Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.18 | ||
Character | \(\chi\) | \(=\) | 384.31 |
Dual form | 384.7.l.b.223.18 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 11.0227 | + | 11.0227i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −45.7781 | − | 45.7781i | −0.366225 | − | 0.366225i | 0.499873 | − | 0.866098i | \(-0.333380\pi\) |
−0.866098 | + | 0.499873i | \(0.833380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −565.544 | −1.64882 | −0.824408 | − | 0.565995i | \(-0.808492\pi\) | ||||
−0.824408 | + | 0.565995i | \(0.808492\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1291.95 | + | 1291.95i | −0.970658 | + | 0.970658i | −0.999582 | − | 0.0289233i | \(-0.990792\pi\) |
0.0289233 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2882.93 | − | 2882.93i | 1.31221 | − | 1.31221i | 0.392433 | − | 0.919781i | \(-0.371634\pi\) |
0.919781 | − | 0.392433i | \(-0.128366\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1009.20i | − | 0.299022i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −662.555 | −0.134858 | −0.0674288 | − | 0.997724i | \(-0.521480\pi\) | ||||
−0.0674288 | + | 0.997724i | \(0.521480\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1940.19 | − | 1940.19i | −0.282868 | − | 0.282868i | 0.551384 | − | 0.834252i | \(-0.314100\pi\) |
−0.834252 | + | 0.551384i | \(0.814100\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6233.83 | − | 6233.83i | −0.673127 | − | 0.673127i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15879.3 | −1.30511 | −0.652557 | − | 0.757740i | \(-0.726304\pi\) | ||||
−0.652557 | + | 0.757740i | \(0.726304\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 11433.7i | − | 0.731758i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2678.52 | + | 2678.52i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11555.8 | + | 11555.8i | −0.473810 | + | 0.473810i | −0.903145 | − | 0.429335i | \(-0.858748\pi\) |
0.429335 | + | 0.903145i | \(0.358748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 39097.9i | − | 1.31241i | −0.754585 | − | 0.656203i | \(-0.772162\pi\) | ||
0.754585 | − | 0.656203i | \(-0.227838\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −28481.5 | −0.792539 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25889.6 | + | 25889.6i | 0.603838 | + | 0.603838i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51336.5 | + | 51336.5i | 1.01349 | + | 1.01349i | 0.999908 | + | 0.0135861i | \(0.00432473\pi\) |
0.0135861 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 63555.4 | 1.07142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66520.0i | 0.965163i | 0.875851 | + | 0.482582i | \(0.160301\pi\) | ||||
−0.875851 | + | 0.482582i | \(0.839699\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −68923.6 | + | 68923.6i | −0.866887 | + | 0.866887i | −0.992127 | − | 0.125239i | \(-0.960030\pi\) |
0.125239 | + | 0.992127i | \(0.460030\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11124.1 | − | 11124.1i | 0.122075 | − | 0.122075i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 107734.i | − | 1.03767i | −0.854873 | − | 0.518837i | \(-0.826365\pi\) | ||
0.854873 | − | 0.518837i | \(-0.173635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 202191. | 1.71860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7303.15 | − | 7303.15i | −0.0550554 | − | 0.0550554i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 108477. | + | 108477.i | 0.728637 | + | 0.728637i | 0.970348 | − | 0.241711i | \(-0.0777086\pi\) |
−0.241711 | + | 0.970348i | \(0.577709\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 118286. | 0.710959 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 42772.3i | − | 0.230961i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 67889.1 | − | 67889.1i | 0.330555 | − | 0.330555i | −0.522242 | − | 0.852797i | \(-0.674904\pi\) |
0.852797 | + | 0.522242i | \(0.174904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 99209.6 | − | 99209.6i | 0.437083 | − | 0.437083i | −0.453946 | − | 0.891029i | \(-0.649984\pi\) |
0.891029 | + | 0.453946i | \(0.149984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 137427.i | − | 0.549606i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −263951. | −0.961131 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 105403. | + | 105403.i | 0.350451 | + | 0.350451i | 0.860277 | − | 0.509826i | \(-0.170290\pi\) |
−0.509826 | + | 0.860277i | \(0.670290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −175033. | − | 175033.i | −0.532810 | − | 0.532810i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 266114. | 0.743520 | 0.371760 | − | 0.928329i | \(-0.378754\pi\) | ||||
0.371760 | + | 0.928329i | \(0.378754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 267965.i | 0.688826i | 0.938818 | + | 0.344413i | \(0.111922\pi\) | ||||
−0.938818 | + | 0.344413i | \(0.888078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 126031. | − | 126031.i | 0.298739 | − | 0.298739i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 730653. | − | 730653.i | 1.60044 | − | 1.60044i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 557984.i | 1.13172i | 0.824500 | + | 0.565862i | \(0.191456\pi\) | ||||
−0.824500 | + | 0.565862i | \(0.808544\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59049.0 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 236224. | + | 236224.i | 0.413133 | + | 0.413133i | 0.882829 | − | 0.469695i | \(-0.155636\pi\) |
−0.469695 | + | 0.882829i | \(0.655636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 30330.5 | + | 30330.5i | 0.0493882 | + | 0.0493882i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −254751. | −0.386864 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 419786.i | 0.595467i | 0.954649 | + | 0.297733i | \(0.0962307\pi\) | ||||
−0.954649 | + | 0.297733i | \(0.903769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.63043e6 | + | 1.63043e6i | −2.16360 | + | 2.16360i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 430964. | − | 430964.i | 0.535787 | − | 0.535787i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 177637.i | 0.207187i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 393308. | 0.430940 | 0.215470 | − | 0.976510i | \(-0.430872\pi\) | ||||
0.215470 | + | 0.976510i | \(0.430872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −313943. | − | 313943.i | −0.323553 | − | 0.323553i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −670944. | − | 670944.i | −0.651212 | − | 0.651212i | 0.302073 | − | 0.953285i | \(-0.402321\pi\) |
−0.953285 | + | 0.302073i | \(0.902321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 456775. | 0.418013 | 0.209007 | − | 0.977914i | \(-0.432977\pi\) | ||||
0.209007 | + | 0.977914i | \(0.432977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 570746.i | 0.493032i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 498780. | − | 498780.i | 0.407153 | − | 0.407153i | −0.473592 | − | 0.880745i | \(-0.657043\pi\) |
0.880745 | + | 0.473592i | \(0.157043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 686021. | − | 686021.i | 0.529734 | − | 0.529734i | −0.390759 | − | 0.920493i | \(-0.627787\pi\) |
0.920493 | + | 0.390759i | \(0.127787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.13173e6i | 0.827514i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.76590e6 | 1.22386 | 0.611930 | − | 0.790912i | \(-0.290394\pi\) | ||||
