Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + 81977088 x^{5} - 3773728 x^{4} - 1245415104 x^{3} + \cdots - 6400833792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.05732\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05732 | 0.186909 | 0.0934545 | − | 0.995624i | \(-0.470209\pi\) | ||||
0.0934545 | + | 0.995624i | \(0.470209\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −30.8821 | −0.965065 | ||||||||
\(5\) | 33.7931 | 0.604510 | 0.302255 | − | 0.953227i | \(-0.402261\pi\) | ||||
0.302255 | + | 0.953227i | \(0.402261\pi\) | |||||||
\(6\) | −9.51585 | −0.107912 | ||||||||
\(7\) | −85.6226 | −0.660455 | −0.330227 | − | 0.943901i | \(-0.607125\pi\) | ||||
−0.330227 | + | 0.943901i | \(0.607125\pi\) | |||||||
\(8\) | −66.4863 | −0.367288 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 35.7300 | 0.112988 | ||||||||
\(11\) | −33.3696 | −0.0831513 | −0.0415757 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415757 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(12\) | 277.939 | 0.557181 | ||||||||
\(13\) | −1043.41 | −1.71237 | −0.856184 | − | 0.516671i | \(-0.827171\pi\) | ||||
−0.856184 | + | 0.516671i | \(0.827171\pi\) | |||||||
\(14\) | −90.5302 | −0.123445 | ||||||||
\(15\) | −304.138 | −0.349014 | ||||||||
\(16\) | 917.930 | 0.896416 | ||||||||
\(17\) | 522.840 | 0.438780 | 0.219390 | − | 0.975637i | \(-0.429593\pi\) | ||||
0.219390 | + | 0.975637i | \(0.429593\pi\) | |||||||
\(18\) | 85.6427 | 0.0623030 | ||||||||
\(19\) | −1300.57 | −0.826514 | −0.413257 | − | 0.910614i | \(-0.635609\pi\) | ||||
−0.413257 | + | 0.910614i | \(0.635609\pi\) | |||||||
\(20\) | −1043.60 | −0.583391 | ||||||||
\(21\) | 770.603 | 0.381314 | ||||||||
\(22\) | −35.2822 | −0.0155417 | ||||||||
\(23\) | 2439.93 | 0.961739 | 0.480869 | − | 0.876792i | \(-0.340321\pi\) | ||||
0.480869 | + | 0.876792i | \(0.340321\pi\) | |||||||
\(24\) | 598.377 | 0.212054 | ||||||||
\(25\) | −1983.02 | −0.634568 | ||||||||
\(26\) | −1103.22 | −0.320057 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2644.20 | 0.637382 | ||||||||
\(29\) | 7069.65 | 1.56100 | 0.780500 | − | 0.625156i | \(-0.214965\pi\) | ||||
0.780500 | + | 0.625156i | \(0.214965\pi\) | |||||||
\(30\) | −321.570 | −0.0652338 | ||||||||
\(31\) | 2519.18 | 0.470821 | 0.235410 | − | 0.971896i | \(-0.424357\pi\) | ||||
0.235410 | + | 0.971896i | \(0.424357\pi\) | |||||||
\(32\) | 3098.10 | 0.534836 | ||||||||
\(33\) | 300.326 | 0.0480074 | ||||||||
\(34\) | 552.807 | 0.0820118 | ||||||||
\(35\) | −2893.45 | −0.399251 | ||||||||
\(36\) | −2501.45 | −0.321688 | ||||||||
\(37\) | −6580.49 | −0.790231 | −0.395115 | − | 0.918632i | \(-0.629295\pi\) | ||||
−0.395115 | + | 0.918632i | \(0.629295\pi\) | |||||||
\(38\) | −1375.12 | −0.154483 | ||||||||
\(39\) | 9390.70 | 0.988636 | ||||||||
\(40\) | −2246.78 | −0.222029 | ||||||||
\(41\) | 19615.8 | 1.82241 | 0.911206 | − | 0.411951i | \(-0.135153\pi\) | ||||
0.911206 | + | 0.411951i | \(0.135153\pi\) | |||||||
\(42\) | 814.771 | 0.0712710 | ||||||||
\(43\) | 18389.9 | 1.51673 | 0.758364 | − | 0.651831i | \(-0.225999\pi\) | ||||
0.758364 | + | 0.651831i | \(0.225999\pi\) | |||||||
\(44\) | 1030.52 | 0.0802464 | ||||||||
\(45\) | 2737.24 | 0.201503 | ||||||||
\(46\) | 2579.77 | 0.179758 | ||||||||
\(47\) | 18005.2 | 1.18892 | 0.594461 | − | 0.804124i | \(-0.297365\pi\) | ||||
0.594461 | + | 0.804124i | \(0.297365\pi\) | |||||||
\(48\) | −8261.37 | −0.517546 | ||||||||
\(49\) | −9475.78 | −0.563799 | ||||||||
\(50\) | −2096.69 | −0.118606 | ||||||||
\(51\) | −4705.56 | −0.253330 | ||||||||
\(52\) | 32222.7 | 1.65255 | ||||||||
\(53\) | 16541.3 | 0.808870 | 0.404435 | − | 0.914567i | \(-0.367468\pi\) | ||||
0.404435 | + | 0.914567i | \(0.367468\pi\) | |||||||
\(54\) | −770.784 | −0.0359706 | ||||||||
\(55\) | −1127.66 | −0.0502658 | ||||||||
\(56\) | 5692.73 | 0.242577 | ||||||||
\(57\) | 11705.1 | 0.477188 | ||||||||
\(58\) | 7474.86 | 0.291765 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 9392.42 | 0.336821 | ||||||||
\(61\) | −29130.6 | −1.00236 | −0.501182 | − | 0.865342i | \(-0.667101\pi\) | ||||
−0.501182 | + | 0.865342i | \(0.667101\pi\) | |||||||
\(62\) | 2663.57 | 0.0880006 | ||||||||
\(63\) | −6935.43 | −0.220152 | ||||||||
\(64\) | −26098.1 | −0.796450 | ||||||||
\(65\) | −35260.1 | −1.03514 | ||||||||
\(66\) | 317.540 | 0.00897302 | ||||||||
\(67\) | −23137.8 | −0.629702 | −0.314851 | − | 0.949141i | \(-0.601955\pi\) | ||||
−0.314851 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(68\) | −16146.4 | −0.423451 | ||||||||
\(69\) | −21959.3 | −0.555260 | ||||||||
\(70\) | −3059.30 | −0.0746237 | ||||||||
\(71\) | −35612.7 | −0.838414 | −0.419207 | − | 0.907891i | \(-0.637692\pi\) | ||||
−0.419207 | + | 0.907891i | \(0.637692\pi\) | |||||||
\(72\) | −5385.39 | −0.122429 | ||||||||
\(73\) | 76489.3 | 1.67994 | 0.839970 | − | 0.542633i | \(-0.182573\pi\) | ||||
0.839970 | + | 0.542633i | \(0.182573\pi\) | |||||||
\(74\) | −6957.66 | −0.147701 | ||||||||
\(75\) | 17847.2 | 0.366368 | ||||||||
\(76\) | 40164.4 | 0.797640 | ||||||||
\(77\) | 2857.19 | 0.0549177 | ||||||||
\(78\) | 9928.95 | 0.184785 | ||||||||
\(79\) | 61578.6 | 1.11010 | 0.555050 | − | 0.831817i | \(-0.312699\pi\) | ||||
0.555050 | + | 0.831817i | \(0.312699\pi\) | |||||||
\(80\) | 31019.7 | 0.541892 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 20740.1 | 0.340625 | ||||||||
\(83\) | −11802.0 | −0.188045 | −0.0940224 | − | 0.995570i | \(-0.529973\pi\) | ||||
−0.0940224 | + | 0.995570i | \(0.529973\pi\) | |||||||
\(84\) | −23797.8 | −0.367993 | ||||||||
\(85\) | 17668.4 | 0.265247 | ||||||||
\(86\) | 19443.9 | 0.283490 | ||||||||
\(87\) | −63626.8 | −0.901243 | ||||||||
\(88\) | 2218.62 | 0.0305405 | ||||||||
\(89\) | 34947.8 | 0.467675 | 0.233838 | − | 0.972276i | \(-0.424872\pi\) | ||||
0.233838 | + | 0.972276i | \(0.424872\pi\) | |||||||
\(90\) | 2894.13 | 0.0376628 | ||||||||
\(91\) | 89339.6 | 1.13094 | ||||||||
\(92\) | −75350.0 | −0.928140 | ||||||||
\(93\) | −22672.6 | −0.271828 | ||||||||
\(94\) | 19037.2 | 0.222220 | ||||||||
\(95\) | −43950.4 | −0.499636 | ||||||||
\(96\) | −27882.9 | −0.308788 | ||||||||
\(97\) | −89284.3 | −0.963487 | −0.481744 | − | 0.876312i | \(-0.659996\pi\) | ||||
−0.481744 | + | 0.876312i | \(0.659996\pi\) | |||||||
\(98\) | −10018.9 | −0.105379 | ||||||||
\(99\) | −2702.94 | −0.0277171 | ||||||||
\(100\) | 61239.9 | 0.612399 | ||||||||
\(101\) | −25180.8 | −0.245621 | −0.122811 | − | 0.992430i | \(-0.539191\pi\) | ||||
−0.122811 | + | 0.992430i | \(0.539191\pi\) | |||||||
\(102\) | −4975.27 | −0.0473496 | ||||||||
\(103\) | 133786. | 1.24256 | 0.621282 | − | 0.783587i | \(-0.286612\pi\) | ||||
0.621282 | + | 0.783587i | \(0.286612\pi\) | |||||||
\(104\) | 69372.5 | 0.628933 | ||||||||
\(105\) | 26041.1 | 0.230508 | ||||||||
\(106\) | 17489.3 | 0.151185 | ||||||||
\(107\) | −71670.6 | −0.605176 | −0.302588 | − | 0.953122i | \(-0.597851\pi\) | ||||
−0.302588 | + | 0.953122i | \(0.597851\pi\) | |||||||
\(108\) | 22513.0 | 0.185727 | ||||||||
\(109\) | −101459. | −0.817948 | −0.408974 | − | 0.912546i | \(-0.634113\pi\) | ||||
−0.408974 | + | 0.912546i | \(0.634113\pi\) | |||||||
\(110\) | −1192.30 | −0.00939512 | ||||||||
\(111\) | 59224.4 | 0.456240 | ||||||||
\(112\) | −78595.5 | −0.592042 | ||||||||
