Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(53,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.ch (of order \(12\), degree \(4\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 242.2 | ||
Character | \(\chi\) | \(=\) | 945.242 |
Dual form | 945.2.ch.a.863.2 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42868 | − | 0.650762i | −1.71733 | − | 0.460158i | −0.740131 | − | 0.672463i | \(-0.765236\pi\) |
−0.977204 | + | 0.212305i | \(0.931903\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.74293 | + | 2.16098i | 1.87147 | + | 1.08049i | ||||
\(5\) | 1.11889 | + | 1.93600i | 0.500383 | + | 0.865804i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.654856 | − | 2.56343i | −0.247512 | − | 0.968885i | ||||
\(8\) | −4.12826 | − | 4.12826i | −1.45956 | − | 1.45956i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.45755 | − | 5.43004i | −0.460917 | − | 1.71713i | ||||
\(11\) | −4.33235 | − | 2.50128i | −1.30625 | − | 0.754165i | −0.324783 | − | 0.945789i | \(-0.605291\pi\) |
−0.981468 | + | 0.191624i | \(0.938625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.46310 | − | 4.46310i | 1.23784 | − | 1.23784i | 0.276960 | − | 0.960882i | \(-0.410673\pi\) |
0.960882 | − | 0.276960i | \(-0.0893268\pi\) | |||||||
\(14\) | −0.0777484 | + | 6.65190i | −0.0207791 | + | 1.77779i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.01772 | + | 5.22685i | 0.754431 | + | 1.30671i | ||||
\(17\) | 0.263965 | + | 0.985130i | 0.0640209 | + | 0.238929i | 0.990520 | − | 0.137367i | \(-0.0438641\pi\) |
−0.926499 | + | 0.376296i | \(0.877197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.51117 | + | 3.18187i | −1.26435 | + | 0.729972i | −0.973913 | − | 0.226922i | \(-0.927134\pi\) |
−0.290436 | + | 0.956894i | \(0.593800\pi\) | |||||||
\(20\) | 0.00427246 | + | 9.66421i | 0.000955351 | + | 2.16098i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.89413 | + | 8.89413i | 1.89624 | + | 1.89624i | ||||
\(23\) | 0.0712184 | − | 0.265791i | 0.0148501 | − | 0.0554212i | −0.958103 | − | 0.286423i | \(-0.907534\pi\) |
0.972953 | + | 0.231002i | \(0.0742004\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.49617 | + | 4.33234i | −0.499234 | + | 0.866467i | ||||
\(26\) | −13.7438 | + | 7.93501i | −2.69539 | + | 1.55618i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.08844 | − | 11.0099i | 0.583661 | − | 2.08067i | ||||
\(29\) | −4.05409 | −0.752826 | −0.376413 | − | 0.926452i | \(-0.622843\pi\) | ||||
−0.376413 | + | 0.926452i | \(0.622843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.12640 | + | 3.68302i | −0.381912 | + | 0.661491i | −0.991336 | − | 0.131354i | \(-0.958068\pi\) |
0.609424 | + | 0.792845i | \(0.291401\pi\) | |||||||
\(32\) | −0.905549 | − | 3.37955i | −0.160080 | − | 0.597426i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.56434i | − | 0.439781i | ||||||
\(35\) | 4.23008 | − | 4.13599i | 0.715014 | − | 0.699110i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.349026 | + | 1.30258i | −0.0573795 | + | 0.214143i | −0.988663 | − | 0.150153i | \(-0.952024\pi\) |
0.931283 | + | 0.364296i | \(0.118690\pi\) | |||||||
\(38\) | 15.4555 | − | 4.14129i | 2.50721 | − | 0.671805i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.37323 | − | 12.6114i | 0.533354 | − | 1.99403i | ||||
\(41\) | − | 2.13805i | − | 0.333907i | −0.985965 | − | 0.166953i | \(-0.946607\pi\) | ||
0.985965 | − | 0.166953i | \(-0.0533930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.22969 | − | 1.22969i | 0.187526 | − | 0.187526i | −0.607100 | − | 0.794626i | \(-0.707667\pi\) |
0.794626 | + | 0.607100i | \(0.207667\pi\) | |||||||
\(44\) | −10.8104 | − | 18.7242i | −1.62974 | − | 2.82279i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.345933 | + | 0.599174i | −0.0510051 | + | 0.0883433i | ||||
\(47\) | −7.54793 | − | 2.02246i | −1.10098 | − | 0.295007i | −0.337816 | − | 0.941212i | \(-0.609688\pi\) |
−0.763163 | + | 0.646206i | \(0.776355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.14233 | + | 3.35735i | −0.877475 | + | 0.479622i | ||||
\(50\) | 8.88171 | − | 8.89743i | 1.25606 | − | 1.25829i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 26.3498 | − | 7.06040i | 3.65405 | − | 0.979101i | ||||
\(53\) | −0.0406498 | + | 0.0108921i | −0.00558367 | + | 0.00149614i | −0.261610 | − | 0.965174i | \(-0.584253\pi\) |
0.256026 | + | 0.966670i | \(0.417587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.00494526 | − | 11.1861i | −0.000666819 | − | 1.50833i | ||||
\(56\) | −7.87908 | + | 13.2859i | −1.05289 | + | 1.77540i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.84608 | + | 2.63825i | 1.29285 | + | 0.346419i | ||||
\(59\) | 5.17288 | − | 8.95970i | 0.673452 | − | 1.16645i | −0.303467 | − | 0.952842i | \(-0.598144\pi\) |
0.976919 | − | 0.213611i | \(-0.0685226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.02281 | + | 1.77155i | 0.130957 | + | 0.226824i | 0.924046 | − | 0.382282i | \(-0.124862\pi\) |
−0.793089 | + | 0.609106i | \(0.791528\pi\) | |||||||
\(62\) | 7.56110 | − | 7.56110i | 0.960261 | − | 0.960261i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 3.27376i | − | 0.409220i | ||||||
\(65\) | 13.6343 | + | 3.64683i | 1.69112 | + | 0.452334i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6943 | + | 3.66938i | −1.67303 | + | 0.448286i | −0.965924 | − | 0.258824i | \(-0.916665\pi\) |
−0.707103 | + | 0.707111i | \(0.749998\pi\) | |||||||
\(68\) | −1.14085 | + | 4.25770i | −0.138348 | + | 0.516322i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.9650 | + | 7.29222i | −1.54962 | + | 0.871587i | ||||
\(71\) | 5.23525i | 0.621310i | 0.950523 | + | 0.310655i | \(0.100548\pi\) | ||||
−0.950523 | + | 0.310655i | \(0.899452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.69518 | − | 10.0585i | −0.315447 | − | 1.17726i | −0.923573 | − | 0.383423i | \(-0.874745\pi\) |
0.608126 | − | 0.793841i | \(-0.291922\pi\) | |||||||
\(74\) | 1.69534 | − | 2.93642i | 0.197079 | − | 0.341352i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27.5039 | −3.15491 | ||||||||
\(77\) | −3.57479 | + | 12.7436i | −0.407385 | + | 1.45227i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5365 | + | 7.23793i | −1.41046 | + | 0.814331i | −0.995432 | − | 0.0954764i | \(-0.969563\pi\) |
−0.415031 | + | 0.909807i | \(0.636229\pi\) | |||||||
\(80\) | −6.74267 | + | 11.6906i | −0.753853 | + | 1.30705i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.39136 | + | 5.19263i | −0.153650 | + | 0.573430i | ||||
\(83\) | −9.98593 | − | 9.98593i | −1.09610 | − | 1.09610i | −0.994863 | − | 0.101235i | \(-0.967721\pi\) |
−0.101235 | − | 0.994863i | \(-0.532279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.61186 | + | 1.61329i | −0.174831 | + | 0.174986i | ||||
\(86\) | −3.78676 | + | 2.18628i | −0.408336 | + | 0.235753i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.55911 | + | 28.2110i | 0.805803 | + | 3.00730i | ||||
\(89\) | 2.39266 | + | 4.14421i | 0.253622 | + | 0.439285i | 0.964520 | − | 0.264009i | \(-0.0850449\pi\) |
−0.710899 | + | 0.703294i | \(0.751712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.3635 | − | 8.51815i | −1.50571 | − | 0.892945i | ||||
\(92\) | 0.840935 | − | 0.840935i | 0.0876735 | − | 0.0876735i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.0154 | + | 9.82382i | 1.75500 | + | 1.01325i | ||||
\(95\) | −12.3265 | − | 7.10944i | −1.26467 | − | 0.729413i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.238144 | + | 0.238144i | 0.0241798 | + | 0.0241798i | 0.719093 | − | 0.694914i | \(-0.244557\pi\) |
−0.694914 | + | 0.719093i | \(0.744557\pi\) | |||||||
\(98\) | 17.1026 | − | 4.15673i | 1.72762 | − | 0.419893i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.7051 | + | 10.8215i | −1.87051 | + | 1.08215i | ||||
\(101\) | 9.68543 | + | 5.59189i | 0.963736 | + | 0.556413i | 0.897321 | − | 0.441379i | \(-0.145510\pi\) |
0.0664154 | + | 0.997792i | \(0.478844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2176 | − | 2.73780i | −1.00677 | − | 0.269763i | −0.282490 | − | 0.959270i | \(-0.591160\pi\) |
−0.724279 | + | 0.689507i | \(0.757827\pi\) | |||||||
\(104\) | −36.8496 | −3.61340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.105813 | 0.0102775 | ||||||||
\(107\) | 13.4143 | + | 3.59435i | 1.29681 | + | 0.347479i | 0.840242 | − | 0.542211i | \(-0.182413\pi\) |
0.456565 | + | 0.889690i | \(0.349079\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.36589 | + | 1.94330i | 0.322394 | + | 0.186134i | 0.652459 | − | 0.757824i | \(-0.273737\pi\) |
−0.330065 | + | 0.943958i | \(0.607071\pi\) | |||||||
\(110\) | −7.26746 | + | 27.1706i | −0.692925 | + | 2.59061i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.4225 | − | 11.1586i | 1.07932 | − | 1.05438i | ||||
\(113\) | −12.1383 | − | 12.1383i | −1.14187 | − | 1.14187i | −0.988107 | − | 0.153768i | \(-0.950859\pi\) |
