Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(23,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("154.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.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: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 23.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.23 |
Dual form | 154.2.e.e.67.1 |
$q$-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 \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.207107 | − | 0.358719i | −0.119573 | − | 0.207107i | 0.800025 | − | 0.599966i | \(-0.204819\pi\) |
−0.919599 | + | 0.392859i | \(0.871486\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.70711 | − | 2.95680i | 0.763441 | − | 1.32232i | −0.177625 | − | 0.984098i | \(-0.556842\pi\) |
0.941067 | − | 0.338221i | \(-0.109825\pi\) | |||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | −2.62132 | − | 0.358719i | −0.990766 | − | 0.135583i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.41421 | − | 2.44949i | 0.471405 | − | 0.816497i | ||||
\(10\) | 1.70711 | + | 2.95680i | 0.539835 | + | 0.935021i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.207107 | + | 0.358719i | −0.0597866 | + | 0.103553i | ||||
\(13\) | 1.82843 | 0.507114 | 0.253557 | − | 0.967320i | \(-0.418399\pi\) | ||||
0.253557 | + | 0.967320i | \(0.418399\pi\) | |||||||
\(14\) | 1.62132 | − | 2.09077i | 0.433316 | − | 0.558782i | ||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.82843 | + | 6.63103i | 0.928530 | + | 1.60826i | 0.785783 | + | 0.618502i | \(0.212260\pi\) |
0.142747 | + | 0.989759i | \(0.454407\pi\) | |||||||
\(18\) | 1.41421 | + | 2.44949i | 0.333333 | + | 0.577350i | ||||
\(19\) | 1.70711 | − | 2.95680i | 0.391637 | − | 0.678335i | −0.601028 | − | 0.799228i | \(-0.705242\pi\) |
0.992666 | + | 0.120892i | \(0.0385755\pi\) | |||||||
\(20\) | −3.41421 | −0.763441 | ||||||||
\(21\) | 0.414214 | + | 1.01461i | 0.0903888 | + | 0.221406i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −1.12132 | + | 1.94218i | −0.233811 | + | 0.404973i | −0.958927 | − | 0.283654i | \(-0.908453\pi\) |
0.725115 | + | 0.688628i | \(0.241787\pi\) | |||||||
\(24\) | −0.207107 | − | 0.358719i | −0.0422755 | − | 0.0732233i | ||||
\(25\) | −3.32843 | − | 5.76500i | −0.665685 | − | 1.15300i | ||||
\(26\) | −0.914214 | + | 1.58346i | −0.179292 | + | 0.310543i | ||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 1.00000 | + | 2.44949i | 0.188982 | + | 0.462910i | ||||
\(29\) | −8.65685 | −1.60754 | −0.803769 | − | 0.594942i | \(-0.797175\pi\) | ||||
−0.803769 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(30\) | 0.707107 | − | 1.22474i | 0.129099 | − | 0.223607i | ||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.207107 | + | 0.358719i | −0.0360527 | + | 0.0624450i | ||||
\(34\) | −7.65685 | −1.31314 | ||||||||
\(35\) | −5.53553 | + | 7.13834i | −0.935676 | + | 1.20660i | ||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | 3.29289 | − | 5.70346i | 0.541348 | − | 0.937643i | −0.457479 | − | 0.889221i | \(-0.651247\pi\) |
0.998827 | − | 0.0484222i | \(-0.0154193\pi\) | |||||||
\(38\) | 1.70711 | + | 2.95680i | 0.276929 | + | 0.479656i | ||||
\(39\) | −0.378680 | − | 0.655892i | −0.0606373 | − | 0.105027i | ||||
\(40\) | 1.70711 | − | 2.95680i | 0.269917 | − | 0.467510i | ||||
\(41\) | −2.58579 | −0.403832 | −0.201916 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201916 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(42\) | −1.08579 | − | 0.148586i | −0.167540 | − | 0.0229274i | ||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | −4.82843 | − | 8.36308i | −0.719779 | − | 1.24669i | ||||
\(46\) | −1.12132 | − | 1.94218i | −0.165330 | − | 0.286359i | ||||
\(47\) | −3.24264 | + | 5.61642i | −0.472988 | + | 0.819239i | −0.999522 | − | 0.0309151i | \(-0.990158\pi\) |
0.526534 | + | 0.850154i | \(0.323491\pi\) | |||||||
\(48\) | 0.414214 | 0.0597866 | ||||||||
\(49\) | 6.74264 | + | 1.88064i | 0.963234 | + | 0.268662i | ||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | 1.58579 | − | 2.74666i | 0.222055 | − | 0.384610i | ||||
\(52\) | −0.914214 | − | 1.58346i | −0.126779 | − | 0.219587i | ||||
\(53\) | 5.94975 | + | 10.3053i | 0.817261 | + | 1.41554i | 0.907693 | + | 0.419634i | \(0.137842\pi\) |
−0.0904325 | + | 0.995903i | \(0.528825\pi\) | |||||||
\(54\) | 1.20711 | − | 2.09077i | 0.164266 | − | 0.284518i | ||||
\(55\) | −3.41421 | −0.460372 | ||||||||
\(56\) | −2.62132 | − | 0.358719i | −0.350289 | − | 0.0479359i | ||||
\(57\) | −1.41421 | −0.187317 | ||||||||
\(58\) | 4.32843 | − | 7.49706i | 0.568350 | − | 0.984412i | ||||
\(59\) | 4.20711 | + | 7.28692i | 0.547719 | + | 0.948677i | 0.998430 | + | 0.0560070i | \(0.0178369\pi\) |
−0.450712 | + | 0.892670i | \(0.648830\pi\) | |||||||
\(60\) | 0.707107 | + | 1.22474i | 0.0912871 | + | 0.158114i | ||||
\(61\) | −3.08579 | + | 5.34474i | −0.395094 | + | 0.684324i | −0.993113 | − | 0.117158i | \(-0.962621\pi\) |
0.598019 | + | 0.801482i | \(0.295955\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | −4.58579 | + | 5.91359i | −0.577755 | + | 0.745042i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.12132 | − | 5.40629i | 0.387152 | − | 0.670567i | ||||
\(66\) | −0.207107 | − | 0.358719i | −0.0254931 | − | 0.0441553i | ||||
\(67\) | −5.62132 | − | 9.73641i | −0.686754 | − | 1.18949i | −0.972882 | − | 0.231301i | \(-0.925702\pi\) |
0.286129 | − | 0.958191i | \(-0.407632\pi\) | |||||||
\(68\) | 3.82843 | − | 6.63103i | 0.464265 | − | 0.804131i | ||||
\(69\) | 0.928932 | 0.111830 | ||||||||
\(70\) | −3.41421 | − | 8.36308i | −0.408077 | − | 0.999579i | ||||
\(71\) | 3.07107 | 0.364469 | 0.182234 | − | 0.983255i | \(-0.441667\pi\) | ||||
0.182234 | + | 0.983255i | \(0.441667\pi\) | |||||||
\(72\) | 1.41421 | − | 2.44949i | 0.166667 | − | 0.288675i | ||||
\(73\) | 3.29289 | + | 5.70346i | 0.385404 | + | 0.667539i | 0.991825 | − | 0.127604i | \(-0.0407288\pi\) |
−0.606421 | + | 0.795144i | \(0.707395\pi\) | |||||||
\(74\) | 3.29289 | + | 5.70346i | 0.382791 | + | 0.663014i | ||||
\(75\) | −1.37868 | + | 2.38794i | −0.159196 | + | 0.275736i | ||||
\(76\) | −3.41421 | −0.391637 | ||||||||
\(77\) | 1.00000 | + | 2.44949i | 0.113961 | + | 0.279145i | ||||
\(78\) | 0.757359 | 0.0857541 | ||||||||
\(79\) | 2.37868 | − | 4.11999i | 0.267622 | − | 0.463536i | −0.700625 | − | 0.713530i | \(-0.747095\pi\) |
0.968247 | + | 0.249994i | \(0.0804287\pi\) | |||||||
\(80\) | 1.70711 | + | 2.95680i | 0.190860 | + | 0.330580i | ||||
\(81\) | −3.74264 | − | 6.48244i | −0.415849 | − | 0.720272i | ||||
\(82\) | 1.29289 | − | 2.23936i | 0.142776 | − | 0.247296i | ||||
\(83\) | 16.1421 | 1.77183 | 0.885915 | − | 0.463848i | \(-0.153532\pi\) | ||||
0.885915 | + | 0.463848i | \(0.153532\pi\) | |||||||
\(84\) | 0.671573 | − | 0.866025i | 0.0732746 | − | 0.0944911i | ||||
\(85\) | 26.1421 | 2.83551 | ||||||||
\(86\) | −2.82843 | + | 4.89898i | −0.304997 | + | 0.528271i | ||||
\(87\) | 1.79289 | + | 3.10538i | 0.192218 | + | 0.332932i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 2.24264 | − | 3.88437i | 0.237719 | − | 0.411742i | −0.722340 | − | 0.691538i | \(-0.756933\pi\) |
0.960060 | + | 0.279796i | \(0.0902668\pi\) | |||||||
\(90\) | 9.65685 | 1.01792 | ||||||||
\(91\) | −4.79289 | − | 0.655892i | −0.502432 | − | 0.0687562i | ||||
\(92\) | 2.24264 | 0.233811 | ||||||||
\(93\) | 0.828427 | − | 1.43488i | 0.0859039 | − | 0.148790i | ||||
\(94\) | −3.24264 | − | 5.61642i | −0.334453 | − | 0.579289i | ||||
\(95\) | −5.82843 | − | 10.0951i | −0.597984 | − | 1.03574i | ||||
\(96\) | −0.207107 | + | 0.358719i | −0.0211377 | + | 0.0366117i | ||||
\(97\) | 1.82843 | 0.185649 | 0.0928243 | − | 0.995683i | \(-0.470411\pi\) | ||||
0.0928243 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(98\) | −5.00000 | + | 4.89898i | −0.505076 | + | 0.494872i | ||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | −3.32843 | + | 5.76500i | −0.332843 | + | 0.576500i | ||||
\(101\) | −5.91421 | − | 10.2437i | −0.588486 | − | 1.01929i | −0.994431 | − | 0.105390i | \(-0.966391\pi\) |
0.405945 | − | 0.913898i | \(-0.366943\pi\) | |||||||
\(102\) | 1.58579 | + | 2.74666i | 0.157016 | + | 0.271960i | ||||
\(103\) | −5.29289 | + | 9.16756i | −0.521524 | + | 0.903307i | 0.478162 | + | 0.878271i | \(0.341303\pi\) |
−0.999687 | + | 0.0250350i | \(0.992030\pi\) | |||||||
\(104\) | 1.82843 | 0.179292 | ||||||||
\(105\) | 3.70711 | + | 0.507306i | 0.361777 | + | 0.0495080i | ||||
\(106\) | −11.8995 | −1.15578 | ||||||||
\(107\) | −5.53553 | + | 9.58783i | −0.535140 | + | 0.926890i | 0.464016 | + | 0.885827i | \(0.346408\pi\) |
−0.999157 | + | 0.0410635i | \(0.986925\pi\) | |||||||
\(108\) | 1.20711 | + | 2.09077i | 0.116154 | + | 0.201184i | ||||
\(109\) | 0.242641 | + | 0.420266i | 0.0232408 | + | 0.0402542i | 0.877412 | − | 0.479738i | \(-0.159268\pi\) |
−0.854171 | + | 0.519992i | \(0.825935\pi\) | |||||||
\(110\) | 1.70711 | − | 2.95680i | 0.162766 | − | 0.281919i | ||||
\(111\) | −2.72792 | −0.258923 | ||||||||
\(112\) | 1.62132 | − | 2.09077i | 0.153200 | − | 0.197559i | ||||
\(113\) | −13.8284 | −1.30087 | −0.650434 | − | 0.759562i | \(-0.725413\pi\) | ||||
−0.650434 | + | 0.759562i | \(0.725413\pi\) | |||||||
\(114\) | 0.707107 | − | 1.22474i | 0.0662266 | − | 0.114708i | ||||
\(115\) | 3.82843 | + | 6.63103i | 0.357003 | + | 0.618347i | ||||
\(116\) | 4.32843 | + | 7.49706i | 0.401884 | + | 0.696084i | ||||
\(117\) | 2.58579 | − | 4.47871i | 0.239056 | − | 0.414057i | ||||
\(118\) | −8.41421 | −0.774591 | ||||||||
\(119\) | −7.65685 | − | 18.7554i | −0.701903 | − | 1.71930i | ||||
