LMFDB - Embedded newform 2646.2.m.b.1763.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, degree $2$, not 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:	$21.1284163748$
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} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1763.2
Root			$-1.70672 + 0.295146i$ of defining polynomial
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.b.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 - 0.837727i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 - 0.837727i) q^{5} -1.00000i q^{8} +0.967324i q^{10} +(4.82689 + 2.78681i) q^{11} +(-3.76893 + 2.17600i) q^{13} +(-0.500000 + 0.866025i) q^{16} +3.94535 q^{17} +4.46634i q^{19} +(0.483662 - 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +(2.29786 - 1.32667i) q^{23} +(2.03214 - 3.51977i) q^{25} +4.35199 q^{26} +(-4.61157 - 2.66249i) q^{29} +(-5.34038 + 3.08327i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.41677 - 1.97267i) q^{34} -0.487217 q^{37} +(2.23317 - 3.86796i) q^{38} +(-0.837727 + 0.483662i) q^{40} +(-0.0818856 - 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} +5.57361i q^{44} -2.65334 q^{46} +(-4.74500 + 8.21859i) q^{47} +(-3.51977 + 2.03214i) q^{50} +(-3.76893 - 2.17600i) q^{52} -2.01518i q^{53} -5.39149i q^{55} +(2.66249 + 4.61157i) q^{58} +(0.836931 + 1.44961i) q^{59} +(-4.47927 - 2.58611i) q^{61} +6.16655 q^{62} -1.00000 q^{64} +(3.64578 + 2.10489i) q^{65} +(2.72126 + 4.71336i) q^{67} +(1.97267 + 3.41677i) q^{68} +3.64006i q^{71} +2.48801i q^{73} +(0.421942 + 0.243608i) q^{74} +(-3.86796 + 2.23317i) q^{76} +(-2.30121 + 3.98581i) q^{79} +0.967324 q^{80} +0.163771i q^{82} +(4.20979 - 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(7.53520 - 4.35045i) q^{86} +(2.78681 - 4.82689i) q^{88} -4.11622 q^{89} +(2.29786 + 1.32667i) q^{92} +(8.21859 - 4.74500i) q^{94} +(3.74157 - 2.16020i) q^{95} +(10.2669 + 5.92762i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 12 q^{11} + 6 q^{13} - 8 q^{16} - 36 q^{17} - 6 q^{23} - 8 q^{25} + 24 q^{26} - 6 q^{29} + 6 q^{31} + 4 q^{37} + 6 q^{41} - 2 q^{43} - 12 q^{46} - 18 q^{47} + 12 q^{50} + 6 q^{52} + 6 q^{58} + 30 q^{59} - 60 q^{61} - 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} - 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{89} - 6 q^{92} - 66 q^{95} + 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^11 + 6 * q^13 - 8 * q^16 - 36 * q^17 - 6 * q^23 - 8 * q^25 + 24 * q^26 - 6 * q^29 + 6 * q^31 + 4 * q^37 + 6 * q^41 - 2 * q^43 - 12 * q^46 - 18 * q^47 + 12 * q^50 + 6 * q^52 + 6 * q^58 + 30 * q^59 - 60 * q^61 - 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^89 - 6 * q^92 - 66 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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
$5$	−0.483662	−	0.837727i	−0.216300	−	0.374643i	0.737374	−	0.675485i	$-0.236066\pi$
$5$	−0.483662	−	0.837727i	−0.216300	−	0.374643i	−0.953674	+	0.300842i	$0.902732\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			0.967324i			0.305895i
$11$	4.82689	+	2.78681i	1.45536	+	0.840254i	0.998778	−	0.0494264i	$-0.0157393\pi$
$11$	4.82689	+	2.78681i	1.45536	+	0.840254i	0.456584	+	0.889680i	$0.349073\pi$
$12$		0			0
$13$	−3.76893	+	2.17600i	−1.04531	+	0.603512i	−0.921334	−	0.388772i	$-0.872899\pi$
$13$	−3.76893	+	2.17600i	−1.04531	+	0.603512i	−0.123980	+	0.992285i	$0.539566\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.94535			0.956887			0.478443	−	0.878118i	$-0.341201\pi$
$17$	3.94535			0.956887			0.478443	+	0.878118i	$0.341201\pi$
$18$		0			0
$19$			4.46634i			1.02465i	0.858792	+	0.512324i	$0.171215\pi$
$19$			4.46634i			1.02465i	−0.858792	+	0.512324i	$0.828785\pi$
$20$	0.483662	−	0.837727i	0.108150	−	0.187322i
$21$		0			0
$22$	−2.78681	−	4.82689i	−0.594149	−	1.02910i
$23$	2.29786	−	1.32667i	0.479137	−	0.276630i	−0.240920	−	0.970545i	$-0.577449\pi$
$23$	2.29786	−	1.32667i	0.479137	−	0.276630i	0.720057	+	0.693915i	$0.244116\pi$
$24$		0			0
$25$	2.03214	−	3.51977i	0.406428	−	0.703955i
$26$	4.35199			0.853496
$27$		0			0
$28$		0			0
$29$	−4.61157	−	2.66249i	−0.856347	−	0.494412i	0.00644015	−	0.999979i	$-0.497950\pi$
$29$	−4.61157	−	2.66249i	−0.856347	−	0.494412i	−0.862787	+	0.505567i	$0.831283\pi$
$30$		0			0
$31$	−5.34038	+	3.08327i	−0.959161	+	0.553772i	−0.895915	−	0.444226i	$-0.853479\pi$
$31$	−5.34038	+	3.08327i	−0.959161	+	0.553772i	−0.0632466	+	0.997998i	$0.520145\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−3.41677	−	1.97267i	−0.585971	−	0.338311i
$35$		0			0
$36$		0			0
$37$	−0.487217			−0.0800980			−0.0400490	−	0.999198i	$-0.512751\pi$
$37$	−0.487217			−0.0800980			−0.0400490	+	0.999198i	$0.512751\pi$
$38$	2.23317	−	3.86796i	0.362268	−	0.627466i
$39$		0			0
$40$	−0.837727	+	0.483662i	−0.132456	+	0.0764737i
$41$	−0.0818856	−	0.141830i	−0.0127884	−	0.0221501i	0.859560	−	0.511034i	$-0.170737\pi$
$41$	−0.0818856	−	0.141830i	−0.0127884	−	0.0221501i	−0.872349	+	0.488884i	$0.837404\pi$
$42$		0			0
$43$	−4.35045	+	7.53520i	−0.663437	+	1.14911i	0.316270	+	0.948669i	$0.397570\pi$
$43$	−4.35045	+	7.53520i	−0.663437	+	1.14911i	−0.979707	+	0.200437i	$0.935764\pi$
$44$			5.57361i			0.840254i
$45$		0			0
$46$	−2.65334			−0.391214
$47$	−4.74500	+	8.21859i	−0.692130	+	1.19880i	0.279009	+	0.960289i	$0.409994\pi$
$47$	−4.74500	+	8.21859i	−0.692130	+	1.19880i	−0.971139	+	0.238516i	$0.923339\pi$
$48$		0			0
$49$		0			0
$50$	−3.51977	+	2.03214i	−0.497771	+	0.287388i
$51$		0			0
$52$	−3.76893	−	2.17600i	−0.522657	−	0.301756i
$53$		−	2.01518i		−	0.276807i	−0.990376	−	0.138403i	$-0.955803\pi$
$53$		−	2.01518i		−	0.276807i	0.990376	−	0.138403i	$-0.0441970\pi$
$54$		0			0
$55$		−	5.39149i		−	0.726988i
$56$		0			0
$57$		0			0
$58$	2.66249	+	4.61157i	0.349602	+	0.605529i
$59$	0.836931	+	1.44961i	0.108959	+	0.188723i	0.915349	−	0.402662i	$-0.131915\pi$
$59$	0.836931	+	1.44961i	0.108959	+	0.188723i	−0.806390	+	0.591384i	$0.798582\pi$
$60$		0			0
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	0.185039	−	0.982731i	$-0.440759\pi$
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	−0.758551	+	0.651614i	$0.774092\pi$
$62$	6.16655			0.783152
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.64578	+	2.10489i	0.452203	+	0.261080i
$66$		0			0
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	0.982993	−	0.183645i	$-0.0587898\pi$
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	−0.650538	+	0.759474i	$0.725456\pi$
$68$	1.97267	+	3.41677i	0.239222	+	0.414344i
$69$		0			0
$70$		0			0
$71$			3.64006i			0.431996i	0.976394	+	0.215998i	$0.0693005\pi$
$71$			3.64006i			0.431996i	−0.976394	+	0.215998i	$0.930700\pi$
$72$		0			0
$73$			2.48801i			0.291200i	0.989344	+	0.145600i	$0.0465112\pi$
$73$			2.48801i			0.291200i	−0.989344	+	0.145600i	$0.953489\pi$
$74$	0.421942	+	0.243608i	0.0490498	+	0.0283189i
$75$		0			0
$76$	−3.86796	+	2.23317i	−0.443686	+	0.256162i
$77$		0			0
$78$		0			0
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	−0.965949	−	0.258732i	$-0.916695\pi$
