Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.1 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.8.d.a.75.2 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.3050 | − | 0.442790i | −0.999234 | − | 0.0391375i | ||||
\(3\) | 16.6522 | 0.356081 | 0.178040 | − | 0.984023i | \(-0.443024\pi\) | ||||
0.178040 | + | 0.984023i | \(0.443024\pi\) | |||||||
\(4\) | 127.608 | + | 10.0115i | 0.996937 | + | 0.0782150i | ||||
\(5\) | 341.116 | 1.22041 | 0.610207 | − | 0.792242i | \(-0.291086\pi\) | ||||
0.610207 | + | 0.792242i | \(0.291086\pi\) | |||||||
\(6\) | −188.254 | − | 7.37345i | −0.355808 | − | 0.0139361i | ||||
\(7\) | − | 1382.96i | − | 1.52393i | −0.647618 | − | 0.761965i | \(-0.724235\pi\) | ||
0.647618 | − | 0.761965i | \(-0.275765\pi\) | |||||||
\(8\) | −1438.18 | − | 169.684i | −0.993112 | − | 0.117173i | ||||
\(9\) | −1909.70 | −0.873207 | ||||||||
\(10\) | −3856.33 | − | 151.043i | −1.21948 | − | 0.0477640i | ||||
\(11\) | − | 3929.55i | − | 0.890161i | −0.895490 | − | 0.445081i | \(-0.853175\pi\) | ||
0.895490 | − | 0.445081i | \(-0.146825\pi\) | |||||||
\(12\) | 2124.96 | + | 166.714i | 0.354990 | + | 0.0278509i | ||||
\(13\) | − | 1276.78i | − | 0.161182i | −0.996747 | − | 0.0805908i | \(-0.974319\pi\) | ||
0.996747 | − | 0.0805908i | \(-0.0256807\pi\) | |||||||
\(14\) | −612.359 | + | 15634.4i | −0.0596428 | + | 1.52276i | ||||
\(15\) | 5680.35 | 0.434566 | ||||||||
\(16\) | 16183.5 | + | 2555.10i | 0.987765 | + | 0.155951i | ||||
\(17\) | −3972.88 | −0.196126 | −0.0980629 | − | 0.995180i | \(-0.531265\pi\) | ||||
−0.0980629 | + | 0.995180i | \(0.531265\pi\) | |||||||
\(18\) | 21589.3 | + | 845.598i | 0.872537 | + | 0.0341751i | ||||
\(19\) | −19789.9 | + | 22410.5i | −0.661921 | + | 0.749573i | ||||
\(20\) | 43529.1 | + | 3415.09i | 1.21667 | + | 0.0954547i | ||||
\(21\) | − | 23029.3i | − | 0.542642i | ||||||
\(22\) | −1739.97 | + | 44423.8i | −0.0348387 | + | 0.889479i | ||||
\(23\) | − | 61712.8i | − | 1.05762i | −0.848741 | − | 0.528808i | \(-0.822639\pi\) | ||
0.848741 | − | 0.528808i | \(-0.177361\pi\) | |||||||
\(24\) | −23948.9 | − | 2825.62i | −0.353628 | − | 0.0417230i | ||||
\(25\) | 38235.1 | 0.489410 | ||||||||
\(26\) | −565.347 | + | 14434.1i | −0.00630825 | + | 0.161058i | ||||
\(27\) | −68219.3 | −0.667013 | ||||||||
\(28\) | 13845.5 | − | 176476.i | 0.119194 | − | 1.51926i | ||||
\(29\) | 237876.i | 1.81116i | 0.424170 | + | 0.905582i | \(0.360566\pi\) | ||||
−0.424170 | + | 0.905582i | \(0.639434\pi\) | |||||||
\(30\) | −64216.6 | − | 2515.20i | −0.434233 | − | 0.0170078i | ||||
\(31\) | −176262. | −1.06266 | −0.531329 | − | 0.847166i | \(-0.678307\pi\) | ||||
−0.531329 | + | 0.847166i | \(0.678307\pi\) | |||||||
\(32\) | −181824. | − | 36051.4i | −0.980904 | − | 0.194490i | ||||
\(33\) | − | 65435.9i | − | 0.316969i | ||||||
\(34\) | 44913.6 | + | 1759.15i | 0.195975 | + | 0.00767587i | ||||
\(35\) | − | 471748.i | − | 1.85983i | ||||||
\(36\) | −243693. | − | 19119.0i | −0.870531 | − | 0.0682979i | ||||
\(37\) | − | 49926.2i | − | 0.162040i | −0.996712 | − | 0.0810200i | \(-0.974182\pi\) | ||
0.996712 | − | 0.0810200i | \(-0.0258178\pi\) | |||||||
\(38\) | 233649. | − | 244589.i | 0.690751 | − | 0.723093i | ||||
\(39\) | − | 21261.3i | − | 0.0573937i | ||||||
\(40\) | −490586. | − | 57882.0i | −1.21201 | − | 0.142999i | ||||
\(41\) | − | 696583.i | − | 1.57844i | −0.614108 | − | 0.789222i | \(-0.710484\pi\) | ||
0.614108 | − | 0.789222i | \(-0.289516\pi\) | |||||||
\(42\) | −10197.2 | + | 260347.i | −0.0212377 | + | 0.542226i | ||||
\(43\) | − | 231172.i | − | 0.443401i | −0.975115 | − | 0.221700i | \(-0.928839\pi\) | ||
0.975115 | − | 0.221700i | \(-0.0711606\pi\) | |||||||
\(44\) | 39340.8 | − | 501442.i | 0.0696240 | − | 0.887434i | ||||
\(45\) | −651430. | −1.06567 | ||||||||
\(46\) | −27325.9 | + | 697666.i | −0.0413925 | + | 1.05681i | ||||
\(47\) | 728161.i | 1.02302i | 0.859277 | + | 0.511511i | \(0.170914\pi\) | ||||
−0.859277 | + | 0.511511i | \(0.829086\pi\) | |||||||
\(48\) | 269492. | + | 42548.1i | 0.351724 | + | 0.0555311i | ||||
\(49\) | −1.08902e6 | −1.32236 | ||||||||
\(50\) | −432250. | − | 16930.1i | −0.489035 | − | 0.0191543i | ||||
\(51\) | −66157.4 | −0.0698366 | ||||||||
\(52\) | 12782.5 | − | 162928.i | 0.0126068 | − | 0.160688i | ||||
\(53\) | − | 1.67316e6i | − | 1.54373i | −0.635785 | − | 0.771866i | \(-0.719323\pi\) | ||
0.635785 | − | 0.771866i | \(-0.280677\pi\) | |||||||
\(54\) | 771222. | + | 30206.9i | 0.666502 | + | 0.0261052i | ||||
\(55\) | − | 1.34043e6i | − | 1.08637i | ||||||
\(56\) | −234666. | + | 1.98894e6i | −0.178563 | + | 1.51343i | ||||
\(57\) | −329547. | + | 373185.i | −0.235697 | + | 0.266909i | ||||
\(58\) | 105329. | − | 2.68920e6i | 0.0708845 | − | 1.80978i | ||||
\(59\) | −2.09273e6 | −1.32657 | −0.663285 | − | 0.748367i | \(-0.730838\pi\) | ||||
−0.663285 | + | 0.748367i | \(0.730838\pi\) | |||||||
\(60\) | 724857. | + | 56869.0i | 0.433234 | + | 0.0339896i | ||||
\(61\) | 488351. | 0.275472 | 0.137736 | − | 0.990469i | \(-0.456017\pi\) | ||||
0.137736 | + | 0.990469i | \(0.456017\pi\) | |||||||
\(62\) | 1.99265e6 | + | 78047.2i | 1.06184 | + | 0.0415898i | ||||
\(63\) | 2.64103e6i | 1.33071i | ||||||||
\(64\) | 2.03957e6 | + | 488073.i | 0.972541 | + | 0.232731i | ||||
\(65\) | − | 435531.i | − | 0.196708i | ||||||
\(66\) | −28974.4 | + | 739755.i | −0.0124054 | + | 0.316726i | ||||
\(67\) | 463413. | 0.188238 | 0.0941189 | − | 0.995561i | \(-0.469997\pi\) | ||||
0.0941189 | + | 0.995561i | \(0.469997\pi\) | |||||||
\(68\) | −506971. | − | 39774.6i | −0.195525 | − | 0.0153400i | ||||
\(69\) | − | 1.02766e6i | − | 0.376597i | ||||||
\(70\) | −208886. | + | 5.33313e6i | −0.0727889 | + | 1.85840i | ||||
\(71\) | 3.96707e6 | 1.31542 | 0.657712 | − | 0.753269i | \(-0.271524\pi\) | ||||
0.657712 | + | 0.753269i | \(0.271524\pi\) | |||||||
\(72\) | 2.74649e6 | + | 324046.i | 0.867191 | + | 0.102316i | ||||
\(73\) | −204855. | −0.0616336 | −0.0308168 | − | 0.999525i | \(-0.509811\pi\) | ||||
−0.0308168 | + | 0.999525i | \(0.509811\pi\) | |||||||
\(74\) | −22106.8 | + | 564417.i | −0.00634184 | + | 0.161916i | ||||
\(75\) | 636701. | 0.174269 | ||||||||
\(76\) | −2.74971e6 | + | 2.66163e6i | −0.718521 | + | 0.695505i | ||||
\(77\) | −5.43440e6 | −1.35654 | ||||||||
\(78\) | −9414.30 | + | 240360.i | −0.00224624 | + | 0.0573497i | ||||
\(79\) | 3.63759e6 | 0.830078 | 0.415039 | − | 0.909804i | \(-0.363768\pi\) | ||||
0.415039 | + | 0.909804i | \(0.363768\pi\) | |||||||
\(80\) | 5.52046e6 | + | 871585.i | 1.20548 | + | 0.190325i | ||||
\(81\) | 3.04051e6 | 0.635696 | ||||||||
\(82\) | −308440. | + | 7.87490e6i | −0.0617764 | + | 1.57724i | ||||
\(83\) | − | 3.67550e6i | − | 0.705575i | −0.935703 | − | 0.352787i | \(-0.885234\pi\) | ||
0.935703 | − | 0.352787i | \(-0.114766\pi\) | |||||||
\(84\) | 230559. | − | 2.93872e6i | 0.0424428 | − | 0.540980i | ||||
\(85\) | −1.35521e6 | −0.239355 | ||||||||
\(86\) | −102361. | + | 2.61341e6i | −0.0173536 | + | 0.443061i | ||||
\(87\) | 3.96117e6i | 0.644921i | ||||||||
\(88\) | −666783. | + | 5.65140e6i | −0.104303 | + | 0.884029i | ||||
\(89\) | − | 9.78887e6i | − | 1.47186i | −0.677055 | − | 0.735932i | \(-0.736744\pi\) | ||
0.677055 | − | 0.735932i | \(-0.263256\pi\) | |||||||
\(90\) | 7.36444e6 | + | 288447.i | 1.06486 | + | 0.0417078i | ||||
\(91\) | −1.76573e6 | −0.245629 | ||||||||
\(92\) | 617840. | − | 7.87504e6i | 0.0827215 | − | 1.05438i | ||||
\(93\) | −2.93516e6 | −0.378392 | ||||||||
\(94\) | 322423. | − | 8.23189e6i | 0.0400385 | − | 1.02224i | ||||
\(95\) | −6.75066e6 | + | 7.64458e6i | −0.807818 | + | 0.914789i | ||||
\(96\) | −3.02778e6 | − | 600337.i | −0.349281 | − | 0.0692542i | ||||
\(97\) | − | 9.38988e6i | − | 1.04462i | −0.852755 | − | 0.522311i | \(-0.825070\pi\) | ||
0.852755 | − | 0.522311i | \(-0.174930\pi\) | |||||||
\(98\) | 1.23114e7 | + | 482209.i | 1.32135 | + | 0.0517540i | ||||
\(99\) | 7.50428e6i | 0.777295i | ||||||||
\(100\) | 4.87910e6 | + | 382792.i | 0.487910 | + | 0.0382792i | ||||
\(101\) | −1.92683e7 | −1.86088 | −0.930439 | − | 0.366447i | \(-0.880574\pi\) | ||||
−0.930439 | + | 0.366447i | \(0.880574\pi\) | |||||||
\(102\) | 747913. | + | 29293.9i | 0.0697831 | + | 0.00273323i | ||||
\(103\) | 8.81693e6 | 0.795037 | 0.397518 | − | 0.917594i | \(-0.369872\pi\) | ||||
0.397518 | + | 0.917594i | \(0.369872\pi\) | |||||||
\(104\) | −216650. | + | 1.83624e6i | −0.0188861 | + | 0.160071i | ||||
\(105\) | − | 7.85567e6i | − | 0.662248i | ||||||
\(106\) | −740859. | + | 1.89151e7i | −0.0604178 | + | 1.54255i | ||||
\(107\) | −8.47923e6 | −0.669134 | −0.334567 | − | 0.942372i | \(-0.608590\pi\) | ||||
−0.334567 | + | 0.942372i | \(0.608590\pi\) | |||||||
\(108\) | −8.70532e6 | − | 682979.i | −0.664969 | − | 0.0521704i | ||||
\(109\) | − | 1.22891e6i | − | 0.0908926i | −0.998967 | − | 0.0454463i | \(-0.985529\pi\) | ||
0.998967 | − | 0.0454463i | \(-0.0144710\pi\) | |||||||
\(110\) | −593531. | + | 1.51537e7i | −0.0425176 | + | 1.08553i | ||||
\(111\) | − | 831383.i | − | 0.0576993i | ||||||
\(112\) | 3.53359e6 | − | 2.23811e7i | 0.237658 | − | 1.50528i | ||||
\(113\) | 904238.i | 0.0589533i | 0.999565 | + | 0.0294767i | \(0.00938407\pi\) | ||||
−0.999565 | + | 0.0294767i | \(0.990616\pi\) | |||||||
\(114\) | 3.89078e6 | − | 4.07296e6i | 0.245963 | − | 0.257479i | ||||
\(115\) | − | 2.10512e7i | − | 1.29073i | ||||||
\(116\) | −2.38150e6 | + | 3.03549e7i | −0.141660 | + | 1.80562i | ||||
\(117\) | 2.43828e6i | 0.140745i | ||||||||