\(120\) | −1.41421 | −0.129099 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −3.08579 | − | 5.34474i | −0.279374 | − | 0.483890i | ||||
\(123\) | 0.535534 | + | 0.927572i | 0.0482875 | + | 0.0836363i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | −2.82843 | − | 6.92820i | −0.251976 | − | 0.617213i | ||||
\(127\) | −9.72792 | −0.863213 | −0.431607 | − | 0.902062i | \(-0.642053\pi\) | ||||
−0.431607 | + | 0.902062i | \(0.642053\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.17157 | − | 2.02922i | −0.103151 | − | 0.178663i | ||||
\(130\) | 3.12132 | + | 5.40629i | 0.273758 | + | 0.474163i | ||||
\(131\) | 1.70711 | − | 2.95680i | 0.149151 | − | 0.258336i | −0.781763 | − | 0.623575i | \(-0.785679\pi\) |
0.930914 | + | 0.365239i | \(0.119013\pi\) | |||||||
\(132\) | 0.414214 | 0.0360527 | ||||||||
\(133\) | −5.53553 | + | 7.13834i | −0.479992 | + | 0.618972i | ||||
\(134\) | 11.2426 | 0.971216 | ||||||||
\(135\) | −4.12132 | + | 7.13834i | −0.354707 | + | 0.614370i | ||||
\(136\) | 3.82843 | + | 6.63103i | 0.328285 | + | 0.568606i | ||||
\(137\) | 2.67157 | + | 4.62730i | 0.228248 | + | 0.395337i | 0.957289 | − | 0.289133i | \(-0.0933670\pi\) |
−0.729041 | + | 0.684470i | \(0.760034\pi\) | |||||||
\(138\) | −0.464466 | + | 0.804479i | −0.0395380 | + | 0.0684818i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 8.94975 | + | 1.22474i | 0.756392 | + | 0.103510i | ||||
\(141\) | 2.68629 | 0.226227 | ||||||||
\(142\) | −1.53553 | + | 2.65962i | −0.128859 | + | 0.223191i | ||||
\(143\) | −0.914214 | − | 1.58346i | −0.0764504 | − | 0.132416i | ||||
\(144\) | 1.41421 | + | 2.44949i | 0.117851 | + | 0.204124i | ||||
\(145\) | −14.7782 | + | 25.5965i | −1.22726 | + | 2.12568i | ||||
\(146\) | −6.58579 | −0.545044 | ||||||||
\(147\) | −0.721825 | − | 2.80821i | −0.0595352 | − | 0.231617i | ||||
\(148\) | −6.58579 | −0.541348 | ||||||||
\(149\) | −3.17157 | + | 5.49333i | −0.259825 | + | 0.450031i | −0.966195 | − | 0.257812i | \(-0.916998\pi\) |
0.706370 | + | 0.707843i | \(0.250332\pi\) | |||||||
\(150\) | −1.37868 | − | 2.38794i | −0.112569 | − | 0.194975i | ||||
\(151\) | −4.86396 | − | 8.42463i | −0.395824 | − | 0.685586i | 0.597382 | − | 0.801957i | \(-0.296207\pi\) |
−0.993206 | + | 0.116370i | \(0.962874\pi\) | |||||||
\(152\) | 1.70711 | − | 2.95680i | 0.138465 | − | 0.239828i | ||||
\(153\) | 21.6569 | 1.75085 | ||||||||
\(154\) | −2.62132 | − | 0.358719i | −0.211232 | − | 0.0289064i | ||||
\(155\) | 13.6569 | 1.09694 | ||||||||
\(156\) | −0.378680 | + | 0.655892i | −0.0303186 | + | 0.0525134i | ||||
\(157\) | −3.17157 | − | 5.49333i | −0.253119 | − | 0.438415i | 0.711264 | − | 0.702925i | \(-0.248123\pi\) |
−0.964383 | + | 0.264510i | \(0.914790\pi\) | |||||||
\(158\) | 2.37868 | + | 4.11999i | 0.189238 | + | 0.327769i | ||||
\(159\) | 2.46447 | − | 4.26858i | 0.195445 | − | 0.338520i | ||||
\(160\) | −3.41421 | −0.269917 | ||||||||
\(161\) | 3.63604 | − | 4.68885i | 0.286560 | − | 0.369533i | ||||
\(162\) | 7.48528 | 0.588099 | ||||||||
\(163\) | 7.86396 | − | 13.6208i | 0.615953 | − | 1.06686i | −0.374264 | − | 0.927322i | \(-0.622104\pi\) |
0.990217 | − | 0.139539i | \(-0.0445622\pi\) | |||||||
\(164\) | 1.29289 | + | 2.23936i | 0.100958 | + | 0.174864i | ||||
\(165\) | 0.707107 | + | 1.22474i | 0.0550482 | + | 0.0953463i | ||||
\(166\) | −8.07107 | + | 13.9795i | −0.626436 | + | 1.08502i | ||||
\(167\) | −11.7279 | −0.907534 | −0.453767 | − | 0.891120i | \(-0.649920\pi\) | ||||
−0.453767 | + | 0.891120i | \(0.649920\pi\) | |||||||
\(168\) | 0.414214 | + | 1.01461i | 0.0319573 | + | 0.0782790i | ||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | −13.0711 | + | 22.6398i | −1.00251 | + | 1.73639i | ||||
\(171\) | −4.82843 | − | 8.36308i | −0.369239 | − | 0.639541i | ||||
\(172\) | −2.82843 | − | 4.89898i | −0.215666 | − | 0.373544i | ||||
\(173\) | 2.08579 | − | 3.61269i | 0.158579 | − | 0.274668i | −0.775777 | − | 0.631007i | \(-0.782642\pi\) |
0.934357 | + | 0.356339i | \(0.115975\pi\) | |||||||
\(174\) | −3.58579 | −0.271838 | ||||||||
\(175\) | 6.65685 | + | 16.3059i | 0.503211 | + | 1.23261i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 1.74264 | − | 3.01834i | 0.130985 | − | 0.226872i | ||||
\(178\) | 2.24264 | + | 3.88437i | 0.168093 | + | 0.291146i | ||||
\(179\) | 9.44975 | + | 16.3674i | 0.706307 | + | 1.22336i | 0.966218 | + | 0.257727i | \(0.0829736\pi\) |
−0.259910 | + | 0.965633i | \(0.583693\pi\) | |||||||
\(180\) | −4.82843 | + | 8.36308i | −0.359890 | + | 0.623347i | ||||
\(181\) | 3.65685 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(182\) | 2.96447 | − | 3.82282i | 0.219741 | − | 0.283366i | ||||
\(183\) | 2.55635 | 0.188971 | ||||||||
\(184\) | −1.12132 | + | 1.94218i | −0.0826648 | + | 0.143180i | ||||
\(185\) | −11.2426 | − | 19.4728i | −0.826575 | − | 1.43167i | ||||
\(186\) | 0.828427 | + | 1.43488i | 0.0607432 | + | 0.105210i | ||||
\(187\) | 3.82843 | − | 6.63103i | 0.279962 | − | 0.484909i | ||||
\(188\) | 6.48528 | 0.472988 | ||||||||
\(189\) | 6.32843 | + | 0.866025i | 0.460325 | + | 0.0629941i | ||||
\(190\) | 11.6569 | 0.845677 | ||||||||
\(191\) | 6.41421 | − | 11.1097i | 0.464116 | − | 0.803873i | −0.535045 | − | 0.844824i | \(-0.679705\pi\) |
0.999161 | + | 0.0409507i | \(0.0130387\pi\) | |||||||
\(192\) | −0.207107 | − | 0.358719i | −0.0149466 | − | 0.0258883i | ||||
\(193\) | −1.05025 | − | 1.81909i | −0.0755988 | − | 0.130941i | 0.825748 | − | 0.564040i | \(-0.190754\pi\) |
−0.901347 | + | 0.433099i | \(0.857420\pi\) | |||||||
\(194\) | −0.914214 | + | 1.58346i | −0.0656367 | + | 0.113686i | ||||
\(195\) | −2.58579 | −0.185172 | ||||||||
\(196\) | −1.74264 | − | 6.77962i | −0.124474 | − | 0.484258i | ||||
\(197\) | −17.4853 | −1.24577 | −0.622887 | − | 0.782312i | \(-0.714041\pi\) | ||||
−0.622887 | + | 0.782312i | \(0.714041\pi\) | |||||||
\(198\) | 1.41421 | − | 2.44949i | 0.100504 | − | 0.174078i | ||||
\(199\) | −9.94975 | − | 17.2335i | −0.705319 | − | 1.22165i | −0.966576 | − | 0.256379i | \(-0.917470\pi\) |
0.261257 | − | 0.965269i | \(-0.415863\pi\) | |||||||
\(200\) | −3.32843 | − | 5.76500i | −0.235355 | − | 0.407647i | ||||
\(201\) | −2.32843 | + | 4.03295i | −0.164235 | + | 0.284463i | ||||
\(202\) | 11.8284 | 0.832245 | ||||||||
\(203\) | 22.6924 | + | 3.10538i | 1.59269 | + | 0.217955i | ||||
\(204\) | −3.17157 | −0.222055 | ||||||||
\(205\) | −4.41421 | + | 7.64564i | −0.308302 | + | 0.533995i | ||||
\(206\) | −5.29289 | − | 9.16756i | −0.368773 | − | 0.638734i | ||||
\(207\) | 3.17157 | + | 5.49333i | 0.220440 | + | 0.381813i | ||||
\(208\) | −0.914214 | + | 1.58346i | −0.0633893 | + | 0.109793i | ||||
\(209\) | −3.41421 | −0.236166 | ||||||||
\(210\) | −2.29289 | + | 2.95680i | −0.158225 | + | 0.204038i | ||||
\(211\) | 4.58579 | 0.315699 | 0.157849 | − | 0.987463i | \(-0.449544\pi\) | ||||
0.157849 | + | 0.987463i | \(0.449544\pi\) | |||||||
\(212\) | 5.94975 | − | 10.3053i | 0.408630 | − | 0.707768i | ||||
\(213\) | −0.636039 | − | 1.10165i | −0.0435807 | − | 0.0754839i | ||||
\(214\) | −5.53553 | − | 9.58783i | −0.378401 | − | 0.655410i | ||||
\(215\) | 9.65685 | − | 16.7262i | 0.658592 | − | 1.14071i | ||||
\(216\) | −2.41421 | −0.164266 | ||||||||
\(217\) | −4.00000 | − | 9.79796i | −0.271538 | − | 0.665129i | ||||
\(218\) | −0.485281 | −0.0328674 | ||||||||
\(219\) | 1.36396 | − | 2.36245i | 0.0921679 | − | 0.159640i | ||||
\(220\) | 1.70711 | + | 2.95680i | 0.115093 | + | 0.199347i | ||||
\(221\) | 7.00000 | + | 12.1244i | 0.470871 | + | 0.815572i | ||||
\(222\) | 1.36396 | − | 2.36245i | 0.0915431 | − | 0.158557i | ||||
\(223\) | 11.4142 | 0.764352 | 0.382176 | − | 0.924089i | \(-0.375175\pi\) | ||||
0.382176 | + | 0.924089i | \(0.375175\pi\) | |||||||
\(224\) | 1.00000 | + | 2.44949i | 0.0668153 | + | 0.163663i | ||||
\(225\) | −18.8284 | −1.25523 | ||||||||
\(226\) | 6.91421 | − | 11.9758i | 0.459927 | − | 0.796616i | ||||
\(227\) | 11.5858 | + | 20.0672i | 0.768976 | + | 1.33190i | 0.938119 | + | 0.346313i | \(0.112567\pi\) |
−0.169143 | + | 0.985591i | \(0.554100\pi\) | |||||||
\(228\) | 0.707107 | + | 1.22474i | 0.0468293 | + | 0.0811107i | ||||
\(229\) | −0.343146 | + | 0.594346i | −0.0226757 | + | 0.0392755i | −0.877141 | − | 0.480234i | \(-0.840552\pi\) |
0.854465 | + | 0.519509i | \(0.173885\pi\) | |||||||
\(230\) | −7.65685 | −0.504878 | ||||||||
\(231\) | 0.671573 | − | 0.866025i | 0.0441863 | − | 0.0569803i | ||||
\(232\) | −8.65685 | −0.568350 | ||||||||
\(233\) | 0.707107 | − | 1.22474i | 0.0463241 | − | 0.0802357i | −0.841934 | − | 0.539581i | \(-0.818583\pi\) |
0.888258 | + | 0.459345i | \(0.151916\pi\) | |||||||
\(234\) | 2.58579 | + | 4.47871i | 0.169038 | + | 0.292783i | ||||
\(235\) | 11.0711 | + | 19.1757i | 0.722197 | + | 1.25088i | ||||
\(236\) | 4.20711 | − | 7.28692i | 0.273859 | − | 0.474338i | ||||
\(237\) | −1.97056 | −0.128002 | ||||||||
\(238\) | 20.0711 | + | 2.74666i | 1.30101 | + | 0.178040i | ||||
\(239\) | −22.2132 | −1.43685 | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695603i | \(0.755137\pi\) | |||||||
\(240\) | 0.707107 | − | 1.22474i | 0.0456435 | − | 0.0790569i | ||||
\(241\) | −1.87868 | − | 3.25397i | −0.121016 | − | 0.209607i | 0.799152 | − | 0.601129i | \(-0.205282\pi\) |
−0.920169 | + | 0.391522i | \(0.871949\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | −5.17157 | + | 8.95743i | −0.331757 | + | 0.574619i | ||||
\(244\) | 6.17157 | 0.395094 | ||||||||
\(245\) | 17.0711 | − | 16.7262i | 1.09063 | − | 1.06860i | ||||
\(246\) | −1.07107 | −0.0682888 | ||||||||
