LMFDB - Embedded newform 90.11.g.a.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,11,Mod(37,90)] 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("90.37"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-32,0,0,-5850] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$57.1821527406$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	90.37
Dual form			90.11.g.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-16.0000 - 16.0000i) q^{2} +512.000i q^{4} +(-2925.00 - 1100.00i) q^{5} +(6953.00 + 6953.00i) q^{7} +(8192.00 - 8192.00i) q^{8} +(29200.0 + 64400.0i) q^{10} -75242.0 q^{11} +(109857. - 109857. i) q^{13} -222496. i q^{14} -262144. q^{16} +(1.52893e6 + 1.52893e6i) q^{17} -4.03868e6i q^{19} +(563200. - 1.49760e6i) q^{20} +(1.20387e6 + 1.20387e6i) q^{22} +(712423. - 712423. i) q^{23} +(7.34562e6 + 6.43500e6i) q^{25} -3.51542e6 q^{26} +(-3.55994e6 + 3.55994e6i) q^{28} -446120. i q^{29} -2.90807e7 q^{31} +(4.19430e6 + 4.19430e6i) q^{32} -4.89257e7i q^{34} +(-1.26892e7 - 2.79858e7i) q^{35} +(-911847. - 911847. i) q^{37} +(-6.46189e7 + 6.46189e7i) q^{38} +(-3.29728e7 + 1.49504e7i) q^{40} +1.63946e8 q^{41} +(1.18423e8 - 1.18423e8i) q^{43} -3.85239e7i q^{44} -2.27975e7 q^{46} +(-2.76320e8 - 2.76320e8i) q^{47} -1.85787e8i q^{49} +(-1.45700e7 - 2.20490e8i) q^{50} +(5.62468e7 + 5.62468e7i) q^{52} +(-3.08460e8 + 3.08460e8i) q^{53} +(2.20083e8 + 8.27662e7i) q^{55} +1.13918e8 q^{56} +(-7.13792e6 + 7.13792e6i) q^{58} +9.40888e8i q^{59} -1.35361e9 q^{61} +(4.65291e8 + 4.65291e8i) q^{62} -1.34218e8i q^{64} +(-4.42174e8 + 2.00489e8i) q^{65} +(8.53571e8 + 8.53571e8i) q^{67} +(-7.82811e8 + 7.82811e8i) q^{68} +(-2.44746e8 + 6.50801e8i) q^{70} -2.82701e9 q^{71} +(-2.75330e9 + 2.75330e9i) q^{73} +2.91791e7i q^{74} +2.06780e9 q^{76} +(-5.23158e8 - 5.23158e8i) q^{77} +3.32450e9i q^{79} +(7.66771e8 + 2.88358e8i) q^{80} +(-2.62313e9 - 2.62313e9i) q^{82} +(-1.34634e9 + 1.34634e9i) q^{83} +(-2.79029e9 - 6.15393e9i) q^{85} -3.78953e9 q^{86} +(-6.16382e8 + 6.16382e8i) q^{88} +2.66745e9i q^{89} +1.52767e9 q^{91} +(3.64761e8 + 3.64761e8i) q^{92} +8.84225e9i q^{94} +(-4.44255e9 + 1.18131e10i) q^{95} +(-5.26563e8 - 5.26563e8i) q^{97} +(-2.97259e9 + 2.97259e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} - 5850 q^{5} + 13906 q^{7} + 16384 q^{8} + 58400 q^{10} - 150484 q^{11} + 219714 q^{13} - 524288 q^{16} + 3057854 q^{17} + 1126400 q^{20} + 2407744 q^{22} + 1424846 q^{23} + 14691250 q^{25}+ \cdots - 5945178592 q^{98}+O(q^{100}) $ 2 * q - 32 * q^2 - 5850 * q^5 + 13906 * q^7 + 16384 * q^8 + 58400 * q^10 - 150484 * q^11 + 219714 * q^13 - 524288 * q^16 + 3057854 * q^17 + 1126400 * q^20 + 2407744 * q^22 + 1424846 * q^23 + 14691250 * q^25 - 7030848 * q^26 - 7119872 * q^28 - 58161436 * q^31 + 8388608 * q^32 - 25378450 * q^35 - 1823694 * q^37 - 129237760 * q^38 - 65945600 * q^40 + 327891356 * q^41 + 236845554 * q^43 - 45595072 * q^46 - 552640626 * q^47 - 29140000 * q^50 + 112493568 * q^52 - 616920194 * q^53 + 440165700 * q^55 + 227835904 * q^56 - 14275840 * q^58 - 2707220076 * q^61 + 930582976 * q^62 - 884348850 * q^65 + 1707141826 * q^67 - 1565621248 * q^68 - 489491200 * q^70 - 5654029124 * q^71 - 5506594366 * q^73 + 4135608320 * q^76 - 1046315252 * q^77 + 1533542400 * q^80 - 5246261696 * q^82 - 2692678194 * q^83 - 5580583550 * q^85 - 7579057728 * q^86 - 1232764928 * q^88 + 3055342884 * q^91 + 729521152 * q^92 - 8885096000 * q^95 - 1053125694 * q^97 - 5945178592 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−16.0000	−	16.0000i	−0.500000	−	0.500000i
$2$	−16.0000	−	16.0000i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			512.000i			0.500000i
$5$	−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	0.883024	−	0.469328i	$-0.155504\pi$
$7$	6953.00	+	6953.00i	0.413697	+	0.413697i	−0.469328	+	0.883024i	$0.655504\pi$
$8$	8192.00	−	8192.00i	0.250000	−	0.250000i
$9$		0			0
$10$	29200.0	+	64400.0i	0.292000	+	0.644000i
$11$	−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	$0.182909\pi$
$14$		−	222496.i		−	0.413697i
$15$		0			0
$16$	−262144.			−0.250000
$17$	1.52893e6	+	1.52893e6i	1.07682	+	1.07682i	0.996793	+	0.0800247i	$0.0254999\pi$
$17$	1.52893e6	+	1.52893e6i	1.07682	+	1.07682i	0.0800247	+	0.996793i	$0.474500\pi$
$18$		0			0
$19$		−	4.03868e6i		−	1.63107i	−0.578711	−	0.815533i	$-0.696444\pi$
$19$		−	4.03868e6i		−	1.63107i	0.578711	−	0.815533i	$-0.303556\pi$
$20$	563200.	−	1.49760e6i	0.176000	−	0.468000i
$21$		0			0
$22$	1.20387e6	+	1.20387e6i	0.233597	+	0.233597i
$23$	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
$26$	−3.51542e6			−0.295877
$27$		0			0
$28$	−3.55994e6	+	3.55994e6i	−0.206848	+	0.206848i
$29$		−	446120.i		−	0.0217501i	−0.999941	−	0.0108751i	$-0.996538\pi$
$29$		−	446120.i		−	0.0217501i	0.999941	−	0.0108751i	$-0.00346171\pi$
$30$		0			0
$31$	−2.90807e7			−1.01577			−0.507886	−	0.861424i	$-0.669573\pi$
$31$	−2.90807e7			−1.01577			−0.507886	+	0.861424i	$0.669573\pi$
$32$	4.19430e6	+	4.19430e6i	0.125000	+	0.125000i
$33$		0			0
$34$		−	4.89257e7i		−	1.07682i
$35$	−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	$0.752960\pi$
$38$	−6.46189e7	+	6.46189e7i	−0.815533	+	0.815533i
$39$		0			0
$40$	−3.29728e7	+	1.49504e7i	−0.322000	+	0.146000i
$41$	1.63946e8			1.41508			0.707540	−	0.706674i	$-0.249805\pi$
$41$	1.63946e8			1.41508			0.707540	+	0.706674i	$0.249805\pi$
$42$		0			0
$43$	1.18423e8	−	1.18423e8i	0.805551	−	0.805551i	−0.178406	−	0.983957i	$-0.557094\pi$
$43$	1.18423e8	−	1.18423e8i	0.805551	−	0.805551i	0.983957	+	0.178406i	$0.0570941\pi$
$44$		−	3.85239e7i		−	0.233597i
$45$		0			0
$46$	−2.27975e7			−0.110688
$47$	−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
$50$	−1.45700e7	−	2.20490e8i	−0.0466240	−	0.705568i
$51$		0			0
$52$	5.62468e7	+	5.62468e7i	0.147938	+	0.147938i
$53$	−3.08460e8	+	3.08460e8i	−0.737598	+	0.737598i	−0.972113	−	0.234515i	$-0.924650\pi$
$53$	−3.08460e8	+	3.08460e8i	−0.737598	+	0.737598i	0.234515	+	0.972113i	$0.424650\pi$
$54$		0			0
$55$	2.20083e8	+	8.27662e7i	0.437293	+	0.164452i
$56$	1.13918e8			0.206848
$57$		0			0
$58$	−7.13792e6	+	7.13792e6i	−0.0108751	+	0.0108751i
