Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(201,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.e (of order \(3\), degree \(2\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.1 | ||
Root | \(1.39564 - 0.228425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.201 |
Dual form | 950.2.e.j.501.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.39564 | + | 2.41733i | −0.805775 | + | 1.39564i | 0.109991 | + | 0.993933i | \(0.464918\pi\) |
−0.915766 | + | 0.401711i | \(0.868416\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.39564 | + | 2.41733i | 0.569769 | + | 0.986869i | ||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.39564 | − | 4.14938i | −0.798548 | − | 1.38313i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.79129 | −1.14312 | −0.571558 | − | 0.820562i | \(-0.693661\pi\) | ||||
−0.571558 | + | 0.820562i | \(0.693661\pi\) | |||||||
\(12\) | 2.79129 | 0.805775 | ||||||||
\(13\) | −0.104356 | − | 0.180750i | −0.0289432 | − | 0.0501310i | 0.851191 | − | 0.524856i | \(-0.175881\pi\) |
−0.880134 | + | 0.474725i | \(0.842548\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.395644 | + | 0.685275i | −0.0959577 | + | 0.166204i | −0.910008 | − | 0.414591i | \(-0.863925\pi\) |
0.814050 | + | 0.580795i | \(0.197258\pi\) | |||||||
\(18\) | −4.79129 | −1.12932 | ||||||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.39564 | + | 2.41733i | −0.304554 | + | 0.527504i | ||||
\(22\) | −1.89564 | + | 3.28335i | −0.404153 | + | 0.700013i | ||||
\(23\) | 2.29129 | + | 3.96863i | 0.477767 | + | 0.827516i | 0.999675 | − | 0.0254855i | \(-0.00811315\pi\) |
−0.521909 | + | 0.853001i | \(0.674780\pi\) | |||||||
\(24\) | 1.39564 | − | 2.41733i | 0.284885 | − | 0.493435i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.208712 | −0.0409318 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | −3.39564 | − | 5.88143i | −0.630555 | − | 1.09215i | −0.987438 | − | 0.158005i | \(-0.949494\pi\) |
0.356883 | − | 0.934149i | \(-0.383839\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.79129 | −0.860541 | −0.430270 | − | 0.902700i | \(-0.641582\pi\) | ||||
−0.430270 | + | 0.902700i | \(0.641582\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 5.29129 | − | 9.16478i | 0.921095 | − | 1.59538i | ||||
\(34\) | 0.395644 | + | 0.685275i | 0.0678524 | + | 0.117524i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.39564 | + | 4.14938i | −0.399274 | + | 0.691563i | ||||
\(37\) | −3.58258 | −0.588972 | −0.294486 | − | 0.955656i | \(-0.595148\pi\) | ||||
−0.294486 | + | 0.955656i | \(0.595148\pi\) | |||||||
\(38\) | −4.00000 | + | 1.73205i | −0.648886 | + | 0.280976i | ||||
\(39\) | 0.582576 | 0.0932868 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.68693 | − | 9.85005i | 0.888150 | − | 1.53832i | 0.0460888 | − | 0.998937i | \(-0.485324\pi\) |
0.842061 | − | 0.539383i | \(-0.181342\pi\) | |||||||
\(42\) | 1.39564 | + | 2.41733i | 0.215353 | + | 0.373002i | ||||
\(43\) | 2.89564 | − | 5.01540i | 0.441582 | − | 0.764842i | −0.556225 | − | 0.831031i | \(-0.687751\pi\) |
0.997807 | + | 0.0661897i | \(0.0210843\pi\) | |||||||
\(44\) | 1.89564 | + | 3.28335i | 0.285779 | + | 0.494984i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.58258 | 0.675664 | ||||||||
\(47\) | −6.08258 | − | 10.5353i | −0.887235 | − | 1.53674i | −0.843131 | − | 0.537709i | \(-0.819290\pi\) |
−0.0441043 | − | 0.999027i | \(-0.514043\pi\) | |||||||
\(48\) | −1.39564 | − | 2.41733i | −0.201444 | − | 0.348911i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.10436 | − | 1.91280i | −0.154641 | − | 0.267846i | ||||
\(52\) | −0.104356 | + | 0.180750i | −0.0144716 | + | 0.0250655i | ||||
\(53\) | −2.29129 | − | 3.96863i | −0.314733 | − | 0.545133i | 0.664648 | − | 0.747157i | \(-0.268582\pi\) |
−0.979381 | + | 0.202024i | \(0.935248\pi\) | |||||||
\(54\) | 2.50000 | − | 4.33013i | 0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 11.1652 | − | 4.83465i | 1.47886 | − | 0.640365i | ||||
\(58\) | −6.79129 | −0.891740 | ||||||||
\(59\) | −2.29129 | + | 3.96863i | −0.298300 | + | 0.516671i | −0.975747 | − | 0.218900i | \(-0.929753\pi\) |
0.677447 | + | 0.735572i | \(0.263086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.686932 | − | 1.18980i | −0.0879526 | − | 0.152338i | 0.818693 | − | 0.574232i | \(-0.194699\pi\) |
−0.906646 | + | 0.421893i | \(0.861366\pi\) | |||||||
\(62\) | −2.39564 | + | 4.14938i | −0.304247 | + | 0.526971i | ||||
\(63\) | −2.39564 | − | 4.14938i | −0.301823 | − | 0.522772i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.29129 | − | 9.16478i | −0.651313 | − | 1.12811i | ||||
\(67\) | 7.79129 | + | 13.4949i | 0.951857 | + | 1.64867i | 0.741401 | + | 0.671062i | \(0.234162\pi\) |
0.210456 | + | 0.977603i | \(0.432505\pi\) | |||||||
\(68\) | 0.791288 | 0.0959577 | ||||||||
\(69\) | −12.7913 | −1.53989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.29129 | − | 3.96863i | 0.271926 | − | 0.470989i | −0.697429 | − | 0.716654i | \(-0.745673\pi\) |
0.969355 | + | 0.245664i | \(0.0790061\pi\) | |||||||
\(72\) | 2.39564 | + | 4.14938i | 0.282329 | + | 0.489009i | ||||
\(73\) | 1.39564 | − | 2.41733i | 0.163348 | − | 0.282927i | −0.772720 | − | 0.634748i | \(-0.781104\pi\) |
0.936067 | + | 0.351821i | \(0.114437\pi\) | |||||||
\(74\) | −1.79129 | + | 3.10260i | −0.208233 | + | 0.360670i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | + | 4.33013i | −0.0573539 | + | 0.496700i | ||||
\(77\) | −3.79129 | −0.432057 | ||||||||
\(78\) | 0.291288 | − | 0.504525i | 0.0329819 | − | 0.0571262i | ||||
\(79\) | −7.47822 | + | 12.9527i | −0.841365 | + | 1.45729i | 0.0473751 | + | 0.998877i | \(0.484914\pi\) |
−0.888741 | + | 0.458411i | \(0.848419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.208712 | − | 0.361500i | 0.0231902 | − | 0.0401667i | ||||
\(82\) | −5.68693 | − | 9.85005i | −0.628017 | − | 1.08776i | ||||
\(83\) | −3.79129 | −0.416148 | −0.208074 | − | 0.978113i | \(-0.566719\pi\) | ||||
−0.208074 | + | 0.978113i | \(0.566719\pi\) | |||||||
\(84\) | 2.79129 | 0.304554 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.89564 | − | 5.01540i | −0.312245 | − | 0.540825i | ||||
\(87\) | 18.9564 | 2.03234 | ||||||||
\(88\) | 3.79129 | 0.404153 | ||||||||
\(89\) | −2.29129 | − | 3.96863i | −0.242876 | − | 0.420674i | 0.718656 | − | 0.695365i | \(-0.244757\pi\) |
−0.961532 | + | 0.274692i | \(0.911424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.104356 | − | 0.180750i | −0.0109395 | − | 0.0189478i | ||||
\(92\) | 2.29129 | − | 3.96863i | 0.238883 | − | 0.413758i | ||||
\(93\) | 6.68693 | − | 11.5821i | 0.693403 | − | 1.20101i | ||||
\(94\) | −12.1652 | −1.25474 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.79129 | −0.284885 | ||||||||
\(97\) | −6.18693 | + | 10.7161i | −0.628188 | + | 1.08805i | 0.359727 | + | 0.933057i | \(0.382870\pi\) |
−0.987915 | + | 0.154996i | \(0.950464\pi\) | |||||||
\(98\) | −3.00000 | + | 5.19615i | −0.303046 | + | 0.524891i | ||||
\(99\) | 9.08258 | + | 15.7315i | 0.912833 | + | 1.58107i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | −2.20871 | −0.218695 | ||||||||
\(103\) | −5.16515 | −0.508937 | −0.254469 | − | 0.967081i | \(-0.581901\pi\) | ||||
−0.254469 | + | 0.967081i | \(0.581901\pi\) | |||||||
\(104\) | 0.104356 | + | 0.180750i | 0.0102330 | + | 0.0177240i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.58258 | −0.445099 | ||||||||
\(107\) | −18.9564 | −1.83259 | −0.916294 | − | 0.400506i | \(-0.868834\pi\) | ||||
−0.916294 | + | 0.400506i | \(0.868834\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | 5.87386 | − | 10.1738i | 0.562614 | − | 0.974476i | −0.434653 | − | 0.900598i | \(-0.643129\pi\) |
0.997267 | − | 0.0738783i | \(-0.0235376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | − | 8.66025i | 0.474579 | − | 0.821995i | ||||
\(112\) | −0.500000 | + | 0.866025i | −0.0472456 | + | 0.0818317i | ||||
\(113\) | −5.37386 | −0.505531 | −0.252765 | − | 0.967528i | \(-0.581340\pi\) | ||||
−0.252765 | + | 0.967528i | \(0.581340\pi\) | |||||||
\(114\) | 1.39564 | − | 12.0866i | 0.130714 | − | 1.13202i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.39564 | + | 5.88143i | −0.315278 | + | 0.546077i | ||||
\(117\) | −0.500000 | + | 0.866025i | −0.0462250 | + | 0.0800641i | ||||
\(118\) | 2.29129 | + | 3.96863i | 0.210930 | + | 0.365342i | ||||
\(119\) | −0.395644 | + | 0.685275i | −0.0362686 | + | 0.0628191i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | −1.37386 | −0.124384 | ||||||||
\(123\) | 15.8739 | + | 27.4943i | 1.43130 | + | 2.47908i | ||||
