Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(1,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, 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("201.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.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: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 3 x^{10} - 74 x^{9} + 208 x^{8} + 1913 x^{7} - 4831 x^{6} - 20432 x^{5} + 42994 x^{4} + 79648 x^{3} - 112288 x^{2} - 85440 x + 3072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.56558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.56558 | −1.96773 | −0.983865 | − | 0.178913i | \(-0.942742\pi\) | ||||
−0.983865 | + | 0.178913i | \(0.942742\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 22.9757 | 2.87196 | ||||||||
\(5\) | −9.37616 | −0.838629 | −0.419315 | − | 0.907841i | \(-0.637730\pi\) | ||||
−0.419315 | + | 0.907841i | \(0.637730\pi\) | |||||||
\(6\) | −16.6967 | −1.13607 | ||||||||
\(7\) | 18.3374 | 0.990128 | 0.495064 | − | 0.868856i | \(-0.335145\pi\) | ||||
0.495064 | + | 0.868856i | \(0.335145\pi\) | |||||||
\(8\) | −83.3483 | −3.68351 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 52.1838 | 1.65020 | ||||||||
\(11\) | 63.5123 | 1.74088 | 0.870440 | − | 0.492274i | \(-0.163834\pi\) | ||||
0.870440 | + | 0.492274i | \(0.163834\pi\) | |||||||
\(12\) | 68.9270 | 1.65813 | ||||||||
\(13\) | −10.7502 | −0.229351 | −0.114676 | − | 0.993403i | \(-0.536583\pi\) | ||||
−0.114676 | + | 0.993403i | \(0.536583\pi\) | |||||||
\(14\) | −102.058 | −1.94830 | ||||||||
\(15\) | −28.1285 | −0.484183 | ||||||||
\(16\) | 280.076 | 4.37619 | ||||||||
\(17\) | −79.2323 | −1.13039 | −0.565196 | − | 0.824957i | \(-0.691199\pi\) | ||||
−0.565196 | + | 0.824957i | \(0.691199\pi\) | |||||||
\(18\) | −50.0902 | −0.655910 | ||||||||
\(19\) | −15.5002 | −0.187158 | −0.0935788 | − | 0.995612i | \(-0.529831\pi\) | ||||
−0.0935788 | + | 0.995612i | \(0.529831\pi\) | |||||||
\(20\) | −215.424 | −2.40851 | ||||||||
\(21\) | 55.0123 | 0.571651 | ||||||||
\(22\) | −353.483 | −3.42558 | ||||||||
\(23\) | 13.8269 | 0.125353 | 0.0626764 | − | 0.998034i | \(-0.480036\pi\) | ||||
0.0626764 | + | 0.998034i | \(0.480036\pi\) | |||||||
\(24\) | −250.045 | −2.12668 | ||||||||
\(25\) | −37.0876 | −0.296701 | ||||||||
\(26\) | 59.8310 | 0.451301 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 421.315 | 2.84361 | ||||||||
\(29\) | 244.274 | 1.56415 | 0.782077 | − | 0.623182i | \(-0.214160\pi\) | ||||
0.782077 | + | 0.623182i | \(0.214160\pi\) | |||||||
\(30\) | 156.551 | 0.952741 | ||||||||
\(31\) | −210.135 | −1.21746 | −0.608730 | − | 0.793377i | \(-0.708321\pi\) | ||||
−0.608730 | + | 0.793377i | \(0.708321\pi\) | |||||||
\(32\) | −892.001 | −4.92766 | ||||||||
\(33\) | 190.537 | 1.00510 | ||||||||
\(34\) | 440.974 | 2.22431 | ||||||||
\(35\) | −171.935 | −0.830351 | ||||||||
\(36\) | 206.781 | 0.957320 | ||||||||
\(37\) | 403.251 | 1.79173 | 0.895866 | − | 0.444324i | \(-0.146556\pi\) | ||||
0.895866 | + | 0.444324i | \(0.146556\pi\) | |||||||
\(38\) | 86.2677 | 0.368275 | ||||||||
\(39\) | −32.2505 | −0.132416 | ||||||||
\(40\) | 781.487 | 3.08910 | ||||||||
\(41\) | 444.299 | 1.69239 | 0.846194 | − | 0.532875i | \(-0.178888\pi\) | ||||
0.846194 | + | 0.532875i | \(0.178888\pi\) | |||||||
\(42\) | −306.175 | −1.12485 | ||||||||
\(43\) | 175.855 | 0.623667 | 0.311833 | − | 0.950137i | \(-0.399057\pi\) | ||||
0.311833 | + | 0.950137i | \(0.399057\pi\) | |||||||
\(44\) | 1459.24 | 4.99974 | ||||||||
\(45\) | −84.3854 | −0.279543 | ||||||||
\(46\) | −76.9549 | −0.246660 | ||||||||
\(47\) | −73.6213 | −0.228485 | −0.114242 | − | 0.993453i | \(-0.536444\pi\) | ||||
−0.114242 | + | 0.993453i | \(0.536444\pi\) | |||||||
\(48\) | 840.229 | 2.52660 | ||||||||
\(49\) | −6.73855 | −0.0196459 | ||||||||
\(50\) | 206.414 | 0.583827 | ||||||||
\(51\) | −237.697 | −0.652632 | ||||||||
\(52\) | −246.993 | −0.658687 | ||||||||
\(53\) | 107.900 | 0.279647 | 0.139823 | − | 0.990176i | \(-0.455347\pi\) | ||||
0.139823 | + | 0.990176i | \(0.455347\pi\) | |||||||
\(54\) | −150.271 | −0.378690 | ||||||||
\(55\) | −595.502 | −1.45995 | ||||||||
\(56\) | −1528.39 | −3.64715 | ||||||||
\(57\) | −46.5006 | −0.108055 | ||||||||
\(58\) | −1359.52 | −3.07783 | ||||||||
\(59\) | 588.147 | 1.29780 | 0.648900 | − | 0.760874i | \(-0.275229\pi\) | ||||
0.648900 | + | 0.760874i | \(0.275229\pi\) | |||||||
\(60\) | −646.271 | −1.39055 | ||||||||
\(61\) | 398.852 | 0.837176 | 0.418588 | − | 0.908176i | \(-0.362525\pi\) | ||||
0.418588 | + | 0.908176i | \(0.362525\pi\) | |||||||
\(62\) | 1169.52 | 2.39563 | ||||||||
\(63\) | 165.037 | 0.330043 | ||||||||
\(64\) | 2723.89 | 5.32010 | ||||||||
\(65\) | 100.795 | 0.192341 | ||||||||
\(66\) | −1060.45 | −1.97776 | ||||||||
\(67\) | 67.0000 | 0.122169 | ||||||||
\(68\) | −1820.42 | −3.24644 | ||||||||
\(69\) | 41.4808 | 0.0723725 | ||||||||
\(70\) | 956.916 | 1.63391 | ||||||||
\(71\) | −2.78311 | −0.00465204 | −0.00232602 | − | 0.999997i | \(-0.500740\pi\) | ||||
−0.00232602 | + | 0.999997i | \(0.500740\pi\) | |||||||
\(72\) | −750.135 | −1.22784 | ||||||||
\(73\) | 459.408 | 0.736571 | 0.368285 | − | 0.929713i | \(-0.379945\pi\) | ||||
0.368285 | + | 0.929713i | \(0.379945\pi\) | |||||||
\(74\) | −2244.33 | −3.52564 | ||||||||
\(75\) | −111.263 | −0.171300 | ||||||||
\(76\) | −356.128 | −0.537509 | ||||||||
\(77\) | 1164.65 | 1.72370 | ||||||||
\(78\) | 179.493 | 0.260559 | ||||||||
\(79\) | 956.408 | 1.36208 | 0.681040 | − | 0.732246i | \(-0.261528\pi\) | ||||
0.681040 | + | 0.732246i | \(0.261528\pi\) | |||||||
\(80\) | −2626.04 | −3.67000 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −2472.78 | −3.33016 | ||||||||
\(83\) | 129.779 | 0.171628 | 0.0858141 | − | 0.996311i | \(-0.472651\pi\) | ||||
0.0858141 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(84\) | 1263.94 | 1.64176 | ||||||||
\(85\) | 742.895 | 0.947980 | ||||||||
\(86\) | −978.736 | −1.22721 | ||||||||
\(87\) | 732.821 | 0.903065 | ||||||||
\(88\) | −5293.65 | −6.41255 | ||||||||
\(89\) | −1258.66 | −1.49907 | −0.749537 | − | 0.661963i | \(-0.769724\pi\) | ||||
−0.749537 | + | 0.661963i | \(0.769724\pi\) | |||||||
\(90\) | 469.654 | 0.550065 | ||||||||
\(91\) | −197.131 | −0.227087 | ||||||||
\(92\) | 317.683 | 0.360008 | ||||||||
\(93\) | −630.404 | −0.702901 | ||||||||
\(94\) | 409.746 | 0.449596 | ||||||||
\(95\) | 145.333 | 0.156956 | ||||||||
\(96\) | −2676.00 | −2.84498 | ||||||||
\(97\) | −2.29216 | −0.00239931 | −0.00119966 | − | 0.999999i | \(-0.500382\pi\) | ||||
−0.00119966 | + | 0.999999i | \(0.500382\pi\) | |||||||
\(98\) | 37.5039 | 0.0386579 | ||||||||
\(99\) | 571.611 | 0.580294 | ||||||||
\(100\) | −852.113 | −0.852113 | ||||||||
\(101\) | −593.678 | −0.584883 | −0.292442 | − | 0.956283i | \(-0.594468\pi\) | ||||
−0.292442 | + | 0.956283i | \(0.594468\pi\) | |||||||
\(102\) | 1322.92 | 1.28420 | ||||||||
\(103\) | −736.895 | −0.704936 | −0.352468 | − | 0.935824i | \(-0.614657\pi\) | ||||
−0.352468 | + | 0.935824i | \(0.614657\pi\) | |||||||
\(104\) | 896.010 | 0.844817 | ||||||||
\(105\) | −515.804 | −0.479403 | ||||||||
\(106\) | −600.529 | −0.550269 | ||||||||
\(107\) | 848.945 | 0.767015 | 0.383508 | − | 0.923538i | \(-0.374716\pi\) | ||||
