LMFDB - Embedded newform 546.2.l.j.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.j.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.27492 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.27492 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.63746 - 2.83616i) q^{10} +(2.00000 - 3.46410i) q^{11} +1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.63746 - 2.83616i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(4.27492 + 7.40437i) q^{19} +(1.63746 + 2.83616i) q^{20} +1.00000 q^{21} +(2.00000 + 3.46410i) q^{22} +(-1.13746 + 1.97014i) q^{23} +(-0.500000 + 0.866025i) q^{24} +5.72508 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-0.362541 + 0.627940i) q^{29} +(1.63746 + 2.83616i) q^{30} +6.27492 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +3.00000 q^{34} +(1.63746 + 2.83616i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.63746 - 6.30026i) q^{37} -8.54983 q^{38} +(-2.50000 + 2.59808i) q^{39} -3.27492 q^{40} +(-0.362541 + 0.627940i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-5.41238 - 9.37451i) q^{43} -4.00000 q^{44} +(1.63746 + 2.83616i) q^{45} +(-1.13746 - 1.97014i) q^{46} +8.54983 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.86254 + 4.95807i) q^{50} +3.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +11.5498 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.54983 + 11.3446i) q^{55} +(-0.500000 - 0.866025i) q^{56} -8.54983 q^{57} +(-0.362541 - 0.627940i) q^{58} +(-5.41238 - 9.37451i) q^{59} -3.27492 q^{60} +(4.50000 + 7.79423i) q^{61} +(-3.13746 + 5.43424i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-11.4622 - 2.83616i) q^{65} -4.00000 q^{66} +(5.13746 - 8.89834i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-1.13746 - 1.97014i) q^{69} -3.27492 q^{70} +(1.13746 + 1.97014i) q^{71} +(-0.500000 - 0.866025i) q^{72} +13.2749 q^{73} +(3.63746 + 6.30026i) q^{74} +(-2.86254 + 4.95807i) q^{75} +(4.27492 - 7.40437i) q^{76} -4.00000 q^{77} +(-1.00000 - 3.46410i) q^{78} -8.00000 q^{79} +(1.63746 - 2.83616i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.362541 - 0.627940i) q^{82} +10.8248 q^{83} +(-0.500000 - 0.866025i) q^{84} +(4.91238 + 8.50848i) q^{85} +10.8248 q^{86} +(-0.362541 - 0.627940i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-4.13746 + 7.16629i) q^{89} -3.27492 q^{90} +(-1.00000 - 3.46410i) q^{91} +2.27492 q^{92} +(-3.13746 + 5.43424i) q^{93} +(-4.27492 + 7.40437i) q^{94} +(-14.0000 - 24.2487i) q^{95} +1.00000 q^{96} +(-7.27492 - 12.6005i) q^{97} +(-0.500000 - 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - q^{10} + 8 q^{11} + 4 q^{12} + 14 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{18} + 2 q^{19} - q^{20} + 4 q^{21} + 8 q^{22} + 3 q^{23} - 2 q^{24} + 38 q^{25} - 10 q^{26} + 4 q^{27} - 2 q^{28} - 9 q^{29} - q^{30} + 10 q^{31} - 2 q^{32} + 8 q^{33} + 12 q^{34} - q^{35} - 2 q^{36} + 7 q^{37} - 4 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} - 2 q^{42} + q^{43} - 16 q^{44} - q^{45} + 3 q^{46} + 4 q^{47} - 2 q^{48} - 2 q^{49} - 19 q^{50} + 12 q^{51} - 4 q^{52} + 16 q^{53} - 2 q^{54} + 4 q^{55} - 2 q^{56} - 4 q^{57} - 9 q^{58} + q^{59} + 2 q^{60} + 18 q^{61} - 5 q^{62} - 2 q^{63} + 4 q^{64} + 7 q^{65} - 16 q^{66} + 13 q^{67} - 6 q^{68} + 3 q^{69} + 2 q^{70} - 3 q^{71} - 2 q^{72} + 38 q^{73} + 7 q^{74} - 19 q^{75} + 2 q^{76} - 16 q^{77} - 4 q^{78} - 32 q^{79} - q^{80} - 2 q^{81} - 9 q^{82} - 2 q^{83} - 2 q^{84} - 3 q^{85} - 2 q^{86} - 9 q^{87} + 8 q^{88} - 9 q^{89} + 2 q^{90} - 4 q^{91} - 6 q^{92} - 5 q^{93} - 2 q^{94} - 56 q^{95} + 4 q^{96} - 14 q^{97} - 2 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - q^10 + 8 * q^11 + 4 * q^12 + 14 * q^13 + 4 * q^14 - q^15 - 2 * q^16 - 6 * q^17 + 4 * q^18 + 2 * q^19 - q^20 + 4 * q^21 + 8 * q^22 + 3 * q^23 - 2 * q^24 + 38 * q^25 - 10 * q^26 + 4 * q^27 - 2 * q^28 - 9 * q^29 - q^30 + 10 * q^31 - 2 * q^32 + 8 * q^33 + 12 * q^34 - q^35 - 2 * q^36 + 7 * q^37 - 4 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 - 2 * q^42 + q^43 - 16 * q^44 - q^45 + 3 * q^46 + 4 * q^47 - 2 * q^48 - 2 * q^49 - 19 * q^50 + 12 * q^51 - 4 * q^52 + 16 * q^53 - 2 * q^54 + 4 * q^55 - 2 * q^56 - 4 * q^57 - 9 * q^58 + q^59 + 2 * q^60 + 18 * q^61 - 5 * q^62 - 2 * q^63 + 4 * q^64 + 7 * q^65 - 16 * q^66 + 13 * q^67 - 6 * q^68 + 3 * q^69 + 2 * q^70 - 3 * q^71 - 2 * q^72 + 38 * q^73 + 7 * q^74 - 19 * q^75 + 2 * q^76 - 16 * q^77 - 4 * q^78 - 32 * q^79 - q^80 - 2 * q^81 - 9 * q^82 - 2 * q^83 - 2 * q^84 - 3 * q^85 - 2 * q^86 - 9 * q^87 + 8 * q^88 - 9 * q^89 + 2 * q^90 - 4 * q^91 - 6 * q^92 - 5 * q^93 - 2 * q^94 - 56 * q^95 + 4 * q^96 - 14 * q^97 - 2 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.27492			−1.46459			−0.732294	−	0.680989i	$-0.761550\pi$
$5$	−3.27492			−1.46459			−0.732294	+	0.680989i	$0.761550\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.63746	−	2.83616i	0.517810	−	0.896873i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	1.00000			0.288675
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	1.00000			0.267261
$15$	1.63746	−	2.83616i	0.422790	−	0.732294i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	1.00000			0.235702
$19$	4.27492	+	7.40437i	0.980733	+	1.69868i	0.659546	+	0.751664i	$0.270749\pi$
$19$	4.27492	+	7.40437i	0.980733	+	1.69868i	0.321187	+	0.947016i	$0.395918\pi$
$20$	1.63746	+	2.83616i	0.366147	+	0.634185i
$21$	1.00000			0.218218
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$	−1.13746	+	1.97014i	−0.237177	+	0.410802i	−0.959903	−	0.280332i	$-0.909555\pi$
$23$	−1.13746	+	1.97014i	−0.237177	+	0.410802i	0.722726	+	0.691134i	$0.242889\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	5.72508			1.14502
$26$	−2.50000	+	2.59808i	−0.490290	+	0.509525i
$27$	1.00000			0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−0.362541	+	0.627940i	−0.0673222	+	0.116606i	−0.897722	−	0.440563i	$-0.854779\pi$
$29$	−0.362541	+	0.627940i	−0.0673222	+	0.116606i	0.830400	+	0.557168i	$0.188112\pi$
$30$	1.63746	+	2.83616i	0.298958	+	0.517810i
$31$	6.27492			1.12701			0.563504	−	0.826113i	$-0.309453\pi$
$31$	6.27492			1.12701			0.563504	+	0.826113i	$0.309453\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$	3.00000			0.514496
$35$	1.63746	+	2.83616i	0.276781	+	0.479399i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.63746	−	6.30026i	0.597995	−	1.03576i	−0.395122	−	0.918629i	$-0.629298\pi$
$37$	3.63746	−	6.30026i	0.597995	−	1.03576i	0.993117	−	0.117128i	$-0.0373689\pi$
$38$	−8.54983			−1.38697
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$	−3.27492			−0.517810
$41$	−0.362541	+	0.627940i	−0.0566195	+	0.0980678i	−0.892946	−	0.450164i	$-0.851366\pi$
