Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), degree \(2\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.h.961.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | 0 | ||||||||
\(3\) | −1.29418 | − | 1.15113i | −0.747196 | − | 0.664603i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58836 | 0.710338 | 0.355169 | − | 0.934802i | \(-0.384423\pi\) | ||||
0.355169 | + | 0.934802i | \(0.384423\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64400 | + | 0.0963576i | 0.999337 | + | 0.0364197i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.349814 | + | 2.97954i | 0.116605 | + | 0.993178i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.58836 | 0.478910 | 0.239455 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239455 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40545 | − | 4.16635i | 0.667151 | − | 1.15554i | −0.311547 | − | 0.950231i | \(-0.600847\pi\) |
0.978697 | − | 0.205308i | \(-0.0658196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.05563 | − | 1.82841i | −0.530762 | − | 0.472093i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.69963 | + | 4.67589i | −0.654756 | + | 1.13407i | 0.327199 | + | 0.944955i | \(0.393895\pi\) |
−0.981955 | + | 0.189115i | \(0.939438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.54944 | + | 6.14781i | 0.814298 | + | 1.41041i | 0.909831 | + | 0.414979i | \(0.136211\pi\) |
−0.0955331 | + | 0.995426i | \(0.530456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.31089 | − | 3.16828i | −0.722496 | − | 0.691375i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.300372 | −0.0626319 | −0.0313159 | − | 0.999510i | \(-0.509970\pi\) | ||||
−0.0313159 | + | 0.999510i | \(0.509970\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.47710 | −0.495420 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.97710 | − | 4.25874i | 0.572943 | − | 0.819595i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.13781 | + | 7.16689i | 0.768371 | + | 1.33086i | 0.938446 | + | 0.345427i | \(0.112266\pi\) |
−0.170074 | + | 0.985431i | \(0.554401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35600 | − | 2.34867i | −0.243545 | − | 0.421833i | 0.718176 | − | 0.695861i | \(-0.244977\pi\) |
−0.961722 | + | 0.274028i | \(0.911644\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.05563 | − | 1.82841i | −0.357840 | − | 0.318285i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.19963 | + | 0.153051i | 0.709867 | + | 0.0258703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.90909 | + | 2.62305i | −1.26647 | + | 0.420024i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.93818 | − | 5.08907i | 0.458866 | − | 0.794780i | −0.540035 | − | 0.841643i | \(-0.681589\pi\) |
0.998901 | + | 0.0468628i | \(0.0149223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.833104 | + | 1.44298i | 0.127047 | + | 0.220052i | 0.922531 | − | 0.385922i | \(-0.126117\pi\) |
−0.795484 | + | 0.605974i | \(0.792783\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.555632 | + | 4.73259i | 0.0828287 | + | 0.705492i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.33310 | − | 2.30900i | 0.194453 | − | 0.336803i | −0.752268 | − | 0.658857i | \(-0.771040\pi\) |
0.946721 | + | 0.322055i | \(0.104373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98143 | + | 0.509538i | 0.997347 | + | 0.0727912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.87636 | − | 2.94384i | 1.24294 | − | 0.412220i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.44437 | − | 4.23377i | 0.335760 | − | 0.581553i | −0.647871 | − | 0.761750i | \(-0.724340\pi\) |
0.983630 | + | 0.180197i | \(0.0576736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.52290 | 0.340188 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.48329 | − | 12.0422i | 0.328920 | − | 1.59503i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.23855 | + | 5.60933i | 0.421623 | + | 0.730273i | 0.996098 | − | 0.0882491i | \(-0.0281271\pi\) |
−0.574475 | + | 0.818522i | \(0.694794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.23855 | − | 3.87728i | 0.286617 | − | 0.496435i | −0.686383 | − | 0.727240i | \(-0.740803\pi\) |
0.973000 | + | 0.230805i | \(0.0741360\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.637806 | + | 7.91159i | 0.0803560 | + | 0.996766i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.82072 | − | 6.61769i | 0.473902 | − | 0.820823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.02654 | − | 8.70623i | −0.614090 | − | 1.06363i | −0.990543 | − | 0.137199i | \(-0.956190\pi\) |
0.376454 | − | 0.926435i | \(-0.377143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.388736 | + | 0.345766i | 0.0467983 | + | 0.0416253i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7207 | −1.50967 | −0.754833 | − | 0.655917i | \(-0.772282\pi\) | ||||
−0.754833 | + | 0.655917i | \(0.772282\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.02654 | − | 13.9024i | 0.939436 | − | 1.62715i | 0.172909 | − | 0.984938i | \(-0.444683\pi\) |
0.766527 | − | 0.642213i | \(-0.221983\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.20582 | + | 2.85146i | 0.370176 | + | 0.329258i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.19963 | + | 0.153051i | 0.478592 | + | 0.0174418i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19344 | − | 7.26325i | 0.471799 | − | 0.817179i | −0.527681 | − | 0.849443i | \(-0.676938\pi\) |
0.999479 | + | 0.0322635i | \(0.0102716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75526 | + | 2.08457i | −0.972807 | + | 0.231619i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.18292 | − | 2.04887i | −0.129842 | − | 0.224893i | 0.793773 | − | 0.608214i | \(-0.208114\pi\) |
−0.923615 | + | 0.383321i | \(0.874780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28799 | + | 7.42702i | −0.465098 | + | 0.805573i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.89493 | − | 14.0384i | 0.310369 | − | 1.50507i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60507 | + | 2.78007i | 0.170138 | + | 0.294687i | 0.938468 | − | 0.345367i | \(-0.112245\pi\) |
−0.768330 | + | 0.640054i | \(0.778912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.76145 | − | 10.7840i | 0.708793 | − | 1.13047i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.948699 | + | 4.60054i | −0.0983755 | + | 0.477053i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.63781 | + | 9.76497i | 0.578427 | + | 1.00186i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.712008 | + | 1.23323i | 0.0722934 | + | 0.125216i | 0.899906 | − | 0.436084i | \(-0.143635\pi\) |
−0.827613 | + | 0.561300i | \(0.810302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.555632 | + | 4.73259i | 0.0558431 | + | 0.475643i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0334 | 1.19737 | 0.598685 | − | 0.800985i | \(-0.295690\pi\) | ||||
0.598685 | + | 0.800985i | \(0.295690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.09888 | 0.600941 | 0.300470 | − | 0.953791i | \(-0.402856\pi\) | ||||
0.300470 | + | 0.953791i | \(0.402856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.25890 | − | 5.03238i | −0.513216 | − | 0.491110i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.54325 | + | 2.67299i | 0.149192 | + | 0.258408i | 0.930929 | − | 0.365200i | \(-0.118999\pi\) |
−0.781737 | + | 0.623608i | \(0.785666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.14400 | − | 1.98146i | 0.109575 | − | 0.189789i | −0.806023 | − | 0.591884i | \(-0.798384\pi\) |
0.915598 | + | 0.402095i | \(0.131718\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.349814 | − | 1.69636i | 0.0332029 | − | 0.161011i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.73236 | + | 16.8569i | −0.915543 | + | 1.58577i | −0.109440 | + | 0.993993i | \(0.534906\pi\) |
