Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(35,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 35.1 | ||
Root | \(0.944649 - 1.05244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.35 |
Dual form | 144.2.l.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32068 | + | 0.505776i | −0.933860 | + | 0.357638i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.48838 | − | 1.33594i | 0.744190 | − | 0.667968i | ||||
\(5\) | −2.10489 | − | 2.10489i | −0.941334 | − | 0.941334i | 0.0570377 | − | 0.998372i | \(-0.481834\pi\) |
−0.998372 | + | 0.0570377i | \(0.981834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.40731 | −1.66581 | −0.832904 | − | 0.553418i | \(-0.813323\pi\) | ||||
−0.832904 | + | 0.553418i | \(0.813323\pi\) | |||||||
\(8\) | −1.28999 | + | 2.51713i | −0.456079 | + | 0.889939i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.84448 | + | 1.71528i | 1.21573 | + | 0.542418i | ||||
\(11\) | 0.215589 | − | 0.215589i | 0.0650026 | − | 0.0650026i | −0.673858 | − | 0.738861i | \(-0.735364\pi\) |
0.738861 | + | 0.673858i | \(0.235364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.73544 | − | 2.73544i | −0.758675 | − | 0.758675i | 0.217406 | − | 0.976081i | \(-0.430240\pi\) |
−0.976081 | + | 0.217406i | \(0.930240\pi\) | |||||||
\(14\) | 5.82064 | − | 2.22912i | 1.55563 | − | 0.595756i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.430552 | − | 3.97676i | 0.107638 | − | 0.994190i | ||||
\(17\) | − | 2.36438i | − | 0.573447i | −0.958013 | − | 0.286724i | \(-0.907434\pi\) | ||
0.958013 | − | 0.286724i | \(-0.0925661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.758681 | − | 0.758681i | 0.174053 | − | 0.174053i | −0.614704 | − | 0.788758i | \(-0.710725\pi\) |
0.788758 | + | 0.614704i | \(0.210725\pi\) | |||||||
\(20\) | −5.94487 | − | 0.320879i | −1.32931 | − | 0.0717507i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.175684 | + | 0.393764i | −0.0374560 | + | 0.0839508i | ||||
\(23\) | 1.75549i | 0.366045i | 0.983109 | + | 0.183023i | \(0.0585881\pi\) | ||||
−0.983109 | + | 0.183023i | \(0.941412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.86110i | 0.772221i | ||||||||
\(26\) | 4.99616 | + | 2.22912i | 0.979827 | + | 0.437165i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.55976 | + | 5.88789i | −1.23968 | + | 1.11271i | ||||
\(29\) | 5.54221 | − | 5.54221i | 1.02916 | − | 1.02916i | 0.0296002 | − | 0.999562i | \(-0.490577\pi\) |
0.999562 | − | 0.0296002i | \(-0.00942341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.01709i | 1.61952i | 0.586763 | + | 0.809759i | \(0.300402\pi\) | ||||
−0.586763 | + | 0.809759i | \(0.699598\pi\) | |||||||
\(32\) | 1.44273 | + | 5.46978i | 0.255041 | + | 0.966930i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.19585 | + | 3.12259i | 0.205086 | + | 0.535520i | ||||
\(35\) | 9.27690 | + | 9.27690i | 1.56808 | + | 1.56808i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10242 | − | 3.10242i | 0.510035 | − | 0.510035i | −0.404502 | − | 0.914537i | \(-0.632555\pi\) |
0.914537 | + | 0.404502i | \(0.132555\pi\) | |||||||
\(38\) | −0.618250 | + | 1.38570i | −0.100293 | + | 0.224789i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.01355 | − | 2.58300i | 1.26705 | − | 0.408408i | ||||
\(41\) | −10.1014 | −1.57757 | −0.788785 | − | 0.614669i | \(-0.789290\pi\) | ||||
−0.788785 | + | 0.614669i | \(0.789290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.54621 | − | 3.54621i | −0.540792 | − | 0.540792i | 0.382969 | − | 0.923761i | \(-0.374901\pi\) |
−0.923761 | + | 0.382969i | \(0.874901\pi\) | |||||||
\(44\) | 0.0328654 | − | 0.608892i | 0.00495465 | − | 0.0917940i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.887886 | − | 2.31844i | −0.130912 | − | 0.341835i | ||||
\(47\) | −3.90136 | −0.569072 | −0.284536 | − | 0.958665i | \(-0.591840\pi\) | ||||
−0.284536 | + | 0.958665i | \(0.591840\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.4244 | 1.77491 | ||||||||
\(50\) | −1.95286 | − | 5.09927i | −0.276175 | − | 0.721146i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.72575 | − | 0.417003i | −1.07137 | − | 0.0578280i | ||||
\(53\) | 2.71378 | + | 2.71378i | 0.372766 | + | 0.372766i | 0.868484 | − | 0.495717i | \(-0.165095\pi\) |
−0.495717 | + | 0.868484i | \(0.665095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.907583 | −0.122378 | ||||||||
\(56\) | 5.68537 | − | 11.0938i | 0.759740 | − | 1.48247i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.51635 | + | 10.1226i | −0.593026 | + | 1.32916i | ||||
\(59\) | −3.40445 | + | 3.40445i | −0.443222 | + | 0.443222i | −0.893093 | − | 0.449871i | \(-0.851470\pi\) |
0.449871 | + | 0.893093i | \(0.351470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.75868 | − | 1.75868i | −0.225176 | − | 0.225176i | 0.585498 | − | 0.810674i | \(-0.300899\pi\) |
−0.810674 | + | 0.585498i | \(0.800899\pi\) | |||||||
\(62\) | −4.56063 | − | 11.9087i | −0.579201 | − | 1.51240i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.67187 | − | 6.49412i | −0.583984 | − | 0.811765i | ||||
\(65\) | 11.5156i | 1.42833i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.11951 | − | 9.11951i | 1.11413 | − | 1.11413i | 0.121539 | − | 0.992587i | \(-0.461217\pi\) |
0.992587 | − | 0.121539i | \(-0.0387831\pi\) | |||||||
\(68\) | −3.15866 | − | 3.51910i | −0.383044 | − | 0.426754i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.9438 | − | 7.55976i | −2.02518 | − | 0.903564i | ||||
\(71\) | − | 11.8897i | − | 1.41105i | −0.708684 | − | 0.705526i | \(-0.750711\pi\) | ||
0.708684 | − | 0.705526i | \(-0.249289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.482639i | − | 0.0564886i | −0.999601 | − | 0.0282443i | \(-0.991008\pi\) | ||
0.999601 | − | 0.0282443i | \(-0.00899163\pi\) | |||||||
\(74\) | −2.52817 | + | 5.66643i | −0.293894 | + | 0.658710i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.115657 | − | 2.14275i | 0.0132667 | − | 0.245791i | ||||
\(77\) | −0.950169 | + | 0.950169i | −0.108282 | + | 0.108282i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.88995i | − | 0.775180i | −0.921832 | − | 0.387590i | \(-0.873308\pi\) | ||
0.921832 | − | 0.387590i | \(-0.126692\pi\) | |||||||
\(80\) | −9.27690 | + | 7.46437i | −1.03719 | + | 0.834542i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.3407 | − | 5.10904i | 1.47323 | − | 0.564199i | ||||
\(83\) | −4.79951 | − | 4.79951i | −0.526814 | − | 0.526814i | 0.392807 | − | 0.919621i | \(-0.371504\pi\) |
−0.919621 | + | 0.392807i | \(0.871504\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97676 | + | 4.97676i | −0.539805 | + | 0.539805i | ||||
\(86\) | 6.47699 | + | 2.88981i | 0.698432 | + | 0.311616i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.264559 | + | 0.820773i | 0.0282021 | + | 0.0874947i | ||||
\(89\) | 7.00534 | 0.742564 | 0.371282 | − | 0.928520i | \(-0.378918\pi\) | ||||
0.371282 | + | 0.928520i | \(0.378918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0559 | + | 12.0559i | 1.26381 | + | 1.26381i | ||||
\(92\) | 2.34522 | + | 2.61284i | 0.244506 | + | 0.272407i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.15244 | − | 1.97322i | 0.531434 | − | 0.203522i | ||||
\(95\) | −3.19387 | −0.327685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34374 | −0.339506 | −0.169753 | − | 0.985487i | \(-0.554297\pi\) | ||||
−0.169753 | + | 0.985487i | \(0.554297\pi\) | |||||||
\(98\) | −16.4086 | + | 6.28397i | −1.65752 | + | 0.634777i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.15819 | + | 5.74679i | 0.515819 | + | 0.574679i | ||||
\(101\) | −1.76361 | − | 1.76361i | −0.175486 | − | 0.175486i | 0.613899 | − | 0.789385i | \(-0.289600\pi\) |
−0.789385 | + | 0.613899i | \(0.789600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.01709 | −0.100217 | −0.0501085 | − | 0.998744i | \(-0.515957\pi\) | ||||
−0.0501085 | + | 0.998744i | \(0.515957\pi\) | |||||||
\(104\) | 10.4141 | − | 3.35678i | 1.02119 | − | 0.329159i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.95660 | − | 2.21146i | −0.481427 | − | 0.214796i | ||||
\(107\) | 2.33152 | − | 2.33152i | 0.225396 | − | 0.225396i | −0.585370 | − | 0.810766i | \(-0.699051\pi\) |
0.810766 | + | 0.585370i | \(0.199051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.07918 | − | 8.07918i | −0.773845 | − | 0.773845i | 0.204931 | − | 0.978776i | \(-0.434303\pi\) |
−0.978776 | + | 0.204931i | \(0.934303\pi\) | |||||||
\(110\) | 1.19862 | − | 0.459034i | 0.114284 | − | 0.0437672i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.89758 | + | 17.5268i | −0.179304 | + | 1.65613i | ||||
\(113\) | 2.09677i | 0.197247i | 0.995125 | + | 0.0986237i | \(0.0314440\pi\) | ||||
