Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,4,Mod(1,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.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: | \(2.06506685020\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 35.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.353553 | 0.176777 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176777 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(3\) | −8.00000 | −1.53960 | −0.769800 | − | 0.638285i | \(-0.779644\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −8.00000 | −0.544331 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −15.0000 | −0.662913 | ||||||||
\(9\) | 37.0000 | 1.37037 | ||||||||
\(10\) | −5.00000 | −0.158114 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 56.0000 | 1.34715 | ||||||||
\(13\) | −78.0000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 7.00000 | 0.133631 | ||||||||
\(15\) | 40.0000 | 0.688530 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | −94.0000 | −1.34108 | −0.670540 | − | 0.741874i | \(-0.733937\pi\) | ||||
−0.670540 | + | 0.741874i | \(0.733937\pi\) | |||||||
\(18\) | 37.0000 | 0.484499 | ||||||||
\(19\) | 40.0000 | 0.482980 | 0.241490 | − | 0.970403i | \(-0.422364\pi\) | ||||
0.241490 | + | 0.970403i | \(0.422364\pi\) | |||||||
\(20\) | 35.0000 | 0.391312 | ||||||||
\(21\) | −56.0000 | −0.581914 | ||||||||
\(22\) | 12.0000 | 0.116291 | ||||||||
\(23\) | 32.0000 | 0.290107 | 0.145054 | − | 0.989424i | \(-0.453665\pi\) | ||||
0.145054 | + | 0.989424i | \(0.453665\pi\) | |||||||
\(24\) | 120.000 | 1.02062 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −78.0000 | −0.588348 | ||||||||
\(27\) | −80.0000 | −0.570222 | ||||||||
\(28\) | −49.0000 | −0.330719 | ||||||||
\(29\) | −50.0000 | −0.320164 | −0.160082 | − | 0.987104i | \(-0.551176\pi\) | ||||
−0.160082 | + | 0.987104i | \(0.551176\pi\) | |||||||
\(30\) | 40.0000 | 0.243432 | ||||||||
\(31\) | −248.000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 161.000 | 0.889408 | ||||||||
\(33\) | −96.0000 | −0.506408 | ||||||||
\(34\) | −94.0000 | −0.474143 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | −259.000 | −1.19907 | ||||||||
\(37\) | −434.000 | −1.92836 | −0.964178 | − | 0.265257i | \(-0.914543\pi\) | ||||
−0.964178 | + | 0.265257i | \(0.914543\pi\) | |||||||
\(38\) | 40.0000 | 0.170759 | ||||||||
\(39\) | 624.000 | 2.56205 | ||||||||
\(40\) | 75.0000 | 0.296464 | ||||||||
\(41\) | 402.000 | 1.53126 | 0.765632 | − | 0.643278i | \(-0.222426\pi\) | ||||
0.765632 | + | 0.643278i | \(0.222426\pi\) | |||||||
\(42\) | −56.0000 | −0.205738 | ||||||||
\(43\) | −68.0000 | −0.241161 | −0.120580 | − | 0.992704i | \(-0.538476\pi\) | ||||
−0.120580 | + | 0.992704i | \(0.538476\pi\) | |||||||
\(44\) | −84.0000 | −0.287806 | ||||||||
\(45\) | −185.000 | −0.612848 | ||||||||
\(46\) | 32.0000 | 0.102568 | ||||||||
\(47\) | 536.000 | 1.66348 | 0.831741 | − | 0.555164i | \(-0.187345\pi\) | ||||
0.831741 | + | 0.555164i | \(0.187345\pi\) | |||||||
\(48\) | −328.000 | −0.986307 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 25.0000 | 0.0707107 | ||||||||
\(51\) | 752.000 | 2.06473 | ||||||||
\(52\) | 546.000 | 1.45609 | ||||||||
\(53\) | 22.0000 | 0.0570176 | 0.0285088 | − | 0.999594i | \(-0.490924\pi\) | ||||
0.0285088 | + | 0.999594i | \(0.490924\pi\) | |||||||
\(54\) | −80.0000 | −0.201604 | ||||||||
\(55\) | −60.0000 | −0.147098 | ||||||||
\(56\) | −105.000 | −0.250557 | ||||||||
\(57\) | −320.000 | −0.743597 | ||||||||
\(58\) | −50.0000 | −0.113195 | ||||||||
\(59\) | −560.000 | −1.23569 | −0.617846 | − | 0.786299i | \(-0.711994\pi\) | ||||
−0.617846 | + | 0.786299i | \(0.711994\pi\) | |||||||
\(60\) | −280.000 | −0.602464 | ||||||||
\(61\) | −278.000 | −0.583512 | −0.291756 | − | 0.956493i | \(-0.594240\pi\) | ||||
−0.291756 | + | 0.956493i | \(0.594240\pi\) | |||||||
\(62\) | −248.000 | −0.508001 | ||||||||
\(63\) | 259.000 | 0.517951 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 390.000 | 0.744208 | ||||||||
\(66\) | −96.0000 | −0.179042 | ||||||||
\(67\) | −164.000 | −0.299042 | −0.149521 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149521 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(68\) | 658.000 | 1.17344 | ||||||||
\(69\) | −256.000 | −0.446649 | ||||||||
\(70\) | −35.0000 | −0.0597614 | ||||||||
\(71\) | 672.000 | 1.12326 | 0.561632 | − | 0.827387i | \(-0.310174\pi\) | ||||
0.561632 | + | 0.827387i | \(0.310174\pi\) | |||||||
\(72\) | −555.000 | −0.908436 | ||||||||
\(73\) | 82.0000 | 0.131471 | 0.0657354 | − | 0.997837i | \(-0.479061\pi\) | ||||
0.0657354 | + | 0.997837i | \(0.479061\pi\) | |||||||
\(74\) | −434.000 | −0.681777 | ||||||||
\(75\) | −200.000 | −0.307920 | ||||||||
\(76\) | −280.000 | −0.422608 | ||||||||
\(77\) | 84.0000 | 0.124321 | ||||||||
\(78\) | 624.000 | 0.905822 | ||||||||
\(79\) | −1000.00 | −1.42416 | −0.712081 | − | 0.702097i | \(-0.752247\pi\) | ||||
−0.712081 | + | 0.702097i | \(0.752247\pi\) | |||||||
\(80\) | −205.000 | −0.286496 | ||||||||
\(81\) | −359.000 | −0.492455 | ||||||||
\(82\) | 402.000 | 0.541384 | ||||||||
\(83\) | −448.000 | −0.592463 | −0.296231 | − | 0.955116i | \(-0.595730\pi\) | ||||
−0.296231 | + | 0.955116i | \(0.595730\pi\) | |||||||
\(84\) | 392.000 | 0.509175 | ||||||||
\(85\) | 470.000 | 0.599749 | ||||||||
\(86\) | −68.0000 | −0.0852631 | ||||||||
\(87\) | 400.000 | 0.492925 | ||||||||
\(88\) | −180.000 | −0.218046 | ||||||||
\(89\) | −870.000 | −1.03618 | −0.518089 | − | 0.855327i | \(-0.673356\pi\) | ||||
−0.518089 | + | 0.855327i | \(0.673356\pi\) | |||||||
\(90\) | −185.000 | −0.216675 | ||||||||
\(91\) | −546.000 | −0.628971 | ||||||||
\(92\) | −224.000 | −0.253844 | ||||||||
\(93\) | 1984.00 | 2.21216 | ||||||||
\(94\) | 536.000 | 0.588130 | ||||||||
\(95\) | −200.000 | −0.215995 | ||||||||
\(96\) | −1288.00 | −1.36933 | ||||||||
\(97\) | 1026.00 | 1.07396 | 0.536982 | − | 0.843594i | \(-0.319564\pi\) | ||||
0.536982 | + | 0.843594i | \(0.319564\pi\) | |||||||
\(98\) | 49.0000 | 0.0505076 | ||||||||
\(99\) | 444.000 | 0.450744 | ||||||||
\(100\) | −175.000 | −0.175000 | ||||||||
\(101\) | 482.000 | 0.474859 | 0.237430 | − | 0.971405i | \(-0.423695\pi\) | ||||
0.237430 | + | 0.971405i | \(0.423695\pi\) | |||||||
\(102\) | 752.000 | 0.729991 | ||||||||
\(103\) | 272.000 | 0.260203 | 0.130102 | − | 0.991501i | \(-0.458470\pi\) | ||||
0.130102 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(104\) | 1170.00 | 1.10315 | ||||||||
\(105\) | 280.000 | 0.260240 | ||||||||
\(106\) | 22.0000 | 0.0201588 | ||||||||
\(107\) | −444.000 | −0.401150 | −0.200575 | − | 0.979678i | \(-0.564281\pi\) | ||||
−0.200575 | + | 0.979678i | \(0.564281\pi\) | |||||||
\(108\) | 560.000 | 0.498945 | ||||||||
\(109\) | −1170.00 | −1.02813 | −0.514063 | − | 0.857753i | \(-0.671860\pi\) | ||||
−0.514063 | + | 0.857753i | \(0.671860\pi\) | |||||||
\(110\) | −60.0000 | −0.0520071 | ||||||||
\(111\) | 3472.00 | 2.96890 | ||||||||
\(112\) | 287.000 | 0.242133 | ||||||||
\(113\) | −798.000 | −0.664332 | −0.332166 | − | 0.943221i | \(-0.607779\pi\) | ||||
−0.332166 | + | 0.943221i | \(0.607779\pi\) | |||||||
\(114\) | −320.000 | −0.262901 | ||||||||
\(115\) | −160.000 | −0.129740 | ||||||||
\(116\) | 350.000 | 0.280144 | ||||||||
\(117\) | −2886.00 | −2.28043 | ||||||||
