Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,6,Mod(1,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, 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("130.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.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: | \(20.8498965757\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1458804.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 361x - 1139 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(20.8905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −27.8905 | −1.78918 | −0.894588 | − | 0.446892i | \(-0.852531\pi\) | ||||
−0.894588 | + | 0.446892i | \(0.852531\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 111.562 | 1.26514 | ||||||||
\(7\) | −240.426 | −1.85454 | −0.927269 | − | 0.374397i | \(-0.877850\pi\) | ||||
−0.927269 | + | 0.374397i | \(0.877850\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 534.880 | 2.20115 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 544.151 | 1.35593 | 0.677966 | − | 0.735093i | \(-0.262862\pi\) | ||||
0.677966 | + | 0.735093i | \(0.262862\pi\) | |||||||
\(12\) | −446.248 | −0.894588 | ||||||||
\(13\) | 169.000 | 0.277350 | ||||||||
\(14\) | 961.702 | 1.31136 | ||||||||
\(15\) | −697.262 | −0.800144 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1629.30 | 1.36735 | 0.683673 | − | 0.729788i | \(-0.260381\pi\) | ||||
0.683673 | + | 0.729788i | \(0.260381\pi\) | |||||||
\(18\) | −2139.52 | −1.55645 | ||||||||
\(19\) | −805.920 | −0.512162 | −0.256081 | − | 0.966655i | \(-0.582431\pi\) | ||||
−0.256081 | + | 0.966655i | \(0.582431\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 6705.59 | 3.31809 | ||||||||
\(22\) | −2176.61 | −0.958789 | ||||||||
\(23\) | 373.152 | 0.147084 | 0.0735421 | − | 0.997292i | \(-0.476570\pi\) | ||||
0.0735421 | + | 0.997292i | \(0.476570\pi\) | |||||||
\(24\) | 1784.99 | 0.632569 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −676.000 | −0.196116 | ||||||||
\(27\) | −8140.67 | −2.14907 | ||||||||
\(28\) | −3846.81 | −0.927269 | ||||||||
\(29\) | 1503.62 | 0.332003 | 0.166001 | − | 0.986126i | \(-0.446914\pi\) | ||||
0.166001 | + | 0.986126i | \(0.446914\pi\) | |||||||
\(30\) | 2789.05 | 0.565787 | ||||||||
\(31\) | −2200.08 | −0.411182 | −0.205591 | − | 0.978638i | \(-0.565912\pi\) | ||||
−0.205591 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −15176.7 | −2.42600 | ||||||||
\(34\) | −6517.20 | −0.966860 | ||||||||
\(35\) | −6010.64 | −0.829374 | ||||||||
\(36\) | 8558.08 | 1.10058 | ||||||||
\(37\) | −13109.1 | −1.57423 | −0.787117 | − | 0.616804i | \(-0.788427\pi\) | ||||
−0.787117 | + | 0.616804i | \(0.788427\pi\) | |||||||
\(38\) | 3223.68 | 0.362154 | ||||||||
\(39\) | −4713.49 | −0.496228 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −17099.9 | −1.58867 | −0.794337 | − | 0.607477i | \(-0.792182\pi\) | ||||
−0.794337 | + | 0.607477i | \(0.792182\pi\) | |||||||
\(42\) | −26822.4 | −2.34625 | ||||||||
\(43\) | −8935.58 | −0.736973 | −0.368487 | − | 0.929633i | \(-0.620124\pi\) | ||||
−0.368487 | + | 0.929633i | \(0.620124\pi\) | |||||||
\(44\) | 8706.42 | 0.677966 | ||||||||
\(45\) | 13372.0 | 0.984385 | ||||||||
\(46\) | −1492.61 | −0.104004 | ||||||||
\(47\) | 15749.7 | 1.03999 | 0.519995 | − | 0.854170i | \(-0.325934\pi\) | ||||
0.519995 | + | 0.854170i | \(0.325934\pi\) | |||||||
\(48\) | −7139.97 | −0.447294 | ||||||||
\(49\) | 40997.5 | 2.43931 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −45442.0 | −2.44642 | ||||||||
\(52\) | 2704.00 | 0.138675 | ||||||||
\(53\) | 40379.7 | 1.97457 | 0.987286 | − | 0.158951i | \(-0.0508112\pi\) | ||||
0.987286 | + | 0.158951i | \(0.0508112\pi\) | |||||||
\(54\) | 32562.7 | 1.51962 | ||||||||
\(55\) | 13603.8 | 0.606391 | ||||||||
\(56\) | 15387.2 | 0.655678 | ||||||||
\(57\) | 22477.5 | 0.916349 | ||||||||
\(58\) | −6014.46 | −0.234761 | ||||||||
\(59\) | −47562.1 | −1.77881 | −0.889407 | − | 0.457116i | \(-0.848882\pi\) | ||||
−0.889407 | + | 0.457116i | \(0.848882\pi\) | |||||||
\(60\) | −11156.2 | −0.400072 | ||||||||
\(61\) | −30280.0 | −1.04191 | −0.520956 | − | 0.853584i | \(-0.674424\pi\) | ||||
−0.520956 | + | 0.853584i | \(0.674424\pi\) | |||||||
\(62\) | 8800.31 | 0.290749 | ||||||||
\(63\) | −128599. | −4.08212 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 4225.00 | 0.124035 | ||||||||
\(66\) | 60706.6 | 1.71544 | ||||||||
\(67\) | 38769.4 | 1.05512 | 0.527561 | − | 0.849517i | \(-0.323107\pi\) | ||||
0.527561 | + | 0.849517i | \(0.323107\pi\) | |||||||
\(68\) | 26068.8 | 0.683673 | ||||||||
\(69\) | −10407.4 | −0.263160 | ||||||||
\(70\) | 24042.6 | 0.586456 | ||||||||
\(71\) | −10519.7 | −0.247660 | −0.123830 | − | 0.992303i | \(-0.539518\pi\) | ||||
−0.123830 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(72\) | −34232.3 | −0.778225 | ||||||||
\(73\) | 1582.12 | 0.0347483 | 0.0173742 | − | 0.999849i | \(-0.494469\pi\) | ||||
0.0173742 | + | 0.999849i | \(0.494469\pi\) | |||||||
\(74\) | 52436.5 | 1.11315 | ||||||||
\(75\) | −17431.6 | −0.357835 | ||||||||
\(76\) | −12894.7 | −0.256081 | ||||||||
\(77\) | −130828. | −2.51463 | ||||||||
\(78\) | 18854.0 | 0.350886 | ||||||||
\(79\) | −6191.23 | −0.111612 | −0.0558058 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558058 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 97071.7 | 1.64392 | ||||||||
\(82\) | 68399.8 | 1.12336 | ||||||||
\(83\) | 37849.2 | 0.603062 | 0.301531 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301531 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(84\) | 107289. | 1.65905 | ||||||||
\(85\) | 40732.5 | 0.611496 | ||||||||
\(86\) | 35742.3 | 0.521119 | ||||||||
\(87\) | −41936.6 | −0.594011 | ||||||||
\(88\) | −34825.7 | −0.479394 | ||||||||
\(89\) | 49151.0 | 0.657744 | 0.328872 | − | 0.944374i | \(-0.393331\pi\) | ||||
0.328872 | + | 0.944374i | \(0.393331\pi\) | |||||||
\(90\) | −53488.0 | −0.696065 | ||||||||
\(91\) | −40631.9 | −0.514356 | ||||||||
\(92\) | 5970.43 | 0.0735421 | ||||||||
\(93\) | 61361.3 | 0.735677 | ||||||||
\(94\) | −62999.0 | −0.735383 | ||||||||
\(95\) | −20148.0 | −0.229046 | ||||||||
\(96\) | 28559.9 | 0.316285 | ||||||||
\(97\) | −15654.2 | −0.168928 | −0.0844641 | − | 0.996427i | \(-0.526918\pi\) | ||||
−0.0844641 | + | 0.996427i | \(0.526918\pi\) | |||||||
\(98\) | −163990. | −1.72485 | ||||||||
\(99\) | 291056. | 2.98461 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −138108. | −1.34714 | −0.673572 | − | 0.739122i | \(-0.735241\pi\) | ||||
−0.673572 | + | 0.739122i | \(0.735241\pi\) | |||||||
\(102\) | 181768. | 1.72988 | ||||||||
\(103\) | −47642.1 | −0.442484 | −0.221242 | − | 0.975219i | \(-0.571011\pi\) | ||||
−0.221242 | + | 0.975219i | \(0.571011\pi\) | |||||||
\(104\) | −10816.0 | −0.0980581 | ||||||||
\(105\) | 167640. | 1.48390 | ||||||||
\(106\) | −161519. | −1.39623 | ||||||||
\(107\) | −186527. | −1.57500 | −0.787501 | − | 0.616313i | \(-0.788626\pi\) | ||||
−0.787501 | + | 0.616313i | \(0.788626\pi\) | |||||||
\(108\) | −130251. | −1.07454 | ||||||||
\(109\) | 14407.1 | 0.116147 | 0.0580736 | − | 0.998312i | \(-0.481504\pi\) | ||||
0.0580736 | + | 0.998312i | \(0.481504\pi\) | |||||||
\(110\) | −54415.1 | −0.428783 | ||||||||
\(111\) | 365620. | 2.81658 | ||||||||
\(112\) | −61548.9 | −0.463634 | ||||||||
