Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(46,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.e (of order \(3\), degree \(2\), not 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: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.15759792.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.1 | ||
Root | \(0.500000 + 2.88506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.46 |
Dual form | 135.4.e.b.91.1 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28679 | + | 3.96084i | −0.808502 | + | 1.40037i | 0.105398 | + | 0.994430i | \(0.466388\pi\) |
−0.913901 | + | 0.405937i | \(0.866945\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.45882 | − | 11.1870i | −0.807352 | − | 1.39838i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0573 | − | 17.4197i | 0.543041 | − | 0.940575i | −0.455686 | − | 0.890141i | \(-0.650606\pi\) |
0.998727 | − | 0.0504348i | \(-0.0160607\pi\) | |||||||
\(8\) | 22.4912 | 0.993981 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −22.8679 | −0.723147 | ||||||||
\(11\) | 33.1708 | − | 57.4535i | 0.909215 | − | 1.57481i | 0.0940582 | − | 0.995567i | \(-0.470016\pi\) |
0.815157 | − | 0.579240i | \(-0.196651\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.4003 | + | 40.5305i | 0.499237 | + | 0.864703i | 1.00000 | 0.000881222i | \(-0.000280502\pi\) | |
−0.500763 | + | 0.865584i | \(0.666947\pi\) | |||||||
\(14\) | 45.9977 | + | 79.6704i | 0.878101 | + | 1.52092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.237854 | − | 0.411975i | 0.00371647 | − | 0.00643711i | ||||
\(17\) | 47.6233 | 0.679432 | 0.339716 | − | 0.940528i | \(-0.389669\pi\) | ||||
0.339716 | + | 0.940528i | \(0.389669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.95276 | −0.120175 | −0.0600874 | − | 0.998193i | \(-0.519138\pi\) | ||||
−0.0600874 | + | 0.998193i | \(0.519138\pi\) | |||||||
\(20\) | 32.2941 | − | 55.9350i | 0.361059 | − | 0.625373i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 151.709 | + | 262.768i | 1.47021 | + | 2.54647i | ||||
\(23\) | 4.79602 | + | 8.30695i | 0.0434800 | + | 0.0753095i | 0.886946 | − | 0.461872i | \(-0.152822\pi\) |
−0.843466 | + | 0.537182i | \(0.819489\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −214.046 | −1.61454 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −259.832 | −1.75370 | ||||||||
\(29\) | −89.3675 | + | 154.789i | −0.572246 | + | 0.991158i | 0.424089 | + | 0.905620i | \(0.360594\pi\) |
−0.996335 | + | 0.0855380i | \(0.972739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −77.0186 | − | 133.400i | −0.446224 | − | 0.772883i | 0.551912 | − | 0.833902i | \(-0.313898\pi\) |
−0.998137 | + | 0.0610190i | \(0.980565\pi\) | |||||||
\(32\) | 91.0527 | + | 157.708i | 0.503000 | + | 0.871222i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −108.905 | + | 188.628i | −0.549323 | + | 0.951455i | ||||
\(35\) | 100.573 | 0.485711 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 248.864 | 1.10576 | 0.552878 | − | 0.833262i | \(-0.313529\pi\) | ||||
0.552878 | + | 0.833262i | \(0.313529\pi\) | |||||||
\(38\) | 22.7599 | − | 39.4213i | 0.0971616 | − | 0.168289i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 56.2280 | + | 97.3898i | 0.222261 | + | 0.384967i | ||||
\(41\) | 124.832 | + | 216.216i | 0.475500 | + | 0.823590i | 0.999606 | − | 0.0280628i | \(-0.00893383\pi\) |
−0.524106 | + | 0.851653i | \(0.675600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 106.122 | − | 183.809i | 0.376361 | − | 0.651876i | −0.614169 | − | 0.789175i | \(-0.710509\pi\) |
0.990530 | + | 0.137299i | \(0.0438420\pi\) | |||||||
\(44\) | −856.976 | −2.93623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −43.8700 | −0.140615 | ||||||||
\(47\) | 237.847 | − | 411.963i | 0.738160 | − | 1.27853i | −0.215163 | − | 0.976578i | \(-0.569028\pi\) |
0.953323 | − | 0.301953i | \(-0.0976384\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30.7973 | − | 53.3425i | −0.0897880 | − | 0.155517i | ||||
\(50\) | −57.1698 | − | 99.0209i | −0.161700 | − | 0.280073i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 302.277 | − | 523.559i | 0.806120 | − | 1.39624i | ||||
\(53\) | 546.314 | 1.41589 | 0.707944 | − | 0.706269i | \(-0.249623\pi\) | ||||
0.707944 | + | 0.706269i | \(0.249623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 331.708 | 0.813227 | ||||||||
\(56\) | 226.200 | − | 391.790i | 0.539773 | − | 0.934914i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −408.729 | − | 707.940i | −0.925324 | − | 1.60271i | ||||
\(59\) | −209.648 | − | 363.121i | −0.462608 | − | 0.801261i | 0.536482 | − | 0.843912i | \(-0.319753\pi\) |
−0.999090 | + | 0.0426512i | \(0.986420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 272.605 | − | 472.165i | 0.572188 | − | 0.991059i | −0.424153 | − | 0.905591i | \(-0.639428\pi\) |
0.996341 | − | 0.0854682i | \(-0.0272386\pi\) | |||||||
\(62\) | 704.502 | 1.44309 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −829.068 | −1.61927 | ||||||||
\(65\) | −117.002 | + | 202.653i | −0.223265 | + | 0.386707i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 223.938 | + | 387.872i | 0.408335 | + | 0.707256i | 0.994703 | − | 0.102788i | \(-0.0327764\pi\) |
−0.586369 | + | 0.810044i | \(0.699443\pi\) | |||||||
\(68\) | −307.590 | − | 532.762i | −0.548541 | − | 0.950102i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −229.989 | + | 398.352i | −0.392699 | + | 0.680174i | ||||
\(71\) | −409.542 | −0.684559 | −0.342279 | − | 0.939598i | \(-0.611199\pi\) | ||||
−0.342279 | + | 0.939598i | \(0.611199\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −358.548 | −0.574861 | −0.287431 | − | 0.957801i | \(-0.592801\pi\) | ||||
−0.287431 | + | 0.957801i | \(0.592801\pi\) | |||||||
\(74\) | −569.100 | + | 985.710i | −0.894007 | + | 1.54847i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 64.2831 | + | 111.342i | 0.0970234 | + | 0.168049i | ||||
\(77\) | −667.215 | − | 1155.65i | −0.987483 | − | 1.71037i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 325.776 | − | 564.260i | 0.463958 | − | 0.803598i | −0.535196 | − | 0.844728i | \(-0.679762\pi\) |
0.999154 | + | 0.0411297i | \(0.0130957\pi\) | |||||||
\(80\) | 2.37854 | 0.00332411 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1141.86 | −1.53777 | ||||||||
\(83\) | −406.571 | + | 704.202i | −0.537675 | + | 0.931280i | 0.461354 | + | 0.887216i | \(0.347364\pi\) |
−0.999029 | + | 0.0440636i | \(0.985970\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 119.058 | + | 206.215i | 0.151926 | + | 0.263143i | ||||
\(86\) | 485.359 | + | 840.667i | 0.608577 | + | 1.05409i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 746.051 | − | 1292.20i | 0.903743 | − | 1.56533i | ||||
\(89\) | 201.000 | 0.239393 | 0.119696 | − | 0.992811i | \(-0.461808\pi\) | ||||
0.119696 | + | 0.992811i | \(0.461808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 941.373 | 1.08442 | ||||||||
\(92\) | 61.9532 | − | 107.306i | 0.0702073 | − | 0.121603i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1087.81 | + | 1884.14i | 1.19361 | + | 2.06739i | ||||
\(95\) | −24.8819 | − | 43.0967i | −0.0268719 | − | 0.0465435i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −126.074 | + | 218.367i | −0.131968 | + | 0.228576i | −0.924435 | − | 0.381339i | \(-0.875463\pi\) |
0.792467 | + | 0.609915i | \(0.208796\pi\) | |||||||
\(98\) | 281.708 | 0.290375 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 322.941 | 0.322941 | ||||||||
\(101\) | 21.8013 | − | 37.7610i | 0.0214783 | − | 0.0372016i | −0.855086 | − | 0.518485i | \(-0.826496\pi\) |
0.876565 | + | 0.481284i | \(0.159829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 720.176 | + | 1247.38i | 0.688942 | + | 1.19328i | 0.972180 | + | 0.234233i | \(0.0752579\pi\) |
−0.283238 | + | 0.959050i | \(0.591409\pi\) | |||||||
\(104\) | 526.301 | + | 911.581i | 0.496232 | + | 0.859498i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1249.31 | + | 2163.86i | −1.14475 | + | 1.98276i | ||||
\(107\) | −355.755 | −0.321422 | −0.160711 | − | 0.987002i | \(-0.551379\pi\) | ||||
−0.160711 | + | 0.987002i | \(0.551379\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1522.51 | −1.33789 | −0.668946 | − | 0.743311i | \(-0.733254\pi\) | ||||
−0.668946 | + | 0.743311i | \(0.733254\pi\) | |||||||
\(110\) | −758.546 | + | 1313.84i | −0.657496 | + | 1.13882i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.78432 | − | 8.28669i | −0.00403639 | − | 0.00699124i | ||||
