LMFDB - Embedded newform 440.2.y.d.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, 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("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.4
Root			$-2.35019 + 1.70752i$ of defining polynomial
Character	$\chi$	$=$	440.361
Dual form			440.2.y.d.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.35019 - 1.70752i) q^{3} +(0.309017 + 0.951057i) q^{5} +(1.76616 + 1.28319i) q^{7} +(1.68075 - 5.17281i) q^{9} +(-2.98460 - 1.44644i) q^{11} +(1.90383 - 5.85939i) q^{13} +(2.35019 + 1.70752i) q^{15} +(2.20273 + 6.77930i) q^{17} +(-5.14521 + 3.73822i) q^{19} +6.34188 q^{21} +2.17735 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-2.18949 - 6.73856i) q^{27} +(2.58318 + 1.87679i) q^{29} +(1.35789 - 4.17917i) q^{31} +(-9.48419 + 1.69684i) q^{33} +(-0.674612 + 2.07624i) q^{35} +(-4.28336 - 3.11205i) q^{37} +(-5.53062 - 17.0215i) q^{39} +(-2.65866 + 1.93163i) q^{41} -6.83874 q^{43} +5.43902 q^{45} +(3.48237 - 2.53009i) q^{47} +(-0.690378 - 2.12477i) q^{49} +(16.7526 + 12.1715i) q^{51} +(-3.28052 + 10.0964i) q^{53} +(0.453350 - 3.28549i) q^{55} +(-5.70918 + 17.5711i) q^{57} +(-11.1568 - 8.10589i) q^{59} +(2.27216 + 6.99299i) q^{61} +(9.60616 - 6.97929i) q^{63} +6.16092 q^{65} -7.67154 q^{67} +(5.11720 - 3.71787i) q^{69} +(1.77417 + 5.46033i) q^{71} +(3.96075 + 2.87765i) q^{73} +(-0.897694 + 2.76282i) q^{75} +(-3.41522 - 6.38444i) q^{77} +(-2.50738 + 7.71694i) q^{79} +(-3.45115 - 2.50741i) q^{81} +(1.30524 + 4.01711i) q^{83} +(-5.76682 + 4.18984i) q^{85} +9.27563 q^{87} +16.8037 q^{89} +(10.8812 - 7.90563i) q^{91} +(-3.94468 - 12.1405i) q^{93} +(-5.14521 - 3.73822i) q^{95} +(-1.01222 + 3.11531i) q^{97} +(-12.4985 + 13.0077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 4 q^{5} + 8 q^{7} - 7 q^{9} - 7 q^{11} - 11 q^{13} - 3 q^{15} + 9 q^{17} - 2 q^{19} + 12 q^{21} + 20 q^{23} - 4 q^{25} - 9 q^{27} + q^{29} - 2 q^{31} - 32 q^{33} - 2 q^{35} - 16 q^{37}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 4 * q^5 + 8 * q^7 - 7 * q^9 - 7 * q^11 - 11 * q^13 - 3 * q^15 + 9 * q^17 - 2 * q^19 + 12 * q^21 + 20 * q^23 - 4 * q^25 - 9 * q^27 + q^29 - 2 * q^31 - 32 * q^33 - 2 * q^35 - 16 * q^37 + 3 * q^39 - 11 * q^41 - 16 * q^43 + 38 * q^45 - 10 * q^47 + 4 * q^49 + 26 * q^51 - 9 * q^53 + 3 * q^55 - 50 * q^57 - 60 * q^59 + 30 * q^61 + 52 * q^63 + 24 * q^65 - 4 * q^67 + 41 * q^69 - 10 * q^71 + q^73 + 2 * q^75 - 4 * q^77 + 19 * q^79 - 31 * q^81 + 64 * q^83 - 11 * q^85 + 30 * q^87 + 24 * q^89 - 9 * q^91 + 45 * q^93 - 2 * q^95 - 3 * q^97 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	2.35019	−	1.70752i	1.35688	−	0.985834i	0.358248	−	0.933626i	$-0.383374\pi$
$3$	2.35019	−	1.70752i	1.35688	−	0.985834i	0.998636	−	0.0522082i	$-0.0166259\pi$
$4$		0			0
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	1.76616	+	1.28319i	0.667545	+	0.485000i	0.869203	−	0.494456i	$-0.164633\pi$
$7$	1.76616	+	1.28319i	0.667545	+	0.485000i	−0.201657	+	0.979456i	$0.564633\pi$
$8$		0			0
$9$	1.68075	−	5.17281i	0.560250	−	1.72427i
$10$		0			0
$11$	−2.98460	−	1.44644i	−0.899890	−	0.436117i
$11$	−2.98460	−	1.44644i	−0.899890	−	0.436117i
$12$		0			0
$13$	1.90383	−	5.85939i	0.528028	−	1.62510i	−0.230223	−	0.973138i	$-0.573945\pi$
$13$	1.90383	−	5.85939i	0.528028	−	1.62510i	0.758250	−	0.651964i	$-0.226055\pi$
$14$		0			0
$15$	2.35019	+	1.70752i	0.606817	+	0.440879i
$16$		0			0
$17$	2.20273	+	6.77930i	0.534240	+	1.64422i	0.745285	+	0.666746i	$0.232314\pi$
$17$	2.20273	+	6.77930i	0.534240	+	1.64422i	−0.211044	+	0.977477i	$0.567686\pi$
$18$		0			0
$19$	−5.14521	+	3.73822i	−1.18039	+	0.857606i	−0.992216	−	0.124529i	$-0.960258\pi$
$19$	−5.14521	+	3.73822i	−1.18039	+	0.857606i	−0.188177	+	0.982135i	$0.560258\pi$
$20$		0			0
$21$	6.34188			1.38391
$22$		0			0
$23$	2.17735			0.454010			0.227005	−	0.973894i	$-0.427107\pi$
$23$	2.17735			0.454010			0.227005	+	0.973894i	$0.427107\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−2.18949	−	6.73856i	−0.421368	−	1.29684i
$28$		0			0
$29$	2.58318	+	1.87679i	0.479685	+	0.348512i	0.801204	−	0.598392i	$-0.204193\pi$
$29$	2.58318	+	1.87679i	0.479685	+	0.348512i	−0.321519	+	0.946903i	$0.604193\pi$
$30$		0			0
$31$	1.35789	−	4.17917i	0.243885	−	0.750601i	−0.751933	−	0.659240i	$-0.770878\pi$
$31$	1.35789	−	4.17917i	0.243885	−	0.750601i	0.995818	−	0.0913612i	$-0.0291218\pi$
$32$		0			0
$33$	−9.48419	+	1.69684i	−1.65099	+	0.295383i
$34$		0			0
$35$	−0.674612	+	2.07624i	−0.114030	+	0.350949i
$36$		0			0
$37$	−4.28336	−	3.11205i	−0.704180	−	0.511617i	0.177111	−	0.984191i	$-0.443325\pi$
$37$	−4.28336	−	3.11205i	−0.704180	−	0.511617i	−0.881291	+	0.472574i	$0.843325\pi$
$38$		0			0
$39$	−5.53062	−	17.0215i	−0.885609	−	2.72562i
$40$		0			0
$41$	−2.65866	+	1.93163i	−0.415214	+	0.301670i	−0.775709	−	0.631091i	$-0.782608\pi$
$41$	−2.65866	+	1.93163i	−0.415214	+	0.301670i	0.360495	+	0.932761i	$0.382608\pi$
$42$		0			0
$43$	−6.83874			−1.04290			−0.521449	−	0.853282i	$-0.674608\pi$
$43$	−6.83874			−1.04290			−0.521449	+	0.853282i	$0.674608\pi$
$44$		0			0
$45$	5.43902			0.810801
$46$		0			0
$47$	3.48237	−	2.53009i	0.507956	−	0.369052i	−0.304092	−	0.952643i	$-0.598353\pi$
$47$	3.48237	−	2.53009i	0.507956	−	0.369052i	0.812048	+	0.583591i	$0.198353\pi$
$48$		0			0
$49$	−0.690378	−	2.12477i	−0.0986255	−	0.303538i
$50$		0			0
$51$	16.7526	+	12.1715i	2.34583	+	1.70435i
$52$		0			0
$53$	−3.28052	+	10.0964i	−0.450614	+	1.38685i	0.425593	+	0.904915i	$0.360066\pi$
$53$	−3.28052	+	10.0964i	−0.450614	+	1.38685i	−0.876207	+	0.481934i	$0.839934\pi$
$54$		0			0
$55$	0.453350	−	3.28549i	0.0611298	−	0.443016i
$56$		0			0
$57$	−5.70918	+	17.5711i	−0.756200	+	2.32734i
$58$		0			0
$59$	−11.1568	−	8.10589i	−1.45249	−	1.05530i	−0.985241	−	0.171171i	$-0.945245\pi$
$59$	−11.1568	−	8.10589i	−1.45249	−	1.05530i	−0.467250	−	0.884125i	$-0.654755\pi$
$60$		0			0
$61$	2.27216	+	6.99299i	0.290920	+	0.895360i	0.984561	+	0.175039i	$0.0560053\pi$
$61$	2.27216	+	6.99299i	0.290920	+	0.895360i	−0.693641	+	0.720321i	$0.743995\pi$
$62$		0			0
$63$	9.60616	−	6.97929i	1.21026	−	0.879308i
$64$		0			0
$65$	6.16092			0.764169
$66$		0			0
$67$	−7.67154			−0.937228			−0.468614	−	0.883403i	$-0.655246\pi$
$67$	−7.67154			−0.937228			−0.468614	+	0.883403i	$0.655246\pi$
$68$		0			0
$69$	5.11720	−	3.71787i	0.616039	−	0.447578i
$70$		0			0
$71$	1.77417	+	5.46033i	0.210555	+	0.648021i	0.999439	+	0.0334799i	$0.0106590\pi$
$71$	1.77417	+	5.46033i	0.210555	+	0.648021i	−0.788884	+	0.614542i	$0.789341\pi$
$72$		0			0
$73$	3.96075	+	2.87765i	0.463570	+	0.336803i	0.794930	−	0.606701i	$-0.207507\pi$
$73$	3.96075	+	2.87765i	0.463570	+	0.336803i	−0.331360	+	0.943504i	$0.607507\pi$
