Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,5,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.c (of order \(2\), degree \(1\), 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: | \(31.0109889252\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.15 | ||
Root | \(1.95664 + 3.48878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.5.c.c.151.16 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.99969 | − | 0.0498899i | 0.999922 | − | 0.0124725i | ||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | 15.9950 | − | 0.399088i | 0.999689 | − | 0.0249430i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.259236 | − | 20.7830i | −0.00720099 | − | 0.577305i | ||||
\(7\) | − | 35.2842i | − | 0.720086i | −0.932936 | − | 0.360043i | \(-0.882762\pi\) | ||
0.932936 | − | 0.360043i | \(-0.117238\pi\) | |||||||
\(8\) | 63.9552 | − | 2.39422i | 0.999300 | − | 0.0374097i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.95158i | 0.0326577i | 0.999867 | + | 0.0163289i | \(0.00519787\pi\) | ||||
−0.999867 | + | 0.0163289i | \(0.994802\pi\) | |||||||
\(12\) | −2.07372 | − | 83.1126i | −0.0144009 | − | 0.577171i | ||||
\(13\) | 41.0572 | 0.242942 | 0.121471 | − | 0.992595i | \(-0.461239\pi\) | ||||
0.121471 | + | 0.992595i | \(0.461239\pi\) | |||||||
\(14\) | −1.76033 | − | 141.126i | −0.00898126 | − | 0.720030i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 255.681 | − | 12.7668i | 0.998756 | − | 0.0498705i | ||||
\(17\) | 186.761 | 0.646233 | 0.323116 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323116 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(18\) | −107.992 | + | 1.34703i | −0.333307 | + | 0.00415749i | ||||
\(19\) | − | 580.932i | − | 1.60923i | −0.593798 | − | 0.804614i | \(-0.702372\pi\) | ||
0.593798 | − | 0.804614i | \(-0.297628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −183.342 | −0.415742 | ||||||||
\(22\) | 0.197144 | + | 15.8051i | 0.000407323 | + | 0.0326552i | ||||
\(23\) | − | 472.336i | − | 0.892885i | −0.894812 | − | 0.446443i | \(-0.852691\pi\) | ||
0.894812 | − | 0.446443i | \(-0.147309\pi\) | |||||||
\(24\) | −12.4407 | − | 332.321i | −0.0215985 | − | 0.576946i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 164.216 | − | 2.04834i | 0.242923 | − | 0.00303009i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | −14.0815 | − | 564.372i | −0.0179611 | − | 0.719862i | ||||
\(29\) | −979.409 | −1.16458 | −0.582288 | − | 0.812982i | \(-0.697843\pi\) | ||||
−0.582288 | + | 0.812982i | \(0.697843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33.2865i | 0.0346373i | 0.999850 | + | 0.0173187i | \(0.00551298\pi\) | ||||
−0.999850 | + | 0.0173187i | \(0.994487\pi\) | |||||||
\(32\) | 1022.01 | − | 63.8193i | 0.998056 | − | 0.0623236i | ||||
\(33\) | 20.5330 | 0.0188549 | ||||||||
\(34\) | 746.987 | − | 9.31750i | 0.646183 | − | 0.00806012i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −431.866 | + | 10.7754i | −0.333230 | + | 0.00831434i | ||||
\(37\) | −623.253 | −0.455262 | −0.227631 | − | 0.973748i | \(-0.573098\pi\) | ||||
−0.227631 | + | 0.973748i | \(0.573098\pi\) | |||||||
\(38\) | −28.9826 | − | 2323.55i | −0.0200711 | − | 1.60910i | ||||
\(39\) | − | 213.340i | − | 0.140263i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 154.478 | 0.0918966 | 0.0459483 | − | 0.998944i | \(-0.485369\pi\) | ||||
0.0459483 | + | 0.998944i | \(0.485369\pi\) | |||||||
\(42\) | −733.312 | + | 9.14693i | −0.415710 | + | 0.00518533i | ||||
\(43\) | − | 2675.32i | − | 1.44690i | −0.690377 | − | 0.723450i | \(-0.742555\pi\) | ||
0.690377 | − | 0.723450i | \(-0.257445\pi\) | |||||||
\(44\) | 1.57703 | + | 63.2057i | 0.000814582 | + | 0.0326476i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23.5648 | − | 1889.20i | −0.0111365 | − | 0.892816i | ||||
\(47\) | 2925.06i | 1.32416i | 0.749434 | + | 0.662079i | \(0.230326\pi\) | ||||
−0.749434 | + | 0.662079i | \(0.769674\pi\) | |||||||
\(48\) | −66.3385 | − | 1328.56i | −0.0287927 | − | 0.576632i | ||||
\(49\) | 1156.02 | 0.481476 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 970.440i | − | 0.373103i | ||||||
\(52\) | 656.711 | − | 16.3855i | 0.242867 | − | 0.00605971i | ||||
\(53\) | 3782.10 | 1.34642 | 0.673212 | − | 0.739450i | \(-0.264914\pi\) | ||||
0.673212 | + | 0.739450i | \(0.264914\pi\) | |||||||
\(54\) | 6.99936 | + | 561.141i | 0.00240033 | + | 0.192435i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −84.4782 | − | 2256.61i | −0.0269382 | − | 0.719582i | ||||
\(57\) | −3018.61 | −0.929089 | ||||||||
\(58\) | −3917.33 | + | 48.8626i | −1.16449 | + | 0.0145252i | ||||
\(59\) | − | 3487.58i | − | 1.00189i | −0.865479 | − | 0.500945i | \(-0.832986\pi\) | ||
0.865479 | − | 0.500945i | \(-0.167014\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −488.539 | −0.131292 | −0.0656462 | − | 0.997843i | \(-0.520911\pi\) | ||||
−0.0656462 | + | 0.997843i | \(0.520911\pi\) | |||||||
\(62\) | 1.66066 | + | 133.135i | 0.000432013 | + | 0.0346346i | ||||
\(63\) | 952.674i | 0.240029i | ||||||||
\(64\) | 4084.54 | − | 306.245i | 0.997201 | − | 0.0747670i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 82.1257 | − | 1.02439i | 0.0188535 | − | 0.000235168i | ||||
\(67\) | 7491.56i | 1.66887i | 0.551107 | + | 0.834435i | \(0.314206\pi\) | ||||
−0.551107 | + | 0.834435i | \(0.685794\pi\) | |||||||
\(68\) | 2987.25 | − | 74.5342i | 0.646032 | − | 0.0161190i | ||||
\(69\) | −2454.33 | −0.515507 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4620.06i | − | 0.916496i | −0.888824 | − | 0.458248i | \(-0.848477\pi\) | ||
0.888824 | − | 0.458248i | \(-0.151523\pi\) | |||||||
\(72\) | −1726.79 | + | 64.6439i | −0.333100 | + | 0.0124699i | ||||
\(73\) | −6959.14 | −1.30590 | −0.652950 | − | 0.757401i | \(-0.726469\pi\) | ||||
−0.652950 | + | 0.757401i | \(0.726469\pi\) | |||||||
\(74\) | −2492.82 | + | 31.0940i | −0.455226 | + | 0.00567824i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −231.843 | − | 9292.01i | −0.0401390 | − | 1.60873i | ||||
\(77\) | 139.429 | 0.0235164 | ||||||||
\(78\) | −10.6435 | − | 853.292i | −0.00174942 | − | 0.140252i | ||||
\(79\) | − | 6756.51i | − | 1.08260i | −0.840829 | − | 0.541300i | \(-0.817932\pi\) | ||
0.840829 | − | 0.541300i | \(-0.182068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 617.865 | − | 7.70690i | 0.0918895 | − | 0.00114618i | ||||
\(83\) | 4862.15i | 0.705785i | 0.935664 | + | 0.352893i | \(0.114802\pi\) | ||||
−0.935664 | + | 0.352893i | \(0.885198\pi\) | |||||||
\(84\) | −2932.56 | + | 73.1697i | −0.415613 | + | 0.0103699i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −133.471 | − | 10700.4i | −0.0180464 | − | 1.44679i | ||||
\(87\) | 5089.16i | 0.672369i | ||||||||
\(88\) | 9.46096 | + | 252.724i | 0.00122171 | + | 0.0326349i | ||||
\(89\) | 513.707 | 0.0648538 | 0.0324269 | − | 0.999474i | \(-0.489676\pi\) | ||||
0.0324269 | + | 0.999474i | \(0.489676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1448.67i | − | 0.174939i | ||||||
\(92\) | −188.504 | − | 7555.03i | −0.0222712 | − | 0.892607i | ||||
\(93\) | 172.962 | 0.0199979 | ||||||||
\(94\) | 145.931 | + | 11699.3i | 0.0165155 | + | 1.32405i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −331.615 | − | 5310.52i | −0.0359825 | − | 0.576228i | ||||
\(97\) | 12119.3 | 1.28805 | 0.644026 | − | 0.765004i | \(-0.277263\pi\) | ||||
0.644026 | + | 0.765004i | \(0.277263\pi\) | |||||||
\(98\) | 4623.73 | − | 57.6739i | 0.481438 | − | 0.00600519i | ||||
\(99\) | − | 106.693i | − | 0.0108859i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7191.20 | −0.704951 | −0.352475 | − | 0.935821i | \(-0.614660\pi\) | ||||
−0.352475 | + | 0.935821i | \(0.614660\pi\) | |||||||
\(102\) | −48.4152 | − | 3881.46i | −0.00465351 | − | 0.373074i | ||||
\(103\) | 10189.6i | 0.960470i | 0.877140 | + | 0.480235i | \(0.159449\pi\) | ||||
−0.877140 | + | 0.480235i | \(0.840551\pi\) | |||||||
\(104\) | 2625.82 | − | 98.3000i | 0.242772 | − | 0.00908839i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15127.2 | − | 188.689i | 1.34632 | − | 0.0167932i | ||||
\(107\) | 21648.8i | 1.89089i | 0.325777 | + | 0.945446i | \(0.394374\pi\) | ||||
−0.325777 | + | 0.945446i | \(0.605626\pi\) | |||||||
\(108\) | 55.9905 | + | 2244.04i | 0.00480028 | + | 0.192390i | ||||
\(109\) | 10655.6 | 0.896859 | 0.448430 | − | 0.893818i | \(-0.351983\pi\) | ||||
0.448430 | + | 0.893818i | \(0.351983\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3238.52i | 0.262845i | ||||||||
\(112\) | −450.468 | − | 9021.52i | −0.0359111 | − | 0.719190i | ||||
\(113\) | 9876.07 | 0.773441 | 0.386721 | − | 0.922197i | \(-0.373608\pi\) | ||||
