Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,4,Mod(1,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, 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("322.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.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: | \(18.9986150218\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 42x^{2} + 26x + 46 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-6.22602\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 6.22602 | 1.19820 | 0.599099 | − | 0.800675i | \(-0.295526\pi\) | ||||
0.599099 | + | 0.800675i | \(0.295526\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −9.89045 | −0.884629 | −0.442315 | − | 0.896860i | \(-0.645843\pi\) | ||||
−0.442315 | + | 0.896860i | \(0.645843\pi\) | |||||||
\(6\) | −12.4520 | −0.847254 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 11.7633 | 0.435678 | ||||||||
\(10\) | 19.7809 | 0.625527 | ||||||||
\(11\) | −41.5157 | −1.13795 | −0.568976 | − | 0.822354i | \(-0.692660\pi\) | ||||
−0.568976 | + | 0.822354i | \(0.692660\pi\) | |||||||
\(12\) | 24.9041 | 0.599099 | ||||||||
\(13\) | 18.7390 | 0.399790 | 0.199895 | − | 0.979817i | \(-0.435940\pi\) | ||||
0.199895 | + | 0.979817i | \(0.435940\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | −61.5782 | −1.05996 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −19.3383 | −0.275895 | −0.137948 | − | 0.990440i | \(-0.544051\pi\) | ||||
−0.137948 | + | 0.990440i | \(0.544051\pi\) | |||||||
\(18\) | −23.5266 | −0.308071 | ||||||||
\(19\) | −52.3251 | −0.631801 | −0.315900 | − | 0.948792i | \(-0.602307\pi\) | ||||
−0.315900 | + | 0.948792i | \(0.602307\pi\) | |||||||
\(20\) | −39.5618 | −0.442315 | ||||||||
\(21\) | 43.5821 | 0.452876 | ||||||||
\(22\) | 83.0315 | 0.804653 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −49.8082 | −0.423627 | ||||||||
\(25\) | −27.1789 | −0.217431 | ||||||||
\(26\) | −37.4781 | −0.282694 | ||||||||
\(27\) | −94.8639 | −0.676169 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −169.213 | −1.08352 | −0.541761 | − | 0.840533i | \(-0.682242\pi\) | ||||
−0.541761 | + | 0.840533i | \(0.682242\pi\) | |||||||
\(30\) | 123.156 | 0.749506 | ||||||||
\(31\) | −191.927 | −1.11197 | −0.555984 | − | 0.831193i | \(-0.687659\pi\) | ||||
−0.555984 | + | 0.831193i | \(0.687659\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −258.478 | −1.36349 | ||||||||
\(34\) | 38.6766 | 0.195088 | ||||||||
\(35\) | −69.2332 | −0.334358 | ||||||||
\(36\) | 47.0533 | 0.217839 | ||||||||
\(37\) | 366.682 | 1.62925 | 0.814623 | − | 0.579990i | \(-0.196944\pi\) | ||||
0.814623 | + | 0.579990i | \(0.196944\pi\) | |||||||
\(38\) | 104.650 | 0.446750 | ||||||||
\(39\) | 116.670 | 0.479028 | ||||||||
\(40\) | 79.1236 | 0.312764 | ||||||||
\(41\) | 81.0378 | 0.308682 | 0.154341 | − | 0.988018i | \(-0.450674\pi\) | ||||
0.154341 | + | 0.988018i | \(0.450674\pi\) | |||||||
\(42\) | −87.1643 | −0.320232 | ||||||||
\(43\) | 202.640 | 0.718658 | 0.359329 | − | 0.933211i | \(-0.383006\pi\) | ||||
0.359329 | + | 0.933211i | \(0.383006\pi\) | |||||||
\(44\) | −166.063 | −0.568976 | ||||||||
\(45\) | −116.345 | −0.385414 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 86.9907 | 0.269977 | 0.134988 | − | 0.990847i | \(-0.456900\pi\) | ||||
0.134988 | + | 0.990847i | \(0.456900\pi\) | |||||||
\(48\) | 99.6163 | 0.299549 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 54.3578 | 0.153747 | ||||||||
\(51\) | −120.401 | −0.330577 | ||||||||
\(52\) | 74.9561 | 0.199895 | ||||||||
\(53\) | −708.249 | −1.83558 | −0.917788 | − | 0.397071i | \(-0.870027\pi\) | ||||
−0.917788 | + | 0.397071i | \(0.870027\pi\) | |||||||
\(54\) | 189.728 | 0.478124 | ||||||||
\(55\) | 410.609 | 1.00666 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | −325.777 | −0.757022 | ||||||||
\(58\) | 338.427 | 0.766165 | ||||||||
\(59\) | −618.357 | −1.36446 | −0.682231 | − | 0.731137i | \(-0.738990\pi\) | ||||
−0.682231 | + | 0.731137i | \(0.738990\pi\) | |||||||
\(60\) | −246.313 | −0.529980 | ||||||||
\(61\) | −258.284 | −0.542129 | −0.271064 | − | 0.962561i | \(-0.587376\pi\) | ||||
−0.271064 | + | 0.962561i | \(0.587376\pi\) | |||||||
\(62\) | 383.853 | 0.786281 | ||||||||
\(63\) | 82.3432 | 0.164671 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −185.338 | −0.353666 | ||||||||
\(66\) | 516.955 | 0.964134 | ||||||||
\(67\) | −167.372 | −0.305191 | −0.152596 | − | 0.988289i | \(-0.548763\pi\) | ||||
−0.152596 | + | 0.988289i | \(0.548763\pi\) | |||||||
\(68\) | −77.3531 | −0.137948 | ||||||||
\(69\) | −143.198 | −0.249842 | ||||||||
\(70\) | 138.466 | 0.236427 | ||||||||
\(71\) | −281.024 | −0.469739 | −0.234869 | − | 0.972027i | \(-0.575466\pi\) | ||||
−0.234869 | + | 0.972027i | \(0.575466\pi\) | |||||||
\(72\) | −94.1065 | −0.154036 | ||||||||
\(73\) | −643.990 | −1.03251 | −0.516256 | − | 0.856434i | \(-0.672675\pi\) | ||||
−0.516256 | + | 0.856434i | \(0.672675\pi\) | |||||||
\(74\) | −733.364 | −1.15205 | ||||||||
\(75\) | −169.216 | −0.260526 | ||||||||
\(76\) | −209.301 | −0.315900 | ||||||||
\(77\) | −290.610 | −0.430105 | ||||||||
\(78\) | −233.339 | −0.338724 | ||||||||
\(79\) | −397.326 | −0.565856 | −0.282928 | − | 0.959141i | \(-0.591306\pi\) | ||||
−0.282928 | + | 0.959141i | \(0.591306\pi\) | |||||||
\(80\) | −158.247 | −0.221157 | ||||||||
\(81\) | −908.234 | −1.24586 | ||||||||
\(82\) | −162.076 | −0.218271 | ||||||||
\(83\) | 1439.93 | 1.90425 | 0.952126 | − | 0.305705i | \(-0.0988921\pi\) | ||||
0.952126 | + | 0.305705i | \(0.0988921\pi\) | |||||||
\(84\) | 174.329 | 0.226438 | ||||||||
\(85\) | 191.264 | 0.244065 | ||||||||
\(86\) | −405.280 | −0.508168 | ||||||||
\(87\) | −1053.53 | −1.29827 | ||||||||
\(88\) | 332.126 | 0.402326 | ||||||||
\(89\) | −497.107 | −0.592058 | −0.296029 | − | 0.955179i | \(-0.595663\pi\) | ||||
−0.296029 | + | 0.955179i | \(0.595663\pi\) | |||||||
\(90\) | 232.689 | 0.272529 | ||||||||
\(91\) | 131.173 | 0.151106 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −1194.94 | −1.33236 | ||||||||
\(94\) | −173.981 | −0.190902 | ||||||||
\(95\) | 517.519 | 0.558909 | ||||||||
\(96\) | −199.233 | −0.211813 | ||||||||
\(97\) | 193.384 | 0.202425 | 0.101212 | − | 0.994865i | \(-0.467728\pi\) | ||||
0.101212 | + | 0.994865i | \(0.467728\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | −488.363 | −0.495781 | ||||||||
\(100\) | −108.716 | −0.108716 | ||||||||
\(101\) | −1188.22 | −1.17061 | −0.585307 | − | 0.810812i | \(-0.699026\pi\) | ||||
−0.585307 | + | 0.810812i | \(0.699026\pi\) | |||||||
\(102\) | 240.801 | 0.233753 | ||||||||
\(103\) | 805.666 | 0.770725 | 0.385362 | − | 0.922765i | \(-0.374076\pi\) | ||||
0.385362 | + | 0.922765i | \(0.374076\pi\) | |||||||
\(104\) | −149.912 | −0.141347 | ||||||||
\(105\) | −431.047 | −0.400628 | ||||||||
\(106\) | 1416.50 | 1.29795 | ||||||||
\(107\) | 558.186 | 0.504317 | 0.252158 | − | 0.967686i | \(-0.418860\pi\) | ||||
0.252158 | + | 0.967686i | \(0.418860\pi\) | |||||||
\(108\) | −379.456 | −0.338085 | ||||||||
\(109\) | 540.293 | 0.474777 | 0.237388 | − | 0.971415i | \(-0.423709\pi\) | ||||
0.237388 | + | 0.971415i | \(0.423709\pi\) | |||||||
