LMFDB - Embedded newform 50.11.c.b.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,11,Mod(7,50)] 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("50.7"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	50.c (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-32,-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:	$31.7678626337$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.43
Dual form			50.11.c.b.7.1

$q$-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} +(-57.0000 - 57.0000i) q^{3} -512.000i q^{4} +1824.00 q^{6} +(-6953.00 + 6953.00i) q^{7} +(8192.00 + 8192.00i) q^{8} -52551.0i q^{9} +75242.0 q^{11} +(-29184.0 + 29184.0i) q^{12} +(-109857. - 109857. i) q^{13} -222496. i q^{14} -262144. q^{16} +(1.52893e6 - 1.52893e6i) q^{17} +(840816. + 840816. i) q^{18} +4.03868e6i q^{19} +792642. q^{21} +(-1.20387e6 + 1.20387e6i) q^{22} +(712423. + 712423. i) q^{23} -933888. i q^{24} +3.51542e6 q^{26} +(-6.36120e6 + 6.36120e6i) q^{27} +(3.55994e6 + 3.55994e6i) q^{28} -446120. i q^{29} -2.90807e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} +(-4.28879e6 - 4.28879e6i) q^{33} +4.89257e7i q^{34} -2.69061e7 q^{36} +(911847. - 911847. i) q^{37} +(-6.46189e7 - 6.46189e7i) q^{38} +1.25237e7i q^{39} -1.63946e8 q^{41} +(-1.26823e7 + 1.26823e7i) q^{42} +(-1.18423e8 - 1.18423e8i) q^{43} -3.85239e7i q^{44} -2.27975e7 q^{46} +(-2.76320e8 + 2.76320e8i) q^{47} +(1.49422e7 + 1.49422e7i) q^{48} +1.85787e8i q^{49} -1.74298e8 q^{51} +(-5.62468e7 + 5.62468e7i) q^{52} +(-3.08460e8 - 3.08460e8i) q^{53} -2.03558e8i q^{54} -1.13918e8 q^{56} +(2.30205e8 - 2.30205e8i) q^{57} +(7.13792e6 + 7.13792e6i) q^{58} +9.40888e8i q^{59} -1.35361e9 q^{61} +(4.65291e8 - 4.65291e8i) q^{62} +(3.65387e8 + 3.65387e8i) q^{63} +1.34218e8i q^{64} +1.37241e8 q^{66} +(-8.53571e8 + 8.53571e8i) q^{67} +(-7.82811e8 - 7.82811e8i) q^{68} -8.12162e7i q^{69} +2.82701e9 q^{71} +(4.30498e8 - 4.30498e8i) q^{72} +(2.75330e9 + 2.75330e9i) q^{73} +2.91791e7i q^{74} +2.06780e9 q^{76} +(-5.23158e8 + 5.23158e8i) q^{77} +(-2.00379e8 - 2.00379e8i) q^{78} -3.32450e9i q^{79} -2.37791e9 q^{81} +(2.62313e9 - 2.62313e9i) q^{82} +(-1.34634e9 - 1.34634e9i) q^{83} -4.05833e8i q^{84} +3.78953e9 q^{86} +(-2.54288e7 + 2.54288e7i) q^{87} +(6.16382e8 + 6.16382e8i) q^{88} +2.66745e9i q^{89} +1.52767e9 q^{91} +(3.64761e8 - 3.64761e8i) q^{92} +(1.65760e9 + 1.65760e9i) q^{93} -8.84225e9i q^{94} -4.78151e8 q^{96} +(5.26563e8 - 5.26563e8i) q^{97} +(-2.97259e9 - 2.97259e9i) q^{98} -3.95404e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} - 114 q^{3} + 3648 q^{6} - 13906 q^{7} + 16384 q^{8} + 150484 q^{11} - 58368 q^{12} - 219714 q^{13} - 524288 q^{16} + 3057854 q^{17} + 1681632 q^{18} + 1585284 q^{21} - 2407744 q^{22} + 1424846 q^{23}+ \cdots - 5945178592 q^{98}+O(q^{100}) $ 2 * q - 32 * q^2 - 114 * q^3 + 3648 * q^6 - 13906 * q^7 + 16384 * q^8 + 150484 * q^11 - 58368 * q^12 - 219714 * q^13 - 524288 * q^16 + 3057854 * q^17 + 1681632 * q^18 + 1585284 * q^21 - 2407744 * q^22 + 1424846 * q^23 + 7030848 * q^26 - 12722400 * q^27 + 7119872 * q^28 - 58161436 * q^31 + 8388608 * q^32 - 8577588 * q^33 - 53812224 * q^36 + 1823694 * q^37 - 129237760 * q^38 - 327891356 * q^41 - 25364544 * q^42 - 236845554 * q^43 - 45595072 * q^46 - 552640626 * q^47 + 29884416 * q^48 - 348595356 * q^51 - 112493568 * q^52 - 616920194 * q^53 - 227835904 * q^56 + 460409520 * q^57 + 14275840 * q^58 - 2707220076 * q^61 + 930582976 * q^62 + 730774206 * q^63 + 274482816 * q^66 - 1707141826 * q^67 - 1565621248 * q^68 + 5654029124 * q^71 + 860995584 * q^72 + 5506594366 * q^73 + 4135608320 * q^76 - 1046315252 * q^77 - 400758336 * q^78 - 4755814398 * q^81 + 5246261696 * q^82 - 2692678194 * q^83 + 7579057728 * q^86 - 50857680 * q^87 + 1232764928 * q^88 + 3055342884 * q^91 + 729521152 * q^92 + 3315201852 * q^93 - 956301312 * q^96 + 1053125694 * q^97 - 5945178592 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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
$3$	−57.0000	−	57.0000i	−0.234568	−	0.234568i	0.580028	−	0.814596i	$-0.303041\pi$
$3$	−57.0000	−	57.0000i	−0.234568	−	0.234568i	−0.814596	+	0.580028i	$0.803041\pi$
$4$		−	512.000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1824.00			0.234568
$7$	−6953.00	+	6953.00i	−0.413697	+	0.413697i	−0.883024	−	0.469328i	$-0.844496\pi$
$7$	−6953.00	+	6953.00i	−0.413697	+	0.413697i	0.469328	+	0.883024i	$0.344496\pi$
$8$	8192.00	+	8192.00i	0.250000	+	0.250000i
$9$		−	52551.0i		−	0.889956i
$10$		0			0
$11$	75242.0			0.467194			0.233597	−	0.972334i	$-0.424950\pi$
$11$	75242.0			0.467194			0.233597	+	0.972334i	$0.424950\pi$
$12$	−29184.0	+	29184.0i	−0.117284	+	0.117284i
$13$	−109857.	−	109857.i	−0.295877	−	0.295877i	0.543520	−	0.839396i	$-0.317091\pi$
$13$	−109857.	−	109857.i	−0.295877	−	0.295877i	−0.839396	+	0.543520i	$0.817091\pi$
$14$		−	222496.i		−	0.413697i
$15$		0			0
$16$	−262144.			−0.250000
$17$	1.52893e6	−	1.52893e6i	1.07682	−	1.07682i	0.0800247	−	0.996793i	$-0.474500\pi$
$17$	1.52893e6	−	1.52893e6i	1.07682	−	1.07682i	0.996793	−	0.0800247i	$-0.0254999\pi$
$18$	840816.	+	840816.i	0.444978	+	0.444978i
$19$			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
$22$	−1.20387e6	+	1.20387e6i	−0.233597	+	0.233597i
$23$	712423.	+	712423.i	0.110688	+	0.110688i	0.760281	−	0.649594i	$-0.225061\pi$
$23$	712423.	+	712423.i	0.110688	+	0.110688i	−0.649594	+	0.760281i	$0.725061\pi$
$24$		−	933888.i		−	0.117284i
$25$		0			0
$26$	3.51542e6			0.295877
$27$	−6.36120e6	+	6.36120e6i	−0.443323	+	0.443323i
$28$	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
$33$	−4.28879e6	−	4.28879e6i	−0.109589	−	0.109589i
$34$			4.89257e7i			1.07682i
$35$		0			0
$36$	−2.69061e7			−0.444978
$37$	911847.	−	911847.i	0.0131496	−	0.0131496i	−0.700501	−	0.713651i	$-0.747040\pi$
$37$	911847.	−	911847.i	0.0131496	−	0.0131496i	0.713651	+	0.700501i	$0.247040\pi$
$38$	−6.46189e7	−	6.46189e7i	−0.815533	−	0.815533i
$39$			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	$0.750195\pi$
$42$	−1.26823e7	+	1.26823e7i	−0.0970400	+	0.0970400i
$43$	−1.18423e8	−	1.18423e8i	−0.805551	−	0.805551i	0.178406	−	0.983957i	$-0.442906\pi$
$43$	−1.18423e8	−	1.18423e8i	−0.805551	−	0.805551i	−0.983957	+	0.178406i	$0.942906\pi$
$44$		−	3.85239e7i		−	0.233597i
$45$		0			0
$46$	−2.27975e7			−0.110688
$47$	−2.76320e8	+	2.76320e8i	−1.20482	+	1.20482i	−0.232142	+	0.972682i	$0.574573\pi$
$47$	−2.76320e8	+	2.76320e8i	−1.20482	+	1.20482i	−0.972682	+	0.232142i	$0.925427\pi$
