LMFDB - Embedded newform 1386.2.bk.b.703.2

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			703.2
Root			$0.500000 + 1.35798i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.b.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(-2.45660 - 0.982398i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(-2.45660 - 0.982398i) q^{7} +1.00000i q^{8} +(1.11200 - 1.92604i) q^{10} +(-2.90045 + 1.60853i) q^{11} +0.112712 q^{13} +(2.61868 - 0.377519i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.119843 - 0.207574i) q^{17} +(0.218080 + 0.377726i) q^{19} +2.22400i q^{20} +(1.70760 - 2.84326i) q^{22} +(0.401617 + 0.695621i) q^{23} +(-0.0269081 + 0.0466061i) q^{25} +(-0.0976119 + 0.0563562i) q^{26} +(-2.07908 + 1.63628i) q^{28} -7.50955i q^{29} +(0.306643 + 0.177040i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.239685i q^{34} +(5.82395 - 0.839603i) q^{35} +(3.67483 + 6.36499i) q^{37} +(-0.377726 - 0.218080i) q^{38} +(-1.11200 - 1.92604i) q^{40} +3.14869 q^{41} -10.1874i q^{43} +(-0.0571978 + 3.31613i) q^{44} +(-0.695621 - 0.401617i) q^{46} +(11.2232 - 6.47974i) q^{47} +(5.06979 + 4.82672i) q^{49} -0.0538161i q^{50} +(0.0563562 - 0.0976119i) q^{52} +(-1.28196 + 2.22041i) q^{53} +(3.79771 - 6.32340i) q^{55} +(0.982398 - 2.45660i) q^{56} +(3.75478 + 6.50347i) q^{58} +(-3.27440 - 1.89048i) q^{59} +(-0.525000 - 0.909326i) q^{61} -0.354081 q^{62} -1.00000 q^{64} +(-0.217089 + 0.125336i) q^{65} +(2.48189 - 4.29875i) q^{67} +(-0.119843 - 0.207574i) q^{68} +(-4.62388 + 3.63909i) q^{70} +7.58067 q^{71} +(-2.39827 + 4.15392i) q^{73} +(-6.36499 - 3.67483i) q^{74} +0.436161 q^{76} +(8.70548 - 1.10212i) q^{77} +(-0.429215 + 0.247807i) q^{79} +(1.92604 + 1.11200i) q^{80} +(-2.72685 + 1.57435i) q^{82} -0.569186 q^{83} +0.533061i q^{85} +(5.09368 + 8.82251i) q^{86} +(-1.60853 - 2.90045i) q^{88} +(12.1232 - 6.99934i) q^{89} +(-0.276890 - 0.110729i) q^{91} +0.803234 q^{92} +(-6.47974 + 11.2232i) q^{94} +(-0.840064 - 0.485011i) q^{95} -10.6708i q^{97} +(-6.80393 - 1.64517i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 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 + 52 * q^77 + 30 * q^79 + 12 * q^80 - 12 * q^82 + 8 * q^83 + 12 * q^86 - 2 * 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
$11$	−2.90045	+	1.60853i	−0.874519	+	0.484990i
$11$	−2.90045	+	1.60853i	−0.874519	+	0.484990i
$12$		0			0
$13$	0.112712			0.0312608			0.0156304	−	0.999878i	$-0.495024\pi$
$13$	0.112712			0.0312608			0.0156304	+	0.999878i	$0.495024\pi$
$14$	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	−0.851126	−	0.524961i	$-0.824080\pi$
$17$	0.119843	−	0.207574i	0.0290661	−	0.0503440i	0.880193	+	0.474617i	$0.157413\pi$
$18$		0			0
$19$	0.218080	+	0.377726i	0.0500311	+	0.0866564i	0.889956	−	0.456046i	$-0.150735\pi$
$19$	0.218080	+	0.377726i	0.0500311	+	0.0866564i	−0.839925	+	0.542702i	$0.817401\pi$
$20$			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	$-0.754409\pi$
$29$		−	7.50955i		−	1.39449i	0.716833	−	0.697245i	$-0.245591\pi$
$30$		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	$-0.420926\pi$
$41$	3.14869			0.491743			0.245872	+	0.969302i	$0.420926\pi$
$42$		0			0
$43$		−	10.1874i		−	1.55356i	−0.629774	−	0.776779i	$-0.716852\pi$
$43$		−	10.1874i		−	1.55356i	0.629774	−	0.776779i	$-0.283148\pi$
$44$	−0.0571978	+	3.31613i	−0.00862289	+	0.499926i
