LMFDB - Embedded newform 588.8.i.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,8,Mod(361,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("588.361");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	588.i (of order $3$, 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:	$183.682394985$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	588.361
Dual form			588.8.i.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 + 23.3827i) q^{3} +(-135.000 - 233.827i) q^{5} +(-364.500 - 631.333i) q^{9} +O(q^{10})$	\(q+(-13.5000 + 23.3827i) q^{3} +(-135.000 - 233.827i) q^{5} +(-364.500 - 631.333i) q^{9} +(2862.00 - 4957.13i) q^{11} -4570.00 q^{13} +7290.00 q^{15} +(18279.0 - 31660.2i) q^{17} +(-25870.0 - 44808.2i) q^{19} +(-11124.0 - 19267.3i) q^{23} +(2612.50 - 4524.98i) q^{25} +19683.0 q^{27} -157194. q^{29} +(51968.0 - 90011.2i) q^{31} +(77274.0 + 133842. i) q^{33} +(47417.0 + 82128.7i) q^{37} +(61695.0 - 106859. i) q^{39} +659610. q^{41} -75772.0 q^{43} +(-98415.0 + 170460. i) q^{45} +(-202824. - 351301. i) q^{47} +(493533. + 854824. i) q^{51} +(673137. - 1.16591e6i) q^{53} -1.54548e6 q^{55} +1.39698e6 q^{57} +(651942. - 1.12920e6i) q^{59} +(-916891. - 1.58810e6i) q^{61} +(616950. + 1.06859e6i) q^{65} +(-684694. + 1.18592e6i) q^{67} +600696. q^{69} +2.71404e6 q^{71} +(-1.43440e6 + 2.48445e6i) q^{73} +(70537.5 + 122175. i) q^{75} +(564824. + 978304. i) q^{79} +(-265720. + 460241. i) q^{81} +5.91203e6 q^{83} -9.87066e6 q^{85} +(2.12212e6 - 3.67562e6i) q^{87} +(448875. + 777474. i) q^{89} +(1.40314e6 + 2.43030e6i) q^{93} +(-6.98490e6 + 1.20982e7i) q^{95} +1.37191e7 q^{97} -4.17280e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 27 q^{3} - 270 q^{5} - 729 q^{9}+O(q^{10}) $ 2 * q - 27 * q^3 - 270 * q^5 - 729 * q^9	$ 2 q - 27 q^{3} - 270 q^{5} - 729 q^{9} + 5724 q^{11} - 9140 q^{13} + 14580 q^{15} + 36558 q^{17} - 51740 q^{19} - 22248 q^{23} + 5225 q^{25} + 39366 q^{27} - 314388 q^{29} + 103936 q^{31} + 154548 q^{33} + 94834 q^{37} + 123390 q^{39} + 1319220 q^{41} - 151544 q^{43} - 196830 q^{45} - 405648 q^{47} + 987066 q^{51} + 1346274 q^{53} - 3090960 q^{55} + 2793960 q^{57} + 1303884 q^{59} - 1833782 q^{61} + 1233900 q^{65} - 1369388 q^{67} + 1201392 q^{69} + 5428080 q^{71} - 2868794 q^{73} + 141075 q^{75} + 1129648 q^{79} - 531441 q^{81} + 11824056 q^{83} - 19741320 q^{85} + 4244238 q^{87} + 897750 q^{89} + 2806272 q^{93} - 13969800 q^{95} + 27438148 q^{97} - 8345592 q^{99}+O(q^{100}) $ 2 * q - 27 * q^3 - 270 * q^5 - 729 * q^9 + 5724 * q^11 - 9140 * q^13 + 14580 * q^15 + 36558 * q^17 - 51740 * q^19 - 22248 * q^23 + 5225 * q^25 + 39366 * q^27 - 314388 * q^29 + 103936 * q^31 + 154548 * q^33 + 94834 * q^37 + 123390 * q^39 + 1319220 * q^41 - 151544 * q^43 - 196830 * q^45 - 405648 * q^47 + 987066 * q^51 + 1346274 * q^53 - 3090960 * q^55 + 2793960 * q^57 + 1303884 * q^59 - 1833782 * q^61 + 1233900 * q^65 - 1369388 * q^67 + 1201392 * q^69 + 5428080 * q^71 - 2868794 * q^73 + 141075 * q^75 + 1129648 * q^79 - 531441 * q^81 + 11824056 * q^83 - 19741320 * q^85 + 4244238 * q^87 + 897750 * q^89 + 2806272 * q^93 - 13969800 * q^95 + 27438148 * q^97 - 8345592 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$4$		0			0
$5$	−135.000	−	233.827i	−0.482991	−	0.836564i	0.516819	−	0.856095i	$-0.327116\pi$
$5$	−135.000	−	233.827i	−0.482991	−	0.836564i	−0.999809	+	0.0195305i	$0.993783\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$		0			0
$11$	2862.00	−	4957.13i	0.648329	−	1.12294i	−0.335193	−	0.942149i	$-0.608802\pi$
$11$	2862.00	−	4957.13i	0.648329	−	1.12294i	0.983522	−	0.180789i	$-0.0578651\pi$
$12$		0			0
$13$	−4570.00			−0.576919			−0.288459	−	0.957492i	$-0.593143\pi$
$13$	−4570.00			−0.576919			−0.288459	+	0.957492i	$0.593143\pi$
$14$		0			0
$15$	7290.00			0.557710
$16$		0			0
$17$	18279.0	−	31660.2i	0.902363	−	1.56294i	0.0779443	−	0.996958i	$-0.475164\pi$
$17$	18279.0	−	31660.2i	0.902363	−	1.56294i	0.824419	−	0.565981i	$-0.191502\pi$
$18$		0			0
$19$	−25870.0	−	44808.2i	−0.865284	−	1.49872i	−0.866765	−	0.498717i	$-0.833805\pi$
$19$	−25870.0	−	44808.2i	−0.865284	−	1.49872i	0.00148030	−	0.999999i	$-0.499529\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−11124.0	−	19267.3i	−0.190640	−	0.330198i	0.754823	−	0.655929i	$-0.227723\pi$
$23$	−11124.0	−	19267.3i	−0.190640	−	0.330198i	−0.945462	+	0.325731i	$0.894390\pi$
$24$		0			0
$25$	2612.50	−	4524.98i	0.0334400	−	0.0579198i
$26$		0			0
$27$	19683.0			0.192450
$28$		0			0
$29$	−157194.			−1.19686			−0.598429	−	0.801175i	$-0.704208\pi$
$29$	−157194.			−1.19686			−0.598429	+	0.801175i	$0.704208\pi$
$30$		0			0
$31$	51968.0	−	90011.2i	0.313307	−	0.542664i	−0.665769	−	0.746158i	$-0.731896\pi$
$31$	51968.0	−	90011.2i	0.313307	−	0.542664i	0.979076	+	0.203494i	$0.0652298\pi$
$32$		0			0
$33$	77274.0	+	133842.i	0.374313	+	0.648329i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	47417.0	+	82128.7i	0.153896	+	0.266556i	0.932657	−	0.360765i	$-0.117485\pi$
$37$	47417.0	+	82128.7i	0.153896	+	0.266556i	−0.778760	+	0.627322i	$0.784151\pi$
$38$		0			0
$39$	61695.0	−	106859.i	0.166542	−	0.288459i
$40$		0			0
$41$	659610.			1.49466			0.747332	−	0.664451i	$-0.231334\pi$
$41$	659610.			1.49466			0.747332	+	0.664451i	$0.231334\pi$
$42$		0			0
$43$	−75772.0			−0.145335			−0.0726673	−	0.997356i	$-0.523151\pi$
$43$	−75772.0			−0.145335			−0.0726673	+	0.997356i	$0.523151\pi$
$44$		0			0
$45$	−98415.0	+	170460.i	−0.160997	+	0.278855i
$46$		0			0
$47$	−202824.	−	351301.i	−0.284955	−	0.493557i	0.687643	−	0.726049i	$-0.258645\pi$
$47$	−202824.	−	351301.i	−0.284955	−	0.493557i	−0.972598	+	0.232492i	$0.925312\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	493533.	+	854824.i	0.520979	+	0.902363i
$52$		0			0
$53$	673137.	−	1.16591e6i	0.621066	−	1.07572i	−0.368221	−	0.929738i	$-0.620033\pi$
$53$	673137.	−	1.16591e6i	0.621066	−	1.07572i	0.989288	−	0.145980i	$-0.0466335\pi$
$54$		0			0
$55$	−1.54548e6			−1.25255
$56$		0			0
$57$	1.39698e6			0.999144
$58$		0			0
$59$	651942.	−	1.12920e6i	0.413263	−	0.715793i	−0.581981	−	0.813202i	$-0.697722\pi$
$59$	651942.	−	1.12920e6i	0.413263	−	0.715793i	0.995244	+	0.0974092i	$0.0310556\pi$
$60$		0			0
$61$	−916891.	−	1.58810e6i	−0.517206	−	0.895827i	−0.999800	−	0.0199827i	$-0.993639\pi$
$61$	−916891.	−	1.58810e6i	−0.517206	−	0.895827i	0.482595	−	0.875844i	$-0.339694\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	616950.	+	1.06859e6i	0.278646	+	0.482629i
$66$		0			0
$67$	−684694.	+	1.18592e6i	−0.278122	+	0.481721i	−0.970918	−	0.239413i	$-0.923045\pi$
$67$	−684694.	+	1.18592e6i	−0.278122	+	0.481721i	0.692796	+	0.721133i	$0.256378\pi$
$68$		0			0
$69$	600696.			0.220132
$70$		0			0