\(113\) | −406.499 | − | 704.077i | −0.338409 | − | 0.586142i | 0.645725 | − | 0.763570i | \(-0.276555\pi\) |
−0.984134 | + | 0.177429i | \(0.943222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.9801 | + | 41.5347i | −0.0194448 | + | 0.0336794i | ||||
\(116\) | 2308.83 | 1.84802 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1917.69 | 1.49608 | ||||||||
\(119\) | 478.960 | − | 829.584i | 0.368960 | − | 0.639057i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1535.10 | − | 2658.87i | −1.15334 | − | 1.99765i | ||||
\(122\) | 1246.78 | + | 2159.49i | 0.925231 | + | 1.60255i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −994.899 | + | 1723.22i | −0.720521 | + | 1.24798i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −864.662 | −0.604144 | −0.302072 | − | 0.953285i | \(-0.597678\pi\) | ||||
−0.302072 | + | 0.953285i | \(0.597678\pi\) | |||||||
\(128\) | 1167.48 | − | 2022.14i | 0.806187 | − | 1.39636i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −535.116 | − | 926.848i | −0.361021 | − | 0.625307i | ||||
\(131\) | −1089.26 | − | 1886.65i | −0.726482 | − | 1.25830i | −0.958361 | − | 0.285559i | \(-0.907821\pi\) |
0.231879 | − | 0.972745i | \(-0.425513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −100.098 | + | 173.374i | −0.0652599 | + | 0.113033i | ||||
\(134\) | −2048.40 | −1.32056 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1071.11 | 0.675343 | ||||||||
\(137\) | −1149.58 | + | 1991.13i | −0.716900 | + | 1.24171i | 0.245322 | + | 0.969442i | \(0.421106\pi\) |
−0.962222 | + | 0.272266i | \(0.912227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1066.98 | + | 1848.06i | 0.651077 | + | 1.12770i | 0.982862 | + | 0.184343i | \(0.0590157\pi\) |
−0.331785 | + | 0.943355i | \(0.607651\pi\) | |||||||
\(140\) | −649.581 | − | 1125.11i | −0.392140 | − | 0.679206i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 936.536 | − | 1622.13i | 0.553467 | − | 0.958634i | ||||
\(143\) | 3104.83 | 1.81565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −893.675 | −0.511832 | ||||||||
\(146\) | 819.924 | − | 1420.15i | 0.464777 | − | 0.805017i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1607.37 | − | 2784.04i | −0.892735 | − | 1.54626i | ||||
\(149\) | 875.309 | + | 1516.08i | 0.481263 | + | 0.833572i | 0.999769 | − | 0.0215024i | \(-0.00684497\pi\) |
−0.518506 | + | 0.855074i | \(0.673512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −437.977 | + | 758.598i | −0.236040 | + | 0.408833i | −0.959574 | − | 0.281455i | \(-0.909183\pi\) |
0.723534 | + | 0.690288i | \(0.242516\pi\) | |||||||
\(152\) | −223.850 | −0.119451 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6103.12 | 3.19353 | ||||||||
\(155\) | 385.093 | − | 667.001i | 0.199558 | − | 0.345644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 129.697 | + | 224.642i | 0.0659298 | + | 0.114194i | 0.897106 | − | 0.441815i | \(-0.145665\pi\) |
−0.831176 | + | 0.556009i | \(0.812332\pi\) | |||||||
\(158\) | 1489.96 | + | 2580.69i | 0.750222 | + | 1.29942i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −455.264 | + | 788.540i | −0.224948 | + | 0.389622i | ||||
\(161\) | 192.939 | 0.0944457 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1201.80 | −0.577498 | −0.288749 | − | 0.957405i | \(-0.593239\pi\) | ||||
−0.288749 | + | 0.957405i | \(0.593239\pi\) | |||||||
\(164\) | 1612.54 | − | 2792.99i | 0.767792 | − | 1.32986i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1859.49 | − | 3220.72i | −0.869422 | − | 1.50588i | ||||
\(167\) | −839.452 | − | 1453.97i | −0.388975 | − | 0.673724i | 0.603337 | − | 0.797486i | \(-0.293837\pi\) |
−0.992312 | + | 0.123762i | \(0.960504\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.35162 | − | 5.80518i | 0.00152554 | − | 0.00264232i | ||||
\(170\) | −1089.05 | −0.491329 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2741.70 | −1.21542 | ||||||||
\(173\) | 465.899 | − | 806.961i | 0.204749 | − | 0.354636i | −0.745303 | − | 0.666725i | \(-0.767695\pi\) |
0.950053 | + | 0.312089i | \(0.101029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 251.432 | + | 435.493i | 0.108608 | + | 0.188115i | ||||
\(176\) | −15.7796 | − | 27.3311i | −0.00675814 | − | 0.0117054i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −459.644 | + | 796.127i | −0.193549 | + | 0.335237i | ||||
\(179\) | −1023.40 | −0.427333 | −0.213667 | − | 0.976907i | \(-0.568541\pi\) | ||||
−0.213667 | + | 0.976907i | \(0.568541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2639.93 | 1.08411 | 0.542056 | − | 0.840342i | \(-0.317646\pi\) | ||||
0.542056 | + | 0.840342i | \(0.317646\pi\) | |||||||
\(182\) | −2152.72 | + | 3728.62i | −0.876760 | + | 1.51859i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 107.868 | + | 186.833i | 0.0432182 | + | 0.0748562i | ||||
\(185\) | 622.160 | + | 1077.61i | 0.247255 | + | 0.428258i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1579.70 | − | 2736.13i | 0.617750 | − | 1.06997i | ||||
\(188\) | −6144.84 | −2.38382 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 227.599 | 0.0869039 | ||||||||
\(191\) | −406.640 | + | 704.322i | −0.154050 | + | 0.266822i | −0.932713 | − | 0.360621i | \(-0.882565\pi\) |
0.778663 | + | 0.627442i | \(0.215898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 407.121 | + | 705.154i | 0.151840 | + | 0.262995i | 0.931904 | − | 0.362705i | \(-0.118147\pi\) |
−0.780064 | + | 0.625700i | \(0.784813\pi\) | |||||||
\(194\) | −576.612 | − | 998.720i | −0.213393 | − | 0.369608i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −397.828 | + | 689.059i | −0.144981 | + | 0.251115i | ||||
\(197\) | −4078.41 | −1.47500 | −0.737499 | − | 0.675348i | \(-0.763994\pi\) | ||||
−0.737499 | + | 0.675348i | \(0.763994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1342.49 | −0.478224 | −0.239112 | − | 0.970992i | \(-0.576856\pi\) | ||||
−0.239112 | + | 0.970992i | \(0.576856\pi\) | |||||||
\(200\) | −281.140 | + | 486.949i | −0.0993981 | + | 0.172163i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 99.7101 | + | 172.703i | 0.0347306 | + | 0.0601551i | ||||
\(203\) | 1797.58 | + | 3113.51i | 0.621506 | + | 1.07648i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −624.161 | + | 1081.08i | −0.212650 | + | 0.368321i | ||||
\(206\) | −6587.56 | −2.22805 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.2634 | 0.00742159 | ||||||||
\(209\) | −330.141 | + | 571.821i | −0.109265 | + | 0.189252i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1477.49 | + | 2559.08i | 0.482059 | + | 0.834950i | 0.999788 | − | 0.0205943i | \(-0.00655583\pi\) |
−0.517729 | + | 0.855545i | \(0.673222\pi\) | |||||||
\(212\) | −3528.55 | − | 6111.62i | −1.14312 | − | 1.97994i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 813.536 | − | 1409.09i | 0.259870 | − | 0.450108i | ||||
\(215\) | 1061.22 | 0.336627 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3098.39 | −0.969273 | ||||||||
\(218\) | 3481.66 | − | 6030.42i | 1.08169 | − | 1.87354i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2142.44 | − | 3710.82i | −0.656561 | − | 1.13720i | ||||
\(221\) | 1114.40 | + | 1930.20i | 0.339198 | + | 0.587507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1753.43 | + | 3037.03i | −0.526539 | + | 0.911993i | 0.472982 | + | 0.881072i | \(0.343177\pi\) |
−0.999522 | + | 0.0309212i | \(0.990156\pi\) | |||||||
\(224\) | 3662.97 | 1.09260 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3718.31 | 1.09442 | ||||||||
\(227\) | 326.413 | − | 565.364i | 0.0954396 | − | 0.165306i | −0.814352 | − | 0.580371i | \(-0.802908\pi\) |
0.909792 | + | 0.415064i | \(0.136241\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2291.78 | − | 3969.47i | −0.661331 | − | 1.14546i | −0.980266 | − | 0.197682i | \(-0.936659\pi\) |
0.318935 | − | 0.947776i | \(-0.396675\pi\) | |||||||
\(230\) | −109.675 | − | 189.962i | −0.0314424 | − | 0.0544598i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2009.98 | + | 3481.39i | −0.568801 | + | 0.985192i | ||||
\(233\) | −317.527 | −0.0892785 | −0.0446392 | − | 0.999003i | \(-0.514214\pi\) | ||||
−0.0446392 | + | 0.999003i | \(0.514214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2378.47 | 0.660230 | ||||||||
\(236\) | −2708.16 | + | 4690.67i | −0.746975 | + | 1.29380i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2190.56 | + | 3794.17i | 0.596610 | + | 1.03336i | ||||