\(124\) | 2.39564 | + | 4.14938i | 0.215135 | + | 0.372625i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.79129 | −0.426842 | ||||||||
\(127\) | 1.31307 | + | 2.27430i | 0.116516 | + | 0.201812i | 0.918385 | − | 0.395689i | \(-0.129494\pi\) |
−0.801869 | + | 0.597500i | \(0.796161\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 8.08258 | + | 13.9994i | 0.711631 | + | 1.23258i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.76951 | + | 9.99308i | −0.504084 | + | 0.873099i | 0.495905 | + | 0.868377i | \(0.334837\pi\) |
−0.999989 | + | 0.00472247i | \(0.998497\pi\) | |||||||
\(132\) | −10.5826 | −0.921095 | ||||||||
\(133\) | −3.50000 | − | 2.59808i | −0.303488 | − | 0.225282i | ||||
\(134\) | 15.5826 | 1.34613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.395644 | − | 0.685275i | 0.0339262 | − | 0.0587619i | ||||
\(137\) | 7.66515 | + | 13.2764i | 0.654878 | + | 1.13428i | 0.981924 | + | 0.189274i | \(0.0606134\pi\) |
−0.327046 | + | 0.945008i | \(0.606053\pi\) | |||||||
\(138\) | −6.39564 | + | 11.0776i | −0.544433 | + | 0.942986i | ||||
\(139\) | 6.10436 | + | 10.5731i | 0.517765 | + | 0.896795i | 0.999787 | + | 0.0206359i | \(0.00656907\pi\) |
−0.482022 | + | 0.876159i | \(0.660098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.9564 | 2.85965 | ||||||||
\(142\) | −2.29129 | − | 3.96863i | −0.192281 | − | 0.333040i | ||||
\(143\) | 0.395644 | + | 0.685275i | 0.0330854 | + | 0.0573056i | ||||
\(144\) | 4.79129 | 0.399274 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.39564 | − | 2.41733i | −0.115504 | − | 0.200059i | ||||
\(147\) | 8.37386 | − | 14.5040i | 0.690665 | − | 1.19627i | ||||
\(148\) | 1.79129 | + | 3.10260i | 0.147243 | + | 0.255032i | ||||
\(149\) | 11.3739 | − | 19.7001i | 0.931783 | − | 1.61390i | 0.151511 | − | 0.988456i | \(-0.451586\pi\) |
0.780272 | − | 0.625440i | \(-0.215081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7477 | 1.28153 | 0.640766 | − | 0.767736i | \(-0.278617\pi\) | ||||
0.640766 | + | 0.767736i | \(0.278617\pi\) | |||||||
\(152\) | 3.50000 | + | 2.59808i | 0.283887 | + | 0.210732i | ||||
\(153\) | 3.79129 | 0.306507 | ||||||||
\(154\) | −1.89564 | + | 3.28335i | −0.152755 | + | 0.264580i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.291288 | − | 0.504525i | −0.0233217 | − | 0.0403944i | ||||
\(157\) | −3.97822 | + | 6.89048i | −0.317496 | + | 0.549920i | −0.979965 | − | 0.199170i | \(-0.936176\pi\) |
0.662469 | + | 0.749090i | \(0.269509\pi\) | |||||||
\(158\) | 7.47822 | + | 12.9527i | 0.594935 | + | 1.03046i | ||||
\(159\) | 12.7913 | 1.01442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.29129 | + | 3.96863i | 0.180579 | + | 0.312772i | ||||
\(162\) | −0.208712 | − | 0.361500i | −0.0163980 | − | 0.0284021i | ||||
\(163\) | 14.5826 | 1.14220 | 0.571098 | − | 0.820882i | \(-0.306518\pi\) | ||||
0.571098 | + | 0.820882i | \(0.306518\pi\) | |||||||
\(164\) | −11.3739 | −0.888150 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.89564 | + | 3.28335i | −0.147131 | + | 0.254838i | ||||
\(167\) | 5.76951 | + | 9.99308i | 0.446458 | + | 0.773288i | 0.998152 | − | 0.0607584i | \(-0.0193519\pi\) |
−0.551695 | + | 0.834046i | \(0.686019\pi\) | |||||||
\(168\) | 1.39564 | − | 2.41733i | 0.107676 | − | 0.186501i | ||||
\(169\) | 6.47822 | − | 11.2206i | 0.498325 | − | 0.863124i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.39564 | + | 20.7469i | −0.183199 | + | 1.58655i | ||||
\(172\) | −5.79129 | −0.441582 | ||||||||
\(173\) | −10.5000 | + | 18.1865i | −0.798300 | + | 1.38270i | 0.122422 | + | 0.992478i | \(0.460934\pi\) |
−0.920722 | + | 0.390218i | \(0.872399\pi\) | |||||||
\(174\) | 9.47822 | − | 16.4168i | 0.718542 | − | 1.24455i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.89564 | − | 3.28335i | 0.142890 | − | 0.247492i | ||||
\(177\) | −6.39564 | − | 11.0776i | −0.480726 | − | 0.832642i | ||||
\(178\) | −4.58258 | −0.343479 | ||||||||
\(179\) | −16.7477 | −1.25178 | −0.625892 | − | 0.779910i | \(-0.715265\pi\) | ||||
−0.625892 | + | 0.779910i | \(0.715265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.81307 | + | 6.60443i | 0.283423 | + | 0.490903i | 0.972226 | − | 0.234046i | \(-0.0751966\pi\) |
−0.688802 | + | 0.724949i | \(0.741863\pi\) | |||||||
\(182\) | −0.208712 | −0.0154708 | ||||||||
\(183\) | 3.83485 | 0.283480 | ||||||||
\(184\) | −2.29129 | − | 3.96863i | −0.168916 | − | 0.292571i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.68693 | − | 11.5821i | −0.490310 | − | 0.849241i | ||||
\(187\) | 1.50000 | − | 2.59808i | 0.109691 | − | 0.189990i | ||||
\(188\) | −6.08258 | + | 10.5353i | −0.443617 | + | 0.768368i | ||||
\(189\) | 5.00000 | 0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.9564 | 1.15457 | 0.577284 | − | 0.816544i | \(-0.304113\pi\) | ||||
0.577284 | + | 0.816544i | \(0.304113\pi\) | |||||||
\(192\) | −1.39564 | + | 2.41733i | −0.100722 | + | 0.174455i | ||||
\(193\) | −1.37386 | + | 2.37960i | −0.0988929 | + | 0.171287i | −0.911227 | − | 0.411905i | \(-0.864863\pi\) |
0.812334 | + | 0.583193i | \(0.198197\pi\) | |||||||
\(194\) | 6.18693 | + | 10.7161i | 0.444196 | + | 0.769370i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | −20.2087 | −1.43981 | −0.719906 | − | 0.694072i | \(-0.755815\pi\) | ||||
−0.719906 | + | 0.694072i | \(0.755815\pi\) | |||||||
\(198\) | 18.1652 | 1.29094 | ||||||||
\(199\) | −1.79129 | − | 3.10260i | −0.126981 | − | 0.219938i | 0.795525 | − | 0.605921i | \(-0.207195\pi\) |
−0.922506 | + | 0.385984i | \(0.873862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −43.4955 | −3.06793 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.39564 | − | 5.88143i | −0.238327 | − | 0.412795i | ||||
\(204\) | −1.10436 | + | 1.91280i | −0.0773204 | + | 0.133923i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.58258 | + | 4.47315i | −0.179937 | + | 0.311659i | ||||
\(207\) | 10.9782 | − | 19.0148i | 0.763039 | − | 1.32162i | ||||
\(208\) | 0.208712 | 0.0144716 | ||||||||
\(209\) | 13.2695 | + | 9.85005i | 0.917871 | + | 0.681343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9782 | + | 20.7469i | −0.824615 | + | 1.42827i | 0.0775988 | + | 0.996985i | \(0.475275\pi\) |
−0.902213 | + | 0.431290i | \(0.858059\pi\) | |||||||
\(212\) | −2.29129 | + | 3.96863i | −0.157366 | + | 0.272566i | ||||
\(213\) | 6.39564 | + | 11.0776i | 0.438222 | + | 0.759023i | ||||
\(214\) | −9.47822 | + | 16.4168i | −0.647918 | + | 1.12223i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −4.79129 | −0.325254 | ||||||||
\(218\) | −5.87386 | − | 10.1738i | −0.397828 | − | 0.689059i | ||||
\(219\) | 3.89564 | + | 6.74745i | 0.263243 | + | 0.455951i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.165151 | 0.0111093 | ||||||||
\(222\) | −5.00000 | − | 8.66025i | −0.335578 | − | 0.581238i | ||||
\(223\) | 9.60436 | − | 16.6352i | 0.643155 | − | 1.11398i | −0.341569 | − | 0.939857i | \(-0.610958\pi\) |
0.984724 | − | 0.174121i | \(-0.0557084\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.68693 | + | 4.65390i | −0.178732 | + | 0.309573i | ||||
\(227\) | −7.74773 | −0.514235 | −0.257117 | − | 0.966380i | \(-0.582773\pi\) | ||||
−0.257117 | + | 0.966380i | \(0.582773\pi\) | |||||||
\(228\) | −9.76951 | − | 7.25198i | −0.647001 | − | 0.480274i | ||||
\(229\) | −25.3303 | −1.67387 | −0.836937 | − | 0.547300i | \(-0.815656\pi\) | ||||
−0.836937 | + | 0.547300i | \(0.815656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.29129 | − | 9.16478i | 0.348141 | − | 0.602998i | ||||
\(232\) | 3.39564 | + | 5.88143i | 0.222935 | + | 0.386135i | ||||
\(233\) | 4.58258 | − | 7.93725i | 0.300215 | − | 0.519987i | −0.675970 | − | 0.736929i | \(-0.736275\pi\) |
0.976184 | + | 0.216942i | \(0.0696084\pi\) | |||||||
\(234\) | 0.500000 | + | 0.866025i | 0.0326860 | + | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.58258 | 0.298300 | ||||||||
\(237\) | −20.8739 | − | 36.1546i | −1.35590 | − | 2.34849i | ||||
\(238\) | 0.395644 | + | 0.685275i | 0.0256458 | + | 0.0444198i | ||||
\(239\) | 16.5826 | 1.07264 | 0.536319 | − | 0.844015i | \(-0.319814\pi\) | ||||
0.536319 | + | 0.844015i | \(0.319814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.39564 | + | 14.5417i | 0.540811 | + | 0.936712i | 0.998858 | + | 0.0477840i | \(0.0152159\pi\) |
−0.458047 | + | 0.888928i | \(0.651451\pi\) | |||||||
\(242\) | 1.68693 | − | 2.92185i | 0.108440 | − | 0.187824i | ||||
\(243\) | 8.08258 | + | 13.9994i | 0.518497 | + | 0.898064i | ||||
