Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("147.146");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + 7244325760 x^{4} - 29387167488 x^{2} + 90230547456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.13 | ||
Root | \(-5.89199 - 3.40174i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.c.146.3 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.80349i | 1.20270i | 0.798986 | + | 0.601349i | \(0.205370\pi\) | ||||
−0.798986 | + | 0.601349i | \(0.794630\pi\) | |||||||
\(3\) | −12.4320 | − | 9.40448i | −0.797516 | − | 0.603297i | ||||
\(4\) | −14.2874 | −0.446483 | ||||||||
\(5\) | −14.9141 | −0.266792 | −0.133396 | − | 0.991063i | \(-0.542588\pi\) | ||||
−0.133396 | + | 0.991063i | \(0.542588\pi\) | |||||||
\(6\) | 63.9832 | − | 84.5813i | 0.725585 | − | 0.959171i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 120.507i | 0.665714i | ||||||||
\(9\) | 66.1117 | + | 233.834i | 0.272065 | + | 0.962279i | ||||
\(10\) | − | 101.468i | − | 0.320870i | ||||||
\(11\) | 96.0737i | 0.239399i | 0.992810 | + | 0.119700i | \(0.0381931\pi\) | ||||
−0.992810 | + | 0.119700i | \(0.961807\pi\) | |||||||
\(12\) | 177.622 | + | 134.366i | 0.356077 | + | 0.269362i | ||||
\(13\) | 416.854i | 0.684109i | 0.939680 | + | 0.342055i | \(0.111123\pi\) | ||||
−0.939680 | + | 0.342055i | \(0.888877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 185.413 | + | 140.259i | 0.212771 | + | 0.160955i | ||||
\(16\) | −1277.07 | −1.24714 | ||||||||
\(17\) | −208.498 | −0.174977 | −0.0874884 | − | 0.996166i | \(-0.527884\pi\) | ||||
−0.0874884 | + | 0.996166i | \(0.527884\pi\) | |||||||
\(18\) | −1590.89 | + | 449.790i | −1.15733 | + | 0.327211i | ||||
\(19\) | − | 2651.38i | − | 1.68495i | −0.538733 | − | 0.842476i | \(-0.681097\pi\) | ||
0.538733 | − | 0.842476i | \(-0.318903\pi\) | |||||||
\(20\) | 213.085 | 0.119118 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −653.636 | −0.287925 | ||||||||
\(23\) | 2617.73i | 1.03182i | 0.856642 | + | 0.515911i | \(0.172546\pi\) | ||||
−0.856642 | + | 0.515911i | \(0.827454\pi\) | |||||||
\(24\) | 1133.31 | − | 1498.15i | 0.401624 | − | 0.530918i | ||||
\(25\) | −2902.57 | −0.928822 | ||||||||
\(26\) | −2836.06 | −0.822777 | ||||||||
\(27\) | 1377.18 | − | 3528.78i | 0.363564 | − | 0.931569i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7220.50i | − | 1.59431i | −0.603776 | − | 0.797154i | \(-0.706338\pi\) | ||
0.603776 | − | 0.797154i | \(-0.293662\pi\) | |||||||
\(30\) | −954.253 | + | 1261.45i | −0.193580 | + | 0.255899i | ||||
\(31\) | − | 4297.41i | − | 0.803160i | −0.915824 | − | 0.401580i | \(-0.868461\pi\) | ||
0.915824 | − | 0.401580i | \(-0.131539\pi\) | |||||||
\(32\) | − | 4832.28i | − | 0.834214i | ||||||
\(33\) | 903.523 | − | 1194.39i | 0.144429 | − | 0.190925i | ||||
\(34\) | − | 1418.52i | − | 0.210444i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −944.567 | − | 3340.89i | −0.121472 | − | 0.429641i | ||||
\(37\) | 3679.00 | 0.441799 | 0.220900 | − | 0.975297i | \(-0.429101\pi\) | ||||
0.220900 | + | 0.975297i | \(0.429101\pi\) | |||||||
\(38\) | 18038.6 | 2.02649 | ||||||||
\(39\) | 3920.29 | − | 5182.35i | 0.412721 | − | 0.545588i | ||||
\(40\) | − | 1797.26i | − | 0.177607i | ||||||
\(41\) | −15452.3 | −1.43560 | −0.717798 | − | 0.696251i | \(-0.754850\pi\) | ||||
−0.717798 | + | 0.696251i | \(0.754850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6011.11 | −0.495774 | −0.247887 | − | 0.968789i | \(-0.579736\pi\) | ||||
−0.247887 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(44\) | − | 1372.65i | − | 0.106888i | ||||||
\(45\) | −985.997 | − | 3487.42i | −0.0725846 | − | 0.256728i | ||||
\(46\) | −17809.7 | −1.24097 | ||||||||
\(47\) | 3907.44 | 0.258016 | 0.129008 | − | 0.991644i | \(-0.458821\pi\) | ||||
0.129008 | + | 0.991644i | \(0.458821\pi\) | |||||||
\(48\) | 15876.6 | + | 12010.1i | 0.994611 | + | 0.752394i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 19747.6i | − | 1.11709i | ||||||
\(51\) | 2592.06 | + | 1960.82i | 0.139547 | + | 0.105563i | ||||
\(52\) | − | 5955.77i | − | 0.305443i | ||||||
\(53\) | − | 36297.2i | − | 1.77494i | −0.460868 | − | 0.887469i | \(-0.652462\pi\) | ||
0.460868 | − | 0.887469i | \(-0.347538\pi\) | |||||||
\(54\) | 24008.0 | + | 9369.63i | 1.12040 | + | 0.437258i | ||||
\(55\) | − | 1432.85i | − | 0.0638697i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24934.8 | + | 32962.1i | −1.01653 | + | 1.34378i | ||||
\(58\) | 49124.6 | 1.91747 | ||||||||
\(59\) | 7827.45 | 0.292746 | 0.146373 | − | 0.989230i | \(-0.453240\pi\) | ||||
0.146373 | + | 0.989230i | \(0.453240\pi\) | |||||||
\(60\) | −2649.08 | − | 2003.95i | −0.0949984 | − | 0.0718635i | ||||
\(61\) | 20193.7i | 0.694850i | 0.937708 | + | 0.347425i | \(0.112944\pi\) | ||||
−0.937708 | + | 0.347425i | \(0.887056\pi\) | |||||||
\(62\) | 29237.3 | 0.965959 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7989.78 | −0.243829 | ||||||||
\(65\) | − | 6217.00i | − | 0.182515i | ||||||
\(66\) | 8126.04 | + | 6147.10i | 0.229625 | + | 0.173704i | ||||
\(67\) | 43937.9 | 1.19578 | 0.597892 | − | 0.801577i | \(-0.296005\pi\) | ||||
0.597892 | + | 0.801577i | \(0.296005\pi\) | |||||||
\(68\) | 2978.91 | 0.0781241 | ||||||||
\(69\) | 24618.3 | − | 32543.7i | 0.622495 | − | 0.822894i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 26028.0i | − | 0.612765i | −0.951908 | − | 0.306383i | \(-0.900881\pi\) | ||
0.951908 | − | 0.306383i | \(-0.0991187\pi\) | |||||||
\(72\) | −28178.6 | + | 7966.93i | −0.640603 | + | 0.181117i | ||||
\(73\) | − | 50911.3i | − | 1.11817i | −0.829111 | − | 0.559084i | \(-0.811153\pi\) | ||
0.829111 | − | 0.559084i | \(-0.188847\pi\) | |||||||
\(74\) | 25030.0i | 0.531351i | ||||||||
\(75\) | 36084.9 | + | 27297.1i | 0.740751 | + | 0.560356i | ||||
\(76\) | 37881.4i | 0.752302i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 35258.0 | + | 26671.6i | 0.656178 | + | 0.496379i | ||||
\(79\) | −50114.3 | −0.903429 | −0.451715 | − | 0.892163i | \(-0.649187\pi\) | ||||
−0.451715 | + | 0.892163i | \(0.649187\pi\) | |||||||
\(80\) | 19046.3 | 0.332726 | ||||||||
\(81\) | −50307.5 | + | 30918.3i | −0.851962 | + | 0.523604i | ||||
\(82\) | − | 105129.i | − | 1.72659i | ||||||
\(83\) | −107835. | −1.71817 | −0.859086 | − | 0.511832i | \(-0.828967\pi\) | ||||
−0.859086 | + | 0.511832i | \(0.828967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3109.57 | 0.0466824 | ||||||||
\(86\) | − | 40896.5i | − | 0.596266i | ||||||
\(87\) | −67905.0 | + | 89765.6i | −0.961842 | + | 1.27149i | ||||
\(88\) | −11577.6 | −0.159371 | ||||||||
\(89\) | −136779. | −1.83039 | −0.915194 | − | 0.403013i | \(-0.867963\pi\) | ||||
−0.915194 | + | 0.403013i | \(0.867963\pi\) | |||||||
\(90\) | 23726.6 | − | 6708.22i | 0.308766 | − | 0.0872973i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 37400.6i | − | 0.460690i | ||||||
\(93\) | −40414.8 | + | 53425.6i | −0.484544 | + | 0.640533i | ||||
\(94\) | 26584.2i | 0.310316i | ||||||||
\(95\) | 39543.0i | 0.449531i | ||||||||
\(96\) | −45445.1 | + | 60075.2i | −0.503279 | + | 0.665299i | ||||
\(97\) | − | 25183.4i | − | 0.271759i | −0.990725 | − | 0.135880i | \(-0.956614\pi\) | ||
0.990725 | − | 0.135880i | \(-0.0433861\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22465.3 | + | 6351.59i | −0.230369 | + | 0.0651320i | ||||
\(100\) | 41470.3 | 0.414703 | ||||||||
\(101\) | −78062.7 | −0.761448 | −0.380724 | − | 0.924689i | \(-0.624325\pi\) | ||||
−0.380724 | + | 0.924689i | \(0.624325\pi\) | |||||||
\(102\) | −13340.4 | + | 17635.1i | −0.126960 | + | 0.167833i | ||||
\(103\) | − | 97991.9i | − | 0.910117i | −0.890462 | − | 0.455059i | \(-0.849618\pi\) | ||
0.890462 | − | 0.455059i | \(-0.150382\pi\) | |||||||
\(104\) | −50233.9 | −0.455421 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 246947. | 2.13471 | ||||||||
\(107\) | 135095.i | 1.14072i | 0.821395 | + | 0.570360i | \(0.193196\pi\) | ||||
−0.821395 | + | 0.570360i | \(0.806804\pi\) | |||||||
\(108\) | −19676.4 | + | 50417.2i | −0.162325 | + | 0.415929i | ||||
\(109\) | 75132.0 | 0.605702 | 0.302851 | − | 0.953038i | \(-0.402062\pi\) | ||||
0.302851 | + | 0.953038i | \(0.402062\pi\) | |||||||
\(110\) | 9748.40 | 0.0768160 | ||||||||
\(111\) | −45737.5 | − | 34599.0i | −0.352342 | − | 0.266536i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 88078.7i | 0.648895i | 0.945904 | + | 0.324448i | \(0.105178\pi\) | ||||