$71$	2.71404e6			0.899937			0.449968	−	0.893044i	$-0.351435\pi$
$71$	2.71404e6			0.899937			0.449968	+	0.893044i	$0.351435\pi$
$72$		0			0
$73$	−1.43440e6	+	2.48445e6i	−0.431558	+	0.747481i	−0.997008	−	0.0773022i	$-0.975369\pi$
$73$	−1.43440e6	+	2.48445e6i	−0.431558	+	0.747481i	0.565450	+	0.824783i	$0.308703\pi$
$74$		0			0
$75$	70537.5	+	122175.i	0.0193066	+	0.0334400i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	564824.	+	978304.i	0.128890	+	0.223244i	0.923247	−	0.384208i	$-0.125525\pi$
$79$	564824.	+	978304.i	0.128890	+	0.223244i	−0.794357	+	0.607451i	$0.792192\pi$
$80$		0			0
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	5.91203e6			1.13491			0.567457	−	0.823403i	$-0.307927\pi$
$83$	5.91203e6			1.13491			0.567457	+	0.823403i	$0.307927\pi$
$84$		0			0
$85$	−9.87066e6			−1.74333
$86$		0			0
$87$	2.12212e6	−	3.67562e6i	0.345503	−	0.598429i
$88$		0			0
$89$	448875.	+	777474.i	0.0674933	+	0.116902i	0.897797	−	0.440409i	$-0.145167\pi$
$89$	448875.	+	777474.i	0.0674933	+	0.116902i	−0.830304	+	0.557311i	$0.811833\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.40314e6	+	2.43030e6i	0.180888	+	0.313307i
$94$		0			0
$95$	−6.98490e6	+	1.20982e7i	−0.835849	+	1.44773i
$96$		0			0
$97$	1.37191e7			1.52624			0.763122	−	0.646255i	$-0.223666\pi$
$97$	1.37191e7			1.52624			0.763122	+	0.646255i	$0.223666\pi$
$98$		0			0
$99$	−4.17280e6			−0.432219
$100$		0			0
$101$	−966519.	+	1.67406e6i	−0.0933438	+	0.161676i	−0.908916	−	0.416979i	$-0.863089\pi$
$101$	−966519.	+	1.67406e6i	−0.0933438	+	0.161676i	0.815572	+	0.578655i	$0.196422\pi$
$102$		0			0
$103$	−2.38064e6	−	4.12338e6i	−0.214666	−	0.371812i	0.738503	−	0.674250i	$-0.235533\pi$
$103$	−2.38064e6	−	4.12338e6i	−0.214666	−	0.371812i	−0.953169	+	0.302438i	$0.902200\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.10522e6	−	1.91429e6i	−0.0872177	−	0.151066i	0.819116	−	0.573627i	$-0.194464\pi$
$107$	−1.10522e6	−	1.91429e6i	−0.0872177	−	0.151066i	−0.906334	+	0.422562i	$0.861131\pi$
$108$		0			0
$109$	1.00464e7	−	1.74009e7i	0.743052	−	1.28700i	−0.208048	−	0.978119i	$-0.566711\pi$
$109$	1.00464e7	−	1.74009e7i	0.743052	−	1.28700i	0.951100	−	0.308885i	$-0.0999557\pi$
$110$		0			0
$111$	−2.56052e6			−0.177704
$112$		0			0
$113$	7.94075e6			0.517711			0.258855	−	0.965916i	$-0.416655\pi$
$113$	7.94075e6			0.517711			0.258855	+	0.965916i	$0.416655\pi$
$114$		0			0
$115$	−3.00348e6	+	5.20218e6i	−0.184154	+	0.318965i
$116$		0			0
$117$	1.66577e6	+	2.88519e6i	0.0961531	+	0.166542i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−6.63850e6	−	1.14982e7i	−0.340660	−	0.590041i
$122$		0			0
$123$	−8.90474e6	+	1.54235e7i	−0.431472	+	0.747332i
$124$		0			0
$125$	−2.25045e7			−1.03059
$126$		0			0
$127$	−2.27395e7			−0.985071			−0.492536	−	0.870292i	$-0.663930\pi$
$127$	−2.27395e7			−0.985071			−0.492536	+	0.870292i	$0.663930\pi$
$128$		0			0
$129$	1.02292e6	−	1.77175e6i	0.0419545	−	0.0726673i
$130$		0			0
$131$	1.13892e7	+	1.97267e7i	0.442633	+	0.766662i	0.997884	−	0.0650204i	$-0.0207112\pi$
$131$	1.13892e7	+	1.97267e7i	0.442633	+	0.766662i	−0.555251	+	0.831683i	$0.687378\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.65720e6	−	4.60241e6i	−0.0929516	−	0.160997i
$136$		0			0
$137$	−2.08494e7	+	3.61122e7i	−0.692741	+	1.19986i	0.278195	+	0.960525i	$0.410264\pi$
$137$	−2.08494e7	+	3.61122e7i	−0.692741	+	1.19986i	−0.970936	+	0.239338i	$0.923069\pi$
$138$		0			0
$139$	−6.19472e6			−0.195645			−0.0978227	−	0.995204i	$-0.531188\pi$
$139$	−6.19472e6			−0.195645			−0.0978227	+	0.995204i	$0.531188\pi$
$140$		0			0
$141$	1.09525e7			0.329038
$142$		0			0
$143$	−1.30793e7	+	2.26541e7i	−0.374033	+	0.647844i
$144$		0			0
$145$	2.12212e7	+	3.67562e7i	0.578072	+	1.00125i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.70829e6	+	4.69089e6i	0.0670723	+	0.116173i	0.897611	−	0.440788i	$-0.145301\pi$
$149$	2.70829e6	+	4.69089e6i	0.0670723	+	0.116173i	−0.830539	+	0.556960i	$0.811968\pi$
$150$		0			0
$151$	−3.54222e7	+	6.13530e7i	−0.837252	+	1.45016i	0.0549324	+	0.998490i	$0.482506\pi$
$151$	−3.54222e7	+	6.13530e7i	−0.837252	+	1.45016i	−0.892184	+	0.451672i	$0.850828\pi$
$152$		0			0
$153$	−2.66508e7			−0.601575
$154$		0			0
$155$	−2.80627e7			−0.605297
$156$		0			0
$157$	3.95401e7	−	6.84854e7i	0.815433	−	1.41237i	−0.0935830	−	0.995611i	$-0.529832\pi$
$157$	3.95401e7	−	6.84854e7i	0.815433	−	1.41237i	0.909016	−	0.416760i	$-0.136835\pi$
$158$		0			0
$159$	1.81747e7	+	3.14795e7i	0.358573	+	0.621066i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.22246e7	+	2.11736e7i	0.221094	+	0.382946i	0.955140	−	0.296153i	$-0.0957039\pi$
$163$	1.22246e7	+	2.11736e7i	0.221094	+	0.382946i	−0.734046	+	0.679099i	$0.762371\pi$
$164$		0			0
$165$	2.08640e7	−	3.61375e7i	0.361579	−	0.626273i
$166$		0			0
$167$	3.55538e7			0.590716			0.295358	−	0.955387i	$-0.404561\pi$
$167$	3.55538e7			0.590716			0.295358	+	0.955387i	$0.404561\pi$
$168$		0			0
$169$	−4.18636e7			−0.667165
$170$		0			0
$171$	−1.88592e7	+	3.26651e7i	−0.288428	+	0.499572i
$172$		0			0
$173$	−5.13970e7	−	8.90222e7i	−0.754704	−	1.30719i	−0.945521	−	0.325560i	$-0.894447\pi$
$173$	−5.13970e7	−	8.90222e7i	−0.754704	−	1.30719i	0.190818	−	0.981625i	$-0.438886\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.76024e7	+	3.04883e7i	0.238598	+	0.413263i
$178$		0			0
$179$	2.07794e7	−	3.59909e7i	0.270799	−	0.469037i	−0.698268	−	0.715837i	$-0.746046\pi$
$179$	2.07794e7	−	3.59909e7i	0.270799	−	0.469037i	0.969067	+	0.246799i	$0.0793789\pi$
$180$		0			0
$181$	−3.35013e7			−0.419939			−0.209969	−	0.977708i	$-0.567336\pi$
$181$	−3.35013e7			−0.419939			−0.209969	+	0.977708i	$0.567336\pi$
$182$		0			0
$183$	4.95121e7			0.597218
$184$		0			0
$185$	1.28026e7	−	2.21747e7i	0.148661	−	0.257488i
$186$		0			0
$187$	−1.04629e8	−	1.81223e8i	−1.17006	−	2.02660i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.45402e7	−	4.25049e7i	−0.254836	−	0.441389i	0.710015	−	0.704187i	$-0.248688\pi$
$191$	−2.45402e7	−	4.25049e7i	−0.254836	−	0.441389i	−0.964851	+	0.262797i	$0.915355\pi$
$192$		0			0
$193$	−3.02242e7	+	5.23498e7i	−0.302624	+	0.524161i	−0.976730	−	0.214475i	$-0.931196\pi$
$193$	−3.02242e7	+	5.23498e7i	−0.302624	+	0.524161i	0.674105	+	0.738635i	$0.264529\pi$
$194$		0			0
$195$	−3.33153e7			−0.321753
$196$		0			0
$197$	5.00456e6			0.0466374			0.0233187	−	0.999728i	$-0.492577\pi$
$197$	5.00456e6			0.0466374			0.0233187	+	0.999728i	$0.492577\pi$
$198$		0			0
$199$	1.10567e8	−	1.91508e8i	0.994584	−	1.72267i	0.407282	−	0.913303i	$-0.366477\pi$
$199$	1.10567e8	−	1.91508e8i	0.994584	−	1.72267i	0.587303	−	0.809368i	$-0.300190\pi$
$200$		0			0
$201$	−1.84867e7	−	3.20200e7i	−0.160574	−	0.278122i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−8.90474e7	−	1.54235e8i	−0.721909	−	1.25038i