\(118\) | −560.000 | −0.436883 | ||||||||
\(119\) | −658.000 | −0.506880 | ||||||||
\(120\) | −600.000 | −0.456435 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | −278.000 | −0.206303 | ||||||||
\(123\) | −3216.00 | −2.35754 | ||||||||
\(124\) | 1736.00 | 1.25724 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 259.000 | 0.183123 | ||||||||
\(127\) | 776.000 | 0.542196 | 0.271098 | − | 0.962552i | \(-0.412613\pi\) | ||||
0.271098 | + | 0.962552i | \(0.412613\pi\) | |||||||
\(128\) | −1455.00 | −1.00473 | ||||||||
\(129\) | 544.000 | 0.371291 | ||||||||
\(130\) | 390.000 | 0.263117 | ||||||||
\(131\) | 1112.00 | 0.741648 | 0.370824 | − | 0.928703i | \(-0.379075\pi\) | ||||
0.370824 | + | 0.928703i | \(0.379075\pi\) | |||||||
\(132\) | 672.000 | 0.443107 | ||||||||
\(133\) | 280.000 | 0.182549 | ||||||||
\(134\) | −164.000 | −0.105727 | ||||||||
\(135\) | 400.000 | 0.255011 | ||||||||
\(136\) | 1410.00 | 0.889018 | ||||||||
\(137\) | −694.000 | −0.432791 | −0.216396 | − | 0.976306i | \(-0.569430\pi\) | ||||
−0.216396 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(138\) | −256.000 | −0.157914 | ||||||||
\(139\) | 360.000 | 0.219675 | 0.109837 | − | 0.993950i | \(-0.464967\pi\) | ||||
0.109837 | + | 0.993950i | \(0.464967\pi\) | |||||||
\(140\) | 245.000 | 0.147902 | ||||||||
\(141\) | −4288.00 | −2.56110 | ||||||||
\(142\) | 672.000 | 0.397134 | ||||||||
\(143\) | −936.000 | −0.547358 | ||||||||
\(144\) | 1517.00 | 0.877894 | ||||||||
\(145\) | 250.000 | 0.143182 | ||||||||
\(146\) | 82.0000 | 0.0464820 | ||||||||
\(147\) | −392.000 | −0.219943 | ||||||||
\(148\) | 3038.00 | 1.68731 | ||||||||
\(149\) | 2270.00 | 1.24809 | 0.624046 | − | 0.781388i | \(-0.285488\pi\) | ||||
0.624046 | + | 0.781388i | \(0.285488\pi\) | |||||||
\(150\) | −200.000 | −0.108866 | ||||||||
\(151\) | 632.000 | 0.340606 | 0.170303 | − | 0.985392i | \(-0.445525\pi\) | ||||
0.170303 | + | 0.985392i | \(0.445525\pi\) | |||||||
\(152\) | −600.000 | −0.320174 | ||||||||
\(153\) | −3478.00 | −1.83778 | ||||||||
\(154\) | 84.0000 | 0.0439540 | ||||||||
\(155\) | 1240.00 | 0.642575 | ||||||||
\(156\) | −4368.00 | −2.24179 | ||||||||
\(157\) | −734.000 | −0.373118 | −0.186559 | − | 0.982444i | \(-0.559734\pi\) | ||||
−0.186559 | + | 0.982444i | \(0.559734\pi\) | |||||||
\(158\) | −1000.00 | −0.503517 | ||||||||
\(159\) | −176.000 | −0.0877843 | ||||||||
\(160\) | −805.000 | −0.397755 | ||||||||
\(161\) | 224.000 | 0.109650 | ||||||||
\(162\) | −359.000 | −0.174109 | ||||||||
\(163\) | 2532.00 | 1.21670 | 0.608348 | − | 0.793670i | \(-0.291832\pi\) | ||||
0.608348 | + | 0.793670i | \(0.291832\pi\) | |||||||
\(164\) | −2814.00 | −1.33986 | ||||||||
\(165\) | 480.000 | 0.226472 | ||||||||
\(166\) | −448.000 | −0.209467 | ||||||||
\(167\) | 416.000 | 0.192761 | 0.0963804 | − | 0.995345i | \(-0.469273\pi\) | ||||
0.0963804 | + | 0.995345i | \(0.469273\pi\) | |||||||
\(168\) | 840.000 | 0.385758 | ||||||||
\(169\) | 3887.00 | 1.76923 | ||||||||
\(170\) | 470.000 | 0.212043 | ||||||||
\(171\) | 1480.00 | 0.661862 | ||||||||
\(172\) | 476.000 | 0.211015 | ||||||||
\(173\) | 3042.00 | 1.33687 | 0.668436 | − | 0.743769i | \(-0.266964\pi\) | ||||
0.668436 | + | 0.743769i | \(0.266964\pi\) | |||||||
\(174\) | 400.000 | 0.174275 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 492.000 | 0.210715 | ||||||||
\(177\) | 4480.00 | 1.90247 | ||||||||
\(178\) | −870.000 | −0.366344 | ||||||||
\(179\) | −180.000 | −0.0751611 | −0.0375805 | − | 0.999294i | \(-0.511965\pi\) | ||||
−0.0375805 | + | 0.999294i | \(0.511965\pi\) | |||||||
\(180\) | 1295.00 | 0.536242 | ||||||||
\(181\) | −1958.00 | −0.804072 | −0.402036 | − | 0.915624i | \(-0.631697\pi\) | ||||
−0.402036 | + | 0.915624i | \(0.631697\pi\) | |||||||
\(182\) | −546.000 | −0.222375 | ||||||||
\(183\) | 2224.00 | 0.898376 | ||||||||
\(184\) | −480.000 | −0.192316 | ||||||||
\(185\) | 2170.00 | 0.862387 | ||||||||
\(186\) | 1984.00 | 0.782118 | ||||||||
\(187\) | −1128.00 | −0.441110 | ||||||||
\(188\) | −3752.00 | −1.45555 | ||||||||
\(189\) | −560.000 | −0.215524 | ||||||||
\(190\) | −200.000 | −0.0763659 | ||||||||
\(191\) | −2888.00 | −1.09408 | −0.547038 | − | 0.837108i | \(-0.684245\pi\) | ||||
−0.547038 | + | 0.837108i | \(0.684245\pi\) | |||||||
\(192\) | 1336.00 | 0.502174 | ||||||||
\(193\) | 1602.00 | 0.597484 | 0.298742 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298742 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(194\) | 1026.00 | 0.379704 | ||||||||
\(195\) | −3120.00 | −1.14578 | ||||||||
\(196\) | −343.000 | −0.125000 | ||||||||
\(197\) | −4794.00 | −1.73380 | −0.866899 | − | 0.498483i | \(-0.833891\pi\) | ||||
−0.866899 | + | 0.498483i | \(0.833891\pi\) | |||||||
\(198\) | 444.000 | 0.159362 | ||||||||
\(199\) | 1280.00 | 0.455964 | 0.227982 | − | 0.973665i | \(-0.426787\pi\) | ||||
0.227982 | + | 0.973665i | \(0.426787\pi\) | |||||||
\(200\) | −375.000 | −0.132583 | ||||||||
\(201\) | 1312.00 | 0.460405 | ||||||||
\(202\) | 482.000 | 0.167888 | ||||||||
\(203\) | −350.000 | −0.121011 | ||||||||
\(204\) | −5264.00 | −1.80664 | ||||||||
\(205\) | −2010.00 | −0.684802 | ||||||||
\(206\) | 272.000 | 0.0919958 | ||||||||
\(207\) | 1184.00 | 0.397554 | ||||||||
\(208\) | −3198.00 | −1.06606 | ||||||||
\(209\) | 480.000 | 0.158863 | ||||||||
\(210\) | 280.000 | 0.0920087 | ||||||||
\(211\) | −68.0000 | −0.0221863 | −0.0110932 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110932 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(212\) | −154.000 | −0.0498904 | ||||||||
\(213\) | −5376.00 | −1.72938 | ||||||||
\(214\) | −444.000 | −0.141828 | ||||||||
\(215\) | 340.000 | 0.107850 | ||||||||
\(216\) | 1200.00 | 0.378008 | ||||||||
\(217\) | −1736.00 | −0.543075 | ||||||||
\(218\) | −1170.00 | −0.363497 | ||||||||
\(219\) | −656.000 | −0.202413 | ||||||||
\(220\) | 420.000 | 0.128711 | ||||||||
\(221\) | 7332.00 | 2.23169 | ||||||||
\(222\) | 3472.00 | 1.04966 | ||||||||
\(223\) | −1728.00 | −0.518903 | −0.259452 | − | 0.965756i | \(-0.583542\pi\) | ||||
−0.259452 | + | 0.965756i | \(0.583542\pi\) | |||||||
\(224\) | 1127.00 | 0.336165 | ||||||||
\(225\) | 925.000 | 0.274074 | ||||||||
\(226\) | −798.000 | −0.234877 | ||||||||
\(227\) | −4864.00 | −1.42218 | −0.711090 | − | 0.703101i | \(-0.751798\pi\) | ||||
−0.711090 | + | 0.703101i | \(0.751798\pi\) | |||||||
\(228\) | 2240.00 | 0.650647 | ||||||||
\(229\) | −5510.00 | −1.59000 | −0.795002 | − | 0.606606i | \(-0.792530\pi\) | ||||
−0.795002 | + | 0.606606i | \(0.792530\pi\) | |||||||
\(230\) | −160.000 | −0.0458699 | ||||||||
\(231\) | −672.000 | −0.191404 | ||||||||
\(232\) | 750.000 | 0.212241 | ||||||||
\(233\) | 5322.00 | 1.49638 | 0.748188 | − | 0.663486i | \(-0.230924\pi\) | ||||
0.748188 | + | 0.663486i | \(0.230924\pi\) | |||||||
\(234\) | −2886.00 | −0.806255 | ||||||||
\(235\) | −2680.00 | −0.743932 | ||||||||
\(236\) | 3920.00 | 1.08123 | ||||||||
\(237\) | 8000.00 | 2.19264 | ||||||||
\(238\) | −658.000 | −0.179209 | ||||||||
\(239\) | −1840.00 | −0.497990 | −0.248995 | − | 0.968505i | \(-0.580100\pi\) | ||||
−0.248995 | + | 0.968505i | \(0.580100\pi\) | |||||||
\(240\) | 1640.00 | 0.441090 | ||||||||
\(241\) | −438.000 | −0.117071 | −0.0585354 | − | 0.998285i | \(-0.518643\pi\) | ||||
