Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(36.0863594579\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{145}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 36 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.52080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.52080 | −0.622395 | −0.311197 | − | 0.950345i | \(-0.600730\pi\) | ||||
−0.311197 | + | 0.950345i | \(0.600730\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −19.6040 | −0.612625 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 80.4159 | 0.620293 | 0.310147 | − | 0.950689i | \(-0.399622\pi\) | ||||
0.310147 | + | 0.950689i | \(0.399622\pi\) | |||||||
\(8\) | 181.687 | 1.00369 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −520.416 | −1.29679 | −0.648394 | − | 0.761305i | \(-0.724559\pi\) | ||||
−0.648394 | + | 0.761305i | \(0.724559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −421.664 | −0.692003 | −0.346001 | − | 0.938234i | \(-0.612461\pi\) | ||||
−0.346001 | + | 0.938234i | \(0.612461\pi\) | |||||||
\(14\) | −283.128 | −0.386067 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.3561 | −0.0120666 | ||||||||
\(17\) | 1162.67 | 0.975736 | 0.487868 | − | 0.872917i | \(-0.337775\pi\) | ||||
0.487868 | + | 0.872917i | \(0.337775\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1170.66 | 0.743952 | 0.371976 | − | 0.928242i | \(-0.378680\pi\) | ||||
0.371976 | + | 0.928242i | \(0.378680\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1832.28 | 0.807114 | ||||||||
\(23\) | 2374.48 | 0.935943 | 0.467971 | − | 0.883744i | \(-0.344985\pi\) | ||||
0.467971 | + | 0.883744i | \(0.344985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1484.59 | 0.430699 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1576.47 | −0.380007 | ||||||||
\(29\) | 7056.62 | 1.55812 | 0.779062 | − | 0.626947i | \(-0.215696\pi\) | ||||
0.779062 | + | 0.626947i | \(0.215696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5561.15 | −1.03935 | −0.519673 | − | 0.854365i | \(-0.673946\pi\) | ||||
−0.519673 | + | 0.854365i | \(0.673946\pi\) | |||||||
\(32\) | −5770.49 | −0.996179 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4093.51 | −0.607293 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2389.95 | −0.287001 | −0.143501 | − | 0.989650i | \(-0.545836\pi\) | ||||
−0.143501 | + | 0.989650i | \(0.545836\pi\) | |||||||
\(38\) | −4121.64 | −0.463032 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8388.28 | −0.779316 | −0.389658 | − | 0.920960i | \(-0.627407\pi\) | ||||
−0.389658 | + | 0.920960i | \(0.627407\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20546.6 | −1.69461 | −0.847304 | − | 0.531108i | \(-0.821776\pi\) | ||||
−0.847304 | + | 0.531108i | \(0.821776\pi\) | |||||||
\(44\) | 10202.2 | 0.794444 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8360.07 | −0.582526 | ||||||||
\(47\) | 8352.17 | 0.551512 | 0.275756 | − | 0.961228i | \(-0.411072\pi\) | ||||
0.275756 | + | 0.961228i | \(0.411072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10340.3 | −0.615236 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8266.29 | 0.423938 | ||||||||
\(53\) | 28390.6 | 1.38831 | 0.694154 | − | 0.719827i | \(-0.255779\pi\) | ||||
0.694154 | + | 0.719827i | \(0.255779\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14610.5 | 0.622582 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −24844.9 | −0.969768 | ||||||||
\(59\) | −37500.4 | −1.40251 | −0.701254 | − | 0.712911i | \(-0.747376\pi\) | ||||
−0.701254 | + | 0.712911i | \(0.747376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57311.1 | −1.97203 | −0.986017 | − | 0.166644i | \(-0.946707\pi\) | ||||
−0.986017 | + | 0.166644i | \(0.946707\pi\) | |||||||
\(62\) | 19579.7 | 0.646884 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 20712.1 | 0.632083 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45848.9 | 1.24779 | 0.623895 | − | 0.781508i | \(-0.285549\pi\) | ||||
0.623895 | + | 0.781508i | \(0.285549\pi\) | |||||||
\(68\) | −22792.9 | −0.597760 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −41510.8 | −0.977271 | −0.488636 | − | 0.872488i | \(-0.662505\pi\) | ||||
−0.488636 | + | 0.872488i | \(0.662505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76806.5 | −1.68691 | −0.843453 | − | 0.537203i | \(-0.819481\pi\) | ||||
−0.843453 | + | 0.537203i | \(0.819481\pi\) | |||||||
\(74\) | 8414.52 | 0.178628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22949.5 | −0.455763 | ||||||||
\(77\) | −41849.7 | −0.804389 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7008.26 | −0.126341 | −0.0631703 | − | 0.998003i | \(-0.520121\pi\) | ||||
−0.0631703 | + | 0.998003i | \(0.520121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 29533.4 | 0.485042 | ||||||||
\(83\) | −93271.1 | −1.48611 | −0.743057 | − | 0.669229i | \(-0.766625\pi\) | ||||
−0.743057 | + | 0.669229i | \(0.766625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 72340.5 | 1.05472 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −94552.9 | −1.30157 | ||||||||
\(89\) | −7074.70 | −0.0946745 | −0.0473372 | − | 0.998879i | \(-0.515074\pi\) | ||||
−0.0473372 | + | 0.998879i | \(0.515074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −33908.5 | −0.429245 | ||||||||
\(92\) | −46549.3 | −0.573382 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −29406.3 | −0.343258 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −22429.9 | −0.242046 | −0.121023 | − | 0.992650i | \(-0.538617\pi\) | ||||
−0.121023 | + | 0.992650i | \(0.538617\pi\) | |||||||
\(98\) | 36406.0 | 0.382920 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107340. | 1.04703 | 0.523515 | − | 0.852017i | \(-0.324621\pi\) | ||||
0.523515 | + | 0.852017i | \(0.324621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14473.5 | 0.134425 | 0.0672125 | − | 0.997739i | \(-0.478589\pi\) | ||||
0.0672125 | + | 0.997739i | \(0.478589\pi\) | |||||||
\(104\) | −76610.9 | −0.694556 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −99957.7 | −0.864075 | ||||||||
\(107\) | 47956.9 | 0.404941 | 0.202470 | − | 0.979288i | \(-0.435103\pi\) | ||||
0.202470 | + | 0.979288i | \(0.435103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −67023.6 | −0.540333 | −0.270167 | − | 0.962814i | \(-0.587079\pi\) | ||||