\(239\) | 928.835 | + | 1608.79i | 0.251386 | + | 0.435414i | 0.963908 | − | 0.266236i | \(-0.0857802\pi\) |
−0.712521 | + | 0.701650i | \(0.752447\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1633.47 | − | 2829.25i | 0.436602 | − | 0.756217i | −0.560823 | − | 0.827936i | \(-0.689515\pi\) |
0.997425 | + | 0.0717190i | \(0.0228485\pi\) | |||||||
\(242\) | 14041.8 | 3.72993 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7042.82 | −1.84783 | ||||||||
\(245\) | 153.986 | − | 266.712i | 0.0401544 | − | 0.0695495i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −232.898 | − | 403.390i | −0.0599956 | − | 0.103915i | ||||
\(248\) | −1732.24 | − | 3000.33i | −0.443538 | − | 0.768231i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 285.849 | − | 495.105i | 0.0723147 | − | 0.125253i | ||||
\(251\) | 5641.37 | 1.41865 | 0.709323 | − | 0.704884i | \(-0.249001\pi\) | ||||
0.709323 | + | 0.704884i | \(0.249001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 636.351 | 0.158131 | ||||||||
\(254\) | 1977.30 | − | 3424.78i | 0.488452 | − | 0.846024i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2023.31 | + | 3504.47i | 0.493971 | + | 0.855584i | ||||
\(257\) | −586.731 | − | 1016.25i | −0.142410 | − | 0.246661i | 0.785994 | − | 0.618234i | \(-0.212152\pi\) |
−0.928404 | + | 0.371574i | \(0.878818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2502.89 | − | 4335.14i | 0.600472 | − | 1.04005i | ||||
\(260\) | 3022.77 | 0.721016 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9963.64 | 2.34945 | ||||||||
\(263\) | −1448.98 | + | 2509.71i | −0.339726 | + | 0.588423i | −0.984381 | − | 0.176051i | \(-0.943668\pi\) |
0.644655 | + | 0.764474i | \(0.277001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1365.79 | + | 2365.61i | 0.316602 | + | 0.548371i | ||||
\(266\) | −457.804 | − | 792.940i | −0.105526 | − | 0.182776i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2892.75 | − | 5010.40i | 0.659340 | − | 1.14201i | ||||
\(269\) | −2930.13 | −0.664138 | −0.332069 | − | 0.943255i | \(-0.607747\pi\) | ||||
−0.332069 | + | 0.943255i | \(0.607747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −668.881 | −0.149932 | −0.0749661 | − | 0.997186i | \(-0.523885\pi\) | ||||
−0.0749661 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(272\) | 11.3274 | − | 19.6196i | 0.00252509 | − | 0.00437358i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5257.70 | − | 9106.60i | −1.15923 | − | 2.00785i | ||||
\(275\) | 829.270 | + | 1436.34i | 0.181843 | + | 0.314961i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 316.315 | − | 547.874i | 0.0686121 | − | 0.118840i | −0.829679 | − | 0.558241i | \(-0.811476\pi\) |
0.898291 | + | 0.439402i | \(0.144810\pi\) | |||||||
\(278\) | −9759.80 | −2.10559 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2262.00 | 0.482787 | ||||||||
\(281\) | −1797.65 | + | 3113.62i | −0.381633 | + | 0.661007i | −0.991296 | − | 0.131653i | \(-0.957971\pi\) |
0.609663 | + | 0.792661i | \(0.291305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −252.184 | − | 436.796i | −0.0529710 | − | 0.0917485i | 0.838324 | − | 0.545172i | \(-0.183536\pi\) |
−0.891295 | + | 0.453424i | \(0.850202\pi\) | |||||||
\(284\) | 2645.16 | + | 4581.55i | 0.552680 | + | 0.957270i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7100.08 | + | 12297.7i | −1.46796 | + | 2.54258i | ||||
\(287\) | 5021.88 | 1.03286 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2645.02 | −0.538372 | ||||||||
\(290\) | 2043.65 | − | 3539.70i | 0.413817 | − | 0.716753i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2315.80 | + | 4011.08i | 0.464116 | + | 0.803872i | ||||
\(293\) | 3099.25 | + | 5368.06i | 0.617953 | + | 1.07033i | 0.989859 | + | 0.142055i | \(0.0453710\pi\) |
−0.371906 | + | 0.928270i | \(0.621296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1048.24 | − | 1815.61i | 0.206885 | − | 0.358335i | ||||
\(296\) | 5597.26 | 1.09910 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8006.60 | −1.55641 | ||||||||
\(299\) | −224.457 | + | 388.770i | −0.0434136 | + | 0.0751945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2134.60 | − | 3697.24i | −0.408759 | − | 0.707991i | ||||
\(302\) | −2003.12 | − | 3469.51i | −0.381678 | − | 0.661086i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.36730 | + | 4.10029i | −0.000446626 | + | 0.000773578i | ||||
\(305\) | 2726.05 | 0.511781 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1966.79 | −0.365636 | −0.182818 | − | 0.983147i | \(-0.558522\pi\) | ||||
−0.182818 | + | 0.983147i | \(0.558522\pi\) | |||||||
\(308\) | −8618.84 | + | 14928.3i | −1.59449 | + | 2.76174i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1761.25 | + | 3050.58i | 0.322686 | + | 0.558908i | ||||
\(311\) | −1153.05 | − | 1997.15i | −0.210237 | − | 0.364141i | 0.741552 | − | 0.670896i | \(-0.234090\pi\) |
−0.951789 | + | 0.306755i | \(0.900757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5151.20 | + | 8922.14i | −0.930234 | + | 1.61121i | −0.147314 | + | 0.989090i | \(0.547063\pi\) |
−0.782920 | + | 0.622122i | \(0.786271\pi\) | |||||||
\(314\) | −1186.36 | −0.213218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8416.51 | −1.49831 | ||||||||
\(317\) | −850.916 | + | 1473.83i | −0.150764 | + | 0.261131i | −0.931509 | − | 0.363719i | \(-0.881507\pi\) |
0.780745 | + | 0.624850i | \(0.214840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5928.78 | + | 10268.9i | 1.04059 | + | 1.80235i | ||||
\(320\) | −2072.67 | − | 3589.97i | −0.362081 | − | 0.627142i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −441.212 | + | 764.201i | −0.0763596 | + | 0.132259i | ||||
\(323\) | −473.983 | −0.0816506 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1170.02 | −0.199695 | ||||||||
\(326\) | 2748.26 | − | 4760.13i | 0.466908 | − | 0.808709i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2807.63 | + | 4862.95i | 0.472638 | + | 0.818633i | ||||
\(329\) | −4784.18 | − | 8286.44i | −0.801703 | − | 1.38859i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4175.74 | − | 7232.60i | 0.693413 | − | 1.20103i | −0.277300 | − | 0.960783i | \(-0.589440\pi\) |
0.970713 | − | 0.240243i | \(-0.0772271\pi\) | |||||||
\(332\) | 10503.9 | 1.73637 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7678.61 | 1.25795 | ||||||||
\(335\) | −1119.69 | + | 1939.36i | −0.182613 | + | 0.316295i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3928.71 | + | 6804.73i | 0.635046 | + | 1.09993i | 0.986505 | + | 0.163729i | \(0.0523523\pi\) |
−0.351459 | + | 0.936203i | \(0.614314\pi\) | |||||||
\(338\) | 15.3289 | + | 26.5504i | 0.00246681 | + | 0.00427264i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1537.95 | − | 2663.81i | 0.245315 | − | 0.424898i | ||||
\(341\) | −10219.1 | −1.62286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5660.34 | 0.891048 | ||||||||
\(344\) | 2386.82 | − | 4134.10i | 0.374095 | − | 0.647952i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2130.83 | + | 3690.70i | 0.331081 | + | 0.573449i | ||||
\(347\) | 606.088 | + | 1049.78i | 0.0937652 | + | 0.162406i | 0.909093 | − | 0.416594i | \(-0.136776\pi\) |
−0.815327 | + | 0.579000i | \(0.803443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −699.332 | + | 1211.28i | −0.107262 | + | 0.185783i | −0.914660 | − | 0.404224i | \(-0.867542\pi\) |
0.807398 | + | 0.590007i | \(0.200875\pi\) | |||||||
\(350\) | −2299.89 | −0.351240 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12081.2 | 1.82934 | ||||||||
\(353\) | 1314.21 | − | 2276.28i | 0.198154 | − | 0.343214i | −0.749776 | − | 0.661692i | \(-0.769839\pi\) |
0.947930 | + | 0.318479i | \(0.103172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1023.85 | − | 1773.37i | −0.153072 | − | 0.265128i | ||||
\(356\) | −1298.22 | − | 2248.59i | −0.193274 | − | 0.334761i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2340.31 | − | 4053.53i | 0.345500 | − | 0.598424i | ||||
\(359\) | −3677.48 | −0.540640 | −0.270320 | − | 0.962770i | \(-0.587130\pi\) | ||||
−0.270320 | + | 0.962770i | \(0.587130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6759.94 | −0.985558 | ||||||||
\(362\) | −6036.96 | + | 10456.3i | −0.876507 | + | 1.51815i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6080.16 | − | 10531.1i | −0.875513 | − | 1.51643i | ||||
