Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,6,Mod(29,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.29");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.f (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: | \(6.41535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.7 | ||
Character | \(\chi\) | \(=\) | 40.29 |
Dual form | 40.6.f.a.29.8 |
$q$-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 \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53479 | − | 4.41648i | −0.624868 | − | 0.780730i | ||||
\(3\) | −21.4357 | −1.37510 | −0.687551 | − | 0.726136i | \(-0.741314\pi\) | ||||
−0.687551 | + | 0.726136i | \(0.741314\pi\) | |||||||
\(4\) | −7.01055 | + | 31.2226i | −0.219080 | + | 0.975707i | ||||
\(5\) | −48.3867 | − | 27.9951i | −0.865568 | − | 0.500792i | ||||
\(6\) | 75.7708 | + | 94.6704i | 0.859258 | + | 1.07358i | ||||
\(7\) | 39.9262i | 0.307973i | 0.988073 | + | 0.153987i | \(0.0492113\pi\) | ||||
−0.988073 | + | 0.153987i | \(0.950789\pi\) | |||||||
\(8\) | 162.675 | − | 79.4034i | 0.898660 | − | 0.438646i | ||||
\(9\) | 216.491 | 0.890908 | ||||||||
\(10\) | 47.3969 | + | 312.656i | 0.149882 | + | 0.988704i | ||||
\(11\) | − | 141.626i | − | 0.352908i | −0.984309 | − | 0.176454i | \(-0.943537\pi\) | ||
0.984309 | − | 0.176454i | \(-0.0564627\pi\) | |||||||
\(12\) | 150.276 | − | 669.280i | 0.301257 | − | 1.34170i | ||||
\(13\) | 700.139 | 1.14902 | 0.574508 | − | 0.818499i | \(-0.305194\pi\) | ||||
0.574508 | + | 0.818499i | \(0.305194\pi\) | |||||||
\(14\) | 176.333 | − | 141.131i | 0.240444 | − | 0.192443i | ||||
\(15\) | 1037.20 | + | 600.096i | 1.19024 | + | 0.688641i | ||||
\(16\) | −925.704 | − | 437.776i | −0.904008 | − | 0.427515i | ||||
\(17\) | − | 960.152i | − | 0.805782i | −0.915248 | − | 0.402891i | \(-0.868005\pi\) | ||
0.915248 | − | 0.402891i | \(-0.131995\pi\) | |||||||
\(18\) | −765.249 | − | 956.126i | −0.556700 | − | 0.695559i | ||||
\(19\) | 2202.13i | 1.39946i | 0.714409 | + | 0.699728i | \(0.246696\pi\) | ||||
−0.714409 | + | 0.699728i | \(0.753304\pi\) | |||||||
\(20\) | 1213.30 | − | 1314.50i | 0.678255 | − | 0.734827i | ||||
\(21\) | − | 855.847i | − | 0.423495i | ||||||
\(22\) | −625.488 | + | 500.618i | −0.275526 | + | 0.220521i | ||||
\(23\) | 4492.21i | 1.77068i | 0.464944 | + | 0.885340i | \(0.346074\pi\) | ||||
−0.464944 | + | 0.885340i | \(0.653926\pi\) | |||||||
\(24\) | −3487.05 | + | 1702.07i | −1.23575 | + | 0.603183i | ||||
\(25\) | 1557.55 | + | 2709.18i | 0.498415 | + | 0.866939i | ||||
\(26\) | −2474.84 | − | 3092.15i | −0.717983 | − | 0.897071i | ||||
\(27\) | 568.247 | 0.150012 | ||||||||
\(28\) | −1246.60 | − | 279.905i | −0.300492 | − | 0.0674707i | ||||
\(29\) | − | 4834.96i | − | 1.06757i | −0.845619 | − | 0.533787i | \(-0.820768\pi\) | ||
0.845619 | − | 0.533787i | \(-0.179232\pi\) | |||||||
\(30\) | −1015.99 | − | 6702.00i | −0.206103 | − | 1.35957i | ||||
\(31\) | −1122.17 | −0.209727 | −0.104864 | − | 0.994487i | \(-0.533441\pi\) | ||||
−0.104864 | + | 0.994487i | \(0.533441\pi\) | |||||||
\(32\) | 1338.74 | + | 5635.80i | 0.231112 | + | 0.972927i | ||||
\(33\) | 3035.86i | 0.485285i | ||||||||
\(34\) | −4240.49 | + | 3393.93i | −0.629098 | + | 0.503507i | ||||
\(35\) | 1117.74 | − | 1931.90i | 0.154231 | − | 0.266572i | ||||
\(36\) | −1517.72 | + | 6759.41i | −0.195180 | + | 0.869265i | ||||
\(37\) | −8779.50 | −1.05430 | −0.527152 | − | 0.849771i | \(-0.676740\pi\) | ||||
−0.527152 | + | 0.849771i | \(0.676740\pi\) | |||||||
\(38\) | 9725.67 | − | 7784.07i | 1.09260 | − | 0.874476i | ||||
\(39\) | −15008.0 | −1.58001 | ||||||||
\(40\) | −10094.2 | − | 712.033i | −0.997521 | − | 0.0703640i | ||||
\(41\) | 11522.4 | 1.07050 | 0.535248 | − | 0.844695i | \(-0.320218\pi\) | ||||
0.535248 | + | 0.844695i | \(0.320218\pi\) | |||||||
\(42\) | −3779.83 | + | 3025.24i | −0.330635 | + | 0.264628i | ||||
\(43\) | 17358.0 | 1.43162 | 0.715811 | − | 0.698295i | \(-0.246057\pi\) | ||||
0.715811 | + | 0.698295i | \(0.246057\pi\) | |||||||
\(44\) | 4421.94 | + | 992.877i | 0.344335 | + | 0.0773150i | ||||
\(45\) | −10475.3 | − | 6060.68i | −0.771141 | − | 0.446160i | ||||
\(46\) | 19839.7 | − | 15879.0i | 1.38242 | − | 1.10644i | ||||
\(47\) | − | 15167.7i | − | 1.00156i | −0.865576 | − | 0.500778i | \(-0.833047\pi\) | ||
0.865576 | − | 0.500778i | \(-0.166953\pi\) | |||||||
\(48\) | 19843.2 | + | 9384.04i | 1.24310 | + | 0.587877i | ||||
\(49\) | 15212.9 | 0.905153 | ||||||||
\(50\) | 6459.46 | − | 16455.3i | 0.365402 | − | 0.930850i | ||||
\(51\) | 20581.6i | 1.10803i | ||||||||
\(52\) | −4908.36 | + | 21860.2i | −0.251726 | + | 1.12110i | ||||
\(53\) | 7119.05 | 0.348123 | 0.174061 | − | 0.984735i | \(-0.444311\pi\) | ||||
0.174061 | + | 0.984735i | \(0.444311\pi\) | |||||||
\(54\) | −2008.63 | − | 2509.65i | −0.0937380 | − | 0.117119i | ||||
\(55\) | −3964.84 | + | 6852.82i | −0.176733 | + | 0.305466i | ||||
\(56\) | 3170.28 | + | 6494.99i | 0.135091 | + | 0.276763i | ||||
\(57\) | − | 47204.3i | − | 1.92440i | ||||||
\(58\) | −21353.5 | + | 17090.6i | −0.833488 | + | 0.667093i | ||||
\(59\) | 41761.3i | 1.56187i | 0.624614 | + | 0.780934i | \(0.285256\pi\) | ||||
−0.624614 | + | 0.780934i | \(0.714744\pi\) | |||||||
\(60\) | −26007.9 | + | 28177.2i | −0.932670 | + | 1.01046i | ||||
\(61\) | 20347.5i | 0.700143i | 0.936723 | + | 0.350072i | \(0.113843\pi\) | ||||
−0.936723 | + | 0.350072i | \(0.886157\pi\) | |||||||
\(62\) | 3966.64 | + | 4956.04i | 0.131052 | + | 0.163740i | ||||
\(63\) | 8643.65i | 0.274376i | ||||||||
\(64\) | 20158.2 | − | 25833.9i | 0.615179 | − | 0.788387i | ||||
\(65\) | −33877.4 | − | 19600.5i | −0.994551 | − | 0.575418i | ||||
\(66\) | 13407.8 | − | 10731.1i | 0.378877 | − | 0.303239i | ||||
\(67\) | −23764.7 | −0.646762 | −0.323381 | − | 0.946269i | \(-0.604820\pi\) | ||||
−0.323381 | + | 0.946269i | \(0.604820\pi\) | |||||||
\(68\) | 29978.4 | + | 6731.19i | 0.786207 | + | 0.176530i | ||||
\(69\) | − | 96293.7i | − | 2.43487i | ||||||
\(70\) | −12483.2 | + | 1892.38i | −0.304494 | + | 0.0461596i | ||||
\(71\) | 881.677 | 0.0207570 | 0.0103785 | − | 0.999946i | \(-0.496696\pi\) | ||||
0.0103785 | + | 0.999946i | \(0.496696\pi\) | |||||||
\(72\) | 35217.6 | − | 17190.1i | 0.800623 | − | 0.390793i | ||||
\(73\) | 7051.66i | 0.154876i | 0.996997 | + | 0.0774381i | \(0.0246740\pi\) | ||||
−0.996997 | + | 0.0774381i | \(0.975326\pi\) | |||||||
\(74\) | 31033.7 | + | 38774.5i | 0.658800 | + | 0.823126i | ||||
\(75\) | −33387.1 | − | 58073.3i | −0.685371 | − | 1.19213i | ||||
\(76\) | −68756.4 | − | 15438.2i | −1.36546 | − | 0.306593i | ||||
\(77\) | 5654.59 | 0.108686 | ||||||||
\(78\) | 53050.1 | + | 66282.5i | 0.987301 | + | 1.23357i | ||||
\(79\) | −47780.1 | −0.861350 | −0.430675 | − | 0.902507i | \(-0.641724\pi\) | ||||
−0.430675 | + | 0.902507i | \(0.641724\pi\) | |||||||
\(80\) | 32536.2 | + | 47097.7i | 0.568384 | + | 0.822763i | ||||
\(81\) | −64788.0 | −1.09719 | ||||||||
\(82\) | −40729.4 | − | 50888.6i | −0.668919 | − | 0.835768i | ||||
\(83\) | 51692.3 | 0.823628 | 0.411814 | − | 0.911268i | \(-0.364895\pi\) | ||||
0.411814 | + | 0.911268i | \(0.364895\pi\) | |||||||
\(84\) | 26721.8 | + | 5999.96i | 0.413207 | + | 0.0927791i | ||||
\(85\) | −26879.6 | + | 46458.6i | −0.403529 | + | 0.697459i | ||||
\(86\) | −61356.8 | − | 76661.1i | −0.894574 | − | 1.11771i | ||||
\(87\) | 103641.i | 1.46802i | ||||||||
\(88\) | −11245.6 | − | 23039.0i | −0.154802 | − | 0.317144i | ||||
\(89\) | 122761. | 1.64281 | 0.821404 | − | 0.570347i | \(-0.193191\pi\) | ||||
0.821404 | + | 0.570347i | \(0.193191\pi\) | |||||||
\(90\) | 10261.0 | + | 67687.0i | 0.133531 | + | 0.880844i | ||||
\(91\) | 27953.9i | 0.353866i | ||||||||
\(92\) | −140258. | − | 31492.8i | −1.72766 | − | 0.387920i | ||||
\(93\) | 24054.6 | 0.288397 | ||||||||
\(94\) | −66987.8 | + | 53614.6i | −0.781945 | + | 0.625840i | ||||
\(95\) | 61649.0 | − | 106554.i | 0.700837 | − | 1.21132i | ||||
\(96\) | −28696.9 | − | 120807.i | −0.317803 | − | 1.33788i | ||||
\(97\) | 155549.i | 1.67856i | 0.543696 | + | 0.839282i | \(0.317024\pi\) | ||||
−0.543696 | + | 0.839282i | \(0.682976\pi\) | |||||||
\(98\) | −53774.4 | − | 67187.4i | −0.565601 | − | 0.706680i | ||||
\(99\) | − | 30660.7i | − | 0.314409i | ||||||
\(100\) | −95507.1 | + | 29637.8i | −0.955071 | + | 0.296378i | ||||
\(101\) | 195692.i | 1.90884i | 0.298466 | + | 0.954420i | \(0.403525\pi\) | ||||
−0.298466 | + | 0.954420i | \(0.596475\pi\) | |||||||
\(102\) | 90898.0 | − | 72751.4i | 0.865075 | − | 0.692374i | ||||
\(103\) | − | 60625.8i | − | 0.563073i | −0.959551 | − | 0.281536i | \(-0.909156\pi\) | ||
0.959551 | − | 0.281536i | \(-0.0908440\pi\) | |||||||
\(104\) | 113895. | − | 55593.4i | 1.03257 | − | 0.504011i | ||||
\(105\) | −23959.6 | + | 41411.6i | −0.212083 | + | 0.366563i | ||||
\(106\) | −25164.3 | − | 31441.1i | −0.217531 | − | 0.271790i | ||||
\(107\) | 10924.2 | 0.0922422 | 0.0461211 | − | 0.998936i | \(-0.485314\pi\) | ||||
0.0461211 | + | 0.998936i | \(0.485314\pi\) | |||||||
\(108\) | −3983.72 | + | 17742.1i | −0.0328647 | + | 0.146368i | ||||
\(109\) | 11344.4i | 0.0914569i | 0.998954 | + | 0.0457285i | \(0.0145609\pi\) | ||||
−0.998954 | + | 0.0457285i | \(0.985439\pi\) | |||||||
\(110\) | 44280.2 | − | 6712.63i | 0.348921 | − | 0.0528946i | ||||
\(111\) | 188195. | 1.44978 | ||||||||
\(112\) | 17478.7 | − | 36959.9i | 0.131663 | − | 0.278410i | ||||
\(113\) | 66586.5i | 0.490557i | 0.969453 | + | 0.245279i | \(0.0788795\pi\) | ||||
−0.969453 | + | 0.245279i | \(0.921121\pi\) | |||||||
\(114\) | −208477. | + | 166857.i | −1.50244 | + | 1.20249i | ||||
\(115\) | 125760. | − | 217363.i | 0.886743 | − | 1.53264i | ||||
\(116\) | 150960. | + | 33895.8i | 1.04164 | + | 0.233884i | ||||