\(113\) | 234915. | 1.73067 | 0.865337 | − | 0.501190i | \(-0.167104\pi\) | ||||
0.865337 | + | 0.501190i | \(0.167104\pi\) | |||||||
\(114\) | 12376.0 | 0.0891907 | ||||||||
\(115\) | 82452.7 | 0.581380 | ||||||||
\(116\) | −218325. | −1.50647 | ||||||||
\(117\) | −84516.3 | −0.570789 | ||||||||
\(118\) | 3680.52 | 0.0243335 | ||||||||
\(119\) | −44766.9 | −0.289794 | ||||||||
\(120\) | 20221.0 | 0.128189 | ||||||||
\(121\) | −159937. | −0.993086 | ||||||||
\(122\) | −30800.3 | −0.187351 | ||||||||
\(123\) | −176542. | −1.05217 | ||||||||
\(124\) | −77797.6 | −0.454372 | ||||||||
\(125\) | −172616. | −0.988112 | ||||||||
\(126\) | −7332.94 | −0.0411483 | ||||||||
\(127\) | 28866.5 | 0.158813 | 0.0794064 | − | 0.996842i | \(-0.474698\pi\) | ||||
0.0794064 | + | 0.996842i | \(0.474698\pi\) | |||||||
\(128\) | −126733. | −0.683700 | ||||||||
\(129\) | −165509. | −0.875684 | ||||||||
\(130\) | −37281.1 | −0.193478 | ||||||||
\(131\) | 119417. | 0.607977 | 0.303989 | − | 0.952676i | \(-0.401682\pi\) | ||||
0.303989 | + | 0.952676i | \(0.401682\pi\) | |||||||
\(132\) | −9274.70 | −0.0463303 | ||||||||
\(133\) | 111358. | 0.545875 | ||||||||
\(134\) | −24464.0 | −0.117697 | ||||||||
\(135\) | −24635.2 | −0.116338 | ||||||||
\(136\) | −34761.7 | −0.161159 | ||||||||
\(137\) | −199935. | −0.910097 | −0.455049 | − | 0.890467i | \(-0.650378\pi\) | ||||
−0.455049 | + | 0.890467i | \(0.650378\pi\) | |||||||
\(138\) | −23218.0 | −0.103783 | ||||||||
\(139\) | 13511.9 | 0.0593172 | 0.0296586 | − | 0.999560i | \(-0.490558\pi\) | ||||
0.0296586 | + | 0.999560i | \(0.490558\pi\) | |||||||
\(140\) | 89355.9 | 0.385304 | ||||||||
\(141\) | −162047. | −0.686425 | ||||||||
\(142\) | −37653.9 | −0.156707 | ||||||||
\(143\) | 34818.2 | 0.142386 | ||||||||
\(144\) | 74352.3 | 0.298805 | ||||||||
\(145\) | 238905. | 0.943640 | ||||||||
\(146\) | 80873.4 | 0.313996 | ||||||||
\(147\) | 85282.0 | 0.325510 | ||||||||
\(148\) | 203219. | 0.762624 | ||||||||
\(149\) | −448024. | −1.65324 | −0.826619 | − | 0.562762i | \(-0.809739\pi\) | ||||
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(150\) | 18870.2 | 0.0684775 | ||||||||
\(151\) | −221792. | −0.791597 | −0.395799 | − | 0.918337i | \(-0.629532\pi\) | ||||
−0.395799 | + | 0.918337i | \(0.629532\pi\) | |||||||
\(152\) | 86470.2 | 0.303569 | ||||||||
\(153\) | 42350.0 | 0.146260 | ||||||||
\(154\) | 3020.95 | 0.0102646 | ||||||||
\(155\) | 85131.0 | 0.284616 | ||||||||
\(156\) | −290004. | −0.954098 | ||||||||
\(157\) | 135887. | 0.439974 | 0.219987 | − | 0.975503i | \(-0.429398\pi\) | ||||
0.219987 | + | 0.975503i | \(0.429398\pi\) | |||||||
\(158\) | 65108.0 | 0.207487 | ||||||||
\(159\) | −148871. | −0.467001 | ||||||||
\(160\) | 104695. | 0.323314 | ||||||||
\(161\) | −208913. | −0.635185 | ||||||||
\(162\) | 6937.06 | 0.0207677 | ||||||||
\(163\) | 301769. | 0.889623 | 0.444812 | − | 0.895624i | \(-0.353271\pi\) | ||||
0.444812 | + | 0.895624i | \(0.353271\pi\) | |||||||
\(164\) | −605777. | −1.75875 | ||||||||
\(165\) | 10149.0 | 0.0290210 | ||||||||
\(166\) | −12478.5 | −0.0351473 | ||||||||
\(167\) | 572098. | 1.58737 | 0.793687 | − | 0.608326i | \(-0.208159\pi\) | ||||
0.793687 | + | 0.608326i | \(0.208159\pi\) | |||||||
\(168\) | −51234.5 | −0.140052 | ||||||||
\(169\) | 717414. | 1.93221 | ||||||||
\(170\) | 18681.1 | 0.0495770 | ||||||||
\(171\) | −105346. | −0.275505 | ||||||||
\(172\) | −567918. | −1.46374 | ||||||||
\(173\) | −279838. | −0.710873 | −0.355436 | − | 0.934700i | \(-0.615668\pi\) | ||||
−0.355436 | + | 0.934700i | \(0.615668\pi\) | |||||||
\(174\) | −67273.7 | −0.168450 | ||||||||
\(175\) | 169792. | 0.419103 | ||||||||
\(176\) | −30630.9 | −0.0745381 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | 36950.8 | 0.0874127 | ||||||||
\(179\) | 421817. | 0.983991 | 0.491995 | − | 0.870598i | \(-0.336268\pi\) | ||||
0.491995 | + | 0.870598i | \(0.336268\pi\) | |||||||
\(180\) | −84531.8 | −0.194464 | ||||||||
\(181\) | −257718. | −0.584720 | −0.292360 | − | 0.956308i | \(-0.594441\pi\) | ||||
−0.292360 | + | 0.956308i | \(0.594441\pi\) | |||||||
\(182\) | 94460.2 | 0.211383 | ||||||||
\(183\) | 262176. | 0.578715 | ||||||||
\(184\) | −162222. | −0.353235 | ||||||||
\(185\) | −222375. | −0.477702 | ||||||||
\(186\) | −23972.2 | −0.0508072 | ||||||||
\(187\) | −17447.0 | −0.0364851 | ||||||||
\(188\) | −556038. | −1.14739 | ||||||||
\(189\) | 62418.8 | 0.127105 | ||||||||
\(190\) | −46469.5 | −0.0933864 | ||||||||
\(191\) | −256126. | −0.508008 | −0.254004 | − | 0.967203i | \(-0.581748\pi\) | ||||
−0.254004 | + | 0.967203i | \(0.581748\pi\) | |||||||
\(192\) | 234883. | 0.459831 | ||||||||
\(193\) | −788156. | −1.52307 | −0.761534 | − | 0.648125i | \(-0.775553\pi\) | ||||
−0.761534 | + | 0.648125i | \(0.775553\pi\) | |||||||
\(194\) | −94401.8 | −0.180084 | ||||||||
\(195\) | 317341. | 0.597640 | ||||||||
\(196\) | 292632. | 0.544103 | ||||||||
\(197\) | 953753. | 1.75094 | 0.875468 | − | 0.483275i | \(-0.160553\pi\) | ||||
0.875468 | + | 0.483275i | \(0.160553\pi\) | |||||||
\(198\) | −2857.86 | −0.00518057 | ||||||||
\(199\) | 694899. | 1.24391 | 0.621955 | − | 0.783053i | \(-0.286339\pi\) | ||||
0.621955 | + | 0.783053i | \(0.286339\pi\) | |||||||
\(200\) | 131844. | 0.233069 | ||||||||
\(201\) | 208240. | 0.363559 | ||||||||
\(202\) | −26624.1 | −0.0459088 | ||||||||
\(203\) | −605321. | −1.03097 | ||||||||
\(204\) | 145317. | 0.244479 | ||||||||
\(205\) | 662879. | 1.10167 | ||||||||
\(206\) | 141454. | 0.232246 | ||||||||
\(207\) | 197634. | 0.320580 | ||||||||
\(208\) | −957778. | −1.53499 | ||||||||
\(209\) | 43399.5 | 0.0687257 | ||||||||
\(210\) | 27533.7 | 0.0430840 | ||||||||
\(211\) | 605261. | 0.935915 | 0.467957 | − | 0.883751i | \(-0.344990\pi\) | ||||
0.467957 | + | 0.883751i | \(0.344990\pi\) | |||||||
\(212\) | −510828. | −0.780612 | ||||||||
\(213\) | 320514. | 0.484059 | ||||||||
\(214\) | −75778.5 | −0.113113 | ||||||||
\(215\) | 621452. | 0.916877 | ||||||||
\(216\) | 48468.5 | 0.0706847 | ||||||||
\(217\) | −215699. | −0.310956 | ||||||||
\(218\) | −107275. | −0.152882 | ||||||||
\(219\) | −688404. | −0.969913 | ||||||||
\(220\) | 34824.6 | 0.0485097 | ||||||||
\(221\) | −545537. | −0.751352 | ||||||||
\(222\) | 62619.0 | 0.0852753 | ||||||||
\(223\) | 1.35183e6 | 1.82037 | 0.910186 | − | 0.414199i | \(-0.135938\pi\) | ||||
0.910186 | + | 0.414199i | \(0.135938\pi\) | |||||||
\(224\) | −265268. | −0.353235 | ||||||||
\(225\) | −160625. | −0.211523 | ||||||||
\(226\) | 248380. | 0.323479 | ||||||||
\(227\) | 289071. | 0.372341 | 0.186170 | − | 0.982517i | \(-0.440392\pi\) | ||||
0.186170 | + | 0.982517i | \(0.440392\pi\) | |||||||
\(228\) | −361479. | −0.460518 | ||||||||
\(229\) | 851974. | 1.07359 | 0.536794 | − | 0.843713i | \(-0.319635\pi\) | ||||
0.536794 | + | 0.843713i | \(0.319635\pi\) | |||||||
\(230\) | 87178.7 | 0.108665 | ||||||||
\(231\) | −25714.7 | −0.0317067 | ||||||||
\(232\) | −470035. | −0.573337 | ||||||||
\(233\) | 1.51708e6 | 1.83071 | 0.915356 | − | 0.402646i | \(-0.131910\pi\) | ||||
0.915356 | + | 0.402646i | \(0.131910\pi\) | |||||||
\(234\) | −89360.5 | −0.106686 | ||||||||
\(235\) | 608452. | 0.718715 | ||||||||
\(236\) | −107501. | −0.125641 | ||||||||
\(237\) | −554207. | −0.640916 | ||||||||
\(238\) | −47332.8 | −0.0541651 | ||||||||
\(239\) | −166996. | −0.189109 | −0.0945543 | − | 0.995520i | \(-0.530143\pi\) | ||||