$41$	−0.362541	+	0.627940i	−0.0566195	+	0.0980678i	0.836326	+	0.548232i	$0.184699\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−5.41238	−	9.37451i	−0.825380	−	1.42960i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−5.41238	−	9.37451i	−0.825380	−	1.42960i	0.0762493	−	0.997089i	$-0.475706\pi$
$44$	−4.00000			−0.603023
$45$	1.63746	+	2.83616i	0.244098	+	0.422790i
$46$	−1.13746	−	1.97014i	−0.167709	−	0.290481i
$47$	8.54983			1.24712			0.623561	−	0.781775i	$-0.285685\pi$
$47$	8.54983			1.24712			0.623561	+	0.781775i	$0.285685\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.86254	+	4.95807i	−0.404824	+	0.701177i
$51$	3.00000			0.420084
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	11.5498			1.58649			0.793246	−	0.608901i	$-0.208390\pi$
$53$	11.5498			1.58649			0.793246	+	0.608901i	$0.208390\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−6.54983	+	11.3446i	−0.883179	+	1.52971i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−8.54983			−1.13245
$58$	−0.362541	−	0.627940i	−0.0476040	−	0.0824526i
$59$	−5.41238	−	9.37451i	−0.704631	−	1.22046i	−0.966824	−	0.255442i	$-0.917779\pi$
$59$	−5.41238	−	9.37451i	−0.704631	−	1.22046i	0.262193	−	0.965015i	$-0.415554\pi$
$60$	−3.27492			−0.422790
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$	−3.13746	+	5.43424i	−0.398458	+	0.690149i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	−11.4622	−	2.83616i	−1.42171	−	0.351783i
$66$	−4.00000			−0.492366
$67$	5.13746	−	8.89834i	0.627640	−	1.08711i	−0.360383	−	0.932804i	$-0.617354\pi$
$67$	5.13746	−	8.89834i	0.627640	−	1.08711i	0.988024	−	0.154301i	$-0.0493125\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	−1.13746	−	1.97014i	−0.136934	−	0.237177i
$70$	−3.27492			−0.391427
$71$	1.13746	+	1.97014i	0.134992	+	0.233812i	0.925594	−	0.378517i	$-0.123566\pi$
$71$	1.13746	+	1.97014i	0.134992	+	0.233812i	−0.790603	+	0.612329i	$0.790233\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	13.2749			1.55371			0.776856	−	0.629679i	$-0.216813\pi$
$73$	13.2749			1.55371			0.776856	+	0.629679i	$0.216813\pi$
$74$	3.63746	+	6.30026i	0.422846	+	0.732391i
$75$	−2.86254	+	4.95807i	−0.330538	+	0.572508i
$76$	4.27492	−	7.40437i	0.490367	−	0.849340i
$77$	−4.00000			−0.455842
$78$	−1.00000	−	3.46410i	−0.113228	−	0.392232i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.63746	−	2.83616i	0.183073	−	0.317092i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.362541	−	0.627940i	−0.0400360	−	0.0693444i
$83$	10.8248			1.18817			0.594085	−	0.804402i	$-0.297514\pi$
$83$	10.8248			1.18817			0.594085	+	0.804402i	$0.297514\pi$
$84$	−0.500000	−	0.866025i	−0.0545545	−	0.0944911i
$85$	4.91238	+	8.50848i	0.532822	+	0.922875i
$86$	10.8248			1.16726
$87$	−0.362541	−	0.627940i	−0.0388685	−	0.0673222i
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	−4.13746	+	7.16629i	−0.438570	+	0.759625i	−0.997579	−	0.0695360i	$-0.977848\pi$
$89$	−4.13746	+	7.16629i	−0.438570	+	0.759625i	0.559010	+	0.829161i	$0.311181\pi$
$90$	−3.27492			−0.345207
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	2.27492			0.237177
$93$	−3.13746	+	5.43424i	−0.325339	+	0.563504i
$94$	−4.27492	+	7.40437i	−0.440924	+	0.763703i
$95$	−14.0000	−	24.2487i	−1.43637	−	2.48787i
$96$	1.00000			0.102062
$97$	−7.27492	−	12.6005i	−0.738656	−	1.27939i	−0.953101	−	0.302653i	$-0.902128\pi$
$97$	−7.27492	−	12.6005i	−0.738656	−	1.27939i	0.214445	−	0.976736i	$-0.431206\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	−4.00000			−0.402015
$100$	−2.86254	−	4.95807i	−0.286254	−	0.495807i
$101$	−4.63746	+	8.03231i	−0.461444	+	0.799245i	−0.999033	−	0.0439620i	$-0.986002\pi$
$101$	−4.63746	+	8.03231i	−0.461444	+	0.799245i	0.537589	+	0.843207i	$0.319335\pi$
$102$	−1.50000	+	2.59808i	−0.148522	+	0.257248i
$103$	−2.27492			−0.224154			−0.112077	−	0.993700i	$-0.535750\pi$
$103$	−2.27492			−0.224154			−0.112077	+	0.993700i	$0.535750\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$	−3.27492			−0.319599
$106$	−5.77492	+	10.0025i	−0.560910	+	0.971524i
$107$	6.27492	−	10.8685i	0.606619	−	1.05070i	−0.385174	−	0.922844i	$-0.625859\pi$
$107$	6.27492	−	10.8685i	0.606619	−	1.05070i	0.991793	−	0.127851i	$-0.0408080\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	10.5498			1.01049			0.505245	−	0.862976i	$-0.331402\pi$
$109$	10.5498			1.01049			0.505245	+	0.862976i	$0.331402\pi$
$110$	−6.54983	−	11.3446i	−0.624502	−	1.08167i
$111$	3.63746	+	6.30026i	0.345252	+	0.597995i
$112$	1.00000			0.0944911
$113$	3.91238	+	6.77643i	0.368045	+	0.637473i	0.989260	−	0.146167i	$-0.0466938\pi$
$113$	3.91238	+	6.77643i	0.368045	+	0.637473i	−0.621215	+	0.783641i	$0.713360\pi$
$114$	4.27492	−	7.40437i	0.400383	−	0.693483i
$115$	3.72508	−	6.45203i	0.347366	−	0.601655i
$116$	0.725083			0.0673222
$117$	−1.00000	−	3.46410i	−0.0924500	−	0.320256i
$118$	10.8248			0.996499
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$	1.63746	−	2.83616i	0.149479	−	0.258905i
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−9.00000			−0.814822
$123$	−0.362541	−	0.627940i	−0.0326893	−	0.0566195i
$124$	−3.13746	−	5.43424i	−0.281752	−	0.488009i
$125$	−2.37459			−0.212389
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	10.8248			0.953066
$130$	8.18729	−	8.50848i	0.718073	−	0.746243i
$131$	−10.2749			−0.897724			−0.448862	−	0.893601i	$-0.648170\pi$
$131$	−10.2749			−0.897724			−0.448862	+	0.893601i	$0.648170\pi$
$132$	2.00000	−	3.46410i	0.174078	−	0.301511i
$133$	4.27492	−	7.40437i	0.370682	−	0.642041i
$134$	5.13746	+	8.89834i	0.443809	+	0.768699i
$135$	−3.27492			−0.281860
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−0.0876242	−	0.151770i	−0.00748624	−	0.0129665i	0.862258	−	0.506469i	$-0.169050\pi$
$137$	−0.0876242	−	0.151770i	−0.00748624	−	0.0129665i	−0.869744	+	0.493503i	$0.835716\pi$
$138$	2.27492			0.193654
$139$	−10.5498	−	18.2728i	−0.894825	−	1.54988i	−0.834021	−	0.551733i	$-0.813967\pi$
$139$	−10.5498	−	18.2728i	−0.894825	−	1.54988i	−0.0608046	−	0.998150i	$-0.519367\pi$
$140$	1.63746	−	2.83616i	0.138391	−	0.239699i
$141$	−4.27492	+	7.40437i	−0.360013	+	0.623561i
$142$	−2.27492			−0.190907
$143$	10.0000	−	10.3923i	0.836242	−	0.869048i
$144$	1.00000			0.0833333
$145$	1.18729	−	2.05645i	0.0985993	−	0.170779i
$146$	−6.63746	+	11.4964i	−0.549320	+	0.951450i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−7.27492			−0.597995
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$	−2.86254	−	4.95807i	−0.233726	−	0.404824i
$151$	−17.0997			−1.39155			−0.695776	−	0.718259i	$-0.744939\pi$
$151$	−17.0997			−1.39155			−0.695776	+	0.718259i	$0.744939\pi$
$152$	4.27492	+	7.40437i	0.346742	+	0.600574i
$153$	−1.50000	+	2.59808i	−0.121268	+	0.210042i
$154$	2.00000	−	3.46410i	0.161165	−	0.279145i