−0.995125 | + | 0.0986237i | \(0.968556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.69511 | − | 3.69511i | 0.344571 | − | 0.344571i | ||||
\(116\) | 0.844880 | − | 15.6529i | 0.0784451 | − | 1.45334i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.77429 | − | 6.21808i | 0.255395 | − | 0.572421i | ||||
\(119\) | 10.4206i | 0.955253i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9070i | 0.991549i | ||||||||
\(122\) | 3.21215 | + | 1.43315i | 0.290814 | + | 0.129751i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0463 | + | 13.4209i | 1.08179 | + | 1.20523i | ||||
\(125\) | −2.39725 | + | 2.39725i | −0.214416 | + | 0.214416i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2802i | 0.912218i | 0.889924 | + | 0.456109i | \(0.150757\pi\) | ||||
−0.889924 | + | 0.456109i | \(0.849243\pi\) | |||||||
\(128\) | 9.45461 | + | 6.21372i | 0.835677 | + | 0.549221i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.82432 | − | 15.2084i | −0.510826 | − | 1.33386i | ||||
\(131\) | −6.80891 | − | 6.80891i | −0.594897 | − | 0.594897i | 0.344053 | − | 0.938950i | \(-0.388200\pi\) |
−0.938950 | + | 0.344053i | \(0.888200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.34374 | + | 3.34374i | −0.289939 | + | 0.289939i | ||||
\(134\) | −7.43151 | + | 16.6564i | −0.641984 | + | 1.43889i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.95146 | + | 3.05002i | 0.510333 | + | 0.261537i | ||||
\(137\) | 13.7922 | 1.17834 | 0.589172 | − | 0.808008i | \(-0.299454\pi\) | ||||
0.589172 | + | 0.808008i | \(0.299454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1195 | − | 13.1195i | −1.11278 | − | 1.11278i | −0.992773 | − | 0.120010i | \(-0.961707\pi\) |
−0.120010 | − | 0.992773i | \(-0.538293\pi\) | |||||||
\(140\) | 26.2009 | + | 1.41421i | 2.21438 | + | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.01355 | + | 15.7025i | 0.504646 | + | 1.31773i | ||||
\(143\) | −1.17946 | −0.0986317 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.3314 | −1.93757 | ||||||||
\(146\) | 0.244107 | + | 0.637410i | 0.0202025 | + | 0.0527525i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.472948 | − | 8.76222i | 0.0388761 | − | 0.720250i | ||||
\(149\) | 7.76174 | + | 7.76174i | 0.635867 | + | 0.635867i | 0.949533 | − | 0.313667i | \(-0.101557\pi\) |
−0.313667 | + | 0.949533i | \(0.601557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.202466 | −0.0164765 | −0.00823823 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823823 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(152\) | 0.931009 | + | 2.88838i | 0.0755148 | + | 0.234279i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.774294 | − | 1.73544i | 0.0623944 | − | 0.139846i | ||||
\(155\) | 18.9800 | − | 18.9800i | 1.52451 | − | 1.52451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.75868 | + | 3.75868i | 0.299975 | + | 0.299975i | 0.841004 | − | 0.541029i | \(-0.181965\pi\) |
−0.541029 | + | 0.841004i | \(0.681965\pi\) | |||||||
\(158\) | 3.48478 | + | 9.09941i | 0.277234 | + | 0.723910i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.47649 | − | 14.5501i | 0.670125 | − | 1.15028i | ||||
\(161\) | − | 7.73700i | − | 0.609761i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.2684 | + | 13.2684i | −1.03926 | + | 1.03926i | −0.0400655 | + | 0.999197i | \(0.512757\pi\) |
−0.999197 | + | 0.0400655i | \(0.987243\pi\) | |||||||
\(164\) | −15.0347 | + | 13.4948i | −1.17401 | + | 1.05377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.76608 | + | 3.91113i | 0.680380 | + | 0.303562i | ||||
\(167\) | − | 20.1644i | − | 1.56037i | −0.625548 | − | 0.780186i | \(-0.715125\pi\) | ||
0.625548 | − | 0.780186i | \(-0.284875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.96528i | 0.151175i | ||||||||
\(170\) | 4.05557 | − | 9.08983i | 0.311048 | − | 0.697158i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0156 | − | 0.540601i | −0.763683 | − | 0.0412204i | ||||
\(173\) | −3.98315 | + | 3.98315i | −0.302833 | + | 0.302833i | −0.842121 | − | 0.539288i | \(-0.818693\pi\) |
0.539288 | + | 0.842121i | \(0.318693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 17.0171i | − | 1.28637i | ||||||
\(176\) | −0.764525 | − | 0.950169i | −0.0576282 | − | 0.0716217i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.25179 | + | 3.54313i | −0.693451 | + | 0.265569i | ||||
\(179\) | −14.7182 | − | 14.7182i | −1.10009 | − | 1.10009i | −0.994399 | − | 0.105688i | \(-0.966296\pi\) |
−0.105688 | − | 0.994399i | \(-0.533704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.26456 | − | 3.26456i | 0.242653 | − | 0.242653i | −0.575294 | − | 0.817947i | \(-0.695112\pi\) |
0.817947 | + | 0.575294i | \(0.195112\pi\) | |||||||
\(182\) | −22.0196 | − | 9.82441i | −1.63220 | − | 0.728233i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.41880 | − | 2.26456i | −0.325758 | − | 0.166945i | ||||
\(185\) | −13.0605 | −0.960227 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.509736 | − | 0.509736i | −0.0372756 | − | 0.0372756i | ||||
\(188\) | −5.80671 | + | 5.21197i | −0.423498 | + | 0.380122i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.21808 | − | 1.61539i | 0.306012 | − | 0.117192i | ||||
\(191\) | 7.69868 | 0.557057 | 0.278528 | − | 0.960428i | \(-0.410153\pi\) | ||||
0.278528 | + | 0.960428i | \(0.410153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.51736 | −0.253185 | −0.126593 | − | 0.991955i | \(-0.540404\pi\) | ||||
−0.126593 | + | 0.991955i | \(0.540404\pi\) | |||||||
\(194\) | 4.41601 | − | 1.69119i | 0.317051 | − | 0.121420i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.4922 | − | 16.5982i | 1.32087 | − | 1.18559i | ||||
\(197\) | 6.40456 | + | 6.40456i | 0.456306 | + | 0.456306i | 0.897441 | − | 0.441135i | \(-0.145424\pi\) |
−0.441135 | + | 0.897441i | \(0.645424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.3491 | 1.65517 | 0.827586 | − | 0.561339i | \(-0.189714\pi\) | ||||
0.827586 | + | 0.561339i | \(0.189714\pi\) | |||||||
\(200\) | −9.71889 | − | 4.98077i | −0.687230 | − | 0.352194i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.22115 | + | 1.43717i | 0.226640 | + | 0.101119i | ||||
\(203\) | −24.4262 | + | 24.4262i | −1.71439 | + | 1.71439i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.2623 | + | 21.2623i | 1.48502 | + | 1.48502i | ||||
\(206\) | 1.34325 | − | 0.514421i | 0.0935887 | − | 0.0358414i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.0559 | + | 9.70045i | −0.835929 | + | 0.672605i | ||||
\(209\) | − | 0.327127i | − | 0.0226278i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.63688 | + | 6.63688i | −0.456901 | + | 0.456901i | −0.897637 | − | 0.440736i | \(-0.854718\pi\) |
0.440736 | + | 0.897637i | \(0.354718\pi\) | |||||||
\(212\) | 7.66457 | + | 0.413701i | 0.526405 | + | 0.0284131i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.89996 | + | 4.25841i | −0.129878 | + | 0.291099i | ||||
\(215\) | 14.9287i | 1.01813i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 39.7411i | − | 2.69780i | ||||||
\(218\) | 14.7563 | + | 6.58374i | 0.999420 | + | 0.445907i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.35083 | + | 1.21247i | −0.0910728 | + | 0.0817448i | ||||
\(221\) | −6.46763 | + | 6.46763i | −0.435060 | + | 0.435060i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.2219i | − | 0.885406i | −0.896668 | − | 0.442703i | \(-0.854020\pi\) | ||
0.896668 | − | 0.442703i | \(-0.145980\pi\) | |||||||
\(224\) | −6.35857 | − | 24.1070i | −0.424850 | − | 1.61072i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.06050 | − | 2.76916i | −0.0705431 | − | 0.184201i | ||||
\(227\) | 16.4029 | + | 16.4029i | 1.08870 | + | 1.08870i | 0.995663 | + | 0.0930369i | \(0.0296574\pi\) |
0.0930369 | + | 0.995663i | \(0.470343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.98677 | + | 4.98677i | −0.329535 | + | 0.329535i | −0.852410 | − | 0.522875i | \(-0.824860\pi\) |
0.522875 | + | 0.852410i | \(0.324860\pi\) | |||||||
\(230\) | −3.01115 | + | 6.74895i | −0.198549 | + | 0.445013i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.80108 | + | 21.0998i | 0.446513 | + | 1.38527i | ||||
\(233\) | −1.05879 | −0.0693634 | −0.0346817 | − | 0.999398i | \(-0.511042\pi\) | ||||
−0.0346817 | + | 0.999398i | \(0.511042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.21193 | + | 8.21193i | 0.535687 | + | 0.535687i | ||||
\(236\) | −0.518991 | + | 9.61525i | −0.0337834 | + | 0.625900i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.27048 | − | 13.7622i | −0.341635 | − | 0.892072i | ||||
\(239\) | −0.317107 | −0.0205119 | −0.0102560 | − | 0.999947i | \(-0.503265\pi\) | ||||
