LMFDB - Embedded newform 1386.2.k.w.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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, 2, 0]))

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

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

chi := DirichletCharacter("1386.793");

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.k (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.500000 - 1.51496i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.w.793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.227452 + 0.393958i) q^{5} +(-0.227452 - 2.63596i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.227452 + 0.393958i) q^{5} +(-0.227452 - 2.63596i) q^{7} -1.00000 q^{8} +(-0.227452 + 0.393958i) q^{10} +(0.500000 - 0.866025i) q^{11} +0.909808 q^{13} +(2.16908 - 1.51496i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-1.94163 - 3.36300i) q^{19} -0.454904 q^{20} +1.00000 q^{22} +(4.16908 + 7.22106i) q^{23} +(2.39653 - 4.15091i) q^{25} +(0.454904 + 0.787917i) q^{26} +(2.39653 + 1.12100i) q^{28} +2.79306 q^{29} +(4.79306 - 8.30183i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(0.986723 - 0.689160i) q^{35} +(-3.94163 - 6.82710i) q^{37} +(1.94163 - 3.36300i) q^{38} +(-0.227452 - 0.393958i) q^{40} +1.79306 q^{41} +7.88325 q^{43} +(0.500000 + 0.866025i) q^{44} +(-4.16908 + 7.22106i) q^{46} +(0.169079 + 0.292854i) q^{47} +(-6.89653 + 1.19911i) q^{49} +4.79306 q^{50} +(-0.454904 + 0.787917i) q^{52} +(0.454904 - 0.787917i) q^{53} +0.454904 q^{55} +(0.227452 + 2.63596i) q^{56} +(1.39653 + 2.41886i) q^{58} +(3.48672 - 6.03918i) q^{59} +(7.02051 + 12.1599i) q^{61} +9.58612 q^{62} +1.00000 q^{64} +(0.206938 + 0.358427i) q^{65} +(1.89653 - 3.28489i) q^{67} +(0.500000 + 0.866025i) q^{68} +(1.09019 + 0.509947i) q^{70} +4.79306 q^{71} +(-5.33816 + 9.24596i) q^{73} +(3.94163 - 6.82710i) q^{74} +3.88325 q^{76} +(-2.39653 - 1.12100i) q^{77} +(-2.68236 - 4.64598i) q^{79} +(0.227452 - 0.393958i) q^{80} +(0.896531 + 1.55284i) q^{82} -1.97345 q^{83} +0.454904 q^{85} +(3.94163 + 6.82710i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-5.54510 - 9.60439i) q^{89} +(-0.206938 - 2.39821i) q^{91} -8.33816 q^{92} +(-0.169079 + 0.292854i) q^{94} +(0.883254 - 1.52984i) q^{95} +14.5861 q^{97} +(-4.48672 - 5.37302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} + 3 q^{11} - 3 q^{14} - 3 q^{16} + 3 q^{17} + 3 q^{19} + 6 q^{22} + 9 q^{23} - 3 q^{25} - 3 q^{28} - 18 q^{29} - 6 q^{31} + 3 q^{32} + 6 q^{34} - 6 q^{35} - 9 q^{37} - 3 q^{38} - 24 q^{41} + 18 q^{43} + 3 q^{44} - 9 q^{46} - 15 q^{47} - 24 q^{49} - 6 q^{50} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} + 6 q^{64} + 36 q^{65} - 6 q^{67} + 3 q^{68} + 12 q^{70} - 6 q^{71} + 9 q^{74} - 6 q^{76} + 3 q^{77} - 12 q^{79} - 12 q^{82} + 12 q^{83} + 9 q^{86} - 3 q^{88} - 36 q^{89} - 36 q^{91} - 18 q^{92} + 15 q^{94} - 24 q^{95} + 18 q^{97} - 15 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 + 3 * q^11 - 3 * q^14 - 3 * q^16 + 3 * q^17 + 3 * q^19 + 6 * q^22 + 9 * q^23 - 3 * q^25 - 3 * q^28 - 18 * q^29 - 6 * q^31 + 3 * q^32 + 6 * q^34 - 6 * q^35 - 9 * q^37 - 3 * q^38 - 24 * q^41 + 18 * q^43 + 3 * q^44 - 9 * q^46 - 15 * q^47 - 24 * q^49 - 6 * q^50 - 9 * q^58 + 9 * q^59 + 6 * q^61 - 12 * q^62 + 6 * q^64 + 36 * q^65 - 6 * q^67 + 3 * q^68 + 12 * q^70 - 6 * q^71 + 9 * q^74 - 6 * q^76 + 3 * q^77 - 12 * q^79 - 12 * q^82 + 12 * q^83 + 9 * q^86 - 3 * q^88 - 36 * q^89 - 36 * q^91 - 18 * q^92 + 15 * q^94 - 24 * q^95 + 18 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.227452	+	0.393958i	0.101720	+	0.176184i	0.912393	−	0.409315i	$-0.134232\pi$
$5$	0.227452	+	0.393958i	0.101720	+	0.176184i	−0.810674	+	0.585498i	$0.800899\pi$
$6$		0			0
$7$	−0.227452	−	2.63596i	−0.0859688	−	0.996298i
$7$	−0.227452	−	2.63596i	−0.0859688	−	0.996298i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.227452	+	0.393958i	−0.0719267	+	0.124581i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	0.909808			0.252335			0.126168	−	0.992009i	$-0.459732\pi$
$13$	0.909808			0.252335			0.126168	+	0.992009i	$0.459732\pi$
$14$	2.16908	−	1.51496i	0.579711	−	0.404889i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$	−1.94163	−	3.36300i	−0.445440	−	0.771524i	0.552643	−	0.833418i	$-0.313619\pi$
$19$	−1.94163	−	3.36300i	−0.445440	−	0.771524i	−0.998083	+	0.0618938i	$0.980286\pi$
$20$	−0.454904			−0.101720
$21$		0			0
$22$	1.00000			0.213201
$23$	4.16908	+	7.22106i	0.869313	+	1.50569i	0.862700	+	0.505716i	$0.168772\pi$
$23$	4.16908	+	7.22106i	0.869313	+	1.50569i	0.00661323	+	0.999978i	$0.497895\pi$
$24$		0			0
$25$	2.39653	−	4.15091i	0.479306	−	0.830183i
$26$	0.454904	+	0.787917i	0.0892140	+	0.154523i
$27$		0			0
$28$	2.39653	+	1.12100i	0.452902	+	0.211849i
$29$	2.79306			0.518659			0.259329	−	0.965789i	$-0.416498\pi$
$29$	2.79306			0.518659			0.259329	+	0.965789i	$0.416498\pi$
$30$		0			0
$31$	4.79306	−	8.30183i	0.860859	−	1.49105i	−0.0102412	−	0.999948i	$-0.503260\pi$
$31$	4.79306	−	8.30183i	0.860859	−	1.49105i	0.871101	−	0.491105i	$-0.163407\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	1.00000			0.171499
$35$	0.986723	−	0.689160i	0.166787	−	0.116489i
$36$		0			0
$37$	−3.94163	−	6.82710i	−0.647999	−	1.12237i	−0.983600	−	0.180364i	$-0.942273\pi$
$37$	−3.94163	−	6.82710i	−0.647999	−	1.12237i	0.335601	−	0.942004i	$-0.391061\pi$
$38$	1.94163	−	3.36300i	0.314973	−	0.545550i
$39$		0			0
$40$	−0.227452	−	0.393958i	−0.0359633	−	0.0622903i
$41$	1.79306			0.280029			0.140015	−	0.990149i	$-0.455285\pi$
$41$	1.79306			0.280029			0.140015	+	0.990149i	$0.455285\pi$
$42$		0			0
$43$	7.88325			1.20218			0.601092	−	0.799179i	$-0.294732\pi$
$43$	7.88325			1.20218			0.601092	+	0.799179i	$0.294732\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	−4.16908	+	7.22106i	−0.614697	+	1.06469i
$47$	0.169079	+	0.292854i	0.0246627	+	0.0427171i	0.878093	−	0.478489i	$-0.158815\pi$
$47$	0.169079	+	0.292854i	0.0246627	+	0.0427171i	−0.853431	+	0.521206i	$0.825482\pi$
$48$		0			0
$49$	−6.89653	+	1.19911i	−0.985219	+	0.171301i
$50$	4.79306			0.677841
$51$		0			0
$52$	−0.454904	+	0.787917i	−0.0630838	+	0.109264i
$53$	0.454904	−	0.787917i	0.0624859	−	0.108229i	−0.833090	−	0.553137i	$-0.813430\pi$
$53$	0.454904	−	0.787917i	0.0624859	−	0.108229i	0.895576	+	0.444909i	$0.146764\pi$
$54$		0			0
$55$	0.454904			0.0613393
$56$	0.227452	+	2.63596i	0.0303946	+	0.352244i
$57$		0			0
$58$	1.39653	+	2.41886i	0.183374	+	0.317612i
$59$	3.48672	−	6.03918i	0.453933	−	0.786234i	−0.544693	−	0.838635i	$-0.683354\pi$
$59$	3.48672	−	6.03918i	0.453933	−	0.786234i	0.998626	+	0.0524008i	$0.0166873\pi$
$60$		0			0
$61$	7.02051	+	12.1599i	0.898885	+	1.55691i	0.828922	+	0.559364i	$0.188955\pi$
$61$	7.02051	+	12.1599i	0.898885	+	1.55691i	0.0699629	+	0.997550i	$0.477712\pi$
$62$	9.58612			1.21744
$63$		0			0
$64$	1.00000			0.125000
$65$	0.206938	+	0.358427i	0.0256675	+	0.0444574i
$66$		0			0
$67$	1.89653	−	3.28489i	0.231698	−	0.401313i	−0.726610	−	0.687050i	$-0.758905\pi$
$67$	1.89653	−	3.28489i	0.231698	−	0.401313i	0.958308	+	0.285737i	$0.0922385\pi$
$68$	0.500000	+	0.866025i	0.0606339	+	0.105021i
$69$		0			0
$70$	1.09019	+	0.509947i	0.130303	+	0.0609503i
$71$	4.79306			0.568832			0.284416	−	0.958701i	$-0.408200\pi$
