Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1421,4,Mod(1,1421)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1421, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1421.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1421 = 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1421.a (trivial) |
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: | yes |
Analytic conductor: | \(83.8417141182\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1421.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.146447 | 0.0732233 | − | 0.997316i | \(-0.476671\pi\) | ||||
0.0732233 | + | 0.997316i | \(0.476671\pi\) | |||||||
\(3\) | 9.24264 | 1.77875 | 0.889374 | − | 0.457181i | \(-0.151141\pi\) | ||||
0.889374 | + | 0.457181i | \(0.151141\pi\) | |||||||
\(4\) | −7.82843 | −0.978553 | ||||||||
\(5\) | −0.656854 | −0.0587508 | −0.0293754 | − | 0.999568i | \(-0.509352\pi\) | ||||
−0.0293754 | + | 0.999568i | \(0.509352\pi\) | |||||||
\(6\) | 3.82843 | 0.260491 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.55635 | −0.289752 | ||||||||
\(9\) | 58.4264 | 2.16394 | ||||||||
\(10\) | −0.272078 | −0.00860386 | ||||||||
\(11\) | −65.3259 | −1.79059 | −0.895295 | − | 0.445473i | \(-0.853036\pi\) | ||||
−0.895295 | + | 0.445473i | \(0.853036\pi\) | |||||||
\(12\) | −72.3553 | −1.74060 | ||||||||
\(13\) | 49.7696 | 1.06181 | 0.530907 | − | 0.847430i | \(-0.321851\pi\) | ||||
0.530907 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.07107 | −0.104503 | ||||||||
\(16\) | 59.9117 | 0.936120 | ||||||||
\(17\) | −55.4558 | −0.791178 | −0.395589 | − | 0.918428i | \(-0.629459\pi\) | ||||
−0.395589 | + | 0.918428i | \(0.629459\pi\) | |||||||
\(18\) | 24.2010 | 0.316902 | ||||||||
\(19\) | 64.7452 | 0.781766 | 0.390883 | − | 0.920440i | \(-0.372170\pi\) | ||||
0.390883 | + | 0.920440i | \(0.372170\pi\) | |||||||
\(20\) | 5.14214 | 0.0574908 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −27.0589 | −0.262226 | ||||||||
\(23\) | 93.8823 | 0.851122 | 0.425561 | − | 0.904930i | \(-0.360077\pi\) | ||||
0.425561 | + | 0.904930i | \(0.360077\pi\) | |||||||
\(24\) | −60.5980 | −0.515396 | ||||||||
\(25\) | −124.569 | −0.996548 | ||||||||
\(26\) | 20.6152 | 0.155499 | ||||||||
\(27\) | 290.463 | 2.07036 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | −2.51472 | −0.0153041 | ||||||||
\(31\) | 236.095 | 1.36787 | 0.683935 | − | 0.729543i | \(-0.260267\pi\) | ||||
0.683935 | + | 0.729543i | \(0.260267\pi\) | |||||||
\(32\) | 77.2670 | 0.426844 | ||||||||
\(33\) | −603.784 | −3.18501 | ||||||||
\(34\) | −22.9706 | −0.115865 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −457.387 | −2.11753 | ||||||||
\(37\) | 76.8040 | 0.341257 | 0.170628 | − | 0.985335i | \(-0.445420\pi\) | ||||
0.170628 | + | 0.985335i | \(0.445420\pi\) | |||||||
\(38\) | 26.8183 | 0.114487 | ||||||||
\(39\) | 460.002 | 1.88870 | ||||||||
\(40\) | 4.30657 | 0.0170232 | ||||||||
\(41\) | −215.161 | −0.819575 | −0.409788 | − | 0.912181i | \(-0.634397\pi\) | ||||
−0.409788 | + | 0.912181i | \(0.634397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 80.8305 | 0.286664 | 0.143332 | − | 0.989675i | \(-0.454218\pi\) | ||||
0.143332 | + | 0.989675i | \(0.454218\pi\) | |||||||
\(44\) | 511.399 | 1.75219 | ||||||||
\(45\) | −38.3776 | −0.127133 | ||||||||
\(46\) | 38.8873 | 0.124644 | ||||||||
\(47\) | 357.742 | 1.11026 | 0.555128 | − | 0.831765i | \(-0.312669\pi\) | ||||
0.555128 | + | 0.831765i | \(0.312669\pi\) | |||||||
\(48\) | 553.742 | 1.66512 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −51.5980 | −0.145941 | ||||||||
\(51\) | −512.558 | −1.40730 | ||||||||
\(52\) | −389.617 | −1.03904 | ||||||||
\(53\) | 328.466 | 0.851288 | 0.425644 | − | 0.904891i | \(-0.360048\pi\) | ||||
0.425644 | + | 0.904891i | \(0.360048\pi\) | |||||||
\(54\) | 120.314 | 0.303197 | ||||||||
\(55\) | 42.9096 | 0.105199 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 598.416 | 1.39056 | ||||||||
\(58\) | 12.0122 | 0.0271945 | ||||||||
\(59\) | 99.2750 | 0.219059 | 0.109530 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109530 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(60\) | 47.5269 | 0.102262 | ||||||||
\(61\) | 725.730 | 1.52328 | 0.761641 | − | 0.647999i | \(-0.224394\pi\) | ||||
0.761641 | + | 0.647999i | \(0.224394\pi\) | |||||||
\(62\) | 97.7939 | 0.200320 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −447.288 | −0.873610 | ||||||||
\(65\) | −32.6913 | −0.0623825 | ||||||||
\(66\) | −250.095 | −0.466434 | ||||||||
\(67\) | 844.479 | 1.53984 | 0.769922 | − | 0.638138i | \(-0.220295\pi\) | ||||
0.769922 | + | 0.638138i | \(0.220295\pi\) | |||||||
\(68\) | 434.132 | 0.774209 | ||||||||
\(69\) | 867.720 | 1.51393 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −378.083 | −0.631975 | −0.315988 | − | 0.948763i | \(-0.602336\pi\) | ||||
−0.315988 | + | 0.948763i | \(0.602336\pi\) | |||||||
\(72\) | −383.064 | −0.627007 | ||||||||
\(73\) | 581.097 | 0.931674 | 0.465837 | − | 0.884870i | \(-0.345753\pi\) | ||||
0.465837 | + | 0.884870i | \(0.345753\pi\) | |||||||
\(74\) | 31.8133 | 0.0499759 | ||||||||
\(75\) | −1151.34 | −1.77261 | ||||||||
\(76\) | −506.853 | −0.765000 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 190.539 | 0.276594 | ||||||||
\(79\) | −353.247 | −0.503081 | −0.251540 | − | 0.967847i | \(-0.580937\pi\) | ||||
−0.251540 | + | 0.967847i | \(0.580937\pi\) | |||||||
\(80\) | −39.3532 | −0.0549978 | ||||||||
\(81\) | 1107.13 | 1.51870 | ||||||||
\(82\) | −89.1228 | −0.120024 | ||||||||
\(83\) | −696.510 | −0.921107 | −0.460553 | − | 0.887632i | \(-0.652349\pi\) | ||||
−0.460553 | + | 0.887632i | \(0.652349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 36.4264 | 0.0464823 | ||||||||
\(86\) | 33.4811 | 0.0419809 | ||||||||
\(87\) | 268.037 | 0.330305 | ||||||||
\(88\) | 428.299 | 0.518828 | ||||||||
\(89\) | −1118.22 | −1.33181 | −0.665905 | − | 0.746037i | \(-0.731954\pi\) | ||||
−0.665905 | + | 0.746037i | \(0.731954\pi\) | |||||||
\(90\) | −15.8965 | −0.0186182 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −734.950 | −0.832868 | ||||||||
\(93\) | 2182.15 | 2.43310 | ||||||||
\(94\) | 148.182 | 0.162593 | ||||||||
\(95\) | −42.5281 | −0.0459294 | ||||||||
\(96\) | 714.151 | 0.759248 | ||||||||
\(97\) | 805.415 | 0.843068 | 0.421534 | − | 0.906813i | \(-0.361492\pi\) | ||||
0.421534 | + | 0.906813i | \(0.361492\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3816.76 | −3.87473 | ||||||||
\(100\) | 975.176 | 0.975176 | ||||||||
\(101\) | 1373.99 | 1.35363 | 0.676817 | − | 0.736151i | \(-0.263359\pi\) | ||||
0.676817 | + | 0.736151i | \(0.263359\pi\) | |||||||
\(102\) | −212.309 | −0.206095 | ||||||||
\(103\) | 634.672 | 0.607147 | 0.303573 | − | 0.952808i | \(-0.401820\pi\) | ||||
0.303573 | + | 0.952808i | \(0.401820\pi\) | |||||||
\(104\) | −326.307 | −0.307663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 136.055 | 0.124668 | ||||||||
\(107\) | −180.956 | −0.163493 | −0.0817463 | − | 0.996653i | \(-0.526050\pi\) | ||||
−0.0817463 | + | 0.996653i | \(0.526050\pi\) | |||||||
\(108\) | −2273.87 | −2.02595 | ||||||||