\(113\) | −50802.0 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(114\) | −89910.0 | −0.647957 | ||||||||
\(115\) | 9328.80 | 0.0657781 | ||||||||
\(116\) | 24057.8 | 0.166001 | ||||||||
\(117\) | 90394.7 | 0.610490 | ||||||||
\(118\) | 190248. | 1.25781 | ||||||||
\(119\) | −391725. | −2.53580 | ||||||||
\(120\) | 44624.8 | 0.282894 | ||||||||
\(121\) | 135050. | 0.838552 | ||||||||
\(122\) | 121120. | 0.736742 | ||||||||
\(123\) | 476926. | 2.84242 | ||||||||
\(124\) | −35201.3 | −0.205591 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 514395. | 2.88649 | ||||||||
\(127\) | −182278. | −1.00282 | −0.501411 | − | 0.865209i | \(-0.667186\pi\) | ||||
−0.501411 | + | 0.865209i | \(0.667186\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 249218. | 1.31858 | ||||||||
\(130\) | −16900.0 | −0.0877058 | ||||||||
\(131\) | 199714. | 1.01679 | 0.508394 | − | 0.861124i | \(-0.330239\pi\) | ||||
0.508394 | + | 0.861124i | \(0.330239\pi\) | |||||||
\(132\) | −242826. | −1.21300 | ||||||||
\(133\) | 193764. | 0.949824 | ||||||||
\(134\) | −155078. | −0.746083 | ||||||||
\(135\) | −203517. | −0.961094 | ||||||||
\(136\) | −104275. | −0.483430 | ||||||||
\(137\) | −345418. | −1.57233 | −0.786165 | − | 0.618017i | \(-0.787936\pi\) | ||||
−0.786165 | + | 0.618017i | \(0.787936\pi\) | |||||||
\(138\) | 41629.6 | 0.186082 | ||||||||
\(139\) | 183088. | 0.803754 | 0.401877 | − | 0.915694i | \(-0.368358\pi\) | ||||
0.401877 | + | 0.915694i | \(0.368358\pi\) | |||||||
\(140\) | −96170.2 | −0.414687 | ||||||||
\(141\) | −439268. | −1.86072 | ||||||||
\(142\) | 42078.7 | 0.175122 | ||||||||
\(143\) | 91961.6 | 0.376068 | ||||||||
\(144\) | 136929. | 0.550288 | ||||||||
\(145\) | 37590.4 | 0.148476 | ||||||||
\(146\) | −6328.50 | −0.0245708 | ||||||||
\(147\) | −1.14344e6 | −4.36435 | ||||||||
\(148\) | −209746. | −0.787117 | ||||||||
\(149\) | −187082. | −0.690344 | −0.345172 | − | 0.938540i | \(-0.612179\pi\) | ||||
−0.345172 | + | 0.938540i | \(0.612179\pi\) | |||||||
\(150\) | 69726.2 | 0.253028 | ||||||||
\(151\) | −10616.3 | −0.0378907 | −0.0189454 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189454 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(152\) | 51578.9 | 0.181077 | ||||||||
\(153\) | 871480. | 3.00974 | ||||||||
\(154\) | 523312. | 1.77811 | ||||||||
\(155\) | −55002.0 | −0.183886 | ||||||||
\(156\) | −75415.9 | −0.248114 | ||||||||
\(157\) | −335884. | −1.08753 | −0.543764 | − | 0.839238i | \(-0.683001\pi\) | ||||
−0.543764 | + | 0.839238i | \(0.683001\pi\) | |||||||
\(158\) | 24764.9 | 0.0789213 | ||||||||
\(159\) | −1.12621e6 | −3.53286 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −89715.3 | −0.272773 | ||||||||
\(162\) | −388287. | −1.16242 | ||||||||
\(163\) | 201881. | 0.595150 | 0.297575 | − | 0.954698i | \(-0.403822\pi\) | ||||
0.297575 | + | 0.954698i | \(0.403822\pi\) | |||||||
\(164\) | −273599. | −0.794337 | ||||||||
\(165\) | −379416. | −1.08494 | ||||||||
\(166\) | −151397. | −0.426429 | ||||||||
\(167\) | −446050. | −1.23764 | −0.618818 | − | 0.785535i | \(-0.712388\pi\) | ||||
−0.618818 | + | 0.785535i | \(0.712388\pi\) | |||||||
\(168\) | −429158. | −1.17312 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | −162930. | −0.432393 | ||||||||
\(171\) | −431070. | −1.12735 | ||||||||
\(172\) | −142969. | −0.368487 | ||||||||
\(173\) | 57408.8 | 0.145835 | 0.0729177 | − | 0.997338i | \(-0.476769\pi\) | ||||
0.0729177 | + | 0.997338i | \(0.476769\pi\) | |||||||
\(174\) | 167746. | 0.420030 | ||||||||
\(175\) | −150266. | −0.370907 | ||||||||
\(176\) | 139303. | 0.338983 | ||||||||
\(177\) | 1.32653e6 | 3.18261 | ||||||||
\(178\) | −196604. | −0.465095 | ||||||||
\(179\) | 87439.4 | 0.203974 | 0.101987 | − | 0.994786i | \(-0.467480\pi\) | ||||
0.101987 | + | 0.994786i | \(0.467480\pi\) | |||||||
\(180\) | 213952. | 0.492192 | ||||||||
\(181\) | 21341.6 | 0.0484206 | 0.0242103 | − | 0.999707i | \(-0.492293\pi\) | ||||
0.0242103 | + | 0.999707i | \(0.492293\pi\) | |||||||
\(182\) | 162528. | 0.363705 | ||||||||
\(183\) | 844523. | 1.86416 | ||||||||
\(184\) | −23881.7 | −0.0520021 | ||||||||
\(185\) | −327728. | −0.704019 | ||||||||
\(186\) | −245445. | −0.520202 | ||||||||
\(187\) | 886586. | 1.85403 | ||||||||
\(188\) | 251996. | 0.519995 | ||||||||
\(189\) | 1.95723e6 | 3.98553 | ||||||||
\(190\) | 80592.0 | 0.161960 | ||||||||
\(191\) | 307517. | 0.609938 | 0.304969 | − | 0.952362i | \(-0.401354\pi\) | ||||
0.304969 | + | 0.952362i | \(0.401354\pi\) | |||||||
\(192\) | −114239. | −0.223647 | ||||||||
\(193\) | 182409. | 0.352496 | 0.176248 | − | 0.984346i | \(-0.443604\pi\) | ||||
0.176248 | + | 0.984346i | \(0.443604\pi\) | |||||||
\(194\) | 62616.9 | 0.119450 | ||||||||
\(195\) | −117837. | −0.221920 | ||||||||
\(196\) | 655959. | 1.21965 | ||||||||
\(197\) | −152508. | −0.279980 | −0.139990 | − | 0.990153i | \(-0.544707\pi\) | ||||
−0.139990 | + | 0.990153i | \(0.544707\pi\) | |||||||
\(198\) | −1.16422e6 | −2.11044 | ||||||||
\(199\) | −586606. | −1.05006 | −0.525029 | − | 0.851084i | \(-0.675946\pi\) | ||||
−0.525029 | + | 0.851084i | \(0.675946\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −1.08130e6 | −1.88780 | ||||||||
\(202\) | 552430. | 0.952574 | ||||||||
\(203\) | −361508. | −0.615711 | ||||||||
\(204\) | −727072. | −1.22321 | ||||||||
\(205\) | −427498. | −0.710477 | ||||||||
\(206\) | 190568. | 0.312884 | ||||||||
\(207\) | 199592. | 0.323755 | ||||||||
\(208\) | 43264.0 | 0.0693375 | ||||||||
\(209\) | −438542. | −0.694458 | ||||||||
\(210\) | −670559. | −1.04927 | ||||||||
\(211\) | −207041. | −0.320147 | −0.160073 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160073 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(212\) | 646075. | 0.987286 | ||||||||
\(213\) | 293399. | 0.443108 | ||||||||
\(214\) | 746106. | 1.11369 | ||||||||
\(215\) | −223390. | −0.329585 | ||||||||
\(216\) | 521003. | 0.759812 | ||||||||
\(217\) | 528955. | 0.762552 | ||||||||
\(218\) | −57628.2 | −0.0821285 | ||||||||
\(219\) | −44126.3 | −0.0621708 | ||||||||
\(220\) | 217661. | 0.303196 | ||||||||
\(221\) | 275352. | 0.379234 | ||||||||
\(222\) | −1.46248e6 | −1.99162 | ||||||||
\(223\) | −1.04889e6 | −1.41243 | −0.706214 | − | 0.707998i | \(-0.749599\pi\) | ||||
−0.706214 | + | 0.707998i | \(0.749599\pi\) | |||||||
\(224\) | 246196. | 0.327839 | ||||||||
\(225\) | 334300. | 0.440230 | ||||||||
\(226\) | 203208. | 0.264649 | ||||||||
\(227\) | −100709. | −0.129719 | −0.0648593 | − | 0.997894i | \(-0.520660\pi\) | ||||
−0.0648593 | + | 0.997894i | \(0.520660\pi\) | |||||||
\(228\) | 359640. | 0.458174 | ||||||||
\(229\) | 487174. | 0.613896 | 0.306948 | − | 0.951726i | \(-0.400692\pi\) | ||||
0.306948 | + | 0.951726i | \(0.400692\pi\) | |||||||
\(230\) | −37315.2 | −0.0465121 | ||||||||
\(231\) | 3.64886e6 | 4.49911 | ||||||||
\(232\) | −96231.4 | −0.117381 | ||||||||
\(233\) | −832844. | −1.00502 | −0.502509 | − | 0.864572i | \(-0.667590\pi\) | ||||
−0.502509 | + | 0.864572i | \(0.667590\pi\) | |||||||
\(234\) | −361579. | −0.431681 | ||||||||
\(235\) | 393744. | 0.465097 | ||||||||
\(236\) | −760993. | −0.889407 | ||||||||
\(237\) | 172677. | 0.199693 | ||||||||
\(238\) | 1.56690e6 | 1.79308 | ||||||||
\(239\) | 1.34919e6 | 1.52785 | 0.763923 | − | 0.645308i | \(-0.223271\pi\) | ||||
0.763923 | + | 0.645308i | \(0.223271\pi\) | |||||||
\(240\) | −178499. | −0.200036 | ||||||||
