Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(36.8882785570\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.27980.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 47x - 106 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.65230\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 | ||||||||
\(3\) | 2.35610 | 0.151144 | 0.0755718 | − | 0.997140i | \(-0.475922\pi\) | ||||
0.0755718 | + | 0.997140i | \(0.475922\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 9.42439 | 0.106875 | ||||||||
\(7\) | −9.44632 | −0.0728648 | −0.0364324 | − | 0.999336i | \(-0.511599\pi\) | ||||
−0.0364324 | + | 0.999336i | \(0.511599\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −237.449 | −0.977156 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −248.872 | −0.620148 | −0.310074 | − | 0.950712i | \(-0.600354\pi\) | ||||
−0.310074 | + | 0.950712i | \(0.600354\pi\) | |||||||
\(12\) | 37.6975 | 0.0755718 | ||||||||
\(13\) | −898.786 | −1.47502 | −0.737510 | − | 0.675336i | \(-0.763998\pi\) | ||||
−0.737510 | + | 0.675336i | \(0.763998\pi\) | |||||||
\(14\) | −37.7853 | −0.0515232 | ||||||||
\(15\) | 58.9024 | 0.0675935 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1177.51 | −0.988193 | −0.494097 | − | 0.869407i | \(-0.664501\pi\) | ||||
−0.494097 | + | 0.869407i | \(0.664501\pi\) | |||||||
\(18\) | −949.795 | −0.690953 | ||||||||
\(19\) | 116.462 | 0.0740117 | 0.0370058 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370058 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −22.2564 | −0.0110130 | ||||||||
\(22\) | −995.490 | −0.438511 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 150.790 | 0.0534374 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3595.14 | −1.04300 | ||||||||
\(27\) | −1131.98 | −0.298835 | ||||||||
\(28\) | −151.141 | −0.0364324 | ||||||||
\(29\) | 2766.81 | 0.610919 | 0.305459 | − | 0.952205i | \(-0.401190\pi\) | ||||
0.305459 | + | 0.952205i | \(0.401190\pi\) | |||||||
\(30\) | 235.610 | 0.0477958 | ||||||||
\(31\) | −661.945 | −0.123714 | −0.0618568 | − | 0.998085i | \(-0.519702\pi\) | ||||
−0.0618568 | + | 0.998085i | \(0.519702\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −586.368 | −0.0937314 | ||||||||
\(34\) | −4710.03 | −0.698758 | ||||||||
\(35\) | −236.158 | −0.0325861 | ||||||||
\(36\) | −3799.18 | −0.488578 | ||||||||
\(37\) | −5965.93 | −0.716430 | −0.358215 | − | 0.933639i | \(-0.616614\pi\) | ||||
−0.358215 | + | 0.933639i | \(0.616614\pi\) | |||||||
\(38\) | 465.848 | 0.0523342 | ||||||||
\(39\) | −2117.63 | −0.222940 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | −7482.54 | −0.695167 | −0.347584 | − | 0.937649i | \(-0.612998\pi\) | ||||
−0.347584 | + | 0.937649i | \(0.612998\pi\) | |||||||
\(42\) | −89.0258 | −0.00778740 | ||||||||
\(43\) | 8158.86 | 0.672912 | 0.336456 | − | 0.941699i | \(-0.390772\pi\) | ||||
0.336456 | + | 0.941699i | \(0.390772\pi\) | |||||||
\(44\) | −3981.96 | −0.310074 | ||||||||
\(45\) | −5936.22 | −0.436997 | ||||||||
\(46\) | −2116.00 | −0.147442 | ||||||||
\(47\) | 14818.9 | 0.978522 | 0.489261 | − | 0.872137i | \(-0.337267\pi\) | ||||
0.489261 | + | 0.872137i | \(0.337267\pi\) | |||||||
\(48\) | 603.161 | 0.0377859 | ||||||||
\(49\) | −16717.8 | −0.994691 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | −2774.32 | −0.149359 | ||||||||
\(52\) | −14380.6 | −0.737510 | ||||||||
\(53\) | −24766.8 | −1.21110 | −0.605551 | − | 0.795807i | \(-0.707047\pi\) | ||||
−0.605551 | + | 0.795807i | \(0.707047\pi\) | |||||||
\(54\) | −4527.94 | −0.211308 | ||||||||
\(55\) | −6221.81 | −0.277339 | ||||||||
\(56\) | −604.565 | −0.0257616 | ||||||||
\(57\) | 274.396 | 0.0111864 | ||||||||
\(58\) | 11067.2 | 0.431985 | ||||||||
\(59\) | −7935.48 | −0.296786 | −0.148393 | − | 0.988928i | \(-0.547410\pi\) | ||||
−0.148393 | + | 0.988928i | \(0.547410\pi\) | |||||||
\(60\) | 942.439 | 0.0337968 | ||||||||
\(61\) | 5864.34 | 0.201788 | 0.100894 | − | 0.994897i | \(-0.467830\pi\) | ||||
0.100894 | + | 0.994897i | \(0.467830\pi\) | |||||||
\(62\) | −2647.78 | −0.0874787 | ||||||||
\(63\) | 2243.02 | 0.0712002 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −22469.6 | −0.659649 | ||||||||
\(66\) | −2345.47 | −0.0662781 | ||||||||
\(67\) | −5691.52 | −0.154896 | −0.0774482 | − | 0.996996i | \(-0.524677\pi\) | ||||
−0.0774482 | + | 0.996996i | \(0.524677\pi\) | |||||||
\(68\) | −18840.1 | −0.494097 | ||||||||
\(69\) | −1246.38 | −0.0315156 | ||||||||
\(70\) | −944.632 | −0.0230419 | ||||||||
\(71\) | −30857.3 | −0.726460 | −0.363230 | − | 0.931699i | \(-0.618326\pi\) | ||||
−0.363230 | + | 0.931699i | \(0.618326\pi\) | |||||||
\(72\) | −15196.7 | −0.345477 | ||||||||
\(73\) | 24861.4 | 0.546032 | 0.273016 | − | 0.962009i | \(-0.411979\pi\) | ||||
0.273016 | + | 0.962009i | \(0.411979\pi\) | |||||||
\(74\) | −23863.7 | −0.506592 | ||||||||
\(75\) | 1472.56 | 0.0302287 | ||||||||
\(76\) | 1863.39 | 0.0370058 | ||||||||
\(77\) | 2350.93 | 0.0451869 | ||||||||
\(78\) | −8470.51 | −0.157642 | ||||||||
\(79\) | −43677.4 | −0.787389 | −0.393694 | − | 0.919241i | \(-0.628803\pi\) | ||||
−0.393694 | + | 0.919241i | \(0.628803\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 55033.0 | 0.931989 | ||||||||
\(82\) | −29930.1 | −0.491557 | ||||||||
\(83\) | −42211.7 | −0.672570 | −0.336285 | − | 0.941760i | \(-0.609170\pi\) | ||||
−0.336285 | + | 0.941760i | \(0.609170\pi\) | |||||||
\(84\) | −356.103 | −0.00550652 | ||||||||
\(85\) | −29437.7 | −0.441933 | ||||||||
\(86\) | 32635.4 | 0.475821 | ||||||||
\(87\) | 6518.86 | 0.0923365 | ||||||||
\(88\) | −15927.8 | −0.219255 | ||||||||
\(89\) | 92378.1 | 1.23621 | 0.618107 | − | 0.786094i | \(-0.287900\pi\) | ||||
0.618107 | + | 0.786094i | \(0.287900\pi\) | |||||||
\(90\) | −23744.9 | −0.309004 | ||||||||
\(91\) | 8490.22 | 0.107477 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | −1559.61 | −0.0186985 | ||||||||
\(94\) | 59275.5 | 0.691920 | ||||||||
\(95\) | 2911.55 | 0.0330990 | ||||||||
\(96\) | 2412.64 | 0.0267187 | ||||||||
\(97\) | −4948.63 | −0.0534018 | −0.0267009 | − | 0.999643i | \(-0.508500\pi\) | ||||
−0.0267009 | + | 0.999643i | \(0.508500\pi\) | |||||||
\(98\) | −66871.1 | −0.703353 | ||||||||
\(99\) | 59094.5 | 0.605981 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −10809.9 | −0.105444 | −0.0527218 | − | 0.998609i | \(-0.516790\pi\) | ||||
−0.0527218 | + | 0.998609i | \(0.516790\pi\) | |||||||
\(102\) | −11097.3 | −0.105613 | ||||||||
\(103\) | −14880.3 | −0.138204 | −0.0691018 | − | 0.997610i | \(-0.522013\pi\) | ||||
−0.0691018 | + | 0.997610i | \(0.522013\pi\) | |||||||
\(104\) | −57522.3 | −0.521498 | ||||||||
\(105\) | −556.411 | −0.00492519 | ||||||||
\(106\) | −99067.3 | −0.856378 | ||||||||
\(107\) | −35453.0 | −0.299360 | −0.149680 | − | 0.988734i | \(-0.547824\pi\) | ||||
−0.149680 | + | 0.988734i | \(0.547824\pi\) | |||||||
\(108\) | −18111.7 | −0.149417 | ||||||||
\(109\) | 98180.7 | 0.791516 | 0.395758 | − | 0.918355i | \(-0.370482\pi\) | ||||
0.395758 | + | 0.918355i | \(0.370482\pi\) | |||||||
\(110\) | −24887.2 | −0.196108 | ||||||||
\(111\) | −14056.3 | −0.108284 | ||||||||
\(112\) | −2418.26 | −0.0182162 | ||||||||
\(113\) | −51475.0 | −0.379228 | −0.189614 | − | 0.981859i | \(-0.560724\pi\) | ||||
−0.189614 | + | 0.981859i | \(0.560724\pi\) | |||||||
