LMFDB - Embedded newform 80.11.p.d.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,11,Mod(17,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("80.17");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, 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:	$50.8285802139$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1334x^{6} + 456089x^{4} + 43159076x^{2} + 31360000 $ x^8 + 1334x^6 + 456089x^4 + 43159076*x^2 + 31360000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.2
Root			$0.855727i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.11.p.d.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-70.6389 + 70.6389i) q^{3} +(1004.90 - 2959.02i) q^{5} +(-2611.74 - 2611.74i) q^{7} +49069.3i q^{9} +O(q^{10})$	\(q+(-70.6389 + 70.6389i) q^{3} +(1004.90 - 2959.02i) q^{5} +(-2611.74 - 2611.74i) q^{7} +49069.3i q^{9} -15694.7 q^{11} +(294351. - 294351. i) q^{13} +(138037. + 280007. i) q^{15} +(1.23520e6 + 1.23520e6i) q^{17} -2.66159e6i q^{19} +368981. q^{21} +(-7.36638e6 + 7.36638e6i) q^{23} +(-7.74599e6 - 5.94702e6i) q^{25} +(-7.63735e6 - 7.63735e6i) q^{27} +1.66720e7i q^{29} +2.74330e7 q^{31} +(1.10866e6 - 1.10866e6i) q^{33} +(-1.03527e7 + 5.10367e6i) q^{35} +(-6.47670e7 - 6.47670e7i) q^{37} +4.15853e7i q^{39} +5.65192e7 q^{41} +(1.85471e8 - 1.85471e8i) q^{43} +(1.45197e8 + 4.93095e7i) q^{45} +(-6.69481e7 - 6.69481e7i) q^{47} -2.68833e8i q^{49} -1.74507e8 q^{51} +(1.86243e8 - 1.86243e8i) q^{53} +(-1.57716e7 + 4.64411e7i) q^{55} +(1.88012e8 + 1.88012e8i) q^{57} -7.53831e8i q^{59} -3.22219e8 q^{61} +(1.28156e8 - 1.28156e8i) q^{63} +(-5.75200e8 - 1.16678e9i) q^{65} +(-9.46635e8 - 9.46635e8i) q^{67} -1.04071e9i q^{69} +1.70508e9 q^{71} +(8.54176e8 - 8.54176e8i) q^{73} +(9.67259e8 - 1.27078e8i) q^{75} +(4.09906e7 + 4.09906e7i) q^{77} -1.15355e9i q^{79} -1.81851e9 q^{81} +(3.46702e9 - 3.46702e9i) q^{83} +(4.89624e9 - 2.41374e9i) q^{85} +(-1.17769e9 - 1.17769e9i) q^{87} -6.69639e9i q^{89} -1.53754e9 q^{91} +(-1.93784e9 + 1.93784e9i) q^{93} +(-7.87570e9 - 2.67462e9i) q^{95} +(1.86215e9 + 1.86215e9i) q^{97} -7.70130e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 60 q^{3} - 5340 q^{5} + 14500 q^{7}+O(q^{10}) $ 8 * q - 60 * q^3 - 5340 * q^5 + 14500 * q^7	$ 8 q - 60 q^{3} - 5340 q^{5} + 14500 q^{7} + 233784 q^{11} + 433520 q^{13} + 3188580 q^{15} + 1045440 q^{17} - 20777784 q^{21} - 24737580 q^{23} - 35382400 q^{25} - 27386640 q^{27} - 258616 q^{31} + 11269320 q^{33} - 113638860 q^{35} + 92216120 q^{37} + 115357416 q^{41} + 262653700 q^{43} + 593742420 q^{45} + 669481140 q^{47} + 768258984 q^{51} - 1321976040 q^{53} - 2597320 q^{55} + 2367269280 q^{57} - 3143200184 q^{61} - 2578662540 q^{63} - 1924527480 q^{65} - 4912566140 q^{67} + 4375053384 q^{71} - 786968920 q^{73} - 5379002700 q^{75} + 7522045800 q^{77} - 2499208992 q^{81} + 11064240660 q^{83} + 15814282160 q^{85} - 2020273920 q^{87} + 12917794184 q^{91} - 40141724280 q^{93} - 14671558800 q^{95} + 24688294760 q^{97}+O(q^{100}) $ 8 * q - 60 * q^3 - 5340 * q^5 + 14500 * q^7 + 233784 * q^11 + 433520 * q^13 + 3188580 * q^15 + 1045440 * q^17 - 20777784 * q^21 - 24737580 * q^23 - 35382400 * q^25 - 27386640 * q^27 - 258616 * q^31 + 11269320 * q^33 - 113638860 * q^35 + 92216120 * q^37 + 115357416 * q^41 + 262653700 * q^43 + 593742420 * q^45 + 669481140 * q^47 + 768258984 * q^51 - 1321976040 * q^53 - 2597320 * q^55 + 2367269280 * q^57 - 3143200184 * q^61 - 2578662540 * q^63 - 1924527480 * q^65 - 4912566140 * q^67 + 4375053384 * q^71 - 786968920 * q^73 - 5379002700 * q^75 + 7522045800 * q^77 - 2499208992 * q^81 + 11064240660 * q^83 + 15814282160 * q^85 - 2020273920 * q^87 + 12917794184 * q^91 - 40141724280 * q^93 - 14671558800 * q^95 + 24688294760 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	−70.6389	+	70.6389i	−0.290695	+	0.290695i	−0.837355	−	0.546660i	$-0.815899\pi$
$3$	−70.6389	+	70.6389i	−0.290695	+	0.290695i	0.546660	+	0.837355i	$0.315899\pi$
$4$		0			0
$5$	1004.90	−	2959.02i	0.321567	−	0.946887i
$5$	1004.90	−	2959.02i	0.321567	−	0.946887i
$6$		0			0
$7$	−2611.74	−	2611.74i	−0.155396	−	0.155396i	0.625127	−	0.780523i	$-0.285047\pi$
$7$	−2611.74	−	2611.74i	−0.155396	−	0.155396i	−0.780523	+	0.625127i	$0.785047\pi$
$8$		0			0
$9$			49069.3i			0.830993i
$10$		0			0
$11$	−15694.7			−0.0974520			−0.0487260	−	0.998812i	$-0.515516\pi$
$11$	−15694.7			−0.0974520			−0.0487260	+	0.998812i	$0.515516\pi$
$12$		0			0
$13$	294351.	−	294351.i	0.792774	−	0.792774i	−0.189170	−	0.981944i	$-0.560580\pi$
$13$	294351.	−	294351.i	0.792774	−	0.792774i	0.981944	+	0.189170i	$0.0605799\pi$
$14$		0			0
$15$	138037.	+	280007.i	0.181777	+	0.368733i
$16$		0			0
$17$	1.23520e6	+	1.23520e6i	0.869948	+	0.869948i	0.992466	−	0.122518i	$-0.0390969\pi$
$17$	1.23520e6	+	1.23520e6i	0.869948	+	0.869948i	−0.122518	+	0.992466i	$0.539097\pi$
$18$		0			0
$19$		−	2.66159e6i		−	1.07491i	−0.843292	−	0.537456i	$-0.819385\pi$
$19$		−	2.66159e6i		−	1.07491i	0.843292	−	0.537456i	$-0.180615\pi$
$20$		0			0
$21$	368981.			0.0903457
$22$		0			0
$23$	−7.36638e6	+	7.36638e6i	−1.14450	+	1.14450i	−0.156880	+	0.987618i	$0.550144\pi$
$23$	−7.36638e6	+	7.36638e6i	−1.14450	+	1.14450i	−0.987618	+	0.156880i	$0.949856\pi$
$24$		0			0
$25$	−7.74599e6	−	5.94702e6i	−0.793190	−	0.608975i
$26$		0			0
$27$	−7.63735e6	−	7.63735e6i	−0.532260	−	0.532260i
$28$		0			0
$29$			1.66720e7i			0.812824i	0.913690	+	0.406412i	$0.133220\pi$
$29$			1.66720e7i			0.812824i	−0.913690	+	0.406412i	$0.866780\pi$
$30$		0			0
$31$	2.74330e7			0.958219			0.479109	−	0.877755i	$-0.340960\pi$
$31$	2.74330e7			0.958219			0.479109	+	0.877755i	$0.340960\pi$
$32$		0			0
$33$	1.10866e6	−	1.10866e6i	0.0283288	−	0.0283288i
$34$		0			0
$35$	−1.03527e7	+	5.10367e6i	−0.197113	+	0.0971723i
$36$		0			0
$37$	−6.47670e7	−	6.47670e7i	−0.933996	−	0.933996i	0.0639563	−	0.997953i	$-0.479628\pi$
$37$	−6.47670e7	−	6.47670e7i	−0.933996	−	0.933996i	−0.997953	+	0.0639563i	$0.979628\pi$
$38$		0			0
$39$			4.15853e7i			0.460911i
$40$		0			0
$41$	5.65192e7			0.487839			0.243920	−	0.969795i	$-0.421567\pi$
$41$	5.65192e7			0.487839			0.243920	+	0.969795i	$0.421567\pi$
$42$		0			0
$43$	1.85471e8	−	1.85471e8i	1.26163	−	1.26163i	0.311335	−	0.950300i	$-0.399224\pi$
$43$	1.85471e8	−	1.85471e8i	1.26163	−	1.26163i	0.950300	−	0.311335i	$-0.100776\pi$
$44$		0			0
$45$	1.45197e8	+	4.93095e7i	0.786856	+	0.267220i
$46$		0			0
$47$	−6.69481e7	−	6.69481e7i	−0.291910	−	0.291910i	0.545924	−	0.837834i	$-0.316179\pi$
$47$	−6.69481e7	−	6.69481e7i	−0.291910	−	0.291910i	−0.837834	+	0.545924i	$0.816179\pi$
$48$		0			0
$49$		−	2.68833e8i		−	0.951704i
$50$		0			0
$51$	−1.74507e8			−0.505779
$52$		0			0
$53$	1.86243e8	−	1.86243e8i	0.445349	−	0.445349i	−0.448456	−	0.893805i	$-0.648026\pi$
$53$	1.86243e8	−	1.86243e8i	0.445349	−	0.445349i	0.893805	+	0.448456i	$0.148026\pi$
$54$		0			0
$55$	−1.57716e7	+	4.64411e7i	−0.0313373	+	0.0922761i
$56$		0			0
$57$	1.88012e8	+	1.88012e8i	0.312471	+	0.312471i
$58$		0			0
