LMFDB - Embedded newform 1386.2.bk.a.703.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.6
Root			$0.500000 + 1.35798i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.a.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(2.45660 + 0.982398i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(2.45660 + 0.982398i) q^{7} -1.00000i q^{8} +(-1.11200 + 1.92604i) q^{10} +(0.0571978 + 3.31613i) q^{11} -0.112712 q^{13} +(2.61868 - 0.377519i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.119843 + 0.207574i) q^{17} +(-0.218080 - 0.377726i) q^{19} +2.22400i q^{20} +(1.70760 + 2.84326i) q^{22} +(0.401617 + 0.695621i) q^{23} +(-0.0269081 + 0.0466061i) q^{25} +(-0.0976119 + 0.0563562i) q^{26} +(2.07908 - 1.63628i) q^{28} +7.50955i q^{29} +(0.306643 + 0.177040i) q^{31} +(-0.866025 - 0.500000i) q^{32} +0.239685i q^{34} +(-5.82395 + 0.839603i) q^{35} +(3.67483 + 6.36499i) q^{37} +(-0.377726 - 0.218080i) q^{38} +(1.11200 + 1.92604i) q^{40} -3.14869 q^{41} +10.1874i q^{43} +(2.90045 + 1.60853i) q^{44} +(0.695621 + 0.401617i) q^{46} +(11.2232 - 6.47974i) q^{47} +(5.06979 + 4.82672i) q^{49} +0.0538161i q^{50} +(-0.0563562 + 0.0976119i) q^{52} +(-1.28196 + 2.22041i) q^{53} +(-3.79771 - 6.32340i) q^{55} +(0.982398 - 2.45660i) q^{56} +(3.75478 + 6.50347i) q^{58} +(-3.27440 - 1.89048i) q^{59} +(0.525000 + 0.909326i) q^{61} +0.354081 q^{62} -1.00000 q^{64} +(0.217089 - 0.125336i) q^{65} +(2.48189 - 4.29875i) q^{67} +(0.119843 + 0.207574i) q^{68} +(-4.62388 + 3.63909i) q^{70} +7.58067 q^{71} +(2.39827 - 4.15392i) q^{73} +(6.36499 + 3.67483i) q^{74} -0.436161 q^{76} +(-3.11725 + 8.20261i) q^{77} +(0.429215 - 0.247807i) q^{79} +(1.92604 + 1.11200i) q^{80} +(-2.72685 + 1.57435i) q^{82} +0.569186 q^{83} -0.533061i q^{85} +(5.09368 + 8.82251i) q^{86} +(3.31613 - 0.0571978i) q^{88} +(12.1232 - 6.99934i) q^{89} +(-0.276890 - 0.110729i) q^{91} +0.803234 q^{92} +(6.47974 - 11.2232i) q^{94} +(0.840064 + 0.485011i) q^{95} -10.6708i q^{97} +(6.80393 + 1.64517i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7	$ 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7} + 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} - 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} + 8 q^{35} + 14 q^{37} + 12 q^{38} - 2 q^{40} - 32 q^{41} - 4 q^{44} + 18 q^{46} + 24 q^{47} - 6 q^{49} - 14 q^{55} - 4 q^{56} + 28 q^{61} + 8 q^{62} - 16 q^{64} - 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} - 44 q^{73} - 24 q^{74} - 20 q^{76} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} + 14 q^{94} - 72 q^{95} + 40 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7 + 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 - 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 + 8 * q^35 + 14 * q^37 + 12 * q^38 - 2 * q^40 - 32 * q^41 - 4 * q^44 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 14 * q^55 - 4 * q^56 + 28 * q^61 + 8 * q^62 - 16 * q^64 - 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 - 44 * q^73 - 24 * q^74 - 20 * q^76 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 + 14 * q^94 - 72 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.92604	+	1.11200i	−0.861352	+	0.497302i	−0.864465	−	0.502693i	$-0.832343\pi$
$5$	−1.92604	+	1.11200i	−0.861352	+	0.497302i	0.00311268	+	0.999995i	$0.499009\pi$
$6$		0			0
$7$	2.45660	+	0.982398i	0.928508	+	0.371312i
$7$	2.45660	+	0.982398i	0.928508	+	0.371312i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.11200	+	1.92604i	−0.351646	+	0.609068i
$11$	0.0571978	+	3.31613i	0.0172458	+	0.999851i
$11$	0.0571978	+	3.31613i	0.0172458	+	0.999851i
$12$		0			0
$13$	−0.112712			−0.0312608			−0.0156304	−	0.999878i	$-0.504976\pi$
$13$	−0.112712			−0.0312608			−0.0156304	+	0.999878i	$0.504976\pi$
$14$	2.61868	−	0.377519i	0.699871	−	0.100896i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.119843	+	0.207574i	−0.0290661	+	0.0503440i	−0.880193	−	0.474617i	$-0.842587\pi$
$17$	−0.119843	+	0.207574i	−0.0290661	+	0.0503440i	0.851126	+	0.524961i	$0.175920\pi$
$18$		0			0
$19$	−0.218080	−	0.377726i	−0.0500311	−	0.0866564i	0.839925	−	0.542702i	$-0.182599\pi$
$19$	−0.218080	−	0.377726i	−0.0500311	−	0.0866564i	−0.889956	+	0.456046i	$0.849265\pi$
$20$			2.22400i			0.497302i
$21$		0			0
$22$	1.70760	+	2.84326i	0.364062	+	0.606184i
$23$	0.401617	+	0.695621i	0.0837429	+	0.145047i	0.904855	−	0.425720i	$-0.139979\pi$
$23$	0.401617	+	0.695621i	0.0837429	+	0.145047i	−0.821112	+	0.570767i	$0.806646\pi$
$24$		0			0
$25$	−0.0269081	+	0.0466061i	−0.00538161	+	0.00932123i
$26$	−0.0976119	+	0.0563562i	−0.0191433	+	0.0110524i
$27$		0			0
$28$	2.07908	−	1.63628i	0.392910	−	0.309228i
$29$			7.50955i			1.39449i	0.716833	+	0.697245i	$0.245591\pi$
$29$			7.50955i			1.39449i	−0.716833	+	0.697245i	$0.754409\pi$
$30$		0			0
$31$	0.306643	+	0.177040i	0.0550747	+	0.0317974i	0.527285	−	0.849689i	$-0.323210\pi$
$31$	0.306643	+	0.177040i	0.0550747	+	0.0317974i	−0.472210	+	0.881486i	$0.656544\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			0.239685i			0.0411057i
$35$	−5.82395	+	0.839603i	−0.984427	+	0.141919i
$36$		0			0
$37$	3.67483	+	6.36499i	0.604138	+	1.04640i	0.992187	+	0.124759i	$0.0398158\pi$
$37$	3.67483	+	6.36499i	0.604138	+	1.04640i	−0.388049	+	0.921639i	$0.626851\pi$
$38$	−0.377726	−	0.218080i	−0.0612753	−	0.0353773i
$39$		0			0
$40$	1.11200	+	1.92604i	0.175823	+	0.304534i
$41$	−3.14869			−0.491743			−0.245872	−	0.969302i	$-0.579074\pi$
$41$	−3.14869			−0.491743			−0.245872	+	0.969302i	$0.579074\pi$
$42$		0			0
$43$			10.1874i			1.55356i	0.629774	+	0.776779i	$0.283148\pi$
$43$			10.1874i			1.55356i	−0.629774	+	0.776779i	$0.716852\pi$
$44$	2.90045	+	1.60853i	0.437260	+	0.242495i
$45$		0			0
$46$	0.695621	+	0.401617i	0.102564	+	0.0592152i
$47$	11.2232	−	6.47974i	1.63708	−	0.945168i	0.655246	−	0.755415i	$-0.272565\pi$
$47$	11.2232	−	6.47974i	1.63708	−	0.945168i	0.981832	−	0.189753i	$-0.0607686\pi$
$48$		0			0
$49$	5.06979	+	4.82672i	0.724255	+	0.689532i
$50$			0.0538161i			0.00761075i
$51$		0			0
$52$	−0.0563562	+	0.0976119i	−0.00781520	+	0.0135363i
$53$	−1.28196	+	2.22041i	−0.176090	+	0.304997i	−0.940538	−	0.339688i	$-0.889678\pi$
$53$	−1.28196	+	2.22041i	−0.176090	+	0.304997i	0.764448	+	0.644686i	$0.223012\pi$
$54$		0			0
$55$	−3.79771	−	6.32340i	−0.512083	−	0.852648i
$56$	0.982398	−	2.45660i	0.131278	−	0.328277i
$57$		0			0
$58$	3.75478	+	6.50347i	0.493026	+	0.853947i
$59$	−3.27440	−	1.89048i	−0.426291	−	0.246119i	0.271474	−	0.962446i	$-0.412489\pi$
$59$	−3.27440	−	1.89048i	−0.426291	−	0.246119i	−0.697765	+	0.716326i	$0.745822\pi$
$60$		0			0
$61$	0.525000	+	0.909326i	0.0672193	+	0.116427i	0.897676	−	0.440655i	$-0.145254\pi$
$61$	0.525000	+	0.909326i	0.0672193	+	0.116427i	−0.830457	+	0.557083i	$0.811921\pi$
$62$	0.354081			0.0449683
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.217089	−	0.125336i	0.0269266	−	0.0155461i
$66$		0			0
$67$	2.48189	−	4.29875i	0.303211	−	0.525176i	−0.673651	−	0.739050i	$-0.735275\pi$
$67$	2.48189	−	4.29875i	0.303211	−	0.525176i	0.976861	+	0.213874i	$0.0686081\pi$
$68$	0.119843	+	0.207574i	0.0145331	+	0.0251720i
$69$		0			0
$70$	−4.62388	+	3.63909i	−0.552660	+	0.434955i
$71$	7.58067			0.899660			0.449830	−	0.893114i	$-0.351485\pi$
$71$	7.58067			0.899660			0.449830	+	0.893114i	$0.351485\pi$
$72$		0			0
$73$	2.39827	−	4.15392i	0.280696	−	0.486179i	−0.690861	−	0.722988i	$-0.742768\pi$
