LMFDB - Embedded newform 252.9.z.c.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (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:	$102.659409735$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 1442 x^{8} + 59551 x^{7} + 2229058 x^{6} + 41253567 x^{5} + 582209889 x^{4} + \cdots + 63214027776 $ x^10 - x^9 + 1442x^8 + 59551x^7 + 2229058x^6 + 41253567x^5 + 582209889x^4 + 4552713792x^3 + 25685059104x^2 + 45666643968x + 63214027776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{9}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$23.4172 - 40.5598i$ of defining polynomial
Character	$\chi$	$=$	252.145
Dual form			252.9.z.c.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-327.308 - 188.971i) q^{5} +(-894.589 + 2228.12i) q^{7} +O(q^{10})$	$q+(-327.308 - 188.971i) q^{5} +(-894.589 + 2228.12i) q^{7} +(9669.77 + 16748.5i) q^{11} -48446.7i q^{13} +(-4752.58 + 2743.90i) q^{17} +(-71330.2 - 41182.5i) q^{19} +(99846.4 - 172939. i) q^{23} +(-123892. - 214587. i) q^{25} -729518. q^{29} +(-657851. + 379810. i) q^{31} +(713857. - 560229. i) q^{35} +(-1.20997e6 + 2.09573e6i) q^{37} +2.65776e6i q^{41} +3.43503e6 q^{43} +(3.34472e6 + 1.93107e6i) q^{47} +(-4.16422e6 - 3.98650e6i) q^{49} +(1.43200e6 + 2.48030e6i) q^{53} -7.30924e6i q^{55} +(1.34642e7 - 7.77355e6i) q^{59} +(-8.84904e6 - 5.10899e6i) q^{61} +(-9.15504e6 + 1.58570e7i) q^{65} +(3.64879e6 + 6.31988e6i) q^{67} +4.30195e7 q^{71} +(1.32896e7 - 7.67277e6i) q^{73} +(-4.59682e7 + 6.56234e6i) q^{77} +(-1.11705e7 + 1.93479e7i) q^{79} -8.50228e7i q^{83} +2.07408e6 q^{85} +(2.69746e7 + 1.55738e7i) q^{89} +(1.07945e8 + 4.33399e7i) q^{91} +(1.55646e7 + 2.69587e7i) q^{95} -9.56779e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) $ 10 * q + 837 * q^5 + 1526 * q^7	$ 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) $ 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−327.308	−	188.971i	−0.523693	−	0.302354i	0.214751	−	0.976669i	$-0.431106\pi$
$5$	−327.308	−	188.971i	−0.523693	−	0.302354i	−0.738444	+	0.674314i	$0.764439\pi$
$6$		0			0
$7$	−894.589	+	2228.12i	−0.372590	+	0.927996i
$7$	−894.589	+	2228.12i	−0.372590	+	0.927996i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	9669.77	+	16748.5i	0.660459	+	1.14395i	0.980495	+	0.196543i	$0.0629714\pi$
$11$	9669.77	+	16748.5i	0.660459	+	1.14395i	−0.320037	+	0.947405i	$0.603695\pi$
$12$		0			0
$13$		−	48446.7i		−	1.69625i	−0.529793	−	0.848127i	$-0.677731\pi$
$13$		−	48446.7i		−	1.69625i	0.529793	−	0.848127i	$-0.322269\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4752.58	+	2743.90i	−0.0569028	+	0.0328529i	−0.528182	−	0.849131i	$-0.677126\pi$
$17$	−4752.58	+	2743.90i	−0.0569028	+	0.0328529i	0.471279	+	0.881984i	$0.343793\pi$
$18$		0			0
$19$	−71330.2	−	41182.5i	−0.547342	−	0.316008i	0.200707	−	0.979651i	$-0.435676\pi$
$19$	−71330.2	−	41182.5i	−0.547342	−	0.316008i	−0.748049	+	0.663643i	$0.769009\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	99846.4	−	172939.i	0.356797	−	0.617990i	−0.630627	−	0.776086i	$-0.717202\pi$
$23$	99846.4	−	172939.i	0.356797	−	0.617990i	0.987424	+	0.158096i	$0.0505355\pi$
$24$		0			0
$25$	−123892.	−	214587.i	−0.317164	−	0.549344i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−729518.			−1.03144			−0.515720	−	0.856757i	$-0.672475\pi$
$29$	−729518.			−1.03144			−0.515720	+	0.856757i	$0.672475\pi$
$30$		0			0
$31$	−657851.	+	379810.i	−0.712329	+	0.411263i	−0.811923	−	0.583765i	$-0.801579\pi$
$31$	−657851.	+	379810.i	−0.712329	+	0.411263i	0.0995939	+	0.995028i	$0.468246\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	713857.	−	560229.i	0.475706	−	0.373331i
$36$		0			0
$37$	−1.20997e6	+	2.09573e6i	−0.645606	+	1.11822i	0.338555	+	0.940947i	$0.390062\pi$
$37$	−1.20997e6	+	2.09573e6i	−0.645606	+	1.11822i	−0.984161	+	0.177276i	$0.943271\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			2.65776e6i			0.940547i	0.882521	+	0.470274i	$0.155845\pi$
$41$			2.65776e6i			0.940547i	−0.882521	+	0.470274i	$0.844155\pi$
$42$		0			0
$43$	3.43503e6			1.00475			0.502374	−	0.864651i	$-0.332460\pi$
$43$	3.43503e6			1.00475			0.502374	+	0.864651i	$0.332460\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.34472e6	+	1.93107e6i	0.685437	+	0.395738i	0.801901	−	0.597458i	$-0.203822\pi$
$47$	3.34472e6	+	1.93107e6i	0.685437	+	0.395738i	−0.116463	+	0.993195i	$0.537156\pi$
$48$		0			0
$49$	−4.16422e6	−	3.98650e6i	−0.722353	−	0.691525i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.43200e6	+	2.48030e6i	0.181485	+	0.314341i	0.942386	−	0.334526i	$-0.108576\pi$
$53$	1.43200e6	+	2.48030e6i	0.181485	+	0.314341i	−0.760901	+	0.648868i	$0.775243\pi$
$54$		0			0
$55$		−	7.30924e6i		−	0.798770i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.34642e7	−	7.77355e6i	1.11115	−	0.641522i	0.172022	−	0.985093i	$-0.444970\pi$
$59$	1.34642e7	−	7.77355e6i	1.11115	−	0.641522i	0.939127	+	0.343571i	$0.111637\pi$
$60$		0			0
$61$	−8.84904e6	−	5.10899e6i	−0.639112	−	0.368991i	0.145161	−	0.989408i	$-0.453630\pi$
$61$	−8.84904e6	−	5.10899e6i	−0.639112	−	0.368991i	−0.784272	+	0.620417i	$0.786963\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.15504e6	+	1.58570e7i	−0.512869	+	0.888316i
$66$		0			0
$67$	3.64879e6	+	6.31988e6i	0.181071	+	0.313624i	0.942246	−	0.334923i	$-0.108710\pi$
$67$	3.64879e6	+	6.31988e6i	0.181071	+	0.313624i	−0.761174	+	0.648547i	$0.775377\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.30195e7			1.69290			0.846451	−	0.532466i	$-0.178735\pi$
$71$	4.30195e7			1.69290			0.846451	+	0.532466i	$0.178735\pi$
$72$		0			0
$73$	1.32896e7	−	7.67277e6i	0.467973	−	0.270185i	−0.247418	−	0.968909i	$-0.579582\pi$
$73$	1.32896e7	−	7.67277e6i	0.467973	−	0.270185i	0.715391	+	0.698724i	$0.246249\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.59682e7	+	6.56234e6i	−1.30766	+	0.186679i
$78$		0			0
$79$	−1.11705e7	+	1.93479e7i	−0.286790	+	0.496735i	−0.973042	−	0.230629i	$-0.925922\pi$
$79$	−1.11705e7	+	1.93479e7i	−0.286790	+	0.496735i	0.686252	+	0.727364i	$0.259255\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	8.50228e7i		−	1.79153i	−0.444533	−	0.895763i	$-0.646630\pi$