−0.0102560 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7334 | 0.755816 | 0.377908 | − | 0.925843i | \(-0.376644\pi\) | ||||
0.377908 | + | 0.925843i | \(0.376644\pi\) | |||||||
\(242\) | −5.51653 | − | 14.4047i | −0.354616 | − | 0.925969i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.96707 | − | 0.268101i | −0.317984 | − | 0.0171634i | ||||
\(245\) | −26.1520 | − | 26.1520i | −1.67079 | − | 1.67079i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.15065 | −0.264100 | ||||||||
\(248\) | −22.6972 | − | 11.6319i | −1.44127 | − | 0.738628i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.95352 | − | 4.37847i | 0.123552 | − | 0.276918i | ||||
\(251\) | −7.02450 | + | 7.02450i | −0.443382 | + | 0.443382i | −0.893147 | − | 0.449765i | \(-0.851508\pi\) |
0.449765 | + | 0.893147i | \(0.351508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.378465 | + | 0.378465i | 0.0237939 | + | 0.0237939i | ||||
\(254\) | −5.19947 | − | 13.5768i | −0.326244 | − | 0.851884i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6293 | − | 3.42440i | −0.976828 | − | 0.214025i | ||||
\(257\) | − | 23.5830i | − | 1.47107i | −0.677487 | − | 0.735535i | \(-0.736931\pi\) | ||
0.677487 | − | 0.735535i | \(-0.263069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6733 | + | 13.6733i | −0.849621 | + | 0.849621i | ||||
\(260\) | 15.3841 | + | 17.1396i | 0.954081 | + | 1.06295i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.4362 | + | 5.54859i | 0.768309 | + | 0.342793i | ||||
\(263\) | 20.1370i | 1.24170i | 0.783928 | + | 0.620851i | \(0.213213\pi\) | ||||
−0.783928 | + | 0.620851i | \(0.786787\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.4244i | − | 0.701796i | ||||||
\(266\) | 2.72482 | − | 6.10719i | 0.167069 | − | 0.374456i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.39022 | − | 25.7564i | 0.0849213 | − | 1.57332i | ||||
\(269\) | 8.62201 | − | 8.62201i | 0.525693 | − | 0.525693i | −0.393592 | − | 0.919285i | \(-0.628768\pi\) |
0.919285 | + | 0.393592i | \(0.128768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.18722i | 0.132864i | 0.997791 | + | 0.0664319i | \(0.0211615\pi\) | ||||
−0.997791 | + | 0.0664319i | \(0.978838\pi\) | |||||||
\(272\) | −9.40259 | − | 1.01799i | −0.570115 | − | 0.0617247i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.2150 | + | 6.97575i | −1.10041 | + | 0.421421i | ||||
\(275\) | 0.832413 | + | 0.832413i | 0.0501964 | + | 0.0501964i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.64248 | − | 8.64248i | 0.519277 | − | 0.519277i | −0.398076 | − | 0.917352i | \(-0.630322\pi\) |
0.917352 | + | 0.398076i | \(0.130322\pi\) | |||||||
\(278\) | 23.9622 | + | 10.6911i | 1.43716 | + | 0.641210i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −35.3182 | + | 11.3841i | −2.11067 | + | 0.680328i | ||||
\(281\) | 14.8081 | 0.883375 | 0.441688 | − | 0.897169i | \(-0.354380\pi\) | ||||
0.441688 | + | 0.897169i | \(0.354380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.12714 | + | 6.12714i | 0.364221 | + | 0.364221i | 0.865364 | − | 0.501144i | \(-0.167087\pi\) |
−0.501144 | + | 0.865364i | \(0.667087\pi\) | |||||||
\(284\) | −15.8839 | − | 17.6964i | −0.942537 | − | 1.05009i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.55769 | − | 0.596545i | 0.0921082 | − | 0.0352744i | ||||
\(287\) | 44.5199 | 2.62793 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4097 | 0.671158 | ||||||||
\(290\) | 30.8133 | − | 11.8005i | 1.80942 | − | 0.692949i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.644774 | − | 0.718350i | −0.0377326 | − | 0.0420383i | ||||
\(293\) | 11.8979 | + | 11.8979i | 0.695080 | + | 0.695080i | 0.963345 | − | 0.268265i | \(-0.0864503\pi\) |
−0.268265 | + | 0.963345i | \(0.586450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3320 | 0.834441 | ||||||||
\(296\) | 3.80711 | + | 11.8113i | 0.221284 | + | 0.686517i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.1765 | − | 6.32505i | −0.821221 | − | 0.366401i | ||||
\(299\) | 4.80204 | − | 4.80204i | 0.277709 | − | 0.277709i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6293 | + | 15.6293i | 0.900855 | + | 0.900855i | ||||
\(302\) | 0.267393 | − | 0.102403i | 0.0153867 | − | 0.00589261i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.69044 | − | 3.34374i | −0.154307 | − | 0.191777i | ||||
\(305\) | 7.40365i | 0.423932i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.91467 | − | 4.91467i | 0.280495 | − | 0.280495i | −0.552811 | − | 0.833306i | \(-0.686445\pi\) |
0.833306 | + | 0.552811i | \(0.186445\pi\) | |||||||
\(308\) | −0.144848 | + | 2.68358i | −0.00825350 | + | 0.152911i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.4668 | + | 34.6660i | −0.878455 | + | 1.96890i | ||||
\(311\) | 20.7712i | 1.17783i | 0.808195 | + | 0.588915i | \(0.200445\pi\) | ||||
−0.808195 | + | 0.588915i | \(0.799555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.3897i | 0.926400i | 0.886254 | + | 0.463200i | \(0.153299\pi\) | ||||
−0.886254 | + | 0.463200i | \(0.846701\pi\) | |||||||
\(314\) | −6.86506 | − | 3.06295i | −0.387418 | − | 0.172853i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.20453 | − | 10.2549i | −0.517795 | − | 0.576881i | ||||
\(317\) | −22.3592 | + | 22.3592i | −1.25582 | + | 1.25582i | −0.302749 | + | 0.953070i | \(0.597904\pi\) |
−0.953070 | + | 0.302749i | \(0.902096\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.38968i | − | 0.133796i | ||||||
\(320\) | −3.83563 | + | 23.5032i | −0.214418 | + | 1.31387i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.91319 | + | 10.2181i | 0.218074 | + | 0.569431i | ||||
\(323\) | −1.79381 | − | 1.79381i | −0.0998103 | − | 0.0998103i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5618 | − | 10.5618i | 0.585865 | − | 0.585865i | ||||
\(326\) | 10.8125 | − | 24.2342i | 0.598846 | − | 1.34221i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.0306 | − | 25.4265i | 0.719497 | − | 1.40394i | ||||
\(329\) | 17.1945 | 0.947965 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.08533 | − | 7.08533i | −0.389445 | − | 0.389445i | 0.485044 | − | 0.874490i | \(-0.338803\pi\) |
−0.874490 | + | 0.485044i | \(0.838803\pi\) | |||||||
\(332\) | −13.5553 | − | 0.731659i | −0.743945 | − | 0.0401550i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.1987 | + | 26.6307i | 0.558048 | + | 1.45717i | ||||
\(335\) | −38.3911 | −2.09753 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.3314 | −1.27094 | −0.635472 | − | 0.772124i | \(-0.719195\pi\) | ||||
−0.635472 | + | 0.772124i | \(0.719195\pi\) | |||||||
\(338\) | −0.993991 | − | 2.59550i | −0.0540660 | − | 0.141177i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.758681 | + | 14.0559i | −0.0411452 | + | 0.762291i | ||||
\(341\) | 1.94399 | + | 1.94399i | 0.105273 | + | 0.105273i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23.9070 | −1.29086 | ||||||||
\(344\) | 13.5008 | − | 4.35170i | 0.727916 | − | 0.234628i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.24587 | − | 7.27503i | 0.174499 | − | 0.391108i | ||||
\(347\) | 21.2074 | − | 21.2074i | 1.13847 | − | 1.13847i | 0.149751 | − | 0.988724i | \(-0.452153\pi\) |
0.988724 | − | 0.149751i | \(-0.0478471\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.38022 | + | 5.38022i | 0.287996 | + | 0.287996i | 0.836288 | − | 0.548291i | \(-0.184721\pi\) |
−0.548291 | + | 0.836288i | \(0.684721\pi\) | |||||||
\(350\) | 8.60684 | + | 22.4741i | 0.460055 | + | 1.20129i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.49026 | + | 0.868189i | 0.0794314 | + | 0.0462746i | ||||
\(353\) | − | 10.5163i | − | 0.559727i | −0.960040 | − | 0.279864i | \(-0.909711\pi\) | ||
0.960040 | − | 0.279864i | \(-0.0902892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.0266 | + | 25.0266i | −1.32827 | + | 1.32827i | ||||
\(356\) | 10.4266 | − | 9.35868i | 0.552609 | − | 0.496009i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.8821 | + | 11.9939i | 1.42076 | + | 0.633895i | ||||
\(359\) | 11.7583i | 0.620578i | 0.950642 | + | 0.310289i | \(0.100426\pi\) | ||||
−0.950642 | + | 0.310289i | \(0.899574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8488i | 0.939411i | ||||||||
\(362\) | −2.66029 | + | 5.96257i | −0.139822 | + | 0.313386i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 34.0498 | + | 1.83786i | 1.78469 | + | 0.0963303i | ||||
\(365\) | −1.01590 | + | 1.01590i | −0.0531747 | + | 0.0531747i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.49973i | 0.182684i | 0.995820 | + | 0.0913422i | \(0.0291157\pi\) | ||||
−0.995820 | + | 0.0913422i | \(0.970884\pi\) | |||||||