−0.945904 | + | 0.324448i | \(0.894822\pi\) | |||||||
\(114\) | −224257. | − | 169644.i | −1.61616 | − | 1.22258i | ||||
\(115\) | − | 39041.0i | − | 0.275281i | ||||||
\(116\) | 103163.i | 0.711831i | ||||||||
\(117\) | −97474.5 | + | 27558.9i | −0.658304 | + | 0.186122i | ||||
\(118\) | 53254.0i | 0.352085i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −16902.3 | + | 22343.6i | −0.107150 | + | 0.141645i | ||||
\(121\) | 151821. | 0.942688 | ||||||||
\(122\) | −137388. | −0.835695 | ||||||||
\(123\) | 192103. | + | 145320.i | 1.14491 | + | 0.866091i | ||||
\(124\) | 61398.9i | 0.358597i | ||||||||
\(125\) | 89895.8 | 0.514594 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −141581. | −0.778923 | −0.389462 | − | 0.921043i | \(-0.627339\pi\) | ||||
−0.389462 | + | 0.921043i | \(0.627339\pi\) | |||||||
\(128\) | − | 208991.i | − | 1.12747i | ||||||
\(129\) | 74730.4 | + | 56531.3i | 0.395388 | + | 0.299099i | ||||
\(130\) | 42297.3 | 0.219510 | ||||||||
\(131\) | 153197. | 0.779959 | 0.389979 | − | 0.920824i | \(-0.372482\pi\) | ||||
0.389979 | + | 0.920824i | \(0.372482\pi\) | |||||||
\(132\) | −12909.0 | + | 17064.8i | −0.0644850 | + | 0.0852446i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 298931.i | 1.43817i | ||||||||
\(135\) | −20539.4 | + | 52628.6i | −0.0969960 | + | 0.248535i | ||||
\(136\) | − | 25125.6i | − | 0.116485i | ||||||
\(137\) | 90239.8i | 0.410768i | 0.978681 | + | 0.205384i | \(0.0658444\pi\) | ||||
−0.978681 | + | 0.205384i | \(0.934156\pi\) | |||||||
\(138\) | 221411. | + | 167491.i | 0.989694 | + | 0.748674i | ||||
\(139\) | 133215.i | 0.584814i | 0.956294 | + | 0.292407i | \(0.0944562\pi\) | ||||
−0.956294 | + | 0.292407i | \(0.905544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −48577.5 | − | 36747.4i | −0.205772 | − | 0.155661i | ||||
\(142\) | 177081. | 0.736972 | ||||||||
\(143\) | −40048.7 | −0.163775 | ||||||||
\(144\) | −84429.1 | − | 298621.i | −0.339301 | − | 1.20009i | ||||
\(145\) | 107687.i | 0.425348i | ||||||||
\(146\) | 346374. | 1.34482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −52563.5 | −0.197256 | ||||||||
\(149\) | − | 28153.3i | − | 0.103888i | −0.998650 | − | 0.0519439i | \(-0.983458\pi\) | ||
0.998650 | − | 0.0519439i | \(-0.0165417\pi\) | |||||||
\(150\) | −185716. | + | 245503.i | −0.673939 | + | 0.890900i | ||||
\(151\) | −6546.74 | −0.0233659 | −0.0116830 | − | 0.999932i | \(-0.503719\pi\) | ||||
−0.0116830 | + | 0.999932i | \(0.503719\pi\) | |||||||
\(152\) | 319510. | 1.12170 | ||||||||
\(153\) | −13784.2 | − | 48754.0i | −0.0476050 | − | 0.168377i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 64092.0i | 0.214276i | ||||||||
\(156\) | −56010.9 | + | 74042.5i | −0.184273 | + | 0.243596i | ||||
\(157\) | 68166.3i | 0.220709i | 0.993892 | + | 0.110355i | \(0.0351986\pi\) | ||||
−0.993892 | + | 0.110355i | \(0.964801\pi\) | |||||||
\(158\) | − | 340952.i | − | 1.08655i | ||||||
\(159\) | −341356. | + | 451248.i | −1.07081 | + | 1.41554i | ||||
\(160\) | 72069.2i | 0.222561i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −210352. | − | 342266.i | −0.629738 | − | 1.02465i | ||||
\(163\) | 423816. | 1.24942 | 0.624709 | − | 0.780857i | \(-0.285217\pi\) | ||||
0.624709 | + | 0.780857i | \(0.285217\pi\) | |||||||
\(164\) | 220773. | 0.640969 | ||||||||
\(165\) | −13475.2 | + | 17813.3i | −0.0385324 | + | 0.0509371i | ||||
\(166\) | − | 733657.i | − | 2.06644i | ||||||
\(167\) | 30916.2 | 0.0857818 | 0.0428909 | − | 0.999080i | \(-0.486343\pi\) | ||||
0.0428909 | + | 0.999080i | \(0.486343\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 197526. | 0.531995 | ||||||||
\(170\) | 21155.9i | 0.0561448i | ||||||||
\(171\) | 619982. | − | 175287.i | 1.62139 | − | 0.458416i | ||||
\(172\) | 85883.4 | 0.221354 | ||||||||
\(173\) | −179220. | −0.455272 | −0.227636 | − | 0.973746i | \(-0.573100\pi\) | ||||
−0.227636 | + | 0.973746i | \(0.573100\pi\) | |||||||
\(174\) | −610719. | − | 461991.i | −1.52921 | − | 1.15681i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 122693.i | − | 0.298563i | ||||||
\(177\) | −97311.3 | − | 73613.1i | −0.233469 | − | 0.176613i | ||||
\(178\) | − | 930572.i | − | 2.20140i | ||||||
\(179\) | 142179.i | 0.331667i | 0.986154 | + | 0.165834i | \(0.0530315\pi\) | ||||
−0.986154 | + | 0.165834i | \(0.946969\pi\) | |||||||
\(180\) | 14087.4 | + | 49826.4i | 0.0324077 | + | 0.114625i | ||||
\(181\) | 321437.i | 0.729288i | 0.931147 | + | 0.364644i | \(0.118809\pi\) | ||||
−0.931147 | + | 0.364644i | \(0.881191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 189911. | − | 251049.i | 0.419201 | − | 0.554154i | ||||
\(184\) | −315455. | −0.686898 | ||||||||
\(185\) | −54869.0 | −0.117868 | ||||||||
\(186\) | −363480. | − | 274962.i | −0.770368 | − | 0.582761i | ||||
\(187\) | − | 20031.2i | − | 0.0418893i | ||||||
\(188\) | −55827.3 | −0.115200 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −269030. | −0.540651 | ||||||||
\(191\) | 528819.i | 1.04887i | 0.851449 | + | 0.524437i | \(0.175724\pi\) | ||||
−0.851449 | + | 0.524437i | \(0.824276\pi\) | |||||||
\(192\) | 99329.4 | + | 75139.7i | 0.194457 | + | 0.147101i | ||||
\(193\) | −95232.1 | −0.184031 | −0.0920153 | − | 0.995758i | \(-0.529331\pi\) | ||||
−0.0920153 | + | 0.995758i | \(0.529331\pi\) | |||||||
\(194\) | 171335. | 0.326844 | ||||||||
\(195\) | −58467.6 | + | 77290.1i | −0.110111 | + | 0.145558i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 705756.i | − | 1.29565i | −0.761787 | − | 0.647827i | \(-0.775678\pi\) | ||
0.761787 | − | 0.647827i | \(-0.224322\pi\) | |||||||
\(198\) | −43213.0 | − | 152842.i | −0.0783342 | − | 0.277064i | ||||
\(199\) | 87307.3i | 0.156285i | 0.996942 | + | 0.0781426i | \(0.0248990\pi\) | ||||
−0.996942 | + | 0.0781426i | \(0.975101\pi\) | |||||||
\(200\) | − | 349780.i | − | 0.618330i | ||||||
\(201\) | −546239. | − | 413213.i | −0.953657 | − | 0.721413i | ||||
\(202\) | − | 531099.i | − | 0.915792i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −37034.0 | − | 28015.1i | −0.0623053 | − | 0.0471321i | ||||
\(205\) | 230457. | 0.383005 | ||||||||
\(206\) | 666687. | 1.09460 | ||||||||
\(207\) | −612113. | + | 173062.i | −0.992900 | + | 0.280722i | ||||
\(208\) | − | 532350.i | − | 0.853177i | ||||||
\(209\) | 254728. | 0.403376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −330657. | −0.511294 | −0.255647 | − | 0.966770i | \(-0.582289\pi\) | ||||
−0.255647 | + | 0.966770i | \(0.582289\pi\) | |||||||
\(212\) | 518594.i | 0.792479i | ||||||||
\(213\) | −244779. | + | 323581.i | −0.369680 | + | 0.488690i | ||||
\(214\) | −919115. | −1.37194 | ||||||||
\(215\) | 89650.4 | 0.132268 | ||||||||
\(216\) | 425243. | + | 165960.i | 0.620159 | + | 0.242030i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 511160.i | 0.728476i | ||||||||
\(219\) | −478794. | + | 632931.i | −0.674587 | + | 0.891757i | ||||
\(220\) | 20471.8i | 0.0285167i | ||||||||
\(221\) | − | 86913.4i | − | 0.119703i | ||||||
\(222\) | 235394. | − | 311174.i | 0.320563 | − | 0.423761i | ||||
\(223\) | − | 232532.i | − | 0.313128i | −0.987668 | − | 0.156564i | \(-0.949958\pi\) | ||
0.987668 | − | 0.156564i | \(-0.0500417\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −191894. | − | 678719.i | −0.252700 | − | 0.893786i | ||||
\(226\) | −599242. | −0.780425 | ||||||||
\(227\) | −448252. | −0.577375 | −0.288687 | − | 0.957423i | \(-0.593219\pi\) | ||||
−0.288687 | + | 0.957423i | \(0.593219\pi\) | |||||||
\(228\) | 356255. | − | 470944.i | 0.453862 | − | 0.599973i | ||||
\(229\) | 576156.i | 0.726025i | 0.931784 | + | 0.363012i | \(0.118252\pi\) | ||||
−0.931784 | + | 0.363012i | \(0.881748\pi\) | |||||||
\(230\) | 265615. | 0.331080 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 870122. | 1.06135 | ||||||||
\(233\) | − | 406966.i | − | 0.491098i | −0.969384 | − | 0.245549i | \(-0.921032\pi\) | ||
0.969384 | − | 0.245549i | \(-0.0789682\pi\) | |||||||
\(234\) | −187497. | − | 663167.i | −0.223848 | − | 0.791741i | ||||
\(235\) | −58276.0 | −0.0688367 | ||||||||
\(236\) | −111834. | −0.130706 | ||||||||
\(237\) | 623024. | + | 471299.i | 0.720499 | + | 0.545036i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 266151.i | 0.301393i | 0.988580 | + | 0.150696i | \(0.0481516\pi\) | ||||
−0.988580 | + | 0.150696i | \(0.951848\pi\) | |||||||