$45$		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	0.830457	−	0.557083i	$-0.188079\pi$
$61$	−0.525000	−	0.909326i	−0.0672193	−	0.116427i	−0.897676	+	0.440655i	$0.854746\pi$
$62$	−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	−0.971556	−	0.236809i	$-0.923899\pi$
$73$	−2.39827	+	4.15392i	−0.280696	+	0.486179i	0.690861	+	0.722988i	$0.257232\pi$
$74$	−6.36499	−	3.67483i	−0.739915	−	0.427190i
$75$		0			0
$76$	0.436161			0.0500311
$77$	8.70548	−	1.10212i	0.992081	−	0.125598i
$78$		0			0
$79$	−0.429215	+	0.247807i	−0.0482905	+	0.0278805i	−0.523951	−	0.851748i	$-0.675542\pi$
$79$	−0.429215	+	0.247807i	−0.0482905	+	0.0278805i	0.475660	+	0.879629i	$0.342209\pi$
$80$	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	$-0.509945\pi$
$83$	−0.569186			−0.0624763			−0.0312381	+	0.999512i	$0.509945\pi$
$84$		0			0
$85$			0.533061i			0.0578186i
$86$	5.09368	+	8.82251i	0.549266	+	0.951356i
$87$		0			0
$88$	−1.60853	−	2.90045i	−0.171470	−	0.309189i
$89$	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	$-0.409177\pi$
$101$	9.76595	−	16.9151i	0.971748	−	1.68312i	0.690274	−	0.723548i	$-0.257490\pi$
$102$		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	−0.923389	−	0.383867i	$-0.874592\pi$
$107$	−10.8886	+	6.28656i	−1.05264	+	0.607745i	−0.129256	+	0.991611i	$0.541259\pi$
$108$		0			0
$109$	14.3351	+	8.27635i	1.37305	+	0.792730i	0.991311	−	0.131540i	$-0.0419921\pi$
$109$	14.3351	+	8.27635i	1.37305	+	0.792730i	0.381739	+	0.924270i	$0.375325\pi$
$110$	−0.127208	+	7.37508i	−0.0121288	+	0.703187i
$111$		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
$121$	5.82526	−	9.33094i	0.529569	−	0.848267i
$122$	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	$-0.927166\pi$
$127$		−	5.11237i		−	0.453650i	0.973936	−	0.226825i	$-0.0728345\pi$
$128$	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	0.817560	−	0.575843i	$-0.195326\pi$
$131$	−1.02912	−	1.78250i	−0.0899150	−	0.155737i	−0.907475	+	0.420106i	$0.861993\pi$
$132$		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	$-0.353047\pi$
$139$	10.5033			0.890880			0.445440	+	0.895312i	$0.353047\pi$
$140$	2.18486	−	5.46349i	0.184654	−	0.461749i
$141$		0			0
$142$	−6.56505	+	3.79033i	−0.550927	+	0.318078i
$143$	−0.326917	+	0.181302i	−0.0273382	+	0.0151612i
$144$		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	−0.918954	−	0.394364i	$-0.870965\pi$
$149$	−12.6570	+	7.30752i	−1.03690	+	0.598656i	−0.117948	+	0.993020i	$0.537631\pi$
$150$		0			0
$151$	1.57663	+	0.910267i	0.128304	+	0.0740764i	0.562778	−	0.826608i	$-0.309732\pi$
$151$	1.57663	+	0.910267i	0.128304	+	0.0740764i	−0.434474	+	0.900684i	$0.643066\pi$
$152$	−0.377726	+	0.218080i	−0.0306377	+	0.0176887i
$153$		0			0
$154$	−6.98810	+	5.30720i	−0.563117	+	0.427667i
$155$	−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	$-0.246271\pi$
$167$	18.4885			1.43068			0.715341	+	0.698775i	$0.246271\pi$
$168$		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	$0.0599988\pi$
$173$	8.59437	+	14.8859i	0.653418	+	1.13175i	−0.328870	+	0.944375i	$0.606668\pi$
$174$		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
$187$	−0.0137095	+	0.794828i	−0.00100254	+	0.0581236i
$188$		−	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	0.740772	−	0.671756i	$-0.234460\pi$