$206$		0			0
$207$	−8.10940e6	+	1.40459e7i	−0.0635466	+	0.110066i
$208$		0			0
$209$	−2.96160e8			−2.24395
$210$		0			0
$211$	−7.16641e7			−0.525186			−0.262593	−	0.964907i	$-0.584578\pi$
$211$	−7.16641e7			−0.525186			−0.262593	+	0.964907i	$0.584578\pi$
$212$		0			0
$213$	−3.66395e7	+	6.34615e7i	−0.259789	+	0.449968i
$214$		0			0
$215$	1.02292e7	+	1.77175e7i	0.0701953	+	0.121582i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.87287e7	−	6.70801e7i	−0.249160	−	0.431558i
$220$		0			0
$221$	−8.35350e7	+	1.44687e8i	−0.520590	+	0.901688i
$222$		0			0
$223$	2.61440e7			0.157872			0.0789360	−	0.996880i	$-0.474848\pi$
$223$	2.61440e7			0.157872			0.0789360	+	0.996880i	$0.474848\pi$
$224$		0			0
$225$	−3.80902e6			−0.0222933
$226$		0			0
$227$	1.70497e7	−	2.95309e7i	0.0967444	−	0.167566i	−0.813591	−	0.581438i	$-0.802490\pi$
$227$	1.70497e7	−	2.95309e7i	0.0967444	−	0.167566i	0.910335	+	0.413871i	$0.135824\pi$
$228$		0			0
$229$	−1.13714e8	−	1.96958e8i	−0.625734	−	1.08380i	−0.988399	−	0.151883i	$-0.951466\pi$
$229$	−1.13714e8	−	1.96958e8i	−0.625734	−	1.08380i	0.362665	−	0.931920i	$-0.381867\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.84530e7	−	4.92821e7i	−0.147361	−	0.255237i	0.782890	−	0.622160i	$-0.213745\pi$
$233$	−2.84530e7	−	4.92821e7i	−0.147361	−	0.255237i	−0.930251	+	0.366923i	$0.880411\pi$
$234$		0			0
$235$	−5.47625e7	+	9.48514e7i	−0.275262	+	0.476767i
$236$		0			0
$237$	−3.05005e7			−0.148829
$238$		0			0
$239$	3.02716e8			1.43431			0.717154	−	0.696915i	$-0.245444\pi$
$239$	3.02716e8			1.43431			0.717154	+	0.696915i	$0.245444\pi$
$240$		0			0
$241$	1.26848e7	−	2.19707e7i	0.0583746	−	0.101108i	−0.835361	−	0.549701i	$-0.814742\pi$
$241$	1.26848e7	−	2.19707e7i	0.0583746	−	0.101108i	0.893736	+	0.448594i	$0.148075\pi$
$242$		0			0
$243$	−7.17445e6	−	1.24265e7i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.18226e8	+	2.04773e8i	0.499199	+	0.864637i
$248$		0			0
$249$	−7.98124e7	+	1.38239e8i	−0.327622	+	0.567457i
$250$		0			0
$251$	−1.46544e7			−0.0584939			−0.0292469	−	0.999572i	$-0.509311\pi$
$251$	−1.46544e7			−0.0584939			−0.0292469	+	0.999572i	$0.509311\pi$
$252$		0			0
$253$	−1.27348e8			−0.494389
$254$		0			0
$255$	1.33254e8	−	2.30803e8i	0.503256	−	0.871666i
$256$		0			0
$257$	1.17326e7	+	2.03215e7i	0.0431150	+	0.0746774i	0.886778	−	0.462196i	$-0.152938\pi$
$257$	1.17326e7	+	2.03215e7i	0.0431150	+	0.0746774i	−0.843663	+	0.536874i	$0.819605\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.72972e7	+	9.92417e7i	0.199476	+	0.345503i
$262$		0			0
$263$	−2.12792e8	+	3.68566e8i	−0.721289	+	1.24931i	0.239194	+	0.970972i	$0.423117\pi$
$263$	−2.12792e8	+	3.68566e8i	−0.721289	+	1.24931i	−0.960483	+	0.278338i	$0.910217\pi$
$264$		0			0
$265$	−3.63494e8			−1.19988
$266$		0			0
$267$	−2.42393e7			−0.0779345
$268$		0			0
$269$	1.96531e8	−	3.40401e8i	0.615599	−	1.06625i	−0.374680	−	0.927154i	$-0.622248\pi$
$269$	1.96531e8	−	3.40401e8i	0.615599	−	1.06625i	0.990279	−	0.139094i	$-0.0444191\pi$
$270$		0			0
$271$	−2.94780e7	−	5.10574e7i	−0.0899716	−	0.155835i	0.817527	−	0.575890i	$-0.195344\pi$
$271$	−2.94780e7	−	5.10574e7i	−0.0899716	−	0.155835i	−0.907499	+	0.420054i	$0.862011\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.49540e7	−	2.59010e7i	−0.0433602	−	0.0751021i
$276$		0			0
$277$	1.07987e7	−	1.87039e7i	0.0305275	−	0.0528752i	−0.850358	−	0.526205i	$-0.823615\pi$
$277$	1.07987e7	−	1.87039e7i	0.0305275	−	0.0528752i	0.880886	+	0.473329i	$0.156948\pi$
$278$		0			0
$279$	−7.57693e7			−0.208871
$280$		0			0
$281$	−3.34718e8			−0.899926			−0.449963	−	0.893047i	$-0.648563\pi$
$281$	−3.34718e8			−0.899926			−0.449963	+	0.893047i	$0.648563\pi$
$282$		0			0
$283$	−1.63403e8	+	2.83023e8i	−0.428557	+	0.742282i	−0.996745	−	0.0806166i	$-0.974311\pi$
$283$	−1.63403e8	+	2.83023e8i	−0.428557	+	0.742282i	0.568189	+	0.822898i	$0.307644\pi$
$284$		0			0
$285$	−1.88592e8	−	3.26651e8i	−0.482577	−	0.835849i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.63074e8	−	8.02068e8i	−1.12852	−	1.95465i
$290$		0			0
$291$	−1.85207e8	+	3.20789e8i	−0.440588	+	0.763122i
$292$		0			0
$293$	−7.28964e8			−1.69305			−0.846525	−	0.532350i	$-0.821309\pi$
$293$	−7.28964e8			−1.69305			−0.846525	+	0.532350i	$0.821309\pi$
$294$		0			0
$295$	−3.52049e8			−0.798409
$296$		0			0
$297$	5.63327e7	−	9.75712e7i	0.124771	−	0.216110i
$298$		0			0
$299$	5.08367e7	+	8.80517e7i	0.109984	+	0.190497i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.60960e7	−	4.51996e7i	−0.0538921	−	0.0933438i
$304$		0			0
$305$	−2.47561e8	+	4.28787e8i	−0.499611	+	0.865352i
$306$		0			0
$307$	−1.26039e8			−0.248612			−0.124306	−	0.992244i	$-0.539670\pi$
$307$	−1.26039e8			−0.248612			−0.124306	+	0.992244i	$0.539670\pi$
$308$		0			0
$309$	1.28554e8			0.247875
$310$		0			0
$311$	3.57884e8	−	6.19873e8i	0.674654	−	1.16853i	−0.301916	−	0.953334i	$-0.597626\pi$
$311$	3.57884e8	−	6.19873e8i	0.674654	−	1.16853i	0.976570	−	0.215200i	$-0.0690404\pi$
$312$		0			0
$313$	1.45598e8	+	2.52183e8i	0.268380	+	0.464848i	0.968444	−	0.249233i	$-0.0801784\pi$
$313$	1.45598e8	+	2.52183e8i	0.268380	+	0.464848i	−0.700064	+	0.714080i	$0.746845\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.12143e7	−	3.67442e7i	−0.0374042	−	0.0647860i	0.846717	−	0.532043i	$-0.178576\pi$
$317$	−2.12143e7	−	3.67442e7i	−0.0374042	−	0.0647860i	−0.884121	+	0.467257i	$0.845242\pi$
$318$		0			0
$319$	−4.49889e8	+	7.79231e8i	−0.775958	+	1.34400i
$320$		0			0
$321$	5.96818e7			0.100710
$322$		0			0
$323$	−1.89151e9			−3.12320
$324$		0			0
$325$	−1.19391e7	+	2.06792e7i	−0.0192922	+	0.0334150i
$326$		0			0
$327$	2.71254e8	+	4.69825e8i	0.429001	+	0.743052i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.73628e8	+	4.73938e8i	0.414728	+	0.718330i	0.995400	−	0.0958080i	$-0.0305435\pi$
$331$	2.73628e8	+	4.73938e8i	0.414728	+	0.718330i	−0.580672	+	0.814138i	$0.697210\pi$
$332$		0			0
$333$	3.45670e7	−	5.98718e7i	0.0512988	−	0.0888520i
$334$		0			0
$335$	3.69735e8			0.537321
$336$		0			0
$337$	−1.85332e8			−0.263783			−0.131891	−	0.991264i	$-0.542105\pi$
$337$	−1.85332e8			−0.263783			−0.131891	+	0.991264i	$0.542105\pi$
$338$		0			0
$339$	−1.07200e8	+	1.85676e8i	−0.149450	+	0.258855i
$340$		0			0
$341$	−2.97465e8	−	5.15224e8i	−0.406252	−	0.703649i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−8.10940e7	−	1.40459e8i	−0.106322	−	0.184154i
$346$		0			0
$347$	−6.48555e8	+	1.12333e9i	−0.833286	+	1.44329i	0.0621327	+	0.998068i	$0.480210\pi$
$347$	−6.48555e8	+	1.12333e9i	−0.833286	+	1.44329i	−0.895419	+	0.445225i	$0.853124\pi$
$348$		0			0
$349$	−6.22136e8			−0.783423			−0.391711	−	0.920088i	$-0.628117\pi$