$59$			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	$0.795877\pi$
$62$	4.65291e8	+	4.65291e8i	0.507886	+	0.507886i
$63$		0			0
$64$		−	1.34218e8i		−	0.125000i
$65$	−4.42174e8	+	2.00489e8i	−0.381089	+	0.172792i
$66$		0			0
$67$	8.53571e8	+	8.53571e8i	0.632216	+	0.632216i	0.948623	−	0.316407i	$-0.102477\pi$
$67$	8.53571e8	+	8.53571e8i	0.632216	+	0.632216i	−0.316407	+	0.948623i	$0.602477\pi$
$68$	−7.82811e8	+	7.82811e8i	−0.538409	+	0.538409i
$69$		0			0
$70$	−2.44746e8	+	6.50801e8i	−0.145621	+	0.387220i
$71$	−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	$0.861637\pi$
$74$			2.91791e7i			0.0131496i
$75$		0			0
$76$	2.06780e9			0.815533
$77$	−5.23158e8	−	5.23158e8i	−0.193276	−	0.193276i
$78$		0			0
$79$			3.32450e9i			1.08042i	0.841532	+	0.540208i	$0.181654\pi$
$79$			3.32450e9i			1.08042i	−0.841532	+	0.540208i	$0.818346\pi$
$80$	7.66771e8	+	2.88358e8i	0.234000	+	0.0880000i
$81$		0			0
$82$	−2.62313e9	−	2.62313e9i	−0.707540	−	0.707540i
$83$	−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
$86$	−3.78953e9			−0.805551
$87$		0			0
$88$	−6.16382e8	+	6.16382e8i	−0.116798	+	0.116798i
$89$			2.66745e9i			0.477690i	0.971058	+	0.238845i	$0.0767688\pi$
$89$			2.66745e9i			0.477690i	−0.971058	+	0.238845i	$0.923231\pi$
$90$		0			0
$91$	1.52767e9			0.244807
$92$	3.64761e8	+	3.64761e8i	0.0553438	+	0.0553438i
$93$		0			0
$94$			8.84225e9i			1.20482i
$95$	−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	$0.763806\pi$
$98$	−2.97259e9	+	2.97259e9i	−0.328855	+	0.328855i
$99$		0			0
$100$	−3.29472e9	+	3.76096e9i	−0.329472	+	0.376096i
$101$	−1.45035e9			−0.137996			−0.0689980	−	0.997617i	$-0.521980\pi$
$101$	−1.45035e9			−0.137996			−0.0689980	+	0.997617i	$0.521980\pi$
$102$		0			0
$103$	−6.94630e9	+	6.94630e9i	−0.599194	+	0.599194i	−0.940098	−	0.340904i	$-0.889267\pi$
$103$	−6.94630e9	+	6.94630e9i	−0.599194	+	0.599194i	0.340904	+	0.940098i	$0.389267\pi$
$104$		−	1.79990e9i		−	0.147938i
$105$		0			0
$106$	9.87072e9			0.737598
$107$	−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	$-0.0193757\pi$
$110$	−2.19707e9	−	4.84558e9i	−0.136421	−	0.300873i
$111$		0			0
$112$	−1.82269e9	−	1.82269e9i	−0.103424	−	0.103424i
$113$	1.41924e9	−	1.41924e9i	0.0770306	−	0.0770306i	−0.667542	−	0.744572i	$-0.732653\pi$
$113$	1.41924e9	−	1.41924e9i	0.0770306	−	0.0770306i	0.744572	+	0.667542i	$0.232653\pi$
$114$		0			0
$115$	−2.86750e9	+	1.30017e9i	−0.142566	+	0.0646415i
$116$	2.28413e8			0.0108751
$117$		0			0
$118$	1.50542e10	−	1.50542e10i	0.658034	−	0.658034i
$119$			2.12613e10i			0.890952i
$120$		0			0
$121$	−2.02761e10			−0.781730
$122$	2.16578e10	+	2.16578e10i	0.801336	+	0.801336i
$123$		0			0
$124$		−	1.48893e10i		−	0.507886i
$125$	−1.44075e10	−	2.69026e10i	−0.472103	−	0.881543i
$126$		0			0
$127$	−2.09209e10	−	2.09209e10i	−0.633231	−	0.633231i	0.315646	−	0.948877i	$-0.397779\pi$
$127$	−2.09209e10	−	2.09209e10i	−0.633231	−	0.633231i	−0.948877	+	0.315646i	$0.897779\pi$
$128$	−2.14748e9	+	2.14748e9i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	1.02826e10	+	3.86697e9i	0.276941	+	0.104149i
$131$	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
$134$		−	2.73143e10i		−	0.632216i
$135$		0			0
$136$	2.50499e10			0.538409
$137$	−5.36302e10	−	5.36302e10i	−1.11124	−	1.11124i	−0.992983	−	0.118254i	$-0.962270\pi$
$137$	−5.36302e10	−	5.36302e10i	−1.11124	−	1.11124i	−0.118254	−	0.992983i	$-0.537730\pi$
$138$		0			0
$139$		−	2.60161e9i		−	0.0501381i	−0.999686	−	0.0250691i	$-0.992019\pi$
$139$		−	2.60161e9i		−	0.0501381i	0.999686	−	0.0250691i	$-0.00798056\pi$
$140$	1.43287e10	−	6.49688e9i	0.266421	−	0.120799i
$141$		0			0
$142$	4.52322e10	+	4.52322e10i	0.783441	+	0.783441i
$143$	−8.26586e9	+	8.26586e9i	−0.138232	+	0.138232i
$144$		0			0
$145$	−4.90732e8	+	1.30490e9i	−0.00765604	+	0.0203581i
$146$	8.81055e10			1.32812
$147$		0			0
$148$	4.66866e8	−	4.66866e8i	0.00657481	−	0.00657481i
$149$		−	7.57271e9i		−	0.103115i	−0.998670	−	0.0515573i	$-0.983582\pi$
$149$		−	7.57271e9i		−	0.103115i	0.998670	−	0.0515573i	$-0.0164185\pi$
$150$		0			0
$151$	−4.01943e10			−0.512012			−0.256006	−	0.966675i	$-0.582407\pi$
$151$	−4.01943e10			−0.512012			−0.256006	+	0.966675i	$0.582407\pi$
$152$	−3.30849e10	−	3.30849e10i	−0.407766	−	0.407766i
$153$		0			0
$154$			1.67410e10i			0.193276i
$155$	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	$0.868092\pi$
$158$	5.31920e10	−	5.31920e10i	0.540208	−	0.540208i
$159$		0			0
$160$	−7.65460e9	−	1.68821e10i	−0.0730000	−	0.161000i
$161$	9.90695e9			0.0915821
$162$		0			0
$163$	−4.65746e9	+	4.65746e9i	−0.0404773	+	0.0404773i	−0.727056	−	0.686578i	$-0.759112\pi$
$163$	−4.65746e9	+	4.65746e9i	−0.0404773	+	0.0404773i	0.686578	+	0.727056i	$0.259112\pi$
$164$			8.39402e10i			0.707540i
$165$		0			0
$166$	4.30829e10			0.341794
$167$	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
$170$	−5.38182e10	+	1.43108e11i	−0.379040	+	1.00790i
$171$		0			0
$172$	6.06325e10	+	6.06325e10i	0.402775	+	0.402775i
$173$	1.06769e11	−	1.06769e11i	0.688994	−	0.688994i	−0.273016	−	0.962010i	$-0.588021\pi$
$173$	1.06769e11	−	1.06769e11i	0.688994	−	0.688994i	0.962010	+	0.273016i	$0.0880211\pi$
$174$		0			0
$175$	6.33158e9	+	9.58167e10i	0.0385764	+	0.583782i
$176$	1.97242e10			0.116798
$177$		0			0
$178$	4.26792e10	−	4.26792e10i	0.238845	−	0.238845i
$179$		−	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	$0.399515\pi$
$182$	−2.44427e10	−	2.44427e10i	−0.122403	−	0.122403i
$183$		0			0
$184$		−	1.16723e10i		−	0.0553438i
$185$	1.66412e9	+	3.67018e9i	0.00767938	+	0.0169367i
$186$		0			0
$187$	−1.15040e11	−	1.15040e11i	−0.503082	−	0.503082i
$188$	1.41476e11	−	1.41476e11i	0.602412	−	0.602412i
$189$		0			0
$190$	2.60091e11	−	1.17929e11i	1.05041	−	0.476271i
$191$	−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	$0.276462\pi$
$194$			1.68500e10i			0.0613185i
$195$		0			0
$196$	9.51229e10			0.328855
$197$	3.78059e10	+	3.78059e10i	0.127417	+	0.127417i	0.767940	−	0.640522i	$-0.221282\pi$
$197$	3.78059e10	+	3.78059e10i	0.127417	+	0.127417i	−0.640522	+	0.767940i	$0.721282\pi$
$198$		0			0
$199$		−	2.82326e11i		−	0.904661i	−0.891850	−	0.452330i	$-0.850593\pi$
$199$		−	2.82326e11i		−	0.904661i	0.891850	−	0.452330i	$-0.149407\pi$