\(109\) | 1038.14 | 0.912251 | 0.456125 | − | 0.889916i | \(-0.349237\pi\) | ||||
0.456125 | + | 0.889916i | \(0.349237\pi\) | |||||||
\(110\) | 17.7737 | 0.0154060 | ||||||||
\(111\) | 709.872 | 0.607010 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −184.765 | −0.153816 | −0.0769082 | − | 0.997038i | \(-0.524505\pi\) | ||||
−0.0769082 | + | 0.997038i | \(0.524505\pi\) | |||||||
\(114\) | 247.872 | 0.203643 | ||||||||
\(115\) | −61.6670 | −0.0500041 | ||||||||
\(116\) | −227.024 | −0.181713 | ||||||||
\(117\) | 2907.86 | 2.29770 | ||||||||
\(118\) | 41.1211 | 0.0320805 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 39.8040 | 0.0302800 | ||||||||
\(121\) | 2936.47 | 2.20622 | ||||||||
\(122\) | 300.607 | 0.223079 | ||||||||
\(123\) | −1988.66 | −1.45782 | ||||||||
\(124\) | −1848.26 | −1.33853 | ||||||||
\(125\) | 163.930 | 0.117299 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1999.58 | 1.39712 | 0.698558 | − | 0.715554i | \(-0.253825\pi\) | ||||
0.698558 | + | 0.715554i | \(0.253825\pi\) | |||||||
\(128\) | −803.409 | −0.554781 | ||||||||
\(129\) | 747.087 | 0.509902 | ||||||||
\(130\) | −13.5412 | −0.00913570 | ||||||||
\(131\) | −561.468 | −0.374471 | −0.187236 | − | 0.982315i | \(-0.559953\pi\) | ||||
−0.187236 | + | 0.982315i | \(0.559953\pi\) | |||||||
\(132\) | 4726.68 | 3.11670 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 349.795 | 0.225505 | ||||||||
\(135\) | −190.792 | −0.121635 | ||||||||
\(136\) | 363.588 | 0.229246 | ||||||||
\(137\) | −250.489 | −0.156210 | −0.0781050 | − | 0.996945i | \(-0.524887\pi\) | ||||
−0.0781050 | + | 0.996945i | \(0.524887\pi\) | |||||||
\(138\) | 359.421 | 0.221710 | ||||||||
\(139\) | 242.244 | 0.147819 | 0.0739096 | − | 0.997265i | \(-0.476452\pi\) | ||||
0.0739096 | + | 0.997265i | \(0.476452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3306.48 | 1.97487 | ||||||||
\(142\) | −156.607 | −0.0925506 | ||||||||
\(143\) | −3251.24 | −1.90128 | ||||||||
\(144\) | 3500.42 | 2.02571 | ||||||||
\(145\) | −19.0488 | −0.0109098 | ||||||||
\(146\) | 240.698 | 0.136441 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −601.255 | −0.333938 | ||||||||
\(149\) | −1632.63 | −0.897652 | −0.448826 | − | 0.893619i | \(-0.648158\pi\) | ||||
−0.448826 | + | 0.893619i | \(0.648158\pi\) | |||||||
\(150\) | −476.902 | −0.259592 | ||||||||
\(151\) | −121.582 | −0.0655245 | −0.0327623 | − | 0.999463i | \(-0.510430\pi\) | ||||
−0.0327623 | + | 0.999463i | \(0.510430\pi\) | |||||||
\(152\) | −424.492 | −0.226519 | ||||||||
\(153\) | −3240.09 | −1.71206 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −155.080 | −0.0803635 | ||||||||
\(156\) | −3601.09 | −1.84819 | ||||||||
\(157\) | 753.163 | 0.382860 | 0.191430 | − | 0.981506i | \(-0.438688\pi\) | ||||
0.191430 | + | 0.981506i | \(0.438688\pi\) | |||||||
\(158\) | −146.320 | −0.0736745 | ||||||||
\(159\) | 3035.89 | 1.51423 | ||||||||
\(160\) | −50.7532 | −0.0250774 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 458.589 | 0.222408 | ||||||||
\(163\) | 537.917 | 0.258484 | 0.129242 | − | 0.991613i | \(-0.458746\pi\) | ||||
0.129242 | + | 0.991613i | \(0.458746\pi\) | |||||||
\(164\) | 1684.38 | 0.801998 | ||||||||
\(165\) | 396.598 | 0.187122 | ||||||||
\(166\) | −288.504 | −0.134893 | ||||||||
\(167\) | −484.613 | −0.224554 | −0.112277 | − | 0.993677i | \(-0.535814\pi\) | ||||
−0.112277 | + | 0.993677i | \(0.535814\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 280.008 | 0.127450 | ||||||||
\(170\) | 15.0883 | 0.00680718 | ||||||||
\(171\) | 3782.83 | 1.69170 | ||||||||
\(172\) | −632.776 | −0.280516 | ||||||||
\(173\) | 3269.70 | 1.43694 | 0.718469 | − | 0.695559i | \(-0.244843\pi\) | ||||
0.718469 | + | 0.695559i | \(0.244843\pi\) | |||||||
\(174\) | 111.024 | 0.0483721 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3913.79 | −1.67621 | ||||||||
\(177\) | 917.563 | 0.389651 | ||||||||
\(178\) | −463.182 | −0.195039 | ||||||||
\(179\) | −562.267 | −0.234781 | −0.117390 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117390 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(180\) | 300.437 | 0.124407 | ||||||||
\(181\) | 1507.32 | 0.618998 | 0.309499 | − | 0.950900i | \(-0.399839\pi\) | ||||
0.309499 | + | 0.950900i | \(0.399839\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6707.66 | 2.70953 | ||||||||
\(184\) | −615.525 | −0.246615 | ||||||||
\(185\) | −50.4491 | −0.0200491 | ||||||||
\(186\) | 903.874 | 0.356319 | ||||||||
\(187\) | 3622.70 | 1.41668 | ||||||||
\(188\) | −2800.56 | −1.08645 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.6157 | −0.00672621 | ||||||||
\(191\) | 4532.00 | 1.71688 | 0.858439 | − | 0.512915i | \(-0.171434\pi\) | ||||
0.858439 | + | 0.512915i | \(0.171434\pi\) | |||||||
\(192\) | −4134.13 | −1.55393 | ||||||||
\(193\) | −2935.17 | −1.09471 | −0.547353 | − | 0.836902i | \(-0.684364\pi\) | ||||
−0.547353 | + | 0.836902i | \(0.684364\pi\) | |||||||
\(194\) | 333.614 | 0.123464 | ||||||||
\(195\) | −302.154 | −0.110963 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2682.20 | 0.970043 | 0.485022 | − | 0.874502i | \(-0.338812\pi\) | ||||
0.485022 | + | 0.874502i | \(0.338812\pi\) | |||||||
\(198\) | −1580.95 | −0.567442 | ||||||||
\(199\) | 648.376 | 0.230966 | 0.115483 | − | 0.993309i | \(-0.463158\pi\) | ||||
0.115483 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(200\) | 816.715 | 0.288752 | ||||||||
\(201\) | 7805.22 | 2.73899 | ||||||||
\(202\) | 569.125 | 0.198235 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4012.53 | 1.37712 | ||||||||
\(205\) | 141.330 | 0.0481507 | ||||||||
\(206\) | 262.890 | 0.0889145 | ||||||||
\(207\) | 5485.20 | 1.84178 | ||||||||
\(208\) | 2981.78 | 0.993986 | ||||||||
\(209\) | −4229.54 | −1.39982 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4949.57 | −1.61489 | −0.807446 | − | 0.589941i | \(-0.799151\pi\) | ||||
−0.807446 | + | 0.589941i | \(0.799151\pi\) | |||||||
\(212\) | −2571.37 | −0.833031 | ||||||||
\(213\) | −3494.49 | −1.12412 | ||||||||
\(214\) | −74.9545 | −0.0239429 | ||||||||
\(215\) | −53.0939 | −0.0168417 | ||||||||
\(216\) | −1904.38 | −0.599891 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 430.010 | 0.133596 | ||||||||
\(219\) | 5370.87 | 1.65721 | ||||||||
\(220\) | −335.915 | −0.102943 | ||||||||
\(221\) | −2760.01 | −0.840084 | ||||||||
\(222\) | 294.039 | 0.0888945 | ||||||||
\(223\) | −2216.94 | −0.665729 | −0.332864 | − | 0.942975i | \(-0.608015\pi\) | ||||
−0.332864 | + | 0.942975i | \(0.608015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7278.09 | −2.15647 | ||||||||
\(226\) | −76.5323 | −0.0225259 | ||||||||
\(227\) | −4546.09 | −1.32923 | −0.664613 | − | 0.747187i | \(-0.731404\pi\) | ||||
−0.664613 | + | 0.747187i | \(0.731404\pi\) | |||||||
\(228\) | −4684.66 | −1.36074 | ||||||||
\(229\) | −3339.05 | −0.963539 | −0.481770 | − | 0.876298i | \(-0.660006\pi\) | ||||
−0.481770 | + | 0.876298i | \(0.660006\pi\) | |||||||
\(230\) | −25.5433 | −0.00732293 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −190.134 | −0.0538057 | ||||||||
