LMFDB - Embedded newform 80.11.p.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,11,Mod(17,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,0,-114] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$50.8285802139$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.11.p.a.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-57.0000 + 57.0000i) q^{3} +(2925.00 + 1100.00i) q^{5} +(-6953.00 - 6953.00i) q^{7} +52551.0i q^{9} -75242.0 q^{11} +(109857. - 109857. i) q^{13} +(-229425. + 104025. i) q^{15} +(-1.52893e6 - 1.52893e6i) q^{17} +4.03868e6i q^{19} +792642. q^{21} +(712423. - 712423. i) q^{23} +(7.34562e6 + 6.43500e6i) q^{25} +(-6.36120e6 - 6.36120e6i) q^{27} +446120. i q^{29} +2.90807e7 q^{31} +(4.28879e6 - 4.28879e6i) q^{33} +(-1.26892e7 - 2.79858e7i) q^{35} +(-911847. - 911847. i) q^{37} +1.25237e7i q^{39} -1.63946e8 q^{41} +(-1.18423e8 + 1.18423e8i) q^{43} +(-5.78061e7 + 1.53712e8i) q^{45} +(-2.76320e8 - 2.76320e8i) q^{47} -1.85787e8i q^{49} +1.74298e8 q^{51} +(3.08460e8 - 3.08460e8i) q^{53} +(-2.20083e8 - 8.27662e7i) q^{55} +(-2.30205e8 - 2.30205e8i) q^{57} +9.40888e8i q^{59} -1.35361e9 q^{61} +(3.65387e8 - 3.65387e8i) q^{63} +(4.42174e8 - 2.00489e8i) q^{65} +(-8.53571e8 - 8.53571e8i) q^{67} +8.12162e7i q^{69} -2.82701e9 q^{71} +(-2.75330e9 + 2.75330e9i) q^{73} +(-7.85496e8 + 5.19056e7i) q^{75} +(5.23158e8 + 5.23158e8i) q^{77} -3.32450e9i q^{79} -2.37791e9 q^{81} +(-1.34634e9 + 1.34634e9i) q^{83} +(-2.79029e9 - 6.15393e9i) q^{85} +(-2.54288e7 - 2.54288e7i) q^{87} -2.66745e9i q^{89} -1.52767e9 q^{91} +(-1.65760e9 + 1.65760e9i) q^{93} +(-4.44255e9 + 1.18131e10i) q^{95} +(-5.26563e8 - 5.26563e8i) q^{97} -3.95404e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 114 q^{3} + 5850 q^{5} - 13906 q^{7} - 150484 q^{11} + 219714 q^{13} - 458850 q^{15} - 3057854 q^{17} + 1585284 q^{21} + 1424846 q^{23} + 14691250 q^{25} - 12722400 q^{27} + 58161436 q^{31} + 8577588 q^{33}+ \cdots - 1053125694 q^{97}+O(q^{100}) $ 2 * q - 114 * q^3 + 5850 * q^5 - 13906 * q^7 - 150484 * q^11 + 219714 * q^13 - 458850 * q^15 - 3057854 * q^17 + 1585284 * q^21 + 1424846 * q^23 + 14691250 * q^25 - 12722400 * q^27 + 58161436 * q^31 + 8577588 * q^33 - 25378450 * q^35 - 1823694 * q^37 - 327891356 * q^41 - 236845554 * q^43 - 115612200 * q^45 - 552640626 * q^47 + 348595356 * q^51 + 616920194 * q^53 - 440165700 * q^55 - 460409520 * q^57 - 2707220076 * q^61 + 730774206 * q^63 + 884348850 * q^65 - 1707141826 * q^67 - 5654029124 * q^71 - 5506594366 * q^73 - 1570991250 * q^75 + 1046315252 * q^77 - 4755814398 * q^81 - 2692678194 * q^83 - 5580583550 * q^85 - 50857680 * q^87 - 3055342884 * q^91 - 3315201852 * q^93 - 8885096000 * q^95 - 1053125694 * q^97

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
$3$	−57.0000	+	57.0000i	−0.234568	+	0.234568i	−0.814596	−	0.580028i	$-0.803041\pi$
$3$	−57.0000	+	57.0000i	−0.234568	+	0.234568i	0.580028	+	0.814596i	$0.303041\pi$
$4$		0			0
$5$	2925.00	+	1100.00i	0.936000	+	0.352000i
$5$	2925.00	+	1100.00i	0.936000	+	0.352000i
$6$		0			0
$7$	−6953.00	−	6953.00i	−0.413697	−	0.413697i	0.469328	−	0.883024i	$-0.344496\pi$
$7$	−6953.00	−	6953.00i	−0.413697	−	0.413697i	−0.883024	+	0.469328i	$0.844496\pi$
$8$		0			0
$9$			52551.0i			0.889956i
$10$		0			0
$11$	−75242.0			−0.467194			−0.233597	−	0.972334i	$-0.575050\pi$
$11$	−75242.0			−0.467194			−0.233597	+	0.972334i	$0.575050\pi$
$12$		0			0
$13$	109857.	−	109857.i	0.295877	−	0.295877i	−0.543520	−	0.839396i	$-0.682909\pi$
$13$	109857.	−	109857.i	0.295877	−	0.295877i	0.839396	+	0.543520i	$0.182909\pi$
$14$		0			0
$15$	−229425.	+	104025.i	−0.302123	+	0.136988i
$16$		0			0
$17$	−1.52893e6	−	1.52893e6i	−1.07682	−	1.07682i	−0.996793	−	0.0800247i	$-0.974500\pi$
$17$	−1.52893e6	−	1.52893e6i	−1.07682	−	1.07682i	−0.0800247	−	0.996793i	$-0.525500\pi$
$18$		0			0
$19$			4.03868e6i			1.63107i	0.578711	+	0.815533i	$0.303556\pi$
$19$			4.03868e6i			1.63107i	−0.578711	+	0.815533i	$0.696444\pi$
$20$		0			0
$21$	792642.			0.194080
$22$		0			0
$23$	712423.	−	712423.i	0.110688	−	0.110688i	−0.649594	−	0.760281i	$-0.725061\pi$
$23$	712423.	−	712423.i	0.110688	−	0.110688i	0.760281	+	0.649594i	$0.225061\pi$
$24$		0			0
$25$	7.34562e6	+	6.43500e6i	0.752192	+	0.658944i
$26$		0			0
$27$	−6.36120e6	−	6.36120e6i	−0.443323	−	0.443323i
$28$		0			0
$29$			446120.i			0.0217501i	0.999941	+	0.0108751i	$0.00346171\pi$
$29$			446120.i			0.0217501i	−0.999941	+	0.0108751i	$0.996538\pi$
$30$		0			0
$31$	2.90807e7			1.01577			0.507886	−	0.861424i	$-0.330427\pi$
$31$	2.90807e7			1.01577			0.507886	+	0.861424i	$0.330427\pi$
$32$		0			0
$33$	4.28879e6	−	4.28879e6i	0.109589	−	0.109589i
$34$		0			0
$35$	−1.26892e7	−	2.79858e7i	−0.241599	−	0.532841i
$36$		0			0
$37$	−911847.	−	911847.i	−0.0131496	−	0.0131496i	0.700501	−	0.713651i	$-0.252960\pi$
$37$	−911847.	−	911847.i	−0.0131496	−	0.0131496i	−0.713651	+	0.700501i	$0.752960\pi$
$38$		0			0
$39$			1.25237e7i			0.138806i
$40$		0			0
$41$	−1.63946e8			−1.41508			−0.707540	−	0.706674i	$-0.750195\pi$
$41$	−1.63946e8			−1.41508			−0.707540	+	0.706674i	$0.750195\pi$
$42$		0			0
$43$	−1.18423e8	+	1.18423e8i	−0.805551	+	0.805551i	−0.983957	−	0.178406i	$-0.942906\pi$
$43$	−1.18423e8	+	1.18423e8i	−0.805551	+	0.805551i	0.178406	+	0.983957i	$0.442906\pi$
$44$		0			0
$45$	−5.78061e7	+	1.53712e8i	−0.313264	+	0.832999i
$46$		0			0
$47$	−2.76320e8	−	2.76320e8i	−1.20482	−	1.20482i	−0.972682	−	0.232142i	$-0.925427\pi$
$47$	−2.76320e8	−	2.76320e8i	−1.20482	−	1.20482i	−0.232142	−	0.972682i	$-0.574573\pi$
$48$		0			0
$49$		−	1.85787e8i		−	0.657710i
$50$		0			0
$51$	1.74298e8			0.505174
$52$		0			0
$53$	3.08460e8	−	3.08460e8i	0.737598	−	0.737598i	−0.234515	−	0.972113i	$-0.575350\pi$
$53$	3.08460e8	−	3.08460e8i	0.737598	−	0.737598i	0.972113	+	0.234515i	$0.0753501\pi$
$54$		0			0
$55$	−2.20083e8	−	8.27662e7i	−0.437293	−	0.164452i
$56$		0			0
$57$	−2.30205e8	−	2.30205e8i	−0.382596	−	0.382596i
$58$		0			0
$59$			9.40888e8i			1.31607i	0.752989	+	0.658034i	$0.228612\pi$
$59$			9.40888e8i			1.31607i	−0.752989	+	0.658034i	$0.771388\pi$
$60$		0			0
$61$	−1.35361e9			−1.60267			−0.801336	−	0.598215i	$-0.795877\pi$
$61$	−1.35361e9			−1.60267			−0.801336	+	0.598215i	$0.795877\pi$
$62$		0			0
$63$	3.65387e8	−	3.65387e8i	0.368172	−	0.368172i
$64$		0			0
$65$	4.42174e8	−	2.00489e8i	0.381089	−	0.172792i
$66$		0			0
$67$	−8.53571e8	−	8.53571e8i	−0.632216	−	0.632216i	0.316407	−	0.948623i	$-0.397523\pi$
$67$	−8.53571e8	−	8.53571e8i	−0.632216	−	0.632216i	−0.948623	+	0.316407i	$0.897523\pi$
$68$		0			0
$69$			8.12162e7i			0.0519275i
$70$		0			0
$71$	−2.82701e9			−1.56688			−0.783441	−	0.621466i	$-0.786537\pi$
$71$	−2.82701e9			−1.56688			−0.783441	+	0.621466i	$0.786537\pi$
$72$		0			0