$200$	1.12891e11	−	7.45984e9i	0.352784	−	0.0233120i
$201$		0			0
$202$	2.32056e10	+	2.32056e10i	0.0689980	+	0.0689980i
$203$	3.10187e9	−	3.10187e9i	0.00899795	−	0.00899795i
$204$		0			0
$205$	−4.79541e11	−	1.80340e11i	−1.32451	−	0.498108i
$206$	2.22281e11			0.599194
$207$		0			0
$208$	−2.87984e10	+	2.87984e10i	−0.0739692	+	0.0739692i
$209$			3.03878e11i			0.762023i
$210$		0			0
$211$	−2.48219e11			−0.593503			−0.296751	−	0.954955i	$-0.595903\pi$
$211$	−2.48219e11			−0.593503			−0.296751	+	0.954955i	$0.595903\pi$
$212$	−1.57932e11	−	1.57932e11i	−0.368799	−	0.368799i
$213$		0			0
$214$			3.63124e11i			0.809071i
$215$	−4.76652e11	+	2.16122e11i	−1.03755	+	0.470442i
$216$		0			0
$217$	−2.02198e11	−	2.02198e11i	−0.420222	−	0.420222i
$218$	−2.99516e10	+	2.99516e10i	−0.0608328	+	0.0608328i
$219$		0			0
$220$	−4.23763e10	+	1.12682e11i	−0.0822261	+	0.218647i
$221$	3.35927e11			0.637211
$222$		0			0
$223$	4.29372e11	−	4.29372e11i	0.778591	−	0.778591i	−0.201000	−	0.979591i	$-0.564419\pi$
$223$	4.29372e11	−	4.29372e11i	0.778591	−	0.778591i	0.979591	+	0.201000i	$0.0644193\pi$
$224$			5.83260e10i			0.103424i
$225$		0			0
$226$	−4.54156e10			−0.0770306
$227$	−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	$0.843903\pi$
$230$	6.66828e10	+	2.50773e10i	0.103604	+	0.0389620i
$231$		0			0
$232$	−3.65462e9	−	3.65462e9i	−0.00543753	−	0.00543753i
$233$	−2.15614e11	+	2.15614e11i	−0.313977	+	0.313977i	−0.846448	−	0.532471i	$-0.821264\pi$
$233$	−2.15614e11	+	2.15614e11i	−0.313977	+	0.313977i	0.532471	+	0.846448i	$0.321264\pi$
$234$		0			0
$235$	5.04285e11	+	1.11219e12i	0.703617	+	1.55181i
$236$	−4.81735e11			−0.658034
$237$		0			0
$238$	3.40180e11	−	3.40180e11i	0.445476	−	0.445476i
$239$			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	$0.757947\pi$
$242$	3.24417e11	+	3.24417e11i	0.390865	+	0.390865i
$243$		0			0
$244$		−	6.93048e11i		−	0.801336i
$245$	−2.04366e11	+	5.43426e11i	−0.231514	+	0.615617i
$246$		0			0
$247$	−4.43677e11	−	4.43677e11i	−0.482595	−	0.482595i
$248$	−2.38229e11	+	2.38229e11i	−0.253943	+	0.253943i
$249$		0			0
$250$	−1.99922e11	+	6.60960e11i	−0.204720	+	0.676823i
$251$	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
$254$			6.69470e11i			0.633231i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$	−8.03958e11	−	8.03958e11i	−0.717081	−	0.717081i	0.250926	−	0.968006i	$-0.419265\pi$
$257$	−8.03958e11	−	8.03958e11i	−0.717081	−	0.717081i	−0.968006	+	0.250926i	$0.919265\pi$
$258$		0			0
$259$		−	1.26801e10i		−	0.0108799i
$260$	−1.02650e11	−	2.26393e11i	−0.0863960	−	0.190545i
$261$		0			0
$262$	−7.53541e11	−	7.53541e11i	−0.610380	−	0.610380i
$263$	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
$266$	−8.98590e11			−0.674766
$267$		0			0
$268$	−4.37028e11	+	4.37028e11i	−0.316108	+	0.316108i
$269$			6.95113e11i			0.493508i	0.969078	+	0.246754i	$0.0793640\pi$
$269$			6.95113e11i			0.493508i	−0.969078	+	0.246754i	$0.920636\pi$
$270$		0			0
$271$	5.08238e11			0.347713			0.173856	−	0.984771i	$-0.444377\pi$
$271$	5.08238e11			0.347713			0.173856	+	0.984771i	$0.444377\pi$
$272$	−4.00799e11	−	4.00799e11i	−0.269204	−	0.269204i
$273$		0			0
$274$			1.71617e12i			1.11124i
$275$	−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	$0.613467\pi$
$278$	−4.16257e10	+	4.16257e10i	−0.0250691	+	0.0250691i
$279$		0			0
$280$	−3.33210e11	−	1.25310e11i	−0.193610	−	0.0728106i
$281$	−6.70898e11			−0.382935			−0.191467	−	0.981499i	$-0.561325\pi$
$281$	−6.70898e11			−0.382935			−0.191467	+	0.981499i	$0.561325\pi$
$282$		0			0
$283$	−1.73203e12	+	1.73203e12i	−0.954162	+	0.954162i	−0.998995	−	0.0448324i	$-0.985725\pi$
$283$	−1.73203e12	+	1.73203e12i	−0.954162	+	0.954162i	0.0448324	+	0.998995i	$0.485725\pi$
$284$		−	1.44743e12i		−	0.783441i
$285$		0			0
$286$	2.64508e11			0.138232
$287$	1.13991e12	+	1.13991e12i	0.585413	+	0.585413i
$288$		0			0
$289$			2.65924e12i			1.31907i
$290$	2.87301e10	−	1.30267e10i	0.0140071	−	0.00635104i
$291$		0			0
$292$	−1.40969e12	−	1.40969e12i	−0.664062	−	0.664062i
$293$	−6.78142e11	+	6.78142e11i	−0.314038	+	0.314038i	−0.846472	−	0.532434i	$-0.821278\pi$
$293$	−6.78142e11	+	6.78142e11i	−0.314038	+	0.314038i	0.532434	+	0.846472i	$0.321278\pi$
$294$		0			0
$295$	1.03498e12	−	2.75210e12i	0.463256	−	1.23184i
$296$	−1.49397e10			−0.00657481
$297$		0			0
$298$	−1.21163e11	+	1.21163e11i	−0.0515573	+	0.0515573i
$299$		−	1.56529e11i		−	0.0654998i
$300$		0			0
$301$	1.64679e12			0.666507
$302$	6.43110e11	+	6.43110e11i	0.256006	+	0.256006i
$303$		0			0
$304$			1.05872e12i			0.407766i
$305$	3.95931e12	+	1.48897e12i	1.50010	+	0.564140i
$306$		0			0
$307$	−9.32237e11	−	9.32237e11i	−0.341849	−	0.341849i	0.515213	−	0.857062i	$-0.327713\pi$
$307$	−9.32237e11	−	9.32237e11i	−0.341849	−	0.341849i	−0.857062	+	0.515213i	$0.827713\pi$
$308$	2.67857e11	−	2.67857e11i	0.0966382	−	0.0966382i
$309$		0			0
$310$	−8.49157e11	−	1.87280e12i	−0.296606	−	0.654158i
$311$	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	$0.0463427\pi$
$314$			1.56504e12i			0.512718i
$315$		0			0
$316$	−1.70214e12			−0.540208
$317$	−9.91586e11	−	9.91586e11i	−0.309766	−	0.309766i	0.535053	−	0.844819i	$-0.320292\pi$
$317$	−9.91586e11	−	9.91586e11i	−0.309766	−	0.309766i	−0.844819	+	0.535053i	$0.820292\pi$
$318$		0			0
$319$			3.35670e10i			0.0101615i
$320$	−1.47640e11	+	3.92587e11i	−0.0440000	+	0.117000i
$321$		0			0
$322$	−1.58511e11	−	1.58511e11i	−0.0457911	−	0.0457911i
$323$	6.17485e12	−	6.17485e12i	1.75636	−	1.75636i
$324$		0			0
$325$	1.51390e12	−	1.00039e11i	0.417522	−	0.0275899i
$326$	1.49039e11			0.0404773
$327$		0			0
$328$	1.34304e12	−	1.34304e12i	0.353770	−	0.353770i
$329$		−	3.84251e12i		−	0.996863i
$330$		0			0
$331$	3.29433e12			0.829140			0.414570	−	0.910017i	$-0.363932\pi$
$331$	3.29433e12			0.829140			0.414570	+	0.910017i	$0.363932\pi$
$332$	−6.89326e11	−	6.89326e11i	−0.170897	−	0.170897i
$333$		0			0
$334$		−	1.87709e12i		−	0.451598i
$335$	−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	$0.737401\pi$
$338$	1.81954e12	−	1.81954e12i	0.412457	−	0.412457i
$339$		0			0
$340$	3.15081e12	−	1.42863e12i	0.693471	−	0.314431i
