Properties

Label 48.16.c.b.47.1
Level $48$
Weight $16$
Character 48.47
Analytic conductor $68.493$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,16,Mod(47,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 16, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.47");
 
S:= CuspForms(chi, 16);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 48.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(68.4928824480\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 32461x^{2} + 32462x + 263623935 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 47.1
Root \(127.913 + 1.65831i\) of defining polynomial
Character \(\chi\) \(=\) 48.47
Dual form 48.16.c.b.47.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2293.43 - 3014.81i) q^{3} +76064.4i q^{5} -1.82913e6i q^{7} +(-3.82928e6 + 1.38285e7i) q^{9} +O(q^{10})\) \(q+(-2293.43 - 3014.81i) q^{3} +76064.4i q^{5} -1.82913e6i q^{7} +(-3.82928e6 + 1.38285e7i) q^{9} -7.64125e7 q^{11} +2.54445e8 q^{13} +(2.29320e8 - 1.74448e8i) q^{15} +7.38677e8i q^{17} -5.32265e8i q^{19} +(-5.51447e9 + 4.19497e9i) q^{21} -1.70562e10 q^{23} +2.47318e10 q^{25} +(5.04725e10 - 2.01702e10i) q^{27} +1.64361e11i q^{29} +1.19565e11i q^{31} +(1.75247e11 + 2.30369e11i) q^{33} +1.39131e11 q^{35} -1.78908e11 q^{37} +(-5.83552e11 - 7.67105e11i) q^{39} -5.29655e11i q^{41} +5.71398e11i q^{43} +(-1.05186e12 - 2.91272e11i) q^{45} +1.37657e12 q^{47} +1.40186e12 q^{49} +(2.22697e12 - 1.69410e12i) q^{51} -1.30462e13i q^{53} -5.81227e12i q^{55} +(-1.60468e12 + 1.22071e12i) q^{57} +6.31592e11 q^{59} -1.44698e13 q^{61} +(2.52941e13 + 7.00422e12i) q^{63} +1.93542e13i q^{65} -8.74692e13i q^{67} +(3.91172e13 + 5.14212e13i) q^{69} +8.26841e13 q^{71} +6.67870e13 q^{73} +(-5.67206e13 - 7.45617e13i) q^{75} +1.39768e14i q^{77} -1.93474e14i q^{79} +(-1.76564e14 - 1.05906e14i) q^{81} +4.13488e14 q^{83} -5.61870e13 q^{85} +(4.95518e14 - 3.76951e14i) q^{87} -5.61280e14i q^{89} -4.65412e14i q^{91} +(3.60466e14 - 2.74214e14i) q^{93} +4.04865e13 q^{95} -3.75171e14 q^{97} +(2.92604e14 - 1.05667e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 15317100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 15317100 q^{9} + 1017781336 q^{13} - 22057873992 q^{21} + 98927122100 q^{25} + 700986197952 q^{33} - 715633821064 q^{37} - 4207432014720 q^{45} + 5607449975596 q^{49} - 6418720383768 q^{57} - 57879101335528 q^{61} + 156468753896832 q^{69} + 267147849446632 q^{73} - 706257752173596 q^{81} - 224748150612480 q^{85} + 14\!\cdots\!64 q^{93}+ \cdots - 15\!\cdots\!20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2293.43 3014.81i −0.605447 0.795886i
\(4\) 0 0
\(5\) 76064.4i 0.435418i 0.976014 + 0.217709i \(0.0698584\pi\)
−0.976014 + 0.217709i \(0.930142\pi\)
\(6\) 0 0
\(7\) 1.82913e6i 0.839476i −0.907645 0.419738i \(-0.862122\pi\)
0.907645 0.419738i \(-0.137878\pi\)
\(8\) 0 0
\(9\) −3.82928e6 + 1.38285e7i −0.266869 + 0.963733i
\(10\) 0 0
\(11\) −7.64125e7 −1.18228 −0.591138 0.806570i \(-0.701321\pi\)
−0.591138 + 0.806570i \(0.701321\pi\)
\(12\) 0 0
\(13\) 2.54445e8 1.12466 0.562328 0.826915i \(-0.309906\pi\)
0.562328 + 0.826915i \(0.309906\pi\)
\(14\) 0 0
\(15\) 2.29320e8 1.74448e8i 0.346543 0.263622i
\(16\) 0 0
\(17\) 7.38677e8i 0.436604i 0.975881 + 0.218302i \(0.0700518\pi\)
−0.975881 + 0.218302i \(0.929948\pi\)
\(18\) 0 0
\(19\) 5.32265e8i 0.136608i −0.997665 0.0683040i \(-0.978241\pi\)
0.997665 0.0683040i \(-0.0217588\pi\)
\(20\) 0 0
\(21\) −5.51447e9 + 4.19497e9i −0.668127 + 0.508258i
\(22\) 0 0
\(23\) −1.70562e10 −1.04454 −0.522268 0.852781i \(-0.674914\pi\)
−0.522268 + 0.852781i \(0.674914\pi\)
\(24\) 0 0
\(25\) 2.47318e10 0.810411
\(26\) 0 0
\(27\) 5.04725e10 2.01702e10i 0.928596 0.371092i
\(28\) 0 0
\(29\) 1.64361e11i 1.76935i 0.466206 + 0.884676i \(0.345620\pi\)
−0.466206 + 0.884676i \(0.654380\pi\)
\(30\) 0 0
\(31\) 1.19565e11i 0.780534i 0.920702 + 0.390267i \(0.127617\pi\)
−0.920702 + 0.390267i \(0.872383\pi\)
\(32\) 0 0