\(233\) | −3995.35 | −1.12336 | −0.561682 | − | 0.827353i | \(-0.689846\pi\) | ||||
−0.561682 | + | 0.827353i | \(0.689846\pi\) | |||||||
\(234\) | 1204.47 | 0.336491 | ||||||||
\(235\) | −234.984 | −0.0652285 | ||||||||
\(236\) | −777.167 | −0.214361 | ||||||||
\(237\) | −3264.93 | −0.894853 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1400.04 | −0.378915 | −0.189458 | − | 0.981889i | \(-0.560673\pi\) | ||||
−0.189458 | + | 0.981889i | \(0.560673\pi\) | |||||||
\(240\) | −363.728 | −0.0978272 | ||||||||
\(241\) | 2040.94 | 0.545513 | 0.272756 | − | 0.962083i | \(-0.412065\pi\) | ||||
0.272756 | + | 0.962083i | \(0.412065\pi\) | |||||||
\(242\) | 1216.33 | 0.323093 | ||||||||
\(243\) | 2390.32 | 0.631026 | ||||||||
\(244\) | −5681.32 | −1.49061 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −823.730 | −0.213492 | ||||||||
\(247\) | 3222.34 | 0.830091 | ||||||||
\(248\) | −1547.92 | −0.396344 | ||||||||
\(249\) | −6437.59 | −1.63842 | ||||||||
\(250\) | 67.9021 | 0.0171780 | ||||||||
\(251\) | −802.648 | −0.201843 | −0.100922 | − | 0.994894i | \(-0.532179\pi\) | ||||
−0.100922 | + | 0.994894i | \(0.532179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6132.94 | −1.52401 | ||||||||
\(254\) | 828.252 | 0.204603 | ||||||||
\(255\) | 336.676 | 0.0826803 | ||||||||
\(256\) | 3245.52 | 0.792364 | ||||||||
\(257\) | 4464.10 | 1.08351 | 0.541756 | − | 0.840536i | \(-0.317760\pi\) | ||||
0.541756 | + | 0.840536i | \(0.317760\pi\) | |||||||
\(258\) | 309.454 | 0.0746734 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 255.922 | 0.0610446 | ||||||||
\(261\) | 1694.37 | 0.401834 | ||||||||
\(262\) | −232.568 | −0.0548400 | ||||||||
\(263\) | −3815.21 | −0.894509 | −0.447255 | − | 0.894407i | \(-0.647598\pi\) | ||||
−0.447255 | + | 0.894407i | \(0.647598\pi\) | |||||||
\(264\) | 3958.62 | 0.922864 | ||||||||
\(265\) | −215.754 | −0.0500139 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10335.3 | −2.36895 | ||||||||
\(268\) | −6610.95 | −1.50682 | ||||||||
\(269\) | −4523.98 | −1.02540 | −0.512699 | − | 0.858569i | \(-0.671354\pi\) | ||||
−0.512699 | + | 0.858569i | \(0.671354\pi\) | |||||||
\(270\) | −79.0286 | −0.0178131 | ||||||||
\(271\) | −3962.65 | −0.888242 | −0.444121 | − | 0.895967i | \(-0.646484\pi\) | ||||
−0.444121 | + | 0.895967i | \(0.646484\pi\) | |||||||
\(272\) | −3322.45 | −0.740637 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −103.756 | −0.0228764 | ||||||||
\(275\) | 8137.55 | 1.78441 | ||||||||
\(276\) | −6792.88 | −1.48146 | ||||||||
\(277\) | 2217.59 | 0.481019 | 0.240509 | − | 0.970647i | \(-0.422685\pi\) | ||||
0.240509 | + | 0.970647i | \(0.422685\pi\) | |||||||
\(278\) | 100.341 | 0.0216476 | ||||||||
\(279\) | 13794.2 | 2.95999 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2562.96 | −0.544105 | −0.272053 | − | 0.962282i | \(-0.587702\pi\) | ||||
−0.272053 | + | 0.962282i | \(0.587702\pi\) | |||||||
\(282\) | 1369.59 | 0.289212 | ||||||||
\(283\) | 3869.29 | 0.812741 | 0.406370 | − | 0.913708i | \(-0.366794\pi\) | ||||
0.406370 | + | 0.913708i | \(0.366794\pi\) | |||||||
\(284\) | 2959.80 | 0.618421 | ||||||||
\(285\) | −393.072 | −0.0816968 | ||||||||
\(286\) | −1346.71 | −0.278435 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4514.43 | 0.923665 | ||||||||
\(289\) | −1837.65 | −0.374038 | ||||||||
\(290\) | −7.89026 | −0.00159770 | ||||||||
\(291\) | 7444.17 | 1.49960 | ||||||||
\(292\) | −4549.07 | −0.911693 | ||||||||
\(293\) | 3883.83 | 0.774388 | 0.387194 | − | 0.921998i | \(-0.373444\pi\) | ||||
0.387194 | + | 0.921998i | \(0.373444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −65.2092 | −0.0128699 | ||||||||
\(296\) | −503.554 | −0.0988800 | ||||||||
\(297\) | −18974.8 | −3.70716 | ||||||||
\(298\) | −676.257 | −0.131458 | ||||||||
\(299\) | 4672.48 | 0.903734 | ||||||||
\(300\) | 9013.20 | 1.73459 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −50.3609 | −0.00959584 | ||||||||
\(303\) | 12699.3 | 2.40777 | ||||||||
\(304\) | 3878.99 | 0.731827 | ||||||||
\(305\) | −476.699 | −0.0894941 | ||||||||
\(306\) | −1342.09 | −0.250726 | ||||||||
\(307\) | 403.210 | 0.0749590 | 0.0374795 | − | 0.999297i | \(-0.488067\pi\) | ||||
0.0374795 | + | 0.999297i | \(0.488067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5866.05 | 1.07996 | ||||||||
\(310\) | −64.2364 | −0.0117690 | ||||||||
\(311\) | 4838.71 | 0.882244 | 0.441122 | − | 0.897447i | \(-0.354581\pi\) | ||||
0.441122 | + | 0.897447i | \(0.354581\pi\) | |||||||
\(312\) | −3015.93 | −0.547255 | ||||||||
\(313\) | 8544.28 | 1.54298 | 0.771488 | − | 0.636244i | \(-0.219513\pi\) | ||||
0.771488 | + | 0.636244i | \(0.219513\pi\) | |||||||
\(314\) | 311.970 | 0.0560685 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2765.37 | 0.492291 | ||||||||
\(317\) | −1773.06 | −0.314148 | −0.157074 | − | 0.987587i | \(-0.550206\pi\) | ||||
−0.157074 | + | 0.987587i | \(0.550206\pi\) | |||||||
\(318\) | 1257.51 | 0.221753 | ||||||||
\(319\) | −1894.45 | −0.332504 | ||||||||
\(320\) | 293.803 | 0.0513253 | ||||||||
\(321\) | −1672.51 | −0.290812 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3590.50 | −0.618516 | ||||||||
\(324\) | −8667.10 | −1.48613 | ||||||||
\(325\) | −6199.72 | −1.05815 | ||||||||
\(326\) | 222.813 | 0.0378541 | ||||||||
\(327\) | 9595.11 | 1.62266 | ||||||||
\(328\) | 1410.67 | 0.237474 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 164.276 | 0.0274034 | ||||||||
\(331\) | 801.875 | 0.133157 | 0.0665786 | − | 0.997781i | \(-0.478792\pi\) | ||||
0.0665786 | + | 0.997781i | \(0.478792\pi\) | |||||||
\(332\) | 5452.58 | 0.901352 | ||||||||
\(333\) | 4487.38 | 0.738460 | ||||||||
\(334\) | −200.733 | −0.0328851 | ||||||||
\(335\) | −554.700 | −0.0904671 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8193.23 | 1.32437 | 0.662186 | − | 0.749339i | \(-0.269629\pi\) | ||||
0.662186 | + | 0.749339i | \(0.269629\pi\) | |||||||
\(338\) | 115.983 | 0.0186647 | ||||||||
\(339\) | −1707.72 | −0.273601 | ||||||||
\(340\) | −285.161 | −0.0454854 | ||||||||
\(341\) | −15423.1 | −2.44930 | ||||||||
\(342\) | 1566.90 | 0.247743 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −529.953 | −0.0830615 | ||||||||
\(345\) | −569.966 | −0.0889447 | ||||||||
\(346\) | 1354.35 | 0.210435 | ||||||||
\(347\) | −10914.9 | −1.68860 | −0.844301 | − | 0.535869i | \(-0.819984\pi\) | ||||
−0.844301 | + | 0.535869i | \(0.819984\pi\) | |||||||
\(348\) | −2098.30 | −0.323221 | ||||||||
\(349\) | −6697.83 | −1.02730 | −0.513649 | − | 0.858001i | \(-0.671706\pi\) | ||||
−0.513649 | + | 0.858001i | \(0.671706\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14456.2 | 2.19833 | ||||||||
\(352\) | −5047.54 | −0.764303 | ||||||||
\(353\) | 3764.83 | 0.567654 | 0.283827 | − | 0.958875i | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958875i | \(0.408396\pi\) | |||||||
\(354\) | 380.067 | 0.0570631 | ||||||||
\(355\) | 248.346 | 0.0371291 | ||||||||
\(356\) | 8753.90 | 1.30325 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −232.898 | −0.0343829 | ||||||||
\(359\) | 6577.13 | 0.966930 | 0.483465 | − | 0.875364i | \(-0.339378\pi\) | ||||