$73$	−2.75330e9	+	2.75330e9i	−1.32812	+	1.32812i	−0.421119	+	0.907005i	$0.638363\pi$
$73$	−2.75330e9	+	2.75330e9i	−1.32812	+	1.32812i	−0.907005	+	0.421119i	$0.861637\pi$
$74$		0			0
$75$	−7.85496e8	+	5.19056e7i	−0.331007	+	0.0218730i
$76$		0			0
$77$	5.23158e8	+	5.23158e8i	0.193276	+	0.193276i
$78$		0			0
$79$		−	3.32450e9i		−	1.08042i	−0.841532	−	0.540208i	$-0.818346\pi$
$79$		−	3.32450e9i		−	1.08042i	0.841532	−	0.540208i	$-0.181654\pi$
$80$		0			0
$81$	−2.37791e9			−0.681977
$82$		0			0
$83$	−1.34634e9	+	1.34634e9i	−0.341794	+	0.341794i	−0.857041	−	0.515248i	$-0.827700\pi$
$83$	−1.34634e9	+	1.34634e9i	−0.341794	+	0.341794i	0.515248	+	0.857041i	$0.327700\pi$
$84$		0			0
$85$	−2.79029e9	−	6.15393e9i	−0.628861	−	1.38694i
$86$		0			0
$87$	−2.54288e7	−	2.54288e7i	−0.00510188	−	0.00510188i
$88$		0			0
$89$		−	2.66745e9i		−	0.477690i	−0.971058	−	0.238845i	$-0.923231\pi$
$89$		−	2.66745e9i		−	0.477690i	0.971058	−	0.238845i	$-0.0767688\pi$
$90$		0			0
$91$	−1.52767e9			−0.244807
$92$		0			0
$93$	−1.65760e9	+	1.65760e9i	−0.238268	+	0.238268i
$94$		0			0
$95$	−4.44255e9	+	1.18131e10i	−0.574135	+	1.52668i
$96$		0			0
$97$	−5.26563e8	−	5.26563e8i	−0.0613185	−	0.0613185i	0.675783	−	0.737101i	$-0.263806\pi$
$97$	−5.26563e8	−	5.26563e8i	−0.0613185	−	0.0613185i	−0.737101	+	0.675783i	$0.763806\pi$
$98$		0			0
$99$		−	3.95404e9i		−	0.415782i
$100$		0			0
$101$	1.45035e9			0.137996			0.0689980	−	0.997617i	$-0.478020\pi$
$101$	1.45035e9			0.137996			0.0689980	+	0.997617i	$0.478020\pi$
$102$		0			0
$103$	6.94630e9	−	6.94630e9i	0.599194	−	0.599194i	−0.340904	−	0.940098i	$-0.610733\pi$
$103$	6.94630e9	−	6.94630e9i	0.599194	−	0.599194i	0.940098	+	0.340904i	$0.110733\pi$
$104$		0			0
$105$	2.31848e9	+	8.71906e8i	0.181659	+	0.0683161i
$106$		0			0
$107$	−1.13476e10	−	1.13476e10i	−0.809071	−	0.809071i	0.175422	−	0.984493i	$-0.443871\pi$
$107$	−1.13476e10	−	1.13476e10i	−0.809071	−	0.809071i	−0.984493	+	0.175422i	$0.943871\pi$
$108$		0			0
$109$		−	1.87198e9i		−	0.121666i	−0.998148	−	0.0608328i	$-0.980624\pi$
$109$		−	1.87198e9i		−	0.121666i	0.998148	−	0.0608328i	$-0.0193757\pi$
$110$		0			0
$111$	1.03951e8			0.00616896
$112$		0			0
$113$	−1.41924e9	+	1.41924e9i	−0.0770306	+	0.0770306i	−0.744572	−	0.667542i	$-0.767347\pi$
$113$	−1.41924e9	+	1.41924e9i	−0.0770306	+	0.0770306i	0.667542	+	0.744572i	$0.267347\pi$
$114$		0			0
$115$	2.86750e9	−	1.30017e9i	0.142566	−	0.0646415i
$116$		0			0
$117$	5.77310e9	+	5.77310e9i	0.263317	+	0.263317i
$118$		0			0
$119$			2.12613e10i			0.890952i
$120$		0			0
$121$	−2.02761e10			−0.781730
$122$		0			0
$123$	9.34490e9	−	9.34490e9i	0.331932	−	0.331932i
$124$		0			0
$125$	1.44075e10	+	2.69026e10i	0.472103	+	0.881543i
$126$		0			0
$127$	2.09209e10	+	2.09209e10i	0.633231	+	0.633231i	0.948877	−	0.315646i	$-0.102221\pi$
$127$	2.09209e10	+	2.09209e10i	0.633231	+	0.633231i	−0.315646	+	0.948877i	$0.602221\pi$
$128$		0			0
$129$		−	1.35002e10i		−	0.377913i
$130$		0			0
$131$	4.70963e10			1.22076			0.610380	−	0.792109i	$-0.291017\pi$
$131$	4.70963e10			1.22076			0.610380	+	0.792109i	$0.291017\pi$
$132$		0			0
$133$	2.80809e10	−	2.80809e10i	0.674766	−	0.674766i
$134$		0			0
$135$	−1.16092e10	−	2.56038e10i	−0.258901	−	0.571000i
$136$		0			0
$137$	5.36302e10	+	5.36302e10i	1.11124	+	1.11124i	0.992983	+	0.118254i	$0.0377297\pi$
$137$	5.36302e10	+	5.36302e10i	1.11124	+	1.11124i	0.118254	+	0.992983i	$0.462270\pi$
$138$		0			0
$139$			2.60161e9i			0.0501381i	0.999686	+	0.0250691i	$0.00798056\pi$
$139$			2.60161e9i			0.0501381i	−0.999686	+	0.0250691i	$0.992019\pi$
$140$		0			0
$141$	3.15005e10			0.565226
$142$		0			0
$143$	−8.26586e9	+	8.26586e9i	−0.138232	+	0.138232i
$144$		0			0
$145$	−4.90732e8	+	1.30490e9i	−0.00765604	+	0.0203581i
$146$		0			0
$147$	1.05898e10	+	1.05898e10i	0.154278	+	0.154278i
$148$		0			0
$149$			7.57271e9i			0.103115i	0.998670	+	0.0515573i	$0.0164185\pi$
$149$			7.57271e9i			0.103115i	−0.998670	+	0.0515573i	$0.983582\pi$
$150$		0			0
$151$	4.01943e10			0.512012			0.256006	−	0.966675i	$-0.417593\pi$
$151$	4.01943e10			0.512012			0.256006	+	0.966675i	$0.417593\pi$
$152$		0			0
$153$	8.03466e10	−	8.03466e10i	0.958320	−	0.958320i
$154$		0			0
$155$	8.50611e10	+	3.19888e10i	0.950764	+	0.357552i
$156$		0			0
$157$	−4.89076e10	−	4.89076e10i	−0.512718	−	0.512718i	0.402641	−	0.915358i	$-0.368092\pi$
$157$	−4.89076e10	−	4.89076e10i	−0.512718	−	0.512718i	−0.915358	+	0.402641i	$0.868092\pi$
$158$		0			0
$159$			3.51645e10i			0.346034i
$160$		0			0
$161$	−9.90695e9			−0.0915821
$162$		0			0
$163$	4.65746e9	−	4.65746e9i	0.0404773	−	0.0404773i	−0.686578	−	0.727056i	$-0.740888\pi$
$163$	4.65746e9	−	4.65746e9i	0.0404773	−	0.0404773i	0.727056	+	0.686578i	$0.240888\pi$
$164$		0			0
$165$	1.72624e10	−	7.82705e9i	0.141150	−	0.0639998i
$166$		0			0
$167$	5.86590e10	+	5.86590e10i	0.451598	+	0.451598i	0.895885	−	0.444287i	$-0.146543\pi$
$167$	5.86590e10	+	5.86590e10i	0.451598	+	0.451598i	−0.444287	+	0.895885i	$0.646543\pi$
$168$		0			0
$169$			1.13721e11i			0.824914i
$170$		0			0
$171$	−2.12237e11			−1.45158
$172$		0			0
$173$	−1.06769e11	+	1.06769e11i	−0.688994	+	0.688994i	−0.962010	−	0.273016i	$-0.911979\pi$
$173$	−1.06769e11	+	1.06769e11i	−0.688994	+	0.688994i	0.273016	+	0.962010i	$0.411979\pi$
$174$		0			0
$175$	−6.33158e9	−	9.58167e10i	−0.0385764	−	0.583782i
$176$		0			0
$177$	−5.36306e10	−	5.36306e10i	−0.308707	−	0.308707i
$178$		0			0
$179$		−	2.46436e11i		−	1.34103i	−0.741897	−	0.670514i	$-0.766073\pi$
$179$		−	2.46436e11i		−	1.34103i	0.741897	−	0.670514i	$-0.233927\pi$
$180$		0			0
$181$	1.20625e11			0.620930			0.310465	−	0.950585i	$-0.399515\pi$
$181$	1.20625e11			0.620930			0.310465	+	0.950585i	$0.399515\pi$
$182$		0			0
$183$	7.71558e10	−	7.71558e10i	0.375935	−	0.375935i
$184$		0			0
$185$	−1.66412e9	−	3.67018e9i	−0.00767938	−	0.0169367i
$186$		0			0
$187$	1.15040e11	+	1.15040e11i	0.503082	+	0.503082i
$188$		0			0
$189$			8.84588e10i			0.366802i
$190$		0			0
$191$	−2.96325e11			−1.16574			−0.582870	−	0.812565i	$-0.698070\pi$
$191$	−2.96325e11			−1.16574			−0.582870	+	0.812565i	$0.698070\pi$
$192$		0			0
$193$	−3.14470e10	+	3.14470e10i	−0.117434	+	0.117434i	−0.763382	−	0.645948i	$-0.776462\pi$
$193$	−3.14470e10	+	3.14470e10i	−0.117434	+	0.117434i	0.645948	+	0.763382i	$0.276462\pi$
$194$		0			0
$195$	−1.37761e10	+	3.66318e10i	−0.0488599	+	0.129923i
$196$		0			0
$197$	−3.78059e10	−	3.78059e10i	−0.127417	−	0.127417i	0.640522	−	0.767940i	$-0.278718\pi$
$197$	−3.78059e10	−	3.78059e10i	−0.127417	−	0.127417i	−0.767940	+	0.640522i	$0.778718\pi$
$198$		0			0
$199$			2.82326e11i			0.904661i	0.891850	+	0.452330i	$0.149407\pi$
$199$			2.82326e11i			0.904661i	−0.891850	+	0.452330i	$0.850593\pi$
$200$		0			0
$201$	9.73071e10			0.296595
$202$		0			0
$203$	3.10187e9	−	3.10187e9i	0.00899795	−	0.00899795i