$155$	−20.5498			−1.65060
$156$	3.50000	+	0.866025i	0.280224	+	0.0693375i
$157$	−11.2749			−0.899836			−0.449918	−	0.893070i	$-0.648547\pi$
$157$	−11.2749			−0.899836			−0.449918	+	0.893070i	$0.648547\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	−5.77492	+	10.0025i	−0.457981	+	0.793246i
$160$	1.63746	+	2.83616i	0.129452	+	0.224218i
$161$	2.27492			0.179289
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	2.86254	+	4.95807i	0.224212	+	0.388346i	0.956083	−	0.293097i	$-0.0946860\pi$
$163$	2.86254	+	4.95807i	0.224212	+	0.388346i	−0.731871	+	0.681443i	$0.761353\pi$
$164$	0.725083			0.0566195
$165$	−6.54983	−	11.3446i	−0.509904	−	0.883179i
$166$	−5.41238	+	9.37451i	−0.420082	+	0.727603i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	1.00000			0.0771517
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−9.82475			−0.753524
$171$	4.27492	−	7.40437i	0.326911	−	0.566227i
$172$	−5.41238	+	9.37451i	−0.412690	+	0.714800i
$173$	−5.27492	−	9.13642i	−0.401045	−	0.694630i	0.592808	−	0.805344i	$-0.298019\pi$
$173$	−5.27492	−	9.13642i	−0.401045	−	0.694630i	−0.993852	+	0.110715i	$0.964686\pi$
$174$	0.725083			0.0549684
$175$	−2.86254	−	4.95807i	−0.216388	−	0.374795i
$176$	2.00000	+	3.46410i	0.150756	+	0.261116i
$177$	10.8248			0.813638
$178$	−4.13746	−	7.16629i	−0.310116	−	0.537136i
$179$	−8.27492	+	14.3326i	−0.618496	+	1.07127i	0.371264	+	0.928527i	$0.378925\pi$
$179$	−8.27492	+	14.3326i	−0.618496	+	1.07127i	−0.989760	+	0.142740i	$0.954409\pi$
$180$	1.63746	−	2.83616i	0.122049	−	0.211395i
$181$	5.82475			0.432950			0.216475	−	0.976288i	$-0.430544\pi$
$181$	5.82475			0.432950			0.216475	+	0.976288i	$0.430544\pi$
$182$	3.50000	+	0.866025i	0.259437	+	0.0641941i
$183$	−9.00000			−0.665299
$184$	−1.13746	+	1.97014i	−0.0838546	+	0.145240i
$185$	−11.9124	+	20.6328i	−0.875815	+	1.51696i
$186$	−3.13746	−	5.43424i	−0.230050	−	0.398458i
$187$	−12.0000			−0.877527
$188$	−4.27492	−	7.40437i	−0.311780	−	0.540019i
$189$	−0.500000	−	0.866025i	−0.0363696	−	0.0629941i
$190$	28.0000			2.03133
$191$	−7.13746	−	12.3624i	−0.516448	−	0.894515i	−0.999818	−	0.0190983i	$-0.993920\pi$
$191$	−7.13746	−	12.3624i	−0.516448	−	0.894515i	0.483369	−	0.875417i	$-0.339413\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	1.08762	−	1.88382i	0.0782889	−	0.135600i	−0.824223	−	0.566266i	$-0.808388\pi$
$193$	1.08762	−	1.88382i	0.0782889	−	0.135600i	0.902512	+	0.430665i	$0.141721\pi$
$194$	14.5498			1.04462
$195$	8.18729	−	8.50848i	0.586304	−	0.609305i
$196$	1.00000			0.0714286
$197$	−0.412376	+	0.714256i	−0.0293806	+	0.0508886i	−0.880342	−	0.474340i	$-0.842687\pi$
$197$	−0.412376	+	0.714256i	−0.0293806	+	0.0508886i	0.850961	+	0.525228i	$0.176020\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	5.41238	+	9.37451i	0.383673	+	0.664541i	0.991584	−	0.129464i	$-0.0413256\pi$
$199$	5.41238	+	9.37451i	0.383673	+	0.664541i	−0.607911	+	0.794005i	$0.707992\pi$
$200$	5.72508			0.404824
$201$	5.13746	+	8.89834i	0.362368	+	0.627640i
$202$	−4.63746	−	8.03231i	−0.326290	−	0.565152i
$203$	0.725083			0.0508908
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$	1.18729	−	2.05645i	0.0829241	−	0.143629i
$206$	1.13746	−	1.97014i	0.0792505	−	0.137266i
$207$	2.27492			0.158118
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	34.1993			2.36562
$210$	1.63746	−	2.83616i	0.112995	−	0.195714i
$211$	4.54983	−	7.88054i	0.313224	−	0.542519i	−0.665835	−	0.746099i	$-0.731924\pi$
$211$	4.54983	−	7.88054i	0.313224	−	0.542519i	0.979058	+	0.203580i	$0.0652578\pi$
$212$	−5.77492	−	10.0025i	−0.396623	−	0.686971i
$213$	−2.27492			−0.155875
$214$	6.27492	+	10.8685i	0.428945	+	0.742954i
$215$	17.7251	+	30.7007i	1.20884	+	2.09377i
$216$	1.00000			0.0680414
$217$	−3.13746	−	5.43424i	−0.212985	−	0.368900i
$218$	−5.27492	+	9.13642i	−0.357262	+	0.618797i
$219$	−6.63746	+	11.4964i	−0.448518	+	0.776856i
$220$	13.0997			0.883179
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$	−7.27492			−0.488260
$223$	−9.13746	+	15.8265i	−0.611889	+	1.05982i	0.379032	+	0.925383i	$0.376257\pi$
$223$	−9.13746	+	15.8265i	−0.611889	+	1.05982i	−0.990922	+	0.134440i	$0.957076\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−2.86254	−	4.95807i	−0.190836	−	0.330538i
$226$	−7.82475			−0.520495
$227$	−4.54983	−	7.88054i	−0.301983	−	0.523050i	0.674602	−	0.738182i	$-0.264315\pi$
$227$	−4.54983	−	7.88054i	−0.301983	−	0.523050i	−0.976585	+	0.215132i	$0.930982\pi$
$228$	4.27492	+	7.40437i	0.283113	+	0.490367i
$229$	20.2749			1.33980			0.669902	−	0.742449i	$-0.266336\pi$
$229$	20.2749			1.33980			0.669902	+	0.742449i	$0.266336\pi$
$230$	3.72508	+	6.45203i	0.245625	+	0.425434i
$231$	2.00000	−	3.46410i	0.131590	−	0.227921i
$232$	−0.362541	+	0.627940i	−0.0238020	+	0.0412263i
$233$	22.5498			1.47729			0.738644	−	0.674095i	$-0.235466\pi$
$233$	22.5498			1.47729			0.738644	+	0.674095i	$0.235466\pi$
$234$	3.50000	+	0.866025i	0.228802	+	0.0566139i
$235$	−28.0000			−1.82652
$236$	−5.41238	+	9.37451i	−0.352316	+	0.610229i
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	2.27492			0.147152			0.0735761	−	0.997290i	$-0.476559\pi$
$239$	2.27492			0.147152			0.0735761	+	0.997290i	$0.476559\pi$
$240$	1.63746	+	2.83616i	0.105697	+	0.183073i
$241$	11.6375	+	20.1567i	0.749635	+	1.29841i	0.947998	+	0.318277i	$0.103104\pi$
$241$	11.6375	+	20.1567i	0.749635	+	1.29841i	−0.198363	+	0.980129i	$0.563563\pi$
$242$	5.00000			0.321412
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.50000	−	7.79423i	0.288083	−	0.498974i
$245$	1.63746	−	2.83616i	0.104613	−	0.181196i
$246$	0.725083			0.0462296
$247$	8.54983	+	29.6175i	0.544013	+	1.88452i
$248$	6.27492			0.398458
$249$	−5.41238	+	9.37451i	−0.342995	+	0.594085i
$250$	1.18729	−	2.05645i	0.0750910	−	0.130061i
$251$	−2.86254	−	4.95807i	−0.180682	−	0.312950i	0.761431	−	0.648246i	$-0.224497\pi$
$251$	−2.86254	−	4.95807i	−0.180682	−	0.312950i	−0.942113	+	0.335296i	$0.891164\pi$
$252$	1.00000			0.0629941
$253$	4.54983	+	7.88054i	0.286046	+	0.495446i
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$	−9.82475			−0.615250
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$	−5.41238	+	9.37451i	−0.336960	+	0.583631i
$259$	−7.27492			−0.452041
$260$	3.27492	+	11.3446i	0.203102	+	0.703565i
$261$	0.725083			0.0448815
$262$	5.13746	−	8.89834i	0.317393	−	0.549741i
$263$	4.54983	−	7.88054i	0.280555	−	0.485935i	−0.690967	−	0.722887i	$-0.742815\pi$
$263$	4.54983	−	7.88054i	0.280555	−	0.485935i	0.971522	+	0.236951i	$0.0761482\pi$
$264$	2.00000	+	3.46410i	0.123091	+	0.213201i
$265$	−37.8248			−2.32356
$266$	4.27492	+	7.40437i	0.262112	+	0.453991i
$267$	−4.13746	−	7.16629i	−0.253208	−	0.438570i
$268$	−10.2749			−0.627640