$83$		−	8.50228e7i		−	1.79153i	0.444533	−	0.895763i	$-0.353370\pi$
$84$		0			0
$85$	2.07408e6			0.0397328
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.69746e7	+	1.55738e7i	0.429927	+	0.248219i	0.699316	−	0.714813i	$-0.253488\pi$
$89$	2.69746e7	+	1.55738e7i	0.429927	+	0.248219i	−0.269388	+	0.963032i	$0.586821\pi$
$90$		0			0
$91$	1.07945e8	+	4.33399e7i	1.57412	+	0.632008i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.55646e7	+	2.69587e7i	0.191093	+	0.330983i
$96$		0			0
$97$		−	9.56779e7i		−	1.08075i	−0.841425	−	0.540375i	$-0.818283\pi$
$97$		−	9.56779e7i		−	1.08075i	0.841425	−	0.540375i	$-0.181717\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.66653e7	−	5.00362e7i	0.832836	−	0.480838i	−0.0219866	−	0.999758i	$-0.506999\pi$
$101$	8.66653e7	−	5.00362e7i	0.832836	−	0.480838i	0.854823	+	0.518920i	$0.173666\pi$
$102$		0			0
$103$	−9.69279e7	−	5.59614e7i	−0.861192	−	0.497209i	0.00321926	−	0.999995i	$-0.498975\pi$
$103$	−9.69279e7	−	5.59614e7i	−0.861192	−	0.497209i	−0.864411	+	0.502785i	$0.832309\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.73411e7	+	1.51279e8i	−0.666321	+	1.15410i	0.312605	+	0.949883i	$0.398798\pi$
$107$	−8.73411e7	+	1.51279e8i	−0.666321	+	1.15410i	−0.978925	+	0.204218i	$0.934535\pi$
$108$		0			0
$109$	1.12720e8	+	1.95236e8i	0.798535	+	1.38310i	0.920570	+	0.390577i	$0.127725\pi$
$109$	1.12720e8	+	1.95236e8i	0.798535	+	1.38310i	−0.122035	+	0.992526i	$0.538942\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.21183e8			1.35655			0.678277	−	0.734806i	$-0.262727\pi$
$113$	2.21183e8			1.35655			0.678277	+	0.734806i	$0.262727\pi$
$114$		0			0
$115$	−6.53611e7	+	3.77362e7i	−0.373704	+	0.215758i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.86213e6	−	1.30440e7i	−0.00928588	−	0.0650462i
$120$		0			0
$121$	−7.98296e7	+	1.38269e8i	−0.372411	+	0.645035i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.41282e8i			0.988292i
$126$		0			0
$127$	4.34179e8			1.66899			0.834495	−	0.551016i	$-0.185760\pi$
$127$	4.34179e8			1.66899			0.834495	+	0.551016i	$0.185760\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.33866e8	+	7.72876e7i	0.454554	+	0.262437i	0.709752	−	0.704452i	$-0.248807\pi$
$131$	1.33866e8	+	7.72876e7i	0.454554	+	0.262437i	−0.255198	+	0.966889i	$0.582141\pi$
$132$		0			0
$133$	1.55571e8	−	1.22091e8i	0.497189	−	0.390190i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.70378e8	−	4.68308e8i	−0.767519	−	1.32938i	−0.938905	−	0.344178i	$-0.888158\pi$
$137$	−2.70378e8	−	4.68308e8i	−0.767519	−	1.32938i	0.171386	−	0.985204i	$-0.445176\pi$
$138$		0			0
$139$		−	4.03527e8i		−	1.08097i	−0.841354	−	0.540484i	$-0.818241\pi$
$139$		−	4.03527e8i		−	1.08097i	0.841354	−	0.540484i	$-0.181759\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.11411e8	−	4.68469e8i	1.94043	−	1.12031i
$144$		0			0
$145$	2.38777e8	+	1.37858e8i	0.540158	+	0.311860i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.20512e8	−	7.28348e8i	0.853166	−	1.47773i	−0.0251707	−	0.999683i	$-0.508013\pi$
$149$	4.20512e8	−	7.28348e8i	0.853166	−	1.47773i	0.878336	−	0.478043i	$-0.158654\pi$
$150$		0			0
$151$	1.71087e8	+	2.96331e8i	0.329085	+	0.569992i	0.982331	−	0.187154i	$-0.0599264\pi$
$151$	1.71087e8	+	2.96331e8i	0.329085	+	0.569992i	−0.653246	+	0.757146i	$0.726593\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.87093e8			0.497389
$156$		0			0
$157$	4.37023e8	−	2.52315e8i	0.719292	−	0.415284i	−0.0951999	−	0.995458i	$-0.530349\pi$
$157$	4.37023e8	−	2.52315e8i	0.719292	−	0.415284i	0.814492	+	0.580175i	$0.197016\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.96007e8	+	3.77179e8i	0.440554	+	0.561363i
$162$		0			0
$163$	3.08409e8	−	5.34179e8i	0.436894	−	0.756723i	−0.560554	−	0.828118i	$-0.689412\pi$
$163$	3.08409e8	−	5.34179e8i	0.436894	−	0.756723i	0.997448	+	0.0713951i	$0.0227451\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			1.27129e9i			1.63448i	0.576300	+	0.817239i	$0.304496\pi$
$167$			1.27129e9i			1.63448i	−0.576300	+	0.817239i	$0.695504\pi$
$168$		0			0
$169$	−1.53135e9			−1.87728
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.10198e9	+	6.36226e8i	1.23023	+	0.710276i	0.967079	−	0.254478i	$-0.0819036\pi$
$173$	1.10198e9	+	6.36226e8i	1.23023	+	0.710276i	0.263155	+	0.964754i	$0.415237\pi$
$174$		0			0
$175$	5.88959e8	−	8.40787e7i	0.627961	−	0.0896466i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.01757e9	+	1.76248e9i	0.991175	+	1.71677i	0.610387	+	0.792103i	$0.291014\pi$
$179$	1.01757e9	+	1.76248e9i	0.991175	+	1.71677i	0.380788	+	0.924662i	$0.375653\pi$
$180$		0			0
$181$			9.83706e8i			0.916539i	0.888813	+	0.458269i	$0.151531\pi$
$181$			9.83706e8i			0.916539i	−0.888813	+	0.458269i	$0.848469\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.92066e8	−	4.57299e8i	0.676199	−	0.390404i
$186$		0			0
$187$	−9.19128e7	−	5.30659e7i	−0.0751639	−	0.0433959i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.66014e8	−	2.87545e8i	0.124742	−	0.216059i	−0.796890	−	0.604124i	$-0.793523\pi$
$191$	1.66014e8	−	2.87545e8i	0.124742	−	0.216059i	0.921632	+	0.388065i	$0.126857\pi$
$192$		0			0
$193$	2.85509e8	+	4.94516e8i	0.205774	+	0.356411i	0.950379	−	0.311094i	$-0.100696\pi$
$193$	2.85509e8	+	4.94516e8i	0.205774	+	0.356411i	−0.744605	+	0.667505i	$0.767362\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.79680e8			0.384878			0.192439	−	0.981309i	$-0.438360\pi$
$197$	5.79680e8			0.384878			0.192439	+	0.981309i	$0.438360\pi$
$198$		0			0
$199$	5.30497e8	−	3.06282e8i	0.338275	−	0.195303i	−0.321234	−	0.947000i	$-0.604098\pi$
$199$	5.30497e8	−	3.06282e8i	0.338275	−	0.195303i	0.659509	+	0.751697i	$0.270764\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.52619e8	−	1.62545e9i	0.384304	−	0.957172i
$204$		0			0
$205$	5.02241e8	−	8.69907e8i	0.284378	−	0.492558i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	1.59290e9i		−	0.834841i
$210$		0			0
$211$	−2.96142e8			−0.149407			−0.0747034	−	0.997206i	$-0.523801\pi$