−0.153768 | − | 0.988107i | \(-0.549141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.594256 | − | 0.159512i | 0.0554146 | − | 0.0148746i | ||||
\(116\) | −15.1742 | − | 8.76082i | −1.40889 | − | 0.813422i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.3939 | + | 18.3939i | −1.69330 | + | 1.69330i | ||||
\(119\) | 2.35245 | − | 1.32177i | 0.215649 | − | 0.121167i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.01282 | + | 12.1466i | 0.637529 | + | 1.10423i | ||||
\(122\) | −1.33121 | − | 4.96813i | −0.120522 | − | 0.449794i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.9179 | + | 9.19021i | −1.42947 | + | 0.825305i | ||||
\(125\) | −11.1803 | + | 0.0148282i | −0.999999 | + | 0.00132627i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.35613 | − | 2.35613i | −0.209072 | − | 0.209072i | 0.594801 | − | 0.803873i | \(-0.297231\pi\) |
−0.803873 | + | 0.594801i | \(0.797231\pi\) | |||||||
\(128\) | −3.94153 | + | 14.7100i | −0.348386 | + | 1.30019i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −30.7400 | − | 17.7296i | −2.69608 | − | 1.55499i | ||||
\(131\) | −4.13205 | + | 2.38564i | −0.361019 | + | 0.208435i | −0.669528 | − | 0.742787i | \(-0.733503\pi\) |
0.308509 | + | 0.951222i | \(0.400170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7655 | + | 12.0438i | 1.02020 | + | 1.04433i | ||||
\(134\) | 35.6470 | 3.07943 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.97716 | − | 5.15658i | 0.255289 | − | 0.442173i | ||||
\(137\) | 0.201380 | + | 0.751559i | 0.0172050 | + | 0.0642100i | 0.973995 | − | 0.226571i | \(-0.0727515\pi\) |
−0.956790 | + | 0.290781i | \(0.906085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.14654i | 0.0972483i | 0.998817 | + | 0.0486241i | \(0.0154837\pi\) | ||||
−0.998817 | + | 0.0486241i | \(0.984516\pi\) | |||||||
\(140\) | 24.7707 | − | 6.33961i | 2.09351 | − | 0.535795i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.40691 | − | 12.7147i | 0.285901 | − | 1.06700i | ||||
\(143\) | −30.4992 | + | 8.17223i | −2.55047 | + | 0.683396i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.53608 | − | 7.84871i | −0.376701 | − | 0.651800i | ||||
\(146\) | 26.1829i | 2.16691i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.12123 | + | 4.12123i | −0.338763 | + | 0.338763i | ||||
\(149\) | −9.23325 | − | 15.9925i | −0.756418 | − | 1.31015i | −0.944666 | − | 0.328032i | \(-0.893614\pi\) |
0.188249 | − | 0.982121i | \(-0.439719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.38096 | − | 11.0522i | 0.519275 | − | 0.899411i | −0.480474 | − | 0.877009i | \(-0.659535\pi\) |
0.999749 | − | 0.0224023i | \(-0.00713146\pi\) | |||||||
\(152\) | 35.8871 | + | 9.61592i | 2.91083 | + | 0.779954i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.9751 | − | 28.6238i | 1.36789 | − | 2.30657i | ||||
\(155\) | −9.50953 | + | 0.00420408i | −0.763824 | + | 0.000337680i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.09943 | − | 1.36639i | 0.406979 | − | 0.109050i | −0.0495210 | − | 0.998773i | \(-0.515769\pi\) |
0.456500 | + | 0.889723i | \(0.349103\pi\) | |||||||
\(158\) | 35.1572 | − | 9.42034i | 2.79696 | − | 0.749442i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.52960 | − | 5.53449i | 0.437153 | − | 0.437540i | ||||
\(161\) | −0.727973 | − | 0.00850867i | −0.0573723 | − | 0.000670577i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.17175 | + | 2.18961i | 0.640061 | + | 0.171504i | 0.564231 | − | 0.825617i | \(-0.309173\pi\) |
0.0758299 | + | 0.997121i | \(0.475839\pi\) | |||||||
\(164\) | 4.62028 | − | 8.00256i | 0.360783 | − | 0.624895i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7541 | + | 30.7511i | 1.37799 | + | 2.38674i | ||||
\(167\) | −0.227335 | + | 0.227335i | −0.0175917 | + | 0.0175917i | −0.715848 | − | 0.698256i | \(-0.753960\pi\) |
0.698256 | + | 0.715848i | \(0.253960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 26.8385i | − | 2.06450i | ||||||
\(170\) | 4.96456 | − | 2.86922i | 0.380764 | − | 0.220059i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.25998 | − | 1.94531i | 0.553569 | − | 0.148328i | ||||
\(173\) | 4.12905 | − | 15.4098i | 0.313926 | − | 1.17159i | −0.611060 | − | 0.791585i | \(-0.709256\pi\) |
0.924985 | − | 0.380003i | \(-0.124077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.7403 | + | 3.56170i | 0.963073 | + | 0.269239i | ||||
\(176\) | − | 30.1927i | − | 2.27586i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.11411 | − | 11.6220i | −0.233412 | − | 0.871106i | ||||
\(179\) | −2.02163 | + | 3.50157i | −0.151104 | + | 0.261720i | −0.931634 | − | 0.363399i | \(-0.881616\pi\) |
0.780530 | + | 0.625119i | \(0.214950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.55204 | −0.709998 | −0.354999 | − | 0.934867i | \(-0.615519\pi\) | ||||
−0.354999 | + | 0.934867i | \(0.615519\pi\) | |||||||
\(182\) | 29.3411 | + | 30.0351i | 2.17491 | + | 2.22635i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.39126 | + | 0.803244i | −0.102565 | + | 0.0592160i | ||||
\(185\) | −2.91231 | + | 0.781733i | −0.214118 | + | 0.0574741i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.32050 | − | 4.92818i | 0.0965646 | − | 0.360384i | ||||
\(188\) | −23.8809 | − | 23.8809i | −1.74169 | − | 1.74169i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.3105 | + | 25.2881i | 1.83622 | + | 1.83459i | ||||
\(191\) | −17.0237 | + | 9.82861i | −1.23179 | + | 0.711173i | −0.967403 | − | 0.253243i | \(-0.918503\pi\) |
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.43496 | − | 5.35533i | −0.103290 | − | 0.385485i | 0.894855 | − | 0.446356i | \(-0.147279\pi\) |
−0.998146 | + | 0.0608716i | \(0.980612\pi\) | |||||||
\(194\) | −0.423399 | − | 0.733349i | −0.0303983 | − | 0.0526514i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.2455 | − | 0.707125i | −2.16039 | − | 0.0505089i | ||||
\(197\) | −7.68996 | + | 7.68996i | −0.547887 | + | 0.547887i | −0.925829 | − | 0.377942i | \(-0.876632\pi\) |
0.377942 | + | 0.925829i | \(0.376632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.99916 | + | 4.04097i | 0.496157 | + | 0.286457i | 0.727125 | − | 0.686505i | \(-0.240856\pi\) |
−0.230968 | + | 0.972961i | \(0.574189\pi\) | |||||||
\(200\) | 28.1898 | − | 7.58016i | 1.99332 | − | 0.535998i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.8838 | − | 19.8838i | −1.39902 | − | 1.39902i | ||||
\(203\) | 2.65485 | + | 10.3924i | 0.186334 | + | 0.729402i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.13925 | − | 2.39224i | 0.289098 | − | 0.167081i | ||||
\(206\) | 23.0336 | + | 13.2984i | 1.60483 | + | 0.926546i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 36.7964 | + | 9.85956i | 2.55137 | + | 0.683637i | ||||
\(209\) | 31.8351 | 2.20208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4885 | 0.928590 | 0.464295 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464295 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(212\) | −0.175687 | − | 0.0470751i | −0.0120662 | − | 0.00323313i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −30.2399 | − | 17.4590i | −2.06716 | − | 1.19347i | ||||
\(215\) | 3.75656 | + | 1.00479i | 0.256196 | + | 0.0685260i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.8337 | + | 3.03901i | 0.735436 | + | 0.206302i | ||||
\(218\) | −6.91003 | − | 6.91003i | −0.468006 | − | 0.468006i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 24.1544 | − | 41.8794i | 1.62849 | − | 2.82351i | ||||
\(221\) | 5.57484 | + | 3.21863i | 0.375004 | + | 0.216509i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.94364 | + | 2.94364i | −0.197121 | + | 0.197121i | −0.798765 | − | 0.601644i | \(-0.794513\pi\) |
0.601644 | + | 0.798765i | \(0.294513\pi\) | |||||||
\(224\) | −8.07024 | + | 4.53443i | −0.539215 | + | 0.302969i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.5809 | + | 37.3792i | 1.43554 | + | 2.48642i | ||||
\(227\) | −5.05613 | − | 18.8697i | −0.335587 | − | 1.25243i | −0.903231 | − | 0.429155i | \(-0.858811\pi\) |
0.567644 | − | 0.823274i | \(-0.307855\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00222 | + | 3.46538i | −0.396638 | + | 0.228999i | −0.685032 | − | 0.728513i | \(-0.740212\pi\) |
0.288394 | + | 0.957512i | \(0.406879\pi\) | |||||||
\(230\) | −1.54706 | 0.000683942i | −0.102010 | 4.50978e-5i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.7363 | + | 16.7363i | 1.09879 | + | 1.09879i | ||||
\(233\) | 5.51176 | − | 20.5702i | 0.361088 | − | 1.34760i | −0.511560 | − | 0.859247i | \(-0.670932\pi\) |
0.872648 | − | 0.488350i | \(-0.162401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.52983 | − | 16.8757i | −0.295493 | − | 1.10085i | ||||
\(236\) | 38.7235 | − | 22.3570i | 2.52069 | − | 1.45532i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.57351 | + | 1.67927i | −0.426097 | + | 0.108851i | ||||
\(239\) | 0.787711 | 0.0509528 | 0.0254764 | − | 0.999675i | \(-0.491890\pi\) | ||||