\(33\) 1.75247e11 + 2.30369e11i 0.715805 + 0.940957i
\(34\) 0 0
\(35\) 1.39131e11 0.365523
\(36\) 0 0
\(37\) −1.78908e11 −0.309826 −0.154913 0.987928i \(-0.549510\pi\)
−0.154913 + 0.987928i \(0.549510\pi\)
\(38\) 0 0
\(39\) −5.83552e11 7.67105e11i −0.680919 0.895097i
\(40\) 0 0
\(41\) 5.29655e11i 0.424731i −0.977190 0.212365i \(-0.931883\pi\)
0.977190 0.212365i \(-0.0681167\pi\)
\(42\) 0 0
\(43\) 5.71398e11i 0.320572i 0.987071 + 0.160286i \(0.0512416\pi\)
−0.987071 + 0.160286i \(0.948758\pi\)
\(44\) 0 0
\(45\) −1.05186e12 2.91272e11i −0.419627 0.116200i
\(46\) 0 0
\(47\) 1.37657e12 0.396337 0.198169 0.980168i \(-0.436501\pi\)
0.198169 + 0.980168i \(0.436501\pi\)
\(48\) 0 0
\(49\) 1.40186e12 0.295281
\(50\) 0 0
\(51\) 2.22697e12 1.69410e12i 0.347487 0.264340i
\(52\) 0 0
\(53\) 1.30462e13i 1.52551i −0.646685 0.762757i \(-0.723845\pi\)
0.646685 0.762757i \(-0.276155\pi\)
\(54\) 0 0
\(55\) 5.81227e12i 0.514785i
\(56\) 0 0
\(57\) −1.60468e12 + 1.22071e12i −0.108724 + 0.0827089i
\(58\) 0 0
\(59\) 6.31592e11 0.0330405 0.0165202 0.999864i \(-0.494741\pi\)
0.0165202 + 0.999864i \(0.494741\pi\)
\(60\) 0 0
\(61\) −1.44698e13 −0.589506 −0.294753 0.955574i \(-0.595237\pi\)
−0.294753 + 0.955574i \(0.595237\pi\)
\(62\) 0 0
\(63\) 2.52941e13 + 7.00422e12i 0.809030 + 0.224030i
\(64\) 0 0
\(65\) 1.93542e13i 0.489695i
\(66\) 0 0
\(67\) 8.74692e13i 1.76317i −0.472025 0.881585i \(-0.656477\pi\)
0.472025 0.881585i \(-0.343523\pi\)
\(68\) 0 0
\(69\) 3.91172e13 + 5.14212e13i 0.632411 + 0.831332i
\(70\) 0 0
\(71\) 8.26841e13 1.07891 0.539454 0.842015i \(-0.318631\pi\)
0.539454 + 0.842015i \(0.318631\pi\)
\(72\) 0 0
\(73\) 6.67870e13 0.707571 0.353786 0.935327i \(-0.384894\pi\)
0.353786 + 0.935327i \(0.384894\pi\)
\(74\) 0 0
\(75\) −5.67206e13 7.45617e13i −0.490661 0.644995i
\(76\) 0 0
\(77\) 1.39768e14i 0.992492i
\(78\) 0 0
\(79\) 1.93474e14i 1.13349i −0.823892 0.566747i \(-0.808202\pi\)
0.823892 0.566747i \(-0.191798\pi\)
\(80\) 0 0
\(81\) −1.76564e14 1.05906e14i −0.857562 0.514380i
\(82\) 0 0
\(83\) 4.13488e14 1.67254 0.836271 0.548316i \(-0.184731\pi\)
0.836271 + 0.548316i \(0.184731\pi\)
\(84\) 0 0
\(85\) −5.61870e13 −0.190105
\(86\) 0 0
\(87\) 4.95518e14 3.76951e14i 1.40820 1.07125i
\(88\) 0 0
\(89\) 5.61280e14i 1.34510i −0.740051 0.672550i \(-0.765199\pi\)
0.740051 0.672550i \(-0.234801\pi\)
\(90\) 0 0
\(91\) 4.65412e14i 0.944121i
\(92\) 0 0
\(93\) 3.60466e14 2.74214e14i 0.621216 0.472572i
\(94\) 0 0
\(95\) 4.04865e13 0.0594816
\(96\) 0 0
\(97\) −3.75171e14 −0.471456 −0.235728 0.971819i \(-0.575747\pi\)
−0.235728 + 0.971819i \(0.575747\pi\)
\(98\) 0 0
\(99\) 2.92604e14 1.05667e15i 0.315513 1.13940i
\(100\) 0 0
\(101\) 8.90919e14i 0.826852i 0.910538 + 0.413426i \(0.135668\pi\)
−0.910538 + 0.413426i \(0.864332\pi\)
\(102\) 0 0
\(103\) 1.87003e15i 1.49820i −0.662458 0.749099i \(-0.730487\pi\)
0.662458 0.749099i \(-0.269513\pi\)
\(104\) 0 0
\(105\) −3.19088e14 4.19455e14i −0.221305 0.290915i
\(106\) 0 0
\(107\) 2.30400e15 1.38709 0.693544 0.720414i \(-0.256048\pi\)
0.693544 + 0.720414i \(0.256048\pi\)
\(108\) 0 0
\(109\) 8.68707e14 0.455171 0.227585 0.973758i \(-0.426917\pi\)
0.227585 + 0.973758i \(0.426917\pi\)
\(110\) 0 0
\(111\) 4.10314e14 + 5.39375e14i 0.187583 + 0.246586i
\(112\) 0 0
\(113\) 1.92630e14i 0.0770259i −0.999258 0.0385129i \(-0.987738\pi\)
0.999258 0.0385129i \(-0.0122621\pi\)
\(114\) 0 0
\(115\) 1.29737e15i 0.454810i
\(116\) 0 0
\(117\) −9.74341e14 + 3.51860e15i −0.300135 + 1.08387i
\(118\) 0 0
\(119\) 1.35113e15 0.366518
\(120\) 0 0
\(121\) 1.66162e15 0.397778
\(122\) 0 0
\(123\) −1.59681e15 + 1.21473e15i −0.338037 + 0.257152i
\(124\) 0 0
\(125\) 4.20251e15i 0.788286i
\(126\) 0 0
\(127\) 1.64302e15i 0.273599i −0.990599 0.136799i \(-0.956318\pi\)
0.990599 0.136799i \(-0.0436816\pi\)
\(128\) 0 0
\(129\) 1.72266e15 1.31046e15i 0.255138 0.194089i
\(130\) 0 0
\(131\) −5.77321e15 −0.761873 −0.380937 0.924601i \(-0.624398\pi\)
−0.380937 + 0.924601i \(0.624398\pi\)
\(132\) 0 0