0.483465 | + | 0.875364i | \(0.339378\pi\) | |||||||
\(360\) | 251.617 | 0.0368372 | ||||||||
\(361\) | −2667.06 | −0.388841 | ||||||||
\(362\) | 624.354 | 0.0906501 | ||||||||
\(363\) | 27140.8 | 3.92430 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −381.696 | −0.0547366 | ||||||||
\(366\) | 2778.40 | 0.396802 | ||||||||
\(367\) | −2274.27 | −0.323477 | −0.161738 | − | 0.986834i | \(-0.551710\pi\) | ||||
−0.161738 | + | 0.986834i | \(0.551710\pi\) | |||||||
\(368\) | 5624.64 | 0.796752 | ||||||||
\(369\) | −12571.1 | −1.77351 | ||||||||
\(370\) | −20.8967 | −0.00293613 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −17082.8 | −2.38091 | ||||||||
\(373\) | 1284.94 | 0.178369 | 0.0891844 | − | 0.996015i | \(-0.471574\pi\) | ||||
0.0891844 | + | 0.996015i | \(0.471574\pi\) | |||||||
\(374\) | 1500.57 | 0.207467 | ||||||||
\(375\) | 1515.15 | 0.208645 | ||||||||
\(376\) | −2345.48 | −0.321700 | ||||||||
\(377\) | 1443.32 | 0.197174 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 174.785 | 0.0236890 | 0.0118445 | − | 0.999930i | \(-0.496230\pi\) | ||||
0.0118445 | + | 0.999930i | \(0.496230\pi\) | |||||||
\(380\) | 332.928 | 0.0449444 | ||||||||
\(381\) | 18481.4 | 2.48512 | ||||||||
\(382\) | 1877.22 | 0.251431 | ||||||||
\(383\) | 5558.62 | 0.741599 | 0.370799 | − | 0.928713i | \(-0.379084\pi\) | ||||
0.370799 | + | 0.928713i | \(0.379084\pi\) | |||||||
\(384\) | −7425.62 | −0.986816 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1215.79 | −0.160316 | ||||||||
\(387\) | 4722.64 | 0.620323 | ||||||||
\(388\) | −6305.14 | −0.824987 | ||||||||
\(389\) | −2556.05 | −0.333154 | −0.166577 | − | 0.986028i | \(-0.553271\pi\) | ||||
−0.166577 | + | 0.986028i | \(0.553271\pi\) | |||||||
\(390\) | −125.156 | −0.0162501 | ||||||||
\(391\) | −5206.32 | −0.673388 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5189.45 | −0.666089 | ||||||||
\(394\) | 1111.00 | 0.142060 | ||||||||
\(395\) | 232.032 | 0.0295564 | ||||||||
\(396\) | 29879.2 | 3.79163 | ||||||||
\(397\) | −5927.27 | −0.749323 | −0.374662 | − | 0.927162i | \(-0.622241\pi\) | ||||
−0.374662 | + | 0.927162i | \(0.622241\pi\) | |||||||
\(398\) | 268.566 | 0.0338241 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7463.11 | −0.932889 | ||||||||
\(401\) | 4747.99 | 0.591280 | 0.295640 | − | 0.955299i | \(-0.404467\pi\) | ||||
0.295640 | + | 0.955299i | \(0.404467\pi\) | |||||||
\(402\) | 3233.03 | 0.401116 | ||||||||
\(403\) | 11750.4 | 1.45243 | ||||||||
\(404\) | −10756.2 | −1.32460 | ||||||||
\(405\) | −727.224 | −0.0892249 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5017.29 | −0.611052 | ||||||||
\(408\) | 3360.51 | 0.407770 | ||||||||
\(409\) | −5200.19 | −0.628686 | −0.314343 | − | 0.949309i | \(-0.601784\pi\) | ||||
−0.314343 | + | 0.949309i | \(0.601784\pi\) | |||||||
\(410\) | 58.5407 | 0.00705151 | ||||||||
\(411\) | −2315.18 | −0.277858 | ||||||||
\(412\) | −4968.48 | −0.594125 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2272.05 | 0.269722 | ||||||||
\(415\) | 457.505 | 0.0541158 | ||||||||
\(416\) | 3845.55 | 0.453229 | ||||||||
\(417\) | 2238.97 | 0.262933 | ||||||||
\(418\) | −1751.93 | −0.204999 | ||||||||
\(419\) | 6425.59 | 0.749189 | 0.374595 | − | 0.927189i | \(-0.377782\pi\) | ||||
0.374595 | + | 0.927189i | \(0.377782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10037.6 | 1.16201 | 0.581003 | − | 0.813902i | \(-0.302661\pi\) | ||||
0.581003 | + | 0.813902i | \(0.302661\pi\) | |||||||
\(422\) | −2050.18 | −0.236496 | ||||||||
\(423\) | 20901.6 | 2.40253 | ||||||||
\(424\) | −2153.54 | −0.246663 | ||||||||
\(425\) | 6908.05 | 0.788447 | ||||||||
\(426\) | −1447.46 | −0.164624 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1416.60 | 0.159986 | ||||||||
\(429\) | −30050.1 | −3.38189 | ||||||||
\(430\) | −21.9922 | −0.00246641 | ||||||||
\(431\) | 16646.8 | 1.86044 | 0.930218 | − | 0.367006i | \(-0.119617\pi\) | ||||
0.930218 | + | 0.367006i | \(0.119617\pi\) | |||||||
\(432\) | 17402.1 | 1.93810 | ||||||||
\(433\) | −15089.1 | −1.67468 | −0.837340 | − | 0.546682i | \(-0.815891\pi\) | ||||
−0.837340 | + | 0.546682i | \(0.815891\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −176.061 | −0.0194057 | ||||||||
\(436\) | −8126.97 | −0.892686 | ||||||||
\(437\) | 6078.42 | 0.665378 | ||||||||
\(438\) | 2224.69 | 0.242693 | ||||||||
\(439\) | 3777.24 | 0.410656 | 0.205328 | − | 0.978693i | \(-0.434174\pi\) | ||||
0.205328 | + | 0.978693i | \(0.434174\pi\) | |||||||
\(440\) | −281.330 | −0.0304816 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1143.23 | −0.123027 | ||||||||
\(443\) | 7992.65 | 0.857206 | 0.428603 | − | 0.903493i | \(-0.359006\pi\) | ||||
0.428603 | + | 0.903493i | \(0.359006\pi\) | |||||||
\(444\) | −5557.18 | −0.593991 | ||||||||
\(445\) | 734.507 | 0.0782449 | ||||||||
\(446\) | −918.288 | −0.0974937 | ||||||||
\(447\) | −15089.8 | −1.59670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6433.54 | 0.676209 | 0.338104 | − | 0.941109i | \(-0.390214\pi\) | ||||
0.338104 | + | 0.941109i | \(0.390214\pi\) | |||||||
\(450\) | −3014.68 | −0.315808 | ||||||||
\(451\) | 14055.6 | 1.46752 | ||||||||
\(452\) | 1446.42 | 0.150518 | ||||||||
\(453\) | −1123.74 | −0.116552 | ||||||||
\(454\) | −1883.05 | −0.194661 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3923.43 | −0.402919 | ||||||||
\(457\) | 6975.18 | 0.713972 | 0.356986 | − | 0.934110i | \(-0.383804\pi\) | ||||
0.356986 | + | 0.934110i | \(0.383804\pi\) | |||||||
\(458\) | −1383.08 | −0.141107 | ||||||||
\(459\) | −16107.9 | −1.63802 | ||||||||
\(460\) | 482.755 | 0.0489317 | ||||||||
\(461\) | 14758.9 | 1.49109 | 0.745543 | − | 0.666458i | \(-0.232190\pi\) | ||||
0.745543 | + | 0.666458i | \(0.232190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18951.2 | −1.90224 | −0.951121 | − | 0.308818i | \(-0.900067\pi\) | ||||
−0.951121 | + | 0.308818i | \(0.900067\pi\) | |||||||
\(464\) | 1737.44 | 0.173833 | ||||||||
\(465\) | −1433.35 | −0.142946 | ||||||||
\(466\) | −1654.93 | −0.164513 | ||||||||
\(467\) | −12442.4 | −1.23290 | −0.616449 | − | 0.787395i | \(-0.711429\pi\) | ||||
−0.616449 | + | 0.787395i | \(0.711429\pi\) | |||||||
\(468\) | −22763.9 | −2.24843 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −97.3338 | −0.00955249 | ||||||||
\(471\) | 6961.22 | 0.681010 | ||||||||
\(472\) | −650.882 | −0.0634730 | ||||||||
\(473\) | −5280.33 | −0.513297 | ||||||||
\(474\) | −1352.38 | −0.131048 | ||||||||
\(475\) | −8065.21 | −0.779068 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19191.1 | 1.84214 | ||||||||
\(478\) | −579.914 | −0.0554909 | ||||||||
\(479\) | −12947.5 | −1.23504 | −0.617522 | − | 0.786554i | \(-0.711863\pi\) | ||||
−0.617522 | + | 0.786554i | \(0.711863\pi\) | |||||||
\(480\) | −469.093 | −0.0446064 | ||||||||
\(481\) | 3822.50 | 0.362352 | ||||||||
\(482\) | 845.385 | 0.0798885 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22988.0 | −2.15890 | ||||||||
\(485\) | −529.041 | −0.0495309 | ||||||||
\(486\) | 990.104 | 0.0924116 | ||||||||
\(487\) | 9844.72 | 0.916030 | 0.458015 | − | 0.888944i | \(-0.348561\pi\) | ||||