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$	1.63746	−	2.83616i	0.0996526	−	0.172603i
$271$	−8.86254	+	15.3504i	−0.538361	+	0.932469i	0.460631	+	0.887591i	$0.347623\pi$
$271$	−8.86254	+	15.3504i	−0.538361	+	0.932469i	−0.998993	+	0.0448772i	$0.985710\pi$
$272$	3.00000			0.181902
$273$	3.50000	+	0.866025i	0.211830	+	0.0524142i
$274$	0.175248			0.0105871
$275$	11.4502	−	19.8323i	0.690471	−	1.19593i
$276$	−1.13746	+	1.97014i	−0.0684670	+	0.118588i
$277$	3.91238	+	6.77643i	0.235072	+	0.407156i	0.959294	−	0.282411i	$-0.0911341\pi$
$277$	3.91238	+	6.77643i	0.235072	+	0.407156i	−0.724222	+	0.689567i	$0.757801\pi$
$278$	21.0997			1.26547
$279$	−3.13746	−	5.43424i	−0.187835	−	0.325339i
$280$	1.63746	+	2.83616i	0.0978569	+	0.169493i
$281$	1.82475			0.108856			0.0544278	−	0.998518i	$-0.482667\pi$
$281$	1.82475			0.108856			0.0544278	+	0.998518i	$0.482667\pi$
$282$	−4.27492	−	7.40437i	−0.254568	−	0.440924i
$283$	12.2749	−	21.2608i	0.729668	−	1.26382i	−0.227355	−	0.973812i	$-0.573008\pi$
$283$	12.2749	−	21.2608i	0.729668	−	1.26382i	0.957024	−	0.290010i	$-0.0936588\pi$
$284$	1.13746	−	1.97014i	0.0674958	−	0.116906i
$285$	28.0000			1.65858
$286$	4.00000	+	13.8564i	0.236525	+	0.819346i
$287$	0.725083			0.0428003
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	1.18729	+	2.05645i	0.0697202	+	0.120759i
$291$	14.5498			0.852926
$292$	−6.63746	−	11.4964i	−0.388428	−	0.672777i
$293$	5.36254	+	9.28819i	0.313283	+	0.542622i	0.979071	−	0.203519i	$-0.0652378\pi$
$293$	5.36254	+	9.28819i	0.313283	+	0.542622i	−0.665788	+	0.746141i	$0.731904\pi$
$294$	1.00000			0.0583212
$295$	17.7251	+	30.7007i	1.03199	+	1.78747i
$296$	3.63746	−	6.30026i	0.211423	−	0.366195i
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$	−1.00000			−0.0579284
$299$	−5.68729	+	5.91041i	−0.328905	+	0.341808i
$300$	5.72508			0.330538
$301$	−5.41238	+	9.37451i	−0.311964	+	0.540338i
$302$	8.54983	−	14.8087i	0.491988	−	0.852148i
$303$	−4.63746	−	8.03231i	−0.266415	−	0.461444i
$304$	−8.54983			−0.490367
$305$	−14.7371	−	25.5255i	−0.843845	−	1.46158i
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	−16.5498			−0.944549			−0.472274	−	0.881452i	$-0.656567\pi$
$307$	−16.5498			−0.944549			−0.472274	+	0.881452i	$0.656567\pi$
$308$	2.00000	+	3.46410i	0.113961	+	0.197386i
$309$	1.13746	−	1.97014i	0.0647078	−	0.112077i
$310$	10.2749	−	17.7967i	0.583576	−	1.01078i
$311$	12.5498			0.711636			0.355818	−	0.934555i	$-0.384202\pi$
$311$	12.5498			0.711636			0.355818	+	0.934555i	$0.384202\pi$
$312$	−2.50000	+	2.59808i	−0.141535	+	0.147087i
$313$	−27.6495			−1.56284			−0.781421	−	0.624004i	$-0.785505\pi$
$313$	−27.6495			−1.56284			−0.781421	+	0.624004i	$0.785505\pi$
$314$	5.63746	−	9.76436i	0.318140	−	0.551035i
$315$	1.63746	−	2.83616i	0.0922603	−	0.159800i
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	7.54983			0.424041			0.212020	−	0.977265i	$-0.431996\pi$
$317$	7.54983			0.424041			0.212020	+	0.977265i	$0.431996\pi$
$318$	−5.77492	−	10.0025i	−0.323841	−	0.560910i
$319$	1.45017	+	2.51176i	0.0811937	+	0.140632i
$320$	−3.27492			−0.183073
$321$	6.27492	+	10.8685i	0.350232	+	0.606619i
$322$	−1.13746	+	1.97014i	−0.0633881	+	0.109791i
$323$	12.8248	−	22.2131i	0.713588	−	1.23597i
$324$	1.00000			0.0555556
$325$	20.0378	+	4.95807i	1.11150	+	0.275024i
$326$	−5.72508			−0.317083
$327$	−5.27492	+	9.13642i	−0.291704	+	0.505245i
$328$	−0.362541	+	0.627940i	−0.0200180	+	0.0346722i
$329$	−4.27492	−	7.40437i	−0.235684	−	0.408216i
$330$	13.0997			0.721113
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	−5.41238	−	9.37451i	−0.297043	−	0.514493i
$333$	−7.27492			−0.398663
$334$		0			0
$335$	−16.8248	+	29.1413i	−0.919234	+	1.59216i
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	−7.27492			−0.396290			−0.198145	−	0.980173i	$-0.563492\pi$
$337$	−7.27492			−0.396290			−0.198145	+	0.980173i	$0.563492\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	−7.82475			−0.424982
$340$	4.91238	−	8.50848i	0.266411	−	0.461437i
$341$	12.5498	−	21.7370i	0.679612	−	1.17712i
$342$	4.27492	+	7.40437i	0.231161	+	0.400383i
$343$	1.00000			0.0539949
$344$	−5.41238	−	9.37451i	−0.291816	−	0.505440i
$345$	3.72508	+	6.45203i	0.200552	+	0.347366i
$346$	10.5498			0.567163
$347$	−7.72508	−	13.3802i	−0.414704	−	0.718289i	0.580693	−	0.814122i	$-0.302782\pi$
$347$	−7.72508	−	13.3802i	−0.414704	−	0.718289i	−0.995397	+	0.0958338i	$0.969448\pi$
$348$	−0.362541	+	0.627940i	−0.0194343	+	0.0336611i
$349$	−8.96221	+	15.5230i	−0.479736	+	0.830927i	−0.999730	−	0.0232427i	$-0.992601\pi$
$349$	−8.96221	+	15.5230i	−0.479736	+	0.830927i	0.519994	+	0.854170i	$0.325934\pi$
$350$	5.72508			0.306019
$351$	3.50000	+	0.866025i	0.186816	+	0.0462250i
$352$	−4.00000			−0.213201
$353$	2.22508	−	3.85396i	0.118429	−	0.205125i	−0.800716	−	0.599044i	$-0.795547\pi$
$353$	2.22508	−	3.85396i	0.118429	−	0.205125i	0.919145	+	0.393919i	$0.128881\pi$
$354$	−5.41238	+	9.37451i	−0.287665	+	0.498250i
$355$	−3.72508	−	6.45203i	−0.197707	−	0.342438i
$356$	8.27492			0.438570
$357$	−1.50000	−	2.59808i	−0.0793884	−	0.137505i
$358$	−8.27492	−	14.3326i	−0.437343	−	0.757500i
$359$	29.0997			1.53582			0.767911	−	0.640557i	$-0.221296\pi$
$359$	29.0997			1.53582			0.767911	+	0.640557i	$0.221296\pi$
$360$	1.63746	+	2.83616i	0.0863016	+	0.149479i
$361$	−27.0498	+	46.8517i	−1.42368	+	2.46588i
$362$	−2.91238	+	5.04438i	−0.153071	+	0.265127i
$363$	5.00000			0.262432
$364$	−2.50000	+	2.59808i	−0.131036	+	0.136176i
$365$	−43.4743			−2.27555
$366$	4.50000	−	7.79423i	0.235219	−	0.407411i
$367$	−2.86254	+	4.95807i	−0.149423	+	0.258809i	−0.931015	−	0.364982i	$-0.881075\pi$
$367$	−2.86254	+	4.95807i	−0.149423	+	0.258809i	0.781591	+	0.623791i	$0.214408\pi$
$368$	−1.13746	−	1.97014i	−0.0592941	−	0.102700i
$369$	0.725083			0.0377463
$370$	−11.9124	−	20.6328i	−0.619295	−	1.07265i
$371$	−5.77492	−	10.0025i	−0.299819	−	0.519301i
$372$	6.27492			0.325339
$373$	−2.08762	−	3.61587i	−0.108093	−	0.187223i	0.806905	−	0.590682i	$-0.201141\pi$
$373$	−2.08762	−	3.61587i	−0.108093	−	0.187223i	−0.914998	+	0.403459i	$0.867808\pi$
$374$	6.00000	−	10.3923i	0.310253	−	0.537373i
$375$	1.18729	−	2.05645i	0.0613115	−	0.106195i
$376$	8.54983			0.440924
$377$	−1.81271	+	1.88382i	−0.0933592	+	0.0970217i
$378$	1.00000			0.0514344
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	−14.0000	+	24.2487i	−0.718185	+	1.24393i
$381$	−4.00000	−	6.92820i	−0.204926	−	0.354943i
$382$	14.2749			0.730368
$383$	19.0997	+	33.0816i	0.975947	+	1.69039i	0.676772	+	0.736192i	$0.263378\pi$
$383$	19.0997	+	33.0816i	0.975947	+	1.69039i	0.299175	+	0.954198i	$0.403288\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	13.0997			0.667621
$386$	1.08762	+	1.88382i	0.0553586	+	0.0958839i
