Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,8,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(1.56192512742\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{19}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.35890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28220 | 0.113332 | 0.0566659 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566659 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(3\) | 79.7424 | 1.70516 | 0.852579 | − | 0.522598i | \(-0.175037\pi\) | ||||
0.852579 | + | 0.522598i | \(0.175037\pi\) | |||||||
\(4\) | −126.356 | −0.987156 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | 102.246 | 0.193249 | ||||||||
\(7\) | −538.197 | −0.593059 | −0.296529 | − | 0.955024i | \(-0.595829\pi\) | ||||
−0.296529 | + | 0.955024i | \(0.595829\pi\) | |||||||
\(8\) | −326.136 | −0.225208 | ||||||||
\(9\) | 4171.85 | 1.90757 | ||||||||
\(10\) | −160.275 | −0.0506835 | ||||||||
\(11\) | −1215.12 | −0.275261 | −0.137630 | − | 0.990484i | \(-0.543949\pi\) | ||||
−0.137630 | + | 0.990484i | \(0.543949\pi\) | |||||||
\(12\) | −10075.9 | −1.68326 | ||||||||
\(13\) | 7070.42 | 0.892573 | 0.446286 | − | 0.894890i | \(-0.352746\pi\) | ||||
0.446286 | + | 0.894890i | \(0.352746\pi\) | |||||||
\(14\) | −690.077 | −0.0672124 | ||||||||
\(15\) | −9967.80 | −0.762570 | ||||||||
\(16\) | 15755.4 | 0.961633 | ||||||||
\(17\) | −3348.13 | −0.165284 | −0.0826420 | − | 0.996579i | \(-0.526336\pi\) | ||||
−0.0826420 | + | 0.996579i | \(0.526336\pi\) | |||||||
\(18\) | 5349.15 | 0.216188 | ||||||||
\(19\) | 22169.7 | 0.741519 | 0.370759 | − | 0.928729i | \(-0.379097\pi\) | ||||
0.370759 | + | 0.928729i | \(0.379097\pi\) | |||||||
\(20\) | 15794.5 | 0.441470 | ||||||||
\(21\) | −42917.1 | −1.01126 | ||||||||
\(22\) | −1558.03 | −0.0311958 | ||||||||
\(23\) | −58513.1 | −1.00278 | −0.501390 | − | 0.865221i | \(-0.667178\pi\) | ||||
−0.501390 | + | 0.865221i | \(0.667178\pi\) | |||||||
\(24\) | −26006.8 | −0.384015 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | 9065.71 | 0.101157 | ||||||||
\(27\) | 158276. | 1.54754 | ||||||||
\(28\) | 68004.4 | 0.585442 | ||||||||
\(29\) | −206301. | −1.57076 | −0.785379 | − | 0.619015i | \(-0.787532\pi\) | ||||
−0.785379 | + | 0.619015i | \(0.787532\pi\) | |||||||
\(30\) | −12780.7 | −0.0864234 | ||||||||
\(31\) | 177822. | 1.07206 | 0.536030 | − | 0.844199i | \(-0.319923\pi\) | ||||
0.536030 | + | 0.844199i | \(0.319923\pi\) | |||||||
\(32\) | 61947.0 | 0.334191 | ||||||||
\(33\) | −96896.5 | −0.469363 | ||||||||
\(34\) | −4292.98 | −0.0187319 | ||||||||
\(35\) | 67274.6 | 0.265224 | ||||||||
\(36\) | −527138. | −1.88307 | ||||||||
\(37\) | −284128. | −0.922163 | −0.461081 | − | 0.887358i | \(-0.652538\pi\) | ||||
−0.461081 | + | 0.887358i | \(0.652538\pi\) | |||||||
\(38\) | 28426.0 | 0.0840376 | ||||||||
\(39\) | 563812. | 1.52198 | ||||||||
\(40\) | 40767.0 | 0.100716 | ||||||||
\(41\) | 627353. | 1.42157 | 0.710785 | − | 0.703409i | \(-0.248340\pi\) | ||||
0.710785 | + | 0.703409i | \(0.248340\pi\) | |||||||
\(42\) | −55028.4 | −0.114608 | ||||||||
\(43\) | −164889. | −0.316266 | −0.158133 | − | 0.987418i | \(-0.550547\pi\) | ||||
−0.158133 | + | 0.987418i | \(0.550547\pi\) | |||||||
\(44\) | 153538. | 0.271725 | ||||||||
\(45\) | −521481. | −0.853090 | ||||||||
\(46\) | −75025.7 | −0.113647 | ||||||||
\(47\) | −449355. | −0.631316 | −0.315658 | − | 0.948873i | \(-0.602225\pi\) | ||||
−0.315658 | + | 0.948873i | \(0.602225\pi\) | |||||||
\(48\) | 1.25637e6 | 1.63974 | ||||||||
\(49\) | −533887. | −0.648281 | ||||||||
\(50\) | 20034.4 | 0.0226663 | ||||||||
\(51\) | −266988. | −0.281835 | ||||||||
\(52\) | −893390. | −0.881108 | ||||||||
\(53\) | −730190. | −0.673706 | −0.336853 | − | 0.941557i | \(-0.609362\pi\) | ||||
−0.336853 | + | 0.941557i | \(0.609362\pi\) | |||||||
\(54\) | 202942. | 0.175386 | ||||||||
\(55\) | 151890. | 0.123100 | ||||||||
\(56\) | 175525. | 0.133562 | ||||||||
\(57\) | 1.76786e6 | 1.26441 | ||||||||
\(58\) | −264520. | −0.178017 | ||||||||
\(59\) | 1.42202e6 | 0.901412 | 0.450706 | − | 0.892673i | \(-0.351172\pi\) | ||||
0.450706 | + | 0.892673i | \(0.351172\pi\) | |||||||
\(60\) | 1.25949e6 | 0.752776 | ||||||||
\(61\) | −266326. | −0.150231 | −0.0751153 | − | 0.997175i | \(-0.523932\pi\) | ||||
−0.0751153 | + | 0.997175i | \(0.523932\pi\) | |||||||
\(62\) | 228004. | 0.121498 | ||||||||
\(63\) | −2.24527e6 | −1.13130 | ||||||||
\(64\) | −1.93726e6 | −0.923758 | ||||||||
\(65\) | −883803. | −0.399171 | ||||||||
\(66\) | −124241. | −0.0531938 | ||||||||
\(67\) | 2.95028e6 | 1.19840 | 0.599200 | − | 0.800599i | \(-0.295485\pi\) | ||||
0.599200 | + | 0.800599i | \(0.295485\pi\) | |||||||
\(68\) | 423056. | 0.163161 | ||||||||
\(69\) | −4.66598e6 | −1.70990 | ||||||||
\(70\) | 86259.6 | 0.0300583 | ||||||||
\(71\) | 921138. | 0.305436 | 0.152718 | − | 0.988270i | \(-0.451197\pi\) | ||||
0.152718 | + | 0.988270i | \(0.451197\pi\) | |||||||
\(72\) | −1.36059e6 | −0.429599 | ||||||||
\(73\) | 4.25657e6 | 1.28065 | 0.640323 | − | 0.768105i | \(-0.278800\pi\) | ||||
0.640323 | + | 0.768105i | \(0.278800\pi\) | |||||||
\(74\) | −364309. | −0.104510 | ||||||||
\(75\) | 1.24597e6 | 0.341032 | ||||||||
\(76\) | −2.80127e6 | −0.731995 | ||||||||
\(77\) | 653973. | 0.163246 | ||||||||
\(78\) | 722921. | 0.172488 | ||||||||
\(79\) | 6.28551e6 | 1.43432 | 0.717159 | − | 0.696910i | \(-0.245442\pi\) | ||||
0.717159 | + | 0.696910i | \(0.245442\pi\) | |||||||
\(80\) | −1.96942e6 | −0.430055 | ||||||||
\(81\) | 3.49751e6 | 0.731243 | ||||||||
\(82\) | 804393. | 0.161109 | ||||||||
\(83\) | −9.17165e6 | −1.76065 | −0.880327 | − | 0.474367i | \(-0.842677\pi\) | ||||
−0.880327 | + | 0.474367i | \(0.842677\pi\) | |||||||
\(84\) | 5.42283e6 | 0.998271 | ||||||||
\(85\) | 418516. | 0.0739172 | ||||||||
\(86\) | −211421. | −0.0358430 | ||||||||
\(87\) | −1.64510e7 | −2.67839 | ||||||||
\(88\) | 396294. | 0.0619909 | ||||||||
\(89\) | 242643. | 0.0364840 | 0.0182420 | − | 0.999834i | \(-0.494193\pi\) | ||||
0.0182420 | + | 0.999834i | \(0.494193\pi\) | |||||||
\(90\) | −668644. | −0.0966821 | ||||||||
\(91\) | −3.80528e6 | −0.529348 | ||||||||
\(92\) | 7.39348e6 | 0.989901 | ||||||||
\(93\) | 1.41799e7 | 1.82803 | ||||||||
\(94\) | −576164. | −0.0715482 | ||||||||
\(95\) | −2.77121e6 | −0.331617 | ||||||||
\(96\) | 4.93980e6 | 0.569849 | ||||||||
\(97\) | −2.59198e6 | −0.288357 | −0.144179 | − | 0.989552i | \(-0.546054\pi\) | ||||
−0.144179 | + | 0.989552i | \(0.546054\pi\) | |||||||
\(98\) | −684551. | −0.0734708 | ||||||||
\(99\) | −5.06929e6 | −0.525078 | ||||||||
\(100\) | −1.97431e6 | −0.197431 | ||||||||
\(101\) | 3.69169e6 | 0.356534 | 0.178267 | − | 0.983982i | \(-0.442951\pi\) | ||||
0.178267 | + | 0.983982i | \(0.442951\pi\) | |||||||
\(102\) | −342332. | −0.0319409 | ||||||||
\(103\) | 8.68203e6 | 0.782873 | 0.391436 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391436 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(104\) | −2.30592e6 | −0.201014 | ||||||||
\(105\) | 5.36464e6 | 0.452249 | ||||||||
\(106\) | −936251. | −0.0763522 | ||||||||
\(107\) | 1.52118e7 | 1.20043 | 0.600216 | − | 0.799838i | \(-0.295081\pi\) | ||||
0.600216 | + | 0.799838i | \(0.295081\pi\) | |||||||
\(108\) | −1.99992e7 | −1.52767 | ||||||||
\(109\) | −1.60843e6 | −0.118963 | −0.0594813 | − | 0.998229i | \(-0.518945\pi\) | ||||
−0.0594813 | + | 0.998229i | \(0.518945\pi\) | |||||||
\(110\) | 194754. | 0.0139512 | ||||||||
\(111\) | −2.26570e7 | −1.57243 | ||||||||
\(112\) | −8.47950e6 | −0.570305 | ||||||||
\(113\) | −2.62766e7 | −1.71315 | −0.856574 | − | 0.516024i | \(-0.827411\pi\) | ||||
