Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 198x^{2} + 43x + 5999 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-12.2094\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 20.4188 | 1.30987 | 0.654933 | − | 0.755687i | \(-0.272697\pi\) | ||||
0.654933 | + | 0.755687i | \(0.272697\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.4943 | −0.384502 | −0.192251 | − | 0.981346i | \(-0.561579\pi\) | ||||
−0.192251 | + | 0.981346i | \(0.561579\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 173.928 | 0.715751 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −647.760 | −1.61411 | −0.807053 | − | 0.590479i | \(-0.798939\pi\) | ||||
−0.807053 | + | 0.590479i | \(0.798939\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 787.030 | 1.29162 | 0.645808 | − | 0.763500i | \(-0.276521\pi\) | ||||
0.645808 | + | 0.763500i | \(0.276521\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −438.888 | −0.503646 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1937.22 | −1.62576 | −0.812879 | − | 0.582432i | \(-0.802101\pi\) | ||||
−0.812879 | + | 0.582432i | \(0.802101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 964.776 | 0.613116 | 0.306558 | − | 0.951852i | \(-0.400823\pi\) | ||||
0.306558 | + | 0.951852i | \(0.400823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1000.52 | 0.495083 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1493.66 | 0.588751 | 0.294375 | − | 0.955690i | \(-0.404888\pi\) | ||||
0.294375 | + | 0.955690i | \(0.404888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2662.99 | −0.852158 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1410.38 | −0.372328 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7167.22 | −1.58254 | −0.791272 | − | 0.611464i | \(-0.790581\pi\) | ||||
−0.791272 | + | 0.611464i | \(0.790581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2225.21 | 0.415879 | 0.207940 | − | 0.978142i | \(-0.433324\pi\) | ||||
0.207940 | + | 0.978142i | \(0.433324\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13226.5 | −2.11426 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1053.22 | −0.145328 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2050.95 | 0.246292 | 0.123146 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123146 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16070.2 | 1.69184 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9009.74 | 0.837053 | 0.418526 | − | 0.908205i | \(-0.362547\pi\) | ||||
0.418526 | + | 0.908205i | \(0.362547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2603.57 | 0.214733 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3738.45 | −0.275208 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22200.2 | −1.46593 | −0.732965 | − | 0.680266i | \(-0.761864\pi\) | ||||
−0.732965 | + | 0.680266i | \(0.761864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −39555.7 | −2.12953 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −27740.0 | −1.35649 | −0.678246 | − | 0.734835i | \(-0.737260\pi\) | ||||
−0.678246 | + | 0.734835i | \(0.737260\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13923.1 | 0.620627 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19699.6 | 0.803100 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43836.3 | −1.63947 | −0.819736 | − | 0.572742i | \(-0.805880\pi\) | ||||
−0.819736 | + | 0.572742i | \(0.805880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31459.4 | −1.08249 | −0.541247 | − | 0.840863i | \(-0.682048\pi\) | ||||
−0.541247 | + | 0.840863i | \(0.682048\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8522.45 | 0.270529 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16916.7 | −0.496628 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5417.61 | 0.147442 | 0.0737210 | − | 0.997279i | \(-0.476513\pi\) | ||||
0.0737210 | + | 0.997279i | \(0.476513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 30498.7 | 0.771185 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48731.4 | 1.14726 | 0.573631 | − | 0.819114i | \(-0.305534\pi\) | ||||
0.573631 | + | 0.819114i | \(0.305534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7553.51 | −0.165898 | −0.0829491 | − | 0.996554i | \(-0.526434\pi\) | ||||
−0.0829491 | + | 0.996554i | \(0.526434\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −54375.2 | −1.11621 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −31740.2 | −0.610075 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 43361.7 | 0.781697 | 0.390849 | − | 0.920455i | \(-0.372182\pi\) | ||||
0.390849 | + | 0.920455i | \(0.372182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −71062.6 | −1.20345 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −71834.6 | −1.14456 | −0.572280 | − | 0.820059i | \(-0.693941\pi\) | ||||
−0.572280 | + | 0.820059i | \(0.693941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41639.1 | 0.625107 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −146346. | −2.07292 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1138.04 | 0.0152294 | 0.00761472 | − | 0.999971i | \(-0.497576\pi\) | ||||
0.00761472 | + | 0.999971i | \(0.497576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38564.5 | 0.488185 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 45436.2 | 0.544746 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20737.2 | −0.235744 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 135062. | 1.45749 | 0.728744 | − | 0.684786i | \(-0.240104\pi\) | ||||
0.728744 | + | 0.684786i | \(0.240104\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −112663. | −1.15530 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 20108.2 | 0.196142 | 0.0980709 | − | 0.995179i | \(-0.468733\pi\) | ||||
0.0980709 | + | 0.995179i | \(0.468733\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14829.7 | 0.137733 | 0.0688665 | − | 0.997626i | \(-0.478062\pi\) | ||||
0.0688665 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −21505.5 | −0.190360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −168416. | −1.42208 | −0.711041 | − | 0.703151i | \(-0.751776\pi\) | ||||
−0.711041 | + | 0.703151i | \(0.751776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 175717. | 1.41660 | 0.708299 | − | 0.705913i | \(-0.249463\pi\) | ||||
0.708299 | + | 0.705913i | \(0.249463\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 41877.9 | 0.322610 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −150362. | −1.10775 | −0.553875 | − | 0.832600i | \(-0.686852\pi\) | ||||