$74$		0			0
$75$	−0.897694	+	2.76282i	−0.103657	+	0.319023i
$76$		0			0
$77$	−3.41522	−	6.38444i	−0.389201	−	0.727574i
$78$		0			0
$79$	−2.50738	+	7.71694i	−0.282103	+	0.868223i	0.705149	+	0.709059i	$0.250880\pi$
$79$	−2.50738	+	7.71694i	−0.282103	+	0.868223i	−0.987252	+	0.159164i	$0.949120\pi$
$80$		0			0
$81$	−3.45115	−	2.50741i	−0.383461	−	0.278601i
$82$		0			0
$83$	1.30524	+	4.01711i	0.143268	+	0.440935i	0.996784	−	0.0801321i	$-0.0255342\pi$
$83$	1.30524	+	4.01711i	0.143268	+	0.440935i	−0.853516	+	0.521067i	$0.825534\pi$
$84$		0			0
$85$	−5.76682	+	4.18984i	−0.625500	+	0.454452i
$86$		0			0
$87$	9.27563			0.994452
$88$		0			0
$89$	16.8037			1.78119			0.890594	−	0.454800i	$-0.150289\pi$
$89$	16.8037			1.78119			0.890594	+	0.454800i	$0.150289\pi$
$90$		0			0
$91$	10.8812	−	7.90563i	1.14066	−	0.828735i
$92$		0			0
$93$	−3.94468	−	12.1405i	−0.409044	−	1.25891i
$94$		0			0
$95$	−5.14521	−	3.73822i	−0.527888	−	0.383533i
$96$		0			0
$97$	−1.01222	+	3.11531i	−0.102776	+	0.316311i	−0.989202	−	0.146559i	$-0.953180\pi$
$97$	−1.01222	+	3.11531i	−0.102776	+	0.316311i	0.886426	+	0.462870i	$0.153180\pi$
$98$		0			0
$99$	−12.4985	+	13.0077i	−1.25615	+	1.30732i
$100$		0			0
$101$	−2.13546	+	6.57226i	−0.212486	+	0.653964i	0.786837	+	0.617161i	$0.211717\pi$
$101$	−2.13546	+	6.57226i	−0.212486	+	0.653964i	−0.999323	+	0.0368028i	$0.988283\pi$
$102$		0			0
$103$	−6.13713	−	4.45889i	−0.604709	−	0.439347i	0.242838	−	0.970067i	$-0.421922\pi$
$103$	−6.13713	−	4.45889i	−0.604709	−	0.439347i	−0.847547	+	0.530720i	$0.821922\pi$
$104$		0			0
$105$	1.95975	+	6.03148i	0.191252	+	0.588613i
$106$		0			0
$107$	−2.26925	+	1.64871i	−0.219377	+	0.159386i	−0.692046	−	0.721853i	$-0.743290\pi$
$107$	−2.26925	+	1.64871i	−0.219377	+	0.159386i	0.472669	+	0.881240i	$0.343290\pi$
$108$		0			0
$109$	8.02896			0.769035			0.384517	−	0.923118i	$-0.374368\pi$
$109$	8.02896			0.769035			0.384517	+	0.923118i	$0.374368\pi$
$110$		0			0
$111$	−15.3806			−1.45986
$112$		0			0
$113$	−5.63030	+	4.09066i	−0.529654	+	0.384816i	−0.820228	−	0.572036i	$-0.806154\pi$
$113$	−5.63030	+	4.09066i	−0.529654	+	0.384816i	0.290574	+	0.956853i	$0.406154\pi$
$114$		0			0
$115$	0.672839	+	2.07079i	0.0627426	+	0.193102i
$116$		0			0
$117$	−27.1097	−	19.6963i	−2.50629	−	1.82092i
$118$		0			0
$119$	−4.80876	+	14.7998i	−0.440818	+	1.35670i
$120$		0			0
$121$	6.81565	+	8.63406i	0.619604	+	0.784914i
$122$		0			0
$123$	−2.95008	+	9.07942i	−0.266000	+	0.818664i
$124$		0			0
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	−3.20983	−	9.87883i	−0.284826	−	0.876604i	−0.986451	−	0.164058i	$-0.947542\pi$
$127$	−3.20983	−	9.87883i	−0.284826	−	0.876604i	0.701625	−	0.712547i	$-0.252458\pi$
$128$		0			0
$129$	−16.0724	+	11.6773i	−1.41509	+	1.02812i
$130$		0			0
$131$	3.48613			0.304585			0.152292	−	0.988335i	$-0.451334\pi$
$131$	3.48613			0.304585			0.152292	+	0.988335i	$0.451334\pi$
$132$		0			0
$133$	−13.8841			−1.20390
$134$		0			0
$135$	5.73216	−	4.16466i	0.493346	−	0.358437i
$136$		0			0
$137$	−4.49530	−	13.8351i	−0.384060	−	1.18201i	−0.937160	−	0.348900i	$-0.886555\pi$
$137$	−4.49530	−	13.8351i	−0.384060	−	1.18201i	0.553100	−	0.833115i	$-0.313445\pi$
$138$		0			0
$139$	0.406040	+	0.295005i	0.0344398	+	0.0250220i	0.604872	−	0.796323i	$-0.293224\pi$
$139$	0.406040	+	0.295005i	0.0344398	+	0.0250220i	−0.570432	+	0.821345i	$0.693224\pi$
$140$		0			0
$141$	3.86407	−	11.8924i	0.325414	−	1.00152i
$142$		0			0
$143$	−14.1574	+	14.7341i	−1.18390	+	1.23213i
$144$		0			0
$145$	−0.986688	+	3.03671i	−0.0819400	+	0.252185i
$146$		0			0
$147$	−5.25059	−	3.81478i	−0.433062	−	0.314638i
$148$		0			0
$149$	0.231027	+	0.711029i	0.0189265	+	0.0582497i	0.960074	−	0.279747i	$-0.0902506\pi$
$149$	0.231027	+	0.711029i	0.0189265	+	0.0582497i	−0.941147	+	0.337997i	$0.890251\pi$
$150$		0			0
$151$	2.64821	−	1.92404i	0.215509	−	0.156576i	−0.474794	−	0.880097i	$-0.657477\pi$
$151$	2.64821	−	1.92404i	0.215509	−	0.156576i	0.690303	+	0.723521i	$0.257477\pi$
$152$		0			0
$153$	38.7703			3.13439
$154$		0			0
$155$	4.39424			0.352954
$156$		0			0
$157$	12.1592	−	8.83418i	0.970410	−	0.705044i	0.0148654	−	0.999890i	$-0.495268\pi$
$157$	12.1592	−	8.83418i	0.970410	−	0.705044i	0.955545	+	0.294845i	$0.0952680\pi$
$158$		0			0
$159$	9.52991	+	29.3301i	0.755771	+	2.32603i
$160$		0			0
$161$	3.84555	+	2.79396i	0.303072	+	0.220195i
$162$		0			0
$163$	4.47497	−	13.7725i	0.350507	−	1.07875i	−0.608063	−	0.793889i	$-0.708053\pi$
$163$	4.47497	−	13.7725i	0.350507	−	1.07875i	0.958569	−	0.284860i	$-0.0919470\pi$
$164$		0			0
$165$	−4.54457	−	8.49565i	−0.353794	−	0.661385i
$166$		0			0
$167$	−0.0941502	+	0.289764i	−0.00728556	+	0.0224226i	−0.954633	−	0.297784i	$-0.903752\pi$
$167$	−0.0941502	+	0.289764i	−0.00728556	+	0.0224226i	0.947348	+	0.320207i	$0.103752\pi$
$168$		0			0
$169$	−20.1906	−	14.6693i	−1.55313	−	1.12841i
$170$		0			0
$171$	10.6893	+	32.8982i	0.817430	+	2.51579i
$172$		0			0
$173$	7.85835	−	5.70942i	0.597459	−	0.434079i	−0.247517	−	0.968884i	$-0.579615\pi$
$173$	7.85835	−	5.70942i	0.597459	−	0.434079i	0.844976	+	0.534804i	$0.179615\pi$
$174$		0			0
$175$	−2.18309			−0.165026
$176$		0			0
$177$	−40.0615			−3.01121
$178$		0			0
$179$	−7.60610	+	5.52616i	−0.568507	+	0.413044i	−0.834562	−	0.550913i	$-0.814279\pi$
$179$	−7.60610	+	5.52616i	−0.568507	+	0.413044i	0.266056	+	0.963958i	$0.414279\pi$
$180$		0			0
$181$	−4.07184	−	12.5318i	−0.302657	−	0.931484i	−0.980541	−	0.196314i	$-0.937103\pi$
$181$	−4.07184	−	12.5318i	−0.302657	−	0.931484i	0.677884	−	0.735169i	$-0.262897\pi$
$182$		0			0
$183$	17.2806	+	12.5551i	1.27742	+	0.928101i
$184$		0			0
$185$	1.63610	−	5.03539i	0.120288	−	0.370210i
$186$		0			0
$187$	3.23156	−	23.4196i	0.236315	−	1.71261i
$188$		0			0
$189$	4.77986	−	14.7109i	0.347684	−	1.07006i
$190$		0			0
$191$	5.95236	+	4.32464i	0.430698	+	0.312920i	0.781928	−	0.623369i	$-0.214236\pi$
$191$	5.95236	+	4.32464i	0.430698	+	0.312920i	−0.351230	+	0.936289i	$0.614236\pi$
$192$		0			0
$193$	−5.70907	−	17.5707i	−0.410948	−	1.26477i	−0.915826	−	0.401576i	$-0.868463\pi$
$193$	−5.70907	−	17.5707i	−0.410948	−	1.26477i	0.504878	−	0.863191i	$-0.331537\pi$
$194$		0			0
$195$	14.4794	−	10.5199i	1.03689	−	0.753344i
$196$		0			0
$197$	9.58209			0.682696			0.341348	−	0.939937i	$-0.389117\pi$
$197$	9.58209			0.682696			0.341348	+	0.939937i	$0.389117\pi$
$198$		0			0
$199$	13.3287			0.944844			0.472422	−	0.881372i	$-0.343380\pi$
$199$	13.3287			0.944844			0.472422	+	0.881372i	$0.343380\pi$
$200$		0			0
$201$	−18.0296	+	13.0993i	−1.27171	+	0.923951i
$202$		0			0
$203$	2.15403	+	6.62943i	0.151183	+	0.465295i
$204$		0			0