\(110\) | −821.219 | −0.711820 | ||||||||
\(111\) | 2282.97 | 1.95216 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1060.50 | 0.882865 | 0.441433 | − | 0.897294i | \(-0.354470\pi\) | ||||
0.441433 | + | 0.897294i | \(0.354470\pi\) | |||||||
\(114\) | 651.555 | 0.535295 | ||||||||
\(115\) | 227.480 | 0.184458 | ||||||||
\(116\) | −676.853 | −0.541761 | ||||||||
\(117\) | 220.433 | 0.174180 | ||||||||
\(118\) | 1236.71 | 0.964820 | ||||||||
\(119\) | −135.368 | −0.104279 | ||||||||
\(120\) | 492.625 | 0.374753 | ||||||||
\(121\) | 392.556 | 0.294933 | ||||||||
\(122\) | 516.568 | 0.383343 | ||||||||
\(123\) | 504.543 | 0.369863 | ||||||||
\(124\) | −767.706 | −0.555984 | ||||||||
\(125\) | 1505.12 | 1.07698 | ||||||||
\(126\) | −164.686 | −0.116440 | ||||||||
\(127\) | 345.613 | 0.241482 | 0.120741 | − | 0.992684i | \(-0.461473\pi\) | ||||
0.120741 | + | 0.992684i | \(0.461473\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 1261.64 | 0.861094 | ||||||||
\(130\) | 370.675 | 0.250080 | ||||||||
\(131\) | 1303.42 | 0.869316 | 0.434658 | − | 0.900596i | \(-0.356869\pi\) | ||||
0.434658 | + | 0.900596i | \(0.356869\pi\) | |||||||
\(132\) | −1033.91 | −0.681745 | ||||||||
\(133\) | −366.276 | −0.238798 | ||||||||
\(134\) | 334.745 | 0.215803 | ||||||||
\(135\) | 938.247 | 0.598159 | ||||||||
\(136\) | 154.706 | 0.0975438 | ||||||||
\(137\) | 335.747 | 0.209378 | 0.104689 | − | 0.994505i | \(-0.466615\pi\) | ||||
0.104689 | + | 0.994505i | \(0.466615\pi\) | |||||||
\(138\) | 286.397 | 0.176665 | ||||||||
\(139\) | −1177.75 | −0.718671 | −0.359335 | − | 0.933209i | \(-0.616997\pi\) | ||||
−0.359335 | + | 0.933209i | \(0.616997\pi\) | |||||||
\(140\) | −276.933 | −0.167179 | ||||||||
\(141\) | 541.606 | 0.323485 | ||||||||
\(142\) | 562.049 | 0.332156 | ||||||||
\(143\) | −777.964 | −0.454942 | ||||||||
\(144\) | 188.213 | 0.108920 | ||||||||
\(145\) | 1673.60 | 0.958515 | ||||||||
\(146\) | 1287.98 | 0.730096 | ||||||||
\(147\) | 305.075 | 0.171171 | ||||||||
\(148\) | 1466.73 | 0.814623 | ||||||||
\(149\) | 597.570 | 0.328556 | 0.164278 | − | 0.986414i | \(-0.447471\pi\) | ||||
0.164278 | + | 0.986414i | \(0.447471\pi\) | |||||||
\(150\) | 338.433 | 0.184219 | ||||||||
\(151\) | 1732.94 | 0.933936 | 0.466968 | − | 0.884274i | \(-0.345346\pi\) | ||||
0.466968 | + | 0.884274i | \(0.345346\pi\) | |||||||
\(152\) | 418.601 | 0.223375 | ||||||||
\(153\) | −227.482 | −0.120202 | ||||||||
\(154\) | 581.220 | 0.304130 | ||||||||
\(155\) | 1898.24 | 0.983680 | ||||||||
\(156\) | 466.678 | 0.239514 | ||||||||
\(157\) | 363.093 | 0.184573 | 0.0922867 | − | 0.995732i | \(-0.470582\pi\) | ||||
0.0922867 | + | 0.995732i | \(0.470582\pi\) | |||||||
\(158\) | 794.651 | 0.400121 | ||||||||
\(159\) | −4409.57 | −2.19938 | ||||||||
\(160\) | 316.495 | 0.156382 | ||||||||
\(161\) | −161.000 | −0.0788110 | ||||||||
\(162\) | 1816.47 | 0.880958 | ||||||||
\(163\) | 2426.28 | 1.16590 | 0.582948 | − | 0.812510i | \(-0.301899\pi\) | ||||
0.582948 | + | 0.812510i | \(0.301899\pi\) | |||||||
\(164\) | 324.151 | 0.154341 | ||||||||
\(165\) | 2556.46 | 1.20618 | ||||||||
\(166\) | −2879.86 | −1.34651 | ||||||||
\(167\) | −3858.78 | −1.78803 | −0.894015 | − | 0.448037i | \(-0.852123\pi\) | ||||
−0.894015 | + | 0.448037i | \(0.852123\pi\) | |||||||
\(168\) | −348.657 | −0.160116 | ||||||||
\(169\) | −1845.85 | −0.840168 | ||||||||
\(170\) | −382.529 | −0.172580 | ||||||||
\(171\) | −615.517 | −0.275262 | ||||||||
\(172\) | 810.559 | 0.359329 | ||||||||
\(173\) | 565.736 | 0.248625 | 0.124313 | − | 0.992243i | \(-0.460327\pi\) | ||||
0.124313 | + | 0.992243i | \(0.460327\pi\) | |||||||
\(174\) | 2107.05 | 0.918018 | ||||||||
\(175\) | −190.252 | −0.0821813 | ||||||||
\(176\) | −664.252 | −0.284488 | ||||||||
\(177\) | −3849.90 | −1.63490 | ||||||||
\(178\) | 994.213 | 0.418648 | ||||||||
\(179\) | 1320.44 | 0.551365 | 0.275682 | − | 0.961249i | \(-0.411096\pi\) | ||||
0.275682 | + | 0.961249i | \(0.411096\pi\) | |||||||
\(180\) | −465.378 | −0.192707 | ||||||||
\(181\) | 3238.75 | 1.33002 | 0.665011 | − | 0.746833i | \(-0.268427\pi\) | ||||
0.665011 | + | 0.746833i | \(0.268427\pi\) | |||||||
\(182\) | −262.346 | −0.106848 | ||||||||
\(183\) | −1608.08 | −0.649578 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −3626.65 | −1.44128 | ||||||||
\(186\) | 2389.88 | 0.942120 | ||||||||
\(187\) | 802.843 | 0.313956 | ||||||||
\(188\) | 347.963 | 0.134988 | ||||||||
\(189\) | −664.047 | −0.255568 | ||||||||
\(190\) | −1035.04 | −0.395208 | ||||||||
\(191\) | 2268.39 | 0.859344 | 0.429672 | − | 0.902985i | \(-0.358629\pi\) | ||||
0.429672 | + | 0.902985i | \(0.358629\pi\) | |||||||
\(192\) | 398.465 | 0.149775 | ||||||||
\(193\) | 4299.35 | 1.60349 | 0.801747 | − | 0.597664i | \(-0.203904\pi\) | ||||
0.801747 | + | 0.597664i | \(0.203904\pi\) | |||||||
\(194\) | −386.768 | −0.143136 | ||||||||
\(195\) | −1153.91 | −0.423762 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −214.502 | −0.0775768 | −0.0387884 | − | 0.999247i | \(-0.512350\pi\) | ||||
−0.0387884 | + | 0.999247i | \(0.512350\pi\) | |||||||
\(198\) | 976.725 | 0.350570 | ||||||||
\(199\) | −4983.74 | −1.77532 | −0.887658 | − | 0.460504i | \(-0.847669\pi\) | ||||
−0.887658 | + | 0.460504i | \(0.847669\pi\) | |||||||
\(200\) | 217.431 | 0.0768735 | ||||||||
\(201\) | −1042.06 | −0.365679 | ||||||||
\(202\) | 2376.43 | 0.827749 | ||||||||
\(203\) | −1184.49 | −0.409533 | ||||||||
\(204\) | −481.602 | −0.165289 | ||||||||
\(205\) | −801.501 | −0.273069 | ||||||||
\(206\) | −1611.33 | −0.544985 | ||||||||
\(207\) | −270.556 | −0.0908452 | ||||||||
\(208\) | 299.824 | 0.0999475 | ||||||||
\(209\) | 2172.32 | 0.718958 | ||||||||
\(210\) | 862.094 | 0.283286 | ||||||||
\(211\) | −1863.75 | −0.608083 | −0.304042 | − | 0.952659i | \(-0.598336\pi\) | ||||
−0.304042 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(212\) | −2833.00 | −0.917788 | ||||||||
\(213\) | −1749.66 | −0.562840 | ||||||||
\(214\) | −1116.37 | −0.356606 | ||||||||
\(215\) | −2004.20 | −0.635746 | ||||||||
\(216\) | 758.911 | 0.239062 | ||||||||
\(217\) | −1343.49 | −0.420285 | ||||||||
\(218\) | −1080.59 | −0.335718 | ||||||||
\(219\) | −4009.49 | −1.23715 | ||||||||
\(220\) | 1642.44 | 0.503332 | ||||||||
\(221\) | −362.381 | −0.110300 | ||||||||
\(222\) | −4565.94 | −1.38039 | ||||||||
\(223\) | 4056.06 | 1.21800 | 0.609000 | − | 0.793170i | \(-0.291571\pi\) | ||||
0.609000 | + | 0.793170i | \(0.291571\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −319.714 | −0.0947301 | ||||||||
\(226\) | −2121.01 | −0.624280 | ||||||||
\(227\) | 3197.93 | 0.935040 | 0.467520 | − | 0.883983i | \(-0.345148\pi\) | ||||
0.467520 | + | 0.883983i | \(0.345148\pi\) | |||||||
\(228\) | −1303.11 | −0.378511 | ||||||||
\(229\) | 1986.22 | 0.573157 | 0.286579 | − | 0.958057i | \(-0.407482\pi\) | ||||
0.286579 | + | 0.958057i | \(0.407482\pi\) | |||||||
\(230\) | −454.961 | −0.130431 | ||||||||
\(231\) | −1809.34 | −0.515351 | ||||||||
\(232\) | 1353.71 | 0.383083 | ||||||||
\(233\) | 625.027 | 0.175738 | 0.0878688 | − | 0.996132i | \(-0.471994\pi\) | ||||
0.0878688 | + | 0.996132i | \(0.471994\pi\) | |||||||
\(234\) | −440.866 | −0.123164 | ||||||||
