Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 616) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.70820 | −1.09854 | −0.549272 | − | 0.835644i | \(-0.685095\pi\) | ||||
−0.549272 | + | 0.835644i | \(0.685095\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.763932 | 0.0683282 | 0.0341641 | − | 0.999416i | \(-0.489123\pi\) | ||||
0.0341641 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.58359 | 0.206800 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.6525 | −1.29400 | −0.646999 | − | 0.762491i | \(-0.723976\pi\) | ||||
−0.646999 | + | 0.762491i | \(0.723976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.36068 | −0.0750615 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 36.2229 | 0.516785 | 0.258393 | − | 0.966040i | \(-0.416807\pi\) | ||||
0.258393 | + | 0.966040i | \(0.416807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −47.7082 | −0.576053 | −0.288027 | − | 0.957622i | \(-0.592999\pi\) | ||||
−0.288027 | + | 0.957622i | \(0.592999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.9574 | −0.415211 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 186.387 | 1.68976 | 0.844878 | − | 0.534960i | \(-0.179673\pi\) | ||||
0.844878 | + | 0.534960i | \(0.179673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.416 | −0.995331 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 122.249 | 0.871366 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.2523 | 0.174504 | 0.0872522 | − | 0.996186i | \(-0.472191\pi\) | ||||
0.0872522 | + | 0.996186i | \(0.472191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −156.079 | −0.904278 | −0.452139 | − | 0.891948i | \(-0.649339\pi\) | ||||
−0.452139 | + | 0.891948i | \(0.649339\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −62.7902 | −0.331224 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.34752 | 0.0258256 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −302.721 | −1.34506 | −0.672528 | − | 0.740072i | \(-0.734792\pi\) | ||||
−0.672528 | + | 0.740072i | \(0.734792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 346.217 | 1.42151 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −73.2724 | −0.279103 | −0.139552 | − | 0.990215i | \(-0.544566\pi\) | ||||
−0.139552 | + | 0.990215i | \(0.544566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.9675 | 0.155930 | 0.0779649 | − | 0.996956i | \(-0.475158\pi\) | ||||
0.0779649 | + | 0.996956i | \(0.475158\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.26548 | 0.0141302 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 112.197 | 0.348203 | 0.174102 | − | 0.984728i | \(-0.444298\pi\) | ||||
0.174102 | + | 0.984728i | \(0.444298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −206.768 | −0.567711 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 264.249 | 0.684857 | 0.342429 | − | 0.939544i | \(-0.388751\pi\) | ||||
0.342429 | + | 0.939544i | \(0.388751\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.40325 | 0.0206017 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 272.328 | 0.632820 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 339.872 | 0.749959 | 0.374980 | − | 0.927033i | \(-0.377650\pi\) | ||||
0.374980 | + | 0.927033i | \(0.377650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −557.459 | −1.17009 | −0.585044 | − | 0.811002i | \(-0.698923\pi\) | ||||
−0.585044 | + | 0.811002i | \(0.698923\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 39.0851 | 0.0781629 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −46.3344 | −0.0884165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −926.906 | −1.69014 | −0.845071 | − | 0.534654i | \(-0.820442\pi\) | ||||
−0.845071 | + | 0.534654i | \(0.820442\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1063.93 | −1.85627 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 78.7601 | 0.131649 | 0.0658247 | − | 0.997831i | \(-0.479032\pi\) | ||||
0.0658247 | + | 0.997831i | \(0.479032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −668.689 | −1.07211 | −0.536056 | − | 0.844183i | \(-0.680086\pi\) | ||||
−0.536056 | + | 0.844183i | \(0.680086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 710.194 | 1.09342 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1218.72 | 1.73565 | 0.867824 | − | 0.496872i | \(-0.165518\pi\) | ||||
0.867824 | + | 0.496872i | \(0.165518\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −848.580 | −1.16403 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1006.86 | −1.33153 | −0.665764 | − | 0.746162i | \(-0.731894\pi\) | ||||
−0.665764 | + | 0.746162i | \(0.731894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.6718 | 0.0353110 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −155.562 | −0.191701 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1146.42 | 1.36540 | 0.682699 | − | 0.730700i | \(-0.260806\pi\) | ||||
0.682699 | + | 0.730700i | \(0.260806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −424.567 | −0.489085 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 890.930 | 0.993389 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.4458 | −0.0393607 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 657.299 | 0.688027 | 0.344013 | − | 0.938965i | \(-0.388213\pi\) | ||||
0.344013 | + | 0.938965i | \(0.388213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 61.4195 | 0.0623525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 398.306 | 0.392405 | 0.196202 | − | 0.980563i | \(-0.437139\pi\) | ||||
0.196202 | + | 0.980563i | \(0.437139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1927.16 | −1.84358 | −0.921791 | − | 0.387687i | \(-0.873274\pi\) | ||||
−0.921791 | + | 0.387687i | \(0.873274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −30.5248 | −0.0283706 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1783.72 | 1.61158 | 0.805788 | − | 0.592204i | \(-0.201742\pi\) | ||||
0.805788 | + | 0.592204i | \(0.201742\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −172.570 | −0.151644 | −0.0758219 | − | 0.997121i | \(-0.524158\pi\) | ||||
−0.0758219 | + | 0.997121i | \(0.524158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1728.00 | 1.47760 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 50.1502 | 0.0417498 | 0.0208749 | − | 0.999782i | \(-0.493355\pi\) | ||||