\(244\) | −0.686932 | + | 1.18980i | −0.0439763 | + | 0.0761692i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 31.7477 | 2.02416 | ||||||||
\(247\) | −0.104356 | + | 0.903750i | −0.00664002 | + | 0.0575042i | ||||
\(248\) | 4.79129 | 0.304247 | ||||||||
\(249\) | 5.29129 | − | 9.16478i | 0.335322 | − | 0.580794i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.56080 | − | 11.3636i | −0.414114 | − | 0.717266i | 0.581221 | − | 0.813746i | \(-0.302575\pi\) |
−0.995335 | + | 0.0964796i | \(0.969242\pi\) | |||||||
\(252\) | −2.39564 | + | 4.14938i | −0.150911 | + | 0.261386i | ||||
\(253\) | −8.68693 | − | 15.0462i | −0.546143 | − | 0.945947i | ||||
\(254\) | 2.62614 | 0.164778 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.60436 | − | 9.70703i | −0.349590 | − | 0.605508i | 0.636587 | − | 0.771205i | \(-0.280346\pi\) |
−0.986177 | + | 0.165697i | \(0.947012\pi\) | |||||||
\(258\) | 16.1652 | 1.00640 | ||||||||
\(259\) | −3.58258 | −0.222610 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.2695 | + | 28.1796i | −1.00706 | + | 1.74427i | ||||
\(262\) | 5.76951 | + | 9.99308i | 0.356441 | + | 0.617375i | ||||
\(263\) | −9.70871 | + | 16.8160i | −0.598665 | + | 1.03692i | 0.394354 | + | 0.918959i | \(0.370969\pi\) |
−0.993018 | + | 0.117959i | \(0.962365\pi\) | |||||||
\(264\) | −5.29129 | + | 9.16478i | −0.325656 | + | 0.564053i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | + | 1.73205i | −0.245256 | + | 0.106199i | ||||
\(267\) | 12.7913 | 0.782814 | ||||||||
\(268\) | 7.79129 | − | 13.4949i | 0.475929 | − | 0.824333i | ||||
\(269\) | −6.56080 | + | 11.3636i | −0.400019 | + | 0.692853i | −0.993728 | − | 0.111827i | \(-0.964330\pi\) |
0.593709 | + | 0.804680i | \(0.297663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.56080 | − | 14.8277i | 0.520031 | − | 0.900721i | −0.479698 | − | 0.877434i | \(-0.659254\pi\) |
0.999729 | − | 0.0232867i | \(-0.00741305\pi\) | |||||||
\(272\) | −0.395644 | − | 0.685275i | −0.0239894 | − | 0.0415509i | ||||
\(273\) | 0.582576 | 0.0352591 | ||||||||
\(274\) | 15.3303 | 0.926137 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.39564 | + | 11.0776i | 0.384973 | + | 0.666792i | ||||
\(277\) | 8.74773 | 0.525600 | 0.262800 | − | 0.964850i | \(-0.415354\pi\) | ||||
0.262800 | + | 0.964850i | \(0.415354\pi\) | |||||||
\(278\) | 12.2087 | 0.732230 | ||||||||
\(279\) | 11.4782 | + | 19.8809i | 0.687183 | + | 1.19024i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.29129 | − | 9.16478i | −0.315652 | − | 0.546725i | 0.663924 | − | 0.747800i | \(-0.268890\pi\) |
−0.979576 | + | 0.201075i | \(0.935556\pi\) | |||||||
\(282\) | 16.9782 | − | 29.4071i | 1.01104 | − | 1.75117i | ||||
\(283\) | 10.5608 | − | 18.2918i | 0.627774 | − | 1.08734i | −0.360223 | − | 0.932866i | \(-0.617299\pi\) |
0.987997 | − | 0.154471i | \(-0.0493672\pi\) | |||||||
\(284\) | −4.58258 | −0.271926 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.791288 | 0.0467898 | ||||||||
\(287\) | 5.68693 | − | 9.85005i | 0.335689 | − | 0.581430i | ||||
\(288\) | 2.39564 | − | 4.14938i | 0.141165 | − | 0.244504i | ||||
\(289\) | 8.18693 | + | 14.1802i | 0.481584 | + | 0.834128i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2695 | − | 29.9117i | −1.01236 | − | 1.75345i | ||||
\(292\) | −2.79129 | −0.163348 | ||||||||
\(293\) | −24.9564 | −1.45797 | −0.728985 | − | 0.684529i | \(-0.760008\pi\) | ||||
−0.728985 | + | 0.684529i | \(0.760008\pi\) | |||||||
\(294\) | −8.37386 | − | 14.5040i | −0.488374 | − | 0.845888i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.58258 | 0.208233 | ||||||||
\(297\) | −18.9564 | −1.09996 | ||||||||
\(298\) | −11.3739 | − | 19.7001i | −0.658870 | − | 1.14120i | ||||
\(299\) | 0.478220 | − | 0.828301i | 0.0276562 | − | 0.0479019i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.89564 | − | 5.01540i | 0.166902 | − | 0.289083i | ||||
\(302\) | 7.87386 | − | 13.6379i | 0.453090 | − | 0.784775i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000 | − | 1.73205i | 0.229416 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.89564 | − | 3.28335i | 0.108367 | − | 0.187697i | ||||
\(307\) | −17.2477 | + | 29.8739i | −0.984380 | + | 1.70500i | −0.339719 | + | 0.940527i | \(0.610332\pi\) |
−0.644661 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(308\) | 1.89564 | + | 3.28335i | 0.108014 | + | 0.187086i | ||||
\(309\) | 7.20871 | − | 12.4859i | 0.410089 | − | 0.710296i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | −0.582576 | −0.0329819 | ||||||||
\(313\) | −5.87386 | − | 10.1738i | −0.332010 | − | 0.575059i | 0.650896 | − | 0.759167i | \(-0.274394\pi\) |
−0.982906 | + | 0.184108i | \(0.941060\pi\) | |||||||
\(314\) | 3.97822 | + | 6.89048i | 0.224504 | + | 0.388852i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.9564 | 0.841365 | ||||||||
\(317\) | −4.58258 | − | 7.93725i | −0.257383 | − | 0.445801i | 0.708157 | − | 0.706055i | \(-0.249527\pi\) |
−0.965540 | + | 0.260254i | \(0.916194\pi\) | |||||||
\(318\) | 6.39564 | − | 11.0776i | 0.358650 | − | 0.621200i | ||||
\(319\) | 12.8739 | + | 22.2982i | 0.720798 | + | 1.24846i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.4564 | − | 45.8239i | 1.47665 | − | 2.55764i | ||||
\(322\) | 4.58258 | 0.255377 | ||||||||
\(323\) | 3.16515 | − | 1.37055i | 0.176114 | − | 0.0762595i | ||||
\(324\) | −0.417424 | −0.0231902 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.29129 | − | 12.6289i | 0.403827 | − | 0.699449i | ||||
\(327\) | 16.3956 | + | 28.3981i | 0.906681 | + | 1.57042i | ||||
\(328\) | −5.68693 | + | 9.85005i | −0.314008 | + | 0.543878i | ||||
\(329\) | −6.08258 | − | 10.5353i | −0.335343 | − | 0.580832i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.9129 | −0.984581 | −0.492290 | − | 0.870431i | \(-0.663840\pi\) | ||||
−0.492290 | + | 0.870431i | \(0.663840\pi\) | |||||||
\(332\) | 1.89564 | + | 3.28335i | 0.104037 | + | 0.180197i | ||||
\(333\) | 8.58258 | + | 14.8655i | 0.470322 | + | 0.814622i | ||||
\(334\) | 11.5390 | 0.631387 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.39564 | − | 2.41733i | −0.0761386 | − | 0.131876i | ||||
\(337\) | 11.6652 | − | 20.2046i | 0.635441 | − | 1.10062i | −0.350980 | − | 0.936383i | \(-0.614152\pi\) |
0.986421 | − | 0.164234i | \(-0.0525151\pi\) | |||||||
\(338\) | −6.47822 | − | 11.2206i | −0.352369 | − | 0.610320i | ||||
\(339\) | 7.50000 | − | 12.9904i | 0.407344 | − | 0.705541i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.1652 | 0.983698 | ||||||||
\(342\) | 16.7695 | + | 12.4481i | 0.906791 | + | 0.673118i | ||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −2.89564 | + | 5.01540i | −0.156123 | + | 0.270412i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5000 | + | 18.1865i | 0.564483 | + | 0.977714i | ||||
\(347\) | 1.81307 | − | 3.14033i | 0.0973306 | − | 0.168582i | −0.813248 | − | 0.581917i | \(-0.802303\pi\) |
0.910579 | + | 0.413335i | \(0.135636\pi\) | |||||||
\(348\) | −9.47822 | − | 16.4168i | −0.508086 | − | 0.880031i | ||||
\(349\) | −5.41742 | −0.289988 | −0.144994 | − | 0.989433i | \(-0.546316\pi\) | ||||
−0.144994 | + | 0.989433i | \(0.546316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.521780 | − | 0.903750i | −0.0278506 | − | 0.0482386i | ||||
\(352\) | −1.89564 | − | 3.28335i | −0.101038 | − | 0.175003i | ||||
\(353\) | 13.7477 | 0.731718 | 0.365859 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365859 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(354\) | −12.7913 | −0.679849 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.29129 | + | 3.96863i | −0.121438 | + | 0.210337i | ||||
\(357\) | −1.10436 | − | 1.91280i | −0.0584487 | − | 0.101236i | ||||
\(358\) | −8.37386 | + | 14.5040i | −0.442572 | + | 0.766558i | ||||
\(359\) | 17.8521 | − | 30.9207i | 0.942197 | − | 1.63193i | 0.180928 | − | 0.983496i | \(-0.442090\pi\) |
0.761269 | − | 0.648437i | \(-0.224577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 7.62614 | 0.400821 | ||||||||
\(363\) | −4.70871 | + | 8.15573i | −0.247143 | + | 0.428065i | ||||
\(364\) | −0.104356 | + | 0.180750i | −0.00546974 | + | 0.00947388i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.91742 | − | 3.32108i | 0.100225 | − | 0.173595i | ||||
\(367\) | 4.39564 | + | 7.61348i | 0.229451 | + | 0.397420i | 0.957645 | − | 0.287950i | \(-0.0929737\pi\) |
−0.728195 | + | 0.685370i | \(0.759640\pi\) | |||||||
\(368\) | −4.58258 | −0.238883 | ||||||||
\(369\) | −54.4955 | −2.83692 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.29129 | − | 3.96863i | −0.118958 | − | 0.206041i | ||||