\(235\) | −860.378 | −0.238829 | ||||||||
\(236\) | −2473.43 | −0.682231 | ||||||||
\(237\) | −2473.76 | −0.678007 | ||||||||
\(238\) | 270.736 | 0.0737362 | ||||||||
\(239\) | −5688.03 | −1.53945 | −0.769724 | − | 0.638377i | \(-0.779606\pi\) | ||||
−0.769724 | + | 0.638377i | \(0.779606\pi\) | |||||||
\(240\) | −985.251 | −0.264990 | ||||||||
\(241\) | 5167.63 | 1.38123 | 0.690614 | − | 0.723223i | \(-0.257340\pi\) | ||||
0.690614 | + | 0.723223i | \(0.257340\pi\) | |||||||
\(242\) | −785.111 | −0.208549 | ||||||||
\(243\) | −3093.36 | −0.816621 | ||||||||
\(244\) | −1033.14 | −0.271064 | ||||||||
\(245\) | −484.632 | −0.126376 | ||||||||
\(246\) | −1009.09 | −0.261532 | ||||||||
\(247\) | −980.522 | −0.252588 | ||||||||
\(248\) | 1535.41 | 0.393140 | ||||||||
\(249\) | 8965.04 | 2.28167 | ||||||||
\(250\) | −3010.24 | −0.761536 | ||||||||
\(251\) | −493.136 | −0.124010 | −0.0620049 | − | 0.998076i | \(-0.519749\pi\) | ||||
−0.0620049 | + | 0.998076i | \(0.519749\pi\) | |||||||
\(252\) | 329.373 | 0.0823355 | ||||||||
\(253\) | 954.862 | 0.237279 | ||||||||
\(254\) | −691.227 | −0.170754 | ||||||||
\(255\) | 1190.82 | 0.292438 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 3505.77 | 0.850910 | 0.425455 | − | 0.904980i | \(-0.360114\pi\) | ||||
0.425455 | + | 0.904980i | \(0.360114\pi\) | |||||||
\(258\) | −2523.28 | −0.608886 | ||||||||
\(259\) | 2566.77 | 0.615797 | ||||||||
\(260\) | −741.350 | −0.176833 | ||||||||
\(261\) | −1990.51 | −0.472067 | ||||||||
\(262\) | −2606.84 | −0.614699 | ||||||||
\(263\) | −1693.68 | −0.397098 | −0.198549 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198549 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(264\) | 2067.82 | 0.482067 | ||||||||
\(265\) | 7004.91 | 1.62380 | ||||||||
\(266\) | 732.552 | 0.168856 | ||||||||
\(267\) | −3094.99 | −0.709403 | ||||||||
\(268\) | −669.490 | −0.152596 | ||||||||
\(269\) | 1108.75 | 0.251308 | 0.125654 | − | 0.992074i | \(-0.459897\pi\) | ||||
0.125654 | + | 0.992074i | \(0.459897\pi\) | |||||||
\(270\) | −1876.49 | −0.422962 | ||||||||
\(271\) | 784.351 | 0.175815 | 0.0879076 | − | 0.996129i | \(-0.471982\pi\) | ||||
0.0879076 | + | 0.996129i | \(0.471982\pi\) | |||||||
\(272\) | −309.412 | −0.0689739 | ||||||||
\(273\) | 816.687 | 0.181055 | ||||||||
\(274\) | −671.493 | −0.148052 | ||||||||
\(275\) | 1128.35 | 0.247426 | ||||||||
\(276\) | −572.794 | −0.124921 | ||||||||
\(277\) | −7088.58 | −1.53759 | −0.768794 | − | 0.639497i | \(-0.779143\pi\) | ||||
−0.768794 | + | 0.639497i | \(0.779143\pi\) | |||||||
\(278\) | 2355.49 | 0.508177 | ||||||||
\(279\) | −2257.69 | −0.484461 | ||||||||
\(280\) | 553.865 | 0.118214 | ||||||||
\(281\) | −7749.43 | −1.64517 | −0.822584 | − | 0.568644i | \(-0.807468\pi\) | ||||
−0.822584 | + | 0.568644i | \(0.807468\pi\) | |||||||
\(282\) | −1083.21 | −0.228739 | ||||||||
\(283\) | −1837.38 | −0.385939 | −0.192969 | − | 0.981205i | \(-0.561812\pi\) | ||||
−0.192969 | + | 0.981205i | \(0.561812\pi\) | |||||||
\(284\) | −1124.10 | −0.234869 | ||||||||
\(285\) | 3222.09 | 0.669684 | ||||||||
\(286\) | 1555.93 | 0.321692 | ||||||||
\(287\) | 567.265 | 0.116671 | ||||||||
\(288\) | −376.426 | −0.0770178 | ||||||||
\(289\) | −4539.03 | −0.923882 | ||||||||
\(290\) | −3347.19 | −0.677772 | ||||||||
\(291\) | 1204.01 | 0.242545 | ||||||||
\(292\) | −2575.96 | −0.516256 | ||||||||
\(293\) | −200.688 | −0.0400147 | −0.0200074 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200074 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(294\) | −610.150 | −0.121036 | ||||||||
\(295\) | 6115.83 | 1.20704 | ||||||||
\(296\) | −2933.45 | −0.576026 | ||||||||
\(297\) | 3938.34 | 0.769447 | ||||||||
\(298\) | −1195.14 | −0.232324 | ||||||||
\(299\) | −430.998 | −0.0833620 | ||||||||
\(300\) | −676.865 | −0.130263 | ||||||||
\(301\) | 1418.48 | 0.271627 | ||||||||
\(302\) | −3465.87 | −0.660393 | ||||||||
\(303\) | −7397.86 | −1.40263 | ||||||||
\(304\) | −837.202 | −0.157950 | ||||||||
\(305\) | 2554.54 | 0.479583 | ||||||||
\(306\) | 454.965 | 0.0849954 | ||||||||
\(307\) | −2168.79 | −0.403190 | −0.201595 | − | 0.979469i | \(-0.564612\pi\) | ||||
−0.201595 | + | 0.979469i | \(0.564612\pi\) | |||||||
\(308\) | −1162.44 | −0.215053 | ||||||||
\(309\) | 5016.09 | 0.923481 | ||||||||
\(310\) | −3796.48 | −0.695567 | ||||||||
\(311\) | −9214.82 | −1.68014 | −0.840072 | − | 0.542475i | \(-0.817487\pi\) | ||||
−0.840072 | + | 0.542475i | \(0.817487\pi\) | |||||||
\(312\) | −933.356 | −0.169362 | ||||||||
\(313\) | 855.244 | 0.154445 | 0.0772224 | − | 0.997014i | \(-0.475395\pi\) | ||||
0.0772224 | + | 0.997014i | \(0.475395\pi\) | |||||||
\(314\) | −726.187 | −0.130513 | ||||||||
\(315\) | −814.412 | −0.145673 | ||||||||
\(316\) | −1589.30 | −0.282928 | ||||||||
\(317\) | −3621.69 | −0.641686 | −0.320843 | − | 0.947132i | \(-0.603966\pi\) | ||||
−0.320843 | + | 0.947132i | \(0.603966\pi\) | |||||||
\(318\) | 8819.15 | 1.55520 | ||||||||
\(319\) | 7025.01 | 1.23299 | ||||||||
\(320\) | −632.989 | −0.110579 | ||||||||
\(321\) | 3475.28 | 0.604271 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 1011.88 | 0.174311 | ||||||||
\(324\) | −3632.94 | −0.622931 | ||||||||
\(325\) | −509.306 | −0.0869268 | ||||||||
\(326\) | −4852.56 | −0.824413 | ||||||||
\(327\) | 3363.87 | 0.568877 | ||||||||
\(328\) | −648.302 | −0.109136 | ||||||||
\(329\) | 608.935 | 0.102042 | ||||||||
\(330\) | −5112.92 | −0.852901 | ||||||||
\(331\) | 2886.49 | 0.479323 | 0.239662 | − | 0.970856i | \(-0.422964\pi\) | ||||
0.239662 | + | 0.970856i | \(0.422964\pi\) | |||||||
\(332\) | 5759.72 | 0.952126 | ||||||||
\(333\) | 4313.39 | 0.709827 | ||||||||
\(334\) | 7717.55 | 1.26433 | ||||||||
\(335\) | 1655.39 | 0.269981 | ||||||||
\(336\) | 697.314 | 0.113219 | ||||||||
\(337\) | −2056.69 | −0.332448 | −0.166224 | − | 0.986088i | \(-0.553158\pi\) | ||||
−0.166224 | + | 0.986088i | \(0.553158\pi\) | |||||||
\(338\) | 3691.70 | 0.594088 | ||||||||
\(339\) | 6602.72 | 1.05785 | ||||||||
\(340\) | 765.058 | 0.122033 | ||||||||
\(341\) | 7967.97 | 1.26537 | ||||||||
\(342\) | 1231.03 | 0.194639 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −1621.12 | −0.254084 | ||||||||
\(345\) | 1416.30 | 0.221017 | ||||||||
\(346\) | −1131.47 | −0.175804 | ||||||||
\(347\) | 3641.32 | 0.563332 | 0.281666 | − | 0.959513i | \(-0.409113\pi\) | ||||
0.281666 | + | 0.959513i | \(0.409113\pi\) | |||||||
\(348\) | −4214.10 | −0.649137 | ||||||||
\(349\) | 7487.45 | 1.14841 | 0.574204 | − | 0.818713i | \(-0.305312\pi\) | ||||
0.574204 | + | 0.818713i | \(0.305312\pi\) | |||||||
\(350\) | 380.505 | 0.0581109 | ||||||||
\(351\) | −1777.66 | −0.270326 | ||||||||
\(352\) | 1328.50 | 0.201163 | ||||||||
\(353\) | 11902.3 | 1.79460 | 0.897302 | − | 0.441416i | \(-0.145524\pi\) | ||||
0.897302 | + | 0.441416i | \(0.145524\pi\) | |||||||
\(354\) | 7699.81 | 1.15605 | ||||||||
\(355\) | 2779.46 | 0.415545 | ||||||||
\(356\) | −1988.43 | −0.296029 | ||||||||
\(357\) | −842.804 | −0.124946 | ||||||||
\(358\) | −2640.88 | −0.389874 | ||||||||
\(359\) | −4802.20 | −0.705991 | −0.352995 | − | 0.935625i | \(-0.614837\pi\) | ||||