0.386721 | + | 0.922197i | \(0.373608\pi\) | |||||||
\(114\) | −12073.5 | + | 150.598i | −0.929017 | + | 0.0115880i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15665.7 | + | 390.871i | −1.16421 | + | 0.0290480i | ||||
\(117\) | −1108.55 | −0.0809807 | ||||||||
\(118\) | −173.995 | − | 13949.2i | −0.0124961 | − | 1.00181i | ||||
\(119\) | − | 6589.73i | − | 0.465343i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14625.4 | 0.998933 | ||||||||
\(122\) | −1954.00 | + | 24.3732i | −0.131282 | + | 0.00163754i | ||||
\(123\) | − | 802.692i | − | 0.0530565i | ||||||
\(124\) | 13.2842 | + | 532.418i | 0.000863959 | + | 0.0346265i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 47.5288 | + | 3810.40i | 0.00299375 | + | 0.240010i | ||||
\(127\) | 19972.7i | 1.23831i | 0.785269 | + | 0.619155i | \(0.212525\pi\) | ||||
−0.785269 | + | 0.619155i | \(0.787475\pi\) | |||||||
\(128\) | 16321.6 | − | 1428.66i | 0.996191 | − | 0.0871987i | ||||
\(129\) | −13901.4 | −0.835368 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 30733.6i | 1.79090i | 0.445164 | + | 0.895449i | \(0.353145\pi\) | ||||
−0.445164 | + | 0.895449i | \(0.646855\pi\) | |||||||
\(132\) | 328.426 | − | 8.19449i | 0.0188491 | − | 0.000470299i | ||||
\(133\) | −20497.7 | −1.15878 | ||||||||
\(134\) | 373.753 | + | 29963.9i | 0.0208149 | + | 1.66874i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11944.4 | − | 447.147i | 0.645780 | − | 0.0241754i | ||||
\(137\) | −7177.05 | −0.382388 | −0.191194 | − | 0.981552i | \(-0.561236\pi\) | ||||
−0.191194 | + | 0.981552i | \(0.561236\pi\) | |||||||
\(138\) | −9816.56 | + | 122.446i | −0.515467 | + | 0.00642965i | ||||
\(139\) | − | 4628.80i | − | 0.239574i | −0.992800 | − | 0.119787i | \(-0.961779\pi\) | ||
0.992800 | − | 0.119787i | \(-0.0382211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15199.1 | 0.764503 | ||||||||
\(142\) | −230.494 | − | 18478.8i | −0.0114310 | − | 0.916425i | ||||
\(143\) | 162.241i | 0.00793394i | ||||||||
\(144\) | −6903.40 | + | 344.705i | −0.332919 | + | 0.0166235i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −27834.4 | + | 347.191i | −1.30580 | + | 0.0162878i | ||||
\(147\) | − | 6006.87i | − | 0.277980i | ||||||
\(148\) | −9968.95 | + | 248.733i | −0.455120 | + | 0.0113556i | ||||
\(149\) | 35128.8 | 1.58231 | 0.791154 | − | 0.611617i | \(-0.209481\pi\) | ||||
0.791154 | + | 0.611617i | \(0.209481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41309.8i | 1.81176i | 0.423539 | + | 0.905878i | \(0.360788\pi\) | ||||
−0.423539 | + | 0.905878i | \(0.639212\pi\) | |||||||
\(152\) | −1390.88 | − | 37153.6i | −0.0602007 | − | 1.60810i | ||||
\(153\) | −5042.55 | −0.215411 | ||||||||
\(154\) | 557.671 | − | 6.95608i | 0.0235146 | − | 0.000293307i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −85.1413 | − | 3412.37i | −0.00349857 | − | 0.140219i | ||||
\(157\) | 3581.96 | 0.145319 | 0.0726594 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726594 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(158\) | −337.082 | − | 27023.9i | −0.0135027 | − | 1.08252i | ||||
\(159\) | − | 19652.4i | − | 0.777358i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16666.0 | −0.642954 | ||||||||
\(162\) | 2915.77 | − | 36.3697i | 0.111102 | − | 0.00138583i | ||||
\(163\) | 14969.6i | 0.563422i | 0.959499 | + | 0.281711i | \(0.0909020\pi\) | ||||
−0.959499 | + | 0.281711i | \(0.909098\pi\) | |||||||
\(164\) | 2470.88 | − | 61.6504i | 0.0918680 | − | 0.00229218i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 242.572 | + | 19447.1i | 0.00880289 | + | 0.705730i | ||||
\(167\) | − | 12510.0i | − | 0.448564i | −0.974524 | − | 0.224282i | \(-0.927996\pi\) | ||
0.974524 | − | 0.224282i | \(-0.0720037\pi\) | |||||||
\(168\) | −11725.7 | + | 438.961i | −0.415451 | + | 0.0155528i | ||||
\(169\) | −26875.3 | −0.940979 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15685.2i | 0.536410i | ||||||||
\(172\) | −1067.69 | − | 42791.8i | −0.0360901 | − | 1.44645i | ||||
\(173\) | 51365.9 | 1.71626 | 0.858129 | − | 0.513434i | \(-0.171627\pi\) | ||||
0.858129 | + | 0.513434i | \(0.171627\pi\) | |||||||
\(174\) | 253.898 | + | 20355.0i | 0.00838610 | + | 0.672316i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 50.4493 | + | 1010.35i | 0.00162866 | + | 0.0326171i | ||||
\(177\) | −18122.0 | −0.578442 | ||||||||
\(178\) | 2054.67 | − | 25.6288i | 0.0648487 | − | 0.000808887i | ||||
\(179\) | − | 29989.3i | − | 0.935967i | −0.883737 | − | 0.467984i | \(-0.844981\pi\) | ||
0.883737 | − | 0.467984i | \(-0.155019\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −47416.2 | −1.44734 | −0.723668 | − | 0.690149i | \(-0.757545\pi\) | ||||
−0.723668 | + | 0.690149i | \(0.757545\pi\) | |||||||
\(182\) | −72.2741 | − | 5794.24i | −0.00218193 | − | 0.174926i | ||||
\(183\) | 2538.52i | 0.0758017i | ||||||||
\(184\) | −1130.88 | − | 30208.4i | −0.0334025 | − | 0.892260i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 691.792 | − | 8.62903i | 0.0199963 | − | 0.000249423i | ||||
\(187\) | 738.003i | 0.0211045i | ||||||||
\(188\) | 1167.36 | + | 46786.5i | 0.0330285 | + | 1.32375i | ||||
\(189\) | 4950.24 | 0.138581 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 41028.6i | 1.12466i | 0.826914 | + | 0.562329i | \(0.190095\pi\) | ||||
−0.826914 | + | 0.562329i | \(0.809905\pi\) | |||||||
\(192\) | −1591.30 | − | 21223.9i | −0.0431667 | − | 0.575734i | ||||
\(193\) | −44180.6 | −1.18609 | −0.593044 | − | 0.805170i | \(-0.702074\pi\) | ||||
−0.593044 | + | 0.805170i | \(0.702074\pi\) | |||||||
\(194\) | 48473.3 | − | 604.629i | 1.28795 | − | 0.0160652i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18490.6 | − | 461.355i | 0.481326 | − | 0.0120094i | ||||
\(197\) | 8724.29 | 0.224801 | 0.112400 | − | 0.993663i | \(-0.464146\pi\) | ||||
0.112400 | + | 0.993663i | \(0.464146\pi\) | |||||||
\(198\) | −5.32289 | − | 426.738i | −0.000135774 | − | 0.0108851i | ||||
\(199\) | − | 6720.98i | − | 0.169717i | −0.996393 | − | 0.0848587i | \(-0.972956\pi\) | ||
0.996393 | − | 0.0848587i | \(-0.0270439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 38927.3 | 0.963522 | ||||||||
\(202\) | −28762.6 | + | 358.768i | −0.704896 | + | 0.00879248i | ||||
\(203\) | 34557.7i | 0.838596i | ||||||||
\(204\) | −387.291 | − | 15522.2i | −0.00930630 | − | 0.372987i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 508.359 | + | 40755.3i | 0.0119794 | + | 0.960395i | ||||
\(207\) | 12753.1i | 0.297628i | ||||||||
\(208\) | 10497.6 | − | 524.171i | 0.242640 | − | 0.0121156i | ||||
\(209\) | 2295.60 | 0.0525537 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8501.81i | 0.190962i | 0.995431 | + | 0.0954808i | \(0.0304389\pi\) | ||||
−0.995431 | + | 0.0954808i | \(0.969561\pi\) | |||||||
\(212\) | 60494.8 | − | 1509.39i | 1.34600 | − | 0.0335839i | ||||
\(213\) | −24006.5 | −0.529139 | ||||||||
\(214\) | 1080.06 | + | 86588.6i | 0.0235841 | + | 1.89075i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 335.900 | + | 8972.67i | 0.00719949 | + | 0.192315i | ||||
\(217\) | 1174.49 | 0.0249419 | ||||||||
\(218\) | 42619.0 | − | 531.606i | 0.896790 | − | 0.0111861i | ||||
\(219\) | 36160.7i | 0.753961i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7667.90 | 0.156997 | ||||||||
\(222\) | 161.569 | + | 12953.1i | 0.00327833 | + | 0.262825i | ||||
\(223\) | 28886.8i | 0.580883i | 0.956893 | + | 0.290442i | \(0.0938022\pi\) | ||||
−0.956893 | + | 0.290442i | \(0.906198\pi\) | |||||||
\(224\) | −2251.82 | − | 36060.8i | −0.0448784 | − | 0.718687i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 39501.2 | − | 492.716i | 0.773381 | − | 0.00964672i | ||||
\(227\) | 17662.3i | 0.342764i | 0.985205 | + | 0.171382i | \(0.0548233\pi\) | ||||
−0.985205 | + | 0.171382i | \(0.945177\pi\) | |||||||
\(228\) | −48282.7 | + | 1204.69i | −0.928800 | + | 0.0231743i | ||||
\(229\) | −99665.8 | −1.90053 | −0.950266 | − | 0.311439i | \(-0.899189\pi\) | ||||
−0.950266 | + | 0.311439i | \(0.899189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 724.492i | − | 0.0135772i | ||||||
\(232\) | −62638.3 | + | 2344.92i | −1.16376 | + | 0.0435664i | ||||
\(233\) | 72559.0 | 1.33653 | 0.668266 | − | 0.743922i | \(-0.267037\pi\) | ||||
0.668266 | + | 0.743922i | \(0.267037\pi\) | |||||||
\(234\) | −4433.84 | + | 55.3052i | −0.0809744 | + | 0.00101003i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1391.85 | − | 55783.9i | −0.0249902 | − | 1.00158i | ||||
\(237\) | −35107.9 | −0.625040 | ||||||||
\(238\) | −328.761 | − | 26356.9i | −0.00580399 | − | 0.465307i | ||||