−0.0945543 | + | 0.995520i | \(0.530143\pi\) | |||||||
\(240\) | −279177. | −0.312862 | ||||||||
\(241\) | −228585. | −0.253516 | −0.126758 | − | 0.991934i | \(-0.540457\pi\) | ||||
−0.126758 | + | 0.991934i | \(0.540457\pi\) | |||||||
\(242\) | −169105. | −0.185617 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 899614. | 0.967346 | ||||||||
\(245\) | −320216. | −0.340822 | ||||||||
\(246\) | −186661. | −0.196660 | ||||||||
\(247\) | 1.35703e6 | 1.41530 | ||||||||
\(248\) | −167491. | −0.172927 | ||||||||
\(249\) | 106218. | 0.108568 | ||||||||
\(250\) | −182510. | −0.184687 | ||||||||
\(251\) | 1.34491e6 | 1.34743 | 0.673717 | − | 0.738989i | \(-0.264697\pi\) | ||||
0.673717 | + | 0.738989i | \(0.264697\pi\) | |||||||
\(252\) | 214180. | 0.212461 | ||||||||
\(253\) | −81419.3 | −0.0799698 | ||||||||
\(254\) | 30521.1 | 0.0296835 | ||||||||
\(255\) | −159016. | −0.153140 | ||||||||
\(256\) | 701141. | 0.668660 | ||||||||
\(257\) | −193589. | −0.182830 | −0.0914151 | − | 0.995813i | \(-0.529139\pi\) | ||||
−0.0914151 | + | 0.995813i | \(0.529139\pi\) | |||||||
\(258\) | −174995. | −0.163673 | ||||||||
\(259\) | 563438. | 0.521912 | ||||||||
\(260\) | 1.08891e6 | 0.998981 | ||||||||
\(261\) | 572641. | 0.520333 | ||||||||
\(262\) | 126261. | 0.113636 | ||||||||
\(263\) | −1.29250e6 | −1.15224 | −0.576118 | − | 0.817367i | \(-0.695433\pi\) | ||||
−0.576118 | + | 0.817367i | \(0.695433\pi\) | |||||||
\(264\) | −19967.6 | −0.0176326 | ||||||||
\(265\) | 558981. | 0.488970 | ||||||||
\(266\) | 117741. | 0.102029 | ||||||||
\(267\) | −314530. | −0.270012 | ||||||||
\(268\) | 714544. | 0.607704 | ||||||||
\(269\) | −2.00558e6 | −1.68990 | −0.844948 | − | 0.534848i | \(-0.820369\pi\) | ||||
−0.844948 | + | 0.534848i | \(0.820369\pi\) | |||||||
\(270\) | −26047.2 | −0.0217446 | ||||||||
\(271\) | 1.28831e6 | 1.06561 | 0.532803 | − | 0.846240i | \(-0.321139\pi\) | ||||
0.532803 | + | 0.846240i | \(0.321139\pi\) | |||||||
\(272\) | 479930. | 0.393329 | ||||||||
\(273\) | −804056. | −0.652950 | ||||||||
\(274\) | −211395. | −0.170105 | ||||||||
\(275\) | 66172.7 | 0.0527651 | ||||||||
\(276\) | 678150. | 0.535862 | ||||||||
\(277\) | 1.13601e6 | 0.889572 | 0.444786 | − | 0.895637i | \(-0.353280\pi\) | ||||
0.444786 | + | 0.895637i | \(0.353280\pi\) | |||||||
\(278\) | 14286.4 | 0.0110869 | ||||||||
\(279\) | 204054. | 0.156940 | ||||||||
\(280\) | 192375. | 0.146640 | ||||||||
\(281\) | 1.45769e6 | 1.10128 | 0.550642 | − | 0.834742i | \(-0.314383\pi\) | ||||
0.550642 | + | 0.834742i | \(0.314383\pi\) | |||||||
\(282\) | −171335. | −0.128299 | ||||||||
\(283\) | −2.50369e6 | −1.85830 | −0.929148 | − | 0.369709i | \(-0.879457\pi\) | ||||
−0.929148 | + | 0.369709i | \(0.879457\pi\) | |||||||
\(284\) | 1.09979e6 | 0.809124 | ||||||||
\(285\) | 395553. | 0.288465 | ||||||||
\(286\) | 36813.9 | 0.0266132 | ||||||||
\(287\) | −1.67956e6 | −1.20362 | ||||||||
\(288\) | 250946. | 0.178279 | ||||||||
\(289\) | −1.14650e6 | −0.807472 | ||||||||
\(290\) | 252599. | 0.176375 | ||||||||
\(291\) | 803559. | 0.556270 | ||||||||
\(292\) | −2.36215e6 | −1.62125 | ||||||||
\(293\) | 1.43176e6 | 0.974322 | 0.487161 | − | 0.873312i | \(-0.338032\pi\) | ||||
0.487161 | + | 0.873312i | \(0.338032\pi\) | |||||||
\(294\) | 90170.1 | 0.0608407 | ||||||||
\(295\) | 117634. | 0.0787005 | ||||||||
\(296\) | 437512. | 0.290242 | ||||||||
\(297\) | 24326.4 | 0.0160025 | ||||||||
\(298\) | −473703. | −0.309005 | ||||||||
\(299\) | −2.54585e6 | −1.64685 | ||||||||
\(300\) | −551159. | −0.353569 | ||||||||
\(301\) | −1.57459e6 | −1.00173 | ||||||||
\(302\) | −234505. | −0.147957 | ||||||||
\(303\) | 226627. | 0.141810 | ||||||||
\(304\) | −1.19383e6 | −0.740900 | ||||||||
\(305\) | −984415. | −0.605938 | ||||||||
\(306\) | 44777.4 | 0.0273373 | ||||||||
\(307\) | −2.16520e6 | −1.31115 | −0.655574 | − | 0.755131i | \(-0.727573\pi\) | ||||
−0.655574 | + | 0.755131i | \(0.727573\pi\) | |||||||
\(308\) | −88235.9 | −0.0529991 | ||||||||
\(309\) | −1.20408e6 | −0.717394 | ||||||||
\(310\) | 90010.5 | 0.0531972 | ||||||||
\(311\) | 1.28475e6 | 0.753216 | 0.376608 | − | 0.926373i | \(-0.377090\pi\) | ||||
0.376608 | + | 0.926373i | \(0.377090\pi\) | |||||||
\(312\) | −624353. | −0.363115 | ||||||||
\(313\) | −191903. | −0.110719 | −0.0553594 | − | 0.998466i | \(-0.517630\pi\) | ||||
−0.0553594 | + | 0.998466i | \(0.517630\pi\) | |||||||
\(314\) | 143675. | 0.0822351 | ||||||||
\(315\) | −234370. | −0.133084 | ||||||||
\(316\) | −1.90167e6 | −1.07132 | ||||||||
\(317\) | 2.80920e6 | 1.57013 | 0.785064 | − | 0.619414i | \(-0.212630\pi\) | ||||
0.785064 | + | 0.619414i | \(0.212630\pi\) | |||||||
\(318\) | −157404. | −0.0872867 | ||||||||
\(319\) | −235911. | −0.129799 | ||||||||
\(320\) | −881935. | −0.481462 | ||||||||
\(321\) | 645035. | 0.349398 | ||||||||
\(322\) | −220887. | −0.118722 | ||||||||
\(323\) | −679991. | −0.362658 | ||||||||
\(324\) | −202617. | −0.107229 | ||||||||
\(325\) | 2.06911e6 | 1.08661 | ||||||||
\(326\) | 319066. | 0.166279 | ||||||||
\(327\) | 913134. | 0.472243 | ||||||||
\(328\) | −1.30418e6 | −0.669351 | ||||||||
\(329\) | −1.54165e6 | −0.785230 | ||||||||
\(330\) | 10730.7 | 0.00542428 | ||||||||
\(331\) | −104756. | −0.0525546 | −0.0262773 | − | 0.999655i | \(-0.508365\pi\) | ||||
−0.0262773 | + | 0.999655i | \(0.508365\pi\) | |||||||
\(332\) | 364471. | 0.181475 | ||||||||
\(333\) | −533020. | −0.263410 | ||||||||
\(334\) | 604889. | 0.296694 | ||||||||
\(335\) | −781899. | −0.380661 | ||||||||
\(336\) | 707359. | 0.341816 | ||||||||
\(337\) | −226616. | −0.108697 | −0.0543483 | − | 0.998522i | \(-0.517308\pi\) | ||||
−0.0543483 | + | 0.998522i | \(0.517308\pi\) | |||||||
\(338\) | 758534. | 0.361147 | ||||||||
\(339\) | −2.11424e6 | −0.999205 | ||||||||
\(340\) | −545637. | −0.255980 | ||||||||
\(341\) | −84064.1 | −0.0391493 | ||||||||
\(342\) | −111384. | −0.0514943 | ||||||||
\(343\) | 2.25040e6 | 1.03282 | ||||||||
\(344\) | −1.22267e6 | −0.557077 | ||||||||
\(345\) | −742075. | −0.335660 | ||||||||
\(346\) | −295878. | −0.132869 | ||||||||
\(347\) | −1.32731e6 | −0.591766 | −0.295883 | − | 0.955224i | \(-0.595614\pi\) | ||||
−0.295883 | + | 0.955224i | \(0.595614\pi\) | |||||||
\(348\) | 1.96493e6 | 0.869759 | ||||||||
\(349\) | −321857. | −0.141449 | −0.0707245 | − | 0.997496i | \(-0.522531\pi\) | ||||
−0.0707245 | + | 0.997496i | \(0.522531\pi\) | |||||||
\(350\) | 179524. | 0.0783342 | ||||||||
\(351\) | 760647. | 0.329545 | ||||||||
\(352\) | −103382. | −0.0444723 | ||||||||
\(353\) | 982643. | 0.419719 | 0.209860 | − | 0.977732i | \(-0.432699\pi\) | ||||
0.209860 | + | 0.977732i | \(0.432699\pi\) | |||||||
\(354\) | −33124.7 | −0.0140489 | ||||||||
\(355\) | −1.20346e6 | −0.506830 | ||||||||
\(356\) | −1.07926e6 | −0.451337 | ||||||||
\(357\) | 402902. | 0.167313 | ||||||||
\(358\) | 445994. | 0.183917 | ||||||||
\(359\) | 937903. | 0.384080 | 0.192040 | − | 0.981387i | \(-0.438490\pi\) | ||||
0.192040 | + | 0.981387i | \(0.438490\pi\) | |||||||
\(360\) | −181989. | −0.0740098 | ||||||||
\(361\) | −784613. | −0.316875 | ||||||||
\(362\) | −272489. | −0.109289 | ||||||||
\(363\) | 1.43944e6 | 0.573358 | ||||||||
\(364\) | −2.75899e6 | −1.09143 | ||||||||
\(365\) | 2.58481e6 | 1.01554 | ||||||||
\(366\) | 277203. | 0.108167 | ||||||||