$205$	−2.65866	−	1.93163i	−0.185689	−	0.134911i
$206$		0			0
$207$	3.65958	−	11.2630i	0.254359	−	0.782836i
$208$		0			0
$209$	20.7635	−	3.71485i	1.43624	−	0.256962i
$210$		0			0
$211$	3.11617	−	9.59060i	0.214526	−	0.660244i	−0.784661	−	0.619926i	$-0.787163\pi$
$211$	3.11617	−	9.59060i	0.214526	−	0.660244i	0.999187	−	0.0403183i	$-0.0128372\pi$
$212$		0			0
$213$	13.4932	+	9.80340i	0.924541	+	0.671718i
$214$		0			0
$215$	−2.11329	−	6.50403i	−0.144125	−	0.443571i
$216$		0			0
$217$	7.76092	−	5.63864i	0.526846	−	0.382776i
$218$		0			0
$219$	14.2221			0.961044
$220$		0			0
$221$	43.9162			2.95412
$222$		0			0
$223$	−8.37329	+	6.08355i	−0.560717	+	0.407385i	−0.831721	−	0.555193i	$-0.812644\pi$
$223$	−8.37329	+	6.08355i	−0.560717	+	0.407385i	0.271004	+	0.962578i	$0.412644\pi$
$224$		0			0
$225$	1.68075	+	5.17281i	0.112050	+	0.344854i
$226$		0			0
$227$	−8.84689	−	6.42764i	−0.587188	−	0.426617i	0.254120	−	0.967173i	$-0.418214\pi$
$227$	−8.84689	−	6.42764i	−0.587188	−	0.426617i	−0.841308	+	0.540555i	$0.818214\pi$
$228$		0			0
$229$	6.91720	−	21.2890i	0.457102	−	1.40681i	−0.411548	−	0.911388i	$-0.635012\pi$
$229$	6.91720	−	21.2890i	0.457102	−	1.40681i	0.868650	−	0.495426i	$-0.164988\pi$
$230$		0			0
$231$	−18.9280	−	9.17312i	−1.24537	−	0.603547i
$232$		0			0
$233$	−4.81006	+	14.8039i	−0.315118	+	0.969833i	0.660588	+	0.750748i	$0.270307\pi$
$233$	−4.81006	+	14.8039i	−0.315118	+	0.969833i	−0.975706	+	0.219084i	$0.929693\pi$
$234$		0			0
$235$	3.48237	+	2.53009i	0.227165	+	0.165045i
$236$		0			0
$237$	7.28395	+	22.4177i	0.473143	+	1.45619i
$238$		0			0
$239$	19.7638	−	14.3592i	1.27841	−	0.928822i	0.278910	−	0.960317i	$-0.410027\pi$
$239$	19.7638	−	14.3592i	1.27841	−	0.928822i	0.999504	+	0.0314955i	$0.0100270\pi$
$240$		0			0
$241$	−5.75661			−0.370816			−0.185408	−	0.982662i	$-0.559361\pi$
$241$	−5.75661			−0.370816			−0.185408	+	0.982662i	$0.559361\pi$
$242$		0			0
$243$	8.86372			0.568608
$244$		0			0
$245$	1.80743	−	1.31318i	0.115473	−	0.0838958i
$246$		0			0
$247$	12.1080	+	37.2647i	0.770416	+	2.37110i
$248$		0			0
$249$	9.92683	+	7.21227i	0.629087	+	0.457059i
$250$		0			0
$251$	3.71563	−	11.4355i	0.234529	−	0.721805i	−0.762655	−	0.646805i	$-0.776105\pi$
$251$	3.71563	−	11.4355i	0.234529	−	0.721805i	0.997184	−	0.0749992i	$-0.0238954\pi$
$252$		0			0
$253$	−6.49853	−	3.14940i	−0.408559	−	0.198001i
$254$		0			0
$255$	−6.39893	+	19.6939i	−0.400716	+	1.23328i
$256$		0			0
$257$	15.8053	+	11.4832i	0.985906	+	0.716303i	0.959021	−	0.283336i	$-0.0914411\pi$
$257$	15.8053	+	11.4832i	0.985906	+	0.716303i	0.0268855	+	0.999639i	$0.491441\pi$
$258$		0			0
$259$	−3.57175	−	10.9927i	−0.221938	−	0.683055i
$260$		0			0
$261$	14.0500	−	10.2079i	0.869672	−	0.631854i
$262$		0			0
$263$	−24.6213			−1.51821			−0.759106	−	0.650967i	$-0.774364\pi$
$263$	−24.6213			−1.51821			−0.759106	+	0.650967i	$0.774364\pi$
$264$		0			0
$265$	−10.6160			−0.652135
$266$		0			0
$267$	39.4919	−	28.6925i	2.41687	−	1.75596i
$268$		0			0
$269$	0.477417	+	1.46934i	0.0291086	+	0.0895871i	0.964555	−	0.263881i	$-0.0850025\pi$
$269$	0.477417	+	1.46934i	0.0291086	+	0.0895871i	−0.935447	+	0.353468i	$0.885002\pi$
$270$		0			0
$271$	−18.2552	−	13.2632i	−1.10893	−	0.805683i	−0.126433	−	0.991975i	$-0.540353\pi$
$271$	−18.2552	−	13.2632i	−1.10893	−	0.805683i	−0.982494	+	0.186292i	$0.940353\pi$
$272$		0			0
$273$	12.0739	−	37.1595i	0.730743	−	2.24900i
$274$		0			0
$275$	3.26478	−	0.584112i	0.196874	−	0.0352233i
$276$		0			0
$277$	−4.27028	+	13.1426i	−0.256576	+	0.789660i	0.736939	+	0.675959i	$0.236270\pi$
$277$	−4.27028	+	13.1426i	−0.256576	+	0.789660i	−0.993515	+	0.113701i	$0.963730\pi$
$278$		0			0
$279$	−19.3358	−	14.0483i	−1.15760	−	0.841048i
$280$		0			0
$281$	−2.69067	−	8.28103i	−0.160512	−	0.494005i	0.838166	−	0.545416i	$-0.183628\pi$
$281$	−2.69067	−	8.28103i	−0.160512	−	0.494005i	−0.998678	+	0.0514109i	$0.983628\pi$
$282$		0			0
$283$	−1.23349	+	0.896181i	−0.0733232	+	0.0532724i	−0.623843	−	0.781550i	$-0.714430\pi$
$283$	−1.23349	+	0.896181i	−0.0733232	+	0.0532724i	0.550520	+	0.834822i	$0.314430\pi$
$284$		0			0
$285$	−18.4753			−1.09438
$286$		0			0
$287$	−7.17427			−0.423484
$288$		0			0
$289$	−27.3537	+	19.8736i	−1.60904	+	1.16904i
$290$		0			0
$291$	2.94051	+	9.04996i	0.172376	+	0.530518i
$292$		0			0
$293$	−19.2037	−	13.9523i	−1.12189	−	0.815103i	−0.137398	−	0.990516i	$-0.543874\pi$
$293$	−19.2037	−	13.9523i	−1.12189	−	0.815103i	−0.984495	+	0.175413i	$0.943874\pi$
$294$		0			0
$295$	4.26152	−	13.1156i	0.248115	−	0.763620i
$296$		0			0
$297$	−3.21214	+	23.2788i	−0.186387	+	1.35078i
$298$		0			0
$299$	4.14531	−	12.7580i	0.239730	−	0.737812i
$300$		0			0
$301$	−12.0783	−	8.77539i	−0.696181	−	0.505805i
$302$		0			0
$303$	6.20349	+	19.0924i	0.356381	+	1.09683i
$304$		0			0
$305$	−5.94859	+	4.32190i	−0.340615	+	0.247471i
$306$		0			0
$307$	−17.7127			−1.01092			−0.505458	−	0.862851i	$-0.668676\pi$
$307$	−17.7127			−1.01092			−0.505458	+	0.862851i	$0.668676\pi$
$308$		0			0
$309$	−22.0371			−1.25364
$310$		0			0
$311$	−5.48912	+	3.98808i	−0.311260	+	0.226143i	−0.732437	−	0.680835i	$-0.761617\pi$
$311$	−5.48912	+	3.98808i	−0.311260	+	0.226143i	0.421177	+	0.906978i	$0.361617\pi$
$312$		0			0
$313$	7.35633	+	22.6405i	0.415804	+	1.27971i	0.911530	+	0.411235i	$0.134902\pi$
$313$	7.35633	+	22.6405i	0.415804	+	1.27971i	−0.495725	+	0.868479i	$0.665098\pi$
$314$		0			0
$315$	9.60616	+	6.97929i	0.541246	+	0.393238i
$316$		0			0
$317$	−0.571055	+	1.75753i	−0.0320737	+	0.0987126i	−0.965812	−	0.259244i	$-0.916527\pi$
$317$	−0.571055	+	1.75753i	−0.0320737	+	0.0987126i	0.933738	+	0.357957i	$0.116527\pi$
$318$		0			0
$319$	−4.99511	−	9.33788i	−0.279672	−	0.522821i
$320$		0			0
$321$	−2.51798	+	7.74955i	−0.140540	+	0.432538i
$322$		0			0
$323$	−36.6760	−	26.6467i	−2.04071	−	1.48266i
$324$		0			0
$325$	1.90383	+	5.85939i	0.105606	+	0.325020i
$326$		0			0
$327$	18.8696	−	13.7096i	1.04349	−	0.758141i
$328$		0			0
$329$	9.39700			0.518073
$330$		0			0
$331$	17.5654			0.965484			0.482742	−	0.875763i	$-0.339641\pi$
$331$	17.5654			0.965484			0.482742	+	0.875763i	$0.339641\pi$
$332$		0			0
$333$	−23.2973	+	16.9265i	−1.27668	+	0.927565i
$334$		0			0
$335$	−2.37064	−	7.29607i	−0.129522	−	0.398627i
$336$		0			0
$337$	−17.2756	−	12.5515i	−0.941064	−	0.683723i	0.00761239	−	0.999971i	$-0.497577\pi$
$337$	−17.2756	−	12.5515i	−0.941064	−	0.683723i	−0.948677	+	0.316248i	$0.897577\pi$
$338$		0			0
$339$	−6.24745	+	19.2277i	−0.339315	+	1.04430i
$340$		0			0
$341$	−10.0977	+	10.5090i	−0.546819	+	0.569096i
$342$		0			0
$343$	6.22945	−	19.1723i	0.336358	−	1.03520i
$344$		0			0
$345$	5.11720	+	3.71787i	0.275501	+	0.200163i
$346$		0			0