\(372\) | −13.3739 | −0.693403 | ||||||||
\(373\) | 21.3739 | 1.10670 | 0.553348 | − | 0.832950i | \(-0.313350\pi\) | ||||
0.553348 | + | 0.832950i | \(0.313350\pi\) | |||||||
\(374\) | −1.50000 | − | 2.59808i | −0.0775632 | − | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.08258 | + | 10.5353i | 0.313685 | + | 0.543318i | ||||
\(377\) | −0.708712 | + | 1.22753i | −0.0365005 | + | 0.0632208i | ||||
\(378\) | 2.50000 | − | 4.33013i | 0.128586 | − | 0.222718i | ||||
\(379\) | 4.83485 | 0.248349 | 0.124175 | − | 0.992260i | \(-0.460372\pi\) | ||||
0.124175 | + | 0.992260i | \(0.460372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.33030 | −0.375543 | ||||||||
\(382\) | 7.97822 | − | 13.8187i | 0.408201 | − | 0.707025i | ||||
\(383\) | 2.29129 | − | 3.96863i | 0.117079 | − | 0.202787i | −0.801530 | − | 0.597955i | \(-0.795980\pi\) |
0.918609 | + | 0.395168i | \(0.129313\pi\) | |||||||
\(384\) | 1.39564 | + | 2.41733i | 0.0712212 | + | 0.123359i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.37386 | + | 2.37960i | 0.0699278 | + | 0.121119i | ||||
\(387\) | −27.7477 | −1.41050 | ||||||||
\(388\) | 12.3739 | 0.628188 | ||||||||
\(389\) | −9.31307 | − | 16.1307i | −0.472191 | − | 0.817859i | 0.527302 | − | 0.849678i | \(-0.323204\pi\) |
−0.999494 | + | 0.0318184i | \(0.989870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.62614 | −0.183382 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | −16.1044 | − | 27.8936i | −0.812357 | − | 1.40704i | ||||
\(394\) | −10.1044 | + | 17.5013i | −0.509050 | + | 0.881701i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.08258 | − | 15.7315i | 0.456417 | − | 0.790537i | ||||
\(397\) | −5.70871 | + | 9.88778i | −0.286512 | + | 0.496253i | −0.972975 | − | 0.230912i | \(-0.925829\pi\) |
0.686463 | + | 0.727165i | \(0.259163\pi\) | |||||||
\(398\) | −3.58258 | −0.179578 | ||||||||
\(399\) | 11.1652 | − | 4.83465i | 0.558957 | − | 0.242035i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | −21.7477 | + | 37.6682i | −1.08468 | + | 1.87872i | ||||
\(403\) | 0.500000 | + | 0.866025i | 0.0249068 | + | 0.0431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.79129 | −0.337046 | ||||||||
\(407\) | 13.5826 | 0.673263 | ||||||||
\(408\) | 1.10436 | + | 1.91280i | 0.0546738 | + | 0.0946978i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.7913 | −2.11074 | ||||||||
\(412\) | 2.58258 | + | 4.47315i | 0.127234 | + | 0.220376i | ||||
\(413\) | −2.29129 | + | 3.96863i | −0.112747 | + | 0.195283i | ||||
\(414\) | −10.9782 | − | 19.0148i | −0.539550 | − | 0.934528i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.104356 | − | 0.180750i | 0.00511648 | − | 0.00886200i | ||||
\(417\) | −34.0780 | −1.66881 | ||||||||
\(418\) | 15.1652 | − | 6.56670i | 0.741752 | − | 0.321188i | ||||
\(419\) | −22.7477 | −1.11130 | −0.555650 | − | 0.831417i | \(-0.687530\pi\) | ||||
−0.555650 | + | 0.831417i | \(0.687530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | + | 17.3205i | −0.487370 | + | 0.844150i | −0.999895 | − | 0.0145228i | \(-0.995377\pi\) |
0.512524 | + | 0.858673i | \(0.328710\pi\) | |||||||
\(422\) | 11.9782 | + | 20.7469i | 0.583091 | + | 1.00994i | ||||
\(423\) | −29.1434 | + | 50.4778i | −1.41700 | + | 2.45431i | ||||
\(424\) | 2.29129 | + | 3.96863i | 0.111275 | + | 0.192734i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.7913 | 0.619740 | ||||||||
\(427\) | −0.686932 | − | 1.18980i | −0.0332430 | − | 0.0575785i | ||||
\(428\) | 9.47822 | + | 16.4168i | 0.458147 | + | 0.793534i | ||||
\(429\) | −2.20871 | −0.106638 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.10436 | − | 7.10895i | −0.197700 | − | 0.342426i | 0.750082 | − | 0.661344i | \(-0.230014\pi\) |
−0.947782 | + | 0.318918i | \(0.896680\pi\) | |||||||
\(432\) | −2.50000 | + | 4.33013i | −0.120281 | + | 0.208333i | ||||
\(433\) | 3.45644 | + | 5.98673i | 0.166106 | + | 0.287704i | 0.937047 | − | 0.349202i | \(-0.113547\pi\) |
−0.770942 | + | 0.636906i | \(0.780214\pi\) | |||||||
\(434\) | −2.39564 | + | 4.14938i | −0.114995 | + | 0.199176i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7477 | −0.562614 | ||||||||
\(437\) | 2.29129 | − | 19.8431i | 0.109607 | − | 0.949226i | ||||
\(438\) | 7.79129 | 0.372282 | ||||||||
\(439\) | 12.6652 | − | 21.9367i | 0.604475 | − | 1.04698i | −0.387660 | − | 0.921803i | \(-0.626716\pi\) |
0.992134 | − | 0.125178i | \(-0.0399503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.3739 | + | 24.8963i | 0.684470 | + | 1.18554i | ||||
\(442\) | 0.0825757 | − | 0.143025i | 0.00392773 | − | 0.00680302i | ||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | −10.0000 | −0.474579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.60436 | − | 16.6352i | −0.454779 | − | 0.787701i | ||||
\(447\) | 31.7477 | + | 54.9887i | 1.50162 | + | 2.60088i | ||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 3.33030 | 0.157167 | 0.0785834 | − | 0.996908i | \(-0.474960\pi\) | ||||
0.0785834 | + | 0.996908i | \(0.474960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.5608 | + | 37.3444i | −1.01526 | + | 1.75848i | ||||
\(452\) | 2.68693 | + | 4.65390i | 0.126383 | + | 0.218901i | ||||
\(453\) | −21.9782 | + | 38.0674i | −1.03263 | + | 1.78856i | ||||
\(454\) | −3.87386 | + | 6.70973i | −0.181809 | + | 0.314903i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.1652 | + | 4.83465i | −0.522856 | + | 0.226403i | ||||
\(457\) | 20.7477 | 0.970538 | 0.485269 | − | 0.874365i | \(-0.338722\pi\) | ||||
0.485269 | + | 0.874365i | \(0.338722\pi\) | |||||||
\(458\) | −12.6652 | + | 21.9367i | −0.591804 | + | 1.02503i | ||||
\(459\) | −1.97822 | + | 3.42638i | −0.0923354 | + | 0.159930i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.39564 | + | 11.0776i | −0.297875 | + | 0.515934i | −0.975650 | − | 0.219335i | \(-0.929611\pi\) |
0.677775 | + | 0.735270i | \(0.262944\pi\) | |||||||
\(462\) | −5.29129 | − | 9.16478i | −0.246173 | − | 0.426384i | ||||
\(463\) | −17.9564 | −0.834507 | −0.417253 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417253 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(464\) | 6.79129 | 0.315278 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.58258 | − | 7.93725i | −0.212284 | − | 0.367686i | ||||
\(467\) | 12.3303 | 0.570578 | 0.285289 | − | 0.958441i | \(-0.407910\pi\) | ||||
0.285289 | + | 0.958441i | \(0.407910\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 7.79129 | + | 13.4949i | 0.359768 | + | 0.623137i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.1044 | − | 19.2333i | −0.511662 | − | 0.886224i | ||||
\(472\) | 2.29129 | − | 3.96863i | 0.105465 | − | 0.182671i | ||||
\(473\) | −10.9782 | + | 19.0148i | −0.504779 | + | 0.874303i | ||||
\(474\) | −41.7477 | −1.91754 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.791288 | 0.0362686 | ||||||||
\(477\) | −10.9782 | + | 19.0148i | −0.502658 | + | 0.870629i | ||||
\(478\) | 8.29129 | − | 14.3609i | 0.379235 | − | 0.656854i | ||||
\(479\) | −15.8739 | − | 27.4943i | −0.725295 | − | 1.25625i | −0.958852 | − | 0.283905i | \(-0.908370\pi\) |
0.233557 | − | 0.972343i | \(-0.424963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.373864 | + | 0.647551i | 0.0170467 | + | 0.0295258i | ||||
\(482\) | 16.7913 | 0.764822 | ||||||||
\(483\) | −12.7913 | −0.582024 | ||||||||
\(484\) | −1.68693 | − | 2.92185i | −0.0766787 | − | 0.132811i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.1652 | 0.733266 | ||||||||
\(487\) | −23.0000 | −1.04223 | −0.521115 | − | 0.853487i | \(-0.674484\pi\) | ||||
−0.521115 | + | 0.853487i | \(0.674484\pi\) | |||||||
\(488\) | 0.686932 | + | 1.18980i | 0.0310959 | + | 0.0538597i | ||||
\(489\) | −20.3521 | + | 35.2508i | −0.920353 | + | 1.59410i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7087 | − | 27.2083i | 0.708924 | − | 1.22789i | −0.256332 | − | 0.966589i | \(-0.582514\pi\) |
0.965257 | − | 0.261304i | \(-0.0841525\pi\) | |||||||
\(492\) | 15.8739 | − | 27.4943i | 0.715649 | − | 1.23954i | ||||
\(493\) | 5.37386 | 0.242027 | ||||||||
\(494\) | 0.730493 | + | 0.542250i | 0.0328664 | + | 0.0243970i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.39564 | − | 4.14938i | 0.107568 | − | 0.186313i | ||||
\(497\) | 2.29129 | − | 3.96863i | 0.102778 | − | 0.178017i | ||||
\(498\) | −5.29129 | − | 9.16478i | −0.237108 | − | 0.410684i | ||||
\(499\) | 9.66515 | − | 16.7405i | 0.432672 | − | 0.749409i | −0.564431 | − | 0.825480i | \(-0.690904\pi\) |
0.997102 | + | 0.0760712i | \(0.0242376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.2087 | −1.43898 | ||||||||
