Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.d (of order \(2\), degree \(1\), not 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: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.5 | ||
Root | \(1.41216 + 0.0762223i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.t.1549.6 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.576222 | − | 1.29150i | 0.407451 | − | 0.913227i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.33594 | − | 1.48838i | −0.667968 | − | 0.744190i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.97676i | 0.747145i | 0.927601 | + | 0.373573i | \(0.121867\pi\) | ||||
−0.927601 | + | 0.373573i | \(0.878133\pi\) | |||||||
\(8\) | −2.69204 | + | 0.867721i | −0.951779 | + | 0.306786i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.43055i | 0.431328i | 0.976468 | + | 0.215664i | \(0.0691915\pi\) | ||||
−0.976468 | + | 0.215664i | \(0.930808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.241319 | −0.0669300 | −0.0334650 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334650 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(14\) | 2.55298 | + | 1.13905i | 0.682313 | + | 0.304425i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.430552 | + | 3.97676i | −0.107638 | + | 0.994190i | ||||
\(17\) | − | 7.38407i | − | 1.79090i | −0.445161 | − | 0.895450i | \(-0.646854\pi\) | ||
0.445161 | − | 0.895450i | \(-0.353146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.04033i | − | 0.697500i | −0.937216 | − | 0.348750i | \(-0.886606\pi\) | ||
0.937216 | − | 0.348750i | \(-0.113394\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.84756 | + | 0.824316i | 0.393900 | + | 0.175745i | ||||
\(23\) | − | 0.874337i | − | 0.182312i | −0.995837 | − | 0.0911560i | \(-0.970944\pi\) | ||
0.995837 | − | 0.0911560i | \(-0.0290562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.139054 | + | 0.311664i | −0.0272707 | + | 0.0611223i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.94217 | − | 2.64082i | 0.556018 | − | 0.499069i | ||||
\(29\) | − | 9.07918i | − | 1.68596i | −0.537943 | − | 0.842981i | \(-0.680799\pi\) | ||
0.537943 | − | 0.842981i | \(-0.319201\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.44764 | −1.33764 | −0.668818 | − | 0.743426i | \(-0.733200\pi\) | ||||
−0.668818 | + | 0.743426i | \(0.733200\pi\) | |||||||
\(32\) | 4.88789 | + | 2.84756i | 0.864064 | + | 0.503381i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.53652 | − | 4.25487i | −1.63550 | − | 0.729704i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.81463 | −1.44912 | −0.724558 | − | 0.689214i | \(-0.757956\pi\) | ||||
−0.724558 | + | 0.689214i | \(0.757956\pi\) | |||||||
\(38\) | −3.92658 | − | 1.75191i | −0.636976 | − | 0.284197i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.91319 | 0.298790 | 0.149395 | − | 0.988778i | \(-0.452267\pi\) | ||||
0.149395 | + | 0.988778i | \(0.452267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2452 | −1.71487 | −0.857437 | − | 0.514589i | \(-0.827944\pi\) | ||||
−0.857437 | + | 0.514589i | \(0.827944\pi\) | |||||||
\(44\) | 2.12921 | − | 1.91113i | 0.320990 | − | 0.288113i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.12921 | − | 0.503813i | −0.166492 | − | 0.0742831i | ||||
\(47\) | − | 3.34374i | − | 0.487735i | −0.969809 | − | 0.243867i | \(-0.921584\pi\) | ||
0.969809 | − | 0.243867i | \(-0.0784162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.09242 | 0.441774 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.322387 | + | 0.359175i | 0.0447071 | + | 0.0498086i | ||||
\(53\) | −9.20632 | −1.26459 | −0.632293 | − | 0.774729i | \(-0.717886\pi\) | ||||
−0.632293 | + | 0.774729i | \(0.717886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.71528 | − | 5.32151i | −0.229213 | − | 0.711117i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.7258 | − | 5.23163i | −1.53967 | − | 0.686946i | ||||
\(59\) | − | 6.43616i | − | 0.837917i | −0.908005 | − | 0.418958i | \(-0.862395\pi\) | ||
0.908005 | − | 0.418958i | \(-0.137605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.57331i | 0.585552i | 0.956181 | + | 0.292776i | \(0.0945790\pi\) | ||||
−0.956181 | + | 0.292776i | \(0.905421\pi\) | |||||||
\(62\) | −4.29150 | + | 9.61862i | −0.545021 | + | 1.22157i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.49412 | − | 4.67187i | 0.811765 | − | 0.583984i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.86671 | −0.594563 | −0.297282 | − | 0.954790i | \(-0.596080\pi\) | ||||
−0.297282 | + | 0.954790i | \(0.596080\pi\) | |||||||
\(68\) | −10.9903 | + | 9.86465i | −1.33277 | + | 1.19626i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.21808 | 0.975307 | 0.487653 | − | 0.873037i | \(-0.337853\pi\) | ||||
0.487653 | + | 0.873037i | \(0.337853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.12714i | − | 0.483045i | −0.970395 | − | 0.241523i | \(-0.922353\pi\) | ||
0.970395 | − | 0.241523i | \(-0.0776468\pi\) | |||||||
\(74\) | −5.07918 | + | 11.3841i | −0.590443 | + | 1.32337i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.52517 | + | 4.06169i | −0.519072 | + | 0.465907i | ||||
\(77\) | −2.82786 | −0.322264 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6757 | 1.53864 | 0.769320 | − | 0.638864i | \(-0.220595\pi\) | ||||
0.769320 | + | 0.638864i | \(0.220595\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.10242 | − | 2.47088i | 0.121742 | − | 0.272863i | ||||
\(83\) | 12.3320 | 1.35361 | 0.676806 | − | 0.736162i | \(-0.263364\pi\) | ||||
0.676806 | + | 0.736162i | \(0.263364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.47972 | + | 14.5231i | −0.698726 | + | 1.56607i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.24132 | − | 3.85110i | −0.132325 | − | 0.410528i | ||||
\(89\) | −8.08066 | −0.856548 | −0.428274 | − | 0.903649i | \(-0.640878\pi\) | ||||
−0.428274 | + | 0.903649i | \(0.640878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.477031i | − | 0.0500064i | ||||||
\(92\) | −1.30135 | + | 1.16806i | −0.135675 | + | 0.121779i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.31844 | − | 1.92674i | −0.445413 | − | 0.198728i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.6757i | − | 1.08396i | −0.840393 | − | 0.541978i | \(-0.817676\pi\) | ||
0.840393 | − | 0.541978i | \(-0.182324\pi\) | |||||||
\(98\) | 1.78192 | − | 3.99385i | 0.180001 | − | 0.403440i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.2063i | − | 1.31408i | −0.753856 | − | 0.657039i | \(-0.771809\pi\) | ||
0.753856 | − | 0.657039i | \(-0.228191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.4244i | 1.91394i | 0.290181 | + | 0.956972i | \(0.406284\pi\) | ||||
−0.290181 | + | 0.956972i | \(0.593716\pi\) | |||||||
\(104\) | 0.649641 | − | 0.209398i | 0.0637025 | − | 0.0205331i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.30489 | + | 11.8900i | −0.515256 | + | 1.15485i | ||||
\(107\) | −14.8085 | −1.43159 | −0.715795 | − | 0.698311i | \(-0.753935\pi\) | ||||