$387$	−5.41238	+	9.37451i	−0.275127	+	0.476533i
$388$	−7.27492	+	12.6005i	−0.369328	+	0.639695i
$389$	20.6495			1.04697			0.523486	−	0.852034i	$-0.324631\pi$
$389$	20.6495			1.04697			0.523486	+	0.852034i	$0.324631\pi$
$390$	3.27492	+	11.3446i	0.165832	+	0.574458i
$391$	6.82475			0.345143
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	5.13746	−	8.89834i	0.259151	−	0.448862i
$394$	−0.412376	−	0.714256i	−0.0207752	−	0.0359837i
$395$	26.1993			1.31823
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−7.86254	−	13.6183i	−0.394610	−	0.683484i	0.598442	−	0.801166i	$-0.295787\pi$
$397$	−7.86254	−	13.6183i	−0.394610	−	0.683484i	−0.993051	+	0.117682i	$0.962454\pi$
$398$	−10.8248			−0.542596
$399$	4.27492	+	7.40437i	0.214014	+	0.370682i
$400$	−2.86254	+	4.95807i	−0.143127	+	0.247903i
$401$	−2.63746	+	4.56821i	−0.131708	+	0.228126i	−0.924335	−	0.381581i	$-0.875380\pi$
$401$	−2.63746	+	4.56821i	−0.131708	+	0.228126i	0.792627	+	0.609707i	$0.208713\pi$
$402$	−10.2749			−0.512466
$403$	21.9622	+	5.43424i	1.09402	+	0.270699i
$404$	9.27492			0.461444
$405$	1.63746	−	2.83616i	0.0813660	−	0.140930i
$406$	−0.362541	+	0.627940i	−0.0179926	+	0.0311641i
$407$	−14.5498	−	25.2011i	−0.721209	−	1.24917i
$408$	3.00000			0.148522
$409$	−11.4622	−	19.8531i	−0.566770	−	0.981674i	−0.996883	−	0.0788990i	$-0.974860\pi$
$409$	−11.4622	−	19.8531i	−0.566770	−	0.981674i	0.430113	−	0.902775i	$-0.358474\pi$
$410$	1.18729	+	2.05645i	0.0586362	+	0.101561i
$411$	0.175248			0.00864436
$412$	1.13746	+	1.97014i	0.0560386	+	0.0970616i
$413$	−5.41238	+	9.37451i	−0.266326	+	0.461289i
$414$	−1.13746	+	1.97014i	−0.0559030	+	0.0968269i
$415$	−35.4502			−1.74018
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$	21.0997			1.03326
$418$	−17.0997	+	29.6175i	−0.836372	+	1.44864i
$419$	−7.68729	+	13.3148i	−0.375549	+	0.650470i	−0.990409	−	0.138166i	$-0.955879\pi$
$419$	−7.68729	+	13.3148i	−0.375549	+	0.650470i	0.614860	+	0.788636i	$0.289212\pi$
$420$	1.63746	+	2.83616i	0.0798998	+	0.138391i
$421$	0.725083			0.0353384			0.0176692	−	0.999844i	$-0.494375\pi$
$421$	0.725083			0.0353384			0.0176692	+	0.999844i	$0.494375\pi$
$422$	4.54983	+	7.88054i	0.221482	+	0.383619i
$423$	−4.27492	−	7.40437i	−0.207854	−	0.360013i
$424$	11.5498			0.560910
$425$	−8.58762	−	14.8742i	−0.416561	−	0.721505i
$426$	1.13746	−	1.97014i	0.0551100	−	0.0954534i
$427$	4.50000	−	7.79423i	0.217770	−	0.377189i
$428$	−12.5498			−0.606619
$429$	4.00000	+	13.8564i	0.193122	+	0.668994i
$430$	−35.4502			−1.70956
$431$	2.86254	−	4.95807i	0.137884	−	0.238822i	−0.788812	−	0.614635i	$-0.789303\pi$
$431$	2.86254	−	4.95807i	0.137884	−	0.238822i	0.926695	+	0.375813i	$0.122637\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	1.36254	+	2.35999i	0.0654796	+	0.113414i	0.896907	−	0.442220i	$-0.145809\pi$
$433$	1.36254	+	2.35999i	0.0654796	+	0.113414i	−0.831427	+	0.555634i	$0.812476\pi$
$434$	6.27492			0.301206
$435$	1.18729	+	2.05645i	0.0569263	+	0.0985993i
$436$	−5.27492	−	9.13642i	−0.252623	−	0.437555i
$437$	−19.4502			−0.930428
$438$	−6.63746	−	11.4964i	−0.317150	−	0.549320i
$439$	8.54983	−	14.8087i	0.408061	−	0.706783i	−0.586611	−	0.809869i	$-0.699538\pi$
$439$	8.54983	−	14.8087i	0.408061	−	0.706783i	0.994672	+	0.103086i	$0.0328716\pi$
$440$	−6.54983	+	11.3446i	−0.312251	+	0.540835i
$441$	1.00000			0.0476190
$442$	10.5000	+	2.59808i	0.499434	+	0.123578i
$443$	19.4502			0.924105			0.462053	−	0.886853i	$-0.347113\pi$
$443$	19.4502			0.924105			0.462053	+	0.886853i	$0.347113\pi$
$444$	3.63746	−	6.30026i	0.172626	−	0.298997i
$445$	13.5498	−	23.4690i	0.642324	−	1.11254i
$446$	−9.13746	−	15.8265i	−0.432671	−	0.749409i
$447$	−1.00000			−0.0472984
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−5.54983	−	9.61260i	−0.261913	−	0.453646i	0.704837	−	0.709369i	$-0.251020\pi$
$449$	−5.54983	−	9.61260i	−0.261913	−	0.453646i	−0.966750	+	0.255723i	$0.917687\pi$
$450$	5.72508			0.269883
$451$	1.45017	+	2.51176i	0.0682856	+	0.118274i
$452$	3.91238	−	6.77643i	0.184023	−	0.318737i
$453$	8.54983	−	14.8087i	0.401706	−	0.695776i
$454$	9.09967			0.427069
$455$	3.27492	+	11.3446i	0.153530	+	0.531845i
$456$	−8.54983			−0.400383
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$	−10.1375	+	17.5586i	−0.473692	+	0.820459i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$	−7.45017			−0.347366
$461$	−9.18729	−	15.9129i	−0.427895	−	0.741136i	0.568791	−	0.822482i	$-0.307411\pi$
$461$	−9.18729	−	15.9129i	−0.427895	−	0.741136i	−0.996686	+	0.0813464i	$0.974078\pi$
$462$	2.00000	+	3.46410i	0.0930484	+	0.161165i
$463$	4.54983			0.211449			0.105724	−	0.994395i	$-0.466284\pi$
$463$	4.54983			0.211449			0.105724	+	0.994395i	$0.466284\pi$
$464$	−0.362541	−	0.627940i	−0.0168306	−	0.0291514i
$465$	10.2749	−	17.7967i	0.476488	−	0.825301i
$466$	−11.2749	+	19.5287i	−0.522300	+	0.904651i
$467$	−30.8248			−1.42640			−0.713200	−	0.700961i	$-0.752755\pi$
$467$	−30.8248			−1.42640			−0.713200	+	0.700961i	$0.752755\pi$
$468$	−2.50000	+	2.59808i	−0.115563	+	0.120096i
$469$	−10.2749			−0.474452
$470$	14.0000	−	24.2487i	0.645772	−	1.11851i
$471$	5.63746	−	9.76436i	0.259760	−	0.449918i
$472$	−5.41238	−	9.37451i	−0.249125	−	0.431497i
$473$	−43.2990			−1.99089
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$	24.4743	+	42.3907i	1.12296	+	1.94502i
$476$	3.00000			0.137505
$477$	−5.77492	−	10.0025i	−0.264415	−	0.457981i
$478$	−1.13746	+	1.97014i	−0.0520261	+	0.0901119i
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$	−3.27492			−0.149479
$481$	18.1873	−	18.9008i	0.829269	−	0.861802i
$482$	−23.2749			−1.06014
$483$	−1.13746	+	1.97014i	−0.0517562	+	0.0896443i
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	23.8248	+	41.2657i	1.08183	+	1.87378i
$486$	1.00000			0.0453609
$487$	−14.5498	−	25.2011i	−0.659316	−	1.14197i	−0.980793	−	0.195051i	$-0.937513\pi$
$487$	−14.5498	−	25.2011i	−0.659316	−	1.14197i	0.321477	−	0.946917i	$-0.395821\pi$
$488$	4.50000	+	7.79423i	0.203705	+	0.352828i
$489$	−5.72508			−0.258897
$490$	1.63746	+	2.83616i	0.0739728	+	0.128125i
$491$	2.54983	−	4.41644i	0.115072	−	0.199311i	−0.802736	−	0.596334i	$-0.796623\pi$
$491$	2.54983	−	4.41644i	0.115072	−	0.199311i	0.917809	+	0.397023i	$0.129957\pi$
$492$	−0.362541	+	0.627940i	−0.0163446	+	0.0283097i
$493$	2.17525			0.0979683
$494$	−29.9244	−	7.40437i	−1.34636	−	0.333139i
$495$	13.0997			0.588786
$496$	−3.13746	+	5.43424i	−0.140876	+	0.244004i
$497$	1.13746	−	1.97014i	0.0510220	−	0.0883727i
$498$	−5.41238	−	9.37451i	−0.242534	−	0.420082i
$499$	−9.17525			−0.410741			−0.205370	−	0.978684i	$-0.565840\pi$
$499$	−9.17525			−0.410741			−0.205370	+	0.978684i	$0.565840\pi$
$500$	1.18729	+	2.05645i	0.0530974	+	0.0919673i
$501$		0			0
$502$	5.72508			0.255523