\(241\) | −1.66283e6 | −1.84419 | −0.922096 | − | 0.386962i | \(-0.873524\pi\) | ||||
−0.922096 | + | 0.386962i | \(0.873524\pi\) | |||||||
\(242\) | −540199. | −0.592946 | ||||||||
\(243\) | −729193. | −0.792185 | ||||||||
\(244\) | −484479. | −0.520956 | ||||||||
\(245\) | 1.02494e6 | 1.09089 | ||||||||
\(246\) | −1.90770e6 | −2.00989 | ||||||||
\(247\) | −136200. | −0.142048 | ||||||||
\(248\) | 140805. | 0.145375 | ||||||||
\(249\) | −1.05563e6 | −1.07898 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −291273. | −0.291820 | −0.145910 | − | 0.989298i | \(-0.546611\pi\) | ||||
−0.145910 | + | 0.989298i | \(0.546611\pi\) | |||||||
\(252\) | −2.05758e6 | −2.04106 | ||||||||
\(253\) | 203051. | 0.199436 | ||||||||
\(254\) | 729110. | 0.709102 | ||||||||
\(255\) | −1.13605e6 | −1.09407 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −548204. | −0.517737 | −0.258868 | − | 0.965913i | \(-0.583350\pi\) | ||||
−0.258868 | + | 0.965913i | \(0.583350\pi\) | |||||||
\(258\) | −996872. | −0.932374 | ||||||||
\(259\) | 3.15177e6 | 2.91947 | ||||||||
\(260\) | 67600.0 | 0.0620174 | ||||||||
\(261\) | 804253. | 0.730788 | ||||||||
\(262\) | −798857. | −0.718978 | ||||||||
\(263\) | 818412. | 0.729596 | 0.364798 | − | 0.931087i | \(-0.381138\pi\) | ||||
0.364798 | + | 0.931087i | \(0.381138\pi\) | |||||||
\(264\) | 971306. | 0.857721 | ||||||||
\(265\) | 1.00949e6 | 0.883056 | ||||||||
\(266\) | −775055. | −0.671627 | ||||||||
\(267\) | −1.37085e6 | −1.17682 | ||||||||
\(268\) | 620311. | 0.527561 | ||||||||
\(269\) | −939455. | −0.791581 | −0.395790 | − | 0.918341i | \(-0.629529\pi\) | ||||
−0.395790 | + | 0.918341i | \(0.629529\pi\) | |||||||
\(270\) | 814067. | 0.679596 | ||||||||
\(271\) | −1.52416e6 | −1.26069 | −0.630345 | − | 0.776315i | \(-0.717087\pi\) | ||||
−0.630345 | + | 0.776315i | \(0.717087\pi\) | |||||||
\(272\) | 417101. | 0.341837 | ||||||||
\(273\) | 1.13324e6 | 0.920274 | ||||||||
\(274\) | 1.38167e6 | 1.11180 | ||||||||
\(275\) | 340095. | 0.271186 | ||||||||
\(276\) | −166518. | −0.131580 | ||||||||
\(277\) | −439704. | −0.344319 | −0.172159 | − | 0.985069i | \(-0.555074\pi\) | ||||
−0.172159 | + | 0.985069i | \(0.555074\pi\) | |||||||
\(278\) | −732352. | −0.568340 | ||||||||
\(279\) | −1.17678e6 | −0.905074 | ||||||||
\(280\) | 384681. | 0.293228 | ||||||||
\(281\) | −592033. | −0.447280 | −0.223640 | − | 0.974672i | \(-0.571794\pi\) | ||||
−0.223640 | + | 0.974672i | \(0.571794\pi\) | |||||||
\(282\) | 1.75707e6 | 1.31573 | ||||||||
\(283\) | −777226. | −0.576875 | −0.288437 | − | 0.957499i | \(-0.593136\pi\) | ||||
−0.288437 | + | 0.957499i | \(0.593136\pi\) | |||||||
\(284\) | −168315. | −0.123830 | ||||||||
\(285\) | 561938. | 0.409804 | ||||||||
\(286\) | −367846. | −0.265920 | ||||||||
\(287\) | 4.11126e6 | 2.94626 | ||||||||
\(288\) | −547717. | −0.389112 | ||||||||
\(289\) | 1.23476e6 | 0.869637 | ||||||||
\(290\) | −150362. | −0.104988 | ||||||||
\(291\) | 436604. | 0.302242 | ||||||||
\(292\) | 25314.0 | 0.0173742 | ||||||||
\(293\) | 609025. | 0.414444 | 0.207222 | − | 0.978294i | \(-0.433558\pi\) | ||||
0.207222 | + | 0.978294i | \(0.433558\pi\) | |||||||
\(294\) | 4.57376e6 | 3.08606 | ||||||||
\(295\) | −1.18905e6 | −0.795510 | ||||||||
\(296\) | 838984. | 0.556576 | ||||||||
\(297\) | −4.42976e6 | −2.91400 | ||||||||
\(298\) | 748326. | 0.488147 | ||||||||
\(299\) | 63062.7 | 0.0407938 | ||||||||
\(300\) | −278905. | −0.178918 | ||||||||
\(301\) | 2.14834e6 | 1.36674 | ||||||||
\(302\) | 42465.4 | 0.0267928 | ||||||||
\(303\) | 3.85189e6 | 2.41028 | ||||||||
\(304\) | −206315. | −0.128041 | ||||||||
\(305\) | −756999. | −0.465957 | ||||||||
\(306\) | −3.48592e6 | −2.12821 | ||||||||
\(307\) | −2.66761e6 | −1.61538 | −0.807692 | − | 0.589604i | \(-0.799284\pi\) | ||||
−0.807692 | + | 0.589604i | \(0.799284\pi\) | |||||||
\(308\) | −2.09325e6 | −1.25731 | ||||||||
\(309\) | 1.32876e6 | 0.791682 | ||||||||
\(310\) | 220008. | 0.130027 | ||||||||
\(311\) | −1.62320e6 | −0.951634 | −0.475817 | − | 0.879544i | \(-0.657847\pi\) | ||||
−0.475817 | + | 0.879544i | \(0.657847\pi\) | |||||||
\(312\) | 301664. | 0.175443 | ||||||||
\(313\) | 592115. | 0.341622 | 0.170811 | − | 0.985304i | \(-0.445361\pi\) | ||||
0.170811 | + | 0.985304i | \(0.445361\pi\) | |||||||
\(314\) | 1.34354e6 | 0.768998 | ||||||||
\(315\) | −3.21497e6 | −1.82558 | ||||||||
\(316\) | −99059.7 | −0.0558058 | ||||||||
\(317\) | −2.61036e6 | −1.45899 | −0.729494 | − | 0.683987i | \(-0.760244\pi\) | ||||
−0.729494 | + | 0.683987i | \(0.760244\pi\) | |||||||
\(318\) | 4.50484e6 | 2.49811 | ||||||||
\(319\) | 818194. | 0.450173 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 5.20232e6 | 2.81796 | ||||||||
\(322\) | 358861. | 0.192880 | ||||||||
\(323\) | −1.31308e6 | −0.700304 | ||||||||
\(324\) | 1.55315e6 | 0.821959 | ||||||||
\(325\) | 105625. | 0.0554700 | ||||||||
\(326\) | −807524. | −0.420834 | ||||||||
\(327\) | −401820. | −0.207808 | ||||||||
\(328\) | 1.09440e6 | 0.561681 | ||||||||
\(329\) | −3.78664e6 | −1.92870 | ||||||||
\(330\) | 1.51767e6 | 0.767169 | ||||||||
\(331\) | 818785. | 0.410771 | 0.205386 | − | 0.978681i | \(-0.434155\pi\) | ||||
0.205386 | + | 0.978681i | \(0.434155\pi\) | |||||||
\(332\) | 605588. | 0.301531 | ||||||||
\(333\) | −7.01180e6 | −3.46513 | ||||||||
\(334\) | 1.78420e6 | 0.875140 | ||||||||
\(335\) | 969236. | 0.471864 | ||||||||
\(336\) | 1.71663e6 | 0.829523 | ||||||||
\(337\) | 3.28910e6 | 1.57762 | 0.788809 | − | 0.614638i | \(-0.210698\pi\) | ||||
0.788809 | + | 0.614638i | \(0.210698\pi\) | |||||||
\(338\) | −114244. | −0.0543928 | ||||||||
\(339\) | 1.41689e6 | 0.669634 | ||||||||
\(340\) | 651720. | 0.305748 | ||||||||
\(341\) | −1.19718e6 | −0.557535 | ||||||||
\(342\) | 1.72428e6 | 0.797155 | ||||||||
\(343\) | −5.81600e6 | −2.66925 | ||||||||
\(344\) | 571877. | 0.260559 | ||||||||
\(345\) | −260185. | −0.117689 | ||||||||
\(346\) | −229635. | −0.103121 | ||||||||
\(347\) | 139108. | 0.0620195 | 0.0310098 | − | 0.999519i | \(-0.490128\pi\) | ||||
0.0310098 | + | 0.999519i | \(0.490128\pi\) | |||||||
\(348\) | −670985. | −0.297006 | ||||||||
\(349\) | 1.41781e6 | 0.623097 | 0.311549 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311549 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(350\) | 601064. | 0.262271 | ||||||||
\(351\) | −1.37577e6 | −0.596045 | ||||||||
\(352\) | −557211. | −0.239697 | ||||||||
\(353\) | 2.45675e6 | 1.04936 | 0.524679 | − | 0.851300i | \(-0.324185\pi\) | ||||
0.524679 | + | 0.851300i | \(0.324185\pi\) | |||||||
\(354\) | −5.30612e6 | −2.25045 | ||||||||
\(355\) | −262992. | −0.110757 | ||||||||
\(356\) | 786416. | 0.328872 | ||||||||
\(357\) | 1.09254e7 | 4.53698 | ||||||||
\(358\) | −349758. | −0.144231 | ||||||||
\(359\) | −2.88601e6 | −1.18185 | −0.590924 | − | 0.806727i | \(-0.701237\pi\) | ||||
−0.590924 | + | 0.806727i | \(0.701237\pi\) | |||||||
\(360\) | −855808. | −0.348033 | ||||||||
\(361\) | −1.82659e6 | −0.737690 | ||||||||
\(362\) | −85366.4 | −0.0342386 | ||||||||
\(363\) | −3.76660e6 | −1.50032 | ||||||||
\(364\) | −650111. | −0.257178 | ||||||||
\(365\) | 39553.1 | 0.0155399 | ||||||||
\(366\) | −3.37809e6 | −1.31816 | ||||||||
\(367\) | −2.83587e6 | −1.09906 | −0.549530 | − | 0.835474i | \(-0.685193\pi\) | ||||
−0.549530 | + | 0.835474i | \(0.685193\pi\) | |||||||