$204$		0			0
$205$	−4.79541e11	−	1.80340e11i	−1.32451	−	0.498108i
$206$		0			0
$207$	3.74385e10	+	3.74385e10i	0.0985070	+	0.0985070i
$208$		0			0
$209$		−	3.03878e11i		−	0.762023i
$210$		0			0
$211$	2.48219e11			0.593503			0.296751	−	0.954955i	$-0.404097\pi$
$211$	2.48219e11			0.593503			0.296751	+	0.954955i	$0.404097\pi$
$212$		0			0
$213$	1.61140e11	−	1.61140e11i	0.367540	−	0.367540i
$214$		0			0
$215$	−4.76652e11	+	2.16122e11i	−1.03755	+	0.470442i
$216$		0			0
$217$	−2.02198e11	−	2.02198e11i	−0.420222	−	0.420222i
$218$		0			0
$219$		−	3.13876e11i		−	0.623071i
$220$		0			0
$221$	−3.35927e11			−0.637211
$222$		0			0
$223$	−4.29372e11	+	4.29372e11i	−0.778591	+	0.778591i	−0.979591	−	0.201000i	$-0.935581\pi$
$223$	−4.29372e11	+	4.29372e11i	−0.778591	+	0.778591i	0.201000	+	0.979591i	$0.435581\pi$
$224$		0			0
$225$	−3.38166e11	+	3.86020e11i	−0.586431	+	0.669418i
$226$		0			0
$227$	−7.98295e11	−	7.98295e11i	−1.32445	−	1.32445i	−0.910136	−	0.414309i	$-0.864023\pi$
$227$	−7.98295e11	−	7.98295e11i	−1.32445	−	1.32445i	−0.414309	−	0.910136i	$-0.635977\pi$
$228$		0			0
$229$			5.93202e11i			0.941944i	0.882148	+	0.470972i	$0.156097\pi$
$229$			5.93202e11i			0.941944i	−0.882148	+	0.470972i	$0.843903\pi$
$230$		0			0
$231$	−5.96400e10			−0.0906729
$232$		0			0
$233$	2.15614e11	−	2.15614e11i	0.313977	−	0.313977i	−0.532471	−	0.846448i	$-0.678736\pi$
$233$	2.15614e11	−	2.15614e11i	0.313977	−	0.313977i	0.846448	+	0.532471i	$0.178736\pi$
$234$		0			0
$235$	−5.04285e11	−	1.11219e12i	−0.703617	−	1.55181i
$236$		0			0
$237$	1.89497e11	+	1.89497e11i	0.253431	+	0.253431i
$238$		0			0
$239$			1.11878e12i			1.43468i	0.696725	+	0.717339i	$0.254640\pi$
$239$			1.11878e12i			1.43468i	−0.696725	+	0.717339i	$0.745360\pi$
$240$		0			0
$241$	−1.17809e12			−1.44908			−0.724539	−	0.689234i	$-0.757947\pi$
$241$	−1.17809e12			−1.44908			−0.724539	+	0.689234i	$0.757947\pi$
$242$		0			0
$243$	5.11163e11	−	5.11163e11i	0.603293	−	0.603293i
$244$		0			0
$245$	2.04366e11	−	5.43426e11i	0.231514	−	0.615617i
$246$		0			0
$247$	4.43677e11	+	4.43677e11i	0.482595	+	0.482595i
$248$		0			0
$249$		−	1.53483e11i		−	0.160348i
$250$		0			0
$251$	7.26605e11			0.729339			0.364670	−	0.931137i	$-0.381182\pi$
$251$	7.26605e11			0.729339			0.364670	+	0.931137i	$0.381182\pi$
$252$		0			0
$253$	−5.36041e10	+	5.36041e10i	−0.0517125	+	0.0517125i
$254$		0			0
$255$	5.09821e11	+	1.91727e11i	0.472843	+	0.177821i
$256$		0			0
$257$	8.03958e11	+	8.03958e11i	0.717081	+	0.717081i	0.968006	−	0.250926i	$-0.0807350\pi$
$257$	8.03958e11	+	8.03958e11i	0.717081	+	0.717081i	−0.250926	+	0.968006i	$0.580735\pi$
$258$		0			0
$259$			1.26801e10i			0.0108799i
$260$		0			0
$261$	−2.34441e10			−0.0193566
$262$		0			0
$263$	2.78593e11	−	2.78593e11i	0.221407	−	0.221407i	−0.587684	−	0.809091i	$-0.699960\pi$
$263$	2.78593e11	−	2.78593e11i	0.221407	−	0.221407i	0.809091	+	0.587684i	$0.199960\pi$
$264$		0			0
$265$	1.24155e12	−	5.62940e11i	0.950026	−	0.430757i
$266$		0			0
$267$	1.52045e11	+	1.52045e11i	0.112051	+	0.112051i
$268$		0			0
$269$		−	6.95113e11i		−	0.493508i	−0.969078	−	0.246754i	$-0.920636\pi$
$269$		−	6.95113e11i		−	0.493508i	0.969078	−	0.246754i	$-0.0793640\pi$
$270$		0			0
$271$	−5.08238e11			−0.347713			−0.173856	−	0.984771i	$-0.555623\pi$
$271$	−5.08238e11			−0.347713			−0.173856	+	0.984771i	$0.555623\pi$
$272$		0			0
$273$	8.70773e10	−	8.70773e10i	0.0574238	−	0.0574238i
$274$		0			0
$275$	−5.52700e11	−	4.84182e11i	−0.351419	−	0.307854i
$276$		0			0
$277$	9.59186e11	+	9.59186e11i	0.588171	+	0.588171i	0.937136	−	0.348964i	$-0.113467\pi$
$277$	9.59186e11	+	9.59186e11i	0.588171	+	0.588171i	−0.348964	+	0.937136i	$0.613467\pi$
$278$		0			0
$279$			1.52822e12i			0.903993i
$280$		0			0
$281$	6.70898e11			0.382935			0.191467	−	0.981499i	$-0.438675\pi$
$281$	6.70898e11			0.382935			0.191467	+	0.981499i	$0.438675\pi$
$282$		0			0
$283$	1.73203e12	−	1.73203e12i	0.954162	−	0.954162i	−0.0448324	−	0.998995i	$-0.514275\pi$
$283$	1.73203e12	−	1.73203e12i	0.954162	−	0.954162i	0.998995	+	0.0448324i	$0.0142754\pi$
$284$		0			0
$285$	−4.20124e11	−	9.26574e11i	−0.223436	−	0.492783i
$286$		0			0
$287$	1.13991e12	+	1.13991e12i	0.585413	+	0.585413i
$288$		0			0
$289$			2.65924e12i			1.31907i
$290$		0			0
$291$	6.00282e10			0.0287667
$292$		0			0
$293$	6.78142e11	−	6.78142e11i	0.314038	−	0.314038i	−0.532434	−	0.846472i	$-0.678722\pi$
$293$	6.78142e11	−	6.78142e11i	0.314038	−	0.314038i	0.846472	+	0.532434i	$0.178722\pi$
$294$		0			0
$295$	−1.03498e12	+	2.75210e12i	−0.463256	+	1.23184i
$296$		0			0
$297$	4.78629e11	+	4.78629e11i	0.207118	+	0.207118i
$298$		0			0
$299$		−	1.56529e11i		−	0.0654998i
$300$		0			0
$301$	1.64679e12			0.666507
$302$		0			0
$303$	−8.26701e10	+	8.26701e10i	−0.0323694	+	0.0323694i
$304$		0			0
$305$	−3.95931e12	−	1.48897e12i	−1.50010	−	0.564140i
$306$		0			0
$307$	9.32237e11	+	9.32237e11i	0.341849	+	0.341849i	0.857062	−	0.515213i	$-0.172287\pi$
$307$	9.32237e11	+	9.32237e11i	0.341849	+	0.341849i	−0.515213	+	0.857062i	$0.672287\pi$
$308$		0			0
$309$			7.91878e11i			0.281103i
$310$		0			0
$311$	6.54904e11			0.225100			0.112550	−	0.993646i	$-0.464098\pi$
$311$	6.54904e11			0.225100			0.112550	+	0.993646i	$0.464098\pi$
$312$		0			0
$313$	2.53654e12	−	2.53654e12i	0.844344	−	0.844344i	−0.145076	−	0.989420i	$-0.546343\pi$
$313$	2.53654e12	−	2.53654e12i	0.844344	−	0.844344i	0.989420	+	0.145076i	$0.0463427\pi$
$314$		0			0
$315$	1.47068e12	−	6.66831e11i	0.474205	−	0.215012i
$316$		0			0
$317$	9.91586e11	+	9.91586e11i	0.309766	+	0.309766i	0.844819	−	0.535053i	$-0.179708\pi$
$317$	9.91586e11	+	9.91586e11i	0.309766	+	0.309766i	−0.535053	+	0.844819i	$0.679708\pi$
$318$		0			0
$319$		−	3.35670e10i		−	0.0101615i
$320$		0			0
$321$	1.29363e12			0.379564
$322$		0			0
$323$	6.17485e12	−	6.17485e12i	1.75636	−	1.75636i
$324$		0			0
$325$	1.51390e12	−	1.00039e11i	0.417522	−	0.0275899i
$326$		0			0
$327$	1.06703e11	+	1.06703e11i	0.0285389	+	0.0285389i
$328$		0			0
$329$			3.84251e12i			0.996863i
$330$		0			0
$331$	−3.29433e12			−0.829140			−0.414570	−	0.910017i	$-0.636068\pi$
$331$	−3.29433e12			−0.829140			−0.414570	+	0.910017i	$0.636068\pi$
$332$		0			0
$333$	4.79185e10	−	4.79185e10i	0.0117026	−	0.0117026i
$334$		0			0
$335$	−1.55777e12	−	3.43562e12i	−0.369214	−	0.814294i
$336$		0			0
$337$	2.43243e11	+	2.43243e11i	0.0559618	+	0.0559618i	0.734534	−	0.678572i	$-0.237401\pi$
$337$	2.43243e11	+	2.43243e11i	0.0559618	+	0.0559618i	−0.678572	+	0.734534i	$0.737401\pi$
$338$		0			0
$339$		−	1.61793e11i		−	0.0361378i
$340$		0			0
$341$	−2.18809e12			−0.474563
$342$		0			0
$343$	−3.25583e12	+	3.25583e12i	−0.685789	+	0.685789i
$344$		0			0
$345$	−8.93378e10	+	2.37557e11i	−0.0182785	+	0.0486041i
$346$		0			0