−0.553875 | + | 0.832600i | \(0.686852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32105.1 | −0.226376 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 136886. | 0.924475 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −94923.6 | −0.614479 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 258542. | 1.60534 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 183968. | 1.09643 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 124409. | 0.712158 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −56065.1 | −0.308449 | −0.154224 | − | 0.988036i | \(-0.549288\pi\) | ||||
−0.154224 | + | 0.988036i | \(0.549288\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 53161.8 | 0.281271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 99935.1 | 0.508791 | 0.254396 | − | 0.967100i | \(-0.418123\pi\) | ||||
0.254396 | + | 0.967100i | \(0.418123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47274.0 | 0.231736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 30315.1 | 0.143161 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 246538. | 1.12223 | 0.561116 | − | 0.827737i | \(-0.310372\pi\) | ||||
0.561116 | + | 0.827737i | \(0.310372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −258431. | −1.13451 | −0.567255 | − | 0.823542i | \(-0.691995\pi\) | ||||
−0.567255 | + | 0.823542i | \(0.691995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −453303. | −1.92017 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −509807. | −2.08480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 154054. | 0.608491 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 49025.5 | 0.187124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −246723. | −0.910425 | −0.455213 | − | 0.890383i | \(-0.650437\pi\) | ||||
−0.455213 | + | 0.890383i | \(0.650437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −248510. | −0.886955 | −0.443478 | − | 0.896285i | \(-0.646255\pi\) | ||||
−0.443478 | + | 0.896285i | \(0.646255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −336935. | −1.16364 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −47829.4 | −0.159906 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −360954. | −1.16870 | −0.584350 | − | 0.811502i | \(-0.698650\pi\) | ||||
−0.584350 | + | 0.811502i | \(0.698650\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −566418. | −1.77682 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 73189.2 | 0.222527 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −486179. | −1.43327 | −0.716634 | − | 0.697449i | \(-0.754318\pi\) | ||||
−0.716634 | + | 0.697449i | \(0.754318\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 284294. | 0.812939 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −275768. | −0.765160 | −0.382580 | − | 0.923922i | \(-0.624964\pi\) | ||||
−0.382580 | + | 0.923922i | \(0.624964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 248124. | 0.668270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 167801. | 0.438838 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −144055. | −0.365942 | −0.182971 | − | 0.983118i | \(-0.558572\pi\) | ||||
−0.182971 | + | 0.983118i | \(0.558572\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −130487. | −0.322086 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −895085. | −2.14749 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 196486. | 0.458353 | 0.229176 | − | 0.973385i | \(-0.426397\pi\) | ||||
0.229176 | + | 0.973385i | \(0.426397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7419.09 | −0.0168327 | −0.00841636 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841636 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −642363. | −1.41792 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −44083.7 | −0.0946997 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.25485e6 | 2.62415 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −69108.4 | −0.140727 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 801615. | 1.58995 | 0.794973 | − | 0.606644i | \(-0.207485\pi\) | ||||
0.794973 | + | 0.606644i | \(0.207485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −304970. | −0.589336 | −0.294668 | − | 0.955600i | \(-0.595209\pi\) | ||||
−0.294668 | + | 0.955600i | \(0.595209\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −345418. | −0.650517 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 382141. | 0.701549 | 0.350775 | − | 0.936460i | \(-0.385918\pi\) | ||||
0.350775 | + | 0.936460i | \(0.385918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −142214. | −0.254572 | −0.127286 | − | 0.991866i | \(-0.540627\pi\) | ||||
−0.127286 | + | 0.991866i | \(0.540627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 110621. | 0.193129 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −351194. | −0.598146 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −193658. | −0.321848 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 259788. | 0.421399 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −624943. | −0.989634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −782360. | −1.20976 | −0.604882 | − | 0.796315i | \(-0.706780\pi\) | ||||
−0.604882 | + | 0.796315i | \(0.706780\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 995036. | 1.50276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −55961.9 | −0.0825651 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 109035. | 0.157188 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −154234. | −0.217304 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.52465e6 | −2.09985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −680812. | −0.916780 | −0.458390 | − | 0.888751i | \(-0.651574\pi\) | ||||
−0.458390 | + | 0.888751i | \(0.651574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −463168. | −0.609933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.03738e6 | 1.33621 | 0.668103 | − | 0.744069i | \(-0.267106\pi\) | ||||
0.668103 | + | 0.744069i | \(0.267106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 323871. | 0.408116 | 0.204058 | − | 0.978959i | \(-0.434587\pi\) | ||||
0.204058 | + | 0.978959i | \(0.434587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −648097. | −0.799117 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.30328e6 | 1.57271 | 0.786353 | − | 0.617777i | \(-0.211966\pi\) | ||||
0.786353 | + | 0.617777i | \(0.211966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 477179. | 0.563653 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 885394. | 1.02392 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 86138.1 | 0.0975440 | 0.0487720 | − | 0.998810i | \(-0.484469\pi\) | ||||