\(368\) | 95526.9 | 0.0367711 | ||||||||
\(369\) | −9.14641e6 | −3.49691 | ||||||||
\(370\) | 1.31091e6 | 0.497816 | ||||||||
\(371\) | −9.70831e6 | −3.66192 | ||||||||
\(372\) | 981781. | 0.367838 | ||||||||
\(373\) | 5.02691e6 | 1.87081 | 0.935403 | − | 0.353583i | \(-0.115037\pi\) | ||||
0.935403 | + | 0.353583i | \(0.115037\pi\) | |||||||
\(374\) | −3.54634e6 | −1.31100 | ||||||||
\(375\) | −435789. | −0.160029 | ||||||||
\(376\) | −1.00798e6 | −0.367692 | ||||||||
\(377\) | 254111. | 0.0920810 | ||||||||
\(378\) | −7.82891e6 | −2.81820 | ||||||||
\(379\) | 2.14892e6 | 0.768462 | 0.384231 | − | 0.923237i | \(-0.374467\pi\) | ||||
0.384231 | + | 0.923237i | \(0.374467\pi\) | |||||||
\(380\) | −322368. | −0.114523 | ||||||||
\(381\) | 5.08381e6 | 1.79423 | ||||||||
\(382\) | −1.23007e6 | −0.431291 | ||||||||
\(383\) | 832971. | 0.290157 | 0.145078 | − | 0.989420i | \(-0.453657\pi\) | ||||
0.145078 | + | 0.989420i | \(0.453657\pi\) | |||||||
\(384\) | 456958. | 0.158142 | ||||||||
\(385\) | −3.27070e6 | −1.12458 | ||||||||
\(386\) | −729637. | −0.249252 | ||||||||
\(387\) | −4.77946e6 | −1.62219 | ||||||||
\(388\) | −250468. | −0.0844641 | ||||||||
\(389\) | −725243. | −0.243002 | −0.121501 | − | 0.992591i | \(-0.538771\pi\) | ||||
−0.121501 | + | 0.992591i | \(0.538771\pi\) | |||||||
\(390\) | 471349. | 0.156921 | ||||||||
\(391\) | 607976. | 0.201115 | ||||||||
\(392\) | −2.62384e6 | −0.862426 | ||||||||
\(393\) | −5.57013e6 | −1.81921 | ||||||||
\(394\) | 610032. | 0.197976 | ||||||||
\(395\) | −154781. | −0.0499142 | ||||||||
\(396\) | 4.65689e6 | 1.49231 | ||||||||
\(397\) | 2.42654e6 | 0.772701 | 0.386351 | − | 0.922352i | \(-0.373735\pi\) | ||||
0.386351 | + | 0.922352i | \(0.373735\pi\) | |||||||
\(398\) | 2.34642e6 | 0.742504 | ||||||||
\(399\) | −5.40417e6 | −1.69940 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −2.14376e6 | −0.665758 | −0.332879 | − | 0.942970i | \(-0.608020\pi\) | ||||
−0.332879 | + | 0.942970i | \(0.608020\pi\) | |||||||
\(402\) | 4.32519e6 | 1.33487 | ||||||||
\(403\) | −371813. | −0.114041 | ||||||||
\(404\) | −2.20972e6 | −0.673572 | ||||||||
\(405\) | 2.42679e6 | 0.735182 | ||||||||
\(406\) | 1.44603e6 | 0.435374 | ||||||||
\(407\) | −7.13335e6 | −2.13455 | ||||||||
\(408\) | 2.90829e6 | 0.864942 | ||||||||
\(409\) | −3.66144e6 | −1.08229 | −0.541145 | − | 0.840929i | \(-0.682009\pi\) | ||||
−0.541145 | + | 0.840929i | \(0.682009\pi\) | |||||||
\(410\) | 1.70999e6 | 0.502383 | ||||||||
\(411\) | 9.63388e6 | 2.81317 | ||||||||
\(412\) | −762273. | −0.221242 | ||||||||
\(413\) | 1.14351e7 | 3.29888 | ||||||||
\(414\) | −798366. | −0.228929 | ||||||||
\(415\) | 946231. | 0.269698 | ||||||||
\(416\) | −173056. | −0.0490290 | ||||||||
\(417\) | −5.10642e6 | −1.43806 | ||||||||
\(418\) | 1.75417e6 | 0.491056 | ||||||||
\(419\) | 3.03786e6 | 0.845341 | 0.422671 | − | 0.906283i | \(-0.361093\pi\) | ||||
0.422671 | + | 0.906283i | \(0.361093\pi\) | |||||||
\(420\) | 2.68224e6 | 0.741948 | ||||||||
\(421\) | −1.88663e6 | −0.518777 | −0.259389 | − | 0.965773i | \(-0.583521\pi\) | ||||
−0.259389 | + | 0.965773i | \(0.583521\pi\) | |||||||
\(422\) | 828162. | 0.226378 | ||||||||
\(423\) | 8.42422e6 | 2.28917 | ||||||||
\(424\) | −2.58430e6 | −0.698117 | ||||||||
\(425\) | 1.01831e6 | 0.273469 | ||||||||
\(426\) | −1.17360e6 | −0.313325 | ||||||||
\(427\) | 7.28008e6 | 1.93226 | ||||||||
\(428\) | −2.98442e6 | −0.787501 | ||||||||
\(429\) | −2.56485e6 | −0.672852 | ||||||||
\(430\) | 893558. | 0.233051 | ||||||||
\(431\) | 717193. | 0.185970 | 0.0929850 | − | 0.995668i | \(-0.470359\pi\) | ||||
0.0929850 | + | 0.995668i | \(0.470359\pi\) | |||||||
\(432\) | −2.08401e6 | −0.537268 | ||||||||
\(433\) | 2.64569e6 | 0.678140 | 0.339070 | − | 0.940761i | \(-0.389888\pi\) | ||||
0.339070 | + | 0.940761i | \(0.389888\pi\) | |||||||
\(434\) | −2.11582e6 | −0.539206 | ||||||||
\(435\) | −1.04841e6 | −0.265650 | ||||||||
\(436\) | 230513. | 0.0580736 | ||||||||
\(437\) | −300731. | −0.0753310 | ||||||||
\(438\) | 176505. | 0.0439614 | ||||||||
\(439\) | 4.47973e6 | 1.10941 | 0.554704 | − | 0.832048i | \(-0.312832\pi\) | ||||
0.554704 | + | 0.832048i | \(0.312832\pi\) | |||||||
\(440\) | −870642. | −0.214392 | ||||||||
\(441\) | 2.19287e7 | 5.36929 | ||||||||
\(442\) | −1.10141e6 | −0.268159 | ||||||||
\(443\) | 4.30731e6 | 1.04279 | 0.521395 | − | 0.853315i | \(-0.325412\pi\) | ||||
0.521395 | + | 0.853315i | \(0.325412\pi\) | |||||||
\(444\) | 5.84992e6 | 1.40829 | ||||||||
\(445\) | 1.22877e6 | 0.294152 | ||||||||
\(446\) | 4.19555e6 | 0.998738 | ||||||||
\(447\) | 5.21780e6 | 1.23515 | ||||||||
\(448\) | −984783. | −0.231817 | ||||||||
\(449\) | −25272.9 | −0.00591615 | −0.00295808 | − | 0.999996i | \(-0.500942\pi\) | ||||
−0.00295808 | + | 0.999996i | \(0.500942\pi\) | |||||||
\(450\) | −1.33720e6 | −0.311290 | ||||||||
\(451\) | −9.30495e6 | −2.15413 | ||||||||
\(452\) | −812832. | −0.187135 | ||||||||
\(453\) | 296095. | 0.0677932 | ||||||||
\(454\) | 402835. | 0.0917250 | ||||||||
\(455\) | −1.01580e6 | −0.230027 | ||||||||
\(456\) | −1.43856e6 | −0.323978 | ||||||||
\(457\) | 1.14360e6 | 0.256143 | 0.128072 | − | 0.991765i | \(-0.459121\pi\) | ||||
0.128072 | + | 0.991765i | \(0.459121\pi\) | |||||||
\(458\) | −1.94869e6 | −0.434090 | ||||||||
\(459\) | −1.32636e7 | −2.93853 | ||||||||
\(460\) | 149261. | 0.0328890 | ||||||||
\(461\) | −8.34911e6 | −1.82973 | −0.914867 | − | 0.403755i | \(-0.867705\pi\) | ||||
−0.914867 | + | 0.403755i | \(0.867705\pi\) | |||||||
\(462\) | −1.45954e7 | −3.18135 | ||||||||
\(463\) | −3.41596e6 | −0.740561 | −0.370280 | − | 0.928920i | \(-0.620738\pi\) | ||||
−0.370280 | + | 0.928920i | \(0.620738\pi\) | |||||||
\(464\) | 384925. | 0.0830007 | ||||||||
\(465\) | 1.53403e6 | 0.329005 | ||||||||
\(466\) | 3.33138e6 | 0.710655 | ||||||||
\(467\) | 5.67105e6 | 1.20329 | 0.601646 | − | 0.798763i | \(-0.294512\pi\) | ||||
0.601646 | + | 0.798763i | \(0.294512\pi\) | |||||||
\(468\) | 1.44632e6 | 0.305245 | ||||||||
\(469\) | −9.32116e6 | −1.95676 | ||||||||
\(470\) | −1.57497e6 | −0.328873 | ||||||||
\(471\) | 9.36797e6 | 1.94578 | ||||||||
\(472\) | 3.04397e6 | 0.628906 | ||||||||
\(473\) | −4.86231e6 | −0.999286 | ||||||||
\(474\) | −690706. | −0.141204 | ||||||||
\(475\) | −503700. | −0.102432 | ||||||||
\(476\) | −6.26760e6 | −1.26790 | ||||||||
\(477\) | 2.15983e7 | 4.34633 | ||||||||
\(478\) | −5.39677e6 | −1.08035 | ||||||||
\(479\) | −6.16340e6 | −1.22739 | −0.613694 | − | 0.789544i | \(-0.710317\pi\) | ||||
−0.613694 | + | 0.789544i | \(0.710317\pi\) | |||||||
\(480\) | 713997. | 0.141447 | ||||||||
\(481\) | −2.21544e6 | −0.436614 | ||||||||
\(482\) | 6.65133e6 | 1.30404 | ||||||||
\(483\) | 2.50220e6 | 0.488039 | ||||||||
\(484\) | 2.16080e6 | 0.419276 | ||||||||
\(485\) | −391356. | −0.0755470 | ||||||||
\(486\) | 2.91677e6 | 0.560160 | ||||||||
\(487\) | −7.32701e6 | −1.39992 | −0.699962 | − | 0.714180i | \(-0.746800\pi\) | ||||
−0.699962 | + | 0.714180i | \(0.746800\pi\) | |||||||
\(488\) | 1.93792e6 | 0.368371 | ||||||||
\(489\) | −5.63056e6 | −1.06483 | ||||||||
\(490\) | −4.09975e6 | −0.771377 | ||||||||
\(491\) | 8.89739e6 | 1.66555 | 0.832777 | − | 0.553608i | \(-0.186750\pi\) | ||||
0.832777 | + | 0.553608i | \(0.186750\pi\) | |||||||
\(492\) | 7.63081e6 | 1.42121 | ||||||||
\(493\) | 2.44984e6 | 0.453963 | ||||||||