$71$	4.79306			0.568832			0.284416	+	0.958701i	$0.408200\pi$
$72$		0			0
$73$	−5.33816	+	9.24596i	−0.624784	+	1.08216i	0.363798	+	0.931478i	$0.381480\pi$
$73$	−5.33816	+	9.24596i	−0.624784	+	1.08216i	−0.988583	+	0.150680i	$0.951854\pi$
$74$	3.94163	−	6.82710i	0.458205	−	0.793634i
$75$		0			0
$76$	3.88325			0.445440
$77$	−2.39653	−	1.12100i	−0.273110	−	0.127750i
$78$		0			0
$79$	−2.68236	−	4.64598i	−0.301789	−	0.522713i	0.674753	−	0.738044i	$-0.264250\pi$
$79$	−2.68236	−	4.64598i	−0.301789	−	0.522713i	−0.976541	+	0.215331i	$0.930917\pi$
$80$	0.227452	−	0.393958i	0.0254299	−	0.0440459i
$81$		0			0
$82$	0.896531	+	1.55284i	0.0990053	+	0.171482i
$83$	−1.97345			−0.216614			−0.108307	−	0.994118i	$-0.534543\pi$
$83$	−1.97345			−0.216614			−0.108307	+	0.994118i	$0.534543\pi$
$84$		0			0
$85$	0.454904			0.0493413
$86$	3.94163	+	6.82710i	0.425037	+	0.736185i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−5.54510	−	9.60439i	−0.587779	−	1.01806i	−0.994523	−	0.104521i	$-0.966669\pi$
$89$	−5.54510	−	9.60439i	−0.587779	−	1.01806i	0.406744	−	0.913542i	$-0.366664\pi$
$90$		0			0
$91$	−0.206938	−	2.39821i	−0.0216930	−	0.251401i
$92$	−8.33816			−0.869313
$93$		0			0
$94$	−0.169079	+	0.292854i	−0.0174392	+	0.0302055i
$95$	0.883254	−	1.52984i	0.0906200	−	0.156958i
$96$		0			0
$97$	14.5861			1.48100			0.740498	−	0.672058i	$-0.234590\pi$
$97$	14.5861			1.48100			0.740498	+	0.672058i	$0.234590\pi$
$98$	−4.48672	−	5.37302i	−0.453227	−	0.542757i
$99$		0			0
$100$	2.39653	+	4.15091i	0.239653	+	0.415091i
$101$	−4.03182	+	6.98332i	−0.401181	+	0.694866i	−0.993869	−	0.110566i	$-0.964733\pi$
$101$	−4.03182	+	6.98332i	−0.401181	+	0.694866i	0.592688	+	0.805432i	$0.298067\pi$
$102$		0			0
$103$	−2.88325	−	4.99394i	−0.284095	−	0.492068i	0.688294	−	0.725432i	$-0.258360\pi$
$103$	−2.88325	−	4.99394i	−0.284095	−	0.492068i	−0.972389	+	0.233364i	$0.925027\pi$
$104$	−0.909808			−0.0892140
$105$		0			0
$106$	0.909808			0.0883684
$107$	7.80634	+	13.5210i	0.754667	+	1.30712i	0.945540	+	0.325507i	$0.105535\pi$
$107$	7.80634	+	13.5210i	0.754667	+	1.30712i	−0.190872	+	0.981615i	$0.561132\pi$
$108$		0			0
$109$	−7.02051	+	12.1599i	−0.672443	+	1.16471i	0.304766	+	0.952427i	$0.401422\pi$
$109$	−7.02051	+	12.1599i	−0.672443	+	1.16471i	−0.977209	+	0.212279i	$0.931912\pi$
$110$	0.227452	+	0.393958i	0.0216867	+	0.0375625i
$111$		0			0
$112$	−2.16908	+	1.51496i	−0.204959	+	0.143150i
$113$	−7.58612			−0.713643			−0.356821	−	0.934173i	$-0.616139\pi$
$113$	−7.58612			−0.713643			−0.356821	+	0.934173i	$0.616139\pi$
$114$		0			0
$115$	−1.89653	+	3.28489i	−0.176852	+	0.306317i
$116$	−1.39653	+	2.41886i	−0.129665	+	0.224586i
$117$		0			0
$118$	6.97345			0.641958
$119$	−2.39653	−	1.12100i	−0.219690	−	0.102762i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−7.02051	+	12.1599i	−0.635608	+	1.10090i
$123$		0			0
$124$	4.79306	+	8.30183i	0.430430	+	0.745526i
$125$	4.45490			0.398459
$126$		0			0
$127$	7.42835			0.659159			0.329580	−	0.944128i	$-0.393093\pi$
$127$	7.42835			0.659159			0.329580	+	0.944128i	$0.393093\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.206938	+	0.358427i	−0.0181496	+	0.0314361i
$131$	−9.70287	−	16.8059i	−0.847744	−	1.46834i	−0.883217	−	0.468965i	$-0.844627\pi$
$131$	−9.70287	−	16.8059i	−0.847744	−	1.46834i	0.0354732	−	0.999371i	$-0.488706\pi$
$132$		0			0
$133$	−8.42309	+	5.88296i	−0.730374	+	0.510118i
$134$	3.79306			0.327671
$135$		0			0
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	0.454904	−	0.787917i	0.0388651	−	0.0673163i	−0.845939	−	0.533280i	$-0.820959\pi$
$137$	0.454904	−	0.787917i	0.0388651	−	0.0673163i	0.884804	+	0.465964i	$0.154292\pi$
$138$		0			0
$139$	−8.37919			−0.710713			−0.355357	−	0.934731i	$-0.615641\pi$
$139$	−8.37919			−0.710713			−0.355357	+	0.934731i	$0.615641\pi$
$140$	0.103469	+	1.19911i	0.00874472	+	0.101343i
$141$		0			0
$142$	2.39653	+	4.15091i	0.201112	+	0.348337i
$143$	0.454904	−	0.787917i	0.0380410	−	0.0658889i
$144$		0			0
$145$	0.635288	+	1.10035i	0.0527578	+	0.0913791i
$146$	−10.6763			−0.883578
$147$		0			0
$148$	7.88325			0.647999
$149$	2.05837	+	3.56521i	0.168628	+	0.292073i	0.937938	−	0.346803i	$-0.112733\pi$
$149$	2.05837	+	3.56521i	0.168628	+	0.292073i	−0.769309	+	0.638876i	$0.779400\pi$
$150$		0			0
$151$	3.07889	−	5.33279i	0.250556	−	0.433976i	−0.713123	−	0.701039i	$-0.752720\pi$
$151$	3.07889	−	5.33279i	0.250556	−	0.433976i	0.963679	+	0.267063i	$0.0860531\pi$
$152$	1.94163	+	3.36300i	0.157487	+	0.272775i
$153$		0			0
$154$	−0.227452	−	2.63596i	−0.0183286	−	0.212411i
$155$	4.36077			0.350265
$156$		0			0
$157$	8.82488	−	15.2851i	0.704302	−	1.21989i	−0.262641	−	0.964894i	$-0.584593\pi$
$157$	8.82488	−	15.2851i	0.704302	−	1.21989i	0.966943	−	0.254993i	$-0.0820733\pi$
$158$	2.68236	−	4.64598i	0.213397	−	0.369614i
$159$		0			0
$160$	0.454904			0.0359633
$161$	18.0861	−	12.6320i	1.42539	−	0.995537i
$162$		0			0
$163$	5.80634	+	10.0569i	0.454788	+	0.787715i	0.998676	−	0.0514424i	$-0.0163818\pi$
$163$	5.80634	+	10.0569i	0.454788	+	0.787715i	−0.543888	+	0.839158i	$0.683049\pi$
$164$	−0.896531	+	1.55284i	−0.0700073	+	0.121256i
$165$		0			0
$166$	−0.986723	−	1.70905i	−0.0765846	−	0.132648i
$167$	4.85670			0.375823			0.187911	−	0.982186i	$-0.439828\pi$
$167$	4.85670			0.375823			0.187911	+	0.982186i	$0.439828\pi$
$168$		0			0
$169$	−12.1722			−0.936327
$170$	0.227452	+	0.393958i	0.0174448	+	0.0302152i
$171$		0			0
$172$	−3.94163	+	6.82710i	−0.300546	+	0.520561i
$173$	−12.7931	−	22.1582i	−0.972639	−	1.68466i	−0.687518	−	0.726168i	$-0.741300\pi$
$173$	−12.7931	−	22.1582i	−0.972639	−	1.68466i	−0.285121	−	0.958492i	$-0.592034\pi$
$174$		0			0
$175$	−11.4867	−	5.37302i	−0.868315	−	0.406162i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	5.54510	−	9.60439i	0.415623	−	0.719879i
$179$	−7.85144	+	13.5991i	−0.586844	+	1.01644i	0.407799	+	0.913072i	$0.366296\pi$
$179$	−7.85144	+	13.5991i	−0.586844	+	1.01644i	−0.994643	+	0.103372i	$0.967037\pi$
$180$		0			0
$181$	−2.49593			−0.185521			−0.0927606	−	0.995688i	$-0.529569\pi$
$181$	−2.49593			−0.185521			−0.0927606	+	0.995688i	$0.529569\pi$
$182$	1.97345	−	1.37832i	0.146282	−	0.102168i
$183$		0			0
$184$	−4.16908	−	7.22106i	−0.307349	−	0.532343i
$185$	1.79306	−	3.10567i	0.131829	−	0.228334i
$186$		0			0
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	−0.338158			−0.0246627
$189$		0			0
$190$	1.76651			0.128156
$191$	4.90981	+	8.50404i	0.355261	+	0.615331i	0.987163	−	0.159718i	$-0.0510586\pi$
$191$	4.90981	+	8.50404i	0.355261	+	0.615331i	−0.631901	+	0.775049i	$0.717725\pi$
$192$		0			0
$193$	−3.42835	+	5.93808i	−0.246778	+	0.427432i	−0.962630	−	0.270820i	$-0.912705\pi$
$193$	−3.42835	+	5.93808i	−0.246778	+	0.427432i	0.715852	+	0.698252i	$0.246039\pi$
$194$	7.29306	+	12.6320i	0.523611	+	0.906921i
$195$		0			0
$196$	2.40981	−	6.57212i	0.172129	−	0.469437i
$197$	−23.4694			−1.67212			−0.836062	−	0.548635i	$-0.815148\pi$
$197$	−23.4694			−1.67212			−0.836062	+	0.548635i	$0.815148\pi$
$198$		0			0
$199$	1.11675	−	1.93426i	0.0791640	−	0.137116i	−0.823725	−	0.566989i	$-0.808108\pi$
$199$	1.11675	−	1.93426i	0.0791640	−	0.137116i	0.902889	+	0.429873i	$0.141442\pi$
$200$	−2.39653	+	4.15091i	−0.169460	+	0.293514i
$201$		0			0
$202$	−8.06364			−0.567356