0.0487720 | + | 0.998810i | \(0.484469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.25796e6 | −1.39516 | −0.697581 | − | 0.716506i | \(-0.745740\pi\) | ||||
−0.697581 | + | 0.716506i | \(0.745740\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.10829e6 | −1.20403 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −51607.8 | −0.0549288 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 759308. | 0.791910 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.46678e6 | −1.49922 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.15904e6 | −1.16122 | −0.580609 | − | 0.814183i | \(-0.697185\pi\) | ||||
−0.580609 | + | 0.814183i | \(0.697185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −967531. | −0.950306 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 850221. | 0.818807 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.53094e6 | 1.44586 | 0.722930 | − | 0.690921i | \(-0.242795\pi\) | ||||
0.722930 | + | 0.690921i | \(0.242795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 100496. | 0.0930896 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.24658e6 | −1.13271 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.06192e6 | 0.946680 | 0.473340 | − | 0.880880i | \(-0.343048\pi\) | ||||
0.473340 | + | 0.880880i | \(0.343048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 596253. | 0.521574 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23237.5 | 0.0199485 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 367406. | 0.309575 | 0.154787 | − | 0.987948i | \(-0.450531\pi\) | ||||
0.154787 | + | 0.987948i | \(0.450531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.12719e6 | 1.75947 | 0.879737 | − | 0.475461i | \(-0.157719\pi\) | ||||
0.879737 | + | 0.475461i | \(0.157719\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 787441. | 0.639457 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.72498e6 | 1.37547 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.24666e6 | 0.976223 | 0.488111 | − | 0.872781i | \(-0.337686\pi\) | ||||
0.488111 | + | 0.872781i | \(0.337686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 387026. | 0.297666 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.79523e6 | 1.35630 | 0.678149 | − | 0.734925i | \(-0.262782\pi\) | ||||
0.678149 | + | 0.734925i | \(0.262782\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.12563e6 | −1.57769 | −0.788844 | − | 0.614593i | \(-0.789320\pi\) | ||||
−0.788844 | + | 0.614593i | \(0.789320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −423429. | −0.308793 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 441477. | 0.316376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.33295e6 | 1.64309 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.75781e6 | 1.90911 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.14547e6 | 0.779494 | 0.389747 | − | 0.920922i | \(-0.372562\pi\) | ||||
0.389747 | + | 0.920922i | \(0.372562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 942231. | 0.630380 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 913585. | 0.600977 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.17555e6 | 0.760439 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 127575. | 0.0811613 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 410586. | 0.256920 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 676198. | 0.416221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.60698e6 | −0.973114 | −0.486557 | − | 0.873649i | \(-0.661747\pi\) | ||||
−0.486557 | + | 0.873649i | \(0.661747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 302804. | 0.180412 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.38046e6 | −1.39560 | −0.697799 | − | 0.716294i | \(-0.745837\pi\) | ||||
−0.697799 | + | 0.716294i | \(0.745837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −600241. | −0.346310 | −0.173155 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173155 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −183184. | −0.104019 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.01742e6 | 1.68650 | 0.843252 | − | 0.537519i | \(-0.180638\pi\) | ||||
0.843252 | + | 0.537519i | \(0.180638\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.64264e6 | 2.55440 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.43886e6 | −1.86274 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.86898e6 | −0.996778 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.09586e6 | −1.10066 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.58792e6 | 1.85555 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.08781e6 | −0.554069 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.68509e6 | 0.845380 | 0.422690 | − | 0.906274i | \(-0.361086\pi\) | ||||
0.422690 | + | 0.906274i | \(0.361086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 356716. | 0.176284 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −116448. | −0.0566917 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.82977e6 | 0.877652 | 0.438826 | − | 0.898572i | \(-0.355395\pi\) | ||||
0.438826 | + | 0.898572i | \(0.355395\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.07021e6 | −1.45101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.44140e6 | −0.671273 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −655548. | −0.296522 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 861788. | 0.384217 | 0.192109 | − | 0.981374i | \(-0.438467\pi\) | ||||
0.192109 | + | 0.981374i | \(0.438467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.11641e6 | 1.80907 | 0.904534 | − | 0.426401i | \(-0.140219\pi\) | ||||
0.904534 | + | 0.426401i | \(0.140219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11001e6 | −0.480904 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.32890e6 | −0.567619 | −0.283809 | − | 0.958881i | \(-0.591598\pi\) | ||||
−0.283809 | + | 0.958881i | \(0.591598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.04745e6 | −0.441125 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.93823e6 | −0.804886 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.94367e6 | −1.61497 | −0.807485 | − | 0.589888i | \(-0.799172\pi\) | ||||
−0.807485 | + | 0.589888i | \(0.799172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.54531e6 | −0.624089 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.27911e6 | 2.10278 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 162357. | 0.0637881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.50971e6 | 1.36021 | 0.680104 | − | 0.733115i | \(-0.261935\pi\) | ||||