$347$	1.83051e12	+	1.83051e12i	0.363851	+	0.363851i	0.865229	−	0.501377i	$-0.167173\pi$
$347$	1.83051e12	+	1.83051e12i	0.363851	+	0.363851i	−0.501377	+	0.865229i	$0.667173\pi$
$348$		0			0
$349$			6.68385e11i			0.129092i	0.997915	+	0.0645460i	$0.0205599\pi$
$349$			6.68385e11i			0.129092i	−0.997915	+	0.0645460i	$0.979440\pi$
$350$		0			0
$351$	−1.39764e12			−0.262338
$352$		0			0
$353$	3.38512e12	−	3.38512e12i	0.617590	−	0.617590i	−0.327323	−	0.944913i	$-0.606146\pi$
$353$	3.38512e12	−	3.38512e12i	0.617590	−	0.617590i	0.944913	+	0.327323i	$0.106146\pi$
$354$		0			0
$355$	−8.26902e12	−	3.10972e12i	−1.46660	−	0.551542i
$356$		0			0
$357$	−1.21189e12	−	1.21189e12i	−0.208989	−	0.208989i
$358$		0			0
$359$			1.01424e13i			1.70085i	0.526095	+	0.850426i	$0.323656\pi$
$359$			1.01424e13i			1.70085i	−0.526095	+	0.850426i	$0.676344\pi$
$360$		0			0
$361$	−1.01799e13			−1.66038
$362$		0			0
$363$	1.15574e12	−	1.15574e12i	0.183369	−	0.183369i
$364$		0			0
$365$	−1.10820e13	+	5.02477e12i	−1.71062	+	0.775625i
$366$		0			0
$367$	6.36244e12	+	6.36244e12i	0.955638	+	0.955638i	0.999057	−	0.0434192i	$-0.0138251\pi$
$367$	6.36244e12	+	6.36244e12i	0.955638	+	0.955638i	−0.0434192	+	0.999057i	$0.513825\pi$
$368$		0			0
$369$		−	8.61551e12i		−	1.25936i
$370$		0			0
$371$	−4.28945e12			−0.610284
$372$		0			0
$373$	6.73657e12	−	6.73657e12i	0.933028	−	0.933028i	−0.0648661	−	0.997894i	$-0.520662\pi$
$373$	6.73657e12	−	6.73657e12i	0.933028	−	0.933028i	0.997894	+	0.0648661i	$0.0206620\pi$
$374$		0			0
$375$	−2.35467e12	−	7.12221e11i	−0.317522	−	0.0960414i
$376$		0			0
$377$	4.90094e10	+	4.90094e10i	0.00643536	+	0.00643536i
$378$		0			0
$379$		−	9.03104e12i		−	1.15489i	−0.816429	−	0.577446i	$-0.804049\pi$
$379$		−	9.03104e12i		−	1.15489i	0.816429	−	0.577446i	$-0.195951\pi$
$380$		0			0
$381$	−2.38499e12			−0.297071
$382$		0			0
$383$	−4.64097e12	+	4.64097e12i	−0.563138	+	0.563138i	−0.930197	−	0.367060i	$-0.880364\pi$
$383$	−4.64097e12	+	4.64097e12i	−0.563138	+	0.563138i	0.367060	+	0.930197i	$0.380364\pi$
$384$		0			0
$385$	9.54763e11	+	2.10571e12i	0.112873	+	0.248940i
$386$		0			0
$387$	−6.22324e12	−	6.22324e12i	−0.716905	−	0.716905i
$388$		0			0
$389$			3.62882e12i			0.407396i	0.979034	+	0.203698i	$0.0652961\pi$
$389$			3.62882e12i			0.407396i	−0.979034	+	0.203698i	$0.934704\pi$
$390$		0			0
$391$	−2.17849e12			−0.238381
$392$		0			0
$393$	−2.68449e12	+	2.68449e12i	−0.286351	+	0.286351i
$394$		0			0
$395$	3.65695e12	−	9.72416e12i	0.380306	−	1.01127i
$396$		0			0
$397$	3.51800e12	+	3.51800e12i	0.356733	+	0.356733i	0.862607	−	0.505874i	$-0.168830\pi$
$397$	3.51800e12	+	3.51800e12i	0.356733	+	0.356733i	−0.505874	+	0.862607i	$0.668830\pi$
$398$		0			0
$399$			3.20123e12i			0.316557i
$400$		0			0
$401$	3.98616e12			0.384444			0.192222	−	0.981351i	$-0.438431\pi$
$401$	3.98616e12			0.384444			0.192222	+	0.981351i	$0.438431\pi$
$402$		0			0
$403$	3.19472e12	−	3.19472e12i	0.300544	−	0.300544i
$404$		0			0
$405$	−6.95538e12	−	2.61570e12i	−0.638331	−	0.240056i
$406$		0			0
$407$	6.86092e10	+	6.86092e10i	0.00614342	+	0.00614342i
$408$		0			0
$409$			1.97360e13i			1.72442i	0.506551	+	0.862210i	$0.330920\pi$
$409$			1.97360e13i			1.72442i	−0.506551	+	0.862210i	$0.669080\pi$
$410$		0			0
$411$	−6.11385e12			−0.521321
$412$		0			0
$413$	6.54200e12	−	6.54200e12i	0.544453	−	0.544453i
$414$		0			0
$415$	−5.41901e12	+	2.45707e12i	−0.440230	+	0.199607i
$416$		0			0
$417$	−1.48292e11	−	1.48292e11i	−0.0117608	−	0.0117608i
$418$		0			0
$419$			6.98875e12i			0.541165i	0.962697	+	0.270582i	$0.0872163\pi$
$419$			6.98875e12i			0.541165i	−0.962697	+	0.270582i	$0.912784\pi$
$420$		0			0
$421$	−2.41687e13			−1.82744			−0.913718	−	0.406349i	$-0.866802\pi$
$421$	−2.41687e13			−1.82744			−0.913718	+	0.406349i	$0.866802\pi$
$422$		0			0
$423$	1.45209e13	−	1.45209e13i	1.07224	−	1.07224i
$424$		0			0
$425$	−1.39228e12	−	2.10696e13i	−0.100411	−	1.51954i
$426$		0			0
$427$	9.41165e12	+	9.41165e12i	0.663020	+	0.663020i
$428$		0			0
$429$		−	9.42308e11i		−	0.0648495i
$430$		0			0
$431$	−2.19757e13			−1.47760			−0.738799	−	0.673926i	$-0.764607\pi$
$431$	−2.19757e13			−1.47760			−0.738799	+	0.673926i	$0.764607\pi$
$432$		0			0
$433$	2.27496e11	−	2.27496e11i	0.0149463	−	0.0149463i	−0.699594	−	0.714540i	$-0.746636\pi$
$433$	2.27496e11	−	2.27496e11i	0.0149463	−	0.0149463i	0.714540	+	0.699594i	$0.246636\pi$
$434$		0			0
$435$	−4.64076e10	−	1.02351e11i	−0.00297950	−	0.00657122i
$436$		0			0
$437$	2.87725e12	+	2.87725e12i	0.180539	+	0.180539i
$438$		0			0
$439$			5.54828e12i			0.340280i	0.985420	+	0.170140i	$0.0544220\pi$
$439$			5.54828e12i			0.340280i	−0.985420	+	0.170140i	$0.945578\pi$
$440$		0			0
$441$	9.76328e12			0.585333
$442$		0			0
$443$	1.02630e12	−	1.02630e12i	0.0601527	−	0.0601527i	−0.676391	−	0.736543i	$-0.736457\pi$
$443$	1.02630e12	−	1.02630e12i	0.0601527	−	0.0601527i	0.736543	+	0.676391i	$0.236457\pi$
$444$		0			0
$445$	2.93420e12	−	7.80229e12i	0.168147	−	0.447118i
$446$		0			0
$447$	−4.31644e11	−	4.31644e11i	−0.0241874	−	0.0241874i
$448$		0			0
$449$			5.71205e12i			0.313011i	0.987677	+	0.156506i	$0.0500229\pi$
$449$			5.71205e12i			0.313011i	−0.987677	+	0.156506i	$0.949977\pi$
$450$		0			0
$451$	1.23356e13			0.661116
$452$		0			0
$453$	−2.29108e12	+	2.29108e12i	−0.120102	+	0.120102i
$454$		0			0
$455$	−4.46844e12	−	1.68044e12i	−0.229139	−	0.0861719i
$456$		0			0
$457$	−4.35652e12	−	4.35652e12i	−0.218554	−	0.218554i	0.589335	−	0.807889i	$-0.299390\pi$
$457$	−4.35652e12	−	4.35652e12i	−0.218554	−	0.218554i	−0.807889	+	0.589335i	$0.799390\pi$
$458$		0			0
$459$			1.94516e13i			0.954756i
$460$		0			0
$461$	3.84281e13			1.84563			0.922813	−	0.385248i	$-0.125884\pi$
$461$	3.84281e13			1.84563			0.922813	+	0.385248i	$0.125884\pi$
$462$		0			0
$463$	2.31064e13	−	2.31064e13i	1.08599	−	1.08599i	0.0900567	−	0.995937i	$-0.471295\pi$
$463$	2.31064e13	−	2.31064e13i	1.08599	−	1.08599i	0.995937	−	0.0900567i	$-0.0287048\pi$
$464$		0			0
$465$	−6.67184e12	+	3.02512e12i	−0.306889	+	0.139148i
$466$		0			0
$467$	−1.27988e12	−	1.27988e12i	−0.0576215	−	0.0576215i	0.677709	−	0.735330i	$-0.262973\pi$
$467$	−1.27988e12	−	1.27988e12i	−0.0576215	−	0.0576215i	−0.735330	+	0.677709i	$0.762973\pi$
$468$		0			0
$469$			1.18698e13i			0.523091i
$470$		0			0
$471$	5.57547e12			0.240534
$472$		0			0
$473$	8.91037e12	−	8.91037e12i	0.376348	−	0.376348i
$474$		0			0
$475$	−2.59889e13	+	2.96666e13i	−1.07478	+	1.22687i
$476$		0			0
$477$	1.62099e13	+	1.62099e13i	0.656429	+	0.656429i
$478$		0			0
$479$		−	1.13388e13i		−	0.449664i	−0.974398	−	0.224832i	$-0.927817\pi$
$479$		−	1.13388e13i		−	0.449664i	0.974398	−	0.224832i	$-0.0721833\pi$
$480$		0			0
$481$	−2.00346e11			−0.00778134
$482$		0			0
$483$	5.64696e11	−	5.64696e11i	0.0214822	−	0.0214822i
$484$		0			0
