Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1133,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.1133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.d (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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.4 | ||
Root | \(-0.0967785 - 1.72934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1133 |
Dual form | 1134.2.d.a.1133.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.366598 | −0.163948 | −0.0819738 | − | 0.996634i | \(-0.526122\pi\) | ||||
−0.0819738 | + | 0.996634i | \(0.526122\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.91449 | + | 1.82612i | −0.723609 | + | 0.690210i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.366598i | 0.115929i | ||||||||
\(11\) | − | 0.669453i | − | 0.201848i | −0.994894 | − | 0.100924i | \(-0.967820\pi\) | ||
0.994894 | − | 0.100924i | \(-0.0321799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00156i | 0.277784i | 0.990308 | + | 0.138892i | \(0.0443541\pi\) | ||||
−0.990308 | + | 0.138892i | \(0.955646\pi\) | |||||||
\(14\) | 1.82612 | + | 1.91449i | 0.488052 | + | 0.511669i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.98906 | 1.21003 | 0.605013 | − | 0.796216i | \(-0.293168\pi\) | ||||
0.605013 | + | 0.796216i | \(0.293168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.35722i | − | 1.45845i | −0.684275 | − | 0.729224i | \(-0.739881\pi\) | ||
0.684275 | − | 0.729224i | \(-0.260119\pi\) | |||||||
\(20\) | 0.366598 | 0.0819738 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.669453 | −0.142728 | ||||||||
\(23\) | − | 7.69459i | − | 1.60443i | −0.597034 | − | 0.802216i | \(-0.703654\pi\) | ||
0.597034 | − | 0.802216i | \(-0.296346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86561 | −0.973121 | ||||||||
\(26\) | 1.00156 | 0.196423 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.91449 | − | 1.82612i | 0.361805 | − | 0.345105i | ||||
\(29\) | − | 1.82898i | − | 0.339633i | −0.985476 | − | 0.169817i | \(-0.945682\pi\) | ||
0.985476 | − | 0.169817i | \(-0.0543175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32588i | − | 1.13616i | −0.822973 | − | 0.568081i | \(-0.807686\pi\) | ||
0.822973 | − | 0.568081i | \(-0.192314\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.98906i | − | 0.855617i | ||||||
\(35\) | 0.701849 | − | 0.669453i | 0.118634 | − | 0.113158i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.16789 | −0.849595 | −0.424798 | − | 0.905288i | \(-0.639655\pi\) | ||||
−0.424798 | + | 0.905288i | \(0.639655\pi\) | |||||||
\(38\) | −6.35722 | −1.03128 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.366598i | − | 0.0579643i | ||||||
\(41\) | −4.31856 | −0.674446 | −0.337223 | − | 0.941425i | \(-0.609488\pi\) | ||||
−0.337223 | + | 0.941425i | \(0.609488\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.49843 | −0.686005 | −0.343002 | − | 0.939335i | \(-0.611444\pi\) | ||||
−0.343002 | + | 0.939335i | \(0.611444\pi\) | |||||||
\(44\) | 0.669453i | 0.100924i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.69459 | −1.13450 | ||||||||
\(47\) | 8.32901 | 1.21491 | 0.607455 | − | 0.794354i | \(-0.292190\pi\) | ||||
0.607455 | + | 0.794354i | \(0.292190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.330547 | − | 6.99219i | 0.0472209 | − | 0.998884i | ||||
\(50\) | 4.86561i | 0.688101i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.00156i | − | 0.138892i | ||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.245420i | 0.0330925i | ||||||||
\(56\) | −1.82612 | − | 1.91449i | −0.244026 | − | 0.255835i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.82898 | −0.240157 | ||||||||
\(59\) | 8.72695 | 1.13615 | 0.568076 | − | 0.822976i | \(-0.307688\pi\) | ||||
0.568076 | + | 0.822976i | \(0.307688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.95771i | − | 0.634770i | −0.948297 | − | 0.317385i | \(-0.897195\pi\) | ||
0.948297 | − | 0.317385i | \(-0.102805\pi\) | |||||||
\(62\) | −6.32588 | −0.803387 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 0.367172i | − | 0.0455420i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8907 | −1.33052 | −0.665258 | − | 0.746614i | \(-0.731678\pi\) | ||||
−0.665258 | + | 0.746614i | \(0.731678\pi\) | |||||||
\(68\) | −4.98906 | −0.605013 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.669453 | − | 0.701849i | −0.0800150 | − | 0.0838869i | ||||
\(71\) | − | 5.49843i | − | 0.652544i | −0.945276 | − | 0.326272i | \(-0.894207\pi\) | ||
0.945276 | − | 0.326272i | \(-0.105793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.07314i | 0.476725i | 0.971176 | + | 0.238363i | \(0.0766106\pi\) | ||||
−0.971176 | + | 0.238363i | \(0.923389\pi\) | |||||||
\(74\) | 5.16789i | 0.600755i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.35722i | 0.729224i | ||||||||
\(77\) | 1.22250 | + | 1.28166i | 0.139317 | + | 0.146059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.35568 | 0.940087 | 0.470044 | − | 0.882643i | \(-0.344238\pi\) | ||||
0.470044 | + | 0.882643i | \(0.344238\pi\) | |||||||
\(80\) | −0.366598 | −0.0409869 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.31856i | 0.476905i | ||||||||
\(83\) | 17.0142 | 1.86756 | 0.933778 | − | 0.357852i | \(-0.116491\pi\) | ||||
0.933778 | + | 0.357852i | \(0.116491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.82898 | −0.198381 | ||||||||
\(86\) | 4.49843i | 0.485079i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.669453 | 0.0713640 | ||||||||
\(89\) | −10.7113 | −1.13540 | −0.567699 | − | 0.823236i | \(-0.692166\pi\) | ||||
−0.567699 | + | 0.823236i | \(0.692166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.82898 | − | 1.91749i | −0.191729 | − | 0.201007i | ||||
\(92\) | 7.69459i | 0.802216i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 8.32901i | − | 0.859071i | ||||||
\(95\) | 2.33055i | 0.239109i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.2157i | − | 1.74799i | −0.485932 | − | 0.873997i | \(-0.661520\pi\) | ||
0.485932 | − | 0.873997i | \(-0.338480\pi\) | |||||||
\(98\) | −6.99219 | − | 0.330547i | −0.706318 | − | 0.0333902i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.86561 | 0.486561 | ||||||||
\(101\) | −15.7317 | −1.56537 | −0.782683 | − | 0.622421i | \(-0.786149\pi\) | ||||
−0.782683 | + | 0.622421i | \(0.786149\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.4445i | 1.12766i | 0.825890 | + | 0.563831i | \(0.190673\pi\) | ||||
−0.825890 | + | 0.563831i | \(0.809327\pi\) | |||||||
\(104\) | −1.00156 | −0.0982115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.0618i | − | 1.06938i | −0.845048 | − | 0.534690i | \(-0.820428\pi\) | ||
0.845048 | − | 0.534690i | \(-0.179572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5633 | −1.01178 | −0.505891 | − | 0.862597i | \(-0.668836\pi\) | ||||
−0.505891 | + | 0.862597i | \(0.668836\pi\) | |||||||
\(110\) | 0.245420 | 0.0233999 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.91449 | + | 1.82612i | −0.180902 | + | 0.172552i | ||||