\(240\) | −236785. | − | 179121.i | −0.265354 | − | 0.200732i | ||||
\(241\) | − | 388486.i | − | 0.430857i | −0.976520 | − | 0.215428i | \(-0.930885\pi\) | ||
0.976520 | − | 0.215428i | \(-0.0691148\pi\) | |||||||
\(242\) | 1.03291e6i | 1.13377i | ||||||||
\(243\) | 916196. | + | 88737.8i | 0.995342 | + | 0.0964036i | ||||
\(244\) | − | 288516.i | − | 0.310238i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −988685. | + | 1.30697e6i | −1.04165 | + | 1.37698i | ||||
\(247\) | 1.10524e6 | 1.15269 | ||||||||
\(248\) | 517868. | 0.534675 | ||||||||
\(249\) | 1.34062e6 | + | 1.01414e6i | 1.37027 | + | 1.03657i | ||||
\(250\) | 611605.i | 0.618901i | ||||||||
\(251\) | −1.09673e6 | −1.09879 | −0.549397 | − | 0.835561i | \(-0.685143\pi\) | ||||
−0.549397 | + | 0.835561i | \(0.685143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −251495. | −0.247017 | ||||||||
\(254\) | − | 963242.i | − | 0.936810i | ||||||
\(255\) | −38658.3 | − | 29243.9i | −0.0372300 | − | 0.0281634i | ||||
\(256\) | 1.16620e6 | 1.11217 | ||||||||
\(257\) | −100324. | −0.0947482 | −0.0473741 | − | 0.998877i | \(-0.515085\pi\) | ||||
−0.0473741 | + | 0.998877i | \(0.515085\pi\) | |||||||
\(258\) | −384610. | + | 508427.i | −0.359726 | + | 0.475532i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 88825.1i | 0.0814896i | ||||||||
\(261\) | 1.68840e6 | − | 477359.i | 1.53417 | − | 0.433755i | ||||
\(262\) | 1.04227e6i | 0.938055i | ||||||||
\(263\) | − | 1.30495e6i | − | 1.16333i | −0.813427 | − | 0.581667i | \(-0.802401\pi\) | ||
0.813427 | − | 0.581667i | \(-0.197599\pi\) | |||||||
\(264\) | 143933. | + | 108881.i | 0.127101 | + | 0.0961484i | ||||
\(265\) | 541340.i | 0.473539i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.70044e6 | + | 1.28633e6i | 1.45976 | + | 1.10427i | ||||
\(268\) | −627761. | −0.533897 | ||||||||
\(269\) | −1.26072e6 | −1.06228 | −0.531139 | − | 0.847285i | \(-0.678236\pi\) | ||||
−0.531139 | + | 0.847285i | \(0.678236\pi\) | |||||||
\(270\) | −358058. | − | 139740.i | −0.298912 | − | 0.116657i | ||||
\(271\) | 1.24738e6i | 1.03176i | 0.856662 | + | 0.515878i | \(0.172534\pi\) | ||||
−0.856662 | + | 0.515878i | \(0.827466\pi\) | |||||||
\(272\) | 266267. | 0.218220 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −613945. | −0.494030 | ||||||||
\(275\) | − | 278861.i | − | 0.222359i | ||||||
\(276\) | −351733. | + | 464966.i | −0.277933 | + | 0.367408i | ||||
\(277\) | 658899. | 0.515964 | 0.257982 | − | 0.966150i | \(-0.416942\pi\) | ||||
0.257982 | + | 0.966150i | \(0.416942\pi\) | |||||||
\(278\) | −906330. | −0.703354 | ||||||||
\(279\) | 1.00488e6 | − | 284109.i | 0.772864 | − | 0.218511i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.28896e6i | − | 0.973809i | −0.873455 | − | 0.486904i | \(-0.838126\pi\) | ||
0.873455 | − | 0.486904i | \(-0.161874\pi\) | |||||||
\(282\) | 250011. | − | 330496.i | 0.187213 | − | 0.247482i | ||||
\(283\) | 1.00909e6i | 0.748966i | 0.927234 | + | 0.374483i | \(0.122180\pi\) | ||||
−0.927234 | + | 0.374483i | \(0.877820\pi\) | |||||||
\(284\) | 371873.i | 0.273589i | ||||||||
\(285\) | 371881. | − | 491600.i | 0.271201 | − | 0.358509i | ||||
\(286\) | − | 272471.i | − | 0.196972i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.12995e6 | − | 319470.i | 0.802746 | − | 0.226960i | ||||
\(289\) | −1.37639e6 | −0.969383 | ||||||||
\(290\) | −732650. | −0.511566 | ||||||||
\(291\) | −236836. | + | 313081.i | −0.163952 | + | 0.216733i | ||||
\(292\) | 727392.i | 0.499242i | ||||||||
\(293\) | −1.94711e6 | −1.32502 | −0.662508 | − | 0.749055i | \(-0.730508\pi\) | ||||
−0.662508 | + | 0.749055i | \(0.730508\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −116739. | −0.0781021 | ||||||||
\(296\) | 443345.i | 0.294112i | ||||||||
\(297\) | 339023. | + | 132311.i | 0.223017 | + | 0.0870371i | ||||
\(298\) | 191541. | 0.124946 | ||||||||
\(299\) | −1.09121e6 | −0.705878 | ||||||||
\(300\) | −515561. | − | 390006.i | −0.330732 | − | 0.250189i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 44540.7i | − | 0.0281022i | ||||||
\(303\) | 970480. | + | 734139.i | 0.607267 | + | 0.459380i | ||||
\(304\) | 3.38599e6i | 2.10137i | ||||||||
\(305\) | − | 301171.i | − | 0.185380i | ||||||
\(306\) | 331697. | − | 93780.5i | 0.202506 | − | 0.0572544i | ||||
\(307\) | 1.97804e6i | 1.19782i | 0.800818 | + | 0.598908i | \(0.204398\pi\) | ||||
−0.800818 | + | 0.598908i | \(0.795602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −921563. | + | 1.21824e6i | −0.549071 | + | 0.725833i | ||||
\(310\) | −436049. | −0.257710 | ||||||||
\(311\) | 1.07146e6 | 0.628169 | 0.314084 | − | 0.949395i | \(-0.398303\pi\) | ||||
0.314084 | + | 0.949395i | \(0.398303\pi\) | |||||||
\(312\) | 624510. | + | 472423.i | 0.363206 | + | 0.274754i | ||||
\(313\) | − | 416279.i | − | 0.240173i | −0.992763 | − | 0.120086i | \(-0.961683\pi\) | ||
0.992763 | − | 0.120086i | \(-0.0383172\pi\) | |||||||
\(314\) | −463768. | −0.265446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 716005. | 0.403365 | ||||||||
\(317\) | − | 2.89214e6i | − | 1.61648i | −0.588851 | − | 0.808242i | \(-0.700420\pi\) | ||
0.588851 | − | 0.808242i | \(-0.299580\pi\) | |||||||
\(318\) | −3.07006e6 | − | 2.32241e6i | −1.70247 | − | 1.28787i | ||||
\(319\) | 693700. | 0.381676 | ||||||||
\(320\) | 119160. | 0.0650515 | ||||||||
\(321\) | 1.27049e6 | − | 1.67950e6i | 0.688193 | − | 0.909743i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 552808.i | 0.294828i | ||||||||
\(324\) | 718765. | − | 441743.i | 0.380386 | − | 0.233780i | ||||
\(325\) | − | 1.20995e6i | − | 0.635416i | ||||||
\(326\) | 2.88342e6i | 1.50267i | ||||||||
\(327\) | −934045. | − | 706577.i | −0.483057 | − | 0.365418i | ||||
\(328\) | − | 1.86211e6i | − | 0.955697i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −121193. | − | 91678.6i | −0.0612620 | − | 0.0463429i | ||||
\(331\) | −3.47755e6 | −1.74463 | −0.872315 | − | 0.488944i | \(-0.837382\pi\) | ||||
−0.872315 | + | 0.488944i | \(0.837382\pi\) | |||||||
\(332\) | 1.54069e6 | 0.767134 | ||||||||
\(333\) | 243225. | + | 860274.i | 0.120198 | + | 0.425134i | ||||
\(334\) | 210338.i | 0.103170i | ||||||||
\(335\) | −655295. | −0.319025 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 916887. | 0.439786 | 0.219893 | − | 0.975524i | \(-0.429429\pi\) | ||||
0.219893 | + | 0.975524i | \(0.429429\pi\) | |||||||
\(338\) | 1.34387e6i | 0.639829i | ||||||||
\(339\) | 828334. | − | 1.09500e6i | 0.391477 | − | 0.517504i | ||||
\(340\) | −44427.8 | −0.0208429 | ||||||||
\(341\) | 412868. | 0.192276 | ||||||||
\(342\) | 1.19256e6 | + | 4.21804e6i | 0.551336 | + | 1.95005i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 724382.i | − | 0.330044i | ||||||
\(345\) | −367161. | + | 485360.i | −0.166077 | + | 0.219541i | ||||
\(346\) | − | 1.21932e6i | − | 0.547555i | ||||||
\(347\) | 1.23792e6i | 0.551912i | 0.961170 | + | 0.275956i | \(0.0889945\pi\) | ||||
−0.961170 | + | 0.275956i | \(0.911006\pi\) | |||||||
\(348\) | 970189. | − | 1.28252e6i | 0.429446 | − | 0.567697i | ||||
\(349\) | − | 2.19902e6i | − | 0.966419i | −0.875505 | − | 0.483210i | \(-0.839471\pi\) | ||
0.875505 | − | 0.483210i | \(-0.160529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.47098e6 | + | 574083.i | 0.637295 | + | 0.248718i | ||||
\(352\) | 464255. | 0.199710 | ||||||||
\(353\) | −2.66911e6 | −1.14006 | −0.570032 | − | 0.821622i | \(-0.693069\pi\) | ||||
−0.570032 | + | 0.821622i | \(0.693069\pi\) | |||||||
\(354\) | 500826. | − | 662056.i | 0.212412 | − | 0.280793i | ||||
\(355\) | 388184.i | 0.163481i | ||||||||
\(356\) | 1.95422e6 | 0.817237 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −967312. | −0.398896 | ||||||||
\(359\) | 4.54793e6i | 1.86242i | 0.364484 | + | 0.931210i | \(0.381245\pi\) | ||||
−0.364484 | + | 0.931210i | \(0.618755\pi\) | |||||||
\(360\) | 420259. | − | 118820.i | 0.170908 | − | 0.0483206i | ||||
\(361\) | −4.55371e6 | −1.83907 | ||||||||
\(362\) | −2.18689e6 | −0.877113 | ||||||||
\(363\) | −1.88744e6 | − | 1.42780e6i | −0.751809 | − | 0.568721i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 759296.i | 0.298318i | ||||||||
\(366\) | 1.70801e6 | + | 1.29206e6i | 0.666480 | + | 0.504173i | ||||
\(367\) | 2.13509e6i | 0.827469i | 0.910398 | + | 0.413735i | \(0.135776\pi\) | ||||
−0.910398 | + | 0.413735i | \(0.864224\pi\) | |||||||
\(368\) | − | 3.34301e6i | − | 1.28682i | ||||||