−0.0585354 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(242\) | −1187.00 | −0.315303 | ||||||||
\(243\) | 5032.00 | 1.32841 | ||||||||
\(244\) | 1946.00 | 0.510573 | ||||||||
\(245\) | −245.000 | −0.0638877 | ||||||||
\(246\) | −3216.00 | −0.833515 | ||||||||
\(247\) | −3120.00 | −0.803728 | ||||||||
\(248\) | 3720.00 | 0.952501 | ||||||||
\(249\) | 3584.00 | 0.912156 | ||||||||
\(250\) | −125.000 | −0.0316228 | ||||||||
\(251\) | 5592.00 | 1.40623 | 0.703115 | − | 0.711076i | \(-0.251792\pi\) | ||||
0.703115 | + | 0.711076i | \(0.251792\pi\) | |||||||
\(252\) | −1813.00 | −0.453207 | ||||||||
\(253\) | 384.000 | 0.0954224 | ||||||||
\(254\) | 776.000 | 0.191695 | ||||||||
\(255\) | −3760.00 | −0.923374 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | −1974.00 | −0.479123 | −0.239562 | − | 0.970881i | \(-0.577004\pi\) | ||||
−0.239562 | + | 0.970881i | \(0.577004\pi\) | |||||||
\(258\) | 544.000 | 0.131271 | ||||||||
\(259\) | −3038.00 | −0.728850 | ||||||||
\(260\) | −2730.00 | −0.651182 | ||||||||
\(261\) | −1850.00 | −0.438744 | ||||||||
\(262\) | 1112.00 | 0.262212 | ||||||||
\(263\) | −728.000 | −0.170686 | −0.0853430 | − | 0.996352i | \(-0.527199\pi\) | ||||
−0.0853430 | + | 0.996352i | \(0.527199\pi\) | |||||||
\(264\) | 1440.00 | 0.335704 | ||||||||
\(265\) | −110.000 | −0.0254990 | ||||||||
\(266\) | 280.000 | 0.0645410 | ||||||||
\(267\) | 6960.00 | 1.59530 | ||||||||
\(268\) | 1148.00 | 0.261661 | ||||||||
\(269\) | 5810.00 | 1.31688 | 0.658442 | − | 0.752631i | \(-0.271216\pi\) | ||||
0.658442 | + | 0.752631i | \(0.271216\pi\) | |||||||
\(270\) | 400.000 | 0.0901601 | ||||||||
\(271\) | −6528.00 | −1.46328 | −0.731638 | − | 0.681693i | \(-0.761244\pi\) | ||||
−0.731638 | + | 0.681693i | \(0.761244\pi\) | |||||||
\(272\) | −3854.00 | −0.859129 | ||||||||
\(273\) | 4368.00 | 0.968364 | ||||||||
\(274\) | −694.000 | −0.153015 | ||||||||
\(275\) | 300.000 | 0.0657843 | ||||||||
\(276\) | 1792.00 | 0.390818 | ||||||||
\(277\) | 5126.00 | 1.11188 | 0.555941 | − | 0.831222i | \(-0.312358\pi\) | ||||
0.555941 | + | 0.831222i | \(0.312358\pi\) | |||||||
\(278\) | 360.000 | 0.0776668 | ||||||||
\(279\) | −9176.00 | −1.96901 | ||||||||
\(280\) | 525.000 | 0.112053 | ||||||||
\(281\) | −2358.00 | −0.500592 | −0.250296 | − | 0.968169i | \(-0.580528\pi\) | ||||
−0.250296 | + | 0.968169i | \(0.580528\pi\) | |||||||
\(282\) | −4288.00 | −0.905485 | ||||||||
\(283\) | 392.000 | 0.0823392 | 0.0411696 | − | 0.999152i | \(-0.486892\pi\) | ||||
0.0411696 | + | 0.999152i | \(0.486892\pi\) | |||||||
\(284\) | −4704.00 | −0.982856 | ||||||||
\(285\) | 1600.00 | 0.332547 | ||||||||
\(286\) | −936.000 | −0.193520 | ||||||||
\(287\) | 2814.00 | 0.578764 | ||||||||
\(288\) | 5957.00 | 1.21882 | ||||||||
\(289\) | 3923.00 | 0.798494 | ||||||||
\(290\) | 250.000 | 0.0506224 | ||||||||
\(291\) | −8208.00 | −1.65348 | ||||||||
\(292\) | −574.000 | −0.115037 | ||||||||
\(293\) | 1202.00 | 0.239664 | 0.119832 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119832 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(294\) | −392.000 | −0.0777616 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | 6510.00 | 1.27833 | ||||||||
\(297\) | −960.000 | −0.187558 | ||||||||
\(298\) | 2270.00 | 0.441267 | ||||||||
\(299\) | −2496.00 | −0.482767 | ||||||||
\(300\) | 1400.00 | 0.269430 | ||||||||
\(301\) | −476.000 | −0.0911501 | ||||||||
\(302\) | 632.000 | 0.120422 | ||||||||
\(303\) | −3856.00 | −0.731094 | ||||||||
\(304\) | 1640.00 | 0.309409 | ||||||||
\(305\) | 1390.00 | 0.260955 | ||||||||
\(306\) | −3478.00 | −0.649752 | ||||||||
\(307\) | −6384.00 | −1.18682 | −0.593411 | − | 0.804900i | \(-0.702219\pi\) | ||||
−0.593411 | + | 0.804900i | \(0.702219\pi\) | |||||||
\(308\) | −588.000 | −0.108781 | ||||||||
\(309\) | −2176.00 | −0.400609 | ||||||||
\(310\) | 1240.00 | 0.227185 | ||||||||
\(311\) | −4968.00 | −0.905818 | −0.452909 | − | 0.891557i | \(-0.649614\pi\) | ||||
−0.452909 | + | 0.891557i | \(0.649614\pi\) | |||||||
\(312\) | −9360.00 | −1.69842 | ||||||||
\(313\) | −2758.00 | −0.498056 | −0.249028 | − | 0.968496i | \(-0.580111\pi\) | ||||
−0.249028 | + | 0.968496i | \(0.580111\pi\) | |||||||
\(314\) | −734.000 | −0.131917 | ||||||||
\(315\) | −1295.00 | −0.231635 | ||||||||
\(316\) | 7000.00 | 1.24614 | ||||||||
\(317\) | −6274.00 | −1.11162 | −0.555809 | − | 0.831310i | \(-0.687591\pi\) | ||||
−0.555809 | + | 0.831310i | \(0.687591\pi\) | |||||||
\(318\) | −176.000 | −0.0310364 | ||||||||
\(319\) | −600.000 | −0.105309 | ||||||||
\(320\) | 835.000 | 0.145868 | ||||||||
\(321\) | 3552.00 | 0.617612 | ||||||||
\(322\) | 224.000 | 0.0387672 | ||||||||
\(323\) | −3760.00 | −0.647715 | ||||||||
\(324\) | 2513.00 | 0.430898 | ||||||||
\(325\) | −1950.00 | −0.332820 | ||||||||
\(326\) | 2532.00 | 0.430167 | ||||||||
\(327\) | 9360.00 | 1.58290 | ||||||||
\(328\) | −6030.00 | −1.01509 | ||||||||
\(329\) | 3752.00 | 0.628737 | ||||||||
\(330\) | 480.000 | 0.0800701 | ||||||||
\(331\) | 1932.00 | 0.320823 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(332\) | 3136.00 | 0.518405 | ||||||||
\(333\) | −16058.0 | −2.64256 | ||||||||
\(334\) | 416.000 | 0.0681512 | ||||||||
\(335\) | 820.000 | 0.133735 | ||||||||
\(336\) | −2296.00 | −0.372789 | ||||||||
\(337\) | 2386.00 | 0.385679 | 0.192839 | − | 0.981230i | \(-0.438230\pi\) | ||||
0.192839 | + | 0.981230i | \(0.438230\pi\) | |||||||
\(338\) | 3887.00 | 0.625518 | ||||||||
\(339\) | 6384.00 | 1.02281 | ||||||||
\(340\) | −3290.00 | −0.524780 | ||||||||
\(341\) | −2976.00 | −0.472608 | ||||||||
\(342\) | 1480.00 | 0.234004 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 1020.00 | 0.159868 | ||||||||
\(345\) | 1280.00 | 0.199747 | ||||||||
\(346\) | 3042.00 | 0.472656 | ||||||||
\(347\) | 6076.00 | 0.939991 | 0.469995 | − | 0.882669i | \(-0.344256\pi\) | ||||
0.469995 | + | 0.882669i | \(0.344256\pi\) | |||||||
\(348\) | −2800.00 | −0.431310 | ||||||||
\(349\) | 2210.00 | 0.338964 | 0.169482 | − | 0.985533i | \(-0.445790\pi\) | ||||
0.169482 | + | 0.985533i | \(0.445790\pi\) | |||||||
\(350\) | 175.000 | 0.0267261 | ||||||||
\(351\) | 6240.00 | 0.948908 | ||||||||
\(352\) | 1932.00 | 0.292545 | ||||||||
\(353\) | −2598.00 | −0.391721 | −0.195861 | − | 0.980632i | \(-0.562750\pi\) | ||||
−0.195861 | + | 0.980632i | \(0.562750\pi\) | |||||||
\(354\) | 4480.00 | 0.672625 | ||||||||
\(355\) | −3360.00 | −0.502339 | ||||||||
\(356\) | 6090.00 | 0.906655 | ||||||||
\(357\) | 5264.00 | 0.780393 | ||||||||
\(358\) | −180.000 | −0.0265735 | ||||||||
\(359\) | −13320.0 | −1.95822 | −0.979112 | − | 0.203320i | \(-0.934827\pi\) | ||||
−0.979112 | + | 0.203320i | \(0.934827\pi\) | |||||||
\(360\) | 2775.00 | 0.406265 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | −1958.00 | −0.284282 | ||||||||
\(363\) | 9496.00 | 1.37303 | ||||||||
\(364\) | 3822.00 | 0.550350 | ||||||||
\(365\) | −410.000 | −0.0587956 | ||||||||
\(366\) | 2224.00 | 0.317624 | ||||||||
\(367\) | 10816.0 | 1.53839 | 0.769197 | − | 0.639012i | \(-0.220656\pi\) | ||||
0.769197 | + | 0.639012i | \(0.220656\pi\) | |||||||
\(368\) | 1312.00 | 0.185850 | ||||||||
\(369\) | 14874.0 | 2.09840 | ||||||||
\(370\) | 2170.00 | 0.304900 | ||||||||
\(371\) | 154.000 | 0.0215506 | ||||||||
\(372\) | −13888.0 | −1.93564 | ||||||||