0.383508 | + | 0.923538i | \(0.374716\pi\) | |||||||
\(108\) | 620.343 | 0.552709 | ||||||||
\(109\) | 915.296 | 0.804307 | 0.402153 | − | 0.915572i | \(-0.368262\pi\) | ||||
0.402153 | + | 0.915572i | \(0.368262\pi\) | |||||||
\(110\) | 3314.31 | 2.87279 | ||||||||
\(111\) | 1209.75 | 1.03446 | ||||||||
\(112\) | 5135.88 | 4.33299 | ||||||||
\(113\) | 476.132 | 0.396379 | 0.198189 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198189 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(114\) | 258.803 | 0.212624 | ||||||||
\(115\) | −129.644 | −0.105125 | ||||||||
\(116\) | 5612.35 | 4.49219 | ||||||||
\(117\) | −96.7516 | −0.0764503 | ||||||||
\(118\) | −3273.38 | −2.55372 | ||||||||
\(119\) | −1452.92 | −1.11923 | ||||||||
\(120\) | 2344.46 | 1.78349 | ||||||||
\(121\) | 2702.82 | 2.03067 | ||||||||
\(122\) | −2219.84 | −1.64734 | ||||||||
\(123\) | 1332.90 | 0.977101 | ||||||||
\(124\) | −4827.98 | −3.49650 | ||||||||
\(125\) | 1519.76 | 1.08745 | ||||||||
\(126\) | −918.526 | −0.649435 | ||||||||
\(127\) | −2247.08 | −1.57005 | −0.785025 | − | 0.619464i | \(-0.787350\pi\) | ||||
−0.785025 | + | 0.619464i | \(0.787350\pi\) | |||||||
\(128\) | −8024.03 | −5.54086 | ||||||||
\(129\) | 527.566 | 0.360074 | ||||||||
\(130\) | −560.985 | −0.378474 | ||||||||
\(131\) | −223.337 | −0.148955 | −0.0744774 | − | 0.997223i | \(-0.523729\pi\) | ||||
−0.0744774 | + | 0.997223i | \(0.523729\pi\) | |||||||
\(132\) | 4377.72 | 2.88660 | ||||||||
\(133\) | −284.234 | −0.185310 | ||||||||
\(134\) | −372.894 | −0.240396 | ||||||||
\(135\) | −253.156 | −0.161394 | ||||||||
\(136\) | 6603.88 | 4.16381 | ||||||||
\(137\) | 472.494 | 0.294656 | 0.147328 | − | 0.989088i | \(-0.452933\pi\) | ||||
0.147328 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(138\) | −230.865 | −0.142409 | ||||||||
\(139\) | −1016.47 | −0.620255 | −0.310128 | − | 0.950695i | \(-0.600372\pi\) | ||||
−0.310128 | + | 0.950695i | \(0.600372\pi\) | |||||||
\(140\) | −3950.32 | −2.38473 | ||||||||
\(141\) | −220.864 | −0.131916 | ||||||||
\(142\) | 15.4896 | 0.00915395 | ||||||||
\(143\) | −682.769 | −0.399273 | ||||||||
\(144\) | 2520.69 | 1.45873 | ||||||||
\(145\) | −2290.35 | −1.31175 | ||||||||
\(146\) | −2556.87 | −1.44937 | ||||||||
\(147\) | −20.2157 | −0.0113426 | ||||||||
\(148\) | 9264.97 | 5.14578 | ||||||||
\(149\) | −674.161 | −0.370667 | −0.185334 | − | 0.982676i | \(-0.559337\pi\) | ||||
−0.185334 | + | 0.982676i | \(0.559337\pi\) | |||||||
\(150\) | 619.242 | 0.337073 | ||||||||
\(151\) | 470.825 | 0.253743 | 0.126871 | − | 0.991919i | \(-0.459506\pi\) | ||||
0.126871 | + | 0.991919i | \(0.459506\pi\) | |||||||
\(152\) | 1291.92 | 0.689397 | ||||||||
\(153\) | −713.091 | −0.376797 | ||||||||
\(154\) | −6481.97 | −3.39177 | ||||||||
\(155\) | 1970.26 | 1.02100 | ||||||||
\(156\) | −740.978 | −0.380293 | ||||||||
\(157\) | −1549.13 | −0.787478 | −0.393739 | − | 0.919222i | \(-0.628819\pi\) | ||||
−0.393739 | + | 0.919222i | \(0.628819\pi\) | |||||||
\(158\) | −5322.96 | −2.68020 | ||||||||
\(159\) | 323.701 | 0.161454 | ||||||||
\(160\) | 8363.54 | 4.13248 | ||||||||
\(161\) | 253.550 | 0.124115 | ||||||||
\(162\) | −450.812 | −0.218637 | ||||||||
\(163\) | −2870.76 | −1.37948 | −0.689741 | − | 0.724057i | \(-0.742275\pi\) | ||||
−0.689741 | + | 0.724057i | \(0.742275\pi\) | |||||||
\(164\) | 10208.1 | 4.86047 | ||||||||
\(165\) | −1786.51 | −0.842905 | ||||||||
\(166\) | −722.298 | −0.337718 | ||||||||
\(167\) | 1972.94 | 0.914194 | 0.457097 | − | 0.889417i | \(-0.348889\pi\) | ||||
0.457097 | + | 0.889417i | \(0.348889\pi\) | |||||||
\(168\) | −4585.18 | −2.10568 | ||||||||
\(169\) | −2081.43 | −0.947398 | ||||||||
\(170\) | −4134.64 | −1.86537 | ||||||||
\(171\) | −139.502 | −0.0623858 | ||||||||
\(172\) | 4040.39 | 1.79115 | ||||||||
\(173\) | −1043.63 | −0.458645 | −0.229323 | − | 0.973350i | \(-0.573651\pi\) | ||||
−0.229323 | + | 0.973350i | \(0.573651\pi\) | |||||||
\(174\) | −4078.57 | −1.77699 | ||||||||
\(175\) | −680.092 | −0.293772 | ||||||||
\(176\) | 17788.3 | 7.61843 | ||||||||
\(177\) | 1764.44 | 0.749285 | ||||||||
\(178\) | 7005.17 | 2.94977 | ||||||||
\(179\) | −2507.53 | −1.04705 | −0.523525 | − | 0.852010i | \(-0.675383\pi\) | ||||
−0.523525 | + | 0.852010i | \(0.675383\pi\) | |||||||
\(180\) | −1938.81 | −0.802837 | ||||||||
\(181\) | −274.593 | −0.112764 | −0.0563821 | − | 0.998409i | \(-0.517957\pi\) | ||||
−0.0563821 | + | 0.998409i | \(0.517957\pi\) | |||||||
\(182\) | 1097.15 | 0.446846 | ||||||||
\(183\) | 1196.55 | 0.483344 | ||||||||
\(184\) | −1152.45 | −0.461738 | ||||||||
\(185\) | −3780.95 | −1.50260 | ||||||||
\(186\) | 3508.56 | 1.38312 | ||||||||
\(187\) | −5032.23 | −1.96788 | ||||||||
\(188\) | −1691.50 | −0.656199 | ||||||||
\(189\) | 495.111 | 0.190550 | ||||||||
\(190\) | −808.860 | −0.308847 | ||||||||
\(191\) | 2152.11 | 0.815293 | 0.407647 | − | 0.913140i | \(-0.366349\pi\) | ||||
0.407647 | + | 0.913140i | \(0.366349\pi\) | |||||||
\(192\) | 8171.67 | 3.07156 | ||||||||
\(193\) | −1602.82 | −0.597788 | −0.298894 | − | 0.954286i | \(-0.596618\pi\) | ||||
−0.298894 | + | 0.954286i | \(0.596618\pi\) | |||||||
\(194\) | 12.7572 | 0.00472120 | ||||||||
\(195\) | 302.386 | 0.111048 | ||||||||
\(196\) | −154.823 | −0.0564223 | ||||||||
\(197\) | 3809.99 | 1.37792 | 0.688960 | − | 0.724799i | \(-0.258068\pi\) | ||||
0.688960 | + | 0.724799i | \(0.258068\pi\) | |||||||
\(198\) | −3181.35 | −1.14186 | ||||||||
\(199\) | −1597.86 | −0.569193 | −0.284596 | − | 0.958647i | \(-0.591860\pi\) | ||||
−0.284596 | + | 0.958647i | \(0.591860\pi\) | |||||||
\(200\) | 3091.19 | 1.09290 | ||||||||
\(201\) | 201.000 | 0.0705346 | ||||||||
\(202\) | 3304.16 | 1.15089 | ||||||||
\(203\) | 4479.35 | 1.54871 | ||||||||
\(204\) | −5461.25 | −1.87433 | ||||||||
\(205\) | −4165.82 | −1.41929 | ||||||||
\(206\) | 4101.25 | 1.38712 | ||||||||
\(207\) | 124.442 | 0.0417843 | ||||||||
\(208\) | −3010.87 | −1.00368 | ||||||||
\(209\) | −984.455 | −0.325819 | ||||||||
\(210\) | 2870.75 | 0.943336 | ||||||||
\(211\) | 1005.09 | 0.327929 | 0.163965 | − | 0.986466i | \(-0.447572\pi\) | ||||
0.163965 | + | 0.986466i | \(0.447572\pi\) | |||||||
\(212\) | 2479.09 | 0.803134 | ||||||||
\(213\) | −8.34933 | −0.00268585 | ||||||||
\(214\) | −4724.87 | −1.50928 | ||||||||
\(215\) | −1648.85 | −0.523025 | ||||||||
\(216\) | −2250.41 | −0.708892 | ||||||||
\(217\) | −3853.33 | −1.20544 | ||||||||
\(218\) | −5094.15 | −1.58266 | ||||||||
\(219\) | 1378.22 | 0.425259 | ||||||||
\(220\) | −13682.1 | −4.19293 | ||||||||
\(221\) | 851.762 | 0.259257 | ||||||||
\(222\) | −6732.98 | −2.03553 | ||||||||
\(223\) | 5789.03 | 1.73839 | 0.869197 | − | 0.494465i | \(-0.164636\pi\) | ||||
0.869197 | + | 0.494465i | \(0.164636\pi\) | |||||||
\(224\) | −16357.0 | −4.87901 | ||||||||
\(225\) | −333.788 | −0.0989003 | ||||||||
\(226\) | −2649.95 | −0.779966 | ||||||||
\(227\) | −5509.30 | −1.61086 | −0.805429 | − | 0.592692i | \(-0.798065\pi\) | ||||
−0.805429 | + | 0.592692i | \(0.798065\pi\) | |||||||
\(228\) | −1068.38 | −0.310331 | ||||||||
\(229\) | 5909.75 | 1.70536 | 0.852679 | − | 0.522434i | \(-0.174976\pi\) | ||||
0.852679 | + | 0.522434i | \(0.174976\pi\) | |||||||
