Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,7,Mod(127,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.127");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.1703840550\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.127 |
Dual form | 192.7.g.a.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −150.000 | −1.20000 | −0.600000 | − | 0.800000i | \(-0.704833\pi\) | ||||
−0.600000 | + | 0.800000i | \(0.704833\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 325.626i | 0.949346i | 0.880162 | + | 0.474673i | \(0.157434\pi\) | ||||
−0.880162 | + | 0.474673i | \(0.842566\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1475.71i | 1.10872i | 0.832277 | + | 0.554360i | \(0.187037\pi\) | ||||
−0.832277 | + | 0.554360i | \(0.812963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3394.00 | −1.54483 | −0.772417 | − | 0.635116i | \(-0.780952\pi\) | ||||
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 2338.27i | − 0.692820i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5178.00 | 1.05394 | 0.526969 | − | 0.849884i | \(-0.323328\pi\) | ||||
0.526969 | + | 0.849884i | \(0.323328\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6810.42i | 0.992918i | 0.868060 | + | 0.496459i | \(0.165367\pi\) | ||||
−0.868060 | + | 0.496459i | \(0.834633\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5076.00 | −0.548105 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3990.65i | 0.327989i | 0.986461 | + | 0.163995i | \(0.0524380\pi\) | ||||
−0.986461 | + | 0.163995i | \(0.947562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6875.00 | 0.440000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3788.00i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −32142.0 | −1.31789 | −0.658945 | − | 0.752191i | \(-0.728997\pi\) | ||||
−0.658945 | + | 0.752191i | \(0.728997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 32611.1i | − 1.09466i | −0.836916 | − | 0.547331i | \(-0.815644\pi\) | ||||
0.836916 | − | 0.547331i | \(-0.184356\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −23004.0 | −0.640120 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 48843.8i | − 1.13921i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 76150.0 | 1.50337 | 0.751683 | − | 0.659525i | \(-0.229242\pi\) | ||||
0.751683 | + | 0.659525i | \(0.229242\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 52907.2i | − 0.891910i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70038.0 | −1.01621 | −0.508103 | − | 0.861296i | \(-0.669653\pi\) | ||||
−0.508103 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 100951.i | − 1.26971i | −0.772631 | − | 0.634855i | \(-0.781060\pi\) | ||||
0.772631 | − | 0.634855i | \(-0.218940\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 36450.0 | 0.400000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 151603.i | 1.46021i | 0.683337 | + | 0.730103i | \(0.260528\pi\) | ||||
−0.683337 | + | 0.730103i | \(0.739472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11617.0 | 0.0987429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 80717.0i | 0.608492i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −66942.0 | −0.449646 | −0.224823 | − | 0.974400i | \(-0.572180\pi\) | ||||
−0.224823 | + | 0.974400i | \(0.572180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 221356.i | − 1.33046i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −106164. | −0.573261 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 390564.i | − 1.90167i | −0.309694 | − | 0.950836i | \(-0.600227\pi\) | ||||
0.309694 | − | 0.950836i | \(-0.399773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 257014. | 1.13232 | 0.566158 | − | 0.824297i | \(-0.308429\pi\) | ||||
0.566158 | + | 0.824297i | \(0.308429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 79127.0i | − 0.316449i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 509100. | 1.85380 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 321198.i | 1.06795i | 0.845502 | + | 0.533973i | \(0.179301\pi\) | ||||
−0.845502 | + | 0.533973i | \(0.820699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −62208.0 | −0.189365 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 343112.i | − 0.958653i | −0.877637 | − | 0.479326i | \(-0.840881\pi\) | ||||
0.877637 | − | 0.479326i | \(-0.159119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 243442. | 0.625788 | 0.312894 | − | 0.949788i | \(-0.398702\pi\) | ||||
0.312894 | + | 0.949788i | \(0.398702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 107171.i | 0.254034i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −480528. | −1.05256 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 474963.i | − 0.963338i | −0.876353 | − | 0.481669i | \(-0.840031\pi\) | ||||
0.876353 | − | 0.481669i | \(-0.159969\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.03406e6i | − 1.80846i | −0.427044 | − | 0.904231i | \(-0.640445\pi\) | ||||
0.427044 | − | 0.904231i | \(-0.359555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −776700. | −1.26473 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 501044.i | − 0.760884i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −686766. | −0.974179 | −0.487090 | − | 0.873352i | \(-0.661941\pi\) | ||||
−0.487090 | + | 0.873352i | \(0.661941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.10517e6i | − 1.46658i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 508356. | 0.632003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 1.02156e6i | − 1.19150i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −942686. | −1.03288 | −0.516442 | − | 0.856322i | \(-0.672744\pi\) | ||||
−0.516442 | + | 0.856322i | \(0.672744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 358597.i | − 0.369574i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 259650. | 0.252014 | 0.126007 | − | 0.992029i | \(-0.459784\pi\) | ||||
0.126007 | + | 0.992029i | \(0.459784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 97971.7i | 0.0896580i | 0.998995 | + | 0.0448290i | \(0.0142743\pi\) | ||||
−0.998995 | + | 0.0448290i | \(0.985726\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 761400. | 0.657726 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 944141.i | 0.770700i | 0.922770 | + | 0.385350i | \(0.125919\pi\) | ||||
−0.922770 | + | 0.385350i | \(0.874081\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.02337e6 | 0.790232 | 0.395116 | − | 0.918631i | \(-0.370704\pi\) | ||||
0.395116 | + | 0.918631i | \(0.370704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.18706e6i | 0.867969i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.31393e6 | −0.910622 | −0.455311 | − | 0.890332i | \(-0.650472\pi\) | ||||