$48$	1.49422e7	+	1.49422e7i	0.0586420	+	0.0586420i
$49$			1.85787e8i			0.657710i
$50$		0			0
$51$	−1.74298e8			−0.505174
$52$	−5.62468e7	+	5.62468e7i	−0.147938	+	0.147938i
$53$	−3.08460e8	−	3.08460e8i	−0.737598	−	0.737598i	0.234515	−	0.972113i	$-0.424650\pi$
$53$	−3.08460e8	−	3.08460e8i	−0.737598	−	0.737598i	−0.972113	+	0.234515i	$0.924650\pi$
$54$		−	2.03558e8i		−	0.443323i
$55$		0			0
$56$	−1.13918e8			−0.206848
$57$	2.30205e8	−	2.30205e8i	0.382596	−	0.382596i
$58$	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
$63$	3.65387e8	+	3.65387e8i	0.368172	+	0.368172i
$64$			1.34218e8i			0.125000i
$65$		0			0
$66$	1.37241e8			0.109589
$67$	−8.53571e8	+	8.53571e8i	−0.632216	+	0.632216i	−0.948623	−	0.316407i	$-0.897523\pi$
$67$	−8.53571e8	+	8.53571e8i	−0.632216	+	0.632216i	0.316407	+	0.948623i	$0.397523\pi$
$68$	−7.82811e8	−	7.82811e8i	−0.538409	−	0.538409i
$69$		−	8.12162e7i		−	0.0519275i
$70$		0			0
$71$	2.82701e9			1.56688			0.783441	−	0.621466i	$-0.213463\pi$
$71$	2.82701e9			1.56688			0.783441	+	0.621466i	$0.213463\pi$
$72$	4.30498e8	−	4.30498e8i	0.222489	−	0.222489i
$73$	2.75330e9	+	2.75330e9i	1.32812	+	1.32812i	0.907005	+	0.421119i	$0.138363\pi$
$73$	2.75330e9	+	2.75330e9i	1.32812	+	1.32812i	0.421119	+	0.907005i	$0.361637\pi$
$74$			2.91791e7i			0.0131496i
$75$		0			0
$76$	2.06780e9			0.815533
$77$	−5.23158e8	+	5.23158e8i	−0.193276	+	0.193276i
$78$	−2.00379e8	−	2.00379e8i	−0.0694032	−	0.0694032i
$79$		−	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
$82$	2.62313e9	−	2.62313e9i	0.707540	−	0.707540i
$83$	−1.34634e9	−	1.34634e9i	−0.341794	−	0.341794i	0.515248	−	0.857041i	$-0.327700\pi$
$83$	−1.34634e9	−	1.34634e9i	−0.341794	−	0.341794i	−0.857041	+	0.515248i	$0.827700\pi$
$84$		−	4.05833e8i		−	0.0970400i
$85$		0			0
$86$	3.78953e9			0.805551
$87$	−2.54288e7	+	2.54288e7i	−0.00510188	+	0.00510188i
$88$	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
$93$	1.65760e9	+	1.65760e9i	0.238268	+	0.238268i
$94$		−	8.84225e9i		−	1.20482i
$95$		0			0
$96$	−4.78151e8			−0.0586420
$97$	5.26563e8	−	5.26563e8i	0.0613185	−	0.0613185i	−0.675783	−	0.737101i	$-0.736194\pi$
$97$	5.26563e8	−	5.26563e8i	0.0613185	−	0.0613185i	0.737101	+	0.675783i	$0.236194\pi$
$98$	−2.97259e9	−	2.97259e9i	−0.328855	−	0.328855i
$99$		−	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	$0.478020\pi$
$102$	2.78876e9	−	2.78876e9i	0.252587	−	0.252587i
$103$	6.94630e9	+	6.94630e9i	0.599194	+	0.599194i	0.940098	−	0.340904i	$-0.110733\pi$
$103$	6.94630e9	+	6.94630e9i	0.599194	+	0.599194i	−0.340904	+	0.940098i	$0.610733\pi$
$104$		−	1.79990e9i		−	0.147938i
$105$		0			0
$106$	9.87072e9			0.737598
$107$	−1.13476e10	+	1.13476e10i	−0.809071	+	0.809071i	−0.984493	−	0.175422i	$-0.943871\pi$
$107$	−1.13476e10	+	1.13476e10i	−0.809071	+	0.809071i	0.175422	+	0.984493i	$0.443871\pi$
$108$	3.25693e9	+	3.25693e9i	0.221661	+	0.221661i
$109$			1.87198e9i			0.121666i	0.998148	+	0.0608328i	$0.0193757\pi$
$109$			1.87198e9i			0.121666i	−0.998148	+	0.0608328i	$0.980624\pi$
$110$		0			0
$111$	−1.03951e8			−0.00616896
$112$	1.82269e9	−	1.82269e9i	0.103424	−	0.103424i
$113$	1.41924e9	+	1.41924e9i	0.0770306	+	0.0770306i	0.744572	−	0.667542i	$-0.232653\pi$
$113$	1.41924e9	+	1.41924e9i	0.0770306	+	0.0770306i	−0.667542	+	0.744572i	$0.732653\pi$
$114$			7.36655e9i			0.382596i
$115$		0			0
$116$	−2.28413e8			−0.0108751
$117$	−5.77310e9	+	5.77310e9i	−0.263317	+	0.263317i
$118$	−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
$123$	9.34490e9	+	9.34490e9i	0.331932	+	0.331932i
$124$			1.48893e10i			0.507886i
$125$		0			0
$126$	−1.16924e10			−0.368172
$127$	2.09209e10	−	2.09209e10i	0.633231	−	0.633231i	−0.315646	−	0.948877i	$-0.602221\pi$
$127$	2.09209e10	−	2.09209e10i	0.633231	−	0.633231i	0.948877	+	0.315646i	$0.102221\pi$
$128$	−2.14748e9	−	2.14748e9i	−0.0625000	−	0.0625000i
$129$			1.35002e10i			0.377913i
$130$		0			0
$131$	−4.70963e10			−1.22076			−0.610380	−	0.792109i	$-0.708983\pi$
$131$	−4.70963e10			−1.22076			−0.610380	+	0.792109i	$0.708983\pi$
$132$	−2.19586e9	+	2.19586e9i	−0.0547943	+	0.0547943i
$133$	−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	−0.118254	+	0.992983i	$0.537730\pi$
$137$	−5.36302e10	+	5.36302e10i	−1.11124	+	1.11124i	−0.992983	+	0.118254i	$0.962270\pi$
$138$	1.29946e9	+	1.29946e9i	0.0259637	+	0.0259637i
$139$			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
$142$	−4.52322e10	+	4.52322e10i	−0.783441	+	0.783441i
$143$	−8.26586e9	−	8.26586e9i	−0.138232	−	0.138232i
$144$			1.37759e10i			0.222489i
$145$		0			0
$146$	−8.81055e10			−1.32812
$147$	1.05898e10	−	1.05898e10i	0.154278	−	0.154278i
$148$	−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
$153$	−8.03466e10	−	8.03466e10i	−0.958320	−	0.958320i
$154$		−	1.67410e10i		−	0.193276i
$155$		0			0
$156$	6.41213e9			0.0694032
$157$	4.89076e10	−	4.89076e10i	0.512718	−	0.512718i	−0.402641	−	0.915358i	$-0.631908\pi$
$157$	4.89076e10	−	4.89076e10i	0.512718	−	0.512718i	0.915358	+	0.402641i	$0.131908\pi$
$158$	5.31920e10	+	5.31920e10i	0.540208	+	0.540208i
$159$			3.51645e10i			0.346034i
$160$		0			0
$161$	−9.90695e9			−0.0915821
$162$	3.80465e10	−	3.80465e10i	0.340989	−	0.340989i
$163$	4.65746e9	+	4.65746e9i	0.0404773	+	0.0404773i	0.727056	−	0.686578i	$-0.240888\pi$
$163$	4.65746e9	+	4.65746e9i	0.0404773	+	0.0404773i	−0.686578	+	0.727056i	$0.740888\pi$
$164$			8.39402e10i			0.707540i
$165$		0			0
$166$	4.30829e10			0.341794
$167$	5.86590e10	−	5.86590e10i	0.451598	−	0.451598i	−0.444287	−	0.895885i	$-0.646543\pi$
$167$	5.86590e10	−	5.86590e10i	0.451598	−	0.451598i	0.895885	+	0.444287i	$0.146543\pi$
$168$	6.49332e9	+	6.49332e9i	0.0485200	+	0.0485200i
$169$		−	1.13721e11i		−	0.824914i
$170$		0			0
$171$	2.12237e11			1.45158
$172$	−6.06325e10	+	6.06325e10i	−0.402775	+	0.402775i
$173$	1.06769e11	+	1.06769e11i	0.688994	+	0.688994i	0.962010	−	0.273016i	$-0.0880211\pi$
$173$	1.06769e11	+	1.06769e11i	0.688994	+	0.688994i	−0.273016	+	0.962010i	$0.588021\pi$
$174$		−	8.13723e8i		−	0.00510188i
$175$		0			0
$176$	−1.97242e10			−0.116798
$177$	5.36306e10	−	5.36306e10i	0.308707	−	0.308707i
$178$	−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
$183$	7.71558e10	+	7.71558e10i	0.375935	+	0.375935i
$184$			1.16723e10i			0.0553438i
$185$		0			0
$186$	−5.30432e10			−0.238268
$187$	1.15040e11	−	1.15040e11i	0.503082	−	0.503082i
$188$	1.41476e11	+	1.41476e11i	0.602412	+	0.602412i
$189$		−	8.84588e10i		−	0.366802i