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	0.707043	+	0.707170i	$0.250029\pi$
$80$	0.967324			0.108150
$81$		0			0
$82$			0.163771i			0.0180855i
$83$	4.20979	−	7.29158i	0.462085	−	0.800355i	−0.536980	−	0.843595i	$-0.680435\pi$
$83$	4.20979	−	7.29158i	0.462085	−	0.800355i	0.999065	+	0.0432405i	$0.0137682\pi$
$84$		0			0
$85$	−1.90821	−	3.30512i	−0.206975	−	0.358491i
$86$	7.53520	−	4.35045i	0.812541	−	0.469121i
$87$		0			0
$88$	2.78681	−	4.82689i	0.297075	−	0.514548i
$89$	−4.11622			−0.436318			−0.218159	−	0.975913i	$-0.570005\pi$
$89$	−4.11622			−0.436318			−0.218159	+	0.975913i	$0.570005\pi$
$90$		0			0
$91$		0			0
$92$	2.29786	+	1.32667i	0.239569	+	0.138315i
$93$		0			0
$94$	8.21859	−	4.74500i	0.847683	−	0.489410i
$95$	3.74157	−	2.16020i	0.383877	−	0.221632i
$96$		0			0
$97$	10.2669	+	5.92762i	1.04245	+	0.601859i	0.920526	−	0.390681i	$-0.127760\pi$
$97$	10.2669	+	5.92762i	1.04245	+	0.601859i	0.121924	+	0.992539i	$0.461094\pi$
$98$		0			0
$99$		0			0
$100$	4.06428			0.406428
$101$	−2.65813	+	4.60402i	−0.264494	+	0.458117i	−0.967431	−	0.253135i	$-0.918538\pi$
$101$	−2.65813	+	4.60402i	−0.264494	+	0.458117i	0.702937	+	0.711252i	$0.251872\pi$
$102$		0			0
$103$	−7.74616	+	4.47225i	−0.763252	+	0.440664i	−0.830462	−	0.557075i	$-0.811924\pi$
$103$	−7.74616	+	4.47225i	−0.763252	+	0.440664i	0.0672102	+	0.997739i	$0.478590\pi$
$104$	2.17600	+	3.76893i	0.213374	+	0.369574i
$105$		0			0
$106$	−1.00759	+	1.74520i	−0.0978659	+	0.169509i
$107$		−	19.1563i		−	1.85191i	−0.377639	−	0.925953i	$-0.623264\pi$
$107$		−	19.1563i		−	1.85191i	0.377639	−	0.925953i	$-0.376736\pi$
$108$		0			0
$109$	19.2434			1.84318			0.921590	−	0.388164i	$-0.126891\pi$
$109$	19.2434			1.84318			0.921590	+	0.388164i	$0.126891\pi$
$110$	−2.69574	+	4.66917i	−0.257029	+	0.445188i
$111$		0			0
$112$		0			0
$113$	−7.31199	+	4.22158i	−0.687854	+	0.397133i	−0.802808	−	0.596238i	$-0.796661\pi$
$113$	−7.31199	+	4.22158i	−0.687854	+	0.397133i	0.114953	+	0.993371i	$0.463328\pi$
$114$		0			0
$115$	−2.22278	−	1.28332i	−0.207275	−	0.119670i
$116$		−	5.32498i		−	0.494412i
$117$		0			0
$118$		−	1.67386i		−	0.154091i
$119$		0			0
$120$		0			0
$121$	10.0326	+	17.3769i	0.912053	+	1.57972i
$122$	2.58611	+	4.47927i	0.234135	+	0.405534i
$123$		0			0
$124$	−5.34038	−	3.08327i	−0.479581	−	0.276886i
$125$	−8.76810			−0.784243
$126$		0			0
$127$	3.31883			0.294498			0.147249	−	0.989099i	$-0.452958\pi$
$127$	3.31883			0.294498			0.147249	+	0.989099i	$0.452958\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.10489	−	3.64578i	−0.184611	−	0.319756i
$131$	9.37335	+	16.2351i	0.818954	+	1.41847i	0.906454	+	0.422305i	$0.138779\pi$
$131$	9.37335	+	16.2351i	0.818954	+	1.41847i	−0.0875000	+	0.996165i	$0.527888\pi$
$132$		0			0
$133$		0			0
$134$		−	5.44252i		−	0.470162i
$135$		0			0
$136$		−	3.94535i		−	0.338311i
$137$	14.6656	+	8.46717i	1.25296	+	0.723399i	0.971697	−	0.236230i	$-0.0759120\pi$
$137$	14.6656	+	8.46717i	1.25296	+	0.723399i	0.281267	+	0.959630i	$0.409245\pi$
$138$		0			0
$139$	−10.5033	+	6.06406i	−0.890875	+	0.514347i	−0.874229	−	0.485514i	$-0.838632\pi$
$139$	−10.5033	+	6.06406i	−0.890875	+	0.514347i	−0.0166466	+	0.999861i	$0.505299\pi$
$140$		0			0
$141$		0			0
$142$	1.82003	−	3.15239i	0.152734	−	0.264543i
$143$	−24.2563			−2.02841
$144$		0			0
$145$			5.15098i			0.427766i
$146$	1.24401	−	2.15468i	0.102955	−	0.178323i
$147$		0			0
$148$	−0.243608	−	0.421942i	−0.0200245	−	0.0346834i
$149$	−7.56951	+	4.37026i	−0.620118	+	0.358025i	−0.776915	−	0.629606i	$-0.783217\pi$
$149$	−7.56951	+	4.37026i	−0.620118	+	0.358025i	0.156797	+	0.987631i	$0.449883\pi$
$150$		0			0
$151$	−11.0471	+	19.1341i	−0.898997	+	1.55711i	−0.0702195	+	0.997532i	$0.522370\pi$
$151$	−11.0471	+	19.1341i	−0.898997	+	1.55711i	−0.828778	+	0.559578i	$0.810963\pi$
$152$	4.46634			0.362268
$153$		0			0
$154$		0			0
$155$	5.16588	+	2.98252i	0.414934	+	0.239562i
$156$		0			0
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	−0.449961	−	0.893048i	$-0.648562\pi$
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	0.548422	+	0.836202i	$0.315229\pi$
$158$	3.98581	−	2.30121i	0.317094	−	0.183074i
$159$		0			0
$160$	−0.837727	−	0.483662i	−0.0662282	−	0.0382368i
$161$		0			0
$162$		0			0
$163$	7.44296			0.582977			0.291489	−	0.956574i	$-0.405849\pi$
$163$	7.44296			0.582977			0.291489	+	0.956574i	$0.405849\pi$
$164$	0.0818856	−	0.141830i	0.00639419	−	0.0110751i
$165$		0			0
$166$	−7.29158	+	4.20979i	−0.565936	+	0.326743i
$167$	3.24855	+	5.62665i	0.251380	+	0.435404i	0.963906	−	0.266242i	$-0.0857822\pi$
$167$	3.24855	+	5.62665i	0.251380	+	0.435404i	−0.712526	+	0.701646i	$0.752449\pi$
$168$		0			0
$169$	2.96991	−	5.14404i	0.228455	−	0.395695i
$170$			3.81643i			0.292707i
$171$		0			0
$172$	−8.70089			−0.663437
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	−0.549057	−	0.835785i	$-0.685013\pi$
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	0.998339	+	0.0576053i	$0.0183465\pi$
$174$		0			0
$175$		0			0
$176$	−4.82689	+	2.78681i	−0.363841	+	0.210063i
$177$		0			0
$178$	3.56475	+	2.05811i	0.267189	+	0.154262i
$179$		−	2.43370i		−	0.181903i	−0.995855	−	0.0909515i	$-0.971009\pi$
$179$		−	2.43370i		−	0.181903i	0.995855	−	0.0909515i	$-0.0289908\pi$
$180$		0			0
$181$		−	11.5342i		−	0.857327i	−0.903464	−	0.428663i	$-0.858985\pi$
$181$		−	11.5342i		−	0.857327i	0.903464	−	0.428663i	$-0.141015\pi$
$182$		0			0
$183$		0			0
$184$	−1.32667	−	2.29786i	−0.0978035	−	0.169401i
$185$	0.235648	+	0.408155i	0.0173252	+	0.0300081i
$186$		0			0
$187$	19.0438	+	10.9949i	1.39262	+	0.804028i
$188$	−9.49001			−0.692130
$189$		0			0
$190$	−4.32040			−0.313435
$191$	19.1122	+	11.0345i	1.38291	+	0.798425i	0.992503	−	0.122216i	$-0.0390002\pi$
$191$	19.1122	+	11.0345i	1.38291	+	0.798425i	0.390409	+	0.920641i	$0.372334\pi$
$192$		0			0
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	0.961932	+	0.273289i	$0.0881116\pi$
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	−0.244291	+	0.969702i	$0.578555\pi$
$194$	−5.92762	−	10.2669i	−0.425578	−	0.737123i
$195$		0			0
$196$		0			0
$197$		−	4.62560i		−	0.329560i	−0.986330	−	0.164780i	$-0.947309\pi$
$197$		−	4.62560i		−	0.329560i	0.986330	−	0.164780i	$-0.0526914\pi$
$198$		0			0
$199$			20.9028i			1.48176i	0.671635	+	0.740882i	$0.265592\pi$
$199$			20.9028i			1.48176i	−0.671635	+	0.740882i	$0.734408\pi$
$200$	−3.51977	−	2.03214i	−0.248886	−	0.143694i
$201$		0			0
$202$	4.60402	−	2.65813i	0.323938	−	0.187025i
$203$		0			0
$204$		0			0
$205$	−0.0792099	+	0.137196i	−0.00553226	+	0.00958215i
$206$	8.94450			0.623193
$207$		0			0
$208$		−	4.35199i		−	0.301756i
$209$	−12.4468	+	21.5585i	−0.860965	+	1.49123i
$210$		0			0
$211$	−3.34310	−	5.79042i	−0.230148	−	0.398629i	0.727703	−	0.685892i	$-0.240588\pi$
$211$	−3.34310	−	5.79042i	−0.230148	−	0.398629i	−0.957852	+	0.287263i	$0.907254\pi$
$212$	1.74520	−	1.00759i	0.119861	−	0.0692017i
$213$		0			0
$214$	−9.57813	+	16.5898i	−0.654747	+	1.13406i
$215$	8.41658			0.574006
$216$		0			0