\(239\) | 70208.6i | 1.22912i | 0.788870 | + | 0.614560i | \(0.210666\pi\) | ||||
−0.788870 | + | 0.614560i | \(0.789334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −51440.5 | −0.885668 | −0.442834 | − | 0.896604i | \(-0.646027\pi\) | ||||
−0.442834 | + | 0.896604i | \(0.646027\pi\) | |||||||
\(242\) | 58497.0 | − | 729.659i | 0.998856 | − | 0.0124592i | ||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | −7814.19 | + | 194.970i | −0.131252 | + | 0.00327483i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −40.0462 | − | 3210.52i | −0.000661746 | − | 0.0530524i | ||||
\(247\) | − | 23851.4i | − | 0.390950i | ||||||
\(248\) | 79.6951 | + | 2128.84i | 0.00129577 | + | 0.0346131i | ||||
\(249\) | 25264.5 | 0.407485 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 72429.1i | − | 1.14965i | −0.818276 | − | 0.574825i | \(-0.805070\pi\) | ||
0.818276 | − | 0.574825i | \(-0.194930\pi\) | |||||||
\(252\) | 380.201 | + | 15238.0i | 0.00598704 | + | 0.239954i | ||||
\(253\) | 1866.48 | 0.0291596 | ||||||||
\(254\) | 996.436 | + | 79884.6i | 0.0154448 | + | 1.23821i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65210.0 | − | 6528.49i | 0.995026 | − | 0.0996169i | ||||
\(257\) | 77711.9 | 1.17658 | 0.588290 | − | 0.808650i | \(-0.299801\pi\) | ||||
0.588290 | + | 0.808650i | \(0.299801\pi\) | |||||||
\(258\) | −55601.1 | + | 693.538i | −0.835303 | + | 0.0104191i | ||||
\(259\) | 21991.0i | 0.327828i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26444.0 | 0.388192 | ||||||||
\(262\) | 1533.30 | + | 122925.i | 0.0223369 | + | 1.79076i | ||||
\(263\) | 2716.70i | 0.0392763i | 0.999807 | + | 0.0196382i | \(0.00625142\pi\) | ||||
−0.999807 | + | 0.0196382i | \(0.993749\pi\) | |||||||
\(264\) | 1313.19 | − | 49.1606i | 0.0188417 | − | 0.000705357i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −81984.5 | + | 1022.63i | −1.15869 | + | 0.0144529i | ||||
\(267\) | − | 2669.30i | − | 0.0374434i | ||||||
\(268\) | 2989.79 | + | 119828.i | 0.0416266 | + | 1.66835i | ||||
\(269\) | 66666.6 | 0.921306 | 0.460653 | − | 0.887580i | \(-0.347615\pi\) | ||||
0.460653 | + | 0.887580i | \(0.347615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 63959.9i | − | 0.870902i | −0.900212 | − | 0.435451i | \(-0.856589\pi\) | ||
0.900212 | − | 0.435451i | \(-0.143411\pi\) | |||||||
\(272\) | 47751.4 | − | 2384.35i | 0.645429 | − | 0.0322280i | ||||
\(273\) | −7527.53 | −0.101001 | ||||||||
\(274\) | −28706.0 | + | 358.062i | −0.382359 | + | 0.00476933i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −39257.1 | + | 979.494i | −0.515347 | + | 0.0128583i | ||||
\(277\) | −36446.7 | −0.475005 | −0.237502 | − | 0.971387i | \(-0.576329\pi\) | ||||
−0.237502 | + | 0.971387i | \(0.576329\pi\) | |||||||
\(278\) | −230.930 | − | 18513.8i | −0.00298808 | − | 0.239555i | ||||
\(279\) | − | 898.734i | − | 0.0115458i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 83688.9 | 1.05988 | 0.529938 | − | 0.848036i | \(-0.322215\pi\) | ||||
0.529938 | + | 0.848036i | \(0.322215\pi\) | |||||||
\(282\) | 60791.6 | − | 758.281i | 0.764443 | − | 0.00953524i | ||||
\(283\) | − | 99210.9i | − | 1.23876i | −0.785092 | − | 0.619379i | \(-0.787384\pi\) | ||
0.785092 | − | 0.619379i | \(-0.212616\pi\) | |||||||
\(284\) | −1843.81 | − | 73897.9i | −0.0228602 | − | 0.916211i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.09419 | + | 648.914i | 9.89558e−5 | + | 0.00793332i | ||||
\(287\) | − | 5450.65i | − | 0.0661735i | ||||||
\(288\) | −27594.3 | + | 1723.12i | −0.332685 | + | 0.0207745i | ||||
\(289\) | −48641.2 | −0.582383 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 62973.6i | − | 0.743657i | ||||||
\(292\) | −111312. | + | 2777.31i | −1.30549 | + | 0.0325731i | ||||
\(293\) | 5554.90 | 0.0647054 | 0.0323527 | − | 0.999477i | \(-0.489700\pi\) | ||||
0.0323527 | + | 0.999477i | \(0.489700\pi\) | |||||||
\(294\) | −299.682 | − | 24025.6i | −0.00346710 | − | 0.277958i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39860.3 | + | 1492.20i | −0.454943 | + | 0.0170312i | ||||
\(297\) | −554.392 | −0.00628498 | ||||||||
\(298\) | 140504. | − | 1752.57i | 1.58219 | − | 0.0197353i | ||||
\(299\) | − | 19392.8i | − | 0.216919i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −94396.6 | −1.04189 | ||||||||
\(302\) | 2060.94 | + | 165226.i | 0.0225971 | + | 1.81161i | ||||
\(303\) | 37366.6i | 0.407004i | ||||||||
\(304\) | −7416.67 | − | 148533.i | −0.0802531 | − | 1.60723i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20168.6 | + | 251.573i | −0.215394 | + | 0.00268671i | ||||
\(307\) | − | 25814.0i | − | 0.273891i | −0.990579 | − | 0.136946i | \(-0.956271\pi\) | ||
0.990579 | − | 0.136946i | \(-0.0437286\pi\) | |||||||
\(308\) | 2230.16 | − | 55.6443i | 0.0235091 | − | 0.000586569i | ||||
\(309\) | 52946.8 | 0.554527 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 106750.i | − | 1.10369i | −0.833947 | − | 0.551844i | \(-0.813924\pi\) | ||
0.833947 | − | 0.551844i | \(-0.186076\pi\) | |||||||
\(312\) | −510.782 | − | 13644.2i | −0.00524718 | − | 0.140165i | ||||
\(313\) | −76334.9 | −0.779174 | −0.389587 | − | 0.920990i | \(-0.627382\pi\) | ||||
−0.389587 | + | 0.920990i | \(0.627382\pi\) | |||||||
\(314\) | 14326.7 | − | 178.704i | 0.145307 | − | 0.00181248i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2696.44 | − | 108071.i | −0.0270033 | − | 1.08226i | ||||
\(317\) | −108286. | −1.07759 | −0.538794 | − | 0.842437i | \(-0.681120\pi\) | ||||
−0.538794 | + | 0.842437i | \(0.681120\pi\) | |||||||
\(318\) | −980.456 | − | 78603.4i | −0.00969558 | − | 0.777298i | ||||
\(319\) | − | 3870.22i | − | 0.0380324i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 112491. | 1.09171 | ||||||||
\(322\) | −66658.9 | + | 831.466i | −0.642904 | + | 0.00801923i | ||||
\(323\) | − | 108496.i | − | 1.03994i | ||||||
\(324\) | 11660.4 | − | 290.935i | 0.111077 | − | 0.00277145i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 746.830 | + | 59873.6i | 0.00702727 | + | 0.563378i | ||||
\(327\) | − | 55368.1i | − | 0.517802i | ||||||
\(328\) | 9879.69 | − | 369.855i | 0.0918323 | − | 0.00343782i | ||||
\(329\) | 103209. | 0.953508 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 109078.i | − | 0.995590i | −0.867295 | − | 0.497795i | \(-0.834143\pi\) | ||
0.867295 | − | 0.497795i | \(-0.165857\pi\) | |||||||
\(332\) | 1940.43 | + | 77770.3i | 0.0176044 | + | 0.705565i | ||||
\(333\) | 16827.8 | 0.151754 | ||||||||
\(334\) | −624.123 | − | 50036.1i | −0.00559471 | − | 0.448529i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −46877.2 | + | 2340.70i | −0.415225 | + | 0.0207333i | ||||
\(337\) | 152574. | 1.34345 | 0.671725 | − | 0.740801i | \(-0.265554\pi\) | ||||
0.671725 | + | 0.740801i | \(0.265554\pi\) | |||||||
\(338\) | −107493. | + | 1340.81i | −0.940906 | + | 0.0117363i | ||||
\(339\) | − | 51317.6i | − | 0.446546i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −131.534 | −0.00113118 | ||||||||
\(342\) | 782.531 | + | 62735.7i | 0.00669036 | + | 0.536368i | ||||
\(343\) | − | 125507.i | − | 1.06679i | ||||||
\(344\) | −6405.30 | − | 171101.i | −0.0541281 | − | 1.44589i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 205448. | − | 2562.64i | 1.71612 | − | 0.0214060i | ||||
\(347\) | − | 168701.i | − | 1.40107i | −0.713618 | − | 0.700535i | \(-0.752945\pi\) | ||
0.713618 | − | 0.700535i | \(-0.247055\pi\) | |||||||
\(348\) | 2031.02 | + | 81401.2i | 0.0167709 | + | 0.672159i | ||||
\(349\) | −19680.8 | −0.161582 | −0.0807910 | − | 0.996731i | \(-0.525745\pi\) | ||||
−0.0807910 | + | 0.996731i | \(0.525745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5760.17i | 0.0467542i | ||||||||
\(352\) | 252.187 | + | 4038.56i | 0.00203535 | + | 0.0325942i | ||||
\(353\) | 55058.2 | 0.441848 | 0.220924 | − | 0.975291i | \(-0.429093\pi\) | ||||
0.220924 | + | 0.975291i | \(0.429093\pi\) | |||||||
\(354\) | −72482.4 | + | 904.105i | −0.578397 | + | 0.00721460i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8216.75 | − | 205.014i | 0.0648336 | − | 0.00161765i | ||||
\(357\) | −34241.2 | −0.268666 | ||||||||
\(358\) | −1496.16 | − | 119948.i | −0.0116738 | − | 0.935894i | ||||
\(359\) | 73206.8i | 0.568019i | 0.958822 | + | 0.284009i | \(0.0916647\pi\) | ||||
−0.958822 | + | 0.284009i | \(0.908335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −207161. | −1.58962 | ||||||||
\(362\) | −189650. | + | 2365.59i | −1.44722 | + | 0.0180519i | ||||
\(363\) | − | 75995.7i | − | 0.576735i | ||||||