$190$		0			0
$191$	2.96325e11			1.16574			0.582870	−	0.812565i	$-0.301930\pi$
$191$	2.96325e11			1.16574			0.582870	+	0.812565i	$0.301930\pi$
$192$	7.65041e9	−	7.65041e9i	0.0293210	−	0.0293210i
$193$	3.14470e10	+	3.14470e10i	0.117434	+	0.117434i	0.763382	−	0.645948i	$-0.223538\pi$
$193$	3.14470e10	+	3.14470e10i	0.117434	+	0.117434i	−0.645948	+	0.763382i	$0.723538\pi$
$194$			1.68500e10i			0.0613185i
$195$		0			0
$196$	9.51229e10			0.328855
$197$	3.78059e10	−	3.78059e10i	0.127417	−	0.127417i	−0.640522	−	0.767940i	$-0.721282\pi$
$197$	3.78059e10	−	3.78059e10i	0.127417	−	0.127417i	0.767940	+	0.640522i	$0.221282\pi$
$198$	6.32647e10	+	6.32647e10i	0.207891	+	0.207891i
$199$			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
$202$	−2.32056e10	+	2.32056e10i	−0.0689980	+	0.0689980i
$203$	3.10187e9	+	3.10187e9i	0.00899795	+	0.00899795i
$204$			8.92404e10i			0.252587i
$205$		0			0
$206$	−2.22281e11			−0.599194
$207$	3.74385e10	−	3.74385e10i	0.0985070	−	0.0985070i
$208$	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
$213$	−1.61140e11	−	1.61140e11i	−0.367540	−	0.367540i
$214$		−	3.63124e11i		−	0.809071i
$215$		0			0
$216$	−1.04222e11			−0.221661
$217$	2.02198e11	−	2.02198e11i	0.420222	−	0.420222i
$218$	−2.99516e10	−	2.99516e10i	−0.0608328	−	0.0608328i
$219$		−	3.13876e11i		−	0.623071i
$220$		0			0
$221$	−3.35927e11			−0.637211
$222$	1.66321e9	−	1.66321e9i	0.00308448	−	0.00308448i
$223$	−4.29372e11	−	4.29372e11i	−0.778591	−	0.778591i	0.201000	−	0.979591i	$-0.435581\pi$
$223$	−4.29372e11	−	4.29372e11i	−0.778591	−	0.778591i	−0.979591	+	0.201000i	$0.935581\pi$
$224$			5.83260e10i			0.103424i
$225$		0			0
$226$	−4.54156e10			−0.0770306
$227$	−7.98295e11	+	7.98295e11i	−1.32445	+	1.32445i	−0.414309	+	0.910136i	$0.635977\pi$
$227$	−7.98295e11	+	7.98295e11i	−1.32445	+	1.32445i	−0.910136	+	0.414309i	$0.864023\pi$
$228$	−1.17865e11	−	1.17865e11i	−0.191298	−	0.191298i
$229$		−	5.93202e11i		−	0.941944i	−0.882148	−	0.470972i	$-0.843903\pi$
$229$		−	5.93202e11i		−	0.941944i	0.882148	−	0.470972i	$-0.156097\pi$
$230$		0			0
$231$	5.96400e10			0.0906729
$232$	3.65462e9	−	3.65462e9i	0.00543753	−	0.00543753i
$233$	−2.15614e11	−	2.15614e11i	−0.313977	−	0.313977i	0.532471	−	0.846448i	$-0.321264\pi$
$233$	−2.15614e11	−	2.15614e11i	−0.313977	−	0.313977i	−0.846448	+	0.532471i	$0.821264\pi$
$234$		−	1.84739e11i		−	0.263317i
$235$		0			0
$236$	4.81735e11			0.658034
$237$	−1.89497e11	+	1.89497e11i	−0.253431	+	0.253431i
$238$	−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
$243$	5.11163e11	+	5.11163e11i	0.603293	+	0.603293i
$244$			6.93048e11i			0.801336i
$245$		0			0
$246$	−2.99037e11			−0.331932
$247$	4.43677e11	−	4.43677e11i	0.482595	−	0.482595i
$248$	−2.38229e11	−	2.38229e11i	−0.253943	−	0.253943i
$249$			1.53483e11i			0.160348i
$250$		0			0
$251$	−7.26605e11			−0.729339			−0.364670	−	0.931137i	$-0.618818\pi$
$251$	−7.26605e11			−0.729339			−0.364670	+	0.931137i	$0.618818\pi$
$252$	1.87078e11	−	1.87078e11i	0.184086	−	0.184086i
$253$	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	−0.968006	−	0.250926i	$-0.919265\pi$
$257$	−8.03958e11	+	8.03958e11i	−0.717081	+	0.717081i	0.250926	+	0.968006i	$0.419265\pi$
$258$	−2.16003e11	−	2.16003e11i	−0.188956	−	0.188956i
$259$			1.26801e10i			0.0108799i
$260$		0			0
$261$	−2.34441e10			−0.0193566
$262$	7.53541e11	−	7.53541e11i	0.610380	−	0.610380i
$263$	2.78593e11	+	2.78593e11i	0.221407	+	0.221407i	0.809091	−	0.587684i	$-0.199960\pi$
$263$	2.78593e11	+	2.78593e11i	0.221407	+	0.221407i	−0.587684	+	0.809091i	$0.699960\pi$
$264$		−	7.02676e10i		−	0.0547943i
$265$		0			0
$266$	8.98590e11			0.674766
$267$	1.52045e11	−	1.52045e11i	0.112051	−	0.112051i
$268$	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
$273$	−8.70773e10	−	8.70773e10i	−0.0574238	−	0.0574238i
$274$		−	1.71617e12i		−	1.11124i
$275$		0			0
$276$	−4.15827e10			−0.0259637
$277$	−9.59186e11	+	9.59186e11i	−0.588171	+	0.588171i	−0.937136	−	0.348964i	$-0.886533\pi$
$277$	−9.59186e11	+	9.59186e11i	−0.588171	+	0.588171i	0.348964	+	0.937136i	$0.386533\pi$
$278$	−4.16257e10	−	4.16257e10i	−0.0250691	−	0.0250691i
$279$			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	$0.438675\pi$
$282$	−5.04008e11	+	5.04008e11i	−0.282613	+	0.282613i
$283$	1.73203e12	+	1.73203e12i	0.954162	+	0.954162i	0.998995	−	0.0448324i	$-0.0142754\pi$
$283$	1.73203e12	+	1.73203e12i	0.954162	+	0.954162i	−0.0448324	+	0.998995i	$0.514275\pi$
$284$		−	1.44743e12i		−	0.783441i
$285$		0			0
$286$	2.64508e11			0.138232
$287$	1.13991e12	−	1.13991e12i	0.585413	−	0.585413i
$288$	−2.20415e11	−	2.20415e11i	−0.111244	−	0.111244i
$289$		−	2.65924e12i		−	1.31907i
$290$		0			0
$291$	−6.00282e10			−0.0287667
$292$	1.40969e12	−	1.40969e12i	0.664062	−	0.664062i
$293$	−6.78142e11	−	6.78142e11i	−0.314038	−	0.314038i	0.532434	−	0.846472i	$-0.321278\pi$
$293$	−6.78142e11	−	6.78142e11i	−0.314038	−	0.314038i	−0.846472	+	0.532434i	$0.821278\pi$
$294$			3.38875e11i			0.154278i
$295$		0			0
$296$	1.49397e10			0.00657481
$297$	−4.78629e11	+	4.78629e11i	−0.207118	+	0.207118i
$298$	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
$303$	−8.26701e10	−	8.26701e10i	−0.0323694	−	0.0323694i
$304$		−	1.05872e12i		−	0.407766i
$305$		0			0
$306$	2.57109e12			0.958320
$307$	9.32237e11	−	9.32237e11i	0.341849	−	0.341849i	−0.515213	−	0.857062i	$-0.672287\pi$
$307$	9.32237e11	−	9.32237e11i	0.341849	−	0.341849i	0.857062	+	0.515213i	$0.172287\pi$
$308$	2.67857e11	+	2.67857e11i	0.0966382	+	0.0966382i
$309$		−	7.91878e11i		−	0.281103i
$310$		0			0
$311$	−6.54904e11			−0.225100			−0.112550	−	0.993646i	$-0.535902\pi$
$311$	−6.54904e11			−0.225100			−0.112550	+	0.993646i	$0.535902\pi$
$312$	−1.02594e11	+	1.02594e11i	−0.0347016	+	0.0347016i
$313$	−2.53654e12	−	2.53654e12i	−0.844344	−	0.844344i	0.145076	−	0.989420i	$-0.453657\pi$
$313$	−2.53654e12	−	2.53654e12i	−0.844344	−	0.844344i	−0.989420	+	0.145076i	$0.953657\pi$
$314$			1.56504e12i			0.512718i
$315$		0			0
$316$	−1.70214e12			−0.540208
$317$	−9.91586e11	+	9.91586e11i	−0.309766	+	0.309766i	−0.844819	−	0.535053i	$-0.820292\pi$
$317$	−9.91586e11	+	9.91586e11i	−0.309766	+	0.309766i	0.535053	+	0.844819i	$0.320292\pi$
$318$	−5.62631e11	−	5.62631e11i	−0.173017	−	0.173017i
$319$		−	3.35670e10i		−	0.0101615i
$320$		0			0
$321$	1.29363e12			0.379564
$322$	1.58511e11	−	1.58511e11i	0.0457911	−	0.0457911i
$323$	6.17485e12	+	6.17485e12i	1.75636	+	1.75636i
$324$			1.21749e12i			0.340989i
$325$		0			0
