LMFDB - Embedded newform 1386.2.bk.a.703.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.1
Root			$0.500000 + 3.43554i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.a.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.72526 + 2.15078i) q^{5} +(-1.43173 - 2.22489i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.72526 + 2.15078i) q^{5} +(-1.43173 - 2.22489i) q^{7} +1.00000i q^{8} +(2.15078 - 3.72526i) q^{10} +(3.27015 - 0.553289i) q^{11} +1.00074 q^{13} +(2.35236 + 1.21095i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.66854 - 2.89000i) q^{17} +(1.61555 + 2.79822i) q^{19} +4.30156i q^{20} +(-2.55539 + 2.11424i) q^{22} +(-2.86499 - 4.96231i) q^{23} +(6.75173 - 11.6943i) q^{25} +(-0.866669 + 0.500372i) q^{26} +(-2.64268 + 0.127470i) q^{28} +7.74872i q^{29} +(-2.77407 - 1.60161i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.33708i q^{34} +(10.1188 + 5.20897i) q^{35} +(1.26472 + 2.19056i) q^{37} +(-2.79822 - 1.61555i) q^{38} +(-2.15078 - 3.72526i) q^{40} -1.45111 q^{41} +4.14572i q^{43} +(1.15591 - 3.10868i) q^{44} +(4.96231 + 2.86499i) q^{46} +(-2.77216 + 1.60050i) q^{47} +(-2.90029 + 6.37090i) q^{49} +13.5035i q^{50} +(0.500372 - 0.866669i) q^{52} +(-5.65774 + 9.79949i) q^{53} +(-10.9922 + 9.09452i) q^{55} +(2.22489 - 1.43173i) q^{56} +(-3.87436 - 6.71059i) q^{58} +(-2.98113 - 1.72116i) q^{59} +(7.42522 + 12.8609i) q^{61} +3.20322 q^{62} -1.00000 q^{64} +(-3.72803 + 2.15238i) q^{65} +(0.165196 - 0.286128i) q^{67} +(-1.66854 - 2.89000i) q^{68} +(-11.3677 + 0.548319i) q^{70} -2.84974 q^{71} +(-7.44790 + 12.9001i) q^{73} +(-2.19056 - 1.26472i) q^{74} +3.23111 q^{76} +(-5.91298 - 6.48357i) q^{77} +(13.9363 - 8.04614i) q^{79} +(3.72526 + 2.15078i) q^{80} +(1.25670 - 0.725556i) q^{82} -1.75062 q^{83} +14.3547i q^{85} +(-2.07286 - 3.59030i) q^{86} +(0.553289 + 3.27015i) q^{88} +(2.41153 - 1.39230i) q^{89} +(-1.43280 - 2.22655i) q^{91} -5.72998 q^{92} +(1.60050 - 2.77216i) q^{94} +(-12.0367 - 6.94940i) q^{95} +12.3347i q^{97} +(-0.673723 - 6.96750i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7	$ 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7} + 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} - 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} + 8 q^{35} + 14 q^{37} + 12 q^{38} - 2 q^{40} - 32 q^{41} - 4 q^{44} + 18 q^{46} + 24 q^{47} - 6 q^{49} - 14 q^{55} - 4 q^{56} + 28 q^{61} + 8 q^{62} - 16 q^{64} - 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} - 44 q^{73} - 24 q^{74} - 20 q^{76} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} + 14 q^{94} - 72 q^{95} + 40 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7 + 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 - 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 + 8 * q^35 + 14 * q^37 + 12 * q^38 - 2 * q^40 - 32 * q^41 - 4 * q^44 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 14 * q^55 - 4 * q^56 + 28 * q^61 + 8 * q^62 - 16 * q^64 - 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 - 44 * q^73 - 24 * q^74 - 20 * q^76 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 + 14 * q^94 - 72 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.72526	+	2.15078i	−1.66599	+	0.961859i	−0.696221	+	0.717827i	$0.745137\pi$
$5$	−3.72526	+	2.15078i	−1.66599	+	0.961859i	−0.969767	+	0.244032i	$0.921530\pi$
$6$		0			0
$7$	−1.43173	−	2.22489i	−0.541144	−	0.840930i
$7$	−1.43173	−	2.22489i	−0.541144	−	0.840930i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.15078	−	3.72526i	0.680137	−	1.17803i
$11$	3.27015	−	0.553289i	0.985987	−	0.166823i
$11$	3.27015	−	0.553289i	0.985987	−	0.166823i
$12$		0			0
$13$	1.00074			0.277556			0.138778	−	0.990324i	$-0.455683\pi$
$13$	1.00074			0.277556			0.138778	+	0.990324i	$0.455683\pi$
$14$	2.35236	+	1.21095i	0.628695	+	0.323639i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.66854	−	2.89000i	0.404681	−	0.700927i	−0.589604	−	0.807693i	$-0.700716\pi$
$17$	1.66854	−	2.89000i	0.404681	−	0.700927i	0.994284	+	0.106765i	$0.0340494\pi$
$18$		0			0
$19$	1.61555	+	2.79822i	0.370633	+	0.641956i	0.989663	−	0.143412i	$-0.0458074\pi$
$19$	1.61555	+	2.79822i	0.370633	+	0.641956i	−0.619030	+	0.785367i	$0.712474\pi$
$20$			4.30156i			0.961859i
$21$		0			0
$22$	−2.55539	+	2.11424i	−0.544810	+	0.450757i
$23$	−2.86499	−	4.96231i	−0.597392	−	1.03471i	−0.993205	−	0.116382i	$-0.962870\pi$
$23$	−2.86499	−	4.96231i	−0.597392	−	1.03471i	0.395813	−	0.918331i	$-0.370463\pi$
$24$		0			0
$25$	6.75173	−	11.6943i	1.35035	−	2.33887i
$26$	−0.866669	+	0.500372i	−0.169968	+	0.0981309i
$27$		0			0
$28$	−2.64268	+	0.127470i	−0.499419	+	0.0240895i
$29$			7.74872i			1.43890i	0.694544	+	0.719450i	$0.255606\pi$
$29$			7.74872i			1.43890i	−0.694544	+	0.719450i	$0.744394\pi$
$30$		0			0
$31$	−2.77407	−	1.60161i	−0.498237	−	0.287657i	0.229748	−	0.973250i	$-0.426210\pi$
$31$	−2.77407	−	1.60161i	−0.498237	−	0.287657i	−0.727985	+	0.685593i	$0.759543\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			3.33708i			0.572305i
$35$	10.1188	+	5.20897i	1.71040	+	0.880476i
$36$		0			0
$37$	1.26472	+	2.19056i	0.207918	+	0.360125i	0.951059	−	0.309010i	$-0.0999978\pi$
$37$	1.26472	+	2.19056i	0.207918	+	0.360125i	−0.743140	+	0.669136i	$0.766664\pi$
$38$	−2.79822	−	1.61555i	−0.453931	−	0.262077i
$39$		0			0
$40$	−2.15078	−	3.72526i	−0.340068	−	0.589016i
$41$	−1.45111			−0.226625			−0.113313	−	0.993559i	$-0.536146\pi$
$41$	−1.45111			−0.226625			−0.113313	+	0.993559i	$0.536146\pi$
$42$		0			0
$43$			4.14572i			0.632216i	0.948723	+	0.316108i	$0.102376\pi$
$43$			4.14572i			0.632216i	−0.948723	+	0.316108i	$0.897624\pi$
$44$	1.15591	−	3.10868i	0.174260	−	0.468651i
$45$		0			0
$46$	4.96231	+	2.86499i	0.731653	+	0.422420i
$47$	−2.77216	+	1.60050i	−0.404360	+	0.233458i	−0.688364	−	0.725366i	$-0.741671\pi$
$47$	−2.77216	+	1.60050i	−0.404360	+	0.233458i	0.284003	+	0.958823i	$0.408337\pi$
$48$		0			0
$49$	−2.90029	+	6.37090i	−0.414327	+	0.910128i
$50$			13.5035i			1.90968i
$51$		0			0
$52$	0.500372	−	0.866669i	0.0693890	−	0.120185i
$53$	−5.65774	+	9.79949i	−0.777150	+	1.34606i	0.156428	+	0.987689i	$0.450002\pi$
$53$	−5.65774	+	9.79949i	−0.777150	+	1.34606i	−0.933578	+	0.358374i	$0.883331\pi$
$54$		0			0
$55$	−10.9922	+	9.09452i	−1.48218	+	1.22631i
$56$	2.22489	−	1.43173i	0.297314	−	0.191323i
$57$		0			0
$58$	−3.87436	−	6.71059i	−0.508728	−	0.881143i
$59$	−2.98113	−	1.72116i	−0.388110	−	0.224075i	0.293231	−	0.956042i	$-0.405270\pi$
$59$	−2.98113	−	1.72116i	−0.388110	−	0.224075i	−0.681341	+	0.731966i	$0.738603\pi$
$60$		0			0
$61$	7.42522	+	12.8609i	0.950702	+	1.64666i	0.743911	+	0.668279i	$0.232969\pi$
$61$	7.42522	+	12.8609i	0.950702	+	1.64666i	0.206791	+	0.978385i	$0.433698\pi$
$62$	3.20322			0.406809
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.72803	+	2.15238i	−0.462405	+	0.266970i
$66$		0			0
$67$	0.165196	−	0.286128i	0.0201819	−	0.0349560i	−0.855758	−	0.517376i	$-0.826909\pi$
$67$	0.165196	−	0.286128i	0.0201819	−	0.0349560i	0.875940	+	0.482420i	$0.160242\pi$
$68$	−1.66854	−	2.89000i	−0.202340	−	0.350464i
$69$		0			0
$70$	−11.3677	+	0.548319i	−1.35869	+	0.0655367i
$71$	−2.84974			−0.338201			−0.169101	−	0.985599i	$-0.554086\pi$
$71$	−2.84974			−0.338201			−0.169101	+	0.985599i	$0.554086\pi$
$72$		0			0
$73$	−7.44790	+	12.9001i	−0.871710	+	1.50985i	−0.0114838	+	0.999934i	$0.503655\pi$