$59$		−	7.53831e8i		−	1.05442i	−0.849735	−	0.527210i	$-0.823238\pi$
$59$		−	7.53831e8i		−	1.05442i	0.849735	−	0.527210i	$-0.176762\pi$
$60$		0			0
$61$	−3.22219e8			−0.381507			−0.190753	−	0.981638i	$-0.561093\pi$
$61$	−3.22219e8			−0.381507			−0.190753	+	0.981638i	$0.561093\pi$
$62$		0			0
$63$	1.28156e8	−	1.28156e8i	0.129133	−	0.129133i
$64$		0			0
$65$	−5.75200e8	−	1.16678e9i	−0.495738	−	1.00560i
$66$		0			0
$67$	−9.46635e8	−	9.46635e8i	−0.701146	−	0.701146i	0.263510	−	0.964657i	$-0.415120\pi$
$67$	−9.46635e8	−	9.46635e8i	−0.701146	−	0.701146i	−0.964657	+	0.263510i	$0.915120\pi$
$68$		0			0
$69$		−	1.04071e9i		−	0.665399i
$70$		0			0
$71$	1.70508e9			0.945043			0.472522	−	0.881319i	$-0.343344\pi$
$71$	1.70508e9			0.945043			0.472522	+	0.881319i	$0.343344\pi$
$72$		0			0
$73$	8.54176e8	−	8.54176e8i	0.412034	−	0.412034i	−0.470413	−	0.882447i	$-0.655895\pi$
$73$	8.54176e8	−	8.54176e8i	0.412034	−	0.412034i	0.882447	+	0.470413i	$0.155895\pi$
$74$		0			0
$75$	9.67259e8	−	1.27078e8i	0.407602	−	0.0535504i
$76$		0			0
$77$	4.09906e7	+	4.09906e7i	0.0151437	+	0.0151437i
$78$		0			0
$79$		−	1.15355e9i		−	0.374888i	−0.982275	−	0.187444i	$-0.939980\pi$
$79$		−	1.15355e9i		−	0.374888i	0.982275	−	0.187444i	$-0.0600203\pi$
$80$		0			0
$81$	−1.81851e9			−0.521542
$82$		0			0
$83$	3.46702e9	−	3.46702e9i	0.880167	−	0.880167i	−0.113384	−	0.993551i	$-0.536169\pi$
$83$	3.46702e9	−	3.46702e9i	0.880167	−	0.880167i	0.993551	+	0.113384i	$0.0361690\pi$
$84$		0			0
$85$	4.89624e9	−	2.41374e9i	1.10349	−	0.543996i
$86$		0			0
$87$	−1.17769e9	−	1.17769e9i	−0.236284	−	0.236284i
$88$		0			0
$89$		−	6.69639e9i		−	1.19920i	−0.800301	−	0.599599i	$-0.795327\pi$
$89$		−	6.69639e9i		−	1.19920i	0.800301	−	0.599599i	$-0.204673\pi$
$90$		0			0
$91$	−1.53754e9			−0.246388
$92$		0			0
$93$	−1.93784e9	+	1.93784e9i	−0.278549	+	0.278549i
$94$		0			0
$95$	−7.87570e9	−	2.67462e9i	−1.01782	−	0.345656i
$96$		0			0
$97$	1.86215e9	+	1.86215e9i	0.216849	+	0.216849i	0.807169	−	0.590320i	$-0.200999\pi$
$97$	1.86215e9	+	1.86215e9i	0.216849	+	0.216849i	−0.590320	+	0.807169i	$0.700999\pi$
$98$		0			0
$99$		−	7.70130e8i		−	0.0809820i
$100$		0			0
$101$	−2.20341e7			−0.00209647			−0.00104824	−	0.999999i	$-0.500334\pi$
$101$	−2.20341e7			−0.00209647			−0.00104824	+	0.999999i	$0.500334\pi$
$102$		0			0
$103$	4.11705e9	−	4.11705e9i	0.355141	−	0.355141i	−0.506877	−	0.862018i	$-0.669200\pi$
$103$	4.11705e9	−	4.11705e9i	0.355141	−	0.355141i	0.862018	+	0.506877i	$0.169200\pi$
$104$		0			0
$105$	3.70787e8	−	1.09182e9i	0.0290522	−	0.0855472i
$106$		0			0
$107$	−4.55710e9	−	4.55710e9i	−0.324915	−	0.324915i	0.525734	−	0.850649i	$-0.323791\pi$
$107$	−4.55710e9	−	4.55710e9i	−0.324915	−	0.324915i	−0.850649	+	0.525734i	$0.823791\pi$
$108$		0			0
$109$		−	4.51896e9i		−	0.293701i	−0.989159	−	0.146851i	$-0.953086\pi$
$109$		−	4.51896e9i		−	0.293701i	0.989159	−	0.146851i	$-0.0469137\pi$
$110$		0			0
$111$	9.15013e9			0.543016
$112$		0			0
$113$	6.46147e9	−	6.46147e9i	0.350703	−	0.350703i	−0.509668	−	0.860371i	$-0.670232\pi$
$113$	6.46147e9	−	6.46147e9i	0.350703	−	0.350703i	0.860371	+	0.509668i	$0.170232\pi$
$114$		0			0
$115$	1.43948e10	+	2.91997e10i	0.715678	+	1.45174i
$116$		0			0
$117$	1.44436e10	+	1.44436e10i	0.658789	+	0.658789i
$118$		0			0
$119$		−	6.45206e9i		−	0.270373i
$120$		0			0
$121$	−2.56911e10			−0.990503
$122$		0			0
$123$	−3.99245e9	+	3.99245e9i	−0.141812	+	0.141812i
$124$		0			0
$125$	−2.53813e10	+	1.69444e10i	−0.831693	+	0.555235i
$126$		0			0
$127$	3.05294e9	+	3.05294e9i	0.0924060	+	0.0924060i	0.751799	−	0.659393i	$-0.229187\pi$
$127$	3.05294e9	+	3.05294e9i	0.0924060	+	0.0924060i	−0.659393	+	0.751799i	$0.729187\pi$
$128$		0			0
$129$			2.62029e10i			0.733502i
$130$		0			0
$131$	−1.32702e10			−0.343971			−0.171986	−	0.985099i	$-0.555018\pi$
$131$	−1.32702e10			−0.343971			−0.171986	+	0.985099i	$0.555018\pi$
$132$		0			0
$133$	−6.95138e9	+	6.95138e9i	−0.167037	+	0.167037i
$134$		0			0
$135$	−3.02738e10	+	1.49243e10i	−0.675147	+	0.332833i
$136$		0			0
$137$	−6.77863e9	−	6.77863e9i	−0.140456	−	0.140456i	0.633383	−	0.773839i	$-0.281666\pi$
$137$	−6.77863e9	−	6.77863e9i	−0.140456	−	0.140456i	−0.773839	+	0.633383i	$0.781666\pi$
$138$		0			0
$139$			6.78011e10i			1.30666i	0.757073	+	0.653330i	$0.226629\pi$
$139$			6.78011e10i			1.30666i	−0.757073	+	0.653330i	$0.773371\pi$
$140$		0			0
$141$	9.45828e9			0.169714
$142$		0			0
$143$	−4.61977e9	+	4.61977e9i	−0.0772574	+	0.0772574i
$144$		0			0
$145$	4.93327e10	+	1.67536e10i	0.769653	+	0.261377i
$146$		0			0
$147$	1.89900e10	+	1.89900e10i	0.276655	+	0.276655i
$148$		0			0
$149$			5.59484e10i			0.761827i	0.924611	+	0.380913i	$0.124390\pi$
$149$			5.59484e10i			0.761827i	−0.924611	+	0.380913i	$0.875610\pi$
$150$		0			0
$151$	−1.02237e11			−1.30233			−0.651167	−	0.758934i	$-0.725720\pi$
$151$	−1.02237e11			−1.30233			−0.651167	+	0.758934i	$0.725720\pi$
$152$		0			0
$153$	−6.06105e10	+	6.06105e10i	−0.722921	+	0.722921i
$154$		0			0
$155$	2.75673e10	−	8.11748e10i	0.308131	−	0.907325i
$156$		0			0
$157$	−1.18836e9	−	1.18836e9i	−0.0124580	−	0.0124580i	0.700850	−	0.713308i	$-0.252804\pi$
$157$	−1.18836e9	−	1.18836e9i	−0.0124580	−	0.0124580i	−0.713308	+	0.700850i	$0.752804\pi$
$158$		0			0
$159$			2.63120e10i			0.258921i
$160$		0			0
$161$	3.84782e10			0.355701
$162$		0			0
$163$	−4.34968e10	+	4.34968e10i	−0.378024	+	0.378024i	−0.870389	−	0.492365i	$-0.836133\pi$
$163$	−4.34968e10	+	4.34968e10i	−0.378024	+	0.378024i	0.492365	+	0.870389i	$0.336133\pi$
$164$		0			0
$165$	−2.16646e9	−	4.39463e9i	−0.0177146	−	0.0359338i
$166$		0			0
$167$	1.31695e11	+	1.31695e11i	1.01388	+	1.01388i	0.999902	+	0.0139823i	$0.00445086\pi$
$167$	1.31695e11	+	1.31695e11i	1.01388	+	1.01388i	0.0139823	+	0.999902i	$0.495549\pi$
$168$		0			0
$169$		−	3.54270e10i		−	0.256981i
$170$		0			0
$171$	1.30602e11			0.893245
$172$		0			0
$173$	1.11305e11	−	1.11305e11i	0.718267	−	0.718267i	−0.249983	−	0.968250i	$-0.580425\pi$
$173$	1.11305e11	−	1.11305e11i	0.718267	−	0.718267i	0.968250	+	0.249983i	$0.0804252\pi$
$174$		0			0
$175$	4.69846e9	+	3.57626e10i	0.0286263	+	0.217891i
$176$		0			0
$177$	5.32497e10	+	5.32497e10i	0.306515	+	0.306515i
$178$		0			0
$179$		−	2.45459e11i		−	1.33572i	−0.744289	−	0.667858i	$-0.767211\pi$
$179$		−	2.45459e11i		−	1.33572i	0.744289	−	0.667858i	$-0.232789\pi$
$180$		0			0
$181$	−1.52111e11			−0.783009			−0.391504	−	0.920176i	$-0.628045\pi$
$181$	−1.52111e11			−0.783009			−0.391504	+	0.920176i	$0.628045\pi$
$182$		0			0
$183$	2.27612e10	−	2.27612e10i	0.110902	−	0.110902i
$184$		0			0
$185$	−2.56731e11	+	1.26563e11i	−1.18473	+	0.584047i
$186$		0			0
$187$	−1.93862e10	−	1.93862e10i	−0.0847782	−	0.0847782i
$188$		0			0
$189$			3.98936e10i			0.165422i
$190$		0			0
$191$	−3.04332e11			−1.19724			−0.598619	−	0.801034i	$-0.704284\pi$
$191$	−3.04332e11			−1.19724			−0.598619	+	0.801034i	$0.704284\pi$
$192$		0			0
$193$	2.42004e11	−	2.42004e11i	0.903726	−	0.903726i	−0.0920301	−	0.995756i	$-0.529336\pi$