−0.455311 | + | 0.890332i | \(0.650472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 598597.i | − 0.393587i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 824742. | 0.514945 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.68609e6i | 1.00055i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −406151. | −0.229262 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.09178e6i | − 0.586707i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.31250e6 | 0.672000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 127139.i | 0.0620682i | 0.999518 | + | 0.0310341i | \(0.00988005\pi\) | ||||
−0.999518 | + | 0.0310341i | \(0.990120\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.57367e6 | 0.733068 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.06920e6i | 1.36525i | 0.730770 | + | 0.682624i | \(0.239161\pi\) | ||||
−0.730770 | + | 0.682624i | \(0.760839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.21765e6 | −0.942622 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 568199.i | 0.230940i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00868e6 | −0.392275 | −0.196138 | − | 0.980576i | \(-0.562840\pi\) | ||||
−0.196138 | + | 0.980576i | \(0.562840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 606031.i | − 0.225658i | −0.993614 | − | 0.112829i | \(-0.964009\pi\) | ||||
0.993614 | − | 0.112829i | \(-0.0359912\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.36326e6 | −0.843050 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 5.00855e6i | − 1.71279i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.82130e6 | 1.58147 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 181091.i | 0.0570092i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.39554e6 | −0.724177 | −0.362089 | − | 0.932144i | \(-0.617936\pi\) | ||||
−0.362089 | + | 0.932144i | \(0.617936\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.25467e6i | 0.945314i | 0.881247 | + | 0.472657i | \(0.156705\pi\) | ||||
−0.881247 | + | 0.472657i | \(0.843295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.25825e6 | −0.351313 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.89166e6i | 1.31359i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.59380e6 | 0.670251 | 0.335125 | − | 0.942174i | \(-0.391221\pi\) | ||||
0.335125 | + | 0.942174i | \(0.391221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 1.04352e6i | − 0.259603i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.29946e6 | −0.311375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.97358e6i | 0.686620i | 0.939222 | + | 0.343310i | \(0.111548\pi\) | ||||
−0.939222 | + | 0.343310i | \(0.888452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.45060e6 | 0.768144 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.37388e6i | 0.724404i | 0.932100 | + | 0.362202i | \(0.117975\pi\) | ||||
−0.932100 | + | 0.362202i | \(0.882025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.69243e6 | 1.38651 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.65493e6i | − 0.330973i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.20327e6 | −1.39121 | −0.695603 | − | 0.718426i | \(-0.744863\pi\) | ||||
−0.695603 | + | 0.718426i | \(0.744863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.23868e6i | 0.417712i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.08828e6 | 1.09793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.11206e6i | − 0.542611i | −0.962493 | − | 0.271306i | \(-0.912545\pi\) | ||||
0.962493 | − | 0.271306i | \(-0.0874554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.01689e6 | 1.18334 | 0.591670 | − | 0.806181i | \(-0.298469\pi\) | ||||
0.591670 | + | 0.806181i | \(0.298469\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00645e6i | 0.653742i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.14225e7 | −1.80404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.64121e6i | 1.16852i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.23347e6 | 0.182702 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.05015e6i | 0.868293i | 0.900842 | + | 0.434146i | \(0.142950\pi\) | ||||
−0.900842 | + | 0.434146i | \(0.857050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.37661e6 | −1.30429 | −0.652144 | − | 0.758095i | \(-0.726130\pi\) | ||||
−0.652144 | + | 0.758095i | \(0.726130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.93608e6i | 1.07029i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.77205e6 | −0.624174 | −0.312087 | − | 0.950053i | \(-0.601028\pi\) | ||||
−0.312087 | + | 0.950053i | \(0.601028\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.58137e6i | 0.708242i | 0.935200 | + | 0.354121i | \(0.115220\pi\) | ||||
−0.935200 | + | 0.354121i | \(0.884780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.00699e6 | −0.616579 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.04663e7i | − 1.25113i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.05057e7 | 1.21945 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 969727.i | − 0.109330i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00502e7 | −1.10087 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.26090e6i | 0.772935i | 0.922303 | + | 0.386468i | \(0.126305\pi\) | ||||
−0.922303 | + | 0.386468i | \(0.873695\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.34859e6 | 0.553478 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.51426e7i | 1.52365i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.06190e7 | 1.03921 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.79489e6i | 0.361299i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.75741e7 | −1.62816 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.79542e6i | − 0.342251i | −0.985249 | − | 0.171125i | \(-0.945260\pi\) | ||||
0.985249 | − | 0.171125i | \(-0.0547404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.67062e6 | −0.146667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50860e7i | 1.28972i | 0.764300 | + | 0.644861i | \(0.223085\pi\) | ||||
−0.764300 | + | 0.644861i | \(0.776915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.90389e6 | −0.491623 | −0.245811 | − | 0.969318i | \(-0.579054\pi\) | ||||
−0.245811 | + | 0.969318i | \(0.579054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 7.49069e6i | − 0.607695i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.30595e7 | 1.03242 | 0.516212 | − | 0.856461i | \(-0.327342\pi\) | ||||
0.516212 | + | 0.856461i | \(0.327342\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.27404e7i | − 1.75225i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.40394e6 | 0.556183 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.85931e6i | − 0.136194i | −0.997679 | − | 0.0680969i | \(-0.978307\pi\) | ||||