$203$	−0.635288	−	7.36239i	−0.0445885	−	0.516738i
$204$		0			0
$205$	0.407836	+	0.706392i	0.0284845	+	0.0493366i
$206$	2.88325	−	4.99394i	0.200886	−	0.347944i
$207$		0			0
$208$	−0.454904	−	0.787917i	−0.0315419	−	0.0546322i
$209$	−3.88325			−0.268610
$210$		0			0
$211$	−18.2624			−1.25724			−0.628619	−	0.777713i	$-0.716380\pi$
$211$	−18.2624			−1.25724			−0.628619	+	0.777713i	$0.716380\pi$
$212$	0.454904	+	0.787917i	0.0312429	+	0.0541144i
$213$		0			0
$214$	−7.80634	+	13.5210i	−0.533630	+	0.924275i
$215$	1.79306	+	3.10567i	0.122286	+	0.211805i
$216$		0			0
$217$	−22.9734	−	10.7460i	−1.55954	−	0.729488i
$218$	−14.0410			−0.950978
$219$		0			0
$220$	−0.227452	+	0.393958i	−0.0153348	+	0.0265607i
$221$	0.454904	−	0.787917i	0.0306002	−	0.0530010i
$222$		0			0
$223$	12.4959			0.836790			0.418395	−	0.908265i	$-0.362593\pi$
$223$	12.4959			0.836790			0.418395	+	0.908265i	$0.362593\pi$
$224$	−2.39653	−	1.12100i	−0.160125	−	0.0748999i
$225$		0			0
$226$	−3.79306	−	6.56978i	−0.252311	−	0.437015i
$227$	4.89653	−	8.48104i	0.324994	−	0.562906i	−0.656517	−	0.754311i	$-0.727971\pi$
$227$	4.89653	−	8.48104i	0.324994	−	0.562906i	0.981511	+	0.191405i	$0.0613043\pi$
$228$		0			0
$229$	−4.33816	−	7.51391i	−0.286674	−	0.496533i	0.686340	−	0.727281i	$-0.259216\pi$
$229$	−4.33816	−	7.51391i	−0.286674	−	0.496533i	−0.973014	+	0.230748i	$0.925883\pi$
$230$	−3.79306			−0.250107
$231$		0			0
$232$	−2.79306			−0.183374
$233$	8.38325	+	14.5202i	0.549205	+	0.951251i	0.998329	+	0.0577819i	$0.0184028\pi$
$233$	8.38325	+	14.5202i	0.549205	+	0.951251i	−0.449124	+	0.893469i	$0.648264\pi$
$234$		0			0
$235$	−0.0769148	+	0.133220i	−0.00501737	+	0.00869033i
$236$	3.48672	+	6.03918i	0.226966	+	0.393117i
$237$		0			0
$238$	−0.227452	−	2.63596i	−0.0147435	−	0.170864i
$239$	26.2624			1.69878			0.849388	−	0.527769i	$-0.176971\pi$
$239$	26.2624			1.69878			0.849388	+	0.527769i	$0.176971\pi$
$240$		0			0
$241$	−3.97345	+	6.88221i	−0.255952	+	0.443322i	−0.965154	−	0.261684i	$-0.915722\pi$
$241$	−3.97345	+	6.88221i	−0.255952	+	0.443322i	0.709202	+	0.705006i	$0.249056\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	−14.0410			−0.898885
$245$	−2.04103	−	2.44421i	−0.130397	−	0.156155i
$246$		0			0
$247$	−1.76651	−	3.05968i	−0.112400	−	0.194683i
$248$	−4.79306	+	8.30183i	−0.304360	+	0.527167i
$249$		0			0
$250$	2.22745	+	3.85806i	0.140876	+	0.244005i
$251$	3.93636			0.248461			0.124230	−	0.992253i	$-0.460354\pi$
$251$	3.93636			0.248461			0.124230	+	0.992253i	$0.460354\pi$
$252$		0			0
$253$	8.33816			0.524216
$254$	3.71417	+	6.43314i	0.233048	+	0.403651i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.54510	−	13.0685i	−0.470650	−	0.815190i	0.528786	−	0.848755i	$-0.322647\pi$
$257$	−7.54510	−	13.0685i	−0.470650	−	0.815190i	−0.999437	+	0.0335650i	$0.989314\pi$
$258$		0			0
$259$	−17.0994	+	11.9428i	−1.06251	+	0.742089i
$260$	−0.413875			−0.0256675
$261$		0			0
$262$	9.70287	−	16.8059i	0.599445	−	1.03827i
$263$	−14.3116	+	24.7884i	−0.882491	+	1.52852i	−0.0339291	+	0.999424i	$0.510802\pi$
$263$	−14.3116	+	24.7884i	−0.882491	+	1.52852i	−0.848562	+	0.529096i	$0.822531\pi$
$264$		0			0
$265$	0.413875			0.0254242
$266$	−9.30634	−	4.35312i	−0.570608	−	0.266907i
$267$		0			0
$268$	1.89653	+	3.28489i	0.115849	+	0.200656i
$269$	−11.4754	+	19.8760i	−0.699669	+	1.21186i	0.268913	+	0.963165i	$0.413336\pi$
$269$	−11.4754	+	19.8760i	−0.699669	+	1.21186i	−0.968581	+	0.248697i	$0.919998\pi$
$270$		0			0
$271$	−4.90981	−	8.50404i	−0.298250	−	0.516583i	0.677486	−	0.735536i	$-0.263069\pi$
$271$	−4.90981	−	8.50404i	−0.298250	−	0.516583i	−0.975736	+	0.218952i	$0.929736\pi$
$272$	−1.00000			−0.0606339
$273$		0			0
$274$	0.909808			0.0549635
$275$	−2.39653	−	4.15091i	−0.144516	−	0.250310i
$276$		0			0
$277$	−5.36471	+	9.29195i	−0.322334	+	0.558299i	−0.980969	−	0.194163i	$-0.937801\pi$
$277$	−5.36471	+	9.29195i	−0.322334	+	0.558299i	0.658635	+	0.752463i	$0.271134\pi$
$278$	−4.18959	−	7.25659i	−0.251275	−	0.435221i
$279$		0			0
$280$	−0.986723	+	0.689160i	−0.0589680	+	0.0411852i
$281$	−2.58612			−0.154275			−0.0771376	−	0.997020i	$-0.524578\pi$
$281$	−2.58612			−0.154275			−0.0771376	+	0.997020i	$0.524578\pi$
$282$		0			0
$283$	10.0410	−	17.3916i	0.596877	−	1.03382i	−0.396402	−	0.918077i	$-0.629741\pi$
$283$	10.0410	−	17.3916i	0.596877	−	1.03382i	0.993279	−	0.115745i	$-0.0369254\pi$
$284$	−2.39653	+	4.15091i	−0.142208	+	0.246311i
$285$		0			0
$286$	0.909808			0.0537981
$287$	−0.407836	−	4.72643i	−0.0240738	−	0.278993i
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	−0.635288	+	1.10035i	−0.0373054	+	0.0646148i
$291$		0			0
$292$	−5.33816	−	9.24596i	−0.312392	−	0.541079i
$293$	−10.3792			−0.606359			−0.303179	−	0.952934i	$-0.598048\pi$
$293$	−10.3792			−0.606359			−0.303179	+	0.952934i	$0.598048\pi$
$294$		0			0
$295$	3.17225			0.184695
$296$	3.94163	+	6.82710i	0.229102	+	0.396817i
$297$		0			0
$298$	−2.05837	+	3.56521i	−0.119238	+	0.206527i
$299$	3.79306	+	6.56978i	0.219358	+	0.379940i
$300$		0			0
$301$	−1.79306	−	20.7799i	−0.103350	−	1.19773i
$302$	6.15777			0.354340
$303$		0			0
$304$	−1.94163	+	3.36300i	−0.111360	+	0.192881i
$305$	−3.19366	+	5.53158i	−0.182868	+	0.316737i
$306$		0			0
$307$	9.76651			0.557404			0.278702	−	0.960378i	$-0.410096\pi$
$307$	9.76651			0.557404			0.278702	+	0.960378i	$0.410096\pi$
$308$	2.16908	−	1.51496i	0.123595	−	0.0863227i
$309$		0			0
$310$	2.18038	+	3.77654i	0.123837	+	0.214493i
$311$	−3.25927	+	5.64522i	−0.184816	+	0.320111i	−0.943515	−	0.331331i	$-0.892502\pi$
$311$	−3.25927	+	5.64522i	−0.184816	+	0.320111i	0.758698	+	0.651442i	$0.225836\pi$
$312$		0			0
$313$	−15.3965	−	26.6676i	−0.870263	−	1.50734i	−0.861724	−	0.507377i	$-0.830615\pi$
$313$	−15.3965	−	26.6676i	−0.870263	−	1.50734i	−0.00853913	−	0.999964i	$-0.502718\pi$
$314$	17.6498			0.996034
$315$		0			0
$316$	5.36471			0.301789
$317$	−13.8136	−	23.9258i	−0.775848	−	1.34381i	−0.934317	−	0.356444i	$-0.883989\pi$
$317$	−13.8136	−	23.9258i	−0.775848	−	1.34381i	0.158469	−	0.987364i	$-0.449344\pi$
$318$		0			0
$319$	1.39653	−	2.41886i	0.0781907	−	0.135430i
$320$	0.227452	+	0.393958i	0.0127150	+	0.0220229i
$321$		0			0
$322$	19.9827	+	9.34707i	1.11359	+	0.520892i
$323$	−3.88325			−0.216070
$324$		0			0
$325$	2.18038	−	3.77654i	0.120946	−	0.209484i
$326$	−5.80634	+	10.0569i	−0.321583	+	0.556999i
$327$		0			0
$328$	−1.79306			−0.0990053
$329$	0.733492	−	0.512295i	0.0404387	−	0.0282438i
$330$		0			0
$331$	14.4827	+	25.0847i	0.796039	+	1.37878i	0.922177	+	0.386767i	$0.126408\pi$
$331$	14.4827	+	25.0847i	0.796039	+	1.37878i	−0.126139	+	0.992013i	$0.540258\pi$
$332$	0.986723	−	1.70905i	0.0541535	−	0.0937965i
$333$		0			0
$334$	2.42835	+	4.20603i	0.132873	+	0.230143i
$335$	1.72548			0.0942730
$336$		0			0
$337$	−9.03708			−0.492281			−0.246141	−	0.969234i	$-0.579163\pi$
$337$	−9.03708			−0.492281			−0.246141	+	0.969234i	$0.579163\pi$
$338$	−6.08612	−	10.5415i	−0.331042	−	0.573381i
$339$		0			0
$340$	−0.227452	+	0.393958i	−0.0123353	+	0.0213654i
$341$	−4.79306	−	8.30183i	−0.259559	−	0.449569i
$342$		0			0
$343$	4.72942	+	17.9062i	0.255365	+	0.966845i
$344$	−7.88325			−0.425037
$345$		0			0
$346$	12.7931	−	22.1582i	0.687759	−	1.19123i
$347$	−10.8063	+	18.7171i	−0.580115	+	1.00479i	0.415350	+	0.909661i	$0.363659\pi$