$193$	7.35467	+	4.24622i	0.529401	+	0.305650i	−0.211372	+	0.977406i	$0.567793\pi$
$194$	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	$0.0422048\pi$
$197$			3.71109i			0.264404i	−0.991223	+	0.132202i	$0.957795\pi$
$198$		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	$-0.707037\pi$
$211$		−	23.1201i		−	1.59165i	0.605524	−	0.795827i	$-0.292963\pi$
$212$	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
$220$	−3.57738	−	6.45061i	−0.241187	−	0.434900i
$221$	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	−0.763875	−	0.645364i	$-0.776706\pi$
$227$	2.66623	−	4.61805i	0.176964	−	0.306510i	0.940839	+	0.338853i	$0.110039\pi$
$228$		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	−0.873765	−	0.486349i	$-0.838328\pi$
$233$	−13.5770	+	7.83866i	−0.889456	+	0.513528i	−0.0156917	+	0.999877i	$0.504995\pi$
$234$		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	$0.219867\pi$
$239$			19.6987i			1.27420i	−0.770780	+	0.637101i	$0.780133\pi$
$240$		0			0
$241$	−3.85279	+	6.67323i	−0.248180	+	0.429861i	−0.963021	−	0.269427i	$-0.913166\pi$
$241$	−3.85279	+	6.67323i	−0.248180	+	0.429861i	0.714841	+	0.699287i	$0.246499\pi$
$242$	−0.379351	+	10.9935i	−0.0243856	+	0.706686i
$243$		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	0.253046	−	0.967454i	$-0.418568\pi$
$263$	−7.43191	−	4.29081i	−0.458271	−	0.264583i	−0.711317	+	0.702871i	$0.751901\pi$
$264$		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	0.809194	−	0.587542i	$-0.199904\pi$
$271$	−1.71583	−	2.97190i	−0.104229	−	0.180530i	−0.913423	+	0.407012i	$0.866571\pi$
$272$	−0.239685			−0.0145331
$273$		0			0
$274$		−	18.8509i		−	1.13882i
$275$	0.00307816	−	0.178461i	0.000185620	−	0.0107616i
$276$		0			0
$277$	1.35959	+	0.784960i	0.0816899	+	0.0471637i	0.540289	−	0.841480i	$-0.318315\pi$
$277$	1.35959	+	0.784960i	0.0816899	+	0.0471637i	−0.458599	+	0.888643i	$0.651648\pi$
$278$	−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	$-0.966721\pi$
$281$		−	3.49877i		−	0.208719i	0.994540	−	0.104360i	$-0.0332793\pi$
$282$		0			0
$283$	11.1106	−	19.2440i	0.660454	−	1.14394i	−0.320043	−	0.947403i	$-0.603697\pi$
$283$	11.1106	−	19.2440i	0.660454	−	1.14394i	0.980496	−	0.196537i	$-0.0629694\pi$
$284$	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	$-0.564177\pi$
$293$	−6.85562			−0.400510			−0.200255	+	0.979744i	$0.564177\pi$
$294$		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	$-0.757377\pi$
$307$	−25.3466			−1.44661			−0.723303	+	0.690531i	$0.757377\pi$
$308$	3.39827	−	8.09022i	0.193635	−	0.460983i
$309$		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
$319$	12.0794	+	21.7811i	0.676314	+	1.21951i
$320$	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	$0.345406\pi$
$337$			32.4695i			1.76872i	−0.466801	+	0.884362i	$0.654594\pi$
$338$	11.2473	−	6.49365i	0.611774	−	0.353208i
$339$		0			0
$340$	0.461644	+	0.266530i	0.0250362	+	0.0144546i
$341$	−1.17418	−	0.0202526i	−0.0635854	−	0.00109674i
$342$		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	−0.432183	−	0.901786i	$-0.642256\pi$
$347$	−26.6239	−	15.3713i	−1.42924	−	0.825174i	−0.997061	+	0.0766119i	$0.975590\pi$
$348$		0			0
$349$	−24.5576			−1.31454			−0.657269	−	0.753656i	$-0.728288\pi$
$349$	−24.5576			−1.31454			−0.657269	+	0.753656i	$0.728288\pi$
$350$	−0.0528689	+	0.132205i	−0.00282596	+	0.00706665i
$351$		0			0