\(117\) | 151574. | 1.02367 | ||||||||
\(118\) | 184438. | − | 147617.i | 1.21940 | − | 0.975961i | ||||
\(119\) | 38335.2 | 0.248159 | ||||||||
\(120\) | 216377. | + | 15263.0i | 1.37169 | + | 0.0967577i | ||||
\(121\) | 140993. | 0.875456 | ||||||||
\(122\) | 89864.4 | − | 71924.2i | 0.546623 | − | 0.437497i | ||||
\(123\) | −246992. | −1.47204 | ||||||||
\(124\) | 7867.04 | − | 35037.1i | 0.0459470 | − | 0.204632i | ||||
\(125\) | 479.446 | − | 174692.i | 0.00274451 | − | 0.999996i | ||||
\(126\) | 38174.5 | − | 30553.5i | 0.214214 | − | 0.171449i | ||||
\(127\) | 88813.9i | 0.488621i | 0.969697 | + | 0.244310i | \(0.0785616\pi\) | ||||
−0.969697 | + | 0.244310i | \(0.921438\pi\) | |||||||
\(128\) | −185350. | + | 2289.02i | −0.999924 | + | 0.0123488i | ||||
\(129\) | −372081. | −1.96863 | ||||||||
\(130\) | 33184.4 | + | 218902.i | 0.172217 | + | 1.13604i | ||||
\(131\) | 83967.1i | 0.427495i | 0.976889 | + | 0.213748i | \(0.0685670\pi\) | ||||
−0.976889 | + | 0.213748i | \(0.931433\pi\) | |||||||
\(132\) | −94787.5 | − | 21283.0i | −0.473496 | − | 0.106316i | ||||
\(133\) | −87922.8 | −0.430995 | ||||||||
\(134\) | 84003.0 | + | 104956.i | 0.404141 | + | 0.504947i | ||||
\(135\) | −27495.6 | − | 15908.1i | −0.129846 | − | 0.0751251i | ||||
\(136\) | −76239.3 | − | 156192.i | −0.353453 | − | 0.724124i | ||||
\(137\) | − | 275285.i | − | 1.25309i | −0.779387 | − | 0.626543i | \(-0.784469\pi\) | ||
0.779387 | − | 0.626543i | \(-0.215531\pi\) | |||||||
\(138\) | −425279. | + | 340378.i | −1.90097 | + | 1.52147i | ||||
\(139\) | − | 153603.i | − | 0.674317i | −0.941448 | − | 0.337158i | \(-0.890534\pi\) | ||
0.941448 | − | 0.337158i | \(-0.109466\pi\) | |||||||
\(140\) | 52482.9 | + | 48442.4i | 0.226307 | + | 0.208884i | ||||
\(141\) | 325131.i | 1.37724i | ||||||||
\(142\) | −3116.54 | − | 3893.91i | −0.0129704 | − | 0.0162056i | ||||
\(143\) | − | 99157.9i | − | 0.405497i | ||||||
\(144\) | −200406. | − | 94774.3i | −0.805388 | − | 0.380877i | ||||
\(145\) | −135355. | + | 233948.i | −0.534633 | + | 0.924058i | ||||
\(146\) | 31143.5 | − | 24926.1i | 0.120916 | − | 0.0967772i | ||||
\(147\) | −326100. | −1.24468 | ||||||||
\(148\) | 61549.1 | − | 274119.i | 0.230976 | − | 1.02869i | ||||
\(149\) | 30715.3i | 0.113342i | 0.998393 | + | 0.0566708i | \(0.0180486\pi\) | ||||
−0.998393 | + | 0.0566708i | \(0.981951\pi\) | |||||||
\(150\) | −138463. | + | 352730.i | −0.502465 | + | 1.28001i | ||||
\(151\) | −25896.6 | −0.0924272 | −0.0462136 | − | 0.998932i | \(-0.514715\pi\) | ||||
−0.0462136 | + | 0.998932i | \(0.514715\pi\) | |||||||
\(152\) | 174857. | + | 358232.i | 0.613866 | + | 1.25764i | ||||
\(153\) | − | 207864.i | − | 0.717878i | ||||||
\(154\) | −19987.8 | − | 24973.4i | −0.0679145 | − | 0.0848546i | ||||
\(155\) | 54298.2 | + | 31415.3i | 0.181533 | + | 0.105030i | ||||
\(156\) | 105214. | − | 468589.i | 0.346149 | − | 1.54163i | ||||
\(157\) | 334928. | 1.08443 | 0.542216 | − | 0.840239i | \(-0.317585\pi\) | ||||
0.542216 | + | 0.840239i | \(0.317585\pi\) | |||||||
\(158\) | 168893. | + | 211020.i | 0.538230 | + | 0.672482i | ||||
\(159\) | −152602. | −0.478704 | ||||||||
\(160\) | 92997.5 | − | 310176.i | 0.287191 | − | 0.957873i | ||||
\(161\) | −179357. | −0.545322 | ||||||||
\(162\) | 229012. | + | 286135.i | 0.685600 | + | 0.856610i | ||||
\(163\) | 203546. | 0.600057 | 0.300029 | − | 0.953930i | \(-0.403004\pi\) | ||||
0.300029 | + | 0.953930i | \(0.403004\pi\) | |||||||
\(164\) | −80778.7 | + | 359761.i | −0.234524 | + | 1.04449i | ||||
\(165\) | 84989.2 | − | 146895.i | 0.243027 | − | 0.420047i | ||||
\(166\) | −182721. | − | 228298.i | −0.514659 | − | 0.643031i | ||||
\(167\) | − | 52221.5i | − | 0.144897i | −0.997372 | − | 0.0724483i | \(-0.976919\pi\) | ||
0.997372 | − | 0.0724483i | \(-0.0230812\pi\) | |||||||
\(168\) | −67957.2 | − | 139225.i | −0.185764 | − | 0.380578i | ||||
\(169\) | 118902. | 0.320236 | ||||||||
\(170\) | 300197. | − | 45508.2i | 0.796680 | − | 0.120772i | ||||
\(171\) | 476741.i | 1.24679i | ||||||||
\(172\) | −121689. | + | 541962.i | −0.313639 | + | 1.39684i | ||||
\(173\) | −503329. | −1.27861 | −0.639303 | − | 0.768955i | \(-0.720777\pi\) | ||||
−0.639303 | + | 0.768955i | \(0.720777\pi\) | |||||||
\(174\) | 457728. | − | 366349.i | 1.14613 | − | 0.917322i | ||||
\(175\) | −108167. | + | 62186.9i | −0.266994 | + | 0.153498i | ||||
\(176\) | −62000.4 | + | 131104.i | −0.150873 | + | 0.319032i | ||||
\(177\) | − | 895185.i | − | 2.14773i | ||||||
\(178\) | −433935. | − | 542173.i | −1.02654 | − | 1.28259i | ||||
\(179\) | − | 249706.i | − | 0.582501i | −0.956647 | − | 0.291251i | \(-0.905929\pi\) | ||
0.956647 | − | 0.291251i | \(-0.0940713\pi\) | |||||||
\(180\) | 262668. | − | 284577.i | 0.604263 | − | 0.654663i | ||||
\(181\) | − | 341157.i | − | 0.774031i | −0.922073 | − | 0.387015i | \(-0.873506\pi\) | ||
0.922073 | − | 0.387015i | \(-0.126494\pi\) | |||||||
\(182\) | 123458. | − | 98811.1i | 0.276274 | − | 0.221120i | ||||
\(183\) | − | 436164.i | − | 0.962769i | ||||||
\(184\) | 356696. | + | 730769.i | 0.776702 | + | 1.59124i | ||||
\(185\) | 424811. | + | 245783.i | 0.912571 | + | 0.527987i | ||||
\(186\) | −85027.8 | − | 106236.i | −0.180210 | − | 0.225160i | ||||
\(187\) | −135982. | −0.284367 | ||||||||
\(188\) | 473575. | + | 106334.i | 0.977225 | + | 0.219420i | ||||
\(189\) | 22687.9i | 0.0461998i | ||||||||
\(190\) | −688509. | + | 104374.i | −1.38365 | + | 0.209753i | ||||
\(191\) | −592636. | −1.17545 | −0.587726 | − | 0.809060i | \(-0.699977\pi\) | ||||
−0.587726 | + | 0.809060i | \(0.699977\pi\) | |||||||
\(192\) | −432106. | + | 553768.i | −0.845935 | + | 1.08411i | ||||
\(193\) | 771725.i | 1.49131i | 0.666330 | + | 0.745657i | \(0.267864\pi\) | ||||
−0.666330 | + | 0.745657i | \(0.732136\pi\) | |||||||
\(194\) | 686979. | − | 549833.i | 1.31051 | − | 1.04888i | ||||
\(195\) | 726187. | + | 420151.i | 1.36761 | + | 0.791259i | ||||
\(196\) | −106651. | + | 474987.i | −0.198301 | + | 0.883164i | ||||
\(197\) | −190213. | −0.349200 | −0.174600 | − | 0.984639i | \(-0.555863\pi\) | ||||
−0.174600 | + | 0.984639i | \(0.555863\pi\) | |||||||
\(198\) | −135412. | + | 108379.i | −0.245468 | + | 0.196464i | ||||
\(199\) | 949154. | 1.69904 | 0.849521 | − | 0.527555i | \(-0.176891\pi\) | ||||
0.849521 | + | 0.527555i | \(0.176891\pi\) | |||||||
\(200\) | 468492. | + | 317042.i | 0.828184 | + | 0.560456i | ||||
\(201\) | 509413. | 0.889364 | ||||||||
\(202\) | 864269. | − | 691730.i | 1.49029 | − | 1.19277i | ||||
\(203\) | 193042. | 0.328784 | ||||||||
\(204\) | −642610. | − | 144288.i | −1.08112 | − | 0.242748i | ||||
\(205\) | −557533. | − | 322572.i | −0.926586 | − | 0.536096i | ||||
\(206\) | −267753. | + | 214299.i | −0.439608 | + | 0.351846i | ||||
\(207\) | 972521.i | 1.57751i | ||||||||
\(208\) | −648122. | − | 306504.i | −1.03872 | − | 0.491222i | ||||
\(209\) | 311879. | 0.493879 | ||||||||
\(210\) | 267585. | − | 40564.5i | 0.418711 | − | 0.0634743i | ||||
\(211\) | 47751.4i | 0.0738380i | 0.999318 | + | 0.0369190i | \(0.0117544\pi\) | ||||
−0.999318 | + | 0.0369190i | \(0.988246\pi\) | |||||||
\(212\) | −49908.4 | + | 222275.i | −0.0762666 | + | 0.339666i | ||||
\(213\) | −18899.4 | −0.0285430 | ||||||||
\(214\) | −38614.7 | − | 48246.4i | −0.0576392 | − | 0.0720163i | ||||
\(215\) | −839896. | − | 485939.i | −1.23916 | − | 0.716945i | ||||
\(216\) | 92439.4 | − | 45120.7i | 0.134810 | − | 0.0658024i | ||||
\(217\) | − | 44804.0i | − | 0.0645904i | ||||||
\(218\) | 50102.4 | − | 40100.2i | 0.0714032 | − | 0.0571485i | ||||
\(219\) | − | 151158.i | − | 0.212971i | ||||||
\(220\) | −186167. | − | 171835.i | −0.259326 | − | 0.239361i | ||||
\(221\) | − | 672239.i | − | 0.925856i | ||||||
\(222\) | −665229. | − | 831159.i | −0.905918 | − | 1.13188i | ||||
\(223\) | 648287.i | 0.872982i | 0.899709 | + | 0.436491i | \(0.143779\pi\) | ||||
−0.899709 | + | 0.436491i | \(0.856221\pi\) | |||||||
\(224\) | −225016. | + | 53450.9i | −0.299635 | + | 0.0711762i | ||||
\(225\) | 337194. | + | 586513.i | 0.444042 | + | 0.772363i | ||||
\(226\) | 294078. | − | 235369.i | 0.382993 | − | 0.306534i | ||||
\(227\) | 17476.8 | 0.0225111 | 0.0112556 | − | 0.999937i | \(-0.496417\pi\) | ||||
0.0112556 | + | 0.999937i | \(0.496417\pi\) | |||||||
\(228\) | 1.47384e6 | + | 330928.i | 1.87765 | + | 0.421596i | ||||
\(229\) | 735371.i | 0.926655i | 0.886187 | + | 0.463327i | \(0.153345\pi\) | ||||
−0.886187 | + | 0.463327i | \(0.846655\pi\) | |||||||
\(230\) | −1.40451e6 | + | 212916.i | −1.75068 | + | 0.265393i | ||||
\(231\) | −121210. | −0.149455 | ||||||||
\(232\) | −383913. | − | 786527.i | −0.468287 | − | 0.959386i | ||||
\(233\) | − | 70875.0i | − | 0.0855270i | −0.999085 | − | 0.0427635i | \(-0.986384\pi\) | ||
0.999085 | − | 0.0427635i | \(-0.0136162\pi\) | |||||||
\(234\) | −535780. | − | 669421.i | −0.639657 | − | 0.799208i | ||||
\(235\) | −424622. | + | 733915.i | −0.501571 | + | 0.866914i | ||||
\(236\) | −1.30390e6 | − | 292770.i | −1.52392 | − | 0.342173i | ||||
\(237\) | 1.02420e6 | 1.18445 | ||||||||
\(238\) | −135507. | − | 169307.i | −0.155067 | − | 0.193745i | ||||
\(239\) | −516369. | −0.584743 | −0.292372 | − | 0.956305i | \(-0.594444\pi\) | ||||
−0.292372 | + | 0.956305i | \(0.594444\pi\) | |||||||
\(240\) | −697437. | − | 1.00957e6i | −0.781587 | − | 1.13138i | ||||
\(241\) | 609937. | 0.676460 | 0.338230 | − | 0.941064i | \(-0.390172\pi\) | ||||
0.338230 | + | 0.941064i | \(0.390172\pi\) | |||||||
\(242\) | −498381. | − | 622693.i | −0.547045 | − | 0.683495i | ||||
\(243\) | 1.25069e6 | 1.35874 | ||||||||
\(244\) | −635303. | − | 142647.i | −0.683135 | − | 0.153387i | ||||
\(245\) | −736102. | − | 425887.i | −0.783471 | − | 0.453293i | ||||