−0.270167 | + | 0.962814i | \(0.587079\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −993.631 | −0.00748480 | ||||||||
\(113\) | −7799.34 | −0.0574595 | −0.0287297 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287297 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −138338. | −0.954545 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 132031. | 0.872914 | ||||||||
\(119\) | 93496.8 | 0.605243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 109782. | 0.681658 | ||||||||
\(122\) | 201781. | 1.22738 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 109021. | 0.636729 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −157992. | −0.869214 | −0.434607 | − | 0.900620i | \(-0.643113\pi\) | ||||
−0.434607 | + | 0.900620i | \(0.643113\pi\) | |||||||
\(128\) | 111732. | 0.602774 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −328644. | −1.67320 | −0.836600 | − | 0.547814i | \(-0.815460\pi\) | ||||
−0.836600 | + | 0.547814i | \(0.815460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 94139.3 | 0.461468 | ||||||||
\(134\) | −161425. | −0.776618 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 211241. | 0.979336 | ||||||||
\(137\) | −297430. | −1.35389 | −0.676944 | − | 0.736034i | \(-0.736696\pi\) | ||||
−0.676944 | + | 0.736034i | \(0.736696\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16801.8 | −0.0737594 | −0.0368797 | − | 0.999320i | \(-0.511742\pi\) | ||||
−0.0368797 | + | 0.999320i | \(0.511742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 146151. | 0.608249 | ||||||||
\(143\) | 219441. | 0.897381 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 270420. | 1.04992 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 46852.5 | 0.175824 | ||||||||
\(149\) | 490724. | 1.81081 | 0.905403 | − | 0.424553i | \(-0.139569\pi\) | ||||
0.905403 | + | 0.424553i | \(0.139569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 132845. | 0.474137 | 0.237069 | − | 0.971493i | \(-0.423813\pi\) | ||||
0.237069 | + | 0.971493i | \(0.423813\pi\) | |||||||
\(152\) | 212693. | 0.746697 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 147344. | 0.500647 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −300751. | −0.973772 | −0.486886 | − | 0.873465i | \(-0.661867\pi\) | ||||
−0.486886 | + | 0.873465i | \(0.661867\pi\) | |||||||
\(158\) | 24674.7 | 0.0786337 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 190946. | 0.580559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 663660. | 1.95649 | 0.978243 | − | 0.207464i | \(-0.0665209\pi\) | ||||
0.978243 | + | 0.207464i | \(0.0665209\pi\) | |||||||
\(164\) | 164444. | 0.477428 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 328389. | 0.924949 | ||||||||
\(167\) | −198828. | −0.551678 | −0.275839 | − | 0.961204i | \(-0.588956\pi\) | ||||
−0.275839 | + | 0.961204i | \(0.588956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −193493. | −0.521132 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 402796. | 1.03816 | ||||||||
\(173\) | −425570. | −1.08108 | −0.540538 | − | 0.841320i | \(-0.681779\pi\) | ||||
−0.540538 | + | 0.841320i | \(0.681779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6430.34 | 0.0156478 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24908.6 | 0.0589249 | ||||||||
\(179\) | −271380. | −0.633061 | −0.316530 | − | 0.948582i | \(-0.602518\pi\) | ||||
−0.316530 | + | 0.948582i | \(0.602518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 390577. | 0.886156 | 0.443078 | − | 0.896483i | \(-0.353886\pi\) | ||||
0.443078 | + | 0.896483i | \(0.353886\pi\) | |||||||
\(182\) | 119385. | 0.267160 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 431413. | 0.939396 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −605070. | −1.26532 | ||||||||
\(188\) | −163736. | −0.337870 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −185922. | −0.368764 | −0.184382 | − | 0.982855i | \(-0.559028\pi\) | ||||
−0.184382 | + | 0.982855i | \(0.559028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 774298. | 1.49629 | 0.748143 | − | 0.663537i | \(-0.230946\pi\) | ||||
0.748143 | + | 0.663537i | \(0.230946\pi\) | |||||||
\(194\) | 78971.1 | 0.150648 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 202711. | 0.376909 | ||||||||
\(197\) | −39823.2 | −0.0731090 | −0.0365545 | − | 0.999332i | \(-0.511638\pi\) | ||||
−0.0365545 | + | 0.999332i | \(0.511638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20033.4 | −0.0358610 | −0.0179305 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179305 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −377923. | −0.651666 | ||||||||
\(203\) | 567465. | 0.966493 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −50958.2 | −0.0836654 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5210.14 | 0.00835009 | ||||||||
\(209\) | −609228. | −0.964748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −231466. | −0.357917 | −0.178958 | − | 0.983857i | \(-0.557273\pi\) | ||||
−0.178958 | + | 0.983857i | \(0.557273\pi\) | |||||||
\(212\) | −556570. | −0.850511 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −168846. | −0.252033 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −447205. | −0.644700 | ||||||||
\(218\) | 235977. | 0.336301 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −490254. | −0.675212 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −134460. | −0.181063 | −0.0905315 | − | 0.995894i | \(-0.528857\pi\) | ||||
−0.0905315 | + | 0.995894i | \(0.528857\pi\) | |||||||
\(224\) | −464039. | −0.617923 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27459.9 | 0.0357625 | ||||||||
\(227\) | 1.48703e6 | 1.91538 | 0.957690 | − | 0.287803i | \(-0.0929248\pi\) | ||||
0.957690 | + | 0.287803i | \(0.0929248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.23314e6 | −1.55390 | −0.776950 | − | 0.629563i | \(-0.783234\pi\) | ||||
−0.776950 | + | 0.629563i | \(0.783234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.28210e6 | 1.56387 | ||||||||
\(233\) | −941066. | −1.13561 | −0.567806 | − | 0.823162i | \(-0.692208\pi\) | ||||
