0.0114687i
$172$		0			0
$173$	5.45640	−	16.7931i	0.414843	−	1.27675i	−0.497549	−	0.867436i	$-0.665766\pi$
$173$	5.45640	−	16.7931i	0.414843	−	1.27675i	0.912392	−	0.409319i	$-0.134234\pi$
$174$		0			0
$175$	−3.70505			−0.280076
$176$		0			0
$177$	−0.674842			−0.0507243
$178$		0			0
$179$	−3.69018	+	11.3572i	−0.275817	+	0.848877i	0.713185	+	0.700976i	$0.247252\pi$
$179$	−3.69018	+	11.3572i	−0.275817	+	0.848877i	−0.989002	+	0.147902i	$0.952748\pi$
$180$		0			0
$181$	0.834670	−	0.606423i	0.0620405	−	0.0450751i	−0.556333	−	0.830960i	$-0.687792\pi$
$181$	0.834670	−	0.606423i	0.0620405	−	0.0450751i	0.618373	+	0.785885i	$0.287792\pi$
$182$		0			0
$183$	−0.953162	−	2.93353i	−0.0704598	−	0.216853i
$184$		0			0
$185$	1.82408	+	1.32527i	0.134109	+	0.0974357i
$186$		0			0
$187$	−5.58776	+	17.0167i	−0.408617	+	1.24439i
$188$		0			0
$189$	15.7426	+	11.4376i	1.14510	+	0.831967i
$190$		0			0
$191$	−5.87606	−	18.0846i	−0.425176	−	1.30856i	−0.902825	−	0.430008i	$-0.858511\pi$
$191$	−5.87606	−	18.0846i	−0.425176	−	1.30856i	0.477649	−	0.878551i	$-0.341489\pi$
$192$		0			0
$193$	−4.37576	+	3.17918i	−0.314974	+	0.228842i	−0.734028	−	0.679119i	$-0.762362\pi$
$193$	−4.37576	+	3.17918i	−0.314974	+	0.228842i	0.419054	+	0.907961i	$0.362362\pi$
$194$		0			0
$195$	−0.623232	+	1.91811i	−0.0446306	+	0.137359i
$196$		0			0
$197$	4.07618			0.290416			0.145208	−	0.989401i	$-0.453615\pi$
$197$	4.07618			0.290416			0.145208	+	0.989401i	$0.453615\pi$
$198$		0			0
$199$	12.0711			0.855700			0.427850	−	0.903850i	$-0.359271\pi$
$199$	12.0711			0.855700			0.427850	+	0.903850i	$0.359271\pi$
$200$		0			0
$201$	−7.61160	+	23.4261i	−0.536881	+	1.65235i
$202$		0			0
$203$	−20.6104	+	14.9743i	−1.44657	+	1.05099i
$204$		0			0
$205$	−0.493602	−	1.51915i	−0.0344746	−	0.106102i
$206$		0			0
$207$	0.465810	+	0.338431i	0.0323760	+	0.0235225i
$208$		0			0
$209$	3.90546	+	12.1485i	0.270146	+	0.840326i
$210$		0			0
$211$	−7.53429	−	5.47398i	−0.518682	−	0.376844i	0.297425	−	0.954745i	$-0.403872\pi$
$211$	−7.53429	−	5.47398i	−0.518682	−	0.376844i	−0.816107	+	0.577901i	$0.803872\pi$
$212$		0			0
$213$	−3.62839	−	11.1670i	−0.248613	−	0.765152i
$214$		0			0
$215$	−3.33298	+	2.42155i	−0.227307	+	0.165148i
$216$		0			0
$217$	10.0243	−	30.8516i	0.680492	−	2.09434i
$218$		0			0
$219$	−17.2224			−1.16378
$220$		0			0
$221$	6.35881			0.427740
$222$		0			0
$223$	1.46586	−	4.51147i	0.0981616	−	0.302110i	−0.889903	−	0.456150i	$-0.849228\pi$
$223$	1.46586	−	4.51147i	0.0981616	−	0.302110i	0.988065	+	0.154039i	$0.0492282\pi$
$224$		0			0
$225$	0.0536500	−	0.0389790i	0.00357667	−	0.00259860i
$226$		0			0
$227$	−1.08627	−	3.34318i	−0.0720980	−	0.221895i	0.908514	−	0.417855i	$-0.137218\pi$
$227$	−1.08627	−	3.34318i	−0.0720980	−	0.221895i	−0.980612	+	0.195960i	$0.937218\pi$
$228$		0			0
$229$	7.38320	+	5.36421i	0.487895	+	0.354477i	0.804374	−	0.594123i	$-0.202501\pi$
$229$	7.38320	+	5.36421i	0.487895	+	0.354477i	−0.316479	+	0.948600i	$0.602501\pi$
$230$		0			0
$231$	−17.0661	+	12.3182i	−1.12287	+	0.810478i
$232$		0			0
$233$	17.4142	+	12.6522i	1.14084	+	0.828870i	0.987236	−	0.159262i	$-0.0509114\pi$
$233$	17.4142	+	12.6522i	1.14084	+	0.828870i	0.153606	+	0.988132i	$0.450911\pi$
$234$		0			0
$235$	−3.91833	−	12.0594i	−0.255603	−	0.786667i
$236$		0			0
$237$	1.54342	−	1.12136i	0.100256	−	0.0728403i
$238$		0			0
$239$	−3.49419	+	10.7540i	−0.226020	+	0.695619i	0.772166	+	0.635421i	$0.219173\pi$
$239$	−3.49419	+	10.7540i	−0.226020	+	0.695619i	−0.998186	+	0.0601983i	$0.980827\pi$
$240$		0			0
$241$	−26.1144			−1.68218			−0.841089	−	0.540897i	$-0.818085\pi$
$241$	−26.1144			−1.68218			−0.841089	+	0.540897i	$0.818085\pi$
$242$		0			0
$243$	−0.689039			−0.0442019
$244$		0			0
$245$	−2.07889	+	6.39816i	−0.132815	+	0.408764i
$246$		0			0
$247$	3.66521	−	2.66293i	0.233212	−	0.169438i
$248$		0			0
$249$	0.00916785	+	0.0282158i	0.000580989	+	0.00178810i
$250$		0			0
$251$	−3.00802	−	2.18545i	−0.189865	−	0.137945i	0.488792	−	0.872400i	$-0.337438\pi$
$251$	−3.00802	−	2.18545i	−0.189865	−	0.137945i	−0.678657	+	0.734456i	$0.737438\pi$
$252$		0			0
$253$	−23.3492	+	16.8533i	−1.46795	+	1.05956i
$254$		0			0
$255$	7.48307	+	5.43677i	0.468608	+	0.340464i
$256$		0			0
$257$	−2.19179	−	6.74564i	−0.136720	−	0.420781i	0.859133	−	0.511752i	$-0.171003\pi$
$257$	−2.19179	−	6.74564i	−0.136720	−	0.420781i	−0.995854	+	0.0909703i	$0.971003\pi$
$258$		0			0
$259$	6.75830	−	4.91019i	0.419940	−	0.305104i
$260$		0			0
$261$	0.140906	−	0.433664i	0.00872185	−	0.0268431i
$262$		0			0
$263$	−23.3578			−1.44030			−0.720151	−	0.693817i	$-0.755927\pi$
$263$	−23.3578			−1.44030			−0.720151	+	0.693817i	$0.755927\pi$
$264$		0			0
$265$	12.3795			0.760468
$266$		0			0
$267$	4.49592	−	13.8370i	0.275146	−	0.846813i
$268$		0			0
$269$	13.8194	−	10.0404i	0.842585	−	0.612174i	−0.0805064	−	0.996754i	$-0.525654\pi$
$269$	13.8194	−	10.0404i	0.842585	−	0.612174i	0.923092	+	0.384580i	$0.125654\pi$
$270$		0			0
$271$	8.47767	+	26.0916i	0.514982	+	1.58495i	0.783315	+	0.621624i	$0.213527\pi$
$271$	8.47767	+	26.0916i	0.514982	+	1.58495i	−0.268334	+	0.963326i	$0.586473\pi$
$272$		0			0
$273$	6.04532	+	4.39218i	0.365880	+	0.265827i
$274$		0			0
$275$	1.01506	+	3.15748i	0.0612103	+	0.190403i
$276$		0			0