$73$	−7.44790	+	12.9001i	−0.871710	+	1.50985i	−0.860226	+	0.509912i	$0.829678\pi$
$74$	−2.19056	−	1.26472i	−0.254647	−	0.147021i
$75$		0			0
$76$	3.23111			0.370633
$77$	−5.91298	−	6.48357i	−0.673847	−	0.738871i
$78$		0			0
$79$	13.9363	−	8.04614i	1.56796	−	0.905261i	0.571552	−	0.820566i	$-0.306342\pi$
$79$	13.9363	−	8.04614i	1.56796	−	0.905261i	0.996407	−	0.0846953i	$-0.0269917\pi$
$80$	3.72526	+	2.15078i	0.416497	+	0.240465i
$81$		0			0
$82$	1.25670	−	0.725556i	0.138779	−	0.0801242i
$83$	−1.75062			−0.192155			−0.0960777	−	0.995374i	$-0.530630\pi$
$83$	−1.75062			−0.192155			−0.0960777	+	0.995374i	$0.530630\pi$
$84$		0			0
$85$			14.3547i			1.55698i
$86$	−2.07286	−	3.59030i	−0.223522	−	0.387152i
$87$		0			0
$88$	0.553289	+	3.27015i	0.0589808	+	0.348599i
$89$	2.41153	−	1.39230i	0.255622	−	0.147583i	−0.366714	−	0.930334i	$-0.619517\pi$
$89$	2.41153	−	1.39230i	0.255622	−	0.147583i	0.622336	+	0.782750i	$0.286184\pi$
$90$		0			0
$91$	−1.43280	−	2.22655i	−0.150198	−	0.233405i
$92$	−5.72998			−0.597392
$93$		0			0
$94$	1.60050	−	2.77216i	0.165079	−	0.285926i
$95$	−12.0367	−	6.94940i	−1.23494	−	0.712994i
$96$		0			0
$97$			12.3347i			1.25240i	0.779661	+	0.626201i	$0.215391\pi$
$97$			12.3347i			1.25240i	−0.779661	+	0.626201i	$0.784609\pi$
$98$	−0.673723	−	6.96750i	−0.0680563	−	0.703824i
$99$		0			0
$100$	−6.75173	−	11.6943i	−0.675173	−	1.16943i
$101$	−0.0281224	+	0.0487094i	−0.00279828	+	0.00484677i	−0.867421	−	0.497575i	$-0.834224\pi$
$101$	−0.0281224	+	0.0487094i	−0.00279828	+	0.00484677i	0.864623	+	0.502421i	$0.167557\pi$
$102$		0			0
$103$	−12.8128	+	7.39746i	−1.26248	+	0.728893i	−0.973554	−	0.228458i	$-0.926632\pi$
$103$	−12.8128	+	7.39746i	−1.26248	+	0.728893i	−0.288926	+	0.957351i	$0.593298\pi$
$104$			1.00074i			0.0981309i
$105$		0			0
$106$		−	11.3155i		−	1.09906i
$107$	9.19190	−	5.30694i	0.888614	−	0.513042i	0.0151251	−	0.999886i	$-0.495185\pi$
$107$	9.19190	−	5.30694i	0.888614	−	0.513042i	0.873489	+	0.486844i	$0.161852\pi$
$108$		0			0
$109$	0.301553	+	0.174102i	0.0288836	+	0.0166759i	0.514372	−	0.857567i	$-0.328025\pi$
$109$	0.301553	+	0.174102i	0.0288836	+	0.0166759i	−0.485489	+	0.874243i	$0.661358\pi$
$110$	4.97223	−	13.3722i	0.474083	−	1.27499i
$111$		0			0
$112$	−1.21095	+	2.35236i	−0.114424	+	0.222277i
$113$	18.9549			1.78313			0.891564	−	0.452895i	$-0.149609\pi$
$113$	18.9549			1.78313			0.891564	+	0.452895i	$0.149609\pi$
$114$		0			0
$115$	21.3457	+	12.3239i	1.99050	+	1.14921i
$116$	6.71059	+	3.87436i	0.623062	+	0.359725i
$117$		0			0
$118$	3.44231			0.316890
$119$	−8.81883	+	0.425377i	−0.808421	+	0.0389942i
$120$		0			0
$121$	10.3877	−	3.61867i	0.944340	−	0.328970i
$122$	−12.8609	−	7.42522i	−1.16437	−	0.672248i
$123$		0			0
$124$	−2.77407	+	1.60161i	−0.249119	+	0.143829i
$125$			36.5781i			3.27165i
$126$		0			0
$127$		−	5.90909i		−	0.524347i	−0.965021	−	0.262173i	$-0.915561\pi$
$127$		−	5.90909i		−	0.524347i	0.965021	−	0.262173i	$-0.0844392\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	2.15238	−	3.72803i	0.188776	−	0.326970i
$131$	6.05214	+	10.4826i	0.528778	+	0.915870i	0.999437	+	0.0335545i	$0.0106827\pi$
$131$	6.05214	+	10.4826i	0.528778	+	0.915870i	−0.470659	+	0.882315i	$0.655984\pi$
$132$		0			0
$133$	3.91270	−	7.60073i	0.339274	−	0.659067i
$134$			0.330392i			0.0285415i
$135$		0			0
$136$	2.89000	+	1.66854i	0.247815	+	0.143076i
$137$	4.94560	−	8.56604i	0.422532	−	0.731846i	−0.573655	−	0.819097i	$-0.694475\pi$
$137$	4.94560	−	8.56604i	0.422532	−	0.731846i	0.996186	+	0.0872511i	$0.0278082\pi$
$138$		0			0
$139$	−1.58746			−0.134647			−0.0673235	−	0.997731i	$-0.521446\pi$
$139$	−1.58746			−0.134647			−0.0673235	+	0.997731i	$0.521446\pi$
$140$	9.57052	−	6.15868i	0.808856	−	0.520504i
$141$		0			0
$142$	2.46794	−	1.42487i	0.207105	−	0.119572i
$143$	3.27258	−	0.553700i	0.273667	−	0.0463027i
$144$		0			0
$145$	−16.6658	−	28.8660i	−1.38402	−	2.39719i
$146$		−	14.8958i		−	1.23278i
$147$		0			0
$148$	2.52944			0.207918
$149$	−14.7912	+	8.53970i	−1.21174	+	0.699599i	−0.963138	−	0.269006i	$-0.913305\pi$
$149$	−14.7912	+	8.53970i	−1.21174	+	0.699599i	−0.248603	+	0.968605i	$0.579971\pi$
$150$		0			0
$151$	7.20145	+	4.15776i	0.586046	+	0.338354i	0.763532	−	0.645770i	$-0.223463\pi$
$151$	7.20145	+	4.15776i	0.586046	+	0.338354i	−0.177487	+	0.984123i	$0.556797\pi$
$152$	−2.79822	+	1.61555i	−0.226966	+	0.131039i
$153$		0			0
$154$	8.36258	+	2.65844i	0.673876	+	0.214223i
$155$	13.7788			1.10674
$156$		0			0
$157$	−1.08351	−	0.625565i	−0.0864735	−	0.0499255i	0.456140	−	0.889908i	$-0.349232\pi$
$157$	−1.08351	−	0.625565i	−0.0864735	−	0.0499255i	−0.542613	+	0.839983i	$0.682565\pi$
$158$	−8.04614	+	13.9363i	−0.640116	+	1.10871i
$159$		0			0
$160$	−4.30156			−0.340068
$161$	−6.93871	+	13.4790i	−0.546847	+	1.06229i
$162$		0			0
$163$	−3.60786	−	6.24899i	−0.282589	−	0.489459i	0.689433	−	0.724350i	$-0.257860\pi$
$163$	−3.60786	−	6.24899i	−0.282589	−	0.489459i	−0.972022	+	0.234891i	$0.924527\pi$
$164$	−0.725556	+	1.25670i	−0.0566564	+	0.0981317i
$165$		0			0
$166$	1.51608	−	0.875309i	0.117671	−	0.0679372i
$167$	−15.4393			−1.19473			−0.597364	−	0.801970i	$-0.703785\pi$
$167$	−15.4393			−1.19473			−0.597364	+	0.801970i	$0.703785\pi$
$168$		0			0
$169$	−11.9985			−0.922963
$170$	−7.17733	−	12.4315i	−0.550476	−	0.953453i
$171$		0			0
$172$	3.59030	+	2.07286i	0.273757	+	0.158054i
$173$	3.11021	+	5.38705i	0.236465	+	0.409569i	0.959697	−	0.281035i	$-0.0906778\pi$
$173$	3.11021	+	5.38705i	0.236465	+	0.409569i	−0.723232	+	0.690605i	$0.757344\pi$
$174$		0			0
$175$	−35.6853	+	1.72128i	−2.69755	+	0.130117i
$176$	−2.11424	−	2.55539i	−0.159367	−	0.192620i
$177$		0			0
$178$	−1.39230	+	2.41153i	−0.104357	+	0.180752i
$179$	1.53946	−	2.66643i	0.115065	−	0.199298i	−0.802741	−	0.596328i	$-0.796626\pi$
$179$	1.53946	−	2.66643i	0.115065	−	0.199298i	0.917806	+	0.397030i	$0.129959\pi$
$180$		0			0
$181$			18.3243i			1.36203i	0.732268	+	0.681016i	$0.238462\pi$
$181$			18.3243i			1.36203i	−0.732268	+	0.681016i	$0.761538\pi$
$182$	2.35411	+	1.21185i	0.174498	+	0.0898281i
$183$		0			0
$184$	4.96231	−	2.86499i	0.365826	−	0.211210i
$185$	−9.42282	−	5.44027i	−0.692779	−	0.399976i
$186$		0			0
$187$	3.85737	−	10.3739i	0.282079	−	0.758615i
$188$			3.20101i			0.233458i
$189$		0			0
$190$	13.8988			1.00833
$191$	10.4101	+	18.0308i	0.753248	+	1.30466i	0.946241	+	0.323464i	$0.104847\pi$
$191$	10.4101	+	18.0308i	0.753248	+	1.30466i	−0.192992	+	0.981200i	$0.561819\pi$
$192$		0			0
$193$	−3.91133	−	2.25821i	−0.281544	−	0.162549i	0.352578	−	0.935782i	$-0.385305\pi$
$193$	−3.91133	−	2.25821i	−0.281544	−	0.162549i	−0.634122	+	0.773233i	$0.718638\pi$
$194$	−6.16737	−	10.6822i	−0.442791	−	0.766937i
$195$		0			0
$196$	4.06721	+	5.69717i	0.290515	+	0.406941i
$197$		−	17.3563i		−	1.23659i	−0.785947	−	0.618293i	$-0.787824\pi$
$197$		−	17.3563i		−	1.23659i	0.785947	−	0.618293i	$-0.212176\pi$
$198$		0			0
$199$	6.76938	+	3.90830i	0.479868	+	0.277052i	0.720362	−	0.693599i	$-0.243976\pi$
$199$	6.76938	+	3.90830i	0.479868	+	0.277052i	−0.240493	+	0.970651i	$0.577309\pi$
$200$	11.6943	+	6.75173i	0.826914	+	0.477419i
$201$		0			0
$202$		−	0.0562448i		−	0.00395737i
$203$	17.2401	−	11.0941i	1.21001	−	0.778652i
$204$		0			0
$205$	5.40577	−	3.12102i	0.377555	−	0.217982i
$206$	7.39746	−	12.8128i	0.515405	−	0.892708i
$207$		0			0
$208$	−0.500372	−	0.866669i	−0.0346945	−	0.0600927i