$73$	2.39827	−	4.15392i	0.280696	−	0.486179i	0.971556	+	0.236809i	$0.0761015\pi$
$74$	6.36499	+	3.67483i	0.739915	+	0.427190i
$75$		0			0
$76$	−0.436161			−0.0500311
$77$	−3.11725	+	8.20261i	−0.355244	+	0.934774i
$78$		0			0
$79$	0.429215	−	0.247807i	0.0482905	−	0.0278805i	−0.475660	−	0.879629i	$-0.657791\pi$
$79$	0.429215	−	0.247807i	0.0482905	−	0.0278805i	0.523951	+	0.851748i	$0.324458\pi$
$80$	1.92604	+	1.11200i	0.215338	+	0.124325i
$81$		0			0
$82$	−2.72685	+	1.57435i	−0.301130	+	0.173857i
$83$	0.569186			0.0624763			0.0312381	−	0.999512i	$-0.490055\pi$
$83$	0.569186			0.0624763			0.0312381	+	0.999512i	$0.490055\pi$
$84$		0			0
$85$		−	0.533061i		−	0.0578186i
$86$	5.09368	+	8.82251i	0.549266	+	0.951356i
$87$		0			0
$88$	3.31613	−	0.0571978i	0.353501	−	0.00609730i
$89$	12.1232	−	6.99934i	1.28506	−	0.741928i	0.307289	−	0.951616i	$-0.400578\pi$
$89$	12.1232	−	6.99934i	1.28506	−	0.741928i	0.977768	+	0.209688i	$0.0672449\pi$
$90$		0			0
$91$	−0.276890	−	0.110729i	−0.0290259	−	0.0116075i
$92$	0.803234			0.0837429
$93$		0			0
$94$	6.47974	−	11.2232i	0.668334	−	1.15759i
$95$	0.840064	+	0.485011i	0.0861888	+	0.0497611i
$96$		0			0
$97$		−	10.6708i		−	1.08345i	−0.840554	−	0.541727i	$-0.817770\pi$
$97$		−	10.6708i		−	1.08345i	0.840554	−	0.541727i	$-0.182230\pi$
$98$	6.80393	+	1.64517i	0.687300	+	0.166187i
$99$		0			0
$100$	0.0269081	+	0.0466061i	0.00269081	+	0.00466061i
$101$	−9.76595	+	16.9151i	−0.971748	+	1.68312i	−0.281474	+	0.959569i	$0.590823\pi$
$101$	−9.76595	+	16.9151i	−0.971748	+	1.68312i	−0.690274	+	0.723548i	$0.742510\pi$
$102$		0			0
$103$	−11.0669	+	6.38947i	−1.09045	+	0.629573i	−0.933697	−	0.358064i	$-0.883437\pi$
$103$	−11.0669	+	6.38947i	−1.09045	+	0.629573i	−0.156756	+	0.987637i	$0.550104\pi$
$104$			0.112712i			0.0110524i
$105$		0			0
$106$			2.56391i			0.249029i
$107$	10.8886	−	6.28656i	1.05264	−	0.607745i	0.129256	−	0.991611i	$-0.458741\pi$
$107$	10.8886	−	6.28656i	1.05264	−	0.607745i	0.923389	+	0.383867i	$0.125408\pi$
$108$		0			0
$109$	−14.3351	−	8.27635i	−1.37305	−	0.792730i	−0.381739	−	0.924270i	$-0.624675\pi$
$109$	−14.3351	−	8.27635i	−1.37305	−	0.792730i	−0.991311	+	0.131540i	$0.958008\pi$
$110$	−6.45061	−	3.57738i	−0.615042	−	0.341089i
$111$		0			0
$112$	−0.377519	−	2.61868i	−0.0356722	−	0.247442i
$113$	8.19898			0.771295			0.385647	−	0.922646i	$-0.373978\pi$
$113$	8.19898			0.771295			0.385647	+	0.922646i	$0.373978\pi$
$114$		0			0
$115$	−1.54706	−	0.893197i	−0.144264	−	0.0832910i
$116$	6.50347	+	3.75478i	0.603832	+	0.348622i
$117$		0			0
$118$	−3.78095			−0.348065
$119$	−0.498326	+	0.392193i	−0.0456815	+	0.0359522i
$120$		0			0
$121$	−10.9935	+	0.379351i	−0.999405	+	0.0344864i
$122$	0.909326	+	0.525000i	0.0823265	+	0.0475312i
$123$		0			0
$124$	0.306643	−	0.177040i	0.0275374	−	0.0158987i
$125$		−	11.2397i		−	1.00531i
$126$		0			0
$127$			5.11237i			0.453650i	0.973936	+	0.226825i	$0.0728345\pi$
$127$			5.11237i			0.453650i	−0.973936	+	0.226825i	$0.927166\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	0.125336	−	0.217089i	0.0109927	−	0.0190400i
$131$	1.02912	+	1.78250i	0.0899150	+	0.155737i	0.907475	−	0.420106i	$-0.138007\pi$
$131$	1.02912	+	1.78250i	0.0899150	+	0.155737i	−0.817560	+	0.575843i	$0.804674\pi$
$132$		0			0
$133$	−0.164659	−	1.14217i	−0.0142778	−	0.0990383i
$134$		−	4.96377i		−	0.428804i
$135$		0			0
$136$	0.207574	+	0.119843i	0.0177993	+	0.0102764i
$137$	−9.42545	+	16.3254i	−0.805271	+	1.39477i	0.110838	+	0.993839i	$0.464647\pi$
$137$	−9.42545	+	16.3254i	−0.805271	+	1.39477i	−0.916108	+	0.400931i	$0.868687\pi$
$138$		0			0
$139$	−10.5033			−0.890880			−0.445440	−	0.895312i	$-0.646953\pi$
$139$	−10.5033			−0.890880			−0.445440	+	0.895312i	$0.646953\pi$
$140$	−2.18486	+	5.46349i	−0.184654	+	0.461749i
$141$		0			0
$142$	6.56505	−	3.79033i	0.550927	−	0.318078i
$143$	−0.00644690	−	0.373769i	−0.000539117	−	0.0312562i
$144$		0			0
$145$	−8.35063	−	14.4637i	−0.693482	−	1.20115i
$146$		−	4.79653i		−	0.396964i
$147$		0			0
$148$	7.34966			0.604138
$149$	12.6570	−	7.30752i	1.03690	−	0.598656i	0.117948	−	0.993020i	$-0.462369\pi$
$149$	12.6570	−	7.30752i	1.03690	−	0.598656i	0.918954	+	0.394364i	$0.129035\pi$
$150$		0			0
$151$	−1.57663	−	0.910267i	−0.128304	−	0.0740764i	0.434474	−	0.900684i	$-0.356934\pi$
$151$	−1.57663	−	0.910267i	−0.128304	−	0.0740764i	−0.562778	+	0.826608i	$0.690268\pi$
$152$	−0.377726	+	0.218080i	−0.0306377	+	0.0176887i
$153$		0			0
$154$	1.40169	+	8.66229i	0.112951	+	0.698027i
$155$	−0.787477			−0.0632516
$156$		0			0
$157$	15.1388	+	8.74037i	1.20821	+	0.697558i	0.962367	−	0.271753i	$-0.0876034\pi$
$157$	15.1388	+	8.74037i	1.20821	+	0.697558i	0.245839	+	0.969311i	$0.420937\pi$
$158$	0.247807	−	0.429215i	0.0197145	−	0.0341465i
$159$		0			0
$160$	2.22400			0.175823
$161$	0.303236	+	2.10341i	0.0238984	+	0.165772i
$162$		0			0
$163$	−5.84566	−	10.1250i	−0.457867	−	0.793049i	0.540981	−	0.841035i	$-0.318053\pi$
$163$	−5.84566	−	10.1250i	−0.457867	−	0.793049i	−0.998848	+	0.0479858i	$0.984720\pi$
$164$	−1.57435	+	2.72685i	−0.122936	+	0.212931i
$165$		0			0
$166$	0.492929	−	0.284593i	0.0382587	−	0.0220887i
$167$	−18.4885			−1.43068			−0.715341	−	0.698775i	$-0.753729\pi$
$167$	−18.4885			−1.43068			−0.715341	+	0.698775i	$0.753729\pi$
$168$		0			0
$169$	−12.9873			−0.999023
$170$	−0.266530	−	0.461644i	−0.0204419	−	0.0354065i
$171$		0			0
$172$	8.82251	+	5.09368i	0.672710	+	0.388389i
$173$	−8.59437	−	14.8859i	−0.653418	−	1.13175i	−0.982288	−	0.187378i	$-0.940001\pi$
$173$	−8.59437	−	14.8859i	−0.653418	−	1.13175i	0.328870	−	0.944375i	$-0.393332\pi$
$174$		0			0
$175$	−0.111888	+	0.0880583i	−0.00845795	+	0.00665658i
$176$	2.84326	−	1.70760i	0.214318	−	0.128715i
$177$		0			0
$178$	6.99934	−	12.1232i	0.524622	−	0.908673i
$179$	5.81838	−	10.0777i	0.434886	−	0.753244i	−0.562400	−	0.826865i	$-0.690122\pi$
$179$	5.81838	−	10.0777i	0.434886	−	0.753244i	0.997286	+	0.0736206i	$0.0234554\pi$
$180$		0			0
$181$		−	21.9534i		−	1.63179i	−0.578203	−	0.815893i	$-0.696246\pi$
$181$		−	21.9534i		−	1.63179i	0.578203	−	0.815893i	$-0.303754\pi$
$182$	−0.295158	+	0.0425511i	−0.0218785	+	0.00315410i
$183$		0			0
$184$	0.695621	−	0.401617i	0.0512818	−	0.0296076i
$185$	−14.1557	−	8.17282i	−1.04075	−	0.600878i
$186$		0			0
$187$	−0.695196	−	0.385541i	−0.0508378	−	0.0281936i
$188$		−	12.9595i		−	0.945168i
$189$		0			0
$190$	0.970023			0.0703728
$191$	−2.99269	−	5.18349i	−0.216543	−	0.375064i	0.737205	−	0.675669i	$-0.236145\pi$
$191$	−2.99269	−	5.18349i	−0.216543	−	0.375064i	−0.953749	+	0.300604i	$0.902812\pi$
$192$		0			0
$193$	−7.35467	−	4.24622i	−0.529401	−	0.305650i	0.211372	−	0.977406i	$-0.432207\pi$
$193$	−7.35467	−	4.24622i	−0.529401	−	0.305650i	−0.740772	+	0.671756i	$0.765540\pi$
$194$	−5.33540	−	9.24118i	−0.383059	−	0.663478i
$195$		0			0
$196$	6.71496	−	1.97720i	0.479640	−	0.141229i
$197$		−	3.71109i		−	0.264404i	−0.991223	−	0.132202i	$-0.957795\pi$
$197$		−	3.71109i		−	0.264404i	0.991223	−	0.132202i	$-0.0422048\pi$
$198$		0			0
$199$	4.99176	+	2.88199i	0.353857	+	0.204299i	0.666383	−	0.745610i	$-0.267842\pi$
$199$	4.99176	+	2.88199i	0.353857	+	0.204299i	−0.312526	+	0.949909i	$0.601175\pi$
$200$	0.0466061	+	0.0269081i	0.00329555	+	0.00190269i
$201$		0			0
$202$			19.5319i			1.37426i
$203$	−7.37737	+	18.4480i	−0.517790	+	1.29479i
$204$		0			0
$205$	6.06451	−	3.50135i	0.423564	−	0.244545i
$206$	−6.38947	+	11.0669i	−0.445176	+	0.771067i
$207$		0			0
$208$	0.0563562	+	0.0976119i	0.00390760	+	0.00676816i