\(133\) −9.73580e14 −0.114679
\(134\) 0 0
\(135\) 1.53423e15 + 3.83916e15i 0.161580 + 0.404328i
\(136\) 0 0
\(137\) 1.98302e16i 1.87035i −0.354185 0.935175i \(-0.615242\pi\)
0.354185 0.935175i \(-0.384758\pi\)
\(138\) 0 0
\(139\) 1.91399e16i 1.61930i 0.586912 + 0.809651i \(0.300343\pi\)
−0.586912 + 0.809651i \(0.699657\pi\)
\(140\) 0 0
\(141\) −3.15707e15 4.15010e15i −0.239961 0.315439i
\(142\) 0 0
\(143\) −1.94428e16 −1.32965
\(144\) 0 0
\(145\) −1.25020e16 −0.770408
\(146\) 0 0
\(147\) −3.21507e15 4.22635e15i −0.178777 0.235010i
\(148\) 0 0
\(149\) 6.29842e15i 0.316472i 0.987401 + 0.158236i \(0.0505806\pi\)
−0.987401 + 0.158236i \(0.949419\pi\)
\(150\) 0 0
\(151\) 2.59510e16i 1.17985i 0.807458 + 0.589925i \(0.200843\pi\)
−0.807458 + 0.589925i \(0.799157\pi\)
\(152\) 0 0
\(153\) −1.02148e16 2.82860e15i −0.420770 0.116516i
\(154\) 0 0
\(155\) −9.09465e15 −0.339859
\(156\) 0 0
\(157\) 4.78146e16 1.62298 0.811490 0.584366i \(-0.198657\pi\)
0.811490 + 0.584366i \(0.198657\pi\)
\(158\) 0 0
\(159\) −3.93319e16 + 2.99206e16i −1.21413 + 0.923617i
\(160\) 0 0
\(161\) 3.11979e16i 0.876863i
\(162\) 0 0
\(163\) 5.01923e16i 1.28597i 0.765880 + 0.642984i \(0.222304\pi\)
−0.765880 + 0.642984i \(0.777696\pi\)
\(164\) 0 0
\(165\) −1.75229e16 + 1.33300e16i −0.409710 + 0.311675i
\(166\) 0 0
\(167\) 2.24657e16 0.479896 0.239948 0.970786i \(-0.422870\pi\)
0.239948 + 0.970786i \(0.422870\pi\)
\(168\) 0 0
\(169\) 1.35565e16 0.264849
\(170\) 0 0
\(171\) 7.36044e15 + 2.03819e15i 0.131654 + 0.0364564i
\(172\) 0 0
\(173\) 3.73031e16i 0.611504i 0.952111 + 0.305752i \(0.0989079\pi\)
−0.952111 + 0.305752i \(0.901092\pi\)
\(174\) 0 0
\(175\) 4.52375e16i 0.680320i
\(176\) 0 0
\(177\) −1.44851e15 1.90413e15i −0.0200043 0.0262965i
\(178\) 0 0
\(179\) −1.37575e17 −1.74639 −0.873197 0.487367i \(-0.837958\pi\)
−0.873197 + 0.487367i \(0.837958\pi\)
\(180\) 0 0
\(181\) −6.36349e16 −0.743201 −0.371600 0.928393i \(-0.621191\pi\)
−0.371600 + 0.928393i \(0.621191\pi\)
\(182\) 0 0
\(183\) 3.31854e16 + 4.36237e16i 0.356914 + 0.469179i
\(184\) 0 0
\(185\) 1.36086e16i 0.134904i
\(186\) 0 0
\(187\) 5.64441e16i 0.516187i
\(188\) 0 0
\(189\) −3.68938e16 9.23206e16i −0.311523 0.779534i
\(190\) 0 0
\(191\) 1.30203e17 1.01595 0.507973 0.861373i \(-0.330395\pi\)
0.507973 + 0.861373i \(0.330395\pi\)
\(192\) 0 0
\(193\) 2.33515e17 1.68513 0.842566 0.538593i \(-0.181044\pi\)
0.842566 + 0.538593i \(0.181044\pi\)
\(194\) 0 0
\(195\) 5.83494e16 4.43876e16i 0.389742 0.296484i
\(196\) 0 0
\(197\) 2.42634e17i 1.50126i −0.660724 0.750629i \(-0.729751\pi\)
0.660724 0.750629i \(-0.270249\pi\)
\(198\) 0 0
\(199\) 1.14963e17i 0.659419i −0.944082 0.329710i \(-0.893049\pi\)
0.944082 0.329710i \(-0.106951\pi\)
\(200\) 0 0
\(201\) −2.63703e17 + 2.00604e17i −1.40328 + 1.06751i
\(202\) 0 0
\(203\) 3.00637e17 1.48533
\(204\) 0 0
\(205\) 4.02879e16 0.184936
\(206\) 0 0
\(207\) 6.53129e16 2.35862e17i 0.278754 1.00665i
\(208\) 0 0
\(209\) 4.06717e16i 0.161508i
\(210\) 0 0
\(211\) 1.14655e17i 0.423913i −0.977279 0.211956i \(-0.932017\pi\)
0.977279 0.211956i \(-0.0679834\pi\)
\(212\) 0 0
\(213\) −1.89630e17 2.49277e17i −0.653221 0.858688i
\(214\) 0 0
\(215\) −4.34630e16 −0.139583
\(216\) 0 0
\(217\) 2.18700e17 0.655239
\(218\) 0 0
\(219\) −1.53171e17 2.01350e17i −0.428397 0.563146i
\(220\) 0 0
\(221\) 1.87953e17i 0.491029i
\(222\) 0 0
\(223\) 4.46157e17i 1.08943i −0.838620 0.544717i \(-0.816637\pi\)
0.838620 0.544717i \(-0.183363\pi\)
\(224\) 0 0
\(225\) −9.47048e16 + 3.42004e17i −0.216273 + 0.781020i
\(226\) 0 0
\(227\) 5.24609e17 1.12109 0.560547 0.828123i \(-0.310591\pi\)
0.560547 + 0.828123i \(0.310591\pi\)
\(228\) 0 0
\(229\) 6.48369e17 1.29735 0.648674 0.761067i \(-0.275324\pi\)
0.648674 + 0.761067i \(0.275324\pi\)
\(230\) 0 0
\(231\) 4.21374e17 3.20548e17i 0.789911 0.600901i
\(232\) 0 0
\(233\) 4.01531e17i 0.705585i 0.935702 + 0.352793i \(0.114768\pi\)
−0.935702 + 0.352793i \(0.885232\pi\)
\(234\) 0 0
\(235\) 1.04708e17i 0.172572i
\(236\) 0 0