0.680104 | + | 0.733115i | \(0.261935\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.56704e6 | 0.599122 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.35926e6 | −0.512706 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.31380e6 | −1.60542 | −0.802709 | − | 0.596371i | \(-0.796609\pi\) | ||||
−0.802709 | + | 0.596371i | \(0.796609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.54028e6 | 0.932833 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.64082e6 | −2.04404 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00478e6 | 1.78973 | 0.894864 | − | 0.446339i | \(-0.147272\pi\) | ||||
0.894864 | + | 0.446339i | \(0.147272\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.14478e6 | −0.404027 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.30249e6 | −0.802050 | −0.401025 | − | 0.916067i | \(-0.631346\pi\) | ||||
−0.401025 | + | 0.916067i | \(0.631346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 682234. | 0.234575 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 452833. | 0.153695 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.52146e6 | 1.51497 | 0.757485 | − | 0.652852i | \(-0.226428\pi\) | ||||
0.757485 | + | 0.652852i | \(0.226428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.89354e6 | −0.957166 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.04055e6 | 0.666449 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −932030. | −0.300564 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.05864e6 | 1.29242 | 0.646212 | − | 0.763158i | \(-0.276352\pi\) | ||||
0.646212 | + | 0.763158i | \(0.276352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 965279. | 0.303543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.20112e6 | 0.373015 | 0.186507 | − | 0.982454i | \(-0.440283\pi\) | ||||
0.186507 | + | 0.982454i | \(0.440283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.75131e6 | 0.537156 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.52744e6 | 0.462729 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.32852e6 | −0.397541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.72738e6 | −0.806190 | −0.403095 | − | 0.915158i | \(-0.632066\pi\) | ||||
−0.403095 | + | 0.915158i | \(0.632066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.03402e6 | 1.46998 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.14798e6 | −0.619662 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.54403e6 | 0.440085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.27686e6 | −1.48606 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 838850. | 0.233426 | 0.116713 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116713 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.09743e6 | −1.12670 | −0.563348 | − | 0.826220i | \(-0.690487\pi\) | ||||
−0.563348 | + | 0.826220i | \(0.690487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.86124e6 | −1.04924 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.15880e6 | 1.38540 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.54151e6 | −0.409145 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.04096e7 | −2.73082 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.21333e6 | 1.61113 | 0.805566 | − | 0.592506i | \(-0.201861\pi\) | ||||
0.805566 | + | 0.592506i | \(0.201861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.48637e6 | 1.40626 | 0.703130 | − | 0.711061i | \(-0.251785\pi\) | ||||
0.703130 | + | 0.711061i | \(0.251785\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.14561e6 | 0.797043 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.44104e6 | 0.360972 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.71784e6 | 0.673073 | 0.336537 | − | 0.941670i | \(-0.390744\pi\) | ||||
0.336537 | + | 0.941670i | \(0.390744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 417600. | 0.102250 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.50234e6 | 1.81630 | 0.908150 | − | 0.418645i | \(-0.137495\pi\) | ||||
0.908150 | + | 0.418645i | \(0.137495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24461.5 | −0.00585575 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.03779e6 | −1.19254 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.28575e6 | 0.300981 | 0.150491 | − | 0.988611i | \(-0.451915\pi\) | ||||
0.150491 | + | 0.988611i | \(0.451915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.83615e6 | −1.35109 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.07428e6 | −1.16179 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −828917. | −0.187708 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −968058. | −0.216826 | −0.108413 | − | 0.994106i | \(-0.534577\pi\) | ||||
−0.108413 | + | 0.994106i | \(0.534577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.73221e6 | 0.605315 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −112166. | −0.0245814 | −0.0122907 | − | 0.999924i | \(-0.503912\pi\) | ||||
−0.0122907 | + | 0.999924i | \(0.503912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −256452. | −0.0555973 | −0.0277986 | − | 0.999614i | \(-0.508850\pi\) | ||||
−0.0277986 | + | 0.999614i | \(0.508850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −976619. | −0.209456 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.22246e6 | −0.471565 | −0.235782 | − | 0.971806i | \(-0.575765\pi\) | ||||
−0.235782 | + | 0.971806i | \(0.575765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 265463. | 0.0557278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.37026e6 | −1.53084 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.68649e6 | −0.346601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.56919e6 | −0.522472 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.82476e6 | −0.970911 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.97880e6 | −0.394061 | −0.197031 | − | 0.980397i | \(-0.563130\pi\) | ||||
−0.197031 | + | 0.980397i | \(0.563130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.61416e6 | 0.318114 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.49444e6 | 0.291480 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.90307e6 | −0.560407 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.11381e6 | −1.74132 | −0.870658 | − | 0.491889i | \(-0.836307\pi\) | ||||
−0.870658 | + | 0.491889i | \(0.836307\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.92720e6 | −1.87739 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.69944e6 | −0.505325 | −0.252662 | − | 0.967555i | \(-0.581306\pi\) | ||||