−0.856574 | + | 0.516024i | \(0.827411\pi\) | |||||||
\(114\) | 2.26676e6 | 0.143297 | ||||||||
\(115\) | 7.31414e6 | 0.448457 | ||||||||
\(116\) | 2.60674e7 | 1.55058 | ||||||||
\(117\) | 2.94967e7 | 1.70264 | ||||||||
\(118\) | 1.82332e6 | 0.102159 | ||||||||
\(119\) | 1.80195e6 | 0.0980231 | ||||||||
\(120\) | 3.25086e6 | 0.171737 | ||||||||
\(121\) | −1.80107e7 | −0.924231 | ||||||||
\(122\) | −341483. | −0.0170259 | ||||||||
\(123\) | 5.00266e7 | 2.42400 | ||||||||
\(124\) | −2.24688e7 | −1.05829 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | −2.87890e6 | −0.128212 | ||||||||
\(127\) | −1.91864e7 | −0.831152 | −0.415576 | − | 0.909559i | \(-0.636420\pi\) | ||||
−0.415576 | + | 0.909559i | \(0.636420\pi\) | |||||||
\(128\) | −1.04132e7 | −0.438882 | ||||||||
\(129\) | −1.31487e7 | −0.539284 | ||||||||
\(130\) | −1.13321e6 | −0.0452387 | ||||||||
\(131\) | 3.07018e7 | 1.19320 | 0.596602 | − | 0.802537i | \(-0.296517\pi\) | ||||
0.596602 | + | 0.802537i | \(0.296517\pi\) | |||||||
\(132\) | 1.22434e7 | 0.463335 | ||||||||
\(133\) | −1.19317e7 | −0.439764 | ||||||||
\(134\) | 3.78286e6 | 0.135817 | ||||||||
\(135\) | −1.97846e7 | −0.692083 | ||||||||
\(136\) | 1.09194e6 | 0.0372232 | ||||||||
\(137\) | −3.16847e7 | −1.05276 | −0.526378 | − | 0.850251i | \(-0.676450\pi\) | ||||
−0.526378 | + | 0.850251i | \(0.676450\pi\) | |||||||
\(138\) | −5.98273e6 | −0.193786 | ||||||||
\(139\) | 2.07581e7 | 0.655596 | 0.327798 | − | 0.944748i | \(-0.393693\pi\) | ||||
0.327798 | + | 0.944748i | \(0.393693\pi\) | |||||||
\(140\) | −8.50054e6 | −0.261817 | ||||||||
\(141\) | −3.58326e7 | −1.07649 | ||||||||
\(142\) | 1.18108e6 | 0.0346156 | ||||||||
\(143\) | −8.59140e6 | −0.245690 | ||||||||
\(144\) | 6.57291e7 | 1.83438 | ||||||||
\(145\) | 2.57877e7 | 0.702464 | ||||||||
\(146\) | 5.45778e6 | 0.145138 | ||||||||
\(147\) | −4.25734e7 | −1.10542 | ||||||||
\(148\) | 3.59012e7 | 0.910318 | ||||||||
\(149\) | 2.94607e7 | 0.729611 | 0.364806 | − | 0.931084i | \(-0.381135\pi\) | ||||
0.364806 | + | 0.931084i | \(0.381135\pi\) | |||||||
\(150\) | 1.59759e6 | 0.0386497 | ||||||||
\(151\) | 4.60002e7 | 1.08728 | 0.543638 | − | 0.839320i | \(-0.317046\pi\) | ||||
0.543638 | + | 0.839320i | \(0.317046\pi\) | |||||||
\(152\) | −7.23033e6 | −0.166996 | ||||||||
\(153\) | −1.39679e7 | −0.315290 | ||||||||
\(154\) | 838526. | 0.0185009 | ||||||||
\(155\) | −2.22277e7 | −0.479440 | ||||||||
\(156\) | −7.12410e7 | −1.50243 | ||||||||
\(157\) | 1.92998e7 | 0.398019 | 0.199010 | − | 0.979998i | \(-0.436227\pi\) | ||||
0.199010 | + | 0.979998i | \(0.436227\pi\) | |||||||
\(158\) | 8.05929e6 | 0.162554 | ||||||||
\(159\) | −5.82271e7 | −1.14878 | ||||||||
\(160\) | −7.74337e6 | −0.149455 | ||||||||
\(161\) | 3.14916e7 | 0.594708 | ||||||||
\(162\) | 4.48452e6 | 0.0828730 | ||||||||
\(163\) | 2.35624e7 | 0.426151 | 0.213076 | − | 0.977036i | \(-0.431652\pi\) | ||||
0.213076 | + | 0.977036i | \(0.431652\pi\) | |||||||
\(164\) | −7.92698e7 | −1.40331 | ||||||||
\(165\) | 1.21121e7 | 0.209906 | ||||||||
\(166\) | −1.17599e7 | −0.199538 | ||||||||
\(167\) | 2.18824e7 | 0.363570 | 0.181785 | − | 0.983338i | \(-0.441813\pi\) | ||||
0.181785 | + | 0.983338i | \(0.441813\pi\) | |||||||
\(168\) | 1.39968e7 | 0.227744 | ||||||||
\(169\) | −1.27577e7 | −0.203314 | ||||||||
\(170\) | 536622. | 0.00837717 | ||||||||
\(171\) | 9.24886e7 | 1.41450 | ||||||||
\(172\) | 2.08347e7 | 0.312204 | ||||||||
\(173\) | −9.62312e7 | −1.41304 | −0.706520 | − | 0.707693i | \(-0.749736\pi\) | ||||
−0.706520 | + | 0.707693i | \(0.749736\pi\) | |||||||
\(174\) | −2.10935e7 | −0.303547 | ||||||||
\(175\) | −8.40932e6 | −0.118612 | ||||||||
\(176\) | −1.91447e7 | −0.264700 | ||||||||
\(177\) | 1.13395e8 | 1.53705 | ||||||||
\(178\) | 311117. | 0.00413479 | ||||||||
\(179\) | 8.46776e7 | 1.10353 | 0.551763 | − | 0.834001i | \(-0.313955\pi\) | ||||
0.551763 | + | 0.834001i | \(0.313955\pi\) | |||||||
\(180\) | 6.58922e7 | 0.842132 | ||||||||
\(181\) | −9.65249e7 | −1.20994 | −0.604971 | − | 0.796248i | \(-0.706815\pi\) | ||||
−0.604971 | + | 0.796248i | \(0.706815\pi\) | |||||||
\(182\) | −4.87913e6 | −0.0599919 | ||||||||
\(183\) | −2.12374e7 | −0.256167 | ||||||||
\(184\) | 1.90832e7 | 0.225834 | ||||||||
\(185\) | 3.55160e7 | 0.412404 | ||||||||
\(186\) | 1.81815e7 | 0.207174 | ||||||||
\(187\) | 4.06837e6 | 0.0454962 | ||||||||
\(188\) | 5.67787e7 | 0.623208 | ||||||||
\(189\) | −8.51839e7 | −0.917785 | ||||||||
\(190\) | −3.55325e6 | −0.0375828 | ||||||||
\(191\) | −1.46467e8 | −1.52098 | −0.760491 | − | 0.649348i | \(-0.775042\pi\) | ||||
−0.760491 | + | 0.649348i | \(0.775042\pi\) | |||||||
\(192\) | −1.54482e8 | −1.57515 | ||||||||
\(193\) | −8.53275e7 | −0.854355 | −0.427177 | − | 0.904168i | \(-0.640492\pi\) | ||||
−0.427177 | + | 0.904168i | \(0.640492\pi\) | |||||||
\(194\) | −3.32345e6 | −0.0326800 | ||||||||
\(195\) | −7.04765e7 | −0.680649 | ||||||||
\(196\) | 6.74598e7 | 0.639954 | ||||||||
\(197\) | 1.44802e8 | 1.34941 | 0.674705 | − | 0.738087i | \(-0.264271\pi\) | ||||
0.674705 | + | 0.738087i | \(0.264271\pi\) | |||||||
\(198\) | −6.49986e6 | −0.0595080 | ||||||||
\(199\) | 1.26870e7 | 0.114123 | 0.0570617 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570617 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(200\) | −5.09587e6 | −0.0450416 | ||||||||
\(201\) | 2.35263e8 | 2.04346 | ||||||||
\(202\) | 4.73349e6 | 0.0404066 | ||||||||
\(203\) | 1.11031e8 | 0.931552 | ||||||||
\(204\) | 3.37355e7 | 0.278215 | ||||||||
\(205\) | −7.84191e7 | −0.635746 | ||||||||
\(206\) | 1.11321e7 | 0.0887243 | ||||||||
\(207\) | −2.44108e8 | −1.91287 | ||||||||
\(208\) | 1.11397e8 | 0.858327 | ||||||||
\(209\) | −2.69388e7 | −0.204111 | ||||||||
\(210\) | 6.87855e6 | 0.0512542 | ||||||||
\(211\) | −9.47331e7 | −0.694246 | −0.347123 | − | 0.937820i | \(-0.612841\pi\) | ||||
−0.347123 | + | 0.937820i | \(0.612841\pi\) | |||||||
\(212\) | 9.22638e7 | 0.665053 | ||||||||
\(213\) | 7.34537e7 | 0.520817 | ||||||||
\(214\) | 1.95046e7 | 0.136047 | ||||||||
\(215\) | 2.06111e7 | 0.141438 | ||||||||
\(216\) | −5.16196e7 | −0.348519 | ||||||||
\(217\) | −9.57031e7 | −0.635795 | ||||||||
\(218\) | −2.06234e6 | −0.0134822 | ||||||||
\(219\) | 3.39429e8 | 2.18371 | ||||||||
\(220\) | −1.91922e7 | −0.121519 | ||||||||
\(221\) | −2.36727e7 | −0.147528 | ||||||||
\(222\) | −2.90509e7 | −0.178207 | ||||||||
\(223\) | −2.28554e8 | −1.38014 | −0.690069 | − | 0.723744i | \(-0.742420\pi\) | ||||
−0.690069 | + | 0.723744i | \(0.742420\pi\) | |||||||
\(224\) | −3.33397e7 | −0.198195 | ||||||||
\(225\) | 6.51851e7 | 0.381513 | ||||||||
\(226\) | −3.36919e7 | −0.194154 | ||||||||
\(227\) | −3.00587e8 | −1.70561 | −0.852806 | − | 0.522229i | \(-0.825101\pi\) | ||||
−0.852806 | + | 0.522229i | \(0.825101\pi\) | |||||||
\(228\) | −2.23380e8 | −1.24817 | ||||||||
\(229\) | −1.05343e8 | −0.579669 | −0.289835 | − | 0.957077i | \(-0.593600\pi\) | ||||
−0.289835 | + | 0.957077i | \(0.593600\pi\) | |||||||
\(230\) | 9.37821e6 | 0.0508244 | ||||||||
\(231\) | 5.21494e7 | 0.278360 | ||||||||
\(232\) | 6.72823e7 | 0.353747 | ||||||||
\(233\) | 3.27196e8 | 1.69458 | 0.847291 | − | 0.531130i | \(-0.178232\pi\) | ||||
0.847291 | + | 0.531130i | \(0.178232\pi\) | |||||||
\(234\) | 3.78208e7 | 0.192963 | ||||||||
\(235\) | 5.61694e7 | 0.282333 | ||||||||
\(236\) | −1.79681e8 | −0.889834 | ||||||||
\(237\) | 5.01221e8 | 2.44574 | ||||||||
\(238\) | 2.31047e6 | 0.0111091 | ||||||||
\(239\) | −5.72888e7 | −0.271442 | −0.135721 | − | 0.990747i | \(-0.543335\pi\) | ||||
−0.135721 | + | 0.990747i | \(0.543335\pi\) | |||||||