0.0254764 | + | 0.999675i | \(0.491890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.438601 | + | 0.759678i | −0.0282527 | + | 0.0489352i | −0.879806 | − | 0.475333i | \(-0.842328\pi\) |
0.851553 | + | 0.524268i | \(0.175661\pi\) | |||||||
\(242\) | −9.12735 | − | 34.0637i | −0.586728 | − | 2.18970i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.84107i | 0.565991i | ||||||||
\(245\) | −13.3724 | − | 8.13502i | −0.854332 | − | 0.519727i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3959 | + | 38.7979i | −0.661473 | + | 2.46865i | ||||
\(248\) | 23.9828 | − | 6.42617i | 1.52291 | − | 0.408062i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 27.1631 | + | 7.23972i | 1.71794 | + | 0.457880i | ||||
\(251\) | 1.76477i | 0.111391i | 0.998448 | + | 0.0556957i | \(0.0177377\pi\) | ||||
−0.998448 | + | 0.0556957i | \(0.982262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.973360 | + | 0.973360i | −0.0611946 | + | 0.0611946i | ||||
\(254\) | 4.18899 | + | 7.25555i | 0.262841 | + | 0.455254i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.8717 | − | 27.4905i | 0.991980 | − | 1.71816i | ||||
\(257\) | −2.54666 | − | 0.682377i | −0.158857 | − | 0.0425655i | 0.178514 | − | 0.983937i | \(-0.442871\pi\) |
−0.337371 | + | 0.941372i | \(0.609538\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.56763 | + | 0.0416991i | 0.221682 | + | 0.00259106i | ||||
\(260\) | 43.1514 | + | 43.1132i | 2.67614 | + | 2.67377i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.5879 | − | 3.10497i | 0.715903 | − | 0.191826i | ||||
\(263\) | 26.8646 | − | 7.19835i | 1.65654 | − | 0.443869i | 0.695108 | − | 0.718905i | \(-0.255356\pi\) |
0.961434 | + | 0.275036i | \(0.0886898\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0665696 | − | 0.0665108i | −0.00408934 | − | 0.00408573i | ||||
\(266\) | −20.7370 | − | 36.9071i | −1.27147 | − | 2.26292i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −59.1864 | − | 15.8589i | −3.61538 | − | 0.968739i | ||||
\(269\) | −10.0436 | + | 17.3961i | −0.612370 | + | 1.06066i | 0.378470 | + | 0.925614i | \(0.376450\pi\) |
−0.990840 | + | 0.135043i | \(0.956883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.546081 | − | 0.945841i | −0.0331721 | − | 0.0574557i | 0.848963 | − | 0.528453i | \(-0.177228\pi\) |
−0.882135 | + | 0.470997i | \(0.843894\pi\) | |||||||
\(272\) | −4.35256 | + | 4.35256i | −0.263913 | + | 0.263913i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.95634i | − | 0.118187i | ||||||
\(275\) | 21.6507 | − | 12.5256i | 1.30558 | − | 0.755319i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.97197 | + | 1.06429i | −0.238653 | + | 0.0639468i | −0.376163 | − | 0.926554i | \(-0.622757\pi\) |
0.137510 | + | 0.990500i | \(0.456090\pi\) | |||||||
\(278\) | 0.746125 | − | 2.78458i | 0.0447496 | − | 0.167008i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −34.5373 | − | 0.388407i | −2.06400 | − | 0.0232117i | ||||
\(281\) | 7.91764i | 0.472327i | 0.971713 | + | 0.236163i | \(0.0758900\pi\) | ||||
−0.971713 | + | 0.236163i | \(0.924110\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.53409 | + | 20.6535i | 0.328967 | + | 1.22772i | 0.910263 | + | 0.414030i | \(0.135879\pi\) |
−0.581296 | + | 0.813692i | \(0.697454\pi\) | |||||||
\(284\) | −11.3133 | + | 19.5952i | −0.671320 | + | 1.16276i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 79.3908 | 4.69448 | ||||||||
\(287\) | −5.48073 | + | 1.40011i | −0.323517 | + | 0.0826460i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.8216 | − | 7.97992i | 0.813037 | − | 0.469407i | ||||
\(290\) | 5.90904 | + | 22.0139i | 0.346991 | + | 1.29270i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6485 | − | 43.4727i | 0.681675 | − | 2.54405i | ||||
\(293\) | 20.6685 | + | 20.6685i | 1.20747 | + | 1.20747i | 0.971845 | + | 0.235620i | \(0.0757121\pi\) |
0.235620 | + | 0.971845i | \(0.424288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.1338 | − | 0.0102273i | 1.34690 | − | 0.000595455i | ||||
\(296\) | 6.81826 | − | 3.93652i | 0.396303 | − | 0.228806i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0173 | + | 44.8492i | 0.696144 | + | 2.59804i | ||||
\(299\) | −0.868396 | − | 1.50411i | −0.0502206 | − | 0.0869847i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.95749 | − | 2.34695i | −0.228106 | − | 0.135276i | ||||
\(302\) | −22.6896 | + | 22.6896i | −1.30564 | + | 1.30564i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −33.2624 | − | 19.2040i | −1.90773 | − | 1.10143i | ||||
\(305\) | −2.28531 | + | 3.96232i | −0.130857 | + | 0.226882i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4383 | − | 10.4383i | −0.595743 | − | 0.595743i | 0.343434 | − | 0.939177i | \(-0.388410\pi\) |
−0.939177 | + | 0.343434i | \(0.888410\pi\) | |||||||
\(308\) | −40.9190 | + | 39.9735i | −2.33158 | + | 2.27770i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.0983 | + | 6.17823i | 1.31190 | + | 0.350900i | ||||
\(311\) | −16.8933 | − | 9.75337i | −0.957933 | − | 0.553063i | −0.0623969 | − | 0.998051i | \(-0.519874\pi\) |
−0.895536 | + | 0.444988i | \(0.853208\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5869 | − | 3.90856i | −0.824502 | − | 0.220925i | −0.178188 | − | 0.983996i | \(-0.557024\pi\) |
−0.646314 | + | 0.763072i | \(0.723690\pi\) | |||||||
\(314\) | −13.2741 | −0.749099 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −62.5642 | −3.51951 | ||||||||
\(317\) | −15.9783 | − | 4.28137i | −0.897431 | − | 0.240466i | −0.219518 | − | 0.975608i | \(-0.570449\pi\) |
−0.677912 | + | 0.735143i | \(0.737115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.5637 | + | 10.1404i | 0.983380 | + | 0.567755i | ||||
\(320\) | 6.33799 | − | 3.66298i | 0.354304 | − | 0.204767i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.76248 | + | 0.494402i | 0.0982189 | + | 0.0275520i | ||||
\(323\) | −4.58931 | − | 4.58931i | −0.255356 | − | 0.255356i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.19499 | + | 30.4763i | 0.454576 | + | 1.69052i | ||||
\(326\) | −18.4216 | − | 10.6357i | −1.02028 | − | 0.589059i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.82641 | + | 8.82641i | −0.487357 | + | 0.487357i | ||||
\(329\) | −0.241629 | + | 20.6730i | −0.0133215 | + | 1.13974i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3963 | − | 23.2031i | −0.736328 | − | 1.27536i | −0.954138 | − | 0.299367i | \(-0.903225\pi\) |
0.217810 | − | 0.975991i | \(-0.430109\pi\) | |||||||
\(332\) | −15.7972 | − | 58.9560i | −0.866985 | − | 3.23563i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.700063 | − | 0.404182i | 0.0383058 | − | 0.0221158i | ||||
\(335\) | −22.4263 | − | 22.4065i | −1.22528 | − | 1.22420i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.48628 | − | 3.48628i | −0.189910 | − | 0.189910i | 0.605747 | − | 0.795657i | \(-0.292874\pi\) |
−0.795657 | + | 0.605747i | \(0.792874\pi\) | |||||||
\(338\) | −17.4655 | + | 65.1821i | −0.949998 | + | 3.54544i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.51937 | + | 2.55522i | −0.516260 | + | 0.138576i | ||||
\(341\) | 18.4246 | − | 10.6374i | 0.997746 | − | 0.576049i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6287 | + | 13.5468i | 0.681884 | + | 0.731460i | ||||
\(344\) | −10.1530 | −0.547410 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.0563 | + | 34.7385i | −1.07823 | + | 1.86755i | ||||
\(347\) | 6.27705 | + | 23.4263i | 0.336970 | + | 1.25759i | 0.901718 | + | 0.432325i | \(0.142307\pi\) |
−0.564748 | + | 0.825263i | \(0.691027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.641866i | − | 0.0343583i | −0.999852 | − | 0.0171792i | \(-0.994531\pi\) | ||
0.999852 | − | 0.0171792i | \(-0.00546857\pi\) | |||||||
\(350\) | −28.6242 | − | 16.9411i | −1.53003 | − | 0.905540i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.53006 | + | 16.9064i | −0.241453 | + | 0.901116i | ||||
\(353\) | 1.88152 | − | 0.504151i | 0.100143 | − | 0.0268332i | −0.208400 | − | 0.978044i | \(-0.566825\pi\) |
0.308543 | + | 0.951211i | \(0.400159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1354 | + | 5.85767i | −0.537933 | + | 0.310893i | ||||
\(356\) | 20.6820i | 1.09614i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.18859 | − | 7.18859i | 0.379929 | − | 0.379929i | ||||
\(359\) | −4.34803 | − | 7.53101i | −0.229480 | − | 0.397471i | 0.728174 | − | 0.685392i | \(-0.240369\pi\) |
−0.957654 | + | 0.287921i | \(0.907036\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.7486 | − | 18.6172i | 0.565718 | − | 0.979853i | ||||
\(362\) | 23.1988 | + | 6.21611i | 1.21930 | + | 0.326711i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −35.3541 | − | 62.9222i | −1.85306 | − | 3.29802i | ||||
\(365\) | 16.4577 | − | 16.4723i | 0.861436 | − | 0.862198i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.4869 | − | 8.43689i | 1.64360 | − | 0.440402i | 0.685790 | − | 0.727799i | \(-0.259457\pi\) |