\(114\) | 1097.58 | 0.00790998 | ||||||||
\(115\) | −13225.0 | −0.0932505 | ||||||||
\(116\) | 44268.9 | 0.305459 | ||||||||
\(117\) | 213416. | 1.44132 | ||||||||
\(118\) | −31741.9 | −0.209859 | ||||||||
\(119\) | 11123.1 | 0.0720045 | ||||||||
\(120\) | 3769.75 | 0.0238979 | ||||||||
\(121\) | −99113.5 | −0.615417 | ||||||||
\(122\) | 23457.4 | 0.142685 | ||||||||
\(123\) | −17629.6 | −0.105070 | ||||||||
\(124\) | −10591.1 | −0.0618568 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 8972.07 | 0.0503462 | ||||||||
\(127\) | 249474. | 1.37251 | 0.686256 | − | 0.727360i | \(-0.259253\pi\) | ||||
0.686256 | + | 0.727360i | \(0.259253\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 19223.1 | 0.101706 | ||||||||
\(130\) | −89878.6 | −0.466442 | ||||||||
\(131\) | −9987.91 | −0.0508507 | −0.0254253 | − | 0.999677i | \(-0.508094\pi\) | ||||
−0.0254253 | + | 0.999677i | \(0.508094\pi\) | |||||||
\(132\) | −9381.88 | −0.0468657 | ||||||||
\(133\) | −1100.14 | −0.00539284 | ||||||||
\(134\) | −22766.1 | −0.109528 | ||||||||
\(135\) | −28299.6 | −0.133643 | ||||||||
\(136\) | −75360.6 | −0.349379 | ||||||||
\(137\) | 9929.64 | 0.0451994 | 0.0225997 | − | 0.999745i | \(-0.492806\pi\) | ||||
0.0225997 | + | 0.999745i | \(0.492806\pi\) | |||||||
\(138\) | −4985.50 | −0.0222849 | ||||||||
\(139\) | 131576. | 0.577615 | 0.288808 | − | 0.957387i | \(-0.406741\pi\) | ||||
0.288808 | + | 0.957387i | \(0.406741\pi\) | |||||||
\(140\) | −3778.53 | −0.0162931 | ||||||||
\(141\) | 34914.7 | 0.147897 | ||||||||
\(142\) | −123429. | −0.513685 | ||||||||
\(143\) | 223683. | 0.914730 | ||||||||
\(144\) | −60786.9 | −0.244289 | ||||||||
\(145\) | 69170.1 | 0.273211 | ||||||||
\(146\) | 99445.5 | 0.386103 | ||||||||
\(147\) | −39388.7 | −0.150341 | ||||||||
\(148\) | −95454.8 | −0.358215 | ||||||||
\(149\) | −70147.9 | −0.258851 | −0.129425 | − | 0.991589i | \(-0.541313\pi\) | ||||
−0.129425 | + | 0.991589i | \(0.541313\pi\) | |||||||
\(150\) | 5890.24 | 0.0213749 | ||||||||
\(151\) | −436974. | −1.55960 | −0.779799 | − | 0.626030i | \(-0.784679\pi\) | ||||
−0.779799 | + | 0.626030i | \(0.784679\pi\) | |||||||
\(152\) | 7453.57 | 0.0261671 | ||||||||
\(153\) | 279598. | 0.965618 | ||||||||
\(154\) | 9403.72 | 0.0319520 | ||||||||
\(155\) | −16548.6 | −0.0553264 | ||||||||
\(156\) | −33882.0 | −0.111470 | ||||||||
\(157\) | −278487. | −0.901688 | −0.450844 | − | 0.892603i | \(-0.648877\pi\) | ||||
−0.450844 | + | 0.892603i | \(0.648877\pi\) | |||||||
\(158\) | −174710. | −0.556768 | ||||||||
\(159\) | −58353.0 | −0.183050 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 4997.10 | 0.0151934 | ||||||||
\(162\) | 220132. | 0.659015 | ||||||||
\(163\) | 409675. | 1.20773 | 0.603865 | − | 0.797086i | \(-0.293627\pi\) | ||||
0.603865 | + | 0.797086i | \(0.293627\pi\) | |||||||
\(164\) | −119721. | −0.347584 | ||||||||
\(165\) | −14659.2 | −0.0419180 | ||||||||
\(166\) | −168847. | −0.475579 | ||||||||
\(167\) | −83087.3 | −0.230538 | −0.115269 | − | 0.993334i | \(-0.536773\pi\) | ||||
−0.115269 | + | 0.993334i | \(0.536773\pi\) | |||||||
\(168\) | −1424.41 | −0.00389370 | ||||||||
\(169\) | 436523. | 1.17568 | ||||||||
\(170\) | −117751. | −0.312494 | ||||||||
\(171\) | −27653.8 | −0.0723209 | ||||||||
\(172\) | 130542. | 0.336456 | ||||||||
\(173\) | 280046. | 0.711400 | 0.355700 | − | 0.934600i | \(-0.384243\pi\) | ||||
0.355700 | + | 0.934600i | \(0.384243\pi\) | |||||||
\(174\) | 26075.4 | 0.0652918 | ||||||||
\(175\) | −5903.95 | −0.0145730 | ||||||||
\(176\) | −63711.4 | −0.155037 | ||||||||
\(177\) | −18696.8 | −0.0448573 | ||||||||
\(178\) | 369512. | 0.874136 | ||||||||
\(179\) | 452794. | 1.05625 | 0.528127 | − | 0.849166i | \(-0.322895\pi\) | ||||
0.528127 | + | 0.849166i | \(0.322895\pi\) | |||||||
\(180\) | −94979.5 | −0.218499 | ||||||||
\(181\) | 467418. | 1.06050 | 0.530248 | − | 0.847842i | \(-0.322099\pi\) | ||||
0.530248 | + | 0.847842i | \(0.322099\pi\) | |||||||
\(182\) | 33960.9 | 0.0759977 | ||||||||
\(183\) | 13817.0 | 0.0304989 | ||||||||
\(184\) | −33856.0 | −0.0737210 | ||||||||
\(185\) | −149148. | −0.320397 | ||||||||
\(186\) | −6238.42 | −0.0132219 | ||||||||
\(187\) | 293050. | 0.612826 | ||||||||
\(188\) | 237102. | 0.489261 | ||||||||
\(189\) | 10693.1 | 0.0217745 | ||||||||
\(190\) | 11646.2 | 0.0234045 | ||||||||
\(191\) | 312868. | 0.620552 | 0.310276 | − | 0.950647i | \(-0.399579\pi\) | ||||
0.310276 | + | 0.950647i | \(0.399579\pi\) | |||||||
\(192\) | 9650.57 | 0.0188930 | ||||||||
\(193\) | 634549. | 1.22623 | 0.613115 | − | 0.789994i | \(-0.289916\pi\) | ||||
0.613115 | + | 0.789994i | \(0.289916\pi\) | |||||||
\(194\) | −19794.5 | −0.0377608 | ||||||||
\(195\) | −52940.7 | −0.0997018 | ||||||||
\(196\) | −267484. | −0.497345 | ||||||||
\(197\) | −526186. | −0.965993 | −0.482997 | − | 0.875622i | \(-0.660452\pi\) | ||||
−0.482997 | + | 0.875622i | \(0.660452\pi\) | |||||||
\(198\) | 236378. | 0.428493 | ||||||||
\(199\) | 333249. | 0.596536 | 0.298268 | − | 0.954482i | \(-0.403591\pi\) | ||||
0.298268 | + | 0.954482i | \(0.403591\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | −13409.8 | −0.0234116 | ||||||||
\(202\) | −43239.8 | −0.0745599 | ||||||||
\(203\) | −26136.1 | −0.0445145 | ||||||||
\(204\) | −44389.2 | −0.0746796 | ||||||||
\(205\) | −187063. | −0.310888 | ||||||||
\(206\) | −59521.3 | −0.0977246 | ||||||||
\(207\) | 125610. | 0.203751 | ||||||||
\(208\) | −230089. | −0.368755 | ||||||||
\(209\) | −28984.2 | −0.0458982 | ||||||||
\(210\) | −2225.64 | −0.00348263 | ||||||||
\(211\) | −500655. | −0.774164 | −0.387082 | − | 0.922045i | \(-0.626517\pi\) | ||||
−0.387082 | + | 0.922045i | \(0.626517\pi\) | |||||||
\(212\) | −396269. | −0.605551 | ||||||||
\(213\) | −72702.7 | −0.109800 | ||||||||
\(214\) | −141812. | −0.211680 | ||||||||
\(215\) | 203971. | 0.300935 | ||||||||
\(216\) | −72447.0 | −0.105654 | ||||||||
\(217\) | 6252.94 | 0.00901436 | ||||||||
\(218\) | 392723. | 0.559687 | ||||||||
\(219\) | 58575.8 | 0.0825293 | ||||||||
\(220\) | −99549.0 | −0.138669 | ||||||||
\(221\) | 1.05833e6 | 1.45760 | ||||||||
\(222\) | −56225.2 | −0.0765682 | ||||||||
\(223\) | −766101. | −1.03163 | −0.515815 | − | 0.856700i | \(-0.672511\pi\) | ||||
−0.515815 | + | 0.856700i | \(0.672511\pi\) | |||||||
\(224\) | −9673.03 | −0.0128808 | ||||||||
\(225\) | −148406. | −0.195431 | ||||||||
\(226\) | −205900. | −0.268154 | ||||||||
\(227\) | −78680.5 | −0.101345 | −0.0506725 | − | 0.998715i | \(-0.516136\pi\) | ||||
−0.0506725 | + | 0.998715i | \(0.516136\pi\) | |||||||
\(228\) | 4390.33 | 0.00559320 | ||||||||
\(229\) | 1.24781e6 | 1.57239 | 0.786197 | − | 0.617977i | \(-0.212047\pi\) | ||||
0.786197 | + | 0.617977i | \(0.212047\pi\) | |||||||
\(230\) | −52900.0 | −0.0659380 | ||||||||
\(231\) | 5539.02 | 0.00682972 | ||||||||
\(232\) | 177076. | 0.215992 | ||||||||
\(233\) | 545547. | 0.658328 | 0.329164 | − | 0.944273i | \(-0.393233\pi\) | ||||
0.329164 | + | 0.944273i | \(0.393233\pi\) | |||||||
\(234\) | 853663. | 1.01917 | ||||||||
\(235\) | 370472. | 0.437608 | ||||||||
\(236\) | −126968. | −0.148393 | ||||||||
\(237\) | −102908. | −0.119009 | ||||||||
\(238\) | 44492.5 | 0.0509148 | ||||||||
\(239\) | 604172. | 0.684173 | 0.342086 | − | 0.939668i | \(-0.388866\pi\) | ||||
0.342086 | + | 0.939668i | \(0.388866\pi\) | |||||||