$349$	−6.22136e8			−0.783423			−0.391711	+	0.920088i	$0.628117\pi$
$350$		0			0
$351$	−8.99513e7			−0.111028
$352$		0			0
$353$	−3.10344e8	+	5.37531e8i	−0.375519	+	0.650417i	−0.990405	−	0.138199i	$-0.955869\pi$
$353$	−3.10344e8	+	5.37531e8i	−0.375519	+	0.650417i	0.614886	+	0.788616i	$0.289202\pi$
$354$		0			0
$355$	−3.66395e8	−	6.34615e8i	−0.434661	−	0.752855i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.03441e8	−	5.25576e8i	−0.346134	−	0.599521i	0.639425	−	0.768853i	$-0.279172\pi$
$359$	−3.03441e8	−	5.25576e8i	−0.346134	−	0.599521i	−0.985559	+	0.169332i	$0.945839\pi$
$360$		0			0
$361$	−8.91578e8	+	1.54426e9i	−0.997434	+	1.72761i
$362$		0			0
$363$	3.58479e8			0.393360
$364$		0			0
$365$	7.74574e8			0.833754
$366$		0			0
$367$	7.02692e8	−	1.21710e9i	0.742051	−	1.28527i	−0.209508	−	0.977807i	$-0.567186\pi$
$367$	7.02692e8	−	1.21710e9i	0.742051	−	1.28527i	0.951560	−	0.307464i	$-0.0994803\pi$
$368$		0			0
$369$	−2.40428e8	−	4.16433e8i	−0.249111	−	0.431472i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.64624e8	+	9.77958e8i	0.563350	+	0.975751i	0.997201	+	0.0747666i	$0.0238212\pi$
$373$	5.64624e8	+	9.77958e8i	0.563350	+	0.975751i	−0.433851	+	0.900985i	$0.642845\pi$
$374$		0			0
$375$	3.03811e8	−	5.26216e8i	0.297505	−	0.515293i
$376$		0			0
$377$	7.18377e8			0.690490
$378$		0			0
$379$	1.63515e9			1.54284			0.771419	−	0.636328i	$-0.219547\pi$
$379$	1.63515e9			1.54284			0.771419	+	0.636328i	$0.219547\pi$
$380$		0			0
$381$	3.06983e8	−	5.31710e8i	0.284366	−	0.492536i
$382$		0			0
$383$	1.13842e8	+	1.97181e8i	0.103540	+	0.179337i	0.913141	−	0.407644i	$-0.133650\pi$
$383$	1.13842e8	+	1.97181e8i	0.103540	+	0.179337i	−0.809601	+	0.586981i	$0.800316\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.76189e7	+	4.78373e7i	0.0242224	+	0.0419545i
$388$		0			0
$389$	3.11560e8	−	5.39638e8i	0.268360	−	0.464813i	−0.700078	−	0.714066i	$-0.746852\pi$
$389$	3.11560e8	−	5.39638e8i	0.268360	−	0.464813i	0.968439	+	0.249253i	$0.0801849\pi$
$390$		0			0
$391$	−8.13342e8			−0.688105
$392$		0			0
$393$	−6.15016e8			−0.511108
$394$		0			0
$395$	1.52502e8	−	2.64142e8i	0.124505	−	0.215649i
$396$		0			0
$397$	747917.	+	1.29543e6i	0.000599911	+	0.00103908i	0.866325	−	0.499480i	$-0.166476\pi$
$397$	747917.	+	1.29543e6i	0.000599911	+	0.00103908i	−0.865725	+	0.500519i	$0.833142\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.53250e8	+	2.65437e8i	0.118685	+	0.205569i	0.919247	−	0.393682i	$-0.128799\pi$
$401$	1.53250e8	+	2.65437e8i	0.118685	+	0.205569i	−0.800562	+	0.599250i	$0.795465\pi$
$402$		0			0
$403$	−2.37494e8	+	4.11351e8i	−0.180753	+	0.313073i
$404$		0			0
$405$	1.43489e8			0.107331
$406$		0			0
$407$	5.42830e8			0.399101
$408$		0			0
$409$	−1.78434e8	+	3.09057e8i	−0.128957	+	0.223361i	−0.923273	−	0.384145i	$-0.874496\pi$
$409$	−1.78434e8	+	3.09057e8i	−0.128957	+	0.223361i	0.794316	+	0.607505i	$0.207830\pi$
$410$		0			0
$411$	−5.62933e8	−	9.75029e8i	−0.399954	−	0.692741i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−7.98124e8	−	1.38239e9i	−0.548153	−	0.949429i
$416$		0			0
$417$	8.36287e7	−	1.44849e8i	0.0564780	−	0.0978227i
$418$		0			0
$419$	−2.28428e9			−1.51705			−0.758526	−	0.651642i	$-0.774080\pi$
$419$	−2.28428e9			−1.51705			−0.758526	+	0.651642i	$0.774080\pi$
$420$		0			0
$421$	2.63135e8			0.171866			0.0859332	−	0.996301i	$-0.472613\pi$
$421$	2.63135e8			0.171866			0.0859332	+	0.996301i	$0.472613\pi$
$422$		0			0
$423$	−1.47859e8	+	2.56099e8i	−0.0949851	+	0.164519i
$424$		0			0
$425$	−9.55078e7	−	1.65424e8i	−0.0603500	−	0.104529i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.53142e8	−	6.11660e8i	−0.215948	−	0.374033i
$430$		0			0
$431$	−7.45265e8	+	1.29084e9i	−0.448374	+	0.776606i	−0.998280	−	0.0586202i	$-0.981330\pi$
$431$	−7.45265e8	+	1.29084e9i	−0.448374	+	0.776606i	0.549907	+	0.835226i	$0.314663\pi$
$432$		0			0
$433$	1.10539e9			0.654347			0.327174	−	0.944964i	$-0.393904\pi$
$433$	1.10539e9			0.654347			0.327174	+	0.944964i	$0.393904\pi$
$434$		0			0
$435$	−1.14594e9			−0.667500
$436$		0			0
$437$	−5.75556e8	+	9.96892e8i	−0.329915	+	0.571430i
$438$		0			0
$439$	−1.48176e8	−	2.56649e8i	−0.0835898	−	0.144782i	0.821200	−	0.570641i	$-0.193305\pi$
$439$	−1.48176e8	−	2.56649e8i	−0.0835898	−	0.144782i	−0.904789	+	0.425859i	$0.859972\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.79472e8	−	3.10855e8i	−0.0980808	−	0.169881i	0.812809	−	0.582530i	$-0.197937\pi$
$443$	−1.79472e8	−	3.10855e8i	−0.0980808	−	0.169881i	−0.910890	+	0.412649i	$0.864604\pi$
$444$		0			0
$445$	1.21196e8	−	2.09918e8i	0.0651972	−	0.112925i
$446$		0			0
$447$	−1.46248e8			−0.0774484
$448$		0			0
$449$	−3.41948e9			−1.78278			−0.891391	−	0.453235i	$-0.850270\pi$
$449$	−3.41948e9			−1.78278			−0.891391	+	0.453235i	$0.850270\pi$
$450$		0			0
$451$	1.88780e9	−	3.26977e9i	0.969034	−	1.67842i
$452$		0			0
$453$	−9.56399e8	−	1.65653e9i	−0.483387	−	0.837252i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.42914e9	+	2.47534e9i	0.700434	+	1.21319i	0.968314	+	0.249735i	$0.0803436\pi$
$457$	1.42914e9	+	2.47534e9i	0.700434	+	1.21319i	−0.267880	+	0.963452i	$0.586323\pi$
$458$		0			0
$459$	3.59786e8	−	6.23167e8i	0.173660	−	0.300788i
$460$		0			0
$461$	9.62700e8			0.457654			0.228827	−	0.973467i	$-0.426511\pi$
$461$	9.62700e8			0.457654			0.228827	+	0.973467i	$0.426511\pi$
$462$		0			0
$463$	6.01893e8			0.281829			0.140914	−	0.990022i	$-0.454996\pi$
$463$	6.01893e8			0.281829			0.140914	+	0.990022i	$0.454996\pi$
$464$		0			0
$465$	3.78847e8	−	6.56182e8i	0.174734	−	0.302649i
$466$		0			0
$467$	−8.60300e8	−	1.49008e9i	−0.390878	−	0.677020i	0.601688	−	0.798731i	$-0.294495\pi$
$467$	−8.60300e8	−	1.49008e9i	−0.390878	−	0.677020i	−0.992566	+	0.121711i	$0.961162\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.06758e9	+	1.84911e9i	0.470791	+	0.815433i
$472$		0			0
$473$	−2.16859e8	+	3.75612e8i	−0.0942246	+	0.163202i
$474$		0			0
$475$	−2.70342e8			−0.115740
$476$		0			0
$477$	−9.81434e8			−0.414044
$478$		0			0
$479$	2.68631e8	−	4.65283e8i	0.111682	−	0.193438i	−0.804767	−	0.593591i	$-0.797710\pi$
$479$	2.68631e8	−	4.65283e8i	0.111682	−	0.193438i	0.916448	+	0.400153i	$0.131043\pi$
$480$		0			0
$481$	−2.16696e8	−	3.75328e8i	−0.0887856	−	0.153781i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.85207e9	−	3.20789e9i	−0.737161	−	1.27680i
$486$		0			0
$487$	2.24811e9	−	3.89383e9i	0.881993	−	1.52766i	0.0328716	−	0.999460i	$-0.489535\pi$
$487$	2.24811e9	−	3.89383e9i	0.881993	−	1.52766i	0.849122	−	0.528197i	$-0.177132\pi$
$488$		0			0
$489$	−6.60127e8			−0.255297
$490$		0			0
$491$	3.32917e9			1.26926			0.634631	−	0.772815i	$-0.281152\pi$
$491$	3.32917e9			1.26926			0.634631	+	0.772815i	$0.281152\pi$