\(367\) | −4.14787e6 | −1.60753 | −0.803766 | − | 0.594946i | \(-0.797174\pi\) | ||||
−0.803766 | + | 0.594946i | \(0.797174\pi\) | |||||||
\(368\) | 2.23968e6 | 0.862118 | ||||||||
\(369\) | 1.58888e6 | 0.607471 | ||||||||
\(370\) | −235121. | −0.0892868 | ||||||||
\(371\) | −1.41630e6 | −0.534222 | ||||||||
\(372\) | 700178. | 0.262332 | ||||||||
\(373\) | −2.43392e6 | −0.905805 | −0.452902 | − | 0.891560i | \(-0.649611\pi\) | ||||
−0.452902 | + | 0.891560i | \(0.649611\pi\) | |||||||
\(374\) | −18447.0 | −0.00681939 | ||||||||
\(375\) | 1.55355e6 | 0.570487 | ||||||||
\(376\) | −1.19710e6 | −0.436677 | ||||||||
\(377\) | −7.37655e6 | −2.67301 | ||||||||
\(378\) | 65996.5 | 0.0237570 | ||||||||
\(379\) | −196709. | −0.0703440 | −0.0351720 | − | 0.999381i | \(-0.511198\pi\) | ||||
−0.0351720 | + | 0.999381i | \(0.511198\pi\) | |||||||
\(380\) | 1.35728e6 | 0.482181 | ||||||||
\(381\) | −259799. | −0.0916906 | ||||||||
\(382\) | −270807. | −0.0949513 | ||||||||
\(383\) | 3.93318e6 | 1.37008 | 0.685041 | − | 0.728504i | \(-0.259784\pi\) | ||||
0.685041 | + | 0.728504i | \(0.259784\pi\) | |||||||
\(384\) | 1.14060e6 | 0.394734 | ||||||||
\(385\) | 96553.3 | 0.0331983 | ||||||||
\(386\) | −833331. | −0.284675 | ||||||||
\(387\) | 1.48958e6 | 0.505576 | ||||||||
\(388\) | 2.75729e6 | 0.929828 | ||||||||
\(389\) | 2.56292e6 | 0.858739 | 0.429369 | − | 0.903129i | \(-0.358736\pi\) | ||||
0.429369 | + | 0.903129i | \(0.358736\pi\) | |||||||
\(390\) | 335530. | 0.111704 | ||||||||
\(391\) | 1.27569e6 | 0.421991 | ||||||||
\(392\) | 630009. | 0.207077 | ||||||||
\(393\) | −1.07475e6 | −0.351016 | ||||||||
\(394\) | 1.00842e6 | 0.327266 | ||||||||
\(395\) | 2.08093e6 | 0.671066 | ||||||||
\(396\) | 83472.3 | 0.0267488 | ||||||||
\(397\) | −4.68608e6 | −1.49222 | −0.746110 | − | 0.665822i | \(-0.768081\pi\) | ||||
−0.746110 | + | 0.665822i | \(0.768081\pi\) | |||||||
\(398\) | 734729. | 0.232498 | ||||||||
\(399\) | −1.00222e6 | −0.315161 | ||||||||
\(400\) | −1.82028e6 | −0.568837 | ||||||||
\(401\) | 1.79185e6 | 0.556468 | 0.278234 | − | 0.960513i | \(-0.410251\pi\) | ||||
0.278234 | + | 0.960513i | \(0.410251\pi\) | |||||||
\(402\) | 220176. | 0.0679524 | ||||||||
\(403\) | −2.62854e6 | −0.806218 | ||||||||
\(404\) | 777635. | 0.237040 | ||||||||
\(405\) | 221717. | 0.0671678 | ||||||||
\(406\) | −640016. | −0.192697 | ||||||||
\(407\) | 219588. | 0.0657087 | ||||||||
\(408\) | 312855. | 0.0930450 | ||||||||
\(409\) | 736446. | 0.217687 | 0.108843 | − | 0.994059i | \(-0.465285\pi\) | ||||
0.108843 | + | 0.994059i | \(0.465285\pi\) | |||||||
\(410\) | 700874. | 0.205911 | ||||||||
\(411\) | 1.79942e6 | 0.525445 | ||||||||
\(412\) | −4.13160e6 | −1.19915 | ||||||||
\(413\) | −298052. | −0.0859839 | ||||||||
\(414\) | 208962. | 0.0599192 | ||||||||
\(415\) | −398827. | −0.113675 | ||||||||
\(416\) | −3.23260e6 | −0.915837 | ||||||||
\(417\) | −121607. | −0.0342468 | ||||||||
\(418\) | 45887.0 | 0.0128455 | ||||||||
\(419\) | 5.71624e6 | 1.59065 | 0.795327 | − | 0.606181i | \(-0.207299\pi\) | ||||
0.795327 | + | 0.606181i | \(0.207299\pi\) | |||||||
\(420\) | −804203. | −0.222455 | ||||||||
\(421\) | −547892. | −0.150657 | −0.0753286 | − | 0.997159i | \(-0.524001\pi\) | ||||
−0.0753286 | + | 0.997159i | \(0.524001\pi\) | |||||||
\(422\) | 639952. | 0.174931 | ||||||||
\(423\) | 1.45842e6 | 0.396308 | ||||||||
\(424\) | −1.09977e6 | −0.297088 | ||||||||
\(425\) | −1.03680e6 | −0.278435 | ||||||||
\(426\) | 338885. | 0.0904749 | ||||||||
\(427\) | 2.49424e6 | 0.662016 | ||||||||
\(428\) | 2.21334e6 | 0.584034 | ||||||||
\(429\) | −313364. | −0.0822064 | ||||||||
\(430\) | 657071. | 0.171373 | ||||||||
\(431\) | −1.20482e6 | −0.312412 | −0.156206 | − | 0.987724i | \(-0.549926\pi\) | ||||
−0.156206 | + | 0.987724i | \(0.549926\pi\) | |||||||
\(432\) | −669171. | −0.172515 | ||||||||
\(433\) | −4.71811e6 | −1.20934 | −0.604669 | − | 0.796477i | \(-0.706695\pi\) | ||||
−0.604669 | + | 0.796477i | \(0.706695\pi\) | |||||||
\(434\) | −228062. | −0.0581204 | ||||||||
\(435\) | −2.15015e6 | −0.544811 | ||||||||
\(436\) | 3.13328e6 | 0.789373 | ||||||||
\(437\) | −3.17330e6 | −0.794890 | ||||||||
\(438\) | −727861. | −0.181286 | ||||||||
\(439\) | −3.47079e6 | −0.859541 | −0.429770 | − | 0.902938i | \(-0.641406\pi\) | ||||
−0.429770 | + | 0.902938i | \(0.641406\pi\) | |||||||
\(440\) | 74974.1 | 0.0184620 | ||||||||
\(441\) | −767538. | −0.187933 | ||||||||
\(442\) | −576806. | −0.140435 | ||||||||
\(443\) | −2.07936e6 | −0.503409 | −0.251705 | − | 0.967804i | \(-0.580991\pi\) | ||||
−0.251705 | + | 0.967804i | \(0.580991\pi\) | |||||||
\(444\) | −1.82897e6 | −0.440301 | ||||||||
\(445\) | 1.18099e6 | 0.282714 | ||||||||
\(446\) | 1.42931e6 | 0.340244 | ||||||||
\(447\) | 4.03222e6 | 0.954498 | ||||||||
\(448\) | 2.23458e6 | 0.526019 | ||||||||
\(449\) | −3.92965e6 | −0.919893 | −0.459947 | − | 0.887947i | \(-0.652131\pi\) | ||||
−0.459947 | + | 0.887947i | \(0.652131\pi\) | |||||||
\(450\) | −169831. | −0.0395355 | ||||||||
\(451\) | −654571. | −0.151536 | ||||||||
\(452\) | −7.25468e6 | −1.67021 | ||||||||
\(453\) | 1.99613e6 | 0.457029 | ||||||||
\(454\) | 305640. | 0.0695938 | ||||||||
\(455\) | 3.01906e6 | 0.683666 | ||||||||
\(456\) | −778231. | −0.175266 | ||||||||
\(457\) | −490813. | −0.109932 | −0.0549662 | − | 0.998488i | \(-0.517505\pi\) | ||||
−0.0549662 | + | 0.998488i | \(0.517505\pi\) | |||||||
\(458\) | 900806. | 0.200663 | ||||||||
\(459\) | −381150. | −0.0844432 | ||||||||
\(460\) | −2.54631e6 | −0.561070 | ||||||||
\(461\) | −6.08206e6 | −1.33290 | −0.666452 | − | 0.745548i | \(-0.732188\pi\) | ||||
−0.666452 | + | 0.745548i | \(0.732188\pi\) | |||||||
\(462\) | −27188.6 | −0.00592627 | ||||||||
\(463\) | 8.92213e6 | 1.93427 | 0.967133 | − | 0.254271i | \(-0.0818354\pi\) | ||||
0.967133 | + | 0.254271i | \(0.0818354\pi\) | |||||||
\(464\) | 6.48944e6 | 1.39930 | ||||||||
\(465\) | −766179. | −0.164323 | ||||||||
\(466\) | 1.60404e6 | 0.342176 | ||||||||
\(467\) | 1.91638e6 | 0.406621 | 0.203310 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203310 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(468\) | 2.61004e6 | 0.550849 | ||||||||
\(469\) | 1.98112e6 | 0.415890 | ||||||||
\(470\) | 643327. | 0.134334 | ||||||||
\(471\) | −1.22298e6 | −0.254019 | ||||||||
\(472\) | −231439. | −0.0478169 | ||||||||
\(473\) | −613663. | −0.126118 | ||||||||
\(474\) | −585972. | −0.119793 | ||||||||
\(475\) | 2.57907e6 | 0.524479 | ||||||||
\(476\) | 1.38249e6 | 0.279670 | ||||||||
\(477\) | 1.33984e6 | 0.269623 | ||||||||
\(478\) | −176568. | −0.0353461 | ||||||||
\(479\) | −2.38919e6 | −0.475786 | −0.237893 | − | 0.971291i | \(-0.576457\pi\) | ||||
−0.237893 | + | 0.971291i | \(0.576457\pi\) | |||||||
\(480\) | −942251. | −0.186665 | ||||||||
\(481\) | 6.86616e6 | 1.35317 | ||||||||
\(482\) | −241686. | −0.0473843 | ||||||||
\(483\) | 1.88021e6 | 0.366724 | ||||||||
\(484\) | 4.93920e6 | 0.958392 | ||||||||
\(485\) | −3.01720e6 | −0.582437 | ||||||||
\(486\) | −62433.5 | −0.0119902 | ||||||||
\(487\) | −876099. | −0.167390 | −0.0836952 | − | 0.996491i | \(-0.526672\pi\) | ||||
−0.0836952 | + | 0.996491i | \(0.526672\pi\) | |||||||
\(488\) | 1.93679e6 | 0.368156 | ||||||||
\(489\) | −2.71592e6 | −0.513624 | ||||||||
\(490\) | −338570. | −0.0637027 | ||||||||
\(491\) | 2.47004e6 | 0.462381 | 0.231190 | − | 0.972909i | \(-0.425738\pi\) | ||||