\(237\) −5.83288e17 + 4.43719e17i −0.902132 + 0.686271i
\(238\) 0 0
\(239\) −1.21318e17 −0.176173 −0.0880867 0.996113i \(-0.528075\pi\)
−0.0880867 + 0.996113i \(0.528075\pi\)
\(240\) 0 0
\(241\) 3.65127e17 0.498100 0.249050 0.968491i \(-0.419882\pi\)
0.249050 + 0.968491i \(0.419882\pi\)
\(242\) 0 0
\(243\) 8.56502e16 + 7.75197e17i 0.109820 + 0.993951i
\(244\) 0 0
\(245\) 1.06632e17i 0.128571i
\(246\) 0 0
\(247\) 1.35432e17i 0.153637i
\(248\) 0 0
\(249\) −9.48305e17 1.24659e18i −1.01263 1.33115i
\(250\) 0 0
\(251\) −1.39376e18 −1.40164 −0.700819 0.713339i \(-0.747182\pi\)
−0.700819 + 0.713339i \(0.747182\pi\)
\(252\) 0 0
\(253\) 1.30331e18 1.23493
\(254\) 0 0
\(255\) 1.28861e17 + 1.69393e17i 0.115099 + 0.151302i
\(256\) 0 0
\(257\) 1.58617e18i 1.33614i −0.744099 0.668070i \(-0.767121\pi\)
0.744099 0.668070i \(-0.232879\pi\)
\(258\) 0 0
\(259\) 3.27246e17i 0.260091i
\(260\) 0 0
\(261\) −2.27287e18 6.29384e17i −1.70518 0.472185i
\(262\) 0 0
\(263\) 1.02896e18 0.729001 0.364501 0.931203i \(-0.381240\pi\)
0.364501 + 0.931203i \(0.381240\pi\)
\(264\) 0 0
\(265\) 9.92354e17 0.664236
\(266\) 0 0
\(267\) −1.69215e18 + 1.28726e18i −1.07055 + 0.814387i
\(268\) 0 0
\(269\) 9.01288e17i 0.539165i 0.962977 + 0.269582i \(0.0868857\pi\)
−0.962977 + 0.269582i \(0.913114\pi\)
\(270\) 0 0
\(271\) 2.19619e18i 1.24280i 0.783494 + 0.621399i \(0.213435\pi\)
−0.783494 + 0.621399i \(0.786565\pi\)
\(272\) 0 0
\(273\) −1.40313e18 + 1.06739e18i −0.751412 + 0.571615i
\(274\) 0 0
\(275\) −1.88982e18 −0.958130
\(276\) 0 0
\(277\) 2.49263e18 1.19690 0.598451 0.801159i \(-0.295783\pi\)
0.598451 + 0.801159i \(0.295783\pi\)
\(278\) 0 0
\(279\) −1.65341e18 4.57848e17i −0.752226 0.208300i
\(280\) 0 0
\(281\) 1.55724e17i 0.0671520i −0.999436 0.0335760i \(-0.989310\pi\)
0.999436 0.0335760i \(-0.0106896\pi\)
\(282\) 0 0
\(283\) 2.54289e18i 1.03975i 0.854242 + 0.519875i \(0.174022\pi\)
−0.854242 + 0.519875i \(0.825978\pi\)
\(284\) 0 0
\(285\) −9.28528e16 1.22059e17i −0.0360129 0.0473406i
\(286\) 0 0
\(287\) −9.68805e17 −0.356551
\(288\) 0 0
\(289\) 2.31678e18 0.809377
\(290\) 0 0
\(291\) 8.60428e17 + 1.13107e18i 0.285441 + 0.375225i
\(292\) 0 0
\(293\) 2.17295e18i 0.684765i 0.939561 + 0.342383i \(0.111234\pi\)
−0.939561 + 0.342383i \(0.888766\pi\)
\(294\) 0 0
\(295\) 4.80417e16i 0.0143864i
\(296\) 0 0
\(297\) −3.85673e18 + 1.54125e18i −1.09786 + 0.438733i
\(298\) 0 0
\(299\) −4.33987e18 −1.17474
\(300\) 0 0
\(301\) 1.04516e18 0.269112
\(302\) 0 0
\(303\) 2.68595e18 2.04326e18i 0.658080 0.500615i
\(304\) 0 0
\(305\) 1.10064e18i 0.256682i
\(306\) 0 0
\(307\) 7.66257e18i 1.70152i 0.525555 + 0.850759i \(0.323858\pi\)
−0.525555 + 0.850759i \(0.676142\pi\)
\(308\) 0 0
\(309\) −5.63779e18 + 4.28878e18i −1.19240 + 0.907079i
\(310\) 0 0
\(311\) 4.84682e18 0.976685 0.488342 0.872652i \(-0.337602\pi\)
0.488342 + 0.872652i \(0.337602\pi\)
\(312\) 0 0
\(313\) 8.77812e18 1.68585 0.842926 0.538030i \(-0.180831\pi\)
0.842926 + 0.538030i \(0.180831\pi\)
\(314\) 0 0
\(315\) −5.32772e17 + 1.92398e18i −0.0975467 + 0.352267i
\(316\) 0 0
\(317\) 6.53956e17i 0.114184i −0.998369 0.0570918i \(-0.981817\pi\)
0.998369 0.0570918i \(-0.0181828\pi\)
\(318\) 0 0
\(319\) 1.25592e19i 2.09186i
\(320\) 0 0
\(321\) −5.28406e18 6.94612e18i −0.839808 1.10396i
\(322\) 0 0
\(323\) 3.93172e17 0.0596436
\(324\) 0 0
\(325\) 6.29289e18 0.911433
\(326\) 0 0
\(327\) −1.99232e18 2.61899e18i −0.275582 0.362264i
\(328\) 0 0
\(329\) 2.51792e18i 0.332715i
\(330\) 0 0
\(331\) 7.41780e18i 0.936623i −0.883563 0.468312i \(-0.844862\pi\)
0.883563 0.468312i \(-0.155138\pi\)
\(332\) 0 0
\(333\) 6.85090e17 2.47404e18i 0.0826829 0.298590i
\(334\) 0 0
\(335\) 6.65330e18 0.767716
\(336\) 0 0
\(337\) −7.56506e18 −0.834811 −0.417405 0.908720i \(-0.637060\pi\)
−0.417405 + 0.908720i \(0.637060\pi\)
\(338\) 0 0
\(339\) −5.80744e17 + 4.41784e17i −0.0613038 + 0.0466350i
\(340\) 0 0
\(341\) 9.13626e18i 0.922807i
\(342\) 0 0
\(343\) 1.12481e19i 1.08736i
\(344\) 0 0