$492$		0			0
$493$	−2.87335e9	+	4.97679e9i	−1.08000	+	1.87062i
$494$		0			0
$495$	5.63327e8	+	9.75712e8i	0.208758	+	0.361579i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.02493e9	+	1.77523e9i	0.369268	+	0.639591i	0.989451	−	0.144866i	$-0.0462751\pi$
$499$	1.02493e9	+	1.77523e9i	0.369268	+	0.639591i	−0.620183	+	0.784457i	$0.712942\pi$
$500$		0			0
$501$	−4.79977e8	+	8.31344e8i	−0.170525	+	0.295358i
$502$		0			0
$503$	7.76491e8			0.272050			0.136025	−	0.990705i	$-0.456567\pi$
$503$	7.76491e8			0.272050			0.136025	+	0.990705i	$0.456567\pi$
$504$		0			0
$505$	5.21920e8			0.180337
$506$		0			0
$507$	5.65159e8	−	9.78884e8i	0.192594	−	0.333583i
$508$		0			0
$509$	2.28340e9	+	3.95496e9i	0.767483	+	1.32932i	0.938924	+	0.344126i	$0.111825\pi$
$509$	2.28340e9	+	3.95496e9i	0.767483	+	1.32932i	−0.171440	+	0.985195i	$0.554842\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−5.09199e8	−	8.81959e8i	−0.166524	−	0.288428i
$514$		0			0
$515$	−6.42772e8	+	1.11331e9i	−0.207363	+	0.359163i
$516$		0			0
$517$	−2.32193e9			−0.738979
$518$		0			0
$519$	2.77544e9			0.871457
$520$		0			0
$521$	1.10580e9	−	1.91530e9i	0.342565	−	0.593340i	−0.642343	−	0.766417i	$-0.722038\pi$
$521$	1.10580e9	−	1.91530e9i	0.342565	−	0.593340i	0.984908	+	0.173077i	$0.0553709\pi$
$522$		0			0
$523$	1.17077e9	+	2.02783e9i	0.357862	+	0.619835i	0.987603	−	0.156970i	$-0.0501725\pi$
$523$	1.17077e9	+	2.02783e9i	0.357862	+	0.619835i	−0.629741	+	0.776805i	$0.716839\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.89985e9	−	3.29063e9i	−0.565433	−	0.979359i
$528$		0			0
$529$	1.45493e9	−	2.52001e9i	0.427313	−	0.740128i
$530$		0			0
$531$	−9.50531e8			−0.275509
$532$		0			0
$533$	−3.01442e9			−0.862300
$534$		0			0
$535$	−2.98409e8	+	5.16859e8i	−0.0842507	+	0.145926i
$536$		0			0
$537$	5.61043e8	+	9.71755e8i	0.156346	+	0.270799i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.17749e9	−	2.03946e9i	−0.319717	−	0.553765i	0.660712	−	0.750639i	$-0.270254\pi$
$541$	−1.17749e9	−	2.03946e9i	−0.319717	−	0.553765i	−0.980429	+	0.196874i	$0.936921\pi$
$542$		0			0
$543$	4.52267e8	−	7.83349e8i	0.121226	−	0.209969i
$544$		0			0
$545$	−5.42507e9			−1.43555
$546$		0			0
$547$	3.41493e9			0.892127			0.446063	−	0.895001i	$-0.352826\pi$
$547$	3.41493e9			0.892127			0.446063	+	0.895001i	$0.352826\pi$
$548$		0			0
$549$	−6.68414e8	+	1.15773e9i	−0.172402	+	0.298609i
$550$		0			0
$551$	4.06661e9	+	7.04357e9i	1.03562	+	1.79375i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.45670e8	+	5.98718e8i	0.0858294	+	0.148661i
$556$		0			0
$557$	2.39647e8	−	4.15080e8i	0.0587595	−	0.101774i	−0.835149	−	0.550023i	$-0.814619\pi$
$557$	2.39647e8	−	4.15080e8i	0.0587595	−	0.101774i	0.893909	+	0.448249i	$0.147952\pi$
$558$		0			0
$559$	3.46278e8			0.0838462
$560$		0			0
$561$	5.64997e9			1.35106
$562$		0			0
$563$	−3.25151e9	+	5.63178e9i	−0.767902	+	1.33005i	0.170796	+	0.985306i	$0.445366\pi$
$563$	−3.25151e9	+	5.63178e9i	−0.767902	+	1.33005i	−0.938699	+	0.344739i	$0.887967\pi$
$564$		0			0
$565$	−1.07200e9	−	1.85676e9i	−0.250049	−	0.433098i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.25812e9	+	3.91118e9i	0.513872	+	0.890052i	0.999871	+	0.0160925i	$0.00512264\pi$
$569$	2.25812e9	+	3.91118e9i	0.513872	+	0.890052i	−0.485999	+	0.873960i	$0.661544\pi$
$570$		0			0
$571$	−1.23688e9	+	2.14233e9i	−0.278035	+	0.481572i	−0.970896	−	0.239500i	$-0.923017\pi$
$571$	−1.23688e9	+	2.14233e9i	−0.278035	+	0.481572i	0.692861	+	0.721071i	$0.256350\pi$
$572$		0			0
$573$	1.32517e9			0.294260
$574$		0			0
$575$	−1.16246e8			−0.0255000
$576$		0			0
$577$	2.65860e8	−	4.60484e8i	0.0576154	−	0.0997927i	−0.835779	−	0.549066i	$-0.814984\pi$
$577$	2.65860e8	−	4.60484e8i	0.0576154	−	0.0997927i	0.893394	+	0.449273i	$0.148317\pi$
$578$		0			0
$579$	−8.16052e8	−	1.41344e9i	−0.174720	−	0.302624i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.85304e9	−	6.67365e9i	−0.805310	−	1.39484i
$584$		0			0
$585$	4.49757e8	−	7.79001e8i	0.0928821	−	0.160876i
$586$		0			0
$587$	8.17110e9			1.66743			0.833715	−	0.552195i	$-0.186210\pi$
$587$	8.17110e9			1.66743			0.833715	+	0.552195i	$0.186210\pi$
$588$		0			0
$589$	−5.37765e9			−1.08440
$590$		0			0
$591$	−6.75615e7	+	1.17020e8i	−0.0134630	+	0.0233187i
$592$		0			0
$593$	7.99614e8	+	1.38497e9i	0.157467	+	0.272740i	0.933955	−	0.357392i	$-0.116334\pi$
$593$	7.99614e8	+	1.38497e9i	0.157467	+	0.272740i	−0.776488	+	0.630132i	$0.783001\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.98532e9	+	5.17073e9i	0.574223	+	0.994584i
$598$		0			0
$599$	4.40165e9	−	7.62388e9i	0.836800	−	1.44938i	−0.0557572	−	0.998444i	$-0.517757\pi$
$599$	4.40165e9	−	7.62388e9i	0.836800	−	1.44938i	0.892557	−	0.450935i	$-0.148909\pi$
$600$		0			0
$601$	8.21235e9			1.54314			0.771572	−	0.636142i	$-0.219471\pi$
$601$	8.21235e9			1.54314			0.771572	+	0.636142i	$0.219471\pi$
$602$		0			0
$603$	9.98284e8			0.185414
$604$		0			0
$605$	−1.79240e9	+	3.10452e9i	−0.329071	+	0.569968i
$606$		0			0
$607$	−2.54596e9	−	4.40973e9i	−0.462052	−	0.800298i	0.537011	−	0.843575i	$-0.319553\pi$
$607$	−2.54596e9	−	4.40973e9i	−0.462052	−	0.800298i	−0.999063	+	0.0432773i	$0.986220\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.26906e8	+	1.60545e9i	0.164396	+	0.284742i
$612$		0			0
$613$	3.50641e9	−	6.07328e9i	0.614824	−	1.06491i	−0.375591	−	0.926785i	$-0.622560\pi$
$613$	3.50641e9	−	6.07328e9i	0.614824	−	1.06491i	0.990415	−	0.138121i	$-0.0441064\pi$
$614$		0			0
$615$	4.80856e9			0.833589
$616$		0			0
$617$	4.63714e9			0.794789			0.397394	−	0.917648i	$-0.369914\pi$
$617$	4.63714e9			0.794789			0.397394	+	0.917648i	$0.369914\pi$
$618$		0			0
$619$	−6.69584e8	+	1.15975e9i	−0.113472	+	0.196539i	−0.917168	−	0.398501i	$-0.869530\pi$
$619$	−6.69584e8	+	1.15975e9i	−0.113472	+	0.196539i	0.803696	+	0.595040i	$0.202864\pi$
$620$		0			0
$621$	−2.18954e8	−	3.79239e8i	−0.0366886	−	0.0635466i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	2.83401e9	+	4.90864e9i	0.464324	+	0.804232i
$626$		0			0
$627$	3.99816e9	−	6.92501e9i	0.647774	−	1.12198i
$628$		0			0
$629$	3.46694e9			0.555481
$630$		0			0
$631$	−1.12354e10			−1.78027			−0.890133	−	0.455700i	$-0.849389\pi$
$631$	−1.12354e10			−1.78027			−0.890133	+	0.455700i	$0.849389\pi$
$632$		0			0
$633$	9.67465e8	−	1.67570e9i	0.151608	−	0.262593i
$634$		0			0
$635$	3.06983e9	+	5.31710e9i	0.475780	+	0.824076i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−9.89268e8	−	1.71346e9i	−0.149989	−	0.259789i
$640$		0			0
$641$	−4.91190e9	+	8.50766e9i	−0.736625	+	1.27587i	0.217381	+	0.976087i	$0.430248\pi$
$641$	−4.91190e9	+	8.50766e9i	−0.736625	+	1.27587i	−0.954007	+	0.299786i	$0.903085\pi$
$642$		0			0
