Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 229x^{3} - 272x^{2} + 7973x - 13998 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(14.6594\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.3187 | −1.75250 | −0.876248 | − | 0.481861i | \(-0.839961\pi\) | ||||
−0.876248 | + | 0.481861i | \(0.839961\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −52.2232 | −0.934197 | −0.467099 | − | 0.884205i | \(-0.654701\pi\) | ||||
−0.467099 | + | 0.884205i | \(0.654701\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 503.312 | 2.07124 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −142.342 | −0.354692 | −0.177346 | − | 0.984149i | \(-0.556751\pi\) | ||||
−0.177346 | + | 0.984149i | \(0.556751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −219.279 | −0.359864 | −0.179932 | − | 0.983679i | \(-0.557588\pi\) | ||||
−0.179932 | + | 0.983679i | \(0.557588\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1426.67 | 1.63718 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1555.97 | −1.30581 | −0.652903 | − | 0.757442i | \(-0.726449\pi\) | ||||
−0.652903 | + | 0.757442i | \(0.726449\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −372.596 | −0.236785 | −0.118393 | − | 0.992967i | \(-0.537774\pi\) | ||||
−0.118393 | + | 0.992967i | \(0.537774\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1338.62 | −0.662381 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3653.43 | 1.44006 | 0.720031 | − | 0.693942i | \(-0.244128\pi\) | ||||
0.720031 | + | 0.693942i | \(0.244128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −397.737 | −0.127276 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7111.38 | −1.87735 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4492.29 | −0.991911 | −0.495955 | − | 0.868348i | \(-0.665182\pi\) | ||||
−0.495955 | + | 0.868348i | \(0.665182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9151.19 | −1.71030 | −0.855152 | − | 0.518378i | \(-0.826536\pi\) | ||||
−0.855152 | + | 0.518378i | \(0.826536\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3888.60 | 0.621596 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2558.94 | −0.353093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3668.75 | −0.440569 | −0.220284 | − | 0.975436i | \(-0.570698\pi\) | ||||
−0.220284 | + | 0.975436i | \(0.570698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5990.41 | 0.630659 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17679.9 | −1.64255 | −0.821277 | − | 0.570530i | \(-0.806738\pi\) | ||||
−0.821277 | + | 0.570530i | \(0.806738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11082.6 | −0.914050 | −0.457025 | − | 0.889454i | \(-0.651085\pi\) | ||||
−0.457025 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −26284.5 | −1.93495 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −19707.8 | −1.30135 | −0.650673 | − | 0.759358i | \(-0.725513\pi\) | ||||
−0.650673 | + | 0.759358i | \(0.725513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42507.0 | 2.28842 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −22932.9 | −1.12142 | −0.560711 | − | 0.828012i | \(-0.689472\pi\) | ||||
−0.560711 | + | 0.828012i | \(0.689472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7433.55 | 0.331352 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10178.9 | 0.414965 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50657.1 | 1.89457 | 0.947284 | − | 0.320395i | \(-0.103816\pi\) | ||||
0.947284 | + | 0.320395i | \(0.103816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23242.6 | −0.799759 | −0.399880 | − | 0.916568i | \(-0.630948\pi\) | ||||
−0.399880 | + | 0.916568i | \(0.630948\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24662.3 | 0.782856 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11451.4 | 0.336183 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34909.7 | 0.950076 | 0.475038 | − | 0.879965i | \(-0.342434\pi\) | ||||
0.475038 | + | 0.879965i | \(0.342434\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −99807.0 | −2.52370 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36659.7 | 0.863064 | 0.431532 | − | 0.902098i | \(-0.357973\pi\) | ||||
0.431532 | + | 0.902098i | \(0.357973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28419.8 | 0.624186 | 0.312093 | − | 0.950052i | \(-0.398970\pi\) | ||||
0.312093 | + | 0.950052i | \(0.398970\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10865.7 | 0.223050 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6974.75 | −0.134061 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15866.1 | −0.286024 | −0.143012 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143012 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 71968.9 | 1.21880 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −26106.6 | −0.415964 | −0.207982 | − | 0.978133i | \(-0.566690\pi\) | ||||
−0.207982 | + | 0.978133i | \(0.566690\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 81257.6 | 1.21988 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 122724. | 1.73832 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 98204.8 | 1.31419 | 0.657094 | − | 0.753809i | \(-0.271785\pi\) | ||||
0.657094 | + | 0.753809i | \(0.271785\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10744.7 | −0.136016 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 249999. | 2.99730 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19458.2 | 0.221204 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −123942. | −1.33749 | −0.668744 | − | 0.743493i | \(-0.733168\pi\) | ||||
−0.668744 | + | 0.743493i | \(0.733168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −71642.3 | −0.734652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −115136. | −1.12307 | −0.561534 | − | 0.827454i | \(-0.689789\pi\) | ||||
−0.561534 | + | 0.827454i | \(0.689789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42730.9 | 0.396871 | 0.198435 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198435 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 69906.8 | 0.618794 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −81647.8 | −0.689422 | −0.344711 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344711 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −117518. | −0.947412 | −0.473706 | − | 0.880683i | \(-0.657084\pi\) | ||||
−0.473706 | + | 0.880683i | \(0.657084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 100225. | 0.772094 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 247972. | 1.82687 | 0.913433 | − | 0.406989i | \(-0.133421\pi\) | ||||