$341$	2.18809e12			0.474563
$342$		0			0
$343$	3.25583e12	−	3.25583e12i	0.685789	−	0.685789i
$344$		−	1.94024e12i		−	0.402775i
$345$		0			0
$346$	−3.41661e12			−0.688994
$347$	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	$0.979440\pi$
$350$	1.43176e12	−	1.63437e12i	0.272603	−	0.311179i
$351$		0			0
$352$	−3.15588e11	−	3.15588e11i	−0.0583992	−	0.0583992i
$353$	−3.38512e12	+	3.38512e12i	−0.617590	+	0.617590i	−0.944913	−	0.327323i	$-0.893854\pi$
$353$	−3.38512e12	+	3.38512e12i	−0.617590	+	0.617590i	0.327323	+	0.944913i	$0.393854\pi$
$354$		0			0
$355$	8.26902e12	+	3.10972e12i	1.46660	+	0.551542i
$356$	−1.36573e12			−0.238845
$357$		0			0
$358$	−3.94297e12	+	3.94297e12i	−0.670514	+	0.670514i
$359$			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
$362$	−1.92999e12	−	1.92999e12i	−0.310465	−	0.310465i
$363$		0			0
$364$			7.82168e11i			0.122403i
$365$	1.10820e13	−	5.02477e12i	1.71062	−	0.775625i
$366$		0			0
$367$	−6.36244e12	−	6.36244e12i	−0.955638	−	0.955638i	0.0434192	−	0.999057i	$-0.486175\pi$
$367$	−6.36244e12	−	6.36244e12i	−0.955638	−	0.955638i	−0.999057	+	0.0434192i	$0.986175\pi$
$368$	−1.86757e11	+	1.86757e11i	−0.0276719	+	0.0276719i
$369$		0			0
$370$	3.20970e10	−	8.53489e10i	0.00462867	−	0.0123080i
$371$	−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	$0.0206620\pi$
$374$			3.68126e12i			0.503082i
$375$		0			0
$376$	−4.52723e12			−0.602412
$377$	−4.90094e10	−	4.90094e10i	−0.00643536	−	0.00643536i
$378$		0			0
$379$			9.03104e12i			1.15489i	0.816429	+	0.577446i	$0.195951\pi$
$379$			9.03104e12i			1.15489i	−0.816429	+	0.577446i	$0.804049\pi$
$380$	−6.04833e12	−	2.27458e12i	−0.763339	−	0.287068i
$381$		0			0
$382$	4.74120e12	+	4.74120e12i	0.582870	+	0.582870i
$383$	−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
$386$	1.00630e12			0.117434
$387$		0			0
$388$	2.69600e11	−	2.69600e11i	0.0306593	−	0.0306593i
$389$		−	3.62882e12i		−	0.407396i	−0.979034	−	0.203698i	$-0.934704\pi$
$389$		−	3.62882e12i		−	0.407396i	0.979034	−	0.203698i	$-0.0652961\pi$
$390$		0			0
$391$	2.17849e12			0.238381
$392$	−1.52197e12	−	1.52197e12i	−0.164428	−	0.164428i
$393$		0			0
$394$		−	1.20979e12i		−	0.127417i
$395$	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	$0.668830\pi$
$398$	−4.51722e12	+	4.51722e12i	−0.452330	+	0.452330i
$399$		0			0
$400$	−1.92561e12	−	1.68690e12i	−0.188048	−	0.164736i
$401$	−3.98616e12			−0.384444			−0.192222	−	0.981351i	$-0.561569\pi$
$401$	−3.98616e12			−0.384444			−0.192222	+	0.981351i	$0.561569\pi$
$402$		0			0
$403$	−3.19472e12	+	3.19472e12i	−0.300544	+	0.300544i
$404$		−	7.42580e11i		−	0.0689980i
$405$		0			0
$406$	−9.92599e10			−0.00899795
$407$	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	$0.669080\pi$
$410$	4.78721e12	+	1.05581e13i	0.413203	+	0.911311i
$411$		0			0
$412$	−3.55650e12	−	3.55650e12i	−0.299597	−	0.299597i
$413$	−6.54200e12	+	6.54200e12i	−0.544453	+	0.544453i
$414$		0			0
$415$	5.41901e12	−	2.45707e12i	0.440230	−	0.199607i
$416$	9.21547e11			0.0739692
$417$		0			0
$418$	4.86205e12	−	4.86205e12i	0.381012	−	0.381012i
$419$			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	$0.866802\pi$
$422$	3.97150e12	+	3.97150e12i	0.296751	+	0.296751i
$423$		0			0
$424$			5.05381e12i			0.368799i
$425$	1.39228e12	+	2.10696e13i	0.100411	+	1.51954i
$426$		0			0
$427$	−9.41165e12	−	9.41165e12i	−0.663020	−	0.663020i
$428$	5.80999e12	−	5.80999e12i	0.404536	−	0.404536i
$429$		0			0
$430$	1.10844e13	+	4.16848e12i	0.753996	+	0.283554i
$431$	−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	$0.246636\pi$
$434$			6.47034e12i			0.420222i
$435$		0			0
$436$	9.58452e11			0.0608328
$437$	−2.87725e12	−	2.87725e12i	−0.180539	−	0.180539i
$438$		0			0
$439$		−	5.54828e12i		−	0.340280i	−0.985420	−	0.170140i	$-0.945578\pi$
$439$		−	5.54828e12i		−	0.340280i	0.985420	−	0.170140i	$-0.0544220\pi$
$440$	2.48094e12	−	1.12490e12i	0.150436	−	0.0682103i
$441$		0			0
$442$	−5.37483e12	−	5.37483e12i	−0.318605	−	0.318605i
$443$	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
$446$	−1.37399e13			−0.778591
$447$		0			0
$448$	9.33216e11	−	9.33216e11i	0.0517121	−	0.0517121i
$449$		−	5.71205e12i		−	0.313011i	−0.987677	−	0.156506i	$-0.949977\pi$
$449$		−	5.71205e12i		−	0.313011i	0.987677	−	0.156506i	$-0.0500229\pi$
$450$		0			0
$451$	−1.23356e13			−0.661116
$452$	7.26650e11	+	7.26650e11i	0.0385153	+	0.0385153i
$453$		0			0
$454$			2.55454e13i			1.32445i
$455$	−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	$0.799390\pi$
$458$	9.49123e12	−	9.49123e12i	0.470972	−	0.470972i
$459$		0			0
$460$	−6.65688e11	−	1.46816e12i	−0.0323208	−	0.0712828i
$461$	−3.84281e13			−1.84563			−0.922813	−	0.385248i	$-0.874116\pi$
$461$	−3.84281e13			−1.84563			−0.922813	+	0.385248i	$0.874116\pi$
$462$		0			0
$463$	−2.31064e13	+	2.31064e13i	−1.08599	+	1.08599i	−0.0900567	+	0.995937i	$0.528705\pi$
$463$	−2.31064e13	+	2.31064e13i	−1.08599	+	1.08599i	−0.995937	+	0.0900567i	$0.971295\pi$
$464$			1.16948e11i			0.00543753i
$465$		0			0
$466$	6.89966e12			0.313977
$467$	−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
$470$	9.72648e12	−	2.58636e13i	0.424098	−	1.12772i
$471$		0			0
$472$	7.70776e12	+	7.70776e12i	0.329017	+	0.329017i
$473$	−8.91037e12	+	8.91037e12i	−0.376348	+	0.376348i
$474$		0			0
$475$	2.59889e13	−	2.96666e13i	1.07478	−	1.22687i
$476$	−1.08858e13			−0.445476
$477$		0			0
$478$	1.79004e13	−	1.79004e13i	0.717339	−	0.717339i
$479$		−	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
$482$	1.88494e13	+	1.88494e13i	0.724539	+	0.724539i
$483$		0			0
$484$		−	1.03813e13i		−	0.390865i
$485$	9.60977e11	+	2.11942e12i	0.0358100	+	0.0789782i
$486$		0			0
$487$	−1.94327e13	−	1.94327e13i	−0.709394	−	0.709394i	0.257014	−	0.966408i	$-0.417261\pi$
$487$	−1.94327e13	−	1.94327e13i	−0.709394	−	0.709394i	−0.966408	+	0.257014i	$0.917261\pi$
$488$	−1.10888e13	+	1.10888e13i	−0.400668	+	0.400668i
$489$		0			0
$490$	1.19647e13	−	5.42498e12i	0.423565	−	0.192051i
$491$	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
$494$			1.41977e13i			0.482595i
$495$		0			0
$496$	7.62334e12			0.253943
$497$	−1.96562e13	−	1.96562e13i	−0.648214	−	0.648214i
$498$		0			0