0.957811 | + | 0.287397i | \(0.0927900\pi\) | |||||||
\(368\) | 1.60417 | − | 0.429835i | 0.0836230 | − | 0.0224067i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.58179 | − | 0.00335185i | 0.394159 | − | 0.000174254i | ||||
\(371\) | 0.0545408 | + | 0.0970700i | 0.00283162 | + | 0.00503962i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9621 | + | 4.81293i | 0.930043 | + | 0.249204i | 0.691873 | − | 0.722019i | \(-0.256786\pi\) |
0.238170 | + | 0.971224i | \(0.423453\pi\) | |||||||
\(374\) | −6.41414 | + | 11.1096i | −0.331667 | + | 0.574465i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.8106 | + | 39.5091i | 1.17636 | + | 2.03752i | ||||
\(377\) | −18.0938 | + | 18.0938i | −0.931879 | + | 0.931879i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6954i | 0.600752i | 0.953821 | + | 0.300376i | \(0.0971122\pi\) | ||||
−0.953821 | + | 0.300376i | \(0.902888\pi\) | |||||||
\(380\) | −30.7738 | − | 53.2475i | −1.57866 | − | 2.73154i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 47.7411 | − | 12.7922i | 2.44264 | − | 0.654505i | ||||
\(383\) | 2.18840 | − | 8.16722i | 0.111822 | − | 0.417326i | −0.887207 | − | 0.461371i | \(-0.847358\pi\) |
0.999030 | + | 0.0440451i | \(0.0140245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.6714 | + | 7.33794i | −1.46123 | + | 0.373976i | ||||
\(386\) | 13.9402i | 0.709536i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.376731 | + | 1.40598i | 0.0191256 | + | 0.0713778i | ||||
\(389\) | −11.1976 | + | 19.3948i | −0.567740 | + | 0.983354i | 0.429049 | + | 0.903281i | \(0.358849\pi\) |
−0.996789 | + | 0.0800731i | \(0.974485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.280638 | 0.0141925 | ||||||||
\(392\) | 39.2171 | + | 11.4971i | 1.98076 | + | 0.580691i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.6808 | − | 13.6721i | 1.19302 | − | 0.688790i | ||||
\(395\) | −28.0395 | − | 16.1721i | −1.41082 | − | 0.813707i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20510 | − | 8.22953i | 0.110671 | − | 0.413028i | −0.888256 | − | 0.459349i | \(-0.848083\pi\) |
0.998927 | + | 0.0463203i | \(0.0147495\pi\) | |||||||
\(398\) | −14.3690 | − | 14.3690i | −0.720253 | − | 0.720253i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −30.1772 | + | 0.0266822i | −1.50886 | + | 0.00133411i | ||||
\(401\) | 10.9993 | − | 6.35044i | 0.549278 | − | 0.317126i | −0.199553 | − | 0.979887i | \(-0.563949\pi\) |
0.748831 | + | 0.662761i | \(0.230616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.94739 | + | 25.9280i | 0.346074 | + | 1.29157i | ||||
\(404\) | 24.1679 | + | 41.8601i | 1.20240 | + | 2.08262i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.315199 | − | 26.9674i | 0.0156431 | − | 1.33837i | ||||
\(407\) | 4.77022 | − | 4.77022i | 0.236451 | − | 0.236451i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.9042 | − | 13.2237i | −1.13254 | − | 0.653871i | −0.187966 | − | 0.982175i | \(-0.560190\pi\) |
−0.944572 | + | 0.328304i | \(0.893523\pi\) | |||||||
\(410\) | −11.6097 | + | 3.11631i | −0.573362 | + | 0.153904i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −32.3274 | − | 32.3274i | −1.59266 | − | 1.59266i | ||||
\(413\) | −26.3550 | − | 7.39301i | −1.29685 | − | 0.363786i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.15957 | − | 30.5059i | 0.400538 | − | 1.49747i | ||||
\(416\) | −19.1248 | − | 11.0417i | −0.937672 | − | 0.541365i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −77.3171 | − | 20.7170i | −3.78170 | − | 1.01330i | ||||
\(419\) | 2.33746 | 0.114192 | 0.0570961 | − | 0.998369i | \(-0.481816\pi\) | ||||
0.0570961 | + | 0.998369i | \(0.481816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1558 | −0.689913 | −0.344957 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344957 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(422\) | −32.7593 | − | 8.77784i | −1.59470 | − | 0.427298i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.212778 | + | 0.122847i | 0.0103334 | + | 0.00596600i | ||||
\(425\) | −4.92682 | − | 1.31547i | −0.238986 | − | 0.0638096i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.87146 | − | 3.78200i | 0.187353 | − | 0.183024i | ||||
\(428\) | 42.4414 | + | 42.4414i | 2.05148 | + | 2.05148i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.46960 | − | 4.88494i | −0.408441 | − | 0.235573i | ||||
\(431\) | 14.4168 | + | 8.32354i | 0.694432 | + | 0.400931i | 0.805270 | − | 0.592908i | \(-0.202020\pi\) |
−0.110838 | + | 0.993838i | \(0.535353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.43208 | − | 8.43208i | 0.405220 | − | 0.405220i | −0.474848 | − | 0.880068i | \(-0.657497\pi\) |
0.880068 | + | 0.474848i | \(0.157497\pi\) | |||||||
\(434\) | −24.3338 | − | 14.4309i | −1.16806 | − | 0.692706i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.39886 | + | 14.5472i | 0.402232 | + | 0.696687i | ||||
\(437\) | 0.453216 | + | 1.69143i | 0.0216803 | + | 0.0809119i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.2457 | + | 16.3077i | −1.34810 | + | 0.778324i | −0.987980 | − | 0.154584i | \(-0.950596\pi\) |
−0.360116 | + | 0.932907i | \(0.617263\pi\) | |||||||
\(440\) | −46.1585 | + | 46.1994i | −2.20052 | + | 2.20247i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.4449 | − | 11.4449i | −0.544379 | − | 0.544379i | ||||
\(443\) | −3.40342 | + | 12.7017i | −0.161701 | + | 0.603477i | 0.836737 | + | 0.547605i | \(0.184460\pi\) |
−0.998438 | + | 0.0558717i | \(0.982206\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.34606 | + | 9.26910i | −0.253427 | + | 0.439398i | ||||
\(446\) | 9.06477 | − | 5.23355i | 0.429229 | − | 0.247816i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.39204 | + | 2.14384i | −0.396487 | + | 0.101287i | ||||
\(449\) | 37.7116 | 1.77972 | 0.889860 | − | 0.456234i | \(-0.150802\pi\) | ||||
0.889860 | + | 0.456234i | \(0.150802\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.34786 | + | 9.26276i | −0.251821 | + | 0.436166i | ||||
\(452\) | −19.2022 | − | 71.6635i | −0.903194 | − | 3.37077i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 49.1189i | 2.30526i | ||||||||
\(455\) | 0.419910 | − | 37.3386i | 0.0196857 | − | 1.75046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.84421 | − | 6.88267i | 0.0862684 | − | 0.321958i | −0.909283 | − | 0.416178i | \(-0.863369\pi\) |
0.995551 | + | 0.0942205i | \(0.0300359\pi\) | |||||||
\(458\) | 16.8326 | − | 4.51028i | 0.786535 | − | 0.210751i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.56896 | + | 0.687134i | 0.119778 | + | 0.0320378i | ||||
\(461\) | 23.2822i | 1.08436i | 0.840262 | + | 0.542181i | \(0.182401\pi\) | ||||
−0.840262 | + | 0.542181i | \(0.817599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0488 | − | 26.0488i | 1.21059 | − | 1.21059i | 0.239757 | − | 0.970833i | \(-0.422932\pi\) |
0.970833 | − | 0.239757i | \(-0.0770677\pi\) | |||||||
\(464\) | −12.2341 | − | 21.1901i | −0.567955 | − | 0.983728i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.7726 | + | 46.3715i | −1.24022 | + | 2.14812i | ||||
\(467\) | −8.90737 | − | 2.38672i | −0.412184 | − | 0.110444i | 0.0467673 | − | 0.998906i | \(-0.485108\pi\) |
−0.458951 | + | 0.888461i | \(0.651775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.3740 | + | 32.7015i | 0.848432 | + | 1.51001i | ||||
\(470\) | 0.0194226 | + | 43.9335i | 0.000895898 | + | 2.02650i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −58.3429 | + | 15.6329i | −2.68545 | + | 0.719564i | ||||
\(473\) | −8.40324 | + | 2.25164i | −0.386382 | + | 0.103531i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0281336 | − | 31.8187i | −0.00129086 | − | 1.45994i | ||||
\(476\) | 11.6614 | + | 0.136300i | 0.534499 | + | 0.00624731i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.91310 | − | 0.512613i | −0.0875030 | − | 0.0234464i | ||||
\(479\) | 9.04651 | − | 15.6690i | 0.413346 | − | 0.715936i | −0.581908 | − | 0.813255i | \(-0.697693\pi\) |
0.995253 | + | 0.0973193i | \(0.0310268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.25581 | + | 7.37129i | 0.194048 | + | 0.336102i | ||||
\(482\) | 1.55959 | − | 1.55959i | 0.0710373 | − | 0.0710373i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 60.6183i | 2.75538i | ||||||||
\(485\) | −0.194589 | + | 0.727502i | −0.00883582 | + | 0.0330342i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.34247 | + | 0.627663i | −0.106148 | + | 0.0284421i | −0.311502 | − | 0.950246i | \(-0.600832\pi\) |
0.205354 | + | 0.978688i | \(0.434165\pi\) | |||||||
\(488\) | 3.09102 | − | 11.5358i | 0.139924 | − | 0.522203i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 27.1833 | + | 28.4596i | 1.22802 | + | 1.28567i | ||||
\(491\) | − | 15.2664i | − | 0.688965i | −0.938793 | − | 0.344483i | \(-0.888054\pi\) | ||