\(230\) | 721.541 | 0.206857 | ||||||||
\(231\) | 3493.96 | 0.995176 | ||||||||
\(232\) | −20359.8 | −5.76158 | ||||||||
\(233\) | −4435.64 | −1.24716 | −0.623580 | − | 0.781760i | \(-0.714322\pi\) | ||||
−0.623580 | + | 0.781760i | \(0.714322\pi\) | |||||||
\(234\) | 538.479 | 0.150434 | ||||||||
\(235\) | 690.286 | 0.191614 | ||||||||
\(236\) | 13513.1 | 3.72723 | ||||||||
\(237\) | 2869.22 | 0.786397 | ||||||||
\(238\) | 8086.33 | 2.20235 | ||||||||
\(239\) | 6913.28 | 1.87106 | 0.935529 | − | 0.353250i | \(-0.114924\pi\) | ||||
0.935529 | + | 0.353250i | \(0.114924\pi\) | |||||||
\(240\) | −7878.12 | −2.11888 | ||||||||
\(241\) | 613.868 | 0.164078 | 0.0820388 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820388 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(242\) | −15042.7 | −3.99580 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 9163.89 | 2.40434 | ||||||||
\(245\) | 63.1817 | 0.0164756 | ||||||||
\(246\) | −7418.35 | −1.92267 | ||||||||
\(247\) | 166.630 | 0.0429248 | ||||||||
\(248\) | 17514.4 | 4.48453 | ||||||||
\(249\) | 389.338 | 0.0990896 | ||||||||
\(250\) | −8458.34 | −2.13981 | ||||||||
\(251\) | −6522.04 | −1.64011 | −0.820054 | − | 0.572286i | \(-0.806057\pi\) | ||||
−0.820054 | + | 0.572286i | \(0.806057\pi\) | |||||||
\(252\) | 3791.83 | 0.947870 | ||||||||
\(253\) | 878.181 | 0.218224 | ||||||||
\(254\) | 12506.3 | 3.08944 | ||||||||
\(255\) | 2228.69 | 0.547316 | ||||||||
\(256\) | 22867.2 | 5.58282 | ||||||||
\(257\) | 3709.96 | 0.900471 | 0.450235 | − | 0.892910i | \(-0.351340\pi\) | ||||
0.450235 | + | 0.892910i | \(0.351340\pi\) | |||||||
\(258\) | −2936.21 | −0.708529 | ||||||||
\(259\) | 7394.59 | 1.77404 | ||||||||
\(260\) | 2315.84 | 0.552394 | ||||||||
\(261\) | 2198.46 | 0.521385 | ||||||||
\(262\) | 1243.00 | 0.293103 | ||||||||
\(263\) | −5209.27 | −1.22136 | −0.610679 | − | 0.791878i | \(-0.709104\pi\) | ||||
−0.610679 | + | 0.791878i | \(0.709104\pi\) | |||||||
\(264\) | −15880.9 | −3.70229 | ||||||||
\(265\) | −1011.69 | −0.234520 | ||||||||
\(266\) | 1581.93 | 0.364640 | ||||||||
\(267\) | −3775.98 | −0.865491 | ||||||||
\(268\) | 1539.37 | 0.350866 | ||||||||
\(269\) | −5274.71 | −1.19556 | −0.597779 | − | 0.801661i | \(-0.703950\pi\) | ||||
−0.597779 | + | 0.801661i | \(0.703950\pi\) | |||||||
\(270\) | 1408.96 | 0.317580 | ||||||||
\(271\) | 5396.33 | 1.20961 | 0.604804 | − | 0.796374i | \(-0.293251\pi\) | ||||
0.604804 | + | 0.796374i | \(0.293251\pi\) | |||||||
\(272\) | −22191.1 | −4.94681 | ||||||||
\(273\) | −591.392 | −0.131109 | ||||||||
\(274\) | −2629.70 | −0.579803 | ||||||||
\(275\) | −2355.52 | −0.516521 | ||||||||
\(276\) | 953.049 | 0.207851 | ||||||||
\(277\) | −6909.29 | −1.49870 | −0.749349 | − | 0.662176i | \(-0.769633\pi\) | ||||
−0.749349 | + | 0.662176i | \(0.769633\pi\) | |||||||
\(278\) | 5657.22 | 1.22050 | ||||||||
\(279\) | −1891.21 | −0.405820 | ||||||||
\(280\) | 14330.5 | 3.05861 | ||||||||
\(281\) | 7176.10 | 1.52345 | 0.761727 | − | 0.647899i | \(-0.224352\pi\) | ||||
0.761727 | + | 0.647899i | \(0.224352\pi\) | |||||||
\(282\) | 1229.24 | 0.259574 | ||||||||
\(283\) | −3277.87 | −0.688513 | −0.344256 | − | 0.938876i | \(-0.611869\pi\) | ||||
−0.344256 | + | 0.938876i | \(0.611869\pi\) | |||||||
\(284\) | −63.9439 | −0.0133605 | ||||||||
\(285\) | 435.998 | 0.0906185 | ||||||||
\(286\) | 3800.01 | 0.785661 | ||||||||
\(287\) | 8147.31 | 1.67568 | ||||||||
\(288\) | −8028.01 | −1.64255 | ||||||||
\(289\) | 1364.76 | 0.277786 | ||||||||
\(290\) | 12747.1 | 2.58116 | ||||||||
\(291\) | −6.87647 | −0.00138524 | ||||||||
\(292\) | 10555.2 | 2.11540 | ||||||||
\(293\) | −4245.73 | −0.846547 | −0.423274 | − | 0.906002i | \(-0.639119\pi\) | ||||
−0.423274 | + | 0.906002i | \(0.639119\pi\) | |||||||
\(294\) | 112.512 | 0.0223191 | ||||||||
\(295\) | −5514.56 | −1.08837 | ||||||||
\(296\) | −33610.3 | −6.59987 | ||||||||
\(297\) | 1714.83 | 0.335033 | ||||||||
\(298\) | 3752.10 | 0.729373 | ||||||||
\(299\) | −148.642 | −0.0287498 | ||||||||
\(300\) | −2556.34 | −0.491968 | ||||||||
\(301\) | 3224.73 | 0.617510 | ||||||||
\(302\) | −2620.41 | −0.499297 | ||||||||
\(303\) | −1781.03 | −0.337682 | ||||||||
\(304\) | −4341.24 | −0.819038 | ||||||||
\(305\) | −3739.70 | −0.702080 | ||||||||
\(306\) | 3968.77 | 0.741435 | ||||||||
\(307\) | −214.823 | −0.0399368 | −0.0199684 | − | 0.999801i | \(-0.506357\pi\) | ||||
−0.0199684 | + | 0.999801i | \(0.506357\pi\) | |||||||
\(308\) | 26758.7 | 4.95038 | ||||||||
\(309\) | −2210.69 | −0.406995 | ||||||||
\(310\) | −10965.6 | −2.00905 | ||||||||
\(311\) | −494.235 | −0.0901141 | −0.0450570 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450570 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(312\) | 2688.03 | 0.487755 | ||||||||
\(313\) | −265.923 | −0.0480220 | −0.0240110 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240110 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(314\) | 8621.81 | 1.54954 | ||||||||
\(315\) | −1547.41 | −0.276784 | ||||||||
\(316\) | 21974.1 | 3.91184 | ||||||||
\(317\) | −678.113 | −0.120147 | −0.0600735 | − | 0.998194i | \(-0.519134\pi\) | ||||
−0.0600735 | + | 0.998194i | \(0.519134\pi\) | |||||||
\(318\) | −1801.59 | −0.317698 | ||||||||
\(319\) | 15514.4 | 2.72301 | ||||||||
\(320\) | −25539.6 | −4.46159 | ||||||||
\(321\) | 2546.84 | 0.442836 | ||||||||
\(322\) | −1411.16 | −0.244225 | ||||||||
\(323\) | 1228.12 | 0.211561 | ||||||||
\(324\) | 1861.03 | 0.319107 | ||||||||
\(325\) | 398.698 | 0.0680487 | ||||||||
\(326\) | 15977.5 | 2.71445 | ||||||||
\(327\) | 2745.89 | 0.464367 | ||||||||
\(328\) | −37031.6 | −6.23393 | ||||||||
\(329\) | −1350.03 | −0.226229 | ||||||||
\(330\) | 9942.94 | 1.65861 | ||||||||
\(331\) | 4855.63 | 0.806313 | 0.403157 | − | 0.915131i | \(-0.367913\pi\) | ||||
0.403157 | + | 0.915131i | \(0.367913\pi\) | |||||||
\(332\) | 2981.77 | 0.492910 | ||||||||
\(333\) | 3629.26 | 0.597244 | ||||||||
\(334\) | −10980.5 | −1.79889 | ||||||||
\(335\) | −628.203 | −0.102455 | ||||||||
\(336\) | 15407.6 | 2.50165 | ||||||||
\(337\) | 7662.97 | 1.23866 | 0.619331 | − | 0.785130i | \(-0.287404\pi\) | ||||
0.619331 | + | 0.785130i | \(0.287404\pi\) | |||||||
\(338\) | 11584.4 | 1.86422 | ||||||||
\(339\) | 1428.40 | 0.228849 | ||||||||
\(340\) | 17068.5 | 2.72256 | ||||||||
\(341\) | −13346.1 | −2.11945 | ||||||||
\(342\) | 776.409 | 0.122758 | ||||||||
\(343\) | −6413.31 | −1.00958 | ||||||||
\(344\) | −14657.2 | −2.29728 | ||||||||
\(345\) | −388.931 | −0.0606937 | ||||||||
\(346\) | 5808.40 | 0.902490 | ||||||||
\(347\) | 1372.20 | 0.212287 | 0.106143 | − | 0.994351i | \(-0.466150\pi\) | ||||
0.106143 | + | 0.994351i | \(0.466150\pi\) | |||||||
\(348\) | 16837.1 | 2.59357 | ||||||||
\(349\) | −1713.78 | −0.262855 | −0.131428 | − | 0.991326i | \(-0.541956\pi\) | ||||
−0.131428 | + | 0.991326i | \(0.541956\pi\) | |||||||
\(350\) | 3785.10 | 0.578064 | ||||||||
\(351\) | −290.255 | −0.0441386 | ||||||||
\(352\) | −56653.1 | −8.57846 | ||||||||
\(353\) | −9043.82 | −1.36361 | −0.681804 | − | 0.731535i | \(-0.738804\pi\) | ||||
−0.681804 | + | 0.731535i | \(0.738804\pi\) | |||||||
\(354\) | −9820.14 | −1.47439 | ||||||||
\(355\) | 26.0949 | 0.00390133 | ||||||||