$217$		0			0
$218$	−16.6652	−	9.62168i	−1.12871	−	0.651663i
$219$		0			0
$220$	4.66917	−	2.69574i	0.314795	−	0.181747i
$221$	−14.8697	+	8.58505i	−1.00025	+	0.577493i
$222$		0			0
$223$	7.08622	+	4.09123i	0.474528	+	0.273969i	0.718133	−	0.695905i	$-0.244997\pi$
$223$	7.08622	+	4.09123i	0.474528	+	0.273969i	−0.243605	+	0.969875i	$0.578330\pi$
$224$		0			0
$225$		0			0
$226$	8.44316			0.561631
$227$	5.34688	−	9.26106i	0.354885	−	0.614678i	−0.632214	−	0.774794i	$-0.717853\pi$
$227$	5.34688	−	9.26106i	0.354885	−	0.614678i	0.987098	+	0.160116i	$0.0511868\pi$
$228$		0			0
$229$	−25.2942	+	14.6036i	−1.67149	+	0.965034i	−0.704682	+	0.709524i	$0.748910\pi$
$229$	−25.2942	+	14.6036i	−1.67149	+	0.965034i	−0.966806	+	0.255510i	$0.917757\pi$
$230$	1.28332	+	2.22278i	0.0846197	+	0.146566i
$231$		0			0
$232$	−2.66249	+	4.61157i	−0.174801	+	0.302764i
$233$		−	6.43935i		−	0.421856i	−0.977502	−	0.210928i	$-0.932352\pi$
$233$		−	6.43935i		−	0.421856i	0.977502	−	0.210928i	$-0.0676485\pi$
$234$		0			0
$235$	9.17991			0.598832
$236$	−0.836931	+	1.44961i	−0.0544796	+	0.0943614i
$237$		0			0
$238$		0			0
$239$	4.01452	−	2.31778i	0.259678	−	0.149925i	−0.364510	−	0.931200i	$-0.618763\pi$
$239$	4.01452	−	2.31778i	0.259678	−	0.149925i	0.624187	+	0.781275i	$0.285430\pi$
$240$		0			0
$241$	−9.08846	−	5.24722i	−0.585439	−	0.338003i	0.177853	−	0.984057i	$-0.443085\pi$
$241$	−9.08846	−	5.24722i	−0.585439	−	0.338003i	−0.763292	+	0.646054i	$0.776418\pi$
$242$		−	20.0652i		−	1.28984i
$243$		0			0
$244$		−	5.17221i		−	0.331117i
$245$		0			0
$246$		0			0
$247$	−9.71873	−	16.8333i	−0.618388	−	1.07108i
$248$	3.08327	+	5.34038i	0.195788	+	0.339115i
$249$		0			0
$250$	7.59340	+	4.38405i	0.480249	+	0.277272i
$251$	−7.85271			−0.495659			−0.247829	−	0.968804i	$-0.579717\pi$
$251$	−7.85271			−0.495659			−0.247829	+	0.968804i	$0.579717\pi$
$252$		0			0
$253$	14.7887			0.929758
$254$	−2.87419	−	1.65941i	−0.180343	−	0.104121i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.71568	+	2.97164i	0.107021	+	0.185366i	0.914562	−	0.404445i	$-0.132535\pi$
$257$	1.71568	+	2.97164i	0.107021	+	0.185366i	−0.807541	+	0.589811i	$0.799202\pi$
$258$		0			0
$259$		0			0
$260$			4.20979i			0.261080i
$261$		0			0
$262$		−	18.7467i		−	1.15818i
$263$	−3.17080	−	1.83066i	−0.195520	−	0.112883i	0.399044	−	0.916932i	$-0.369342\pi$
$263$	−3.17080	−	1.83066i	−0.195520	−	0.112883i	−0.594564	+	0.804048i	$0.702675\pi$
$264$		0			0
$265$	−1.68817	+	0.974668i	−0.103704	+	0.0598734i
$266$		0			0
$267$		0			0
$268$	−2.72126	+	4.71336i	−0.166227	+	0.287914i
$269$	−12.6861			−0.773483			−0.386741	−	0.922188i	$-0.626399\pi$
$269$	−12.6861			−0.773483			−0.386741	+	0.922188i	$0.626399\pi$
$270$		0			0
$271$		−	19.8766i		−	1.20742i	−0.797206	−	0.603708i	$-0.793689\pi$
$271$		−	19.8766i		−	1.20742i	0.797206	−	0.603708i	$-0.206311\pi$
$272$	−1.97267	+	3.41677i	−0.119611	+	0.207172i
$273$		0			0
$274$	−8.46717	−	14.6656i	−0.511520	−	0.885979i
$275$	19.6179	−	11.3264i	1.18300	−	0.683006i
$276$		0			0
$277$	3.73302	−	6.46579i	0.224296	−	0.388491i	−0.731812	−	0.681506i	$-0.761325\pi$
$277$	3.73302	−	6.46579i	0.224296	−	0.388491i	0.956108	+	0.293015i	$0.0946585\pi$
$278$	12.1281			0.727397
$279$		0			0
$280$		0			0
$281$	19.2746	+	11.1282i	1.14983	+	0.663854i	0.948845	−	0.315741i	$-0.102253\pi$
$281$	19.2746	+	11.1282i	1.14983	+	0.663854i	0.200983	+	0.979595i	$0.435586\pi$
$282$		0			0
$283$	14.0125	−	8.09012i	0.832957	−	0.480908i	−0.0219073	−	0.999760i	$-0.506974\pi$
$283$	14.0125	−	8.09012i	0.832957	−	0.480908i	0.854864	+	0.518852i	$0.173641\pi$
$284$	−3.15239	+	1.82003i	−0.187060	+	0.107999i
$285$		0			0
$286$	21.0066	+	12.1282i	1.24215	+	0.717153i
$287$		0			0
$288$		0			0
$289$	−1.43425			−0.0843675
$290$	2.57549	−	4.46088i	0.151238	−	0.261952i
$291$		0			0
$292$	−2.15468	+	1.24401i	−0.126093	+	0.0727999i
$293$	4.43406	+	7.68002i	0.259041	+	0.448672i	0.965985	−	0.258597i	$-0.0832603\pi$
$293$	4.43406	+	7.68002i	0.259041	+	0.448672i	−0.706944	+	0.707269i	$0.749927\pi$
$294$		0			0
$295$	0.809584	−	1.40224i	0.0471358	−	0.0816416i
$296$			0.487217i			0.0283189i
$297$		0			0
$298$	8.74051			0.506324
$299$	−5.77366	+	10.0003i	−0.333899	+	0.578331i
$300$		0			0
$301$		0			0
$302$	19.1341	−	11.0471i	1.10104	−	0.635687i
$303$		0			0
$304$	−3.86796	−	2.23317i	−0.221843	−	0.128081i
$305$			5.00321i			0.286483i
$306$		0			0
$307$			27.1427i			1.54912i	0.632501	+	0.774559i	$0.282028\pi$
$307$			27.1427i			1.54912i	−0.632501	+	0.774559i	$0.717972\pi$
$308$		0			0
$309$		0			0
$310$	−2.98252	−	5.16588i	−0.169396	−	0.293402i
$311$	8.44774	+	14.6319i	0.479028	+	0.829700i	0.999711	−	0.0240499i	$-0.00765605\pi$
$311$	8.44774	+	14.6319i	0.479028	+	0.829700i	−0.520683	+	0.853750i	$0.674323\pi$
$312$		0			0
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	0.601024	−	0.799231i	$-0.294760\pi$
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	−0.391643	+	0.920117i	$0.628093\pi$
$314$	−1.42457			−0.0803934
$315$		0			0
$316$	−4.60242			−0.258906
$317$	−5.74123	−	3.31470i	−0.322460	−	0.186172i	0.330029	−	0.943971i	$-0.392942\pi$
$317$	−5.74123	−	3.31470i	−0.322460	−	0.186172i	−0.652488	+	0.757799i	$0.726275\pi$
$318$		0			0
$319$	−14.8397	−	25.7031i	−0.830864	−	1.43910i
$320$	0.483662	+	0.837727i	0.0270375	+	0.0468304i
$321$		0			0
$322$		0			0
$323$			17.6212i			0.980472i
$324$		0			0
$325$			17.6877i			0.981138i
$326$	−6.44579	−	3.72148i	−0.356999	−	0.206114i
$327$		0			0
$328$	−0.141830	+	0.0818856i	−0.00783125	+	0.00452137i
$329$		0			0
$330$		0			0
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	−0.855425	−	0.517927i	$-0.826704\pi$
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	0.876251	+	0.481856i	$0.160037\pi$
$332$	8.41959			0.462085
$333$		0			0
$334$		−	6.49710i		−	0.355506i
$335$	2.63234	−	4.55935i	0.143820	−	0.249104i
$336$		0			0
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	0.892244	−	0.451553i	$-0.149130\pi$
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	−0.837178	+	0.546930i	$0.815796\pi$
$338$	−5.14404	+	2.96991i	−0.279799	+	0.161542i
$339$		0			0
$340$	1.90821	−	3.30512i	0.103487	−	0.179245i
$341$	−34.3699			−1.86124
$342$		0			0
$343$		0			0
$344$	7.53520	+	4.35045i	0.406271	+	0.234560i
$345$		0			0
$346$	−10.2354	+	5.90938i	−0.550256	+	0.317690i
$347$	18.1572	−	10.4831i	0.974730	−	0.562761i	0.0740550	−	0.997254i	$-0.476406\pi$
$347$	18.1572	−	10.4831i	0.974730	−	0.562761i	0.900675	+	0.434494i	$0.143073\pi$
$348$		0			0
$349$	−5.36406	−	3.09694i	−0.287132	−	0.165776i	0.349516	−	0.936930i	$-0.386346\pi$
$349$	−5.36406	−	3.09694i	−0.287132	−	0.165776i	−0.636648	+	0.771155i	$0.719679\pi$
$350$		0			0
$351$		0			0
$352$	5.57361			0.297075
$353$	−9.41889	+	16.3140i	−0.501317	+	0.868306i	0.498682	+	0.866785i	$0.333818\pi$
$353$	−9.41889	+	16.3140i	−0.501317	+	0.868306i	−0.999999	+	0.00152110i	$0.999516\pi$
$354$		0			0
$355$	3.04938	−	1.76056i	0.161844	−	0.0934409i
$356$	−2.05811	−	3.56475i	−0.109080	−	0.188931i
$357$		0			0