0.938793 | − | 0.344483i | \(-0.111946\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.07014 | − | 3.99381i | −0.0481966 | − | 0.179872i | ||||
\(494\) | 50.4964 | − | 87.4624i | 2.27194 | − | 3.93512i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.6675 | −1.15250 | ||||||||
\(497\) | 13.4202 | − | 3.42834i | 0.601978 | − | 0.153782i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.192077 | − | 0.110896i | 0.00859855 | − | 0.00496437i | −0.495695 | − | 0.868497i | \(-0.665086\pi\) |
0.504293 | + | 0.863533i | \(0.331753\pi\) | |||||||
\(500\) | −41.8792 | − | 24.1050i | −1.87290 | − | 1.07801i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.14845 | − | 4.28606i | 0.0512576 | − | 0.191296i | ||||
\(503\) | 16.5305 | + | 16.5305i | 0.737057 | + | 0.737057i | 0.972007 | − | 0.234951i | \(-0.0754929\pi\) |
−0.234951 | + | 0.972007i | \(0.575493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0110557 | + | 25.0077i | 0.000491971 | + | 1.11283i | ||||
\(506\) | 2.99740 | − | 1.73055i | 0.133251 | − | 0.0769324i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.72727 | − | 13.9104i | −0.165371 | − | 0.617173i | ||||
\(509\) | 1.68470 | + | 2.91798i | 0.0746729 | + | 0.129337i | 0.900944 | − | 0.433935i | \(-0.142875\pi\) |
−0.826271 | + | 0.563273i | \(0.809542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0194 | + | 13.4958i | −1.06256 | + | 0.597019i | ||||
\(512\) | −34.9000 | + | 34.9000i | −1.54238 | + | 1.54238i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.74096 | + | 3.31455i | 0.253223 | + | 0.146198i | ||||
\(515\) | −6.13200 | − | 22.8445i | −0.270208 | − | 1.00665i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.6415 | + | 27.6415i | 1.21567 | + | 1.21567i | ||||
\(518\) | −8.63750 | − | 2.42296i | −0.379510 | − | 0.106459i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −41.2307 | − | 71.3408i | −1.80809 | − | 3.12850i | ||||
\(521\) | 23.3214 | + | 13.4646i | 1.02173 | + | 0.589895i | 0.914604 | − | 0.404351i | \(-0.132503\pi\) |
0.107124 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0465 | + | 4.03169i | 0.657936 | + | 0.176294i | 0.572315 | − | 0.820034i | \(-0.306046\pi\) |
0.0856218 | + | 0.996328i | \(0.472712\pi\) | |||||||
\(524\) | −20.6213 | −0.900847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −69.9299 | −3.04909 | ||||||||
\(527\) | −4.18955 | − | 1.12259i | −0.182500 | − | 0.0489007i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.8530 | + | 11.4621i | 0.863174 | + | 0.498354i | ||||
\(530\) | 0.118393 | + | 0.204854i | 0.00514268 | + | 0.00889830i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.0111 | + | 70.5043i | 0.780880 | + | 3.05675i | ||||
\(533\) | −9.54232 | − | 9.54232i | −0.413324 | − | 0.413324i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.05046 | + | 29.9917i | 0.348052 | + | 1.29665i | ||||
\(536\) | 71.6818 | + | 41.3855i | 3.09618 | + | 1.78758i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 35.7134 | − | 35.7134i | 1.53971 | − | 1.53971i | ||||
\(539\) | 35.0084 | + | 0.818479i | 1.50792 | + | 0.0352544i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.35172 | − | 7.53741i | −0.187095 | − | 0.324059i | 0.757185 | − | 0.653200i | \(-0.226574\pi\) |
−0.944281 | + | 0.329142i | \(0.893241\pi\) | |||||||
\(542\) | 0.710738 | + | 2.65251i | 0.0305288 | + | 0.113935i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.09027 | − | 1.78417i | 0.132494 | − | 0.0764955i | ||||
\(545\) | 0.00384208 | + | 8.69068i | 0.000164576 | + | 0.372268i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.42064 | − | 9.42064i | −0.402798 | − | 0.402798i | 0.476420 | − | 0.879218i | \(-0.341934\pi\) |
−0.879218 | + | 0.476420i | \(0.841934\pi\) | |||||||
\(548\) | −0.870355 | + | 3.24821i | −0.0371797 | + | 0.138757i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −60.7336 | + | 16.3311i | −2.58969 | + | 0.696360i | ||||
\(551\) | 22.3428 | − | 12.8996i | 0.951834 | − | 0.549542i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.7635 | + | 27.3965i | 1.13810 | + | 1.16502i | ||||
\(554\) | 10.3392 | 0.439272 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.47765 | + | 4.29142i | −0.105076 | + | 0.181997i | ||||
\(557\) | 11.1018 | + | 41.4325i | 0.470398 | + | 1.75555i | 0.638341 | + | 0.769754i | \(0.279621\pi\) |
−0.167943 | + | 0.985797i | \(0.553712\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.9765i | − | 0.464255i | ||||||
\(560\) | 34.3834 | + | 9.62871i | 1.45297 | + | 0.406887i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.15250 | − | 19.2294i | 0.217345 | − | 0.811143i | ||||
\(563\) | −0.0807657 | + | 0.0216411i | −0.00340387 | + | 0.000912064i | −0.260521 | − | 0.965468i | \(-0.583894\pi\) |
0.257117 | + | 0.966380i | \(0.417228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.91829 | − | 37.0811i | 0.417266 | − | 1.56001i | ||||
\(566\) | − | 53.7620i | − | 2.25979i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.6125 | − | 21.6125i | 0.906839 | − | 0.906839i | ||||
\(569\) | 6.87752 | + | 11.9122i | 0.288321 | + | 0.499386i | 0.973409 | − | 0.229074i | \(-0.0735698\pi\) |
−0.685088 | + | 0.728460i | \(0.740236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2197 | − | 19.4331i | 0.469530 | − | 0.813251i | −0.529863 | − | 0.848083i | \(-0.677757\pi\) |
0.999393 | + | 0.0348328i | \(0.0110899\pi\) | |||||||
\(572\) | −131.816 | − | 35.3201i | −5.51152 | − | 1.47681i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.2221 | + | 0.166230i | 0.593618 | + | 0.00693830i | ||||
\(575\) | 0.973722 | + | 0.972001i | 0.0406070 | + | 0.0405353i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7976 | + | 5.03680i | −0.782554 | + | 0.209685i | −0.627910 | − | 0.778286i | \(-0.716090\pi\) |
−0.154644 | + | 0.987970i | \(0.549423\pi\) | |||||||
\(578\) | −38.7613 | + | 10.3861i | −1.61226 | + | 0.432003i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0173209 | − | 39.1796i | −0.000719213 | − | 1.62684i | ||||
\(581\) | −19.0589 | + | 32.1375i | −0.790695 | + | 1.33329i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.203353 | + | 0.0544883i | 0.00842202 | + | 0.00225667i | ||||
\(584\) | −30.3979 | + | 52.6506i | −1.25787 | + | 2.17870i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.7468 | − | 63.6473i | −1.51800 | − | 2.62925i | ||||
\(587\) | −15.2148 | + | 15.2148i | −0.627982 | + | 0.627982i | −0.947560 | − | 0.319578i | \(-0.896459\pi\) |
0.319578 | + | 0.947560i | \(0.396459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 27.0637i | − | 1.11514i | ||||||
\(590\) | −56.1913 | − | 15.0298i | −2.31336 | − | 0.618767i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.86166 | + | 2.10653i | −0.323112 | + | 0.0865777i | ||||
\(593\) | −7.62569 | + | 28.4595i | −0.313150 | + | 1.16869i | 0.612550 | + | 0.790432i | \(0.290144\pi\) |
−0.925700 | + | 0.378259i | \(0.876523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.19108 | + | 3.07542i | 0.212814 | + | 0.126080i | ||||
\(596\) | − | 79.8116i | − | 3.26921i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.13024 | + | 4.21811i | 0.0462189 | + | 0.172491i | ||||
\(599\) | 19.0653 | − | 33.0220i | 0.778986 | − | 1.34924i | −0.153541 | − | 0.988142i | \(-0.549068\pi\) |
0.932527 | − | 0.361101i | \(-0.117599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.21756 | 0.0904563 | 0.0452282 | − | 0.998977i | \(-0.485599\pi\) | ||||
0.0452282 | + | 0.998977i | \(0.485599\pi\) | |||||||
\(602\) | 8.08416 | + | 8.27538i | 0.329486 | + | 0.337279i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 47.7670 | − | 27.5783i | 1.94361 | − | 1.12215i | ||||
\(605\) | −15.6691 | + | 27.1675i | −0.637041 | + | 1.10451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.919787 | − | 3.43269i | 0.0373330 | − | 0.139329i | −0.944744 | − | 0.327809i | \(-0.893690\pi\) |
0.982077 | + | 0.188481i | \(0.0603563\pi\) | |||||||
\(608\) | 15.7439 | + | 15.7439i | 0.638501 | + | 0.638501i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.12882 | − | 8.13601i | 0.329126 | − | 0.329417i | ||||
\(611\) | −42.7136 | + | 24.6607i | −1.72801 | + | 0.997666i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.08899 | − | 30.1885i | −0.326711 | − | 1.21930i | −0.912580 | − | 0.408897i | \(-0.865913\pi\) |
0.585869 | − | 0.810406i | \(-0.300753\pi\) | |||||||
\(614\) | 18.5584 | + | 32.1440i | 0.748954 | + | 1.29723i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 67.3667 | − | 37.8513i | 2.71428 | − | 1.52507i | ||||
\(617\) | −22.1284 | + | 22.1284i | −0.890857 | + | 0.890857i | −0.994604 | − | 0.103747i | \(-0.966917\pi\) |
0.103747 | + | 0.994604i | \(0.466917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.9430 | + | 23.0611i | 1.60544 | + | 0.926903i | 0.990372 | + | 0.138433i | \(0.0442064\pi\) |
0.615072 | + | 0.788471i | \(0.289127\pi\) | |||||||
