Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.58378\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58378 | 0.913504 | 0.456752 | − | 0.889594i | \(-0.349013\pi\) | ||||
0.456752 | + | 0.889594i | \(0.349013\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −1.32408 | −0.165510 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −7.75134 | −0.527412 | ||||||||
\(7\) | −26.6398 | −1.43842 | −0.719208 | − | 0.694795i | \(-0.755495\pi\) | ||||
−0.719208 | + | 0.694795i | \(0.755495\pi\) | |||||||
\(8\) | −24.0914 | −1.06470 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 12.9189 | 0.408531 | ||||||||
\(11\) | −8.03338 | −0.220196 | −0.110098 | − | 0.993921i | \(-0.535116\pi\) | ||||
−0.110098 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(12\) | 3.97225 | 0.0955574 | ||||||||
\(13\) | 49.9367 | 1.06538 | 0.532691 | − | 0.846310i | \(-0.321181\pi\) | ||||
0.532691 | + | 0.846310i | \(0.321181\pi\) | |||||||
\(14\) | −68.8314 | −1.31400 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −51.6541 | −0.807096 | ||||||||
\(17\) | 116.617 | 1.66375 | 0.831874 | − | 0.554964i | \(-0.187268\pi\) | ||||
0.831874 | + | 0.554964i | \(0.187268\pi\) | |||||||
\(18\) | 23.2540 | 0.304501 | ||||||||
\(19\) | 22.6617 | 0.273629 | 0.136815 | − | 0.990597i | \(-0.456314\pi\) | ||||
0.136815 | + | 0.990597i | \(0.456314\pi\) | |||||||
\(20\) | −6.62041 | −0.0740185 | ||||||||
\(21\) | 79.9195 | 0.830470 | ||||||||
\(22\) | −20.7565 | −0.201150 | ||||||||
\(23\) | 38.2616 | 0.346874 | 0.173437 | − | 0.984845i | \(-0.444513\pi\) | ||||
0.173437 | + | 0.984845i | \(0.444513\pi\) | |||||||
\(24\) | 72.2741 | 0.614704 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 129.025 | 0.973230 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 35.2733 | 0.238073 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | −38.7567 | −0.235866 | ||||||||
\(31\) | −8.82528 | −0.0511312 | −0.0255656 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255656 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(32\) | 59.2681 | 0.327413 | ||||||||
\(33\) | 24.1002 | 0.127130 | ||||||||
\(34\) | 301.312 | 1.51984 | ||||||||
\(35\) | −133.199 | −0.643279 | ||||||||
\(36\) | −11.9167 | −0.0551701 | ||||||||
\(37\) | 301.022 | 1.33750 | 0.668752 | − | 0.743486i | \(-0.266829\pi\) | ||||
0.668752 | + | 0.743486i | \(0.266829\pi\) | |||||||
\(38\) | 58.5529 | 0.249962 | ||||||||
\(39\) | −149.810 | −0.615098 | ||||||||
\(40\) | −120.457 | −0.476148 | ||||||||
\(41\) | 305.401 | 1.16331 | 0.581654 | − | 0.813436i | \(-0.302406\pi\) | ||||
0.581654 | + | 0.813436i | \(0.302406\pi\) | |||||||
\(42\) | 206.494 | 0.758637 | ||||||||
\(43\) | 275.872 | 0.978374 | 0.489187 | − | 0.872179i | \(-0.337294\pi\) | ||||
0.489187 | + | 0.872179i | \(0.337294\pi\) | |||||||
\(44\) | 10.6369 | 0.0364447 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 98.8596 | 0.316871 | ||||||||
\(47\) | −479.282 | −1.48746 | −0.743729 | − | 0.668481i | \(-0.766945\pi\) | ||||
−0.743729 | + | 0.668481i | \(0.766945\pi\) | |||||||
\(48\) | 154.962 | 0.465977 | ||||||||
\(49\) | 366.680 | 1.06904 | ||||||||
\(50\) | 64.5945 | 0.182701 | ||||||||
\(51\) | −349.850 | −0.960566 | ||||||||
\(52\) | −66.1204 | −0.176332 | ||||||||
\(53\) | −496.683 | −1.28726 | −0.643629 | − | 0.765338i | \(-0.722572\pi\) | ||||
−0.643629 | + | 0.765338i | \(0.722572\pi\) | |||||||
\(54\) | −69.7621 | −0.175804 | ||||||||
\(55\) | −40.1669 | −0.0984747 | ||||||||
\(56\) | 641.790 | 1.53148 | ||||||||
\(57\) | −67.9852 | −0.157980 | ||||||||
\(58\) | 74.9296 | 0.169633 | ||||||||
\(59\) | −563.505 | −1.24342 | −0.621712 | − | 0.783246i | \(-0.713563\pi\) | ||||
−0.621712 | + | 0.783246i | \(0.713563\pi\) | |||||||
\(60\) | 19.8612 | 0.0427346 | ||||||||
\(61\) | 485.346 | 1.01872 | 0.509362 | − | 0.860552i | \(-0.329881\pi\) | ||||
0.509362 | + | 0.860552i | \(0.329881\pi\) | |||||||
\(62\) | −22.8026 | −0.0467085 | ||||||||
\(63\) | −239.758 | −0.479472 | ||||||||
\(64\) | 566.369 | 1.10619 | ||||||||
\(65\) | 249.684 | 0.476453 | ||||||||
\(66\) | 62.2695 | 0.116134 | ||||||||
\(67\) | 217.176 | 0.396004 | 0.198002 | − | 0.980202i | \(-0.436555\pi\) | ||||
0.198002 | + | 0.980202i | \(0.436555\pi\) | |||||||
\(68\) | −154.410 | −0.275368 | ||||||||
\(69\) | −114.785 | −0.200268 | ||||||||
\(70\) | −344.157 | −0.587638 | ||||||||
\(71\) | 628.023 | 1.04975 | 0.524877 | − | 0.851178i | \(-0.324111\pi\) | ||||
0.524877 | + | 0.851178i | \(0.324111\pi\) | |||||||
\(72\) | −216.822 | −0.354899 | ||||||||
\(73\) | −682.502 | −1.09426 | −0.547128 | − | 0.837049i | \(-0.684279\pi\) | ||||
−0.547128 | + | 0.837049i | \(0.684279\pi\) | |||||||
\(74\) | 777.773 | 1.22182 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −30.0060 | −0.0452885 | ||||||||
\(77\) | 214.008 | 0.316733 | ||||||||
\(78\) | −387.076 | −0.561895 | ||||||||
\(79\) | 1159.26 | 1.65097 | 0.825484 | − | 0.564425i | \(-0.190902\pi\) | ||||
0.825484 | + | 0.564425i | \(0.190902\pi\) | |||||||
\(80\) | −258.271 | −0.360944 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 789.089 | 1.06269 | ||||||||
\(83\) | 668.594 | 0.884189 | 0.442095 | − | 0.896968i | \(-0.354236\pi\) | ||||
0.442095 | + | 0.896968i | \(0.354236\pi\) | |||||||
\(84\) | −105.820 | −0.137451 | ||||||||
\(85\) | 583.084 | 0.744051 | ||||||||
\(86\) | 712.792 | 0.893748 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | 193.535 | 0.234442 | ||||||||