$485$	−9.60977e11	−	2.11942e12i	−0.0358100	−	0.0789782i
$486$		0			0
$487$	1.94327e13	+	1.94327e13i	0.709394	+	0.709394i	0.966408	−	0.257014i	$-0.0827386\pi$
$487$	1.94327e13	+	1.94327e13i	0.709394	+	0.709394i	−0.257014	+	0.966408i	$0.582739\pi$
$488$		0			0
$489$			5.30951e11i			0.0189893i
$490$		0			0
$491$	5.13556e13			1.79962			0.899808	−	0.436286i	$-0.143706\pi$
$491$	5.13556e13			1.79962			0.899808	+	0.436286i	$0.143706\pi$
$492$		0			0
$493$	6.82085e11	−	6.82085e11i	0.0234209	−	0.0234209i
$494$		0			0
$495$	4.34945e12	−	1.15656e13i	0.146355	−	0.389172i
$496$		0			0
$497$	1.96562e13	+	1.96562e13i	0.648214	+	0.648214i
$498$		0			0
$499$			1.74585e13i			0.564292i	0.959371	+	0.282146i	$0.0910463\pi$
$499$			1.74585e13i			0.564292i	−0.959371	+	0.282146i	$0.908954\pi$
$500$		0			0
$501$	−6.68712e12			−0.211861
$502$		0			0
$503$	1.47498e13	−	1.47498e13i	0.458085	−	0.458085i	−0.439942	−	0.898026i	$-0.645001\pi$
$503$	1.47498e13	−	1.47498e13i	0.458085	−	0.458085i	0.898026	+	0.439942i	$0.145001\pi$
$504$		0			0
$505$	4.24228e12	+	1.59539e12i	0.129164	+	0.0485746i
$506$		0			0
$507$	−6.48212e12	−	6.48212e12i	−0.193498	−	0.193498i
$508$		0			0
$509$		−	2.66714e13i		−	0.780650i	−0.920677	−	0.390325i	$-0.872363\pi$
$509$		−	2.66714e13i		−	0.780650i	0.920677	−	0.390325i	$-0.127637\pi$
$510$		0			0
$511$	3.82874e13			1.09888
$512$		0			0
$513$	2.56909e13	−	2.56909e13i	0.723089	−	0.723089i
$514$		0			0
$515$	2.79588e13	−	1.26770e13i	0.771761	−	0.349929i
$516$		0			0
$517$	2.07909e13	+	2.07909e13i	0.562886	+	0.562886i
$518$		0			0
$519$		−	1.21717e13i		−	0.323232i
$520$		0			0
$521$	−4.68604e13			−1.22072			−0.610362	−	0.792123i	$-0.708976\pi$
$521$	−4.68604e13			−1.22072			−0.610362	+	0.792123i	$0.708976\pi$
$522$		0			0
$523$	−4.18752e13	+	4.18752e13i	−1.07016	+	1.07016i	−0.0728136	+	0.997346i	$0.523198\pi$
$523$	−4.18752e13	+	4.18752e13i	−1.07016	+	1.07016i	−0.997346	+	0.0728136i	$0.976802\pi$
$524$		0			0
$525$	5.82245e12	+	5.10065e12i	0.145985	+	0.127888i
$526$		0			0
$527$	−4.44623e13	−	4.44623e13i	−1.09380	−	1.09380i
$528$		0			0
$529$			4.04114e13i			0.975497i
$530$		0			0
$531$	−4.94446e13			−1.17124
$532$		0			0
$533$	−1.80106e13	+	1.80106e13i	−0.418689	+	0.418689i
$534$		0			0
$535$	−2.07094e13	−	4.56743e13i	−0.472498	−	1.04208i
$536$		0			0
$537$	1.40468e13	+	1.40468e13i	0.314562	+	0.314562i
$538$		0			0
$539$			1.39790e13i			0.307278i
$540$		0			0
$541$	−1.39500e12			−0.0301014			−0.0150507	−	0.999887i	$-0.504791\pi$
$541$	−1.39500e12			−0.0301014			−0.0150507	+	0.999887i	$0.504791\pi$
$542$		0			0
$543$	−6.87560e12	+	6.87560e12i	−0.145650	+	0.145650i
$544$		0			0
$545$	2.05917e12	−	5.47553e12i	0.0428263	−	0.113879i
$546$		0			0
$547$	3.93459e13	+	3.93459e13i	0.803457	+	0.803457i	0.983634	−	0.180177i	$-0.0576671\pi$
$547$	3.93459e13	+	3.93459e13i	0.803457	+	0.803457i	−0.180177	+	0.983634i	$0.557667\pi$
$548$		0			0
$549$		−	7.11336e13i		−	1.42631i
$550$		0			0
$551$	−1.80174e12			−0.0354759
$552$		0			0
$553$	−2.31153e13	+	2.31153e13i	−0.446964	+	0.446964i
$554$		0			0
$555$	3.04055e11	+	1.14346e11i	0.00577415	+	0.00217147i
$556$		0			0
$557$	−4.14369e13	−	4.14369e13i	−0.772879	−	0.772879i	0.205730	−	0.978609i	$-0.434043\pi$
$557$	−4.14369e13	−	4.14369e13i	−0.772879	−	0.772879i	−0.978609	+	0.205730i	$0.934043\pi$
$558$		0			0
$559$			2.60191e13i			0.476688i
$560$		0			0
$561$	−1.31145e13			−0.236014
$562$		0			0
$563$	−3.17638e12	+	3.17638e12i	−0.0561553	+	0.0561553i	−0.734627	−	0.678471i	$-0.762643\pi$
$563$	−3.17638e12	+	3.17638e12i	−0.0561553	+	0.0561553i	0.678471	+	0.734627i	$0.262643\pi$
$564$		0			0
$565$	−5.71243e12	+	2.59011e12i	−0.0992154	+	0.0449858i
$566$		0			0
$567$	1.65336e13	+	1.65336e13i	0.282132	+	0.282132i
$568$		0			0
$569$		−	3.75308e13i		−	0.629254i	−0.949215	−	0.314627i	$-0.898121\pi$
$569$		−	3.75308e13i		−	0.629254i	0.949215	−	0.314627i	$-0.101879\pi$
$570$		0			0
$571$	−5.58913e13			−0.920796			−0.460398	−	0.887713i	$-0.652293\pi$
$571$	−5.58913e13			−0.920796			−0.460398	+	0.887713i	$0.652293\pi$
$572$		0			0
$573$	1.68905e13	−	1.68905e13i	0.273445	−	0.273445i
$574$		0			0
$575$	9.81763e12	−	6.48750e11i	0.156195	−	0.0103214i
$576$		0			0
$577$	−7.40732e13	−	7.40732e13i	−1.15820	−	1.15820i	−0.984863	−	0.173332i	$-0.944547\pi$
$577$	−7.40732e13	−	7.40732e13i	−1.15820	−	1.15820i	−0.173332	−	0.984863i	$-0.555453\pi$
$578$		0			0
$579$		−	3.58496e12i		−	0.0550923i
$580$		0			0
$581$	1.87222e13			0.282798
$582$		0			0
$583$	−2.32092e13	+	2.32092e13i	−0.344601	+	0.344601i
$584$		0			0
$585$	1.05359e13	+	2.32367e13i	0.153777	+	0.339153i
$586$		0			0
$587$	−2.68740e13	−	2.68740e13i	−0.385604	−	0.385604i	0.487512	−	0.873116i	$-0.337904\pi$
$587$	−2.68740e13	−	2.68740e13i	−0.385604	−	0.385604i	−0.873116	+	0.487512i	$0.837904\pi$
$588$		0			0
$589$			1.17448e14i			1.65679i
$590$		0			0
$591$	4.30987e12			0.0597760
$592$		0			0
$593$	−7.07818e11	+	7.07818e11i	−0.00965269	+	0.00965269i	−0.711917	−	0.702264i	$-0.752173\pi$
$593$	−7.07818e11	+	7.07818e11i	−0.00965269	+	0.00965269i	0.702264	+	0.711917i	$0.252173\pi$
$594$		0			0
$595$	−2.33874e13	+	6.21892e13i	−0.313615	+	0.833931i
$596$		0			0
$597$	−1.60926e13	−	1.60926e13i	−0.212204	−	0.212204i
$598$		0			0
$599$		−	1.43124e14i		−	1.85600i	−0.372586	−	0.927998i	$-0.621529\pi$
$599$		−	1.43124e14i		−	1.85600i	0.372586	−	0.927998i	$-0.378471\pi$
$600$		0			0
$601$	7.54546e13			0.962306			0.481153	−	0.876637i	$-0.340218\pi$
$601$	7.54546e13			0.962306			0.481153	+	0.876637i	$0.340218\pi$
$602$		0			0
$603$	4.48560e13	−	4.48560e13i	0.562644	−	0.562644i
$604$		0			0
$605$	−5.93075e13	−	2.23037e13i	−0.731699	−	0.275169i
$606$		0			0
$607$	−3.59141e13	−	3.59141e13i	−0.435835	−	0.435835i	0.454773	−	0.890607i	$-0.349720\pi$
$607$	−3.59141e13	−	3.59141e13i	−0.435835	−	0.435835i	−0.890607	+	0.454773i	$0.849720\pi$
$608$		0			0
$609$			3.53613e11i			0.00422126i
$610$		0			0
$611$	−6.07114e13			−0.712959
$612$		0			0
$613$	−7.56469e13	+	7.56469e13i	−0.873955	+	0.873955i	−0.992901	−	0.118946i	$-0.962049\pi$
$613$	−7.56469e13	+	7.56469e13i	−0.873955	+	0.873955i	0.118946	+	0.992901i	$0.462049\pi$
$614$		0			0
$615$	3.76132e13	−	1.70544e13i	0.427529	−	0.193848i
$616$		0			0
$617$	1.50165e12	+	1.50165e12i	0.0167936	+	0.0167936i	0.715454	−	0.698660i	$-0.246220\pi$
$617$	1.50165e12	+	1.50165e12i	0.0167936	+	0.0167936i	−0.698660	+	0.715454i	$0.746220\pi$
$618$		0			0
$619$			3.68182e13i			0.405144i	0.979267	+	0.202572i	$0.0649300\pi$
$619$			3.68182e13i			0.405144i	−0.979267	+	0.202572i	$0.935070\pi$
$620$		0			0
$621$	−9.06373e12			−0.0981407
$622$		0			0
$623$	−1.85468e13	+	1.85468e13i	−0.197619	+	0.197619i
$624$		0			0
$625$	1.25490e13	+	9.45382e13i	0.131586	+	0.991305i
$626$		0			0
$627$	1.73211e13	+	1.73211e13i	0.178746	+	0.178746i