$352$	−3.31613	−	0.0571978i	−0.176750	−	0.00304865i
$353$	−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	−0.817519	−	0.575901i	$-0.804651\pi$
$359$	−13.7848	+	7.95866i	−0.727534	+	0.420042i	0.0899854	+	0.995943i	$0.471318\pi$
$360$		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	−0.981813	−	0.189850i	$-0.939200\pi$
$373$	−25.2676	+	14.5882i	−1.30831	+	0.755350i	−0.326492	+	0.945200i	$0.605867\pi$
$374$	−0.385541	−	0.695196i	−0.0199359	−	0.0359477i
$375$		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
$385$	−15.5416	+	11.8032i	−0.792071	+	0.601548i
$386$	−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	$-0.645644\pi$
$409$	11.2457	−	19.4781i	0.556065	−	0.963132i	0.997820	−	0.0659967i	$-0.0210227\pi$
$410$	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
$418$	1.44637	+	0.0249474i	0.0707441	+	0.00122022i
$419$		−	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	0.992854	−	0.119338i	$-0.0380771\pi$
$431$	28.7727	+	16.6119i	1.38593	+	0.800168i	0.393077	+	0.919505i	$0.371410\pi$
$432$		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	0.992095	−	0.125486i	$-0.0400492\pi$
$439$	8.11637	+	14.0580i	0.387373	+	0.670950i	−0.604722	+	0.796437i	$0.706716\pi$
$440$	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
$451$	−9.13263	+	5.06477i	−0.430039	+	0.238491i
$452$	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	−0.905941	−	0.423404i	$-0.860835\pi$
$457$	−21.2115	+	12.2465i	−0.992233	+	0.572866i	−0.0862919	+	0.996270i	$0.527502\pi$
$458$	−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	$-0.440217\pi$
$461$	8.01773			0.373423			0.186712	+	0.982415i	$0.440217\pi$
$462$		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
$473$	16.3867	+	29.5480i	0.753460	+	1.35862i
$474$		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	$-0.541679\pi$
$479$	17.3629	−	30.0734i	0.793330	−	1.37409i	0.923894	−	0.382648i	$-0.124988\pi$
$480$		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	$-0.746974\pi$
$491$		−	31.6334i		−	1.42760i	0.700352	−	0.713798i	$-0.253026\pi$
$492$		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	$-0.282194\pi$
$503$	28.3530			1.26420			0.632098	+	0.774889i	$0.282194\pi$
$504$		0			0
$505$			43.4390i			1.93301i
$506$	2.66363	+	0.0459432i	0.118413	+	0.00204242i
$507$		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	$-0.902283\pi$
$523$	−16.8849	−	29.2456i	−0.738327	−	1.27882i	0.214921	−	0.976631i	$-0.431050\pi$
$524$	−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
$539$	−22.4686	−	5.84477i	−0.967792	−	0.251752i
$540$		0			0
$541$	19.6218	−	11.3286i	0.843607	−	0.487057i	−0.0148819	−	0.999889i	$-0.504737\pi$
$541$	19.6218	−	11.3286i	0.843607	−	0.487057i	0.858489	+	0.512833i	$0.171404\pi$
$542$	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	$0.0787163\pi$
$547$			11.4499i			0.489563i	−0.969578	+	0.244782i	$0.921284\pi$
$548$	9.42545	+	16.3254i	0.402635	+	0.697385i
$549$		0			0
$550$	0.0865649	+	0.156091i	0.00369114	+	0.00665575i
$551$	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	$0.0755552\pi$
$557$	39.2147	+	22.6406i	1.66158	+	0.959314i	0.689619	+	0.724173i	$0.257778\pi$
$558$		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	$-0.634709\pi$
$563$	13.8636	−	24.0125i	0.584283	−	1.01201i	0.994964	−	0.100228i	$-0.0319573\pi$