0.0208749 | + | 0.999782i | \(0.493355\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 142.387 | 0.115458 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −338.659 | −0.267598 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 253.560 | 0.195326 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 418.254 | 0.306607 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −190.537 | −0.136337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2143.92 | 1.49797 | 0.748986 | − | 0.662586i | \(-0.230541\pi\) | ||||
0.748986 | + | 0.662586i | \(0.230541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −250.975 | −0.171296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1351.35 | 0.901281 | 0.450640 | − | 0.892706i | \(-0.351196\pi\) | ||||
0.450640 | + | 0.892706i | \(0.351196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −333.957 | −0.217728 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 93.3901 | 0.0595388 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1732.64 | 1.08051 | 0.540253 | − | 0.841503i | \(-0.318329\pi\) | ||||
0.540253 | + | 0.841503i | \(0.318329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2803.08 | 1.71046 | 0.855231 | − | 0.518248i | \(-0.173415\pi\) | ||||
0.855231 | + | 0.518248i | \(0.173415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −640.441 | −0.382517 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −667.177 | −0.390155 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.8189 | 0.0119236 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −279.702 | −0.156935 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −170.271 | −0.0936183 | −0.0468091 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468091 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1685.42 | 0.908327 | 0.454163 | − | 0.890918i | \(-0.349938\pi\) | ||||
0.454163 | + | 0.890918i | \(0.349938\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 202.254 | 0.106871 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −119.234 | −0.0617876 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 663.459 | 0.337260 | 0.168630 | − | 0.985679i | \(-0.446066\pi\) | ||||
0.168630 | + | 0.985679i | \(0.446066\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1508.39 | −0.752346 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1304.71 | 0.638668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 334.906 | 0.160931 | 0.0804657 | − | 0.996757i | \(-0.474359\pi\) | ||||
0.0804657 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −47.9675 | −0.0226319 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1724.13 | 0.798903 | 0.399452 | − | 0.916754i | \(-0.369201\pi\) | ||||
0.399452 | + | 0.916754i | \(0.369201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1481.72 | 0.674430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −266.383 | −0.119128 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 119.044 | 0.0523166 | 0.0261583 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261583 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −870.915 | −0.376200 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1940.06 | −0.823864 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4589.64 | 1.91646 | 0.958229 | − | 0.286001i | \(-0.0923261\pi\) | ||||
0.958229 | + | 0.286001i | \(0.0923261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2645.91 | 1.08657 | 0.543285 | − | 0.839548i | \(-0.317180\pi\) | ||||
0.543285 | + | 0.839548i | \(0.317180\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3182.09 | 1.28539 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −231.259 | −0.0919052 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 398.452 | 0.155817 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 855.745 | 0.329345 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −794.404 | −0.300948 | −0.150474 | − | 0.988614i | \(-0.548080\pi\) | ||||
−0.150474 | + | 0.988614i | \(0.548080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4888.02 | 1.82305 | 0.911523 | − | 0.411250i | \(-0.134908\pi\) | ||||
0.911523 | + | 0.411250i | \(0.134908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 264.486 | 0.0971294 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2962.03 | −1.07125 | −0.535624 | − | 0.844457i | \(-0.679923\pi\) | ||||
−0.535624 | + | 0.844457i | \(0.679923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1649.76 | −0.587679 | −0.293840 | − | 0.955855i | \(-0.594933\pi\) | ||||
−0.293840 | + | 0.955855i | \(0.594933\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5290.97 | 1.85670 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 190.766 | 0.0659565 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −55.9752 | −0.0190706 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1040.71 | 0.349441 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −524.790 | −0.173687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3304.44 | −1.07814 | −0.539069 | − | 0.842262i | \(-0.681224\pi\) | ||||
−0.539069 | + | 0.842262i | \(0.681224\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −449.579 | −0.144623 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33.5882 | 0.0106544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1092.55 | −0.341785 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3817.01 | 1.17776 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2197.01 | −0.668719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 998.421 | 0.299817 | 0.149909 | − | 0.988700i | \(-0.452102\pi\) | ||||
0.149909 | + | 0.988700i | \(0.452102\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −694.690 | −0.205834 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3490.81 | −1.02067 | −0.510337 | − | 0.859974i | \(-0.670479\pi\) | ||||
−0.510337 | + | 0.859974i | \(0.670479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1228.13 | 0.354398 | 0.177199 | − | 0.984175i | \(-0.443296\pi\) | ||||
0.177199 | + | 0.984175i | \(0.443296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −439.532 | −0.125191 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4361.81 | 1.22640 | 0.613201 | − | 0.789927i | \(-0.289882\pi\) | ||||
0.613201 | + | 0.789927i | \(0.289882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 85.7106 | 0.0237921 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6956.67 | −1.90669 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2804.52 | −0.759034 | −0.379517 | − | 0.925185i | \(-0.623910\pi\) | ||||