−0.252662 | + | 0.967555i | \(0.581306\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.38845e7 | 2.57283 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.42162e6 | 0.444215 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.38784e6 | 0.433624 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −435566. | −0.0783074 | −0.0391537 | − | 0.999233i | \(-0.512466\pi\) | ||||
−0.0391537 | + | 0.999233i | \(0.512466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.63085e6 | −1.00226 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 92382.1 | 0.0162805 | 0.00814025 | − | 0.999967i | \(-0.497409\pi\) | ||||
0.00814025 | + | 0.999967i | \(0.497409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −432212. | −0.0754169 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.06639e6 | 0.875344 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.86197e6 | 0.489634 | 0.244817 | − | 0.969569i | \(-0.421272\pi\) | ||||
0.244817 | + | 0.969569i | \(0.421272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −370122. | −0.0627036 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.36070e6 | −0.228280 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −318753. | −0.0529586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.43804e7 | 2.36617 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.94143e6 | −0.479336 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.45599e6 | 0.719200 | 0.359600 | − | 0.933107i | \(-0.382913\pi\) | ||||
0.359600 | + | 0.933107i | \(0.382913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.35927e6 | −0.696882 | −0.348441 | − | 0.937331i | \(-0.613289\pi\) | ||||
−0.348441 | + | 0.937331i | \(0.613289\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.66438e6 | −0.421889 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.31072e6 | −0.676119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.20533e6 | −0.653373 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.62434e6 | −1.17345 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.09094e6 | 1.08115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.61999e6 | 0.546793 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.01202e6 | 0.600381 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.55527e6 | −0.230587 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.30648e6 | −0.191915 | −0.0959576 | − | 0.995385i | \(-0.530591\pi\) | ||||
−0.0959576 | + | 0.995385i | \(0.530591\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −151489. | −0.0220486 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.77691e6 | −0.544685 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.33330e7 | −1.90528 | −0.952640 | − | 0.304102i | \(-0.901644\pi\) | ||||
−0.952640 | + | 0.304102i | \(0.901644\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.47166e6 | −0.774797 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.91476e6 | −0.970283 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.12472e6 | 0.295454 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −900136. | −0.124044 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.06595e7 | 1.45579 | 0.727894 | − | 0.685690i | \(-0.240499\pi\) | ||||
0.727894 | + | 0.685690i | \(0.240499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.04909e6 | 0.277352 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.56226e7 | 3.43728 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.43316e6 | 1.25426 | 0.627128 | − | 0.778916i | \(-0.284230\pi\) | ||||
0.627128 | + | 0.778916i | \(0.284230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.23193e6 | 0.425932 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.48207e6 | −0.454862 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.64441e6 | −0.212927 | −0.106463 | − | 0.994317i | \(-0.533953\pi\) | ||||
−0.106463 | + | 0.994317i | \(0.533953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.16956e6 | −1.17695 | −0.588475 | − | 0.808515i | \(-0.700272\pi\) | ||||
−0.588475 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.63680e7 | 2.08262 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.97760e6 | −0.501709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 546566. | 0.0683444 | 0.0341722 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341722 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.22711e6 | −0.771952 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.51989e6 | −0.432603 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.79689e7 | 2.18952 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.94228e6 | −0.355462 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.60611e6 | 0.312175 | 0.156087 | − | 0.987743i | \(-0.450112\pi\) | ||||
0.156087 | + | 0.987743i | \(0.450112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.14683e6 | 0.254982 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.80286e6 | 0.918936 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.08057e6 | 0.242966 | 0.121483 | − | 0.992594i | \(-0.461235\pi\) | ||||
0.121483 | + | 0.992594i | \(0.461235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.04032e6 | 0.236268 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.90385e6 | −0.333455 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.40857e7 | −1.60403 | −0.802015 | − | 0.597304i | \(-0.796239\pi\) | ||||
−0.802015 | + | 0.597304i | \(0.796239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.33576e6 | −1.05430 | −0.527149 | − | 0.849773i | \(-0.676739\pi\) | ||||
−0.527149 | + | 0.849773i | \(0.676739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 942272. | 0.105532 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.55717e6 | −0.617256 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.05476e7 | 1.16193 | 0.580967 | − | 0.813927i | \(-0.302675\pi\) | ||||
0.580967 | + | 0.813927i | \(0.302675\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.17096e6 | −0.783491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.74723e7 | −1.89342 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.90712e6 | −0.957384 | −0.478692 | − | 0.877983i | \(-0.658889\pi\) | ||||
−0.478692 | + | 0.877983i | \(0.658889\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.95427e6 | −0.421578 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.75653e6 | 0.291507 | 0.145754 | − | 0.989321i | \(-0.453439\pi\) | ||||