\(89\) | 798.300 | 0.950782 | 0.475391 | − | 0.879775i | \(-0.342307\pi\) | ||||
0.475391 | + | 0.879775i | \(0.342307\pi\) | |||||||
\(90\) | 116.270 | 0.136177 | ||||||||
\(91\) | −1330.31 | −1.53246 | ||||||||
\(92\) | −50.6616 | −0.0574112 | ||||||||
\(93\) | 26.4758 | 0.0295206 | ||||||||
\(94\) | −1238.36 | −1.35880 | ||||||||
\(95\) | 113.309 | 0.122371 | ||||||||
\(96\) | −177.804 | −0.189032 | ||||||||
\(97\) | 867.116 | 0.907653 | 0.453826 | − | 0.891090i | \(-0.350059\pi\) | ||||
0.453826 | + | 0.891090i | \(0.350059\pi\) | |||||||
\(98\) | 947.421 | 0.976571 | ||||||||
\(99\) | −72.3005 | −0.0733987 | ||||||||
\(100\) | −33.1021 | −0.0331021 | ||||||||
\(101\) | 1270.57 | 1.25174 | 0.625872 | − | 0.779926i | \(-0.284743\pi\) | ||||
0.625872 | + | 0.779926i | \(0.284743\pi\) | |||||||
\(102\) | −903.936 | −0.877481 | ||||||||
\(103\) | −884.596 | −0.846232 | −0.423116 | − | 0.906076i | \(-0.639064\pi\) | ||||
−0.423116 | + | 0.906076i | \(0.639064\pi\) | |||||||
\(104\) | −1203.04 | −1.13431 | ||||||||
\(105\) | 399.597 | 0.371397 | ||||||||
\(106\) | −1283.32 | −1.17591 | ||||||||
\(107\) | 925.937 | 0.836577 | 0.418288 | − | 0.908314i | \(-0.362630\pi\) | ||||
0.418288 | + | 0.908314i | \(0.362630\pi\) | |||||||
\(108\) | 35.7502 | 0.0318525 | ||||||||
\(109\) | 73.4989 | 0.0645864 | 0.0322932 | − | 0.999478i | \(-0.489719\pi\) | ||||
0.0322932 | + | 0.999478i | \(0.489719\pi\) | |||||||
\(110\) | −103.782 | −0.0899570 | ||||||||
\(111\) | −903.065 | −0.772208 | ||||||||
\(112\) | 1376.06 | 1.16094 | ||||||||
\(113\) | −2068.68 | −1.72217 | −0.861086 | − | 0.508459i | \(-0.830215\pi\) | ||||
−0.861086 | + | 0.508459i | \(0.830215\pi\) | |||||||
\(114\) | −175.659 | −0.144315 | ||||||||
\(115\) | 191.308 | 0.155127 | ||||||||
\(116\) | −38.3984 | −0.0307345 | ||||||||
\(117\) | 449.431 | 0.355127 | ||||||||
\(118\) | −1455.97 | −1.13587 | ||||||||
\(119\) | −3106.65 | −2.39316 | ||||||||
\(120\) | 361.371 | 0.274904 | ||||||||
\(121\) | −1266.46 | −0.951514 | ||||||||
\(122\) | 1254.03 | 0.930609 | ||||||||
\(123\) | −916.204 | −0.671637 | ||||||||
\(124\) | 11.6854 | 0.00846274 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −619.483 | −0.437999 | ||||||||
\(127\) | −708.738 | −0.495199 | −0.247600 | − | 0.968862i | \(-0.579642\pi\) | ||||
−0.247600 | + | 0.968862i | \(0.579642\pi\) | |||||||
\(128\) | 989.228 | 0.683095 | ||||||||
\(129\) | −827.616 | −0.564864 | ||||||||
\(130\) | 645.127 | 0.435242 | ||||||||
\(131\) | −2033.80 | −1.35644 | −0.678220 | − | 0.734859i | \(-0.737248\pi\) | ||||
−0.678220 | + | 0.734859i | \(0.737248\pi\) | |||||||
\(132\) | −31.9106 | −0.0210414 | ||||||||
\(133\) | −603.705 | −0.393593 | ||||||||
\(134\) | 561.135 | 0.361752 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −2809.46 | −1.77139 | ||||||||
\(137\) | 2635.96 | 1.64383 | 0.821917 | − | 0.569608i | \(-0.192905\pi\) | ||||
0.821917 | + | 0.569608i | \(0.192905\pi\) | |||||||
\(138\) | −296.579 | −0.182945 | ||||||||
\(139\) | −1284.05 | −0.783539 | −0.391769 | − | 0.920063i | \(-0.628137\pi\) | ||||
−0.391769 | + | 0.920063i | \(0.628137\pi\) | |||||||
\(140\) | 176.367 | 0.106469 | ||||||||
\(141\) | 1437.85 | 0.858784 | ||||||||
\(142\) | 1622.67 | 0.958955 | ||||||||
\(143\) | −401.161 | −0.234593 | ||||||||
\(144\) | −464.887 | −0.269032 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | −1763.43 | −0.999608 | ||||||||
\(147\) | −1100.04 | −0.617210 | ||||||||
\(148\) | −398.578 | −0.221371 | ||||||||
\(149\) | 261.843 | 0.143966 | 0.0719832 | − | 0.997406i | \(-0.477067\pi\) | ||||
0.0719832 | + | 0.997406i | \(0.477067\pi\) | |||||||
\(150\) | −193.783 | −0.105482 | ||||||||
\(151\) | 2760.20 | 1.48756 | 0.743781 | − | 0.668424i | \(-0.233031\pi\) | ||||
0.743781 | + | 0.668424i | \(0.233031\pi\) | |||||||
\(152\) | −545.952 | −0.291333 | ||||||||
\(153\) | 1049.55 | 0.554583 | ||||||||
\(154\) | 552.949 | 0.289337 | ||||||||
\(155\) | −44.1264 | −0.0228666 | ||||||||
\(156\) | 198.361 | 0.101805 | ||||||||
\(157\) | 1922.00 | 0.977019 | 0.488509 | − | 0.872559i | \(-0.337541\pi\) | ||||
0.488509 | + | 0.872559i | \(0.337541\pi\) | |||||||
\(158\) | 2995.26 | 1.50817 | ||||||||
\(159\) | 1490.05 | 0.743198 | ||||||||
\(160\) | 296.340 | 0.146424 | ||||||||
\(161\) | −1019.28 | −0.498949 | ||||||||
\(162\) | 209.286 | 0.101500 | ||||||||
\(163\) | −2784.04 | −1.33781 | −0.668904 | − | 0.743349i | \(-0.733236\pi\) | ||||
−0.668904 | + | 0.743349i | \(0.733236\pi\) | |||||||
\(164\) | −404.376 | −0.192540 | ||||||||
\(165\) | 120.501 | 0.0568544 | ||||||||
\(166\) | 1727.50 | 0.807711 | ||||||||
\(167\) | −1669.58 | −0.773627 | −0.386814 | − | 0.922158i | \(-0.626424\pi\) | ||||
−0.386814 | + | 0.922158i | \(0.626424\pi\) | |||||||
\(168\) | −1925.37 | −0.884200 | ||||||||
\(169\) | 296.677 | 0.135037 | ||||||||
\(170\) | 1506.56 | 0.679694 | ||||||||
\(171\) | 203.956 | 0.0912098 | ||||||||
\(172\) | −365.277 | −0.161931 | ||||||||
\(173\) | −3488.62 | −1.53315 | −0.766574 | − | 0.642156i | \(-0.778040\pi\) | ||||
−0.766574 | + | 0.642156i | \(0.778040\pi\) | |||||||
\(174\) | −224.789 | −0.0979379 | ||||||||
\(175\) | −665.996 | −0.287683 | ||||||||
\(176\) | 414.958 | 0.177719 | ||||||||
\(177\) | 1690.51 | 0.717892 | ||||||||
\(178\) | 2062.63 | 0.868543 | ||||||||
\(179\) | 4016.48 | 1.67713 | 0.838564 | − | 0.544803i | \(-0.183396\pi\) | ||||