−0.715795 | + | 0.698311i | \(0.753935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2296i | 1.45873i | 0.684126 | + | 0.729364i | \(0.260184\pi\) | ||||
−0.684126 | + | 0.729364i | \(0.739816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.86110 | − | 0.851098i | −0.742804 | − | 0.0804212i | ||||
\(113\) | 1.13890i | 0.107138i | 0.998564 | + | 0.0535692i | \(0.0170598\pi\) | ||||
−0.998564 | + | 0.0535692i | \(0.982940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.5133 | + | 12.1292i | −1.25468 | + | 1.12617i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.31229 | − | 3.70866i | −0.765208 | − | 0.341410i | ||||
\(119\) | 14.5965 | 1.33806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.95352 | 0.813956 | ||||||||
\(122\) | 5.90642 | + | 2.63524i | 0.534742 | + | 0.238583i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.94957 | + | 11.0849i | 0.893498 | + | 0.995456i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.43616i | − | 0.216174i | −0.994141 | − | 0.108087i | \(-0.965527\pi\) | ||
0.994141 | − | 0.108087i | \(-0.0344725\pi\) | |||||||
\(128\) | −2.29166 | − | 11.0792i | −0.202556 | − | 0.979271i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.90143i | 0.602981i | 0.953469 | + | 0.301491i | \(0.0974842\pi\) | ||||
−0.953469 | + | 0.301491i | \(0.902516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.01001 | 0.521134 | ||||||||
\(134\) | −2.80431 | + | 6.28535i | −0.242255 | + | 0.542972i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.40731 | + | 19.8782i | 0.549423 | + | 1.70454i | ||||
\(137\) | − | 5.39022i | − | 0.460518i | −0.973129 | − | 0.230259i | \(-0.926043\pi\) | ||
0.973129 | − | 0.230259i | \(-0.0739573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.4244i | − | 1.47792i | −0.673750 | − | 0.738959i | \(-0.735318\pi\) | ||
0.673750 | − | 0.738959i | \(-0.264682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.73544 | − | 10.6136i | 0.397389 | − | 0.890677i | ||||
\(143\) | − | 0.345220i | − | 0.0288687i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.33019 | − | 2.37815i | −0.441130 | − | 0.196817i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.7758 | + | 13.1195i | 0.967962 | + | 1.07842i | ||||
\(149\) | − | 2.28551i | − | 0.187236i | −0.995608 | − | 0.0936180i | \(-0.970157\pi\) | ||
0.995608 | − | 0.0936180i | \(-0.0298432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.66425 | 0.542329 | 0.271164 | − | 0.962533i | \(-0.412591\pi\) | ||||
0.271164 | + | 0.962533i | \(0.412591\pi\) | |||||||
\(152\) | 2.63816 | + | 8.18468i | 0.213983 | + | 0.663865i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.62948 | + | 3.65217i | −0.131307 | + | 0.294301i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4144 | −1.38982 | −0.694910 | − | 0.719097i | \(-0.744556\pi\) | ||||
−0.694910 | + | 0.719097i | \(0.744556\pi\) | |||||||
\(158\) | 7.88026 | − | 17.6622i | 0.626920 | − | 1.40513i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.72836 | 0.136214 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.66187 | 0.365145 | 0.182573 | − | 0.983192i | \(-0.441557\pi\) | ||||
0.182573 | + | 0.983192i | \(0.441557\pi\) | |||||||
\(164\) | −2.55590 | − | 2.84756i | −0.199582 | − | 0.222357i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.10597 | − | 15.9267i | 0.551530 | − | 1.23615i | ||||
\(167\) | − | 0.137419i | − | 0.0106338i | −0.999986 | − | 0.00531690i | \(-0.998308\pi\) | ||
0.999986 | − | 0.00531690i | \(-0.00169243\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9418 | −0.995520 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.0228 | + | 16.7371i | 1.14548 | + | 1.27619i | ||||
\(173\) | 3.96675 | 0.301587 | 0.150793 | − | 0.988565i | \(-0.451817\pi\) | ||||
0.150793 | + | 0.988565i | \(0.451817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.68896 | − | 0.615927i | −0.428822 | − | 0.0464272i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.65626 | + | 10.4362i | −0.349001 | + | 0.782223i | ||||
\(179\) | 4.68749i | 0.350359i | 0.984537 | + | 0.175180i | \(0.0560506\pi\) | ||||
−0.984537 | + | 0.175180i | \(0.943949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.10242i | 0.676578i | 0.941042 | + | 0.338289i | \(0.109848\pi\) | ||||
−0.941042 | + | 0.338289i | \(0.890152\pi\) | |||||||
\(182\) | −0.616084 | − | 0.274876i | −0.0456672 | − | 0.0203751i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.758681 | + | 2.35375i | 0.0559307 | + | 0.173521i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.5633 | 0.772465 | ||||||||
\(188\) | −4.97676 | + | 4.46702i | −0.362968 | + | 0.325791i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2063 | −1.10029 | −0.550145 | − | 0.835069i | \(-0.685428\pi\) | ||||
−0.550145 | + | 0.835069i | \(0.685428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 20.7564i | − | 1.49408i | −0.664780 | − | 0.747039i | \(-0.731475\pi\) | ||
0.664780 | − | 0.747039i | \(-0.268525\pi\) | |||||||
\(194\) | −13.7877 | − | 6.15159i | −0.989898 | − | 0.441659i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.13127 | − | 4.60269i | −0.295091 | − | 0.328764i | ||||
\(197\) | −23.2508 | −1.65655 | −0.828275 | − | 0.560322i | \(-0.810677\pi\) | ||||
−0.828275 | + | 0.560322i | \(0.810677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.21633 | 0.511552 | 0.255776 | − | 0.966736i | \(-0.417669\pi\) | ||||
0.255776 | + | 0.966736i | \(0.417669\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.0559 | − | 7.60978i | −1.20005 | − | 0.535422i | ||||
\(203\) | 17.9474 | 1.25966 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 25.0866 | + | 11.1928i | 1.74787 | + | 0.779838i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.103901 | − | 0.959669i | 0.00720420 | − | 0.0665411i | ||||
\(209\) | 4.34935 | 0.300851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.38407i | − | 0.301812i | −0.988548 | − | 0.150906i | \(-0.951781\pi\) | ||
0.988548 | − | 0.150906i | \(-0.0482191\pi\) | |||||||
\(212\) | 12.2991 | + | 13.7025i | 0.844703 | + | 0.941092i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.53298 | + | 19.1251i | −0.583302 | + | 1.30737i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.7222i | − | 0.999409i | ||||||
\(218\) | 19.6690 | + | 8.77561i | 1.33215 | + | 0.594360i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.78192i | 0.119865i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.98852i | − | 0.334056i | −0.985952 | − | 0.167028i | \(-0.946583\pi\) | ||
0.985952 | − | 0.167028i | \(-0.0534170\pi\) | |||||||
\(224\) | −5.62894 | + | 9.66218i | −0.376099 | + | 0.645582i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.47088 | + | 0.656257i | 0.0978416 | + | 0.0436536i | ||||
\(227\) | −11.2569 | −0.747149 | −0.373574 | − | 0.927600i | \(-0.621868\pi\) | ||||
−0.373574 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.8364i | − | 1.04650i | −0.852180 | − | 0.523249i | \(-0.824720\pi\) | ||