\(368\) | 6.98117 | + | 0.755830i | 0.363918 | + | 0.0394004i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.2487 | − | 6.60570i | 0.896718 | − | 0.343414i | ||||
\(371\) | −11.9605 | − | 11.9605i | −0.620957 | − | 0.620957i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.1831 | − | 19.1831i | 0.993262 | − | 0.993262i | −0.00671500 | − | 0.999977i | \(-0.502137\pi\) |
0.999977 | + | 0.00671500i | \(0.00213747\pi\) | |||||||
\(374\) | 0.931009 | + | 0.415384i | 0.0481413 | + | 0.0214790i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.03271 | − | 9.82023i | 0.259542 | − | 0.506440i | ||||
\(377\) | −30.3208 | −1.56160 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9977 | − | 14.9977i | −0.770381 | − | 0.770381i | 0.207792 | − | 0.978173i | \(-0.433372\pi\) |
−0.978173 | + | 0.207792i | \(0.933372\pi\) | |||||||
\(380\) | −4.75370 | + | 4.26681i | −0.243860 | + | 0.218883i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.1675 | + | 3.89381i | −0.520213 | + | 0.199225i | ||||
\(383\) | 30.4027 | 1.55351 | 0.776754 | − | 0.629805i | \(-0.216865\pi\) | ||||
0.776754 | + | 0.629805i | \(0.216865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 4.64530 | − | 1.77900i | 0.236440 | − | 0.0905486i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.97676 | + | 4.46702i | −0.252657 | + | 0.226779i | ||||
\(389\) | −19.4571 | − | 19.4571i | −0.986516 | − | 0.986516i | 0.0133943 | − | 0.999910i | \(-0.495736\pi\) |
−0.999910 | + | 0.0133943i | \(0.995736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.15065 | 0.209908 | ||||||||
\(392\) | −16.0273 | + | 31.2738i | −0.809501 | + | 1.57957i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.6976 | − | 5.21909i | −0.589319 | − | 0.262934i | ||||
\(395\) | −14.5026 | + | 14.5026i | −0.729704 | + | 0.729704i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4339 | − | 20.4339i | −1.02555 | − | 1.02555i | −0.999665 | − | 0.0258815i | \(-0.991761\pi\) |
−0.0258815 | − | 0.999665i | \(-0.508239\pi\) | |||||||
\(398\) | −30.8366 | + | 11.8094i | −1.54570 | + | 0.591952i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.3547 | + | 1.66241i | 0.767734 | + | 0.0831203i | ||||
\(401\) | − | 22.5671i | − | 1.12695i | −0.826133 | − | 0.563475i | \(-0.809464\pi\) | ||
0.826133 | − | 0.563475i | \(-0.190536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.6657 | − | 24.6657i | 1.22869 | − | 1.22869i | ||||
\(404\) | −4.98099 | − | 0.268853i | −0.247814 | − | 0.0133759i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.9050 | − | 44.6134i | 0.987867 | − | 2.21413i | ||||
\(407\) | − | 1.33770i | − | 0.0663073i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.78286i | − | 0.483731i | −0.970310 | − | 0.241866i | \(-0.922241\pi\) | ||
0.970310 | − | 0.241866i | \(-0.0777593\pi\) | |||||||
\(410\) | −38.8346 | − | 17.3267i | −1.91790 | − | 0.855702i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.51382 | + | 1.35877i | −0.0745805 | + | 0.0669417i | ||||
\(413\) | 15.0045 | − | 15.0045i | 0.738323 | − | 0.738323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.2048i | 0.991817i | ||||||||
\(416\) | 11.0158 | − | 18.9088i | 0.540092 | − | 0.927079i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.165453 | + | 0.432029i | 0.00809257 | + | 0.0211312i | ||||
\(419\) | 9.09125 | + | 9.09125i | 0.444137 | + | 0.444137i | 0.893400 | − | 0.449263i | \(-0.148313\pi\) |
−0.449263 | + | 0.893400i | \(0.648313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9862 | + | 17.9862i | −0.876595 | + | 0.876595i | −0.993181 | − | 0.116586i | \(-0.962805\pi\) |
0.116586 | + | 0.993181i | \(0.462805\pi\) | |||||||
\(422\) | 5.40840 | − | 12.1220i | 0.263277 | − | 0.590087i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.3317 | + | 3.33019i | −0.501750 | + | 0.161729i | ||||
\(425\) | 9.12913 | 0.442828 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.75106 | + | 7.75106i | 0.375100 | + | 0.375100i | ||||
\(428\) | 0.355427 | − | 6.58494i | 0.0171802 | − | 0.318295i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.55061 | − | 19.7161i | −0.364123 | − | 0.950793i | ||||
\(431\) | −30.7707 | −1.48217 | −0.741085 | − | 0.671411i | \(-0.765689\pi\) | ||||
−0.741085 | + | 0.671411i | \(0.765689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.49735 | 0.168072 | 0.0840360 | − | 0.996463i | \(-0.473219\pi\) | ||||
0.0840360 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(434\) | 20.1001 | + | 52.4852i | 0.964837 | + | 2.51937i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.8182 | − | 1.23163i | −1.09279 | − | 0.0589843i | ||||
\(437\) | 1.33186 | + | 1.33186i | 0.0637113 | + | 0.0637113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1290 | −1.00843 | −0.504216 | − | 0.863578i | \(-0.668218\pi\) | ||||
−0.504216 | + | 0.863578i | \(0.668218\pi\) | |||||||
\(440\) | 1.17077 | − | 2.28450i | 0.0558142 | − | 0.108909i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.27048 | − | 11.8128i | 0.250691 | − | 0.561879i | ||||
\(443\) | 12.6022 | − | 12.6022i | 0.598750 | − | 0.598750i | −0.341230 | − | 0.939980i | \(-0.610843\pi\) |
0.939980 | + | 0.341230i | \(0.110843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.7454 | − | 14.7454i | −0.699001 | − | 0.699001i | ||||
\(446\) | 6.68735 | + | 17.4619i | 0.316655 | + | 0.826846i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.5904 | + | 28.6216i | 0.972805 | + | 1.35224i | ||||
\(449\) | 9.98731i | 0.471330i | 0.971834 | + | 0.235665i | \(0.0757268\pi\) | ||||
−0.971834 | + | 0.235665i | \(0.924273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17775 | + | 2.17775i | −0.102546 | + | 0.102546i | ||||
\(452\) | 2.80115 | + | 3.12079i | 0.131755 | + | 0.146790i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −29.9592 | − | 13.3668i | −1.40605 | − | 0.627333i | ||||
\(455\) | − | 50.7528i | − | 2.37933i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.2508i | − | 0.713402i | −0.934219 | − | 0.356701i | \(-0.883902\pi\) | ||
0.934219 | − | 0.356701i | \(-0.116098\pi\) | |||||||
\(458\) | 4.06372 | − | 9.10810i | 0.189885 | − | 0.425594i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.563300 | − | 10.4362i | 0.0262640 | − | 0.486588i | ||||
\(461\) | 14.3850 | − | 14.3850i | 0.669976 | − | 0.669976i | −0.287734 | − | 0.957710i | \(-0.592902\pi\) |
0.957710 | + | 0.287734i | \(0.0929019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.1295i | − | 1.02845i | −0.857657 | − | 0.514223i | \(-0.828080\pi\) | ||
0.857657 | − | 0.514223i | \(-0.171920\pi\) | |||||||
\(464\) | −19.6538 | − | 24.4262i | −0.912406 | − | 1.13396i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.39832 | − | 0.535509i | 0.0647757 | − | 0.0248070i | ||||
\(467\) | −4.79951 | − | 4.79951i | −0.222095 | − | 0.222095i | 0.587285 | − | 0.809380i | \(-0.300197\pi\) |
−0.809380 | + | 0.587285i | \(0.800197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.1926 | + | 40.1926i | −1.85592 | + | 1.85592i | ||||
\(470\) | −14.9987 | − | 6.69192i | −0.691839 | − | 0.308675i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.17775 | − | 12.9611i | −0.192297 | − | 0.596585i | ||||
\(473\) | −1.52905 | −0.0703058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.92934 | + | 2.92934i | 0.134408 | + | 0.134408i | ||||
\(476\) | 13.9212 | + | 15.5098i | 0.638078 | + | 0.710890i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.418796 | − | 0.160385i | 0.0191553 | − | 0.00733584i | ||||
\(479\) | −23.2801 | −1.06369 | −0.531847 | − | 0.846840i | \(-0.678502\pi\) | ||||
−0.531847 | + | 0.846840i | \(0.678502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9730 | −0.773902 | ||||||||
\(482\) | −15.4961 | + | 5.93449i | −0.705827 | + | 0.270309i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.5711 | + | 16.2338i | 0.662323 | + | 0.737901i | ||||
\(485\) | 7.03820 | + | 7.03820i | 0.319588 | + | 0.319588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0748 | 0.954990 | 0.477495 | − | 0.878635i | \(-0.341545\pi\) | ||||
0.477495 | + | 0.878635i | \(0.341545\pi\) | |||||||
\(488\) | 6.69550 | − | 2.15815i | 0.303091 | − | 0.0976949i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 47.7654 | + | 21.3113i | 2.15782 | + | 0.962746i | ||||
\(491\) | −26.1459 | + | 26.1459i | −1.17995 | + | 1.17995i | −0.200194 | + | 0.979756i | \(0.564157\pi\) |
−0.979756 | + | 0.200194i | \(0.935843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.1039 | − | 13.1039i | −0.590170 | − | 0.590170i | ||||
\(494\) | 5.48168 | − | 2.09930i | 0.246632 | − | 0.0944521i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 35.8588 | + | 3.88233i | 1.61011 | + | 0.174322i | ||||