$564$		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	−0.762314	−	0.647207i	$-0.775937\pi$
$569$	−13.9061	+	8.02868i	−0.582973	+	0.336580i	0.179341	+	0.983787i	$0.442603\pi$
$570$		0			0
$571$	8.42022	+	4.86141i	0.352375	+	0.203444i	0.665731	−	0.746192i	$-0.268120\pi$
$571$	8.42022	+	4.86141i	0.352375	+	0.203444i	−0.313356	+	0.949636i	$0.601453\pi$
$572$	−0.00644690	+	0.373769i	−0.000269559	+	0.0156281i
$573$		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
$583$	0.146650	−	8.50227i	0.00607363	−	0.352128i
$584$	−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	0.932273	−	0.361756i	$-0.117823\pi$
$593$	3.72204	+	6.44677i	0.152846	+	0.264737i	−0.779427	+	0.626494i	$0.784489\pi$
$594$		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	$-0.543988\pi$
$601$	−6.75417			−0.275508			−0.137754	+	0.990466i	$0.543988\pi$
$602$	−3.84592	−	26.6774i	−0.156748	−	1.08729i
$603$		0			0
$604$	1.57663	−	0.910267i	0.0641521	−	0.0370382i
$605$	−0.843677	+	24.4495i	−0.0343003	+	0.994012i
$606$		0			0
$607$	18.7854	+	32.5373i	0.762476	+	1.32065i	0.941571	+	0.336815i	$0.109350\pi$
$607$	18.7854	+	32.5373i	0.762476	+	1.32065i	−0.179095	+	0.983832i	$0.557317\pi$
$608$			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	−0.326544	−	0.945182i	$-0.605884\pi$
$613$	−32.3937	−	18.7025i	−1.30837	−	0.755387i	−0.981824	+	0.189795i	$0.939218\pi$
$614$	21.9508	−	12.6733i	0.885861	−	0.511452i
$615$		0			0
$616$	1.10212	+	8.70548i	0.0444057	+	0.350754i
$617$	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
$649$	12.5381	+	0.216262i	0.492165	+	0.00848903i
$650$		−	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	$-0.553524\pi$
$659$		−	50.6179i		−	1.97179i	0.167358	−	0.985896i	$-0.446476\pi$
$660$		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	$-0.839848\pi$
$673$		−	25.0173i		−	0.964345i	0.876076	−	0.482172i	$-0.160152\pi$
$674$	−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	$0.215323\pi$
$677$	24.2515	+	42.0048i	0.932059	+	1.61437i	0.152263	+	0.988340i	$0.451344\pi$
$678$		0			0
$679$	−10.4830	+	26.2139i	−0.402299	+	1.00600i
$680$	−0.533061			−0.0204419
$681$		0			0
$682$	1.02700	−	0.569550i	0.0393257	−	0.0218092i
$683$	−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	$0.203097\pi$
$701$			31.5402i			1.19126i	−0.803260	+	0.595628i	$0.796903\pi$
$702$		0			0
$703$	−1.60282	+	2.77616i	−0.0604514	+	0.104705i
$704$	2.90045	−	1.60853i	0.109315	−	0.0606238i
$705$		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	0.569772	−	0.821803i	$-0.307031\pi$
$733$	−11.5556	−	20.0149i	−0.426816	−	0.739266i	−0.996588	+	0.0825361i	$0.973698\pi$
$734$	25.7459			0.950297
$735$		0			0
$736$			0.803234i			0.0296076i
$737$	−0.283917	+	16.4605i	−0.0104582	+	0.606331i
$738$		0			0
$739$	−24.3934	−	14.0836i	−0.897327	−	0.518072i	−0.0209949	−	0.999780i	$-0.506683\pi$
$739$	−24.3934	−	14.0836i	−0.897327	−	0.518072i	−0.876332	+	0.481708i	$0.840017\pi$
$740$	−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	$-0.996173\pi$
$743$		−	0.655454i		−	0.0240463i	0.999928	−	0.0120231i	$-0.00382718\pi$
$744$		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	$-0.881564\pi$
$761$	−21.5347	−	37.2992i	−0.780632	−	1.35209i	0.150942	−	0.988543i	$-0.451769\pi$
$762$		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	$-0.229563\pi$