0.852180 | − | 0.523249i | \(-0.175280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.87820 | + | 24.4415i | 0.517229 | + | 1.60466i | ||||
\(233\) | 10.9591i | 0.717956i | 0.933346 | + | 0.358978i | \(0.116875\pi\) | ||||
−0.933346 | + | 0.358978i | \(0.883125\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.57945 | + | 8.59830i | −0.623569 | + | 0.559701i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.41086 | − | 18.8514i | 0.545195 | − | 1.22196i | ||||
\(239\) | 17.3182 | 1.12022 | 0.560111 | − | 0.828418i | \(-0.310758\pi\) | ||||
0.560111 | + | 0.828418i | \(0.310758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.76869 | 0.307178 | 0.153589 | − | 0.988135i | \(-0.450917\pi\) | ||||
0.153589 | + | 0.988135i | \(0.450917\pi\) | |||||||
\(242\) | 5.15922 | − | 11.5635i | 0.331647 | − | 0.743327i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.80682 | − | 6.10964i | 0.435762 | − | 0.391130i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.733691i | 0.0466836i | ||||||||
\(248\) | 20.0493 | − | 6.46247i | 1.27313 | − | 0.410367i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.15837i | − | 0.388713i | −0.980931 | − | 0.194356i | \(-0.937738\pi\) | ||
0.980931 | − | 0.194356i | \(-0.0622618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.25079 | 0.0786362 | ||||||||
\(254\) | −3.14630 | − | 1.40377i | −0.197416 | − | 0.0880804i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6293 | − | 3.42440i | −0.976828 | − | 0.214025i | ||||
\(257\) | − | 14.1584i | − | 0.883175i | −0.897218 | − | 0.441587i | \(-0.854416\pi\) | ||
0.897218 | − | 0.441587i | \(-0.145584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 17.4244i | − | 1.08270i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.91319 | + | 3.97676i | 0.550659 | + | 0.245685i | ||||
\(263\) | 15.5960i | 0.961691i | 0.876805 | + | 0.480845i | \(0.159670\pi\) | ||||
−0.876805 | + | 0.480845i | \(0.840330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.46310 | − | 7.76191i | 0.212336 | − | 0.475913i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.50161 | + | 7.24352i | 0.397149 | + | 0.442468i | ||||
\(269\) | 11.3182i | 0.690084i | 0.938587 | + | 0.345042i | \(0.112135\pi\) | ||||
−0.938587 | + | 0.345042i | \(0.887865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.20485 | −0.376918 | −0.188459 | − | 0.982081i | \(-0.560349\pi\) | ||||
−0.188459 | + | 0.982081i | \(0.560349\pi\) | |||||||
\(272\) | 29.3647 | + | 3.17923i | 1.78050 | + | 0.192769i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.96146 | − | 3.10597i | −0.420557 | − | 0.187638i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9288 | 1.13732 | 0.568661 | − | 0.822572i | \(-0.307462\pi\) | ||||
0.568661 | + | 0.822572i | \(0.307462\pi\) | |||||||
\(278\) | −22.5036 | − | 10.0403i | −1.34968 | − | 0.602179i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.6231 | 1.28993 | 0.644963 | − | 0.764214i | \(-0.276873\pi\) | ||||
0.644963 | + | 0.764214i | \(0.276873\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.1522 | 1.73292 | 0.866460 | − | 0.499247i | \(-0.166390\pi\) | ||||
0.866460 | + | 0.499247i | \(0.166390\pi\) | |||||||
\(284\) | −10.9788 | − | 12.2316i | −0.651473 | − | 0.725814i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.445851 | − | 0.198923i | −0.0263637 | − | 0.0117626i | ||||
\(287\) | 3.78192i | 0.223240i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.5245 | −2.20733 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.14275 | + | 5.51359i | −0.359477 | + | 0.322659i | ||||
\(293\) | −2.32427 | −0.135785 | −0.0678927 | − | 0.997693i | \(-0.521628\pi\) | ||||
−0.0678927 | + | 0.997693i | \(0.521628\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.7293 | − | 7.64863i | 1.37924 | − | 0.444568i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.95173 | − | 1.31696i | −0.170989 | − | 0.0762895i | ||||
\(299\) | 0.210995i | 0.0122021i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 22.2290i | − | 1.28126i | ||||||
\(302\) | 3.84009 | − | 8.60686i | 0.220972 | − | 0.495269i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.0907 | + | 1.30902i | 0.693447 | + | 0.0750775i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.52297 | 0.201066 | 0.100533 | − | 0.994934i | \(-0.467945\pi\) | ||||
0.100533 | + | 0.994934i | \(0.467945\pi\) | |||||||
\(308\) | 3.77784 | + | 4.20893i | 0.215262 | + | 0.239826i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.6757 | 1.22912 | 0.614559 | − | 0.788871i | \(-0.289334\pi\) | ||||
0.614559 | + | 0.788871i | \(0.289334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.5486i | − | 0.709288i | −0.935001 | − | 0.354644i | \(-0.884602\pi\) | ||
0.935001 | − | 0.354644i | \(-0.115398\pi\) | |||||||
\(314\) | −10.0346 | + | 22.4907i | −0.566283 | + | 1.26922i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.2699 | − | 20.3547i | −1.02776 | − | 1.14504i | ||||
\(317\) | 10.8611 | 0.610020 | 0.305010 | − | 0.952349i | \(-0.401340\pi\) | ||||
0.305010 | + | 0.952349i | \(0.401340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.9882 | 0.727202 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.995917 | − | 2.23217i | 0.0555003 | − | 0.124394i | ||||
\(323\) | −22.4500 | −1.24915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.68627 | − | 6.02079i | 0.148779 | − | 0.333461i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.15038 | + | 1.66011i | −0.284382 | + | 0.0916645i | ||||
\(329\) | 6.60978 | 0.364409 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.23185i | 0.0677088i | 0.999427 | + | 0.0338544i | \(0.0107783\pi\) | ||||
−0.999427 | + | 0.0338544i | \(0.989222\pi\) | |||||||
\(332\) | −16.4747 | − | 18.3547i | −0.904169 | − | 1.00734i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.177476 | − | 0.0791838i | −0.00971107 | − | 0.00433275i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.13890i | − | 0.225460i | −0.993626 | − | 0.112730i | \(-0.964040\pi\) | ||
0.993626 | − | 0.112730i | \(-0.0359595\pi\) | |||||||
\(338\) | −7.45733 | + | 16.7143i | −0.405625 | + | 0.909136i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.6542i | − | 0.576959i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9503i | 1.07721i | ||||||||
\(344\) | 30.2724 | − | 9.75767i | 1.63218 | − | 0.526098i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.28573 | − | 5.12306i | 0.122882 | − | 0.275417i | ||||
\(347\) | 17.4586 | 0.937226 | 0.468613 | − | 0.883404i | \(-0.344754\pi\) | ||||
0.468613 | + | 0.883404i | \(0.344754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2196i | 1.13586i | 0.823078 | + | 0.567928i | \(0.192255\pi\) | ||||
−0.823078 | + | 0.567928i | \(0.807745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.07358 | + | 6.99237i | −0.217122 | + | 0.372695i | ||||
\(353\) | − | 21.0398i | − | 1.11984i | −0.828548 | − | 0.559918i | \(-0.810833\pi\) | ||
0.828548 | − | 0.559918i | \(-0.189167\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.7952 | + | 12.0271i | 0.572147 | + | 0.637435i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.05388 | + | 2.70103i | 0.319957 | + | 0.142754i | ||||