0.997679 | − | 0.0680969i | \(-0.0216927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.65134e6 | −0.403739 | −0.201869 | − | 0.979412i | \(-0.564702\pi\) | ||||
−0.201869 | + | 0.979412i | \(0.564702\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.74255e6 | −0.118491 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.31146e7i | − 1.53389i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.61193e7 | 1.04412 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.92421e7i | − 1.84921i | −0.380925 | − | 0.924606i | \(-0.624394\pi\) | ||||
0.380925 | − | 0.924606i | \(-0.375606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.88902e6 | −0.363648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 1.21076e7i | − 0.730190i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.19328e6 | 0.482679 | 0.241340 | − | 0.970441i | \(-0.422413\pi\) | ||||
0.241340 | + | 0.970441i | \(0.422413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.47964e7i | 1.42721i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.81051e6 | 0.439296 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 6.82637e6i | − 0.375252i | −0.982241 | − | 0.187626i | \(-0.939921\pi\) | ||||
0.982241 | − | 0.187626i | \(-0.0600793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00413e7 | 0.539576 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.07056e7i | − 0.562443i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.42950e7 | −0.734389 | −0.367194 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367194 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 2.05403e7i | − 1.03205i | −0.856575 | − | 0.516023i | \(-0.827412\pi\) | ||||
0.856575 | − | 0.516023i | \(-0.172588\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.72279e7 | 0.846731 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.01455e7i | 0.487837i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.92093e6 | 0.0903798 | 0.0451899 | − | 0.998978i | \(-0.485611\pi\) | ||||
0.0451899 | + | 0.998978i | \(0.485611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.92449e6i | 0.364887i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.88921e7 | −1.30215 | −0.651074 | − | 0.759015i | \(-0.725681\pi\) | ||||
−0.651074 | + | 0.759015i | \(0.725681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.82163e6i | − 0.389215i | −0.980881 | − | 0.194608i | \(-0.937657\pi\) | ||||
0.980881 | − | 0.194608i | \(-0.0623433\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.59246e7 | 0.687914 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.28062e7i | − 0.964732i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.67412e6 | 0.110786 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.46950e7i | − 0.596336i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.06685e6 | −0.121924 | −0.0609620 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609620 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.85845e7i | 2.28201i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.58997e6 | 0.213373 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.35442e7i | − 0.506689i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.28722e7 | 1.20539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.04754e6i | 0.145500i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.85521e7 | −1.35878 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.33706e7i | − 1.84453i | −0.386553 | − | 0.922267i | \(-0.626334\pi\) | ||||
0.386553 | − | 0.922267i | \(-0.373666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.52723e6 | −0.0517641 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 1.11399e7i | − 0.370340i | −0.982706 | − | 0.185170i | \(-0.940716\pi\) | ||||
0.982706 | − | 0.185170i | \(-0.0592837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.26509e7 | −0.412561 | −0.206280 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206280 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.18691e7i | 0.379738i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.49712e6 | −0.109782 | −0.0548912 | − | 0.998492i | \(-0.517481\pi\) | ||||
−0.0548912 | + | 0.998492i | \(0.517481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4.74322e7i | − 1.46117i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.47177e7 | −0.444964 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.52644e7i | 1.04647i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.33338e7 | −0.679727 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.59528e7i | 0.456241i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.93658e7 | −1.38624 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.50036e7i | − 0.965227i | −0.875834 | − | 0.482613i | \(-0.839688\pi\) | ||||
0.875834 | − | 0.482613i | \(-0.160312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.85045e7 | −0.501122 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 4.81798e7i | − 1.28153i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.96237e7 | 1.03530 | 0.517649 | − | 0.855593i | \(-0.326807\pi\) | ||||
0.517649 | + | 0.855593i | \(0.326807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2.04822e7i | − 0.525748i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.81244e7 | 1.21367 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.20923e7i | 1.04309i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.33120e6 | 0.227238 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.49793e7i | − 0.358512i | −0.983802 | − | 0.179256i | \(-0.942631\pi\) | ||||
0.983802 | − | 0.179256i | \(-0.0573690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.40951e6 | −0.0802077 | −0.0401039 | − | 0.999196i | \(-0.512769\pi\) | ||||
−0.0401039 | + | 0.999196i | \(0.512769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.28565e7i | 0.297303i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.55995e6 | 0.194602 | 0.0973010 | − | 0.995255i | \(-0.468979\pi\) | ||||
0.0973010 | + | 0.995255i | \(0.468979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.14669e7i | 1.15038i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.62835e7 | −0.577669 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 2.57477e7i | − 0.556488i | −0.960510 | − | 0.278244i | \(-0.910248\pi\) | ||||
0.960510 | − | 0.278244i | \(-0.0897523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 664009. | 0.0141141 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6.33127e6i | − 0.132364i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.65163e7 | −0.750945 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7.22681e7i | − 1.46200i | −0.682375 | − | 0.731002i | \(-0.739053\pi\) | ||||