$326$	−1.49039e11			−0.0404773
$327$	1.06703e11	−	1.06703e11i	0.0285389	−	0.0285389i
$328$	−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
$333$	−4.79185e10	−	4.79185e10i	−0.0117026	−	0.0117026i
$334$			1.87709e12i			0.451598i
$335$		0			0
$336$	−2.07786e11			−0.0485200
$337$	−2.43243e11	+	2.43243e11i	−0.0559618	+	0.0559618i	−0.734534	−	0.678572i	$-0.762599\pi$
$337$	−2.43243e11	+	2.43243e11i	−0.0559618	+	0.0559618i	0.678572	+	0.734534i	$0.262599\pi$
$338$	1.81954e12	+	1.81954e12i	0.412457	+	0.412457i
$339$		−	1.61793e11i		−	0.0361378i
$340$		0			0
$341$	−2.18809e12			−0.474563
$342$	−3.39579e12	+	3.39579e12i	−0.725788	+	0.725788i
$343$	−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	−0.501377	−	0.865229i	$-0.667173\pi$
$347$	1.83051e12	−	1.83051e12i	0.363851	−	0.363851i	0.865229	+	0.501377i	$0.167173\pi$
$348$	1.30196e10	+	1.30196e10i	0.00255094	+	0.00255094i
$349$		−	6.68385e11i		−	0.129092i	−0.997915	−	0.0645460i	$-0.979440\pi$
$349$		−	6.68385e11i		−	0.129092i	0.997915	−	0.0645460i	$-0.0205599\pi$
$350$		0			0
$351$	1.39764e12			0.262338
$352$	3.15588e11	−	3.15588e11i	0.0583992	−	0.0583992i
$353$	−3.38512e12	−	3.38512e12i	−0.617590	−	0.617590i	0.327323	−	0.944913i	$-0.393854\pi$
$353$	−3.38512e12	−	3.38512e12i	−0.617590	−	0.617590i	−0.944913	+	0.327323i	$0.893854\pi$
$354$			1.71618e12i			0.308707i
$355$		0			0
$356$	1.36573e12			0.238845
$357$	1.21189e12	−	1.21189e12i	0.208989	−	0.208989i
$358$	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
$363$	1.15574e12	+	1.15574e12i	0.183369	+	0.183369i
$364$		−	7.82168e11i		−	0.122403i
$365$		0			0
$366$	−2.46898e12			−0.375935
$367$	6.36244e12	−	6.36244e12i	0.955638	−	0.955638i	−0.0434192	−	0.999057i	$-0.513825\pi$
$367$	6.36244e12	−	6.36244e12i	0.955638	−	0.955638i	0.999057	+	0.0434192i	$0.0138251\pi$
$368$	−1.86757e11	−	1.86757e11i	−0.0276719	−	0.0276719i
$369$			8.61551e12i			1.25936i
$370$		0			0
$371$	4.28945e12			0.610284
$372$	8.48692e11	−	8.48692e11i	0.119134	−	0.119134i
$373$	−6.73657e12	−	6.73657e12i	−0.933028	−	0.933028i	0.0648661	−	0.997894i	$-0.479338\pi$
$373$	−6.73657e12	−	6.73657e12i	−0.933028	−	0.933028i	−0.997894	+	0.0648661i	$0.979338\pi$
$374$			3.68126e12i			0.503082i
$375$		0			0
$376$	−4.52723e12			−0.602412
$377$	−4.90094e10	+	4.90094e10i	−0.00643536	+	0.00643536i
$378$	1.41534e12	+	1.41534e12i	0.183401	+	0.183401i
$379$		−	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
$382$	−4.74120e12	+	4.74120e12i	−0.582870	+	0.582870i
$383$	−4.64097e12	−	4.64097e12i	−0.563138	−	0.563138i	0.367060	−	0.930197i	$-0.380364\pi$
$383$	−4.64097e12	−	4.64097e12i	−0.563138	−	0.563138i	−0.930197	+	0.367060i	$0.880364\pi$
$384$			2.44813e11i			0.0293210i
$385$		0			0
$386$	−1.00630e12			−0.117434
$387$	−6.22324e12	+	6.22324e12i	−0.716905	+	0.716905i
$388$	−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
$393$	2.68449e12	+	2.68449e12i	0.286351	+	0.286351i
$394$			1.20979e12i			0.127417i
$395$		0			0
$396$	−2.02447e12			−0.207891
$397$	−3.51800e12	+	3.51800e12i	−0.356733	+	0.356733i	−0.862607	−	0.505874i	$-0.831170\pi$
$397$	−3.51800e12	+	3.51800e12i	−0.356733	+	0.356733i	0.505874	+	0.862607i	$0.331170\pi$
$398$	−4.51722e12	−	4.51722e12i	−0.452330	−	0.452330i
$399$			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	$0.438431\pi$
$402$	−1.55691e12	+	1.55691e12i	−0.148298	+	0.148298i
$403$	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
$408$	−1.42785e12	−	1.42785e12i	−0.126293	−	0.126293i
$409$		−	1.97360e13i		−	1.72442i	−0.506551	−	0.862210i	$-0.669080\pi$
$409$		−	1.97360e13i		−	1.72442i	0.506551	−	0.862210i	$-0.330920\pi$
$410$		0			0
$411$	6.11385e12			0.521321
$412$	3.55650e12	−	3.55650e12i	0.299597	−	0.299597i
$413$	−6.54200e12	−	6.54200e12i	−0.544453	−	0.544453i
$414$			1.19803e12i			0.0985070i
$415$		0			0
$416$	−9.21547e11			−0.0739692
$417$	1.48292e11	−	1.48292e11i	0.0117608	−	0.0117608i
$418$	−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
$423$	1.45209e13	+	1.45209e13i	1.07224	+	1.07224i
$424$		−	5.05381e12i		−	0.368799i
$425$		0			0
$426$	5.15647e12			0.367540
$427$	9.41165e12	−	9.41165e12i	0.663020	−	0.663020i
$428$	5.80999e12	+	5.80999e12i	0.404536	+	0.404536i
$429$			9.42308e11i			0.0648495i
$430$		0			0
$431$	2.19757e13			1.47760			0.738799	−	0.673926i	$-0.235393\pi$
$431$	2.19757e13			1.47760			0.738799	+	0.673926i	$0.235393\pi$
$432$	1.66755e12	−	1.66755e12i	0.110831	−	0.110831i
$433$	−2.27496e11	−	2.27496e11i	−0.0149463	−	0.0149463i	0.699594	−	0.714540i	$-0.253364\pi$
$433$	−2.27496e11	−	2.27496e11i	−0.0149463	−	0.0149463i	−0.714540	+	0.699594i	$0.753364\pi$
$434$			6.47034e12i			0.420222i
$435$		0			0
$436$	9.58452e11			0.0608328
$437$	−2.87725e12	+	2.87725e12i	−0.180539	+	0.180539i
$438$	5.02201e12	+	5.02201e12i	0.311535	+	0.311535i
$439$			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
$442$	5.37483e12	−	5.37483e12i	0.318605	−	0.318605i
$443$	1.02630e12	+	1.02630e12i	0.0601527	+	0.0601527i	0.736543	−	0.676391i	$-0.236457\pi$
$443$	1.02630e12	+	1.02630e12i	0.0601527	+	0.0601527i	−0.676391	+	0.736543i	$0.736457\pi$
$444$			5.32227e10i			0.00308448i
$445$		0			0
$446$	1.37399e13			0.778591
$447$	−4.31644e11	+	4.31644e11i	−0.0241874	+	0.0241874i
$448$	−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
$453$	2.29108e12	+	2.29108e12i	0.120102	+	0.120102i
$454$		−	2.55454e13i		−	1.32445i
$455$		0			0
$456$	3.77167e12			0.191298
$457$	4.35652e12	−	4.35652e12i	0.218554	−	0.218554i	−0.589335	−	0.807889i	$-0.700610\pi$
$457$	4.35652e12	−	4.35652e12i	0.218554	−	0.218554i	0.807889	+	0.589335i	$0.200610\pi$
$458$	9.49123e12	+	9.49123e12i	0.470972	+	0.470972i
$459$			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	$0.125884\pi$
$462$	−9.54240e11	+	9.54240e11i	−0.0453365	+	0.0453365i
$463$	2.31064e13	+	2.31064e13i	1.08599	+	1.08599i	0.995937	+	0.0900567i	$0.0287048\pi$
$463$	2.31064e13	+	2.31064e13i	1.08599	+	1.08599i	0.0900567	+	0.995937i	$0.471295\pi$
$464$			1.16948e11i			0.00543753i
$465$		0			0
$466$	6.89966e12			0.313977
$467$	−1.27988e12	+	1.27988e12i	−0.0576215	+	0.0576215i	−0.735330	−	0.677709i	$-0.762973\pi$
$467$	−1.27988e12	+	1.27988e12i	−0.0576215	+	0.0576215i	0.677709	+	0.735330i	$0.262973\pi$
$468$	2.95582e12	+	2.95582e12i	0.131659	+	0.131659i
$469$		−	1.18698e13i		−	0.523091i
$470$		0			0
$471$	−5.57547e12			−0.240534
$472$	−7.70776e12	+	7.70776e12i	−0.329017	+	0.329017i
$473$	−8.91037e12	−	8.91037e12i	−0.376348	−	0.376348i