\(502\) | −13.1216 | −0.585645 | ||||||||
\(503\) | −2.29129 | − | 3.96863i | −0.102163 | − | 0.176952i | 0.810412 | − | 0.585860i | \(-0.199243\pi\) |
−0.912576 | + | 0.408908i | \(0.865910\pi\) | |||||||
\(504\) | 2.39564 | + | 4.14938i | 0.106710 | + | 0.184828i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.3739 | −0.772362 | ||||||||
\(507\) | 18.0826 | + | 31.3199i | 0.803075 | + | 1.39097i | ||||
\(508\) | 1.31307 | − | 2.27430i | 0.0582580 | − | 0.100906i | ||||
\(509\) | −11.2087 | − | 19.4141i | −0.496817 | − | 0.860513i | 0.503176 | − | 0.864184i | \(-0.332165\pi\) |
−0.999993 | + | 0.00367102i | \(0.998831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39564 | − | 2.41733i | 0.0617397 | − | 0.106936i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.5000 | − | 12.9904i | −0.772644 | − | 0.573539i | ||||
\(514\) | −11.2087 | −0.494395 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.08258 | − | 13.9994i | 0.355816 | − | 0.616291i | ||||
\(517\) | 23.0608 | + | 39.9425i | 1.01421 | + | 1.75667i | ||||
\(518\) | −1.79129 | + | 3.10260i | −0.0787047 | + | 0.136320i | ||||
\(519\) | −29.3085 | − | 50.7638i | −1.28650 | − | 2.22829i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2523 | 0.580593 | 0.290296 | − | 0.956937i | \(-0.406246\pi\) | ||||
0.290296 | + | 0.956937i | \(0.406246\pi\) | |||||||
\(522\) | 16.2695 | + | 28.1796i | 0.712097 | + | 1.23339i | ||||
\(523\) | −8.87386 | − | 15.3700i | −0.388027 | − | 0.672082i | 0.604157 | − | 0.796865i | \(-0.293510\pi\) |
−0.992184 | + | 0.124783i | \(0.960177\pi\) | |||||||
\(524\) | 11.5390 | 0.504084 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.70871 | + | 16.8160i | 0.423320 | + | 0.733212i | ||||
\(527\) | 1.89564 | − | 3.28335i | 0.0825755 | − | 0.143025i | ||||
\(528\) | 5.29129 | + | 9.16478i | 0.230274 | + | 0.398846i | ||||
\(529\) | 1.00000 | − | 1.73205i | 0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.9564 | 0.952828 | ||||||||
\(532\) | −0.500000 | + | 4.33013i | −0.0216777 | + | 0.187735i | ||||
\(533\) | −2.37386 | −0.102823 | ||||||||
\(534\) | 6.39564 | − | 11.0776i | 0.276767 | − | 0.479374i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.79129 | − | 13.4949i | −0.336532 | − | 0.582891i | ||||
\(537\) | 23.3739 | − | 40.4847i | 1.00866 | − | 1.74704i | ||||
\(538\) | 6.56080 | + | 11.3636i | 0.282856 | + | 0.489921i | ||||
\(539\) | 22.7477 | 0.979814 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.56080 | + | 14.8277i | 0.368057 | + | 0.637494i | 0.989262 | − | 0.146155i | \(-0.0466897\pi\) |
−0.621204 | + | 0.783649i | \(0.713356\pi\) | |||||||
\(542\) | −8.56080 | − | 14.8277i | −0.367718 | − | 0.636906i | ||||
\(543\) | −21.2867 | −0.913502 | ||||||||
\(544\) | −0.791288 | −0.0339262 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.291288 | − | 0.504525i | 0.0124660 | − | 0.0215917i | ||||
\(547\) | 8.41742 | + | 14.5794i | 0.359903 | + | 0.623370i | 0.987944 | − | 0.154810i | \(-0.0494764\pi\) |
−0.628041 | + | 0.778180i | \(0.716143\pi\) | |||||||
\(548\) | 7.66515 | − | 13.2764i | 0.327439 | − | 0.567141i | ||||
\(549\) | −3.29129 | + | 5.70068i | −0.140469 | + | 0.243299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.39564 | + | 29.4071i | −0.144659 | + | 1.25279i | ||||
\(552\) | 12.7913 | 0.544433 | ||||||||
\(553\) | −7.47822 | + | 12.9527i | −0.318006 | + | 0.550803i | ||||
\(554\) | 4.37386 | − | 7.57575i | 0.185828 | − | 0.321863i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.10436 | − | 10.5731i | 0.258882 | − | 0.448397i | ||||
\(557\) | 4.97822 | + | 8.62253i | 0.210934 | + | 0.365348i | 0.952007 | − | 0.306076i | \(-0.0990162\pi\) |
−0.741073 | + | 0.671424i | \(0.765683\pi\) | |||||||
\(558\) | 22.9564 | 0.971824 | ||||||||
\(559\) | −1.20871 | −0.0511231 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.18693 | + | 7.25198i | 0.176772 | + | 0.306179i | ||||
\(562\) | −10.5826 | −0.446399 | ||||||||
\(563\) | 14.3739 | 0.605786 | 0.302893 | − | 0.953025i | \(-0.402047\pi\) | ||||
0.302893 | + | 0.953025i | \(0.402047\pi\) | |||||||
\(564\) | −16.9782 | − | 29.4071i | −0.714912 | − | 1.23826i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.5608 | − | 18.2918i | −0.443903 | − | 0.768863i | ||||
\(567\) | 0.208712 | − | 0.361500i | 0.00876509 | − | 0.0151816i | ||||
\(568\) | −2.29129 | + | 3.96863i | −0.0961403 | + | 0.166520i | ||||
\(569\) | −8.83485 | −0.370376 | −0.185188 | − | 0.982703i | \(-0.559289\pi\) | ||||
−0.185188 | + | 0.982703i | \(0.559289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0.395644 | − | 0.685275i | 0.0165427 | − | 0.0286528i | ||||
\(573\) | −22.2695 | + | 38.5719i | −0.930322 | + | 1.61137i | ||||
\(574\) | −5.68693 | − | 9.85005i | −0.237368 | − | 0.411133i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.39564 | − | 4.14938i | −0.0998185 | − | 0.172891i | ||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 16.3739 | 0.681063 | ||||||||
\(579\) | −3.83485 | − | 6.64215i | −0.159371 | − | 0.276038i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.79129 | −0.157289 | ||||||||
\(582\) | −34.5390 | −1.43169 | ||||||||
\(583\) | 8.68693 | + | 15.0462i | 0.359776 | + | 0.623150i | ||||
\(584\) | −1.39564 | + | 2.41733i | −0.0577522 | + | 0.100030i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.4782 | + | 21.6129i | −0.515471 | + | 0.892821i | ||||
\(587\) | −4.74773 | + | 8.22330i | −0.195960 | + | 0.339412i | −0.947215 | − | 0.320600i | \(-0.896116\pi\) |
0.751255 | + | 0.660012i | \(0.229449\pi\) | |||||||
\(588\) | −16.7477 | −0.690665 | ||||||||
\(589\) | 16.7695 | + | 12.4481i | 0.690976 | + | 0.512916i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.2042 | − | 48.8510i | 1.16016 | − | 2.00946i | ||||
\(592\) | 1.79129 | − | 3.10260i | 0.0736215 | − | 0.127516i | ||||
\(593\) | −5.91742 | − | 10.2493i | −0.242999 | − | 0.420887i | 0.718568 | − | 0.695457i | \(-0.244798\pi\) |
−0.961567 | + | 0.274569i | \(0.911465\pi\) | |||||||
\(594\) | −9.47822 | + | 16.4168i | −0.388896 | + | 0.673588i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.7477 | −0.931783 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | −0.478220 | − | 0.828301i | −0.0195559 | − | 0.0338717i | ||||
\(599\) | 18.5608 | + | 32.1482i | 0.758374 | + | 1.31354i | 0.943680 | + | 0.330861i | \(0.107339\pi\) |
−0.185306 | + | 0.982681i | \(0.559328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.91288 | 0.404355 | 0.202177 | − | 0.979349i | \(-0.435198\pi\) | ||||
0.202177 | + | 0.979349i | \(0.435198\pi\) | |||||||
\(602\) | −2.89564 | − | 5.01540i | −0.118018 | − | 0.204413i | ||||
\(603\) | 37.3303 | − | 64.6580i | 1.52021 | − | 2.63308i | ||||
\(604\) | −7.87386 | − | 13.6379i | −0.320383 | − | 0.554920i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.2087 | 0.739069 | 0.369534 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369534 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(608\) | 0.500000 | − | 4.33013i | 0.0202777 | − | 0.175610i | ||||
\(609\) | 18.9564 | 0.768154 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.26951 | + | 2.19885i | −0.0513588 | + | 0.0889560i | ||||
\(612\) | −1.89564 | − | 3.28335i | −0.0766269 | − | 0.132722i | ||||
\(613\) | 7.24773 | − | 12.5534i | 0.292733 | − | 0.507028i | −0.681722 | − | 0.731611i | \(-0.738769\pi\) |
0.974455 | + | 0.224583i | \(0.0721020\pi\) | |||||||
\(614\) | 17.2477 | + | 29.8739i | 0.696062 | + | 1.20561i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.79129 | 0.152755 | ||||||||
\(617\) | −16.5000 | − | 28.5788i | −0.664265 | − | 1.15054i | −0.979484 | − | 0.201522i | \(-0.935411\pi\) |
0.315219 | − | 0.949019i | \(-0.397922\pi\) | |||||||
\(618\) | −7.20871 | − | 12.4859i | −0.289977 | − | 0.502255i | ||||
\(619\) | −24.3739 | −0.979668 | −0.489834 | − | 0.871816i | \(-0.662943\pi\) | ||||
−0.489834 | + | 0.871816i | \(0.662943\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.4564 | + | 19.8431i | 0.459731 | + | 0.796278i | ||||
\(622\) | −7.50000 | + | 12.9904i | −0.300723 | + | 0.520867i | ||||
\(623\) | −2.29129 | − | 3.96863i | −0.0917985 | − | 0.159000i | ||||
\(624\) | −0.291288 | + | 0.504525i | −0.0116608 | + | 0.0201972i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.7477 | −0.469534 | ||||||||
\(627\) | −42.3303 | + | 18.3296i | −1.69051 | + | 0.732012i | ||||
\(628\) | 7.95644 | 0.317496 | ||||||||