$347$	1.65675	+	5.09894i	0.0889387	+	0.273725i	0.985627	−	0.168938i	$-0.0540337\pi$
$347$	1.65675	+	5.09894i	0.0889387	+	0.273725i	−0.896688	+	0.442663i	$0.854034\pi$
$348$		0			0
$349$	9.31693	−	6.76914i	0.498724	−	0.362344i	−0.309806	−	0.950800i	$-0.600264\pi$
$349$	9.31693	−	6.76914i	0.498724	−	0.362344i	0.808529	+	0.588456i	$0.200264\pi$
$350$		0			0
$351$	−43.6523			−2.32998
$352$		0			0
$353$	9.70208			0.516389			0.258195	−	0.966093i	$-0.416872\pi$
$353$	9.70208			0.516389			0.258195	+	0.966093i	$0.416872\pi$
$354$		0			0
$355$	−4.64483	+	3.37467i	−0.246522	+	0.179109i
$356$		0			0
$357$	13.9694	+	42.9935i	0.739341	+	2.27546i
$358$		0			0
$359$	26.3383	+	19.1359i	1.39008	+	1.00995i	0.995857	+	0.0909376i	$0.0289864\pi$
$359$	26.3383	+	19.1359i	1.39008	+	1.00995i	0.394223	+	0.919015i	$0.371014\pi$
$360$		0			0
$361$	6.62764	−	20.3978i	0.348823	−	1.07357i
$362$		0			0
$363$	30.7609	+	8.65388i	1.61453	+	0.454211i
$364$		0			0
$365$	−1.51287	+	4.65614i	−0.0791872	+	0.243713i
$366$		0			0
$367$	21.4415	+	15.5781i	1.11924	+	0.813172i	0.984093	−	0.177654i	$-0.0568509\pi$
$367$	21.4415	+	15.5781i	1.11924	+	0.813172i	0.135142	+	0.990826i	$0.456851\pi$
$368$		0			0
$369$	5.52343	+	16.9994i	0.287538	+	0.884952i
$370$		0			0
$371$	−18.7495	+	13.6223i	−0.973427	+	0.707236i
$372$		0			0
$373$	25.2185			1.30577			0.652883	−	0.757459i	$-0.273559\pi$
$373$	25.2185			1.30577			0.652883	+	0.757459i	$0.273559\pi$
$374$		0			0
$375$	−2.90500			−0.150013
$376$		0			0
$377$	15.9148	−	11.5628i	0.819654	−	0.595513i
$378$		0			0
$379$	−5.41871	−	16.6771i	−0.278340	−	0.856644i	−0.988316	−	0.152418i	$-0.951294\pi$
$379$	−5.41871	−	16.6771i	−0.278340	−	0.856644i	0.709976	−	0.704226i	$-0.248706\pi$
$380$		0			0
$381$	−24.4120	−	17.7363i	−1.25066	−	0.908660i
$382$		0			0
$383$	−4.08098	+	12.5600i	−0.208528	+	0.641784i	0.791022	+	0.611788i	$0.209549\pi$
$383$	−4.08098	+	12.5600i	−0.208528	+	0.641784i	−0.999550	+	0.0299959i	$0.990451\pi$
$384$		0			0
$385$	5.01660	−	5.22097i	0.255670	−	0.266085i
$386$		0			0
$387$	−11.4942	+	35.3755i	−0.584283	+	1.79824i
$388$		0			0
$389$	−26.5730	−	19.3064i	−1.34731	−	0.978876i	−0.999141	−	0.0414426i	$-0.986805\pi$
$389$	−26.5730	−	19.3064i	−1.34731	−	0.978876i	−0.348166	−	0.937433i	$-0.613195\pi$
$390$		0			0
$391$	4.79612	+	14.7609i	0.242550	+	0.746493i
$392$		0			0
$393$	8.19309	−	5.95263i	0.413287	−	0.300270i
$394$		0			0
$395$	−8.11407			−0.408263
$396$		0			0
$397$	25.2290			1.26621			0.633104	−	0.774066i	$-0.281780\pi$
$397$	25.2290			1.26621			0.633104	+	0.774066i	$0.281780\pi$
$398$		0			0
$399$	−32.6303	+	23.7073i	−1.63356	+	1.18685i
$400$		0			0
$401$	5.27641	+	16.2391i	0.263492	+	0.810944i	0.992037	+	0.125946i	$0.0401967\pi$
$401$	5.27641	+	16.2391i	0.263492	+	0.810944i	−0.728546	+	0.684997i	$0.759803\pi$
$402$		0			0
$403$	−21.9022	−	15.9129i	−1.09102	−	0.792676i
$404$		0			0
$405$	1.31822	−	4.05707i	0.0655030	−	0.201597i
$406$		0			0
$407$	8.28274	+	15.4838i	0.410560	+	0.767504i
$408$		0			0
$409$	−0.246762	+	0.759454i	−0.0122016	+	0.0375526i	−0.956972	−	0.290180i	$-0.906285\pi$
$409$	−0.246762	+	0.759454i	−0.0122016	+	0.0375526i	0.944770	+	0.327733i	$0.106285\pi$
$410$		0			0
$411$	−34.1885	−	24.8394i	−1.68639	−	1.22524i
$412$		0			0
$413$	−9.30328	−	28.6326i	−0.457784	−	1.40892i
$414$		0			0
$415$	−3.41716	+	2.48271i	−0.167742	+	0.121871i
$416$		0			0
$417$	1.45800			0.0713984
$418$		0			0
$419$	−3.76575			−0.183969			−0.0919844	−	0.995760i	$-0.529321\pi$
$419$	−3.76575			−0.183969			−0.0919844	+	0.995760i	$0.529321\pi$
$420$		0			0
$421$	13.7158	−	9.96512i	0.668468	−	0.485670i	−0.201044	−	0.979582i	$-0.564433\pi$
$421$	13.7158	−	9.96512i	0.668468	−	0.485670i	0.869512	+	0.493912i	$0.164433\pi$
$422$		0			0
$423$	−7.23469	−	22.2661i	−0.351763	−	1.08261i
$424$		0			0
$425$	−5.76682	−	4.18984i	−0.279732	−	0.203237i
$426$		0			0
$427$	−4.96033	+	15.2663i	−0.240047	+	0.738789i
$428$		0			0
$429$	−8.11383	+	58.8021i	−0.391739	+	2.83899i
$430$		0			0
$431$	8.04778	−	24.7685i	0.387648	−	1.19306i	−0.546893	−	0.837202i	$-0.684190\pi$
$431$	8.04778	−	24.7685i	0.387648	−	1.19306i	0.934541	−	0.355855i	$-0.115810\pi$
$432$		0			0
$433$	18.0358	+	13.1038i	0.866746	+	0.629728i	0.929712	−	0.368288i	$-0.120056\pi$
$433$	18.0358	+	13.1038i	0.866746	+	0.629728i	−0.0629661	+	0.998016i	$0.520056\pi$
$434$		0			0
$435$	2.86633	+	8.82165i	0.137430	+	0.422966i
$436$		0			0
$437$	−11.2030	+	8.13942i	−0.535910	+	0.389361i
$438$		0			0
$439$	13.8298			0.660060			0.330030	−	0.943970i	$-0.392941\pi$
$439$	13.8298			0.660060			0.330030	+	0.943970i	$0.392941\pi$
$440$		0			0
$441$	−12.1514			−0.578637
$442$		0			0
$443$	−12.2099	+	8.87103i	−0.580111	+	0.421475i	−0.838764	−	0.544495i	$-0.816721\pi$
$443$	−12.2099	+	8.87103i	−0.580111	+	0.421475i	0.258653	+	0.965970i	$0.416721\pi$
$444$		0			0
$445$	5.19262	+	15.9813i	0.246154	+	0.757584i
$446$		0			0
$447$	1.75705	+	1.27657i	0.0831057	+	0.0603798i
$448$		0			0
$449$	5.46057	−	16.8059i	0.257700	−	0.793120i	−0.735585	−	0.677432i	$-0.763093\pi$
$449$	5.46057	−	16.8059i	0.257700	−	0.793120i	0.993286	−	0.115688i	$-0.0369073\pi$
$450$		0			0
$451$	10.7290	−	1.91956i	0.505210	−	0.0903886i
$452$		0			0
$453$	2.93849	−	9.04373i	0.138062	−	0.424911i
$454$		0			0
$455$	10.8812	+	7.90563i	0.510117	+	0.370622i
$456$		0			0
$457$	−10.5786	−	32.5574i	−0.494844	−	1.52297i	−0.817200	−	0.576354i	$-0.804475\pi$
$457$	−10.5786	−	32.5574i	−0.494844	−	1.52297i	0.322356	−	0.946618i	$-0.395525\pi$
$458$		0			0
$459$	40.8599	−	29.6865i	1.90718	−	1.38564i
$460$		0			0
$461$	−10.1143			−0.471069			−0.235534	−	0.971866i	$-0.575684\pi$
$461$	−10.1143			−0.471069			−0.235534	+	0.971866i	$0.575684\pi$
$462$		0			0
$463$	−11.2505			−0.522857			−0.261429	−	0.965223i	$-0.584194\pi$
$463$	−11.2505			−0.522857			−0.261429	+	0.965223i	$0.584194\pi$
$464$		0			0
$465$	10.3273	−	7.50323i	0.478918	−	0.347954i
$466$		0			0
$467$	10.6269	+	32.7063i	0.491755	+	1.51347i	0.821953	+	0.569555i	$0.192884\pi$
$467$	10.6269	+	32.7063i	0.491755	+	1.51347i	−0.330198	+	0.943912i	$0.607116\pi$
$468$		0			0
$469$	−13.5492	−	9.84403i	−0.625642	−	0.454555i
$470$		0			0
$471$	13.4920	−	41.5241i	0.621678	−	1.91333i
$472$		0			0
$473$	20.4109	+	9.89179i	0.938494	+	0.454825i
$474$		0			0
$475$	1.96530	−	6.04856i	0.0901740	−	0.277527i
$476$		0			0
$477$	46.7131	+	33.9391i	2.13885	+	1.55396i
$478$		0			0
$479$	−7.93273	−	24.4144i	−0.362456	−	1.11552i	−0.951559	−	0.307466i	$-0.900519\pi$
$479$	−7.93273	−	24.4144i	−0.362456	−	1.11552i	0.589103	−	0.808058i	$-0.299481\pi$
$480$		0			0
$481$	−26.3895	+	19.1731i	−1.20326	+	0.874217i
$482$		0			0