\(118\) | 2.36584e7 | + | 926639.i | 1.32555 | + | 0.0519187i | ||||
\(119\) | 5.49432e6i | 0.298882i | ||||||||
\(120\) | −8.16936e6 | − | 963866.i | −0.431572 | − | 0.0509193i | ||||
\(121\) | 4.04579e6 | 0.207613 | ||||||||
\(122\) | −5.52083e6 | − | 216237.i | −0.275261 | − | 0.0107813i | ||||
\(123\) | − | 1.15997e7i | − | 0.562054i | ||||||
\(124\) | −2.24925e7 | − | 1.76465e6i | −1.05940 | − | 0.0831158i | ||||
\(125\) | −1.36071e7 | −0.623132 | ||||||||
\(126\) | 1.16942e6 | − | 2.98570e7i | 0.0520805 | − | 1.32969i | ||||
\(127\) | 1.67092e7 | 0.723841 | 0.361920 | − | 0.932209i | \(-0.382121\pi\) | ||||
0.361920 | + | 0.932209i | \(0.382121\pi\) | |||||||
\(128\) | −2.28413e7 | − | 6.42078e6i | −0.962687 | − | 0.270616i | ||||
\(129\) | − | 3.84954e6i | − | 0.157886i | ||||||
\(130\) | −192849. | + | 4.92370e6i | −0.00769867 | + | 0.196557i | ||||
\(131\) | − | 2.17373e7i | − | 0.844804i | −0.906409 | − | 0.422402i | \(-0.861187\pi\) | ||
0.906409 | − | 0.422402i | \(-0.138813\pi\) | |||||||
\(132\) | 655113. | − | 8.35013e6i | 0.0247918 | − | 0.315998i | ||||
\(133\) | 3.09927e7 | + | 2.73686e7i | 1.14230 | + | 1.00872i | ||||
\(134\) | −5.23891e6 | − | 205195.i | −0.188093 | − | 0.00736716i | ||||
\(135\) | −2.32707e7 | −0.814031 | ||||||||
\(136\) | 5.71372e6 | + | 674136.i | 0.194775 | + | 0.0229806i | ||||
\(137\) | 5.05332e7 | 1.67902 | 0.839508 | − | 0.543347i | \(-0.182843\pi\) | ||||
0.839508 | + | 0.543347i | \(0.182843\pi\) | |||||||
\(138\) | −455037. | + | 1.16177e7i | −0.0147391 | + | 0.376308i | ||||
\(139\) | 2.00717e7i | 0.633917i | 0.948439 | + | 0.316958i | \(0.102662\pi\) | ||||
−0.948439 | + | 0.316958i | \(0.897338\pi\) | |||||||
\(140\) | 4.72292e6 | − | 6.01988e7i | 0.145466 | − | 1.85413i | ||||
\(141\) | 1.21255e7i | 0.364279i | ||||||||
\(142\) | −4.48479e7 | − | 1.75658e6i | −1.31442 | − | 0.0514824i | ||||
\(143\) | −5.01719e6 | −0.143478 | ||||||||
\(144\) | −3.09057e7 | − | 4.87948e6i | −0.862523 | − | 0.136177i | ||||
\(145\) | 8.11434e7i | 2.21037i | ||||||||
\(146\) | 2.31590e6 | + | 90708.0i | 0.0615863 | + | 0.00241218i | ||||
\(147\) | −1.81347e7 | −0.470868 | ||||||||
\(148\) | 499837. | − | 6.37097e6i | 0.0126740 | − | 0.161544i | ||||
\(149\) | −7.42164e6 | −0.183801 | −0.0919006 | − | 0.995768i | \(-0.529294\pi\) | ||||
−0.0919006 | + | 0.995768i | \(0.529294\pi\) | |||||||
\(150\) | −7.19793e6 | − | 281925.i | −0.174136 | − | 0.00682047i | ||||
\(151\) | 4.07360e7 | 0.962851 | 0.481426 | − | 0.876487i | \(-0.340119\pi\) | ||||
0.481426 | + | 0.876487i | \(0.340119\pi\) | |||||||
\(152\) | 3.22642e7 | − | 2.88723e7i | 0.745191 | − | 0.666851i | ||||
\(153\) | 7.58703e6 | 0.171258 | ||||||||
\(154\) | 6.14361e7 | + | 2.40630e6i | 1.35550 | + | 0.0530917i | ||||
\(155\) | −6.01259e7 | −1.29688 | ||||||||
\(156\) | 212858. | − | 2.71311e6i | 0.00448905 | − | 0.0572178i | ||||
\(157\) | 5.41329e7 | 1.11638 | 0.558190 | − | 0.829713i | \(-0.311496\pi\) | ||||
0.558190 | + | 0.829713i | \(0.311496\pi\) | |||||||
\(158\) | −4.11231e7 | − | 1.61069e6i | −0.829442 | − | 0.0324872i | ||||
\(159\) | − | 2.78619e7i | − | 0.549693i | ||||||
\(160\) | −6.20231e7 | − | 1.22977e7i | −1.19711 | − | 0.237358i | ||||
\(161\) | −8.53461e7 | −1.61173 | ||||||||
\(162\) | −3.43731e7 | − | 1.34631e6i | −0.635209 | − | 0.0248796i | ||||
\(163\) | 4.49136e7i | 0.812310i | 0.913804 | + | 0.406155i | \(0.133131\pi\) | ||||
−0.913804 | + | 0.406155i | \(0.866869\pi\) | |||||||
\(164\) | 6.97386e6 | − | 8.88895e7i | 0.123458 | − | 1.57361i | ||||
\(165\) | − | 2.23212e7i | − | 0.386834i | ||||||
\(166\) | −1.62748e6 | + | 4.15517e7i | −0.0276144 | + | 0.705034i | ||||
\(167\) | −3.74649e7 | −0.622468 | −0.311234 | − | 0.950333i | \(-0.600742\pi\) | ||||
−0.311234 | + | 0.950333i | \(0.600742\pi\) | |||||||
\(168\) | −3.90771e6 | + | 3.31203e7i | −0.0635829 | + | 0.538904i | ||||
\(169\) | 6.11183e7 | 0.974020 | ||||||||
\(170\) | 1.53208e7 | + | 600076.i | 0.239171 | + | 0.00936774i | ||||
\(171\) | 3.77929e7 | − | 4.27974e7i | 0.577994 | − | 0.654532i | ||||
\(172\) | 2.31439e6 | − | 2.94994e7i | 0.0346806 | − | 0.442042i | ||||
\(173\) | − | 1.03878e8i | − | 1.52532i | −0.646799 | − | 0.762660i | \(-0.723893\pi\) | ||
0.646799 | − | 0.762660i | \(-0.276107\pi\) | |||||||
\(174\) | 1.75397e6 | − | 4.47812e7i | 0.0252406 | − | 0.644427i | ||||
\(175\) | − | 5.28775e7i | − | 0.745826i | ||||||
\(176\) | 1.00404e7 | − | 6.35941e7i | 0.138821 | − | 0.879270i | ||||
\(177\) | −3.48486e7 | −0.472366 | ||||||||
\(178\) | −4.33442e6 | + | 1.10664e8i | −0.0576051 | + | 1.47074i | ||||
\(179\) | 5.04771e7 | 0.657823 | 0.328911 | − | 0.944361i | \(-0.393318\pi\) | ||||
0.328911 | + | 0.944361i | \(0.393318\pi\) | |||||||
\(180\) | −8.31276e7 | − | 6.52181e6i | −1.06241 | − | 0.0833517i | ||||
\(181\) | 7.05772e7i | 0.884686i | 0.896846 | + | 0.442343i | \(0.145853\pi\) | ||||
−0.896846 | + | 0.442343i | \(0.854147\pi\) | |||||||
\(182\) | 1.99617e7 | + | 781850.i | 0.245441 | + | 0.00961333i | ||||
\(183\) | 8.13214e6 | 0.0980903 | ||||||||
\(184\) | −1.04717e7 | + | 8.87541e7i | −0.123924 | + | 1.05033i | ||||
\(185\) | − | 1.70306e7i | − | 0.197756i | ||||||
\(186\) | 3.31821e7 | + | 1.29966e6i | 0.378102 | + | 0.0148093i | ||||
\(187\) | 1.56117e7i | 0.174584i | ||||||||
\(188\) | −7.29001e6 | + | 9.29191e7i | −0.0800157 | + | 1.01989i | ||||
\(189\) | 9.43443e7i | 1.01648i | ||||||||
\(190\) | 7.97014e7 | − | 8.34332e7i | 0.843002 | − | 0.882473i | ||||
\(191\) | 9.92474e7i | 1.03063i | 0.857001 | + | 0.515314i | \(0.172325\pi\) | ||||
−0.857001 | + | 0.515314i | \(0.827675\pi\) | |||||||
\(192\) | 3.39634e7 | + | 8.12751e6i | 0.346303 | + | 0.0828711i | ||||
\(193\) | 1.52590e8i | 1.52784i | 0.645313 | + | 0.763918i | \(0.276727\pi\) | ||||
−0.645313 | + | 0.763918i | \(0.723273\pi\) | |||||||
\(194\) | −4.15775e6 | + | 1.06153e8i | −0.0408839 | + | 1.04382i | ||||
\(195\) | − | 7.25257e6i | − | 0.0700440i | ||||||
\(196\) | −1.38968e8 | − | 1.09028e7i | −1.31831 | − | 0.103429i | ||||
\(197\) | 1.15293e8 | 1.07441 | 0.537207 | − | 0.843450i | \(-0.319479\pi\) | ||||
0.537207 | + | 0.843450i | \(0.319479\pi\) | |||||||
\(198\) | 3.32282e6 | − | 8.48362e7i | 0.0304214 | − | 0.776699i | ||||
\(199\) | 7.81895e7i | 0.703336i | 0.936125 | + | 0.351668i | \(0.114385\pi\) | ||||
−0.936125 | + | 0.351668i | \(0.885615\pi\) | |||||||
\(200\) | −5.49890e7 | − | 6.48790e6i | −0.486038 | − | 0.0573455i | ||||
\(201\) | 7.71687e6 | 0.0670278 | ||||||||
\(202\) | 2.17829e8 | + | 8.53180e6i | 1.85945 | + | 0.0728301i | ||||
\(203\) | 3.28972e8 | 2.76009 | ||||||||
\(204\) | −8.44221e6 | − | 662337.i | −0.0696227 | − | 0.00546227i | ||||
\(205\) | − | 2.37616e8i | − | 1.92636i | ||||||
\(206\) | −9.96757e7 | − | 3.90405e6i | −0.794427 | − | 0.0311158i | ||||
\(207\) | 1.17853e8i | 0.923517i | ||||||||
\(208\) | 3.26231e6 | − | 2.06629e7i | 0.0251364 | − | 0.159209i | ||||
\(209\) | 8.80633e7 | + | 7.77655e7i | 0.667241 | + | 0.589217i | ||||
\(210\) | −3.47841e6 | + | 8.88086e7i | −0.0259187 | + | 0.661741i | ||||
\(211\) | −2.29615e8 | −1.68272 | −0.841359 | − | 0.540476i | \(-0.818244\pi\) | ||||
−0.841359 | + | 0.540476i | \(0.818244\pi\) | |||||||
\(212\) | 1.67509e7 | − | 2.13508e8i | 0.120743 | − | 1.53900i | ||||
\(213\) | 6.60607e7 | 0.468397 | ||||||||
\(214\) | 9.58581e7 | + | 3.75452e6i | 0.668622 | + | 0.0261883i | ||||
\(215\) | − | 7.88566e7i | − | 0.541132i | ||||||
\(216\) | 9.81116e7 | + | 1.15757e7i | 0.662418 | + | 0.0781557i | ||||
\(217\) | 2.43763e8i | 1.61942i | ||||||||
\(218\) | −544151. | + | 1.38929e7i | −0.00355731 | + | 0.0908230i | ||||
\(219\) | −3.41130e6 | −0.0219465 | ||||||||
\(220\) | 1.34198e7 | − | 1.71050e8i | 0.0849701 | − | 1.08304i | ||||
\(221\) | 5.07251e6i | 0.0316119i | ||||||||
\(222\) | −368128. | + | 9.39882e6i | −0.00225821 | + | 0.0576551i | ||||
\(223\) | 7.73459e7 | 0.467057 | 0.233529 | − | 0.972350i | \(-0.424973\pi\) | ||||
0.233529 | + | 0.972350i | \(0.424973\pi\) | |||||||
\(224\) | −4.98575e7 | + | 2.51455e8i | −0.296389 | + | 1.49483i | ||||
\(225\) | −7.30177e7 | −0.427356 | ||||||||
\(226\) | 400388. | − | 1.02224e7i | 0.00230729 | − | 0.0589082i | ||||
\(227\) | −1.80672e8 | −1.02518 | −0.512589 | − | 0.858634i | \(-0.671314\pi\) | ||||
−0.512589 | + | 0.858634i | \(0.671314\pi\) | |||||||
\(228\) | −4.57889e7 | + | 4.43221e7i | −0.255852 | + | 0.247656i | ||||
\(229\) | 1.03804e8 | 0.571204 | 0.285602 | − | 0.958348i | \(-0.407806\pi\) | ||||
0.285602 | + | 0.958348i | \(0.407806\pi\) | |||||||
\(230\) | −9.32129e6 | + | 2.37985e8i | −0.0505159 | + | 1.28974i | ||||
\(231\) | −9.04949e7 | −0.483039 | ||||||||
\(232\) | 4.03638e7 | − | 3.42109e8i | 0.212219 | − | 1.79869i | ||||
\(233\) | −1.12943e8 | −0.584942 | −0.292471 | − | 0.956274i | \(-0.594477\pi\) | ||||
−0.292471 | + | 0.956274i | \(0.594477\pi\) | |||||||
\(234\) | 1.07965e6 | − | 2.75648e7i | 0.00550840 | − | 0.140637i | ||||
\(235\) | 2.48387e8i | 1.24851i | ||||||||
\(236\) | −2.67048e8 | − | 2.09514e7i | −1.32251 | − | 0.103758i | ||||
\(237\) | 6.05741e7 | 0.295575 | ||||||||
\(238\) | 2.43283e6 | − | 6.21135e7i | 0.0116975 | − | 0.298653i | ||||
\(239\) | − | 4.08044e8i | − | 1.93337i | −0.255971 | − | 0.966685i | \(-0.582395\pi\) | ||
0.255971 | − | 0.966685i | \(-0.417605\pi\) | |||||||
\(240\) | 9.19281e7 | + | 1.45139e7i | 0.429249 | + | 0.0677709i | ||||
\(241\) | − | 2.81664e8i | − | 1.29620i | −0.761555 | − | 0.648100i | \(-0.775564\pi\) | ||