$209$	1.24012	−	0.744789i	0.0857807	−	0.0515181i
$210$		0			0
$211$			23.1201i			1.59165i	0.605524	+	0.795827i	$0.292963\pi$
$211$			23.1201i			1.59165i	−0.605524	+	0.795827i	$0.707037\pi$
$212$	1.28196	+	2.22041i	0.0880451	+	0.152499i
$213$		0			0
$214$	6.28656	−	10.8886i	0.429740	−	0.744332i
$215$	−11.3284	−	19.6213i	−0.772587	−	1.33816i
$216$		0			0
$217$	0.579376	+	0.736164i	0.0393306	+	0.0499740i
$218$	−16.5527			−1.12109
$219$		0			0
$220$	−7.37508	+	0.127208i	−0.497228	+	0.00857636i
$221$	0.0135078	−	0.0233961i	0.000908631	−	0.00157379i
$222$		0			0
$223$		−	11.3233i		−	0.758267i	−0.925342	−	0.379134i	$-0.876222\pi$
$223$		−	11.3233i		−	0.758267i	0.925342	−	0.379134i	$-0.123778\pi$
$224$	−1.63628	−	2.07908i	−0.109329	−	0.138915i
$225$		0			0
$226$	7.10052	−	4.09949i	0.472320	−	0.272694i
$227$	−2.66623	+	4.61805i	−0.176964	+	0.306510i	−0.940839	−	0.338853i	$-0.889961\pi$
$227$	−2.66623	+	4.61805i	−0.176964	+	0.306510i	0.763875	+	0.645364i	$0.223294\pi$
$228$		0			0
$229$	15.6189	−	9.01755i	1.03212	−	0.595897i	0.114531	−	0.993420i	$-0.463463\pi$
$229$	15.6189	−	9.01755i	1.03212	−	0.595897i	0.917592	+	0.397523i	$0.130130\pi$
$230$	−1.78639			−0.117791
$231$		0			0
$232$	7.50955			0.493026
$233$	13.5770	−	7.83866i	0.889456	−	0.513528i	0.0156917	−	0.999877i	$-0.495005\pi$
$233$	13.5770	−	7.83866i	0.889456	−	0.513528i	0.873765	+	0.486349i	$0.161672\pi$
$234$		0			0
$235$	−14.4110	+	24.9605i	−0.940067	+	1.62824i
$236$	−3.27440	+	1.89048i	−0.213145	+	0.123060i
$237$		0			0
$238$	−0.235467	+	0.588812i	−0.0152630	+	0.0381670i
$239$		−	19.6987i		−	1.27420i	−0.770780	−	0.637101i	$-0.780133\pi$
$239$		−	19.6987i		−	1.27420i	0.770780	−	0.637101i	$-0.219867\pi$
$240$		0			0
$241$	3.85279	−	6.67323i	0.248180	−	0.429861i	−0.714841	−	0.699287i	$-0.753501\pi$
$241$	3.85279	−	6.67323i	0.248180	−	0.429861i	0.963021	+	0.269427i	$0.0868342\pi$
$242$	−9.33094	+	5.82526i	−0.599815	+	0.374462i
$243$		0			0
$244$	1.05000			0.0672193
$245$	−15.1319	−	3.65886i	−0.966744	−	0.233756i
$246$		0			0
$247$	0.0245804	+	0.0425745i	0.00156401	+	0.00270895i
$248$	0.177040	−	0.306643i	0.0112421	−	0.0194719i
$249$		0			0
$250$	−5.61985	−	9.73386i	−0.355430	−	0.615624i
$251$			11.3888i			0.718857i	0.933173	+	0.359428i	$0.117028\pi$
$251$			11.3888i			0.718857i	−0.933173	+	0.359428i	$0.882972\pi$
$252$		0			0
$253$	−2.28380	+	1.37160i	−0.143581	+	0.0862319i
$254$	2.55619	+	4.42744i	0.160389	+	0.277803i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.9973	+	8.08134i	−0.873127	+	0.504100i	−0.868386	−	0.495888i	$-0.834842\pi$
$257$	−13.9973	+	8.08134i	−0.873127	+	0.504100i	−0.00474110	+	0.999989i	$0.501509\pi$
$258$		0			0
$259$	2.77464	+	19.2464i	0.172407	+	1.19591i
$260$		−	0.250673i		−	0.0155461i
$261$		0			0
$262$	1.78250	+	1.02912i	0.110123	+	0.0635795i
$263$	7.43191	+	4.29081i	0.458271	+	0.264583i	0.711317	−	0.702871i	$-0.248099\pi$
$263$	7.43191	+	4.29081i	0.458271	+	0.264583i	−0.253046	+	0.967454i	$0.581432\pi$
$264$		0			0
$265$		−	5.70215i		−	0.350280i
$266$	−0.713682	−	0.906815i	−0.0437586	−	0.0556004i
$267$		0			0
$268$	−2.48189	−	4.29875i	−0.151605	−	0.262588i
$269$	−3.58587	−	2.07030i	−0.218634	−	0.126229i	0.386683	−	0.922213i	$-0.373621\pi$
$269$	−3.58587	−	2.07030i	−0.218634	−	0.126229i	−0.605318	+	0.795984i	$0.706954\pi$
$270$		0			0
$271$	1.71583	+	2.97190i	0.104229	+	0.180530i	0.913423	−	0.407012i	$-0.133429\pi$
$271$	1.71583	+	2.97190i	0.104229	+	0.180530i	−0.809194	+	0.587542i	$0.800096\pi$
$272$	0.239685			0.0145331
$273$		0			0
$274$			18.8509i			1.13882i
$275$	−0.156091	−	0.0865649i	−0.00941265	−	0.00522006i
$276$		0			0
$277$	−1.35959	−	0.784960i	−0.0816899	−	0.0471637i	0.458599	−	0.888643i	$-0.348352\pi$
$277$	−1.35959	−	0.784960i	−0.0816899	−	0.0471637i	−0.540289	+	0.841480i	$0.681685\pi$
$278$	−9.09614	+	5.25166i	−0.545550	+	0.314974i
$279$		0			0
$280$	0.839603	+	5.82395i	0.0501759	+	0.348047i
$281$			3.49877i			0.208719i	0.994540	+	0.104360i	$0.0332793\pi$
$281$			3.49877i			0.208719i	−0.994540	+	0.104360i	$0.966721\pi$
$282$		0			0
$283$	−11.1106	+	19.2440i	−0.660454	+	1.14394i	0.320043	+	0.947403i	$0.396303\pi$
$283$	−11.1106	+	19.2440i	−0.660454	+	1.14394i	−0.980496	+	0.196537i	$0.937031\pi$
$284$	3.79033	−	6.56505i	0.224915	−	0.389564i
$285$		0			0
$286$	−0.192468	−	0.320470i	−0.0113809	−	0.0189498i
$287$	−7.73508	−	3.09327i	−0.456588	−	0.182590i
$288$		0			0
$289$	8.47128	+	14.6727i	0.498310	+	0.863099i
$290$	−14.4637	−	8.35063i	−0.849339	−	0.490366i
$291$		0			0
$292$	−2.39827	−	4.15392i	−0.140348	−	0.243090i
$293$	6.85562			0.400510			0.200255	−	0.979744i	$-0.435823\pi$
$293$	6.85562			0.400510			0.200255	+	0.979744i	$0.435823\pi$
$294$		0			0
$295$	8.40885			0.489582
$296$	6.36499	−	3.67483i	0.369957	−	0.213595i
$297$		0			0
$298$	7.30752	−	12.6570i	0.423313	−	0.733200i
$299$	−0.0452672	−	0.0784051i	−0.00261787	−	0.00453429i
$300$		0			0
$301$	−10.0080	+	25.0263i	−0.576854	+	1.44249i
$302$	−1.82053			−0.104760
$303$		0			0
$304$	−0.218080	+	0.377726i	−0.0125078	+	0.0216641i
$305$	−2.02234	−	1.16760i	−0.115799	−	0.0668566i
$306$		0			0
$307$	25.3466			1.44661			0.723303	−	0.690531i	$-0.242623\pi$
$307$	25.3466			1.44661			0.723303	+	0.690531i	$0.242623\pi$
$308$	5.54504	+	6.80092i	0.315958	+	0.387518i
$309$		0			0
$310$	−0.681975	+	0.393738i	−0.0387336	+	0.0223628i
$311$	−12.0093	−	6.93356i	−0.680984	−	0.393166i	0.119242	−	0.992865i	$-0.461954\pi$
$311$	−12.0093	−	6.93356i	−0.680984	−	0.393166i	−0.800226	+	0.599699i	$0.795287\pi$
$312$		0			0
$313$	10.4414	−	6.02834i	0.590183	−	0.340742i	−0.174987	−	0.984571i	$-0.555988\pi$
$313$	10.4414	−	6.02834i	0.590183	−	0.340742i	0.765170	+	0.643829i	$0.222655\pi$
$314$	17.4807			0.986496
$315$		0			0
$316$		−	0.495615i		−	0.0278805i
$317$	−3.77629	−	6.54073i	−0.212098	−	0.367364i	0.740273	−	0.672306i	$-0.234696\pi$
$317$	−3.77629	−	6.54073i	−0.212098	−	0.367364i	−0.952371	+	0.304942i	$0.901363\pi$
$318$		0			0
$319$	−24.9027	+	0.429530i	−1.39428	+	0.0240491i
$320$	1.92604	−	1.11200i	0.107669	−	0.0621627i
$321$		0			0
$322$	1.31432	+	1.66999i	0.0732439	+	0.0930649i
$323$	0.104541			0.00581684
$324$		0			0
$325$	0.00303287	−	0.00525309i	0.000168234	−	0.000291389i
$326$	−10.1250	−	5.84566i	−0.560770	−	0.323761i
$327$		0			0
$328$			3.14869i			0.173857i
$329$	33.9367	−	4.89245i	1.87099	−	0.269730i
$330$		0			0
$331$	−11.2835	−	19.5435i	−0.620195	−	1.07421i	−0.989449	−	0.144880i	$-0.953720\pi$
$331$	−11.2835	−	19.5435i	−0.620195	−	1.07421i	0.369255	−	0.929328i	$-0.379613\pi$
$332$	0.284593	−	0.492929i	0.0156191	−	0.0270530i
$333$		0			0
$334$	−16.0115	+	9.24425i	−0.876111	+	0.505823i
$335$			11.0394i			0.603149i
$336$		0			0
$337$		−	32.4695i		−	1.76872i	−0.466801	−	0.884362i	$-0.654594\pi$
$337$		−	32.4695i		−	1.76872i	0.466801	−	0.884362i	$-0.345406\pi$
$338$	−11.2473	+	6.49365i	−0.611774	+	0.353208i
$339$		0			0
$340$	−0.461644	−	0.266530i	−0.0250362	−	0.0144546i
$341$	−0.569550	+	1.02700i	−0.0308429	+	0.0556149i
$342$		0			0
$343$	7.71269	+	16.8379i	0.416446	+	0.909161i
$344$	10.1874			0.549266
$345$		0			0
$346$	−14.8859	−	8.59437i	−0.800270	−	0.462036i
$347$	26.6239	+	15.3713i	1.42924	+	0.825174i	0.997061	−	0.0766119i	$-0.0244102\pi$
$347$	26.6239	+	15.3713i	1.42924	+	0.825174i	0.432183	+	0.901786i	$0.357744\pi$
$348$		0			0
$349$	24.5576			1.31454			0.657269	−	0.753656i	$-0.271712\pi$