\(345\) −3.91133e18 + 2.97543e18i −0.361977 + 0.275363i
\(346\) 0 0
\(347\) 5.19618e18 0.460483 0.230241 0.973134i \(-0.426048\pi\)
0.230241 + 0.973134i \(0.426048\pi\)
\(348\) 0 0
\(349\) −3.25826e18 −0.276563 −0.138282 0.990393i \(-0.544158\pi\)
−0.138282 + 0.990393i \(0.544158\pi\)
\(350\) 0 0
\(351\) 1.28425e19 5.13221e18i 1.04435 0.417350i
\(352\) 0 0
\(353\) 1.05498e19i 0.822121i 0.911608 + 0.411060i \(0.134841\pi\)
−0.911608 + 0.411060i \(0.865159\pi\)
\(354\) 0 0
\(355\) 6.28932e18i 0.469776i
\(356\) 0 0
\(357\) −3.09873e18 4.07341e18i −0.221907 0.291707i
\(358\) 0 0
\(359\) 2.60617e19 1.78976 0.894880 0.446308i \(-0.147261\pi\)
0.894880 + 0.446308i \(0.147261\pi\)
\(360\) 0 0
\(361\) 1.48978e19 0.981338
\(362\) 0 0
\(363\) −3.81080e18 5.00946e18i −0.240833 0.316586i
\(364\) 0 0
\(365\) 5.08011e18i 0.308089i
\(366\) 0 0
\(367\) 3.03458e19i 1.76646i −0.468942 0.883229i \(-0.655365\pi\)
0.468942 0.883229i \(-0.344635\pi\)
\(368\) 0 0
\(369\) 7.32434e18 + 2.02819e18i 0.409327 + 0.113347i
\(370\) 0 0
\(371\) −2.38632e19 −1.28063
\(372\) 0 0
\(373\) 9.93056e18 0.511868 0.255934 0.966694i \(-0.417617\pi\)
0.255934 + 0.966694i \(0.417617\pi\)
\(374\) 0 0
\(375\) 1.26698e19 9.63816e18i 0.627386 0.477265i
\(376\) 0 0
\(377\) 4.18209e19i 1.98991i
\(378\) 0 0
\(379\) 4.08110e19i 1.86631i 0.359480 + 0.933153i \(0.382954\pi\)
−0.359480 + 0.933153i \(0.617046\pi\)
\(380\) 0 0
\(381\) −4.95339e18 + 3.76814e18i −0.217753 + 0.165650i
\(382\) 0 0
\(383\) −2.12130e19 −0.896626 −0.448313 0.893877i \(-0.647975\pi\)
−0.448313 + 0.893877i \(0.647975\pi\)
\(384\) 0 0
\(385\) −1.06314e19 −0.432149
\(386\) 0 0
\(387\) −7.90158e18 2.18804e18i −0.308945 0.0855505i
\(388\) 0 0
\(389\) 3.25171e19i 1.22318i −0.791176 0.611588i \(-0.790531\pi\)
0.791176 0.611588i \(-0.209469\pi\)
\(390\) 0 0
\(391\) 1.25990e19i 0.456049i
\(392\) 0 0
\(393\) 1.32404e19 + 1.74051e19i 0.461273 + 0.606364i
\(394\) 0 0
\(395\) 1.47165e19 0.493544
\(396\) 0 0
\(397\) −3.17360e19 −1.02476 −0.512382 0.858758i \(-0.671237\pi\)
−0.512382 + 0.858758i \(0.671237\pi\)
\(398\) 0 0
\(399\) 2.23284e18 + 2.93516e18i 0.0694321 + 0.0912715i
\(400\) 0 0
\(401\) 5.30666e19i 1.58942i −0.606989 0.794710i \(-0.707623\pi\)
0.606989 0.794710i \(-0.292377\pi\)
\(402\) 0 0
\(403\) 3.04228e19i 0.877831i
\(404\) 0 0
\(405\) 8.05571e18 1.34303e19i 0.223971 0.373398i
\(406\) 0 0
\(407\) 1.36708e19 0.366300
\(408\) 0 0
\(409\) −2.32775e19 −0.601189 −0.300595 0.953752i \(-0.597185\pi\)
−0.300595 + 0.953752i \(0.597185\pi\)
\(410\) 0 0
\(411\) −5.97844e19 + 4.54792e19i −1.48859 + 1.13240i
\(412\) 0 0
\(413\) 1.15526e18i 0.0277367i
\(414\) 0 0
\(415\) 3.14517e19i 0.728255i
\(416\) 0 0
\(417\) 5.77031e19 4.38959e19i 1.28878 0.980401i
\(418\) 0 0
\(419\) −6.13766e19 −1.32251 −0.661253 0.750163i \(-0.729975\pi\)
−0.661253 + 0.750163i \(0.729975\pi\)
\(420\) 0 0
\(421\) −3.49520e19 −0.726703 −0.363351 0.931652i \(-0.618368\pi\)
−0.363351 + 0.931652i \(0.618368\pi\)
\(422\) 0 0
\(423\) −5.27127e18 + 1.90359e19i −0.105770 + 0.381963i
\(424\) 0 0
\(425\) 1.82688e19i 0.353829i
\(426\) 0 0
\(427\) 2.64670e19i 0.494876i
\(428\) 0 0
\(429\) 4.45907e19 + 5.86164e19i 0.805034 + 1.05825i
\(430\) 0 0
\(431\) −6.15689e17 −0.0107345 −0.00536725 0.999986i \(-0.501708\pi\)
−0.00536725 + 0.999986i \(0.501708\pi\)
\(432\) 0 0
\(433\) −6.85272e19 −1.15399 −0.576997 0.816746i \(-0.695776\pi\)
−0.576997 + 0.816746i \(0.695776\pi\)
\(434\) 0 0
\(435\) 2.86725e19 + 3.76913e19i 0.466441 + 0.613157i
\(436\) 0 0
\(437\) 9.07843e18i 0.142692i
\(438\) 0 0
\(439\) 7.27308e18i 0.110467i −0.998473 0.0552337i \(-0.982410\pi\)
0.998473 0.0552337i \(-0.0175904\pi\)
\(440\) 0 0
\(441\) −5.36812e18 + 1.93857e19i −0.0788011 + 0.284572i
\(442\) 0 0
\(443\) −8.96453e19 −1.27204 −0.636018 0.771674i \(-0.719420\pi\)
−0.636018 + 0.771674i \(0.719420\pi\)
\(444\) 0 0
\(445\) 4.26935e19 0.585681
\(446\) 0 0
\(447\) 1.89886e19 1.44450e19i 0.251875 0.191607i
\(448\) 0 0