−0.567806 | + | 0.823162i | \(0.692208\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 735157. | 0.859211 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −329183. | −0.376700 | ||||||||
\(239\) | −835483. | −0.946113 | −0.473056 | − | 0.881032i | \(-0.656849\pi\) | ||||
−0.473056 | + | 0.881032i | \(0.656849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 32145.1 | 0.0356511 | 0.0178255 | − | 0.999841i | \(-0.494326\pi\) | ||||
0.0178255 | + | 0.999841i | \(0.494326\pi\) | |||||||
\(242\) | −386519. | −0.424261 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.12353e6 | 1.20812 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −493623. | −0.514817 | ||||||||
\(248\) | −1.01039e6 | −1.04318 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 680645. | 0.681924 | 0.340962 | − | 0.940077i | \(-0.389247\pi\) | ||||
0.340962 | + | 0.940077i | \(0.389247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23572e6 | −1.21372 | ||||||||
\(254\) | 556259. | 0.540995 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.05617e6 | −1.00725 | ||||||||
\(257\) | −959946. | −0.906596 | −0.453298 | − | 0.891359i | \(-0.649753\pi\) | ||||
−0.453298 | + | 0.891359i | \(0.649753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −192190. | −0.178025 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.15709e6 | 1.04139 | ||||||||
\(263\) | 828601. | 0.738680 | 0.369340 | − | 0.929294i | \(-0.379584\pi\) | ||||
0.369340 | + | 0.929294i | \(0.379584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −331446. | −0.287216 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −898821. | −0.764427 | ||||||||
\(269\) | 1.47945e6 | 1.24658 | 0.623290 | − | 0.781991i | \(-0.285796\pi\) | ||||
0.623290 | + | 0.781991i | \(0.285796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −812554. | −0.672093 | −0.336046 | − | 0.941845i | \(-0.609090\pi\) | ||||
−0.336046 | + | 0.941845i | \(0.609090\pi\) | |||||||
\(272\) | −14366.1 | −0.0117738 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.04719e6 | 0.842653 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −275667. | −0.215866 | −0.107933 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107933 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(278\) | 59155.6 | 0.0459075 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 509442. | 0.384883 | 0.192442 | − | 0.981308i | \(-0.438359\pi\) | ||||
0.192442 | + | 0.981308i | \(0.438359\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −986519. | −0.732216 | −0.366108 | − | 0.930572i | \(-0.619310\pi\) | ||||
−0.366108 | + | 0.930572i | \(0.619310\pi\) | |||||||
\(284\) | 813777. | 0.598700 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −772606. | −0.558525 | ||||||||
\(287\) | −674552. | −0.483404 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −68065.9 | −0.0479386 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.50571e6 | 1.03344 | ||||||||
\(293\) | 201092. | 0.136844 | 0.0684219 | − | 0.997656i | \(-0.478204\pi\) | ||||
0.0684219 | + | 0.997656i | \(0.478204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −434223. | −0.288060 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.72774e6 | −1.12704 | ||||||||
\(299\) | −1.00123e6 | −0.647675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.65228e6 | −1.05115 | ||||||||
\(302\) | −467722. | −0.295101 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14464.8 | −0.00897694 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 982845. | 0.595167 | 0.297584 | − | 0.954696i | \(-0.403819\pi\) | ||||
0.297584 | + | 0.954696i | \(0.403819\pi\) | |||||||
\(308\) | 820422. | 0.492788 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.70689e6 | −1.00070 | −0.500351 | − | 0.865823i | \(-0.666796\pi\) | ||||
−0.500351 | + | 0.865823i | \(0.666796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 511933. | 0.295360 | 0.147680 | − | 0.989035i | \(-0.452819\pi\) | ||||
0.147680 | + | 0.989035i | \(0.452819\pi\) | |||||||
\(314\) | 1.05888e6 | 0.606071 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 137390. | 0.0773993 | ||||||||
\(317\) | 2.51314e6 | 1.40465 | 0.702325 | − | 0.711857i | \(-0.252145\pi\) | ||||
0.702325 | + | 0.711857i | \(0.252145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.67238e6 | −2.02055 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −672283. | −0.361337 | ||||||||
\(323\) | 1.36108e6 | 0.725901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.33661e6 | −1.21771 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.52404e6 | −0.782191 | ||||||||
\(329\) | 671648. | 0.342099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.89334e6 | −0.949857 | −0.474928 | − | 0.880024i | \(-0.657526\pi\) | ||||
−0.474928 | + | 0.880024i | \(0.657526\pi\) | |||||||
\(332\) | 1.82849e6 | 0.910430 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 700032. | 0.343361 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.29119e6 | −1.57862 | −0.789310 | − | 0.613994i | \(-0.789562\pi\) | ||||
−0.789310 | + | 0.613994i | \(0.789562\pi\) | |||||||
\(338\) | 681248. | 0.324350 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.89411e6 | 1.34781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.18307e6 | −1.00192 | ||||||||
\(344\) | −3.73306e6 | −1.70086 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.49835e6 | 0.672856 | ||||||||
\(347\) | −182036. | −0.0811584 | −0.0405792 | − | 0.999176i | \(-0.512920\pi\) | ||||
−0.0405792 | + | 0.999176i | \(0.512920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 796176. | 0.349901 | 0.174951 | − | 0.984577i | \(-0.444023\pi\) | ||||
0.174951 | + | 0.984577i | \(0.444023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00305e6 | 1.29183 | ||||||||
\(353\) | 727614. | 0.310788 | 0.155394 | − | 0.987853i | \(-0.450335\pi\) | ||||
0.155394 | + | 0.987853i | \(0.450335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 138692. | 0.0579999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 955475. | 0.394014 | ||||||||
\(359\) | 2.55650e6 | 1.04691 | 0.523454 | − | 0.852054i | \(-0.324643\pi\) | ||||
0.523454 | + | 0.852054i | \(0.324643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.10567e6 | −0.446535 | ||||||||