\(247\) | 3.12132 | − | 5.40629i | 0.198605 | − | 0.343994i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | −3.34315 | − | 5.79050i | −0.211863 | − | 0.366958i | ||||
\(250\) | 2.82843 | − | 4.89898i | 0.178885 | − | 0.309839i | ||||
\(251\) | 2.14214 | 0.135210 | 0.0676052 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676052 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(252\) | 7.41421 | + | 1.01461i | 0.467052 | + | 0.0639145i | ||||
\(253\) | 2.24264 | 0.140994 | ||||||||
\(254\) | 4.86396 | − | 8.42463i | 0.305192 | − | 0.528608i | ||||
\(255\) | −5.41421 | − | 9.37769i | −0.339051 | − | 0.587254i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.57107 | + | 2.72117i | −0.0980005 | + | 0.169742i | −0.910857 | − | 0.412722i | \(-0.864578\pi\) |
0.812856 | + | 0.582464i | \(0.197911\pi\) | |||||||
\(258\) | 2.34315 | 0.145878 | ||||||||
\(259\) | −10.6777 | + | 13.7694i | −0.663478 | + | 0.855587i | ||||
\(260\) | −6.24264 | −0.387152 | ||||||||
\(261\) | −12.2426 | + | 21.2049i | −0.757800 | + | 1.31255i | ||||
\(262\) | 1.70711 | + | 2.95680i | 0.105465 | + | 0.182671i | ||||
\(263\) | −15.5208 | − | 26.8828i | −0.957054 | − | 1.65767i | −0.729595 | − | 0.683879i | \(-0.760291\pi\) |
−0.227459 | − | 0.973788i | \(-0.573042\pi\) | |||||||
\(264\) | −0.207107 | + | 0.358719i | −0.0127465 | + | 0.0220777i | ||||
\(265\) | 40.6274 | 2.49572 | ||||||||
\(266\) | −3.41421 | − | 8.36308i | −0.209339 | − | 0.512773i | ||||
\(267\) | −1.85786 | −0.113699 | ||||||||
\(268\) | −5.62132 | + | 9.73641i | −0.343377 | + | 0.594746i | ||||
\(269\) | −6.82843 | − | 11.8272i | −0.416337 | − | 0.721116i | 0.579231 | − | 0.815163i | \(-0.303353\pi\) |
−0.995568 | + | 0.0940473i | \(0.970020\pi\) | |||||||
\(270\) | −4.12132 | − | 7.13834i | −0.250816 | − | 0.434425i | ||||
\(271\) | 13.2782 | − | 22.9985i | 0.806592 | − | 1.39706i | −0.108620 | − | 0.994083i | \(-0.534643\pi\) |
0.915211 | − | 0.402974i | \(-0.132024\pi\) | |||||||
\(272\) | −7.65685 | −0.464265 | ||||||||
\(273\) | 0.757359 | + | 1.85514i | 0.0458375 | + | 0.112278i | ||||
\(274\) | −5.34315 | −0.322791 | ||||||||
\(275\) | −3.32843 | + | 5.76500i | −0.200712 | + | 0.347643i | ||||
\(276\) | −0.464466 | − | 0.804479i | −0.0279576 | − | 0.0484239i | ||||
\(277\) | 1.91421 | + | 3.31552i | 0.115014 | + | 0.199210i | 0.917785 | − | 0.397077i | \(-0.129975\pi\) |
−0.802771 | + | 0.596287i | \(0.796642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3137 | 0.677334 | ||||||||
\(280\) | −5.53553 | + | 7.13834i | −0.330811 | + | 0.426597i | ||||
\(281\) | −16.7279 | −0.997904 | −0.498952 | − | 0.866630i | \(-0.666282\pi\) | ||||
−0.498952 | + | 0.866630i | \(0.666282\pi\) | |||||||
\(282\) | −1.34315 | + | 2.32640i | −0.0799832 | + | 0.138535i | ||||
\(283\) | 10.2929 | + | 17.8278i | 0.611849 | + | 1.05975i | 0.990929 | + | 0.134389i | \(0.0429073\pi\) |
−0.379080 | + | 0.925364i | \(0.623759\pi\) | |||||||
\(284\) | −1.53553 | − | 2.65962i | −0.0911172 | − | 0.157820i | ||||
\(285\) | −2.41421 | + | 4.18154i | −0.143006 | + | 0.247693i | ||||
\(286\) | 1.82843 | 0.108117 | ||||||||
\(287\) | 6.77817 | + | 0.927572i | 0.400103 | + | 0.0547528i | ||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | −20.8137 | + | 36.0504i | −1.22434 | + | 2.12061i | ||||
\(290\) | −14.7782 | − | 25.5965i | −0.867804 | − | 1.50308i | ||||
\(291\) | −0.378680 | − | 0.655892i | −0.0221986 | − | 0.0384491i | ||||
\(292\) | 3.29289 | − | 5.70346i | 0.192702 | − | 0.333770i | ||||
\(293\) | −5.17157 | −0.302127 | −0.151063 | − | 0.988524i | \(-0.548270\pi\) | ||||
−0.151063 | + | 0.988524i | \(0.548270\pi\) | |||||||
\(294\) | 2.79289 | + | 0.778985i | 0.162885 | + | 0.0454314i | ||||
\(295\) | 28.7279 | 1.67260 | ||||||||
\(296\) | 3.29289 | − | 5.70346i | 0.191396 | − | 0.331507i | ||||
\(297\) | 1.20711 | + | 2.09077i | 0.0700434 | + | 0.121319i | ||||
\(298\) | −3.17157 | − | 5.49333i | −0.183724 | − | 0.318220i | ||||
\(299\) | −2.05025 | + | 3.55114i | −0.118569 | + | 0.205368i | ||||
\(300\) | 2.75736 | 0.159196 | ||||||||
\(301\) | −14.8284 | − | 2.02922i | −0.854696 | − | 0.116963i | ||||
\(302\) | 9.72792 | 0.559779 | ||||||||
\(303\) | −2.44975 | + | 4.24309i | −0.140734 | + | 0.243759i | ||||
\(304\) | 1.70711 | + | 2.95680i | 0.0979093 | + | 0.169584i | ||||
\(305\) | 10.5355 | + | 18.2481i | 0.603263 | + | 1.04488i | ||||
\(306\) | −10.8284 | + | 18.7554i | −0.619020 | + | 1.07217i | ||||
\(307\) | −9.89949 | −0.564994 | −0.282497 | − | 0.959268i | \(-0.591163\pi\) | ||||
−0.282497 | + | 0.959268i | \(0.591163\pi\) | |||||||
\(308\) | 1.62132 | − | 2.09077i | 0.0923833 | − | 0.119133i | ||||
\(309\) | 4.38478 | 0.249441 | ||||||||
\(310\) | −6.82843 | + | 11.8272i | −0.387829 | + | 0.671739i | ||||
\(311\) | 4.36396 | + | 7.55860i | 0.247458 | + | 0.428609i | 0.962820 | − | 0.270145i | \(-0.0870716\pi\) |
−0.715362 | + | 0.698754i | \(0.753738\pi\) | |||||||
\(312\) | −0.378680 | − | 0.655892i | −0.0214385 | − | 0.0371326i | ||||
\(313\) | 4.67157 | − | 8.09140i | 0.264053 | − | 0.457353i | −0.703262 | − | 0.710931i | \(-0.748274\pi\) |
0.967315 | + | 0.253578i | \(0.0816073\pi\) | |||||||
\(314\) | 6.34315 | 0.357964 | ||||||||
\(315\) | 9.65685 | + | 23.6544i | 0.544102 | + | 1.33277i | ||||
\(316\) | −4.75736 | −0.267622 | ||||||||
\(317\) | −15.6569 | + | 27.1185i | −0.879377 | + | 1.52312i | −0.0273502 | + | 0.999626i | \(0.508707\pi\) |
−0.852026 | + | 0.523499i | \(0.824626\pi\) | |||||||
\(318\) | 2.46447 | + | 4.26858i | 0.138200 | + | 0.239370i | ||||
\(319\) | 4.32843 | + | 7.49706i | 0.242345 | + | 0.419755i | ||||
\(320\) | 1.70711 | − | 2.95680i | 0.0954302 | − | 0.165290i | ||||
\(321\) | 4.58579 | 0.255954 | ||||||||
\(322\) | 2.24264 | + | 5.49333i | 0.124977 | + | 0.306131i | ||||
\(323\) | 26.1421 | 1.45459 | ||||||||
\(324\) | −3.74264 | + | 6.48244i | −0.207924 | + | 0.360136i | ||||
\(325\) | −6.08579 | − | 10.5409i | −0.337579 | − | 0.584703i | ||||
\(326\) | 7.86396 | + | 13.6208i | 0.435545 | + | 0.754385i | ||||
\(327\) | 0.100505 | − | 0.174080i | 0.00555794 | − | 0.00962664i | ||||
\(328\) | −2.58579 | −0.142776 | ||||||||
\(329\) | 10.5147 | − | 13.5592i | 0.579695 | − | 0.747545i | ||||
\(330\) | −1.41421 | −0.0778499 | ||||||||
\(331\) | 4.96447 | − | 8.59871i | 0.272872 | − | 0.472628i | −0.696724 | − | 0.717339i | \(-0.745360\pi\) |
0.969596 | + | 0.244711i | \(0.0786932\pi\) | |||||||
\(332\) | −8.07107 | − | 13.9795i | −0.442957 | − | 0.767225i | ||||
\(333\) | −9.31371 | − | 16.1318i | −0.510388 | − | 0.884018i | ||||
\(334\) | 5.86396 | − | 10.1567i | 0.320862 | − | 0.555749i | ||||
\(335\) | −38.3848 | −2.09718 | ||||||||
\(336\) | −1.08579 | − | 0.148586i | −0.0592345 | − | 0.00810606i | ||||
\(337\) | −19.7574 | −1.07625 | −0.538126 | − | 0.842864i | \(-0.680868\pi\) | ||||
−0.538126 | + | 0.842864i | \(0.680868\pi\) | |||||||
\(338\) | 4.82843 | − | 8.36308i | 0.262632 | − | 0.454892i | ||||
\(339\) | 2.86396 | + | 4.96053i | 0.155549 | + | 0.269419i | ||||
\(340\) | −13.0711 | − | 22.6398i | −0.708878 | − | 1.22781i | ||||
\(341\) | 2.00000 | − | 3.46410i | 0.108306 | − | 0.187592i | ||||
\(342\) | 9.65685 | 0.522183 | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | 5.65685 | 0.304997 | ||||||||
\(345\) | 1.58579 | − | 2.74666i | 0.0853759 | − | 0.147875i | ||||
\(346\) | 2.08579 | + | 3.61269i | 0.112133 | + | 0.194219i | ||||
\(347\) | −7.29289 | − | 12.6317i | −0.391503 | − | 0.678103i | 0.601145 | − | 0.799140i | \(-0.294711\pi\) |
−0.992648 | + | 0.121037i | \(0.961378\pi\) | |||||||
\(348\) | 1.79289 | − | 3.10538i | 0.0961092 | − | 0.166466i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −17.4497 | − | 2.38794i | −0.932728 | − | 0.127641i | ||||
\(351\) | −4.41421 | −0.235613 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 12.6569 | + | 21.9223i | 0.673656 | + | 1.16681i | 0.976860 | + | 0.213881i | \(0.0686105\pi\) |
−0.303203 | + | 0.952926i | \(0.598056\pi\) | |||||||
\(354\) | 1.74264 | + | 3.01834i | 0.0926203 | + | 0.160423i | ||||
\(355\) | 5.24264 | − | 9.08052i | 0.278250 | − | 0.481944i | ||||
\(356\) | −4.48528 | −0.237719 | ||||||||
\(357\) | −5.14214 | + | 6.63103i | −0.272151 | + | 0.350951i | ||||
\(358\) | −18.8995 | −0.998869 | ||||||||
\(359\) | −5.37868 | + | 9.31615i | −0.283876 | + | 0.491687i | −0.972336 | − | 0.233587i | \(-0.924954\pi\) |
0.688460 | + | 0.725274i | \(0.258287\pi\) | |||||||
\(360\) | −4.82843 | − | 8.36308i | −0.254480 | − | 0.440773i | ||||
\(361\) | 3.67157 | + | 6.35935i | 0.193241 | + | 0.334703i | ||||
\(362\) | −1.82843 | + | 3.16693i | −0.0961000 | + | 0.166450i | ||||
\(363\) | 0.414214 | 0.0217406 | ||||||||
\(364\) | 1.82843 | + | 4.47871i | 0.0958356 | + | 0.234748i | ||||
\(365\) | 22.4853 | 1.17693 | ||||||||
\(366\) | −1.27817 | + | 2.21386i | −0.0668113 | + | 0.115720i | ||||
\(367\) | −7.36396 | − | 12.7548i | −0.384396 | − | 0.665793i | 0.607290 | − | 0.794481i | \(-0.292257\pi\) |
−0.991685 | + | 0.128688i | \(0.958923\pi\) | |||||||
\(368\) | −1.12132 | − | 1.94218i | −0.0584529 | − | 0.101243i | ||||
\(369\) | −3.65685 | + | 6.33386i | −0.190368 | + | 0.329727i | ||||
\(370\) | 22.4853 | 1.16895 | ||||||||
\(371\) | −11.8995 | − | 29.1477i | −0.617791 | − | 1.51327i | ||||
\(372\) | −1.65685 | −0.0859039 | ||||||||
\(373\) | −6.98528 | + | 12.0989i | −0.361684 | + | 0.626455i | −0.988238 | − | 0.152923i | \(-0.951131\pi\) |
0.626554 | + | 0.779378i | \(0.284465\pi\) | |||||||
\(374\) | 3.82843 | + | 6.63103i | 0.197963 | + | 0.342882i | ||||