$211$	−2.96142e8			−0.149407			−0.0747034	+	0.997206i	$0.523801\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.12431e9	−	6.49123e8i	−0.526179	−	0.303790i
$216$		0			0
$217$	−2.57756e8	−	1.80554e9i	−0.116244	−	0.814271i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.32933e8	+	2.30247e8i	0.0557268	+	0.0965216i
$222$		0			0
$223$			1.61451e9i			0.652862i	0.945221	+	0.326431i	$0.105846\pi$
$223$			1.61451e9i			0.652862i	−0.945221	+	0.326431i	$0.894154\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.24050e7	−	5.33501e7i	0.0348010	−	0.0200924i	−0.482499	−	0.875897i	$-0.660271\pi$
$227$	9.24050e7	−	5.33501e7i	0.0348010	−	0.0200924i	0.517300	+	0.855804i	$0.326937\pi$
$228$		0			0
$229$	4.19529e9	+	2.42215e9i	1.52553	+	0.880763i	0.999542	+	0.0302696i	$0.00963658\pi$
$229$	4.19529e9	+	2.42215e9i	1.52553	+	0.880763i	0.525985	+	0.850494i	$0.323697\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.88395e8	−	1.19234e9i	0.233568	−	0.404552i	−0.725287	−	0.688446i	$-0.758293\pi$
$233$	6.88395e8	−	1.19234e9i	0.233568	−	0.404552i	0.958856	+	0.283894i	$0.0916264\pi$
$234$		0			0
$235$	−7.29835e8	−	1.26411e9i	−0.239306	−	0.414490i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.43290e9			−0.745647			−0.372824	−	0.927902i	$-0.621610\pi$
$239$	−2.43290e9			−0.745647			−0.372824	+	0.927902i	$0.621610\pi$
$240$		0			0
$241$	−7.63518e7	+	4.40817e7i	−0.0226335	+	0.0130674i	−0.511274	−	0.859418i	$-0.670826\pi$
$241$	−7.63518e7	+	4.40817e7i	−0.0226335	+	0.0130674i	0.488641	+	0.872485i	$0.337493\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.09648e8	+	2.09173e9i	0.169206	+	0.580553i
$246$		0			0
$247$	−1.99516e9	+	3.45571e9i	−0.536030	+	0.928431i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			2.17652e8i			0.0548362i	0.999624	+	0.0274181i	$0.00872854\pi$
$251$			2.17652e8i			0.0548362i	−0.999624	+	0.0274181i	$0.991271\pi$
$252$		0			0
$253$	3.86197e9			0.942598
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.91538e8	−	5.72465e8i	−0.227288	−	0.131225i	0.382032	−	0.924149i	$-0.375224\pi$
$257$	−9.91538e8	−	5.72465e8i	−0.227288	−	0.131225i	−0.609320	+	0.792924i	$0.708558\pi$
$258$		0			0
$259$	−3.58711e9	−	4.57077e9i	−0.797160	−	1.01576i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.63387e9	+	4.56199e9i	0.550517	+	0.953524i	0.998237	+	0.0593498i	$0.0189027\pi$
$263$	2.63387e9	+	4.56199e9i	0.550517	+	0.953524i	−0.447720	+	0.894174i	$0.647764\pi$
$264$		0			0
$265$		−	1.08243e9i		−	0.219491i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.99560e9	+	3.46156e9i	−1.14505	+	0.661093i	−0.947675	−	0.319236i	$-0.896574\pi$
$269$	−5.99560e9	+	3.46156e9i	−1.14505	+	0.661093i	−0.197371	+	0.980329i	$0.563240\pi$
$270$		0			0
$271$	−1.03483e9	−	5.97462e8i	−0.191864	−	0.110773i	0.400991	−	0.916082i	$-0.368666\pi$
$271$	−1.03483e9	−	5.97462e8i	−0.191864	−	0.110773i	−0.592855	+	0.805309i	$0.701999\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.39602e9	−	4.15002e9i	0.418947	−	0.725638i
$276$		0			0
$277$	5.25716e8	+	9.10566e8i	0.0892960	+	0.154665i	0.907214	−	0.420670i	$-0.138205\pi$
$277$	5.25716e8	+	9.10566e8i	0.0892960	+	0.154665i	−0.817918	+	0.575335i	$0.804872\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.39931e9			0.224434			0.112217	−	0.993684i	$-0.464205\pi$
$281$	1.39931e9			0.224434			0.112217	+	0.993684i	$0.464205\pi$
$282$		0			0
$283$	8.63101e9	−	4.98311e9i	1.34560	−	0.776882i	0.357976	−	0.933731i	$-0.383467\pi$
$283$	8.63101e9	−	4.98311e9i	1.34560	−	0.776882i	0.987623	+	0.156849i	$0.0501335\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.92181e9	−	2.37760e9i	−0.872824	−	0.350439i
$288$		0			0
$289$	−3.47282e9	+	6.01510e9i	−0.497841	+	0.862287i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	9.23400e9i		−	1.25291i	−0.779458	−	0.626454i	$-0.784506\pi$
$293$		−	9.23400e9i		−	1.25291i	0.779458	−	0.626454i	$-0.215494\pi$
$294$		0			0
$295$	−5.87592e9			−0.775867
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.37833e9	−	4.83723e9i	−1.04827	−	0.605218i
$300$		0			0
$301$	−3.07294e9	+	7.65366e9i	−0.374359	+	0.932402i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.93091e9	+	3.34443e9i	0.223132	+	0.386476i
$306$		0			0
$307$		−	1.40040e8i		−	0.0157652i	−0.999969	−	0.00788259i	$-0.997491\pi$
$307$		−	1.40040e8i		−	0.0157652i	0.999969	−	0.00788259i	$-0.00250913\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.15689e9	+	3.55468e9i	−0.658143	+	0.379979i	−0.791569	−	0.611080i	$-0.790735\pi$
$311$	−6.15689e9	+	3.55468e9i	−0.658143	+	0.379979i	0.133426	+	0.991059i	$0.457402\pi$
$312$		0			0
$313$	−6.86699e8	−	3.96466e8i	−0.0715466	−	0.0413075i	0.463800	−	0.885940i	$-0.346486\pi$
$313$	−6.86699e8	−	3.96466e8i	−0.0715466	−	0.0413075i	−0.535347	+	0.844633i	$0.679819\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.37244e9	+	1.45015e10i	−0.829115	+	1.43607i	0.0696182	+	0.997574i	$0.477822\pi$
$317$	−8.37244e9	+	1.45015e10i	−0.829115	+	1.43607i	−0.898733	+	0.438496i	$0.855511\pi$
$318$		0			0
$319$	−7.05427e9	−	1.22184e10i	−0.681223	−	1.17991i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.52003e8			0.0415271
$324$		0			0
$325$	−1.03961e10	+	6.00216e9i	−0.931826	+	0.537990i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.29481e9	+	5.72491e9i	−0.622630	+	0.488635i
$330$		0			0
$331$	−6.81682e9	+	1.18071e10i	−0.567897	+	0.983627i	0.428876	+	0.903363i	$0.358910\pi$
$331$	−6.81682e9	+	1.18071e10i	−0.567897	+	0.983627i	−0.996774	+	0.0802640i	$0.974424\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	2.75806e9i		−	0.218990i
$336$		0			0
$337$	−1.81834e10			−1.40979			−0.704897	−	0.709309i	$-0.749007\pi$
$337$	−1.81834e10			−1.40979			−0.704897	+	0.709309i	$0.749007\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.27225e10	−	7.34536e9i	−0.940927	−	0.543245i
$342$		0			0
$343$	1.26077e10	−	5.71210e9i	0.910874	−	0.412685i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.16239e8	−	1.06736e9i	−0.0425041	−	0.0736193i	0.843991	−	0.536358i	$-0.180200\pi$
$347$	−6.16239e8	−	1.06736e9i	−0.0425041	−	0.0736193i	−0.886495	+	0.462738i	$0.846867\pi$
$348$		0			0