\(373\) | −11098.0 | −1.54057 | −0.770285 | − | 0.637700i | \(-0.779886\pi\) | ||||
−0.770285 | + | 0.637700i | \(0.779886\pi\) | |||||||
\(374\) | −1128.00 | −0.155956 | ||||||||
\(375\) | 1000.00 | 0.137706 | ||||||||
\(376\) | −8040.00 | −1.10274 | ||||||||
\(377\) | 3900.00 | 0.532786 | ||||||||
\(378\) | −560.000 | −0.0761992 | ||||||||
\(379\) | 7100.00 | 0.962276 | 0.481138 | − | 0.876645i | \(-0.340224\pi\) | ||||
0.481138 | + | 0.876645i | \(0.340224\pi\) | |||||||
\(380\) | 1400.00 | 0.188996 | ||||||||
\(381\) | −6208.00 | −0.834765 | ||||||||
\(382\) | −2888.00 | −0.386814 | ||||||||
\(383\) | −728.000 | −0.0971255 | −0.0485627 | − | 0.998820i | \(-0.515464\pi\) | ||||
−0.0485627 | + | 0.998820i | \(0.515464\pi\) | |||||||
\(384\) | 11640.0 | 1.54688 | ||||||||
\(385\) | −420.000 | −0.0555979 | ||||||||
\(386\) | 1602.00 | 0.211243 | ||||||||
\(387\) | −2516.00 | −0.330479 | ||||||||
\(388\) | −7182.00 | −0.939719 | ||||||||
\(389\) | −6810.00 | −0.887611 | −0.443806 | − | 0.896123i | \(-0.646372\pi\) | ||||
−0.443806 | + | 0.896123i | \(0.646372\pi\) | |||||||
\(390\) | −3120.00 | −0.405096 | ||||||||
\(391\) | −3008.00 | −0.389057 | ||||||||
\(392\) | −735.000 | −0.0947018 | ||||||||
\(393\) | −8896.00 | −1.14184 | ||||||||
\(394\) | −4794.00 | −0.612990 | ||||||||
\(395\) | 5000.00 | 0.636905 | ||||||||
\(396\) | −3108.00 | −0.394401 | ||||||||
\(397\) | −574.000 | −0.0725648 | −0.0362824 | − | 0.999342i | \(-0.511552\pi\) | ||||
−0.0362824 | + | 0.999342i | \(0.511552\pi\) | |||||||
\(398\) | 1280.00 | 0.161208 | ||||||||
\(399\) | −2240.00 | −0.281053 | ||||||||
\(400\) | 1025.00 | 0.128125 | ||||||||
\(401\) | 6162.00 | 0.767371 | 0.383685 | − | 0.923464i | \(-0.374655\pi\) | ||||
0.383685 | + | 0.923464i | \(0.374655\pi\) | |||||||
\(402\) | 1312.00 | 0.162778 | ||||||||
\(403\) | 19344.0 | 2.39105 | ||||||||
\(404\) | −3374.00 | −0.415502 | ||||||||
\(405\) | 1795.00 | 0.220233 | ||||||||
\(406\) | −350.000 | −0.0427838 | ||||||||
\(407\) | −5208.00 | −0.634278 | ||||||||
\(408\) | −11280.0 | −1.36873 | ||||||||
\(409\) | 8210.00 | 0.992563 | 0.496282 | − | 0.868162i | \(-0.334698\pi\) | ||||
0.496282 | + | 0.868162i | \(0.334698\pi\) | |||||||
\(410\) | −2010.00 | −0.242114 | ||||||||
\(411\) | 5552.00 | 0.666326 | ||||||||
\(412\) | −1904.00 | −0.227678 | ||||||||
\(413\) | −3920.00 | −0.467047 | ||||||||
\(414\) | 1184.00 | 0.140557 | ||||||||
\(415\) | 2240.00 | 0.264957 | ||||||||
\(416\) | −12558.0 | −1.48006 | ||||||||
\(417\) | −2880.00 | −0.338212 | ||||||||
\(418\) | 480.000 | 0.0561664 | ||||||||
\(419\) | 4800.00 | 0.559655 | 0.279827 | − | 0.960050i | \(-0.409723\pi\) | ||||
0.279827 | + | 0.960050i | \(0.409723\pi\) | |||||||
\(420\) | −1960.00 | −0.227710 | ||||||||
\(421\) | −9938.00 | −1.15047 | −0.575236 | − | 0.817988i | \(-0.695090\pi\) | ||||
−0.575236 | + | 0.817988i | \(0.695090\pi\) | |||||||
\(422\) | −68.0000 | −0.00784405 | ||||||||
\(423\) | 19832.0 | 2.27959 | ||||||||
\(424\) | −330.000 | −0.0377977 | ||||||||
\(425\) | −2350.00 | −0.268216 | ||||||||
\(426\) | −5376.00 | −0.611427 | ||||||||
\(427\) | −1946.00 | −0.220547 | ||||||||
\(428\) | 3108.00 | 0.351007 | ||||||||
\(429\) | 7488.00 | 0.842713 | ||||||||
\(430\) | 340.000 | 0.0381308 | ||||||||
\(431\) | −9248.00 | −1.03355 | −0.516776 | − | 0.856121i | \(-0.672868\pi\) | ||||
−0.516776 | + | 0.856121i | \(0.672868\pi\) | |||||||
\(432\) | −3280.00 | −0.365299 | ||||||||
\(433\) | −1118.00 | −0.124082 | −0.0620412 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620412 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(434\) | −1736.00 | −0.192006 | ||||||||
\(435\) | −2000.00 | −0.220443 | ||||||||
\(436\) | 8190.00 | 0.899610 | ||||||||
\(437\) | 1280.00 | 0.140116 | ||||||||
\(438\) | −656.000 | −0.0715637 | ||||||||
\(439\) | −11960.0 | −1.30027 | −0.650136 | − | 0.759818i | \(-0.725288\pi\) | ||||
−0.650136 | + | 0.759818i | \(0.725288\pi\) | |||||||
\(440\) | 900.000 | 0.0975132 | ||||||||
\(441\) | 1813.00 | 0.195767 | ||||||||
\(442\) | 7332.00 | 0.789022 | ||||||||
\(443\) | 7332.00 | 0.786352 | 0.393176 | − | 0.919463i | \(-0.371376\pi\) | ||||
0.393176 | + | 0.919463i | \(0.371376\pi\) | |||||||
\(444\) | −24304.0 | −2.59779 | ||||||||
\(445\) | 4350.00 | 0.463393 | ||||||||
\(446\) | −1728.00 | −0.183460 | ||||||||
\(447\) | −18160.0 | −1.92156 | ||||||||
\(448\) | −1169.00 | −0.123281 | ||||||||
\(449\) | 1890.00 | 0.198652 | 0.0993259 | − | 0.995055i | \(-0.468331\pi\) | ||||
0.0993259 | + | 0.995055i | \(0.468331\pi\) | |||||||
\(450\) | 925.000 | 0.0968998 | ||||||||
\(451\) | 4824.00 | 0.503666 | ||||||||
\(452\) | 5586.00 | 0.581291 | ||||||||
\(453\) | −5056.00 | −0.524396 | ||||||||
\(454\) | −4864.00 | −0.502817 | ||||||||
\(455\) | 2730.00 | 0.281284 | ||||||||
\(456\) | 4800.00 | 0.492940 | ||||||||
\(457\) | −7014.00 | −0.717945 | −0.358973 | − | 0.933348i | \(-0.616873\pi\) | ||||
−0.358973 | + | 0.933348i | \(0.616873\pi\) | |||||||
\(458\) | −5510.00 | −0.562152 | ||||||||
\(459\) | 7520.00 | 0.764714 | ||||||||
\(460\) | 1120.00 | 0.113522 | ||||||||
\(461\) | −8318.00 | −0.840364 | −0.420182 | − | 0.907440i | \(-0.638034\pi\) | ||||
−0.420182 | + | 0.907440i | \(0.638034\pi\) | |||||||
\(462\) | −672.000 | −0.0676716 | ||||||||
\(463\) | 6432.00 | 0.645616 | 0.322808 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322808 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(464\) | −2050.00 | −0.205105 | ||||||||
\(465\) | −9920.00 | −0.989310 | ||||||||
\(466\) | 5322.00 | 0.529049 | ||||||||
\(467\) | −10064.0 | −0.997230 | −0.498615 | − | 0.866824i | \(-0.666158\pi\) | ||||
−0.498615 | + | 0.866824i | \(0.666158\pi\) | |||||||
\(468\) | 20202.0 | 1.99538 | ||||||||
\(469\) | −1148.00 | −0.113027 | ||||||||
\(470\) | −2680.00 | −0.263020 | ||||||||
\(471\) | 5872.00 | 0.574453 | ||||||||
\(472\) | 8400.00 | 0.819155 | ||||||||
\(473\) | −816.000 | −0.0793229 | ||||||||
\(474\) | 8000.00 | 0.775216 | ||||||||
\(475\) | 1000.00 | 0.0965961 | ||||||||
\(476\) | 4606.00 | 0.443520 | ||||||||
\(477\) | 814.000 | 0.0781352 | ||||||||
\(478\) | −1840.00 | −0.176066 | ||||||||
\(479\) | 1400.00 | 0.133544 | 0.0667721 | − | 0.997768i | \(-0.478730\pi\) | ||||
0.0667721 | + | 0.997768i | \(0.478730\pi\) | |||||||
\(480\) | 6440.00 | 0.612384 | ||||||||
\(481\) | 33852.0 | 3.20898 | ||||||||
\(482\) | −438.000 | −0.0413908 | ||||||||
\(483\) | −1792.00 | −0.168817 | ||||||||
\(484\) | 8309.00 | 0.780334 | ||||||||
\(485\) | −5130.00 | −0.480291 | ||||||||
\(486\) | 5032.00 | 0.469663 | ||||||||
\(487\) | 13376.0 | 1.24461 | 0.622304 | − | 0.782775i | \(-0.286197\pi\) | ||||
0.622304 | + | 0.782775i | \(0.286197\pi\) | |||||||
\(488\) | 4170.00 | 0.386818 | ||||||||
\(489\) | −20256.0 | −1.87323 | ||||||||
\(490\) | −245.000 | −0.0225877 | ||||||||
\(491\) | 7092.00 | 0.651848 | 0.325924 | − | 0.945396i | \(-0.394325\pi\) | ||||
0.325924 | + | 0.945396i | \(0.394325\pi\) | |||||||
\(492\) | 22512.0 | 2.06284 | ||||||||
\(493\) | 4700.00 | 0.429366 | ||||||||
\(494\) | −3120.00 | −0.284161 | ||||||||
\(495\) | −2220.00 | −0.201579 | ||||||||
\(496\) | −10168.0 | −0.920477 | ||||||||
\(497\) | 4704.00 | 0.424554 | ||||||||
\(498\) | 3584.00 | 0.322496 | ||||||||
\(499\) | −820.000 | −0.0735636 | −0.0367818 | − | 0.999323i | \(-0.511711\pi\) | ||||