$349$	24.5576			1.31454			0.657269	+	0.753656i	$0.271712\pi$
$350$	−0.0528689	+	0.132205i	−0.00282596	+	0.00706665i
$351$		0			0
$352$	1.60853	−	2.90045i	0.0857350	−	0.154595i
$353$	−3.74418	−	2.16170i	−0.199283	−	0.115056i	0.397038	−	0.917802i	$-0.370038\pi$
$353$	−3.74418	−	2.16170i	−0.199283	−	0.115056i	−0.596321	+	0.802746i	$0.703371\pi$
$354$		0			0
$355$	−14.6007	+	8.42971i	−0.774924	+	0.447402i
$356$		−	13.9987i		−	0.741928i
$357$		0			0
$358$		−	11.6368i		−	0.615021i
$359$	13.7848	−	7.95866i	0.727534	−	0.420042i	−0.0899854	−	0.995943i	$-0.528682\pi$
$359$	13.7848	−	7.95866i	0.727534	−	0.420042i	0.817519	+	0.575901i	$0.195349\pi$
$360$		0			0
$361$	9.40488	−	16.2897i	0.494994	−	0.857354i
$362$	−10.9767	−	19.0122i	−0.576923	−	0.999260i
$363$		0			0
$364$	−0.234339	+	0.184429i	−0.0122827	+	0.00966672i
$365$			10.6675i			0.558362i
$366$		0			0
$367$	−22.2966	−	12.8729i	−1.16387	−	0.671962i	−0.211643	−	0.977347i	$-0.567881\pi$
$367$	−22.2966	−	12.8729i	−1.16387	−	0.671962i	−0.952229	+	0.305385i	$0.901215\pi$
$368$	0.401617	−	0.695621i	0.0209357	−	0.0362617i
$369$		0			0
$370$	−16.3456			−0.849770
$371$	−5.33059	+	4.19528i	−0.276750	+	0.217808i
$372$		0			0
$373$	25.2676	−	14.5882i	1.30831	−	0.755350i	0.326492	−	0.945200i	$-0.394133\pi$
$373$	25.2676	−	14.5882i	1.30831	−	0.755350i	0.981813	+	0.189850i	$0.0608000\pi$
$374$	−0.794828	+	0.0137095i	−0.0410996	+	0.000708900i
$375$		0			0
$376$	−6.47974	−	11.2232i	−0.334167	−	0.578795i
$377$		−	0.846420i		−	0.0435929i
$378$		0			0
$379$	−28.8200			−1.48039			−0.740193	−	0.672395i	$-0.765266\pi$
$379$	−28.8200			−1.48039			−0.740193	+	0.672395i	$0.765266\pi$
$380$	0.840064	−	0.485011i	0.0430944	−	0.0248806i
$381$		0			0
$382$	−5.18349	−	2.99269i	−0.265210	−	0.153119i
$383$	6.12468	−	3.53608i	0.312956	−	0.180685i	−0.335292	−	0.942114i	$-0.608835\pi$
$383$	6.12468	−	3.53608i	0.312956	−	0.180685i	0.648249	+	0.761429i	$0.275502\pi$
$384$		0			0
$385$	−3.11735	−	19.2649i	−0.158875	−	0.981833i
$386$	−8.49244			−0.432254
$387$		0			0
$388$	−9.24118	−	5.33540i	−0.469150	−	0.270864i
$389$	6.18937	−	10.7203i	0.313813	−	0.543541i	−0.665371	−	0.746513i	$-0.731727\pi$
$389$	6.18937	−	10.7203i	0.313813	−	0.543541i	0.979185	+	0.202972i	$0.0650601\pi$
$390$		0			0
$391$	−0.192523			−0.00973633
$392$	4.82672	−	5.06979i	0.243786	−	0.256063i
$393$		0			0
$394$	−1.85555	−	3.21390i	−0.0934811	−	0.161914i
$395$	−0.551124	+	0.954575i	−0.0277301	+	0.0480299i
$396$		0			0
$397$	17.2980	−	9.98702i	0.868163	−	0.501234i	0.00142581	−	0.999999i	$-0.499546\pi$
$397$	17.2980	−	9.98702i	0.868163	−	0.501234i	0.866737	+	0.498765i	$0.166213\pi$
$398$	5.76399			0.288923
$399$		0			0
$400$	0.0538161			0.00269081
$401$	5.27945	+	9.14428i	0.263643	+	0.456643i	0.967207	−	0.253988i	$-0.0817425\pi$
$401$	5.27945	+	9.14428i	0.263643	+	0.456643i	−0.703564	+	0.710632i	$0.748409\pi$
$402$		0			0
$403$	−0.0345625	−	0.0199547i	−0.00172168	−	0.000994013i
$404$	9.76595	+	16.9151i	0.485874	+	0.841558i
$405$		0			0
$406$	2.83500	+	19.6651i	0.140699	+	0.975963i
$407$	−20.8969	+	12.5503i	−1.03582	+	0.622094i
$408$		0			0
$409$	−11.2457	+	19.4781i	−0.556065	+	0.963132i	0.441755	+	0.897136i	$0.354356\pi$
$409$	−11.2457	+	19.4781i	−0.556065	+	0.963132i	−0.997820	+	0.0659967i	$0.978977\pi$
$410$	3.50135	−	6.06451i	0.172919	−	0.299505i
$411$		0			0
$412$			12.7789i			0.629573i
$413$	−6.18670	−	7.86092i	−0.304428	−	0.386811i
$414$		0			0
$415$	−1.09628	+	0.632935i	−0.0538141	+	0.0310696i
$416$	0.0976119	+	0.0563562i	0.00478582	+	0.00276309i
$417$		0			0
$418$	0.701578	−	1.26506i	0.0343153	−	0.0618763i
$419$		−	25.5522i		−	1.24831i	−0.781302	−	0.624154i	$-0.785444\pi$
$419$		−	25.5522i		−	1.24831i	0.781302	−	0.624154i	$-0.214556\pi$
$420$		0			0
$421$	−2.88784			−0.140745			−0.0703723	−	0.997521i	$-0.522419\pi$
$421$	−2.88784			−0.140745			−0.0703723	+	0.997521i	$0.522419\pi$
$422$	11.5601	+	20.0226i	0.562735	+	0.974685i
$423$		0			0
$424$	2.22041	+	1.28196i	0.107833	+	0.0622573i
$425$	−0.00644947	−	0.0111708i	−0.000312845	−	0.000541864i
$426$		0			0
$427$	0.396395	+	2.74961i	0.0191829	+	0.133063i
$428$		−	12.5731i		−	0.607745i
$429$		0			0
$430$	−19.6213	−	11.3284i	−0.946222	−	0.546302i
$431$	−28.7727	−	16.6119i	−1.38593	−	0.800168i	−0.393077	−	0.919505i	$-0.628590\pi$
$431$	−28.7727	−	16.6119i	−1.38593	−	0.800168i	−0.992854	+	0.119338i	$0.961923\pi$
$432$		0			0
$433$		−	0.741961i		−	0.0356564i	−0.999841	−	0.0178282i	$-0.994325\pi$
$433$		−	0.741961i		−	0.0356564i	0.999841	−	0.0178282i	$-0.00567519\pi$
$434$	0.869836	+	0.347849i	0.0417535	+	0.0166973i
$435$		0			0
$436$	−14.3351	+	8.27635i	−0.686525	+	0.396365i
$437$	0.175170	−	0.303403i	0.00837950	−	0.0145137i
$438$		0			0
$439$	−8.11637	−	14.0580i	−0.387373	−	0.670950i	0.604722	−	0.796437i	$-0.293284\pi$
$439$	−8.11637	−	14.0580i	−0.387373	−	0.670950i	−0.992095	+	0.125486i	$0.959951\pi$
$440$	−6.32340	+	3.79771i	−0.301456	+	0.181049i
$441$		0			0
$442$		−	0.0270155i		−	0.00128500i
$443$	−5.45671	−	9.45129i	−0.259256	−	0.449044i	0.706787	−	0.707427i	$-0.250144\pi$
$443$	−5.45671	−	9.45129i	−0.259256	−	0.449044i	−0.966043	+	0.258382i	$0.916811\pi$
$444$		0			0
$445$	−15.5665	+	26.9620i	−0.737925	+	1.27812i
$446$	−5.66167	−	9.80630i	−0.268088	−	0.464342i
$447$		0			0
$448$	−2.45660	−	0.982398i	−0.116064	−	0.0464140i
$449$	23.6594			1.11656			0.558278	−	0.829654i	$-0.311462\pi$
$449$	23.6594			1.11656			0.558278	+	0.829654i	$0.311462\pi$
$450$		0			0
$451$	−0.180098	−	10.4415i	−0.00848049	−	0.491670i
$452$	4.09949	−	7.10052i	0.192824	−	0.333980i
$453$		0			0
$454$			5.33246i			0.250265i
$455$	0.656431	−	0.0946338i	0.0307740	−	0.00443650i
$456$		0			0
$457$	21.2115	−	12.2465i	0.992233	−	0.572866i	0.0862919	−	0.996270i	$-0.472498\pi$
$457$	21.2115	−	12.2465i	0.992233	−	0.572866i	0.905941	+	0.423404i	$0.139165\pi$
$458$	9.01755	−	15.6189i	0.421363	−	0.729821i
$459$		0			0
$460$	−1.54706	+	0.893197i	−0.0721321	+	0.0416455i
$461$	−8.01773			−0.373423			−0.186712	−	0.982415i	$-0.559783\pi$
$461$	−8.01773			−0.373423			−0.186712	+	0.982415i	$0.559783\pi$
$462$		0			0
$463$	32.2209			1.49743			0.748716	−	0.662891i	$-0.230671\pi$
$463$	32.2209			1.49743			0.748716	+	0.662891i	$0.230671\pi$
$464$	6.50347	−	3.75478i	0.301916	−	0.174311i
$465$		0			0
$466$	7.83866	−	13.5770i	0.363119	−	0.628941i
$467$	−11.5836	+	6.68782i	−0.536027	+	0.309475i	−0.743467	−	0.668772i	$-0.766820\pi$
$467$	−11.5836	+	6.68782i	−0.536027	+	0.309475i	0.207440	+	0.978248i	$0.433487\pi$
$468$		0			0
$469$	10.3201	−	8.12212i	0.476538	−	0.375045i
$470$			28.8219i			1.32946i
$471$		0			0
$472$	−1.89048	+	3.27440i	−0.0870163	+	0.150717i
$473$	−33.7826	+	0.582694i	−1.55333	+	0.0267923i
$474$		0			0
$475$	0.0234725			0.00107699
$476$	0.0904858	+	0.627659i	0.00414741	+	0.0287687i
$477$		0			0
$478$	−9.84934	−	17.0596i	−0.450498	−	0.780286i
$479$	−17.3629	+	30.0734i	−0.793330	+	1.37409i	0.130564	+	0.991440i	$0.458321\pi$
$479$	−17.3629	+	30.0734i	−0.793330	+	1.37409i	−0.923894	+	0.382648i	$0.875012\pi$
$480$		0			0
$481$	−0.414199	−	0.717414i	−0.0188858	−	0.0327112i
$482$		−	7.70558i		−	0.350980i
$483$		0			0
$484$	−5.16820	+	9.71029i	−0.234918	+	0.441377i
$485$	11.8659	+	20.5524i	0.538804	+	0.933236i
$486$		0			0
$487$	−9.83069	+	17.0272i	−0.445471	+	0.771578i	−0.998085	−	0.0618591i	$-0.980297\pi$
$487$	−9.83069	+	17.0272i	−0.445471	+	0.771578i	0.552614	+	0.833437i	$0.313630\pi$