0.838564 | + | 0.544803i | \(0.183396\pi\) | |||||||
\(180\) | −59.5837 | −0.0246728 | ||||||||
\(181\) | −2275.81 | −0.934583 | −0.467291 | − | 0.884103i | \(-0.654770\pi\) | ||||
−0.467291 | + | 0.884103i | \(0.654770\pi\) | |||||||
\(182\) | −3437.22 | −1.39991 | ||||||||
\(183\) | −1456.04 | −0.588161 | ||||||||
\(184\) | −921.775 | −0.369316 | ||||||||
\(185\) | 1505.11 | 0.598150 | ||||||||
\(186\) | 68.4077 | 0.0269672 | ||||||||
\(187\) | −936.827 | −0.366351 | ||||||||
\(188\) | 634.610 | 0.246190 | ||||||||
\(189\) | 719.275 | 0.276823 | ||||||||
\(190\) | 292.765 | 0.111786 | ||||||||
\(191\) | 3204.35 | 1.21392 | 0.606961 | − | 0.794732i | \(-0.292389\pi\) | ||||
0.606961 | + | 0.794732i | \(0.292389\pi\) | |||||||
\(192\) | −1699.11 | −0.638659 | ||||||||
\(193\) | −71.0310 | −0.0264918 | −0.0132459 | − | 0.999912i | \(-0.504216\pi\) | ||||
−0.0132459 | + | 0.999912i | \(0.504216\pi\) | |||||||
\(194\) | 2240.44 | 0.829144 | ||||||||
\(195\) | −749.051 | −0.275080 | ||||||||
\(196\) | −485.515 | −0.176937 | ||||||||
\(197\) | 1260.52 | 0.455881 | 0.227941 | − | 0.973675i | \(-0.426801\pi\) | ||||
0.227941 | + | 0.973675i | \(0.426801\pi\) | |||||||
\(198\) | −186.808 | −0.0670500 | ||||||||
\(199\) | 2365.21 | 0.842539 | 0.421270 | − | 0.906935i | \(-0.361585\pi\) | ||||
0.421270 | + | 0.906935i | \(0.361585\pi\) | |||||||
\(200\) | −602.284 | −0.212940 | ||||||||
\(201\) | −651.529 | −0.228633 | ||||||||
\(202\) | 3282.87 | 1.14347 | ||||||||
\(203\) | −772.555 | −0.267107 | ||||||||
\(204\) | 463.231 | 0.158984 | ||||||||
\(205\) | 1527.01 | 0.520247 | ||||||||
\(206\) | −2285.60 | −0.773036 | ||||||||
\(207\) | 344.355 | 0.115625 | ||||||||
\(208\) | −2579.44 | −0.859865 | ||||||||
\(209\) | −182.050 | −0.0602521 | ||||||||
\(210\) | 1032.47 | 0.339273 | ||||||||
\(211\) | −1604.41 | −0.523468 | −0.261734 | − | 0.965140i | \(-0.584294\pi\) | ||||
−0.261734 | + | 0.965140i | \(0.584294\pi\) | |||||||
\(212\) | 657.649 | 0.213054 | ||||||||
\(213\) | −1884.07 | −0.606076 | ||||||||
\(214\) | 2392.42 | 0.764216 | ||||||||
\(215\) | 1379.36 | 0.437542 | ||||||||
\(216\) | 650.467 | 0.204901 | ||||||||
\(217\) | 235.104 | 0.0735479 | ||||||||
\(218\) | 189.905 | 0.0589999 | ||||||||
\(219\) | 2047.50 | 0.631770 | ||||||||
\(220\) | 53.1843 | 0.0162986 | ||||||||
\(221\) | 5823.46 | 1.77253 | ||||||||
\(222\) | −2333.32 | −0.705415 | ||||||||
\(223\) | −2789.26 | −0.837591 | −0.418795 | − | 0.908081i | \(-0.637548\pi\) | ||||
−0.418795 | + | 0.908081i | \(0.637548\pi\) | |||||||
\(224\) | −1578.89 | −0.470956 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −5345.02 | −1.57321 | ||||||||
\(227\) | 3091.67 | 0.903971 | 0.451985 | − | 0.892025i | \(-0.350716\pi\) | ||||
0.451985 | + | 0.892025i | \(0.350716\pi\) | |||||||
\(228\) | 90.0180 | 0.0261473 | ||||||||
\(229\) | −6479.99 | −1.86991 | −0.934955 | − | 0.354766i | \(-0.884561\pi\) | ||||
−0.934955 | + | 0.354766i | \(0.884561\pi\) | |||||||
\(230\) | 494.298 | 0.141709 | ||||||||
\(231\) | −642.024 | −0.182866 | ||||||||
\(232\) | −698.650 | −0.197710 | ||||||||
\(233\) | −3647.01 | −1.02542 | −0.512712 | − | 0.858561i | \(-0.671359\pi\) | ||||
−0.512712 | + | 0.858561i | \(0.671359\pi\) | |||||||
\(234\) | 1161.23 | 0.324410 | ||||||||
\(235\) | −2396.41 | −0.665211 | ||||||||
\(236\) | 746.127 | 0.205800 | ||||||||
\(237\) | −3477.77 | −0.953187 | ||||||||
\(238\) | −8026.90 | −2.18616 | ||||||||
\(239\) | 3863.00 | 1.04551 | 0.522754 | − | 0.852483i | \(-0.324905\pi\) | ||||
0.522754 | + | 0.852483i | \(0.324905\pi\) | |||||||
\(240\) | 774.812 | 0.208391 | ||||||||
\(241\) | 6207.76 | 1.65924 | 0.829620 | − | 0.558329i | \(-0.188557\pi\) | ||||
0.829620 | + | 0.558329i | \(0.188557\pi\) | |||||||
\(242\) | −3272.27 | −0.869212 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −642.638 | −0.168609 | ||||||||
\(245\) | 1833.40 | 0.478089 | ||||||||
\(246\) | −2367.27 | −0.613543 | ||||||||
\(247\) | 1131.65 | 0.291520 | ||||||||
\(248\) | 212.613 | 0.0544393 | ||||||||
\(249\) | −2005.78 | −0.510487 | ||||||||
\(250\) | 322.972 | 0.0817063 | ||||||||
\(251\) | 4942.68 | 1.24294 | 0.621472 | − | 0.783436i | \(-0.286535\pi\) | ||||
0.621472 | + | 0.783436i | \(0.286535\pi\) | |||||||
\(252\) | 317.460 | 0.0793575 | ||||||||
\(253\) | −307.370 | −0.0763803 | ||||||||
\(254\) | −1831.22 | −0.452367 | ||||||||
\(255\) | −1749.25 | −0.429578 | ||||||||
\(256\) | −1975.00 | −0.482179 | ||||||||
\(257\) | 3343.25 | 0.811465 | 0.405732 | − | 0.913992i | \(-0.367016\pi\) | ||||
0.405732 | + | 0.913992i | \(0.367016\pi\) | |||||||
\(258\) | −2138.38 | −0.516006 | ||||||||
\(259\) | −8019.16 | −1.92389 | ||||||||
\(260\) | −330.602 | −0.0788579 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | −5254.88 | −1.23911 | ||||||||
\(263\) | 1053.61 | 0.247027 | 0.123514 | − | 0.992343i | \(-0.460584\pi\) | ||||
0.123514 | + | 0.992343i | \(0.460584\pi\) | |||||||
\(264\) | −580.606 | −0.135355 | ||||||||
\(265\) | −2483.41 | −0.575679 | ||||||||
\(266\) | −1559.84 | −0.359549 | ||||||||
\(267\) | −2394.90 | −0.548934 | ||||||||
\(268\) | −287.559 | −0.0655428 | ||||||||
\(269\) | 2348.05 | 0.532205 | 0.266103 | − | 0.963945i | \(-0.414264\pi\) | ||||
0.266103 | + | 0.963945i | \(0.414264\pi\) | |||||||
\(270\) | −348.810 | −0.0786219 | ||||||||
\(271\) | 4230.65 | 0.948316 | 0.474158 | − | 0.880440i | \(-0.342753\pi\) | ||||