$503$	−4.54983	−	7.88054i	−0.202867	−	0.351376i	0.746584	−	0.665291i	$-0.231693\pi$
$503$	−4.54983	−	7.88054i	−0.202867	−	0.351376i	−0.949451	+	0.313915i	$0.898359\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	15.1873	−	26.3052i	0.675826	−	1.17056i
$506$	−9.09967			−0.404530
$507$	−11.0000	+	6.92820i	−0.488527	+	0.307692i
$508$	8.00000			0.354943
$509$	17.9124	−	31.0251i	0.793952	−	1.37517i	−0.129550	−	0.991573i	$-0.541353\pi$
$509$	17.9124	−	31.0251i	0.793952	−	1.37517i	0.923502	−	0.383593i	$-0.125313\pi$
$510$	4.91238	−	8.50848i	0.217524	−	0.376762i
$511$	−6.63746	−	11.4964i	−0.293624	−	0.508571i
$512$	1.00000			0.0441942
$513$	4.27492	+	7.40437i	0.188742	+	0.326911i
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	7.45017			0.328294
$516$	−5.41238	−	9.37451i	−0.238267	−	0.412690i
$517$	17.0997	−	29.6175i	0.752043	−	1.30258i
$518$	3.63746	−	6.30026i	0.159821	−	0.276818i
$519$	10.5498			0.463086
$520$	−11.4622	−	2.83616i	−0.502651	−	0.124374i
$521$	1.82475			0.0799438			0.0399719	−	0.999201i	$-0.487273\pi$
$521$	1.82475			0.0799438			0.0399719	+	0.999201i	$0.487273\pi$
$522$	−0.362541	+	0.627940i	−0.0158680	+	0.0274842i
$523$	−17.0997	+	29.6175i	−0.747716	+	1.29508i	0.201199	+	0.979550i	$0.435516\pi$
$523$	−17.0997	+	29.6175i	−0.747716	+	1.29508i	−0.948915	+	0.315532i	$0.897817\pi$
$524$	5.13746	+	8.89834i	0.224431	+	0.388726i
$525$	5.72508			0.249863
$526$	4.54983	+	7.88054i	0.198382	+	0.343608i
$527$	−9.41238	−	16.3027i	−0.410010	−	0.710157i
$528$	−4.00000			−0.174078
$529$	8.91238	+	15.4367i	0.387495	+	0.671160i
$530$	18.9124	−	32.7572i	0.821501	−	1.42288i
$531$	−5.41238	+	9.37451i	−0.234877	+	0.406819i
$532$	−8.54983			−0.370682
$533$	−1.81271	+	1.88382i	−0.0785171	+	0.0815973i
$534$	8.27492			0.358091
$535$	−20.5498	+	35.5934i	−0.888447	+	1.53884i
$536$	5.13746	−	8.89834i	0.221904	−	0.384350i
$537$	−8.27492	−	14.3326i	−0.357089	−	0.618496i
$538$	−18.0000			−0.776035
$539$	2.00000	+	3.46410i	0.0861461	+	0.149209i
$540$	1.63746	+	2.83616i	0.0704650	+	0.122049i
$541$	−12.3746			−0.532025			−0.266013	−	0.963970i	$-0.585706\pi$
$541$	−12.3746			−0.532025			−0.266013	+	0.963970i	$0.585706\pi$
$542$	−8.86254	−	15.3504i	−0.380679	−	0.659355i
$543$	−2.91238	+	5.04438i	−0.124982	+	0.216475i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−34.5498			−1.47995
$546$	−2.50000	+	2.59808i	−0.106990	+	0.111187i
$547$	33.0997			1.41524			0.707620	−	0.706593i	$-0.249769\pi$
$547$	33.0997			1.41524			0.707620	+	0.706593i	$0.249769\pi$
$548$	−0.0876242	+	0.151770i	−0.00374312	+	0.00648327i
$549$	4.50000	−	7.79423i	0.192055	−	0.332650i
$550$	11.4502	+	19.8323i	0.488237	+	0.845651i
$551$	−6.19934			−0.264101
$552$	−1.13746	−	1.97014i	−0.0484135	−	0.0838546i
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	−7.82475			−0.332442
$555$	−11.9124	−	20.6328i	−0.505652	−	0.875815i
$556$	−10.5498	+	18.2728i	−0.447413	+	0.774941i
$557$	−12.5997	+	21.8233i	−0.533865	+	0.924681i	0.465352	+	0.885126i	$0.345928\pi$
$557$	−12.5997	+	21.8233i	−0.533865	+	0.924681i	−0.999217	+	0.0395559i	$0.987406\pi$
$558$	6.27492			0.265638
$559$	−10.8248	−	37.4980i	−0.457838	−	1.58600i
$560$	−3.27492			−0.138391
$561$	6.00000	−	10.3923i	0.253320	−	0.438763i
$562$	−0.912376	+	1.58028i	−0.0384863	+	0.0666601i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	8.54983			0.360013
$565$	−12.8127	−	22.1923i	−0.539035	−	0.933635i
$566$	12.2749	+	21.2608i	0.515953	+	0.893657i
$567$	1.00000			0.0419961
$568$	1.13746	+	1.97014i	0.0477267	+	0.0826651i
$569$	−17.5498	+	30.3972i	−0.735727	+	1.27432i	0.218676	+	0.975797i	$0.429826\pi$
$569$	−17.5498	+	30.3972i	−0.735727	+	1.27432i	−0.954403	+	0.298520i	$0.903507\pi$
$570$	−14.0000	+	24.2487i	−0.586395	+	1.01567i
$571$	−22.2749			−0.932176			−0.466088	−	0.884738i	$-0.654337\pi$
$571$	−22.2749			−0.932176			−0.466088	+	0.884738i	$0.654337\pi$
$572$	−14.0000	−	3.46410i	−0.585369	−	0.144841i
$573$	14.2749			0.596343
$574$	−0.362541	+	0.627940i	−0.0151322	+	0.0262097i
$575$	−6.51204	+	11.2792i	−0.271571	+	0.470375i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−28.3746			−1.18125			−0.590625	−	0.806946i	$-0.701119\pi$
$577$	−28.3746			−1.18125			−0.590625	+	0.806946i	$0.701119\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	1.08762	+	1.88382i	0.0452001	+	0.0782889i
$580$	−2.37459			−0.0985993
$581$	−5.41238	−	9.37451i	−0.224543	−	0.388920i
$582$	−7.27492	+	12.6005i	−0.301555	+	0.522309i
$583$	23.0997	−	40.0098i	0.956691	−	1.65704i
$584$	13.2749			0.549320
$585$	3.27492	+	11.3446i	0.135401	+	0.469043i
$586$	−10.7251			−0.443049
$587$	21.9622	−	38.0397i	0.906477	−	1.57006i	0.0875558	−	0.996160i	$-0.472094\pi$
$587$	21.9622	−	38.0397i	0.906477	−	1.57006i	0.818922	−	0.573905i	$-0.194572\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	26.8248	+	46.4618i	1.10529	+	1.91443i
$590$	−35.4502			−1.45946
$591$	−0.412376	−	0.714256i	−0.0169629	−	0.0293806i
$592$	3.63746	+	6.30026i	0.149499	+	0.258939i
$593$	19.5498			0.802815			0.401408	−	0.915899i	$-0.368521\pi$
$593$	19.5498			0.802815			0.401408	+	0.915899i	$0.368521\pi$
$594$	2.00000	+	3.46410i	0.0820610	+	0.142134i
$595$	4.91238	−	8.50848i	0.201388	−	0.348814i
$596$	0.500000	−	0.866025i	0.0204808	−	0.0354738i
$597$	−10.8248			−0.443028
$598$	−2.27492	−	7.88054i	−0.0930283	−	0.322259i
$599$	−18.2749			−0.746693			−0.373346	−	0.927692i	$-0.621790\pi$
$599$	−18.2749			−0.746693			−0.373346	+	0.927692i	$0.621790\pi$
$600$	−2.86254	+	4.95807i	−0.116863	+	0.202412i
$601$	7.63746	−	13.2285i	0.311538	−	0.539600i	−0.667157	−	0.744917i	$-0.732489\pi$
$601$	7.63746	−	13.2285i	0.311538	−	0.539600i	0.978696	+	0.205317i	$0.0658224\pi$
$602$	−5.41238	−	9.37451i	−0.220592	−	0.382077i
$603$	−10.2749			−0.418427
$604$	8.54983	+	14.8087i	0.347888	+	0.602559i
$605$	8.18729	+	14.1808i	0.332861	+	0.576532i
$606$	9.27492			0.376768
$607$	−11.1375	−	19.2906i	−0.452055	−	0.782983i	0.546458	−	0.837486i	$-0.315976\pi$
$607$	−11.1375	−	19.2906i	−0.452055	−	0.782983i	−0.998514	+	0.0545034i	$0.982642\pi$
$608$	4.27492	−	7.40437i	0.173371	−	0.300287i
$609$	−0.362541	+	0.627940i	−0.0146909	+	0.0254454i
$610$	29.4743			1.19338
$611$	29.9244	+	7.40437i	1.21061	+	0.299549i
$612$	3.00000			0.121268
$613$	4.18729	−	7.25260i	0.169123	−	0.292930i	−0.768989	−	0.639262i	$-0.779240\pi$
$613$	4.18729	−	7.25260i	0.169123	−	0.292930i	0.938112	+	0.346332i	$0.112573\pi$
$614$	8.27492	−	14.3326i	0.333948	−	0.578416i
$615$	1.18729	+	2.05645i	0.0478763	+	0.0829241i
$616$	−4.00000			−0.161165
$617$	6.46221	+	11.1929i	0.260159	+	0.450608i	0.966284	−	0.257479i	$-0.0828918\pi$
$617$	6.46221	+	11.1929i	0.260159	+	0.450608i	−0.706125	+	0.708087i	$0.749558\pi$