\(364\) | −578.148 | − | 23171.6i | −0.00436351 | − | 0.174885i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 126.647 | + | 10153.3i | 0.000945435 | + | 0.0757958i | ||||
\(367\) | − | 156333.i | − | 1.16069i | −0.814370 | − | 0.580346i | \(-0.802917\pi\) | ||
0.814370 | − | 0.580346i | \(-0.197083\pi\) | |||||||
\(368\) | −6030.24 | − | 120768.i | −0.0445286 | − | 0.891774i | ||||
\(369\) | −4170.91 | −0.0306322 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 133449.i | − | 0.969542i | ||||||
\(372\) | 2766.52 | − | 69.0269i | 0.0199916 | − | 0.000498807i | ||||
\(373\) | −233763. | −1.68019 | −0.840096 | − | 0.542438i | \(-0.817501\pi\) | ||||
−0.840096 | + | 0.542438i | \(0.817501\pi\) | |||||||
\(374\) | 36.8189 | + | 2951.78i | 0.000263225 | + | 0.0211028i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7003.24 | + | 187073.i | 0.0495363 | + | 1.32323i | ||||
\(377\) | −40211.8 | −0.282925 | ||||||||
\(378\) | 19799.4 | − | 246.967i | 0.138570 | − | 0.00172844i | ||||
\(379\) | 25001.6i | 0.174056i | 0.996206 | + | 0.0870282i | \(0.0277370\pi\) | ||||
−0.996206 | + | 0.0870282i | \(0.972263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 103781. | 0.714938 | ||||||||
\(382\) | 2046.92 | + | 164102.i | 0.0140273 | + | 1.12457i | ||||
\(383\) | − | 165132.i | − | 1.12573i | −0.826549 | − | 0.562864i | \(-0.809699\pi\) | ||
0.826549 | − | 0.562864i | \(-0.190301\pi\) | |||||||
\(384\) | −7423.55 | − | 84809.5i | −0.0503442 | − | 0.575151i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −176709. | + | 2204.17i | −1.18600 | + | 0.0147935i | ||||
\(387\) | 72233.6i | 0.482300i | ||||||||
\(388\) | 193848. | − | 4836.66i | 1.28765 | − | 0.0321279i | ||||
\(389\) | 46311.3 | 0.306047 | 0.153023 | − | 0.988223i | \(-0.451099\pi\) | ||||
0.153023 | + | 0.988223i | \(0.451099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 88214.1i | − | 0.577012i | ||||||
\(392\) | 73933.7 | − | 2767.77i | 0.481138 | − | 0.0180118i | ||||
\(393\) | 159696. | 1.03398 | ||||||||
\(394\) | 34894.4 | − | 435.254i | 0.224783 | − | 0.00280382i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −42.5798 | − | 1706.55i | −0.000271527 | − | 0.0108825i | ||||
\(397\) | 244029. | 1.54832 | 0.774161 | − | 0.632989i | \(-0.218172\pi\) | ||||
0.774161 | + | 0.632989i | \(0.218172\pi\) | |||||||
\(398\) | −335.309 | − | 26881.8i | −0.00211680 | − | 0.169704i | ||||
\(399\) | 106509.i | 0.669024i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 102342. | 0.636451 | 0.318225 | − | 0.948015i | \(-0.396913\pi\) | ||||
0.318225 | + | 0.948015i | \(0.396913\pi\) | |||||||
\(402\) | 155697. | − | 1942.08i | 0.963447 | − | 0.0120175i | ||||
\(403\) | 1366.65i | 0.00841487i | ||||||||
\(404\) | −115023. | + | 2869.92i | −0.704732 | + | 0.0175836i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1724.08 | + | 138220.i | 0.0104594 | + | 0.838531i | ||||
\(407\) | − | 2462.84i | − | 0.0148678i | ||||||
\(408\) | −2323.45 | − | 62064.7i | −0.0139576 | − | 0.372842i | ||||
\(409\) | −110640. | −0.661405 | −0.330702 | − | 0.943735i | \(-0.607286\pi\) | ||||
−0.330702 | + | 0.943735i | \(0.607286\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 37293.0i | 0.220772i | ||||||||
\(412\) | 4066.56 | + | 162983.i | 0.0239570 | + | 0.960171i | ||||
\(413\) | −123057. | −0.721448 | ||||||||
\(414\) | 636.250 | + | 51008.3i | 0.00371216 | + | 0.297605i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 41960.9 | − | 2620.25i | 0.242470 | − | 0.0151410i | ||||
\(417\) | −24052.0 | −0.138318 | ||||||||
\(418\) | 9181.69 | − | 114.527i | 0.0525497 | − | 0.000655475i | ||||
\(419\) | − | 2345.08i | − | 0.0133576i | −0.999978 | − | 0.00667882i | \(-0.997874\pi\) | ||
0.999978 | − | 0.00667882i | \(-0.00212595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −158819. | −0.896062 | −0.448031 | − | 0.894018i | \(-0.647875\pi\) | ||||
−0.448031 | + | 0.894018i | \(0.647875\pi\) | |||||||
\(422\) | 424.154 | + | 34004.6i | 0.00238176 | + | 0.190947i | ||||
\(423\) | − | 78976.7i | − | 0.441386i | ||||||
\(424\) | 241885. | − | 9055.18i | 1.34548 | − | 0.0503693i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −96018.6 | + | 1197.68i | −0.529098 | + | 0.00659968i | ||||
\(427\) | 17237.7i | 0.0945419i | ||||||||
\(428\) | 8639.79 | + | 346274.i | 0.0471646 | + | 1.89030i | ||||
\(429\) | 843.029 | 0.00458066 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 269669.i | 1.45170i | 0.687853 | + | 0.725850i | \(0.258553\pi\) | ||||
−0.687853 | + | 0.725850i | \(0.741447\pi\) | |||||||
\(432\) | 1791.14 | + | 35871.1i | 0.00959758 | + | 0.192211i | ||||
\(433\) | 161609. | 0.861967 | 0.430983 | − | 0.902360i | \(-0.358167\pi\) | ||||
0.430983 | + | 0.902360i | \(0.358167\pi\) | |||||||
\(434\) | 4697.58 | − | 58.5951i | 0.0249399 | − | 0.000311087i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 170436. | − | 4252.52i | 0.896580 | − | 0.0223704i | ||||
\(437\) | −274395. | −1.43686 | ||||||||
\(438\) | 1804.06 | + | 144632.i | 0.00940376 | + | 0.753903i | ||||
\(439\) | 171500.i | 0.889885i | 0.895559 | + | 0.444943i | \(0.146776\pi\) | ||||
−0.895559 | + | 0.444943i | \(0.853224\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31212.6 | −0.160492 | ||||||||
\(442\) | 30669.2 | − | 382.551i | 0.156985 | − | 0.00195814i | ||||
\(443\) | 78491.9i | 0.399961i | 0.979800 | + | 0.199980i | \(0.0640878\pi\) | ||||
−0.979800 | + | 0.199980i | \(0.935912\pi\) | |||||||
\(444\) | 1292.45 | + | 51800.2i | 0.00655616 | + | 0.262764i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1441.16 | + | 115538.i | 0.00724505 | + | 0.580838i | ||||
\(447\) | − | 182535.i | − | 0.913546i | ||||||
\(448\) | −10805.6 | − | 144120.i | −0.0538387 | − | 0.718071i | ||||
\(449\) | −256874. | −1.27417 | −0.637085 | − | 0.770794i | \(-0.719860\pi\) | ||||
−0.637085 | + | 0.770794i | \(0.719860\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 610.434i | 0.00300113i | ||||||||
\(452\) | 157968. | − | 3941.42i | 0.773200 | − | 0.0192919i | ||||
\(453\) | 214652. | 1.04602 | ||||||||
\(454\) | 881.170 | + | 70643.7i | 0.00427512 | + | 0.342738i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −193056. | + | 7227.21i | −0.928438 | + | 0.0347569i | ||||
\(457\) | 182963. | 0.876053 | 0.438027 | − | 0.898962i | \(-0.355678\pi\) | ||||
0.438027 | + | 0.898962i | \(0.355678\pi\) | |||||||
\(458\) | −398632. | + | 4972.32i | −1.90038 | + | 0.0237043i | ||||
\(459\) | 26201.9i | 0.124368i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 328023. | 1.54348 | 0.771742 | − | 0.635936i | \(-0.219386\pi\) | ||||
0.771742 | + | 0.635936i | \(0.219386\pi\) | |||||||
\(462\) | −36.1449 | − | 2897.74i | −0.000169341 | − | 0.0135761i | ||||
\(463\) | 288300.i | 1.34488i | 0.740153 | + | 0.672439i | \(0.234753\pi\) | ||||
−0.740153 | + | 0.672439i | \(0.765247\pi\) | |||||||
\(464\) | −250417. | + | 12504.0i | −1.16313 | + | 0.0580780i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 290213. | − | 3619.96i | 1.33643 | − | 0.0166699i | ||||
\(467\) | − | 187893.i | − | 0.861542i | −0.902461 | − | 0.430771i | \(-0.858242\pi\) | ||
0.902461 | − | 0.430771i | \(-0.141758\pi\) | |||||||
\(468\) | −17731.2 | + | 442.407i | −0.0809555 | + | 0.00201990i | ||||
\(469\) | 264334. | 1.20173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 18612.4i | − | 0.0838998i | ||||||
\(472\) | −8350.03 | − | 223049.i | −0.0374804 | − | 1.00119i | ||||
\(473\) | 10571.7 | 0.0472525 | ||||||||
\(474\) | −140420. | + | 1751.53i | −0.624991 | + | 0.00779579i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2629.88 | − | 105403.i | −0.0116071 | − | 0.465199i | ||||
\(477\) | −102117. | −0.448808 | ||||||||
\(478\) | 3502.70 | + | 280812.i | 0.0153302 | + | 1.22902i | ||||
\(479\) | 42484.8i | 0.185167i | 0.995705 | + | 0.0925833i | \(0.0295125\pi\) | ||||
−0.995705 | + | 0.0925833i | \(0.970488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25589.1 | −0.110602 | ||||||||
\(482\) | −205746. | + | 2566.36i | −0.885599 | + | 0.0110465i | ||||
\(483\) | 86599.2i | 0.371210i | ||||||||
\(484\) | 233933. | − | 5836.82i | 0.998623 | − | 0.0249164i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −188.983 | − | 15150.8i | −0.000800110 | − | 0.0641450i | ||||
\(487\) | − | 115941.i | − | 0.488854i | −0.969668 | − | 0.244427i | \(-0.921400\pi\) | ||
0.969668 | − | 0.244427i | \(-0.0785998\pi\) | |||||||
\(488\) | −31244.6 | + | 1169.67i | −0.131200 | + | 0.00491160i | ||||
\(489\) | 77784.1 | 0.325292 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 254668.i | − | 1.05636i | −0.849133 | − | 0.528179i | \(-0.822875\pi\) | ||