\(246\) | 873064. | + | 1.09083e6i | 0.919832 | + | 1.14927i | ||||
\(247\) | 1.54180e6i | 1.60800i | ||||||||
\(248\) | −182549. | + | 89104.2i | −0.188474 | + | 0.0919960i | ||||
\(249\) | −1.10806e6 | −1.13257 | ||||||||
\(250\) | −773219. | + | 615382.i | −0.782442 | + | 0.622723i | ||||
\(251\) | 327106.i | 0.327721i | 0.986484 | + | 0.163860i | \(0.0523947\pi\) | ||||
−0.986484 | + | 0.163860i | \(0.947605\pi\) | |||||||
\(252\) | −269877. | − | 60596.7i | −0.267710 | − | 0.0601102i | ||||
\(253\) | 636213. | 0.624887 | ||||||||
\(254\) | 392245. | − | 313938.i | 0.381481 | − | 0.305323i | ||||
\(255\) | 576183. | − | 995873.i | 0.554894 | − | 0.959077i | ||||
\(256\) | 665281. | + | 810501.i | 0.634462 | + | 0.772954i | ||||
\(257\) | − | 882853.i | − | 0.833788i | −0.908955 | − | 0.416894i | \(-0.863119\pi\) | ||
0.908955 | − | 0.416894i | \(-0.136881\pi\) | |||||||
\(258\) | 1.31523e6 | + | 1.64329e6i | 1.23013 | + | 1.53697i | ||||
\(259\) | − | 350532.i | − | 0.324697i | ||||||
\(260\) | 849478. | − | 920332.i | 0.779325 | − | 0.844328i | ||||
\(261\) | − | 1.04672e6i | − | 0.951111i | ||||||
\(262\) | 370839. | − | 296806.i | 0.333758 | − | 0.267128i | ||||
\(263\) | 454062.i | 0.404786i | 0.979304 | + | 0.202393i | \(0.0648719\pi\) | ||||
−0.979304 | + | 0.202393i | \(0.935128\pi\) | |||||||
\(264\) | 241058. | + | 493858.i | 0.212868 | + | 0.436106i | ||||
\(265\) | −344467. | − | 199299.i | −0.301324 | − | 0.174337i | ||||
\(266\) | 310788. | + | 388309.i | 0.269315 | + | 0.336491i | ||||
\(267\) | −2.63148e6 | −2.25903 | ||||||||
\(268\) | 166603. | − | 741995.i | 0.141692 | − | 0.631050i | ||||
\(269\) | − | 384748.i | − | 0.324187i | −0.986775 | − | 0.162093i | \(-0.948175\pi\) | ||
0.986775 | − | 0.162093i | \(-0.0518246\pi\) | |||||||
\(270\) | 26933.1 | + | 177665.i | 0.0224842 | + | 0.148318i | ||||
\(271\) | 1.36818e6 | 1.13167 | 0.565837 | − | 0.824517i | \(-0.308553\pi\) | ||||
0.565837 | + | 0.824517i | \(0.308553\pi\) | |||||||
\(272\) | −420331. | + | 888816.i | −0.344484 | + | 0.728433i | ||||
\(273\) | − | 599212.i | − | 0.486602i | ||||||
\(274\) | −1.21579e6 | + | 973073.i | −0.978322 | + | 0.783013i | ||||
\(275\) | 383691. | − | 220589.i | 0.305950 | − | 0.175894i | ||||
\(276\) | 3.00654e6 | + | 675072.i | 2.37572 | + | 0.533430i | ||||
\(277\) | 567739. | 0.444579 | 0.222290 | − | 0.974981i | \(-0.428647\pi\) | ||||
0.222290 | + | 0.974981i | \(0.428647\pi\) | |||||||
\(278\) | −678386. | + | 542955.i | −0.526459 | + | 0.421359i | ||||
\(279\) | −242940. | −0.186848 | ||||||||
\(280\) | 28428.8 | − | 403023.i | 0.0216702 | − | 0.307210i | ||||
\(281\) | −1.90809e6 | −1.44156 | −0.720779 | − | 0.693165i | \(-0.756216\pi\) | ||||
−0.720779 | + | 0.693165i | \(0.756216\pi\) | |||||||
\(282\) | 1.43593e6 | − | 1.14927e6i | 1.07525 | − | 0.860594i | ||||
\(283\) | −873157. | −0.648077 | −0.324038 | − | 0.946044i | \(-0.605041\pi\) | ||||
−0.324038 | + | 0.946044i | \(0.605041\pi\) | |||||||
\(284\) | −6181.04 | + | 27528.3i | −0.00454743 | + | 0.0202527i | ||||
\(285\) | −1.32149e6 | + | 2.28406e6i | −0.963723 | + | 1.66570i | ||||
\(286\) | −437929. | + | 350502.i | −0.316584 | + | 0.253382i | ||||
\(287\) | 460047.i | 0.329684i | ||||||||
\(288\) | 289825. | + | 1.22010e6i | 0.205899 | + | 0.866789i | ||||
\(289\) | 497966. | 0.350716 | ||||||||
\(290\) | 1.51168e6 | − | 229162.i | 1.05552 | − | 0.160010i | ||||
\(291\) | − | 3.33431e6i | − | 2.30820i | ||||||
\(292\) | −220171. | − | 49436.0i | −0.151114 | − | 0.0339302i | ||||
\(293\) | 422723. | 0.287665 | 0.143832 | − | 0.989602i | \(-0.454057\pi\) | ||||
0.143832 | + | 0.989602i | \(0.454057\pi\) | |||||||
\(294\) | 1.15269e6 | + | 1.44021e6i | 0.777760 | + | 0.971758i | ||||
\(295\) | 1.16911e6 | − | 2.02069e6i | 0.782171 | − | 1.35190i | ||||
\(296\) | −1.42820e6 | + | 697122.i | −0.947460 | + | 0.462466i | ||||
\(297\) | − | 80478.5i | − | 0.0529406i | ||||||
\(298\) | 135654. | − | 108572.i | 0.0884893 | − | 0.0708236i | ||||
\(299\) | 3.14517e6i | 2.03454i | ||||||||
\(300\) | 2.04726e6 | − | 635308.i | 1.31332 | − | 0.407550i | ||||
\(301\) | 693038.i | 0.440901i | ||||||||
\(302\) | 91538.9 | + | 114372.i | 0.0577548 | + | 0.0721608i | ||||
\(303\) | − | 4.19480e6i | − | 2.62485i | ||||||
\(304\) | 964040. | − | 2.03852e6i | 0.598289 | − | 1.26512i | ||||
\(305\) | 569632. | − | 984550.i | 0.350626 | − | 0.606021i | ||||
\(306\) | −918026. | + | 734755.i | −0.560469 | + | 0.448579i | ||||
\(307\) | 1.38323e6 | 0.837624 | 0.418812 | − | 0.908073i | \(-0.362447\pi\) | ||||
0.418812 | + | 0.908073i | \(0.362447\pi\) | |||||||
\(308\) | −39641.8 | + | 176551.i | −0.0238109 | + | 0.106046i | ||||
\(309\) | 1.29956e6i | 0.774283i | ||||||||
\(310\) | −53187.4 | − | 350853.i | −0.0314344 | − | 0.207358i | ||||
\(311\) | −1.96775e6 | −1.15363 | −0.576817 | − | 0.816873i | \(-0.695706\pi\) | ||||
−0.576817 | + | 0.816873i | \(0.695706\pi\) | |||||||
\(312\) | −2.44142e6 | + | 1.19169e6i | −1.41990 | + | 0.693067i | ||||
\(313\) | 2.42724e6i | 1.40040i | 0.713948 | + | 0.700199i | \(0.246905\pi\) | ||||
−0.713948 | + | 0.700199i | \(0.753095\pi\) | |||||||
\(314\) | −1.18390e6 | − | 1.47920e6i | −0.677627 | − | 0.846650i | ||||
\(315\) | 241980. | − | 418238.i | 0.137405 | − | 0.237491i | ||||
\(316\) | 334965. | − | 1.49182e6i | 0.188704 | − | 0.840425i | ||||
\(317\) | 1.28631e6 | 0.718951 | 0.359475 | − | 0.933155i | \(-0.382956\pi\) | ||||
0.359475 | + | 0.933155i | \(0.382956\pi\) | |||||||
\(318\) | 539416. | + | 673963.i | 0.299127 | + | 0.373739i | ||||
\(319\) | −684757. | −0.376756 | ||||||||
\(320\) | −1.69861e6 | + | 685684.i | −0.927297 | + | 0.374325i | ||||
\(321\) | −234168. | −0.126843 | ||||||||
\(322\) | 633988. | + | 792125.i | 0.340754 | + | 0.425749i | ||||
\(323\) | 2.11438e6 | 1.12766 | ||||||||
\(324\) | 454200. | − | 2.02285e6i | 0.240372 | − | 1.07054i | ||||
\(325\) | 1.09050e6 | + | 1.89680e6i | 0.572686 | + | 0.996126i | ||||
\(326\) | −719491. | − | 898955.i | −0.374957 | − | 0.468483i | ||||
\(327\) | − | 243176.i | − | 0.125763i | ||||||
\(328\) | 1.87441e6 | − | 914921.i | 0.962012 | − | 0.469569i | ||||
\(329\) | 605588. | 0.308452 | ||||||||
\(330\) | −949178. | + | 143890.i | −0.479803 | + | 0.0727355i | ||||
\(331\) | − | 3.07996e6i | − | 1.54517i | −0.634913 | − | 0.772584i | \(-0.718964\pi\) | ||
0.634913 | − | 0.772584i | \(-0.281036\pi\) | |||||||
\(332\) | −362392. | + | 1.61397e6i | −0.180440 | + | 0.803619i | ||||
\(333\) | −1.90068e6 | −0.939287 | ||||||||
\(334\) | −230635. | + | 184592.i | −0.113125 | + | 0.0905413i | ||||
\(335\) | 1.14989e6 | + | 665294.i | 0.559816 | + | 0.323893i | ||||
\(336\) | −374669. | + | 792262.i | −0.181050 | + | 0.382843i | ||||
\(337\) | − | 1.51034e6i | − | 0.724437i | −0.932093 | − | 0.362218i | \(-0.882019\pi\) | ||
0.932093 | − | 0.362218i | \(-0.117981\pi\) | |||||||
\(338\) | −420292. | − | 525126.i | −0.200105 | − | 0.250018i | ||||
\(339\) | − | 1.42733e6i | − | 0.674567i | ||||||
\(340\) | −1.26212e6 | − | 1.16495e6i | −0.592110 | − | 0.546525i | ||||
\(341\) | 158929.i | 0.0740144i | ||||||||
\(342\) | 2.10552e6 | − | 1.68518e6i | 0.973405 | − | 0.779078i | ||||
\(343\) | 1.27843e6i | 0.586736i | ||||||||
\(344\) | 2.82371e6 | − | 1.37828e6i | 1.28654 | − | 0.627975i | ||||
\(345\) | −2.69576e6 | + | 4.65934e6i | −1.21936 | + | 2.10754i | ||||
\(346\) | 1.77916e6 | + | 2.22294e6i | 0.798960 | + | 0.998246i | ||||
\(347\) | −4.01257e6 | −1.78895 | −0.894477 | − | 0.447113i | \(-0.852452\pi\) | ||||
−0.894477 | + | 0.447113i | \(0.852452\pi\) | |||||||
\(348\) | −3.23594e6 | − | 726580.i | −1.43236 | − | 0.321614i | ||||
\(349\) | − | 595449.i | − | 0.261686i | −0.991403 | − | 0.130843i | \(-0.958232\pi\) | ||
0.991403 | − | 0.130843i | \(-0.0417684\pi\) | |||||||
\(350\) | 656996. | + | 257902.i | 0.286677 | + | 0.112534i | ||||
\(351\) | 397852. | 0.172367 | ||||||||
\(352\) | 798176. | − | 189601.i | 0.343354 | − | 0.0815612i | ||||
\(353\) | 1.05328e6i | 0.449890i | 0.974371 | + | 0.224945i | \(0.0722203\pi\) | ||||
−0.974371 | + | 0.224945i | \(0.927780\pi\) | |||||||
\(354\) | −3.95356e6 | + | 3.16429e6i | −1.67680 | + | 1.34205i | ||||
\(355\) | −42661.5 | − | 24682.7i | −0.0179666 | − | 0.0103949i | ||||
\(356\) | −860624. | + | 3.83293e6i | −0.359906 | + | 1.60290i | ||||
\(357\) | −821743. | −0.341244 | ||||||||
\(358\) | −1.10282e6 | + | 882659.i | −0.454776 | + | 0.363986i | ||||
\(359\) | 549662. | 0.225092 | 0.112546 | − | 0.993647i | \(-0.464099\pi\) | ||||
0.112546 | + | 0.993647i | \(0.464099\pi\) | |||||||
\(360\) | −2.18530e6 | − | 154149.i | −0.888700 | − | 0.0626878i | ||||
\(361\) | −2.37329e6 | −0.958480 | ||||||||
\(362\) | −1.50671e6 | + | 1.20592e6i | −0.604309 | + | 0.483667i | ||||
\(363\) | −3.02229e6 | −1.20384 | ||||||||
\(364\) | −872794. | − | 195972.i | −0.345269 | − | 0.0775248i | ||||
\(365\) | 197412. | − | 341207.i | 0.0775607 | − | 0.134056i | ||||
\(366\) | −1.92631e6 | + | 1.54175e6i | −0.751663 | + | 0.601604i | ||||
\(367\) | − | 313163.i | − | 0.121368i | −0.998157 | − | 0.0606842i | \(-0.980672\pi\) | ||
0.998157 | − | 0.0606842i | \(-0.0193283\pi\) | |||||||
\(368\) | 1.96658e6 | − | 4.15845e6i | 0.756993 | − | 1.60071i | ||||
\(369\) | 2.49450e6 | 0.953713 | ||||||||
\(370\) | −416121. | − | 2.74496e6i | −0.158021 | − | 1.04239i | ||||
\(371\) | 284236.i | 0.107212i | ||||||||
\(372\) | −168636. | + | 751047.i | −0.0631818 | + | 0.281391i | ||||
\(373\) | 251757. | 0.0936935 | 0.0468468 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468468 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(374\) | 480669. | + | 600564.i | 0.177692 | + | 0.222014i | ||||
\(375\) | −10277.3 | + | 3.74465e6i | −0.00377399 | + | 1.37510i | ||||