−0.0367818 | + | 0.999323i | \(0.511711\pi\) | |||||||
\(500\) | 875.000 | 0.0782624 | ||||||||
\(501\) | −3328.00 | −0.296775 | ||||||||
\(502\) | 5592.00 | 0.497178 | ||||||||
\(503\) | −4568.00 | −0.404925 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(504\) | −3885.00 | −0.343356 | ||||||||
\(505\) | −2410.00 | −0.212364 | ||||||||
\(506\) | 384.000 | 0.0337369 | ||||||||
\(507\) | −31096.0 | −2.72391 | ||||||||
\(508\) | −5432.00 | −0.474421 | ||||||||
\(509\) | 19810.0 | 1.72507 | 0.862537 | − | 0.505994i | \(-0.168874\pi\) | ||||
0.862537 | + | 0.505994i | \(0.168874\pi\) | |||||||
\(510\) | −3760.00 | −0.326462 | ||||||||
\(511\) | 574.000 | 0.0496913 | ||||||||
\(512\) | 11521.0 | 0.994455 | ||||||||
\(513\) | −3200.00 | −0.275406 | ||||||||
\(514\) | −1974.00 | −0.169396 | ||||||||
\(515\) | −1360.00 | −0.116367 | ||||||||
\(516\) | −3808.00 | −0.324880 | ||||||||
\(517\) | 6432.00 | 0.547155 | ||||||||
\(518\) | −3038.00 | −0.257687 | ||||||||
\(519\) | −24336.0 | −2.05825 | ||||||||
\(520\) | −5850.00 | −0.493345 | ||||||||
\(521\) | −1838.00 | −0.154557 | −0.0772785 | − | 0.997010i | \(-0.524623\pi\) | ||||
−0.0772785 | + | 0.997010i | \(0.524623\pi\) | |||||||
\(522\) | −1850.00 | −0.155119 | ||||||||
\(523\) | 2072.00 | 0.173236 | 0.0866178 | − | 0.996242i | \(-0.472394\pi\) | ||||
0.0866178 | + | 0.996242i | \(0.472394\pi\) | |||||||
\(524\) | −7784.00 | −0.648942 | ||||||||
\(525\) | −1400.00 | −0.116383 | ||||||||
\(526\) | −728.000 | −0.0603466 | ||||||||
\(527\) | 23312.0 | 1.92692 | ||||||||
\(528\) | −3936.00 | −0.324417 | ||||||||
\(529\) | −11143.0 | −0.915838 | ||||||||
\(530\) | −110.000 | −0.00901527 | ||||||||
\(531\) | −20720.0 | −1.69335 | ||||||||
\(532\) | −1960.00 | −0.159731 | ||||||||
\(533\) | −31356.0 | −2.54818 | ||||||||
\(534\) | 6960.00 | 0.564024 | ||||||||
\(535\) | 2220.00 | 0.179400 | ||||||||
\(536\) | 2460.00 | 0.198238 | ||||||||
\(537\) | 1440.00 | 0.115718 | ||||||||
\(538\) | 5810.00 | 0.465589 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | −2800.00 | −0.223135 | ||||||||
\(541\) | −3498.00 | −0.277987 | −0.138993 | − | 0.990293i | \(-0.544387\pi\) | ||||
−0.138993 | + | 0.990293i | \(0.544387\pi\) | |||||||
\(542\) | −6528.00 | −0.517346 | ||||||||
\(543\) | 15664.0 | 1.23795 | ||||||||
\(544\) | −15134.0 | −1.19277 | ||||||||
\(545\) | 5850.00 | 0.459792 | ||||||||
\(546\) | 4368.00 | 0.342368 | ||||||||
\(547\) | 5076.00 | 0.396772 | 0.198386 | − | 0.980124i | \(-0.436430\pi\) | ||||
0.198386 | + | 0.980124i | \(0.436430\pi\) | |||||||
\(548\) | 4858.00 | 0.378692 | ||||||||
\(549\) | −10286.0 | −0.799628 | ||||||||
\(550\) | 300.000 | 0.0232583 | ||||||||
\(551\) | −2000.00 | −0.154633 | ||||||||
\(552\) | 3840.00 | 0.296089 | ||||||||
\(553\) | −7000.00 | −0.538283 | ||||||||
\(554\) | 5126.00 | 0.393110 | ||||||||
\(555\) | −17360.0 | −1.32773 | ||||||||
\(556\) | −2520.00 | −0.192215 | ||||||||
\(557\) | −8674.00 | −0.659837 | −0.329918 | − | 0.944009i | \(-0.607021\pi\) | ||||
−0.329918 | + | 0.944009i | \(0.607021\pi\) | |||||||
\(558\) | −9176.00 | −0.696149 | ||||||||
\(559\) | 5304.00 | 0.401315 | ||||||||
\(560\) | −1435.00 | −0.108285 | ||||||||
\(561\) | 9024.00 | 0.679133 | ||||||||
\(562\) | −2358.00 | −0.176986 | ||||||||
\(563\) | 16072.0 | 1.20312 | 0.601558 | − | 0.798829i | \(-0.294547\pi\) | ||||
0.601558 | + | 0.798829i | \(0.294547\pi\) | |||||||
\(564\) | 30016.0 | 2.24096 | ||||||||
\(565\) | 3990.00 | 0.297098 | ||||||||
\(566\) | 392.000 | 0.0291113 | ||||||||
\(567\) | −2513.00 | −0.186131 | ||||||||
\(568\) | −10080.0 | −0.744626 | ||||||||
\(569\) | 2730.00 | 0.201138 | 0.100569 | − | 0.994930i | \(-0.467934\pi\) | ||||
0.100569 | + | 0.994930i | \(0.467934\pi\) | |||||||
\(570\) | 1600.00 | 0.117573 | ||||||||
\(571\) | 19932.0 | 1.46082 | 0.730410 | − | 0.683009i | \(-0.239329\pi\) | ||||
0.730410 | + | 0.683009i | \(0.239329\pi\) | |||||||
\(572\) | 6552.00 | 0.478939 | ||||||||
\(573\) | 23104.0 | 1.68444 | ||||||||
\(574\) | 2814.00 | 0.204624 | ||||||||
\(575\) | 800.000 | 0.0580214 | ||||||||
\(576\) | −6179.00 | −0.446976 | ||||||||
\(577\) | −20054.0 | −1.44690 | −0.723448 | − | 0.690379i | \(-0.757444\pi\) | ||||
−0.723448 | + | 0.690379i | \(0.757444\pi\) | |||||||
\(578\) | 3923.00 | 0.282310 | ||||||||
\(579\) | −12816.0 | −0.919887 | ||||||||
\(580\) | −1750.00 | −0.125284 | ||||||||
\(581\) | −3136.00 | −0.223930 | ||||||||
\(582\) | −8208.00 | −0.584592 | ||||||||
\(583\) | 264.000 | 0.0187543 | ||||||||
\(584\) | −1230.00 | −0.0871537 | ||||||||
\(585\) | 14430.0 | 1.01984 | ||||||||
\(586\) | 1202.00 | 0.0847341 | ||||||||
\(587\) | −2544.00 | −0.178879 | −0.0894396 | − | 0.995992i | \(-0.528508\pi\) | ||||
−0.0894396 | + | 0.995992i | \(0.528508\pi\) | |||||||
\(588\) | 2744.00 | 0.192450 | ||||||||
\(589\) | −9920.00 | −0.693967 | ||||||||
\(590\) | 2800.00 | 0.195380 | ||||||||
\(591\) | 38352.0 | 2.66936 | ||||||||
\(592\) | −17794.0 | −1.23535 | ||||||||
\(593\) | 14202.0 | 0.983484 | 0.491742 | − | 0.870741i | \(-0.336360\pi\) | ||||
0.491742 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(594\) | −960.000 | −0.0663119 | ||||||||
\(595\) | 3290.00 | 0.226684 | ||||||||
\(596\) | −15890.0 | −1.09208 | ||||||||
\(597\) | −10240.0 | −0.702002 | ||||||||
\(598\) | −2496.00 | −0.170684 | ||||||||
\(599\) | −19600.0 | −1.33695 | −0.668476 | − | 0.743734i | \(-0.733053\pi\) | ||||
−0.668476 | + | 0.743734i | \(0.733053\pi\) | |||||||
\(600\) | 3000.00 | 0.204124 | ||||||||
\(601\) | −27078.0 | −1.83783 | −0.918914 | − | 0.394458i | \(-0.870932\pi\) | ||||
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(602\) | −476.000 | −0.0322264 | ||||||||
\(603\) | −6068.00 | −0.409798 | ||||||||
\(604\) | −4424.00 | −0.298030 | ||||||||
\(605\) | 5935.00 | 0.398830 | ||||||||
\(606\) | −3856.00 | −0.258481 | ||||||||
\(607\) | −2704.00 | −0.180811 | −0.0904053 | − | 0.995905i | \(-0.528816\pi\) | ||||
−0.0904053 | + | 0.995905i | \(0.528816\pi\) | |||||||
\(608\) | 6440.00 | 0.429567 | ||||||||
\(609\) | 2800.00 | 0.186308 | ||||||||
\(610\) | 1390.00 | 0.0922614 | ||||||||
\(611\) | −41808.0 | −2.76820 | ||||||||
\(612\) | 24346.0 | 1.60805 | ||||||||
\(613\) | 12702.0 | 0.836915 | 0.418458 | − | 0.908236i | \(-0.362571\pi\) | ||||
0.418458 | + | 0.908236i | \(0.362571\pi\) | |||||||
\(614\) | −6384.00 | −0.419605 | ||||||||
\(615\) | 16080.0 | 1.05432 | ||||||||
\(616\) | −1260.00 | −0.0824137 | ||||||||
\(617\) | 12666.0 | 0.826441 | 0.413220 | − | 0.910631i | \(-0.364404\pi\) | ||||
0.413220 | + | 0.910631i | \(0.364404\pi\) | |||||||
\(618\) | −2176.00 | −0.141637 | ||||||||
\(619\) | 960.000 | 0.0623355 | 0.0311677 | − | 0.999514i | \(-0.490077\pi\) | ||||
0.0311677 | + | 0.999514i | \(0.490077\pi\) | |||||||
\(620\) | −8680.00 | −0.562254 | ||||||||
\(621\) | −2560.00 | −0.165426 | ||||||||
\(622\) | −4968.00 | −0.320255 | ||||||||
\(623\) | −6090.00 | −0.391638 | ||||||||
\(624\) | 25584.0 | 1.64131 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −2758.00 | −0.176089 | ||||||||
\(627\) | −3840.00 | −0.244585 | ||||||||
\(628\) | 5138.00 | 0.326479 | ||||||||
\(629\) | 40796.0 | 2.58608 | ||||||||
\(630\) | −1295.00 | −0.0818953 | ||||||||
\(631\) | 23232.0 | 1.46569 | 0.732846 | − | 0.680395i | \(-0.238192\pi\) | ||||