0.145754 | + | 0.989321i | \(0.453439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −792026. | −0.0830831 | −0.0415416 | − | 0.999137i | \(-0.513227\pi\) | ||||
−0.0415416 | + | 0.999137i | \(0.513227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.10662e6 | −0.219208 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55764.1 | 0.00575619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.64777e6 | 0.578332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.27606e7 | −1.29629 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.97313e6 | −0.400411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.72493e6 | 0.372430 | 0.186215 | − | 0.982509i | \(-0.440378\pi\) | ||||
0.186215 | + | 0.982509i | \(0.440378\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.59749e7 | −1.58463 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.20508e6 | 0.118599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.88966e6 | 0.184516 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.47573e6 | 0.821155 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.67519e6 | −0.257163 | −0.128582 | − | 0.991699i | \(-0.541042\pi\) | ||||
−0.128582 | + | 0.991699i | \(0.541042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.82378e7 | −1.73958 | −0.869792 | − | 0.493418i | \(-0.835747\pi\) | ||||
−0.869792 | + | 0.493418i | \(0.835747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.14268e6 | −0.108149 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.16473e6 | −0.766798 | −0.383399 | − | 0.923583i | \(-0.625247\pi\) | ||||
−0.383399 | + | 0.923583i | \(0.625247\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.83954e7 | 2.64628 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.22637e6 | 0.205895 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.04750e7 | −1.87906 | −0.939528 | − | 0.342471i | \(-0.888736\pi\) | ||||
−0.939528 | + | 0.342471i | \(0.888736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.14804e6 | −0.195631 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.31376e6 | −0.118742 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.15848e7 | −1.03914 | −0.519572 | − | 0.854427i | \(-0.673908\pi\) | ||||
−0.519572 | + | 0.854427i | \(0.673908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.60142e7 | −1.42562 | −0.712809 | − | 0.701359i | \(-0.752577\pi\) | ||||
−0.712809 | + | 0.701359i | \(0.752577\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.11315e7 | −2.75053 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.01612e6 | −0.0891029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.07054e7 | −0.931724 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.39014e7 | −1.20086 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.03781e7 | 1.74726 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.14532e7 | −0.974739 | −0.487370 | − | 0.873196i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873196i | \(0.662044\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.75583e6 | 0.317282 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.11530e7 | 1.77378 | 0.886891 | − | 0.461979i | \(-0.152860\pi\) | ||||
0.886891 | + | 0.461979i | \(0.152860\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.61805e6 | 0.550879 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.11821e7 | 1.75025 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.37808e6 | 0.113037 | 0.0565187 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565187 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.29917e6 | −0.431500 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.61306e6 | 0.534577 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.18323e7 | −1.75207 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.77460e7 | 1.41386 | 0.706930 | − | 0.707284i | \(-0.250080\pi\) | ||||
0.706930 | + | 0.707284i | \(0.250080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.52050e6 | −0.436662 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.55480e6 | 0.436221 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.74538e7 | −1.36085 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.66114e7 | 2.06004 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −841648. | −0.0646898 | −0.0323449 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323449 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.97870e6 | 0.151005 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.74342e6 | 0.738310 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 985303. | 0.0741347 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.61436e6 | 0.494165 | 0.247082 | − | 0.968994i | \(-0.420528\pi\) | ||||
0.247082 | + | 0.968994i | \(0.420528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.54180e6 | 0.559501 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.32370e6 | 0.244849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.09579e7 | 0.801611 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.75884e6 | 0.127770 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11026e7 | −0.800948 | −0.400474 | − | 0.916308i | \(-0.631154\pi\) | ||||
−0.400474 | + | 0.916308i | \(0.631154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 726653. | 0.0520582 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.56861e7 | −1.82748 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.90863e7 | 1.34858 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44518e7 | 1.01411 | 0.507057 | − | 0.861913i | \(-0.330733\pi\) | ||||
0.507057 | + | 0.861913i | \(0.330733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.36178e6 | −0.373672 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.04368e6 | −0.349103 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.29283e6 | −0.157620 | −0.0788102 | − | 0.996890i | \(-0.525112\pi\) | ||||
−0.0788102 | + | 0.996890i | \(0.525112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.05377e6 | −0.0719495 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.50931e6 | −0.237987 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.02688e7 | −0.691686 | −0.345843 | − | 0.938292i | \(-0.612407\pi\) | ||||
−0.345843 | + | 0.938292i | \(0.612407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.55042e7 | 1.03730 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.42827e6 | −0.0949159 | −0.0474579 | − | 0.998873i | \(-0.515112\pi\) | ||||