\(113\) | 4.15953i | 0.391295i | 0.980674 | + | 0.195648i | \(0.0626809\pi\) | ||||
−0.980674 | + | 0.195648i | \(0.937319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82082i | 0.263043i | ||||||||
\(116\) | 1.82898i | 0.169817i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.72695i | − | 0.803381i | ||||||
\(119\) | −9.55151 | + | 9.11064i | −0.875586 | + | 0.835171i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5518 | 0.959257 | ||||||||
\(122\) | −4.95771 | −0.448850 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.32588i | 0.568081i | ||||||||
\(125\) | 3.61671 | 0.323489 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.66945 | −0.148140 | −0.0740700 | − | 0.997253i | \(-0.523599\pi\) | ||||
−0.0740700 | + | 0.997253i | \(0.523599\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.367172 | −0.0322031 | ||||||||
\(131\) | 13.5321 | 1.18231 | 0.591154 | − | 0.806558i | \(-0.298672\pi\) | ||||
0.591154 | + | 0.806558i | \(0.298672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6091 | + | 12.1708i | 1.00663 | + | 1.05535i | ||||
\(134\) | 10.8907i | 0.940817i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.98906i | 0.427809i | ||||||||
\(137\) | − | 8.98851i | − | 0.767940i | −0.923346 | − | 0.383970i | \(-0.874557\pi\) | ||
0.923346 | − | 0.383970i | \(-0.125443\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.29922i | 0.788750i | 0.918950 | + | 0.394375i | \(0.129039\pi\) | ||||
−0.918950 | + | 0.394375i | \(0.870961\pi\) | |||||||
\(140\) | −0.701849 | + | 0.669453i | −0.0593170 | + | 0.0565791i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.49843 | −0.461418 | ||||||||
\(143\) | 0.670501 | 0.0560701 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.670501i | 0.0556821i | ||||||||
\(146\) | 4.07314 | 0.337096 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.16789 | 0.424798 | ||||||||
\(149\) | − | 2.83211i | − | 0.232016i | −0.993248 | − | 0.116008i | \(-0.962990\pi\) | ||
0.993248 | − | 0.116008i | \(-0.0370098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5518 | −1.34697 | −0.673484 | − | 0.739201i | \(-0.735203\pi\) | ||||
−0.673484 | + | 0.739201i | \(0.735203\pi\) | |||||||
\(152\) | 6.35722 | 0.515639 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.28166 | − | 1.22250i | 0.103279 | − | 0.0985122i | ||||
\(155\) | 2.31905i | 0.186271i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.83456i | − | 0.226222i | −0.993582 | − | 0.113111i | \(-0.963918\pi\) | ||
0.993582 | − | 0.113111i | \(-0.0360816\pi\) | |||||||
\(158\) | − | 8.35568i | − | 0.664742i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.366598i | 0.0289821i | ||||||||
\(161\) | 14.0513 | + | 14.7312i | 1.10739 | + | 1.16098i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.7281 | 1.93685 | 0.968426 | − | 0.249300i | \(-0.0802005\pi\) | ||||
0.968426 | + | 0.249300i | \(0.0802005\pi\) | |||||||
\(164\) | 4.31856 | 0.337223 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 17.0142i | − | 1.32056i | ||||||
\(167\) | −19.3484 | −1.49723 | −0.748614 | − | 0.663006i | \(-0.769280\pi\) | ||||
−0.748614 | + | 0.663006i | \(0.769280\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9969 | 0.922836 | ||||||||
\(170\) | 1.82898i | 0.140276i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.49843 | 0.343002 | ||||||||
\(173\) | −4.83654 | −0.367715 | −0.183858 | − | 0.982953i | \(-0.558859\pi\) | ||||
−0.183858 | + | 0.982953i | \(0.558859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.31516 | − | 8.88520i | 0.704160 | − | 0.671658i | ||||
\(176\) | − | 0.669453i | − | 0.0504619i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.7113i | 0.802847i | ||||||||
\(179\) | − | 3.65796i | − | 0.273409i | −0.990612 | − | 0.136704i | \(-0.956349\pi\) | ||
0.990612 | − | 0.136704i | \(-0.0436511\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.66796i | 0.421296i | 0.977562 | + | 0.210648i | \(0.0675574\pi\) | ||||
−0.977562 | + | 0.210648i | \(0.932443\pi\) | |||||||
\(182\) | −1.91749 | + | 1.82898i | −0.142134 | + | 0.135573i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.69459 | 0.567252 | ||||||||
\(185\) | 1.89454 | 0.139289 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.33994i | − | 0.244241i | ||||||
\(188\) | −8.32901 | −0.607455 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.33055 | 0.169076 | ||||||||
\(191\) | − | 27.3777i | − | 1.98098i | −0.137587 | − | 0.990490i | \(-0.543935\pi\) | ||
0.137587 | − | 0.990490i | \(-0.456065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0283 | −0.721850 | −0.360925 | − | 0.932595i | \(-0.617539\pi\) | ||||
−0.360925 | + | 0.932595i | \(0.617539\pi\) | |||||||
\(194\) | −17.2157 | −1.23602 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.330547 | + | 6.99219i | −0.0236105 | + | 0.499442i | ||||
\(197\) | 18.8258i | 1.34129i | 0.741780 | + | 0.670643i | \(0.233982\pi\) | ||||
−0.741780 | + | 0.670643i | \(0.766018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.36406i | − | 0.380248i | −0.981760 | − | 0.190124i | \(-0.939111\pi\) | ||
0.981760 | − | 0.190124i | \(-0.0608890\pi\) | |||||||
\(200\) | − | 4.86561i | − | 0.344050i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.7317i | 1.10688i | ||||||||
\(203\) | 3.33994 | + | 3.50157i | 0.234418 | + | 0.245762i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.58318 | 0.110574 | ||||||||
\(206\) | 11.4445 | 0.797377 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00156i | 0.0694460i | ||||||||
\(209\) | −4.25587 | −0.294384 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.65796 | 0.114139 | 0.0570694 | − | 0.998370i | \(-0.481824\pi\) | ||||
0.0570694 | + | 0.998370i | \(0.481824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.0618 | −0.756166 | ||||||||
\(215\) | 1.64912 | 0.112469 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5518 | + | 12.1108i | 0.784189 | + | 0.822137i | ||||
\(218\) | 10.5633i | 0.715439i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 0.245420i | − | 0.0165462i | ||||||
\(221\) | 4.99687i | 0.336126i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.0372i | 1.14090i | 0.821334 | + | 0.570448i | \(0.193230\pi\) | ||||
−0.821334 | + | 0.570448i | \(0.806770\pi\) | |||||||
\(224\) | 1.82612 | + | 1.91449i | 0.122013 | + | 0.127917i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.15953 | 0.276688 | ||||||||
\(227\) | 5.11024 | 0.339179 | 0.169589 | − | 0.985515i | \(-0.445756\pi\) | ||||
0.169589 | + | 0.985515i | \(0.445756\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.2669i | 1.00887i | 0.863451 | + | 0.504433i | \(0.168298\pi\) | ||||
−0.863451 | + | 0.504433i | \(0.831702\pi\) | |||||||
\(230\) | 2.82082 | 0.185999 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.82898 | 0.120078 | ||||||||
\(233\) | − | 10.1930i | − | 0.667767i | −0.942614 | − | 0.333883i | \(-0.891641\pi\) | ||
0.942614 | − | 0.333883i | \(-0.108359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.05340 | −0.199182 | ||||||||