$474$		−	6.06389e12i		−	0.253431i
$475$		0			0
$476$	1.08858e13			0.445476
$477$	−1.62099e13	+	1.62099e13i	−0.656429	+	0.656429i
$478$	−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
$483$	5.64696e11	+	5.64696e11i	0.0214822	+	0.0214822i
$484$			1.03813e13i			0.390865i
$485$		0			0
$486$	−1.63572e13			−0.603293
$487$	1.94327e13	−	1.94327e13i	0.709394	−	0.709394i	−0.257014	−	0.966408i	$-0.582739\pi$
$487$	1.94327e13	−	1.94327e13i	0.709394	−	0.709394i	0.966408	+	0.257014i	$0.0827386\pi$
$488$	−1.10888e13	−	1.10888e13i	−0.400668	−	0.400668i
$489$		−	5.30951e11i		−	0.0189893i
$490$		0			0
$491$	−5.13556e13			−1.79962			−0.899808	−	0.436286i	$-0.856294\pi$
$491$	−5.13556e13			−1.79962			−0.899808	+	0.436286i	$0.856294\pi$
$492$	4.78459e12	−	4.78459e12i	0.165966	−	0.165966i
$493$	−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
$498$	−2.45572e12	−	2.45572e12i	−0.0801738	−	0.0801738i
$499$			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
$502$	1.16257e13	−	1.16257e13i	0.364670	−	0.364670i
$503$	1.47498e13	+	1.47498e13i	0.458085	+	0.458085i	0.898026	−	0.439942i	$-0.145001\pi$
$503$	1.47498e13	+	1.47498e13i	0.458085	+	0.458085i	−0.439942	+	0.898026i	$0.645001\pi$
$504$			5.98650e12i			0.184086i
$505$		0			0
$506$	−1.71533e12			−0.0517125
$507$	−6.48212e12	+	6.48212e12i	−0.193498	+	0.193498i
$508$	−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
$513$	−2.56909e13	−	2.56909e13i	−0.723089	−	0.723089i
$514$		−	2.57267e13i		−	0.717081i
$515$		0			0
$516$	6.91210e12			0.188956
$517$	−2.07909e13	+	2.07909e13i	−0.562886	+	0.562886i
$518$	−2.02882e11	−	2.02882e11i	−0.00543996	−	0.00543996i
$519$		−	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	$0.708976\pi$
$522$	3.75105e11	−	3.75105e11i	0.00967832	−	0.00967832i
$523$	−4.18752e13	−	4.18752e13i	−1.07016	−	1.07016i	−0.997346	−	0.0728136i	$-0.976802\pi$
$523$	−4.18752e13	−	4.18752e13i	−1.07016	−	1.07016i	−0.0728136	−	0.997346i	$-0.523198\pi$
$524$			2.41133e13i			0.610380i
$525$		0			0
$526$	−8.91498e12			−0.221407
$527$	−4.44623e13	+	4.44623e13i	−1.09380	+	1.09380i
$528$	1.12428e12	+	1.12428e12i	0.0273972	+	0.0273972i
$529$		−	4.04114e13i		−	0.975497i
$530$		0			0
$531$	4.94446e13			1.17124
$532$	−1.43774e13	+	1.43774e13i	−0.337383	+	0.337383i
$533$	1.80106e13	+	1.80106e13i	0.418689	+	0.418689i
$534$			4.86543e12i			0.112051i
$535$		0			0
$536$	−1.39849e13			−0.316108
$537$	−1.40468e13	+	1.40468e13i	−0.314562	+	0.314562i
$538$	−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
$543$	−6.87560e12	−	6.87560e12i	−0.145650	−	0.145650i
$544$		−	1.28256e13i		−	0.269204i
$545$		0			0
$546$	2.78647e12			0.0574238
$547$	3.93459e13	−	3.93459e13i	0.803457	−	0.803457i	−0.180177	−	0.983634i	$-0.557667\pi$
$547$	3.93459e13	−	3.93459e13i	0.803457	−	0.803457i	0.983634	+	0.180177i	$0.0576671\pi$
$548$	2.74587e13	+	2.74587e13i	0.555619	+	0.555619i
$549$			7.11336e13i			1.42631i
$550$		0			0
$551$	1.80174e12			0.0354759
$552$	6.65323e11	−	6.65323e11i	0.0129819	−	0.0129819i
$553$	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	−0.205730	−	0.978609i	$-0.565957\pi$
$557$	4.14369e13	−	4.14369e13i	0.772879	−	0.772879i	0.978609	+	0.205730i	$0.0659568\pi$
$558$	−2.44515e13	−	2.44515e13i	−0.451997	−	0.451997i
$559$			2.60191e13i			0.476688i
$560$		0			0
$561$	−1.31145e13			−0.236014
$562$	−1.07344e13	+	1.07344e13i	−0.191467	+	0.191467i
$563$	−3.17638e12	−	3.17638e12i	−0.0561553	−	0.0561553i	0.678471	−	0.734627i	$-0.262643\pi$
$563$	−3.17638e12	−	3.17638e12i	−0.0561553	−	0.0561553i	−0.734627	+	0.678471i	$0.762643\pi$
$564$		−	1.61283e13i		−	0.282613i
$565$		0			0
$566$	−5.54248e13			−0.954162
$567$	1.65336e13	−	1.65336e13i	0.282132	−	0.282132i
$568$	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
$573$	−1.68905e13	−	1.68905e13i	−0.273445	−	0.273445i
$574$			3.64773e13i			0.585413i
$575$		0			0
$576$	7.05328e12			0.111244
$577$	7.40732e13	−	7.40732e13i	1.15820	−	1.15820i	0.173332	−	0.984863i	$-0.444547\pi$
$577$	7.40732e13	−	7.40732e13i	1.15820	−	1.15820i	0.984863	−	0.173332i	$-0.0554533\pi$
$578$	4.25479e13	+	4.25479e13i	0.659536	+	0.659536i
$579$		−	3.58496e12i		−	0.0550923i
$580$		0			0
$581$	1.87222e13			0.282798
$582$	9.60451e11	−	9.60451e11i	0.0143834	−	0.0143834i
$583$	−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	−0.873116	−	0.487512i	$-0.837904\pi$
$587$	−2.68740e13	+	2.68740e13i	−0.385604	+	0.385604i	0.487512	+	0.873116i	$0.337904\pi$
$588$	−5.42200e12	−	5.42200e12i	−0.0771388	−	0.0771388i
$589$		−	1.17448e14i		−	1.65679i
$590$		0			0
$591$	−4.30987e12			−0.0597760
$592$	−2.39035e11	+	2.39035e11i	−0.00328741	+	0.00328741i
$593$	7.07818e11	+	7.07818e11i	0.00965269	+	0.00965269i	0.711917	−	0.702264i	$-0.247827\pi$
$593$	7.07818e11	+	7.07818e11i	0.00965269	+	0.00965269i	−0.702264	+	0.711917i	$0.747827\pi$
$594$		−	1.53161e13i		−	0.207118i
$595$		0			0
$596$	−3.87723e12			−0.0515573
$597$	1.60926e13	−	1.60926e13i	0.212204	−	0.212204i
$598$	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
$603$	4.48560e13	+	4.48560e13i	0.562644	+	0.562644i
$604$			2.05795e13i			0.256006i
$605$		0			0
$606$	2.64544e12			0.0323694
$607$	−3.59141e13	+	3.59141e13i	−0.435835	+	0.435835i	−0.890607	−	0.454773i	$-0.849720\pi$
$607$	−3.59141e13	+	3.59141e13i	−0.435835	+	0.435835i	0.454773	+	0.890607i	$0.349720\pi$
$608$	1.69395e13	+	1.69395e13i	0.203883	+	0.203883i
$609$		−	3.53613e11i		−	0.00422126i
$610$		0			0
$611$	6.07114e13			0.712959
$612$	−4.11375e13	+	4.11375e13i	−0.479160	+	0.479160i
$613$	7.56469e13	+	7.56469e13i	0.873955	+	0.873955i	0.992901	−	0.118946i	$-0.0379515\pi$
$613$	7.56469e13	+	7.56469e13i	0.873955	+	0.873955i	−0.118946	+	0.992901i	$0.537951\pi$
$614$			2.98316e13i			0.341849i
$615$		0			0
$616$	−8.57141e12			−0.0966382
$617$	−1.50165e12	+	1.50165e12i	−0.0167936	+	0.0167936i	−0.715454	−	0.698660i	$-0.753780\pi$
$617$	−1.50165e12	+	1.50165e12i	−0.0167936	+	0.0167936i	0.698660	+	0.715454i	$0.253780\pi$
$618$	1.26700e13	+	1.26700e13i	0.140552	+	0.140552i
$619$			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
$622$	1.04785e13	−	1.04785e13i	0.112550	−	0.112550i
$623$	−1.85468e13	−	1.85468e13i	−0.197619	−	0.197619i
$624$		−	3.28301e12i		−	0.0347016i
$625$		0			0
$626$	8.11692e13			0.844344
$627$	1.73211e13	−	1.73211e13i	0.178746	−	0.178746i
$628$	−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
$633$	1.41485e13	+	1.41485e13i	0.139217	+	0.139217i
$634$		−	3.17307e13i		−	0.309766i