0.474158 | + | 0.880440i | \(0.342753\pi\) | |||||||
\(272\) | −6023.74 | −1.34280 | ||||||||
\(273\) | 3990.92 | 0.884767 | ||||||||
\(274\) | 6810.74 | 1.50165 | ||||||||
\(275\) | −200.835 | −0.0440392 | ||||||||
\(276\) | 151.985 | 0.0331464 | ||||||||
\(277\) | 2146.72 | 0.465647 | 0.232823 | − | 0.972519i | \(-0.425204\pi\) | ||||
0.232823 | + | 0.972519i | \(0.425204\pi\) | |||||||
\(278\) | −3317.71 | −0.715766 | ||||||||
\(279\) | −79.4275 | −0.0170437 | ||||||||
\(280\) | 3208.95 | 0.684898 | ||||||||
\(281\) | −1445.80 | −0.306937 | −0.153469 | − | 0.988154i | \(-0.549044\pi\) | ||||
−0.153469 | + | 0.988154i | \(0.549044\pi\) | |||||||
\(282\) | 3715.08 | 0.784503 | ||||||||
\(283\) | 3775.85 | 0.793113 | 0.396557 | − | 0.918010i | \(-0.370205\pi\) | ||||
0.396557 | + | 0.918010i | \(0.370205\pi\) | |||||||
\(284\) | −831.554 | −0.173745 | ||||||||
\(285\) | −339.926 | −0.0706508 | ||||||||
\(286\) | −1036.51 | −0.214301 | ||||||||
\(287\) | −8135.83 | −1.67332 | ||||||||
\(288\) | 533.413 | 0.109138 | ||||||||
\(289\) | 8686.48 | 1.76806 | ||||||||
\(290\) | 374.648 | 0.0758624 | ||||||||
\(291\) | −2601.35 | −0.524033 | ||||||||
\(292\) | 903.688 | 0.181111 | ||||||||
\(293\) | 6451.38 | 1.28633 | 0.643164 | − | 0.765729i | \(-0.277622\pi\) | ||||
0.643164 | + | 0.765729i | \(0.277622\pi\) | |||||||
\(294\) | −2842.26 | −0.563824 | ||||||||
\(295\) | −2817.52 | −0.556076 | ||||||||
\(296\) | −7252.02 | −1.42404 | ||||||||
\(297\) | 216.901 | 0.0423767 | ||||||||
\(298\) | 676.544 | 0.131514 | ||||||||
\(299\) | 1910.66 | 0.369553 | ||||||||
\(300\) | 99.3062 | 0.0191115 | ||||||||
\(301\) | −7349.18 | −1.40731 | ||||||||
\(302\) | 7131.74 | 1.35889 | ||||||||
\(303\) | −3811.70 | −0.722695 | ||||||||
\(304\) | −1170.57 | −0.220845 | ||||||||
\(305\) | 2426.73 | 0.455587 | ||||||||
\(306\) | 2711.81 | 0.506614 | ||||||||
\(307\) | 4197.07 | 0.780258 | 0.390129 | − | 0.920760i | \(-0.372430\pi\) | ||||
0.390129 | + | 0.920760i | \(0.372430\pi\) | |||||||
\(308\) | −283.364 | −0.0524227 | ||||||||
\(309\) | 2653.79 | 0.488572 | ||||||||
\(310\) | −114.013 | −0.0208887 | ||||||||
\(311\) | 6909.28 | 1.25977 | 0.629886 | − | 0.776687i | \(-0.283102\pi\) | ||||
0.629886 | + | 0.776687i | \(0.283102\pi\) | |||||||
\(312\) | 3609.13 | 0.654894 | ||||||||
\(313\) | 835.311 | 0.150845 | 0.0754226 | − | 0.997152i | \(-0.475969\pi\) | ||||
0.0754226 | + | 0.997152i | \(0.475969\pi\) | |||||||
\(314\) | 4966.01 | 0.892510 | ||||||||
\(315\) | −1198.79 | −0.214426 | ||||||||
\(316\) | −1534.95 | −0.273252 | ||||||||
\(317\) | −454.133 | −0.0804626 | −0.0402313 | − | 0.999190i | \(-0.512809\pi\) | ||||
−0.0402313 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(318\) | 3849.96 | 0.678915 | ||||||||
\(319\) | −232.968 | −0.0408894 | ||||||||
\(320\) | 2831.84 | 0.494703 | ||||||||
\(321\) | −2777.81 | −0.482998 | ||||||||
\(322\) | −2633.60 | −0.455792 | ||||||||
\(323\) | 2642.74 | 0.455250 | ||||||||
\(324\) | −107.251 | −0.0183900 | ||||||||
\(325\) | 1248.42 | 0.213076 | ||||||||
\(326\) | −7193.34 | −1.22209 | ||||||||
\(327\) | −220.497 | −0.0372890 | ||||||||
\(328\) | −7357.53 | −1.23857 | ||||||||
\(329\) | 12768.0 | 2.13958 | ||||||||
\(330\) | 311.347 | 0.0519367 | ||||||||
\(331\) | −6368.25 | −1.05749 | −0.528747 | − | 0.848779i | \(-0.677338\pi\) | ||||
−0.528747 | + | 0.848779i | \(0.677338\pi\) | |||||||
\(332\) | −885.274 | −0.146343 | ||||||||
\(333\) | 2709.19 | 0.445835 | ||||||||
\(334\) | −4313.82 | −0.706712 | ||||||||
\(335\) | 1085.88 | 0.177099 | ||||||||
\(336\) | −4128.17 | −0.670269 | ||||||||
\(337\) | −8096.70 | −1.30877 | −0.654384 | − | 0.756162i | \(-0.727072\pi\) | ||||
−0.654384 | + | 0.756162i | \(0.727072\pi\) | |||||||
\(338\) | 766.547 | 0.123357 | ||||||||
\(339\) | 6206.05 | 0.994297 | ||||||||
\(340\) | −772.051 | −0.123148 | ||||||||
\(341\) | 70.8968 | 0.0112589 | ||||||||
\(342\) | 526.976 | 0.0833205 | ||||||||
\(343\) | −630.841 | −0.0993067 | ||||||||
\(344\) | −6646.13 | −1.04167 | ||||||||
\(345\) | −573.924 | −0.0895625 | ||||||||
\(346\) | −9013.82 | −1.40054 | ||||||||
\(347\) | −2438.20 | −0.377202 | −0.188601 | − | 0.982054i | \(-0.560395\pi\) | ||||
−0.188601 | + | 0.982054i | \(0.560395\pi\) | |||||||
\(348\) | 115.195 | 0.0177446 | ||||||||
\(349\) | −777.284 | −0.119218 | −0.0596090 | − | 0.998222i | \(-0.518985\pi\) | ||||
−0.0596090 | + | 0.998222i | \(0.518985\pi\) | |||||||
\(350\) | −1720.79 | −0.262800 | ||||||||
\(351\) | −1348.29 | −0.205033 | ||||||||
\(352\) | −476.123 | −0.0720950 | ||||||||
\(353\) | −9649.81 | −1.45498 | −0.727489 | − | 0.686119i | \(-0.759313\pi\) | ||||
−0.727489 | + | 0.686119i | \(0.759313\pi\) | |||||||
\(354\) | 4367.92 | 0.655797 | ||||||||
\(355\) | 3140.11 | 0.469465 | ||||||||
\(356\) | −1057.02 | −0.157364 | ||||||||
\(357\) | 9319.95 | 1.38169 | ||||||||
\(358\) | 10377.7 | 1.53206 | ||||||||
\(359\) | 9657.56 | 1.41980 | 0.709898 | − | 0.704304i | \(-0.248741\pi\) | ||||
0.709898 | + | 0.704304i | \(0.248741\pi\) | |||||||
\(360\) | −1084.11 | −0.158716 | ||||||||
\(361\) | −6345.45 | −0.925127 | ||||||||
\(362\) | −5880.19 | −0.853745 | ||||||||
\(363\) | 3799.39 | 0.549357 | ||||||||
\(364\) | 1761.43 | 0.253638 | ||||||||
\(365\) | −3412.51 | −0.489367 | ||||||||
\(366\) | −3762.08 | −0.537287 | ||||||||
\(367\) | −9173.93 | −1.30484 | −0.652419 | − | 0.757859i | \(-0.726246\pi\) | ||||