0.913433 | + | 0.406989i | \(0.133421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −190794. | −1.34530 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −110365. | −0.745364 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −76242.4 | −0.493548 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140790. | −0.874194 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 482991. | 2.87857 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 183969. | 1.05310 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −118457. | −0.651704 | −0.325852 | − | 0.945421i | \(-0.605651\pi\) | ||||
−0.325852 | + | 0.945421i | \(0.605651\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 302762. | 1.60187 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 282312. | 1.43731 | 0.718656 | − | 0.695366i | \(-0.244758\pi\) | ||||
0.718656 | + | 0.695366i | \(0.244758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18257.2 | −0.0894964 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 371379. | 1.75381 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −268767. | −1.22342 | −0.611708 | − | 0.791084i | \(-0.709517\pi\) | ||||
−0.611708 | + | 0.791084i | \(0.709517\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 241896. | 1.06192 | 0.530961 | − | 0.847396i | \(-0.321831\pi\) | ||||
0.530961 | + | 0.847396i | \(0.321831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 538391. | 2.28060 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31212.5 | 0.127641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 234602. | 0.926640 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −65592.2 | −0.250357 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 319446. | 1.17878 | 0.589389 | − | 0.807850i | \(-0.299369\pi\) | ||||
0.589389 | + | 0.807850i | \(0.299369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −154017. | −0.549701 | −0.274851 | − | 0.961487i | \(-0.588628\pi\) | ||||
−0.274851 | + | 0.961487i | \(0.588628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −783137. | −2.70464 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 477904. | 1.59776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 148158. | 0.479706 | 0.239853 | − | 0.970809i | \(-0.422901\pi\) | ||||
0.239853 | + | 0.970809i | \(0.422901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 626497. | 1.96529 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 179018. | 0.544292 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 433962. | 1.27933 | 0.639666 | − | 0.768653i | \(-0.279073\pi\) | ||||
0.639666 | + | 0.768653i | \(0.279073\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −203075. | −0.580693 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −568533. | −1.57748 | −0.788741 | − | 0.614726i | \(-0.789267\pi\) | ||||
−0.788741 | + | 0.614726i | \(0.789267\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −323210. | −0.870498 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −187532. | −0.490439 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −373172. | −0.947969 | −0.473984 | − | 0.880533i | \(-0.657185\pi\) | ||||
−0.473984 | + | 0.880533i | \(0.657185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19489.1 | −0.0481058 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.38389e6 | −3.32022 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −149898. | −0.349674 | −0.174837 | − | 0.984597i | \(-0.555940\pi\) | ||||
−0.174837 | + | 0.984597i | \(0.555940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −115243. | −0.261468 | −0.130734 | − | 0.991417i | \(-0.541733\pi\) | ||||
−0.130734 | + | 0.991417i | \(0.541733\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 634957. | 1.40157 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 191594. | 0.411578 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 221479. | 0.463158 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −348457. | −0.709570 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18013.1 | 0.0357278 | 0.0178639 | − | 0.999840i | \(-0.494313\pi\) | ||||
0.0178639 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 873827. | 1.68862 | 0.844310 | − | 0.535855i | \(-0.180011\pi\) | ||||
0.844310 | + | 0.535855i | \(0.180011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −312838. | −0.589160 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 148925. | 0.273402 | 0.136701 | − | 0.990612i | \(-0.456350\pi\) | ||||
0.136701 | + | 0.990612i | \(0.456350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −764586. | −1.36865 | −0.684327 | − | 0.729175i | \(-0.739904\pi\) | ||||
−0.684327 | + | 0.729175i | \(0.739904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −953686. | −1.66500 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −220122. | −0.374907 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 923300. | 1.53447 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.83881e6 | 2.98272 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 53036.1 | 0.0839858 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −852579. | −1.31834 | −0.659172 | − | 0.751992i | \(-0.729093\pi\) | ||||
−0.659172 | + | 0.751992i | \(0.729093\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.00150e6 | −1.51252 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 578768. | 0.853903 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −448408. | −0.646434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −776392. | −1.09388 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 341191. | 0.469912 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −276149. | −0.371862 | −0.185931 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185931 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −200186. | −0.263619 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.01983e6 | 1.31360 | 0.656802 | − | 0.754063i | \(-0.271909\pi\) | ||||
0.656802 | + | 0.754063i | \(0.271909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.07254e6 | −1.35153 | −0.675765 | − | 0.737117i | \(-0.736187\pi\) | ||||
−0.675765 | + | 0.737117i | \(0.736187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 190541. | 0.234941 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −376769. | −0.454658 | −0.227329 | − | 0.973818i | \(-0.572999\pi\) | ||||
−0.227329 | + | 0.973818i | \(0.572999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.02920e6 | 1.21571 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 433441. | 0.501256 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −286565. | −0.324510 | −0.162255 | − | 0.986749i | \(-0.551877\pi\) | ||||