$643$	3.56240e9			0.528450			0.264225	−	0.964461i	$-0.414884\pi$
$643$	3.56240e9			0.528450			0.264225	+	0.964461i	$0.414884\pi$
$644$		0			0
$645$	−5.52378e8			−0.0810545
$646$		0			0
$647$	−2.95560e9	+	5.11924e9i	−0.429022	+	0.743089i	−0.996787	−	0.0801026i	$-0.974475\pi$
$647$	−2.95560e9	+	5.11924e9i	−0.429022	+	0.743089i	0.567764	+	0.823191i	$0.307809\pi$
$648$		0			0
$649$	−3.73172e9	−	6.46352e9i	−0.535861	−	0.928138i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.85269e8	+	6.67306e8i	0.0541462	+	0.0937840i	0.891828	−	0.452375i	$-0.149423\pi$
$653$	3.85269e8	+	6.67306e8i	0.0541462	+	0.0937840i	−0.837682	+	0.546158i	$0.816090\pi$
$654$		0			0
$655$	3.07508e9	−	5.32620e9i	0.427575	−	0.740581i
$656$		0			0
$657$	2.09135e9			0.287705
$658$		0			0
$659$	4.95271e9			0.674130			0.337065	−	0.941481i	$-0.390566\pi$
$659$	4.95271e9			0.674130			0.337065	+	0.941481i	$0.390566\pi$
$660$		0			0
$661$	6.01593e8	−	1.04199e9i	0.0810210	−	0.140332i	−0.822668	−	0.568522i	$-0.807515\pi$
$661$	6.01593e8	−	1.04199e9i	0.0810210	−	0.140332i	0.903689	+	0.428190i	$0.140849\pi$
$662$		0			0
$663$	−2.25545e9	−	3.90655e9i	−0.300563	−	0.520590i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.74863e9	+	3.02871e9i	0.228169	+	0.395200i
$668$		0			0
$669$	−3.52944e8	+	6.11317e8i	−0.0455737	+	0.0789360i
$670$		0			0
$671$	−1.04966e10			−1.34128
$672$		0			0
$673$	1.30823e10			1.65436			0.827181	−	0.561936i	$-0.189943\pi$
$673$	1.30823e10			1.65436			0.827181	+	0.561936i	$0.189943\pi$
$674$		0			0
$675$	5.14218e7	−	8.90652e7i	0.00643553	−	0.0111467i
$676$		0			0
$677$	7.46898e9	+	1.29367e10i	0.925126	+	1.60237i	0.791358	+	0.611353i	$0.209374\pi$
$677$	7.46898e9	+	1.29367e10i	0.925126	+	1.60237i	0.133768	+	0.991013i	$0.457292\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	4.60342e8	+	7.97335e8i	0.0558554	+	0.0967444i
$682$		0			0
$683$	4.75208e9	−	8.23084e9i	0.570704	−	0.988488i	−0.425790	−	0.904822i	$-0.640004\pi$
$683$	4.75208e9	−	8.23084e9i	0.570704	−	0.988488i	0.996494	−	0.0836663i	$-0.0266630\pi$
$684$		0			0
$685$	1.12587e10			1.33835
$686$		0			0
$687$	6.14055e9			0.722535
$688$		0			0
$689$	−3.07624e9	+	5.32820e9i	−0.358305	+	0.620602i
$690$		0			0
$691$	−9.39463e8	−	1.62720e9i	−0.108320	−	0.187615i	0.806770	−	0.590866i	$-0.201214\pi$
$691$	−9.39463e8	−	1.62720e9i	−0.108320	−	0.187615i	−0.915090	+	0.403251i	$0.867880\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.36287e8	+	1.44849e9i	0.0944949	+	0.163670i
$696$		0			0
$697$	1.20570e10	−	2.08834e10i	1.34873	−	2.33607i
$698$		0			0
$699$	1.53646e9			0.170158
$700$		0			0
$701$	−1.06591e10			−1.16872			−0.584359	−	0.811496i	$-0.698654\pi$
$701$	−1.06591e10			−1.16872			−0.584359	+	0.811496i	$0.698654\pi$
$702$		0			0
$703$	2.45336e9	−	4.24934e9i	0.266328	−	0.461294i
$704$		0			0
$705$	−1.47859e9	−	2.56099e9i	−0.158922	−	0.275262i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.92322e9	+	1.37234e10i	0.834911	+	1.44611i	0.894103	+	0.447861i	$0.147814\pi$
$709$	7.92322e9	+	1.37234e10i	0.834911	+	1.44611i	−0.0591921	+	0.998247i	$0.518852\pi$
$710$		0			0
$711$	4.11757e8	−	7.13184e8i	0.0429632	−	0.0744145i
$712$		0			0
$713$	−2.31237e9			−0.238915
$714$		0			0
$715$	7.06284e9			0.722617
$716$		0			0
$717$	−4.08666e9	+	7.07831e9i	−0.414049	+	0.717154i
$718$		0			0
$719$	8.92412e9	+	1.54570e10i	0.895394	+	1.55087i	0.833316	+	0.552797i	$0.186440\pi$
$719$	8.92412e9	+	1.54570e10i	0.895394	+	1.55087i	0.0620787	+	0.998071i	$0.480227\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	3.42489e8	+	5.93209e8i	0.0337026	+	0.0583746i
$724$		0			0
$725$	−4.10669e8	+	7.11300e8i	−0.0400230	+	0.0693218i
$726$		0			0
$727$	1.41123e10			1.36216			0.681081	−	0.732208i	$-0.261510\pi$
$727$	1.41123e10			1.36216			0.681081	+	0.732208i	$0.261510\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$		0			0
$731$	−1.38504e9	+	2.39895e9i	−0.131145	+	0.227149i
$732$		0			0
$733$	2.77662e9	+	4.80925e9i	0.260407	+	0.451038i	0.966350	−	0.257230i	$-0.0828099\pi$
$733$	2.77662e9	+	4.80925e9i	0.260407	+	0.451038i	−0.705943	+	0.708269i	$0.749477\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.91919e9	+	6.78823e9i	0.360628	+	0.624627i
$738$		0			0
$739$	−4.86307e9	+	8.42308e9i	−0.443256	+	0.767742i	−0.997929	−	0.0643262i	$-0.979510\pi$
$739$	−4.86307e9	+	8.42308e9i	−0.443256	+	0.767742i	0.554673	+	0.832069i	$0.312844\pi$
$740$		0			0
$741$	−6.38420e9			−0.576425
$742$		0			0
$743$	8.37462e8			0.0749038			0.0374519	−	0.999298i	$-0.488076\pi$
$743$	8.37462e8			0.0749038			0.0374519	+	0.999298i	$0.488076\pi$
$744$		0			0
$745$	7.31238e8	−	1.26654e9i	0.0647906	−	0.112221i
$746$		0			0
$747$	−2.15493e9	−	3.73246e9i	−0.189152	−	0.327622i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.52711e9	+	2.64503e9i	0.131562	+	0.227872i	0.924279	−	0.381718i	$-0.124667\pi$
$751$	1.52711e9	+	2.64503e9i	0.131562	+	0.227872i	−0.792717	+	0.609590i	$0.791334\pi$
$752$		0			0
$753$	1.97835e8	−	3.42660e8i	0.0168857	−	0.0292469i
$754$		0			0
$755$	1.91280e10			1.61754
$756$		0			0
$757$	1.77250e10			1.48508			0.742541	−	0.669800i	$-0.233620\pi$
$757$	1.77250e10			1.48508			0.742541	+	0.669800i	$0.233620\pi$
$758$		0			0
$759$	1.71919e9	−	2.97773e9i	0.142718	−	0.247194i
$760$		0			0
$761$	−6.41340e8	−	1.11083e9i	−0.0527524	−	0.0913698i	0.838443	−	0.544989i	$-0.183466\pi$
$761$	−6.41340e8	−	1.11083e9i	−0.0527524	−	0.0913698i	−0.891196	+	0.453619i	$0.850133\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.59786e9	+	6.23167e9i	0.290555	+	0.503256i
$766$		0			0
$767$	−2.97937e9	+	5.16043e9i	−0.238419	+	0.412954i
$768$		0			0
$769$	1.50778e10			1.19562			0.597812	−	0.801636i	$-0.296037\pi$
$769$	1.50778e10			1.19562			0.597812	+	0.801636i	$0.296037\pi$
$770$		0			0
$771$	−6.33561e8			−0.0497849
$772$		0			0
$773$	−6.33683e9	+	1.09757e10i	−0.493451	+	0.854682i	−0.999972	−	0.00754572i	$-0.997598\pi$
$773$	−6.33683e9	+	1.09757e10i	−0.493451	+	0.854682i	0.506521	+	0.862228i	$0.330931\pi$
$774$		0			0
$775$	−2.71533e8	−	4.70309e8i	−0.0209540	−	0.0362933i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.70641e10	−	2.95559e10i	−1.29331	−	2.24008i
$780$		0			0
$781$	7.76758e9	−	1.34538e10i	0.583455	−	1.01057i
$782$		0			0
$783$	−3.09405e9			−0.230336
$784$		0			0
$785$	−2.13516e10			−1.57539
$786$		0			0
$787$	7.33422e8	−	1.27032e9i	0.0536342	−	0.0928972i	−0.837962	−	0.545729i	$-0.816253\pi$
$787$	7.33422e8	−	1.27032e9i	0.0536342	−	0.0928972i	0.891596	+	0.452832i	$0.149586\pi$
$788$		0			0
$789$	−5.74537e9	−	9.95128e9i	−0.416437	−	0.721289i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.19019e9	+	7.25763e9i	0.298386	+	0.516819i
$794$		0			0