0.732846 | + | 0.680395i | \(0.238192\pi\) | |||||||
\(632\) | 15000.0 | 0.944095 | ||||||||
\(633\) | 544.000 | 0.0341581 | ||||||||
\(634\) | −6274.00 | −0.393016 | ||||||||
\(635\) | −3880.00 | −0.242477 | ||||||||
\(636\) | 1232.00 | 0.0768113 | ||||||||
\(637\) | −3822.00 | −0.237729 | ||||||||
\(638\) | −600.000 | −0.0372323 | ||||||||
\(639\) | 24864.0 | 1.53929 | ||||||||
\(640\) | 7275.00 | 0.449328 | ||||||||
\(641\) | 12162.0 | 0.749407 | 0.374704 | − | 0.927145i | \(-0.377744\pi\) | ||||
0.374704 | + | 0.927145i | \(0.377744\pi\) | |||||||
\(642\) | 3552.00 | 0.218359 | ||||||||
\(643\) | −488.000 | −0.0299298 | −0.0149649 | − | 0.999888i | \(-0.504764\pi\) | ||||
−0.0149649 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(644\) | −1568.00 | −0.0959439 | ||||||||
\(645\) | −2720.00 | −0.166046 | ||||||||
\(646\) | −3760.00 | −0.229002 | ||||||||
\(647\) | −3984.00 | −0.242082 | −0.121041 | − | 0.992647i | \(-0.538623\pi\) | ||||
−0.121041 | + | 0.992647i | \(0.538623\pi\) | |||||||
\(648\) | 5385.00 | 0.326455 | ||||||||
\(649\) | −6720.00 | −0.406445 | ||||||||
\(650\) | −1950.00 | −0.117670 | ||||||||
\(651\) | 13888.0 | 0.836119 | ||||||||
\(652\) | −17724.0 | −1.06461 | ||||||||
\(653\) | −30538.0 | −1.83008 | −0.915042 | − | 0.403360i | \(-0.867842\pi\) | ||||
−0.915042 | + | 0.403360i | \(0.867842\pi\) | |||||||
\(654\) | 9360.00 | 0.559641 | ||||||||
\(655\) | −5560.00 | −0.331675 | ||||||||
\(656\) | 16482.0 | 0.980966 | ||||||||
\(657\) | 3034.00 | 0.180164 | ||||||||
\(658\) | 3752.00 | 0.222292 | ||||||||
\(659\) | 22740.0 | 1.34420 | 0.672098 | − | 0.740463i | \(-0.265394\pi\) | ||||
0.672098 | + | 0.740463i | \(0.265394\pi\) | |||||||
\(660\) | −3360.00 | −0.198163 | ||||||||
\(661\) | −18718.0 | −1.10143 | −0.550715 | − | 0.834693i | \(-0.685645\pi\) | ||||
−0.550715 | + | 0.834693i | \(0.685645\pi\) | |||||||
\(662\) | 1932.00 | 0.113428 | ||||||||
\(663\) | −58656.0 | −3.43591 | ||||||||
\(664\) | 6720.00 | 0.392751 | ||||||||
\(665\) | −1400.00 | −0.0816386 | ||||||||
\(666\) | −16058.0 | −0.934287 | ||||||||
\(667\) | −1600.00 | −0.0928819 | ||||||||
\(668\) | −2912.00 | −0.168666 | ||||||||
\(669\) | 13824.0 | 0.798904 | ||||||||
\(670\) | 820.000 | 0.0472826 | ||||||||
\(671\) | −3336.00 | −0.191930 | ||||||||
\(672\) | −9016.00 | −0.517559 | ||||||||
\(673\) | 10802.0 | 0.618702 | 0.309351 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309351 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(674\) | 2386.00 | 0.136358 | ||||||||
\(675\) | −2000.00 | −0.114044 | ||||||||
\(676\) | −27209.0 | −1.54808 | ||||||||
\(677\) | 346.000 | 0.0196423 | 0.00982117 | − | 0.999952i | \(-0.496874\pi\) | ||||
0.00982117 | + | 0.999952i | \(0.496874\pi\) | |||||||
\(678\) | 6384.00 | 0.361617 | ||||||||
\(679\) | 7182.00 | 0.405920 | ||||||||
\(680\) | −7050.00 | −0.397581 | ||||||||
\(681\) | 38912.0 | 2.18959 | ||||||||
\(682\) | −2976.00 | −0.167092 | ||||||||
\(683\) | −11628.0 | −0.651439 | −0.325720 | − | 0.945466i | \(-0.605607\pi\) | ||||
−0.325720 | + | 0.945466i | \(0.605607\pi\) | |||||||
\(684\) | −10360.0 | −0.579129 | ||||||||
\(685\) | 3470.00 | 0.193550 | ||||||||
\(686\) | 343.000 | 0.0190901 | ||||||||
\(687\) | 44080.0 | 2.44797 | ||||||||
\(688\) | −2788.00 | −0.154493 | ||||||||
\(689\) | −1716.00 | −0.0948830 | ||||||||
\(690\) | 1280.00 | 0.0706214 | ||||||||
\(691\) | 2472.00 | 0.136092 | 0.0680458 | − | 0.997682i | \(-0.478324\pi\) | ||||
0.0680458 | + | 0.997682i | \(0.478324\pi\) | |||||||
\(692\) | −21294.0 | −1.16976 | ||||||||
\(693\) | 3108.00 | 0.170365 | ||||||||
\(694\) | 6076.00 | 0.332337 | ||||||||
\(695\) | −1800.00 | −0.0982416 | ||||||||
\(696\) | −6000.00 | −0.326766 | ||||||||
\(697\) | −37788.0 | −2.05355 | ||||||||
\(698\) | 2210.00 | 0.119842 | ||||||||
\(699\) | −42576.0 | −2.30382 | ||||||||
\(700\) | −1225.00 | −0.0661438 | ||||||||
\(701\) | −2018.00 | −0.108729 | −0.0543643 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543643 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(702\) | 6240.00 | 0.335489 | ||||||||
\(703\) | −17360.0 | −0.931358 | ||||||||
\(704\) | −2004.00 | −0.107285 | ||||||||
\(705\) | 21440.0 | 1.14536 | ||||||||
\(706\) | −2598.00 | −0.138494 | ||||||||
\(707\) | 3374.00 | 0.179480 | ||||||||
\(708\) | −31360.0 | −1.66466 | ||||||||
\(709\) | 790.000 | 0.0418464 | 0.0209232 | − | 0.999781i | \(-0.493339\pi\) | ||||
0.0209232 | + | 0.999781i | \(0.493339\pi\) | |||||||
\(710\) | −3360.00 | −0.177604 | ||||||||
\(711\) | −37000.0 | −1.95163 | ||||||||
\(712\) | 13050.0 | 0.686895 | ||||||||
\(713\) | −7936.00 | −0.416838 | ||||||||
\(714\) | 5264.00 | 0.275911 | ||||||||
\(715\) | 4680.00 | 0.244786 | ||||||||
\(716\) | 1260.00 | 0.0657659 | ||||||||
\(717\) | 14720.0 | 0.766706 | ||||||||
\(718\) | −13320.0 | −0.692337 | ||||||||
\(719\) | 18200.0 | 0.944013 | 0.472007 | − | 0.881595i | \(-0.343530\pi\) | ||||
0.472007 | + | 0.881595i | \(0.343530\pi\) | |||||||
\(720\) | −7585.00 | −0.392606 | ||||||||
\(721\) | 1904.00 | 0.0983477 | ||||||||
\(722\) | −5259.00 | −0.271080 | ||||||||
\(723\) | 3504.00 | 0.180242 | ||||||||
\(724\) | 13706.0 | 0.703563 | ||||||||
\(725\) | −1250.00 | −0.0640329 | ||||||||
\(726\) | 9496.00 | 0.485440 | ||||||||
\(727\) | 29056.0 | 1.48229 | 0.741147 | − | 0.671343i | \(-0.234282\pi\) | ||||
0.741147 | + | 0.671343i | \(0.234282\pi\) | |||||||
\(728\) | 8190.00 | 0.416953 | ||||||||
\(729\) | −30563.0 | −1.55276 | ||||||||
\(730\) | −410.000 | −0.0207874 | ||||||||
\(731\) | 6392.00 | 0.323415 | ||||||||
\(732\) | −15568.0 | −0.786079 | ||||||||
\(733\) | 7082.00 | 0.356862 | 0.178431 | − | 0.983952i | \(-0.442898\pi\) | ||||
0.178431 | + | 0.983952i | \(0.442898\pi\) | |||||||
\(734\) | 10816.0 | 0.543904 | ||||||||
\(735\) | 1960.00 | 0.0983615 | ||||||||
\(736\) | 5152.00 | 0.258023 | ||||||||
\(737\) | −1968.00 | −0.0983612 | ||||||||
\(738\) | 14874.0 | 0.741896 | ||||||||
\(739\) | 11060.0 | 0.550539 | 0.275270 | − | 0.961367i | \(-0.411233\pi\) | ||||
0.275270 | + | 0.961367i | \(0.411233\pi\) | |||||||
\(740\) | −15190.0 | −0.754589 | ||||||||
\(741\) | 24960.0 | 1.23742 | ||||||||
\(742\) | 154.000 | 0.00761930 | ||||||||
\(743\) | 33072.0 | 1.63297 | 0.816483 | − | 0.577369i | \(-0.195921\pi\) | ||||
0.816483 | + | 0.577369i | \(0.195921\pi\) | |||||||
\(744\) | −29760.0 | −1.46647 | ||||||||
\(745\) | −11350.0 | −0.558164 | ||||||||
\(746\) | −11098.0 | −0.544674 | ||||||||
\(747\) | −16576.0 | −0.811893 | ||||||||
\(748\) | 7896.00 | 0.385971 | ||||||||
\(749\) | −3108.00 | −0.151621 | ||||||||
\(750\) | 1000.00 | 0.0486864 | ||||||||
\(751\) | 29072.0 | 1.41259 | 0.706293 | − | 0.707919i | \(-0.250366\pi\) | ||||
0.706293 | + | 0.707919i | \(0.250366\pi\) | |||||||
\(752\) | 21976.0 | 1.06567 | ||||||||
\(753\) | −44736.0 | −2.16503 | ||||||||
\(754\) | 3900.00 | 0.188368 | ||||||||
\(755\) | −3160.00 | −0.152323 | ||||||||
\(756\) | 3920.00 | 0.188583 | ||||||||
\(757\) | −13234.0 | −0.635400 | −0.317700 | − | 0.948191i | \(-0.602911\pi\) | ||||
−0.317700 | + | 0.948191i | \(0.602911\pi\) | |||||||
\(758\) | 7100.00 | 0.340216 | ||||||||
\(759\) | −3072.00 | −0.146912 | ||||||||
\(760\) | 3000.00 | 0.143186 | ||||||||