−0.162255 | + | 0.986749i | \(0.551877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 809660. | 0.897966 | 0.448983 | − | 0.893540i | \(-0.351786\pi\) | ||||
0.448983 | + | 0.893540i | \(0.351786\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −238032. | −0.258594 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −125388. | −0.133457 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 81702.4 | 0.0852104 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 713199. | 0.728975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 672198. | 0.673462 | 0.336731 | − | 0.941601i | \(-0.390679\pi\) | ||||
0.336731 | + | 0.941601i | \(0.390679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −520036. | −0.510778 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.21985e6 | −2.13783 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 593485. | 0.560501 | 0.280251 | − | 0.959927i | \(-0.409582\pi\) | ||||
0.280251 | + | 0.959927i | \(0.409582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −179769. | −0.166519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.26102e6 | −2.05449 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.58789e6 | 1.41556 | 0.707782 | − | 0.706430i | \(-0.249696\pi\) | ||||
0.707782 | + | 0.706430i | \(0.249696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.19763e6 | 1.04763 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.68283e6 | −2.30311 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.77916e6 | 1.49911 | 0.749556 | − | 0.661941i | \(-0.230267\pi\) | ||||
0.749556 | + | 0.661941i | \(0.230267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.07288e6 | −0.887414 | −0.443707 | − | 0.896172i | \(-0.646337\pi\) | ||||
−0.443707 | + | 0.896172i | \(0.646337\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 293530. | 0.238367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 56614.7 | 0.0451437 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.99945e6 | 1.56571 | 0.782856 | − | 0.622202i | \(-0.213762\pi\) | ||||
0.782856 | + | 0.622202i | \(0.213762\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.60590e6 | −3.54245 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26939.8 | 0.0203530 | 0.0101765 | − | 0.999948i | \(-0.496761\pi\) | ||||
0.0101765 | + | 0.999948i | \(0.496761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −462556. | −0.343320 | −0.171660 | − | 0.985156i | \(-0.554913\pi\) | ||||
−0.171660 | + | 0.985156i | \(0.554913\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −531572. | −0.387659 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −866314. | −0.620827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00118e6 | 0.705127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.38594e6 | 2.34394 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.74537e6 | 1.18773 | 0.593867 | − | 0.804563i | \(-0.297600\pi\) | ||||
0.593867 | + | 0.804563i | \(0.297600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.64548e6 | −1.76990 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.01225e6 | 0.665879 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −801119. | −0.518226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −543047. | −0.345479 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.14535e6 | 1.96817 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.21380e6 | 0.747133 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.61327e6 | −0.976924 | −0.488462 | − | 0.872585i | \(-0.662442\pi\) | ||||
−0.488462 | + | 0.872585i | \(0.662442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.16735e6 | −0.695514 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −985033. | −0.577497 | −0.288749 | − | 0.957405i | \(-0.593239\pi\) | ||||
−0.288749 | + | 0.957405i | \(0.593239\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.06442e6 | 0.614116 | 0.307058 | − | 0.951691i | \(-0.400655\pi\) | ||||
0.307058 | + | 0.951691i | \(0.400655\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.28794e6 | −0.731341 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −180539. | −0.100907 | −0.0504536 | − | 0.998726i | \(-0.516067\pi\) | ||||
−0.0504536 | + | 0.998726i | \(0.516067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 639441. | 0.351823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.23051e6 | 1.20821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 579748. | 0.309195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 87215.2 | 0.0458020 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.21045e6 | 1.66034 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −965681. | −0.491863 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 192466. | 0.0965571 | 0.0482786 | − | 0.998834i | \(-0.484626\pi\) | ||||
0.0482786 | + | 0.998834i | \(0.484626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.84652e6 | −0.912524 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.82309e6 | −0.887559 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.10014e6 | 1.96664 | 0.983318 | − | 0.181892i | \(-0.0582222\pi\) | ||||
0.983318 | + | 0.181892i | \(0.0582222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.77428e6 | −3.20158 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.30260e6 | 0.606631 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.21224e6 | 2.35764 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.68642e6 | 1.19770 | 0.598852 | − | 0.800860i | \(-0.295624\pi\) | ||||
0.598852 | + | 0.800860i | \(0.295624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.01244e6 | −1.32390 | −0.661948 | − | 0.749549i | \(-0.730270\pi\) | ||||
−0.661948 | + | 0.749549i | \(0.730270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.55937e6 | 0.675588 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.40559e6 | −1.88177 | −0.940886 | − | 0.338724i | \(-0.890005\pi\) | ||||
−0.940886 | + | 0.338724i | \(0.890005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.91449e6 | −0.806272 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.08284e6 | 0.864941 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.08572e6 | 0.444611 | 0.222306 | − | 0.974977i | \(-0.428642\pi\) | ||||