−0.806104 | + | 0.591774i | \(0.798428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.477100 | −0.0444898 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.2553 | + | 5.70966i | 1.22545 | + | 0.527858i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.58836 | + | 12.1029i | −0.695624 | + | 1.10947i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.47710 | −0.770645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.66071 | + | 3.20397i | −0.871077 | + | 0.288892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8764 | −1.06225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4400 | 1.19260 | 0.596302 | − | 0.802760i | \(-0.296636\pi\) | ||||
0.596302 | + | 0.802760i | \(0.296636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.582863 | − | 2.82648i | 0.0513182 | − | 0.248858i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.17673 | 0.277552 | 0.138776 | − | 0.990324i | \(-0.455683\pi\) | ||||
0.138776 | + | 0.990324i | \(0.455683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.79232 | + | 16.5968i | 0.762391 | + | 1.43913i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.72872 | − | 6.76443i | 0.406983 | − | 0.582190i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.2632 | −1.81664 | −0.908320 | − | 0.418275i | \(-0.862635\pi\) | ||||
−0.908320 | + | 0.418275i | \(0.862635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.52654 | + | 11.3043i | −0.553574 | + | 0.958818i | 0.444439 | + | 0.895809i | \(0.353403\pi\) |
−0.998013 | + | 0.0630092i | \(0.979930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.38323 | + | 1.45370i | −0.369135 | + | 0.122424i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.82072 | − | 6.61769i | 0.319505 | − | 0.553399i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.57234 | + | 11.3836i | 0.545803 | + | 0.945359i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.44870 | − | 8.69595i | −0.696837 | − | 0.717230i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.20877 | 0.426719 | 0.213360 | − | 0.976974i | \(-0.431559\pi\) | ||||
0.213360 | + | 0.976974i | \(0.431559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.522900 | 0.0425530 | 0.0212765 | − | 0.999774i | \(-0.493227\pi\) | ||||
0.0212765 | + | 0.999774i | \(0.493227\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.8764 | − | 6.40794i | −1.20268 | − | 0.518052i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.15383 | − | 3.73054i | −0.173000 | − | 0.299644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.43199 | − | 7.67643i | −0.353711 | − | 0.612646i | 0.633185 | − | 0.774000i | \(-0.281747\pi\) |
−0.986897 | + | 0.161354i | \(0.948414\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.03706 | + | 2.66549i | −0.637381 | + | 0.211387i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.794182 | − | 0.0289431i | −0.0625903 | − | 0.00228104i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9814 | − | 19.0204i | −0.860132 | − | 1.48979i | −0.871801 | − | 0.489860i | \(-0.837048\pi\) |
0.0116689 | − | 0.999932i | \(-0.496286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.26509 | − | 2.90418i | −0.254187 | − | 0.226090i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.65019 | + | 2.85821i | −0.127695 | + | 0.221175i | −0.922783 | − | 0.385319i | \(-0.874091\pi\) |
0.795088 | + | 0.606494i | \(0.207425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.07234 | − | 8.78555i | −0.390180 | − | 0.675812i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.0760 | + | 12.7263i | −1.30583 | + | 0.973203i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.55377 | + | 16.5476i | −0.726360 | + | 1.25809i | 0.232052 | + | 0.972703i | \(0.425456\pi\) |
−0.958412 | + | 0.285389i | \(0.907877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.54944 | − | 0.238687i | −0.495091 | − | 0.0180431i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.26578 | − | 10.9875i | 0.170307 | − | 0.825870i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.03706 | − | 13.9206i | 0.600718 | − | 1.04047i | −0.391994 | − | 0.919968i | \(-0.628215\pi\) |
0.992712 | − | 0.120507i | \(-0.0384520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.05308 | 0.598581 | 0.299291 | − | 0.954162i | \(-0.403250\pi\) | ||||
0.299291 | + | 0.954162i | \(0.403250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.36033 | + | 2.44105i | −0.544092 | + | 0.180448i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.794182 | + | 1.37556i | 0.0583894 | + | 0.101133i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.28799 | + | 7.42702i | −0.313569 | + | 0.543118i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.28180 | − | 10.9732i | 0.602412 | − | 0.798185i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9814 | + | 20.7524i | −0.866946 | + | 1.50159i | −0.00184390 | + | 0.999998i | \(0.500587\pi\) |
−0.865102 | + | 0.501596i | \(0.832746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.88255 | − | 8.45682i | −0.351453 | − | 0.608735i | 0.635051 | − | 0.772470i | \(-0.280979\pi\) |
−0.986504 | + | 0.163735i | \(0.947646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.5625 | + | 4.16635i | −0.899620 | + | 0.298359i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.2436 | −1.29980 | −0.649900 | − | 0.760020i | \(-0.725189\pi\) | ||||
−0.649900 | + | 0.760020i | \(0.725189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.04944 | + | 15.6741i | −0.641498 | + | 1.11111i | 0.343601 | + | 0.939116i | \(0.388353\pi\) |
−0.985098 | + | 0.171991i | \(0.944980\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.51671 | + | 17.0536i | −0.248050 | + | 1.20287i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.2498 | + | 19.3479i | 0.719392 | + | 1.35796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.66690 | − | 8.08330i | 0.325950 | − | 0.564562i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.105074 | − | 0.894969i | −0.00730317 | − | 0.0622046i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.63781 | + | 9.76497i | 0.389975 | + | 0.675457i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.166208 | + | 0.287880i | −0.0114422 | + | 0.0198185i | −0.871690 | − | 0.490058i | \(-0.836976\pi\) |
0.860248 | + | 0.509877i | \(0.170309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.4629 | + | 14.6431i | 1.12802 | + | 1.00333i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.32327 | + | 2.29197i | 0.0902464 | + | 0.156311i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.35896 | − | 6.34053i | −0.228021 | − | 0.430423i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.3912 | + | 8.75264i | −1.78335 | + | 0.591449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9876 | + | 22.4952i | 0.873642 | + | 1.51319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.16621 | − | 5.48403i | −0.212025 | − | 0.367238i | 0.740323 | − | 0.672251i | \(-0.234672\pi\) |
−0.952348 | + | 0.305013i | \(0.901339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.866524 | − | 7.38061i | −0.0577683 | − | 0.492040i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3090 | 1.54707 | 0.773537 | − | 0.633751i | \(-0.218485\pi\) | ||||
0.773537 | + | 0.633751i | \(0.218485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.95420 | −0.327383 | −0.163691 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163691 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.25890 | − | 5.03238i | −0.346010 | − | 0.331106i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.13781 | − | 12.3630i | −0.467613 | − | 0.809930i | 0.531702 | − | 0.846932i | \(-0.321553\pi\) |
−0.999315 | + | 0.0370017i | \(0.988219\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.11745 | − | 3.66754i | 0.138127 | − | 0.239244i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.7880 | + | 4.57279i | −0.895626 | + | 0.297034i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.48762 | + | 4.30868i | −0.160911 | + | 0.278706i | −0.935196 | − | 0.354132i | \(-0.884776\pi\) |