−0.379517 | + | 0.925185i | \(0.623910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4410.82 | 1.17895 | 0.589473 | − | 0.807788i | \(-0.299336\pi\) | ||||
0.589473 | + | 0.807788i | \(0.299336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1543.14 | 0.407377 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 37.4327 | 0.00976117 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2893.62 | 0.745412 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5747.34 | 1.46274 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 183.800 | 0.0462204 | 0.0231102 | − | 0.999733i | \(-0.492643\pi\) | ||||
0.0231102 | + | 0.999733i | \(0.492643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2050.26 | 0.509480 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −157.957 | −0.0387907 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3718.53 | 0.902550 | 0.451275 | − | 0.892385i | \(-0.350969\pi\) | ||||
0.451275 | + | 0.892385i | \(0.350969\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2119.05 | −0.508384 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 152.166 | 0.0360875 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2361.30 | 0.553627 | 0.276813 | − | 0.960924i | \(-0.410722\pi\) | ||||
0.276813 | + | 0.960924i | \(0.410722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 201.868 | 0.0467950 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6544.00 | −1.49995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2676.42 | 0.606633 | 0.303317 | − | 0.952890i | \(-0.401906\pi\) | ||||
0.303317 | + | 0.952890i | \(0.401906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4672.14 | 1.04728 | 0.523639 | − | 0.851940i | \(-0.324574\pi\) | ||||
0.523639 | + | 0.851940i | \(0.324574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2423.52 | 0.537282 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1368.58 | −0.300104 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8630.05 | 1.87195 | 0.935974 | − | 0.352070i | \(-0.114522\pi\) | ||||
0.935974 | + | 0.352070i | \(0.114522\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −871.481 | −0.187004 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1533.41 | −0.325536 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3075.10 | 0.645921 | 0.322961 | − | 0.946412i | \(-0.395322\pi\) | ||||
0.322961 | + | 0.946412i | \(0.395322\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 208.040 | 0.0432394 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −512.907 | −0.105491 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3600.90 | −0.732933 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3752.00 | −0.755828 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6705.90 | −1.33707 | −0.668537 | − | 0.743679i | \(-0.733079\pi\) | ||||
−0.668537 | + | 0.743679i | \(0.733079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 259.639 | 0.0512433 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1344.74 | 0.262727 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11304.8 | −2.18654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 307.772 | 0.0589359 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2273.61 | −0.431074 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −425.861 | −0.0799499 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8182.05 | −1.52109 | −0.760544 | − | 0.649286i | \(-0.775068\pi\) | ||||
−0.760544 | + | 0.649286i | \(0.775068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11000.6 | 2.02526 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6563.79 | 1.19678 | 0.598389 | − | 0.801205i | \(-0.295808\pi\) | ||||
0.598389 | + | 0.801205i | \(0.295808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6609.11 | 1.19351 | 0.596755 | − | 0.802423i | \(-0.296456\pi\) | ||||
0.596755 | + | 0.802423i | \(0.296456\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.8584 | 0.00534073 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3777.95 | 0.669371 | 0.334686 | − | 0.942330i | \(-0.391370\pi\) | ||||
0.334686 | + | 0.942330i | \(0.391370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 299.776 | 0.0526151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10181.8 | −1.77039 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1728.13 | −0.297696 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7546.16 | 1.28796 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 985.063 | 0.166587 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 785.376 | 0.131608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1059.15 | −0.175879 | −0.0879397 | − | 0.996126i | \(-0.528028\pi\) | ||||
−0.0879397 | + | 0.996126i | \(0.528028\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1690.27 | −0.278157 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −708.093 | −0.115484 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −583.077 | −0.0942500 | −0.0471250 | − | 0.998889i | \(-0.515006\pi\) | ||||
−0.0471250 | + | 0.998889i | \(0.515006\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −286.268 | −0.0458641 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1716.87 | −0.272650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −812.774 | −0.126836 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −993.813 | −0.153748 | −0.0768742 | − | 0.997041i | \(-0.524494\pi\) | ||||
−0.0768742 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6624.74 | −1.01609 | −0.508043 | − | 0.861332i | \(-0.669631\pi\) | ||||
−0.508043 | + | 0.861332i | \(0.669631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7414.72 | −1.12755 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1136.14 | −0.171305 | −0.0856524 | − | 0.996325i | \(-0.527297\pi\) | ||||
−0.0856524 | + | 0.996325i | \(0.527297\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 60.1674 | 0.00899536 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1447.37 | −0.214575 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5362.89 | −0.788419 | −0.394210 | − | 0.919021i | \(-0.628982\pi\) | ||||
−0.394210 | + | 0.919021i | \(0.628982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4582.93 | −0.668163 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −690.693 | −0.0998677 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −510.833 | −0.0732554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11782.1 | −1.67581 | −0.837904 | − | 0.545818i | \(-0.816219\pi\) | ||||