\(236\) | −8.72695 | −0.568076 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.11064 | + | 9.55151i | 0.590555 | + | 0.619132i | ||||
\(239\) | − | 19.1815i | − | 1.24075i | −0.784305 | − | 0.620375i | \(-0.786980\pi\) | ||
0.784305 | − | 0.620375i | \(-0.213020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6853i | 1.33245i | 0.745749 | + | 0.666227i | \(0.232092\pi\) | ||||
−0.745749 | + | 0.666227i | \(0.767908\pi\) | |||||||
\(242\) | − | 10.5518i | − | 0.678297i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.95771i | 0.317385i | ||||||||
\(245\) | −0.121178 | + | 2.56332i | −0.00774176 | + | 0.163765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.36717 | 0.405133 | ||||||||
\(248\) | 6.32588 | 0.401694 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 3.61671i | − | 0.228741i | ||||||
\(251\) | 1.81200 | 0.114373 | 0.0571864 | − | 0.998364i | \(-0.481787\pi\) | ||||
0.0571864 | + | 0.998364i | \(0.481787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.15117 | −0.323851 | ||||||||
\(254\) | 1.66945i | 0.104751i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.45545 | 0.402680 | 0.201340 | − | 0.979521i | \(-0.435470\pi\) | ||||
0.201340 | + | 0.979521i | \(0.435470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.89387 | − | 9.43720i | 0.614775 | − | 0.586399i | ||||
\(260\) | 0.367172i | 0.0227710i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 13.5321i | − | 0.836018i | ||||||
\(263\) | 8.82062i | 0.543903i | 0.962311 | + | 0.271951i | \(0.0876690\pi\) | ||||
−0.962311 | + | 0.271951i | \(0.912331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.1708 | − | 11.6091i | 0.746242 | − | 0.711798i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.8907 | 0.665258 | ||||||||
\(269\) | −14.2653 | −0.869773 | −0.434886 | − | 0.900485i | \(-0.643212\pi\) | ||||
−0.434886 | + | 0.900485i | \(0.643212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.05281i | 0.185445i | 0.995692 | + | 0.0927226i | \(0.0295570\pi\) | ||||
−0.995692 | + | 0.0927226i | \(0.970443\pi\) | |||||||
\(272\) | 4.98906 | 0.302506 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.98851 | −0.543016 | ||||||||
\(275\) | 3.25730i | 0.196422i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.26566 | 0.0760459 | 0.0380230 | − | 0.999277i | \(-0.487894\pi\) | ||||
0.0380230 | + | 0.999277i | \(0.487894\pi\) | |||||||
\(278\) | 9.29922 | 0.557730 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.669453 | + | 0.701849i | 0.0400075 | + | 0.0419435i | ||||
\(281\) | − | 10.5267i | − | 0.627970i | −0.949428 | − | 0.313985i | \(-0.898336\pi\) | ||
0.949428 | − | 0.313985i | \(-0.101664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8718i | 1.18125i | 0.806945 | + | 0.590627i | \(0.201119\pi\) | ||||
−0.806945 | + | 0.590627i | \(0.798881\pi\) | |||||||
\(284\) | 5.49843i | 0.326272i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.670501i | − | 0.0396475i | ||||||
\(287\) | 8.26784 | − | 7.88623i | 0.488035 | − | 0.465509i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.89074 | 0.464161 | ||||||||
\(290\) | 0.670501 | 0.0393732 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 4.07314i | − | 0.238363i | ||||||
\(293\) | 13.4121 | 0.783544 | 0.391772 | − | 0.920062i | \(-0.371862\pi\) | ||||
0.391772 | + | 0.920062i | \(0.371862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.19928 | −0.186270 | ||||||||
\(296\) | − | 5.16789i | − | 0.300377i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.83211 | −0.164060 | ||||||||
\(299\) | 7.70663 | 0.445686 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.61221 | − | 8.21470i | 0.496399 | − | 0.473487i | ||||
\(302\) | 16.5518i | 0.952451i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.35722i | − | 0.364612i | ||||||
\(305\) | 1.81749i | 0.104069i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.653728i | 0.0373102i | 0.999826 | + | 0.0186551i | \(0.00593845\pi\) | ||||
−0.999826 | + | 0.0186551i | \(0.994062\pi\) | |||||||
\(308\) | −1.22250 | − | 1.28166i | −0.0696587 | − | 0.0730295i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.31905 | 0.131713 | ||||||||
\(311\) | 9.24493 | 0.524232 | 0.262116 | − | 0.965036i | \(-0.415580\pi\) | ||||
0.262116 | + | 0.965036i | \(0.415580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.16414i | − | 0.348418i | −0.984709 | − | 0.174209i | \(-0.944263\pi\) | ||
0.984709 | − | 0.174209i | \(-0.0557368\pi\) | |||||||
\(314\) | −2.83456 | −0.159963 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.35568 | −0.470044 | ||||||||
\(317\) | 20.6548i | 1.16009i | 0.814584 | + | 0.580045i | \(0.196965\pi\) | ||||
−0.814584 | + | 0.580045i | \(0.803035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.22442 | −0.0685542 | ||||||||
\(320\) | 0.366598 | 0.0204935 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.7312 | − | 14.0513i | 0.820938 | − | 0.783046i | ||||
\(323\) | − | 31.7166i | − | 1.76476i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.87322i | − | 0.270318i | ||||||
\(326\) | − | 24.7281i | − | 1.36956i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4.31856i | − | 0.238453i | ||||||
\(329\) | −15.9458 | + | 15.2098i | −0.879121 | + | 0.838543i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7114 | 0.588750 | 0.294375 | − | 0.955690i | \(-0.404889\pi\) | ||||
0.294375 | + | 0.955690i | \(0.404889\pi\) | |||||||
\(332\) | −17.0142 | −0.933778 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.3484i | 1.05870i | ||||||||
\(335\) | 3.99252 | 0.218135 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.55183 | −0.411375 | −0.205687 | − | 0.978618i | \(-0.565943\pi\) | ||||
−0.205687 | + | 0.978618i | \(0.565943\pi\) | |||||||
\(338\) | − | 11.9969i | − | 0.652544i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.82898 | 0.0991904 | ||||||||
\(341\) | −4.23488 | −0.229332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.1358 | + | 13.9901i | 0.655270 | + | 0.755394i | ||||
\(344\) | − | 4.49843i | − | 0.242539i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.83654i | 0.260014i | ||||||||
\(347\) | − | 10.9320i | − | 0.586859i | −0.955981 | − | 0.293430i | \(-0.905203\pi\) | ||
0.955981 | − | 0.293430i | \(-0.0947967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.18429i | 0.0633936i | 0.999498 | + | 0.0316968i | \(0.0100911\pi\) | ||||
−0.999498 | + | 0.0316968i | \(0.989909\pi\) | |||||||
\(350\) | −8.88520 | − | 9.31516i | −0.474934 | − | 0.497916i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.669453 | −0.0356820 | ||||||||
\(353\) | 33.5824 | 1.78741 | 0.893706 | − | 0.448653i | \(-0.148096\pi\) | ||||
0.893706 | + | 0.448653i | \(0.148096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.01572i | 0.106983i | ||||||||
\(356\) | 10.7113 | 0.567699 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.65796 | −0.193329 | ||||||||
\(359\) | 10.1281i | 0.534542i | 0.963621 | + | 0.267271i | \(0.0861219\pi\) | ||||