0.761555 | − | 0.648100i | \(-0.224436\pi\) | |||||||
\(242\) | −4.57378e7 | − | 1.79144e6i | −0.207454 | − | 0.00812545i | ||||
\(243\) | 1.99827e8 | 0.893372 | ||||||||
\(244\) | 6.23174e7 | + | 4.88914e6i | 0.274628 | + | 0.0215461i | ||||
\(245\) | −3.71483e8 | −1.61383 | ||||||||
\(246\) | −5.13622e6 | + | 1.31135e8i | −0.0219974 | + | 0.561623i | ||||
\(247\) | 2.86134e7 | + | 2.52674e7i | 0.120817 | + | 0.106690i | ||||
\(248\) | 2.53497e8 | + | 2.99089e7i | 1.05534 | + | 0.124515i | ||||
\(249\) | − | 6.12053e7i | − | 0.251242i | ||||||
\(250\) | 1.53829e8 | + | 6.02508e6i | 0.622654 | + | 0.0243878i | ||||
\(251\) | 6.78510e7i | 0.270831i | 0.990789 | + | 0.135416i | \(0.0432369\pi\) | ||||
−0.990789 | + | 0.135416i | \(0.956763\pi\) | |||||||
\(252\) | −2.64408e7 | + | 3.37017e8i | −0.104081 | + | 1.32663i | ||||
\(253\) | −2.42504e8 | −0.941449 | ||||||||
\(254\) | −1.88898e8 | − | 7.39868e6i | −0.723286 | − | 0.0283293i | ||||
\(255\) | −2.25674e7 | −0.0852295 | ||||||||
\(256\) | 2.55378e8 | + | 8.27011e7i | 0.951359 | + | 0.308086i | ||||
\(257\) | 1.35735e7i | 0.0498799i | 0.999689 | + | 0.0249400i | \(0.00793946\pi\) | ||||
−0.999689 | + | 0.0249400i | \(0.992061\pi\) | |||||||
\(258\) | −1.70454e6 | + | 4.35192e7i | −0.00617928 | + | 0.157765i | ||||
\(259\) | −6.90457e7 | −0.246938 | ||||||||
\(260\) | 4.36033e6 | − | 5.55772e7i | 0.0153855 | − | 0.196106i | ||||
\(261\) | − | 4.54273e8i | − | 1.58152i | ||||||
\(262\) | −9.62506e6 | + | 2.45741e8i | −0.0330635 | + | 0.844156i | ||||
\(263\) | 4.95451e7i | 0.167940i | 0.996468 | + | 0.0839702i | \(0.0267601\pi\) | ||||
−0.996468 | + | 0.0839702i | \(0.973240\pi\) | |||||||
\(264\) | −1.11034e7 | + | 9.41085e7i | −0.0371402 | + | 0.314786i | ||||
\(265\) | − | 5.70742e8i | − | 1.88399i | ||||||
\(266\) | −3.38256e8 | − | 3.23126e8i | −1.10194 | − | 1.05266i | ||||
\(267\) | − | 1.63007e8i | − | 0.524102i | ||||||
\(268\) | 5.91352e7 | + | 4.63947e6i | 0.187661 | + | 0.0147230i | ||||
\(269\) | 3.42904e8i | 1.07409i | 0.843555 | + | 0.537043i | \(0.180459\pi\) | ||||
−0.843555 | + | 0.537043i | \(0.819541\pi\) | |||||||
\(270\) | 2.63076e8 | + | 1.03040e7i | 0.813408 | + | 0.0318592i | ||||
\(271\) | − | 3.03598e8i | − | 0.926629i | −0.886194 | − | 0.463314i | \(-0.846660\pi\) | ||
0.886194 | − | 0.463314i | \(-0.153340\pi\) | |||||||
\(272\) | −6.42953e7 | − | 1.01511e7i | −0.193726 | − | 0.0305860i | ||||
\(273\) | −2.94034e7 | −0.0874639 | ||||||||
\(274\) | −5.71280e8 | − | 2.23756e7i | −1.67773 | − | 0.0657125i | ||||
\(275\) | − | 1.50247e8i | − | 0.435653i | ||||||
\(276\) | 1.02884e7 | − | 1.31137e8i | 0.0294555 | − | 0.375443i | ||||
\(277\) | −2.85659e8 | −0.807547 | −0.403774 | − | 0.914859i | \(-0.632302\pi\) | ||||
−0.403774 | + | 0.914859i | \(0.632302\pi\) | |||||||
\(278\) | 8.88755e6 | − | 2.26911e8i | 0.0248099 | − | 0.633431i | ||||
\(279\) | 3.36609e8 | 0.927920 | ||||||||
\(280\) | −8.00482e7 | + | 6.78458e8i | −0.217921 | + | 1.84701i | ||||
\(281\) | − | 2.23933e8i | − | 0.602068i | −0.953613 | − | 0.301034i | \(-0.902668\pi\) | ||
0.953613 | − | 0.301034i | \(-0.0973318\pi\) | |||||||
\(282\) | 5.36907e6 | − | 1.37080e8i | 0.0142570 | − | 0.363999i | ||||
\(283\) | 2.12357e8i | 0.556946i | 0.960444 | + | 0.278473i | \(0.0898283\pi\) | ||||
−0.960444 | + | 0.278473i | \(0.910172\pi\) | |||||||
\(284\) | 5.06230e8 | + | 3.97165e7i | 1.31139 | + | 0.102886i | ||||
\(285\) | −1.12414e8 | + | 1.27299e8i | −0.287648 | + | 0.325739i | ||||
\(286\) | 5.67195e7 | + | 2.22156e6i | 0.143368 | + | 0.00561536i | ||||
\(287\) | −9.63343e8 | −2.40544 | ||||||||
\(288\) | 3.47230e8 | + | 6.88475e7i | 0.856532 | + | 0.169830i | ||||
\(289\) | −3.94555e8 | −0.961535 | ||||||||
\(290\) | 3.59295e7 | − | 9.17329e8i | 0.0865084 | − | 2.20868i | ||||
\(291\) | − | 1.56363e8i | − | 0.371970i | ||||||
\(292\) | −2.61411e7 | − | 2.05091e6i | −0.0614447 | − | 0.00482067i | ||||
\(293\) | − | 5.27037e8i | − | 1.22407i | −0.790832 | − | 0.612033i | \(-0.790352\pi\) | ||
0.790832 | − | 0.612033i | \(-0.209648\pi\) | |||||||
\(294\) | 2.05013e8 | + | 8.02986e6i | 0.470507 | + | 0.0184286i | ||||
\(295\) | −7.13862e8 | −1.61896 | ||||||||
\(296\) | −8.47168e6 | + | 7.18028e7i | −0.0189867 | + | 0.160924i | ||||
\(297\) | 2.68071e8i | 0.593749i | ||||||||
\(298\) | 8.39020e7 | + | 3.28623e6i | 0.183660 | + | 0.00719352i | ||||
\(299\) | −7.87939e7 | −0.170468 | ||||||||
\(300\) | 8.12480e7 | + | 6.37435e6i | 0.173735 | + | 0.0136305i | ||||
\(301\) | −3.19701e8 | −0.675711 | ||||||||
\(302\) | −4.60522e8 | − | 1.80375e7i | −0.962114 | − | 0.0376836i | ||||
\(303\) | −3.20860e8 | −0.662623 | ||||||||
\(304\) | −3.77532e8 | + | 3.12116e8i | −0.770719 | + | 0.637175i | ||||
\(305\) | 1.66584e8 | 0.336190 | ||||||||
\(306\) | −8.57716e7 | − | 3.35946e6i | −0.171127 | − | 0.00670262i | ||||
\(307\) | 4.84311e8 | 0.955300 | 0.477650 | − | 0.878550i | \(-0.341489\pi\) | ||||
0.477650 | + | 0.878550i | \(0.341489\pi\) | |||||||
\(308\) | −6.93472e8 | − | 5.44066e7i | −1.35239 | − | 0.106102i | ||||
\(309\) | 1.46822e8 | 0.283097 | ||||||||
\(310\) | 6.79725e8 | + | 2.66232e7i | 1.29589 | + | 0.0507567i | ||||
\(311\) | − | 5.70320e8i | − | 1.07512i | −0.843225 | − | 0.537561i | \(-0.819346\pi\) | ||
0.843225 | − | 0.537561i | \(-0.180654\pi\) | |||||||
\(312\) | −3.60771e6 | + | 3.05776e7i | −0.00672497 | + | 0.0569983i | ||||
\(313\) | 6.70728e8 | 1.23635 | 0.618175 | − | 0.786041i | \(-0.287872\pi\) | ||||
0.618175 | + | 0.786041i | \(0.287872\pi\) | |||||||
\(314\) | −6.11974e8 | − | 2.39695e7i | −1.11553 | − | 0.0436924i | ||||
\(315\) | 9.00899e8i | 1.62401i | ||||||||
\(316\) | 4.64185e8 | + | 3.64178e7i | 0.827536 | + | 0.0649246i | ||||
\(317\) | 7.09547e8i | 1.25105i | 0.780205 | + | 0.625524i | \(0.215115\pi\) | ||||
−0.780205 | + | 0.625524i | \(0.784885\pi\) | |||||||
\(318\) | −1.23370e7 | + | 3.14980e8i | −0.0215136 | + | 0.549272i | ||||
\(319\) | 9.34747e8 | 1.61223 | ||||||||
\(320\) | 6.95729e8 | + | 1.66489e8i | 1.18690 | + | 0.284028i | ||||
\(321\) | −1.41198e8 | −0.238266 | ||||||||
\(322\) | 9.64841e8 | + | 3.77904e7i | 1.61050 | + | 0.0630792i | ||||
\(323\) | 7.86230e7 | − | 8.90343e7i | 0.129820 | − | 0.147011i | ||||
\(324\) | 3.87994e8 | + | 3.04402e7i | 0.633749 | + | 0.0497210i | ||||
\(325\) | − | 4.88180e7i | − | 0.0788838i | ||||||
\(326\) | 1.98873e7 | − | 5.07751e8i | 0.0317918 | − | 0.811687i | ||||
\(327\) | − | 2.04642e7i | − | 0.0323651i | ||||||
\(328\) | −1.18199e8 | + | 1.00181e9i | −0.184951 | + | 1.56757i | ||||
\(329\) | 1.00701e9 | 1.55901 | ||||||||
\(330\) | −9.88362e6 | + | 2.52342e8i | −0.0151397 | + | 0.386537i | ||||
\(331\) | 9.88943e8 | 1.49890 | 0.749451 | − | 0.662060i | \(-0.230317\pi\) | ||||
0.749451 | + | 0.662060i | \(0.230317\pi\) | |||||||
\(332\) | 3.67974e7 | − | 4.69023e8i | 0.0551866 | − | 0.703413i | ||||
\(333\) | 9.53441e7i | 0.141494i | ||||||||
\(334\) | 4.23542e8 | + | 1.65891e7i | 0.621991 | + | 0.0243619i | ||||
\(335\) | 1.58078e8 | 0.229728 | ||||||||
\(336\) | 5.88422e7 | − | 3.72696e8i | 0.0846255 | − | 0.536003i | ||||
\(337\) | − | 1.89407e8i | − | 0.269582i | −0.990874 | − | 0.134791i | \(-0.956964\pi\) | ||
0.990874 | − | 0.134791i | \(-0.0430363\pi\) | |||||||
\(338\) | −6.90945e8 | − | 2.70626e7i | −0.973274 | − | 0.0381207i | ||||
\(339\) | 1.50576e7i | 0.0209921i | ||||||||
\(340\) | −1.72936e8 | − | 1.35678e7i | −0.238621 | − | 0.0187211i | ||||
\(341\) | 6.92632e8i | 0.945937i | ||||||||
\(342\) | −4.46200e8 | + | 4.67092e8i | −0.603168 | + | 0.631410i | ||||
\(343\) | 3.67147e8i | 0.491259i | ||||||||
\(344\) | −3.92263e7 | + | 3.32467e8i | −0.0519544 | + | 0.440346i | ||||
\(345\) | − | 3.50550e8i | − | 0.459604i | ||||||
\(346\) | −4.59961e7 | + | 1.17434e9i | −0.0596973 | + | 1.52415i | ||||
\(347\) | 1.24000e9i | 1.59320i | 0.604510 | + | 0.796598i | \(0.293369\pi\) | ||||
−0.604510 | + | 0.796598i | \(0.706631\pi\) | |||||||
\(348\) | −3.96574e7 | + | 5.05477e8i | −0.0504425 | + | 0.642945i | ||||
\(349\) | −8.25219e8 | −1.03915 | −0.519577 | − | 0.854423i | \(-0.673911\pi\) | ||||
−0.519577 | + | 0.854423i | \(0.673911\pi\) | |||||||
\(350\) | −2.34136e7 | + | 5.97782e8i | −0.0291898 | + | 0.745255i | ||||
\(351\) | 8.71013e7i | 0.107510i | ||||||||
\(352\) | −1.41666e8 | + | 7.14488e8i | −0.173128 | + | 0.873163i | ||||
\(353\) | 5.70208e7 | 0.0689957 | 0.0344979 | − | 0.999405i | \(-0.489017\pi\) | ||||
0.0344979 | + | 0.999405i | \(0.489017\pi\) | |||||||
\(354\) | 3.93965e8 | + | 1.54306e7i | 0.472004 | + | 0.0184872i | ||||
\(355\) | 1.35323e9 | 1.60536 | ||||||||
\(356\) | 9.80016e7 | − | 1.24914e9i | 0.115122 | − | 1.46735i | ||||
\(357\) | 9.14928e7i | 0.106426i | ||||||||
\(358\) | −5.70646e8 | − | 2.23508e7i | −0.657319 | − | 0.0257456i | ||||
\(359\) | − | 1.45777e9i | − | 1.66287i | −0.555624 | − | 0.831434i | \(-0.687521\pi\) | ||
0.555624 | − | 0.831434i | \(-0.312479\pi\) | |||||||
\(360\) | 9.36873e8 | + | 1.10537e8i | 1.05833 | + | 0.124868i | ||||
\(361\) | −1.10590e8 | − | 8.87004e8i | −0.123720 | − | 0.992317i | ||||
\(362\) | 3.12509e7 | − | 7.97878e8i | 0.0346244 | − | 0.884009i | ||||
\(363\) | 6.73714e7 | 0.0739269 | ||||||||
\(364\) | −2.25322e8 | − | 1.76777e7i | −0.244877 | − | 0.0192119i | ||||
\(365\) | −6.98794e7 | −0.0752184 | ||||||||
\(366\) | −9.19342e7 | − | 3.60083e6i | −0.0980151 | − | 0.00383901i | ||||
\(367\) | 1.02185e9i | 1.07908i | 0.841958 | + | 0.539542i | \(0.181403\pi\) | ||||
−0.841958 | + | 0.539542i | \(0.818597\pi\) | |||||||