$209$	6.83132	+	8.25673i	0.472532	+	0.571130i
$210$		0			0
$211$			21.9923i			1.51401i	0.653406	+	0.757007i	$0.273339\pi$
$211$			21.9923i			1.51401i	−0.653406	+	0.757007i	$0.726661\pi$
$212$	5.65774	+	9.79949i	0.388575	+	0.673032i
$213$		0			0
$214$	−5.30694	+	9.19190i	−0.362775	+	0.628345i
$215$	−8.91653	−	15.4439i	−0.608102	−	1.05326i
$216$		0			0
$217$	0.408313	+	8.46507i	0.0277181	+	0.574646i
$218$	−0.348204			−0.0235833
$219$		0			0
$220$	2.38001	+	14.0668i	0.160460	+	0.948380i
$221$	1.66978	−	2.89214i	0.112322	−	0.194547i
$222$		0			0
$223$		−	8.30245i		−	0.555973i	−0.960585	−	0.277987i	$-0.910333\pi$
$223$		−	8.30245i		−	0.555973i	0.960585	−	0.277987i	$-0.0896671\pi$
$224$	−0.127470	−	2.64268i	−0.00851693	−	0.176571i
$225$		0			0
$226$	−16.4154	+	9.47745i	−1.09194	+	0.630431i
$227$	−3.95627	+	6.85245i	−0.262587	+	0.454813i	−0.966929	−	0.255048i	$-0.917909\pi$
$227$	−3.95627	+	6.85245i	−0.262587	+	0.454813i	0.704342	+	0.709861i	$0.251242\pi$
$228$		0			0
$229$	−9.27450	+	5.35463i	−0.612876	+	0.353844i	−0.774090	−	0.633075i	$-0.781792\pi$
$229$	−9.27450	+	5.35463i	−0.612876	+	0.353844i	0.161214	+	0.986919i	$0.448459\pi$
$230$	−24.6479			−1.62523
$231$		0			0
$232$	−7.74872			−0.508728
$233$	15.3378	−	8.85528i	1.00481	−	0.580129i	0.0951440	−	0.995464i	$-0.469669\pi$
$233$	15.3378	−	8.85528i	1.00481	−	0.580129i	0.909669	+	0.415335i	$0.136336\pi$
$234$		0			0
$235$	6.88467	−	11.9246i	0.449107	−	0.777876i
$236$	−2.98113	+	1.72116i	−0.194055	+	0.112038i
$237$		0			0
$238$	7.42465	−	4.77780i	0.481268	−	0.309699i
$239$			26.6356i			1.72291i	0.507832	+	0.861456i	$0.330447\pi$
$239$			26.6356i			1.72291i	−0.507832	+	0.861456i	$0.669553\pi$
$240$		0			0
$241$	1.85521	−	3.21331i	0.119504	−	0.206987i	−0.800067	−	0.599911i	$-0.795203\pi$
$241$	1.85521	−	3.21331i	0.119504	−	0.206987i	0.919571	+	0.392923i	$0.128536\pi$
$242$	−7.18671	+	8.32774i	−0.461979	+	0.535327i
$243$		0			0
$244$	14.8504			0.950702
$245$	−2.89806	−	29.9712i	−0.185150	−	1.91479i
$246$		0			0
$247$	1.61675	+	2.80030i	0.102872	+	0.178179i
$248$	1.60161	−	2.77407i	0.101702	−	0.176153i
$249$		0			0
$250$	−18.2891	−	31.6776i	−1.15670	−	2.00347i
$251$		−	10.6948i		−	0.675051i	−0.941316	−	0.337526i	$-0.890410\pi$
$251$		−	10.6948i		−	0.675051i	0.941316	−	0.337526i	$-0.109590\pi$
$252$		0			0
$253$	−12.1145	−	14.6423i	−0.761634	−	0.920555i
$254$	2.95454	+	5.11742i	0.185385	+	0.321095i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−20.6304	+	11.9110i	−1.28689	+	0.742987i	−0.978099	−	0.208142i	$-0.933258\pi$
$257$	−20.6304	+	11.9110i	−1.28689	+	0.742987i	−0.308793	+	0.951129i	$0.599925\pi$
$258$		0			0
$259$	3.06302	−	5.95015i	0.190327	−	0.369724i
$260$			4.30476i			0.266970i
$261$		0			0
$262$	−10.4826	−	6.05214i	−0.647618	−	0.373902i
$263$	14.7672	+	8.52582i	0.910582	+	0.525725i	0.880618	−	0.473826i	$-0.157127\pi$
$263$	14.7672	+	8.52582i	0.910582	+	0.525725i	0.0299637	+	0.999551i	$0.490461\pi$
$264$		0			0
$265$		−	48.6743i		−	2.99004i
$266$	0.411868	+	8.53877i	0.0252532	+	0.523546i
$267$		0			0
$268$	−0.165196	−	0.286128i	−0.0100909	−	0.0174780i
$269$	−8.32306	−	4.80532i	−0.507466	−	0.292986i	0.224326	−	0.974514i	$-0.427982\pi$
$269$	−8.32306	−	4.80532i	−0.507466	−	0.292986i	−0.731791	+	0.681529i	$0.761315\pi$
$270$		0			0
$271$	2.55614	+	4.42736i	0.155274	+	0.268943i	0.933159	−	0.359464i	$-0.117040\pi$
$271$	2.55614	+	4.42736i	0.155274	+	0.268943i	−0.777884	+	0.628407i	$0.783707\pi$
$272$	−3.33708			−0.202340
$273$		0			0
$274$			9.89121i			0.597550i
$275$	15.6088	−	41.9779i	0.941246	−	2.53136i
$276$		0			0
$277$	−22.8002	−	13.1637i	−1.36993	−	0.790931i	−0.379013	−	0.925391i	$-0.623736\pi$
$277$	−22.8002	−	13.1637i	−1.36993	−	0.790931i	−0.990919	+	0.134461i	$0.957070\pi$
$278$	1.37478	−	0.793732i	0.0824541	−	0.0476049i
$279$		0			0
$280$	−5.20897	+	10.1188i	−0.311295	+	0.604716i
$281$			10.5684i			0.630459i	0.949015	+	0.315230i	$0.102082\pi$
$281$			10.5684i			0.630459i	−0.949015	+	0.315230i	$0.897918\pi$
$282$		0			0
$283$	−5.20379	+	9.01323i	−0.309333	+	0.535781i	−0.978217	−	0.207586i	$-0.933439\pi$
$283$	−5.20379	+	9.01323i	−0.309333	+	0.535781i	0.668883	+	0.743367i	$0.266773\pi$
$284$	−1.42487	+	2.46794i	−0.0845504	+	0.146446i
$285$		0			0
$286$	−2.55729	+	2.11581i	−0.151215	+	0.125110i
$287$	2.07760	+	3.22857i	0.122637	+	0.190576i
$288$		0			0
$289$	2.93194	+	5.07828i	0.172467	+	0.298722i
$290$	28.8660	+	16.6658i	1.69507	+	0.978649i
$291$		0			0
$292$	7.44790	+	12.9001i	0.435855	+	0.754923i
$293$	31.4600			1.83792			0.918958	−	0.394356i	$-0.129032\pi$
$293$	31.4600			1.83792			0.918958	+	0.394356i	$0.129032\pi$
$294$		0			0
$295$	14.8073			0.862116
$296$	−2.19056	+	1.26472i	−0.127324	+	0.0735103i
$297$		0			0
$298$	8.53970	−	14.7912i	0.494691	−	0.856831i
$299$	−2.86712	−	4.96600i	−0.165810	−	0.287191i
$300$		0			0
$301$	9.22377	−	5.93555i	0.531649	−	0.342120i
$302$	−8.31552			−0.478504
$303$		0			0
$304$	1.61555	−	2.79822i	0.0926583	−	0.160489i
$305$	−55.3218	−	31.9401i	−3.16772	−	1.82888i
$306$		0			0
$307$	18.4994			1.05582			0.527910	−	0.849301i	$-0.322976\pi$
$307$	18.4994			1.05582			0.527910	+	0.849301i	$0.322976\pi$
$308$	−8.57142	+	1.87901i	−0.488402	+	0.107067i
$309$		0			0
$310$	−11.9328	+	6.88942i	−0.677739	+	0.391293i
$311$	26.8449	+	15.4989i	1.52224	+	0.878864i	0.999655	+	0.0262743i	$0.00836432\pi$
$311$	26.8449	+	15.4989i	1.52224	+	0.878864i	0.522582	+	0.852589i	$0.324969\pi$
$312$		0			0
$313$	8.31513	−	4.80074i	0.469999	−	0.271354i	−0.246240	−	0.969209i	$-0.579195\pi$
$313$	8.31513	−	4.80074i	0.469999	−	0.271354i	0.716239	+	0.697855i	$0.245862\pi$
$314$	1.25113			0.0706053
$315$		0			0
$316$		−	16.0923i		−	0.905261i
$317$	−5.97126	−	10.3425i	−0.335379	−	0.580894i	0.648178	−	0.761489i	$-0.275531\pi$
$317$	−5.97126	−	10.3425i	−0.335379	−	0.580894i	−0.983558	+	0.180595i	$0.942198\pi$
$318$		0			0
$319$	4.28728	+	25.3395i	0.240042	+	1.41874i
$320$	3.72526	−	2.15078i	0.208249	−	0.120232i
$321$		0			0
$322$	−0.730399	−	15.1425i	−0.0407035	−	0.843859i
$323$	10.7825			0.599952
$324$		0			0
$325$	6.75674	−	11.7030i	0.374797	−	0.649167i
$326$	6.24899	+	3.60786i	0.346100	+	0.199821i
$327$		0			0
$328$		−	1.45111i		−	0.0801242i
$329$	7.52993	+	3.87625i	0.415139	+	0.213705i
$330$		0			0
$331$	−3.24581	−	5.62191i	−0.178406	−	0.309008i	0.762929	−	0.646482i	$-0.223761\pi$
$331$	−3.24581	−	5.62191i	−0.178406	−	0.309008i	−0.941335	+	0.337474i	$0.890427\pi$
$332$	−0.875309	+	1.51608i	−0.0480388	+	0.0832057i
$333$		0			0
$334$	13.3708	−	7.71964i	0.731618	−	0.422400i
$335$			1.42120i			0.0776485i
$336$		0			0
$337$		−	5.74869i		−	0.313151i	−0.987666	−	0.156576i	$-0.949955\pi$
$337$		−	5.74869i		−	0.313151i	0.987666	−	0.156576i	$-0.0500455\pi$
$338$	10.3910	−	5.99926i	0.565197	−	0.326317i
$339$		0			0
$340$	12.4315	+	7.17733i	0.674193	+	0.389246i
$341$	−9.95776	−	3.70264i	−0.539243	−	0.200509i
$342$		0			0
$343$	18.3270	−	2.66858i	0.989565	−	0.144090i
$344$	−4.14572			−0.223522
$345$		0			0
$346$	−5.38705	−	3.11021i	−0.289609	−	0.167206i
$347$	−12.6658	−	7.31263i	−0.679938	−	0.392563i	0.119893	−	0.992787i	$-0.461745\pi$
$347$	−12.6658	−	7.31263i	−0.679938	−	0.392563i	−0.799832	+	0.600224i	$0.795078\pi$
$348$		0			0
$349$	15.2458			0.816091			0.408046	−	0.912962i	$-0.366210\pi$
$349$	15.2458			0.816091			0.408046	+	0.912962i	$0.366210\pi$