\(494\) | 544802. | 0.100443 | ||||||||
\(495\) | 7.27639e6 | 1.33476 | ||||||||
\(496\) | −563220. | −0.102795 | ||||||||
\(497\) | 2.52920e6 | 0.459295 | ||||||||
\(498\) | 4.22254e6 | 0.762957 | ||||||||
\(499\) | 3.02237e6 | 0.543371 | 0.271686 | − | 0.962386i | \(-0.412419\pi\) | ||||
0.271686 | + | 0.962386i | \(0.412419\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 1.24406e7 | 2.21435 | ||||||||
\(502\) | 1.16509e6 | 0.206348 | ||||||||
\(503\) | −7.48799e6 | −1.31961 | −0.659805 | − | 0.751437i | \(-0.729361\pi\) | ||||
−0.659805 | + | 0.751437i | \(0.729361\pi\) | |||||||
\(504\) | 8.23032e6 | 1.44325 | ||||||||
\(505\) | −3.45269e6 | −0.602461 | ||||||||
\(506\) | −812205. | −0.141023 | ||||||||
\(507\) | −796581. | −0.137629 | ||||||||
\(508\) | −2.91644e6 | −0.501411 | ||||||||
\(509\) | 4.87997e6 | 0.834878 | 0.417439 | − | 0.908705i | \(-0.362928\pi\) | ||||
0.417439 | + | 0.908705i | \(0.362928\pi\) | |||||||
\(510\) | 4.54420e6 | 0.773627 | ||||||||
\(511\) | −380383. | −0.0644420 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 6.56073e6 | 1.10067 | ||||||||
\(514\) | 2.19281e6 | 0.366095 | ||||||||
\(515\) | −1.19105e6 | −0.197885 | ||||||||
\(516\) | 3.98749e6 | 0.659288 | ||||||||
\(517\) | 8.57024e6 | 1.41015 | ||||||||
\(518\) | −1.26071e7 | −2.06438 | ||||||||
\(519\) | −1.60116e6 | −0.260925 | ||||||||
\(520\) | −270400. | −0.0438529 | ||||||||
\(521\) | −3.79679e6 | −0.612805 | −0.306403 | − | 0.951902i | \(-0.599125\pi\) | ||||
−0.306403 | + | 0.951902i | \(0.599125\pi\) | |||||||
\(522\) | −3.21701e6 | −0.516745 | ||||||||
\(523\) | −5.66643e6 | −0.905848 | −0.452924 | − | 0.891549i | \(-0.649619\pi\) | ||||
−0.452924 | + | 0.891549i | \(0.649619\pi\) | |||||||
\(524\) | 3.19543e6 | 0.508394 | ||||||||
\(525\) | 4.19099e6 | 0.663619 | ||||||||
\(526\) | −3.27365e6 | −0.515902 | ||||||||
\(527\) | −3.58459e6 | −0.562228 | ||||||||
\(528\) | −3.88522e6 | −0.606500 | ||||||||
\(529\) | −6.29710e6 | −0.978366 | ||||||||
\(530\) | −4.03797e6 | −0.624415 | ||||||||
\(531\) | −2.54400e7 | −3.91544 | ||||||||
\(532\) | 3.10022e6 | 0.474912 | ||||||||
\(533\) | −2.88989e6 | −0.440619 | ||||||||
\(534\) | 5.48338e6 | 0.832138 | ||||||||
\(535\) | −4.66316e6 | −0.704362 | ||||||||
\(536\) | −2.48124e6 | −0.373042 | ||||||||
\(537\) | −2.43873e6 | −0.364945 | ||||||||
\(538\) | 3.75782e6 | 0.559732 | ||||||||
\(539\) | 2.23088e7 | 3.30754 | ||||||||
\(540\) | −3.25627e6 | −0.480547 | ||||||||
\(541\) | 1.15648e7 | 1.69881 | 0.849403 | − | 0.527745i | \(-0.176962\pi\) | ||||
0.849403 | + | 0.527745i | \(0.176962\pi\) | |||||||
\(542\) | 6.09665e6 | 0.891442 | ||||||||
\(543\) | −595228. | −0.0866330 | ||||||||
\(544\) | −1.66840e6 | −0.241715 | ||||||||
\(545\) | 360176. | 0.0519426 | ||||||||
\(546\) | −4.53298e6 | −0.650732 | ||||||||
\(547\) | −1.28104e7 | −1.83060 | −0.915299 | − | 0.402776i | \(-0.868045\pi\) | ||||
−0.915299 | + | 0.402776i | \(0.868045\pi\) | |||||||
\(548\) | −5.52669e6 | −0.786165 | ||||||||
\(549\) | −1.61961e7 | −2.29340 | ||||||||
\(550\) | −1.36038e6 | −0.191758 | ||||||||
\(551\) | −1.21179e6 | −0.170039 | ||||||||
\(552\) | 666073. | 0.0930410 | ||||||||
\(553\) | 1.48853e6 | 0.206988 | ||||||||
\(554\) | 1.75881e6 | 0.243470 | ||||||||
\(555\) | 9.14050e6 | 1.25961 | ||||||||
\(556\) | 2.92941e6 | 0.401877 | ||||||||
\(557\) | 3.51737e6 | 0.480374 | 0.240187 | − | 0.970727i | \(-0.422791\pi\) | ||||
0.240187 | + | 0.970727i | \(0.422791\pi\) | |||||||
\(558\) | 4.70711e6 | 0.639984 | ||||||||
\(559\) | −1.51011e6 | −0.204400 | ||||||||
\(560\) | −1.53872e6 | −0.207344 | ||||||||
\(561\) | −2.47273e7 | −3.31719 | ||||||||
\(562\) | 2.36813e6 | 0.316275 | ||||||||
\(563\) | 9.45258e6 | 1.25684 | 0.628419 | − | 0.777875i | \(-0.283702\pi\) | ||||
0.628419 | + | 0.777875i | \(0.283702\pi\) | |||||||
\(564\) | −7.02829e6 | −0.930362 | ||||||||
\(565\) | −1.27005e6 | −0.167378 | ||||||||
\(566\) | 3.10891e6 | 0.407912 | ||||||||
\(567\) | −2.33385e7 | −3.04871 | ||||||||
\(568\) | 673259. | 0.0875611 | ||||||||
\(569\) | 1.11315e7 | 1.44136 | 0.720679 | − | 0.693269i | \(-0.243830\pi\) | ||||
0.720679 | + | 0.693269i | \(0.243830\pi\) | |||||||
\(570\) | −2.24775e6 | −0.289775 | ||||||||
\(571\) | 4.92935e6 | 0.632702 | 0.316351 | − | 0.948642i | \(-0.397542\pi\) | ||||
0.316351 | + | 0.948642i | \(0.397542\pi\) | |||||||
\(572\) | 1.47139e6 | 0.188034 | ||||||||
\(573\) | −8.57680e6 | −1.09129 | ||||||||
\(574\) | −1.64450e7 | −2.08332 | ||||||||
\(575\) | 233220. | 0.0294169 | ||||||||
\(576\) | 2.19087e6 | 0.275144 | ||||||||
\(577\) | 1.09437e7 | 1.36843 | 0.684217 | − | 0.729279i | \(-0.260144\pi\) | ||||
0.684217 | + | 0.729279i | \(0.260144\pi\) | |||||||
\(578\) | −4.93904e6 | −0.614926 | ||||||||
\(579\) | −5.08749e6 | −0.630677 | ||||||||
\(580\) | 601446. | 0.0742381 | ||||||||
\(581\) | −9.09993e6 | −1.11840 | ||||||||
\(582\) | −1.74642e6 | −0.213718 | ||||||||
\(583\) | 2.19727e7 | 2.67739 | ||||||||
\(584\) | −101256. | −0.0122854 | ||||||||
\(585\) | 2.25987e6 | 0.273019 | ||||||||
\(586\) | −2.43610e6 | −0.293056 | ||||||||
\(587\) | 7.96444e6 | 0.954025 | 0.477013 | − | 0.878896i | \(-0.341720\pi\) | ||||
0.477013 | + | 0.878896i | \(0.341720\pi\) | |||||||
\(588\) | −1.82950e7 | −2.18218 | ||||||||
\(589\) | 1.77309e6 | 0.210592 | ||||||||
\(590\) | 4.75621e6 | 0.562510 | ||||||||
\(591\) | 4.25352e6 | 0.500934 | ||||||||
\(592\) | −3.35593e6 | −0.393558 | ||||||||
\(593\) | −1.19793e7 | −1.39892 | −0.699460 | − | 0.714671i | \(-0.746576\pi\) | ||||
−0.699460 | + | 0.714671i | \(0.746576\pi\) | |||||||
\(594\) | 1.77190e7 | 2.06051 | ||||||||
\(595\) | −9.79313e6 | −1.13404 | ||||||||
\(596\) | −2.99330e6 | −0.345172 | ||||||||
\(597\) | 1.63607e7 | 1.87874 | ||||||||
\(598\) | −252251. | −0.0288456 | ||||||||
\(599\) | 7.45663e6 | 0.849132 | 0.424566 | − | 0.905397i | \(-0.360427\pi\) | ||||
0.424566 | + | 0.905397i | \(0.360427\pi\) | |||||||
\(600\) | 1.11562e6 | 0.126514 | ||||||||
\(601\) | −1.04196e7 | −1.17670 | −0.588351 | − | 0.808606i | \(-0.700223\pi\) | ||||
−0.588351 | + | 0.808606i | \(0.700223\pi\) | |||||||
\(602\) | −8.59337e6 | −0.966434 | ||||||||
\(603\) | 2.07370e7 | 2.32248 | ||||||||
\(604\) | −169862. | −0.0189454 | ||||||||
\(605\) | 3.37624e6 | 0.375012 | ||||||||
\(606\) | −1.54075e7 | −1.70432 | ||||||||
\(607\) | 571939. | 0.0630054 | 0.0315027 | − | 0.999504i | \(-0.489971\pi\) | ||||
0.0315027 | + | 0.999504i | \(0.489971\pi\) | |||||||
\(608\) | 825262. | 0.0905384 | ||||||||
\(609\) | 1.00826e7 | 1.10162 | ||||||||
\(610\) | 3.02800e6 | 0.329481 | ||||||||
\(611\) | 2.66171e6 | 0.288441 | ||||||||
\(612\) | 1.39437e7 | 1.50487 | ||||||||
\(613\) | −1.61323e7 | −1.73398 | −0.866991 | − | 0.498323i | \(-0.833949\pi\) | ||||
−0.866991 | + | 0.498323i | \(0.833949\pi\) | |||||||
\(614\) | 1.06704e7 | 1.14225 | ||||||||
\(615\) | 1.19231e7 | 1.27117 | ||||||||
\(616\) | 8.37299e6 | 0.889055 | ||||||||
\(617\) | −6.39133e6 | −0.675894 | −0.337947 | − | 0.941165i | \(-0.609732\pi\) | ||||
−0.337947 | + | 0.941165i | \(0.609732\pi\) | |||||||
\(618\) | −5.31505e6 | −0.559804 | ||||||||
\(619\) | 1.27062e7 | 1.33287 | 0.666435 | − | 0.745563i | \(-0.267819\pi\) | ||||
0.666435 | + | 0.745563i | \(0.267819\pi\) | |||||||
\(620\) | −880031. | −0.0919431 | ||||||||