0.611930 | + | 0.790912i | \(0.290394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 726926. | + | 726926.i | 0.477965 | + | 0.477965i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 700553. | + | 700553.i | 0.437404 | + | 0.437404i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 374704. | 0.222355 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.56669e6i | − | 0.884355i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −733230. | + | 733230.i | −0.394026 | + | 0.394026i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.23870e6 | + | 1.23870e6i | −0.634213 | + | 0.634213i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.52519e6i | − | 1.23277i | −0.787445 | − | 0.616385i | \(-0.788596\pi\) | ||
0.787445 | − | 0.616385i | \(-0.211404\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.51945e6 | −0.707810 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.20532e6 | + | 2.20532e6i | 0.980976 | + | 0.980976i | 0.999822 | − | 0.0188466i | \(-0.00599941\pi\) |
−0.0188466 | + | 0.999822i | \(0.505999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.09726e6 | + | 1.09726e6i | 0.466398 | + | 0.466398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 245235. | 0.0996738 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 210985.i | − | 0.0820520i | −0.999158 | − | 0.0410260i | \(-0.986937\pi\) | ||
0.999158 | − | 0.0410260i | \(-0.0130626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 678952. | − | 678952.i | 0.252810 | − | 0.252810i | −0.569312 | − | 0.822122i | \(-0.692790\pi\) |
0.822122 | + | 0.569312i | \(0.192790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.18752e6 | − | 1.18752e6i | 0.423629 | − | 0.423629i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.44919e6i | 2.54742i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05800e6 | 0.347042 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.22869e6 | + | 2.22869e6i | 0.701614 | + | 0.701614i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.62816e6 | + | 2.62816e6i | 0.794497 | + | 0.794497i | 0.982222 | − | 0.187724i | \(-0.0601111\pi\) |
−0.187724 | + | 0.982222i | \(0.560111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.88045e6 | 0.836622 | 0.418311 | − | 0.908304i | \(-0.362622\pi\) | ||||
0.418311 | + | 0.908304i | \(0.362622\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 161001.i | − | 0.0449525i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.78983e6 | + | 1.78983e6i | −0.480636 | + | 0.480636i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 501498. | − | 501498.i | 0.129590 | − | 0.129590i | −0.639337 | − | 0.768927i | \(-0.720791\pi\) |
0.768927 | + | 0.639337i | \(0.220791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.39143e6i | 0.594930i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.98046e6 | 2.15189 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.30009e6 | − | 1.30009e6i | −0.300199 | − | 0.300199i | 0.540893 | − | 0.841092i | \(-0.318087\pi\) |
−0.841092 | + | 0.540893i | \(0.818087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.30383e6 | + | 1.30383e6i | 0.290248 | + | 0.290248i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.60262e6 | −1.84706 | −0.923531 | − | 0.383524i | \(-0.874710\pi\) | ||||
−0.923531 | + | 0.383524i | \(0.874710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.17958e7i | − | 2.44381i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 471467. | − | 471467.i | 0.0942894 | − | 0.0942894i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 891920. | − | 891920.i | 0.172261 | − | 0.172261i | −0.615711 | − | 0.787972i | \(-0.711131\pi\) |
0.787972 | + | 0.615711i | \(0.211131\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.46628e6i | 1.20654i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.49664e6 | 0.269897 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.89580e6 | + | 2.89580e6i | 0.504904 | + | 0.504904i | 0.912958 | − | 0.408054i | \(-0.133792\pi\) |
−0.408054 | + | 0.912958i | \(0.633792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.14643e6 | − | 2.14643e6i | −0.361977 | − | 0.361977i | 0.502563 | − | 0.864541i | \(-0.332390\pi\) |
−0.864541 | + | 0.502563i | \(0.832390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.18712e6 | 0.356877 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.70018e6i | − | 0.742334i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 855986. | − | 855986.i | 0.130901 | − | 0.130901i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.51482e6 | − | 1.51482e6i | 0.224376 | − | 0.224376i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.12449e6i | − | 0.161382i | −0.996739 | − | 0.0806912i | \(-0.974287\pi\) | ||
0.996739 | − | 0.0806912i | \(-0.0257128\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.65489e6 | 0.925697 | 0.462848 | − | 0.886437i | \(-0.346827\pi\) | ||||
0.462848 | + | 0.886437i | \(0.346827\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.90945e6 | − | 2.90945e6i | −0.392380 | − | 0.392380i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.01919e6 | − | 1.01919e6i | −0.133307 | − | 0.133307i | 0.637305 | − | 0.770612i | \(-0.280049\pi\) |
−0.770612 | + | 0.637305i | \(0.780049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 889727. | 0.112901 | 0.0564505 | − | 0.998405i | \(-0.482022\pi\) | ||||
0.0564505 | + | 0.998405i | \(0.482022\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.32365e6i | 0.286142i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.53529e6 | − | 6.53529e6i | 0.781226 | − | 0.781226i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.04516e6 | − | 3.04516e6i | 0.353467 | − | 0.353467i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.85867e6i | − | 0.435038i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.01325e6 | 0.549137 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.10371e6 | + | 6.10371e6i | 0.649750 | + | 0.649750i | 0.952933 | − | 0.303182i | \(-0.0980491\pi\) |
−0.303182 | + | 0.952933i | \(0.598049\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.93330e6 | + | 2.93330e6i | 0.303541 | + | 0.303541i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.31039e6 | 0.634952 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.21116e7i | 2.16392i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.95370e6 | + | 2.95370e6i | −0.281212 | + | 0.281212i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.91010e6 | + | 1.91010e6i | −0.176962 | + | 0.176962i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.07405e6i | 0.728077i | 0.931384 | + | 0.364038i | \(0.118602\pi\) | ||||
−0.931384 | + | 0.364038i | \(0.881398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.77840e6 | 0.243919 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.13774e6 | + | 4.13774e6i | 0.353741 | + | 0.353741i | 0.861500 | − | 0.507758i | \(-0.169526\pi\) |
−0.507758 | + | 0.861500i | \(0.669526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.19667e7 | + | 1.19667e7i | 0.996480 | + | 0.996480i | 0.999994 | − | 0.00351356i | \(-0.00111840\pi\) |
−0.00351356 | + | 0.999994i | \(0.501118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.61075e7 | 1.30675 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.46761e6i | 0.116023i | 0.998316 | + | 0.0580114i | \(0.0184760\pi\) | ||||
−0.998316 | + | 0.0580114i | \(0.981524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.93188e6 | + | 4.93188e6i | −0.380022 | + | 0.380022i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.15049e6 | + | 6.15049e6i | −0.462024 | + | 0.462024i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.28489e7i | 0.941177i | 0.882353 | + | 0.470588i | \(0.155958\pi\) | ||||
−0.882353 | + | 0.470588i | \(0.844042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.87104e6 | −0.133670 | −0.0668348 | − | 0.997764i | \(-0.521290\pi\) | ||||