−0.352995 | + | 0.935625i | \(0.614837\pi\) | |||||||
\(360\) | 930.756 | 0.136264 | ||||||||
\(361\) | −4121.08 | −0.600828 | ||||||||
\(362\) | −6477.49 | −0.940468 | ||||||||
\(363\) | 2444.06 | 0.353388 | ||||||||
\(364\) | 524.693 | 0.0755532 | ||||||||
\(365\) | 6369.35 | 0.913390 | ||||||||
\(366\) | 3216.16 | 0.459321 | ||||||||
\(367\) | −9127.37 | −1.29822 | −0.649108 | − | 0.760697i | \(-0.724857\pi\) | ||||
−0.649108 | + | 0.760697i | \(0.724857\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 953.273 | 0.134486 | ||||||||
\(370\) | 7253.30 | 1.01914 | ||||||||
\(371\) | −4957.74 | −0.693782 | ||||||||
\(372\) | −4779.75 | −0.666179 | ||||||||
\(373\) | −12900.8 | −1.79083 | −0.895413 | − | 0.445237i | \(-0.853120\pi\) | ||||
−0.895413 | + | 0.445237i | \(0.853120\pi\) | |||||||
\(374\) | −1605.69 | −0.222000 | ||||||||
\(375\) | 9370.90 | 1.29043 | ||||||||
\(376\) | −695.926 | −0.0954511 | ||||||||
\(377\) | −3170.89 | −0.433181 | ||||||||
\(378\) | 1328.09 | 0.180714 | ||||||||
\(379\) | −1830.25 | −0.248058 | −0.124029 | − | 0.992279i | \(-0.539582\pi\) | ||||
−0.124029 | + | 0.992279i | \(0.539582\pi\) | |||||||
\(380\) | 2070.08 | 0.279455 | ||||||||
\(381\) | 2151.80 | 0.289343 | ||||||||
\(382\) | −4536.78 | −0.607648 | ||||||||
\(383\) | −8010.59 | −1.06873 | −0.534363 | − | 0.845255i | \(-0.679448\pi\) | ||||
−0.534363 | + | 0.845255i | \(0.679448\pi\) | |||||||
\(384\) | −796.930 | −0.105907 | ||||||||
\(385\) | 2874.27 | 0.380484 | ||||||||
\(386\) | −8598.70 | −1.13384 | ||||||||
\(387\) | 2383.72 | 0.313104 | ||||||||
\(388\) | 773.537 | 0.101212 | ||||||||
\(389\) | 4424.06 | 0.576629 | 0.288315 | − | 0.957536i | \(-0.406905\pi\) | ||||
0.288315 | + | 0.957536i | \(0.406905\pi\) | |||||||
\(390\) | 2307.83 | 0.299645 | ||||||||
\(391\) | 444.780 | 0.0575282 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 8115.12 | 1.04161 | ||||||||
\(394\) | 429.004 | 0.0548551 | ||||||||
\(395\) | 3929.73 | 0.500573 | ||||||||
\(396\) | −1953.45 | −0.247890 | ||||||||
\(397\) | −6976.76 | −0.881999 | −0.440999 | − | 0.897507i | \(-0.645376\pi\) | ||||
−0.440999 | + | 0.897507i | \(0.645376\pi\) | |||||||
\(398\) | 9967.48 | 1.25534 | ||||||||
\(399\) | −2280.44 | −0.286127 | ||||||||
\(400\) | −434.862 | −0.0543578 | ||||||||
\(401\) | −9824.95 | −1.22353 | −0.611764 | − | 0.791040i | \(-0.709540\pi\) | ||||
−0.611764 | + | 0.791040i | \(0.709540\pi\) | |||||||
\(402\) | 2084.13 | 0.258574 | ||||||||
\(403\) | −3596.52 | −0.444554 | ||||||||
\(404\) | −4752.87 | −0.585307 | ||||||||
\(405\) | 8982.85 | 1.10213 | ||||||||
\(406\) | 2368.99 | 0.289583 | ||||||||
\(407\) | −15223.1 | −1.85400 | ||||||||
\(408\) | 963.204 | 0.116877 | ||||||||
\(409\) | 8036.27 | 0.971559 | 0.485780 | − | 0.874081i | \(-0.338536\pi\) | ||||
0.485780 | + | 0.874081i | \(0.338536\pi\) | |||||||
\(410\) | 1603.00 | 0.193089 | ||||||||
\(411\) | 2090.36 | 0.250876 | ||||||||
\(412\) | 3222.66 | 0.385362 | ||||||||
\(413\) | −4328.50 | −0.515718 | ||||||||
\(414\) | 541.112 | 0.0642373 | ||||||||
\(415\) | −14241.6 | −1.68456 | ||||||||
\(416\) | −599.649 | −0.0706736 | ||||||||
\(417\) | −7332.68 | −0.861110 | ||||||||
\(418\) | −4344.63 | −0.508380 | ||||||||
\(419\) | 4471.23 | 0.521322 | 0.260661 | − | 0.965430i | \(-0.416060\pi\) | ||||
0.260661 | + | 0.965430i | \(0.416060\pi\) | |||||||
\(420\) | −1724.19 | −0.200314 | ||||||||
\(421\) | −8709.07 | −1.00820 | −0.504102 | − | 0.863644i | \(-0.668177\pi\) | ||||
−0.504102 | + | 0.863644i | \(0.668177\pi\) | |||||||
\(422\) | 3727.49 | 0.429980 | ||||||||
\(423\) | 1023.30 | 0.117623 | ||||||||
\(424\) | 5665.99 | 0.648974 | ||||||||
\(425\) | 525.593 | 0.0599883 | ||||||||
\(426\) | 3499.33 | 0.397988 | ||||||||
\(427\) | −1807.99 | −0.204905 | ||||||||
\(428\) | 2232.75 | 0.252158 | ||||||||
\(429\) | −4843.62 | −0.545110 | ||||||||
\(430\) | 4008.40 | 0.449540 | ||||||||
\(431\) | −11847.9 | −1.32411 | −0.662056 | − | 0.749455i | \(-0.730316\pi\) | ||||
−0.662056 | + | 0.749455i | \(0.730316\pi\) | |||||||
\(432\) | −1517.82 | −0.169042 | ||||||||
\(433\) | 6306.04 | 0.699882 | 0.349941 | − | 0.936772i | \(-0.386202\pi\) | ||||
0.349941 | + | 0.936772i | \(0.386202\pi\) | |||||||
\(434\) | 2686.97 | 0.297186 | ||||||||
\(435\) | 10419.8 | 1.14849 | ||||||||
\(436\) | 2161.17 | 0.237388 | ||||||||
\(437\) | 1203.48 | 0.131740 | ||||||||
\(438\) | 8018.99 | 0.874799 | ||||||||
\(439\) | −26.8997 | −0.00292449 | −0.00146225 | − | 0.999999i | \(-0.500465\pi\) | ||||
−0.00146225 | + | 0.999999i | \(0.500465\pi\) | |||||||
\(440\) | −3284.88 | −0.355910 | ||||||||
\(441\) | 576.402 | 0.0622398 | ||||||||
\(442\) | 724.761 | 0.0779941 | ||||||||
\(443\) | −12573.3 | −1.34848 | −0.674241 | − | 0.738512i | \(-0.735529\pi\) | ||||
−0.674241 | + | 0.738512i | \(0.735529\pi\) | |||||||
\(444\) | 9131.87 | 0.976080 | ||||||||
\(445\) | 4916.61 | 0.523752 | ||||||||
\(446\) | −8112.13 | −0.861256 | ||||||||
\(447\) | 3720.48 | 0.393675 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 2972.66 | 0.312446 | 0.156223 | − | 0.987722i | \(-0.450068\pi\) | ||||
0.156223 | + | 0.987722i | \(0.450068\pi\) | |||||||
\(450\) | 639.428 | 0.0669843 | ||||||||
\(451\) | −3364.34 | −0.351266 | ||||||||
\(452\) | 4242.01 | 0.441433 | ||||||||
\(453\) | 10789.3 | 1.11904 | ||||||||
\(454\) | −6395.86 | −0.661173 | ||||||||
\(455\) | −1297.36 | −0.133673 | ||||||||
\(456\) | 2606.22 | 0.267648 | ||||||||
\(457\) | 11841.7 | 1.21210 | 0.606050 | − | 0.795426i | \(-0.292753\pi\) | ||||
0.606050 | + | 0.795426i | \(0.292753\pi\) | |||||||
\(458\) | −3972.44 | −0.405284 | ||||||||
\(459\) | 1834.50 | 0.186552 | ||||||||
\(460\) | 909.922 | 0.0922290 | ||||||||
\(461\) | −5145.33 | −0.519831 | −0.259915 | − | 0.965631i | \(-0.583695\pi\) | ||||
−0.259915 | + | 0.965631i | \(0.583695\pi\) | |||||||
\(462\) | 3618.69 | 0.364408 | ||||||||
\(463\) | −10743.6 | −1.07840 | −0.539200 | − | 0.842177i | \(-0.681273\pi\) | ||||
−0.539200 | + | 0.842177i | \(0.681273\pi\) | |||||||
\(464\) | −2707.41 | −0.270880 | ||||||||
\(465\) | 11818.5 | 1.17864 | ||||||||
\(466\) | −1250.05 | −0.124265 | ||||||||
\(467\) | −6047.05 | −0.599195 | −0.299597 | − | 0.954066i | \(-0.596852\pi\) | ||||
−0.299597 | + | 0.954066i | \(0.596852\pi\) | |||||||
\(468\) | 881.732 | 0.0870899 | ||||||||
\(469\) | −1171.61 | −0.115351 | ||||||||
\(470\) | 1720.76 | 0.168878 | ||||||||
\(471\) | 2260.63 | 0.221155 | ||||||||
\(472\) | 4946.86 | 0.482410 | ||||||||
\(473\) | −8412.74 | −0.817797 | ||||||||
\(474\) | 4947.51 | 0.479424 | ||||||||
\(475\) | 1422.14 | 0.137373 | ||||||||
\(476\) | −541.472 | −0.0521393 | ||||||||
\(477\) | −8331.36 | −0.799720 | ||||||||
\(478\) | 11376.1 | 1.08855 | ||||||||
\(479\) | −1039.14 | −0.0991223 | −0.0495612 | − | 0.998771i | \(-0.515782\pi\) | ||||
−0.0495612 | + | 0.998771i | \(0.515782\pi\) | |||||||
\(480\) | 1970.50 | 0.187376 | ||||||||
\(481\) | 6871.26 | 0.651357 | ||||||||
\(482\) | −10335.3 | −0.976676 | ||||||||
\(483\) | −1002.39 | −0.0944312 | ||||||||
\(484\) | 1570.22 | 0.147466 | ||||||||
\(485\) | −1912.66 | −0.179071 | ||||||||
\(486\) | 6186.71 | 0.577438 | ||||||||