0.222306 | + | 0.974977i | \(0.428642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.33727e6 | −0.943933 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.84619e6 | 1.53202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.48417e6 | −0.583113 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.46765e6 | 1.34391 | 0.671955 | − | 0.740592i | \(-0.265455\pi\) | ||||
0.671955 | + | 0.740592i | \(0.265455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.89849e6 | −3.40213 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.12371e6 | −0.423858 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.77398e6 | −1.03236 | −0.516180 | − | 0.856480i | \(-0.672646\pi\) | ||||
−0.516180 | + | 0.856480i | \(0.672646\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.02578e6 | −1.84555 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 985063. | 0.356953 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.31407e6 | −1.18512 | −0.592562 | − | 0.805525i | \(-0.701884\pi\) | ||||
−0.592562 | + | 0.805525i | \(0.701884\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.23609e6 | 1.14211 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.13229e6 | 1.09110 | 0.545551 | − | 0.838078i | \(-0.316321\pi\) | ||||
0.545551 | + | 0.838078i | \(0.316321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 364244. | 0.125239 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.57800e6 | −1.89322 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.78999e6 | 0.934823 | 0.467411 | − | 0.884040i | \(-0.345187\pi\) | ||||
0.467411 | + | 0.884040i | \(0.345187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.68462e6 | −1.88044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.71240e6 | −2.51888 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 828578. | 0.267203 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 397948. | 0.126721 | 0.0633607 | − | 0.997991i | \(-0.479818\pi\) | ||||
0.0633607 | + | 0.997991i | \(0.479818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 498764. | 0.156842 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 741928. | 0.230410 | 0.115205 | − | 0.993342i | \(-0.463248\pi\) | ||||
0.115205 | + | 0.993342i | \(0.463248\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00666e6 | 0.615476 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.75844e6 | −1.13860 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 522216. | 0.156266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.16438e6 | 0.639771 | 0.319886 | − | 0.947456i | \(-0.396356\pi\) | ||||
0.319886 | + | 0.947456i | \(0.396356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.34235e6 | 2.14403 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.48220e6 | 0.716079 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.36337e6 | 0.388592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.60830e6 | −1.86101 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.07575e6 | −1.13415 | −0.567077 | − | 0.823665i | \(-0.691926\pi\) | ||||
−0.567077 | + | 0.823665i | \(0.691926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.95488e6 | 0.812522 | 0.406261 | − | 0.913757i | \(-0.366832\pi\) | ||||
0.406261 | + | 0.913757i | \(0.366832\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.91915e6 | −2.69540 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 618866. | 0.166198 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13889e6 | −0.302281 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −852686. | −0.223690 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.59736e6 | −0.414200 | −0.207100 | − | 0.978320i | \(-0.566403\pi\) | ||||
−0.207100 | + | 0.978320i | \(0.566403\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.52435e6 | −0.647039 | −0.323519 | − | 0.946222i | \(-0.604866\pi\) | ||||
−0.323519 | + | 0.946222i | \(0.604866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.40901e6 | −1.62393 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.36125e6 | −0.340985 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −297743. | −0.0737360 | −0.0368680 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368680 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.20845e6 | 0.295892 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.09616e6 | −0.265377 | −0.132689 | − | 0.991158i | \(-0.542361\pi\) | ||||
−0.132689 | + | 0.991158i | \(0.542361\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.12857e6 | −1.22771 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.72685e6 | −2.06580 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.14561e6 | −0.268177 | −0.134088 | − | 0.990969i | \(-0.542811\pi\) | ||||
−0.134088 | + | 0.990969i | \(0.542811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.51659e6 | 0.582600 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.20755e6 | 0.963349 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 561120. | 0.127065 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50626e6 | 1.90523 | 0.952617 | − | 0.304173i | \(-0.0983800\pi\) | ||||
0.952617 | + | 0.304173i | \(0.0983800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.10651e7 | 2.45145 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.07074e6 | −0.892115 | −0.446058 | − | 0.895004i | \(-0.647172\pi\) | ||||
−0.446058 | + | 0.895004i | \(0.647172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.48385e6 | 0.972072 | 0.486036 | − | 0.873939i | \(-0.338442\pi\) | ||||
0.486036 | + | 0.873939i | \(0.338442\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.30557e7 | −2.80007 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −229548. | −0.0487059 | −0.0243529 | − | 0.999703i | \(-0.507753\pi\) | ||||
−0.0243529 | + | 0.999703i | \(0.507753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71057e6 | 0.359095 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.04748e6 | −0.840683 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.57752e6 | 0.324206 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 148195. | 0.0301371 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.15424e7 | −2.32274 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.50619e6 | −0.499085 | −0.249542 | − | 0.968364i | \(-0.580280\pi\) | ||||
−0.249542 | + | 0.968364i | \(0.580280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 804478. | 0.158545 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.89054e6 | −0.953870 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.47266e6 | 1.24948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.24551e6 | 1.57542 | 0.787708 | − | 0.616049i | \(-0.211268\pi\) | ||||
