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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.39075800976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.1 | ||
Root | \(1.51772 - 2.62877i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.201 |
Dual form | 950.2.e.m.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 | ||||
\(3\) | −1.51772 | + | 2.62877i | −0.876255 | + | 1.51772i | −0.0208358 | + | 0.999783i | \(0.506633\pi\) |
−0.855419 | + | 0.517936i | \(0.826701\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.51772 | + | 2.62877i | 0.619606 | + | 1.07319i | ||||
\(7\) | −4.93155 | −1.86395 | −0.931975 | − | 0.362521i | \(-0.881916\pi\) | ||||
−0.931975 | + | 0.362521i | \(0.881916\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.10694 | − | 5.38138i | −1.03565 | − | 1.79379i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.28233 | 0.386637 | 0.193318 | − | 0.981136i | \(-0.438075\pi\) | ||||
0.193318 | + | 0.981136i | \(0.438075\pi\) | |||||||
\(12\) | 3.03544 | 0.876255 | ||||||||
\(13\) | 1.98349 | + | 3.43551i | 0.550122 | + | 0.952840i | 0.998265 | + | 0.0588778i | \(0.0187522\pi\) |
−0.448143 | + | 0.893962i | \(0.647914\pi\) | |||||||
\(14\) | −2.46578 | + | 4.27085i | −0.659006 | + | 1.14143i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.10694 | − | 1.91728i | 0.268472 | − | 0.465008i | −0.699995 | − | 0.714148i | \(-0.746815\pi\) |
0.968468 | + | 0.249140i | \(0.0801478\pi\) | |||||||
\(18\) | −6.21388 | −1.46463 | ||||||||
\(19\) | 3.12466 | − | 3.03916i | 0.716846 | − | 0.697232i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.48471 | − | 12.9639i | 1.63330 | − | 2.82895i | ||||
\(22\) | 0.641165 | − | 1.11053i | 0.136697 | − | 0.236766i | ||||
\(23\) | −3.84233 | − | 6.65511i | −0.801181 | − | 1.38769i | −0.918839 | − | 0.394632i | \(-0.870872\pi\) |
0.117658 | − | 0.993054i | \(-0.462461\pi\) | |||||||
\(24\) | 1.51772 | − | 2.62877i | 0.309803 | − | 0.536595i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.96699 | 0.777990 | ||||||||
\(27\) | 9.75553 | 1.87745 | ||||||||
\(28\) | 2.46578 | + | 4.27085i | 0.465988 | + | 0.807114i | ||||
\(29\) | 2.14116 | + | 3.70861i | 0.397604 | + | 0.688671i | 0.993430 | − | 0.114443i | \(-0.0365083\pi\) |
−0.595825 | + | 0.803114i | \(0.703175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.14543 | −0.744541 | −0.372271 | − | 0.928124i | \(-0.621421\pi\) | ||||
−0.372271 | + | 0.928124i | \(0.621421\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1.94622 | + | 3.37094i | −0.338793 | + | 0.586806i | ||||
\(34\) | −1.10694 | − | 1.91728i | −0.189839 | − | 0.328810i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.10694 | + | 5.38138i | −0.517823 | + | 0.896896i | ||||
\(37\) | 9.38864 | 1.54348 | 0.771742 | − | 0.635936i | \(-0.219386\pi\) | ||||
0.771742 | + | 0.635936i | \(0.219386\pi\) | |||||||
\(38\) | −1.06966 | − | 4.22562i | −0.173522 | − | 0.685485i | ||||
\(39\) | −12.0415 | −1.92819 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.30005 | − | 3.98380i | 0.359207 | − | 0.622165i | −0.628621 | − | 0.777711i | \(-0.716380\pi\) |
0.987829 | + | 0.155546i | \(0.0497138\pi\) | |||||||
\(42\) | −7.48471 | − | 12.9639i | −1.15492 | − | 2.00037i | ||||
\(43\) | 3.32461 | − | 5.75839i | 0.506998 | − | 0.878147i | −0.492969 | − | 0.870047i | \(-0.664088\pi\) |
0.999967 | − | 0.00809994i | \(-0.00257832\pi\) | |||||||
\(44\) | −0.641165 | − | 1.11053i | −0.0966592 | − | 0.167419i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.68466 | −1.13304 | ||||||||
\(47\) | −3.46578 | − | 6.00290i | −0.505535 | − | 0.875613i | −0.999979 | − | 0.00640345i | \(-0.997962\pi\) |
0.494444 | − | 0.869209i | \(-0.335372\pi\) | |||||||
\(48\) | −1.51772 | − | 2.62877i | −0.219064 | − | 0.379430i | ||||
\(49\) | 17.3202 | 2.47431 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.36005 | + | 5.81977i | 0.470501 | + | 0.814931i | ||||
\(52\) | 1.98349 | − | 3.43551i | 0.275061 | − | 0.476420i | ||||
\(53\) | 3.46578 | + | 6.00290i | 0.476061 | + | 0.824562i | 0.999624 | − | 0.0274254i | \(-0.00873086\pi\) |
−0.523563 | + | 0.851987i | \(0.675398\pi\) | |||||||
\(54\) | 4.87777 | − | 8.44854i | 0.663780 | − | 1.14970i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.93155 | 0.659006 | ||||||||
\(57\) | 3.24689 | + | 12.8266i | 0.430061 | + | 1.69892i | ||||
\(58\) | 4.28233 | 0.562297 | ||||||||
\(59\) | 3.15888 | − | 5.47135i | 0.411252 | − | 0.712309i | −0.583775 | − | 0.811915i | \(-0.698425\pi\) |
0.995027 | + | 0.0996066i | \(0.0317584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.64238 | − | 9.77288i | −0.722432 | − | 1.25129i | −0.960022 | − | 0.279924i | \(-0.909691\pi\) |
0.237590 | − | 0.971366i | \(-0.423643\pi\) | |||||||
\(62\) | −2.07272 | + | 3.59005i | −0.263235 | + | 0.455937i | ||||
\(63\) | 15.3220 | + | 26.5385i | 1.93039 | + | 3.34354i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.94622 | + | 3.37094i | 0.239563 | + | 0.414935i | ||||
\(67\) | 0.965775 | + | 1.67277i | 0.117988 | + | 0.204362i | 0.918970 | − | 0.394327i | \(-0.129022\pi\) |
−0.800982 | + | 0.598688i | \(0.795689\pi\) | |||||||
\(68\) | −2.21388 | −0.268472 | ||||||||
\(69\) | 23.3263 | 2.80816 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.16010 | + | 7.20550i | −0.493713 | + | 0.855135i | −0.999974 | − | 0.00724489i | \(-0.997694\pi\) |
0.506261 | + | 0.862380i | \(0.331027\pi\) | |||||||
\(72\) | 3.10694 | + | 5.38138i | 0.366156 | + | 0.634202i | ||||
\(73\) | 3.41383 | − | 5.91293i | 0.399559 | − | 0.692056i | −0.594113 | − | 0.804382i | \(-0.702497\pi\) |
0.993671 | + | 0.112326i | \(0.0358300\pi\) | |||||||
\(74\) | 4.69432 | − | 8.13080i | 0.545704 | − | 0.945187i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.19432 | − | 1.18645i | −0.481122 | − | 0.136095i | ||||
\(77\) | −6.32387 | −0.720672 | ||||||||
\(78\) | −6.02077 | + | 10.4283i | −0.681718 | + | 1.18077i | ||||
\(79\) | −1.76961 | + | 3.06506i | −0.199097 | + | 0.344846i | −0.948236 | − | 0.317567i | \(-0.897134\pi\) |
0.749139 | + | 0.662413i | \(0.230468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.48533 | + | 9.50088i | −0.609482 | + | 1.05565i | ||||
\(82\) | −2.30005 | − | 3.98380i | −0.253998 | − | 0.439937i | ||||
\(83\) | −3.28476 | −0.360549 | −0.180274 | − | 0.983616i | \(-0.557699\pi\) | ||||
−0.180274 | + | 0.983616i | \(0.557699\pi\) | |||||||
\(84\) | −14.9694 | −1.63330 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.32461 | − | 5.75839i | −0.358502 | − | 0.620944i | ||||
\(87\) | −12.9987 | −1.39361 | ||||||||
\(88\) | −1.28233 | −0.136697 | ||||||||
\(89\) | −4.46699 | − | 7.73705i | −0.473500 | − | 0.820126i | 0.526040 | − | 0.850460i | \(-0.323676\pi\) |
−0.999540 | + | 0.0303341i | \(0.990343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.78170 | − | 16.9424i | −1.02540 | − | 1.77605i | ||||
\(92\) | −3.84233 | + | 6.65511i | −0.400591 | + | 0.693843i | ||||
\(93\) | 6.29160 | − | 10.8974i | 0.652408 | − | 1.13000i | ||||
\(94\) | −6.93155 | −0.714935 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.03544 | −0.309803 | ||||||||
\(97\) | 1.07150 | − | 1.85590i | 0.108795 | − | 0.188438i | −0.806488 | − | 0.591251i | \(-0.798634\pi\) |
0.915282 | + | 0.402813i | \(0.131968\pi\) | |||||||
\(98\) | 8.66010 | − | 14.9997i | 0.874802 | − | 1.51520i | ||||
\(99\) | −3.98412 | − | 6.90070i | −0.400419 | − | 0.693547i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.27267 | − | 9.13253i | −0.524650 | − | 0.908720i | −0.999588 | − | 0.0287012i | \(-0.990863\pi\) |
0.474938 | − | 0.880019i | \(-0.342470\pi\) | |||||||
\(102\) | 6.72010 | 0.665389 | ||||||||
\(103\) | −3.64311 | −0.358967 | −0.179483 | − | 0.983761i | \(-0.557443\pi\) | ||||
−0.179483 | + | 0.983761i | \(0.557443\pi\) | |||||||
\(104\) | −1.98349 | − | 3.43551i | −0.194498 | − | 0.336880i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.93155 | 0.673252 | ||||||||
\(107\) | 5.07456 | 0.490576 | 0.245288 | − | 0.969450i | \(-0.421117\pi\) | ||||
0.245288 | + | 0.969450i | \(0.421117\pi\) | |||||||
\(108\) | −4.87777 | − | 8.44854i | −0.469363 | − | 0.812961i | ||||
\(109\) | −2.37155 | + | 4.10765i | −0.227153 | + | 0.393441i | −0.956963 | − | 0.290209i | \(-0.906275\pi\) |
0.729810 | + | 0.683650i | \(0.239609\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.2493 | + | 24.6805i | −1.35249 | + | 2.34257i | ||||
\(112\) | 2.46578 | − | 4.27085i | 0.232994 | − | 0.403557i | ||||
\(113\) | −12.4414 | −1.17039 | −0.585196 | − | 0.810892i | \(-0.698983\pi\) | ||||
−0.585196 | + | 0.810892i | \(0.698983\pi\) | |||||||
\(114\) | 12.7316 | + | 3.60140i | 1.19242 | + | 0.337302i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.14116 | − | 3.70861i | 0.198802 | − | 0.344335i | ||||