$277$	19.5985	+	14.2391i	1.17756	+	0.855546i	0.991894	−	0.127067i	$-0.0405565\pi$
$277$	19.5985	+	14.2391i	1.17756	+	0.855546i	0.185664	+	0.982613i	$0.440556\pi$
$278$		0			0
$279$	0.179420	+	0.552198i	0.0107416	+	0.0330592i
$280$		0			0
$281$	13.8855	−	10.0884i	0.828338	−	0.601823i	−0.0907503	−	0.995874i	$-0.528927\pi$
$281$	13.8855	−	10.0884i	0.828338	−	0.601823i	0.919089	+	0.394051i	$0.128927\pi$
$282$		0			0
$283$	−1.43047	+	4.40252i	−0.0850324	+	0.261703i	−0.984528	−	0.175227i	$-0.943934\pi$
$283$	−1.43047	+	4.40252i	−0.0850324	+	0.261703i	0.899496	+	0.436930i	$0.143934\pi$
$284$		0			0
$285$	6.59004			0.390360
$286$		0			0
$287$	−5.91819			−0.349340
$288$		0			0
$289$	3.75855	−	11.5676i	0.221091	−	0.680449i
$290$		0			0
$291$	14.5711	−	10.5865i	0.854174	−	0.620594i
$292$		0			0
$293$	−5.71701	−	17.5951i	−0.333991	−	1.02792i	−0.967217	−	0.253952i	$-0.918270\pi$
$293$	−5.71701	−	17.5951i	−0.333991	−	1.02792i	0.633226	−	0.773967i	$-0.281730\pi$
$294$		0			0
$295$	0.318752	+	0.231587i	0.0185585	+	0.0134835i
$296$		0			0
$297$	5.43432	−	16.5495i	0.315331	−	0.960298i
$298$		0			0
$299$	8.27098	+	6.00922i	0.478323	+	0.347522i
$300$		0			0
$301$	4.71685	+	14.5170i	0.271874	+	0.836744i
$302$		0			0
$303$	9.94730	−	7.22714i	0.571458	−	0.415188i
$304$		0			0
$305$	−0.556493	+	1.71271i	−0.0318647	+	0.0980695i
$306$		0			0
$307$	27.2021			1.55250			0.776252	−	0.630422i	$-0.217118\pi$
$307$	27.2021			1.55250			0.776252	+	0.630422i	$0.217118\pi$
$308$		0			0
$309$	−6.42328			−0.365408
$310$		0			0
$311$	−9.96884	+	30.6809i	−0.565281	+	1.73976i	0.101834	+	0.994801i	$0.467529\pi$
$311$	−9.96884	+	30.6809i	−0.565281	+	1.73976i	−0.667115	+	0.744955i	$0.732471\pi$
$312$		0			0
$313$	0.235220	−	0.170898i	0.0132954	−	0.00965970i	−0.581118	−	0.813820i	$-0.697384\pi$
$313$	0.235220	−	0.170898i	0.0132954	−	0.00965970i	0.594413	+	0.804160i	$0.297384\pi$
$314$		0			0
$315$	−0.0759258	−	0.233676i	−0.00427793	−	0.0131661i
$316$		0			0
$317$	−18.4735	−	13.4218i	−1.03758	−	0.753844i	−0.0677665	−	0.997701i	$-0.521587\pi$
$317$	−18.4735	−	13.4218i	−1.03758	−	0.753844i	−0.969811	+	0.243857i	$0.921587\pi$
$318$		0			0
$319$	18.4078	+	13.4619i	1.03064	+	0.753721i
$320$		0			0
$321$	8.80087	+	6.39420i	0.491216	+	0.356890i
$322$		0			0
$323$	−6.42065	−	19.7607i	−0.357254	−	1.09952i
$324$		0			0
$325$	0.952617	−	0.692117i	0.0528417	−	0.0383917i
$326$		0			0
$327$	−0.700810	+	2.15687i	−0.0387549	+	0.119275i
$328$		0			0
$329$	−46.9800			−2.59009
$330$		0			0
$331$	14.5262			0.798433			0.399217	−	0.916857i	$-0.369282\pi$
$331$	14.5262			0.798433			0.399217	+	0.916857i	$0.369282\pi$
$332$		0			0
$333$	−0.0462040	+	0.142201i	−0.00253197	+	0.00779259i
$334$		0			0
$335$	11.6344	−	8.45289i	0.635656	−	0.461831i
$336$		0			0
$337$	4.33684	+	13.3474i	0.236243	+	0.727081i	0.996954	+	0.0779903i	$0.0248503\pi$
$337$	4.33684	+	13.3474i	0.236243	+	0.727081i	−0.760711	+	0.649090i	$0.775150\pi$
$338$		0			0
$339$	7.38804	+	5.36773i	0.401263	+	0.291535i
$340$		0			0
$341$	−29.0383	−	0.0904916i	−1.57251	−	0.00490040i
$342$		0			0
$343$	−0.817029	−	0.593607i	−0.0441154	−	0.0320517i
$344$		0			0
$345$	4.59544	+	14.1433i	0.247410	+	0.761451i
$346$		0			0
$347$	−22.0640	+	16.0304i	−1.18446	+	0.860558i	−0.992667	−	0.120878i	$-0.961429\pi$
$347$	−22.0640	+	16.0304i	−1.18446	+	0.860558i	−0.191789	+	0.981436i	$0.561429\pi$
$348$		0			0
$349$	−7.69815	+	23.6925i	−0.412073	+	1.26823i	0.502771	+	0.864420i	$0.332314\pi$
$349$	−7.69815	+	23.6925i	−0.412073	+	1.26823i	−0.914843	+	0.403809i	$0.867686\pi$
$350$		0			0
$351$	−6.18421			−0.330089
$352$		0			0
$353$	−22.2916			−1.18646			−0.593232	−	0.805031i	$-0.702148\pi$
$353$	−22.2916			−1.18646			−0.593232	+	0.805031i	$0.702148\pi$
$354$		0			0
$355$	−2.11839	+	6.51975i	−0.112433	+	0.346032i
$356$		0			0
$357$	27.7252	−	20.1435i	1.46737	−	1.06611i
$358$		0			0
$359$	−0.577219	−	1.77650i	−0.0304645	−	0.0937599i	0.934668	−	0.355521i	$-0.115697\pi$
$359$	−0.577219	−	1.77650i	−0.0304645	−	0.0937599i	−0.965133	+	0.261761i	$0.915697\pi$
$360$		0			0
$361$	3.39510	+	2.46669i	0.178690	+	0.129826i
$362$		0			0
$363$	15.1732	+	11.1691i	0.796387	+	0.586227i
$364$		0			0
$365$	8.13474	+	5.91023i	0.425792	+	0.309356i
$366$		0			0
$367$	−0.796316	−	2.45081i	−0.0415674	−	0.127931i	0.928119	−	0.372283i	$-0.121425\pi$
$367$	−0.796316	−	2.45081i	−0.0415674	−	0.127931i	−0.969687	+	0.244352i	$0.921425\pi$
$368$		0			0
$369$	0.0856968	−	0.0622623i	0.00446120	−	0.00324125i
$370$		0			0
$371$	14.1736	−	43.6219i	0.735858	−	2.26474i
$372$		0			0
$373$	7.12031			0.368675			0.184338	−	0.982863i	$-0.440986\pi$
$373$	7.12031			0.368675			0.184338	+	0.982863i	$0.440986\pi$
$374$		0			0
$375$	1.71280			0.0884486
$376$		0			0
$377$	2.50194	−	7.70018i	0.128857	−	0.396580i
$378$		0			0
$379$	−23.0912	+	16.7768i	−1.18612	+	0.861765i	−0.992849	−	0.119381i	$-0.961909\pi$
$379$	−23.0912	+	16.7768i	−1.18612	+	0.861765i	−0.193269	+	0.981146i	$0.561909\pi$
$380$		0			0
$381$	7.74904	+	23.8491i	0.396995	+	1.22183i
$382$		0			0
$383$	−7.54866	−	5.48442i	−0.385718	−	0.280241i	0.377980	−	0.925814i	$-0.376619\pi$
$383$	−7.54866	−	5.48442i	−0.385718	−	0.280241i	−0.763699	+	0.645573i	$0.776619\pi$
$384$		0			0
$385$	12.2882	+	0.0382936i	0.626265	+	0.00195162i