\(240\) | −1.57047e8 | −0.733312 | ||||||||
\(241\) | 2.84287e8 | 1.30827 | 0.654134 | − | 0.756379i | \(-0.273033\pi\) | ||||
0.654134 | + | 0.756379i | \(0.273033\pi\) | |||||||
\(242\) | −2.30933e7 | −0.104745 | ||||||||
\(243\) | −6.72506e7 | −0.300659 | ||||||||
\(244\) | 3.36518e7 | 0.148301 | ||||||||
\(245\) | 6.67359e7 | 0.289920 | ||||||||
\(246\) | 6.41442e7 | 0.274717 | ||||||||
\(247\) | 1.56749e8 | 0.661859 | ||||||||
\(248\) | −5.79941e7 | −0.241436 | ||||||||
\(249\) | −7.31369e8 | −3.00219 | ||||||||
\(250\) | −2.50430e6 | −0.0101367 | ||||||||
\(251\) | −2.69178e7 | −0.107444 | −0.0537220 | − | 0.998556i | \(-0.517108\pi\) | ||||
−0.0537220 | + | 0.998556i | \(0.517108\pi\) | |||||||
\(252\) | 2.83704e8 | 1.11677 | ||||||||
\(253\) | 7.11004e7 | 0.276026 | ||||||||
\(254\) | −2.46008e7 | −0.0941959 | ||||||||
\(255\) | 3.33735e7 | 0.126041 | ||||||||
\(256\) | 2.34618e8 | 0.874019 | ||||||||
\(257\) | −3.28749e8 | −1.20809 | −0.604044 | − | 0.796951i | \(-0.706445\pi\) | ||||
−0.604044 | + | 0.796951i | \(0.706445\pi\) | |||||||
\(258\) | −1.68592e7 | −0.0611179 | ||||||||
\(259\) | 1.52917e8 | 0.546897 | ||||||||
\(260\) | 1.11674e8 | 0.394044 | ||||||||
\(261\) | −8.60658e8 | −2.99632 | ||||||||
\(262\) | 3.93660e7 | 0.135228 | ||||||||
\(263\) | 1.85590e8 | 0.629084 | 0.314542 | − | 0.949244i | \(-0.398149\pi\) | ||||
0.314542 | + | 0.949244i | \(0.398149\pi\) | |||||||
\(264\) | 3.16014e7 | 0.105704 | ||||||||
\(265\) | 9.12737e7 | 0.301290 | ||||||||
\(266\) | −1.52988e7 | −0.0498393 | ||||||||
\(267\) | 1.93489e7 | 0.0622109 | ||||||||
\(268\) | −3.72786e8 | −1.18301 | ||||||||
\(269\) | 2.70876e8 | 0.848471 | 0.424236 | − | 0.905552i | \(-0.360543\pi\) | ||||
0.424236 | + | 0.905552i | \(0.360543\pi\) | |||||||
\(270\) | −2.53678e7 | −0.0784350 | ||||||||
\(271\) | 2.30743e8 | 0.704263 | 0.352132 | − | 0.935950i | \(-0.385457\pi\) | ||||
0.352132 | + | 0.935950i | \(0.385457\pi\) | |||||||
\(272\) | −5.27511e7 | −0.158942 | ||||||||
\(273\) | −3.03442e8 | −0.902623 | ||||||||
\(274\) | −4.06262e7 | −0.119311 | ||||||||
\(275\) | −1.89862e7 | −0.0550522 | ||||||||
\(276\) | 5.89574e8 | 1.68794 | ||||||||
\(277\) | 1.42059e8 | 0.401595 | 0.200798 | − | 0.979633i | \(-0.435647\pi\) | ||||
0.200798 | + | 0.979633i | \(0.435647\pi\) | |||||||
\(278\) | 2.66161e7 | 0.0742998 | ||||||||
\(279\) | 7.41846e8 | 2.04503 | ||||||||
\(280\) | −2.19406e7 | −0.0597305 | ||||||||
\(281\) | −1.15362e8 | −0.310164 | −0.155082 | − | 0.987902i | \(-0.549564\pi\) | ||||
−0.155082 | + | 0.987902i | \(0.549564\pi\) | |||||||
\(282\) | −4.59447e7 | −0.122001 | ||||||||
\(283\) | 2.18080e8 | 0.571958 | 0.285979 | − | 0.958236i | \(-0.407681\pi\) | ||||
0.285979 | + | 0.958236i | \(0.407681\pi\) | |||||||
\(284\) | −1.16391e8 | −0.301513 | ||||||||
\(285\) | −2.20983e8 | −0.565460 | ||||||||
\(286\) | −1.10159e7 | −0.0278445 | ||||||||
\(287\) | −3.37639e8 | −0.843075 | ||||||||
\(288\) | 2.58433e8 | 0.637492 | ||||||||
\(289\) | −3.99129e8 | −0.972681 | ||||||||
\(290\) | 3.30650e7 | 0.0796115 | ||||||||
\(291\) | −2.06691e8 | −0.491695 | ||||||||
\(292\) | −5.37842e8 | −1.26420 | ||||||||
\(293\) | 4.12384e8 | 0.957778 | 0.478889 | − | 0.877875i | \(-0.341040\pi\) | ||||
0.478889 | + | 0.877875i | \(0.341040\pi\) | |||||||
\(294\) | −5.45878e7 | −0.125279 | ||||||||
\(295\) | −1.77752e8 | −0.403124 | ||||||||
\(296\) | 9.26642e7 | 0.207678 | ||||||||
\(297\) | −1.92325e8 | −0.425979 | ||||||||
\(298\) | 3.77746e7 | 0.0826881 | ||||||||
\(299\) | −4.13713e8 | −0.895055 | ||||||||
\(300\) | −1.57436e8 | −0.336652 | ||||||||
\(301\) | 8.87428e7 | 0.187564 | ||||||||
\(302\) | 5.89815e7 | 0.123223 | ||||||||
\(303\) | 2.94384e8 | 0.607946 | ||||||||
\(304\) | 3.49292e8 | 0.713069 | ||||||||
\(305\) | 3.32907e7 | 0.0671852 | ||||||||
\(306\) | −1.79096e7 | −0.0357324 | ||||||||
\(307\) | 1.57983e8 | 0.311621 | 0.155810 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155810 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(308\) | −8.26334e7 | −0.161149 | ||||||||
\(309\) | 6.92326e8 | 1.33492 | ||||||||
\(310\) | −2.85004e7 | −0.0543357 | ||||||||
\(311\) | −1.69169e8 | −0.318904 | −0.159452 | − | 0.987206i | \(-0.550973\pi\) | ||||
−0.159452 | + | 0.987206i | \(0.550973\pi\) | |||||||
\(312\) | −1.83879e8 | −0.342761 | ||||||||
\(313\) | −5.22117e8 | −0.962415 | −0.481208 | − | 0.876607i | \(-0.659802\pi\) | ||||
−0.481208 | + | 0.876607i | \(0.659802\pi\) | |||||||
\(314\) | 2.47463e7 | 0.0451082 | ||||||||
\(315\) | 2.80659e8 | 0.505932 | ||||||||
\(316\) | −7.94211e8 | −1.41590 | ||||||||
\(317\) | 4.73280e8 | 0.834470 | 0.417235 | − | 0.908799i | \(-0.362999\pi\) | ||||
0.417235 | + | 0.908799i | \(0.362999\pi\) | |||||||
\(318\) | −7.46589e7 | −0.130193 | ||||||||
\(319\) | 2.50681e8 | 0.432368 | ||||||||
\(320\) | 2.42158e8 | 0.413117 | ||||||||
\(321\) | 1.21303e9 | 2.04693 | ||||||||
\(322\) | 4.03786e7 | 0.0673993 | ||||||||
\(323\) | −7.42270e7 | −0.122561 | ||||||||
\(324\) | −4.41932e8 | −0.721851 | ||||||||
\(325\) | 1.10475e8 | 0.178515 | ||||||||
\(326\) | 3.02118e7 | 0.0482965 | ||||||||
\(327\) | −1.28260e8 | −0.202850 | ||||||||
\(328\) | −2.04602e8 | −0.320149 | ||||||||
\(329\) | 2.41841e8 | 0.374408 | ||||||||
\(330\) | 1.55301e7 | 0.0237890 | ||||||||
\(331\) | −8.75892e7 | −0.132756 | −0.0663778 | − | 0.997795i | \(-0.521144\pi\) | ||||
−0.0663778 | + | 0.997795i | \(0.521144\pi\) | |||||||
\(332\) | 1.15889e9 | 1.73804 | ||||||||
\(333\) | −1.18534e9 | −1.75909 | ||||||||
\(334\) | 2.80577e7 | 0.0412040 | ||||||||
\(335\) | −3.68785e8 | −0.535941 | ||||||||
\(336\) | −6.76175e8 | −0.972460 | ||||||||
\(337\) | −3.04119e8 | −0.432851 | −0.216426 | − | 0.976299i | \(-0.569440\pi\) | ||||
−0.216426 | + | 0.976299i | \(0.569440\pi\) | |||||||
\(338\) | −1.63579e7 | −0.0230419 | ||||||||
\(339\) | −2.09536e9 | −2.92119 | ||||||||
\(340\) | −5.28820e7 | −0.0729678 | ||||||||
\(341\) | −2.16075e8 | −0.295096 | ||||||||
\(342\) | 1.18589e8 | 0.160307 | ||||||||
\(343\) | 7.30565e8 | 0.977528 | ||||||||
\(344\) | 5.37762e7 | 0.0712256 | ||||||||
\(345\) | 5.83247e8 | 0.764691 | ||||||||
\(346\) | −1.23388e8 | −0.160142 | ||||||||
\(347\) | 3.15347e8 | 0.405169 | 0.202584 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202584 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(348\) | 2.07868e9 | 2.64399 | ||||||||
\(349\) | −5.23418e8 | −0.659112 | −0.329556 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329556 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(350\) | −1.07825e7 | −0.0134425 | ||||||||
\(351\) | 1.11908e9 | 1.38130 | ||||||||
\(352\) | −7.52730e7 | −0.0919898 | ||||||||
\(353\) | −4.13964e8 | −0.500900 | −0.250450 | − | 0.968130i | \(-0.580579\pi\) | ||||
−0.250450 | + | 0.968130i | \(0.580579\pi\) | |||||||
\(354\) | 1.45395e8 | 0.174197 | ||||||||
\(355\) | −1.15142e8 | −0.136595 | ||||||||
\(356\) | −3.06593e7 | −0.0360154 | ||||||||
\(357\) | 1.43692e8 | 0.167145 | ||||||||
\(358\) | 1.08574e8 | 0.125065 | ||||||||
\(359\) | −2.48768e8 | −0.283768 | −0.141884 | − | 0.989883i | \(-0.545316\pi\) | ||||
−0.141884 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(360\) | 1.70074e8 | 0.192122 | ||||||||
\(361\) | −4.02376e8 | −0.450150 | ||||||||
\(362\) | −1.23764e8 | −0.137125 | ||||||||
\(363\) | −1.43621e9 | −1.57596 | ||||||||
\(364\) | 4.80819e8 | 0.522549 | ||||||||
\(365\) | −5.32071e8 | −0.572723 | ||||||||
\(366\) | −2.72307e7 | −0.0290319 | ||||||||
\(367\) | 1.45884e9 | 1.54056 | 0.770278 | − | 0.637708i | \(-0.220117\pi\) | ||||
0.770278 | + | 0.637708i | \(0.220117\pi\) | |||||||