\(356\) | −28918.5 | −4.30528 | ||||||||
\(357\) | −4358.75 | −0.646190 | ||||||||
\(358\) | 13955.9 | 2.06031 | ||||||||
\(359\) | 2963.70 | 0.435706 | 0.217853 | − | 0.975982i | \(-0.430095\pi\) | ||||
0.217853 | + | 0.975982i | \(0.430095\pi\) | |||||||
\(360\) | 7033.39 | 1.02970 | ||||||||
\(361\) | −6618.74 | −0.964972 | ||||||||
\(362\) | 1528.27 | 0.221890 | ||||||||
\(363\) | 8108.45 | 1.17241 | ||||||||
\(364\) | −4529.21 | −0.652185 | ||||||||
\(365\) | −4307.48 | −0.617710 | ||||||||
\(366\) | −6659.52 | −0.951090 | ||||||||
\(367\) | −637.767 | −0.0907117 | −0.0453558 | − | 0.998971i | \(-0.514442\pi\) | ||||
−0.0453558 | + | 0.998971i | \(0.514442\pi\) | |||||||
\(368\) | 3872.60 | 0.548568 | ||||||||
\(369\) | 3998.70 | 0.564129 | ||||||||
\(370\) | 21043.2 | 2.95671 | ||||||||
\(371\) | 1978.62 | 0.276886 | ||||||||
\(372\) | −14484.0 | −2.01870 | ||||||||
\(373\) | 3834.52 | 0.532289 | 0.266144 | − | 0.963933i | \(-0.414250\pi\) | ||||
0.266144 | + | 0.963933i | \(0.414250\pi\) | |||||||
\(374\) | 28007.3 | 3.87225 | ||||||||
\(375\) | 4559.28 | 0.627840 | ||||||||
\(376\) | 6136.22 | 0.841626 | ||||||||
\(377\) | −2625.99 | −0.358740 | ||||||||
\(378\) | −2755.58 | −0.374951 | ||||||||
\(379\) | −566.636 | −0.0767972 | −0.0383986 | − | 0.999263i | \(-0.512226\pi\) | ||||
−0.0383986 | + | 0.999263i | \(0.512226\pi\) | |||||||
\(380\) | 3339.11 | 0.450771 | ||||||||
\(381\) | −6741.25 | −0.906469 | ||||||||
\(382\) | −11977.7 | −1.60428 | ||||||||
\(383\) | −9217.20 | −1.22971 | −0.614853 | − | 0.788642i | \(-0.710784\pi\) | ||||
−0.614853 | + | 0.788642i | \(0.710784\pi\) | |||||||
\(384\) | −24072.1 | −3.19902 | ||||||||
\(385\) | −10920.0 | −1.44554 | ||||||||
\(386\) | 8920.60 | 1.17629 | ||||||||
\(387\) | 1582.70 | 0.207889 | ||||||||
\(388\) | −52.6639 | −0.00689073 | ||||||||
\(389\) | −12751.8 | −1.66206 | −0.831031 | − | 0.556226i | \(-0.812249\pi\) | ||||
−0.831031 | + | 0.556226i | \(0.812249\pi\) | |||||||
\(390\) | −1682.95 | −0.218512 | ||||||||
\(391\) | −1095.54 | −0.141698 | ||||||||
\(392\) | 561.647 | 0.0723660 | ||||||||
\(393\) | −670.012 | −0.0859991 | ||||||||
\(394\) | −21204.8 | −2.71137 | ||||||||
\(395\) | −8967.43 | −1.14228 | ||||||||
\(396\) | 13133.2 | 1.66658 | ||||||||
\(397\) | 2193.72 | 0.277329 | 0.138664 | − | 0.990339i | \(-0.455719\pi\) | ||||
0.138664 | + | 0.990339i | \(0.455719\pi\) | |||||||
\(398\) | 8893.02 | 1.12002 | ||||||||
\(399\) | −852.702 | −0.106989 | ||||||||
\(400\) | −10387.4 | −1.29842 | ||||||||
\(401\) | 1852.85 | 0.230741 | 0.115371 | − | 0.993323i | \(-0.463194\pi\) | ||||
0.115371 | + | 0.993323i | \(0.463194\pi\) | |||||||
\(402\) | −1118.68 | −0.138793 | ||||||||
\(403\) | 2258.98 | 0.279226 | ||||||||
\(404\) | −13640.2 | −1.67976 | ||||||||
\(405\) | −759.469 | −0.0931810 | ||||||||
\(406\) | −24930.2 | −3.04745 | ||||||||
\(407\) | 25611.4 | 3.11919 | ||||||||
\(408\) | 19811.7 | 2.40398 | ||||||||
\(409\) | −9730.07 | −1.17633 | −0.588167 | − | 0.808739i | \(-0.700150\pi\) | ||||
−0.588167 | + | 0.808739i | \(0.700150\pi\) | |||||||
\(410\) | 23185.2 | 2.79277 | ||||||||
\(411\) | 1417.48 | 0.170120 | ||||||||
\(412\) | −16930.7 | −2.02455 | ||||||||
\(413\) | 10785.1 | 1.28499 | ||||||||
\(414\) | −692.594 | −0.0822201 | ||||||||
\(415\) | −1216.83 | −0.143933 | ||||||||
\(416\) | 9589.17 | 1.13016 | ||||||||
\(417\) | −3049.40 | −0.358105 | ||||||||
\(418\) | 5479.06 | 0.641124 | ||||||||
\(419\) | −13507.7 | −1.57493 | −0.787465 | − | 0.616359i | \(-0.788607\pi\) | ||||
−0.787465 | + | 0.616359i | \(0.788607\pi\) | |||||||
\(420\) | −11851.0 | −1.37683 | ||||||||
\(421\) | 5819.08 | 0.673645 | 0.336823 | − | 0.941568i | \(-0.390648\pi\) | ||||
0.336823 | + | 0.941568i | \(0.390648\pi\) | |||||||
\(422\) | −5593.90 | −0.645277 | ||||||||
\(423\) | −662.592 | −0.0761615 | ||||||||
\(424\) | −8993.32 | −1.03008 | ||||||||
\(425\) | 2938.54 | 0.335388 | ||||||||
\(426\) | 46.4689 | 0.00528503 | ||||||||
\(427\) | 7313.92 | 0.828911 | ||||||||
\(428\) | 19505.1 | 2.20284 | ||||||||
\(429\) | −2048.31 | −0.230520 | ||||||||
\(430\) | 9176.79 | 1.02917 | ||||||||
\(431\) | 10170.6 | 1.13667 | 0.568333 | − | 0.822799i | \(-0.307589\pi\) | ||||
0.568333 | + | 0.822799i | \(0.307589\pi\) | |||||||
\(432\) | 7562.06 | 0.842199 | ||||||||
\(433\) | 780.624 | 0.0866383 | 0.0433192 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433192 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(434\) | 21446.0 | 2.37198 | ||||||||
\(435\) | −6871.05 | −0.757337 | ||||||||
\(436\) | 21029.5 | 2.30994 | ||||||||
\(437\) | −214.320 | −0.0234607 | ||||||||
\(438\) | −7670.62 | −0.836795 | ||||||||
\(439\) | −9387.18 | −1.02056 | −0.510280 | − | 0.860008i | \(-0.670458\pi\) | ||||
−0.510280 | + | 0.860008i | \(0.670458\pi\) | |||||||
\(440\) | 49634.1 | 5.37776 | ||||||||
\(441\) | −60.6470 | −0.00654864 | ||||||||
\(442\) | −4740.55 | −0.510147 | ||||||||
\(443\) | −16622.6 | −1.78276 | −0.891381 | − | 0.453254i | \(-0.850263\pi\) | ||||
−0.891381 | + | 0.453254i | \(0.850263\pi\) | |||||||
\(444\) | 27794.9 | 2.97092 | ||||||||
\(445\) | 11801.4 | 1.25717 | ||||||||
\(446\) | −32219.3 | −3.42069 | ||||||||
\(447\) | −2022.48 | −0.214005 | ||||||||
\(448\) | 49949.2 | 5.26758 | ||||||||
\(449\) | 986.558 | 0.103694 | 0.0518469 | − | 0.998655i | \(-0.483489\pi\) | ||||
0.0518469 | + | 0.998655i | \(0.483489\pi\) | |||||||
\(450\) | 1857.73 | 0.194609 | ||||||||
\(451\) | 28218.5 | 2.94625 | ||||||||
\(452\) | 10939.5 | 1.13838 | ||||||||
\(453\) | 1412.47 | 0.146498 | ||||||||
\(454\) | 30662.4 | 3.16973 | ||||||||
\(455\) | 1848.33 | 0.190442 | ||||||||
\(456\) | 3875.75 | 0.398023 | ||||||||
\(457\) | 6599.18 | 0.675485 | 0.337742 | − | 0.941239i | \(-0.390337\pi\) | ||||
0.337742 | + | 0.941239i | \(0.390337\pi\) | |||||||
\(458\) | −32891.2 | −3.35569 | ||||||||
\(459\) | −2139.27 | −0.217544 | ||||||||
\(460\) | −2978.65 | −0.301913 | ||||||||
\(461\) | −17494.0 | −1.76741 | −0.883704 | − | 0.468047i | \(-0.844958\pi\) | ||||
−0.883704 | + | 0.468047i | \(0.844958\pi\) | |||||||
\(462\) | −19445.9 | −1.95824 | ||||||||
\(463\) | 1622.80 | 0.162890 | 0.0814450 | − | 0.996678i | \(-0.474047\pi\) | ||||
0.0814450 | + | 0.996678i | \(0.474047\pi\) | |||||||
\(464\) | 68415.3 | 6.84504 | ||||||||
\(465\) | 5910.77 | 0.589473 | ||||||||
\(466\) | 24686.9 | 2.45407 | ||||||||
\(467\) | 3130.69 | 0.310217 | 0.155108 | − | 0.987897i | \(-0.450427\pi\) | ||||
0.155108 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(468\) | −2222.93 | −0.219562 | ||||||||
\(469\) | 1228.61 | 0.120963 | ||||||||
\(470\) | −3841.84 | −0.377044 | ||||||||
\(471\) | −4647.39 | −0.454651 | ||||||||
\(472\) | −49021.1 | −4.78046 | ||||||||
\(473\) | 11169.0 | 1.08573 | ||||||||
\(474\) | −15968.9 | −1.54742 | ||||||||
\(475\) | 574.866 | 0.0555298 | ||||||||
\(476\) | −33381.8 | −3.21439 | ||||||||
\(477\) | 971.104 | 0.0932155 | ||||||||
\(478\) | −38476.4 | −3.68174 | ||||||||
\(479\) | 498.066 | 0.0475099 | 0.0237549 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237549 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(480\) | 25090.6 | 2.38589 | ||||||||