$386$		0			0
$387$	−0.221027	−	0.160585i	−0.0112354	−	0.00816301i
$388$		0			0
$389$	0.137494	+	0.423163i	0.00697123	+	0.0214552i	0.954482	−	0.298270i	$-0.0964095\pi$
$389$	0.137494	+	0.423163i	0.00697123	+	0.0214552i	−0.947510	+	0.319725i	$0.896409\pi$
$390$		0			0
$391$	37.9325	−	27.5596i	1.91833	−	1.39375i
$392$		0			0
$393$	3.14354	−	9.67481i	0.158570	−	0.488030i
$394$		0			0
$395$	−1.11383			−0.0560431
$396$		0			0
$397$	1.66941			0.0837850			0.0418925	−	0.999122i	$-0.486661\pi$
$397$	1.66941			0.0837850			0.0418925	+	0.999122i	$0.486661\pi$
$398$		0			0
$399$	7.54510	−	23.2214i	0.377727	−	1.16252i
$400$		0			0
$401$	−27.3906	+	19.9004i	−1.36782	+	0.993780i	−0.369917	+	0.929065i	$0.620614\pi$
$401$	−27.3906	+	19.9004i	−1.36782	+	0.993780i	−0.997904	+	0.0647154i	$0.979386\pi$
$402$		0			0
$403$	3.18581	+	9.80490i	0.158696	+	0.488417i
$404$		0			0
$405$	−7.11665	−	5.17055i	−0.353629	−	0.256926i
$406$		0			0
$407$	−6.03605	−	4.41425i	−0.299196	−	0.218806i
$408$		0			0
$409$	17.5651	+	12.7618i	0.868539	+	0.631031i	0.930195	−	0.367067i	$-0.119638\pi$
$409$	17.5651	+	12.7618i	0.868539	+	0.631031i	−0.0616554	+	0.998097i	$0.519638\pi$
$410$		0			0
$411$	−7.81741	−	24.0595i	−0.385605	−	1.18677i
$412$		0			0
$413$	1.18099	−	0.858043i	0.0581129	−	0.0422215i
$414$		0			0
$415$	0.00535255	−	0.0164735i	0.000262746	−	0.000808651i
$416$		0			0
$417$	2.21382			0.108411
$418$		0			0
$419$	26.5502			1.29706			0.648532	−	0.761187i	$-0.275383\pi$
$419$	26.5502			1.29706			0.648532	+	0.761187i	$0.275383\pi$
$420$		0			0
$421$	−3.23989	+	9.97137i	−0.157903	+	0.485975i	−0.998443	−	0.0557736i	$-0.982237\pi$
$421$	−3.23989	+	9.97137i	−0.157903	+	0.485975i	0.840541	+	0.541749i	$0.182237\pi$
$422$		0			0
$423$	0.680281	−	0.494253i	0.0330764	−	0.0240314i
$424$		0			0
$425$	−1.66878	−	5.13596i	−0.0809475	−	0.249131i
$426$		0			0
$427$	5.39796	+	3.92185i	0.261226	+	0.189792i
$428$		0			0
$429$	2.08684	−	6.35518i	0.100754	−	0.306831i
$430$		0			0
$431$	4.37855	+	3.18120i	0.210907	+	0.153233i	0.688224	−	0.725498i	$-0.258391\pi$
$431$	4.37855	+	3.18120i	0.210907	+	0.153233i	−0.477317	+	0.878731i	$0.658391\pi$
$432$		0			0
$433$	2.80625	+	8.63676i	0.134860	+	0.415056i	0.995568	−	0.0940422i	$-0.0299789\pi$
$433$	2.80625	+	8.63676i	0.134860	+	0.415056i	−0.860708	+	0.509099i	$0.829979\pi$
$434$		0			0
$435$	9.52793	−	6.92245i	0.456829	−	0.331906i
$436$		0			0
$437$	10.3229	−	31.7706i	0.493811	−	1.51980i
$438$		0			0
$439$	−17.3683			−0.828945			−0.414473	−	0.910062i	$-0.636034\pi$
$439$	−17.3683			−0.828945			−0.414473	+	0.910062i	$0.636034\pi$
$440$		0			0
$441$	−0.446130			−0.0212443
$442$		0			0
$443$	4.22224	−	12.9947i	0.200604	−	0.617397i	−0.799261	−	0.600984i	$-0.794775\pi$
$443$	4.22224	−	12.9947i	0.200604	−	0.617397i	0.999865	−	0.0164128i	$-0.00522459\pi$
$444$		0			0
$445$	−6.87207	+	4.99285i	−0.325767	+	0.236684i
$446$		0			0
$447$	−12.6531	−	38.9422i	−0.598471	−	1.84190i
$448$		0			0
$449$	12.1532	+	8.82983i	0.573546	+	0.416706i	0.836392	−	0.548132i	$-0.184661\pi$
$449$	12.1532	+	8.82983i	0.573546	+	0.416706i	−0.262846	+	0.964838i	$0.584661\pi$
$450$		0			0
$451$	1.62138	+	5.04353i	0.0763479	+	0.237490i
$452$		0			0
$453$	−11.4741	−	8.33645i	−0.539102	−	0.391681i
$454$		0			0
$455$	−1.34815	−	4.14917i	−0.0632021	−	0.194516i
$456$		0			0
$457$	2.12304	−	1.54248i	0.0993115	−	0.0721540i	−0.537021	−	0.843569i	$-0.680451\pi$
$457$	2.12304	−	1.54248i	0.0993115	−	0.0721540i	0.636333	+	0.771415i	$0.280451\pi$
$458$		0			0
$459$	−8.76438	+	26.9740i	−0.409086	+	1.25904i
$460$		0			0
$461$	39.2715			1.82906			0.914529	−	0.404521i	$-0.132562\pi$
$461$	39.2715			1.82906			0.914529	+	0.404521i	$0.132562\pi$
$462$		0			0
$463$	3.26421			0.151701			0.0758505	−	0.997119i	$-0.475833\pi$
$463$	3.26421			0.151701			0.0758505	+	0.997119i	$0.475833\pi$
$464$		0			0
$465$	−4.63410	+	14.2623i	−0.214901	+	0.661398i
$466$		0			0
$467$	−20.3484	+	14.7840i	−0.941613	+	0.684122i	−0.948809	−	0.315852i	$-0.897710\pi$
$467$	−20.3484	+	14.7840i	−0.941613	+	0.684122i	0.00719505	+	0.999974i	$0.497710\pi$
$468$		0			0
$469$	−16.4651	−	50.6743i	−0.760286	−	2.33992i
$470$		0			0
$471$	−11.0362	−	8.01827i	−0.508521	−	0.369462i
$472$		0			0
$473$	11.0792	−	7.99689i	0.509423	−	0.367697i
$474$		0			0
$475$	−3.11271	−	2.26152i	−0.142821	−	0.103765i
$476$		0			0
$477$	0.253687	+	0.780769i	0.0116155	+	0.0357490i
$478$		0			0
$479$	24.1885	−	17.5740i	1.10520	−	0.802977i	0.123301	−	0.992369i	$-0.460652\pi$
$479$	24.1885	−	17.5740i	1.10520	−	0.802977i	0.981901	+	0.189393i	$0.0606519\pi$
$480$		0			0
$481$	−0.820405	+	2.52495i	−0.0374072	+	0.115128i
$482$		0			0
$483$	55.0985			2.50707
$484$		0			0
$485$	−10.5155			−0.477483
$486$		0			0
$487$	−9.66165	+	29.7355i	−0.437811	+	1.34744i	0.452367	+	0.891832i	$0.350580\pi$
$487$	−9.66165	+	29.7355i	−0.437811	+	1.34744i	−0.890178	+	0.455612i	$0.849420\pi$
$488$		0			0
$489$	5.66438	−	4.11541i	0.256152	−	0.186105i
$490$		0			0
$491$	−2.52081	−	7.75827i	−0.113763	−	0.350126i	0.877924	−	0.478800i	$-0.158928\pi$
$491$	−2.52081	−	7.75827i	−0.113763	−	0.350126i	−0.991687	+	0.128674i	$0.958928\pi$
$492$		0			0
$493$	−30.0405	−	21.8257i	−1.35296	−	0.982980i
$494$		0			0