$483$	13.8085			0.628309
$484$		0			0
$485$	−3.27563			−0.148739
$486$		0			0
$487$	15.6164	−	11.3460i	0.707646	−	0.514135i	−0.174768	−	0.984610i	$-0.555917\pi$
$487$	15.6164	−	11.3460i	0.707646	−	0.514135i	0.882413	+	0.470475i	$0.155917\pi$
$488$		0			0
$489$	−12.9998	−	40.0092i	−0.587870	−	1.80928i
$490$		0			0
$491$	13.8850	+	10.0880i	0.626620	+	0.455266i	0.855227	−	0.518253i	$-0.173417\pi$
$491$	13.8850	+	10.0880i	0.626620	+	0.455266i	−0.228608	+	0.973519i	$0.573417\pi$
$492$		0			0
$493$	−7.03330	+	21.6463i	−0.316764	+	0.974899i
$494$		0			0
$495$	−16.2333	−	7.86719i	−0.729632	−	0.353604i
$496$		0			0
$497$	−3.87317	+	11.9204i	−0.173735	+	0.534703i
$498$		0			0
$499$	33.3620	+	24.2389i	1.49349	+	1.08508i	0.972886	+	0.231285i	$0.0742931\pi$
$499$	33.3620	+	24.2389i	1.49349	+	1.08508i	0.520604	+	0.853798i	$0.325707\pi$
$500$		0			0
$501$	0.273506	+	0.841765i	0.0122194	+	0.0376073i
$502$		0			0
$503$	−21.6639	+	15.7397i	−0.965944	+	0.701799i	−0.954524	−	0.298135i	$-0.903635\pi$
$503$	−21.6639	+	15.7397i	−0.965944	+	0.701799i	−0.0114203	+	0.999935i	$0.503635\pi$
$504$		0			0
$505$	−6.91048			−0.307512
$506$		0			0
$507$	−72.5000			−3.21984
$508$		0			0
$509$	20.2770	−	14.7321i	0.898764	−	0.652990i	−0.0393843	−	0.999224i	$-0.512540\pi$
$509$	20.2770	−	14.7321i	0.898764	−	0.652990i	0.938148	+	0.346234i	$0.112540\pi$
$510$		0			0
$511$	3.30273	+	10.1648i	0.146104	+	0.449663i
$512$		0			0
$513$	36.4556	+	26.4865i	1.60955	+	1.16941i
$514$		0			0
$515$	2.34417	−	7.21463i	0.103297	−	0.317914i
$516$		0			0
$517$	−14.0531	+	2.51428i	−0.618054	+	0.110578i
$518$		0			0
$519$	8.71971	−	26.8365i	0.382753	−	1.17799i
$520$		0			0
$521$	−0.776493	−	0.564155i	−0.0340188	−	0.0247161i	0.570646	−	0.821196i	$-0.306693\pi$
$521$	−0.776493	−	0.564155i	−0.0340188	−	0.0247161i	−0.604665	+	0.796480i	$0.706693\pi$
$522$		0			0
$523$	−0.871151	−	2.68113i	−0.0380928	−	0.117238i	0.930202	−	0.367048i	$-0.119632\pi$
$523$	−0.871151	−	2.68113i	−0.0380928	−	0.117238i	−0.968295	+	0.249811i	$0.919632\pi$
$524$		0			0
$525$	−5.13069	+	3.72766i	−0.223922	+	0.162689i
$526$		0			0
$527$	31.3229			1.36445
$528$		0			0
$529$	−18.2591			−0.793875
$530$		0			0
$531$	−60.6820	+	44.0881i	−2.63337	+	1.91326i
$532$		0			0
$533$	6.25654	+	19.2556i	0.271001	+	0.834055i
$534$		0			0
$535$	−2.26925	−	1.64871i	−0.0981082	−	0.0712798i
$536$		0			0
$537$	−8.43981	+	25.9751i	−0.364205	+	1.12091i
$538$		0			0
$539$	−1.01284	+	7.34016i	−0.0436259	+	0.316163i
$540$		0			0
$541$	−7.51400	+	23.1257i	−0.323052	+	0.994253i	0.649260	+	0.760567i	$0.275079\pi$
$541$	−7.51400	+	23.1257i	−0.323052	+	0.994253i	−0.972312	+	0.233686i	$0.924921\pi$
$542$		0			0
$543$	−30.9679	−	22.4995i	−1.32896	−	0.965546i
$544$		0			0
$545$	2.48108	+	7.63599i	0.106278	+	0.327090i
$546$		0			0
$547$	34.9573	−	25.3980i	1.49467	−	1.08594i	0.522220	−	0.852811i	$-0.325104\pi$
$547$	34.9573	−	25.3980i	1.49467	−	1.08594i	0.972446	−	0.233128i	$-0.0748960\pi$
$548$		0			0
$549$	39.9923			1.70683
$550$		0			0
$551$	−20.3069			−0.865103
$552$		0			0
$553$	−14.3307	+	10.4119i	−0.609404	+	0.442758i
$554$		0			0
$555$	−4.75287	−	14.6278i	−0.201748	−	0.620916i
$556$		0			0
$557$	−6.78989	−	4.93314i	−0.287697	−	0.209024i	0.434571	−	0.900638i	$-0.356900\pi$
$557$	−6.78989	−	4.93314i	−0.287697	−	0.209024i	−0.722268	+	0.691614i	$0.756900\pi$
$558$		0			0
$559$	−13.0198	+	40.0708i	−0.550679	+	1.69482i
$560$		0			0
$561$	−32.3945	−	60.5585i	−1.36770	−	2.55678i
$562$		0			0
$563$	−1.90302	+	5.85688i	−0.0802026	+	0.246838i	−0.983116	−	0.182985i	$-0.941424\pi$
$563$	−1.90302	+	5.85688i	−0.0802026	+	0.246838i	0.902913	+	0.429823i	$0.141424\pi$
$564$		0			0
$565$	−5.63030	−	4.09066i	−0.236869	−	0.172095i
$566$		0			0
$567$	−2.87780	−	8.85696i	−0.120856	−	0.371957i
$568$		0			0
$569$	−3.30458	+	2.40092i	−0.138535	+	0.100652i	−0.654894	−	0.755720i	$-0.727287\pi$
$569$	−3.30458	+	2.40092i	−0.138535	+	0.100652i	0.516359	+	0.856372i	$0.327287\pi$
$570$		0			0
$571$	30.8820			1.29237			0.646185	−	0.763181i	$-0.276363\pi$
$571$	30.8820			1.29237			0.646185	+	0.763181i	$0.276363\pi$
$572$		0			0
$573$	21.3736			0.892895
$574$		0			0
$575$	−1.76152	+	1.27982i	−0.0734603	+	0.0533720i
$576$		0			0
$577$	−4.46694	−	13.7478i	−0.185961	−	0.572329i	0.814003	−	0.580861i	$-0.197284\pi$
$577$	−4.46694	−	13.7478i	−0.185961	−	0.572329i	−0.999964	+	0.00853208i	$0.997284\pi$
$578$		0			0
$579$	−43.4197	−	31.5462i	−1.80446	−	1.31102i
$580$		0			0
$581$	−2.84945	+	8.76971i	−0.118215	+	0.363829i
$582$		0			0
$583$	24.3948	−	25.3887i	1.01033	−	1.05149i
$584$		0			0
$585$	10.3550	−	31.8693i	0.428125	−	1.31763i
$586$		0			0
$587$	−24.9981	−	18.1622i	−1.03178	−	0.749633i	−0.0631164	−	0.998006i	$-0.520104\pi$
$587$	−24.9981	−	18.1622i	−1.03178	−	0.749633i	−0.968664	+	0.248374i	$0.920104\pi$
$588$		0			0
$589$	8.63598	+	26.5788i	0.355840	+	1.09516i
$590$		0			0
$591$	22.5198	−	16.3616i	0.926339	−	0.673025i
$592$		0			0
$593$	−29.6191			−1.21631			−0.608156	−	0.793818i	$-0.708090\pi$
$593$	−29.6191			−1.21631			−0.608156	+	0.793818i	$0.708090\pi$
$594$		0			0
$595$	−15.5615			−0.637958
$596$		0			0
$597$	31.3250	−	22.7589i	1.28205	−	0.931460i
$598$		0			0
$599$	−2.09562	−	6.44965i	−0.0856247	−	0.263526i	0.899072	−	0.437800i	$-0.144242\pi$
$599$	−2.09562	−	6.44965i	−0.0856247	−	0.263526i	−0.984697	+	0.174274i	$0.944242\pi$
$600$		0			0
$601$	14.3815	+	10.4488i	0.586634	+	0.426215i	0.841110	−	0.540865i	$-0.181903\pi$
$601$	14.3815	+	10.4488i	0.586634	+	0.426215i	−0.254476	+	0.967079i	$0.581903\pi$
$602$		0			0
$603$	−12.8939	+	39.6834i	−0.525081	+	1.61603i
$604$		0			0
$605$	−6.10532	+	9.15014i	−0.248217	+	0.372006i
$606$		0			0
$607$	−12.0194	+	36.9918i	−0.487851	+	1.50145i	0.339958	+	0.940441i	$0.389587\pi$
$607$	−12.0194	+	36.9918i	−0.487851	+	1.50145i	−0.827809	+	0.561010i	$0.810413\pi$
$608$		0			0
$609$	16.3822	+	11.9024i	0.663842	+	0.482309i
$610$		0			0
$611$	−8.19493	−	25.2214i	−0.331532	−	1.02035i
$612$		0			0
$613$	−24.8817	+	18.0776i	−1.00496	+	0.730147i	−0.963146	−	0.268979i	$-0.913314\pi$
$613$	−24.8817	+	18.0776i	−1.00496	+	0.730147i	−0.0418146	+	0.999125i	$0.513314\pi$
$614$		0			0
$615$	−9.54667			−0.384959
$616$		0			0
$617$	23.3088			0.938377			0.469188	−	0.883098i	$-0.344547\pi$
$617$	23.3088			0.938377			0.469188	+	0.883098i	$0.344547\pi$
$618$		0			0
$619$	−27.9978	+	20.3416i	−1.12533	+	0.817598i	−0.985008	−	0.172508i	$-0.944813\pi$
$619$	−27.9978	+	20.3416i	−1.12533	+	0.817598i	−0.140319	+	0.990106i	$0.544813\pi$
$620$		0			0
$621$	−4.76730	−	14.6722i	−0.191305	−	0.588776i
$622$		0			0
$623$	29.6780	+	21.5623i	1.18902	+	0.863875i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	42.4550	−	44.1846i	1.69549	−	1.76456i