0.682375 | − | 0.731002i | \(-0.260947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.70192e7 | 0.338736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.17980e7i | − 0.426870i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.64405e7 | 1.08759 | 0.543794 | − | 0.839219i | \(-0.316987\pi\) | ||||
0.543794 | + | 0.839219i | \(0.316987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.04599e7i | 0.387979i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.09090e8 | 2.03592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3.92134e7i | − 0.720305i | −0.932893 | − | 0.360153i | \(-0.882725\pi\) | ||||
0.932893 | − | 0.360153i | \(-0.117275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.98191e6 | −0.0358351 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 2.32420e7i | − 0.413692i | −0.978373 | − | 0.206846i | \(-0.933680\pi\) | ||||
0.978373 | − | 0.206846i | \(-0.0663200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.20792e7 | 1.26307 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.45311e7i | 0.423237i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.01266e8 | −1.72034 | −0.860169 | − | 0.510009i | \(-0.829642\pi\) | ||||
−0.860169 | + | 0.510009i | \(0.829642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.06636e7i | 0.345680i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.78441e7 | −0.788226 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.12444e7i | 1.15601i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.04857e8 | −1.67581 | −0.837906 | − | 0.545815i | \(-0.816220\pi\) | ||||
−0.837906 | + | 0.545815i | \(0.816220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 3.45697e7i | − 0.544223i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.68500e7 | −1.50199 | −0.750994 | − | 0.660309i | \(-0.770425\pi\) | ||||
−0.750994 | + | 0.660309i | \(0.770425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.10682e8i | 1.69107i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.85735e6 | −0.133333 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.12375e8i | 1.66681i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.23021e7 | −1.20293 | −0.601466 | − | 0.798898i | \(-0.705416\pi\) | ||||
−0.601466 | + | 0.798898i | \(0.705416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.57237e7i | − 0.226480i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.27177e8 | 1.80534 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.55108e8i | 2.17015i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.44708e6 | 0.130284 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.87082e7i | 0.798099i | 0.916929 | + | 0.399050i | \(0.130660\pi\) | ||||
−0.916929 | + | 0.399050i | \(0.869340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.33609e7 | 0.983146 | 0.491573 | − | 0.870836i | \(-0.336422\pi\) | ||||
0.491573 | + | 0.870836i | \(0.336422\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3.68395e7i | − 0.486735i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.55988e7 | 0.463733 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.36903e7i | 1.07496i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.80756e7 | 0.988879 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.26607e8i | 1.58134i | 0.612240 | + | 0.790672i | \(0.290268\pi\) | ||||
−0.612240 | + | 0.790672i | \(0.709732\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.59750e7 | 0.689493 | 0.344747 | − | 0.938696i | \(-0.387965\pi\) | ||||
0.344747 | + | 0.938696i | \(0.387965\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.51566e7i | 0.913060i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.71780e7 | −0.325666 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 1.59949e7i | − 0.189055i | −0.995522 | − | 0.0945277i | \(-0.969866\pi\) | ||||
0.995522 | − | 0.0945277i | \(-0.0301341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.82293e6 | −0.0329143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.15233e8i | − 1.32545i | −0.748861 | − | 0.662727i | \(-0.769399\pi\) | ||||
0.748861 | − | 0.662727i | \(-0.230601\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03015e8 | 1.16901 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.73428e7i | − 0.418104i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.55375e7 | 1.05544 | 0.527721 | − | 0.849418i | \(-0.323047\pi\) | ||||
0.527721 | + | 0.849418i | \(0.323047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.03356e8i | − 1.12669i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.07353e7 | −0.545777 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.65776e8i | 1.75990i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.29504e8 | −1.35686 | −0.678428 | − | 0.734667i | \(-0.737339\pi\) | ||||
−0.678428 | + | 0.734667i | \(0.737339\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.96142e7i | − 0.202831i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.05039e8 | 1.07213 | 0.536066 | − | 0.844176i | \(-0.319910\pi\) | ||||
0.536066 | + | 0.844176i | \(0.319910\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.04436e8i | − 1.05223i | −0.850415 | − | 0.526113i | \(-0.823649\pi\) | ||||
0.850415 | − | 0.526113i | \(-0.176351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.62534e7 | −0.758404 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.54569e7i | 0.151765i | 0.997117 | + | 0.0758824i | \(0.0241774\pi\) | ||||
−0.997117 | + | 0.0758824i | \(0.975823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.04590e8 | −1.01385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.04333e7i | 0.386969i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.48974e8 | 1.40775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.68217e7i | 0.436884i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.62669e7 | 0.149882 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 1.25737e7i | − 0.114408i | −0.998363 | − | 0.0572042i | \(-0.981781\pi\) | ||||
0.998363 | − | 0.0572042i | \(-0.0182186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.58453e8 | −2.32245 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.02565e7i | − 0.179773i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.41403e8 | 1.23946 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.25365e7i | − 0.454856i | −0.973795 | − | 0.227428i | \(-0.926968\pi\) | ||||
0.973795 | − | 0.227428i | \(-0.0730317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.63535e7 | −0.396420 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.04753e7i | − 0.341936i | −0.985277 | − | 0.170968i | \(-0.945310\pi\) | ||||