\(369\) | −1.02157e6 | − | 3.61326e6i | −0.390575 | − | 1.38144i | ||||
\(370\) | − | 373300.i | − | 0.141760i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 577425. | − | 763315.i | 0.216341 | − | 0.285987i | ||||
\(373\) | −3.25854e6 | −1.21269 | −0.606346 | − | 0.795201i | \(-0.707365\pi\) | ||||
−0.606346 | + | 0.795201i | \(0.707365\pi\) | |||||||
\(374\) | 136282. | 0.0503802 | ||||||||
\(375\) | −1.11759e6 | − | 845423.i | −0.410397 | − | 0.310453i | ||||
\(376\) | 470874.i | 0.171765i | ||||||||
\(377\) | 3.00989e6 | 1.09068 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.32017e6 | −1.18730 | −0.593652 | − | 0.804722i | \(-0.702314\pi\) | ||||
−0.593652 | + | 0.804722i | \(0.702314\pi\) | |||||||
\(380\) | − | 564968.i | − | 0.200708i | ||||||
\(381\) | 1.76014e6 | + | 1.33149e6i | 0.621204 | + | 0.469922i | ||||
\(382\) | −3.59781e6 | −1.26148 | ||||||||
\(383\) | 3.46201e6 | 1.20596 | 0.602978 | − | 0.797758i | \(-0.293981\pi\) | ||||
0.602978 | + | 0.797758i | \(0.293981\pi\) | |||||||
\(384\) | −1.96545e6 | + | 2.59819e6i | −0.680197 | + | 0.899173i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 647910.i | − | 0.221333i | ||||||
\(387\) | −397405. | − | 1.40560e6i | −0.134882 | − | 0.477073i | ||||
\(388\) | 359806.i | 0.121336i | ||||||||
\(389\) | − | 2.49213e6i | − | 0.835018i | −0.908673 | − | 0.417509i | \(-0.862903\pi\) | ||
0.908673 | − | 0.417509i | \(-0.137097\pi\) | |||||||
\(390\) | −525842. | − | 397784.i | −0.175063 | − | 0.132430i | ||||
\(391\) | − | 545792.i | − | 0.180545i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.90455e6 | − | 1.44074e6i | −0.622030 | − | 0.470547i | ||||
\(394\) | 4.80161e6 | 1.55828 | ||||||||
\(395\) | 747410. | 0.241027 | ||||||||
\(396\) | 320971. | − | 90748.0i | 0.102856 | − | 0.0290803i | ||||
\(397\) | 3.04840e6i | 0.970722i | 0.874314 | + | 0.485361i | \(0.161312\pi\) | ||||
−0.874314 | + | 0.485361i | \(0.838688\pi\) | |||||||
\(398\) | −593994. | −0.187964 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.70678e6 | 1.15837 | ||||||||
\(401\) | − | 51572.9i | − | 0.0160162i | −0.999968 | − | 0.00800812i | \(-0.997451\pi\) | ||
0.999968 | − | 0.00800812i | \(-0.00254909\pi\) | |||||||
\(402\) | 2.81129e6 | − | 3.71633e6i | 0.867642 | − | 1.14696i | ||||
\(403\) | 1.79139e6 | 0.549449 | ||||||||
\(404\) | 1.11532e6 | 0.339973 | ||||||||
\(405\) | 750291. | − | 461119.i | 0.227296 | − | 0.139693i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 353455.i | 0.105766i | ||||||||
\(408\) | −236293. | + | 312362.i | −0.0702748 | + | 0.0928983i | ||||
\(409\) | − | 4.53920e6i | − | 1.34175i | −0.741571 | − | 0.670875i | \(-0.765919\pi\) | ||
0.741571 | − | 0.670875i | \(-0.234081\pi\) | |||||||
\(410\) | 1.56791e6i | 0.460639i | ||||||||
\(411\) | 848658. | − | 1.12187e6i | 0.247815 | − | 0.327594i | ||||
\(412\) | 1.40005e6i | 0.406351i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.17743e6 | − | 4.16450e6i | −0.337624 | − | 1.19416i | ||||
\(415\) | 1.60827e6 | 0.458394 | ||||||||
\(416\) | 2.01435e6 | 0.570693 | ||||||||
\(417\) | 1.25282e6 | − | 1.65614e6i | 0.352817 | − | 0.466399i | ||||
\(418\) | 1.73304e6i | 0.485140i | ||||||||
\(419\) | −1.89078e6 | −0.526145 | −0.263072 | − | 0.964776i | \(-0.584736\pi\) | ||||
−0.263072 | + | 0.964776i | \(0.584736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.04901e6 | −1.38836 | −0.694178 | − | 0.719803i | \(-0.744232\pi\) | ||||
−0.694178 | + | 0.719803i | \(0.744232\pi\) | |||||||
\(422\) | − | 2.24962e6i | − | 0.614933i | ||||||
\(423\) | 258327. | + | 913691.i | 0.0701971 | + | 0.248284i | ||||
\(424\) | 4.37407e6 | 1.18160 | ||||||||
\(425\) | 605181. | 0.162522 | ||||||||
\(426\) | −2.20148e6 | − | 1.66535e6i | −0.587747 | − | 0.444613i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 1.93016e6i | − | 0.509312i | ||||||
\(429\) | 497887. | + | 376637.i | 0.130613 | + | 0.0988051i | ||||
\(430\) | 609935.i | 0.159079i | ||||||||
\(431\) | − | 3.26850e6i | − | 0.847530i | −0.905772 | − | 0.423765i | \(-0.860708\pi\) | ||
0.905772 | − | 0.423765i | \(-0.139292\pi\) | |||||||
\(432\) | −1.75875e6 | + | 4.50649e6i | −0.453414 | + | 1.16179i | ||||
\(433\) | − | 1.69788e6i | − | 0.435198i | −0.976038 | − | 0.217599i | \(-0.930177\pi\) | ||
0.976038 | − | 0.217599i | \(-0.0698226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.01274e6 | − | 1.33877e6i | 0.256612 | − | 0.339222i | ||||
\(436\) | −1.07344e6 | −0.270435 | ||||||||
\(437\) | 6.94058e6 | 1.73857 | ||||||||
\(438\) | −4.30614e6 | − | 3.25747e6i | −1.07251 | − | 0.811325i | ||||
\(439\) | − | 4.42320e6i | − | 1.09541i | −0.836673 | − | 0.547703i | \(-0.815502\pi\) | ||
0.836673 | − | 0.547703i | \(-0.184498\pi\) | |||||||
\(440\) | 172669. | 0.0425190 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 591314. | 0.143967 | ||||||||
\(443\) | − | 5.22017e6i | − | 1.26379i | −0.775054 | − | 0.631895i | \(-0.782277\pi\) | ||
0.775054 | − | 0.631895i | \(-0.217723\pi\) | |||||||
\(444\) | 653471. | + | 494332.i | 0.157315 | + | 0.119004i | ||||
\(445\) | 2.03993e6 | 0.488332 | ||||||||
\(446\) | 1.58203e6 | 0.376598 | ||||||||
\(447\) | −264767. | + | 350004.i | −0.0626752 | + | 0.0828522i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.80274e6i | 0.890186i | 0.895484 | + | 0.445093i | \(0.146829\pi\) | ||||
−0.895484 | + | 0.445093i | \(0.853171\pi\) | |||||||
\(450\) | 4.61765e6 | − | 1.30555e6i | 1.07495 | − | 0.303921i | ||||
\(451\) | − | 1.48456e6i | − | 0.343681i | ||||||
\(452\) | − | 1.25842e6i | − | 0.289720i | ||||||
\(453\) | 81389.4 | + | 61568.7i | 0.0186347 | + | 0.0140966i | ||||
\(454\) | − | 3.04968e6i | − | 0.694407i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.97217e6 | − | 3.00482e6i | −0.894572 | − | 0.676717i | ||||
\(457\) | 1.83749e6 | 0.411561 | 0.205781 | − | 0.978598i | \(-0.434027\pi\) | ||||
0.205781 | + | 0.978598i | \(0.434027\pi\) | |||||||
\(458\) | −3.91987e6 | −0.873188 | ||||||||
\(459\) | −287140. | + | 735745.i | −0.0636154 | + | 0.163003i | ||||
\(460\) | 557797.i | 0.122908i | ||||||||
\(461\) | 7.79775e6 | 1.70890 | 0.854450 | − | 0.519533i | \(-0.173894\pi\) | ||||
0.854450 | + | 0.519533i | \(0.173894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 254809. | 0.0552410 | 0.0276205 | − | 0.999618i | \(-0.491207\pi\) | ||||
0.0276205 | + | 0.999618i | \(0.491207\pi\) | |||||||
\(464\) | 9.22106e6i | 1.98832i | ||||||||
\(465\) | 602751. | − | 796795.i | 0.129272 | − | 0.170889i | ||||
\(466\) | 2.76878e6 | 0.590642 | ||||||||
\(467\) | 4.98525e6 | 1.05778 | 0.528889 | − | 0.848691i | \(-0.322609\pi\) | ||||
0.528889 | + | 0.848691i | \(0.322609\pi\) | |||||||
\(468\) | 1.39266e6 | − | 393746.i | 0.293921 | − | 0.0831002i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 396480.i | − | 0.0827897i | ||||||
\(471\) | 641068. | − | 847446.i | 0.133153 | − | 0.176019i | ||||
\(472\) | 943264.i | 0.194885i | ||||||||
\(473\) | − | 577509.i | − | 0.118688i | ||||||
\(474\) | −3.20648e6 | + | 4.23873e6i | −0.655514 | + | 0.866543i | ||||
\(475\) | 7.69581e6i | 1.56502i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.48750e6 | − | 2.39967e6i | 1.70798 | − | 0.482897i | ||||
\(478\) | −1.81075e6 | −0.362485 | ||||||||
\(479\) | −7.71216e6 | −1.53581 | −0.767904 | − | 0.640564i | \(-0.778700\pi\) | ||||
−0.767904 | + | 0.640564i | \(0.778700\pi\) | |||||||
\(480\) | 677773. | − | 895968.i | 0.134271 | − | 0.177496i | ||||
\(481\) | 1.53360e6i | 0.302239i | ||||||||
\(482\) | 2.64306e6 | 0.518191 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.16913e6 | −0.420894 | ||||||||
\(485\) | 375588.i | 0.0725031i | ||||||||
\(486\) | −603727. | + | 6.23332e6i | −0.115944 | + | 1.19710i | ||||
\(487\) | −8.12051e6 | −1.55153 | −0.775767 | − | 0.631020i | \(-0.782637\pi\) | ||||
−0.775767 | + | 0.631020i | \(0.782637\pi\) | |||||||
\(488\) | −2.43348e6 | −0.462572 | ||||||||
\(489\) | −5.26890e6 | − | 3.98576e6i | −0.996432 | − | 0.753771i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.72726e6i | 1.44651i | 0.690581 | + | 0.723255i | \(0.257355\pi\) | ||||
−0.690581 | + | 0.723255i | \(0.742645\pi\) | |||||||
\(492\) | −2.74466e6 | − | 2.07626e6i | −0.511183 | − | 0.386695i | ||||
\(493\) | 1.50546e6i | 0.278967i | ||||||||
\(494\) | 7.51947e6i | 1.38634i | ||||||||
\(495\) | 335050. | − | 94728.4i | 0.0614605 | − | 0.0173767i | ||||