\(368\) | 1.57682e8 | − | 9.98732e8i | 0.164936 | − | 1.04468i | ||||
\(369\) | 1.33027e9i | 1.37831i | ||||||||
\(370\) | −7.54099e6 | + | 1.92532e8i | −0.00773967 | + | 0.197604i | ||||
\(371\) | −2.31391e9 | −2.35254 | ||||||||
\(372\) | −3.74550e8 | − | 2.93855e7i | −0.377233 | − | 0.0295959i | ||||
\(373\) | − | 8.51247e8i | − | 0.849326i | −0.905351 | − | 0.424663i | \(-0.860393\pi\) | ||
0.905351 | − | 0.424663i | \(-0.139607\pi\) | |||||||
\(374\) | 6.91269e6 | − | 1.76490e8i | 0.00683277 | − | 0.174450i | ||||
\(375\) | −2.26588e8 | −0.221885 | ||||||||
\(376\) | 1.23558e8 | − | 1.04723e9i | 0.119870 | − | 1.01598i | ||||
\(377\) | 3.03716e8 | 0.291926 | ||||||||
\(378\) | 4.17747e7 | − | 1.06657e9i | 0.0397825 | − | 1.01570i | ||||
\(379\) | −2.22179e8 | −0.209636 | −0.104818 | − | 0.994491i | \(-0.533426\pi\) | ||||
−0.104818 | + | 0.994491i | \(0.533426\pi\) | |||||||
\(380\) | −9.37971e8 | + | 9.07925e8i | −0.876893 | + | 0.848804i | ||||
\(381\) | 2.78246e8 | 0.257746 | ||||||||
\(382\) | 4.39458e7 | − | 1.12200e9i | 0.0403362 | − | 1.02984i | ||||
\(383\) | −7.90357e8 | −0.718832 | −0.359416 | − | 0.933177i | \(-0.617024\pi\) | ||||
−0.359416 | + | 0.933177i | \(0.617024\pi\) | |||||||
\(384\) | −3.80358e8 | − | 1.06920e8i | −0.342794 | − | 0.0963610i | ||||
\(385\) | −1.85376e9 | −1.65554 | ||||||||
\(386\) | 6.75656e7 | − | 1.72504e9i | 0.0597957 | − | 1.52667i | ||||
\(387\) | 4.41470e8i | 0.387180i | ||||||||
\(388\) | 9.40070e7 | − | 1.19822e9i | 0.0817051 | − | 1.04142i | ||||
\(389\) | 1.68344e9 | 1.45002 | 0.725012 | − | 0.688736i | \(-0.241834\pi\) | ||||
0.725012 | + | 0.688736i | \(0.241834\pi\) | |||||||
\(390\) | −3.21137e6 | + | 8.19906e7i | −0.00274135 | + | 0.0699903i | ||||
\(391\) | 2.45178e8i | 0.207426i | ||||||||
\(392\) | 1.56621e9 | + | 1.84790e8i | 1.31325 | + | 0.154945i | ||||
\(393\) | − | 3.61975e8i | − | 0.300818i | ||||||
\(394\) | −1.30339e9 | − | 5.10507e7i | −1.07359 | − | 0.0420499i | ||||
\(395\) | 1.24084e9 | 1.01304 | ||||||||
\(396\) | −7.51293e7 | + | 9.57605e8i | −0.0607961 | + | 0.774913i | ||||
\(397\) | 1.69708e9 | 1.36125 | 0.680623 | − | 0.732634i | \(-0.261709\pi\) | ||||
0.680623 | + | 0.732634i | \(0.261709\pi\) | |||||||
\(398\) | 3.46216e7 | − | 8.83936e8i | 0.0275268 | − | 0.702797i | ||||
\(399\) | 5.16099e8 | + | 4.55748e8i | 0.406750 | + | 0.359186i | ||||
\(400\) | 6.18780e8 | + | 9.76945e7i | 0.483422 | + | 0.0763238i | ||||
\(401\) | 1.20644e9i | 0.934328i | 0.884171 | + | 0.467164i | \(0.154724\pi\) | ||||
−0.884171 | + | 0.467164i | \(0.845276\pi\) | |||||||
\(402\) | −8.72396e7 | − | 3.41696e6i | −0.0669765 | − | 0.00262330i | ||||
\(403\) | 2.25049e8i | 0.171281i | ||||||||
\(404\) | −2.45878e9 | − | 1.92905e8i | −1.85518 | − | 0.145549i | ||||
\(405\) | 1.03717e9 | 0.775812 | ||||||||
\(406\) | −3.71904e9 | − | 1.45666e8i | −2.75797 | − | 0.108023i | ||||
\(407\) | −1.96187e8 | −0.144242 | ||||||||
\(408\) | 9.51463e7 | + | 1.12259e7i | 0.0693555 | + | 0.00818295i | ||||
\(409\) | 8.49225e8i | 0.613750i | 0.951750 | + | 0.306875i | \(0.0992833\pi\) | ||||
−0.951750 | + | 0.306875i | \(0.900717\pi\) | |||||||
\(410\) | −1.05214e8 | + | 2.68625e9i | −0.0753928 | + | 1.92488i | ||||
\(411\) | 8.41491e8 | 0.597865 | ||||||||
\(412\) | 1.12511e9 | + | 8.82709e7i | 0.792601 | + | 0.0621838i | ||||
\(413\) | 2.89415e9i | 2.02160i | ||||||||
\(414\) | 5.21843e7 | − | 1.33233e9i | 0.0361442 | − | 0.922810i | ||||
\(415\) | − | 1.25377e9i | − | 0.861093i | ||||||
\(416\) | −4.60298e7 | + | 2.32150e8i | −0.0313482 | + | 0.158104i | ||||
\(417\) | 3.34239e8i | 0.225726i | ||||||||
\(418\) | −9.61125e8 | − | 9.18136e8i | −0.643669 | − | 0.614879i | ||||
\(419\) | − | 2.09310e9i | − | 1.39008i | −0.718969 | − | 0.695042i | \(-0.755386\pi\) | ||
0.718969 | − | 0.695042i | \(-0.244614\pi\) | |||||||
\(420\) | 7.86472e7 | − | 1.00245e9i | 0.0517978 | − | 0.660219i | ||||
\(421\) | − | 6.68196e8i | − | 0.436432i | −0.975900 | − | 0.218216i | \(-0.929976\pi\) | ||
0.975900 | − | 0.218216i | \(-0.0700237\pi\) | |||||||
\(422\) | 2.59581e9 | + | 1.01671e8i | 1.68143 | + | 0.0658574i | ||||
\(423\) | − | 1.39057e9i | − | 0.893310i | ||||||
\(424\) | −2.83909e8 | + | 2.40630e9i | −0.180883 | + | 1.53310i | ||||
\(425\) | −1.51904e8 | −0.0959858 | ||||||||
\(426\) | −7.46819e8 | − | 2.92510e7i | −0.468039 | − | 0.0183319i | ||||
\(427\) | − | 6.75367e8i | − | 0.419800i | ||||||
\(428\) | −1.08202e9 | − | 8.48901e7i | −0.667085 | − | 0.0523364i | ||||
\(429\) | −8.35474e7 | −0.0510896 | ||||||||
\(430\) | −3.49169e7 | + | 8.91477e8i | −0.0211786 | + | 0.540717i | ||||
\(431\) | 9.56966e8 | 0.575740 | 0.287870 | − | 0.957670i | \(-0.407053\pi\) | ||||
0.287870 | + | 0.957670i | \(0.407053\pi\) | |||||||
\(432\) | −1.10403e9 | − | 1.74307e8i | −0.658852 | − | 0.104021i | ||||
\(433\) | 2.67539e9i | 1.58372i | 0.610700 | + | 0.791862i | \(0.290888\pi\) | ||||
−0.610700 | + | 0.791862i | \(0.709112\pi\) | |||||||
\(434\) | 1.07936e8 | − | 2.75575e9i | 0.0633799 | − | 1.61818i | ||||
\(435\) | 1.35122e9i | 0.787070i | ||||||||
\(436\) | 1.23033e7 | − | 1.56819e8i | 0.00710917 | − | 0.0906142i | ||||
\(437\) | 1.38302e9 | + | 1.22129e9i | 0.792761 | + | 0.700059i | ||||
\(438\) | 3.85649e7 | + | 1.51049e6i | 0.0219297 | + | 0.000858932i | ||||
\(439\) | −2.69019e9 | −1.51760 | −0.758801 | − | 0.651323i | \(-0.774214\pi\) | ||||
−0.758801 | + | 0.651323i | \(0.774214\pi\) | |||||||
\(440\) | −2.27450e8 | + | 1.92778e9i | −0.127292 | + | 1.07888i | ||||
\(441\) | 2.07971e9 | 1.15470 | ||||||||
\(442\) | 2.24606e6 | − | 5.73449e7i | 0.00123721 | − | 0.0315876i | ||||
\(443\) | − | 9.26357e8i | − | 0.506251i | −0.967433 | − | 0.253125i | \(-0.918542\pi\) | ||
0.967433 | − | 0.253125i | \(-0.0814585\pi\) | |||||||
\(444\) | 8.32341e6 | − | 1.06091e8i | 0.00451295 | − | 0.0575226i | ||||
\(445\) | − | 3.33914e9i | − | 1.79628i | ||||||
\(446\) | −8.74399e8 | − | 3.42480e7i | −0.466700 | − | 0.0182795i | ||||
\(447\) | −1.23587e8 | −0.0654480 | ||||||||
\(448\) | 6.74983e8 | − | 2.82063e9i | 0.354666 | − | 1.48208i | ||||
\(449\) | − | 1.13367e9i | − | 0.591048i | −0.955335 | − | 0.295524i | \(-0.904506\pi\) | ||
0.955335 | − | 0.295524i | \(-0.0954942\pi\) | |||||||
\(450\) | 8.25468e8 | + | 3.23315e7i | 0.427028 | + | 0.0167256i | ||||
\(451\) | −2.73726e9 | −1.40507 | ||||||||
\(452\) | −9.05280e6 | + | 1.15388e8i | −0.00461104 | + | 0.0587727i | ||||
\(453\) | 6.78346e8 | 0.342853 | ||||||||
\(454\) | 2.04250e9 | + | 7.99997e7i | 1.02439 | + | 0.0401229i | ||||
\(455\) | −6.02320e8 | −0.299770 | ||||||||
\(456\) | 5.37271e8 | − | 4.80788e8i | 0.265348 | − | 0.237453i | ||||
\(457\) | −2.33566e8 | −0.114473 | −0.0572365 | − | 0.998361i | \(-0.518229\pi\) | ||||
−0.0572365 | + | 0.998361i | \(0.518229\pi\) | |||||||
\(458\) | −1.17351e9 | − | 4.59636e7i | −0.570766 | − | 0.0223555i | ||||
\(459\) | 2.71027e8 | 0.130818 | ||||||||
\(460\) | 2.10755e8 | − | 2.68630e9i | 0.100954 | − | 1.28678i | ||||
\(461\) | −3.21670e9 | −1.52918 | −0.764588 | − | 0.644519i | \(-0.777058\pi\) | ||||
−0.764588 | + | 0.644519i | \(0.777058\pi\) | |||||||
\(462\) | 1.02305e9 | + | 4.00703e7i | 0.482669 | + | 0.0189049i | ||||
\(463\) | − | 7.50901e8i | − | 0.351600i | −0.984426 | − | 0.175800i | \(-0.943749\pi\) | ||
0.984426 | − | 0.175800i | \(-0.0562513\pi\) | |||||||
\(464\) | −6.07797e8 | + | 3.84968e9i | −0.282453 | + | 1.78900i | ||||
\(465\) | −1.00123e9 | −0.461795 | ||||||||
\(466\) | 1.27682e9 | + | 5.00099e7i | 0.584493 | + | 0.0228932i | ||||
\(467\) | − | 2.12548e9i | − | 0.965712i | −0.875700 | − | 0.482856i | \(-0.839600\pi\) | ||
0.875700 | − | 0.482856i | \(-0.160400\pi\) | |||||||
\(468\) | −2.44109e7 | + | 3.11143e8i | −0.0110084 | + | 0.140314i | ||||
\(469\) | − | 6.40880e8i | − | 0.286861i | ||||||
\(470\) | 1.09984e8 | − | 2.80803e9i | 0.0488636 | − | 1.24755i | ||||
\(471\) | 9.01434e8 | 0.397522 | ||||||||
\(472\) | 3.00972e9 | + | 3.55103e8i | 1.31743 | + | 0.155438i | ||||
\(473\) | −9.08404e8 | −0.394698 | ||||||||
\(474\) | −6.84792e8 | − | 2.68216e7i | −0.295348 | − | 0.0115681i | ||||
\(475\) | −7.56670e8 | + | 8.56868e8i | −0.323951 | + | 0.366848i | ||||
\(476\) | −5.50065e7 | + | 7.01119e8i | −0.0233771 | + | 0.297966i | ||||
\(477\) | 3.19524e9i | 1.34800i | ||||||||
\(478\) | −1.80678e8 | + | 4.61296e9i | −0.0756673 | + | 1.93189i | ||||
\(479\) | − | 1.56967e8i | − | 0.0652579i | −0.999468 | − | 0.0326289i | \(-0.989612\pi\) | ||
0.999468 | − | 0.0326289i | \(-0.0103880\pi\) | |||||||
\(480\) | −1.03282e9 | − | 2.04785e8i | −0.426268 | − | 0.0845187i | ||||
\(481\) | −6.37449e7 | −0.0261179 | ||||||||
\(482\) | −1.24718e8 | + | 3.18422e9i | −0.0507300 | + | 1.29521i | ||||
\(483\) | −1.42120e9 | −0.573907 | ||||||||
\(484\) | 5.16274e8 | + | 4.05045e7i | 0.206977 | + | 0.0162384i | ||||
\(485\) | − | 3.20304e9i | − | 1.27487i | ||||||
\(486\) | −2.25905e9 | − | 8.84815e7i | −0.892687 | − | 0.0349643i | ||||
\(487\) | 2.15061e9 | 0.843744 | 0.421872 | − | 0.906655i | \(-0.361373\pi\) | ||||
0.421872 | + | 0.906655i | \(0.361373\pi\) | |||||||
\(488\) | −7.02336e8 | − | 8.28654e7i | −0.273574 | − | 0.0322778i | ||||
\(489\) | 7.47913e8i | 0.289248i | ||||||||
\(490\) | 4.19963e9 | + | 1.64489e8i | 1.61259 | + | 0.0631613i | ||||
\(491\) | 3.14545e9i | 1.19922i | 0.800293 | + | 0.599609i | \(0.204677\pi\) | ||||
−0.800293 | + | 0.599609i | \(0.795323\pi\) | |||||||
\(492\) | 1.16130e8 | − | 1.48021e9i | 0.0439611 | − | 0.560332i | ||||