0.774285 | + | 0.632837i | \(0.218110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7305 | + | 7.38061i | 0.880812 | + | 0.473466i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.0891 | + | 0.809332i | 0.708454 | + | 0.0517063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.1520 | 2.17304 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.827603 | + | 4.01330i | −0.0524472 | + | 0.254333i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.43268 | −0.153549 | −0.0767746 | − | 0.997048i | \(-0.524462\pi\) | ||||
−0.0767746 | + | 0.997048i | \(0.524462\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.477100 | −0.0299950 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.0989 | − | 4.67589i | 0.882906 | − | 0.292816i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.987620 | −0.0616061 | −0.0308030 | − | 0.999525i | \(-0.509806\pi\) | ||||
−0.0308030 | + | 0.999525i | \(0.509806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.23855 | + | 2.33795i | 0.0769597 | + | 0.145273i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.9065 | + | 14.8358i | −1.23218 | + | 0.918314i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.1854 | −1.05970 | −0.529848 | − | 0.848092i | \(-0.677751\pi\) | ||||
−0.529848 | + | 0.848092i | \(0.677751\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.88255 | − | 6.72477i | 0.238503 | − | 0.413099i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.12296 | − | 5.44556i | 0.0687237 | − | 0.333263i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4523 | − | 19.8360i | 0.698262 | − | 1.20942i | −0.270807 | − | 0.962634i | \(-0.587291\pi\) |
0.969069 | − | 0.246791i | \(-0.0793761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00364 | − | 12.1307i | −0.425441 | − | 0.736885i | 0.571021 | − | 0.820936i | \(-0.306548\pi\) |
−0.996462 | + | 0.0840504i | \(0.973214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.1643 | + | 6.17323i | −1.28092 | + | 0.373621i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.93454 | −0.237261 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2953 | 1.70010 | 0.850049 | − | 0.526703i | \(-0.176572\pi\) | ||||
0.850049 | + | 0.526703i | \(0.176572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.52359 | − | 4.86186i | 0.390557 | − | 0.291072i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.79782 | − | 15.2383i | −0.524834 | − | 0.909039i | −0.999582 | − | 0.0289175i | \(-0.990794\pi\) |
0.474748 | − | 0.880122i | \(-0.342539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.26145 | − | 16.0413i | −0.550536 | − | 0.953556i | −0.998236 | − | 0.0593725i | \(-0.981090\pi\) |
0.447700 | − | 0.894184i | \(-0.352243\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.94437 | − | 19.1275i | 0.233644 | − | 1.13301i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.25890 | − | 13.1724i | 0.487508 | − | 0.777541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.07598 | − | 10.5239i | −0.357411 | − | 0.619054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.498141 | − | 2.41564i | 0.0292015 | − | 0.141607i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.04256 | + | 12.1981i | −0.411431 | + | 0.712619i | −0.995046 | − | 0.0994108i | \(-0.968304\pi\) |
0.583616 | + | 0.812030i | \(0.301638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.14400 | + | 8.90966i | 0.299495 | + | 0.518741i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.72872 | − | 6.76443i | 0.274388 | − | 0.392512i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.722528 | + | 1.25146i | −0.0417849 | + | 0.0723736i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.06368 | + | 3.89550i | 0.118949 | + | 0.224533i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.5734 | − | 13.8520i | −0.894671 | − | 0.795776i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.55563 | − | 6.15854i | 0.203595 | − | 0.352637i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.85532 | 0.334180 | 0.167090 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167090 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.89307 | − | 7.02059i | −0.449021 | − | 0.399387i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.405446 | + | 0.702253i | 0.0229907 | + | 0.0398211i | 0.877292 | − | 0.479957i | \(-0.159348\pi\) |
−0.854301 | + | 0.519778i | \(0.826015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.28799 | + | 9.15907i | −0.298895 | + | 0.517701i | −0.975883 | − | 0.218292i | \(-0.929951\pi\) |
0.676988 | + | 0.735994i | \(0.263285\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.01307 | + | 12.5665i | 0.0570799 | + | 0.708041i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.09820 | + | 10.5624i | −0.342509 | + | 0.593243i | −0.984898 | − | 0.173136i | \(-0.944610\pi\) |
0.642389 | + | 0.766379i | \(0.277943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.57234 | + | 11.3836i | 0.367981 | + | 0.637361i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.07970 | − | 5.23582i | 0.0602631 | − | 0.292235i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −38.3287 | −2.13267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.95853 | + | 10.3205i | −0.330520 | + | 0.572477i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.76145 | + | 1.24748i | −0.208009 | + | 0.0689860i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.74721 | − | 5.97654i | 0.206590 | − | 0.329497i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.83310 | + | 13.5673i | −0.430546 | + | 0.745728i | −0.996920 | − | 0.0784202i | \(-0.975012\pi\) |
0.566374 | + | 0.824148i | \(0.308346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.40545 | + | 1.79272i | −0.131818 | + | 0.0982402i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.98398 | − | 13.8287i | −0.436211 | − | 0.755540i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.21201 | + | 7.29541i | −0.229443 | + | 0.397406i | −0.957643 | − | 0.287958i | \(-0.907024\pi\) |
0.728200 | + | 0.685364i | \(0.240357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.9999 | − | 10.6128i | 1.73800 | − | 0.576407i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.15383 | − | 3.73054i | −0.116636 | − | 0.202020i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4098 | + | 2.01993i | 0.994035 | + | 0.109066i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.617454 | + | 0.549202i | 0.0332426 | + | 0.0295681i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.283662 | + | 0.491316i | 0.0152277 | + | 0.0263752i | 0.873539 | − | 0.486754i | \(-0.161819\pi\) |
−0.858311 | + | 0.513130i | \(0.828486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.00364189 | − | 0.00630794i | −0.000194946 | − | 0.000337656i | 0.865928 | − | 0.500169i | \(-0.166729\pi\) |
−0.866123 | + | 0.499831i | \(0.833395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.5822 | − | 22.6478i | −0.564835 | − | 1.20885i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.65383 | 0.354148 | 0.177074 | − | 0.984198i | \(-0.443337\pi\) | ||||
0.177074 | + | 0.984198i | \(0.443337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.2051 | −1.07237 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.7527 | − | 6.92820i | 1.25713 | − | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.398568 | + | 0.690339i | 0.0210356 | + | 0.0364347i | 0.876352 | − | 0.481672i | \(-0.159970\pi\) |
−0.855316 | + | 0.518107i | \(0.826637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6971 | + | 27.1881i | −0.826162 | + | 1.43095i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9709 | + | 9.75822i | 0.575823 | + | 0.512174i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.7491 | − | 22.0820i | 0.667317 | − | 1.15583i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4327 | 0.805579 | 0.402790 | − | 0.915293i | \(-0.368041\pi\) | ||||