\(375\) | 1.17157 | + | 2.02922i | 0.0604998 | + | 0.104789i | ||||
\(376\) | −3.24264 | + | 5.61642i | −0.167226 | + | 0.289645i | ||||
\(377\) | −15.8284 | −0.815205 | ||||||||
\(378\) | −3.91421 | + | 5.04757i | −0.201325 | + | 0.259619i | ||||
\(379\) | −25.8701 | −1.32886 | −0.664428 | − | 0.747352i | \(-0.731325\pi\) | ||||
−0.664428 | + | 0.747352i | \(0.731325\pi\) | |||||||
\(380\) | −5.82843 | + | 10.0951i | −0.298992 | + | 0.517869i | ||||
\(381\) | 2.01472 | + | 3.48960i | 0.103217 | + | 0.178777i | ||||
\(382\) | 6.41421 | + | 11.1097i | 0.328180 | + | 0.568424i | ||||
\(383\) | −15.1924 | + | 26.3140i | −0.776295 | + | 1.34458i | 0.157769 | + | 0.987476i | \(0.449570\pi\) |
−0.934064 | + | 0.357106i | \(0.883764\pi\) | |||||||
\(384\) | 0.414214 | 0.0211377 | ||||||||
\(385\) | 8.94975 | + | 1.22474i | 0.456121 | + | 0.0624188i | ||||
\(386\) | 2.10051 | 0.106913 | ||||||||
\(387\) | 8.00000 | − | 13.8564i | 0.406663 | − | 0.704361i | ||||
\(388\) | −0.914214 | − | 1.58346i | −0.0464122 | − | 0.0803882i | ||||
\(389\) | −1.36396 | − | 2.36245i | −0.0691556 | − | 0.119781i | 0.829374 | − | 0.558693i | \(-0.188697\pi\) |
−0.898530 | + | 0.438912i | \(0.855364\pi\) | |||||||
\(390\) | 1.29289 | − | 2.23936i | 0.0654682 | − | 0.113394i | ||||
\(391\) | −17.1716 | −0.868404 | ||||||||
\(392\) | 6.74264 | + | 1.88064i | 0.340555 | + | 0.0949865i | ||||
\(393\) | −1.41421 | −0.0713376 | ||||||||
\(394\) | 8.74264 | − | 15.1427i | 0.440448 | − | 0.762878i | ||||
\(395\) | −8.12132 | − | 14.0665i | −0.408628 | − | 0.707764i | ||||
\(396\) | 1.41421 | + | 2.44949i | 0.0710669 | + | 0.123091i | ||||
\(397\) | −11.0000 | + | 19.0526i | −0.552074 | + | 0.956221i | 0.446051 | + | 0.895008i | \(0.352830\pi\) |
−0.998125 | + | 0.0612128i | \(0.980503\pi\) | |||||||
\(398\) | 19.8995 | 0.997472 | ||||||||
\(399\) | 3.70711 | + | 0.507306i | 0.185587 | + | 0.0253971i | ||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | 2.15685 | − | 3.73578i | 0.107708 | − | 0.186556i | −0.807133 | − | 0.590369i | \(-0.798982\pi\) |
0.914841 | + | 0.403813i | \(0.132315\pi\) | |||||||
\(402\) | −2.32843 | − | 4.03295i | −0.116131 | − | 0.201145i | ||||
\(403\) | 3.65685 | + | 6.33386i | 0.182161 | + | 0.315512i | ||||
\(404\) | −5.91421 | + | 10.2437i | −0.294243 | + | 0.509644i | ||||
\(405\) | −25.5563 | −1.26991 | ||||||||
\(406\) | −14.0355 | + | 18.0995i | −0.696572 | + | 0.898263i | ||||
\(407\) | −6.58579 | −0.326445 | ||||||||
\(408\) | 1.58579 | − | 2.74666i | 0.0785081 | − | 0.135980i | ||||
\(409\) | 11.3640 | + | 19.6830i | 0.561912 | + | 0.973260i | 0.997330 | + | 0.0730312i | \(0.0232673\pi\) |
−0.435418 | + | 0.900228i | \(0.643399\pi\) | |||||||
\(410\) | −4.41421 | − | 7.64564i | −0.218002 | − | 0.377591i | ||||
\(411\) | 1.10660 | − | 1.91669i | 0.0545846 | − | 0.0945434i | ||||
\(412\) | 10.5858 | 0.521524 | ||||||||
\(413\) | −8.41421 | − | 20.6105i | −0.414036 | − | 1.01418i | ||||
\(414\) | −6.34315 | −0.311749 | ||||||||
\(415\) | 27.5563 | − | 47.7290i | 1.35269 | − | 2.34292i | ||||
\(416\) | −0.914214 | − | 1.58346i | −0.0448230 | − | 0.0776357i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.70711 | − | 2.95680i | 0.0834973 | − | 0.144622i | ||||
\(419\) | 2.14214 | 0.104650 | 0.0523251 | − | 0.998630i | \(-0.483337\pi\) | ||||
0.0523251 | + | 0.998630i | \(0.483337\pi\) | |||||||
\(420\) | −1.41421 | − | 3.46410i | −0.0690066 | − | 0.169031i | ||||
\(421\) | 23.3137 | 1.13624 | 0.568120 | − | 0.822946i | \(-0.307671\pi\) | ||||
0.568120 | + | 0.822946i | \(0.307671\pi\) | |||||||
\(422\) | −2.29289 | + | 3.97141i | −0.111616 | + | 0.193325i | ||||
\(423\) | 9.17157 | + | 15.8856i | 0.445937 | + | 0.772386i | ||||
\(424\) | 5.94975 | + | 10.3053i | 0.288945 | + | 0.500468i | ||||
\(425\) | 25.4853 | − | 44.1418i | 1.23622 | − | 2.14119i | ||||
\(426\) | 1.27208 | 0.0616324 | ||||||||
\(427\) | 10.0061 | − | 12.9033i | 0.484229 | − | 0.624436i | ||||
\(428\) | 11.0711 | 0.535140 | ||||||||
\(429\) | −0.378680 | + | 0.655892i | −0.0182828 | + | 0.0316668i | ||||
\(430\) | 9.65685 | + | 16.7262i | 0.465695 | + | 0.806607i | ||||
\(431\) | 10.2071 | + | 17.6792i | 0.491659 | + | 0.851578i | 0.999954 | − | 0.00960469i | \(-0.00305731\pi\) |
−0.508295 | + | 0.861183i | \(0.669724\pi\) | |||||||
\(432\) | 1.20711 | − | 2.09077i | 0.0580770 | − | 0.100592i | ||||
\(433\) | −2.14214 | −0.102944 | −0.0514722 | − | 0.998674i | \(-0.516391\pi\) | ||||
−0.0514722 | + | 0.998674i | \(0.516391\pi\) | |||||||
\(434\) | 10.4853 | + | 1.43488i | 0.503310 | + | 0.0688763i | ||||
\(435\) | 12.2426 | 0.586990 | ||||||||
\(436\) | 0.242641 | − | 0.420266i | 0.0116204 | − | 0.0201271i | ||||
\(437\) | 3.82843 | + | 6.63103i | 0.183139 | + | 0.317205i | ||||
\(438\) | 1.36396 | + | 2.36245i | 0.0651726 | + | 0.112882i | ||||
\(439\) | −4.69239 | + | 8.12745i | −0.223955 | + | 0.387902i | −0.956006 | − | 0.293349i | \(-0.905230\pi\) |
0.732050 | + | 0.681251i | \(0.238564\pi\) | |||||||
\(440\) | −3.41421 | −0.162766 | ||||||||
\(441\) | 14.1421 | − | 13.8564i | 0.673435 | − | 0.659829i | ||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | 16.3137 | − | 28.2562i | 0.775088 | − | 1.34249i | −0.159658 | − | 0.987172i | \(-0.551039\pi\) |
0.934745 | − | 0.355319i | \(-0.115628\pi\) | |||||||
\(444\) | 1.36396 | + | 2.36245i | 0.0647307 | + | 0.112117i | ||||
\(445\) | −7.65685 | − | 13.2621i | −0.362970 | − | 0.628682i | ||||
\(446\) | −5.70711 | + | 9.88500i | −0.270239 | + | 0.468068i | ||||
\(447\) | 2.62742 | 0.124273 | ||||||||
\(448\) | −2.62132 | − | 0.358719i | −0.123846 | − | 0.0169479i | ||||
\(449\) | 33.6569 | 1.58837 | 0.794183 | − | 0.607679i | \(-0.207899\pi\) | ||||
0.794183 | + | 0.607679i | \(0.207899\pi\) | |||||||
\(450\) | 9.41421 | − | 16.3059i | 0.443790 | − | 0.768667i | ||||
\(451\) | 1.29289 | + | 2.23936i | 0.0608800 | + | 0.105447i | ||||
\(452\) | 6.91421 | + | 11.9758i | 0.325217 | + | 0.563293i | ||||
\(453\) | −2.01472 | + | 3.48960i | −0.0946597 | + | 0.163955i | ||||
\(454\) | −23.1716 | −1.08750 | ||||||||
\(455\) | −10.1213 | + | 13.0519i | −0.474495 | + | 0.611884i | ||||
\(456\) | −1.41421 | −0.0662266 | ||||||||
\(457\) | 0.171573 | − | 0.297173i | 0.00802584 | − | 0.0139012i | −0.861985 | − | 0.506934i | \(-0.830779\pi\) |
0.870010 | + | 0.493033i | \(0.164112\pi\) | |||||||
\(458\) | −0.343146 | − | 0.594346i | −0.0160341 | − | 0.0277720i | ||||
\(459\) | −9.24264 | − | 16.0087i | −0.431410 | − | 0.747223i | ||||
\(460\) | 3.82843 | − | 6.63103i | 0.178501 | − | 0.309173i | ||||
\(461\) | 14.3137 | 0.666656 | 0.333328 | − | 0.942811i | \(-0.391828\pi\) | ||||
0.333328 | + | 0.942811i | \(0.391828\pi\) | |||||||
\(462\) | 0.414214 | + | 1.01461i | 0.0192710 | + | 0.0472040i | ||||
\(463\) | 7.17157 | 0.333291 | 0.166646 | − | 0.986017i | \(-0.446706\pi\) | ||||
0.166646 | + | 0.986017i | \(0.446706\pi\) | |||||||
\(464\) | 4.32843 | − | 7.49706i | 0.200942 | − | 0.348042i | ||||
\(465\) | −2.82843 | − | 4.89898i | −0.131165 | − | 0.227185i | ||||
\(466\) | 0.707107 | + | 1.22474i | 0.0327561 | + | 0.0567352i | ||||
\(467\) | 17.0000 | − | 29.4449i | 0.786666 | − | 1.36255i | −0.141332 | − | 0.989962i | \(-0.545139\pi\) |
0.927999 | − | 0.372584i | \(-0.121528\pi\) | |||||||
\(468\) | −5.17157 | −0.239056 | ||||||||
\(469\) | 11.2426 | + | 27.5387i | 0.519137 | + | 1.27162i | ||||
\(470\) | −22.1421 | −1.02134 | ||||||||
\(471\) | −1.31371 | + | 2.27541i | −0.0605325 | + | 0.104845i | ||||
\(472\) | 4.20711 | + | 7.28692i | 0.193648 | + | 0.335408i | ||||
\(473\) | −2.82843 | − | 4.89898i | −0.130051 | − | 0.225255i | ||||
\(474\) | 0.985281 | − | 1.70656i | 0.0452555 | − | 0.0783848i | ||||
\(475\) | −22.7279 | −1.04283 | ||||||||
\(476\) | −12.4142 | + | 16.0087i | −0.569005 | + | 0.733759i | ||||
\(477\) | 33.6569 | 1.54104 | ||||||||
\(478\) | 11.1066 | − | 19.2372i | 0.508004 | − | 0.879889i | ||||
\(479\) | 13.0355 | + | 22.5782i | 0.595609 | + | 1.03162i | 0.993461 | + | 0.114175i | \(0.0364224\pi\) |
−0.397852 | + | 0.917450i | \(0.630244\pi\) | |||||||
\(480\) | 0.707107 | + | 1.22474i | 0.0322749 | + | 0.0559017i | ||||
\(481\) | 6.02082 | − | 10.4284i | 0.274526 | − | 0.475492i | ||||
\(482\) | 3.75736 | 0.171143 | ||||||||
\(483\) | −2.43503 | − | 0.333226i | −0.110798 | − | 0.0151623i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.12132 | − | 5.40629i | 0.141732 | − | 0.245487i | ||||
\(486\) | −5.17157 | − | 8.95743i | −0.234587 | − | 0.406317i | ||||
\(487\) | −0.828427 | − | 1.43488i | −0.0375396 | − | 0.0650205i | 0.846645 | − | 0.532158i | \(-0.178619\pi\) |
−0.884185 | + | 0.467137i | \(0.845285\pi\) | |||||||
\(488\) | −3.08579 | + | 5.34474i | −0.139687 | + | 0.241945i | ||||
\(489\) | −6.51472 | −0.294606 | ||||||||
\(490\) | 5.94975 | + | 23.1471i | 0.268782 | + | 1.04568i | ||||
\(491\) | 24.8284 | 1.12049 | 0.560246 | − | 0.828327i | \(-0.310707\pi\) | ||||
0.560246 | + | 0.828327i | \(0.310707\pi\) | |||||||
\(492\) | 0.535534 | − | 0.927572i | 0.0241437 | − | 0.0418182i | ||||
\(493\) | −33.1421 | − | 57.4039i | −1.49265 | − | 2.58534i | ||||
\(494\) | 3.12132 | + | 5.40629i | 0.140435 | + | 0.243240i | ||||
\(495\) | −4.82843 | + | 8.36308i | −0.217022 | + | 0.375893i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −8.05025 | − | 1.10165i | −0.361103 | − | 0.0494158i | ||||
\(498\) | 6.68629 | 0.299620 | ||||||||
\(499\) | 3.07107 | − | 5.31925i | 0.137480 | − | 0.238122i | −0.789062 | − | 0.614313i | \(-0.789433\pi\) |
0.926542 | + | 0.376191i | \(0.122766\pi\) | |||||||
\(500\) | 2.82843 | + | 4.89898i | 0.126491 | + | 0.219089i | ||||