\(368\) | −9.21897e8 | −0.964307 | ||||||||
\(369\) | 2.61722e9 | 2.71174 | ||||||||
\(370\) | 4.55386e7 | 0.0467384 | ||||||||
\(371\) | 3.92986e8 | 0.399547 | ||||||||
\(372\) | −1.79172e9 | −1.80455 | ||||||||
\(373\) | 6.29125e8 | 0.627706 | 0.313853 | − | 0.949472i | \(-0.398380\pi\) | ||||
0.313853 | + | 0.949472i | \(0.398380\pi\) | |||||||
\(374\) | 5.21648e6 | 0.00515616 | ||||||||
\(375\) | −1.55747e8 | −0.152514 | ||||||||
\(376\) | 1.46551e8 | 0.142177 | ||||||||
\(377\) | −1.45864e9 | −1.40202 | ||||||||
\(378\) | −1.09223e8 | −0.104014 | ||||||||
\(379\) | 8.54658e7 | 0.0806409 | 0.0403204 | − | 0.999187i | \(-0.487162\pi\) | ||||
0.0403204 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(380\) | 3.50159e8 | 0.327358 | ||||||||
\(381\) | −1.52997e9 | −1.41725 | ||||||||
\(382\) | −1.87801e8 | −0.172376 | ||||||||
\(383\) | −7.56340e8 | −0.687893 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(384\) | −8.30371e8 | −0.748364 | ||||||||
\(385\) | −8.17466e7 | −0.0730058 | ||||||||
\(386\) | −1.09407e8 | −0.0968255 | ||||||||
\(387\) | −6.87892e8 | −0.603298 | ||||||||
\(388\) | 3.27512e8 | 0.284654 | ||||||||
\(389\) | 1.42837e9 | 1.23032 | 0.615160 | − | 0.788402i | \(-0.289092\pi\) | ||||
0.615160 | + | 0.788402i | \(0.289092\pi\) | |||||||
\(390\) | −9.03652e7 | −0.0771392 | ||||||||
\(391\) | 1.95909e8 | 0.165744 | ||||||||
\(392\) | 1.74120e8 | 0.145998 | ||||||||
\(393\) | 2.44824e9 | 2.03460 | ||||||||
\(394\) | 1.85666e8 | 0.152931 | ||||||||
\(395\) | −7.85688e8 | −0.641446 | ||||||||
\(396\) | 6.40535e8 | 0.518334 | ||||||||
\(397\) | −1.67152e8 | −0.134074 | −0.0670372 | − | 0.997750i | \(-0.521355\pi\) | ||||
−0.0670372 | + | 0.997750i | \(0.521355\pi\) | |||||||
\(398\) | 1.62673e7 | 0.0129338 | ||||||||
\(399\) | −9.51459e8 | −0.749868 | ||||||||
\(400\) | 2.46178e8 | 0.192327 | ||||||||
\(401\) | 2.32051e9 | 1.79712 | 0.898561 | − | 0.438848i | \(-0.144613\pi\) | ||||
0.898561 | + | 0.438848i | \(0.144613\pi\) | |||||||
\(402\) | 3.01654e8 | 0.231589 | ||||||||
\(403\) | 1.25728e9 | 0.956892 | ||||||||
\(404\) | −4.66467e8 | −0.351954 | ||||||||
\(405\) | −4.37189e8 | −0.327022 | ||||||||
\(406\) | 1.42364e8 | 0.105574 | ||||||||
\(407\) | 3.45249e8 | 0.253835 | ||||||||
\(408\) | 8.70742e7 | 0.0634715 | ||||||||
\(409\) | −8.24735e8 | −0.596050 | −0.298025 | − | 0.954558i | \(-0.596328\pi\) | ||||
−0.298025 | + | 0.954558i | \(0.596328\pi\) | |||||||
\(410\) | −1.00549e8 | −0.0720502 | ||||||||
\(411\) | −2.52661e9 | −1.79512 | ||||||||
\(412\) | −1.09703e9 | −0.772817 | ||||||||
\(413\) | −7.65326e8 | −0.534590 | ||||||||
\(414\) | −3.12996e8 | −0.216789 | ||||||||
\(415\) | 1.14646e9 | 0.787389 | ||||||||
\(416\) | 4.37991e8 | 0.298290 | ||||||||
\(417\) | 1.65530e9 | 1.11790 | ||||||||
\(418\) | −3.45410e7 | −0.0231323 | ||||||||
\(419\) | 8.23968e8 | 0.547219 | 0.273610 | − | 0.961841i | \(-0.411782\pi\) | ||||
0.273610 | + | 0.961841i | \(0.411782\pi\) | |||||||
\(420\) | −6.77854e8 | −0.446440 | ||||||||
\(421\) | −2.12046e8 | −0.138498 | −0.0692488 | − | 0.997599i | \(-0.522060\pi\) | ||||
−0.0692488 | + | 0.997599i | \(0.522060\pi\) | |||||||
\(422\) | −1.21467e8 | −0.0786801 | ||||||||
\(423\) | −1.87464e9 | −1.20428 | ||||||||
\(424\) | 2.38141e8 | 0.151724 | ||||||||
\(425\) | −5.23145e7 | −0.0330568 | ||||||||
\(426\) | 9.41825e7 | 0.0590251 | ||||||||
\(427\) | 1.43336e8 | 0.0890956 | ||||||||
\(428\) | −1.92210e9 | −1.18501 | ||||||||
\(429\) | −6.85099e8 | −0.418941 | ||||||||
\(430\) | 2.64276e7 | 0.0160295 | ||||||||
\(431\) | 7.44023e8 | 0.447627 | 0.223813 | − | 0.974632i | \(-0.428149\pi\) | ||||
0.223813 | + | 0.974632i | \(0.428149\pi\) | |||||||
\(432\) | 2.49371e9 | 1.48817 | ||||||||
\(433\) | −1.93573e9 | −1.14588 | −0.572938 | − | 0.819598i | \(-0.694197\pi\) | ||||
−0.572938 | + | 0.819598i | \(0.694197\pi\) | |||||||
\(434\) | −1.22711e8 | −0.0720557 | ||||||||
\(435\) | 2.05637e9 | 1.19781 | ||||||||
\(436\) | 2.03235e8 | 0.117435 | ||||||||
\(437\) | −1.29722e9 | −0.743581 | ||||||||
\(438\) | 4.35216e8 | 0.247483 | ||||||||
\(439\) | −1.35485e9 | −0.764300 | −0.382150 | − | 0.924100i | \(-0.624816\pi\) | ||||
−0.382150 | + | 0.924100i | \(0.624816\pi\) | |||||||
\(440\) | −4.95367e7 | −0.0277232 | ||||||||
\(441\) | −2.22730e9 | −1.23664 | ||||||||
\(442\) | −3.03531e7 | −0.0167196 | ||||||||
\(443\) | 1.05985e9 | 0.579203 | 0.289601 | − | 0.957147i | \(-0.406477\pi\) | ||||
0.289601 | + | 0.957147i | \(0.406477\pi\) | |||||||
\(444\) | 2.86285e9 | 1.55224 | ||||||||
\(445\) | −3.03303e7 | −0.0163161 | ||||||||
\(446\) | −2.93053e8 | −0.156413 | ||||||||
\(447\) | 2.34927e9 | 1.24410 | ||||||||
\(448\) | 1.04263e9 | 0.547843 | ||||||||
\(449\) | −1.70272e9 | −0.887730 | −0.443865 | − | 0.896094i | \(-0.646393\pi\) | ||||
−0.443865 | + | 0.896094i | \(0.646393\pi\) | |||||||
\(450\) | 8.35805e7 | 0.0432376 | ||||||||
\(451\) | −7.62309e8 | −0.391303 | ||||||||
\(452\) | 3.32021e9 | 1.69114 | ||||||||
\(453\) | 3.66816e9 | 1.85398 | ||||||||
\(454\) | −3.85414e8 | −0.193300 | ||||||||
\(455\) | 4.75660e8 | 0.236732 | ||||||||
\(456\) | −5.76564e8 | −0.284754 | ||||||||
\(457\) | −3.76431e9 | −1.84493 | −0.922463 | − | 0.386085i | \(-0.873827\pi\) | ||||
−0.922463 | + | 0.386085i | \(0.873827\pi\) | |||||||
\(458\) | −1.35071e8 | −0.0656949 | ||||||||
\(459\) | −5.29930e8 | −0.255784 | ||||||||
\(460\) | −9.24185e8 | −0.442697 | ||||||||
\(461\) | 3.59084e9 | 1.70704 | 0.853519 | − | 0.521062i | \(-0.174464\pi\) | ||||
0.853519 | + | 0.521062i | \(0.174464\pi\) | |||||||
\(462\) | 6.68660e7 | 0.0315470 | ||||||||
\(463\) | −2.45649e8 | −0.115022 | −0.0575111 | − | 0.998345i | \(-0.518316\pi\) | ||||
−0.0575111 | + | 0.998345i | \(0.518316\pi\) | |||||||
\(464\) | −3.25036e9 | −1.51049 | ||||||||
\(465\) | −1.77249e9 | −0.817521 | ||||||||
\(466\) | 4.19532e8 | 0.192050 | ||||||||
\(467\) | −4.04985e8 | −0.184005 | −0.0920025 | − | 0.995759i | \(-0.529327\pi\) | ||||
−0.0920025 | + | 0.995759i | \(0.529327\pi\) | |||||||
\(468\) | −3.72709e9 | −1.68077 | ||||||||
\(469\) | −1.58783e9 | −0.710722 | ||||||||
\(470\) | 7.20205e7 | 0.0319973 | ||||||||
\(471\) | 1.53901e9 | 0.678686 | ||||||||
\(472\) | −4.63771e8 | −0.203005 | ||||||||
\(473\) | 2.00360e8 | 0.0870556 | ||||||||
\(474\) | 6.42667e8 | 0.277180 | ||||||||
\(475\) | 3.46401e8 | 0.148304 | ||||||||
\(476\) | −2.27687e8 | −0.0967641 | ||||||||
\(477\) | −3.04624e9 | −1.28514 | ||||||||
\(478\) | −7.34559e7 | −0.0307630 | ||||||||
\(479\) | 4.18334e9 | 1.73920 | 0.869598 | − | 0.493760i | \(-0.164378\pi\) | ||||
0.869598 | + | 0.493760i | \(0.164378\pi\) | |||||||
\(480\) | −6.17475e8 | −0.254844 | ||||||||
\(481\) | −2.00890e9 | −0.823097 | ||||||||
\(482\) | 3.64513e8 | 0.148268 | ||||||||
\(483\) | 2.51121e9 | 1.01407 | ||||||||
\(484\) | 2.27575e9 | 0.912361 | ||||||||
\(485\) | 3.23998e8 | 0.128957 | ||||||||
\(486\) | −8.62289e7 | −0.0340742 | ||||||||
\(487\) | 3.25089e9 | 1.27541 | 0.637706 | − | 0.770280i | \(-0.279883\pi\) | ||||
0.637706 | + | 0.770280i | \(0.279883\pi\) | |||||||
\(488\) | 8.68583e7 | 0.0338331 | ||||||||
\(489\) | 1.87893e9 | 0.726656 | ||||||||
\(490\) | 8.55689e7 | 0.0328571 | ||||||||
\(491\) | −3.37360e9 | −1.28620 | −0.643100 | − | 0.765782i | \(-0.722352\pi\) | ||||
−0.643100 | + | 0.765782i | \(0.722352\pi\) | |||||||
\(492\) | −6.32116e9 | −2.39287 | ||||||||
\(493\) | 6.90723e8 | 0.259621 | ||||||||
\(494\) | 2.00984e8 | 0.0750097 | ||||||||
\(495\) | 6.33662e8 | 0.234822 | ||||||||
\(496\) | 2.80165e9 | 1.03093 | ||||||||
\(497\) | −4.95753e8 | −0.181142 | ||||||||