−0.0668348 | + | 0.997764i | \(0.521290\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −650880. | − | 650880.i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.25593e6 | − | 9.25593e6i | −0.629393 | − | 0.629393i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.11869e7 | −0.742367 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.20766e6i | 0.337322i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.06552e7 | − | 2.06552e7i | 1.30619 | − | 1.30619i | 0.382052 | − | 0.924141i | \(-0.375218\pi\) |
0.924141 | − | 0.382052i | \(-0.124782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.05152e7 | − | 2.05152e7i | 1.26682 | − | 1.26682i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 668649.i | 0.0403253i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 960591. | 0.0565900 | 0.0282950 | − | 0.999600i | \(-0.490992\pi\) | ||||
0.0282950 | + | 0.999600i | \(0.490992\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.90331e7 | − | 2.90331e7i | −1.67107 | − | 1.67107i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.80805e6 | − | 2.80805e6i | −0.157937 | − | 0.157937i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.66308e7 | −1.46392 | −0.731960 | − | 0.681348i | \(-0.761394\pi\) | ||||
−0.731960 | + | 0.681348i | \(0.761394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.93178e6i | − | 0.533690i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.62717e6 | + | 4.62717e6i | −0.243098 | + | 0.243098i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00276e7 | + | 2.00276e7i | −1.02890 | + | 1.02890i | −0.0293254 | + | 0.999570i | \(0.509336\pi\) |
−0.999570 | + | 0.0293254i | \(0.990664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.33995e7i | − | 0.673256i | −0.941638 | − | 0.336628i | \(-0.890714\pi\) | ||
0.941638 | − | 0.336628i | \(-0.109286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.59434e7 | −1.76657 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.47718e7 | + | 1.47718e7i | 0.710287 | + | 0.710287i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.43027e6 | + | 1.43027e6i | 0.0672942 | + | 0.0672942i | 0.739953 | − | 0.672659i | \(-0.234848\pi\) |
−0.672659 | + | 0.739953i | \(0.734848\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.50078e6 | 0.437469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.75247e7i | − | 0.789825i | −0.918719 | − | 0.394912i | \(-0.870775\pi\) | ||
0.918719 | − | 0.394912i | \(-0.129225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.40129e7 | + | 2.40129e7i | −1.05946 | + | 1.05946i | −0.0613460 | + | 0.998117i | \(0.519539\pi\) |
−0.998117 | + | 0.0613460i | \(0.980461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.95804e6 | + | 1.95804e6i | −0.0845837 | + | 0.0845837i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 3.76200e7i | − | 1.59138i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.36986e7 | −0.981813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.33531e6 | + | 4.33531e6i | 0.175931 | + | 0.175931i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.49680e7 | − | 2.49680e7i | −0.992617 | − | 0.992617i | 0.00735615 | − | 0.999973i | \(-0.497658\pi\) |
−0.999973 | + | 0.00735615i | \(0.997658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.21568e6 | −0.242115 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.92100e6i | − | 0.264180i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.57790e7 | + | 4.57790e7i | −1.71259 | + | 1.71259i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.89793e7 | − | 3.89793e7i | 1.42934 | − | 1.42934i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.47912e7i | − | 0.531712i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.08326e6 | −0.320142 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.13583e6 | − | 3.13583e6i | −0.108377 | − | 0.108377i | 0.650839 | − | 0.759216i | \(-0.274417\pi\) |
−0.759216 | + | 0.650839i | \(0.774417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.03489e6 | + | 5.03489e6i | 0.170653 | + | 0.170653i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.82703e7 | 0.939830 | 0.469915 | − | 0.882712i | \(-0.344285\pi\) | ||||
0.469915 | + | 0.882712i | \(0.344285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.17098e6i | − | 0.136021i | −0.997685 | − | 0.0680104i | \(-0.978335\pi\) | ||
0.997685 | − | 0.0680104i | \(-0.0216651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.29116e6 | + | 6.29116e6i | −0.201279 | + | 0.201279i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.49603e7 | + | 3.49603e7i | −1.09748 | + | 1.09748i | −0.102779 | + | 0.994704i | \(0.532773\pi\) |
−0.994704 | + | 0.102779i | \(0.967227\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.98588e7i | − | 0.919815i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.09958e7 | 0.332439 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.28548e6 | + | 1.28548e6i | 0.0381469 | + | 0.0381469i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.29627e7 | − | 3.29627e7i | −0.960223 | − | 0.960223i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.51236e7 | 0.432526 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.09286e7i | 1.71093i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.32895e7 | − | 2.32895e7i | 0.642210 | − | 0.642210i | −0.308888 | − | 0.951098i | \(-0.599957\pi\) |
0.951098 | + | 0.308888i | \(0.0999569\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.24748e7 | + | 1.24748e7i | −0.337831 | + | 0.337831i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.65029e6i | − | 0.256688i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.28256e7 | −0.335110 | −0.167555 | − | 0.985863i | \(-0.553587\pi\) | ||||
−0.167555 | + | 0.985863i | \(0.553587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.94650e7 | + | 1.94650e7i | 0.499638 | + | 0.499638i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.05124e7 | + | 5.05124e7i | 1.27390 | + | 1.27390i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.78123e7 | −1.18483 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.60254e7i | 0.390257i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.91869e7 | − | 3.91869e7i | 0.937891 | − | 0.937891i | −0.0602903 | − | 0.998181i | \(-0.519203\pi\) |
0.998181 | + | 0.0602903i | \(0.0192026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.06672e7 | + | 4.06672e7i | −0.956682 | + | 0.956682i | −0.999100 | − | 0.0424175i | \(-0.986494\pi\) |
0.0424175 | + | 0.999100i | \(0.486494\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54440e7i | 0.357139i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.01960e7 | −0.686475 | −0.343237 | − | 0.939249i | \(-0.611524\pi\) | ||||
−0.343237 | + | 0.939249i | \(0.611524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.21822e7 | − | 1.21822e7i | −0.272296 | − | 0.272296i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.13025e6 | + | 4.13025e6i | 0.0907762 | + | 0.0907762i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.27234e7 | 1.35565 | 0.677823 | − | 0.735225i | \(-0.262924\pi\) | ||||
0.677823 | + | 0.735225i | \(0.262924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3.95172e7i | − | 0.839971i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.72691e7 | − | 1.72691e7i | 0.361036 | − | 0.361036i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.22669e7 | − | 1.22669e7i | 0.252265 | − | 0.252265i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.63574e7i | − | 1.54473i | −0.635179 | − | 0.772365i | \(-0.719073\pi\) | ||