\(501\) | 2.42893 | + | 4.20703i | 0.108517 | + | 0.187956i | ||||
\(502\) | −1.07107 | + | 1.85514i | −0.0478041 | + | 0.0827991i | ||||
\(503\) | −38.2132 | −1.70384 | −0.851921 | − | 0.523670i | \(-0.824563\pi\) | ||||
−0.851921 | + | 0.523670i | \(0.824563\pi\) | |||||||
\(504\) | −4.58579 | + | 5.91359i | −0.204267 | + | 0.263412i | ||||
\(505\) | −40.3848 | −1.79710 | ||||||||
\(506\) | −1.12132 | + | 1.94218i | −0.0498488 | + | 0.0863406i | ||||
\(507\) | 2.00000 | + | 3.46410i | 0.0888231 | + | 0.153846i | ||||
\(508\) | 4.86396 | + | 8.42463i | 0.215803 | + | 0.373782i | ||||
\(509\) | 6.65685 | − | 11.5300i | 0.295060 | − | 0.511059i | −0.679939 | − | 0.733269i | \(-0.737994\pi\) |
0.974999 | + | 0.222210i | \(0.0713271\pi\) | |||||||
\(510\) | 10.8284 | 0.479491 | ||||||||
\(511\) | −6.58579 | − | 16.1318i | −0.291338 | − | 0.713630i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.12132 | + | 7.13834i | −0.181961 | + | 0.315165i | ||||
\(514\) | −1.57107 | − | 2.72117i | −0.0692968 | − | 0.120026i | ||||
\(515\) | 18.0711 | + | 31.3000i | 0.796306 | + | 1.37924i | ||||
\(516\) | −1.17157 | + | 2.02922i | −0.0515756 | + | 0.0893316i | ||||
\(517\) | 6.48528 | 0.285222 | ||||||||
\(518\) | −6.58579 | − | 16.1318i | −0.289363 | − | 0.708791i | ||||
\(519\) | −1.72792 | −0.0758474 | ||||||||
\(520\) | 3.12132 | − | 5.40629i | 0.136879 | − | 0.237081i | ||||
\(521\) | −14.1421 | − | 24.4949i | −0.619578 | − | 1.07314i | −0.989563 | − | 0.144103i | \(-0.953970\pi\) |
0.369984 | − | 0.929038i | \(-0.379363\pi\) | |||||||
\(522\) | −12.2426 | − | 21.2049i | −0.535846 | − | 0.928112i | ||||
\(523\) | −6.36396 | + | 11.0227i | −0.278277 | + | 0.481989i | −0.970957 | − | 0.239256i | \(-0.923097\pi\) |
0.692680 | + | 0.721245i | \(0.256430\pi\) | |||||||
\(524\) | −3.41421 | −0.149151 | ||||||||
\(525\) | 4.47056 | − | 5.76500i | 0.195111 | − | 0.251605i | ||||
\(526\) | 31.0416 | 1.35348 | ||||||||
\(527\) | −15.3137 | + | 26.5241i | −0.667076 | + | 1.15541i | ||||
\(528\) | −0.207107 | − | 0.358719i | −0.00901317 | − | 0.0156113i | ||||
\(529\) | 8.98528 | + | 15.5630i | 0.390664 | + | 0.676651i | ||||
\(530\) | −20.3137 | + | 35.1844i | −0.882371 | + | 1.52831i | ||||
\(531\) | 23.7990 | 1.03279 | ||||||||
\(532\) | 8.94975 | + | 1.22474i | 0.388021 | + | 0.0530994i | ||||
\(533\) | −4.72792 | −0.204789 | ||||||||
\(534\) | 0.928932 | − | 1.60896i | 0.0401988 | − | 0.0696264i | ||||
\(535\) | 18.8995 | + | 32.7349i | 0.817096 | + | 1.41525i | ||||
\(536\) | −5.62132 | − | 9.73641i | −0.242804 | − | 0.420549i | ||||
\(537\) | 3.91421 | − | 6.77962i | 0.168911 | − | 0.292562i | ||||
\(538\) | 13.6569 | 0.588789 | ||||||||
\(539\) | −1.74264 | − | 6.77962i | −0.0750608 | − | 0.292019i | ||||
\(540\) | 8.24264 | 0.354707 | ||||||||
\(541\) | 20.5711 | − | 35.6301i | 0.884419 | − | 1.53186i | 0.0380415 | − | 0.999276i | \(-0.487888\pi\) |
0.846378 | − | 0.532583i | \(-0.178779\pi\) | |||||||
\(542\) | 13.2782 | + | 22.9985i | 0.570346 | + | 0.987869i | ||||
\(543\) | −0.757359 | − | 1.31178i | −0.0325014 | − | 0.0562941i | ||||
\(544\) | 3.82843 | − | 6.63103i | 0.164142 | − | 0.284303i | ||||
\(545\) | 1.65685 | 0.0709718 | ||||||||
\(546\) | −1.98528 | − | 0.271680i | −0.0849622 | − | 0.0116268i | ||||
\(547\) | −18.8701 | −0.806825 | −0.403413 | − | 0.915018i | \(-0.632176\pi\) | ||||
−0.403413 | + | 0.915018i | \(0.632176\pi\) | |||||||
\(548\) | 2.67157 | − | 4.62730i | 0.114124 | − | 0.197668i | ||||
\(549\) | 8.72792 | + | 15.1172i | 0.372499 | + | 0.645187i | ||||
\(550\) | −3.32843 | − | 5.76500i | −0.141925 | − | 0.245821i | ||||
\(551\) | −14.7782 | + | 25.5965i | −0.629571 | + | 1.09045i | ||||
\(552\) | 0.928932 | 0.0395380 | ||||||||
\(553\) | −7.71320 | + | 9.94655i | −0.327999 | + | 0.422970i | ||||
\(554\) | −3.82843 | −0.162654 | ||||||||
\(555\) | −4.65685 | + | 8.06591i | −0.197672 | + | 0.342379i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2426 | − | 21.2049i | −0.518737 | − | 0.898479i | −0.999763 | − | 0.0217729i | \(-0.993069\pi\) |
0.481026 | − | 0.876707i | \(-0.340264\pi\) | |||||||
\(558\) | −5.65685 | + | 9.79796i | −0.239474 | + | 0.414781i | ||||
\(559\) | 10.3431 | 0.437468 | ||||||||
\(560\) | −3.41421 | − | 8.36308i | −0.144277 | − | 0.353405i | ||||
\(561\) | −3.17157 | −0.133904 | ||||||||
\(562\) | 8.36396 | − | 14.4868i | 0.352812 | − | 0.611089i | ||||
\(563\) | 2.53553 | + | 4.39167i | 0.106860 | + | 0.185087i | 0.914497 | − | 0.404594i | \(-0.132587\pi\) |
−0.807637 | + | 0.589681i | \(0.799254\pi\) | |||||||
\(564\) | −1.34315 | − | 2.32640i | −0.0565566 | − | 0.0979590i | ||||
\(565\) | −23.6066 | + | 40.8878i | −0.993137 | + | 1.72016i | ||||
\(566\) | −20.5858 | −0.865285 | ||||||||
\(567\) | 7.48528 | + | 18.3351i | 0.314352 | + | 0.770003i | ||||
\(568\) | 3.07107 | 0.128859 | ||||||||
\(569\) | 2.00000 | − | 3.46410i | 0.0838444 | − | 0.145223i | −0.821054 | − | 0.570851i | \(-0.806613\pi\) |
0.904898 | + | 0.425628i | \(0.139947\pi\) | |||||||
\(570\) | −2.41421 | − | 4.18154i | −0.101120 | − | 0.175145i | ||||
\(571\) | 5.19239 | + | 8.99348i | 0.217295 | + | 0.376365i | 0.953980 | − | 0.299870i | \(-0.0969434\pi\) |
−0.736685 | + | 0.676236i | \(0.763610\pi\) | |||||||
\(572\) | −0.914214 | + | 1.58346i | −0.0382252 | + | 0.0662080i | ||||
\(573\) | −5.31371 | −0.221983 | ||||||||
\(574\) | −4.19239 | + | 5.40629i | −0.174987 | + | 0.225654i | ||||
\(575\) | 14.9289 | 0.622580 | ||||||||
\(576\) | 1.41421 | − | 2.44949i | 0.0589256 | − | 0.102062i | ||||
\(577\) | 16.1569 | + | 27.9845i | 0.672619 | + | 1.16501i | 0.977159 | + | 0.212510i | \(0.0681639\pi\) |
−0.304540 | + | 0.952499i | \(0.598503\pi\) | |||||||
\(578\) | −20.8137 | − | 36.0504i | −0.865736 | − | 1.49950i | ||||
\(579\) | −0.435029 | + | 0.753492i | −0.0180792 | + | 0.0313141i | ||||
\(580\) | 29.5563 | 1.22726 | ||||||||
\(581\) | −42.3137 | − | 5.79050i | −1.75547 | − | 0.240230i | ||||
\(582\) | 0.757359 | 0.0313936 | ||||||||
\(583\) | 5.94975 | − | 10.3053i | 0.246413 | − | 0.426800i | ||||
\(584\) | 3.29289 | + | 5.70346i | 0.136261 | + | 0.236011i | ||||
\(585\) | −8.82843 | − | 15.2913i | −0.365011 | − | 0.632217i | ||||
\(586\) | 2.58579 | − | 4.47871i | 0.106818 | − | 0.185014i | ||||
\(587\) | −44.8995 | −1.85320 | −0.926600 | − | 0.376048i | \(-0.877283\pi\) | ||||
−0.926600 | + | 0.376048i | \(0.877283\pi\) | |||||||
\(588\) | −2.07107 | + | 2.02922i | −0.0854094 | + | 0.0836838i | ||||
\(589\) | 13.6569 | 0.562721 | ||||||||
\(590\) | −14.3640 | + | 24.8791i | −0.591355 | + | 1.02426i | ||||
\(591\) | 3.62132 | + | 6.27231i | 0.148961 | + | 0.258008i | ||||
\(592\) | 3.29289 | + | 5.70346i | 0.135337 | + | 0.234411i | ||||
\(593\) | 17.8492 | − | 30.9158i | 0.732981 | − | 1.26956i | −0.222623 | − | 0.974905i | \(-0.571462\pi\) |
0.955604 | − | 0.294655i | \(-0.0952047\pi\) | |||||||
\(594\) | −2.41421 | −0.0990564 | ||||||||
\(595\) | −68.5269 | − | 9.37769i | −2.80933 | − | 0.384448i | ||||
\(596\) | 6.34315 | 0.259825 | ||||||||
\(597\) | −4.12132 | + | 7.13834i | −0.168674 | + | 0.292153i | ||||
\(598\) | −2.05025 | − | 3.55114i | −0.0838411 | − | 0.145217i | ||||
\(599\) | 1.31371 | + | 2.27541i | 0.0536767 | + | 0.0929707i | 0.891615 | − | 0.452794i | \(-0.149573\pi\) |
−0.837939 | + | 0.545765i | \(0.816239\pi\) | |||||||
\(600\) | −1.37868 | + | 2.38794i | −0.0562844 | + | 0.0974874i | ||||
\(601\) | −35.9411 | −1.46607 | −0.733035 | − | 0.680191i | \(-0.761897\pi\) | ||||
−0.733035 | + | 0.680191i | \(0.761897\pi\) | |||||||
\(602\) | 9.17157 | − | 11.8272i | 0.373805 | − | 0.482040i | ||||
\(603\) | −31.7990 | −1.29495 | ||||||||
\(604\) | −4.86396 | + | 8.42463i | −0.197912 | + | 0.342793i | ||||
\(605\) | 1.70711 | + | 2.95680i | 0.0694038 | + | 0.120211i | ||||
\(606\) | −2.44975 | − | 4.24309i | −0.0995142 | − | 0.172364i | ||||
\(607\) | 4.51472 | − | 7.81972i | 0.183247 | − | 0.317393i | −0.759738 | − | 0.650230i | \(-0.774673\pi\) |
0.942984 | + | 0.332837i | \(0.108006\pi\) | |||||||
\(608\) | −3.41421 | −0.138465 | ||||||||
\(609\) | −3.58579 | − | 8.78335i | −0.145303 | − | 0.355919i | ||||
\(610\) | −21.0711 | −0.853143 | ||||||||
\(611\) | −5.92893 | + | 10.2692i | −0.239859 | + | 0.415448i | ||||
\(612\) | −10.8284 | − | 18.7554i | −0.437713 | − | 0.758142i | ||||
\(613\) | 8.31371 | + | 14.3998i | 0.335788 | + | 0.581601i | 0.983636 | − | 0.180168i | \(-0.0576643\pi\) |
−0.647848 | + | 0.761769i | \(0.724331\pi\) | |||||||
\(614\) | 4.94975 | − | 8.57321i | 0.199756 | − | 0.345987i | ||||
\(615\) | 3.65685 | 0.147459 | ||||||||
\(616\) | 1.00000 | + | 2.44949i | 0.0402911 | + | 0.0986928i | ||||
\(617\) | −8.02944 | −0.323253 | −0.161626 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161626 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(618\) | −2.19239 | + | 3.79733i | −0.0881908 | + | 0.152751i | ||||
\(619\) | −22.9706 | − | 39.7862i | −0.923265 | − | 1.59914i | −0.794328 | − | 0.607489i | \(-0.792177\pi\) |
−0.128937 | − | 0.991653i | \(-0.541156\pi\) | |||||||
\(620\) | −6.82843 | − | 11.8272i | −0.274236 | − | 0.474991i | ||||
\(621\) | 2.70711 | − | 4.68885i | 0.108632 | − | 0.188157i | ||||
\(622\) | −8.72792 | −0.349958 | ||||||||
\(623\) | −7.27208 | + | 9.37769i | −0.291350 | + | 0.375709i | ||||
\(624\) | 0.757359 | 0.0303186 | ||||||||
\(625\) | 6.98528 | − | 12.0989i | 0.279411 | − | 0.483954i | ||||
\(626\) | 4.67157 | + | 8.09140i | 0.186714 | + | 0.323397i | ||||
\(627\) | 0.707107 | + | 1.22474i | 0.0282391 | + | 0.0489116i | ||||