\(362\) | −1.37514e6 | −0.551539 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 664742. | 0.262966 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.15447e6 | −0.834977 | −0.417489 | − | 0.908682i | \(-0.637090\pi\) | ||||
−0.417489 | + | 0.908682i | \(0.637090\pi\) | |||||||
\(368\) | −29339.5 | −0.0112936 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.28306e6 | 0.861158 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.61293e6 | 1.34458 | 0.672291 | − | 0.740287i | \(-0.265311\pi\) | ||||
0.672291 | + | 0.740287i | \(0.265311\pi\) | |||||||
\(374\) | 2.13033e6 | 0.787531 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.51748e6 | 0.553547 | ||||||||
\(377\) | −2.97552e6 | −1.07823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 660411. | 0.236165 | 0.118083 | − | 0.993004i | \(-0.462325\pi\) | ||||
0.118083 | + | 0.993004i | \(0.462325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 654595. | 0.229517 | ||||||||
\(383\) | −5.10573e6 | −1.77853 | −0.889264 | − | 0.457395i | \(-0.848783\pi\) | ||||
−0.889264 | + | 0.457395i | \(0.848783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.72615e6 | −0.931281 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 439715. | 0.148283 | ||||||||
\(389\) | −492425. | −0.164993 | −0.0824966 | − | 0.996591i | \(-0.526289\pi\) | ||||
−0.0824966 | + | 0.996591i | \(0.526289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.76073e6 | 0.913233 | ||||||||
\(392\) | −1.87870e6 | −0.617506 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 140210. | 0.0455027 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.72078e6 | 0.866397 | 0.433199 | − | 0.901298i | \(-0.357385\pi\) | ||||
0.433199 | + | 0.901298i | \(0.357385\pi\) | |||||||
\(398\) | 70533.6 | 0.0223197 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −204131. | −0.0633941 | −0.0316970 | − | 0.999498i | \(-0.510091\pi\) | ||||
−0.0316970 | + | 0.999498i | \(0.510091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.34494e6 | 0.719231 | ||||||||
\(404\) | −2.10429e6 | −0.641436 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.99793e6 | −0.601541 | ||||||||
\(407\) | 1.24377e6 | 0.372180 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −468364. | −0.138444 | −0.0692221 | − | 0.997601i | \(-0.522052\pi\) | ||||
−0.0692221 | + | 0.997601i | \(0.522052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −283738. | −0.0823521 | ||||||||
\(413\) | −3.01563e6 | −0.869967 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.43321e6 | 0.689359 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.14497e6 | 0.600454 | ||||||||
\(419\) | −2.45205e6 | −0.682328 | −0.341164 | − | 0.940004i | \(-0.610821\pi\) | ||||
−0.341164 | + | 0.940004i | \(0.610821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.51677e6 | 1.51698 | 0.758489 | − | 0.651686i | \(-0.225938\pi\) | ||||
0.758489 | + | 0.651686i | \(0.225938\pi\) | |||||||
\(422\) | 814946. | 0.222765 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.15822e6 | 1.39343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.60873e6 | −1.22324 | ||||||||
\(428\) | −940146. | −0.248077 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.25875e6 | 0.585701 | 0.292850 | − | 0.956158i | \(-0.405396\pi\) | ||||
0.292850 | + | 0.956158i | \(0.405396\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.02853e6 | 0.519951 | 0.259976 | − | 0.965615i | \(-0.416285\pi\) | ||||
0.259976 | + | 0.965615i | \(0.416285\pi\) | |||||||
\(434\) | 1.57452e6 | 0.401258 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.31393e6 | 0.331021 | ||||||||
\(437\) | 2.77970e6 | 0.696297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.74449e6 | −0.432024 | −0.216012 | − | 0.976391i | \(-0.569305\pi\) | ||||
−0.216012 | + | 0.976391i | \(0.569305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.72608e6 | 0.420249 | ||||||||
\(443\) | 987200. | 0.238999 | 0.119499 | − | 0.992834i | \(-0.461871\pi\) | ||||
0.119499 | + | 0.992834i | \(0.461871\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 473405. | 0.112693 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.66558e6 | 0.392077 | ||||||||
\(449\) | −7.78246e6 | −1.82180 | −0.910901 | − | 0.412624i | \(-0.864612\pi\) | ||||
−0.910901 | + | 0.412624i | \(0.864612\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.36540e6 | 1.01061 | ||||||||
\(452\) | 152898. | 0.0352011 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.23553e6 | −1.19212 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.01729e6 | −0.899793 | −0.449896 | − | 0.893081i | \(-0.648539\pi\) | ||||
−0.449896 | + | 0.893081i | \(0.648539\pi\) | |||||||
\(458\) | 4.34163e6 | 0.967139 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.42822e6 | −0.313000 | −0.156500 | − | 0.987678i | \(-0.550021\pi\) | ||||
−0.156500 | + | 0.987678i | \(0.550021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.56420e6 | 0.555904 | 0.277952 | − | 0.960595i | \(-0.410344\pi\) | ||||
0.277952 | + | 0.960595i | \(0.410344\pi\) | |||||||
\(464\) | −87192.7 | −0.0188012 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.31330e6 | 0.706800 | ||||||||
\(467\) | 2.07027e6 | 0.439272 | 0.219636 | − | 0.975582i | \(-0.429513\pi\) | ||||
0.219636 | + | 0.975582i | \(0.429513\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.68698e6 | 0.773996 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.81334e6 | −1.40768 | ||||||||
\(473\) | 1.06928e7 | 2.19755 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.83291e6 | −0.370787 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.94157e6 | 0.588856 | ||||||||
\(479\) | 3.78107e6 | 0.752967 | 0.376484 | − | 0.926423i | \(-0.377133\pi\) | ||||
0.376484 | + | 0.926423i | \(0.377133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00775e6 | 0.198606 | ||||||||
\(482\) | −113176. | −0.0221890 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.15216e6 | −0.417601 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.73232e6 | 1.47736 | 0.738682 | − | 0.674054i | \(-0.235449\pi\) | ||||
0.738682 | + | 0.674054i | \(0.235449\pi\) | |||||||
\(488\) | −1.04127e7 | −1.97931 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.20848e6 | −1.53659 | −0.768296 | − | 0.640094i | \(-0.778895\pi\) | ||||