\(449\) 2.97759e19i 0.381959i −0.981594 0.190980i \(-0.938834\pi\)
0.981594 0.190980i \(-0.0611665\pi\)
\(450\) 0 0
\(451\) 4.04722e19i 0.502149i
\(452\) 0 0
\(453\) 7.82374e19 5.95168e19i 0.939026 0.714336i
\(454\) 0 0
\(455\) 3.54013e19 0.411087
\(456\) 0 0
\(457\) −5.35657e19 −0.601887 −0.300944 0.953642i \(-0.597302\pi\)
−0.300944 + 0.953642i \(0.597302\pi\)
\(458\) 0 0
\(459\) 1.48992e19 + 3.72829e19i 0.162020 + 0.405429i
\(460\) 0 0
\(461\) 1.88829e20i 1.98752i 0.111527 + 0.993761i \(0.464426\pi\)
−0.111527 + 0.993761i \(0.535574\pi\)
\(462\) 0 0
\(463\) 2.55431e19i 0.260265i −0.991497 0.130133i \(-0.958460\pi\)
0.991497 0.130133i \(-0.0415403\pi\)
\(464\) 0 0
\(465\) 2.08579e19 + 2.74187e19i 0.205766 + 0.270489i
\(466\) 0 0
\(467\) −5.46072e19 −0.521642 −0.260821 0.965387i \(-0.583993\pi\)
−0.260821 + 0.965387i \(0.583993\pi\)
\(468\) 0 0
\(469\) −1.59992e20 −1.48014
\(470\) 0 0
\(471\) −1.09659e20 1.44152e20i −0.982628 1.29171i
\(472\) 0 0
\(473\) 4.36619e19i 0.379004i
\(474\) 0 0
\(475\) 1.31639e19i 0.110709i
\(476\) 0 0
\(477\) 1.80410e20 + 4.99576e19i 1.47019 + 0.407112i
\(478\) 0 0
\(479\) 1.65419e20 1.30638 0.653188 0.757196i \(-0.273431\pi\)
0.653188 + 0.757196i \(0.273431\pi\)
\(480\) 0 0
\(481\) −4.55224e19 −0.348447
\(482\) 0 0
\(483\) 9.40559e19 7.15502e19i 0.697883 0.530894i
\(484\) 0 0
\(485\) 2.85372e19i 0.205280i
\(486\) 0 0
\(487\) 5.27556e19i 0.367960i −0.982930 0.183980i \(-0.941102\pi\)
0.982930 0.183980i \(-0.0588982\pi\)
\(488\) 0 0
\(489\) 1.51320e20 1.15112e20i 1.02348 0.778585i
\(490\) 0 0
\(491\) 2.76893e20 1.81636 0.908178 0.418584i \(-0.137474\pi\)
0.908178 + 0.418584i \(0.137474\pi\)
\(492\) 0 0
\(493\) −1.21410e20 −0.772506
\(494\) 0 0
\(495\) 8.03751e19 + 2.22568e19i 0.496115 + 0.137380i
\(496\) 0 0
\(497\) 1.51240e20i 0.905717i
\(498\) 0 0
\(499\) 1.21401e20i 0.705453i −0.935726 0.352727i \(-0.885255\pi\)
0.935726 0.352727i \(-0.114745\pi\)
\(500\) 0 0
\(501\) −5.15235e19 6.77299e19i −0.290551 0.381942i
\(502\) 0 0
\(503\) −1.34169e20 −0.734330 −0.367165 0.930156i \(-0.619672\pi\)
−0.367165 + 0.930156i \(0.619672\pi\)
\(504\) 0 0
\(505\) −6.77672e19 −0.360026
\(506\) 0 0
\(507\) −3.10909e19 4.08704e19i −0.160352 0.210790i
\(508\) 0 0
\(509\) 1.59029e20i 0.796328i −0.917314 0.398164i \(-0.869647\pi\)
0.917314 0.398164i \(-0.130353\pi\)
\(510\) 0 0
\(511\) 1.22162e20i 0.593989i
\(512\) 0 0
\(513\) −1.07359e19 2.68648e19i −0.0506941 0.126854i
\(514\) 0 0
\(515\) 1.42243e20 0.652343
\(516\) 0 0
\(517\) −1.05187e20 −0.468580
\(518\) 0 0
\(519\) 1.12462e20 8.55521e19i 0.486688 0.370233i
\(520\) 0 0
\(521\) 2.22638e20i 0.936087i 0.883706 + 0.468043i \(0.155041\pi\)
−0.883706 + 0.468043i \(0.844959\pi\)
\(522\) 0 0
\(523\) 4.79645e20i 1.95955i −0.200093 0.979777i \(-0.564124\pi\)
0.200093 0.979777i \(-0.435876\pi\)
\(524\) 0 0
\(525\) −1.36383e20 + 1.03749e20i −0.541457 + 0.411898i
\(526\) 0 0
\(527\) −8.83200e19 −0.340784
\(528\) 0 0
\(529\) 2.42788e19 0.0910563
\(530\) 0 0
\(531\) −2.41854e18 + 8.73398e18i −0.00881747 + 0.0318422i
\(532\) 0 0
\(533\) 1.34768e20i 0.477676i
\(534\) 0 0
\(535\) 1.75252e20i 0.603963i
\(536\) 0 0
\(537\) 3.15519e20 + 4.14763e20i 1.05735 + 1.38993i
\(538\) 0 0
\(539\) −1.07120e20 −0.349103
\(540\) 0 0
\(541\) 4.62548e20 1.46615 0.733074 0.680149i \(-0.238085\pi\)
0.733074 + 0.680149i \(0.238085\pi\)
\(542\) 0 0
\(543\) 1.45942e20 + 1.91847e20i 0.449968 + 0.591503i
\(544\) 0 0
\(545\) 6.60777e19i 0.198190i
\(546\) 0 0
\(547\) 1.52374e20i 0.444638i 0.974974 + 0.222319i \(0.0713626\pi\)
−0.974974 + 0.222319i \(0.928637\pi\)
\(548\) 0 0
\(549\) 5.54087e19 2.00095e20i 0.157321 0.568126i
\(550\) 0 0
\(551\) 8.74838e19 0.241708
\(552\) 0 0
\(553\) −3.53888e20 −0.951541
\(554\) 0 0
\(555\) −4.10273e19 + 3.12103e19i −0.107368 + 0.0816771i
\(556\) 0 0
\(557\) 5.19363e20i 1.32299i 0.749949 + 0.661495i \(0.230078\pi\)
−0.749949 + 0.661495i \(0.769922\pi\)
\(558\) 0 0
\(559\) 1.45389e20i 0.360532i
\(560\) 0 0