$628$		0			0
$629$			2.78829e12i			0.0283195i
$630$		0			0
$631$	−1.00278e14			−1.00244			−0.501222	−	0.865319i	$-0.667116\pi$
$631$	−1.00278e14			−1.00244			−0.501222	+	0.865319i	$0.667116\pi$
$632$		0			0
$633$	−1.41485e13	+	1.41485e13i	−0.139217	+	0.139217i
$634$		0			0
$635$	3.81807e13	+	8.42067e13i	0.369807	+	0.815602i
$636$		0			0
$637$	−2.04100e13	−	2.04100e13i	−0.194601	−	0.194601i
$638$		0			0
$639$		−	1.48562e14i		−	1.39446i
$640$		0			0
$641$	−6.77897e13			−0.626431			−0.313216	−	0.949682i	$-0.601406\pi$
$641$	−6.77897e13			−0.626431			−0.313216	+	0.949682i	$0.601406\pi$
$642$		0			0
$643$	−1.15028e14	+	1.15028e14i	−1.04652	+	1.04652i	−0.0476578	+	0.998864i	$0.515176\pi$
$643$	−1.15028e14	+	1.15028e14i	−1.04652	+	1.04652i	−0.998864	+	0.0476578i	$0.984824\pi$
$644$		0			0
$645$	1.48502e13	−	3.94881e13i	0.133025	−	0.353726i
$646$		0			0
$647$	−1.38195e13	−	1.38195e13i	−0.121891	−	0.121891i	0.643530	−	0.765421i	$-0.277469\pi$
$647$	−1.38195e13	−	1.38195e13i	−0.121891	−	0.121891i	−0.765421	+	0.643530i	$0.777469\pi$
$648$		0			0
$649$		−	7.07943e13i		−	0.614858i
$650$		0			0
$651$	2.30506e13			0.197141
$652$		0			0
$653$	4.92287e13	−	4.92287e13i	0.414622	−	0.414622i	−0.468723	−	0.883345i	$-0.655286\pi$
$653$	4.92287e13	−	4.92287e13i	0.414622	−	0.414622i	0.883345	+	0.468723i	$0.155286\pi$
$654$		0			0
$655$	1.37757e14	+	5.18059e13i	1.14263	+	0.429707i
$656$		0			0
$657$	−1.44689e14	−	1.44689e14i	−1.18197	−	1.18197i
$658$		0			0
$659$			7.07781e13i			0.569471i	0.958606	+	0.284736i	$0.0919058\pi$
$659$			7.07781e13i			0.569471i	−0.958606	+	0.284736i	$0.908094\pi$
$660$		0			0
$661$	4.24894e13			0.336723			0.168362	−	0.985725i	$-0.446152\pi$
$661$	4.24894e13			0.336723			0.168362	+	0.985725i	$0.446152\pi$
$662$		0			0
$663$	1.91478e13	−	1.91478e13i	0.149469	−	0.149469i
$664$		0			0
$665$	1.13026e14	−	5.12477e13i	0.869099	−	0.394064i
$666$		0			0
$667$	3.17826e11	+	3.17826e11i	0.00240747	+	0.00240747i
$668$		0			0
$669$		−	4.89484e13i		−	0.365265i
$670$		0			0
$671$	1.01848e14			0.748758
$672$		0			0
$673$	−4.51609e13	+	4.51609e13i	−0.327105	+	0.327105i	−0.851485	−	0.524380i	$-0.824297\pi$
$673$	−4.51609e13	+	4.51609e13i	−0.327105	+	0.327105i	0.524380	+	0.851485i	$0.324297\pi$
$674$		0			0
$675$	−5.79267e12	−	8.76613e13i	−0.0413390	−	0.625589i
$676$		0			0
$677$	4.91332e13	+	4.91332e13i	0.345487	+	0.345487i	0.858426	−	0.512938i	$-0.171443\pi$
$677$	4.91332e13	+	4.91332e13i	0.345487	+	0.345487i	−0.512938	+	0.858426i	$0.671443\pi$
$678$		0			0
$679$			7.32238e12i			0.0507345i
$680$		0			0
$681$	9.10056e13			0.621345
$682$		0			0
$683$	−5.34107e13	+	5.34107e13i	−0.359356	+	0.359356i	−0.863575	−	0.504220i	$-0.831780\pi$
$683$	−5.34107e13	+	5.34107e13i	−0.359356	+	0.359356i	0.504220	+	0.863575i	$0.331780\pi$
$684$		0			0
$685$	9.78752e13	+	2.15862e14i	0.648963	+	1.43127i
$686$		0			0
$687$	−3.38125e13	−	3.38125e13i	−0.220950	−	0.220950i
$688$		0			0
$689$		−	6.77730e13i		−	0.436476i
$690$		0			0
$691$	1.93717e14			1.22964			0.614819	−	0.788668i	$-0.289229\pi$
$691$	1.93717e14			1.22964			0.614819	+	0.788668i	$0.289229\pi$
$692$		0			0
$693$	−2.74925e13	+	2.74925e13i	−0.172007	+	0.172007i
$694$		0			0
$695$	−2.86177e12	+	7.60970e12i	−0.0176486	+	0.0469293i
$696$		0			0
$697$	2.50661e14	+	2.50661e14i	1.52378	+	1.52378i
$698$		0			0
$699$			2.45801e13i			0.147298i
$700$		0			0
$701$	1.14090e14			0.673995			0.336998	−	0.941506i	$-0.390589\pi$
$701$	1.14090e14			0.673995			0.336998	+	0.941506i	$0.390589\pi$
$702$		0			0
$703$	3.68266e12	−	3.68266e12i	0.0214479	−	0.0214479i
$704$		0			0
$705$	9.21390e13	+	3.46506e13i	0.529051	+	0.198960i
$706$		0			0
$707$	−1.00843e13	−	1.00843e13i	−0.0570885	−	0.0570885i
$708$		0			0
$709$		−	2.99856e14i		−	1.67371i	−0.547421	−	0.836857i	$-0.684390\pi$
$709$		−	2.99856e14i		−	1.67371i	0.547421	−	0.836857i	$-0.315610\pi$
$710$		0			0
$711$	1.74706e14			0.961522
$712$		0			0
$713$	2.07178e13	−	2.07178e13i	0.112433	−	0.112433i
$714$		0			0
$715$	−3.32701e13	+	1.50852e13i	−0.178043	+	0.0807274i
$716$		0			0
$717$	−6.37703e13	−	6.37703e13i	−0.336529	−	0.336529i
$718$		0			0
$719$		−	9.81480e13i		−	0.510784i	−0.966838	−	0.255392i	$-0.917795\pi$
$719$		−	9.81480e13i		−	0.510784i	0.966838	−	0.255392i	$-0.0822045\pi$
$720$		0			0
$721$	−9.65952e13			−0.495769
$722$		0			0
$723$	6.71509e13	−	6.71509e13i	0.339907	−	0.339907i
$724$		0			0
$725$	−2.87078e12	+	3.27703e12i	−0.0143321	+	0.0163603i
$726$		0			0
$727$	−9.01780e12	−	9.01780e12i	−0.0444046	−	0.0444046i	0.684556	−	0.728960i	$-0.259996\pi$
$727$	−9.01780e12	−	9.01780e12i	−0.0444046	−	0.0444046i	−0.728960	+	0.684556i	$0.759996\pi$
$728$		0			0
$729$		−	8.21404e13i		−	0.398951i
$730$		0			0
$731$	3.62120e14			1.73486
$732$		0			0
$733$	−2.22715e14	+	2.22715e14i	−1.05252	+	1.05252i	−0.0539778	+	0.998542i	$0.517190\pi$
$733$	−2.22715e14	+	2.22715e14i	−1.05252	+	1.05252i	−0.998542	+	0.0539778i	$0.982810\pi$
$734$		0			0
$735$	1.93265e13	+	4.26241e13i	0.0900982	+	0.198710i
$736$		0			0
$737$	6.42244e13	+	6.42244e13i	0.295367	+	0.295367i
$738$		0			0
$739$			4.88296e13i			0.221545i	0.993846	+	0.110772i	$0.0353324\pi$
$739$			4.88296e13i			0.221545i	−0.993846	+	0.110772i	$0.964668\pi$
$740$		0			0
$741$	−5.05792e13			−0.226402
$742$		0			0
$743$	−2.49851e14	+	2.49851e14i	−1.10341	+	1.10341i	−0.109416	+	0.993996i	$0.534898\pi$
$743$	−2.49851e14	+	2.49851e14i	−1.10341	+	1.10341i	−0.993996	+	0.109416i	$0.965102\pi$
$744$		0			0
$745$	−8.32998e12	+	2.21502e13i	−0.0362963	+	0.0965152i
$746$		0			0
$747$	−7.07515e13	−	7.07515e13i	−0.304181	−	0.304181i
$748$		0			0
$749$			1.57800e14i			0.669420i
$750$		0			0
$751$	−1.99588e14			−0.835478			−0.417739	−	0.908567i	$-0.637177\pi$
$751$	−1.99588e14			−0.835478			−0.417739	+	0.908567i	$0.637177\pi$
$752$		0			0
$753$	−4.14165e13	+	4.14165e13i	−0.171080	+	0.171080i
$754$		0			0
$755$	1.17568e14	+	4.42138e13i	0.479243	+	0.180228i
$756$		0			0
$757$	5.52263e13	+	5.52263e13i	0.222160	+	0.222160i	0.809408	−	0.587247i	$-0.199788\pi$
$757$	5.52263e13	+	5.52263e13i	0.222160	+	0.222160i	−0.587247	+	0.809408i	$0.699788\pi$
$758$		0			0
$759$		−	6.11087e12i		−	0.0242602i
$760$		0			0
$761$	−2.80397e13			−0.109863			−0.0549313	−	0.998490i	$-0.517494\pi$
$761$	−2.80397e13			−0.109863			−0.0549313	+	0.998490i	$0.517494\pi$
$762$		0			0
$763$	−1.30159e13	+	1.30159e13i	−0.0503327	+	0.0503327i
$764$		0			0
$765$	3.23395e14	−	1.46633e14i	1.23432	−	0.559659i
$766$		0			0
$767$	1.03363e14	+	1.03363e14i	0.389394	+	0.389394i
$768$		0			0
$769$			1.29006e14i			0.479711i	0.970809	+	0.239855i	$0.0771000\pi$
$769$			1.29006e14i			0.479711i	−0.970809	+	0.239855i	$0.922900\pi$
$770$		0			0
$771$	−9.16513e13			−0.336408
$772$		0			0