\(376\) | −1.20437e6 | − | 2.46740e6i | −0.439328 | − | 0.900058i | ||||
\(377\) | − | 3.38515e6i | − | 1.22666i | ||||||
\(378\) | 100201. | − | 80197.0i | 0.0360696 | − | 0.0288688i | ||||
\(379\) | 862618.i | 0.308476i | 0.988034 | + | 0.154238i | \(0.0492922\pi\) | ||||
−0.988034 | + | 0.154238i | \(0.950708\pi\) | |||||||
\(380\) | 2.89470e6 | + | 2.67185e6i | 1.02836 | + | 0.949188i | ||||
\(381\) | − | 1.90379e6i | − | 0.671904i | ||||||
\(382\) | 2.09484e6 | + | 2.61736e6i | 0.734502 | + | 0.917711i | ||||
\(383\) | 4.09103e6i | 1.42507i | 0.701638 | + | 0.712534i | \(0.252453\pi\) | ||||
−0.701638 | + | 0.712534i | \(0.747547\pi\) | |||||||
\(384\) | 3.97311e6 | − | 49066.9i | 1.37500 | − | 0.0169809i | ||||
\(385\) | −273607. | − | 158301.i | −0.0940752 | − | 0.0544292i | ||||
\(386\) | 3.40831e6 | − | 2.72788e6i | 1.16431 | − | 0.931875i | ||||
\(387\) | 3.75784e6 | 1.27544 | ||||||||
\(388\) | −4.85665e6 | − | 1.09048e6i | −1.63779 | − | 0.367739i | ||||
\(389\) | − | 5.39187e6i | − | 1.80661i | −0.428995 | − | 0.903307i | \(-0.641132\pi\) | ||
0.428995 | − | 0.903307i | \(-0.358868\pi\) | |||||||
\(390\) | −711332. | − | 4.69233e6i | −0.236816 | − | 1.56217i | ||||
\(391\) | 4.31320e6 | 1.42678 | ||||||||
\(392\) | 2.47476e6 | − | 1.20796e6i | 0.813424 | − | 0.397042i | ||||
\(393\) | − | 1.79990e6i | − | 0.587850i | ||||||
\(394\) | 672363. | + | 840072.i | 0.218204 | + | 0.272631i | ||||
\(395\) | 2.31192e6 | + | 1.33761e6i | 0.745557 | + | 0.431357i | ||||
\(396\) | 957308. | + | 214949.i | 0.306771 | + | 0.0688805i | ||||
\(397\) | 5.41902e6 | 1.72562 | 0.862809 | − | 0.505529i | \(-0.168703\pi\) | ||||
0.862809 | + | 0.505529i | \(0.168703\pi\) | |||||||
\(398\) | −3.35506e6 | − | 4.19192e6i | −1.06168 | − | 1.32649i | ||||
\(399\) | 1.88469e6 | 0.592663 | ||||||||
\(400\) | −255812. | − | 3.18976e6i | −0.0799414 | − | 0.996800i | ||||
\(401\) | 3.22720e6 | 1.00222 | 0.501112 | − | 0.865383i | \(-0.332925\pi\) | ||||
0.501112 | + | 0.865383i | \(0.332925\pi\) | |||||||
\(402\) | −1.80067e6 | − | 2.24981e6i | −0.555735 | − | 0.694354i | ||||
\(403\) | −785676. | −0.240980 | ||||||||
\(404\) | −6.11002e6 | − | 1.37191e6i | −1.86247 | − | 0.418188i | ||||
\(405\) | 3.13488e6 | + | 1.81375e6i | 0.949693 | + | 0.549464i | ||||
\(406\) | −682361. | − | 852564.i | −0.205447 | − | 0.256692i | ||||
\(407\) | 1.24341e6i | 0.372072i | ||||||||
\(408\) | 1.63425e6 | + | 3.34810e6i | 0.486034 | + | 0.995745i | ||||
\(409\) | 523436. | 0.154723 | 0.0773616 | − | 0.997003i | \(-0.475350\pi\) | ||||
0.0773616 | + | 0.997003i | \(0.475350\pi\) | |||||||
\(410\) | 546128. | + | 3.60256e6i | 0.160448 | + | 1.05840i | ||||
\(411\) | 5.90093e6i | 1.72312i | ||||||||
\(412\) | 1.89290e6 | + | 425020.i | 0.549394 | + | 0.123358i | ||||
\(413\) | −1.66737e6 | −0.481013 | ||||||||
\(414\) | 4.29512e6 | − | 3.43765e6i | 1.23161 | − | 0.985738i | ||||
\(415\) | −2.50122e6 | − | 1.44713e6i | −0.712906 | − | 0.412466i | ||||
\(416\) | 937306. | + | 3.94584e6i | 0.265551 | + | 1.11791i | ||||
\(417\) | 3.29260e6i | 0.927255i | ||||||||
\(418\) | −1.10243e6 | − | 1.37741e6i | −0.308610 | − | 0.385587i | ||||
\(419\) | 3.66116e6i | 1.01879i | 0.860534 | + | 0.509393i | \(0.170130\pi\) | ||||
−0.860534 | + | 0.509393i | \(0.829870\pi\) | |||||||
\(420\) | −1.12501e6 | − | 1.03840e6i | −0.311195 | − | 0.287237i | ||||
\(421\) | 3.15337e6i | 0.867101i | 0.901129 | + | 0.433550i | \(0.142739\pi\) | ||||
−0.901129 | + | 0.433550i | \(0.857261\pi\) | |||||||
\(422\) | 210893. | − | 168791.i | 0.0576476 | − | 0.0461390i | ||||
\(423\) | − | 3.28366e6i | − | 0.892294i | ||||||
\(424\) | 1.15809e6 | − | 565277.i | 0.312844 | − | 0.152703i | ||||
\(425\) | 2.60123e6 | − | 1.49548e6i | 0.698564 | − | 0.401613i | ||||
\(426\) | 66805.4 | + | 83468.8i | 0.0178356 | + | 0.0222844i | ||||
\(427\) | −812399. | −0.215625 | ||||||||
\(428\) | −76584.6 | + | 341082.i | −0.0202084 | + | 0.0900014i | ||||
\(429\) | 2.12552e6i | 0.557600i | ||||||||
\(430\) | 822714. | + | 5.42707e6i | 0.214574 | + | 1.41545i | ||||
\(431\) | −1.92170e6 | −0.498301 | −0.249151 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249151 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(432\) | −526028. | − | 248764.i | −0.135613 | − | 0.0641326i | ||||
\(433\) | − | 3.16413e6i | − | 0.811025i | −0.914089 | − | 0.405513i | \(-0.867093\pi\) | ||
0.914089 | − | 0.405513i | \(-0.132907\pi\) | |||||||
\(434\) | −197876. | + | 158373.i | −0.0504277 | + | 0.0403605i | ||||
\(435\) | 2.90144e6 | − | 5.01485e6i | 0.735175 | − | 1.27067i | ||||
\(436\) | −354203. | − | 79530.7i | −0.0892352 | − | 0.0200364i | ||||
\(437\) | −9.89244e6 | −2.47799 | ||||||||
\(438\) | −667584. | + | 534310.i | −0.166273 | + | 0.133079i | ||||
\(439\) | −7.05163e6 | −1.74634 | −0.873169 | − | 0.487417i | \(-0.837939\pi\) | ||||
−0.873169 | + | 0.487417i | \(0.837939\pi\) | |||||||
\(440\) | −100842. | + | 1.42960e6i | −0.0248320 | + | 0.352033i | ||||
\(441\) | 3.29345e6 | 0.806408 | ||||||||
\(442\) | −2.96893e6 | + | 2.37622e6i | −0.722844 | + | 0.578538i | ||||
\(443\) | −722258. | −0.174857 | −0.0874285 | − | 0.996171i | \(-0.527865\pi\) | ||||
−0.0874285 | + | 0.996171i | \(0.527865\pi\) | |||||||
\(444\) | −1.31935e6 | + | 5.87594e6i | −0.317616 | + | 1.41456i | ||||
\(445\) | −5.94002e6 | − | 3.43672e6i | −1.42196 | − | 0.822705i | ||||
\(446\) | 2.86314e6 | − | 2.29156e6i | 0.681563 | − | 0.545498i | ||||
\(447\) | − | 658406.i | − | 0.155856i | ||||||
\(448\) | 1.03145e6 | + | 804840.i | 0.242802 | + | 0.189459i | ||||
\(449\) | 1.24334e6 | 0.291055 | 0.145528 | − | 0.989354i | \(-0.453512\pi\) | ||||
0.145528 | + | 0.989354i | \(0.453512\pi\) | |||||||
\(450\) | 1.39841e6 | − | 3.56241e6i | 0.325540 | − | 0.829302i | ||||
\(451\) | − | 1.63188e6i | − | 0.377786i | ||||||
\(452\) | −2.07900e6 | − | 466808.i | −0.478640 | − | 0.107471i | ||||
\(453\) | 555112. | 0.127097 | ||||||||
\(454\) | −61776.8 | − | 77185.9i | −0.0140665 | − | 0.0175751i | ||||
\(455\) | 782573. | − | 1.35260e6i | 0.177213 | − | 0.306295i | ||||
\(456\) | −3.74819e6 | − | 7.67896e6i | −0.844129 | − | 1.72938i | ||||
\(457\) | 4.26434e6i | 0.955127i | 0.878597 | + | 0.477564i | \(0.158480\pi\) | ||||
−0.878597 | + | 0.477564i | \(0.841520\pi\) | |||||||
\(458\) | 3.24775e6 | − | 2.59938e6i | 0.723467 | − | 0.579037i | ||||
\(459\) | − | 545603.i | − | 0.120877i | ||||||
\(460\) | 5.90500e6 | + | 5.45039e6i | 1.30114 | + | 1.20097i | ||||
\(461\) | − | 3.17128e6i | − | 0.694997i | −0.937681 | − | 0.347498i | \(-0.887031\pi\) | ||
0.937681 | − | 0.347498i | \(-0.112969\pi\) | |||||||
\(462\) | 428453. | + | 535323.i | 0.0933895 | + | 0.116684i | ||||
\(463\) | − | 605017.i | − | 0.131164i | −0.997847 | − | 0.0655821i | \(-0.979110\pi\) | ||
0.997847 | − | 0.0655821i | \(-0.0208904\pi\) | |||||||
\(464\) | −2.11663e6 | + | 4.47575e6i | −0.456404 | + | 0.965096i | ||||
\(465\) | −1.16392e6 | − | 673411.i | −0.249627 | − | 0.144427i | ||||
\(466\) | −313018. | + | 250528.i | −0.0667735 | + | 0.0534431i | ||||
\(467\) | 7.35248e6 | 1.56006 | 0.780031 | − | 0.625741i | \(-0.215203\pi\) | ||||
0.780031 | + | 0.625741i | \(0.215203\pi\) | |||||||
\(468\) | −1.06261e6 | + | 4.73252e6i | −0.224265 | + | 0.998799i | ||||
\(469\) | − | 948832.i | − | 0.199185i | ||||||
\(470\) | 4.74227e6 | − | 718901.i | 0.990242 | − | 0.150115i | ||||
\(471\) | −7.17943e6 | −1.49121 | ||||||||
\(472\) | 3.31599e6 | + | 6.79352e6i | 0.685107 | + | 1.40359i | ||||
\(473\) | − | 2.45834e6i | − | 0.505230i | ||||||
\(474\) | −3.62034e6 | − | 4.52337e6i | −0.740122 | − | 0.924732i | ||||
\(475\) | −5.96598e6 | + | 3.42992e6i | −1.21324 | + | 0.697510i | ||||
\(476\) | −268751. | + | 1.19693e6i | −0.0543666 | + | 0.242131i | ||||
\(477\) | 1.54121e6 | 0.310145 | ||||||||
\(478\) | 1.82525e6 | + | 2.28053e6i | 0.365388 | + | 0.456527i | ||||
\(479\) | −3.01150e6 | −0.599714 | −0.299857 | − | 0.953984i | \(-0.596939\pi\) | ||||
−0.299857 | + | 0.953984i | \(0.596939\pi\) | |||||||
\(480\) | −1.99347e6 | + | 6.64885e6i | −0.394918 | + | 1.31717i | ||||
\(481\) | −6.14687e6 | −1.21141 | ||||||||
\(482\) | −2.15600e6 | − | 2.69377e6i | −0.422698 | − | 0.528133i | ||||
\(483\) | 3.84464e6 | 0.749874 | ||||||||
\(484\) | −988439. | + | 4.40217e6i | −0.191795 | + | 0.854189i | ||||
\(485\) | 4.35461e6 | − | 7.52650e6i | 0.840612 | − | 1.45291i | ||||
\(486\) | −4.42094e6 | − | 5.52367e6i | −0.849032 | − | 1.06081i | ||||
\(487\) | − | 3.76217e6i | − | 0.718813i | −0.933181 | − | 0.359407i | \(-0.882979\pi\) | ||
0.933181 | − | 0.359407i | \(-0.117021\pi\) | |||||||
\(488\) | 1.61566e6 | + | 3.31003e6i | 0.307115 | + | 0.629191i | ||||
\(489\) | −4.36315e6 | −0.825141 | ||||||||
\(490\) | 721044. | + | 4.75640e6i | 0.135666 | + | 0.894928i | ||||
\(491\) | 5.68936e6i | 1.06502i | 0.846422 | + | 0.532512i | \(0.178752\pi\) | ||||
−0.846422 | + | 0.532512i | \(0.821248\pi\) | |||||||
\(492\) | 1.73155e6 | − | 7.71174e6i | 0.322494 | − | 1.43628i | ||||
\(493\) | −4.64230e6 | −0.860232 | ||||||||
\(494\) | 6.80932e6 | − | 5.44993e6i | 1.25541 | − | 1.00479i | ||||
\(495\) | −858351. | + | 1.48357e6i | −0.157453 | + | 0.272142i | ||||
\(496\) | 1.03880e6 | + | 491259.i | 0.189595 | + | 0.0896616i | ||||
\(497\) | 35202.0i | 0.00639259i | ||||||||
\(498\) | 3.91677e6 | + | 4.89374e6i | 0.707709 | + | 0.884234i | ||||
\(499\) | − | 8.16772e6i | − | 1.46842i | −0.678924 | − | 0.734208i | \(-0.737553\pi\) | ||
0.678924 | − | 0.734208i | \(-0.262447\pi\) | |||||||
\(500\) | 5.45099e6 | + | 1.23966e6i | 0.975102 | + | 0.221757i | ||||
\(501\) | 1.11941e6i | 0.199248i | ||||||||
\(502\) | 1.44466e6 | − | 1.15625e6i | 0.255862 | − | 0.204782i | ||||