$358$	−1.21685	+	2.10764i	−0.0643124	+	0.111392i
$359$			27.7977i			1.46711i	0.679633	+	0.733553i	$0.262139\pi$
$359$			27.7977i			1.46711i	−0.679633	+	0.733553i	$0.737861\pi$
$360$		0			0
$361$	−0.948177			−0.0499041
$362$	−5.76708	+	9.98887i	−0.303111	+	0.525003i
$363$		0			0
$364$		0			0
$365$	2.08428	−	1.20336i	0.109096	−	0.0629866i
$366$		0			0
$367$	18.8390	+	10.8767i	0.983388	+	0.567759i	0.903291	−	0.429028i	$-0.141144\pi$
$367$	18.8390	+	10.8767i	0.983388	+	0.567759i	0.0800968	+	0.996787i	$0.474477\pi$
$368$			2.65334i			0.138315i
$369$		0			0
$370$		−	0.471297i		−	0.0245016i
$371$		0			0
$372$		0			0
$373$	−5.86560	−	10.1595i	−0.303709	−	0.526040i	0.673264	−	0.739402i	$-0.264892\pi$
$373$	−5.86560	−	10.1595i	−0.303709	−	0.526040i	−0.976973	+	0.213362i	$0.931558\pi$
$374$	−10.9949	−	19.0438i	−0.568533	−	0.984729i
$375$		0			0
$376$	8.21859	+	4.74500i	0.423841	+	0.244705i
$377$	23.1743			1.19354
$378$		0			0
$379$	34.8881			1.79208			0.896041	−	0.443971i	$-0.146431\pi$
$379$	34.8881			1.79208			0.896041	+	0.443971i	$0.146431\pi$
$380$	3.74157	+	2.16020i	0.191939	+	0.110816i
$381$		0			0
$382$	−11.0345	−	19.1122i	−0.564572	−	0.977867i
$383$	−5.92412	−	10.2609i	−0.302708	−	0.524306i	0.674040	−	0.738695i	$-0.264557\pi$
$383$	−5.92412	−	10.2609i	−0.302708	−	0.524306i	−0.976748	+	0.214389i	$0.931224\pi$
$384$		0			0
$385$		0			0
$386$		−	19.9396i		−	1.01490i
$387$		0			0
$388$			11.8552i			0.601859i
$389$	−5.50224	−	3.17672i	−0.278975	−	0.161066i	0.353984	−	0.935251i	$-0.384827\pi$
$389$	−5.50224	−	3.17672i	−0.278975	−	0.161066i	−0.632959	+	0.774185i	$0.718160\pi$
$390$		0			0
$391$	9.06586	−	5.23418i	0.458480	−	0.264704i
$392$		0			0
$393$		0			0
$394$	−2.31280	+	4.00588i	−0.116517	+	0.201814i
$395$	4.45203			0.224006
$396$		0			0
$397$		−	8.57535i		−	0.430385i	−0.976572	−	0.215192i	$-0.930962\pi$
$397$		−	8.57535i		−	0.430385i	0.976572	−	0.215192i	$-0.0690378\pi$
$398$	10.4514	−	18.1024i	0.523883	−	0.907391i
$399$		0			0
$400$	2.03214	+	3.51977i	0.101607	+	0.175989i
$401$	−20.0216	+	11.5595i	−0.999833	+	0.577254i	−0.908199	−	0.418539i	$-0.862542\pi$
$401$	−20.0216	+	11.5595i	−0.999833	+	0.577254i	−0.0916343	+	0.995793i	$0.529209\pi$
$402$		0			0
$403$	13.4184	−	23.2413i	0.668417	−	1.15773i
$404$	−5.31626			−0.264494
$405$		0			0
$406$		0			0
$407$	−2.35174	−	1.35778i	−0.116572	−	0.0673026i
$408$		0			0
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	−0.533027	−	0.846098i	$-0.678946\pi$
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	0.466229	+	0.884664i	$0.345612\pi$
$410$	0.137196	−	0.0792099i	0.00677561	−	0.00391190i
$411$		0			0
$412$	−7.74616	−	4.47225i	−0.381626	−	0.220332i
$413$		0			0
$414$		0			0
$415$	−8.14447			−0.399796
$416$	−2.17600	+	3.76893i	−0.106687	+	0.184787i
$417$		0			0
$418$	21.5585	−	12.4468i	1.05446	−	0.608794i
$419$	−3.40822	−	5.90321i	−0.166502	−	0.288391i	0.770685	−	0.637216i	$-0.219914\pi$
$419$	−3.40822	−	5.90321i	−0.166502	−	0.288391i	−0.937188	+	0.348825i	$0.886581\pi$
$420$		0			0
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	−0.982379	−	0.186900i	$-0.940156\pi$
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	0.653050	+	0.757315i	$0.273489\pi$
$422$			6.68620i			0.325479i
$423$		0			0
$424$	−2.01518			−0.0978659
$425$	8.01750	−	13.8867i	0.388906	−	0.673605i
$426$		0			0
$427$		0			0
$428$	16.5898	−	9.57813i	0.801899	−	0.462976i
$429$		0			0
$430$	−7.28898	−	4.20829i	−0.351506	−	0.202942i
$431$			14.1598i			0.682054i	0.940053	+	0.341027i	$0.110775\pi$
$431$			14.1598i			0.682054i	−0.940053	+	0.341027i	$0.889225\pi$
$432$		0			0
$433$		−	23.4830i		−	1.12852i	−0.825597	−	0.564260i	$-0.809161\pi$
$433$		−	23.4830i		−	1.12852i	0.825597	−	0.564260i	$-0.190839\pi$
$434$		0			0
$435$		0			0
$436$	9.62168	+	16.6652i	0.460795	+	0.798121i
$437$	5.92536	+	10.2630i	0.283449	+	0.490947i
$438$		0			0
$439$	3.66398	+	2.11540i	0.174872	+	0.100963i	0.584881	−	0.811119i	$-0.301141\pi$
$439$	3.66398	+	2.11540i	0.174872	+	0.100963i	−0.410009	+	0.912081i	$0.634474\pi$
$440$	−5.39149			−0.257029
$441$		0			0
$442$	17.1701			0.816699
$443$	−25.8161	−	14.9049i	−1.22656	−	0.708154i	−0.260250	−	0.965541i	$-0.583805\pi$
$443$	−25.8161	−	14.9049i	−1.22656	−	0.708154i	−0.966308	+	0.257388i	$0.917138\pi$
$444$		0			0
$445$	1.99086	+	3.44827i	0.0943757	+	0.163464i
$446$	−4.09123	−	7.08622i	−0.193725	−	0.335542i
$447$		0			0
$448$		0			0
$449$			8.41716i			0.397230i	0.980078	+	0.198615i	$0.0636444\pi$
$449$			8.41716i			0.397230i	−0.980078	+	0.198615i	$0.936356\pi$
$450$		0			0
$451$		−	0.912797i		−	0.0429819i
$452$	−7.31199	−	4.22158i	−0.343927	−	0.198566i
$453$		0			0
$454$	−9.26106	+	5.34688i	−0.434643	+	0.250941i
$455$		0			0
$456$		0			0
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	−0.817048	−	0.576570i	$-0.804391\pi$
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	0.907848	+	0.419299i	$0.137724\pi$
$458$	29.2072			1.36476
$459$		0			0
$460$		−	2.56664i		−	0.119670i
$461$	17.0423	−	29.5181i	0.793739	−	1.37480i	−0.129898	−	0.991527i	$-0.541465\pi$
$461$	17.0423	−	29.5181i	0.793739	−	1.37480i	0.923637	−	0.383269i	$-0.125202\pi$
$462$		0			0
$463$	−6.10962	−	10.5822i	−0.283938	−	0.491796i	0.688413	−	0.725319i	$-0.258308\pi$
$463$	−6.10962	−	10.5822i	−0.283938	−	0.491796i	−0.972351	+	0.233523i	$0.924974\pi$
$464$	4.61157	−	2.66249i	0.214087	−	0.123603i
$465$		0			0
$466$	−3.21967	+	5.57664i	−0.149148	+	0.258333i
$467$	30.8115			1.42579			0.712893	−	0.701273i	$-0.247385\pi$
$467$	30.8115			1.42579			0.712893	+	0.701273i	$0.247385\pi$
$468$		0			0
$469$		0			0
$470$	−7.95004	−	4.58996i	−0.366708	−	0.211719i
$471$		0			0
$472$	1.44961	−	0.836931i	0.0667236	−	0.0385229i
$473$	−41.9983	+	24.2477i	−1.93108	+	1.11491i
$474$		0			0
$475$	15.7205	+	9.07623i	0.721306	+	0.416446i
$476$		0			0
$477$		0			0
$478$	−4.63557			−0.212026
$479$	20.8747	−	36.1560i	0.953788	−	1.65201i	0.216670	−	0.976245i	$-0.430481\pi$
$479$	20.8747	−	36.1560i	0.953788	−	1.65201i	0.737118	−	0.675764i	$-0.236186\pi$
$480$		0			0
$481$	1.83629	−	1.06018i	0.0837276	−	0.0483401i
$482$	5.24722	+	9.08846i	0.239004	+	0.413968i
$483$		0			0
$484$	−10.0326	+	17.3769i	−0.456026	+	0.789861i
$485$		−	11.4679i		−	0.520729i
$486$		0			0
$487$	−21.1663			−0.959137			−0.479568	−	0.877504i	$-0.659207\pi$
$487$	−21.1663			−0.959137			−0.479568	+	0.877504i	$0.659207\pi$
$488$	−2.58611	+	4.47927i	−0.117068	+	0.202767i
$489$		0			0
$490$		0			0
$491$	−32.3428	+	18.6731i	−1.45961	+	0.842707i	−0.998992	−	0.0448915i	$-0.985706\pi$
$491$	−32.3428	+	18.6731i	−1.45961	+	0.842707i	−0.460619	+	0.887598i	$0.652372\pi$
$492$		0			0
$493$	−18.1942	−	10.5044i	−0.819427	−	0.473097i
$494$			19.4375i			0.874533i
$495$		0			0
$496$		−	6.16655i		−	0.276886i
$497$		0			0
$498$		0			0
$499$	−13.7099	−	23.7462i	−0.613738	−	1.06303i	−0.990605	−	0.136758i	$-0.956332\pi$
$499$	−13.7099	−	23.7462i	−0.613738	−	1.06303i	0.376867	−	0.926267i	$-0.377001\pi$
$500$	−4.38405	−	7.59340i	−0.196061	−	0.339587i