\(359\) | 23.5153 | 1.24109 | 0.620546 | − | 0.784170i | \(-0.286911\pi\) | ||||
0.620546 | + | 0.784170i | \(0.286911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.75639 | 0.513494 | ||||||||
\(362\) | 11.7558 | + | 5.24502i | 0.617869 | + | 0.275672i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.710003 | + | 0.637282i | −0.0372143 | + | 0.0334027i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.4012i | 1.32593i | 0.748650 | + | 0.662965i | \(0.230702\pi\) | ||||
−0.748650 | + | 0.662965i | \(0.769298\pi\) | |||||||
\(368\) | 3.47703 | + | 0.376448i | 0.181253 | + | 0.0196237i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 18.1987i | − | 0.944829i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0677 | 0.521286 | 0.260643 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260643 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(374\) | 6.08681 | − | 13.6425i | 0.314741 | − | 0.705436i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.90143 | + | 9.00148i | 0.149630 | + | 0.464216i | ||||
\(377\) | 2.19098i | 0.112841i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.9674i | 0.974289i | 0.873321 | + | 0.487145i | \(0.161962\pi\) | ||||
−0.873321 | + | 0.487145i | \(0.838038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.76222 | + | 19.6389i | −0.448314 | + | 1.00482i | ||||
\(383\) | 28.7446i | 1.46878i | 0.678727 | + | 0.734391i | \(0.262532\pi\) | ||||
−0.678727 | + | 0.734391i | \(0.737468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.8068 | − | 11.9603i | −1.36443 | − | 0.608763i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.8895 | + | 14.2621i | −0.806669 | + | 0.724048i | ||||
\(389\) | 29.8161i | 1.51174i | 0.654724 | + | 0.755868i | \(0.272785\pi\) | ||||
−0.654724 | + | 0.755868i | \(0.727215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.45617 | −0.326503 | ||||||||
\(392\) | −8.32490 | + | 2.68335i | −0.420471 | + | 0.135530i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.3976 | + | 30.0283i | −0.674962 | + | 1.51281i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.73167 | 0.137099 | 0.0685494 | − | 0.997648i | \(-0.478163\pi\) | ||||
0.0685494 | + | 0.997648i | \(0.478163\pi\) | |||||||
\(398\) | 4.15821 | − | 9.31988i | 0.208432 | − | 0.467163i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.8744 | −1.29211 | −0.646054 | − | 0.763292i | \(-0.723582\pi\) | ||||
−0.646054 | + | 0.763292i | \(0.723582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.79726 | 0.0895279 | ||||||||
\(404\) | −19.6560 | + | 17.6428i | −0.977924 | + | 0.877762i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.3417 | − | 23.1790i | 0.513249 | − | 1.15035i | ||||
\(407\) | − | 12.6098i | − | 0.625044i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.4786 | −1.11150 | −0.555748 | − | 0.831351i | \(-0.687568\pi\) | ||||
−0.555748 | + | 0.831351i | \(0.687568\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.9109 | − | 25.9498i | 1.42434 | − | 1.27845i | ||||
\(413\) | 12.7227 | 0.626045 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.17954 | − | 0.687170i | −0.0578318 | − | 0.0336913i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.50619 | − | 5.61718i | 0.122582 | − | 0.274745i | ||||
\(419\) | − | 24.5307i | − | 1.19840i | −0.800598 | − | 0.599201i | \(-0.795485\pi\) | ||
0.800598 | − | 0.599201i | \(-0.204515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 33.3856i | − | 1.62712i | −0.581483 | − | 0.813558i | \(-0.697527\pi\) | ||
0.581483 | − | 0.813558i | \(-0.302473\pi\) | |||||||
\(422\) | −5.66202 | − | 2.52620i | −0.275623 | − | 0.122974i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.7838 | − | 7.98852i | 1.20361 | − | 0.387957i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.04033 | −0.437492 | ||||||||
\(428\) | 19.7832 | + | 22.0406i | 0.956256 | + | 1.06537i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6548 | −0.561391 | −0.280696 | − | 0.959797i | \(-0.590565\pi\) | ||||
−0.280696 | + | 0.959797i | \(0.590565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7681i | 0.949996i | 0.879987 | + | 0.474998i | \(0.157551\pi\) | ||||
−0.879987 | + | 0.474998i | \(0.842449\pi\) | |||||||
\(434\) | −19.0137 | − | 8.48326i | −0.912687 | − | 0.407210i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.6674 | − | 20.3457i | 1.08557 | − | 0.974383i | ||||
\(437\) | −2.65827 | −0.127163 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1699 | 1.20129 | 0.600646 | − | 0.799515i | \(-0.294910\pi\) | ||||
0.600646 | + | 0.799515i | \(0.294910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.30135 | + | 1.02678i | 0.109464 | + | 0.0488390i | ||||
\(443\) | −19.5515 | −0.928922 | −0.464461 | − | 0.885594i | \(-0.653752\pi\) | ||||
−0.464461 | + | 0.885594i | \(0.653752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.44266 | − | 2.87449i | −0.305069 | − | 0.136111i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.23517 | + | 12.8373i | 0.436321 | + | 0.606507i | ||||
\(449\) | −19.9612 | −0.942029 | −0.471014 | − | 0.882125i | \(-0.656112\pi\) | ||||
−0.471014 | + | 0.882125i | \(0.656112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.73692i | 0.128876i | ||||||||
\(452\) | 1.69511 | − | 1.52149i | 0.0797313 | − | 0.0715650i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.48650 | + | 14.5383i | −0.304426 | + | 0.682317i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.01176i | 0.234440i | 0.993106 | + | 0.117220i | \(0.0373983\pi\) | ||||
−0.993106 | + | 0.117220i | \(0.962602\pi\) | |||||||
\(458\) | −20.4527 | − | 9.12528i | −0.955690 | − | 0.426396i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.12566i | 0.238726i | 0.992851 | + | 0.119363i | \(0.0380852\pi\) | ||||
−0.992851 | + | 0.119363i | \(0.961915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.79515i | − | 0.269324i | −0.990892 | − | 0.134662i | \(-0.957005\pi\) | ||
0.990892 | − | 0.134662i | \(-0.0429948\pi\) | |||||||
\(464\) | 36.1057 | + | 3.90906i | 1.67617 | + | 0.181474i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.1537 | + | 6.31490i | 0.655657 | + | 0.292532i | ||||
\(467\) | 16.8208 | 0.778373 | 0.389186 | − | 0.921159i | \(-0.372756\pi\) | ||||
0.389186 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.62032i | − | 0.444225i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.58479 | + | 17.3264i | 0.257061 | + | 0.797511i | ||||
\(473\) | − | 16.0868i | − | 0.739672i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.5000 | − | 21.7252i | −0.893783 | − | 0.995773i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.97914 | − | 22.3664i | 0.456435 | − | 1.02302i | ||||
\(479\) | −36.9065 | −1.68630 | −0.843151 | − | 0.537678i | \(-0.819302\pi\) | ||||
−0.843151 | + | 0.537678i | \(0.819302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.12714 | 0.0969892 | ||||||||