$193$	2.42004e11	−	2.42004e11i	0.903726	−	0.903726i	0.995756	+	0.0920301i	$0.0293356\pi$
$194$		0			0
$195$	1.23052e11	+	4.17889e10i	0.436430	+	0.148213i
$196$		0			0
$197$	−1.95726e11	−	1.95726e11i	−0.659655	−	0.659655i	0.295643	−	0.955298i	$-0.404466\pi$
$197$	−1.95726e11	−	1.95726e11i	−0.659655	−	0.659655i	−0.955298	+	0.295643i	$0.904466\pi$
$198$		0			0
$199$			1.32708e11i			0.425238i	0.977135	+	0.212619i	$0.0681993\pi$
$199$			1.32708e11i			0.425238i	−0.977135	+	0.212619i	$0.931801\pi$
$200$		0			0
$201$	1.33738e11			0.407639
$202$		0			0
$203$	4.35429e10	−	4.35429e10i	0.126310	−	0.126310i
$204$		0			0
$205$	5.67959e10	−	1.67242e11i	0.156873	−	0.461929i
$206$		0			0
$207$	−3.61463e11	−	3.61463e11i	−0.951070	−	0.951070i
$208$		0			0
$209$			4.17730e10i			0.104752i
$210$		0			0
$211$	2.87300e11			0.686948			0.343474	−	0.939162i	$-0.388396\pi$
$211$	2.87300e11			0.686948			0.343474	+	0.939162i	$0.388396\pi$
$212$		0			0
$213$	−1.20445e11	+	1.20445e11i	−0.274719	+	0.274719i
$214$		0			0
$215$	−3.62434e11	−	7.35192e11i	−0.788926	−	1.60033i
$216$		0			0
$217$	−7.16479e10	−	7.16479e10i	−0.148903	−	0.148903i
$218$		0			0
$219$			1.20676e11i			0.239552i
$220$		0			0
$221$	7.27167e11			1.37934
$222$		0			0
$223$	4.39899e11	−	4.39899e11i	0.797680	−	0.797680i	−0.185049	−	0.982729i	$-0.559245\pi$
$223$	4.39899e11	−	4.39899e11i	0.797680	−	0.797680i	0.982729	+	0.185049i	$0.0592445\pi$
$224$		0			0
$225$	2.91816e11	−	3.80091e11i	0.506054	−	0.659135i
$226$		0			0
$227$	6.77659e11	+	6.77659e11i	1.12430	+	1.12430i	0.991088	+	0.133211i	$0.0425288\pi$
$227$	6.77659e11	+	6.77659e11i	1.12430	+	1.12430i	0.133211	+	0.991088i	$0.457471\pi$
$228$		0			0
$229$		−	4.76659e11i		−	0.756887i	−0.925624	−	0.378443i	$-0.876460\pi$
$229$		−	4.76659e11i		−	0.756887i	0.925624	−	0.378443i	$-0.123540\pi$
$230$		0			0
$231$	−5.79106e9			−0.00880437
$232$		0			0
$233$	2.19919e11	−	2.19919e11i	0.320246	−	0.320246i	−0.528615	−	0.848862i	$-0.677289\pi$
$233$	2.19919e11	−	2.19919e11i	0.320246	−	0.320246i	0.848862	+	0.528615i	$0.177289\pi$
$234$		0			0
$235$	−2.65377e11	+	1.30825e11i	−0.370275	+	0.182537i
$236$		0			0
$237$	8.14855e10	+	8.14855e10i	0.108978	+	0.108978i
$238$		0			0
$239$		−	1.40281e11i		−	0.179891i	−0.995947	−	0.0899454i	$-0.971331\pi$
$239$		−	1.40281e11i		−	0.179891i	0.995947	−	0.0899454i	$-0.0286692\pi$
$240$		0			0
$241$	−7.40125e11			−0.910374			−0.455187	−	0.890396i	$-0.650428\pi$
$241$	−7.40125e11			−0.910374			−0.455187	+	0.890396i	$0.650428\pi$
$242$		0			0
$243$	5.79435e11	−	5.79435e11i	0.683870	−	0.683870i
$244$		0			0
$245$	−7.95482e11	−	2.70149e11i	−0.901156	−	0.306036i
$246$		0			0
$247$	−7.83442e11	−	7.83442e11i	−0.852162	−	0.852162i
$248$		0			0
$249$			4.89812e11i			0.511720i
$250$		0			0
$251$	9.97549e11			1.00130			0.500652	−	0.865649i	$-0.333094\pi$
$251$	9.97549e11			1.00130			0.500652	+	0.865649i	$0.333094\pi$
$252$		0			0
$253$	1.15613e11	−	1.15613e11i	0.111534	−	0.111534i
$254$		0			0
$255$	−1.75361e11	+	5.16369e11i	−0.162642	+	0.478915i
$256$		0			0
$257$	4.29300e11	+	4.29300e11i	0.382909	+	0.382909i	0.872149	−	0.489240i	$-0.162726\pi$
$257$	4.29300e11	+	4.29300e11i	0.382909	+	0.382909i	−0.489240	+	0.872149i	$0.662726\pi$
$258$		0			0
$259$			3.38309e11i			0.290279i
$260$		0			0
$261$	−8.18082e11			−0.675451
$262$		0			0
$263$	−1.26771e12	+	1.26771e12i	−1.00749	+	1.00749i	−0.00751567	+	0.999972i	$0.502392\pi$
$263$	−1.26771e12	+	1.26771e12i	−1.00749	+	1.00749i	−0.999972	+	0.00751567i	$0.997608\pi$
$264$		0			0
$265$	−3.63942e11	−	7.38251e11i	−0.278486	−	0.564904i
$266$		0			0
$267$	4.73026e11	+	4.73026e11i	0.348601	+	0.348601i
$268$		0			0
$269$			1.33804e12i			0.949966i	0.879995	+	0.474983i	$0.157546\pi$
$269$			1.33804e12i			0.949966i	−0.879995	+	0.474983i	$0.842454\pi$
$270$		0			0
$271$	−1.64105e12			−1.12273			−0.561364	−	0.827569i	$-0.689723\pi$
$271$	−1.64105e12			−1.12273			−0.561364	+	0.827569i	$0.689723\pi$
$272$		0			0
$273$	1.08610e11	−	1.08610e11i	0.0716237	−	0.0716237i
$274$		0			0
$275$	1.21571e11	+	9.33369e10i	0.0772979	+	0.0593458i
$276$		0			0
$277$	1.88551e12	+	1.88551e12i	1.15619	+	1.15619i	0.985287	+	0.170905i	$0.0546692\pi$
$277$	1.88551e12	+	1.88551e12i	1.15619	+	1.15619i	0.170905	+	0.985287i	$0.445331\pi$
$278$		0			0
$279$			1.34612e12i			0.796273i
$280$		0			0
$281$	−8.00428e11			−0.456868			−0.228434	−	0.973559i	$-0.573360\pi$
$281$	−8.00428e11			−0.456868			−0.228434	+	0.973559i	$0.573360\pi$
$282$		0			0
$283$	1.51030e12	−	1.51030e12i	0.832013	−	0.832013i	−0.155779	−	0.987792i	$-0.549789\pi$
$283$	1.51030e12	−	1.51030e12i	0.832013	−	0.832013i	0.987792	+	0.155779i	$0.0497886\pi$
$284$		0			0
$285$	7.45262e11	−	3.67398e11i	0.396356	−	0.195395i
$286$		0			0
$287$	−1.47614e11	−	1.47614e11i	−0.0758083	−	0.0758083i
$288$		0			0
$289$			1.03545e12i			0.513620i
$290$		0			0
$291$	−2.63081e11			−0.126074
$292$		0			0
$293$	−2.02228e11	+	2.02228e11i	−0.0936489	+	0.0936489i	−0.752379	−	0.658730i	$-0.771094\pi$
$293$	−2.02228e11	+	2.02228e11i	−0.0936489	+	0.0936489i	0.658730	+	0.752379i	$0.271094\pi$
$294$		0			0
$295$	−2.23060e12	−	7.57521e11i	−0.998417	−	0.339066i
$296$		0			0
$297$	1.19866e11	+	1.19866e11i	0.0518698	+	0.0518698i
$298$		0			0
$299$			4.33661e12i			1.81466i
$300$		0			0
$301$	−9.68805e11			−0.392106
$302$		0			0
$303$	1.55647e9	−	1.55647e9i	0.000609433	−	0.000609433i
$304$		0			0
$305$	−3.23797e11	+	9.53453e11i	−0.122680	+	0.361244i
$306$		0			0
$307$	2.37230e12	+	2.37230e12i	0.869915	+	0.869915i	0.992463	−	0.122548i	$-0.0391064\pi$
$307$	2.37230e12	+	2.37230e12i	0.869915	+	0.869915i	−0.122548	+	0.992463i	$0.539106\pi$
$308$		0			0
$309$			5.81648e11i			0.206475i
$310$		0			0
$311$	−1.53573e12			−0.527853			−0.263926	−	0.964543i	$-0.585018\pi$
$311$	−1.53573e12			−0.527853			−0.263926	+	0.964543i	$0.585018\pi$
$312$		0			0
$313$	−8.40022e11	+	8.40022e11i	−0.279621	+	0.279621i	−0.832958	−	0.553337i	$-0.813354\pi$
$313$	−8.40022e11	+	8.40022e11i	−0.279621	+	0.279621i	0.553337	+	0.832958i	$0.313354\pi$
$314$		0			0
$315$	−2.50434e11	−	5.08001e11i	−0.0807495	−	0.163799i
$316$		0			0
$317$	3.01880e11	+	3.01880e11i	0.0943057	+	0.0943057i	0.752686	−	0.658380i	$-0.228758\pi$
$317$	3.01880e11	+	3.01880e11i	0.0943057	+	0.0943057i	−0.658380	+	0.752686i	$0.728758\pi$
$318$		0			0
$319$		−	2.61662e11i		−	0.0792114i
$320$		0			0
$321$	6.43817e11			0.188902
$322$		0			0
$323$	3.28760e12	−	3.28760e12i	0.935118	−	0.935118i
$324$		0			0
$325$	−4.03056e12	+	5.29531e11i	−1.11160	+	0.146041i
$326$		0			0
$327$	3.19214e11	+	3.19214e11i	0.0853775	+	0.0853775i
$328$		0			0
$329$			3.49703e11i			0.0907234i
$330$		0			0
$331$	2.77221e12			0.697727			0.348863	−	0.937174i	$-0.386568\pi$
$331$	2.77221e12			0.697727			0.348863	+	0.937174i	$0.386568\pi$
$332$		0			0
$333$	3.17807e12	−	3.17807e12i	0.776144	−	0.776144i
$334$		0			0
$335$	−3.75238e12	+	1.84984e12i	−0.889371	+	0.438441i
$336$		0			0
$337$	−5.71886e11	−	5.71886e11i	−0.131571	−	0.131571i	0.638254	−	0.769825i	$-0.279657\pi$