\(497\) | 52.4018i | 2.35054i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0195 | − | 21.0195i | 0.940961 | − | 0.940961i | −0.0573910 | − | 0.998352i | \(-0.518278\pi\) |
0.998352 | + | 0.0573910i | \(0.0182782\pi\) | |||||||
\(500\) | −0.365448 | + | 6.77059i | −0.0163433 | + | 0.302790i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.72427 | − | 12.8299i | 0.255487 | − | 0.572628i | ||||
\(503\) | − | 44.4925i | − | 1.98382i | −0.126929 | − | 0.991912i | \(-0.540512\pi\) | ||
0.126929 | − | 0.991912i | \(-0.459488\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.42440i | 0.330382i | ||||||||
\(506\) | −0.691249 | − | 0.308412i | −0.0307298 | − | 0.0137106i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.7336 | + | 15.3008i | 0.609332 | + | 0.678864i | ||||
\(509\) | 11.7664 | − | 11.7664i | 0.521536 | − | 0.521536i | −0.396499 | − | 0.918035i | \(-0.629775\pi\) |
0.918035 | + | 0.396499i | \(0.129775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.12714i | 0.0940991i | ||||||||
\(512\) | 22.3732 | − | 3.38237i | 0.988765 | − | 0.149481i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.9277 | + | 31.1456i | 0.526110 | + | 1.37377i | ||||
\(515\) | 2.14086 | + | 2.14086i | 0.0943377 | + | 0.0943377i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.841092 | + | 0.841092i | −0.0369912 | + | 0.0369912i | ||||
\(518\) | 11.1424 | − | 24.9737i | 0.489570 | − | 1.09728i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −28.9862 | − | 14.8550i | −1.27113 | − | 0.651433i | ||||
\(521\) | −29.6216 | −1.29775 | −0.648873 | − | 0.760897i | \(-0.724759\pi\) | ||||
−0.648873 | + | 0.760897i | \(0.724759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.96353 | + | 4.96353i | 0.217040 | + | 0.217040i | 0.807250 | − | 0.590210i | \(-0.200955\pi\) |
−0.590210 | + | 0.807250i | \(0.700955\pi\) | |||||||
\(524\) | −19.2305 | − | 1.03798i | −0.840089 | − | 0.0453444i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1848 | − | 26.5945i | −0.444080 | − | 1.15958i | ||||
\(527\) | 21.3199 | 0.928708 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9183 | 0.866011 | ||||||||
\(530\) | 5.77819 | + | 15.0880i | 0.250989 | + | 0.655379i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.509736 | + | 9.44379i | −0.0220998 | + | 0.409440i | ||||
\(533\) | 27.6317 | + | 27.6317i | 1.19686 | + | 1.19686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.81517 | −0.424347 | ||||||||
\(536\) | 11.1909 | + | 34.7190i | 0.483375 | + | 1.49963i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.02609 | + | 15.7477i | −0.302916 | + | 0.678932i | ||||
\(539\) | 2.67857 | − | 2.67857i | 0.115374 | − | 0.115374i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0792 | + | 10.0792i | 0.433338 | + | 0.433338i | 0.889762 | − | 0.456424i | \(-0.150870\pi\) |
−0.456424 | + | 0.889762i | \(0.650870\pi\) | |||||||
\(542\) | −1.10624 | − | 2.88861i | −0.0475172 | − | 0.124076i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.9327 | − | 3.41117i | 0.554483 | − | 0.146253i | ||||
\(545\) | 34.0115i | 1.45689i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.48797 | − | 2.48797i | 0.106378 | − | 0.106378i | −0.651914 | − | 0.758293i | \(-0.726034\pi\) |
0.758293 | + | 0.651914i | \(0.226034\pi\) | |||||||
\(548\) | 20.5280 | − | 18.4254i | 0.876912 | − | 0.787096i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.52036 | − | 0.678334i | −0.0648285 | − | 0.0289243i | ||||
\(551\) | − | 8.40953i | − | 0.358258i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3662i | 1.29130i | ||||||||
\(554\) | −7.04277 | + | 15.7851i | −0.299219 | + | 0.670645i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.0537 | − | 2.00000i | −1.57142 | − | 0.0848189i | ||||
\(557\) | −24.2575 | + | 24.2575i | −1.02782 | + | 1.02782i | −0.0282205 | + | 0.999602i | \(0.508984\pi\) |
−0.999602 | + | 0.0282205i | \(0.991016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.4009i | 0.820570i | ||||||||
\(560\) | 40.8862 | − | 32.8978i | 1.72776 | − | 1.39019i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5567 | + | 7.48957i | −0.824949 | + | 0.315928i | ||||
\(563\) | 14.4061 | + | 14.4061i | 0.607143 | + | 0.607143i | 0.942198 | − | 0.335055i | \(-0.108755\pi\) |
−0.335055 | + | 0.942198i | \(0.608755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.41346 | − | 4.41346i | 0.185676 | − | 0.185676i | ||||
\(566\) | −11.1909 | − | 4.99302i | −0.470390 | − | 0.209872i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.9280 | + | 15.3376i | 1.25575 | + | 0.643551i | ||||
\(569\) | 33.5254 | 1.40546 | 0.702729 | − | 0.711457i | \(-0.251964\pi\) | ||||
0.702729 | + | 0.711457i | \(0.251964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5368 | + | 14.5368i | 0.608348 | + | 0.608348i | 0.942514 | − | 0.334167i | \(-0.108455\pi\) |
−0.334167 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(572\) | −1.75549 | + | 1.57569i | −0.0734008 | + | 0.0658828i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −58.7965 | + | 22.5171i | −2.45412 | + | 0.939847i | ||||
\(575\) | −6.77813 | −0.282668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3662 | 0.847855 | 0.423927 | − | 0.905696i | \(-0.360651\pi\) | ||||
0.423927 | + | 0.905696i | \(0.360651\pi\) | |||||||
\(578\) | −15.0685 | + | 5.77075i | −0.626768 | + | 0.240032i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −34.7261 | + | 31.1693i | −1.44192 | + | 1.29424i | ||||
\(581\) | 21.1529 | + | 21.1529i | 0.877571 | + | 0.877571i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17012 | 0.0484616 | ||||||||
\(584\) | 1.21486 | + | 0.622597i | 0.0502714 | + | 0.0257633i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.7309 | − | 9.69558i | −0.897695 | − | 0.400521i | ||||
\(587\) | 17.4809 | − | 17.4809i | 0.721512 | − | 0.721512i | −0.247401 | − | 0.968913i | \(-0.579576\pi\) |
0.968913 | + | 0.247401i | \(0.0795765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.84109 | + | 6.84109i | 0.281882 | + | 0.281882i | ||||
\(590\) | −18.9279 | + | 7.24878i | −0.779251 | + | 0.298428i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.0018 | − | 13.6733i | −0.452173 | − | 0.561971i | ||||
\(593\) | − | 25.6632i | − | 1.05386i | −0.849908 | − | 0.526930i | \(-0.823343\pi\) | ||
0.849908 | − | 0.526930i | \(-0.176657\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.9341 | − | 21.9341i | 0.899212 | − | 0.899212i | ||||
\(596\) | 21.9216 | + | 1.18324i | 0.897944 | + | 0.0484672i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.91319 | + | 8.77071i | −0.160022 | + | 0.358661i | ||||
\(599\) | 22.4652i | 0.917902i | 0.888461 | + | 0.458951i | \(0.151775\pi\) | ||||
−0.888461 | + | 0.458951i | \(0.848225\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8106i | 1.29758i | 0.760967 | + | 0.648790i | \(0.224725\pi\) | ||||
−0.760967 | + | 0.648790i | \(0.775275\pi\) | |||||||
\(602\) | −28.5461 | − | 12.7363i | −1.16345 | − | 0.519093i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.301347 | + | 0.270482i | −0.0122616 | + | 0.0110057i | ||||
\(605\) | 22.9581 | − | 22.9581i | 0.933379 | − | 0.933379i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9829i | 0.608138i | 0.952650 | + | 0.304069i | \(0.0983453\pi\) | ||||
−0.952650 | + | 0.304069i | \(0.901655\pi\) | |||||||
\(608\) | 5.24439 | + | 3.05525i | 0.212688 | + | 0.123907i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.74459 | − | 9.77784i | −0.151614 | − | 0.395893i | ||||
\(611\) | 10.6720 | + | 10.6720i | 0.431741 | + | 0.431741i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.6734 | − | 25.6734i | 1.03694 | − | 1.03694i | 0.0376494 | − | 0.999291i | \(-0.488013\pi\) |
0.999291 | − | 0.0376494i | \(-0.0119870\pi\) | |||||||
\(614\) | −4.00497 | + | 8.97642i | −0.161627 | + | 0.362259i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.16599 | − | 3.61740i | −0.0469792 | − | 0.145749i | ||||
\(617\) | −27.1598 | −1.09341 | −0.546705 | − | 0.837325i | \(-0.684118\pi\) | ||||
−0.546705 | + | 0.837325i | \(0.684118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.4244 | − | 29.4244i | −1.18267 | − | 1.18267i | −0.979051 | − | 0.203616i | \(-0.934731\pi\) |
−0.203616 | − | 0.979051i | \(-0.565269\pi\) | |||||||
\(620\) | 2.89339 | − | 53.6054i | 0.116202 | − | 2.15285i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.5056 | − | 27.4321i | −0.421236 | − | 1.09993i | ||||
\(623\) | −30.8747 | −1.23697 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.3974 | 1.17590 | ||||||||
\(626\) | −8.28952 | − | 21.6455i | −0.331316 | − | 0.865128i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.6157 | + | 0.572991i | 0.423613 | + | 0.0228648i | ||||