$488$	0.909326	−	0.525000i	0.0411633	−	0.0237656i
$489$		0			0
$490$	−14.9341	+	4.39730i	−0.674653	+	0.198650i
$491$			31.6334i			1.42760i	0.700352	+	0.713798i	$0.253026\pi$
$491$			31.6334i			1.42760i	−0.700352	+	0.713798i	$0.746974\pi$
$492$		0			0
$493$	−1.55879	−	0.899965i	−0.0702042	−	0.0405324i
$494$	0.0425745	+	0.0245804i	0.00191552	+	0.00110592i
$495$		0			0
$496$		−	0.354081i		−	0.0158987i
$497$	18.6227	+	7.44723i	0.835341	+	0.334054i
$498$		0			0
$499$	18.1190	+	31.3830i	0.811118	+	1.40490i	0.912082	+	0.410007i	$0.134474\pi$
$499$	18.1190	+	31.3830i	0.811118	+	1.40490i	−0.100965	+	0.994890i	$0.532193\pi$
$500$	−9.73386	−	5.61985i	−0.435312	−	0.251327i
$501$		0			0
$502$	5.69442	+	9.86302i	0.254154	+	0.440208i
$503$	−28.3530			−1.26420			−0.632098	−	0.774889i	$-0.717806\pi$
$503$	−28.3530			−1.26420			−0.632098	+	0.774889i	$0.717806\pi$
$504$		0			0
$505$		−	43.4390i		−	1.93301i
$506$	−1.29203	+	2.32974i	−0.0574376	+	0.103570i
$507$		0			0
$508$	4.42744	+	2.55619i	0.196436	+	0.113412i
$509$	31.4337	−	18.1483i	1.39328	−	0.804408i	0.399600	−	0.916690i	$-0.369149\pi$
$509$	31.4337	−	18.1483i	1.39328	−	0.804408i	0.993676	+	0.112281i	$0.0358158\pi$
$510$		0			0
$511$	9.97239	−	7.84847i	0.441152	−	0.347196i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−8.08134	+	13.9973i	−0.356453	+	0.617394i
$515$	14.2102	−	24.6128i	0.626176	−	1.08457i
$516$		0			0
$517$	22.1296	+	36.8471i	0.973260	+	1.62053i
$518$	12.0261	+	15.2805i	0.528396	+	0.671389i
$519$		0			0
$520$	−0.125336	−	0.217089i	−0.00549636	−	0.00951998i
$521$	7.10021	+	4.09931i	0.311066	+	0.179594i	0.647403	−	0.762148i	$-0.275855\pi$
$521$	7.10021	+	4.09931i	0.311066	+	0.179594i	−0.336338	+	0.941741i	$0.609188\pi$
$522$		0			0
$523$	16.8849	+	29.2456i	0.738327	+	1.27882i	0.953248	+	0.302188i	$0.0977171\pi$
$523$	16.8849	+	29.2456i	0.738327	+	1.27882i	−0.214921	+	0.976631i	$0.568950\pi$
$524$	2.05825			0.0899150
$525$		0			0
$526$	8.58163			0.374177
$527$	−0.0734979	+	0.0424340i	−0.00320162	+	0.00184845i
$528$		0			0
$529$	11.1774	−	19.3598i	0.485974	−	0.841732i
$530$	−2.85107	−	4.93820i	−0.123843	−	0.214502i
$531$		0			0
$532$	−1.07147	−	0.428484i	−0.0464543	−	0.0185771i
$533$	0.354897			0.0153723
$534$		0			0
$535$	−13.9813	+	24.2164i	−0.604465	+	1.04696i
$536$	−4.29875	−	2.48189i	−0.185678	−	0.107201i
$537$		0			0
$538$	−4.14061			−0.178514
$539$	−15.7161	+	17.0882i	−0.676939	+	0.736039i
$540$		0			0
$541$	−19.6218	+	11.3286i	−0.843607	+	0.487057i	−0.858489	−	0.512833i	$-0.828596\pi$
$541$	−19.6218	+	11.3286i	−0.843607	+	0.487057i	0.0148819	+	0.999889i	$0.495263\pi$
$542$	2.97190	+	1.71583i	0.127654	+	0.0737011i
$543$		0			0
$544$	0.207574	−	0.119843i	0.00889965	−	0.00513821i
$545$	36.8132			1.57691
$546$		0			0
$547$		−	11.4499i		−	0.489563i	−0.969578	−	0.244782i	$-0.921284\pi$
$547$		−	11.4499i		−	0.489563i	0.969578	−	0.244782i	$-0.0787163\pi$
$548$	9.42545	+	16.3254i	0.402635	+	0.697385i
$549$		0			0
$550$	−0.178461	+	0.00307816i	−0.00760962	+	0.000131253i
$551$	2.83656	−	1.63769i	0.120841	−	0.0697678i
$552$		0			0
$553$	1.29786	−	0.187104i	0.0551904	−	0.00795647i
$554$	−1.56992			−0.0666995
$555$		0			0
$556$	−5.25166	+	9.09614i	−0.222720	+	0.385762i
$557$	−39.2147	−	22.6406i	−1.66158	−	0.959314i	−0.971961	−	0.235141i	$-0.924445\pi$
$557$	−39.2147	−	22.6406i	−1.66158	−	0.959314i	−0.689619	−	0.724173i	$-0.742222\pi$
$558$		0			0
$559$		−	1.14824i		−	0.0485655i
$560$	3.63909	+	4.62388i	0.153780	+	0.195395i
$561$		0			0
$562$	1.74939	+	3.03003i	0.0737934	+	0.127814i
$563$	−13.8636	+	24.0125i	−0.584283	+	1.01201i	0.410682	+	0.911779i	$0.365291\pi$
$563$	−13.8636	+	24.0125i	−0.584283	+	1.01201i	−0.994964	+	0.100228i	$0.968043\pi$
$564$		0			0
$565$	−15.7916	+	9.11727i	−0.664356	+	0.383566i
$566$			22.2211i			0.934023i
$567$		0			0
$568$		−	7.58067i		−	0.318078i
$569$	13.9061	−	8.02868i	0.582973	−	0.336580i	−0.179341	−	0.983787i	$-0.557397\pi$
$569$	13.9061	−	8.02868i	0.582973	−	0.336580i	0.762314	+	0.647207i	$0.224063\pi$
$570$		0			0
$571$	−8.42022	−	4.86141i	−0.352375	−	0.203444i	0.313356	−	0.949636i	$-0.398547\pi$
$571$	−8.42022	−	4.86141i	−0.352375	−	0.203444i	−0.665731	+	0.746192i	$0.731880\pi$
$572$	−0.326917	−	0.181302i	−0.0136691	−	0.00758060i
$573$		0			0
$574$	−8.24541	+	1.18869i	−0.344157	+	0.0496150i
$575$	−0.0432269			−0.00180269
$576$		0			0
$577$	2.22544	+	1.28486i	0.0926462	+	0.0534893i	0.545607	−	0.838041i	$-0.316299\pi$
$577$	2.22544	+	1.28486i	0.0926462	+	0.0534893i	−0.452961	+	0.891530i	$0.649632\pi$
$578$	14.6727	+	8.47128i	0.610303	+	0.352359i
$579$		0			0
$580$	−16.7013			−0.693482
$581$	1.39826	+	0.559167i	0.0580097	+	0.0231982i
$582$		0			0
$583$	−7.43651	−	4.12413i	−0.307989	−	0.170804i
$584$	−4.15392	−	2.39827i	−0.171890	−	0.0992409i
$585$		0			0
$586$	5.93714	−	3.42781i	0.245261	−	0.141602i
$587$			25.9150i			1.06963i	0.844970	+	0.534814i	$0.179618\pi$
$587$			25.9150i			1.06963i	−0.844970	+	0.534814i	$0.820382\pi$
$588$		0			0
$589$		−	0.154436i		−	0.00636344i
$590$	7.28228	−	4.20443i	0.299807	−	0.173093i
$591$		0			0
$592$	3.67483	−	6.36499i	0.151034	−	0.261599i
$593$	−3.72204	−	6.44677i	−0.152846	−	0.264737i	0.779427	−	0.626494i	$-0.215511\pi$
$593$	−3.72204	−	6.44677i	−0.152846	−	0.264737i	−0.932273	+	0.361756i	$0.882177\pi$
$594$		0			0
$595$	0.523678	−	1.30952i	0.0214687	−	0.0536850i
$596$		−	14.6150i		−	0.598656i
$597$		0			0
$598$	−0.0784051	−	0.0452672i	−0.00320622	−	0.00185111i
$599$	12.3177	−	21.3348i	0.503286	−	0.871717i	−0.496707	−	0.867918i	$-0.665458\pi$
$599$	12.3177	−	21.3348i	0.503286	−	0.871717i	0.999993	−	0.00379841i	$-0.00120908\pi$
$600$		0			0
$601$	6.75417			0.275508			0.137754	−	0.990466i	$-0.456012\pi$
$601$	6.75417			0.275508			0.137754	+	0.990466i	$0.456012\pi$
$602$	3.84592	+	26.6774i	0.156748	+	1.08729i
$603$		0			0
$604$	−1.57663	+	0.910267i	−0.0641521	+	0.0370382i
$605$	20.7520	−	12.9554i	0.843690	−	0.526711i
$606$		0			0
$607$	−18.7854	−	32.5373i	−0.762476	−	1.32065i	−0.941571	−	0.336815i	$-0.890650\pi$
$607$	−18.7854	−	32.5373i	−0.762476	−	1.32065i	0.179095	−	0.983832i	$-0.442683\pi$
$608$			0.436161i			0.0176887i
$609$		0			0
$610$	−2.33520			−0.0945495
$611$	−1.26500	+	0.730348i	−0.0511764	+	0.0295467i
$612$		0			0
$613$	32.3937	+	18.7025i	1.30837	+	0.755387i	0.981824	−	0.189795i	$-0.0607824\pi$
$613$	32.3937	+	18.7025i	1.30837	+	0.755387i	0.326544	+	0.945182i	$0.394116\pi$
$614$	21.9508	−	12.6733i	0.885861	−	0.511452i
$615$		0			0
$616$	8.20261	+	3.11725i	0.330492	+	0.125598i
$617$	12.6245			0.508243			0.254122	−	0.967172i	$-0.418214\pi$
$617$	12.6245			0.508243			0.254122	+	0.967172i	$0.418214\pi$
$618$		0			0
$619$	−5.03418	−	2.90648i	−0.202341	−	0.116821i	0.395406	−	0.918506i	$-0.370604\pi$
$619$	−5.03418	−	2.90648i	−0.202341	−	0.116821i	−0.597747	+	0.801685i	$0.703937\pi$
$620$	−0.393738	+	0.681975i	−0.0158129	+	0.0273888i
$621$		0			0
$622$	−13.8671			−0.556021
$623$	36.6580	−	5.28477i	1.46867	−	0.211730i
$624$		0			0
$625$	12.3640	+	21.4151i	0.494560	+	0.856604i
$626$	6.02834	−	10.4414i	0.240941	−	0.417322i
$627$		0			0
$628$	15.1388	−	8.74037i	0.604103	−	0.348779i
$629$	−1.76161			−0.0702398
$630$		0			0
$631$	45.0951			1.79521			0.897604	−	0.440804i	$-0.145307\pi$
$631$	45.0951			1.79521			0.897604	+	0.440804i	$0.145307\pi$
$632$	−0.247807	−	0.429215i	−0.00985725	−	0.0170733i
$633$		0			0
$634$	−6.54073	−	3.77629i	−0.259766	−	0.149976i