0.849133 | − | 0.528179i | \(-0.177125\pi\) | |||||||
\(492\) | −320.345 | − | 12839.1i | −0.00132339 | − | 0.0530400i | ||||
\(493\) | −182916. | −0.752588 | ||||||||
\(494\) | −1189.95 | − | 95398.3i | −0.00487611 | − | 0.390919i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 424.963 | + | 8510.73i | 0.00172738 | + | 0.0345942i | ||||
\(497\) | −163015. | −0.659956 | ||||||||
\(498\) | 101050. | − | 1260.44i | 0.407454 | − | 0.00508235i | ||||
\(499\) | 139763.i | 0.561296i | 0.959811 | + | 0.280648i | \(0.0905494\pi\) | ||||
−0.959811 | + | 0.280648i | \(0.909451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −65003.9 | −0.258979 | ||||||||
\(502\) | −3613.48 | − | 289694.i | −0.0143390 | − | 1.14956i | ||||
\(503\) | 416958.i | 1.64800i | 0.566592 | + | 0.823998i | \(0.308261\pi\) | ||||
−0.566592 | + | 0.823998i | \(0.691739\pi\) | |||||||
\(504\) | 2280.91 | + | 60928.5i | 0.00897940 | + | 0.239861i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7465.32 | − | 93.1183i | 0.0291573 | − | 0.000363692i | ||||
\(507\) | 139648.i | 0.543275i | ||||||||
\(508\) | 7970.87 | + | 319464.i | 0.0308872 | + | 1.23792i | ||||
\(509\) | −414530. | −1.60000 | −0.800000 | − | 0.600000i | \(-0.795167\pi\) | ||||
−0.800000 | + | 0.600000i | \(0.795167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 245548.i | 0.940360i | ||||||||
\(512\) | 260494. | − | 29365.3i | 0.993706 | − | 0.112020i | ||||
\(513\) | 81502.5 | 0.309696 | ||||||||
\(514\) | 310823. | − | 3877.04i | 1.17649 | − | 0.0146749i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −222353. | + | 5547.87i | −0.835108 | + | 0.0208366i | ||||
\(517\) | −11558.6 | −0.0432440 | ||||||||
\(518\) | 1097.13 | + | 87957.2i | 0.00408882 | + | 0.327802i | ||||
\(519\) | − | 266905.i | − | 0.990882i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7651.52 | 0.0281885 | 0.0140943 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140943 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(522\) | 105768. | − | 1319.29i | 0.388162 | − | 0.00484172i | ||||
\(523\) | 120269.i | 0.439692i | 0.975535 | + | 0.219846i | \(0.0705555\pi\) | ||||
−0.975535 | + | 0.219846i | \(0.929444\pi\) | |||||||
\(524\) | 12265.4 | + | 491585.i | 0.0446704 | + | 1.79034i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 135.536 | + | 10866.0i | 0.000489873 | + | 0.0392732i | ||||
\(527\) | 6216.62i | 0.0223838i | ||||||||
\(528\) | 5249.92 | − | 262.142i | 0.0188315 | − | 0.000940305i | ||||
\(529\) | 56739.5 | 0.202756 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 94164.7i | 0.333964i | ||||||||
\(532\) | −327862. | + | 8180.40i | −1.15842 | + | 0.0289036i | ||||
\(533\) | 6342.45 | 0.0223256 | ||||||||
\(534\) | −133.171 | − | 10676.4i | −0.000467011 | − | 0.0374404i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17936.4 | + | 479124.i | 0.0624319 | + | 1.66770i | ||||
\(537\) | −155829. | −0.540381 | ||||||||
\(538\) | 266646. | − | 3325.99i | 0.921234 | − | 0.0114910i | ||||
\(539\) | 4568.12i | 0.0157239i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −479201. | −1.63728 | −0.818640 | − | 0.574307i | \(-0.805272\pi\) | ||||
−0.818640 | + | 0.574307i | \(0.805272\pi\) | |||||||
\(542\) | −3190.95 | − | 255820.i | −0.0108623 | − | 0.870834i | ||||
\(543\) | 246382.i | 0.835619i | ||||||||
\(544\) | 190872. | − | 11919.0i | 0.644977 | − | 0.0402755i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −30107.8 | + | 375.547i | −0.100993 | + | 0.00125974i | ||||
\(547\) | 327802.i | 1.09556i | 0.836622 | + | 0.547781i | \(0.184527\pi\) | ||||
−0.836622 | + | 0.547781i | \(0.815473\pi\) | |||||||
\(548\) | −114797. | + | 2864.28i | −0.382269 | + | 0.00953792i | ||||
\(549\) | 13190.6 | 0.0437641 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 568970.i | 1.87407i | ||||||||
\(552\) | −156967. | + | 5876.20i | −0.515147 | + | 0.0192850i | ||||
\(553\) | −238398. | −0.779566 | ||||||||
\(554\) | −145775. | + | 1818.32i | −0.474968 | + | 0.00592449i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1847.30 | − | 74037.8i | −0.00597569 | − | 0.239499i | ||||
\(557\) | 131341. | 0.423342 | 0.211671 | − | 0.977341i | \(-0.432109\pi\) | ||||
0.211671 | + | 0.977341i | \(0.432109\pi\) | |||||||
\(558\) | −44.8378 | − | 3594.66i | −0.000144004 | − | 0.0115449i | ||||
\(559\) | − | 109841.i | − | 0.351513i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3834.78 | 0.0121847 | ||||||||
\(562\) | 334730. | − | 4175.23i | 1.05979 | − | 0.0132193i | ||||
\(563\) | − | 137401.i | − | 0.433485i | −0.976229 | − | 0.216742i | \(-0.930457\pi\) | ||
0.976229 | − | 0.216742i | \(-0.0695432\pi\) | |||||||
\(564\) | 243110. | − | 6065.77i | 0.764265 | − | 0.0190690i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4949.62 | − | 396813.i | −0.0154504 | − | 1.23866i | ||||
\(567\) | − | 25722.2i | − | 0.0800096i | ||||||
\(568\) | −11061.4 | − | 295477.i | −0.0342858 | − | 0.915855i | ||||
\(569\) | 152095. | 0.469775 | 0.234887 | − | 0.972023i | \(-0.424528\pi\) | ||||
0.234887 | + | 0.972023i | \(0.424528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 150818.i | 0.462573i | 0.972886 | + | 0.231286i | \(0.0742935\pi\) | ||||
−0.972886 | + | 0.231286i | \(0.925707\pi\) | |||||||
\(572\) | 64.7485 | + | 2595.05i | 0.000197896 | + | 0.00793147i | ||||
\(573\) | 213191. | 0.649322 | ||||||||
\(574\) | −271.932 | − | 21800.9i | −0.000825348 | − | 0.0661684i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −110282. | + | 8268.63i | −0.332400 | + | 0.0249223i | ||||
\(577\) | 258173. | 0.775461 | 0.387730 | − | 0.921773i | \(-0.373259\pi\) | ||||
0.387730 | + | 0.921773i | \(0.373259\pi\) | |||||||
\(578\) | −194550. | + | 2426.71i | −0.582338 | + | 0.00726376i | ||||
\(579\) | 229569.i | 0.684788i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 171557. | 0.508226 | ||||||||
\(582\) | −3141.75 | − | 251875.i | −0.00927524 | − | 0.743599i | ||||
\(583\) | 14945.3i | 0.0439711i | ||||||||
\(584\) | −445073. | + | 16661.7i | −1.30499 | + | 0.0488533i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22217.9 | − | 277.133i | 0.0647004 | − | 0.000807037i | ||||
\(587\) | 574134.i | 1.66624i | 0.553095 | + | 0.833118i | \(0.313447\pi\) | ||||
−0.553095 | + | 0.833118i | \(0.686553\pi\) | |||||||
\(588\) | −2397.27 | − | 96080.0i | −0.00693366 | − | 0.277894i | ||||
\(589\) | 19337.2 | 0.0557394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 45332.7i | − | 0.129789i | ||||||
\(592\) | −159354. | + | 7956.98i | −0.454695 | + | 0.0227041i | ||||
\(593\) | −275339. | −0.782995 | −0.391497 | − | 0.920179i | \(-0.628043\pi\) | ||||
−0.391497 | + | 0.920179i | \(0.628043\pi\) | |||||||
\(594\) | −2217.39 | + | 27.6586i | −0.00628449 | + | 7.83893e-5i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 561886. | − | 14019.5i | 1.58182 | − | 0.0394675i | ||||
\(597\) | −34923.2 | −0.0979864 | ||||||||
\(598\) | −967.506 | − | 77565.2i | −0.00270552 | − | 0.216903i | ||||
\(599\) | 86528.9i | 0.241161i | 0.992704 | + | 0.120581i | \(0.0384756\pi\) | ||||
−0.992704 | + | 0.120581i | \(0.961524\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −391085. | −1.08273 | −0.541367 | − | 0.840786i | \(-0.682093\pi\) | ||||
−0.541367 | + | 0.840786i | \(0.682093\pi\) | |||||||
\(602\) | −377557. | + | 4709.44i | −1.04181 | + | 0.0129950i | ||||
\(603\) | − | 202272.i | − | 0.556290i | ||||||
\(604\) | 16486.3 | + | 660752.i | 0.0451906 | + | 1.81119i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1864.22 | + | 149455.i | 0.00507634 | + | 0.406972i | ||||
\(607\) | − | 86135.8i | − | 0.233779i | −0.993145 | − | 0.116890i | \(-0.962708\pi\) | ||
0.993145 | − | 0.116890i | \(-0.0372924\pi\) | |||||||
\(608\) | −37074.7 | − | 593718.i | −0.100293 | − | 1.60610i | ||||
\(609\) | 179567. | 0.484164 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 120095.i | 0.321694i | ||||||||
\(612\) | −80655.8 | + | 2012.42i | −0.215344 | + | 0.00537300i | ||||
\(613\) | 161510. | 0.429811 | 0.214906 | − | 0.976635i | \(-0.431056\pi\) | ||||
0.214906 | + | 0.976635i | \(0.431056\pi\) | |||||||
\(614\) | −1287.86 | − | 103248.i | −0.00341610 | − | 0.273870i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8917.19 | − | 333.823i | 0.0234999 | − | 0.000879740i | ||||
\(617\) | −3300.03 | −0.00866857 | −0.00433428 | − | 0.999991i | \(-0.501380\pi\) | ||||
−0.00433428 | + | 0.999991i | \(0.501380\pi\) | |||||||
\(618\) | 211771. | − | 2641.51i | 0.554484 | − | 0.00691633i | ||||
\(619\) | − | 670945.i | − | 1.75108i | −0.483147 | − | 0.875539i | \(-0.660506\pi\) | ||