$349$		−	1.23418e10i		−	0.831910i	−0.909385	−	0.415955i	$-0.863447\pi$
$349$		−	1.23418e10i		−	0.831910i	0.909385	−	0.415955i	$-0.136553\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.51638e10	−	8.75484e9i	0.976585	−	0.563831i	0.0753473	−	0.997157i	$-0.475993\pi$
$353$	1.51638e10	−	8.75484e9i	0.976585	−	0.563831i	0.901237	+	0.433326i	$0.142660\pi$
$354$		0			0
$355$	−1.40806e10	−	8.12945e9i	−0.886561	−	0.511856i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.45738e8	+	4.25631e8i	−0.0147943	+	0.0256245i	−0.873328	−	0.487133i	$-0.838043\pi$
$359$	−2.45738e8	+	4.25631e8i	−0.0147943	+	0.0256245i	0.858533	+	0.512758i	$0.171376\pi$
$360$		0			0
$361$	−5.09978e9	−	8.83308e9i	−0.300278	−	0.520096i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.79973e9			−0.326766
$366$		0			0
$367$	3.21943e9	−	1.85874e9i	0.177466	−	0.102460i	−0.408636	−	0.912698i	$-0.633995\pi$
$367$	3.21943e9	−	1.85874e9i	0.177466	−	0.102460i	0.586102	+	0.810238i	$0.300662\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.80747e9	+	9.71821e8i	−0.359327	+	0.0512969i
$372$		0			0
$373$	4.50275e9	−	7.79900e9i	0.232618	−	0.402906i	−0.725960	−	0.687737i	$-0.758604\pi$
$373$	4.50275e9	−	7.79900e9i	0.232618	−	0.402906i	0.958578	+	0.284831i	$0.0919376\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			3.53427e10i			1.74958i
$378$		0			0
$379$	1.72072e9			0.0833974			0.0416987	−	0.999130i	$-0.486723\pi$
$379$	1.72072e9			0.0833974			0.0416987	+	0.999130i	$0.486723\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.02302e10	−	5.90640e9i	−0.475432	−	0.274491i	0.243079	−	0.970007i	$-0.421843\pi$
$383$	−1.02302e10	−	5.90640e9i	−0.475432	−	0.274491i	−0.718511	+	0.695516i	$0.755176\pi$
$384$		0			0
$385$	1.62859e10	+	6.53877e9i	0.741255	+	0.297614i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.12760e10	−	1.95307e10i	−0.492445	−	0.852940i	0.507517	−	0.861642i	$-0.330563\pi$
$389$	−1.12760e10	−	1.95307e10i	−0.492445	−	0.852940i	−0.999962	+	0.00870164i	$0.997230\pi$
$390$		0			0
$391$			1.09588e9i			0.0468872i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.31239e9	−	4.22181e9i	0.300380	−	0.173424i
$396$		0			0
$397$	2.50595e10	+	1.44681e10i	1.00881	+	0.582438i	0.910844	−	0.412751i	$-0.135432\pi$
$397$	2.50595e10	+	1.44681e10i	1.00881	+	0.582438i	0.0979687	+	0.995189i	$0.468765\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.68401e10	−	2.91679e10i	0.651280	−	1.12805i	−0.331533	−	0.943444i	$-0.607566\pi$
$401$	1.68401e10	−	2.91679e10i	0.651280	−	1.12805i	0.982813	−	0.184606i	$-0.0591008\pi$
$402$		0			0
$403$	1.84006e10	+	3.18707e10i	0.697607	+	1.20829i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.68005e10			−1.70558
$408$		0			0
$409$	−2.44482e10	+	1.41152e10i	−0.873683	+	0.504421i	−0.868570	−	0.495566i	$-0.834961\pi$
$409$	−2.44482e10	+	1.41152e10i	−0.873683	+	0.504421i	−0.00511242	+	0.999987i	$0.501627\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.27548e9	+	3.69539e10i	0.181327	+	1.27017i
$414$		0			0
$415$	−1.60669e10	+	2.78286e10i	−0.541675	+	0.938209i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			2.39616e10i			0.777426i	0.921359	+	0.388713i	$0.127080\pi$
$419$			2.39616e10i			0.777426i	−0.921359	+	0.388713i	$0.872920\pi$
$420$		0			0
$421$	2.62773e9			0.0836474			0.0418237	−	0.999125i	$-0.486683\pi$
$421$	2.62773e9			0.0836474			0.0418237	+	0.999125i	$0.486683\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.17761e9	+	6.79896e8i	0.0360950	+	0.0208395i
$426$		0			0
$427$	1.92997e10	−	1.51463e10i	0.580549	−	0.455610i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.51439e10	−	2.62300e10i	−0.438863	−	0.760132i	0.558739	−	0.829343i	$-0.311285\pi$
$431$	−1.51439e10	−	2.62300e10i	−0.438863	−	0.760132i	−0.997602	+	0.0692109i	$0.977952\pi$
$432$		0			0
$433$		−	3.52520e10i		−	1.00284i	−0.865204	−	0.501420i	$-0.832811\pi$
$433$		−	3.52520e10i		−	1.00284i	0.865204	−	0.501420i	$-0.167189\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.42441e10	+	8.22385e9i	−0.390580	+	0.225502i
$438$		0			0
$439$	−6.83835e9	−	3.94812e9i	−0.184117	−	0.106300i	0.405109	−	0.914269i	$-0.367234\pi$
$439$	−6.83835e9	−	3.94812e9i	−0.184117	−	0.106300i	−0.589225	+	0.807969i	$0.700567\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.09947e10	−	5.36844e10i	0.804771	−	1.39390i	−0.111675	−	0.993745i	$-0.535622\pi$
$443$	3.09947e10	−	5.36844e10i	0.804771	−	1.39390i	0.916446	−	0.400159i	$-0.131045\pi$
$444$		0			0
$445$	−5.88601e9	−	1.01949e10i	−0.150100	−	0.259981i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	3.41615e10			0.840526			0.420263	−	0.907402i	$-0.361938\pi$
$449$	3.41615e10			0.840526			0.420263	+	0.907402i	$0.361938\pi$
$450$		0			0
$451$	−4.45136e10	+	2.57000e10i	−1.07594	+	0.621192i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.71413e10	−	3.45840e10i	−0.633263	−	0.806919i
$456$		0			0
$457$	3.83643e10	−	6.64489e10i	0.879554	−	1.52343i	0.0277221	−	0.999616i	$-0.491175\pi$
$457$	3.83643e10	−	6.64489e10i	0.879554	−	1.52343i	0.851832	−	0.523816i	$-0.175492\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	1.69291e10i		−	0.374826i	−0.982281	−	0.187413i	$-0.939990\pi$
$461$		−	1.69291e10i		−	0.374826i	0.982281	−	0.187413i	$-0.0600103\pi$
$462$		0			0
$463$	1.31514e10			0.286185			0.143093	−	0.989709i	$-0.454295\pi$
$463$	1.31514e10			0.286185			0.143093	+	0.989709i	$0.454295\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.04029e10	+	1.75531e10i	0.639215	+	0.369051i	0.784312	−	0.620367i	$-0.213016\pi$
$467$	3.04029e10	+	1.75531e10i	0.639215	+	0.369051i	−0.145097	+	0.989417i	$0.546349\pi$
$468$		0			0
$469$	−1.73456e10	+	2.47623e9i	−0.358507	+	0.0511799i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.32160e10	+	5.75318e10i	0.663594	+	1.14938i
$474$		0			0
$475$			2.04088e10i			0.400906i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.02789e10	−	1.74815e10i	0.575172	−	0.332076i	−0.184040	−	0.982919i	$-0.558918\pi$
$479$	3.02789e10	−	1.74815e10i	0.575172	−	0.332076i	0.759213	+	0.650843i	$0.225584\pi$
$480$		0			0