\(629\) | −7.33532 | − | 7.33532i | −0.292478 | − | 0.292478i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.84697 | −0.312383 | −0.156191 | − | 0.987727i | \(-0.549922\pi\) | ||||
−0.156191 | + | 0.987727i | \(0.549922\pi\) | |||||||
\(632\) | 17.3429 | + | 8.88794i | 0.689863 | + | 0.353543i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.2206 | − | 40.8381i | 0.723631 | − | 1.62189i | ||||
\(635\) | 21.6386 | − | 21.6386i | 0.858702 | − | 0.858702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.9862 | − | 33.9862i | −1.34658 | − | 1.34658i | ||||
\(638\) | 1.20864 | + | 3.15600i | 0.0478507 | + | 0.124947i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.82171 | − | 32.9801i | −0.269652 | − | 1.30365i | ||||
\(641\) | 37.7956i | 1.49284i | 0.665477 | + | 0.746418i | \(0.268228\pi\) | ||||
−0.665477 | + | 0.746418i | \(0.731772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.3026 | − | 27.3026i | 1.07671 | − | 1.07671i | 0.0799071 | − | 0.996802i | \(-0.474538\pi\) |
0.996802 | − | 0.0799071i | \(-0.0254624\pi\) | |||||||
\(644\) | −10.3361 | − | 11.5156i | −0.407301 | − | 0.453778i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.27632 | + | 1.46178i | 0.128905 | + | 0.0575130i | ||||
\(647\) | − | 0.100686i | − | 0.00395836i | −0.999998 | − | 0.00197918i | \(-0.999370\pi\) | ||
0.999998 | − | 0.00197918i | \(-0.000629993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.46793i | 0.0576212i | ||||||||
\(650\) | −8.60684 | + | 19.2907i | −0.337588 | + | 0.756643i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.02270 | + | 37.4742i | −0.0792150 | + | 1.46760i | ||||
\(653\) | 9.10477 | − | 9.10477i | 0.356297 | − | 0.356297i | −0.506149 | − | 0.862446i | \(-0.668931\pi\) |
0.862446 | + | 0.506149i | \(0.168931\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.6640i | 1.11999i | ||||||||
\(656\) | −4.34917 | + | 40.1708i | −0.169806 | + | 1.56840i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.7084 | + | 8.69659i | −0.885267 | + | 0.339028i | ||||
\(659\) | −14.6141 | − | 14.6141i | −0.569285 | − | 0.569285i | 0.362643 | − | 0.931928i | \(-0.381874\pi\) |
−0.931928 | + | 0.362643i | \(0.881874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.87057 | − | 5.87057i | 0.228339 | − | 0.228339i | −0.583660 | − | 0.811998i | \(-0.698380\pi\) |
0.811998 | + | 0.583660i | \(0.198380\pi\) | |||||||
\(662\) | 12.9410 | + | 5.77385i | 0.502968 | + | 0.224407i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.2723 | − | 5.88968i | 0.709102 | − | 0.228564i | ||||
\(665\) | 14.0764 | 0.545860 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.72929 | + | 9.72929i | 0.376720 | + | 0.376720i | ||||
\(668\) | −26.9384 | − | 30.0124i | −1.04228 | − | 1.16121i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 50.7023 | − | 19.4173i | 1.95880 | − | 0.750156i | ||||
\(671\) | −0.758305 | −0.0292741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3515 | −1.05432 | −0.527161 | − | 0.849766i | \(-0.676743\pi\) | ||||
−0.527161 | + | 0.849766i | \(0.676743\pi\) | |||||||
\(674\) | 30.8133 | − | 11.8005i | 1.18688 | − | 0.454538i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.62548 | + | 2.92508i | 0.100980 | + | 0.112503i | ||||
\(677\) | −31.2462 | − | 31.2462i | −1.20089 | − | 1.20089i | −0.973897 | − | 0.226992i | \(-0.927111\pi\) |
−0.226992 | − | 0.973897i | \(-0.572889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.7369 | 0.565551 | ||||||||
\(680\) | −6.10719 | − | 18.9471i | −0.234200 | − | 0.726588i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.55061 | − | 1.58416i | −0.135960 | − | 0.0606606i | ||||
\(683\) | −15.0378 | + | 15.0378i | −0.575406 | + | 0.575406i | −0.933634 | − | 0.358228i | \(-0.883381\pi\) |
0.358228 | + | 0.933634i | \(0.383381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.0310 | − | 29.0310i | −1.10922 | − | 1.10922i | ||||
\(686\) | 31.5735 | − | 12.0916i | 1.20548 | − | 0.461660i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.6293 | + | 12.5756i | −0.595860 | + | 0.479440i | ||||
\(689\) | − | 14.8468i | − | 0.565617i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.24894 | − | 4.24894i | 0.161637 | − | 0.161637i | −0.621654 | − | 0.783292i | \(-0.713539\pi\) |
0.783292 | + | 0.621654i | \(0.213539\pi\) | |||||||
\(692\) | −0.607209 | + | 11.2497i | −0.0230826 | + | 0.427648i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.2820 | + | 38.7344i | −0.656014 | + | 1.47034i | ||||
\(695\) | 55.2302i | 2.09500i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.8835i | 0.904653i | ||||||||
\(698\) | −9.82672 | − | 4.38435i | −0.371947 | − | 0.165950i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22.7337 | − | 25.3279i | −0.859255 | − | 0.957305i | ||||
\(701\) | −23.4629 | + | 23.4629i | −0.886183 | + | 0.886183i | −0.994154 | − | 0.107971i | \(-0.965565\pi\) |
0.107971 | + | 0.994154i | \(0.465565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.70750i | − | 0.177547i | ||||||
\(704\) | −2.40727 | − | 0.392858i | −0.0907274 | − | 0.0148064i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.31891 | + | 13.8887i | 0.200180 | + | 0.522707i | ||||
\(707\) | 7.77278 | + | 7.77278i | 0.292326 | + | 0.292326i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.79314 | − | 2.79314i | 0.104898 | − | 0.104898i | −0.652710 | − | 0.757608i | \(-0.726368\pi\) |
0.757608 | + | 0.652710i | \(0.226368\pi\) | |||||||
\(710\) | 20.3942 | − | 45.7099i | 0.765380 | − | 1.71546i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.03679 | + | 17.6333i | −0.338668 | + | 0.660837i | ||||
\(713\) | −15.8294 | −0.592816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.48264 | + | 2.48264i | 0.0928454 | + | 0.0928454i | ||||
\(716\) | −41.5687 | − | 2.24371i | −1.55350 | − | 0.0838512i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.94706 | − | 15.5289i | −0.221942 | − | 0.579533i | ||||
\(719\) | −33.8130 | −1.26101 | −0.630507 | − | 0.776184i | \(-0.717153\pi\) | ||||
−0.630507 | + | 0.776184i | \(0.717153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.48264 | 0.166942 | ||||||||
\(722\) | −9.02751 | − | 23.5725i | −0.335969 | − | 0.877279i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.497665 | − | 9.22015i | 0.0184956 | − | 0.342664i | ||||
\(725\) | 21.3990 | + | 21.3990i | 0.794740 | + | 0.794740i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.42732 | −0.0900245 | −0.0450122 | − | 0.998986i | \(-0.514333\pi\) | ||||
−0.0450122 | + | 0.998986i | \(0.514333\pi\) | |||||||
\(728\) | −45.8984 | + | 14.7944i | −1.70111 | + | 0.548315i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.827859 | − | 1.85550i | 0.0306404 | − | 0.0686750i | ||||
\(731\) | −8.38460 | + | 8.38460i | −0.310115 | + | 0.310115i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.8596 | + | 16.8596i | 0.622725 | + | 0.622725i | 0.946227 | − | 0.323503i | \(-0.104860\pi\) |
−0.323503 | + | 0.946227i | \(0.604860\pi\) | |||||||
\(734\) | −1.77008 | − | 4.62202i | −0.0653349 | − | 0.170602i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.60215 | + | 2.53270i | −0.353940 | + | 0.0933566i | ||||
\(737\) | − | 3.93214i | − | 0.144842i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.2243 | − | 25.2243i | 0.927892 | − | 0.927892i | −0.0696780 | − | 0.997570i | \(-0.522197\pi\) |
0.997570 | + | 0.0696780i | \(0.0221972\pi\) | |||||||
\(740\) | −19.4390 | + | 17.4480i | −0.714592 | + | 0.641401i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.8453 | + | 9.74661i | 0.801965 | + | 0.357809i | ||||
\(743\) | − | 33.4926i | − | 1.22872i | −0.789025 | − | 0.614361i | \(-0.789414\pi\) | ||
0.789025 | − | 0.614361i | \(-0.210586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 32.6752i | − | 1.19713i | ||||||
\(746\) | −15.6323 | + | 35.0370i | −0.572340 | + | 1.28280i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.43965 | − | 0.0777065i | −0.0526390 | − | 0.00284123i | ||||
\(749\) | −10.2757 | + | 10.2757i | −0.375467 | + | 0.375467i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 17.9247i | − | 0.654081i | −0.945010 | − | 0.327040i | \(-0.893949\pi\) | ||
0.945010 | − | 0.327040i | \(-0.106051\pi\) | |||||||
\(752\) | −1.67974 | + | 15.5148i | −0.0612538 | + | 0.565766i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 40.0440 | − | 15.3355i | 1.45832 | − | 0.558487i | ||||
\(755\) | 0.426168 | + | 0.426168i | 0.0155099 | + | 0.0155099i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.10619 | − | 3.10619i | 0.112896 | − | 0.112896i | −0.648402 | − | 0.761298i | \(-0.724562\pi\) |
0.761298 | + | 0.648402i | \(0.224562\pi\) | |||||||