−0.963621 | + | 0.267271i | \(0.913878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.4143 | −1.12707 | ||||||||
\(362\) | 5.66796 | 0.297901 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.82898 | + | 1.91749i | 0.0958646 | + | 0.100504i | ||||
\(365\) | − | 1.49321i | − | 0.0781580i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.0021i | − | 0.939701i | −0.882746 | − | 0.469850i | \(-0.844308\pi\) | ||
0.882746 | − | 0.469850i | \(-0.155692\pi\) | |||||||
\(368\) | − | 7.69459i | − | 0.401108i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1.89454i | − | 0.0984923i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4090 | 0.849627 | 0.424814 | − | 0.905281i | \(-0.360340\pi\) | ||||
0.424814 | + | 0.905281i | \(0.360340\pi\) | |||||||
\(374\) | −3.33994 | −0.172704 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.32901i | 0.429536i | ||||||||
\(377\) | 1.83184 | 0.0943447 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.91372 | −0.149668 | −0.0748339 | − | 0.997196i | \(-0.523843\pi\) | ||||
−0.0748339 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(380\) | − | 2.33055i | − | 0.119555i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27.3777 | −1.40076 | ||||||||
\(383\) | −8.57443 | −0.438133 | −0.219066 | − | 0.975710i | \(-0.570301\pi\) | ||||
−0.219066 | + | 0.975710i | \(0.570301\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.448168 | − | 0.469855i | −0.0228407 | − | 0.0239460i | ||||
\(386\) | 10.0283i | 0.510425i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.2157i | 0.873997i | ||||||||
\(389\) | 35.5539i | 1.80266i | 0.433137 | + | 0.901328i | \(0.357406\pi\) | ||||
−0.433137 | + | 0.901328i | \(0.642594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 38.3888i | − | 1.94140i | ||||||
\(392\) | 6.99219 | + | 0.330547i | 0.353159 | + | 0.0166951i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8258 | 0.948433 | ||||||||
\(395\) | −3.06318 | −0.154125 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.58034i | − | 0.179692i | −0.995956 | − | 0.0898460i | \(-0.971363\pi\) | ||
0.995956 | − | 0.0898460i | \(-0.0286375\pi\) | |||||||
\(398\) | −5.36406 | −0.268876 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.86561 | −0.243280 | ||||||||
\(401\) | 0.190871i | 0.00953167i | 0.999989 | + | 0.00476583i | \(0.00151702\pi\) | ||||
−0.999989 | + | 0.00476583i | \(0.998483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.33577 | 0.315607 | ||||||||
\(404\) | 15.7317 | 0.782683 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.50157 | − | 3.33994i | 0.173780 | − | 0.165759i | ||||
\(407\) | 3.45966i | 0.171489i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.47371i | 0.171764i | 0.996305 | + | 0.0858819i | \(0.0273708\pi\) | ||||
−0.996305 | + | 0.0858819i | \(0.972629\pi\) | |||||||
\(410\) | − | 1.58318i | − | 0.0781875i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 11.4445i | − | 0.563831i | ||||||
\(413\) | −16.7077 | + | 15.9365i | −0.822130 | + | 0.784183i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.23739 | −0.306182 | ||||||||
\(416\) | 1.00156 | 0.0491057 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.25587i | 0.208161i | ||||||||
\(419\) | 1.40791 | 0.0687809 | 0.0343905 | − | 0.999408i | \(-0.489051\pi\) | ||||
0.0343905 | + | 0.999408i | \(0.489051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3860 | −1.48093 | −0.740463 | − | 0.672098i | \(-0.765393\pi\) | ||||
−0.740463 | + | 0.672098i | \(0.765393\pi\) | |||||||
\(422\) | − | 1.65796i | − | 0.0807083i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.2748 | −1.17750 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.05340 | + | 9.49150i | 0.438125 | + | 0.459326i | ||||
\(428\) | 11.0618i | 0.534690i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 1.64912i | − | 0.0795275i | ||||||
\(431\) | 27.2747i | 1.31378i | 0.753988 | + | 0.656888i | \(0.228127\pi\) | ||||
−0.753988 | + | 0.656888i | \(0.771873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.15047i | 0.391686i | 0.980635 | + | 0.195843i | \(0.0627444\pi\) | ||||
−0.980635 | + | 0.195843i | \(0.937256\pi\) | |||||||
\(434\) | 12.1108 | − | 11.5518i | 0.581338 | − | 0.554506i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.5633 | 0.505891 | ||||||||
\(437\) | −48.9162 | −2.33998 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2404i | 0.584203i | 0.956387 | + | 0.292101i | \(0.0943545\pi\) | ||||
−0.956387 | + | 0.292101i | \(0.905646\pi\) | |||||||
\(440\) | −0.245420 | −0.0117000 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.99687 | 0.237677 | ||||||||
\(443\) | − | 8.00836i | − | 0.380489i | −0.981737 | − | 0.190244i | \(-0.939072\pi\) | ||
0.981737 | − | 0.190244i | \(-0.0609280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.92675 | 0.186146 | ||||||||
\(446\) | 17.0372 | 0.806735 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.91449 | − | 1.82612i | 0.0904512 | − | 0.0862762i | ||||
\(449\) | − | 14.5183i | − | 0.685163i | −0.939488 | − | 0.342581i | \(-0.888699\pi\) | ||
0.939488 | − | 0.342581i | \(-0.111301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.89108i | 0.136135i | ||||||||
\(452\) | − | 4.15953i | − | 0.195648i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 5.11024i | − | 0.239835i | ||||||
\(455\) | 0.670501 | + | 0.702947i | 0.0314336 | + | 0.0329547i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.95501 | 0.465676 | 0.232838 | − | 0.972516i | \(-0.425199\pi\) | ||||
0.232838 | + | 0.972516i | \(0.425199\pi\) | |||||||
\(458\) | 15.2669 | 0.713375 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 2.82082i | − | 0.131521i | ||||||
\(461\) | −32.3270 | −1.50562 | −0.752810 | − | 0.658237i | \(-0.771302\pi\) | ||||
−0.752810 | + | 0.658237i | \(0.771302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.45032 | 0.439193 | 0.219597 | − | 0.975591i | \(-0.429526\pi\) | ||||
0.219597 | + | 0.975591i | \(0.429526\pi\) | |||||||
\(464\) | − | 1.82898i | − | 0.0849083i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.1930 | −0.472183 | ||||||||
\(467\) | −20.6623 | −0.956138 | −0.478069 | − | 0.878322i | \(-0.658663\pi\) | ||||
−0.478069 | + | 0.878322i | \(0.658663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.8502 | − | 19.8878i | 0.962773 | − | 0.918335i | ||||
\(470\) | 3.05340i | 0.140843i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.72695i | 0.401691i | ||||||||
\(473\) | 3.01149i | 0.138469i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.9317i | 1.41925i | ||||||||
\(476\) | 9.55151 | − | 9.11064i | 0.437793 | − | 0.417586i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.1815 | −0.877343 | ||||||||
\(479\) | −10.1608 | −0.464261 | −0.232131 | − | 0.972685i | \(-0.574570\pi\) | ||||
−0.232131 | + | 0.972685i | \(0.574570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.17597i | − | 0.236004i | ||||||
\(482\) | 20.6853 | 0.942188 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5518 | −0.479629 | ||||||||