$628$		0			0
$629$	11.6624	−	35.8932i	0.465011	−	1.43116i
$630$		0			0
$631$	−9.05056	−	6.57562i	−0.360297	−	0.261771i	0.392879	−	0.919590i	$-0.371479\pi$
$631$	−9.05056	−	6.57562i	−0.360297	−	0.261771i	−0.753176	+	0.657819i	$0.771479\pi$
$632$		0			0
$633$	−9.05248	−	27.8607i	−0.359804	−	1.10736i
$634$		0			0
$635$	8.40343	−	6.10545i	0.333480	−	0.242287i
$636$		0			0
$637$	−13.7642			−0.545357
$638$		0			0
$639$	31.2272			1.23533
$640$		0			0
$641$	−28.1482	+	20.4508i	−1.11179	+	0.807759i	−0.982944	−	0.183906i	$-0.941126\pi$
$641$	−28.1482	+	20.4508i	−1.11179	+	0.807759i	−0.128842	+	0.991665i	$0.541126\pi$
$642$		0			0
$643$	7.55669	+	23.2571i	0.298007	+	0.917171i	0.982195	+	0.187865i	$0.0601567\pi$
$643$	7.55669	+	23.2571i	0.298007	+	0.917171i	−0.684188	+	0.729306i	$0.739843\pi$
$644$		0			0
$645$	−16.0724	−	11.6773i	−0.632848	−	0.459791i
$646$		0			0
$647$	5.80359	−	17.8616i	0.228163	−	0.702212i	−0.769793	−	0.638294i	$-0.779640\pi$
$647$	5.80359	−	17.8616i	0.228163	−	0.702212i	0.997955	−	0.0639180i	$-0.0203596\pi$
$648$		0			0
$649$	21.5739	+	40.3304i	0.846850	+	1.58311i
$650$		0			0
$651$	8.61160	−	26.5038i	0.337515	−	1.03877i
$652$		0			0
$653$	−32.2823	−	23.4545i	−1.26330	−	0.917844i	−0.264390	−	0.964416i	$-0.585170\pi$
$653$	−32.2823	−	23.4545i	−1.26330	−	0.917844i	−0.998915	+	0.0465715i	$0.985170\pi$
$654$		0			0
$655$	1.07727	+	3.31551i	0.0420926	+	0.129548i
$656$		0			0
$657$	21.5426	−	15.6516i	0.840455	−	0.610627i
$658$		0			0
$659$	17.6187			0.686326			0.343163	−	0.939276i	$-0.388502\pi$
$659$	17.6187			0.686326			0.343163	+	0.939276i	$0.388502\pi$
$660$		0			0
$661$	42.4404			1.65074			0.825371	−	0.564591i	$-0.190966\pi$
$661$	42.4404			1.65074			0.825371	+	0.564591i	$0.190966\pi$
$662$		0			0
$663$	103.212	−	74.9876i	4.00840	−	2.91228i
$664$		0			0
$665$	−4.29042	−	13.2046i	−0.166375	−	0.512051i
$666$		0			0
$667$	5.62451	+	4.08644i	0.217782	+	0.158228i
$668$		0			0
$669$	−9.29110	+	28.5951i	−0.359214	+	1.10555i
$670$		0			0
$671$	3.33342	−	24.1578i	0.128685	−	0.932601i
$672$		0			0
$673$	1.88078	−	5.78844i	0.0724987	−	0.223128i	−0.908241	−	0.418448i	$-0.862574\pi$
$673$	1.88078	−	5.78844i	0.0724987	−	0.223128i	0.980740	+	0.195319i	$0.0625744\pi$
$674$		0			0
$675$	5.73216	+	4.16466i	0.220631	+	0.160298i
$676$		0			0
$677$	−3.22714	−	9.93211i	−0.124029	−	0.381722i	0.869694	−	0.493591i	$-0.164316\pi$
$677$	−3.22714	−	9.93211i	−0.124029	−	0.381722i	−0.993723	+	0.111869i	$0.964316\pi$
$678$		0			0
$679$	−5.78527	+	4.20325i	−0.222018	+	0.161306i
$680$		0			0
$681$	−31.7672			−1.21732
$682$		0			0
$683$	28.7312			1.09937			0.549685	−	0.835372i	$-0.314748\pi$
$683$	28.7312			1.09937			0.549685	+	0.835372i	$0.314748\pi$
$684$		0			0
$685$	11.7689	−	8.55057i	0.449665	−	0.326701i
$686$		0			0
$687$	−20.0945	−	61.8444i	−0.766652	−	2.35951i
$688$		0			0
$689$	52.9132	+	38.4437i	2.01583	+	1.46459i
$690$		0			0
$691$	−8.67788	+	26.7078i	−0.330122	+	1.01601i	0.638953	+	0.769246i	$0.279368\pi$
$691$	−8.67788	+	26.7078i	−0.330122	+	1.01601i	−0.969075	+	0.246766i	$0.920632\pi$
$692$		0			0
$693$	−38.7656	+	6.93567i	−1.47258	+	0.263464i
$694$		0			0
$695$	−0.155093	+	0.477328i	−0.00588303	+	0.0181061i
$696$		0			0
$697$	−18.9514	−	13.7690i	−0.717837	−	0.521539i
$698$		0			0
$699$	13.9732	+	43.0052i	0.528516	+	1.62661i
$700$		0			0
$701$	−9.76350	+	7.09360i	−0.368762	+	0.267921i	−0.756698	−	0.653765i	$-0.773188\pi$
$701$	−9.76350	+	7.09360i	−0.368762	+	0.267921i	0.387935	+	0.921687i	$0.373188\pi$
$702$		0			0
$703$	33.6723			1.26998
$704$		0			0
$705$	12.5044			0.470943
$706$		0			0
$707$	−12.2050	+	8.86745i	−0.459016	+	0.333495i
$708$		0			0
$709$	9.86241	+	30.3534i	0.370390	+	1.13994i	0.946536	+	0.322598i	$0.104556\pi$
$709$	9.86241	+	30.3534i	0.370390	+	1.13994i	−0.576146	+	0.817347i	$0.695444\pi$
$710$		0			0
$711$	35.7040	+	25.9405i	1.33900	+	0.972843i
$712$		0			0
$713$	2.95662	−	9.09953i	0.110726	−	0.340780i
$714$		0			0
$715$	−18.3879	−	8.91138i	−0.687668	−	0.333267i
$716$		0			0
$717$	21.9301	−	67.4940i	0.818995	−	2.52061i
$718$		0			0
$719$	2.14443	+	1.55802i	0.0799739	+	0.0581044i	0.627054	−	0.778976i	$-0.284261\pi$
$719$	2.14443	+	1.55802i	0.0799739	+	0.0581044i	−0.547080	+	0.837080i	$0.684261\pi$
$720$		0			0
$721$	−5.11755	−	15.7502i	−0.190587	−	0.586568i
$722$		0			0
$723$	−13.5291	+	9.82950i	−0.503154	+	0.365563i
$724$		0			0
$725$	−3.19299			−0.118585
$726$		0			0
$727$	−1.73626			−0.0643944			−0.0321972	−	0.999482i	$-0.510250\pi$
$727$	−1.73626			−0.0643944			−0.0321972	+	0.999482i	$0.510250\pi$
$728$		0			0
$729$	31.1849	−	22.6572i	1.15500	−	0.839154i
$730$		0			0
$731$	−15.0639	−	46.3619i	−0.557158	−	1.71476i
$732$		0			0
$733$	−27.0175	−	19.6294i	−0.997914	−	0.725027i	−0.0362742	−	0.999342i	$-0.511549\pi$
$733$	−27.0175	−	19.6294i	−0.997914	−	0.725027i	−0.961640	+	0.274315i	$0.911549\pi$
$734$		0			0
$735$	2.00555	−	6.17244i	0.0739758	−	0.227674i
$736$		0			0
$737$	22.8965	+	11.0964i	0.843402	+	0.408741i
$738$		0			0
$739$	−12.6811	+	39.0284i	−0.466482	+	1.43568i	0.390627	+	0.920549i	$0.372258\pi$
$739$	−12.6811	+	39.0284i	−0.466482	+	1.43568i	−0.857109	+	0.515135i	$0.827742\pi$
$740$		0			0
$741$	92.0864	+	66.9047i	3.38288	+	2.45780i
$742$		0			0
$743$	12.9409	+	39.8280i	0.474755	+	1.46115i	0.846287	+	0.532727i	$0.178833\pi$
$743$	12.9409	+	39.8280i	0.474755	+	1.46115i	−0.371532	+	0.928420i	$0.621167\pi$
$744$		0			0
$745$	−0.604837	+	0.439440i	−0.0221595	+	0.0160998i
$746$		0			0
$747$	22.9735			0.840557
$748$		0			0
$749$	−6.12345			−0.223746
$750$		0			0
$751$	15.0799	−	10.9562i	0.550274	−	0.399798i	−0.277612	−	0.960693i	$-0.589543\pi$
$751$	15.0799	−	10.9562i	0.550274	−	0.399798i	0.827887	+	0.560895i	$0.189543\pi$
$752$		0			0
$753$	−10.7939	−	33.2202i	−0.393352	−	1.21061i
$754$		0			0
$755$	2.64821	+	1.92404i	0.0963783	+	0.0700230i
$756$		0			0
$757$	−4.41678	+	13.5934i	−0.160531	+	0.494062i	−0.998679	−	0.0513797i	$-0.983638\pi$
$757$	−4.41678	+	13.5934i	−0.160531	+	0.494062i	0.838149	+	0.545442i	$0.183638\pi$
$758$		0			0
$759$	−20.6504	+	3.69463i	−0.749564	+	0.134107i
$760$		0			0
$761$	−4.87309	+	14.9978i	−0.176649	+	0.543671i	−0.999705	−	0.0242900i	$-0.992267\pi$
$761$	−4.87309	+	14.9978i	−0.176649	+	0.543671i	0.823056	+	0.567961i	$0.192267\pi$
$762$		0			0
$763$	14.1804	+	10.3027i	0.513365	+	0.372982i
$764$		0			0
$765$	11.9807	+	36.8728i	0.433163	+	1.33314i
$766$		0			0
$767$	−68.7362	+	49.9397i	−2.48192	+	1.80322i
$768$		0			0
$769$	−16.5268			−0.595971			−0.297986	−	0.954570i	$-0.596315\pi$
$769$	−16.5268			−0.595971			−0.297986	+	0.954570i	$0.596315\pi$