$635$	−5.68496	−	9.84664i	−0.225601	−	0.390752i
$636$		0			0
$637$	−0.571428	−	0.544032i	−0.0226408	−	0.0215553i
$638$	−21.3516	+	12.8233i	−0.845317	+	0.507680i
$639$		0			0
$640$	1.11200	−	1.92604i	0.0439557	−	0.0761335i
$641$	−9.27227	+	16.0600i	−0.366233	+	0.634333i	−0.988973	−	0.148095i	$-0.952686\pi$
$641$	−9.27227	+	16.0600i	−0.366233	+	0.634333i	0.622741	+	0.782428i	$0.286019\pi$
$642$		0			0
$643$			9.80715i			0.386756i	0.981124	+	0.193378i	$0.0619444\pi$
$643$			9.80715i			0.386756i	−0.981124	+	0.193378i	$0.938056\pi$
$644$	1.97323	+	0.789095i	0.0777560	+	0.0310947i
$645$		0			0
$646$	0.0905355	−	0.0522707i	0.00356207	−	0.00205656i
$647$	16.4510	+	9.49800i	0.646756	+	0.373405i	0.787212	−	0.616682i	$-0.211524\pi$
$647$	16.4510	+	9.49800i	0.646756	+	0.373405i	−0.140456	+	0.990087i	$0.544857\pi$
$648$		0			0
$649$	6.08178	−	10.9665i	0.238731	−	0.430472i
$650$		−	0.00606575i		−	0.000237918i
$651$		0			0
$652$	−11.6913			−0.457867
$653$	7.65833	+	13.2646i	0.299694	+	0.519084i	0.976066	−	0.217476i	$-0.0697822\pi$
$653$	7.65833	+	13.2646i	0.299694	+	0.519084i	−0.676372	+	0.736560i	$0.736449\pi$
$654$		0			0
$655$	−3.96427	−	2.28877i	−0.154897	−	0.0894298i
$656$	1.57435	+	2.72685i	0.0614679	+	0.106465i
$657$		0			0
$658$	26.9438	−	21.2054i	1.05038	−	0.826671i
$659$			50.6179i			1.97179i	0.167358	+	0.985896i	$0.446476\pi$
$659$			50.6179i			1.97179i	−0.167358	+	0.985896i	$0.553524\pi$
$660$		0			0
$661$	33.9093	+	19.5776i	1.31892	+	0.761478i	0.983555	−	0.180610i	$-0.0578072\pi$
$661$	33.9093	+	19.5776i	1.31892	+	0.761478i	0.335365	+	0.942088i	$0.391141\pi$
$662$	−19.5435	−	11.2835i	−0.759580	−	0.438544i
$663$		0			0
$664$		−	0.569186i		−	0.0220887i
$665$	1.58723	+	2.01676i	0.0615501	+	0.0782065i
$666$		0			0
$667$	−5.22380	+	3.01596i	−0.202266	+	0.116779i
$668$	−9.24425	+	16.0115i	−0.357671	+	0.619504i
$669$		0			0
$670$	5.51972	+	9.56043i	0.213245	+	0.369352i
$671$	−2.98542	+	1.79298i	−0.115251	+	0.0692172i
$672$		0			0
$673$			25.0173i			0.964345i	0.876076	+	0.482172i	$0.160152\pi$
$673$			25.0173i			0.964345i	−0.876076	+	0.482172i	$0.839848\pi$
$674$	−16.2347	−	28.1194i	−0.625339	−	1.08312i
$675$		0			0
$676$	−6.49365	+	11.2473i	−0.249756	+	0.432590i
$677$	−24.2515	−	42.0048i	−0.932059	−	1.61437i	−0.779796	−	0.626034i	$-0.784677\pi$
$677$	−24.2515	−	42.0048i	−0.932059	−	1.61437i	−0.152263	−	0.988340i	$-0.548656\pi$
$678$		0			0
$679$	10.4830	−	26.2139i	0.402299	−	1.00600i
$680$	−0.533061			−0.0204419
$681$		0			0
$682$	0.0202526	+	1.17418i	0.000775514	+	0.0449616i
$683$	−3.55626	+	6.15962i	−0.136076	+	0.235691i	−0.926008	−	0.377504i	$-0.876783\pi$
$683$	−3.55626	+	6.15962i	−0.136076	+	0.235691i	0.789932	+	0.613195i	$0.210116\pi$
$684$		0			0
$685$		−	41.9244i		−	1.60185i
$686$	15.0983	+	10.7257i	0.576457	+	0.409509i
$687$		0			0
$688$	8.82251	−	5.09368i	0.336355	−	0.194195i
$689$	0.144492	−	0.250268i	0.00550472	−	0.00953446i
$690$		0			0
$691$	37.8547	−	21.8554i	1.44006	−	0.831420i	0.442209	−	0.896912i	$-0.354195\pi$
$691$	37.8547	−	21.8554i	1.44006	−	0.831420i	0.997853	+	0.0654915i	$0.0208615\pi$
$692$	−17.1887			−0.653418
$693$		0			0
$694$	30.7426			1.16697
$695$	20.2298	−	11.6797i	0.767361	−	0.443036i
$696$		0			0
$697$	0.377348	−	0.653585i	0.0142931	−	0.0247563i
$698$	21.2675	−	12.2788i	0.804986	−	0.464759i
$699$		0			0
$700$	0.0203166	+	0.140927i	0.000767896	+	0.00532655i
$701$		−	31.5402i		−	1.19126i	−0.803260	−	0.595628i	$-0.796903\pi$
$701$		−	31.5402i		−	1.19126i	0.803260	−	0.595628i	$-0.203097\pi$
$702$		0			0
$703$	1.60282	−	2.77616i	0.0604514	−	0.104705i
$704$	−0.0571978	−	3.31613i	−0.00215572	−	0.124981i
$705$		0			0
$706$	−4.32341			−0.162714
$707$	−40.6084	+	31.9597i	−1.52724	+	1.20197i
$708$		0			0
$709$	20.1759	+	34.9457i	0.757723	+	1.31241i	0.944009	+	0.329919i	$0.107021\pi$
$709$	20.1759	+	34.9457i	0.757723	+	1.31241i	−0.186287	+	0.982495i	$0.559645\pi$
$710$	−8.42971	+	14.6007i	−0.316361	+	0.547954i
$711$		0			0
$712$	−6.99934	−	12.1232i	−0.262311	−	0.454336i
$713$			0.284410i			0.0106512i
$714$		0			0
$715$	0.428049	+	0.712727i	0.0160081	+	0.0266545i
$716$	−5.81838	−	10.0777i	−0.217443	−	0.376622i
$717$		0			0
$718$	7.95866	−	13.7848i	0.297014	−	0.514444i
$719$	5.72561	−	3.30568i	0.213529	−	0.123281i	−0.389421	−	0.921060i	$-0.627325\pi$
$719$	5.72561	−	3.30568i	0.213529	−	0.123281i	0.602950	+	0.797779i	$0.293992\pi$
$720$		0			0
$721$	−33.4639	+	4.82430i	−1.24626	+	0.179666i
$722$		−	18.8098i		−	0.700027i
$723$		0			0
$724$	−19.0122	−	10.9767i	−0.706584	−	0.407946i
$725$	−0.349991	−	0.202068i	−0.0129984	−	0.00750460i
$726$		0			0
$727$		−	37.4392i		−	1.38854i	−0.719714	−	0.694271i	$-0.755727\pi$
$727$		−	37.4392i		−	1.38854i	0.719714	−	0.694271i	$-0.244273\pi$
$728$	−0.110729	+	0.276890i	−0.00410387	+	0.0102622i
$729$		0			0
$730$	5.33375	+	9.23832i	0.197411	+	0.341926i
$731$	−2.11463	−	1.22088i	−0.0782123	−	0.0451559i
$732$		0			0
$733$	11.5556	+	20.0149i	0.426816	+	0.739266i	0.996588	−	0.0825361i	$-0.0263020\pi$
$733$	11.5556	+	20.0149i	0.426816	+	0.739266i	−0.569772	+	0.821803i	$0.692969\pi$
$734$	−25.7459			−0.950297
$735$		0			0
$736$		−	0.803234i		−	0.0296076i
$737$	14.3972	+	7.98438i	0.530327	+	0.294108i
$738$		0			0
$739$	24.3934	+	14.0836i	0.897327	+	0.518072i	0.876332	−	0.481708i	$-0.159983\pi$
$739$	24.3934	+	14.0836i	0.897327	+	0.518072i	0.0209949	+	0.999780i	$0.493317\pi$
$740$	−14.1557	+	8.17282i	−0.520376	+	0.300439i
$741$		0			0
$742$	−2.51878	+	6.29851i	−0.0924674	+	0.231226i
$743$			0.655454i			0.0240463i	0.999928	+	0.0120231i	$0.00382718\pi$
$743$			0.655454i			0.0240463i	−0.999928	+	0.0120231i	$0.996173\pi$
$744$		0			0
$745$	−16.2519	+	28.1492i	−0.595425	+	1.03131i
$746$	14.5882	−	25.2676i	0.534113	−	0.925112i
$747$		0			0
$748$	−0.681487	+	0.409287i	−0.0249176	+	0.0149650i
$749$	32.9250	−	4.74659i	1.20305	−	0.173437i
$750$		0			0
$751$	−2.65126	−	4.59211i	−0.0967457	−	0.167568i	0.813590	−	0.581439i	$-0.197510\pi$
$751$	−2.65126	−	4.59211i	−0.0967457	−	0.167568i	−0.910336	+	0.413870i	$0.864177\pi$
$752$	−11.2232	−	6.47974i	−0.409270	−	0.236292i
$753$		0			0
$754$	−0.423210	−	0.733022i	−0.0154124	−	0.0266951i
$755$	4.04887			0.147353
$756$		0			0
$757$	−5.79544			−0.210639			−0.105319	−	0.994438i	$-0.533586\pi$
$757$	−5.79544			−0.210639			−0.105319	+	0.994438i	$0.533586\pi$
$758$	−24.9589	+	14.4100i	−0.906547	+	0.523395i
$759$		0			0
$760$	0.485011	−	0.840064i	0.0175932	−	0.0304723i
$761$	21.5347	+	37.2992i	0.780632	+	1.35209i	0.931574	+	0.363552i	$0.118436\pi$
$761$	21.5347	+	37.2992i	0.780632	+	1.35209i	−0.150942	+	0.988543i	$0.548231\pi$
$762$		0			0
$763$	−27.0849	−	34.4144i	−0.980538	−	1.24589i
$764$	−5.98538			−0.216543
$765$		0			0
$766$	3.53608	−	6.12468i	0.127764	−	0.221294i
$767$	0.369066	+	0.213080i	0.0133262	+	0.00769389i
$768$		0			0
$769$	−41.6527			−1.50204			−0.751018	−	0.660282i	$-0.770437\pi$
$769$	−41.6527			−1.50204			−0.751018	+	0.660282i	$0.770437\pi$
$770$	−12.3322	−	15.1253i	−0.444421	−	0.545077i
$771$		0			0
$772$	−7.35467	+	4.24622i	−0.264700	+	0.152825i
$773$	18.5314	+	10.6991i	0.666527	+	0.384820i	0.794759	−	0.606925i	$-0.207597\pi$
$773$	18.5314	+	10.6991i	0.666527	+	0.384820i	−0.128232	+	0.991744i	$0.540930\pi$
$774$		0			0
$775$	−0.0165023	+	0.00952763i	−0.000592782	+	0.000342243i
$776$	−10.6708			−0.383059
$777$		0			0
$778$		−	12.3787i		−	0.443799i
$779$	0.686668	+	1.18934i	0.0246024	+	0.0426127i