\(117\) | 12.3252 | − | 21.3479i | 1.13946 | − | 1.97361i | ||||
\(118\) | −3.15888 | − | 5.47135i | −0.290799 | − | 0.503678i | ||||
\(119\) | −5.45893 | + | 9.45515i | −0.500419 | + | 0.866752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.35563 | −0.850512 | ||||||||
\(122\) | −11.2848 | −1.02167 | ||||||||
\(123\) | 6.98165 | + | 12.0926i | 0.629514 | + | 1.09035i | ||||
\(124\) | 2.07272 | + | 3.59005i | 0.186135 | + | 0.322396i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 30.6441 | 2.72999 | ||||||||
\(127\) | −1.94806 | − | 3.37413i | −0.172862 | − | 0.299406i | 0.766557 | − | 0.642176i | \(-0.221968\pi\) |
−0.939419 | + | 0.342770i | \(0.888635\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 10.0916 | + | 17.4792i | 0.888520 | + | 1.53896i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.41504 | − | 9.37913i | 0.473115 | − | 0.819459i | −0.526412 | − | 0.850230i | \(-0.676463\pi\) |
0.999526 | + | 0.0307711i | \(0.00979629\pi\) | |||||||
\(132\) | 3.89243 | 0.338793 | ||||||||
\(133\) | −15.4094 | + | 14.9878i | −1.33617 | + | 1.29961i | ||||
\(134\) | 1.93155 | 0.166861 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.10694 | + | 1.91728i | −0.0949193 | + | 0.164405i | ||||
\(137\) | −10.2994 | − | 17.8391i | −0.879939 | − | 1.52410i | −0.851407 | − | 0.524506i | \(-0.824250\pi\) |
−0.0285321 | − | 0.999593i | \(-0.509083\pi\) | |||||||
\(138\) | 11.6632 | − | 20.2012i | 0.992833 | − | 1.71964i | ||||
\(139\) | 3.39427 | + | 5.87905i | 0.287898 | + | 0.498655i | 0.973308 | − | 0.229503i | \(-0.0737101\pi\) |
−0.685409 | + | 0.728158i | \(0.740377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.0403 | 1.77191 | ||||||||
\(142\) | 4.16010 | + | 7.20550i | 0.349108 | + | 0.604672i | ||||
\(143\) | 2.54349 | + | 4.40546i | 0.212698 | + | 0.368403i | ||||
\(144\) | 6.21388 | 0.517823 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.41383 | − | 5.91293i | −0.282531 | − | 0.489358i | ||||
\(147\) | −26.2872 | + | 45.5307i | −2.16813 | + | 3.75531i | ||||
\(148\) | −4.69432 | − | 8.13080i | −0.385871 | − | 0.668348i | ||||
\(149\) | −11.3790 | + | 19.7090i | −0.932202 | + | 1.61462i | −0.152654 | + | 0.988280i | \(0.548782\pi\) |
−0.779548 | + | 0.626342i | \(0.784551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5478 | 0.939743 | 0.469872 | − | 0.882735i | \(-0.344300\pi\) | ||||
0.469872 | + | 0.882735i | \(0.344300\pi\) | |||||||
\(152\) | −3.12466 | + | 3.03916i | −0.253443 | + | 0.246509i | ||||
\(153\) | −13.7568 | −1.11217 | ||||||||
\(154\) | −3.16194 | + | 5.47664i | −0.254796 | + | 0.441320i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.02077 | + | 10.4283i | 0.482048 | + | 0.834931i | ||||
\(157\) | 5.44927 | − | 9.43841i | 0.434899 | − | 0.753267i | −0.562388 | − | 0.826873i | \(-0.690117\pi\) |
0.997287 | + | 0.0736060i | \(0.0234507\pi\) | |||||||
\(158\) | 1.76961 | + | 3.06506i | 0.140783 | + | 0.243843i | ||||
\(159\) | −21.0403 | −1.66860 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.9486 | + | 32.8200i | 1.49336 | + | 2.58658i | ||||
\(162\) | 5.48533 | + | 9.50088i | 0.430969 | + | 0.746460i | ||||
\(163\) | −11.8240 | −0.926126 | −0.463063 | − | 0.886325i | \(-0.653250\pi\) | ||||
−0.463063 | + | 0.886325i | \(0.653250\pi\) | |||||||
\(164\) | −4.60010 | −0.359207 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.64238 | + | 2.84468i | −0.127473 | + | 0.220790i | ||||
\(167\) | −8.83549 | − | 15.3035i | −0.683710 | − | 1.18422i | −0.973840 | − | 0.227234i | \(-0.927032\pi\) |
0.290130 | − | 0.956987i | \(-0.406302\pi\) | |||||||
\(168\) | −7.48471 | + | 12.9639i | −0.577458 | + | 1.00019i | ||||
\(169\) | −1.36850 | + | 2.37031i | −0.105269 | + | 0.182331i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.0630 | − | 7.37248i | −1.99309 | − | 0.563787i | ||||
\(172\) | −6.64922 | −0.506998 | ||||||||
\(173\) | 6.22855 | − | 10.7882i | 0.473548 | − | 0.820208i | −0.525994 | − | 0.850488i | \(-0.676307\pi\) |
0.999541 | + | 0.0302799i | \(0.00963987\pi\) | |||||||
\(174\) | −6.49937 | + | 11.2572i | −0.492716 | + | 0.853409i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.641165 | + | 1.11053i | −0.0483296 | + | 0.0837094i | ||||
\(177\) | 9.58859 | + | 16.6079i | 0.720723 | + | 1.24833i | ||||
\(178\) | −8.93398 | −0.669630 | ||||||||
\(179\) | 13.7971 | 1.03124 | 0.515621 | − | 0.856817i | \(-0.327561\pi\) | ||||
0.515621 | + | 0.856817i | \(0.327561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.96883 | + | 12.0704i | 0.517989 | + | 0.897183i | 0.999782 | + | 0.0208980i | \(0.00665251\pi\) |
−0.481793 | + | 0.876285i | \(0.660014\pi\) | |||||||
\(182\) | −19.5634 | −1.45014 | ||||||||
\(183\) | 34.2542 | 2.53214 | ||||||||
\(184\) | 3.84233 | + | 6.65511i | 0.283260 | + | 0.490621i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.29160 | − | 10.8974i | −0.461322 | − | 0.799034i | ||||
\(187\) | 1.41946 | − | 2.45858i | 0.103801 | − | 0.179789i | ||||
\(188\) | −3.46578 | + | 6.00290i | −0.252768 | + | 0.437806i | ||||
\(189\) | −48.1099 | −3.49948 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.28233 | 0.309859 | 0.154929 | − | 0.987926i | \(-0.450485\pi\) | ||||
0.154929 | + | 0.987926i | \(0.450485\pi\) | |||||||
\(192\) | −1.51772 | + | 2.62877i | −0.109532 | + | 0.189715i | ||||
\(193\) | −4.80310 | + | 8.31922i | −0.345735 | + | 0.598830i | −0.985487 | − | 0.169751i | \(-0.945704\pi\) |
0.639752 | + | 0.768581i | \(0.279037\pi\) | |||||||
\(194\) | −1.07150 | − | 1.85590i | −0.0769294 | − | 0.133246i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.66010 | − | 14.9997i | −0.618578 | − | 1.07141i | ||||
\(197\) | 23.7834 | 1.69450 | 0.847248 | − | 0.531197i | \(-0.178258\pi\) | ||||
0.847248 | + | 0.531197i | \(0.178258\pi\) | |||||||
\(198\) | −7.96824 | −0.566278 | ||||||||
\(199\) | −7.51588 | − | 13.0179i | −0.532786 | − | 0.922813i | −0.999267 | − | 0.0382818i | \(-0.987812\pi\) |
0.466481 | − | 0.884531i | \(-0.345522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.86310 | −0.413551 | ||||||||
\(202\) | −10.5453 | −0.741967 | ||||||||
\(203\) | −10.5593 | − | 18.2892i | −0.741115 | − | 1.28365i | ||||
\(204\) | 3.36005 | − | 5.81977i | 0.235250 | − | 0.407466i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.82156 | + | 3.15503i | −0.126914 | + | 0.219821i | ||||
\(207\) | −23.8758 | + | 41.3541i | −1.65948 | + | 2.87431i | ||||
\(208\) | −3.96699 | −0.275061 | ||||||||
\(209\) | 4.00684 | − | 3.89721i | 0.277159 | − | 0.269576i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.73281 | + | 16.8577i | −0.670034 | + | 1.16053i | 0.307859 | + | 0.951432i | \(0.400387\pi\) |
−0.977894 | + | 0.209102i | \(0.932946\pi\) | |||||||
\(212\) | 3.46578 | − | 6.00290i | 0.238030 | − | 0.412281i | ||||
\(213\) | −12.6277 | − | 21.8718i | −0.865237 | − | 1.49863i | ||||
\(214\) | 2.53728 | − | 4.39469i | 0.173445 | − | 0.300415i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.75553 | −0.663780 | ||||||||
\(217\) | 20.4434 | 1.38779 | ||||||||
\(218\) | 2.37155 | + | 4.10765i | 0.160622 | + | 0.278205i | ||||
\(219\) | 10.3625 | + | 17.9483i | 0.700231 | + | 1.21284i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.78244 | 0.590771 | ||||||||
\(222\) | 14.2493 | + | 24.6805i | 0.956352 | + | 1.65645i | ||||
\(223\) | 2.82582 | − | 4.89447i | 0.189231 | − | 0.327758i | −0.755763 | − | 0.654845i | \(-0.772734\pi\) |
0.944994 | + | 0.327087i | \(0.106067\pi\) | |||||||
\(224\) | −2.46578 | − | 4.27085i | −0.164752 | − | 0.285358i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.22072 | + | 10.7746i | −0.413796 | + | 0.716716i | ||||
\(227\) | 8.45952 | 0.561478 | 0.280739 | − | 0.959784i | \(-0.409420\pi\) | ||||
0.280739 | + | 0.959784i | \(0.409420\pi\) | |||||||
\(228\) | 9.48471 | − | 9.22519i | 0.628140 | − | 0.610953i | ||||
\(229\) | 1.54291 | 0.101958 | 0.0509791 | − | 0.998700i | \(-0.483766\pi\) | ||||
0.0509791 | + | 0.998700i | \(0.483766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.59786 | − | 16.6240i | 0.631493 | − | 1.09378i | ||||
\(232\) | −2.14116 | − | 3.70861i | −0.140574 | − | 0.243482i | ||||
\(233\) | 2.04631 | − | 3.54432i | 0.134058 | − | 0.232196i | −0.791179 | − | 0.611585i | \(-0.790532\pi\) |
0.925237 | + | 0.379389i | \(0.123866\pi\) | |||||||
\(234\) | −12.3252 | − | 21.3479i | −0.805723 | − | 1.39555i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.31777 | −0.411252 | ||||||||
\(237\) | −5.37155 | − | 9.30380i | −0.348920 | − | 0.604347i | ||||
\(238\) | 5.45893 | + | 9.45515i | 0.353850 | + | 0.612886i | ||||
\(239\) | 25.1442 | 1.62644 | 0.813221 | − | 0.581955i | \(-0.197712\pi\) | ||||
0.813221 | + | 0.581955i | \(0.197712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7170 | − | 23.7586i | −0.883592 | − | 1.53043i | −0.847319 | − | 0.531085i | \(-0.821784\pi\) |