\(621\) | −3.03771e6 | −0.316095 | ||||||||
\(622\) | 6.49278e6 | 0.672907 | ||||||||
\(623\) | −1.18172e7 | −1.21981 | ||||||||
\(624\) | −1.20665e6 | −0.124057 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −2.36846e6 | −0.241563 | ||||||||
\(627\) | 1.22312e7 | 1.24251 | ||||||||
\(628\) | −5.37414e6 | −0.543764 | ||||||||
\(629\) | −2.13587e7 | −2.15252 | ||||||||
\(630\) | 1.28599e7 | 1.29088 | ||||||||
\(631\) | −694354. | −0.0694237 | −0.0347118 | − | 0.999397i | \(-0.511051\pi\) | ||||
−0.0347118 | + | 0.999397i | \(0.511051\pi\) | |||||||
\(632\) | 396239. | 0.0394607 | ||||||||
\(633\) | 5.77447e6 | 0.572799 | ||||||||
\(634\) | 1.04414e7 | 1.03166 | ||||||||
\(635\) | −4.55694e6 | −0.448476 | ||||||||
\(636\) | −1.80193e7 | −1.76643 | ||||||||
\(637\) | 6.92857e6 | 0.676542 | ||||||||
\(638\) | −3.27278e6 | −0.318321 | ||||||||
\(639\) | −5.62676e6 | −0.545138 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −8.71863e6 | −0.838114 | −0.419057 | − | 0.907960i | \(-0.637639\pi\) | ||||
−0.419057 | + | 0.907960i | \(0.637639\pi\) | |||||||
\(642\) | −2.08093e7 | −1.99260 | ||||||||
\(643\) | 5.98737e6 | 0.571096 | 0.285548 | − | 0.958364i | \(-0.407824\pi\) | ||||
0.285548 | + | 0.958364i | \(0.407824\pi\) | |||||||
\(644\) | −1.43544e6 | −0.136387 | ||||||||
\(645\) | 6.23045e6 | 0.589685 | ||||||||
\(646\) | 5.25234e6 | 0.495189 | ||||||||
\(647\) | −1.09581e7 | −1.02914 | −0.514571 | − | 0.857448i | \(-0.672049\pi\) | ||||
−0.514571 | + | 0.857448i | \(0.672049\pi\) | |||||||
\(648\) | −6.21259e6 | −0.581212 | ||||||||
\(649\) | −2.58810e7 | −2.41195 | ||||||||
\(650\) | −422500. | −0.0392232 | ||||||||
\(651\) | −1.47528e7 | −1.36434 | ||||||||
\(652\) | 3.23009e6 | 0.297575 | ||||||||
\(653\) | 6.47503e6 | 0.594236 | 0.297118 | − | 0.954841i | \(-0.403975\pi\) | ||||
0.297118 | + | 0.954841i | \(0.403975\pi\) | |||||||
\(654\) | 1.60728e6 | 0.146942 | ||||||||
\(655\) | 4.99285e6 | 0.454722 | ||||||||
\(656\) | −4.37758e6 | −0.397169 | ||||||||
\(657\) | 846247. | 0.0764863 | ||||||||
\(658\) | 1.51466e7 | 1.36380 | ||||||||
\(659\) | 501723. | 0.0450039 | 0.0225020 | − | 0.999747i | \(-0.492837\pi\) | ||||
0.0225020 | + | 0.999747i | \(0.492837\pi\) | |||||||
\(660\) | −6.07066e6 | −0.542471 | ||||||||
\(661\) | 4.00659e6 | 0.356674 | 0.178337 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178337 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(662\) | −3.27514e6 | −0.290459 | ||||||||
\(663\) | −7.67969e6 | −0.678516 | ||||||||
\(664\) | −2.42235e6 | −0.213215 | ||||||||
\(665\) | 4.84409e6 | 0.424774 | ||||||||
\(666\) | 2.80472e7 | 2.45021 | ||||||||
\(667\) | 561077. | 0.0488324 | ||||||||
\(668\) | −7.13681e6 | −0.618818 | ||||||||
\(669\) | 2.92540e7 | 2.52708 | ||||||||
\(670\) | −3.87694e6 | −0.333659 | ||||||||
\(671\) | −1.64769e7 | −1.41276 | ||||||||
\(672\) | −6.86652e6 | −0.586562 | ||||||||
\(673\) | 8.17473e6 | 0.695722 | 0.347861 | − | 0.937546i | \(-0.386908\pi\) | ||||
0.347861 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(674\) | −1.31564e7 | −1.11554 | ||||||||
\(675\) | −5.08792e6 | −0.429814 | ||||||||
\(676\) | 456976. | 0.0384615 | ||||||||
\(677\) | 1.00935e6 | 0.0846392 | 0.0423196 | − | 0.999104i | \(-0.486525\pi\) | ||||
0.0423196 | + | 0.999104i | \(0.486525\pi\) | |||||||
\(678\) | −5.66757e6 | −0.473503 | ||||||||
\(679\) | 3.76368e6 | 0.313284 | ||||||||
\(680\) | −2.60688e6 | −0.216196 | ||||||||
\(681\) | 2.80882e6 | 0.232090 | ||||||||
\(682\) | 4.78870e6 | 0.394237 | ||||||||
\(683\) | 1.99189e7 | 1.63386 | 0.816928 | − | 0.576739i | \(-0.195675\pi\) | ||||
0.816928 | + | 0.576739i | \(0.195675\pi\) | |||||||
\(684\) | −6.89712e6 | −0.563674 | ||||||||
\(685\) | −8.63545e6 | −0.703167 | ||||||||
\(686\) | 2.32640e7 | 1.88745 | ||||||||
\(687\) | −1.35875e7 | −1.09837 | ||||||||
\(688\) | −2.28751e6 | −0.184243 | ||||||||
\(689\) | 6.82417e6 | 0.547648 | ||||||||
\(690\) | 1.04074e6 | 0.0832184 | ||||||||
\(691\) | −677407. | −0.0539703 | −0.0269851 | − | 0.999636i | \(-0.508591\pi\) | ||||
−0.0269851 | + | 0.999636i | \(0.508591\pi\) | |||||||
\(692\) | 918541. | 0.0729177 | ||||||||
\(693\) | −6.99772e7 | −5.53508 | ||||||||
\(694\) | −556432. | −0.0438544 | ||||||||
\(695\) | 4.57720e6 | 0.359450 | ||||||||
\(696\) | 2.68394e6 | 0.210015 | ||||||||
\(697\) | −2.78609e7 | −2.17227 | ||||||||
\(698\) | −5.67126e6 | −0.440596 | ||||||||
\(699\) | 2.32284e7 | 1.79815 | ||||||||
\(700\) | −2.40426e6 | −0.185454 | ||||||||
\(701\) | 1.04542e7 | 0.803518 | 0.401759 | − | 0.915745i | \(-0.368399\pi\) | ||||
0.401759 | + | 0.915745i | \(0.368399\pi\) | |||||||
\(702\) | 5.50310e6 | 0.421468 | ||||||||
\(703\) | 1.05649e7 | 0.806263 | ||||||||
\(704\) | 2.22884e6 | 0.169492 | ||||||||
\(705\) | −1.09817e7 | −0.832141 | ||||||||
\(706\) | −9.82700e6 | −0.742009 | ||||||||
\(707\) | 3.32046e7 | 2.49833 | ||||||||
\(708\) | 2.12245e7 | 1.59131 | ||||||||
\(709\) | −2.25125e7 | −1.68193 | −0.840964 | − | 0.541091i | \(-0.818011\pi\) | ||||
−0.840964 | + | 0.541091i | \(0.818011\pi\) | |||||||
\(710\) | 1.05197e6 | 0.0783170 | ||||||||
\(711\) | −3.31157e6 | −0.245674 | ||||||||
\(712\) | −3.14566e6 | −0.232548 | ||||||||
\(713\) | −820964. | −0.0604784 | ||||||||
\(714\) | −4.37017e7 | −3.20813 | ||||||||
\(715\) | 2.29904e6 | 0.168183 | ||||||||
\(716\) | 1.39903e6 | 0.101987 | ||||||||
\(717\) | −3.76297e7 | −2.73358 | ||||||||
\(718\) | 1.15440e7 | 0.835693 | ||||||||
\(719\) | −2.77678e6 | −0.200317 | −0.100159 | − | 0.994971i | \(-0.531935\pi\) | ||||
−0.100159 | + | 0.994971i | \(0.531935\pi\) | |||||||
\(720\) | 3.42323e6 | 0.246096 | ||||||||
\(721\) | 1.14544e7 | 0.820603 | ||||||||
\(722\) | 7.30637e6 | 0.521625 | ||||||||
\(723\) | 4.63772e7 | 3.29958 | ||||||||
\(724\) | 341466. | 0.0242103 | ||||||||
\(725\) | 939759. | 0.0664006 | ||||||||
\(726\) | 1.50664e7 | 1.06089 | ||||||||
\(727\) | 2.76872e6 | 0.194287 | 0.0971434 | − | 0.995270i | \(-0.469029\pi\) | ||||
0.0971434 | + | 0.995270i | \(0.469029\pi\) | |||||||
\(728\) | 2.60044e6 | 0.181852 | ||||||||
\(729\) | −3.25086e6 | −0.226558 | ||||||||
\(730\) | −158212. | −0.0109884 | ||||||||
\(731\) | −1.45587e7 | −1.00770 | ||||||||
\(732\) | 1.35124e7 | 0.932081 | ||||||||
\(733\) | −1.80998e7 | −1.24427 | −0.622133 | − | 0.782911i | \(-0.713734\pi\) | ||||
−0.622133 | + | 0.782911i | \(0.713734\pi\) | |||||||
\(734\) | 1.13435e7 | 0.777152 | ||||||||
\(735\) | −2.85860e7 | −1.95180 | ||||||||
\(736\) | −382108. | −0.0260011 | ||||||||
\(737\) | 2.10964e7 | 1.43067 | ||||||||
\(738\) | 3.65857e7 | 2.47269 | ||||||||
\(739\) | −3.57016e6 | −0.240479 | −0.120239 | − | 0.992745i | \(-0.538366\pi\) | ||||
−0.120239 | + | 0.992745i | \(0.538366\pi\) | |||||||
\(740\) | −5.24365e6 | −0.352009 | ||||||||
\(741\) | 3.79870e6 | 0.254149 | ||||||||
\(742\) | 3.88332e7 | 2.58937 | ||||||||
\(743\) | −1.73285e7 | −1.15157 | −0.575783 | − | 0.817603i | \(-0.695303\pi\) | ||||
−0.575783 | + | 0.817603i | \(0.695303\pi\) | |||||||
\(744\) | −3.92712e6 | −0.260101 | ||||||||
\(745\) | −4.67704e6 | −0.308731 | ||||||||
\(746\) | −2.01076e7 | −1.32286 | ||||||||
\(747\) | 2.02448e7 | 1.32743 | ||||||||
\(748\) | 1.41854e7 | 0.927015 | ||||||||
\(749\) | 4.48457e7 | 2.92090 | ||||||||
\(750\) | 1.74316e6 | 0.113157 | ||||||||
\(751\) | 3.04634e6 | 0.197096 | 0.0985480 | − | 0.995132i | \(-0.468580\pi\) | ||||
0.0985480 | + | 0.995132i | \(0.468580\pi\) | |||||||
\(752\) | 4.03193e6 | 0.259997 | ||||||||
\(753\) | 8.12374e6 | 0.522118 | ||||||||
\(754\) | −1.01644e6 | −0.0651111 | ||||||||
\(755\) | −265409. | −0.0169452 | ||||||||
\(756\) | 3.13156e7 | 1.99277 | ||||||||
\(757\) | −8.98398e6 | −0.569808 | −0.284904 | − | 0.958556i | \(-0.591962\pi\) | ||||
−0.284904 | + | 0.958556i | \(0.591962\pi\) | |||||||
\(758\) | −8.59568e6 | −0.543384 | ||||||||
\(759\) | −5.66320e6 | −0.356827 | ||||||||
\(760\) | 1.28947e6 | 0.0809800 | ||||||||
\(761\) | 1.31757e7 | 0.824731 | 0.412366 | − | 0.911018i | \(-0.364703\pi\) | ||||
0.412366 | + | 0.911018i | \(0.364703\pi\) | |||||||
\(762\) | −2.03352e7 | −1.26871 | ||||||||
\(763\) | −3.46382e6 | −0.215399 | ||||||||
\(764\) | 4.92027e6 | 0.304969 | ||||||||
\(765\) | 2.17870e7 | 1.34600 | ||||||||
\(766\) | −3.33188e6 | −0.205172 | ||||||||
\(767\) | −8.03799e6 | −0.493354 | ||||||||
\(768\) | −1.82783e6 | −0.111824 | ||||||||
\(769\) | 3.53661e6 | 0.215661 | 0.107830 | − | 0.994169i | \(-0.465610\pi\) | ||||
0.107830 | + | 0.994169i | \(0.465610\pi\) | |||||||
\(770\) | 1.30828e7 | 0.795195 | ||||||||
\(771\) | 1.52897e7 | 0.926322 | ||||||||
\(772\) | 2.91855e6 | 0.176248 | ||||||||
\(773\) | −3.14397e7 | −1.89247 | −0.946235 | − | 0.323479i | \(-0.895147\pi\) | ||||
−0.946235 | + | 0.323479i | \(0.895147\pi\) | |||||||
\(774\) | 1.91179e7 | 1.14706 | ||||||||
\(775\) | −1.37505e6 | −0.0822364 | ||||||||
\(776\) | 1.00187e6 | 0.0597251 | ||||||||
\(777\) | −8.79044e7 | −5.22346 | ||||||||
\(778\) | 2.90097e6 | 0.171828 | ||||||||
\(779\) | 1.37812e7 | 0.813659 | ||||||||
\(780\) | −1.88540e6 | −0.110960 | ||||||||
\(781\) | −5.72429e6 | −0.335810 | ||||||||
\(782\) | −2.43191e6 | −0.142210 | ||||||||
\(783\) | −1.22404e7 | −0.713498 | ||||||||
\(784\) | 1.04953e7 | 0.609827 | ||||||||
\(785\) | −8.39710e6 | −0.486357 | ||||||||
\(786\) | 2.22805e7 | 1.28638 | ||||||||
\(787\) | 1.27213e7 | 0.732139 | 0.366069 | − | 0.930588i | \(-0.380703\pi\) | ||||
0.366069 | + | 0.930588i | \(0.380703\pi\) | |||||||
\(788\) | −2.44013e6 | −0.139990 | ||||||||
\(789\) | −2.28259e7 | −1.30538 | ||||||||
\(790\) | 619123. | 0.0352947 | ||||||||
\(791\) | 1.22141e7 | 0.694097 | ||||||||
\(792\) | −1.86276e7 | −1.05522 | ||||||||
\(793\) | −5.11731e6 | −0.288974 | ||||||||
\(794\) | −9.70617e6 | −0.546382 | ||||||||
\(795\) | −2.81552e7 | −1.57994 | ||||||||
\(796\) | −9.38569e6 | −0.525029 | ||||||||
\(797\) | 1.84237e7 | 1.02738 | 0.513689 | − | 0.857977i | \(-0.328279\pi\) | ||||
0.513689 | + | 0.857977i | \(0.328279\pi\) | |||||||
\(798\) | 2.16167e7 | 1.20166 | ||||||||
\(799\) | 2.56610e7 | 1.42203 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 2.62899e7 | 1.44780 | ||||||||
\(802\) | 8.57506e6 | 0.470762 | ||||||||
\(803\) | 860915. | 0.0471164 | ||||||||
\(804\) | −1.73008e7 | −0.943899 | ||||||||
\(805\) | −2.24288e6 | −0.121988 | ||||||||
\(806\) | 1.48725e6 | 0.0806394 | ||||||||
\(807\) | 2.62019e7 | 1.41628 | ||||||||
\(808\) | 8.83888e6 | 0.476287 | ||||||||
\(809\) | 2.10360e7 | 1.13004 | 0.565018 | − | 0.825079i | \(-0.308869\pi\) | ||||
0.565018 | + | 0.825079i | \(0.308869\pi\) | |||||||
\(810\) | −9.70717e6 | −0.519852 | ||||||||
\(811\) | 3.53571e7 | 1.88767 | 0.943833 | − | 0.330424i | \(-0.107192\pi\) | ||||
0.943833 | + | 0.330424i | \(0.107192\pi\) | |||||||
\(812\) | −5.78412e6 | −0.307856 | ||||||||
\(813\) | 4.25097e7 | 2.25560 | ||||||||
\(814\) | 2.85334e7 | 1.50936 | ||||||||
\(815\) | 5.04702e6 | 0.266159 | ||||||||
\(816\) | −1.16331e7 | −0.611606 | ||||||||
\(817\) | 7.20136e6 | 0.377450 | ||||||||
\(818\) | 1.46458e7 | 0.765295 | ||||||||
\(819\) | −2.17332e7 | −1.13218 | ||||||||
\(820\) | −6.83998e6 | −0.355238 | ||||||||
\(821\) | 1.72038e7 | 0.890770 | 0.445385 | − | 0.895339i | \(-0.353067\pi\) | ||||
0.445385 | + | 0.895339i | \(0.353067\pi\) | |||||||
\(822\) | −3.85355e7 | −1.98921 | ||||||||
\(823\) | −947098. | −0.0487411 | −0.0243705 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243705 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(824\) | 3.04909e6 | 0.156442 | ||||||||
\(825\) | −9.48541e6 | −0.485200 | ||||||||
\(826\) | −4.57405e7 | −2.33266 | ||||||||
\(827\) | −3.05385e7 | −1.55269 | −0.776345 | − | 0.630308i | \(-0.782928\pi\) | ||||
−0.776345 | + | 0.630308i | \(0.782928\pi\) | |||||||
\(828\) | 3.19346e6 | 0.161877 | ||||||||
\(829\) | −1.57415e7 | −0.795538 | −0.397769 | − | 0.917486i | \(-0.630215\pi\) | ||||
−0.397769 | + | 0.917486i | \(0.630215\pi\) | |||||||
\(830\) | −3.78492e6 | −0.190705 | ||||||||
\(831\) | 1.22636e7 | 0.616047 | ||||||||
\(832\) | 692224. | 0.0346688 | ||||||||
\(833\) | 6.67971e7 | 3.33538 | ||||||||
\(834\) | 2.04257e7 | 1.01686 | ||||||||
\(835\) | −1.11513e7 | −0.553487 | ||||||||
\(836\) | −7.01668e6 | −0.347229 | ||||||||
\(837\) | 1.79101e7 | 0.883659 | ||||||||
\(838\) | −1.21514e7 | −0.597746 | ||||||||
\(839\) | 2.07700e7 | 1.01867 | 0.509333 | − | 0.860570i | \(-0.329892\pi\) | ||||
0.509333 | + | 0.860570i | \(0.329892\pi\) | |||||||
\(840\) | −1.07289e7 | −0.524637 | ||||||||
\(841\) | −1.82503e7 | −0.889774 | ||||||||
\(842\) | 7.54651e6 | 0.366831 | ||||||||
\(843\) | 1.65121e7 | 0.800263 | ||||||||
\(844\) | −3.31265e6 | −0.160073 | ||||||||
\(845\) | 714025. | 0.0344010 | ||||||||
\(846\) | −3.36969e7 | −1.61869 | ||||||||
\(847\) | −3.24694e7 | −1.55513 | ||||||||
\(848\) | 1.03372e7 | 0.493643 | ||||||||
\(849\) | 2.16772e7 | 1.03213 | ||||||||
\(850\) | −4.07325e6 | −0.193372 | ||||||||
\(851\) | −4.89169e6 | −0.231545 | ||||||||
\(852\) | 4.69438e6 | 0.221554 | ||||||||
\(853\) | −1.91838e7 | −0.902740 | −0.451370 | − | 0.892337i | \(-0.649064\pi\) | ||||
−0.451370 | + | 0.892337i | \(0.649064\pi\) | |||||||
\(854\) | −2.91203e7 | −1.36632 | ||||||||
\(855\) | −1.07768e7 | −0.504165 | ||||||||
\(856\) | 1.19377e7 | 0.556847 | ||||||||
\(857\) | 2.64211e7 | 1.22885 | 0.614425 | − | 0.788975i | \(-0.289388\pi\) | ||||
0.614425 | + | 0.788975i | \(0.289388\pi\) | |||||||
\(858\) | 1.02594e7 | 0.475778 | ||||||||
\(859\) | −3.30576e7 | −1.52858 | −0.764289 | − | 0.644873i | \(-0.776910\pi\) | ||||
−0.764289 | + | 0.644873i | \(0.776910\pi\) | |||||||
\(860\) | −3.57423e6 | −0.164792 | ||||||||
\(861\) | −1.14665e8 | −5.27137 | ||||||||
\(862\) | −2.86877e6 | −0.131501 | ||||||||
\(863\) | 1.19324e7 | 0.545380 | 0.272690 | − | 0.962102i | \(-0.412087\pi\) | ||||
0.272690 | + | 0.962102i | \(0.412087\pi\) | |||||||
\(864\) | 8.33605e6 | 0.379906 | ||||||||
\(865\) | 1.43522e6 | 0.0652196 | ||||||||
\(866\) | −1.05828e7 | −0.479518 | ||||||||
\(867\) | −3.44381e7 | −1.55593 | ||||||||
\(868\) | 8.46328e6 | 0.381276 | ||||||||
\(869\) | −3.36897e6 | −0.151338 | ||||||||
\(870\) | 4.19366e6 | 0.187843 | ||||||||
\(871\) | 6.55203e6 | 0.292638 | ||||||||
\(872\) | −922051. | −0.0410643 | ||||||||
\(873\) | −8.37313e6 | −0.371837 | ||||||||
\(874\) | 1.20292e6 | 0.0532671 | ||||||||
\(875\) | −3.75665e6 | −0.165875 | ||||||||
\(876\) | −706020. | −0.0310854 | ||||||||
\(877\) | 3.88434e6 | 0.170537 | 0.0852684 | − | 0.996358i | \(-0.472825\pi\) | ||||
0.0852684 | + | 0.996358i | \(0.472825\pi\) | |||||||
\(878\) | −1.79189e7 | −0.784469 | ||||||||
\(879\) | −1.69860e7 | −0.741513 | ||||||||
\(880\) | 3.48257e6 | 0.151598 | ||||||||
\(881\) | −8.93397e6 | −0.387797 | −0.193899 | − | 0.981022i | \(-0.562113\pi\) | ||||
−0.193899 | + | 0.981022i | \(0.562113\pi\) | |||||||
\(882\) | −8.77148e7 | −3.79666 | ||||||||
\(883\) | −4.32552e6 | −0.186697 | −0.0933484 | − | 0.995634i | \(-0.529757\pi\) | ||||
−0.0933484 | + | 0.995634i | \(0.529757\pi\) | |||||||
\(884\) | 4.40563e6 | 0.189617 | ||||||||
\(885\) | 3.31632e7 | 1.42331 | ||||||||
\(886\) | −1.72292e7 | −0.737364 | ||||||||
\(887\) | 3.55552e7 | 1.51738 | 0.758689 | − | 0.651453i | \(-0.225840\pi\) | ||||
0.758689 | + | 0.651453i | \(0.225840\pi\) | |||||||
\(888\) | −2.33997e7 | −0.995812 | ||||||||
\(889\) | 4.38242e7 | 1.85977 | ||||||||
\(890\) | −4.91510e6 | −0.207997 | ||||||||
\(891\) | 5.28217e7 | 2.22904 | ||||||||
\(892\) | −1.67822e7 | −0.706214 | ||||||||
\(893\) | −1.26930e7 | −0.532643 | ||||||||
\(894\) | −2.08712e7 | −0.873380 | ||||||||
\(895\) | 2.18599e6 | 0.0912199 | ||||||||
\(896\) | 3.93913e6 | 0.163919 | ||||||||
\(897\) | −1.75885e6 | −0.0729874 | ||||||||
\(898\) | 101092. | 0.00418335 | ||||||||
\(899\) | −3.30807e6 | −0.136514 | ||||||||
\(900\) | 5.34880e6 | 0.220115 | ||||||||
\(901\) | 6.57906e7 | 2.69993 | ||||||||
\(902\) | 3.72198e7 | 1.52320 | ||||||||
\(903\) | −5.99184e7 | −2.44535 | ||||||||
\(904\) | 3.25133e6 | 0.132324 | ||||||||
\(905\) | 533540. | 0.0216544 | ||||||||
\(906\) | −1.18438e6 | −0.0479370 | ||||||||
\(907\) | 2.44157e7 | 0.985486 | 0.492743 | − | 0.870175i | \(-0.335994\pi\) | ||||
0.492743 | + | 0.870175i | \(0.335994\pi\) | |||||||
\(908\) | −1.61134e6 | −0.0648593 | ||||||||
\(909\) | −7.38709e7 | −2.96527 | ||||||||
\(910\) | 4.06319e6 | 0.162654 | ||||||||
\(911\) | 3.00267e7 | 1.19870 | 0.599352 | − | 0.800486i | \(-0.295425\pi\) | ||||
0.599352 | + | 0.800486i | \(0.295425\pi\) | |||||||
\(912\) | 5.75424e6 | 0.229087 | ||||||||
\(913\) | 2.05957e7 | 0.817711 | ||||||||
\(914\) | −4.57439e6 | −0.181120 | ||||||||
\(915\) | 2.11131e7 | 0.833679 | ||||||||
\(916\) | 7.79478e6 | 0.306948 | ||||||||
\(917\) | −4.80164e7 | −1.88567 | ||||||||
\(918\) | 5.30544e7 | 2.07785 | ||||||||
\(919\) | −1.30118e7 | −0.508216 | −0.254108 | − | 0.967176i | \(-0.581782\pi\) | ||||
−0.254108 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(920\) | −597043. | −0.0232561 | ||||||||
\(921\) | 7.44009e7 | 2.89021 | ||||||||
\(922\) | 3.33964e7 | 1.29382 | ||||||||
\(923\) | −1.77782e6 | −0.0686886 | ||||||||
\(924\) | 5.83817e7 | 2.24956 | ||||||||
\(925\) | −8.19320e6 | −0.314847 | ||||||||
\(926\) | 1.36639e7 | 0.523656 | ||||||||
\(927\) | −2.54828e7 | −0.973975 | ||||||||
\(928\) | −1.53970e6 | −0.0586904 | ||||||||
\(929\) | −5.16678e7 | −1.96418 | −0.982089 | − | 0.188419i | \(-0.939664\pi\) | ||||
−0.982089 | + | 0.188419i | \(0.939664\pi\) | |||||||
\(930\) | −6.13613e6 | −0.232641 | ||||||||
\(931\) | −3.30407e7 | −1.24932 | ||||||||
\(932\) | −1.33255e7 | −0.502509 | ||||||||
\(933\) | 4.52717e7 | 1.70264 | ||||||||
\(934\) | −2.26842e7 | −0.850857 | ||||||||
\(935\) | 2.21646e7 | 0.829147 | ||||||||
\(936\) | −5.78526e6 | −0.215841 | ||||||||
\(937\) | −4.04703e6 | −0.150587 | −0.0752936 | − | 0.997161i | \(-0.523989\pi\) | ||||
−0.0752936 | + | 0.997161i | \(0.523989\pi\) | |||||||
\(938\) | 3.72846e7 | 1.38364 | ||||||||
\(939\) | −1.65144e7 | −0.611221 | ||||||||
\(940\) | 6.29990e6 | 0.232549 | ||||||||
\(941\) | −4.43008e7 | −1.63094 | −0.815470 | − | 0.578799i | \(-0.803521\pi\) | ||||
−0.815470 | + | 0.578799i | \(0.803521\pi\) | |||||||
\(942\) | −3.74719e7 | −1.37587 | ||||||||
\(943\) | −6.38088e6 | −0.233669 | ||||||||
\(944\) | −1.21759e7 | −0.444704 | ||||||||
\(945\) | 4.89307e7 | 1.78239 | ||||||||
\(946\) | 1.94492e7 | 0.706602 | ||||||||
\(947\) | −3.60463e7 | −1.30613 | −0.653064 | − | 0.757303i | \(-0.726517\pi\) | ||||
−0.653064 | + | 0.757303i | \(0.726517\pi\) | |||||||
\(948\) | 2.76283e6 | 0.0998464 | ||||||||
\(949\) | 267379. | 0.00963745 | ||||||||
\(950\) | 2.01480e6 | 0.0724307 | ||||||||
\(951\) | 7.28042e7 | 2.61039 | ||||||||
\(952\) | 2.50704e7 | 0.896539 | ||||||||
\(953\) | −1.31248e7 | −0.468123 | −0.234061 | − | 0.972222i | \(-0.575202\pi\) | ||||
−0.234061 | + | 0.972222i | \(0.575202\pi\) | |||||||
\(954\) | −8.63931e7 | −3.07332 | ||||||||
\(955\) | 7.68792e6 | 0.272773 | ||||||||
\(956\) | 2.15871e7 | 0.763923 | ||||||||
\(957\) | −2.28198e7 | −0.805439 | ||||||||
\(958\) | 2.46536e7 | 0.867894 | ||||||||
\(959\) | 8.30473e7 | 2.91594 | ||||||||
\(960\) | −2.85599e6 | −0.100018 | ||||||||
\(961\) | −2.37888e7 | −0.830929 | ||||||||
\(962\) | 8.86176e6 | 0.308733 | ||||||||
\(963\) | −9.97693e7 | −3.46682 | ||||||||
\(964\) | −2.66053e7 | −0.922096 | ||||||||
\(965\) | 4.56023e6 | 0.157641 | ||||||||
\(966\) | −1.00088e7 | −0.345096 | ||||||||
\(967\) | 2.48150e7 | 0.853390 | 0.426695 | − | 0.904396i | \(-0.359678\pi\) | ||||
0.426695 | + | 0.904396i | \(0.359678\pi\) | |||||||
\(968\) | −8.64318e6 | −0.296473 | ||||||||
\(969\) | 3.66226e7 | 1.25297 | ||||||||
\(970\) | 1.56542e6 | 0.0534198 | ||||||||
\(971\) | −3.54227e6 | −0.120569 | −0.0602843 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602843 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(972\) | −1.16671e7 | −0.396093 | ||||||||
\(973\) | −4.40191e7 | −1.49059 | ||||||||
\(974\) | 2.93080e7 | 0.989896 | ||||||||
\(975\) | −2.94593e6 | −0.0992456 | ||||||||
\(976\) | −7.75167e6 | −0.260478 | ||||||||
\(977\) | 9.16916e6 | 0.307322 | 0.153661 | − | 0.988124i | \(-0.450894\pi\) | ||||
0.153661 | + | 0.988124i | \(0.450894\pi\) | |||||||
\(978\) | 2.25222e7 | 0.752947 | ||||||||
\(979\) | 2.67456e7 | 0.891857 | ||||||||
\(980\) | 1.63990e7 | 0.545446 | ||||||||
\(981\) | 7.70604e6 | 0.255658 | ||||||||
\(982\) | −3.55895e7 | −1.17772 | ||||||||
\(983\) | −3.05912e7 | −1.00975 | −0.504874 | − | 0.863193i | \(-0.668461\pi\) | ||||
−0.504874 | + | 0.863193i | \(0.668461\pi\) | |||||||
\(984\) | −3.05233e7 | −1.00495 | ||||||||
\(985\) | −3.81270e6 | −0.125211 | ||||||||
\(986\) | −9.79936e6 | −0.321000 | ||||||||
\(987\) | 1.05611e8 | 3.45078 | ||||||||
\(988\) | −2.17921e6 | −0.0710242 | ||||||||
\(989\) | −3.33433e6 | −0.108397 | ||||||||
\(990\) | −2.91056e7 | −0.943817 | ||||||||
\(991\) | 3.47852e7 | 1.12515 | 0.562575 | − | 0.826746i | \(-0.309811\pi\) | ||||
0.562575 | + | 0.826746i | \(0.309811\pi\) | |||||||
\(992\) | 2.25288e6 | 0.0726874 | ||||||||
\(993\) | −2.28363e7 | −0.734942 | ||||||||
\(994\) | −1.01168e7 | −0.324771 | ||||||||
\(995\) | −1.46651e7 | −0.469600 | ||||||||
\(996\) | −1.68902e7 | −0.539492 | ||||||||
\(997\) | −4.21812e7 | −1.34394 | −0.671972 | − | 0.740577i | \(-0.734552\pi\) | ||||
−0.671972 | + | 0.740577i | \(0.734552\pi\) | |||||||
\(998\) | −1.20895e7 | −0.384222 | ||||||||
\(999\) | 1.06717e8 | 3.38314 |
(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 | 130.6.a.f.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 1040.6.a.l.1.3 | 3 | |||
5.2 | odd | 4 | 650.6.b.j.599.3 | 6 | |||
5.3 | odd | 4 | 650.6.b.j.599.4 | 6 | |||
5.4 | even | 2 | 650.6.a.j.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.6.a.f.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
650.6.a.j.1.3 | 3 | 5.4 | even | 2 | |||
650.6.b.j.599.3 | 6 | 5.2 | odd | 4 | |||
650.6.b.j.599.4 | 6 | 5.3 | odd | 4 | |||
1040.6.a.l.1.3 | 3 | 4.3 | odd | 2 |