$481$	1.01531e11	+	5.86191e10i	1.89679	+	1.09511i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.80804e10	+	3.13162e10i	−0.326769	+	0.565981i
$486$		0			0
$487$	−4.13971e10	−	7.17018e10i	−0.735959	−	1.27472i	−0.954301	−	0.298846i	$-0.903398\pi$
$487$	−4.13971e10	−	7.17018e10i	−0.735959	−	1.27472i	0.218342	−	0.975872i	$-0.429935\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.23248e10			1.07235			0.536173	−	0.844108i	$-0.319870\pi$
$491$	6.23248e10			1.07235			0.536173	+	0.844108i	$0.319870\pi$
$492$		0			0
$493$	3.46709e9	−	2.00173e9i	0.0586918	−	0.0338857i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.84848e10	+	9.58525e10i	−0.630759	+	1.57101i
$498$		0			0
$499$	7.15575e9	−	1.23941e10i	0.115412	−	0.199900i	−0.802532	−	0.596609i	$-0.796514\pi$
$499$	7.15575e9	−	1.23941e10i	0.115412	−	0.199900i	0.917945	+	0.396709i	$0.129848\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	7.69313e10i		−	1.20180i	−0.799325	−	0.600899i	$-0.794809\pi$
$503$		−	7.69313e10i		−	1.20180i	0.799325	−	0.600899i	$-0.205191\pi$
$504$		0			0
$505$	−3.78217e10			−0.581534
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.47817e10	+	4.31752e10i	1.11410	+	0.643226i	0.939888	−	0.341482i	$-0.110929\pi$
$509$	7.47817e10	+	4.31752e10i	1.11410	+	0.643226i	0.174212	+	0.984708i	$0.444262\pi$
$510$		0			0
$511$	5.20708e9	+	3.64748e10i	0.0763679	+	0.534946i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.11502e10	+	3.66332e10i	0.300667	+	0.520770i
$516$		0			0
$517$			7.46921e10i			1.04547i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.35013e10	−	2.51155e10i	0.590407	−	0.340872i	−0.174851	−	0.984595i	$-0.555944\pi$
$521$	4.35013e10	−	2.51155e10i	0.590407	−	0.340872i	0.765259	+	0.643723i	$0.222611\pi$
$522$		0			0
$523$	3.93369e10	+	2.27112e10i	0.525767	+	0.303552i	0.739291	−	0.673386i	$-0.235161\pi$
$523$	3.93369e10	+	2.27112e10i	0.525767	+	0.303552i	−0.213524	+	0.976938i	$0.568494\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.08433e9	−	3.61016e9i	0.0270223	−	0.0468041i
$528$		0			0
$529$	1.92169e10	+	3.32846e10i	0.245392	+	0.425031i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.28760e11			1.59541
$534$		0			0
$535$	5.71749e10	−	3.30099e10i	0.697895	−	0.402930i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.65010e10	−	1.08293e11i	0.313984	−	1.28306i
$540$		0			0
$541$	−2.94658e10	+	5.10362e10i	−0.343976	+	0.595784i	−0.985167	−	0.171597i	$-0.945107\pi$
$541$	−2.94658e10	+	5.10362e10i	−0.343976	+	0.595784i	0.641191	+	0.767381i	$0.278441\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	8.52032e10i		−	0.965762i
$546$		0			0
$547$	9.83691e10			1.09878			0.549388	−	0.835567i	$-0.314861\pi$
$547$	9.83691e10			1.09878			0.549388	+	0.835567i	$0.314861\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.20366e10	+	3.00434e10i	0.564551	+	0.325943i
$552$		0			0
$553$	−3.31163e10	−	4.21976e10i	−0.354113	−	0.451219i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.69551e10	+	9.86492e10i	0.591714	+	1.02488i	0.994002	+	0.109366i	$0.0348820\pi$
$557$	5.69551e10	+	9.86492e10i	0.591714	+	1.02488i	−0.402287	+	0.915514i	$0.631785\pi$
$558$		0			0
$559$		−	1.66416e11i		−	1.70431i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.01740e10	+	4.62885e10i	−0.797995	+	0.460723i	−0.842770	−	0.538275i	$-0.819076\pi$
$563$	−8.01740e10	+	4.62885e10i	−0.797995	+	0.460723i	0.0447747	+	0.998997i	$0.485743\pi$
$564$		0			0
$565$	−7.23949e10	−	4.17972e10i	−0.710418	−	0.410160i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.57486e8	−	7.92389e8i	0.00436444	−	0.00755943i	−0.863835	−	0.503775i	$-0.831944\pi$
$569$	4.57486e8	−	7.92389e8i	0.00436444	−	0.00755943i	0.868199	+	0.496216i	$0.165277\pi$
$570$		0			0
$571$	−5.01821e10	−	8.69179e10i	−0.472068	−	0.817645i	0.527421	−	0.849604i	$-0.323159\pi$
$571$	−5.01821e10	−	8.69179e10i	−0.472068	−	0.817645i	−0.999489	+	0.0319584i	$0.989826\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.94807e10			−0.452652
$576$		0			0
$577$	9.75665e10	−	5.63301e10i	0.880233	−	0.508203i	0.00949770	−	0.999955i	$-0.496977\pi$
$577$	9.75665e10	−	5.63301e10i	0.880233	−	0.508203i	0.870735	+	0.491752i	$0.163643\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.89441e11	+	7.60605e10i	1.66253	+	0.667505i
$582$		0			0
$583$	−2.76943e10	+	4.79680e10i	−0.239727	+	0.415219i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	1.51553e10i		−	0.127647i	−0.997961	−	0.0638236i	$-0.979671\pi$
$587$		−	1.51553e10i		−	0.127647i	0.997961	−	0.0638236i	$-0.0203295\pi$
$588$		0			0
$589$	6.25662e10			0.519850
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.22390e10	−	4.17072e10i	−0.584189	−	0.337281i	0.178608	−	0.983920i	$-0.442841\pi$
$593$	−7.22390e10	−	4.17072e10i	−0.584189	−	0.337281i	−0.762796	+	0.646639i	$0.776174\pi$
$594$		0			0
$595$	−1.85545e9	+	4.62129e9i	−0.0148041	+	0.0368719i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.83703e10	+	3.18183e10i	0.142695	+	0.247155i	0.928511	−	0.371306i	$-0.121090\pi$
$599$	1.83703e10	+	3.18183e10i	0.142695	+	0.247155i	−0.785816	+	0.618461i	$0.787756\pi$
$600$		0			0
$601$			5.77240e10i			0.442444i	0.975223	+	0.221222i	$0.0710046\pi$
$601$			5.77240e10i			0.442444i	−0.975223	+	0.221222i	$0.928995\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.22577e10	−	3.01710e10i	0.390058	−	0.225200i
$606$		0			0
$607$	−4.58050e10	−	2.64455e10i	−0.337410	−	0.194804i	0.321716	−	0.946836i	$-0.395740\pi$
$607$	−4.58050e10	−	2.64455e10i	−0.337410	−	0.194804i	−0.659126	+	0.752032i	$0.729074\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.35541e10	−	1.62040e11i	0.671271	−	1.16268i
$612$		0			0
$613$	9.82662e10	+	1.70202e11i	0.695925	+	1.20538i	0.969868	+	0.243632i	$0.0783388\pi$
$613$	9.82662e10	+	1.70202e11i	0.695925	+	1.20538i	−0.273943	+	0.961746i	$0.588328\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.78844e11			−1.23405			−0.617027	−	0.786942i	$-0.711663\pi$
$617$	−1.78844e11			−1.23405			−0.617027	+	0.786942i	$0.711663\pi$
$618$		0			0
$619$	3.70567e9	−	2.13947e9i	0.0252408	−	0.0145728i	−0.487326	−	0.873220i	$-0.662028\pi$