$499$		−	1.74585e13i		−	0.564292i	−0.959371	−	0.282146i	$-0.908954\pi$
$499$		−	1.74585e13i		−	0.564292i	0.959371	−	0.282146i	$-0.0910463\pi$
$500$	1.37741e13	−	7.37662e12i	0.440772	−	0.236052i
$501$		0			0
$502$	−1.16257e13	−	1.16257e13i	−0.364670	−	0.364670i
$503$	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
$506$	1.71533e12			0.0517125
$507$		0			0
$508$	1.07115e13	−	1.07115e13i	0.316616	−	0.316616i
$509$			2.66714e13i			0.780650i	0.920677	+	0.390325i	$0.127637\pi$
$509$			2.66714e13i			0.780650i	−0.920677	+	0.390325i	$0.872363\pi$
$510$		0			0
$511$	−3.82874e13			−1.09888
$512$	−1.09951e12	−	1.09951e12i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			2.57267e13i			0.717081i
$515$	2.79588e13	−	1.26770e13i	0.771761	−	0.349929i
$516$		0			0
$517$	2.07909e13	+	2.07909e13i	0.562886	+	0.562886i
$518$	−2.02882e11	+	2.02882e11i	−0.00543996	+	0.00543996i
$519$		0			0
$520$	−1.97989e12	+	5.26470e12i	−0.0520743	+	0.138470i
$521$	4.68604e13			1.22072			0.610362	−	0.792123i	$-0.291024\pi$
$521$	4.68604e13			1.22072			0.610362	+	0.792123i	$0.291024\pi$
$522$		0			0
$523$	4.18752e13	−	4.18752e13i	1.07016	−	1.07016i	0.0728136	−	0.997346i	$-0.476802\pi$
$523$	4.18752e13	−	4.18752e13i	1.07016	−	1.07016i	0.997346	−	0.0728136i	$-0.0231978\pi$
$524$			2.41133e13i			0.610380i
$525$		0			0
$526$	−8.91498e12			−0.221407
$527$	−4.44623e13	−	4.44623e13i	−1.09380	−	1.09380i
$528$		0			0
$529$			4.04114e13i			0.975497i
$530$	−2.88719e13	−	1.08578e13i	−0.690392	−	0.259634i
$531$		0			0
$532$	1.43774e13	+	1.43774e13i	0.337383	+	0.337383i
$533$	1.80106e13	−	1.80106e13i	0.418689	−	0.418689i
$534$		0			0
$535$	2.07094e13	+	4.56743e13i	0.472498	+	1.04208i
$536$	1.39849e13			0.316108
$537$		0			0
$538$	1.11218e13	−	1.11218e13i	0.246754	−	0.246754i
$539$			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	$0.504791\pi$
$542$	−8.13181e12	−	8.13181e12i	−0.173856	−	0.173856i
$543$		0			0
$544$			1.28256e13i			0.269204i
$545$	−2.05917e12	+	5.47553e12i	−0.0428263	+	0.113879i
$546$		0			0
$547$	−3.93459e13	−	3.93459e13i	−0.803457	−	0.803457i	0.180177	−	0.983634i	$-0.442333\pi$
$547$	−3.93459e13	−	3.93459e13i	−0.803457	−	0.803457i	−0.983634	+	0.180177i	$0.942333\pi$
$548$	2.74587e13	−	2.74587e13i	0.555619	−	0.555619i
$549$		0			0
$550$	1.09628e12	+	1.65901e13i	0.0217824	+	0.329637i
$551$	−1.80174e12			−0.0354759
$552$		0			0
$553$	−2.31153e13	+	2.31153e13i	−0.446964	+	0.446964i
$554$		−	3.06940e13i		−	0.588171i
$555$		0			0
$556$	1.33202e12			0.0250691
$557$	4.14369e13	+	4.14369e13i	0.772879	+	0.772879i	0.978609	−	0.205730i	$-0.0659568\pi$
$557$	4.14369e13	+	4.14369e13i	0.772879	+	0.772879i	−0.205730	+	0.978609i	$0.565957\pi$
$558$		0			0
$559$		−	2.60191e13i		−	0.476688i
$560$	3.32640e12	+	7.33632e12i	0.0603997	+	0.133210i
$561$		0			0
$562$	1.07344e13	+	1.07344e13i	0.191467	+	0.191467i
$563$	−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
$566$	5.54248e13			0.954162
$567$		0			0
$568$	−2.31589e13	+	2.31589e13i	−0.391721	+	0.391721i
$569$			3.75308e13i			0.629254i	0.949215	+	0.314627i	$0.101879\pi$
$569$			3.75308e13i			0.629254i	−0.949215	+	0.314627i	$0.898121\pi$
$570$		0			0
$571$	5.58913e13			0.920796			0.460398	−	0.887713i	$-0.347707\pi$
$571$	5.58913e13			0.920796			0.460398	+	0.887713i	$0.347707\pi$
$572$	−4.23212e12	−	4.23212e12i	−0.0691159	−	0.0691159i
$573$		0			0
$574$		−	3.64773e13i		−	0.585413i
$575$	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	$-0.555453\pi$
$578$	4.25479e13	−	4.25479e13i	0.659536	−	0.659536i
$579$		0			0
$580$	−6.68109e11	−	2.51255e11i	−0.0101791	−	0.00382802i
$581$	−1.87222e13			−0.282798
$582$		0			0
$583$	2.32092e13	−	2.32092e13i	0.344601	−	0.344601i
$584$			4.51100e13i			0.664062i
$585$		0			0
$586$	2.17005e13			0.314038
$587$	−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
$590$	−6.05932e13	+	2.74739e13i	−0.847547	+	0.384292i
$591$		0			0
$592$	2.39035e11	+	2.39035e11i	0.00328741	+	0.00328741i
$593$	7.07818e11	−	7.07818e11i	0.00965269	−	0.00965269i	−0.702264	−	0.711917i	$-0.747827\pi$
$593$	7.07818e11	−	7.07818e11i	0.00965269	−	0.00965269i	0.711917	+	0.702264i	$0.247827\pi$
$594$		0			0
$595$	2.33874e13	−	6.21892e13i	0.313615	−	0.833931i
$596$	3.87723e12			0.0515573
$597$		0			0
$598$	−2.50447e12	+	2.50447e12i	−0.0327499	+	0.0327499i
$599$		−	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	$0.340218\pi$
$602$	−2.63486e13	−	2.63486e13i	−0.333254	−	0.333254i
$603$		0			0
$604$		−	2.05795e13i		−	0.256006i
$605$	5.93075e13	+	2.23037e13i	0.731699	+	0.275169i
$606$		0			0
$607$	3.59141e13	+	3.59141e13i	0.435835	+	0.435835i	0.890607	−	0.454773i	$-0.150280\pi$
$607$	3.59141e13	+	3.59141e13i	0.435835	+	0.435835i	−0.454773	+	0.890607i	$0.650280\pi$
$608$	1.69395e13	−	1.69395e13i	0.203883	−	0.203883i
$609$		0			0
$610$	−3.95254e13	−	8.71725e13i	−0.467980	−	1.03212i
$611$	−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	$0.462049\pi$
$614$			2.98316e13i			0.341849i
$615$		0			0
$616$	−8.57141e12			−0.0966382
$617$	−1.50165e12	−	1.50165e12i	−0.0167936	−	0.0167936i	0.698660	−	0.715454i	$-0.253780\pi$
$617$	−1.50165e12	−	1.50165e12i	−0.0167936	−	0.0167936i	−0.715454	+	0.698660i	$0.753780\pi$
$618$		0			0
$619$		−	3.68182e13i		−	0.405144i	−0.979267	−	0.202572i	$-0.935070\pi$
$619$		−	3.68182e13i		−	0.405144i	0.979267	−	0.202572i	$-0.0649300\pi$
$620$	−1.63783e13	+	4.35513e13i	−0.178776	+	0.475382i
$621$		0			0
$622$	−1.04785e13	−	1.04785e13i	−0.112550	−	0.112550i
$623$	−1.85468e13	+	1.85468e13i	−0.197619	+	0.197619i
$624$		0			0
$625$	1.25490e13	+	9.45382e13i	0.131586	+	0.991305i
$626$	−8.11692e13			−0.844344
$627$		0			0
$628$	2.50407e13	−	2.50407e13i	0.256359	−	0.256359i
$629$		−	2.78829e12i		−	0.0283195i
$630$		0			0
$631$	1.00278e14			1.00244			0.501222	−	0.865319i	$-0.332884\pi$
$631$	1.00278e14			1.00244			0.501222	+	0.865319i	$0.332884\pi$
$632$	2.72343e13	+	2.72343e13i	0.270104	+	0.270104i
$633$		0			0
$634$			3.17307e13i			0.309766i
$635$	3.81807e13	+	8.42067e13i	0.369807	+	0.815602i
$636$		0			0
$637$	−2.04100e13	−	2.04100e13i	−0.194601	−	0.194601i
$638$	5.37071e11	−	5.37071e11i	0.00508076	−	0.00508076i