$347$	−10.8063	+	18.7171i	−0.580115	+	1.00479i	−0.995465	+	0.0951267i	$0.969674\pi$
$348$		0			0
$349$	14.2745			0.764098			0.382049	−	0.924142i	$-0.375219\pi$
$349$	14.2745			0.764098			0.382049	+	0.924142i	$0.375219\pi$
$350$	−1.09019	−	12.6343i	−0.0582732	−	0.675332i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−14.2480	+	24.6782i	−0.758343	+	1.31349i	0.185353	+	0.982672i	$0.440657\pi$
$353$	−14.2480	+	24.6782i	−0.758343	+	1.31349i	−0.943695	+	0.330816i	$0.892676\pi$
$354$		0			0
$355$	1.09019	+	1.88827i	0.0578614	+	0.100219i
$356$	11.0902			0.587779
$357$		0			0
$358$	−15.7029			−0.829922
$359$	−6.81962	−	11.8119i	−0.359926	−	0.623409i	0.628022	−	0.778195i	$-0.283865\pi$
$359$	−6.81962	−	11.8119i	−0.359926	−	0.623409i	−0.987948	+	0.154786i	$0.950531\pi$
$360$		0			0
$361$	1.96017	−	3.39511i	0.103167	−	0.178690i
$362$	−1.24797	−	2.16154i	−0.0655917	−	0.113608i
$363$		0			0
$364$	2.18038	+	1.01989i	0.114283	+	0.0534570i
$365$	−4.85670			−0.254211
$366$		0			0
$367$	−11.3647	+	19.6843i	−0.593233	+	1.02751i	0.400560	+	0.916270i	$0.368815\pi$
$367$	−11.3647	+	19.6843i	−0.593233	+	1.02751i	−0.993794	+	0.111240i	$0.964518\pi$
$368$	4.16908	−	7.22106i	0.217328	−	0.376424i
$369$		0			0
$370$	3.58612			0.186434
$371$	−2.18038	−	1.01989i	−0.113200	−	0.0529503i
$372$		0			0
$373$	−5.20090	−	9.00822i	−0.269292	−	0.466428i	0.699387	−	0.714743i	$-0.253456\pi$
$373$	−5.20090	−	9.00822i	−0.269292	−	0.466428i	−0.968679	+	0.248315i	$0.920123\pi$
$374$	0.500000	−	0.866025i	0.0258544	−	0.0447811i
$375$		0			0
$376$	−0.169079	−	0.292854i	−0.00871959	−	0.0151028i
$377$	2.54115			0.130876
$378$		0			0
$379$	7.61268			0.391037			0.195519	−	0.980700i	$-0.437361\pi$
$379$	7.61268			0.391037			0.195519	+	0.980700i	$0.437361\pi$
$380$	0.883254	+	1.52984i	0.0453100	+	0.0784792i
$381$		0			0
$382$	−4.90981	+	8.50404i	−0.251208	+	0.435104i
$383$	−11.0728	−	19.1787i	−0.565796	−	0.979988i	−0.996975	−	0.0777212i	$-0.975236\pi$
$383$	−11.0728	−	19.1787i	−0.565796	−	0.979988i	0.431179	−	0.902266i	$-0.358098\pi$
$384$		0			0
$385$	−0.103469	−	1.19911i	−0.00527326	−	0.0611122i
$386$	−6.85670			−0.348997
$387$		0			0
$388$	−7.29306	+	12.6320i	−0.370249	+	0.641290i
$389$	−1.77255	+	3.07014i	−0.0898717	+	0.155662i	−0.907457	−	0.420145i	$-0.861979\pi$
$389$	−1.77255	+	3.07014i	−0.0898717	+	0.155662i	0.817585	+	0.575808i	$0.195312\pi$
$390$		0			0
$391$	8.33816			0.421679
$392$	6.89653	−	1.19911i	0.348327	−	0.0605641i
$393$		0			0
$394$	−11.7347	−	20.3251i	−0.591185	−	1.02396i
$395$	1.22021	−	2.11347i	0.0613957	−	0.106340i
$396$		0			0
$397$	1.27979	+	2.21665i	0.0642306	+	0.111251i	0.896352	−	0.443342i	$-0.146207\pi$
$397$	1.27979	+	2.21665i	0.0642306	+	0.111251i	−0.832122	+	0.554593i	$0.812874\pi$
$398$	2.23349			0.111955
$399$		0			0
$400$	−4.79306			−0.239653
$401$	5.24797	+	9.08974i	0.262071	+	0.453920i	0.966792	−	0.255564i	$-0.0822612\pi$
$401$	5.24797	+	9.08974i	0.262071	+	0.453920i	−0.704721	+	0.709484i	$0.748928\pi$
$402$		0			0
$403$	4.36077	−	7.55307i	0.217225	−	0.376245i
$404$	−4.03182	−	6.98332i	−0.200590	−	0.347433i
$405$		0			0
$406$	6.05837	−	4.23137i	0.300672	−	0.209999i
$407$	−7.88325			−0.390758
$408$		0			0
$409$	−7.92428	+	13.7253i	−0.391831	+	0.678670i	−0.992691	−	0.120683i	$-0.961491\pi$
$409$	−7.92428	+	13.7253i	−0.391831	+	0.678670i	0.600860	+	0.799354i	$0.294825\pi$
$410$	−0.407836	+	0.706392i	−0.0201416	+	0.0348862i
$411$		0			0
$412$	5.76651			0.284095
$413$	−16.7121	−	7.81723i	−0.822348	−	0.384661i
$414$		0			0
$415$	−0.448864	−	0.777456i	−0.0220339	−	0.0381638i
$416$	0.454904	−	0.787917i	0.0223035	−	0.0386308i
$417$		0			0
$418$	−1.94163	−	3.36300i	−0.0949681	−	0.164490i
$419$	9.52249			0.465204			0.232602	−	0.972572i	$-0.425276\pi$
$419$	9.52249			0.465204			0.232602	+	0.972572i	$0.425276\pi$
$420$		0			0
$421$	−0.530621			−0.0258609			−0.0129305	−	0.999916i	$-0.504116\pi$
$421$	−0.530621			−0.0258609			−0.0129305	+	0.999916i	$0.504116\pi$
$422$	−9.13122	−	15.8157i	−0.444501	−	0.769898i
$423$		0			0
$424$	−0.454904	+	0.787917i	−0.0220921	+	0.0382646i
$425$	−2.39653	−	4.15091i	−0.116249	−	0.201349i
$426$		0			0
$427$	30.4561	−	21.2716i	1.47387	−	1.02940i
$428$	−15.6127			−0.754667
$429$		0			0
$430$	−1.79306	+	3.10567i	−0.0864691	+	0.149769i
$431$	10.4018	−	18.0164i	0.501037	−	0.867821i	−0.498962	−	0.866624i	$-0.666285\pi$
$431$	10.4018	−	18.0164i	0.501037	−	0.867821i	0.999999	−	0.00119770i	$-0.000381239\pi$
$432$		0			0
$433$	−4.40574			−0.211726			−0.105863	−	0.994381i	$-0.533761\pi$
$433$	−4.40574			−0.211726			−0.105863	+	0.994381i	$0.533761\pi$
$434$	−2.18038	−	25.2686i	−0.104662	−	1.21293i
$435$		0			0
$436$	−7.02051	−	12.1599i	−0.336222	−	0.582353i
$437$	16.1896	−	28.0412i	0.774453	−	1.34139i
$438$		0			0
$439$	7.59743	+	13.1591i	0.362606	+	0.628051i	0.988389	−	0.151946i	$-0.0485539\pi$
$439$	7.59743	+	13.1591i	0.362606	+	0.628051i	−0.625783	+	0.779997i	$0.715221\pi$
$440$	−0.454904			−0.0216867
$441$		0			0
$442$	0.909808			0.0432752
$443$	−5.69366	−	9.86171i	−0.270514	−	0.468544i	0.698480	−	0.715630i	$-0.253860\pi$
$443$	−5.69366	−	9.86171i	−0.270514	−	0.468544i	−0.968994	+	0.247086i	$0.920527\pi$
$444$		0			0
$445$	2.52249	−	4.36908i	0.119577	−	0.207114i
$446$	6.24797	+	10.8218i	0.295850	+	0.512427i
$447$		0			0
$448$	−0.227452	−	2.63596i	−0.0107461	−	0.124537i
$449$	24.0821			1.13650			0.568251	−	0.822855i	$-0.307620\pi$
$449$	24.0821			1.13650			0.568251	+	0.822855i	$0.307620\pi$
$450$		0			0
$451$	0.896531	−	1.55284i	0.0422160	−	0.0731203i
$452$	3.79306	−	6.56978i	0.178411	−	0.309016i
$453$		0			0
$454$	9.79306			0.459611
$455$	0.897729	−	0.627004i	0.0420862	−	0.0293944i
$456$		0			0
$457$	14.7665	+	25.5763i	0.690748	+	1.19641i	0.971593	+	0.236658i	$0.0760520\pi$
$457$	14.7665	+	25.5763i	0.690748	+	1.19641i	−0.280845	+	0.959753i	$0.590615\pi$
$458$	4.33816	−	7.51391i	0.202709	−	0.351102i
$459$		0			0
$460$	−1.89653	−	3.28489i	−0.0884262	−	0.153159i
$461$	−4.14569			−0.193084			−0.0965421	−	0.995329i	$-0.530778\pi$
$461$	−4.14569			−0.193084			−0.0965421	+	0.995329i	$0.530778\pi$
$462$		0			0
$463$	−9.32368			−0.433308			−0.216654	−	0.976248i	$-0.569514\pi$
$463$	−9.32368			−0.433308			−0.216654	+	0.976248i	$0.569514\pi$
$464$	−1.39653	−	2.41886i	−0.0648323	−	0.112293i
$465$		0			0
$466$	−8.38325	+	14.5202i	−0.388347	+	0.672636i
$467$	18.2798	+	31.6615i	0.845888	+	1.46512i	0.884848	+	0.465880i	$0.154262\pi$
$467$	18.2798	+	31.6615i	0.845888	+	1.46512i	−0.0389606	+	0.999241i	$0.512405\pi$
$468$		0			0
$469$	−9.09019	−	4.25202i	−0.419746	−	0.196340i
$470$	−0.153830			−0.00709563
$471$		0			0
$472$	−3.48672	+	6.03918i	−0.160489	+	0.277976i
$473$	3.94163	−	6.82710i	0.181236	−	0.313910i
$474$		0			0
$475$	−18.6127			−0.854008
$476$	2.16908	−	1.51496i	0.0994196	−	0.0694380i
$477$		0			0
$478$	13.1312	+	22.7439i	0.600608	+	1.04028i
$479$	0.364712	−	0.631700i	0.0166641	−	0.0288631i	−0.857573	−	0.514362i	$-0.828029\pi$
$479$	0.364712	−	0.631700i	0.0166641	−	0.0288631i	0.874237	+	0.485499i	$0.161362\pi$
$480$		0			0
$481$	−3.58612	−	6.21135i	−0.163513	−	0.283213i
$482$	−7.94689			−0.361971
$483$		0			0
$484$	1.00000			0.0454545
$485$	3.31764	+	5.74633i	0.150646	+	0.260927i