$618$	1.13746	+	1.97014i	0.0457553	+	0.0792505i
$619$	29.6495			1.19171			0.595857	−	0.803090i	$-0.296812\pi$
$619$	29.6495			1.19171			0.595857	+	0.803090i	$0.296812\pi$
$620$	10.2749	+	17.7967i	0.412651	+	0.714732i
$621$	−1.13746	+	1.97014i	−0.0456446	+	0.0790588i
$622$	−6.27492	+	10.8685i	−0.251601	+	0.435786i
$623$	8.27492			0.331528
$624$	−1.00000	−	3.46410i	−0.0400320	−	0.138675i
$625$	−20.8488			−0.833954
$626$	13.8248	−	23.9452i	0.552548	−	0.957042i
$627$	−17.0997	+	29.6175i	−0.682895	+	1.18281i
$628$	5.63746	+	9.76436i	0.224959	+	0.389641i
$629$	−21.8248			−0.870210
$630$	1.63746	+	2.83616i	0.0652379	+	0.112995i
$631$	−0.549834	−	0.952341i	−0.0218886	−	0.0379121i	0.854874	−	0.518836i	$-0.173635\pi$
$631$	−0.549834	−	0.952341i	−0.0218886	−	0.0379121i	−0.876762	+	0.480924i	$0.840301\pi$
$632$	−8.00000			−0.318223
$633$	4.54983	+	7.88054i	0.180840	+	0.313224i
$634$	−3.77492	+	6.53835i	−0.149921	+	0.259671i
$635$	13.0997	−	22.6893i	0.519845	−	0.900397i
$636$	11.5498			0.457981
$637$	−2.50000	+	2.59808i	−0.0990536	+	0.102940i
$638$	−2.90033			−0.114825
$639$	1.13746	−	1.97014i	0.0449972	−	0.0779374i
$640$	1.63746	−	2.83616i	0.0647262	−	0.112109i
$641$	1.91238	+	3.31233i	0.0755343	+	0.130829i	0.901318	−	0.433157i	$-0.142600\pi$
$641$	1.91238	+	3.31233i	0.0755343	+	0.130829i	−0.825784	+	0.563986i	$0.809267\pi$
$642$	−12.5498			−0.495302
$643$	−21.3746	−	37.0219i	−0.842931	−	1.46000i	−0.887406	−	0.460989i	$-0.847495\pi$
$643$	−21.3746	−	37.0219i	−0.842931	−	1.46000i	0.0444742	−	0.999011i	$-0.485839\pi$
$644$	−1.13746	−	1.97014i	−0.0448221	−	0.0776342i
$645$	−35.4502			−1.39585
$646$	12.8248	+	22.2131i	0.504583	+	0.873964i
$647$	−12.2749	+	21.2608i	−0.482577	+	0.835848i	−0.999800	−	0.0200031i	$-0.993632\pi$
$647$	−12.2749	+	21.2608i	−0.482577	+	0.835848i	0.517223	+	0.855851i	$0.326966\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−43.2990			−1.69963
$650$	−14.3127	+	14.8742i	−0.561391	+	0.583414i
$651$	6.27492			0.245933
$652$	2.86254	−	4.95807i	0.112106	−	0.194173i
$653$	17.2371	−	29.8556i	0.674541	−	1.16834i	−0.302062	−	0.953288i	$-0.597675\pi$
$653$	17.2371	−	29.8556i	0.674541	−	1.16834i	0.976603	−	0.215051i	$-0.0689917\pi$
$654$	−5.27492	−	9.13642i	−0.206266	−	0.357262i
$655$	33.6495			1.31479
$656$	−0.362541	−	0.627940i	−0.0141549	−	0.0245169i
$657$	−6.63746	−	11.4964i	−0.258952	−	0.448518i
$658$	8.54983			0.333307
$659$	14.2749	+	24.7249i	0.556072	+	0.963145i	0.997819	+	0.0660052i	$0.0210254\pi$
$659$	14.2749	+	24.7249i	0.556072	+	0.963145i	−0.441747	+	0.897139i	$0.645641\pi$
$660$	−6.54983	+	11.3446i	−0.254952	+	0.441590i
$661$	−20.0498	+	34.7273i	−0.779848	+	1.35074i	0.152181	+	0.988353i	$0.451370\pi$
$661$	−20.0498	+	34.7273i	−0.779848	+	1.35074i	−0.932029	+	0.362384i	$0.881963\pi$
$662$	4.00000			0.155464
$663$	10.5000	+	2.59808i	0.407786	+	0.100901i
$664$	10.8248			0.420082
$665$	−14.0000	+	24.2487i	−0.542897	+	0.940325i
$666$	3.63746	−	6.30026i	0.140949	−	0.244130i
$667$	−0.824752	−	1.42851i	−0.0319345	−	0.0553122i
$668$		0			0
$669$	−9.13746	−	15.8265i	−0.353275	−	0.611889i
$670$	−16.8248	−	29.1413i	−0.649997	−	1.12583i
$671$	36.0000			1.38976
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−6.04983	+	10.4786i	−0.233204	+	0.403921i	−0.958749	−	0.284253i	$-0.908254\pi$
$673$	−6.04983	+	10.4786i	−0.233204	+	0.403921i	0.725545	+	0.688174i	$0.241588\pi$
$674$	3.63746	−	6.30026i	0.140110	−	0.242677i
$675$	5.72508			0.220359
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	11.6495			0.447727			0.223863	−	0.974621i	$-0.428133\pi$
$677$	11.6495			0.447727			0.223863	+	0.974621i	$0.428133\pi$
$678$	3.91238	−	6.77643i	0.150254	−	0.260247i
$679$	−7.27492	+	12.6005i	−0.279186	+	0.483564i
$680$	4.91238	+	8.50848i	0.188381	+	0.326285i
$681$	9.09967			0.348700
$682$	12.5498	+	21.7370i	0.480558	+	0.832351i
$683$	24.8248	+	42.9977i	0.949893	+	1.64526i	0.745645	+	0.666343i	$0.232141\pi$
$683$	24.8248	+	42.9977i	0.949893	+	1.64526i	0.204248	+	0.978919i	$0.434525\pi$
$684$	−8.54983			−0.326911
$685$	0.286962	+	0.497033i	0.0109643	+	0.0189906i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−10.1375	+	17.5586i	−0.386768	+	0.669902i
$688$	10.8248			0.412690
$689$	40.4244	+	10.0025i	1.54005	+	0.381063i
$690$	−7.45017			−0.283623
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−5.27492	+	9.13642i	−0.200522	+	0.347315i
$693$	2.00000	+	3.46410i	0.0759737	+	0.131590i
$694$	15.4502			0.586480
$695$	34.5498	+	59.8421i	1.31055	+	2.26994i
$696$	−0.362541	−	0.627940i	−0.0137421	−	0.0238020i
$697$	2.17525			0.0823934
$698$	−8.96221	−	15.5230i	−0.339225	−	0.587554i
$699$	−11.2749	+	19.5287i	−0.426457	+	0.738644i
$700$	−2.86254	+	4.95807i	−0.108194	+	0.187397i
$701$	−37.9244			−1.43239			−0.716193	−	0.697902i	$-0.754117\pi$
$701$	−37.9244			−1.43239			−0.716193	+	0.697902i	$0.754117\pi$
$702$	−2.50000	+	2.59808i	−0.0943564	+	0.0980581i
$703$	62.1993			2.34589
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$	14.0000	−	24.2487i	0.527271	−	0.913259i
$706$	2.22508	+	3.85396i	0.0837421	+	0.145046i
$707$	9.27492			0.348819
$708$	−5.41238	−	9.37451i	−0.203410	−	0.352316i
$709$	4.81271	+	8.33585i	0.180745	+	0.313060i	0.942134	−	0.335235i	$-0.108816\pi$
$709$	4.81271	+	8.33585i	0.180745	+	0.313060i	−0.761389	+	0.648295i	$0.775482\pi$
$710$	7.45017			0.279600
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	−4.13746	+	7.16629i	−0.155058	+	0.268568i
$713$	−7.13746	+	12.3624i	−0.267300	+	0.462977i
$714$	3.00000			0.112272
$715$	−32.7492	+	34.0339i	−1.22475	+	1.27280i
$716$	16.5498			0.618496
$717$	−1.13746	+	1.97014i	−0.0424792	+	0.0735761i
$718$	−14.5498	+	25.2011i	−0.542995	+	0.940495i
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$	−3.27492			−0.122049
$721$	1.13746	+	1.97014i	0.0423612	+	0.0733717i
$722$	−27.0498	−	46.8517i	−1.00669	−	1.74364i
$723$	−23.2749			−0.865603
$724$	−2.91238	−	5.04438i	−0.108238	−	0.187473i
$725$	−2.07558	+	3.59501i	−0.0770851	+	0.133515i
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$	−2.82475			−0.104764			−0.0523821	−	0.998627i	$-0.516681\pi$
$727$	−2.82475			−0.104764			−0.0523821	+	0.998627i	$0.516681\pi$
$728$	−1.00000	−	3.46410i	−0.0370625	−	0.128388i
$729$	1.00000			0.0370370
$730$	21.7371	−	37.6498i	0.804527	−	1.39348i
$731$	−16.2371	+	28.1235i	−0.600552	+	1.04019i
$732$	4.50000	+	7.79423i	0.166325	+	0.288083i
$733$	12.6495			0.467220			0.233610	−	0.972330i	$-0.424946\pi$
$733$	12.6495			0.467220			0.233610	+	0.972330i	$0.424946\pi$
$734$	−2.86254	−	4.95807i	−0.105658	−	0.183006i
$735$	1.63746	+	2.83616i	0.0603986	+	0.104613i
$736$	2.27492			0.0838546
$737$	−20.5498	−	35.5934i	−0.756963	−	1.31110i