\(493\) | − | 9.45055e8i | − | 0.355216i | ||||||
\(494\) | −3.12287e8 | − | 2.98319e8i | −0.116549 | − | 0.111336i | ||||
\(495\) | 2.55983e9i | 0.948621i | ||||||||
\(496\) | −2.85255e9 | − | 4.50368e8i | −1.04966 | − | 0.165722i | ||||
\(497\) | − | 5.48629e9i | − | 2.00462i | ||||||
\(498\) | −2.71011e7 | + | 6.91929e8i | −0.00983297 | + | 0.251049i | ||||
\(499\) | 1.35215e9i | 0.487160i | 0.969881 | + | 0.243580i | \(0.0783219\pi\) | ||||
−0.969881 | + | 0.243580i | \(0.921678\pi\) | |||||||
\(500\) | −1.73637e9 | − | 1.36228e8i | −0.621223 | − | 0.0487383i | ||||
\(501\) | −6.23875e8 | −0.221649 | ||||||||
\(502\) | 3.00438e7 | − | 7.67059e8i | 0.0105997 | − | 0.270624i | ||||
\(503\) | 7.68337e8i | 0.269193i | 0.990900 | + | 0.134597i | \(0.0429739\pi\) | ||||
−0.990900 | + | 0.134597i | \(0.957026\pi\) | |||||||
\(504\) | 4.48142e8 | − | 3.79828e9i | 0.155922 | − | 1.32154i | ||||
\(505\) | −6.57271e9 | −2.27104 | ||||||||
\(506\) | 2.74152e9 | + | 1.07378e8i | 0.940728 | + | 0.0368460i | ||||
\(507\) | 1.01776e9 | 0.346830 | ||||||||
\(508\) | 2.13223e9 | + | 1.67285e8i | 0.721623 | + | 0.0566152i | ||||
\(509\) | 6.08575e8i | 0.204551i | 0.994756 | + | 0.102276i | \(0.0326123\pi\) | ||||
−0.994756 | + | 0.102276i | \(0.967388\pi\) | |||||||
\(510\) | 2.55125e8 | + | 9.99261e6i | 0.0851642 | + | 0.00333567i | ||||
\(511\) | 2.83306e8i | 0.0939252i | ||||||||
\(512\) | −2.85044e9 | − | 1.04802e9i | −0.938572 | − | 0.345083i | ||||
\(513\) | 1.35005e9 | − | 1.52883e9i | 0.441510 | − | 0.499975i | ||||
\(514\) | 6.01021e6 | − | 1.53449e8i | 0.00195218 | − | 0.0498417i | ||||
\(515\) | 3.00760e9 | 0.970274 | ||||||||
\(516\) | 3.85398e7 | − | 4.91231e8i | 0.0123491 | − | 0.157403i | ||||
\(517\) | 2.86135e9 | 0.910655 | ||||||||
\(518\) | 7.80564e8 | + | 3.05728e7i | 0.246748 | + | 0.00966452i | ||||
\(519\) | − | 1.72980e9i | − | 0.543137i | ||||||
\(520\) | −7.39028e7 | + | 6.26372e8i | −0.0230488 | + | 0.195353i | ||||
\(521\) | 1.19148e8i | 0.0369108i | 0.999830 | + | 0.0184554i | \(0.00587487\pi\) | ||||
−0.999830 | + | 0.0184554i | \(0.994125\pi\) | |||||||
\(522\) | −2.01148e8 | + | 5.13557e9i | −0.0618968 | + | 1.58031i | ||||
\(523\) | 3.57520e9 | 1.09281 | 0.546404 | − | 0.837522i | \(-0.315996\pi\) | ||||
0.546404 | + | 0.837522i | \(0.315996\pi\) | |||||||
\(524\) | 2.17623e8 | − | 2.77385e9i | 0.0660764 | − | 0.842216i | ||||
\(525\) | − | 8.80529e8i | − | 0.265574i | ||||||
\(526\) | 2.19381e7 | − | 5.60109e8i | 0.00657277 | − | 0.167812i | ||||
\(527\) | 7.00270e8 | 0.208415 | ||||||||
\(528\) | 1.67195e8 | − | 1.05898e9i | 0.0494316 | − | 0.313091i | ||||
\(529\) | −4.03650e8 | −0.118552 | ||||||||
\(530\) | −2.52719e8 | + | 6.45226e9i | −0.0737348 | + | 1.88255i | ||||
\(531\) | 3.99648e9 | 1.15837 | ||||||||
\(532\) | 3.68092e9 | + | 3.80273e9i | 1.05990 | + | 1.09498i | ||||
\(533\) | −8.89385e8 | −0.254416 | ||||||||
\(534\) | −7.21778e7 | + | 1.84280e9i | −0.0205121 | + | 0.523701i | ||||
\(535\) | −2.89240e9 | −0.816621 | ||||||||
\(536\) | −6.66471e8 | − | 7.86339e7i | −0.186941 | − | 0.0220563i | ||||
\(537\) | 8.40558e8 | 0.234238 | ||||||||
\(538\) | 1.51835e8 | − | 3.87654e9i | 0.0420371 | − | 1.07326i | ||||
\(539\) | 4.27937e9i | 1.17712i | ||||||||
\(540\) | −2.96952e9 | − | 2.32975e8i | −0.811538 | − | 0.0636695i | ||||
\(541\) | −5.19745e8 | −0.141124 | −0.0705618 | − | 0.997507i | \(-0.522479\pi\) | ||||
−0.0705618 | + | 0.997507i | \(0.522479\pi\) | |||||||
\(542\) | −1.34430e8 | + | 3.43218e9i | −0.0362659 | + | 0.925919i | ||||
\(543\) | 1.17527e9i | 0.315020i | ||||||||
\(544\) | 7.22366e8 | + | 1.43228e8i | 0.192381 | + | 0.0381445i | ||||
\(545\) | − | 4.19202e8i | − | 0.110927i | ||||||
\(546\) | 3.32407e8 | + | 1.30196e7i | 0.0873969 | + | 0.00342312i | ||||
\(547\) | −2.69595e8 | −0.0704297 | −0.0352149 | − | 0.999380i | \(-0.511212\pi\) | ||||
−0.0352149 | + | 0.999380i | \(0.511212\pi\) | |||||||
\(548\) | 6.44844e9 | + | 5.05915e8i | 1.67387 | + | 0.131324i | ||||
\(549\) | −9.32605e8 | −0.240544 | ||||||||
\(550\) | −6.65279e7 | + | 1.69855e9i | −0.0170504 | + | 0.435320i | ||||
\(551\) | −5.33093e9 | − | 4.70755e9i | −1.35760 | − | 1.19885i | ||||
\(552\) | −1.74377e8 | + | 1.47796e9i | −0.0441269 | + | 0.374003i | ||||
\(553\) | − | 5.03063e9i | − | 1.26498i | ||||||
\(554\) | 3.22938e9 | + | 1.26487e8i | 0.806929 | + | 0.0316054i | ||||
\(555\) | − | 2.83598e8i | − | 0.0704170i | ||||||
\(556\) | −2.00948e8 | + | 2.56131e9i | −0.0495818 | + | 0.631975i | ||||
\(557\) | −3.40830e9 | −0.835688 | −0.417844 | − | 0.908519i | \(-0.637214\pi\) | ||||
−0.417844 | + | 0.908519i | \(0.637214\pi\) | |||||||
\(558\) | −3.80537e9 | − | 1.49047e8i | −0.927209 | − | 0.0363165i | ||||
\(559\) | −2.95157e8 | −0.0714680 | ||||||||
\(560\) | 1.20536e9 | − | 7.63456e9i | 0.290041 | − | 1.83707i | ||||
\(561\) | 2.59969e8i | 0.0621658i | ||||||||
\(562\) | −9.91553e7 | + | 2.53157e9i | −0.0235635 | + | 0.601607i | ||||
\(563\) | 4.67616e9 | 1.10436 | 0.552179 | − | 0.833726i | \(-0.313797\pi\) | ||||
0.552179 | + | 0.833726i | \(0.313797\pi\) | |||||||
\(564\) | −1.21395e8 | + | 1.54731e9i | −0.0284921 | + | 0.363163i | ||||
\(565\) | 3.08450e8i | 0.0719474i | ||||||||
\(566\) | 9.40294e7 | − | 2.40070e9i | 0.0217975 | − | 0.556519i | ||||
\(567\) | − | 4.20490e9i | − | 0.968757i | ||||||
\(568\) | −5.70536e9 | − | 6.73150e8i | −1.30636 | − | 0.154132i | ||||
\(569\) | 2.38691e9i | 0.543179i | 0.962413 | + | 0.271590i | \(0.0875493\pi\) | ||||
−0.962413 | + | 0.271590i | \(0.912451\pi\) | |||||||
\(570\) | 1.32721e9 | − | 1.38935e9i | 0.300177 | − | 0.314231i | ||||
\(571\) | 5.45658e9i | 1.22657i | 0.789860 | + | 0.613287i | \(0.210153\pi\) | ||||
−0.789860 | + | 0.613287i | \(0.789847\pi\) | |||||||
\(572\) | −6.40232e8 | − | 5.02297e7i | −0.143038 | − | 0.0112221i | ||||
\(573\) | 1.65269e9i | 0.366987i | ||||||||
\(574\) | 1.08906e10 | + | 4.26559e8i | 2.40360 | + | 0.0941429i | ||||
\(575\) | − | 2.35960e9i | − | 0.517608i | ||||||
\(576\) | −3.89497e9 | − | 9.32074e8i | −0.849229 | − | 0.203222i | ||||
\(577\) | −2.30793e9 | −0.500159 | −0.250079 | − | 0.968225i | \(-0.580457\pi\) | ||||
−0.250079 | + | 0.968225i | \(0.580457\pi\) | |||||||
\(578\) | 4.46046e9 | + | 1.74705e8i | 0.960798 | + | 0.0376321i | ||||
\(579\) | 2.54097e9i | 0.544033i | ||||||||
\(580\) | −8.12369e8 | + | 1.03545e10i | −0.172884 | + | 2.20360i | ||||
\(581\) | −5.08305e9 | −1.07525 | ||||||||
\(582\) | −6.92358e7 | + | 1.76769e9i | −0.0145580 | + | 0.371685i | ||||
\(583\) | −6.57477e9 | −1.37417 | ||||||||
\(584\) | 2.94619e8 | + | 3.47607e7i | 0.0612090 | + | 0.00722177i | ||||
\(585\) | 8.31735e8i | 0.171767i | ||||||||
\(586\) | −2.33367e8 | + | 5.95818e9i | −0.0479069 | + | 1.22313i | ||||
\(587\) | 2.65678e9i | 0.542154i | 0.962558 | + | 0.271077i | \(0.0873799\pi\) | ||||
−0.962558 | + | 0.271077i | \(0.912620\pi\) | |||||||
\(588\) | −2.31413e9 | − | 1.81556e8i | −0.469426 | − | 0.0368290i | ||||
\(589\) | 3.48822e9 | − | 3.95013e9i | 0.703396 | − | 0.796540i | ||||
\(590\) | 8.07024e9 | + | 3.16091e8i | 1.61772 | + | 0.0633623i | ||||
\(591\) | 1.91989e9 | 0.382578 | ||||||||
\(592\) | 1.27566e8 | − | 8.07982e8i | 0.0252703 | − | 0.160057i | ||||
\(593\) | 6.41729e9 | 1.26375 | 0.631874 | − | 0.775071i | \(-0.282286\pi\) | ||||
0.631874 | + | 0.775071i | \(0.282286\pi\) | |||||||
\(594\) | 1.18699e8 | − | 3.03056e9i | 0.0232379 | − | 0.593294i | ||||
\(595\) | 1.87420e9i | 0.364760i | ||||||||
\(596\) | −9.47060e8 | − | 7.43020e7i | −0.183238 | − | 0.0143760i | ||||
\(597\) | 1.30203e9i | 0.250444i | ||||||||
\(598\) | 8.90768e8 | + | 3.48892e7i | 0.170338 | + | 0.00667170i | ||||
\(599\) | −3.51493e9 | −0.668226 | −0.334113 | − | 0.942533i | \(-0.608437\pi\) | ||||
−0.334113 | + | 0.942533i | \(0.608437\pi\) | |||||||
\(600\) | −9.15690e8 | − | 1.08038e8i | −0.173069 | − | 0.0204196i | ||||
\(601\) | − | 3.72426e9i | − | 0.699808i | −0.936786 | − | 0.349904i | \(-0.886214\pi\) | ||
0.936786 | − | 0.349904i | \(-0.113786\pi\) | |||||||
\(602\) | 3.61423e9 | + | 1.41561e8i | 0.675194 | + | 0.0264457i | ||||
\(603\) | −8.84982e8 | −0.164370 | ||||||||
\(604\) | 5.19824e9 | + | 4.07830e8i | 0.959902 | + | 0.0753095i | ||||
\(605\) | 1.38008e9 | 0.253374 | ||||||||
\(606\) | 3.62733e9 | + | 1.42074e8i | 0.662115 | + | 0.0259334i | ||||
\(607\) | 8.69807e9 | 1.57856 | 0.789282 | − | 0.614031i | \(-0.210453\pi\) | ||||
0.789282 | + | 0.614031i | \(0.210453\pi\) | |||||||
\(608\) | 4.40622e9 | − | 3.36132e9i | 0.795066 | − | 0.606523i | ||||
\(609\) | 5.47813e9 | 0.982814 | ||||||||
\(610\) | −1.88324e9 | − | 7.37619e7i | −0.335932 | − | 0.0131576i | ||||
\(611\) | 9.29704e8 | 0.164892 | ||||||||
\(612\) | 9.68164e8 | + | 7.59577e7i | 0.170734 | + | 0.0133950i | ||||
\(613\) | −9.45776e9 | −1.65835 | −0.829176 | − | 0.558988i | \(-0.811190\pi\) | ||||
−0.829176 | + | 0.558988i | \(0.811190\pi\) | |||||||
\(614\) | −5.47515e9 | − | 2.14448e8i | −0.954568 | − | 0.0373881i | ||||
\(615\) | − | 3.95683e9i | − | 0.685938i | ||||||
\(616\) | 7.81564e9 | + | 9.22131e8i | 1.34720 | + | 0.158950i | ||||
\(617\) | 7.94564e9 | 1.36185 | 0.680927 | − | 0.732351i | \(-0.261577\pi\) | ||||
0.680927 | + | 0.732351i | \(0.261577\pi\) | |||||||
\(618\) | −1.65983e9 | − | 6.50112e7i | −0.282880 | − | 0.0110797i | ||||
\(619\) | − | 7.11840e8i | − | 0.120633i | −0.998179 | − | 0.0603164i | \(-0.980789\pi\) | ||
0.998179 | − | 0.0603164i | \(-0.0192110\pi\) | |||||||
\(620\) | −7.67254e9 | − | 6.01952e8i | −1.29291 | − | 0.101436i | ||||