$501$		0			0
$502$	6.80065	+	3.92635i	0.303528	+	0.175242i
$503$	11.2791			0.502909			0.251454	−	0.967869i	$-0.419091\pi$
$503$	11.2791			0.502909			0.251454	+	0.967869i	$0.419091\pi$
$504$		0			0
$505$	5.14255			0.228840
$506$	−12.8074	−	7.39435i	−0.569358	−	0.328719i
$507$		0			0
$508$	1.65941	+	2.87419i	0.0736246	+	0.127522i
$509$	−9.31667	−	16.1370i	−0.412954	−	0.715258i	0.582257	−	0.813005i	$-0.302170\pi$
$509$	−9.31667	−	16.1370i	−0.412954	−	0.715258i	−0.995211	+	0.0977470i	$0.968836\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	3.43136i		−	0.151351i
$515$	7.49305	+	4.32611i	0.330183	+	0.190631i
$516$		0			0
$517$	−45.8072	+	26.4468i	−2.01460	+	1.16313i
$518$		0			0
$519$		0			0
$520$	2.10489	−	3.64578i	0.0923056	−	0.159878i
$521$	−15.2851			−0.669652			−0.334826	−	0.942280i	$-0.608678\pi$
$521$	−15.2851			−0.669652			−0.334826	+	0.942280i	$0.608678\pi$
$522$		0			0
$523$		−	36.4875i		−	1.59549i	−0.602997	−	0.797743i	$-0.706027\pi$
$523$		−	36.4875i		−	1.59549i	0.602997	−	0.797743i	$-0.293973\pi$
$524$	−9.37335	+	16.2351i	−0.409477	+	0.709235i
$525$		0			0
$526$	1.83066	+	3.17080i	0.0798207	+	0.138253i
$527$	−21.0697	+	12.1646i	−0.917809	+	0.529897i
$528$		0			0
$529$	−7.97989	+	13.8216i	−0.346952	+	0.600938i
$530$	1.94934			0.0846737
$531$		0			0
$532$		0			0
$533$	0.617243	+	0.356365i	0.0267358	+	0.0154359i
$534$		0			0
$535$	−16.0477	+	9.26516i	−0.693803	+	0.400568i
$536$	4.71336	−	2.72126i	0.203586	−	0.117540i
$537$		0			0
$538$	10.9865	+	6.34303i	0.473660	+	0.273467i
$539$		0			0
$540$		0			0
$541$	−5.27293			−0.226701			−0.113351	−	0.993555i	$-0.536158\pi$
$541$	−5.27293			−0.226701			−0.113351	+	0.993555i	$0.536158\pi$
$542$	−9.93828	+	17.2136i	−0.426886	+	0.739388i
$543$		0			0
$544$	3.41677	−	1.97267i	0.146493	−	0.0845776i
$545$	−9.30729	−	16.1207i	−0.398680	−	0.690535i
$546$		0			0
$547$	−9.29831	+	16.1051i	−0.397567	+	0.688606i	−0.993425	−	0.114484i	$-0.963479\pi$
$547$	−9.29831	+	16.1051i	−0.397567	+	0.688606i	0.595858	+	0.803090i	$0.296812\pi$
$548$			16.9343i			0.723399i
$549$		0			0
$550$	−22.6527			−0.965916
$551$	11.8916	−	20.5968i	0.506599	−	0.877455i
$552$		0			0
$553$		0			0
$554$	−6.46579	+	3.73302i	−0.274705	+	0.158601i
$555$		0			0
$556$	−10.5033	−	6.06406i	−0.445438	−	0.257174i
$557$			27.5620i			1.16784i	0.811811	+	0.583920i	$0.198482\pi$
$557$			27.5620i			1.16784i	−0.811811	+	0.583920i	$0.801518\pi$
$558$		0			0
$559$		−	37.8662i		−	1.60157i
$560$		0			0
$561$		0			0
$562$	−11.1282	−	19.2746i	−0.469416	−	0.813052i
$563$	−9.42577	−	16.3259i	−0.397249	−	0.688055i	0.596137	−	0.802883i	$-0.296702\pi$
$563$	−9.42577	−	16.3259i	−0.397249	−	0.688055i	−0.993385	+	0.114828i	$0.963368\pi$
$564$		0			0
$565$	7.07306	+	4.08364i	0.297566	+	0.171800i
$566$	−16.1802			−0.680106
$567$		0			0
$568$	3.64006			0.152734
$569$	3.87103	+	2.23494i	0.162282	+	0.0936936i	0.578942	−	0.815369i	$-0.303466\pi$
$569$	3.87103	+	2.23494i	0.162282	+	0.0936936i	−0.416659	+	0.909063i	$0.636799\pi$
$570$		0			0
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	0.602697	−	0.797970i	$-0.294093\pi$
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	−0.992411	+	0.122966i	$0.960759\pi$
$572$	−12.1282	−	21.0066i	−0.507104	−	0.878329i
$573$		0			0
$574$		0			0
$575$		−	10.7839i		−	0.449721i
$576$		0			0
$577$		−	36.8833i		−	1.53547i	−0.640767	−	0.767735i	$-0.721384\pi$
$577$		−	36.8833i		−	1.53547i	0.640767	−	0.767735i	$-0.278616\pi$
$578$	1.24210	+	0.717124i	0.0516644	+	0.0298284i
$579$		0			0
$580$	−4.46088	+	2.57549i	−0.185228	+	0.106941i
$581$		0			0
$582$		0			0
$583$	5.61593	−	9.72707i	0.232588	−	0.402854i
$584$	2.48801			0.102955
$585$		0			0
$586$		−	8.86813i		−	0.366339i
$587$	−13.2295	+	22.9141i	−0.546039	+	0.945766i	0.452502	+	0.891763i	$0.350531\pi$
$587$	−13.2295	+	22.9141i	−0.546039	+	0.945766i	−0.998541	+	0.0540032i	$0.982802\pi$
$588$		0			0
$589$	−13.7709	−	23.8520i	−0.567422	−	0.982803i
$590$	−1.40224	+	0.809584i	−0.0577293	+	0.0333300i
$591$		0			0
$592$	0.243608	−	0.421942i	0.0100122	−	0.0173417i
$593$	−34.6703			−1.42374			−0.711869	−	0.702312i	$-0.752151\pi$
$593$	−34.6703			−1.42374			−0.711869	+	0.702312i	$0.752151\pi$
$594$		0			0
$595$		0			0
$596$	−7.56951	−	4.37026i	−0.310059	−	0.179013i
$597$		0			0
$598$	10.0003	−	5.77366i	0.408942	−	0.236103i
$599$	21.2079	−	12.2444i	0.866530	−	0.500291i	0.000336253	−	1.00000i	$-0.499893\pi$
$599$	21.2079	−	12.2444i	0.866530	−	0.500291i	0.866193	+	0.499709i	$0.166560\pi$
$600$		0			0
$601$	−19.3812	−	11.1898i	−0.790577	−	0.456440i	0.0495885	−	0.998770i	$-0.484209\pi$
$601$	−19.3812	−	11.1898i	−0.790577	−	0.456440i	−0.840166	+	0.542330i	$0.817542\pi$
$602$		0			0
$603$		0			0
$604$	−22.0941			−0.898997
$605$	9.70476	−	16.8091i	0.394554	−	0.683388i
$606$		0			0
$607$	28.2180	−	16.2917i	1.14533	−	0.661259i	0.197589	−	0.980285i	$-0.436689\pi$
$607$	28.2180	−	16.2917i	1.14533	−	0.661259i	0.947746	+	0.319026i	$0.103356\pi$
$608$	2.23317	+	3.86796i	0.0905670	+	0.156867i
$609$		0			0
$610$	2.50160	−	4.33290i	0.101287	−	0.175434i
$611$		−	41.3004i		−	1.67084i
$612$		0			0
$613$	−11.7386			−0.474118			−0.237059	−	0.971495i	$-0.576183\pi$
$613$	−11.7386			−0.474118			−0.237059	+	0.971495i	$0.576183\pi$
$614$	13.5714	−	23.5063i	0.547696	−	0.948637i
$615$		0			0
$616$		0			0
$617$	38.1947	−	22.0517i	1.53766	−	0.887770i	0.538687	−	0.842506i	$-0.318920\pi$
$617$	38.1947	−	22.0517i	1.53766	−	0.887770i	0.998975	−	0.0452639i	$-0.0144129\pi$
$618$		0			0
$619$	4.28374	+	2.47322i	0.172178	+	0.0994070i	0.583612	−	0.812032i	$-0.301639\pi$
$619$	4.28374	+	2.47322i	0.172178	+	0.0994070i	−0.411434	+	0.911439i	$0.634972\pi$
$620$			5.96505i			0.239562i
$621$		0			0
$622$		−	16.8955i		−	0.677447i
$623$		0			0
$624$		0			0
$625$	−5.91991	−	10.2536i	−0.236797	−	0.410144i
$626$	−2.13870	−	3.70433i	−0.0854795	−	0.148055i
$627$		0			0
$628$	1.23372	+	0.712287i	0.0492307	+	0.0284233i
$629$	−1.92224			−0.0766447
$630$		0			0
$631$	−9.08478			−0.361659			−0.180830	−	0.983514i	$-0.557878\pi$
$631$	−9.08478			−0.361659			−0.180830	+	0.983514i	$0.557878\pi$
$632$	3.98581	+	2.30121i	0.158547	+	0.0915371i
$633$		0			0
$634$	3.31470	+	5.74123i	0.131644	+	0.228013i
$635$	−1.60519	−	2.78027i	−0.0637001	−	0.110332i
$636$		0			0
$637$		0			0
$638$			29.6794i			1.17502i
$639$		0			0
$640$		−	0.967324i		−	0.0382368i
$641$	−12.1954	−	7.04105i	−0.481691	−	0.278105i	0.239430	−	0.970914i	$-0.423040\pi$
$641$	−12.1954	−	7.04105i	−0.481691	−	0.278105i	−0.721121	+	0.692809i	$0.756373\pi$
$642$		0			0
$643$	7.33157	−	4.23288i	0.289129	−	0.166929i	−0.348420	−	0.937339i	$-0.613282\pi$
$643$	7.33157	−	4.23288i	0.289129	−	0.166929i	0.637549	+	0.770410i	$0.279948\pi$
$644$		0			0
$645$		0			0
$646$	8.81062	−	15.2604i	0.346649	−	0.600414i
$647$	−24.3324			−0.956607			−0.478304	−	0.878195i	$-0.658748\pi$
$647$	−24.3324			−0.956607			−0.478304	+	0.878195i	$0.658748\pi$
$648$		0			0
$649$			9.32946i			0.366213i
$650$	8.84386	−	15.3180i	0.346885	−	0.600822i