0.985277 | − | 0.170968i | \(-0.0546895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.66431e8 | −1.38897 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.37895e7i | 0.443488i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.11726e8 | 0.910093 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.91720e8i | 1.54300i | 0.636230 | + | 0.771499i | \(0.280493\pi\) | ||||
−0.636230 | + | 0.771499i | \(0.719507\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.25936e7 | −0.418235 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 3.32464e7i | − 0.261241i | −0.991432 | − | 0.130620i | \(-0.958303\pi\) | ||||
0.991432 | − | 0.130620i | \(-0.0416969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.89475e7 | −0.302416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.04325e8i | 0.800503i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.87407e8 | −1.42112 | −0.710562 | − | 0.703634i | \(-0.751559\pi\) | ||||
−0.710562 | + | 0.703634i | \(0.751559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.92709e7i | 0.594089i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.57979e7 | 0.191087 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.46958e7i | − 0.107590i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.23722e8 | −1.61896 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 1.12288e8i | − 0.803213i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.24378e8 | 0.879486 | 0.439743 | − | 0.898124i | \(-0.355069\pi\) | ||||
0.439743 | + | 0.898124i | \(0.355069\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.67205e8i | − 1.16881i | −0.811463 | − | 0.584404i | \(-0.801328\pi\) | ||||
0.811463 | − | 0.584404i | \(-0.198672\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.48975e7 | −0.241166 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.68860e8i | − 1.15371i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.32111e8 | 0.892423 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.49070e7i | 0.633891i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.37709e8 | 1.56987 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1.41621e8i | − 0.924840i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.85122e7 | 0.313277 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.71433e7i | 0.109478i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.84248e6 | −0.0621603 | −0.0310801 | − | 0.999517i | \(-0.509895\pi\) | ||||
−0.0310801 | + | 0.999517i | \(0.509895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.09383e8i | 0.683201i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.53506e8 | −0.948279 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.24398e8i | − 0.760064i | −0.924973 | − | 0.380032i | \(-0.875913\pi\) | ||||
0.924973 | − | 0.380032i | \(-0.124087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.24544e7 | −0.377438 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 2.18901e8i | − 1.30856i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54660e8 | 0.914540 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.78059e8i | − 1.04156i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.33942e8 | −0.775091 | −0.387545 | − | 0.921851i | \(-0.626677\pi\) | ||||
−0.387545 | + | 0.921851i | \(0.626677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.42627e8i | 1.96149i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.19115e8 | −0.674647 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.20675e7i | − 0.0676228i | −0.999428 | − | 0.0338114i | \(-0.989235\pi\) | ||||
0.999428 | − | 0.0338114i | \(-0.0107646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.97090e8 | 1.09275 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.92279e7i | 0.105483i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.50088e7 | 0.190038 | 0.0950191 | − | 0.995475i | \(-0.469709\pi\) | ||||
0.0950191 | + | 0.995475i | \(0.469709\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.91768e8i | 1.03007i | 0.857168 | + | 0.515037i | \(0.172222\pi\) | ||||
−0.857168 | + | 0.515037i | \(0.827778\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.43125e7 | −0.501309 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.74357e7i | 0.144315i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.40733e8 | 1.25317 | 0.626583 | − | 0.779354i | \(-0.284453\pi\) | ||||
0.626583 | + | 0.779354i | \(0.284453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.46167e8i | − 0.753031i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.36715e8 | 1.71686 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.87868e7i | − 0.498532i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.23711e8 | −0.617934 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.66145e8i | 1.81025i | 0.425147 | + | 0.905124i | \(0.360222\pi\) | ||||
−0.425147 | + | 0.905124i | \(0.639778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.22095e8 | 1.08691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 7.43888e7i | − 0.360367i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.91532e7 | 0.139805 | 0.0699024 | − | 0.997554i | \(-0.477731\pi\) | ||||
0.0699024 | + | 0.997554i | \(0.477731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.52913e8i | − 1.20066i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.70049e7 | −0.408903 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.30694e8i | − 0.608100i | −0.952656 | − | 0.304050i | \(-0.901661\pi\) | ||||
0.952656 | − | 0.304050i | \(-0.0983389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.80928e8 | −1.75477 | −0.877383 | − | 0.479791i | \(-0.840712\pi\) | ||||
−0.877383 | + | 0.479791i | \(0.840712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 7.80512e7i | − 0.355982i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.09226e7 | 0.275114 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3.04928e8i | − 1.36342i | −0.731620 | − | 0.681712i | \(-0.761236\pi\) | ||||
0.731620 | − | 0.681712i | \(-0.238764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.63153e8 | 0.722342 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 5.14540e8i | − 2.25578i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.34479e7 | −0.275445 | −0.137723 | − | 0.990471i | \(-0.543978\pi\) | ||||
−0.137723 | + | 0.990471i | \(0.543978\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.63768e8i | 0.704049i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.34561e7 | −0.142436 | −0.0712181 | − | 0.997461i | \(-0.522689\pi\) | ||||
−0.0712181 | + | 0.997461i | \(0.522689\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.89984e8i | − 0.801022i | −0.916292 | − | 0.400511i | \(-0.868833\pi\) | ||||