\(485\) | 6.31126i | 0.286579i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.2296 | −1.41515 | −0.707575 | − | 0.706638i | \(-0.750211\pi\) | ||||
−0.707575 | + | 0.706638i | \(0.750211\pi\) | |||||||
\(488\) | 4.95771 | 0.224425 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.56332 | + | 0.121178i | 0.115799 | + | 0.00547425i | ||||
\(491\) | 20.5899i | 0.929211i | 0.885518 | + | 0.464605i | \(0.153804\pi\) | ||||
−0.885518 | + | 0.464605i | \(0.846196\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.12490i | − | 0.410965i | ||||||
\(494\) | − | 6.36717i | − | 0.286473i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.32588i | − | 0.284040i | ||||||
\(497\) | 10.0408 | + | 10.5267i | 0.450392 | + | 0.472187i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.1533 | −1.12601 | −0.563007 | − | 0.826452i | \(-0.690356\pi\) | ||||
−0.563007 | + | 0.826452i | \(0.690356\pi\) | |||||||
\(500\) | −3.61671 | −0.161744 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 1.81200i | − | 0.0808737i | ||||||
\(503\) | 31.1553 | 1.38915 | 0.694574 | − | 0.719421i | \(-0.255593\pi\) | ||||
0.694574 | + | 0.719421i | \(0.255593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.76722 | 0.256638 | ||||||||
\(506\) | 5.15117i | 0.228997i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.66945 | 0.0740700 | ||||||||
\(509\) | −4.83347 | −0.214240 | −0.107120 | − | 0.994246i | \(-0.534163\pi\) | ||||
−0.107120 | + | 0.994246i | \(0.534163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.43806 | − | 7.79799i | −0.329040 | − | 0.344963i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 6.45545i | − | 0.284738i | ||||||
\(515\) | − | 4.19554i | − | 0.184877i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.57588i | − | 0.245227i | ||||||
\(518\) | −9.43720 | − | 9.89387i | −0.414647 | − | 0.434712i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.367172 | 0.0161015 | ||||||||
\(521\) | −17.5322 | −0.768101 | −0.384050 | − | 0.923312i | \(-0.625471\pi\) | ||||
−0.384050 | + | 0.923312i | \(0.625471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 19.1019i | − | 0.835267i | −0.908616 | − | 0.417633i | \(-0.862860\pi\) | ||
0.908616 | − | 0.417633i | \(-0.137140\pi\) | |||||||
\(524\) | −13.5321 | −0.591154 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.82062 | 0.384597 | ||||||||
\(527\) | − | 31.5602i | − | 1.37478i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −36.2067 | −1.57420 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.6091 | − | 12.1708i | −0.503317 | − | 0.527673i | ||||
\(533\) | − | 4.32532i | − | 0.187350i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.05522i | 0.175322i | ||||||||
\(536\) | − | 10.8907i | − | 0.470408i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.2653i | 0.615022i | ||||||||
\(539\) | −4.68095 | − | 0.221286i | −0.201623 | − | 0.00953144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.6642 | 0.587471 | 0.293735 | − | 0.955887i | \(-0.405102\pi\) | ||||
0.293735 | + | 0.955887i | \(0.405102\pi\) | |||||||
\(542\) | 3.05281 | 0.131130 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 4.98906i | − | 0.213904i | ||||||
\(545\) | 3.87249 | 0.165879 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.88761 | −0.422764 | −0.211382 | − | 0.977404i | \(-0.567796\pi\) | ||||
−0.211382 | + | 0.977404i | \(0.567796\pi\) | |||||||
\(548\) | 8.98851i | 0.383970i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.25730 | 0.138892 | ||||||||
\(551\) | −11.6272 | −0.495337 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.9969 | + | 15.2585i | −0.680256 | + | 0.648858i | ||||
\(554\) | − | 1.26566i | − | 0.0537726i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.29922i | − | 0.394375i | ||||||
\(557\) | 12.5800i | 0.533034i | 0.963830 | + | 0.266517i | \(0.0858728\pi\) | ||||
−0.963830 | + | 0.266517i | \(0.914127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.50547i | − | 0.190561i | ||||||
\(560\) | 0.701849 | − | 0.669453i | 0.0296585 | − | 0.0282896i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5267 | −0.444042 | ||||||||
\(563\) | 24.3333 | 1.02553 | 0.512763 | − | 0.858530i | \(-0.328622\pi\) | ||||
0.512763 | + | 0.858530i | \(0.328622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.52487i | − | 0.0641520i | ||||||
\(566\) | 19.8718 | 0.835272 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.49843 | 0.230709 | ||||||||
\(569\) | 9.45406i | 0.396335i | 0.980168 | + | 0.198167i | \(0.0634990\pi\) | ||||
−0.980168 | + | 0.198167i | \(0.936501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.5686 | −1.32110 | −0.660551 | − | 0.750781i | \(-0.729677\pi\) | ||||
−0.660551 | + | 0.750781i | \(0.729677\pi\) | |||||||
\(572\) | −0.670501 | −0.0280351 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.88623 | − | 8.26784i | −0.329165 | − | 0.345093i | ||||
\(575\) | 37.4388i | 1.56131i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 33.5794i | − | 1.39793i | −0.715157 | − | 0.698964i | \(-0.753645\pi\) | ||
0.715157 | − | 0.698964i | \(-0.246355\pi\) | |||||||
\(578\) | − | 7.89074i | − | 0.328211i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 0.670501i | − | 0.0278410i | ||||||
\(581\) | −32.5736 | + | 31.0701i | −1.35138 | + | 1.28901i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.07314 | −0.168548 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 13.4121i | − | 0.554049i | ||||||
\(587\) | −19.3171 | −0.797302 | −0.398651 | − | 0.917103i | \(-0.630521\pi\) | ||||
−0.398651 | + | 0.917103i | \(0.630521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.2150 | −1.65703 | ||||||||
\(590\) | 3.19928i | 0.131712i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.16789 | −0.212399 | ||||||||
\(593\) | −0.733196 | −0.0301088 | −0.0150544 | − | 0.999887i | \(-0.504792\pi\) | ||||
−0.0150544 | + | 0.999887i | \(0.504792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.50157 | − | 3.33994i | 0.143550 | − | 0.136924i | ||||
\(596\) | 2.83211i | 0.116008i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 7.70663i | − | 0.315147i | ||||||
\(599\) | 30.7783i | 1.25757i | 0.777580 | + | 0.628785i | \(0.216447\pi\) | ||||
−0.777580 | + | 0.628785i | \(0.783553\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.908670i | − | 0.0370654i | −0.999828 | − | 0.0185327i | \(-0.994101\pi\) | ||
0.999828 | − | 0.0185327i | \(-0.00589948\pi\) | |||||||
\(602\) | −8.21470 | − | 8.61221i | −0.334806 | − | 0.351007i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.5518 | 0.673484 | ||||||||
\(605\) | −3.86828 | −0.157268 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 44.7773i | − | 1.81746i | −0.417389 | − | 0.908728i | \(-0.637055\pi\) | ||
0.417389 | − | 0.908728i | \(-0.362945\pi\) | |||||||
\(608\) | −6.35722 | −0.257820 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.81749 | 0.0735880 | ||||||||
\(611\) | 8.34204i | 0.337483i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.1480 | 0.732992 | 0.366496 | − | 0.930420i | \(-0.380557\pi\) | ||||