$769$	41.6527			1.50204			0.751018	+	0.660282i	$0.229563\pi$
$770$	7.55777	−	17.9927i	0.272363	−	0.648411i
$771$		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
$781$	−21.9874	+	12.1937i	−0.786770	+	0.436326i
$782$	−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	−0.589356	−	0.807873i	$-0.700619\pi$
$787$	11.3606	−	19.6771i	0.404961	−	0.701413i	0.994317	+	0.106461i	$0.0339519\pi$
$788$	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
$803$	0.274351	−	15.9059i	0.00968163	−	0.561308i
$804$		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	0.457306	−	0.889310i	$-0.348815\pi$
$809$	−2.39507	−	1.38280i	−0.0842063	−	0.0486165i	−0.541512	+	0.840693i	$0.682148\pi$
$810$		0			0
$811$	25.2486			0.886597			0.443298	−	0.896374i	$-0.353808\pi$
$811$	25.2486			0.886597			0.443298	+	0.896374i	$0.353808\pi$
$812$	12.2877	+	15.6130i	0.431215	+	0.547908i
$813$		0			0
$814$	24.3724	+	0.420384i	0.854253	+	0.0147345i
$815$	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	0.201009	−	0.979589i	$-0.435578\pi$
$821$	32.9471	−	19.0220i	1.14986	−	0.663874i	0.948854	+	0.315716i	$0.102245\pi$
$822$		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	$-0.960903\pi$
$827$		−	7.04659i		−	0.245034i	0.992466	−	0.122517i	$-0.0390966\pi$
$828$		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
$836$	−1.26506	+	0.701578i	−0.0437532	+	0.0242646i
$837$		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
$847$	−23.4770	+	17.1997i	−0.806680	+	0.590988i
$848$	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	$-0.724707\pi$
$853$	−37.8949			−1.29750			−0.648749	+	0.761003i	$0.724707\pi$
$854$	−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	−0.999924	−	0.0123352i	$-0.996073\pi$
$857$	−14.3234	+	24.8089i	−0.489279	+	0.847457i	0.510645	+	0.859792i	$0.329407\pi$
$858$		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	−0.684951	−	0.728589i	$-0.740176\pi$
$877$	−11.7405	+	6.77841i	−0.396450	+	0.228890i	0.288501	+	0.957480i	$0.406843\pi$
$878$	−14.0580	−	8.11637i	−0.474433	−	0.273914i
$879$		0			0
$880$	−7.37508	−	0.127208i	−0.248614	−	0.00428818i
$881$		−	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	$-0.948043\pi$
$887$	−18.8847	−	32.7092i	−0.634085	−	1.09827i	0.352623	−	0.935766i	$-0.385290\pi$
$888$		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
$913$	1.65090	−	0.915553i	0.0546367	−	0.0303004i
$914$	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	−0.845943	−	0.533273i	$-0.820962\pi$
$919$	−24.4668	+	14.1259i	−0.807086	+	0.465971i	0.0388569	+	0.999245i	$0.487628\pi$
$920$	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
$935$	−0.857445	−	1.54612i	−0.0280414	−	0.0505635i
$936$		0			0
$937$	8.64381			0.282381			0.141190	−	0.989982i	$-0.454907\pi$
$937$	8.64381			0.282381			0.141190	+	0.989982i	$0.454907\pi$
$938$	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	−0.959746	−	0.280869i	$-0.909377\pi$
$941$	−7.25889	+	12.5728i	−0.236633	+	0.409861i	0.723113	+	0.690730i	$0.242711\pi$
$942$		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	$-0.969877\pi$
$953$		−	5.83407i		−	0.188984i	0.995526	−	0.0944920i	$-0.0301227\pi$
$954$		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	$-0.676069\pi$
$967$		−	52.9190i		−	1.70176i	0.525359	−	0.850881i	$-0.323931\pi$
$968$	9.33094	+	5.82526i	0.299908	+	0.187231i