−0.0362738 | − | 0.999342i | \(-0.511549\pi\) | |||||||
\(242\) | −4.67782 | + | 8.10221i | −0.300701 | + | 0.520830i | ||||
\(243\) | −2.01709 | − | 3.49370i | −0.129396 | − | 0.224121i | ||||
\(244\) | −5.64238 | + | 9.77288i | −0.361216 | + | 0.625645i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.9633 | 0.890268 | ||||||||
\(247\) | 16.6388 | + | 4.70665i | 1.05870 | + | 0.299477i | ||||
\(248\) | 4.14543 | 0.263235 | ||||||||
\(249\) | 4.98533 | − | 8.63485i | 0.315933 | − | 0.547212i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.30263 | − | 3.98826i | −0.145340 | − | 0.251737i | 0.784159 | − | 0.620559i | \(-0.213094\pi\) |
−0.929500 | + | 0.368822i | \(0.879761\pi\) | |||||||
\(252\) | 15.3220 | − | 26.5385i | 0.965197 | − | 1.67177i | ||||
\(253\) | −4.92713 | − | 8.53404i | −0.309766 | − | 0.536531i | ||||
\(254\) | −3.89611 | −0.244464 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.86247 | − | 17.0823i | −0.615204 | − | 1.06556i | −0.990349 | − | 0.138599i | \(-0.955740\pi\) |
0.375144 | − | 0.926966i | \(-0.377593\pi\) | |||||||
\(258\) | 20.1833 | 1.25656 | ||||||||
\(259\) | −46.3006 | −2.87698 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.3049 | − | 23.0448i | 0.823555 | − | 1.42644i | ||||
\(262\) | −5.41504 | − | 9.37913i | −0.334543 | − | 0.579445i | ||||
\(263\) | 4.16010 | − | 7.20550i | 0.256523 | − | 0.444310i | −0.708785 | − | 0.705424i | \(-0.750757\pi\) |
0.965308 | + | 0.261114i | \(0.0840899\pi\) | |||||||
\(264\) | 1.94622 | − | 3.37094i | 0.119781 | − | 0.207467i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.27509 | + | 20.8388i | 0.323437 | + | 1.27771i | ||||
\(267\) | 27.1185 | 1.65963 | ||||||||
\(268\) | 0.965775 | − | 1.67277i | 0.0589941 | − | 0.102181i | ||||
\(269\) | −7.67281 | + | 13.2897i | −0.467820 | + | 0.810287i | −0.999324 | − | 0.0367683i | \(-0.988294\pi\) |
0.531504 | + | 0.847056i | \(0.321627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.68039 | + | 2.91052i | −0.102077 | + | 0.176802i | −0.912540 | − | 0.408987i | \(-0.865882\pi\) |
0.810463 | + | 0.585789i | \(0.199215\pi\) | |||||||
\(272\) | 1.10694 | + | 1.91728i | 0.0671181 | + | 0.116252i | ||||
\(273\) | 59.3835 | 3.59405 | ||||||||
\(274\) | −20.5988 | −1.24442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.6632 | − | 20.2012i | −0.702039 | − | 1.21597i | ||||
\(277\) | −31.2517 | −1.87774 | −0.938868 | − | 0.344278i | \(-0.888124\pi\) | ||||
−0.938868 | + | 0.344278i | \(0.888124\pi\) | |||||||
\(278\) | 6.78855 | 0.407150 | ||||||||
\(279\) | 12.8796 | + | 22.3081i | 0.771082 | + | 1.33555i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.46699 | − | 2.54090i | −0.0875132 | − | 0.151577i | 0.818946 | − | 0.573870i | \(-0.194559\pi\) |
−0.906459 | + | 0.422293i | \(0.861225\pi\) | |||||||
\(282\) | 10.5201 | − | 18.2214i | 0.626465 | − | 1.08507i | ||||
\(283\) | −7.34660 | + | 12.7247i | −0.436710 | + | 0.756404i | −0.997433 | − | 0.0715995i | \(-0.977190\pi\) |
0.560724 | + | 0.828003i | \(0.310523\pi\) | |||||||
\(284\) | 8.32019 | 0.493713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.08699 | 0.300800 | ||||||||
\(287\) | −11.3428 | + | 19.6463i | −0.669545 | + | 1.15969i | ||||
\(288\) | 3.10694 | − | 5.38138i | 0.183078 | − | 0.317101i | ||||
\(289\) | 6.04937 | + | 10.4778i | 0.355845 | + | 0.616342i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.25248 | + | 5.63346i | 0.190664 | + | 0.330239i | ||||
\(292\) | −6.82766 | −0.399559 | ||||||||
\(293\) | 8.58320 | 0.501436 | 0.250718 | − | 0.968060i | \(-0.419333\pi\) | ||||
0.250718 | + | 0.968060i | \(0.419333\pi\) | |||||||
\(294\) | 26.2872 | + | 45.5307i | 1.53310 | + | 2.65541i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.38864 | −0.545704 | ||||||||
\(297\) | 12.5098 | 0.725893 | ||||||||
\(298\) | 11.3790 | + | 19.7090i | 0.659167 | + | 1.14171i | ||||
\(299\) | 15.2425 | − | 26.4007i | 0.881495 | − | 1.52679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.3955 | + | 28.3978i | −0.945020 | + | 1.63682i | ||||
\(302\) | 5.77388 | − | 10.0007i | 0.332249 | − | 0.575473i | ||||
\(303\) | 32.0097 | 1.83891 | ||||||||
\(304\) | 1.06966 | + | 4.22562i | 0.0613493 | + | 0.242356i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.87839 | + | 11.9137i | −0.393212 | + | 0.681063i | ||||
\(307\) | −2.66757 | + | 4.62036i | −0.152246 | + | 0.263698i | −0.932053 | − | 0.362322i | \(-0.881984\pi\) |
0.779807 | + | 0.626020i | \(0.215317\pi\) | |||||||
\(308\) | 3.16194 | + | 5.47664i | 0.180168 | + | 0.312060i | ||||
\(309\) | 5.52922 | − | 9.57689i | 0.314546 | − | 0.544810i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2933 | 1.32084 | 0.660421 | − | 0.750896i | \(-0.270378\pi\) | ||||
0.660421 | + | 0.750896i | \(0.270378\pi\) | |||||||
\(312\) | 12.0415 | 0.681718 | ||||||||
\(313\) | 5.35699 | + | 9.27859i | 0.302795 | + | 0.524457i | 0.976768 | − | 0.214299i | \(-0.0687468\pi\) |
−0.673973 | + | 0.738756i | \(0.735414\pi\) | |||||||
\(314\) | −5.44927 | − | 9.43841i | −0.307520 | − | 0.532640i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.53923 | 0.199097 | ||||||||
\(317\) | 7.16267 | + | 12.4061i | 0.402296 | + | 0.696797i | 0.994003 | − | 0.109356i | \(-0.0348790\pi\) |
−0.591707 | + | 0.806153i | \(0.701546\pi\) | |||||||
\(318\) | −10.5201 | + | 18.2214i | −0.589940 | + | 1.02181i | ||||
\(319\) | 2.74568 | + | 4.75566i | 0.153729 | + | 0.266266i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.70175 | + | 13.3398i | −0.429870 | + | 0.744556i | ||||
\(322\) | 37.8973 | 2.11193 | ||||||||
\(323\) | −2.36810 | − | 9.35501i | −0.131765 | − | 0.520527i | ||||
\(324\) | 10.9707 | 0.609482 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.91199 | + | 10.2399i | −0.327435 | + | 0.567134i | ||||
\(327\) | −7.19870 | − | 12.4685i | −0.398089 | − | 0.689510i | ||||
\(328\) | −2.30005 | + | 3.98380i | −0.126999 | + | 0.219969i | ||||
\(329\) | 17.0916 | + | 29.6036i | 0.942293 | + | 1.63210i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5695 | −0.580953 | −0.290476 | − | 0.956882i | \(-0.593814\pi\) | ||||
−0.290476 | + | 0.956882i | \(0.593814\pi\) | |||||||
\(332\) | 1.64238 | + | 2.84468i | 0.0901372 | + | 0.156122i | ||||
\(333\) | −29.1700 | − | 50.5238i | −1.59850 | − | 2.76869i | ||||
\(334\) | −17.6710 | −0.966913 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.48471 | + | 12.9639i | 0.408324 | + | 0.707238i | ||||
\(337\) | 5.85931 | − | 10.1486i | 0.319177 | − | 0.552831i | −0.661140 | − | 0.750263i | \(-0.729927\pi\) |
0.980317 | + | 0.197432i | \(0.0632602\pi\) | |||||||
\(338\) | 1.36850 | + | 2.37031i | 0.0744365 | + | 0.128928i | ||||
\(339\) | 18.8826 | − | 32.7057i | 1.02556 | − | 1.77633i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.31581 | −0.287867 | ||||||||
\(342\) | −19.4163 | + | 18.8850i | −1.04991 | + | 1.02118i | ||||
\(343\) | −50.8946 | −2.74805 | ||||||||
\(344\) | −3.32461 | + | 5.75839i | −0.179251 | + | 0.310472i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.22855 | − | 10.7882i | −0.334849 | − | 0.579975i | ||||
\(347\) | 10.4505 | − | 18.1008i | 0.561011 | − | 0.971700i | −0.436397 | − | 0.899754i | \(-0.643746\pi\) |
0.997409 | − | 0.0719459i | \(-0.0229209\pi\) | |||||||
\(348\) | 6.49937 | + | 11.2572i | 0.348403 | + | 0.603452i | ||||
\(349\) | 35.4817 | 1.89929 | 0.949647 | − | 0.313322i | \(-0.101442\pi\) | ||||
0.949647 | + | 0.313322i | \(0.101442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3500 | + | 33.5153i | 1.03283 | + | 1.78891i | ||||
\(352\) | 0.641165 | + | 1.11053i | 0.0341742 | + | 0.0591915i | ||||
\(353\) | 14.2984 | 0.761029 | 0.380515 | − | 0.924775i | \(-0.375747\pi\) | ||||
0.380515 | + | 0.924775i | \(0.375747\pi\) | |||||||
\(354\) | 19.1772 | 1.01926 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.46699 | + | 7.73705i | −0.236750 | + | 0.410063i | ||||
\(357\) | −16.5702 | − | 28.7005i | −0.876990 | − | 1.51899i | ||||
\(358\) | 6.89854 | − | 11.9486i | 0.364599 | − | 0.631504i | ||||
\(359\) | −2.11073 | + | 3.65589i | −0.111400 | + | 0.192951i | −0.916335 | − | 0.400413i | \(-0.868867\pi\) |
0.804935 | + | 0.593363i | \(0.202200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.526988 | − | 18.9927i | 0.0277362 | − | 0.999615i | ||||
\(362\) | 13.9377 | 0.732547 | ||||||||
\(363\) | 14.1992 | − | 24.5938i | 0.745266 | − | 1.29084i | ||||
\(364\) | −9.78170 | + | 16.9424i | −0.512700 | + | 0.888023i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 17.1271 | − | 29.6650i | 0.895247 | − | 1.55061i | ||||
\(367\) | 7.08238 | + | 12.2670i | 0.369697 | + | 0.640334i | 0.989518 | − | 0.144409i | \(-0.0461281\pi\) |
−0.619821 | + | 0.784743i | \(0.712795\pi\) | |||||||