$795$	4.90717e9	−	8.49947e9i	0.346375	−	0.599938i
$796$		0			0
$797$	−1.49629e10			−1.04692			−0.523459	−	0.852051i	$-0.675359\pi$
$797$	−1.49629e10			−1.04692			−0.523459	+	0.852051i	$0.675359\pi$
$798$		0			0
$799$	−1.48297e10			−1.02853
$800$		0			0
$801$	3.27230e8	−	5.66779e8i	0.0224978	−	0.0389673i
$802$		0			0
$803$	8.21049e9	+	1.42210e10i	0.559583	+	0.969226i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.30633e9	+	9.19084e9i	0.355416	+	0.615599i
$808$		0			0
$809$	−5.31315e9	+	9.20265e9i	−0.352803	+	0.611073i	−0.986739	−	0.162312i	$-0.948105\pi$
$809$	−5.31315e9	+	9.20265e9i	−0.352803	+	0.611073i	0.633936	+	0.773385i	$0.281438\pi$
$810$		0			0
$811$	−2.44306e10			−1.60828			−0.804139	−	0.594442i	$-0.797373\pi$
$811$	−2.44306e10			−1.60828			−0.804139	+	0.594442i	$0.797373\pi$
$812$		0			0
$813$	1.59181e9			0.103890
$814$		0			0
$815$	3.30063e9	−	5.71687e9i	0.213573	−	0.369919i
$816$		0			0
$817$	1.96022e9	+	3.39520e9i	0.125756	+	0.217815i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.34284e10	−	2.32586e10i	−0.846882	−	1.46684i	−0.883977	−	0.467530i	$-0.845144\pi$
$821$	−1.34284e10	−	2.32586e10i	−0.846882	−	1.46684i	0.0370955	−	0.999312i	$-0.488189\pi$
$822$		0			0
$823$	−2.91457e9	+	5.04818e9i	−0.182253	+	0.315672i	−0.942647	−	0.333790i	$-0.891672\pi$
$823$	−2.91457e9	+	5.04818e9i	−0.182253	+	0.315672i	0.760394	+	0.649462i	$0.225006\pi$
$824$		0			0
$825$	8.07513e8			0.0500681
$826$		0			0
$827$	−1.31761e10			−0.810062			−0.405031	−	0.914303i	$-0.632739\pi$
$827$	−1.31761e10			−0.810062			−0.405031	+	0.914303i	$0.632739\pi$
$828$		0			0
$829$	−9.98170e9	+	1.72888e10i	−0.608504	+	1.05396i	0.382983	+	0.923755i	$0.374897\pi$
$829$	−9.98170e9	+	1.72888e10i	−0.608504	+	1.05396i	−0.991487	+	0.130205i	$0.958437\pi$
$830$		0			0
$831$	2.91564e8	+	5.05004e8i	0.0176251	+	0.0305275i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−4.79977e9	−	8.31344e9i	−0.285310	−	0.494172i
$836$		0			0
$837$	1.02289e9	−	1.77169e9i	0.0602960	−	0.104436i
$838$		0			0
$839$	2.19433e10			1.28273			0.641365	−	0.767236i	$-0.278368\pi$
$839$	2.19433e10			1.28273			0.641365	+	0.767236i	$0.278368\pi$
$840$		0			0
$841$	7.46008e9			0.432471
$842$		0			0
$843$	4.51869e9	−	7.82661e9i	0.259786	−	0.449963i
$844$		0			0
$845$	5.65159e9	+	9.78884e9i	0.322234	+	0.558127i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.41189e9	−	7.64161e9i	−0.247427	−	0.428557i
$850$		0			0
$851$	1.05493e9	−	1.82720e9i	0.0586775	−	0.101632i
$852$		0			0
$853$	−2.13102e10			−1.17562			−0.587808	−	0.809000i	$-0.700009\pi$
$853$	−2.13102e10			−1.17562			−0.587808	+	0.809000i	$0.700009\pi$
$854$		0			0
$855$	1.01840e10			0.557232
$856$		0			0
$857$	−2.32998e9	+	4.03564e9i	−0.126450	+	0.219018i	−0.922299	−	0.386478i	$-0.873692\pi$
$857$	−2.32998e9	+	4.03564e9i	−0.126450	+	0.219018i	0.795849	+	0.605495i	$0.207025\pi$
$858$		0			0
$859$	8.42102e8	+	1.45856e9i	0.0453303	+	0.0785144i	0.887800	−	0.460229i	$-0.152233\pi$
$859$	8.42102e8	+	1.45856e9i	0.0453303	+	0.0785144i	−0.842470	+	0.538743i	$0.818899\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.43162e8	−	9.40784e8i	−0.0287668	−	0.0498255i	0.851284	−	0.524706i	$-0.175825\pi$
$863$	−5.43162e8	−	9.40784e8i	−0.0287668	−	0.0498255i	−0.880050	+	0.474880i	$0.842491\pi$
$864$		0			0
$865$	−1.38772e10	+	2.40360e10i	−0.729030	+	1.26272i
$866$		0			0
$867$	2.50060e10			1.30310
$868$		0			0
$869$	6.46611e9			0.334252
$870$		0			0
$871$	3.12905e9	−	5.41968e9i	0.160453	−	0.277914i
$872$		0			0
$873$	−5.00060e9	−	8.66130e9i	−0.254374	−	0.440588i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.57215e9	−	9.65124e9i	−0.278948	−	0.483153i	0.692175	−	0.721729i	$-0.256653\pi$
$877$	−5.57215e9	−	9.65124e9i	−0.278948	−	0.483153i	−0.971124	+	0.238577i	$0.923319\pi$
$878$		0			0
$879$	9.84102e9	−	1.70451e10i	0.488741	−	0.846525i
$880$		0			0
$881$	−3.78845e10			−1.86658			−0.933288	−	0.359130i	$-0.883074\pi$
$881$	−3.78845e10			−1.86658			−0.933288	+	0.359130i	$0.883074\pi$
$882$		0			0
$883$	1.58131e10			0.772956			0.386478	−	0.922299i	$-0.373692\pi$
$883$	1.58131e10			0.772956			0.386478	+	0.922299i	$0.373692\pi$
$884$		0			0
$885$	4.75266e9	−	8.23184e9i	0.230481	−	0.399205i
$886$		0			0
$887$	7.60855e9	+	1.31784e10i	0.366074	+	0.634059i	0.988948	−	0.148263i	$-0.0473683\pi$
$887$	7.60855e9	+	1.31784e10i	0.366074	+	0.634059i	−0.622874	+	0.782322i	$0.714035\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.52098e9	+	2.63442e9i	0.0720365	+	0.124771i
$892$		0			0
$893$	−1.04941e10	+	1.81763e10i	−0.493135	+	0.854135i
$894$		0			0
$895$	−1.12209e10			−0.523173
$896$		0			0
$897$	−2.74518e9			−0.126998
$898$		0			0
$899$	−8.16906e9	+	1.41492e10i	−0.374984	+	0.649492i
$900$		0			0
$901$	−2.46085e10	−	4.26232e10i	−1.12085	−	1.94138i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.52267e9	+	7.83349e9i	0.202827	+	0.351306i
$906$		0			0
$907$	7.61976e9	−	1.31978e10i	0.339091	−	0.587322i	−0.645171	−	0.764038i	$-0.723214\pi$
$907$	7.61976e9	−	1.31978e10i	0.339091	−	0.587322i	0.984262	+	0.176716i	$0.0565473\pi$
$908$		0			0
$909$	1.40918e9			0.0622292
$910$		0			0
$911$	−1.49447e10			−0.654895			−0.327448	−	0.944869i	$-0.606189\pi$
$911$	−1.49447e10			−0.654895			−0.327448	+	0.944869i	$0.606189\pi$
$912$		0			0
$913$	1.69202e10	−	2.93067e10i	0.735798	−	1.27444i
$914$		0			0
$915$	−6.68414e9	−	1.15773e10i	−0.288451	−	0.499611i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.26457e9	+	1.43147e10i	0.351250	+	0.608383i	0.986469	−	0.163950i	$-0.0524234\pi$
$919$	8.26457e9	+	1.43147e10i	0.351250	+	0.608383i	−0.635219	+	0.772332i	$0.719090\pi$
$920$		0			0
$921$	1.70153e9	−	2.94714e9i	0.0717681	−	0.124306i
$922$		0			0
$923$	−1.24032e10			−0.519190
$924$		0			0
$925$	4.95508e8			0.0205852
$926$		0			0
$927$	−1.73548e9	+	3.00595e9i	−0.0715552	+	0.123937i
$928$		0			0
$929$	1.29085e10	+	2.23582e10i	0.528228	+	0.914918i	0.999458	+	0.0329078i	$0.0104768\pi$
$929$	1.29085e10	+	2.23582e10i	0.528228	+	0.914918i	−0.471230	+	0.882010i	$0.656190\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	9.66287e9	+	1.67366e10i	0.389512	+	0.674654i
$934$		0			0
$935$	−2.82498e10	+	4.89301e10i	−1.13025	+	1.95765i
$936$		0			0
$937$	−1.83428e10			−0.728411			−0.364206	−	0.931319i	$-0.618659\pi$
$937$	−1.83428e10			−0.728411			−0.364206	+	0.931319i	$0.618659\pi$
$938$		0			0
$939$	−7.86229e9			−0.309899
$940$		0			0
$941$	3.16673e9	−	5.48494e9i	0.123893	−	0.214589i	−0.797407	−	0.603442i	$-0.793795\pi$
$941$	3.16673e9	−	5.48494e9i	0.123893	−	0.214589i	0.921300	+	0.388853i	$0.127129\pi$
$942$		0			0
$943$	−7.33750e9	−	1.27089e10i	−0.284943	−	0.493535i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.00979e10	−	1.74901e10i	−0.386372	−	0.669216i	0.605587	−	0.795779i	$-0.292939\pi$