0.231190 | + | 0.972909i | \(0.425738\pi\) | |||||||
\(492\) | 5.45199e6 | 1.01541 | ||||||||
\(493\) | 3.69629e6 | 0.684935 | ||||||||
\(494\) | 1.43481e6 | 0.264532 | ||||||||
\(495\) | −91340.7 | −0.0167553 | ||||||||
\(496\) | 2.31243e6 | 0.422051 | ||||||||
\(497\) | 3.04925e6 | 0.553735 | ||||||||
\(498\) | 112306. | 0.0202923 | ||||||||
\(499\) | −1.91170e6 | −0.343691 | −0.171846 | − | 0.985124i | \(-0.554973\pi\) | ||||
−0.171846 | + | 0.985124i | \(0.554973\pi\) | |||||||
\(500\) | 5.33075e6 | 0.953593 | ||||||||
\(501\) | −5.14888e6 | −0.916471 | ||||||||
\(502\) | 1.42199e6 | 0.251848 | ||||||||
\(503\) | 4.85098e6 | 0.854888 | 0.427444 | − | 0.904042i | \(-0.359414\pi\) | ||||
0.427444 | + | 0.904042i | \(0.359414\pi\) | |||||||
\(504\) | 461111. | 0.0808591 | ||||||||
\(505\) | −850938. | −0.148480 | ||||||||
\(506\) | −86086.0 | −0.0149471 | ||||||||
\(507\) | −6.45673e6 | −1.11556 | ||||||||
\(508\) | −891459. | −0.153265 | ||||||||
\(509\) | 7.45465e6 | 1.27536 | 0.637680 | − | 0.770301i | \(-0.279894\pi\) | ||||
0.637680 | + | 0.770301i | \(0.279894\pi\) | |||||||
\(510\) | −168130. | −0.0286233 | ||||||||
\(511\) | −6.54921e6 | −1.10952 | ||||||||
\(512\) | 4.79679e6 | 0.808679 | ||||||||
\(513\) | 948117. | 0.159063 | ||||||||
\(514\) | −204685. | −0.0341726 | ||||||||
\(515\) | 4.52106e6 | 0.751142 | ||||||||
\(516\) | 5.11126e6 | 0.845092 | ||||||||
\(517\) | −600826. | −0.0988605 | ||||||||
\(518\) | 595733. | 0.0975500 | ||||||||
\(519\) | 2.51854e6 | 0.410423 | ||||||||
\(520\) | 2.34432e6 | 0.380196 | ||||||||
\(521\) | 3.66620e6 | 0.591727 | 0.295864 | − | 0.955230i | \(-0.404393\pi\) | ||||
0.295864 | + | 0.955230i | \(0.404393\pi\) | |||||||
\(522\) | 605463. | 0.0972549 | ||||||||
\(523\) | 9.66704e6 | 1.54539 | 0.772697 | − | 0.634774i | \(-0.218907\pi\) | ||||
0.772697 | + | 0.634774i | \(0.218907\pi\) | |||||||
\(524\) | −3.68784e6 | −0.586738 | ||||||||
\(525\) | −1.52812e6 | −0.241969 | ||||||||
\(526\) | −1.36658e6 | −0.215363 | ||||||||
\(527\) | 1.31713e6 | 0.206586 | ||||||||
\(528\) | 275678. | 0.0430346 | ||||||||
\(529\) | −483104. | −0.0750587 | ||||||||
\(530\) | 591020. | 0.0913928 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −3.43897e6 | −0.526805 | ||||||||
\(533\) | −2.04674e7 | −3.12064 | ||||||||
\(534\) | −332558. | −0.0504677 | ||||||||
\(535\) | −2.42197e6 | −0.365835 | ||||||||
\(536\) | 1.53835e6 | 0.231282 | ||||||||
\(537\) | −3.79635e6 | −0.568107 | ||||||||
\(538\) | −2.12054e6 | −0.315857 | ||||||||
\(539\) | 316203. | 0.0468807 | ||||||||
\(540\) | 760786. | 0.112274 | ||||||||
\(541\) | 7.32547e6 | 1.07608 | 0.538038 | − | 0.842921i | \(-0.319166\pi\) | ||||
0.538038 | + | 0.842921i | \(0.319166\pi\) | |||||||
\(542\) | 1.36215e6 | 0.199171 | ||||||||
\(543\) | 2.31946e6 | 0.337588 | ||||||||
\(544\) | 1.61981e6 | 0.234675 | ||||||||
\(545\) | −3.42863e6 | −0.494458 | ||||||||
\(546\) | −850142. | −0.122042 | ||||||||
\(547\) | 6.36157e6 | 0.909067 | 0.454533 | − | 0.890730i | \(-0.349806\pi\) | ||||
0.454533 | + | 0.890730i | \(0.349806\pi\) | |||||||
\(548\) | 6.17441e6 | 0.878303 | ||||||||
\(549\) | −2.35958e6 | −0.334121 | ||||||||
\(550\) | 69965.5 | 0.00986228 | ||||||||
\(551\) | −9.19458e6 | −1.29019 | ||||||||
\(552\) | 1.45999e6 | 0.203941 | ||||||||
\(553\) | −5.27251e6 | −0.733170 | ||||||||
\(554\) | 1.20112e6 | 0.166269 | ||||||||
\(555\) | 2.00138e6 | 0.275802 | ||||||||
\(556\) | −417277. | −0.0572449 | ||||||||
\(557\) | 4.74906e6 | 0.648589 | 0.324295 | − | 0.945956i | \(-0.394873\pi\) | ||||
0.324295 | + | 0.945956i | \(0.394873\pi\) | |||||||
\(558\) | 215749. | 0.0293335 | ||||||||
\(559\) | −1.91882e7 | −2.59720 | ||||||||
\(560\) | −2.65599e6 | −0.357895 | ||||||||
\(561\) | 157023. | 0.0210647 | ||||||||
\(562\) | 1.54124e6 | 0.205840 | ||||||||
\(563\) | 3.15470e6 | 0.419457 | 0.209729 | − | 0.977760i | \(-0.432742\pi\) | ||||
0.209729 | + | 0.977760i | \(0.432742\pi\) | |||||||
\(564\) | 5.00435e6 | 0.662445 | ||||||||
\(565\) | 7.93853e6 | 1.04621 | ||||||||
\(566\) | −2.64720e6 | −0.347332 | ||||||||
\(567\) | −561770. | −0.0733839 | ||||||||
\(568\) | 2.36775e6 | 0.307940 | ||||||||
\(569\) | 8.64099e6 | 1.11888 | 0.559439 | − | 0.828872i | \(-0.311017\pi\) | ||||
0.559439 | + | 0.828872i | \(0.311017\pi\) | |||||||
\(570\) | 418225. | 0.0539167 | ||||||||
\(571\) | 6.75178e6 | 0.866619 | 0.433310 | − | 0.901245i | \(-0.357346\pi\) | ||||
0.433310 | + | 0.901245i | \(0.357346\pi\) | |||||||
\(572\) | −1.07526e6 | −0.137411 | ||||||||
\(573\) | 2.30514e6 | 0.293299 | ||||||||
\(574\) | −1.77582e6 | −0.224967 | ||||||||
\(575\) | −4.83843e6 | −0.610288 | ||||||||
\(576\) | −2.11394e6 | −0.265483 | ||||||||
\(577\) | −80122.8 | −0.0100188 | −0.00500941 | − | 0.999987i | \(-0.501595\pi\) | ||||
−0.00500941 | + | 0.999987i | \(0.501595\pi\) | |||||||
\(578\) | −1.21221e6 | −0.150924 | ||||||||
\(579\) | 7.09341e6 | 0.879343 | ||||||||
\(580\) | −7.37790e6 | −0.910674 | ||||||||
\(581\) | 1.01052e6 | 0.124195 | ||||||||
\(582\) | 849616. | 0.103972 | ||||||||
\(583\) | −551975. | −0.0672586 | ||||||||
\(584\) | −5.08549e6 | −0.617022 | ||||||||
\(585\) | −2.85607e6 | −0.345048 | ||||||||
\(586\) | 1.51383e6 | 0.182110 | ||||||||
\(587\) | 8.20721e6 | 0.983106 | 0.491553 | − | 0.870848i | \(-0.336429\pi\) | ||||
0.491553 | + | 0.870848i | \(0.336429\pi\) | |||||||
\(588\) | −2.63369e6 | −0.314138 | ||||||||
\(589\) | −3.27638e6 | −0.389140 | ||||||||
\(590\) | 124376. | 0.0147098 | ||||||||
\(591\) | −8.58378e6 | −1.01090 | ||||||||
\(592\) | −6.04043e6 | −0.708375 | ||||||||
\(593\) | 3.34469e6 | 0.390588 | 0.195294 | − | 0.980745i | \(-0.437434\pi\) | ||||
0.195294 | + | 0.980745i | \(0.437434\pi\) | |||||||
\(594\) | 25720.7 | 0.00299101 | ||||||||
\(595\) | −1.51281e6 | −0.175183 | ||||||||
\(596\) | 1.38359e7 | 1.59548 | ||||||||
\(597\) | −6.25409e6 | −0.718172 | ||||||||
\(598\) | −2.69177e6 | −0.307811 | ||||||||
\(599\) | −1.54909e7 | −1.76405 | −0.882024 | − | 0.471204i | \(-0.843819\pi\) | ||||
−0.882024 | + | 0.471204i | \(0.843819\pi\) | |||||||
\(600\) | −1.18660e6 | −0.134563 | ||||||||
\(601\) | −6.02417e6 | −0.680317 | −0.340158 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340158 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(602\) | −1.66484e6 | −0.187232 | ||||||||
\(603\) | −1.87416e6 | −0.209901 | ||||||||
\(604\) | 6.84941e6 | 0.763943 | ||||||||
\(605\) | −5.40479e6 | −0.600330 | ||||||||
\(606\) | 239617. | 0.0265055 | ||||||||
\(607\) | −1.80813e7 | −1.99186 | −0.995930 | − | 0.0901349i | \(-0.971270\pi\) | ||||
−0.995930 | + | 0.0901349i | \(0.971270\pi\) | |||||||
\(608\) | −4.02930e6 | −0.442050 | ||||||||
\(609\) | 5.44789e6 | 0.595231 | ||||||||
\(610\) | −1.04084e6 | −0.113255 | ||||||||
\(611\) | −1.87868e7 | −2.03587 | ||||||||
\(612\) | −1.30786e6 | −0.141150 | ||||||||
\(613\) | 1.63982e7 | 1.76256 | 0.881281 | − | 0.472593i | \(-0.156682\pi\) | ||||
0.881281 | + | 0.472593i | \(0.156682\pi\) | |||||||
\(614\) | −2.28930e6 | −0.245065 | ||||||||
\(615\) | −5.96592e6 | −0.636047 | ||||||||
\(616\) | −189964. | −0.0201706 | ||||||||
\(617\) | −1.39449e7 | −1.47470 | −0.737350 | − | 0.675511i | \(-0.763923\pi\) | ||||
−0.737350 | + | 0.675511i | \(0.763923\pi\) | |||||||