0.916292 | − | 0.400511i | \(-0.131167\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.51165e7 | 0.0631216 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.23629e8i | − 0.924833i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.04297e8 | −1.24640 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.56667e8i | − 0.635587i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.94305e8 | 1.58446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.35903e8i | 1.33698i | 0.743719 | + | 0.668492i | \(0.233060\pi\) | ||||
−0.743719 | + | 0.668492i | \(0.766940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.13186e8 | −0.446255 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.90709e7i | − 0.0744818i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.94281e7 | −0.152541 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.33763e7i | 0.319551i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.60654e8 | −0.989671 | −0.494835 | − | 0.868987i | \(-0.664772\pi\) | ||||
−0.494835 | + | 0.868987i | \(0.664772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.73815e8i | − 1.40612i | −0.711128 | − | 0.703062i | \(-0.751815\pi\) | ||||
0.711128 | − | 0.703062i | \(-0.248185\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.36050e8 | −0.879681 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.43406e8i | − 0.898708i | −0.893354 | − | 0.449354i | \(-0.851654\pi\) | ||||
0.893354 | − | 0.449354i | \(-0.148346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.76358e8 | 2.10842 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.65534e8i | 0.599989i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.12306e7 | 0.148074 | 0.0740372 | − | 0.997255i | \(-0.476412\pi\) | ||||
0.0740372 | + | 0.997255i | \(0.476412\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 4.60380e8i | − 1.63830i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.91564e7 | −0.208596 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.91383e7i | 0.346406i | 0.984886 | + | 0.173203i | \(0.0554117\pi\) | ||||
−0.984886 | + | 0.173203i | \(0.944588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.85360e8 | −1.33433 | −0.667163 | − | 0.744912i | \(-0.732492\pi\) | ||||
−0.667163 | + | 0.744912i | \(0.732492\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.73954e8i | − 0.940019i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.32647e8 | 1.13115 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.28267e8i | − 0.432253i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.91647e7 | 0.197599 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.79277e8i | 1.25542i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.80231e7 | 0.157545 | 0.0787726 | − | 0.996893i | \(-0.474900\pi\) | ||||
0.0787726 | + | 0.996893i | \(0.474900\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2.60425e7i | − 0.0846780i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.63635e8 | −0.849644 | −0.424822 | − | 0.905277i | \(-0.639663\pi\) | ||||
−0.424822 | + | 0.905277i | \(0.639663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 3.06963e8i | − 0.980565i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.35167e8 | −0.744622 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.05574e8i | 1.58680i | 0.608699 | + | 0.793401i | \(0.291692\pi\) | ||||
−0.608699 | + | 0.793401i | \(0.708308\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.51302e8 | 0.470730 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 9.20325e7i | − 0.283838i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.27201e8 | 0.694629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.79953e7i | 0.236393i | 0.992990 | + | 0.118196i | \(0.0377113\pi\) | ||||
−0.992990 | + | 0.118196i | \(0.962289\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.16768e8 | 0.350853 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.09046e7i | 0.270789i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.62657e8 | −1.07102 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.03577e8i | 0.596070i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.66810e8 | −1.35515 | −0.677573 | − | 0.735456i | \(-0.736968\pi\) | ||||
−0.677573 | + | 0.735456i | \(0.736968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.18614e8i | 1.49272i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.54488e8 | 1.01166 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.45487e7i | 0.239248i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.77560e8 | −0.498203 | −0.249101 | − | 0.968477i | \(-0.580135\pi\) | ||||
−0.249101 | + | 0.968477i | \(0.580135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.15416e8i | 0.321113i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.30139e8 | 0.359037 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.51283e8i | 2.05535i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.89837e7 | 0.0786316 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.87726e8i | 0.774093i | 0.922060 | + | 0.387046i | \(0.126505\pi\) | ||||
−0.922060 | + | 0.387046i | \(0.873495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.19021e7 | −0.0851164 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.80957e7i | − 0.233099i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.20976e8 | −0.579871 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.20038e8i | − 0.312404i | −0.987725 | − | 0.156202i | \(-0.950075\pi\) | ||||
0.987725 | − | 0.156202i | \(-0.0499251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 5.22723e8i | − 1.33820i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.05697e8 | 0.522295 | 0.261147 | − | 0.965299i | \(-0.415899\pi\) | ||||
0.261147 | + | 0.965299i | \(0.415899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 2.71637e7i | − 0.0684111i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.73995e8 | −1.18405 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.80558e8i | 1.19073i | 0.803456 | + | 0.595364i | \(0.202992\pi\) | ||||
−0.803456 | + | 0.595364i | \(0.797008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.60321e8 | 0.885594 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.96089e8i | − 0.478065i | −0.971012 | − | 0.239032i | \(-0.923170\pi\) | ||||
0.971012 | − | 0.239032i | \(-0.0768302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.59331e8 | 0.869013 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.51275e8i | 0.602821i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.07436e8 | −0.731661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.78956e8i | 0.422501i | 0.977432 | + | 0.211250i | \(0.0677535\pi\) | ||||
−0.977432 | + | 0.211250i | \(0.932246\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.55839e8 | 1.06764 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.88200e8i | − 1.13438i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.54288e8 | −0.586190 | −0.293095 | − | 0.956083i | \(-0.594685\pi\) | ||||