0.458015 | + | 0.888944i | \(0.348561\pi\) | |||||||
\(488\) | −4758.14 | −0.441375 | ||||||||
\(489\) | 4971.77 | 0.459778 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6809.50 | −0.625883 | −0.312941 | − | 0.949772i | \(-0.601314\pi\) | ||||
−0.312941 | + | 0.949772i | \(0.601314\pi\) | |||||||
\(492\) | 15568.1 | 1.42655 | ||||||||
\(493\) | −1608.22 | −0.146918 | ||||||||
\(494\) | 1334.74 | 0.121564 | ||||||||
\(495\) | 2507.05 | 0.227644 | ||||||||
\(496\) | 14144.9 | 1.28049 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2666.54 | −0.239940 | ||||||||
\(499\) | −15953.8 | −1.43124 | −0.715622 | − | 0.698488i | \(-0.753857\pi\) | ||||
−0.715622 | + | 0.698488i | \(0.753857\pi\) | |||||||
\(500\) | −1283.32 | −0.114783 | ||||||||
\(501\) | −4479.11 | −0.399424 | ||||||||
\(502\) | −332.468 | −0.0295593 | ||||||||
\(503\) | 14582.7 | 1.29267 | 0.646334 | − | 0.763054i | \(-0.276301\pi\) | ||||
0.646334 | + | 0.763054i | \(0.276301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −902.511 | −0.0795272 | ||||||||
\(506\) | −2540.35 | −0.223186 | ||||||||
\(507\) | 2588.02 | 0.226702 | ||||||||
\(508\) | −15653.5 | −1.36715 | ||||||||
\(509\) | −20906.4 | −1.82055 | −0.910273 | − | 0.414008i | \(-0.864129\pi\) | ||||
−0.910273 | + | 0.414008i | \(0.864129\pi\) | |||||||
\(510\) | 139.456 | 0.0121083 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7771.61 | 0.670820 | ||||||||
\(513\) | 18806.1 | 1.61854 | ||||||||
\(514\) | 1849.09 | 0.158677 | ||||||||
\(515\) | −416.887 | −0.0356704 | ||||||||
\(516\) | −5848.52 | −0.498967 | ||||||||
\(517\) | −23369.8 | −1.98802 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30220.6 | 2.55595 | ||||||||
\(520\) | 214.336 | 0.0180755 | ||||||||
\(521\) | 15131.7 | 1.27242 | 0.636212 | − | 0.771515i | \(-0.280500\pi\) | ||||
0.636212 | + | 0.771515i | \(0.280500\pi\) | |||||||
\(522\) | 701.829 | 0.0588472 | ||||||||
\(523\) | −12146.9 | −1.01558 | −0.507790 | − | 0.861481i | \(-0.669537\pi\) | ||||
−0.507790 | + | 0.861481i | \(0.669537\pi\) | |||||||
\(524\) | 4395.41 | 0.366440 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1580.31 | −0.130998 | ||||||||
\(527\) | −13092.9 | −1.08223 | ||||||||
\(528\) | −36173.7 | −2.98155 | ||||||||
\(529\) | −3353.12 | −0.275592 | ||||||||
\(530\) | −89.3683 | −0.00732436 | ||||||||
\(531\) | 5800.28 | 0.474032 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10708.5 | −0.870237 | ||||||||
\(534\) | −4281.02 | −0.346925 | ||||||||
\(535\) | 118.862 | 0.00960532 | ||||||||
\(536\) | −5536.70 | −0.446174 | ||||||||
\(537\) | −5196.83 | −0.417616 | ||||||||
\(538\) | −1873.89 | −0.150166 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1493.60 | 0.119027 | ||||||||
\(541\) | −22291.8 | −1.77153 | −0.885767 | − | 0.464130i | \(-0.846367\pi\) | ||||
−0.885767 | + | 0.464130i | \(0.846367\pi\) | |||||||
\(542\) | −1641.38 | −0.130080 | ||||||||
\(543\) | 13931.7 | 1.10104 | ||||||||
\(544\) | −4284.91 | −0.337709 | ||||||||
\(545\) | −681.904 | −0.0535955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15439.4 | −1.20684 | −0.603421 | − | 0.797423i | \(-0.706196\pi\) | ||||
−0.603421 | + | 0.797423i | \(0.706196\pi\) | |||||||
\(548\) | 1960.94 | 0.152860 | ||||||||
\(549\) | 42401.8 | 3.29629 | ||||||||
\(550\) | 3370.68 | 0.261321 | ||||||||
\(551\) | 1877.61 | 0.145170 | ||||||||
\(552\) | −5689.07 | −0.438665 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 918.557 | 0.0704436 | ||||||||
\(555\) | −466.283 | −0.0356623 | ||||||||
\(556\) | −1896.39 | −0.144649 | ||||||||
\(557\) | 2336.99 | 0.177776 | 0.0888881 | − | 0.996042i | \(-0.471669\pi\) | ||||
0.0888881 | + | 0.996042i | \(0.471669\pi\) | |||||||
\(558\) | 5713.75 | 0.433481 | ||||||||
\(559\) | 4022.90 | 0.304384 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33483.3 | 2.51991 | ||||||||
\(562\) | −1061.61 | −0.0796824 | ||||||||
\(563\) | −19833.3 | −1.48468 | −0.742340 | − | 0.670023i | \(-0.766284\pi\) | ||||
−0.742340 | + | 0.670023i | \(0.766284\pi\) | |||||||
\(564\) | −25884.6 | −1.93251 | ||||||||
\(565\) | 121.364 | 0.00903685 | ||||||||
\(566\) | 1602.71 | 0.119023 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2478.85 | 0.183116 | ||||||||
\(569\) | 11063.7 | 0.815141 | 0.407571 | − | 0.913174i | \(-0.366376\pi\) | ||||
0.407571 | + | 0.913174i | \(0.366376\pi\) | |||||||
\(570\) | −162.816 | −0.0119642 | ||||||||
\(571\) | −665.827 | −0.0487986 | −0.0243993 | − | 0.999702i | \(-0.507767\pi\) | ||||
−0.0243993 | + | 0.999702i | \(0.507767\pi\) | |||||||
\(572\) | 25452.1 | 1.86050 | ||||||||
\(573\) | 41887.6 | 3.05389 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11694.8 | −0.848184 | ||||||||
\(576\) | −26133.5 | −1.89044 | ||||||||
\(577\) | 7165.21 | 0.516970 | 0.258485 | − | 0.966015i | \(-0.416777\pi\) | ||||
0.258485 | + | 0.966015i | \(0.416777\pi\) | |||||||
\(578\) | −761.179 | −0.0547766 | ||||||||
\(579\) | −27128.7 | −1.94720 | ||||||||
\(580\) | 149.122 | 0.0106758 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3083.47 | 0.219612 | ||||||||
\(583\) | −21457.3 | −1.52431 | ||||||||
\(584\) | −3809.87 | −0.269955 | ||||||||
\(585\) | −1910.04 | −0.134992 | ||||||||
\(586\) | 1608.73 | 0.113406 | ||||||||
\(587\) | 10375.2 | 0.729525 | 0.364763 | − | 0.931101i | \(-0.381150\pi\) | ||||
0.364763 | + | 0.931101i | \(0.381150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15286.0 | 1.06936 | ||||||||
\(590\) | −27.0105 | −0.00188476 | ||||||||
\(591\) | 24790.6 | 1.72546 | ||||||||
\(592\) | 4601.46 | 0.319457 | ||||||||
\(593\) | −18931.5 | −1.31100 | −0.655501 | − | 0.755194i | \(-0.727542\pi\) | ||||
−0.655501 | + | 0.755194i | \(0.727542\pi\) | |||||||
\(594\) | −7859.60 | −0.542901 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12780.9 | 0.878401 | ||||||||
\(597\) | 5992.71 | 0.410829 | ||||||||
\(598\) | 1935.40 | 0.132349 | ||||||||
\(599\) | −12244.2 | −0.835199 | −0.417600 | − | 0.908631i | \(-0.637129\pi\) | ||||
−0.417600 | + | 0.908631i | \(0.637129\pi\) | |||||||
\(600\) | 7548.60 | 0.513617 | ||||||||
\(601\) | −15596.9 | −1.05859 | −0.529293 | − | 0.848439i | \(-0.677543\pi\) | ||||
−0.529293 | + | 0.848439i | \(0.677543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 49339.9 | 3.33213 | ||||||||
\(604\) | 951.796 | 0.0641192 | ||||||||
\(605\) | −1928.84 | −0.129617 | ||||||||
\(606\) | 5260.22 | 0.352610 | ||||||||
\(607\) | 10155.5 | 0.679076 | 0.339538 | − | 0.940592i | \(-0.389729\pi\) | ||||
0.339538 | + | 0.940592i | \(0.389729\pi\) | |||||||
\(608\) | 5002.67 | 0.333692 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −197.455 | −0.0131061 | ||||||||
\(611\) | 17804.7 | 1.17889 | ||||||||
\(612\) | 25364.8 | 1.67534 | ||||||||
\(613\) | −6227.67 | −0.410331 | −0.205166 | − | 0.978727i | \(-0.565773\pi\) | ||||
−0.205166 | + | 0.978727i | \(0.565773\pi\) | |||||||
\(614\) | 167.015 | 0.0109775 | ||||||||
\(615\) | 1306.26 | 0.0856479 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14357.5 | 0.936808 | 0.468404 | − | 0.883514i | \(-0.344829\pi\) | ||||