0.635179 | − | 0.772365i | \(-0.280927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.61644e7 | −0.321721 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.13487e7 | − | 6.13487e7i | −1.20139 | − | 1.20139i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.70594e7 | − | 3.70594e7i | −0.714121 | − | 0.714121i | 0.253274 | − | 0.967395i | \(-0.418493\pi\) |
−0.967395 | + | 0.253274i | \(0.918493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.73076e7 | −0.517833 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.66289e7i | 1.24348i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.65182e7 | − | 4.65182e7i | 0.854487 | − | 0.854487i | −0.136195 | − | 0.990682i | \(-0.543487\pi\) |
0.990682 | + | 0.136195i | \(0.0434873\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.78344e7 | − | 2.78344e7i | 0.503276 | − | 0.503276i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.38162e7i | 0.245919i | 0.992412 | + | 0.122959i | \(0.0392385\pi\) | ||||
−0.992412 | + | 0.122959i | \(0.960762\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.68958e7 | −1.17224 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.67484e7 | − | 1.67484e7i | −0.288962 | − | 0.288962i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.29148e7 | − | 3.29148e7i | −0.559168 | − | 0.559168i | 0.369902 | − | 0.929071i | \(-0.379391\pi\) |
−0.929071 | + | 0.369902i | \(0.879391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.05209e7 | 0.176004 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.86172e7i | 0.800963i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.55435e7 | − | 2.55435e7i | 0.414465 | − | 0.414465i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.09263e6 | + | 9.09263e6i | −0.145318 | + | 0.145318i | −0.776023 | − | 0.630705i | \(-0.782766\pi\) |
0.630705 | + | 0.776023i | \(0.282766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.41896e7i | 0.380812i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.10274e7 | 0.791353 | 0.395677 | − | 0.918390i | \(-0.370510\pi\) | ||||
0.395677 | + | 0.918390i | \(0.370510\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12717e8 | − | 1.12717e8i | −1.72216 | − | 1.72216i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.70315e6 | + | 2.70315e6i | 0.0406917 | + | 0.0406917i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.32648e8 | −1.96751 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.06130e7i | − | 1.17824i | −0.808044 | − | 0.589122i | \(-0.799474\pi\) | ||
0.808044 | − | 0.589122i | \(-0.200526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.32562e6 | − | 2.32562e6i | 0.0334976 | − | 0.0334976i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.83943e7 | + | 3.83943e7i | −0.545025 | + | 0.545025i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.16278e7i | − | 0.302599i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.49678e7 | 0.206419 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.05454e7 | + | 8.05454e7i | 1.09496 | + | 1.09496i | 0.994990 | + | 0.0999711i | \(0.0318750\pi\) |
0.0999711 | + | 0.994990i | \(0.468125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.99109e7 | + | 1.99109e7i | 0.266837 | + | 0.266837i | 0.827824 | − | 0.560988i | \(-0.189578\pi\) |
−0.560988 | + | 0.827824i | \(0.689578\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.61795e7 | 0.345891 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.57548e6i | 0.0986832i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.61074e7 | + | 5.61074e7i | −0.720670 | + | 0.720670i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.21102e7 | + | 8.21102e7i | −1.03998 | + | 1.03998i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.56500e7i | 0.695078i | 0.937666 | + | 0.347539i | \(0.112982\pi\) | ||||
−0.937666 | + | 0.347539i | \(0.887018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.28922e8 | 1.58804 | 0.794022 | − | 0.607889i | \(-0.207984\pi\) | ||||
0.794022 | + | 0.607889i | \(0.207984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.16620e7 | + | 1.16620e7i | 0.141679 | + | 0.141679i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.08089e7 | + | 3.08089e7i | 0.369175 | + | 0.369175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.16571e8 | −1.37784 | −0.688918 | − | 0.724839i | \(-0.741914\pi\) | ||||
−0.688918 | + | 0.724839i | \(0.741914\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.91325e7i | 0.572865i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.56146e7 | − | 8.56146e7i | 0.984775 | − | 0.984775i | −0.0151112 | − | 0.999886i | \(-0.504810\pi\) |
0.999886 | + | 0.0151112i | \(0.00481022\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.92170e7 | − | 1.92170e7i | 0.218075 | − | 0.218075i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.79388e7i | 0.648704i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.62296e8 | −1.79295 | −0.896474 | − | 0.443096i | \(-0.853880\pi\) | ||||
−0.896474 | + | 0.443096i | \(0.853880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.59403e7 | − | 8.59403e7i | −0.936844 | − | 0.936844i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.17503e7 | + | 3.17503e7i | 0.341550 | + | 0.341550i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.49276e8 | 1.58473 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.31224e8i | − | 1.37488i | −0.726241 | − | 0.687440i | \(-0.758734\pi\) | ||
0.726241 | − | 0.687440i | \(-0.241266\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.77467e6 | − | 1.77467e6i | 0.0183518 | − | 0.0183518i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.76397e7 | + | 3.76397e7i | −0.384188 | + | 0.384188i | −0.872608 | − | 0.488421i | \(-0.837573\pi\) |
0.488421 | + | 0.872608i | \(0.337573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.50458e6i | − | 0.0554602i | −0.999615 | − | 0.0277301i | \(-0.991172\pi\) | ||
0.999615 | − | 0.0277301i | \(-0.00882789\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.94575e7 | −0.392438 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.63536e6 | + | 9.63536e6i | 0.0946057 | + | 0.0946057i | 0.752826 | − | 0.658220i | \(-0.228690\pi\) |
−0.658220 | + | 0.752826i | \(0.728690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.96099e7 | − | 5.96099e7i | −0.577830 | − | 0.577830i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.10557e7 | 0.105809 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.78091e8i | − | 1.68290i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.21836e7 | + | 2.21836e7i | −0.206991 | + | 0.206991i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.63600e7 | + | 2.63600e7i | −0.242879 | + | 0.242879i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.68794e6i | 0.0335566i | 0.999859 | + | 0.0167783i | \(0.00534095\pi\) | ||||
−0.999859 | + | 0.0167783i | \(0.994659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.95999e8 | 2.65984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.89889e7 | + | 9.89889e7i | 0.878507 | + | 0.878507i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.80049e7 | − | 1.80049e7i | −0.157821 | − | 0.157821i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.06471e7 | −0.525077 | −0.262539 | − | 0.964921i | \(-0.584560\pi\) | ||||
−0.262539 | + | 0.964921i | \(0.584560\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.86609e7i | − | 0.245112i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.63117e7 | + | 2.63117e7i | −0.222282 | + | 0.222282i | −0.809459 | − | 0.587177i | \(-0.800239\pi\) |