$486$		0			0
$487$	18.4283	−	31.9188i	0.835068	−	1.44638i	−0.0589066	−	0.998263i	$-0.518761\pi$
$487$	18.4283	−	31.9188i	0.835068	−	1.44638i	0.893975	−	0.448117i	$-0.147905\pi$
$488$	−7.02051	−	12.1599i	−0.317804	−	0.550452i
$489$		0			0
$490$	1.09623	−	2.98969i	0.0495227	−	0.135060i
$491$	−25.5065			−1.15109			−0.575545	−	0.817770i	$-0.695210\pi$
$491$	−25.5065			−1.15109			−0.575545	+	0.817770i	$0.695210\pi$
$492$		0			0
$493$	1.39653	−	2.41886i	0.0628966	−	0.108940i
$494$	1.76651	−	3.05968i	0.0794790	−	0.137662i
$495$		0			0
$496$	−9.58612			−0.430430
$497$	−1.09019	−	12.6343i	−0.0489018	−	0.566726i
$498$		0			0
$499$	2.06364	+	3.57433i	0.0923811	+	0.160009i	0.908513	−	0.417857i	$-0.137219\pi$
$499$	2.06364	+	3.57433i	0.0923811	+	0.160009i	−0.816131	+	0.577866i	$0.803886\pi$
$500$	−2.22745	+	3.85806i	−0.0996147	+	0.172538i
$501$		0			0
$502$	1.96818	+	3.40899i	0.0878442	+	0.152151i
$503$	6.85670			0.305725			0.152863	−	0.988247i	$-0.451151\pi$
$503$	6.85670			0.305725			0.152863	+	0.988247i	$0.451151\pi$
$504$		0			0
$505$	−3.66818			−0.163232
$506$	4.16908	+	7.22106i	0.185338	+	0.321015i
$507$		0			0
$508$	−3.71417	+	6.43314i	−0.164790	+	0.285424i
$509$	8.22141	+	14.2399i	0.364408	+	0.631173i	0.988681	−	0.150033i	$-0.0479381\pi$
$509$	8.22141	+	14.2399i	0.364408	+	0.631173i	−0.624273	+	0.781206i	$0.714605\pi$
$510$		0			0
$511$	25.5861	+	11.9681i	1.13186	+	0.529439i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.54510	−	13.0685i	0.332800	−	0.576426i
$515$	1.31160	−	2.27176i	0.0577962	−	0.100106i
$516$		0			0
$517$	0.338158			0.0148722
$518$	−18.8925	−	8.83712i	−0.830087	−	0.388281i
$519$		0			0
$520$	−0.206938	−	0.358427i	−0.00907482	−	0.0157180i
$521$	−2.81962	+	4.88372i	−0.123530	+	0.213960i	−0.921157	−	0.389191i	$-0.872755\pi$
$521$	−2.81962	+	4.88372i	−0.123530	+	0.213960i	0.797628	+	0.603150i	$0.206088\pi$
$522$		0			0
$523$	2.04103	+	3.53517i	0.0892480	+	0.154582i	0.907193	−	0.420714i	$-0.138220\pi$
$523$	2.04103	+	3.53517i	0.0892480	+	0.154582i	−0.817946	+	0.575296i	$0.804887\pi$
$524$	19.4057			0.847744
$525$		0			0
$526$	−28.6232			−1.24803
$527$	−4.79306	−	8.30183i	−0.208789	−	0.361633i
$528$		0			0
$529$	−23.2624	+	40.2917i	−1.01141	+	1.75181i
$530$	0.206938	+	0.358427i	0.00898880	+	0.0155691i
$531$		0			0
$532$	−0.883254	−	10.2361i	−0.0382939	−	0.443791i
$533$	1.63134			0.0706613
$534$		0			0
$535$	−3.55114	+	6.15075i	−0.153529	+	0.265920i
$536$	−1.89653	+	3.28489i	−0.0819177	+	0.141886i
$537$		0			0
$538$	−22.9508			−0.989481
$539$	−2.40981	+	6.57212i	−0.103798	+	0.283081i
$540$		0			0
$541$	2.44886	+	4.24156i	0.105285	+	0.182359i	0.913855	−	0.406042i	$-0.133091\pi$
$541$	2.44886	+	4.24156i	0.105285	+	0.182359i	−0.808570	+	0.588400i	$0.799758\pi$
$542$	4.90981	−	8.50404i	0.210894	−	0.365280i
$543$		0			0
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	−6.38732			−0.273603
$546$		0			0
$547$	21.4694			0.917964			0.458982	−	0.888445i	$-0.348214\pi$
$547$	21.4694			0.917964			0.458982	+	0.888445i	$0.348214\pi$
$548$	0.454904	+	0.787917i	0.0194325	+	0.0336581i
$549$		0			0
$550$	2.39653	−	4.15091i	0.102188	−	0.176996i
$551$	−5.42309	−	9.39306i	−0.231031	−	0.400158i
$552$		0			0
$553$	−11.6365	+	8.12731i	−0.494834	+	0.345608i
$554$	−10.7294			−0.455850
$555$		0			0
$556$	4.18959	−	7.25659i	0.177678	−	0.307748i
$557$	−19.7347	+	34.1815i	−0.836186	+	1.44832i	0.0568758	+	0.998381i	$0.481886\pi$
$557$	−19.7347	+	34.1815i	−0.836186	+	1.44832i	−0.893061	+	0.449935i	$0.851447\pi$
$558$		0			0
$559$	7.17225			0.303354
$560$	−1.09019	−	0.509947i	−0.0460690	−	0.0215492i
$561$		0			0
$562$	−1.29306	−	2.23965i	−0.0545445	−	0.0944739i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	−1.72548	−	2.98862i	−0.0725915	−	0.125732i
$566$	20.0821			0.844112
$567$		0			0
$568$	−4.79306			−0.201112
$569$	17.0994	+	29.6170i	0.716844	+	1.24161i	0.962244	+	0.272189i	$0.0877475\pi$
$569$	17.0994	+	29.6170i	0.716844	+	1.24161i	−0.245400	+	0.969422i	$0.578919\pi$
$570$		0			0
$571$	−7.39653	+	12.8112i	−0.309535	+	0.536131i	−0.978261	−	0.207379i	$-0.933507\pi$
$571$	−7.39653	+	12.8112i	−0.309535	+	0.536131i	0.668726	+	0.743509i	$0.266840\pi$
$572$	0.454904	+	0.787917i	0.0190205	+	0.0329445i
$573$		0			0
$574$	3.88929	−	2.71641i	0.162336	−	0.113381i
$575$	39.9653			1.66667
$576$		0			0
$577$	3.59940	−	6.23435i	0.149845	−	0.259539i	−0.781325	−	0.624124i	$-0.785456\pi$
$577$	3.59940	−	6.23435i	0.149845	−	0.259539i	0.931170	+	0.364585i	$0.118789\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$		0			0
$580$	−1.27058			−0.0527578
$581$	0.448864	+	5.20192i	0.0186220	+	0.215812i
$582$		0			0
$583$	−0.454904	−	0.787917i	−0.0188402	−	0.0326322i
$584$	5.33816	−	9.24596i	0.220895	−	0.382601i
$585$		0			0
$586$	−5.18959	−	8.98864i	−0.214380	−	0.371317i
$587$	44.4959			1.83654			0.918272	−	0.395951i	$-0.129585\pi$
$587$	44.4959			1.83654			0.918272	+	0.395951i	$0.129585\pi$
$588$		0			0
$589$	−37.2254			−1.53384
$590$	1.58612	+	2.74725i	0.0652997	+	0.113102i
$591$		0			0
$592$	−3.94163	+	6.82710i	−0.162000	+	0.280592i
$593$	8.98266	+	15.5584i	0.368873	+	0.638908i	0.989390	−	0.145286i	$-0.0464102\pi$
$593$	8.98266	+	15.5584i	0.368873	+	0.638908i	−0.620516	+	0.784194i	$0.713077\pi$
$594$		0			0
$595$	−0.103469	−	1.19911i	−0.00424181	−	0.0491586i
$596$	−4.11675			−0.168628
$597$		0			0
$598$	−3.79306	+	6.56978i	−0.155110	+	0.268658i
$599$	−12.9038	+	22.3500i	−0.527234	+	0.913196i	0.472263	+	0.881458i	$0.343437\pi$
$599$	−12.9038	+	22.3500i	−0.527234	+	0.913196i	−0.999496	+	0.0317376i	$0.989896\pi$
$600$		0			0
$601$	10.4139			0.424791			0.212395	−	0.977184i	$-0.431874\pi$
$601$	10.4139			0.424791			0.212395	+	0.977184i	$0.431874\pi$
$602$	17.0994	−	11.9428i	0.696920	−	0.486752i
$603$		0			0
$604$	3.07889	+	5.33279i	0.125278	+	0.216988i
$605$	0.227452	−	0.393958i	0.00924724	−	0.0160167i
$606$		0			0
$607$	4.44886	+	7.70566i	0.180574	+	0.312763i	0.942076	−	0.335399i	$-0.108871\pi$
$607$	4.44886	+	7.70566i	0.180574	+	0.312763i	−0.761502	+	0.648162i	$0.775538\pi$
$608$	−3.88325			−0.157487
$609$		0			0
$610$	−6.38732			−0.258615
$611$	0.153830	+	0.266441i	0.00622328	+	0.0107790i
$612$		0			0
$613$	11.8136	−	20.4617i	0.477146	−	0.826441i	−0.522511	−	0.852632i	$-0.675005\pi$
$613$	11.8136	−	20.4617i	0.477146	−	0.826441i	0.999657	+	0.0261916i	$0.00833800\pi$
$614$	4.88325	+	8.45804i	0.197072	+	0.341339i
$615$		0			0
$616$	2.39653	+	1.12100i	0.0965590	+	0.0451663i
$617$	35.8486			1.44321			0.721604	−	0.692306i	$-0.243405\pi$
$617$	35.8486			1.44321			0.721604	+	0.692306i	$0.243405\pi$
$618$		0			0
$619$	−13.9602	+	24.1797i	−0.561107	+	0.971865i	0.436294	+	0.899804i	$0.356291\pi$
$619$	−13.9602	+	24.1797i	−0.561107	+	0.971865i	−0.997400	+	0.0720607i	$0.977042\pi$
$620$	−2.18038	+	3.77654i	−0.0875663	+	0.151669i
$621$		0			0
$622$	−6.51854			−0.261370
$623$	−24.0555	+	16.8012i	−0.963763	+	0.673125i
$624$		0			0
$625$	−10.9694	−	18.9995i	−0.438775	−	0.759981i
$626$	15.3965	−	26.6676i	0.615369	−	1.06585i
$627$		0			0
$628$	8.82488	+	15.2851i	0.352151	+	0.609944i
$629$	−7.88325			−0.314326
$630$		0			0
$631$	43.6682			1.73840			0.869201	−	0.494458i	$-0.164633\pi$
$631$	43.6682			1.73840			0.869201	+	0.494458i	$0.164633\pi$