\(365\) | −896.370 | − | 1552.56i | −0.128543 | − | 0.222643i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5714.88 | + | 9898.47i | −0.812846 | + | 1.40789i | 0.0980185 | + | 0.995185i | \(0.468750\pi\) |
−0.910864 | + | 0.412706i | \(0.864584\pi\) | |||||||
\(368\) | 4.56301 | 0.000646368 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5691.00 | −0.799624 | ||||||||
\(371\) | 5494.43 | − | 9516.63i | 0.768886 | − | 1.33175i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1129.95 | − | 1957.13i | −0.156854 | − | 0.271679i | 0.776879 | − | 0.629650i | \(-0.216802\pi\) |
−0.933733 | + | 0.357971i | \(0.883469\pi\) | |||||||
\(374\) | 7224.90 | + | 12513.9i | 0.998905 | + | 1.73015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5349.47 | − | 9265.55i | 0.733717 | − | 1.27084i | ||||
\(377\) | −8364.90 | −1.14274 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11815.8 | −1.60142 | −0.800709 | − | 0.599053i | \(-0.795544\pi\) | ||||
−0.800709 | + | 0.599053i | \(0.795544\pi\) | |||||||
\(380\) | −321.415 | + | 556.708i | −0.0433902 | + | 0.0751540i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1859.80 | − | 3221.27i | −0.249099 | − | 0.431452i | ||||
\(383\) | −4040.11 | − | 6997.68i | −0.539008 | − | 0.933589i | −0.998958 | − | 0.0456440i | \(-0.985466\pi\) |
0.459950 | − | 0.887945i | \(-0.347867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3336.07 | − | 5778.25i | 0.441616 | − | 0.764901i | ||||
\(386\) | −3724.00 | −0.491054 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3257.17 | 0.426180 | ||||||||
\(389\) | 1550.22 | − | 2685.05i | 0.202054 | − | 0.349968i | −0.747136 | − | 0.664671i | \(-0.768572\pi\) |
0.949190 | + | 0.314703i | \(0.101905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 228.402 | + | 395.604i | 0.0295417 | + | 0.0511677i | ||||
\(392\) | −692.669 | − | 1199.74i | −0.0892476 | − | 0.154581i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9326.47 | − | 16153.9i | 1.19254 | − | 2.06554i | ||||
\(395\) | 3257.76 | 0.414976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11990.1 | −1.51578 | −0.757890 | − | 0.652382i | \(-0.773770\pi\) | ||||
−0.757890 | + | 0.652382i | \(0.773770\pi\) | |||||||
\(398\) | 3069.99 | − | 5317.38i | 0.386645 | − | 0.669689i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.94635 | + | 10.2994i | 0.000743294 | + | 0.00128742i | ||||
\(401\) | 6426.63 | + | 11131.3i | 0.800326 | + | 1.38620i | 0.919402 | + | 0.393320i | \(0.128673\pi\) |
−0.119076 | + | 0.992885i | \(0.537993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3604.52 | − | 6243.21i | 0.445543 | − | 0.771703i | ||||
\(404\) | −563.243 | −0.0693623 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16442.8 | −2.00996 | ||||||||
\(407\) | 8255.02 | − | 14298.1i | 1.00537 | − | 1.74135i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1112.54 | − | 1926.98i | −0.134503 | − | 0.232966i | 0.790904 | − | 0.611940i | \(-0.209610\pi\) |
−0.925408 | + | 0.378974i | \(0.876277\pi\) | |||||||
\(410\) | −2854.65 | − | 4944.40i | −0.343856 | − | 0.595576i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9302.97 | − | 16113.2i | 1.11244 | − | 1.92680i | ||||
\(413\) | −8433.95 | −1.00486 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4065.71 | −0.480911 | ||||||||
\(416\) | −4261.32 | + | 7380.83i | −0.502232 | + | 0.869891i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1509.93 | − | 2615.27i | −0.176682 | − | 0.306021i | ||||
\(419\) | 4838.33 | + | 8380.23i | 0.564123 | + | 0.977090i | 0.997131 | + | 0.0756998i | \(0.0241191\pi\) |
−0.433007 | + | 0.901390i | \(0.642548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4981.30 | − | 8627.87i | 0.576660 | − | 0.998804i | −0.419199 | − | 0.907894i | \(-0.637689\pi\) |
0.995859 | − | 0.0909098i | \(-0.0289775\pi\) | |||||||
\(422\) | −13514.8 | −1.55898 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12287.3 | 1.40737 | ||||||||
\(425\) | −595.291 | + | 1031.08i | −0.0679432 | + | 0.117681i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5483.32 | − | 9497.39i | −0.621444 | − | 1.07637i | ||||
\(428\) | 2297.76 | + | 3979.83i | 0.259500 | + | 0.449468i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2426.80 | + | 4203.33i | −0.272164 | + | 0.471402i | ||||
\(431\) | 2461.47 | 0.275092 | 0.137546 | − | 0.990495i | \(-0.456078\pi\) | ||||
0.137546 | + | 0.990495i | \(0.456078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7818.49 | 0.867743 | 0.433871 | − | 0.900975i | \(-0.357147\pi\) | ||||
0.433871 | + | 0.900975i | \(0.357147\pi\) | |||||||
\(434\) | 7085.36 | − | 12272.2i | 0.783660 | − | 1.35734i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9833.63 | + | 17032.3i | 1.08015 | + | 1.87087i | ||||
\(437\) | −47.7336 | − | 82.6770i | −0.00522519 | − | 0.00905030i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3105.91 | + | 5379.60i | −0.337670 | + | 0.584862i | −0.983994 | − | 0.178201i | \(-0.942972\pi\) |
0.646324 | + | 0.763063i | \(0.276306\pi\) | |||||||
\(440\) | 7460.51 | 0.808332 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10193.6 | −1.09697 | ||||||||
\(443\) | 1492.17 | − | 2584.52i | 0.160034 | − | 0.277188i | −0.774846 | − | 0.632150i | \(-0.782173\pi\) |
0.934881 | + | 0.354962i | \(0.115506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 502.499 | + | 870.355i | 0.0535298 | + | 0.0927163i | ||||
\(446\) | −8019.45 | − | 13890.1i | −0.851417 | − | 1.47470i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8338.16 | + | 14442.1i | −0.879333 | + | 1.52305i | ||||
\(449\) | 810.476 | 0.0851865 | 0.0425932 | − | 0.999092i | \(-0.486438\pi\) | ||||
0.0425932 | + | 0.999092i | \(0.486438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16563.1 | 1.72933 | ||||||||
\(452\) | −5251.01 | + | 9095.01i | −0.546431 | + | 0.946446i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1492.88 | + | 2585.74i | 0.154326 | + | 0.267301i | ||||
\(455\) | 2353.43 | + | 4076.26i | 0.242485 | + | 0.419996i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −785.887 | + | 1361.20i | −0.0804425 | + | 0.139331i | −0.903440 | − | 0.428714i | \(-0.858967\pi\) |
0.822998 | + | 0.568045i | \(0.192300\pi\) | |||||||
\(458\) | 20963.2 | 2.13875 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 619.532 | 0.0627953 | ||||||||
\(461\) | 1031.35 | − | 1786.34i | 0.104196 | − | 0.180474i | −0.809213 | − | 0.587515i | \(-0.800106\pi\) |
0.913410 | + | 0.407042i | \(0.133440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1391.62 | − | 2410.35i | −0.139684 | − | 0.241940i | 0.787693 | − | 0.616068i | \(-0.211275\pi\) |
−0.927377 | + | 0.374128i | \(0.877942\pi\) | |||||||
\(464\) | 42.5128 | + | 73.6344i | 0.00425347 | + | 0.00736722i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 726.118 | − | 1257.67i | 0.0721819 | − | 0.125023i | ||||
\(467\) | −10939.7 | −1.08400 | −0.541999 | − | 0.840379i | \(-0.682332\pi\) | ||||
−0.541999 | + | 0.840379i | \(0.682332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9008.83 | 0.886970 | ||||||||
\(470\) | −5439.06 | + | 9420.72i | −0.533798 | + | 0.924565i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4715.24 | − | 8167.04i | −0.459823 | − | 0.796438i | ||||
\(473\) | −7040.33 | − | 12194.2i | −0.684386 | − | 1.18539i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 124.409 | − | 215.484i | 0.0120175 | − | 0.0208149i | ||||
\(476\) | −12374.1 | −1.19152 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8496.21 | −0.812986 | ||||||||
\(479\) | 7311.85 | − | 12664.5i | 0.697467 | − | 1.20805i | −0.271875 | − | 0.962333i | \(-0.587644\pi\) |
0.969342 | − | 0.245716i | \(-0.0790230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5823.49 | + | 10086.6i | 0.552034 | + | 0.956151i | ||||
\(482\) | 7470.81 | + | 12939.8i | 0.705987 | + | 1.22281i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19829.9 | + | 34346.4i | −1.86231 | + | 3.22562i | ||||
\(485\) | −1260.74 | −0.118036 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16473.6 | 1.53284 | 0.766419 | − | 0.642341i | \(-0.222037\pi\) | ||||
0.766419 | + | 0.642341i | \(0.222037\pi\) | |||||||
\(488\) | 6131.22 | − | 10619.6i | 0.568744 | − | 0.985093i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 704.270 | + | 1219.83i | 0.0649299 | + | 0.112462i | ||||
\(491\) | 10264.6 | + | 17778.8i | 0.943450 | + | 1.63410i | 0.758825 | + | 0.651295i | \(0.225774\pi\) |
0.184626 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4255.97 | + | 7371.56i | −0.388802 | + | 0.673425i | ||||