0.402790 | + | 0.915293i | \(0.368041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.1909 | + | 6.97418i | 0.842864 | + | 0.363061i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.87085 | − | 10.9585i | 0.356717 | − | 0.568939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2422 | 0.530321 | 0.265160 | − | 0.964204i | \(-0.414575\pi\) | ||||
0.265160 | + | 0.964204i | \(0.414575\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.3702 | + | 13.6712i | 0.793712 | + | 0.705977i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.8131 | 2.05048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0087 | −1.28461 | −0.642304 | − | 0.766450i | \(-0.722021\pi\) | ||||
−0.642304 | + | 0.766450i | \(0.722021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3938 | − | 15.4711i | −0.891109 | − | 0.792608i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.26695 | 0.320226 | 0.160113 | − | 0.987099i | \(-0.448814\pi\) | ||||
0.160113 | + | 0.987099i | \(0.448814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.67054 | + | 0.243101i | 0.339962 | + | 0.0123896i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00797 | + | 2.98704i | −0.203737 | + | 0.151840i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6342 | −1.09690 | −0.548448 | − | 0.836185i | \(-0.684781\pi\) | ||||
−0.548448 | + | 0.836185i | \(0.684781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.810892 | − | 1.40451i | 0.0410086 | − | 0.0710290i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.11126 | − | 3.65682i | −0.207386 | − | 0.184462i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.66071 | − | 11.5367i | 0.335137 | − | 0.580473i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05308 | + | 3.55605i | 0.103041 | + | 0.178473i | 0.912936 | − | 0.408102i | \(-0.133809\pi\) |
−0.809895 | + | 0.586575i | \(0.800476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.72617 | − | 31.6004i | 0.386792 | − | 1.58200i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7417 | 0.836041 | 0.418021 | − | 0.908438i | \(-0.362724\pi\) | ||||
0.418021 | + | 0.908438i | \(0.362724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0472 | −0.649926 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.9065 | + | 3.31105i | −0.691022 | + | 0.164527i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.794182 | + | 1.37556i | 0.0393661 | + | 0.0681842i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.38255 | + | 7.59079i | 0.216703 | + | 0.375341i | 0.953798 | − | 0.300449i | \(-0.0971364\pi\) |
−0.737095 | + | 0.675789i | \(0.763803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.5185 | + | 24.4767i | 1.35739 | + | 1.20735i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.02221 | + | 15.1431i | 0.394747 | + | 0.745144i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.87890 | − | 3.25436i | −0.0922318 | − | 0.159750i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.4592 | − | 7.11695i | 1.05086 | − | 0.348518i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.210149 | − | 0.363988i | 0.0102664 | − | 0.0177820i | −0.860847 | − | 0.508865i | \(-0.830065\pi\) |
0.871113 | + | 0.491083i | \(0.163399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.28799 | + | 5.69497i | 0.160247 | + | 0.277556i | 0.934957 | − | 0.354761i | \(-0.115438\pi\) |
−0.774710 | + | 0.632316i | \(0.782104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.34610 | + | 3.16431i | 0.357179 | + | 0.153854i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.68725 | − | 11.5827i | 0.324379 | − | 0.561841i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.29232 | − | 10.0358i | 0.304507 | − | 0.485667i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.5625 | + | 4.16635i | −0.606524 | + | 0.201154i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.0439 | + | 19.1287i | −0.531968 | + | 0.921395i | 0.467336 | + | 0.884080i | \(0.345214\pi\) |
−0.999304 | + | 0.0373155i | \(0.988119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.43268 | −0.453306 | −0.226653 | − | 0.973976i | \(-0.572778\pi\) | ||||
−0.226653 | + | 0.973976i | \(0.572778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.59820 | − | 22.2981i | 0.220467 | − | 1.06911i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.06615 | − | 1.84663i | −0.0510010 | − | 0.0883363i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.6032 | + | 27.0256i | −0.744701 | + | 1.28986i | 0.205634 | + | 0.978629i | \(0.434074\pi\) |
−0.950334 | + | 0.311231i | \(0.899259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.924016 | + | 20.9797i | 0.0440007 | + | 0.999031i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.52723 | − | 11.3055i | 0.310118 | − | 0.537140i | −0.668270 | − | 0.743919i | \(-0.732965\pi\) |
0.978388 | + | 0.206779i | \(0.0662981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.54944 | + | 4.41576i | 0.120855 | + | 0.209327i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.74110 | − | 5.99596i | −0.318843 | − | 0.283599i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.91706 | −0.468015 | −0.234008 | − | 0.972235i | \(-0.575184\pi\) | ||||
−0.234008 | + | 0.972235i | \(0.575184\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.66690 | − | 8.08330i | 0.219756 | − | 0.380628i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.676728 | − | 0.601924i | −0.0317955 | − | 0.0282809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7396 | − | 17.1290i | 0.503482 | − | 0.803019i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2615 | − | 21.2375i | 0.573566 | − | 0.993446i | −0.422629 | − | 0.906303i | \(-0.638893\pi\) |
0.996196 | − | 0.0871436i | \(-0.0277739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.8764 | + | 25.4176i | 0.554341 | + | 1.18639i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.75526 | + | 3.04020i | 0.0817506 | + | 0.141596i | 0.904002 | − | 0.427528i | \(-0.140616\pi\) |
−0.822251 | + | 0.569125i | \(0.807282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.69413 | + | 15.0587i | −0.404050 | + | 0.699836i | −0.994210 | − | 0.107451i | \(-0.965731\pi\) |
0.590160 | + | 0.807286i | \(0.299065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.50688 | + | 7.30733i | −0.0698798 | + | 0.338869i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.69894 | − | 11.6029i | −0.309990 | − | 0.536918i | 0.668370 | − | 0.743829i | \(-0.266992\pi\) |
−0.978360 | + | 0.206911i | \(0.933659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4512 | − | 23.5036i | −0.574945 | − | 1.08529i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.10074 | + | 15.0365i | −0.142875 | + | 0.692844i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.32327 | + | 2.29197i | 0.0608441 | + | 0.105385i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.79232 | − | 15.2287i | −0.403419 | − | 0.698743i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.4697 | + | 5.80205i | 0.616737 | + | 0.265658i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.8058 | −0.950641 | −0.475321 | − | 0.879813i | \(-0.657668\pi\) | ||||
−0.475321 | + | 0.879813i | \(0.657668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.81089 | 0.219358 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.994499 | + | 0.951662i | 0.0452513 | + | 0.0433021i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.13093 | + | 1.95882i | 0.0513528 | + | 0.0889456i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2472 | + | 28.1410i | −0.736231 | + | 1.27519i | 0.217950 | + | 0.975960i | \(0.430063\pi\) |