$619$	3.70567e9	−	2.13947e9i	0.0252408	−	0.0145728i	0.512567	+	0.858647i	$0.328695\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.88315e10	+	4.61705e10i	−0.390533	+	0.306487i
$624$		0			0
$625$	−2.79992e9	+	4.84961e9i	−0.0183496	+	0.0317824i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.32802e10i		−	0.0848400i
$630$		0			0
$631$	−7.52207e10			−0.474482			−0.237241	−	0.971451i	$-0.576243\pi$
$631$	−7.52207e10			−0.474482			−0.237241	+	0.971451i	$0.576243\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.42110e11	−	8.20474e10i	−0.874038	−	0.504626i
$636$		0			0
$637$	−1.93133e11	+	2.01743e11i	−1.17300	+	1.22529i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.42255e10	+	4.19597e10i	0.143496	+	0.248542i	0.928811	−	0.370554i	$-0.120832\pi$
$641$	2.42255e10	+	4.19597e10i	0.143496	+	0.248542i	−0.785315	+	0.619097i	$0.787499\pi$
$642$		0			0
$643$		−	9.91856e10i		−	0.580236i	−0.956991	−	0.290118i	$-0.906305\pi$
$643$		−	9.91856e10i		−	0.580236i	0.956991	−	0.290118i	$-0.0936946\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.08123e10	+	6.24247e9i	−0.0617021	+	0.0356237i	−0.530534	−	0.847664i	$-0.678008\pi$
$647$	−1.08123e10	+	6.24247e9i	−0.0617021	+	0.0356237i	0.468832	+	0.883288i	$0.344675\pi$
$648$		0			0
$649$	2.60391e11	+	1.50337e11i	1.46773	+	0.847397i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.02174e11	+	1.76970e11i	−0.561936	+	0.973302i	0.435391	+	0.900241i	$0.356610\pi$
$653$	−1.02174e11	+	1.76970e11i	−0.561936	+	0.973302i	−0.997327	+	0.0730610i	$0.976723\pi$
$654$		0			0
$655$	−2.92103e10	−	5.05937e10i	−0.158698	−	0.274873i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.69754e11			−1.43030			−0.715149	−	0.698973i	$-0.753641\pi$
$659$	−2.69754e11			−1.43030			−0.715149	+	0.698973i	$0.753641\pi$
$660$		0			0
$661$	1.16400e11	−	6.72037e10i	0.609745	−	0.352036i	−0.163121	−	0.986606i	$-0.552156\pi$
$661$	1.16400e11	−	6.72037e10i	0.609745	−	0.352036i	0.772866	+	0.634570i	$0.218823\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.39912e10	+	1.05628e10i	−0.378350	+	0.0540125i
$666$		0			0
$667$	−7.28397e10	+	1.26162e11i	−0.368015	+	0.637420i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	1.97611e11i		−	0.974814i
$672$		0			0
$673$	−1.85348e11			−0.903499			−0.451750	−	0.892145i	$-0.649200\pi$
$673$	−1.85348e11			−0.903499			−0.451750	+	0.892145i	$0.649200\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.28495e11	+	1.31922e11i	1.08773	+	0.628003i	0.932972	−	0.359950i	$-0.117206\pi$
$677$	2.28495e11	+	1.31922e11i	1.08773	+	0.628003i	0.154760	+	0.987952i	$0.450539\pi$
$678$		0			0
$679$	2.13182e11	+	8.55925e10i	1.00293	+	0.402677i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.06407e11	−	3.57507e11i	−0.948509	−	1.64287i	−0.748568	−	0.663059i	$-0.769258\pi$
$683$	−2.06407e11	−	3.57507e11i	−0.948509	−	1.64287i	−0.199942	−	0.979808i	$-0.564075\pi$
$684$		0			0
$685$			2.04375e11i			0.928250i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.20163e11	−	6.93759e10i	0.533203	−	0.307845i
$690$		0			0
$691$	−3.41227e11	−	1.97007e11i	−1.49669	−	0.864113i	−0.496694	−	0.867926i	$-0.665453\pi$
$691$	−3.41227e11	−	1.97007e11i	−1.49669	−	0.864113i	−0.999993	+	0.00381313i	$0.998786\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.62550e10	+	1.32078e11i	−0.326835	+	0.566096i
$696$		0			0
$697$	−7.29264e9	−	1.26312e10i	−0.0308997	−	0.0535198i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.63008e11			−1.08917			−0.544587	−	0.838704i	$-0.683314\pi$
$701$	−2.63008e11			−1.08917			−0.544587	+	0.838704i	$0.683314\pi$
$702$		0			0
$703$	1.72615e11	−	9.96592e10i	0.706735	−	0.408034i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.39568e10	+	2.37862e11i	0.135909	+	0.952024i
$708$		0			0
$709$	2.26127e11	−	3.91664e11i	0.894886	−	1.54999i	0.0609414	−	0.998141i	$-0.480590\pi$
$709$	2.26127e11	−	3.91664e11i	0.894886	−	1.54999i	0.833945	−	0.551848i	$-0.186077\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			1.51691e11i			0.586950i
$714$		0			0
$715$	−3.54109e11			−1.35492
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.41212e11	+	1.39264e11i	0.902574	+	0.521102i	0.878035	−	0.478597i	$-0.158855\pi$
$719$	2.41212e11	+	1.39264e11i	0.902574	+	0.521102i	0.0245399	+	0.999699i	$0.492188\pi$
$720$		0			0
$721$	2.11399e11	−	1.65904e11i	0.782280	−	0.613927i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.03815e10	+	1.56545e11i	0.327135	+	0.566615i
$726$		0			0
$727$			1.13459e11i			0.406165i	0.979162	+	0.203083i	$0.0650960\pi$
$727$			1.13459e11i			0.406165i	−0.979162	+	0.203083i	$0.934904\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.63253e10	+	9.42540e9i	−0.0571730	+	0.0330088i
$732$		0			0
$733$	−3.59122e11	−	2.07339e11i	−1.24402	−	0.718234i	−0.274108	−	0.961699i	$-0.588382\pi$
$733$	−3.59122e11	−	2.07339e11i	−1.24402	−	0.718234i	−0.969910	+	0.243465i	$0.921716\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.05659e10	+	1.22224e11i	−0.239180	+	0.414272i
$738$		0			0
$739$	−2.59283e10	−	4.49092e10i	−0.0869354	−	0.150577i	0.819279	−	0.573395i	$-0.194374\pi$
$739$	−2.59283e10	−	4.49092e10i	−0.0869354	−	0.150577i	−0.906214	+	0.422819i	$0.861041\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.16614e11			−1.03890			−0.519451	−	0.854500i	$-0.673863\pi$
$743$	−3.16614e11			−1.03890			−0.519451	+	0.854500i	$0.673863\pi$
$744$		0			0
$745$	−2.75274e11	+	1.58930e11i	−0.893594	+	0.515917i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.58933e11	−	3.29939e11i	−0.822737	−	1.04835i
$750$		0			0
$751$	1.00643e11	−	1.74319e11i	0.316392	−	0.548006i	−0.663341	−	0.748318i	$-0.730862\pi$
$751$	1.00643e11	−	1.74319e11i	0.316392	−	0.548006i	0.979732	+	0.200311i	$0.0641953\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	1.29322e11i		−	0.398001i
$756$		0			0
$757$	−4.64675e10			−0.141503			−0.0707515	−	0.997494i	$-0.522540\pi$
$757$	−4.64675e10			−0.141503			−0.0707515	+	0.997494i	$0.522540\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.01663e11	−	5.86953e10i	−0.303128	−	0.175011i	0.340719	−	0.940165i	$-0.389329\pi$