$639$		0			0
$640$	8.64362e12	−	3.91916e12i	0.0805000	−	0.0365000i
$641$	6.77897e13			0.626431			0.313216	−	0.949682i	$-0.398594\pi$
$641$	6.77897e13			0.626431			0.313216	+	0.949682i	$0.398594\pi$
$642$		0			0
$643$	1.15028e14	−	1.15028e14i	1.04652	−	1.04652i	0.0476578	−	0.998864i	$-0.484824\pi$
$643$	1.15028e14	−	1.15028e14i	1.04652	−	1.04652i	0.998864	−	0.0476578i	$-0.0151757\pi$
$644$			5.07236e12i			0.0457911i
$645$		0			0
$646$	−1.97595e14			−1.75636
$647$	−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
$650$	−2.58230e13	−	2.26218e13i	−0.222556	−	0.194966i
$651$		0			0
$652$	−2.38462e12	−	2.38462e12i	−0.0202386	−	0.0202386i
$653$	−4.92287e13	+	4.92287e13i	−0.414622	+	0.414622i	−0.883345	−	0.468723i	$-0.844714\pi$
$653$	−4.92287e13	+	4.92287e13i	−0.414622	+	0.414622i	0.468723	+	0.883345i	$0.344714\pi$
$654$		0			0
$655$	−1.37757e14	−	5.18059e13i	−1.14263	−	0.429707i
$656$	−4.29774e13			−0.353770
$657$		0			0
$658$	−6.14802e13	+	6.14802e13i	−0.498432	+	0.498432i
$659$			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	$0.446152\pi$
$662$	−5.27094e13	−	5.27094e13i	−0.414570	−	0.414570i
$663$		0			0
$664$			2.20584e13i			0.170897i
$665$	−1.13026e14	+	5.12477e13i	−0.869099	+	0.394064i
$666$		0			0
$667$	−3.17826e11	−	3.17826e11i	−0.00240747	−	0.00240747i
$668$	−3.00334e13	+	3.00334e13i	−0.225799	+	0.225799i
$669$		0			0
$670$	−3.00457e13	+	7.98942e13i	−0.222540	+	0.591754i
$671$	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	$0.324297\pi$
$674$		−	7.78379e12i		−	0.0559618i
$675$		0			0
$676$	−5.82253e13			−0.412457
$677$	−4.91332e13	−	4.91332e13i	−0.345487	−	0.345487i	0.512938	−	0.858426i	$-0.328557\pi$
$677$	−4.91332e13	−	4.91332e13i	−0.345487	−	0.345487i	−0.858426	+	0.512938i	$0.828557\pi$
$678$		0			0
$679$		−	7.32238e12i		−	0.0507345i
$680$	−7.32711e13	−	2.75549e13i	−0.503951	−	0.189520i
$681$		0			0
$682$	−3.50095e13	−	3.50095e13i	−0.237281	−	0.237281i
$683$	−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
$686$	−1.04186e14			−0.685789
$687$		0			0
$688$	−3.10438e13	+	3.10438e13i	−0.201388	+	0.201388i
$689$			6.77730e13i			0.436476i
$690$		0			0
$691$	−1.93717e14			−1.22964			−0.614819	−	0.788668i	$-0.710771\pi$
$691$	−1.93717e14			−1.22964			−0.614819	+	0.788668i	$0.710771\pi$
$692$	5.46658e13	+	5.46658e13i	0.344497	+	0.344497i
$693$		0			0
$694$		−	5.85762e13i		−	0.363851i
$695$	−2.86177e12	+	7.60970e12i	−0.0176486	+	0.0469293i
$696$		0			0
$697$	2.50661e14	+	2.50661e14i	1.52378	+	1.52378i
$698$	1.06942e13	−	1.06942e13i	0.0645460	−	0.0645460i
$699$		0			0
$700$	−4.90581e13	+	3.24177e12i	−0.291891	+	0.0192882i
$701$	−1.14090e14			−0.673995			−0.336998	−	0.941506i	$-0.609411\pi$
$701$	−1.14090e14			−0.673995			−0.336998	+	0.941506i	$0.609411\pi$
$702$		0			0
$703$	−3.68266e12	+	3.68266e12i	−0.0214479	+	0.0214479i
$704$			1.00988e13i			0.0583992i
$705$		0			0
$706$	1.08324e14			0.617590
$707$	−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	$-0.315610\pi$
$710$	−8.25488e13	−	1.82060e14i	−0.457530	−	1.00907i
$711$		0			0
$712$	2.18518e13	+	2.18518e13i	0.119423	+	0.119423i
$713$	−2.07178e13	+	2.07178e13i	−0.112433	+	0.112433i
$714$		0			0
$715$	3.32701e13	−	1.50852e13i	0.178043	−	0.0807274i
$716$	1.26175e14			0.670514
$717$		0			0
$718$	1.62278e14	−	1.62278e14i	0.850426	−	0.850426i
$719$		−	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
$722$	1.62878e14	+	1.62878e14i	0.830188	+	0.830188i
$723$		0			0
$724$			6.17598e13i			0.310465i
$725$	2.87078e12	−	3.27703e12i	0.0143321	−	0.0163603i
$726$		0			0
$727$	9.01780e12	+	9.01780e12i	0.0444046	+	0.0444046i	0.728960	−	0.684556i	$-0.240004\pi$
$727$	9.01780e12	+	9.01780e12i	0.0444046	+	0.0444046i	−0.684556	+	0.728960i	$0.740004\pi$
$728$	1.25147e13	−	1.25147e13i	0.0612016	−	0.0612016i
$729$		0			0
$730$	−2.57709e14	−	9.69161e13i	−1.24312	−	0.467500i
$731$	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	$0.982810\pi$
$734$			2.03598e14i			0.955638i
$735$		0			0
$736$	5.97624e12			0.0276719
$737$	−6.42244e13	−	6.42244e13i	−0.295367	−	0.295367i
$738$		0			0
$739$		−	4.88296e13i		−	0.221545i	−0.993846	−	0.110772i	$-0.964668\pi$
$739$		−	4.88296e13i		−	0.221545i	0.993846	−	0.110772i	$-0.0353324\pi$
$740$	−1.87913e12	+	8.52030e11i	−0.00846836	+	0.00383969i
$741$		0			0
$742$	6.86311e13	+	6.86311e13i	0.305142	+	0.305142i
$743$	−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
$746$	−2.15570e14			−0.933028
$747$		0			0
$748$	5.89002e13	−	5.89002e13i	0.251541	−	0.251541i
$749$		−	1.57800e14i		−	0.669420i
$750$		0			0
$751$	1.99588e14			0.835478			0.417739	−	0.908567i	$-0.362823\pi$
$751$	1.99588e14			0.835478			0.417739	+	0.908567i	$0.362823\pi$
$752$	7.24357e13	+	7.24357e13i	0.301206	+	0.301206i
$753$		0			0
$754$			1.56830e12i			0.00643536i
$755$	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	$0.699788\pi$
$758$	1.44497e14	−	1.44497e14i	0.577446	−	0.577446i
$759$		0			0
$760$	6.03799e13	+	1.33167e14i	0.238136	+	0.525203i
$761$	2.80397e13			0.109863			0.0549313	−	0.998490i	$-0.482506\pi$
$761$	2.80397e13			0.109863			0.0549313	+	0.998490i	$0.482506\pi$
$762$		0			0
$763$	1.30159e13	−	1.30159e13i	0.0503327	−	0.0503327i
$764$		−	1.51718e14i		−	0.582870i
$765$		0			0
$766$	1.48511e14			0.563138
$767$	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	$0.922900\pi$
$770$	1.84151e13	−	4.89676e13i	0.0680333	−	0.180907i
$771$		0			0
$772$	−1.61009e13	−	1.61009e13i	−0.0587168	−	0.0587168i
$773$	−1.09209e14	+	1.09209e14i	−0.395695	+	0.395695i	−0.876711	−	0.481017i	$-0.840268\pi$
$773$	−1.09209e14	+	1.09209e14i	−0.395695	+	0.395695i	0.481017	+	0.876711i	$0.340268\pi$
$774$		0			0
$775$	−2.13616e14	−	1.87134e14i	−0.764056	−	0.669338i
$776$	−8.62721e12			−0.0306593
$777$		0			0
$778$	−5.80611e13	+	5.80611e13i	−0.203698	+	0.203698i
$779$		−	6.62124e14i		−	2.30809i
$780$		0			0
$781$	2.12710e14			0.732037
$782$	−3.48558e13	−	3.48558e13i	−0.119190	−	0.119190i
$783$		0			0
$784$			4.87029e13i			0.164428i
$785$	8.92564e13	+	1.96853e14i	0.299427	+	0.660380i
$786$		0			0
$787$	2.88376e14	+	2.88376e14i	0.955181	+	0.955181i	0.999038	−	0.0438564i	$-0.0139644\pi$