$350$	30.0437	−	19.3333i	1.60590	−	1.03341i
$351$		0			0
$352$	3.10868	+	1.15591i	0.165693	+	0.0616103i
$353$	23.7709	+	13.7242i	1.26520	+	0.730463i	0.974076	−	0.226222i	$-0.0726374\pi$
$353$	23.7709	+	13.7242i	1.26520	+	0.730463i	0.291124	+	0.956685i	$0.405971\pi$
$354$		0			0
$355$	10.6160	−	6.12916i	0.563440	−	0.325302i
$356$		−	2.78460i		−	0.147583i
$357$		0			0
$358$			3.07893i			0.162726i
$359$	14.1129	−	8.14808i	0.744850	−	0.430039i	−0.0789804	−	0.996876i	$-0.525166\pi$
$359$	14.1129	−	8.14808i	0.744850	−	0.430039i	0.823830	+	0.566837i	$0.191833\pi$
$360$		0			0
$361$	4.27998	−	7.41314i	0.225262	−	0.390165i
$362$	−9.16214	−	15.8693i	−0.481551	−	0.834071i
$363$		0			0
$364$	−2.64464	+	0.127564i	−0.138617	+	0.00668619i
$365$		−	64.0752i		−	3.35385i
$366$		0			0
$367$	−2.93922	−	1.69696i	−0.153426	−	0.0885807i	0.421321	−	0.906911i	$-0.361566\pi$
$367$	−2.93922	−	1.69696i	−0.153426	−	0.0885807i	−0.574748	+	0.818331i	$0.694900\pi$
$368$	−2.86499	+	4.96231i	−0.149348	+	0.258678i
$369$		0			0
$370$	10.8805			0.565652
$371$	29.9032	−	1.44238i	1.55250	−	0.0748847i
$372$		0			0
$373$	−5.64289	+	3.25792i	−0.292178	+	0.168689i	−0.638923	−	0.769270i	$-0.720620\pi$
$373$	−5.64289	+	3.25792i	−0.292178	+	0.168689i	0.346746	+	0.937959i	$0.387287\pi$
$374$	1.84637	+	10.9128i	0.0954735	+	0.564285i
$375$		0			0
$376$	−1.60050	−	2.77216i	−0.0825397	−	0.142963i
$377$			7.75447i			0.399376i
$378$		0			0
$379$	−27.4324			−1.40911			−0.704555	−	0.709650i	$-0.748853\pi$
$379$	−27.4324			−1.40911			−0.704555	+	0.709650i	$0.748853\pi$
$380$	−12.0367	+	6.94940i	−0.617471	+	0.356497i
$381$		0			0
$382$	−18.0308	−	10.4101i	−0.922537	−	0.532627i
$383$	7.65298	−	4.41845i	0.391049	−	0.225772i	−0.291565	−	0.956551i	$-0.594176\pi$
$383$	7.65298	−	4.41845i	0.391049	−	0.225772i	0.682615	+	0.730779i	$0.260843\pi$
$384$		0			0
$385$	35.9722	+	11.4355i	1.83331	+	0.582805i
$386$	4.51641			0.229879
$387$		0			0
$388$	10.6822	+	6.16737i	0.542306	+	0.313101i
$389$	4.46153	−	7.72760i	0.226209	−	0.391805i	−0.730473	−	0.682942i	$-0.760700\pi$
$389$	4.46153	−	7.72760i	0.226209	−	0.391805i	0.956681	+	0.291137i	$0.0940336\pi$
$390$		0			0
$391$	−19.1214			−0.967011
$392$	−6.37090	−	2.90029i	−0.321779	−	0.146487i
$393$		0			0
$394$	8.67816	+	15.0310i	0.437200	+	0.757252i
$395$	−34.6110	+	59.9480i	−1.74147	+	3.01631i
$396$		0			0
$397$	−4.13575	+	2.38778i	−0.207567	+	0.119839i	−0.600180	−	0.799865i	$-0.704905\pi$
$397$	−4.13575	+	2.38778i	−0.207567	+	0.119839i	0.392613	+	0.919704i	$0.371571\pi$
$398$	−7.81660			−0.391811
$399$		0			0
$400$	−13.5035			−0.675173
$401$	1.26986	+	2.19946i	0.0634137	+	0.109836i	0.895989	−	0.444076i	$-0.146468\pi$
$401$	1.26986	+	2.19946i	0.0634137	+	0.109836i	−0.832576	+	0.553912i	$0.813135\pi$
$402$		0			0
$403$	−2.77613	−	1.60280i	−0.138289	−	0.0798411i
$404$	0.0281224	+	0.0487094i	0.00139914	+	0.00242338i
$405$		0			0
$406$	−9.38329	+	18.2278i	−0.465685	+	0.904630i
$407$	5.34783	+	6.46369i	0.265082	+	0.320393i
$408$		0			0
$409$	−0.0321007	+	0.0556000i	−0.00158728	+	0.00274924i	−0.866818	−	0.498625i	$-0.833839\pi$
$409$	−0.0321007	+	0.0556000i	−0.00158728	+	0.00274924i	0.865231	+	0.501374i	$0.167172\pi$
$410$	−3.12102	+	5.40577i	−0.154136	+	0.266972i
$411$		0			0
$412$			14.7949i			0.728893i
$413$	0.438790	+	9.09692i	0.0215915	+	0.447630i
$414$		0			0
$415$	6.52152	−	3.76520i	0.320129	−	0.184826i
$416$	0.866669	+	0.500372i	0.0424919	+	0.0245327i
$417$		0			0
$418$	−10.0445	−	3.73487i	−0.491291	−	0.182679i
$419$		−	23.7720i		−	1.16134i	−0.814140	−	0.580669i	$-0.802791\pi$
$419$		−	23.7720i		−	1.16134i	0.814140	−	0.580669i	$-0.197209\pi$
$420$		0			0
$421$	−1.11501			−0.0543422			−0.0271711	−	0.999631i	$-0.508650\pi$
$421$	−1.11501			−0.0543422			−0.0271711	+	0.999631i	$0.508650\pi$
$422$	−10.9962	−	19.0459i	−0.535285	−	0.927141i
$423$		0			0
$424$	−9.79949	−	5.65774i	−0.475905	−	0.274764i
$425$	−22.5311	−	39.0249i	−1.09292	−	1.89299i
$426$		0			0
$427$	17.9831	−	34.9336i	0.870263	−	1.69056i
$428$		−	10.6139i		−	0.513042i
$429$		0			0
$430$	15.4439	+	8.91653i	0.744770	+	0.429993i
$431$	−25.4430	−	14.6895i	−1.22555	−	0.707569i	−0.259451	−	0.965756i	$-0.583542\pi$
$431$	−25.4430	−	14.6895i	−1.22555	−	0.707569i	−0.966095	+	0.258187i	$0.916875\pi$
$432$		0			0
$433$			13.1705i			0.632934i	0.948604	+	0.316467i	$0.102497\pi$
$433$			13.1705i			0.632934i	−0.948604	+	0.316467i	$0.897503\pi$
$434$	−4.58614	−	7.12681i	−0.220142	−	0.342098i
$435$		0			0
$436$	0.301553	−	0.174102i	0.0144418	−	0.00833797i
$437$	9.25709	−	16.0337i	0.442826	−	0.766998i
$438$		0			0
$439$	−5.10665	−	8.84498i	−0.243727	−	0.422148i	0.718046	−	0.695996i	$-0.245037\pi$
$439$	−5.10665	−	8.84498i	−0.243727	−	0.422148i	−0.961773	+	0.273848i	$0.911703\pi$
$440$	−9.09452	−	10.9922i	−0.433564	−	0.524031i
$441$		0			0
$442$			3.33956i			0.158847i
$443$	13.6862	+	23.7051i	0.650250	+	1.12627i	0.983062	+	0.183272i	$0.0586690\pi$
$443$	13.6862	+	23.7051i	0.650250	+	1.12627i	−0.332813	+	0.942993i	$0.607998\pi$
$444$		0			0
$445$	−5.98906	+	10.3734i	−0.283909	+	0.491744i
$446$	4.15123	+	7.19014i	0.196566	+	0.340463i
$447$		0			0
$448$	1.43173	+	2.22489i	0.0676430	+	0.105116i
$449$	−1.35953			−0.0641602			−0.0320801	−	0.999485i	$-0.510213\pi$
$449$	−1.35953			−0.0641602			−0.0320801	+	0.999485i	$0.510213\pi$
$450$		0			0
$451$	−4.74535	+	0.802884i	−0.223450	+	0.0378063i
$452$	9.47745	−	16.4154i	0.445782	−	0.772117i
$453$		0			0
$454$		−	7.91253i		−	0.371354i
$455$	10.1264	+	5.21284i	0.474731	+	0.244382i
$456$		0			0
$457$	18.9644	−	10.9491i	0.887115	−	0.512176i	0.0141173	−	0.999900i	$-0.495506\pi$
$457$	18.9644	−	10.9491i	0.887115	−	0.512176i	0.872998	+	0.487724i	$0.162173\pi$
$458$	5.35463	−	9.27450i	0.250206	−	0.433369i
$459$		0			0
$460$	21.3457	−	12.3239i	0.995248	−	0.574607i
$461$	13.4227			0.625159			0.312579	−	0.949892i	$-0.398807\pi$
$461$	13.4227			0.625159			0.312579	+	0.949892i	$0.398807\pi$
$462$		0			0
$463$	−21.1422			−0.982562			−0.491281	−	0.871001i	$-0.663471\pi$
$463$	−21.1422			−0.982562			−0.491281	+	0.871001i	$0.663471\pi$
$464$	6.71059	−	3.87436i	0.311531	−	0.179863i
$465$		0			0
$466$	−8.85528	+	15.3378i	−0.410213	+	0.710510i
$467$	−2.48960	+	1.43737i	−0.115205	+	0.0665137i	−0.556495	−	0.830851i	$-0.687854\pi$
$467$	−2.48960	+	1.43737i	−0.115205	+	0.0665137i	0.441290	+	0.897364i	$0.354521\pi$
$468$		0			0
$469$	−0.873119	+	0.0421149i	−0.0403169	+	0.00194469i
$470$			13.7693i			0.635133i
$471$		0			0
$472$	1.72116	−	2.98113i	0.0792226	−	0.137218i
$473$	2.29378	+	13.5571i	0.105468	+	0.623356i
$474$		0			0
$475$	43.6311			2.00193
$476$	−4.04103	+	7.85002i	−0.185220	+	0.359805i
$477$		0			0
$478$	−13.3178	−	23.0671i	−0.609141	−	1.05506i
$479$	1.91941	−	3.32451i	0.0877000	−	0.151901i	−0.818839	−	0.574024i	$-0.805382\pi$
$479$	1.91941	−	3.32451i	0.0877000	−	0.151901i	0.906539	+	0.422123i	$0.138715\pi$
$480$		0			0
$481$	1.26566	+	2.19218i	0.0577091	+	0.0999550i
$482$			3.71041i			0.169005i
$483$		0			0
$484$	2.06001	−	10.8054i	0.0936367	−	0.491154i
$485$	−26.5293	−	45.9502i	−1.20463	−	2.08649i
$486$		0			0
$487$	4.84042	−	8.38386i	0.219340	−	0.379909i	−0.735266	−	0.677779i	$-0.762943\pi$
$487$	4.84042	−	8.38386i	0.219340	−	0.379909i	0.954607	+	0.297870i	$0.0962761\pi$
$488$	−12.8609	+	7.42522i	−0.582184	+	0.336124i
$489$		0			0