−0.652419 | + | 0.757859i | \(0.726246\pi\) | |||||||
\(368\) | −1976.37 | −0.279961 | ||||||||
\(369\) | 2748.61 | 0.387770 | ||||||||
\(370\) | 3888.87 | 0.546412 | ||||||||
\(371\) | 13231.5 | 1.85161 | ||||||||
\(372\) | −35.0562 | −0.00488597 | ||||||||
\(373\) | 2899.69 | 0.402521 | 0.201261 | − | 0.979538i | \(-0.435496\pi\) | ||||
0.201261 | + | 0.979538i | \(0.435496\pi\) | |||||||
\(374\) | −2420.56 | −0.334663 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 11546.6 | 1.58369 | ||||||||
\(377\) | 1448.17 | 0.197836 | ||||||||
\(378\) | 1858.45 | 0.252879 | ||||||||
\(379\) | −5819.59 | −0.788739 | −0.394370 | − | 0.918952i | \(-0.629037\pi\) | ||||
−0.394370 | + | 0.918952i | \(0.629037\pi\) | |||||||
\(380\) | −150.030 | −0.0202536 | ||||||||
\(381\) | 2126.21 | 0.285903 | ||||||||
\(382\) | 8279.34 | 1.10892 | ||||||||
\(383\) | −5805.80 | −0.774576 | −0.387288 | − | 0.921959i | \(-0.626588\pi\) | ||||
−0.387288 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(384\) | −2967.68 | −0.394385 | ||||||||
\(385\) | 1070.04 | 0.141647 | ||||||||
\(386\) | −183.528 | −0.0242004 | ||||||||
\(387\) | 2482.85 | 0.326125 | ||||||||
\(388\) | −1148.13 | −0.150226 | ||||||||
\(389\) | 7690.82 | 1.00242 | 0.501208 | − | 0.865327i | \(-0.332889\pi\) | ||||
0.501208 | + | 0.865327i | \(0.332889\pi\) | |||||||
\(390\) | −1935.38 | −0.251287 | ||||||||
\(391\) | 4461.95 | 0.577111 | ||||||||
\(392\) | −8833.83 | −1.13820 | ||||||||
\(393\) | 6101.39 | 0.783141 | ||||||||
\(394\) | 3256.92 | 0.416449 | ||||||||
\(395\) | 5796.28 | 0.738336 | ||||||||
\(396\) | 95.7318 | 0.0121482 | ||||||||
\(397\) | −1638.24 | −0.207105 | −0.103553 | − | 0.994624i | \(-0.533021\pi\) | ||||
−0.103553 | + | 0.994624i | \(0.533021\pi\) | |||||||
\(398\) | 6111.18 | 0.769663 | ||||||||
\(399\) | 1811.11 | 0.227241 | ||||||||
\(400\) | −1291.35 | −0.161419 | ||||||||
\(401\) | 3780.89 | 0.470845 | 0.235422 | − | 0.971893i | \(-0.424353\pi\) | ||||
0.235422 | + | 0.971893i | \(0.424353\pi\) | |||||||
\(402\) | −1683.41 | −0.208857 | ||||||||
\(403\) | −440.705 | −0.0544742 | ||||||||
\(404\) | −1682.34 | −0.207177 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −1996.11 | −0.244003 | ||||||||
\(407\) | −2418.22 | −0.294513 | ||||||||
\(408\) | 8428.38 | 1.02271 | ||||||||
\(409\) | −330.980 | −0.0400145 | −0.0200073 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200073 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(410\) | 3945.45 | 0.475248 | ||||||||
\(411\) | −7907.88 | −0.949068 | ||||||||
\(412\) | 1171.28 | 0.140060 | ||||||||
\(413\) | 15011.7 | 1.78856 | ||||||||
\(414\) | 889.736 | 0.105624 | ||||||||
\(415\) | 3342.97 | 0.395422 | ||||||||
\(416\) | 2959.65 | 0.348820 | ||||||||
\(417\) | 3852.16 | 0.452376 | ||||||||
\(418\) | −470.378 | −0.0550405 | ||||||||
\(419\) | 9913.43 | 1.15585 | 0.577927 | − | 0.816089i | \(-0.303862\pi\) | ||||
0.577927 | + | 0.816089i | \(0.303862\pi\) | |||||||
\(420\) | −529.100 | −0.0614701 | ||||||||
\(421\) | 6286.56 | 0.727763 | 0.363881 | − | 0.931445i | \(-0.381451\pi\) | ||||
0.363881 | + | 0.931445i | \(0.381451\pi\) | |||||||
\(422\) | −4145.43 | −0.478190 | ||||||||
\(423\) | −4313.54 | −0.495819 | ||||||||
\(424\) | 11965.8 | 1.37054 | ||||||||
\(425\) | 2915.42 | 0.332750 | ||||||||
\(426\) | −4868.02 | −0.553653 | ||||||||
\(427\) | −12929.5 | −1.46535 | ||||||||
\(428\) | −1226.02 | −0.138462 | ||||||||
\(429\) | 1203.48 | 0.135442 | ||||||||
\(430\) | 3563.96 | 0.399696 | ||||||||
\(431\) | 5798.56 | 0.648044 | 0.324022 | − | 0.946050i | \(-0.394965\pi\) | ||||
0.324022 | + | 0.946050i | \(0.394965\pi\) | |||||||
\(432\) | 1394.66 | 0.155326 | ||||||||
\(433\) | 11476.3 | 1.27371 | 0.636856 | − | 0.770983i | \(-0.280235\pi\) | ||||
0.636856 | + | 0.770983i | \(0.280235\pi\) | |||||||
\(434\) | 607.457 | 0.0671863 | ||||||||
\(435\) | −435.000 | −0.0479463 | ||||||||
\(436\) | −97.3186 | −0.0106897 | ||||||||
\(437\) | 867.075 | 0.0949149 | ||||||||
\(438\) | 5290.30 | 0.577124 | ||||||||
\(439\) | 14429.5 | 1.56875 | 0.784377 | − | 0.620285i | \(-0.212983\pi\) | ||||
0.784377 | + | 0.620285i | \(0.212983\pi\) | |||||||
\(440\) | 967.676 | 0.104846 | ||||||||
\(441\) | 3300.12 | 0.356346 | ||||||||
\(442\) | 15046.5 | 1.61921 | ||||||||
\(443\) | −11892.0 | −1.27541 | −0.637703 | − | 0.770283i | \(-0.720115\pi\) | ||||
−0.637703 | + | 0.770283i | \(0.720115\pi\) | |||||||
\(444\) | 1195.73 | 0.127808 | ||||||||
\(445\) | 3991.50 | 0.425203 | ||||||||
\(446\) | −7206.84 | −0.765143 | ||||||||
\(447\) | −785.528 | −0.0831190 | ||||||||
\(448\) | −15088.0 | −1.59116 | ||||||||
\(449\) | −9881.53 | −1.03862 | −0.519308 | − | 0.854587i | \(-0.673810\pi\) | ||||
−0.519308 | + | 0.854587i | \(0.673810\pi\) | |||||||
\(450\) | 581.350 | 0.0609003 | ||||||||
\(451\) | −2453.40 | −0.256156 | ||||||||
\(452\) | 2739.11 | 0.285037 | ||||||||
\(453\) | −8280.59 | −0.858844 | ||||||||
\(454\) | 7988.20 | 0.825781 | ||||||||
\(455\) | −6651.53 | −0.685337 | ||||||||
\(456\) | 1637.86 | 0.168201 | ||||||||
\(457\) | 11641.2 | 1.19158 | 0.595792 | − | 0.803139i | \(-0.296838\pi\) | ||||
0.595792 | + | 0.803139i | \(0.296838\pi\) | |||||||
\(458\) | −16742.9 | −1.70817 | ||||||||
\(459\) | −3148.65 | −0.320189 | ||||||||
\(460\) | −253.308 | −0.0256751 | ||||||||
\(461\) | −8045.29 | −0.812812 | −0.406406 | − | 0.913693i | \(-0.633218\pi\) | ||||