\(629\) | 1.41742 | − | 2.45505i | 0.0565164 | − | 0.0978893i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1044 | + | 31.3577i | 0.720723 | + | 1.24833i | 0.960710 | + | 0.277553i | \(0.0895234\pi\) |
−0.239987 | + | 0.970776i | \(0.577143\pi\) | |||||||
\(632\) | 7.47822 | − | 12.9527i | 0.297468 | − | 0.515229i | ||||
\(633\) | −33.4347 | − | 57.9105i | −1.32891 | − | 2.30174i | ||||
\(634\) | −9.16515 | −0.363995 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.39564 | − | 11.0776i | −0.253604 | − | 0.439255i | ||||
\(637\) | 0.626136 | + | 1.08450i | 0.0248084 | + | 0.0429695i | ||||
\(638\) | 25.7477 | 1.01936 | ||||||||
\(639\) | −21.9564 | −0.868583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.52178 | + | 14.7602i | −0.336590 | + | 0.582991i | −0.983789 | − | 0.179330i | \(-0.942607\pi\) |
0.647199 | + | 0.762321i | \(0.275940\pi\) | |||||||
\(642\) | −26.4564 | − | 45.8239i | −1.04415 | − | 1.80852i | ||||
\(643\) | 14.7477 | − | 25.5438i | 0.581594 | − | 1.00735i | −0.413697 | − | 0.910415i | \(-0.635763\pi\) |
0.995291 | − | 0.0969351i | \(-0.0309039\pi\) | |||||||
\(644\) | 2.29129 | − | 3.96863i | 0.0902894 | − | 0.156386i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.395644 | − | 3.42638i | 0.0155664 | − | 0.134809i | ||||
\(647\) | −18.7913 | −0.738762 | −0.369381 | − | 0.929278i | \(-0.620430\pi\) | ||||
−0.369381 | + | 0.929278i | \(0.620430\pi\) | |||||||
\(648\) | −0.208712 | + | 0.361500i | −0.00819899 | + | 0.0142011i | ||||
\(649\) | 8.68693 | − | 15.0462i | 0.340992 | − | 0.590615i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.68693 | − | 11.5821i | 0.262082 | − | 0.453939i | ||||
\(652\) | −7.29129 | − | 12.6289i | −0.285549 | − | 0.494585i | ||||
\(653\) | 27.3303 | 1.06952 | 0.534759 | − | 0.845005i | \(-0.320403\pi\) | ||||
0.534759 | + | 0.845005i | \(0.320403\pi\) | |||||||
\(654\) | 32.7913 | 1.28224 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.68693 | + | 9.85005i | 0.222037 | + | 0.384580i | ||||
\(657\) | −13.3739 | −0.521764 | ||||||||
\(658\) | −12.1652 | −0.474247 | ||||||||
\(659\) | −0.873864 | − | 1.51358i | −0.0340409 | − | 0.0589606i | 0.848503 | − | 0.529190i | \(-0.177504\pi\) |
−0.882544 | + | 0.470230i | \(0.844171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4347 | − | 40.5900i | −0.911503 | − | 1.57877i | −0.811943 | − | 0.583737i | \(-0.801590\pi\) |
−0.0995599 | − | 0.995032i | \(-0.531744\pi\) | |||||||
\(662\) | −8.95644 | + | 15.5130i | −0.348102 | + | 0.602930i | ||||
\(663\) | −0.230493 | + | 0.399225i | −0.00895159 | + | 0.0155046i | ||||
\(664\) | 3.79129 | 0.147131 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.1652 | 0.665136 | ||||||||
\(667\) | 15.5608 | − | 26.9521i | 0.602516 | − | 1.04359i | ||||
\(668\) | 5.76951 | − | 9.99308i | 0.223229 | − | 0.386644i | ||||
\(669\) | 26.8085 | + | 46.4337i | 1.03648 | + | 1.79523i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.60436 | + | 4.51088i | 0.100540 | + | 0.174140i | ||||
\(672\) | −2.79129 | −0.107676 | ||||||||
\(673\) | −2.79129 | −0.107596 | −0.0537981 | − | 0.998552i | \(-0.517133\pi\) | ||||
−0.0537981 | + | 0.998552i | \(0.517133\pi\) | |||||||
\(674\) | −11.6652 | − | 20.2046i | −0.449325 | − | 0.778253i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9564 | −0.498325 | ||||||||
\(677\) | 35.2432 | 1.35451 | 0.677253 | − | 0.735750i | \(-0.263170\pi\) | ||||
0.677253 | + | 0.735750i | \(0.263170\pi\) | |||||||
\(678\) | −7.50000 | − | 12.9904i | −0.288036 | − | 0.498893i | ||||
\(679\) | −6.18693 | + | 10.7161i | −0.237433 | + | 0.411245i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8131 | − | 18.7288i | 0.414358 | − | 0.717689i | ||||
\(682\) | 9.08258 | − | 15.7315i | 0.347790 | − | 0.602390i | ||||
\(683\) | 36.1652 | 1.38382 | 0.691911 | − | 0.721983i | \(-0.256769\pi\) | ||||
0.691911 | + | 0.721983i | \(0.256769\pi\) | |||||||
\(684\) | 19.1652 | − | 8.29875i | 0.732798 | − | 0.317311i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | + | 11.2583i | −0.248171 | + | 0.429845i | ||||
\(687\) | 35.3521 | − | 61.2316i | 1.34877 | − | 2.33613i | ||||
\(688\) | 2.89564 | + | 5.01540i | 0.110395 | + | 0.191210i | ||||
\(689\) | −0.478220 | + | 0.828301i | −0.0182187 | + | 0.0315557i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1216 | −1.22196 | −0.610981 | − | 0.791645i | \(-0.709225\pi\) | ||||
−0.610981 | + | 0.791645i | \(0.709225\pi\) | |||||||
\(692\) | 21.0000 | 0.798300 | ||||||||
\(693\) | 9.08258 | + | 15.7315i | 0.345019 | + | 0.597590i | ||||
\(694\) | −1.81307 | − | 3.14033i | −0.0688231 | − | 0.119205i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.9564 | −0.718542 | ||||||||
\(697\) | 4.50000 | + | 7.79423i | 0.170450 | + | 0.295227i | ||||
\(698\) | −2.70871 | + | 4.69163i | −0.102526 | + | 0.177581i | ||||
\(699\) | 12.7913 | + | 22.1552i | 0.483811 | + | 0.837985i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.47822 | − | 11.2206i | 0.244679 | − | 0.423796i | −0.717362 | − | 0.696700i | \(-0.754651\pi\) |
0.962041 | + | 0.272904i | \(0.0879841\pi\) | |||||||
\(702\) | −1.04356 | −0.0393867 | ||||||||
\(703\) | 12.5390 | + | 9.30780i | 0.472918 | + | 0.351051i | ||||
\(704\) | −3.79129 | −0.142890 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.87386 | − | 11.9059i | 0.258701 | − | 0.448084i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.39564 | + | 11.0776i | −0.240363 | + | 0.416321i | ||||
\(709\) | 13.3739 | + | 23.1642i | 0.502266 | + | 0.869950i | 0.999997 | + | 0.00261852i | \(0.000833501\pi\) |
−0.497731 | + | 0.867332i | \(0.665833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 71.6606 | 2.68748 | ||||||||
\(712\) | 2.29129 | + | 3.96863i | 0.0858696 | + | 0.148731i | ||||
\(713\) | −10.9782 | − | 19.0148i | −0.411138 | − | 0.712111i | ||||
\(714\) | −2.20871 | −0.0826590 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.37386 | + | 14.5040i | 0.312946 | + | 0.542038i | ||||
\(717\) | −23.1434 | + | 40.0855i | −0.864305 | + | 1.49702i | ||||
\(718\) | −17.8521 | − | 30.9207i | −0.666234 | − | 1.15395i | ||||
\(719\) | 6.08258 | − | 10.5353i | 0.226842 | − | 0.392902i | −0.730029 | − | 0.683417i | \(-0.760493\pi\) |
0.956870 | + | 0.290515i | \(0.0938266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.16515 | −0.192360 | ||||||||
\(722\) | 18.5000 | + | 4.33013i | 0.688499 | + | 0.161151i | ||||
\(723\) | −46.8693 | −1.74309 | ||||||||
\(724\) | 3.81307 | − | 6.60443i | 0.141712 | − | 0.245452i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.70871 | + | 8.15573i | 0.174757 | + | 0.302687i | ||||
\(727\) | −2.08258 | + | 3.60713i | −0.0772385 | + | 0.133781i | −0.902058 | − | 0.431616i | \(-0.857944\pi\) |
0.824819 | + | 0.565397i | \(0.191277\pi\) | |||||||
\(728\) | 0.104356 | + | 0.180750i | 0.00386769 | + | 0.00669904i | ||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.29129 | + | 3.96863i | 0.0847463 | + | 0.146785i | ||||
\(732\) | −1.91742 | − | 3.32108i | −0.0708700 | − | 0.122751i | ||||
\(733\) | −12.7477 | −0.470848 | −0.235424 | − | 0.971893i | \(-0.575648\pi\) | ||||
−0.235424 | + | 0.971893i | \(0.575648\pi\) | |||||||
\(734\) | 8.79129 | 0.324492 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.29129 | + | 3.96863i | −0.0844580 | + | 0.146286i | ||||
\(737\) | −29.5390 | − | 51.1631i | −1.08808 | − | 1.88462i | ||||
\(738\) | −27.2477 | + | 47.1944i | −1.00300 | + | 1.73725i | ||||
\(739\) | 17.8739 | − | 30.9584i | 0.657501 | − | 1.13882i | −0.323760 | − | 0.946139i | \(-0.604947\pi\) |
0.981261 | − | 0.192685i | \(-0.0617197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.03901 | − | 1.51358i | −0.0749051 | − | 0.0556026i | ||||
\(742\) | −4.58258 | −0.168232 | ||||||||
\(743\) | 9.70871 | − | 16.8160i | 0.356178 | − | 0.616919i | −0.631141 | − | 0.775668i | \(-0.717413\pi\) |
0.987319 | + | 0.158750i | \(0.0507463\pi\) | |||||||
\(744\) | −6.68693 | + | 11.5821i | −0.245155 | + | 0.424621i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.6869 | − | 18.5103i | 0.391276 | − | 0.677711i | ||||
\(747\) | 9.08258 | + | 15.7315i | 0.332314 | + | 0.575585i | ||||
\(748\) | −3.00000 | −0.109691 | ||||||||
\(749\) | −18.9564 | −0.692653 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7913 | − | 18.6911i | −0.393780 | − | 0.682046i | 0.599165 | − | 0.800626i | \(-0.295499\pi\) |
−0.992945 | + | 0.118579i | \(0.962166\pi\) | |||||||
\(752\) | 12.1652 | 0.443617 | ||||||||
\(753\) | 36.6261 | 1.33473 | ||||||||
\(754\) | 0.708712 | + | 1.22753i | 0.0258098 | + | 0.0447038i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.50000 | − | 4.33013i | −0.0909241 | − | 0.157485i | ||||