$632$	2.68236	+	4.64598i	0.106698	+	0.184807i
$633$		0			0
$634$	13.8136	−	23.9258i	0.548607	−	0.950216i
$635$	1.68959	+	2.92646i	0.0670495	+	0.116133i
$636$		0			0
$637$	−6.27452	+	1.09096i	−0.248606	+	0.0432253i
$638$	2.79306			0.110578
$639$		0			0
$640$	−0.227452	+	0.393958i	−0.00899083	+	0.0155726i
$641$	−9.88325	+	17.1183i	−0.390365	+	0.676132i	−0.992498	−	0.122264i	$-0.960985\pi$
$641$	−9.88325	+	17.1183i	−0.390365	+	0.676132i	0.602133	+	0.798396i	$0.294318\pi$
$642$		0			0
$643$	24.7584			0.976375			0.488187	−	0.872739i	$-0.337658\pi$
$643$	24.7584			0.976375			0.488187	+	0.872739i	$0.337658\pi$
$644$	1.89653	+	21.9790i	0.0747338	+	0.866095i
$645$		0			0
$646$	−1.94163	−	3.36300i	−0.0763923	−	0.132315i
$647$	15.5391	−	26.9144i	0.610903	−	1.05812i	−0.380185	−	0.924910i	$-0.624140\pi$
$647$	15.5391	−	26.9144i	0.610903	−	1.05812i	0.991088	−	0.133205i	$-0.0425269\pi$
$648$		0			0
$649$	−3.48672	−	6.03918i	−0.136866	−	0.237059i
$650$	4.36077			0.171043
$651$		0			0
$652$	−11.6127			−0.454788
$653$	11.3587	+	19.6738i	0.444499	+	0.769895i	0.998017	−	0.0629420i	$-0.0200483\pi$
$653$	11.3587	+	19.6738i	0.444499	+	0.769895i	−0.553518	+	0.832837i	$0.686715\pi$
$654$		0			0
$655$	4.41388	−	7.64506i	0.172464	−	0.298717i
$656$	−0.896531	−	1.55284i	−0.0350037	−	0.0606281i
$657$		0			0
$658$	0.810407	+	0.379075i	0.0315929	+	0.0147779i
$659$	−43.6127			−1.69891			−0.849454	−	0.527662i	$-0.823069\pi$
$659$	−43.6127			−1.69891			−0.849454	+	0.527662i	$0.823069\pi$
$660$		0			0
$661$	3.96818	−	6.87309i	0.154344	−	0.267332i	−0.778476	−	0.627675i	$-0.784007\pi$
$661$	3.96818	−	6.87309i	0.154344	−	0.267332i	0.932820	+	0.360342i	$0.117340\pi$
$662$	−14.4827	+	25.0847i	−0.562884	+	0.974944i
$663$		0			0
$664$	1.97345			0.0765846
$665$	−4.23349	−	1.98025i	−0.164168	−	0.0767909i
$666$		0			0
$667$	11.6445	+	20.1689i	0.450877	+	0.780941i
$668$	−2.42835	+	4.20603i	−0.0939557	+	0.162736i
$669$		0			0
$670$	0.862740	+	1.49431i	0.0333305	+	0.0577302i
$671$	14.0410			0.542048
$672$		0			0
$673$	36.9388			1.42388			0.711942	−	0.702238i	$-0.247816\pi$
$673$	36.9388			1.42388			0.711942	+	0.702238i	$0.247816\pi$
$674$	−4.51854	−	7.82634i	−0.174048	−	0.301460i
$675$		0			0
$676$	6.08612	−	10.5415i	0.234082	−	0.405441i
$677$	−19.8249	−	34.3377i	−0.761932	−	1.31971i	−0.941853	−	0.336024i	$-0.890918\pi$
$677$	−19.8249	−	34.3377i	−0.761932	−	1.31971i	0.179921	−	0.983681i	$-0.442416\pi$
$678$		0			0
$679$	−3.31764	−	38.4484i	−0.127319	−	1.47551i
$680$	−0.454904			−0.0174448
$681$		0			0
$682$	4.79306	−	8.30183i	0.183536	−	0.317893i
$683$	−22.7757	+	39.4487i	−0.871489	+	1.50946i	−0.0110318	+	0.999939i	$0.503512\pi$
$683$	−22.7757	+	39.4487i	−0.871489	+	1.50946i	−0.860457	+	0.509523i	$0.829822\pi$
$684$		0			0
$685$	0.413875			0.0158134
$686$	−13.1425	+	13.0489i	−0.501784	+	0.498210i
$687$		0			0
$688$	−3.94163	−	6.82710i	−0.150273	−	0.260281i
$689$	0.413875	−	0.716853i	0.0157674	−	0.0273099i
$690$		0			0
$691$	9.59940	+	16.6267i	0.365178	+	0.632508i	0.988805	−	0.149215i	$-0.0476746\pi$
$691$	9.59940	+	16.6267i	0.365178	+	0.632508i	−0.623626	+	0.781723i	$0.714341\pi$
$692$	25.5861			0.972639
$693$		0			0
$694$	−21.6127			−0.820406
$695$	−1.90586	−	3.30105i	−0.0722935	−	0.125216i
$696$		0			0
$697$	0.896531	−	1.55284i	0.0339585	−	0.0588179i
$698$	7.13726	+	12.3621i	0.270149	+	0.467912i
$699$		0			0
$700$	10.3965	−	7.26129i	0.392952	−	0.274451i
$701$	−23.2890			−0.879613			−0.439807	−	0.898093i	$-0.644953\pi$
$701$	−23.2890			−0.879613			−0.439807	+	0.898093i	$0.644953\pi$
$702$		0			0
$703$	−15.3063	+	26.5114i	−0.577290	+	0.999895i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	−28.4959			−1.07246
$707$	19.3248	+	9.03933i	0.726782	+	0.339959i
$708$		0			0
$709$	10.3965	+	18.0073i	0.390450	+	0.676279i	0.992509	−	0.122173i	$-0.0389861\pi$
$709$	10.3965	+	18.0073i	0.390450	+	0.676279i	−0.602059	+	0.798452i	$0.705653\pi$
$710$	−1.09019	+	1.88827i	−0.0409142	+	0.0708654i
$711$		0			0
$712$	5.54510	+	9.60439i	0.207811	+	0.359940i
$713$	79.9306			2.99343
$714$		0			0
$715$	0.413875			0.0154781
$716$	−7.85144	−	13.5991i	−0.293422	−	0.508222i
$717$		0			0
$718$	6.81962	−	11.8119i	0.254506	−	0.440817i
$719$	−2.74073	−	4.74708i	−0.102212	−	0.177036i	0.810384	−	0.585899i	$-0.199259\pi$
$719$	−2.74073	−	4.74708i	−0.102212	−	0.177036i	−0.912596	+	0.408863i	$0.865925\pi$
$720$		0			0
$721$	−12.5080	+	8.73601i	−0.465823	+	0.325346i
$722$	3.92034			0.145900
$723$		0			0
$724$	1.24797	−	2.16154i	0.0463803	−	0.0803330i
$725$	6.69366	−	11.5938i	0.248596	−	0.430581i
$726$		0			0
$727$	25.5330			0.946967			0.473484	−	0.880803i	$-0.342996\pi$
$727$	25.5330			0.946967			0.473484	+	0.880803i	$0.342996\pi$
$728$	0.206938	+	2.39821i	0.00766962	+	0.0888837i
$729$		0			0
$730$	−2.42835	−	4.20603i	−0.0898773	−	0.155672i
$731$	3.94163	−	6.82710i	0.145786	−	0.252509i
$732$		0			0
$733$	−8.11071	−	14.0482i	−0.299576	−	0.518880i	0.676463	−	0.736476i	$-0.263512\pi$
$733$	−8.11071	−	14.0482i	−0.299576	−	0.518880i	−0.976039	+	0.217596i	$0.930178\pi$
$734$	−22.7294			−0.838958
$735$		0			0
$736$	8.33816			0.307349
$737$	−1.89653	−	3.28489i	−0.0698596	−	0.121000i
$738$		0			0
$739$	−9.37919	+	16.2452i	−0.345019	+	0.597590i	−0.985357	−	0.170503i	$-0.945461\pi$
$739$	−9.37919	+	16.2452i	−0.345019	+	0.597590i	0.640338	+	0.768093i	$0.278794\pi$
$740$	1.79306	+	3.10567i	0.0659143	+	0.114167i
$741$		0			0
$742$	−0.206938	−	2.39821i	−0.00759692	−	0.0880412i
$743$	44.6763			1.63902			0.819508	−	0.573068i	$-0.194247\pi$
$743$	44.6763			1.63902			0.819508	+	0.573068i	$0.194247\pi$
$744$		0			0
$745$	−0.936362	+	1.62183i	−0.0343057	+	0.0594191i
$746$	5.20090	−	9.00822i	0.190418	−	0.329814i
$747$		0			0
$748$	1.00000			0.0365636
$749$	33.8651	−	23.6525i	1.23741	−	0.864245i
$750$		0			0
$751$	1.48146	+	2.56596i	0.0540592	+	0.0936332i	0.891789	−	0.452452i	$-0.149451\pi$
$751$	1.48146	+	2.56596i	0.0540592	+	0.0936332i	−0.837729	+	0.546085i	$0.816117\pi$
$752$	0.169079	−	0.292854i	0.00616568	−	0.0106793i
$753$		0			0
$754$	1.27058	+	2.20070i	0.0462716	+	0.0801448i
$755$	2.80120			0.101946
$756$		0			0
$757$	26.1988			0.952212			0.476106	−	0.879388i	$-0.342048\pi$
$757$	26.1988			0.952212			0.476106	+	0.879388i	$0.342048\pi$
$758$	3.80634	+	6.59277i	0.138252	+	0.239460i
$759$		0			0
$760$	−0.883254	+	1.52984i	−0.0320390	+	0.0554932i
$761$	12.8965	+	22.3374i	0.467499	+	0.809732i	0.999310	−	0.0371309i	$-0.0118219\pi$
$761$	12.8965	+	22.3374i	0.467499	+	0.809732i	−0.531812	+	0.846863i	$0.678489\pi$
$762$		0			0
$763$	33.6498	+	15.7400i	1.21820	+	0.569825i
$764$	−9.81962			−0.355261
$765$		0			0
$766$	11.0728	−	19.1787i	0.400078	−	0.692956i
$767$	3.17225	−	5.49450i	0.114543	−	0.198395i
$768$		0			0
$769$	−37.2012			−1.34151			−0.670755	−	0.741679i	$-0.734030\pi$
$769$	−37.2012			−1.34151			−0.670755	+	0.741679i	$0.734030\pi$
$770$	0.986723	−	0.689160i	0.0355590	−	0.0248356i
$771$		0			0
$772$	−3.42835	−	5.93808i	−0.123389	−	0.213716i
$773$	−20.3852	+	35.3082i	−0.733206	+	1.26995i	0.222300	+	0.974978i	$0.428643\pi$
$773$	−20.3852	+	35.3082i	−0.733206	+	1.26995i	−0.955506	+	0.294971i	$0.904690\pi$
$774$		0			0
$775$	−22.9734	−	39.7912i	−0.825231	−	1.42934i
$776$	−14.5861			−0.523611
$777$		0			0