\(496\) | 5.48808e6i | 1.00165i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.89966e6 | + | 9.12086e6i | −1.24668 | + | 1.64802i | ||||
\(499\) | 2.33074e6 | 0.419028 | 0.209514 | − | 0.977806i | \(-0.432812\pi\) | ||||
0.209514 | + | 0.977806i | \(0.432812\pi\) | |||||||
\(500\) | −1.28438e6 | −0.229757 | ||||||||
\(501\) | −384352. | − | 290751.i | −0.0684124 | − | 0.0517519i | ||||
\(502\) | − | 7.46161e6i | − | 1.32152i | ||||||
\(503\) | −3.86914e6 | −0.681859 | −0.340930 | − | 0.940089i | \(-0.610742\pi\) | ||||
−0.340930 | + | 0.940089i | \(0.610742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.16424e6 | 0.203148 | ||||||||
\(506\) | − | 1.71104e6i | − | 0.297087i | ||||||
\(507\) | −2.45565e6 | − | 1.85763e6i | −0.424275 | − | 0.320951i | ||||
\(508\) | 2.02283e6 | 0.347776 | ||||||||
\(509\) | 4.29903e6 | 0.735489 | 0.367744 | − | 0.929927i | \(-0.380130\pi\) | ||||
0.367744 | + | 0.929927i | \(0.380130\pi\) | |||||||
\(510\) | 198960. | − | 263011.i | 0.0338720 | − | 0.0447764i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.24648e6i | 0.210142i | ||||||||
\(513\) | −9.35613e6 | − | 3.65143e6i | −1.56965 | − | 0.612589i | ||||
\(514\) | − | 682552.i | − | 0.113953i | ||||||
\(515\) | 1.46146e6i | 0.242812i | ||||||||
\(516\) | −1.06771e6 | − | 807688.i | −0.176534 | − | 0.133543i | ||||
\(517\) | 375402.i | 0.0617689i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.22807e6 | + | 1.68547e6i | 0.363087 | + | 0.274664i | ||||
\(520\) | 749193. | 0.121503 | ||||||||
\(521\) | 4.57032e6 | 0.737653 | 0.368827 | − | 0.929498i | \(-0.379760\pi\) | ||||
0.368827 | + | 0.929498i | \(0.379760\pi\) | |||||||
\(522\) | 3.24771e6 | + | 1.14870e7i | 0.521676 | + | 1.84514i | ||||
\(523\) | − | 2.15375e6i | − | 0.344304i | −0.985070 | − | 0.172152i | \(-0.944928\pi\) | ||
0.985070 | − | 0.172152i | \(-0.0550720\pi\) | |||||||
\(524\) | −2.18879e6 | −0.348238 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.87821e6 | 1.39914 | ||||||||
\(527\) | 896002.i | 0.140534i | ||||||||
\(528\) | −1.15386e6 | + | 1.52532e6i | −0.180122 | + | 0.238109i | ||||
\(529\) | −416145. | −0.0646555 | ||||||||
\(530\) | −3.68300e6 | −0.569524 | ||||||||
\(531\) | 517486. | + | 1.83032e6i | 0.0796457 | + | 0.281703i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.44133e6i | − | 0.982104i | ||||||
\(534\) | −8.75154e6 | + | 1.15689e7i | −1.32810 | + | 1.75566i | ||||
\(535\) | − | 2.01482e6i | − | 0.304335i | ||||||
\(536\) | 5.29484e6i | 0.796051i | ||||||||
\(537\) | 1.33712e6 | − | 1.76757e6i | 0.200094 | − | 0.264510i | ||||
\(538\) | − | 8.57730e6i | − | 1.27760i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 293456. | − | 751928.i | 0.0433070 | − | 0.110967i | ||||
\(541\) | −5.46624e6 | −0.802963 | −0.401481 | − | 0.915867i | \(-0.631505\pi\) | ||||
−0.401481 | + | 0.915867i | \(0.631505\pi\) | |||||||
\(542\) | −8.48656e6 | −1.24089 | ||||||||
\(543\) | 3.02294e6 | − | 3.99612e6i | 0.439978 | − | 0.581619i | ||||
\(544\) | 1.00752e6i | 0.145968i | ||||||||
\(545\) | −1.12053e6 | −0.161596 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.32611e6 | 1.04690 | 0.523450 | − | 0.852056i | \(-0.324645\pi\) | ||||
0.523450 | + | 0.852056i | \(0.324645\pi\) | |||||||
\(548\) | − | 1.28930e6i | − | 0.183401i | ||||||
\(549\) | −4.72197e6 | + | 1.33504e6i | −0.668640 | + | 0.189044i | ||||
\(550\) | 1.89722e6 | 0.267431 | ||||||||
\(551\) | −1.91443e7 | −2.68633 | ||||||||
\(552\) | 3.92175e6 | + | 2.96669e6i | 0.547813 | + | 0.414404i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.48281e6i | 0.620549i | ||||||||
\(555\) | 682134. | + | 516014.i | 0.0940020 | + | 0.0711097i | ||||
\(556\) | − | 1.90331e6i | − | 0.261109i | ||||||
\(557\) | 7.63525e6i | 1.04276i | 0.853324 | + | 0.521381i | \(0.174583\pi\) | ||||
−0.853324 | + | 0.521381i | \(0.825417\pi\) | |||||||
\(558\) | 1.93293e6 | + | 6.83668e6i | 0.262803 | + | 0.929522i | ||||
\(559\) | − | 2.50575e6i | − | 0.339163i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −188383. | + | 249029.i | −0.0252717 | + | 0.0334074i | ||||
\(562\) | 8.76942e6 | 1.17120 | ||||||||
\(563\) | −2.17576e6 | −0.289295 | −0.144648 | − | 0.989483i | \(-0.546205\pi\) | ||||
−0.144648 | + | 0.989483i | \(0.546205\pi\) | |||||||
\(564\) | 694048. | + | 525026.i | 0.0918738 | + | 0.0694998i | ||||
\(565\) | − | 1.31361e6i | − | 0.173120i | ||||||
\(566\) | −6.86531e6 | −0.900780 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.13656e6 | 0.407927 | ||||||||
\(569\) | − | 8.38705e6i | − | 1.08600i | −0.839734 | − | 0.542998i | \(-0.817289\pi\) | ||
0.839734 | − | 0.542998i | \(-0.182711\pi\) | |||||||
\(570\) | 3.34459e6 | + | 2.53009e6i | 0.431178 | + | 0.326173i | ||||
\(571\) | 2.54473e6 | 0.326626 | 0.163313 | − | 0.986574i | \(-0.447782\pi\) | ||||
0.163313 | + | 0.986574i | \(0.447782\pi\) | |||||||
\(572\) | 572193. | 0.0731228 | ||||||||
\(573\) | 4.97326e6 | − | 6.57430e6i | 0.632783 | − | 0.836494i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.59813e6i | − | 0.958379i | ||||||
\(576\) | −528218. | − | 1.86828e6i | −0.0663372 | − | 0.234631i | ||||
\(577\) | 1.02039e7i | 1.27592i | 0.770068 | + | 0.637962i | \(0.220222\pi\) | ||||
−0.770068 | + | 0.637962i | \(0.779778\pi\) | |||||||
\(578\) | − | 9.36422e6i | − | 1.16588i | ||||||
\(579\) | 1.18393e6 | + | 895608.i | 0.146767 | + | 0.111025i | ||||
\(580\) | − | 1.53858e6i | − | 0.189911i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.13004e6 | − | 1.61131e6i | −0.260664 | − | 0.197184i | ||||
\(583\) | 3.48720e6 | 0.424919 | ||||||||
\(584\) | 6.13517e6 | 0.744380 | ||||||||
\(585\) | 1.45375e6 | − | 411017.i | 0.175630 | − | 0.0496558i | ||||
\(586\) | − | 1.32471e7i | − | 1.59359i | ||||||
\(587\) | 1.90974e6 | 0.228760 | 0.114380 | − | 0.993437i | \(-0.463512\pi\) | ||||
0.114380 | + | 0.993437i | \(0.463512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.13940e7 | −1.35329 | ||||||||
\(590\) | − | 794235.i | − | 0.0939332i | ||||||
\(591\) | −6.63727e6 | + | 8.77400e6i | −0.781665 | + | 1.03331i | ||||
\(592\) | −4.69833e6 | −0.550984 | ||||||||
\(593\) | 9.68502e6 | 1.13100 | 0.565502 | − | 0.824747i | \(-0.308683\pi\) | ||||
0.565502 | + | 0.824747i | \(0.308683\pi\) | |||||||
\(594\) | −900175. | + | 2.30654e6i | −0.104679 | + | 0.268222i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 402239.i | 0.0463841i | ||||||||
\(597\) | 821080. | − | 1.08541e6i | 0.0942865 | − | 0.124640i | ||||
\(598\) | − | 7.42403e6i | − | 0.848959i | ||||||
\(599\) | − | 4.03346e6i | − | 0.459315i | −0.973271 | − | 0.229658i | \(-0.926239\pi\) | ||
0.973271 | − | 0.229658i | \(-0.0737606\pi\) | |||||||
\(600\) | −3.28950e6 | + | 4.34849e6i | −0.373037 | + | 0.493128i | ||||
\(601\) | 1.16260e7i | 1.31293i | 0.754356 | + | 0.656466i | \(0.227949\pi\) | ||||
−0.754356 | + | 0.656466i | \(0.772051\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.90481e6 | + | 1.02742e7i | 0.325330 | + | 1.15068i | ||||
\(604\) | 93536.2 | 0.0104325 | ||||||||
\(605\) | −2.26427e6 | −0.251501 | ||||||||
\(606\) | −4.99471e6 | + | 6.60265e6i | −0.552495 | + | 0.730359i | ||||
\(607\) | 7.51421e6i | 0.827774i | 0.910328 | + | 0.413887i | \(0.135829\pi\) | ||||
−0.910328 | + | 0.413887i | \(0.864171\pi\) | |||||||
\(608\) | −1.28122e7 | −1.40561 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.04901e6 | 0.222956 | ||||||||
\(611\) | 1.62883e6i | 0.176511i | ||||||||
\(612\) | 196941. | + | 696570.i | 0.0212548 | + | 0.0751772i | ||||
\(613\) | 3.74103e6 | 0.402105 | 0.201053 | − | 0.979580i | \(-0.435564\pi\) | ||||
0.201053 | + | 0.979580i | \(0.435564\pi\) | |||||||
\(614\) | −1.34576e7 | −1.44061 | ||||||||
\(615\) | −2.86505e6 | − | 2.16732e6i | −0.305453 | − | 0.231066i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.48513e7i | − | 1.57055i | −0.619146 | − | 0.785276i | \(-0.712521\pi\) | ||
0.619146 | − | 0.785276i | \(-0.287479\pi\) | |||||||
\(618\) | −8.28828e6 | − | 6.26984e6i | −0.872958 | − | 0.660367i | ||||
\(619\) | − | 8.36596e6i | − | 0.877585i | −0.898588 | − | 0.438793i | \(-0.855406\pi\) | ||
0.898588 | − | 0.438793i | \(-0.144594\pi\) | |||||||
\(620\) | − | 915711.i | − | 0.0956707i | ||||||
\(621\) | 9.23738e6 | + | 3.60508e6i | 0.961213 | + | 0.375134i | ||||
\(622\) | 7.28969e6i | 0.755497i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.00647e6 | + | 6.61820e6i | −0.514719 | + | 0.680423i | ||||