$495$	−0.178339	+	0.128724i	−0.00801574	+	0.00578570i
$496$		0			0
$497$	20.5483	+	14.9292i	0.921719	+	0.669668i
$498$		0			0
$499$	−2.63513	−	8.11010i	−0.117965	−	0.363058i	0.874589	−	0.484865i	$-0.161131\pi$
$499$	−2.63513	−	8.11010i	−0.117965	−	0.363058i	−0.992554	+	0.121807i	$0.961131\pi$
$500$		0			0
$501$	5.51820	−	4.00921i	0.246535	−	0.179118i
$502$		0			0
$503$	−3.04027	+	9.35700i	−0.135559	+	0.417208i	−0.995677	−	0.0928880i	$-0.970390\pi$
$503$	−3.04027	+	9.35700i	−0.135559	+	0.417208i	0.860117	+	0.510096i	$0.170390\pi$
$504$		0			0
$505$	−7.17862			−0.319444
$506$		0			0
$507$	19.8916			0.883417
$508$		0			0
$509$	−0.151062	+	0.464920i	−0.00669569	+	0.0206072i	−0.954349	−	0.298695i	$-0.903449\pi$
$509$	−0.151062	+	0.464920i	−0.00669569	+	0.0206072i	0.947653	+	0.319302i	$0.103449\pi$
$510$		0			0
$511$	30.1397	−	21.8977i	1.33330	−	0.968699i
$512$		0			0
$513$	6.24435	+	19.2181i	0.275695	+	0.848501i
$514$		0			0
$515$	3.03395	+	2.20429i	0.133692	+	0.0971327i
$516$		0			0
$517$	12.8709	+	40.0367i	0.566062	+	1.76081i
$518$		0			0
$519$	24.4674	+	17.7766i	1.07400	+	0.780308i
$520$		0			0
$521$	3.44666	+	10.6077i	0.151001	+	0.464734i	0.997734	−	0.0672849i	$-0.0214337\pi$
$521$	3.44666	+	10.6077i	0.151001	+	0.464734i	−0.846733	+	0.532019i	$0.821434\pi$
$522$		0			0
$523$	2.72056	−	1.97660i	0.118962	−	0.0864307i	−0.526714	−	0.850043i	$-0.676576\pi$
$523$	2.72056	−	1.97660i	0.118962	−	0.0864307i	0.645675	+	0.763612i	$0.276576\pi$
$524$		0			0
$525$	1.96103	−	6.03542i	0.0855862	−	0.263407i
$526$		0			0
$527$	47.2816			2.05962
$528$		0			0
$529$	52.3836			2.27755
$530$		0			0
$531$	−0.00807403	+	0.0248493i	−0.000350383	+	0.00107837i
$532$		0			0
$533$	1.52164	−	1.10554i	0.0659097	−	0.0478862i
$534$		0			0
$535$	−1.96265	−	6.04042i	−0.0848529	−	0.261150i
$536$		0			0
$537$	−16.5474	−	12.0224i	−0.714072	−	0.518804i
$538$		0			0
$539$	6.96099	−	21.1987i	0.299831	−	0.913093i
$540$		0			0
$541$	−2.13323	−	1.54988i	−0.0917145	−	0.0666345i	0.540983	−	0.841034i	$-0.318052\pi$
$541$	−2.13323	−	1.54988i	−0.0917145	−	0.0666345i	−0.632697	+	0.774399i	$0.718052\pi$
$542$		0			0
$543$	0.546067	+	1.68062i	0.0234340	+	0.0721224i
$544$		0			0
$545$	1.07120	−	0.778270i	0.0458850	−	0.0333374i
$546$		0			0
$547$	−11.8276	+	36.4018i	−0.505714	+	1.55643i	0.293854	+	0.955850i	$0.405062\pi$
$547$	−11.8276	+	36.4018i	−0.505714	+	1.55643i	−0.799567	+	0.600577i	$0.794938\pi$
$548$		0			0
$549$	−0.119424			−0.00509687
$550$		0			0
$551$	−26.4555			−1.12704
$552$		0			0
$553$	−1.27526	+	3.92483i	−0.0542294	+	0.166901i
$554$		0			0
$555$	−3.12428	+	2.26992i	−0.132618	+	0.0963528i
$556$		0			0
$557$	−5.59589	−	17.2224i	−0.237105	−	0.729736i	−0.996835	−	0.0794966i	$-0.974669\pi$
$557$	−5.59589	−	17.2224i	−0.237105	−	0.729736i	0.759730	−	0.650239i	$-0.225331\pi$
$558$		0			0
$559$	−3.92458	−	2.85137i	−0.165992	−	0.120600i
$560$		0			0
$561$	−24.7622	−	18.1090i	−1.04546	−	0.764562i
$562$		0			0
$563$	2.88702	+	2.09754i	0.121673	+	0.0884008i	0.646958	−	0.762526i	$-0.276041\pi$
$563$	2.88702	+	2.09754i	0.121673	+	0.0884008i	−0.525284	+	0.850927i	$0.676041\pi$
$564$		0			0
$565$	−1.64758	−	5.07074i	−0.0693143	−	0.213328i
$566$		0			0
$567$	−26.3676	+	19.1571i	−1.10733	+	0.804525i
$568$		0			0
$569$	−12.4766	+	38.3990i	−0.523046	+	1.60977i	0.245100	+	0.969498i	$0.421179\pi$
$569$	−12.4766	+	38.3990i	−0.523046	+	1.60977i	−0.768147	+	0.640274i	$0.778821\pi$
$570$		0			0
$571$	−36.3873			−1.52276			−0.761381	−	0.648305i	$-0.775478\pi$
$571$	−36.3873			−1.52276			−0.761381	+	0.648305i	$0.775478\pi$
$572$		0			0
$573$	32.5694			1.36061
$574$		0			0
$575$	2.68300	−	8.25743i	0.111889	−	0.344359i
$576$		0			0
$577$	1.20076	−	0.872400i	0.0499881	−	0.0363185i	−0.562511	−	0.826790i	$-0.690164\pi$
$577$	1.20076	−	0.872400i	0.0499881	−	0.0363185i	0.612499	+	0.790472i	$0.290164\pi$
$578$		0			0
$579$	−2.86276	−	8.81067i	−0.118972	−	0.366159i
$580$		0			0
$581$	−0.0519195	−	0.0377217i	−0.00215399	−	0.00156496i
$582$		0			0
$583$	−41.0580	−	0.127949i	−1.70045	−	0.00529909i
$584$		0			0
$585$	0.0631729	+	0.0458978i	0.00261188	+	0.00189764i
$586$		0			0
$587$	12.1618	+	37.4300i	0.501969	+	1.54490i	0.805806	+	0.592179i	$0.201732\pi$
$587$	12.1618	+	37.4300i	0.501969	+	1.54490i	−0.303837	+	0.952724i	$0.598268\pi$
$588$		0			0
$589$	27.2530	−	19.8005i	1.12294	−	0.815865i
$590$		0			0
$591$	−2.15746	+	6.63998i	−0.0887460	+	0.273132i
$592$		0			0
$593$	27.2990			1.12104			0.560518	−	0.828142i	$-0.310602\pi$
$593$	27.2990			1.12104			0.560518	+	0.828142i	$0.310602\pi$
$594$		0			0
$595$	−20.0083			−0.820260
$596$		0			0
$597$	−6.38907	+	19.6635i	−0.261487	+	0.804774i
$598$		0			0
$599$	17.0954	−	12.4205i	0.698499	−	0.507490i	−0.180944	−	0.983493i	$-0.557915\pi$
$599$	17.0954	−	12.4205i	0.698499	−	0.507490i	0.879443	+	0.476004i	$0.157915\pi$
$600$		0			0
$601$	−0.884593	−	2.72250i	−0.0360833	−	0.111053i	0.931393	−	0.364016i	$-0.118595\pi$
$601$	−0.884593	−	2.72250i	−0.0360833	−	0.111053i	−0.967476	+	0.252963i	$0.918595\pi$
$602$		0			0
$603$	0.771537	+	0.560554i	0.0314194	+	0.0228275i
$604$		0			0
$605$	−3.33392	−	10.4826i	−0.135543	−	0.426178i
$606$		0			0
$607$	25.8840	+	18.8058i	1.05060	+	0.763305i	0.972326	−	0.233627i	$-0.0750593\pi$