0.483147 | − | 0.875539i | \(-0.339494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 66266.9 | 0.171836 | ||||||||
\(622\) | −5325.74 | − | 426966.i | −0.0137657 | − | 1.10360i | ||||
\(623\) | − | 18125.8i | − | 0.0467003i | ||||||
\(624\) | −2723.67 | − | 54547.0i | −0.00699497 | − | 0.140088i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −305316. | + | 3808.34i | −0.779113 | + | 0.00971822i | ||||
\(627\) | − | 11928.3i | − | 0.0303419i | ||||||
\(628\) | 57293.6 | − | 1429.52i | 0.145274 | − | 0.00362469i | ||||
\(629\) | −116400. | −0.294205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 563090.i | 1.41423i | 0.707100 | + | 0.707113i | \(0.250003\pi\) | ||||
−0.707100 | + | 0.707113i | \(0.749997\pi\) | |||||||
\(632\) | −16176.6 | − | 432114.i | −0.0404997 | − | 1.08184i | ||||
\(633\) | 44176.7 | 0.110252 | ||||||||
\(634\) | −433110. | + | 5402.37i | −1.07750 | + | 0.0134402i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7843.04 | − | 314340.i | −0.0193897 | − | 0.777116i | ||||
\(637\) | 47463.1 | 0.116971 | ||||||||
\(638\) | −193.085 | − | 15479.7i | −0.000474358 | − | 0.0380295i | ||||
\(639\) | 124742.i | 0.305499i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 758985. | 1.84721 | 0.923607 | − | 0.383341i | \(-0.125226\pi\) | ||||
0.923607 | + | 0.383341i | \(0.125226\pi\) | |||||||
\(642\) | 449928. | − | 5612.15i | 1.09162 | − | 0.0136163i | ||||
\(643\) | − | 572545.i | − | 1.38480i | −0.721513 | − | 0.692401i | \(-0.756553\pi\) | ||
0.721513 | − | 0.692401i | \(-0.243447\pi\) | |||||||
\(644\) | −266573. | + | 6651.21i | −0.642754 | + | 0.0160372i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5412.83 | − | 433948.i | −0.0129706 | − | 1.03986i | ||||
\(647\) | 263241.i | 0.628847i | 0.949283 | + | 0.314423i | \(0.101811\pi\) | ||||
−0.949283 | + | 0.314423i | \(0.898189\pi\) | |||||||
\(648\) | 46623.3 | − | 1745.39i | 0.111033 | − | 0.00415663i | ||||
\(649\) | 13781.5 | 0.0327195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 6102.82i | − | 0.0144002i | ||||||
\(652\) | 5974.18 | + | 239439.i | 0.0140534 | + | 0.563247i | ||||
\(653\) | −224745. | −0.527065 | −0.263532 | − | 0.964651i | \(-0.584888\pi\) | ||||
−0.263532 | + | 0.964651i | \(0.584888\pi\) | |||||||
\(654\) | −2762.31 | − | 221455.i | −0.00645827 | − | 0.517762i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 39497.2 | − | 1972.20i | 0.0917823 | − | 0.00458293i | ||||
\(657\) | 187897. | 0.435300 | ||||||||
\(658\) | 412803. | − | 5149.07i | 0.953434 | − | 0.0118926i | ||||
\(659\) | − | 778617.i | − | 1.79289i | −0.443158 | − | 0.896444i | \(-0.646142\pi\) | ||
0.443158 | − | 0.896444i | \(-0.353858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 339420. | 0.776844 | 0.388422 | − | 0.921482i | \(-0.373020\pi\) | ||||
0.388422 | + | 0.921482i | \(0.373020\pi\) | |||||||
\(662\) | −5441.88 | − | 436277.i | −0.0124175 | − | 0.995512i | ||||
\(663\) | − | 39843.6i | − | 0.0906424i | ||||||
\(664\) | 11641.1 | + | 310960.i | 0.0264032 | + | 0.705291i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 67306.1 | − | 839.539i | 0.151742 | − | 0.00189275i | ||||
\(667\) | 462610.i | 1.03983i | ||||||||
\(668\) | −4992.60 | − | 200098.i | −0.0111885 | − | 0.448425i | ||||
\(669\) | 150100. | 0.335373 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1930.50i | − | 0.00428771i | ||||||
\(672\) | −187378. | + | 11700.8i | −0.414934 | + | 0.0259105i | ||||
\(673\) | −20796.2 | −0.0459149 | −0.0229574 | − | 0.999736i | \(-0.507308\pi\) | ||||
−0.0229574 | + | 0.999736i | \(0.507308\pi\) | |||||||
\(674\) | 610250. | − | 7611.92i | 1.34335 | − | 0.0167561i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −429871. | + | 10725.6i | −0.940686 | + | 0.0234709i | ||||
\(677\) | −202957. | −0.442820 | −0.221410 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221410 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(678\) | −2560.23 | − | 205254.i | −0.00556954 | − | 0.446512i | ||||
\(679\) | − | 427619.i | − | 0.927508i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 91776.0 | 0.197895 | ||||||||
\(682\) | −526.096 | + | 6.56223i | −0.00113109 | + | 1.41086e-5i | ||||
\(683\) | − | 74248.4i | − | 0.159164i | −0.996828 | − | 0.0795821i | \(-0.974641\pi\) | ||
0.996828 | − | 0.0795821i | \(-0.0253586\pi\) | |||||||
\(684\) | 6259.76 | + | 250884.i | 0.0133797 | + | 0.536243i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6261.52 | − | 501988.i | −0.0133055 | − | 1.06671i | ||||
\(687\) | 517879.i | 1.09727i | ||||||||
\(688\) | −34155.4 | − | 684029.i | −0.0721577 | − | 1.44510i | ||||
\(689\) | 155283. | 0.327103 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 628006.i | − | 1.31525i | −0.753346 | − | 0.657624i | \(-0.771562\pi\) | ||
0.753346 | − | 0.657624i | \(-0.228438\pi\) | |||||||
\(692\) | 821599. | − | 20499.5i | 1.71572 | − | 0.0428086i | ||||
\(693\) | −3764.57 | −0.00783879 | ||||||||
\(694\) | −8416.50 | − | 674753.i | −0.0174748 | − | 1.40096i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12184.6 | + | 325478.i | 0.0251531 | + | 0.671898i | ||||
\(697\) | 28850.6 | 0.0593866 | ||||||||
\(698\) | −78717.3 | + | 981.876i | −0.161569 | + | 0.00201533i | ||||
\(699\) | − | 377028.i | − | 0.771647i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −508002. | −1.03378 | −0.516892 | − | 0.856051i | \(-0.672911\pi\) | ||||
−0.516892 | + | 0.856051i | \(0.672911\pi\) | |||||||
\(702\) | 287.374 | + | 23038.9i | 0.000583141 | + | 0.0467506i | ||||
\(703\) | 362068.i | 0.732620i | ||||||||
\(704\) | 1210.15 | + | 16140.4i | 0.00244172 | + | 0.0325663i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 220216. | − | 2746.85i | 0.441813 | − | 0.00551094i | ||||
\(707\) | 253736.i | 0.507626i | ||||||||
\(708\) | −289862. | + | 7232.28i | −0.578262 | + | 0.0144281i | ||||
\(709\) | −60762.6 | −0.120877 | −0.0604385 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604385 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 182426.i | 0.360867i | ||||||||
\(712\) | 32854.2 | − | 1229.93i | 0.0648084 | − | 0.00242616i | ||||
\(713\) | 15722.4 | 0.0309271 | ||||||||
\(714\) | −136954. | + | 1708.29i | −0.268645 | + | 0.00335093i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11968.4 | − | 479680.i | −0.0233458 | − | 0.935676i | ||||
\(717\) | 364814. | 0.709633 | ||||||||
\(718\) | 3652.28 | + | 292804.i | 0.00708460 | + | 0.567974i | ||||
\(719\) | − | 240815.i | − | 0.465828i | −0.972497 | − | 0.232914i | \(-0.925174\pi\) | ||
0.972497 | − | 0.232914i | \(-0.0748261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 359533. | 0.691621 | ||||||||
\(722\) | −828578. | + | 10335.2i | −1.58949 | + | 0.0198265i | ||||
\(723\) | 267292.i | 0.511340i | ||||||||
\(724\) | −758422. | + | 18923.2i | −1.44689 | + | 0.0361009i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3791.42 | − | 303959.i | −0.00719331 | − | 0.576690i | ||||
\(727\) | 447387.i | 0.846476i | 0.906018 | + | 0.423238i | \(0.139107\pi\) | ||||
−0.906018 | + | 0.423238i | \(0.860893\pi\) | |||||||
\(728\) | −3468.44 | − | 92650.2i | −0.00654442 | − | 0.174817i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 499646.i | − | 0.935035i | ||||||
\(732\) | 1013.09 | + | 40603.7i | 0.00189072 | + | 0.0757781i | ||||
\(733\) | 855174. | 1.59165 | 0.795823 | − | 0.605529i | \(-0.207039\pi\) | ||||
0.795823 | + | 0.605529i | \(0.207039\pi\) | |||||||
\(734\) | −7799.41 | − | 625282.i | −0.0144767 | − | 1.16060i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30144.2 | − | 482732.i | −0.0556478 | − | 0.891149i | ||||
\(737\) | −29603.5 | −0.0545015 | ||||||||
\(738\) | −16682.4 | + | 208.086i | −0.0306298 | + | 0.000382059i | ||||
\(739\) | 234148.i | 0.428747i | 0.976752 | + | 0.214374i | \(0.0687710\pi\) | ||||
−0.976752 | + | 0.214374i | \(0.931229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −123936. | −0.225715 | ||||||||
\(742\) | −6657.74 | − | 533753.i | −0.0120926 | − | 0.969466i | ||||
\(743\) | 242702.i | 0.439639i | 0.975541 | + | 0.219819i | \(0.0705468\pi\) | ||||
−0.975541 | + | 0.219819i | \(0.929453\pi\) | |||||||
\(744\) | 11061.8 | − | 414.108i | 0.0199839 | − | 0.000748113i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −934981. | + | 11662.4i | −1.68006 | + | 0.0209562i | ||||
\(747\) | − | 131278.i | − | 0.235262i | ||||||
\(748\) | 294.528 | + | 11804.4i | 0.000526409 | + | 0.0210979i | ||||
\(749\) | 763863. | 1.36161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 328095.i | 0.581728i | 0.956764 | + | 0.290864i | \(0.0939428\pi\) | ||||