$337$	−5.71886e11	−	5.71886e11i	−0.131571	−	0.131571i	−0.769825	+	0.638254i	$0.779657\pi$
$338$		0			0
$339$			9.12862e11i			0.203895i
$340$		0			0
$341$	−4.30554e11			−0.0933804
$342$		0			0
$343$	−1.43987e12	+	1.43987e12i	−0.303287	+	0.303287i
$344$		0			0
$345$	−3.07947e12	−	1.04580e12i	−0.630058	−	0.213970i
$346$		0			0
$347$	1.13487e12	+	1.13487e12i	0.225580	+	0.225580i	0.810843	−	0.585263i	$-0.199009\pi$
$347$	1.13487e12	+	1.13487e12i	0.225580	+	0.225580i	−0.585263	+	0.810843i	$0.699009\pi$
$348$		0			0
$349$			5.63803e12i			1.08893i	0.838783	+	0.544465i	$0.183267\pi$
$349$			5.63803e12i			1.08893i	−0.838783	+	0.544465i	$0.816733\pi$
$350$		0			0
$351$	−4.49613e12			−0.843924
$352$		0			0
$353$	7.43074e12	−	7.43074e12i	1.35568	−	1.35568i	0.476520	−	0.879164i	$-0.341898\pi$
$353$	7.43074e12	−	7.43074e12i	1.35568	−	1.35568i	0.879164	−	0.476520i	$-0.158102\pi$
$354$		0			0
$355$	1.71342e12	−	5.04535e12i	0.303894	−	0.894849i
$356$		0			0
$357$	4.55766e11	+	4.55766e11i	0.0785961	+	0.0785961i
$358$		0			0
$359$		−	7.02776e12i		−	1.17854i	−0.807936	−	0.589270i	$-0.799415\pi$
$359$		−	7.02776e12i		−	1.17854i	0.807936	−	0.589270i	$-0.200585\pi$
$360$		0			0
$361$	−9.52990e11			−0.155436
$362$		0			0
$363$	1.81479e12	−	1.81479e12i	0.287934	−	0.287934i
$364$		0			0
$365$	−1.66917e12	−	3.38588e12i	−0.257653	−	0.522646i
$366$		0			0
$367$	−4.10757e11	−	4.10757e11i	−0.0616956	−	0.0616956i	0.675586	−	0.737281i	$-0.263891\pi$
$367$	−4.10757e11	−	4.10757e11i	−0.0616956	−	0.0616956i	−0.737281	+	0.675586i	$0.763891\pi$
$368$		0			0
$369$			2.77336e12i			0.405391i
$370$		0			0
$371$	−9.72837e11			−0.138411
$372$		0			0
$373$	5.37175e12	−	5.37175e12i	0.743998	−	0.743998i	−0.229347	−	0.973345i	$-0.573659\pi$
$373$	5.37175e12	−	5.37175e12i	0.743998	−	0.743998i	0.973345	+	0.229347i	$0.0736589\pi$
$374$		0			0
$375$	5.95969e11	−	2.98984e12i	0.0803651	−	0.403173i
$376$		0			0
$377$	4.90742e12	+	4.90742e12i	0.644386	+	0.644386i
$378$		0			0
$379$			3.45301e12i			0.441573i	0.975322	+	0.220786i	$0.0708624\pi$
$379$			3.45301e12i			0.441573i	−0.975322	+	0.220786i	$0.929138\pi$
$380$		0			0
$381$	−4.31313e11			−0.0537239
$382$		0			0
$383$	7.95493e12	−	7.95493e12i	0.965256	−	0.965256i	−0.0341606	−	0.999416i	$-0.510876\pi$
$383$	7.95493e12	−	7.95493e12i	0.965256	−	0.965256i	0.999416	+	0.0341606i	$0.0108758\pi$
$384$		0			0
$385$	1.62483e11	−	8.01008e10i	0.0192090	−	0.00946964i
$386$		0			0
$387$	9.10093e12	+	9.10093e12i	1.04841	+	1.04841i
$388$		0			0
$389$		−	1.31059e13i		−	1.47136i	−0.677329	−	0.735680i	$-0.736863\pi$
$389$		−	1.31059e13i		−	1.47136i	0.677329	−	0.735680i	$-0.263137\pi$
$390$		0			0
$391$	−1.81979e13			−1.99131
$392$		0			0
$393$	9.37394e11	−	9.37394e11i	0.0999906	−	0.0999906i
$394$		0			0
$395$	−3.41338e12	−	1.15920e12i	−0.354976	−	0.120551i
$396$		0			0
$397$	−5.77637e12	−	5.77637e12i	−0.585736	−	0.585736i	0.350738	−	0.936474i	$-0.385931\pi$
$397$	−5.77637e12	−	5.77637e12i	−0.585736	−	0.585736i	−0.936474	+	0.350738i	$0.885931\pi$
$398$		0			0
$399$		−	9.82076e11i		−	0.0971137i
$400$		0			0
$401$	−1.00597e13			−0.970202			−0.485101	−	0.874458i	$-0.661217\pi$
$401$	−1.00597e13			−0.970202			−0.485101	+	0.874458i	$0.661217\pi$
$402$		0			0
$403$	8.07494e12	−	8.07494e12i	0.759651	−	0.759651i
$404$		0			0
$405$	−1.82741e12	+	5.38100e12i	−0.167711	+	0.493842i
$406$		0			0
$407$	1.01650e12	+	1.01650e12i	0.0910198	+	0.0910198i
$408$		0			0
$409$			5.81279e12i			0.507888i	0.967219	+	0.253944i	$0.0817279\pi$
$409$			5.81279e12i			0.507888i	−0.967219	+	0.253944i	$0.918272\pi$
$410$		0			0
$411$	9.57669e11			0.0816594
$412$		0			0
$413$	−1.96881e12	+	1.96881e12i	−0.163853	+	0.163853i
$414$		0			0
$415$	−6.77498e12	−	1.37430e13i	−0.550387	−	1.11645i
$416$		0			0
$417$	−4.78939e12	−	4.78939e12i	−0.379839	−	0.379839i
$418$		0			0
$419$			4.24519e12i			0.328721i	0.986400	+	0.164360i	$0.0525560\pi$
$419$			4.24519e12i			0.328721i	−0.986400	+	0.164360i	$0.947444\pi$
$420$		0			0
$421$	2.54080e12			0.192115			0.0960574	−	0.995376i	$-0.469377\pi$
$421$	2.54080e12			0.192115			0.0960574	+	0.995376i	$0.469377\pi$
$422$		0			0
$423$	3.28510e12	−	3.28510e12i	0.242575	−	0.242575i
$424$		0			0
$425$	−2.22210e12	−	1.69136e13i	−0.160258	−	1.21981i
$426$		0			0
$427$	8.41553e11	+	8.41553e11i	0.0592846	+	0.0592846i
$428$		0			0
$429$		−	6.52671e11i		−	0.0449167i
$430$		0			0
$431$	2.15279e13			1.44749			0.723743	−	0.690070i	$-0.242420\pi$
$431$	2.15279e13			1.44749			0.723743	+	0.690070i	$0.242420\pi$
$432$		0			0
$433$	9.99110e12	−	9.99110e12i	0.656408	−	0.656408i	−0.298121	−	0.954528i	$-0.596360\pi$
$433$	9.99110e12	−	9.99110e12i	0.656408	−	0.656408i	0.954528	+	0.298121i	$0.0963598\pi$
$434$		0			0
$435$	−4.66826e12	+	2.30135e12i	−0.299715	+	0.147753i
$436$		0			0
$437$	1.96063e13	+	1.96063e13i	1.23023	+	1.23023i
$438$		0			0
$439$			2.33293e13i			1.43080i	0.698714	+	0.715401i	$0.253756\pi$
$439$			2.33293e13i			1.43080i	−0.698714	+	0.715401i	$0.746244\pi$
$440$		0			0
$441$	1.31914e13			0.790859
$442$		0			0
$443$	−2.92902e12	+	2.92902e12i	−0.171673	+	0.171673i	−0.787714	−	0.616041i	$-0.788736\pi$
$443$	−2.92902e12	+	2.92902e12i	−0.171673	+	0.171673i	0.616041	+	0.787714i	$0.288736\pi$
$444$		0			0
$445$	−1.98148e13	−	6.72918e12i	−1.13550	−	0.385622i
$446$		0			0
$447$	−3.95213e12	−	3.95213e12i	−0.221459	−	0.221459i
$448$		0			0
$449$			3.40161e13i			1.86403i	0.362419	+	0.932015i	$0.381951\pi$
$449$			3.40161e13i			1.86403i	−0.362419	+	0.932015i	$0.618049\pi$
$450$		0			0
$451$	−8.87055e11			−0.0475409
$452$		0			0
$453$	7.22189e12	−	7.22189e12i	0.378582	−	0.378582i
$454$		0			0
$455$	−1.54507e12	+	4.54961e12i	−0.0792301	+	0.233301i
$456$		0			0
$457$	4.38241e12	+	4.38241e12i	0.219853	+	0.219853i	0.808436	−	0.588584i	$-0.200314\pi$
$457$	4.38241e12	+	4.38241e12i	0.219853	+	0.219853i	−0.588584	+	0.808436i	$0.700314\pi$
$458$		0			0
$459$		−	1.88673e13i		−	0.926078i
$460$		0			0
$461$	−6.09175e12			−0.292575			−0.146288	−	0.989242i	$-0.546732\pi$
$461$	−6.09175e12			−0.292575			−0.146288	+	0.989242i	$0.546732\pi$
$462$		0			0
$463$	−5.30861e12	+	5.30861e12i	−0.249503	+	0.249503i	−0.820767	−	0.571264i	$-0.806453\pi$
$463$	−5.30861e12	+	5.30861e12i	−0.249503	+	0.249503i	0.571264	+	0.820767i	$0.306453\pi$
$464$		0			0
$465$	3.78677e12	+	7.68142e12i	0.174183	+	0.353327i
$466$		0			0
$467$	−1.33139e13	−	1.33139e13i	−0.599407	−	0.599407i	0.340747	−	0.940155i	$-0.389320\pi$
$467$	−1.33139e13	−	1.33139e13i	−0.599407	−	0.599407i	−0.940155	+	0.340747i	$0.889320\pi$
$468$		0			0
$469$			4.94473e12i			0.217911i
$470$		0			0
$471$	1.67888e11			0.00724295
$472$		0			0
$473$	−2.91092e12	+	2.91092e12i	−0.122949	+	0.122949i
$474$		0			0
$475$	−1.58285e13	+	2.06167e13i	−0.654594	+	0.852609i
$476$		0			0
$477$	9.13881e12	+	9.13881e12i	0.370082	+	0.370082i
$478$		0			0
$479$			4.52816e13i			1.79574i	0.440257	+	0.897872i	$0.354887\pi$
$479$			4.52816e13i			1.79574i	−0.440257	+	0.897872i	$0.645113\pi$