0.587177 | + | 0.809459i | \(0.300239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.65633e6 | − | 7.65633e6i | 0.0638969 | − | 0.0638969i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.87434e7i | 0.236986i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.50499e8 | −1.22593 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.17267e8 | + | 1.17267e8i | 0.943788 | + | 0.943788i | 0.998502 | − | 0.0547144i | \(-0.0174248\pi\) |
−0.0547144 | + | 0.998502i | \(0.517425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.48241e7 | − | 9.48241e7i | −0.754060 | − | 0.754060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.84245e7 | 0.694814 | 0.347407 | − | 0.937714i | \(-0.387062\pi\) | ||||
0.347407 | + | 0.937714i | \(0.387062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.14291e7i | 0.476980i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.30022e8 | − | 1.30022e8i | 0.997681 | − | 0.997681i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.88133e7 | − | 9.88133e7i | 0.749311 | − | 0.749311i | −0.225039 | − | 0.974350i | \(-0.572251\pi\) |
0.974350 | + | 0.225039i | \(0.0722509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.51546e8i | − | 1.13575i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.03937e7 | 0.0769870 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.09103e7 | − | 2.09103e7i | −0.153087 | − | 0.153087i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.39187e8 | + | 1.39187e8i | 1.00723 | + | 1.00723i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.96627e7 | 0.140651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.96978e8i | 1.39285i | 0.717629 | + | 0.696425i | \(0.245227\pi\) | ||||
−0.717629 | + | 0.696425i | \(0.754773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.96274e7 | + | 7.96274e7i | −0.556618 | + | 0.556618i | −0.928343 | − | 0.371725i | \(-0.878767\pi\) |
0.371725 | + | 0.928343i | \(0.378767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.12758e7 | + | 7.12758e7i | −0.492566 | + | 0.492566i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.59045e7i | 0.176988i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.04117e8 | 0.703322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.64971e7 | + | 1.64971e7i | 0.110185 | + | 0.110185i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.91773e8 | + | 1.91773e8i | 1.26650 | + | 1.26650i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.56664e7 | −0.298219 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.38390e7i | 0.412252i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.61220e8 | + | 2.61220e8i | −1.66817 | + | 1.66817i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.92069e8 | − | 1.92069e8i | 1.21302 | − | 1.21302i | 0.242986 | − | 0.970030i | \(-0.421873\pi\) |
0.970030 | − | 0.242986i | \(-0.0781268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 4.73190e7i | − | 0.295553i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.28095e7 | −0.388004 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.48181e7 | + | 7.48181e7i | 0.457135 | + | 0.457135i | 0.897714 | − | 0.440579i | \(-0.145227\pi\) |
−0.440579 | + | 0.897714i | \(0.645227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.41079e7 | + | 2.41079e7i | 0.145694 | + | 0.145694i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.48408e7 | 0.268052 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.15564e8i | − | 1.86600i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.18087e7 | − | 5.18087e7i | 0.303056 | − | 0.303056i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.38814e8 | − | 1.38814e8i | 0.803281 | − | 0.803281i | −0.180326 | − | 0.983607i | \(-0.557715\pi\) |
0.983607 | + | 0.180326i | \(0.0577152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.97404e8i | 2.27508i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.88706e7 | 0.106880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.37839e8 | + | 1.37839e8i | 0.772411 | + | 0.772411i | 0.978527 | − | 0.206117i | \(-0.0660827\pi\) |
−0.206117 | + | 0.978527i | \(0.566083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.08397e7 | − | 8.08397e7i | −0.448208 | − | 0.448208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.33948e7 | 0.183202 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.94110e8i | 1.05368i | 0.849963 | + | 0.526842i | \(0.176624\pi\) | ||||
−0.849963 | + | 0.526842i | \(0.823376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.50758e7 | + | 5.50758e7i | −0.295837 | + | 0.295837i | −0.839381 | − | 0.543544i | \(-0.817082\pi\) |
0.543544 | + | 0.839381i | \(0.317082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.23949e7 | − | 1.23949e7i | 0.0658841 | − | 0.0658841i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.81560e8i | 0.955028i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.62355e8 | −0.845158 | −0.422579 | − | 0.906326i | \(-0.638875\pi\) | ||||
−0.422579 | + | 0.906326i | \(0.638875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.33548e7 | + | 7.33548e7i | 0.377914 | + | 0.377914i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.33595e8 | − | 1.33595e8i | −0.681181 | − | 0.681181i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.80294e8 | −1.41452 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 6.41400e7i | − | 0.320377i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.11238e8 | + | 1.11238e8i | −0.549968 | + | 0.549968i | −0.926431 | − | 0.376464i | \(-0.877140\pi\) |
0.376464 | + | 0.926431i | \(0.377140\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.58574e7 | + | 7.58574e7i | −0.371238 | + | 0.371238i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.24683e7i | − | 0.108845i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.77045e8 | 1.80813 | 0.904064 | − | 0.427397i | \(-0.140569\pi\) | ||||
0.904064 | + | 0.427397i | \(0.140569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.71533e7 | − | 1.71533e7i | −0.0814321 | − | 0.0814321i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.80720e6 | + | 9.80720e6i | 0.0460916 | + | 0.0460916i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.55681e8 | 1.65493 | 0.827465 | − | 0.561517i | \(-0.189782\pi\) | ||||
0.827465 | + | 0.561517i | \(0.189782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.48769e8i | 0.685313i | 0.939461 | + | 0.342656i | \(0.111327\pi\) | ||||
−0.939461 | + | 0.342656i | \(0.888673\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.56129e7 | + | 2.56129e7i | −0.116817 | + | 0.116817i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.17201e7 | + | 7.17201e7i | −0.323873 | + | 0.323873i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.97217e7i | 0.132894i | 0.997790 | + | 0.0664472i | \(0.0211664\pi\) | ||||
−0.997790 | + | 0.0664472i | \(0.978834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.44073e8 | 0.637868 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.10591e8 | − | 3.10591e8i | −1.36165 | − | 1.36165i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.04355e8 | − | 1.04355e8i | −0.453034 | − | 0.453034i | 0.443326 | − | 0.896360i | \(-0.353798\pi\) |
−0.896360 | + | 0.443326i | \(0.853798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.71318e7 | 0.288605 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.67053e8i | − | 0.711213i | −0.934636 | − | 0.355606i | \(-0.884274\pi\) | ||
0.934636 | − | 0.355606i | \(-0.115726\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.33498e7 | − | 3.33498e7i | 0.140612 | − | 0.140612i | −0.633297 | − | 0.773909i | \(-0.718299\pi\) |