−0.406406 | + | 0.913693i | \(0.633218\pi\) | |||||||
\(462\) | −1658.85 | −0.167049 | ||||||||
\(463\) | −4340.54 | −0.435684 | −0.217842 | − | 0.975984i | \(-0.569902\pi\) | ||||
−0.217842 | + | 0.975984i | \(0.569902\pi\) | |||||||
\(464\) | −1497.97 | −0.149874 | ||||||||
\(465\) | 132.379 | 0.0132020 | ||||||||
\(466\) | −9423.08 | −0.936729 | ||||||||
\(467\) | −3461.65 | −0.343011 | −0.171506 | − | 0.985183i | \(-0.554863\pi\) | ||||
−0.171506 | + | 0.985183i | \(0.554863\pi\) | |||||||
\(468\) | −595.083 | −0.0587772 | ||||||||
\(469\) | −5785.54 | −0.569619 | ||||||||
\(470\) | −6191.80 | −0.607673 | ||||||||
\(471\) | −5765.99 | −0.564082 | ||||||||
\(472\) | 13575.6 | 1.32387 | ||||||||
\(473\) | −2216.18 | −0.215434 | ||||||||
\(474\) | −8985.79 | −0.870740 | ||||||||
\(475\) | 566.543 | 0.0547259 | ||||||||
\(476\) | 4113.46 | 0.396093 | ||||||||
\(477\) | −4470.14 | −0.429086 | ||||||||
\(478\) | 9981.14 | 0.955076 | ||||||||
\(479\) | 6284.62 | 0.599481 | 0.299741 | − | 0.954021i | \(-0.403100\pi\) | ||||
0.299741 | + | 0.954021i | \(0.403100\pi\) | |||||||
\(480\) | −889.021 | −0.0845377 | ||||||||
\(481\) | 15032.0 | 1.42495 | ||||||||
\(482\) | 16039.5 | 1.51572 | ||||||||
\(483\) | 3057.85 | 0.288068 | ||||||||
\(484\) | 1676.90 | 0.157485 | ||||||||
\(485\) | 4335.58 | 0.405915 | ||||||||
\(486\) | −627.858 | −0.0586013 | ||||||||
\(487\) | −1809.63 | −0.168382 | −0.0841912 | − | 0.996450i | \(-0.526831\pi\) | ||||
−0.0841912 | + | 0.996450i | \(0.526831\pi\) | |||||||
\(488\) | −11692.7 | −1.08463 | ||||||||
\(489\) | 8352.12 | 0.772384 | ||||||||
\(490\) | 4737.11 | 0.436736 | ||||||||
\(491\) | 9550.28 | 0.877796 | 0.438898 | − | 0.898537i | \(-0.355369\pi\) | ||||
0.438898 | + | 0.898537i | \(0.355369\pi\) | |||||||
\(492\) | 1213.13 | 0.111163 | ||||||||
\(493\) | 3381.89 | 0.308950 | ||||||||
\(494\) | 2923.94 | 0.266304 | ||||||||
\(495\) | −361.502 | −0.0328249 | ||||||||
\(496\) | 455.862 | 0.0412678 | ||||||||
\(497\) | −16730.4 | −1.50998 | ||||||||
\(498\) | −5182.50 | −0.466332 | ||||||||
\(499\) | −13672.9 | −1.22662 | −0.613309 | − | 0.789843i | \(-0.710162\pi\) | ||||
−0.613309 | + | 0.789843i | \(0.710162\pi\) | |||||||
\(500\) | −165.510 | −0.0148037 | ||||||||
\(501\) | 5008.73 | 0.446654 | ||||||||
\(502\) | 12770.8 | 1.13544 | ||||||||
\(503\) | 13406.0 | 1.18836 | 0.594181 | − | 0.804332i | \(-0.297476\pi\) | ||||
0.594181 | + | 0.804332i | \(0.297476\pi\) | |||||||
\(504\) | 5776.11 | 0.510493 | ||||||||
\(505\) | 6352.84 | 0.559797 | ||||||||
\(506\) | −794.177 | −0.0697737 | ||||||||
\(507\) | −890.030 | −0.0779638 | ||||||||
\(508\) | 938.428 | 0.0819606 | ||||||||
\(509\) | −13537.0 | −1.17882 | −0.589409 | − | 0.807835i | \(-0.700639\pi\) | ||||
−0.589409 | + | 0.807835i | \(0.700639\pi\) | |||||||
\(510\) | −4519.68 | −0.392421 | ||||||||
\(511\) | 18181.7 | 1.57400 | ||||||||
\(512\) | −13016.8 | −1.12357 | ||||||||
\(513\) | −611.867 | −0.0526600 | ||||||||
\(514\) | 8638.23 | 0.741276 | ||||||||
\(515\) | −4422.98 | −0.378446 | ||||||||
\(516\) | 1095.83 | 0.0934909 | ||||||||
\(517\) | 3850.26 | 0.327532 | ||||||||
\(518\) | −20719.8 | −1.75748 | ||||||||
\(519\) | 10465.9 | 0.885163 | ||||||||
\(520\) | −6015.22 | −0.507279 | ||||||||
\(521\) | −6612.84 | −0.556073 | −0.278036 | − | 0.960571i | \(-0.589684\pi\) | ||||
−0.278036 | + | 0.960571i | \(0.589684\pi\) | |||||||
\(522\) | 674.366 | 0.0565445 | ||||||||
\(523\) | −11689.8 | −0.977363 | −0.488682 | − | 0.872462i | \(-0.662522\pi\) | ||||
−0.488682 | + | 0.872462i | \(0.662522\pi\) | |||||||
\(524\) | 2692.91 | 0.224505 | ||||||||
\(525\) | 1997.99 | 0.166094 | ||||||||
\(526\) | 2722.29 | 0.225660 | ||||||||
\(527\) | −1029.18 | −0.0850694 | ||||||||
\(528\) | −1244.87 | −0.102606 | ||||||||
\(529\) | −10703.0 | −0.879678 | ||||||||
\(530\) | −6416.59 | −0.525885 | ||||||||
\(531\) | −5071.54 | −0.414475 | ||||||||
\(532\) | 799.355 | 0.0651437 | ||||||||
\(533\) | 15250.7 | 1.23937 | ||||||||
\(534\) | −6187.89 | −0.501454 | ||||||||
\(535\) | 4629.68 | 0.374128 | ||||||||
\(536\) | −5232.07 | −0.421625 | ||||||||
\(537\) | −12049.4 | −0.968290 | ||||||||
\(538\) | 6066.85 | 0.486172 | ||||||||
\(539\) | −2945.68 | −0.235398 | ||||||||
\(540\) | 178.751 | 0.0142449 | ||||||||
\(541\) | −170.114 | −0.0135190 | −0.00675951 | − | 0.999977i | \(-0.502152\pi\) | ||||
−0.00675951 | + | 0.999977i | \(0.502152\pi\) | |||||||
\(542\) | 10931.1 | 0.866291 | ||||||||
\(543\) | 6827.42 | 0.539582 | ||||||||
\(544\) | 6911.65 | 0.544733 | ||||||||
\(545\) | 367.494 | 0.0288839 | ||||||||
\(546\) | 10311.7 | 0.808238 | ||||||||
\(547\) | −6453.08 | −0.504413 | −0.252206 | − | 0.967673i | \(-0.581156\pi\) | ||||
−0.252206 | + | 0.967673i | \(0.581156\pi\) | |||||||
\(548\) | −3490.23 | −0.272071 | ||||||||
\(549\) | 4368.11 | 0.339575 | ||||||||
\(550\) | −518.912 | −0.0402300 | ||||||||
\(551\) | 657.190 | 0.0508117 | ||||||||
\(552\) | 2765.33 | 0.213225 | ||||||||
\(553\) | −30882.4 | −2.37478 | ||||||||
\(554\) | 5546.66 | 0.425370 | ||||||||
\(555\) | −4515.32 | −0.345342 | ||||||||
\(556\) | 1700.19 | 0.129684 | ||||||||
\(557\) | −12800.7 | −0.973759 | −0.486879 | − | 0.873469i | \(-0.661865\pi\) | ||||
−0.486879 | + | 0.873469i | \(0.661865\pi\) | |||||||
\(558\) | −205.223 | −0.0155695 | ||||||||
\(559\) | 13776.1 | 1.04234 | ||||||||
\(560\) | 6880.29 | 0.519188 | ||||||||