\(481\) | −4335.02 | −0.410936 | ||||||||
\(482\) | −3416.53 | −0.322860 | ||||||||
\(483\) | 760.651 | 0.0716580 | ||||||||
\(484\) | 62099.0 | 5.83199 | ||||||||
\(485\) | 21.4916 | 0.00201213 | ||||||||
\(486\) | −1352.44 | −0.126230 | ||||||||
\(487\) | −8164.16 | −0.759658 | −0.379829 | − | 0.925057i | \(-0.624017\pi\) | ||||
−0.379829 | + | 0.925057i | \(0.624017\pi\) | |||||||
\(488\) | −33243.6 | −3.08375 | ||||||||
\(489\) | −8612.29 | −0.796444 | ||||||||
\(490\) | −351.643 | −0.0324196 | ||||||||
\(491\) | 6914.18 | 0.635505 | 0.317752 | − | 0.948174i | \(-0.397072\pi\) | ||||
0.317752 | + | 0.948174i | \(0.397072\pi\) | |||||||
\(492\) | 30624.2 | 2.80619 | ||||||||
\(493\) | −19354.4 | −1.76811 | ||||||||
\(494\) | −927.393 | −0.0844644 | ||||||||
\(495\) | −5359.52 | −0.486651 | ||||||||
\(496\) | −58853.7 | −5.32784 | ||||||||
\(497\) | −51.0351 | −0.00460611 | ||||||||
\(498\) | −2166.89 | −0.194982 | ||||||||
\(499\) | −10976.7 | −0.984743 | −0.492372 | − | 0.870385i | \(-0.663870\pi\) | ||||
−0.492372 | + | 0.870385i | \(0.663870\pi\) | |||||||
\(500\) | 34917.5 | 3.12312 | ||||||||
\(501\) | 5918.81 | 0.527810 | ||||||||
\(502\) | 36298.9 | 3.22729 | ||||||||
\(503\) | 4883.56 | 0.432897 | 0.216449 | − | 0.976294i | \(-0.430553\pi\) | ||||
0.216449 | + | 0.976294i | \(0.430553\pi\) | |||||||
\(504\) | −13755.6 | −1.21572 | ||||||||
\(505\) | 5566.42 | 0.490500 | ||||||||
\(506\) | −4887.58 | −0.429406 | ||||||||
\(507\) | −6244.30 | −0.546981 | ||||||||
\(508\) | −51628.3 | −4.50912 | ||||||||
\(509\) | −3071.69 | −0.267486 | −0.133743 | − | 0.991016i | \(-0.542700\pi\) | ||||
−0.133743 | + | 0.991016i | \(0.542700\pi\) | |||||||
\(510\) | −12403.9 | −1.07697 | ||||||||
\(511\) | 8424.36 | 0.729299 | ||||||||
\(512\) | −63077.2 | −5.44462 | ||||||||
\(513\) | −418.506 | −0.0360185 | ||||||||
\(514\) | −20648.1 | −1.77188 | ||||||||
\(515\) | 6909.25 | 0.591180 | ||||||||
\(516\) | 12121.2 | 1.03412 | ||||||||
\(517\) | −4675.86 | −0.397764 | ||||||||
\(518\) | −41155.2 | −3.49084 | ||||||||
\(519\) | −3130.89 | −0.264799 | ||||||||
\(520\) | −8401.13 | −0.708488 | ||||||||
\(521\) | −10466.6 | −0.880134 | −0.440067 | − | 0.897965i | \(-0.645045\pi\) | ||||
−0.440067 | + | 0.897965i | \(0.645045\pi\) | |||||||
\(522\) | −12235.7 | −1.02594 | ||||||||
\(523\) | 17015.5 | 1.42263 | 0.711317 | − | 0.702872i | \(-0.248099\pi\) | ||||
0.711317 | + | 0.702872i | \(0.248099\pi\) | |||||||
\(524\) | −5131.33 | −0.427792 | ||||||||
\(525\) | −2040.27 | −0.169609 | ||||||||
\(526\) | 28992.6 | 2.40330 | ||||||||
\(527\) | 16649.4 | 1.37621 | ||||||||
\(528\) | 53364.9 | 4.39850 | ||||||||
\(529\) | −11975.8 | −0.984287 | ||||||||
\(530\) | 5630.65 | 0.461472 | ||||||||
\(531\) | 5293.32 | 0.432600 | ||||||||
\(532\) | −6530.47 | −0.532203 | ||||||||
\(533\) | −4776.30 | −0.388151 | ||||||||
\(534\) | 21015.5 | 1.70305 | ||||||||
\(535\) | −7959.85 | −0.643241 | ||||||||
\(536\) | −5584.34 | −0.450012 | ||||||||
\(537\) | −7522.60 | −0.604514 | ||||||||
\(538\) | 29356.8 | 2.35253 | ||||||||
\(539\) | −427.981 | −0.0342012 | ||||||||
\(540\) | −5816.44 | −0.463518 | ||||||||
\(541\) | 196.265 | 0.0155972 | 0.00779861 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779861 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(542\) | −30033.7 | −2.38018 | ||||||||
\(543\) | −823.779 | −0.0651045 | ||||||||
\(544\) | 70675.3 | 5.57018 | ||||||||
\(545\) | −8581.96 | −0.674515 | ||||||||
\(546\) | 3291.44 | 0.257987 | ||||||||
\(547\) | −15657.7 | −1.22390 | −0.611952 | − | 0.790895i | \(-0.709615\pi\) | ||||
−0.611952 | + | 0.790895i | \(0.709615\pi\) | |||||||
\(548\) | 10855.9 | 0.846240 | ||||||||
\(549\) | 3589.66 | 0.279059 | ||||||||
\(550\) | 13109.8 | 1.01637 | ||||||||
\(551\) | −3786.29 | −0.292743 | ||||||||
\(552\) | −3457.36 | −0.266585 | ||||||||
\(553\) | 17538.1 | 1.34863 | ||||||||
\(554\) | 38454.2 | 2.94903 | ||||||||
\(555\) | −11342.8 | −0.867526 | ||||||||
\(556\) | −23354.0 | −1.78135 | ||||||||
\(557\) | 10543.5 | 0.802050 | 0.401025 | − | 0.916067i | \(-0.368654\pi\) | ||||
0.401025 | + | 0.916067i | \(0.368654\pi\) | |||||||
\(558\) | 10525.7 | 0.798544 | ||||||||
\(559\) | −1890.48 | −0.143039 | ||||||||
\(560\) | −48154.9 | −3.63378 | ||||||||
\(561\) | −15096.7 | −1.13615 | ||||||||
\(562\) | −39939.2 | −2.99774 | ||||||||
\(563\) | 3882.05 | 0.290602 | 0.145301 | − | 0.989387i | \(-0.453585\pi\) | ||||
0.145301 | + | 0.989387i | \(0.453585\pi\) | |||||||
\(564\) | −5074.50 | −0.378856 | ||||||||
\(565\) | −4464.29 | −0.332415 | ||||||||
\(566\) | 18243.2 | 1.35481 | ||||||||
\(567\) | 1485.33 | 0.110014 | ||||||||
\(568\) | 231.968 | 0.0171358 | ||||||||
\(569\) | −8596.23 | −0.633344 | −0.316672 | − | 0.948535i | \(-0.602565\pi\) | ||||
−0.316672 | + | 0.948535i | \(0.602565\pi\) | |||||||
\(570\) | −2426.58 | −0.178313 | ||||||||
\(571\) | 9931.35 | 0.727871 | 0.363935 | − | 0.931424i | \(-0.381433\pi\) | ||||
0.363935 | + | 0.931424i | \(0.381433\pi\) | |||||||
\(572\) | −15687.1 | −1.14670 | ||||||||
\(573\) | 6456.32 | 0.470710 | ||||||||
\(574\) | −45344.5 | −3.29729 | ||||||||
\(575\) | −512.808 | −0.0371923 | ||||||||
\(576\) | 24515.0 | 1.77337 | ||||||||
\(577\) | 19338.0 | 1.39524 | 0.697619 | − | 0.716469i | \(-0.254243\pi\) | ||||
0.697619 | + | 0.716469i | \(0.254243\pi\) | |||||||
\(578\) | −7595.70 | −0.546608 | ||||||||
\(579\) | −4808.45 | −0.345133 | ||||||||
\(580\) | −52622.3 | −3.76728 | ||||||||
\(581\) | 2379.82 | 0.169934 | ||||||||
\(582\) | 38.2716 | 0.00272579 | ||||||||
\(583\) | 6853.01 | 0.486831 | ||||||||
\(584\) | −38290.9 | −2.71317 | ||||||||
\(585\) | 907.159 | 0.0641135 | ||||||||
\(586\) | 23630.0 | 1.66578 | ||||||||
\(587\) | −17190.3 | −1.20872 | −0.604360 | − | 0.796712i | \(-0.706571\pi\) | ||||
−0.604360 | + | 0.796712i | \(0.706571\pi\) | |||||||
\(588\) | −464.468 | −0.0325754 | ||||||||
\(589\) | 3257.13 | 0.227857 | ||||||||
\(590\) | 30691.7 | 2.14162 | ||||||||
\(591\) | 11430.0 | 0.795543 | ||||||||
\(592\) | 112941. | 7.84097 | ||||||||
\(593\) | −2497.07 | −0.172921 | −0.0864607 | − | 0.996255i | \(-0.527556\pi\) | ||||
−0.0864607 | + | 0.996255i | \(0.527556\pi\) | |||||||
\(594\) | −9544.04 | −0.659254 | ||||||||
\(595\) | 13622.8 | 0.938622 | ||||||||
\(596\) | −15489.3 | −1.06454 | ||||||||
\(597\) | −4793.58 | −0.328624 | ||||||||
\(598\) | 827.279 | 0.0565718 | ||||||||
\(599\) | 16534.3 | 1.12784 | 0.563918 | − | 0.825831i | \(-0.309293\pi\) | ||||
0.563918 | + | 0.825831i | \(0.309293\pi\) | |||||||
\(600\) | 9273.57 | 0.630987 | ||||||||
\(601\) | 14103.7 | 0.957238 | 0.478619 | − | 0.878023i | \(-0.341137\pi\) | ||||
0.478619 | + | 0.878023i | \(0.341137\pi\) | |||||||
\(602\) | −17947.5 | −1.21509 | ||||||||
\(603\) | 603.000 | 0.0407231 | ||||||||
\(604\) | 10817.5 | 0.728739 | ||||||||
\(605\) | −25342.0 | −1.70298 | ||||||||
\(606\) | 9912.49 | 0.664468 | ||||||||
\(607\) | 7489.59 | 0.500812 | 0.250406 | − | 0.968141i | \(-0.419436\pi\) | ||||
0.250406 | + | 0.968141i | \(0.419436\pi\) | |||||||
\(608\) | 13826.2 | 0.922248 | ||||||||
\(609\) | 13438.1 | 0.894150 | ||||||||
\(610\) | 20813.6 | 1.38150 | ||||||||
\(611\) | 791.443 | 0.0524032 | ||||||||