−0.956764 | + | 0.290864i | \(0.906057\pi\) | |||||||
\(752\) | 37343.9 | + | 747885.i | 0.0660364 | + | 1.32251i | ||||
\(753\) | −376353. | −0.663751 | ||||||||
\(754\) | −160835. | + | 2006.16i | −0.282903 | + | 0.00352877i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 79179.2 | − | 1975.58i | 0.138538 | − | 0.00345662i | ||||
\(757\) | −270737. | −0.472450 | −0.236225 | − | 0.971698i | \(-0.575910\pi\) | ||||
−0.236225 | + | 0.971698i | \(0.575910\pi\) | |||||||
\(758\) | 1247.33 | + | 99998.8i | 0.00217092 | + | 0.174043i | ||||
\(759\) | − | 9698.49i | − | 0.0168353i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −718672. | −1.24097 | −0.620485 | − | 0.784218i | \(-0.713064\pi\) | ||||
−0.620485 | + | 0.784218i | \(0.713064\pi\) | |||||||
\(762\) | 415092. | − | 5177.63i | 0.714883 | − | 0.00891705i | ||||
\(763\) | − | 375974.i | − | 0.645816i | ||||||
\(764\) | 16374.0 | + | 656254.i | 0.0280524 | + | 1.12431i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8238.42 | − | 660476.i | −0.0140406 | − | 1.12564i | ||||
\(767\) | − | 143190.i | − | 0.243401i | ||||||
\(768\) | −33923.0 | − | 338841.i | −0.0575138 | − | 0.574478i | ||||
\(769\) | −654646. | −1.10702 | −0.553508 | − | 0.832844i | \(-0.686711\pi\) | ||||
−0.553508 | + | 0.832844i | \(0.686711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 403803.i | − | 0.679298i | ||||||
\(772\) | −706670. | + | 17632.0i | −1.18572 | + | 0.0295846i | ||||
\(773\) | −547589. | −0.916423 | −0.458211 | − | 0.888843i | \(-0.651510\pi\) | ||||
−0.458211 | + | 0.888843i | \(0.651510\pi\) | |||||||
\(774\) | 3603.73 | + | 288912.i | 0.00601548 | + | 0.482263i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 775091. | − | 29016.2i | 1.28715 | − | 0.0481856i | ||||
\(777\) | 114269. | 0.189271 | ||||||||
\(778\) | 185231. | − | 2310.46i | 0.306023 | − | 0.00381716i | ||||
\(779\) | − | 89741.3i | − | 0.147883i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18256.5 | 0.0299307 | ||||||||
\(782\) | −4400.99 | − | 352829.i | −0.00719676 | − | 0.576967i | ||||
\(783\) | − | 137407.i | − | 0.224123i | ||||||
\(784\) | 295574. | − | 14758.8i | 0.480876 | − | 0.0240114i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 638736. | − | 7967.24i | 1.03389 | − | 0.0128962i | ||||
\(787\) | 709361.i | 1.14530i | 0.819801 | + | 0.572648i | \(0.194084\pi\) | ||||
−0.819801 | + | 0.572648i | \(0.805916\pi\) | |||||||
\(788\) | 139545. | − | 3481.76i | 0.224731 | − | 0.00560721i | ||||
\(789\) | 14116.4 | 0.0226762 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 348470.i | − | 0.556944i | ||||||
\(792\) | −255.446 | − | 6823.56i | −0.000407238 | − | 0.0108783i | ||||
\(793\) | −20058.1 | −0.0318965 | ||||||||
\(794\) | 976042. | − | 12174.6i | 1.54820 | − | 0.0193114i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2682.26 | − | 107502.i | −0.00423327 | − | 0.169665i | ||||
\(797\) | 431065. | 0.678620 | 0.339310 | − | 0.940675i | \(-0.389806\pi\) | ||||
0.339310 | + | 0.940675i | \(0.389806\pi\) | |||||||
\(798\) | 5313.74 | + | 426004.i | 0.00834439 | + | 0.668972i | ||||
\(799\) | 546289.i | 0.855714i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13870.1 | −0.0216179 | ||||||||
\(802\) | 409336. | − | 5105.83i | 0.636401 | − | 0.00793811i | ||||
\(803\) | − | 27499.6i | − | 0.0426477i | ||||||
\(804\) | 622642. | − | 15535.4i | 0.963223 | − | 0.0240331i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 68.1820 | + | 5466.17i | 0.000104954 | + | 0.00841421i | ||||
\(807\) | − | 346410.i | − | 0.531916i | ||||||
\(808\) | −459915. | + | 17217.3i | −0.704457 | + | 0.0263720i | ||||
\(809\) | −179022. | −0.273533 | −0.136767 | − | 0.990603i | \(-0.543671\pi\) | ||||
−0.136767 | + | 0.990603i | \(0.543671\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 979088.i | − | 1.48861i | −0.667841 | − | 0.744304i | \(-0.732782\pi\) | ||
0.667841 | − | 0.744304i | \(-0.267218\pi\) | |||||||
\(812\) | 13791.6 | + | 552751.i | 0.0209171 | + | 0.838335i | ||||
\(813\) | −332345. | −0.502815 | ||||||||
\(814\) | −122.871 | − | 9850.58i | −0.000185438 | − | 0.0148667i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12389.5 | − | 248124.i | −0.0186068 | − | 0.372638i | ||||
\(817\) | −1.55418e6 | −2.32839 | ||||||||
\(818\) | −442528. | + | 5519.84i | −0.661354 | + | 0.00824936i | ||||
\(819\) | 39114.2i | 0.0583131i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 154045. | 0.228540 | 0.114270 | − | 0.993450i | \(-0.463547\pi\) | ||||
0.114270 | + | 0.993450i | \(0.463547\pi\) | |||||||
\(822\) | 1860.55 | + | 149161.i | 0.00275357 | + | 0.220755i | ||||
\(823\) | 844036.i | 1.24612i | 0.782173 | + | 0.623062i | \(0.214111\pi\) | ||||
−0.782173 | + | 0.623062i | \(0.785889\pi\) | |||||||
\(824\) | 24396.2 | + | 651679.i | 0.0359309 | + | 0.959797i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −492188. | + | 6139.28i | −0.721392 | + | 0.00899824i | ||||
\(827\) | 1.00992e6i | 1.47665i | 0.674445 | + | 0.738325i | \(0.264383\pi\) | ||||
−0.674445 | + | 0.738325i | \(0.735617\pi\) | |||||||
\(828\) | 5089.60 | + | 203986.i | 0.00742375 | + | 0.297536i | ||||
\(829\) | −617007. | −0.897803 | −0.448901 | − | 0.893581i | \(-0.648185\pi\) | ||||
−0.448901 | + | 0.893581i | \(0.648185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 189382.i | 0.274244i | ||||||||
\(832\) | 167700. | − | 12573.6i | 0.242262 | − | 0.0181640i | ||||
\(833\) | 215900. | 0.311145 | ||||||||
\(834\) | −96200.3 | + | 1199.95i | −0.138307 | + | 0.00172517i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 36718.2 | − | 916.147i | 0.0525374 | − | 0.00131085i | ||||
\(837\) | −4669.96 | −0.00666595 | ||||||||
\(838\) | −116.996 | − | 9379.60i | −0.000166603 | − | 0.0133566i | ||||
\(839\) | 1.04364e6i | 1.48261i | 0.671171 | + | 0.741303i | \(0.265792\pi\) | ||||
−0.671171 | + | 0.741303i | \(0.734208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 251961. | 0.356239 | ||||||||
\(842\) | −635227. | + | 7923.46i | −0.895993 | + | 0.0111761i | ||||
\(843\) | − | 434860.i | − | 0.611920i | ||||||
\(844\) | 3392.97 | + | 135987.i | 0.00476316 | + | 0.190902i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3940.14 | − | 315882.i | −0.00550518 | − | 0.441352i | ||||
\(847\) | − | 516046.i | − | 0.719318i | ||||||
\(848\) | 967014. | − | 48285.6i | 1.34475 | − | 0.0671468i | ||||
\(849\) | −515515. | −0.715197 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 294385.i | 0.406496i | ||||||||
\(852\) | −383985. | + | 9580.72i | −0.528975 | + | 0.0131983i | ||||
\(853\) | 103215. | 0.141856 | 0.0709278 | − | 0.997481i | \(-0.477404\pi\) | ||||
0.0709278 | + | 0.997481i | \(0.477404\pi\) | |||||||
\(854\) | 859.988 | + | 68945.5i | 0.00117917 | + | 0.0945345i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 51832.0 | + | 1.38456e6i | 0.0707377 | + | 1.88957i | ||||
\(857\) | −240186. | −0.327029 | −0.163515 | − | 0.986541i | \(-0.552283\pi\) | ||||
−0.163515 | + | 0.986541i | \(0.552283\pi\) | |||||||
\(858\) | 3371.86 | − | 42.0587i | 0.00458030 | − | 5.71322e-5i | ||||
\(859\) | − | 75055.7i | − | 0.101718i | −0.998706 | − | 0.0508590i | \(-0.983804\pi\) | ||
0.998706 | − | 0.0508590i | \(-0.0161959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28322.4 | −0.0382053 | ||||||||
\(862\) | 13453.8 | + | 1.07859e6i | 0.0181063 | + | 1.45159i | ||||
\(863\) | − | 539137.i | − | 0.723898i | −0.932198 | − | 0.361949i | \(-0.882111\pi\) | ||
0.932198 | − | 0.361949i | \(-0.117889\pi\) | |||||||
\(864\) | 8953.61 | + | 143384.i | 0.0119942 | + | 0.192076i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 646387. | − | 8062.67i | 0.861900 | − | 0.0107509i | ||||
\(867\) | 252747.i | 0.336239i | ||||||||
\(868\) | 18786.0 | − | 468.724i | 0.0249341 | − | 0.000622125i | ||||
\(869\) | 26698.9 | 0.0353553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 307583.i | 0.405439i | ||||||||
\(872\) | 681480. | − | 25511.8i | 0.896232 | − | 0.0335512i | ||||
\(873\) | −327220. | −0.429350 | ||||||||
\(874\) | −1.09749e6 | + | 13689.5i | −1.43674 | + | 0.0179212i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14431.3 | + | 578392.i | 0.0188061 | + | 0.753727i | ||||
\(877\) | 851207. | 1.10672 | 0.553358 | − | 0.832944i | \(-0.313346\pi\) | ||||
0.553358 | + | 0.832944i | \(0.313346\pi\) | |||||||
\(878\) | 8556.10 | + | 685945.i | 0.0110991 | + | 0.889816i | ||||
\(879\) | − | 28864.1i | − | 0.0373577i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.32290e6 | −1.70442 | −0.852209 | − | 0.523201i | \(-0.824738\pi\) | ||||
−0.852209 | + | 0.523201i | \(0.824738\pi\) | |||||||