$635$		0			0
$636$	1.80042e13			0.173017
$637$	2.04100e13	−	2.04100e13i	0.194601	−	0.194601i
$638$	5.37071e11	+	5.37071e11i	0.00508076	+	0.00508076i
$639$		−	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	$0.601406\pi$
$642$	−2.06981e13	+	2.06981e13i	−0.189782	+	0.189782i
$643$	−1.15028e14	−	1.15028e14i	−1.04652	−	1.04652i	−0.998864	−	0.0476578i	$-0.984824\pi$
$643$	−1.15028e14	−	1.15028e14i	−1.04652	−	1.04652i	−0.0476578	−	0.998864i	$-0.515176\pi$
$644$			5.07236e12i			0.0457911i
$645$		0			0
$646$	−1.97595e14			−1.75636
$647$	−1.38195e13	+	1.38195e13i	−0.121891	+	0.121891i	−0.765421	−	0.643530i	$-0.777469\pi$
$647$	−1.38195e13	+	1.38195e13i	−0.121891	+	0.121891i	0.643530	+	0.765421i	$0.277469\pi$
$648$	−1.94798e13	−	1.94798e13i	−0.170494	−	0.170494i
$649$			7.07943e13i			0.614858i
$650$		0			0
$651$	−2.30506e13			−0.197141
$652$	2.38462e12	−	2.38462e12i	0.0202386	−	0.0202386i
$653$	−4.92287e13	−	4.92287e13i	−0.414622	−	0.414622i	0.468723	−	0.883345i	$-0.344714\pi$
$653$	−4.92287e13	−	4.92287e13i	−0.414622	−	0.414622i	−0.883345	+	0.468723i	$0.844714\pi$
$654$			3.41449e12i			0.0285389i
$655$		0			0
$656$	4.29774e13			0.353770
$657$	1.44689e14	−	1.44689e14i	1.18197	−	1.18197i
$658$	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
$663$	1.91478e13	+	1.91478e13i	0.149469	+	0.149469i
$664$		−	2.20584e13i		−	0.170897i
$665$		0			0
$666$	1.53339e12			0.0117026
$667$	3.17826e11	−	3.17826e11i	0.00240747	−	0.00240747i
$668$	−3.00334e13	−	3.00334e13i	−0.225799	−	0.225799i
$669$			4.89484e13i			0.365265i
$670$		0			0
$671$	−1.01848e14			−0.748758
$672$	3.32458e12	−	3.32458e12i	0.0242600	−	0.0242600i
$673$	4.51609e13	+	4.51609e13i	0.327105	+	0.327105i	0.851485	−	0.524380i	$-0.175703\pi$
$673$	4.51609e13	+	4.51609e13i	0.327105	+	0.327105i	−0.524380	+	0.851485i	$0.675703\pi$
$674$		−	7.78379e12i		−	0.0559618i
$675$		0			0
$676$	−5.82253e13			−0.412457
$677$	−4.91332e13	+	4.91332e13i	−0.345487	+	0.345487i	−0.858426	−	0.512938i	$-0.828557\pi$
$677$	−4.91332e13	+	4.91332e13i	−0.345487	+	0.345487i	0.512938	+	0.858426i	$0.328557\pi$
$678$	2.58869e12	+	2.58869e12i	0.0180689	+	0.0180689i
$679$			7.32238e12i			0.0507345i
$680$		0			0
$681$	9.10056e13			0.621345
$682$	3.50095e13	−	3.50095e13i	0.237281	−	0.237281i
$683$	−5.34107e13	−	5.34107e13i	−0.359356	−	0.359356i	0.504220	−	0.863575i	$-0.331780\pi$
$683$	−5.34107e13	−	5.34107e13i	−0.359356	−	0.359356i	−0.863575	+	0.504220i	$0.831780\pi$
$684$		−	1.08665e14i		−	0.725788i
$685$		0			0
$686$	1.04186e14			0.685789
$687$	−3.38125e13	+	3.38125e13i	−0.220950	+	0.220950i
$688$	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
$693$	2.74925e13	+	2.74925e13i	0.172007	+	0.172007i
$694$			5.85762e13i			0.363851i
$695$		0			0
$696$	−4.16626e11			−0.00255094
$697$	−2.50661e14	+	2.50661e14i	−1.52378	+	1.52378i
$698$	1.06942e13	+	1.06942e13i	0.0645460	+	0.0645460i
$699$			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	$0.390589\pi$
$702$	−2.23623e13	+	2.23623e13i	−0.131169	+	0.131169i
$703$	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
$708$	−2.74589e13	−	2.74589e13i	−0.154354	−	0.154354i
$709$			2.99856e14i			1.67371i	0.547421	+	0.836857i	$0.315610\pi$
$709$			2.99856e14i			1.67371i	−0.547421	+	0.836857i	$0.684390\pi$
$710$		0			0
$711$	−1.74706e14			−0.961522
$712$	−2.18518e13	+	2.18518e13i	−0.119423	+	0.119423i
$713$	−2.07178e13	−	2.07178e13i	−0.112433	−	0.112433i
$714$			3.87805e13i			0.208989i
$715$		0			0
$716$	−1.26175e14			−0.670514
$717$	6.37703e13	−	6.37703e13i	0.336529	−	0.336529i
$718$	−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
$723$	6.71509e13	+	6.71509e13i	0.339907	+	0.339907i
$724$		−	6.17598e13i		−	0.310465i
$725$		0			0
$726$	−3.69835e13			−0.183369
$727$	−9.01780e12	+	9.01780e12i	−0.0444046	+	0.0444046i	−0.728960	−	0.684556i	$-0.759996\pi$
$727$	−9.01780e12	+	9.01780e12i	−0.0444046	+	0.0444046i	0.684556	+	0.728960i	$0.259996\pi$
$728$	1.25147e13	+	1.25147e13i	0.0612016	+	0.0612016i
$729$			8.21404e13i			0.398951i
$730$		0			0
$731$	−3.62120e14			−1.73486
$732$	3.95038e13	−	3.95038e13i	0.187968	−	0.187968i
$733$	2.22715e14	+	2.22715e14i	1.05252	+	1.05252i	0.998542	+	0.0539778i	$0.0171900\pi$
$733$	2.22715e14	+	2.22715e14i	1.05252	+	1.05252i	0.0539778	+	0.998542i	$0.482810\pi$
$734$			2.03598e14i			0.955638i
$735$		0			0
$736$	5.97624e12			0.0276719
$737$	−6.42244e13	+	6.42244e13i	−0.295367	+	0.295367i
$738$	−1.37848e14	−	1.37848e14i	−0.629679	−	0.629679i
$739$			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
$742$	−6.86311e13	+	6.86311e13i	−0.305142	+	0.305142i
$743$	−2.49851e14	−	2.49851e14i	−1.10341	−	1.10341i	−0.993996	−	0.109416i	$-0.965102\pi$
$743$	−2.49851e14	−	2.49851e14i	−1.10341	−	1.10341i	−0.109416	−	0.993996i	$-0.534898\pi$
$744$			2.71581e13i			0.119134i
$745$		0			0
$746$	2.15570e14			0.933028
$747$	−7.07515e13	+	7.07515e13i	−0.304181	+	0.304181i
$748$	−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
$753$	4.14165e13	+	4.14165e13i	0.171080	+	0.171080i
$754$		−	1.56830e12i		−	0.00643536i
$755$		0			0
$756$	−4.52909e13			−0.183401
$757$	−5.52263e13	+	5.52263e13i	−0.222160	+	0.222160i	−0.809408	−	0.587247i	$-0.800212\pi$
$757$	−5.52263e13	+	5.52263e13i	−0.222160	+	0.222160i	0.587247	+	0.809408i	$0.300212\pi$
$758$	1.44497e14	+	1.44497e14i	0.577446	+	0.577446i
$759$		−	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	$0.517494\pi$
$762$	3.81598e13	−	3.81598e13i	0.148536	−	0.148536i
$763$	−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
$768$	−3.91701e12	−	3.91701e12i	−0.0146605	−	0.0146605i
$769$		−	1.29006e14i		−	0.479711i	−0.970809	−	0.239855i	$-0.922900\pi$
$769$		−	1.29006e14i		−	0.479711i	0.970809	−	0.239855i	$-0.0771000\pi$
$770$		0			0
$771$	9.16513e13			0.336408
$772$	1.61009e13	−	1.61009e13i	0.0587168	−	0.0587168i
$773$	−1.09209e14	−	1.09209e14i	−0.395695	−	0.395695i	0.481017	−	0.876711i	$-0.340268\pi$
$773$	−1.09209e14	−	1.09209e14i	−0.395695	−	0.395695i	−0.876711	+	0.481017i	$0.840268\pi$
$774$		−	1.99144e14i		−	0.716905i
$775$		0			0
$776$	8.62721e12			0.0306593
$777$	7.22768e11	−	7.22768e11i	0.00255208	−	0.00255208i
$778$	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
$783$	2.83786e12	+	2.83786e12i	0.00964233	+	0.00964233i
$784$		−	4.87029e13i		−	0.164428i
$785$		0			0
$786$	−8.59036e13			−0.286351
$787$	−2.88376e14	+	2.88376e14i	−0.955181	+	0.955181i	−0.999038	−	0.0438564i	$-0.986036\pi$