\(757\) | 22.8739 | − | 39.6187i | 0.831365 | − | 1.43997i | −0.0655915 | − | 0.997847i | \(-0.520893\pi\) |
0.896956 | − | 0.442119i | \(-0.145773\pi\) | |||||||
\(758\) | 2.41742 | − | 4.18710i | 0.0878048 | − | 0.152082i | ||||
\(759\) | 48.4955 | 1.76027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.2523 | 0.915394 | 0.457697 | − | 0.889108i | \(-0.348674\pi\) | ||||
0.457697 | + | 0.889108i | \(0.348674\pi\) | |||||||
\(762\) | −3.66515 | + | 6.34823i | −0.132774 | + | 0.229972i | ||||
\(763\) | 5.87386 | − | 10.1738i | 0.212648 | − | 0.368317i | ||||
\(764\) | −7.97822 | − | 13.8187i | −0.288642 | − | 0.499942i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.29129 | − | 3.96863i | −0.0827876 | − | 0.143392i | ||||
\(767\) | 0.956439 | 0.0345350 | ||||||||
\(768\) | 2.79129 | 0.100722 | ||||||||
\(769\) | 11.1652 | + | 19.3386i | 0.402626 | + | 0.697368i | 0.994042 | − | 0.108998i | \(-0.0347643\pi\) |
−0.591416 | + | 0.806366i | \(0.701431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2867 | 1.12676 | ||||||||
\(772\) | 2.74773 | 0.0988929 | ||||||||
\(773\) | −10.6652 | − | 18.4726i | −0.383599 | − | 0.664413i | 0.607975 | − | 0.793956i | \(-0.291982\pi\) |
−0.991574 | + | 0.129544i | \(0.958649\pi\) | |||||||
\(774\) | −13.8739 | + | 24.0302i | −0.498686 | + | 0.863749i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.18693 | − | 10.7161i | 0.222098 | − | 0.384685i | ||||
\(777\) | 5.00000 | − | 8.66025i | 0.179374 | − | 0.310685i | ||||
\(778\) | −18.6261 | −0.667779 | ||||||||
\(779\) | −45.4955 | + | 19.7001i | −1.63004 | + | 0.705830i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.68693 | + | 15.0462i | −0.310843 | + | 0.538396i | ||||
\(782\) | −1.81307 | + | 3.14033i | −0.0648352 | + | 0.112298i | ||||
\(783\) | −16.9782 | − | 29.4071i | −0.606752 | − | 1.05093i | ||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.2087 | −1.14885 | ||||||||
\(787\) | 23.7477 | 0.846515 | 0.423258 | − | 0.906009i | \(-0.360887\pi\) | ||||
0.423258 | + | 0.906009i | \(0.360887\pi\) | |||||||
\(788\) | 10.1044 | + | 17.5013i | 0.359953 | + | 0.623457i | ||||
\(789\) | −27.0998 | − | 46.9382i | −0.964779 | − | 1.67105i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.37386 | −0.191073 | ||||||||
\(792\) | −9.08258 | − | 15.7315i | −0.322735 | − | 0.558994i | ||||
\(793\) | −0.143371 | + | 0.248326i | −0.00509125 | + | 0.00881831i | ||||
\(794\) | 5.70871 | + | 9.88778i | 0.202595 | + | 0.350904i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.79129 | + | 3.10260i | −0.0634905 | + | 0.109969i | ||||
\(797\) | 38.5390 | 1.36512 | 0.682561 | − | 0.730829i | \(-0.260866\pi\) | ||||
0.682561 | + | 0.730829i | \(0.260866\pi\) | |||||||
\(798\) | 1.39564 | − | 12.0866i | 0.0494053 | − | 0.427862i | ||||
\(799\) | 9.62614 | 0.340548 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.9782 | + | 19.0148i | −0.387896 | + | 0.671856i | ||||
\(802\) | −6.00000 | − | 10.3923i | −0.211867 | − | 0.366965i | ||||
\(803\) | −5.29129 | + | 9.16478i | −0.186725 | + | 0.323418i | ||||
\(804\) | 21.7477 | + | 37.6682i | 0.766983 | + | 1.32845i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | −18.3131 | − | 31.7192i | −0.644651 | − | 1.11657i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.53901 | −0.0892670 | −0.0446335 | − | 0.999003i | \(-0.514212\pi\) | ||||
−0.0446335 | + | 0.999003i | \(0.514212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.9347 | − | 22.4035i | −0.454197 | − | 0.786693i | 0.544444 | − | 0.838797i | \(-0.316741\pi\) |
−0.998642 | + | 0.0521042i | \(0.983407\pi\) | |||||||
\(812\) | −3.39564 | + | 5.88143i | −0.119164 | + | 0.206398i | ||||
\(813\) | 23.8956 | + | 41.3885i | 0.838057 | + | 1.45156i | ||||
\(814\) | 6.79129 | − | 11.7629i | 0.238035 | − | 0.412288i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.20871 | 0.0773204 | ||||||||
\(817\) | −23.1652 | + | 10.0308i | −0.810446 | + | 0.350933i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −0.500000 | + | 0.866025i | −0.0174714 | + | 0.0302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1652 | + | 31.4630i | 0.633968 | + | 1.09807i | 0.986733 | + | 0.162353i | \(0.0519083\pi\) |
−0.352765 | + | 0.935712i | \(0.614758\pi\) | |||||||
\(822\) | −21.3956 | + | 37.0583i | −0.746259 | + | 1.29256i | ||||
\(823\) | 18.3739 | + | 31.8245i | 0.640473 | + | 1.10933i | 0.985327 | + | 0.170675i | \(0.0545948\pi\) |
−0.344855 | + | 0.938656i | \(0.612072\pi\) | |||||||
\(824\) | 5.16515 | 0.179937 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.29129 | + | 3.96863i | 0.0797241 | + | 0.138086i | ||||
\(827\) | −14.4564 | − | 25.0393i | −0.502700 | − | 0.870701i | −0.999995 | − | 0.00312009i | \(-0.999007\pi\) |
0.497295 | − | 0.867581i | \(-0.334326\pi\) | |||||||
\(828\) | −21.9564 | −0.763039 | ||||||||
\(829\) | 31.5390 | 1.09540 | 0.547698 | − | 0.836676i | \(-0.315504\pi\) | ||||
0.547698 | + | 0.836676i | \(0.315504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.2087 | + | 21.1461i | −0.423516 | + | 0.733550i | ||||
\(832\) | −0.104356 | − | 0.180750i | −0.00361790 | − | 0.00626638i | ||||
\(833\) | 2.37386 | − | 4.11165i | 0.0822495 | − | 0.142460i | ||||
\(834\) | −17.0390 | + | 29.5124i | −0.590013 | + | 1.02193i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.89564 | − | 16.4168i | 0.0655622 | − | 0.567785i | ||||
\(837\) | −23.9564 | −0.828056 | ||||||||
\(838\) | −11.3739 | + | 19.7001i | −0.392904 | + | 0.680529i | ||||
\(839\) | −25.9782 | + | 44.9956i | −0.896868 | + | 1.55342i | −0.0653918 | + | 0.997860i | \(0.520830\pi\) |
−0.831476 | + | 0.555561i | \(0.812504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.56080 | + | 14.8277i | −0.295200 | + | 0.511301i | ||||
\(842\) | 10.0000 | + | 17.3205i | 0.344623 | + | 0.596904i | ||||
\(843\) | 29.5390 | 1.01738 | ||||||||
\(844\) | 23.9564 | 0.824615 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.1434 | + | 50.4778i | 1.00197 | + | 1.73546i | ||||
\(847\) | 3.37386 | 0.115927 | ||||||||
\(848\) | 4.58258 | 0.157366 | ||||||||
\(849\) | 29.4782 | + | 51.0578i | 1.01169 | + | 1.75230i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.20871 | − | 14.2179i | −0.281391 | − | 0.487384i | ||||
\(852\) | 6.39564 | − | 11.0776i | 0.219111 | − | 0.379512i | ||||
\(853\) | −26.0172 | + | 45.0632i | −0.890813 | + | 1.54293i | −0.0519108 | + | 0.998652i | \(0.516531\pi\) |
−0.838902 | + | 0.544282i | \(0.816802\pi\) | |||||||
\(854\) | −1.37386 | −0.0470126 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9564 | 0.647918 | ||||||||
\(857\) | 1.50000 | − | 2.59808i | 0.0512390 | − | 0.0887486i | −0.839268 | − | 0.543718i | \(-0.817016\pi\) |
0.890507 | + | 0.454969i | \(0.150350\pi\) | |||||||
\(858\) | −1.10436 | + | 1.91280i | −0.0377021 | + | 0.0653019i | ||||
\(859\) | −8.35208 | − | 14.4662i | −0.284969 | − | 0.493581i | 0.687632 | − | 0.726059i | \(-0.258650\pi\) |
−0.972602 | + | 0.232478i | \(0.925317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.8739 | + | 27.4943i | 0.540980 | + | 0.937005i | ||||
\(862\) | −8.20871 | −0.279590 | ||||||||
\(863\) | 4.41742 | 0.150371 | 0.0751854 | − | 0.997170i | \(-0.476045\pi\) | ||||
0.0751854 | + | 0.997170i | \(0.476045\pi\) | |||||||
\(864\) | 2.50000 | + | 4.33013i | 0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.91288 | 0.234909 | ||||||||
\(867\) | −45.7042 | −1.55219 | ||||||||
\(868\) | 2.39564 | + | 4.14938i | 0.0813135 | + | 0.140839i | ||||
\(869\) | 28.3521 | − | 49.1072i | 0.961779 | − | 1.66585i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.62614 | − | 2.81655i | 0.0550995 | − | 0.0954352i | ||||
\(872\) | −5.87386 | + | 10.1738i | −0.198914 | + | 0.344529i | ||||
\(873\) | 59.2867 | 2.00655 | ||||||||
\(874\) | −16.0390 | − | 11.9059i | −0.542528 | − | 0.402722i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.89564 | − | 6.74745i | 0.131622 | − | 0.227975i | ||||
\(877\) | 13.2477 | − | 22.9457i | 0.447344 | − | 0.774822i | −0.550868 | − | 0.834592i | \(-0.685703\pi\) |
0.998212 | + | 0.0597698i | \(0.0190367\pi\) | |||||||
\(878\) | −12.6652 | − | 21.9367i | −0.427428 | − | 0.740327i | ||||
\(879\) | 34.8303 | − | 60.3279i | 1.17480 | − | 2.03481i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.791288 | −0.0266592 | −0.0133296 | − | 0.999911i | \(-0.504243\pi\) | ||||
−0.0133296 | + | 0.999911i | \(0.504243\pi\) | |||||||
\(882\) | 28.7477 | 0.967986 | ||||||||