\(561\) | 2810.48 | 0.211513 | ||||||||
\(562\) | −3735.63 | −0.280388 | ||||||||
\(563\) | 6454.48 | 0.483169 | 0.241584 | − | 0.970380i | \(-0.422333\pi\) | ||||
0.241584 | + | 0.970380i | \(0.422333\pi\) | |||||||
\(564\) | −1903.83 | −0.142138 | ||||||||
\(565\) | −10343.4 | −0.770179 | ||||||||
\(566\) | 9755.97 | 0.724512 | ||||||||
\(567\) | −2157.83 | −0.159824 | ||||||||
\(568\) | −15129.9 | −1.11767 | ||||||||
\(569\) | 2900.88 | 0.213728 | 0.106864 | − | 0.994274i | \(-0.465919\pi\) | ||||
0.106864 | + | 0.994274i | \(0.465919\pi\) | |||||||
\(570\) | −878.294 | −0.0645398 | ||||||||
\(571\) | −13437.3 | −0.984823 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(572\) | 531.170 | 0.0388275 | ||||||||
\(573\) | −9613.06 | −0.700858 | ||||||||
\(574\) | −21021.2 | −1.52859 | ||||||||
\(575\) | 956.541 | 0.0693748 | ||||||||
\(576\) | 5097.32 | 0.368730 | ||||||||
\(577\) | −5402.33 | −0.389778 | −0.194889 | − | 0.980825i | \(-0.562435\pi\) | ||||
−0.194889 | + | 0.980825i | \(0.562435\pi\) | |||||||
\(578\) | 22443.9 | 1.61513 | ||||||||
\(579\) | 213.093 | 0.0152951 | ||||||||
\(580\) | −191.992 | −0.0137449 | ||||||||
\(581\) | −17811.2 | −1.27183 | ||||||||
\(582\) | −6721.31 | −0.478707 | ||||||||
\(583\) | 3990.04 | 0.283449 | ||||||||
\(584\) | 16442.4 | 1.16505 | ||||||||
\(585\) | 2247.15 | 0.158818 | ||||||||
\(586\) | 16669.0 | 1.17507 | ||||||||
\(587\) | −17702.2 | −1.24471 | −0.622357 | − | 0.782733i | \(-0.713825\pi\) | ||||
−0.622357 | + | 0.782733i | \(0.713825\pi\) | |||||||
\(588\) | 1456.55 | 0.102155 | ||||||||
\(589\) | −199.996 | −0.0139910 | ||||||||
\(590\) | −7279.86 | −0.507978 | ||||||||
\(591\) | −3781.57 | −0.263203 | ||||||||
\(592\) | −15549.0 | −1.07949 | ||||||||
\(593\) | −13235.5 | −0.916558 | −0.458279 | − | 0.888808i | \(-0.651534\pi\) | ||||
−0.458279 | + | 0.888808i | \(0.651534\pi\) | |||||||
\(594\) | 560.425 | 0.0387113 | ||||||||
\(595\) | −15533.3 | −1.07025 | ||||||||
\(596\) | −346.701 | −0.0238279 | ||||||||
\(597\) | −7095.63 | −0.486440 | ||||||||
\(598\) | 4936.73 | 0.337588 | ||||||||
\(599\) | −22931.4 | −1.56419 | −0.782095 | − | 0.623159i | \(-0.785849\pi\) | ||||
−0.782095 | + | 0.623159i | \(0.785849\pi\) | |||||||
\(600\) | 1806.85 | 0.122941 | ||||||||
\(601\) | −11714.0 | −0.795051 | −0.397525 | − | 0.917591i | \(-0.630131\pi\) | ||||
−0.397525 | + | 0.917591i | \(0.630131\pi\) | |||||||
\(602\) | −18988.7 | −1.28558 | ||||||||
\(603\) | 1954.59 | 0.132001 | ||||||||
\(604\) | −3654.73 | −0.246207 | ||||||||
\(605\) | −6332.32 | −0.425530 | ||||||||
\(606\) | −9848.60 | −0.660185 | ||||||||
\(607\) | 4567.18 | 0.305397 | 0.152699 | − | 0.988273i | \(-0.451204\pi\) | ||||
0.152699 | + | 0.988273i | \(0.451204\pi\) | |||||||
\(608\) | 1343.12 | 0.0895898 | ||||||||
\(609\) | 2317.66 | 0.154214 | ||||||||
\(610\) | 6270.14 | 0.416181 | ||||||||
\(611\) | −23933.8 | −1.58471 | ||||||||
\(612\) | −1389.69 | −0.0917892 | ||||||||
\(613\) | −19389.4 | −1.27754 | −0.638768 | − | 0.769399i | \(-0.720556\pi\) | ||||
−0.638768 | + | 0.769399i | \(0.720556\pi\) | |||||||
\(614\) | 10844.3 | 0.712769 | ||||||||
\(615\) | −4581.02 | −0.300365 | ||||||||
\(616\) | −5155.75 | −0.337226 | ||||||||
\(617\) | −1918.52 | −0.125181 | −0.0625905 | − | 0.998039i | \(-0.519936\pi\) | ||||
−0.0625905 | + | 0.998039i | \(0.519936\pi\) | |||||||
\(618\) | 6856.81 | 0.446313 | ||||||||
\(619\) | 25281.1 | 1.64157 | 0.820785 | − | 0.571237i | \(-0.193536\pi\) | ||||
0.820785 | + | 0.571237i | \(0.193536\pi\) | |||||||
\(620\) | 58.4270 | 0.00378465 | ||||||||
\(621\) | −1033.06 | −0.0667559 | ||||||||
\(622\) | 17852.1 | 1.15081 | ||||||||
\(623\) | −21266.6 | −1.36762 | ||||||||
\(624\) | 7738.32 | 0.496443 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 2158.26 | 0.137798 | ||||||||
\(627\) | 546.151 | 0.0347866 | ||||||||
\(628\) | −2544.88 | −0.161707 | ||||||||
\(629\) | 35104.2 | 2.22527 | ||||||||
\(630\) | −3097.41 | −0.195879 | ||||||||
\(631\) | −21718.6 | −1.37022 | −0.685108 | − | 0.728442i | \(-0.740245\pi\) | ||||
−0.685108 | + | 0.728442i | \(0.740245\pi\) | |||||||
\(632\) | −27928.1 | −1.75778 | ||||||||
\(633\) | 4813.22 | 0.302225 | ||||||||
\(634\) | −1173.38 | −0.0735029 | ||||||||
\(635\) | −3543.69 | −0.221460 | ||||||||
\(636\) | −1972.95 | −0.123007 | ||||||||
\(637\) | 18310.8 | 1.13893 | ||||||||
\(638\) | −601.938 | −0.0373526 | ||||||||
\(639\) | 5652.20 | 0.349918 | ||||||||
\(640\) | 4946.14 | 0.305489 | ||||||||
\(641\) | 9371.00 | 0.577429 | 0.288715 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288715 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(642\) | −7177.25 | −0.441220 | ||||||||
\(643\) | −7538.94 | −0.462375 | −0.231187 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231187 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(644\) | 1349.62 | 0.0825812 | ||||||||
\(645\) | −4138.08 | −0.252615 | ||||||||
\(646\) | 6828.25 | 0.415873 | ||||||||
\(647\) | 15345.6 | 0.932455 | 0.466228 | − | 0.884665i | \(-0.345613\pi\) | ||||
0.466228 | + | 0.884665i | \(0.345613\pi\) | |||||||
\(648\) | −1951.40 | −0.118300 | ||||||||
\(649\) | 4526.85 | 0.273797 | ||||||||
\(650\) | 3225.64 | 0.194646 | ||||||||
\(651\) | −705.312 | −0.0424629 | ||||||||
\(652\) | 3686.30 | 0.221421 | ||||||||
\(653\) | −19648.0 | −1.17747 | −0.588735 | − | 0.808326i | \(-0.700374\pi\) | ||||
−0.588735 | + | 0.808326i | \(0.700374\pi\) | |||||||