$490$	17.4954	+	24.5068i	0.790360	+	1.10710i
$491$			15.8886i			0.717041i	0.933522	+	0.358520i	$0.116719\pi$
$491$			15.8886i			0.717041i	−0.933522	+	0.358520i	$0.883281\pi$
$492$		0			0
$493$	22.3938	+	12.9290i	1.00856	+	0.582295i
$494$	−2.80030	−	1.61675i	−0.125991	−	0.0727412i
$495$		0			0
$496$			3.20322i			0.143829i
$497$	4.08006	+	6.34036i	0.183016	+	0.284404i
$498$		0			0
$499$	15.0220	+	26.0188i	0.672477	+	1.16476i	0.977200	+	0.212323i	$0.0681027\pi$
$499$	15.0220	+	26.0188i	0.672477	+	1.16476i	−0.304723	+	0.952441i	$0.598564\pi$
$500$	31.6776	+	18.2891i	1.41667	+	0.817912i
$501$		0			0
$502$	5.34741	+	9.26199i	0.238667	+	0.413383i
$503$	−4.66798			−0.208135			−0.104067	−	0.994570i	$-0.533186\pi$
$503$	−4.66798			−0.208135			−0.104067	+	0.994570i	$0.533186\pi$
$504$		0			0
$505$		−	0.241941i		−	0.0107662i
$506$	17.8127	+	6.62335i	0.791869	+	0.294444i
$507$		0			0
$508$	−5.11742	−	2.95454i	−0.227049	−	0.131087i
$509$	−26.8000	+	15.4730i	−1.18789	+	0.685829i	−0.957827	−	0.287346i	$-0.907227\pi$
$509$	−26.8000	+	15.4730i	−1.18789	+	0.685829i	−0.230064	+	0.973175i	$0.573894\pi$
$510$		0			0
$511$	39.3648	−	1.89876i	1.74140	−	0.0839963i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	11.9110	−	20.6304i	0.525371	−	0.909970i
$515$	31.8206	−	55.1150i	1.40219	−	2.42866i
$516$		0			0
$517$	−8.17982	+	6.76769i	−0.359748	+	0.297643i
$518$	0.322427	+	6.68449i	0.0141666	+	0.293700i
$519$		0			0
$520$	−2.15238	−	3.72803i	−0.0943881	−	0.163485i
$521$	−9.57271	−	5.52680i	−0.419388	−	0.242134i	0.275427	−	0.961322i	$-0.411181\pi$
$521$	−9.57271	−	5.52680i	−0.419388	−	0.242134i	−0.694815	+	0.719188i	$0.744514\pi$
$522$		0			0
$523$	2.06741	+	3.58085i	0.0904013	+	0.156580i	0.907680	−	0.419663i	$-0.137852\pi$
$523$	2.06741	+	3.58085i	0.0904013	+	0.156580i	−0.817279	+	0.576243i	$0.804518\pi$
$524$	12.1043			0.528778
$525$		0			0
$526$	−17.0516			−0.743487
$527$	−9.25728	+	5.34470i	−0.403254	+	0.232819i
$528$		0			0
$529$	−4.91634	+	8.51535i	−0.213754	+	0.370233i
$530$	24.3371	+	42.1531i	1.05714	+	1.83102i
$531$		0			0
$532$	−4.62607	−	7.18886i	−0.200566	−	0.311677i
$533$	−1.45219			−0.0629013
$534$		0			0
$535$	−22.8282	+	39.5395i	−0.986947	+	1.70944i
$536$	0.286128	+	0.165196i	0.0123588	+	0.00713537i
$537$		0			0
$538$	9.61064			0.414344
$539$	−5.95943	+	22.4385i	−0.256691	+	0.966494i
$540$		0			0
$541$	−34.4914	+	19.9136i	−1.48290	+	0.856153i	−0.999811	−	0.0194190i	$-0.993818\pi$
$541$	−34.4914	+	19.9136i	−1.48290	+	0.856153i	−0.483088	+	0.875572i	$0.660485\pi$
$542$	−4.42736	−	2.55614i	−0.190172	−	0.109796i
$543$		0			0
$544$	2.89000	−	1.66854i	0.123908	−	0.0715381i
$545$	−1.49782			−0.0641596
$546$		0			0
$547$			37.7080i			1.61228i	0.591728	+	0.806138i	$0.298446\pi$
$547$			37.7080i			1.61228i	−0.591728	+	0.806138i	$0.701554\pi$
$548$	−4.94560	−	8.56604i	−0.211266	−	0.365923i
$549$		0			0
$550$	7.47131	+	44.1583i	0.318578	+	1.88292i
$551$	−21.6826	+	12.5185i	−0.923710	+	0.533304i
$552$		0			0
$553$	−37.8549	−	19.4869i	−1.60975	−	0.828667i
$554$	26.3274			1.11854
$555$		0			0
$556$	−0.793732	+	1.37478i	−0.0336617	+	0.0583039i
$557$	27.3188	+	15.7725i	1.15754	+	0.668304i	0.950712	−	0.310074i	$-0.100354\pi$
$557$	27.3188	+	15.7725i	1.15754	+	0.668304i	0.206824	+	0.978378i	$0.433687\pi$
$558$		0			0
$559$			4.14880i			0.175475i
$560$	−0.548319	−	11.3677i	−0.0231707	−	0.480371i
$561$		0			0
$562$	−5.28421	−	9.15252i	−0.222901	−	0.386076i
$563$	18.8993	−	32.7345i	0.796511	−	1.37960i	−0.125365	−	0.992111i	$-0.540010\pi$
$563$	18.8993	−	32.7345i	0.796511	−	1.37960i	0.921876	−	0.387486i	$-0.126656\pi$
$564$		0			0
$565$	−70.6120	+	40.7679i	−2.97067	+	1.71512i
$566$		−	10.4076i		−	0.437463i
$567$		0			0
$568$		−	2.84974i		−	0.119572i
$569$	−16.0111	+	9.24404i	−0.671222	+	0.387530i	−0.796540	−	0.604586i	$-0.793338\pi$
$569$	−16.0111	+	9.24404i	−0.671222	+	0.387530i	0.125317	+	0.992117i	$0.460005\pi$
$570$		0			0
$571$	−13.1984	−	7.62013i	−0.552338	−	0.318892i	0.197727	−	0.980257i	$-0.436644\pi$
$571$	−13.1984	−	7.62013i	−0.552338	−	0.318892i	−0.750064	+	0.661365i	$0.769978\pi$
$572$	1.15677	−	3.11099i	0.0483670	−	0.130077i
$573$		0			0
$574$	−3.41354	−	1.75722i	−0.142478	−	0.0733449i
$575$	−77.3745			−3.22674
$576$		0			0
$577$	−23.7188	−	13.6941i	−0.987428	−	0.570092i	−0.0829237	−	0.996556i	$-0.526426\pi$
$577$	−23.7188	−	13.6941i	−0.987428	−	0.570092i	−0.904505	+	0.426464i	$0.859759\pi$
$578$	−5.07828	−	2.93194i	−0.211228	−	0.121953i
$579$		0			0
$580$	−33.3316			−1.38402
$581$	2.50642	+	3.89494i	0.103984	+	0.161589i
$582$		0			0
$583$	−13.0797	+	35.1762i	−0.541706	+	1.45685i
$584$	−12.9001	−	7.44790i	−0.533811	−	0.308196i
$585$		0			0
$586$	−27.2452	+	15.7300i	−1.12549	+	0.649801i
$587$		−	17.1517i		−	0.707927i	−0.935259	−	0.353964i	$-0.884834\pi$
$587$		−	17.1517i		−	0.707927i	0.935259	−	0.353964i	$-0.115166\pi$
$588$		0			0
$589$		−	10.3499i		−	0.426461i
$590$	−12.8235	+	7.40366i	−0.527936	+	0.304804i
$591$		0			0
$592$	1.26472	−	2.19056i	0.0519796	−	0.0900313i
$593$	2.63071	+	4.55652i	0.108030	+	0.187114i	0.914972	−	0.403517i	$-0.132212\pi$
$593$	2.63071	+	4.55652i	0.108030	+	0.187114i	−0.806942	+	0.590631i	$0.798879\pi$
$594$		0			0
$595$	31.9376	−	20.5520i	1.30931	−	0.842551i
$596$			17.0794i			0.699599i
$597$		0			0
$598$	4.96600	+	2.86712i	0.203075	+	0.117245i
$599$	−17.8442	+	30.9071i	−0.729096	+	1.26283i	0.228169	+	0.973621i	$0.426726\pi$
$599$	−17.8442	+	30.9071i	−0.729096	+	1.26283i	−0.957266	+	0.289210i	$0.906607\pi$
$600$		0			0
$601$	−9.98679			−0.407370			−0.203685	−	0.979036i	$-0.565292\pi$
$601$	−9.98679			−0.407370			−0.203685	+	0.979036i	$0.565292\pi$
$602$	−5.02024	+	9.75222i	−0.204610	+	0.397471i
$603$		0			0
$604$	7.20145	−	4.15776i	0.293023	−	0.169177i
$605$	−30.9141	+	35.8223i	−1.25684	+	1.45638i
$606$		0			0
$607$	11.8496	+	20.5242i	0.480962	+	0.833050i	0.999761	−	0.0218456i	$-0.00695422\pi$
$607$	11.8496	+	20.5242i	0.480962	+	0.833050i	−0.518800	+	0.854896i	$0.673621\pi$
$608$			3.23111i			0.131039i
$609$		0			0
$610$	63.8801			2.58643
$611$	−2.77422	+	1.60169i	−0.112233	+	0.0647976i
$612$		0			0
$613$	−22.3572	−	12.9080i	−0.903000	−	0.521347i	−0.0248276	−	0.999692i	$-0.507904\pi$
$613$	−22.3572	−	12.9080i	−0.903000	−	0.521347i	−0.878172	+	0.478345i	$0.841237\pi$
$614$	−16.0210	+	9.24972i	−0.646555	+	0.373288i
$615$		0			0
$616$	6.48357	−	5.91298i	0.261230	−	0.238241i
$617$	−4.44499			−0.178949			−0.0894743	−	0.995989i	$-0.528519\pi$
$617$	−4.44499			−0.178949			−0.0894743	+	0.995989i	$0.528519\pi$
$618$		0			0
$619$	−30.0167	−	17.3301i	−1.20647	−	0.696557i	−0.244485	−	0.969653i	$-0.578619\pi$
$619$	−30.0167	−	17.3301i	−1.20647	−	0.696557i	−0.961987	+	0.273096i	$0.911952\pi$
$620$	6.88942	−	11.9328i	0.276686	−	0.479234i
$621$		0			0
$622$	−30.9979			−1.24290
$623$	−6.55038	−	3.37200i	−0.262435	−	0.135096i
$624$		0			0
$625$	−44.9130	−	77.7916i	−1.79652	−	3.11166i
$626$	−4.80074	+	8.31513i	−0.191876	+	0.332339i
$627$		0			0
$628$	−1.08351	+	0.625565i	−0.0432368	+	0.0249627i
$629$	8.44094			0.336562
$630$		0			0
$631$	32.7549			1.30395			0.651975	−	0.758240i	$-0.273941\pi$
$631$	32.7549			1.30395			0.651975	+	0.758240i	$0.273941\pi$
$632$	8.04614	+	13.9363i	0.320058	+	0.554357i
$633$		0			0
$634$	10.3425	+	5.97126i	0.410754	+	0.237149i
$635$	12.7092	+	22.0129i	0.504348	+	0.873556i