0.366496 | + | 0.930420i | \(0.380557\pi\) | |||||||
\(614\) | 0.653728 | 0.0263823 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.28166 | + | 1.22250i | −0.0516396 | + | 0.0492561i | ||||
\(617\) | − | 22.7930i | − | 0.917610i | −0.888537 | − | 0.458805i | \(-0.848278\pi\) | ||
0.888537 | − | 0.458805i | \(-0.151722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 44.3668i | − | 1.78325i | −0.452772 | − | 0.891626i | \(-0.649565\pi\) | ||
0.452772 | − | 0.891626i | \(-0.350435\pi\) | |||||||
\(620\) | − | 2.31905i | − | 0.0931355i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 9.24493i | − | 0.370688i | ||||||
\(623\) | 20.5067 | − | 19.5602i | 0.821584 | − | 0.783663i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0021 | 0.920086 | ||||||||
\(626\) | −6.16414 | −0.246368 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.83456i | 0.113111i | ||||||||
\(629\) | −25.7829 | −1.02803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.5707 | −1.29662 | −0.648310 | − | 0.761377i | \(-0.724524\pi\) | ||||
−0.648310 | + | 0.761377i | \(0.724524\pi\) | |||||||
\(632\) | 8.35568i | 0.332371i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.6548 | 0.820308 | ||||||||
\(635\) | 0.612018 | 0.0242872 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00313 | + | 0.331064i | 0.277474 | + | 0.0131172i | ||||
\(638\) | 1.22442i | 0.0484751i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 0.366598i | − | 0.0144911i | ||||||
\(641\) | 11.8091i | 0.466433i | 0.972425 | + | 0.233216i | \(0.0749250\pi\) | ||||
−0.972425 | + | 0.233216i | \(0.925075\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.2964i | − | 1.15534i | −0.816272 | − | 0.577668i | \(-0.803963\pi\) | ||
0.816272 | − | 0.577668i | \(-0.196037\pi\) | |||||||
\(644\) | −14.0513 | − | 14.7312i | −0.553697 | − | 0.580491i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.7166 | −1.24787 | ||||||||
\(647\) | 28.1683 | 1.10741 | 0.553705 | − | 0.832713i | \(-0.313214\pi\) | ||||
0.553705 | + | 0.832713i | \(0.313214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.84229i | − | 0.229330i | ||||||
\(650\) | −4.87322 | −0.191143 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.7281 | −0.968426 | ||||||||
\(653\) | 45.0974i | 1.76480i | 0.470502 | + | 0.882399i | \(0.344073\pi\) | ||||
−0.470502 | + | 0.882399i | \(0.655927\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.96086 | −0.193837 | ||||||||
\(656\) | −4.31856 | −0.168611 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.2098 | + | 15.9458i | 0.592939 | + | 0.621632i | ||||
\(659\) | − | 31.8045i | − | 1.23893i | −0.785026 | − | 0.619463i | \(-0.787350\pi\) | ||
0.785026 | − | 0.619463i | \(-0.212650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.7724i | − | 0.769056i | −0.923113 | − | 0.384528i | \(-0.874364\pi\) | ||
0.923113 | − | 0.384528i | \(-0.125636\pi\) | |||||||
\(662\) | − | 10.7114i | − | 0.416309i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.0142i | 0.660281i | ||||||||
\(665\) | −4.25587 | − | 4.46181i | −0.165035 | − | 0.173022i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.0733 | −0.544918 | ||||||||
\(668\) | 19.3484 | 0.748614 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 3.99252i | − | 0.154245i | ||||||
\(671\) | −3.31896 | −0.128127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.89074 | 0.0728826 | 0.0364413 | − | 0.999336i | \(-0.488398\pi\) | ||||
0.0364413 | + | 0.999336i | \(0.488398\pi\) | |||||||
\(674\) | 7.55183i | 0.290886i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.9969 | −0.461418 | ||||||||
\(677\) | 21.1322 | 0.812175 | 0.406088 | − | 0.913834i | \(-0.366893\pi\) | ||||
0.406088 | + | 0.913834i | \(0.366893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.4381 | + | 32.9594i | 1.20648 | + | 1.26486i | ||||
\(680\) | − | 1.82898i | − | 0.0701382i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.23488i | 0.162162i | ||||||||
\(683\) | 8.71972i | 0.333651i | 0.985986 | + | 0.166825i | \(0.0533516\pi\) | ||||
−0.985986 | + | 0.166825i | \(0.946648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.29517i | 0.125902i | ||||||||
\(686\) | 13.9901 | − | 12.1358i | 0.534145 | − | 0.463346i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.49843 | −0.171501 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.1370i | − | 0.689964i | −0.938609 | − | 0.344982i | \(-0.887885\pi\) | ||
0.938609 | − | 0.344982i | \(-0.112115\pi\) | |||||||
\(692\) | 4.83654 | 0.183858 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.9320 | −0.414972 | ||||||||
\(695\) | − | 3.40908i | − | 0.129314i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.5456 | −0.816097 | ||||||||
\(698\) | 1.18429 | 0.0448260 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.31516 | + | 8.88520i | −0.352080 | + | 0.335829i | ||||
\(701\) | − | 35.6167i | − | 1.34523i | −0.739995 | − | 0.672613i | \(-0.765172\pi\) | ||
0.739995 | − | 0.672613i | \(-0.234828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.8534i | 1.23909i | ||||||||
\(704\) | 0.669453i | 0.0252310i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 33.5824i | − | 1.26389i | ||||||
\(707\) | 30.1182 | − | 28.7281i | 1.13271 | − | 1.08043i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.60770 | −0.135490 | −0.0677449 | − | 0.997703i | \(-0.521580\pi\) | ||||
−0.0677449 | + | 0.997703i | \(0.521580\pi\) | |||||||
\(710\) | 2.01572 | 0.0756485 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 10.7113i | − | 0.401424i | ||||||
\(713\) | −48.6750 | −1.82289 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.245804 | −0.00919256 | ||||||||
\(716\) | 3.65796i | 0.136704i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.1281 | 0.377978 | ||||||||
\(719\) | 25.7829 | 0.961540 | 0.480770 | − | 0.876847i | \(-0.340357\pi\) | ||||
0.480770 | + | 0.876847i | \(0.340357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.8991 | − | 21.9104i | −0.778323 | − | 0.815987i | ||||
\(722\) | 21.4143i | 0.796958i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 5.66796i | − | 0.210648i | ||||||
\(725\) | 8.89910i | 0.330504i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.52909i | 0.0567107i | 0.999598 | + | 0.0283554i | \(0.00902700\pi\) | ||||
−0.999598 | + | 0.0283554i | \(0.990973\pi\) | |||||||
\(728\) | 1.91749 | − | 1.82898i | 0.0710668 | − | 0.0677865i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.49321 | −0.0552660 | ||||||||
\(731\) | −22.4430 | −0.830083 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7739i | 0.767303i | 0.923478 | + | 0.383651i | \(0.125334\pi\) | ||||
−0.923478 | + | 0.383651i | \(0.874666\pi\) | |||||||
\(734\) | −18.0021 | −0.664469 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.69459 | −0.283626 | ||||||||