\(494\) | 2130.35 | 0.194026 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −73.2768 | −0.00663352 | ||||||||
\(497\) | −4118.87 | + | 7134.10i | −0.371744 | + | 0.643879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7202.31 | + | 12474.8i | 0.646131 | + | 1.11913i | 0.984039 | + | 0.177953i | \(0.0569475\pi\) |
−0.337908 | + | 0.941179i | \(0.609719\pi\) | |||||||
\(500\) | 807.352 | + | 1398.38i | 0.0722118 | + | 0.125075i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12900.6 | + | 22344.5i | −1.14698 | + | 1.98663i | ||||
\(503\) | 2953.63 | 0.261821 | 0.130910 | − | 0.991394i | \(-0.458210\pi\) | ||||
0.130910 | + | 0.991394i | \(0.458210\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 218.013 | 0.0192108 | ||||||||
\(506\) | −1455.20 | + | 2520.48i | −0.127849 | + | 0.221441i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5584.69 | + | 9672.98i | 0.487757 | + | 0.844821i | ||||
\(509\) | −8684.44 | − | 15041.9i | −0.756250 | − | 1.30986i | −0.944750 | − | 0.327790i | \(-0.893696\pi\) |
0.188500 | − | 0.982073i | \(-0.439637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3606.02 | + | 6245.80i | −0.312174 | + | 0.540701i | ||||
\(512\) | 172.223 | 0.0148657 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5366.92 | 0.460554 | ||||||||
\(515\) | −3600.88 | + | 6236.91i | −0.308104 | + | 0.533652i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15779.1 | − | 27330.3i | −1.34229 | − | 2.32492i | ||||
\(518\) | 11447.2 | + | 19827.1i | 0.970966 | + | 1.68176i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2631.51 | + | 4557.90i | −0.221922 | + | 0.384379i | ||||
\(521\) | 6146.30 | 0.516841 | 0.258421 | − | 0.966033i | \(-0.416798\pi\) | ||||
0.258421 | + | 0.966033i | \(0.416798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4554.68 | −0.380807 | −0.190404 | − | 0.981706i | \(-0.560980\pi\) | ||||
−0.190404 | + | 0.981706i | \(0.560980\pi\) | |||||||
\(524\) | −14070.7 | + | 24371.1i | −1.17305 | + | 2.03179i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6627.03 | − | 11478.4i | −0.549339 | − | 0.951483i | ||||
\(527\) | −3667.88 | − | 6352.96i | −0.303179 | − | 0.525122i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6037.50 | − | 10457.3i | 0.496219 | − | 0.859476i | ||||
\(530\) | −12493.1 | −1.02389 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2586.05 | 0.210751 | ||||||||
\(533\) | −5842.22 | + | 10119.0i | −0.474774 | + | 0.822333i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −889.387 | − | 1540.46i | −0.0718720 | − | 0.124486i | ||||
\(536\) | 5036.64 | + | 8723.72i | 0.405877 | + | 0.702999i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6700.59 | − | 11605.8i | 0.536957 | − | 0.930037i | ||||
\(539\) | −4086.28 | −0.326547 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18091.8 | 1.43776 | 0.718879 | − | 0.695135i | \(-0.244655\pi\) | ||||
0.718879 | + | 0.695135i | \(0.244655\pi\) | |||||||
\(542\) | 1529.59 | − | 2649.33i | 0.121221 | − | 0.209960i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4336.23 | + | 7510.58i | 0.341754 | + | 0.591936i | ||||
\(545\) | −3806.28 | − | 6592.67i | −0.299162 | − | 0.518163i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7890.69 | + | 13667.1i | −0.616786 | + | 1.06830i | 0.373283 | + | 0.927718i | \(0.378232\pi\) |
−0.990068 | + | 0.140586i | \(0.955101\pi\) | |||||||
\(548\) | 29699.7 | 2.31516 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7585.46 | −0.588082 | ||||||||
\(551\) | 889.453 | − | 1540.58i | 0.0687694 | − | 0.119112i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6552.83 | − | 11349.8i | −0.503896 | − | 0.872774i | ||||
\(554\) | 1446.69 | + | 2505.75i | 0.110946 | + | 0.192164i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13782.8 | − | 23872.5i | 1.05130 | − | 1.82090i | ||||
\(557\) | 13954.5 | 1.06153 | 0.530766 | − | 0.847519i | \(-0.321904\pi\) | ||||
0.530766 | + | 0.847519i | \(0.321904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9933.18 | 0.751572 | ||||||||
\(560\) | 23.9216 | − | 41.4335i | 0.00180513 | − | 0.00312658i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8221.69 | − | 14240.4i | −0.617102 | − | 1.06885i | ||||
\(563\) | −6801.97 | − | 11781.4i | −0.509181 | − | 0.881927i | −0.999943 | − | 0.0106339i | \(-0.996615\pi\) |
0.490762 | − | 0.871293i | \(-0.336718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2032.50 | − | 3520.39i | 0.151341 | − | 0.262131i | ||||
\(566\) | 2306.77 | 0.171309 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9211.10 | −0.680438 | ||||||||
\(569\) | −6229.30 | + | 10789.5i | −0.458956 | + | 0.794935i | −0.998906 | − | 0.0467619i | \(-0.985110\pi\) |
0.539950 | + | 0.841697i | \(0.318443\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6728.56 | + | 11654.2i | 0.493137 | + | 0.854139i | 0.999969 | − | 0.00790629i | \(-0.00251668\pi\) |
−0.506831 | + | 0.862045i | \(0.669183\pi\) | |||||||
\(572\) | −20053.5 | − | 34733.7i | −1.46587 | − | 2.53897i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11484.0 | + | 19890.8i | −0.835074 | + | 1.44639i | ||||
\(575\) | −239.801 | −0.0173920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3722.70 | 0.268592 | 0.134296 | − | 0.990941i | \(-0.457123\pi\) | ||||
0.134296 | + | 0.990941i | \(0.457123\pi\) | |||||||
\(578\) | 6048.61 | − | 10476.5i | 0.435275 | − | 0.753918i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5772.08 | + | 9997.54i | 0.413229 | + | 0.715733i | ||||
\(581\) | 8177.99 | + | 14164.7i | 0.583959 | + | 1.01145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18121.7 | − | 31387.7i | 1.28735 | − | 2.22975i | ||||
\(584\) | −8064.19 | −0.571401 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28349.3 | −1.99847 | ||||||||
\(587\) | −8770.16 | + | 15190.4i | −0.616667 | + | 1.06810i | 0.373423 | + | 0.927661i | \(0.378184\pi\) |
−0.990090 | + | 0.140437i | \(0.955149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 766.548 | + | 1327.70i | 0.0536249 | + | 0.0928810i | ||||
\(590\) | 4794.21 | + | 8303.82i | 0.334533 | + | 0.579429i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 59.1933 | − | 102.526i | 0.00410951 | − | 0.00711788i | ||||
\(593\) | 22350.6 | 1.54777 | 0.773886 | − | 0.633325i | \(-0.218310\pi\) | ||||
0.773886 | + | 0.633325i | \(0.218310\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4789.60 | 0.330008 | ||||||||
\(596\) | 11306.9 | − | 19584.2i | 0.777097 | − | 1.34597i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1026.57 | − | 1778.07i | −0.0702000 | − | 0.121590i | ||||
\(599\) | −1280.81 | − | 2218.43i | −0.0873665 | − | 0.151323i | 0.819031 | − | 0.573750i | \(-0.194512\pi\) |
−0.906397 | + | 0.422427i | \(0.861178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6692.51 | + | 11591.8i | −0.454232 | + | 0.786752i | −0.998644 | − | 0.0520656i | \(-0.983420\pi\) |
0.544412 | + | 0.838818i | \(0.316753\pi\) | |||||||
\(602\) | 19525.6 | 1.32193 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11315.3 | 0.762270 | ||||||||
\(605\) | 7675.51 | − | 13294.4i | 0.515791 | − | 0.893377i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14314.3 | + | 24793.1i | 0.957166 | + | 1.65786i | 0.729331 | + | 0.684161i | \(0.239831\pi\) |
0.227835 | + | 0.973700i | \(0.426835\pi\) | |||||||
\(608\) | −906.226 | − | 1569.63i | −0.0604479 | − | 0.104699i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6233.90 | + | 10797.4i | −0.413776 | + | 0.716681i | ||||
\(611\) | 22262.8 | 1.47407 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7188.12 | 0.473614 | 0.236807 | − | 0.971557i | \(-0.423899\pi\) | ||||
0.236807 | + | 0.971557i | \(0.423899\pi\) | |||||||
\(614\) | 4497.63 | − | 7790.12i | 0.295618 | − | 0.512025i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15006.5 | − | 25992.0i | −0.981539 | − | 1.70008i | ||||
\(617\) | 7766.88 | + | 13452.6i | 0.506779 | + | 0.877767i | 0.999969 | + | 0.00784559i | \(0.00249736\pi\) |
−0.493190 | + | 0.869922i | \(0.664169\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11079.9 | − | 19191.0i | 0.719450 | − | 1.24612i | −0.241769 | − | 0.970334i | \(-0.577728\pi\) |
0.961218 | − | 0.275789i | \(-0.0889392\pi\) | |||||||
\(620\) | −9948.99 | −0.644453 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10547.2 | 0.679908 | ||||||||