\(625\) | 7.72981e6 | 0.791533 | ||||||||
\(626\) | 2.83215e6 | 0.288855 | ||||||||
\(627\) | −3.16679e6 | − | 2.39558e6i | −0.321699 | − | 0.243356i | ||||
\(628\) | − | 973922.i | − | 0.0985428i | ||||||
\(629\) | −767065. | −0.0773047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.21939e6 | 0.821800 | 0.410900 | − | 0.911680i | \(-0.365215\pi\) | ||||
0.410900 | + | 0.911680i | \(0.365215\pi\) | |||||||
\(632\) | − | 6.03913e6i | − | 0.601426i | ||||||
\(633\) | 4.11074e6 | + | 3.10965e6i | 0.407766 | + | 0.308463i | ||||
\(634\) | 1.96766e7 | 1.94414 | ||||||||
\(635\) | 2.11155e6 | 0.207810 | ||||||||
\(636\) | 4.87710e6 | − | 6.44718e6i | 0.478100 | − | 0.632015i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.71958e6i | 0.459041i | ||||||||
\(639\) | 6.08622e6 | − | 1.72075e6i | 0.589651 | − | 0.166712i | ||||
\(640\) | 3.11692e6i | 0.300799i | ||||||||
\(641\) | 4.93371e6i | 0.474273i | 0.971476 | + | 0.237137i | \(0.0762089\pi\) | ||||
−0.971476 | + | 0.237137i | \(0.923791\pi\) | |||||||
\(642\) | 1.14265e7 | + | 8.64380e6i | 1.09415 | + | 0.827689i | ||||
\(643\) | 1.06965e7i | 1.02027i | 0.860094 | + | 0.510135i | \(0.170405\pi\) | ||||
−0.860094 | + | 0.510135i | \(0.829595\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.11454e6 | − | 843115.i | −0.105486 | − | 0.0797971i | ||||
\(646\) | −3.76102e6 | −0.354589 | ||||||||
\(647\) | 8.71767e6 | 0.818728 | 0.409364 | − | 0.912371i | \(-0.365751\pi\) | ||||
0.409364 | + | 0.912371i | \(0.365751\pi\) | |||||||
\(648\) | −3.72588e6 | − | 6.06241e6i | −0.348571 | − | 0.567163i | ||||
\(649\) | 752012.i | 0.0700831i | ||||||||
\(650\) | 8.23186e6 | 0.764213 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.05524e6 | −0.557844 | ||||||||
\(653\) | 9.86209e6i | 0.905078i | 0.891745 | + | 0.452539i | \(0.149482\pi\) | ||||
−0.891745 | + | 0.452539i | \(0.850518\pi\) | |||||||
\(654\) | 4.80719e6 | − | 6.35476e6i | 0.439488 | − | 0.580972i | ||||
\(655\) | −2.28479e6 | −0.208087 | ||||||||
\(656\) | 1.97336e7 | 1.79038 | ||||||||
\(657\) | 1.19048e7 | − | 3.36583e6i | 1.07599 | − | 0.304214i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.63431e6i | 0.684788i | 0.939556 | + | 0.342394i | \(0.111238\pi\) | ||||
−0.939556 | + | 0.342394i | \(0.888762\pi\) | |||||||
\(660\) | 192527. | − | 254507.i | 0.0172041 | − | 0.0227426i | ||||
\(661\) | − | 1.40247e7i | − | 1.24850i | −0.781223 | − | 0.624252i | \(-0.785404\pi\) | ||
0.781223 | − | 0.624252i | \(-0.214596\pi\) | |||||||
\(662\) | − | 2.36595e7i | − | 2.09826i | ||||||
\(663\) | −817375. | + | 1.08051e6i | −0.0722166 | + | 0.0954653i | ||||
\(664\) | − | 1.29949e7i | − | 1.14381i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.85286e6 | + | 1.65478e6i | −0.511308 | + | 0.144562i | ||||
\(667\) | 1.89013e7 | 1.64504 | ||||||||
\(668\) | −441714. | −0.0383001 | ||||||||
\(669\) | −2.18684e6 | + | 2.89085e6i | −0.188909 | + | 0.249724i | ||||
\(670\) | − | 4.45829e6i | − | 0.383691i | ||||||
\(671\) | −1.94008e6 | −0.166347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.03156e7 | −0.877920 | −0.438960 | − | 0.898507i | \(-0.644653\pi\) | ||||
−0.438960 | + | 0.898507i | \(0.644653\pi\) | |||||||
\(674\) | 6.23803e6i | 0.528930i | ||||||||
\(675\) | −3.99736e6 | + | 1.02425e7i | −0.337687 | + | 0.865262i | ||||
\(676\) | −2.82214e6 | −0.237526 | ||||||||
\(677\) | −4.53726e6 | −0.380472 | −0.190236 | − | 0.981738i | \(-0.560925\pi\) | ||||
−0.190236 | + | 0.981738i | \(0.560925\pi\) | |||||||
\(678\) | 7.44981e6 | + | 5.63556e6i | 0.622402 | + | 0.470828i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 374725.i | 0.0310771i | ||||||||
\(681\) | 5.57269e6 | + | 4.21558e6i | 0.460466 | + | 0.348329i | ||||
\(682\) | 2.80894e6i | 0.231250i | ||||||||
\(683\) | − | 901559.i | − | 0.0739507i | −0.999316 | − | 0.0369754i | \(-0.988228\pi\) | ||
0.999316 | − | 0.0369754i | \(-0.0117723\pi\) | |||||||
\(684\) | −8.85796e6 | + | 2.50440e6i | −0.723925 | + | 0.204675i | ||||
\(685\) | − | 1.34585e6i | − | 0.109590i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.41844e6 | − | 7.16280e6i | 0.438009 | − | 0.579016i | ||||
\(688\) | 7.67659e6 | 0.618297 | ||||||||
\(689\) | 1.51306e7 | 1.21425 | ||||||||
\(690\) | −3.30214e6 | − | 2.49797e6i | −0.264042 | − | 0.199740i | ||||
\(691\) | 1.71097e7i | 1.36316i | 0.731742 | + | 0.681582i | \(0.238708\pi\) | ||||
−0.731742 | + | 0.681582i | \(0.761292\pi\) | |||||||
\(692\) | 2.56059e6 | 0.203271 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.42220e6 | −0.663784 | ||||||||
\(695\) | − | 1.98679e6i | − | 0.156023i | ||||||
\(696\) | −1.08174e7 | − | 8.18304e6i | −0.846447 | − | 0.640312i | ||||
\(697\) | 3.22177e6 | 0.251196 | ||||||||
\(698\) | 1.49610e7 | 1.16231 | ||||||||
\(699\) | −3.82730e6 | + | 5.05942e6i | −0.296278 | + | 0.391658i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.02857e6i | 0.155917i | 0.996957 | + | 0.0779587i | \(0.0248402\pi\) | ||||
−0.996957 | + | 0.0779587i | \(0.975160\pi\) | |||||||
\(702\) | −3.90577e6 | + | 1.00078e7i | −0.299132 | + | 0.766473i | ||||
\(703\) | − | 9.75441e6i | − | 0.744411i | ||||||
\(704\) | − | 767608.i | − | 0.0583724i | ||||||
\(705\) | 724490. | + | 548055.i | 0.0548984 | + | 0.0415290i | ||||
\(706\) | − | 1.81592e7i | − | 1.37115i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.39033e6 | + | 1.05174e6i | 0.104240 | + | 0.0788545i | ||||
\(709\) | −1.67894e7 | −1.25435 | −0.627176 | − | 0.778878i | \(-0.715789\pi\) | ||||
−0.627176 | + | 0.778878i | \(0.715789\pi\) | |||||||
\(710\) | −2.64100e6 | −0.196618 | ||||||||
\(711\) | −3.31314e6 | − | 1.17184e7i | −0.245791 | − | 0.869351i | ||||
\(712\) | − | 1.64828e7i | − | 1.21852i | ||||||
\(713\) | 1.12494e7 | 0.828718 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 597290. | 0.0436939 | ||||||||
\(716\) | − | 2.03137e6i | − | 0.148084i | ||||||
\(717\) | 2.50301e6 | − | 3.30880e6i | 0.181829 | − | 0.240366i | ||||
\(718\) | −3.09418e7 | −2.23993 | ||||||||
\(719\) | −2.63704e7 | −1.90237 | −0.951183 | − | 0.308627i | \(-0.900130\pi\) | ||||
−0.951183 | + | 0.308627i | \(0.900130\pi\) | |||||||
\(720\) | 1.25918e6 | + | 4.45367e6i | 0.0905228 | + | 0.320175i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 3.09811e7i | − | 2.21184i | ||||||
\(723\) | −3.65351e6 | + | 4.82968e6i | −0.259935 | + | 0.343615i | ||||
\(724\) | − | 4.59251e6i | − | 0.325614i | ||||||
\(725\) | 2.09580e7i | 1.48083i | ||||||||
\(726\) | 9.71399e6 | − | 1.28412e7i | 0.684000 | − | 0.904199i | ||||
\(727\) | 1.63660e7i | 1.14844i | 0.818702 | + | 0.574218i | \(0.194694\pi\) | ||||
−0.818702 | + | 0.574218i | \(0.805306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.05557e7 | − | 9.71953e6i | −0.735642 | − | 0.677371i | ||||
\(730\) | −5.16586e6 | −0.358786 | ||||||||
\(731\) | 1.25331e6 | 0.0867489 | ||||||||
\(732\) | −2.71334e6 | + | 3.58685e6i | −0.187166 | + | 0.247420i | ||||
\(733\) | − | 2.65023e7i | − | 1.82189i | −0.412525 | − | 0.910946i | \(-0.635353\pi\) | ||
0.412525 | − | 0.910946i | \(-0.364647\pi\) | |||||||
\(734\) | −1.45261e7 | −0.995196 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.26496e7 | 0.860759 | ||||||||
\(737\) | 4.22128e6i | 0.286270i | ||||||||
\(738\) | 2.45828e7 | − | 6.95027e6i | 1.66146 | − | 0.469743i | ||||
\(739\) | −1.36791e7 | −0.921397 | −0.460698 | − | 0.887557i | \(-0.652401\pi\) | ||||
−0.460698 | + | 0.887557i | \(0.652401\pi\) | |||||||
\(740\) | 783937. | 0.0526262 | ||||||||
\(741\) | −1.37404e7 | − | 1.03942e7i | −0.919290 | − | 0.695416i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.39766e6i | 0.624522i | 0.949996 | + | 0.312261i | \(0.101086\pi\) | ||||
−0.949996 | + | 0.312261i | \(0.898914\pi\) | |||||||
\(744\) | −6.43816e6 | − | 4.87028e6i | −0.426412 | − | 0.322568i | ||||
\(745\) | 419882.i | 0.0277164i | ||||||||
\(746\) | − | 2.21694e7i | − | 1.45850i | ||||||
\(747\) | −7.12918e6 | − | 2.52156e7i | −0.467453 | − | 1.65336i | ||||
\(748\) | 286195.i | 0.0187029i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.75183e6 | − | 7.60351e6i | 0.373381 | − | 0.493584i | ||||
\(751\) | −1.35043e7 | −0.873723 | −0.436862 | − | 0.899529i | \(-0.643910\pi\) | ||||
−0.436862 | + | 0.899529i | \(0.643910\pi\) | |||||||
\(752\) | −4.99006e6 | −0.321782 | ||||||||