\(561\) −1.70168e20 + 1.29451e20i −0.410826 + 0.312523i
\(562\) 0 0
\(563\) 1.10226e20 0.259102 0.129551 0.991573i \(-0.458646\pi\)
0.129551 + 0.991573i \(0.458646\pi\)
\(564\) 0 0
\(565\) 1.46523e19 0.0335385
\(566\) 0 0
\(567\) −1.93716e20 + 3.22958e20i −0.431810 + 0.719903i
\(568\) 0 0
\(569\) 1.11868e20i 0.242864i 0.992600 + 0.121432i \(0.0387486\pi\)
−0.992600 + 0.121432i \(0.961251\pi\)
\(570\) 0 0
\(571\) 2.44274e20i 0.516543i 0.966072 + 0.258271i \(0.0831529\pi\)
−0.966072 + 0.258271i \(0.916847\pi\)
\(572\) 0 0
\(573\) −2.98611e20 3.92537e20i −0.615101 0.808577i
\(574\) 0 0
\(575\) −4.21830e20 −0.846504
\(576\) 0 0
\(577\) 2.24168e20 0.438284 0.219142 0.975693i \(-0.429674\pi\)
0.219142 + 0.975693i \(0.429674\pi\)
\(578\) 0 0
\(579\) −5.35549e20 7.04002e20i −1.02026 1.34117i
\(580\) 0 0
\(581\) 7.56321e20i 1.40406i
\(582\) 0 0
\(583\) 9.96895e20i 1.80358i
\(584\) 0 0
\(585\) −2.67640e20 7.41127e19i −0.471935 0.130684i
\(586\) 0 0
\(587\) −1.36189e19 −0.0234075 −0.0117038 0.999932i \(-0.503726\pi\)
−0.0117038 + 0.999932i \(0.503726\pi\)
\(588\) 0 0
\(589\) 6.36404e19 0.106627
\(590\) 0 0
\(591\) −7.31497e20 + 5.56464e20i −1.19483 + 0.908932i
\(592\) 0 0
\(593\) 5.06250e20i 0.806222i −0.915151 0.403111i \(-0.867929\pi\)
0.915151 0.403111i \(-0.132071\pi\)
\(594\) 0 0
\(595\) 1.02773e20i 0.159589i
\(596\) 0 0
\(597\) −3.46593e20 + 2.63661e20i −0.524823 + 0.399243i
\(598\) 0 0
\(599\) −1.02091e21 −1.50760 −0.753802 0.657102i \(-0.771782\pi\)
−0.753802 + 0.657102i \(0.771782\pi\)
\(600\) 0 0
\(601\) 1.06150e21 1.52884 0.764421 0.644717i \(-0.223025\pi\)
0.764421 + 0.644717i \(0.223025\pi\)
\(602\) 0 0
\(603\) 1.20957e21 + 3.34944e20i 1.69922 + 0.470535i
\(604\) 0 0
\(605\) 1.26390e20i 0.173200i
\(606\) 0 0
\(607\) 4.51118e20i 0.603080i 0.953453 + 0.301540i \(0.0975007\pi\)
−0.953453 + 0.301540i \(0.902499\pi\)
\(608\) 0 0
\(609\) −6.89490e20 9.06364e20i −0.899287 1.18215i
\(610\) 0 0
\(611\) 3.50262e20 0.445743
\(612\) 0 0
\(613\) 4.84225e20 0.601304 0.300652 0.953734i \(-0.402796\pi\)
0.300652 + 0.953734i \(0.402796\pi\)
\(614\) 0 0
\(615\) −9.23974e19 1.21460e20i −0.111969 0.147188i
\(616\) 0 0
\(617\) 1.04009e21i 1.23008i 0.788497 + 0.615038i \(0.210859\pi\)
−0.788497 + 0.615038i \(0.789141\pi\)
\(618\) 0 0
\(619\) 5.15454e19i 0.0594990i −0.999557 0.0297495i \(-0.990529\pi\)
0.999557 0.0297495i \(-0.00947096\pi\)
\(620\) 0 0
\(621\) −8.60870e20 + 3.44026e20i −0.969953 + 0.387619i
\(622\) 0 0
\(623\) −1.02665e21 −1.12918
\(624\) 0 0
\(625\) 4.35092e20 0.467177
\(626\) 0 0
\(627\) 1.22618e20 9.32777e19i 0.128542 0.0977848i
\(628\) 0 0
\(629\) 1.32156e20i 0.135271i
\(630\) 0 0
\(631\) 2.22096e20i 0.221984i −0.993821 0.110992i \(-0.964597\pi\)
0.993821 0.110992i \(-0.0354028\pi\)
\(632\) 0 0
\(633\) −3.45665e20 + 2.62954e20i −0.337386 + 0.256656i
\(634\) 0 0
\(635\) 1.24975e20 0.119130
\(636\) 0 0
\(637\) 3.56697e20 0.332089
\(638\) 0 0
\(639\) −3.16620e20 + 1.14340e21i −0.287927 + 1.03978i
\(640\) 0 0
\(641\) 5.19914e19i 0.0461845i 0.999733 + 0.0230922i \(0.00735114\pi\)
−0.999733 + 0.0230922i \(0.992649\pi\)
\(642\) 0 0
\(643\) 6.41865e20i 0.557008i −0.960435 0.278504i \(-0.910161\pi\)
0.960435 0.278504i \(-0.0898385\pi\)
\(644\) 0 0
\(645\) 9.96794e19 + 1.31033e20i 0.0845099 + 0.111092i
\(646\) 0 0
\(647\) 1.59499e21 1.32122 0.660611 0.750729i \(-0.270297\pi\)
0.660611 + 0.750729i \(0.270297\pi\)
\(648\) 0 0
\(649\) −4.82615e19 −0.0390630
\(650\) 0 0
\(651\) −5.01572e20 6.59338e20i −0.396712 0.521496i
\(652\) 0 0
\(653\) 3.61572e17i 0.000279477i −1.00000 0.000139739i \(-0.999956\pi\)
1.00000 0.000139739i \(-4.44802e-5\pi\)
\(654\) 0 0
\(655\) 4.39136e20i 0.331733i
\(656\) 0 0
\(657\) −2.55746e20 + 9.23564e20i −0.188829 + 0.681910i
\(658\) 0 0
\(659\) 9.68333e20 0.698851 0.349425 0.936964i \(-0.386377\pi\)
0.349425 + 0.936964i \(0.386377\pi\)
\(660\) 0 0
\(661\) 1.92498e21 1.35805 0.679025 0.734115i \(-0.262403\pi\)
0.679025 + 0.734115i \(0.262403\pi\)
\(662\) 0 0