\(761\) | −22398.0 | −1.06692 | −0.533460 | − | 0.845825i | \(-0.679109\pi\) | ||||
−0.533460 | + | 0.845825i | \(0.679109\pi\) | |||||||
\(762\) | −6208.00 | −0.295134 | ||||||||
\(763\) | −8190.00 | −0.388595 | ||||||||
\(764\) | 20216.0 | 0.957316 | ||||||||
\(765\) | 17390.0 | 0.821878 | ||||||||
\(766\) | −728.000 | −0.0343390 | ||||||||
\(767\) | 43680.0 | 2.05631 | ||||||||
\(768\) | 952.000 | 0.0447296 | ||||||||
\(769\) | 6890.00 | 0.323095 | 0.161547 | − | 0.986865i | \(-0.448352\pi\) | ||||
0.161547 | + | 0.986865i | \(0.448352\pi\) | |||||||
\(770\) | −420.000 | −0.0196568 | ||||||||
\(771\) | 15792.0 | 0.737659 | ||||||||
\(772\) | −11214.0 | −0.522799 | ||||||||
\(773\) | 16722.0 | 0.778071 | 0.389035 | − | 0.921223i | \(-0.372808\pi\) | ||||
0.389035 | + | 0.921223i | \(0.372808\pi\) | |||||||
\(774\) | −2516.00 | −0.116842 | ||||||||
\(775\) | −6200.00 | −0.287368 | ||||||||
\(776\) | −15390.0 | −0.711944 | ||||||||
\(777\) | 24304.0 | 1.12214 | ||||||||
\(778\) | −6810.00 | −0.313818 | ||||||||
\(779\) | 16080.0 | 0.739571 | ||||||||
\(780\) | 21840.0 | 1.00256 | ||||||||
\(781\) | 8064.00 | 0.369466 | ||||||||
\(782\) | −3008.00 | −0.137552 | ||||||||
\(783\) | 4000.00 | 0.182565 | ||||||||
\(784\) | 2009.00 | 0.0915179 | ||||||||
\(785\) | 3670.00 | 0.166864 | ||||||||
\(786\) | −8896.00 | −0.403702 | ||||||||
\(787\) | −32624.0 | −1.47766 | −0.738831 | − | 0.673891i | \(-0.764622\pi\) | ||||
−0.738831 | + | 0.673891i | \(0.764622\pi\) | |||||||
\(788\) | 33558.0 | 1.51707 | ||||||||
\(789\) | 5824.00 | 0.262788 | ||||||||
\(790\) | 5000.00 | 0.225180 | ||||||||
\(791\) | −5586.00 | −0.251094 | ||||||||
\(792\) | −6660.00 | −0.298804 | ||||||||
\(793\) | 21684.0 | 0.971023 | ||||||||
\(794\) | −574.000 | −0.0256555 | ||||||||
\(795\) | 880.000 | 0.0392583 | ||||||||
\(796\) | −8960.00 | −0.398968 | ||||||||
\(797\) | 11346.0 | 0.504261 | 0.252130 | − | 0.967693i | \(-0.418869\pi\) | ||||
0.252130 | + | 0.967693i | \(0.418869\pi\) | |||||||
\(798\) | −2240.00 | −0.0993673 | ||||||||
\(799\) | −50384.0 | −2.23086 | ||||||||
\(800\) | 4025.00 | 0.177882 | ||||||||
\(801\) | −32190.0 | −1.41995 | ||||||||
\(802\) | 6162.00 | 0.271306 | ||||||||
\(803\) | 984.000 | 0.0432436 | ||||||||
\(804\) | −9184.00 | −0.402854 | ||||||||
\(805\) | −1120.00 | −0.0490370 | ||||||||
\(806\) | 19344.0 | 0.845364 | ||||||||
\(807\) | −46480.0 | −2.02748 | ||||||||
\(808\) | −7230.00 | −0.314790 | ||||||||
\(809\) | −35190.0 | −1.52931 | −0.764657 | − | 0.644438i | \(-0.777091\pi\) | ||||
−0.764657 | + | 0.644438i | \(0.777091\pi\) | |||||||
\(810\) | 1795.00 | 0.0778640 | ||||||||
\(811\) | 30432.0 | 1.31765 | 0.658824 | − | 0.752297i | \(-0.271054\pi\) | ||||
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(812\) | 2450.00 | 0.105884 | ||||||||
\(813\) | 52224.0 | 2.25286 | ||||||||
\(814\) | −5208.00 | −0.224251 | ||||||||
\(815\) | −12660.0 | −0.544123 | ||||||||
\(816\) | 30832.0 | 1.32272 | ||||||||
\(817\) | −2720.00 | −0.116476 | ||||||||
\(818\) | 8210.00 | 0.350924 | ||||||||
\(819\) | −20202.0 | −0.861923 | ||||||||
\(820\) | 14070.0 | 0.599202 | ||||||||
\(821\) | 12702.0 | 0.539955 | 0.269977 | − | 0.962867i | \(-0.412984\pi\) | ||||
0.269977 | + | 0.962867i | \(0.412984\pi\) | |||||||
\(822\) | 5552.00 | 0.235582 | ||||||||
\(823\) | 16952.0 | 0.717995 | 0.358997 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358997 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(824\) | −4080.00 | −0.172492 | ||||||||
\(825\) | −2400.00 | −0.101282 | ||||||||
\(826\) | −3920.00 | −0.165126 | ||||||||
\(827\) | −25404.0 | −1.06818 | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||||
−0.534089 | + | 0.845428i | \(0.679345\pi\) | |||||||
\(828\) | −8288.00 | −0.347860 | ||||||||
\(829\) | 26250.0 | 1.09976 | 0.549879 | − | 0.835244i | \(-0.314674\pi\) | ||||
0.549879 | + | 0.835244i | \(0.314674\pi\) | |||||||
\(830\) | 2240.00 | 0.0936765 | ||||||||
\(831\) | −41008.0 | −1.71186 | ||||||||
\(832\) | 13026.0 | 0.542783 | ||||||||
\(833\) | −4606.00 | −0.191583 | ||||||||
\(834\) | −2880.00 | −0.119576 | ||||||||
\(835\) | −2080.00 | −0.0862052 | ||||||||
\(836\) | −3360.00 | −0.139005 | ||||||||
\(837\) | 19840.0 | 0.819320 | ||||||||
\(838\) | 4800.00 | 0.197868 | ||||||||
\(839\) | −15360.0 | −0.632045 | −0.316023 | − | 0.948752i | \(-0.602348\pi\) | ||||
−0.316023 | + | 0.948752i | \(0.602348\pi\) | |||||||
\(840\) | −4200.00 | −0.172516 | ||||||||
\(841\) | −21889.0 | −0.897495 | ||||||||
\(842\) | −9938.00 | −0.406753 | ||||||||
\(843\) | 18864.0 | 0.770713 | ||||||||
\(844\) | 476.000 | 0.0194130 | ||||||||
\(845\) | −19435.0 | −0.791224 | ||||||||
\(846\) | 19832.0 | 0.805955 | ||||||||
\(847\) | −8309.00 | −0.337073 | ||||||||
\(848\) | 902.000 | 0.0365269 | ||||||||
\(849\) | −3136.00 | −0.126769 | ||||||||
\(850\) | −2350.00 | −0.0948286 | ||||||||
\(851\) | −13888.0 | −0.559430 | ||||||||
\(852\) | 37632.0 | 1.51321 | ||||||||
\(853\) | 10362.0 | 0.415930 | 0.207965 | − | 0.978136i | \(-0.433316\pi\) | ||||
0.207965 | + | 0.978136i | \(0.433316\pi\) | |||||||
\(854\) | −1946.00 | −0.0779751 | ||||||||
\(855\) | −7400.00 | −0.295994 | ||||||||
\(856\) | 6660.00 | 0.265928 | ||||||||
\(857\) | 4506.00 | 0.179606 | 0.0898028 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898028 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(858\) | 7488.00 | 0.297944 | ||||||||
\(859\) | 24200.0 | 0.961226 | 0.480613 | − | 0.876933i | \(-0.340414\pi\) | ||||
0.480613 | + | 0.876933i | \(0.340414\pi\) | |||||||
\(860\) | −2380.00 | −0.0943690 | ||||||||
\(861\) | −22512.0 | −0.891065 | ||||||||
\(862\) | −9248.00 | −0.365415 | ||||||||
\(863\) | −37008.0 | −1.45975 | −0.729877 | − | 0.683579i | \(-0.760422\pi\) | ||||
−0.729877 | + | 0.683579i | \(0.760422\pi\) | |||||||
\(864\) | −12880.0 | −0.507160 | ||||||||
\(865\) | −15210.0 | −0.597868 | ||||||||
\(866\) | −1118.00 | −0.0438697 | ||||||||
\(867\) | −31384.0 | −1.22936 | ||||||||
\(868\) | 12152.0 | 0.475191 | ||||||||
\(869\) | −12000.0 | −0.468437 | ||||||||
\(870\) | −2000.00 | −0.0779383 | ||||||||
\(871\) | 12792.0 | 0.497635 | ||||||||
\(872\) | 17550.0 | 0.681557 | ||||||||
\(873\) | 37962.0 | 1.47173 | ||||||||
\(874\) | 1280.00 | 0.0495385 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | 4592.00 | 0.177111 | ||||||||
\(877\) | 3446.00 | 0.132683 | 0.0663416 | − | 0.997797i | \(-0.478867\pi\) | ||||
0.0663416 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(878\) | −11960.0 | −0.459716 | ||||||||
\(879\) | −9616.00 | −0.368987 | ||||||||
\(880\) | −2460.00 | −0.0942348 | ||||||||
\(881\) | −16158.0 | −0.617908 | −0.308954 | − | 0.951077i | \(-0.599979\pi\) | ||||
−0.308954 | + | 0.951077i | \(0.599979\pi\) | |||||||
\(882\) | 1813.00 | 0.0692142 | ||||||||
\(883\) | −44708.0 | −1.70390 | −0.851950 | − | 0.523623i | \(-0.824580\pi\) | ||||
−0.851950 | + | 0.523623i | \(0.824580\pi\) | |||||||
\(884\) | −51324.0 | −1.95273 | ||||||||
\(885\) | −22400.0 | −0.850811 | ||||||||
\(886\) | 7332.00 | 0.278017 | ||||||||
\(887\) | −23504.0 | −0.889726 | −0.444863 | − | 0.895599i | \(-0.646748\pi\) | ||||
−0.444863 | + | 0.895599i | \(0.646748\pi\) | |||||||
\(888\) | −52080.0 | −1.96812 | ||||||||
\(889\) | 5432.00 | 0.204931 | ||||||||
\(890\) | 4350.00 | 0.163834 | ||||||||