$607$	25.8840	+	18.8058i	1.05060	+	0.763305i	0.0782733	+	0.996932i	$0.475059\pi$
$608$		0			0
$609$	−13.4840	−	41.4994i	−0.546398	−	1.68164i
$610$		0			0
$611$	12.0792	−	8.77602i	0.488670	−	0.355040i
$612$		0			0
$613$	−11.0013	+	33.8584i	−0.444337	+	1.36753i	0.438873	+	0.898549i	$0.355378\pi$
$613$	−11.0013	+	33.8584i	−0.444337	+	1.36753i	−0.883209	+	0.468979i	$0.844622\pi$
$614$		0			0
$615$	2.73591			0.110322
$616$		0			0
$617$	−36.9894			−1.48914			−0.744568	−	0.667546i	$-0.767345\pi$
$617$	−36.9894			−1.48914			−0.744568	+	0.667546i	$0.767345\pi$
$618$		0			0
$619$	−10.5038	+	32.3274i	−0.422184	+	1.29935i	0.483480	+	0.875355i	$0.339372\pi$
$619$	−10.5038	+	32.3274i	−0.422184	+	1.29935i	−0.905665	+	0.423995i	$0.860628\pi$
$620$		0			0
$621$	−36.8909	+	26.8028i	−1.48038	+	1.07556i
$622$		0			0
$623$	9.72538	+	29.9317i	0.389639	+	1.19919i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−21.8566	−	0.0681114i	−0.872867	−	0.00272011i
$628$		0			0
$629$	9.85050	+	7.15681i	0.392765	+	0.285361i
$630$		0			0
$631$	−0.891987	−	2.74525i	−0.0355094	−	0.109287i	0.931731	−	0.363150i	$-0.118299\pi$
$631$	−0.891987	−	2.74525i	−0.0355094	−	0.109287i	−0.967240	+	0.253863i	$0.918299\pi$
$632$		0			0
$633$	12.9047	−	9.37584i	0.512917	−	0.372656i
$634$		0			0
$635$	4.52419	−	13.9240i	0.179537	−	0.552558i
$636$		0			0
$637$	−7.92154			−0.313863
$638$		0			0
$639$	−0.454608			−0.0179840
$640$		0			0
$641$	3.59179	−	11.0544i	0.141867	−	0.436623i	−0.854728	−	0.519077i	$-0.826276\pi$
$641$	3.59179	−	11.0544i	0.141867	−	0.436623i	0.996595	+	0.0824541i	$0.0262758\pi$
$642$		0			0
$643$	−21.9133	+	15.9210i	−0.864178	+	0.627862i	−0.929018	−	0.370033i	$-0.879346\pi$
$643$	−21.9133	+	15.9210i	−0.864178	+	0.627862i	0.0648403	+	0.997896i	$0.479346\pi$
$644$		0			0
$645$	−2.18054	−	6.71101i	−0.0858586	−	0.264246i
$646$		0			0
$647$	1.34353	+	0.976135i	0.0528198	+	0.0383758i	0.613882	−	0.789398i	$-0.289607\pi$
$647$	1.34353	+	0.976135i	0.0528198	+	0.0383758i	−0.561062	+	0.827774i	$0.689607\pi$
$648$		0			0
$649$	−1.05478	−	0.771378i	−0.0414039	−	0.0302792i
$650$		0			0
$651$	44.9506	+	32.6585i	1.76175	+	1.27999i
$652$		0			0
$653$	−12.4505	−	38.3186i	−0.487224	−	1.49952i	−0.828734	−	0.559643i	$-0.810938\pi$
$653$	−12.4505	−	38.3186i	−0.487224	−	1.49952i	0.341510	−	0.939878i	$-0.389062\pi$
$654$		0			0
$655$	−4.80493	+	3.49099i	−0.187744	+	0.136404i
$656$		0			0
$657$	−0.206054	+	0.634169i	−0.00803893	+	0.0247413i
$658$		0			0
$659$	−33.7115			−1.31321			−0.656607	−	0.754233i	$-0.728009\pi$
$659$	−33.7115			−1.31321			−0.656607	+	0.754233i	$0.728009\pi$
$660$		0			0
$661$	42.4279			1.65026			0.825128	−	0.564946i	$-0.191103\pi$
$661$	42.4279			1.65026			0.825128	+	0.564946i	$0.191103\pi$
$662$		0			0
$663$	−3.36562	+	10.3583i	−0.130710	+	0.402284i
$664$		0			0
$665$	−11.5328	+	8.37904i	−0.447221	+	0.324925i
$666$		0			0
$667$	−18.4482	−	56.7779i	−0.714319	−	2.19845i
$668$		0			0
$669$	6.57319	+	4.77570i	0.254134	+	0.184639i
$670$		0			0
$671$	1.86337	−	5.67464i	0.0719347	−	0.219067i
$672$		0			0
$673$	30.8456	+	22.4107i	1.18901	+	0.863868i	0.993160	−	0.116765i	$-0.0372525\pi$
$673$	30.8456	+	22.4107i	1.18901	+	0.863868i	0.195853	+	0.980633i	$0.437253\pi$
$674$		0			0
$675$	1.62295	+	4.99493i	0.0624675	+	0.192255i
$676$		0			0
$677$	9.71587	−	7.05899i	0.373411	−	0.271299i	−0.385213	−	0.922828i	$-0.625872\pi$
$677$	9.71587	−	7.05899i	0.373411	−	0.271299i	0.758624	+	0.651529i	$0.225872\pi$
$678$		0			0
$679$	−12.0394	+	37.0535i	−0.462030	+	1.42198i
$680$		0			0
$681$	6.02089			0.230721
$682$		0			0
$683$	−37.6564			−1.44088			−0.720441	−	0.693516i	$-0.756061\pi$
$683$	−37.6564			−1.44088			−0.720441	+	0.693516i	$0.756061\pi$
$684$		0			0
$685$	−4.56411	+	14.0469i	−0.174386	+	0.536704i
$686$		0			0
$687$	−12.6459	+	9.18782i	−0.482473	+	0.350537i
$688$		0			0
$689$	4.50450	+	13.8634i	0.171608	+	0.528155i
$690$		0			0
$691$	−8.03817	−	5.84007i	−0.305786	−	0.222167i	0.424300	−	0.905522i	$-0.360520\pi$
$691$	−8.03817	−	5.84007i	−0.305786	−	0.222167i	−0.730086	+	0.683355i	$0.760520\pi$
$692$		0			0
$693$	0.249401	+	0.775795i	0.00947396	+	0.0294700i
$694$		0			0
$695$	−1.04567	−	0.759722i	−0.0396644	−	0.0288179i
$696$		0			0
$697$	−2.66558	−	8.20382i	−0.100966	−	0.310742i
$698$		0			0
$699$	−29.8270	+	21.6706i	−1.12816	+	0.819658i
$700$		0			0
$701$	3.11652	−	9.59166i	0.117709	−	0.362272i	−0.874793	−	0.484497i	$-0.839003\pi$
$701$	3.11652	−	9.59166i	0.117709	−	0.362272i	0.992502	+	0.122225i	$0.0390028\pi$
$702$		0			0
$703$	8.67494			0.327181
$704$		0			0
$705$	21.7183			0.817957
$706$		0			0
$707$	−8.21898	+	25.2954i	−0.309106	+	0.951332i
$708$		0			0
$709$	−4.22013	+	3.06611i	−0.158490	+	0.115150i	−0.664204	−	0.747552i	$-0.731229\pi$
$709$	−4.22013	+	3.06611i	−0.158490	+	0.115150i	0.505713	+	0.862702i	$0.331229\pi$
$710$		0			0
$711$	−0.0228252	−	0.0702488i	−0.000856013	−	0.00263454i
$712$		0			0
$713$	61.4996	+	44.6821i	2.30318	+	1.67336i
$714$		0			0
$715$	−3.16661	+	2.28563i	−0.118425	+	0.0854779i
$716$		0			0
$717$	−15.6685	−	11.3839i	−0.585152	−	0.425138i
$718$		0			0
$719$	2.44416	+	7.52235i	0.0911518	+	0.280536i	0.986232	−	0.165369i	$-0.0528816\pi$
$719$	2.44416	+	7.52235i	0.0911518	+	0.280536i	−0.895080	+	0.445906i	$0.852882\pi$