\(612\) | −16383.8 | −1.08215 | ||||||||
\(613\) | 17712.9 | 1.16708 | 0.583539 | − | 0.812085i | \(-0.301668\pi\) | ||||
0.583539 | + | 0.812085i | \(0.301668\pi\) | |||||||
\(614\) | 1195.62 | 0.0785849 | ||||||||
\(615\) | −12497.5 | −0.819425 | ||||||||
\(616\) | −97071.9 | −6.34925 | ||||||||
\(617\) | −15231.7 | −0.993847 | −0.496924 | − | 0.867794i | \(-0.665537\pi\) | ||||
−0.496924 | + | 0.867794i | \(0.665537\pi\) | |||||||
\(618\) | 12303.7 | 0.800856 | ||||||||
\(619\) | −1777.52 | −0.115420 | −0.0577098 | − | 0.998333i | \(-0.518380\pi\) | ||||
−0.0577098 | + | 0.998333i | \(0.518380\pi\) | |||||||
\(620\) | 45267.9 | 2.93227 | ||||||||
\(621\) | 373.327 | 0.0241242 | ||||||||
\(622\) | 2750.70 | 0.177320 | ||||||||
\(623\) | −23080.6 | −1.48428 | ||||||||
\(624\) | −9032.62 | −0.579478 | ||||||||
\(625\) | −9613.56 | −0.615268 | ||||||||
\(626\) | 1480.02 | 0.0944943 | ||||||||
\(627\) | −2953.36 | −0.188112 | ||||||||
\(628\) | −35592.3 | −2.26161 | ||||||||
\(629\) | −31950.5 | −2.02536 | ||||||||
\(630\) | 8612.25 | 0.544635 | ||||||||
\(631\) | −29832.3 | −1.88210 | −0.941049 | − | 0.338271i | \(-0.890158\pi\) | ||||
−0.941049 | + | 0.338271i | \(0.890158\pi\) | |||||||
\(632\) | −79715.0 | −5.01724 | ||||||||
\(633\) | 3015.26 | 0.189330 | ||||||||
\(634\) | 3774.09 | 0.236417 | ||||||||
\(635\) | 21069.0 | 1.31669 | ||||||||
\(636\) | 7437.26 | 0.463689 | ||||||||
\(637\) | 72.4406 | 0.00450581 | ||||||||
\(638\) | −86346.6 | −5.35814 | ||||||||
\(639\) | −25.0480 | −0.00155068 | ||||||||
\(640\) | 75234.6 | 4.64673 | ||||||||
\(641\) | −12016.1 | −0.740418 | −0.370209 | − | 0.928949i | \(-0.620714\pi\) | ||||
−0.370209 | + | 0.928949i | \(0.620714\pi\) | |||||||
\(642\) | −14174.6 | −0.871382 | ||||||||
\(643\) | −14193.2 | −0.870490 | −0.435245 | − | 0.900312i | \(-0.643338\pi\) | ||||
−0.435245 | + | 0.900312i | \(0.643338\pi\) | |||||||
\(644\) | 5825.49 | 0.356454 | ||||||||
\(645\) | −4946.54 | −0.301969 | ||||||||
\(646\) | −6835.19 | −0.416296 | ||||||||
\(647\) | 26400.1 | 1.60416 | 0.802082 | − | 0.597214i | \(-0.203726\pi\) | ||||
0.802082 | + | 0.597214i | \(0.203726\pi\) | |||||||
\(648\) | −6751.22 | −0.409279 | ||||||||
\(649\) | 37354.6 | 2.25932 | ||||||||
\(650\) | −2218.99 | −0.133901 | ||||||||
\(651\) | −11560.0 | −0.695962 | ||||||||
\(652\) | −65957.7 | −3.96181 | ||||||||
\(653\) | −9641.82 | −0.577815 | −0.288908 | − | 0.957357i | \(-0.593292\pi\) | ||||
−0.288908 | + | 0.957357i | \(0.593292\pi\) | |||||||
\(654\) | −15282.5 | −0.913748 | ||||||||
\(655\) | 2094.05 | 0.124918 | ||||||||
\(656\) | 124438. | 7.40622 | ||||||||
\(657\) | 4134.67 | 0.245524 | ||||||||
\(658\) | 7513.68 | 0.445158 | ||||||||
\(659\) | −9945.53 | −0.587895 | −0.293948 | − | 0.955822i | \(-0.594969\pi\) | ||||
−0.293948 | + | 0.955822i | \(0.594969\pi\) | |||||||
\(660\) | −41046.2 | −2.42079 | ||||||||
\(661\) | −16881.2 | −0.993348 | −0.496674 | − | 0.867937i | \(-0.665446\pi\) | ||||
−0.496674 | + | 0.867937i | \(0.665446\pi\) | |||||||
\(662\) | −27024.4 | −1.58661 | ||||||||
\(663\) | 2555.29 | 0.149682 | ||||||||
\(664\) | −10816.9 | −0.632195 | ||||||||
\(665\) | 2665.03 | 0.155406 | ||||||||
\(666\) | −20198.9 | −1.17521 | ||||||||
\(667\) | 3377.56 | 0.196071 | ||||||||
\(668\) | 45329.6 | 2.62553 | ||||||||
\(669\) | 17367.1 | 1.00366 | ||||||||
\(670\) | 3496.31 | 0.201604 | ||||||||
\(671\) | 25332.0 | 1.45742 | ||||||||
\(672\) | −49071.0 | −2.81690 | ||||||||
\(673\) | 18318.3 | 1.04921 | 0.524606 | − | 0.851345i | \(-0.324213\pi\) | ||||
0.524606 | + | 0.851345i | \(0.324213\pi\) | |||||||
\(674\) | −42648.9 | −2.43735 | ||||||||
\(675\) | −1001.37 | −0.0571001 | ||||||||
\(676\) | −47822.4 | −2.72089 | ||||||||
\(677\) | 5568.23 | 0.316107 | 0.158054 | − | 0.987431i | \(-0.449478\pi\) | ||||
0.158054 | + | 0.987431i | \(0.449478\pi\) | |||||||
\(678\) | −7949.86 | −0.450313 | ||||||||
\(679\) | −42.0323 | −0.00237563 | ||||||||
\(680\) | −61919.1 | −3.49189 | ||||||||
\(681\) | −16527.9 | −0.930029 | ||||||||
\(682\) | 74279.0 | 4.17051 | ||||||||
\(683\) | 12021.4 | 0.673476 | 0.336738 | − | 0.941598i | \(-0.390676\pi\) | ||||
0.336738 | + | 0.941598i | \(0.390676\pi\) | |||||||
\(684\) | −3205.15 | −0.179170 | ||||||||
\(685\) | −4430.18 | −0.247107 | ||||||||
\(686\) | 35693.8 | 1.98658 | ||||||||
\(687\) | 17729.2 | 0.984589 | ||||||||
\(688\) | 49252.9 | 2.72929 | ||||||||
\(689\) | −1159.95 | −0.0641372 | ||||||||
\(690\) | 2164.62 | 0.119429 | ||||||||
\(691\) | 21089.9 | 1.16107 | 0.580534 | − | 0.814236i | \(-0.302844\pi\) | ||||
0.580534 | + | 0.814236i | \(0.302844\pi\) | |||||||
\(692\) | −23978.1 | −1.31721 | ||||||||
\(693\) | 10481.9 | 0.574565 | ||||||||
\(694\) | −7637.09 | −0.417723 | ||||||||
\(695\) | 9530.55 | 0.520164 | ||||||||
\(696\) | −61079.4 | −3.32645 | ||||||||
\(697\) | −35202.9 | −1.91306 | ||||||||
\(698\) | 9538.16 | 0.517228 | ||||||||
\(699\) | −13306.9 | −0.720048 | ||||||||
\(700\) | −15625.6 | −0.843701 | ||||||||
\(701\) | 23160.3 | 1.24786 | 0.623932 | − | 0.781479i | \(-0.285534\pi\) | ||||
0.623932 | + | 0.781479i | \(0.285534\pi\) | |||||||
\(702\) | 1615.44 | 0.0868529 | ||||||||
\(703\) | −6250.48 | −0.335336 | ||||||||
\(704\) | 173001. | 9.26166 | ||||||||
\(705\) | 2070.86 | 0.110628 | ||||||||
\(706\) | 50334.1 | 2.68321 | ||||||||
\(707\) | −10886.5 | −0.579109 | ||||||||
\(708\) | 40539.2 | 2.15192 | ||||||||
\(709\) | −9142.60 | −0.484284 | −0.242142 | − | 0.970241i | \(-0.577850\pi\) | ||||
−0.242142 | + | 0.970241i | \(0.577850\pi\) | |||||||
\(710\) | −145.233 | −0.00767677 | ||||||||
\(711\) | 8607.67 | 0.454027 | ||||||||
\(712\) | 104907. | 5.52185 | ||||||||
\(713\) | −2905.52 | −0.152612 | ||||||||
\(714\) | 24259.0 | 1.27153 | ||||||||
\(715\) | 6401.75 | 0.334842 | ||||||||
\(716\) | −57612.3 | −3.00708 | ||||||||
\(717\) | 20739.8 | 1.08026 | ||||||||
\(718\) | −16494.7 | −0.857351 | ||||||||
\(719\) | −4851.00 | −0.251616 | −0.125808 | − | 0.992055i | \(-0.540152\pi\) | ||||
−0.125808 | + | 0.992055i | \(0.540152\pi\) | |||||||
\(720\) | −23634.4 | −1.22333 | ||||||||
\(721\) | −13512.8 | −0.697977 | ||||||||
\(722\) | 36837.1 | 1.89880 | ||||||||
\(723\) | 1841.60 | 0.0947303 | ||||||||
\(724\) | −6308.96 | −0.323854 | ||||||||
\(725\) | −9059.53 | −0.464086 | ||||||||
\(726\) | −45128.2 | −2.30698 | ||||||||
\(727\) | 393.072 | 0.0200526 | 0.0100263 | − | 0.999950i | \(-0.496808\pi\) | ||||
0.0100263 | + | 0.999950i | \(0.496808\pi\) | |||||||
\(728\) | 16430.5 | 0.836477 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 23973.6 | 1.21549 | ||||||||
\(731\) | −13933.4 | −0.704988 | ||||||||
\(732\) | 27491.7 | 1.38814 | ||||||||
\(733\) | 9672.93 | 0.487419 | 0.243709 | − | 0.969848i | \(-0.421636\pi\) | ||||
0.243709 | + | 0.969848i | \(0.421636\pi\) | |||||||
\(734\) | 3549.54 | 0.178496 | ||||||||
\(735\) | 189.545 | 0.00951222 | ||||||||
\(736\) | −12333.6 | −0.617695 | ||||||||
\(737\) | 4255.33 | 0.212682 | ||||||||
\(738\) | −22255.1 | −1.11005 | ||||||||
\(739\) | −16379.8 | −0.815344 | −0.407672 | − | 0.913128i | \(-0.633659\pi\) | ||||
−0.407672 | + | 0.913128i | \(0.633659\pi\) | |||||||
\(740\) | −86869.9 | −4.31540 | ||||||||