\(737\) | 7.29084i | 0.268562i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.8709 | −0.436678 | −0.218339 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218339 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(740\) | −1.89454 | −0.0696446 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.4059i | − | 1.59241i | −0.605028 | − | 0.796204i | \(-0.706838\pi\) | ||
0.605028 | − | 0.796204i | \(-0.293162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.03825i | 0.0380384i | ||||||||
\(746\) | − | 16.4090i | − | 0.600777i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.33994i | 0.122120i | ||||||||
\(749\) | 20.2001 | + | 21.1776i | 0.738097 | + | 0.773814i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.31383 | 0.0844327 | 0.0422164 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422164 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(752\) | 8.32901 | 0.303728 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1.83184i | − | 0.0667118i | ||||||
\(755\) | 6.06787 | 0.220832 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0946 | −0.548624 | −0.274312 | − | 0.961641i | \(-0.588450\pi\) | ||||
−0.274312 | + | 0.961641i | \(0.588450\pi\) | |||||||
\(758\) | 2.91372i | 0.105831i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.33055 | −0.0845378 | ||||||||
\(761\) | 23.3379 | 0.845998 | 0.422999 | − | 0.906130i | \(-0.360977\pi\) | ||||
0.422999 | + | 0.906130i | \(0.360977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.2234 | − | 19.2899i | 0.732136 | − | 0.698342i | ||||
\(764\) | 27.3777i | 0.990490i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.57443i | 0.309807i | ||||||||
\(767\) | 8.74061i | 0.315605i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.2750i | 0.659012i | 0.944153 | + | 0.329506i | \(0.106882\pi\) | ||||
−0.944153 | + | 0.329506i | \(0.893118\pi\) | |||||||
\(770\) | −0.469855 | + | 0.448168i | −0.0169324 | + | 0.0161508i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.0283 | 0.360925 | ||||||||
\(773\) | 0.438507 | 0.0157720 | 0.00788600 | − | 0.999969i | \(-0.497490\pi\) | ||||
0.00788600 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.7792i | 1.10562i | ||||||||
\(776\) | 17.2157 | 0.618009 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.5539 | 1.27467 | ||||||||
\(779\) | 27.4541i | 0.983644i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.68095 | −0.131715 | ||||||||
\(782\) | −38.3888 | −1.37278 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.330547 | − | 6.99219i | 0.0118052 | − | 0.249721i | ||||
\(785\) | 1.03914i | 0.0370886i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.2572i | 1.36372i | 0.731481 | + | 0.681861i | \(0.238829\pi\) | ||||
−0.731481 | + | 0.681861i | \(0.761171\pi\) | |||||||
\(788\) | − | 18.8258i | − | 0.670643i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.06318i | 0.108983i | ||||||||
\(791\) | −7.59581 | − | 7.96337i | −0.270076 | − | 0.283145i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.96547 | 0.176329 | ||||||||
\(794\) | −3.58034 | −0.127061 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.36406i | 0.190124i | ||||||||
\(797\) | 35.3225 | 1.25119 | 0.625594 | − | 0.780149i | \(-0.284857\pi\) | ||||
0.625594 | + | 0.780149i | \(0.284857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.5539 | 1.47007 | ||||||||
\(800\) | 4.86561i | 0.172025i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.190871 | 0.00673991 | ||||||||
\(803\) | 2.72678 | 0.0962259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.15117 | − | 5.40043i | −0.181555 | − | 0.190340i | ||||
\(806\) | − | 6.33577i | − | 0.223168i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 15.7317i | − | 0.553440i | ||||||
\(809\) | − | 21.7669i | − | 0.765282i | −0.923897 | − | 0.382641i | \(-0.875015\pi\) | ||
0.923897 | − | 0.382641i | \(-0.124985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.0184i | − | 0.597598i | −0.954316 | − | 0.298799i | \(-0.903414\pi\) | ||
0.954316 | − | 0.298799i | \(-0.0965860\pi\) | |||||||
\(812\) | −3.33994 | − | 3.50157i | −0.117209 | − | 0.122881i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.45966 | 0.121261 | ||||||||
\(815\) | −9.06527 | −0.317542 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.5976i | 1.00050i | ||||||||
\(818\) | 3.47371 | 0.121455 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.58318 | −0.0552869 | ||||||||
\(821\) | 24.8013i | 0.865572i | 0.901497 | + | 0.432786i | \(0.142469\pi\) | ||||
−0.901497 | + | 0.432786i | \(0.857531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.3144 | 0.742973 | 0.371486 | − | 0.928438i | \(-0.378848\pi\) | ||||
0.371486 | + | 0.928438i | \(0.378848\pi\) | |||||||
\(824\) | −11.4445 | −0.398689 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.9365 | + | 16.7077i | 0.554501 | + | 0.581334i | ||||
\(827\) | − | 49.7585i | − | 1.73027i | −0.501537 | − | 0.865136i | \(-0.667232\pi\) | ||
0.501537 | − | 0.865136i | \(-0.332768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.1190i | 1.49759i | 0.662804 | + | 0.748793i | \(0.269366\pi\) | ||||
−0.662804 | + | 0.748793i | \(0.730634\pi\) | |||||||
\(830\) | 6.23739i | 0.216503i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.00156i | − | 0.0347230i | ||||||
\(833\) | 1.64912 | − | 34.8845i | 0.0571385 | − | 1.20868i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.09310 | 0.245467 | ||||||||
\(836\) | 4.25587 | 0.147192 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 1.40791i | − | 0.0486354i | ||||||
\(839\) | 29.9971 | 1.03561 | 0.517807 | − | 0.855498i | \(-0.326749\pi\) | ||||
0.517807 | + | 0.855498i | \(0.326749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6548 | 0.884649 | ||||||||
\(842\) | 30.3860i | 1.04717i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.65796 | −0.0570694 | ||||||||
\(845\) | −4.39803 | −0.151297 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.2014 | + | 19.2689i | −0.694128 | + | 0.662089i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.2748i | 0.832619i | ||||||||
\(851\) | 39.7648i | 1.36312i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 29.7559i | − | 1.01882i | −0.860524 | − | 0.509411i | \(-0.829863\pi\) | ||
0.860524 | − | 0.509411i | \(-0.170137\pi\) | |||||||
\(854\) | 9.49150 | − | 9.05340i | 0.324792 | − | 0.309801i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0618 | 0.378083 | ||||||||
\(857\) | 45.8592 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.74208i | 0.127678i | 0.997960 | + | 0.0638390i | \(0.0203344\pi\) | ||||
−0.997960 | + | 0.0638390i | \(0.979666\pi\) | |||||||
\(860\) | −1.64912 | −0.0562344 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.2747 | 0.928979 | ||||||||
\(863\) | − | 31.3944i | − | 1.06868i | −0.845270 | − | 0.534339i | \(-0.820561\pi\) | ||
0.845270 | − | 0.534339i | \(-0.179439\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.77307 | 0.0602860 | ||||||||
\(866\) | 8.15047 | 0.276964 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.5518 | − | 12.1108i | −0.392095 | − | 0.411068i | ||||
\(869\) | − | 5.59374i | − | 0.189755i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.9078i | − | 0.369596i | ||||||