$720$		0			0
$721$	11.2409	−	8.16702i	0.418634	−	0.304156i
$722$		0			0
$723$	13.8220	−	42.5396i	0.514044	−	1.58206i
$724$		0			0
$725$	−6.87597			−0.255367
$726$		0			0
$727$	−10.2281			−0.379338			−0.189669	−	0.981848i	$-0.560742\pi$
$727$	−10.2281			−0.379338			−0.189669	+	0.981848i	$0.560742\pi$
$728$		0			0
$729$	8.51965	−	26.2208i	0.315542	−	0.971140i
$730$		0			0
$731$	−17.9990	+	13.0770i	−0.665716	+	0.483671i
$732$		0			0
$733$	−4.74873	−	14.6151i	−0.175398	−	0.539821i	0.824253	−	0.566222i	$-0.191595\pi$
$733$	−4.74873	−	14.6151i	−0.175398	−	0.539821i	−0.999651	+	0.0264009i	$0.991595\pi$
$734$		0			0
$735$	−9.32209	−	6.77289i	−0.343850	−	0.249822i
$736$		0			0
$737$	−38.6742	+	27.9147i	−1.42458	+	1.02825i
$738$		0			0
$739$	−22.8200	−	16.5797i	−0.839449	−	0.609895i	0.0827676	−	0.996569i	$-0.473624\pi$
$739$	−22.8200	−	16.5797i	−0.839449	−	0.609895i	−0.922217	+	0.386673i	$0.873624\pi$
$740$		0			0
$741$	2.39790	+	7.37997i	0.0880890	+	0.271110i
$742$		0			0
$743$	35.6824	−	25.9248i	1.30906	−	0.951089i	0.309061	−	0.951042i	$-0.399985\pi$
$743$	35.6824	−	25.9248i	1.30906	−	0.951089i	1.00000		4.66582e-5i	$-1.48518e-5\pi$
$744$		0			0
$745$	−7.38737	+	22.7360i	−0.270652	+	0.832982i
$746$		0			0
$747$	0.00114866			4.20272e−5
$748$		0			0
$749$	−23.5318			−0.859834
$750$		0			0
$751$	13.3439	−	41.0682i	0.486924	−	1.49860i	−0.342250	−	0.939609i	$-0.611189\pi$
$751$	13.3439	−	41.0682i	0.486924	−	1.49860i	0.829174	−	0.558990i	$-0.188811\pi$
$752$		0			0
$753$	5.15214	−	3.74325i	0.187754	−	0.136411i
$754$		0			0
$755$	2.55881	+	7.87521i	0.0931246	+	0.286608i
$756$		0			0
$757$	−15.5978	−	11.3325i	−0.566913	−	0.411886i	0.267070	−	0.963677i	$-0.413945\pi$
$757$	−15.5978	−	11.3325i	−0.566913	−	0.411886i	−0.833982	+	0.551791i	$0.813945\pi$
$758$		0			0
$759$	−15.0951	−	46.9554i	−0.547918	−	1.70437i
$760$		0			0
$761$	−28.2423	−	20.5193i	−1.02378	−	0.743823i	−0.0567289	−	0.998390i	$-0.518067\pi$
$761$	−28.2423	−	20.5193i	−1.02378	−	0.743823i	−0.967055	+	0.254567i	$0.918067\pi$
$762$		0			0
$763$	−1.51596	−	4.66565i	−0.0548815	−	0.168908i
$764$		0			0
$765$	0.289725	−	0.210497i	0.0104750	−	0.00761055i
$766$		0			0
$767$	−0.143364	+	0.441228i	−0.00517656	+	0.0159318i
$768$		0			0
$769$	10.7367			0.387177			0.193588	−	0.981083i	$-0.437987\pi$
$769$	10.7367			0.387177			0.193588	+	0.981083i	$0.437987\pi$
$770$		0			0
$771$	12.1485			0.437518
$772$		0			0
$773$	9.77736	−	30.0916i	0.351667	−	1.08232i	−0.606249	−	0.795275i	$-0.707327\pi$
$773$	9.77736	−	30.0916i	0.351667	−	1.08232i	0.957917	−	0.287046i	$-0.0926733\pi$
$774$		0			0
$775$	7.08327	−	5.14630i	0.254439	−	0.184860i
$776$		0			0
$777$	4.42149	+	13.6080i	0.158620	+	0.488183i
$778$		0			0
$779$	−4.97202	−	3.61239i	−0.178141	−	0.129427i
$780$		0			0
$781$	7.09327	−	21.6016i	0.253817	−	0.772964i
$782$		0			0
$783$	29.2156	+	21.2264i	1.04408	+	0.758570i
$784$		0			0
$785$	2.46115	+	7.57463i	0.0878421	+	0.270350i
$786$		0			0
$787$	12.6566	−	9.19553i	0.451158	−	0.327785i	−0.338895	−	0.940824i	$-0.610053\pi$
$787$	12.6566	−	9.19553i	0.451158	−	0.327785i	0.790053	+	0.613039i	$0.210053\pi$
$788$		0			0
$789$	12.3629	−	38.0491i	0.440131	−	1.35458i
$790$		0			0
$791$	−19.7542			−0.702379
$792$		0			0
$793$	−2.12050			−0.0753011
$794$		0			0
$795$	−6.55229	+	20.1659i	−0.232386	+	0.715209i
$796$		0			0
$797$	4.02872	−	2.92704i	0.142705	−	0.103681i	−0.514142	−	0.857705i	$-0.671890\pi$
$797$	4.02872	−	2.92704i	0.142705	−	0.103681i	0.656847	+	0.754024i	$0.271890\pi$
$798$		0			0
$799$	−21.1600	−	65.1239i	−0.748588	−	2.30392i
$800$		0			0
$801$	−0.455722	−	0.331101i	−0.0161021	−	0.0116989i
$802$		0			0
$803$	−26.9187	−	19.6860i	−0.949939	−	0.694704i
$804$		0			0
$805$	−26.0250	−	18.9083i	−0.917261	−	0.666429i
$806$		0			0
$807$	9.04110	+	27.8257i	0.318262	+	0.979510i
$808$		0			0
$809$	−24.9907	+	18.1568i	−0.878627	+	0.638360i	−0.932888	−	0.360167i	$-0.882720\pi$
$809$	−24.9907	+	18.1568i	−0.878627	+	0.638360i	0.0542612	+	0.998527i	$0.482720\pi$
$810$		0			0
$811$	−1.38422	+	4.26019i	−0.0486066	+	0.149596i	−0.972414	−	0.233262i	$-0.925060\pi$
$811$	−1.38422	+	4.26019i	−0.0486066	+	0.149596i	0.923807	+	0.382858i	$0.125060\pi$
$812$		0			0
$813$	−46.9895			−1.64799
$814$		0			0
$815$	−4.08778			−0.143189
$816$		0			0
$817$	−4.89822	+	15.0752i	−0.171367	+	0.527413i
$818$		0			0
$819$	0.234059	−	0.170054i	0.00817868	−	0.00594216i
$820$		0			0
$821$	3.85678	+	11.8699i	0.134603	+	0.414264i	0.995528	−	0.0944672i	$-0.0301147\pi$
$821$	3.85678	+	11.8699i	0.134603	+	0.414264i	−0.860925	+	0.508731i	$0.830115\pi$
$822$		0			0
$823$	13.3519	+	9.70071i	0.465417	+	0.338146i	0.795653	−	0.605753i	$-0.207128\pi$
$823$	13.3519	+	9.70071i	0.465417	+	0.338146i	−0.330235	+	0.943899i	$0.607128\pi$
$824$		0			0
$825$	−5.68069	−	0.0177027i	−0.197776	−	0.000616328i
$826$		0			0
$827$	−36.5649	−	26.5660i	−1.27149	−	0.923789i	−0.272225	−	0.962233i	$-0.587760\pi$
$827$	−36.5649	−	26.5660i	−1.27149	−	0.923789i	−0.999261	+	0.0384447i	$0.987760\pi$
$828$		0			0
$829$	−3.51891	−	10.8301i	−0.122217	−	0.376144i	0.871167	−	0.490987i	$-0.163364\pi$
$829$	−3.51891	−	10.8301i	−0.122217	−	0.376144i	−0.993384	+	0.114842i	$0.963364\pi$
$830$		0			0
$831$	−33.5683	+	24.3888i	−1.16447	+	0.846037i