\(240\) | 15079.0 | 0.0168984 | ||||||||
\(241\) | −720233. | −0.798786 | −0.399393 | − | 0.916780i | \(-0.630779\pi\) | ||||
−0.399393 | + | 0.916780i | \(0.630779\pi\) | |||||||
\(242\) | −396454. | −0.435165 | ||||||||
\(243\) | 404735. | 0.439699 | ||||||||
\(244\) | 93829.5 | 0.100894 | ||||||||
\(245\) | −417944. | −0.444839 | ||||||||
\(246\) | −70518.3 | −0.0742958 | ||||||||
\(247\) | −104674. | −0.109169 | ||||||||
\(248\) | −42364.5 | −0.0437394 | ||||||||
\(249\) | −99454.8 | −0.101655 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | −667638. | −0.668893 | −0.334447 | − | 0.942415i | \(-0.608549\pi\) | ||||
−0.334447 | + | 0.942415i | \(0.608549\pi\) | |||||||
\(252\) | 35888.3 | 0.0356001 | ||||||||
\(253\) | 131654. | 0.129310 | ||||||||
\(254\) | 997897. | 0.970513 | ||||||||
\(255\) | −69358.1 | −0.0667954 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −671078. | −0.633783 | −0.316891 | − | 0.948462i | \(-0.602639\pi\) | ||||
−0.316891 | + | 0.948462i | \(0.602639\pi\) | |||||||
\(258\) | 76892.2 | 0.0719173 | ||||||||
\(259\) | 56356.0 | 0.0522025 | ||||||||
\(260\) | −359514. | −0.329824 | ||||||||
\(261\) | −656975. | −0.596963 | ||||||||
\(262\) | −39951.7 | −0.0359568 | ||||||||
\(263\) | −962332. | −0.857898 | −0.428949 | − | 0.903329i | \(-0.641116\pi\) | ||||
−0.428949 | + | 0.903329i | \(0.641116\pi\) | |||||||
\(264\) | −37527.5 | −0.0331391 | ||||||||
\(265\) | −619171. | −0.541621 | ||||||||
\(266\) | −4400.55 | −0.00381332 | ||||||||
\(267\) | 217652. | 0.186846 | ||||||||
\(268\) | −91064.3 | −0.0774482 | ||||||||
\(269\) | 405581. | 0.341741 | 0.170870 | − | 0.985294i | \(-0.445342\pi\) | ||||
0.170870 | + | 0.985294i | \(0.445342\pi\) | |||||||
\(270\) | −113198. | −0.0944998 | ||||||||
\(271\) | −763574. | −0.631579 | −0.315790 | − | 0.948829i | \(-0.602269\pi\) | ||||
−0.315790 | + | 0.948829i | \(0.602269\pi\) | |||||||
\(272\) | −301442. | −0.247048 | ||||||||
\(273\) | 20003.8 | 0.0162445 | ||||||||
\(274\) | 39718.6 | 0.0319608 | ||||||||
\(275\) | −155545. | −0.124030 | ||||||||
\(276\) | −19942.0 | −0.0157578 | ||||||||
\(277\) | −1.25365e6 | −0.981697 | −0.490848 | − | 0.871245i | \(-0.663313\pi\) | ||||
−0.490848 | + | 0.871245i | \(0.663313\pi\) | |||||||
\(278\) | 526303. | 0.408436 | ||||||||
\(279\) | 157178. | 0.120887 | ||||||||
\(280\) | −15114.1 | −0.0115209 | ||||||||
\(281\) | 864071. | 0.652805 | 0.326403 | − | 0.945231i | \(-0.394164\pi\) | ||||
0.326403 | + | 0.945231i | \(0.394164\pi\) | |||||||
\(282\) | 139659. | 0.104579 | ||||||||
\(283\) | −906004. | −0.672457 | −0.336228 | − | 0.941781i | \(-0.609151\pi\) | ||||
−0.336228 | + | 0.941781i | \(0.609151\pi\) | |||||||
\(284\) | −493717. | −0.363230 | ||||||||
\(285\) | 6859.89 | 0.00500271 | ||||||||
\(286\) | 894732. | 0.646812 | ||||||||
\(287\) | 70682.4 | 0.0506532 | ||||||||
\(288\) | −243148. | −0.172738 | ||||||||
\(289\) | −33330.4 | −0.0234745 | ||||||||
\(290\) | 276681. | 0.193190 | ||||||||
\(291\) | −11659.5 | −0.00807134 | ||||||||
\(292\) | 397782. | 0.273016 | ||||||||
\(293\) | −2.59187e6 | −1.76378 | −0.881888 | − | 0.471459i | \(-0.843727\pi\) | ||||
−0.881888 | + | 0.471459i | \(0.843727\pi\) | |||||||
\(294\) | −157555. | −0.106307 | ||||||||
\(295\) | −198387. | −0.132727 | ||||||||
\(296\) | −381819. | −0.253296 | ||||||||
\(297\) | 281720. | 0.185322 | ||||||||
\(298\) | −280592. | −0.183035 | ||||||||
\(299\) | 475458. | 0.307563 | ||||||||
\(300\) | 23561.0 | 0.0151144 | ||||||||
\(301\) | −77071.2 | −0.0490316 | ||||||||
\(302\) | −1.74789e6 | −1.10280 | ||||||||
\(303\) | −25469.3 | −0.0159371 | ||||||||
\(304\) | 29814.3 | 0.0185029 | ||||||||
\(305\) | 146609. | 0.0902422 | ||||||||
\(306\) | 1.11839e6 | 0.682795 | ||||||||
\(307\) | −2.38503e6 | −1.44427 | −0.722134 | − | 0.691753i | \(-0.756839\pi\) | ||||
−0.722134 | + | 0.691753i | \(0.756839\pi\) | |||||||
\(308\) | 37614.9 | 0.0225935 | ||||||||
\(309\) | −35059.5 | −0.0208886 | ||||||||
\(310\) | −66194.5 | −0.0391217 | ||||||||
\(311\) | −1.75699e6 | −1.03008 | −0.515038 | − | 0.857167i | \(-0.672222\pi\) | ||||
−0.515038 | + | 0.857167i | \(0.672222\pi\) | |||||||
\(312\) | −135528. | −0.0788212 | ||||||||
\(313\) | 840202. | 0.484756 | 0.242378 | − | 0.970182i | \(-0.422073\pi\) | ||||
0.242378 | + | 0.970182i | \(0.422073\pi\) | |||||||
\(314\) | −1.11395e6 | −0.637590 | ||||||||
\(315\) | 56075.4 | 0.0318417 | ||||||||
\(316\) | −698839. | −0.393694 | ||||||||
\(317\) | −3.07745e6 | −1.72006 | −0.860028 | − | 0.510247i | \(-0.829554\pi\) | ||||
−0.860028 | + | 0.510247i | \(0.829554\pi\) | |||||||
\(318\) | −233412. | −0.129436 | ||||||||
\(319\) | −688582. | −0.378860 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | −83530.8 | −0.0452464 | ||||||||
\(322\) | 19988.4 | 0.0107433 | ||||||||
\(323\) | −137135. | −0.0731378 | ||||||||
\(324\) | 880528. | 0.465994 | ||||||||
\(325\) | −561741. | −0.295004 | ||||||||
\(326\) | 1.63870e6 | 0.853994 | ||||||||
\(327\) | 231323. | 0.119633 | ||||||||
\(328\) | −478882. | −0.245779 | ||||||||
\(329\) | −139984. | −0.0712998 | ||||||||
\(330\) | −58636.8 | −0.0296405 | ||||||||
\(331\) | −1.77017e6 | −0.888068 | −0.444034 | − | 0.896010i | \(-0.646453\pi\) | ||||
−0.444034 | + | 0.896010i | \(0.646453\pi\) | |||||||
\(332\) | −675387. | −0.336285 | ||||||||
\(333\) | 1.41660e6 | 0.700063 | ||||||||
\(334\) | −332349. | −0.163015 | ||||||||
\(335\) | −142288. | −0.0692717 | ||||||||
\(336\) | −5697.65 | −0.00275326 | ||||||||
\(337\) | −185971. | −0.0892010 | −0.0446005 | − | 0.999005i | \(-0.514201\pi\) | ||||
−0.0446005 | + | 0.999005i | \(0.514201\pi\) | |||||||
\(338\) | 1.74609e6 | 0.831334 | ||||||||
\(339\) | −121280. | −0.0573179 | ||||||||
\(340\) | −471003. | −0.220967 | ||||||||
\(341\) | 164740. | 0.0767207 | ||||||||
\(342\) | −110615. | −0.0511386 | ||||||||
\(343\) | 316686. | 0.145343 | ||||||||
\(344\) | 522167. | 0.237910 | ||||||||
\(345\) | −31159.4 | −0.0140942 | ||||||||
\(346\) | 1.12018e6 | 0.503035 | ||||||||
\(347\) | −2.14626e6 | −0.956882 | −0.478441 | − | 0.878120i | \(-0.658798\pi\) | ||||
−0.478441 | + | 0.878120i | \(0.658798\pi\) | |||||||
\(348\) | 104302. | 0.0461683 | ||||||||
\(349\) | −1.83833e6 | −0.807903 | −0.403951 | − | 0.914780i | \(-0.632364\pi\) | ||||
−0.403951 | + | 0.914780i | \(0.632364\pi\) | |||||||
\(350\) | −23615.8 | −0.0103046 | ||||||||
\(351\) | 1.01741e6 | 0.440787 | ||||||||
\(352\) | −254845. | −0.109628 | ||||||||
\(353\) | 1.45416e6 | 0.621119 | 0.310559 | − | 0.950554i | \(-0.399484\pi\) | ||||
0.310559 | + | 0.950554i | \(0.399484\pi\) | |||||||
\(354\) | −74787.0 | −0.0317189 | ||||||||
\(355\) | −771432. | −0.324883 | ||||||||
\(356\) | 1.47805e6 | 0.618107 | ||||||||
\(357\) | 26207.2 | 0.0108830 | ||||||||
\(358\) | 1.81118e6 | 0.746884 | ||||||||
\(359\) | −158990. | −0.0651079 | −0.0325540 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325540 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(360\) | −379918. | −0.154502 | ||||||||
\(361\) | −2.46254e6 | −0.994522 | ||||||||
\(362\) | 1.86967e6 | 0.749884 | ||||||||
\(363\) | −233521. | −0.0930163 | ||||||||
\(364\) | 135844. | 0.0537385 | ||||||||
\(365\) | 621535. | 0.244193 | ||||||||
\(366\) | 55267.8 | 0.0215660 | ||||||||