−0.768296 | + | 0.640094i | \(0.778895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.20449e6 | 1.52032 | ||||||||
\(494\) | 1.73795e6 | 0.320419 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 68714.4 | 0.0125413 | ||||||||
\(497\) | −3.33813e6 | −0.606195 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 58456.0 | 0.0105094 | 0.00525470 | − | 0.999986i | \(-0.498327\pi\) | ||||
0.00525470 | + | 0.999986i | \(0.498327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.39641e6 | −0.424426 | ||||||||
\(503\) | −4.83775e6 | −0.852557 | −0.426278 | − | 0.904592i | \(-0.640176\pi\) | ||||
−0.426278 | + | 0.904592i | \(0.640176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.35071e6 | 0.755413 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.09728e6 | 0.532502 | ||||||||
\(509\) | 1.42306e6 | 0.243460 | 0.121730 | − | 0.992563i | \(-0.461156\pi\) | ||||
0.121730 | + | 0.992563i | \(0.461156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.17647e6 | −1.04638 | ||||||||
\(512\) | 143140. | 0.0241315 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.37977e6 | 0.564261 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.34660e6 | −0.715194 | ||||||||
\(518\) | 676662. | 0.110802 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.26166e6 | −0.849236 | −0.424618 | − | 0.905373i | \(-0.639592\pi\) | ||||
−0.424618 | + | 0.905373i | \(0.639592\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.53462e6 | −1.04464 | −0.522319 | − | 0.852750i | \(-0.674933\pi\) | ||||
−0.522319 | + | 0.852750i | \(0.674933\pi\) | |||||||
\(524\) | 6.44274e6 | 1.02504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.91734e6 | −0.459751 | ||||||||
\(527\) | −6.46576e6 | −1.01413 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −798179. | −0.124011 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.84551e6 | −0.282707 | ||||||||
\(533\) | 3.53704e6 | 0.539289 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.33015e6 | 1.25239 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.20885e6 | −0.775865 | ||||||||
\(539\) | 5.38124e6 | 0.797831 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.38001e6 | 1.37788 | 0.688938 | − | 0.724820i | \(-0.258077\pi\) | ||||
0.688938 | + | 0.724820i | \(0.258077\pi\) | |||||||
\(542\) | 2.86084e6 | 0.418307 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.70915e6 | −0.972008 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.75854e6 | 1.10869 | 0.554347 | − | 0.832286i | \(-0.312968\pi\) | ||||
0.554347 | + | 0.832286i | \(0.312968\pi\) | |||||||
\(548\) | 5.83081e6 | 0.829425 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.26087e6 | 1.15917 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −563576. | −0.0783682 | ||||||||
\(554\) | 970567. | 0.134354 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 329381. | 0.0451868 | ||||||||
\(557\) | 7.61675e6 | 1.04024 | 0.520118 | − | 0.854094i | \(-0.325888\pi\) | ||||
0.520118 | + | 0.854094i | \(0.325888\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.66377e6 | 1.17267 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.79364e6 | −0.239549 | ||||||||
\(563\) | 2.87806e6 | 0.382674 | 0.191337 | − | 0.981524i | \(-0.438718\pi\) | ||||
0.191337 | + | 0.981524i | \(0.438718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.47333e6 | 0.455728 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.54198e6 | −0.980876 | ||||||||
\(569\) | 6.23789e6 | 0.807713 | 0.403856 | − | 0.914822i | \(-0.367670\pi\) | ||||
0.403856 | + | 0.914822i | \(0.367670\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.14465e7 | −1.46920 | −0.734601 | − | 0.678499i | \(-0.762631\pi\) | ||||
−0.734601 | + | 0.678499i | \(0.762631\pi\) | |||||||
\(572\) | −4.30191e6 | −0.549758 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.37496e6 | 0.300868 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.48097e7 | 1.85186 | 0.925928 | − | 0.377700i | \(-0.123285\pi\) | ||||
0.925928 | + | 0.377700i | \(0.123285\pi\) | |||||||
\(578\) | 239646. | 0.0298367 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.50048e6 | −0.921826 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.47749e7 | −1.80034 | ||||||||
\(584\) | −1.39548e7 | −1.69313 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −708003. | −0.0851708 | ||||||||
\(587\) | −7.19551e6 | −0.861919 | −0.430959 | − | 0.902371i | \(-0.641825\pi\) | ||||
−0.430959 | + | 0.902371i | \(0.641825\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.51019e6 | −0.773224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 29530.6 | 0.00346312 | ||||||||
\(593\) | −2.20920e6 | −0.257987 | −0.128994 | − | 0.991645i | \(-0.541175\pi\) | ||||
−0.128994 | + | 0.991645i | \(0.541175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.62015e6 | −1.10934 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.52514e6 | 0.403110 | ||||||||
\(599\) | 309553. | 0.0352508 | 0.0176254 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176254 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.93532e6 | −0.670283 | −0.335141 | − | 0.942168i | \(-0.608784\pi\) | ||||
−0.335141 | + | 0.942168i | \(0.608784\pi\) | |||||||
\(602\) | 5.81733e6 | 0.654233 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.60430e6 | −0.290468 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.30961e6 | −0.474751 | −0.237376 | − | 0.971418i | \(-0.576287\pi\) | ||||
−0.237376 | + | 0.971418i | \(0.576287\pi\) | |||||||
\(608\) | −6.75525e6 | −0.741110 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.52181e6 | −0.381648 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.06508e7 | −1.14480 | −0.572402 | − | 0.819973i | \(-0.693988\pi\) | ||||
−0.572402 | + | 0.819973i | \(0.693988\pi\) | |||||||
\(614\) | −3.46040e6 | −0.370429 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.60356e6 | −0.807356 | ||||||||
\(617\) | 1.57352e7 | 1.66403 | 0.832014 | − | 0.554754i | \(-0.187188\pi\) | ||||
0.832014 | + | 0.554754i | \(0.187188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.90140e6 | 0.409255 | 0.204627 | − | 0.978840i | \(-0.434402\pi\) | ||||