$770$		0			0
$771$	56.7532			2.04392
$772$		0			0
$773$	−31.6031	+	22.9610i	−1.13669	+	0.825851i	−0.986654	−	0.162830i	$-0.947938\pi$
$773$	−31.6031	+	22.9610i	−1.13669	+	0.825851i	−0.150032	+	0.988681i	$0.547938\pi$
$774$		0			0
$775$	1.35789	+	4.17917i	0.0487770	+	0.150120i
$776$		0			0
$777$	−27.1646	−	19.7362i	−0.974523	−	0.708033i
$778$		0			0
$779$	6.45854	−	19.8773i	0.231401	−	0.712179i
$780$		0			0
$781$	2.60283	−	18.8631i	0.0931367	−	0.674975i
$782$		0			0
$783$	6.99102	−	21.5162i	0.249839	−	0.768925i
$784$		0			0
$785$	12.1592	+	8.83418i	0.433981	+	0.315305i
$786$		0			0
$787$	1.52369	+	4.68945i	0.0543138	+	0.167161i	0.974534	−	0.224241i	$-0.0719903\pi$
$787$	1.52369	+	4.68945i	0.0543138	+	0.167161i	−0.920220	+	0.391402i	$0.871990\pi$
$788$		0			0
$789$	−57.8647	+	42.0412i	−2.06004	+	1.49671i
$790$		0			0
$791$	−15.1931			−0.540204
$792$		0			0
$793$	45.3004			1.60866
$794$		0			0
$795$	−24.9496	+	18.1270i	−0.884873	+	0.642898i
$796$		0			0
$797$	−15.5757	−	47.9370i	−0.551719	−	1.69802i	−0.704455	−	0.709748i	$-0.748809\pi$
$797$	−15.5757	−	47.9370i	−0.551719	−	1.69802i	0.152737	−	0.988267i	$-0.451191\pi$
$798$		0			0
$799$	24.8230	+	18.0349i	0.878174	+	0.638030i
$800$		0			0
$801$	28.2428	−	86.9223i	0.997909	−	3.07125i
$802$		0			0
$803$	−7.65890	−	14.3176i	−0.270277	−	0.505257i
$804$		0			0
$805$	−1.46887	+	4.52072i	−0.0517709	+	0.159334i
$806$		0			0
$807$	3.63094	+	2.63803i	0.127815	+	0.0928630i
$808$		0			0
$809$	−16.8685	−	51.9158i	−0.593064	−	1.82526i	−0.564136	−	0.825682i	$-0.690790\pi$
$809$	−16.8685	−	51.9158i	−0.593064	−	1.82526i	−0.0289285	−	0.999581i	$-0.509210\pi$
$810$		0			0
$811$	−11.0409	+	8.02170i	−0.387699	+	0.281680i	−0.764512	−	0.644609i	$-0.777020\pi$
$811$	−11.0409	+	8.02170i	−0.387699	+	0.281680i	0.376813	+	0.926289i	$0.377020\pi$
$812$		0			0
$813$	−65.5505			−2.29896
$814$		0			0
$815$	14.4813			0.507258
$816$		0			0
$817$	35.1868	−	25.5647i	1.23103	−	0.894395i
$818$		0			0
$819$	−22.6058	−	69.5736i	−0.789912	−	2.43110i
$820$		0			0
$821$	30.2323	+	21.9651i	1.05512	+	0.766586i	0.973178	−	0.230052i	$-0.0738895\pi$
$821$	30.2323	+	21.9651i	1.05512	+	0.766586i	0.0819367	+	0.996638i	$0.473889\pi$
$822$		0			0
$823$	−8.50293	+	26.1693i	−0.296394	+	0.912206i	0.686356	+	0.727266i	$0.259209\pi$
$823$	−8.50293	+	26.1693i	−0.296394	+	0.912206i	−0.982750	+	0.184940i	$0.940791\pi$
$824$		0			0
$825$	6.67549	−	6.94744i	0.232411	−	0.241879i
$826$		0			0
$827$	−12.0378	+	37.0486i	−0.418596	+	1.28831i	0.490399	+	0.871498i	$0.336851\pi$
$827$	−12.0378	+	37.0486i	−0.418596	+	1.28831i	−0.908995	+	0.416807i	$0.863149\pi$
$828$		0			0
$829$	−6.48669	−	4.71286i	−0.225292	−	0.163684i	0.469413	−	0.882978i	$-0.344465\pi$
$829$	−6.48669	−	4.71286i	−0.225292	−	0.163684i	−0.694706	+	0.719294i	$0.744465\pi$
$830$		0			0
$831$	12.4051	+	38.1791i	0.430330	+	1.32442i
$832$		0			0
$833$	12.8837	−	9.36057i	0.446394	−	0.324325i
$834$		0			0
$835$	−0.304676			−0.0105438
$836$		0			0
$837$	−31.1347			−1.07617
$838$		0			0
$839$	16.0692	−	11.6749i	0.554769	−	0.403064i	−0.274771	−	0.961510i	$-0.588602\pi$
$839$	16.0692	−	11.6749i	0.554769	−	0.403064i	0.829541	+	0.558446i	$0.188602\pi$
$840$		0			0
$841$	−5.81101	−	17.8844i	−0.200379	−	0.616705i
$842$		0			0
$843$	−20.4636	−	14.8677i	−0.704803	−	0.512069i
$844$		0			0
$845$	7.71213	−	23.7355i	0.265305	−	0.816526i
$846$		0			0
$847$	0.958388	+	23.9949i	0.0329306	+	0.824474i
$848$		0			0
$849$	−1.36869	+	4.21240i	−0.0469733	+	0.144569i
$850$		0			0
$851$	−9.32640	−	6.77602i	−0.319705	−	0.232279i
$852$		0			0
$853$	7.58692	+	23.3501i	0.259771	+	0.799493i	0.992852	+	0.119352i	$0.0380816\pi$
$853$	7.58692	+	23.3501i	0.259771	+	0.799493i	−0.733081	+	0.680141i	$0.761918\pi$
$854$		0			0
$855$	−27.9849	+	20.3322i	−0.957064	+	0.695347i
$856$		0			0
$857$	9.17203			0.313311			0.156655	−	0.987653i	$-0.449929\pi$
$857$	9.17203			0.313311			0.156655	+	0.987653i	$0.449929\pi$
$858$		0			0
$859$	2.83353			0.0966786			0.0483393	−	0.998831i	$-0.484607\pi$
$859$	2.83353			0.0966786			0.0483393	+	0.998831i	$0.484607\pi$
$860$		0			0
$861$	−16.8609	+	12.2502i	−0.574619	+	0.417485i
$862$		0			0
$863$	12.5909	+	38.7509i	0.428601	+	1.31910i	0.899504	+	0.436913i	$0.143928\pi$
$863$	12.5909	+	38.7509i	0.428601	+	1.31910i	−0.470903	+	0.882185i	$0.656072\pi$
$864$		0			0
$865$	7.85835	+	5.70942i	0.267192	+	0.194126i
$866$		0			0
$867$	−30.3519	+	93.4136i	−1.03081	+	3.17249i
$868$		0			0
$869$	18.6456	−	19.4052i	0.632508	−	0.658276i
$870$		0			0
$871$	−14.6053	+	44.9505i	−0.494882	+	1.52309i
$872$		0			0
$873$	14.4136	+	10.4721i	0.487826	+	0.354427i
$874$		0			0
$875$	−0.674612	−	2.07624i	−0.0228061	−	0.0701898i
$876$		0			0
$877$	2.30156	−	1.67218i	0.0777183	−	0.0564656i	−0.548248	−	0.836316i	$-0.684705\pi$
$877$	2.30156	−	1.67218i	0.0777183	−	0.0564656i	0.625966	+	0.779850i	$0.284705\pi$
$878$		0			0
$879$	−68.9562			−2.32584
$880$		0			0
$881$	−25.7884			−0.868834			−0.434417	−	0.900712i	$-0.643046\pi$
$881$	−25.7884			−0.868834			−0.434417	+	0.900712i	$0.643046\pi$
$882$		0			0
$883$	−6.87135	+	4.99233i	−0.231239	+	0.168005i	−0.697371	−	0.716710i	$-0.745647\pi$
$883$	−6.87135	+	4.99233i	−0.231239	+	0.168005i	0.466132	+	0.884715i	$0.345647\pi$
$884$		0			0
$885$	−12.3797	−	38.1008i	−0.416139	−	1.28074i
$886$		0			0
$887$	−20.7442	−	15.0716i	−0.696524	−	0.506054i	0.182275	−	0.983248i	$-0.441654\pi$
$887$	−20.7442	−	15.0716i	−0.696524	−	0.506054i	−0.878798	+	0.477194i	$0.841654\pi$
$888$		0			0
$889$	7.00734	−	21.5664i	0.235019	−	0.723313i
$890$		0			0
$891$	6.67349	+	12.4755i	0.223570	+	0.417944i
$892$		0			0
$893$	−8.45951	+	26.0357i	−0.283087	+	0.871252i
$894$		0			0
$895$	−7.60610	−	5.52616i	−0.254244	−	0.184719i
$896$		0			0
$897$	−12.0421	−	37.0619i	−0.402075	−	1.23746i
$898$		0			0
$899$	11.3511	−	8.24708i	0.378581	−	0.275055i
$900$		0			0
$901$	−75.6728			−2.52102
$902$		0			0
$903$	−43.3704			−1.44328
$904$		0			0
$905$	10.6602	−	7.74510i	0.354357	−	0.257456i
$906$		0			0
$907$	−7.30339	−	22.4775i	−0.242505	−	0.746354i	−0.996037	−	0.0889426i	$-0.971651\pi$
$907$	−7.30339	−	22.4775i	−0.242505	−	0.746354i	0.753532	−	0.657412i	$-0.228349\pi$
$908$		0			0
$909$	30.4079	+	22.0926i	1.00857	+	0.732766i
$910$		0			0
$911$	−14.6445	+	45.0710i	−0.485193	+	1.49327i	0.346509	+	0.938047i	$0.387367\pi$
$911$	−14.6445	+	45.0710i	−0.485193	+	1.49327i	−0.831701	+	0.555223i	$0.812633\pi$
$912$		0			0
$913$	1.91488	−	13.8774i	0.0633732	−	0.459275i
$914$		0			0
$915$	−6.60062	+	20.3146i	−0.218210	+	0.671580i
$916$		0			0
$917$	6.15706	+	4.47337i	0.203324	+	0.147724i
$918$		0			0