0.787708 | + | 0.616049i | \(0.211268\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.18553e7 | −2.24202 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.08374e6 | −0.202872 | −0.101436 | − | 0.994842i | \(-0.532344\pi\) | ||||
−0.101436 | + | 0.994842i | \(0.532344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.98986e6 | 1.29524 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.74139e6 | 0.686310 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.79632e6 | 0.326207 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.19035e6 | 0.573571 | 0.286785 | − | 0.957995i | \(-0.407413\pi\) | ||||
0.286785 | + | 0.957995i | \(0.407413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.55316e7 | 2.76453 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.20859e6 | 0.917910 | 0.458955 | − | 0.888459i | \(-0.348224\pi\) | ||||
0.458955 | + | 0.888459i | \(0.348224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.01274e6 | 1.04917 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.82968e6 | 1.52554 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.19140e6 | 1.05924 | 0.529620 | − | 0.848235i | \(-0.322334\pi\) | ||||
0.529620 | + | 0.848235i | \(0.322334\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39257e6 | 0.235920 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.64967e6 | 0.444528 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.23154e6 | −0.370755 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.80524e6 | 0.461577 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.01946e7 | 1.66131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.49044e6 | 0.401959 | 0.200979 | − | 0.979595i | \(-0.435588\pi\) | ||||
0.200979 | + | 0.979595i | \(0.435588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.62094e6 | −0.259128 | −0.129564 | − | 0.991571i | \(-0.541358\pi\) | ||||
−0.129564 | + | 0.991571i | \(0.541358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 532418. | 0.0843051 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.42390e7 | 2.23332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.91121e6 | 1.07378 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.54963e7 | 3.92411 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.87682e6 | 0.591095 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.26391e6 | 0.644056 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.09501e6 | 0.612801 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −341763. | −0.0506702 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −215848. | −0.0317070 | −0.0158535 | − | 0.999874i | \(-0.505047\pi\) | ||||
−0.0158535 | + | 0.999874i | \(0.505047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.14829e6 | 0.458221 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.13718e6 | 0.885070 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.41491e6 | −1.20249 | −0.601244 | − | 0.799065i | \(-0.705328\pi\) | ||||
−0.601244 | + | 0.799065i | \(0.705328\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.16983e7 | −1.65649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.67381e6 | 0.234870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −777439. | −0.108107 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.23409e6 | −0.721288 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.81520e6 | −0.384478 | −0.192239 | − | 0.981348i | \(-0.561575\pi\) | ||||
−0.192239 | + | 0.981348i | \(0.561575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.43018e6 | 0.328933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.05053e6 | −0.811683 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.14460e6 | −0.418114 | −0.209057 | − | 0.977903i | \(-0.567039\pi\) | ||||
−0.209057 | + | 0.977903i | \(0.567039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.29499e7 | −1.70665 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.52647e6 | 0.460663 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.38913e6 | 0.309356 | 0.154678 | − | 0.987965i | \(-0.450566\pi\) | ||||
0.154678 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.59235e6 | −0.204384 | −0.102192 | − | 0.994765i | \(-0.532586\pi\) | ||||
−0.102192 | + | 0.994765i | \(0.532586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −492096. | −0.0626128 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.45310e6 | −0.183285 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.33877e7 | 1.67405 | 0.837023 | − | 0.547168i | \(-0.184294\pi\) | ||||
0.837023 | + | 0.547168i | \(0.184294\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.38718e7 | −2.95930 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.27922e6 | −0.157220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.26431e6 | 0.397759 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.76364e6 | 0.696317 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.10664e6 | 0.252346 | 0.126173 | − | 0.992008i | \(-0.459731\pi\) | ||||
0.126173 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.40970e6 | 0.404975 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.06844e6 | −0.479136 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.06143e6 | −0.240731 | −0.120365 | − | 0.992730i | \(-0.538407\pi\) | ||||
−0.120365 | + | 0.992730i | \(0.538407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.98162e6 | 0.461071 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.08875e7 | 2.39856 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.01049e7 | −1.15071 | −0.575355 | − | 0.817904i | \(-0.695136\pi\) | ||||
−0.575355 | + | 0.817904i | \(0.695136\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.52826e6 | 0.850176 | 0.425088 | − | 0.905152i | \(-0.360243\pi\) | ||||
0.425088 | + | 0.905152i | \(0.360243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.75704e7 | 1.96784 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.35249e6 | 0.816669 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.03624e6 | 0.224314 | 0.112157 | − | 0.993691i | \(-0.464224\pi\) | ||||
0.112157 | + | 0.993691i | \(0.464224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.01345e6 | 0.657023 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.32149e6 | 0.468307 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.08503e7 | −1.16625 | −0.583123 | − | 0.812384i | \(-0.698169\pi\) | ||||
−0.583123 | + | 0.812384i | \(0.698169\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.52234e7 | −2.68915 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.55938e7 | −1.64907 | −0.824533 | − | 0.565814i | \(-0.808562\pi\) | ||||