−0.0474579 | + | 0.998873i | \(0.515112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.30314e6 | 0.350060 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.24940e7 | −0.819220 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.25239e6 | −0.537496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.23504e7 | −0.799064 | −0.399532 | − | 0.916719i | \(-0.630827\pi\) | ||||
−0.399532 | + | 0.916719i | \(0.630827\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.36662e7 | −1.52104 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.34155e6 | 0.341036 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.11463e6 | −0.514670 | −0.257335 | − | 0.966322i | \(-0.582844\pi\) | ||||
−0.257335 | + | 0.966322i | \(0.582844\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.97558e7 | −1.24477 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.67506e6 | 0.104850 | 0.0524249 | − | 0.998625i | \(-0.483305\pi\) | ||||
0.0524249 | + | 0.998625i | \(0.483305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.61011e6 | 0.535424 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.24219e6 | 0.447421 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.45005e7 | −2.11757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.68837e7 | −1.63935 | −0.819677 | − | 0.572826i | \(-0.805847\pi\) | ||||
−0.819677 | + | 0.572826i | \(0.805847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.12600e7 | 1.89388 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 400610. | 0.0241142 | 0.0120571 | − | 0.999927i | \(-0.496162\pi\) | ||||
0.0120571 | + | 0.999927i | \(0.496162\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.92573e6 | −0.354395 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.05202e6 | 0.121935 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.69238e6 | 0.513210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.15662e7 | −1.85180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.01085e7 | 0.589225 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.75846e6 | 0.449367 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.47190e7 | 0.847113 | 0.423557 | − | 0.905870i | \(-0.360782\pi\) | ||||
0.423557 | + | 0.905870i | \(0.360782\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.16832e7 | 1.24002 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.36774e6 | −0.418690 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.47595e7 | −1.39817 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.21748e7 | 0.683192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.00867e7 | −0.562474 | −0.281237 | − | 0.959638i | \(-0.590745\pi\) | ||||
−0.281237 | + | 0.959638i | \(0.590745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.30067e7 | 2.38325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 197937. | 0.0109005 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.89286e6 | 0.267777 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.57315e6 | −0.0855620 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.50199e6 | 0.405502 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.96759e7 | 1.05697 | 0.528487 | − | 0.848941i | \(-0.322760\pi\) | ||||
0.528487 | + | 0.848941i | \(0.322760\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.07488e7 | −1.10775 | −0.553874 | − | 0.832601i | \(-0.686851\pi\) | ||||
−0.553874 | + | 0.832601i | \(0.686851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.34346e7 | 2.30468 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.04501e7 | 0.551094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.51186e6 | 0.131656 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.70743e6 | 0.349419 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −946675. | −0.0490166 | −0.0245083 | − | 0.999700i | \(-0.507802\pi\) | ||||
−0.0245083 | + | 0.999700i | \(0.507802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.80402e7 | −0.928412 | −0.464206 | − | 0.885727i | \(-0.653660\pi\) | ||||
−0.464206 | + | 0.885727i | \(0.653660\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.52220e7 | 1.80169 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.98123e6 | 0.507482 | 0.253741 | − | 0.967272i | \(-0.418339\pi\) | ||||
0.253741 | + | 0.967272i | \(0.418339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.24005e6 | −0.416432 | −0.208216 | − | 0.978083i | \(-0.566766\pi\) | ||||
−0.208216 | + | 0.978083i | \(0.566766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.54553e7 | 1.27872 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.65126e6 | −0.232251 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.92744e6 | 0.294205 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.13839e6 | −0.154843 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.34565e7 | −0.659973 | −0.329986 | − | 0.943986i | \(-0.607044\pi\) | ||||
−0.329986 | + | 0.943986i | \(0.607044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.08579e7 | 1.50445 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.66565e7 | 1.77657 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.33325e6 | −0.256951 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.26685e7 | 0.606762 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.34028e7 | −2.06656 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.06341e6 | 0.145004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.38794e6 | 0.253542 | 0.126771 | − | 0.991932i | \(-0.459539\pi\) | ||||
0.126771 | + | 0.991932i | \(0.459539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.60677e6 | −0.168734 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.96394e6 | −0.184364 | −0.0921818 | − | 0.995742i | \(-0.529384\pi\) | ||||
−0.0921818 | + | 0.995742i | \(0.529384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.95904e7 | −0.905859 | −0.452930 | − | 0.891546i | \(-0.649621\pi\) | ||||
−0.452930 | + | 0.891546i | \(0.649621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.01444e6 | 0.414411 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.83066e7 | −1.75084 | −0.875420 | − | 0.483363i | \(-0.839415\pi\) | ||||
−0.875420 | + | 0.483363i | \(0.839415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.09636e6 | 0.140706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.76361e7 | 2.15223 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.80880e7 | −1.26174 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.26383e6 | 0.190438 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.34911e7 | 1.04320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.09604e6 | 0.269171 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.52390e7 | −0.669048 | −0.334524 | − | 0.942387i | \(-0.608576\pi\) | ||||
−0.334524 | + | 0.942387i | \(0.608576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.33890e7 | 1.02103 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.13058e7 | 1.35889 | 0.679445 | − | 0.733726i | \(-0.262220\pi\) | ||||
0.679445 | + | 0.733726i | \(0.262220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.58868e6 | 0.413864 | 0.206932 | − | 0.978355i | \(-0.433652\pi\) | ||||
0.206932 | + | 0.978355i | \(0.433652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.92392e7 | 0.825714 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.49529e6 | −0.362551 | −0.181275 | − | 0.983432i | \(-0.558023\pi\) | ||||
−0.181275 | + | 0.983432i | \(0.558023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.74719e6 | −0.116583 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.60315e7 | 1.94250 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.14183e7 | −0.898785 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.22334e6 | −0.176238 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.40034e7 | 0.996074 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.59486e7 | −0.658147 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.37385e7 | 2.20533 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.60493e6 | 0.106311 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 159468. | 0.00647221 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.16843e6 | −0.127887 | −0.0639435 | − | 0.997954i | \(-0.520368\pi\) | ||||
−0.0639435 | + | 0.997954i | \(0.520368\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.49737e6 | 0.140389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.14906e7 | −0.857932 | −0.428966 | − | 0.903321i | \(-0.641122\pi\) | ||||
−0.428966 | + | 0.903321i | \(0.641122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.65315e7 | 1.84744 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.38072e7 | 0.545194 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.89682e6 | 0.192305 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.43349e7 | 0.950473 | 0.475237 | − | 0.879858i | \(-0.342362\pi\) | ||||
0.475237 | + | 0.879858i | \(0.342362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.28126e7 | −1.27465 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.83531e7 | 1.48182 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.46166e6 | −0.209880 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.57929e6 | 0.0985826 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.95011e7 | 1.50165 | 0.750827 | − | 0.660499i | \(-0.229655\pi\) | ||||
0.750827 | + | 0.660499i | \(0.229655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.31643e6 | 0.0875880 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.86062e7 | −1.82805 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.69722e7 | −1.00899 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.80717e7 | 1.41662 | 0.708310 | − | 0.705901i | \(-0.249458\pi\) | ||||
0.708310 | + | 0.705901i | \(0.249458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.22562e7 | −0.453620 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.78889e7 | −1.02673 | −0.513367 | − | 0.858169i | \(-0.671602\pi\) | ||||
−0.513367 | + | 0.858169i | \(0.671602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.34575e7 | 0.492815 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.48544e6 | 0.0541097 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.95348e7 | −1.43253 | −0.716266 | − | 0.697828i | \(-0.754150\pi\) | ||||
−0.716266 | + | 0.697828i | \(0.754150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.94484e6 | −0.214277 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.16120e7 | 2.20909 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.46155e7 | −0.877964 | −0.438982 | − | 0.898496i | \(-0.644661\pi\) | ||||
−0.438982 | + | 0.898496i | \(0.644661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.72302e7 | −0.611337 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.47971e7 | 3.34592 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.20804e7 | 0.424164 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.36776e7 | −0.827045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.92922e7 | −1.01786 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.55511e6 | 0.226601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.95008e7 | 1.01453 | 0.507267 | − | 0.861789i | \(-0.330656\pi\) | ||||
0.507267 | + | 0.861789i | \(0.330656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.81623e7 | −1.30565 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.46448e7 | −1.17921 | −0.589604 | − | 0.807692i | \(-0.700716\pi\) | ||||
−0.589604 | + | 0.807692i | \(0.700716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.26631e7 | −0.428804 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.27949e7 | −1.44172 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.52468e7 | −1.18136 | −0.590681 | − | 0.806905i | \(-0.701141\pi\) | ||||
−0.590681 | + | 0.806905i | \(0.701141\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −737179. | −0.0245819 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.05620e7 | 1.01393 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.34734e7 | 1.76504 | 0.882519 | − | 0.470277i | \(-0.155846\pi\) | ||||
0.882519 | + | 0.470277i | \(0.155846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.21386e6 | −0.269747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.22118e7 | −0.725757 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.88884e6 | 0.126424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.45979e7 | 0.472177 | 0.236089 | − | 0.971732i | \(-0.424134\pi\) | ||||
0.236089 | + | 0.971732i | \(0.424134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.44074e7 | 1.10734 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.05680e6 | 0.0978834 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.69407e6 | −0.181420 | −0.0907100 | − | 0.995877i | \(-0.528914\pi\) | ||||
−0.0907100 | + | 0.995877i | \(0.528914\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.89261e6 | −0.0917013 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 448.6.a.bc.1.4 | 4 | ||
4.3 | odd | 2 | 448.6.a.bd.1.1 | 4 | |||
8.3 | odd | 2 | 224.6.a.g.1.4 | ✓ | 4 | ||
8.5 | even | 2 | 224.6.a.h.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.g.1.4 | ✓ | 4 | 8.3 | odd | 2 | ||
224.6.a.h.1.1 | yes | 4 | 8.5 | even | 2 | ||
448.6.a.bc.1.4 | 4 | 1.1 | even | 1 | trivial | ||
448.6.a.bd.1.1 | 4 | 4.3 | odd | 2 |