0.204627 | + | 0.978840i | \(0.434402\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.00962e6 | 0.622832 | ||||||||
\(623\) | −568918. | −0.0587259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.80241e6 | −0.183831 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.89591e6 | 0.596557 | ||||||||
\(629\) | −2.77871e6 | −0.280038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.35074e7 | −1.35051 | −0.675254 | − | 0.737586i | \(-0.735966\pi\) | ||||
−0.675254 | + | 0.737586i | \(0.735966\pi\) | |||||||
\(632\) | −1.27331e6 | −0.126807 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.84825e6 | −0.874247 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.36012e6 | 0.425745 | ||||||||
\(638\) | 1.29297e7 | 1.25758 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.66035e6 | −0.736382 | −0.368191 | − | 0.929750i | \(-0.620023\pi\) | ||||
−0.368191 | + | 0.929750i | \(0.620023\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.12191e7 | −1.07012 | −0.535060 | − | 0.844814i | \(-0.679711\pi\) | ||||
−0.535060 | + | 0.844814i | \(0.679711\pi\) | |||||||
\(644\) | −3.74331e6 | −0.355665 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.79209e6 | −0.451797 | ||||||||
\(647\) | −1.67988e7 | −1.57767 | −0.788835 | − | 0.614604i | \(-0.789316\pi\) | ||||
−0.788835 | + | 0.614604i | \(0.789316\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.95158e7 | 1.81876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.30104e7 | −1.19859 | ||||||||
\(653\) | −9.92579e6 | −0.910924 | −0.455462 | − | 0.890255i | \(-0.650526\pi\) | ||||
−0.455462 | + | 0.890255i | \(0.650526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 103647. | 0.00940365 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.36474e6 | −0.212921 | ||||||||
\(659\) | −7.26028e6 | −0.651238 | −0.325619 | − | 0.945501i | \(-0.605573\pi\) | ||||
−0.325619 | + | 0.945501i | \(0.605573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.89224e6 | 0.435516 | 0.217758 | − | 0.976003i | \(-0.430126\pi\) | ||||
0.217758 | + | 0.976003i | \(0.430126\pi\) | |||||||
\(662\) | 6.66606e6 | 0.591186 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.69462e7 | −1.49160 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.67558e7 | 1.45831 | ||||||||
\(668\) | 3.89781e6 | 0.337971 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.98256e7 | 2.55731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.33639e6 | −0.709481 | −0.354740 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354740 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(674\) | 1.15876e7 | 0.982526 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.79323e6 | 0.319258 | ||||||||
\(677\) | −1.56824e7 | −1.31505 | −0.657525 | − | 0.753433i | \(-0.728396\pi\) | ||||
−0.657525 | + | 0.753433i | \(0.728396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.80372e6 | −0.150140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.01896e7 | −0.838871 | ||||||||
\(683\) | −1.39324e7 | −1.14281 | −0.571407 | − | 0.820667i | \(-0.693602\pi\) | ||||
−0.571407 | + | 0.820667i | \(0.693602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.68616e6 | 0.623590 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 253877. | 0.0204481 | ||||||||
\(689\) | −1.19713e7 | −0.960713 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.60504e6 | −0.287220 | −0.143610 | − | 0.989634i | \(-0.545871\pi\) | ||||
−0.143610 | + | 0.989634i | \(0.545871\pi\) | |||||||
\(692\) | 8.34288e6 | 0.662294 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 640912. | 0.0505126 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.75277e6 | −0.760407 | ||||||||
\(698\) | −2.80318e6 | −0.217777 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.10596e6 | 0.392448 | 0.196224 | − | 0.980559i | \(-0.437132\pi\) | ||||
0.196224 | + | 0.980559i | \(0.437132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.79781e6 | −0.213515 | ||||||||
\(704\) | −1.07789e7 | −0.819678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.56178e6 | −0.193433 | ||||||||
\(707\) | 8.63186e6 | 0.649465 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.89610e6 | −0.664637 | −0.332318 | − | 0.943167i | \(-0.607831\pi\) | ||||
−0.332318 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.28538e6 | −0.0950237 | ||||||||
\(713\) | −1.32049e7 | −0.972769 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.32013e6 | 0.387829 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.00090e6 | −0.651591 | ||||||||
\(719\) | 1.71802e7 | 1.23938 | 0.619691 | − | 0.784846i | \(-0.287258\pi\) | ||||
0.619691 | + | 0.784846i | \(0.287258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.16390e6 | 0.0833829 | ||||||||
\(722\) | 3.89282e6 | 0.277921 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.65687e6 | −0.542881 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.48569e7 | 1.04254 | 0.521270 | − | 0.853392i | \(-0.325458\pi\) | ||||
0.521270 | + | 0.853392i | \(0.325458\pi\) | |||||||
\(728\) | −6.16074e6 | −0.430828 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.38888e7 | −1.65349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.97878e7 | 1.36031 | 0.680154 | − | 0.733069i | \(-0.261913\pi\) | ||||
0.680154 | + | 0.733069i | \(0.261913\pi\) | |||||||
\(734\) | 7.58544e6 | 0.519686 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.37019e7 | −0.932367 | ||||||||
\(737\) | −2.38605e7 | −1.61812 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26011e7 | 0.848783 | 0.424392 | − | 0.905479i | \(-0.360488\pi\) | ||||
0.424392 | + | 0.905479i | \(0.360488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.03819e6 | −0.535980 | ||||||||
\(743\) | 1.19632e7 | 0.795014 | 0.397507 | − | 0.917599i | \(-0.369875\pi\) | ||||
0.397507 | + | 0.917599i | \(0.369875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.27204e7 | −0.836860 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.18618e7 | 0.775168 | ||||||||
\(749\) | 3.85650e6 | 0.251182 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.44504e7 | 0.934933 | 0.467466 | − | 0.884011i | \(-0.345167\pi\) | ||||
0.467466 | + | 0.884011i | \(0.345167\pi\) | |||||||