\(367\) | −4.39291e6 | −1.70250 | −0.851251 | − | 0.524759i | \(-0.824155\pi\) | ||||
−0.851251 | + | 0.524759i | \(0.824155\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | 1.77672e6 | 0.679286 | ||||||||
\(370\) | −596593. | −0.226555 | ||||||||
\(371\) | 233955. | 0.0882467 | ||||||||
\(372\) | −24953.7 | −0.00934926 | ||||||||
\(373\) | 853721. | 0.317720 | 0.158860 | − | 0.987301i | \(-0.449218\pi\) | ||||
0.158860 | + | 0.987301i | \(0.449218\pi\) | |||||||
\(374\) | 1.17220e6 | 0.433333 | ||||||||
\(375\) | 36814.0 | 0.0135187 | ||||||||
\(376\) | 948408. | 0.345960 | ||||||||
\(377\) | −2.48677e6 | −0.901117 | ||||||||
\(378\) | 42772.3 | 0.0153969 | ||||||||
\(379\) | 4.83295e6 | 1.72828 | 0.864141 | − | 0.503250i | \(-0.167862\pi\) | ||||
0.864141 | + | 0.503250i | \(0.167862\pi\) | |||||||
\(380\) | 46584.8 | 0.0165495 | ||||||||
\(381\) | 587786. | 0.207447 | ||||||||
\(382\) | 1.25147e6 | 0.438796 | ||||||||
\(383\) | −1.95110e6 | −0.679646 | −0.339823 | − | 0.940489i | \(-0.610367\pi\) | ||||
−0.339823 | + | 0.940489i | \(0.610367\pi\) | |||||||
\(384\) | 38602.3 | 0.0133593 | ||||||||
\(385\) | 58773.2 | 0.0202082 | ||||||||
\(386\) | 2.53820e6 | 0.867075 | ||||||||
\(387\) | −1.93731e6 | −0.657540 | ||||||||
\(388\) | −79178.1 | −0.0267009 | ||||||||
\(389\) | 2.32918e6 | 0.780422 | 0.390211 | − | 0.920725i | \(-0.372402\pi\) | ||||
0.390211 | + | 0.920725i | \(0.372402\pi\) | |||||||
\(390\) | −211763. | −0.0704998 | ||||||||
\(391\) | 622902. | 0.206052 | ||||||||
\(392\) | −1.06994e6 | −0.351676 | ||||||||
\(393\) | −23532.5 | −0.00768576 | ||||||||
\(394\) | −2.10475e6 | −0.683060 | ||||||||
\(395\) | −1.09194e6 | −0.352131 | ||||||||
\(396\) | 945512. | 0.302990 | ||||||||
\(397\) | −2.30502e6 | −0.734004 | −0.367002 | − | 0.930220i | \(-0.619616\pi\) | ||||
−0.367002 | + | 0.930220i | \(0.619616\pi\) | |||||||
\(398\) | 1.33300e6 | 0.421814 | ||||||||
\(399\) | −2592.03 | −0.000815094 0 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 904601. | 0.280929 | 0.140464 | − | 0.990086i | \(-0.455140\pi\) | ||||
0.140464 | + | 0.990086i | \(0.455140\pi\) | |||||||
\(402\) | −53639.1 | −0.0165545 | ||||||||
\(403\) | 594946. | 0.182480 | ||||||||
\(404\) | −172959. | −0.0527218 | ||||||||
\(405\) | 1.37582e6 | 0.416798 | ||||||||
\(406\) | −104545. | −0.0314765 | ||||||||
\(407\) | 1.48475e6 | 0.444292 | ||||||||
\(408\) | −177557. | −0.0528064 | ||||||||
\(409\) | 4.80236e6 | 1.41954 | 0.709768 | − | 0.704436i | \(-0.248800\pi\) | ||||
0.709768 | + | 0.704436i | \(0.248800\pi\) | |||||||
\(410\) | −748254. | −0.219831 | ||||||||
\(411\) | 23395.2 | 0.00683160 | ||||||||
\(412\) | −238085. | −0.0691018 | ||||||||
\(413\) | 74961.1 | 0.0216252 | ||||||||
\(414\) | 502442. | 0.144074 | ||||||||
\(415\) | −1.05529e6 | −0.300782 | ||||||||
\(416\) | −920357. | −0.260749 | ||||||||
\(417\) | 310005. | 0.0873029 | ||||||||
\(418\) | −115937. | −0.0324549 | ||||||||
\(419\) | −1.55511e6 | −0.432739 | −0.216370 | − | 0.976312i | \(-0.569422\pi\) | ||||
−0.216370 | + | 0.976312i | \(0.569422\pi\) | |||||||
\(420\) | −8902.58 | −0.00246259 | ||||||||
\(421\) | 2.15341e6 | 0.592137 | 0.296069 | − | 0.955167i | \(-0.404324\pi\) | ||||
0.296069 | + | 0.955167i | \(0.404324\pi\) | |||||||
\(422\) | −2.00262e6 | −0.547416 | ||||||||
\(423\) | −3.51873e6 | −0.956168 | ||||||||
\(424\) | −1.58508e6 | −0.428189 | ||||||||
\(425\) | −735943. | −0.197639 | ||||||||
\(426\) | −290811. | −0.0776402 | ||||||||
\(427\) | −55396.5 | −0.0147032 | ||||||||
\(428\) | −567249. | −0.149680 | ||||||||
\(429\) | 527019. | 0.138256 | ||||||||
\(430\) | 815886. | 0.212793 | ||||||||
\(431\) | 2.75892e6 | 0.715394 | 0.357697 | − | 0.933838i | \(-0.383562\pi\) | ||||
0.357697 | + | 0.933838i | \(0.383562\pi\) | |||||||
\(432\) | −289788. | −0.0747086 | ||||||||
\(433\) | 7.76317e6 | 1.98985 | 0.994923 | − | 0.100643i | \(-0.0320901\pi\) | ||||
0.994923 | + | 0.100643i | \(0.0320901\pi\) | |||||||
\(434\) | 25011.8 | 0.00637412 | ||||||||
\(435\) | 162972. | 0.0412942 | ||||||||
\(436\) | 1.57089e6 | 0.395758 | ||||||||
\(437\) | −61608.4 | −0.0154325 | ||||||||
\(438\) | 234303. | 0.0583570 | ||||||||
\(439\) | 5.38240e6 | 1.33295 | 0.666476 | − | 0.745527i | \(-0.267802\pi\) | ||||
0.666476 | + | 0.745527i | \(0.267802\pi\) | |||||||
\(440\) | −398196. | −0.0980540 | ||||||||
\(441\) | 3.96961e6 | 0.971968 | ||||||||
\(442\) | 4.23331e6 | 1.03068 | ||||||||
\(443\) | −3.25646e6 | −0.788382 | −0.394191 | − | 0.919029i | \(-0.628975\pi\) | ||||
−0.394191 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(444\) | −224901. | −0.0541419 | ||||||||
\(445\) | 2.30945e6 | 0.552852 | ||||||||
\(446\) | −3.06440e6 | −0.729472 | ||||||||
\(447\) | −165275. | −0.0391236 | ||||||||
\(448\) | −38692.1 | −0.00910810 | ||||||||
\(449\) | 4.19928e6 | 0.983013 | 0.491506 | − | 0.870874i | \(-0.336446\pi\) | ||||
0.491506 | + | 0.870874i | \(0.336446\pi\) | |||||||
\(450\) | −593622. | −0.138191 | ||||||||
\(451\) | 1.86220e6 | 0.431106 | ||||||||
\(452\) | −823600. | −0.189614 | ||||||||
\(453\) | −1.02955e6 | −0.235723 | ||||||||
\(454\) | −314722. | −0.0716618 | ||||||||
\(455\) | 212255. | 0.0480652 | ||||||||
\(456\) | 17561.3 | 0.00395499 | ||||||||
\(457\) | 2.83004e6 | 0.633872 | 0.316936 | − | 0.948447i | \(-0.397346\pi\) | ||||
0.316936 | + | 0.948447i | \(0.397346\pi\) | |||||||
\(458\) | 4.99126e6 | 1.11185 | ||||||||
\(459\) | 1.33292e6 | 0.295306 | ||||||||
\(460\) | −211600. | −0.0466252 | ||||||||
\(461\) | 4.05115e6 | 0.887821 | 0.443911 | − | 0.896071i | \(-0.353591\pi\) | ||||
0.443911 | + | 0.896071i | \(0.353591\pi\) | |||||||
\(462\) | 22156.1 | 0.00482934 | ||||||||
\(463\) | −4.15579e6 | −0.900951 | −0.450476 | − | 0.892789i | \(-0.648746\pi\) | ||||
−0.450476 | + | 0.892789i | \(0.648746\pi\) | |||||||
\(464\) | 708302. | 0.152730 | ||||||||
\(465\) | −38990.1 | −0.00836223 | ||||||||
\(466\) | 2.18219e6 | 0.465508 | ||||||||
\(467\) | −4.22033e6 | −0.895477 | −0.447738 | − | 0.894165i | \(-0.647770\pi\) | ||||
−0.447738 | + | 0.894165i | \(0.647770\pi\) | |||||||
\(468\) | 3.41465e6 | 0.720662 | ||||||||
\(469\) | 53763.9 | 0.0112865 | ||||||||
\(470\) | 1.48189e6 | 0.309436 | ||||||||
\(471\) | −656143. | −0.136284 | ||||||||
\(472\) | −507871. | −0.104930 | ||||||||
\(473\) | −2.03052e6 | −0.417305 | ||||||||
\(474\) | −411633. | −0.0841519 | ||||||||
\(475\) | 72788.7 | 0.0148023 | ||||||||
\(476\) | 177970. | 0.0360022 | ||||||||
\(477\) | 5.88085e6 | 1.18343 | ||||||||
\(478\) | 2.41669e6 | 0.483783 | ||||||||
\(479\) | 6.35763e6 | 1.26607 | 0.633033 | − | 0.774125i | \(-0.281810\pi\) | ||||
0.633033 | + | 0.774125i | \(0.281810\pi\) | |||||||
\(480\) | 60316.1 | 0.0119490 | ||||||||
\(481\) | 5.36209e6 | 1.05675 | ||||||||
\(482\) | −2.88093e6 | −0.564827 | ||||||||
\(483\) | 11773.7 | 0.00229638 | ||||||||
\(484\) | −1.58582e6 | −0.307708 | ||||||||
\(485\) | −123716. | −0.0238820 | ||||||||
\(486\) | 1.61894e6 | 0.310914 | ||||||||
\(487\) | −5.24048e6 | −1.00126 | −0.500632 | − | 0.865660i | \(-0.666899\pi\) | ||||
−0.500632 | + | 0.865660i | \(0.666899\pi\) | |||||||
\(488\) | 375318. | 0.0713427 | ||||||||
\(489\) | 965233. | 0.182541 | ||||||||
\(490\) | −1.67178e6 | −0.314549 | ||||||||