\(368\) | 7.68466 | 0.400591 | ||||||||
\(369\) | −28.5845 | −1.48805 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.0916 | − | 29.6036i | −0.887354 | − | 1.53694i | ||||
\(372\) | −12.5832 | −0.652408 | ||||||||
\(373\) | −16.6541 | −0.862315 | −0.431158 | − | 0.902277i | \(-0.641895\pi\) | ||||
−0.431158 | + | 0.902277i | \(0.641895\pi\) | |||||||
\(374\) | −1.41946 | − | 2.45858i | −0.0733987 | − | 0.127130i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.46578 | + | 6.00290i | 0.178734 | + | 0.309576i | ||||
\(377\) | −8.49398 | + | 14.7120i | −0.437462 | + | 0.757706i | ||||
\(378\) | −24.0550 | + | 41.6644i | −1.23725 | + | 2.14299i | ||||
\(379\) | 3.36689 | 0.172946 | 0.0864728 | − | 0.996254i | \(-0.472440\pi\) | ||||
0.0864728 | + | 0.996254i | \(0.472440\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.8264 | 0.605885 | ||||||||
\(382\) | 2.14116 | − | 3.70861i | 0.109552 | − | 0.189749i | ||||
\(383\) | 4.16010 | − | 7.20550i | 0.212571 | − | 0.368184i | −0.739947 | − | 0.672665i | \(-0.765150\pi\) |
0.952518 | + | 0.304481i | \(0.0984830\pi\) | |||||||
\(384\) | 1.51772 | + | 2.62877i | 0.0774508 | + | 0.134149i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.80310 | + | 8.31922i | 0.244471 | + | 0.423437i | ||||
\(387\) | −41.3175 | −2.10028 | ||||||||
\(388\) | −2.14301 | −0.108795 | ||||||||
\(389\) | −12.4076 | − | 21.4905i | −0.629089 | − | 1.08961i | −0.987735 | − | 0.156140i | \(-0.950095\pi\) |
0.358646 | − | 0.933474i | \(-0.383239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.0129 | −0.860380 | ||||||||
\(392\) | −17.3202 | −0.874802 | ||||||||
\(393\) | 16.4370 | + | 28.4698i | 0.829138 | + | 1.43611i | ||||
\(394\) | 11.8917 | − | 20.5970i | 0.599095 | − | 1.03766i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.98412 | + | 6.90070i | −0.200210 | + | 0.346773i | ||||
\(397\) | −6.15043 | + | 10.6529i | −0.308681 | + | 0.534652i | −0.978074 | − | 0.208257i | \(-0.933221\pi\) |
0.669393 | + | 0.742909i | \(0.266554\pi\) | |||||||
\(398\) | −15.0318 | −0.753474 | ||||||||
\(399\) | −16.0122 | − | 63.2550i | −0.801613 | − | 3.16671i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.52320 | − | 13.0306i | 0.375691 | − | 0.650715i | −0.614740 | − | 0.788730i | \(-0.710739\pi\) |
0.990430 | + | 0.138015i | \(0.0440722\pi\) | |||||||
\(402\) | −2.93155 | + | 5.07759i | −0.146212 | + | 0.253247i | ||||
\(403\) | −8.22244 | − | 14.2417i | −0.409589 | − | 0.709429i | ||||
\(404\) | −5.27267 | + | 9.13253i | −0.262325 | + | 0.454360i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.1185 | −1.04809 | ||||||||
\(407\) | 12.0393 | 0.596768 | ||||||||
\(408\) | −3.36005 | − | 5.81977i | −0.166347 | − | 0.288122i | ||||
\(409\) | −13.0170 | − | 22.5461i | −0.643648 | − | 1.11483i | −0.984612 | − | 0.174755i | \(-0.944087\pi\) |
0.340964 | − | 0.940077i | \(-0.389247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 62.5265 | 3.08420 | ||||||||
\(412\) | 1.82156 | + | 3.15503i | 0.0897417 | + | 0.155437i | ||||
\(413\) | −15.5782 | + | 26.9822i | −0.766553 | + | 1.32771i | ||||
\(414\) | 23.8758 | + | 41.3541i | 1.17343 | + | 2.03244i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.98349 | + | 3.43551i | −0.0972488 | + | 0.168440i | ||||
\(417\) | −20.6062 | −1.00909 | ||||||||
\(418\) | −1.37166 | − | 5.41863i | −0.0670901 | − | 0.265034i | ||||
\(419\) | 9.69640 | 0.473700 | 0.236850 | − | 0.971546i | \(-0.423885\pi\) | ||||
0.236850 | + | 0.971546i | \(0.423885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.04154 | + | 15.6604i | −0.440658 | + | 0.763242i | −0.997738 | − | 0.0672166i | \(-0.978588\pi\) |
0.557080 | + | 0.830459i | \(0.311921\pi\) | |||||||
\(422\) | 9.73281 | + | 16.8577i | 0.473786 | + | 0.820621i | ||||
\(423\) | −21.5359 | + | 37.3013i | −1.04711 | + | 1.81365i | ||||
\(424\) | −3.46578 | − | 6.00290i | −0.168313 | − | 0.291527i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −25.2554 | −1.22363 | ||||||||
\(427\) | 27.8257 | + | 48.1955i | 1.34658 | + | 2.33234i | ||||
\(428\) | −2.53728 | − | 4.39469i | −0.122644 | − | 0.212426i | ||||
\(429\) | −15.4412 | −0.745510 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.08981 | + | 15.7440i | 0.437841 | + | 0.758362i | 0.997523 | − | 0.0703453i | \(-0.0224101\pi\) |
−0.559682 | + | 0.828707i | \(0.689077\pi\) | |||||||
\(432\) | −4.87777 | + | 8.44854i | −0.234682 | + | 0.406481i | ||||
\(433\) | 2.35699 | + | 4.08243i | 0.113270 | + | 0.196189i | 0.917087 | − | 0.398687i | \(-0.130534\pi\) |
−0.803817 | + | 0.594877i | \(0.797201\pi\) | |||||||
\(434\) | 10.2217 | − | 17.7045i | 0.490657 | − | 0.849844i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.74310 | 0.227153 | ||||||||
\(437\) | −32.2319 | − | 9.11749i | −1.54186 | − | 0.436149i | ||||
\(438\) | 20.7249 | 0.990276 | ||||||||
\(439\) | 7.08554 | − | 12.2725i | 0.338174 | − | 0.585735i | −0.645915 | − | 0.763409i | \(-0.723524\pi\) |
0.984089 | + | 0.177674i | \(0.0568573\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −53.8128 | − | 93.2065i | −2.56251 | − | 4.43841i | ||||
\(442\) | 4.39122 | − | 7.60581i | 0.208869 | − | 0.361772i | ||||
\(443\) | −6.24811 | − | 10.8220i | −0.296856 | − | 0.514170i | 0.678559 | − | 0.734546i | \(-0.262605\pi\) |
−0.975415 | + | 0.220376i | \(0.929272\pi\) | |||||||
\(444\) | 28.4986 | 1.35249 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.82582 | − | 4.89447i | −0.133807 | − | 0.231760i | ||||
\(447\) | −34.5402 | − | 59.8253i | −1.63369 | − | 2.82964i | ||||
\(448\) | −4.93155 | −0.232994 | ||||||||
\(449\) | −29.3326 | −1.38429 | −0.692146 | − | 0.721757i | \(-0.743335\pi\) | ||||
−0.692146 | + | 0.721757i | \(0.743335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.94942 | − | 5.10855i | 0.138883 | − | 0.240552i | ||||
\(452\) | 6.22072 | + | 10.7746i | 0.292598 | + | 0.506795i | ||||
\(453\) | −17.5263 | + | 30.3564i | −0.823455 | + | 1.42627i | ||||
\(454\) | 4.22976 | − | 7.32616i | 0.198512 | − | 0.343834i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.24689 | − | 12.8266i | −0.152050 | − | 0.600660i | ||||
\(457\) | 26.2126 | 1.22617 | 0.613087 | − | 0.790015i | \(-0.289927\pi\) | ||||
0.613087 | + | 0.790015i | \(0.289927\pi\) | |||||||
\(458\) | 0.771454 | − | 1.33620i | 0.0360477 | − | 0.0624364i | ||||
\(459\) | 10.7988 | − | 18.7041i | 0.504044 | − | 0.873031i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.85641 | + | 8.41155i | −0.226186 | + | 0.391765i | −0.956674 | − | 0.291160i | \(-0.905959\pi\) |
0.730489 | + | 0.682925i | \(0.239292\pi\) | |||||||
\(462\) | −9.59786 | − | 16.6240i | −0.446533 | − | 0.773418i | ||||
\(463\) | 5.34146 | 0.248239 | 0.124119 | − | 0.992267i | \(-0.460389\pi\) | ||||
0.124119 | + | 0.992267i | \(0.460389\pi\) | |||||||
\(464\) | −4.28233 | −0.198802 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.04631 | − | 3.54432i | −0.0947936 | − | 0.164187i | ||||
\(467\) | 30.3642 | 1.40509 | 0.702543 | − | 0.711641i | \(-0.252048\pi\) | ||||
0.702543 | + | 0.711641i | \(0.252048\pi\) | |||||||
\(468\) | −24.6504 | −1.13946 | ||||||||
\(469\) | −4.76277 | − | 8.24936i | −0.219924 | − | 0.380920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.5409 | + | 28.6497i | 0.762165 | + | 1.32011i | ||||
\(472\) | −3.15888 | + | 5.47135i | −0.145399 | + | 0.251839i | ||||
\(473\) | 4.26325 | − | 7.38416i | 0.196024 | − | 0.339524i | ||||
\(474\) | −10.7431 | −0.493447 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.9179 | 0.500419 | ||||||||
\(477\) | 21.5359 | − | 37.3013i | 0.986062 | − | 1.70791i | ||||
\(478\) | 12.5721 | − | 21.7755i | 0.575034 | − | 0.995988i | ||||
\(479\) | −0.994997 | − | 1.72339i | −0.0454626 | − | 0.0787435i | 0.842399 | − | 0.538855i | \(-0.181143\pi\) |
−0.887861 | + | 0.460111i | \(0.847810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.6223 | + | 32.2548i | 0.849105 | + | 1.47069i | ||||
\(482\) | −27.4341 | −1.24959 | ||||||||
\(483\) | −115.035 | −5.23427 | ||||||||
\(484\) | 4.67782 | + | 8.10221i | 0.212628 | + | 0.368282i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.03418 | −0.182994 | ||||||||
\(487\) | −29.2102 | −1.32364 | −0.661820 | − | 0.749663i | \(-0.730216\pi\) | ||||
−0.661820 | + | 0.749663i | \(0.730216\pi\) | |||||||
\(488\) | 5.64238 | + | 9.77288i | 0.255418 | + | 0.442398i | ||||
\(489\) | 17.9455 | − | 31.0825i | 0.811523 | − | 1.40560i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.44853 | − | 14.6333i | 0.381277 | − | 0.660391i | −0.609968 | − | 0.792426i | \(-0.708818\pi\) |
0.991245 | + | 0.132035i | \(0.0421511\pi\) | |||||||
\(492\) | 6.98165 | − | 12.0926i | 0.314757 | − | 0.545176i | ||||
\(493\) | 9.48057 | 0.426983 | ||||||||