$636$		0			0
$637$	−2.90245	+	6.37563i	−0.114999	+	0.252612i
$638$	−16.3826	−	19.8010i	−0.648594	−	0.783928i
$639$		0			0
$640$	−2.15078	+	3.72526i	−0.0850171	+	0.147254i
$641$	−17.5417	+	30.3831i	−0.692854	+	1.20006i	0.278044	+	0.960568i	$0.410314\pi$
$641$	−17.5417	+	30.3831i	−0.692854	+	1.20006i	−0.970899	+	0.239491i	$0.923020\pi$
$642$		0			0
$643$			4.02224i			0.158622i	0.996850	+	0.0793109i	$0.0252720\pi$
$643$			4.02224i			0.158622i	−0.996850	+	0.0793109i	$0.974728\pi$
$644$	8.20379	+	12.7486i	0.323275	+	0.502365i
$645$		0			0
$646$	−9.33788	+	5.39123i	−0.367394	+	0.212115i
$647$	4.94497	+	2.85498i	0.194407	+	0.112241i	0.594044	−	0.804433i	$-0.297530\pi$
$647$	4.94497	+	2.85498i	0.194407	+	0.112241i	−0.399637	+	0.916673i	$0.630864\pi$
$648$		0			0
$649$	−10.7010	−	3.97901i	−0.420052	−	0.156190i
$650$			13.5135i			0.530043i
$651$		0			0
$652$	−7.21571			−0.282589
$653$	−7.19689	−	12.4654i	−0.281636	−	0.487808i	0.690152	−	0.723665i	$-0.257544\pi$
$653$	−7.19689	−	12.4654i	−0.281636	−	0.487808i	−0.971788	+	0.235857i	$0.924210\pi$
$654$		0			0
$655$	−45.0916	−	26.0336i	−1.76187	−	1.01722i
$656$	0.725556	+	1.25670i	0.0283282	+	0.0490659i
$657$		0			0
$658$	−8.45924	+	0.408032i	−0.329776	+	0.0159067i
$659$		−	1.73466i		−	0.0675728i	−0.999429	−	0.0337864i	$-0.989243\pi$
$659$		−	1.73466i		−	0.0675728i	0.999429	−	0.0337864i	$-0.0107566\pi$
$660$		0			0
$661$	−24.2717	−	14.0132i	−0.944058	−	0.545052i	−0.0528280	−	0.998604i	$-0.516823\pi$
$661$	−24.2717	−	14.0132i	−0.944058	−	0.545052i	−0.891230	+	0.453551i	$0.850157\pi$
$662$	5.62191	+	3.24581i	0.218502	+	0.126152i
$663$		0			0
$664$		−	1.75062i		−	0.0679372i
$665$	1.77168	+	36.7301i	0.0687027	+	1.42433i
$666$		0			0
$667$	38.4515	−	22.2000i	1.48885	−	0.859587i
$668$	−7.71964	+	13.3708i	−0.298682	+	0.517332i
$669$		0			0
$670$	−0.710600	−	1.23080i	−0.0274529	−	0.0475498i
$671$	31.3973	+	37.9486i	1.21208	+	1.46499i
$672$		0			0
$673$		−	11.9436i		−	0.460394i	−0.973144	−	0.230197i	$-0.926063\pi$
$673$		−	11.9436i		−	0.460394i	0.973144	−	0.230197i	$-0.0739370\pi$
$674$	2.87434	+	4.97851i	0.110716	+	0.191765i
$675$		0			0
$676$	−5.99926	+	10.3910i	−0.230741	+	0.399655i
$677$	−20.2334	−	35.0453i	−0.777634	−	1.34690i	−0.933302	−	0.359092i	$-0.883086\pi$
$677$	−20.2334	−	35.0453i	−0.777634	−	1.34690i	0.155668	−	0.987809i	$-0.450247\pi$
$678$		0			0
$679$	27.4435	−	17.6600i	1.05318	−	0.677730i
$680$	−14.3547			−0.550476
$681$		0			0
$682$	10.4750	−	1.77230i	0.401108	−	0.0678650i
$683$	−9.15993	+	15.8655i	−0.350495	+	0.607075i	−0.986336	−	0.164745i	$-0.947320\pi$
$683$	−9.15993	+	15.8655i	−0.350495	+	0.607075i	0.635841	+	0.771820i	$0.280653\pi$
$684$		0			0
$685$			42.5477i			1.62566i
$686$	−14.5374	+	11.4746i	−0.555039	+	0.438100i
$687$		0			0
$688$	3.59030	−	2.07286i	0.136879	−	0.0790270i
$689$	−5.66194	+	9.80677i	−0.215703	+	0.373608i
$690$		0			0
$691$	38.6960	−	22.3412i	1.47207	−	0.849898i	0.472560	−	0.881299i	$-0.343330\pi$
$691$	38.6960	−	22.3412i	1.47207	−	0.849898i	0.999507	+	0.0314005i	$0.00999673\pi$
$692$	6.22042			0.236465
$693$		0			0
$694$	14.6253			0.555167
$695$	5.91372	−	3.41429i	0.224320	−	0.129511i
$696$		0			0
$697$	−2.42124	+	4.19371i	−0.0917109	+	0.158848i
$698$	−13.2033	+	7.62292i	−0.499752	+	0.288532i
$699$		0			0
$700$	−16.3520	+	31.7650i	−0.618046	+	1.20060i
$701$			18.6437i			0.704161i	0.935970	+	0.352081i	$0.114526\pi$
$701$			18.6437i			0.704161i	−0.935970	+	0.352081i	$0.885474\pi$
$702$		0			0
$703$	−4.08644	+	7.07792i	−0.154123	+	0.266949i
$704$	−3.27015	+	0.553289i	−0.123248	+	0.0208529i
$705$		0			0
$706$	−27.4483			−1.03303
$707$	0.148637	−	0.00716950i	0.00559007	−	0.000269637i
$708$		0			0
$709$	2.45067	+	4.24468i	0.0920368	+	0.159412i	0.908368	−	0.418172i	$-0.137329\pi$
$709$	2.45067	+	4.24468i	0.0920368	+	0.159412i	−0.816331	+	0.577584i	$0.803996\pi$
$710$	−6.12916	+	10.6160i	−0.230023	+	0.398412i
$711$		0			0
$712$	1.39230	+	2.41153i	0.0521786	+	0.0903759i
$713$			18.3544i			0.687376i
$714$		0			0
$715$	−11.0003	+	9.10128i	−0.411389	+	0.340369i
$716$	−1.53946	−	2.66643i	−0.0575325	−	0.0996492i
$717$		0			0
$718$	−8.14808	+	14.1129i	−0.304084	+	0.526688i
$719$	19.2665	−	11.1235i	0.718518	−	0.414837i	−0.0956887	−	0.995411i	$-0.530505\pi$
$719$	19.2665	−	11.1235i	0.718518	−	0.414837i	0.814207	+	0.580575i	$0.197172\pi$
$720$		0			0
$721$	34.8030	+	17.9159i	1.29613	+	0.667222i
$722$			8.55996i			0.318569i
$723$		0			0
$724$	15.8693	+	9.16214i	0.589777	+	0.340508i
$725$	90.6161	+	52.3172i	3.36540	+	1.94301i
$726$		0			0
$727$		−	27.5807i		−	1.02291i	−0.859310	−	0.511456i	$-0.829106\pi$
$727$		−	27.5807i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$728$	2.22655	−	1.43280i	0.0825213	−	0.0531029i
$729$		0			0
$730$	32.0376	+	55.4907i	1.18576	+	2.05380i
$731$	11.9811	+	6.91730i	0.443137	+	0.255845i
$732$		0			0
$733$	−8.95070	−	15.5031i	−0.330602	−	0.572619i	0.652028	−	0.758195i	$-0.273918\pi$
$733$	−8.95070	−	15.5031i	−0.330602	−	0.572619i	−0.982630	+	0.185576i	$0.940585\pi$
$734$	3.39392			0.125272
$735$		0			0
$736$		−	5.72998i		−	0.211210i
$737$	0.381904	−	1.02708i	0.0140676	−	0.0378330i
$738$		0			0
$739$	24.9947	+	14.4307i	0.919443	+	0.530841i	0.883457	−	0.468511i	$-0.155210\pi$
$739$	24.9947	+	14.4307i	0.919443	+	0.530841i	0.0359860	+	0.999352i	$0.488543\pi$
$740$	−9.42282	+	5.44027i	−0.346390	+	0.199988i
$741$		0			0
$742$	−25.1757	+	16.2007i	−0.924230	+	0.594747i
$743$			34.0656i			1.24975i	0.780726	+	0.624873i	$0.214849\pi$
$743$			34.0656i			1.24975i	−0.780726	+	0.624873i	$0.785151\pi$
$744$		0			0
$745$	36.7341	−	63.6253i	1.34583	−	2.33105i
$746$	3.25792	−	5.64289i	0.119281	−	0.206601i
$747$		0			0
$748$	−7.05538	−	8.52753i	−0.257970	−	0.311798i
$749$	−24.9677	−	12.8529i	−0.912300	−	0.469633i
$750$		0			0
$751$	6.28179	+	10.8804i	0.229226	+	0.397031i	0.957579	−	0.288171i	$-0.0930472\pi$
$751$	6.28179	+	10.8804i	0.229226	+	0.397031i	−0.728353	+	0.685202i	$0.759714\pi$
$752$	2.77216	+	1.60050i	0.101090	+	0.0583644i
$753$		0			0
$754$	−3.87724	−	6.71557i	−0.141201	−	0.244567i
$755$	−35.7697			−1.30179
$756$		0			0
$757$	7.03843			0.255816			0.127908	−	0.991786i	$-0.459174\pi$
$757$	7.03843			0.255816			0.127908	+	0.991786i	$0.459174\pi$
$758$	23.7572	−	13.7162i	0.862900	−	0.498195i
$759$		0			0
$760$	6.94940	−	12.0367i	0.252081	−	0.436618i
$761$	−0.820725	−	1.42154i	−0.0297512	−	0.0515307i	0.850766	−	0.525544i	$-0.176138\pi$
$761$	−0.820725	−	1.42154i	−0.0297512	−	0.0515307i	−0.880518	+	0.474013i	$0.842805\pi$
$762$		0			0
$763$	−0.0443854	−	0.920191i	−0.00160686	−	0.0333131i
$764$	20.8202			0.753248
$765$		0			0
$766$	−4.41845	+	7.65298i	−0.159645	+	0.276514i
$767$	−2.98334	−	1.72243i	−0.107722	−	0.0621935i
$768$		0			0
$769$	5.29585			0.190973			0.0954867	−	0.995431i	$-0.469559\pi$
$769$	5.29585			0.190973			0.0954867	+	0.995431i	$0.469559\pi$
$770$	−36.8705	+	8.08268i	−1.32872	+	0.291280i
$771$		0			0
$772$	−3.91133	+	2.25821i	−0.140772	+	0.0812746i
$773$	17.0683	+	9.85437i	0.613903	+	0.354437i	0.774491	−	0.632584i	$-0.218006\pi$
$773$	17.0683	+	9.85437i	0.613903	+	0.354437i	−0.160588	+	0.987021i	$0.551339\pi$
$774$		0			0
$775$	−37.4595	+	21.6272i	−1.34558	+	0.776873i
$776$	−12.3347			−0.442791
$777$		0			0
$778$			8.92306i			0.319907i
$779$	−2.34435	−	4.06053i	−0.0839949	−	0.145483i
$780$		0			0