$787$	2.88376e14	+	2.88376e14i	0.955181	+	0.955181i	−0.0438564	+	0.999038i	$0.513964\pi$
$788$	−1.93566e13	+	1.93566e13i	−0.0637087	+	0.0637087i
$789$		0			0
$790$	−2.14098e14	+	9.70754e13i	−0.695788	+	0.315481i
$791$	1.97359e13			0.0637346
$792$		0			0
$793$	−1.48704e14	+	1.48704e14i	−0.474193	+	0.474193i
$794$		−	1.12576e14i		−	0.356733i
$795$		0			0
$796$	1.44551e14			0.452330
$797$	2.45303e14	+	2.45303e14i	0.762801	+	0.762801i	0.976828	−	0.214027i	$-0.0686581\pi$
$797$	2.45303e14	+	2.45303e14i	0.762801	+	0.762801i	−0.214027	+	0.976828i	$0.568658\pi$
$798$		0			0
$799$		−	8.44947e14i		−	2.59475i
$800$	3.81944e12	+	5.78001e13i	0.0116560	+	0.176392i
$801$		0			0
$802$	6.37785e13	+	6.37785e13i	0.192222	+	0.192222i
$803$	2.07164e14	−	2.07164e14i	0.620491	−	0.620491i
$804$		0			0
$805$	−2.89778e13	−	1.08976e13i	−0.0857209	−	0.0322369i
$806$	1.02231e14			0.300544
$807$		0			0
$808$	−1.18813e13	+	1.18813e13i	−0.0344990	+	0.0344990i
$809$			2.91623e13i			0.0841548i	0.999114	+	0.0420774i	$0.0133976\pi$
$809$			2.91623e13i			0.0841548i	−0.999114	+	0.0420774i	$0.986602\pi$
$810$		0			0
$811$	2.84391e14			0.810609			0.405304	−	0.914182i	$-0.367166\pi$
$811$	2.84391e14			0.810609			0.405304	+	0.914182i	$0.367166\pi$
$812$	1.58816e12	+	1.58816e12i	0.00449898	+	0.00449898i
$813$		0			0
$814$		−	2.19549e12i		−	0.00614342i
$815$	1.87463e13	−	8.49987e12i	0.0521348	−	0.0236387i
$816$		0			0
$817$	−4.78272e14	−	4.78272e14i	−1.31391	−	1.31391i
$818$	3.15776e14	−	3.15776e14i	0.862210	−	0.862210i
$819$		0			0
$820$	9.23342e13	−	2.45525e14i	0.249054	−	0.662257i
$821$	2.09755e14			0.562338			0.281169	−	0.959658i	$-0.409278\pi$
$821$	2.09755e14			0.562338			0.281169	+	0.959658i	$0.409278\pi$
$822$		0			0
$823$	1.06255e14	−	1.06255e14i	0.281417	−	0.281417i	−0.552257	−	0.833674i	$-0.686233\pi$
$823$	1.06255e14	−	1.06255e14i	0.281417	−	0.281417i	0.833674	+	0.552257i	$0.186233\pi$
$824$			1.13808e14i			0.299597i
$825$		0			0
$826$	2.09344e14			0.544453
$827$	−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	$-0.129792\pi$
$830$	−1.26017e14	−	4.73911e13i	−0.319919	−	0.120311i
$831$		0			0
$832$	−1.47448e13	−	1.47448e13i	−0.0369846	−	0.0369846i
$833$	2.84055e14	−	2.84055e14i	0.708234	−	0.708234i
$834$		0			0
$835$	−1.07053e14	−	2.36102e14i	−0.263733	−	0.581658i
$836$	−1.55586e14			−0.381012
$837$		0			0
$838$	1.11820e14	−	1.11820e14i	0.270582	−	0.270582i
$839$		−	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
$842$	3.86699e14	+	3.86699e14i	0.913718	+	0.913718i
$843$		0			0
$844$		−	1.27088e14i		−	0.296751i
$845$	1.25094e14	−	3.32635e14i	0.290370	−	0.772119i
$846$		0			0
$847$	−1.40979e14	−	1.40979e14i	−0.323399	−	0.323399i
$848$	8.08610e13	−	8.08610e13i	0.184399	−	0.184399i
$849$		0			0
$850$	3.14837e14	−	3.59390e14i	0.709562	−	0.809974i
$851$	−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	$0.927082\pi$
$854$			3.01173e14i			0.663020i
$855$		0			0
$856$	−1.85920e14			−0.404536
$857$	2.19826e14	+	2.19826e14i	0.475527	+	0.475527i	0.903698	−	0.428171i	$-0.140842\pi$
$857$	2.19826e14	+	2.19826e14i	0.475527	+	0.475527i	−0.428171	+	0.903698i	$0.640842\pi$
$858$		0			0
$859$			3.31148e14i			0.708037i	0.935238	+	0.354019i	$0.115185\pi$
$859$			3.31148e14i			0.708037i	−0.935238	+	0.354019i	$0.884815\pi$
$860$	−1.10654e14	−	2.44046e14i	−0.235221	−	0.518775i
$861$		0			0
$862$	3.51611e14	+	3.51611e14i	0.738799	+	0.738799i
$863$	−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
$866$	−7.27986e12			−0.0149463
$867$		0			0
$868$	1.03525e14	−	1.03525e14i	0.210111	−	0.210111i
$869$		−	2.50142e14i		−	0.504763i
$870$		0			0
$871$	1.87541e14			0.374116
$872$	−1.53352e13	−	1.53352e13i	−0.0304164	−	0.0304164i
$873$		0			0
$874$			9.20720e13i			0.180539i
$875$	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	$0.345431\pi$
$878$	−8.87726e13	+	8.87726e13i	−0.170140	+	0.170140i
$879$		0			0
$880$	−5.76934e13	−	2.16967e13i	−0.109323	−	0.0411130i
$881$	−2.47093e13			−0.0465566			−0.0232783	−	0.999729i	$-0.507410\pi$
$881$	−2.47093e13			−0.0465566			−0.0232783	+	0.999729i	$0.507410\pi$
$882$		0			0
$883$	−1.88710e14	+	1.88710e14i	−0.351553	+	0.351553i	−0.860687	−	0.509134i	$-0.829966\pi$
$883$	−1.88710e14	+	1.88710e14i	−0.351553	+	0.351553i	0.509134	+	0.860687i	$0.329966\pi$
$884$			1.71994e14i			0.318605i
$885$		0			0
$886$	−3.28415e13			−0.0601527
$887$	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
$890$	−1.71784e14	+	7.78895e13i	−0.307632	+	0.139486i
$891$		0			0
$892$	2.19838e14	+	2.19838e14i	0.389295	+	0.389295i
$893$	−1.11597e15	+	1.11597e15i	−1.96515	+	1.96515i
$894$		0			0
$895$	−2.71079e14	+	7.20824e14i	−0.472042	+	1.25520i
$896$	−2.98629e13			−0.0517121
$897$		0			0
$898$	−9.13928e13	+	9.13928e13i	−0.156506	+	0.156506i
$899$			1.29735e13i			0.0220932i
$900$		0			0
$901$	−9.43226e14			−1.58852
$902$	1.97370e14	+	1.97370e14i	0.330558	+	0.330558i
$903$		0			0
$904$		−	2.32528e13i		−	0.0385153i
$905$	−3.52827e14	−	1.32687e14i	−0.581191	−	0.218567i
$906$		0			0
$907$	−6.88961e14	−	6.88961e14i	−1.12243	−	1.12243i	−0.991376	−	0.131052i	$-0.958165\pi$
$907$	−6.88961e14	−	6.88961e14i	−1.12243	−	1.12243i	−0.131052	−	0.991376i	$-0.541835\pi$
$908$	4.08727e14	−	4.08727e14i	0.662223	−	0.662223i
$909$		0			0
$910$	4.46080e13	+	9.83820e13i	0.0714835	+	0.157655i
$911$	−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
$914$			1.39409e14i			0.218554i
$915$		0			0
$916$	−3.03719e14			−0.470972
$917$	3.27461e14	+	3.27461e14i	0.505024	+	0.505024i
$918$		0			0
$919$		−	7.09097e14i		−	1.08175i	−0.841102	−	0.540876i	$-0.818093\pi$
$919$		−	7.09097e14i		−	1.08175i	0.841102	−	0.540876i	$-0.181907\pi$
$920$	−1.28396e13	+	3.41416e13i	−0.0194810	+	0.0518018i
$921$		0			0
$922$	6.14849e14	+	6.14849e14i	0.922813	+	0.922813i
$923$	−3.10567e14	+	3.10567e14i	−0.463604	+	0.463604i
$924$		0			0
$925$	−8.30351e11	−	1.25658e13i	−0.00122618	−	0.0185559i
$926$	7.39404e14			1.08599
$927$		0			0
$928$	1.87116e12	−	1.87116e12i	0.00271877	−	0.00271877i
$929$			6.96190e14i			1.00612i	0.864252	+	0.503059i	$0.167792\pi$
$929$			6.96190e14i			1.00612i	−0.864252	+	0.503059i	$0.832208\pi$
$930$		0			0
$931$	−7.50334e14			−1.07277