\(491\) | 1.05280e6 | 0.197080 | 0.0985402 | − | 0.995133i | \(-0.468583\pi\) | ||||
0.0985402 | + | 0.995133i | \(0.468583\pi\) | |||||||
\(492\) | −282073. | −0.0525351 | ||||||||
\(493\) | −3.25794e6 | −0.603706 | ||||||||
\(494\) | −418698. | −0.0771939 | ||||||||
\(495\) | 1.47736e6 | 0.271003 | ||||||||
\(496\) | −169458. | −0.0309284 | ||||||||
\(497\) | 291488. | 0.0529334 | ||||||||
\(498\) | −397819. | −0.0718807 | ||||||||
\(499\) | −9.41686e6 | −1.69299 | −0.846496 | − | 0.532395i | \(-0.821292\pi\) | ||||
−0.846496 | + | 0.532395i | \(0.821292\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | −195762. | −0.0348444 | ||||||||
\(502\) | −2.67055e6 | −0.472979 | ||||||||
\(503\) | 2.05520e6 | 0.362188 | 0.181094 | − | 0.983466i | \(-0.442036\pi\) | ||||
0.181094 | + | 0.983466i | \(0.442036\pi\) | |||||||
\(504\) | 143553. | 0.0251731 | ||||||||
\(505\) | −270249. | −0.0471558 | ||||||||
\(506\) | 526614. | 0.0914358 | ||||||||
\(507\) | 1.02849e6 | 0.177697 | ||||||||
\(508\) | 3.99159e6 | 0.686256 | ||||||||
\(509\) | −1.07533e6 | −0.183970 | −0.0919848 | − | 0.995760i | \(-0.529321\pi\) | ||||
−0.0919848 | + | 0.995760i | \(0.529321\pi\) | |||||||
\(510\) | −277432. | −0.0472315 | ||||||||
\(511\) | −234849. | −0.0397865 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −131833. | −0.0221172 | ||||||||
\(514\) | −2.68431e6 | −0.448152 | ||||||||
\(515\) | −372008. | −0.0618065 | ||||||||
\(516\) | 307569. | 0.0508532 | ||||||||
\(517\) | −3.68801e6 | −0.606828 | ||||||||
\(518\) | 225424. | 0.0369127 | ||||||||
\(519\) | 659815. | 0.107524 | ||||||||
\(520\) | −1.43806e6 | −0.233221 | ||||||||
\(521\) | 313555. | 0.0506080 | 0.0253040 | − | 0.999680i | \(-0.491945\pi\) | ||||
0.0253040 | + | 0.999680i | \(0.491945\pi\) | |||||||
\(522\) | −2.62790e6 | −0.422116 | ||||||||
\(523\) | −5.21202e6 | −0.833205 | −0.416603 | − | 0.909089i | \(-0.636779\pi\) | ||||
−0.416603 | + | 0.909089i | \(0.636779\pi\) | |||||||
\(524\) | −159807. | −0.0254253 | ||||||||
\(525\) | −13910.3 | −0.00220261 | ||||||||
\(526\) | −3.84933e6 | −0.606626 | ||||||||
\(527\) | 779445. | 0.122253 | ||||||||
\(528\) | −150110. | −0.0234329 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −2.47668e6 | −0.382984 | ||||||||
\(531\) | 1.88427e6 | 0.290006 | ||||||||
\(532\) | −17602.2 | −0.00269642 | ||||||||
\(533\) | 6.72520e6 | 1.02539 | ||||||||
\(534\) | 870607. | 0.132120 | ||||||||
\(535\) | −886326. | −0.133878 | ||||||||
\(536\) | −364257. | −0.0547641 | ||||||||
\(537\) | 1.06683e6 | 0.159646 | ||||||||
\(538\) | 1.62232e6 | 0.241647 | ||||||||
\(539\) | 4.16059e6 | 0.616855 | ||||||||
\(540\) | −452794. | −0.0668214 | ||||||||
\(541\) | −1.03751e6 | −0.152405 | −0.0762024 | − | 0.997092i | \(-0.524280\pi\) | ||||
−0.0762024 | + | 0.997092i | \(0.524280\pi\) | |||||||
\(542\) | −3.05430e6 | −0.446594 | ||||||||
\(543\) | 1.10128e6 | 0.160287 | ||||||||
\(544\) | −1.20577e6 | −0.174690 | ||||||||
\(545\) | 2.45452e6 | 0.353977 | ||||||||
\(546\) | 80015.1 | 0.0114866 | ||||||||
\(547\) | −1.37643e7 | −1.96692 | −0.983461 | − | 0.181119i | \(-0.942028\pi\) | ||||
−0.983461 | + | 0.181119i | \(0.942028\pi\) | |||||||
\(548\) | 158874. | 0.0225997 | ||||||||
\(549\) | −1.39248e6 | −0.197178 | ||||||||
\(550\) | −622181. | −0.0877021 | ||||||||
\(551\) | 322228. | 0.0452151 | ||||||||
\(552\) | −79768.0 | −0.0111425 | ||||||||
\(553\) | 412591. | 0.0573729 | ||||||||
\(554\) | −5.01460e6 | −0.694164 | ||||||||
\(555\) | −351407. | −0.0484260 | ||||||||
\(556\) | 2.10521e6 | 0.288808 | ||||||||
\(557\) | 6.55713e6 | 0.895522 | 0.447761 | − | 0.894153i | \(-0.352222\pi\) | ||||
0.447761 | + | 0.894153i | \(0.352222\pi\) | |||||||
\(558\) | 628712. | 0.0854803 | ||||||||
\(559\) | −7.33307e6 | −0.992558 | ||||||||
\(560\) | −60456.5 | −0.00814653 | ||||||||
\(561\) | 690453. | 0.0926247 | ||||||||
\(562\) | 3.45628e6 | 0.461603 | ||||||||
\(563\) | 1.03758e6 | 0.137960 | 0.0689799 | − | 0.997618i | \(-0.478026\pi\) | ||||
0.0689799 | + | 0.997618i | \(0.478026\pi\) | |||||||
\(564\) | 558635. | 0.0739487 | ||||||||
\(565\) | −1.28687e6 | −0.169596 | ||||||||
\(566\) | −3.62402e6 | −0.475499 | ||||||||
\(567\) | −519859. | −0.0679091 | ||||||||
\(568\) | −1.97487e6 | −0.256842 | ||||||||
\(569\) | 2.73424e6 | 0.354043 | 0.177022 | − | 0.984207i | \(-0.443354\pi\) | ||||
0.177022 | + | 0.984207i | \(0.443354\pi\) | |||||||
\(570\) | 27439.6 | 0.00353745 | ||||||||
\(571\) | 304642. | 0.0391021 | 0.0195510 | − | 0.999809i | \(-0.493776\pi\) | ||||
0.0195510 | + | 0.999809i | \(0.493776\pi\) | |||||||
\(572\) | 3.57893e6 | 0.457365 | ||||||||
\(573\) | 737148. | 0.0937925 | ||||||||
\(574\) | 282730. | 0.0358172 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | −972590. | −0.122144 | ||||||||
\(577\) | −4.26839e6 | −0.533734 | −0.266867 | − | 0.963733i | \(-0.585988\pi\) | ||||
−0.266867 | + | 0.963733i | \(0.585988\pi\) | |||||||
\(578\) | −133321. | −0.0165989 | ||||||||
\(579\) | 1.49506e6 | 0.185337 | ||||||||
\(580\) | 1.10672e6 | 0.136606 | ||||||||
\(581\) | 398745. | 0.0490066 | ||||||||
\(582\) | −46637.8 | −0.00570730 | ||||||||
\(583\) | 6.16378e6 | 0.751062 | ||||||||
\(584\) | 1.59113e6 | 0.193051 | ||||||||
\(585\) | 5.33539e6 | 0.644580 | ||||||||
\(586\) | −1.03675e7 | −1.24718 | ||||||||
\(587\) | 8.95255e6 | 1.07239 | 0.536193 | − | 0.844095i | \(-0.319862\pi\) | ||||
0.536193 | + | 0.844095i | \(0.319862\pi\) | |||||||
\(588\) | −630219. | −0.0751706 | ||||||||
\(589\) | −77091.4 | −0.00915625 | ||||||||
\(590\) | −793548. | −0.0938519 | ||||||||
\(591\) | −1.23975e6 | −0.146004 | ||||||||
\(592\) | −1.52728e6 | −0.179107 | ||||||||
\(593\) | 891844. | 0.104148 | 0.0520742 | − | 0.998643i | \(-0.483417\pi\) | ||||
0.0520742 | + | 0.998643i | \(0.483417\pi\) | |||||||
\(594\) | 1.12688e6 | 0.131042 | ||||||||
\(595\) | 278078. | 0.0322014 | ||||||||
\(596\) | −1.12237e6 | −0.129425 | ||||||||
\(597\) | 785167. | 0.0901626 | ||||||||
\(598\) | 1.90183e6 | 0.217480 | ||||||||
\(599\) | 8.36368e6 | 0.952424 | 0.476212 | − | 0.879331i | \(-0.342010\pi\) | ||||
0.476212 | + | 0.879331i | \(0.342010\pi\) | |||||||
\(600\) | 94243.9 | 0.0106875 | ||||||||
\(601\) | −8.54102e6 | −0.964547 | −0.482273 | − | 0.876021i | \(-0.660189\pi\) | ||||
−0.482273 | + | 0.876021i | \(0.660189\pi\) | |||||||
\(602\) | −308285. | −0.0346706 | ||||||||
\(603\) | 1.35144e6 | 0.151358 | ||||||||
\(604\) | −6.99158e6 | −0.779799 | ||||||||
\(605\) | −2.47784e6 | −0.275223 | ||||||||
\(606\) | −101877. | −0.0112693 | ||||||||
\(607\) | −1.68584e7 | −1.85714 | −0.928568 | − | 0.371162i | \(-0.878959\pi\) | ||||
−0.928568 | + | 0.371162i | \(0.878959\pi\) | |||||||
\(608\) | 119257. | 0.0130835 | ||||||||
\(609\) | −61579.2 | −0.00672808 | ||||||||
\(610\) | 586434. | 0.0638109 | ||||||||
\(611\) | −1.33190e7 | −1.44334 | ||||||||
\(612\) | 4.47357e6 | 0.482809 | ||||||||
\(613\) | −1.14220e7 | −1.22769 | −0.613847 | − | 0.789425i | \(-0.710379\pi\) | ||||
−0.613847 | + | 0.789425i | \(0.710379\pi\) | |||||||
\(614\) | −9.54012e6 | −1.02125 | ||||||||
\(615\) | −440739. | −0.0469888 | ||||||||
\(616\) | 150459. | 0.0159760 | ||||||||
\(617\) | −4.05632e6 | −0.428962 | −0.214481 | − | 0.976728i | \(-0.568806\pi\) | ||||
−0.214481 | + | 0.976728i | \(0.568806\pi\) | |||||||
\(618\) | −140238. | −0.0147705 | ||||||||