\(482\) | 2.74782 | − | 6.15875i | 0.125160 | − | 0.280523i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.9613 | − | 13.3262i | −0.543697 | − | 0.605738i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.14984i | 0.233361i | 0.993169 | + | 0.116681i | \(0.0372254\pi\) | ||||
−0.993169 | + | 0.116681i | \(0.962775\pi\) | |||||||
\(488\) | −3.96835 | − | 12.3115i | −0.179639 | − | 0.557316i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.1154i | − | 1.04318i | −0.853195 | − | 0.521591i | \(-0.825339\pi\) | ||
0.853195 | − | 0.521591i | \(-0.174661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −67.0414 | −3.01939 | ||||||||
\(494\) | 0.947560 | + | 0.422769i | 0.0426328 | + | 0.0190213i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.20660 | − | 29.6175i | 0.143980 | − | 1.32986i | ||||
\(497\) | 16.2452i | 0.728696i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3111i | 0.640654i | 0.947307 | + | 0.320327i | \(0.103793\pi\) | ||||
−0.947307 | + | 0.320327i | \(0.896207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.95352 | − | 3.54859i | −0.354983 | − | 0.158381i | ||||
\(503\) | − | 15.4224i | − | 0.687650i | −0.939034 | − | 0.343825i | \(-0.888277\pi\) | ||
0.939034 | − | 0.343825i | \(-0.111723\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.720730 | − | 1.61539i | 0.0320404 | − | 0.0718127i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.62593 | + | 3.25455i | −0.160875 | + | 0.144397i | ||||
\(509\) | − | 43.1578i | − | 1.91294i | −0.291835 | − | 0.956469i | \(-0.594266\pi\) | ||
0.291835 | − | 0.956469i | \(-0.405734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.15837 | 0.360905 | ||||||||
\(512\) | −13.4285 | + | 18.2119i | −0.593463 | + | 0.804861i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.2855 | − | 8.15837i | −0.806539 | − | 0.359850i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.78340 | 0.210374 | ||||||||
\(518\) | −22.5036 | − | 10.0403i | −0.988751 | − | 0.441147i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8232 | 0.780848 | 0.390424 | − | 0.920635i | \(-0.372328\pi\) | ||||
0.390424 | + | 0.920635i | \(0.372328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.7502 | 1.08225 | 0.541126 | − | 0.840941i | \(-0.317998\pi\) | ||||
0.541126 | + | 0.840941i | \(0.317998\pi\) | |||||||
\(524\) | 10.2720 | − | 9.21987i | 0.448733 | − | 0.402772i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.1422 | + | 8.98677i | 0.878242 | + | 0.391842i | ||||
\(527\) | 54.9939i | 2.39557i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.2355 | 0.966762 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.02898 | − | 8.94517i | −0.348100 | − | 0.387822i | ||||
\(533\) | −0.461690 | −0.0199980 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.1014 | − | 4.22295i | 0.565893 | − | 0.182403i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.6175 | + | 6.52181i | 0.630203 | + | 0.281175i | ||||
\(539\) | 4.42386i | 0.190549i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16.9982i | − | 0.730812i | −0.930848 | − | 0.365406i | \(-0.880930\pi\) | ||
0.930848 | − | 0.365406i | \(-0.119070\pi\) | |||||||
\(542\) | −3.57537 | + | 8.01355i | −0.153575 | + | 0.344211i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.0266 | − | 36.0925i | 0.901506 | − | 1.54745i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.2385 | 1.59220 | 0.796101 | − | 0.605163i | \(-0.206892\pi\) | ||||
0.796101 | + | 0.605163i | \(0.206892\pi\) | |||||||
\(548\) | −8.02270 | + | 7.20099i | −0.342713 | + | 0.307611i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.6037 | −1.17596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.0336i | 1.14959i | ||||||||
\(554\) | 10.9072 | − | 24.4465i | 0.463403 | − | 1.03863i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.9341 | + | 23.2779i | −1.09985 | + | 0.987202i | ||||
\(557\) | 14.7604 | 0.625420 | 0.312710 | − | 0.949849i | \(-0.398763\pi\) | ||||
0.312710 | + | 0.949849i | \(0.398763\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.71368 | 0.114776 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.4597 | − | 27.9262i | 0.525581 | − | 1.17800i | ||||
\(563\) | 3.00561 | 0.126671 | 0.0633356 | − | 0.997992i | \(-0.479826\pi\) | ||||
0.0633356 | + | 0.997992i | \(0.479826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.7982 | − | 37.6500i | 0.706079 | − | 1.58255i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.1234 | + | 7.13100i | −0.928276 | + | 0.299210i | ||||
\(569\) | −23.1840 | −0.971923 | −0.485962 | − | 0.873980i | \(-0.661531\pi\) | ||||
−0.485962 | + | 0.873980i | \(0.661531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.202739i | − | 0.00848438i | −0.999991 | − | 0.00424219i | \(-0.998650\pi\) | ||
0.999991 | − | 0.00424219i | \(-0.00135033\pi\) | |||||||
\(572\) | −0.513819 | + | 0.461192i | −0.0214838 | + | 0.0192834i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.88434 | + | 2.17923i | 0.203869 | + | 0.0909592i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.8023i | − | 0.907643i | −0.891093 | − | 0.453821i | \(-0.850060\pi\) | ||
0.891093 | − | 0.453821i | \(-0.149940\pi\) | |||||||
\(578\) | −21.6225 | + | 48.4629i | −0.899376 | + | 2.01579i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.3774i | 1.01134i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 13.1701i | − | 0.545451i | ||||||
\(584\) | 3.58120 | + | 11.1104i | 0.148191 | + | 0.459752i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.33930 | + | 3.00179i | −0.0553258 | + | 0.124003i | ||||
\(587\) | 36.7126 | 1.51529 | 0.757645 | − | 0.652667i | \(-0.226350\pi\) | ||||
0.757645 | + | 0.652667i | \(0.226350\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.6433i | 0.933001i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.79515 | − | 35.0537i | 0.155980 | − | 1.44070i | ||||
\(593\) | − | 10.6036i | − | 0.435439i | −0.976011 | − | 0.217719i | \(-0.930138\pi\) | ||
0.976011 | − | 0.217719i | \(-0.0698618\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.40170 | + | 3.05329i | −0.139339 | + | 0.125068i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.272499 | + | 0.121580i | 0.0111433 | + | 0.00497177i | ||||
\(599\) | −25.7988 | −1.05411 | −0.527056 | − | 0.849831i | \(-0.676704\pi\) | ||||
−0.527056 | + | 0.849831i | \(0.676704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5021 | 0.754717 | 0.377358 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377358 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(602\) | −28.7087 | − | 12.8089i | −1.17008 | − | 0.522050i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.90300 | − | 9.91893i | −0.362258 | − | 0.403596i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.5828i | 1.52544i | 0.646730 | + | 0.762719i | \(0.276136\pi\) | ||||
−0.646730 | + | 0.762719i | \(0.723864\pi\) | |||||||
\(608\) | 8.65751 | − | 14.8608i | 0.351108 | − | 0.602685i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.806910i | 0.0326441i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.93405 | 0.199284 | 0.0996422 | − | 0.995023i | \(-0.468230\pi\) | ||||