$480$		0			0
$481$	−3.81285e13			−1.48090
$482$		0			0
$483$	−2.71805e12	+	2.71805e12i	−0.103400	+	0.103400i
$484$		0			0
$485$	7.38142e12	−	3.63888e12i	0.275062	−	0.135600i
$486$		0			0
$487$	1.68828e13	+	1.68828e13i	0.616309	+	0.616309i	0.944583	−	0.328273i	$-0.106467\pi$
$487$	1.68828e13	+	1.68828e13i	0.616309	+	0.616309i	−0.328273	+	0.944583i	$0.606467\pi$
$488$		0			0
$489$		−	6.14513e12i		−	0.219779i
$490$		0			0
$491$	−2.30176e13			−0.806590			−0.403295	−	0.915070i	$-0.632135\pi$
$491$	−2.30176e13			−0.806590			−0.403295	+	0.915070i	$0.632135\pi$
$492$		0			0
$493$	−2.05932e13	+	2.05932e13i	−0.707115	+	0.707115i
$494$		0			0
$495$	−2.27883e12	−	7.73901e11i	−0.0766808	−	0.0260411i
$496$		0			0
$497$	−4.45322e12	−	4.45322e12i	−0.146856	−	0.146856i
$498$		0			0
$499$			9.09915e12i			0.294102i	0.989129	+	0.147051i	$0.0469782\pi$
$499$			9.09915e12i			0.294102i	−0.989129	+	0.147051i	$0.953022\pi$
$500$		0			0
$501$	−1.86056e13			−0.589462
$502$		0			0
$503$	2.81006e13	−	2.81006e13i	0.872721	−	0.872721i	−0.120048	−	0.992768i	$-0.538305\pi$
$503$	2.81006e13	−	2.81006e13i	0.872721	−	0.872721i	0.992768	+	0.120048i	$0.0383047\pi$
$504$		0			0
$505$	−2.21420e10	+	6.51994e10i	−0.000674155	+	0.00198512i
$506$		0			0
$507$	2.50252e12	+	2.50252e12i	0.0747030	+	0.0747030i
$508$		0			0
$509$			4.20563e13i			1.23095i	0.788155	+	0.615477i	$0.211037\pi$
$509$			4.20563e13i			1.23095i	−0.788155	+	0.615477i	$0.788963\pi$
$510$		0			0
$511$	−4.46177e12			−0.128057
$512$		0			0
$513$	−2.03275e13	+	2.03275e13i	−0.572133	+	0.572133i
$514$		0			0
$515$	−8.04524e12	−	1.63197e13i	−0.222077	−	0.450479i
$516$		0			0
$517$	1.05073e12	+	1.05073e12i	0.0284472	+	0.0284472i
$518$		0			0
$519$			1.57250e13i			0.417593i
$520$		0			0
$521$	3.53219e13			0.920143			0.460072	−	0.887882i	$-0.347824\pi$
$521$	3.53219e13			0.920143			0.460072	+	0.887882i	$0.347824\pi$
$522$		0			0
$523$	−1.01996e13	+	1.01996e13i	−0.260661	+	0.260661i	−0.825322	−	0.564662i	$-0.809007\pi$
$523$	−1.01996e13	+	1.01996e13i	−0.260661	+	0.260661i	0.564662	+	0.825322i	$0.309007\pi$
$524$		0			0
$525$	−2.85812e12	−	2.19434e12i	−0.0716613	−	0.0550182i
$526$		0			0
$527$	3.38853e13	+	3.38853e13i	0.833601	+	0.833601i
$528$		0			0
$529$		−	6.71007e13i		−	1.61975i
$530$		0			0
$531$	3.69900e13			0.876216
$532$		0			0
$533$	1.66365e13	−	1.66365e13i	0.386746	−	0.386746i
$534$		0			0
$535$	−1.80640e13	+	8.90515e12i	−0.412140	+	0.203176i
$536$		0			0
$537$	1.73390e13	+	1.73390e13i	0.388286	+	0.388286i
$538$		0			0
$539$			4.21926e12i			0.0927455i
$540$		0			0
$541$	5.17386e13			1.11642			0.558211	−	0.829699i	$-0.311488\pi$
$541$	5.17386e13			1.11642			0.558211	+	0.829699i	$0.311488\pi$
$542$		0			0
$543$	1.07449e13	−	1.07449e13i	0.227617	−	0.227617i
$544$		0			0
$545$	−1.33717e13	−	4.54109e12i	−0.278102	−	0.0944446i
$546$		0			0
$547$	−5.40393e13	−	5.40393e13i	−1.10350	−	1.10350i	−0.993985	−	0.109516i	$-0.965070\pi$
$547$	−5.40393e13	−	5.40393e13i	−1.10350	−	1.10350i	−0.109516	−	0.993985i	$-0.534930\pi$
$548$		0			0
$549$		−	1.58111e13i		−	0.317029i
$550$		0			0
$551$	4.43739e13			0.873715
$552$		0			0
$553$	−3.01278e12	+	3.01278e12i	−0.0582561	+	0.0582561i
$554$		0			0
$555$	9.19493e12	−	2.70754e13i	0.174616	−	0.514175i
$556$		0			0
$557$	−2.64732e12	−	2.64732e12i	−0.0493777	−	0.0493777i	0.681987	−	0.731365i	$-0.261116\pi$
$557$	−2.64732e12	−	2.64732e12i	−0.0493777	−	0.0493777i	−0.731365	+	0.681987i	$0.761116\pi$
$558$		0			0
$559$		−	1.09187e14i		−	2.00038i
$560$		0			0
$561$	2.73884e12			0.0492892
$562$		0			0
$563$	−5.45245e13	+	5.45245e13i	−0.963940	+	0.963940i	−0.999372	−	0.0354321i	$-0.988719\pi$
$563$	−5.45245e13	+	5.45245e13i	−0.963940	+	0.963940i	0.0354321	+	0.999372i	$0.488719\pi$
$564$		0			0
$565$	−1.26265e13	−	2.56128e13i	−0.219302	−	0.444850i
$566$		0			0
$567$	4.74947e12	+	4.74947e12i	0.0810456	+	0.0810456i
$568$		0			0
$569$			8.15865e13i			1.36791i	0.729525	+	0.683955i	$0.239741\pi$
$569$			8.15865e13i			1.36791i	−0.729525	+	0.683955i	$0.760259\pi$
$570$		0			0
$571$	−9.85629e13			−1.62380			−0.811901	−	0.583795i	$-0.801567\pi$
$571$	−9.85629e13			−1.62380			−0.811901	+	0.583795i	$0.801567\pi$
$572$		0			0
$573$	2.14977e13	−	2.14977e13i	0.348031	−	0.348031i
$574$		0			0
$575$	1.00868e14	−	1.32519e13i	1.60477	−	0.210834i
$576$		0			0
$577$	−3.53230e13	−	3.53230e13i	−0.552305	−	0.552305i	0.374801	−	0.927105i	$-0.377711\pi$
$577$	−3.53230e13	−	3.53230e13i	−0.552305	−	0.552305i	−0.927105	+	0.374801i	$0.877711\pi$
$578$		0			0
$579$			3.41898e13i			0.525417i
$580$		0			0
$581$	−1.81099e13			−0.273549
$582$		0			0
$583$	−2.92303e12	+	2.92303e12i	−0.0434001	+	0.0434001i
$584$		0			0
$585$	5.72533e13	−	2.82246e13i	0.835644	−	0.411954i
$586$		0			0
$587$	−4.08411e12	−	4.08411e12i	−0.0586012	−	0.0586012i	0.677199	−	0.735800i	$-0.263194\pi$
$587$	−4.08411e12	−	4.08411e12i	−0.0586012	−	0.0586012i	−0.735800	+	0.677199i	$0.763194\pi$
$588$		0			0
$589$		−	7.30154e13i		−	1.03000i
$590$		0			0
$591$	2.76517e13			0.383517
$592$		0			0
$593$	8.89286e13	−	8.89286e13i	1.21274	−	1.21274i	0.242619	−	0.970122i	$-0.421994\pi$
$593$	8.89286e13	−	8.89286e13i	1.21274	−	1.21274i	0.970122	−	0.242619i	$-0.0780064\pi$
$594$		0			0
$595$	−1.90918e13	−	6.48365e12i	−0.256013	−	0.0869430i
$596$		0			0
$597$	−9.37434e12	−	9.37434e12i	−0.123614	−	0.123614i
$598$		0			0
$599$		−	8.84354e13i		−	1.14681i	−0.819272	−	0.573406i	$-0.805622\pi$
$599$		−	8.84354e13i		−	1.14681i	0.819272	−	0.573406i	$-0.194378\pi$
$600$		0			0
$601$	−1.24727e14			−1.59070			−0.795352	−	0.606148i	$-0.792714\pi$
$601$	−1.24727e14			−1.59070			−0.795352	+	0.606148i	$0.792714\pi$
$602$		0			0
$603$	4.64507e13	−	4.64507e13i	0.582648	−	0.582648i
$604$		0			0
$605$	−2.58169e13	+	7.60205e13i	−0.318513	+	0.937894i
$606$		0			0
$607$	7.90250e12	+	7.90250e12i	0.0959005	+	0.0959005i	0.753429	−	0.657529i	$-0.228398\pi$
$607$	7.90250e12	+	7.90250e12i	0.0959005	+	0.0959005i	−0.657529	+	0.753429i	$0.728398\pi$
$608$		0			0
$609$			6.15164e12i			0.0734352i
$610$		0			0
$611$	−3.94126e13			−0.462837
$612$		0			0
$613$	−7.87997e13	+	7.87997e13i	−0.910378	+	0.910378i	−0.996302	−	0.0859234i	$-0.972616\pi$
$613$	−7.87997e13	+	7.87997e13i	−0.910378	+	0.910378i	0.0859234	+	0.996302i	$0.472616\pi$
$614$		0			0
$615$	7.80175e12	+	1.58258e13i	0.0886782	+	0.179882i
$616$		0			0
$617$	−8.06967e13	−	8.06967e13i	−0.902464	−	0.902464i	0.0931846	−	0.995649i	$-0.470295\pi$
$617$	−8.06967e13	−	8.06967e13i	−0.902464	−	0.902464i	−0.995649	+	0.0931846i	$0.970295\pi$
$618$		0			0
$619$		−	1.91232e13i		−	0.210430i	−0.994450	−	0.105215i	$-0.966447\pi$
$619$		−	1.91232e13i		−	0.210430i	0.994450	−	0.105215i	$-0.0335530\pi$
$620$		0			0
$621$	1.12519e14			1.21834
$622$		0			0
$623$	−1.74893e13	+	1.74893e13i	−0.186351	+	0.186351i
$624$		0			0
$625$	2.46334e13	+	9.21311e13i	0.258300	+	0.966065i
$626$		0			0
$627$	−2.95079e12	−	2.95079e12i	−0.0304510	−	0.0304510i
$628$		0			0
$629$		−	1.60001e14i		−	1.62506i
$630$		0			0