−0.824533 | + | 0.565814i | \(0.808562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.72263e6 | 0.810099 | 0.405050 | − | 0.914295i | \(-0.367254\pi\) | ||||
0.405050 | + | 0.914295i | \(0.367254\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.59809e7 | −2.70349 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.81203e6 | 0.496716 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.36450e6 | −0.856525 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.44888e6 | −0.147185 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.70845e6 | 0.575297 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.01204e7 | −1.01187 | −0.505936 | − | 0.862571i | \(-0.668853\pi\) | ||||
−0.505936 | + | 0.862571i | \(0.668853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.32914e7 | 2.31039 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.18619e6 | 0.608820 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −526488. | −0.0514091 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.84512e7 | 1.78761 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.11080e7 | 1.06780 | 0.533902 | − | 0.845546i | \(-0.320725\pi\) | ||||
0.533902 | + | 0.845546i | \(0.320725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.36445e7 | 1.30146 | 0.650730 | − | 0.759309i | \(-0.274463\pi\) | ||||
0.650730 | + | 0.759309i | \(0.274463\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.58112e7 | −1.49646 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.88459e7 | 1.76993 | 0.884965 | − | 0.465658i | \(-0.154182\pi\) | ||||
0.884965 | + | 0.465658i | \(0.154182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.21063e6 | −0.671988 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.22499e7 | 1.13287 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.89196e6 | 0.173632 | 0.0868158 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868158 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.47432e7 | −1.34273 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.43040e7 | 1.29284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.03246e6 | 0.630803 | 0.315402 | − | 0.948958i | \(-0.397861\pi\) | ||||
0.315402 | + | 0.948958i | \(0.397861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.49186e7 | −1.32808 | −0.664040 | − | 0.747697i | \(-0.731160\pi\) | ||||
−0.664040 | + | 0.747697i | \(0.731160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.32088e6 | −0.823518 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 953451. | 0.0836073 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.64123e7 | −1.42841 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.54404e6 | 0.651686 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.30839e6 | 0.283668 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.40310e6 | 0.289625 | 0.144813 | − | 0.989459i | \(-0.453742\pi\) | ||||
0.144813 | + | 0.989459i | \(0.453742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82846e6 | 0.238941 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.76032e6 | −0.818450 | −0.409225 | − | 0.912433i | \(-0.634201\pi\) | ||||
−0.409225 | + | 0.912433i | \(0.634201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.07317e6 | −0.505523 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.78605e7 | −2.30209 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.43814e6 | 0.282015 | 0.141007 | − | 0.990009i | \(-0.454966\pi\) | ||||
0.141007 | + | 0.990009i | \(0.454966\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.40359e7 | 1.14291 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.93005e7 | 2.36855 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.02869e6 | 0.403559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.45739e6 | 0.514472 | 0.257236 | − | 0.966349i | \(-0.417188\pi\) | ||||
0.257236 | + | 0.966349i | \(0.417188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.51047e6 | −0.277672 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.26326e7 | −0.992044 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.75093e7 | 2.14486 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.02928e7 | 0.796787 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.90115e6 | −0.453567 | −0.226784 | − | 0.973945i | \(-0.572821\pi\) | ||||
−0.226784 | + | 0.973945i | \(0.572821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.36696e6 | 0.104320 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.81165e7 | −2.13053 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.64164e6 | −0.424480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.36046e7 | −1.01641 | −0.508205 | − | 0.861236i | \(-0.669691\pi\) | ||||
−0.508205 | + | 0.861236i | \(0.669691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.98559e6 | −0.592424 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.34332e7 | −2.46294 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.63002e6 | −0.119241 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.82858e6 | 0.568703 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.94690e7 | 1.40450 | 0.702248 | − | 0.711932i | \(-0.252180\pi\) | ||||
0.702248 | + | 0.711932i | \(0.252180\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.09381e6 | 0.150003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.21189e7 | −1.57368 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.78675e6 | 0.126246 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.13596e6 | 0.0797129 | 0.0398564 | − | 0.999205i | \(-0.487310\pi\) | ||||
0.0398564 | + | 0.999205i | \(0.487310\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.09857e7 | −0.765613 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.72442e7 | 1.19357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.50171e7 | −1.71980 | −0.859898 | − | 0.510466i | \(-0.829473\pi\) | ||||
−0.859898 | + | 0.510466i | \(0.829473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.42544e6 | 0.233882 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.96911e6 | −0.336984 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.83852e7 | −1.91197 | −0.955985 | − | 0.293416i | \(-0.905208\pi\) | ||||
−0.955985 | + | 0.293416i | \(0.905208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.23200e6 | −0.149331 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.77193e7 | −1.17754 | −0.588769 | − | 0.808301i | \(-0.700387\pi\) | ||||