$919$	−12.3341	−	37.9604i	−0.406864	−	1.25220i	−0.919329	−	0.393490i	$-0.871268\pi$
$919$	−12.3341	−	37.9604i	−0.406864	−	1.25220i	0.512465	−	0.858708i	$-0.328732\pi$
$920$		0			0
$921$	−41.6282	+	30.2447i	−1.37170	+	0.996595i
$922$		0			0
$923$	35.3719			1.16428
$924$		0			0
$925$	5.29453			0.174083
$926$		0			0
$927$	−33.3799	+	24.2520i	−1.09634	+	0.796539i
$928$		0			0
$929$	−3.33281	−	10.2573i	−0.109346	−	0.336533i	0.881380	−	0.472408i	$-0.156615\pi$
$929$	−3.33281	−	10.2573i	−0.109346	−	0.336533i	−0.990726	+	0.135876i	$0.956615\pi$
$930$		0			0
$931$	11.4950	+	8.35159i	0.376733	+	0.273712i
$932$		0			0
$933$	−6.09079	+	18.7455i	−0.199404	+	0.613701i
$934$		0			0
$935$	23.2720	−	4.16366i	0.761075	−	0.136166i
$936$		0			0
$937$	−11.7069	+	36.0300i	−0.382447	+	1.17705i	0.555869	+	0.831270i	$0.312386\pi$
$937$	−11.7069	+	36.0300i	−0.382447	+	1.17705i	−0.938316	+	0.345780i	$0.887614\pi$
$938$		0			0
$939$	55.9477	+	40.6484i	1.82578	+	1.32651i
$940$		0			0
$941$	0.367150	+	1.12997i	0.0119688	+	0.0368361i	0.956863	−	0.290541i	$-0.0938353\pi$
$941$	0.367150	+	1.12997i	0.0119688	+	0.0368361i	−0.944894	+	0.327377i	$0.893835\pi$
$942$		0			0
$943$	−5.78885	+	4.20585i	−0.188511	+	0.136961i
$944$		0			0
$945$	15.4679			0.503172
$946$		0			0
$947$	4.75475			0.154508			0.0772542	−	0.997011i	$-0.475385\pi$
$947$	4.75475			0.154508			0.0772542	+	0.997011i	$0.475385\pi$
$948$		0			0
$949$	24.4019	−	17.7290i	0.792118	−	0.575507i
$950$		0			0
$951$	1.65892	+	5.10562i	0.0537940	+	0.165561i
$952$		0			0
$953$	−1.55624	−	1.13067i	−0.0504115	−	0.0366261i	0.562294	−	0.826937i	$-0.309919\pi$
$953$	−1.55624	−	1.13067i	−0.0504115	−	0.0366261i	−0.612706	+	0.790311i	$0.709919\pi$
$954$		0			0
$955$	−2.27360	+	6.99742i	−0.0735720	+	0.226431i
$956$		0			0
$957$	−27.6840	−	13.4166i	−0.894898	−	0.433697i
$958$		0			0
$959$	9.81366	−	30.2033i	0.316900	−	0.975317i
$960$		0			0
$961$	9.45795	+	6.87160i	0.305095	+	0.221665i
$962$		0			0
$963$	4.71441	+	14.5095i	0.151920	+	0.467561i
$964$		0			0
$965$	14.9465	−	10.8593i	0.481146	−	0.349573i
$966$		0			0
$967$	−14.4688			−0.465284			−0.232642	−	0.972562i	$-0.574737\pi$
$967$	−14.4688			−0.465284			−0.232642	+	0.972562i	$0.574737\pi$
$968$		0			0
$969$	−131.695			−4.23067
$970$		0			0
$971$	11.1092	−	8.07132i	0.356512	−	0.259021i	−0.395084	−	0.918645i	$-0.629285\pi$
$971$	11.1092	−	8.07132i	0.356512	−	0.259021i	0.751596	+	0.659624i	$0.229285\pi$
$972$		0			0
$973$	0.338583	+	1.04205i	0.0108545	+	0.0334066i
$974$		0			0
$975$	14.4794	+	10.5199i	0.463711	+	0.336906i
$976$		0			0
$977$	−13.3023	+	40.9404i	−0.425579	+	1.30980i	0.476859	+	0.878980i	$0.341775\pi$
$977$	−13.3023	+	40.9404i	−0.425579	+	1.30980i	−0.902439	+	0.430818i	$0.858225\pi$
$978$		0			0
$979$	−50.1522	−	24.3054i	−1.60287	−	0.776805i
$980$		0			0
$981$	13.4947	−	41.5323i	0.430851	−	1.32602i
$982$		0			0
$983$	−16.8472	−	12.2402i	−0.537341	−	0.390401i	0.285756	−	0.958302i	$-0.407755\pi$
$983$	−16.8472	−	12.2402i	−0.537341	−	0.390401i	−0.823096	+	0.567902i	$0.807755\pi$
$984$		0			0
$985$	2.96103	+	9.11311i	0.0943462	+	0.290368i
$986$		0			0
$987$	22.0848	−	16.0455i	0.702966	−	0.510735i
$988$		0			0
$989$	−14.8904			−0.473486
$990$		0			0
$991$	42.9441			1.36417			0.682083	−	0.731275i	$-0.261074\pi$
$991$	42.9441			1.36417			0.682083	+	0.731275i	$0.261074\pi$
$992$		0			0
$993$	41.2822	−	29.9933i	1.31005	−	0.951807i
$994$		0			0
$995$	4.11879	+	12.6763i	0.130574	+	0.401866i
$996$		0			0
$997$	24.1408	+	17.5393i	0.764547	+	0.555476i	0.900302	−	0.435267i	$-0.143346\pi$
$997$	24.1408	+	17.5393i	0.764547	+	0.555476i	−0.135755	+	0.990742i	$0.543346\pi$
$998$		0			0
$999$	−11.5923	+	35.6775i	−0.366765	+	1.12879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.d.361.4	✓	16
4.3	odd	2		880.2.bo.k.801.1		16
11.4	even	5		4840.2.a.bg.1.1		8
11.5	even	5	inner	440.2.y.d.401.4	yes	16
11.7	odd	10		4840.2.a.bh.1.1		8
44.7	even	10		9680.2.a.de.1.8		8
44.15	odd	10		9680.2.a.df.1.8		8
44.27	odd	10		880.2.bo.k.401.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.361.4	✓	16	1.1	even	1	trivial
440.2.y.d.401.4	yes	16	11.5	even	5	inner
880.2.bo.k.401.1		16	44.27	odd	10
880.2.bo.k.801.1		16	4.3	odd	2
4840.2.a.bg.1.1		8	11.4	even	5
4840.2.a.bh.1.1		8	11.7	odd	10
9680.2.a.de.1.8		8	44.7	even	10
9680.2.a.df.1.8		8	44.15	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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.35019 - 1.70752i) q^{3} +(0.309017 + 0.951057i) q^{5} +(1.76616 + 1.28319i) q^{7} +(1.68075 - 5.17281i) q^{9} +(-2.98460 - 1.44644i) q^{11} +(1.90383 - 5.85939i) q^{13} +(2.35019 + 1.70752i) q^{15} +(2.20273 + 6.77930i) q^{17} +(-5.14521 + 3.73822i) q^{19} +6.34188 q^{21} +2.17735 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-2.18949 - 6.73856i) q^{27} +(2.58318 + 1.87679i) q^{29} +(1.35789 - 4.17917i) q^{31} +(-9.48419 + 1.69684i) q^{33} +(-0.674612 + 2.07624i) q^{35} +(-4.28336 - 3.11205i) q^{37} +(-5.53062 - 17.0215i) q^{39} +(-2.65866 + 1.93163i) q^{41} -6.83874 q^{43} +5.43902 q^{45} +(3.48237 - 2.53009i) q^{47} +(-0.690378 - 2.12477i) q^{49} +(16.7526 + 12.1715i) q^{51} +(-3.28052 + 10.0964i) q^{53} +(0.453350 - 3.28549i) q^{55} +(-5.70918 + 17.5711i) q^{57} +(-11.1568 - 8.10589i) q^{59} +(2.27216 + 6.99299i) q^{61} +(9.60616 - 6.97929i) q^{63} +6.16092 q^{65} -7.67154 q^{67} +(5.11720 - 3.71787i) q^{69} +(1.77417 + 5.46033i) q^{71} +(3.96075 + 2.87765i) q^{73} +(-0.897694 + 2.76282i) q^{75} +(-3.41522 - 6.38444i) q^{77} +(-2.50738 + 7.71694i) q^{79} +(-3.45115 - 2.50741i) q^{81} +(1.30524 + 4.01711i) q^{83} +(-5.76682 + 4.18984i) q^{85} +9.27563 q^{87} +16.8037 q^{89} +(10.8812 - 7.90563i) q^{91} +(-3.94468 - 12.1405i) q^{93} +(-5.14521 - 3.73822i) q^{95} +(-1.01222 + 3.11531i) q^{97} +(-12.4985 + 13.0077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 4 q^{5} + 8 q^{7} - 7 q^{9} - 7 q^{11} - 11 q^{13} - 3 q^{15} + 9 q^{17} - 2 q^{19} + 12 q^{21} + 20 q^{23} - 4 q^{25} - 9 q^{27} + q^{29} - 2 q^{31} - 32 q^{33} - 2 q^{35} - 16 q^{37}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 4 * q^5 + 8 * q^7 - 7 * q^9 - 7 * q^11 - 11 * q^13 - 3 * q^15 + 9 * q^17 - 2 * q^19 + 12 * q^21 + 20 * q^23 - 4 * q^25 - 9 * q^27 + q^29 - 2 * q^31 - 32 * q^33 - 2 * q^35 - 16 * q^37 + 3 * q^39 - 11 * q^41 - 16 * q^43 + 38 * q^45 - 10 * q^47 + 4 * q^49 + 26 * q^51 - 9 * q^53 + 3 * q^55 - 50 * q^57 - 60 * q^59 + 30 * q^61 + 52 * q^63 + 24 * q^65 - 4 * q^67 + 41 * q^69 - 10 * q^71 + q^73 + 2 * q^75 - 4 * q^77 + 19 * q^79 - 31 * q^81 + 64 * q^83 - 11 * q^85 + 30 * q^87 + 24 * q^89 - 9 * q^91 + 45 * q^93 - 2 * q^95 - 3 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more