\(663\) 5.66643e20 4.31057e20i 0.390803 0.297292i
\(664\) 0 0
\(665\) 7.40548e19i 0.0499334i
\(666\) 0 0
\(667\) 2.80338e21i 1.84815i
\(668\) 0 0
\(669\) −1.34508e21 + 1.02323e21i −0.867065 + 0.659594i
\(670\) 0 0
\(671\) 1.10567e21 0.696959
\(672\) 0 0
\(673\) 5.09103e20 0.313829 0.156914 0.987612i \(-0.449845\pi\)
0.156914 + 0.987612i \(0.449845\pi\)
\(674\) 0 0
\(675\) 1.24828e21 4.98844e20i 0.752545 0.300737i
\(676\) 0 0
\(677\) 1.96477e21i 1.15850i 0.815148 + 0.579252i \(0.196655\pi\)
−0.815148 + 0.579252i \(0.803345\pi\)
\(678\) 0 0
\(679\) 6.86234e20i 0.395776i
\(680\) 0 0
\(681\) −1.20315e21 1.58160e21i −0.678762 0.892262i
\(682\) 0 0
\(683\) 2.40991e20 0.132998 0.0664991 0.997786i \(-0.478817\pi\)
0.0664991 + 0.997786i \(0.478817\pi\)
\(684\) 0 0
\(685\) 1.50837e21 0.814385
\(686\) 0 0
\(687\) −1.48699e21 1.95471e21i −0.785474 1.03254i
\(688\) 0 0
\(689\) 3.31955e21i 1.71568i
\(690\) 0 0
\(691\) 9.40696e20i 0.475734i −0.971298 0.237867i \(-0.923552\pi\)
0.971298 0.237867i \(-0.0764482\pi\)
\(692\) 0 0
\(693\) −1.93278e21 5.35210e20i −0.956498 0.264865i
\(694\) 0 0
\(695\) −1.45586e21 −0.705073
\(696\) 0 0
\(697\) 3.91244e20 0.185439
\(698\) 0 0
\(699\) 1.21054e21 9.20883e20i 0.561565 0.427194i
\(700\) 0 0
\(701\) 2.13672e21i 0.970201i −0.874458 0.485101i \(-0.838783\pi\)
0.874458 0.485101i \(-0.161217\pi\)
\(702\) 0 0
\(703\) 9.52268e19i 0.0423247i
\(704\) 0 0
\(705\) 3.15675e20 2.40141e20i 0.137348 0.104483i
\(706\) 0 0
\(707\) 1.62960e21 0.694122
\(708\) 0 0
\(709\) −5.05315e20 −0.210724 −0.105362 0.994434i \(-0.533600\pi\)
−0.105362 + 0.994434i \(0.533600\pi\)
\(710\) 0 0
\(711\) 2.67546e21 + 7.40865e20i 1.09239 + 0.302494i
\(712\) 0 0
\(713\) 2.03933e21i 0.815296i
\(714\) 0 0
\(715\) 1.47891e21i 0.578955i
\(716\) 0 0
\(717\) 2.78234e20 + 3.65750e20i 0.106664 + 0.140214i
\(718\) 0 0
\(719\) 1.96314e21 0.737030 0.368515 0.929622i \(-0.379866\pi\)
0.368515 + 0.929622i \(0.379866\pi\)
\(720\) 0 0
\(721\) −3.42052e21 −1.25770
\(722\) 0 0
\(723\) −8.37393e20 1.10079e21i −0.301573 0.396430i
\(724\) 0 0
\(725\) 4.06494e21i 1.43390i
\(726\) 0 0
\(727\) 1.15913e21i 0.400519i 0.979743 + 0.200259i \(0.0641785\pi\)
−0.979743 + 0.200259i \(0.935822\pi\)
\(728\) 0 0
\(729\) 2.14064e21 2.03608e21i 0.724582 0.689189i
\(730\) 0 0
\(731\) −4.22078e20 −0.139963
\(732\) 0 0
\(733\) 2.01215e21 0.653703 0.326852 0.945076i \(-0.394012\pi\)
0.326852 + 0.945076i \(0.394012\pi\)
\(734\) 0 0
\(735\) 3.21475e20 2.44553e20i 0.102327 0.0778426i
\(736\) 0 0
\(737\) 6.68374e21i 2.08455i
\(738\) 0 0
\(739\) 3.78711e21i 1.15738i 0.815549 + 0.578688i \(0.196435\pi\)
−0.815549 + 0.578688i \(0.803565\pi\)
\(740\) 0 0
\(741\) −4.08303e20 + 3.10605e20i −0.122277 + 0.0930190i
\(742\) 0 0
\(743\) −3.73122e21 −1.09505 −0.547525 0.836789i \(-0.684430\pi\)
−0.547525 + 0.836789i \(0.684430\pi\)
\(744\) 0 0
\(745\) −4.79086e20 −0.137798
\(746\) 0 0
\(747\) −1.58336e21 + 5.71792e21i −0.446349 + 1.61188i
\(748\) 0 0
\(749\) 4.21430e21i 1.16443i
\(750\) 0 0
\(751\) 1.59970e21i 0.433251i −0.976255 0.216626i \(-0.930495\pi\)
0.976255 0.216626i \(-0.0695051\pi\)
\(752\) 0 0
\(753\) 3.19650e21 + 4.20193e21i 0.848617 + 1.11554i
\(754\) 0 0
\(755\) −1.97395e21 −0.513728
\(756\) 0 0
\(757\) 1.89582e21 0.483702 0.241851 0.970313i \(-0.422245\pi\)
0.241851 + 0.970313i \(0.422245\pi\)
\(758\) 0 0
\(759\) −2.98904e21 3.92922e21i −0.747685 0.982864i
\(760\) 0 0
\(761\) 2.60427e21i 0.638706i 0.947636 + 0.319353i \(0.103466\pi\)
−0.947636 + 0.319353i \(0.896534\pi\)
\(762\) 0 0
\(763\) 1.58897e21i 0.382105i
\(764\) 0 0
\(765\) 2.15156e20 7.76983e20i 0.0507332 0.183211i
\(766\) 0 0
\(767\) 1.60706e20 0.0371592
\(768\) 0 0
\(769\) −1.38301e21 −0.313601 −0.156801 0.987630i \(-0.550118\pi\)
−0.156801 + 0.987630i \(0.550118\pi\)
\(770\) 0 0
\(771\) −4.78201e21 + 3.63777e21i −1.06341 + 0.808961i
\(772\) 0 0
\(773\) 2.47373e21i 0.539519i −0.962928 0.269760i \(-0.913056\pi\)
0.962928 0.269760i \(-0.0869442\pi\)
\(774\) 0 0