$651$		0			0
$652$	3.72148	+	6.44579i	0.145744	+	0.252437i
$653$	−36.0653	+	20.8223i	−1.41134	+	0.814840i	−0.995515	−	0.0946029i	$-0.969842\pi$
$653$	−36.0653	+	20.8223i	−1.41134	+	0.814840i	−0.415829	+	0.909443i	$0.636509\pi$
$654$		0			0
$655$	9.06707	−	15.7046i	0.354280	−	0.613631i
$656$	0.163771			0.00639419
$657$		0			0
$658$		0			0
$659$	9.09866	+	5.25312i	0.354434	+	0.204632i	0.666636	−	0.745383i	$-0.267733\pi$
$659$	9.09866	+	5.25312i	0.354434	+	0.204632i	−0.312203	+	0.950016i	$0.601067\pi$
$660$		0			0
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	−0.791243	−	0.611502i	$-0.790566\pi$
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	0.133954	+	0.990987i	$0.457232\pi$
$662$	−0.656267	+	0.378896i	−0.0255065	+	0.0147262i
$663$		0			0
$664$	−7.29158	−	4.20979i	−0.282968	−	0.163372i
$665$		0			0
$666$		0			0
$667$	−14.1290			−0.547077
$668$	−3.24855	+	5.62665i	−0.125690	+	0.217702i
$669$		0			0
$670$	−4.55935	+	2.63234i	−0.176143	+	0.101696i
$671$	−14.4140	−	24.9657i	−0.556445	−	0.963790i
$672$		0			0
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	−0.919610	−	0.392832i	$-0.871495\pi$
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	0.800007	+	0.599990i	$0.204829\pi$
$674$		−	2.02176i		−	0.0778751i
$675$		0			0
$676$	5.93982			0.228455
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	−0.523942	−	0.851754i	$-0.675539\pi$
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	0.999612	+	0.0278703i	$0.00887255\pi$
$678$		0			0
$679$		0			0
$680$	−3.30512	+	1.90821i	−0.126746	+	0.0731767i
$681$		0			0
$682$	29.7652	+	17.1850i	1.13977	+	0.658046i
$683$		−	21.1448i		−	0.809083i	−0.914520	−	0.404542i	$-0.867431\pi$
$683$		−	21.1448i		−	0.809083i	0.914520	−	0.404542i	$-0.132569\pi$
$684$		0			0
$685$		−	16.3810i		−	0.625886i
$686$		0			0
$687$		0			0
$688$	−4.35045	−	7.53520i	−0.165859	−	0.287277i
$689$	4.38503	+	7.59509i	0.167056	+	0.289350i
$690$		0			0
$691$	5.58127	+	3.22235i	0.212322	+	0.122584i	0.602390	−	0.798202i	$-0.294215\pi$
$691$	5.58127	+	3.22235i	0.212322	+	0.122584i	−0.390068	+	0.920786i	$0.627549\pi$
$692$	11.8188			0.449282
$693$		0			0
$694$	−20.9661			−0.795864
$695$	10.1601	+	5.86591i	0.385393	+	0.222507i
$696$		0			0
$697$	−0.323067	−	0.559568i	−0.0122370	−	0.0211952i
$698$	3.09694	+	5.36406i	0.117221	+	0.203033i
$699$		0			0
$700$		0			0
$701$		−	24.5717i		−	0.928061i	−0.885819	−	0.464031i	$-0.846403\pi$
$701$		−	24.5717i		−	0.928061i	0.885819	−	0.464031i	$-0.153597\pi$
$702$		0			0
$703$		−	2.17608i		−	0.0820723i
$704$	−4.82689	−	2.78681i	−0.181920	−	0.105032i
$705$		0			0
$706$	16.3140	−	9.41889i	0.613985	−	0.354484i
$707$		0			0
$708$		0			0
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	0.0655765	+	0.997848i	$0.479111\pi$
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	−0.896950	+	0.442133i	$0.854222\pi$
$710$	−3.52112			−0.132145
$711$		0			0
$712$			4.11622i			0.154262i
$713$	−8.18098	+	14.1699i	−0.306380	+	0.530666i
$714$		0			0
$715$	11.7319	+	20.3202i	0.438747	+	0.759931i
$716$	2.10764	−	1.21685i	0.0787663	−	0.0454757i
$717$		0			0
$718$	13.8988	−	24.0735i	0.518700	−	0.898415i
$719$	4.44867			0.165907			0.0829537	−	0.996553i	$-0.473565\pi$
$719$	4.44867			0.165907			0.0829537	+	0.996553i	$0.473565\pi$
$720$		0			0
$721$		0			0
$722$	0.821146	+	0.474089i	0.0305599	+	0.0176438i
$723$		0			0
$724$	9.98887	−	5.76708i	0.371233	−	0.214332i
$725$	−18.7427	+	10.8211i	−0.696088	+	0.401886i
$726$		0			0
$727$	30.4270	+	17.5670i	1.12848	+	0.651525i	0.943551	−	0.331227i	$-0.107463\pi$
$727$	30.4270	+	17.5670i	1.12848	+	0.651525i	0.184924	+	0.982753i	$0.440796\pi$
$728$		0			0
$729$		0			0
$730$	−2.40671			−0.0890765
$731$	−17.1640	+	29.7289i	−0.634834	+	1.09956i
$732$		0			0
$733$	5.03789	−	2.90863i	0.186079	−	0.107433i	−0.404067	−	0.914729i	$-0.632404\pi$
$733$	5.03789	−	2.90863i	0.186079	−	0.107433i	0.590145	+	0.807297i	$0.299070\pi$
$734$	−10.8767	−	18.8390i	−0.401467	−	0.695360i
$735$		0			0
$736$	1.32667	−	2.29786i	0.0489018	−	0.0847003i
$737$			30.3345i			1.11739i
$738$		0			0
$739$	11.0335			0.405874			0.202937	−	0.979192i	$-0.434951\pi$
$739$	11.0335			0.405874			0.202937	+	0.979192i	$0.434951\pi$
$740$	−0.235648	+	0.408155i	−0.00866261	+	0.0150041i
$741$		0			0
$742$		0			0
$743$	0.543196	−	0.313615i	0.0199279	−	0.0115054i	−0.490003	−	0.871721i	$-0.663004\pi$
$743$	0.543196	−	0.313615i	0.0199279	−	0.0115054i	0.509931	+	0.860215i	$0.329671\pi$
$744$		0			0
$745$	7.32216	+	4.22745i	0.268263	+	0.154882i
$746$			11.7312i			0.429510i
$747$		0			0
$748$			21.9898i			0.804028i
$749$		0			0
$750$		0			0
$751$	−2.23529	−	3.87163i	−0.0815668	−	0.141278i	0.822356	−	0.568973i	$-0.192659\pi$
$751$	−2.23529	−	3.87163i	−0.0815668	−	0.141278i	−0.903923	+	0.427695i	$0.859326\pi$
$752$	−4.74500	−	8.21859i	−0.173033	−	0.299701i
$753$		0			0
$754$	−20.0695	−	11.5871i	−0.730889	−	0.421979i
$755$	21.3722			0.777813
$756$		0			0
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$	−30.2140	−	17.4441i	−1.09742	−	0.633597i
$759$		0			0
$760$	−2.16020	−	3.74157i	−0.0783586	−	0.135721i
$761$	10.4970	+	18.1813i	0.380516	+	0.659073i	0.991136	−	0.132851i	$-0.0424131\pi$
$761$	10.4970	+	18.1813i	0.380516	+	0.659073i	−0.610620	+	0.791924i	$0.709080\pi$
$762$		0			0
$763$		0			0
$764$			22.0689i			0.798425i
$765$		0			0
$766$			11.8482i			0.428094i
$767$	−6.30868	−	3.64232i	−0.227793	−	0.131516i
$768$		0			0
$769$	34.1729	−	19.7298i	1.23231	−	0.711473i	0.264797	−	0.964304i	$-0.414695\pi$
$769$	34.1729	−	19.7298i	1.23231	−	0.711473i	0.967511	+	0.252831i	$0.0813616\pi$
$770$		0			0
$771$		0			0
$772$	−9.96979	+	17.2682i	−0.358821	+	0.621496i
$773$	34.6328			1.24566			0.622829	−	0.782358i	$-0.285983\pi$
$773$	34.6328			1.24566			0.622829	+	0.782358i	$0.285983\pi$
$774$		0			0
$775$			25.0626i			0.900275i
$776$	5.92762	−	10.2669i	0.212789	−	0.368562i
$777$		0			0
$778$	3.17672	+	5.50224i	0.113891	+	0.197265i
$779$	0.633461	−	0.365729i	0.0226961	−	0.0131036i
$780$		0			0
$781$	−10.1442	+	17.5702i	−0.362986	+	0.628711i
$782$	−10.4684			−0.374348
$783$		0			0
$784$		0			0
$785$	−1.19340	−	0.689012i	−0.0425944	−	0.0245919i
$786$		0			0
$787$	30.5793	−	17.6550i	1.09003	−	0.629332i	0.156449	−	0.987686i	$-0.449995\pi$
$787$	30.5793	−	17.6550i	1.09003	−	0.629332i	0.933586	+	0.358355i	$0.116662\pi$
$788$	4.00588	−	2.31280i	0.142704	−	0.0823900i
$789$		0			0
$790$	−3.85557	−	2.22601i	−0.137175	−	0.0791980i
$791$		0			0
$792$		0			0
$793$	22.5094			0.799333
$794$	−4.28768	+	7.42647i	−0.152164	+	0.263556i
$795$		0			0
$796$	−18.1024	+	10.4514i	−0.641622	+	0.370441i
$797$	−9.60992	−	16.6449i	−0.340401	−	0.589591i	0.644106	−	0.764936i	$-0.277229\pi$
$797$	−9.60992	−	16.6449i	−0.340401	−	0.589591i	−0.984507	+	0.175344i	$0.943896\pi$
$798$		0			0
$799$	−18.7207	+	32.4252i	−0.662290	+	1.14712i
$800$		−	4.06428i		−	0.143694i
$801$		0			0
$802$	23.1190			0.816360
$803$	−6.93361	+	12.0094i	−0.244682	+	0.423801i
$804$		0			0
$805$		0			0