0.468404 | + | 0.883514i | \(0.344829\pi\) | |||||||
\(618\) | 2429.80 | 0.158156 | ||||||||
\(619\) | 13220.6 | 0.858453 | 0.429227 | − | 0.903197i | \(-0.358786\pi\) | ||||
0.429227 | + | 0.903197i | \(0.358786\pi\) | |||||||
\(620\) | 1214.03 | 0.0786400 | ||||||||
\(621\) | 27269.3 | 1.76213 | ||||||||
\(622\) | 2004.26 | 0.129202 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 27559.5 | 1.76805 | ||||||||
\(625\) | 15463.4 | 0.989657 | ||||||||
\(626\) | 3539.16 | 0.225963 | ||||||||
\(627\) | −39092.1 | −2.48993 | ||||||||
\(628\) | −5896.08 | −0.374649 | ||||||||
\(629\) | −4259.23 | −0.269995 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1828.97 | 0.115389 | 0.0576943 | − | 0.998334i | \(-0.481625\pi\) | ||||
0.0576943 | + | 0.998334i | \(0.481625\pi\) | |||||||
\(632\) | 2316.01 | 0.145769 | ||||||||
\(633\) | −45747.1 | −2.87249 | ||||||||
\(634\) | −734.426 | −0.0460059 | ||||||||
\(635\) | −1313.43 | −0.0820817 | ||||||||
\(636\) | −23766.3 | −1.48175 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −784.707 | −0.0486941 | ||||||||
\(639\) | −22090.0 | −1.36756 | ||||||||
\(640\) | 527.723 | 0.0325939 | ||||||||
\(641\) | −22644.1 | −1.39530 | −0.697651 | − | 0.716437i | \(-0.745772\pi\) | ||||
−0.697651 | + | 0.716437i | \(0.745772\pi\) | |||||||
\(642\) | −692.778 | −0.0425884 | ||||||||
\(643\) | −22728.4 | −1.39397 | −0.696983 | − | 0.717088i | \(-0.745475\pi\) | ||||
−0.696983 | + | 0.717088i | \(0.745475\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −490.728 | −0.0299572 | ||||||||
\(646\) | −1487.23 | −0.0905796 | ||||||||
\(647\) | 5844.85 | 0.355154 | 0.177577 | − | 0.984107i | \(-0.443174\pi\) | ||||
0.177577 | + | 0.984107i | \(0.443174\pi\) | |||||||
\(648\) | −7258.74 | −0.440047 | ||||||||
\(649\) | −6485.23 | −0.392246 | ||||||||
\(650\) | −2568.01 | −0.154962 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4211.04 | −0.252941 | ||||||||
\(653\) | 15174.1 | 0.909355 | 0.454677 | − | 0.890656i | \(-0.349755\pi\) | ||||
0.454677 | + | 0.890656i | \(0.349755\pi\) | |||||||
\(654\) | 3974.43 | 0.237634 | ||||||||
\(655\) | 368.803 | 0.0220005 | ||||||||
\(656\) | −12890.7 | −0.767221 | ||||||||
\(657\) | 33951.4 | 2.01609 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27857.0 | −1.64667 | −0.823333 | − | 0.567558i | \(-0.807888\pi\) | ||||
−0.823333 | + | 0.567558i | \(0.807888\pi\) | |||||||
\(660\) | −3104.74 | −0.183109 | ||||||||
\(661\) | 4966.64 | 0.292254 | 0.146127 | − | 0.989266i | \(-0.453319\pi\) | ||||
0.146127 | + | 0.989266i | \(0.453319\pi\) | |||||||
\(662\) | 332.148 | 0.0195004 | ||||||||
\(663\) | −25509.8 | −1.49430 | ||||||||
\(664\) | 4566.56 | 0.266893 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1858.74 | 0.108145 | ||||||||
\(667\) | 2722.59 | 0.158049 | ||||||||
\(668\) | 3793.76 | 0.219738 | ||||||||
\(669\) | −20490.4 | −1.18416 | ||||||||
\(670\) | −229.764 | −0.0132486 | ||||||||
\(671\) | −47409.0 | −2.72758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2338.02 | −0.133914 | −0.0669569 | − | 0.997756i | \(-0.521329\pi\) | ||||
−0.0669569 | + | 0.997756i | \(0.521329\pi\) | |||||||
\(674\) | 3393.75 | 0.193950 | ||||||||
\(675\) | −36182.6 | −2.06321 | ||||||||
\(676\) | −2192.03 | −0.124717 | ||||||||
\(677\) | −6342.30 | −0.360051 | −0.180025 | − | 0.983662i | \(-0.557618\pi\) | ||||
−0.180025 | + | 0.983662i | \(0.557618\pi\) | |||||||
\(678\) | −707.361 | −0.0400679 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −238.824 | −0.0134684 | ||||||||
\(681\) | −42017.9 | −2.36436 | ||||||||
\(682\) | −6388.48 | −0.358691 | ||||||||
\(683\) | −30366.6 | −1.70124 | −0.850620 | − | 0.525780i | \(-0.823773\pi\) | ||||
−0.850620 | + | 0.525780i | \(0.823773\pi\) | |||||||
\(684\) | −29613.6 | −1.65542 | ||||||||
\(685\) | 164.535 | 0.00917746 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30861.6 | −1.71389 | ||||||||
\(688\) | 4842.69 | 0.268352 | ||||||||
\(689\) | 16347.6 | 0.903910 | ||||||||
\(690\) | −236.087 | −0.0130256 | ||||||||
\(691\) | 11826.5 | 0.651089 | 0.325545 | − | 0.945527i | \(-0.394452\pi\) | ||||
0.325545 | + | 0.945527i | \(0.394452\pi\) | |||||||
\(692\) | −25596.6 | −1.40612 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4521.12 | −0.247290 | ||||||||
\(695\) | −159.119 | −0.00868450 | ||||||||
\(696\) | −1757.34 | −0.0957067 | ||||||||
\(697\) | 11932.0 | 0.648429 | ||||||||
\(698\) | −2774.33 | −0.150444 | ||||||||
\(699\) | −36927.6 | −1.99818 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2776.33 | −0.149587 | −0.0747936 | − | 0.997199i | \(-0.523830\pi\) | ||||
−0.0747936 | + | 0.997199i | \(0.523830\pi\) | |||||||
\(702\) | 5987.96 | 0.321939 | ||||||||
\(703\) | 4972.69 | 0.266783 | ||||||||
\(704\) | 29219.5 | 1.56428 | ||||||||
\(705\) | −2171.88 | −0.116025 | ||||||||
\(706\) | 1559.45 | 0.0831310 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7183.08 | −0.381295 | ||||||||
\(709\) | −15962.7 | −0.845543 | −0.422772 | − | 0.906236i | \(-0.638943\pi\) | ||||
−0.422772 | + | 0.906236i | \(0.638943\pi\) | |||||||
\(710\) | 102.868 | 0.00543742 | ||||||||
\(711\) | −20638.9 | −1.08864 | ||||||||
\(712\) | 7331.44 | 0.385895 | ||||||||
\(713\) | 22165.2 | 1.16422 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2135.59 | 0.111702 | ||||||||
\(716\) | 4401.66 | 0.229746 | ||||||||
\(717\) | −12940.0 | −0.673994 | ||||||||
\(718\) | 2724.34 | 0.141604 | ||||||||
\(719\) | 20832.9 | 1.08058 | 0.540289 | − | 0.841480i | \(-0.318315\pi\) | ||||
0.540289 | + | 0.841480i | \(0.318315\pi\) | |||||||
\(720\) | −2299.27 | −0.119012 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1104.73 | −0.0569445 | ||||||||
\(723\) | 18863.7 | 0.970329 | ||||||||
\(724\) | −11800.0 | −0.605722 | ||||||||
\(725\) | −3612.49 | −0.185054 | ||||||||
\(726\) | 11242.1 | 0.574700 | ||||||||
\(727\) | −4452.04 | −0.227121 | −0.113561 | − | 0.993531i | \(-0.536226\pi\) | ||||
−0.113561 | + | 0.993531i | \(0.536226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7799.67 | −0.396264 | ||||||||
\(730\) | −158.104 | −0.00801599 | ||||||||
\(731\) | −4482.52 | −0.226802 | ||||||||
\(732\) | −52510.4 | −2.65142 | ||||||||
\(733\) | 12107.2 | 0.610082 | 0.305041 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305041 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(734\) | −942.034 | −0.0473721 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7254.00 | 0.363296 | ||||||||
\(737\) | −55166.4 | −2.75723 | ||||||||
\(738\) | −5207.12 | −0.259725 | ||||||||
\(739\) | −4506.27 | −0.224311 | −0.112156 | − | 0.993691i | \(-0.535775\pi\) | ||||
−0.112156 | + | 0.993691i | \(0.535775\pi\) | |||||||
\(740\) | 394.937 | 0.0196191 | ||||||||
\(741\) | 29782.9 | 1.47652 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1177.19 | 0.0581253 | 0.0290626 | − | 0.999578i | \(-0.490748\pi\) | ||||
0.0290626 | + | 0.999578i | \(0.490748\pi\) | |||||||
\(744\) | −14306.9 | −0.704996 | ||||||||
\(745\) | 1072.40 | 0.0527378 | ||||||||
\(746\) | 532.239 | 0.0261215 | ||||||||
\(747\) | −40694.6 | −1.99322 | ||||||||