−0.293095 | + | 0.956083i | \(0.594685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 9.18008e7i | − 0.209953i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.52852e8 | 1.02755 | 0.513775 | − | 0.857925i | \(-0.328247\pi\) | ||||
0.513775 | + | 0.857925i | \(0.328247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.33237e8i | 0.750204i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.88738e8 | 0.421575 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.32557e9i | 2.93777i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.75007e8 | −1.26443 | −0.632214 | − | 0.774794i | \(-0.717854\pi\) | ||||
−0.632214 | + | 0.774794i | \(0.717854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.27721e8i | 0.278675i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.85200e8 | 0.617464 | 0.308732 | − | 0.951149i | \(-0.400095\pi\) | ||||
0.308732 | + | 0.951149i | \(0.400095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 2.24201e8i | − 0.481651i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.86537e8 | −0.824002 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.76988e8i | − 1.00901i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.06333e8 | 1.06288 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.21754e8i | 0.253628i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.89070e8 | −0.804301 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.03737e8i | − 0.417971i | −0.977919 | − | 0.208986i | \(-0.932984\pi\) | ||||
0.977919 | − | 0.208986i | \(-0.0670162\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.06413e8 | 0.216652 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 4.27850e8i | − 0.864495i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.72306e8 | −1.74924 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.56528e8i | 0.311524i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.73958e8 | 0.343612 | 0.171806 | − | 0.985131i | \(-0.445040\pi\) | ||||
0.171806 | + | 0.985131i | \(0.445040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.85000e8i | 1.53897i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.66884e8 | 0.324726 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.59249e8i | 0.693824i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.94918e8 | 0.373650 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.22836e8i | − 0.424000i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.47671e8 | −0.845500 | −0.422750 | − | 0.906246i | \(-0.638935\pi\) | ||||
−0.422750 | + | 0.906246i | \(0.638935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.93222e7i | 0.111213i | 0.998453 | + | 0.0556064i | \(0.0177092\pi\) | ||||
−0.998453 | + | 0.0556064i | \(0.982291\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.20192e8 | 0.595852 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 4.46037e8i | − 0.823944i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.87518e8 | 1.26072 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.68557e8i | 0.488860i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.86250e7 | 0.0697974 | 0.0348987 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348987 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.03810e8i | 0.724399i | 0.932101 | + | 0.362200i | \(0.117974\pi\) | ||||
−0.932101 | + | 0.362200i | \(0.882026\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.58152e8 | −0.281653 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.21027e8i | 0.567578i | 0.958887 | + | 0.283789i | \(0.0915915\pi\) | ||||
−0.958887 | + | 0.283789i | \(0.908408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.98016e7 | 0.122519 | 0.0612593 | − | 0.998122i | \(-0.480488\pi\) | ||||
0.0612593 | + | 0.998122i | \(0.480488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.99443e7i | 0.0521808i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.01528e7 | 0.104069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5.06082e8i | − 0.869284i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.23531e8 | −0.210668 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.16728e8i | 0.874936i | 0.899234 | + | 0.437468i | \(0.144125\pi\) | ||||
−0.899234 | + | 0.437468i | \(0.855875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.38285e8 | 0.736832 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.50383e8i | − 0.751795i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00386e9 | −1.66381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.32253e8i | − 0.217649i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.37516e8 | 0.224713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.03888e8i | 0.493088i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.41054e7 | 0.0549510 | 0.0274755 | − | 0.999622i | \(-0.491253\pi\) | ||||
0.0274755 | + | 0.999622i | \(0.491253\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.48240e8i | 0.397167i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.96601e8 | 0.947854 | 0.473927 | − | 0.880564i | \(-0.342836\pi\) | ||||
0.473927 | + | 0.880564i | \(0.342836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.96999e8i | 0.784109i | 0.919942 | + | 0.392054i | \(0.128236\pi\) | ||||
−0.919942 | + | 0.392054i | \(0.871764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.55513e8 | 0.556988 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.28718e8i | 0.511435i | 0.966752 | + | 0.255718i | \(0.0823117\pi\) | ||||
−0.966752 | + | 0.255718i | \(0.917688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.08049e9 | 1.66945 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.16853e7i | 0.0639626i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.00906e8 | 1.06807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.09015e9i | − 1.64980i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.29073e8 | 0.344295 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.27384e8i | 0.637960i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.37191e8 | 1.09290 | 0.546451 | − | 0.837491i | \(-0.315979\pi\) | ||||
0.546451 | + | 0.837491i | \(0.315979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 4.78074e7i | − 0.0703928i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.05804e9 | −1.54730 | −0.773649 | − | 0.633614i | \(-0.781571\pi\) | ||||
−0.773649 | + | 0.633614i | \(0.781571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 9.53856e7i | − 0.138548i | −0.997598 | − | 0.0692741i | \(-0.977932\pi\) | ||||
0.997598 | − | 0.0692741i | \(-0.0220683\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.13243e8 | −1.31752 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.48931e8i | 0.929882i | 0.885342 | + | 0.464941i | \(0.153925\pi\) | ||||