\(503\) | − | 207353.i | − | 0.0365419i | −0.999833 | − | 0.0182709i | \(-0.994184\pi\) | ||
0.999833 | − | 0.0182709i | \(-0.00581615\pi\) | |||||||
\(504\) | 686335. | + | 1.40610e6i | 0.120354 | + | 0.246571i | ||||
\(505\) | 5.47842e6 | − | 9.46889e6i | 0.955932 | − | 1.65223i | ||||
\(506\) | −2.24888e6 | − | 2.80982e6i | −0.390472 | − | 0.487868i | ||||
\(507\) | −2.54874e6 | −0.440358 | ||||||||
\(508\) | −2.77300e6 | − | 622635.i | −0.476751 | − | 0.107047i | ||||
\(509\) | 4.43777e6i | 0.759224i | 0.925146 | + | 0.379612i | \(0.123943\pi\) | ||||
−0.925146 | + | 0.379612i | \(0.876057\pi\) | |||||||
\(510\) | −6.43494e6 | + | 975501.i | −1.09552 | + | 0.166074i | ||||
\(511\) | −281546. | −0.0476977 | ||||||||
\(512\) | 1.22793e6 | − | 5.80315e6i | 0.207014 | − | 0.978338i | ||||
\(513\) | 1.25135e6i | 0.209936i | ||||||||
\(514\) | −3.89910e6 | + | 3.12070e6i | −0.650963 | + | 0.521007i | ||||
\(515\) | −1.69723e6 | + | 2.93348e6i | −0.281982 | + | 0.487377i | ||||
\(516\) | 2.60849e6 | − | 1.16173e7i | 0.431286 | − | 1.92080i | ||||
\(517\) | −2.14814e6 | −0.353457 | ||||||||
\(518\) | −1.54812e6 | + | 1.23906e6i | −0.253501 | + | 0.202893i | ||||
\(519\) | 1.07892e7 | 1.75821 | ||||||||
\(520\) | −7.06735e6 | − | 498522.i | −1.14617 | − | 0.0808493i | ||||
\(521\) | 8.59405e6 | 1.38709 | 0.693543 | − | 0.720415i | \(-0.256049\pi\) | ||||
0.693543 | + | 0.720415i | \(0.256049\pi\) | |||||||
\(522\) | −4.62284e6 | + | 3.69995e6i | −0.742561 | + | 0.594319i | ||||
\(523\) | −4.23189e6 | −0.676519 | −0.338259 | − | 0.941053i | \(-0.609838\pi\) | ||||
−0.338259 | + | 0.941053i | \(0.609838\pi\) | |||||||
\(524\) | −2.62167e6 | − | 588656.i | −0.417110 | − | 0.0936555i | ||||
\(525\) | 2.31865e6 | − | 1.33302e6i | 0.367144 | − | 0.211076i | ||||
\(526\) | 2.00535e6 | − | 1.60501e6i | 0.316029 | − | 0.252938i | ||||
\(527\) | 1.07745e6i | 0.168994i | ||||||||
\(528\) | 1.32902e6 | − | 2.81031e6i | 0.207467 | − | 0.438701i | ||||
\(529\) | −1.37436e7 | −2.13531 | ||||||||
\(530\) | 337420. | + | 2.22581e6i | 0.0521773 | + | 0.344190i | ||||
\(531\) | 9.04094e6i | 1.39148i | ||||||||
\(532\) | 616387. | − | 2.74518e6i | 0.0944223 | − | 0.420525i | ||||
\(533\) | 8.06731e6 | 1.23002 | ||||||||
\(534\) | 9.30172e6 | + | 1.16219e7i | 1.41160 | + | 1.76369i | ||||
\(535\) | −528585. | − | 305824.i | −0.0798419 | − | 0.0461942i | ||||
\(536\) | −3.86591e6 | + | 1.88699e6i | −0.581219 | + | 0.283700i | ||||
\(537\) | 5.35264e6i | 0.800999i | ||||||||
\(538\) | −1.69923e6 | + | 1.36000e6i | −0.253103 | + | 0.202574i | ||||
\(539\) | − | 2.15454e6i | − | 0.319436i | ||||||
\(540\) | 689453. | − | 746959.i | 0.101747 | − | 0.110233i | ||||
\(541\) | 1.04071e7i | 1.52875i | 0.644770 | + | 0.764377i | \(0.276953\pi\) | ||||
−0.644770 | + | 0.764377i | \(0.723047\pi\) | |||||||
\(542\) | −4.83624e6 | − | 6.04255e6i | −0.707147 | − | 0.883532i | ||||
\(543\) | 7.31296e6i | 1.06437i | ||||||||
\(544\) | 5.41122e6 | − | 1.28540e6i | 0.783967 | − | 0.186226i | ||||
\(545\) | 317589. | − | 548920.i | 0.0458009 | − | 0.0791622i | ||||
\(546\) | −2.64641e6 | + | 2.11809e6i | −0.379905 | + | 0.304062i | ||||
\(547\) | 2.44104e6 | 0.348825 | 0.174412 | − | 0.984673i | \(-0.444197\pi\) | ||||
0.174412 | + | 0.984673i | \(0.444197\pi\) | |||||||
\(548\) | 8.59511e6 | + | 1.92990e6i | 1.22264 | + | 0.274526i | ||||
\(549\) | 4.40505e6i | 0.623763i | ||||||||
\(550\) | −2.33049e6 | − | 914827.i | −0.328504 | − | 0.128953i | ||||
\(551\) | 1.06472e7 | 1.49402 | ||||||||
\(552\) | −7.64605e6 | − | 1.56646e7i | −1.06804 | − | 2.18812i | ||||
\(553\) | − | 1.90768e6i | − | 0.265273i | ||||||
\(554\) | −2.00684e6 | − | 2.50740e6i | −0.277803 | − | 0.347096i | ||||
\(555\) | −9.10614e6 | − | 5.26854e6i | −1.25488 | − | 0.726036i | ||||
\(556\) | 4.79590e6 | + | 1.07684e6i | 0.657935 | + | 0.147729i | ||||
\(557\) | 2.55398e6 | 0.348803 | 0.174402 | − | 0.984675i | \(-0.444201\pi\) | ||||
0.174402 | + | 0.984675i | \(0.444201\pi\) | |||||||
\(558\) | 858740. | + | 1.07294e6i | 0.116755 | + | 0.145878i | ||||
\(559\) | 1.21530e7 | 1.64495 | ||||||||
\(560\) | −1.88043e6 | + | 1.29905e6i | −0.253389 | + | 0.175047i | ||||
\(561\) | 2.91488e6 | 0.391034 | ||||||||
\(562\) | 6.74468e6 | + | 8.42702e6i | 0.900784 | + | 1.12547i | ||||
\(563\) | 6.75752e6 | 0.898496 | 0.449248 | − | 0.893407i | \(-0.351692\pi\) | ||||
0.449248 | + | 0.893407i | \(0.351692\pi\) | |||||||
\(564\) | −1.01514e7 | − | 2.27934e6i | −1.34378 | − | 0.301726i | ||||
\(565\) | 1.86410e6 | − | 3.22190e6i | 0.245667 | − | 0.424611i | ||||
\(566\) | 3.08643e6 | + | 3.85628e6i | 0.404963 | + | 0.505973i | ||||
\(567\) | − | 2.58674e6i | − | 0.337905i | ||||||
\(568\) | 143427. | − | 70008.2i | 0.0186535 | − | 0.00910496i | ||||
\(569\) | 9.34676e6 | 1.21027 | 0.605133 | − | 0.796125i | \(-0.293120\pi\) | ||||
0.605133 | + | 0.796125i | \(0.293120\pi\) | |||||||
\(570\) | 1.47587e7 | − | 2.23734e6i | 1.90266 | − | 0.288433i | ||||
\(571\) | 1.78748e6i | 0.229431i | 0.993398 | + | 0.114715i | \(0.0365956\pi\) | ||||
−0.993398 | + | 0.114715i | \(0.963404\pi\) | |||||||
\(572\) | 3.09597e6 | + | 695152.i | 0.395646 | + | 0.0888361i | ||||
\(573\) | 1.27036e7 | 1.61637 | ||||||||
\(574\) | 2.03179e6 | − | 1.62617e6i | 0.257394 | − | 0.206009i | ||||
\(575\) | −1.21702e7 | + | 6.99682e6i | −1.53507 | + | 0.882533i | ||||
\(576\) | 4.36406e6 | − | 5.59279e6i | 0.548068 | − | 0.702381i | ||||
\(577\) | 8.09579e6i | 1.01232i | 0.862438 | + | 0.506162i | \(0.168936\pi\) | ||||
−0.862438 | + | 0.506162i | \(0.831064\pi\) | |||||||
\(578\) | −1.76020e6 | − | 2.19926e6i | −0.219151 | − | 0.273814i | ||||
\(579\) | − | 1.65425e7i | − | 2.05071i | ||||||
\(580\) | −6.35555e6 | − | 5.86626e6i | −0.784483 | − | 0.724087i | ||||
\(581\) | 2.06388e6i | 0.253655i | ||||||||
\(582\) | −1.47259e7 | + | 1.17861e7i | −1.80208 | + | 1.44232i | ||||
\(583\) | − | 1.00824e6i | − | 0.122855i | ||||||
\(584\) | 559926. | + | 1.14713e6i | 0.0679358 | + | 0.139181i | ||||
\(585\) | −7.33414e6 | − | 4.24332e6i | −0.886053 | − | 0.512644i | ||||
\(586\) | −1.49424e6 | − | 1.86695e6i | −0.179753 | − | 0.224589i | ||||
\(587\) | 3.38443e6 | 0.405407 | 0.202703 | − | 0.979240i | \(-0.435027\pi\) | ||||
0.202703 | + | 0.979240i | \(0.435027\pi\) | |||||||
\(588\) | 2.28614e6 | − | 1.01817e7i | 0.272684 | − | 1.21444i | ||||
\(589\) | − | 2.47117e6i | − | 0.293504i | ||||||
\(590\) | −1.30569e7 | + | 1.97936e6i | −1.54422 | + | 0.234096i | ||||
\(591\) | 4.07736e6 | 0.480186 | ||||||||
\(592\) | 8.12722e6 | + | 3.84345e6i | 0.953099 | + | 0.450731i | ||||
\(593\) | 1.19814e7i | 1.39917i | 0.714549 | + | 0.699585i | \(0.246632\pi\) | ||||
−0.714549 | + | 0.699585i | \(0.753368\pi\) | |||||||
\(594\) | −355432. | + | 284475.i | −0.0413323 | + | 0.0330809i | ||||
\(595\) | −1.85491e6 | − | 1.07320e6i | −0.214799 | − | 0.124276i | ||||
\(596\) | −959013. | − | 215331.i | −0.110588 | − | 0.0248309i | ||||
\(597\) | −2.03458e7 | −2.33636 | ||||||||
\(598\) | 1.38906e7 | − | 1.11175e7i | 1.58843 | − | 1.27132i | ||||
\(599\) | −5.66907e6 | −0.645572 | −0.322786 | − | 0.946472i | \(-0.604619\pi\) | ||||
−0.322786 | + | 0.946472i | \(0.604619\pi\) | |||||||
\(600\) | −1.00425e7 | − | 6.79602e6i | −1.13884 | − | 0.770684i | ||||
\(601\) | −2.59514e6 | −0.293072 | −0.146536 | − | 0.989205i | \(-0.546812\pi\) | ||||
−0.146536 | + | 0.989205i | \(0.546812\pi\) | |||||||
\(602\) | 3.06079e6 | − | 2.44974e6i | 0.344225 | − | 0.275505i | ||||
\(603\) | −5.14483e6 | −0.576206 | ||||||||
\(604\) | 181549. | − | 808559.i | 0.0202489 | − | 0.0901819i | ||||
\(605\) | −6.82219e6 | − | 3.94712e6i | −0.757766 | − | 0.438421i | ||||
\(606\) | −1.85262e7 | + | 1.48277e7i | −2.04930 | + | 1.64019i | ||||
\(607\) | − | 1.37152e7i | − | 1.51089i | −0.655214 | − | 0.755443i | \(-0.727422\pi\) | ||
0.655214 | − | 0.755443i | \(-0.272578\pi\) | |||||||
\(608\) | −1.24108e7 | + | 2.94809e6i | −1.36157 | + | 0.323431i | ||||
\(609\) | −4.13799e6 | −0.452112 | ||||||||
\(610\) | −6.36177e6 | + | 964409.i | −0.692234 | + | 0.104939i | ||||
\(611\) | − | 1.06195e7i | − | 1.15080i | ||||||
\(612\) | 6.49006e6 | + | 1.45724e6i | 0.700438 | + | 0.157272i | ||||
\(613\) | 8.09513e6 | 0.870107 | 0.435054 | − | 0.900405i | \(-0.356729\pi\) | ||||
0.435054 | + | 0.900405i | \(0.356729\pi\) | |||||||
\(614\) | −4.88943e6 | − | 6.10902e6i | −0.523405 | − | 0.653959i | ||||
\(615\) | 1.19511e7 | + | 6.91457e6i | 1.27415 | + | 0.737187i | ||||
\(616\) | 919859. | − | 448994.i | 0.0976719 | − | 0.0476748i | ||||
\(617\) | 5.98284e6i | 0.632695i | 0.948643 | + | 0.316347i | \(0.102457\pi\) | ||||
−0.948643 | + | 0.316347i | \(0.897543\pi\) | |||||||
\(618\) | 5.73947e6 | − | 4.59366e6i | 0.604506 | − | 0.483825i | ||||
\(619\) | − | 719050.i | − | 0.0754280i | −0.999289 | − | 0.0377140i | \(-0.987992\pi\) | ||
0.999289 | − | 0.0377140i | \(-0.0120076\pi\) | |||||||
\(620\) | −1.36153e6 | + | 1.47509e6i | −0.142248 | + | 0.154113i | ||||
\(621\) | 2.55268e6i | 0.265624i | ||||||||
\(622\) | 6.95557e6 | + | 8.69051e6i | 0.720870 | + | 0.900678i | ||||
\(623\) | 4.90139e6i | 0.505940i | ||||||||
\(624\) | 1.38930e7 | + | 6.57013e6i | 1.42835 | + | 0.675480i | ||||
\(625\) | −4.91373e6 | + | 8.43935e6i | −0.503166 | + | 0.864190i | ||||
\(626\) | 1.07198e7 | − | 8.57977e6i | 1.09333 | − | 0.875064i | ||||
\(627\) | −6.68536e6 | −0.679135 | ||||||||
\(628\) | −2.34803e6 | + | 1.04573e7i | −0.237577 | + | 1.05809i | ||||
\(629\) | 8.42965e6i | 0.849538i | ||||||||
\(630\) | −2.70249e6 | + | 409682.i | −0.271276 | + | 0.0411240i | ||||
\(631\) | −8.84500e6 | −0.884350 | −0.442175 | − | 0.896929i | \(-0.645793\pi\) | ||||
−0.442175 | + | 0.896929i | \(0.645793\pi\) | |||||||