\(882\) | −124841. | + | 1557.19i | −0.160479 | + | 0.00200173i | ||||
\(883\) | 222639.i | 0.285548i | 0.989755 | + | 0.142774i | \(0.0456023\pi\) | ||||
−0.989755 | + | 0.142774i | \(0.954398\pi\) | |||||||
\(884\) | 122648. | − | 3060.17i | 0.156948 | − | 0.00391598i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3915.95 | + | 313943.i | 0.00498850 | + | 0.399929i | ||||
\(887\) | − | 1.27431e6i | − | 1.61967i | −0.586655 | − | 0.809837i | \(-0.699555\pi\) | ||
0.586655 | − | 0.809837i | \(-0.300445\pi\) | |||||||
\(888\) | 7753.72 | + | 207120.i | 0.00983296 | + | 0.262661i | ||||
\(889\) | 704721. | 0.891690 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2880.70i | 0.00362864i | ||||||||
\(892\) | 11528.4 | + | 462044.i | 0.0144890 | + | 0.580703i | ||||
\(893\) | 1.69926e6 | 2.13087 | ||||||||
\(894\) | −9106.64 | − | 730082.i | −0.0113942 | − | 0.913475i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −50409.3 | − | 575895.i | −0.0627906 | − | 0.717344i | ||||
\(897\) | −100768. | −0.125238 | ||||||||
\(898\) | −1.02742e6 | + | 12815.4i | −1.27407 | + | 0.0158920i | ||||
\(899\) | − | 32601.1i | − | 0.0403378i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 706351. | 0.870103 | ||||||||
\(902\) | 30.4545 | + | 2441.54i | 3.74316e−5 | + | 0.00300090i | ||||
\(903\) | 490499.i | 0.601537i | ||||||||
\(904\) | 631626. | − | 23645.5i | 0.772900 | − | 0.0289342i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 858542. | − | 10709.0i | 1.04594 | − | 0.0130464i | ||||
\(907\) | − | 1.23551e6i | − | 1.50187i | −0.660377 | − | 0.750934i | \(-0.729604\pi\) | ||
0.660377 | − | 0.750934i | \(-0.270396\pi\) | |||||||
\(908\) | 7048.81 | + | 282509.i | 0.00854957 | + | 0.342658i | ||||
\(909\) | 194162. | 0.234984 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 830747.i | 1.00100i | 0.865738 | + | 0.500498i | \(0.166850\pi\) | ||||
−0.865738 | + | 0.500498i | \(0.833150\pi\) | |||||||
\(912\) | −771802. | + | 38538.1i | −0.927933 | + | 0.0463341i | ||||
\(913\) | −19213.2 | −0.0230493 | ||||||||
\(914\) | 731795. | − | 9128.00i | 0.875985 | − | 0.0109266i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.59416e6 | + | 39775.4i | −1.89994 | + | 0.0474050i | ||||
\(917\) | 1.08441e6 | 1.28960 | ||||||||
\(918\) | 1307.21 | + | 104799.i | 0.00155117 | + | 0.124358i | ||||
\(919\) | 189522.i | 0.224403i | 0.993685 | + | 0.112201i | \(0.0357902\pi\) | ||||
−0.993685 | + | 0.112201i | \(0.964210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −134133. | −0.158131 | ||||||||
\(922\) | 1.31199e6 | − | 16365.0i | 1.54336 | − | 0.0192511i | ||||
\(923\) | − | 189687.i | − | 0.222656i | ||||||
\(924\) | −289.136 | − | 11588.3i | −0.000338656 | − | 0.0135730i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14383.3 | + | 1.15311e6i | 0.0167739 | + | 1.34477i | ||||
\(927\) | − | 275120.i | − | 0.320157i | ||||||
\(928\) | −1.00097e6 | + | 62505.2i | −1.16231 | + | 0.0725806i | ||||
\(929\) | 125410. | 0.145312 | 0.0726558 | − | 0.997357i | \(-0.476853\pi\) | ||||
0.0726558 | + | 0.997357i | \(0.476853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 671570.i | − | 0.774804i | ||||||
\(932\) | 1.16058e6 | − | 28957.4i | 1.33612 | − | 0.0333371i | ||||
\(933\) | −554689. | −0.637215 | ||||||||
\(934\) | −9373.96 | − | 751513.i | −0.0107456 | − | 0.861475i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −70897.2 | + | 2654.10i | −0.0809240 | + | 0.00302946i | ||||
\(937\) | −1.18087e6 | −1.34500 | −0.672502 | − | 0.740095i | \(-0.734780\pi\) | ||||
−0.672502 | + | 0.740095i | \(0.734780\pi\) | |||||||
\(938\) | 1.05725e6 | − | 13187.6i | 1.20164 | − | 0.0149886i | ||||
\(939\) | 396648.i | 0.449856i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 259343. | 0.292883 | 0.146442 | − | 0.989219i | \(-0.453218\pi\) | ||||
0.146442 | + | 0.989219i | \(0.453218\pi\) | |||||||
\(942\) | −928.572 | − | 74443.9i | −0.00104644 | − | 0.0838933i | ||||
\(943\) | − | 72965.7i | − | 0.0820531i | ||||||
\(944\) | −44525.4 | − | 891710.i | −0.0499648 | − | 1.00064i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42283.7 | − | 527.423i | 0.0472488 | − | 0.000589355i | ||||
\(947\) | − | 658326.i | − | 0.734076i | −0.930206 | − | 0.367038i | \(-0.880372\pi\) | ||
0.930206 | − | 0.367038i | \(-0.119628\pi\) | |||||||
\(948\) | −561551. | + | 14011.1i | −0.624845 | + | 0.0155904i | ||||
\(949\) | −285723. | −0.317258 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 562670.i | 0.622146i | ||||||||
\(952\) | −15777.3 | − | 421447.i | −0.0174083 | − | 0.465018i | ||||
\(953\) | 710654. | 0.782478 | 0.391239 | − | 0.920289i | \(-0.372047\pi\) | ||||
0.391239 | + | 0.920289i | \(0.372047\pi\) | |||||||
\(954\) | −408435. | + | 5094.60i | −0.448773 | + | 0.00559775i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28019.4 | + | 1.12299e6i | 0.0306580 | + | 1.22874i | ||||
\(957\) | −20110.2 | −0.0219580 | ||||||||
\(958\) | 2119.56 | + | 169926.i | 0.00230949 | + | 0.185152i | ||||
\(959\) | 253237.i | 0.275353i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 922413. | 0.998800 | ||||||||
\(962\) | −102348. | + | 1276.64i | −0.110594 | + | 0.00137948i | ||||
\(963\) | − | 584519.i | − | 0.630298i | ||||||
\(964\) | −822791. | + | 20529.3i | −0.885392 | + | 0.0220912i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4320.42 | + | 346370.i | 0.00462991 | + | 0.371181i | ||||
\(967\) | − | 1.34932e6i | − | 1.44298i | −0.692423 | − | 0.721491i | \(-0.743457\pi\) | ||
0.692423 | − | 0.721491i | \(-0.256543\pi\) | |||||||
\(968\) | 935369. | − | 35016.4i | 0.998234 | − | 0.0373698i | ||||
\(969\) | −563759. | −0.600408 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.17569e6i | − | 1.24696i | −0.781838 | − | 0.623482i | \(-0.785718\pi\) | ||
0.781838 | − | 0.623482i | \(-0.214282\pi\) | |||||||
\(972\) | −1511.74 | − | 60589.1i | −0.00160009 | − | 0.0641301i | ||||
\(973\) | −163324. | −0.172514 | ||||||||
\(974\) | −5784.28 | − | 463728.i | −0.00609722 | − | 0.488816i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −124910. | + | 6237.10i | −0.131129 | + | 0.00654762i | ||||
\(977\) | 1.31383e6 | 1.37642 | 0.688211 | − | 0.725511i | \(-0.258396\pi\) | ||||
0.688211 | + | 0.725511i | \(0.258396\pi\) | |||||||
\(978\) | 311112. | − | 3880.64i | 0.325267 | − | 0.00405720i | ||||
\(979\) | 2029.96i | 0.00211798i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −287701. | −0.298953 | ||||||||
\(982\) | −12705.3 | − | 1.01859e6i | −0.0131754 | − | 1.05628i | ||||
\(983\) | 915869.i | 0.947821i | 0.880573 | + | 0.473911i | \(0.157158\pi\) | ||||
−0.880573 | + | 0.473911i | \(0.842842\pi\) | |||||||
\(984\) | −1921.82 | − | 51336.4i | −0.00198483 | − | 0.0530194i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −731606. | + | 9125.64i | −0.752529 | + | 0.00938663i | ||||
\(987\) | − | 536288.i | − | 0.550508i | ||||||
\(988\) | −9518.83 | − | 381504.i | −0.00975146 | − | 0.390828i | ||||
\(989\) | −1.26365e6 | −1.29192 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.25784e6i | 1.28079i | 0.768046 | + | 0.640394i | \(0.221229\pi\) | ||||
−0.768046 | + | 0.640394i | \(0.778771\pi\) | |||||||
\(992\) | 2124.32 | + | 34019.1i | 0.00215872 | + | 0.0345700i | ||||
\(993\) | −566785. | −0.574804 | ||||||||
\(994\) | −652010. | + | 8132.81i | −0.659905 | + | 0.00823129i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 404106. | − | 10082.8i | 0.407358 | − | 0.0101639i | ||||
\(997\) | −1.20780e6 | −1.21508 | −0.607538 | − | 0.794291i | \(-0.707843\pi\) | ||||
−0.607538 | + | 0.794291i | \(0.707843\pi\) | |||||||
\(998\) | 6972.78 | + | 559010.i | 0.00700075 | + | 0.561253i | ||||
\(999\) | − | 87440.0i | − | 0.0876152i |
(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 | 300.5.c.c.151.15 | yes | 16 | |
4.3 | odd | 2 | inner | 300.5.c.c.151.16 | yes | 16 | |
5.2 | odd | 4 | 300.5.f.c.199.18 | 32 | |||
5.3 | odd | 4 | 300.5.f.c.199.15 | 32 | |||
5.4 | even | 2 | 300.5.c.b.151.2 | yes | 16 | ||
20.3 | even | 4 | 300.5.f.c.199.17 | 32 | |||
20.7 | even | 4 | 300.5.f.c.199.16 | 32 | |||
20.19 | odd | 2 | 300.5.c.b.151.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.5.c.b.151.1 | ✓ | 16 | 20.19 | odd | 2 | ||
300.5.c.b.151.2 | yes | 16 | 5.4 | even | 2 | ||
300.5.c.c.151.15 | yes | 16 | 1.1 | even | 1 | trivial | |
300.5.c.c.151.16 | yes | 16 | 4.3 | odd | 2 | inner | |
300.5.f.c.199.15 | 32 | 5.3 | odd | 4 | |||
300.5.f.c.199.16 | 32 | 20.7 | even | 4 | |||
300.5.f.c.199.17 | 32 | 20.3 | even | 4 | |||
300.5.f.c.199.18 | 32 | 5.2 | odd | 4 |