$806$	−23.2413	+	13.4184i	−0.818640	+	0.472642i
$807$		0			0
$808$	4.60402	+	2.65813i	0.161969	+	0.0935127i
$809$		−	39.2779i		−	1.38094i	−0.723362	−	0.690469i	$-0.757404\pi$
$809$		−	39.2779i		−	1.38094i	0.723362	−	0.690469i	$-0.242596\pi$
$810$		0			0
$811$			9.68436i			0.340064i	0.985439	+	0.170032i	$0.0543871\pi$
$811$			9.68436i			0.340064i	−0.985439	+	0.170032i	$0.945613\pi$
$812$		0			0
$813$		0			0
$814$	1.35778	+	2.35174i	0.0475901	+	0.0824285i
$815$	−3.59987	−	6.23517i	−0.126098	−	0.218408i
$816$		0			0
$817$	−33.6547	−	19.4306i	−1.17743	−	0.679790i
$818$	1.55989			0.0545404
$819$		0			0
$820$	−0.158420			−0.00553226
$821$	10.9919	+	6.34620i	0.383621	+	0.221484i	0.679393	−	0.733775i	$-0.262243\pi$
$821$	10.9919	+	6.34620i	0.383621	+	0.221484i	−0.295771	+	0.955259i	$0.595577\pi$
$822$		0			0
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	0.672572	−	0.740032i	$-0.265190\pi$
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	−0.977172	+	0.212448i	$0.931856\pi$
$824$	4.47225	+	7.74616i	0.155798	+	0.269850i
$825$		0			0
$826$		0			0
$827$		−	46.9482i		−	1.63255i	−0.577665	−	0.816274i	$-0.696036\pi$
$827$		−	46.9482i		−	1.63255i	0.577665	−	0.816274i	$-0.303964\pi$
$828$		0			0
$829$			2.30706i			0.0801275i	0.999197	+	0.0400637i	$0.0127561\pi$
$829$			2.30706i			0.0801275i	−0.999197	+	0.0400637i	$0.987244\pi$
$830$	7.05332	+	4.07224i	0.244824	+	0.141349i
$831$		0			0
$832$	3.76893	−	2.17600i	0.130664	−	0.0754391i
$833$		0			0
$834$		0			0
$835$	3.14240	−	5.44280i	0.108747	−	0.188356i
$836$	−24.8936			−0.860965
$837$		0			0
$838$			6.81644i			0.235470i
$839$	−8.51664	+	14.7513i	−0.294027	+	0.509270i	−0.974758	−	0.223264i	$-0.928329\pi$
$839$	−8.51664	+	14.7513i	−0.294027	+	0.509270i	0.680731	+	0.732533i	$0.261662\pi$
$840$		0			0
$841$	−0.322276	−	0.558199i	−0.0111130	−	0.0192482i
$842$	11.7039	−	6.75727i	0.403344	−	0.232871i
$843$		0			0
$844$	3.34310	−	5.79042i	0.115074	−	0.199314i
$845$	−5.74573			−0.197659
$846$		0			0
$847$		0			0
$848$	1.74520	+	1.00759i	0.0599304	+	0.0346008i
$849$		0			0
$850$	−13.8867	+	8.01750i	−0.476311	+	0.274998i
$851$	−1.11956	+	0.646377i	−0.0383779	+	0.0221575i
$852$		0			0
$853$	2.87158	+	1.65791i	0.0983209	+	0.0567656i	0.548354	−	0.836246i	$-0.315255\pi$
$853$	2.87158	+	1.65791i	0.0983209	+	0.0567656i	−0.450033	+	0.893012i	$0.648588\pi$
$854$		0			0
$855$		0			0
$856$	−19.1563			−0.654747
$857$	4.74512	−	8.21879i	0.162090	−	0.280748i	−0.773528	−	0.633762i	$-0.781510\pi$
$857$	4.74512	−	8.21879i	0.162090	−	0.280748i	0.935618	+	0.353014i	$0.114843\pi$
$858$		0			0
$859$	25.5104	−	14.7284i	0.870404	−	0.502528i	0.00292142	−	0.999996i	$-0.499070\pi$
$859$	25.5104	−	14.7284i	0.870404	−	0.502528i	0.867482	+	0.497468i	$0.165737\pi$
$860$	4.20829	+	7.28898i	0.143502	+	0.248552i
$861$		0			0
$862$	7.07990	−	12.2628i	0.241143	−	0.417671i
$863$		−	15.5434i		−	0.529105i	−0.964371	−	0.264553i	$-0.914776\pi$
$863$		−	15.5434i		−	0.529105i	0.964371	−	0.264553i	$-0.0852243\pi$
$864$		0			0
$865$	−11.4326			−0.388719
$866$	−11.7415	+	20.3369i	−0.398992	+	0.691075i
$867$		0			0
$868$		0			0
$869$	−22.2154	+	12.8260i	−0.753604	+	0.435094i
$870$		0			0
$871$	−20.5125	−	11.8429i	−0.695039	−	0.401281i
$872$		−	19.2434i		−	0.651663i
$873$		0			0
$874$		−	11.8507i		−	0.400857i
$875$		0			0
$876$		0			0
$877$	22.7249	+	39.3606i	0.767364	+	1.32911i	0.938988	+	0.343950i	$0.111765\pi$
$877$	22.7249	+	39.3606i	0.767364	+	1.32911i	−0.171624	+	0.985163i	$0.554901\pi$
$878$	−2.11540	−	3.66398i	−0.0713913	−	0.123653i
$879$		0			0
$880$	4.66917	+	2.69574i	0.157398	+	0.0908735i
$881$	−15.6912			−0.528651			−0.264326	−	0.964433i	$-0.585149\pi$
$881$	−15.6912			−0.528651			−0.264326	+	0.964433i	$0.585149\pi$
$882$		0			0
$883$	−10.5344			−0.354510			−0.177255	−	0.984165i	$-0.556722\pi$
$883$	−10.5344			−0.354510			−0.177255	+	0.984165i	$0.556722\pi$
$884$	−14.8697	−	8.58505i	−0.500124	−	0.288747i
$885$		0			0
$886$	14.9049	+	25.8161i	0.500740	+	0.867307i
$887$	−0.0302741	−	0.0524362i	−0.00101650	−	0.00176064i	0.865517	−	0.500880i	$-0.166990\pi$
$887$	−0.0302741	−	0.0524362i	−0.00101650	−	0.00176064i	−0.866533	+	0.499119i	$0.833657\pi$
$888$		0			0
$889$		0			0
$890$		−	3.98172i		−	0.133467i
$891$		0			0
$892$			8.18246i			0.273969i
$893$	−36.7070	−	21.1928i	−1.22835	−	0.709190i
$894$		0			0
$895$	−2.03877	+	1.17709i	−0.0681487	+	0.0393456i
$896$		0			0
$897$		0			0
$898$	4.20858	−	7.28948i	0.140442	−	0.243253i
$899$	32.8368			1.09517
$900$		0			0
$901$		−	7.95059i		−	0.264873i
$902$	−0.456399	+	0.790505i	−0.0151964	+	0.0263210i
$903$		0			0
$904$	4.22158	+	7.31199i	0.140408	+	0.243193i
$905$	−9.66247	+	5.57863i	−0.321192	+	0.185440i
$906$		0			0
$907$	−12.0490	+	20.8695i	−0.400081	+	0.692961i	−0.993735	−	0.111760i	$-0.964351\pi$
$907$	−12.0490	+	20.8695i	−0.400081	+	0.692961i	0.593654	+	0.804720i	$0.297685\pi$
$908$	10.6938			0.354885
$909$		0			0
$910$		0			0
$911$	−22.0494	−	12.7302i	−0.730528	−	0.421771i	0.0880873	−	0.996113i	$-0.471925\pi$
$911$	−22.0494	−	12.7302i	−0.730528	−	0.421771i	−0.818615	+	0.574342i	$0.805258\pi$
$912$		0			0
$913$	40.6404	−	23.4638i	1.34500	−	0.776537i
$914$	−3.36207	+	1.94109i	−0.111208	+	0.0642057i
$915$		0			0
$916$	−25.2942	−	14.6036i	−0.835744	−	0.482517i
$917$		0			0
$918$		0			0
$919$	−22.9067			−0.755623			−0.377812	−	0.925882i	$-0.623323\pi$
$919$	−22.9067			−0.755623			−0.377812	+	0.925882i	$0.623323\pi$
$920$	−1.28332	+	2.22278i	−0.0423098	+	0.0732828i
$921$		0			0
$922$	−29.5181	+	17.0423i	−0.972128	+	0.561258i
$923$	−7.92076	−	13.7192i	−0.260715	−	0.451572i
$924$		0			0
$925$	−0.990094	+	1.71489i	−0.0325541	+	0.0563853i
$926$			12.2192i			0.401549i
$927$		0			0
$928$	−5.32498			−0.174801
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	−0.527097	−	0.849805i	$-0.676720\pi$
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	0.999501	+	0.0315768i	$0.0100529\pi$
$930$		0			0
$931$		0			0
$932$	5.57664	−	3.21967i	0.182669	−	0.105464i
$933$		0			0
$934$	−26.6835	−	15.4057i	−0.873112	−	0.504091i
$935$		−	21.2713i		−	0.695646i
$936$		0			0
$937$			53.6825i			1.75373i	0.480736	+	0.876865i	$0.340369\pi$
$937$			53.6825i			1.75373i	−0.480736	+	0.876865i	$0.659631\pi$
$938$		0			0
$939$		0			0
$940$	4.58996	+	7.95004i	0.149708	+	0.259302i
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	−0.948693	−	0.316200i	$-0.897593\pi$
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	0.200509	−	0.979692i	$-0.435740\pi$
$942$		0			0
$943$	−0.376324	−	0.217271i	−0.0122548	−	0.00707530i
$944$	−1.67386			−0.0544796
$945$		0			0
$946$	48.4954			1.57672
$947$	−25.0440	−	14.4591i	−0.813820	−	0.469859i	0.0344607	−	0.999406i	$-0.489029\pi$
$947$	−25.0440	−	14.4591i	−0.813820	−	0.469859i	−0.848281	+	0.529547i	$0.822362\pi$
$948$		0			0
$949$	−5.41390	−	9.37715i	−0.175743	−	0.304395i
$950$	−9.07623	−	15.7205i	−0.294472	−	0.510040i
$951$		0			0
$952$		0			0
$953$		−	12.8715i		−	0.416949i	−0.978028	−	0.208475i	$-0.933150\pi$