\(618\) | −1.27309e6 | −0.134087 | ||||||||
\(619\) | 3.47959e6 | 0.365007 | 0.182504 | − | 0.983205i | \(-0.441580\pi\) | ||||
0.182504 | + | 0.983205i | \(0.441580\pi\) | |||||||
\(620\) | −2.62902e6 | −0.274673 | ||||||||
\(621\) | −1.77871e6 | −0.185087 | ||||||||
\(622\) | 1.35839e6 | 0.140783 | ||||||||
\(623\) | −2.99232e6 | −0.308878 | ||||||||
\(624\) | 8.62000e6 | 0.886229 | ||||||||
\(625\) | 363714. | 0.0372443 | ||||||||
\(626\) | −202902. | −0.0206943 | ||||||||
\(627\) | −390596. | −0.0396788 | ||||||||
\(628\) | −4.19646e6 | −0.424604 | ||||||||
\(629\) | −3.44054e6 | −0.346737 | ||||||||
\(630\) | −247803. | −0.0248746 | ||||||||
\(631\) | 1.90874e6 | 0.190842 | 0.0954210 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954210 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(632\) | −4.09413e6 | −0.407726 | ||||||||
\(633\) | −5.44735e6 | −0.540351 | ||||||||
\(634\) | 2.97022e6 | 0.293471 | ||||||||
\(635\) | 975491. | 0.0960039 | ||||||||
\(636\) | 4.59745e6 | 0.450687 | ||||||||
\(637\) | 9.88714e6 | 0.965432 | ||||||||
\(638\) | −249433. | −0.0242606 | ||||||||
\(639\) | −2.88463e6 | −0.279471 | ||||||||
\(640\) | −4.28271e6 | −0.413303 | ||||||||
\(641\) | 1.01908e7 | 0.979632 | 0.489816 | − | 0.871826i | \(-0.337064\pi\) | ||||
0.489816 | + | 0.871826i | \(0.337064\pi\) | |||||||
\(642\) | 682006. | 0.0653057 | ||||||||
\(643\) | 1.55416e7 | 1.48241 | 0.741205 | − | 0.671279i | \(-0.234255\pi\) | ||||
0.741205 | + | 0.671279i | \(0.234255\pi\) | |||||||
\(644\) | 6.45166e6 | 0.612995 | ||||||||
\(645\) | −5.59306e6 | −0.529359 | ||||||||
\(646\) | −718966. | −0.0677839 | ||||||||
\(647\) | −3.01771e6 | −0.283411 | −0.141705 | − | 0.989909i | \(-0.545259\pi\) | ||||
−0.141705 | + | 0.989909i | \(0.545259\pi\) | |||||||
\(648\) | −436216. | −0.0408098 | ||||||||
\(649\) | −116160. | −0.0108254 | ||||||||
\(650\) | 2.18771e6 | 0.203098 | ||||||||
\(651\) | 1.94129e6 | 0.179530 | ||||||||
\(652\) | −9.31927e6 | −0.858544 | ||||||||
\(653\) | −5.97669e6 | −0.548502 | −0.274251 | − | 0.961658i | \(-0.588430\pi\) | ||||
−0.274251 | + | 0.961658i | \(0.588430\pi\) | |||||||
\(654\) | 965472. | 0.0882664 | ||||||||
\(655\) | 4.03547e6 | 0.367528 | ||||||||
\(656\) | 1.80059e7 | 1.63364 | ||||||||
\(657\) | 6.19563e6 | 0.559980 | ||||||||
\(658\) | −1.63001e6 | −0.146766 | ||||||||
\(659\) | −3.91411e6 | −0.351091 | −0.175546 | − | 0.984471i | \(-0.556169\pi\) | ||||
−0.175546 | + | 0.984471i | \(0.556169\pi\) | |||||||
\(660\) | −313421. | −0.0280071 | ||||||||
\(661\) | 7.35500e6 | 0.654755 | 0.327378 | − | 0.944894i | \(-0.393835\pi\) | ||||
0.327378 | + | 0.944894i | \(0.393835\pi\) | |||||||
\(662\) | −110761. | −0.00982293 | ||||||||
\(663\) | 4.90983e6 | 0.433794 | ||||||||
\(664\) | 784673. | 0.0690667 | ||||||||
\(665\) | 3.76314e6 | 0.329987 | ||||||||
\(666\) | −563571. | −0.0492337 | ||||||||
\(667\) | 1.72494e7 | 1.50127 | ||||||||
\(668\) | −1.76676e7 | −1.53192 | ||||||||
\(669\) | −1.21665e7 | −1.05099 | ||||||||
\(670\) | −826715. | −0.0711490 | ||||||||
\(671\) | 972077. | 0.0833478 | ||||||||
\(672\) | 2.38741e6 | 0.203940 | ||||||||
\(673\) | −1.68761e6 | −0.143627 | −0.0718134 | − | 0.997418i | \(-0.522879\pi\) | ||||
−0.0718134 | + | 0.997418i | \(0.522879\pi\) | |||||||
\(674\) | −239605. | −0.0203164 | ||||||||
\(675\) | 1.44562e6 | 0.122123 | ||||||||
\(676\) | −2.21553e7 | −1.86470 | ||||||||
\(677\) | −8.90194e6 | −0.746471 | −0.373236 | − | 0.927737i | \(-0.621752\pi\) | ||||
−0.373236 | + | 0.927737i | \(0.621752\pi\) | |||||||
\(678\) | −2.23542e6 | −0.186760 | ||||||||
\(679\) | 7.64475e6 | 0.636340 | ||||||||
\(680\) | −1.17471e6 | −0.0974220 | ||||||||
\(681\) | −2.60164e6 | −0.214971 | ||||||||
\(682\) | −88882.3 | −0.00731736 | ||||||||
\(683\) | 6.04714e6 | 0.496019 | 0.248010 | − | 0.968758i | \(-0.420224\pi\) | ||||
0.248010 | + | 0.968758i | \(0.420224\pi\) | |||||||
\(684\) | 3.25331e6 | 0.265880 | ||||||||
\(685\) | −6.75643e6 | −0.550163 | ||||||||
\(686\) | 2.37938e6 | 0.193043 | ||||||||
\(687\) | −7.66776e6 | −0.619836 | ||||||||
\(688\) | 1.68806e7 | 1.35962 | ||||||||
\(689\) | −1.72593e7 | −1.38508 | ||||||||
\(690\) | −784608. | −0.0627379 | ||||||||
\(691\) | −3.65486e6 | −0.291189 | −0.145595 | − | 0.989344i | \(-0.546509\pi\) | ||||
−0.145595 | + | 0.989344i | \(0.546509\pi\) | |||||||
\(692\) | 8.64199e6 | 0.686039 | ||||||||
\(693\) | 231432. | 0.0183059 | ||||||||
\(694\) | −1.40339e6 | −0.110606 | ||||||||
\(695\) | 456610. | 0.0358578 | ||||||||
\(696\) | 4.23031e6 | 0.331016 | ||||||||
\(697\) | 1.02559e7 | 0.799637 | ||||||||
\(698\) | −340305. | −0.0264381 | ||||||||
\(699\) | −1.36538e7 | −1.05696 | ||||||||
\(700\) | −5.24352e6 | −0.404462 | ||||||||
\(701\) | −1.63664e7 | −1.25793 | −0.628966 | − | 0.777432i | \(-0.716522\pi\) | ||||
−0.628966 | + | 0.777432i | \(0.716522\pi\) | |||||||
\(702\) | 804245. | 0.0615950 | ||||||||
\(703\) | 8.55840e6 | 0.653137 | ||||||||
\(704\) | 870882. | 0.0662258 | ||||||||
\(705\) | −5.47607e6 | −0.414951 | ||||||||
\(706\) | 1.03896e6 | 0.0784493 | ||||||||
\(707\) | 2.15604e6 | 0.162222 | ||||||||
\(708\) | 967505. | 0.0725387 | ||||||||
\(709\) | −2.45108e7 | −1.83123 | −0.915613 | − | 0.402061i | \(-0.868294\pi\) | ||||
−0.915613 | + | 0.402061i | \(0.868294\pi\) | |||||||
\(710\) | −1.27244e6 | −0.0947310 | ||||||||
\(711\) | 4.98786e6 | 0.370033 | ||||||||
\(712\) | −2.32355e6 | −0.171772 | ||||||||
\(713\) | 6.14662e6 | 0.452806 | ||||||||
\(714\) | 425995. | 0.0312722 | ||||||||
\(715\) | 1.17662e6 | 0.0860735 | ||||||||
\(716\) | −1.30266e7 | −0.949615 | ||||||||
\(717\) | 1.50296e6 | 0.109182 | ||||||||
\(718\) | 991661. | 0.0717880 | ||||||||
\(719\) | 1.16640e7 | 0.841446 | 0.420723 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420723 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(720\) | 2.51260e6 | 0.180631 | ||||||||
\(721\) | −1.14551e7 | −0.820657 | ||||||||
\(722\) | −829584. | −0.0592267 | ||||||||
\(723\) | 2.05726e6 | 0.146367 | ||||||||
\(724\) | 7.95886e6 | 0.564293 | ||||||||
\(725\) | −1.40193e7 | −0.990560 | ||||||||
\(726\) | 1.52194e6 | 0.107166 | ||||||||
\(727\) | 1.76785e7 | 1.24054 | 0.620268 | − | 0.784390i | \(-0.287024\pi\) | ||||
0.620268 | + | 0.784390i | \(0.287024\pi\) | |||||||
\(728\) | −5.93985e6 | −0.415382 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.73297e6 | 0.189813 | ||||||||
\(731\) | 9.61497e6 | 0.665510 | ||||||||
\(732\) | −8.09653e6 | −0.558497 | ||||||||
\(733\) | 1.31251e6 | 0.0902279 | 0.0451140 | − | 0.998982i | \(-0.485635\pi\) | ||||
0.0451140 | + | 0.998982i | \(0.485635\pi\) | |||||||
\(734\) | −4.38561e6 | −0.300462 | ||||||||
\(735\) | 2.88195e6 | 0.196774 | ||||||||
\(736\) | 7.55914e6 | 0.514373 | ||||||||
\(737\) | 772099. | 0.0523606 | ||||||||
\(738\) | 1.67995e6 | 0.113542 | ||||||||
\(739\) | 2.62184e6 | 0.176602 | 0.0883010 | − | 0.996094i | \(-0.471856\pi\) | ||||
0.0883010 | + | 0.996094i | \(0.471856\pi\) | |||||||
\(740\) | 6.86741e6 | 0.461014 | ||||||||
\(741\) | −1.22133e7 | −0.817122 | ||||||||
\(742\) | −1.49748e6 | −0.0998509 | ||||||||
\(743\) | 7.41645e6 | 0.492861 | 0.246430 | − | 0.969161i | \(-0.420742\pi\) | ||||
0.246430 | + | 0.969161i | \(0.420742\pi\) | |||||||
\(744\) | 1.50742e6 | 0.0998394 | ||||||||
\(745\) | −1.51401e7 | −0.999399 | ||||||||