\(741\) | 499.890 | 0.0247826 | ||||||||
\(742\) | −11012.2 | −0.544837 | ||||||||
\(743\) | 1918.02 | 0.0947043 | 0.0473522 | − | 0.998878i | \(-0.484922\pi\) | ||||
0.0473522 | + | 0.998878i | \(0.484922\pi\) | |||||||
\(744\) | 52543.1 | 2.58914 | ||||||||
\(745\) | 6321.04 | 0.310852 | ||||||||
\(746\) | −21341.3 | −1.04740 | ||||||||
\(747\) | 1168.02 | 0.0572094 | ||||||||
\(748\) | −115619. | −5.65167 | ||||||||
\(749\) | 15567.5 | 0.759444 | ||||||||
\(750\) | −25375.0 | −1.23542 | ||||||||
\(751\) | 18041.6 | 0.876627 | 0.438313 | − | 0.898822i | \(-0.355576\pi\) | ||||
0.438313 | + | 0.898822i | \(0.355576\pi\) | |||||||
\(752\) | −20619.6 | −0.999893 | ||||||||
\(753\) | −19566.1 | −0.946917 | ||||||||
\(754\) | 14615.1 | 0.705904 | ||||||||
\(755\) | −4414.53 | −0.212796 | ||||||||
\(756\) | 11375.5 | 0.547253 | ||||||||
\(757\) | −4736.09 | −0.227393 | −0.113696 | − | 0.993516i | \(-0.536269\pi\) | ||||
−0.113696 | + | 0.993516i | \(0.536269\pi\) | |||||||
\(758\) | 3153.66 | 0.151116 | ||||||||
\(759\) | 2634.54 | 0.125992 | ||||||||
\(760\) | −12113.2 | −0.578148 | ||||||||
\(761\) | −37890.8 | −1.80491 | −0.902457 | − | 0.430781i | \(-0.858238\pi\) | ||||
−0.902457 | + | 0.430781i | \(0.858238\pi\) | |||||||
\(762\) | 37519.0 | 1.78369 | ||||||||
\(763\) | 16784.2 | 0.796367 | ||||||||
\(764\) | 49446.1 | 2.34149 | ||||||||
\(765\) | 6686.06 | 0.315993 | ||||||||
\(766\) | 51299.1 | 2.41973 | ||||||||
\(767\) | −6322.69 | −0.297652 | ||||||||
\(768\) | 68601.7 | 3.22324 | ||||||||
\(769\) | −10807.3 | −0.506791 | −0.253395 | − | 0.967363i | \(-0.581547\pi\) | ||||
−0.253395 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(770\) | 60776.0 | 2.84443 | ||||||||
\(771\) | 11129.9 | 0.519887 | ||||||||
\(772\) | −36825.8 | −1.71682 | ||||||||
\(773\) | 35806.3 | 1.66606 | 0.833029 | − | 0.553230i | \(-0.186605\pi\) | ||||
0.833029 | + | 0.553230i | \(0.186605\pi\) | |||||||
\(774\) | −8808.63 | −0.409069 | ||||||||
\(775\) | 7793.39 | 0.361222 | ||||||||
\(776\) | 191.048 | 0.00883790 | ||||||||
\(777\) | 22183.8 | 1.02425 | ||||||||
\(778\) | 70971.2 | 3.27049 | ||||||||
\(779\) | −6886.74 | −0.316743 | ||||||||
\(780\) | 6947.53 | 0.318925 | ||||||||
\(781\) | −176.762 | −0.00809864 | ||||||||
\(782\) | 6097.32 | 0.278823 | ||||||||
\(783\) | 6595.39 | 0.301022 | ||||||||
\(784\) | −1887.31 | −0.0859744 | ||||||||
\(785\) | 14524.9 | 0.660402 | ||||||||
\(786\) | 3729.01 | 0.169223 | ||||||||
\(787\) | 19577.1 | 0.886722 | 0.443361 | − | 0.896343i | \(-0.353786\pi\) | ||||
0.443361 | + | 0.896343i | \(0.353786\pi\) | |||||||
\(788\) | 87537.0 | 3.95733 | ||||||||
\(789\) | −15627.8 | −0.705152 | ||||||||
\(790\) | 49909.0 | 2.24770 | ||||||||
\(791\) | 8731.05 | 0.392466 | ||||||||
\(792\) | −47642.8 | −2.13752 | ||||||||
\(793\) | −4287.73 | −0.192007 | ||||||||
\(794\) | −12209.3 | −0.545708 | ||||||||
\(795\) | −3035.08 | −0.135400 | ||||||||
\(796\) | −36711.9 | −1.63470 | ||||||||
\(797\) | 24351.5 | 1.08228 | 0.541139 | − | 0.840933i | \(-0.317993\pi\) | ||||
0.541139 | + | 0.840933i | \(0.317993\pi\) | |||||||
\(798\) | 4745.78 | 0.210525 | ||||||||
\(799\) | 5833.19 | 0.258277 | ||||||||
\(800\) | 33082.2 | 1.46204 | ||||||||
\(801\) | −11327.9 | −0.499691 | ||||||||
\(802\) | −10312.2 | −0.454036 | ||||||||
\(803\) | 29178.1 | 1.28228 | ||||||||
\(804\) | 4618.11 | 0.202572 | ||||||||
\(805\) | −2377.33 | −0.104087 | ||||||||
\(806\) | −12572.6 | −0.549441 | ||||||||
\(807\) | −15824.1 | −0.690255 | ||||||||
\(808\) | 49482.1 | 2.15442 | ||||||||
\(809\) | −19396.6 | −0.842953 | −0.421476 | − | 0.906839i | \(-0.638488\pi\) | ||||
−0.421476 | + | 0.906839i | \(0.638488\pi\) | |||||||
\(810\) | 4226.89 | 0.183355 | ||||||||
\(811\) | −24238.5 | −1.04948 | −0.524739 | − | 0.851263i | \(-0.675837\pi\) | ||||
−0.524739 | + | 0.851263i | \(0.675837\pi\) | |||||||
\(812\) | 102916. | 4.44784 | ||||||||
\(813\) | 16189.0 | 0.698368 | ||||||||
\(814\) | −142542. | −6.13773 | ||||||||
\(815\) | 26916.7 | 1.15687 | ||||||||
\(816\) | −66573.3 | −2.85604 | ||||||||
\(817\) | −2725.79 | −0.116724 | ||||||||
\(818\) | 54153.5 | 2.31471 | ||||||||
\(819\) | −1774.18 | −0.0756957 | ||||||||
\(820\) | −95712.6 | −4.07613 | ||||||||
\(821\) | −13774.7 | −0.585554 | −0.292777 | − | 0.956181i | \(-0.594579\pi\) | ||||
−0.292777 | + | 0.956181i | \(0.594579\pi\) | |||||||
\(822\) | −7889.10 | −0.334749 | ||||||||
\(823\) | −29087.7 | −1.23200 | −0.615998 | − | 0.787748i | \(-0.711247\pi\) | ||||
−0.615998 | + | 0.787748i | \(0.711247\pi\) | |||||||
\(824\) | 61419.0 | 2.59664 | ||||||||
\(825\) | −7066.56 | −0.298213 | ||||||||
\(826\) | −60025.4 | −2.52851 | ||||||||
\(827\) | 24698.3 | 1.03850 | 0.519252 | − | 0.854621i | \(-0.326211\pi\) | ||||
0.519252 | + | 0.854621i | \(0.326211\pi\) | |||||||
\(828\) | 2859.15 | 0.120003 | ||||||||
\(829\) | −9009.94 | −0.377477 | −0.188738 | − | 0.982027i | \(-0.560440\pi\) | ||||
−0.188738 | + | 0.982027i | \(0.560440\pi\) | |||||||
\(830\) | 6772.38 | 0.283220 | ||||||||
\(831\) | −20727.9 | −0.865273 | ||||||||
\(832\) | −29282.3 | −1.22017 | ||||||||
\(833\) | 533.911 | 0.0222076 | ||||||||
\(834\) | 16971.7 | 0.704653 | ||||||||
\(835\) | −18498.6 | −0.766670 | ||||||||
\(836\) | −22618.5 | −0.935739 | ||||||||
\(837\) | −5673.63 | −0.234300 | ||||||||
\(838\) | 75178.4 | 3.09904 | ||||||||
\(839\) | −18900.3 | −0.777726 | −0.388863 | − | 0.921296i | \(-0.627132\pi\) | ||||
−0.388863 | + | 0.921296i | \(0.627132\pi\) | |||||||
\(840\) | 42991.4 | 1.76589 | ||||||||
\(841\) | 35280.6 | 1.44658 | ||||||||
\(842\) | −32386.5 | −1.32555 | ||||||||
\(843\) | 21528.3 | 0.879566 | ||||||||
\(844\) | 23092.6 | 0.941800 | ||||||||
\(845\) | 19515.9 | 0.794516 | ||||||||
\(846\) | 3687.71 | 0.149865 | ||||||||
\(847\) | 49562.7 | 2.01062 | ||||||||
\(848\) | 30220.4 | 1.22379 | ||||||||
\(849\) | −9833.61 | −0.397513 | ||||||||
\(850\) | −16354.7 | −0.659953 | ||||||||
\(851\) | 5575.73 | 0.224599 | ||||||||
\(852\) | −191.832 | −0.00771366 | ||||||||
\(853\) | 15100.3 | 0.606123 | 0.303062 | − | 0.952971i | \(-0.401991\pi\) | ||||
0.303062 | + | 0.952971i | \(0.401991\pi\) | |||||||
\(854\) | −40706.2 | −1.63107 | ||||||||
\(855\) | 1307.99 | 0.0523186 | ||||||||
\(856\) | −70758.2 | −2.82531 | ||||||||
\(857\) | −36278.5 | −1.44603 | −0.723016 | − | 0.690831i | \(-0.757245\pi\) | ||||
−0.723016 | + | 0.690831i | \(0.757245\pi\) | |||||||
\(858\) | 11400.0 | 0.453602 | ||||||||
\(859\) | 22352.9 | 0.887861 | 0.443931 | − | 0.896061i | \(-0.353584\pi\) | ||||
0.443931 | + | 0.896061i | \(0.353584\pi\) | |||||||
\(860\) | −37883.4 | −1.50211 | ||||||||
\(861\) | 24441.9 | 0.967455 | ||||||||
\(862\) | −56605.5 | −2.23665 | ||||||||
\(863\) | −11591.1 | −0.457204 | −0.228602 | − | 0.973520i | \(-0.573415\pi\) | ||||
−0.228602 | + | 0.973520i | \(0.573415\pi\) | |||||||
\(864\) | −24084.0 | −0.948328 | ||||||||
\(865\) | 9785.23 | 0.384633 | ||||||||
\(866\) | −4344.62 | −0.170481 | ||||||||
\(867\) | 4094.29 | 0.160380 | ||||||||
\(868\) | −88532.8 | −3.46198 | ||||||||
\(869\) | 60743.7 | 2.37122 | ||||||||
\(870\) | 38241.4 | 1.49023 | ||||||||
\(871\) | −720.262 | −0.0280197 | ||||||||