0.0996422 | + | 0.995023i | \(0.468230\pi\) | |||||||
\(614\) | 2.03001 | − | 4.54991i | 0.0819247 | − | 0.183619i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.61270 | − | 2.45379i | 0.306724 | − | 0.0988661i | ||||
\(617\) | − | 6.26043i | − | 0.252035i | −0.992028 | − | 0.126018i | \(-0.959780\pi\) | ||
0.992028 | − | 0.126018i | \(-0.0402196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.02562i | 0.322577i | 0.986907 | + | 0.161288i | \(0.0515649\pi\) | ||||
−0.986907 | + | 0.161288i | \(0.948435\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4900 | − | 27.9942i | 0.500805 | − | 1.12246i | ||||
\(623\) | − | 15.9735i | − | 0.639966i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.2065 | − | 7.23078i | −0.647741 | − | 0.289000i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.2645 | + | 25.9192i | 0.928355 | + | 1.03429i | ||||
\(629\) | 65.0878i | 2.59522i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5248 | −1.05594 | −0.527968 | − | 0.849264i | \(-0.677046\pi\) | ||||
−0.527968 | + | 0.849264i | \(0.677046\pi\) | |||||||
\(632\) | −36.8156 | + | 11.8667i | −1.46444 | + | 0.472032i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.25841 | − | 14.0271i | 0.248553 | − | 0.557087i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.746260 | −0.0295679 | ||||||||
\(638\) | 7.48412 | − | 16.7743i | 0.296299 | − | 0.664101i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5863 | 1.05009 | 0.525047 | − | 0.851073i | \(-0.324048\pi\) | ||||
0.525047 | + | 0.851073i | \(0.324048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.89233 | −0.114062 | −0.0570312 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570312 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(644\) | −2.30897 | − | 2.57245i | −0.0909862 | − | 0.101369i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.9362 | + | 28.9942i | −0.508968 | + | 1.14076i | ||||
\(647\) | − | 12.3472i | − | 0.485420i | −0.970099 | − | 0.242710i | \(-0.921964\pi\) | ||
0.970099 | − | 0.242710i | \(-0.0780363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.20726 | 0.361417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.22795 | − | 6.93863i | −0.243905 | − | 0.271738i | ||||
\(653\) | 39.0507 | 1.52817 | 0.764086 | − | 0.645114i | \(-0.223190\pi\) | ||||
0.764086 | + | 0.645114i | \(0.223190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.823728 | + | 7.60830i | −0.0321612 | + | 0.297054i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.80870 | − | 8.53652i | 0.148479 | − | 0.332788i | ||||
\(659\) | − | 23.7738i | − | 0.926094i | −0.886334 | − | 0.463047i | \(-0.846756\pi\) | ||
0.886334 | − | 0.463047i | \(-0.153244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.5051i | 0.836450i | 0.908343 | + | 0.418225i | \(0.137348\pi\) | ||||
−0.908343 | + | 0.418225i | \(0.862652\pi\) | |||||||
\(662\) | 1.59094 | + | 0.709822i | 0.0618335 | + | 0.0275880i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.1982 | + | 10.7007i | −1.28834 | + | 0.415268i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.93827 | −0.307371 | ||||||||
\(668\) | −0.204532 | + | 0.183583i | −0.00791356 | + | 0.00710303i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.54235 | −0.252565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.1896i | − | 1.39501i | −0.716582 | − | 0.697503i | \(-0.754294\pi\) | ||
0.716582 | − | 0.697503i | \(-0.245706\pi\) | |||||||
\(674\) | −5.34538 | − | 2.38492i | −0.205896 | − | 0.0918639i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.2894 | + | 19.2623i | 0.664976 | + | 0.740856i | ||||
\(677\) | −9.17214 | −0.352514 | −0.176257 | − | 0.984344i | \(-0.556399\pi\) | ||||
−0.176257 | + | 0.984344i | \(0.556399\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.1034 | 0.809873 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.7599 | − | 6.13921i | −0.526895 | − | 0.235083i | ||||
\(683\) | −16.3974 | −0.627429 | −0.313714 | − | 0.949517i | \(-0.601573\pi\) | ||||
−0.313714 | + | 0.949517i | \(0.601573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.7658 | + | 11.4958i | 0.983742 | + | 0.438912i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.84163 | − | 44.7194i | 0.184586 | − | 1.70491i | ||||
\(689\) | 2.22166 | 0.0846387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.4904i | 0.931657i | 0.884875 | + | 0.465828i | \(0.154244\pi\) | ||||
−0.884875 | + | 0.465828i | \(0.845756\pi\) | |||||||
\(692\) | −5.29933 | − | 5.90404i | −0.201450 | − | 0.224438i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.0600 | − | 22.5477i | 0.381873 | − | 0.855900i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 14.1271i | − | 0.535104i | ||||||
\(698\) | 27.4050 | + | 12.2272i | 1.03730 | + | 0.462806i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.3887i | 0.467916i | 0.972247 | + | 0.233958i | \(0.0751679\pi\) | ||||
−0.972247 | + | 0.233958i | \(0.924832\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.7994i | 1.01076i | ||||||||
\(704\) | 6.68335 | + | 9.29018i | 0.251888 | + | 0.350137i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.1729 | − | 12.1236i | −1.02266 | − | 0.456278i | ||||
\(707\) | 26.1057 | 0.981807 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 33.4144i | − | 1.25490i | −0.778655 | − | 0.627452i | \(-0.784098\pi\) | ||
0.778655 | − | 0.627452i | \(-0.215902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.7534 | − | 7.01176i | 0.815244 | − | 0.262777i | ||||
\(713\) | 6.51175i | 0.243867i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.97676 | − | 6.26218i | 0.260734 | − | 0.234029i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.5501 | − | 30.3700i | 0.505684 | − | 1.13340i | ||||
\(719\) | −33.8938 | −1.26403 | −0.632013 | − | 0.774958i | \(-0.717771\pi\) | ||||
−0.632013 | + | 0.774958i | \(0.717771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.3974 | −1.42999 | ||||||||
\(722\) | 5.62185 | − | 12.6004i | 0.209224 | − | 0.468937i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.5479 | − | 12.1603i | 0.503503 | − | 0.451932i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.1846i | − | 0.526076i | −0.964785 | − | 0.263038i | \(-0.915275\pi\) | ||
0.964785 | − | 0.263038i | \(-0.0847245\pi\) | |||||||
\(728\) | 0.413929 | + | 1.28418i | 0.0153412 | + | 0.0475950i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 83.0352i | 3.07117i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.09296 | −0.298920 | −0.149460 | − | 0.988768i | \(-0.547754\pi\) | ||||
−0.149460 | + | 0.988768i | \(0.547754\pi\) | |||||||
\(734\) | 32.8056 | + | 14.6367i | 1.21088 | + | 0.540251i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.48972 | − | 4.27366i | 0.0917725 | − | 0.157529i | ||||
\(737\) | − | 6.96208i | − | 0.256452i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0919i | 0.812663i | 0.913726 | + | 0.406331i | \(0.133192\pi\) | ||||