$832$		0			0
$833$	−11.2266	+	34.5518i	−0.388977	+	1.19715i
$834$		0			0
$835$	−3.98229			−0.137813
$836$		0			0
$837$	−45.9833			−1.58941
$838$		0			0
$839$	4.36023	−	13.4194i	0.150532	−	0.463289i	−0.847149	−	0.531355i	$-0.821683\pi$
$839$	4.36023	−	13.4194i	0.150532	−	0.463289i	0.997681	+	0.0680663i	$0.0216829\pi$
$840$		0			0
$841$	−14.7880	+	10.7441i	−0.509932	+	0.370487i
$842$		0			0
$843$	9.08432	+	27.9587i	0.312881	+	0.962948i
$844$		0			0
$845$	−9.39552	−	6.82624i	−0.323216	−	0.234830i
$846$		0			0
$847$	−40.7548	−	0.254010i	−1.40035	−	0.00872789i
$848$		0			0
$849$	−6.41445	−	4.66037i	−0.220143	−	0.159944i
$850$		0			0
$851$	6.04931	+	18.6179i	0.207368	+	0.638212i
$852$		0			0
$853$	16.9736	−	12.3320i	0.581165	−	0.422241i	−0.257979	−	0.966151i	$-0.583056\pi$
$853$	16.9736	−	12.3320i	0.581165	−	0.422241i	0.839144	+	0.543909i	$0.183056\pi$
$854$		0			0
$855$	0.0788453	−	0.242661i	0.00269645	−	0.00829883i
$856$		0			0
$857$	25.0649			0.856201			0.428101	−	0.903731i	$-0.359183\pi$
$857$	25.0649			0.856201			0.428101	+	0.903731i	$0.359183\pi$
$858$		0			0
$859$	38.0496			1.29823			0.649117	−	0.760689i	$-0.275139\pi$
$859$	38.0496			1.29823			0.649117	+	0.760689i	$0.275139\pi$
$860$		0			0
$861$	3.13241	−	9.64055i	0.106752	−	0.328549i
$862$		0			0
$863$	−6.94855	+	5.04842i	−0.236531	+	0.171850i	−0.699737	−	0.714401i	$-0.746699\pi$
$863$	−6.94855	+	5.04842i	−0.236531	+	0.171850i	0.463205	+	0.886251i	$0.346699\pi$
$864$		0			0
$865$	−5.45640	−	16.7931i	−0.185523	−	0.570982i
$866$		0			0
$867$	16.8540	+	12.2451i	0.572391	+	0.415866i
$868$		0			0
$869$	3.69415	+	0.0115120i	0.125315	+	0.000390519i
$870$		0			0
$871$	13.6995	+	9.95328i	0.464190	+	0.337254i
$872$		0			0
$873$	−0.215488	−	0.663204i	−0.00729316	−	0.0224461i
$874$		0			0
$875$	−2.99745	+	2.17778i	−0.101332	+	0.0736223i
$876$		0			0
$877$	−3.26516	+	10.0491i	−0.110257	+	0.339335i	−0.990928	−	0.134392i	$-0.957092\pi$
$877$	−3.26516	+	10.0491i	−0.110257	+	0.339335i	0.880671	+	0.473727i	$0.157092\pi$
$878$		0			0
$879$	31.6879			1.06881
$880$		0			0
$881$	−35.5069			−1.19626			−0.598129	−	0.801400i	$-0.704089\pi$
$881$	−35.5069			−1.19626			−0.598129	+	0.801400i	$0.704089\pi$
$882$		0			0
$883$	10.5115	−	32.3511i	0.353740	−	1.08870i	−0.602996	−	0.797744i	$-0.706026\pi$
$883$	10.5115	−	32.3511i	0.353740	−	1.08870i	0.956736	−	0.290957i	$-0.0939736\pi$
$884$		0			0
$885$	−0.545959	+	0.396662i	−0.0183522	+	0.0133337i
$886$		0			0
$887$	3.08945	+	9.50834i	0.103733	+	0.319259i	0.989431	−	0.145004i	$-0.0463194\pi$
$887$	3.08945	+	9.50834i	0.103733	+	0.319259i	−0.885698	+	0.464263i	$0.846319\pi$
$888$		0			0
$889$	−43.8845	−	31.8839i	−1.47184	−	1.06935i
$890$		0			0
$891$	23.5497	+	17.2222i	0.788944	+	0.576966i
$892$		0			0
$893$	−39.4691	−	28.6760i	−1.32078	−	0.959605i
$894$		0			0
$895$	3.69018	+	11.3572i	0.123349	+	0.379629i
$896$		0			0
$897$	−14.1665	+	10.2926i	−0.473007	+	0.343659i
$898$		0			0
$899$	18.6034	−	57.2554i	0.620459	−	1.90958i
$900$		0			0
$901$	66.8528			2.22719
$902$		0			0
$903$	−26.1442			−0.870026
$904$		0			0
$905$	0.318815	−	0.981213i	0.0105978	−	0.0326166i
$906$		0			0
$907$	11.6476	−	8.46245i	0.386751	−	0.280991i	−0.377372	−	0.926062i	$-0.623172\pi$
$907$	11.6476	−	8.46245i	0.386751	−	0.280991i	0.764123	+	0.645071i	$0.223172\pi$
$908$		0			0
$909$	−0.147108	−	0.452751i	−0.00487926	−	0.0150168i
$910$		0			0
$911$	−13.0870	−	9.50830i	−0.433593	−	0.315024i	0.349491	−	0.936940i	$-0.386355\pi$
$911$	−13.0870	−	9.50830i	−0.433593	−	0.315024i	−0.783084	+	0.621916i	$0.786355\pi$
$912$		0			0
$913$	−0.0179226	+	0.0545807i	−0.000593151	+	0.00180636i
$914$		0			0
$915$	−2.49541	−	1.81302i	−0.0824957	−	0.0599366i
$916$		0			0
$917$	6.79996	+	20.9281i	0.224555	+	0.691108i
$918$		0			0
$919$	−14.7072	+	10.6854i	−0.485144	+	0.352478i	−0.803314	−	0.595556i	$-0.796932\pi$
$919$	−14.7072	+	10.6854i	−0.485144	+	0.352478i	0.318170	+	0.948034i	$0.396932\pi$
$920$		0			0
$921$	−14.3976	+	44.3114i	−0.474418	+	1.46011i
$922$		0			0
$923$	−8.07207			−0.265696
$924$		0			0
$925$	2.25468			0.0741335
$926$		0			0
$927$	−0.0768502	+	0.236521i	−0.00252409	+	0.00776836i
$928$		0			0
$929$	19.6811	−	14.2992i	0.645717	−	0.469141i	−0.216092	−	0.976373i	$-0.569331\pi$
$929$	19.6811	−	14.2992i	0.645717	−	0.469141i	0.861810	+	0.507232i	$0.169331\pi$
$930$		0			0
$931$	7.99857	+	24.6171i	0.262143	+	0.806792i
$932$		0			0
$933$	−44.7020	−	32.4779i	−1.46348	−	1.06328i
$934$		0			0
$935$	5.48159	+	17.0512i	0.179267	+	0.557635i
$936$		0			0
$937$	−19.5700	−	14.2184i	−0.639323	−	0.464495i	0.220295	−	0.975433i	$-0.429298\pi$
$937$	−19.5700	−	14.2184i	−0.639323	−	0.464495i	−0.859617	+	0.510938i	$0.829298\pi$
$938$		0			0
$939$	0.153889	+	0.473620i	0.00502196	+	0.0154560i
$940$		0			0
$941$	4.95329	−	3.59878i	0.161473	−	0.117317i	−0.504115	−	0.863637i	$-0.668181\pi$
$941$	4.95329	−	3.59878i	0.161473	−	0.117317i	0.665587	+	0.746320i	$0.268181\pi$
$942$		0			0
$943$	4.28564	−	13.1898i	0.139559	−	0.429520i
$944$		0			0
$945$	19.4589			0.632998
$946$		0			0
$947$	−30.4758			−0.990330			−0.495165	−	0.868799i	$-0.664892\pi$
$947$	−30.4758			−0.990330			−0.495165	+	0.868799i	$0.664892\pi$
$948$		0			0
$949$	−3.65872	+	11.2604i	−0.118767	+	0.365527i