\(632\) | −7.77263e6 | + | 3.79391e6i | −0.774061 | + | 0.377828i | ||||
\(633\) | − | 1.02359e6i | − | 0.101535i | ||||||
\(634\) | −4.54685e6 | − | 5.68098e6i | −0.449249 | − | 0.561307i | ||||
\(635\) | 2.48636e6 | − | 4.29741e6i | 0.244697 | − | 0.422934i | ||||
\(636\) | 1.06982e6 | − | 4.76463e6i | 0.104874 | − | 0.467075i | ||||
\(637\) | 1.06511e7 | 1.04003 | ||||||||
\(638\) | 2.42047e6 | + | 3.02421e6i | 0.235423 | + | 0.294144i | ||||
\(639\) | 190875. | 0.0184925 | ||||||||
\(640\) | 9.03254e6 | + | 5.07813e6i | 0.871686 | + | 0.490065i | ||||
\(641\) | −1.09511e7 | −1.05272 | −0.526360 | − | 0.850262i | \(-0.676443\pi\) | ||||
−0.526360 | + | 0.850262i | \(0.676443\pi\) | |||||||
\(642\) | 827734. | + | 1.03420e6i | 0.0792599 | + | 0.0990298i | ||||
\(643\) | −3.55893e6 | −0.339462 | −0.169731 | − | 0.985490i | \(-0.554290\pi\) | ||||
−0.169731 | + | 0.985490i | \(0.554290\pi\) | |||||||
\(644\) | 1.25739e6 | − | 5.59999e6i | 0.119469 | − | 0.532074i | ||||
\(645\) | 1.80038e7 | + | 1.04165e7i | 1.70398 | + | 0.985873i | ||||
\(646\) | −7.47389e6 | − | 9.33812e6i | −0.704637 | − | 0.880396i | ||||
\(647\) | − | 2.00678e7i | − | 1.88469i | −0.334649 | − | 0.942343i | \(-0.608618\pi\) | ||
0.334649 | − | 0.942343i | \(-0.391382\pi\) | |||||||
\(648\) | −1.05394e7 | + | 5.14439e6i | −0.986001 | + | 0.481278i | ||||
\(649\) | 5.91449e6 | 0.551195 | ||||||||
\(650\) | 4.52252e6 | − | 1.15210e7i | 0.419853 | − | 1.06956i | ||||
\(651\) | 960407.i | 0.0888184i | ||||||||
\(652\) | −1.42697e6 | + | 6.35523e6i | −0.131460 | + | 0.585480i | ||||
\(653\) | −1.67704e7 | −1.53907 | −0.769537 | − | 0.638602i | \(-0.779513\pi\) | ||||
−0.769537 | + | 0.638602i | \(0.779513\pi\) | |||||||
\(654\) | −1.07398e6 | + | 859576.i | −0.0981867 | + | 0.0785851i | ||||
\(655\) | 2.35067e6 | − | 4.06289e6i | 0.214086 | − | 0.370026i | ||||
\(656\) | −1.06664e7 | − | 5.04424e6i | −0.967737 | − | 0.457653i | ||||
\(657\) | 1.52662e6i | 0.137980i | ||||||||
\(658\) | −2.14063e6 | − | 2.67457e6i | −0.192742 | − | 0.240818i | ||||
\(659\) | 1.99619e7i | 1.79055i | 0.445510 | + | 0.895277i | \(0.353022\pi\) | ||||
−0.445510 | + | 0.895277i | \(0.646978\pi\) | |||||||
\(660\) | 3.99063e6 | + | 3.68340e6i | 0.356600 | + | 0.329147i | ||||
\(661\) | 4.41003e6i | 0.392589i | 0.980545 | + | 0.196295i | \(0.0628909\pi\) | ||||
−0.980545 | + | 0.196295i | \(0.937109\pi\) | |||||||
\(662\) | −1.36026e7 | + | 1.08870e7i | −1.20636 | + | 0.965526i | ||||
\(663\) | 1.44099e7i | 1.27315i | ||||||||
\(664\) | 8.40904e6 | − | 4.10455e6i | 0.740161 | − | 0.361281i | ||||
\(665\) | 4.25429e6 | + | 2.46141e6i | 0.373055 | + | 0.215839i | ||||
\(666\) | 6.71850e6 | + | 8.39431e6i | 0.586931 | + | 0.733330i | ||||
\(667\) | 2.17197e7 | 1.89033 | ||||||||
\(668\) | 1.63049e6 | + | 366102.i | 0.141377 | + | 0.0317439i | ||||
\(669\) | − | 1.38965e7i | − | 1.20044i | ||||||
\(670\) | −1.12637e6 | − | 7.43015e6i | −0.0969380 | − | 0.639456i | ||||
\(671\) | 2.88174e6 | 0.247086 | ||||||||
\(672\) | 4.82338e6 | − | 1.14576e6i | 0.412030 | − | 0.0978747i | ||||
\(673\) | − | 1.91274e7i | − | 1.62787i | −0.580959 | − | 0.813933i | \(-0.697322\pi\) | ||
0.580959 | − | 0.813933i | \(-0.302678\pi\) | |||||||
\(674\) | −6.67039e6 | + | 5.33874e6i | −0.565590 | + | 0.452677i | ||||
\(675\) | 885070. | + | 1.53948e6i | 0.0747684 | + | 0.130052i | ||||
\(676\) | −833565. | + | 3.71242e6i | −0.0701573 | + | 0.312457i | ||||
\(677\) | −1.47330e7 | −1.23544 | −0.617718 | − | 0.786399i | \(-0.711943\pi\) | ||||
−0.617718 | + | 0.786399i | \(0.711943\pi\) | |||||||
\(678\) | −6.30377e6 | + | 5.04531e6i | −0.526655 | + | 0.421515i | ||||
\(679\) | −6.21048e6 | −0.516953 | ||||||||
\(680\) | −683660. | + | 9.69197e6i | −0.0566980 | + | 0.803785i | ||||
\(681\) | −374628. | −0.0309551 | ||||||||
\(682\) | 701905. | − | 561779.i | 0.0577853 | − | 0.0462493i | ||||
\(683\) | −2.53230e6 | −0.207713 | −0.103856 | − | 0.994592i | \(-0.533118\pi\) | ||||
−0.103856 | + | 0.994592i | \(0.533118\pi\) | |||||||
\(684\) | −1.48851e7 | − | 3.34222e6i | −1.21650 | − | 0.273146i | ||||
\(685\) | −7.70663e6 | + | 1.33201e7i | −0.627535 | + | 1.08463i | ||||
\(686\) | 5.64617e6 | − | 4.51899e6i | 0.458082 | − | 0.366633i | ||||
\(687\) | − | 1.57632e7i | − | 1.27425i | ||||||
\(688\) | −1.60684e7 | − | 7.59890e6i | −1.29420 | − | 0.612040i | ||||
\(689\) | 4.98432e6 | 0.399998 | ||||||||
\(690\) | 3.01068e7 | − | 4.56402e6i | 2.40736 | − | 0.364943i | ||||
\(691\) | − | 2.97284e6i | − | 0.236852i | −0.992963 | − | 0.118426i | \(-0.962215\pi\) | ||
0.992963 | − | 0.118426i | \(-0.0377848\pi\) | |||||||
\(692\) | 3.52861e6 | − | 1.57152e7i | 0.280116 | − | 1.24754i | ||||
\(693\) | 1.22417e6 | 0.0968294 | ||||||||
\(694\) | 1.41836e7 | + | 1.77214e7i | 1.11786 | + | 1.39669i | ||||
\(695\) | −4.30015e6 | + | 7.43236e6i | −0.337692 | + | 0.583667i | ||||
\(696\) | 8.22945e6 | + | 1.68598e7i | 0.643943 | + | 1.31926i | ||||
\(697\) | − | 1.10633e7i | − | 0.862586i | ||||||
\(698\) | −2.62979e6 | + | 2.10479e6i | −0.204306 | + | 0.163519i | ||||
\(699\) | 1.51926e6i | 0.117608i | ||||||||
\(700\) | −1.18332e6 | − | 3.81323e6i | −0.0912764 | − | 0.294136i | ||||
\(701\) | − | 9.09229e6i | − | 0.698841i | −0.936966 | − | 0.349420i | \(-0.886379\pi\) | ||
0.936966 | − | 0.349420i | \(-0.113621\pi\) | |||||||
\(702\) | −1.40632e6 | − | 1.75710e6i | −0.107706 | − | 0.134572i | ||||
\(703\) | − | 1.93336e7i | − | 1.47545i | ||||||
\(704\) | −3.65875e6 | − | 2.85493e6i | −0.278228 | − | 0.217102i | ||||
\(705\) | 9.10207e6 | − | 1.57320e7i | 0.689712 | − | 1.19210i | ||||
\(706\) | 4.65178e6 | − | 3.72312e6i | 0.351243 | − | 0.281122i | ||||
\(707\) | −7.81324e6 | −0.587872 | ||||||||
\(708\) | 2.79500e7 | + | 6.27574e6i | 2.09555 | + | 0.470524i | ||||
\(709\) | − | 3.91601e6i | − | 0.292569i | −0.989243 | − | 0.146284i | \(-0.953269\pi\) | ||
0.989243 | − | 0.146284i | \(-0.0467315\pi\) | |||||||
\(710\) | 41788.7 | + | 275661.i | 0.00311110 | + | 0.0205225i | ||||
\(711\) | −1.03440e7 | −0.767384 | ||||||||
\(712\) | 1.99702e7 | − | 9.74767e6i | 1.47632 | − | 0.720611i | ||||
\(713\) | − | 5.04103e6i | − | 0.371360i | ||||||
\(714\) | 2.90469e6 | + | 3.62921e6i | 0.213233 | + | 0.266420i | ||||
\(715\) | −2.77594e6 | + | 4.79792e6i | −0.203070 | + | 0.350985i | ||||
\(716\) | 7.79648e6 | + | 1.75058e6i | 0.568350 | + | 0.127614i | ||||
\(717\) | 1.10687e7 | 0.804082 | ||||||||
\(718\) | −1.94294e6 | − | 2.42757e6i | −0.140653 | − | 0.175736i | ||||
\(719\) | −1.30009e7 | −0.937890 | −0.468945 | − | 0.883227i | \(-0.655366\pi\) | ||||
−0.468945 | + | 0.883227i | \(0.655366\pi\) | |||||||
\(720\) | 7.04378e6 | + | 1.01962e7i | 0.506378 | + | 0.733007i | ||||
\(721\) | 2.42056e6 | 0.173411 | ||||||||
\(722\) | 8.38908e6 | + | 1.04816e7i | 0.598924 | + | 0.748314i | ||||
\(723\) | −1.30744e7 | −0.930202 | ||||||||
\(724\) | 1.06518e7 | + | 2.39170e6i | 0.755227 | + | 0.169574i | ||||
\(725\) | 1.30988e7 | − | 7.53068e6i | 0.925522 | − | 0.532095i | ||||
\(726\) | 1.06832e7 | + | 1.33479e7i | 0.752243 | + | 0.939876i | ||||
\(727\) | 2.08574e7i | 1.46361i | 0.681515 | + | 0.731804i | \(0.261321\pi\) | ||||
−0.681515 | + | 0.731804i | \(0.738679\pi\) | |||||||
\(728\) | 2.21963e6 | + | 4.54739e6i | 0.155222 | + | 0.318005i | ||||
\(729\) | −1.10661e7 | −0.771214 | ||||||||
\(730\) | −2.20474e6 | + | 334227.i | −0.153127 | + | 0.0232132i | ||||
\(731\) | − | 1.66663e7i | − | 1.15357i | ||||||
\(732\) | 1.36182e7 | + | 3.05775e6i | 0.939381 | + | 0.210923i | ||||
\(733\) | −2.35771e6 | −0.162081 | −0.0810403 | − | 0.996711i | \(-0.525824\pi\) | ||||
−0.0810403 | + | 0.996711i | \(0.525824\pi\) | |||||||
\(734\) | −1.38308e6 | + | 1.10697e6i | −0.0947560 | + | 0.0758393i | ||||
\(735\) | 1.57789e7 | + | 9.12920e6i | 1.07735 | + | 0.623325i | ||||
\(736\) | −2.53172e7 | + | 6.01391e6i | −1.72274 | + | 0.409225i | ||||
\(737\) | 3.36569e6i | 0.228247i | ||||||||
\(738\) | −8.81753e6 | − | 1.10169e7i | −0.595945 | − | 0.744593i | ||||
\(739\) | 1.75976e7i | 1.18534i | 0.805445 | + | 0.592670i | \(0.201926\pi\) | ||||
−0.805445 | + | 0.592670i | \(0.798074\pi\) | |||||||
\(740\) | −1.06522e7 | + | 1.15406e7i | −0.715086 | + | 0.774730i | ||||
\(741\) | − | 3.30496e7i | − | 2.21116i | ||||||
\(742\) | 1.25532e6 | − | 1.00472e6i | 0.0837040 | − | 0.0669936i | ||||
\(743\) | − | 2.71312e6i | − | 0.180301i | −0.995928 | − | 0.0901504i | \(-0.971265\pi\) | ||
0.995928 | − | 0.0901504i | \(-0.0287348\pi\) | |||||||
\(744\) | 3.91307e6 | − | 1.91001e6i | 0.259170 | − | 0.126504i | ||||
\(745\) | 859880. | − | 1.48621e6i | 0.0567606 | − | 0.0981049i | ||||
\(746\) | −889908. | − | 1.11188e6i | −0.0585461 | − | 0.0731494i | ||||
\(747\) | 1.11909e7 | 0.733777 | ||||||||
\(748\) | 953312. | − | 4.24573e6i | 0.0622990 | − | 0.277459i | ||||
\(749\) | 436161.i | 0.0284081i | ||||||||
\(750\) | 1.65745e7 | − | 1.31912e7i | 1.07594 | − | 0.856308i | ||||
\(751\) | 1.51201e7 | 0.978262 | 0.489131 | − | 0.872210i | \(-0.337314\pi\) | ||||
0.489131 | + | 0.872210i | \(0.337314\pi\) | |||||||
\(752\) | −6.64005e6 | + | 1.40408e7i | −0.428180 | + | 0.905414i | ||||
\(753\) | − | 7.01176e6i | − | 0.450650i | ||||||
\(754\) | −1.49504e7 | + | 1.19658e7i | −0.957690 | + | 0.766500i | ||||
\(755\) | 1.25305e6 | + | 724978.i | 0.0800020 | + | 0.0462868i | ||||
\(756\) | −708377. | − | 159055.i | −0.0450775 | − | 0.0101214i | ||||
\(757\) | −1.87944e7 | −1.19204 | −0.596018 | − | 0.802971i | \(-0.703251\pi\) | ||||
−0.596018 | + | 0.802971i | \(0.703251\pi\) | |||||||
\(758\) | 3.80974e6 | − | 3.04917e6i | 0.240836 | − | 0.192757i | ||||
\(759\) | −1.36377e7 | −0.859284 | ||||||||
\(760\) | 1.56799e6 | − | 2.22288e7i | 0.0984714 | − | 1.39599i | ||||