\(494\) | 12.3955 | − | 12.0563i | 0.557699 | − | 0.542439i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.07272 | − | 3.59005i | 0.0930677 | − | 0.161198i | ||||
\(497\) | 20.5157 | − | 35.5343i | 0.920256 | − | 1.59393i | ||||
\(498\) | −4.98533 | − | 8.63485i | −0.223398 | − | 0.386937i | ||||
\(499\) | −0.629662 | + | 1.09061i | −0.0281875 | + | 0.0488222i | −0.879775 | − | 0.475390i | \(-0.842307\pi\) |
0.851588 | + | 0.524212i | \(0.175640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.6391 | 2.39642 | ||||||||
\(502\) | −4.60525 | −0.205542 | ||||||||
\(503\) | 4.56966 | + | 7.91489i | 0.203751 | + | 0.352907i | 0.949734 | − | 0.313058i | \(-0.101353\pi\) |
−0.745983 | + | 0.665965i | \(0.768020\pi\) | |||||||
\(504\) | −15.3220 | − | 26.5385i | −0.682498 | − | 1.18212i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.85427 | −0.438076 | ||||||||
\(507\) | −4.15399 | − | 7.19492i | −0.184485 | − | 0.319538i | ||||
\(508\) | −1.94806 | + | 3.37413i | −0.0864310 | + | 0.149703i | ||||
\(509\) | −17.3005 | − | 29.9654i | −0.766832 | − | 1.32819i | −0.939272 | − | 0.343172i | \(-0.888498\pi\) |
0.172440 | − | 0.985020i | \(-0.444835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.8355 | + | 29.1599i | −0.744758 | + | 1.28996i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 30.4827 | − | 29.6486i | 1.34584 | − | 1.30902i | ||||
\(514\) | −19.7249 | −0.870030 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.0916 | − | 17.4792i | 0.444260 | − | 0.769481i | ||||
\(517\) | −4.44427 | − | 7.69770i | −0.195459 | − | 0.338544i | ||||
\(518\) | −23.1503 | + | 40.0975i | −1.01717 | + | 1.76178i | ||||
\(519\) | 18.9064 | + | 32.7468i | 0.829897 | + | 1.43742i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.2542 | 1.01878 | 0.509392 | − | 0.860535i | \(-0.329870\pi\) | ||||
0.509392 | + | 0.860535i | \(0.329870\pi\) | |||||||
\(522\) | −13.3049 | − | 23.0448i | −0.582342 | − | 1.00865i | ||||
\(523\) | 11.7066 | + | 20.2765i | 0.511896 | + | 0.886630i | 0.999905 | + | 0.0137910i | \(0.00438994\pi\) |
−0.488009 | + | 0.872839i | \(0.662277\pi\) | |||||||
\(524\) | −10.8301 | −0.473115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.16010 | − | 7.20550i | −0.181389 | − | 0.314175i | ||||
\(527\) | −4.58874 | + | 7.94794i | −0.199889 | + | 0.346218i | ||||
\(528\) | −1.94622 | − | 3.37094i | −0.0846982 | − | 0.146702i | ||||
\(529\) | −18.0270 | + | 31.2237i | −0.783782 | + | 1.35755i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.2579 | −1.70365 | ||||||||
\(532\) | 20.6845 | + | 5.85105i | 0.896787 | + | 0.253675i | ||||
\(533\) | 18.2485 | 0.790432 | ||||||||
\(534\) | 13.5593 | − | 23.4853i | 0.586767 | − | 1.01631i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.965775 | − | 1.67277i | −0.0417151 | − | 0.0722527i | ||||
\(537\) | −20.9401 | + | 36.2693i | −0.903631 | + | 1.56514i | ||||
\(538\) | 7.67281 | + | 13.2897i | 0.330798 | + | 0.572960i | ||||
\(539\) | 22.2102 | 0.956661 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.39291 | − | 5.87669i | −0.145873 | − | 0.252659i | 0.783826 | − | 0.620981i | \(-0.213266\pi\) |
−0.929698 | + | 0.368322i | \(0.879932\pi\) | |||||||
\(542\) | 1.68039 | + | 2.91052i | 0.0721790 | + | 0.125018i | ||||
\(543\) | −42.3069 | −1.81556 | ||||||||
\(544\) | 2.21388 | 0.0949193 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 29.6917 | − | 51.4276i | 1.27069 | − | 2.20090i | ||||
\(547\) | −14.3705 | − | 24.8905i | −0.614439 | − | 1.06424i | −0.990483 | − | 0.137638i | \(-0.956049\pi\) |
0.376043 | − | 0.926602i | \(-0.377284\pi\) | |||||||
\(548\) | −10.2994 | + | 17.8391i | −0.439969 | + | 0.762049i | ||||
\(549\) | −35.0611 | + | 60.7275i | −1.49637 | + | 2.59179i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.9615 | + | 5.08078i | 0.765184 | + | 0.216449i | ||||
\(552\) | −23.3263 | −0.992833 | ||||||||
\(553\) | 8.72694 | − | 15.1155i | 0.371107 | − | 0.642777i | ||||
\(554\) | −15.6259 | + | 27.0648i | −0.663880 | + | 1.14987i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.39427 | − | 5.87905i | 0.143949 | − | 0.249327i | ||||
\(557\) | 5.48471 | + | 9.49979i | 0.232394 | + | 0.402519i | 0.958512 | − | 0.285051i | \(-0.0920106\pi\) |
−0.726118 | + | 0.687570i | \(0.758677\pi\) | |||||||
\(558\) | 25.7592 | 1.09047 | ||||||||
\(559\) | 26.3774 | 1.11564 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.30869 | + | 7.46287i | 0.181913 | + | 0.315083i | ||||
\(562\) | −2.93398 | −0.123762 | ||||||||
\(563\) | 1.10389 | 0.0465233 | 0.0232616 | − | 0.999729i | \(-0.492595\pi\) | ||||
0.0232616 | + | 0.999729i | \(0.492595\pi\) | |||||||
\(564\) | −10.5201 | − | 18.2214i | −0.442978 | − | 0.767260i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.34660 | + | 12.7247i | 0.308800 | + | 0.534858i | ||||
\(567\) | 27.0512 | − | 46.8541i | 1.13604 | − | 1.96769i | ||||
\(568\) | 4.16010 | − | 7.20550i | 0.174554 | − | 0.302336i | ||||
\(569\) | −3.17844 | −0.133247 | −0.0666236 | − | 0.997778i | \(-0.521223\pi\) | ||||
−0.0666236 | + | 0.997778i | \(0.521223\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.3717 | −1.39656 | −0.698282 | − | 0.715823i | \(-0.746052\pi\) | ||||
−0.698282 | + | 0.715823i | \(0.746052\pi\) | |||||||
\(572\) | 2.54349 | − | 4.40546i | 0.106349 | − | 0.184202i | ||||
\(573\) | −6.49937 | + | 11.2572i | −0.271515 | + | 0.470278i | ||||
\(574\) | 11.3428 | + | 19.6463i | 0.473440 | + | 0.820021i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.10694 | − | 5.38138i | −0.129456 | − | 0.224224i | ||||
\(577\) | 6.96331 | 0.289886 | 0.144943 | − | 0.989440i | \(-0.453700\pi\) | ||||
0.144943 | + | 0.989440i | \(0.453700\pi\) | |||||||
\(578\) | 12.0987 | 0.503241 | ||||||||
\(579\) | −14.5795 | − | 25.2525i | −0.605904 | − | 1.04946i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.1989 | 0.672045 | ||||||||
\(582\) | 6.50496 | 0.269639 | ||||||||
\(583\) | 4.44427 | + | 7.69770i | 0.184063 | + | 0.318806i | ||||
\(584\) | −3.41383 | + | 5.91293i | −0.141265 | + | 0.244679i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.29160 | − | 7.43327i | 0.177284 | − | 0.307065i | ||||
\(587\) | −5.49500 | + | 9.51761i | −0.226803 | + | 0.392834i | −0.956859 | − | 0.290553i | \(-0.906161\pi\) |
0.730056 | + | 0.683387i | \(0.239494\pi\) | |||||||
\(588\) | 52.5744 | 2.16813 | ||||||||
\(589\) | −12.9531 | + | 12.5986i | −0.533722 | + | 0.519118i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.0965 | + | 62.5210i | −1.48481 | + | 2.57177i | ||||
\(592\) | −4.69432 | + | 8.13080i | −0.192935 | + | 0.334174i | ||||
\(593\) | −19.3949 | − | 33.5929i | −0.796451 | − | 1.37949i | −0.921914 | − | 0.387396i | \(-0.873375\pi\) |
0.125462 | − | 0.992098i | \(-0.459959\pi\) | |||||||
\(594\) | 6.25491 | − | 10.8338i | 0.256642 | − | 0.444517i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.7580 | 0.932202 | ||||||||
\(597\) | 45.6280 | 1.86743 | ||||||||
\(598\) | −15.2425 | − | 26.4007i | −0.623311 | − | 1.07961i | ||||
\(599\) | −1.47262 | − | 2.55065i | −0.0601696 | − | 0.104217i | 0.834372 | − | 0.551202i | \(-0.185831\pi\) |
−0.894541 | + | 0.446986i | \(0.852497\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.62059 | −0.392432 | −0.196216 | − | 0.980561i | \(-0.562865\pi\) | ||||
−0.196216 | + | 0.980561i | \(0.562865\pi\) | |||||||
\(602\) | 16.3955 | + | 28.3978i | 0.668230 | + | 1.15741i | ||||
\(603\) | 6.00121 | − | 10.3944i | 0.244388 | − | 0.423293i | ||||
\(604\) | −5.77388 | − | 10.0007i | −0.234936 | − | 0.406921i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.0049 | − | 27.7212i | 0.650153 | − | 1.12610i | ||||
\(607\) | 32.8499 | 1.33334 | 0.666668 | − | 0.745355i | \(-0.267720\pi\) | ||||
0.666668 | + | 0.745355i | \(0.267720\pi\) | |||||||
\(608\) | 4.19432 | + | 1.18645i | 0.170102 | + | 0.0481170i | ||||
\(609\) | 64.1040 | 2.59762 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.7487 | − | 23.8134i | 0.556212 | − | 0.963388i | ||||
\(612\) | 6.87839 | + | 11.9137i | 0.278043 | + | 0.481584i | ||||
\(613\) | −5.29101 | + | 9.16430i | −0.213702 | + | 0.370143i | −0.952870 | − | 0.303378i | \(-0.901885\pi\) |
0.739168 | + | 0.673521i | \(0.235219\pi\) | |||||||
\(614\) | 2.66757 | + | 4.62036i | 0.107654 | + | 0.186463i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.32387 | 0.254796 | ||||||||
\(617\) | −14.0478 | − | 24.3314i | −0.565542 | − | 0.979547i | −0.996999 | − | 0.0774134i | \(-0.975334\pi\) |
0.431458 | − | 0.902133i | \(-0.357999\pi\) | |||||||
\(618\) | −5.52922 | − | 9.57689i | −0.222418 | − | 0.385239i | ||||
\(619\) | 2.32903 | 0.0936115 | 0.0468058 | − | 0.998904i | \(-0.485096\pi\) | ||||
0.0468058 | + | 0.998904i | \(0.485096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −37.4840 | − | 64.9241i | −1.50418 | − | 2.60532i | ||||