\(623\) | 2021.51 | − | 3501.36i | 0.130000 | − | 0.225167i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −23559.4 | − | 40806.1i | −1.50419 | − | 2.60534i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1675.38 | − | 2901.85i | 0.106457 | − | 0.184389i | ||||
\(629\) | 11851.7 | 0.751287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25582.8 | −1.61400 | −0.807002 | − | 0.590549i | \(-0.798911\pi\) | ||||
−0.807002 | + | 0.590549i | \(0.798911\pi\) | |||||||
\(632\) | 7327.10 | − | 12690.9i | 0.461165 | − | 0.798761i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3891.73 | − | 6740.68i | −0.243786 | − | 0.422250i | ||||
\(635\) | −2161.65 | − | 3744.10i | −0.135091 | − | 0.233984i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1441.33 | − | 2496.46i | 0.0896510 | − | 0.155280i | ||||
\(638\) | −54231.5 | −3.36527 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11674.8 | 0.721076 | ||||||||
\(641\) | 1905.34 | − | 3300.14i | 0.117405 | − | 0.203351i | −0.801334 | − | 0.598217i | \(-0.795876\pi\) |
0.918738 | + | 0.394867i | \(0.129209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13360.0 | − | 23140.3i | −0.819391 | − | 1.41923i | −0.906131 | − | 0.422996i | \(-0.860978\pi\) |
0.0867402 | − | 0.996231i | \(-0.472355\pi\) | |||||||
\(644\) | −1246.16 | − | 2158.41i | −0.0762509 | − | 0.132071i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1083.90 | − | 1877.37i | 0.0660147 | − | 0.114341i | ||||
\(647\) | −5114.23 | −0.310759 | −0.155380 | − | 0.987855i | \(-0.549660\pi\) | ||||
−0.155380 | + | 0.987855i | \(0.549660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27816.8 | −1.68244 | ||||||||
\(650\) | 2675.58 | − | 4634.24i | 0.161454 | − | 0.279646i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7762.20 | + | 13444.5i | 0.466244 | + | 0.807559i | ||||
\(653\) | −4435.53 | − | 7682.56i | −0.265813 | − | 0.460401i | 0.701964 | − | 0.712213i | \(-0.252307\pi\) |
−0.967776 | + | 0.251812i | \(0.918974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5446.30 | − | 9433.27i | 0.324893 | − | 0.562730i | ||||
\(656\) | 118.767 | 0.00706872 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43761.7 | 2.59272 | ||||||||
\(659\) | −12102.2 | + | 20961.7i | −0.715382 | + | 1.23908i | 0.247430 | + | 0.968906i | \(0.420414\pi\) |
−0.962812 | + | 0.270172i | \(0.912920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10689.8 | − | 18515.2i | −0.629023 | − | 1.08950i | −0.987748 | − | 0.156056i | \(-0.950122\pi\) |
0.358726 | − | 0.933443i | \(-0.383211\pi\) | |||||||
\(662\) | 19098.1 | + | 33078.9i | 1.12125 | + | 1.94207i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9144.28 | + | 15838.4i | −0.534438 | + | 0.925674i | ||||
\(665\) | −1000.98 | −0.0583702 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1714.43 | −0.0995248 | ||||||||
\(668\) | −10843.7 | + | 18781.9i | −0.628079 | + | 1.08787i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5121.00 | − | 8869.83i | −0.295286 | − | 0.511450i | ||||
\(671\) | −18085.0 | − | 31324.2i | −1.04048 | − | 1.80217i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14850.7 | + | 25722.1i | −0.850597 | + | 1.47328i | 0.0300732 | + | 0.999548i | \(0.490426\pi\) |
−0.880670 | + | 0.473730i | \(0.842907\pi\) | |||||||
\(674\) | −35936.6 | −2.05375 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −86.5900 | −0.00492661 | ||||||||
\(677\) | 1330.74 | − | 2304.91i | 0.0755459 | − | 0.130849i | −0.825778 | − | 0.563996i | \(-0.809263\pi\) |
0.901324 | + | 0.433147i | \(0.142597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2535.93 | + | 4392.36i | 0.143328 | + | 0.248252i | ||||
\(680\) | 2677.77 | + | 4638.03i | 0.151011 | + | 0.261559i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23368.9 | − | 40476.1i | 1.31208 | − | 2.27259i | ||||
\(683\) | −28698.1 | −1.60776 | −0.803882 | − | 0.594789i | \(-0.797235\pi\) | ||||
−0.803882 | + | 0.594789i | \(0.797235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11495.8 | −0.641215 | ||||||||
\(686\) | −12944.0 | + | 22419.7i | −0.720415 | + | 1.24780i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −50.4833 | − | 87.4396i | −0.00279747 | − | 0.00484535i | ||||
\(689\) | 12783.9 | + | 22142.4i | 0.706863 | + | 1.22432i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8412.62 | + | 14571.1i | −0.463142 | + | 0.802186i | −0.999116 | − | 0.0420492i | \(-0.986611\pi\) |
0.535973 | + | 0.844235i | \(0.319945\pi\) | |||||||
\(692\) | −12036.6 | −0.661220 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5543.99 | −0.303238 | ||||||||
\(695\) | −5334.88 | + | 9240.28i | −0.291170 | + | 0.504322i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5944.92 | + | 10296.9i | 0.323070 | + | 0.559574i | ||||
\(698\) | −3198.45 | − | 5539.88i | −0.173443 | − | 0.300412i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3247.90 | − | 5625.54i | 0.175370 | − | 0.303750i | ||||
\(701\) | 998.795 | 0.0538145 | 0.0269073 | − | 0.999638i | \(-0.491434\pi\) | ||||
0.0269073 | + | 0.999638i | \(0.491434\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2476.88 | −0.132884 | ||||||||
\(704\) | −27500.8 | + | 47632.9i | −1.47227 | + | 2.55004i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6010.66 | + | 10410.8i | 0.320417 | + | 0.554978i | ||||
\(707\) | −438.523 | − | 759.545i | −0.0233272 | − | 0.0404040i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16626.9 | + | 28798.6i | −0.880727 | + | 1.52546i | −0.0301937 | + | 0.999544i | \(0.509612\pi\) |
−0.850534 | + | 0.525921i | \(0.823721\pi\) | |||||||
\(710\) | 9365.36 | 0.495036 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4520.73 | 0.237952 | ||||||||
\(713\) | 738.765 | − | 1279.58i | 0.0388036 | − | 0.0672099i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7762.06 | + | 13444.3i | 0.405993 | + | 0.703200i | ||||
\(716\) | 6609.97 | + | 11448.8i | 0.345009 | + | 0.597573i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8409.62 | − | 14565.9i | 0.437109 | − | 0.757095i | ||||
\(719\) | −1178.94 | −0.0611503 | −0.0305752 | − | 0.999532i | \(-0.509734\pi\) | ||||
−0.0305752 | + | 0.999532i | \(0.509734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28972.0 | 1.49650 | ||||||||
\(722\) | 15458.6 | − | 26775.0i | 0.796826 | − | 1.38014i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17050.8 | − | 29532.9i | −0.875260 | − | 1.51600i | ||||
\(725\) | −2234.19 | − | 3869.72i | −0.114449 | − | 0.198232i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6338.35 | + | 10978.3i | −0.323351 | + | 0.560061i | −0.981177 | − | 0.193109i | \(-0.938143\pi\) |
0.657826 | + | 0.753170i | \(0.271476\pi\) | |||||||
\(728\) | 21172.6 | 1.07790 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8199.24 | 0.415709 | ||||||||
\(731\) | 5053.90 | − | 8753.61i | 0.255712 | − | 0.442906i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4903.42 | − | 8492.98i | −0.247083 | − | 0.427961i | 0.715632 | − | 0.698478i | \(-0.246139\pi\) |
−0.962715 | + | 0.270517i | \(0.912805\pi\) | |||||||
\(734\) | −26137.5 | − | 45271.4i | −1.31438 | − | 2.27657i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −873.381 | + | 1512.74i | −0.0437408 | + | 0.0757613i | ||||
\(737\) | 29712.8 | 1.48506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29970.4 | −1.49185 | −0.745927 | − | 0.666028i | \(-0.767993\pi\) | ||||
−0.745927 | + | 0.666028i | \(0.767993\pi\) | |||||||
\(740\) | 8036.84 | − | 13920.2i | 0.399243 | − | 0.691510i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25129.2 | + | 43525.1i | 1.24329 | + | 2.15345i | ||||
\(743\) | 10848.8 | + | 18790.6i | 0.535670 | + | 0.927808i | 0.999131 | + | 0.0416904i | \(0.0132743\pi\) |
−0.463460 | + | 0.886118i | \(0.653392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4376.55 | + | 7580.40i | −0.215227 | + | 0.372785i | ||||
\(746\) | 10335.8 | 0.507267 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40812.1 | −1.99497 | ||||||||
\(749\) | −3577.92 | + | 6197.14i | −0.174545 | + | 0.302321i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8512.10 | − | 14743.4i | −0.413596 | − | 0.716370i | 0.581684 | − | 0.813415i | \(-0.302394\pi\) |
−0.995280 | + | 0.0970452i | \(0.969061\pi\) | |||||||
\(752\) | −113.146 | − | 195.974i | −0.00548670 | − | 0.00950324i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19128.8 | − | 33132.0i | 0.923911 | − | 1.60026i | ||||