\(761\) | −1.06723e7 | −0.668031 | −0.334016 | − | 0.942567i | \(-0.608404\pi\) | ||||
−0.334016 | + | 0.942567i | \(0.608404\pi\) | |||||||
\(762\) | −8.40805e6 | + | 6.72950e6i | −0.524576 | + | 0.419851i | ||||
\(763\) | −452940. | −0.0281663 | ||||||||
\(764\) | 4.15471e6 | − | 1.85037e7i | 0.257518 | − | 1.14690i | ||||
\(765\) | −5.81918e6 | + | 1.00578e7i | −0.359507 | + | 0.621372i | ||||
\(766\) | 1.80679e7 | − | 1.44609e7i | 1.11259 | − | 0.890480i | ||||
\(767\) | 2.92387e7i | 1.79461i | ||||||||
\(768\) | −1.42608e7 | − | 1.73737e7i | −0.872450 | − | 1.06289i | ||||
\(769\) | 2.98430e7 | 1.81981 | 0.909905 | − | 0.414816i | \(-0.136154\pi\) | ||||
0.909905 | + | 0.414816i | \(0.136154\pi\) | |||||||
\(770\) | 268010. | + | 1.76794e6i | 0.0162901 | + | 0.107458i | ||||
\(771\) | 1.89246e7i | 1.14654i | ||||||||
\(772\) | −2.40953e7 | − | 5.41022e6i | −1.45509 | − | 0.326717i | ||||
\(773\) | −1.33577e6 | −0.0804049 | −0.0402024 | − | 0.999192i | \(-0.512800\pi\) | ||||
−0.0402024 | + | 0.999192i | \(0.512800\pi\) | |||||||
\(774\) | −1.32832e7 | − | 1.65964e7i | −0.796984 | − | 0.995777i | ||||
\(775\) | −1.74783e6 | − | 3.04017e6i | −0.104531 | − | 0.181821i | ||||
\(776\) | 1.23511e7 | + | 2.53039e7i | 0.736295 | + | 1.50846i | ||||
\(777\) | 7.51391e6i | 0.446492i | ||||||||
\(778\) | −2.38131e7 | + | 1.90591e7i | −1.41048 | + | 1.12890i | ||||
\(779\) | 2.53740e7i | 1.49811i | ||||||||
\(780\) | −1.82092e7 | + | 1.97280e7i | −1.07165 | + | 1.16104i | ||||
\(781\) | − | 124868.i | − | 0.00732530i | ||||||
\(782\) | −1.52462e7 | − | 1.90491e7i | −0.891550 | − | 1.11393i | ||||
\(783\) | − | 2.74745e6i | − | 0.160150i | ||||||
\(784\) | −1.40826e7 | − | 6.65983e6i | −0.818265 | − | 0.386966i | ||||
\(785\) | −1.62061e7 | − | 9.37636e6i | −0.938650 | − | 0.543075i | ||||
\(786\) | −7.94921e6 | + | 6.36226e6i | −0.458952 | + | 0.367329i | ||||
\(787\) | 1.08897e7 | 0.626729 | 0.313364 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313364 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(788\) | 1.33350e6 | − | 5.93895e6i | 0.0765027 | − | 0.340717i | ||||
\(789\) | − | 9.73315e6i | − | 0.556623i | ||||||
\(790\) | −2.26463e6 | − | 1.49387e7i | −0.129101 | − | 0.851620i | ||||
\(791\) | −2.65854e6 | −0.151078 | ||||||||
\(792\) | −2.43457e6 | − | 4.98773e6i | −0.137914 | − | 0.282546i | ||||
\(793\) | 1.42461e7i | 0.804476i | ||||||||
\(794\) | −1.91551e7 | − | 2.39330e7i | −1.07828 | − | 1.34724i | ||||
\(795\) | 7.38391e6 | + | 4.27211e6i | 0.414351 | + | 0.239731i | ||||
\(796\) | −6.65409e6 | + | 2.96351e7i | −0.372226 | + | 1.65777i | ||||
\(797\) | 1.87183e7 | 1.04381 | 0.521904 | − | 0.853004i | \(-0.325222\pi\) | ||||
0.521904 | + | 0.853004i | \(0.325222\pi\) | |||||||
\(798\) | −6.66198e6 | − | 8.32369e6i | −0.370336 | − | 0.462710i | ||||
\(799\) | −1.45633e7 | −0.807035 | ||||||||
\(800\) | −1.31833e7 | + | 1.24049e7i | −0.728279 | + | 0.685281i | ||||
\(801\) | 2.65767e7 | 1.46359 | ||||||||
\(802\) | −1.14075e7 | − | 1.42528e7i | −0.626258 | − | 0.782466i | ||||
\(803\) | 998699. | 0.0546570 | ||||||||
\(804\) | −3.57126e6 | + | 1.59052e7i | −0.194842 | + | 0.867759i | ||||
\(805\) | 8.67848e6 | + | 5.02111e6i | 0.472013 | + | 0.273093i | ||||
\(806\) | 2.77720e6 | + | 3.46992e6i | 0.150581 | + | 0.188140i | ||||
\(807\) | 8.24735e6i | 0.445790i | ||||||||
\(808\) | 1.55386e7 | + | 3.18342e7i | 0.837305 | + | 1.71540i | ||||
\(809\) | −1.03428e6 | −0.0555608 | −0.0277804 | − | 0.999614i | \(-0.508844\pi\) | ||||
−0.0277804 | + | 0.999614i | \(0.508844\pi\) | |||||||
\(810\) | −3.07075e6 | − | 2.02563e7i | −0.164449 | − | 1.08480i | ||||
\(811\) | − | 2.15728e7i | − | 1.15174i | −0.817542 | − | 0.575870i | \(-0.804664\pi\) | ||
0.817542 | − | 0.575870i | \(-0.195336\pi\) | |||||||
\(812\) | −1.35333e6 | + | 6.02727e6i | −0.0720300 | + | 0.320797i | ||||
\(813\) | −2.93280e7 | −1.55617 | ||||||||
\(814\) | 5.49147e6 | − | 4.39518e6i | 0.290488 | − | 0.232496i | ||||
\(815\) | −9.84890e6 | − | 5.69829e6i | −0.519390 | − | 0.300504i | ||||
\(816\) | 9.01010e6 | − | 1.90524e7i | 0.473701 | − | 1.00167i | ||||
\(817\) | 3.82246e7i | 2.00349i | ||||||||
\(818\) | −1.85024e6 | − | 2.31174e6i | −0.0966816 | − | 0.120797i | ||||
\(819\) | 6.05176e6i | 0.315262i | ||||||||
\(820\) | 1.39802e7 | − | 1.51462e7i | 0.726069 | − | 0.786629i | ||||
\(821\) | 1.19912e7i | 0.620874i | 0.950594 | + | 0.310437i | \(0.100475\pi\) | ||||
−0.950594 | + | 0.310437i | \(0.899525\pi\) | |||||||
\(822\) | 2.60613e7 | − | 2.08585e7i | 1.34529 | − | 1.07672i | ||||
\(823\) | 1.47880e7i | 0.761045i | 0.924772 | + | 0.380523i | \(0.124256\pi\) | ||||
−0.924772 | + | 0.380523i | \(0.875744\pi\) | |||||||
\(824\) | −4.81390e6 | − | 9.86229e6i | −0.246990 | − | 0.506011i | ||||
\(825\) | −8.22470e6 | + | 4.72849e6i | −0.420712 | + | 0.241873i | ||||
\(826\) | 5.89380e6 | + | 7.36391e6i | 0.300570 | + | 0.375542i | ||||
\(827\) | −3.13464e6 | −0.159376 | −0.0796882 | − | 0.996820i | \(-0.525392\pi\) | ||||
−0.0796882 | + | 0.996820i | \(0.525392\pi\) | |||||||
\(828\) | −3.03647e7 | − | 6.81791e6i | −1.53919 | − | 0.345601i | ||||
\(829\) | − | 1.80218e7i | − | 0.910777i | −0.890293 | − | 0.455389i | \(-0.849500\pi\) | ||
0.890293 | − | 0.455389i | \(-0.150500\pi\) | |||||||
\(830\) | 2.45006e6 | + | 1.61619e7i | 0.123447 | + | 0.814324i | ||||
\(831\) | −1.21699e7 | −0.611342 | ||||||||
\(832\) | 1.41135e7 | − | 1.80873e7i | 0.706851 | − | 0.905869i | ||||
\(833\) | − | 1.46067e7i | − | 0.729355i | ||||||
\(834\) | 1.45417e7 | − | 1.16386e7i | 0.723936 | − | 0.579412i | ||||
\(835\) | −1.46195e6 | + | 2.52683e6i | −0.0725631 | + | 0.125418i | ||||
\(836\) | −2.18645e6 | + | 9.73769e6i | −0.108199 | + | 0.481882i | ||||
\(837\) | −637670. | −0.0314617 | ||||||||
\(838\) | 1.61694e7 | − | 1.29414e7i | 0.795398 | − | 0.636607i | ||||
\(839\) | 3.26760e7 | 1.60260 | 0.801298 | − | 0.598265i | \(-0.204143\pi\) | ||||
0.801298 | + | 0.598265i | \(0.204143\pi\) | |||||||
\(840\) | −609392. | + | 8.63910e6i | −0.0297988 | + | 0.422445i | ||||
\(841\) | −2.86572e6 | −0.139715 | ||||||||
\(842\) | 1.39268e7 | − | 1.11465e7i | 0.676972 | − | 0.541824i | ||||
\(843\) | 4.09012e7 | 1.98229 | ||||||||
\(844\) | −1.49092e6 | − | 334764.i | −0.0720443 | − | 0.0161764i | ||||
\(845\) | −5.75325e6 | − | 3.32866e6i | −0.277186 | − | 0.160372i | ||||
\(846\) | −1.45022e7 | + | 1.16071e7i | −0.696641 | + | 0.557566i | ||||
\(847\) | 5.62932e6i | 0.269617i | ||||||||
\(848\) | −6.59013e6 | − | 3.11654e6i | −0.314706 | − | 0.148828i | ||||
\(849\) | 1.87168e7 | 0.891172 | ||||||||
\(850\) | −1.57995e7 | − | 6.20206e6i | −0.750062 | − | 0.294434i | ||||
\(851\) | − | 3.94393e7i | − | 1.86683i | ||||||
\(852\) | 132495. | − | 590089.i | 0.00625318 | − | 0.0278496i | ||||
\(853\) | −3.87723e6 | −0.182452 | −0.0912261 | − | 0.995830i | \(-0.529079\pi\) | ||||
−0.0912261 | + | 0.995830i | \(0.529079\pi\) | |||||||
\(854\) | 2.87166e6 | + | 3.58794e6i | 0.134737 | + | 0.168345i | ||||
\(855\) | 1.33464e7 | − | 2.30679e7i | 0.624381 | − | 1.07918i | ||||
\(856\) | 1.77709e6 | − | 867418.i | 0.0828944 | − | 0.0404617i | ||||
\(857\) | 3.53502e6i | 0.164414i | 0.996615 | + | 0.0822071i | \(0.0261969\pi\) | ||||
−0.996615 | + | 0.0822071i | \(0.973803\pi\) | |||||||
\(858\) | 9.38732e6 | − | 7.51327e6i | 0.435335 | − | 0.348426i | ||||
\(859\) | − | 2.22265e7i | − | 1.02775i | −0.857864 | − | 0.513877i | \(-0.828209\pi\) | ||
0.857864 | − | 0.513877i | \(-0.171791\pi\) | |||||||
\(860\) | 2.10604e7 | − | 2.28170e7i | 0.971004 | − | 1.05199i | ||||
\(861\) | − | 9.86145e6i | − | 0.453349i | ||||||
\(862\) | 6.79279e6 | + | 8.48714e6i | 0.311373 | + | 0.389039i | ||||
\(863\) | − | 1.10828e7i | − | 0.506549i | −0.967394 | − | 0.253274i | \(-0.918492\pi\) | ||
0.967394 | − | 0.253274i | \(-0.0815075\pi\) | |||||||
\(864\) | 760736. | + | 3.20252e6i | 0.0346697 | + | 0.145951i | ||||
\(865\) | 2.43544e7 | + | 1.40908e7i | 1.10672 | + | 0.640315i | ||||
\(866\) | −1.39743e7 | + | 1.11845e7i | −0.633192 | + | 0.506784i | ||||
\(867\) | −1.06743e7 | −0.482270 | ||||||||
\(868\) | 1.39890e6 | + | 314101.i | 0.0630213 | + | 0.0141504i | ||||
\(869\) | 6.76691e6i | 0.303977i | ||||||||
\(870\) | −3.24039e7 | + | 4.91226e6i | −1.45144 | + | 0.220031i | ||||
\(871\) | −1.66386e7 | −0.743139 | ||||||||
\(872\) | 900787. | + | 1.84545e6i | 0.0401172 | + | 0.0821887i | ||||
\(873\) | 3.36749e7i | 1.49545i | ||||||||
\(874\) | 3.49677e7 | + | 4.36897e7i | 1.54842 | + | 1.93464i | ||||
\(875\) | 6.97479e6 | + | 19142.5i | 0.307972 | + | 0.000845236i | ||||
\(876\) | 4.71954e6 | + | 1.05970e6i | 0.207797 | + | 0.0466575i | ||||
\(877\) | 1.24789e7 | 0.547869 | 0.273934 | − | 0.961748i | \(-0.411675\pi\) | ||||
0.273934 | + | 0.961748i | \(0.411675\pi\) | |||||||
\(878\) | 2.49260e7 | + | 3.11434e7i | 1.09123 | + | 1.36342i | ||||
\(879\) | −9.06137e6 | −0.395569 | ||||||||
\(880\) | 6.67026e6 | − | 4.60797e6i | 0.290360 | − | 0.200587i | ||||
\(881\) | −5.51270e6 | −0.239290 | −0.119645 | − | 0.992817i | \(-0.538176\pi\) | ||||
−0.119645 | + | 0.992817i | \(0.538176\pi\) | |||||||
\(882\) | −1.16417e7 | − | 1.45455e7i | −0.503899 | − | 0.629587i | ||||
\(883\) | −3.28692e7 | −1.41869 | −0.709346 | − | 0.704861i | \(-0.751009\pi\) | ||||
−0.709346 | + | 0.704861i | \(0.751009\pi\) | |||||||
\(884\) | 2.09891e7 | + | 4.71277e6i | 0.903364 | + | 0.202836i | ||||
\(885\) | −2.50608e7 | + | 4.33150e7i | −1.07557 | + | 1.85900i | ||||
\(886\) | 2.55303e6 | + | 3.18984e6i | 0.109263 | + | 0.136516i | ||||
\(887\) | − | 2.60618e7i | − | 1.11223i | −0.831105 | − | 0.556115i | \(-0.812291\pi\) | ||
0.831105 | − | 0.556115i | \(-0.187709\pi\) | |||||||
\(888\) | 3.06146e7 | − | 1.49433e7i | 1.30285 | − | 0.635938i | ||||