−0.954181 | + | 0.299230i | \(0.903270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.68292 | + | 37.2569i | −0.347434 | + | 1.68481i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.66071 | − | 16.7328i | 0.435982 | − | 0.755142i | −0.561394 | − | 0.827549i | \(-0.689735\pi\) |
0.997375 | + | 0.0724067i | \(0.0230679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.6822 | −2.01238 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.882546 | + | 7.51707i | 0.0396675 | + | 0.337867i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33.6334 | − | 1.22573i | −1.50866 | − | 0.0549816i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1506 | 0.499169 | 0.249585 | − | 0.968353i | \(-0.419706\pi\) | ||||
0.249585 | + | 0.968353i | \(0.419706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.42580 | − | 1.79947i | 0.242407 | − | 0.0803942i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.7651 | 1.81763 | 0.908813 | − | 0.417204i | \(-0.136990\pi\) | ||||
0.908813 | + | 0.417204i | \(0.136990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1135 | 0.850537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.54875 | + | 17.2090i | −0.157606 | + | 0.764279i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.44506 | 0.0640510 | 0.0320255 | − | 0.999487i | \(-0.489804\pi\) | ||||
0.0320255 | + | 0.999487i | \(0.489804\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.5617 | − | 35.9844i | 0.998073 | − | 1.59186i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.7490 | + | 3.18650i | 1.62251 | + | 0.140687i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.68725 | 0.426871 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.11745 | − | 3.66754i | 0.0931255 | − | 0.161298i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.4127 | − | 10.4180i | 1.37887 | − | 0.457301i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.64214 | − | 16.7007i | 0.422430 | − | 0.731670i | −0.573747 | − | 0.819033i | \(-0.694511\pi\) |
0.996177 | + | 0.0873630i | \(0.0278440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.3454 | + | 31.7752i | 0.802189 | + | 1.38943i | 0.918173 | + | 0.396180i | \(0.129665\pi\) |
−0.115984 | + | 0.993251i | \(0.537002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.20141 | + | 7.84814i | 0.357939 | + | 0.342521i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.6428 | 0.637851 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9098 | −0.996077 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.5803 | + | 11.6116i | −0.676128 | + | 0.503900i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.1353 | − | 24.4830i | −0.612266 | − | 1.06048i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.45125 | + | 4.24568i | 0.105977 | + | 0.183557i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.4258 | + | 8.76411i | −1.14036 | + | 0.378199i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0891 | + | 0.809332i | 0.477639 | + | 0.0348604i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.62543 | − | 2.81532i | −0.0698825 | − | 0.121040i | 0.828967 | − | 0.559298i | \(-0.188929\pi\) |
−0.898849 | + | 0.438258i | \(0.855596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.4222 | − | 9.27012i | −0.447258 | − | 0.397819i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.81708 | − | 3.14728i | 0.0778352 | − | 0.134815i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.95853 | + | 5.12432i | 0.126498 | + | 0.219100i | 0.922317 | − | 0.386433i | \(-0.126293\pi\) |
−0.795820 | + | 0.605534i | \(0.792960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.3356 | + | 5.31351i | 0.526470 | + | 0.226775i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.3738 | + | 50.8769i | −1.25137 | + | 2.16743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7873 | − | 18.7999i | 0.501247 | − | 0.799454i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.555632 | − | 2.69443i | 0.0235853 | − | 0.114372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.8040 | − | 22.1772i | 0.542523 | − | 0.939678i | −0.456235 | − | 0.889859i | \(-0.650802\pi\) |
0.998758 | − | 0.0498188i | \(-0.0158644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.01594 | 0.339038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.0989 | − | 4.67589i | 0.595255 | − | 0.197416i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.3189 | − | 40.3895i | −0.982773 | − | 1.70221i | −0.651443 | − | 0.758698i | \(-0.725836\pi\) |
−0.331330 | − | 0.943515i | \(-0.607497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.4585 | + | 26.7750i | −0.650345 | + | 1.12643i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.3497 | + | 4.66795i | −0.980597 | + | 0.196035i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.5989 | + | 27.0181i | −0.653939 | + | 1.13266i | 0.328219 | + | 0.944602i | \(0.393551\pi\) |
−0.982159 | + | 0.188054i | \(0.939782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.83812 | − | 13.5760i | −0.328015 | − | 0.568139i | 0.654103 | − | 0.756406i | \(-0.273046\pi\) |
−0.982118 | + | 0.188267i | \(0.939713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.3948 | − | 13.0653i | 1.64574 | − | 0.545811i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.744051 | 0.0310291 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.99567 | − | 12.1169i | 0.291234 | − | 0.504431i | −0.682868 | − | 0.730542i | \(-0.739268\pi\) |
0.974102 | + | 0.226110i | \(0.0726010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.41597 | + | 16.5651i | −0.141963 | + | 0.688422i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.93021 | − | 5.53120i | −0.121565 | − | 0.229473i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.88255 | − | 6.72477i | 0.160799 | − | 0.278511i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.0542 | + | 9.06902i | 0.870483 | + | 0.374958i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.44801 | − | 2.50803i | −0.0597658 | − | 0.103517i | 0.834594 | − | 0.550865i | \(-0.185702\pi\) |
−0.894360 | + | 0.447348i | \(0.852369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.62612 | − | 16.6729i | 0.396637 | − | 0.686996i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6105 | + | 21.0007i | 0.971206 | + | 0.863852i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.04394 | − | 3.54021i | −0.0839346 | − | 0.145379i | 0.821002 | − | 0.570925i | \(-0.193415\pi\) |
−0.904937 | + | 0.425546i | \(0.860082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0531 | + | 19.2238i | −0.494128 | + | 0.788100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.7545 | − | 9.86807i | 1.21777 | − | 0.403873i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.88255 | − | 17.1171i | −0.403790 | − | 0.699385i | 0.590390 | − | 0.807118i | \(-0.298974\pi\) |
−0.994180 | + | 0.107734i | \(0.965641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4320 | − | 23.2649i | −0.547902 | − | 0.948994i | −0.998418 | − | 0.0562261i | \(-0.982093\pi\) |
0.450516 | − | 0.892768i | \(-0.351240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.1822 | − | 18.0223i | 0.984773 | − | 0.733926i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.4647 | −0.547419 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.2422 | 0.618661 | 0.309331 | − | 0.950955i | \(-0.399895\pi\) | ||||
0.309331 | + | 0.950955i | \(0.399895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.00688 | − | 36.8385i | 0.364977 | − | 1.49277i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.41342 | − | 11.1084i | −0.259459 | − | 0.449396i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.36033 | + | 2.35617i | −0.0549434 | + | 0.0951648i | −0.892189 | − | 0.451662i | \(-0.850831\pi\) |