\(619\) | −9.02063e6 | −0.946259 | −0.473130 | − | 0.880993i | \(-0.656876\pi\) | ||||
−0.473130 | + | 0.880993i | \(0.656876\pi\) | |||||||
\(620\) | −264778. | −0.0276632 | ||||||||
\(621\) | 598819. | 0.0623113 | ||||||||
\(622\) | −7.02797e6 | −0.728374 | ||||||||
\(623\) | −872633. | −0.0900765 | ||||||||
\(624\) | −542112. | −0.0557350 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 3.36081e6 | 0.342774 | ||||||||
\(627\) | −68289.5 | −0.00693722 | ||||||||
\(628\) | −4.45580e6 | −0.450844 | ||||||||
\(629\) | 7.02493e6 | 0.707971 | ||||||||
\(630\) | 224302. | 0.0225155 | ||||||||
\(631\) | −1.61649e7 | −1.61622 | −0.808110 | − | 0.589032i | \(-0.799509\pi\) | ||||
−0.808110 | + | 0.589032i | \(0.799509\pi\) | |||||||
\(632\) | −2.79535e6 | −0.278384 | ||||||||
\(633\) | −1.17959e6 | −0.117010 | ||||||||
\(634\) | −1.23098e7 | −1.21626 | ||||||||
\(635\) | 6.23686e6 | 0.613806 | ||||||||
\(636\) | −933649. | −0.0915252 | ||||||||
\(637\) | 1.50257e7 | 1.46719 | ||||||||
\(638\) | −2.75433e6 | −0.267894 | ||||||||
\(639\) | 7.32703e6 | 0.709865 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −1.60205e7 | −1.54003 | −0.770017 | − | 0.638023i | \(-0.779752\pi\) | ||||
−0.770017 | + | 0.638023i | \(0.779752\pi\) | |||||||
\(642\) | −334123. | −0.0319940 | ||||||||
\(643\) | −8.32578e6 | −0.794140 | −0.397070 | − | 0.917788i | \(-0.629973\pi\) | ||||
−0.397070 | + | 0.917788i | \(0.629973\pi\) | |||||||
\(644\) | 79953.7 | 0.00759668 | ||||||||
\(645\) | 480576. | 0.0454845 | ||||||||
\(646\) | −548540. | −0.0517162 | ||||||||
\(647\) | 6.02871e6 | 0.566192 | 0.283096 | − | 0.959092i | \(-0.408639\pi\) | ||||
0.283096 | + | 0.959092i | \(0.408639\pi\) | |||||||
\(648\) | 3.52211e6 | 0.329508 | ||||||||
\(649\) | 1.97492e6 | 0.184051 | ||||||||
\(650\) | −2.24696e6 | −0.208599 | ||||||||
\(651\) | 14732.5 | 0.00136246 | ||||||||
\(652\) | 6.55479e6 | 0.603865 | ||||||||
\(653\) | 8.22531e6 | 0.754865 | 0.377433 | − | 0.926037i | \(-0.376807\pi\) | ||||
0.377433 | + | 0.926037i | \(0.376807\pi\) | |||||||
\(654\) | 925293. | 0.0845931 | ||||||||
\(655\) | −249698. | −0.0227411 | ||||||||
\(656\) | −1.91553e6 | −0.173792 | ||||||||
\(657\) | −5.90331e6 | −0.533558 | ||||||||
\(658\) | −559936. | −0.0504166 | ||||||||
\(659\) | 1.68658e7 | 1.51284 | 0.756420 | − | 0.654086i | \(-0.226946\pi\) | ||||
0.756420 | + | 0.654086i | \(0.226946\pi\) | |||||||
\(660\) | −234547. | −0.0209590 | ||||||||
\(661\) | −992213. | −0.0883286 | −0.0441643 | − | 0.999024i | \(-0.514063\pi\) | ||||
−0.0441643 | + | 0.999024i | \(0.514063\pi\) | |||||||
\(662\) | −7.08070e6 | −0.627959 | ||||||||
\(663\) | 2.49352e6 | 0.220308 | ||||||||
\(664\) | −2.70155e6 | −0.237789 | ||||||||
\(665\) | −27503.4 | −0.00241175 | ||||||||
\(666\) | 5.66641e6 | 0.495019 | ||||||||
\(667\) | −1.46364e6 | −0.127385 | ||||||||
\(668\) | −1.32940e6 | −0.115269 | ||||||||
\(669\) | −1.80501e6 | −0.155924 | ||||||||
\(670\) | −569152. | −0.0489825 | ||||||||
\(671\) | −1.45947e6 | −0.125138 | ||||||||
\(672\) | −22790.6 | −0.00194685 | ||||||||
\(673\) | −8.36599e6 | −0.711999 | −0.356000 | − | 0.934486i | \(-0.615860\pi\) | ||||
−0.356000 | + | 0.934486i | \(0.615860\pi\) | |||||||
\(674\) | −743883. | −0.0630746 | ||||||||
\(675\) | −707490. | −0.0597669 | ||||||||
\(676\) | 6.98437e6 | 0.587842 | ||||||||
\(677\) | 1.59336e7 | 1.33611 | 0.668054 | − | 0.744113i | \(-0.267128\pi\) | ||||
0.668054 | + | 0.744113i | \(0.267128\pi\) | |||||||
\(678\) | −485120. | −0.0405299 | ||||||||
\(679\) | 46746.4 | 0.00389111 | ||||||||
\(680\) | −1.88401e6 | −0.156247 | ||||||||
\(681\) | −185379. | −0.0153177 | ||||||||
\(682\) | 658959. | 0.0542497 | ||||||||
\(683\) | 4.02204e6 | 0.329909 | 0.164955 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164955 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(684\) | −442460. | −0.0361605 | ||||||||
\(685\) | 248241. | 0.0202138 | ||||||||
\(686\) | 1.26674e6 | 0.102773 | ||||||||
\(687\) | 2.93997e6 | 0.237657 | ||||||||
\(688\) | 2.08867e6 | 0.168228 | ||||||||
\(689\) | 2.22601e7 | 1.78640 | ||||||||
\(690\) | −124638. | −0.00996612 | ||||||||
\(691\) | 8.51156e6 | 0.678132 | 0.339066 | − | 0.940763i | \(-0.389889\pi\) | ||||
0.339066 | + | 0.940763i | \(0.389889\pi\) | |||||||
\(692\) | 4.48073e6 | 0.355700 | ||||||||
\(693\) | −558225. | −0.0441547 | ||||||||
\(694\) | −8.58503e6 | −0.676617 | ||||||||
\(695\) | 3.28939e6 | 0.258317 | ||||||||
\(696\) | 417207. | 0.0326459 | ||||||||
\(697\) | 8.81075e6 | 0.686959 | ||||||||
\(698\) | −7.35331e6 | −0.571274 | ||||||||
\(699\) | 1.28536e6 | 0.0995020 | ||||||||
\(700\) | −94463.2 | −0.00728648 | ||||||||
\(701\) | 1.13383e7 | 0.871472 | 0.435736 | − | 0.900074i | \(-0.356488\pi\) | ||||
0.435736 | + | 0.900074i | \(0.356488\pi\) | |||||||
\(702\) | 4.06964e6 | 0.311683 | ||||||||
\(703\) | −694804. | −0.0530241 | ||||||||
\(704\) | −1.01938e6 | −0.0775185 | ||||||||
\(705\) | 872868. | 0.0661417 | ||||||||
\(706\) | 5.81663e6 | 0.439197 | ||||||||
\(707\) | 102114. | 0.00768312 | ||||||||
\(708\) | −299148. | −0.0224286 | ||||||||
\(709\) | 6.85924e6 | 0.512460 | 0.256230 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256230 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(710\) | −3.08573e6 | −0.229727 | ||||||||
\(711\) | 1.03712e7 | 0.769401 | ||||||||
\(712\) | 5.91220e6 | 0.437068 | ||||||||
\(713\) | 350169. | 0.0257961 | ||||||||
\(714\) | 104829. | 0.00769546 | ||||||||
\(715\) | 5.59208e6 | 0.409080 | ||||||||
\(716\) | 7.24471e6 | 0.528127 | ||||||||
\(717\) | 1.42349e6 | 0.103408 | ||||||||
\(718\) | −635960. | −0.0460383 | ||||||||
\(719\) | −1.86207e7 | −1.34330 | −0.671652 | − | 0.740867i | \(-0.734415\pi\) | ||||
−0.671652 | + | 0.740867i | \(0.734415\pi\) | |||||||
\(720\) | −1.51967e6 | −0.109249 | ||||||||
\(721\) | 140564. | 0.0100702 | ||||||||
\(722\) | −9.85014e6 | −0.703233 | ||||||||
\(723\) | −1.69694e6 | −0.120732 | ||||||||
\(724\) | 7.47869e6 | 0.530248 | ||||||||
\(725\) | 1.72925e6 | 0.122184 | ||||||||
\(726\) | −934084. | −0.0657725 | ||||||||
\(727\) | 9.72770e6 | 0.682612 | 0.341306 | − | 0.939952i | \(-0.389131\pi\) | ||||
0.341306 | + | 0.939952i | \(0.389131\pi\) | |||||||
\(728\) | 543374. | 0.0379988 | ||||||||
\(729\) | −1.24194e7 | −0.865531 | ||||||||
\(730\) | 2.48614e6 | 0.172671 | ||||||||
\(731\) | −9.60713e6 | −0.664967 | ||||||||
\(732\) | 221071. | 0.0152495 | ||||||||
\(733\) | −2.08414e7 | −1.43274 | −0.716370 | − | 0.697720i | \(-0.754198\pi\) | ||||
−0.716370 | + | 0.697720i | \(0.754198\pi\) | |||||||
\(734\) | −1.75717e7 | −1.20385 | ||||||||
\(735\) | −984717. | −0.0672346 | ||||||||
\(736\) | −541696. | −0.0368605 | ||||||||
\(737\) | 1.41646e6 | 0.0960586 | ||||||||
\(738\) | 7.10688e6 | 0.480328 | ||||||||
\(739\) | −2.75701e7 | −1.85707 | −0.928533 | − | 0.371250i | \(-0.878929\pi\) | ||||
−0.928533 | + | 0.371250i | \(0.878929\pi\) | |||||||
\(740\) | −2.38637e6 | −0.160199 | ||||||||
\(741\) | −246623. | −0.0165002 | ||||||||
\(742\) | 935822. | 0.0623998 | ||||||||
\(743\) | −2.42438e6 | −0.161112 | −0.0805560 | − | 0.996750i | \(-0.525670\pi\) | ||||
−0.0805560 | + | 0.996750i | \(0.525670\pi\) | |||||||
\(744\) | −99814.7 | −0.00661093 | ||||||||
\(745\) | −1.75370e6 | −0.115762 | ||||||||