\(872\) | − | 10.5633i | − | 0.357719i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 48.9162i | 1.65462i | ||||||||
\(875\) | −6.92416 | + | 6.60456i | −0.234079 | + | 0.223275i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3923 | −0.688599 | −0.344300 | − | 0.938860i | \(-0.611884\pi\) | ||||
−0.344300 | + | 0.938860i | \(0.611884\pi\) | |||||||
\(878\) | 12.2404 | 0.413094 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.245420i | 0.00827312i | ||||||||
\(881\) | −21.2010 | −0.714280 | −0.357140 | − | 0.934051i | \(-0.616248\pi\) | ||||
−0.357140 | + | 0.934051i | \(0.616248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.6157 | 1.29952 | 0.649761 | − | 0.760139i | \(-0.274869\pi\) | ||||
0.649761 | + | 0.760139i | \(0.274869\pi\) | |||||||
\(884\) | − | 4.99687i | − | 0.168063i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.00836 | −0.269046 | ||||||||
\(887\) | −6.19211 | −0.207911 | −0.103955 | − | 0.994582i | \(-0.533150\pi\) | ||||
−0.103955 | + | 0.994582i | \(0.533150\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.19615 | − | 3.04863i | 0.107196 | − | 0.102248i | ||||
\(890\) | − | 3.92675i | − | 0.131625i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 17.0372i | − | 0.570448i | ||||||
\(893\) | − | 52.9494i | − | 1.77188i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.34100i | 0.0448247i | ||||||||
\(896\) | −1.82612 | − | 1.91449i | −0.0610065 | − | 0.0639586i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.5183 | −0.484483 | ||||||||
\(899\) | −11.5699 | −0.385878 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.89108 | 0.0962623 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.15953 | −0.138344 | ||||||||
\(905\) | − | 2.07786i | − | 0.0690705i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.129113 | −0.00428714 | −0.00214357 | − | 0.999998i | \(-0.500682\pi\) | ||||
−0.00214357 | + | 0.999998i | \(0.500682\pi\) | |||||||
\(908\) | −5.11024 | −0.169589 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.702947 | − | 0.670501i | 0.0233025 | − | 0.0222269i | ||||
\(911\) | − | 34.2579i | − | 1.13502i | −0.823368 | − | 0.567508i | \(-0.807908\pi\) | ||
0.823368 | − | 0.567508i | \(-0.192092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11.3902i | − | 0.376962i | ||||||
\(914\) | − | 9.95501i | − | 0.329283i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 15.2669i | − | 0.504433i | ||||||
\(917\) | −25.9072 | + | 24.7114i | −0.855530 | + | 0.816041i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3054 | 0.471892 | 0.235946 | − | 0.971766i | \(-0.424181\pi\) | ||||
0.235946 | + | 0.971766i | \(0.424181\pi\) | |||||||
\(920\) | −2.82082 | −0.0929997 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.3270i | 1.06463i | ||||||||
\(923\) | 5.50704 | 0.181266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.1449 | 0.826759 | ||||||||
\(926\) | − | 9.45032i | − | 0.310557i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.82898 | −0.0600392 | ||||||||
\(929\) | 11.7473 | 0.385415 | 0.192708 | − | 0.981256i | \(-0.438273\pi\) | ||||
0.192708 | + | 0.981256i | \(0.438273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.4509 | − | 2.10136i | −1.45682 | − | 0.0688693i | ||||
\(932\) | 10.1930i | 0.333883i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.6623i | 0.676091i | ||||||||
\(935\) | 1.22442i | 0.0400427i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.63611i | 0.0861179i | 0.999073 | + | 0.0430589i | \(0.0137103\pi\) | ||||
−0.999073 | + | 0.0430589i | \(0.986290\pi\) | |||||||
\(938\) | −19.8878 | − | 20.8502i | −0.649361 | − | 0.680784i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.05340 | 0.0995909 | ||||||||
\(941\) | −11.9311 | −0.388944 | −0.194472 | − | 0.980908i | \(-0.562299\pi\) | ||||
−0.194472 | + | 0.980908i | \(0.562299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.2295i | 1.08210i | ||||||||
\(944\) | 8.72695 | 0.284038 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.01149 | 0.0979121 | ||||||||
\(947\) | − | 7.73957i | − | 0.251502i | −0.992062 | − | 0.125751i | \(-0.959866\pi\) | ||
0.992062 | − | 0.125751i | \(-0.0401341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.07951 | −0.132427 | ||||||||
\(950\) | 30.9317 | 1.00356 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.11064 | − | 9.55151i | −0.295278 | − | 0.309566i | ||||
\(953\) | − | 3.76685i | − | 0.122020i | −0.998137 | − | 0.0610102i | \(-0.980568\pi\) | ||
0.998137 | − | 0.0610102i | \(-0.0194322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0366i | 0.324777i | ||||||||
\(956\) | 19.1815i | 0.620375i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.1608i | 0.328282i | ||||||||
\(959\) | 16.4141 | + | 17.2084i | 0.530040 | + | 0.555689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.01672 | −0.290862 | ||||||||
\(962\) | −5.17597 | −0.166880 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 20.6853i | − | 0.666227i | ||||||
\(965\) | 3.67634 | 0.118346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.57482 | 0.147116 | 0.0735581 | − | 0.997291i | \(-0.476565\pi\) | ||||
0.0735581 | + | 0.997291i | \(0.476565\pi\) | |||||||
\(968\) | 10.5518i | 0.339149i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.31126 | 0.202642 | ||||||||
\(971\) | 25.8445 | 0.829388 | 0.414694 | − | 0.909961i | \(-0.363889\pi\) | ||||
0.414694 | + | 0.909961i | \(0.363889\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.9815 | − | 17.8033i | −0.544403 | − | 0.570747i | ||||
\(974\) | 31.2296i | 1.00066i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 4.95771i | − | 0.158693i | ||||||
\(977\) | − | 30.1319i | − | 0.964004i | −0.876170 | − | 0.482002i | \(-0.839910\pi\) | ||
0.876170 | − | 0.482002i | \(-0.160090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.17073i | 0.229178i | ||||||||
\(980\) | 0.121178 | − | 2.56332i | 0.00387088 | − | 0.0818824i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.5899 | 0.657051 | ||||||||
\(983\) | −12.6059 | −0.402064 | −0.201032 | − | 0.979585i | \(-0.564430\pi\) | ||||
−0.201032 | + | 0.979585i | \(0.564430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.90152i | − | 0.219901i | ||||||
\(986\) | −9.12490 | −0.290596 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.36717 | −0.202567 | ||||||||
\(989\) | 34.6136i | 1.10065i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.6852 | 1.64184 | 0.820918 | − | 0.571046i | \(-0.193462\pi\) | ||||
0.820918 | + | 0.571046i | \(0.193462\pi\) | |||||||
\(992\) | −6.32588 | −0.200847 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.5267 | − | 10.0408i | 0.333887 | − | 0.318475i | ||||
\(995\) | 1.96645i | 0.0623408i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.5841i | 1.28531i | 0.766155 | + | 0.642656i | \(0.222168\pi\) | ||||
−0.766155 | + | 0.642656i | \(0.777832\pi\) | |||||||
\(998\) | 25.1533i | 0.796213i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))