$778$	−3.54510			−0.127098
$779$	−3.48146	−	6.03006i	−0.124736	−	0.216049i
$780$		0			0
$781$	2.39653	−	4.15091i	0.0857546	−	0.148531i
$782$	4.16908	+	7.22106i	0.149086	+	0.258224i
$783$		0			0
$784$	4.48672	+	5.37302i	0.160240	+	0.191893i
$785$	8.02895			0.286565
$786$		0			0
$787$	−27.2943	+	47.2750i	−0.972935	+	1.68517i	−0.286348	+	0.958126i	$0.592441\pi$
$787$	−27.2943	+	47.2750i	−0.972935	+	1.68517i	−0.686587	+	0.727048i	$0.740892\pi$
$788$	11.7347	−	20.3251i	0.418031	−	0.724051i
$789$		0			0
$790$	2.44043			0.0868266
$791$	1.72548	+	19.9967i	0.0613510	+	0.711001i
$792$		0			0
$793$	6.38732	+	11.0632i	0.226820	+	0.392865i
$794$	−1.27979	+	2.21665i	−0.0454179	+	0.0786661i
$795$		0			0
$796$	1.11675	+	1.93426i	0.0395820	+	0.0685581i
$797$	16.7705			0.594040			0.297020	−	0.954871i	$-0.404007\pi$
$797$	16.7705			0.594040			0.297020	+	0.954871i	$0.404007\pi$
$798$		0			0
$799$	0.338158			0.0119632
$800$	−2.39653	−	4.15091i	−0.0847302	−	0.146757i
$801$		0			0
$802$	−5.24797	+	9.08974i	−0.185312	+	0.320970i
$803$	5.33816	+	9.24596i	0.188380	+	0.326283i
$804$		0			0
$805$	9.09019	+	4.25202i	0.320387	+	0.149864i
$806$	8.72153			0.307203
$807$		0			0
$808$	4.03182	−	6.98332i	0.141839	−	0.245672i
$809$	−5.10347	+	8.83947i	−0.179428	+	0.310779i	−0.941685	−	0.336496i	$-0.890758\pi$
$809$	−5.10347	+	8.83947i	−0.179428	+	0.310779i	0.762257	+	0.647275i	$0.224091\pi$
$810$		0			0
$811$	−28.4139			−0.997746			−0.498873	−	0.866675i	$-0.666253\pi$
$811$	−28.4139			−0.997746			−0.498873	+	0.866675i	$0.666253\pi$
$812$	6.69366	+	3.13102i	0.234901	+	0.109877i
$813$		0			0
$814$	−3.94163	−	6.82710i	−0.138154	−	0.239290i
$815$	−2.64133	+	4.57491i	−0.0925217	+	0.160252i
$816$		0			0
$817$	−15.3063	−	26.5114i	−0.535501	−	0.927515i
$818$	−15.8486			−0.554132
$819$		0			0
$820$	−0.815671			−0.0284845
$821$	−1.70287	−	2.94946i	−0.0594306	−	0.102937i	0.834779	−	0.550585i	$-0.185595\pi$
$821$	−1.70287	−	2.94946i	−0.0594306	−	0.102937i	−0.894210	+	0.447648i	$0.852262\pi$
$822$		0			0
$823$	19.0145	−	32.9340i	0.662803	−	1.14801i	−0.317073	−	0.948401i	$-0.602700\pi$
$823$	19.0145	−	32.9340i	0.662803	−	1.14801i	0.979876	−	0.199607i	$-0.0639666\pi$
$824$	2.88325	+	4.99394i	0.100443	+	0.173972i
$825$		0			0
$826$	−1.58612	−	18.3817i	−0.0551883	−	0.639581i
$827$	12.9653			0.450848			0.225424	−	0.974261i	$-0.427623\pi$
$827$	12.9653			0.450848			0.225424	+	0.974261i	$0.427623\pi$
$828$		0			0
$829$	−25.9416	+	44.9322i	−0.900990	+	1.56056i	−0.0747785	+	0.997200i	$0.523825\pi$
$829$	−25.9416	+	44.9322i	−0.900990	+	1.56056i	−0.826211	+	0.563360i	$0.809508\pi$
$830$	0.448864	−	0.777456i	0.0155803	−	0.0269859i
$831$		0			0
$832$	0.909808			0.0315419
$833$	−2.40981	+	6.57212i	−0.0834949	+	0.227711i
$834$		0			0
$835$	1.10467	+	1.91334i	0.0382286	+	0.0662138i
$836$	1.94163	−	3.36300i	0.0671526	−	0.116312i
$837$		0			0
$838$	4.76124	+	8.24672i	0.164474	+	0.284878i
$839$	50.2504			1.73484			0.867418	−	0.497581i	$-0.165778\pi$
$839$	50.2504			1.73484			0.867418	+	0.497581i	$0.165778\pi$
$840$		0			0
$841$	−21.1988			−0.730993
$842$	−0.265311	−	0.459532i	−0.00914321	−	0.0158365i
$843$		0			0
$844$	9.13122	−	15.8157i	0.314310	−	0.544400i
$845$	−2.76860	−	4.79536i	−0.0952428	−	0.164965i
$846$		0			0
$847$	−2.16908	+	1.51496i	−0.0745304	+	0.0520546i
$848$	−0.909808			−0.0312429
$849$		0			0
$850$	2.39653	−	4.15091i	0.0822003	−	0.142375i
$851$	32.8659	−	56.9254i	1.12663	−	1.95138i
$852$		0			0
$853$	13.3647			0.457599			0.228800	−	0.973474i	$-0.426520\pi$
$853$	13.3647			0.457599			0.228800	+	0.973474i	$0.426520\pi$
$854$	33.6498	+	15.7400i	1.15147	+	0.538611i
$855$		0			0
$856$	−7.80634	−	13.5210i	−0.266815	−	0.462137i
$857$	13.1763	−	22.8220i	0.450094	−	0.779586i	−0.548297	−	0.836284i	$-0.684724\pi$
$857$	13.1763	−	22.8220i	0.450094	−	0.779586i	0.998391	+	0.0566973i	$0.0180570\pi$
$858$		0			0
$859$	−0.986723	−	1.70905i	−0.0336666	−	0.0583122i	0.848701	−	0.528873i	$-0.177385\pi$
$859$	−0.986723	−	1.70905i	−0.0336666	−	0.0583122i	−0.882368	+	0.470560i	$0.844052\pi$
$860$	−3.58612			−0.122286
$861$		0			0
$862$	20.8036			0.708573
$863$	−24.9038	−	43.1346i	−0.847734	−	1.46832i	−0.883225	−	0.468949i	$-0.844633\pi$
$863$	−24.9038	−	43.1346i	−0.847734	−	1.46832i	0.0354913	−	0.999370i	$-0.488700\pi$
$864$		0			0
$865$	5.81962	−	10.0799i	0.197873	−	0.342726i
$866$	−2.20287	−	3.81548i	−0.0748566	−	0.129655i
$867$		0			0
$868$	20.7931	−	14.5226i	0.705763	−	0.492928i
$869$	−5.36471			−0.181985
$870$		0			0
$871$	1.72548	−	2.98862i	0.0584656	−	0.101265i
$872$	7.02051	−	12.1599i	0.237745	−	0.411786i
$873$		0			0
$874$	32.3792			1.09524
$875$	−1.01328	−	11.7429i	−0.0342550	−	0.396984i
$876$		0			0
$877$	12.2685	+	21.2496i	0.414277	+	0.717549i	0.995352	−	0.0963008i	$-0.0307011\pi$
$877$	12.2685	+	21.2496i	0.414277	+	0.717549i	−0.581075	+	0.813850i	$0.697368\pi$
$878$	−7.59743	+	13.1591i	−0.256401	+	0.444099i
$879$		0			0
$880$	−0.227452	−	0.393958i	−0.00766741	−	0.0132803i
$881$	−11.5861			−0.390346			−0.195173	−	0.980769i	$-0.562527\pi$
$881$	−11.5861			−0.390346			−0.195173	+	0.980769i	$0.562527\pi$
$882$		0			0
$883$	−44.1376			−1.48535			−0.742674	−	0.669654i	$-0.766443\pi$
$883$	−44.1376			−1.48535			−0.742674	+	0.669654i	$0.766443\pi$
$884$	0.454904	+	0.787917i	0.0153001	+	0.0265005i
$885$		0			0
$886$	5.69366	−	9.86171i	0.191282	−	0.331311i
$887$	−10.0145	−	17.3456i	−0.336253	−	0.582408i	0.647472	−	0.762090i	$-0.275826\pi$
$887$	−10.0145	−	17.3456i	−0.336253	−	0.582408i	−0.983725	+	0.179682i	$0.942493\pi$
$888$		0			0
$889$	−1.68959	−	19.5808i	−0.0566671	−	0.656719i
$890$	5.04497			0.169108
$891$		0			0
$892$	−6.24797	+	10.8218i	−0.209197	+	0.362341i
$893$	0.656577	−	1.13722i	0.0219715	−	0.0380558i
$894$		0			0
$895$	−7.14330			−0.238774
$896$	2.16908	−	1.51496i	0.0724638	−	0.0506112i
$897$		0			0
$898$	12.0410	+	20.8557i	0.401814	+	0.695963i
$899$	13.3873	−	23.1875i	0.446492	−	0.773347i
$900$		0			0
$901$	−0.454904	−	0.787917i	−0.0151551	−	0.0262493i
$902$	1.79306			0.0597024
$903$		0			0
$904$	7.58612			0.252311
$905$	−0.567705	−	0.983294i	−0.0188712	−	0.0326858i
$906$		0			0
$907$	8.96017	−	15.5195i	0.297518	−	0.515315i	−0.678050	−	0.735016i	$-0.737175\pi$
$907$	8.96017	−	15.5195i	0.297518	−	0.515315i	0.975567	+	0.219700i	$0.0705080\pi$
$908$	4.89653	+	8.48104i	0.162497	+	0.281453i
$909$		0			0
$910$	0.991865	+	0.463954i	0.0328800	+	0.0153799i
$911$	−13.9695			−0.462830			−0.231415	−	0.972855i	$-0.574336\pi$
$911$	−13.9695			−0.462830			−0.231415	+	0.972855i	$0.574336\pi$
$912$		0			0
$913$	−0.986723	+	1.70905i	−0.0326558	+	0.0565614i
$914$	−14.7665	+	25.5763i	−0.488433	+	0.845990i
$915$		0			0
$916$	8.67632			0.286674
$917$	−42.0926	+	29.3989i	−1.39002	+	0.970836i
$918$		0			0
$919$	21.4807	+	37.2056i	0.708582	+	1.22730i	0.965383	+	0.260836i	$0.0839983\pi$
$919$	21.4807	+	37.2056i	0.708582	+	1.22730i	−0.256801	+	0.966464i	$0.582668\pi$
$920$	1.89653	−	3.28489i	0.0625268	−	0.108300i
$921$		0			0
$922$	−2.07285	−	3.59028i	−0.0682656	−	0.118239i
$923$	4.36077			0.143536
$924$		0			0
$925$	−37.7849			−1.24236
$926$	−4.66184	−	8.07455i	−0.153198	−	0.265346i
$927$		0			0
$928$	1.39653	−	2.41886i	0.0458434	−	0.0794031i