\(487\) | 4060.20 | 0.377793 | 0.188896 | − | 0.981997i | \(-0.439509\pi\) | ||||
0.188896 | + | 0.981997i | \(0.439509\pi\) | |||||||
\(488\) | 2066.27 | 0.191671 | ||||||||
\(489\) | 15106.1 | 1.39697 | ||||||||
\(490\) | 969.265 | 0.0893610 | ||||||||
\(491\) | 7755.82 | 0.712862 | 0.356431 | − | 0.934322i | \(-0.383993\pi\) | ||||
0.356431 | + | 0.934322i | \(0.383993\pi\) | |||||||
\(492\) | 2018.17 | 0.184931 | ||||||||
\(493\) | 3272.29 | 0.298939 | ||||||||
\(494\) | 1961.04 | 0.178606 | ||||||||
\(495\) | 4830.13 | 0.438582 | ||||||||
\(496\) | −3070.83 | −0.277992 | ||||||||
\(497\) | −1967.17 | −0.177545 | ||||||||
\(498\) | −17930.1 | −1.61339 | ||||||||
\(499\) | 12482.6 | 1.11984 | 0.559919 | − | 0.828547i | \(-0.310832\pi\) | ||||
0.559919 | + | 0.828547i | \(0.310832\pi\) | |||||||
\(500\) | 6020.47 | 0.538488 | ||||||||
\(501\) | −24024.8 | −2.14241 | ||||||||
\(502\) | 986.272 | 0.0876882 | ||||||||
\(503\) | 7263.00 | 0.643819 | 0.321910 | − | 0.946770i | \(-0.395675\pi\) | ||||
0.321910 | + | 0.946770i | \(0.395675\pi\) | |||||||
\(504\) | −658.746 | −0.0582200 | ||||||||
\(505\) | 11752.0 | 1.03556 | ||||||||
\(506\) | −1909.72 | −0.167782 | ||||||||
\(507\) | −11492.3 | −1.00669 | ||||||||
\(508\) | 1382.45 | 0.120741 | ||||||||
\(509\) | −9298.85 | −0.809753 | −0.404876 | − | 0.914371i | \(-0.632685\pi\) | ||||
−0.404876 | + | 0.914371i | \(0.632685\pi\) | |||||||
\(510\) | −2381.63 | −0.206785 | ||||||||
\(511\) | −4507.93 | −0.390253 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 4963.77 | 0.427204 | ||||||||
\(514\) | −7011.54 | −0.601684 | ||||||||
\(515\) | −7968.40 | −0.681805 | ||||||||
\(516\) | 5046.56 | 0.430547 | ||||||||
\(517\) | −3611.48 | −0.307220 | ||||||||
\(518\) | −5133.55 | −0.435434 | ||||||||
\(519\) | 3522.28 | 0.297902 | ||||||||
\(520\) | 1482.70 | 0.125040 | ||||||||
\(521\) | 17700.1 | 1.48840 | 0.744200 | − | 0.667957i | \(-0.232831\pi\) | ||||
0.744200 | + | 0.667957i | \(0.232831\pi\) | |||||||
\(522\) | 3981.02 | 0.333802 | ||||||||
\(523\) | −4985.36 | −0.416815 | −0.208408 | − | 0.978042i | \(-0.566828\pi\) | ||||
−0.208408 | + | 0.978042i | \(0.566828\pi\) | |||||||
\(524\) | 5213.68 | 0.434658 | ||||||||
\(525\) | −1184.51 | −0.0984694 | ||||||||
\(526\) | 3387.36 | 0.280791 | ||||||||
\(527\) | 3711.53 | 0.306787 | ||||||||
\(528\) | −4135.64 | −0.340873 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −14009.8 | −1.14820 | ||||||||
\(531\) | −7273.93 | −0.594467 | ||||||||
\(532\) | −1465.10 | −0.119399 | ||||||||
\(533\) | 1518.57 | 0.123408 | ||||||||
\(534\) | 6189.99 | 0.501624 | ||||||||
\(535\) | −5520.72 | −0.446133 | ||||||||
\(536\) | 1338.98 | 0.107901 | ||||||||
\(537\) | 8221.08 | 0.660644 | ||||||||
\(538\) | −2217.51 | −0.177702 | ||||||||
\(539\) | −2034.27 | −0.162564 | ||||||||
\(540\) | 3752.99 | 0.299079 | ||||||||
\(541\) | 15877.9 | 1.26182 | 0.630910 | − | 0.775856i | \(-0.282682\pi\) | ||||
0.630910 | + | 0.775856i | \(0.282682\pi\) | |||||||
\(542\) | −1568.70 | −0.124320 | ||||||||
\(543\) | 20164.5 | 1.59363 | ||||||||
\(544\) | 618.825 | 0.0487719 | ||||||||
\(545\) | −5343.74 | −0.420001 | ||||||||
\(546\) | −1633.37 | −0.128026 | ||||||||
\(547\) | −8542.53 | −0.667737 | −0.333869 | − | 0.942620i | \(-0.608354\pi\) | ||||
−0.333869 | + | 0.942620i | \(0.608354\pi\) | |||||||
\(548\) | 1342.99 | 0.104689 | ||||||||
\(549\) | −3038.27 | −0.236194 | ||||||||
\(550\) | −2256.70 | −0.174957 | ||||||||
\(551\) | 8854.11 | 0.684569 | ||||||||
\(552\) | 1145.59 | 0.0883323 | ||||||||
\(553\) | −2781.28 | −0.213873 | ||||||||
\(554\) | 14177.2 | 1.08724 | ||||||||
\(555\) | −22579.6 | −1.72694 | ||||||||
\(556\) | −4710.99 | −0.359335 | ||||||||
\(557\) | −14999.9 | −1.14106 | −0.570528 | − | 0.821278i | \(-0.693261\pi\) | ||||
−0.570528 | + | 0.821278i | \(0.693261\pi\) | |||||||
\(558\) | 4515.39 | 0.342565 | ||||||||
\(559\) | 3797.27 | 0.287312 | ||||||||
\(560\) | −1107.73 | −0.0835896 | ||||||||
\(561\) | 4998.51 | 0.376181 | ||||||||
\(562\) | 15498.9 | 1.16331 | ||||||||
\(563\) | 19048.3 | 1.42592 | 0.712959 | − | 0.701206i | \(-0.247355\pi\) | ||||
0.712959 | + | 0.701206i | \(0.247355\pi\) | |||||||
\(564\) | 2166.42 | 0.161743 | ||||||||
\(565\) | −10488.9 | −0.781008 | ||||||||
\(566\) | 3674.75 | 0.272900 | ||||||||
\(567\) | −6357.64 | −0.470892 | ||||||||
\(568\) | 2248.20 | 0.166078 | ||||||||
\(569\) | −4524.55 | −0.333355 | −0.166678 | − | 0.986011i | \(-0.553304\pi\) | ||||
−0.166678 | + | 0.986011i | \(0.553304\pi\) | |||||||
\(570\) | −6444.17 | −0.473538 | ||||||||
\(571\) | −21959.6 | −1.60942 | −0.804712 | − | 0.593666i | \(-0.797680\pi\) | ||||
−0.804712 | + | 0.593666i | \(0.797680\pi\) | |||||||
\(572\) | −3111.86 | −0.227471 | ||||||||
\(573\) | 14123.0 | 1.02966 | ||||||||
\(574\) | −1134.53 | −0.0824988 | ||||||||
\(575\) | 625.115 | 0.0453375 | ||||||||
\(576\) | 752.852 | 0.0544598 | ||||||||
\(577\) | 6815.71 | 0.491753 | 0.245877 | − | 0.969301i | \(-0.420924\pi\) | ||||
0.245877 | + | 0.969301i | \(0.420924\pi\) | |||||||
\(578\) | 9078.06 | 0.653283 | ||||||||
\(579\) | 26767.9 | 1.92130 | ||||||||
\(580\) | 6694.39 | 0.479257 | ||||||||
\(581\) | 10079.5 | 0.719740 | ||||||||
\(582\) | −2408.03 | −0.171505 | ||||||||
\(583\) | 29403.5 | 2.08880 | ||||||||
\(584\) | 5151.92 | 0.365048 | ||||||||
\(585\) | −2180.18 | −0.154085 | ||||||||
\(586\) | 401.376 | 0.0282947 | ||||||||
\(587\) | −10153.0 | −0.713898 | −0.356949 | − | 0.934124i | \(-0.616183\pi\) | ||||
−0.356949 | + | 0.934124i | \(0.616183\pi\) | |||||||
\(588\) | 1220.30 | 0.0855856 | ||||||||
\(589\) | 10042.6 | 0.702542 | ||||||||
\(590\) | −12231.7 | −0.853508 | ||||||||
\(591\) | −1335.49 | −0.0929523 | ||||||||
\(592\) | 5866.91 | 0.407312 | ||||||||
\(593\) | 5891.25 | 0.407968 | 0.203984 | − | 0.978974i | \(-0.434611\pi\) | ||||
0.203984 | + | 0.978974i | \(0.434611\pi\) | |||||||
\(594\) | −7876.69 | −0.544081 | ||||||||
\(595\) | 1338.85 | 0.0922479 | ||||||||
\(596\) | 2390.28 | 0.164278 | ||||||||
\(597\) | −31028.8 | −2.12718 | ||||||||
\(598\) | 861.995 | 0.0589458 | ||||||||
\(599\) | −26348.6 | −1.79728 | −0.898642 | − | 0.438683i | \(-0.855445\pi\) | ||||
−0.898642 | + | 0.438683i | \(0.855445\pi\) | |||||||
\(600\) | 1353.73 | 0.0921097 | ||||||||
\(601\) | −11213.6 | −0.761088 | −0.380544 | − | 0.924763i | \(-0.624263\pi\) | ||||
−0.380544 | + | 0.924763i | \(0.624263\pi\) | |||||||
\(602\) | −2836.96 | −0.192069 | ||||||||
\(603\) | −1968.85 | −0.132965 | ||||||||
\(604\) | 6931.74 | 0.466968 | ||||||||
\(605\) | −3882.55 | −0.260906 | ||||||||
\(606\) | 14795.7 | 0.991807 | ||||||||
\(607\) | −17937.3 | −1.19943 | −0.599713 | − | 0.800215i | \(-0.704719\pi\) | ||||
−0.599713 | + | 0.800215i | \(0.704719\pi\) | |||||||
\(608\) | 1674.40 | 0.111688 | ||||||||
\(609\) | −7374.68 | −0.490701 | ||||||||
\(610\) | −5109.09 | −0.339116 | ||||||||
\(611\) | 1630.12 | 0.107934 | ||||||||
\(612\) | −909.929 | −0.0601008 | ||||||||
\(613\) | 6735.03 | 0.443761 | 0.221880 | − | 0.975074i | \(-0.428781\pi\) | ||||
0.221880 | + | 0.975074i | \(0.428781\pi\) | |||||||
\(614\) | 4337.57 | 0.285098 | ||||||||