\(621\) | 4.21001e9i | 0.705444i | ||||||||
\(622\) | −2.52532e8 | + | 6.44749e9i | −0.0420776 | + | 1.07430i | ||||
\(623\) | −1.35376e10 | −2.24302 | ||||||||
\(624\) | 5.43247e7 | − | 3.44083e8i | 0.00895059 | − | 0.0566914i | ||||
\(625\) | −7.62871e9 | −1.24989 | ||||||||
\(626\) | −7.58260e9 | − | 2.96992e8i | −1.23540 | − | 0.0483876i | ||||
\(627\) | 1.46645e9 | + | 1.29497e9i | 0.237592 | + | 0.209809i | ||||
\(628\) | 6.90778e9 | + | 5.41953e8i | 1.11296 | + | 0.0873178i | ||||
\(629\) | 1.98351e8i | 0.0317802i | ||||||||
\(630\) | 3.98909e8 | − | 1.01847e10i | 0.0635598 | − | 1.62277i | ||||
\(631\) | − | 1.07070e10i | − | 1.69655i | −0.529557 | − | 0.848274i | \(-0.677642\pi\) | ||
0.529557 | − | 0.848274i | \(-0.322358\pi\) | |||||||
\(632\) | −5.23151e9 | − | 6.17242e8i | −0.824361 | − | 0.0972626i | ||||
\(633\) | −3.82361e9 | −0.599184 | ||||||||
\(634\) | 3.14181e8 | − | 8.02146e9i | 0.0489629 | − | 1.25009i | ||||
\(635\) | 5.69978e9 | 0.883385 | ||||||||
\(636\) | 2.78940e8 | − | 3.55540e9i | 0.0429943 | − | 0.548009i | ||||
\(637\) | 1.39045e9i | 0.213141i | ||||||||
\(638\) | −1.05674e10 | − | 4.13897e8i | −1.61099 | − | 0.0630986i | ||||
\(639\) | −7.57593e9 | −1.14864 | ||||||||
\(640\) | −7.79152e9 | − | 2.19023e9i | −1.17488 | − | 0.330263i | ||||
\(641\) | − | 5.39388e9i | − | 0.808906i | −0.914559 | − | 0.404453i | \(-0.867462\pi\) | ||
0.914559 | − | 0.404453i | \(-0.132538\pi\) | |||||||
\(642\) | 1.59625e9 | + | 6.25213e7i | 0.238083 | + | 0.00932513i | ||||
\(643\) | 5.02019e9i | 0.744701i | 0.928092 | + | 0.372350i | \(0.121448\pi\) | ||||
−0.928092 | + | 0.372350i | \(0.878552\pi\) | |||||||
\(644\) | −1.08908e10 | − | 8.54445e8i | −1.60680 | − | 0.126062i | ||||
\(645\) | − | 1.31314e9i | − | 0.192687i | ||||||
\(646\) | −9.28260e8 | + | 9.71723e8i | −0.135474 | + | 0.141817i | ||||
\(647\) | − | 1.12648e10i | − | 1.63515i | −0.575822 | − | 0.817575i | \(-0.695318\pi\) | ||
0.575822 | − | 0.817575i | \(-0.304682\pi\) | |||||||
\(648\) | −4.37281e9 | − | 5.15927e8i | −0.631317 | − | 0.0744863i | ||||
\(649\) | 8.22348e9i | 1.18086i | ||||||||
\(650\) | −2.16161e7 | + | 5.51889e8i | −0.00308732 | + | 0.0788234i | ||||
\(651\) | 4.05920e9i | 0.576643i | ||||||||
\(652\) | −4.49654e8 | + | 5.73133e9i | −0.0635349 | + | 0.809821i | ||||
\(653\) | −1.68561e9 | −0.236898 | −0.118449 | − | 0.992960i | \(-0.537792\pi\) | ||||
−0.118449 | + | 0.992960i | \(0.537792\pi\) | |||||||
\(654\) | −9.06134e6 | + | 2.31348e8i | −0.00126669 | + | 0.0323403i | ||||
\(655\) | − | 7.41494e9i | − | 1.03101i | ||||||
\(656\) | 1.77984e9 | − | 1.12732e10i | 0.246160 | − | 1.55913i | ||||
\(657\) | 3.91213e8 | 0.0538188 | ||||||||
\(658\) | −1.13843e10 | − | 4.45896e8i | −1.55782 | − | 0.0610160i | ||||
\(659\) | −2.26846e9 | −0.308768 | −0.154384 | − | 0.988011i | \(-0.549339\pi\) | ||||
−0.154384 | + | 0.988011i | \(0.549339\pi\) | |||||||
\(660\) | 2.23470e8 | − | 2.84836e9i | 0.0302562 | − | 0.385649i | ||||
\(661\) | − | 8.80186e9i | − | 1.18541i | −0.805419 | − | 0.592706i | \(-0.798060\pi\) | ||
0.805419 | − | 0.592706i | \(-0.201940\pi\) | |||||||
\(662\) | −1.11800e10 | − | 4.37894e8i | −1.49775 | − | 0.0586633i | ||||
\(663\) | 8.44687e7i | 0.0112564i | ||||||||
\(664\) | −6.23675e8 | + | 5.28603e9i | −0.0826742 | + | 0.700715i | ||||
\(665\) | 1.05721e10 | + | 9.33586e9i | 1.39408 | + | 1.23106i | ||||
\(666\) | 4.22175e7 | − | 1.07787e9i | 0.00553774 | − | 0.141386i | ||||
\(667\) | 1.46800e10 | 1.91552 | ||||||||
\(668\) | −4.78082e9 | − | 3.75081e8i | −0.620561 | − | 0.0486864i | ||||
\(669\) | 1.28798e9 | 0.166310 | ||||||||
\(670\) | −1.78707e9 | − | 6.99953e7i | −0.229552 | − | 0.00899098i | ||||
\(671\) | − | 1.91900e9i | − | 0.245215i | ||||||
\(672\) | −8.30239e8 | + | 4.18729e9i | −0.105538 | + | 0.532280i | ||||
\(673\) | 7.03798e8i | 0.0890011i | 0.999009 | + | 0.0445006i | \(0.0141696\pi\) | ||||
−0.999009 | + | 0.0445006i | \(0.985830\pi\) | |||||||
\(674\) | −8.38675e7 | + | 2.14125e9i | −0.0105508 | + | 0.269375i | ||||
\(675\) | −2.60837e9 | −0.326442 | ||||||||
\(676\) | 7.79918e9 | + | 6.11888e8i | 0.971037 | + | 0.0761831i | ||||
\(677\) | 1.53717e10i | 1.90398i | 0.306126 | + | 0.951991i | \(0.400967\pi\) | ||||
−0.306126 | + | 0.951991i | \(0.599033\pi\) | |||||||
\(678\) | 6.66736e6 | − | 1.70227e8i | 0.000821580 | − | 0.0209761i | ||||
\(679\) | −1.29858e10 | −1.59193 | ||||||||
\(680\) | 1.94904e9 | + | 2.29959e8i | 0.237706 | + | 0.0280458i | ||||
\(681\) | −3.00859e9 | −0.365046 | ||||||||
\(682\) | 3.06691e8 | − | 7.83023e9i | 0.0370216 | − | 0.945212i | ||||
\(683\) | 6.42983e9 | 0.772195 | 0.386098 | − | 0.922458i | \(-0.373823\pi\) | ||||
0.386098 | + | 0.922458i | \(0.373823\pi\) | |||||||
\(684\) | 5.25113e9 | − | 5.08292e9i | 0.627418 | − | 0.607319i | ||||
\(685\) | 1.72377e10 | 2.04909 | ||||||||
\(686\) | 1.62569e8 | − | 4.15061e9i | 0.0192267 | − | 0.490883i | ||||
\(687\) | 1.72858e9 | 0.203395 | ||||||||
\(688\) | 5.90668e8 | − | 3.74119e9i | 0.0691487 | − | 0.437975i | ||||
\(689\) | −2.13626e9 | −0.248821 | ||||||||
\(690\) | −1.55220e8 | + | 3.96299e9i | −0.0179878 | + | 0.459252i | ||||
\(691\) | − | 1.42377e9i | − | 0.164160i | −0.996626 | − | 0.0820801i | \(-0.973844\pi\) | ||
0.996626 | − | 0.0820801i | \(-0.0261563\pi\) | |||||||
\(692\) | 1.03997e9 | − | 1.32556e10i | 0.119303 | − | 1.52065i | ||||
\(693\) | 1.03781e10 | 1.18454 | ||||||||
\(694\) | 5.49061e8 | − | 1.40183e10i | 0.0623537 | − | 1.59197i | ||||
\(695\) | 6.84678e9i | 0.773641i | ||||||||
\(696\) | 6.72149e8 | − | 5.69688e9i | 0.0755671 | − | 0.640478i | ||||
\(697\) | 2.76744e9i | 0.309574i | ||||||||
\(698\) | 9.32913e9 | + | 3.65399e8i | 1.03836 | + | 0.0406699i | ||||
\(699\) | −1.88075e9 | −0.208286 | ||||||||
\(700\) | 5.29384e8 | − | 6.74758e9i | 0.0583348 | − | 0.743541i | ||||
\(701\) | −2.62220e9 | −0.287510 | −0.143755 | − | 0.989613i | \(-0.545918\pi\) | ||||
−0.143755 | + | 0.989613i | \(0.545918\pi\) | |||||||
\(702\) | 3.85676e7 | − | 9.84683e8i | 0.00420768 | − | 0.107428i | ||||
\(703\) | 1.11887e9 | + | 9.88035e8i | 0.121461 | + | 0.107258i | ||||
\(704\) | 1.91791e9 | − | 8.01458e9i | 0.207168 | − | 0.865718i | ||||
\(705\) | 4.13621e9i | 0.444571i | ||||||||
\(706\) | −6.44623e8 | − | 2.52483e7i | −0.0689428 | − | 0.00270032i | ||||
\(707\) | 2.66472e10i | 2.83585i | ||||||||
\(708\) | −4.44696e9 | − | 3.48888e8i | −0.470919 | − | 0.0369461i | ||||
\(709\) | −3.91774e8 | −0.0412832 | −0.0206416 | − | 0.999787i | \(-0.506571\pi\) | ||||
−0.0206416 | + | 0.999787i | \(0.506571\pi\) | |||||||
\(710\) | −1.52983e10 | − | 5.99198e8i | −1.60413 | − | 0.0628299i | ||||
\(711\) | −6.94672e9 | −0.724830 | ||||||||
\(712\) | −1.66102e9 | + | 1.40782e10i | −0.172462 | + | 1.46173i | ||||
\(713\) | 1.08776e10i | 1.12388i | ||||||||
\(714\) | 4.05121e7 | − | 1.03433e9i | 0.00416525 | − | 0.106345i | ||||
\(715\) | −1.71144e9 | −0.175102 | ||||||||
\(716\) | 6.44128e9 | + | 5.05353e8i | 0.655808 | + | 0.0514517i | ||||
\(717\) | − | 6.79486e9i | − | 0.688435i | ||||||
\(718\) | −6.45485e8 | + | 1.64801e10i | −0.0650805 | + | 1.66159i | ||||
\(719\) | − | 1.00281e9i | − | 0.100616i | −0.998734 | − | 0.0503081i | \(-0.983980\pi\) | ||
0.998734 | − | 0.0503081i | \(-0.0160203\pi\) | |||||||
\(720\) | −1.05424e10 | − | 1.66447e9i | −1.05263 | − | 0.166193i | ||||
\(721\) | − | 1.21934e10i | − | 1.21158i | ||||||
\(722\) | 8.57468e8 | + | 1.00766e10i | 0.0847886 | + | 0.996399i | ||||
\(723\) | − | 4.69034e9i | − | 0.461552i | ||||||
\(724\) | −7.06585e8 | + | 9.00620e9i | −0.0691958 | + | 0.881976i | ||||
\(725\) | 9.09523e9i | 0.886401i | ||||||||
\(726\) | −7.61637e8 | − | 2.98314e7i | −0.0738703 | − | 0.00289332i | ||||
\(727\) | − | 2.26549e8i | − | 0.0218671i | −0.999940 | − | 0.0109336i | \(-0.996520\pi\) | ||
0.999940 | − | 0.0109336i | \(-0.00348033\pi\) | |||||||
\(728\) | 2.53944e9 | + | 2.99617e8i | 0.243937 | + | 0.0287811i | ||||
\(729\) | −3.32204e9 | −0.317584 | ||||||||
\(730\) | 7.89990e8 | + | 3.09419e7i | 0.0751608 | + | 0.00294386i | ||||
\(731\) | 9.18421e8i | 0.0869623i | ||||||||
\(732\) | 1.03772e9 | + | 8.14151e7i | 0.0977898 | + | 0.00767214i | ||||
\(733\) | 1.63102e9 | 0.152966 | 0.0764831 | − | 0.997071i | \(-0.475631\pi\) | ||||
0.0764831 | + | 0.997071i | \(0.475631\pi\) | |||||||
\(734\) | 4.52465e8 | − | 1.15520e10i | 0.0422327 | − | 1.07826i | ||||
\(735\) | −6.18603e9 | −0.574654 | ||||||||
\(736\) | −2.22484e9 | + | 1.12209e10i | −0.205696 | + | 1.03742i | ||||
\(737\) | − | 1.82101e9i | − | 0.167562i | ||||||
\(738\) | 5.89029e8 | − | 1.50387e10i | 0.0539436 | − | 1.37725i | ||||
\(739\) | − | 1.46814e10i | − | 1.33817i | −0.743184 | − | 0.669087i | \(-0.766685\pi\) | ||
0.743184 | − | 0.669087i | \(-0.233315\pi\) | |||||||
\(740\) | 1.70502e8 | − | 2.17324e9i | 0.0154675 | − | 0.197150i | ||||
\(741\) | 4.76477e8 | + | 4.20760e8i | 0.0430207 | + | 0.0379901i | ||||
\(742\) | 2.61588e10 | + | 1.02458e9i | 2.35074 | + | 0.0920726i | ||||
\(743\) | 2.11568e10 | 1.89229 | 0.946147 | − | 0.323738i | \(-0.104940\pi\) | ||||
0.946147 | + | 0.323738i | \(0.104940\pi\) | |||||||
\(744\) | 4.22129e9 | + | 4.98051e8i | 0.375785 | + | 0.0443372i | ||||
\(745\) | −2.53164e9 | −0.224313 | ||||||||
\(746\) | −3.76924e8 | + | 9.62338e9i | −0.0332405 | + | 0.848675i | ||||
\(747\) | 7.01911e9i | 0.616113i | ||||||||
\(748\) | −1.56297e8 | + | 1.99217e9i | −0.0136551 | + | 0.174049i | ||||
\(749\) | 1.17264e10i | 1.01971i | ||||||||