−0.588769 | + | 0.808301i | \(0.700387\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.66825e7 | −1.10121 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.31398e7 | −0.861561 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00074e6 | −0.260577 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −528823. | −0.0342145 | −0.0171073 | − | 0.999854i | \(-0.505446\pi\) | ||||
−0.0171073 | + | 0.999854i | \(0.505446\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.83636e7 | −1.18024 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.04327e6 | 0.513529 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.09456e6 | −0.0694222 | −0.0347111 | − | 0.999397i | \(-0.511051\pi\) | ||||
−0.0347111 | + | 0.999397i | \(0.511051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.42067e7 | 0.895136 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.33654e6 | −0.0836607 | −0.0418304 | − | 0.999125i | \(-0.513319\pi\) | ||||
−0.0418304 | + | 0.999125i | \(0.513319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.75839e6 | −0.358088 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.08979e7 | 2.52666 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.11080e7 | −0.681786 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.94041e6 | −0.179305 | −0.0896523 | − | 0.995973i | \(-0.528576\pi\) | ||||
−0.0896523 | + | 0.995973i | \(0.528576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.62132e7 | −0.982276 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.93399e6 | 0.417383 | 0.208691 | − | 0.977982i | \(-0.433080\pi\) | ||||
0.208691 | + | 0.977982i | \(0.433080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.63977e6 | 0.217680 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.91105e6 | 0.291824 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.58746e6 | 0.388933 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.21821e6 | −0.306122 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.19464e7 | 1.86216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.73727e6 | −0.448140 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.39059e6 | −0.425346 | −0.212673 | − | 0.977123i | \(-0.568217\pi\) | ||||
−0.212673 | + | 0.977123i | \(0.568217\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.33790e7 | −2.48077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.21506e7 | 0.690491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.09660e6 | 0.287804 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.27177e7 | −1.83597 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.35937e7 | 1.87332 | 0.936659 | − | 0.350242i | \(-0.113901\pi\) | ||||
0.936659 | + | 0.350242i | \(0.113901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.06647e7 | 1.69930 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.94276e7 | 2.72200 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.04533e6 | −0.221394 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.34890e6 | −0.508476 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.86043e7 | −2.62719 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.75845e6 | 0.255619 | 0.127810 | − | 0.991799i | \(-0.459205\pi\) | ||||
0.127810 | + | 0.991799i | \(0.459205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.12488e6 | 0.380387 | 0.190193 | − | 0.981747i | \(-0.439088\pi\) | ||||
0.190193 | + | 0.981747i | \(0.439088\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.93096e7 | 1.55519 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.26629e7 | −1.19515 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.12933e6 | 0.216434 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.40791e6 | −0.281721 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.59860e6 | −0.238105 | −0.119052 | − | 0.992888i | \(-0.537986\pi\) | ||||
−0.119052 | + | 0.992888i | \(0.537986\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.21796e7 | −1.14144 | −0.570722 | − | 0.821144i | \(-0.693336\pi\) | ||||
−0.570722 | + | 0.821144i | \(0.693336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.54664e6 | −0.0791141 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.75259e6 | 0.190795 | 0.0953975 | − | 0.995439i | \(-0.469588\pi\) | ||||
0.0953975 | + | 0.995439i | \(0.469588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.26844e6 | −0.468404 | −0.234202 | − | 0.972188i | \(-0.575248\pi\) | ||||
−0.234202 | + | 0.972188i | \(0.575248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.46225e7 | −2.74390 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.73588e6 | −0.186544 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.96906e7 | 1.47368 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.50775e7 | 3.21083 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.88364e7 | 1.41428 | 0.707141 | − | 0.707073i | \(-0.249985\pi\) | ||||
0.707141 | + | 0.707073i | \(0.249985\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −330491. | −0.0161127 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −735960. | −0.0356685 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.68791e7 | 0.813217 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.89870e6 | −0.330414 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.26364e7 | 0.601666 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.34035e7 | −0.634446 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.97102e7 | −1.86866 | −0.934329 | − | 0.356411i | \(-0.884000\pi\) | ||||
−0.934329 | + | 0.356411i | \(0.884000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.79353e6 | 0.458167 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.42053e7 | −1.12579 | −0.562897 | − | 0.826527i | \(-0.690313\pi\) | ||||
−0.562897 | + | 0.826527i | \(0.690313\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.20350e7 | 0.556497 | 0.278248 | − | 0.960509i | \(-0.410246\pi\) | ||||
0.278248 | + | 0.960509i | \(0.410246\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.36666e7 | 1.08800 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.84727e7 | 0.844313 | 0.422157 | − | 0.906523i | \(-0.361273\pi\) | ||||
0.422157 | + | 0.906523i | \(0.361273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.94882e7 | 0.885590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.73509e7 | −1.23573 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.25841e6 | 0.101450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.65494e6 | −0.341898 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.23815e7 | −2.77026 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.01446e6 | 0.398034 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.26802e7 | 0.556706 | 0.278353 | − | 0.960479i | \(-0.410212\pi\) | ||||