\(622\) | 11.6466 | − | 20.1726i | 0.466988 | − | 0.808847i | ||||
\(623\) | 22.0292 | + | 38.1557i | 0.882580 | + | 1.52867i | ||||
\(624\) | 6.02077 | − | 10.4283i | 0.241024 | − | 0.417465i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.7140 | 0.428217 | ||||||||
\(627\) | 4.16359 | + | 16.4479i | 0.166278 | + | 0.656867i | ||||
\(628\) | −10.8985 | −0.434899 | ||||||||
\(629\) | 10.3927 | − | 18.0006i | 0.414383 | − | 0.717732i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.20704 | + | 10.7509i | 0.247098 | + | 0.427987i | 0.962719 | − | 0.270502i | \(-0.0871896\pi\) |
−0.715621 | + | 0.698489i | \(0.753856\pi\) | |||||||
\(632\) | 1.76961 | − | 3.06506i | 0.0703914 | − | 0.121922i | ||||
\(633\) | −29.5433 | − | 51.1706i | −1.17424 | − | 2.03385i | ||||
\(634\) | 14.3253 | 0.568932 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.5201 | + | 18.2214i | 0.417151 | + | 0.722526i | ||||
\(637\) | 34.3545 | + | 59.5037i | 1.36117 | + | 2.35762i | ||||
\(638\) | 5.49136 | 0.217405 | ||||||||
\(639\) | 51.7007 | 2.04525 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.2279 | − | 19.4473i | 0.443476 | − | 0.768123i | −0.554469 | − | 0.832205i | \(-0.687078\pi\) |
0.997945 | + | 0.0640815i | \(0.0204118\pi\) | |||||||
\(642\) | 7.70175 | + | 13.3398i | 0.303964 | + | 0.526481i | ||||
\(643\) | −15.5465 | + | 26.9274i | −0.613096 | + | 1.06191i | 0.377619 | + | 0.925961i | \(0.376743\pi\) |
−0.990715 | + | 0.135952i | \(0.956591\pi\) | |||||||
\(644\) | 18.9486 | − | 32.8200i | 0.746681 | − | 1.29329i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.28573 | − | 2.62667i | −0.365342 | − | 0.103345i | ||||
\(647\) | 23.8320 | 0.936934 | 0.468467 | − | 0.883481i | \(-0.344806\pi\) | ||||
0.468467 | + | 0.883481i | \(0.344806\pi\) | |||||||
\(648\) | 5.48533 | − | 9.50088i | 0.215484 | − | 0.373230i | ||||
\(649\) | 4.05073 | − | 7.01607i | 0.159005 | − | 0.275405i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.0273 | + | 53.7409i | −1.21606 | + | 2.10627i | ||||
\(652\) | 5.91199 | + | 10.2399i | 0.231531 | + | 0.401024i | ||||
\(653\) | 25.2762 | 0.989135 | 0.494568 | − | 0.869139i | \(-0.335326\pi\) | ||||
0.494568 | + | 0.869139i | \(0.335326\pi\) | |||||||
\(654\) | −14.3974 | −0.562983 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.30005 | + | 3.98380i | 0.0898018 | + | 0.155541i | ||||
\(657\) | −42.4263 | −1.65521 | ||||||||
\(658\) | 34.1833 | 1.33260 | ||||||||
\(659\) | 0.0195595 | + | 0.0338780i | 0.000761929 | + | 0.00131970i | 0.866406 | − | 0.499340i | \(-0.166424\pi\) |
−0.865644 | + | 0.500660i | \(0.833091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9014 | + | 22.3458i | 0.501805 | + | 0.869151i | 0.999998 | + | 0.00208512i | \(0.000663715\pi\) |
−0.498193 | + | 0.867066i | \(0.666003\pi\) | |||||||
\(662\) | −5.28476 | + | 9.15346i | −0.205398 | + | 0.355760i | ||||
\(663\) | −13.3293 | + | 23.0870i | −0.517666 | + | 0.896624i | ||||
\(664\) | 3.28476 | 0.127473 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −58.3399 | −2.26063 | ||||||||
\(667\) | 16.4541 | − | 28.4994i | 0.637106 | − | 1.10350i | ||||
\(668\) | −8.83549 | + | 15.3035i | −0.341855 | + | 0.592111i | ||||
\(669\) | 8.57761 | + | 14.8569i | 0.331630 | + | 0.574399i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.23539 | − | 12.5321i | −0.279319 | − | 0.483795i | ||||
\(672\) | 14.9694 | 0.577458 | ||||||||
\(673\) | 24.6682 | 0.950891 | 0.475445 | − | 0.879745i | \(-0.342287\pi\) | ||||
0.475445 | + | 0.879745i | \(0.342287\pi\) | |||||||
\(674\) | −5.85931 | − | 10.1486i | −0.225692 | − | 0.390910i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.73700 | 0.105269 | ||||||||
\(677\) | −47.3964 | −1.82159 | −0.910796 | − | 0.412858i | \(-0.864531\pi\) | ||||
−0.910796 | + | 0.412858i | \(0.864531\pi\) | |||||||
\(678\) | −18.8826 | − | 32.7057i | −0.725183 | − | 1.25605i | ||||
\(679\) | −5.28417 | + | 9.15245i | −0.202788 | + | 0.351239i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.8392 | + | 22.2381i | −0.491998 | + | 0.852165i | ||||
\(682\) | −2.65790 | + | 4.60363i | −0.101776 | + | 0.176282i | ||||
\(683\) | −1.61136 | −0.0616569 | −0.0308284 | − | 0.999525i | \(-0.509815\pi\) | ||||
−0.0308284 | + | 0.999525i | \(0.509815\pi\) | |||||||
\(684\) | 6.64675 | + | 26.2575i | 0.254145 | + | 1.00398i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −25.4473 | + | 44.0760i | −0.971582 | + | 1.68283i | ||||
\(687\) | −2.34170 | + | 4.05595i | −0.0893415 | + | 0.154744i | ||||
\(688\) | 3.32461 | + | 5.75839i | 0.126750 | + | 0.219537i | ||||
\(689\) | −13.7487 | + | 23.8134i | −0.523783 | + | 0.907219i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.9474 | −1.17729 | −0.588647 | − | 0.808391i | \(-0.700339\pi\) | ||||
−0.588647 | + | 0.808391i | \(0.700339\pi\) | |||||||
\(692\) | −12.4571 | −0.473548 | ||||||||
\(693\) | 19.6479 | + | 34.0312i | 0.746362 | + | 1.29274i | ||||
\(694\) | −10.4505 | − | 18.1008i | −0.396695 | − | 0.687096i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.9987 | 0.492716 | ||||||||
\(697\) | −5.09203 | − | 8.81966i | −0.192874 | − | 0.334068i | ||||
\(698\) | 17.7409 | − | 30.7281i | 0.671502 | − | 1.16308i | ||||
\(699\) | 6.21145 | + | 10.7586i | 0.234939 | + | 0.406926i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.39904 | + | 2.42321i | −0.0528410 | + | 0.0915234i | −0.891236 | − | 0.453540i | \(-0.850161\pi\) |
0.838395 | + | 0.545063i | \(0.183494\pi\) | |||||||
\(702\) | 38.7001 | 1.46064 | ||||||||
\(703\) | 29.3363 | − | 28.5336i | 1.10644 | − | 1.07617i | ||||
\(704\) | 1.28233 | 0.0483296 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.14922 | − | 12.3828i | 0.269064 | − | 0.466033i | ||||
\(707\) | 26.0024 | + | 45.0375i | 0.977922 | + | 1.69381i | ||||
\(708\) | 9.58859 | − | 16.6079i | 0.360361 | − | 0.624164i | ||||
\(709\) | −20.7910 | − | 36.0110i | −0.780821 | − | 1.35242i | −0.931464 | − | 0.363834i | \(-0.881468\pi\) |
0.150643 | − | 0.988588i | \(-0.451866\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.9923 | 0.824777 | ||||||||
\(712\) | 4.46699 | + | 7.73705i | 0.167407 | + | 0.289958i | ||||
\(713\) | 15.9281 | + | 27.5883i | 0.596512 | + | 1.03319i | ||||
\(714\) | −33.1405 | −1.24025 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.89854 | − | 11.9486i | −0.257811 | − | 0.446541i | ||||
\(717\) | −38.1618 | + | 66.0982i | −1.42518 | + | 2.46848i | ||||
\(718\) | 2.11073 | + | 3.65589i | 0.0787717 | + | 0.136437i | ||||
\(719\) | −9.88375 | + | 17.1192i | −0.368602 | + | 0.638437i | −0.989347 | − | 0.145575i | \(-0.953497\pi\) |
0.620746 | + | 0.784012i | \(0.286830\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.9662 | 0.669096 | ||||||||
\(722\) | −16.1847 | − | 9.95273i | −0.602331 | − | 0.370402i | ||||
\(723\) | 83.2744 | 3.09701 | ||||||||
\(724\) | 6.96883 | − | 12.0704i | 0.258994 | − | 0.448592i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.1992 | − | 24.5938i | −0.526982 | − | 0.912760i | ||||
\(727\) | −8.38398 | + | 14.5215i | −0.310945 | + | 0.538572i | −0.978567 | − | 0.205928i | \(-0.933979\pi\) |
0.667622 | + | 0.744500i | \(0.267312\pi\) | |||||||
\(728\) | 9.78170 | + | 16.9424i | 0.362534 | + | 0.627927i | ||||
\(729\) | −20.6665 | −0.765426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.36029 | − | 12.7484i | −0.272230 | − | 0.471516i | ||||
\(732\) | −17.1271 | − | 29.6650i | −0.633035 | − | 1.09645i | ||||
\(733\) | −7.20019 | −0.265945 | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(734\) | 14.1648 | 0.522831 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.84233 | − | 6.65511i | 0.141630 | − | 0.245311i | ||||
\(737\) | 1.23844 | + | 2.14505i | 0.0456186 | + | 0.0790138i | ||||
\(738\) | −14.2922 | + | 24.7549i | −0.526104 | + | 0.911239i | ||||
\(739\) | 1.26645 | − | 2.19356i | 0.0465872 | − | 0.0806914i | −0.841792 | − | 0.539803i | \(-0.818499\pi\) |
0.888379 | + | 0.459111i | \(0.151832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.6257 | + | 36.5962i | −1.38222 | + | 1.34440i | ||||
\(742\) | −34.1833 | −1.25491 | ||||||||
\(743\) | −10.1601 | + | 17.5978i | −0.372738 | + | 0.645601i | −0.989986 | − | 0.141168i | \(-0.954914\pi\) |
0.617248 | + | 0.786769i | \(0.288248\pi\) | |||||||
\(744\) | −6.29160 | + | 10.8974i | −0.230661 | + | 0.399517i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.32704 | + | 14.4228i | −0.304874 | + | 0.528058i | ||||
\(747\) | 10.2055 | + | 17.6765i | 0.373401 | + | 0.646750i | ||||
\(748\) | −2.83892 | −0.103801 | ||||||||
\(749\) | −25.0254 | −0.914409 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.67855 | − | 15.0317i | −0.316685 | − | 0.548514i | 0.663109 | − | 0.748523i | \(-0.269236\pi\) |
−0.979794 | + | 0.200008i | \(0.935903\pi\) | |||||||