$631$	7.38246e13			0.737997			0.368998	−	0.929430i	$-0.379701\pi$
$631$	7.38246e13			0.737997			0.368998	+	0.929430i	$0.379701\pi$
$632$		0			0
$633$	−2.02946e13	+	2.02946e13i	−0.199692	+	0.199692i
$634$		0			0
$635$	1.21016e13	−	5.96583e12i	0.117213	−	0.0577833i
$636$		0			0
$637$	−7.91313e13	−	7.91313e13i	−0.754486	−	0.754486i
$638$		0			0
$639$			8.36668e13i			0.785324i
$640$		0			0
$641$	2.06509e14			1.90831			0.954154	−	0.299317i	$-0.0967587\pi$
$641$	2.06509e14			1.90831			0.954154	+	0.299317i	$0.0967587\pi$
$642$		0			0
$643$	4.65598e13	−	4.65598e13i	0.423600	−	0.423600i	−0.462841	−	0.886441i	$-0.653170\pi$
$643$	4.65598e13	−	4.65598e13i	0.423600	−	0.423600i	0.886441	+	0.462841i	$0.153170\pi$
$644$		0			0
$645$	7.75350e13	+	2.63312e13i	0.694543	+	0.235870i
$646$		0			0
$647$	3.93706e13	+	3.93706e13i	0.347257	+	0.347257i	0.859087	−	0.511830i	$-0.171032\pi$
$647$	3.93706e13	+	3.93706e13i	0.347257	+	0.347257i	−0.511830	+	0.859087i	$0.671032\pi$
$648$		0			0
$649$			1.18312e13i			0.102755i
$650$		0			0
$651$	1.01223e13			0.0865710
$652$		0			0
$653$	−2.83045e12	+	2.83045e12i	−0.0238391	+	0.0238391i	−0.718926	−	0.695087i	$-0.755366\pi$
$653$	−2.83045e12	+	2.83045e12i	−0.0238391	+	0.0238391i	0.695087	+	0.718926i	$0.255366\pi$
$654$		0			0
$655$	−1.33352e13	+	3.92669e13i	−0.110610	+	0.325702i
$656$		0			0
$657$	4.19138e13	+	4.19138e13i	0.342397	+	0.342397i
$658$		0			0
$659$		−	1.73272e14i		−	1.39412i	−0.717011	−	0.697062i	$-0.754490\pi$
$659$		−	1.73272e14i		−	1.39412i	0.717011	−	0.697062i	$-0.245510\pi$
$660$		0			0
$661$	−8.78289e13			−0.696034			−0.348017	−	0.937488i	$-0.613145\pi$
$661$	−8.78289e13			−0.696034			−0.348017	+	0.937488i	$0.613145\pi$
$662$		0			0
$663$	−5.13662e13	+	5.13662e13i	−0.400968	+	0.400968i
$664$		0			0
$665$	1.35839e13	+	2.75547e13i	0.104452	+	0.211879i
$666$		0			0
$667$	−1.22812e14	−	1.22812e14i	−0.930276	−	0.930276i
$668$		0			0
$669$			6.21479e13i			0.463763i
$670$		0			0
$671$	5.05715e12			0.0371786
$672$		0			0
$673$	−5.27984e13	+	5.27984e13i	−0.382424	+	0.382424i	−0.871975	−	0.489551i	$-0.837161\pi$
$673$	−5.27984e13	+	5.27984e13i	−0.382424	+	0.382424i	0.489551	+	0.871975i	$0.337161\pi$
$674$		0			0
$675$	1.37394e13	+	1.04578e14i	0.0980504	+	0.746316i
$676$		0			0
$677$	6.90074e13	+	6.90074e13i	0.485235	+	0.485235i	0.906799	−	0.421563i	$-0.138519\pi$
$677$	6.90074e13	+	6.90074e13i	0.485235	+	0.485235i	−0.421563	+	0.906799i	$0.638519\pi$
$678$		0			0
$679$		−	9.72692e12i		−	0.0673948i
$680$		0			0
$681$	−9.57381e13			−0.653656
$682$		0			0
$683$	−1.63496e14	+	1.63496e14i	−1.10003	+	1.10003i	−0.105625	+	0.994406i	$0.533684\pi$
$683$	−1.63496e14	+	1.63496e14i	−1.10003	+	1.10003i	−0.994406	+	0.105625i	$0.966316\pi$
$684$		0			0
$685$	−2.68699e13	+	1.32463e13i	−0.178161	+	0.0878297i
$686$		0			0
$687$	3.36707e13	+	3.36707e13i	0.220023	+	0.220023i
$688$		0			0
$689$		−	1.09642e14i		−	0.706122i
$690$		0			0
$691$	−1.36873e14			−0.868818			−0.434409	−	0.900716i	$-0.643043\pi$
$691$	−1.36873e14			−0.868818			−0.434409	+	0.900716i	$0.643043\pi$
$692$		0			0
$693$	−2.01138e12	+	2.01138e12i	−0.0125843	+	0.0125843i
$694$		0			0
$695$	2.00625e14	+	6.81330e13i	1.23726	+	0.420178i
$696$		0			0
$697$	6.98126e13	+	6.98126e13i	0.424395	+	0.424395i
$698$		0			0
$699$			3.10697e13i			0.186188i
$700$		0			0
$701$	−1.67987e13			−0.0992398			−0.0496199	−	0.998768i	$-0.515801\pi$
$701$	−1.67987e13			−0.0992398			−0.0496199	+	0.998768i	$0.515801\pi$
$702$		0			0
$703$	−1.72383e14	+	1.72383e14i	−1.00396	+	1.00396i
$704$		0			0
$705$	9.50459e12	−	2.79873e13i	0.0545742	−	0.160700i
$706$		0			0
$707$	5.75474e10	+	5.75474e10i	0.000325783	+	0.000325783i
$708$		0			0
$709$			1.26548e14i			0.706356i	0.935556	+	0.353178i	$0.114899\pi$
$709$			1.26548e14i			0.706356i	−0.935556	+	0.353178i	$0.885101\pi$
$710$		0			0
$711$	5.66039e13			0.311529
$712$		0			0
$713$	−2.02082e14	+	2.02082e14i	−1.09668	+	1.09668i
$714$		0			0
$715$	9.02761e12	+	1.83124e13i	0.0483106	+	0.0979975i
$716$		0			0
$717$	9.90927e12	+	9.90927e12i	0.0522933	+	0.0522933i
$718$		0			0
$719$		−	8.16574e11i		−	0.00424963i	−0.999998	−	0.00212481i	$-0.999324\pi$
$719$		−	8.16574e11i		−	0.00424963i	0.999998	−	0.00212481i	$-0.000676350\pi$
$720$		0			0
$721$	−2.15054e13			−0.110375
$722$		0			0
$723$	5.22816e13	−	5.22816e13i	0.264641	−	0.264641i
$724$		0			0
$725$	9.91485e13	−	1.29141e14i	0.494989	−	0.644724i
$726$		0			0
$727$	−1.34638e14	−	1.34638e14i	−0.662974	−	0.662974i	0.293106	−	0.956080i	$-0.405311\pi$
$727$	−1.34638e14	−	1.34638e14i	−0.662974	−	0.662974i	−0.956080	+	0.293106i	$0.905311\pi$
$728$		0			0
$729$		−	2.55197e13i		−	0.123947i
$730$		0			0
$731$	4.58188e14			2.19511
$732$		0			0
$733$	−1.94919e14	+	1.94919e14i	−0.921157	+	0.921157i	−0.997111	−	0.0759543i	$-0.975800\pi$
$733$	−1.94919e14	+	1.94919e14i	−0.921157	+	0.921157i	0.0759543	+	0.997111i	$0.475800\pi$
$734$		0			0
$735$	7.52750e13	−	3.71089e13i	0.350925	−	0.172998i
$736$		0			0
$737$	1.48572e13	+	1.48572e13i	0.0683281	+	0.0683281i
$738$		0			0
$739$			1.67761e14i			0.761146i	0.924751	+	0.380573i	$0.124273\pi$
$739$			1.67761e14i			0.761146i	−0.924751	+	0.380573i	$0.875727\pi$
$740$		0			0
$741$	1.10683e14			0.495438
$742$		0			0
$743$	−6.39674e13	+	6.39674e13i	−0.282497	+	0.282497i	−0.834104	−	0.551607i	$-0.814015\pi$
$743$	−6.39674e13	+	6.39674e13i	−0.282497	+	0.282497i	0.551607	+	0.834104i	$0.314015\pi$
$744$		0			0
$745$	1.65552e14	+	5.62223e13i	0.721364	+	0.244978i
$746$		0			0
$747$	1.70124e14	+	1.70124e14i	0.731413	+	0.731413i
$748$		0			0
$749$			2.38039e13i			0.100981i
$750$		0			0
$751$	−1.82829e14			−0.765323			−0.382661	−	0.923889i	$-0.624992\pi$
$751$	−1.82829e14			−0.765323			−0.382661	+	0.923889i	$0.624992\pi$
$752$		0			0
$753$	−7.04657e13	+	7.04657e13i	−0.291074	+	0.291074i
$754$		0			0
$755$	−1.02737e14	+	3.02521e14i	−0.418787	+	1.23316i
$756$		0			0
$757$	−2.32023e14	−	2.32023e14i	−0.933363	−	0.933363i	0.0645511	−	0.997914i	$-0.479438\pi$
$757$	−2.32023e14	−	2.32023e14i	−0.933363	−	0.933363i	−0.997914	+	0.0645511i	$0.979438\pi$
$758$		0			0
$759$			1.63336e13i			0.0648445i
$760$		0			0
$761$	−6.14463e13			−0.240753			−0.120377	−	0.992728i	$-0.538410\pi$
$761$	−6.14463e13			−0.240753			−0.120377	+	0.992728i	$0.538410\pi$
$762$		0			0
$763$	−1.18024e13	+	1.18024e13i	−0.0456401	+	0.0456401i
$764$		0			0
$765$	1.18441e14	+	2.40255e14i	0.452057	+	0.916992i
$766$		0			0
$767$	−2.21891e14	−	2.21891e14i	−0.835917	−	0.835917i
$768$		0			0
$769$		−	2.33449e14i		−	0.868080i	−0.900894	−	0.434040i	$-0.857088\pi$
$769$		−	2.33449e14i		−	0.868080i	0.900894	−	0.434040i	$-0.142912\pi$
$770$		0			0
$771$	−6.06505e13			−0.222619
$772$		0			0
$773$	1.25932e13	−	1.25932e13i	0.0456288	−	0.0456288i	−0.683924	−	0.729553i	$-0.739728\pi$
$773$	1.25932e13	−	1.25932e13i	0.0456288	−	0.0456288i	0.729553	+	0.683924i	$0.239728\pi$
$774$		0			0
$775$	−2.12496e14	−	1.63145e14i	−0.760049	−	0.583531i
$776$		0			0