−0.837904 | + | 0.545818i | \(0.816219\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −409.123 | −0.0577185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1849.74 | 0.258852 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5670.15 | −0.787103 | −0.393551 | − | 0.919303i | \(-0.628754\pi\) | ||||
−0.393551 | + | 0.919303i | \(0.628754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1087.63 | 0.149773 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1652.92 | −0.225808 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4988.40 | −0.676087 | −0.338043 | − | 0.941131i | \(-0.609765\pi\) | ||||
−0.338043 | + | 0.941131i | \(0.609765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12237.9 | −1.64559 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6793.64 | 0.906368 | 0.453184 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453184 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 58.8228 | 0.00778672 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 245.496 | 0.0322462 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6302.89 | 0.821515 | 0.410757 | − | 0.911745i | \(-0.365264\pi\) | ||||
0.410757 | + | 0.911745i | \(0.365264\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6751.48 | 0.873240 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7713.77 | −0.990097 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 931.016 | 0.118594 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2970.47 | 0.375525 | 0.187762 | − | 0.982214i | \(-0.439876\pi\) | ||||
0.187762 | + | 0.982214i | \(0.439876\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1906.30 | 0.239184 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11810.8 | 1.47084 | 0.735418 | − | 0.677614i | \(-0.236986\pi\) | ||||
0.735418 | + | 0.677614i | \(0.236986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9466.57 | 1.17013 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −648.258 | −0.0795363 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3329.93 | −0.405550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6050.63 | −0.731502 | −0.365751 | − | 0.930713i | \(-0.619188\pi\) | ||||
−0.365751 | + | 0.930713i | \(0.619188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9890.25 | −1.18698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2379.11 | 0.283458 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −769.170 | −0.0909809 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16000.6 | −1.87902 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 979.679 | 0.114225 | 0.0571127 | − | 0.998368i | \(-0.481811\pi\) | ||||
0.0571127 | + | 0.998368i | \(0.481811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4273.53 | −0.494725 | −0.247363 | − | 0.968923i | \(-0.579564\pi\) | ||||
−0.247363 | + | 0.968923i | \(0.579564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 626.460 | 0.0720083 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4506.72 | −0.514372 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3902.21 | −0.442251 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3808.38 | 0.428603 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11923.4 | 1.33255 | 0.666277 | − | 0.745704i | \(-0.267887\pi\) | ||||
0.666277 | + | 0.745704i | \(0.267887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2942.85 | 0.326615 | 0.163308 | − | 0.986575i | \(-0.447784\pi\) | ||||
0.163308 | + | 0.986575i | \(0.447784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −118.839 | −0.0130986 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8892.19 | −0.973389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9664.14 | −1.05067 | −0.525335 | − | 0.850895i | \(-0.676060\pi\) | ||||
−0.525335 | + | 0.850895i | \(0.676060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 273.596 | 0.0295428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6781.33 | 0.727293 | 0.363647 | − | 0.931537i | \(-0.381532\pi\) | ||||
0.363647 | + | 0.931537i | \(0.381532\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 875.788 | 0.0932951 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 971.940 | 0.102844 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8117.32 | −0.853184 | −0.426592 | − | 0.904444i | \(-0.640286\pi\) | ||||
−0.426592 | + | 0.904444i | \(0.640286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −805.997 | −0.0841528 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9620.71 | −0.997837 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −324.341 | −0.0334183 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12449.4 | 1.27431 | 0.637153 | − | 0.770737i | \(-0.280112\pi\) | ||||
0.637153 | + | 0.770737i | \(0.280112\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4428.22 | 0.450309 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12149.6 | −1.22746 | −0.613732 | − | 0.789514i | \(-0.710333\pi\) | ||||
−0.613732 | + | 0.789514i | \(0.710333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15806.0 | 1.58654 | 0.793269 | − | 0.608871i | \(-0.208377\pi\) | ||||
0.793269 | + | 0.608871i | \(0.208377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 680.610 | 0.0678764 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5659.39 | −0.560783 | −0.280391 | − | 0.959886i | \(-0.590464\pi\) | ||||
−0.280391 | + | 0.959886i | \(0.590464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6488.34 | −0.638814 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3787.16 | −0.370495 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 483.642 | 0.0470146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5935.68 | 0.573364 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1475.46 | 0.141628 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16251.4 | 1.55020 | 0.775101 | − | 0.631837i | \(-0.217699\pi\) | ||||
0.775101 | + | 0.631837i | \(0.217699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18360.8 | 1.74050 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7447.54 | −0.701605 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 502.132 | 0.0470116 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18908.5 | 1.75939 | 0.879696 | − | 0.475536i | \(-0.157746\pi\) | ||||
0.879696 | + | 0.475536i | \(0.157746\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1911.71 | −0.176790 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 46.7115 | 0.00429340 | 0.00214670 | − | 0.999998i | \(-0.499317\pi\) | ||||