$773$	1.09209e14	−	1.09209e14i	0.395695	−	0.395695i	−0.481017	−	0.876711i	$-0.659732\pi$
$773$	1.09209e14	−	1.09209e14i	0.395695	−	0.395695i	0.876711	+	0.481017i	$0.159732\pi$
$774$		0			0
$775$	2.13616e14	+	1.87134e14i	0.764056	+	0.669338i
$776$		0			0
$777$	−7.22768e11	−	7.22768e11i	−0.00255208	−	0.00255208i
$778$		0			0
$779$		−	6.62124e14i		−	2.30809i
$780$		0			0
$781$	2.12710e14			0.732037
$782$		0			0
$783$	2.83786e12	−	2.83786e12i	0.00964233	−	0.00964233i
$784$		0			0
$785$	−8.92564e13	−	1.96853e14i	−0.299427	−	0.660380i
$786$		0			0
$787$	−2.88376e14	−	2.88376e14i	−0.955181	−	0.955181i	0.0438564	−	0.999038i	$-0.486036\pi$
$787$	−2.88376e14	−	2.88376e14i	−0.955181	−	0.955181i	−0.999038	+	0.0438564i	$0.986036\pi$
$788$		0			0
$789$			3.17596e13i			0.103870i
$790$		0			0
$791$	1.97359e13			0.0637346
$792$		0			0
$793$	−1.48704e14	+	1.48704e14i	−0.474193	+	0.474193i
$794$		0			0
$795$	−3.86809e13	+	1.02856e14i	−0.121804	+	0.323887i
$796$		0			0
$797$	−2.45303e14	−	2.45303e14i	−0.762801	−	0.762801i	0.214027	−	0.976828i	$-0.431342\pi$
$797$	−2.45303e14	−	2.45303e14i	−0.762801	−	0.762801i	−0.976828	+	0.214027i	$0.931342\pi$
$798$		0			0
$799$			8.44947e14i			2.59475i
$800$		0			0
$801$	1.40177e14			0.425123
$802$		0			0
$803$	2.07164e14	−	2.07164e14i	0.620491	−	0.620491i
$804$		0			0
$805$	−2.89778e13	−	1.08976e13i	−0.0857209	−	0.0322369i
$806$		0			0
$807$	3.96215e13	+	3.96215e13i	0.115761	+	0.115761i
$808$		0			0
$809$		−	2.91623e13i		−	0.0841548i	−0.999114	−	0.0420774i	$-0.986602\pi$
$809$		−	2.91623e13i		−	0.0841548i	0.999114	−	0.0420774i	$-0.0133976\pi$
$810$		0			0
$811$	−2.84391e14			−0.810609			−0.405304	−	0.914182i	$-0.632834\pi$
$811$	−2.84391e14			−0.810609			−0.405304	+	0.914182i	$0.632834\pi$
$812$		0			0
$813$	2.89696e13	−	2.89696e13i	0.0815623	−	0.0815623i
$814$		0			0
$815$	1.87463e13	−	8.49987e12i	0.0521348	−	0.0236387i
$816$		0			0
$817$	−4.78272e14	−	4.78272e14i	−1.31391	−	1.31391i
$818$		0			0
$819$		−	8.02807e13i		−	0.217867i
$820$		0			0
$821$	−2.09755e14			−0.562338			−0.281169	−	0.959658i	$-0.590722\pi$
$821$	−2.09755e14			−0.562338			−0.281169	+	0.959658i	$0.590722\pi$
$822$		0			0
$823$	−1.06255e14	+	1.06255e14i	−0.281417	+	0.281417i	−0.833674	−	0.552257i	$-0.813767\pi$
$823$	−1.06255e14	+	1.06255e14i	−0.281417	+	0.281417i	0.552257	+	0.833674i	$0.313767\pi$
$824$		0			0
$825$	5.91023e13	−	3.90548e12i	0.154644	−	0.0102189i
$826$		0			0
$827$	−3.71353e14	−	3.71353e14i	−0.959974	−	0.959974i	0.0392548	−	0.999229i	$-0.487502\pi$
$827$	−3.71353e14	−	3.71353e14i	−0.959974	−	0.959974i	−0.999229	+	0.0392548i	$0.987502\pi$
$828$		0			0
$829$		−	3.10526e14i		−	0.793094i	−0.918014	−	0.396547i	$-0.870208\pi$
$829$		−	3.10526e14i		−	0.793094i	0.918014	−	0.396547i	$-0.129792\pi$
$830$		0			0
$831$	−1.09347e14			−0.275932
$832$		0			0
$833$	−2.84055e14	+	2.84055e14i	−0.708234	+	0.708234i
$834$		0			0
$835$	1.07053e14	+	2.36102e14i	0.263733	+	0.581658i
$836$		0			0
$837$	−1.84988e14	−	1.84988e14i	−0.450315	−	0.450315i
$838$		0			0
$839$		−	4.17806e14i		−	1.00500i	−0.864578	−	0.502498i	$-0.832414\pi$
$839$		−	4.17806e14i		−	1.00500i	0.864578	−	0.502498i	$-0.167586\pi$
$840$		0			0
$841$	4.20508e14			0.999527
$842$		0			0
$843$	−3.82412e13	+	3.82412e13i	−0.0898242	+	0.0898242i
$844$		0			0
$845$	−1.25094e14	+	3.32635e14i	−0.290370	+	0.772119i
$846$		0			0
$847$	1.40979e14	+	1.40979e14i	0.323399	+	0.323399i
$848$		0			0
$849$			1.97451e14i			0.447632i
$850$		0			0
$851$	−1.29924e12			−0.00291100
$852$		0			0
$853$	−5.42341e14	+	5.42341e14i	−1.20096	+	1.20096i	−0.227079	+	0.973876i	$0.572918\pi$
$853$	−5.42341e14	+	5.42341e14i	−1.20096	+	1.20096i	−0.973876	+	0.227079i	$0.927082\pi$
$854$		0			0
$855$	−6.20792e14	−	2.33460e14i	−1.35868	−	0.510955i
$856$		0			0
$857$	−2.19826e14	−	2.19826e14i	−0.475527	−	0.475527i	0.428171	−	0.903698i	$-0.359158\pi$
$857$	−2.19826e14	−	2.19826e14i	−0.475527	−	0.475527i	−0.903698	+	0.428171i	$0.859158\pi$
$858$		0			0
$859$		−	3.31148e14i		−	0.708037i	−0.935238	−	0.354019i	$-0.884815\pi$
$859$		−	3.31148e14i		−	0.708037i	0.935238	−	0.354019i	$-0.115185\pi$
$860$		0			0
$861$	−1.29950e14			−0.274638
$862$		0			0
$863$	−5.28472e14	+	5.28472e14i	−1.10400	+	1.10400i	−0.110074	+	0.993923i	$0.535109\pi$
$863$	−5.28472e14	+	5.28472e14i	−1.10400	+	1.10400i	−0.993923	+	0.110074i	$0.964891\pi$
$864$		0			0
$865$	−4.29746e14	+	1.94854e14i	−0.887424	+	0.402372i
$866$		0			0
$867$	−1.51577e14	−	1.51577e14i	−0.309412	−	0.309412i
$868$		0			0
$869$			2.50142e14i			0.504763i
$870$		0			0
$871$	−1.87541e14			−0.374116
$872$		0			0
$873$	2.76714e13	−	2.76714e13i	0.0545708	−	0.0545708i
$874$		0			0
$875$	8.68785e13	−	2.87229e14i	0.169384	−	0.559999i
$876$		0			0
$877$	7.00963e14	+	7.00963e14i	1.35113	+	1.35113i	0.884399	+	0.466732i	$0.154569\pi$
$877$	7.00963e14	+	7.00963e14i	1.35113	+	1.35113i	0.466732	+	0.884399i	$0.345431\pi$
$878$		0			0
$879$			7.73081e13i			0.147326i
$880$		0			0
$881$	2.47093e13			0.0465566			0.0232783	−	0.999729i	$-0.492590\pi$
$881$	2.47093e13			0.0465566			0.0232783	+	0.999729i	$0.492590\pi$
$882$		0			0
$883$	1.88710e14	−	1.88710e14i	0.351553	−	0.351553i	−0.509134	−	0.860687i	$-0.670034\pi$
$883$	1.88710e14	−	1.88710e14i	0.351553	−	0.351553i	0.860687	+	0.509134i	$0.170034\pi$
$884$		0			0
$885$	−9.78759e13	−	2.15863e14i	−0.180285	−	0.397615i
$886$		0			0
$887$	1.88830e14	+	1.88830e14i	0.343916	+	0.343916i	0.857837	−	0.513921i	$-0.171808\pi$
$887$	1.88830e14	+	1.88830e14i	0.343916	+	0.343916i	−0.513921	+	0.857837i	$0.671808\pi$
$888$		0			0
$889$		−	2.90926e14i		−	0.523931i
$890$		0			0
$891$	1.78918e14			0.318615
$892$		0			0
$893$	1.11597e15	−	1.11597e15i	1.96515	−	1.96515i
$894$		0			0
$895$	2.71079e14	−	7.20824e14i	0.472042	−	1.25520i
$896$		0			0
$897$	8.92217e12	+	8.92217e12i	0.0153641	+	0.0153641i
$898$		0			0
$899$			1.29735e13i			0.0220932i
$900$		0			0
$901$	−9.43226e14			−1.58852
$902$		0			0
$903$	−9.38669e13	+	9.38669e13i	−0.156341	+	0.156341i
$904$		0			0
$905$	3.52827e14	+	1.32687e14i	0.581191	+	0.218567i
$906$		0			0
$907$	6.88961e14	+	6.88961e14i	1.12243	+	1.12243i	0.991376	+	0.131052i	$0.0418354\pi$
$907$	6.88961e14	+	6.88961e14i	1.12243	+	1.12243i	0.131052	+	0.991376i	$0.458165\pi$
$908$		0			0
$909$			7.62175e13i			0.122810i
$910$		0			0
$911$	−3.16488e14			−0.504389			−0.252195	−	0.967677i	$-0.581152\pi$
$911$	−3.16488e14			−0.504389			−0.252195	+	0.967677i	$0.581152\pi$
$912$		0			0
$913$	1.01301e14	−	1.01301e14i	0.159684	−	0.159684i
$914$		0			0
$915$	3.10552e14	−	1.40809e14i	0.484205	−	0.219546i
$916$		0			0
$917$	−3.27461e14	−	3.27461e14i	−0.505024	−	0.505024i
$918$		0			0
$919$			7.09097e14i			1.08175i	0.841102	+	0.540876i	$0.181907\pi$
$919$			7.09097e14i			1.08175i	−0.841102	+	0.540876i	$0.818093\pi$