\(889\) | −3.54600e6 | −0.150482 | ||||||||
\(890\) | 5.81850e6 | + | 3.83820e7i | 0.246227 | + | 1.62425i | ||||
\(891\) | 9.17567e6i | 0.387207i | ||||||||
\(892\) | −2.02412e7 | − | 4.54485e6i | −0.851774 | − | 0.191253i | ||||
\(893\) | 3.34013e7 | 1.40163 | ||||||||
\(894\) | −2.90783e6 | + | 2.32732e6i | −0.121682 | + | 0.0973897i | ||||
\(895\) | −6.99056e6 | + | 1.20825e7i | −0.291712 | + | 0.504194i | ||||
\(896\) | −91392.0 | − | 7.40031e6i | −0.00380311 | − | 0.307950i | ||||
\(897\) | − | 6.74190e7i | − | 2.79770i | ||||||
\(898\) | −4.39496e6 | − | 5.49120e6i | −0.181871 | − | 0.227236i | ||||
\(899\) | 5.42566e6i | 0.223900i | ||||||||
\(900\) | −2.06764e7 | + | 6.41631e6i | −0.850880 | + | 0.264046i | ||||
\(901\) | − | 6.83536e6i | − | 0.280511i | ||||||
\(902\) | −7.20715e6 | + | 5.76834e6i | −0.294949 | + | 0.236067i | ||||
\(903\) | − | 1.48558e7i | − | 0.606284i | ||||||
\(904\) | 5.28719e6 | + | 1.08319e7i | 0.215181 | + | 0.440844i | ||||
\(905\) | −9.55074e6 | + | 1.65075e7i | −0.387628 | + | 0.669976i | ||||
\(906\) | −1.96220e6 | − | 2.45164e6i | −0.0794189 | − | 0.0992285i | ||||
\(907\) | −1.70037e7 | −0.686319 | −0.343160 | − | 0.939277i | \(-0.611497\pi\) | ||||
−0.343160 | + | 0.939277i | \(0.611497\pi\) | |||||||
\(908\) | −122522. | + | 545672.i | −0.00493173 | + | 0.0219643i | ||||
\(909\) | 4.23655e7i | 1.70060i | ||||||||
\(910\) | −8.73994e6 | + | 1.32493e6i | −0.349869 | + | 0.0530381i | ||||
\(911\) | 2.80920e7 | 1.12147 | 0.560734 | − | 0.827996i | \(-0.310519\pi\) | ||||
0.560734 | + | 0.827996i | \(0.310519\pi\) | |||||||
\(912\) | −2.06649e7 | + | 4.36973e7i | −0.822709 | + | 1.73967i | ||||
\(913\) | − | 7.32098e6i | − | 0.290665i | ||||||
\(914\) | 1.88334e7 | − | 1.50735e7i | 0.745697 | − | 0.596829i | ||||
\(915\) | −1.22105e7 | + | 2.11045e7i | −0.482147 | + | 0.833342i | ||||
\(916\) | −2.29602e7 | − | 5.15536e6i | −0.904143 | − | 0.203011i | ||||
\(917\) | −3.35249e6 | −0.131657 | ||||||||
\(918\) | −2.40964e6 | + | 1.92859e6i | −0.0943726 | + | 0.0755324i | ||||
\(919\) | 4.45468e7 | 1.73992 | 0.869958 | − | 0.493126i | \(-0.164146\pi\) | ||||
0.869958 | + | 0.493126i | \(0.164146\pi\) | |||||||
\(920\) | 3.19860e6 | − | 4.53453e7i | 0.124592 | − | 1.76629i | ||||
\(921\) | −2.96506e7 | −1.15182 | ||||||||
\(922\) | −1.40059e7 | + | 1.12098e7i | −0.542605 | + | 0.434281i | ||||
\(923\) | 617297. | 0.0238501 | ||||||||
\(924\) | 849751. | − | 3.78450e6i | 0.0327425 | − | 0.145824i | ||||
\(925\) | −1.36745e7 | − | 2.37853e7i | −0.525480 | − | 0.914016i | ||||
\(926\) | −2.67204e6 | + | 2.13861e6i | −0.102404 | + | 0.0819603i | ||||
\(927\) | − | 1.31249e7i | − | 0.501646i | ||||||
\(928\) | 2.72489e7 | − | 6.47277e6i | 1.03867 | − | 0.246729i | ||||
\(929\) | −2.74746e7 | −1.04446 | −0.522229 | − | 0.852805i | \(-0.674900\pi\) | ||||
−0.522229 | + | 0.852805i | \(0.674900\pi\) | |||||||
\(930\) | 1.14011e6 | + | 7.52080e6i | 0.0432255 | + | 0.285139i | ||||
\(931\) | 3.35008e7i | 1.26672i | ||||||||
\(932\) | 2.21290e6 | + | 496873.i | 0.0834493 | + | 0.0187372i | ||||
\(933\) | 4.21801e7 | 1.58637 | ||||||||
\(934\) | −2.59895e7 | − | 3.24721e7i | −0.974833 | − | 1.21799i | ||||
\(935\) | 6.57974e6 | + | 3.80685e6i | 0.246139 | + | 0.142409i | ||||
\(936\) | 2.46572e7 | − | 1.20355e7i | 0.919929 | − | 0.449028i | ||||
\(937\) | − | 2.68158e7i | − | 0.997795i | −0.866661 | − | 0.498898i | \(-0.833738\pi\) | ||
0.866661 | − | 0.498898i | \(-0.166262\pi\) | |||||||
\(938\) | −4.19050e6 | + | 3.35392e6i | −0.155510 | + | 0.124465i | ||||
\(939\) | − | 5.20296e7i | − | 1.92569i | ||||||
\(940\) | −1.99379e7 | − | 1.84029e7i | −0.735970 | − | 0.679309i | ||||
\(941\) | 431928.i | 0.0159015i | 0.999968 | + | 0.00795074i | \(0.00253083\pi\) | ||||
−0.999968 | + | 0.00795074i | \(0.997469\pi\) | |||||||
\(942\) | 2.53778e7 | + | 3.17078e7i | 0.931807 | + | 1.16423i | ||||
\(943\) | 5.17612e7i | 1.89551i | ||||||||
\(944\) | 1.82821e7 | − | 3.86586e7i | 0.667722 | − | 1.41194i | ||||
\(945\) | 635151. | − | 1.09779e6i | 0.0231365 | − | 0.0399891i | ||||
\(946\) | −1.08572e7 | + | 8.68972e6i | −0.394449 | + | 0.315702i | ||||
\(947\) | −4.14162e7 | −1.50070 | −0.750352 | − | 0.661039i | \(-0.770116\pi\) | ||||
−0.750352 | + | 0.661039i | \(0.770116\pi\) | |||||||
\(948\) | −7.18022e6 | + | 3.19783e7i | −0.259488 | + | 1.15567i | ||||
\(949\) | 4.93714e6i | 0.177955i | ||||||||
\(950\) | 3.62367e7 | + | 1.42246e7i | 1.30268 | + | 0.511364i | ||||
\(951\) | −2.75731e7 | −0.988631 | ||||||||
\(952\) | 6.23617e6 | − | 3.04395e6i | 0.223011 | − | 0.108854i | ||||
\(953\) | − | 2.33270e7i | − | 0.832006i | −0.909363 | − | 0.416003i | \(-0.863431\pi\) | ||
0.909363 | − | 0.416003i | \(-0.136569\pi\) | |||||||
\(954\) | −5.44784e6 | − | 6.80671e6i | −0.193800 | − | 0.242140i | ||||
\(955\) | 2.86757e7 | + | 1.65909e7i | 1.01743 | + | 0.588657i | ||||
\(956\) | 3.62003e6 | − | 1.61224e7i | 0.128105 | − | 0.570538i | ||||
\(957\) | 1.46783e7 | 0.518078 | ||||||||
\(958\) | 1.06450e7 | + | 1.33002e7i | 0.374742 | + | 0.468215i | ||||
\(959\) | 1.09911e7 | 0.385917 | ||||||||
\(960\) | 3.64110e7 | − | 1.46982e7i | 1.27513 | − | 0.514736i | ||||
\(961\) | −2.73699e7 | −0.956014 | ||||||||
\(962\) | 2.17279e7 | + | 2.71475e7i | 0.756972 | + | 0.945785i | ||||
\(963\) | 2.36498e6 | 0.0821793 | ||||||||
\(964\) | −4.27599e6 | + | 1.90438e7i | −0.148199 | + | 0.660027i | ||||
\(965\) | 2.16045e7 | − | 3.73412e7i | 0.746838 | − | 1.29083i | ||||
\(966\) | −1.35900e7 | − | 1.69798e7i | −0.468572 | − | 0.585449i | ||||
\(967\) | 2.07177e7i | 0.712485i | 0.934393 | + | 0.356243i | \(0.115942\pi\) | ||||
−0.934393 | + | 0.356243i | \(0.884058\pi\) | |||||||
\(968\) | 2.29360e7 | − | 1.11953e7i | 0.786737 | − | 0.384015i | ||||
\(969\) | −4.53233e7 | −1.55064 | ||||||||
\(970\) | −4.86333e7 | + | 7.37254e6i | −1.65960 | + | 0.251587i | ||||
\(971\) | − | 1.95292e7i | − | 0.664716i | −0.943153 | − | 0.332358i | \(-0.892156\pi\) | ||
0.943153 | − | 0.332358i | \(-0.107844\pi\) | |||||||
\(972\) | −8.76806e6 | + | 3.90500e7i | −0.297672 | + | 1.32573i | ||||
\(973\) | 6.13280e6 | 0.207671 | ||||||||
\(974\) | −1.66155e7 | + | 1.32985e7i | −0.561199 | + | 0.449164i | ||||
\(975\) | −2.33756e7 | − | 4.06594e7i | −0.787502 | − | 1.36978i | ||||
\(976\) | 8.90765e6 | − | 1.88358e7i | 0.299322 | − | 0.632935i | ||||
\(977\) | − | 3.94484e7i | − | 1.32219i | −0.750304 | − | 0.661093i | \(-0.770093\pi\) | ||
0.750304 | − | 0.661093i | \(-0.229907\pi\) | |||||||
\(978\) | 1.54228e7 | + | 1.92698e7i | 0.515604 | + | 0.644212i | ||||
\(979\) | − | 1.73862e7i | − | 0.579760i | ||||||
\(980\) | 1.84578e7 | − | 1.99973e7i | 0.613924 | − | 0.665131i | ||||
\(981\) | 2.45596e6i | 0.0814797i | ||||||||
\(982\) | 2.51269e7 | − | 2.01107e7i | 0.831497 | − | 0.665500i | ||||
\(983\) | − | 5.47261e7i | − | 1.80639i | −0.429233 | − | 0.903194i | \(-0.641216\pi\) | ||
0.429233 | − | 0.903194i | \(-0.358784\pi\) | |||||||
\(984\) | −4.01794e7 | + | 1.96120e7i | −1.32287 | + | 0.645705i | ||||
\(985\) | 9.20378e6 | + | 5.32504e6i | 0.302257 | + | 0.174877i | ||||
\(986\) | 1.64095e7 | + | 2.05026e7i | 0.537532 | + | 0.671609i | ||||
\(987\) | −1.29812e7 | −0.424153 | ||||||||
\(988\) | −4.81390e7 | − | 1.08089e7i | −1.56893 | − | 0.352280i | ||||
\(989\) | 7.79756e7i | 2.53494i | ||||||||
\(990\) | 9.58625e6 | − | 1.45322e6i | 0.310857 | − | 0.0471242i | ||||
\(991\) | 3.95278e7 | 1.27855 | 0.639276 | − | 0.768977i | \(-0.279234\pi\) | ||||
0.639276 | + | 0.768977i | \(0.279234\pi\) | |||||||
\(992\) | −1.50230e6 | − | 6.32433e6i | −0.0484705 | − | 0.204049i | ||||
\(993\) | 6.60213e7i | 2.12476i | ||||||||
\(994\) | 155469. | − | 124432.i | 0.00499089 | − | 0.00399452i | ||||
\(995\) | −4.59264e7 | − | 2.65717e7i | −1.47064 | − | 0.850867i | ||||
\(996\) | 7.76813e6 | − | 3.45966e7i | 0.248124 | − | 1.10506i | ||||
\(997\) | 1.20027e7 | 0.382421 | 0.191210 | − | 0.981549i | \(-0.438759\pi\) | ||||
0.191210 | + | 0.981549i | \(0.438759\pi\) | |||||||
\(998\) | −3.60725e7 | + | 2.88711e7i | −1.14644 | + | 0.917567i | ||||
\(999\) | −4.98892e6 | −0.158159 |
(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 | 40.6.f.a.29.7 | ✓ | 28 | |
4.3 | odd | 2 | 160.6.f.a.49.23 | 28 | |||
5.2 | odd | 4 | 200.6.d.e.101.21 | 28 | |||
5.3 | odd | 4 | 200.6.d.e.101.8 | 28 | |||
5.4 | even | 2 | inner | 40.6.f.a.29.22 | yes | 28 | |
8.3 | odd | 2 | 160.6.f.a.49.5 | 28 | |||
8.5 | even | 2 | inner | 40.6.f.a.29.21 | yes | 28 | |
20.3 | even | 4 | 800.6.d.e.401.12 | 28 | |||
20.7 | even | 4 | 800.6.d.e.401.17 | 28 | |||
20.19 | odd | 2 | 160.6.f.a.49.6 | 28 | |||
40.3 | even | 4 | 800.6.d.e.401.11 | 28 | |||
40.13 | odd | 4 | 200.6.d.e.101.7 | 28 | |||
40.19 | odd | 2 | 160.6.f.a.49.24 | 28 | |||
40.27 | even | 4 | 800.6.d.e.401.18 | 28 | |||
40.29 | even | 2 | inner | 40.6.f.a.29.8 | yes | 28 | |
40.37 | odd | 4 | 200.6.d.e.101.22 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.f.a.29.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
40.6.f.a.29.8 | yes | 28 | 40.29 | even | 2 | inner | |
40.6.f.a.29.21 | yes | 28 | 8.5 | even | 2 | inner | |
40.6.f.a.29.22 | yes | 28 | 5.4 | even | 2 | inner | |
160.6.f.a.49.5 | 28 | 8.3 | odd | 2 | |||
160.6.f.a.49.6 | 28 | 20.19 | odd | 2 | |||
160.6.f.a.49.23 | 28 | 4.3 | odd | 2 | |||
160.6.f.a.49.24 | 28 | 40.19 | odd | 2 | |||
200.6.d.e.101.7 | 28 | 40.13 | odd | 4 | |||
200.6.d.e.101.8 | 28 | 5.3 | odd | 4 | |||
200.6.d.e.101.21 | 28 | 5.2 | odd | 4 | |||
200.6.d.e.101.22 | 28 | 40.37 | odd | 4 | |||
800.6.d.e.401.11 | 28 | 40.3 | even | 4 | |||
800.6.d.e.401.12 | 28 | 20.3 | even | 4 | |||
800.6.d.e.401.17 | 28 | 20.7 | even | 4 | |||
800.6.d.e.401.18 | 28 | 40.27 | even | 4 |