\(498\) | −9.37763e8 | −0.340244 | ||||||||
\(499\) | 3.74951e9 | 1.35090 | 0.675449 | − | 0.737406i | \(-0.263950\pi\) | ||||
0.675449 | + | 0.737406i | \(0.263950\pi\) | |||||||
\(500\) | 2.46789e8 | 0.0882939 | ||||||||
\(501\) | 1.74496e9 | 0.619945 | ||||||||
\(502\) | −3.45141e7 | −0.0121768 | ||||||||
\(503\) | −3.09301e9 | −1.08366 | −0.541830 | − | 0.840488i | \(-0.682268\pi\) | ||||
−0.541830 | + | 0.840488i | \(0.682268\pi\) | |||||||
\(504\) | 7.32264e8 | 0.254777 | ||||||||
\(505\) | −4.61461e8 | −0.159447 | ||||||||
\(506\) | 9.11651e7 | 0.0312825 | ||||||||
\(507\) | −1.01733e9 | −0.346683 | ||||||||
\(508\) | 2.42432e9 | 0.820476 | ||||||||
\(509\) | 1.36862e9 | 0.460015 | 0.230007 | − | 0.973189i | \(-0.426125\pi\) | ||||
0.230007 | + | 0.973189i | \(0.426125\pi\) | |||||||
\(510\) | 4.27915e7 | 0.0142844 | ||||||||
\(511\) | −2.29087e9 | −0.759499 | ||||||||
\(512\) | 1.63371e9 | 0.537937 | ||||||||
\(513\) | 3.50894e9 | 1.14753 | ||||||||
\(514\) | −4.21523e8 | −0.136915 | ||||||||
\(515\) | −1.08525e9 | −0.350111 | ||||||||
\(516\) | 1.66141e9 | 0.532357 | ||||||||
\(517\) | 5.46020e8 | 0.173777 | ||||||||
\(518\) | 1.96070e8 | 0.0619808 | ||||||||
\(519\) | −7.67371e9 | −2.40946 | ||||||||
\(520\) | 2.88240e8 | 0.0898963 | ||||||||
\(521\) | −4.47414e9 | −1.38604 | −0.693022 | − | 0.720916i | \(-0.743721\pi\) | ||||
−0.693022 | + | 0.720916i | \(0.743721\pi\) | |||||||
\(522\) | −1.10354e9 | −0.339579 | ||||||||
\(523\) | −3.01993e9 | −0.923085 | −0.461542 | − | 0.887118i | \(-0.652704\pi\) | ||||
−0.461542 | + | 0.887118i | \(0.652704\pi\) | |||||||
\(524\) | −3.87936e9 | −1.17788 | ||||||||
\(525\) | −6.70579e8 | −0.202252 | ||||||||
\(526\) | 2.37963e8 | 0.0712952 | ||||||||
\(527\) | −5.95370e8 | −0.177194 | ||||||||
\(528\) | −1.52664e9 | −0.451355 | ||||||||
\(529\) | 1.89619e7 | 0.00556913 | ||||||||
\(530\) | 1.17031e8 | 0.0341458 | ||||||||
\(531\) | 5.93244e9 | 1.71950 | ||||||||
\(532\) | 1.50764e9 | 0.434116 | ||||||||
\(533\) | 4.43565e9 | 1.26885 | ||||||||
\(534\) | 2.48092e7 | 0.00705047 | ||||||||
\(535\) | −1.90148e9 | −0.536850 | ||||||||
\(536\) | −9.62193e8 | −0.269889 | ||||||||
\(537\) | 6.75239e9 | 1.88169 | ||||||||
\(538\) | 3.47318e8 | 0.0961587 | ||||||||
\(539\) | 6.48737e8 | 0.178446 | ||||||||
\(540\) | 2.49990e9 | 0.683194 | ||||||||
\(541\) | 3.23946e9 | 0.879593 | 0.439796 | − | 0.898097i | \(-0.355051\pi\) | ||||
0.439796 | + | 0.898097i | \(0.355051\pi\) | |||||||
\(542\) | 2.95859e8 | 0.0798154 | ||||||||
\(543\) | −7.69713e9 | −2.06314 | ||||||||
\(544\) | −2.07406e8 | −0.0552365 | ||||||||
\(545\) | 2.01054e8 | 0.0532017 | ||||||||
\(546\) | −3.89074e8 | −0.102296 | ||||||||
\(547\) | 4.25742e9 | 1.11222 | 0.556111 | − | 0.831108i | \(-0.312293\pi\) | ||||
0.556111 | + | 0.831108i | \(0.312293\pi\) | |||||||
\(548\) | 4.00355e9 | 1.03923 | ||||||||
\(549\) | −1.11107e9 | −0.286575 | ||||||||
\(550\) | −2.43442e7 | −0.00623916 | ||||||||
\(551\) | −4.57364e9 | −1.16475 | ||||||||
\(552\) | 1.52174e9 | 0.385083 | ||||||||
\(553\) | −3.38284e9 | −0.850635 | ||||||||
\(554\) | 1.82148e8 | 0.0455135 | ||||||||
\(555\) | 2.83213e9 | 0.703214 | ||||||||
\(556\) | −2.62291e9 | −0.647175 | ||||||||
\(557\) | −5.65828e9 | −1.38737 | −0.693684 | − | 0.720280i | \(-0.744013\pi\) | ||||
−0.693684 | + | 0.720280i | \(0.744013\pi\) | |||||||
\(558\) | 9.51196e8 | 0.231766 | ||||||||
\(559\) | −1.16584e9 | −0.282290 | ||||||||
\(560\) | 1.05994e9 | 0.255048 | ||||||||
\(561\) | 3.24422e8 | 0.0775783 | ||||||||
\(562\) | −1.47918e8 | −0.0351515 | ||||||||
\(563\) | 4.37511e9 | 1.03326 | 0.516630 | − | 0.856209i | \(-0.327186\pi\) | ||||
0.516630 | + | 0.856209i | \(0.327186\pi\) | |||||||
\(564\) | 4.52767e9 | 1.06267 | ||||||||
\(565\) | 3.28458e9 | 0.766143 | ||||||||
\(566\) | 2.79623e8 | 0.0648210 | ||||||||
\(567\) | −1.88235e9 | −0.433670 | ||||||||
\(568\) | −3.00416e8 | −0.0687866 | ||||||||
\(569\) | 1.67226e9 | 0.380550 | 0.190275 | − | 0.981731i | \(-0.439062\pi\) | ||||
0.190275 | + | 0.981731i | \(0.439062\pi\) | |||||||
\(570\) | −2.83345e8 | −0.0640846 | ||||||||
\(571\) | 6.39802e8 | 0.143820 | 0.0719100 | − | 0.997411i | \(-0.477091\pi\) | ||||
0.0719100 | + | 0.997411i | \(0.477091\pi\) | |||||||
\(572\) | 1.08558e9 | 0.242535 | ||||||||
\(573\) | −1.16797e10 | −2.59352 | ||||||||
\(574\) | −4.32922e8 | −0.0955472 | ||||||||
\(575\) | −9.14268e8 | −0.200556 | ||||||||
\(576\) | −8.08196e9 | −1.76213 | ||||||||
\(577\) | 4.87101e9 | 1.05561 | 0.527805 | − | 0.849366i | \(-0.323015\pi\) | ||||
0.527805 | + | 0.849366i | \(0.323015\pi\) | |||||||
\(578\) | −5.11764e8 | −0.110236 | ||||||||
\(579\) | −6.80422e9 | −1.45681 | ||||||||
\(580\) | −3.25843e9 | −0.693442 | ||||||||
\(581\) | 4.93615e9 | 1.04417 | ||||||||
\(582\) | −2.65019e8 | −0.0557246 | ||||||||
\(583\) | 8.87268e8 | 0.185445 | ||||||||
\(584\) | −1.38822e9 | −0.288412 | ||||||||
\(585\) | −3.68709e9 | −0.761444 | ||||||||
\(586\) | 5.28760e8 | 0.108547 | ||||||||
\(587\) | −2.32406e9 | −0.474258 | −0.237129 | − | 0.971478i | \(-0.576206\pi\) | ||||
−0.237129 | + | 0.971478i | \(0.576206\pi\) | |||||||
\(588\) | 5.37941e9 | 1.09122 | ||||||||
\(589\) | 3.94226e9 | 0.794953 | ||||||||
\(590\) | −2.27914e8 | −0.0456867 | ||||||||
\(591\) | 1.15469e10 | 2.30096 | ||||||||
\(592\) | −4.47654e9 | −0.886782 | ||||||||
\(593\) | 4.27080e9 | 0.841043 | 0.420522 | − | 0.907283i | \(-0.361847\pi\) | ||||
0.420522 | + | 0.907283i | \(0.361847\pi\) | |||||||
\(594\) | −2.46599e8 | −0.0482769 | ||||||||
\(595\) | −2.25244e8 | −0.0438373 | ||||||||
\(596\) | −3.72254e9 | −0.720240 | ||||||||
\(597\) | 1.01169e9 | 0.194598 | ||||||||
\(598\) | −5.30463e8 | −0.101438 | ||||||||
\(599\) | 3.50335e9 | 0.666023 | 0.333012 | − | 0.942923i | \(-0.391935\pi\) | ||||
0.333012 | + | 0.942923i | \(0.391935\pi\) | |||||||
\(600\) | −4.06357e8 | −0.0768030 | ||||||||
\(601\) | 2.98866e9 | 0.561585 | 0.280792 | − | 0.959769i | \(-0.409403\pi\) | ||||
0.280792 | + | 0.959769i | \(0.409403\pi\) | |||||||
\(602\) | 1.13786e8 | 0.0212570 | ||||||||
\(603\) | 1.23081e10 | 2.28603 | ||||||||
\(604\) | −5.81240e9 | −1.07331 | ||||||||
\(605\) | 2.25133e9 | 0.413329 | ||||||||
\(606\) | 3.77460e8 | 0.0688996 | ||||||||
\(607\) | −7.31901e9 | −1.32829 | −0.664143 | − | 0.747605i | \(-0.731203\pi\) | ||||
−0.664143 | + | 0.747605i | \(0.731203\pi\) | |||||||
\(608\) | 1.37335e9 | 0.247809 | ||||||||
\(609\) | 8.85386e9 | 1.58844 | ||||||||
\(610\) | 4.26854e7 | 0.00761421 | ||||||||
\(611\) | −3.17713e9 | −0.563496 | ||||||||
\(612\) | 1.76492e9 | 0.311241 | ||||||||
\(613\) | −8.32799e9 | −1.46026 | −0.730128 | − | 0.683311i | \(-0.760539\pi\) | ||||
−0.730128 | + | 0.683311i | \(0.760539\pi\) | |||||||
\(614\) | 2.02566e8 | 0.0353165 | ||||||||
\(615\) | −6.25333e9 | −1.08405 | ||||||||
\(616\) | −2.13284e8 | −0.0367643 | ||||||||
\(617\) | −2.88456e9 | −0.494403 | −0.247201 | − | 0.968964i | \(-0.579511\pi\) | ||||
−0.247201 | + | 0.968964i | \(0.579511\pi\) | |||||||
\(618\) | 8.87702e8 | 0.151289 | ||||||||
\(619\) | −2.27213e9 | −0.385049 | −0.192525 | − | 0.981292i | \(-0.561668\pi\) | ||||
−0.192525 | + | 0.981292i | \(0.561668\pi\) | |||||||
\(620\) | 2.80861e9 | 0.473282 | ||||||||
\(621\) | −9.26125e9 | −1.55185 | ||||||||
\(622\) | −2.16909e8 | −0.0361420 | ||||||||
\(623\) | −1.30589e8 | −0.0216371 | ||||||||
\(624\) | 8.88308e9 | 1.46358 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −6.69459e8 | −0.109072 | ||||||||
\(627\) | −2.14817e9 | −0.348042 | ||||||||
\(628\) | −2.43865e9 | −0.392907 | ||||||||
\(629\) | 9.51296e8 | 0.152419 | ||||||||
\(630\) | 3.59862e8 | 0.0573382 | ||||||||
\(631\) | −2.90856e7 | −0.00460867 | −0.00230434 | − | 0.999997i | \(-0.500733\pi\) | ||||
−0.00230434 | + | 0.999997i | \(0.500733\pi\) | |||||||
\(632\) | −2.04993e9 | −0.323020 | ||||||||
\(633\) | −7.55424e9 | −1.18380 | ||||||||
\(634\) | 6.06841e8 | 0.0945719 | ||||||||
\(635\) | 2.39830e9 | 0.371702 | ||||||||
\(636\) | 7.35734e9 | 1.13402 | ||||||||
\(637\) | −3.77481e9 | −0.578638 | ||||||||
\(638\) | 3.21423e8 | 0.0490010 | ||||||||
\(639\) | 3.84285e9 | 0.582640 | ||||||||
\(640\) | 1.30165e9 | 0.196274 | ||||||||
\(641\) | −3.12634e9 | −0.468849 | −0.234424 | − | 0.972134i | \(-0.575320\pi\) | ||||
−0.234424 | + | 0.972134i | \(0.575320\pi\) | |||||||
\(642\) | 1.55534e9 | 0.231982 | ||||||||
\(643\) | 2.48120e9 | 0.368064 | 0.184032 | − | 0.982920i | \(-0.441085\pi\) | ||||
0.184032 | + | 0.982920i | \(0.441085\pi\) | |||||||
\(644\) | −3.97915e9 | −0.587070 | ||||||||
\(645\) | 1.64358e9 | 0.241175 | ||||||||
\(646\) | −9.51740e7 | −0.0138901 | ||||||||
\(647\) | 3.10080e9 | 0.450100 | 0.225050 | − | 0.974347i | \(-0.427746\pi\) | ||||
0.225050 | + | 0.974347i | \(0.427746\pi\) | |||||||
\(648\) | −1.14066e9 | −0.164682 | ||||||||
\(649\) | −1.72792e9 | −0.248123 | ||||||||
\(650\) | 1.41652e8 | 0.0202314 | ||||||||
\(651\) | −7.63159e9 | −1.08413 | ||||||||
\(652\) | −2.97726e9 | −0.420678 | ||||||||
\(653\) | 9.64911e8 | 0.135610 | 0.0678049 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678049 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(654\) | −1.64456e8 | −0.0229894 | ||||||||
\(655\) | −3.83773e9 | −0.533617 | ||||||||
\(656\) | 9.88419e9 | 1.36703 | ||||||||
\(657\) | 1.77577e10 | 2.44292 | ||||||||
\(658\) | 3.10089e8 | 0.0424323 | ||||||||
\(659\) | −7.70039e9 | −1.04813 | −0.524063 | − | 0.851679i | \(-0.675584\pi\) | ||||
−0.524063 | + | 0.851679i | \(0.675584\pi\) | |||||||
\(660\) | −1.53043e9 | −0.207210 | ||||||||
\(661\) | 1.30650e10 | 1.75956 | 0.879779 | − | 0.475382i | \(-0.157690\pi\) | ||||
0.879779 | + | 0.475382i | \(0.157690\pi\) | |||||||
\(662\) | −1.12307e8 | −0.0150454 | ||||||||
\(663\) | −1.88772e9 | −0.251559 | ||||||||
\(664\) | 2.99120e9 | 0.396513 | ||||||||
\(665\) | 1.49146e9 | 0.196669 | ||||||||
\(666\) | −1.51984e9 | −0.199360 | ||||||||
\(667\) | 1.20713e10 | 1.57513 | ||||||||
\(668\) | −2.76498e9 | −0.358900 | ||||||||
\(669\) | −1.82255e10 | −2.35335 | ||||||||
\(670\) | −4.72857e8 | −0.0607391 | ||||||||
\(671\) | 3.23617e8 | 0.0413526 | ||||||||
\(672\) | −2.65858e9 | −0.337954 | ||||||||
\(673\) | 1.31771e10 | 1.66636 | 0.833179 | − | 0.553003i | \(-0.186518\pi\) | ||||
0.833179 | + | 0.553003i | \(0.186518\pi\) | |||||||
\(674\) | −3.89942e8 | −0.0490558 | ||||||||
\(675\) | 2.47307e9 | 0.309509 | ||||||||
\(676\) | 1.61201e9 | 0.200703 | ||||||||
\(677\) | −3.18151e9 | −0.394069 | −0.197035 | − | 0.980397i | \(-0.563131\pi\) | ||||
−0.197035 | + | 0.980397i | \(0.563131\pi\) | |||||||
\(678\) | −2.68667e9 | −0.331063 | ||||||||
\(679\) | 1.39500e9 | 0.171013 | ||||||||
\(680\) | −1.36493e8 | −0.0166467 | ||||||||
\(681\) | −2.39695e10 | −2.90834 | ||||||||
\(682\) | −2.77051e8 | −0.0334438 | ||||||||
\(683\) | −3.33139e8 | −0.0400086 | −0.0200043 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200043 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(684\) | −1.16865e10 | −1.39633 | ||||||||
\(685\) | 3.96059e9 | 0.470807 | ||||||||
\(686\) | 9.36731e8 | 0.110785 | ||||||||
\(687\) | −8.40028e9 | −0.988428 | ||||||||
\(688\) | −2.59789e9 | −0.304132 | ||||||||
\(689\) | −5.16275e9 | −0.601331 | ||||||||
\(690\) | 7.47841e8 | 0.0866637 | ||||||||
\(691\) | −4.45248e9 | −0.513368 | −0.256684 | − | 0.966495i | \(-0.582630\pi\) | ||||
−0.256684 | + | 0.966495i | \(0.582630\pi\) | |||||||
\(692\) | 1.21594e10 | 1.39489 | ||||||||
\(693\) | 2.72828e9 | 0.311402 | ||||||||
\(694\) | 4.04339e8 | 0.0459185 | ||||||||
\(695\) | −2.59476e9 | −0.293191 | ||||||||
\(696\) | 5.36525e9 | 0.603195 | ||||||||
\(697\) | −2.10046e9 | −0.234963 | ||||||||
\(698\) | −6.71127e8 | −0.0746983 | ||||||||
\(699\) | 2.60914e10 | 2.88953 | ||||||||
\(700\) | 1.06257e9 | 0.117088 | ||||||||
\(701\) | −1.91380e9 | −0.209838 | −0.104919 | − | 0.994481i | \(-0.533458\pi\) | ||||
−0.104919 | + | 0.994481i | \(0.533458\pi\) | |||||||
\(702\) | 1.43489e9 | 0.156545 | ||||||||
\(703\) | −6.29902e9 | −0.683801 | ||||||||
\(704\) | 2.35400e9 | 0.254274 | ||||||||
\(705\) | 4.47908e9 | 0.481423 | ||||||||
\(706\) | −5.30785e8 | −0.0567679 | ||||||||
\(707\) | −1.98686e9 | −0.211445 | ||||||||
\(708\) | −1.43282e10 | −1.51731 | ||||||||
\(709\) | 1.38704e9 | 0.146160 | 0.0730799 | − | 0.997326i | \(-0.476717\pi\) | ||||
0.0730799 | + | 0.997326i | \(0.476717\pi\) | |||||||
\(710\) | −1.47636e8 | −0.0154806 | ||||||||
\(711\) | 2.62222e10 | 2.73606 | ||||||||
\(712\) | −7.91344e7 | −0.00821647 | ||||||||
\(713\) | −1.04049e10 | −1.07504 | ||||||||
\(714\) | 1.84242e8 | 0.0189428 | ||||||||
\(715\) | 1.07393e9 | 0.109876 | ||||||||
\(716\) | −1.06995e10 | −1.08935 | ||||||||
\(717\) | −4.56835e9 | −0.462852 | ||||||||
\(718\) | −3.18970e8 | −0.0321599 | ||||||||
\(719\) | 9.42958e9 | 0.946109 | 0.473055 | − | 0.881033i | \(-0.343151\pi\) | ||||
0.473055 | + | 0.881033i | \(0.343151\pi\) | |||||||
\(720\) | −8.21614e9 | −0.820359 | ||||||||
\(721\) | −4.67264e9 | −0.464290 | ||||||||
\(722\) | −5.15928e8 | −0.0510163 | ||||||||
\(723\) | 2.26697e10 | 2.23081 | ||||||||
\(724\) | 1.21965e10 | 1.19440 | ||||||||
\(725\) | −3.22346e9 | −0.314152 | ||||||||
\(726\) | −1.84151e9 | −0.178606 | ||||||||
\(727\) | −2.99387e9 | −0.288976 | −0.144488 | − | 0.989507i | \(-0.546154\pi\) | ||||
−0.144488 | + | 0.989507i | \(0.546154\pi\) | |||||||
\(728\) | 1.24104e9 | 0.119213 | ||||||||
\(729\) | −1.30118e10 | −1.24391 | ||||||||
\(730\) | −6.82222e8 | −0.0649076 | ||||||||
\(731\) | 5.52070e8 | 0.0522737 | ||||||||
\(732\) | 2.68348e9 | 0.252877 | ||||||||
\(733\) | 1.11711e10 | 1.04768 | 0.523842 | − | 0.851815i | \(-0.324498\pi\) | ||||
0.523842 | + | 0.851815i | \(0.324498\pi\) | |||||||
\(734\) | 1.87053e9 | 0.174594 | ||||||||
\(735\) | 5.32168e9 | 0.494360 | ||||||||
\(736\) | −3.62471e9 | −0.335121 | ||||||||
\(737\) | −3.58495e9 | −0.329873 | ||||||||
\(738\) | 3.35581e9 | 0.307326 | ||||||||
\(739\) | −6.96449e9 | −0.634796 | −0.317398 | − | 0.948292i | \(-0.602809\pi\) | ||||
−0.317398 | + | 0.948292i | \(0.602809\pi\) | |||||||
\(740\) | −4.48765e9 | −0.407107 | ||||||||
\(741\) | 1.24995e10 | 1.12858 | ||||||||
\(742\) | 5.03887e8 | 0.0452814 | ||||||||
\(743\) | 1.27161e9 | 0.113734 | 0.0568672 | − | 0.998382i | \(-0.481889\pi\) | ||||
0.0568672 | + | 0.998382i | \(0.481889\pi\) | |||||||
\(744\) | −4.62458e9 | −0.411687 | ||||||||
\(745\) | −3.68259e9 | −0.326292 | ||||||||
\(746\) | 8.06666e8 | 0.0711390 | ||||||||
\(747\) | −3.82627e10 | −3.35856 | ||||||||
\(748\) | −5.14063e8 | −0.0449119 | ||||||||
\(749\) | −8.18695e9 | −0.711927 | ||||||||
\(750\) | −1.99699e8 | −0.0172847 | ||||||||
\(751\) | −1.70771e10 | −1.47121 | −0.735603 | − | 0.677413i | \(-0.763101\pi\) | ||||
−0.735603 | + | 0.677413i | \(0.763101\pi\) | |||||||
\(752\) | −7.07976e9 | −0.607094 | ||||||||
\(753\) | −2.14649e9 | −0.183209 | ||||||||
\(754\) | −1.87027e9 | −0.158893 | ||||||||
\(755\) | −5.75002e9 | −0.486245 | ||||||||
\(756\) | 1.07635e10 | 0.905997 | ||||||||
\(757\) | 1.37933e10 | 1.15567 | 0.577833 | − | 0.816155i | \(-0.303899\pi\) | ||||
0.577833 | + | 0.816155i | \(0.303899\pi\) | |||||||
\(758\) | 1.09584e8 | 0.00913917 | ||||||||
\(759\) | 5.66972e9 | 0.470669 | ||||||||
\(760\) | 9.03791e8 | 0.0746828 | ||||||||
\(761\) | 1.71364e10 | 1.40953 | 0.704765 | − | 0.709441i | \(-0.251053\pi\) | ||||
0.704765 | + | 0.709441i | \(0.251053\pi\) | |||||||
\(762\) | −1.96173e9 | −0.160619 | ||||||||
\(763\) | 8.65654e8 | 0.0705518 | ||||||||
\(764\) | 1.85070e10 | 1.50145 | ||||||||
\(765\) | 1.74598e9 | 0.141002 | ||||||||
\(766\) | −9.69780e8 | −0.0779602 | ||||||||
\(767\) | 1.00543e10 | 0.804575 | ||||||||
\(768\) | 1.87090e10 | 1.49034 | ||||||||
\(769\) | −4.41529e9 | −0.350120 | −0.175060 | − | 0.984558i | \(-0.556012\pi\) | ||||
−0.175060 | + | 0.984558i | \(0.556012\pi\) | |||||||
\(770\) | −1.04816e8 | −0.00827387 | ||||||||
\(771\) | −2.62152e10 | −2.05998 | ||||||||
\(772\) | 1.07816e10 | 0.843381 | ||||||||
\(773\) | −5.87300e8 | −0.0457332 | −0.0228666 | − | 0.999739i | \(-0.507279\pi\) | ||||
−0.0228666 | + | 0.999739i | \(0.507279\pi\) | |||||||
\(774\) | −8.82017e8 | −0.0683728 | ||||||||
\(775\) | 2.77847e9 | 0.214412 | ||||||||
\(776\) | 8.45338e8 | 0.0649403 | ||||||||
\(777\) | 1.21939e10 | 0.932546 | ||||||||
\(778\) | 1.83146e9 | 0.139434 | ||||||||
\(779\) | 1.39082e10 | 1.05412 | ||||||||
\(780\) | 8.90513e9 | 0.671907 | ||||||||
\(781\) | −1.11929e9 | −0.0840746 | ||||||||
\(782\) | 2.51195e8 | 0.0187840 | ||||||||
\(783\) | −3.26527e10 | −2.43082 | ||||||||
\(784\) | −8.41160e9 | −0.623408 | ||||||||
\(785\) | −2.41248e9 | −0.178000 | ||||||||
\(786\) | 3.13914e9 | 0.230585 | ||||||||
\(787\) | −2.30069e10 | −1.68247 | −0.841235 | − | 0.540670i | \(-0.818171\pi\) | ||||
−0.841235 | + | 0.540670i | \(0.818171\pi\) | |||||||
\(788\) | −1.82967e10 | −1.33208 | ||||||||
\(789\) | 1.47994e10 | 1.07269 | ||||||||
\(790\) | −1.00741e9 | −0.0726962 | ||||||||
\(791\) | 1.41420e10 | 1.01600 | ||||||||
\(792\) | 1.65328e9 | 0.118252 | ||||||||
\(793\) | −1.88303e9 | −0.134092 | ||||||||
\(794\) | −2.14323e8 | −0.0151949 | ||||||||
\(795\) | 7.27838e9 | 0.513748 | ||||||||
\(796\) | −1.60308e9 | −0.112658 | ||||||||
\(797\) | 2.49526e10 | 1.74587 | 0.872935 | − | 0.487836i | \(-0.162213\pi\) | ||||
0.872935 | + | 0.487836i | \(0.162213\pi\) | |||||||
\(798\) | −1.21996e9 | −0.0849838 | ||||||||
\(799\) | 1.50450e9 | 0.104346 | ||||||||
\(800\) | 9.67921e8 | 0.0668383 | ||||||||
\(801\) | 1.01227e9 | 0.0695956 | ||||||||
\(802\) | 2.97536e9 | 0.203671 | ||||||||
\(803\) | −5.17223e9 | −0.352512 | ||||||||
\(804\) | −2.97268e10 | −2.01722 | ||||||||
\(805\) | −3.93645e9 | −0.265962 | ||||||||
\(806\) | 1.61208e9 | 0.108446 | ||||||||
\(807\) | 2.16003e10 | 1.44678 | ||||||||
\(808\) | −1.20399e9 | −0.0802942 | ||||||||
\(809\) | −1.29758e10 | −0.861616 | −0.430808 | − | 0.902443i | \(-0.641771\pi\) | ||||
−0.430808 | + | 0.902443i | \(0.641771\pi\) | |||||||
\(810\) | −5.60565e8 | −0.0370620 | ||||||||
\(811\) | −2.04887e10 | −1.34878 | −0.674391 | − | 0.738374i | \(-0.735594\pi\) | ||||
−0.674391 | + | 0.738374i | \(0.735594\pi\) | |||||||
\(812\) | −1.40294e10 | −0.919587 | ||||||||
\(813\) | 1.84000e10 | 1.20088 | ||||||||
\(814\) | 4.42679e8 | 0.0287676 | ||||||||
\(815\) | −2.94531e9 | −0.190581 | ||||||||
\(816\) | −4.20649e9 | −0.271022 | ||||||||
\(817\) | −3.65554e9 | −0.234517 | ||||||||
\(818\) | −1.05748e9 | −0.0675514 | ||||||||
\(819\) | −1.58750e10 | −1.00977 | ||||||||
\(820\) | 9.90872e9 | 0.627580 | ||||||||
\(821\) | −7.97556e9 | −0.502991 | −0.251495 | − | 0.967858i | \(-0.580922\pi\) | ||||
−0.251495 | + | 0.967858i | \(0.580922\pi\) | |||||||
\(822\) | −3.23963e9 | −0.203444 | ||||||||
\(823\) | 5.64462e9 | 0.352968 | 0.176484 | − | 0.984304i | \(-0.443528\pi\) | ||||
0.176484 | + | 0.984304i | \(0.443528\pi\) | |||||||
\(824\) | −2.83152e9 | −0.176309 | ||||||||
\(825\) | −1.51401e9 | −0.0938727 | ||||||||
\(826\) | −9.81302e8 | −0.0605860 | ||||||||
\(827\) | 1.22946e10 | 0.755866 | 0.377933 | − | 0.925833i | \(-0.376635\pi\) | ||||
0.377933 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(828\) | 3.08445e10 | 1.88830 | ||||||||
\(829\) | −1.72844e10 | −1.05369 | −0.526845 | − | 0.849962i | \(-0.676625\pi\) | ||||
−0.526845 | + | 0.849962i | \(0.676625\pi\) | |||||||
\(830\) | 1.46999e9 | 0.0892361 | ||||||||
\(831\) | 1.13281e10 | 0.684784 | ||||||||
\(832\) | −1.36973e10 | −0.824521 | ||||||||
\(833\) | 1.78752e9 | 0.107150 | ||||||||
\(834\) | 2.12243e9 | 0.126693 | ||||||||
\(835\) | −2.73530e9 | −0.162593 | ||||||||
\(836\) | 3.40388e9 | 0.201489 | ||||||||
\(837\) | 2.81450e10 | 1.65906 | ||||||||
\(838\) | 1.05649e9 | 0.0620173 | ||||||||
\(839\) | −4.87580e9 | −0.285023 | −0.142511 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142511 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(840\) | −1.74960e9 | −0.101850 | ||||||||
\(841\) | 2.53104e10 | 1.46728 | ||||||||
\(842\) | −2.71885e8 | −0.0156962 | ||||||||
\(843\) | −9.19927e9 | −0.528879 | ||||||||
\(844\) | 1.19701e10 | 0.685329 | ||||||||
\(845\) | 1.59471e9 | 0.0909249 | ||||||||
\(846\) | −2.40367e9 | −0.136483 | ||||||||
\(847\) | 9.69328e9 | 0.548124 | ||||||||
\(848\) | −1.15044e10 | −0.647857 | ||||||||
\(849\) | 1.73903e10 | 0.975279 | ||||||||
\(850\) | −6.70777e7 | −0.00374638 | ||||||||
\(851\) | 1.66252e10 | 0.924727 | ||||||||
\(852\) | −9.28132e9 | −0.514128 | ||||||||
\(853\) | −1.67542e10 | −0.924277 | −0.462138 | − | 0.886808i | \(-0.652918\pi\) | ||||
−0.462138 | + | 0.886808i | \(0.652918\pi\) | |||||||
\(854\) | 1.83785e8 | 0.0100974 | ||||||||
\(855\) | −1.15611e10 | −0.632582 | ||||||||
\(856\) | −4.96112e9 | −0.270347 | ||||||||
\(857\) | −1.45198e10 | −0.788001 | −0.394001 | − | 0.919110i | \(-0.628909\pi\) | ||||
−0.394001 | + | 0.919110i | \(0.628909\pi\) | |||||||
\(858\) | −8.78435e8 | −0.0474793 | ||||||||
\(859\) | 2.44108e10 | 1.31403 | 0.657016 | − | 0.753877i | \(-0.271819\pi\) | ||||
0.657016 | + | 0.753877i | \(0.271819\pi\) | |||||||
\(860\) | −2.60434e9 | −0.139622 | ||||||||
\(861\) | −2.69242e10 | −1.43758 | ||||||||
\(862\) | 9.53988e8 | 0.0507303 | ||||||||
\(863\) | −2.03914e10 | −1.07996 | −0.539981 | − | 0.841677i | \(-0.681569\pi\) | ||||
−0.539981 | + | 0.841677i | \(0.681569\pi\) | |||||||
\(864\) | 9.80475e9 | 0.517176 | ||||||||
\(865\) | 1.20289e10 | 0.631931 | ||||||||
\(866\) | −2.48200e9 | −0.129864 | ||||||||
\(867\) | −3.18275e10 | −1.65858 | ||||||||
\(868\) | 1.20927e10 | 0.627629 | ||||||||
\(869\) | −7.63764e9 | −0.394812 | ||||||||
\(870\) | 2.63668e9 | 0.135750 | ||||||||
\(871\) | 2.08597e10 | 1.06966 | ||||||||
\(872\) | 5.24568e8 | 0.0267913 | ||||||||
\(873\) | −1.08134e10 | −0.550061 | ||||||||
\(874\) | −1.66330e9 | −0.0842713 | ||||||||
\(875\) | 1.05117e9 | 0.0530448 | ||||||||
\(876\) | −4.28888e10 | −2.15566 | ||||||||
\(877\) | −3.75418e10 | −1.87939 | −0.939693 | − | 0.342018i | \(-0.888890\pi\) | ||||
−0.939693 | + | 0.342018i | \(0.888890\pi\) | |||||||
\(878\) | −1.73719e9 | −0.0866194 | ||||||||
\(879\) | 3.28845e10 | 1.63316 | ||||||||
\(880\) | 2.39308e9 | 0.118377 | ||||||||
\(881\) | 1.05852e10 | 0.521533 | 0.260767 | − | 0.965402i | \(-0.416025\pi\) | ||||
0.260767 | + | 0.965402i | \(0.416025\pi\) | |||||||
\(882\) | −2.85584e9 | −0.140150 | ||||||||
\(883\) | 3.45129e10 | 1.68702 | 0.843509 | − | 0.537116i | \(-0.180486\pi\) | ||||
0.843509 | + | 0.537116i | \(0.180486\pi\) | |||||||
\(884\) | 2.99118e9 | 0.145633 | ||||||||
\(885\) | −1.41744e10 | −0.687390 | ||||||||
\(886\) | 1.35894e9 | 0.0656420 | ||||||||
\(887\) | 1.68685e10 | 0.811602 | 0.405801 | − | 0.913961i | \(-0.366993\pi\) | ||||
0.405801 | + | 0.913961i | \(0.366993\pi\) | |||||||
\(888\) | 7.38926e9 | 0.354124 | ||||||||
\(889\) | 1.03261e10 | 0.492922 | ||||||||
\(890\) | −3.88896e7 | −0.00184913 | ||||||||
\(891\) | −4.24990e9 | −0.201283 | ||||||||
\(892\) | 2.88792e10 | 1.36241 | ||||||||
\(893\) | −9.96206e9 | −0.468133 | ||||||||
\(894\) | 3.01224e9 | 0.140996 | ||||||||
\(895\) | −1.05847e10 | −0.493512 | ||||||||
\(896\) | 5.60434e9 | 0.260283 | ||||||||
\(897\) | −3.29904e10 | −1.52621 | ||||||||
\(898\) | −2.18323e9 | −0.100608 | ||||||||
\(899\) | −3.66849e10 | −1.68395 | ||||||||
\(900\) | −8.23653e9 | −0.376613 | ||||||||
\(901\) | 2.44477e9 | 0.111353 | ||||||||
\(902\) | −9.77434e8 | −0.0443470 | ||||||||
\(903\) | 7.07656e9 | 0.319827 | ||||||||
\(904\) | 8.56974e9 | 0.385814 | ||||||||
\(905\) | 1.20656e10 | 0.541102 | ||||||||
\(906\) | 4.70333e9 | 0.210115 | ||||||||
\(907\) | −1.14713e10 | −0.510492 | −0.255246 | − | 0.966876i | \(-0.582156\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582156\pi\) | |||||||
\(908\) | 3.79810e10 | 1.68370 | ||||||||
\(909\) | 1.54012e10 | 0.680112 | ||||||||
\(910\) | 6.09892e8 | 0.0268292 | ||||||||
\(911\) | 1.62306e10 | 0.711248 | 0.355624 | − | 0.934629i | \(-0.384268\pi\) | ||||
0.355624 | + | 0.934629i | \(0.384268\pi\) | |||||||
\(912\) | 2.78534e10 | 1.21590 | ||||||||
\(913\) | 1.11446e10 | 0.484639 | ||||||||
\(914\) | −4.82661e9 | −0.209089 | ||||||||
\(915\) | 2.65468e9 | 0.114561 | ||||||||
\(916\) | 1.33107e10 | 0.572224 | ||||||||
\(917\) | −1.65236e10 | −0.707641 | ||||||||
\(918\) | −6.79477e8 | −0.0289885 | ||||||||
\(919\) | −4.36259e10 | −1.85413 | −0.927065 | − | 0.374900i | \(-0.877677\pi\) | ||||
−0.927065 | + | 0.374900i | \(0.877677\pi\) | |||||||
\(920\) | −2.38540e9 | −0.100996 | ||||||||
\(921\) | 1.25979e10 | 0.531363 | ||||||||
\(922\) | 4.60419e9 | 0.193462 | ||||||||
\(923\) | 6.51283e9 | 0.272624 | ||||||||
\(924\) | −6.58938e9 | −0.274785 | ||||||||
\(925\) | −4.43950e9 | −0.184433 | ||||||||
\(926\) | −3.14972e8 | −0.0130357 | ||||||||
\(927\) | 3.62201e10 | 1.49338 | ||||||||
\(928\) | −1.27797e10 | −0.524934 | ||||||||
\(929\) | 1.67801e10 | 0.686656 | 0.343328 | − | 0.939216i | \(-0.388446\pi\) | ||||
0.343328 | + | 0.939216i | \(0.388446\pi\) | |||||||
\(930\) | −2.27269e9 | −0.0926511 | ||||||||
\(931\) | −1.18361e10 | −0.480713 | ||||||||
\(932\) | −4.13432e10 | −1.67282 | ||||||||
\(933\) | −1.34900e10 | −0.543782 | ||||||||
\(934\) | −5.19273e8 | −0.0208536 | ||||||||
\(935\) | −5.08547e8 | −0.0203465 | ||||||||
\(936\) | −9.61993e9 | −0.383448 | ||||||||
\(937\) | 1.94934e10 | 0.774105 | 0.387053 | − | 0.922058i | \(-0.373493\pi\) | ||||
0.387053 | + | 0.922058i | \(0.373493\pi\) | |||||||
\(938\) | −2.03592e9 | −0.0805474 | ||||||||
\(939\) | −4.16348e10 | −1.64107 | ||||||||
\(940\) | −7.09733e9 | −0.278707 | ||||||||
\(941\) | −4.91523e10 | −1.92300 | −0.961502 | − | 0.274797i | \(-0.911389\pi\) | ||||
−0.961502 | + | 0.274797i | \(0.911389\pi\) | |||||||
\(942\) | 1.97333e9 | 0.0769167 | ||||||||
\(943\) | −3.67084e10 | −1.42552 | ||||||||
\(944\) | 2.24045e10 | 0.866827 | ||||||||
\(945\) | 1.06480e10 | 0.410446 | ||||||||
\(946\) | 2.56902e8 | 0.00986617 | ||||||||
\(947\) | 3.01570e10 | 1.15389 | 0.576944 | − | 0.816784i | \(-0.304245\pi\) | ||||
0.576944 | + | 0.816784i | \(0.304245\pi\) | |||||||
\(948\) | −6.33323e10 | −2.41433 | ||||||||
\(949\) | 3.00957e10 | 1.14307 | ||||||||
\(950\) | 4.44157e8 | 0.0168075 | ||||||||
\(951\) | 3.77405e10 | 1.42290 | ||||||||
\(952\) | −5.87681e8 | −0.0220756 | ||||||||
\(953\) | −1.86916e10 | −0.699554 | −0.349777 | − | 0.936833i | \(-0.613743\pi\) | ||||
−0.349777 | + | 0.936833i | \(0.613743\pi\) | |||||||
\(954\) | −3.90590e9 | −0.145647 | ||||||||
\(955\) | 1.83084e10 | 0.680204 | ||||||||
\(956\) | 7.23879e9 | 0.267956 | ||||||||
\(957\) | 1.99899e10 | 0.737256 | ||||||||
\(958\) | 5.36388e9 | 0.197106 | ||||||||
\(959\) | 1.70526e10 | 0.624346 | ||||||||
\(960\) | 1.93102e10 | 0.704430 | ||||||||
\(961\) | 4.10799e9 | 0.149313 | ||||||||
\(962\) | −2.57582e9 | −0.0932830 | ||||||||
\(963\) | 6.34614e10 | 2.28990 | ||||||||
\(964\) | −3.59213e10 | −1.29146 | ||||||||
\(965\) | 1.06659e10 | 0.382079 | ||||||||
\(966\) | 3.21988e9 | 0.114926 | ||||||||
\(967\) | −7.61328e9 | −0.270757 | −0.135378 | − | 0.990794i | \(-0.543225\pi\) | ||||
−0.135378 | + | 0.990794i | \(0.543225\pi\) | |||||||
\(968\) | 5.87392e9 | 0.208144 | ||||||||
\(969\) | −5.91903e9 | −0.208986 | ||||||||
\(970\) | 4.15431e8 | 0.0146150 | ||||||||
\(971\) | −4.83242e10 | −1.69394 | −0.846969 | − | 0.531643i | \(-0.821575\pi\) | ||||
−0.846969 | + | 0.531643i | \(0.821575\pi\) | |||||||
\(972\) | 8.49752e9 | 0.296797 | ||||||||
\(973\) | −1.11720e10 | −0.388807 | ||||||||
\(974\) | 4.16829e9 | 0.144545 | ||||||||
\(975\) | 8.80957e9 | 0.304396 | ||||||||
\(976\) | −4.19606e9 | −0.144467 | ||||||||
\(977\) | 1.42491e9 | 0.0488829 | 0.0244414 | − | 0.999701i | \(-0.492219\pi\) | ||||
0.0244414 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(978\) | 2.40916e9 | 0.0823531 | ||||||||
\(979\) | −2.94840e8 | −0.0100426 | ||||||||
\(980\) | −8.43248e9 | −0.286196 | ||||||||
\(981\) | −6.71014e9 | −0.226929 | ||||||||
\(982\) | −4.32564e9 | −0.145767 | ||||||||
\(983\) | 4.85675e10 | 1.63083 | 0.815415 | − | 0.578877i | \(-0.196509\pi\) | ||||
0.815415 | + | 0.578877i | \(0.196509\pi\) | |||||||
\(984\) | −1.63155e10 | −0.545905 | ||||||||
\(985\) | −1.81003e10 | −0.603475 | ||||||||
\(986\) | 8.85647e8 | 0.0294233 | ||||||||
\(987\) | 1.92850e10 | 0.638425 | ||||||||
\(988\) | −1.98062e10 | −0.653358 | ||||||||
\(989\) | 9.64818e9 | 0.317145 | ||||||||
\(990\) | 8.12482e8 | 0.0266128 | ||||||||
\(991\) | −1.69341e10 | −0.552719 | −0.276360 | − | 0.961054i | \(-0.589128\pi\) | ||||
−0.276360 | + | 0.961054i | \(0.589128\pi\) | |||||||
\(992\) | 1.10155e10 | 0.358273 | ||||||||
\(993\) | −6.98457e9 | −0.226369 | ||||||||
\(994\) | −6.35656e8 | −0.0205291 | ||||||||
\(995\) | −1.58588e9 | −0.0510375 | ||||||||
\(996\) | 9.24128e10 | 2.96363 | ||||||||
\(997\) | 2.36849e10 | 0.756900 | 0.378450 | − | 0.925622i | \(-0.376457\pi\) | ||||
0.378450 | + | 0.925622i | \(0.376457\pi\) | |||||||
\(998\) | 4.80763e9 | 0.153100 | ||||||||
\(999\) | −4.49707e10 | −1.42709 |
(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 | 5.8.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 45.8.a.h.1.2 | 2 | |||
4.3 | odd | 2 | 80.8.a.g.1.1 | 2 | |||
5.2 | odd | 4 | 25.8.b.c.24.3 | 4 | |||
5.3 | odd | 4 | 25.8.b.c.24.2 | 4 | |||
5.4 | even | 2 | 25.8.a.b.1.2 | 2 | |||
7.6 | odd | 2 | 245.8.a.c.1.1 | 2 | |||
8.3 | odd | 2 | 320.8.a.u.1.2 | 2 | |||
8.5 | even | 2 | 320.8.a.l.1.1 | 2 | |||
11.10 | odd | 2 | 605.8.a.d.1.2 | 2 | |||
15.2 | even | 4 | 225.8.b.m.199.2 | 4 | |||
15.8 | even | 4 | 225.8.b.m.199.3 | 4 | |||
15.14 | odd | 2 | 225.8.a.w.1.1 | 2 | |||
20.3 | even | 4 | 400.8.c.m.49.1 | 4 | |||
20.7 | even | 4 | 400.8.c.m.49.4 | 4 | |||
20.19 | odd | 2 | 400.8.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.8.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
25.8.a.b.1.2 | 2 | 5.4 | even | 2 | |||
25.8.b.c.24.2 | 4 | 5.3 | odd | 4 | |||
25.8.b.c.24.3 | 4 | 5.2 | odd | 4 | |||
45.8.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
80.8.a.g.1.1 | 2 | 4.3 | odd | 2 | |||
225.8.a.w.1.1 | 2 | 15.14 | odd | 2 | |||
225.8.b.m.199.2 | 4 | 15.2 | even | 4 | |||
225.8.b.m.199.3 | 4 | 15.8 | even | 4 | |||
245.8.a.c.1.1 | 2 | 7.6 | odd | 2 | |||
320.8.a.l.1.1 | 2 | 8.5 | even | 2 | |||
320.8.a.u.1.2 | 2 | 8.3 | odd | 2 | |||
400.8.a.bb.1.2 | 2 | 20.19 | odd | 2 | |||
400.8.c.m.49.1 | 4 | 20.3 | even | 4 | |||
400.8.c.m.49.4 | 4 | 20.7 | even | 4 | |||
605.8.a.d.1.2 | 2 | 11.10 | odd | 2 |