0.00214670 | + | 0.999998i | \(0.499317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 987.159 | 0.0901813 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 46.9203 | 0.00426043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 551.321 | 0.0497588 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15520.5 | −1.39237 | −0.696183 | − | 0.717864i | \(-0.745120\pi\) | ||||
−0.696183 | + | 0.717864i | \(0.745120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9841.66 | −0.877631 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12124.3 | 1.07474 | 0.537369 | − | 0.843347i | \(-0.319418\pi\) | ||||
0.537369 | + | 0.843347i | \(0.319418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 304.278 | 0.0268123 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8457.98 | −0.740891 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21982.8 | −1.91429 | −0.957143 | − | 0.289616i | \(-0.906473\pi\) | ||||
−0.957143 | + | 0.289616i | \(0.906473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4680.82 | −0.405220 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5832.29 | −0.501953 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1472.22 | −0.125969 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1234.16 | 0.104987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −679.529 | −0.0574721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20822.5 | −1.75096 | −0.875479 | − | 0.483257i | \(-0.839454\pi\) | ||||
−0.875479 | + | 0.483257i | \(0.839454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9380.10 | 0.784251 | 0.392125 | − | 0.919912i | \(-0.371740\pi\) | ||||
0.392125 | + | 0.919912i | \(0.371740\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4971.36 | 0.413272 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5653.63 | −0.467317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22573.1 | 1.85527 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1897.71 | 0.155091 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4444.15 | 0.361159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1362.64 | 0.110116 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26198.6 | −2.10531 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1561.29 | −0.124076 | −0.0620382 | − | 0.998074i | \(-0.519760\pi\) | ||||
−0.0620382 | + | 0.998074i | \(0.519760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15103.4 | −1.19365 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −131.832 | −0.0103615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13736.3 | −1.07372 | −0.536859 | − | 0.843672i | \(-0.680389\pi\) | ||||
−0.536859 | + | 0.843672i | \(0.680389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3112.62 | −0.241974 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1300.16 | −0.100524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8531.01 | 0.656013 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1320.07 | 0.100962 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15896.8 | 1.20928 | 0.604639 | − | 0.796499i | \(-0.293317\pi\) | ||||
0.604639 | + | 0.796499i | \(0.293317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2666.74 | −0.201773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2274.45 | −0.171171 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3750.20 | 0.280732 | 0.140366 | − | 0.990100i | \(-0.455172\pi\) | ||||
0.140366 | + | 0.990100i | \(0.455172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.3113 | 0.00285269 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5940.06 | −0.439963 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6212.45 | 0.457714 | 0.228857 | − | 0.973460i | \(-0.426501\pi\) | ||||
0.228857 | + | 0.973460i | \(0.426501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9826.17 | 0.720162 | 0.360081 | − | 0.932921i | \(-0.382749\pi\) | ||||
0.360081 | + | 0.932921i | \(0.382749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4534.62 | 0.330605 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23189.6 | −1.68187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16223.1 | −1.17050 | −0.585248 | − | 0.810854i | \(-0.699003\pi\) | ||||
−0.585248 | + | 0.810854i | \(0.699003\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27901.8 | −2.00270 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7048.00 | −0.503271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2906.74 | 0.206492 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −258.712 | −0.0182845 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6898.95 | 0.485094 | 0.242547 | − | 0.970140i | \(-0.422017\pi\) | ||||
0.242547 | + | 0.970140i | \(0.422017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7446.25 | 0.520912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16907.9 | 1.17681 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17914.3 | −1.24056 | −0.620282 | − | 0.784379i | \(-0.712982\pi\) | ||||
−0.620282 | + | 0.784379i | \(0.712982\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 193.703 | 0.0133463 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9417.15 | 0.645592 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26256.9 | 1.79103 | 0.895517 | − | 0.445027i | \(-0.146806\pi\) | ||||
0.895517 | + | 0.445027i | \(0.146806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25416.8 | −1.72508 | −0.862538 | − | 0.505991i | \(-0.831127\pi\) | ||||
−0.862538 | + | 0.505991i | \(0.831127\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5175.46 | −0.349521 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 92.4358 | 0.00621165 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11099.0 | 0.742166 | 0.371083 | − | 0.928600i | \(-0.378987\pi\) | ||||
0.371083 | + | 0.928600i | \(0.378987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1088.93 | −0.0724561 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6805.00 | −0.450574 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8870.82 | −0.584484 | −0.292242 | − | 0.956344i | \(-0.594401\pi\) | ||||
−0.292242 | + | 0.956344i | \(0.594401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 319.518 | 0.0209499 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5428.99 | −0.354235 | −0.177117 | − | 0.984190i | \(-0.556677\pi\) | ||||