\(748\) | −28360.1 | −1.38629 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 627.595 | 0.0305554 | ||||||||
\(751\) | 27631.6 | 1.34260 | 0.671300 | − | 0.741186i | \(-0.265736\pi\) | ||||
0.671300 | + | 0.741186i | \(0.265736\pi\) | |||||||
\(752\) | 21432.9 | 1.03933 | ||||||||
\(753\) | −7418.59 | −0.359028 | ||||||||
\(754\) | 597.841 | 0.0288755 | ||||||||
\(755\) | 79.8616 | 0.00384962 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11336.6 | 0.544300 | 0.272150 | − | 0.962255i | \(-0.412265\pi\) | ||||
0.272150 | + | 0.962255i | \(0.412265\pi\) | |||||||
\(758\) | 72.3984 | 0.00346917 | ||||||||
\(759\) | −56684.6 | −2.71083 | ||||||||
\(760\) | 278.829 | 0.0133082 | ||||||||
\(761\) | −4356.58 | −0.207524 | −0.103762 | − | 0.994602i | \(-0.533088\pi\) | ||||
−0.103762 | + | 0.994602i | \(0.533088\pi\) | |||||||
\(762\) | 7655.23 | 0.363937 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35478.4 | −1.68006 | ||||||||
\(765\) | 2128.26 | 0.100585 | ||||||||
\(766\) | 2302.46 | 0.108605 | ||||||||
\(767\) | 4940.87 | 0.232601 | ||||||||
\(768\) | 29997.2 | 1.40942 | ||||||||
\(769\) | 21718.1 | 1.01843 | 0.509217 | − | 0.860638i | \(-0.329935\pi\) | ||||
0.509217 | + | 0.860638i | \(0.329935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41260.0 | 1.92729 | ||||||||
\(772\) | 22977.8 | 1.07123 | ||||||||
\(773\) | −22688.4 | −1.05568 | −0.527842 | − | 0.849343i | \(-0.676999\pi\) | ||||
−0.527842 | + | 0.849343i | \(0.676999\pi\) | |||||||
\(774\) | 1956.18 | 0.0908442 | ||||||||
\(775\) | −29410.1 | −1.36315 | ||||||||
\(776\) | −5280.58 | −0.244281 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1058.75 | −0.0487893 | ||||||||
\(779\) | −13930.7 | −0.640716 | ||||||||
\(780\) | 2365.39 | 0.108583 | ||||||||
\(781\) | 24698.6 | 1.13161 | ||||||||
\(782\) | −2156.53 | −0.0986155 | ||||||||
\(783\) | 8423.43 | 0.384456 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −494.718 | −0.0224933 | ||||||||
\(786\) | −2149.54 | −0.0975465 | ||||||||
\(787\) | 32890.9 | 1.48975 | 0.744875 | − | 0.667204i | \(-0.232509\pi\) | ||||
0.744875 | + | 0.667204i | \(0.232509\pi\) | |||||||
\(788\) | −20997.4 | −0.949239 | ||||||||
\(789\) | −35262.6 | −1.59111 | ||||||||
\(790\) | 96.1107 | 0.00432844 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 25024.0 | 1.12271 | ||||||||
\(793\) | 36119.3 | 1.61744 | ||||||||
\(794\) | −2455.16 | −0.109736 | ||||||||
\(795\) | −1994.14 | −0.0889620 | ||||||||
\(796\) | −5075.76 | −0.226012 | ||||||||
\(797\) | −30404.1 | −1.35128 | −0.675638 | − | 0.737233i | \(-0.736132\pi\) | ||||
−0.675638 | + | 0.737233i | \(0.736132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19838.9 | −0.878410 | ||||||||
\(800\) | −9625.04 | −0.425371 | ||||||||
\(801\) | −65333.5 | −2.88196 | ||||||||
\(802\) | 1966.68 | 0.0865909 | ||||||||
\(803\) | −37960.7 | −1.66825 | ||||||||
\(804\) | −61102.6 | −2.68025 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4867.16 | 0.212703 | ||||||||
\(807\) | −41813.5 | −1.82392 | ||||||||
\(808\) | −9008.36 | −0.392219 | ||||||||
\(809\) | −37889.3 | −1.64662 | −0.823311 | − | 0.567591i | \(-0.807876\pi\) | ||||
−0.823311 | + | 0.567591i | \(0.807876\pi\) | |||||||
\(810\) | −301.226 | −0.0130667 | ||||||||
\(811\) | 8123.23 | 0.351720 | 0.175860 | − | 0.984415i | \(-0.443729\pi\) | ||||
0.175860 | + | 0.984415i | \(0.443729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36625.3 | −1.57996 | ||||||||
\(814\) | −2078.23 | −0.0894864 | ||||||||
\(815\) | −353.333 | −0.0151862 | ||||||||
\(816\) | −30708.2 | −1.31741 | ||||||||
\(817\) | 5233.39 | 0.224104 | ||||||||
\(818\) | −2153.99 | −0.0920690 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1106.39 | −0.0471180 | ||||||||
\(821\) | 13226.8 | 0.562264 | 0.281132 | − | 0.959669i | \(-0.409290\pi\) | ||||
0.281132 | + | 0.959669i | \(0.409290\pi\) | |||||||
\(822\) | −958.981 | −0.0406914 | ||||||||
\(823\) | −29575.2 | −1.25265 | −0.626323 | − | 0.779563i | \(-0.715441\pi\) | ||||
−0.626323 | + | 0.779563i | \(0.715441\pi\) | |||||||
\(824\) | −4161.13 | −0.175922 | ||||||||
\(825\) | 75212.5 | 3.17401 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36661.2 | −1.54152 | −0.770758 | − | 0.637128i | \(-0.780122\pi\) | ||||
−0.770758 | + | 0.637128i | \(0.780122\pi\) | |||||||
\(828\) | −42940.5 | −1.80228 | ||||||||
\(829\) | −11277.0 | −0.472455 | −0.236228 | − | 0.971698i | \(-0.575911\pi\) | ||||
−0.236228 | + | 0.971698i | \(0.575911\pi\) | |||||||
\(830\) | 189.505 | 0.00792507 | ||||||||
\(831\) | 20496.4 | 0.855611 | ||||||||
\(832\) | −22261.3 | −0.927612 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 927.413 | 0.0385056 | ||||||||
\(835\) | 318.320 | 0.0131927 | ||||||||
\(836\) | 33110.6 | 1.36980 | ||||||||
\(837\) | 68577.0 | 2.83198 | ||||||||
\(838\) | 2661.56 | 0.109716 | ||||||||
\(839\) | 18965.7 | 0.780417 | 0.390208 | − | 0.920727i | \(-0.372403\pi\) | ||||
0.390208 | + | 0.920727i | \(0.372403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 4157.72 | 0.170172 | ||||||||
\(843\) | −23688.5 | −0.967825 | ||||||||
\(844\) | 38747.3 | 1.58026 | ||||||||
\(845\) | −183.925 | −0.00748781 | ||||||||
\(846\) | 8657.72 | 0.351842 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19678.9 | 0.796908 | ||||||||
\(849\) | 35762.5 | 1.44566 | ||||||||
\(850\) | 2861.41 | 0.115465 | ||||||||
\(851\) | 7210.54 | 0.290451 | ||||||||
\(852\) | 27356.3 | 1.10002 | ||||||||
\(853\) | −8067.23 | −0.323818 | −0.161909 | − | 0.986806i | \(-0.551765\pi\) | ||||
−0.161909 | + | 0.986806i | \(0.551765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2484.77 | −0.0993886 | ||||||||
\(856\) | 1186.41 | 0.0473724 | ||||||||
\(857\) | −15281.7 | −0.609118 | −0.304559 | − | 0.952493i | \(-0.598509\pi\) | ||||
−0.304559 | + | 0.952493i | \(0.598509\pi\) | |||||||
\(858\) | −12447.1 | −0.495266 | ||||||||
\(859\) | 36789.1 | 1.46127 | 0.730634 | − | 0.682770i | \(-0.239225\pi\) | ||||
0.730634 | + | 0.682770i | \(0.239225\pi\) | |||||||
\(860\) | 415.641 | 0.0164805 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6895.33 | 0.272455 | ||||||||
\(863\) | 40907.8 | 1.61358 | 0.806788 | − | 0.590840i | \(-0.201204\pi\) | ||||
0.806788 | + | 0.590840i | \(0.201204\pi\) | |||||||
\(864\) | 22443.2 | 0.883719 | ||||||||
\(865\) | −2147.71 | −0.0844213 | ||||||||
\(866\) | −6250.12 | −0.245251 | ||||||||
\(867\) | −16984.7 | −0.665319 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23076.2 | 0.900812 | ||||||||
\(870\) | −72.9268 | −0.00284190 | ||||||||
\(871\) | 42029.4 | 1.63503 | ||||||||
\(872\) | −6806.38 | −0.264327 | ||||||||
\(873\) | 47057.5 | 1.82435 | ||||||||
\(874\) | 2517.76 | 0.0974424 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −42045.4 | −1.62167 | ||||||||
\(877\) | 2391.60 | 0.0920852 | 0.0460426 | − | 0.998939i | \(-0.485339\pi\) | ||||
0.0460426 | + | 0.998939i | \(0.485339\pi\) | |||||||
\(878\) | 1564.59 | 0.0601392 | ||||||||
\(879\) | 35896.8 | 1.37744 | ||||||||
\(880\) | 2570.79 | 0.0984786 | ||||||||
\(881\) | −5487.72 | −0.209859 | −0.104930 | − | 0.994480i | \(-0.533462\pi\) | ||||