$787$	−2.88376e14	+	2.88376e14i	−0.955181	+	0.955181i	0.0438564	+	0.999038i	$0.486036\pi$
$788$	−1.93566e13	−	1.93566e13i	−0.0637087	−	0.0637087i
$789$		−	3.17596e13i		−	0.103870i
$790$		0			0
$791$	−1.97359e13			−0.0637346
$792$	3.23915e13	−	3.23915e13i	0.103945	−	0.103945i
$793$	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	−0.214027	−	0.976828i	$-0.568658\pi$
$797$	2.45303e14	−	2.45303e14i	0.762801	−	0.762801i	0.976828	+	0.214027i	$0.0686581\pi$
$798$	−5.12196e13	−	5.12196e13i	−0.158279	−	0.158279i
$799$			8.44947e14i			2.59475i
$800$		0			0
$801$	1.40177e14			0.425123
$802$	−6.37785e13	+	6.37785e13i	−0.192222	+	0.192222i
$803$	2.07164e14	+	2.07164e14i	0.620491	+	0.620491i
$804$		−	4.98212e13i		−	0.148298i
$805$		0			0
$806$	−1.02231e14			−0.300544
$807$	3.96215e13	−	3.96215e13i	0.115761	−	0.115761i
$808$	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
$813$	−2.89696e13	−	2.89696e13i	−0.0815623	−	0.0815623i
$814$			2.19549e12i			0.00614342i
$815$		0			0
$816$	4.56911e13			0.126293
$817$	4.78272e14	−	4.78272e14i	1.31391	−	1.31391i
$818$	3.15776e14	+	3.15776e14i	0.862210	+	0.862210i
$819$		−	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	$0.590722\pi$
$822$	−9.78215e13	+	9.78215e13i	−0.260661	+	0.260661i
$823$	−1.06255e14	−	1.06255e14i	−0.281417	−	0.281417i	0.552257	−	0.833674i	$-0.313767\pi$
$823$	−1.06255e14	−	1.06255e14i	−0.281417	−	0.281417i	−0.833674	+	0.552257i	$0.813767\pi$
$824$			1.13808e14i			0.299597i
$825$		0			0
$826$	2.09344e14			0.544453
$827$	−3.71353e14	+	3.71353e14i	−0.959974	+	0.959974i	−0.999229	−	0.0392548i	$-0.987502\pi$
$827$	−3.71353e14	+	3.71353e14i	−0.959974	+	0.959974i	0.0392548	+	0.999229i	$0.487502\pi$
$828$	−1.91685e13	−	1.91685e13i	−0.0492535	−	0.0492535i
$829$			3.10526e14i			0.793094i	0.918014	+	0.396547i	$0.129792\pi$
$829$			3.10526e14i			0.793094i	−0.918014	+	0.396547i	$0.870208\pi$
$830$		0			0
$831$	1.09347e14			0.275932
$832$	1.47448e13	−	1.47448e13i	0.0369846	−	0.0369846i
$833$	2.84055e14	+	2.84055e14i	0.708234	+	0.708234i
$834$			4.74533e12i			0.0117608i
$835$		0			0
$836$	1.55586e14			0.381012
$837$	1.84988e14	−	1.84988e14i	0.450315	−	0.450315i
$838$	−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
$843$	−3.82412e13	−	3.82412e13i	−0.0898242	−	0.0898242i
$844$			1.27088e14i			0.296751i
$845$		0			0
$846$	−4.64669e14			−1.07224
$847$	1.40979e14	−	1.40979e14i	0.323399	−	0.323399i
$848$	8.08610e13	+	8.08610e13i	0.184399	+	0.184399i
$849$		−	1.97451e14i		−	0.447632i
$850$		0			0
$851$	1.29924e12			0.00291100
$852$	−8.25036e13	+	8.25036e13i	−0.183770	+	0.183770i
$853$	5.42341e14	+	5.42341e14i	1.20096	+	1.20096i	0.973876	+	0.227079i	$0.0729177\pi$
$853$	5.42341e14	+	5.42341e14i	1.20096	+	1.20096i	0.227079	+	0.973876i	$0.427082\pi$
$854$			3.01173e14i			0.663020i
$855$		0			0
$856$	−1.85920e14			−0.404536
$857$	2.19826e14	−	2.19826e14i	0.475527	−	0.475527i	−0.428171	−	0.903698i	$-0.640842\pi$
$857$	2.19826e14	−	2.19826e14i	0.475527	−	0.475527i	0.903698	+	0.428171i	$0.140842\pi$
$858$	−1.50769e13	−	1.50769e13i	−0.0324247	−	0.0324247i
$859$		−	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
$862$	−3.51611e14	+	3.51611e14i	−0.738799	+	0.738799i
$863$	−5.28472e14	−	5.28472e14i	−1.10400	−	1.10400i	−0.993923	−	0.110074i	$-0.964891\pi$
$863$	−5.28472e14	−	5.28472e14i	−1.10400	−	1.10400i	−0.110074	−	0.993923i	$-0.535109\pi$
$864$			5.33616e13i			0.110831i
$865$		0			0
$866$	7.27986e12			0.0149463
$867$	−1.51577e14	+	1.51577e14i	−0.309412	+	0.309412i
$868$	−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
$873$	−2.76714e13	−	2.76714e13i	−0.0545708	−	0.0545708i
$874$		−	9.20720e13i		−	0.180539i
$875$		0			0
$876$	−1.60704e14			−0.311535
$877$	−7.00963e14	+	7.00963e14i	−1.35113	+	1.35113i	−0.466732	+	0.884399i	$0.654569\pi$
$877$	−7.00963e14	+	7.00963e14i	−1.35113	+	1.35113i	−0.884399	+	0.466732i	$0.845431\pi$
$878$	−8.87726e13	−	8.87726e13i	−0.170140	−	0.170140i
$879$			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	$0.492590\pi$
$882$	−1.56213e14	+	1.56213e14i	−0.292666	+	0.292666i
$883$	1.88710e14	+	1.88710e14i	0.351553	+	0.351553i	0.860687	−	0.509134i	$-0.170034\pi$
$883$	1.88710e14	+	1.88710e14i	0.351553	+	0.351553i	−0.509134	+	0.860687i	$0.670034\pi$
$884$			1.71994e14i			0.318605i
$885$		0			0
$886$	−3.28415e13			−0.0601527
$887$	1.88830e14	−	1.88830e14i	0.343916	−	0.343916i	−0.513921	−	0.857837i	$-0.671808\pi$
$887$	1.88830e14	−	1.88830e14i	0.343916	−	0.343916i	0.857837	+	0.513921i	$0.171808\pi$
$888$	−8.51563e11	−	8.51563e11i	−0.00154224	−	0.00154224i
$889$			2.90926e14i			0.523931i
$890$		0			0
$891$	−1.78918e14			−0.318615
$892$	−2.19838e14	+	2.19838e14i	−0.389295	+	0.389295i
$893$	−1.11597e15	−	1.11597e15i	−1.96515	−	1.96515i
$894$		−	1.38126e13i		−	0.0241874i
$895$		0			0
$896$	2.98629e13			0.0517121
$897$	−8.92217e12	+	8.92217e12i	−0.0153641	+	0.0153641i
$898$	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
$903$	−9.38669e13	−	9.38669e13i	−0.156341	−	0.156341i
$904$			2.32528e13i			0.0385153i
$905$		0			0
$906$	−7.33145e13			−0.120102
$907$	6.88961e14	−	6.88961e14i	1.12243	−	1.12243i	0.131052	−	0.991376i	$-0.458165\pi$
$907$	6.88961e14	−	6.88961e14i	1.12243	−	1.12243i	0.991376	−	0.131052i	$-0.0418354\pi$
$908$	4.08727e14	+	4.08727e14i	0.662223	+	0.662223i
$909$		−	7.62175e13i		−	0.122810i
$910$		0			0
$911$	3.16488e14			0.504389			0.252195	−	0.967677i	$-0.418848\pi$
$911$	3.16488e14			0.504389			0.252195	+	0.967677i	$0.418848\pi$
$912$	−6.03468e13	+	6.03468e13i	−0.0956489	+	0.0956489i
$913$	−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
$918$	−3.11226e14	−	3.11226e14i	−0.477378	−	0.477378i
$919$			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
$922$	−6.14849e14	+	6.14849e14i	−0.922813	+	0.922813i
$923$	−3.10567e14	−	3.10567e14i	−0.463604	−	0.463604i
$924$		−	3.05357e13i		−	0.0453365i
$925$		0			0
$926$	−7.39404e14			−1.08599
$927$	3.65035e14	−	3.65035e14i	0.533256	−	0.533256i
$928$	−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
$933$	3.73296e13	+	3.73296e13i	0.0528013	+	0.0528013i
$934$		−	4.09562e13i		−	0.0576215i
$935$		0			0
$936$	−9.45864e13			−0.131659
$937$	−7.02940e14	+	7.02940e14i	−0.973241	+	0.973241i	−0.999651	−	0.0264102i	$-0.991592\pi$
$937$	−7.02940e14	+	7.02940e14i	−0.973241	+	0.973241i	0.0264102	+	0.999651i	$0.491592\pi$
$938$	1.89916e14	+	1.89916e14i	0.261546	+	0.261546i
$939$			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	$0.401643\pi$