\(883\) | 12.3739 | + | 21.4322i | 0.416414 | + | 0.721250i | 0.995576 | − | 0.0939628i | \(-0.0299535\pi\) |
−0.579162 | + | 0.815212i | \(0.696620\pi\) | |||||||
\(884\) | −0.0825757 | − | 0.143025i | −0.00277732 | − | 0.00481046i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | −0.806296 | ||||||||
\(887\) | −17.0608 | − | 29.5502i | −0.572845 | − | 0.992197i | −0.996272 | − | 0.0862670i | \(-0.972506\pi\) |
0.423427 | − | 0.905930i | \(-0.360827\pi\) | |||||||
\(888\) | −5.00000 | + | 8.66025i | −0.167789 | + | 0.290619i | ||||
\(889\) | 1.31307 | + | 2.27430i | 0.0440389 | + | 0.0762776i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.791288 | + | 1.37055i | −0.0265091 | + | 0.0459152i | ||||
\(892\) | −19.2087 | −0.643155 | ||||||||
\(893\) | −6.08258 | + | 52.6767i | −0.203546 | + | 1.76276i | ||||
\(894\) | 63.4955 | 2.12361 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | 1.33485 | + | 2.31203i | 0.0445693 | + | 0.0771963i | ||||
\(898\) | 1.66515 | − | 2.88413i | 0.0555668 | − | 0.0962446i | ||||
\(899\) | 16.2695 | + | 28.1796i | 0.542618 | + | 0.939843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.62614 | 0.120804 | ||||||||
\(902\) | 21.5608 | + | 37.3444i | 0.717896 | + | 1.24343i | ||||
\(903\) | 8.08258 | + | 13.9994i | 0.268971 | + | 0.465872i | ||||
\(904\) | 5.37386 | 0.178732 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21.9782 | + | 38.0674i | 0.730177 | + | 1.26470i | ||||
\(907\) | −16.9347 | + | 29.3317i | −0.562306 | + | 0.973943i | 0.434989 | + | 0.900436i | \(0.356752\pi\) |
−0.997295 | + | 0.0735068i | \(0.976581\pi\) | |||||||
\(908\) | 3.87386 | + | 6.70973i | 0.128559 | + | 0.222670i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.6606 | −1.61220 | −0.806099 | − | 0.591781i | \(-0.798425\pi\) | ||||
−0.806099 | + | 0.591781i | \(0.798425\pi\) | |||||||
\(912\) | −1.39564 | + | 12.0866i | −0.0462144 | + | 0.400228i | ||||
\(913\) | 14.3739 | 0.475705 | ||||||||
\(914\) | 10.3739 | − | 17.9681i | 0.343137 | − | 0.594331i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6652 | + | 21.9367i | 0.418468 | + | 0.724808i | ||||
\(917\) | −5.76951 | + | 9.99308i | −0.190526 | + | 0.330001i | ||||
\(918\) | 1.97822 | + | 3.42638i | 0.0652910 | + | 0.113087i | ||||
\(919\) | −46.7913 | −1.54350 | −0.771751 | − | 0.635925i | \(-0.780619\pi\) | ||||
−0.771751 | + | 0.635925i | \(0.780619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.1434 | − | 83.3868i | −1.58638 | − | 2.74769i | ||||
\(922\) | 6.39564 | + | 11.0776i | 0.210629 | + | 0.364821i | ||||
\(923\) | −0.956439 | −0.0314816 | ||||||||
\(924\) | −10.5826 | −0.348141 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.97822 | + | 15.5507i | −0.295043 | + | 0.511029i | ||||
\(927\) | 12.3739 | + | 21.4322i | 0.406411 | + | 0.703925i | ||||
\(928\) | 3.39564 | − | 5.88143i | 0.111467 | − | 0.193067i | ||||
\(929\) | −5.43920 | + | 9.42098i | −0.178455 | + | 0.309092i | −0.941351 | − | 0.337428i | \(-0.890443\pi\) |
0.762897 | + | 0.646520i | \(0.223776\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.0000 | + | 15.5885i | 0.688247 | + | 0.510891i | ||||
\(932\) | −9.16515 | −0.300215 | ||||||||
\(933\) | 20.9347 | − | 36.2599i | 0.685370 | − | 1.18710i | ||||
\(934\) | 6.16515 | − | 10.6784i | 0.201730 | − | 0.349406i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 0.866025i | 0.0163430 | − | 0.0283069i | ||||
\(937\) | 3.06080 | + | 5.30145i | 0.0999918 | + | 0.173191i | 0.911681 | − | 0.410899i | \(-0.134785\pi\) |
−0.811689 | + | 0.584090i | \(0.801452\pi\) | |||||||
\(938\) | 15.5826 | 0.508789 | ||||||||
\(939\) | 32.7913 | 1.07010 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2913 | + | 35.1455i | 0.661477 | + | 1.14571i | 0.980228 | + | 0.197873i | \(0.0634034\pi\) |
−0.318751 | + | 0.947839i | \(0.603263\pi\) | |||||||
\(942\) | −22.2087 | −0.723599 | ||||||||
\(943\) | 52.1216 | 1.69731 | ||||||||
\(944\) | −2.29129 | − | 3.96863i | −0.0745751 | − | 0.129168i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.9782 | + | 19.0148i | 0.356933 | + | 0.618226i | ||||
\(947\) | −14.2913 | + | 24.7532i | −0.464404 | + | 0.804372i | −0.999174 | − | 0.0406256i | \(-0.987065\pi\) |
0.534770 | + | 0.844998i | \(0.320398\pi\) | |||||||
\(948\) | −20.8739 | + | 36.1546i | −0.677952 | + | 1.17425i | ||||
\(949\) | −0.582576 | −0.0189112 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.5826 | 0.829572 | ||||||||
\(952\) | 0.395644 | − | 0.685275i | 0.0128229 | − | 0.0222099i | ||||
\(953\) | −8.06080 | + | 13.9617i | −0.261115 | + | 0.452264i | −0.966538 | − | 0.256522i | \(-0.917423\pi\) |
0.705424 | + | 0.708786i | \(0.250757\pi\) | |||||||
\(954\) | 10.9782 | + | 19.0148i | 0.355433 | + | 0.615628i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.29129 | − | 14.3609i | −0.268159 | − | 0.464466i | ||||
\(957\) | −71.8693 | −2.32321 | ||||||||
\(958\) | −31.7477 | −1.02572 | ||||||||
\(959\) | 7.66515 | + | 13.2764i | 0.247521 | + | 0.428718i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.04356 | −0.259470 | ||||||||
\(962\) | 0.747727 | 0.0241077 | ||||||||
\(963\) | 45.4129 | + | 78.6574i | 1.46341 | + | 2.53470i | ||||
\(964\) | 8.39564 | − | 14.5417i | 0.270405 | − | 0.468356i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.39564 | + | 11.0776i | −0.205776 | + | 0.356415i | ||||
\(967\) | −25.5390 | + | 44.2349i | −0.821279 | + | 1.42250i | 0.0834506 | + | 0.996512i | \(0.473406\pi\) |
−0.904730 | + | 0.425986i | \(0.859927\pi\) | |||||||
\(968\) | −3.37386 | −0.108440 | ||||||||
\(969\) | −1.10436 | + | 9.56400i | −0.0354770 | + | 0.307240i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.543561 | − | 0.941475i | 0.0174437 | − | 0.0302134i | −0.857172 | − | 0.515031i | \(-0.827781\pi\) |
0.874615 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(972\) | 8.08258 | − | 13.9994i | 0.259249 | − | 0.449032i | ||||
\(973\) | 6.10436 | + | 10.5731i | 0.195697 | + | 0.338957i | ||||
\(974\) | −11.5000 | + | 19.9186i | −0.368484 | + | 0.638233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.37386 | 0.0439763 | ||||||||
\(977\) | −32.3739 | −1.03573 | −0.517866 | − | 0.855462i | \(-0.673273\pi\) | ||||
−0.517866 | + | 0.855462i | \(0.673273\pi\) | |||||||
\(978\) | 20.3521 | + | 35.2508i | 0.650788 | + | 1.12720i | ||||
\(979\) | 8.68693 | + | 15.0462i | 0.277636 | + | 0.480879i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −56.2867 | −1.79710 | ||||||||
\(982\) | −15.7087 | − | 27.2083i | −0.501285 | − | 0.868251i | ||||
\(983\) | 24.7913 | − | 42.9398i | 0.790719 | − | 1.36957i | −0.134803 | − | 0.990872i | \(-0.543040\pi\) |
0.925522 | − | 0.378694i | \(-0.123627\pi\) | |||||||
\(984\) | −15.8739 | − | 27.4943i | −0.506040 | − | 0.876487i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.68693 | − | 4.65390i | 0.0855693 | − | 0.148210i | ||||
\(987\) | 33.9564 | 1.08085 | ||||||||
\(988\) | 0.834849 | − | 0.361500i | 0.0265601 | − | 0.0115008i | ||||
\(989\) | 26.5390 | 0.843892 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0608 | + | 20.8899i | −0.383124 | + | 0.663590i | −0.991507 | − | 0.130054i | \(-0.958485\pi\) |
0.608383 | + | 0.793643i | \(0.291818\pi\) | |||||||
\(992\) | −2.39564 | − | 4.14938i | −0.0760618 | − | 0.131743i | ||||
\(993\) | 25.0000 | − | 43.3013i | 0.793351 | − | 1.37412i | ||||
\(994\) | −2.29129 | − | 3.96863i | −0.0726752 | − | 0.125877i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.5826 | −0.335322 | ||||||||
\(997\) | −0.500000 | − | 0.866025i | −0.0158352 | − | 0.0274273i | 0.857999 | − | 0.513651i | \(-0.171707\pi\) |
−0.873834 | + | 0.486224i | \(0.838374\pi\) | |||||||
\(998\) | −9.66515 | − | 16.7405i | −0.305945 | − | 0.529912i | ||||
\(999\) | −17.9129 | −0.566738 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 950.2.e.j.201.1 | yes | 4 | |
5.2 | odd | 4 | 950.2.j.h.49.4 | 8 | |||
5.3 | odd | 4 | 950.2.j.h.49.1 | 8 | |||
5.4 | even | 2 | 950.2.e.i.201.2 | ✓ | 4 | ||
19.7 | even | 3 | inner | 950.2.e.j.501.1 | yes | 4 | |
95.7 | odd | 12 | 950.2.j.h.349.1 | 8 | |||
95.64 | even | 6 | 950.2.e.i.501.2 | yes | 4 | ||
95.83 | odd | 12 | 950.2.j.h.349.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.i.201.2 | ✓ | 4 | 5.4 | even | 2 | ||
950.2.e.i.501.2 | yes | 4 | 95.64 | even | 6 | ||
950.2.e.j.201.1 | yes | 4 | 1.1 | even | 1 | trivial | |
950.2.e.j.501.1 | yes | 4 | 19.7 | even | 3 | inner | |
950.2.j.h.49.1 | 8 | 5.3 | odd | 4 | |||
950.2.j.h.49.4 | 8 | 5.2 | odd | 4 | |||
950.2.j.h.349.1 | 8 | 95.7 | odd | 12 | |||
950.2.j.h.349.4 | 8 | 95.83 | odd | 12 |