−0.104930 | + | 0.994480i | \(0.533462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 170.008 | 0.00647931 | 0.00323966 | − | 0.999995i | \(-0.498969\pi\) | ||||
0.00323966 | + | 0.999995i | \(0.498969\pi\) | |||||||
\(884\) | 21606.6 | 0.822067 | ||||||||
\(885\) | −602.705 | −0.0228923 | ||||||||
\(886\) | 3310.66 | 0.125535 | ||||||||
\(887\) | −25867.3 | −0.979188 | −0.489594 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489594 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(888\) | −4654.17 | −0.175883 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 304.243 | 0.0114587 | ||||||||
\(891\) | −72324.4 | −2.71937 | ||||||||
\(892\) | 17355.2 | 0.651451 | ||||||||
\(893\) | 23162.1 | 0.867961 | ||||||||
\(894\) | −6250.40 | −0.233831 | ||||||||
\(895\) | 369.327 | 0.0137936 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43186.0 | 1.60751 | ||||||||
\(898\) | 2664.86 | 0.0990285 | ||||||||
\(899\) | 6846.77 | 0.254007 | ||||||||
\(900\) | 56976.0 | 2.11022 | ||||||||
\(901\) | −18215.4 | −0.673520 | ||||||||
\(902\) | 5822.03 | 0.214914 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1211.39 | 0.0445687 | ||||||||
\(905\) | −990.093 | −0.0363666 | ||||||||
\(906\) | −465.468 | −0.0170686 | ||||||||
\(907\) | 11411.5 | 0.417765 | 0.208882 | − | 0.977941i | \(-0.433017\pi\) | ||||
0.208882 | + | 0.977941i | \(0.433017\pi\) | |||||||
\(908\) | 35588.7 | 1.30072 | ||||||||
\(909\) | 80277.3 | 2.92919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38718.5 | −1.40813 | −0.704063 | − | 0.710138i | \(-0.748633\pi\) | ||||
−0.704063 | + | 0.710138i | \(0.748633\pi\) | |||||||
\(912\) | 35852.1 | 1.30174 | ||||||||
\(913\) | 45500.1 | 1.64933 | ||||||||
\(914\) | 2889.21 | 0.104559 | ||||||||
\(915\) | −4405.96 | −0.159187 | ||||||||
\(916\) | 26139.5 | 0.942875 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6672.10 | −0.239882 | ||||||||
\(919\) | −48465.3 | −1.73963 | −0.869817 | − | 0.493374i | \(-0.835763\pi\) | ||||
−0.869817 | + | 0.493374i | \(0.835763\pi\) | |||||||
\(920\) | 404.310 | 0.0144888 | ||||||||
\(921\) | 3726.72 | 0.133333 | ||||||||
\(922\) | 6113.34 | 0.218364 | ||||||||
\(923\) | −18817.0 | −0.671040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9567.37 | −0.340079 | ||||||||
\(926\) | −7849.85 | −0.278577 | ||||||||
\(927\) | 37081.6 | 1.31383 | ||||||||
\(928\) | 2240.74 | 0.0792630 | ||||||||
\(929\) | −10560.1 | −0.372946 | −0.186473 | − | 0.982460i | \(-0.559706\pi\) | ||||
−0.186473 | + | 0.982460i | \(0.559706\pi\) | |||||||
\(930\) | −593.714 | −0.0209340 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 31277.3 | 1.09927 | ||||||||
\(933\) | 44722.4 | 1.56929 | ||||||||
\(934\) | −5153.79 | −0.180554 | ||||||||
\(935\) | −2379.59 | −0.0832309 | ||||||||
\(936\) | −19064.9 | −0.665765 | ||||||||
\(937\) | 23025.0 | 0.802769 | 0.401384 | − | 0.915910i | \(-0.368529\pi\) | ||||
0.401384 | + | 0.915910i | \(0.368529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 78971.7 | 2.74456 | ||||||||
\(940\) | 1839.56 | 0.0638296 | ||||||||
\(941\) | −40778.1 | −1.41268 | −0.706338 | − | 0.707874i | \(-0.749654\pi\) | ||||
−0.706338 | + | 0.707874i | \(0.749654\pi\) | |||||||
\(942\) | 2883.43 | 0.0997317 | ||||||||
\(943\) | −20199.8 | −0.697558 | ||||||||
\(944\) | 5947.74 | 0.205066 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2187.18 | −0.0751707 | ||||||||
\(947\) | 36129.8 | 1.23977 | 0.619884 | − | 0.784693i | \(-0.287179\pi\) | ||||
0.619884 | + | 0.784693i | \(0.287179\pi\) | |||||||
\(948\) | 25559.3 | 0.875662 | ||||||||
\(949\) | 28920.9 | 0.989265 | ||||||||
\(950\) | −3340.72 | −0.114092 | ||||||||
\(951\) | −16387.8 | −0.558790 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20831.4 | 0.708075 | 0.354037 | − | 0.935231i | \(-0.384809\pi\) | ||||
0.354037 | + | 0.935231i | \(0.384809\pi\) | |||||||
\(954\) | 7949.21 | 0.269775 | ||||||||
\(955\) | −2976.86 | −0.100868 | ||||||||
\(956\) | 10960.1 | 0.370789 | ||||||||
\(957\) | −17509.7 | −0.591441 | ||||||||
\(958\) | −5363.02 | −0.180868 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2715.52 | 0.0912948 | ||||||||
\(961\) | 25950.1 | 0.871071 | ||||||||
\(962\) | 1583.33 | 0.0530652 | ||||||||
\(963\) | −10572.6 | −0.353788 | ||||||||
\(964\) | −15977.4 | −0.533813 | ||||||||
\(965\) | 1927.98 | 0.0643149 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49242.5 | 1.63757 | 0.818785 | − | 0.574100i | \(-0.194648\pi\) | ||||
0.818785 | + | 0.574100i | \(0.194648\pi\) | |||||||
\(968\) | −19252.5 | −0.639256 | ||||||||
\(969\) | −33185.7 | −1.10018 | ||||||||
\(970\) | −219.136 | −0.00725363 | ||||||||
\(971\) | 2352.05 | 0.0777351 | 0.0388675 | − | 0.999244i | \(-0.487625\pi\) | ||||
0.0388675 | + | 0.999244i | \(0.487625\pi\) | |||||||
\(972\) | −18712.5 | −0.617493 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4077.82 | 0.134150 | ||||||||
\(975\) | −57301.8 | −1.88218 | ||||||||
\(976\) | 43479.7 | 1.42598 | ||||||||
\(977\) | 18768.3 | 0.614588 | 0.307294 | − | 0.951615i | \(-0.400577\pi\) | ||||
0.307294 | + | 0.951615i | \(0.400577\pi\) | |||||||
\(978\) | 2059.38 | 0.0673329 | ||||||||
\(979\) | 73048.7 | 2.38473 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 60654.5 | 1.97406 | ||||||||
\(982\) | −2820.59 | −0.0916584 | ||||||||
\(983\) | 49014.5 | 1.59036 | 0.795179 | − | 0.606375i | \(-0.207377\pi\) | ||||
0.795179 | + | 0.606375i | \(0.207377\pi\) | |||||||
\(984\) | 13038.4 | 0.422406 | ||||||||
\(985\) | −1761.81 | −0.0569908 | ||||||||
\(986\) | −666.146 | −0.0215156 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25225.8 | −0.812288 | ||||||||
\(989\) | 7588.55 | 0.243986 | ||||||||
\(990\) | 1038.46 | 0.0333377 | ||||||||
\(991\) | −48860.6 | −1.56620 | −0.783102 | − | 0.621893i | \(-0.786364\pi\) | ||||
−0.783102 | + | 0.621893i | \(0.786364\pi\) | |||||||
\(992\) | 18242.4 | 0.583868 | ||||||||
\(993\) | 7411.44 | 0.236853 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −425.888 | −0.0135694 | ||||||||
\(996\) | 50396.2 | 1.60328 | ||||||||
\(997\) | −2934.57 | −0.0932184 | −0.0466092 | − | 0.998913i | \(-0.514842\pi\) | ||||
−0.0466092 | + | 0.998913i | \(0.514842\pi\) | |||||||
\(998\) | −6608.29 | −0.209601 | ||||||||
\(999\) | 22308.7 | 0.706524 |
(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 | 1421.4.a.c.1.2 | 2 | ||
7.6 | odd | 2 | 29.4.a.a.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 261.4.a.b.1.1 | 2 | |||
28.27 | even | 2 | 464.4.a.f.1.2 | 2 | |||
35.34 | odd | 2 | 725.4.a.b.1.1 | 2 | |||
56.13 | odd | 2 | 1856.4.a.n.1.2 | 2 | |||
56.27 | even | 2 | 1856.4.a.h.1.1 | 2 | |||
203.202 | odd | 2 | 841.4.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.a.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
261.4.a.b.1.1 | 2 | 21.20 | even | 2 | |||
464.4.a.f.1.2 | 2 | 28.27 | even | 2 | |||
725.4.a.b.1.1 | 2 | 35.34 | odd | 2 | |||
841.4.a.a.1.1 | 2 | 203.202 | odd | 2 | |||
1421.4.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1856.4.a.h.1.1 | 2 | 56.27 | even | 2 | |||
1856.4.a.n.1.2 | 2 | 56.13 | odd | 2 |