\(755\) | −4379.77 | −0.211121 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30745.2 | 1.47616 | 0.738080 | − | 0.674714i | \(-0.235733\pi\) | ||||
0.738080 | + | 0.674714i | \(0.235733\pi\) | |||||||
\(758\) | 27020.3 | − | 46800.5i | 1.29475 | − | 2.24257i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −559.624 | − | 969.298i | −0.0267101 | − | 0.0462633i | ||||
\(761\) | 10748.3 | + | 18616.6i | 0.511992 | + | 0.886797i | 0.999903 | + | 0.0139035i | \(0.00442575\pi\) |
−0.487911 | + | 0.872893i | \(0.662241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15312.3 | + | 26521.7i | −0.726530 | + | 1.25839i | ||||
\(764\) | 10505.7 | 0.497489 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36955.5 | 1.74316 | ||||||||
\(767\) | 9811.66 | − | 16994.3i | 0.461902 | − | 0.800037i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11028.7 | − | 19102.4i | −0.517174 | − | 0.895772i | −0.999801 | − | 0.0199457i | \(-0.993651\pi\) |
0.482627 | − | 0.875826i | \(-0.339683\pi\) | |||||||
\(770\) | 15257.8 | + | 26427.3i | 0.714095 | + | 1.23685i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5259.04 | − | 9108.93i | 0.245178 | − | 0.424660i | ||||
\(773\) | −30155.8 | −1.40314 | −0.701570 | − | 0.712601i | \(-0.747517\pi\) | ||||
−0.701570 | + | 0.712601i | \(0.747517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3850.93 | 0.178490 | ||||||||
\(776\) | −2835.57 | + | 4911.35i | −0.131174 | + | 0.227200i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7090.04 | + | 12280.3i | 0.326723 | + | 0.565900i | ||||
\(779\) | −1242.42 | − | 2151.94i | −0.0571431 | − | 0.0989747i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13584.8 | + | 23529.6i | −0.622411 | + | 1.07805i | ||||
\(782\) | −2089.23 | −0.0955381 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29.3010 | −0.00133478 | ||||||||
\(785\) | −648.487 | + | 1123.21i | −0.0294847 | + | 0.0510690i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1624.36 | + | 2813.47i | 0.0735733 | + | 0.127433i | 0.900465 | − | 0.434929i | \(-0.143226\pi\) |
−0.826892 | + | 0.562361i | \(0.809893\pi\) | |||||||
\(788\) | 26341.7 | + | 45625.2i | 1.19084 | + | 2.06260i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7449.81 | + | 12903.4i | −0.335509 | + | 0.581119i | ||||
\(791\) | −16353.1 | −0.735081 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25516.1 | 1.14263 | ||||||||
\(794\) | 27418.8 | − | 47490.8i | 1.22551 | − | 2.12265i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8670.90 | + | 15018.4i | 0.386095 | + | 0.668737i | ||||
\(797\) | −13855.1 | − | 23997.7i | −0.615775 | − | 1.06655i | −0.990248 | − | 0.139316i | \(-0.955510\pi\) |
0.374473 | − | 0.927238i | \(-0.377824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11327.1 | − | 19619.0i | 0.501530 | − | 0.868675i | ||||
\(800\) | −4552.64 | −0.201200 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −58785.4 | −2.58826 | ||||||||
\(803\) | −11893.3 | + | 20599.8i | −0.522673 | + | 0.905296i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 482.348 | + | 835.452i | 0.0211187 | + | 0.0365786i | ||||
\(806\) | 16485.6 | + | 28553.8i | 0.720445 | + | 1.24785i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 490.338 | − | 849.290i | 0.0213491 | − | 0.0369776i | ||||
\(809\) | 2244.10 | 0.0975259 | 0.0487630 | − | 0.998810i | \(-0.484472\pi\) | ||||
0.0487630 | + | 0.998810i | \(0.484472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2739.73 | −0.118625 | −0.0593126 | − | 0.998239i | \(-0.518891\pi\) | ||||
−0.0593126 | + | 0.998239i | \(0.518891\pi\) | |||||||
\(812\) | 23220.6 | − | 40219.2i | 1.00355 | − | 1.73820i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 37755.0 | + | 65393.5i | 1.62569 | + | 2.81578i | ||||
\(815\) | −3004.50 | − | 5203.94i | −0.129132 | − | 0.223664i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1056.21 | + | 1829.41i | −0.0452290 | + | 0.0783390i | ||||
\(818\) | 10176.6 | 0.434984 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16125.4 | 0.686734 | ||||||||
\(821\) | −8616.06 | + | 14923.5i | −0.366264 | + | 0.634388i | −0.988978 | − | 0.148062i | \(-0.952697\pi\) |
0.622714 | + | 0.782449i | \(0.286030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9642.94 | − | 16702.1i | −0.408422 | − | 0.707409i | 0.586291 | − | 0.810101i | \(-0.300588\pi\) |
−0.994713 | + | 0.102692i | \(0.967254\pi\) | |||||||
\(824\) | 16197.6 | + | 28055.1i | 0.684795 | + | 1.18610i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19286.7 | − | 33405.5i | 0.812433 | − | 1.40717i | ||||
\(827\) | −26379.4 | −1.10919 | −0.554595 | − | 0.832120i | \(-0.687127\pi\) | ||||
−0.554595 | + | 0.832120i | \(0.687127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8718.15 | −0.365252 | −0.182626 | − | 0.983182i | \(-0.558460\pi\) | ||||
−0.182626 | + | 0.983182i | \(0.558460\pi\) | |||||||
\(830\) | 9297.43 | − | 16103.6i | 0.388818 | − | 0.673452i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19400.4 | − | 33602.6i | −0.808401 | − | 1.40019i | ||||
\(833\) | −1466.67 | − | 2540.35i | −0.0610049 | − | 0.105664i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4197.26 | − | 7269.87i | 0.173955 | − | 0.301299i | ||||
\(836\) | 8529.28 | 0.352860 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44256.9 | −1.82438 | ||||||||
\(839\) | −6738.10 | + | 11670.7i | −0.277265 | + | 0.480236i | −0.970704 | − | 0.240279i | \(-0.922761\pi\) |
0.693439 | + | 0.720515i | \(0.256095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3778.58 | − | 6544.70i | −0.154930 | − | 0.268346i | ||||
\(842\) | 22782.4 | + | 39460.2i | 0.932462 | + | 1.61507i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19085.6 | − | 33057.3i | 0.778383 | − | 1.34820i | ||||
\(845\) | 33.5162 | 0.00136449 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −61755.7 | −2.50526 | ||||||||
\(848\) | 129.943 | − | 225.068i | 0.00526210 | − | 0.00911423i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2722.61 | − | 4715.70i | −0.109865 | − | 0.190291i | ||||
\(851\) | 1193.56 | + | 2067.30i | 0.0480783 | + | 0.0832740i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14118.3 | − | 24453.6i | 0.566708 | − | 0.981567i | −0.430181 | − | 0.902743i | \(-0.641550\pi\) |
0.996889 | − | 0.0788242i | \(-0.0251166\pi\) | |||||||
\(854\) | 50156.8 | 2.00975 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8001.36 | −0.319487 | ||||||||
\(857\) | 4229.08 | − | 7324.98i | 0.168568 | − | 0.291968i | −0.769349 | − | 0.638829i | \(-0.779419\pi\) |
0.937917 | + | 0.346861i | \(0.112752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11527.2 | + | 19965.6i | 0.457860 | + | 0.793036i | 0.998848 | − | 0.0479940i | \(-0.0152828\pi\) |
−0.540988 | + | 0.841030i | \(0.681950\pi\) | |||||||
\(860\) | −6854.25 | − | 11871.9i | −0.271777 | − | 0.470731i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5628.86 | + | 9749.48i | −0.222413 | + | 0.385230i | ||||
\(863\) | 42314.4 | 1.66906 | 0.834529 | − | 0.550963i | \(-0.185740\pi\) | ||||
0.834529 | + | 0.550963i | \(0.185740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4658.99 | 0.183133 | ||||||||
\(866\) | −17879.2 | + | 30967.8i | −0.701572 | + | 1.21516i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20011.9 | + | 34661.7i | 0.782545 | + | 1.35541i | ||||
\(869\) | −21612.5 | − | 37433.9i | −0.843674 | − | 1.46129i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10480.4 | + | 18152.7i | −0.407711 | + | 0.706176i | ||||
\(872\) | −34243.1 | −1.32984 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 436.627 | 0.0168983 | ||||||||
\(875\) | −1257.16 | + | 2177.46i | −0.0485711 | + | 0.0841276i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5090.00 | + | 8816.15i | 0.195983 | + | 0.339453i | 0.947222 | − | 0.320577i | \(-0.103877\pi\) |
−0.751239 | + | 0.660030i | \(0.770544\pi\) | |||||||
\(878\) | −14205.2 | − | 24604.0i | −0.546014 | − | 0.945725i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 78.8980 | − | 136.655i | 0.00302233 | − | 0.00523483i | ||||
\(881\) | −6030.64 | −0.230621 | −0.115311 | − | 0.993329i | \(-0.536786\pi\) | ||||
−0.115311 | + | 0.993329i | \(0.536786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30238.0 | −1.15242 | −0.576211 | − | 0.817301i | \(-0.695469\pi\) | ||||
−0.576211 | + | 0.817301i | \(0.695469\pi\) | |||||||
\(884\) | 14395.4 | − | 24933.6i | 0.547704 | − | 0.948651i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6824.57 | + | 11820.5i | 0.258776 | + | 0.448214i | ||||