0.278353 | + | 0.960479i | \(0.410212\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.76813e7 | −2.08150 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.82766e7 | −1.22740 | −0.613701 | − | 0.789538i | \(-0.710320\pi\) | ||||
−0.613701 | + | 0.789538i | \(0.710320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.31253e7 | 0.998127 | 0.499064 | − | 0.866565i | \(-0.333677\pi\) | ||||
0.499064 | + | 0.866565i | \(0.333677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.22710e7 | 3.10174 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.07655e6 | −0.216650 | −0.108325 | − | 0.994116i | \(-0.534549\pi\) | ||||
−0.108325 | + | 0.994116i | \(0.534549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.80438e6 | −0.246321 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.02442e7 | −0.432298 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.34304e6 | 0.308140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.82814e6 | 0.326664 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.18855e7 | 0.908188 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.11098e7 | 1.69647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.56828e7 | 1.46436 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.48353e7 | 0.605450 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.01836e6 | 0.244262 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.81858e6 | −0.0734029 | −0.0367015 | − | 0.999326i | \(-0.511685\pi\) | ||||
−0.0367015 | + | 0.999326i | \(0.511685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.79490e7 | −2.32614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.78317e7 | −1.11108 | −0.555539 | − | 0.831491i | \(-0.687488\pi\) | ||||
−0.555539 | + | 0.831491i | \(0.687488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.71607e6 | 0.147539 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.31595e7 | −1.30935 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.38333e7 | 0.543253 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.51945e7 | −1.37463 | −0.687316 | − | 0.726359i | \(-0.741211\pi\) | ||||
−0.687316 | + | 0.726359i | \(0.741211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.40724e7 | 1.71206 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.03868e6 | −0.310585 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.45920e6 | 0.0560738 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.15070e7 | 0.822015 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.41933e6 | 0.0539565 | 0.0269783 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269783 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −894604. | −0.0338265 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.69098e7 | 1.01206 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.15664e7 | −0.432681 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.77633e6 | −0.177724 | −0.0888618 | − | 0.996044i | \(-0.528323\pi\) | ||||
−0.0888618 | + | 0.996044i | \(0.528323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.90785e7 | −1.07624 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.25077e6 | −0.266938 | −0.133469 | − | 0.991053i | \(-0.542612\pi\) | ||||
−0.133469 | + | 0.991053i | \(0.542612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.45922e7 | −2.36538 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.81976e7 | 0.662878 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.13887e6 | 0.186206 | 0.0931028 | − | 0.995656i | \(-0.470321\pi\) | ||||
0.0931028 | + | 0.995656i | \(0.470321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.23185e6 | −0.224622 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.93208e6 | 0.176839 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.22957e7 | 0.438553 | 0.219276 | − | 0.975663i | \(-0.429630\pi\) | ||||
0.219276 | + | 0.975663i | \(0.429630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −940704. | −0.0333768 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.74687e7 | −0.616568 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31696e7 | −0.462407 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.51151e7 | 1.92514 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.10943e7 | −1.42796 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.56340e7 | −1.57750 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.91017e7 | −0.656911 | −0.328455 | − | 0.944520i | \(-0.606528\pi\) | ||||
−0.328455 | + | 0.944520i | \(0.606528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.58380e7 | −0.541864 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.17949e6 | −0.176295 | −0.0881473 | − | 0.996107i | \(-0.528095\pi\) | ||||
−0.0881473 | + | 0.996107i | \(0.528095\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.18529e7 | 0.401369 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.38261e6 | −0.0802677 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.66564e6 | −0.122861 | −0.0614304 | − | 0.998111i | \(-0.519566\pi\) | ||||
−0.0614304 | + | 0.998111i | \(0.519566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.39787e7 | −0.466132 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.91483e7 | −1.96232 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.05592e7 | 1.33877 | 0.669384 | − | 0.742916i | \(-0.266558\pi\) | ||||
0.669384 | + | 0.742916i | \(0.266558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.77734e6 | −0.255411 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.63811e7 | 0.861987 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.04895e7 | −1.31629 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.01285e6 | −0.0651068 | −0.0325534 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325534 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.25792e6 | −0.169216 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.99291e7 | 1.27859 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.05641e6 | 0.0336585 | 0.0168293 | − | 0.999858i | \(-0.494643\pi\) | ||||
0.0168293 | + | 0.999858i | \(0.494643\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.60898e7 | 0.827099 |
(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 | 448.6.a.bf.1.1 | 5 | ||
4.3 | odd | 2 | 448.6.a.be.1.5 | 5 | |||
8.3 | odd | 2 | 224.6.a.j.1.1 | yes | 5 | ||
8.5 | even | 2 | 224.6.a.i.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.i.1.5 | ✓ | 5 | 8.5 | even | 2 | ||
224.6.a.j.1.1 | yes | 5 | 8.3 | odd | 2 | ||
448.6.a.be.1.5 | 5 | 4.3 | odd | 2 | |||
448.6.a.bf.1.1 | 5 | 1.1 | even | 1 | trivial |