$929$	−12.8341	−	22.2293i	−0.421073	−	0.729320i	0.574972	−	0.818173i	$-0.305013\pi$
$929$	−12.8341	−	22.2293i	−0.421073	−	0.729320i	−0.996045	+	0.0888536i	$0.971680\pi$
$930$		0			0
$931$	17.4231	+	20.8648i	0.571019	+	0.683816i
$932$	−16.7665			−0.549205
$933$		0			0
$934$	−18.2798	+	31.6615i	−0.598133	+	1.03600i
$935$	0.227452	−	0.393958i	0.00743848	−	0.0128838i
$936$		0			0
$937$	26.7584			0.874158			0.437079	−	0.899423i	$-0.356013\pi$
$937$	26.7584			0.874158			0.437079	+	0.899423i	$0.356013\pi$
$938$	−0.862740	−	9.99835i	−0.0281695	−	0.326458i
$939$		0			0
$940$	−0.0769148	−	0.133220i	−0.00250868	−	0.00434517i
$941$	−7.81041	+	13.5280i	−0.254612	+	0.441001i	−0.964790	−	0.263021i	$-0.915281\pi$
$941$	−7.81041	+	13.5280i	−0.254612	+	0.441001i	0.710178	+	0.704022i	$0.248614\pi$
$942$		0			0
$943$	7.47542	+	12.9478i	0.243433	+	0.421639i
$944$	−6.97345			−0.226966
$945$		0			0
$946$	7.88325			0.256307
$947$	9.89246	+	17.1343i	0.321462	+	0.556788i	0.980790	−	0.195067i	$-0.0624925\pi$
$947$	9.89246	+	17.1343i	0.321462	+	0.556788i	−0.659328	+	0.751855i	$0.729159\pi$
$948$		0			0
$949$	−4.85670	+	8.41205i	−0.157655	+	0.273067i
$950$	−9.30634	−	16.1191i	−0.301938	−	0.522971i
$951$		0			0
$952$	2.39653	+	1.12100i	0.0776720	+	0.0363318i
$953$	−43.5065			−1.40931			−0.704656	−	0.709549i	$-0.748899\pi$
$953$	−43.5065			−1.40931			−0.704656	+	0.709549i	$0.748899\pi$
$954$		0			0
$955$	−2.23349	+	3.86852i	−0.0722741	+	0.125182i
$956$	−13.1312	+	22.7439i	−0.424694	+	0.735592i
$957$		0			0
$958$	0.729425			0.0235666
$959$	−2.18038	−	1.01989i	−0.0704083	−	0.0329341i
$960$		0			0
$961$	−30.4469	−	52.7356i	−0.982158	−	1.70115i
$962$	3.58612	−	6.21135i	0.115621	−	0.200262i
$963$		0			0
$964$	−3.97345	−	6.88221i	−0.127976	−	0.221661i
$965$	−3.11914			−0.100409
$966$		0			0
$967$	34.5185			1.11004			0.555021	−	0.831837i	$-0.312710\pi$
$967$	34.5185			1.11004			0.555021	+	0.831837i	$0.312710\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	−3.31764	+	5.74633i	−0.106523	+	0.184503i
$971$	−22.4694	−	38.9181i	−0.721077	−	1.24894i	−0.960569	−	0.278043i	$-0.910314\pi$
$971$	−22.4694	−	38.9181i	−0.721077	−	1.24894i	0.239492	−	0.970898i	$-0.423019\pi$
$972$		0			0
$973$	1.90586	+	22.0872i	0.0610992	+	0.708082i
$974$	36.8567			1.18096
$975$		0			0
$976$	7.02051	−	12.1599i	0.224721	−	0.389229i
$977$	16.2624	−	28.1674i	0.520282	−	0.901154i	−0.479440	−	0.877574i	$-0.659160\pi$
$977$	16.2624	−	28.1674i	0.520282	−	0.901154i	0.999722	−	0.0235797i	$-0.00750634\pi$
$978$		0			0
$979$	−11.0902			−0.354444
$980$	3.13726	−	0.545479i	0.100216	−	0.0174247i
$981$		0			0
$982$	−12.7532	−	22.0892i	−0.406972	−	0.704896i
$983$	−23.5974	+	40.8719i	−0.752641	+	1.30361i	0.193897	+	0.981022i	$0.437887\pi$
$983$	−23.5974	+	40.8719i	−0.752641	+	1.30361i	−0.946539	+	0.322591i	$0.895446\pi$
$984$		0			0
$985$	−5.33816	−	9.24596i	−0.170088	−	0.294601i
$986$	2.79306			0.0889492
$987$		0			0
$988$	3.53302			0.112400
$989$	32.8659	+	56.9254i	1.04508	+	1.81012i
$990$		0			0
$991$	−6.27452	+	10.8678i	−0.199317	+	0.345227i	−0.948307	−	0.317354i	$-0.897206\pi$
$991$	−6.27452	+	10.8678i	−0.199317	+	0.345227i	0.748990	+	0.662581i	$0.230539\pi$
$992$	−4.79306	−	8.30183i	−0.152180	−	0.263583i
$993$		0			0
$994$	10.3965	−	7.26129i	0.329758	−	0.230314i
$995$	1.01602			0.0322101
$996$		0			0
$997$	−20.4549	+	35.4289i	−0.647813	+	1.12205i	0.335831	+	0.941922i	$0.390983\pi$
$997$	−20.4549	+	35.4289i	−0.647813	+	1.12205i	−0.983644	+	0.180123i	$0.942350\pi$
$998$	−2.06364	+	3.57433i	−0.0653233	+	0.113143i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.w.991.2		6
3.2	odd	2		462.2.i.f.67.2	✓	6
7.2	even	3	inner	1386.2.k.w.793.2		6
7.3	odd	6		9702.2.a.du.1.2		3
7.4	even	3		9702.2.a.dt.1.2		3
21.2	odd	6		462.2.i.f.331.2	yes	6
21.11	odd	6		3234.2.a.bi.1.2		3
21.17	even	6		3234.2.a.bg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.f.67.2	✓	6	3.2	odd	2
462.2.i.f.331.2	yes	6	21.2	odd	6
1386.2.k.w.793.2		6	7.2	even	3	inner
1386.2.k.w.991.2		6	1.1	even	1	trivial
3234.2.a.bg.1.2		3	21.17	even	6
3234.2.a.bi.1.2		3	21.11	odd	6
9702.2.a.dt.1.2		3	7.4	even	3
9702.2.a.du.1.2		3	7.3	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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.227452 + 0.393958i) q^{5} +(-0.227452 - 2.63596i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.227452 + 0.393958i) q^{5} +(-0.227452 - 2.63596i) q^{7} -1.00000 q^{8} +(-0.227452 + 0.393958i) q^{10} +(0.500000 - 0.866025i) q^{11} +0.909808 q^{13} +(2.16908 - 1.51496i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-1.94163 - 3.36300i) q^{19} -0.454904 q^{20} +1.00000 q^{22} +(4.16908 + 7.22106i) q^{23} +(2.39653 - 4.15091i) q^{25} +(0.454904 + 0.787917i) q^{26} +(2.39653 + 1.12100i) q^{28} +2.79306 q^{29} +(4.79306 - 8.30183i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(0.986723 - 0.689160i) q^{35} +(-3.94163 - 6.82710i) q^{37} +(1.94163 - 3.36300i) q^{38} +(-0.227452 - 0.393958i) q^{40} +1.79306 q^{41} +7.88325 q^{43} +(0.500000 + 0.866025i) q^{44} +(-4.16908 + 7.22106i) q^{46} +(0.169079 + 0.292854i) q^{47} +(-6.89653 + 1.19911i) q^{49} +4.79306 q^{50} +(-0.454904 + 0.787917i) q^{52} +(0.454904 - 0.787917i) q^{53} +0.454904 q^{55} +(0.227452 + 2.63596i) q^{56} +(1.39653 + 2.41886i) q^{58} +(3.48672 - 6.03918i) q^{59} +(7.02051 + 12.1599i) q^{61} +9.58612 q^{62} +1.00000 q^{64} +(0.206938 + 0.358427i) q^{65} +(1.89653 - 3.28489i) q^{67} +(0.500000 + 0.866025i) q^{68} +(1.09019 + 0.509947i) q^{70} +4.79306 q^{71} +(-5.33816 + 9.24596i) q^{73} +(3.94163 - 6.82710i) q^{74} +3.88325 q^{76} +(-2.39653 - 1.12100i) q^{77} +(-2.68236 - 4.64598i) q^{79} +(0.227452 - 0.393958i) q^{80} +(0.896531 + 1.55284i) q^{82} -1.97345 q^{83} +0.454904 q^{85} +(3.94163 + 6.82710i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-5.54510 - 9.60439i) q^{89} +(-0.206938 - 2.39821i) q^{91} -8.33816 q^{92} +(-0.169079 + 0.292854i) q^{94} +(0.883254 - 1.52984i) q^{95} +14.5861 q^{97} +(-4.48672 - 5.37302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} + 3 q^{11} - 3 q^{14} - 3 q^{16} + 3 q^{17} + 3 q^{19} + 6 q^{22} + 9 q^{23} - 3 q^{25} - 3 q^{28} - 18 q^{29} - 6 q^{31} + 3 q^{32} + 6 q^{34} - 6 q^{35} - 9 q^{37} - 3 q^{38} - 24 q^{41} + 18 q^{43} + 3 q^{44} - 9 q^{46} - 15 q^{47} - 24 q^{49} - 6 q^{50} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} + 6 q^{64} + 36 q^{65} - 6 q^{67} + 3 q^{68} + 12 q^{70} - 6 q^{71} + 9 q^{74} - 6 q^{76} + 3 q^{77} - 12 q^{79} - 12 q^{82} + 12 q^{83} + 9 q^{86} - 3 q^{88} - 36 q^{89} - 36 q^{91} - 18 q^{92} + 15 q^{94} - 24 q^{95} + 18 q^{97} - 15 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 + 3 * q^11 - 3 * q^14 - 3 * q^16 + 3 * q^17 + 3 * q^19 + 6 * q^22 + 9 * q^23 - 3 * q^25 - 3 * q^28 - 18 * q^29 - 6 * q^31 + 3 * q^32 + 6 * q^34 - 6 * q^35 - 9 * q^37 - 3 * q^38 - 24 * q^41 + 18 * q^43 + 3 * q^44 - 9 * q^46 - 15 * q^47 - 24 * q^49 - 6 * q^50 - 9 * q^58 + 9 * q^59 + 6 * q^61 - 12 * q^62 + 6 * q^64 + 36 * q^65 - 6 * q^67 + 3 * q^68 + 12 * q^70 - 6 * q^71 + 9 * q^74 - 6 * q^76 + 3 * q^77 - 12 * q^79 - 12 * q^82 + 12 * q^83 + 9 * q^86 - 3 * q^88 - 36 * q^89 - 36 * q^91 - 18 * q^92 + 15 * q^94 - 24 * q^95 + 18 * q^97 - 15 * q^98

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