\(872\) | −76288.4 | −2.96267 | ||||||||
\(873\) | −20.6294 | −0.000799771 0 | ||||||||
\(874\) | 1192.82 | 0.0461644 | ||||||||
\(875\) | 27868.5 | 1.07672 | ||||||||
\(876\) | 31665.6 | 1.22133 | ||||||||
\(877\) | 1593.02 | 0.0613368 | 0.0306684 | − | 0.999530i | \(-0.490236\pi\) | ||||
0.0306684 | + | 0.999530i | \(0.490236\pi\) | |||||||
\(878\) | 52245.1 | 2.00819 | ||||||||
\(879\) | −12737.2 | −0.488754 | ||||||||
\(880\) | −166786. | −6.38904 | ||||||||
\(881\) | 33123.4 | 1.26669 | 0.633347 | − | 0.773868i | \(-0.281681\pi\) | ||||
0.633347 | + | 0.773868i | \(0.281681\pi\) | |||||||
\(882\) | 337.536 | 0.0128860 | ||||||||
\(883\) | −5020.60 | −0.191344 | −0.0956720 | − | 0.995413i | \(-0.530500\pi\) | ||||
−0.0956720 | + | 0.995413i | \(0.530500\pi\) | |||||||
\(884\) | 19569.8 | 0.744575 | ||||||||
\(885\) | −16543.7 | −0.628373 | ||||||||
\(886\) | 92514.4 | 3.50799 | ||||||||
\(887\) | 16806.2 | 0.636185 | 0.318093 | − | 0.948060i | \(-0.396958\pi\) | ||||
0.318093 | + | 0.948060i | \(0.396958\pi\) | |||||||
\(888\) | −100831. | −3.81043 | ||||||||
\(889\) | −41205.8 | −1.55455 | ||||||||
\(890\) | −65681.6 | −2.47377 | ||||||||
\(891\) | 5144.50 | 0.193431 | ||||||||
\(892\) | 133007. | 4.99260 | ||||||||
\(893\) | 1141.15 | 0.0427626 | ||||||||
\(894\) | 11256.3 | 0.421104 | ||||||||
\(895\) | 23511.0 | 0.878087 | ||||||||
\(896\) | −147140. | −5.48616 | ||||||||
\(897\) | −445.926 | −0.0165987 | ||||||||
\(898\) | −5490.76 | −0.204041 | ||||||||
\(899\) | −51330.3 | −1.90430 | ||||||||
\(900\) | −7669.02 | −0.284038 | ||||||||
\(901\) | −8549.20 | −0.316110 | ||||||||
\(902\) | −157052. | −5.79742 | ||||||||
\(903\) | 9674.20 | 0.356520 | ||||||||
\(904\) | −39684.8 | −1.46006 | ||||||||
\(905\) | 2574.63 | 0.0945674 | ||||||||
\(906\) | −7861.24 | −0.288269 | ||||||||
\(907\) | 42624.3 | 1.56044 | 0.780219 | − | 0.625506i | \(-0.215107\pi\) | ||||
0.780219 | + | 0.625506i | \(0.215107\pi\) | |||||||
\(908\) | −126580. | −4.62632 | ||||||||
\(909\) | −5343.10 | −0.194961 | ||||||||
\(910\) | −10287.0 | −0.374738 | ||||||||
\(911\) | 17061.2 | 0.620486 | 0.310243 | − | 0.950657i | \(-0.399590\pi\) | ||||
0.310243 | + | 0.950657i | \(0.399590\pi\) | |||||||
\(912\) | −13023.7 | −0.472872 | ||||||||
\(913\) | 8242.60 | 0.298784 | ||||||||
\(914\) | −36728.3 | −1.32917 | ||||||||
\(915\) | −11219.1 | −0.405346 | ||||||||
\(916\) | 135780. | 4.89772 | ||||||||
\(917\) | −4095.44 | −0.147484 | ||||||||
\(918\) | 11906.3 | 0.428068 | ||||||||
\(919\) | −40517.4 | −1.45435 | −0.727175 | − | 0.686452i | \(-0.759167\pi\) | ||||
−0.727175 | + | 0.686452i | \(0.759167\pi\) | |||||||
\(920\) | 10805.6 | 0.387227 | ||||||||
\(921\) | −644.470 | −0.0230575 | ||||||||
\(922\) | 97364.0 | 3.47778 | ||||||||
\(923\) | 29.9189 | 0.00106695 | ||||||||
\(924\) | 80276.1 | 2.85811 | ||||||||
\(925\) | −14955.6 | −0.531609 | ||||||||
\(926\) | −9031.84 | −0.320524 | ||||||||
\(927\) | −6632.06 | −0.234979 | ||||||||
\(928\) | −217892. | −7.70761 | ||||||||
\(929\) | −45913.3 | −1.62149 | −0.810746 | − | 0.585398i | \(-0.800938\pi\) | ||||
−0.810746 | + | 0.585398i | \(0.800938\pi\) | |||||||
\(930\) | −32896.8 | −1.15992 | ||||||||
\(931\) | 104.449 | 0.00367688 | ||||||||
\(932\) | −101912. | −3.58179 | ||||||||
\(933\) | −1482.70 | −0.0520274 | ||||||||
\(934\) | −17424.1 | −0.610423 | ||||||||
\(935\) | 47183.0 | 1.65032 | ||||||||
\(936\) | 8064.09 | 0.281606 | ||||||||
\(937\) | 20590.8 | 0.717900 | 0.358950 | − | 0.933357i | \(-0.383135\pi\) | ||||
0.358950 | + | 0.933357i | \(0.383135\pi\) | |||||||
\(938\) | −6837.92 | −0.238023 | ||||||||
\(939\) | −797.770 | −0.0277255 | ||||||||
\(940\) | 15859.8 | 0.550307 | ||||||||
\(941\) | −403.036 | −0.0139624 | −0.00698120 | − | 0.999976i | \(-0.502222\pi\) | ||||
−0.00698120 | + | 0.999976i | \(0.502222\pi\) | |||||||
\(942\) | 25865.4 | 0.894630 | ||||||||
\(943\) | 6143.30 | 0.212146 | ||||||||
\(944\) | 164726. | 5.67943 | ||||||||
\(945\) | −4642.24 | −0.159801 | ||||||||
\(946\) | −62161.8 | −2.13642 | ||||||||
\(947\) | 8234.78 | 0.282571 | 0.141285 | − | 0.989969i | \(-0.454877\pi\) | ||||
0.141285 | + | 0.989969i | \(0.454877\pi\) | |||||||
\(948\) | 65922.4 | 2.25850 | ||||||||
\(949\) | −4938.72 | −0.168933 | ||||||||
\(950\) | −3199.46 | −0.109268 | ||||||||
\(951\) | −2034.34 | −0.0693669 | ||||||||
\(952\) | 121098. | 4.12271 | ||||||||
\(953\) | −33516.2 | −1.13924 | −0.569620 | − | 0.821908i | \(-0.692910\pi\) | ||||
−0.569620 | + | 0.821908i | \(0.692910\pi\) | |||||||
\(954\) | −5404.76 | −0.183423 | ||||||||
\(955\) | −20178.5 | −0.683729 | ||||||||
\(956\) | 158837. | 5.37360 | ||||||||
\(957\) | 46543.2 | 1.57213 | ||||||||
\(958\) | −2772.03 | −0.0934866 | ||||||||
\(959\) | 8664.32 | 0.291747 | ||||||||
\(960\) | −76618.9 | −2.57590 | ||||||||
\(961\) | 14365.5 | 0.482210 | ||||||||
\(962\) | 24126.9 | 0.808610 | ||||||||
\(963\) | 7640.51 | 0.255672 | ||||||||
\(964\) | 14104.0 | 0.471224 | ||||||||
\(965\) | 15028.3 | 0.501323 | ||||||||
\(966\) | −4233.47 | −0.141004 | ||||||||
\(967\) | −20602.4 | −0.685139 | −0.342570 | − | 0.939492i | \(-0.611297\pi\) | ||||
−0.342570 | + | 0.939492i | \(0.611297\pi\) | |||||||
\(968\) | −225275. | −7.47998 | ||||||||
\(969\) | 3684.35 | 0.122145 | ||||||||
\(970\) | −119.613 | −0.00395934 | ||||||||
\(971\) | 4984.98 | 0.164754 | 0.0823768 | − | 0.996601i | \(-0.473749\pi\) | ||||
0.0823768 | + | 0.996601i | \(0.473749\pi\) | |||||||
\(972\) | 5583.09 | 0.184236 | ||||||||
\(973\) | −18639.4 | −0.614132 | ||||||||
\(974\) | 45438.3 | 1.49480 | ||||||||
\(975\) | 1196.10 | 0.0392879 | ||||||||
\(976\) | 111709. | 3.66364 | ||||||||
\(977\) | −52420.8 | −1.71657 | −0.858286 | − | 0.513172i | \(-0.828470\pi\) | ||||
−0.858286 | + | 0.513172i | \(0.828470\pi\) | |||||||
\(978\) | 47932.4 | 1.56719 | ||||||||
\(979\) | −79940.4 | −2.60971 | ||||||||
\(980\) | 1451.64 | 0.0473174 | ||||||||
\(981\) | 8237.66 | 0.268102 | ||||||||
\(982\) | −38481.4 | −1.25050 | ||||||||
\(983\) | 36852.7 | 1.19575 | 0.597873 | − | 0.801591i | \(-0.296013\pi\) | ||||
0.597873 | + | 0.801591i | \(0.296013\pi\) | |||||||
\(984\) | −111095. | −3.59916 | ||||||||
\(985\) | −35723.0 | −1.15556 | ||||||||
\(986\) | 107718. | 3.47916 | ||||||||
\(987\) | −4050.08 | −0.130613 | ||||||||
\(988\) | 3828.44 | 0.123278 | ||||||||
\(989\) | 2431.54 | 0.0781784 | ||||||||
\(990\) | 29828.8 | 0.957598 | ||||||||
\(991\) | 11437.3 | 0.366618 | 0.183309 | − | 0.983055i | \(-0.441319\pi\) | ||||
0.183309 | + | 0.983055i | \(0.441319\pi\) | |||||||
\(992\) | 187440. | 5.99923 | ||||||||
\(993\) | 14566.9 | 0.465525 | ||||||||
\(994\) | 284.040 | 0.00906358 | ||||||||
\(995\) | 14981.8 | 0.477342 | ||||||||
\(996\) | 8945.32 | 0.284581 | ||||||||
\(997\) | 34016.8 | 1.08057 | 0.540283 | − | 0.841484i | \(-0.318317\pi\) | ||||
0.540283 | + | 0.841484i | \(0.318317\pi\) | |||||||
\(998\) | 61092.0 | 1.93771 | ||||||||
\(999\) | 10887.8 | 0.344819 |
(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 | 201.4.a.e.1.1 | ✓ | 11 | |
3.2 | odd | 2 | 603.4.a.g.1.11 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.a.e.1.1 | ✓ | 11 | 1.1 | even | 1 | trivial | |
603.4.a.g.1.11 | 11 | 3.2 | odd | 2 |