$953$		−	12.8715i		−	0.416949i	0.978028	−	0.208475i	$-0.0668498\pi$
$954$		0			0
$955$		−	21.3478i		−	0.690798i
$956$	4.01452	+	2.31778i	0.129839	+	0.0749624i
$957$		0			0
$958$	−36.1560	+	20.8747i	−1.16815	+	0.674430i
$959$		0			0
$960$		0			0
$961$	3.51314	−	6.08494i	0.113327	−	0.196288i
$962$	−2.12036			−0.0683633
$963$		0			0
$964$		−	10.4944i		−	0.338003i
$965$	9.64402	−	16.7039i	0.310452	−	0.537719i
$966$		0			0
$967$	3.11725	+	5.39923i	0.100244	+	0.173627i	0.911785	−	0.410668i	$-0.134704\pi$
$967$	3.11725	+	5.39923i	0.100244	+	0.173627i	−0.811541	+	0.584295i	$0.801371\pi$
$968$	17.3769	−	10.0326i	0.558516	−	0.322459i
$969$		0			0
$970$	−5.73393	+	9.93146i	−0.184105	+	0.318880i
$971$	−39.3727			−1.26353			−0.631764	−	0.775160i	$-0.717669\pi$
$971$	−39.3727			−1.26353			−0.631764	+	0.775160i	$0.717669\pi$
$972$		0			0
$973$		0			0
$974$	18.3306	+	10.5832i	0.587349	+	0.339106i
$975$		0			0
$976$	4.47927	−	2.58611i	0.143378	−	0.0827793i
$977$	23.2474	−	13.4219i	0.743751	−	0.429405i	−0.0796807	−	0.996820i	$-0.525390\pi$
$977$	23.2474	−	13.4219i	0.743751	−	0.429405i	0.823431	+	0.567416i	$0.192057\pi$
$978$		0			0
$979$	−19.8685	−	11.4711i	−0.635001	−	0.366618i
$980$		0			0
$981$		0			0
$982$	37.3463			1.19177
$983$	−5.98457	+	10.3656i	−0.190878	+	0.330611i	−0.945541	−	0.325502i	$-0.894467\pi$
$983$	−5.98457	+	10.3656i	−0.190878	+	0.330611i	0.754663	+	0.656112i	$0.227800\pi$
$984$		0			0
$985$	−3.87499	+	2.23723i	−0.123467	+	0.0712839i
$986$	10.5044	+	18.1942i	0.334530	+	0.579423i
$987$		0			0
$988$	9.71873	−	16.8333i	0.309194	−	0.535540i
$989$			23.0865i			0.734107i
$990$		0			0
$991$	10.8084			0.343340			0.171670	−	0.985154i	$-0.445084\pi$
$991$	10.8084			0.343340			0.171670	+	0.985154i	$0.445084\pi$
$992$	−3.08327	+	5.34038i	−0.0978940	+	0.169557i
$993$		0			0
$994$		0			0
$995$	17.5109	−	10.1099i	0.555132	−	0.320506i
$996$		0			0
$997$	11.6653	+	6.73498i	0.369445	+	0.213299i	0.673216	−	0.739446i	$-0.264912\pi$
$997$	11.6653	+	6.73498i	0.369445	+	0.213299i	−0.303771	+	0.952745i	$0.598246\pi$
$998$			27.4197i			0.867956i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.b.1763.2		16
3.2	odd	2		882.2.m.b.587.6		16
7.2	even	3		378.2.l.a.143.6		16
7.3	odd	6		378.2.t.a.89.6		16
7.4	even	3		2646.2.t.b.1979.7		16
7.5	odd	6		2646.2.l.a.521.7		16
7.6	odd	2		2646.2.m.a.1763.3		16
9.4	even	3		882.2.m.a.293.7		16
9.5	odd	6		2646.2.m.a.881.3		16
21.2	odd	6		126.2.l.a.101.3	yes	16
21.5	even	6		882.2.l.b.227.2		16
21.11	odd	6		882.2.t.a.803.4		16
21.17	even	6		126.2.t.a.47.1	yes	16
21.20	even	2		882.2.m.a.587.7		16
28.3	even	6		3024.2.df.c.1601.4		16
28.23	odd	6		3024.2.ca.c.2033.4		16
63.2	odd	6		1134.2.k.a.647.3		16
63.4	even	3		882.2.l.b.509.6		16
63.5	even	6		2646.2.t.b.2285.7		16
63.13	odd	6		882.2.m.b.293.6		16
63.16	even	3		1134.2.k.b.647.6		16
63.23	odd	6		378.2.t.a.17.6		16
63.31	odd	6		126.2.l.a.5.7	✓	16
63.32	odd	6		2646.2.l.a.1097.3		16
63.38	even	6		1134.2.k.b.971.6		16
63.40	odd	6		882.2.t.a.815.4		16
63.41	even	6	inner	2646.2.m.b.881.2		16
63.52	odd	6		1134.2.k.a.971.3		16
63.58	even	3		126.2.t.a.59.1	yes	16
63.59	even	6		378.2.l.a.341.2		16
84.23	even	6		1008.2.ca.c.353.5		16
84.59	odd	6		1008.2.df.c.929.7		16
252.23	even	6		3024.2.df.c.17.4		16
252.31	even	6		1008.2.ca.c.257.5		16
252.59	odd	6		3024.2.ca.c.2609.4		16
252.247	odd	6		1008.2.df.c.689.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	63.31	odd	6
126.2.l.a.101.3	yes	16	21.2	odd	6
126.2.t.a.47.1	yes	16	21.17	even	6
126.2.t.a.59.1	yes	16	63.58	even	3
378.2.l.a.143.6		16	7.2	even	3
378.2.l.a.341.2		16	63.59	even	6
378.2.t.a.17.6		16	63.23	odd	6
378.2.t.a.89.6		16	7.3	odd	6
882.2.l.b.227.2		16	21.5	even	6
882.2.l.b.509.6		16	63.4	even	3
882.2.m.a.293.7		16	9.4	even	3
882.2.m.a.587.7		16	21.20	even	2
882.2.m.b.293.6		16	63.13	odd	6
882.2.m.b.587.6		16	3.2	odd	2
882.2.t.a.803.4		16	21.11	odd	6
882.2.t.a.815.4		16	63.40	odd	6
1008.2.ca.c.257.5		16	252.31	even	6
1008.2.ca.c.353.5		16	84.23	even	6
1008.2.df.c.689.7		16	252.247	odd	6
1008.2.df.c.929.7		16	84.59	odd	6
1134.2.k.a.647.3		16	63.2	odd	6
1134.2.k.a.971.3		16	63.52	odd	6
1134.2.k.b.647.6		16	63.16	even	3
1134.2.k.b.971.6		16	63.38	even	6
2646.2.l.a.521.7		16	7.5	odd	6
2646.2.l.a.1097.3		16	63.32	odd	6
2646.2.m.a.881.3		16	9.5	odd	6
2646.2.m.a.1763.3		16	7.6	odd	2
2646.2.m.b.881.2		16	63.41	even	6	inner
2646.2.m.b.1763.2		16	1.1	even	1	trivial
2646.2.t.b.1979.7		16	7.4	even	3
2646.2.t.b.2285.7		16	63.5	even	6
3024.2.ca.c.2033.4		16	28.23	odd	6
3024.2.ca.c.2609.4		16	252.59	odd	6
3024.2.df.c.17.4		16	252.23	even	6
3024.2.df.c.1601.4		16	28.3	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 - 0.837727i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 - 0.837727i) q^{5} -1.00000i q^{8} +0.967324i q^{10} +(4.82689 + 2.78681i) q^{11} +(-3.76893 + 2.17600i) q^{13} +(-0.500000 + 0.866025i) q^{16} +3.94535 q^{17} +4.46634i q^{19} +(0.483662 - 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +(2.29786 - 1.32667i) q^{23} +(2.03214 - 3.51977i) q^{25} +4.35199 q^{26} +(-4.61157 - 2.66249i) q^{29} +(-5.34038 + 3.08327i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.41677 - 1.97267i) q^{34} -0.487217 q^{37} +(2.23317 - 3.86796i) q^{38} +(-0.837727 + 0.483662i) q^{40} +(-0.0818856 - 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} +5.57361i q^{44} -2.65334 q^{46} +(-4.74500 + 8.21859i) q^{47} +(-3.51977 + 2.03214i) q^{50} +(-3.76893 - 2.17600i) q^{52} -2.01518i q^{53} -5.39149i q^{55} +(2.66249 + 4.61157i) q^{58} +(0.836931 + 1.44961i) q^{59} +(-4.47927 - 2.58611i) q^{61} +6.16655 q^{62} -1.00000 q^{64} +(3.64578 + 2.10489i) q^{65} +(2.72126 + 4.71336i) q^{67} +(1.97267 + 3.41677i) q^{68} +3.64006i q^{71} +2.48801i q^{73} +(0.421942 + 0.243608i) q^{74} +(-3.86796 + 2.23317i) q^{76} +(-2.30121 + 3.98581i) q^{79} +0.967324 q^{80} +0.163771i q^{82} +(4.20979 - 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(7.53520 - 4.35045i) q^{86} +(2.78681 - 4.82689i) q^{88} -4.11622 q^{89} +(2.29786 + 1.32667i) q^{92} +(8.21859 - 4.74500i) q^{94} +(3.74157 - 2.16020i) q^{95} +(10.2669 + 5.92762i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 12 q^{11} + 6 q^{13} - 8 q^{16} - 36 q^{17} - 6 q^{23} - 8 q^{25} + 24 q^{26} - 6 q^{29} + 6 q^{31} + 4 q^{37} + 6 q^{41} - 2 q^{43} - 12 q^{46} - 18 q^{47} + 12 q^{50} + 6 q^{52} + 6 q^{58} + 30 q^{59} - 60 q^{61} - 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} - 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{89} - 6 q^{92} - 66 q^{95} + 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^11 + 6 * q^13 - 8 * q^16 - 36 * q^17 - 6 * q^23 - 8 * q^25 + 24 * q^26 - 6 * q^29 + 6 * q^31 + 4 * q^37 + 6 * q^41 - 2 * q^43 - 12 * q^46 - 18 * q^47 + 12 * q^50 + 6 * q^52 + 6 * q^58 + 30 * q^59 - 60 * q^61 - 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^89 - 6 * q^92 - 66 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

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