−0.177117 | + | 0.984190i | \(0.556677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20949.9 | −1.36033 | −0.680167 | − | 0.733058i | \(-0.738093\pi\) | ||||
−0.680167 | + | 0.733058i | \(0.738093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22785.7 | 1.47239 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8024.95 | 0.516072 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15406.5 | 0.986016 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2995.61 | 0.190802 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10965.4 | −0.695105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21743.8 | −1.37180 | −0.685900 | − | 0.727696i | \(-0.740591\pi\) | ||||
−0.685900 | + | 0.727696i | \(0.740591\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18862.4 | 1.18438 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1637.81 | 0.102354 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2971.97 | −0.184857 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 439.764 | 0.0272250 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16087.6 | −0.991299 | −0.495650 | − | 0.868523i | \(-0.665070\pi\) | ||||
−0.495650 | + | 0.868523i | \(0.665070\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17284.9 | 1.06011 | 0.530055 | − | 0.847963i | \(-0.322171\pi\) | ||||
0.530055 | + | 0.847963i | \(0.322171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −191.728 | −0.0117043 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18965.9 | 1.15244 | 0.576220 | − | 0.817295i | \(-0.304527\pi\) | ||||
0.576220 | + | 0.817295i | \(0.304527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3738.60 | 0.226121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6236.51 | 0.375466 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24866.7 | 1.49021 | 0.745105 | − | 0.666947i | \(-0.232399\pi\) | ||||
0.745105 | + | 0.666947i | \(0.232399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1032.34 | 0.0615829 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3733.69 | −0.221712 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4941.55 | 0.292102 | 0.146051 | − | 0.989277i | \(-0.453344\pi\) | ||||
0.146051 | + | 0.989277i | \(0.453344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13734.2 | −0.808166 | −0.404083 | − | 0.914722i | \(-0.632409\pi\) | ||||
−0.404083 | + | 0.914722i | \(0.632409\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12541.0 | 0.734617 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −255.121 | −0.0148769 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5079.48 | 0.294870 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5699.19 | −0.329362 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6132.05 | −0.352795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10123.4 | 0.579833 | 0.289916 | − | 0.957052i | \(-0.406373\pi\) | ||||
0.289916 | + | 0.957052i | \(0.406373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15209.8 | −0.867298 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20357.5 | 1.15569 | 0.577845 | − | 0.816147i | \(-0.303894\pi\) | ||||
0.577845 | + | 0.816147i | \(0.303894\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4601.09 | 0.260050 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19926.2 | 1.12126 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32651.4 | 1.82924 | 0.914620 | − | 0.404314i | \(-0.132490\pi\) | ||||
0.914620 | + | 0.404314i | \(0.132490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1323.62 | 0.0738289 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7010.42 | −0.389322 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16027.4 | −0.886203 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24765.5 | −1.36342 | −0.681711 | − | 0.731621i | \(-0.738764\pi\) | ||||
−0.681711 | + | 0.731621i | \(0.738764\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 429.937 | 0.0235670 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2141.36 | 0.116873 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2654.14 | −0.144236 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24898.1 | −1.34726 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7358.42 | −0.396467 | −0.198234 | − | 0.980155i | \(-0.563520\pi\) | ||||
−0.198234 | + | 0.980155i | \(0.563520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14442.3 | 0.774824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −489.253 | −0.0261367 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2788.14 | 0.148315 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27601.6 | 1.46206 | 0.731030 | − | 0.682345i | \(-0.239040\pi\) | ||||
0.731030 | + | 0.682345i | \(0.239040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6804.81 | 0.358931 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29091.1 | −1.52801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −509.678 | −0.0266586 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16008.8 | 0.833832 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16126.4 | 0.836459 | 0.418229 | − | 0.908341i | \(-0.362651\pi\) | ||||
0.418229 | + | 0.908341i | \(0.362651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13490.1 | −0.696809 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25177.9 | −1.29512 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3390.64 | −0.173690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5873.33 | 0.299628 | 0.149814 | − | 0.988714i | \(-0.452132\pi\) | ||||
0.149814 | + | 0.988714i | \(0.452132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14103.1 | 0.716512 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1592.63 | 0.0805821 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20612.5 | −1.03866 | −0.519332 | − | 0.854573i | \(-0.673819\pi\) | ||||
−0.519332 | + | 0.854573i | \(0.673819\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −213.673 | −0.0107231 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10196.0 | −0.509597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5091.41 | −0.253438 | −0.126719 | − | 0.991939i | \(-0.540445\pi\) | ||||
−0.126719 | + | 0.991939i | \(0.540445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16517.4 | −0.818868 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20493.0 | −1.01186 | −0.505931 | − | 0.862574i | \(-0.668851\pi\) | ||||