$780$		0			0
$781$	0.433597	+	25.1385i	0.0155153	+	0.899526i
$782$	−0.166730	+	0.0962617i	−0.00596226	+	0.00344231i
$783$		0			0
$784$	1.64517	−	6.80393i	0.0587561	−	0.242997i
$785$	−38.8772			−1.38759
$786$		0			0
$787$	−11.3606	+	19.6771i	−0.404961	+	0.701413i	−0.994317	−	0.106461i	$-0.966048\pi$
$787$	−11.3606	+	19.6771i	−0.404961	+	0.701413i	0.589356	+	0.807873i	$0.299381\pi$
$788$	−3.21390	−	1.85555i	−0.114490	−	0.0661011i
$789$		0			0
$790$			1.10225i			0.0392162i
$791$	20.1416	+	8.05466i	0.716154	+	0.286391i
$792$		0			0
$793$	−0.0591740	−	0.102492i	−0.00210133	−	0.00363961i
$794$	9.98702	−	17.2980i	0.354426	−	0.613884i
$795$		0			0
$796$	4.99176	−	2.88199i	0.176928	−	0.102150i
$797$		−	20.0434i		−	0.709972i	−0.934872	−	0.354986i	$-0.884486\pi$
$797$		−	20.0434i		−	0.709972i	0.934872	−	0.354986i	$-0.115514\pi$
$798$		0			0
$799$			3.10620i			0.109889i
$800$	0.0466061	−	0.0269081i	0.00164778	−	0.000951344i
$801$		0			0
$802$	9.14428	+	5.27945i	0.322896	+	0.186424i
$803$	13.9121	+	7.71537i	0.490948	+	0.272269i
$804$		0			0
$805$	−2.92304	−	3.71406i	−0.103024	−	0.130903i
$806$	−0.0399093			−0.00140575
$807$		0			0
$808$	16.9151	+	9.76595i	0.595072	+	0.343565i
$809$	2.39507	+	1.38280i	0.0842063	+	0.0486165i	0.541512	−	0.840693i	$-0.317852\pi$
$809$	2.39507	+	1.38280i	0.0842063	+	0.0486165i	−0.457306	+	0.889310i	$0.651185\pi$
$810$		0			0
$811$	−25.2486			−0.886597			−0.443298	−	0.896374i	$-0.646192\pi$
$811$	−25.2486			−0.886597			−0.443298	+	0.896374i	$0.646192\pi$
$812$	12.2877	+	15.6130i	0.431215	+	0.547908i
$813$		0			0
$814$	−11.8221	+	21.3173i	−0.414366	+	0.747172i
$815$	22.5180	+	13.0007i	0.788770	+	0.455396i
$816$		0			0
$817$	3.84803	−	2.22166i	0.134626	−	0.0777262i
$818$			22.4914i			0.786394i
$819$		0			0
$820$		−	7.00270i		−	0.244545i
$821$	−32.9471	+	19.0220i	−1.14986	+	0.663874i	−0.948854	−	0.315716i	$-0.897755\pi$
$821$	−32.9471	+	19.0220i	−1.14986	+	0.663874i	−0.201009	+	0.979589i	$0.564422\pi$
$822$		0			0
$823$	13.2848	−	23.0100i	0.463079	−	0.802076i	−0.536033	−	0.844197i	$-0.680078\pi$
$823$	13.2848	−	23.0100i	0.463079	−	0.802076i	0.999113	+	0.0421202i	$0.0134113\pi$
$824$	6.38947	+	11.0669i	0.222588	+	0.385533i
$825$		0			0
$826$	−9.28830	−	3.71440i	−0.323181	−	0.129241i
$827$			7.04659i			0.245034i	0.992466	+	0.122517i	$0.0390966\pi$
$827$			7.04659i			0.245034i	−0.992466	+	0.122517i	$0.960903\pi$
$828$		0			0
$829$	15.5644	+	8.98614i	0.540576	+	0.312102i	0.745312	−	0.666716i	$-0.232300\pi$
$829$	15.5644	+	8.98614i	0.540576	+	0.312102i	−0.204737	+	0.978817i	$0.565634\pi$
$830$	−0.632935	+	1.09628i	−0.0219695	+	0.0380523i
$831$		0			0
$832$	0.112712			0.00390760
$833$	−1.60948	+	0.473907i	−0.0557651	+	0.0164199i
$834$		0			0
$835$	35.6096	−	20.5592i	1.23232	−	0.711481i
$836$	−0.0249474	−	1.44637i	−0.000862825	−	0.0500236i
$837$		0			0
$838$	−12.7761	−	22.1289i	−0.441343	−	0.764429i
$839$			12.2437i			0.422699i	0.977411	+	0.211350i	$0.0677859\pi$
$839$			12.2437i			0.422699i	−0.977411	+	0.211350i	$0.932214\pi$
$840$		0			0
$841$	−27.3934			−0.944601
$842$	−2.50094	+	1.44392i	−0.0861882	+	0.0497608i
$843$		0			0
$844$	20.0226	+	11.5601i	0.689206	+	0.397913i
$845$	25.0141	−	14.4419i	0.860510	−	0.496816i
$846$		0			0
$847$	−27.3792	−	9.86804i	−0.940761	−	0.339070i
$848$	2.56391			0.0880451
$849$		0			0
$850$	−0.0111708	−	0.00644947i	−0.000383156	−	0.000221215i
$851$	−2.95175	+	5.11257i	−0.101185	+	0.175257i
$852$		0			0
$853$	37.8949			1.29750			0.648749	−	0.761003i	$-0.275293\pi$
$853$	37.8949			1.29750			0.648749	+	0.761003i	$0.275293\pi$
$854$	1.71809	+	2.18304i	0.0587920	+	0.0747020i
$855$		0			0
$856$	−6.28656	−	10.8886i	−0.214870	−	0.372166i
$857$	14.3234	−	24.8089i	0.489279	−	0.847457i	−0.510645	−	0.859792i	$-0.670593\pi$
$857$	14.3234	−	24.8089i	0.489279	−	0.847457i	0.999924	+	0.0123352i	$0.00392651\pi$
$858$		0			0
$859$	4.55274	−	2.62852i	0.155337	−	0.0896841i	−0.420316	−	0.907378i	$-0.638081\pi$
$859$	4.55274	−	2.62852i	0.155337	−	0.0896841i	0.575654	+	0.817694i	$0.304748\pi$
$860$	−22.6567			−0.772587
$861$		0			0
$862$	−33.2238			−1.13161
$863$	−17.4901	−	30.2937i	−0.595369	−	1.03121i	−0.993495	−	0.113879i	$-0.963673\pi$
$863$	−17.4901	−	30.2937i	−0.595369	−	1.03121i	0.398126	−	0.917331i	$-0.369661\pi$
$864$		0			0
$865$	33.1062	+	19.1139i	1.12565	+	0.649892i
$866$	−0.370981	−	0.642557i	−0.0126064	−	0.0218350i
$867$		0			0
$868$	0.927224	−	0.133672i	0.0314720	−	0.00453714i
$869$	0.846312	+	1.40916i	0.0287092	+	0.0478024i
$870$		0			0
$871$	−0.279739	+	0.484523i	−0.00947861	+	0.0164174i
$872$	−8.27635	+	14.3351i	−0.280273	+	0.485446i
$873$		0			0
$874$		−	0.350339i		−	0.0118504i
$875$	11.0419	−	27.6115i	0.373283	−	0.933438i
$876$		0			0
$877$	11.7405	−	6.77841i	0.396450	−	0.228890i	−0.288501	−	0.957480i	$-0.593157\pi$
$877$	11.7405	−	6.77841i	0.396450	−	0.228890i	0.684951	+	0.728589i	$0.259824\pi$
$878$	−14.0580	−	8.11637i	−0.474433	−	0.273914i
$879$		0			0
$880$	−3.57738	+	6.45061i	−0.120593	+	0.217450i
$881$		−	57.2399i		−	1.92846i	−0.265064	−	0.964231i	$-0.585393\pi$
$881$		−	57.2399i		−	1.92846i	0.265064	−	0.964231i	$-0.414607\pi$
$882$		0			0
$883$	−1.33594			−0.0449579			−0.0224789	−	0.999747i	$-0.507156\pi$
$883$	−1.33594			−0.0449579			−0.0224789	+	0.999747i	$0.507156\pi$
$884$	−0.0135078	−	0.0233961i	−0.000454315	−	0.000786897i
$885$		0			0
$886$	−9.45129	−	5.45671i	−0.317522	−	0.183322i
$887$	18.8847	+	32.7092i	0.634085	+	1.09827i	0.986708	+	0.162502i	$0.0519565\pi$
$887$	18.8847	+	32.7092i	0.634085	+	1.09827i	−0.352623	+	0.935766i	$0.614710\pi$
$888$		0			0
$889$	−5.02238	+	12.5591i	−0.168445	+	0.421217i
$890$			31.1331i			1.04358i
$891$		0			0
$892$	−9.80630	−	5.66167i	−0.328339	−	0.189567i
$893$	−4.89514	−	2.82621i	−0.163810	−	0.0945755i
$894$		0			0
$895$			25.8802i			0.865078i
$896$	−2.61868	+	0.377519i	−0.0874839	+	0.0126120i
$897$		0			0
$898$	20.4896	−	11.8297i	0.683748	−	0.394762i
$899$	−1.32950	+	2.30275i	−0.0443411	+	0.0768011i
$900$		0			0
$901$	−0.307266	−	0.532201i	−0.0102365	−	0.0177302i
$902$	−5.37671	−	8.95253i	−0.179025	−	0.298087i
$903$		0			0
$904$		−	8.19898i		−	0.272694i
$905$	24.4122	+	42.2832i	0.811490	+	1.40554i
$906$		0			0
$907$	−22.2803	+	38.5907i	−0.739807	+	1.28138i	0.212775	+	0.977101i	$0.431750\pi$
$907$	−22.2803	+	38.5907i	−0.739807	+	1.28138i	−0.952582	+	0.304282i	$0.901584\pi$
$908$	2.66623	+	4.61805i	0.0884819	+	0.153255i
$909$		0			0
$910$	0.521169	−	0.410171i	0.0172766	−	0.0135970i
$911$	17.1268			0.567436			0.283718	−	0.958908i	$-0.408432\pi$
$911$	17.1268			0.567436			0.283718	+	0.958908i	$0.408432\pi$
$912$		0			0
$913$	0.0325562	+	1.88750i	0.00107745	+	0.0624670i
$914$	12.2465	−	21.2115i	0.405077	−	0.701615i
$915$		0			0
$916$		−	18.0351i		−	0.595897i
$917$	0.777028	+	5.38989i	0.0256597	+	0.177990i
$918$		0			0
$919$	24.4668	−	14.1259i	0.807086	−	0.465971i	−0.0388569	−	0.999245i	$-0.512372\pi$
$919$	24.4668	−	14.1259i	0.807086	−	0.465971i	0.845943	+	0.533273i	$0.179038\pi$
$920$	−0.893197	+	1.54706i	−0.0294478	+	0.0510051i
$921$		0			0
$922$	−6.94356	+	4.00887i	−0.228674	+	0.132025i
$923$	−0.854436			−0.0281241
$924$		0			0
$925$	−0.395530			−0.0130049
$926$	27.9041	−	16.1105i	0.916986	−	0.529422i
$927$		0			0
$928$	3.75478	−	6.50347i	0.123257	−	0.213487i
$929$	23.1670	−	13.3755i	0.760085	−	0.438836i	−0.0692410	−	0.997600i	$-0.522058\pi$