0.837246 | + | 0.546827i | \(0.184165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.3447 | + | 5.08907i | −0.618759 | + | 0.205211i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.21812 | + | 15.9663i | −0.371108 | + | 0.642777i | −0.989736 | − | 0.142906i | \(-0.954355\pi\) |
0.618629 | + | 0.785684i | \(0.287689\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.107546 | −0.00432262 | −0.00216131 | − | 0.999998i | \(-0.500688\pi\) | ||||
−0.00216131 | + | 0.999998i | \(0.500688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.894237 | + | 1.27921i | −0.0358845 | + | 0.0513328i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.97593 | + | 7.50516i | 0.159292 | + | 0.300688i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.47848 | −0.259139 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.94437 | − | 19.1275i | 0.157523 | − | 0.763878i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.39926 | −0.215282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7266 | −1.42225 | −0.711126 | − | 0.703064i | \(-0.751815\pi\) | ||||
−0.711126 | + | 0.703064i | \(0.751815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.546489 | − | 0.181243i | 0.0217210 | − | 0.00720376i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.3475 | 0.847152 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9164 | − | 27.8615i | 0.749494 | − | 1.10391i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.44987 | − | 37.9017i | −0.176034 | − | 1.49937i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3128 | 0.683813 | 0.341906 | − | 0.939734i | \(-0.388927\pi\) | ||||
0.341906 | + | 0.939734i | \(0.388927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.4821 | + | 25.0838i | −0.571119 | + | 0.989207i | 0.425332 | + | 0.905037i | \(0.360157\pi\) |
−0.996451 | + | 0.0841700i | \(0.973176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.925798 | − | 4.48949i | 0.0364533 | − | 0.176773i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.27816 | + | 2.21384i | −0.0502497 | + | 0.0870350i | −0.890056 | − | 0.455851i | \(-0.849335\pi\) |
0.839807 | + | 0.542886i | \(0.182668\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.14400 | + | 8.90966i | 0.201920 | + | 0.349735i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.95165 | + | 12.0724i | −0.115684 | + | 0.473154i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.9766 | 1.17308 | 0.586538 | − | 0.809922i | \(-0.300491\pi\) | ||||
0.586538 | + | 0.809922i | \(0.300491\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.04580 | 0.197156 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 44.2304 | + | 19.0521i | 1.72559 | + | 0.743294i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.63162 | + | 13.2183i | 0.297286 | + | 0.514914i | 0.975514 | − | 0.219937i | \(-0.0705853\pi\) |
−0.678228 | + | 0.734851i | \(0.737252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6261 | + | 23.6011i | 0.529994 | + | 0.917977i | 0.999388 | + | 0.0349881i | \(0.0111393\pi\) |
−0.469393 | + | 0.882989i | \(0.655527\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.08650 | − | 44.0633i | 0.352891 | − | 1.71128i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.9654 | + | 26.3618i | 0.541555 | + | 1.02227i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.24288 | − | 2.15273i | −0.0481245 | − | 0.0833541i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.21517 | + | 10.7420i | −0.0856433 | + | 0.415311i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.55563 | − | 6.15854i | 0.137264 | − | 0.237748i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2280 | + | 40.2320i | 0.895372 | + | 1.55083i | 0.833344 | + | 0.552755i | \(0.186423\pi\) |
0.0620280 | + | 0.998074i | \(0.480243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.37457 | + | 10.5493i | −0.283847 | + | 0.406044i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.54944 | + | 4.41576i | −0.0979830 | + | 0.169712i | −0.910850 | − | 0.412738i | \(-0.864572\pi\) |
0.812867 | + | 0.582450i | \(0.197906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76371 | + | 3.32927i | 0.0676852 | + | 0.127766i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.1661 | − | 26.8317i | −1.15597 | − | 1.02819i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.77197 | − | 13.4614i | 0.297386 | − | 0.515088i | −0.678151 | − | 0.734923i | \(-0.737218\pi\) |
0.975537 | + | 0.219835i | \(0.0705518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.7738 | −1.29043 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.41164 | + | 5.70291i | 0.244619 | + | 0.217580i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.7596 | − | 20.3682i | −0.448005 | − | 0.775967i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.6483 | − | 20.1755i | 0.443123 | − | 0.767512i | −0.554796 | − | 0.831986i | \(-0.687204\pi\) |
0.997919 | + | 0.0644744i | \(0.0205371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.01307 | + | 12.5665i | 0.0384833 | + | 0.477361i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3665 | + | 17.9553i | −0.393225 | + | 0.681085i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.8640 | + | 27.4772i | 0.600891 | + | 1.04077i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.99381 | + | 24.2165i | −0.188883 | + | 0.915954i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.6464 | −1.72404 | −0.862020 | − | 0.506874i | \(-0.830801\pi\) | ||||
−0.862020 | + | 0.506874i | \(0.830801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.54944 | + | 6.14781i | −0.133870 | + | 0.231869i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.96217 | + | 2.30900i | −0.262211 | + | 0.0869621i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.8163 | + | 1.15951i | 1.19658 | + | 0.0436079i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.00069 | + | 15.5897i | −0.338028 | + | 0.585482i | −0.984062 | − | 0.177827i | \(-0.943093\pi\) |
0.646034 | + | 0.763309i | \(0.276427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.1080 | + | 9.95371i | 0.866619 | + | 0.373293i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.407305 | + | 0.705474i | 0.0152537 | + | 0.0264202i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.06870 | − | 10.5113i | 0.226957 | − | 0.393100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.17928 | − | 2.71266i | 0.305461 | − | 0.101306i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.4389 | − | 31.9371i | −0.687654 | − | 1.19105i | −0.972595 | − | 0.232506i | \(-0.925307\pi\) |
0.284941 | − | 0.958545i | \(-0.408026\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.1254 | + | 0.587674i | 0.600542 | + | 0.0218861i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.8244 | + | 14.9646i | 0.625705 | + | 0.556541i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.2498 | − | 17.7531i | −0.380666 | − | 0.659334i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2429 | − | 26.4014i | −0.565327 | − | 0.979175i | −0.997019 | − | 0.0771543i | \(-0.975417\pi\) |
0.431692 | − | 0.902021i | \(-0.357917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.27375 | − | 25.3574i | −0.343472 | − | 0.939163i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.99628 | −0.332739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.15059 | 0.227177 | 0.113589 | − | 0.993528i | \(-0.463765\pi\) | ||||
0.113589 | + | 0.993528i | \(0.463765\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.4196 | − | 13.8123i | −0.494990 | − | 0.509475i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.98398 | − | 13.8287i | −0.294094 | − | 0.509385i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3912 | − | 35.3186i | 0.750103 | − | 1.29922i | −0.197670 | − | 0.980269i | \(-0.563337\pi\) |
0.947772 | − | 0.318947i | \(-0.103329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −44.1989 | − | 39.3132i | −1.62369 | − | 1.44421i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.25271 | + | 12.5621i | −0.266076 | + | 0.460858i | −0.967845 | − | 0.251547i | \(-0.919061\pi\) |