$777$	−2.38978e13	−	2.38978e13i	−0.0843826	−	0.0843826i
$778$		0			0
$779$		−	1.50431e14i		−	0.524384i
$780$		0			0
$781$	−2.67607e13			−0.0920964
$782$		0			0
$783$	1.27330e14	−	1.27330e14i	0.432634	−	0.432634i
$784$		0			0
$785$	−4.71055e12	+	2.32220e12i	−0.0158024	+	0.00779024i
$786$		0			0
$787$	−9.94162e12	−	9.94162e12i	−0.0329294	−	0.0329294i	0.690450	−	0.723380i	$-0.257412\pi$
$787$	−9.94162e12	−	9.94162e12i	−0.0329294	−	0.0329294i	−0.723380	+	0.690450i	$0.757412\pi$
$788$		0			0
$789$		−	1.79099e14i		−	0.585743i
$790$		0			0
$791$	−3.37514e13			−0.108996
$792$		0			0
$793$	−9.48456e13	+	9.48456e13i	−0.302448	+	0.302448i
$794$		0			0
$795$	7.78577e13	+	2.64408e13i	0.245169	+	0.0832604i
$796$		0			0
$797$	3.81477e14	+	3.81477e14i	1.18625	+	1.18625i	0.978096	+	0.208155i	$0.0667457\pi$
$797$	3.81477e14	+	3.81477e14i	1.18625	+	1.18625i	0.208155	+	0.978096i	$0.433254\pi$
$798$		0			0
$799$		−	1.65389e14i		−	0.507893i
$800$		0			0
$801$	3.28587e14			0.996525
$802$		0			0
$803$	−1.34061e13	+	1.34061e13i	−0.0401535	+	0.0401535i
$804$		0			0
$805$	3.86666e13	−	1.13858e14i	0.114382	−	0.336809i
$806$		0			0
$807$	−9.45177e13	−	9.45177e13i	−0.276150	−	0.276150i
$808$		0			0
$809$		−	7.59808e13i		−	0.219261i	−0.993972	−	0.109630i	$-0.965033\pi$
$809$		−	7.59808e13i		−	0.219261i	0.993972	−	0.109630i	$-0.0349668\pi$
$810$		0			0
$811$	3.51474e14			1.00182			0.500909	−	0.865500i	$-0.332999\pi$
$811$	3.51474e14			1.00182			0.500909	+	0.865500i	$0.332999\pi$
$812$		0			0
$813$	1.15922e14	−	1.15922e14i	0.326371	−	0.326371i
$814$		0			0
$815$	8.49983e13	+	1.72418e14i	0.236386	+	0.479506i
$816$		0			0
$817$	−4.93648e14	−	4.93648e14i	−1.35615	−	1.35615i
$818$		0			0
$819$		−	7.54460e13i		−	0.204747i
$820$		0			0
$821$	−5.87456e13			−0.157492			−0.0787462	−	0.996895i	$-0.525092\pi$
$821$	−5.87456e13			−0.157492			−0.0787462	+	0.996895i	$0.525092\pi$
$822$		0			0
$823$	−2.06649e14	+	2.06649e14i	−0.547311	+	0.547311i	−0.925662	−	0.378351i	$-0.876491\pi$
$823$	−2.06649e14	+	2.06649e14i	−0.547311	+	0.547311i	0.378351	+	0.925662i	$0.376491\pi$
$824$		0			0
$825$	−1.51809e13	+	1.99445e12i	−0.0397216	+	0.00521859i
$826$		0			0
$827$	−2.86687e14	−	2.86687e14i	−0.741107	−	0.741107i	0.231684	−	0.972791i	$-0.425576\pi$
$827$	−2.86687e14	−	2.86687e14i	−0.741107	−	0.741107i	−0.972791	+	0.231684i	$0.925576\pi$
$828$		0			0
$829$		−	9.04765e13i		−	0.231080i	−0.993303	−	0.115540i	$-0.963140\pi$
$829$		−	9.04765e13i		−	0.231080i	0.993303	−	0.115540i	$-0.0368599\pi$
$830$		0			0
$831$	−2.66381e14			−0.672199
$832$		0			0
$833$	3.32063e14	−	3.32063e14i	0.827933	−	0.827933i
$834$		0			0
$835$	5.22030e14	−	2.57350e14i	1.28607	−	0.634003i
$836$		0			0
$837$	−2.09515e14	−	2.09515e14i	−0.510022	−	0.510022i
$838$		0			0
$839$		−	3.57580e14i		−	0.860128i	−0.902798	−	0.430064i	$-0.858491\pi$
$839$		−	3.57580e14i		−	0.860128i	0.902798	−	0.430064i	$-0.141509\pi$
$840$		0			0
$841$	1.42753e14			0.339316
$842$		0			0
$843$	5.65413e13	−	5.65413e13i	0.132809	−	0.132809i
$844$		0			0
$845$	−1.04829e14	−	3.56004e13i	−0.243332	−	0.0826364i
$846$		0			0
$847$	6.70985e13	+	6.70985e13i	0.153920	+	0.153920i
$848$		0			0
$849$			2.13371e14i			0.483724i
$850$		0			0
$851$	9.54197e14			2.13791
$852$		0			0
$853$	7.28675e13	−	7.28675e13i	0.161357	−	0.161357i	−0.621810	−	0.783168i	$-0.713603\pi$
$853$	7.28675e13	−	7.28675e13i	0.161357	−	0.161357i	0.783168	+	0.621810i	$0.213603\pi$
$854$		0			0
$855$	1.31242e14	−	3.86455e14i	0.287238	−	0.845802i
$856$		0			0
$857$	3.16590e14	+	3.16590e14i	0.684847	+	0.684847i	0.961088	−	0.276242i	$-0.0890890\pi$
$857$	3.16590e14	+	3.16590e14i	0.684847	+	0.684847i	−0.276242	+	0.961088i	$0.589089\pi$
$858$		0			0
$859$			1.37150e13i			0.0293244i	0.999893	+	0.0146622i	$0.00466729\pi$
$859$			1.37150e13i			0.0293244i	−0.999893	+	0.0146622i	$0.995333\pi$
$860$		0			0
$861$	2.08545e13			0.0440742
$862$		0			0
$863$	−2.41396e13	+	2.41396e13i	−0.0504286	+	0.0504286i	−0.731871	−	0.681443i	$-0.761353\pi$
$863$	−2.41396e13	+	2.41396e13i	−0.0504286	+	0.0504286i	0.681443	+	0.731871i	$0.261353\pi$
$864$		0			0
$865$	−2.17505e14	−	4.41205e14i	−0.449147	−	0.911088i
$866$		0			0
$867$	−7.31433e13	−	7.31433e13i	−0.149307	−	0.149307i
$868$		0			0
$869$			1.81047e13i			0.0365336i
$870$		0			0
$871$	−5.57287e14			−1.11170
$872$		0			0
$873$	−9.13745e13	+	9.13745e13i	−0.180200	+	0.180200i
$874$		0			0
$875$	1.10544e14	+	2.20349e13i	0.215523	+	0.0429606i
$876$		0			0
$877$	−3.68225e14	−	3.68225e14i	−0.709766	−	0.709766i	0.256720	−	0.966486i	$-0.417358\pi$
$877$	−3.68225e14	−	3.68225e14i	−0.709766	−	0.709766i	−0.966486	+	0.256720i	$0.917358\pi$
$878$		0			0
$879$		−	2.85703e13i		−	0.0544465i
$880$		0			0
$881$	1.21911e14			0.229700			0.114850	−	0.993383i	$-0.463361\pi$
$881$	1.21911e14			0.229700			0.114850	+	0.993383i	$0.463361\pi$
$882$		0			0
$883$	−7.38601e13	+	7.38601e13i	−0.137596	+	0.137596i	−0.772550	−	0.634954i	$-0.781019\pi$
$883$	−7.38601e13	+	7.38601e13i	−0.137596	+	0.137596i	0.634954	+	0.772550i	$0.281019\pi$
$884$		0			0
$885$	2.11078e14	−	1.04057e14i	0.388800	−	0.191670i
$886$		0			0
$887$	4.03967e14	+	4.03967e14i	0.735746	+	0.735746i	0.971752	−	0.236005i	$-0.0758383\pi$
$887$	4.03967e14	+	4.03967e14i	0.735746	+	0.735746i	−0.236005	+	0.971752i	$0.575838\pi$
$888$		0			0
$889$		−	1.59470e13i		−	0.0287191i
$890$		0			0
$891$	2.85410e13			0.0508254
$892$		0			0
$893$	−1.78188e14	+	1.78188e14i	−0.313778	+	0.313778i
$894$		0			0
$895$	−7.26319e14	−	2.46661e14i	−1.26477	−	0.429522i
$896$		0			0
$897$	−3.06333e14	−	3.06333e14i	−0.527511	−	0.527511i
$898$		0			0
$899$			4.57362e14i			0.778864i
$900$		0			0
$901$	4.60095e14			0.774861
$902$		0			0
$903$	6.84353e13	−	6.84353e13i	0.113983	−	0.113983i
$904$		0			0
$905$	−1.52855e14	+	4.50098e14i	−0.251789	+	0.741421i
$906$		0			0
$907$	1.93179e14	+	1.93179e14i	0.314719	+	0.314719i	0.846734	−	0.532016i	$-0.178565\pi$
$907$	1.93179e14	+	1.93179e14i	0.314719	+	0.314719i	−0.532016	+	0.846734i	$0.678565\pi$
$908$		0			0
$909$		−	1.08120e12i		−	0.00174215i
$910$		0			0
$911$	−8.80416e14			−1.40312			−0.701562	−	0.712608i	$-0.747514\pi$
$911$	−8.80416e14			−1.40312			−0.701562	+	0.712608i	$0.747514\pi$
$912$		0			0
$913$	−5.44139e13	+	5.44139e13i	−0.0857741	+	0.0857741i
$914$		0			0
$915$	−4.44782e13	−	9.02234e13i	−0.0693493	−	0.140674i
$916$		0			0
$917$	3.46584e13	+	3.46584e13i	0.0534518	+	0.0534518i
$918$		0			0
$919$		−	2.50083e14i		−	0.381510i	−0.981638	−	0.190755i	$-0.938906\pi$
$919$		−	2.50083e14i		−	0.381510i	0.981638	−	0.190755i	$-0.0610937\pi$
$920$		0			0
$921$	−3.35152e14			−0.505760
$922$		0			0
$923$	5.01891e14	−	5.01891e14i	0.749206	−	0.749206i
$924$		0			0
$925$	1.16514e14	+	8.86855e14i	0.172056	+	1.30962i
$926$		0			0
$927$	2.02021e14	+	2.02021e14i	0.295119	+	0.295119i
$928$		0			0
$929$			4.22608e12i			0.00610744i	0.999995	+	0.00305372i	$0.000972031\pi$
$929$			4.22608e12i			0.00610744i	−0.999995	+	0.00305372i	$0.999028\pi$
$930$		0			0
$931$	−7.15523e14			−1.02300