$761$	−1.01663e11	−	5.86953e10i	−0.303128	−	0.175011i	−0.643847	+	0.765154i	$0.722663\pi$
$762$		0			0
$763$	−5.35847e11	+	7.64966e10i	−1.58104	+	0.225706i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.76603e11	−	6.52295e11i	−1.08818	−	1.88479i
$768$		0			0
$769$		−	3.16824e11i		−	0.905967i	−0.891519	−	0.452984i	$-0.850360\pi$
$769$		−	3.16824e11i		−	0.905967i	0.891519	−	0.452984i	$-0.149640\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.18087e10	−	2.99118e10i	0.145106	−	0.0837769i	−0.425689	−	0.904869i	$-0.639968\pi$
$773$	5.18087e10	−	2.99118e10i	0.145106	−	0.0837769i	0.570795	+	0.821092i	$0.306635\pi$
$774$		0			0
$775$	1.63005e11	+	9.41110e10i	0.451850	+	0.260876i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.09453e11	−	1.89579e11i	0.297221	−	0.514801i
$780$		0			0
$781$	4.15989e11	+	7.20514e11i	1.11809	+	1.93659i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.90721e11			−0.502251
$786$		0			0
$787$	−1.91607e11	+	1.10624e11i	−0.499473	+	0.288371i	−0.728496	−	0.685050i	$-0.759780\pi$
$787$	−1.91607e11	+	1.10624e11i	−0.499473	+	0.288371i	0.229023	+	0.973421i	$0.426447\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.97868e11	+	4.92821e11i	−0.505439	+	1.25888i
$792$		0			0
$793$	−2.47514e11	+	4.28707e11i	−0.625903	+	1.08410i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	2.22900e11i		−	0.552429i	−0.961096	−	0.276215i	$-0.910920\pi$
$797$		−	2.22900e11i		−	0.552429i	0.961096	−	0.276215i	$-0.0890800\pi$
$798$		0			0
$799$	−2.11947e10			−0.0520044
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.57015e11	+	1.48388e11i	0.618154	+	0.356891i
$804$		0			0
$805$	−2.56095e10	−	1.79391e11i	−0.0609842	−	0.427185i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.60307e11	+	4.50865e11i	0.607703	+	1.05257i	0.991618	+	0.129204i	$0.0412422\pi$
$809$	2.60307e11	+	4.50865e11i	0.607703	+	1.05257i	−0.383915	+	0.923368i	$0.625424\pi$
$810$		0			0
$811$		−	7.42722e11i		−	1.71689i	−0.512904	−	0.858446i	$-0.671430\pi$
$811$		−	7.42722e11i		−	1.71689i	0.512904	−	0.858446i	$-0.328570\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.01889e11	+	1.16561e11i	−0.457597	+	0.264194i
$816$		0			0
$817$	−2.45022e11	−	1.41463e11i	−0.549941	−	0.317509i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.95281e11	+	3.38237e11i	−0.429821	+	0.744472i	−0.996857	−	0.0792213i	$-0.974757\pi$
$821$	−1.95281e11	+	3.38237e11i	−0.429821	+	0.744472i	0.567036	+	0.823693i	$0.308090\pi$
$822$		0			0
$823$	3.11169e11	+	5.38960e11i	0.678261	+	1.17478i	0.975504	+	0.219980i	$0.0705993\pi$
$823$	3.11169e11	+	5.38960e11i	0.678261	+	1.17478i	−0.297244	+	0.954802i	$0.596067\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.76465e11			−1.01861			−0.509307	−	0.860585i	$-0.670098\pi$
$827$	−4.76465e11			−1.01861			−0.509307	+	0.860585i	$0.670098\pi$
$828$		0			0
$829$	−5.95189e11	+	3.43632e11i	−1.26019	+	0.727572i	−0.973111	−	0.230335i	$-0.926018\pi$
$829$	−5.95189e11	+	3.43632e11i	−1.26019	+	0.727572i	−0.287080	+	0.957907i	$0.592685\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.07294e10	+	7.51995e9i	0.0638225	+	0.0156183i
$834$		0			0
$835$	2.40238e11	−	4.16104e11i	0.494191	−	0.855964i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	2.54247e11i		−	0.513106i	−0.966530	−	0.256553i	$-0.917413\pi$
$839$		−	2.54247e11i		−	0.513106i	0.966530	−	0.256553i	$-0.0825868\pi$
$840$		0			0
$841$	3.19496e10			0.0638677
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.01224e11	+	2.89382e11i	0.983116	+	0.567602i
$846$		0			0
$847$	−2.36665e11	−	3.01564e11i	−0.459833	−	0.585929i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.41622e11	+	4.18502e11i	0.460701	+	0.797957i
$852$		0			0
$853$			3.25449e11i			0.614733i	0.951591	+	0.307367i	$0.0994478\pi$
$853$			3.25449e11i			0.614733i	−0.951591	+	0.307367i	$0.900552\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.78614e11	−	3.34063e11i	1.07267	−	0.619305i	0.143759	−	0.989613i	$-0.454081\pi$
$857$	5.78614e11	−	3.34063e11i	1.07267	−	0.619305i	0.928909	+	0.370307i	$0.120748\pi$
$858$		0			0
$859$	8.40365e11	+	4.85185e11i	1.54346	+	0.891116i	0.998617	+	0.0525777i	$0.0167437\pi$
$859$	8.40365e11	+	4.85185e11i	1.54346	+	0.891116i	0.544842	+	0.838539i	$0.316590\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.65239e11	+	2.86202e11i	−0.297899	+	0.515976i	−0.975655	−	0.219311i	$-0.929619\pi$
$863$	−1.65239e11	+	2.86202e11i	−0.297899	+	0.515976i	0.677756	+	0.735287i	$0.262952\pi$
$864$		0			0
$865$	−2.40457e11	−	4.16484e11i	−0.429510	−	0.743933i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.32065e11			−0.757652
$870$		0			0
$871$	3.06177e11	−	1.76772e11i	0.531986	−	0.307142i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.37605e11	−	2.15848e11i	−0.917131	−	0.368228i
$876$		0			0
$877$	2.99474e11	−	5.18704e11i	0.506244	−	0.876841i	−0.493729	−	0.869616i	$-0.664367\pi$
$877$	2.99474e11	−	5.18704e11i	0.506244	−	0.876841i	0.999974	−	0.00722558i	$-0.00229999\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	2.08291e11i		−	0.345754i	−0.984943	−	0.172877i	$-0.944694\pi$
$881$		−	2.08291e11i		−	0.345754i	0.984943	−	0.172877i	$-0.0553064\pi$
$882$		0			0
$883$	−7.84994e11			−1.29129			−0.645645	−	0.763638i	$-0.723411\pi$
$883$	−7.84994e11			−1.29129			−0.645645	+	0.763638i	$0.723411\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.11593e11	+	2.37634e11i	0.664927	+	0.383896i	0.794152	−	0.607720i	$-0.207916\pi$
$887$	4.11593e11	+	2.37634e11i	0.664927	+	0.383896i	−0.129225	+	0.991615i	$0.541249\pi$
$888$		0			0
$889$	−3.88412e11	+	9.67402e11i	−0.621849	+	1.54882i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.59053e11	−	2.75488e11i	−0.250113	−	0.433208i
$894$		0			0
$895$		−	7.69163e11i		−	1.19874i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.79914e11	−	2.77078e11i	0.734724	−	0.424193i
$900$		0			0
$901$	−1.36114e10	−	7.85856e9i	−0.0206540	−	0.0119246i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.85892e11	−	3.21975e11i	0.277119	−	0.479985i