\(615\) | −4990.16 | −0.327191 | ||||||||
\(616\) | 2324.88 | 0.152065 | ||||||||
\(617\) | 21561.2 | 1.40684 | 0.703421 | − | 0.710773i | \(-0.251655\pi\) | ||||
0.703421 | + | 0.710773i | \(0.251655\pi\) | |||||||
\(618\) | −10032.2 | −0.652999 | ||||||||
\(619\) | −811.525 | −0.0526946 | −0.0263473 | − | 0.999653i | \(-0.508388\pi\) | ||||
−0.0263473 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(620\) | 7592.96 | 0.491840 | ||||||||
\(621\) | 2181.87 | 0.140991 | ||||||||
\(622\) | 18429.6 | 1.18804 | ||||||||
\(623\) | −3479.75 | −0.223777 | ||||||||
\(624\) | 1866.71 | 0.119757 | ||||||||
\(625\) | −11488.9 | −0.735292 | ||||||||
\(626\) | −1710.49 | −0.109209 | ||||||||
\(627\) | 13524.9 | 0.861454 | ||||||||
\(628\) | 1452.37 | 0.0922867 | ||||||||
\(629\) | −7091.00 | −0.449502 | ||||||||
\(630\) | 1628.82 | 0.103006 | ||||||||
\(631\) | −6015.69 | −0.379526 | −0.189763 | − | 0.981830i | \(-0.560772\pi\) | ||||
−0.189763 | + | 0.981830i | \(0.560772\pi\) | |||||||
\(632\) | 3178.60 | 0.200060 | ||||||||
\(633\) | −11603.7 | −0.728604 | ||||||||
\(634\) | 7243.39 | 0.453741 | ||||||||
\(635\) | −3418.27 | −0.213622 | ||||||||
\(636\) | −17638.3 | −1.09969 | ||||||||
\(637\) | 918.212 | 0.0571129 | ||||||||
\(638\) | −14050.0 | −0.871859 | ||||||||
\(639\) | −3305.78 | −0.204655 | ||||||||
\(640\) | 1265.98 | 0.0781909 | ||||||||
\(641\) | −28011.7 | −1.72604 | −0.863022 | − | 0.505166i | \(-0.831431\pi\) | ||||
−0.863022 | + | 0.505166i | \(0.831431\pi\) | |||||||
\(642\) | −6950.56 | −0.427284 | ||||||||
\(643\) | −8896.79 | −0.545653 | −0.272827 | − | 0.962063i | \(-0.587959\pi\) | ||||
−0.272827 | + | 0.962063i | \(0.587959\pi\) | |||||||
\(644\) | −644.000 | −0.0394055 | ||||||||
\(645\) | −12478.2 | −0.761749 | ||||||||
\(646\) | −2023.76 | −0.123256 | ||||||||
\(647\) | −15429.8 | −0.937570 | −0.468785 | − | 0.883312i | \(-0.655308\pi\) | ||||
−0.468785 | + | 0.883312i | \(0.655308\pi\) | |||||||
\(648\) | 7265.87 | 0.440479 | ||||||||
\(649\) | 25671.6 | 1.55269 | ||||||||
\(650\) | 1018.61 | 0.0614666 | ||||||||
\(651\) | −8364.57 | −0.503584 | ||||||||
\(652\) | 9705.12 | 0.582948 | ||||||||
\(653\) | 11711.0 | 0.701820 | 0.350910 | − | 0.936409i | \(-0.385872\pi\) | ||||
0.350910 | + | 0.936409i | \(0.385872\pi\) | |||||||
\(654\) | −6727.75 | −0.402257 | ||||||||
\(655\) | −12891.4 | −0.769022 | ||||||||
\(656\) | 1296.60 | 0.0771706 | ||||||||
\(657\) | −7575.46 | −0.449843 | ||||||||
\(658\) | −1217.87 | −0.0721543 | ||||||||
\(659\) | 10814.5 | 0.639258 | 0.319629 | − | 0.947543i | \(-0.396442\pi\) | ||||
0.319629 | + | 0.947543i | \(0.396442\pi\) | |||||||
\(660\) | 10225.8 | 0.603092 | ||||||||
\(661\) | 4122.46 | 0.242580 | 0.121290 | − | 0.992617i | \(-0.461297\pi\) | ||||
0.121290 | + | 0.992617i | \(0.461297\pi\) | |||||||
\(662\) | −5772.99 | −0.338933 | ||||||||
\(663\) | −2256.19 | −0.132162 | ||||||||
\(664\) | −11519.4 | −0.673255 | ||||||||
\(665\) | 3622.64 | 0.211248 | ||||||||
\(666\) | −8626.79 | −0.501924 | ||||||||
\(667\) | 3891.91 | 0.225930 | ||||||||
\(668\) | −15435.1 | −0.894015 | ||||||||
\(669\) | 25253.1 | 1.45941 | ||||||||
\(670\) | −3310.78 | −0.190905 | ||||||||
\(671\) | 10722.8 | 0.616916 | ||||||||
\(672\) | −1394.63 | −0.0800580 | ||||||||
\(673\) | −21192.2 | −1.21382 | −0.606909 | − | 0.794771i | \(-0.707591\pi\) | ||||
−0.606909 | + | 0.794771i | \(0.707591\pi\) | |||||||
\(674\) | 4113.38 | 0.235077 | ||||||||
\(675\) | 2578.30 | 0.147020 | ||||||||
\(676\) | −7383.40 | −0.420084 | ||||||||
\(677\) | −29376.9 | −1.66772 | −0.833860 | − | 0.551976i | \(-0.813874\pi\) | ||||
−0.833860 | + | 0.551976i | \(0.813874\pi\) | |||||||
\(678\) | −13205.4 | −0.748011 | ||||||||
\(679\) | 1353.69 | 0.0765093 | ||||||||
\(680\) | −1530.12 | −0.0862901 | ||||||||
\(681\) | 19910.4 | 1.12036 | ||||||||
\(682\) | −15935.9 | −0.894749 | ||||||||
\(683\) | −2923.77 | −0.163800 | −0.0818998 | − | 0.996641i | \(-0.526099\pi\) | ||||
−0.0818998 | + | 0.996641i | \(0.526099\pi\) | |||||||
\(684\) | −2462.07 | −0.137631 | ||||||||
\(685\) | −3320.69 | −0.185222 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 12366.2 | 0.686756 | ||||||||
\(688\) | 3242.24 | 0.179664 | ||||||||
\(689\) | −13271.9 | −0.733845 | ||||||||
\(690\) | −2832.60 | −0.156283 | ||||||||
\(691\) | −19904.1 | −1.09579 | −0.547893 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547893 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(692\) | 2262.94 | 0.124313 | ||||||||
\(693\) | −3418.54 | −0.187387 | ||||||||
\(694\) | −7282.64 | −0.398336 | ||||||||
\(695\) | 11648.5 | 0.635757 | ||||||||
\(696\) | 8428.20 | 0.459009 | ||||||||
\(697\) | −1567.13 | −0.0851641 | ||||||||
\(698\) | −14974.9 | −0.812047 | ||||||||
\(699\) | 3891.43 | 0.210569 | ||||||||
\(700\) | −761.009 | −0.0410906 | ||||||||
\(701\) | −15700.8 | −0.845949 | −0.422974 | − | 0.906142i | \(-0.639014\pi\) | ||||
−0.422974 | + | 0.906142i | \(0.639014\pi\) | |||||||
\(702\) | 3555.31 | 0.191149 | ||||||||
\(703\) | −19186.7 | −1.02936 | ||||||||
\(704\) | −2657.01 | −0.142244 | ||||||||
\(705\) | −5356.73 | −0.286165 | ||||||||
\(706\) | −23804.6 | −1.26898 | ||||||||
\(707\) | −8317.52 | −0.442451 | ||||||||
\(708\) | −15399.6 | −0.817448 | ||||||||
\(709\) | −11130.6 | −0.589588 | −0.294794 | − | 0.955561i | \(-0.595251\pi\) | ||||
−0.294794 | + | 0.955561i | \(0.595251\pi\) | |||||||
\(710\) | −5558.92 | −0.293835 | ||||||||
\(711\) | −4673.87 | −0.246531 | ||||||||
\(712\) | 3976.85 | 0.209324 | ||||||||
\(713\) | 4414.31 | 0.231862 | ||||||||
\(714\) | 1685.61 | 0.0883505 | ||||||||
\(715\) | 7694.42 | 0.402455 | ||||||||
\(716\) | 5281.76 | 0.275682 | ||||||||
\(717\) | −35413.8 | −1.84456 | ||||||||
\(718\) | 9604.41 | 0.499211 | ||||||||
\(719\) | 26480.8 | 1.37353 | 0.686766 | − | 0.726879i | \(-0.259030\pi\) | ||||
0.686766 | + | 0.726879i | \(0.259030\pi\) | |||||||
\(720\) | −1861.51 | −0.0963534 | ||||||||
\(721\) | 5639.66 | 0.291307 | ||||||||
\(722\) | 8242.16 | 0.424850 | ||||||||
\(723\) | 32173.7 | 1.65498 | ||||||||
\(724\) | 12955.0 | 0.665011 | ||||||||
\(725\) | 4599.03 | 0.235591 | ||||||||
\(726\) | −4888.12 | −0.249883 | ||||||||
\(727\) | 15809.9 | 0.806542 | 0.403271 | − | 0.915081i | \(-0.367873\pi\) | ||||
0.403271 | + | 0.915081i | \(0.367873\pi\) | |||||||
\(728\) | −1049.39 | −0.0534242 | ||||||||
\(729\) | 5263.02 | 0.267389 | ||||||||
\(730\) | −12738.7 | −0.645864 | ||||||||
\(731\) | −3918.71 | −0.198274 | ||||||||
\(732\) | −6432.32 | −0.324789 | ||||||||
\(733\) | −16659.7 | −0.839481 | −0.419740 | − | 0.907644i | \(-0.637879\pi\) | ||||
−0.419740 | + | 0.907644i | \(0.637879\pi\) | |||||||
\(734\) | 18254.7 | 0.917977 | ||||||||
\(735\) | −3017.33 | −0.151423 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 6948.59 | 0.347292 | ||||||||
\(738\) | −1906.55 | −0.0950961 | ||||||||
\(739\) | −36041.7 | −1.79407 | −0.897033 | − | 0.441963i | \(-0.854282\pi\) | ||||
−0.897033 | + | 0.441963i | \(0.854282\pi\) | |||||||
\(740\) | −14506.6 | −0.720640 | ||||||||
\(741\) | −6104.75 | −0.302650 | ||||||||
\(742\) | 9915.49 | 0.490578 | ||||||||
\(743\) | −14639.2 | −0.722828 | −0.361414 | − | 0.932405i | \(-0.617706\pi\) | ||||