\(891\) | −4308.00 | −0.161979 | ||||||||
\(892\) | 12096.0 | 0.454040 | ||||||||
\(893\) | 21440.0 | 0.803429 | ||||||||
\(894\) | −18160.0 | −0.679375 | ||||||||
\(895\) | 900.000 | 0.0336131 | ||||||||
\(896\) | −10185.0 | −0.379751 | ||||||||
\(897\) | 19968.0 | 0.743269 | ||||||||
\(898\) | 1890.00 | 0.0702340 | ||||||||
\(899\) | 12400.0 | 0.460026 | ||||||||
\(900\) | −6475.00 | −0.239815 | ||||||||
\(901\) | −2068.00 | −0.0764651 | ||||||||
\(902\) | 4824.00 | 0.178073 | ||||||||
\(903\) | 3808.00 | 0.140335 | ||||||||
\(904\) | 11970.0 | 0.440394 | ||||||||
\(905\) | 9790.00 | 0.359592 | ||||||||
\(906\) | −5056.00 | −0.185402 | ||||||||
\(907\) | 42436.0 | 1.55354 | 0.776772 | − | 0.629782i | \(-0.216856\pi\) | ||||
0.776772 | + | 0.629782i | \(0.216856\pi\) | |||||||
\(908\) | 34048.0 | 1.24441 | ||||||||
\(909\) | 17834.0 | 0.650733 | ||||||||
\(910\) | 2730.00 | 0.0994490 | ||||||||
\(911\) | −7968.00 | −0.289782 | −0.144891 | − | 0.989448i | \(-0.546283\pi\) | ||||
−0.144891 | + | 0.989448i | \(0.546283\pi\) | |||||||
\(912\) | −13120.0 | −0.476367 | ||||||||
\(913\) | −5376.00 | −0.194874 | ||||||||
\(914\) | −7014.00 | −0.253832 | ||||||||
\(915\) | −11120.0 | −0.401766 | ||||||||
\(916\) | 38570.0 | 1.39125 | ||||||||
\(917\) | 7784.00 | 0.280317 | ||||||||
\(918\) | 7520.00 | 0.270367 | ||||||||
\(919\) | 14880.0 | 0.534109 | 0.267054 | − | 0.963681i | \(-0.413950\pi\) | ||||
0.267054 | + | 0.963681i | \(0.413950\pi\) | |||||||
\(920\) | 2400.00 | 0.0860061 | ||||||||
\(921\) | 51072.0 | 1.82723 | ||||||||
\(922\) | −8318.00 | −0.297114 | ||||||||
\(923\) | −52416.0 | −1.86922 | ||||||||
\(924\) | 4704.00 | 0.167479 | ||||||||
\(925\) | −10850.0 | −0.385671 | ||||||||
\(926\) | 6432.00 | 0.228260 | ||||||||
\(927\) | 10064.0 | 0.356575 | ||||||||
\(928\) | −8050.00 | −0.284757 | ||||||||
\(929\) | 27610.0 | 0.975086 | 0.487543 | − | 0.873099i | \(-0.337893\pi\) | ||||
0.487543 | + | 0.873099i | \(0.337893\pi\) | |||||||
\(930\) | −9920.00 | −0.349774 | ||||||||
\(931\) | 1960.00 | 0.0689972 | ||||||||
\(932\) | −37254.0 | −1.30933 | ||||||||
\(933\) | 39744.0 | 1.39460 | ||||||||
\(934\) | −10064.0 | −0.352574 | ||||||||
\(935\) | 5640.00 | 0.197270 | ||||||||
\(936\) | 43290.0 | 1.51173 | ||||||||
\(937\) | −28094.0 | −0.979499 | −0.489750 | − | 0.871863i | \(-0.662912\pi\) | ||||
−0.489750 | + | 0.871863i | \(0.662912\pi\) | |||||||
\(938\) | −1148.00 | −0.0399611 | ||||||||
\(939\) | 22064.0 | 0.766807 | ||||||||
\(940\) | 18760.0 | 0.650940 | ||||||||
\(941\) | −12198.0 | −0.422575 | −0.211288 | − | 0.977424i | \(-0.567766\pi\) | ||||
−0.211288 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(942\) | 5872.00 | 0.203100 | ||||||||
\(943\) | 12864.0 | 0.444231 | ||||||||
\(944\) | −22960.0 | −0.791615 | ||||||||
\(945\) | 2800.00 | 0.0963852 | ||||||||
\(946\) | −816.000 | −0.0280449 | ||||||||
\(947\) | 31316.0 | 1.07459 | 0.537293 | − | 0.843396i | \(-0.319447\pi\) | ||||
0.537293 | + | 0.843396i | \(0.319447\pi\) | |||||||
\(948\) | −56000.0 | −1.91856 | ||||||||
\(949\) | −6396.00 | −0.218781 | ||||||||
\(950\) | 1000.00 | 0.0341519 | ||||||||
\(951\) | 50192.0 | 1.71145 | ||||||||
\(952\) | 9870.00 | 0.336017 | ||||||||
\(953\) | 27322.0 | 0.928695 | 0.464348 | − | 0.885653i | \(-0.346289\pi\) | ||||
0.464348 | + | 0.885653i | \(0.346289\pi\) | |||||||
\(954\) | 814.000 | 0.0276250 | ||||||||
\(955\) | 14440.0 | 0.489285 | ||||||||
\(956\) | 12880.0 | 0.435742 | ||||||||
\(957\) | 4800.00 | 0.162134 | ||||||||
\(958\) | 1400.00 | 0.0472150 | ||||||||
\(959\) | −4858.00 | −0.163580 | ||||||||
\(960\) | −6680.00 | −0.224579 | ||||||||
\(961\) | 31713.0 | 1.06452 | ||||||||
\(962\) | 33852.0 | 1.13454 | ||||||||
\(963\) | −16428.0 | −0.549725 | ||||||||
\(964\) | 3066.00 | 0.102437 | ||||||||
\(965\) | −8010.00 | −0.267203 | ||||||||
\(966\) | −1792.00 | −0.0596860 | ||||||||
\(967\) | 5296.00 | 0.176120 | 0.0880599 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880599 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(968\) | 17805.0 | 0.591193 | ||||||||
\(969\) | 30080.0 | 0.997223 | ||||||||
\(970\) | −5130.00 | −0.169809 | ||||||||
\(971\) | 512.000 | 0.0169216 | 0.00846079 | − | 0.999964i | \(-0.497307\pi\) | ||||
0.00846079 | + | 0.999964i | \(0.497307\pi\) | |||||||
\(972\) | −35224.0 | −1.16236 | ||||||||
\(973\) | 2520.00 | 0.0830293 | ||||||||
\(974\) | 13376.0 | 0.440036 | ||||||||
\(975\) | 15600.0 | 0.512410 | ||||||||
\(976\) | −11398.0 | −0.373813 | ||||||||
\(977\) | −20734.0 | −0.678955 | −0.339478 | − | 0.940614i | \(-0.610250\pi\) | ||||
−0.339478 | + | 0.940614i | \(0.610250\pi\) | |||||||
\(978\) | −20256.0 | −0.662286 | ||||||||
\(979\) | −10440.0 | −0.340821 | ||||||||
\(980\) | 1715.00 | 0.0559017 | ||||||||
\(981\) | −43290.0 | −1.40891 | ||||||||
\(982\) | 7092.00 | 0.230463 | ||||||||
\(983\) | −61168.0 | −1.98470 | −0.992348 | − | 0.123472i | \(-0.960597\pi\) | ||||
−0.992348 | + | 0.123472i | \(0.960597\pi\) | |||||||
\(984\) | 48240.0 | 1.56284 | ||||||||
\(985\) | 23970.0 | 0.775378 | ||||||||
\(986\) | 4700.00 | 0.151804 | ||||||||
\(987\) | −30016.0 | −0.968004 | ||||||||
\(988\) | 21840.0 | 0.703262 | ||||||||
\(989\) | −2176.00 | −0.0699624 | ||||||||
\(990\) | −2220.00 | −0.0712689 | ||||||||
\(991\) | −47928.0 | −1.53631 | −0.768155 | − | 0.640264i | \(-0.778825\pi\) | ||||
−0.768155 | + | 0.640264i | \(0.778825\pi\) | |||||||
\(992\) | −39928.0 | −1.27794 | ||||||||
\(993\) | −15456.0 | −0.493939 | ||||||||
\(994\) | 4704.00 | 0.150102 | ||||||||
\(995\) | −6400.00 | −0.203913 | ||||||||
\(996\) | −25088.0 | −0.798136 | ||||||||
\(997\) | −9454.00 | −0.300312 | −0.150156 | − | 0.988662i | \(-0.547978\pi\) | ||||
−0.150156 | + | 0.988662i | \(0.547978\pi\) | |||||||
\(998\) | −820.000 | −0.0260087 | ||||||||
\(999\) | 34720.0 | 1.09959 |
(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 | 35.4.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 315.4.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 560.4.a.p.1.1 | 1 | |||
5.2 | odd | 4 | 175.4.b.a.99.2 | 2 | |||
5.3 | odd | 4 | 175.4.b.a.99.1 | 2 | |||
5.4 | even | 2 | 175.4.a.a.1.1 | 1 | |||
7.2 | even | 3 | 245.4.e.e.116.1 | 2 | |||
7.3 | odd | 6 | 245.4.e.b.226.1 | 2 | |||
7.4 | even | 3 | 245.4.e.e.226.1 | 2 | |||
7.5 | odd | 6 | 245.4.e.b.116.1 | 2 | |||
7.6 | odd | 2 | 245.4.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 2240.4.a.b.1.1 | 1 | |||
8.5 | even | 2 | 2240.4.a.bk.1.1 | 1 | |||
15.14 | odd | 2 | 1575.4.a.g.1.1 | 1 | |||
21.20 | even | 2 | 2205.4.a.i.1.1 | 1 | |||
35.34 | odd | 2 | 1225.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
175.4.a.a.1.1 | 1 | 5.4 | even | 2 | |||
175.4.b.a.99.1 | 2 | 5.3 | odd | 4 | |||
175.4.b.a.99.2 | 2 | 5.2 | odd | 4 | |||
245.4.a.d.1.1 | 1 | 7.6 | odd | 2 | |||
245.4.e.b.116.1 | 2 | 7.5 | odd | 6 | |||
245.4.e.b.226.1 | 2 | 7.3 | odd | 6 | |||
245.4.e.e.116.1 | 2 | 7.2 | even | 3 | |||
245.4.e.e.226.1 | 2 | 7.4 | even | 3 | |||
315.4.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
560.4.a.p.1.1 | 1 | 4.3 | odd | 2 | |||
1225.4.a.e.1.1 | 1 | 35.34 | odd | 2 | |||
1575.4.a.g.1.1 | 1 | 15.14 | odd | 2 | |||
2205.4.a.i.1.1 | 1 | 21.20 | even | 2 | |||
2240.4.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
2240.4.a.bk.1.1 | 1 | 8.5 | even | 2 |