\(620\) | −35.6026 | − | 20.5342i | −1.42983 | − | 0.824673i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.6813 | + | 34.6813i | 1.39059 | + | 1.39059i | ||||
\(623\) | 9.05654 | − | 8.84728i | 0.362843 | − | 0.354459i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5383 | − | 21.6285i | −0.501531 | − | 0.865140i | ||||
\(626\) | 32.8834 | + | 18.9852i | 1.31429 | + | 0.758803i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.0396 | + | 5.90548i | 0.879475 | + | 0.235654i | ||||
\(629\) | −1.37534 | −0.0548385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0682 | 1.59509 | 0.797545 | − | 0.603260i | \(-0.206132\pi\) | ||||
0.797545 | + | 0.603260i | \(0.206132\pi\) | |||||||
\(632\) | 81.6338 | + | 21.8737i | 3.24722 | + | 0.870089i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.0200 | + | 20.7961i | 1.43054 | + | 0.825920i | ||||
\(635\) | 1.92521 | − | 7.19770i | 0.0763996 | − | 0.285632i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.4296 | + | 42.3980i | −0.492480 | + | 1.67987i | ||||
\(638\) | −36.0576 | − | 36.0576i | −1.42754 | − | 1.42754i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −32.8887 | + | 8.82808i | −1.30004 | + | 0.348961i | ||||
\(641\) | 25.8536 | + | 14.9266i | 1.02116 | + | 0.589566i | 0.914439 | − | 0.404724i | \(-0.132632\pi\) |
0.106719 | + | 0.994289i | \(0.465966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.3585 | + | 17.3585i | −0.684554 | + | 0.684554i | −0.961023 | − | 0.276469i | \(-0.910836\pi\) |
0.276469 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(644\) | −2.70637 | − | 1.60498i | −0.106646 | − | 0.0632453i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.15941 | + | 14.1325i | 0.321028 | + | 0.556036i | ||||
\(647\) | −0.324212 | − | 1.20998i | −0.0127461 | − | 0.0475691i | 0.959260 | − | 0.282525i | \(-0.0911721\pi\) |
−0.972006 | + | 0.234956i | \(0.924505\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.8215 | + | 25.8777i | −1.75940 | + | 1.01579i | ||||
\(650\) | −0.0701600 | − | 79.3501i | −0.00275190 | − | 3.11237i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25.8546 | + | 25.8546i | 1.01254 | + | 1.01254i | ||||
\(653\) | −2.58041 | + | 9.63022i | −0.100979 | + | 0.376859i | −0.997858 | − | 0.0654169i | \(-0.979162\pi\) |
0.896879 | + | 0.442276i | \(0.145829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.24191 | − | 5.33037i | −0.361111 | − | 0.208275i | ||||
\(656\) | 11.1753 | − | 6.45204i | 0.436321 | − | 0.251910i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.0401 | − | 50.0508i | 0.547338 | − | 1.95118i | ||||
\(659\) | 40.7659 | 1.58801 | 0.794007 | − | 0.607908i | \(-0.207991\pi\) | ||||
0.794007 | + | 0.607908i | \(0.207991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.2529 | − | 19.4907i | 0.437689 | − | 0.758099i | −0.559822 | − | 0.828613i | \(-0.689131\pi\) |
0.997511 | + | 0.0705137i | \(0.0224639\pi\) | |||||||
\(662\) | 17.4356 | + | 65.0707i | 0.677655 | + | 2.52904i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 82.4489i | 3.19964i | ||||||||
\(665\) | −10.1525 | + | 36.2537i | −0.393696 | + | 1.40586i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.288726 | + | 1.07754i | −0.0111795 | + | 0.0417225i | ||||
\(668\) | −1.34216 | + | 0.359632i | −0.0519299 | + | 0.0139146i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 39.8850 | + | 69.0124i | 1.54089 | + | 2.66618i | ||||
\(671\) | − | 10.2333i | − | 0.395052i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.4767 | − | 27.4767i | 1.05915 | − | 1.05915i | 0.0610132 | − | 0.998137i | \(-0.480567\pi\) |
0.998137 | − | 0.0610132i | \(-0.0194332\pi\) | |||||||
\(674\) | 6.19831 | + | 10.7358i | 0.238750 | + | 0.413527i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 57.9976 | − | 100.455i | 2.23068 | − | 3.86364i | ||||
\(677\) | −17.7812 | − | 4.76445i | −0.683386 | − | 0.183113i | −0.0996090 | − | 0.995027i | \(-0.531759\pi\) |
−0.583777 | + | 0.811914i | \(0.698426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.454514 | − | 0.766414i | 0.0174427 | − | 0.0294123i | ||||
\(680\) | 13.3142 | − | 0.00588611i | 0.510578 | − | 0.000225722i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −51.6697 | + | 13.8449i | −1.97854 | + | 0.530147i | ||||
\(683\) | −31.0627 | + | 8.32323i | −1.18858 | + | 0.318480i | −0.798325 | − | 0.602226i | \(-0.794280\pi\) |
−0.390257 | + | 0.920706i | \(0.627614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.22969 | + | 1.23078i | −0.0469842 | + | 0.0470257i | ||||
\(686\) | −21.8552 | − | 41.1191i | −0.834435 | − | 1.56994i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.1383 | + | 2.71654i | 0.386518 | + | 0.103567i | ||||
\(689\) | −0.132812 | + | 0.230036i | −0.00505972 | + | 0.00876369i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.08405 | + | 10.5379i | 0.231448 | + | 0.400880i | 0.958235 | − | 0.285984i | \(-0.0923203\pi\) |
−0.726786 | + | 0.686864i | \(0.758987\pi\) | |||||||
\(692\) | 48.7551 | − | 48.7551i | 1.85339 | − | 1.85339i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 60.9797i | − | 2.31476i | ||||||
\(695\) | −2.21970 | + | 1.28285i | −0.0841980 | + | 0.0486614i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.10625 | − | 0.564369i | 0.0797801 | − | 0.0213770i | ||||
\(698\) | −0.417702 | + | 1.55889i | −0.0158103 | + | 0.0590047i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 39.9892 | + | 40.8627i | 1.51145 | + | 1.54446i | ||||
\(701\) | − | 30.7110i | − | 1.15994i | −0.814639 | − | 0.579969i | \(-0.803065\pi\) | ||
0.814639 | − | 0.579969i | \(-0.196935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.22111 | − | 8.28930i | −0.0837708 | − | 0.312637i | ||||
\(704\) | −8.18859 | + | 14.1831i | −0.308619 | + | 0.534544i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.89768 | −0.184326 | ||||||||
\(707\) | 7.99184 | − | 28.4898i | 0.300564 | − | 1.07147i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.92357 | + | 2.84263i | −0.184909 | + | 0.106757i | −0.589597 | − | 0.807698i | \(-0.700713\pi\) |
0.404688 | + | 0.914455i | \(0.367380\pi\) | |||||||
\(710\) | 28.4277 | − | 7.63064i | 1.06687 | − | 0.286373i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.23085 | − | 26.9859i | 0.270987 | − | 1.01134i | ||||
\(713\) | 0.827475 | + | 0.827475i | 0.0309892 | + | 0.0309892i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.9466 | − | 49.9025i | −1.86790 | − | 1.86625i | ||||
\(716\) | −15.1337 | + | 8.73743i | −0.565572 | + | 0.326533i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.65906 | + | 21.1199i | 0.211194 | + | 0.788188i | ||||
\(719\) | 4.06871 | + | 7.04721i | 0.151737 | + | 0.262817i | 0.931866 | − | 0.362802i | \(-0.118180\pi\) |
−0.780129 | + | 0.625619i | \(0.784847\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.327092 | + | 27.9849i | −0.0121816 | + | 1.04221i | ||||
\(722\) | −38.2204 | + | 38.2204i | −1.42241 | + | 1.42241i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.7526 | − | 20.6418i | −1.32874 | − | 0.767146i | ||||
\(725\) | 10.1197 | − | 17.5637i | 0.375836 | − | 0.652299i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.4261 | + | 37.4261i | 1.38806 | + | 1.38806i | 0.829392 | + | 0.558666i | \(0.188687\pi\) |
0.558666 | + | 0.829392i | \(0.311313\pi\) | |||||||
\(728\) | 24.1312 | + | 94.4614i | 0.894362 | + | 3.50097i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −50.6900 | + | 29.2958i | −1.87612 | + | 1.08428i | ||||
\(731\) | 1.53600 | + | 0.886810i | 0.0568110 | + | 0.0327998i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.7501 | − | 10.9190i | −1.50514 | − | 0.403301i | −0.590321 | − | 0.807168i | \(-0.700999\pi\) |
−0.914817 | + | 0.403868i | \(0.867666\pi\) | |||||||
\(734\) | −81.9619 | −3.02527 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.962746 | −0.0354873 | ||||||||
\(737\) | 68.5067 | + | 18.3563i | 2.52348 | + | 0.676163i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.4476 | − | 24.5071i | −1.56146 | − | 0.901510i | −0.997110 | − | 0.0759743i | \(-0.975793\pi\) |
−0.564351 | − | 0.825535i | \(-0.690873\pi\) | |||||||
\(740\) | −12.5899 | − | 3.36749i | −0.462814 | − | 0.123791i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.0692925 | − | 0.271245i | −0.00254381 | − | 0.00995771i | ||||
\(743\) | −28.7264 | − | 28.7264i | −1.05387 | − | 1.05387i | −0.998464 | − | 0.0554047i | \(-0.982355\pi\) |
−0.0554047 | − | 0.998464i | \(-0.517645\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.6304 | − | 35.7694i | 0.755838 | − | 1.31049i | ||||
\(746\) | −40.4921 | − | 23.3781i | −1.48252 | − | 0.855934i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.5922 | − | 15.5922i | 0.570109 | − | 0.570109i | ||||
\(749\) | 0.429427 | − | 36.7403i | 0.0156909 | − | 1.34246i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.29587 | + | 7.44067i | 0.156759 | + | 0.271514i | 0.933698 | − | 0.358061i | \(-0.116562\pi\) |