$906$		0			0
$907$	3.01929e11	+	5.22956e11i	0.446144	+	0.772745i	0.998131	−	0.0611081i	$-0.0194634\pi$
$907$	3.01929e11	+	5.22956e11i	0.446144	+	0.772745i	−0.551987	+	0.833853i	$0.686130\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.64766e10			−0.0819965			−0.0409982	−	0.999159i	$-0.513054\pi$
$911$	−5.64766e10			−0.0819965			−0.0409982	+	0.999159i	$0.513054\pi$
$912$		0			0
$913$	1.42401e12	−	8.22151e11i	2.04941	−	1.18323i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.91961e11	+	2.29129e11i	−0.412903	+	0.324043i
$918$		0			0
$919$	−3.53883e10	+	6.12943e10i	−0.0496132	+	0.0859327i	−0.889766	−	0.456418i	$-0.849132\pi$
$919$	−3.53883e10	+	6.12943e10i	−0.0496132	+	0.0859327i	0.840152	+	0.542351i	$0.182466\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	2.08415e12i		−	2.87159i
$924$		0			0
$925$	5.99623e11			0.819052
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.88996e11	+	3.97792e11i	0.925026	+	0.534064i	0.885235	−	0.465144i	$-0.153998\pi$
$929$	6.88996e11	+	3.97792e11i	0.925026	+	0.534064i	0.0397908	+	0.999208i	$0.487331\pi$
$930$		0			0
$931$	1.32861e11	+	4.55851e11i	0.176847	+	0.606770i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.00559e10	+	3.47378e10i	0.0262419	+	0.0454523i
$936$		0			0
$937$			9.34401e11i			1.21220i	0.795388	+	0.606101i	$0.207267\pi$
$937$			9.34401e11i			1.21220i	−0.795388	+	0.606101i	$0.792733\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.21783e12	+	7.03113e11i	−1.55320	+	0.896741i	−0.555322	+	0.831636i	$0.687405\pi$
$941$	−1.21783e12	+	7.03113e11i	−1.55320	+	0.896741i	−0.997878	+	0.0651050i	$0.979262\pi$
$942$		0			0
$943$	4.59631e11	+	2.65368e11i	0.581249	+	0.335584i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.50197e10	−	7.79763e10i	0.0559760	−	0.0969534i	−0.836680	−	0.547693i	$-0.815506\pi$
$947$	4.50197e10	−	7.79763e10i	0.0559760	−	0.0969534i	0.892656	+	0.450739i	$0.148840\pi$
$948$		0			0
$949$	−3.71720e11	−	6.43838e11i	−0.458302	−	0.793802i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.15644e11			0.746376			0.373188	−	0.927756i	$-0.378265\pi$
$953$	6.15644e11			0.746376			0.373188	+	0.927756i	$0.378265\pi$
$954$		0			0
$955$	−1.08675e11	+	6.27438e10i	−0.130653	+	0.0754323i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.28532e12	−	1.83490e11i	1.51963	−	0.216940i
$960$		0			0
$961$	−1.37934e11	+	2.38908e11i	−0.161725	+	0.280116i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	2.15812e11i		−	0.248866i
$966$		0			0
$967$	4.52860e11			0.517914			0.258957	−	0.965889i	$-0.416621\pi$
$967$	4.52860e11			0.517914			0.258957	+	0.965889i	$0.416621\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.65973e10	+	4.99970e10i	0.0974154	+	0.0562428i	0.547916	−	0.836533i	$-0.315421\pi$
$971$	8.65973e10	+	4.99970e10i	0.0974154	+	0.0562428i	−0.450501	+	0.892776i	$0.648755\pi$
$972$		0			0
$973$	8.99105e11	+	3.60991e11i	1.00313	+	0.402758i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.56681e11	+	7.90994e11i	0.501227	+	0.868151i	0.999999	+	0.00141736i	$0.000451159\pi$
$977$	4.56681e11	+	7.90994e11i	0.501227	+	0.868151i	−0.498772	+	0.866733i	$0.666216\pi$
$978$		0			0
$979$			6.02380e11i			0.655753i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.08072e11	−	4.66541e11i	0.865438	−	0.499661i	−0.000391493	−	1.00000i	$-0.500125\pi$
$983$	8.08072e11	−	4.66541e11i	0.865438	−	0.499661i	0.865830	+	0.500339i	$0.166791\pi$
$984$		0			0
$985$	−1.89734e11	−	1.09543e11i	−0.201558	−	0.116370i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.42976e11	−	5.94051e11i	0.358491	−	0.620924i
$990$		0			0
$991$	−8.26833e11	−	1.43212e12i	−0.857280	−	1.48485i	−0.874513	−	0.485002i	$-0.838819\pi$
$991$	−8.26833e11	−	1.43212e12i	−0.857280	−	1.48485i	0.0172326	−	0.999852i	$-0.494514\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.31515e11			−0.236203
$996$		0			0
$997$	9.26012e11	−	5.34633e11i	0.937208	−	0.541097i	0.0481238	−	0.998841i	$-0.484676\pi$
$997$	9.26012e11	−	5.34633e11i	0.937208	−	0.541097i	0.889084	+	0.457744i	$0.151342\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.c.145.3		10
3.2	odd	2		28.9.h.a.5.2	✓	10
7.3	odd	6	inner	252.9.z.c.73.3		10
12.11	even	2		112.9.s.b.33.4		10
21.2	odd	6		196.9.b.a.97.3		10
21.5	even	6		196.9.b.a.97.8		10
21.11	odd	6		196.9.h.a.129.4		10
21.17	even	6		28.9.h.a.17.2	yes	10
21.20	even	2		196.9.h.a.117.4		10
84.59	odd	6		112.9.s.b.17.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.h.a.5.2	✓	10	3.2	odd	2
28.9.h.a.17.2	yes	10	21.17	even	6
112.9.s.b.17.4		10	84.59	odd	6
112.9.s.b.33.4		10	12.11	even	2
196.9.b.a.97.3		10	21.2	odd	6
196.9.b.a.97.8		10	21.5	even	6
196.9.h.a.117.4		10	21.20	even	2
196.9.h.a.129.4		10	21.11	odd	6
252.9.z.c.73.3		10	7.3	odd	6	inner
252.9.z.c.145.3		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-327.308 - 188.971i) q^{5} +(-894.589 + 2228.12i) q^{7} +O(q^{10})\)	\(q+(-327.308 - 188.971i) q^{5} +(-894.589 + 2228.12i) q^{7} +(9669.77 + 16748.5i) q^{11} -48446.7i q^{13} +(-4752.58 + 2743.90i) q^{17} +(-71330.2 - 41182.5i) q^{19} +(99846.4 - 172939. i) q^{23} +(-123892. - 214587. i) q^{25} -729518. q^{29} +(-657851. + 379810. i) q^{31} +(713857. - 560229. i) q^{35} +(-1.20997e6 + 2.09573e6i) q^{37} +2.65776e6i q^{41} +3.43503e6 q^{43} +(3.34472e6 + 1.93107e6i) q^{47} +(-4.16422e6 - 3.98650e6i) q^{49} +(1.43200e6 + 2.48030e6i) q^{53} -7.30924e6i q^{55} +(1.34642e7 - 7.77355e6i) q^{59} +(-8.84904e6 - 5.10899e6i) q^{61} +(-9.15504e6 + 1.58570e7i) q^{65} +(3.64879e6 + 6.31988e6i) q^{67} +4.30195e7 q^{71} +(1.32896e7 - 7.67277e6i) q^{73} +(-4.59682e7 + 6.56234e6i) q^{77} +(-1.11705e7 + 1.93479e7i) q^{79} -8.50228e7i q^{83} +2.07408e6 q^{85} +(2.69746e7 + 1.55738e7i) q^{89} +(1.07945e8 + 4.33399e7i) q^{91} +(1.55646e7 + 2.69587e7i) q^{95} -9.56779e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) \) 10 * q + 837 * q^5 + 1526 * q^7	\( 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) \) 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Introduction

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