\(752\) | 6.93155 | 0.252768 | ||||||||
\(753\) | 13.9790 | 0.509421 | ||||||||
\(754\) | 8.49398 | + | 14.7120i | 0.309332 | + | 0.535779i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 24.0550 | + | 41.6644i | 0.874870 | + | 1.51532i | ||||
\(757\) | 21.5624 | − | 37.3472i | 0.783700 | − | 1.35741i | −0.146073 | − | 0.989274i | \(-0.546663\pi\) |
0.929773 | − | 0.368134i | \(-0.120003\pi\) | |||||||
\(758\) | 1.68345 | − | 2.91581i | 0.0611455 | − | 0.105907i | ||||
\(759\) | 29.9120 | 1.08574 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.1711 | 0.477451 | 0.238726 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238726 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(762\) | 5.91320 | − | 10.2420i | 0.214213 | − | 0.371027i | ||||
\(763\) | 11.6954 | − | 20.2571i | 0.423403 | − | 0.733355i | ||||
\(764\) | −2.14116 | − | 3.70861i | −0.0774646 | − | 0.134173i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.16010 | − | 7.20550i | −0.150310 | − | 0.260345i | ||||
\(767\) | 25.0625 | 0.904955 | ||||||||
\(768\) | 3.03544 | 0.109532 | ||||||||
\(769\) | −11.3839 | − | 19.7174i | −0.410513 | − | 0.711029i | 0.584433 | − | 0.811442i | \(-0.301317\pi\) |
−0.994946 | + | 0.100413i | \(0.967984\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 59.8738 | 2.15630 | ||||||||
\(772\) | 9.60620 | 0.345735 | ||||||||
\(773\) | −5.64054 | − | 9.76970i | −0.202876 | − | 0.351392i | 0.746578 | − | 0.665298i | \(-0.231696\pi\) |
−0.949454 | + | 0.313906i | \(0.898362\pi\) | |||||||
\(774\) | −20.6587 | + | 35.7820i | −0.742563 | + | 1.28616i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.07150 | + | 1.85590i | −0.0384647 | + | 0.0666228i | ||||
\(777\) | 70.2712 | − | 121.713i | 2.52097 | − | 4.36644i | ||||
\(778\) | −24.8151 | −0.889666 | ||||||||
\(779\) | −4.92055 | − | 19.4382i | −0.176297 | − | 0.696447i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.33462 | + | 9.23983i | −0.190888 | + | 0.330627i | ||||
\(782\) | −8.50646 | + | 14.7336i | −0.304190 | + | 0.526873i | ||||
\(783\) | 20.8882 | + | 36.1794i | 0.746484 | + | 1.29295i | ||||
\(784\) | −8.66010 | + | 14.9997i | −0.309289 | + | 0.535705i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 32.8741 | 1.17258 | ||||||||
\(787\) | −9.72573 | −0.346685 | −0.173342 | − | 0.984862i | \(-0.555457\pi\) | ||||
−0.173342 | + | 0.984862i | \(0.555457\pi\) | |||||||
\(788\) | −11.8917 | − | 20.5970i | −0.423624 | − | 0.733738i | ||||
\(789\) | 12.6277 | + | 21.8718i | 0.449558 | + | 0.778658i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.3556 | 2.18156 | ||||||||
\(792\) | 3.98412 | + | 6.90070i | 0.141570 | + | 0.245206i | ||||
\(793\) | 22.3832 | − | 38.7689i | 0.794852 | − | 1.37672i | ||||
\(794\) | 6.15043 | + | 10.6529i | 0.218271 | + | 0.378056i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.51588 | + | 13.0179i | −0.266393 | + | 0.461407i | ||||
\(797\) | −38.9279 | −1.37890 | −0.689448 | − | 0.724335i | \(-0.742147\pi\) | ||||
−0.689448 | + | 0.724335i | \(0.742147\pi\) | |||||||
\(798\) | −62.7865 | − | 17.7605i | −2.22262 | − | 0.628715i | ||||
\(799\) | −15.3456 | −0.542889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.7573 | + | 48.0771i | −0.980757 | + | 1.69872i | ||||
\(802\) | −7.52320 | − | 13.0306i | −0.265653 | − | 0.460125i | ||||
\(803\) | 4.37766 | − | 7.58233i | 0.154484 | − | 0.267575i | ||||
\(804\) | 2.93155 | + | 5.07759i | 0.103388 | + | 0.179073i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.4449 | −0.579246 | ||||||||
\(807\) | −23.2903 | − | 40.3401i | −0.819859 | − | 1.42004i | ||||
\(808\) | 5.27267 | + | 9.13253i | 0.185492 | + | 0.321281i | ||||
\(809\) | 9.10610 | 0.320153 | 0.160077 | − | 0.987105i | \(-0.448826\pi\) | ||||
0.160077 | + | 0.987105i | \(0.448826\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.2000 | − | 21.1309i | −0.428398 | − | 0.742008i | 0.568333 | − | 0.822799i | \(-0.307589\pi\) |
−0.996731 | + | 0.0807913i | \(0.974255\pi\) | |||||||
\(812\) | −10.5593 | + | 18.2892i | −0.370557 | + | 0.641824i | ||||
\(813\) | −5.10072 | − | 8.83471i | −0.178890 | − | 0.309847i | ||||
\(814\) | 6.01967 | − | 10.4264i | 0.210989 | − | 0.365444i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.72010 | −0.235250 | ||||||||
\(817\) | −7.11242 | − | 28.0970i | −0.248832 | − | 0.982991i | ||||
\(818\) | −26.0340 | −0.910256 | ||||||||
\(819\) | −60.7823 | + | 105.278i | −2.12391 | + | 3.67871i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8680 | + | 36.1444i | 0.728297 | + | 1.26145i | 0.957603 | + | 0.288092i | \(0.0930210\pi\) |
−0.229306 | + | 0.973354i | \(0.573646\pi\) | |||||||
\(822\) | 31.2632 | − | 54.1495i | 1.09043 | − | 1.88868i | ||||
\(823\) | 2.58190 | + | 4.47198i | 0.0899994 | + | 0.155884i | 0.907511 | − | 0.420029i | \(-0.137980\pi\) |
−0.817511 | + | 0.575913i | \(0.804647\pi\) | |||||||
\(824\) | 3.64311 | 0.126914 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.5782 | + | 26.9822i | 0.542035 | + | 0.938832i | ||||
\(827\) | 21.8677 | + | 37.8760i | 0.760415 | + | 1.31708i | 0.942637 | + | 0.333820i | \(0.108338\pi\) |
−0.182222 | + | 0.983257i | \(0.558329\pi\) | |||||||
\(828\) | 47.7515 | 1.65948 | ||||||||
\(829\) | 7.63968 | 0.265337 | 0.132669 | − | 0.991160i | \(-0.457645\pi\) | ||||
0.132669 | + | 0.991160i | \(0.457645\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 47.4314 | − | 82.1535i | 1.64538 | − | 2.84987i | ||||
\(832\) | 1.98349 | + | 3.43551i | 0.0687653 | + | 0.119105i | ||||
\(833\) | 19.1724 | − | 33.2076i | 0.664285 | − | 1.15058i | ||||
\(834\) | −10.3031 | + | 17.8455i | −0.356767 | + | 0.617939i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.37850 | − | 1.52142i | −0.186019 | − | 0.0526196i | ||||
\(837\) | −40.4409 | −1.39784 | ||||||||
\(838\) | 4.84820 | − | 8.39733i | 0.167478 | − | 0.290081i | ||||
\(839\) | −2.92005 | + | 5.05767i | −0.100811 | + | 0.174610i | −0.912019 | − | 0.410148i | \(-0.865477\pi\) |
0.811208 | + | 0.584758i | \(0.198810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.33083 | − | 9.23326i | 0.183822 | − | 0.318388i | ||||
\(842\) | 9.04154 | + | 15.6604i | 0.311592 | + | 0.539694i | ||||
\(843\) | 8.90590 | 0.306736 | ||||||||
\(844\) | 19.4656 | 0.670034 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 21.5359 | + | 37.3013i | 0.740420 | + | 1.28245i | ||||
\(847\) | 46.1378 | 1.58531 | ||||||||
\(848\) | −6.93155 | −0.238030 | ||||||||
\(849\) | −22.3001 | − | 38.6250i | −0.765339 | − | 1.32561i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0743 | − | 62.4824i | −1.23661 | − | 2.14187i | ||||
\(852\) | −12.6277 | + | 21.8718i | −0.432618 | + | 0.749317i | ||||
\(853\) | −11.6485 | + | 20.1758i | −0.398837 | + | 0.690805i | −0.993583 | − | 0.113108i | \(-0.963919\pi\) |
0.594746 | + | 0.803914i | \(0.297253\pi\) | |||||||
\(854\) | 55.6513 | 1.90435 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.07456 | −0.173445 | ||||||||
\(857\) | 10.5000 | − | 18.1865i | 0.358673 | − | 0.621240i | −0.629066 | − | 0.777352i | \(-0.716563\pi\) |
0.987739 | + | 0.156112i | \(0.0498959\pi\) | |||||||
\(858\) | −7.72062 | + | 13.3725i | −0.263577 | + | 0.456530i | ||||
\(859\) | −27.0164 | − | 46.7937i | −0.921786 | − | 1.59658i | −0.796650 | − | 0.604441i | \(-0.793397\pi\) |
−0.125136 | − | 0.992140i | \(-0.539937\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.4304 | − | 59.6352i | −1.17338 | − | 2.03236i | ||||
\(862\) | 18.1796 | 0.619200 | ||||||||
\(863\) | 49.3001 | 1.67819 | 0.839097 | − | 0.543981i | \(-0.183084\pi\) | ||||
0.839097 | + | 0.543981i | \(0.183084\pi\) | |||||||
\(864\) | 4.87777 | + | 8.44854i | 0.165945 | + | 0.287425i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.71399 | 0.160188 | ||||||||
\(867\) | −36.7249 | −1.24724 | ||||||||
\(868\) | −10.2217 | − | 17.7045i | −0.346947 | − | 0.600930i | ||||
\(869\) | −2.26923 | + | 3.93042i | −0.0769783 | + | 0.133330i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.83122 | + | 6.63587i | −0.129816 | + | 0.224848i | ||||
\(872\) | 2.37155 | − | 4.10765i | 0.0803109 | − | 0.139102i | ||||
\(873\) | −13.3164 | −0.450691 | ||||||||
\(874\) | −24.0119 | + | 23.3549i | −0.812216 | + | 0.789992i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.3625 | − | 17.9483i | 0.350116 | − | 0.606418i | ||||
\(877\) | −26.5645 | + | 46.0111i | −0.897020 | + | 1.55368i | −0.0657348 | + | 0.997837i | \(0.520939\pi\) |
−0.831285 | + | 0.555847i | \(0.812394\pi\) | |||||||
\(878\) | −7.08554 | − | 12.2725i | −0.239125 | − | 0.414177i | ||||
\(879\) | −13.0269 | + | 22.5632i | −0.439386 | + | 0.761038i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.71737 | −0.293696 | −0.146848 | − | 0.989159i | \(-0.546913\pi\) | ||||
−0.146848 | + | 0.989159i | \(0.546913\pi\) | |||||||