$929$	23.1670	−	13.3755i	0.760085	−	0.438836i	0.829326	+	0.558764i	$0.188724\pi$
$930$		0			0
$931$	0.717559	−	2.96761i	0.0235171	−	0.0972594i
$932$		−	15.6773i		−	0.513528i
$933$		0			0
$934$	−6.68782	+	11.5836i	−0.218832	+	0.379028i
$935$	1.76770	−	0.0304899i	0.0578100	−	0.000997126i
$936$		0			0
$937$	−8.64381			−0.282381			−0.141190	−	0.989982i	$-0.545093\pi$
$937$	−8.64381			−0.282381			−0.141190	+	0.989982i	$0.545093\pi$
$938$	4.87640	−	12.1940i	0.159220	−	0.398149i
$939$		0			0
$940$	14.4110	+	24.9605i	0.470034	+	0.814122i
$941$	7.25889	−	12.5728i	0.236633	−	0.409861i	−0.723113	−	0.690730i	$-0.757289\pi$
$941$	7.25889	−	12.5728i	0.236633	−	0.409861i	0.959746	+	0.280869i	$0.0906227\pi$
$942$		0			0
$943$	−1.26457	−	2.19030i	−0.0411800	−	0.0713258i
$944$			3.78095i			0.123060i
$945$		0			0
$946$	−28.9653	+	17.3959i	−0.941742	+	0.565591i
$947$	−5.90549	−	10.2286i	−0.191903	−	0.332385i	0.753978	−	0.656899i	$-0.228132\pi$
$947$	−5.90549	−	10.2286i	−0.191903	−	0.332385i	−0.945881	+	0.324515i	$0.894799\pi$
$948$		0			0
$949$	−0.270314	+	0.468198i	−0.00877478	+	0.0151984i
$950$	0.0203278	−	0.0117362i	0.000659520	−	0.000380774i
$951$		0			0
$952$	0.392193	+	0.498326i	0.0127110	+	0.0161508i
$953$			5.83407i			0.188984i	0.995526	+	0.0944920i	$0.0301227\pi$
$953$			5.83407i			0.188984i	−0.995526	+	0.0944920i	$0.969877\pi$
$954$		0			0
$955$	11.5281	+	6.65575i	0.373040	+	0.215375i
$956$	−17.0596	−	9.84934i	−0.551746	−	0.318550i
$957$		0			0
$958$			34.7257i			1.12194i
$959$	−39.1926	+	30.8454i	−1.26559	+	0.996049i
$960$		0			0
$961$	−15.4373	−	26.7382i	−0.497978	−	0.862523i
$962$	−0.717414	−	0.414199i	−0.0231303	−	0.0133543i
$963$		0			0
$964$	−3.85279	−	6.67323i	−0.124090	−	0.214930i
$965$	18.8872			0.608001
$966$		0			0
$967$			52.9190i			1.70176i	0.525359	+	0.850881i	$0.323931\pi$
$967$			52.9190i			1.70176i	−0.525359	+	0.850881i	$0.676069\pi$
$968$	0.379351	+	10.9935i	0.0121928	+	0.353343i
$969$		0			0
$970$	20.5524	+	11.8659i	0.659898	+	0.380992i
$971$	−37.2182	+	21.4879i	−1.19439	+	0.689580i	−0.959299	−	0.282394i	$-0.908872\pi$
$971$	−37.2182	+	21.4879i	−1.19439	+	0.689580i	−0.235089	+	0.971974i	$0.575538\pi$
$972$		0			0
$973$	−25.8025	−	10.3184i	−0.827189	−	0.330794i
$974$			19.6614i			0.629991i
$975$		0			0
$976$	0.525000	−	0.909326i	0.0168048	−	0.0291068i
$977$	−5.72694	+	9.91935i	−0.183221	+	0.317348i	−0.942976	−	0.332862i	$-0.891986\pi$
$977$	−5.72694	+	9.91935i	−0.183221	+	0.317348i	0.759755	+	0.650210i	$0.225319\pi$
$978$		0			0
$979$	23.9041	+	39.8018i	0.763980	+	1.27207i
$980$	−10.7346	+	11.2752i	−0.342906	+	0.360174i
$981$		0			0
$982$	15.8167	+	27.3953i	0.504731	+	0.874220i
$983$	41.5723	+	24.0018i	1.32595	+	0.765538i	0.984671	−	0.174423i	$-0.0558061\pi$
$983$	41.5723	+	24.0018i	1.32595	+	0.765538i	0.341281	+	0.939961i	$0.389139\pi$
$984$		0			0
$985$	4.12674	+	7.14772i	0.131489	+	0.227745i
$986$	−1.79993			−0.0573215
$987$		0			0
$988$	0.0491608			0.00156401
$989$	−7.08654	+	4.09141i	−0.225339	+	0.130099i
$990$		0			0
$991$	−1.92802	+	3.33943i	−0.0612456	+	0.106081i	−0.895022	−	0.446021i	$-0.852841\pi$
$991$	−1.92802	+	3.33943i	−0.0612456	+	0.106081i	0.833777	+	0.552102i	$0.186174\pi$
$992$	−0.177040	−	0.306643i	−0.00562104	−	0.00973593i
$993$		0			0
$994$	19.8513	−	2.86185i	0.629646	−	0.0907723i
$995$	−12.8191			−0.406393
$996$		0			0
$997$	−2.19567	+	3.80302i	−0.0695376	+	0.120443i	−0.898698	−	0.438568i	$-0.855486\pi$
$997$	−2.19567	+	3.80302i	−0.0695376	+	0.120443i	0.829160	+	0.559011i	$0.188819\pi$
$998$	31.3830	+	18.1190i	0.993412	+	0.573547i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.a.703.6		16
3.2	odd	2		462.2.p.a.241.3	✓	16
7.5	odd	6		1386.2.bk.b.901.2		16
11.10	odd	2		1386.2.bk.b.703.2		16
21.5	even	6		462.2.p.b.439.7	yes	16
21.11	odd	6		3234.2.e.a.2155.6		16
21.17	even	6		3234.2.e.b.2155.3		16
33.32	even	2		462.2.p.b.241.7	yes	16
77.54	even	6	inner	1386.2.bk.a.901.6		16
231.32	even	6		3234.2.e.b.2155.14		16
231.131	odd	6		462.2.p.a.439.3	yes	16
231.164	odd	6		3234.2.e.a.2155.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.3	✓	16	3.2	odd	2
462.2.p.a.439.3	yes	16	231.131	odd	6
462.2.p.b.241.7	yes	16	33.32	even	2
462.2.p.b.439.7	yes	16	21.5	even	6
1386.2.bk.a.703.6		16	1.1	even	1	trivial
1386.2.bk.a.901.6		16	77.54	even	6	inner
1386.2.bk.b.703.2		16	11.10	odd	2
1386.2.bk.b.901.2		16	7.5	odd	6
3234.2.e.a.2155.6		16	21.11	odd	6
3234.2.e.a.2155.11		16	231.164	odd	6
3234.2.e.b.2155.3		16	21.17	even	6
3234.2.e.b.2155.14		16	231.32	even	6

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(2.45660 + 0.982398i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(2.45660 + 0.982398i) q^{7} -1.00000i q^{8} +(-1.11200 + 1.92604i) q^{10} +(0.0571978 + 3.31613i) q^{11} -0.112712 q^{13} +(2.61868 - 0.377519i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.119843 + 0.207574i) q^{17} +(-0.218080 - 0.377726i) q^{19} +2.22400i q^{20} +(1.70760 + 2.84326i) q^{22} +(0.401617 + 0.695621i) q^{23} +(-0.0269081 + 0.0466061i) q^{25} +(-0.0976119 + 0.0563562i) q^{26} +(2.07908 - 1.63628i) q^{28} +7.50955i q^{29} +(0.306643 + 0.177040i) q^{31} +(-0.866025 - 0.500000i) q^{32} +0.239685i q^{34} +(-5.82395 + 0.839603i) q^{35} +(3.67483 + 6.36499i) q^{37} +(-0.377726 - 0.218080i) q^{38} +(1.11200 + 1.92604i) q^{40} -3.14869 q^{41} +10.1874i q^{43} +(2.90045 + 1.60853i) q^{44} +(0.695621 + 0.401617i) q^{46} +(11.2232 - 6.47974i) q^{47} +(5.06979 + 4.82672i) q^{49} +0.0538161i q^{50} +(-0.0563562 + 0.0976119i) q^{52} +(-1.28196 + 2.22041i) q^{53} +(-3.79771 - 6.32340i) q^{55} +(0.982398 - 2.45660i) q^{56} +(3.75478 + 6.50347i) q^{58} +(-3.27440 - 1.89048i) q^{59} +(0.525000 + 0.909326i) q^{61} +0.354081 q^{62} -1.00000 q^{64} +(0.217089 - 0.125336i) q^{65} +(2.48189 - 4.29875i) q^{67} +(0.119843 + 0.207574i) q^{68} +(-4.62388 + 3.63909i) q^{70} +7.58067 q^{71} +(2.39827 - 4.15392i) q^{73} +(6.36499 + 3.67483i) q^{74} -0.436161 q^{76} +(-3.11725 + 8.20261i) q^{77} +(0.429215 - 0.247807i) q^{79} +(1.92604 + 1.11200i) q^{80} +(-2.72685 + 1.57435i) q^{82} +0.569186 q^{83} -0.533061i q^{85} +(5.09368 + 8.82251i) q^{86} +(3.31613 - 0.0571978i) q^{88} +(12.1232 - 6.99934i) q^{89} +(-0.276890 - 0.110729i) q^{91} +0.803234 q^{92} +(6.47974 - 11.2232i) q^{94} +(0.840064 + 0.485011i) q^{95} -10.6708i q^{97} +(6.80393 + 1.64517i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7} + 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} - 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} + 8 q^{35} + 14 q^{37} + 12 q^{38} - 2 q^{40} - 32 q^{41} - 4 q^{44} + 18 q^{46} + 24 q^{47} - 6 q^{49} - 14 q^{55} - 4 q^{56} + 28 q^{61} + 8 q^{62} - 16 q^{64} - 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} - 44 q^{73} - 24 q^{74} - 20 q^{76} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} + 14 q^{94} - 72 q^{95} + 40 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7 + 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 - 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 + 8 * q^35 + 14 * q^37 + 12 * q^38 - 2 * q^40 - 32 * q^41 - 4 * q^44 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 14 * q^55 - 4 * q^56 + 28 * q^61 + 8 * q^62 - 16 * q^64 - 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 - 44 * q^73 - 24 * q^74 - 20 * q^76 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 + 14 * q^94 - 72 * q^95 + 40 * q^98

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