\(628\) | −3.17157 | + | 5.49333i | −0.126560 | + | 0.219208i | ||||
\(629\) | 50.4264 | 2.01063 | ||||||||
\(630\) | −25.3137 | − | 3.46410i | −1.00852 | − | 0.138013i | ||||
\(631\) | 48.7279 | 1.93983 | 0.969914 | − | 0.243448i | \(-0.0782785\pi\) | ||||
0.969914 | + | 0.243448i | \(0.0782785\pi\) | |||||||
\(632\) | 2.37868 | − | 4.11999i | 0.0946188 | − | 0.163885i | ||||
\(633\) | −0.949747 | − | 1.64501i | −0.0377491 | − | 0.0653833i | ||||
\(634\) | −15.6569 | − | 27.1185i | −0.621813 | − | 1.07701i | ||||
\(635\) | −16.6066 | + | 28.7635i | −0.659013 | + | 1.14144i | ||||
\(636\) | −4.92893 | −0.195445 | ||||||||
\(637\) | 12.3284 | + | 3.43861i | 0.488470 | + | 0.136243i | ||||
\(638\) | −8.65685 | −0.342728 | ||||||||
\(639\) | 4.34315 | − | 7.52255i | 0.171812 | − | 0.297587i | ||||
\(640\) | 1.70711 | + | 2.95680i | 0.0674793 | + | 0.116878i | ||||
\(641\) | 20.6421 | + | 35.7532i | 0.815315 | + | 1.41217i | 0.909101 | + | 0.416575i | \(0.136770\pi\) |
−0.0937859 | + | 0.995592i | \(0.529897\pi\) | |||||||
\(642\) | −2.29289 | + | 3.97141i | −0.0904933 | + | 0.156739i | ||||
\(643\) | 4.41421 | 0.174080 | 0.0870398 | − | 0.996205i | \(-0.472259\pi\) | ||||
0.0870398 | + | 0.996205i | \(0.472259\pi\) | |||||||
\(644\) | −5.87868 | − | 0.804479i | −0.231652 | − | 0.0317009i | ||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | −13.0711 | + | 22.6398i | −0.514274 | + | 0.890749i | ||||
\(647\) | 23.0919 | + | 39.9963i | 0.907836 | + | 1.57242i | 0.817065 | + | 0.576546i | \(0.195600\pi\) |
0.0907706 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(648\) | −3.74264 | − | 6.48244i | −0.147025 | − | 0.254654i | ||||
\(649\) | 4.20711 | − | 7.28692i | 0.165143 | − | 0.286037i | ||||
\(650\) | 12.1716 | 0.477408 | ||||||||
\(651\) | −2.68629 | + | 3.46410i | −0.105284 | + | 0.135769i | ||||
\(652\) | −15.7279 | −0.615953 | ||||||||
\(653\) | −9.19239 | + | 15.9217i | −0.359726 | + | 0.623064i | −0.987915 | − | 0.154997i | \(-0.950463\pi\) |
0.628189 | + | 0.778061i | \(0.283796\pi\) | |||||||
\(654\) | 0.100505 | + | 0.174080i | 0.00393006 | + | 0.00680706i | ||||
\(655\) | −5.82843 | − | 10.0951i | −0.227735 | − | 0.394449i | ||||
\(656\) | 1.29289 | − | 2.23936i | 0.0504790 | − | 0.0874322i | ||||
\(657\) | 18.6274 | 0.726725 | ||||||||
\(658\) | 6.48528 | + | 15.8856i | 0.252823 | + | 0.619286i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0.707107 | − | 1.22474i | 0.0275241 | − | 0.0476731i | ||||
\(661\) | 7.48528 | + | 12.9649i | 0.291144 | + | 0.504276i | 0.974080 | − | 0.226202i | \(-0.0726309\pi\) |
−0.682937 | + | 0.730478i | \(0.739298\pi\) | |||||||
\(662\) | 4.96447 | + | 8.59871i | 0.192949 | + | 0.334198i | ||||
\(663\) | 2.89949 | − | 5.02207i | 0.112607 | − | 0.195041i | ||||
\(664\) | 16.1421 | 0.626436 | ||||||||
\(665\) | 11.6569 | + | 28.5533i | 0.452033 | + | 1.10725i | ||||
\(666\) | 18.6274 | 0.721798 | ||||||||
\(667\) | 9.70711 | − | 16.8132i | 0.375861 | − | 0.651010i | ||||
\(668\) | 5.86396 | + | 10.1567i | 0.226883 | + | 0.392974i | ||||
\(669\) | −2.36396 | − | 4.09450i | −0.0913960 | − | 0.158303i | ||||
\(670\) | 19.1924 | − | 33.2422i | 0.741467 | − | 1.28426i | ||||
\(671\) | 6.17157 | 0.238251 | ||||||||
\(672\) | 0.671573 | − | 0.866025i | 0.0259065 | − | 0.0334077i | ||||
\(673\) | −25.5563 | −0.985125 | −0.492562 | − | 0.870277i | \(-0.663940\pi\) | ||||
−0.492562 | + | 0.870277i | \(0.663940\pi\) | |||||||
\(674\) | 9.87868 | − | 17.1104i | 0.380513 | − | 0.659067i | ||||
\(675\) | 8.03553 | + | 13.9180i | 0.309288 | + | 0.535702i | ||||
\(676\) | 4.82843 | + | 8.36308i | 0.185709 | + | 0.321657i | ||||
\(677\) | 6.34315 | − | 10.9867i | 0.243787 | − | 0.422251i | −0.718003 | − | 0.696040i | \(-0.754944\pi\) |
0.961790 | + | 0.273789i | \(0.0882769\pi\) | |||||||
\(678\) | −5.72792 | −0.219980 | ||||||||
\(679\) | −4.79289 | − | 0.655892i | −0.183934 | − | 0.0251708i | ||||
\(680\) | 26.1421 | 1.00251 | ||||||||
\(681\) | 4.79899 | − | 8.31209i | 0.183898 | − | 0.318520i | ||||
\(682\) | 2.00000 | + | 3.46410i | 0.0765840 | + | 0.132647i | ||||
\(683\) | −8.20711 | − | 14.2151i | −0.314036 | − | 0.543927i | 0.665196 | − | 0.746669i | \(-0.268348\pi\) |
−0.979232 | + | 0.202742i | \(0.935015\pi\) | |||||||
\(684\) | −4.82843 | + | 8.36308i | −0.184620 | + | 0.319770i | ||||
\(685\) | 18.2426 | 0.697015 | ||||||||
\(686\) | 14.8640 | − | 11.0482i | 0.567509 | − | 0.421822i | ||||
\(687\) | 0.284271 | 0.0108456 | ||||||||
\(688\) | −2.82843 | + | 4.89898i | −0.107833 | + | 0.186772i | ||||
\(689\) | 10.8787 | + | 18.8424i | 0.414445 | + | 0.717839i | ||||
\(690\) | 1.58579 | + | 2.74666i | 0.0603699 | + | 0.104564i | ||||
\(691\) | −6.96447 | + | 12.0628i | −0.264941 | + | 0.458891i | −0.967548 | − | 0.252687i | \(-0.918686\pi\) |
0.702607 | + | 0.711578i | \(0.252019\pi\) | |||||||
\(692\) | −4.17157 | −0.158579 | ||||||||
\(693\) | 7.41421 | + | 1.01461i | 0.281643 | + | 0.0385419i | ||||
\(694\) | 14.5858 | 0.553669 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.79289 | + | 3.10538i | 0.0679594 | + | 0.117709i | ||||
\(697\) | −9.89949 | − | 17.1464i | −0.374970 | − | 0.649467i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.585786 | −0.0221565 | ||||||||
\(700\) | 10.7929 | − | 13.9180i | 0.407933 | − | 0.526049i | ||||
\(701\) | 36.1127 | 1.36396 | 0.681979 | − | 0.731372i | \(-0.261120\pi\) | ||||
0.681979 | + | 0.731372i | \(0.261120\pi\) | |||||||
\(702\) | 2.20711 | − | 3.82282i | 0.0833019 | − | 0.144283i | ||||
\(703\) | −11.2426 | − | 19.4728i | −0.424024 | − | 0.734432i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 4.58579 | − | 7.94282i | 0.172711 | − | 0.299144i | ||||
\(706\) | −25.3137 | −0.952694 | ||||||||
\(707\) | 11.8284 | + | 28.9736i | 0.444854 | + | 1.08966i | ||||
\(708\) | −3.48528 | −0.130985 | ||||||||
\(709\) | −18.0208 | + | 31.2130i | −0.676786 | + | 1.17223i | 0.299158 | + | 0.954204i | \(0.403294\pi\) |
−0.975943 | + | 0.218024i | \(0.930039\pi\) | |||||||
\(710\) | 5.24264 | + | 9.08052i | 0.196753 | + | 0.340786i | ||||
\(711\) | −6.72792 | − | 11.6531i | −0.252317 | − | 0.437026i | ||||
\(712\) | 2.24264 | − | 3.88437i | 0.0840465 | − | 0.145573i | ||||
\(713\) | −8.97056 | −0.335950 | ||||||||
\(714\) | −3.17157 | − | 7.76874i | −0.118693 | − | 0.290738i | ||||
\(715\) | −6.24264 | −0.233462 | ||||||||
\(716\) | 9.44975 | − | 16.3674i | 0.353154 | − | 0.611680i | ||||
\(717\) | 4.60051 | + | 7.96831i | 0.171809 | + | 0.297582i | ||||
\(718\) | −5.37868 | − | 9.31615i | −0.200731 | − | 0.347675i | ||||
\(719\) | 9.24264 | − | 16.0087i | 0.344692 | − | 0.597025i | −0.640605 | − | 0.767870i | \(-0.721317\pi\) |
0.985298 | + | 0.170846i | \(0.0546499\pi\) | |||||||
\(720\) | 9.65685 | 0.359890 | ||||||||
\(721\) | 17.1630 | − | 22.1324i | 0.639182 | − | 0.824255i | ||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | −0.778175 | + | 1.34784i | −0.0289406 | + | 0.0501266i | ||||
\(724\) | −1.82843 | − | 3.16693i | −0.0679530 | − | 0.117698i | ||||
\(725\) | 28.8137 | + | 49.9068i | 1.07011 | + | 1.85349i | ||||
\(726\) | −0.207107 | + | 0.358719i | −0.00768645 | + | 0.0133133i | ||||
\(727\) | −48.4264 | −1.79604 | −0.898018 | − | 0.439959i | \(-0.854993\pi\) | ||||
−0.898018 | + | 0.439959i | \(0.854993\pi\) | |||||||
\(728\) | −4.79289 | − | 0.655892i | −0.177636 | − | 0.0243090i | ||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | −11.2426 | + | 19.4728i | −0.416109 | + | 0.720722i | ||||
\(731\) | 21.6569 | + | 37.5108i | 0.801008 | + | 1.38739i | ||||
\(732\) | −1.27817 | − | 2.21386i | −0.0472427 | − | 0.0818267i | ||||
\(733\) | 6.50000 | − | 11.2583i | 0.240083 | − | 0.415836i | −0.720655 | − | 0.693294i | \(-0.756159\pi\) |
0.960738 | + | 0.277458i | \(0.0894920\pi\) | |||||||
\(734\) | 14.7279 | 0.543618 | ||||||||
\(735\) | −9.53553 | − | 2.65962i | −0.351723 | − | 0.0981017i | ||||
\(736\) | 2.24264 | 0.0826648 | ||||||||
\(737\) | −5.62132 | + | 9.73641i | −0.207064 | + | 0.358645i | ||||
\(738\) | −3.65685 | − | 6.33386i | −0.134611 | − | 0.233153i | ||||
\(739\) | −16.2132 | − | 28.0821i | −0.596412 | − | 1.03302i | −0.993346 | − | 0.115169i | \(-0.963259\pi\) |
0.396934 | − | 0.917847i | \(-0.370074\pi\) | |||||||
\(740\) | −11.2426 | + | 19.4728i | −0.413288 | + | 0.715835i | ||||
\(741\) | −2.58579 | −0.0949912 | ||||||||
\(742\) | 31.1924 | + | 4.26858i | 1.14511 | + | 0.156705i | ||||
\(743\) | 9.31371 | 0.341687 | 0.170843 | − | 0.985298i | \(-0.445351\pi\) | ||||
0.170843 | + | 0.985298i | \(0.445351\pi\) | |||||||
\(744\) | 0.828427 | − | 1.43488i | 0.0303716 | − | 0.0526052i | ||||
\(745\) | 10.8284 | + | 18.7554i | 0.396723 | + | 0.687144i | ||||
\(746\) | −6.98528 | − | 12.0989i | −0.255749 | − | 0.442971i | ||||
\(747\) | 22.8284 | − | 39.5400i | 0.835248 | − | 1.44669i | ||||
\(748\) | −7.65685 | −0.279962 | ||||||||
\(749\) | 17.9497 | − | 23.1471i | 0.655869 | − | 0.845775i | ||||
\(750\) | −2.34315 | −0.0855596 | ||||||||
\(751\) | −17.1716 | + | 29.7420i | −0.626600 | + | 1.08530i | 0.361630 | + | 0.932322i | \(0.382220\pi\) |
−0.988229 | + | 0.152980i | \(0.951113\pi\) | |||||||
\(752\) | −3.24264 | − | 5.61642i | −0.118247 | − | 0.204810i | ||||
\(753\) | −0.443651 | − | 0.768426i | −0.0161675 | − | 0.0280030i | ||||
\(754\) | 7.91421 | − | 13.7078i | 0.288219 | − | 0.499209i | ||||
\(755\) | −33.2132 | −1.20875 | ||||||||
\(756\) | −2.41421 | − | 5.91359i | −0.0878041 | − | 0.215075i | ||||
\(757\) | 19.6569 | 0.714441 | 0.357220 | − | 0.934020i | \(-0.383725\pi\) | ||||
0.357220 | + | 0.934020i | \(0.383725\pi\) | |||||||