\(882\) | −107.626 | −3.62394 | ||||||||
\(883\) | 18.5732 | + | 32.1697i | 0.625038 | + | 1.08260i | 0.988534 | + | 0.151001i | \(0.0482497\pi\) |
−0.363496 | + | 0.931596i | \(0.618417\pi\) | |||||||
\(884\) | −4.39122 | − | 7.60581i | −0.147693 | − | 0.255811i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.4962 | −0.419818 | ||||||||
\(887\) | 4.01295 | + | 6.95063i | 0.134742 | + | 0.233379i | 0.925499 | − | 0.378751i | \(-0.123646\pi\) |
−0.790757 | + | 0.612130i | \(0.790313\pi\) | |||||||
\(888\) | 14.2493 | − | 24.6805i | 0.478176 | − | 0.828225i | ||||
\(889\) | 9.60694 | + | 16.6397i | 0.322206 | + | 0.558078i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.03401 | + | 12.1833i | −0.235648 | + | 0.408155i | ||||
\(892\) | −5.65165 | −0.189231 | ||||||||
\(893\) | −29.0731 | − | 8.22396i | −0.972896 | − | 0.275204i | ||||
\(894\) | −69.0804 | −2.31039 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.46578 | + | 4.27085i | −0.0823758 | + | 0.142679i | ||||
\(897\) | 46.2676 | + | 80.1378i | 1.54483 | + | 2.67572i | ||||
\(898\) | −14.6663 | + | 25.4028i | −0.489421 | + | 0.847702i | ||||
\(899\) | −8.87605 | − | 15.3738i | −0.296033 | − | 0.512744i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3456 | 0.511237 | ||||||||
\(902\) | −2.94942 | − | 5.10855i | −0.0982050 | − | 0.170096i | ||||
\(903\) | −49.7675 | − | 86.1998i | −1.65616 | − | 2.86855i | ||||
\(904\) | 12.4414 | 0.413796 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.5263 | + | 30.3564i | 0.582271 | + | 1.00852i | ||||
\(907\) | −29.2999 | + | 50.7489i | −0.972887 | + | 1.68509i | −0.286149 | + | 0.958185i | \(0.592375\pi\) |
−0.686738 | + | 0.726905i | \(0.740958\pi\) | |||||||
\(908\) | −4.22976 | − | 7.32616i | −0.140369 | − | 0.243127i | ||||
\(909\) | −32.7637 | + | 56.7484i | −1.08670 | + | 1.88223i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.2835 | −1.33465 | −0.667326 | − | 0.744766i | \(-0.732561\pi\) | ||||
−0.667326 | + | 0.744766i | \(0.732561\pi\) | |||||||
\(912\) | −12.7316 | − | 3.60140i | −0.421585 | − | 0.119254i | ||||
\(913\) | −4.21214 | −0.139401 | ||||||||
\(914\) | 13.1063 | − | 22.7008i | 0.433518 | − | 0.750876i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.771454 | − | 1.33620i | −0.0254896 | − | 0.0441492i | ||||
\(917\) | −26.7046 | + | 46.2537i | −0.881863 | + | 1.52743i | ||||
\(918\) | −10.7988 | − | 18.7041i | −0.356413 | − | 0.617326i | ||||
\(919\) | −0.0107924 | −0.000356010 | −0.000178005 | − | 1.00000i | \(-0.500057\pi\) | ||||
−0.000178005 | 1.00000i | \(0.500057\pi\) | ||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.09723 | − | 14.0248i | −0.266813 | − | 0.462134i | ||||
\(922\) | 4.85641 | + | 8.41155i | 0.159937 | + | 0.277020i | ||||
\(923\) | −33.0061 | −1.08641 | ||||||||
\(924\) | −19.1957 | −0.631493 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.67073 | − | 4.62584i | 0.0877656 | − | 0.152015i | ||||
\(927\) | 11.3189 | + | 19.6050i | 0.371763 | + | 0.643912i | ||||
\(928\) | −2.14116 | + | 3.70861i | −0.0702872 | + | 0.121741i | ||||
\(929\) | −25.0297 | + | 43.3526i | −0.821196 | + | 1.42235i | 0.0835955 | + | 0.996500i | \(0.473360\pi\) |
−0.904792 | + | 0.425854i | \(0.859974\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.1197 | − | 52.6389i | 1.77370 | − | 1.72517i | ||||
\(932\) | −4.09263 | −0.134058 | ||||||||
\(933\) | −35.3527 | + | 61.2326i | −1.15739 | + | 2.00467i | ||||
\(934\) | 15.1821 | − | 26.2961i | 0.496773 | − | 0.860436i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.3252 | + | 21.3479i | −0.402862 | + | 0.697777i | ||||
\(937\) | 2.76238 | + | 4.78458i | 0.0902429 | + | 0.156305i | 0.907613 | − | 0.419807i | \(-0.137902\pi\) |
−0.817370 | + | 0.576113i | \(0.804569\pi\) | |||||||
\(938\) | −9.52554 | −0.311020 | ||||||||
\(939\) | −32.5216 | −1.06130 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.07956 | − | 1.86985i | −0.0351926 | − | 0.0609554i | 0.847893 | − | 0.530168i | \(-0.177871\pi\) |
−0.883085 | + | 0.469213i | \(0.844538\pi\) | |||||||
\(942\) | 33.0818 | 1.07786 | ||||||||
\(943\) | −35.3502 | −1.15116 | ||||||||
\(944\) | 3.15888 | + | 5.47135i | 0.102813 | + | 0.178077i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.26325 | − | 7.38416i | −0.138610 | − | 0.240080i | ||||
\(947\) | 12.0501 | − | 20.8714i | 0.391576 | − | 0.678229i | −0.601082 | − | 0.799187i | \(-0.705263\pi\) |
0.992658 | + | 0.120958i | \(0.0385968\pi\) | |||||||
\(948\) | −5.37155 | + | 9.30380i | −0.174460 | + | 0.302173i | ||||
\(949\) | 27.0853 | 0.879225 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.4837 | −1.41006 | ||||||||
\(952\) | 5.45893 | − | 9.45515i | 0.176925 | − | 0.306443i | ||||
\(953\) | −27.5618 | + | 47.7384i | −0.892814 | + | 1.54640i | −0.0563275 | + | 0.998412i | \(0.517939\pi\) |
−0.836487 | + | 0.547987i | \(0.815394\pi\) | |||||||
\(954\) | −21.5359 | − | 37.3013i | −0.697251 | − | 1.20767i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.5721 | − | 21.7755i | −0.406610 | − | 0.704270i | ||||
\(957\) | −16.6687 | −0.538822 | ||||||||
\(958\) | −1.98999 | −0.0642938 | ||||||||
\(959\) | 50.7921 | + | 87.9745i | 1.64016 | + | 2.84085i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.8154 | −0.445658 | ||||||||
\(962\) | 37.2446 | 1.20082 | ||||||||
\(963\) | −15.7663 | − | 27.3081i | −0.508063 | − | 0.879991i | ||||
\(964\) | −13.7170 | + | 23.7586i | −0.441796 | + | 0.765213i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −57.5174 | + | 99.6231i | −1.85059 | + | 3.20532i | ||||
\(967\) | −28.3445 | + | 49.0941i | −0.911498 | + | 1.57876i | −0.0995477 | + | 0.995033i | \(0.531740\pi\) |
−0.811950 | + | 0.583727i | \(0.801594\pi\) | |||||||
\(968\) | 9.35563 | 0.300701 | ||||||||
\(969\) | 28.1862 | + | 7.97308i | 0.905472 | + | 0.256132i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.09923 | − | 1.90392i | 0.0352759 | − | 0.0610996i | −0.847848 | − | 0.530239i | \(-0.822102\pi\) |
0.883124 | + | 0.469139i | \(0.155436\pi\) | |||||||
\(972\) | −2.01709 | + | 3.49370i | −0.0646982 | + | 0.112061i | ||||
\(973\) | −16.7390 | − | 28.9928i | −0.536629 | − | 0.929468i | ||||
\(974\) | −14.6051 | + | 25.2968i | −0.467978 | + | 0.810561i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.2848 | 0.361216 | ||||||||
\(977\) | 23.7523 | 0.759904 | 0.379952 | − | 0.925006i | \(-0.375940\pi\) | ||||
0.379952 | + | 0.925006i | \(0.375940\pi\) | |||||||
\(978\) | −17.9455 | − | 31.0825i | −0.573833 | − | 0.993908i | ||||
\(979\) | −5.72815 | − | 9.92145i | −0.183073 | − | 0.317091i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.4731 | 0.941003 | ||||||||
\(982\) | −8.44853 | − | 14.6333i | −0.269604 | − | 0.466967i | ||||
\(983\) | −8.26543 | + | 14.3161i | −0.263626 | + | 0.456614i | −0.967203 | − | 0.254005i | \(-0.918252\pi\) |
0.703577 | + | 0.710620i | \(0.251585\pi\) | |||||||
\(984\) | −6.98165 | − | 12.0926i | −0.222567 | − | 0.385497i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.74028 | − | 8.21041i | 0.150961 | − | 0.261473i | ||||
\(987\) | −103.761 | −3.30276 | ||||||||
\(988\) | −4.24334 | − | 16.7630i | −0.134999 | − | 0.533301i | ||||
\(989\) | −51.0970 | −1.62479 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4564 | − | 18.1109i | 0.332157 | − | 0.575313i | −0.650777 | − | 0.759269i | \(-0.725557\pi\) |
0.982935 | + | 0.183956i | \(0.0588903\pi\) | |||||||
\(992\) | −2.07272 | − | 3.59005i | −0.0658088 | − | 0.113984i | ||||
\(993\) | 16.0415 | − | 27.7848i | 0.509063 | − | 0.881723i | ||||
\(994\) | −20.5157 | − | 35.5343i | −0.650719 | − | 1.12708i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.97067 | −0.315933 | ||||||||
\(997\) | 1.31436 | + | 2.27654i | 0.0416263 | + | 0.0720989i | 0.886088 | − | 0.463517i | \(-0.153413\pi\) |
−0.844462 | + | 0.535616i | \(0.820079\pi\) | |||||||
\(998\) | 0.629662 | + | 1.09061i | 0.0199316 | + | 0.0345225i | ||||
\(999\) | 91.5912 | 2.89782 |
(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.m.201.1 | yes | 8 | |
5.2 | odd | 4 | 950.2.j.i.49.8 | 16 | |||
5.3 | odd | 4 | 950.2.j.i.49.1 | 16 | |||
5.4 | even | 2 | 950.2.e.l.201.4 | ✓ | 8 | ||
19.7 | even | 3 | inner | 950.2.e.m.501.1 | yes | 8 | |
95.7 | odd | 12 | 950.2.j.i.349.1 | 16 | |||
95.64 | even | 6 | 950.2.e.l.501.4 | yes | 8 | ||
95.83 | odd | 12 | 950.2.j.i.349.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.l.201.4 | ✓ | 8 | 5.4 | even | 2 | ||
950.2.e.l.501.4 | yes | 8 | 95.64 | even | 6 | ||
950.2.e.m.201.1 | yes | 8 | 1.1 | even | 1 | trivial | |
950.2.e.m.501.1 | yes | 8 | 19.7 | even | 3 | inner | |
950.2.j.i.49.1 | 16 | 5.3 | odd | 4 | |||
950.2.j.i.49.8 | 16 | 5.2 | odd | 4 | |||
950.2.j.i.349.1 | 16 | 95.7 | odd | 12 | |||
950.2.j.i.349.8 | 16 | 95.83 | odd | 12 |