−0.505931 | + | 0.862574i | \(0.668851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −130.075 | −0.00639677 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5621.88 | −0.275360 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12486.0 | 0.609119 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2488.12 | −0.120896 | −0.0604479 | − | 0.998171i | \(-0.519253\pi\) | ||||
−0.0604479 | + | 0.998171i | \(0.519253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1049.17 | −0.0507752 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1287.54 | 0.0620643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7386.41 | 0.354642 | 0.177321 | − | 0.984153i | \(-0.443257\pi\) | ||||
0.177321 | + | 0.984153i | \(0.443257\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11703.3 | −0.559687 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22577.9 | −1.07549 | −0.537746 | − | 0.843107i | \(-0.680724\pi\) | ||||
−0.537746 | + | 0.843107i | \(0.680724\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1207.99 | −0.0573160 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 154.508 | 0.00730230 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20614.1 | −0.970446 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23886.7 | −1.12012 | −0.560062 | − | 0.828451i | \(-0.689223\pi\) | ||||
−0.560062 | + | 0.828451i | \(0.689223\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21226.1 | −0.991492 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5087.32 | 0.236712 | 0.118356 | − | 0.992971i | \(-0.462238\pi\) | ||||
0.118356 | + | 0.992971i | \(0.462238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19418.8 | 0.900056 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12096.0 | 0.558482 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3495.70 | 0.160778 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 866.361 | 0.0396938 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3331.58 | 0.152057 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 506.838 | 0.0230443 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3776.28 | −0.171042 | −0.0855209 | − | 0.996336i | \(-0.527255\pi\) | ||||
−0.0855209 | + | 0.996336i | \(0.527255\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13478.8 | −0.608184 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 351.051 | 0.0157800 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33811.3 | 1.51409 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1152.31 | −0.0514064 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1500.95 | 0.0667083 | 0.0333542 | − | 0.999444i | \(-0.489381\pi\) | ||||
0.0333542 | + | 0.999444i | \(0.489381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4064.09 | 0.179946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6401.15 | 0.282364 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7355.58 | −0.323254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 996.709 | 0.0436390 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15277.6 | −0.666413 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3940.35 | 0.171243 | 0.0856213 | − | 0.996328i | \(-0.472712\pi\) | ||||
0.0856213 | + | 0.996328i | \(0.472712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17138.0 | −0.742044 | −0.371022 | − | 0.928624i | \(-0.620992\pi\) | ||||
−0.371022 | + | 0.928624i | \(0.620992\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26669.5 | −1.15048 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 255.845 | 0.0109961 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2097.61 | −0.0898238 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2370.61 | −0.101143 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6162.19 | −0.261951 | −0.130976 | − | 0.991386i | \(-0.541811\pi\) | ||||
−0.130976 | + | 0.991386i | \(0.541811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44961.7 | 1.90433 | 0.952166 | − | 0.305581i | \(-0.0988506\pi\) | ||||
0.952166 | + | 0.305581i | \(0.0988506\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7812.14 | 0.329677 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23796.0 | 1.00057 | 0.500283 | − | 0.865862i | \(-0.333229\pi\) | ||||
0.500283 | + | 0.865862i | \(0.333229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5578.25 | 0.233704 | 0.116852 | − | 0.993149i | \(-0.462720\pi\) | ||||
0.116852 | + | 0.993149i | \(0.462720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49262.1 | −2.05642 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1774.92 | 0.0738264 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1317.11 | 0.0545876 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19080.5 | −0.787956 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1184.55 | −0.0487427 | −0.0243713 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243713 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23646.3 | −0.969548 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8753.03 | 0.357616 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1131.94 | 0.0460826 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17553.3 | −0.709573 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56423.3 | −2.27282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3979.23 | −0.159726 | −0.0798630 | − | 0.996806i | \(-0.525448\pi\) | ||||
−0.0798630 | + | 0.996806i | \(0.525448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −203.499 | −0.00813977 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23815.6 | −0.949271 | −0.474636 | − | 0.880182i | \(-0.657420\pi\) | ||||
−0.474636 | + | 0.880182i | \(0.657420\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41886.5 | −1.66374 | −0.831869 | − | 0.554973i | \(-0.812729\pi\) | ||||
−0.831869 | + | 0.554973i | \(0.812729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2927.78 | 0.115887 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8287.00 | 0.326875 | 0.163437 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163437 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 90.9417 | 0.00357469 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20554.7 | 0.805160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13405.9 | 0.523317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56219.1 | 2.18704 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3670.09 | 0.142284 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1333.76 | −0.0515307 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32181.9 | 1.23912 | 0.619559 | − | 0.784950i | \(-0.287311\pi\) | ||||