\(887\) | 9388.09 | + | 16260.7i | 0.355379 | + | 0.615535i | 0.987183 | − | 0.159594i | \(-0.0510184\pi\) |
−0.631804 | + | 0.775129i | \(0.717685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8696.14 | + | 15062.1i | −0.328075 | + | 0.568243i | ||||
\(890\) | −4596.44 | −0.173116 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45300.3 | 1.70041 | ||||||||
\(893\) | −2367.23 | + | 4100.17i | −0.0887082 | + | 0.153647i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2558.51 | − | 4431.46i | −0.0955547 | − | 0.165506i | ||||
\(896\) | −23483.4 | − | 40674.4i | −0.875586 | − | 1.51656i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1853.39 | + | 3210.16i | −0.0688735 | + | 0.119292i | ||||
\(899\) | 27531.8 | 1.02140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26017.3 | 0.962000 | ||||||||
\(902\) | −37876.4 | + | 65603.8i | −1.39817 | + | 2.42169i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9142.66 | − | 15835.6i | −0.336372 | − | 0.582614i | ||||
\(905\) | 6599.82 | + | 11431.2i | 0.242415 | + | 0.419875i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18826.3 | − | 32608.1i | 0.689213 | − | 1.19375i | −0.282880 | − | 0.959155i | \(-0.591290\pi\) |
0.972093 | − | 0.234597i | \(-0.0753769\pi\) | |||||||
\(908\) | −8432.97 | −0.308214 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21527.2 | −0.784198 | ||||||||
\(911\) | −23793.1 | + | 41210.8i | −0.865312 | + | 1.49877i | 0.00142411 | + | 0.999999i | \(0.499547\pi\) |
−0.866737 | + | 0.498766i | \(0.833787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26972.6 | + | 46717.9i | 0.977724 | + | 1.69347i | ||||
\(914\) | −3594.32 | − | 6225.54i | −0.130076 | − | 0.225298i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29604.3 | + | 51276.2i | −1.06785 | + | 1.84958i | ||||
\(917\) | −43819.9 | −1.57804 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32177.3 | 1.15499 | 0.577493 | − | 0.816396i | \(-0.304031\pi\) | ||||
0.577493 | + | 0.816396i | \(0.304031\pi\) | |||||||
\(920\) | −539.341 | + | 934.167i | −0.0193278 | + | 0.0334767i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4716.94 | + | 8169.99i | 0.168486 | + | 0.291827i | ||||
\(923\) | −9583.40 | − | 16598.9i | −0.341757 | − | 0.591940i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3110.80 | + | 5388.07i | −0.110576 | + | 0.191523i | ||||
\(926\) | 12729.3 | 0.451741 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32548.6 | −1.15136 | ||||||||
\(929\) | 20321.8 | − | 35198.4i | 0.717694 | − | 1.24308i | −0.244218 | − | 0.969720i | \(-0.578531\pi\) |
0.961911 | − | 0.273362i | \(-0.0881355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 306.518 | + | 530.905i | 0.0107903 | + | 0.0186893i | ||||
\(932\) | 2050.85 | + | 3552.18i | 0.0720792 | + | 0.124845i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25016.7 | − | 43330.2i | 0.876415 | − | 1.51799i | ||||
\(935\) | 15797.0 | 0.552533 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6077.87 | 0.211905 | 0.105953 | − | 0.994371i | \(-0.466211\pi\) | ||||
0.105953 | + | 0.994371i | \(0.466211\pi\) | |||||||
\(938\) | −20601.3 | + | 35682.5i | −0.717118 | + | 1.24208i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15362.1 | − | 26607.9i | −0.533039 | − | 0.923250i | ||||
\(941\) | 732.293 | + | 1268.37i | 0.0253688 | + | 0.0439401i | 0.878431 | − | 0.477869i | \(-0.158591\pi\) |
−0.853062 | + | 0.521809i | \(0.825257\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1197.39 | + | 2073.95i | −0.0413494 | + | 0.0716193i | ||||
\(944\) | −199.463 | −0.00687707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64399.0 | 2.21331 | ||||||||
\(947\) | −5304.36 | + | 9187.43i | −0.182015 | + | 0.315260i | −0.942567 | − | 0.334018i | \(-0.891595\pi\) |
0.760551 | + | 0.649278i | \(0.224929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8390.14 | − | 14532.1i | −0.286992 | − | 0.497085i | ||||
\(950\) | 568.997 | + | 985.531i | 0.0194323 | + | 0.0336577i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10772.4 | − | 18658.4i | 0.366739 | − | 0.635211i | ||||
\(953\) | 43623.4 | 1.48279 | 0.741396 | − | 0.671068i | \(-0.234164\pi\) | ||||
0.741396 | + | 0.671068i | \(0.234164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4066.40 | −0.137786 | ||||||||
\(956\) | 11998.4 | − | 20781.8i | 0.405915 | − | 0.703065i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33441.3 | + | 57922.1i | 1.12781 | + | 1.95342i | ||||
\(959\) | 23123.3 | + | 40050.7i | 0.778613 | + | 1.34860i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3031.76 | − | 5251.17i | 0.101768 | − | 0.176267i | ||||
\(962\) | −53268.4 | −1.78528 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −42201.2 | −1.40997 | ||||||||
\(965\) | −2035.61 | + | 3525.77i | −0.0679051 | + | 0.117615i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2540.19 | − | 4399.73i | −0.0844745 | − | 0.146314i | 0.820693 | − | 0.571370i | \(-0.193588\pi\) |
−0.905167 | + | 0.425056i | \(0.860254\pi\) | |||||||
\(968\) | −34526.3 | − | 59801.3i | −1.14640 | − | 1.98563i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2883.06 | − | 4993.60i | 0.0954324 | − | 0.165294i | ||||
\(971\) | −9875.60 | −0.326388 | −0.163194 | − | 0.986594i | \(-0.552180\pi\) | ||||
−0.163194 | + | 0.986594i | \(0.552180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42923.4 | 1.41425 | ||||||||
\(974\) | −37671.8 | + | 65249.4i | −1.23930 | + | 2.14654i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −129.680 | − | 224.613i | −0.00425304 | − | 0.00736648i | ||||
\(977\) | 12290.4 | + | 21287.6i | 0.402461 | + | 0.697084i | 0.994022 | − | 0.109177i | \(-0.0348214\pi\) |
−0.591561 | + | 0.806260i | \(0.701488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6667.32 | − | 11548.1i | 0.217659 | − | 0.376997i | ||||
\(980\) | −3978.28 | −0.129675 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −93891.8 | −3.05113 | ||||||||
\(983\) | −15930.3 | + | 27592.1i | −0.516885 | + | 0.895270i | 0.482923 | + | 0.875663i | \(0.339575\pi\) |
−0.999808 | + | 0.0196076i | \(0.993758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10196.0 | − | 17660.0i | −0.329820 | − | 0.571265i | ||||
\(986\) | −19465.0 | − | 33714.4i | −0.628695 | − | 1.08893i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3008.49 | + | 5210.85i | −0.0968752 | + | 0.167793i | ||||
\(989\) | 2035.86 | 0.0654566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36921.3 | −1.18350 | −0.591748 | − | 0.806123i | \(-0.701562\pi\) | ||||
−0.591748 | + | 0.806123i | \(0.701562\pi\) | |||||||
\(992\) | 14025.5 | − | 24292.9i | 0.448902 | − | 0.777520i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18838.0 | − | 32628.4i | −0.601112 | − | 1.04116i | ||||
\(995\) | −3356.22 | − | 5813.15i | −0.106934 | − | 0.185215i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1867.06 | − | 3233.84i | 0.0593083 | − | 0.102725i | −0.834847 | − | 0.550482i | \(-0.814444\pi\) |
0.894155 | + | 0.447757i | \(0.147777\pi\) | |||||||
\(998\) | −65880.7 | −2.08959 | ||||||||
\(999\) | 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 | 135.4.e.b.46.1 | 6 | ||
3.2 | odd | 2 | 45.4.e.b.16.3 | ✓ | 6 | ||
9.2 | odd | 6 | 405.4.a.h.1.1 | 3 | |||
9.4 | even | 3 | inner | 135.4.e.b.91.1 | 6 | ||
9.5 | odd | 6 | 45.4.e.b.31.3 | yes | 6 | ||
9.7 | even | 3 | 405.4.a.j.1.3 | 3 | |||
15.2 | even | 4 | 225.4.k.c.124.6 | 12 | |||
15.8 | even | 4 | 225.4.k.c.124.1 | 12 | |||
15.14 | odd | 2 | 225.4.e.c.151.1 | 6 | |||
45.14 | odd | 6 | 225.4.e.c.76.1 | 6 | |||
45.23 | even | 12 | 225.4.k.c.49.6 | 12 | |||
45.29 | odd | 6 | 2025.4.a.s.1.3 | 3 | |||
45.32 | even | 12 | 225.4.k.c.49.1 | 12 | |||
45.34 | even | 6 | 2025.4.a.q.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.3 | ✓ | 6 | 3.2 | odd | 2 | ||
45.4.e.b.31.3 | yes | 6 | 9.5 | odd | 6 | ||
135.4.e.b.46.1 | 6 | 1.1 | even | 1 | trivial | ||
135.4.e.b.91.1 | 6 | 9.4 | even | 3 | inner | ||
225.4.e.c.76.1 | 6 | 45.14 | odd | 6 | |||
225.4.e.c.151.1 | 6 | 15.14 | odd | 2 | |||
225.4.k.c.49.1 | 12 | 45.32 | even | 12 | |||
225.4.k.c.49.6 | 12 | 45.23 | even | 12 | |||
225.4.k.c.124.1 | 12 | 15.8 | even | 4 | |||
225.4.k.c.124.6 | 12 | 15.2 | even | 4 | |||
405.4.a.h.1.1 | 3 | 9.2 | odd | 6 | |||
405.4.a.j.1.3 | 3 | 9.7 | even | 3 | |||
2025.4.a.q.1.1 | 3 | 45.34 | even | 6 | |||
2025.4.a.s.1.3 | 3 | 45.29 | odd | 6 |