−0.776939 | + | 0.629575i | \(0.783229\pi\) | |||||||
\(752\) | −12.2065 | − | 45.5552i | −0.445124 | − | 1.66123i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 55.7188 | − | 32.1693i | 2.02916 | − | 1.17154i | ||||
\(755\) | 28.5365 | − | 0.0126158i | 1.03855 | − | 0.000459134i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94682 | + | 1.94682i | 0.0707583 | + | 0.0707583i | 0.741600 | − | 0.670842i | \(-0.234067\pi\) |
−0.670842 | + | 0.741600i | \(0.734067\pi\) | |||||||
\(758\) | 7.61092 | − | 28.4044i | 0.276441 | − | 1.03169i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 21.5373 | + | 80.2365i | 0.781241 | + | 2.91048i | ||||
\(761\) | −17.3244 | + | 10.0023i | −0.628011 | + | 0.362582i | −0.779981 | − | 0.625803i | \(-0.784771\pi\) |
0.151971 | + | 0.988385i | \(0.451438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.77733 | − | 9.90079i | 0.100546 | − | 0.358433i | ||||
\(764\) | −84.9578 | −3.07367 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.6298 | + | 18.4114i | −0.384072 | + | 0.665232i | ||||
\(767\) | −16.9009 | − | 63.0751i | −0.610257 | − | 2.27751i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.7665i | 1.14553i | 0.819720 | + | 0.572764i | \(0.194129\pi\) | ||||
−0.819720 | + | 0.572764i | \(0.805871\pi\) | |||||||
\(770\) | 74.4089 | + | 0.836804i | 2.68151 | + | 0.0301563i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.20183 | − | 23.1455i | 0.223209 | − | 0.833026i | ||||
\(773\) | 28.9093 | − | 7.74623i | 1.03980 | − | 0.278613i | 0.301768 | − | 0.953382i | \(-0.402423\pi\) |
0.738029 | + | 0.674769i | \(0.235757\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.6483 | − | 18.4057i | −0.382497 | − | 0.661153i | ||||
\(776\) | − | 1.96624i | − | 0.0705837i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.8167 | − | 39.8167i | 1.42750 | − | 1.42750i | ||||
\(779\) | 6.80300 | + | 11.7831i | 0.243743 | + | 0.422175i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.0948 | − | 22.6809i | 0.468570 | − | 0.811588i | ||||
\(782\) | −0.681578 | − | 0.182628i | −0.0243732 | − | 0.00653078i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −36.0842 | − | 21.9735i | −1.28872 | − | 0.784767i | ||||
\(785\) | 8.35103 | + | 8.34365i | 0.298061 | + | 0.297798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.61451 | + | 0.700556i | −0.0931973 | + | 0.0249721i | −0.305116 | − | 0.952315i | \(-0.598695\pi\) |
0.211919 | + | 0.977287i | \(0.432029\pi\) | |||||||
\(788\) | −45.4008 | + | 12.1651i | −1.61734 | + | 0.433364i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 57.5748 | + | 57.5239i | 2.04842 | + | 2.04661i | ||||
\(791\) | −23.1668 | + | 39.0645i | −0.823717 | + | 1.38897i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.4715 | + | 3.34173i | 0.442876 | + | 0.118668i | ||||
\(794\) | −10.7109 | + | 18.5519i | −0.380117 | + | 0.658382i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4649 | + | 30.2501i | 0.619028 | + | 1.07219i | ||||
\(797\) | −19.5221 | + | 19.5221i | −0.691508 | + | 0.691508i | −0.962564 | − | 0.271056i | \(-0.912627\pi\) |
0.271056 | + | 0.962564i | \(0.412627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.96956i | − | 0.281943i | ||||||
\(800\) | 16.9018 | + | 4.51280i | 0.597568 | + | 0.159552i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.8463 | + | 8.26525i | −1.08922 | + | 0.291856i | ||||
\(803\) | −13.4828 | + | 50.3185i | −0.475798 | + | 1.77570i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.798049 | − | 1.41887i | −0.0281275 | − | 0.0500088i | ||||
\(806\) | − | 67.4919i | − | 2.37730i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.8992 | − | 63.0687i | −0.594512 | − | 2.21875i | ||||
\(809\) | −2.93046 | + | 5.07571i | −0.103030 | + | 0.178452i | −0.912931 | − | 0.408113i | \(-0.866187\pi\) |
0.809902 | + | 0.586565i | \(0.199520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1090 | −0.565662 | −0.282831 | − | 0.959170i | \(-0.591274\pi\) | ||||
−0.282831 | + | 0.959170i | \(0.591274\pi\) | |||||||
\(812\) | −12.5208 | + | 44.6350i | −0.439395 | + | 1.56638i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.6896 | + | 8.48105i | −0.514871 | + | 0.297261i | ||||
\(815\) | 4.90420 | + | 18.2704i | 0.171787 | + | 0.639985i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.86431 | + | 10.6897i | −0.100210 | + | 0.373987i | ||||
\(818\) | 47.0213 | + | 47.0213i | 1.64406 | + | 1.64406i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.6625 | − | 0.00913472i | 0.721567 | − | 0.000318998i | ||||
\(821\) | 36.8611 | − | 21.2817i | 1.28646 | − | 0.742738i | 0.308439 | − | 0.951244i | \(-0.400194\pi\) |
0.978021 | + | 0.208507i | \(0.0668602\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.56545 | − | 31.9667i | −0.298573 | − | 1.11429i | −0.938338 | − | 0.345719i | \(-0.887635\pi\) |
0.639765 | − | 0.768570i | \(-0.279032\pi\) | |||||||
\(824\) | 30.8785 | + | 53.4832i | 1.07570 | + | 1.86317i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 59.1968 | + | 35.1061i | 2.05972 | + | 1.22150i | ||||
\(827\) | −7.78145 | + | 7.78145i | −0.270587 | + | 0.270587i | −0.829337 | − | 0.558749i | \(-0.811281\pi\) |
0.558749 | + | 0.829337i | \(0.311281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.4643 | − | 18.7432i | −1.12753 | − | 0.650980i | −0.184218 | − | 0.982885i | \(-0.558975\pi\) |
−0.943313 | + | 0.331906i | \(0.892308\pi\) | |||||||
\(830\) | −39.6690 | + | 68.7790i | −1.37693 | + | 2.38735i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.6111 | − | 14.6111i | −0.506549 | − | 0.506549i | ||||
\(833\) | −4.92879 | − | 5.16477i | −0.170772 | − | 0.178949i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.694482 | − | 0.185757i | −0.0240335 | − | 0.00642838i | ||||
\(836\) | 119.156 | + | 68.7950i | 4.12111 | + | 2.37932i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.67693 | − | 1.52113i | −0.196106 | − | 0.0525465i | ||||
\(839\) | 0.118993 | 0.00410811 | 0.00205406 | − | 0.999998i | \(-0.499346\pi\) | ||||
0.00205406 | + | 0.999998i | \(0.499346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.5643 | −0.433253 | ||||||||
\(842\) | 34.3800 | + | 9.21208i | 1.18481 | + | 0.317469i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 50.4867 | + | 29.1485i | 1.73782 | + | 1.00333i | ||||
\(845\) | 51.9593 | − | 30.0294i | 1.78745 | − | 1.03304i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.5444 | − | 25.9311i | 0.912078 | − | 0.891003i | ||||
\(848\) | −0.179601 | − | 0.179601i | −0.00616753 | − | 0.00616753i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.1096 | + | 6.40103i | 0.381056 | + | 0.219554i | ||||
\(851\) | 0.321357 | + | 0.185536i | 0.0110160 | + | 0.00636008i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.51907 | − | 6.51907i | 0.223209 | − | 0.223209i | −0.586639 | − | 0.809848i | \(-0.699549\pi\) |
0.809848 | + | 0.586639i | \(0.199549\pi\) | |||||||
\(854\) | −11.8637 | + | 6.66587i | −0.405968 | + | 0.228101i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.5392 | − | 70.2160i | −1.38560 | − | 2.39993i | ||||
\(857\) | −7.94363 | − | 29.6460i | −0.271349 | − | 1.01269i | −0.958249 | − | 0.285936i | \(-0.907695\pi\) |
0.686899 | − | 0.726752i | \(-0.258971\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5614 | − | 17.6447i | 1.04274 | − | 0.602028i | 0.122134 | − | 0.992514i | \(-0.461026\pi\) |
0.920609 | + | 0.390486i | \(0.127693\pi\) | |||||||
\(860\) | 11.8892 | + | 11.8787i | 0.405419 | + | 0.405061i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.5971 | − | 29.5971i | −1.00808 | − | 1.00808i | ||||
\(863\) | 13.4253 | − | 50.1038i | 0.457002 | − | 1.70555i | −0.225134 | − | 0.974328i | \(-0.572282\pi\) |
0.682136 | − | 0.731225i | \(-0.261051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.4533 | − | 9.24807i | 1.17145 | − | 0.314444i | ||||
\(866\) | −25.9661 | + | 14.9915i | −0.882363 | + | 0.509433i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33.9824 | + | 34.7861i | 1.15344 | + | 1.18072i | ||||
\(869\) | 72.4164 | 2.45656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.7423 | + | 77.4959i | −1.51603 | + | 2.62585i | ||||
\(872\) | −5.87282 | − | 21.9177i | −0.198879 | − | 0.742226i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 4.40286i | − | 0.148929i | ||||||
\(875\) | 7.35952 | + | 28.6503i | 0.248797 | + | 0.968556i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.32717 | − | 19.8813i | 0.179886 | − | 0.671343i | −0.815782 | − | 0.578360i | \(-0.803693\pi\) |
0.995668 | − | 0.0929832i | \(-0.0296403\pi\) | |||||||
\(878\) | 79.2122 | − | 21.2249i | 2.67328 | − | 0.716304i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 58.4530 | − | 33.7823i | 1.97045 | − | 1.13880i | ||||
\(881\) | − | 18.4194i | − | 0.620564i | −0.950645 | − | 0.310282i | \(-0.899577\pi\) | ||