$738$	−0.362541	+	0.627940i	−0.0133453	+	0.0231148i
$739$	20.8625	−	36.1350i	0.767441	−	1.32925i	−0.171505	−	0.985183i	$-0.554863\pi$
$739$	20.8625	−	36.1350i	0.767441	−	1.32925i	0.938946	−	0.344064i	$-0.111804\pi$
$740$	23.8248			0.875815
$741$	−29.9244	−	7.40437i	−1.09930	−	0.272006i
$742$	11.5498			0.424008
$743$	13.4124	−	23.2309i	0.492052	−	0.852260i	−0.507906	−	0.861413i	$-0.669580\pi$
$743$	13.4124	−	23.2309i	0.492052	−	0.852260i	0.999958	+	0.00915297i	$0.00291352\pi$
$744$	−3.13746	+	5.43424i	−0.115025	+	0.199229i
$745$	−1.63746	−	2.83616i	−0.0599918	−	0.103909i
$746$	4.17525			0.152867
$747$	−5.41238	−	9.37451i	−0.198028	−	0.342995i
$748$	6.00000	+	10.3923i	0.219382	+	0.379980i
$749$	−12.5498			−0.458561
$750$	1.18729	+	2.05645i	0.0433538	+	0.0750910i
$751$	1.72508	−	2.98793i	0.0629492	−	0.109031i	−0.832833	−	0.553524i	$-0.813283\pi$
$751$	1.72508	−	2.98793i	0.0629492	−	0.109031i	0.895782	+	0.444493i	$0.146616\pi$
$752$	−4.27492	+	7.40437i	−0.155890	+	0.270010i
$753$	5.72508			0.208634
$754$	−0.725083	−	2.51176i	−0.0264060	−	0.0914729i
$755$	56.0000			2.03805
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	−0.527011	−	0.849858i	$-0.676688\pi$
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	0.999505	+	0.0314762i	$0.0100208\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$	−9.09967			−0.330297
$760$	−14.0000	−	24.2487i	−0.507833	−	0.879593i
$761$	20.0997	+	34.8136i	0.728612	+	1.26199i	0.957470	+	0.288534i	$0.0931677\pi$
$761$	20.0997	+	34.8136i	0.728612	+	1.26199i	−0.228857	+	0.973460i	$0.573499\pi$
$762$	8.00000			0.289809
$763$	−5.27492	−	9.13642i	−0.190965	−	0.330761i
$764$	−7.13746	+	12.3624i	−0.258224	+	0.447257i
$765$	4.91238	−	8.50848i	0.177607	−	0.307625i
$766$	−38.1993			−1.38020
$767$	−10.8248	−	37.4980i	−0.390859	−	1.35398i
$768$	1.00000			0.0360844
$769$	1.82475	−	3.16056i	0.0658022	−	0.113973i	−0.831247	−	0.555903i	$-0.812373\pi$
$769$	1.82475	−	3.16056i	0.0658022	−	0.113973i	0.897050	+	0.441930i	$0.145706\pi$
$770$	−6.54983	+	11.3446i	−0.236040	+	0.408833i
$771$	−7.50000	−	12.9904i	−0.270106	−	0.467837<

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.27492 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.27492 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.63746 - 2.83616i) q^{10} +(2.00000 - 3.46410i) q^{11} +1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.63746 - 2.83616i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(4.27492 + 7.40437i) q^{19} +(1.63746 + 2.83616i) q^{20} +1.00000 q^{21} +(2.00000 + 3.46410i) q^{22} +(-1.13746 + 1.97014i) q^{23} +(-0.500000 + 0.866025i) q^{24} +5.72508 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-0.362541 + 0.627940i) q^{29} +(1.63746 + 2.83616i) q^{30} +6.27492 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +3.00000 q^{34} +(1.63746 + 2.83616i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.63746 - 6.30026i) q^{37} -8.54983 q^{38} +(-2.50000 + 2.59808i) q^{39} -3.27492 q^{40} +(-0.362541 + 0.627940i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-5.41238 - 9.37451i) q^{43} -4.00000 q^{44} +(1.63746 + 2.83616i) q^{45} +(-1.13746 - 1.97014i) q^{46} +8.54983 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.86254 + 4.95807i) q^{50} +3.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +11.5498 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.54983 + 11.3446i) q^{55} +(-0.500000 - 0.866025i) q^{56} -8.54983 q^{57} +(-0.362541 - 0.627940i) q^{58} +(-5.41238 - 9.37451i) q^{59} -3.27492 q^{60} +(4.50000 + 7.79423i) q^{61} +(-3.13746 + 5.43424i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-11.4622 - 2.83616i) q^{65} -4.00000 q^{66} +(5.13746 - 8.89834i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-1.13746 - 1.97014i) q^{69} -3.27492 q^{70} +(1.13746 + 1.97014i) q^{71} +(-0.500000 - 0.866025i) q^{72} +13.2749 q^{73} +(3.63746 + 6.30026i) q^{74} +(-2.86254 + 4.95807i) q^{75} +(4.27492 - 7.40437i) q^{76} -4.00000 q^{77} +(-1.00000 - 3.46410i) q^{78} -8.00000 q^{79} +(1.63746 - 2.83616i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.362541 - 0.627940i) q^{82} +10.8248 q^{83} +(-0.500000 - 0.866025i) q^{84} +(4.91238 + 8.50848i) q^{85} +10.8248 q^{86} +(-0.362541 - 0.627940i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-4.13746 + 7.16629i) q^{89} -3.27492 q^{90} +(-1.00000 - 3.46410i) q^{91} +2.27492 q^{92} +(-3.13746 + 5.43424i) q^{93} +(-4.27492 + 7.40437i) q^{94} +(-14.0000 - 24.2487i) q^{95} +1.00000 q^{96} +(-7.27492 - 12.6005i) q^{97} +(-0.500000 - 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - q^{10} + 8 q^{11} + 4 q^{12} + 14 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{18} + 2 q^{19} - q^{20} + 4 q^{21} + 8 q^{22} + 3 q^{23} - 2 q^{24} + 38 q^{25} - 10 q^{26} + 4 q^{27} - 2 q^{28} - 9 q^{29} - q^{30} + 10 q^{31} - 2 q^{32} + 8 q^{33} + 12 q^{34} - q^{35} - 2 q^{36} + 7 q^{37} - 4 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} - 2 q^{42} + q^{43} - 16 q^{44} - q^{45} + 3 q^{46} + 4 q^{47} - 2 q^{48} - 2 q^{49} - 19 q^{50} + 12 q^{51} - 4 q^{52} + 16 q^{53} - 2 q^{54} + 4 q^{55} - 2 q^{56} - 4 q^{57} - 9 q^{58} + q^{59} + 2 q^{60} + 18 q^{61} - 5 q^{62} - 2 q^{63} + 4 q^{64} + 7 q^{65} - 16 q^{66} + 13 q^{67} - 6 q^{68} + 3 q^{69} + 2 q^{70} - 3 q^{71} - 2 q^{72} + 38 q^{73} + 7 q^{74} - 19 q^{75} + 2 q^{76} - 16 q^{77} - 4 q^{78} - 32 q^{79} - q^{80} - 2 q^{81} - 9 q^{82} - 2 q^{83} - 2 q^{84} - 3 q^{85} - 2 q^{86} - 9 q^{87} + 8 q^{88} - 9 q^{89} + 2 q^{90} - 4 q^{91} - 6 q^{92} - 5 q^{93} - 2 q^{94} - 56 q^{95} + 4 q^{96} - 14 q^{97} - 2 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - q^10 + 8 * q^11 + 4 * q^12 + 14 * q^13 + 4 * q^14 - q^15 - 2 * q^16 - 6 * q^17 + 4 * q^18 + 2 * q^19 - q^20 + 4 * q^21 + 8 * q^22 + 3 * q^23 - 2 * q^24 + 38 * q^25 - 10 * q^26 + 4 * q^27 - 2 * q^28 - 9 * q^29 - q^30 + 10 * q^31 - 2 * q^32 + 8 * q^33 + 12 * q^34 - q^35 - 2 * q^36 + 7 * q^37 - 4 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 - 2 * q^42 + q^43 - 16 * q^44 - q^45 + 3 * q^46 + 4 * q^47 - 2 * q^48 - 2 * q^49 - 19 * q^50 + 12 * q^51 - 4 * q^52 + 16 * q^53 - 2 * q^54 + 4 * q^55 - 2 * q^56 - 4 * q^57 - 9 * q^58 + q^59 + 2 * q^60 + 18 * q^61 - 5 * q^62 - 2 * q^63 + 4 * q^64 + 7 * q^65 - 16 * q^66 + 13 * q^67 - 6 * q^68 + 3 * q^69 + 2 * q^70 - 3 * q^71 - 2 * q^72 + 38 * q^73 + 7 * q^74 - 19 * q^75 + 2 * q^76 - 16 * q^77 - 4 * q^78 - 32 * q^79 - q^80 - 2 * q^81 - 9 * q^82 - 2 * q^83 - 2 * q^84 - 3 * q^85 - 2 * q^86 - 9 * q^87 + 8 * q^88 - 9 * q^89 + 2 * q^90 - 4 * q^91 - 6 * q^92 - 5 * q^93 - 2 * q^94 - 56 * q^95 + 4 * q^96 - 14 * q^97 - 2 * q^98 - 16 * q^99

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