$950$		0			0
$951$	31.6415	−	22.9889i	1.02605	−	0.745466i
$952$		0			0
$953$	3.80261	+	11.7032i	0.123179	+	0.379105i	0.993565	−	0.113265i	$-0.0361309\pi$
$953$	3.80261	+	11.7032i	0.123179	+	0.379105i	−0.870386	+	0.492370i	$0.836131\pi$
$954$		0			0
$955$	−15.3837	−	11.1769i	−0.497805	−	0.361677i
$956$		0			0
$957$	−31.6720	+	22.8606i	−1.02381	+	0.738977i
$958$		0			0
$959$	44.2717	+	32.1653i	1.42961	+	1.03867i
$960$		0			0
$961$	14.1088	+	43.4225i	0.455123	+	1.40073i
$962$		0			0
$963$	0.340746	−	0.247567i	0.0109804	−	0.00797772i
$964$		0			0
$965$	−1.67139	+	5.14402i	−0.0538040	+	0.165592i
$966$		0			0
$967$	−22.5927			−0.726532			−0.363266	−	0.931685i	$-0.618338\pi$
$967$	−22.5927			−0.726532			−0.363266	+	0.931685i	$0.618338\pi$
$968$		0			0
$969$	35.5880			1.14325
$970$		0			0
$971$	−13.3663	+	41.1374i	−0.428946	+	1.32016i	0.470218	+	0.882550i	$0.344175\pi$
$971$	−13.3663	+	41.1374i	−0.428946	+	1.32016i	−0.899164	+	0.437611i	$0.855825\pi$
$972$		0			0
$973$	−3.87426	+	2.81481i	−0.124203	+	0.0902387i
$974$		0			0
$975$	0.623232	+	1.91811i	0.0199594	+	0.0614287i
$976$		0			0
$977$	−12.1952	−	8.86033i	−0.390159	−	0.283467i	0.375362	−	0.926878i	$-0.377518\pi$
$977$	−12.1952	−	8.86033i	−0.390159	−	0.283467i	−0.765521	+	0.643411i	$0.777518\pi$
$978$		0			0
$979$	22.8436	−	16.4883i	0.730084	−	0.526969i
$980$		0			0
$981$	0.0710365	+	0.0516110i	0.00226802	+	0.00164781i
$982$		0			0
$983$	12.9536	+	39.8672i	0.413157	+	1.27157i	0.913889	+	0.405964i	$0.133064\pi$
$983$	12.9536	+	39.8672i	0.413157	+	1.27157i	−0.500732	+	0.865602i	$0.666936\pi$
$984$		0			0
$985$	3.29770	−	2.39592i	0.105073	−	0.0763403i
$986$		0			0
$987$	24.8658	−	76.5290i	0.791486	−	2.43594i
$988$		0			0
$989$	−35.7695			−1.13740
$990$		0			0
$991$	−29.5068			−0.937314			−0.468657	−	0.883380i	$-0.655262\pi$
$991$	−29.5068			−0.937314			−0.468657	+	0.883380i	$0.655262\pi$
$992$		0			0
$993$	−7.68850	+	23.6628i	−0.243987	+	0.750916i
$994$		0			0
$995$	9.76576	−	7.09524i	0.309595	−	0.224934i
$996$		0			0
$997$	15.0230	+	46.2361i	0.475784	+	1.46431i	0.844897	+	0.534929i	$0.179661\pi$
$997$	15.0230	+	46.2361i	0.475784	+	1.46431i	−0.369113	+	0.929384i	$0.620339\pi$
$998$		0			0
$999$	−9.58002	−	6.96029i	−0.303098	−	0.220214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.i.81.1		12
4.3	odd	2		440.2.y.c.81.3	✓	12
11.3	even	5	inner	880.2.bo.i.641.1		12
11.5	even	5		9680.2.a.dc.1.1		6
11.6	odd	10		9680.2.a.dd.1.1		6
44.3	odd	10		440.2.y.c.201.3	yes	12
44.27	odd	10		4840.2.a.bb.1.6		6
44.39	even	10		4840.2.a.ba.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.c.81.3	✓	12	4.3	odd	2
440.2.y.c.201.3	yes	12	44.3	odd	10
880.2.bo.i.81.1		12	1.1	even	1	trivial
880.2.bo.i.641.1		12	11.3	even	5	inner
4840.2.a.ba.1.6		6	44.39	even	10
4840.2.a.bb.1.6		6	44.27	odd	10
9680.2.a.dc.1.1		6	11.5	even	5
9680.2.a.dd.1.1		6	11.6	odd	10

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.529284 + 1.62897i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-1.14492 - 3.52372i) q^{7} +(0.0536500 + 0.0389790i) q^{9} +(-2.68927 + 1.94109i) q^{11} +(0.952617 + 0.692117i) q^{13} +(0.529284 + 1.62897i) q^{15} +(4.36891 - 3.17420i) q^{17} +(1.18895 - 3.65921i) q^{19} +6.34602 q^{21} +8.68237 q^{23} +(0.309017 - 0.951057i) q^{25} +(-4.24895 + 3.08704i) q^{27} +(-2.12479 - 6.53944i) q^{29} +(7.08327 + 5.14630i) q^{31} +(-1.73859 - 5.40813i) q^{33} +(-2.99745 - 2.17778i) q^{35} +(0.696735 + 2.14433i) q^{37} +(-1.63164 + 1.18546i) q^{39} +(0.493602 - 1.51915i) q^{41} -4.11979 q^{43} +0.0663151 q^{45} +(3.91833 - 12.0594i) q^{47} +(-5.44260 + 3.95428i) q^{49} +(2.85828 + 8.79688i) q^{51} +(10.0152 + 7.27650i) q^{53} +(-1.03472 + 3.15109i) q^{55} +(5.33145 + 3.87353i) q^{57} +(0.121753 + 0.374716i) q^{59} +(-1.45692 + 1.05851i) q^{61} +(0.0759258 - 0.233676i) q^{63} +1.17750 q^{65} +14.3809 q^{67} +(-4.59544 + 14.1433i) q^{69} +(-5.54603 + 4.02943i) q^{71} +(3.10719 + 9.56296i) q^{73} +(1.38568 + 1.00676i) q^{75} +(9.91887 + 7.25381i) q^{77} +(-0.901110 - 0.654695i) q^{79} +(-2.71832 - 8.36612i) q^{81} +(0.0140132 - 0.0101812i) q^{83} +(1.66878 - 5.13596i) q^{85} +11.7772 q^{87} -8.49434 q^{89} +(1.34815 - 4.14917i) q^{91} +(-12.1322 + 8.81458i) q^{93} +(-1.18895 - 3.65921i) q^{95} +(-8.50719 - 6.18083i) q^{97} +(-0.219941 - 0.000685401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} + 18 q^{13} - q^{15} + 3 q^{17} - 4 q^{19} - 28 q^{21} + 18 q^{23} - 3 q^{25} - 23 q^{27} + 15 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{35} + 6 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) \) 12 * q + q^3 + 3 * q^5 + q^7 - 10 * q^9 - 4 * q^11 + 18 * q^13 - q^15 + 3 * q^17 - 4 * q^19 - 28 * q^21 + 18 * q^23 - 3 * q^25 - 23 * q^27 + 15 * q^29 + 8 * q^31 + 4 * q^33 - 6 * q^35 + 6 * q^37 + 33 * q^39 + 2 * q^41 + 36 * q^43 - 10 * q^45 + 16 * q^47 - 16 * q^49 + 10 * q^51 + 19 * q^53 - 6 * q^55 + 62 * q^57 - 46 * q^59 + 18 * q^61 + 7 * q^63 + 2 * q^65 + 44 * q^67 - q^69 + 6 * q^71 + 25 * q^73 - 4 * q^75 + 10 * q^77 - 19 * q^79 + 30 * q^81 - 3 * q^85 - 6 * q^87 - 50 * q^89 + 46 * q^91 - 37 * q^93 + 4 * q^95 - 31 * q^97 - 79 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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