\(746\) | −2.57343e6 | −0.169303 | ||||||||
\(747\) | −955964. | −0.0626816 | ||||||||
\(748\) | 538798. | 0.0352105 | ||||||||
\(749\) | 6.13662e6 | 0.399691 | ||||||||
\(750\) | 1.64259e6 | 0.106629 | ||||||||
\(751\) | 1.89341e7 | 1.22503 | 0.612514 | − | 0.790460i | \(-0.290158\pi\) | ||||
0.612514 | + | 0.790460i | \(0.290158\pi\) | |||||||
\(752\) | 1.65275e7 | 1.06577 | ||||||||
\(753\) | −1.21042e7 | −0.777942 | ||||||||
\(754\) | −7.79935e6 | −0.499609 | ||||||||
\(755\) | −7.49506e6 | −0.478528 | ||||||||
\(756\) | −1.92762e6 | −0.122664 | ||||||||
\(757\) | −3.95313e6 | −0.250727 | −0.125364 | − | 0.992111i | \(-0.540010\pi\) | ||||
−0.125364 | + | 0.992111i | \(0.540010\pi\) | |||||||
\(758\) | −207984. | −0.0131479 | ||||||||
\(759\) | 732774. | 0.0461706 | ||||||||
\(760\) | 2.92210e6 | 0.183510 | ||||||||
\(761\) | 2.27391e7 | 1.42335 | 0.711675 | − | 0.702509i | \(-0.247937\pi\) | ||||
0.711675 | + | 0.702509i | \(0.247937\pi\) | |||||||
\(762\) | −274690. | −0.0171378 | ||||||||
\(763\) | 8.68721e6 | 0.540218 | ||||||||
\(764\) | 7.90971e6 | 0.490261 | ||||||||
\(765\) | 1.43114e6 | 0.0884155 | ||||||||
\(766\) | 4.15862e6 | 0.256081 | ||||||||
\(767\) | −3.63212e6 | −0.222931 | ||||||||
\(768\) | −6.31027e6 | −0.386051 | ||||||||
\(769\) | −6.06544e6 | −0.369867 | −0.184934 | − | 0.982751i | \(-0.559207\pi\) | ||||
−0.184934 | + | 0.982751i | \(0.559207\pi\) | |||||||
\(770\) | 102087. | 0.00620505 | ||||||||
\(771\) | 1.74230e6 | 0.105557 | ||||||||
\(772\) | 2.43399e7 | 1.46986 | ||||||||
\(773\) | 2.81598e7 | 1.69504 | 0.847521 | − | 0.530762i | \(-0.178094\pi\) | ||||
0.847521 | + | 0.530762i | \(0.178094\pi\) | |||||||
\(774\) | 1.57496e6 | 0.0944967 | ||||||||
\(775\) | −4.99560e6 | −0.298768 | ||||||||
\(776\) | 5.93618e6 | 0.353878 | ||||||||
\(777\) | −5.07095e6 | −0.301326 | ||||||||
\(778\) | 2.70982e6 | 0.160506 | ||||||||
\(779\) | −2.55118e7 | −1.50625 | ||||||||
\(780\) | −9.80016e6 | −0.576762 | ||||||||
\(781\) | 1.18838e6 | 0.0697153 | ||||||||
\(782\) | 1.34881e6 | 0.0788740 | ||||||||
\(783\) | −5.15377e6 | −0.300414 | ||||||||
\(784\) | −8.69810e6 | −0.505399 | ||||||||
\(785\) | 4.59203e6 | 0.265969 | ||||||||
\(786\) | −1.13635e6 | −0.0656080 | ||||||||
\(787\) | 1.35985e7 | 0.782627 | 0.391313 | − | 0.920257i | \(-0.372021\pi\) | ||||
0.391313 | + | 0.920257i | \(0.372021\pi\) | |||||||
\(788\) | −2.94539e7 | −1.68977 | ||||||||
\(789\) | 1.16325e7 | 0.665243 | ||||||||
\(790\) | 2.20020e6 | 0.125428 | ||||||||
\(791\) | −2.01141e7 | −1.14303 | ||||||||
\(792\) | 179708. | 0.0101802 | ||||||||
\(793\) | 3.03952e7 | 1.71642 | ||||||||
\(794\) | −4.95467e6 | −0.278909 | ||||||||
\(795\) | −5.03083e6 | −0.282307 | ||||||||
\(796\) | −2.14599e7 | −1.20045 | ||||||||
\(797\) | 3.47277e6 | 0.193656 | 0.0968279 | − | 0.995301i | \(-0.469130\pi\) | ||||
0.0968279 | + | 0.995301i | \(0.469130\pi\) | |||||||
\(798\) | −1.05967e6 | −0.0589064 | ||||||||
\(799\) | 9.41384e6 | 0.521675 | ||||||||
\(800\) | −6.14361e6 | −0.339390 | ||||||||
\(801\) | 2.83077e6 | 0.155892 | ||||||||
\(802\) | 1.89455e6 | 0.104009 | ||||||||
\(803\) | −2.55242e6 | −0.139689 | ||||||||
\(804\) | −6.43089e6 | −0.350858 | ||||||||
\(805\) | −7.05981e6 | −0.383976 | ||||||||
\(806\) | −2.77920e6 | −0.150689 | ||||||||
\(807\) | 1.80503e7 | 0.975662 | ||||||||
\(808\) | 1.67418e6 | 0.0902138 | ||||||||
\(809\) | −4.11626e6 | −0.221122 | −0.110561 | − | 0.993869i | \(-0.535265\pi\) | ||||
−0.110561 | + | 0.993869i | \(0.535265\pi\) | |||||||
\(810\) | 234425. | 0.0125543 | ||||||||
\(811\) | −1.46103e7 | −0.780022 | −0.390011 | − | 0.920810i | \(-0.627529\pi\) | ||||
−0.390011 | + | 0.920810i | \(0.627529\pi\) | |||||||
\(812\) | 1.86936e7 | 0.994953 | ||||||||
\(813\) | −1.15948e7 | −0.615227 | ||||||||
\(814\) | 232174. | 0.0122815 | ||||||||
\(815\) | 1.01977e7 | 0.537786 | ||||||||
\(816\) | −4.31937e6 | −0.227089 | ||||||||
\(817\) | −2.39174e7 | −1.25360 | ||||||||
\(818\) | 778656. | 0.0406876 | ||||||||
\(819\) | 7.23650e6 | 0.376981 | ||||||||
\(820\) | −2.04711e7 | −1.06318 | ||||||||
\(821\) | −2.36586e7 | −1.22498 | −0.612492 | − | 0.790477i | \(-0.709833\pi\) | ||||
−0.612492 | + | 0.790477i | \(0.709833\pi\) | |||||||
\(822\) | 1.90255e6 | 0.0982104 | ||||||||
\(823\) | 2.73951e6 | 0.140985 | 0.0704925 | − | 0.997512i | \(-0.477543\pi\) | ||||
0.0704925 | + | 0.997512i | \(0.477543\pi\) | |||||||
\(824\) | −8.89495e6 | −0.456379 | ||||||||
\(825\) | −595554. | −0.0304640 | ||||||||
\(826\) | −315135. | −0.0160712 | ||||||||
\(827\) | 2.71855e7 | 1.38221 | 0.691103 | − | 0.722756i | \(-0.257125\pi\) | ||||
0.691103 | + | 0.722756i | \(0.257125\pi\) | |||||||
\(828\) | −6.10335e6 | −0.309380 | ||||||||
\(829\) | −2.81195e6 | −0.142109 | −0.0710545 | − | 0.997472i | \(-0.522636\pi\) | ||||
−0.0710545 | + | 0.997472i | \(0.522636\pi\) | |||||||
\(830\) | −421687. | −0.0212469 | ||||||||
\(831\) | −1.02241e7 | −0.513595 | ||||||||
\(832\) | 2.72310e7 | 1.36382 | ||||||||
\(833\) | −4.95432e6 | −0.247384 | ||||||||
\(834\) | −128578. | −0.00640103 | ||||||||
\(835\) | 1.93330e7 | 0.959583 | ||||||||
\(836\) | −1.34027e6 | −0.0663248 | ||||||||
\(837\) | −1.83648e6 | −0.0906094 | ||||||||
\(838\) | 6.04388e6 | 0.297308 | ||||||||
\(839\) | −2.10069e6 | −0.103028 | −0.0515142 | − | 0.998672i | \(-0.516405\pi\) | ||||
−0.0515142 | + | 0.998672i | \(0.516405\pi\) | |||||||
\(840\) | −1.73137e6 | −0.0846628 | ||||||||
\(841\) | 2.94688e7 | 1.43672 | ||||||||
\(842\) | −579296. | −0.0281592 | ||||||||
\(843\) | −1.31192e7 | −0.635827 | ||||||||
\(844\) | −1.86917e7 | −0.903219 | ||||||||
\(845\) | 2.42437e7 | 1.16804 | ||||||||
\(846\) | 1.54201e6 | 0.0740734 | ||||||||
\(847\) | 1.36943e7 | 0.655888 | ||||||||
\(848\) | 1.51837e7 | 0.725084 | ||||||||
\(849\) | 2.25332e7 | 1.07289 | ||||||||
\(850\) | −1.09623e6 | −0.0520421 | ||||||||
\(851\) | −1.60559e7 | −0.759995 | ||||||||
\(852\) | −9.89814e6 | −0.467148 | ||||||||
\(853\) | 1.91254e7 | 0.899991 | 0.449996 | − | 0.893031i | \(-0.351426\pi\) | ||||
0.449996 | + | 0.893031i | \(0.351426\pi\) | |||||||
\(854\) | 2.63720e6 | 0.123737 | ||||||||
\(855\) | −3.55998e6 | −0.166545 | ||||||||
\(856\) | 4.76511e6 | 0.222274 | ||||||||
\(857\) | −1.08164e7 | −0.503072 | −0.251536 | − | 0.967848i | \(-0.580936\pi\) | ||||
−0.251536 | + | 0.967848i | \(0.580936\pi\) | |||||||
\(858\) | −331325. | −0.0153651 | ||||||||
\(859\) | −4.44481e6 | −0.205528 | −0.102764 | − | 0.994706i | \(-0.532769\pi\) | ||||
−0.102764 | + | 0.994706i | \(0.532769\pi\) | |||||||
\(860\) | −1.91917e7 | −0.884846 | ||||||||
\(861\) | 1.51160e7 | 0.694911 | ||||||||
\(862\) | −1.27387e6 | −0.0583926 | ||||||||
\(863\) | 3.43899e7 | 1.57183 | 0.785913 | − | 0.618337i | \(-0.212193\pi\) | ||||
0.785913 | + | 0.618337i | \(0.212193\pi\) | |||||||
\(864\) | −2.25852e6 | −0.102929 | ||||||||
\(865\) | −9.45661e6 | −0.429730 | ||||||||
\(866\) | −4.98853e6 | −0.226036 | ||||||||
\(867\) | 1.03185e7 | 0.466194 | ||||||||
\(868\) | 6.66123e6 | 0.300092 | ||||||||
\(869\) | −2.05485e6 | −0.0923062 | ||||||||
\(870\) | −2.27339e6 | −0.101830 | ||||||||
\(871\) | 2.41423e7 | 1.07828 | ||||||||
\(872\) | 6.74566e6 | 0.300423 | ||||||||
\(873\) | −7.23203e6 | −0.321162 | ||||||||
\(874\) | −3.35518e6 | −0.148572 | ||||||||
\(875\) | 1.47798e7 | 0.652604 | ||||||||