$942$	8.92075e13	−	8.92075e13i	0.120267	−	0.120267i
$943$	−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	−0.998911	−	0.0466554i	$-0.985144\pi$
$947$	−7.25276e14	+	7.25276e14i	−0.952256	+	0.952256i	0.0466554	+	0.998911i	$0.485144\pi$
$948$	9.70222e13	+	9.70222e13i	0.126715	+	0.126715i
$949$		−	6.04938e14i		−	0.785923i
$950$		0			0
$951$	1.13041e14			0.145322
$952$	−1.74172e14	+	1.74172e14i	−0.222738	+	0.222738i
$953$	−4.88196e14	−	4.88196e14i	−0.621055	−	0.621055i	0.324746	−	0.945801i	$-0.394721\pi$
$953$	−4.88196e14	−	4.88196e14i	−0.621055	−	0.621055i	−0.945801	+	0.324746i	$0.894721\pi$
$954$		−	5.18716e14i		−	0.656429i
$955$		0			0
$956$	5.72814e14			0.717339
$957$	−1.91332e12	+	1.91332e12i	−0.00238357	+	0.00238357i
$958$	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
$963$	5.96330e14	+	5.96330e14i	0.720037	+	0.720037i
$964$			6.03180e14i			0.724539i
$965$		0			0
$966$	−1.80703e13			−0.0214822
$967$	4.94497e14	−	4.94497e14i	0.584832	−	0.584832i	−0.351395	−	0.936227i	$-0.614293\pi$
$967$	4.94497e14	−	4.94497e14i	0.584832	−	0.584832i	0.936227	+	0.351395i	$0.114293\pi$
$968$	−1.66102e14	−	1.66102e14i	−0.195433	−	0.195433i
$969$		−	7.03933e14i		−	0.823971i
$970$		0			0
$971$	−1.74459e14			−0.202115			−0.101057	−	0.994881i	$-0.532223\pi$
$971$	−1.74459e14			−0.202115			−0.101057	+	0.994881i	$0.532223\pi$
$972$	2.61716e14	−	2.61716e14i	0.301646	−	0.301646i
$973$	−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	−0.955510	−	0.294959i	$-0.904694\pi$
$977$	−5.88002e14	+	5.88002e14i	−0.660551	+	0.660551i	0.294959	+	0.955510i	$0.404694\pi$
$978$	8.49521e12	+	8.49521e12i	0.00949467	+	0.00949467i
$979$			2.00704e14i			0.223174i
$980$		0			0
$981$	9.83743e13			0.108277
$982$	8.21689e14	−	8.21689e14i	0.899808	−	0.899808i
$983$	9.62314e14	+	9.62314e14i	1.04845	+	1.04845i	0.998765	+	0.0496890i	$0.0158230\pi$
$983$	9.62314e14	+	9.62314e14i	1.04845	+	1.04845i	0.0496890	+	0.998765i	$0.484177\pi$
$984$			1.53107e14i			0.165966i
$985$		0			0
$986$	2.18267e13			0.0234209
$987$	−2.19023e14	+	2.19023e14i	−0.233832	+	0.233832i
$988$	−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
$993$	−1.87777e14	−	1.87777e14i	−0.194490	−	0.194490i
$994$		−	6.28999e14i		−	0.648214i
$995$		0			0
$996$	7.85831e13			0.0801738
$997$	8.16894e14	−	8.16894e14i	0.829259	−	0.829259i	−0.158155	−	0.987414i	$-0.550555\pi$
$997$	8.16894e14	−	8.16894e14i	0.829259	−	0.829259i	0.987414	+	0.158155i	$0.0505547\pi$
$998$	−2.79336e14	−	2.79336e14i	−0.282146	−	0.282146i
$999$			1.16009e13i			0.0116591i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.11.c.b.3.1	✓	2	5.4	even	2
10.11.c.b.7.1	yes	2	5.3	odd	4
50.11.c.b.7.1		2	5.2	odd	4	inner
50.11.c.b.43.1		2	1.1	even	1	trivial
80.11.p.a.17.1		2	20.3	even	4
80.11.p.a.33.1		2	20.19	odd	2
90.11.g.a.37.1		2	15.8	even	4
90.11.g.a.73.1		2	15.14	odd	2

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	50.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.0000 + 16.0000i) q^{2} +(-57.0000 - 57.0000i) q^{3} -512.000i q^{4} +1824.00 q^{6} +(-6953.00 + 6953.00i) q^{7} +(8192.00 + 8192.00i) q^{8} -52551.0i q^{9} +75242.0 q^{11} +(-29184.0 + 29184.0i) q^{12} +(-109857. - 109857. i) q^{13} -222496. i q^{14} -262144. q^{16} +(1.52893e6 - 1.52893e6i) q^{17} +(840816. + 840816. i) q^{18} +4.03868e6i q^{19} +792642. q^{21} +(-1.20387e6 + 1.20387e6i) q^{22} +(712423. + 712423. i) q^{23} -933888. i q^{24} +3.51542e6 q^{26} +(-6.36120e6 + 6.36120e6i) q^{27} +(3.55994e6 + 3.55994e6i) q^{28} -446120. i q^{29} -2.90807e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} +(-4.28879e6 - 4.28879e6i) q^{33} +4.89257e7i q^{34} -2.69061e7 q^{36} +(911847. - 911847. i) q^{37} +(-6.46189e7 - 6.46189e7i) q^{38} +1.25237e7i q^{39} -1.63946e8 q^{41} +(-1.26823e7 + 1.26823e7i) q^{42} +(-1.18423e8 - 1.18423e8i) q^{43} -3.85239e7i q^{44} -2.27975e7 q^{46} +(-2.76320e8 + 2.76320e8i) q^{47} +(1.49422e7 + 1.49422e7i) q^{48} +1.85787e8i q^{49} -1.74298e8 q^{51} +(-5.62468e7 + 5.62468e7i) q^{52} +(-3.08460e8 - 3.08460e8i) q^{53} -2.03558e8i q^{54} -1.13918e8 q^{56} +(2.30205e8 - 2.30205e8i) q^{57} +(7.13792e6 + 7.13792e6i) q^{58} +9.40888e8i q^{59} -1.35361e9 q^{61} +(4.65291e8 - 4.65291e8i) q^{62} +(3.65387e8 + 3.65387e8i) q^{63} +1.34218e8i q^{64} +1.37241e8 q^{66} +(-8.53571e8 + 8.53571e8i) q^{67} +(-7.82811e8 - 7.82811e8i) q^{68} -8.12162e7i q^{69} +2.82701e9 q^{71} +(4.30498e8 - 4.30498e8i) q^{72} +(2.75330e9 + 2.75330e9i) q^{73} +2.91791e7i q^{74} +2.06780e9 q^{76} +(-5.23158e8 + 5.23158e8i) q^{77} +(-2.00379e8 - 2.00379e8i) q^{78} -3.32450e9i q^{79} -2.37791e9 q^{81} +(2.62313e9 - 2.62313e9i) q^{82} +(-1.34634e9 - 1.34634e9i) q^{83} -4.05833e8i q^{84} +3.78953e9 q^{86} +(-2.54288e7 + 2.54288e7i) q^{87} +(6.16382e8 + 6.16382e8i) q^{88} +2.66745e9i q^{89} +1.52767e9 q^{91} +(3.64761e8 - 3.64761e8i) q^{92} +(1.65760e9 + 1.65760e9i) q^{93} -8.84225e9i q^{94} -4.78151e8 q^{96} +(5.26563e8 - 5.26563e8i) q^{97} +(-2.97259e9 - 2.97259e9i) q^{98} -3.95404e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} - 114 q^{3} + 3648 q^{6} - 13906 q^{7} + 16384 q^{8} + 150484 q^{11} - 58368 q^{12} - 219714 q^{13} - 524288 q^{16} + 3057854 q^{17} + 1681632 q^{18} + 1585284 q^{21} - 2407744 q^{22} + 1424846 q^{23}+ \cdots - 5945178592 q^{98}+O(q^{100}) \) 2 * q - 32 * q^2 - 114 * q^3 + 3648 * q^6 - 13906 * q^7 + 16384 * q^8 + 150484 * q^11 - 58368 * q^12 - 219714 * q^13 - 524288 * q^16 + 3057854 * q^17 + 1681632 * q^18 + 1585284 * q^21 - 2407744 * q^22 + 1424846 * q^23 + 7030848 * q^26 - 12722400 * q^27 + 7119872 * q^28 - 58161436 * q^31 + 8388608 * q^32 - 8577588 * q^33 - 53812224 * q^36 + 1823694 * q^37 - 129237760 * q^38 - 327891356 * q^41 - 25364544 * q^42 - 236845554 * q^43 - 45595072 * q^46 - 552640626 * q^47 + 29884416 * q^48 - 348595356 * q^51 - 112493568 * q^52 - 616920194 * q^53 - 227835904 * q^56 + 460409520 * q^57 + 14275840 * q^58 - 2707220076 * q^61 + 930582976 * q^62 + 730774206 * q^63 + 274482816 * q^66 - 1707141826 * q^67 - 1565621248 * q^68 + 5654029124 * q^71 + 860995584 * q^72 + 5506594366 * q^73 + 4135608320 * q^76 - 1046315252 * q^77 - 400758336 * q^78 - 4755814398 * q^81 + 5246261696 * q^82 - 2692678194 * q^83 + 7579057728 * q^86 - 50857680 * q^87 + 1232764928 * q^88 + 3055342884 * q^91 + 729521152 * q^92 + 3315201852 * q^93 - 956301312 * q^96 + 1053125694 * q^97 - 5945178592 * q^98

Introduction

L-functions

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