$969$		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	−0.829160	−	0.559011i	$-0.811181\pi$
$997$	2.19567	−	3.80302i	0.0695376	−	0.120443i	0.898698	+	0.438568i	$0.144514\pi$
$998$	−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.b.703.2		16
3.2	odd	2		462.2.p.b.241.7	yes	16
7.5	odd	6		1386.2.bk.a.901.6		16
11.10	odd	2		1386.2.bk.a.703.6		16
21.5	even	6		462.2.p.a.439.3	yes	16
21.11	odd	6		3234.2.e.b.2155.14		16
21.17	even	6		3234.2.e.a.2155.11		16
33.32	even	2		462.2.p.a.241.3	✓	16
77.54	even	6	inner	1386.2.bk.b.901.2		16
231.32	even	6		3234.2.e.a.2155.6		16
231.131	odd	6		462.2.p.b.439.7	yes	16
231.164	odd	6		3234.2.e.b.2155.3		16

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(-2.45660 - 0.982398i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.92604 + 1.11200i) q^{5} +(-2.45660 - 0.982398i) q^{7} +1.00000i q^{8} +(1.11200 - 1.92604i) q^{10} +(-2.90045 + 1.60853i) q^{11} +0.112712 q^{13} +(2.61868 - 0.377519i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.119843 - 0.207574i) q^{17} +(0.218080 + 0.377726i) q^{19} +2.22400i q^{20} +(1.70760 - 2.84326i) q^{22} +(0.401617 + 0.695621i) q^{23} +(-0.0269081 + 0.0466061i) q^{25} +(-0.0976119 + 0.0563562i) q^{26} +(-2.07908 + 1.63628i) q^{28} -7.50955i q^{29} +(0.306643 + 0.177040i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.239685i q^{34} +(5.82395 - 0.839603i) q^{35} +(3.67483 + 6.36499i) q^{37} +(-0.377726 - 0.218080i) q^{38} +(-1.11200 - 1.92604i) q^{40} +3.14869 q^{41} -10.1874i q^{43} +(-0.0571978 + 3.31613i) q^{44} +(-0.695621 - 0.401617i) q^{46} +(11.2232 - 6.47974i) q^{47} +(5.06979 + 4.82672i) q^{49} -0.0538161i q^{50} +(0.0563562 - 0.0976119i) q^{52} +(-1.28196 + 2.22041i) q^{53} +(3.79771 - 6.32340i) q^{55} +(0.982398 - 2.45660i) q^{56} +(3.75478 + 6.50347i) q^{58} +(-3.27440 - 1.89048i) q^{59} +(-0.525000 - 0.909326i) q^{61} -0.354081 q^{62} -1.00000 q^{64} +(-0.217089 + 0.125336i) q^{65} +(2.48189 - 4.29875i) q^{67} +(-0.119843 - 0.207574i) q^{68} +(-4.62388 + 3.63909i) q^{70} +7.58067 q^{71} +(-2.39827 + 4.15392i) q^{73} +(-6.36499 - 3.67483i) q^{74} +0.436161 q^{76} +(8.70548 - 1.10212i) q^{77} +(-0.429215 + 0.247807i) q^{79} +(1.92604 + 1.11200i) q^{80} +(-2.72685 + 1.57435i) q^{82} -0.569186 q^{83} +0.533061i q^{85} +(5.09368 + 8.82251i) q^{86} +(-1.60853 - 2.90045i) q^{88} +(12.1232 - 6.99934i) q^{89} +(-0.276890 - 0.110729i) q^{91} +0.803234 q^{92} +(-6.47974 + 11.2232i) q^{94} +(-0.840064 - 0.485011i) q^{95} -10.6708i q^{97} +(-6.80393 - 1.64517i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7} - 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} + 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} - 8 q^{35} + 14 q^{37} + 12 q^{38} + 2 q^{40} + 32 q^{41} - 4 q^{44} - 18 q^{46} + 24 q^{47} - 6 q^{49} + 14 q^{55} - 4 q^{56} - 28 q^{61} - 8 q^{62} - 16 q^{64} + 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} + 44 q^{73} + 24 q^{74} + 20 q^{76} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} - 14 q^{94} + 72 q^{95} - 40 q^{98}+O(q^{100}) \) 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 + 52 * q^77 + 30 * q^79 + 12 * q^80 - 12 * q^82 + 8 * q^83 + 12 * q^86 - 2 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 - 14 * q^94 + 72 * q^95 - 40 * q^98

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