$947$	−1.00979e10	−	1.74901e10i	−0.386372	−	0.669216i	−0.991958	+	0.126564i	$0.959605\pi$
$948$		0			0
$949$	6.55519e9	−	1.13539e10i	0.248974	−	0.431235i
$950$		0			0
$951$	1.14557e9			0.0431906
$952$		0			0
$953$	4.86172e10			1.81955			0.909777	−	0.415096i	$-0.136252\pi$
$953$	4.86172e10			1.81955			0.909777	+	0.415096i	$0.136252\pi$
$954$		0			0
$955$	−6.62585e9	+	1.14763e10i	−0.246167	+	0.426374i
$956$		0			0
$957$	−1.21470e10	−	2.10392e10i	−0.448000	−	0.775958i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	8.35496e9	+	1.44712e10i	0.303677	+	0.525985i
$962$		0			0
$963$	−8.05704e8	+	1.39552e9i	−0.0290726	+	0.0503552i
$964$		0			0
$965$	1.63210e10			0.584659
$966$		0			0
$967$	1.23778e10			0.440201			0.220100	−	0.975477i	$-0.429362\pi$
$967$	1.23778e10			0.440201			0.220100	+	0.975477i	$0.429362\pi$
$968$		0			0
$969$	2.55354e10	−	4.42286e10i	0.901591	−	1.56160i
$970$		0			0
$971$	8.52984e9	+	1.47741e10i	0.299001	+	0.517886i	0.975908	−	0.218183i	$-0.0700131\pi$
$971$	8.52984e9	+	1.47741e10i	0.299001	+	0.517886i	−0.676906	+	0.736069i	$0.736680\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.22356e8	−	5.58338e8i	−0.0111383	−	0.0192922i
$976$		0			0
$977$	−1.98472e10	+	3.43764e10i	−0.680878	+	1.17932i	0.293835	+	0.955856i	$0.405068\pi$
$977$	−1.98472e10	+	3.43764e10i	−0.680878	+	1.17932i	−0.974713	+	0.223459i	$0.928265\pi$
$978$		0			0
$979$	5.13872e9			0.175031
$980$		0			0
$981$	−1.46477e10			−0.495368
$982$		0			0
$983$	3.77699e7	−	6.54193e7i	0.00126826	−	0.00219669i	−0.865391	−	0.501098i	$-0.832930\pi$
$983$	3.77699e7	−	6.54193e7i	0.00126826	−	0.00219669i	0.866659	+	0.498901i	$0.166263\pi$
$984$		0			0
$985$	−6.75615e8	−	1.17020e9i	−0.0225254	−	0.0390152i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.42888e8	+	1.45992e9i	0.0277066	+	0.0479892i
$990$		0			0
$991$	1.49513e10	−	2.58964e10i	0.488001	−	0.845243i	−0.511904	−	0.859043i	$-0.671059\pi$
$991$	1.49513e10	−	2.58964e10i	0.488001	−	0.845243i	0.999905	+	0.0138000i	$0.00439281\pi$
$992$		0			0
$993$	−1.47759e10			−0.478886
$994$		0			0
$995$	−5.97064e10			−1.92150
$996$		0			0
$997$	−6.21272e9	+	1.07607e10i	−0.198540	+	0.343882i	−0.948055	−	0.318105i	$-0.896953\pi$
$997$	−6.21272e9	+	1.07607e10i	−0.198540	+	0.343882i	0.749515	+	0.661987i	$0.230287\pi$
$998$		0			0
$999$	9.33309e8	+	1.61654e9i	0.0296173	+	0.0512988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.8.i.b.361.1		2
7.2	even	3	inner	588.8.i.b.373.1		2
7.3	odd	6		588.8.a.a.1.1		1
7.4	even	3		12.8.a.b.1.1	✓	1
7.5	odd	6		588.8.i.g.373.1		2
7.6	odd	2		588.8.i.g.361.1		2
21.11	odd	6		36.8.a.a.1.1		1
28.11	odd	6		48.8.a.d.1.1		1
35.4	even	6		300.8.a.a.1.1		1
35.18	odd	12		300.8.d.a.49.2		2
35.32	odd	12		300.8.d.a.49.1		2
56.11	odd	6		192.8.a.j.1.1		1
56.53	even	6		192.8.a.b.1.1		1
63.4	even	3		324.8.e.b.217.1		2
63.11	odd	6		324.8.e.e.109.1		2
63.25	even	3		324.8.e.b.109.1		2
63.32	odd	6		324.8.e.e.217.1		2
84.11	even	6		144.8.a.c.1.1		1
168.11	even	6		576.8.a.u.1.1		1
168.53	odd	6		576.8.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.8.a.b.1.1	✓	1	7.4	even	3
36.8.a.a.1.1		1	21.11	odd	6
48.8.a.d.1.1		1	28.11	odd	6
144.8.a.c.1.1		1	84.11	even	6
192.8.a.b.1.1		1	56.53	even	6
192.8.a.j.1.1		1	56.11	odd	6
300.8.a.a.1.1		1	35.4	even	6
300.8.d.a.49.1		2	35.32	odd	12
300.8.d.a.49.2		2	35.18	odd	12
324.8.e.b.109.1		2	63.25	even	3
324.8.e.b.217.1		2	63.4	even	3
324.8.e.e.109.1		2	63.11	odd	6
324.8.e.e.217.1		2	63.32	odd	6
576.8.a.u.1.1		1	168.11	even	6
576.8.a.v.1.1		1	168.53	odd	6
588.8.a.a.1.1		1	7.3	odd	6
588.8.i.b.361.1		2	1.1	even	1	trivial
588.8.i.b.373.1		2	7.2	even	3	inner
588.8.i.g.361.1		2	7.6	odd	2
588.8.i.g.373.1		2	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	588.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.5000 + 23.3827i) q^{3} +(-135.000 - 233.827i) q^{5} +(-364.500 - 631.333i) q^{9} +O(q^{10})\)	\(q+(-13.5000 + 23.3827i) q^{3} +(-135.000 - 233.827i) q^{5} +(-364.500 - 631.333i) q^{9} +(2862.00 - 4957.13i) q^{11} -4570.00 q^{13} +7290.00 q^{15} +(18279.0 - 31660.2i) q^{17} +(-25870.0 - 44808.2i) q^{19} +(-11124.0 - 19267.3i) q^{23} +(2612.50 - 4524.98i) q^{25} +19683.0 q^{27} -157194. q^{29} +(51968.0 - 90011.2i) q^{31} +(77274.0 + 133842. i) q^{33} +(47417.0 + 82128.7i) q^{37} +(61695.0 - 106859. i) q^{39} +659610. q^{41} -75772.0 q^{43} +(-98415.0 + 170460. i) q^{45} +(-202824. - 351301. i) q^{47} +(493533. + 854824. i) q^{51} +(673137. - 1.16591e6i) q^{53} -1.54548e6 q^{55} +1.39698e6 q^{57} +(651942. - 1.12920e6i) q^{59} +(-916891. - 1.58810e6i) q^{61} +(616950. + 1.06859e6i) q^{65} +(-684694. + 1.18592e6i) q^{67} +600696. q^{69} +2.71404e6 q^{71} +(-1.43440e6 + 2.48445e6i) q^{73} +(70537.5 + 122175. i) q^{75} +(564824. + 978304. i) q^{79} +(-265720. + 460241. i) q^{81} +5.91203e6 q^{83} -9.87066e6 q^{85} +(2.12212e6 - 3.67562e6i) q^{87} +(448875. + 777474. i) q^{89} +(1.40314e6 + 2.43030e6i) q^{93} +(-6.98490e6 + 1.20982e7i) q^{95} +1.37191e7 q^{97} -4.17280e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 27 q^{3} - 270 q^{5} - 729 q^{9}+O(q^{10}) \) 2 * q - 27 * q^3 - 270 * q^5 - 729 * q^9	\( 2 q - 27 q^{3} - 270 q^{5} - 729 q^{9} + 5724 q^{11} - 9140 q^{13} + 14580 q^{15} + 36558 q^{17} - 51740 q^{19} - 22248 q^{23} + 5225 q^{25} + 39366 q^{27} - 314388 q^{29} + 103936 q^{31} + 154548 q^{33} + 94834 q^{37} + 123390 q^{39} + 1319220 q^{41} - 151544 q^{43} - 196830 q^{45} - 405648 q^{47} + 987066 q^{51} + 1346274 q^{53} - 3090960 q^{55} + 2793960 q^{57} + 1303884 q^{59} - 1833782 q^{61} + 1233900 q^{65} - 1369388 q^{67} + 1201392 q^{69} + 5428080 q^{71} - 2868794 q^{73} + 141075 q^{75} + 1129648 q^{79} - 531441 q^{81} + 11824056 q^{83} - 19741320 q^{85} + 4244238 q^{87} + 897750 q^{89} + 2806272 q^{93} - 13969800 q^{95} + 27438148 q^{97} - 8345592 q^{99}+O(q^{100}) \) 2 * q - 27 * q^3 - 270 * q^5 - 729 * q^9 + 5724 * q^11 - 9140 * q^13 + 14580 * q^15 + 36558 * q^17 - 51740 * q^19 - 22248 * q^23 + 5225 * q^25 + 39366 * q^27 - 314388 * q^29 + 103936 * q^31 + 154548 * q^33 + 94834 * q^37 + 123390 * q^39 + 1319220 * q^41 - 151544 * q^43 - 196830 * q^45 - 405648 * q^47 + 987066 * q^51 + 1346274 * q^53 - 3090960 * q^55 + 2793960 * q^57 + 1303884 * q^59 - 1833782 * q^61 + 1233900 * q^65 - 1369388 * q^67 + 1201392 * q^69 + 5428080 * q^71 - 2868794 * q^73 + 141075 * q^75 + 1129648 * q^79 - 531441 * q^81 + 11824056 * q^83 - 19741320 * q^85 + 4244238 * q^87 + 897750 * q^89 + 2806272 * q^93 - 13969800 * q^95 + 27438148 * q^97 - 8345592 * q^99

Introduction

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