\(750\) | 2.56159e9 | + | 1.00331e8i | 0.221715 | + | 0.00868403i | ||||
\(751\) | 6.87719e9 | 0.592477 | 0.296238 | − | 0.955114i | \(-0.404268\pi\) | ||||
0.296238 | + | 0.955114i | \(0.404268\pi\) | |||||||
\(752\) | −1.86052e9 | + | 1.17842e10i | −0.159541 | + | 1.01051i | ||||
\(753\) | 1.12987e9i | 0.0964377i | ||||||||
\(754\) | −3.43353e9 | − | 1.34483e8i | −0.291703 | − | 0.0114253i | ||||
\(755\) | 1.38957e10 | 1.17508 | ||||||||
\(756\) | −9.44530e8 | + | 1.20391e10i | −0.0795041 | + | 1.01337i | ||||
\(757\) | −1.31587e10 | −1.10250 | −0.551249 | − | 0.834341i | \(-0.685849\pi\) | ||||
−0.551249 | + | 0.834341i | \(0.685849\pi\) | |||||||
\(758\) | 2.51175e9 | + | 9.83788e7i | 0.209476 | + | 0.00820464i | ||||
\(759\) | −4.03823e9 | −0.335232 | ||||||||
\(760\) | 1.10058e10 | − | 9.84880e9i | 0.909442 | − | 0.813834i | ||||
\(761\) | 2.03795e10 | 1.67628 | 0.838140 | − | 0.545455i | \(-0.183643\pi\) | ||||
0.838140 | + | 0.545455i | \(0.183643\pi\) | |||||||
\(762\) | −3.14558e9 | − | 1.23205e8i | −0.257548 | − | 0.0100875i | ||||
\(763\) | −1.69953e9 | −0.138514 | ||||||||
\(764\) | −9.93618e8 | + | 1.26647e10i | −0.0806107 | + | 1.02747i | ||||
\(765\) | 2.58806e9 | 0.209006 | ||||||||
\(766\) | 8.93502e9 | + | 3.49962e8i | 0.718281 | + | 0.0281333i | ||||
\(767\) | 2.67196e9i | 0.213819i | ||||||||
\(768\) | 4.25262e9 | + | 1.37716e9i | 0.338760 | + | 0.109703i | ||||
\(769\) | −4.03215e9 | −0.319738 | −0.159869 | − | 0.987138i | \(-0.551107\pi\) | ||||
−0.159869 | + | 0.987138i | \(0.551107\pi\) | |||||||
\(770\) | 2.09568e10 | + | 8.20827e8i | 1.65428 | + | 0.0647939i | ||||
\(771\) | 2.26029e8i | 0.0177613i | ||||||||
\(772\) | −1.52766e9 | + | 1.94717e10i | −0.119500 | + | 1.52316i | ||||
\(773\) | − | 1.43109e10i | − | 1.11440i | −0.830380 | − | 0.557198i | \(-0.811877\pi\) | ||
0.830380 | − | 0.557198i | \(-0.188123\pi\) | |||||||
\(774\) | 1.95479e8 | − | 4.99084e9i | 0.0151533 | − | 0.386884i | ||||
\(775\) | −6.73941e9 | −0.520075 | ||||||||
\(776\) | −1.59331e9 | + | 1.35043e10i | −0.122401 | + | 1.03743i | ||||
\(777\) | −1.14977e9 | −0.0879297 | ||||||||
\(778\) | −1.90314e10 | − | 7.45413e8i | −1.44891 | − | 0.0567503i | ||||
\(779\) | 1.56108e10 | + | 1.37853e10i | 1.18316 | + | 1.04481i | ||||
\(780\) | 7.26093e7 | − | 9.25485e8i | 0.00547849 | − | 0.0698294i | ||||
\(781\) | − | 1.55888e10i | − | 1.17094i | ||||||
\(782\) | 1.08562e8 | − | 2.77175e9i | 0.00811813 | − | 0.207267i | ||||
\(783\) | − | 1.62277e10i | − | 1.20807i | ||||||
\(784\) | −1.76242e10 | − | 2.78256e9i | −1.30618 | − | 0.206224i | ||||
\(785\) | 1.84656e10 | 1.36245 | ||||||||
\(786\) | −1.60279e8 | + | 4.09214e9i | −0.0117733 | + | 0.300588i | ||||
\(787\) | 2.06321e9 | 0.150880 | 0.0754399 | − | 0.997150i | \(-0.475964\pi\) | ||||
0.0754399 | + | 0.997150i | \(0.475964\pi\) | |||||||
\(788\) | 1.47123e10 | + | 1.15426e9i | 1.07112 | + | 0.0840354i | ||||
\(789\) | 8.25036e8i | 0.0598003i | ||||||||
\(790\) | −1.40278e10 | − | 5.49432e8i | −1.01226 | − | 0.0396478i | ||||
\(791\) | 1.25052e9 | 0.0898407 | ||||||||
\(792\) | 1.27336e9 | − | 1.07925e10i | 0.0910777 | − | 0.771940i | ||||
\(793\) | − | 6.23518e8i | − | 0.0444010i | ||||||
\(794\) | −1.91856e10 | − | 7.51452e8i | −1.36020 | − | 0.0532758i | ||||
\(795\) | − | 9.50413e9i | − | 0.670853i | ||||||
\(796\) | −7.82797e8 | + | 9.97760e9i | −0.0550115 | + | 0.701181i | ||||
\(797\) | 6.81836e9i | 0.477063i | 0.971135 | + | 0.238532i | \(0.0766661\pi\) | ||||
−0.971135 | + | 0.238532i | \(0.923334\pi\) | |||||||
\(798\) | −5.63272e9 | − | 5.38078e9i | −0.392381 | − | 0.374830i | ||||
\(799\) | − | 2.89290e9i | − | 0.200641i | ||||||
\(800\) | −6.95207e9 | − | 1.37843e9i | −0.480064 | − | 0.0951853i | ||||
\(801\) | 1.86938e10i | 1.28524i | ||||||||
\(802\) | 5.34199e8 | − | 1.36388e10i | 0.0365673 | − | 0.933612i | ||||
\(803\) | 8.04990e8i | 0.0548638i | ||||||||
\(804\) | 9.84734e8 | + | 7.72577e7i | 0.0668225 | + | 0.00524258i | ||||
\(805\) | −2.91129e10 | −1.96698 | ||||||||
\(806\) | 9.96494e7 | − | 2.54418e9i | 0.00670351 | − | 0.171150i | ||||
\(807\) | 5.71012e9i | 0.382462i | ||||||||
\(808\) | 2.77112e10 | + | 3.26952e9i | 1.84806 | + | 0.218044i | ||||
\(809\) | −2.06110e10 | −1.36861 | −0.684304 | − | 0.729196i | \(-0.739894\pi\) | ||||
−0.684304 | + | 0.729196i | \(0.739894\pi\) | |||||||
\(810\) | −1.17252e10 | − | 4.59248e8i | −0.775218 | − | 0.0303634i | ||||
\(811\) | −2.17656e10 | −1.43284 | −0.716419 | − | 0.697670i | \(-0.754220\pi\) | ||||
−0.716419 | + | 0.697670i | \(0.754220\pi\) | |||||||
\(812\) | 4.19794e10 | + | 3.29351e9i | 2.75163 | + | 0.215880i | ||||
\(813\) | − | 5.05558e9i | − | 0.329955i | ||||||
\(814\) | 2.21791e9 | + | 8.68699e7i | 0.144131 | + | 0.00564526i | ||||
\(815\) | 1.53208e10i | 0.991354i | ||||||||
\(816\) | −1.07066e9 | − | 1.69039e8i | −0.0689821 | − | 0.0108911i | ||||
\(817\) | 5.18069e9 | + | 4.57488e9i | 0.332361 | + | 0.293496i | ||||
\(818\) | 3.76029e8 | − | 9.60053e9i | 0.0240206 | − | 0.613280i | ||||
\(819\) | 3.37203e9 | 0.214485 | ||||||||
\(820\) | 2.37889e9 | − | 3.03216e10i | 0.150670 | − | 1.92045i | ||||
\(821\) | 2.36908e10 | 1.49410 | 0.747048 | − | 0.664770i | \(-0.231471\pi\) | ||||
0.747048 | + | 0.664770i | \(0.231471\pi\) | |||||||
\(822\) | −9.51310e9 | − | 3.72604e8i | −0.597407 | − | 0.0233990i | ||||
\(823\) | 1.69861e10i | 1.06217i | 0.847318 | + | 0.531085i | \(0.178216\pi\) | ||||
−0.847318 | + | 0.531085i | \(0.821784\pi\) | |||||||
\(824\) | −1.26803e10 | − | 1.49609e9i | −0.789560 | − | 0.0931566i | ||||
\(825\) | − | 2.50195e9i | − | 0.155128i | ||||||
\(826\) | 1.28150e9 | − | 3.27185e10i | 0.0791204 | − | 2.02005i | ||||
\(827\) | −4.08965e9 | −0.251430 | −0.125715 | − | 0.992066i | \(-0.540122\pi\) | ||||
−0.125715 | + | 0.992066i | \(0.540122\pi\) | |||||||
\(828\) | −1.17989e9 | + | 1.50390e10i | −0.0722330 | + | 0.920688i | ||||
\(829\) | − | 9.54054e9i | − | 0.581610i | −0.956782 | − | 0.290805i | \(-0.906077\pi\) | ||
0.956782 | − | 0.290805i | \(-0.0939231\pi\) | |||||||
\(830\) | −5.55158e8 | + | 1.41739e10i | −0.0337011 | + | 0.860434i | ||||
\(831\) | −4.75686e9 | −0.287552 | ||||||||
\(832\) | 6.23163e8 | − | 2.60408e9i | 0.0375120 | − | 0.156756i | ||||
\(833\) | 4.32656e9 | 0.259349 | ||||||||
\(834\) | 1.47998e8 | − | 3.77858e9i | 0.00883433 | − | 0.225553i | ||||
\(835\) | −1.27799e10 | −0.759669 | ||||||||
\(836\) | 1.04590e10 | + | 1.08051e10i | 0.619111 | + | 0.639600i | ||||
\(837\) | 1.20245e10 | 0.708806 | ||||||||
\(838\) | −9.26805e8 | + | 2.36626e10i | −0.0544044 | + | 1.38902i | ||||
\(839\) | −8.77153e9 | −0.512753 | −0.256377 | − | 0.966577i | \(-0.582529\pi\) | ||||
−0.256377 | + | 0.966577i | \(0.582529\pi\) | |||||||
\(840\) | −1.33298e9 | + | 1.12979e10i | −0.0775974 | + | 0.657686i | ||||
\(841\) | −3.93352e10 | −2.28032 | ||||||||
\(842\) | −2.95871e8 | + | 7.55398e9i | −0.0170809 | + | 0.436098i | ||||
\(843\) | − | 3.72899e9i | − | 0.214385i | ||||||
\(844\) | −2.93007e10 | − | 2.29880e9i | −1.67756 | − | 0.131614i | ||||
\(845\) | 2.08484e10 | 1.18871 | ||||||||
\(846\) | −6.15732e8 | + | 1.57205e10i | −0.0349619 | + | 0.892625i | ||||
\(847\) | − | 5.59514e9i | − | 0.316388i | ||||||
\(848\) | 4.27509e9 | − | 2.70777e10i | 0.240746 | − | 1.52484i | ||||
\(849\) | 3.53621e9i | 0.198318i | ||||||||
\(850\) | 1.71728e9 | + | 6.72615e7i | 0.0959123 | + | 0.00375665i | ||||
\(851\) | −3.08109e9 | −0.171376 | ||||||||
\(852\) | 8.42986e9 | + | 6.61368e8i | 0.466962 | + | 0.0366357i | ||||
\(853\) | −1.64301e10 | −0.906398 | −0.453199 | − | 0.891409i | \(-0.649717\pi\) | ||||
−0.453199 | + | 0.891409i | \(0.649717\pi\) | |||||||
\(854\) | −2.99046e8 | + | 7.63506e9i | −0.0164299 | + | 0.419478i | ||||
\(855\) | 1.28917e10 | − | 1.45989e10i | 0.705392 | − | 0.798800i | ||||
\(856\) | 1.21947e10 | + | 1.43879e9i | 0.664525 | + | 0.0784043i | ||||
\(857\) | − | 1.62196e10i | − | 0.880250i | −0.897936 | − | 0.440125i | \(-0.854934\pi\) | ||
0.897936 | − | 0.440125i | \(-0.145066\pi\) | |||||||
\(858\) | 9.44507e8 | + | 3.69940e7i | 0.0510505 | + | 0.00199952i | ||||
\(859\) | − | 1.31545e10i | − | 0.708108i | −0.935225 | − | 0.354054i | \(-0.884803\pi\) | ||
0.935225 | − | 0.354054i | \(-0.115197\pi\) | |||||||
\(860\) | 7.89475e8 | − | 1.00627e10i | 0.0423247 | − | 0.539474i | ||||
\(861\) | −1.60418e10 | −0.856531 | ||||||||
\(862\) | −1.08185e10 | − | 4.23736e8i | −0.575299 | − | 0.0225330i | ||||
\(863\) | 1.14711e9 | 0.0607529 | 0.0303764 | − | 0.999539i | \(-0.490329\pi\) | ||||
0.0303764 | + | 0.999539i | \(0.490329\pi\) | |||||||
\(864\) | 1.24039e10 | + | 2.45940e9i | 0.654276 | + | 0.129727i | ||||
\(865\) | − | 3.54344e10i | − | 1.86152i | ||||||
\(866\) | 1.18464e9 | − | 3.02454e10i | 0.0619830 | − | 1.58251i | ||||
\(867\) | −6.57023e9 | −0.342384 | ||||||||
\(868\) | −2.44044e9 | + | 3.11061e10i | −0.126663 | + | 1.61446i | ||||
\(869\) | − | 1.42941e10i | − | 0.738904i | ||||||
\(870\) | 5.98307e8 | − | 1.52756e10i | 0.0308040 | − | 0.786467i | ||||
\(871\) | − | 5.91678e8i | − | 0.0303405i | ||||||
\(872\) | −2.08527e8 | + | 1.76740e9i | −0.0106501 | + | 0.0902665i | ||||
\(873\) | 1.79319e10i | 0.912170i | ||||||||
\(874\) | −1.50943e10 | − | 1.44191e10i | −0.764755 | − | 0.730549i | ||||
\(875\) | 1.88180e10i | 0.949609i | ||||||||
\(876\) | −4.35309e8 | − | 3.41523e7i | −0.0218793 | − | 0.00171655i | ||||
\(877\) | − | 2.64207e10i | − | 1.32265i | −0.750098 | − | 0.661327i | \(-0.769994\pi\) | ||