0.619559 | + | 0.784950i | \(0.287311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38278.6 | 1.46884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26654.6 | 1.01932 | 0.509658 | − | 0.860377i | \(-0.329772\pi\) | ||||
0.509658 | + | 0.860377i | \(0.329772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8951.70 | −0.341165 | −0.170582 | − | 0.985343i | \(-0.554565\pi\) | ||||
−0.170582 | + | 0.985343i | \(0.554565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1482.07 | −0.0562931 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6233.31 | −0.235957 | −0.117979 | − | 0.993016i | \(-0.537641\pi\) | ||||
−0.117979 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15007.5 | 0.566180 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9334.39 | −0.350969 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5352.70 | −0.200584 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3506.18 | 0.130948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 64530.3 | 2.40201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4253.51 | −0.157801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9571.88 | 0.353924 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1756.83 | −0.0647437 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2021.30 | 0.0742434 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15545.4 | −0.569104 | −0.284552 | − | 0.958661i | \(-0.591845\pi\) | ||||
−0.284552 | + | 0.958661i | \(0.591845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2223.98 | 0.0811492 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12274.7 | 0.446409 | 0.223205 | − | 0.974772i | \(-0.428348\pi\) | ||||
0.223205 | + | 0.974772i | \(0.428348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11075.4 | −0.401471 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2430.90 | 0.0878285 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9459.43 | 0.340652 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12058.6 | −0.432836 | −0.216418 | − | 0.976301i | \(-0.569437\pi\) | ||||
−0.216418 | + | 0.976301i | \(0.569437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46704.8 | 1.67098 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4776.99 | −0.170354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37663.5 | 1.33878 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10760.5 | −0.381252 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29126.1 | −1.02863 | −0.514315 | − | 0.857601i | \(-0.671954\pi\) | ||||
−0.514315 | + | 0.857601i | \(0.671954\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2337.70 | −0.0822933 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37467.4 | −1.31471 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 304.390 | 0.0106467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21291.5 | −0.742331 | −0.371165 | − | 0.928567i | \(-0.621042\pi\) | ||||
−0.371165 | + | 0.928567i | \(0.621042\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37726.1 | −1.31112 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33899.2 | 1.17437 | 0.587184 | − | 0.809453i | \(-0.300236\pi\) | ||||
0.587184 | + | 0.809453i | \(0.300236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13657.0 | −0.471616 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 653.731 | 0.0225036 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3661.41 | −0.125639 | −0.0628194 | − | 0.998025i | \(-0.520009\pi\) | ||||
−0.0628194 | + | 0.998025i | \(0.520009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40557.6 | 1.38731 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21565.3 | −0.735334 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6827.41 | −0.232069 | −0.116034 | − | 0.993245i | \(-0.537018\pi\) | ||||
−0.116034 | + | 0.993245i | \(0.537018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −606.871 | −0.0205632 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1711.18 | −0.0578000 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12128.5 | 0.408393 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5430.37 | −0.182282 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9959.56 | 0.333274 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3734.12 | 0.124565 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18184.0 | −0.604714 | −0.302357 | − | 0.953195i | \(-0.597774\pi\) | ||||
−0.302357 | + | 0.953195i | \(0.597774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9864.52 | 0.327032 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25014.6 | 0.826731 | 0.413366 | − | 0.910565i | \(-0.364353\pi\) | ||||
0.413366 | + | 0.910565i | \(0.364353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19621.6 | 0.646494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −43075.0 | −1.41488 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35342.1 | −1.15731 | −0.578656 | − | 0.815572i | \(-0.696423\pi\) | ||||
−0.578656 | + | 0.815572i | \(0.696423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12610.6 | 0.411683 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −963.559 | −0.0313599 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10482.2 | 0.340114 | 0.170057 | − | 0.985434i | \(-0.445605\pi\) | ||||
0.170057 | + | 0.985434i | \(0.445605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2262.79 | −0.0731964 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4483.09 | −0.144578 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8194.97 | 0.263483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12086.9 | 0.387440 | 0.193720 | − | 0.981057i | \(-0.437945\pi\) | ||||
0.193720 | + | 0.981057i | \(0.437945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6045.84 | 0.193211 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1260.30 | −0.0401550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25242.6 | 0.801847 | 0.400924 | − | 0.916111i | \(-0.368689\pi\) | ||||
0.400924 | + | 0.916111i | \(0.368689\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37007.5 | −1.17204 |
(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 | 1232.4.a.l.1.1 | 2 | ||
4.3 | odd | 2 | 616.4.a.d.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.4.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1232.4.a.l.1.1 | 2 | 1.1 | even | 1 | trivial |