\(758\) | 27.3926 | + | 12.2217i | 0.994945 | + | 0.443910i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.12005 | − | 8.03939i | 0.149450 | − | 0.291619i | ||||
\(761\) | 1.10917 | 0.0402073 | 0.0201037 | − | 0.999798i | \(-0.493600\pi\) | ||||
0.0201037 | + | 0.999798i | \(0.493600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.6075 | + | 35.6075i | 1.28908 | + | 1.28908i | ||||
\(764\) | 11.4586 | − | 10.2849i | 0.414556 | − | 0.372096i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.1522 | + | 15.3770i | −1.45076 | + | 0.555593i | ||||
\(767\) | 18.6254 | 0.672523 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4591 | 0.809897 | 0.404948 | − | 0.914340i | \(-0.367289\pi\) | ||||
0.404948 | + | 0.914340i | \(0.367289\pi\) | |||||||
\(770\) | −5.28271 | + | 2.02311i | −0.190376 | + | 0.0729077i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.23517 | + | 4.69897i | −0.188418 | + | 0.169120i | ||||
\(773\) | −22.6327 | − | 22.6327i | −0.814041 | − | 0.814041i | 0.171196 | − | 0.985237i | \(-0.445237\pi\) |
−0.985237 | + | 0.171196i | \(0.945237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.8159 | −1.25062 | ||||||||
\(776\) | 4.31338 | − | 8.41663i | 0.154841 | − | 0.302139i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.5376 | + | 15.8556i | 1.27408 | + | 0.568453i | ||||
\(779\) | −7.66372 | + | 7.66372i | −0.274581 | + | 0.274581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56330 | − | 2.56330i | −0.0917221 | − | 0.0917221i | ||||
\(782\) | −5.48168 | + | 2.09930i | −0.196024 | + | 0.0750709i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.34935 | − | 49.4089i | 0.191048 | − | 1.76460i | ||||
\(785\) | − | 15.8232i | − | 0.564754i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.6505 | + | 38.6505i | −1.37774 | + | 1.37774i | −0.529315 | + | 0.848425i | \(0.677551\pi\) |
−0.848425 | + | 0.529315i | \(0.822449\pi\) | |||||||
\(788\) | 18.0885 | + | 0.976342i | 0.644377 | + | 0.0347807i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.8182 | − | 26.4883i | 0.420472 | − | 0.942411i | ||||
\(791\) | − | 9.24111i | − | 0.328576i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.62153i | 0.341671i | ||||||||
\(794\) | 37.3215 | + | 16.6516i | 1.32449 | + | 0.590943i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.7523 | − | 31.1929i | 1.23176 | − | 1.10560i | ||||
\(797\) | 37.8969 | − | 37.8969i | 1.34238 | − | 1.34238i | 0.448686 | − | 0.893689i | \(-0.351892\pi\) |
0.893689 | − | 0.448686i | \(-0.148108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.22432i | 0.326333i | ||||||||
\(800\) | −21.1194 | + | 5.57054i | −0.746684 | + | 0.196948i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.4139 | + | 29.8039i | 0.403040 | + | 1.05241i | ||||
\(803\) | −0.104052 | − | 0.104052i | −0.00367191 | − | 0.00367191i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.2855 | + | 16.2855i | −0.573989 | + | 0.573989i | ||||
\(806\) | −20.1001 | + | 45.0508i | −0.707997 | + | 1.58685i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.71427 | − | 2.16420i | 0.236207 | − | 0.0761363i | ||||
\(809\) | 27.0719 | 0.951799 | 0.475899 | − | 0.879500i | \(-0.342123\pi\) | ||||
0.475899 | + | 0.879500i | \(0.342123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0554 | − | 19.0554i | −0.669126 | − | 0.669126i | 0.288388 | − | 0.957514i | \(-0.406881\pi\) |
−0.957514 | + | 0.288388i | \(0.906881\pi\) | |||||||
\(812\) | −3.72365 | + | 68.9874i | −0.130674 | + | 2.42098i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.676576 | + | 1.76667i | 0.0237140 | + | 0.0619217i | ||||
\(815\) | 55.8571 | 1.95659 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.38088 | −0.188253 | ||||||||
\(818\) | 4.94794 | + | 12.9200i | 0.173001 | + | 0.451737i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 60.0514 | + | 3.24132i | 2.09708 | + | 0.113192i | ||||
\(821\) | −37.5393 | − | 37.5393i | −1.31013 | − | 1.31013i | −0.921315 | − | 0.388817i | \(-0.872884\pi\) |
−0.388817 | − | 0.921315i | \(-0.627116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.9589 | −0.974584 | −0.487292 | − | 0.873239i | \(-0.662015\pi\) | ||||
−0.487292 | + | 0.873239i | \(0.662015\pi\) | |||||||
\(824\) | 1.31203 | − | 2.56015i | 0.0457069 | − | 0.0891870i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.2272 | + | 27.4050i | −0.425438 | + | 0.953543i | ||||
\(827\) | −2.04182 | + | 2.04182i | −0.0710011 | + | 0.0710011i | −0.741716 | − | 0.670715i | \(-0.765988\pi\) |
0.670715 | + | 0.741716i | \(0.265988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5808 | + | 34.5808i | 1.20104 | + | 1.20104i | 0.973851 | + | 0.227188i | \(0.0729533\pi\) |
0.227188 | + | 0.973851i | \(0.427047\pi\) | |||||||
\(830\) | −10.2191 | − | 26.6841i | −0.354711 | − | 0.926218i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.98466 | + | 30.5439i | −0.172812 | + | 1.05892i | ||||
\(833\) | − | 29.3760i | − | 1.01782i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.4439 | + | 42.4439i | −1.46883 | + | 1.46883i | ||||
\(836\) | −0.437020 | − | 0.486889i | −0.0151147 | − | 0.0168394i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.6048 | − | 7.40847i | −0.573602 | − | 0.255922i | ||||
\(839\) | − | 0.865723i | − | 0.0298881i | −0.999888 | − | 0.0149440i | \(-0.995243\pi\) | ||
0.999888 | − | 0.0149440i | \(-0.00475701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 32.4321i | − | 1.11835i | ||||||
\(842\) | 14.6570 | − | 32.8510i | 0.505114 | − | 1.13212i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.01176 | + | 18.7446i | −0.0348261 | + | 0.645217i | ||||
\(845\) | 4.13669 | − | 4.13669i | 0.142306 | − | 0.142306i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 48.0707i | − | 1.65173i | ||||||
\(848\) | 11.9605 | − | 9.62363i | 0.410724 | − | 0.330477i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.0566 | + | 4.61730i | −0.413539 | + | 0.158372i | ||||
\(851\) | 5.44628 | + | 5.44628i | 0.186696 | + | 0.186696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.4262 | + | 14.4262i | −0.493942 | + | 0.493942i | −0.909546 | − | 0.415604i | \(-0.863570\pi\) |
0.415604 | + | 0.909546i | \(0.363570\pi\) | |||||||
\(854\) | −14.1569 | − | 6.31635i | −0.484441 | − | 0.216141i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.86110 | + | 8.87635i | 0.0977905 | + | 0.303388i | ||||
\(857\) | −37.6532 | −1.28621 | −0.643105 | − | 0.765778i | \(-0.722354\pi\) | ||||
−0.643105 | + | 0.765778i | \(0.722354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.7470 | − | 38.7470i | −1.32203 | − | 1.32203i | −0.912130 | − | 0.409901i | \(-0.865563\pi\) |
−0.409901 | − | 0.912130i | \(-0.634437\pi\) | |||||||
\(860\) | 19.9438 | + | 22.2196i | 0.680079 | + | 0.757684i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.6381 | − | 15.5631i | 1.38414 | − | 0.530080i | ||||
\(863\) | 14.8672 | 0.506085 | 0.253043 | − | 0.967455i | \(-0.418569\pi\) | ||||
0.253043 | + | 0.967455i | \(0.418569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7681 | 0.570134 | ||||||||
\(866\) | −4.61887 | + | 1.76888i | −0.156956 | + | 0.0601089i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −53.0916 | − | 59.1499i | −1.80205 | − | 2.00768i | ||||
\(869\) | −1.48540 | − | 1.48540i | −0.0503887 | − | 0.0503887i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.8918 | −1.69052 | ||||||||
\(872\) | 30.7584 | − | 9.91431i | 1.04161 | − | 0.335741i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.43258 | − | 1.08533i | −0.0822831 | − | 0.0367119i | ||||
\(875\) | 10.5654 | − | 10.5654i | 0.357176 | − | 0.357176i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.7699 | − | 13.7699i | −0.464976 | − | 0.464976i | 0.435306 | − | 0.900283i | \(-0.356640\pi\) |
−0.900283 | + | 0.435306i | \(0.856640\pi\) | |||||||
\(878\) | 27.9046 | − | 10.6865i | 0.941734 | − | 0.360653i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.390761 | + | 3.60924i | −0.0131726 | + | 0.121667i | ||||
\(881\) | − | 20.6232i | − | 0.694812i | −0.937715 | − | 0.347406i | \(-0.887063\pi\) | ||
0.937715 | − | 0.347406i | \(-0.112937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.5416 | + | 41.5416i | −1.39799 | + | 1.39799i | −0.592185 | + | 0.805802i | \(0.701735\pi\) |
−0.805802 | + | 0.592185i | \(0.798265\pi\) | |||||||
\(884\) | −0.985956 | + | 18.2666i | −0.0331613 | + | 0.614373i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.2696 | + | 23.0174i | −0.345013 | + | 0.773285i | ||||
\(887\) | 7.44312i | 0.249916i | 0.992162 | + | 0.124958i | \(0.0398795\pi\) | ||||
−0.992162 | + | 0.124958i | \(0.960120\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 45.3079i | − | 1.51958i | ||||||