\(752\) | −103201. | −0.00665485 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.04762e7 | 0.671082 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.08448e7 | 1.32208 | 0.661040 | − | 0.750351i | \(-0.270115\pi\) | ||||
0.661040 | + | 0.750351i | \(0.270115\pi\) | |||||||
\(758\) | −2.32517e6 | −0.146988 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.27907e6 | 0.393037 | 0.196518 | − | 0.980500i | \(-0.437036\pi\) | ||||
0.196518 | + | 0.980500i | \(0.437036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.38977e6 | −0.335165 | ||||||||
\(764\) | 3.64482e6 | 0.225914 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.79762e7 | 1.10695 | ||||||||
\(767\) | 1.58126e7 | 0.970540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.28302e6 | 0.383136 | 0.191568 | − | 0.981479i | \(-0.438643\pi\) | ||||
0.191568 | + | 0.981479i | \(0.438643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.51793e7 | −0.916662 | ||||||||
\(773\) | 2.10517e7 | 1.26718 | 0.633591 | − | 0.773668i | \(-0.281580\pi\) | ||||
0.633591 | + | 0.773668i | \(0.281580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.07522e6 | −0.242939 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.73373e6 | 0.102691 | ||||||||
\(779\) | −9.81979e6 | −0.579774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.16029e7 | 1.26731 | ||||||||
\(782\) | −9.71996e6 | −0.568392 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 127766. | 0.00742378 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.95429e6 | 0.112474 | 0.0562370 | − | 0.998417i | \(-0.482090\pi\) | ||||
0.0562370 | + | 0.998417i | \(0.482090\pi\) | |||||||
\(788\) | 780694. | 0.0447884 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −627191. | −0.0356417 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.41660e7 | 1.36465 | ||||||||
\(794\) | −9.57931e6 | −0.539241 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 392735. | 0.0219693 | ||||||||
\(797\) | 1.56292e7 | 0.871547 | 0.435774 | − | 0.900056i | \(-0.356475\pi\) | ||||
0.435774 | + | 0.900056i | \(0.356475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.71078e6 | 0.538130 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 718705. | 0.0394562 | ||||||||
\(803\) | 3.99713e7 | 2.18756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.25604e6 | −0.447646 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.95023e7 | 1.05089 | ||||||||
\(809\) | 8.57518e6 | 0.460651 | 0.230326 | − | 0.973114i | \(-0.426021\pi\) | ||||
0.230326 | + | 0.973114i | \(0.426021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.81206e6 | −0.310297 | −0.155149 | − | 0.987891i | \(-0.549586\pi\) | ||||
−0.155149 | + | 0.987891i | \(0.549586\pi\) | |||||||
\(812\) | −1.11246e7 | −0.592098 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.37905e6 | −0.231643 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.40530e7 | −1.26071 | ||||||||
\(818\) | 1.64901e6 | 0.0861670 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.43637e6 | −0.436815 | −0.218408 | − | 0.975858i | \(-0.570086\pi\) | ||||
−0.218408 | + | 0.975858i | \(0.570086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.48078e6 | 0.179133 | 0.0895667 | − | 0.995981i | \(-0.471452\pi\) | ||||
0.0895667 | + | 0.995981i | \(0.471452\pi\) | |||||||
\(824\) | 2.62965e6 | 0.134921 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.06174e7 | 0.541463 | ||||||||
\(827\) | 3.76000e7 | 1.91172 | 0.955861 | − | 0.293820i | \(-0.0949268\pi\) | ||||
0.955861 | + | 0.293820i | \(0.0949268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.78630e7 | 0.902752 | 0.451376 | − | 0.892334i | \(-0.350933\pi\) | ||||
0.451376 | + | 0.892334i | \(0.350933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.73355e6 | −0.437404 | ||||||||
\(833\) | −1.20223e7 | −0.600308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.19433e7 | 0.591028 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.63315e6 | 0.424678 | ||||||||
\(839\) | 1.01511e7 | 0.497861 | 0.248931 | − | 0.968521i | \(-0.419921\pi\) | ||||
0.248931 | + | 0.968521i | \(0.419921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.92847e7 | 1.42775 | ||||||||
\(842\) | −1.94234e7 | −0.944160 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.53766e6 | 0.219269 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.82820e6 | 0.422828 | ||||||||
\(848\) | −350799. | −0.0167521 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.67489e6 | −0.268617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.57022e7 | 1.20948 | 0.604738 | − | 0.796425i | \(-0.293278\pi\) | ||||
0.604738 | + | 0.796425i | \(0.293278\pi\) | |||||||
\(854\) | 1.62264e7 | 0.761338 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.71315e6 | 0.406435 | ||||||||
\(857\) | 2.47250e7 | 1.14996 | 0.574982 | − | 0.818166i | \(-0.305009\pi\) | ||||
0.574982 | + | 0.818166i | \(0.305009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.01446e7 | −1.85628 | −0.928141 | − | 0.372228i | \(-0.878594\pi\) | ||||
−0.928141 | + | 0.372228i | \(0.878594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.95261e6 | −0.364537 | ||||||||
\(863\) | −3.30616e7 | −1.51111 | −0.755556 | − | 0.655084i | \(-0.772633\pi\) | ||||
−0.755556 | + | 0.655084i | \(0.772633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.14206e6 | −0.323615 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.76700e6 | 0.394959 | ||||||||
\(869\) | 3.64721e6 | 0.163837 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.93328e7 | −0.863475 | ||||||||
\(872\) | −1.21773e7 | −0.542327 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.78676e6 | −0.433371 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.39879e7 | −1.05316 | −0.526579 | − | 0.850126i | \(-0.676525\pi\) | ||||
−0.526579 | + | 0.850126i | \(0.676525\pi\) | |||||||
\(878\) | 6.14200e6 | 0.268889 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.84976e7 | 1.67107 | 0.835534 | − | 0.549439i | \(-0.185158\pi\) | ||||
0.835534 | + | 0.549439i | \(0.185158\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.51833e7 | −1.08695 | −0.543476 | − | 0.839425i | \(-0.682892\pi\) | ||||
−0.543476 | + | 0.839425i | \(0.682892\pi\) | |||||||