−0.913726 | + | 0.406331i | \(0.866808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.5036 | − | 10.4865i | −0.862844 | − | 0.384971i | ||||
\(743\) | 8.78340i | 0.322232i | 0.986936 | + | 0.161116i | \(0.0515093\pi\) | ||||
−0.986936 | + | 0.161116i | \(0.948491\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.80123 | − | 13.0024i | 0.212398 | − | 0.476052i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.1119 | − | 15.7222i | −0.515982 | − | 0.574861i | ||||
\(749\) | − | 29.2728i | − | 1.06961i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3779 | 0.488167 | 0.244084 | − | 0.969754i | \(-0.421513\pi\) | ||||
0.244084 | + | 0.969754i | \(0.421513\pi\) | |||||||
\(752\) | 13.2973 | + | 1.43965i | 0.484901 | + | 0.0524988i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.82965 | + | 1.26249i | 0.103050 | + | 0.0459773i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.72450 | 0.353443 | 0.176721 | − | 0.984261i | \(-0.443451\pi\) | ||||
0.176721 | + | 0.984261i | \(0.443451\pi\) | |||||||
\(758\) | 24.4963 | + | 10.9294i | 0.889747 | + | 0.396975i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.8835 | −1.22828 | −0.614138 | − | 0.789198i | \(-0.710496\pi\) | ||||
−0.614138 | + | 0.789198i | \(0.710496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.1052 | −1.08988 | ||||||||
\(764\) | 20.3147 | + | 22.6328i | 0.734959 | + | 0.818826i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.1236 | + | 16.5633i | 1.34133 | + | 0.598456i | ||||
\(767\) | 1.55317i | 0.0560817i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.7334 | −0.675545 | −0.337772 | − | 0.941228i | \(-0.609673\pi\) | ||||
−0.337772 | + | 0.941228i | \(0.609673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.8934 | + | 27.7292i | −1.11188 | + | 0.997996i | ||||
\(773\) | −22.5006 | −0.809292 | −0.404646 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404646 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.26355 | + | 28.7395i | 0.332542 | + | 1.03169i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.5074 | + | 17.1807i | 1.38056 | + | 0.615958i | ||||
\(779\) | − | 5.81673i | − | 0.208406i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7564i | 0.420677i | ||||||||
\(782\) | −3.72019 | + | 8.33813i | −0.133034 | + | 0.298171i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.33145 | + | 12.2978i | −0.0475517 | + | 0.439207i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.1063 | −1.00188 | −0.500940 | − | 0.865482i | \(-0.667012\pi\) | ||||
−0.500940 | + | 0.865482i | \(0.667012\pi\) | |||||||
\(788\) | 31.0616 | + | 34.6060i | 1.10652 | + | 1.23279i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.25133 | −0.0800479 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.10363i | − | 0.0391910i | ||||||
\(794\) | 1.57405 | − | 3.52795i | 0.0558610 | − | 0.125202i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.64055 | − | 10.7406i | −0.341700 | − | 0.380692i | ||||
\(797\) | 38.1461 | 1.35120 | 0.675602 | − | 0.737267i | \(-0.263884\pi\) | ||||
0.675602 | + | 0.737267i | \(0.263884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.6904 | −0.873485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.9094 | + | 33.4168i | −0.526470 | + | 1.17999i | ||||
\(803\) | 5.90409 | 0.208351 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.03562 | − | 2.32116i | 0.0364782 | − | 0.0817593i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.4594 | + | 35.5519i | 0.403140 | + | 1.25071i | ||||
\(809\) | −10.0745 | −0.354201 | −0.177101 | − | 0.984193i | \(-0.556672\pi\) | ||||
−0.177101 | + | 0.984193i | \(0.556672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.6001i | 1.42566i | 0.701335 | + | 0.712832i | \(0.252588\pi\) | ||||
−0.701335 | + | 0.712832i | \(0.747412\pi\) | |||||||
\(812\) | −23.9765 | − | 26.7125i | −0.841411 | − | 0.937426i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.2855 | − | 7.26604i | −0.570807 | − | 0.254674i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.1891i | 1.19612i | ||||||||
\(818\) | −12.9527 | + | 29.0311i | −0.452879 | + | 1.01505i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.3397i | 0.360858i | 0.983588 | + | 0.180429i | \(0.0577486\pi\) | ||||
−0.983588 | + | 0.180429i | \(0.942251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.5013i | − | 0.993493i | −0.867896 | − | 0.496746i | \(-0.834528\pi\) | ||
0.867896 | − | 0.496746i | \(-0.165472\pi\) | |||||||
\(824\) | −16.8550 | − | 52.2912i | −0.587170 | − | 1.82165i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.33113 | − | 16.4314i | 0.255083 | − | 0.571722i | ||||
\(827\) | −32.1957 | −1.11956 | −0.559778 | − | 0.828643i | \(-0.689114\pi\) | ||||
−0.559778 | + | 0.828643i | \(0.689114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5286i | 1.09503i | 0.836795 | + | 0.547516i | \(0.184427\pi\) | ||||
−0.836795 | + | 0.547516i | \(0.815573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.56716 | + | 1.12741i | −0.0543314 | + | 0.0390860i | ||||
\(833\) | − | 22.8346i | − | 0.791173i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.81045 | − | 6.47349i | −0.200959 | − | 0.223890i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.6813 | − | 14.1351i | −1.09441 | − | 0.488290i | ||||
\(839\) | 54.9816 | 1.89818 | 0.949089 | − | 0.315009i | \(-0.102008\pi\) | ||||
0.949089 | + | 0.315009i | \(0.102008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −53.4316 | −1.84247 | ||||||||
\(842\) | −43.1175 | − | 19.2376i | −1.48593 | − | 0.662970i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.52517 | + | 5.85684i | −0.224606 | + | 0.201601i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.6990i | 0.608144i | ||||||||
\(848\) | 3.96380 | − | 36.6113i | 0.136117 | − | 1.25724i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.70696i | 0.264191i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.22607 | −0.144698 | −0.0723489 | − | 0.997379i | \(-0.523050\pi\) | ||||
−0.0723489 | + | 0.997379i | \(0.523050\pi\) | |||||||
\(854\) | −5.20924 | + | 11.6756i | −0.178257 | + | 0.399530i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.8650 | − | 12.8496i | 1.36256 | − | 0.439191i | ||||
\(857\) | 54.8223i | 1.87270i | 0.351074 | + | 0.936348i | \(0.385817\pi\) | ||||
−0.351074 | + | 0.936348i | \(0.614183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.2126i | − | 0.484926i | −0.970161 | − | 0.242463i | \(-0.922045\pi\) | ||
0.970161 | − | 0.242463i | \(-0.0779554\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.71574 | + | 15.0521i | −0.228739 | + | 0.512678i | ||||
\(863\) | − | 40.7446i | − | 1.38696i | −0.720474 | − | 0.693482i | \(-0.756076\pi\) | ||
0.720474 | − | 0.693482i | \(-0.243924\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.5305 | + | 11.3908i | 0.867563 | + | 0.387077i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −21.9122 | + | 19.6679i | −0.743750 | + | 0.667573i | ||||