\(876\) | 2.12593e7 | 0.936030 | ||||||||
\(877\) | 2.34437e7 | 1.02926 | 0.514632 | − | 0.857411i | \(-0.327929\pi\) | ||||
0.514632 | + | 0.857411i | \(0.327929\pi\) | |||||||
\(878\) | −3.66972e6 | −0.160656 | ||||||||
\(879\) | −1.28859e7 | −0.562525 | ||||||||
\(880\) | −1.03511e6 | −0.0450590 | ||||||||
\(881\) | 1.52635e7 | 0.662542 | 0.331271 | − | 0.943536i | \(-0.392523\pi\) | ||||
0.331271 | + | 0.943536i | \(0.392523\pi\) | |||||||
\(882\) | −811531. | −0.0351264 | ||||||||
\(883\) | 1.88369e7 | 0.813034 | 0.406517 | − | 0.913643i | \(-0.366743\pi\) | ||||
0.406517 | + | 0.913643i | \(0.366743\pi\) | |||||||
\(884\) | 1.68473e7 | 0.725104 | ||||||||
\(885\) | −1.05870e6 | −0.0454377 | ||||||||
\(886\) | −2.19855e6 | −0.0940917 | ||||||||
\(887\) | 3.45462e7 | 1.47432 | 0.737160 | − | 0.675718i | \(-0.236166\pi\) | ||||
0.737160 | + | 0.675718i | \(0.236166\pi\) | |||||||
\(888\) | −3.93761e6 | −0.167572 | ||||||||
\(889\) | −2.47163e6 | −0.104889 | ||||||||
\(890\) | 1.24868e6 | 0.0528418 | ||||||||
\(891\) | −218938. | −0.00923903 | ||||||||
\(892\) | −4.17474e7 | −1.75678 | ||||||||
\(893\) | −2.34171e7 | −0.982661 | ||||||||
\(894\) | 4.26333e6 | 0.178404 | ||||||||
\(895\) | 1.42545e7 | 0.594832 | ||||||||
\(896\) | 1.08512e7 | 0.451553 | ||||||||
\(897\) | 2.29126e7 | 0.950810 | ||||||||
\(898\) | −4.15488e6 | −0.171936 | ||||||||
\(899\) | 1.78097e7 | 0.734951 | ||||||||
\(900\) | 4.96043e6 | 0.204133 | ||||||||
\(901\) | 8.64843e6 | 0.354916 | ||||||||
\(902\) | −692089. | −0.0283234 | ||||||||
\(903\) | 1.41713e7 | 0.578349 | ||||||||
\(904\) | −1.56186e7 | −0.635656 | ||||||||
\(905\) | −8.70909e6 | −0.353469 | ||||||||
\(906\) | 2.11054e6 | 0.0854228 | ||||||||
\(907\) | −1.49504e7 | −0.603440 | −0.301720 | − | 0.953397i | \(-0.597561\pi\) | ||||
−0.301720 | + | 0.953397i | \(0.597561\pi\) | |||||||
\(908\) | −8.92713e6 | −0.359333 | ||||||||
\(909\) | −2.03964e6 | −0.0818738 | ||||||||
\(910\) | 3.19211e6 | 0.127783 | ||||||||
\(911\) | −4.82835e7 | −1.92754 | −0.963768 | − | 0.266741i | \(-0.914053\pi\) | ||||
−0.963768 | + | 0.266741i | \(0.914053\pi\) | |||||||
\(912\) | 1.07445e7 | 0.427759 | ||||||||
\(913\) | 393829. | 0.0156362 | ||||||||
\(914\) | −518945. | −0.0205473 | ||||||||
\(915\) | 8.85973e6 | 0.349839 | ||||||||
\(916\) | −2.63107e7 | −1.03608 | ||||||||
\(917\) | −1.02248e7 | −0.401541 | ||||||||
\(918\) | −402997. | −0.0157832 | ||||||||
\(919\) | 2.12186e7 | 0.828758 | 0.414379 | − | 0.910105i | \(-0.363999\pi\) | ||||
0.414379 | + | 0.910105i | \(0.363999\pi\) | |||||||
\(920\) | −5.48198e6 | −0.213534 | ||||||||
\(921\) | 1.94868e7 | 0.756991 | ||||||||
\(922\) | −6.43067e6 | −0.249132 | ||||||||
\(923\) | 3.71587e7 | 1.43567 | ||||||||
\(924\) | 794123. | 0.0305991 | ||||||||
\(925\) | 1.30493e7 | 0.501455 | ||||||||
\(926\) | 9.43352e6 | 0.361532 | ||||||||
\(927\) | 1.08367e7 | 0.414188 | ||||||||
\(928\) | 2.19025e7 | 0.834879 | ||||||||
\(929\) | 1.47484e6 | 0.0560667 | 0.0280333 | − | 0.999607i | \(-0.491076\pi\) | ||||
0.0280333 | + | 0.999607i | \(0.491076\pi\) | |||||||
\(930\) | −810094. | −0.0307134 | ||||||||
\(931\) | 1.23239e7 | 0.465988 | ||||||||
\(932\) | −4.68507e7 | −1.76676 | ||||||||
\(933\) | −1.15628e7 | −0.434869 | ||||||||
\(934\) | 2.02622e6 | 0.0760011 | ||||||||
\(935\) | −589587. | −0.0220556 | ||||||||
\(936\) | 5.61918e6 | 0.209644 | ||||||||
\(937\) | −2.87501e7 | −1.06977 | −0.534885 | − | 0.844925i | \(-0.679645\pi\) | ||||
−0.534885 | + | 0.844925i | \(0.679645\pi\) | |||||||
\(938\) | 2.09467e6 | 0.0777335 | ||||||||
\(939\) | 1.72713e6 | 0.0639235 | ||||||||
\(940\) | −1.87903e7 | −0.693607 | ||||||||
\(941\) | 4.42692e7 | 1.62978 | 0.814888 | − | 0.579618i | \(-0.196798\pi\) | ||||
0.814888 | + | 0.579618i | \(0.196798\pi\) | |||||||
\(942\) | −1.29308e6 | −0.0474785 | ||||||||
\(943\) | 4.78611e7 | 1.75268 | ||||||||
\(944\) | 3.19531e6 | 0.116703 | ||||||||
\(945\) | 2.10933e6 | 0.0768360 | ||||||||
\(946\) | −648836. | −0.0235726 | ||||||||
\(947\) | −8.37611e6 | −0.303506 | −0.151753 | − | 0.988418i | \(-0.548492\pi\) | ||||
−0.151753 | + | 0.988418i | \(0.548492\pi\) | |||||||
\(948\) | 1.71151e7 | 0.618526 | ||||||||
\(949\) | −7.98098e7 | −2.87668 | ||||||||
\(950\) | 2.72689e6 | 0.0980299 | ||||||||
\(951\) | −2.52828e7 | −0.906514 | ||||||||
\(952\) | 2.97638e6 | 0.106438 | ||||||||
\(953\) | 1.04083e7 | 0.371232 | 0.185616 | − | 0.982622i | \(-0.440572\pi\) | ||||
0.185616 | + | 0.982622i | \(0.440572\pi\) | |||||||
\(954\) | 1.41664e6 | 0.0503950 | ||||||||
\(955\) | −8.65531e6 | −0.307096 | ||||||||
\(956\) | 5.15719e6 | 0.182502 | ||||||||
\(957\) | 2.12320e6 | 0.0749396 | ||||||||
\(958\) | −2.52613e6 | −0.0889287 | ||||||||
\(959\) | 1.71190e7 | 0.601078 | ||||||||
\(960\) | 7.93742e6 | 0.277972 | ||||||||
\(961\) | −2.22829e7 | −0.778328 | ||||||||
\(962\) | 7.25970e6 | 0.252919 | ||||||||
\(963\) | −5.80532e6 | −0.201725 | ||||||||
\(964\) | 7.05917e6 | 0.244659 | ||||||||
\(965\) | −2.66343e7 | −0.920709 | ||||||||
\(966\) | 1.98798e6 | 0.0685440 | ||||||||
\(967\) | −3.41560e7 | −1.17463 | −0.587315 | − | 0.809358i | \(-0.699815\pi\) | ||||
−0.587315 | + | 0.809358i | \(0.699815\pi\) | |||||||
\(968\) | 1.06336e7 | 0.364749 | ||||||||
\(969\) | 6.11992e6 | 0.209380 | ||||||||
\(970\) | −3.19013e6 | −0.108863 | ||||||||
\(971\) | −2.80041e7 | −0.953176 | −0.476588 | − | 0.879127i | \(-0.658127\pi\) | ||||
−0.476588 | + | 0.879127i | \(0.658127\pi\) | |||||||
\(972\) | 1.82356e6 | 0.0619090 | ||||||||
\(973\) | −1.15693e6 | −0.0391763 | ||||||||
\(974\) | −926314. | −0.0312868 | ||||||||
\(975\) | −1.86220e7 | −0.627357 | ||||||||
\(976\) | −2.67399e7 | −0.898534 | ||||||||
\(977\) | −4.46833e6 | −0.149764 | −0.0748822 | − | 0.997192i | \(-0.523858\pi\) | ||||
−0.0748822 | + | 0.997192i | \(0.523858\pi\) | |||||||
\(978\) | −2.87159e6 | −0.0960010 | ||||||||
\(979\) | −1.16619e6 | −0.0388878 | ||||||||
\(980\) | 9.88894e6 | 0.328916 | ||||||||
\(981\) | −8.21821e6 | −0.272649 | ||||||||
\(982\) | 2.61161e6 | 0.0864231 | ||||||||
\(983\) | −2.39250e7 | −0.789711 | −0.394856 | − | 0.918743i | \(-0.629205\pi\) | ||||
−0.394856 | + | 0.918743i | \(0.629205\pi\) | |||||||
\(984\) | 1.17376e7 | 0.386450 | ||||||||
\(985\) | 3.22303e7 | 1.05846 | ||||||||
\(986\) | 3.90815e6 | 0.128020 | ||||||||
\(987\) | 1.38749e7 | 0.453353 | ||||||||
\(988\) | −4.19079e7 | −1.36585 | ||||||||
\(989\) | 4.48700e7 | 1.45870 | ||||||||
\(990\) | −96576.0 | −0.00313171 | ||||||||
\(991\) | −7.93514e6 | −0.256667 | −0.128334 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128334 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(992\) | 7.80469e6 | 0.251812 | ||||||||
\(993\) | 942808. | 0.0303424 | ||||||||
\(994\) | 3.22402e6 | 0.103498 | ||||||||
\(995\) | 2.34828e7 | 0.751956 | ||||||||
\(996\) | −3.28024e6 | −0.104775 | ||||||||
\(997\) | −7.07884e6 | −0.225540 | −0.112770 | − | 0.993621i | \(-0.535972\pi\) | ||||
−0.112770 | + | 0.993621i | \(0.535972\pi\) | |||||||
\(998\) | −2.02127e6 | −0.0642390 | ||||||||
\(999\) | 4.79718e6 | 0.152080 |
(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 | 177.6.a.d.1.7 | ✓ | 13 | |
3.2 | odd | 2 | 531.6.a.e.1.7 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.d.1.7 | ✓ | 13 | 1.1 | even | 1 | trivial | |
531.6.a.e.1.7 | 13 | 3.2 | odd | 2 |