0.773909 | + | 0.633297i | \(0.218299\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.25330e7 | − | 4.25330e7i | 0.177603 | − | 0.177603i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.37407e8i | − | 0.981816i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.52414e7 | −0.267229 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.52596e7 | + | 5.52596e7i | 0.224184 | + | 0.224184i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.40133e7 | − | 3.40133e7i | −0.136677 | − | 0.136677i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.26476e8 | 0.503408 | 0.251704 | − | 0.967804i | \(-0.419009\pi\) | ||||
0.251704 | + | 0.967804i | \(0.419009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.34559e8i | 0.530519i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.15598e8 | + | 1.15598e8i | −0.451471 | + | 0.451471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.82904e8 | − | 5.82904e8i | 2.25517 | − | 2.25517i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.46657e7i | 0.247840i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.79771e8 | −1.44194 | −0.720971 | − | 0.692965i | \(-0.756304\pi\) | ||||
−0.720971 | + | 0.692965i | \(0.756304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.19573e8 | − | 2.19573e8i | −0.825937 | − | 0.825937i | 0.161015 | − | 0.986952i | \(-0.448523\pi\) |
−0.986952 | + | 0.161015i | \(0.948523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.95575e7 | + | 6.95575e7i | 0.259218 | + | 0.259218i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.63625e8 | 0.604139 | 0.302069 | − | 0.953286i | \(-0.402323\pi\) | ||||
0.302069 | + | 0.953286i | \(0.402323\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75418e8i | 0.641713i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.43729e8 | + | 2.43729e8i | −0.883415 | + | 0.883415i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.17072e8 | − | 2.17072e8i | 0.779587 | − | 0.779587i | −0.200173 | − | 0.979761i | \(-0.564151\pi\) |
0.979761 | + | 0.200173i | \(0.0641505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.01911e8i | − | 0.718516i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.51155e7 | −0.229609 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.75232e8 | + | 3.75232e8i | 1.31112 | + | 1.31112i | 0.920588 | + | 0.390535i | \(0.127710\pi\) |
0.390535 | + | 0.920588i | \(0.372290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.25679e7 | + | 9.25679e7i | 0.320521 | + | 0.320521i | 0.848967 | − | 0.528446i | \(-0.177225\pi\) |
−0.528446 | + | 0.848967i | \(0.677225\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.21090e7 | −0.144489 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.00461e8i | − | 0.341613i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.83498e8 | − | 1.83498e8i | 0.618376 | − | 0.618376i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.89979e7 | + | 8.89979e7i | −0.297236 | + | 0.297236i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.56347e8i | 0.848517i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.35988e8 | 1.75837 | 0.879185 | − | 0.476481i | \(-0.158088\pi\) | ||||
0.879185 | + | 0.476481i | \(0.158088\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.06254e7 | + | 3.06254e7i | 0.0995797 | + | 0.0995797i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.17164e8 | + | 3.17164e8i | 1.02216 | + | 1.02216i | 0.999749 | + | 0.0224072i | \(0.00713303\pi\) |
0.0224072 | + | 0.999749i | \(0.492867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.22433e8 | −0.710542 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.12182e7i | 0.288829i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.38997e8 | − | 2.38997e8i | 0.750121 | − | 0.750121i | −0.224381 | − | 0.974502i | \(-0.572036\pi\) |
0.974502 | + | 0.224381i | \(0.0720359\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.65848e6 | + | 9.65848e6i | −0.0300495 | + | 0.0300495i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.63811e8i | 0.813623i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.25466e8 | 1.91226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.14977e8 | + | 1.14977e8i | 0.348478 | + | 0.348478i | 0.859542 | − | 0.511065i | \(-0.170749\pi\) |
−0.511065 | + | 0.859542i | \(0.670749\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.77549e8 | + | 1.77549e8i | 0.533479 | + | 0.533479i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.21623e7 | −0.185171 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.40732e7i | − | 0.130160i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.61770e7 | + | 1.61770e7i | −0.0473661 | + | 0.0473661i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.52614e8 | + | 1.52614e8i | −0.443036 | + | 0.443036i | −0.893031 | − | 0.449995i | \(-0.851426\pi\) |
0.449995 | + | 0.893031i | \(0.351426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.99205e8i | − | 0.573370i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.08725e8 | −0.310287 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.79448e8 | + | 3.79448e8i | 1.07373 | + | 1.07373i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.20534e8 | − | 2.20534e8i | −0.618780 | − | 0.618780i | 0.326439 | − | 0.945218i | \(-0.394151\pi\) |
−0.945218 | + | 0.326439i | \(0.894151\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.35590e8 | −0.377241 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.20848e8i | 1.71284i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.41010e8 | − | 3.41010e8i | 0.932930 | − | 0.932930i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.41629e8 | + | 1.41629e8i | −0.384234 | + | 0.384234i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.10928e8i | 0.298439i | 0.988804 | + | 0.149220i | \(0.0476762\pi\) | ||||
−0.988804 | + | 0.149220i | \(0.952324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.58326e8 | −0.689228 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.06240e7 | − | 2.06240e7i | −0.0545704 | − | 0.0545704i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.32125e8 | + | 1.32125e8i | 0.346714 | + | 0.346714i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.40388e8 | 1.14613 | 0.573063 | − | 0.819512i | \(-0.305755\pi\) | ||||
0.573063 | + | 0.819512i | \(0.305755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.43489e7i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.56657e7 | − | 4.56657e7i | 0.116906 | − | 0.116906i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.77336e7 | + | 8.77336e7i | −0.222769 | + | 0.222769i | −0.809663 | − | 0.586895i | \(-0.800350\pi\) |
0.586895 | + | 0.809663i | \(0.300350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 2.04051e8i | − | 0.513897i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.72349e8 | −0.680337 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.75595e8 | − | 1.75595e8i | −0.435089 | − | 0.435089i | 0.455266 | − | 0.890355i | \(-0.349544\pi\) |
−0.890355 | + | 0.455266i | \(0.849544\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23310e8 | − | 1.23310e8i | −0.303070 | − | 0.303070i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.99950e8 | 0.487478 | 0.243739 | − | 0.969841i | \(-0.421626\pi\) | ||||
0.243739 | + | 0.969841i | \(0.421626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.40624e8i | − | 0.581930i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.74025e7 | + | 5.74025e7i | −0.137711 | + | 0.137711i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.82082e8 | + | 2.82082e8i | −0.671320 | + | 0.671320i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.31676e7i | − | 0.101915i | −0.998701 | − | 0.0509575i | \(-0.983773\pi\) | ||