\(753\) | 1.36346e7 | + | 1.03142e7i | 0.876307 | + | 0.662900i | ||||
\(754\) | 2.04778e7i | 1.31176i | ||||||||
\(755\) | 97638.9 | 0.00623383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.36283e6 | −0.466987 | −0.233494 | − | 0.972358i | \(-0.575016\pi\) | ||||
−0.233494 | + | 0.972358i | \(0.575016\pi\) | |||||||
\(758\) | − | 2.25887e7i | − | 1.42797i | ||||||
\(759\) | 3.12659e6 | + | 2.36517e6i | 0.197000 | + | 0.149025i | ||||
\(760\) | −4.76521e6 | −0.299259 | ||||||||
\(761\) | −2.48311e6 | −0.155430 | −0.0777150 | − | 0.996976i | \(-0.524762\pi\) | ||||
−0.0777150 | + | 0.996976i | \(0.524762\pi\) | |||||||
\(762\) | −9.05879e6 | + | 1.19751e7i | −0.565175 | + | 0.747121i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 7.55547e6i | − | 0.468304i | ||||||
\(765\) | 205579. | + | 727122.i | 0.0127006 | + | 0.0449215i | ||||
\(766\) | 2.35538e7i | 1.45040i | ||||||||
\(767\) | 3.26290e6i | 0.200270i | ||||||||
\(768\) | −1.44982e7 | − | 1.09675e7i | −0.886976 | − | 0.670971i | ||||
\(769\) | − | 2.15050e7i | − | 1.31136i | −0.755038 | − | 0.655681i | \(-0.772382\pi\) | ||
0.755038 | − | 0.655681i | \(-0.227618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.24723e6 | + | 943492.i | 0.0755632 | + | 0.0571614i | ||||
\(772\) | 1.36062e6 | 0.0821664 | ||||||||
\(773\) | 9.92550e6 | 0.597453 | 0.298726 | − | 0.954339i | \(-0.403438\pi\) | ||||
0.298726 | + | 0.954339i | \(0.403438\pi\) | |||||||
\(774\) | 9.56299e6 | − | 2.70374e6i | 0.573774 | − | 0.162223i | ||||
\(775\) | 1.24735e7i | 0.745993i | ||||||||
\(776\) | 3.03478e6 | 0.180914 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.69551e7 | 1.00427 | ||||||||
\(779\) | 4.09698e7i | 2.41891i | ||||||||
\(780\) | 835353. | − | 1.10428e6i | 0.0491625 | − | 0.0649893i | ||||
\(781\) | 2.50060e6 | 0.146696 | ||||||||
\(782\) | 3.71329e6 | 0.217141 | ||||||||
\(783\) | −2.54796e7 | − | 9.94393e6i | −1.48521 | − | 0.579634i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.01664e6i | − | 0.0588834i | ||||||
\(786\) | 9.80203e6 | − | 1.29576e7i | 0.565926 | − | 0.748114i | ||||
\(787\) | 1.03681e6i | 0.0596708i | 0.999555 | + | 0.0298354i | \(0.00949831\pi\) | ||||
−0.999555 | + | 0.0298354i | \(0.990502\pi\) | |||||||
\(788\) | 1.00835e7i | 0.578487i | ||||||||
\(789\) | −1.22724e7 | + | 1.62232e7i | −0.701836 | + | 0.927778i | ||||
\(790\) | 5.08500e6i | 0.289883i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −765412. | − | 2.70723e6i | −0.0433593 | − | 0.153360i | ||||
\(793\) | −8.41782e6 | −0.475353 | ||||||||
\(794\) | −2.07397e7 | −1.16749 | ||||||||
\(795\) | 5.09102e6 | − | 6.72996e6i | 0.285685 | − | 0.377655i | ||||
\(796\) | − | 1.24740e6i | − | 0.0697786i | ||||||
\(797\) | 1.52399e7 | 0.849838 | 0.424919 | − | 0.905231i | \(-0.360303\pi\) | ||||
0.424919 | + | 0.905231i | \(0.360303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −814695. | −0.0451469 | ||||||||
\(800\) | 1.40260e7i | 0.774836i | ||||||||
\(801\) | −9.04267e6 | − | 3.19835e7i | −0.497984 | − | 1.76134i | ||||
\(802\) | 350875. | 0.0192627 | ||||||||
\(803\) | 4.89123e6 | 0.267688 | ||||||||
\(804\) | 7.80435e6 | + | 5.90376e6i | 0.425791 | + | 0.322099i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.21877e7i | 0.660821i | ||||||||
\(807\) | 1.56733e7 | + | 1.18564e7i | 0.847184 | + | 0.640869i | ||||
\(808\) | − | 9.40712e6i | − | 0.506907i | ||||||
\(809\) | 5.45336e6i | 0.292949i | 0.989214 | + | 0.146475i | \(0.0467927\pi\) | ||||
−0.989214 | + | 0.146475i | \(0.953207\pi\) | |||||||
\(810\) | 3.13722e6 | + | 5.10460e6i | 0.168009 | + | 0.273369i | ||||
\(811\) | − | 9.69507e6i | − | 0.517605i | −0.965930 | − | 0.258803i | \(-0.916672\pi\) | ||
0.965930 | − | 0.258803i | \(-0.0833279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.17310e7 | − | 1.55075e7i | 0.622456 | − | 0.822842i | ||||
\(814\) | −2.40473e6 | −0.127205 | ||||||||
\(815\) | −6.32083e6 | −0.333335 | ||||||||
\(816\) | −3.31024e6 | − | 2.50410e6i | −0.174034 | − | 0.131651i | ||||
\(817\) | 1.59377e7i | 0.835355i | ||||||||
\(818\) | 3.08824e7 | 1.61372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.29264e6 | −0.171005 | ||||||||
\(821\) | − | 1.63719e7i | − | 0.847699i | −0.905733 | − | 0.423849i | \(-0.860679\pi\) | ||
0.905733 | − | 0.423849i | \(-0.139321\pi\) | |||||||
\(822\) | 7.63260e6 | + | 5.77384e6i | 0.393997 | + | 0.298047i | ||||
\(823\) | 2.37540e7 | 1.22247 | 0.611233 | − | 0.791451i | \(-0.290674\pi\) | ||||
0.611233 | + | 0.791451i | \(0.290674\pi\) | |||||||
\(824\) | 1.18087e7 | 0.605878 | ||||||||
\(825\) | −2.62254e6 | + | 3.46681e6i | −0.134149 | + | 0.177335i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.87632e7i | 1.46242i | 0.682151 | + | 0.731211i | \(0.261045\pi\) | ||||
−0.682151 | + | 0.731211i | \(0.738955\pi\) | |||||||
\(828\) | 8.74553e6 | − | 2.47262e6i | 0.443313 | − | 0.125338i | ||||
\(829\) | 3.69015e7i | 1.86491i | 0.361286 | + | 0.932455i | \(0.382338\pi\) | ||||
−0.361286 | + | 0.932455i | \(0.617662\pi\) | |||||||
\(830\) | 1.09418e7i | 0.551309i | ||||||||
\(831\) | −8.19146e6 | − | 6.19660e6i | −0.411490 | − | 0.311280i | ||||
\(832\) | − | 3.33057e6i | − | 0.166805i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.12675e7 | + | 8.52356e6i | 0.560937 | + | 0.424332i | ||||
\(835\) | −461088. | −0.0228859 | ||||||||
\(836\) | −3.63941e6 | −0.180101 | ||||||||
\(837\) | −1.51646e7 | − | 5.91830e6i | −0.748199 | − | 0.292000i | ||||
\(838\) | − | 1.28639e7i | − | 0.632793i | ||||||
\(839\) | −2.41096e7 | −1.18246 | −0.591229 | − | 0.806504i | \(-0.701357\pi\) | ||||
−0.591229 | + | 0.806504i | \(0.701357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.16245e7 | −1.54182 | ||||||||
\(842\) | − | 3.43509e7i | − | 1.66977i | ||||||
\(843\) | −1.21220e7 | + | 1.60244e7i | −0.587496 | + | 0.776628i | ||||
\(844\) | 4.72424e6 | 0.228284 | ||||||||
\(845\) | −2.94592e6 | −0.141932 | ||||||||
\(846\) | −6.21629e6 | + | 1.75753e6i | −0.298611 | + | 0.0844260i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.63539e7i | 2.21359i | ||||||||
\(849\) | 9.48993e6 | − | 1.25450e7i | 0.451849 | − | 0.597313i | ||||
\(850\) | 4.11734e6i | 0.195465i | ||||||||
\(851\) | 9.63060e6i | 0.455858i | ||||||||
\(852\) | 3.49727e6 | − | 4.62314e6i | 0.165056 | − | 0.218192i | ||||
\(853\) | 1.08498e7i | 0.510561i | 0.966867 | + | 0.255281i | \(0.0821678\pi\) | ||||
−0.966867 | + | 0.255281i | \(0.917832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.24648e6 | + | 2.61425e6i | −0.432575 | + | 0.122302i | ||||
\(856\) | −1.62799e7 | −0.759393 | ||||||||
\(857\) | −2.90805e7 | −1.35254 | −0.676270 | − | 0.736654i | \(-0.736405\pi\) | ||||
−0.676270 | + | 0.736654i | \(0.736405\pi\) | |||||||
\(858\) | −2.56244e6 | + | 3.38737e6i | −0.118833 | + | 0.157088i | ||||
\(859\) | 3.67954e7i | 1.70142i | 0.525636 | + | 0.850709i | \(0.323827\pi\) | ||||
−0.525636 | + | 0.850709i | \(0.676173\pi\) | |||||||
\(860\) | −1.28087e6 | −0.0590555 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.22372e7 | 1.01932 | ||||||||
\(863\) | − | 2.85606e6i | − | 0.130539i | −0.997868 | − | 0.0652695i | \(-0.979209\pi\) | ||
0.997868 | − | 0.0652695i | \(-0.0207907\pi\) | |||||||
\(864\) | −1.70521e7 | − | 6.65492e6i | −0.777128 | − | 0.303290i | ||||
\(865\) | 2.67290e6 | 0.121463 | ||||||||
\(866\) | 1.15515e7 | 0.523412 | ||||||||
\(867\) | 1.71113e7 | + | 1.29442e7i | 0.773099 | + | 0.584826i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.81467e6i | − | 0.216280i | ||||||
\(870\) | 9.10834e6 | + | 6.89018e6i | 0.407982 | + | 0.308626i | ||||
\(871\) | 1.83157e7i | 0.818047i | ||||||||
\(872\) | 9.05395e6i | 0.403224i | ||||||||
\(873\) | 5.88872e6 | − | 1.66491e6i | 0.261508 | − | 0.0739361i | ||||
\(874\) | 4.72202e7i | 2.09098i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.84074e6 | − | 9.04297e6i | 0.301192 | − | 0.398154i | ||||
\(877\) | −5.35187e6 | −0.234967 | −0.117483 | − | 0.993075i | \(-0.537483\pi\) | ||||
−0.117483 | + | 0.993075i | \(0.537483\pi\) | |||||||
\(878\) | 3.00932e7 | 1.31744 | ||||||||
\(879\) | 2.42065e7 | + | 1.83115e7i | 1.05672 | + | 0.799378i | ||||
\(880\) | 1.82985e6i | 0.0796542i | ||||||||
\(881\) | 2.78347e6 | 0.120822 | 0.0604111 | − | 0.998174i | \(-0.480759\pi\) | ||||
0.0604111 | + | 0.998174i | \(0.480759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −626626. | −0.0270462 | −0.0135231 | − | 0.999909i | \(-0.504305\pi\) | ||||