\(758\) | 12.9350 | − | 22.4041i | 0.469821 | − | 0.813755i | ||||
\(759\) | −0.464466 | − | 0.804479i | −0.0168591 | − | 0.0292007i | ||||
\(760\) | −5.82843 | − | 10.0951i | −0.211419 | − | 0.366189i | ||||
\(761\) | 1.48528 | − | 2.57258i | 0.0538414 | − | 0.0932561i | −0.837849 | − | 0.545903i | \(-0.816187\pi\) |
0.891690 | + | 0.452647i | \(0.149520\pi\) | |||||||
\(762\) | −4.02944 | −0.145971 | ||||||||
\(763\) | −0.485281 | − | 1.18869i | −0.0175684 | − | 0.0430335i | ||||
\(764\) | −12.8284 | −0.464116 | ||||||||
\(765\) | 36.9706 | − | 64.0349i | 1.33667 | − | 2.31519i | ||||
\(766\) | −15.1924 | − | 26.3140i | −0.548923 | − | 0.950763i | ||||
\(767\) | 7.69239 | + | 13.3236i | 0.277756 | + | 0.481088i | ||||
\(768\) | −0.207107 | + | 0.358719i | −0.00747332 | + | 0.0129442i | ||||
\(769\) | −10.9706 | −0.395609 | −0.197804 | − | 0.980242i | \(-0.563381\pi\) | ||||
−0.197804 | + | 0.980242i | \(0.563381\pi\) | |||||||
\(770\) | −5.53553 | + | 7.13834i | −0.199487 | + | 0.257248i | ||||
\(771\) | 1.30152 | 0.0468729 | ||||||||
\(772\) | −1.05025 | + | 1.81909i | −0.0377994 | + | 0.0654705i | ||||
\(773\) | −22.9706 | − | 39.7862i | −0.826194 | − | 1.43101i | −0.901004 | − | 0.433812i | \(-0.857168\pi\) |
0.0748099 | − | 0.997198i | \(-0.476165\pi\) | |||||||
\(774\) | 8.00000 | + | 13.8564i | 0.287554 | + | 0.498058i | ||||
\(775\) | 13.3137 | − | 23.0600i | 0.478243 | − | 0.828340i | ||||
\(776\) | 1.82843 | 0.0656367 | ||||||||
\(777\) | 7.15076 | + | 0.978559i | 0.256532 | + | 0.0351056i | ||||
\(778\) | 2.72792 | 0.0978007 | ||||||||
\(779\) | −4.41421 | + | 7.64564i | −0.158156 | + | 0.273934i | ||||
\(780\) | 1.29289 | + | 2.23936i | 0.0462930 | + | 0.0801818i | ||||
\(781\) | −1.53553 | − | 2.65962i | −0.0549457 | − | 0.0951688i | ||||
\(782\) | 8.58579 | − | 14.8710i | 0.307027 | − | 0.531787i | ||||
\(783\) | 20.8995 | 0.746887 | ||||||||
\(784\) | −5.00000 | + | 4.89898i | −0.178571 | + | 0.174964i | ||||
\(785\) | −21.6569 | −0.772966 | ||||||||
\(786\) | 0.707107 | − | 1.22474i | 0.0252217 | − | 0.0436852i | ||||
\(787\) | 8.77817 | + | 15.2042i | 0.312908 | + | 0.541973i | 0.978991 | − | 0.203905i | \(-0.0653635\pi\) |
−0.666082 | + | 0.745878i | \(0.732030\pi\) | |||||||
\(788\) | 8.74264 | + | 15.1427i | 0.311444 | + | 0.539436i | ||||
\(789\) | −6.42893 | + | 11.1352i | −0.228876 | + | 0.396425i | ||||
\(790\) | 16.2426 | 0.577887 | ||||||||
\(791\) | 36.2487 | + | 4.96053i | 1.28886 | + | 0.176376i | ||||
\(792\) | −2.82843 | −0.100504 | ||||||||
\(793\) | −5.64214 | + | 9.77247i | −0.200358 | + | 0.347030i | ||||
\(794\) | −11.0000 | − | 19.0526i | −0.390375 | − | 0.676150i | ||||
\(795\) | −8.41421 | − | 14.5738i | −0.298421 | − | 0.516881i | ||||
\(796\) | −9.94975 | + | 17.2335i | −0.352659 | + | 0.610824i | ||||
\(797\) | 3.65685 | 0.129532 | 0.0647662 | − | 0.997900i | \(-0.479370\pi\) | ||||
0.0647662 | + | 0.997900i | \(0.479370\pi\) | |||||||
\(798\) | −2.29289 | + | 2.95680i | −0.0811675 | + | 0.104669i | ||||
\(799\) | −49.6569 | −1.75673 | ||||||||
\(800\) | −3.32843 | + | 5.76500i | −0.117678 | + | 0.203824i | ||||
\(801\) | −6.34315 | − | 10.9867i | −0.224124 | − | 0.388194i | ||||
\(802\) | 2.15685 | + | 3.73578i | 0.0761612 | + | 0.131915i | ||||
\(803\) | 3.29289 | − | 5.70346i | 0.116204 | − | 0.201271i | ||||
\(804\) | 4.65685 | 0.164235 | ||||||||
\(805\) | −7.65685 | − | 18.7554i | −0.269869 | − | 0.661040i | ||||
\(806\) | −7.31371 | −0.257614 | ||||||||
\(807\) | −2.82843 | + | 4.89898i | −0.0995654 | + | 0.172452i | ||||
\(808\) | −5.91421 | − | 10.2437i | −0.208061 | − | 0.360373i | ||||
\(809\) | 0.686292 | + | 1.18869i | 0.0241287 | + | 0.0417922i | 0.877838 | − | 0.478958i | \(-0.158986\pi\) |
−0.853709 | + | 0.520751i | \(0.825652\pi\) | |||||||
\(810\) | 12.7782 | − | 22.1324i | 0.448979 | − | 0.777655i | ||||
\(811\) | 32.2843 | 1.13365 | 0.566827 | − | 0.823837i | \(-0.308171\pi\) | ||||
0.566827 | + | 0.823837i | \(0.308171\pi\) | |||||||
\(812\) | −8.65685 | − | 21.2049i | −0.303796 | − | 0.744145i | ||||
\(813\) | −11.0000 | −0.385787 | ||||||||
\(814\) | 3.29289 | − | 5.70346i | 0.115416 | − | 0.199906i | ||||
\(815\) | −26.8492 | − | 46.5043i | −0.940488 | − | 1.62897i | ||||
\(816\) | 1.58579 | + | 2.74666i | 0.0555136 | + | 0.0961524i | ||||
\(817\) | 9.65685 | − | 16.7262i | 0.337851 | − | 0.585174i | ||||
\(818\) | −22.7279 | −0.794663 | ||||||||
\(819\) | −8.38478 | + | 10.8126i | −0.292988 | + | 0.377822i | ||||
\(820\) | 8.82843 | 0.308302 | ||||||||
\(821\) | 6.25736 | − | 10.8381i | 0.218383 | − | 0.378251i | −0.735931 | − | 0.677057i | \(-0.763255\pi\) |
0.954314 | + | 0.298806i | \(0.0965884\pi\) | |||||||
\(822\) | 1.10660 | + | 1.91669i | 0.0385972 | + | 0.0668523i | ||||
\(823\) | −3.72792 | − | 6.45695i | −0.129947 | − | 0.225075i | 0.793709 | − | 0.608298i | \(-0.208147\pi\) |
−0.923656 | + | 0.383223i | \(0.874814\pi\) | |||||||
\(824\) | −5.29289 | + | 9.16756i | −0.184387 | + | 0.319367i | ||||
\(825\) | 2.75736 | 0.0959989 | ||||||||
\(826\) | 22.0563 | + | 3.01834i | 0.767439 | + | 0.105022i | ||||
\(827\) | 49.3553 | 1.71625 | 0.858127 | − | 0.513438i | \(-0.171628\pi\) | ||||
0.858127 | + | 0.513438i | \(0.171628\pi\) | |||||||
\(828\) | 3.17157 | − | 5.49333i | 0.110220 | − | 0.190906i | ||||
\(829\) | −15.1213 | − | 26.1909i | −0.525185 | − | 0.909647i | −0.999570 | − | 0.0293297i | \(-0.990663\pi\) |
0.474385 | − | 0.880318i | \(-0.342671\pi\) | |||||||
\(830\) | 27.5563 | + | 47.7290i | 0.956495 | + | 1.65670i | ||||
\(831\) | 0.792893 | − | 1.37333i | 0.0275052 | − | 0.0476403i | ||||
\(832\) | 1.82843 | 0.0633893 | ||||||||
\(833\) | 13.3431 | + | 51.9105i | 0.462313 | + | 1.79859i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.0208 | + | 34.6771i | −0.692849 | + | 1.20005i | ||||
\(836\) | 1.70711 | + | 2.95680i | 0.0590415 | + | 0.102263i | ||||
\(837\) | −4.82843 | − | 8.36308i | −0.166895 | − | 0.289070i | ||||
\(838\) | −1.07107 | + | 1.85514i | −0.0369994 | + | 0.0640849i | ||||
\(839\) | −1.51472 | −0.0522939 | −0.0261469 | − | 0.999658i | \(-0.508324\pi\) | ||||
−0.0261469 | + | 0.999658i | \(0.508324\pi\) | |||||||
\(840\) | 3.70711 | + | 0.507306i | 0.127907 | + | 0.0175037i | ||||
\(841\) | 45.9411 | 1.58418 | ||||||||
\(842\) | −11.6569 | + | 20.1903i | −0.401722 | + | 0.695802i | ||||
\(843\) | 3.46447 | + | 6.00063i | 0.119323 | + | 0.206673i | ||||
\(844\) | −2.29289 | − | 3.97141i | −0.0789246 | − | 0.136701i | ||||
\(845\) | −16.4853 | + | 28.5533i | −0.567111 | + | 0.982265i | ||||
\(846\) | −18.3431 | −0.630650 | ||||||||
\(847\) | 1.62132 | − | 2.09077i | 0.0557092 | − | 0.0718397i | ||||
\(848\) | −11.8995 | −0.408630 | ||||||||
\(849\) | 4.26346 | − | 7.38452i | 0.146321 | − | 0.253436i | ||||
\(850\) | 25.4853 | + | 44.1418i | 0.874138 | + | 1.51405i | ||||
\(851\) | 7.38478 | + | 12.7908i | 0.253147 | + | 0.438463i | ||||
\(852\) | −0.636039 | + | 1.10165i | −0.0217903 | + | 0.0377420i | ||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 6.17157 | + | 15.1172i | 0.211187 | + | 0.517300i | ||||
\(855\) | −32.9706 | −1.12757 | ||||||||
\(856\) | −5.53553 | + | 9.58783i | −0.189201 | + | 0.327705i | ||||
\(857\) | −5.31371 | − | 9.20361i | −0.181513 | − | 0.314389i | 0.760883 | − | 0.648889i | \(-0.224766\pi\) |
−0.942396 | + | 0.334500i | \(0.891433\pi\) | |||||||
\(858\) | −0.378680 | − | 0.655892i | −0.0129279 | − | 0.0223918i | ||||
\(859\) | −9.86396 | + | 17.0849i | −0.336554 | + | 0.582929i | −0.983782 | − | 0.179368i | \(-0.942595\pi\) |
0.647228 | + | 0.762296i | \(0.275928\pi\) | |||||||
\(860\) | −19.3137 | −0.658592 | ||||||||
\(861\) | −1.07107 | − | 2.62357i | −0.0365019 | − | 0.0894110i | ||||
\(862\) | −20.4142 | −0.695311 | ||||||||
\(863\) | 3.60660 | − | 6.24682i | 0.122770 | − | 0.212644i | −0.798089 | − | 0.602540i | \(-0.794156\pi\) |
0.920859 | + | 0.389895i | \(0.127489\pi\) | |||||||
\(864\) | 1.20711 | + | 2.09077i | 0.0410666 | + | 0.0711294i | ||||
\(865\) | −7.12132 | − | 12.3345i | −0.242132 | − | 0.419385i | ||||
\(866\) | 1.07107 | − | 1.85514i | 0.0363964 | − | 0.0630404i | ||||
\(867\) | 17.2426 | 0.585591 | ||||||||
\(868\) | −6.48528 | + | 8.36308i | −0.220125 | + | 0.283861i | ||||
\(869\) | −4.75736 | −0.161382 | ||||||||
\(870\) | −6.12132 | + | 10.6024i | −0.207532 | + | 0.359456i | ||||
\(871\) | −10.2782 | − | 17.8023i | −0.348263 | − | 0.603209i | ||||
\(872\) | 0.242641 | + | 0.420266i | 0.00821685 | + | 0.0142320i | ||||
\(873\) | 2.58579 | − | 4.47871i | 0.0875156 | − | 0.151581i | ||||
\(874\) | −7.65685 | −0.258997 | ||||||||
\(875\) | 14.8284 | + | 2.02922i | 0.501292 | + | 0.0686003i | ||||
\(876\) | −2.72792 | −0.0921679 | ||||||||
\(877\) | 12.8137 | − | 22.1940i | 0.432688 | − | 0.749438i | −0.564416 | − | 0.825491i | \(-0.690898\pi\) |
0.997104 | + | 0.0760529i | \(0.0242318\pi\) | |||||||
\(878\) | −4.69239 | − | 8.12745i | −0.158360 | − | 0.274288i | ||||
\(879\) | 1.07107 | + | 1.85514i | 0.0361262 | + | 0.0625724i | ||||
\(880\) | 1.70711 | − | 2.95680i | 0.0575466 | − | 0.0996736i | ||||
\(881\) | −44.4558 | −1.49776 | −0.748878 | − | 0.662708i | \(-0.769407\pi\) | ||||
−0.748878 | + | 0.662708i | \(0.769407\pi\) | |||||||
\(882\) | 4.92893 | + | 19.1757i | 0.165966 | + | 0.645678i | ||||
\(883\) | −9.72792 | −0.327371 | −0.163685 | − | 0.986513i | \(-0.552338\pi\) | ||||
−0.163685 | + | 0.986513i | \(0.552338\pi\) | |||||||
\(884\) | 7.00000 | − | 12.1244i | 0.235435 | − | 0.407786i | ||||
\(885\) | −5.94975 | − | 10.3053i | −0.199999 | − | 0.346408i | ||||