\(869\) | 19.5638i | 0.663658i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.17443 | 0.0397941 | ||||||||
\(872\) | −13.2150 | − | 40.9985i | −0.447517 | − | 1.38839i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.53176 | + | 3.43316i | −0.0518125 | + | 0.116128i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.4568 | −1.16352 | −0.581762 | − | 0.813359i | \(-0.697637\pi\) | ||||
−0.581762 | + | 0.813359i | \(0.697637\pi\) | |||||||
\(878\) | 14.5034 | − | 32.5068i | 0.489467 | − | 1.09705i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.8528 | −0.803623 | −0.401811 | − | 0.915722i | \(-0.631619\pi\) | ||||
−0.401811 | + | 0.915722i | \(0.631619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2417 | 0.815798 | 0.407899 | − | 0.913027i | \(-0.366262\pi\) | ||||
0.407899 | + | 0.913027i | \(0.366262\pi\) | |||||||
\(884\) | 2.65217 | − | 2.38053i | 0.0892023 | − | 0.0800659i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.2660 | + | 25.2508i | −0.378490 | + | 0.848317i | ||||
\(887\) | − | 39.1843i | − | 1.31568i | −0.753158 | − | 0.657840i | \(-0.771470\pi\) | ||
0.753158 | − | 0.657840i | \(-0.228530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.81571 | 0.161514 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.42481 | + | 6.66434i | −0.248601 | + | 0.223139i | ||||
\(893\) | −10.1661 | −0.340195 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 21.9009 | − | 4.53005i | 0.731658 | − | 0.151339i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.5021 | + | 25.7799i | −0.383830 | + | 0.860286i | ||||
\(899\) | 67.6185i | 2.25520i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.9802i | 2.26475i | ||||||||
\(902\) | 3.53473 | + | 1.57707i | 0.117693 | + | 0.0525108i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.988244 | − | 3.06595i | −0.0328685 | − | 0.101972i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9418 | −0.628951 | −0.314475 | − | 0.949266i | \(-0.601829\pi\) | ||||
−0.314475 | + | 0.949266i | \(0.601829\pi\) | |||||||
\(908\) | 15.0385 | + | 16.7546i | 0.499071 | + | 0.556021i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8493 | −0.591375 | −0.295688 | − | 0.955285i | \(-0.595549\pi\) | ||||
−0.295688 | + | 0.955285i | \(0.595549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6415i | 0.583850i | ||||||||
\(914\) | 6.47267 | + | 2.88789i | 0.214097 | + | 0.0955228i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.5706 | + | 21.1564i | −0.778793 | + | 0.699027i | ||||
\(917\) | −13.6425 | −0.450515 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.4983 | −0.808126 | −0.404063 | − | 0.914731i | \(-0.632402\pi\) | ||||
−0.404063 | + | 0.914731i | \(0.632402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.61978 | + | 2.95352i | 0.218011 | + | 0.0972690i | ||||
\(923\) | −1.98318 | −0.0652772 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.48443 | − | 3.33930i | −0.245954 | − | 0.109736i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.8535 | − | 44.3780i | 0.848682 | − | 1.45678i | ||||
\(929\) | 11.5577 | 0.379196 | 0.189598 | − | 0.981862i | \(-0.439282\pi\) | ||||
0.189598 | + | 0.981862i | \(0.439282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.40197i | − | 0.308137i | ||||||
\(932\) | 16.3114 | − | 14.6407i | 0.534296 | − | 0.479572i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.69251 | − | 21.7240i | 0.317148 | − | 0.710831i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.5587i | 1.94570i | 0.231440 | + | 0.972849i | \(0.425656\pi\) | ||||
−0.231440 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(938\) | −12.4246 | − | 5.54345i | −0.405679 | − | 0.181000i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.9289i | 1.82323i | 0.411044 | + | 0.911615i | \(0.365164\pi\) | ||||
−0.411044 | + | 0.911615i | \(0.634836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.67277i | − | 0.0544730i | ||||||
\(944\) | 25.5951 | + | 2.77110i | 0.833048 | + | 0.0901917i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.7761 | − | 9.26958i | −0.675489 | − | 0.301380i | ||||
\(947\) | −30.0945 | −0.977941 | −0.488970 | − | 0.872300i | \(-0.662627\pi\) | ||||
−0.488970 | + | 0.872300i | \(0.662627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.995959i | 0.0323302i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −39.2944 | + | 12.6657i | −1.27354 | + | 0.410498i | ||||
\(953\) | − | 12.4097i | − | 0.401989i | −0.979592 | − | 0.200995i | \(-0.935583\pi\) | ||
0.979592 | − | 0.200995i | \(-0.0644174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.1360 | − | 25.7761i | −0.748272 | − | 0.833658i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.2664 | + | 47.6647i | −0.687085 | + | 1.53998i | ||||
\(959\) | 10.6552 | 0.344074 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4674 | 0.789271 | ||||||||
\(962\) | 1.22571 | − | 2.74720i | 0.0395183 | − | 0.0885732i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.37066 | − | 7.09762i | −0.205185 | − | 0.228599i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41.8371i | − | 1.34539i | −0.739920 | − | 0.672694i | \(-0.765137\pi\) | ||
0.739920 | − | 0.672694i | \(-0.234863\pi\) | |||||||
\(968\) | −24.1032 | + | 7.76916i | −0.774706 | + | 0.249710i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 40.6875i | − | 1.30572i | −0.757477 | − | 0.652862i | \(-0.773568\pi\) | ||
0.757477 | − | 0.652862i | \(-0.226432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.4439 | 1.10422 | ||||||||
\(974\) | 6.65101 | + | 2.96745i | 0.213112 | + | 0.0950833i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.1869 | − | 1.96905i | −0.582150 | − | 0.0630276i | ||||
\(977\) | 1.67923i | 0.0537233i | 0.999639 | + | 0.0268617i | \(0.00855136\pi\) | ||||
−0.999639 | + | 0.0268617i | \(0.991449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.5598i | − | 0.369453i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −29.8535 | − | 13.3196i | −0.952663 | − | 0.425046i | ||||
\(983\) | 13.4944i | 0.430404i | 0.976570 | + | 0.215202i | \(0.0690411\pi\) | ||||
−0.976570 | + | 0.215202i | \(0.930959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −38.6307 | + | 86.5838i | −1.23025 | + | 2.75739i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.09201 | − | 0.980164i | 0.0347415 | − | 0.0311832i | ||||
\(989\) | 9.83208i | 0.312642i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8502 | −0.344667 | −0.172333 | − | 0.985039i | \(-0.555131\pi\) | ||||
−0.172333 | + | 0.985039i | \(0.555131\pi\) | |||||||
\(992\) | −36.4032 | − | 21.2076i | −1.15580 | − | 0.673341i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.9806 | + | 9.36083i | 0.665465 | + | 0.296908i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.0972 | 1.23822 | 0.619110 | − | 0.785304i | \(-0.287493\pi\) | ||||
0.619110 | + | 0.785304i | \(0.287493\pi\) | |||||||
\(998\) | 18.4828 | + | 8.24639i | 0.585063 | + | 0.261035i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))