$932$		0			0
$933$	1.08482e14	−	1.08482e14i	0.153444	−	0.153444i
$934$		0			0
$935$	−7.68452e13	+	3.78830e13i	−0.107537	+	0.0530135i
$936$		0			0
$937$	8.53049e14	+	8.53049e14i	1.18107	+	1.18107i	0.979467	+	0.201604i	$0.0646154\pi$
$937$	8.53049e14	+	8.53049e14i	1.18107	+	1.18107i	0.201604	+	0.979467i	$0.435385\pi$
$938$		0			0
$939$		−	1.18676e14i		−	0.162569i
$940$		0			0
$941$	−7.60983e14			−1.03140			−0.515699	−	0.856770i	$-0.672468\pi$
$941$	−7.60983e14			−1.03140			−0.515699	+	0.856770i	$0.672468\pi$
$942$		0			0
$943$	−4.16342e14	+	4.16342e14i	−0.558331	+	0.558331i
$944$		0			0
$945$	1.18046e14	+	4.00889e13i	0.156636	+	0.0531943i
$946$		0			0
$947$	2.06394e14	+	2.06394e14i	0.270987	+	0.270987i	0.829497	−	0.558511i	$-0.188627\pi$
$947$	2.06394e14	+	2.06394e14i	0.270987	+	0.270987i	−0.558511	+	0.829497i	$0.688627\pi$
$948$		0			0
$949$		−	5.02855e14i		−	0.653299i
$950$		0			0
$951$	−4.26489e13			−0.0548284
$952$		0			0
$953$	3.44966e14	−	3.44966e14i	0.438845	−	0.438845i	−0.452778	−	0.891623i	$-0.649567\pi$
$953$	3.44966e14	−	3.44966e14i	0.438845	−	0.438845i	0.891623	+	0.452778i	$0.149567\pi$
$954$		0			0
$955$	−3.05822e14	+	9.00524e14i	−0.384992	+	1.13365i
$956$		0			0
$957$	1.84835e13	+	1.84835e13i	0.0230263	+	0.0230263i
$958$		0			0
$959$			3.54081e13i			0.0436525i
$960$		0			0
$961$	−6.70591e13			−0.0818165
$962$		0			0
$963$	2.23614e14	−	2.23614e14i	0.270002	−	0.270002i
$964$		0			0
$965$	−4.72907e14	−	9.59286e14i	−0.565118	−	1.14633i
$966$		0			0
$967$	5.84321e14	+	5.84321e14i	0.691065	+	0.691065i	0.962466	−	0.271401i	$-0.0874870\pi$
$967$	5.84321e14	+	5.84321e14i	0.691065	+	0.691065i	−0.271401	+	0.962466i	$0.587487\pi$
$968$		0			0
$969$			4.64465e14i			0.543668i
$970$		0			0
$971$	1.97850e14			0.229213			0.114606	−	0.993411i	$-0.463439\pi$
$971$	1.97850e14			0.229213			0.114606	+	0.993411i	$0.463439\pi$
$972$		0			0
$973$	1.77079e14	−	1.77079e14i	0.203050	−	0.203050i
$974$		0			0
$975$	2.47308e14	−	3.22119e14i	0.280683	−	0.365590i
$976$		0			0
$977$	2.11691e14	+	2.11691e14i	0.237809	+	0.237809i	0.815942	−	0.578133i	$-0.196219\pi$
$977$	2.11691e14	+	2.11691e14i	0.237809	+	0.237809i	−0.578133	+	0.815942i	$0.696219\pi$
$978$		0			0
$979$			1.05098e14i			0.116864i
$980$		0			0
$981$	2.21742e14			0.244064
$982$		0			0
$983$	−6.31966e14	+	6.31966e14i	−0.688535	+	0.688535i	−0.961908	−	0.273373i	$-0.911861\pi$
$983$	−6.31966e14	+	6.31966e14i	−0.688535	+	0.688535i	0.273373	+	0.961908i	$0.411861\pi$
$984$		0			0
$985$	−7.75841e14	+	3.82473e14i	−0.836742	+	0.412496i
$986$		0			0
$987$	−2.47026e13	−	2.47026e13i	−0.0263728	−	0.0263728i
$988$		0			0
$989$			2.73250e15i			2.88788i
$990$		0			0
$991$	1.45360e15			1.52082			0.760409	−	0.649445i	$-0.224999\pi$
$991$	1.45360e15			1.52082			0.760409	+	0.649445i	$0.224999\pi$
$992$		0			0
$993$	−1.95825e14	+	1.95825e14i	−0.202826	+	0.202826i
$994$		0			0
$995$	3.92686e14	+	1.33358e14i	0.402652	+	0.136742i
$996$		0			0
$997$	4.52019e14	+	4.52019e14i	0.458861	+	0.458861i	0.898282	−	0.439420i	$-0.144816\pi$
$997$	4.52019e14	+	4.52019e14i	0.458861	+	0.458861i	−0.439420	+	0.898282i	$0.644816\pi$
$998$		0			0
$999$			9.89297e14i			0.994258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.11.p.d.17.2		8
4.3	odd	2		5.11.c.a.2.2	✓	8
5.3	odd	4	inner	80.11.p.d.33.2		8
12.11	even	2		45.11.g.a.37.3		8
20.3	even	4		5.11.c.a.3.2	yes	8
20.7	even	4		25.11.c.a.18.3		8
20.19	odd	2		25.11.c.a.7.3		8
60.23	odd	4		45.11.g.a.28.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.11.c.a.2.2	✓	8	4.3	odd	2
5.11.c.a.3.2	yes	8	20.3	even	4
25.11.c.a.7.3		8	20.19	odd	2
25.11.c.a.18.3		8	20.7	even	4
45.11.g.a.28.3		8	60.23	odd	4
45.11.g.a.37.3		8	12.11	even	2
80.11.p.d.17.2		8	1.1	even	1	trivial
80.11.p.d.33.2		8	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-70.6389 + 70.6389i) q^{3} +(1004.90 - 2959.02i) q^{5} +(-2611.74 - 2611.74i) q^{7} +49069.3i q^{9} +O(q^{10})\)	\(q+(-70.6389 + 70.6389i) q^{3} +(1004.90 - 2959.02i) q^{5} +(-2611.74 - 2611.74i) q^{7} +49069.3i q^{9} -15694.7 q^{11} +(294351. - 294351. i) q^{13} +(138037. + 280007. i) q^{15} +(1.23520e6 + 1.23520e6i) q^{17} -2.66159e6i q^{19} +368981. q^{21} +(-7.36638e6 + 7.36638e6i) q^{23} +(-7.74599e6 - 5.94702e6i) q^{25} +(-7.63735e6 - 7.63735e6i) q^{27} +1.66720e7i q^{29} +2.74330e7 q^{31} +(1.10866e6 - 1.10866e6i) q^{33} +(-1.03527e7 + 5.10367e6i) q^{35} +(-6.47670e7 - 6.47670e7i) q^{37} +4.15853e7i q^{39} +5.65192e7 q^{41} +(1.85471e8 - 1.85471e8i) q^{43} +(1.45197e8 + 4.93095e7i) q^{45} +(-6.69481e7 - 6.69481e7i) q^{47} -2.68833e8i q^{49} -1.74507e8 q^{51} +(1.86243e8 - 1.86243e8i) q^{53} +(-1.57716e7 + 4.64411e7i) q^{55} +(1.88012e8 + 1.88012e8i) q^{57} -7.53831e8i q^{59} -3.22219e8 q^{61} +(1.28156e8 - 1.28156e8i) q^{63} +(-5.75200e8 - 1.16678e9i) q^{65} +(-9.46635e8 - 9.46635e8i) q^{67} -1.04071e9i q^{69} +1.70508e9 q^{71} +(8.54176e8 - 8.54176e8i) q^{73} +(9.67259e8 - 1.27078e8i) q^{75} +(4.09906e7 + 4.09906e7i) q^{77} -1.15355e9i q^{79} -1.81851e9 q^{81} +(3.46702e9 - 3.46702e9i) q^{83} +(4.89624e9 - 2.41374e9i) q^{85} +(-1.17769e9 - 1.17769e9i) q^{87} -6.69639e9i q^{89} -1.53754e9 q^{91} +(-1.93784e9 + 1.93784e9i) q^{93} +(-7.87570e9 - 2.67462e9i) q^{95} +(1.86215e9 + 1.86215e9i) q^{97} -7.70130e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 60 q^{3} - 5340 q^{5} + 14500 q^{7}+O(q^{10}) \) 8 * q - 60 * q^3 - 5340 * q^5 + 14500 * q^7	\( 8 q - 60 q^{3} - 5340 q^{5} + 14500 q^{7} + 233784 q^{11} + 433520 q^{13} + 3188580 q^{15} + 1045440 q^{17} - 20777784 q^{21} - 24737580 q^{23} - 35382400 q^{25} - 27386640 q^{27} - 258616 q^{31} + 11269320 q^{33} - 113638860 q^{35} + 92216120 q^{37} + 115357416 q^{41} + 262653700 q^{43} + 593742420 q^{45} + 669481140 q^{47} + 768258984 q^{51} - 1321976040 q^{53} - 2597320 q^{55} + 2367269280 q^{57} - 3143200184 q^{61} - 2578662540 q^{63} - 1924527480 q^{65} - 4912566140 q^{67} + 4375053384 q^{71} - 786968920 q^{73} - 5379002700 q^{75} + 7522045800 q^{77} - 2499208992 q^{81} + 11064240660 q^{83} + 15814282160 q^{85} - 2020273920 q^{87} + 12917794184 q^{91} - 40141724280 q^{93} - 14671558800 q^{95} + 24688294760 q^{97}+O(q^{100}) \) 8 * q - 60 * q^3 - 5340 * q^5 + 14500 * q^7 + 233784 * q^11 + 433520 * q^13 + 3188580 * q^15 + 1045440 * q^17 - 20777784 * q^21 - 24737580 * q^23 - 35382400 * q^25 - 27386640 * q^27 - 258616 * q^31 + 11269320 * q^33 - 113638860 * q^35 + 92216120 * q^37 + 115357416 * q^41 + 262653700 * q^43 + 593742420 * q^45 + 669481140 * q^47 + 768258984 * q^51 - 1321976040 * q^53 - 2597320 * q^55 + 2367269280 * q^57 - 3143200184 * q^61 - 2578662540 * q^63 - 1924527480 * q^65 - 4912566140 * q^67 + 4375053384 * q^71 - 786968920 * q^73 - 5379002700 * q^75 + 7522045800 * q^77 - 2499208992 * q^81 + 11064240660 * q^83 + 15814282160 * q^85 - 2020273920 * q^87 + 12917794184 * q^91 - 40141724280 * q^93 - 14671558800 * q^95 + 24688294760 * q^97

Introduction

L-functions

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