\(746\) | 3.41488e6 | 0.224662 | ||||||||
\(747\) | 1.00231e7 | 0.657205 | ||||||||
\(748\) | 4.68879e6 | 0.306413 | ||||||||
\(749\) | 334901. | 0.0218128 | ||||||||
\(750\) | 147256. | 0.00955917 | ||||||||
\(751\) | −1.70442e7 | −1.10275 | −0.551375 | − | 0.834258i | \(-0.685897\pi\) | ||||
−0.551375 | + | 0.834258i | \(0.685897\pi\) | |||||||
\(752\) | 3.79363e6 | 0.244631 | ||||||||
\(753\) | −1.57302e6 | −0.101099 | ||||||||
\(754\) | −9.94706e6 | −0.637186 | ||||||||
\(755\) | −1.09243e7 | −0.697474 | ||||||||
\(756\) | 171089. | 0.0108873 | ||||||||
\(757\) | 4.90700e6 | 0.311226 | 0.155613 | − | 0.987818i | \(-0.450265\pi\) | ||||
0.155613 | + | 0.987818i | \(0.450265\pi\) | |||||||
\(758\) | 1.93318e7 | 1.22208 | ||||||||
\(759\) | 310188. | 0.0195444 | ||||||||
\(760\) | 186339. | 0.0117023 | ||||||||
\(761\) | −9.97216e6 | −0.624206 | −0.312103 | − | 0.950048i | \(-0.601033\pi\) | ||||
−0.312103 | + | 0.950048i | \(0.601033\pi\) | |||||||
\(762\) | 2.35114e6 | 0.146687 | ||||||||
\(763\) | −927447. | −0.0576737 | ||||||||
\(764\) | 5.00589e6 | 0.310276 | ||||||||
\(765\) | 6.98995e6 | 0.431838 | ||||||||
\(766\) | −7.80441e6 | −0.480583 | ||||||||
\(767\) | 7.13229e6 | 0.437765 | ||||||||
\(768\) | 154409. | 0.00944648 | ||||||||
\(769\) | 7.81599e6 | 0.476615 | 0.238308 | − | 0.971190i | \(-0.423407\pi\) | ||||
0.238308 | + | 0.971190i | \(0.423407\pi\) | |||||||
\(770\) | 235093. | 0.0142894 | ||||||||
\(771\) | −1.58113e6 | −0.0957923 | ||||||||
\(772\) | 1.01528e7 | 0.613115 | ||||||||
\(773\) | −2.20716e7 | −1.32857 | −0.664287 | − | 0.747478i | \(-0.731265\pi\) | ||||
−0.664287 | + | 0.747478i | \(0.731265\pi\) | |||||||
\(774\) | −7.74924e6 | −0.464951 | ||||||||
\(775\) | −413715. | −0.0247427 | ||||||||
\(776\) | −316713. | −0.0188804 | ||||||||
\(777\) | 132780. | 0.00789007 | ||||||||
\(778\) | 9.31673e6 | 0.551842 | ||||||||
\(779\) | −871431. | −0.0514505 | ||||||||
\(780\) | −847051. | −0.0498509 | ||||||||
\(781\) | 7.67953e6 | 0.450513 | ||||||||
\(782\) | 2.49161e6 | 0.145701 | ||||||||
\(783\) | −3.13198e6 | −0.182564 | ||||||||
\(784\) | −4.27975e6 | −0.248673 | ||||||||
\(785\) | −6.96218e6 | −0.403247 | ||||||||
\(786\) | −94130.0 | −0.00543465 | ||||||||
\(787\) | 2.88969e7 | 1.66308 | 0.831542 | − | 0.555462i | \(-0.187459\pi\) | ||||
0.831542 | + | 0.555462i | \(0.187459\pi\) | |||||||
\(788\) | −8.41898e6 | −0.482997 | ||||||||
\(789\) | −2.26735e6 | −0.129666 | ||||||||
\(790\) | −4.36774e6 | −0.248994 | ||||||||
\(791\) | 486249. | 0.0276323 | ||||||||
\(792\) | 3.78205e6 | 0.214247 | ||||||||
\(793\) | −5.27079e6 | −0.297641 | ||||||||
\(794\) | −9.22008e6 | −0.519019 | ||||||||
\(795\) | −1.45883e6 | −0.0818626 | ||||||||
\(796\) | 5.33199e6 | 0.298268 | ||||||||
\(797\) | 3.54790e7 | 1.97845 | 0.989226 | − | 0.146394i | \(-0.0467669\pi\) | ||||
0.989226 | + | 0.146394i | \(0.0467669\pi\) | |||||||
\(798\) | −10368.1 | −0.000576359 0 | ||||||||
\(799\) | −1.74494e7 | −0.966969 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | −2.19351e7 | −1.20797 | ||||||||
\(802\) | 3.61840e6 | 0.198647 | ||||||||
\(803\) | −6.18731e6 | −0.338621 | ||||||||
\(804\) | −214556. | −0.0117058 | ||||||||
\(805\) | 124928. | 0.00679467 | ||||||||
\(806\) | 2.37979e6 | 0.129033 | ||||||||
\(807\) | 955588. | 0.0516520 | ||||||||
\(808\) | −691837. | −0.0372799 | ||||||||
\(809\) | 1.54874e7 | 0.831970 | 0.415985 | − | 0.909371i | \(-0.363437\pi\) | ||||
0.415985 | + | 0.909371i | \(0.363437\pi\) | |||||||
\(810\) | 5.50330e6 | 0.294721 | ||||||||
\(811\) | −1.51749e7 | −0.810167 | −0.405083 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405083 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(812\) | −418178. | −0.0222572 | ||||||||
\(813\) | −1.79905e6 | −0.0954592 | ||||||||
\(814\) | 5.93902e6 | 0.314162 | ||||||||
\(815\) | 1.02419e7 | 0.540113 | ||||||||
\(816\) | −710227. | −0.0373398 | ||||||||
\(817\) | 950197. | 0.0498033 | ||||||||
\(818\) | 1.92094e7 | 1.00376 | ||||||||
\(819\) | −2.01599e6 | −0.105022 | ||||||||
\(820\) | −2.99301e6 | −0.155444 | ||||||||
\(821\) | 3.55262e7 | 1.83946 | 0.919730 | − | 0.392552i | \(-0.128408\pi\) | ||||
0.919730 | + | 0.392552i | \(0.128408\pi\) | |||||||
\(822\) | 93580.8 | 0.00483067 | ||||||||
\(823\) | −3.14372e7 | −1.61787 | −0.808935 | − | 0.587898i | \(-0.799956\pi\) | ||||
−0.808935 | + | 0.587898i | \(0.799956\pi\) | |||||||
\(824\) | −952340. | −0.0488623 | ||||||||
\(825\) | −366480. | −0.0187463 | ||||||||
\(826\) | 299844. | 0.0152913 | ||||||||
\(827\) | 1.46845e7 | 0.746615 | 0.373307 | − | 0.927708i | \(-0.378224\pi\) | ||||
0.373307 | + | 0.927708i | \(0.378224\pi\) | |||||||
\(828\) | 2.00977e6 | 0.101876 | ||||||||
\(829\) | 2.18365e7 | 1.10356 | 0.551781 | − | 0.833989i | \(-0.313949\pi\) | ||||
0.551781 | + | 0.833989i | \(0.313949\pi\) | |||||||
\(830\) | −4.22117e6 | −0.212685 | ||||||||
\(831\) | −2.95372e6 | −0.148377 | ||||||||
\(832\) | −3.68143e6 | −0.184377 | ||||||||
\(833\) | 1.96853e7 | 0.982946 | ||||||||
\(834\) | 1.24002e6 | 0.0617324 | ||||||||
\(835\) | −2.07718e6 | −0.103100 | ||||||||
\(836\) | −463747. | −0.0229491 | ||||||||
\(837\) | 749311. | 0.0369699 | ||||||||
\(838\) | −6.22044e6 | −0.305993 | ||||||||
\(839\) | 8.00659e6 | 0.392684 | 0.196342 | − | 0.980536i | \(-0.437094\pi\) | ||||
0.196342 | + | 0.980536i | \(0.437094\pi\) | |||||||
\(840\) | −35610.3 | −0.00174132 | ||||||||
\(841\) | −1.28559e7 | −0.626778 | ||||||||
\(842\) | 8.61365e6 | 0.418704 | ||||||||
\(843\) | 2.03583e6 | 0.0986673 | ||||||||
\(844\) | −8.01049e6 | −0.387082 | ||||||||
\(845\) | 1.09131e7 | 0.525782 | ||||||||
\(846\) | −1.40749e7 | −0.676113 | ||||||||
\(847\) | 936258. | 0.0448422 | ||||||||
\(848\) | −6.34031e6 | −0.302775 | ||||||||
\(849\) | −2.13463e6 | −0.101638 | ||||||||
\(850\) | −2.94377e6 | −0.139752 | ||||||||
\(851\) | 3.15597e6 | 0.149386 | ||||||||
\(852\) | −1.16324e6 | −0.0548999 | ||||||||
\(853\) | −2.73958e7 | −1.28917 | −0.644587 | − | 0.764531i | \(-0.722971\pi\) | ||||
−0.644587 | + | 0.764531i | \(0.722971\pi\) | |||||||
\(854\) | −221586. | −0.0103967 | ||||||||
\(855\) | −691344. | −0.0323429 | ||||||||
\(856\) | −2.26900e6 | −0.105840 | ||||||||
\(857\) | −1.73328e7 | −0.806153 | −0.403076 | − | 0.915166i | \(-0.632059\pi\) | ||||
−0.403076 | + | 0.915166i | \(0.632059\pi\) | |||||||
\(858\) | 2.10808e6 | 0.0977615 | ||||||||
\(859\) | 1.52183e6 | 0.0703693 | 0.0351847 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351847 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(860\) | 3.26354e6 | 0.150468 | ||||||||
\(861\) | 166535. | 0.00765591 | ||||||||
\(862\) | 1.10357e7 | 0.505860 | ||||||||
\(863\) | −1.94346e7 | −0.888276 | −0.444138 | − | 0.895958i | \(-0.646490\pi\) | ||||
−0.444138 | + | 0.895958i | \(0.646490\pi\) | |||||||
\(864\) | −1.15915e6 | −0.0528270 | ||||||||
\(865\) | 7.00114e6 | 0.318148 | ||||||||
\(866\) | 3.10527e7 | 1.40703 | ||||||||
\(867\) | −78529.6 | −0.00354802 | ||||||||
\(868\) | 100047. | 0.00450718 | ||||||||
\(869\) | 1.08701e7 | 0.488297 | ||||||||
\(870\) | 651886. | 0.0291994 | ||||||||
\(871\) | 5.11546e6 | 0.228475 | ||||||||
\(872\) | 6.28357e6 | 0.279843 | ||||||||
\(873\) | 1.17505e6 | 0.0521819 | ||||||||
\(874\) | −246434. | −0.0109124 | ||||||||