0.950645 | − | 0.310282i | \(-0.100423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6058 | + | 14.6058i | −0.491526 | + | 0.491526i | −0.908787 | − | 0.417261i | \(-0.862990\pi\) |
0.417261 | + | 0.908787i | \(0.362990\pi\) | |||||||
\(884\) | 13.9108 | + | 24.0942i | 0.467871 | + | 0.810377i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.5316 | − | 28.6336i | 0.555390 | − | 0.961963i | ||||
\(887\) | 14.6042 | + | 3.91318i | 0.490361 | + | 0.131392i | 0.495523 | − | 0.868595i | \(-0.334976\pi\) |
−0.00516191 | + | 0.999987i | \(0.501643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.49684 | + | 7.58269i | −0.150819 | + | 0.254315i | ||||
\(890\) | 19.0158 | − | 19.0326i | 0.637412 | − | 0.637976i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.3790 | + | 4.65669i | −0.581892 | + | 0.155918i | ||||
\(893\) | 48.0332 | − | 12.8704i | 1.60737 | − | 0.430693i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.04102 | + | 0.00399696i | −0.302208 | + | 0.000133604i | ||||
\(896\) | 40.2892 | + | 0.470906i | 1.34597 | + | 0.0157319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −91.5893 | − | 24.5413i | −3.05637 | − | 0.818953i | ||||
\(899\) | 8.62060 | − | 14.9313i | 0.287513 | − | 0.497987i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0214602 | − | 0.0371702i | −0.000714943 | − | 0.00123832i | ||||
\(902\) | 19.0161 | − | 19.0161i | 0.633166 | − | 0.633166i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 100.220i | 3.33327i | ||||||||
\(905\) | −10.6877 | − | 18.4927i | −0.355271 | − | 0.614719i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.7656 | + | 8.24361i | −1.02155 | + | 0.273725i | −0.730449 | − | 0.682967i | \(-0.760689\pi\) |
−0.291104 | + | 0.956691i | \(0.594023\pi\) | |||||||
\(908\) | 21.8524 | − | 81.5544i | 0.725198 | − | 2.70648i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −25.3184 | + | 90.4102i | −0.839296 | + | 2.99707i | ||||
\(911\) | − | 44.5563i | − | 1.47621i | −0.674683 | − | 0.738107i | \(-0.735720\pi\) | ||
0.674683 | − | 0.738107i | \(-0.264280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.2849 | + | 68.2401i | 0.605141 | + | 2.25842i | ||||
\(914\) | −8.95797 | + | 15.5157i | −0.296303 | + | 0.513212i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.9545 | −0.989725 | ||||||||
\(917\) | 8.82132 | + | 9.02997i | 0.291306 | + | 0.298196i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1834 | − | 16.8490i | 0.962671 | − | 0.555798i | 0.0656768 | − | 0.997841i | \(-0.479079\pi\) |
0.896994 | + | 0.442043i | \(0.145746\pi\) | |||||||
\(920\) | −3.11175 | − | 1.79473i | −0.102591 | − | 0.0591706i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.1512 | − | 56.5450i | 0.498978 | − | 1.86221i | ||||
\(923\) | 23.3655 | + | 23.3655i | 0.769084 | + | 0.769084i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.77199 | − | 4.76356i | −0.156902 | − | 0.156625i | ||||
\(926\) | −80.2157 | + | 46.3125i | −2.63605 | + | 1.52192i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.67118 | + | 13.7010i | 0.120512 | + | 0.449758i | ||||
\(929\) | −8.87442 | − | 15.3710i | −0.291160 | − | 0.504305i | 0.682924 | − | 0.730489i | \(-0.260708\pi\) |
−0.974084 | + | 0.226185i | \(0.927375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.1687 | − | 38.0470i | 0.759324 | − | 1.24694i | ||||
\(932\) | 65.0819 | − | 65.0819i | 2.13183 | − | 2.13183i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.0799 | + | 11.5932i | 0.657036 | + | 0.379340i | ||||
\(935\) | 11.0184 | − | 2.95760i | 0.360341 | − | 0.0967239i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.1626 | − | 30.1626i | −0.985368 | − | 0.985368i | 0.0145268 | − | 0.999894i | \(-0.495376\pi\) |
−0.999894 | + | 0.0145268i | \(0.995376\pi\) | |||||||
\(938\) | −23.3436 | − | 91.3785i | −0.762197 | − | 2.98361i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.5133 | − | 72.9534i | 0.636452 | − | 2.37948i | ||||
\(941\) | −29.0798 | − | 16.7893i | −0.947976 | − | 0.547314i | −0.0555241 | − | 0.998457i | \(-0.517683\pi\) |
−0.892451 | + | 0.451143i | \(0.851016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.568273 | − | 0.152268i | −0.0185055 | − | 0.00495854i | ||||
\(944\) | 62.4414 | 2.03229 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.8741 | 0.711187 | ||||||||
\(947\) | −28.6266 | − | 7.67048i | −0.930240 | − | 0.249257i | −0.238283 | − | 0.971196i | \(-0.576585\pi\) |
−0.691957 | + | 0.721939i | \(0.743251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.9211 | − | 32.8634i | −1.84774 | − | 1.06679i | ||||
\(950\) | −20.6381 | + | 77.2957i | −0.669588 | + | 2.50780i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.1681 | − | 4.25490i | −0.491602 | − | 0.137902i | ||||
\(953\) | −16.1133 | − | 16.1133i | −0.521961 | − | 0.521961i | 0.396202 | − | 0.918163i | \(-0.370328\pi\) |
−0.918163 | + | 0.396202i | \(0.870328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.0758 | − | 21.9606i | −1.23210 | − | 0.710629i | ||||
\(956\) | 2.94835 | + | 1.70223i | 0.0953564 | + | 0.0550540i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.1679 | + | 32.1679i | −1.03930 | + | 1.03930i | ||||
\(959\) | 1.79469 | − | 1.00838i | 0.0579536 | − | 0.0325624i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.45689 | + | 11.1837i | 0.208287 | + | 0.360763i | ||||
\(962\) | −5.53905 | − | 20.6720i | −0.178586 | − | 0.666492i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.28330 | + | 1.89562i | −0.105748 | + | 0.0610537i | ||||
\(965\) | 8.76234 | − | 8.77009i | 0.282070 | − | 0.282319i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.9843 | + | 32.9843i | 1.06070 | + | 1.06070i | 0.998034 | + | 0.0626698i | \(0.0199615\pi\) |
0.0626698 | + | 0.998034i | \(0.480039\pi\) | |||||||
\(968\) | 21.1934 | − | 79.0948i | 0.681181 | − | 2.54220i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.946024 | − | 1.64024i | 0.0303750 | − | 0.0526648i | ||||
\(971\) | −33.4151 | + | 19.2922i | −1.07234 | + | 0.619117i | −0.928820 | − | 0.370531i | \(-0.879176\pi\) |
−0.143521 | + | 0.989647i | \(0.545842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.93907 | − | 0.750819i | 0.0942224 | − | 0.0240701i | ||||
\(974\) | 6.09757 | 0.195379 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.17310 | + | 10.6921i | −0.197596 | + | 0.342246i | ||||
\(977\) | 0.612947 | + | 2.28755i | 0.0196099 | + | 0.0731852i | 0.975037 | − | 0.222041i | \(-0.0712718\pi\) |
−0.955428 | + | 0.295226i | \(0.904605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23.9389i | − | 0.765090i | ||||||
\(980\) | −32.4724 | − | 59.3464i | −1.03729 | − | 1.89575i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.93483 | + | 37.0773i | −0.317033 | + | 1.18318i | ||||
\(983\) | 27.5427 | − | 7.38005i | 0.878476 | − | 0.235387i | 0.208727 | − | 0.977974i | \(-0.433068\pi\) |
0.669750 | + | 0.742587i | \(0.266401\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.4919 | − | 6.28352i | −0.748516 | − | 0.200210i | ||||
\(986\) | 10.3961i | 0.331078i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −122.753 | + | 122.753i | −3.90528 | + | 3.90528i | ||||
\(989\) | −0.239264 | − | 0.414417i | −0.00760814 | − | 0.0131777i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.85117 | + | 15.3307i | −0.281167 | + | 0.486995i | −0.971672 | − | 0.236332i | \(-0.924055\pi\) |
0.690506 | + | 0.723327i | \(0.257388\pi\) | |||||||
\(992\) | 14.3725 | + | 3.85111i | 0.456328 | + | 0.122273i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −34.8244 | − | 0.407033i | −1.10456 | − | 0.0129103i | ||||
\(995\) | 0.00798936 | + | 18.0718i | 0.000253280 | + | 0.572913i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.3174 | + | 13.7505i | −1.62524 | + | 0.435481i | −0.952535 | − | 0.304431i | \(-0.901534\pi\) |
−0.672704 | + | 0.739912i | \(0.734867\pi\) | |||||||
\(998\) | −0.538660 | + | 0.144333i | −0.0170510 | + | 0.00456880i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.ch.a.242.2 | yes | 128 | |
3.2 | odd | 2 | inner | 945.2.ch.a.242.31 | yes | 128 | |
5.3 | odd | 4 | inner | 945.2.ch.a.53.2 | ✓ | 128 | |
7.2 | even | 3 | inner | 945.2.ch.a.107.31 | yes | 128 | |
15.8 | even | 4 | inner | 945.2.ch.a.53.31 | yes | 128 | |
21.2 | odd | 6 | inner | 945.2.ch.a.107.2 | yes | 128 | |
35.23 | odd | 12 | inner | 945.2.ch.a.863.31 | yes | 128 | |
105.23 | even | 12 | inner | 945.2.ch.a.863.2 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.ch.a.53.2 | ✓ | 128 | 5.3 | odd | 4 | inner | |
945.2.ch.a.53.31 | yes | 128 | 15.8 | even | 4 | inner | |
945.2.ch.a.107.2 | yes | 128 | 21.2 | odd | 6 | inner | |
945.2.ch.a.107.31 | yes | 128 | 7.2 | even | 3 | inner | |
945.2.ch.a.242.2 | yes | 128 | 1.1 | even | 1 | trivial | |
945.2.ch.a.242.31 | yes | 128 | 3.2 | odd | 2 | inner | |
945.2.ch.a.863.2 | yes | 128 | 105.23 | even | 12 | inner | |
945.2.ch.a.863.31 | yes | 128 | 35.23 | odd | 12 | inner |