−0.361414 | + | 0.932405i | \(0.617706\pi\) | |||||||
\(744\) | 9559.51 | 0.471060 | ||||||||
\(745\) | −5910.24 | −0.290650 | ||||||||
\(746\) | 25801.6 | 1.26631 | ||||||||
\(747\) | 16938.4 | 0.829642 | ||||||||
\(748\) | 3211.37 | 0.156978 | ||||||||
\(749\) | 3907.30 | 0.190614 | ||||||||
\(750\) | −18741.8 | −0.912471 | ||||||||
\(751\) | −15263.2 | −0.741629 | −0.370814 | − | 0.928707i | \(-0.620921\pi\) | ||||
−0.370814 | + | 0.928707i | \(0.620921\pi\) | |||||||
\(752\) | 1391.85 | 0.0674941 | ||||||||
\(753\) | −3070.27 | −0.148588 | ||||||||
\(754\) | 6341.79 | 0.306305 | ||||||||
\(755\) | −17139.5 | −0.826187 | ||||||||
\(756\) | −2656.19 | −0.127784 | ||||||||
\(757\) | −25812.5 | −1.23933 | −0.619663 | − | 0.784868i | \(-0.712731\pi\) | ||||
−0.619663 | + | 0.784868i | \(0.712731\pi\) | |||||||
\(758\) | 3660.51 | 0.175403 | ||||||||
\(759\) | 5944.99 | 0.284307 | ||||||||
\(760\) | −4140.16 | −0.197604 | ||||||||
\(761\) | 8641.54 | 0.411637 | 0.205818 | − | 0.978590i | \(-0.434014\pi\) | ||||
0.205818 | + | 0.978590i | \(0.434014\pi\) | |||||||
\(762\) | −4303.59 | −0.204597 | ||||||||
\(763\) | 3782.05 | 0.179449 | ||||||||
\(764\) | 9073.55 | 0.429672 | ||||||||
\(765\) | 2249.90 | 0.106334 | ||||||||
\(766\) | 16021.2 | 0.755703 | ||||||||
\(767\) | −11587.4 | −0.545498 | ||||||||
\(768\) | 1593.86 | 0.0748874 | ||||||||
\(769\) | 7300.25 | 0.342333 | 0.171166 | − | 0.985242i | \(-0.445246\pi\) | ||||
0.171166 | + | 0.985242i | \(0.445246\pi\) | |||||||
\(770\) | −5748.53 | −0.269042 | ||||||||
\(771\) | 21827.0 | 1.01956 | ||||||||
\(772\) | 17197.4 | 0.801747 | ||||||||
\(773\) | 16068.9 | 0.747684 | 0.373842 | − | 0.927492i | \(-0.378040\pi\) | ||||
0.373842 | + | 0.927492i | \(0.378040\pi\) | |||||||
\(774\) | −4767.43 | −0.221398 | ||||||||
\(775\) | 5216.35 | 0.241777 | ||||||||
\(776\) | −1547.07 | −0.0715679 | ||||||||
\(777\) | 15980.8 | 0.737847 | ||||||||
\(778\) | −8848.12 | −0.407739 | ||||||||
\(779\) | −4240.31 | −0.195026 | ||||||||
\(780\) | −4615.66 | −0.211881 | ||||||||
\(781\) | 11666.9 | 0.534540 | ||||||||
\(782\) | −889.561 | −0.0406786 | ||||||||
\(783\) | 16052.2 | 0.732644 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −3591.16 | −0.163279 | ||||||||
\(786\) | −16230.2 | −0.736531 | ||||||||
\(787\) | −754.116 | −0.0341567 | −0.0170783 | − | 0.999854i | \(-0.505436\pi\) | ||||
−0.0170783 | + | 0.999854i | \(0.505436\pi\) | |||||||
\(788\) | −858.007 | −0.0387884 | ||||||||
\(789\) | −10544.9 | −0.475802 | ||||||||
\(790\) | −7859.46 | −0.353958 | ||||||||
\(791\) | 7423.52 | 0.333692 | ||||||||
\(792\) | 3906.90 | 0.175285 | ||||||||
\(793\) | −4839.99 | −0.216738 | ||||||||
\(794\) | 13953.5 | 0.623667 | ||||||||
\(795\) | 43612.7 | 1.94564 | ||||||||
\(796\) | −19935.0 | −0.887658 | ||||||||
\(797\) | −6159.16 | −0.273737 | −0.136869 | − | 0.990589i | \(-0.543704\pi\) | ||||
−0.136869 | + | 0.990589i | \(0.543704\pi\) | |||||||
\(798\) | 4560.88 | 0.202323 | ||||||||
\(799\) | −1682.25 | −0.0744853 | ||||||||
\(800\) | 869.725 | 0.0384368 | ||||||||
\(801\) | −5847.62 | −0.257947 | ||||||||
\(802\) | 19649.9 | 0.865165 | ||||||||
\(803\) | 26735.7 | 1.17495 | ||||||||
\(804\) | −4168.26 | −0.182840 | ||||||||
\(805\) | 1592.36 | 0.0697185 | ||||||||
\(806\) | 7193.03 | 0.314347 | ||||||||
\(807\) | 6903.13 | 0.301117 | ||||||||
\(808\) | 9505.74 | 0.413875 | ||||||||
\(809\) | −1676.54 | −0.0728602 | −0.0364301 | − | 0.999336i | \(-0.511599\pi\) | ||||
−0.0364301 | + | 0.999336i | \(0.511599\pi\) | |||||||
\(810\) | −17965.7 | −0.779321 | ||||||||
\(811\) | 16726.0 | 0.724205 | 0.362102 | − | 0.932138i | \(-0.382059\pi\) | ||||
0.362102 | + | 0.932138i | \(0.382059\pi\) | |||||||
\(812\) | −4737.97 | −0.204766 | ||||||||
\(813\) | 4883.39 | 0.210662 | ||||||||
\(814\) | 30446.1 | 1.31098 | ||||||||
\(815\) | −23997.0 | −1.03139 | ||||||||
\(816\) | −1926.41 | −0.0826443 | ||||||||
\(817\) | −10603.2 | −0.454048 | ||||||||
\(818\) | −16072.5 | −0.686996 | ||||||||
\(819\) | 1543.03 | 0.0658338 | ||||||||
\(820\) | −3206.00 | −0.136535 | ||||||||
\(821\) | −11588.4 | −0.492617 | −0.246309 | − | 0.969191i | \(-0.579218\pi\) | ||||
−0.246309 | + | 0.969191i | \(0.579218\pi\) | |||||||
\(822\) | −4180.73 | −0.177396 | ||||||||
\(823\) | −42240.5 | −1.78908 | −0.894538 | − | 0.446991i | \(-0.852496\pi\) | ||||
−0.894538 | + | 0.446991i | \(0.852496\pi\) | |||||||
\(824\) | −6445.33 | −0.272492 | ||||||||
\(825\) | 7025.14 | 0.296465 | ||||||||
\(826\) | 8657.00 | 0.364668 | ||||||||
\(827\) | 30885.9 | 1.29868 | 0.649341 | − | 0.760498i | \(-0.275045\pi\) | ||||
0.649341 | + | 0.760498i | \(0.275045\pi\) | |||||||
\(828\) | −1082.22 | −0.0454226 | ||||||||
\(829\) | 11743.9 | 0.492017 | 0.246008 | − | 0.969268i | \(-0.420881\pi\) | ||||
0.246008 | + | 0.969268i | \(0.420881\pi\) | |||||||
\(830\) | 28483.1 | 1.19116 | ||||||||
\(831\) | −44133.7 | −1.84233 | ||||||||
\(832\) | 1199.30 | 0.0499738 | ||||||||
\(833\) | −947.576 | −0.0394136 | ||||||||
\(834\) | 14665.4 | 0.608897 | ||||||||
\(835\) | 38165.0 | 1.58174 | ||||||||
\(836\) | 8689.26 | 0.359479 | ||||||||
\(837\) | 18206.9 | 0.751879 | ||||||||
\(838\) | −8942.46 | −0.368630 | ||||||||
\(839\) | 30404.4 | 1.25110 | 0.625552 | − | 0.780183i | \(-0.284874\pi\) | ||||
0.625552 | + | 0.780183i | \(0.284874\pi\) | |||||||
\(840\) | 3448.38 | 0.141643 | ||||||||
\(841\) | 4244.15 | 0.174019 | ||||||||
\(842\) | 17418.1 | 0.712908 | ||||||||
\(843\) | −48248.1 | −1.97124 | ||||||||
\(844\) | −7454.98 | −0.304042 | ||||||||
\(845\) | 18256.3 | 0.743237 | ||||||||
\(846\) | −2046.60 | −0.0831720 | ||||||||
\(847\) | 2747.89 | 0.111474 | ||||||||
\(848\) | −11332.0 | −0.458894 | ||||||||
\(849\) | −11439.5 | −0.462431 | ||||||||
\(850\) | −1051.19 | −0.0424181 | ||||||||
\(851\) | −8433.68 | −0.339721 | ||||||||
\(852\) | −6998.65 | −0.281420 | ||||||||
\(853\) | 1256.30 | 0.0504276 | 0.0252138 | − | 0.999682i | \(-0.491973\pi\) | ||||
0.0252138 | + | 0.999682i | \(0.491973\pi\) | |||||||
\(854\) | 3615.97 | 0.144890 | ||||||||
\(855\) | 6087.74 | 0.243505 | ||||||||
\(856\) | −4465.49 | −0.178303 | ||||||||
\(857\) | −7524.50 | −0.299921 | −0.149960 | − | 0.988692i | \(-0.547915\pi\) | ||||
−0.149960 | + | 0.988692i | \(0.547915\pi\) | |||||||
\(858\) | 9687.24 | 0.385451 | ||||||||
\(859\) | 32543.0 | 1.29261 | 0.646306 | − | 0.763078i | \(-0.276313\pi\) | ||||
0.646306 | + | 0.763078i | \(0.276313\pi\) | |||||||
\(860\) | −8016.80 | −0.317873 | ||||||||
\(861\) | 3531.80 | 0.139795 | ||||||||
\(862\) | 23695.8 | 0.936288 | ||||||||
\(863\) | 17286.5 | 0.681852 | 0.340926 | − | 0.940090i | \(-0.389259\pi\) | ||||
0.340926 | + | 0.940090i | \(0.389259\pi\) | |||||||
\(864\) | 3035.64 | 0.119531 | ||||||||
\(865\) | −5595.39 | −0.219941 | ||||||||
\(866\) | −12612.1 | −0.494891 | ||||||||
\(867\) | −28260.1 | −1.10699 | ||||||||
\(868\) | −5373.94 | −0.210142 | ||||||||
\(869\) | 16495.3 | 0.643916 | ||||||||
\(870\) | −20839.7 | −0.812105 | ||||||||
\(871\) | −3136.40 | −0.122012 | ||||||||
\(872\) | −4322.34 | −0.167859 | ||||||||
\(873\) | 2274.84 | 0.0881920 | ||||||||