\(875\) | −147599. | −0.00651722 | ||||||||
\(876\) | 937213. | 0.0412646 | ||||||||
\(877\) | −2.54795e7 | −1.11865 | −0.559323 | − | 0.828950i | \(-0.688939\pi\) | ||||
−0.559323 | + | 0.828950i | \(0.688939\pi\) | |||||||
\(878\) | 2.15296e7 | 0.942539 | ||||||||
\(879\) | −6.10669e6 | −0.266584 | ||||||||
\(880\) | −1.59278e6 | −0.0693346 | ||||||||
\(881\) | −6.59781e6 | −0.286391 | −0.143196 | − | 0.989694i | \(-0.545738\pi\) | ||||
−0.143196 | + | 0.989694i | \(0.545738\pi\) | |||||||
\(882\) | 1.58785e7 | 0.687285 | ||||||||
\(883\) | −2.37423e7 | −1.02476 | −0.512378 | − | 0.858760i | \(-0.671235\pi\) | ||||
−0.512378 | + | 0.858760i | \(0.671235\pi\) | |||||||
\(884\) | 1.69332e7 | 0.728802 | ||||||||
\(885\) | −467419. | −0.0200608 | ||||||||
\(886\) | −1.30258e7 | −0.557470 | ||||||||
\(887\) | 2.96051e7 | 1.26345 | 0.631724 | − | 0.775194i | \(-0.282348\pi\) | ||||
0.631724 | + | 0.775194i | \(0.282348\pi\) | |||||||
\(888\) | −899603. | −0.0382841 | ||||||||
\(889\) | −2.35661e6 | −0.100008 | ||||||||
\(890\) | 9.23781e6 | 0.390925 | ||||||||
\(891\) | −1.36962e7 | −0.577971 | ||||||||
\(892\) | −1.22576e7 | −0.515815 | ||||||||
\(893\) | 1.72584e6 | 0.0724221 | ||||||||
\(894\) | −661101. | −0.0276646 | ||||||||
\(895\) | 1.13199e7 | 0.472371 | ||||||||
\(896\) | −154769. | −0.00644040 | ||||||||
\(897\) | 1.12022e6 | 0.0464862 | ||||||||
\(898\) | 1.67971e7 | 0.695095 | ||||||||
\(899\) | −1.83147e6 | −0.0755790 | ||||||||
\(900\) | −2.37449e6 | −0.0977156 | ||||||||
\(901\) | 2.91632e7 | 1.19680 | ||||||||
\(902\) | 7.44879e6 | 0.304838 | ||||||||
\(903\) | −181587. | −0.00741081 | ||||||||
\(904\) | −3.29440e6 | −0.134077 | ||||||||
\(905\) | 1.16855e7 | 0.474268 | ||||||||
\(906\) | −4.11821e6 | −0.166682 | ||||||||
\(907\) | −1.29526e7 | −0.522803 | −0.261402 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261402 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(908\) | −1.25889e6 | −0.0506725 | ||||||||
\(909\) | 2.56681e6 | 0.103035 | ||||||||
\(910\) | 849022. | 0.0339872 | ||||||||
\(911\) | −2.62067e7 | −1.04620 | −0.523102 | − | 0.852270i | \(-0.675225\pi\) | ||||
−0.523102 | + | 0.852270i | \(0.675225\pi\) | |||||||
\(912\) | 70245.3 | 0.00279660 | ||||||||
\(913\) | 1.05053e7 | 0.417093 | ||||||||
\(914\) | 1.13201e7 | 0.448215 | ||||||||
\(915\) | 345424. | 0.0136395 | ||||||||
\(916\) | 1.99650e7 | 0.786197 | ||||||||
\(917\) | 94349.0 | 0.00370522 | ||||||||
\(918\) | 5.33168e6 | 0.208813 | ||||||||
\(919\) | 2.24232e7 | 0.875807 | 0.437904 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437904 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(920\) | −846400. | −0.0329690 | ||||||||
\(921\) | −5.61936e6 | −0.218292 | ||||||||
\(922\) | 1.62046e7 | 0.627784 | ||||||||
\(923\) | 2.77341e7 | 1.07154 | ||||||||
\(924\) | 88624.3 | 0.00341486 | ||||||||
\(925\) | −3.72870e6 | −0.143286 | ||||||||
\(926\) | −1.66232e7 | −0.637069 | ||||||||
\(927\) | 3.53331e6 | 0.135046 | ||||||||
\(928\) | 2.83321e6 | 0.107996 | ||||||||
\(929\) | 5.75572e6 | 0.218807 | 0.109403 | − | 0.993997i | \(-0.465106\pi\) | ||||
0.109403 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(930\) | −155961. | −0.00591299 | ||||||||
\(931\) | −1.94698e6 | −0.0736187 | ||||||||
\(932\) | 8.72874e6 | 0.329164 | ||||||||
\(933\) | −4.13965e6 | −0.155689 | ||||||||
\(934\) | −1.68813e7 | −0.633198 | ||||||||
\(935\) | 7.32624e6 | 0.274064 | ||||||||
\(936\) | 1.36586e7 | 0.509585 | ||||||||
\(937\) | −1.96217e6 | −0.0730109 | −0.0365055 | − | 0.999333i | \(-0.511623\pi\) | ||||
−0.0365055 | + | 0.999333i | \(0.511623\pi\) | |||||||
\(938\) | 215056. | 0.00798075 | ||||||||
\(939\) | 1.97960e6 | 0.0732678 | ||||||||
\(940\) | 5.92755e6 | 0.218804 | ||||||||
\(941\) | 2.26215e7 | 0.832813 | 0.416406 | − | 0.909179i | \(-0.363289\pi\) | ||||
0.416406 | + | 0.909179i | \(0.363289\pi\) | |||||||
\(942\) | −2.62457e6 | −0.0963676 | ||||||||
\(943\) | 3.95826e6 | 0.144952 | ||||||||
\(944\) | −2.03148e6 | −0.0741964 | ||||||||
\(945\) | 267327. | 0.00973786 | ||||||||
\(946\) | −8.12206e6 | −0.295079 | ||||||||
\(947\) | 9.29545e6 | 0.336818 | 0.168409 | − | 0.985717i | \(-0.446137\pi\) | ||||
0.168409 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(948\) | −1.64653e6 | −0.0595044 | ||||||||
\(949\) | −2.23451e7 | −0.805408 | ||||||||
\(950\) | 291155. | 0.0104668 | ||||||||
\(951\) | −7.25076e6 | −0.259975 | ||||||||
\(952\) | 711880. | 0.0254574 | ||||||||
\(953\) | −1.09761e7 | −0.391484 | −0.195742 | − | 0.980655i | \(-0.562712\pi\) | ||||
−0.195742 | + | 0.980655i | \(0.562712\pi\) | |||||||
\(954\) | 2.35234e7 | 0.836815 | ||||||||
\(955\) | 7.82171e6 | 0.277519 | ||||||||
\(956\) | 9.66675e6 | 0.342086 | ||||||||
\(957\) | −1.62237e6 | −0.0572623 | ||||||||
\(958\) | 2.54305e7 | 0.895244 | ||||||||
\(959\) | −93798.6 | −0.00329344 | ||||||||
\(960\) | 241264. | 0.00844919 | ||||||||
\(961\) | −2.81910e7 | −0.984695 | ||||||||
\(962\) | 2.14484e7 | 0.747234 | ||||||||
\(963\) | 8.41828e6 | 0.292522 | ||||||||
\(964\) | −1.15237e7 | −0.399393 | ||||||||
\(965\) | 1.58637e7 | 0.548386 | ||||||||
\(966\) | 47094.6 | 0.00162379 | ||||||||
\(967\) | 1.31788e7 | 0.453219 | 0.226610 | − | 0.973986i | \(-0.427236\pi\) | ||||
0.226610 | + | 0.973986i | \(0.427236\pi\) | |||||||
\(968\) | −6.34326e6 | −0.217583 | ||||||||
\(969\) | −323103. | −0.0110543 | ||||||||
\(970\) | −494863. | −0.0168871 | ||||||||
\(971\) | 3.36061e7 | 1.14385 | 0.571927 | − | 0.820305i | \(-0.306196\pi\) | ||||
0.571927 | + | 0.820305i | \(0.306196\pi\) | |||||||
\(972\) | 6.47576e6 | 0.219849 | ||||||||
\(973\) | −1.24291e6 | −0.0420878 | ||||||||
\(974\) | −2.09619e7 | −0.708000 | ||||||||
\(975\) | −1.32352e6 | −0.0445880 | ||||||||
\(976\) | 1.50127e6 | 0.0504469 | ||||||||
\(977\) | −5.56285e7 | −1.86449 | −0.932246 | − | 0.361824i | \(-0.882154\pi\) | ||||
−0.932246 | + | 0.361824i | \(0.882154\pi\) | |||||||
\(978\) | 3.86093e6 | 0.129076 | ||||||||
\(979\) | −2.29904e7 | −0.766636 | ||||||||
\(980\) | −6.68711e6 | −0.222420 | ||||||||
\(981\) | −2.33129e7 | −0.773435 | ||||||||
\(982\) | 4.21121e6 | 0.139357 | ||||||||
\(983\) | −1.76368e7 | −0.582150 | −0.291075 | − | 0.956700i | \(-0.594013\pi\) | ||||
−0.291075 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(984\) | −1.12829e6 | −0.0371479 | ||||||||
\(985\) | −1.31547e7 | −0.432005 | ||||||||
\(986\) | −1.30317e7 | −0.426884 | ||||||||
\(987\) | −329816. | −0.0107765 | ||||||||
\(988\) | −1.67479e6 | −0.0545843 | ||||||||
\(989\) | −4.31604e6 | −0.140312 | ||||||||
\(990\) | 5.90945e6 | 0.191628 | ||||||||
\(991\) | 1.13075e7 | 0.365749 | 0.182875 | − | 0.983136i | \(-0.441460\pi\) | ||||
0.182875 | + | 0.983136i | \(0.441460\pi\) | |||||||
\(992\) | −677831. | −0.0218697 | ||||||||
\(993\) | −4.17070e6 | −0.134226 | ||||||||
\(994\) | 1.16595e6 | 0.0374295 | ||||||||
\(995\) | 8.33123e6 | 0.266779 | ||||||||
\(996\) | −1.59128e6 | −0.0508273 | ||||||||
\(997\) | 2.57849e6 | 0.0821538 | 0.0410769 | − | 0.999156i | \(-0.486921\pi\) | ||||
0.0410769 | + | 0.999156i | \(0.486921\pi\) | |||||||
\(998\) | −3.76674e7 | −1.19713 | ||||||||
\(999\) | 6.75333e6 | 0.214094 |
(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 | 230.6.a.d.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |