Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,6,Mod(1,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.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: | \(35.9259756381\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{61}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 15 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.40512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.1 |
$q$-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 | ||||||||
\(3\) | −0.810250 | −0.0519775 | −0.0259888 | − | 0.999662i | \(-0.508273\pi\) | ||||
−0.0259888 | + | 0.999662i | \(0.508273\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 71.6717 | 1.28210 | 0.641052 | − | 0.767498i | \(-0.278498\pi\) | ||||
0.641052 | + | 0.767498i | \(0.278498\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −242.343 | −0.997298 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −569.271 | −1.41853 | −0.709264 | − | 0.704943i | \(-0.750972\pi\) | ||||
−0.709264 | + | 0.704943i | \(0.750972\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 137.702 | 0.225987 | 0.112993 | − | 0.993596i | \(-0.463956\pi\) | ||||
0.112993 | + | 0.993596i | \(0.463956\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −58.0720 | −0.0666406 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −418.657 | −0.351346 | −0.175673 | − | 0.984449i | \(-0.556210\pi\) | ||||
−0.175673 | + | 0.984449i | \(0.556210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2552.13 | −1.62188 | −0.810941 | − | 0.585128i | \(-0.801044\pi\) | ||||
−0.810941 | + | 0.585128i | \(0.801044\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.7022 | −0.0196457 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 127.036 | 0.0500734 | 0.0250367 | − | 0.999687i | \(-0.492030\pi\) | ||||
0.0250367 | + | 0.999687i | \(0.492030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2011.84 | 0.643789 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 393.249 | 0.103815 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2312.40 | 0.510584 | 0.255292 | − | 0.966864i | \(-0.417828\pi\) | ||||
0.255292 | + | 0.966864i | \(0.417828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3992.18 | 0.746115 | 0.373058 | − | 0.927808i | \(-0.378309\pi\) | ||||
0.373058 | + | 0.927808i | \(0.378309\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 461.252 | 0.0737316 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3511.92 | 0.484589 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3853.34 | −0.462736 | −0.231368 | − | 0.972866i | \(-0.574320\pi\) | ||||
−0.231368 | + | 0.972866i | \(0.574320\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −111.573 | −0.0117462 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4940.82 | −0.459029 | −0.229514 | − | 0.973305i | \(-0.573714\pi\) | ||||
−0.229514 | + | 0.973305i | \(0.573714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13679.2 | −1.12821 | −0.564103 | − | 0.825704i | \(-0.690778\pi\) | ||||
−0.564103 | + | 0.825704i | \(0.690778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17369.2 | −1.27864 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −27624.7 | −1.82412 | −0.912059 | − | 0.410058i | \(-0.865508\pi\) | ||||
−0.912059 | + | 0.410058i | \(0.865508\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 339.216 | 0.0182621 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37400.0 | 1.82886 | 0.914432 | − | 0.404740i | \(-0.132638\pi\) | ||||
0.914432 | + | 0.404740i | \(0.132638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −40800.7 | −1.81870 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2067.86 | 0.0843014 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −37000.0 | −1.38379 | −0.691897 | − | 0.721996i | \(-0.743225\pi\) | ||||
−0.691897 | + | 0.721996i | \(0.743225\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3803.32 | −0.130869 | −0.0654347 | − | 0.997857i | \(-0.520843\pi\) | ||||
−0.0654347 | + | 0.997857i | \(0.520843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11874.8 | −0.376943 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9869.36 | 0.289738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22454.7 | 0.611111 | 0.305555 | − | 0.952174i | \(-0.401158\pi\) | ||||
0.305555 | + | 0.952174i | \(0.401158\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −102.931 | −0.00260269 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −55088.9 | −1.29693 | −0.648467 | − | 0.761243i | \(-0.724590\pi\) | ||||
−0.648467 | + | 0.761243i | \(0.724590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −69256.6 | −1.52109 | −0.760543 | − | 0.649287i | \(-0.775067\pi\) | ||||
−0.760543 | + | 0.649287i | \(0.775067\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1630.09 | −0.0334625 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27894.3 | −0.536153 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40937.8 | −0.738000 | −0.369000 | − | 0.929429i | \(-0.620300\pi\) | ||||
−0.369000 | + | 0.929429i | \(0.620300\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 58570.8 | 0.991902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 19789.0 | 0.315303 | 0.157652 | − | 0.987495i | \(-0.449608\pi\) | ||||
0.157652 | + | 0.987495i | \(0.449608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30005.8 | −0.450462 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1873.62 | −0.0265389 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 104148. | 1.39373 | 0.696864 | − | 0.717203i | \(-0.254578\pi\) | ||||
0.696864 | + | 0.717203i | \(0.254578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6747.41 | 0.0854149 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3234.66 | −0.0387812 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −182916. | −2.07942 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −96649.8 | −1.04297 | −0.521485 | − | 0.853261i | \(-0.674622\pi\) | ||||
−0.521485 | + | 0.853261i | \(0.674622\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 137959. | 1.41469 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 26636.2 | 0.259817 | 0.129909 | − | 0.991526i | \(-0.458532\pi\) | ||||
0.129909 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 62232.5 | 0.577995 | 0.288998 | − | 0.957330i | \(-0.406678\pi\) | ||||
0.288998 | + | 0.957330i | \(0.406678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2845.53 | −0.0251878 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −111445. | −0.941026 | −0.470513 | − | 0.882393i | \(-0.655931\pi\) | ||||
−0.470513 | + | 0.882393i | \(0.655931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 163349. | 1.31690 | 0.658448 | − | 0.752627i | \(-0.271213\pi\) | ||||
0.658448 | + | 0.752627i | \(0.271213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3122.17 | 0.0240519 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −180728. | −1.33146 | −0.665732 | − | 0.746191i | \(-0.731881\pi\) | ||||
−0.665732 | + | 0.746191i | \(0.731881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9104.89 | 0.0641993 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −33371.2 | −0.225376 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20514.2 | −0.132796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 163019. | 1.01222 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4003.30 | 0.0238592 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −79782.2 | −0.456700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −121589. | −0.668938 | −0.334469 | − | 0.942407i | \(-0.608557\pi\) | ||||
−0.334469 | + | 0.942407i | \(0.608557\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11083.5 | 0.0586414 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 119712. | 0.609482 | 0.304741 | − | 0.952435i | \(-0.401430\pi\) | ||||
0.304741 | + | 0.952435i | \(0.401430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −125054. | −0.613014 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 28184.9 | 0.133101 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4767.80 | −0.0217028 | −0.0108514 | − | 0.999941i | \(-0.503454\pi\) | ||||
−0.0108514 | + | 0.999941i | \(0.503454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 173481. | 0.761578 | 0.380789 | − | 0.924662i | \(-0.375652\pi\) | ||||
0.380789 | + | 0.924662i | \(0.375652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22382.9 | 0.0948132 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −78390.0 | −0.320568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 165733. | 0.654621 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1945.41 | −0.00742536 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −236401. | −0.872337 | −0.436169 | − | 0.899865i | \(-0.643665\pi\) | ||||
−0.436169 | + | 0.899865i | \(0.643665\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 280973. | 1.00282 | 0.501410 | − | 0.865210i | \(-0.332815\pi\) | ||||
0.501410 | + | 0.865210i | \(0.332815\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 101459. | 0.350397 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 286127. | 0.956597 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 343000. | 1.11057 | 0.555284 | − | 0.831661i | \(-0.312610\pi\) | ||||
0.555284 | + | 0.831661i | \(0.312610\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −30303.3 | −0.0950598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6224.76 | 0.0189260 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 631306. | 1.86110 | 0.930552 | − | 0.366160i | \(-0.119328\pi\) | ||||
0.930552 | + | 0.366160i | \(0.119328\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 33058.7 | 0.0945315 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −174139. | −0.483176 | −0.241588 | − | 0.970379i | \(-0.577668\pi\) | ||||
−0.241588 | + | 0.970379i | \(0.577668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −352331. | −0.948930 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 618493. | 1.61750 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −389487. | −0.989412 | −0.494706 | − | 0.869060i | \(-0.664724\pi\) | ||||
−0.494706 | + | 0.869060i | \(0.664724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 98580.1 | 0.243329 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29979.2 | 0.0719262 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 827314. | 1.92991 | 0.964956 | − | 0.262411i | \(-0.0845178\pi\) | ||||
0.964956 | + | 0.262411i | \(0.0845178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 250850. | 0.569138 | 0.284569 | − | 0.958656i | \(-0.408150\pi\) | ||||
0.284569 | + | 0.958656i | \(0.408150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3081.64 | 0.00680227 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −276176. | −0.593275 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 238329. | 0.498395 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19269.2 | 0.0392383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −166405. | −0.330052 | −0.165026 | − | 0.986289i | \(-0.552771\pi\) | ||||
−0.165026 | + | 0.986289i | \(0.552771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −408270. | −0.788959 | −0.394480 | − | 0.918905i | \(-0.629075\pi\) | ||||
−0.394480 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7996.65 | −0.0150599 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 895496. | 1.64399 | 0.821993 | − | 0.569497i | \(-0.192862\pi\) | ||||
0.821993 | + | 0.569497i | \(0.192862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −177488. | −0.317714 | −0.158857 | − | 0.987302i | \(-0.550781\pi\) | ||||
−0.158857 | + | 0.987302i | \(0.550781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18193.9 | −0.0317640 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 113307. | 0.192983 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −354117. | −0.588522 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30786.3 | −0.0499381 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.45286e6 | 2.30068 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −963464. | −1.48981 | −0.744903 | − | 0.667173i | \(-0.767504\pi\) | ||||
−0.744903 | + | 0.667173i | \(0.767504\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 44635.7 | 0.0674114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −980410. | −1.44648 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 195617. | 0.282005 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 56115.1 | 0.0790623 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −57649.9 | −0.0793996 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 513529. | 0.691518 | 0.345759 | − | 0.938323i | \(-0.387622\pi\) | ||||
0.345759 | + | 0.938323i | \(0.387622\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −487556. | −0.642049 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 251707. | 0.324213 | 0.162106 | − | 0.986773i | \(-0.448171\pi\) | ||||
0.162106 | + | 0.986773i | \(0.448171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.11802e6 | −1.40884 | −0.704419 | − | 0.709784i | \(-0.748793\pi\) | ||||
−0.704419 | + | 0.709784i | \(0.748793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22601.3 | 0.0278679 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.09444e6 | −1.32070 | −0.660349 | − | 0.750959i | \(-0.729592\pi\) | ||||
−0.660349 | + | 0.750959i | \(0.729592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.97991e6 | −2.33871 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33169.8 | 0.0383594 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.61769e6 | 1.83190 | 0.915949 | − | 0.401295i | \(-0.131440\pi\) | ||||
0.915949 | + | 0.401295i | \(0.131440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 368001. | 0.408137 | 0.204069 | − | 0.978957i | \(-0.434583\pi\) | ||||
0.204069 | + | 0.978957i | \(0.434583\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −143017. | −0.155371 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 172084. | 0.183158 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −351434. | −0.366523 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16034.0 | −0.0163887 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 132644. | 0.132893 | 0.0664466 | − | 0.997790i | \(-0.478834\pi\) | ||||
0.0664466 | + | 0.997790i | \(0.478834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −72318.0 | −0.0710305 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24312.2 | 0.0234139 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −648941. | −0.612876 | −0.306438 | − | 0.951891i | \(-0.599137\pi\) | ||||
−0.306438 | + | 0.951891i | \(0.599137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −188814. | −0.174898 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −560394. | −0.509205 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 559540. | 0.498818 | 0.249409 | − | 0.968398i | \(-0.419764\pi\) | ||||
0.249409 | + | 0.968398i | \(0.419764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.68052e6 | 2.34479 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −84386.3 | −0.0724425 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.11891e6 | 0.942793 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.85235e6 | 1.53214 | 0.766072 | − | 0.642754i | \(-0.222208\pi\) | ||||
0.766072 | + | 0.642754i | \(0.222208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5467.09 | −0.00443966 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.14528e6 | −0.913232 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −150989. | −0.118235 | −0.0591173 | − | 0.998251i | \(-0.518829\pi\) | ||||
−0.0591173 | + | 0.998251i | \(0.518829\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −967479. | −0.744099 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −658293. | −0.497340 | −0.248670 | − | 0.968588i | \(-0.579994\pi\) | ||||
−0.248670 | + | 0.968588i | \(0.579994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.88185e6 | −1.39675 | −0.698376 | − | 0.715731i | \(-0.746094\pi\) | ||||
−0.698376 | + | 0.715731i | \(0.746094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 148207. | 0.108083 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −242100. | −0.173496 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.24458e6 | −0.876556 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 78310.5 | 0.0542110 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.04860e6 | 0.713577 | 0.356789 | − | 0.934185i | \(-0.383872\pi\) | ||||
0.356789 | + | 0.934185i | \(0.383872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.65185e6 | −1.77417 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −223866. | −0.147264 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17493.1 | 0.0113159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −670279. | −0.426422 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21581.9 | −0.0135047 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −272591. | −0.167788 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.11586e6 | −1.28127 | −0.640634 | − | 0.767846i | \(-0.721329\pi\) | ||||
−0.640634 | + | 0.767846i | \(0.721329\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −50423.9 | −0.0300428 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.58928e6 | −0.931749 | −0.465875 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 150833. | 0.0870235 | 0.0435118 | − | 0.999053i | \(-0.486145\pi\) | ||||
0.0435118 | + | 0.999053i | \(0.486145\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −851090. | −0.483280 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17178.1 | −0.00960122 | −0.00480061 | − | 0.999988i | \(-0.501528\pi\) | ||||
−0.00480061 | + | 0.999988i | \(0.501528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.31638e6 | −0.724277 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 90298.4 | 0.0489122 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.06847e6 | 0.569842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 277035. | 0.145488 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −132354. | −0.0684490 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.35361e6 | −0.689452 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.47433e6 | −1.24133 | −0.620666 | − | 0.784075i | \(-0.713138\pi\) | ||||
−0.620666 | + | 0.784075i | \(0.713138\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 933833. | 0.461486 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.60937e6 | 0.783507 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.92911e6 | −0.925302 | −0.462651 | − | 0.886541i | \(-0.653102\pi\) | ||||
−0.462651 | + | 0.886541i | \(0.653102\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 146435. | 0.0692062 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.27263e6 | −1.05838 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7377.24 | −0.00333692 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 566575. | 0.252600 | 0.126300 | − | 0.991992i | \(-0.459690\pi\) | ||||
0.126300 | + | 0.991992i | \(0.459690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.91470e6 | 0.841469 | 0.420734 | − | 0.907184i | \(-0.361772\pi\) | ||||
0.420734 | + | 0.907184i | \(0.361772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54151.3 | 0.0234607 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.75846e6 | 1.60536 | 0.802681 | − | 0.596409i | \(-0.203406\pi\) | ||||
0.802681 | + | 0.596409i | \(0.203406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.94831e6 | −1.66280 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16621.6 | 0.00690243 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.88170e6 | 1.18008 | 0.590042 | − | 0.807373i | \(-0.299111\pi\) | ||||
0.590042 | + | 0.807373i | \(0.299111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.03728e6 | 1.63050 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −132086. | −0.0526127 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.96374e6 | −1.95019 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00494e6 | 1.55214 | 0.776070 | − | 0.630647i | \(-0.217211\pi\) | ||||
0.776070 | + | 0.630647i | \(0.217211\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.19738e6 | 0.457788 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.83260e6 | 0.691246 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −527856. | −0.196446 | −0.0982230 | − | 0.995164i | \(-0.531316\pi\) | ||||
−0.0982230 | + | 0.995164i | \(0.531316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 64643.5 | 0.0237381 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 318422. | 0.115385 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −771013. | −0.275717 | −0.137858 | − | 0.990452i | \(-0.544022\pi\) | ||||
−0.137858 | + | 0.990452i | \(0.544022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 98517.6 | 0.0347697 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.49145e6 | 0.519530 | 0.259765 | − | 0.965672i | \(-0.416355\pi\) | ||||
0.259765 | + | 0.965672i | \(0.416355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.99923e6 | −0.687403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.31506e6 | 1.12516 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.84613e6 | 1.62376 | 0.811878 | − | 0.583827i | \(-0.198445\pi\) | ||||
0.811878 | + | 0.583827i | \(0.198445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53184.4 | −0.0175931 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −96997.0 | −0.0316794 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.93408e6 | −0.946192 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 241537. | 0.0769144 | 0.0384572 | − | 0.999260i | \(-0.487756\pi\) | ||||
0.0384572 | + | 0.999260i | \(0.487756\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 101325. | 0.0318629 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.33211e6 | −1.03481 | −0.517403 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517403 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 549732. | 0.168612 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.19787e6 | 1.27172 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.19360e6 | 0.656404 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.42388e6 | −1.30766 | −0.653831 | − | 0.756641i | \(-0.726839\pi\) | ||||
−0.653831 | + | 0.756641i | \(0.726839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3863.11 | 0.00112806 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.81300e6 | −0.523025 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41831e6 | 0.404251 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −140563. | −0.0395849 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.05733e6 | 1.40730 | 0.703649 | − | 0.710548i | \(-0.251553\pi\) | ||||
0.703649 | + | 0.710548i | \(0.251553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.46515e6 | −1.77776 | −0.888881 | − | 0.458139i | \(-0.848516\pi\) | ||||
−0.888881 | + | 0.458139i | \(0.848516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.69467e6 | 1.81919 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −842270. | −0.226193 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −186363. | −0.0494640 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 63515.4 | 0.0166623 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.92475e6 | 1.27700 | 0.638500 | − | 0.769622i | \(-0.279555\pi\) | ||||
0.638500 | + | 0.769622i | \(0.279555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.99870e6 | 0.768622 | 0.384311 | − | 0.923204i | \(-0.374439\pi\) | ||||
0.384311 | + | 0.923204i | \(0.374439\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −134286. | −0.0340256 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −324213. | −0.0812131 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.09504e6 | −1.26179 | −0.630894 | − | 0.775869i | \(-0.717312\pi\) | ||||
−0.630894 | + | 0.775869i | \(0.717312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −581867. | −0.142471 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.63893e6 | −0.638878 | −0.319439 | − | 0.947607i | \(-0.603494\pi\) | ||||
−0.319439 | + | 0.947607i | \(0.603494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.46450e6 | 1.78690 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 191544. | 0.0453419 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.01164e6 | 1.17318 | 0.586589 | − | 0.809885i | \(-0.300470\pi\) | ||||
0.586589 | + | 0.809885i | \(0.300470\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.81267e6 | 0.651145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −227659. | −0.0521241 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 483599. | 0.109511 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.62960e6 | −1.26092 | −0.630460 | − | 0.776222i | \(-0.717134\pi\) | ||||
−0.630460 | + | 0.776222i | \(0.717134\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −164636. | −0.0364749 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.21775e6 | 0.924334 | 0.462167 | − | 0.886793i | \(-0.347072\pi\) | ||||
0.462167 | + | 0.886793i | \(0.347072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.79250e6 | 0.388603 | 0.194301 | − | 0.980942i | \(-0.437756\pi\) | ||||
0.194301 | + | 0.980942i | \(0.437756\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −231834. | −0.0497215 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.56530e6 | 1.18085 | 0.590427 | − | 0.807091i | \(-0.298959\pi\) | ||||
0.590427 | + | 0.807091i | \(0.298959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.10028e6 | 0.230978 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −277916. | −0.0577246 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.78716e6 | 1.60039 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.13448e6 | −1.04415 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.06363e6 | −1.82392 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.98318e6 | −1.58978 | −0.794890 | − | 0.606753i | \(-0.792472\pi\) | ||||
−0.794890 | + | 0.606753i | \(0.792472\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −530614. | −0.104572 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5043.61 | −0.000983726 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.92706e6 | −1.33719 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.89273e6 | −0.361631 | −0.180815 | − | 0.983517i | \(-0.557874\pi\) | ||||
−0.180815 | + | 0.983517i | \(0.557874\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −511515. | −0.0967356 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −714559. | −0.133762 | −0.0668812 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668812 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −968100. | −0.179392 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.88778e6 | 1.81378 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.69935e6 | −0.490195 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.55243e6 | 1.17802 | 0.589008 | − | 0.808127i | \(-0.299519\pi\) | ||||
0.589008 | + | 0.808127i | \(0.299519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 141096. | 0.0251143 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −990048. | −0.174476 | −0.0872381 | − | 0.996187i | \(-0.527804\pi\) | ||||
−0.0872381 | + | 0.996187i | \(0.527804\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90906e6 | 0.333113 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 285476. | 0.0493231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.01675e6 | −0.858277 | −0.429139 | − | 0.903239i | \(-0.641183\pi\) | ||||
−0.429139 | + | 0.903239i | \(0.641183\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.39357e6 | −0.574917 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00362e6 | −0.168375 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.46031e6 | 0.741049 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.57260e7 | 2.58756 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 315581. | 0.0514272 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −196789. | −0.0317619 | −0.0158809 | − | 0.999874i | \(-0.505055\pi\) | ||||
−0.0158809 | + | 0.999874i | \(0.505055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.81508e6 | 0.769749 | 0.384875 | − | 0.922969i | \(-0.374245\pi\) | ||||
0.384875 | + | 0.922969i | \(0.374245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −79874.5 | −0.0126477 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.67135e6 | −0.262145 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.42020e6 | −0.997493 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.96671e6 | 1.38006 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −680362. | −0.103734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.98747e6 | −1.20649 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −670330. | −0.100312 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.36682e6 | −0.202647 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.47799e6 | 0.364005 | 0.182002 | − | 0.983298i | \(-0.441742\pi\) | ||||
0.182002 | + | 0.983298i | \(0.441742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −203251. | −0.0295824 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.17075e7 | 1.68840 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.97032e6 | 0.853158 | 0.426579 | − | 0.904450i | \(-0.359719\pi\) | ||||
0.426579 | + | 0.904450i | \(0.359719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 921710. | 0.130516 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.90154e6 | −0.828107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00595e6 | −0.278938 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 223771. | 0.0308370 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.59368e6 | 1.03708 | 0.518542 | − | 0.855052i | \(-0.326475\pi\) | ||||
0.518542 | + | 0.855052i | \(0.326475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.88365e6 | −0.254960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −193106. | −0.0259053 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.11744e7 | 1.48578 | 0.742888 | − | 0.669416i | \(-0.233456\pi\) | ||||
0.742888 | + | 0.669416i | \(0.233456\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.29531e7 | −1.70707 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.86997e6 | 0.374904 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.18434e7 | −1.53354 | −0.766771 | − | 0.641921i | \(-0.778138\pi\) | ||||
−0.766771 | + | 0.641921i | \(0.778138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00356e7 | −1.28811 | −0.644057 | − | 0.764977i | \(-0.722750\pi\) | ||||
−0.644057 | + | 0.764977i | \(0.722750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 134829. | 0.0171553 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 255576. | 0.0322367 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.12162e7 | 1.40251 | 0.701256 | − | 0.712909i | \(-0.252623\pi\) | ||||
0.701256 | + | 0.712909i | \(0.252623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 330801. | 0.0410082 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 969661. | 0.119173 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.12907e7 | −2.59429 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.39178e6 | −0.288955 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.16178e6 | −0.378736 | −0.189368 | − | 0.981906i | \(-0.560644\pi\) | ||||
−0.189368 | + | 0.981906i | \(0.560644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.01886e7 | −1.21011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −725575. | −0.0854504 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.55501e6 | −0.882264 | −0.441132 | − | 0.897442i | \(-0.645423\pi\) | ||||
−0.441132 | + | 0.897442i | \(0.645423\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.47029e6 | −0.170259 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 143810. | 0.0165140 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.56629e7 | −1.78364 | −0.891818 | − | 0.452394i | \(-0.850570\pi\) | ||||
−0.891818 | + | 0.452394i | \(0.850570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.07168e7 | 1.21027 | 0.605133 | − | 0.796125i | \(-0.293120\pi\) | ||||
0.605133 | + | 0.796125i | \(0.293120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.44175e6 | −0.609460 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.16839e7 | 1.29777 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.24101e7 | −1.36711 | −0.683557 | − | 0.729897i | \(-0.739568\pi\) | ||||
−0.683557 | + | 0.729897i | \(0.739568\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −91807.3 | −0.0100308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.80398e6 | −0.412226 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.92284e6 | −0.959074 | −0.479537 | − | 0.877522i | \(-0.659195\pi\) | ||||
−0.479537 | + | 0.877522i | \(0.659195\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 286924. | 0.0305899 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.46678e6 | 0.578121 | 0.289060 | − | 0.957311i | \(-0.406657\pi\) | ||||
0.289060 | + | 0.957311i | \(0.406657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.14856e6 | −0.435181 | −0.217591 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217591 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 49956.8 | 0.00519835 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.10328e6 | 0.526780 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20051e7 | −1.22932 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.17718e6 | −0.119584 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.61323e6 | 0.162581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.66340e7 | −1.66312 | −0.831561 | − | 0.555433i | \(-0.812553\pi\) | ||||
−0.831561 | + | 0.555433i | \(0.812553\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 780647. | 0.0774364 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.71451e6 | −0.857647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 330623. | 0.0322838 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.33504e7 | 1.29343 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.54577e7 | −1.48594 | −0.742968 | − | 0.669327i | \(-0.766582\pi\) | ||||
−0.742968 | + | 0.669327i | \(0.766582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.42448e7 | −1.35872 | −0.679360 | − | 0.733805i | \(-0.737743\pi\) | ||||
−0.679360 | + | 0.733805i | \(0.737743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 794377. | 0.0751843 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.78031e6 | −0.918527 | −0.459264 | − | 0.888300i | \(-0.651887\pi\) | ||||
−0.459264 | + | 0.888300i | \(0.651887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.10630e7 | 1.96295 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −158498. | −0.0146579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.43600e6 | 0.223560 | 0.111780 | − | 0.993733i | \(-0.464345\pi\) | ||||
0.111780 | + | 0.993733i | \(0.464345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.58000e6 | 0.781419 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.67839e7 | 1.51698 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.49022e6 | 0.313069 | 0.156534 | − | 0.987673i | \(-0.449968\pi\) | ||||
0.156534 | + | 0.987673i | \(0.449968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.38495e7 | 1.23291 | 0.616453 | − | 0.787392i | \(-0.288569\pi\) | ||||
0.616453 | + | 0.787392i | \(0.288569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46710.8 | 0.00412699 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.96287e6 | −0.785947 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 293758. | 0.0255667 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −416087. | −0.0359434 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.16512e6 | 0.185642 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.47132e7 | −1.25219 | −0.626093 | − | 0.779748i | \(-0.715347\pi\) | ||||
−0.626093 | + | 0.779748i | \(0.715347\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 791155. | 0.0668347 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.00252e7 | −1.67921 | −0.839605 | − | 0.543198i | \(-0.817213\pi\) | ||||
−0.839605 | + | 0.543198i | \(0.817213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.73584e6 | −0.394205 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −203945. | −0.0168518 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.84454e7 | 1.51299 | 0.756495 | − | 0.654000i | \(-0.226910\pi\) | ||||
0.756495 | + | 0.654000i | \(0.226910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −341717. | −0.0278253 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 905876. | 0.0732280 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.15006e6 | 0.413299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.52332e6 | −0.440053 | −0.220027 | − | 0.975494i | \(-0.570614\pi\) | ||||
−0.220027 | + | 0.975494i | \(0.570614\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.76000e6 | 0.534704 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.24337e7 | 0.976421 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.06851e6 | 0.161278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 886772. | 0.0686466 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.11961e6 | 0.393497 | 0.196749 | − | 0.980454i | \(-0.436962\pi\) | ||||
0.196749 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.83424e6 | 0.750503 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.60422e6 | 0.121560 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.30517e6 | 0.0982017 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.98577e6 | 0.223070 | 0.111535 | − | 0.993761i | \(-0.464423\pi\) | ||||
0.111535 | + | 0.993761i | \(0.464423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.92100e6 | 0.736006 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 507151. | 0.0373605 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.61835e6 | −0.411001 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.31073e6 | −0.0952175 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.51554e6 | 0.181472 | 0.0907360 | − | 0.995875i | \(-0.471078\pi\) | ||||
0.0907360 | + | 0.995875i | \(0.471078\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.04939e6 | 0.218462 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −298173. | −0.0212140 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.65217e6 | 0.328708 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.55008e7 | −1.08772 | −0.543862 | − | 0.839175i | \(-0.683038\pi\) | ||||
−0.543862 | + | 0.839175i | \(0.683038\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.41168e7 | −0.983826 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.72687e6 | 0.396391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.88611e7 | −1.29660 | −0.648302 | − | 0.761384i | \(-0.724520\pi\) | ||||
−0.648302 | + | 0.761384i | \(0.724520\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −139431. | −0.00952008 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.27828e7 | −0.866877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.73270e6 | −0.184069 | −0.0920346 | − | 0.995756i | \(-0.529337\pi\) | ||||
−0.0920346 | + | 0.995756i | \(0.529337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 284749. | 0.0190510 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −108079. | −0.00718239 | −0.00359119 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359119 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.69433e7 | −1.11843 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.79574e6 | −0.314452 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.46081e6 | −0.355675 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.41662e7 | −0.916543 | −0.458272 | − | 0.888812i | \(-0.651531\pi\) | ||||
−0.458272 | + | 0.888812i | \(0.651531\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −107475. | −0.00690747 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.01379e7 | 1.28572 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.35016e6 | −0.0856339 | −0.0428169 | − | 0.999083i | \(-0.513633\pi\) | ||||
−0.0428169 | + | 0.999083i | \(0.513633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 58595.6 | 0.00369199 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.16646e7 | 0.730146 | 0.365073 | − | 0.930979i | \(-0.381044\pi\) | ||||
0.365073 | + | 0.930979i | \(0.381044\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00412e6 | 0.497740 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.27172e6 | 0.449245 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.09498e6 | −0.312719 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.99473e7 | 1.21638 | 0.608188 | − | 0.793793i | \(-0.291897\pi\) | ||||
0.608188 | + | 0.793793i | \(0.291897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 525804. | 0.0318558 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.52976e7 | 0.920818 | 0.460409 | − | 0.887707i | \(-0.347703\pi\) | ||||
0.460409 | + | 0.887707i | \(0.347703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.03163e6 | 0.480340 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 152986. | 0.00909076 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.26096e7 | 0.744490 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.13605e7 | 1.83974 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 909348. | 0.0530061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.45834e7 | 1.42386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.34094e7 | −1.92279 | −0.961394 | − | 0.275176i | \(-0.911264\pi\) | ||||
−0.961394 | + | 0.275176i | \(0.911264\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −453367. | −0.0259273 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.85568e6 | −0.503246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −523726. | −0.0295747 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.17189e6 | −0.121877 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.12154e7 | −1.74070 | −0.870349 | − | 0.492436i | \(-0.836107\pi\) | ||||
−0.870349 | + | 0.492436i | \(0.836107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.15653e7 | 0.640898 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.52397e7 | −1.38996 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.94258e7 | 2.15770 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 446140. | 0.0242651 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −906600. | −0.0490041 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.90944e6 | 0.424888 | 0.212444 | − | 0.977173i | \(-0.431858\pi\) | ||||
0.212444 | + | 0.977173i | \(0.431858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.94124e6 | 0.263805 | 0.131903 | − | 0.991263i | \(-0.457891\pi\) | ||||
0.131903 | + | 0.991263i | \(0.457891\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.50087e6 | −0.0796371 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.52468e7 | 2.38613 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.49110e7 | 1.82982 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.63519e6 | −0.0851841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.08881e6 | 0.211709 | 0.105855 | − | 0.994382i | \(-0.466242\pi\) | ||||
0.105855 | + | 0.994382i | \(0.466242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.11809e6 | −0.469250 | −0.234625 | − | 0.972086i | \(-0.575386\pi\) | ||||
−0.234625 | + | 0.972086i | \(0.575386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 927965. | 0.0474675 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.21913e6 | 0.417890 | 0.208945 | − | 0.977927i | \(-0.432997\pi\) | ||||
0.208945 | + | 0.977927i | \(0.432997\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.40529e7 | −1.21557 | −0.607787 | − | 0.794100i | \(-0.707943\pi\) | ||||
−0.607787 | + | 0.794100i | \(0.707943\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 122338. | 0.00614555 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.00519e6 | −0.0501923 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.24809e7 | −0.619482 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.56992e6 | 0.0774577 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.55100e6 | 0.223204 | 0.111602 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111602 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.51640e7 | −0.739304 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 533382. | 0.0258505 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.52522e7 | −1.21663 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.98793e6 | 0.382583 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.52477e6 | 0.0725998 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −489513. | −0.0231708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.92326e7 | −0.905033 | −0.452517 | − | 0.891756i | \(-0.649474\pi\) | ||||
−0.452517 | + | 0.891756i | \(0.649474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.43284e7 | 2.07380 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.44005e7 | −1.13487 | −0.567435 | − | 0.823418i | \(-0.692064\pi\) | ||||
−0.567435 | + | 0.823418i | \(0.692064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.80489e7 | −0.834581 | −0.417291 | − | 0.908773i | \(-0.637020\pi\) | ||||
−0.417291 | + | 0.908773i | \(0.637020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 196162. | 0.00901792 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.08506e7 | 0.952999 | 0.476499 | − | 0.879175i | \(-0.341905\pi\) | ||||
0.476499 | + | 0.879175i | \(0.341905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.79152e7 | −1.26853 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00842e6 | 0.0455612 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.33047e7 | 1.04687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.09206e6 | 0.138103 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.34224e7 | 1.04015 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.90933e6 | −0.172616 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.18628e7 | 0.520819 | 0.260409 | − | 0.965498i | \(-0.416142\pi\) | ||||
0.260409 | + | 0.965498i | \(0.416142\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −849628. | −0.0370900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.67453e7 | −0.726866 | −0.363433 | − | 0.931620i | \(-0.618395\pi\) | ||||
−0.363433 | + | 0.931620i | \(0.618395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.53639e6 | 0.152637 | 0.0763183 | − | 0.997084i | \(-0.475683\pi\) | ||||
0.0763183 | + | 0.997084i | \(0.475683\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.14866e6 | 0.0922169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.80164e7 | 1.62242 | 0.811208 | − | 0.584758i | \(-0.198811\pi\) | ||||
0.811208 | + | 0.584758i | \(0.198811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.95787e6 | −0.252835 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.33427e7 | −1.40704 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.05019e7 | 2.95850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.92950e7 | 2.47435 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14173.8 | −0.000588174 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.23150e6 | 0.380955 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.56577e7 | −0.642565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 543094. | 0.0221644 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.79788e7 | 0.729693 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.50380e7 | −1.01060 | −0.505302 | − | 0.862943i | \(-0.668619\pi\) | ||||
−0.505302 | + | 0.862943i | \(0.668619\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.45510e6 | −0.259115 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.36962e7 | −0.945982 | −0.472991 | − | 0.881067i | \(-0.656826\pi\) | ||||
−0.472991 | + | 0.881067i | \(0.656826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.12653e7 | −0.447266 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 220866. | 0.00872122 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.86591e6 | 0.230363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.73462e7 | 1.06809 | 0.534044 | − | 0.845456i | \(-0.320671\pi\) | ||||
0.534044 | + | 0.845456i | \(0.320671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.71437e6 | 0.0665972 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.58586e6 | −0.293090 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.75231e6 | −0.297904 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.50816e7 | −0.576434 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.14288e7 | 1.19478 | 0.597390 | − | 0.801951i | \(-0.296204\pi\) | ||||
0.597390 | + | 0.801951i | \(0.296204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.12767e6 | −0.231697 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.28771e6 | 0.0484300 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.70815e7 | 0.638993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.07773e7 | −1.51729 | −0.758646 | − | 0.651503i | \(-0.774139\pi\) | ||||
−0.758646 | + | 0.651503i | \(0.774139\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −122213. | −0.00452327 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.38493e7 | 0.509863 | 0.254931 | − | 0.966959i | \(-0.417947\pi\) | ||||
0.254931 | + | 0.966959i | \(0.417947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −627662. | −0.0229851 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.38106e6 | 0.0503075 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.45927e7 | 0.528762 | 0.264381 | − | 0.964418i | \(-0.414832\pi\) | ||||
0.264381 | + | 0.964418i | \(0.414832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.53679e6 | −0.343745 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13918.5 | 0.000499048 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.78156e7 | 0.992100 | 0.496050 | − | 0.868294i | \(-0.334783\pi\) | ||||
0.496050 | + | 0.868294i | \(0.334783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.19265e7 | −0.423161 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.06660e6 | 0.0376462 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −233622. | −0.00820290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.26916e7 | −0.443312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.70080e7 | 0.938484 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.92615e7 | −1.01153 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.97734e7 | −1.02391 | −0.511956 | − | 0.859012i | \(-0.671079\pi\) | ||||
−0.511956 | + | 0.859012i | \(0.671079\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −865725. | −0.0296190 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00707e7 | −1.36389 | −0.681944 | − | 0.731404i | \(-0.738865\pi\) | ||||
−0.681944 | + | 0.731404i | \(0.738865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.50055e6 | 0.287849 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −224467. | −0.00756209 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.66964e7 | −1.22995 | −0.614974 | − | 0.788547i | \(-0.710834\pi\) | ||||
−0.614974 | + | 0.788547i | \(0.710834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.92888e7 | −1.97704 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.95867e7 | −1.31334 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.14382e7 | −0.377550 | −0.188775 | − | 0.982020i | \(-0.560452\pi\) | ||||
−0.188775 | + | 0.982020i | \(0.560452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.41818e7 | 2.10776 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09676e6 | 0.0358360 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.73775e6 | −0.0564932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.22413e7 | 1.04286 | 0.521432 | − | 0.853293i | \(-0.325398\pi\) | ||||
0.521432 | + | 0.853293i | \(0.325398\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00483e6 | 0.0645213 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.27209e7 | −0.407343 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.17997e7 | 0.694566 | 0.347283 | − | 0.937760i | \(-0.387104\pi\) | ||||
0.347283 | + | 0.937760i | \(0.387104\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.51533e6 | −0.0480388 |
(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 | 224.6.a.d.1.1 | yes | 2 | |
4.3 | odd | 2 | 224.6.a.c.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 448.6.a.y.1.1 | 2 | |||
8.5 | even | 2 | 448.6.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.c.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
224.6.a.d.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
448.6.a.s.1.2 | 2 | 8.5 | even | 2 | |||
448.6.a.y.1.1 | 2 | 8.3 | odd | 2 |