$920$		0			0
$921$	−1.06275e14			−0.160374
$922$		0			0
$923$	−3.10567e14	+	3.10567e14i	−0.463604	+	0.463604i
$924$		0			0
$925$	−8.30351e11	−	1.25658e13i	−0.00122618	−	0.0185559i
$926$		0			0
$927$	3.65035e14	+	3.65035e14i	0.533256	+	0.533256i
$928$		0			0
$929$		−	6.96190e14i		−	1.00612i	−0.864252	−	0.503059i	$-0.832208\pi$
$929$		−	6.96190e14i		−	1.00612i	0.864252	−	0.503059i	$-0.167792\pi$
$930$		0			0
$931$	7.50334e14			1.07277
$932$		0			0
$933$	−3.73296e13	+	3.73296e13i	−0.0528013	+	0.0528013i
$934$		0			0
$935$	2.09947e14	+	4.63034e14i	0.293800	+	0.647970i
$936$		0			0
$937$	7.02940e14	+	7.02940e14i	0.973241	+	0.973241i	0.999651	−	0.0264102i	$-0.00840759\pi$
$937$	7.02940e14	+	7.02940e14i	0.973241	+	0.973241i	−0.0264102	+	0.999651i	$0.508408\pi$
$938$		0			0
$939$			2.89165e14i			0.396112i
$940$		0			0
$941$	4.48743e14			0.608205			0.304102	−	0.952639i	$-0.401643\pi$
$941$	4.48743e14			0.608205			0.304102	+	0.952639i	$0.401643\pi$
$942$		0			0
$943$	−1.16799e14	+	1.16799e14i	−0.156632	+	0.156632i
$944$		0			0
$945$	−9.73047e13	+	2.58742e14i	−0.129114	+	0.343327i
$946$		0			0
$947$	−7.25276e14	−	7.25276e14i	−0.952256	−	0.952256i	0.0466554	−	0.998911i	$-0.485144\pi$
$947$	−7.25276e14	−	7.25276e14i	−0.952256	−	0.952256i	−0.998911	+	0.0466554i	$0.985144\pi$
$948$		0			0
$949$			6.04938e14i			0.785923i
$950$		0			0
$951$	−1.13041e14			−0.145322
$952$		0			0
$953$	4.88196e14	−	4.88196e14i	0.621055	−	0.621055i	−0.324746	−	0.945801i	$-0.605279\pi$
$953$	4.88196e14	−	4.88196e14i	0.621055	−	0.621055i	0.945801	+	0.324746i	$0.105279\pi$
$954$		0			0
$955$	−8.66751e14	−	3.25958e14i	−1.09113	−	0.410341i
$956$		0			0
$957$	1.91332e12	+	1.91332e12i	0.00238357	+	0.00238357i
$958$		0			0
$959$		−	7.45782e14i		−	0.919430i
$960$		0			0
$961$	2.60599e13			0.0317947
$962$		0			0
$963$	5.96330e14	−	5.96330e14i	0.720037	−	0.720037i
$964$		0			0
$965$	−1.26574e14	+	5.73908e13i	−0.151255	+	0.0685812i
$966$		0			0
$967$	4.94497e14	+	4.94497e14i	0.584832	+	0.584832i	0.936227	−	0.351395i	$-0.114293\pi$
$967$	4.94497e14	+	4.94497e14i	0.584832	+	0.584832i	−0.351395	+	0.936227i	$0.614293\pi$
$968$		0			0
$969$			7.03933e14i			0.823971i
$970$		0			0
$971$	1.74459e14			0.202115			0.101057	−	0.994881i	$-0.467777\pi$
$971$	1.74459e14			0.202115			0.101057	+	0.994881i	$0.467777\pi$
$972$		0			0
$973$	1.80890e13	−	1.80890e13i	0.0207420	−	0.0207420i
$974$		0			0
$975$	−8.05900e13	+	9.19944e13i	−0.0914657	+	0.104409i
$976$		0			0
$977$	5.88002e14	+	5.88002e14i	0.660551	+	0.660551i	0.955510	−	0.294959i	$-0.0953060\pi$
$977$	5.88002e14	+	5.88002e14i	0.660551	+	0.660551i	−0.294959	+	0.955510i	$0.595306\pi$
$978$		0			0
$979$			2.00704e14i			0.223174i
$980$		0			0
$981$	9.83743e13			0.108277
$982$		0			0
$983$	9.62314e14	−	9.62314e14i	1.04845	−	1.04845i	0.0496890	−	0.998765i	$-0.484177\pi$
$983$	9.62314e14	−	9.62314e14i	1.04845	−	1.04845i	0.998765	−	0.0496890i	$-0.0158230\pi$
$984$		0			0
$985$	−6.89958e13	−	1.52169e14i	−0.0744117	−	0.164114i
$986$		0			0
$987$	−2.19023e14	−	2.19023e14i	−0.233832	−	0.233832i
$988$		0			0
$989$			1.68734e14i			0.178329i
$990$		0			0
$991$	−5.56497e14			−0.582230			−0.291115	−	0.956688i	$-0.594026\pi$
$991$	−5.56497e14			−0.582230			−0.291115	+	0.956688i	$0.594026\pi$
$992$		0			0
$993$	1.87777e14	−	1.87777e14i	0.194490	−	0.194490i
$994$		0			0
$995$	−3.10559e14	+	8.25804e14i	−0.318441	+	0.846763i
$996$		0			0
$997$	−8.16894e14	−	8.16894e14i	−0.829259	−	0.829259i	0.158155	−	0.987414i	$-0.449445\pi$
$997$	−8.16894e14	−	8.16894e14i	−0.829259	−	0.829259i	−0.987414	+	0.158155i	$0.949445\pi$
$998$		0			0
$999$			1.16009e13i			0.0116591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.11.p.a.17.1		2
4.3	odd	2		10.11.c.b.7.1	yes	2
5.3	odd	4	inner	80.11.p.a.33.1		2
12.11	even	2		90.11.g.a.37.1		2
20.3	even	4		10.11.c.b.3.1	✓	2
20.7	even	4		50.11.c.b.43.1		2
20.19	odd	2		50.11.c.b.7.1		2
60.23	odd	4		90.11.g.a.73.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.11.c.b.3.1	✓	2	20.3	even	4
10.11.c.b.7.1	yes	2	4.3	odd	2
50.11.c.b.7.1		2	20.19	odd	2
50.11.c.b.43.1		2	20.7	even	4
80.11.p.a.17.1		2	1.1	even	1	trivial
80.11.p.a.33.1		2	5.3	odd	4	inner
90.11.g.a.37.1		2	12.11	even	2
90.11.g.a.73.1		2	60.23	odd	4

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-57.0000 + 57.0000i) q^{3} +(2925.00 + 1100.00i) q^{5} +(-6953.00 - 6953.00i) q^{7} +52551.0i q^{9} -75242.0 q^{11} +(109857. - 109857. i) q^{13} +(-229425. + 104025. i) q^{15} +(-1.52893e6 - 1.52893e6i) q^{17} +4.03868e6i q^{19} +792642. q^{21} +(712423. - 712423. i) q^{23} +(7.34562e6 + 6.43500e6i) q^{25} +(-6.36120e6 - 6.36120e6i) q^{27} +446120. i q^{29} +2.90807e7 q^{31} +(4.28879e6 - 4.28879e6i) q^{33} +(-1.26892e7 - 2.79858e7i) q^{35} +(-911847. - 911847. i) q^{37} +1.25237e7i q^{39} -1.63946e8 q^{41} +(-1.18423e8 + 1.18423e8i) q^{43} +(-5.78061e7 + 1.53712e8i) q^{45} +(-2.76320e8 - 2.76320e8i) q^{47} -1.85787e8i q^{49} +1.74298e8 q^{51} +(3.08460e8 - 3.08460e8i) q^{53} +(-2.20083e8 - 8.27662e7i) q^{55} +(-2.30205e8 - 2.30205e8i) q^{57} +9.40888e8i q^{59} -1.35361e9 q^{61} +(3.65387e8 - 3.65387e8i) q^{63} +(4.42174e8 - 2.00489e8i) q^{65} +(-8.53571e8 - 8.53571e8i) q^{67} +8.12162e7i q^{69} -2.82701e9 q^{71} +(-2.75330e9 + 2.75330e9i) q^{73} +(-7.85496e8 + 5.19056e7i) q^{75} +(5.23158e8 + 5.23158e8i) q^{77} -3.32450e9i q^{79} -2.37791e9 q^{81} +(-1.34634e9 + 1.34634e9i) q^{83} +(-2.79029e9 - 6.15393e9i) q^{85} +(-2.54288e7 - 2.54288e7i) q^{87} -2.66745e9i q^{89} -1.52767e9 q^{91} +(-1.65760e9 + 1.65760e9i) q^{93} +(-4.44255e9 + 1.18131e10i) q^{95} +(-5.26563e8 - 5.26563e8i) q^{97} -3.95404e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 114 q^{3} + 5850 q^{5} - 13906 q^{7} - 150484 q^{11} + 219714 q^{13} - 458850 q^{15} - 3057854 q^{17} + 1585284 q^{21} + 1424846 q^{23} + 14691250 q^{25} - 12722400 q^{27} + 58161436 q^{31} + 8577588 q^{33}+ \cdots - 1053125694 q^{97}+O(q^{100}) \) 2 * q - 114 * q^3 + 5850 * q^5 - 13906 * q^7 - 150484 * q^11 + 219714 * q^13 - 458850 * q^15 - 3057854 * q^17 + 1585284 * q^21 + 1424846 * q^23 + 14691250 * q^25 - 12722400 * q^27 + 58161436 * q^31 + 8577588 * q^33 - 25378450 * q^35 - 1823694 * q^37 - 327891356 * q^41 - 236845554 * q^43 - 115612200 * q^45 - 552640626 * q^47 + 348595356 * q^51 + 616920194 * q^53 - 440165700 * q^55 - 460409520 * q^57 - 2707220076 * q^61 + 730774206 * q^63 + 884348850 * q^65 - 1707141826 * q^67 - 5654029124 * q^71 - 5506594366 * q^73 - 1570991250 * q^75 + 1046315252 * q^77 - 4755814398 * q^81 - 2692678194 * q^83 - 5580583550 * q^85 - 50857680 * q^87 - 3055342884 * q^91 - 3315201852 * q^93 - 8885096000 * q^95 - 1053125694 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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