0.701769 | + | 0.712405i | \(0.252394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.27342 | 0.303115 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.69089 | − | 4.24127i | 0.208219 | − | 0.155180i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.82279 | + | 7.21608i | 0.139682 | + | 0.263670i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.18911 | −0.152863 | −0.0764314 | − | 0.997075i | \(-0.524353\pi\) | ||||
−0.0764314 | + | 0.997075i | \(0.524353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.14833 | + | 2.80032i | 0.114731 | + | 0.102049i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.830556 | 0.0302270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.38688 | 0.0867525 | 0.0433763 | − | 0.999059i | \(-0.486189\pi\) | ||||
0.0433763 | + | 0.999059i | \(0.486189\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.617454 | + | 0.549202i | 0.0224122 | + | 0.0199348i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.63416 | 0.131738 | 0.0658692 | − | 0.997828i | \(-0.479018\pi\) | ||||
0.0658692 | + | 0.997828i | \(0.479018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.21565 | − | 5.12874i | 0.116414 | − | 0.185673i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.6291 | − | 10.1781i | −0.854311 | − | 0.367992i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.1606 | 1.12515 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.9672 | + | 34.5842i | −0.720035 | + | 1.24714i | 0.240950 | + | 0.970538i | \(0.422541\pi\) |
−0.960985 | + | 0.276600i | \(0.910792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.27816 | + | 1.13688i | 0.0460318 | + | 0.0409436i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0698 | − | 31.2978i | 0.649925 | − | 1.12570i | −0.333215 | − | 0.942851i | \(-0.608133\pi\) |
0.983140 | − | 0.182853i | \(-0.0585332\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.35896 | + | 5.81788i | 0.120657 | + | 0.208985i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.08836 | − | 4.45146i | 0.0390448 | − | 0.159695i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.7156 | 1.49462 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2051 | −0.722994 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.8406 | + | 3.71470i | 1.53100 | + | 0.132753i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.03961 | − | 12.1930i | −0.251254 | − | 0.435186i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.3189 | − | 38.6574i | −0.795582 | − | 1.37799i | −0.922469 | − | 0.386071i | \(-0.873832\pi\) |
0.126888 | − | 0.991917i | \(-0.459501\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.2410 | + | 19.7826i | 0.791801 | + | 0.704278i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.3566 | + | 43.6319i | −0.972689 | + | 1.55137i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7694 | − | 18.6532i | −0.382433 | − | 0.662394i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.7658 | + | 4.23377i | −0.452756 | + | 0.150156i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.2836 | − | 45.5245i | 0.931012 | − | 1.61256i | 0.149418 | − | 0.988774i | \(-0.452260\pi\) |
0.781595 | − | 0.623786i | \(-0.214407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.19777 | + | 12.4669i | 0.254639 | + | 0.441047i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.72184 | + | 5.75488i | −0.272838 | + | 0.203339i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.7491 | − | 22.0820i | 0.449905 | − | 0.779258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.26145 | − | 0.0459722i | −0.0444603 | − | 0.00162031i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.6552 | + | 12.4883i | −1.32553 | + | 0.439611i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.40290 | − | 12.8222i | 0.260272 | − | 0.450804i | −0.706042 | − | 0.708170i | \(-0.749521\pi\) |
0.966314 | + | 0.257365i | \(0.0828544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0704 | −0.950571 | −0.475285 | − | 0.879832i | \(-0.657655\pi\) | ||||
−0.475285 | + | 0.879832i | \(0.657655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.89995 | + | 23.7614i | −0.171849 | + | 0.833348i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.4425 | − | 30.2113i | −0.610984 | − | 1.05826i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.91411 | + | 10.2435i | −0.206908 | + | 0.358376i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.4967 | + | 16.3736i | 1.20541 | + | 0.572139i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.9091 | + | 37.9477i | −0.764632 | + | 1.32438i | 0.175808 | + | 0.984424i | \(0.443746\pi\) |
−0.940441 | + | 0.339958i | \(0.889587\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6712 | + | 27.1434i | 0.546265 | + | 0.946158i | 0.998526 | + | 0.0542727i | \(0.0172840\pi\) |
−0.452262 | + | 0.891885i | \(0.649383\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.09201 | + | 4.52915i | 0.177281 | + | 0.157685i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.7665 | 0.513480 | 0.256740 | − | 0.966480i | \(-0.417352\pi\) | ||||
0.256740 | + | 0.966480i | \(0.417352\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0036 | + | 25.9871i | −0.521098 | + | 0.902568i | 0.478601 | + | 0.878033i | \(0.341144\pi\) |
−0.999699 | + | 0.0245357i | \(0.992189\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.6192 | − | 32.5715i | −1.27031 | − | 1.12989i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.2298 | + | 31.2689i | −0.735569 | + | 1.08340i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.62110 | + | 4.53987i | −0.0907068 | + | 0.157109i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.0393 | − | 1.21735i | −0.485270 | − | 0.0420777i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0167 | − | 31.2059i | −0.622006 | − | 1.07735i | −0.989112 | − | 0.147167i | \(-0.952985\pi\) |
0.367106 | − | 0.930179i | \(-0.380349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7429 | + | 34.1957i | −0.680789 | + | 1.17916i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.15521 | + | 29.8485i | −0.211997 | + | 1.02804i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.05673 | − | 13.9547i | −0.277160 | − | 0.480055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.4134 | − | 0.816833i | −0.770134 | − | 0.0280667i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.47957 | + | 31.4215i | −0.222378 | + | 1.07838i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.150186 | − | 0.260130i | −0.00514831 | − | 0.00891713i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2658 | − | 21.2450i | −0.419972 | − | 0.727413i | 0.575964 | − | 0.817475i | \(-0.304627\pi\) |
−0.995936 | + | 0.0900617i | \(0.971294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.1229 | + | 20.2140i | −0.927583 | + | 0.691303i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.0480 | 0.992260 | 0.496130 | − | 0.868248i | \(-0.334754\pi\) | ||||
0.496130 | + | 0.868248i | \(0.334754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.2953 | −0.863064 | −0.431532 | − | 0.902098i | \(-0.642027\pi\) | ||||
−0.431532 | + | 0.902098i | \(0.642027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.8516 | + | 7.54041i | −0.881020 | + | 0.256976i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.34981 | + | 2.33795i | 0.0459482 | + | 0.0795846i | 0.888085 | − | 0.459680i | \(-0.152036\pi\) |