$781$	−9.31906	+	1.57673i	−0.333462	+	0.0564197i
$782$	16.5596	−	9.56071i	0.592171	−	0.341890i
$783$		0			0
$784$	6.96750	−	0.673723i	0.248839	−	0.0240615i
$785$	5.38181			0.192085
$786$		0			0
$787$	−26.0498	+	45.1196i	−0.928576	+	1.60834i	−0.142870	+	0.989741i	$0.545633\pi$
$787$	−26.0498	+	45.1196i	−0.928576	+	1.60834i	−0.785706	+	0.618600i	$0.787700\pi$
$788$	−15.0310	−	8.67816i	−0.535458	−	0.309147i
$789$		0			0
$790$		−	69.2220i		−	2.46281i
$791$	−27.1383	−	42.1726i	−0.964928	−	1.49949i
$792$		0			0
$793$	7.43074	+	12.8704i	0.263873	+	0.457042i
$794$	2.38778	−	4.13575i	0.0847390	−	0.146772i
$795$		0			0
$796$	6.76938	−	3.90830i	0.239934	−	0.138526i
$797$		−	39.4609i		−	1.39778i	−0.715230	−	0.698889i	$-0.753678\pi$
$797$		−	39.4609i		−	1.39778i	0.715230	−	0.698889i	$-0.246322\pi$
$798$		0			0
$799$			10.6820i			0.377903i
$800$	11.6943	−	6.75173i	0.413457	−	0.238710i
$801$		0			0
$802$	−2.19946	−	1.26986i	−0.0776656	−	0.0448403i
$803$	−17.2182	+	46.3062i	−0.607618	+	1.63411i
$804$		0			0
$805$	−3.14186	−	65.1364i	−0.110736	−	2.29576i
$806$	3.20560			0.112912
$807$		0			0
$808$	−0.0487094	−	0.0281224i	−0.00171359	−	0.000989342i
$809$	1.42371	+	0.821978i	0.0500549	+	0.0288992i	0.524819	−	0.851214i	$-0.324133\pi$
$809$	1.42371	+	0.821978i	0.0500549	+	0.0288992i	−0.474764	+	0.880113i	$0.657466\pi$
$810$		0			0
$811$	18.9381			0.665006			0.332503	−	0.943102i	$-0.392107\pi$
$811$	18.9381			0.665006			0.332503	+	0.943102i	$0.392107\pi$
$812$	−0.987726	−	20.4774i	−0.0346624	−	0.718615i
$813$		0			0
$814$	−7.86320	−	2.92381i	−0.275605	−	0.102479i
$815$	26.8804	+	15.5194i	0.941581	+	0.543622i
$816$		0			0
$817$	−11.6006	+	6.69762i	−0.405854	+	0.234320i
$818$		−	0.0642013i		−	0.00224475i
$819$		0			0
$820$		−	6.24205i		−	0.217982i
$821$	14.0021	−	8.08410i	0.488676	−	0.282137i	−0.235349	−	0.971911i	$-0.575623\pi$
$821$	14.0021	−	8.08410i	0.488676	−	0.282137i	0.724025	+	0.689774i	$0.242290\pi$
$822$		0			0
$823$	−1.93640	+	3.35394i	−0.0674986	+	0.116911i	−0.897800	−	0.440404i	$-0.854835\pi$
$823$	−1.93640	+	3.35394i	−0.0674986	+	0.116911i	0.830301	+	0.557315i	$0.188168\pi$
$824$	−7.39746	−	12.8128i	−0.257703	−	0.446354i
$825$		0			0
$826$	−4.92846	−	7.65877i	−0.171483	−	0.266483i
$827$			17.5641i			0.610762i	0.952230	+	0.305381i	$0.0987838\pi$
$827$			17.5641i			0.610762i	−0.952230	+	0.305381i	$0.901216\pi$
$828$		0			0
$829$	27.5947	+	15.9318i	0.958405	+	0.553335i	0.895682	−	0.444696i	$-0.146688\pi$
$829$	27.5947	+	15.9318i	0.958405	+	0.553335i	0.0627229	+	0.998031i	$0.480022\pi$
$830$	−3.76520	+	6.52152i	−0.130692	+	0.226365i
$831$		0			0
$832$	−1.00074			−0.0346945
$833$	13.5726	+	19.0119i	0.470263	+	0.658724i
$834$		0			0
$835$	57.5154	−	33.2065i	1.99040	−	1.14916i
$836$	10.5662	−	1.78773i	0.365439	−	0.0618301i
$837$		0			0
$838$	11.8860	+	20.5872i	0.410595	+	0.711171i
$839$		−	13.8360i		−	0.477670i	−0.971060	−	0.238835i	$-0.923234\pi$
$839$		−	13.8360i		−	0.477670i	0.971060	−	0.238835i	$-0.0767656\pi$
$840$		0			0
$841$	−31.0426			−1.07043
$842$	0.965627	−	0.557505i	0.0332777	−	0.0192129i
$843$		0			0
$844$	19.0459	+	10.9962i	0.655588	+	0.378504i
$845$	44.6976	−	25.8062i	1.53765	−	0.887760i
$846$		0			0
$847$	−22.9236	−	17.9306i	−0.787665	−	0.616104i
$848$	11.3155			0.388575
$849$		0			0
$850$	39.0249	+	22.5311i	1.33854	+	0.772809i
$851$	7.24681	−	12.5518i	0.248418	−	0.430272i
$852$		0			0
$853$	−9.77894			−0.334825			−0.167412	−	0.985887i	$-0.553541\pi$
$853$	−9.77894			−0.334825			−0.167412	+	0.985887i	$0.553541\pi$
$854$	1.89298	+	39.2449i	0.0647765	+	1.34293i
$855$		0			0
$856$	5.30694	+	9.19190i	0.181388	+	0.314173i
$857$	−21.8559	+	37.8555i	−0.746583	+	1.29312i	0.202869	+	0.979206i	$0.434973\pi$
$857$	−21.8559	+	37.8555i	−0.746583	+	1.29312i	−0.949452	+	0.313913i	$0.898360\pi$
$858$		0			0
$859$	40.0841	−	23.1426i	1.36765	−	0.789614i	0.377023	−	0.926204i	$-0.376948\pi$
$859$	40.0841	−	23.1426i	1.36765	−	0.789614i	0.990628	+	0.136590i	$0.0436143\pi$
$860$	−17.8331			−0.608102
$861$		0			0
$862$	29.3790			1.00065
$863$	−14.3077	−	24.7817i	−0.487041	−	0.843579i	0.512848	−	0.858479i	$-0.328590\pi$
$863$	−14.3077	−	24.7817i	−0.487041	−	0.843579i	−0.999889	+	0.0149001i	$0.995257\pi$
$864$		0			0
$865$	−23.1727	−	13.3788i	−0.787896	−	0.454892i
$866$	−6.58525	−	11.4060i	−0.223776	−	0.387591i
$867$		0			0
$868$	7.53512	+	3.87893i	0.255759	+	0.131659i
$869$	41.1220	−	34.0229i	1.39497	−	1.15415i
$870$		0			0
$871$	0.165319	−	0.286340i	0.00560161	−	0.00970227i
$872$	−0.174102	+	0.301553i	−0.00589583	+	0.0102119i
$873$		0			0
$874$			18.5142i			0.626251i
$875$	81.3824	−	52.3701i	2.75123	−	1.77043i
$876$		0			0
$877$	−48.1559	+	27.8028i	−1.62611	+	0.938834i	−0.640869	+	0.767650i	$0.721426\pi$
$877$	−48.1559	+	27.8028i	−1.62611	+	0.938834i	−0.985239	+	0.171184i	$0.945241\pi$
$878$	8.84498	+	5.10665i	0.298504	+	0.172341i
$879$		0			0
$880$	13.3722	+	4.97223i	0.450776	+	0.167614i
$881$			31.8585i			1.07334i	0.843792	+	0.536671i	$0.180318\pi$
$881$			31.8585i			1.07334i	−0.843792	+	0.536671i	$0.819682\pi$
$882$		0			0
$883$	55.9427			1.88262			0.941311	−	0.337539i	$-0.109595\pi$
$883$	55.9427			1.88262			0.941311	+	0.337539i	$0.109595\pi$
$884$	−1.66978	−	2.89214i	−0.0561608	−	0.0972734i
$885$		0			0
$886$	−23.7051	−	13.6862i	−0.796390	−	0.459796i
$887$	−5.49008	−	9.50910i	−0.184339	−	0.319284i	0.759015	−	0.651073i	$-0.225681\pi$
$887$	−5.49008	−	9.50910i	−0.184339	−	0.319284i	−0.943354	+	0.331789i	$0.892348\pi$
$888$		0			0
$889$	−13.1471	+	8.46023i	−0.440939	+	0.283747i
$890$		−	11.9781i		−	0.401507i
$891$		0			0
$892$	−7.19014	−	4.15123i	−0.240744	−	0.138993i
$893$	−8.95713	−	5.17140i	−0.299739	−	0.173054i
$894$		0			0
$895$			13.2442i			0.442705i
$896$	−2.35236	−	1.21095i	−0.0785869	−	0.0404549i
$897$		0			0
$898$	1.17739	−	0.679765i	0.0392899	−	0.0226840i
$899$	12.4104	−	21.4955i	0.413910	−	0.716913i
$900$		0			0
$901$	18.8803	+	32.7017i	0.628995	+	1.08945i
$902$	3.70815	−	3.06799i	0.123468	−	0.102153i
$903$		0			0
$904$			18.9549i			0.630431i
$905$	−39.4115	−	68.2627i	−1.31008	−	2.26913i
$906$		0			0
$907$	−1.05966	+	1.83539i	−0.0351856	+	0.0609432i	−0.883082	−	0.469219i	$-0.844536\pi$
$907$	−1.05966	+	1.83539i	−0.0351856	+	0.0609432i	0.847896	+	0.530162i	$0.177869\pi$
$908$	3.95627	+	6.85245i	0.131293	+	0.227407i
$909$		0			0
$910$	−11.3761	+	0.548726i	−0.377114	+	0.0181901i
$911$	−1.06472			−0.0352757			−0.0176379	−	0.999844i	$-0.505615\pi$
$911$	−1.06472			−0.0352757			−0.0176379	+	0.999844i	$0.505615\pi$
$912$		0			0
$913$	−5.72478	+	0.968598i	−0.189463	+	0.0320559i
$914$	−10.9491	+	18.9644i	−0.362163	+	0.627285i
$915$		0			0
$916$			10.7093i			0.353844i
$917$	14.6576	−	28.4736i	0.484038	−	0.940282i
$918$		0			0
$919$	35.7439	−	20.6368i	1.17908	−	0.680744i	0.223280	−	0.974754i	$-0.428323\pi$
$919$	35.7439	−	20.6368i	1.17908	−	0.680744i	0.955802	+	0.294011i	$0.0949901\pi$
$920$	−12.3239	+	21.3457i	−0.406308	+	0.703747i
$921$		0			0
$922$	−11.6244	+	6.71136i	−0.382830	+	0.221027i
$923$	−2.85185			−0.0938699
$924$		0			0
$925$	34.1561			1.12305
$926$	18.3097	−	10.5711i	0.601694	−	0.347388i
$927$		0			0
$928$	−3.87436	+	6.71059i	−0.127182	+	0.220286i
$929$	−17.6201	+	10.1730i	−0.578096	+	0.333764i	−0.760376	−	0.649483i	$-0.774985\pi$
$929$	−17.6201	+	10.1730i	−0.578096	+	0.333764i	0.182280	+	0.983247i	$0.441652\pi$