\(890\) | 26.9319 | + | 12.0161i | 0.902759 | + | 0.402780i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.6637 | − | 19.6793i | −0.591423 | − | 0.658911i | ||||
\(893\) | −2.95989 | + | 2.95989i | −0.0990489 | + | 0.0990489i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 61.9602i | 2.07110i | ||||||||
\(896\) | −41.6694 | − | 27.3858i | −1.39208 | − | 0.914896i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.05135 | − | 13.1900i | −0.168566 | − | 0.440157i | ||||
\(899\) | 49.9746 | + | 49.9746i | 1.66675 | + | 1.66675i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.41642 | − | 6.41642i | 0.213762 | − | 0.213762i | ||||
\(902\) | 1.77465 | − | 3.97756i | 0.0590894 | − | 0.132438i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.27783 | − | 2.70480i | −0.175538 | − | 0.0899604i | ||||
\(905\) | −13.7431 | −0.456835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.75106 | + | 3.75106i | 0.124552 | + | 0.124552i | 0.766635 | − | 0.642083i | \(-0.221930\pi\) |
−0.642083 | + | 0.766635i | \(0.721930\pi\) | |||||||
\(908\) | 46.3270 | + | 2.50054i | 1.53742 | + | 0.0829832i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 25.6696 | + | 67.0281i | 0.850938 | + | 2.22196i | ||||
\(911\) | 29.9816 | 0.993334 | 0.496667 | − | 0.867941i | \(-0.334557\pi\) | ||||
0.496667 | + | 0.867941i | \(0.334557\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.06944 | −0.0684886 | ||||||||
\(914\) | 7.71349 | + | 20.1414i | 0.255140 | + | 0.666217i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.760206 | + | 14.0842i | −0.0251179 | + | 0.465355i | ||||
\(917\) | 30.0090 | + | 30.0090i | 0.990984 | + | 0.990984i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1402 | 1.25813 | 0.629064 | − | 0.777353i | \(-0.283438\pi\) | ||||
0.629064 | + | 0.777353i | \(0.283438\pi\) | |||||||
\(920\) | 4.53443 | + | 14.0677i | 0.149496 | + | 0.463799i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.7224 | + | 26.2736i | −0.386055 | + | 0.865273i | ||||
\(923\) | −32.5237 | + | 32.5237i | −1.07053 | + | 1.07053i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.9788 | + | 11.9788i | 0.393860 | + | 0.393860i | ||||
\(926\) | 11.1926 | + | 29.2260i | 0.367811 | + | 0.960425i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 38.3106 | + | 22.3188i | 1.25761 | + | 0.732649i | ||||
\(929\) | − | 13.8738i | − | 0.455183i | −0.973757 | − | 0.227592i | \(-0.926915\pi\) | ||
0.973757 | − | 0.227592i | \(-0.0730851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.42615 | − | 9.42615i | 0.308930 | − | 0.308930i | ||||
\(932\) | −1.57588 | + | 1.41447i | −0.0516195 | + | 0.0463325i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.76608 | + | 3.91113i | 0.286835 | + | 0.127976i | ||||
\(935\) | 2.14587i | 0.0701775i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.4097i | 0.862767i | 0.902169 | + | 0.431384i | \(0.141974\pi\) | ||||
−0.902169 | + | 0.431384i | \(0.858026\pi\) | |||||||
\(938\) | 32.7530 | − | 73.4099i | 1.06942 | − | 2.39692i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.1931 | + | 1.25187i | 0.756475 | + | 0.0408313i | ||||
\(941\) | −4.91123 | + | 4.91123i | −0.160102 | + | 0.160102i | −0.782612 | − | 0.622510i | \(-0.786113\pi\) |
0.622510 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 17.7329i | − | 0.577462i | ||||||
\(944\) | 12.0729 | + | 15.0045i | 0.392940 | + | 0.488355i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.01938 | − | 0.773357i | 0.0656558 | − | 0.0251440i | ||||
\(947\) | −6.84386 | − | 6.84386i | −0.222396 | − | 0.222396i | 0.587111 | − | 0.809507i | \(-0.300265\pi\) |
−0.809507 | + | 0.587111i | \(0.800265\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.32023 | + | 1.32023i | −0.0428565 | + | 0.0428565i | ||||
\(950\) | −5.35031 | − | 2.38713i | −0.173587 | − | 0.0774486i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.2299 | − | 13.4424i | −0.850117 | − | 0.435671i | ||||
\(953\) | 4.33045 | 0.140277 | 0.0701386 | − | 0.997537i | \(-0.477656\pi\) | ||||
0.0701386 | + | 0.997537i | \(0.477656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2048 | − | 16.2048i | −0.524377 | − | 0.524377i | ||||
\(956\) | −0.471975 | + | 0.423634i | −0.0152648 | + | 0.0137013i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.7455 | − | 11.7745i | 0.993342 | − | 0.380417i | ||||
\(959\) | −60.7864 | −1.96289 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.3079 | −1.62284 | ||||||||
\(962\) | 22.4159 | − | 8.58454i | 0.722716 | − | 0.276777i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.4638 | − | 15.6751i | 0.562471 | − | 0.504861i | ||||
\(965\) | 7.40365 | + | 7.40365i | 0.238332 | + | 0.238332i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.6664 | 1.30774 | 0.653871 | − | 0.756606i | \(-0.273144\pi\) | ||||
0.653871 | + | 0.756606i | \(0.273144\pi\) | |||||||
\(968\) | −27.4544 | − | 14.0699i | −0.882419 | − | 0.452225i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.8550 | − | 5.73544i | −0.412748 | − | 0.184154i | ||||
\(971\) | 24.0742 | − | 24.0742i | 0.772577 | − | 0.772577i | −0.205979 | − | 0.978556i | \(-0.566038\pi\) |
0.978556 | + | 0.205979i | \(0.0660379\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.8218 | + | 57.8218i | 1.85368 | + | 1.85368i | ||||
\(974\) | −27.8330 | + | 10.6591i | −0.891827 | + | 0.341541i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.75106 | + | 6.23665i | −0.248105 | + | 0.199630i | ||||
\(977\) | 21.0381i | 0.673068i | 0.941671 | + | 0.336534i | \(0.109255\pi\) | ||||
−0.941671 | + | 0.336534i | \(0.890745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.51028 | − | 1.51028i | 0.0482686 | − | 0.0482686i | ||||
\(980\) | −73.8614 | − | 3.98673i | −2.35942 | − | 0.127351i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.3064 | − | 47.7544i | 0.679913 | − | 1.52390i | ||||
\(983\) | 14.1206i | 0.450376i | 0.974315 | + | 0.225188i | \(0.0722997\pi\) | ||||
−0.974315 | + | 0.225188i | \(0.927700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 26.9618i | − | 0.859074i | ||||||
\(986\) | 23.9337 | + | 10.6784i | 0.762204 | + | 0.340069i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.17775 | + | 5.54500i | −0.196540 | + | 0.176410i | ||||
\(989\) | 6.22534 | − | 6.22534i | 0.197954 | − | 0.197954i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 33.3338i | − | 1.05888i | −0.848346 | − | 0.529442i | \(-0.822401\pi\) | ||
0.848346 | − | 0.529442i | \(-0.177599\pi\) | |||||||
\(992\) | −49.3215 | + | 13.0092i | −1.56596 | + | 0.413044i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −26.5036 | − | 69.2059i | −0.840643 | − | 2.19508i | ||||
\(995\) | −49.1472 | − | 49.1472i | −1.55807 | − | 1.55807i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.8358 | − | 24.8358i | 0.786559 | − | 0.786559i | −0.194369 | − | 0.980928i | \(-0.562266\pi\) |
0.980928 | + | 0.194369i | \(0.0622660\pi\) | |||||||
\(998\) | −17.1288 | + | 38.3911i | −0.542203 | + | 1.21525i | ||||
\(999\) | 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 | 144.2.l.a.35.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 144.2.l.a.35.8 | yes | 16 | |
4.3 | odd | 2 | 576.2.l.a.431.2 | 16 | |||
8.3 | odd | 2 | 1152.2.l.b.863.7 | 16 | |||
8.5 | even | 2 | 1152.2.l.a.863.7 | 16 | |||
12.11 | even | 2 | 576.2.l.a.431.7 | 16 | |||
16.3 | odd | 4 | 1152.2.l.a.287.2 | 16 | |||
16.5 | even | 4 | 576.2.l.a.143.7 | 16 | |||
16.11 | odd | 4 | inner | 144.2.l.a.107.8 | yes | 16 | |
16.13 | even | 4 | 1152.2.l.b.287.2 | 16 | |||
24.5 | odd | 2 | 1152.2.l.a.863.2 | 16 | |||
24.11 | even | 2 | 1152.2.l.b.863.2 | 16 | |||
48.5 | odd | 4 | 576.2.l.a.143.2 | 16 | |||
48.11 | even | 4 | inner | 144.2.l.a.107.1 | yes | 16 | |
48.29 | odd | 4 | 1152.2.l.b.287.7 | 16 | |||
48.35 | even | 4 | 1152.2.l.a.287.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.l.a.35.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
144.2.l.a.35.8 | yes | 16 | 3.2 | odd | 2 | inner | |
144.2.l.a.107.1 | yes | 16 | 48.11 | even | 4 | inner | |
144.2.l.a.107.8 | yes | 16 | 16.11 | odd | 4 | inner | |
576.2.l.a.143.2 | 16 | 48.5 | odd | 4 | |||
576.2.l.a.143.7 | 16 | 16.5 | even | 4 | |||
576.2.l.a.431.2 | 16 | 4.3 | odd | 2 | |||
576.2.l.a.431.7 | 16 | 12.11 | even | 2 | |||
1152.2.l.a.287.2 | 16 | 16.3 | odd | 4 | |||
1152.2.l.a.287.7 | 16 | 48.35 | even | 4 | |||
1152.2.l.a.863.2 | 16 | 24.5 | odd | 2 | |||
1152.2.l.a.863.7 | 16 | 8.5 | even | 2 | |||
1152.2.l.b.287.2 | 16 | 16.13 | even | 4 | |||
1152.2.l.b.287.7 | 16 | 48.29 | odd | 4 | |||
1152.2.l.b.863.2 | 16 | 24.11 | even | 2 | |||
1152.2.l.b.863.7 | 16 | 8.3 | odd | 2 |