−0.0135231 | + | 0.999909i | \(0.504305\pi\) | |||||||
\(884\) | 1.24177e6i | 0.0534454i | ||||||||
\(885\) | 1.45131e6 | + | 1.09787e6i | 0.0622877 | + | 0.0471188i | ||||
\(886\) | 3.55153e7 | 1.51996 | ||||||||
\(887\) | 4.27454e7 | 1.82423 | 0.912117 | − | 0.409930i | \(-0.134447\pi\) | ||||
0.912117 | + | 0.409930i | \(0.134447\pi\) | |||||||
\(888\) | 4.16943e6 | − | 5.51169e6i | 0.177437 | − | 0.234559i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.38786e7i | 0.587316i | ||||||||
\(891\) | −2.97043e6 | − | 4.83323e6i | −0.125350 | − | 0.203959i | ||||
\(892\) | 3.32229e6i | 0.139806i | ||||||||
\(893\) | − | 1.03601e7i | − | 0.434746i | ||||||
\(894\) | −2.38125e6 | − | 1.80134e6i | −0.0996461 | − | 0.0753793i | ||||
\(895\) | − | 2.12047e6i | − | 0.0884861i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.35660e7 | + | 1.02622e7i | 0.562950 | + | 0.425855i | ||||
\(898\) | −2.58719e7 | −1.07062 | ||||||||
\(899\) | −3.10294e7 | −1.28048 | ||||||||
\(900\) | 2.74167e6 | + | 9.69716e6i | 0.112826 | + | 0.399060i | ||||
\(901\) | 7.56790e6i | 0.310573i | ||||||||
\(902\) | 1.01002e7 | 0.413344 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.06141e7 | −0.431979 | ||||||||
\(905\) | − | 4.79394e6i | − | 0.194568i | ||||||
\(906\) | −418882. | + | 553732.i | −0.0169540 | + | 0.0224119i | ||||
\(907\) | 7.04109e6 | 0.284198 | 0.142099 | − | 0.989852i | \(-0.454615\pi\) | ||||
0.142099 | + | 0.989852i | \(0.454615\pi\) | |||||||
\(908\) | 6.40438e6 | 0.257788 | ||||||||
\(909\) | −5.16086e6 | − | 1.82537e7i | −0.207163 | − | 0.732726i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.05335e6i | − | 0.0420509i | −0.999779 | − | 0.0210255i | \(-0.993307\pi\) | ||
0.999779 | − | 0.0210255i | \(-0.00669310\pi\) | |||||||
\(912\) | 3.18434e7 | − | 4.20948e7i | 1.26775 | − | 1.67587i | ||||
\(913\) | − | 1.03602e7i | − | 0.411329i | ||||||
\(914\) | 1.25013e7i | 0.494984i | ||||||||
\(915\) | −2.83235e6 | + | 3.74417e6i | −0.111839 | + | 0.147844i | ||||
\(916\) | − | 8.23180e6i | − | 0.324157i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.00563e6 | − | 1.95355e6i | −0.196043 | − | 0.0765101i | ||||
\(919\) | 1.81997e7 | 0.710844 | 0.355422 | − | 0.934706i | \(-0.384337\pi\) | ||||
0.355422 | + | 0.934706i | \(0.384337\pi\) | |||||||
\(920\) | 4.70473e6 | 0.183259 | ||||||||
\(921\) | 1.86025e7 | − | 2.45911e7i | 0.722639 | − | 0.955278i | ||||
\(922\) | 5.30519e7i | 2.05529i | ||||||||
\(923\) | 1.08499e7 | 0.419198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.06785e7 | −0.410353 | ||||||||
\(926\) | 1.73359e6i | 0.0664383i | ||||||||
\(927\) | 2.29138e7 | − | 6.47841e6i | 0.875787 | − | 0.247611i | ||||
\(928\) | −3.48915e7 | −1.32999 | ||||||||
\(929\) | −3.36714e7 | −1.28004 | −0.640018 | − | 0.768360i | \(-0.721073\pi\) | ||||
−0.640018 | + | 0.768360i | \(0.721073\pi\) | |||||||
\(930\) | 5.42098e6 | + | 4.10081e6i | 0.205528 | + | 0.155476i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.81450e6i | 0.219267i | ||||||||
\(933\) | −1.33205e7 | − | 1.00765e7i | −0.500975 | − | 0.378973i | ||||
\(934\) | 3.39171e7i | 1.27219i | ||||||||
\(935\) | 298748.i | 0.0111757i | ||||||||
\(936\) | −3.32105e6 | − | 1.17464e7i | −0.123904 | − | 0.438242i | ||||
\(937\) | − | 3.25239e7i | − | 1.21019i | −0.796153 | − | 0.605095i | \(-0.793135\pi\) | ||
0.796153 | − | 0.605095i | \(-0.206865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.91489e6 | + | 5.17520e6i | −0.144896 | + | 0.191542i | ||||
\(940\) | 832615. | 0.0307344 | ||||||||
\(941\) | −1.62948e7 | −0.599895 | −0.299947 | − | 0.953956i | \(-0.596969\pi\) | ||||
−0.299947 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(942\) | 5.76559e6 | + | 4.36150e6i | 0.211698 | + | 0.160143i | ||||
\(943\) | − | 4.04498e7i | − | 1.48128i | ||||||
\(944\) | −9.99618e6 | −0.365093 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.92908e6 | 0.142746 | ||||||||
\(947\) | 1.21518e7i | 0.440317i | 0.975464 | + | 0.220158i | \(0.0706574\pi\) | ||||
−0.975464 | + | 0.220158i | \(0.929343\pi\) | |||||||
\(948\) | −8.90142e6 | − | 6.73366e6i | −0.321690 | − | 0.243349i | ||||
\(949\) | 2.12226e7 | 0.764948 | ||||||||
\(950\) | −5.23583e7 | −1.88225 | ||||||||
\(951\) | −2.71991e7 | + | 3.59552e7i | −0.975220 | + | 1.28917i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.91378e7i | − | 1.03926i | −0.854391 | − | 0.519630i | \(-0.826070\pi\) | ||
0.854391 | − | 0.519630i | \(-0.173930\pi\) | |||||||
\(954\) | 1.63261e7 | + | 5.77446e7i | 0.580780 | + | 2.05419i | ||||
\(955\) | − | 7.88686e6i | − | 0.279831i | ||||||
\(956\) | − | 3.80261e6i | − | 0.134567i | ||||||
\(957\) | −8.62411e6 | − | 6.52389e6i | −0.304393 | − | 0.230264i | ||||
\(958\) | − | 5.24696e7i | − | 1.84711i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.48141e6 | − | 1.12064e6i | −0.0518796 | − | 0.0392454i | ||||
\(961\) | 1.01615e7 | 0.354934 | ||||||||
\(962\) | −1.04339e7 | −0.363502 | ||||||||
\(963\) | −3.15897e7 | + | 8.93134e6i | −1.09769 | + | 0.310349i | ||||
\(964\) | 5.55047e6i | 0.192370i | ||||||||
\(965\) | 1.42030e6 | 0.0490978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.05970e7 | 1.39614 | 0.698068 | − | 0.716032i | \(-0.254043\pi\) | ||||
0.698068 | + | 0.716032i | \(0.254043\pi\) | |||||||
\(968\) | 1.82955e7i | 0.627561i | ||||||||
\(969\) | 5.19887e6 | − | 6.87254e6i | 0.177869 | − | 0.235130i | ||||
\(970\) | −2.55531e6 | −0.0871994 | ||||||||
\(971\) | 1.12136e7 | 0.381677 | 0.190838 | − | 0.981621i | \(-0.438879\pi\) | ||||
0.190838 | + | 0.981621i | \(0.438879\pi\) | |||||||
\(972\) | −1.30901e7 | − | 1.26784e6i | −0.444403 | − | 0.0430425i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 5.52478e7i | − | 1.86603i | ||||||
\(975\) | −1.13789e7 | + | 1.50421e7i | −0.383345 | + | 0.506754i | ||||
\(976\) | − | 2.57887e7i | − | 0.866572i | ||||||
\(977\) | − | 2.82925e7i | − | 0.948276i | −0.880451 | − | 0.474138i | \(-0.842760\pi\) | ||
0.880451 | − | 0.474138i | \(-0.157240\pi\) | |||||||
\(978\) | 2.71171e7 | − | 3.58469e7i | 0.906559 | − | 1.19841i | ||||
\(979\) | − | 1.31408e7i | − | 0.438194i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.96710e6 | + | 1.75684e7i | 0.164790 | + | 0.582854i | ||||
\(982\) | −5.25723e7 | −1.73972 | ||||||||
\(983\) | 3.44078e7 | 1.13573 | 0.567863 | − | 0.823123i | \(-0.307770\pi\) | ||||
0.567863 | + | 0.823123i | \(0.307770\pi\) | |||||||
\(984\) | −1.75121e7 | + | 2.31498e7i | −0.576569 | + | 0.762184i | ||||
\(985\) | 1.05257e7i | 0.345670i | ||||||||
\(986\) | −1.02424e7 | −0.335513 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.57910e7 | −0.514657 | ||||||||
\(989\) | − | 1.57354e7i | − | 0.511550i | ||||||
\(990\) | 644483. | + | 2.27951e6i | 0.0208989 | + | 0.0739184i | ||||
\(991\) | −4.97942e7 | −1.61063 | −0.805313 | − | 0.592850i | \(-0.798003\pi\) | ||||
−0.805313 | + | 0.592850i | \(0.798003\pi\) | |||||||
\(992\) | −2.07663e7 | −0.670007 | ||||||||
\(993\) | 4.32331e7 | + | 3.27045e7i | 1.39137 | + | 1.05253i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.30211e6i | − | 0.0416956i | ||||||
\(996\) | −1.91540e7 | − | 1.44894e7i | −0.611802 | − | 0.462810i | ||||
\(997\) | − | 1.01229e7i | − | 0.322529i | −0.986911 | − | 0.161265i | \(-0.948443\pi\) | ||
0.986911 | − | 0.161265i | \(-0.0515572\pi\) | |||||||
\(998\) | 1.58572e7i | 0.503964i | ||||||||
\(999\) | 5.06664e6 | − | 1.29824e7i | 0.160623 | − | 0.411567i |
(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 | 147.6.c.c.146.13 | 16 | ||
3.2 | odd | 2 | inner | 147.6.c.c.146.4 | 16 | ||
7.2 | even | 3 | 21.6.g.c.17.7 | yes | 16 | ||
7.3 | odd | 6 | 21.6.g.c.5.2 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 147.6.c.c.146.14 | 16 | ||
21.2 | odd | 6 | 21.6.g.c.17.2 | yes | 16 | ||
21.17 | even | 6 | 21.6.g.c.5.7 | yes | 16 | ||
21.20 | even | 2 | inner | 147.6.c.c.146.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.g.c.5.2 | ✓ | 16 | 7.3 | odd | 6 | ||
21.6.g.c.5.7 | yes | 16 | 21.17 | even | 6 | ||
21.6.g.c.17.2 | yes | 16 | 21.2 | odd | 6 | ||
21.6.g.c.17.7 | yes | 16 | 7.2 | even | 3 | ||
147.6.c.c.146.3 | 16 | 21.20 | even | 2 | inner | ||
147.6.c.c.146.4 | 16 | 3.2 | odd | 2 | inner | ||
147.6.c.c.146.13 | 16 | 1.1 | even | 1 | trivial | ||
147.6.c.c.146.14 | 16 | 7.6 | odd | 2 | inner |