$930$		0			0
$931$	−22.5127	+	2.17687i	−0.737825	+	0.0713440i
$932$		−	17.7106i		−	0.580129i
$933$		0			0
$934$	1.43737	−	2.48960i	0.0470323	−	0.0814623i
$935$	7.94228	+	46.9419i	0.259740	+	1.53516i
$936$		0			0
$937$	−21.9119			−0.715831			−0.357916	−	0.933754i	$-0.616512\pi$
$937$	−21.9119			−0.715831			−0.357916	+	0.933754i	$0.616512\pi$
$938$	0.735086	−	0.473032i	0.0240014	−	0.0154450i
$939$		0			0
$940$	−6.88467	−	11.9246i	−0.224553	−	0.388938i
$941$	−26.3049	+	45.5614i	−0.857514	+	1.48526i	0.0167786	+	0.999859i	$0.494659\pi$
$941$	−26.3049	+	45.5614i	−0.857514	+	1.48526i	−0.874293	+	0.485399i	$0.838674\pi$
$942$		0			0
$943$	4.15742	+	7.20086i	0.135384	+	0.234492i
$944$			3.44231i			0.112038i
$945$		0			0
$946$	−8.76502	−	10.5939i	−0.284976	−	0.344438i
$947$	−12.5178	−	21.6815i	−0.406775	−	0.704555i	0.587751	−	0.809042i	$-0.300013\pi$
$947$	−12.5178	−	21.6815i	−0.406775	−	0.704555i	−0.994526	+	0.104487i	$0.966680\pi$
$948$		0			0
$949$	−7.45343	+	12.9097i	−0.241949	+	0.419067i
$950$	−37.7856	+	21.8155i	−1.22593	+	0.707790i
$951$		0			0
$952$	−0.425377	−	8.81883i	−0.0137865	−	0.285820i
$953$		−	27.4386i		−	0.888823i	−0.895823	−	0.444411i	$-0.853413\pi$
$953$		−	27.4386i		−	0.888823i	0.895823	−	0.444411i	$-0.146587\pi$
$954$		0			0
$955$	−77.5607	−	44.7797i	−2.50981	−	1.44904i
$956$	23.0671	+	13.3178i	0.746043	+	0.430728i
$957$		0			0
$958$			3.83882i			0.124027i
$959$	−26.1393	+	1.26083i	−0.844082	+	0.0407143i
$960$		0			0
$961$	−10.3697	−	17.9609i	−0.334507	−	0.579382i
$962$	−2.19218	−	1.26566i	−0.0706789	−	0.0408065i
$963$		0			0
$964$	−1.85521	−	3.21331i	−0.0597521	−	0.103494i
$965$	19.4276			0.625398
$966$		0			0
$967$		−	44.4870i		−	1.43061i	−0.698815	−	0.715303i	$-0.746289\pi$
$967$		−	44.4870i		−	1.43061i	0.698815	−	0.715303i	$-0.253711\pi$
$968$	3.61867	+	10.3877i	0.116309	+	0.333875i
$969$		0			0
$970$	45.9502	+	26.5293i	1.47537	+	0.851806i
$971$	7.16677	−	4.13774i	0.229993	−	0.132786i	−0.380576	−	0.924750i	$-0.624274\pi$
$971$	7.16677	−	4.13774i	0.229993	−	0.132786i	0.610569	+	0.791963i	$0.290941\pi$
$972$		0			0
$973$	2.27282	+	3.53194i	0.0728634	+	0.113229i
$974$			9.68084i			0.310194i
$975$		0			0
$976$	7.42522	−	12.8609i	0.237675	−	0.411666i
$977$	14.4351	−	25.0022i	0.461818	−	0.799893i	−0.537233	−	0.843434i	$-0.680531\pi$
$977$	14.4351	−	25.0022i	0.461818	−	0.799893i	0.999052	+	0.0435409i	$0.0138639\pi$
$978$		0			0
$979$	7.11572	−	5.88729i	0.227419	−	0.188159i
$980$	−27.4048	−	12.4758i	−0.875415	−	0.398524i
$981$		0			0
$982$	−7.94428	−	13.7599i	−0.253512	−	0.439096i
$983$	−38.6365	−	22.3068i	−1.23231	−	0.711476i	−0.264800	−	0.964303i	$-0.585306\pi$
$983$	−38.6365	−	22.3068i	−1.23231	−	0.711476i	−0.967511	+	0.252828i	$0.918639\pi$
$984$		0			0
$985$	37.3297	+	64.6569i	1.18942	+	2.06014i
$986$	−25.8581			−0.823490
$987$		0			0
$988$	3.23351			0.102872
$989$	20.5723	−	11.8774i	0.654162	−	0.377681i
$990$		0			0
$991$	18.5281	−	32.0916i	0.588565	−	1.01942i	−0.405856	−	0.913937i	$-0.633026\pi$
$991$	18.5281	−	32.0916i	0.588565	−	1.01942i	0.994421	−	0.105487i	$-0.0336402\pi$
$992$	−1.60161	−	2.77407i	−0.0508511	−	0.0880767i
$993$		0			0
$994$	−6.70361	−	3.45088i	−0.212626	−	0.109455i
$995$	−33.6236			−1.06594
$996$		0			0
$997$	17.2468	−	29.8724i	0.546213	−	0.946068i	−0.452317	−	0.891857i	$-0.649402\pi$
$997$	17.2468	−	29.8724i	0.546213	−	0.946068i	0.998530	−	0.0542108i	$-0.0172643\pi$
$998$	−26.0188	−	15.0220i	−0.823612	−	0.475513i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.a.703.1		16
3.2	odd	2		462.2.p.a.241.8	✓	16
7.5	odd	6		1386.2.bk.b.901.5		16
11.10	odd	2		1386.2.bk.b.703.5		16
21.5	even	6		462.2.p.b.439.4	yes	16
21.11	odd	6		3234.2.e.a.2155.16		16
21.17	even	6		3234.2.e.b.2155.9		16
33.32	even	2		462.2.p.b.241.4	yes	16
77.54	even	6	inner	1386.2.bk.a.901.1		16
231.32	even	6		3234.2.e.b.2155.8		16
231.131	odd	6		462.2.p.a.439.8	yes	16
231.164	odd	6		3234.2.e.a.2155.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.8	✓	16	3.2	odd	2
462.2.p.a.439.8	yes	16	231.131	odd	6
462.2.p.b.241.4	yes	16	33.32	even	2
462.2.p.b.439.4	yes	16	21.5	even	6
1386.2.bk.a.703.1		16	1.1	even	1	trivial
1386.2.bk.a.901.1		16	77.54	even	6	inner
1386.2.bk.b.703.5		16	11.10	odd	2
1386.2.bk.b.901.5		16	7.5	odd	6
3234.2.e.a.2155.1		16	231.164	odd	6
3234.2.e.a.2155.16		16	21.11	odd	6
3234.2.e.b.2155.8		16	231.32	even	6
3234.2.e.b.2155.9		16	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.72526 + 2.15078i) q^{5} +(-1.43173 - 2.22489i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.72526 + 2.15078i) q^{5} +(-1.43173 - 2.22489i) q^{7} +1.00000i q^{8} +(2.15078 - 3.72526i) q^{10} +(3.27015 - 0.553289i) q^{11} +1.00074 q^{13} +(2.35236 + 1.21095i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.66854 - 2.89000i) q^{17} +(1.61555 + 2.79822i) q^{19} +4.30156i q^{20} +(-2.55539 + 2.11424i) q^{22} +(-2.86499 - 4.96231i) q^{23} +(6.75173 - 11.6943i) q^{25} +(-0.866669 + 0.500372i) q^{26} +(-2.64268 + 0.127470i) q^{28} +7.74872i q^{29} +(-2.77407 - 1.60161i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.33708i q^{34} +(10.1188 + 5.20897i) q^{35} +(1.26472 + 2.19056i) q^{37} +(-2.79822 - 1.61555i) q^{38} +(-2.15078 - 3.72526i) q^{40} -1.45111 q^{41} +4.14572i q^{43} +(1.15591 - 3.10868i) q^{44} +(4.96231 + 2.86499i) q^{46} +(-2.77216 + 1.60050i) q^{47} +(-2.90029 + 6.37090i) q^{49} +13.5035i q^{50} +(0.500372 - 0.866669i) q^{52} +(-5.65774 + 9.79949i) q^{53} +(-10.9922 + 9.09452i) q^{55} +(2.22489 - 1.43173i) q^{56} +(-3.87436 - 6.71059i) q^{58} +(-2.98113 - 1.72116i) q^{59} +(7.42522 + 12.8609i) q^{61} +3.20322 q^{62} -1.00000 q^{64} +(-3.72803 + 2.15238i) q^{65} +(0.165196 - 0.286128i) q^{67} +(-1.66854 - 2.89000i) q^{68} +(-11.3677 + 0.548319i) q^{70} -2.84974 q^{71} +(-7.44790 + 12.9001i) q^{73} +(-2.19056 - 1.26472i) q^{74} +3.23111 q^{76} +(-5.91298 - 6.48357i) q^{77} +(13.9363 - 8.04614i) q^{79} +(3.72526 + 2.15078i) q^{80} +(1.25670 - 0.725556i) q^{82} -1.75062 q^{83} +14.3547i q^{85} +(-2.07286 - 3.59030i) q^{86} +(0.553289 + 3.27015i) q^{88} +(2.41153 - 1.39230i) q^{89} +(-1.43280 - 2.22655i) q^{91} -5.72998 q^{92} +(1.60050 - 2.77216i) q^{94} +(-12.0367 - 6.94940i) q^{95} +12.3347i q^{97} +(-0.673723 - 6.96750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7} + 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} - 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} + 8 q^{35} + 14 q^{37} + 12 q^{38} - 2 q^{40} - 32 q^{41} - 4 q^{44} + 18 q^{46} + 24 q^{47} - 6 q^{49} - 14 q^{55} - 4 q^{56} + 28 q^{61} + 8 q^{62} - 16 q^{64} - 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} - 44 q^{73} - 24 q^{74} - 20 q^{76} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} + 14 q^{94} - 72 q^{95} + 40 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7 + 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 - 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 + 8 * q^35 + 14 * q^37 + 12 * q^38 - 2 * q^40 - 32 * q^41 - 4 * q^44 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 14 * q^55 - 4 * q^56 + 28 * q^61 + 8 * q^62 - 16 * q^64 - 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 - 44 * q^73 - 24 * q^74 - 20 * q^76 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 + 14 * q^94 - 72 * q^95 + 40 * q^98

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