$932$	−1.10395e14	−	1.10395e14i	−0.156989	−	0.156989i
$933$		0			0
$934$			4.09562e13i			0.0576215i
$935$	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	$0.508408\pi$
$938$	1.89916e14	−	1.89916e14i	0.261546	−	0.261546i
$939$		0			0
$940$	−5.69441e14	+	2.58194e14i	−0.775906	+	0.351809i
$941$	−4.48743e14			−0.608205			−0.304102	−	0.952639i	$-0.598357\pi$
$941$	−4.48743e14			−0.608205			−0.304102	+	0.952639i	$0.598357\pi$
$942$		0			0
$943$	1.16799e14	−	1.16799e14i	0.156632	−	0.156632i
$944$		−	2.46648e14i		−	0.329017i
$945$		0			0
$946$	2.85132e14			0.376348
$947$	−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
$950$	−8.90489e14	+	5.88436e13i	−1.15083	+	0.0760468i
$951$		0			0
$952$	1.74172e14	+	1.74172e14i	0.222738	+	0.222738i
$953$	−4.88196e14	+	4.88196e14i	−0.621055	+	0.621055i	−0.945801	−	0.324746i	$-0.894721\pi$
$953$	−4.88196e14	+	4.88196e14i	−0.621055	+	0.621055i	0.324746	+	0.945801i	$0.394721\pi$
$954$		0			0
$955$	8.66751e14	+	3.25958e14i	1.09113	+	0.410341i
$956$	−5.72814e14			−0.717339
$957$		0			0
$958$	−1.81420e14	+	1.81420e14i	−0.224832	+	0.224832i
$959$		−	7.45782e14i		−	0.919430i
$960$		0			0
$961$	2.60599e13			0.0317947
$962$	3.20553e12	+	3.20553e12i	0.00389067	+	0.00389067i
$963$		0			0
$964$		−	6.03180e14i		−	0.724539i
$965$	1.26574e14	−	5.73908e13i	0.151255	−	0.0685812i
$966$		0			0
$967$	−4.94497e14	−	4.94497e14i	−0.584832	−	0.584832i	0.351395	−	0.936227i	$-0.385707\pi$
$967$	−4.94497e14	−	4.94497e14i	−0.584832	−	0.584832i	−0.936227	+	0.351395i	$0.885707\pi$
$968$	−1.66102e14	+	1.66102e14i	−0.195433	+	0.195433i
$969$		0			0
$970$	1.85350e13	−	4.92863e13i	0.0215841	−	0.0573941i
$971$	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
$974$			6.21845e14i			0.709394i
$975$		0			0
$976$	3.54841e14			0.400668
$977$	−5.88002e14	−	5.88002e14i	−0.660551	−	0.660551i	0.294959	−	0.955510i	$-0.404694\pi$
$977$	−5.88002e14	−	5.88002e14i	−0.660551	−	0.660551i	−0.955510	+	0.294959i	$0.904694\pi$
$978$		0			0
$979$		−	2.00704e14i		−	0.223174i
$980$	−2.78234e14	−	1.04635e14i	−0.307808	−	0.115757i
$981$		0			0
$982$	−8.21689e14	−	8.21689e14i	−0.899808	−	0.899808i
$983$	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
$986$	−2.18267e13			−0.0234209
$987$		0			0
$988$	2.27163e14	−	2.27163e14i	0.241297	−	0.241297i
$989$		−	1.68734e14i		−	0.178329i
$990$		0			0
$991$	5.56497e14			0.582230			0.291115	−	0.956688i	$-0.405974\pi$
$991$	5.56497e14			0.582230			0.291115	+	0.956688i	$0.405974\pi$
$992$	−1.21973e14	−	1.21973e14i	−0.126972	−	0.126972i
$993$		0			0
$994$			6.28999e14i			0.648214i
$995$	−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	$0.949445\pi$
$998$	−2.79336e14	+	2.79336e14i	−0.282146	+	0.282146i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.11.c.b.3.1	✓	2	15.8	even	4
10.11.c.b.7.1	yes	2	3.2	odd	2
50.11.c.b.7.1		2	15.14	odd	2
50.11.c.b.43.1		2	15.2	even	4
80.11.p.a.17.1		2	12.11	even	2
80.11.p.a.33.1		2	60.23	odd	4
90.11.g.a.37.1		2	1.1	even	1	trivial
90.11.g.a.73.1		2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.0000 - 16.0000i) q^{2} +512.000i q^{4} +(-2925.00 - 1100.00i) q^{5} +(6953.00 + 6953.00i) q^{7} +(8192.00 - 8192.00i) q^{8} +(29200.0 + 64400.0i) q^{10} -75242.0 q^{11} +(109857. - 109857. i) q^{13} -222496. i q^{14} -262144. q^{16} +(1.52893e6 + 1.52893e6i) q^{17} -4.03868e6i q^{19} +(563200. - 1.49760e6i) q^{20} +(1.20387e6 + 1.20387e6i) q^{22} +(712423. - 712423. i) q^{23} +(7.34562e6 + 6.43500e6i) q^{25} -3.51542e6 q^{26} +(-3.55994e6 + 3.55994e6i) q^{28} -446120. i q^{29} -2.90807e7 q^{31} +(4.19430e6 + 4.19430e6i) q^{32} -4.89257e7i q^{34} +(-1.26892e7 - 2.79858e7i) q^{35} +(-911847. - 911847. i) q^{37} +(-6.46189e7 + 6.46189e7i) q^{38} +(-3.29728e7 + 1.49504e7i) q^{40} +1.63946e8 q^{41} +(1.18423e8 - 1.18423e8i) q^{43} -3.85239e7i q^{44} -2.27975e7 q^{46} +(-2.76320e8 - 2.76320e8i) q^{47} -1.85787e8i q^{49} +(-1.45700e7 - 2.20490e8i) q^{50} +(5.62468e7 + 5.62468e7i) q^{52} +(-3.08460e8 + 3.08460e8i) q^{53} +(2.20083e8 + 8.27662e7i) q^{55} +1.13918e8 q^{56} +(-7.13792e6 + 7.13792e6i) q^{58} +9.40888e8i q^{59} -1.35361e9 q^{61} +(4.65291e8 + 4.65291e8i) q^{62} -1.34218e8i q^{64} +(-4.42174e8 + 2.00489e8i) q^{65} +(8.53571e8 + 8.53571e8i) q^{67} +(-7.82811e8 + 7.82811e8i) q^{68} +(-2.44746e8 + 6.50801e8i) q^{70} -2.82701e9 q^{71} +(-2.75330e9 + 2.75330e9i) q^{73} +2.91791e7i q^{74} +2.06780e9 q^{76} +(-5.23158e8 - 5.23158e8i) q^{77} +3.32450e9i q^{79} +(7.66771e8 + 2.88358e8i) q^{80} +(-2.62313e9 - 2.62313e9i) q^{82} +(-1.34634e9 + 1.34634e9i) q^{83} +(-2.79029e9 - 6.15393e9i) q^{85} -3.78953e9 q^{86} +(-6.16382e8 + 6.16382e8i) q^{88} +2.66745e9i q^{89} +1.52767e9 q^{91} +(3.64761e8 + 3.64761e8i) q^{92} +8.84225e9i q^{94} +(-4.44255e9 + 1.18131e10i) q^{95} +(-5.26563e8 - 5.26563e8i) q^{97} +(-2.97259e9 + 2.97259e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} - 5850 q^{5} + 13906 q^{7} + 16384 q^{8} + 58400 q^{10} - 150484 q^{11} + 219714 q^{13} - 524288 q^{16} + 3057854 q^{17} + 1126400 q^{20} + 2407744 q^{22} + 1424846 q^{23} + 14691250 q^{25}+ \cdots - 5945178592 q^{98}+O(q^{100}) \) 2 * q - 32 * q^2 - 5850 * q^5 + 13906 * q^7 + 16384 * q^8 + 58400 * q^10 - 150484 * q^11 + 219714 * q^13 - 524288 * q^16 + 3057854 * q^17 + 1126400 * q^20 + 2407744 * q^22 + 1424846 * q^23 + 14691250 * q^25 - 7030848 * q^26 - 7119872 * q^28 - 58161436 * q^31 + 8388608 * q^32 - 25378450 * q^35 - 1823694 * q^37 - 129237760 * q^38 - 65945600 * q^40 + 327891356 * q^41 + 236845554 * q^43 - 45595072 * q^46 - 552640626 * q^47 - 29140000 * q^50 + 112493568 * q^52 - 616920194 * q^53 + 440165700 * q^55 + 227835904 * q^56 - 14275840 * q^58 - 2707220076 * q^61 + 930582976 * q^62 - 884348850 * q^65 + 1707141826 * q^67 - 1565621248 * q^68 - 489491200 * q^70 - 5654029124 * q^71 - 5506594366 * q^73 + 4135608320 * q^76 - 1046315252 * q^77 + 1533542400 * q^80 - 5246261696 * q^82 - 2692678194 * q^83 - 5580583550 * q^85 - 7579057728 * q^86 - 1232764928 * q^88 + 3055342884 * q^91 + 729521152 * q^92 - 8885096000 * q^95 - 1053125694 * q^97 - 5945178592 * q^98

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