\(884\) | 9.61093e6 | 0.413652 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.47573e6 | −0.148752 | ||||||||
\(887\) | −3.20905e7 | −1.36952 | −0.684759 | − | 0.728770i | \(-0.740092\pi\) | ||||
−0.684759 | + | 0.728770i | \(0.740092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.27051e7 | −0.539168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.63594e6 | 0.110924 | ||||||||
\(893\) | 9.77751e6 | 0.410298 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.98507e6 | 0.373896 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.74005e7 | 1.13388 | ||||||||
\(899\) | −3.92429e7 | −1.61943 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.30088e7 | 1.35462 | ||||||||
\(902\) | −1.53697e7 | −0.628997 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.41704e6 | −0.0576715 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 463821. | 0.0187211 | 0.00936057 | − | 0.999956i | \(-0.497020\pi\) | ||||
0.00936057 | + | 0.999956i | \(0.497020\pi\) | |||||||
\(908\) | −2.91517e7 | −1.17341 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.98906e7 | −1.19327 | −0.596634 | − | 0.802513i | \(-0.703496\pi\) | ||||
−0.596634 | + | 0.802513i | \(0.703496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.85398e7 | 1.92717 | ||||||||
\(914\) | 1.41441e7 | 0.560026 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.41744e7 | 0.951957 | ||||||||
\(917\) | −2.64282e7 | −1.03787 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.02895e7 | 1.18305 | 0.591524 | − | 0.806287i | \(-0.298526\pi\) | ||||
0.591524 | + | 0.806287i | \(0.298526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.02849e6 | 0.194809 | ||||||||
\(923\) | 1.75036e7 | 0.676274 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.02803e6 | −0.345992 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.07201e7 | −1.55217 | ||||||||
\(929\) | 2.64394e7 | 1.00511 | 0.502554 | − | 0.864546i | \(-0.332394\pi\) | ||||
0.502554 | + | 0.864546i | \(0.332394\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.21049e7 | −0.457706 | ||||||||
\(932\) | 1.84486e7 | 0.695704 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.28899e6 | −0.273401 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.87274e7 | −0.696833 | −0.348416 | − | 0.937340i | \(-0.613280\pi\) | ||||
−0.348416 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(938\) | −1.29811e7 | −0.481731 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.91313e7 | 1.07247 | 0.536236 | − | 0.844068i | \(-0.319846\pi\) | ||||
0.536236 | + | 0.844068i | \(0.319846\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.99178e7 | −0.729395 | ||||||||
\(944\) | 463360. | 0.0169234 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.76471e7 | −1.36774 | ||||||||
\(947\) | 9.75601e6 | 0.353506 | 0.176753 | − | 0.984255i | \(-0.443441\pi\) | ||||
0.176753 | + | 0.984255i | \(0.443441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.23865e7 | 1.16734 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.69872e7 | 0.607476 | ||||||||
\(953\) | 4.75019e6 | 0.169425 | 0.0847127 | − | 0.996405i | \(-0.473003\pi\) | ||||
0.0847127 | + | 0.996405i | \(0.473003\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.63788e7 | 0.579612 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.33124e7 | −0.468643 | ||||||||
\(959\) | −2.39181e7 | −0.839808 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.29725e6 | 0.0802415 | ||||||||
\(962\) | −3.54810e6 | −0.123611 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −630173. | −0.0218407 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 208056. | 0.00715508 | 0.00357754 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357754 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(968\) | 1.99459e7 | 0.684173 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.65816e7 | −0.564388 | −0.282194 | − | 0.959357i | \(-0.591062\pi\) | ||||
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.35113e6 | −0.0457525 | ||||||||
\(974\) | −2.72239e7 | −0.919503 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 708145. | 0.0237957 | ||||||||
\(977\) | 1.41891e7 | 0.475575 | 0.237787 | − | 0.971317i | \(-0.423578\pi\) | ||||
0.237787 | + | 0.971317i | \(0.423578\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.68179e6 | 0.122773 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.89004e7 | 0.956367 | ||||||||
\(983\) | −4.24448e7 | −1.40101 | −0.700504 | − | 0.713649i | \(-0.747041\pi\) | ||||
−0.700504 | + | 0.713649i | \(0.747041\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.88863e7 | −0.946238 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.67698e6 | 0.315390 | ||||||||
\(989\) | −4.87876e7 | −1.58606 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.61915e7 | −1.17064 | −0.585320 | − | 0.810803i | \(-0.699031\pi\) | ||||
−0.585320 | + | 0.810803i | \(0.699031\pi\) | |||||||
\(992\) | 3.20905e7 | 1.03538 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.17529e7 | 0.377292 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.68344e6 | 0.308526 | 0.154263 | − | 0.988030i | \(-0.450700\pi\) | ||||
0.154263 | + | 0.988030i | \(0.450700\pi\) | |||||||
\(998\) | −205812. | −0.00654100 | ||||||||
\(999\) | 0 | 0 |
(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 | 225.6.a.r.1.1 | 2 | ||
3.2 | odd | 2 | 225.6.a.k.1.2 | 2 | |||
5.2 | odd | 4 | 225.6.b.j.199.2 | 4 | |||
5.3 | odd | 4 | 225.6.b.j.199.3 | 4 | |||
5.4 | even | 2 | 45.6.a.d.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 225.6.b.k.199.3 | 4 | |||
15.8 | even | 4 | 225.6.b.k.199.2 | 4 | |||
15.14 | odd | 2 | 45.6.a.f.1.1 | yes | 2 | ||
20.19 | odd | 2 | 720.6.a.y.1.2 | 2 | |||
60.59 | even | 2 | 720.6.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.6.a.d.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
45.6.a.f.1.1 | yes | 2 | 15.14 | odd | 2 | ||
225.6.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
225.6.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
225.6.b.j.199.2 | 4 | 5.2 | odd | 4 | |||
225.6.b.j.199.3 | 4 | 5.3 | odd | 4 | |||
225.6.b.k.199.2 | 4 | 15.8 | even | 4 | |||
225.6.b.k.199.3 | 4 | 15.2 | even | 4 | |||
720.6.a.y.1.2 | 2 | 20.19 | odd | 2 | |||
720.6.a.be.1.2 | 2 | 60.59 | even | 2 |