−0.885342 | + | 0.464941i | \(0.846075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.13999e7 | −0.0589242 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.71390e7i | 0.123191i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.03248e9 | −1.44986 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.66809e8i | 0.651133i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.11134e8 | 0.292537 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.04818e9i | 1.44264i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.46626e8 | −0.473900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.12427e8i | 0.695934i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.05253e9 | −1.42001 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.09067e6i | 0.00816288i | 0.999992 | + | 0.00408144i | \(0.00129917\pi\) | ||||
−0.999992 | + | 0.00408144i | \(0.998701\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.30950e7 | −0.0840046 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.17870e9i | − 1.55901i | −0.626397 | − | 0.779504i | \(-0.715471\pi\) | ||||
0.626397 | − | 0.779504i | \(-0.284529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52596e9 | 2.00508 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 6.00968e8i | − 0.784491i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.99410e8 | −1.29609 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 4.51537e7i | − 0.0581764i | −0.999577 | − | 0.0290882i | \(-0.990740\pi\) | ||||
0.999577 | − | 0.0290882i | \(-0.00926037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.31965e8 | 1.06494 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.16452e9i | 1.48096i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.23531e8 | 0.661481 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.38071e7i | − 0.0298860i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.05122e8 | −0.879463 | −0.439731 | − | 0.898129i | \(-0.644926\pi\) | ||||
−0.439731 | + | 0.898129i | \(0.644926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.91167e7i | 0.0980436i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.73654e8 | 0.213816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1.14618e9i | − 1.40223i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.32052e8 | −0.889864 | −0.444932 | − | 0.895564i | \(-0.646772\pi\) | ||||
−0.444932 | + | 0.895564i | \(0.646772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.97208e8i | − 0.238192i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.64058e9 | −1.96892 | −0.984461 | − | 0.175603i | \(-0.943813\pi\) | ||||
−0.984461 | + | 0.175603i | \(0.943813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.79497e8i | − 0.333305i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.85020e8 | −0.219242 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.04106e9i | − 1.22581i | −0.790156 | − | 0.612906i | \(-0.790000\pi\) | ||||
0.790156 | − | 0.612906i | \(-0.210000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.26242e8 | −0.966738 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 5.45147e7i | − 0.0633829i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.01652e9 | −1.17446 | −0.587231 | − | 0.809419i | \(-0.699782\pi\) | ||||
−0.587231 | + | 0.809419i | \(0.699782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9.07523e8i | − 1.04195i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.39395e8 | 0.843608 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 3.28451e8i | − 0.372405i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75977e8 | −0.198283 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2.29426e8i | − 0.256900i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.40649e9 | 1.56515 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.48126e8i | 1.04854i | 0.851551 | + | 0.524272i | \(0.175662\pi\) | ||||
−0.851551 | + | 0.524272i | \(0.824338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.49717e8 | −0.604182 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.06242e9i | − 1.16048i | −0.814446 | − | 0.580240i | \(-0.802959\pi\) | ||||
0.814446 | − | 0.580240i | \(-0.197041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.97339e8 | 0.214227 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 3.63737e8i | − 0.392441i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.10671e9 | −1.18673 | −0.593363 | − | 0.804935i | \(-0.702200\pi\) | ||||
−0.593363 | + | 0.804935i | \(0.702200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.01347e9i | − 1.08009i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.48680e8 | −0.263411 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.37448e9i | − 1.44703i | −0.690310 | − | 0.723513i | \(-0.742526\pi\) | ||||
0.690310 | − | 0.723513i | \(-0.257474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.15807e8 | 0.749009 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 7.69537e8i | − 0.800346i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.02859e8 | 0.416451 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 6.25564e8i | − 0.642762i | −0.946950 | − | 0.321381i | \(-0.895853\pi\) | ||||
0.946950 | − | 0.321381i | \(-0.104147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.45653e8 | 0.557274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 8.37205e8i | − 0.849890i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.20853e9 | 1.21947 | 0.609736 | − | 0.792604i | \(-0.291275\pi\) | ||||
0.609736 | + | 0.792604i | \(0.291275\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 2.88456e8i | − 0.289323i |
(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 | 192.7.g.a.127.2 | 2 | ||
3.2 | odd | 2 | 576.7.g.j.127.2 | 2 | |||
4.3 | odd | 2 | inner | 192.7.g.a.127.1 | 2 | ||
8.3 | odd | 2 | 48.7.g.c.31.2 | yes | 2 | ||
8.5 | even | 2 | 48.7.g.c.31.1 | ✓ | 2 | ||
12.11 | even | 2 | 576.7.g.j.127.1 | 2 | |||
16.3 | odd | 4 | 768.7.b.d.127.4 | 4 | |||
16.5 | even | 4 | 768.7.b.d.127.3 | 4 | |||
16.11 | odd | 4 | 768.7.b.d.127.1 | 4 | |||
16.13 | even | 4 | 768.7.b.d.127.2 | 4 | |||
24.5 | odd | 2 | 144.7.g.b.127.2 | 2 | |||
24.11 | even | 2 | 144.7.g.b.127.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.g.c.31.1 | ✓ | 2 | 8.5 | even | 2 | ||
48.7.g.c.31.2 | yes | 2 | 8.3 | odd | 2 | ||
144.7.g.b.127.1 | 2 | 24.11 | even | 2 | |||
144.7.g.b.127.2 | 2 | 24.5 | odd | 2 | |||
192.7.g.a.127.1 | 2 | 4.3 | odd | 2 | inner | ||
192.7.g.a.127.2 | 2 | 1.1 | even | 1 | trivial | ||
576.7.g.j.127.1 | 2 | 12.11 | even | 2 | |||
576.7.g.j.127.2 | 2 | 3.2 | odd | 2 | |||
768.7.b.d.127.1 | 4 | 16.11 | odd | 4 | |||
768.7.b.d.127.2 | 4 | 16.13 | even | 4 | |||
768.7.b.d.127.3 | 4 | 16.5 | even | 4 | |||
768.7.b.d.127.4 | 4 | 16.3 | odd | 4 |