0.998701 | − | 0.0509575i | \(-0.0162273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.55351e8 | 1.06650 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.31862e8 | − | 1.31862e8i | −0.306392 | − | 0.306392i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.04827e8 | + | 3.04827e8i | 0.702692 | + | 0.702692i | 0.964988 | − | 0.262295i | \(-0.0844794\pi\) |
−0.262295 | + | 0.964988i | \(0.584479\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.52267e8 | 1.03435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.91137e8i | − | 1.11442i | −0.830372 | − | 0.557209i | \(-0.811872\pi\) | ||
0.830372 | − | 0.557209i | \(-0.188128\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.87975e8 | + | 3.87975e8i | −0.873434 | + | 0.873434i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.37032e6 | + | 7.37032e6i | −0.0164627 | + | 0.0164627i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.91440e8i | − | 0.867519i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.18352e8 | −1.57964 | −0.789820 | − | 0.613338i | \(-0.789826\pi\) | ||||
−0.789820 | + | 0.613338i | \(0.789826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.05883e7 | + | 1.05883e7i | 0.0231028 | + | 0.0231028i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.46865e8 | − | 4.46865e8i | −0.967471 | − | 0.967471i | 0.0320160 | − | 0.999487i | \(-0.489807\pi\) |
−0.999487 | + | 0.0320160i | \(0.989807\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.47034e8 | −0.960364 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.40046e8i | − | 1.36442i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.29062e8 | − | 1.29062e8i | 0.273014 | − | 0.273014i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.43805e8 | + | 3.43805e8i | −0.721704 | + | 0.721704i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.19046e7i | − | 0.128955i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.59153e7 | −0.0949179 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27217e8 | − | 1.27217e8i | −0.260989 | − | 0.260989i | 0.564467 | − | 0.825456i | \(-0.309082\pi\) |
−0.825456 | + | 0.564467i | \(0.809082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.93544e8 | − | 2.93544e8i | −0.597643 | − | 0.597643i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.98696e8 | −2.01792 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.72029e8i | − | 1.14709i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.09475e8 | − | 1.09475e8i | 0.217878 | − | 0.217878i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.09748e7 | + | 5.09748e7i | −0.100689 | + | 0.100689i | −0.755657 | − | 0.654968i | \(-0.772682\pi\) |
0.654968 | + | 0.755657i | \(0.272682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.13800e7i | 0.139938i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.02008e8 | −0.198489 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.46196e8 | − | 3.46196e8i | −0.668615 | − | 0.668615i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.11109e8 | − | 4.11109e8i | −0.788077 | − | 0.788077i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.41516e8 | −0.840090 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.47571e8i | − | 1.78964i | −0.446424 | − | 0.894822i | \(-0.647303\pi\) | ||
0.446424 | − | 0.894822i | \(-0.352697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.22998e7 | + | 9.22998e7i | −0.173037 | + | 0.173037i | −0.788312 | − | 0.615275i | \(-0.789045\pi\) |
0.615275 | + | 0.788312i | \(0.289045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.47699e8 | − | 1.47699e8i | 0.274856 | − | 0.274856i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.19031e8i | 0.219881i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.67450e8 | 0.490429 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.96193e8 | − | 3.96193e8i | −0.721200 | − | 0.721200i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.05480e8 | + | 5.05480e8i | 0.913429 | + | 0.913429i | 0.996540 | − | 0.0831113i | \(-0.0264857\pi\) |
−0.0831113 | + | 0.996540i | \(0.526486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.69057e7 | −0.0662055 | −0.0331027 | − | 0.999452i | \(-0.510539\pi\) | ||||
−0.0331027 | + | 0.999452i | \(0.510539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.25649e8i | 0.579947i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.45689e8 | − | 1.45689e8i | 0.257579 | − | 0.257579i | −0.566490 | − | 0.824069i | \(-0.691699\pi\) |
0.824069 | + | 0.566490i | \(0.191699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.21154e8 | + | 6.21154e8i | −1.09027 | + | 1.09027i | −0.0947757 | + | 0.995499i | \(0.530213\pi\) |
−0.995499 | + | 0.0947757i | \(0.969787\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.15308e7i | 0.0549455i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.33963e8 | −0.231766 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.93812e8 | + | 3.93812e8i | 0.676440 | + | 0.676440i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.04724e8 | + | 1.04724e8i | 0.178596 | + | 0.178596i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.28215e8 | −1.23303 | −0.616515 | − | 0.787343i | \(-0.711456\pi\) | ||||
−0.616515 | + | 0.787343i | \(0.711456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.27752e8i | 0.551008i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.93169e8 | − | 1.93169e8i | 0.322445 | − | 0.322445i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.39990e8 | + | 5.39990e8i | −0.894984 | + | 0.894984i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.86032e8i | 1.45814i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.29375e8 | −0.865048 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.15189e8 | − | 8.15189e8i | −1.32272 | − | 1.32272i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.95707e8 | + | 3.95707e8i | 0.637568 | + | 0.637568i | 0.949955 | − | 0.312387i | \(-0.101128\pi\) |
−0.312387 | + | 0.949955i | \(0.601128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.31657e7 | −0.0690623 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.60780e8i | 1.20870i | 0.796721 | + | 0.604348i | \(0.206566\pi\) | ||||
−0.796721 | + | 0.604348i | \(0.793434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.52493e8 | + | 2.52493e8i | −0.398354 | + | 0.398354i | −0.877652 | − | 0.479298i | \(-0.840891\pi\) |
0.479298 | + | 0.877652i | \(0.340891\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.14674e8 | − | 4.14674e8i | 0.649677 | − | 0.649677i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.25728e7i | 0.112912i | 0.998405 | + | 0.0564562i | \(0.0179801\pi\) | ||||
−0.998405 | + | 0.0564562i | \(0.982020\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.16609e7 | −0.126173 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.61223e8 | − | 2.61223e8i | −0.400824 | − | 0.400824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.20885e8 | − | 7.20885e8i | −1.09852 | − | 1.09852i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.07738e8 | 0.919734 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.55738e7i | 0.143647i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.00538e8 | − | 7.00538e8i | 1.04570 | − | 1.04570i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.64497e8 | + | 5.64497e8i | −0.836879 | + | 0.836879i | −0.988447 | − | 0.151568i | \(-0.951568\pi\) |
0.151568 | + | 0.988447i | \(0.451568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 5.50431e8i | − | 0.810468i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.73736e7 | 0.142401 | 0.0712006 | − | 0.997462i | \(-0.477317\pi\) | ||||