\(874\) | −2406.96 | −0.0931539 | ||||||||
\(875\) | 10535.8 | 0.407058 | ||||||||
\(876\) | −16038.0 | −0.618577 | ||||||||
\(877\) | −10416.4 | −0.401068 | −0.200534 | − | 0.979687i | \(-0.564268\pi\) | ||||
−0.200534 | + | 0.979687i | \(0.564268\pi\) | |||||||
\(878\) | 53.7994 | 0.00206793 | ||||||||
\(879\) | −1249.49 | −0.0479456 | ||||||||
\(880\) | 6569.75 | 0.251666 | ||||||||
\(881\) | 48386.4 | 1.85037 | 0.925186 | − | 0.379514i | \(-0.123909\pi\) | ||||
0.925186 | + | 0.379514i | \(0.123909\pi\) | |||||||
\(882\) | −1152.80 | −0.0440102 | ||||||||
\(883\) | 4310.85 | 0.164294 | 0.0821471 | − | 0.996620i | \(-0.473822\pi\) | ||||
0.0821471 | + | 0.996620i | \(0.473822\pi\) | |||||||
\(884\) | −1449.52 | −0.0551501 | ||||||||
\(885\) | 38077.3 | 1.44628 | ||||||||
\(886\) | 25146.7 | 0.953521 | ||||||||
\(887\) | 4359.56 | 0.165028 | 0.0825139 | − | 0.996590i | \(-0.473705\pi\) | ||||
0.0825139 | + | 0.996590i | \(0.473705\pi\) | |||||||
\(888\) | −18263.7 | −0.690193 | ||||||||
\(889\) | 2419.29 | 0.0912716 | ||||||||
\(890\) | −9833.22 | −0.370349 | ||||||||
\(891\) | 37706.0 | 1.41773 | ||||||||
\(892\) | 16224.3 | 0.609000 | ||||||||
\(893\) | −4551.80 | −0.170571 | ||||||||
\(894\) | −7440.96 | −0.278370 | ||||||||
\(895\) | −13059.8 | −0.487753 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | −2683.40 | −0.0998842 | ||||||||
\(898\) | −5945.32 | −0.220933 | ||||||||
\(899\) | 32476.5 | 1.20484 | ||||||||
\(900\) | −1278.86 | −0.0473650 | ||||||||
\(901\) | 13696.3 | 0.506427 | ||||||||
\(902\) | 6728.69 | 0.248382 | ||||||||
\(903\) | 8831.48 | 0.325463 | ||||||||
\(904\) | −8484.03 | −0.312140 | ||||||||
\(905\) | −32032.7 | −1.17658 | ||||||||
\(906\) | −21578.6 | −0.791281 | ||||||||
\(907\) | −50399.3 | −1.84507 | −0.922537 | − | 0.385908i | \(-0.873888\pi\) | ||||
−0.922537 | + | 0.385908i | \(0.873888\pi\) | |||||||
\(908\) | 12791.7 | 0.467520 | ||||||||
\(909\) | −13977.4 | −0.510011 | ||||||||
\(910\) | 2594.73 | 0.0945212 | ||||||||
\(911\) | 46810.4 | 1.70241 | 0.851206 | − | 0.524832i | \(-0.175872\pi\) | ||||
0.851206 | + | 0.524832i | \(0.175872\pi\) | |||||||
\(912\) | −5212.44 | −0.189256 | ||||||||
\(913\) | −59779.8 | −2.16695 | ||||||||
\(914\) | −23683.3 | −0.857085 | ||||||||
\(915\) | 15904.6 | 0.574635 | ||||||||
\(916\) | 7944.88 | 0.286579 | ||||||||
\(917\) | 9123.94 | 0.328570 | ||||||||
\(918\) | −3669.01 | −0.131912 | ||||||||
\(919\) | 19768.2 | 0.709569 | 0.354785 | − | 0.934948i | \(-0.384554\pi\) | ||||
0.354785 | + | 0.934948i | \(0.384554\pi\) | |||||||
\(920\) | −1819.84 | −0.0652157 | ||||||||
\(921\) | −13502.9 | −0.483101 | ||||||||
\(922\) | 10290.7 | 0.367576 | ||||||||
\(923\) | −5266.12 | −0.187797 | ||||||||
\(924\) | −7237.38 | −0.257676 | ||||||||
\(925\) | −9966.01 | −0.354249 | ||||||||
\(926\) | 21487.3 | 0.762545 | ||||||||
\(927\) | 9477.30 | 0.335788 | ||||||||
\(928\) | 5414.83 | 0.191541 | ||||||||
\(929\) | 30117.9 | 1.06366 | 0.531828 | − | 0.846852i | \(-0.321505\pi\) | ||||
0.531828 | + | 0.846852i | \(0.321505\pi\) | |||||||
\(930\) | −23637.0 | −0.833427 | ||||||||
\(931\) | −2563.93 | −0.0902572 | ||||||||
\(932\) | 2500.11 | 0.0878688 | ||||||||
\(933\) | −57371.7 | −2.01314 | ||||||||
\(934\) | 12094.1 | 0.423695 | ||||||||
\(935\) | −7940.48 | −0.277734 | ||||||||
\(936\) | −1763.46 | −0.0615819 | ||||||||
\(937\) | −54880.6 | −1.91342 | −0.956708 | − | 0.291049i | \(-0.905996\pi\) | ||||
−0.956708 | + | 0.291049i | \(0.905996\pi\) | |||||||
\(938\) | 2343.21 | 0.0815657 | ||||||||
\(939\) | 5324.77 | 0.185056 | ||||||||
\(940\) | −3441.51 | −0.119415 | ||||||||
\(941\) | 42264.7 | 1.46417 | 0.732087 | − | 0.681211i | \(-0.238546\pi\) | ||||
0.732087 | + | 0.681211i | \(0.238546\pi\) | |||||||
\(942\) | −4521.25 | −0.156380 | ||||||||
\(943\) | −1863.87 | −0.0643647 | ||||||||
\(944\) | −9893.72 | −0.341115 | ||||||||
\(945\) | 6567.73 | 0.226083 | ||||||||
\(946\) | 16825.5 | 0.578270 | ||||||||
\(947\) | 16330.6 | 0.560373 | 0.280186 | − | 0.959946i | \(-0.409604\pi\) | ||||
0.280186 | + | 0.959946i | \(0.409604\pi\) | |||||||
\(948\) | −9895.03 | −0.339004 | ||||||||
\(949\) | −12067.7 | −0.412788 | ||||||||
\(950\) | −2844.28 | −0.0971375 | ||||||||
\(951\) | −22548.7 | −0.768867 | ||||||||
\(952\) | 1082.94 | 0.0368681 | ||||||||
\(953\) | −55484.1 | −1.88595 | −0.942973 | − | 0.332868i | \(-0.891984\pi\) | ||||
−0.942973 | + | 0.332868i | \(0.891984\pi\) | |||||||
\(954\) | 16662.7 | 0.565488 | ||||||||
\(955\) | −22435.4 | −0.760201 | ||||||||
\(956\) | −22752.1 | −0.769724 | ||||||||
\(957\) | 43737.9 | 1.47737 | ||||||||
\(958\) | 2078.28 | 0.0700901 | ||||||||
\(959\) | 2350.23 | 0.0791374 | ||||||||
\(960\) | −3941.00 | −0.132495 | ||||||||
\(961\) | 7044.81 | 0.236474 | ||||||||
\(962\) | −13742.5 | −0.460579 | ||||||||
\(963\) | 6566.12 | 0.219720 | ||||||||
\(964\) | 20670.5 | 0.690614 | ||||||||
\(965\) | −42522.6 | −1.41850 | ||||||||
\(966\) | 2004.78 | 0.0667730 | ||||||||
\(967\) | 49602.8 | 1.64956 | 0.824778 | − | 0.565457i | \(-0.191300\pi\) | ||||
0.824778 | + | 0.565457i | \(0.191300\pi\) | |||||||
\(968\) | −3140.45 | −0.104275 | ||||||||
\(969\) | 6299.97 | 0.208859 | ||||||||
\(970\) | 3825.31 | 0.126622 | ||||||||
\(971\) | 45053.6 | 1.48902 | 0.744510 | − | 0.667611i | \(-0.232683\pi\) | ||||
0.744510 | + | 0.667611i | \(0.232683\pi\) | |||||||
\(972\) | −12373.4 | −0.408311 | ||||||||
\(973\) | −8244.23 | −0.271632 | ||||||||
\(974\) | −8120.39 | −0.267140 | ||||||||
\(975\) | −3170.95 | −0.104156 | ||||||||
\(976\) | −4132.54 | −0.135532 | ||||||||
\(977\) | −7977.63 | −0.261235 | −0.130618 | − | 0.991433i | \(-0.541696\pi\) | ||||
−0.130618 | + | 0.991433i | \(0.541696\pi\) | |||||||
\(978\) | −30212.1 | −0.987810 | ||||||||
\(979\) | 20637.7 | 0.673733 | ||||||||
\(980\) | −1938.53 | −0.0631878 | ||||||||
\(981\) | 6355.64 | 0.206850 | ||||||||
\(982\) | −15511.6 | −0.504070 | ||||||||
\(983\) | 745.180 | 0.0241786 | 0.0120893 | − | 0.999927i | \(-0.496152\pi\) | ||||
0.0120893 | + | 0.999927i | \(0.496152\pi\) | |||||||
\(984\) | −4036.34 | −0.130766 | ||||||||
\(985\) | 2121.52 | 0.0686267 | ||||||||
\(986\) | −6544.59 | −0.211382 | ||||||||
\(987\) | 3791.24 | 0.122266 | ||||||||
\(988\) | −3922.09 | −0.126294 | ||||||||
\(989\) | −4660.72 | −0.149850 | ||||||||
\(990\) | −9660.26 | −0.310124 | ||||||||
\(991\) | −30814.7 | −0.987752 | −0.493876 | − | 0.869532i | \(-0.664420\pi\) | ||||
−0.493876 | + | 0.869532i | \(0.664420\pi\) | |||||||
\(992\) | 6141.65 | 0.196570 | ||||||||
\(993\) | 17971.4 | 0.574324 | ||||||||
\(994\) | 3934.34 | 0.125543 | ||||||||
\(995\) | 49291.4 | 1.57050 | ||||||||
\(996\) | 35860.2 | 1.14084 | ||||||||
\(997\) | 37297.4 | 1.18477 | 0.592387 | − | 0.805654i | \(-0.298186\pi\) | ||||
0.592387 | + | 0.805654i | \(0.298186\pi\) | |||||||
\(998\) | −24965.3 | −0.791845 | ||||||||
\(999\) | −34784.9 | −1.10165 |
(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 | 322.4.a.f.1.4 | ✓ | 4 | |
7.6 | odd | 2 | 2254.4.a.j.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.a.f.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2254.4.a.j.1.1 | 4 | 7.6 | odd | 2 |