−0.842137 | + | 0.539264i | \(0.818702\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1749 | + | 26.2836i | −0.515961 | + | 0.893671i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.25093 | + | 20.6141i | −0.144369 | + | 0.700091i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.66071 | − | 11.5367i | 0.225949 | − | 0.391355i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.3643 | −1.63876 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.42539 | + | 2.55286i | −0.115932 | + | 0.0864011i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.4010 | − | 1.14438i | −1.06155 | − | 0.0386870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0916 | −0.374537 | −0.187268 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187268 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.1559 | − | 7.67965i | 0.781029 | − | 0.259028i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.3942 | −1.36091 | −0.680457 | − | 0.732788i | \(-0.738219\pi\) | ||||
−0.680457 | + | 0.732788i | \(0.738219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2581 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.59888 | − | 17.4521i | 0.120975 | − | 0.586646i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.5672 | −1.36211 | −0.681056 | − | 0.732231i | \(-0.738479\pi\) | ||||
−0.681056 | + | 0.732231i | \(0.738479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.5352 | + | 1.29504i | 1.19181 | + | 0.0434343i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.9065 | + | 3.31105i | −0.465887 | + | 0.110924i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.9271 | 0.633371 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7658 | − | 22.1110i | 0.426713 | − | 0.739089i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.37567 | − | 0.787890i | 0.0793212 | − | 0.0263069i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.2218 | − | 19.4367i | 0.374267 | − | 0.648249i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1978 | + | 22.8592i | 0.439681 | + | 0.761551i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.81344 | − | 7.41705i | 0.0603475 | − | 0.246824i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.7912 | 0.425195 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.1135 | −0.999901 | −0.499950 | − | 0.866054i | \(-0.666648\pi\) | ||||
−0.499950 | + | 0.866054i | \(0.666648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.20946 | + | 35.8540i | 0.139619 | + | 1.18920i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6113 | − | 25.3075i | −0.484093 | − | 0.838473i | 0.515740 | − | 0.856745i | \(-0.327517\pi\) |
−0.999833 | + | 0.0182717i | \(0.994184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.87890 | − | 3.25436i | −0.0621826 | − | 0.107704i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.6909 | + | 3.87728i | −0.386489 | + | 0.128179i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.39926 | + | 0.306102i | 0.277368 | + | 0.0101084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.52359 | + | 9.56714i | 0.182206 | + | 0.315591i | 0.942632 | − | 0.333835i | \(-0.108343\pi\) |
−0.760425 | + | 0.649426i | \(0.775009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.57784 | − | 6.74021i | −0.249698 | − | 0.222097i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.5989 | + | 52.9988i | −1.00717 | + | 1.74448i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.23855 | − | 2.14523i | −0.0407233 | − | 0.0705348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.13348 | + | 18.1718i | 0.0700725 | + | 0.596842i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.1669 | − | 36.6621i | 0.694463 | − | 1.20285i | −0.275898 | − | 0.961187i | \(-0.588975\pi\) |
0.970361 | − | 0.241659i | \(-0.0776915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.6476 | + | 44.7291i | 0.709473 | + | 1.46594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.283662 | − | 1.37556i | 0.00928666 | − | 0.0450339i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.81089 | + | 11.7968i | −0.222740 | + | 0.385797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7651 | −0.384349 | −0.192174 | − | 0.981361i | \(-0.561554\pi\) | ||||
−0.192174 | + | 0.981361i | \(0.561554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.3869 | − | 5.76636i | 0.567399 | − | 0.188178i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.28799 | − | 12.6232i | −0.237582 | − | 0.411504i | 0.722438 | − | 0.691436i | \(-0.243021\pi\) |
−0.960020 | + | 0.279932i | \(0.909688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.882546 | + | 1.52861i | −0.0287397 | + | 0.0497785i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.1545 | − | 17.4295i | 0.427916 | − | 0.566981i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.12178 | − | 5.40709i | 0.101444 | − | 0.175707i | −0.810836 | − | 0.585274i | \(-0.800987\pi\) |
0.912280 | + | 0.409567i | \(0.134320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.6148 | − | 66.8828i | −1.25349 | − | 2.17111i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.0508 | − | 6.64985i | 0.650192 | − | 0.215636i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0173 | 0.907570 | 0.453785 | − | 0.891111i | \(-0.350073\pi\) | ||||
0.453785 | + | 0.891111i | \(0.350073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.0309 | + | 32.9624i | −0.615825 | + | 1.06664i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.59820 | − | 22.2981i | 0.148639 | − | 0.720795i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56.2199 | − | 2.04887i | −1.81544 | − | 0.0661616i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.8225 | − | 20.4772i | 0.381371 | − | 0.660554i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.42442 | + | 5.53322i | −0.239249 | + | 0.178306i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.75526 | − | 13.4325i | −0.249651 | − | 0.432408i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.7837 | + | 27.3381i | −0.507568 | + | 0.879134i | 0.492393 | + | 0.870373i | \(0.336122\pi\) |
−0.999962 | + | 0.00876132i | \(0.997211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.6043 | + | 44.1212i | 1.59352 | + | 1.41738i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.82141 | − | 4.88683i | −0.0905434 | − | 0.156826i | 0.817196 | − | 0.576359i | \(-0.195527\pi\) |
−0.907740 | + | 0.419533i | \(0.862194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3454 | + | 29.2596i | −0.588127 | + | 0.938021i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.5916 | − | 6.49755i | 0.627433 | − | 0.208088i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.24652 | − | 5.62314i | −0.103865 | − | 0.179900i | 0.809409 | − | 0.587246i | \(-0.199788\pi\) |
−0.913274 | + | 0.407346i | \(0.866454\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.54944 | + | 4.41576i | 0.0814805 | + | 0.141128i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.30401 | + | 2.71543i | 0.201272 | + | 0.0866971i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.3063 | 0.966620 | 0.483310 | − | 0.875449i | \(-0.339434\pi\) | ||||
0.483310 | + | 0.875449i | \(0.339434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.9774 | −0.923298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.7293 | + | 3.42122i | −0.373349 | + | 0.108899i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.250241 | − | 0.433430i | −0.00795720 | − | 0.0137823i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1669 | + | 19.3416i | −0.354728 | + | 0.614407i | −0.987071 | − | 0.160281i | \(-0.948760\pi\) |
0.632343 | + | 0.774688i | \(0.282093\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.7552 | − | 8.54170i | 0.817316 | − | 0.271063i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3738 | + | 24.8962i | −0.455680 | + | 0.789262i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.76509 | −0.277593 | −0.138797 | − | 0.990321i | \(-0.544323\pi\) | ||||
−0.138797 | + | 0.990321i | \(0.544323\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.17673 | + | 0.448873i | 0.163784 | + | 0.0142017i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))