\(886\) | 16.3137 | + | 28.2562i | 0.548070 | + | 0.949285i | ||||
\(887\) | 11.4497 | − | 19.8315i | 0.384445 | − | 0.665878i | −0.607247 | − | 0.794513i | \(-0.707726\pi\) |
0.991692 | + | 0.128635i | \(0.0410595\pi\) | |||||||
\(888\) | −2.72792 | −0.0915431 | ||||||||
\(889\) | 25.5000 | + | 3.48960i | 0.855243 | + | 0.117037i | ||||
\(890\) | 15.3137 | 0.513317 | ||||||||
\(891\) | −3.74264 | + | 6.48244i | −0.125383 | + | 0.217170i | ||||
\(892\) | −5.70711 | − | 9.88500i | −0.191088 | − | 0.330974i | ||||
\(893\) | 11.0711 | + | 19.1757i | 0.370479 | + | 0.641689i | ||||
\(894\) | −1.31371 | + | 2.27541i | −0.0439370 | + | 0.0761011i | ||||
\(895\) | 64.5269 | 2.15690 | ||||||||
\(896\) | 1.62132 | − | 2.09077i | 0.0541645 | − | 0.0698477i | ||||
\(897\) | 1.69848 | 0.0567108 | ||||||||
\(898\) | −16.8284 | + | 29.1477i | −0.561572 | + | 0.972671i | ||||
\(899\) | −17.3137 | − | 29.9882i | −0.577445 | − | 1.00016i | ||||
\(900\) | 9.41421 | + | 16.3059i | 0.313807 | + | 0.543530i | ||||
\(901\) | −45.5563 | + | 78.9059i | −1.51770 | + | 2.62874i | ||||
\(902\) | −2.58579 | −0.0860973 | ||||||||
\(903\) | 2.34315 | + | 5.73951i | 0.0779750 | + | 0.190999i | ||||
\(904\) | −13.8284 | −0.459927 | ||||||||
\(905\) | 6.24264 | − | 10.8126i | 0.207512 | − | 0.359422i | ||||
\(906\) | −2.01472 | − | 3.48960i | −0.0669345 | − | 0.115934i | ||||
\(907\) | −16.6569 | − | 28.8505i | −0.553082 | − | 0.957966i | −0.998050 | − | 0.0624194i | \(-0.980118\pi\) |
0.444968 | − | 0.895546i | \(-0.353215\pi\) | |||||||
\(908\) | 11.5858 | − | 20.0672i | 0.384488 | − | 0.665952i | ||||
\(909\) | −33.4558 | −1.10966 | ||||||||
\(910\) | −6.24264 | − | 15.2913i | −0.206942 | − | 0.506901i | ||||
\(911\) | −13.5147 | −0.447763 | −0.223881 | − | 0.974616i | \(-0.571873\pi\) | ||||
−0.223881 | + | 0.974616i | \(0.571873\pi\) | |||||||
\(912\) | 0.707107 | − | 1.22474i | 0.0234146 | − | 0.0405554i | ||||
\(913\) | −8.07107 | − | 13.9795i | −0.267113 | − | 0.462654i | ||||
\(914\) | 0.171573 | + | 0.297173i | 0.00567513 | + | 0.00982961i | ||||
\(915\) | 4.36396 | − | 7.55860i | 0.144268 | − | 0.249880i | ||||
\(916\) | 0.686292 | 0.0226757 | ||||||||
\(917\) | −5.53553 | + | 7.13834i | −0.182799 | + | 0.235729i | ||||
\(918\) | 18.4853 | 0.610105 | ||||||||
\(919\) | 3.07107 | − | 5.31925i | 0.101305 | − | 0.175466i | −0.810917 | − | 0.585161i | \(-0.801031\pi\) |
0.912223 | + | 0.409695i | \(0.134365\pi\) | |||||||
\(920\) | 3.82843 | + | 6.63103i | 0.126220 | + | 0.218619i | ||||
\(921\) | 2.05025 | + | 3.55114i | 0.0675581 | + | 0.117014i | ||||
\(922\) | −7.15685 | + | 12.3960i | −0.235698 | + | 0.408242i | ||||
\(923\) | 5.61522 | 0.184827 | ||||||||
\(924\) | −1.08579 | − | 0.148586i | −0.0357198 | − | 0.00488814i | ||||
\(925\) | −43.8406 | −1.44147 | ||||||||
\(926\) | −3.58579 | + | 6.21076i | −0.117836 | + | 0.204098i | ||||
\(927\) | 14.9706 | + | 25.9298i | 0.491698 | + | 0.851646i | ||||
\(928\) | 4.32843 | + | 7.49706i | 0.142088 | + | 0.246103i | ||||
\(929\) | −5.22792 | + | 9.05503i | −0.171523 | + | 0.297086i | −0.938952 | − | 0.344047i | \(-0.888202\pi\) |
0.767430 | + | 0.641133i | \(0.221535\pi\) | |||||||
\(930\) | 5.65685 | 0.185496 | ||||||||
\(931\) | 17.0711 | − | 16.7262i | 0.559482 | − | 0.548178i | ||||
\(932\) | −1.41421 | −0.0463241 | ||||||||
\(933\) | 1.80761 | − | 3.13088i | 0.0591786 | − | 0.102500i | ||||
\(934\) | 17.0000 | + | 29.4449i | 0.556257 | + | 0.963465i | ||||
\(935\) | −13.0711 | − | 22.6398i | −0.427470 | − | 0.740399i | ||||
\(936\) | 2.58579 | − | 4.47871i | 0.0845191 | − | 0.146391i | ||||
\(937\) | −16.5858 | −0.541834 | −0.270917 | − | 0.962603i | \(-0.587327\pi\) | ||||
−0.270917 | + | 0.962603i | \(0.587327\pi\) | |||||||
\(938\) | −29.4706 | − | 4.03295i | −0.962248 | − | 0.131681i | ||||
\(939\) | −3.87006 | −0.126295 | ||||||||
\(940\) | 11.0711 | − | 19.1757i | 0.361098 | − | 0.625441i | ||||
\(941\) | −6.67157 | − | 11.5555i | −0.217487 | − | 0.376699i | 0.736552 | − | 0.676381i | \(-0.236453\pi\) |
−0.954039 | + | 0.299682i | \(0.903119\pi\) | |||||||
\(942\) | −1.31371 | − | 2.27541i | −0.0428029 | − | 0.0741369i | ||||
\(943\) | 2.89949 | − | 5.02207i | 0.0944205 | − | 0.163541i | ||||
\(944\) | −8.41421 | −0.273859 | ||||||||
\(945\) | 13.3640 | − | 17.2335i | 0.434730 | − | 0.560605i | ||||
\(946\) | 5.65685 | 0.183920 | ||||||||
\(947\) | −14.5858 | + | 25.2633i | −0.473974 | + | 0.820948i | −0.999556 | − | 0.0297955i | \(-0.990514\pi\) |
0.525582 | + | 0.850743i | \(0.323848\pi\) | |||||||
\(948\) | 0.985281 | + | 1.70656i | 0.0320005 | + | 0.0554264i | ||||
\(949\) | 6.02082 | + | 10.4284i | 0.195444 | + | 0.338519i | ||||
\(950\) | 11.3640 | − | 19.6830i | 0.368696 | − | 0.638599i | ||||
\(951\) | 12.9706 | 0.420599 | ||||||||
\(952\) | −7.65685 | − | 18.7554i | −0.248160 | − | 0.607866i | ||||
\(953\) | −25.5563 | −0.827851 | −0.413926 | − | 0.910311i | \(-0.635843\pi\) | ||||
−0.413926 | + | 0.910311i | \(0.635843\pi\) | |||||||
\(954\) | −16.8284 | + | 29.1477i | −0.544840 | + | 0.943691i | ||||
\(955\) | −21.8995 | − | 37.9310i | −0.708651 | − | 1.22742i | ||||
\(956\) | 11.1066 | + | 19.2372i | 0.359213 | + | 0.622175i | ||||
\(957\) | 1.79289 | − | 3.10538i | 0.0579560 | − | 0.100383i | ||||
\(958\) | −26.0711 | −0.842318 | ||||||||
\(959\) | −5.34315 | − | 13.0880i | −0.172539 | − | 0.422633i | ||||
\(960\) | −1.41421 | −0.0456435 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 6.02082 | + | 10.4284i | 0.194119 | + | 0.336224i | ||||
\(963\) | 15.6569 | + | 27.1185i | 0.504535 | + | 0.873880i | ||||
\(964\) | −1.87868 | + | 3.25397i | −0.0605082 | + | 0.104803i | ||||
\(965\) | −7.17157 | −0.230861 | ||||||||
\(966\) | 1.50610 | − | 1.94218i | 0.0484579 | − | 0.0624887i | ||||
\(967\) | 20.2843 | 0.652298 | 0.326149 | − | 0.945318i | \(-0.394249\pi\) | ||||
0.326149 | + | 0.945318i | \(0.394249\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | −5.41421 | − | 9.37769i | −0.173930 | − | 0.301255i | ||||
\(970\) | 3.12132 | + | 5.40629i | 0.100220 | + | 0.173585i | ||||
\(971\) | −23.8640 | + | 41.3336i | −0.765831 | + | 1.32646i | 0.173975 | + | 0.984750i | \(0.444339\pi\) |
−0.939806 | + | 0.341708i | \(0.888995\pi\) | |||||||
\(972\) | 10.3431 | 0.331757 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.65685 | 0.0530890 | ||||||||
\(975\) | −2.52082 | + | 4.36618i | −0.0807307 | + | 0.139830i | ||||
\(976\) | −3.08579 | − | 5.34474i | −0.0987736 | − | 0.171081i | ||||
\(977\) | −20.0000 | − | 34.6410i | −0.639857 | − | 1.10826i | −0.985464 | − | 0.169885i | \(-0.945660\pi\) |
0.345607 | − | 0.938379i | \(-0.387673\pi\) | |||||||
\(978\) | 3.25736 | − | 5.64191i | 0.104159 | − | 0.180408i | ||||
\(979\) | −4.48528 | −0.143350 | ||||||||
\(980\) | −23.0208 | − | 6.42090i | −0.735373 | − | 0.205108i | ||||
\(981\) | 1.37258 | 0.0438232 | ||||||||
\(982\) | −12.4142 | + | 21.5020i | −0.396153 | + | 0.686158i | ||||
\(983\) | 26.2132 | + | 45.4026i | 0.836071 | + | 1.44812i | 0.893155 | + | 0.449749i | \(0.148486\pi\) |
−0.0570838 | + | 0.998369i | \(0.518180\pi\) | |||||||
\(984\) | 0.535534 | + | 0.927572i | 0.0170722 | + | 0.0295699i | ||||
\(985\) | −29.8492 | + | 51.7004i | −0.951076 | + | 1.64731i | ||||
\(986\) | 66.2843 | 2.11092 | ||||||||
\(987\) | −7.04163 | − | 0.963625i | −0.224138 | − | 0.0306725i | ||||
\(988\) | −6.24264 | −0.198605 | ||||||||
\(989\) | −6.34315 | + | 10.9867i | −0.201700 | + | 0.349355i | ||||
\(990\) | −4.82843 | − | 8.36308i | −0.153457 | − | 0.265796i | ||||
\(991\) | 19.1924 | + | 33.2422i | 0.609666 | + | 1.05597i | 0.991295 | + | 0.131657i | \(0.0420299\pi\) |
−0.381629 | + | 0.924316i | \(0.624637\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | −4.11270 | −0.130513 | ||||||||
\(994\) | 4.97918 | − | 6.42090i | 0.157930 | − | 0.203658i | ||||
\(995\) | −67.9411 | −2.15388 | ||||||||
\(996\) | −3.34315 | + | 5.79050i | −0.105932 | + | 0.183479i | ||||
\(997\) | −9.41421 | − | 16.3059i | −0.298151 | − | 0.516413i | 0.677562 | − | 0.735466i | \(-0.263037\pi\) |
−0.975713 | + | 0.219053i | \(0.929703\pi\) | |||||||
\(998\) | 3.07107 | + | 5.31925i | 0.0972130 | + | 0.168378i | ||||
\(999\) | −7.94975 | + | 13.7694i | −0.251519 | + | 0.435643i |
(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 | 154.2.e.e.23.1 | ✓ | 4 | |
3.2 | odd | 2 | 1386.2.k.t.793.1 | 4 | |||
4.3 | odd | 2 | 1232.2.q.f.177.2 | 4 | |||
7.2 | even | 3 | 1078.2.a.t.1.2 | 2 | |||
7.3 | odd | 6 | 1078.2.e.m.67.2 | 4 | |||
7.4 | even | 3 | inner | 154.2.e.e.67.1 | yes | 4 | |
7.5 | odd | 6 | 1078.2.a.x.1.1 | 2 | |||
7.6 | odd | 2 | 1078.2.e.m.177.2 | 4 | |||
21.2 | odd | 6 | 9702.2.a.cx.1.2 | 2 | |||
21.5 | even | 6 | 9702.2.a.ch.1.1 | 2 | |||
21.11 | odd | 6 | 1386.2.k.t.991.1 | 4 | |||
28.11 | odd | 6 | 1232.2.q.f.529.2 | 4 | |||
28.19 | even | 6 | 8624.2.a.bh.1.2 | 2 | |||
28.23 | odd | 6 | 8624.2.a.cc.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.e.23.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
154.2.e.e.67.1 | yes | 4 | 7.4 | even | 3 | inner | |
1078.2.a.t.1.2 | 2 | 7.2 | even | 3 | |||
1078.2.a.x.1.1 | 2 | 7.5 | odd | 6 | |||
1078.2.e.m.67.2 | 4 | 7.3 | odd | 6 | |||
1078.2.e.m.177.2 | 4 | 7.6 | odd | 2 | |||
1232.2.q.f.177.2 | 4 | 4.3 | odd | 2 | |||
1232.2.q.f.529.2 | 4 | 28.11 | odd | 6 | |||
1386.2.k.t.793.1 | 4 | 3.2 | odd | 2 | |||
1386.2.k.t.991.1 | 4 | 21.11 | odd | 6 | |||
8624.2.a.bh.1.2 | 2 | 28.19 | even | 6 | |||
8624.2.a.cc.1.1 | 2 | 28.23 | odd | 6 | |||
9702.2.a.ch.1.1 | 2 | 21.5 | even | 6 | |||
9702.2.a.cx.1.2 | 2 | 21.2 | odd | 6 |