0.750098 | − | 0.661327i | \(-0.230006\pi\) | |||||||
\(878\) | 3.04127e10 | + | 1.19119e9i | 1.51644 | + | 0.0593951i | ||||
\(879\) | − | 8.77635e9i | − | 0.435866i | ||||||
\(880\) | 3.42494e9 | − | 2.16930e10i | 0.169420 | − | 1.07307i | ||||
\(881\) | −2.65953e10 | −1.31036 | −0.655178 | − | 0.755474i | \(-0.727406\pi\) | ||||
−0.655178 | + | 0.755474i | \(0.727406\pi\) | |||||||
\(882\) | −2.35112e10 | − | 9.20876e8i | −1.15381 | − | 0.0451919i | ||||
\(883\) | 1.86252e10i | 0.910413i | 0.890386 | + | 0.455207i | \(0.150435\pi\) | ||||
−0.890386 | + | 0.455207i | \(0.849565\pi\) | |||||||
\(884\) | −5.07836e7 | + | 6.47292e8i | −0.00247252 | + | 0.0315150i | ||||
\(885\) | −1.18874e10 | −0.576482 | ||||||||
\(886\) | −4.10182e8 | + | 1.04725e10i | −0.0198134 | + | 0.505863i | ||||
\(887\) | 1.57386e10 | 0.757239 | 0.378620 | − | 0.925552i | \(-0.376399\pi\) | ||||
0.378620 | + | 0.925552i | \(0.376399\pi\) | |||||||
\(888\) | −1.41073e8 | + | 1.19568e9i | −0.00676079 | + | 0.0573019i | ||||
\(889\) | − | 2.31081e10i | − | 1.10308i | ||||||
\(890\) | −1.47854e9 | + | 3.77491e10i | −0.0703020 | + | 1.79491i | ||||
\(891\) | − | 1.19479e10i | − | 0.565872i | ||||||
\(892\) | 9.86995e9 | + | 7.74351e8i | 0.465627 | + | 0.0365309i | ||||
\(893\) | −1.63185e10 | − | 1.44103e10i | −0.766830 | − | 0.677160i | ||||
\(894\) | 1.39716e9 | + | 5.47232e7i | 0.0653979 | + | 0.00256147i | ||||
\(895\) | 1.72186e10 | 0.802816 | ||||||||
\(896\) | −8.87966e9 | + | 3.15885e10i | −0.412399 | + | 1.46707i | ||||
\(897\) | −1.31210e9 | −0.0607005 | ||||||||
\(898\) | −5.01976e8 | + | 1.28161e10i | −0.0231321 | + | 0.590595i | ||||
\(899\) | − | 4.19286e10i | − | 1.92465i | ||||||
\(900\) | −9.31763e9 | − | 7.31019e8i | −0.426046 | − | 0.0334256i | ||||
\(901\) | 6.64727e9i | 0.302766i | ||||||||
\(902\) | 3.09448e10 | + | 1.21203e9i | 1.40399 | + | 0.0549910i | ||||
\(903\) | −5.32374e9 | −0.240608 | ||||||||
\(904\) | 1.53435e8 | − | 1.30046e9i | 0.00690772 | − | 0.0585472i | ||||
\(905\) | 2.40750e10i | 1.07968i | ||||||||
\(906\) | −7.66873e9 | − | 3.00365e8i | −0.342590 | − | 0.0134184i | ||||
\(907\) | −1.00339e10 | −0.446525 | −0.223263 | − | 0.974758i | \(-0.571671\pi\) | ||||
−0.223263 | + | 0.974758i | \(0.571671\pi\) | |||||||
\(908\) | −2.30551e10 | − | 1.80880e9i | −1.02204 | − | 0.0801844i | ||||
\(909\) | 3.67967e10 | 1.62493 | ||||||||
\(910\) | 6.80925e9 | + | 2.66702e8i | 0.299540 | + | 0.0117322i | ||||
\(911\) | −1.58345e10 | −0.693888 | −0.346944 | − | 0.937886i | \(-0.612781\pi\) | ||||
−0.346944 | + | 0.937886i | \(0.612781\pi\) | |||||||
\(912\) | −6.28676e9 | + | 5.19743e9i | −0.274438 | + | 0.226886i | ||||
\(913\) | −1.44431e10 | −0.628076 | ||||||||
\(914\) | 2.64048e9 | + | 1.03421e8i | 0.114385 | + | 0.00448019i | ||||
\(915\) | 2.77400e9 | 0.119711 | ||||||||
\(916\) | 1.32463e10 | + | 1.03924e9i | 0.569454 | + | 0.0446768i | ||||
\(917\) | −3.00617e10 | −1.28742 | ||||||||
\(918\) | −3.06398e9 | − | 1.20008e8i | −0.130718 | − | 0.00511991i | ||||
\(919\) | 6.01772e9i | 0.255757i | 0.991790 | + | 0.127879i | \(0.0408168\pi\) | ||||
−0.991790 | + | 0.127879i | \(0.959183\pi\) | |||||||
\(920\) | −3.57206e9 | + | 3.02755e10i | −0.151238 | + | 1.28184i | ||||
\(921\) | 8.06487e9 | 0.340164 | ||||||||
\(922\) | 3.63649e10 | + | 1.42432e9i | 1.52800 | + | 0.0598482i | ||||
\(923\) | − | 5.06509e9i | − | 0.212022i | ||||||
\(924\) | −1.15479e10 | − | 9.05992e8i | −0.481559 | − | 0.0377809i | ||||
\(925\) | − | 1.90893e9i | − | 0.0793039i | ||||||
\(926\) | −3.32492e8 | + | 8.48897e9i | −0.0137608 | + | 0.351331i | ||||
\(927\) | −1.68377e10 | −0.694231 | ||||||||
\(928\) | 8.57577e9 | − | 4.32516e10i | 0.352254 | − | 1.77658i | ||||
\(929\) | 4.56774e9 | 0.186916 | 0.0934579 | − | 0.995623i | \(-0.470208\pi\) | ||||
0.0934579 | + | 0.995623i | \(0.470208\pi\) | |||||||
\(930\) | 1.13190e10 | + | 4.43335e8i | 0.461441 | + | 0.0180735i | ||||
\(931\) | 2.15517e10 | − | 2.44056e10i | 0.875300 | − | 0.991208i | ||||
\(932\) | −1.44124e10 | − | 1.13073e9i | −0.583150 | − | 0.0457512i | ||||
\(933\) | − | 9.49712e9i | − | 0.382830i | ||||||
\(934\) | −9.41141e8 | + | 2.40286e10i | −0.0377955 | + | 0.964972i | ||||
\(935\) | 5.32539e9i | 0.213064i | ||||||||
\(936\) | 4.13737e8 | − | 3.50668e9i | 0.0164915 | − | 0.139775i | ||||
\(937\) | 1.10333e10 | 0.438146 | 0.219073 | − | 0.975709i | \(-0.429697\pi\) | ||||
0.219073 | + | 0.975709i | \(0.429697\pi\) | |||||||
\(938\) | −2.83775e8 | + | 7.24517e9i | −0.0112270 | + | 0.286641i | ||||
\(939\) | 1.11691e10 | 0.440240 | ||||||||
\(940\) | −2.48674e9 | + | 3.16962e10i | −0.0976523 | + | 1.24469i | ||||
\(941\) | 2.95981e10i | 1.15798i | 0.815335 | + | 0.578990i | \(0.196553\pi\) | ||||
−0.815335 | + | 0.578990i | \(0.803447\pi\) | |||||||
\(942\) | −1.01907e10 | − | 3.99146e8i | −0.397217 | − | 0.0155580i | ||||
\(943\) | −4.29881e10 | −1.66939 | ||||||||
\(944\) | −3.38677e10 | − | 5.34712e9i | −1.31034 | − | 0.206880i | ||||
\(945\) | 3.21823e10i | 1.24053i | ||||||||
\(946\) | 1.02695e10 | + | 4.02232e8i | 0.394396 | + | 0.0154475i | ||||
\(947\) | 2.38397e10i | 0.912169i | 0.889937 | + | 0.456084i | \(0.150748\pi\) | ||||
−0.889937 | + | 0.456084i | \(0.849252\pi\) | |||||||
\(948\) | 7.72973e9 | + | 6.06439e8i | 0.294669 | + | 0.0231184i | ||||
\(949\) | 2.61556e8i | 0.00993419i | ||||||||
\(950\) | 8.93360e9 | − | 9.35189e9i | 0.338060 | − | 0.353889i | ||||
\(951\) | 1.18156e10i | 0.445474i | ||||||||
\(952\) | 9.32300e8 | − | 7.90182e9i | 0.0350208 | − | 0.296823i | ||||
\(953\) | − | 3.29758e10i | − | 1.23416i | −0.786902 | − | 0.617078i | \(-0.788316\pi\) | ||
0.786902 | − | 0.617078i | \(-0.211684\pi\) | |||||||
\(954\) | 1.41482e9 | − | 3.61223e10i | 0.0527573 | − | 1.34696i | ||||
\(955\) | 3.38549e10i | 1.25779i | ||||||||
\(956\) | 4.08515e9 | − | 5.20697e10i | 0.151219 | − | 1.92745i | ||||
\(957\) | 1.55656e10 | 0.574084 | ||||||||
\(958\) | −6.95033e7 | + | 1.77451e9i | −0.00255403 | + | 0.0652079i | ||||
\(959\) | − | 6.98852e10i | − | 2.55870i | ||||||
\(960\) | 1.15854e10 | + | 2.77242e9i | 0.422633 | + | 0.101137i | ||||
\(961\) | 3.55577e9 | 0.129242 | ||||||||
\(962\) | 7.20639e8 | + | 2.82256e7i | 0.0260978 | + | 0.00102219i | ||||
\(963\) | 1.61928e10 | 0.584293 | ||||||||
\(964\) | 2.81989e9 | − | 3.59426e10i | 0.101382 | − | 1.29223i | ||||
\(965\) | 5.20510e10i | 1.86459i | ||||||||
\(966\) | 1.60668e10 | + | 6.29296e8i | 0.573467 | + | 0.0224613i | ||||
\(967\) | 3.06333e10i | 1.08943i | 0.838620 | + | 0.544717i | \(0.183363\pi\) | ||||
−0.838620 | + | 0.544717i | \(0.816637\pi\) | |||||||
\(968\) | −5.81857e9 | − | 6.86506e8i | −0.206183 | − | 0.0243266i | ||||
\(969\) | 1.30925e9 | − | 1.48262e9i | 0.0462263 | − | 0.0523477i | ||||
\(970\) | −1.41827e9 | + | 3.62105e10i | −0.0498952 | + | 1.27389i | ||||
\(971\) | 1.86762e10 | 0.654667 | 0.327334 | − | 0.944909i | \(-0.393850\pi\) | ||||
0.327334 | + | 0.944909i | \(0.393850\pi\) | |||||||
\(972\) | 2.54995e10 | + | 2.00057e9i | 0.890635 | + | 0.0698751i | ||||
\(973\) | 2.77583e10 | 0.966045 | ||||||||
\(974\) | −2.43128e10 | − | 9.52270e8i | −0.843098 | − | 0.0330220i | ||||
\(975\) | − | 8.12929e8i | − | 0.0280890i | ||||||
\(976\) | 7.90324e9 | + | 1.24778e9i | 0.272102 | + | 0.0429601i | ||||
\(977\) | − | 4.63388e10i | − | 1.58970i | −0.606809 | − | 0.794848i | \(-0.707551\pi\) | ||
0.606809 | − | 0.794848i | \(-0.292449\pi\) | |||||||
\(978\) | 3.31169e8 | − | 8.45519e9i | 0.0113204 | − | 0.289026i | ||||
\(979\) | −3.84659e10 | −1.31020 | ||||||||
\(980\) | −4.74042e10 | − | 3.71911e9i | −1.60889 | − | 0.126226i | ||||
\(981\) | 2.34686e9i | 0.0793680i | ||||||||
\(982\) | 1.39278e9 | − | 3.55595e10i | 0.0469344 | − | 1.19830i | ||||
\(983\) | −1.38258e10 | −0.464251 | −0.232126 | − | 0.972686i | \(-0.574568\pi\) | ||||
−0.232126 | + | 0.972686i | \(0.574568\pi\) | |||||||
\(984\) | −1.96828e9 | + | 1.66824e10i | −0.0658574 | + | 0.558182i | ||||
\(985\) | 3.93284e10 | 1.31123 | ||||||||
\(986\) | −4.18461e8 | + | 1.06839e10i | −0.0139023 | + | 0.354944i | ||||
\(987\) | 1.67691e10 | 0.555135 | ||||||||
\(988\) | 3.39832e9 | + | 3.51079e9i | 0.112103 | + | 0.115812i | ||||
\(989\) | −1.42663e10 | −0.468948 | ||||||||
\(990\) | 1.13347e9 | − | 2.89390e10i | 0.0371267 | − | 0.947894i | ||||
\(991\) | −4.33942e10 | −1.41636 | −0.708180 | − | 0.706032i | \(-0.750483\pi\) | ||||
−0.708180 | + | 0.706032i | \(0.750483\pi\) | |||||||
\(992\) | 3.20487e10 | + | 6.35450e9i | 1.04237 | + | 0.206676i | ||||
\(993\) | 1.64681e10 | 0.533730 | ||||||||
\(994\) | −2.42927e9 | + | 6.20227e10i | −0.0784557 | + | 2.00308i | ||||
\(995\) | 2.66717e10i | 0.858361i | ||||||||
\(996\) | 6.12759e8 | − | 7.81028e9i | 0.0196509 | − | 0.250472i | ||||
\(997\) | −3.34859e10 | −1.07011 | −0.535055 | − | 0.844817i | \(-0.679709\pi\) | ||||
−0.535055 | + | 0.844817i | \(0.679709\pi\) | |||||||
\(998\) | 5.98718e8 | − | 1.52861e10i | 0.0190662 | − | 0.486787i | ||||
\(999\) | 3.40593e9i | 0.108083i |
(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 | 76.8.d.a.75.1 | ✓ | 68 | |
4.3 | odd | 2 | inner | 76.8.d.a.75.67 | yes | 68 | |
19.18 | odd | 2 | inner | 76.8.d.a.75.68 | yes | 68 | |
76.75 | even | 2 | inner | 76.8.d.a.75.2 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.d.a.75.1 | ✓ | 68 | 1.1 | even | 1 | trivial | |
76.8.d.a.75.2 | yes | 68 | 76.75 | even | 2 | inner | |
76.8.d.a.75.67 | yes | 68 | 4.3 | odd | 2 | inner | |
76.8.d.a.75.68 | yes | 68 | 19.18 | odd | 2 | inner |