0.0712006 | + | 0.997462i | \(0.477317\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.90645e7 | + | 6.90645e7i | 0.100317 | + | 0.100317i | 0.755484 | − | 0.655167i | \(-0.227402\pi\) |
−0.655167 | + | 0.755484i | \(0.727402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.85136e7 | − | 6.85136e7i | −0.0988432 | − | 0.0988432i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.66487e8 | −0.668450 | −0.334225 | − | 0.942493i | \(-0.608474\pi\) | ||||
−0.334225 | + | 0.942493i | \(0.608474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.42810e9i | 2.03261i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.62881e7 | − | 7.62881e7i | 0.107851 | − | 0.107851i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.09026e8 | + | 2.09026e8i | −0.293525 | + | 0.293525i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.65128e8i | − | 0.369817i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.00922e9 | −1.39832 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.51805e8 | + | 4.51805e8i | 0.621831 | + | 0.621831i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.18722e7 | − | 7.18722e7i | −0.0982623 | − | 0.0982623i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.59315e8 | 1.16705 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.96519e8i | 0.265130i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.99657e8 | − | 1.99657e8i | 0.267585 | − | 0.267585i | −0.560541 | − | 0.828126i | \(-0.689407\pi\) |
0.828126 | + | 0.560541i | \(0.189407\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.63039e8 | − | 1.63039e8i | 0.217071 | − | 0.217071i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.71797e8i | − | 1.02082i | −0.859932 | − | 0.510409i | \(-0.829494\pi\) | ||
0.859932 | − | 0.510409i | \(-0.170506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.10378e8 | −0.802022 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.00122e8 | − | 1.00122e8i | −0.130697 | − | 0.130697i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.24721e9 | − | 1.24721e9i | −1.61745 | − | 1.61745i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.94727e8 | 1.15277 | 0.576387 | − | 0.817177i | \(-0.304462\pi\) | ||||
0.576387 | + | 0.817177i | \(0.304462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.91307e7i | − | 0.0884896i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.67189e8 | − | 7.67189e8i | 0.975658 | − | 0.975658i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.86967e8 | − | 5.86967e8i | 0.741633 | − | 0.741633i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.10996e8i | 0.139338i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.16188e8 | 0.643814 | 0.321907 | − | 0.946771i | \(-0.395676\pi\) | ||||
0.321907 | + | 0.946771i | \(0.395676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.92290e8 | − | 3.92290e8i | −0.486136 | − | 0.486136i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.11615e8 | + | 3.11615e8i | 0.383684 | + | 0.383684i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.83709e7 | −0.0958782 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.89366e8i | 0.716418i | 0.933641 | + | 0.358209i | \(0.116612\pi\) | ||||
−0.933641 | + | 0.358209i | \(0.883388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.59755e7 | − | 4.59755e7i | 0.0555303 | − | 0.0555303i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.11063e7 | + | 4.11063e7i | −0.0493333 | + | 0.0493333i | −0.731343 | − | 0.682010i | \(-0.761106\pi\) |
0.682010 | + | 0.731343i | \(0.261106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.05629e9i | − | 1.25965i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.38691e8 | −0.164344 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.82225e8 | + | 1.82225e8i | 0.214565 | + | 0.214565i | 0.806203 | − | 0.591639i | \(-0.201519\pi\) |
−0.591639 | + | 0.806203i | \(0.701519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.72525e8 | + | 7.72525e8i | 0.903887 | + | 0.903887i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.70715e8 | −0.896091 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.41084e9i | 1.63004i | 0.579433 | + | 0.815020i | \(0.303274\pi\) | ||||
−0.579433 | + | 0.815020i | \(0.696726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.14771e7 | + | 5.14771e7i | −0.0591023 | + | 0.0591023i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.29125e8 | − | 3.29125e8i | 0.375513 | − | 0.375513i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.19321e8i | 0.135289i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.41141e8 | −0.722409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.21203e8 | + | 1.21203e8i | 0.135718 | + | 0.135718i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.04648e8 | − | 3.04648e8i | −0.339013 | − | 0.339013i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.62310e8 | 1.06423 | 0.532115 | − | 0.846672i | \(-0.321397\pi\) | ||||
0.532115 | + | 0.846672i | \(0.321397\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.83390e7i | 0.0311468i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.97286e8 | + | 8.97286e8i | −0.980106 | + | 0.980106i | −0.999806 | − | 0.0196995i | \(-0.993729\pi\) |
0.0196995 | + | 0.999806i | \(0.493729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.83977e8 | + | 3.83977e8i | −0.416838 | + | 0.416838i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 7.26675e8i | − | 0.784019i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.56733e8 | −0.168065 | −0.0840324 | − | 0.996463i | \(-0.526780\pi\) | ||||
−0.0840324 | + | 0.996463i | \(0.526780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.42341e8 | − | 5.42341e8i | −0.577995 | − | 0.577995i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.66703e8 | + | 1.66703e8i | 0.176578 | + | 0.176578i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.49727e7 | 0.0262909 | 0.0131454 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131454 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.33128e7i | 0.0976411i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.71598e8 | + | 6.71598e8i | −0.698486 | + | 0.698486i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.09446e9 | − | 1.09446e9i | 1.13139 | − | 1.13139i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.63587e8i | − | 0.476333i | −0.971224 | − | 0.238166i | \(-0.923454\pi\) | ||
0.971224 | − | 0.238166i | \(-0.0765463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.13428e8 | 0.524362 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.07300e7 | − | 4.07300e7i | −0.0413472 | − | 0.0413472i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.19997e7 | + | 9.19997e7i | 0.0928327 | + | 0.0928327i | 0.751998 | − | 0.659165i | \(-0.229090\pi\) |
−0.659165 | + | 0.751998i | \(0.729090\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.75011e8 | −0.275838 |
(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 | 384.7.l.b.31.18 | 48 | ||
4.3 | odd | 2 | 384.7.l.a.31.7 | 48 | |||
8.3 | odd | 2 | 192.7.l.a.79.18 | 48 | |||
8.5 | even | 2 | 48.7.l.a.43.18 | yes | 48 | ||
16.3 | odd | 4 | inner | 384.7.l.b.223.18 | 48 | ||
16.5 | even | 4 | 192.7.l.a.175.18 | 48 | |||
16.11 | odd | 4 | 48.7.l.a.19.18 | ✓ | 48 | ||
16.13 | even | 4 | 384.7.l.a.223.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.l.a.19.18 | ✓ | 48 | 16.11 | odd | 4 | ||
48.7.l.a.43.18 | yes | 48 | 8.5 | even | 2 | ||
192.7.l.a.79.18 | 48 | 8.3 | odd | 2 | |||
192.7.l.a.175.18 | 48 | 16.5 | even | 4 | |||
384.7.l.a.31.7 | 48 | 4.3 | odd | 2 | |||
384.7.l.a.223.7 | 48 | 16.13 | even | 4 | |||
384.7.l.b.31.18 | 48 | 1.1 | even | 1 | trivial | ||
384.7.l.b.223.18 | 48 | 16.3 | odd | 4 | inner |