\(654\) | −569.715 | −0.0340636 | ||||||||
\(655\) | −10169.0 | −0.606618 | ||||||||
\(656\) | −15775.2 | −0.938902 | ||||||||
\(657\) | −6142.51 | −0.364752 | ||||||||
\(658\) | 32989.7 | 1.95452 | ||||||||
\(659\) | −24207.8 | −1.43096 | −0.715481 | − | 0.698633i | \(-0.753792\pi\) | ||||
−0.715481 | + | 0.698633i | \(0.753792\pi\) | |||||||
\(660\) | −159.553 | −0.00940999 | ||||||||
\(661\) | 3864.20 | 0.227383 | 0.113691 | − | 0.993516i | \(-0.463733\pi\) | ||||
0.113691 | + | 0.993516i | \(0.463733\pi\) | |||||||
\(662\) | −16454.2 | −0.966026 | ||||||||
\(663\) | −17470.4 | −1.02337 | ||||||||
\(664\) | −16107.3 | −0.941395 | ||||||||
\(665\) | −3018.52 | −0.176020 | ||||||||
\(666\) | 6999.96 | 0.407272 | ||||||||
\(667\) | 1109.59 | 0.0644129 | ||||||||
\(668\) | 2210.66 | 0.128043 | ||||||||
\(669\) | 8367.78 | 0.483583 | ||||||||
\(670\) | 2805.68 | 0.161780 | ||||||||
\(671\) | −3898.97 | −0.224319 | ||||||||
\(672\) | 4736.67 | 0.271907 | ||||||||
\(673\) | 17574.4 | 1.00660 | 0.503300 | − | 0.864112i | \(-0.332119\pi\) | ||||
0.503300 | + | 0.864112i | \(0.332119\pi\) | |||||||
\(674\) | −20920.1 | −1.19557 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −392.825 | −0.0223501 | ||||||||
\(677\) | −26672.9 | −1.51421 | −0.757106 | − | 0.653292i | \(-0.773387\pi\) | ||||
−0.757106 | + | 0.653292i | \(0.773387\pi\) | |||||||
\(678\) | 16035.1 | 0.908294 | ||||||||
\(679\) | −23099.8 | −1.30558 | ||||||||
\(680\) | −14047.3 | −0.792190 | ||||||||
\(681\) | −9275.01 | −0.521908 | ||||||||
\(682\) | 183.182 | 0.0102850 | ||||||||
\(683\) | 2985.36 | 0.167250 | 0.0836249 | − | 0.996497i | \(-0.473350\pi\) | ||||
0.0836249 | + | 0.996497i | \(0.473350\pi\) | |||||||
\(684\) | −270.054 | −0.0150962 | ||||||||
\(685\) | 13179.8 | 0.735145 | ||||||||
\(686\) | −1629.95 | −0.0907171 | ||||||||
\(687\) | 19440.0 | 1.07959 | ||||||||
\(688\) | −14249.9 | −0.789642 | ||||||||
\(689\) | −24802.7 | −1.37142 | ||||||||
\(690\) | −1482.89 | −0.0818157 | ||||||||
\(691\) | 15067.6 | 0.829518 | 0.414759 | − | 0.909931i | \(-0.363866\pi\) | ||||
0.414759 | + | 0.909931i | \(0.363866\pi\) | |||||||
\(692\) | 4619.22 | 0.253752 | ||||||||
\(693\) | 1926.07 | 0.105578 | ||||||||
\(694\) | −6299.76 | −0.344576 | ||||||||
\(695\) | −6420.26 | −0.350409 | ||||||||
\(696\) | 2095.95 | 0.114148 | ||||||||
\(697\) | 35614.9 | 1.93545 | ||||||||
\(698\) | −2008.33 | −0.108906 | ||||||||
\(699\) | 10941.0 | 0.592029 | ||||||||
\(700\) | 881.833 | 0.0476145 | ||||||||
\(701\) | 32060.7 | 1.72741 | 0.863707 | − | 0.503994i | \(-0.168137\pi\) | ||||
0.863707 | + | 0.503994i | \(0.168137\pi\) | |||||||
\(702\) | −3483.69 | −0.187298 | ||||||||
\(703\) | 6821.67 | 0.365980 | ||||||||
\(704\) | −4549.86 | −0.243578 | ||||||||
\(705\) | 7189.24 | 0.384060 | ||||||||
\(706\) | −24933.0 | −1.32913 | ||||||||
\(707\) | −33847.7 | −1.80053 | ||||||||
\(708\) | −2238.38 | −0.118818 | ||||||||
\(709\) | −6089.76 | −0.322575 | −0.161288 | − | 0.986907i | \(-0.551565\pi\) | ||||
−0.161288 | + | 0.986907i | \(0.551565\pi\) | |||||||
\(710\) | 8113.36 | 0.428858 | ||||||||
\(711\) | 10433.3 | 0.550323 | ||||||||
\(712\) | −19232.1 | −1.01230 | ||||||||
\(713\) | −337.669 | −0.0177361 | ||||||||
\(714\) | 24080.7 | 1.26218 | ||||||||
\(715\) | −2005.80 | −0.104913 | ||||||||
\(716\) | −5318.15 | −0.277582 | ||||||||
\(717\) | −11589.0 | −0.603625 | ||||||||
\(718\) | 24953.0 | 1.29699 | ||||||||
\(719\) | 2735.79 | 0.141902 | 0.0709511 | − | 0.997480i | \(-0.477397\pi\) | ||||
0.0709511 | + | 0.997480i | \(0.477397\pi\) | |||||||
\(720\) | −2324.44 | −0.120315 | ||||||||
\(721\) | 23565.5 | 1.21723 | ||||||||
\(722\) | −16395.2 | −0.845107 | ||||||||
\(723\) | −18623.3 | −0.957963 | ||||||||
\(724\) | 3013.36 | 0.154683 | ||||||||
\(725\) | 725.000 | 0.0371391 | ||||||||
\(726\) | 9816.80 | 0.501840 | ||||||||
\(727\) | −23072.1 | −1.17702 | −0.588511 | − | 0.808489i | \(-0.700286\pi\) | ||||
−0.588511 | + | 0.808489i | \(0.700286\pi\) | |||||||
\(728\) | 32048.9 | 1.63161 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −8817.17 | −0.447038 | ||||||||
\(731\) | 32171.3 | 1.62777 | ||||||||
\(732\) | 1927.92 | 0.0973467 | ||||||||
\(733\) | 2341.92 | 0.118009 | 0.0590047 | − | 0.998258i | \(-0.481207\pi\) | ||||
0.0590047 | + | 0.998258i | \(0.481207\pi\) | |||||||
\(734\) | −23703.4 | −1.19197 | ||||||||
\(735\) | −5500.21 | −0.276025 | ||||||||
\(736\) | 2267.69 | 0.113571 | ||||||||
\(737\) | −1744.66 | −0.0871986 | ||||||||
\(738\) | 7101.80 | 0.354229 | ||||||||
\(739\) | 30372.4 | 1.51186 | 0.755932 | − | 0.654651i | \(-0.227184\pi\) | ||||
0.755932 | + | 0.654651i | \(0.227184\pi\) | |||||||
\(740\) | −1992.89 | −0.0990000 | ||||||||
\(741\) | −3394.96 | −0.168309 | ||||||||
\(742\) | 34187.4 | 1.69145 | ||||||||
\(743\) | 16456.7 | 0.812566 | 0.406283 | − | 0.913747i | \(-0.366825\pi\) | ||||
0.406283 | + | 0.913747i | \(0.366825\pi\) | |||||||
\(744\) | −637.839 | −0.0314305 | ||||||||
\(745\) | 1309.21 | 0.0643837 | ||||||||
\(746\) | 7492.17 | 0.367705 | ||||||||
\(747\) | 6017.35 | 0.294730 | ||||||||
\(748\) | 1240.44 | 0.0606349 | ||||||||
\(749\) | −24666.8 | −1.20334 | ||||||||
\(750\) | −968.917 | −0.0471731 | ||||||||
\(751\) | −28265.3 | −1.37339 | −0.686694 | − | 0.726947i | \(-0.740939\pi\) | ||||
−0.686694 | + | 0.726947i | \(0.740939\pi\) | |||||||
\(752\) | 24756.9 | 1.20052 | ||||||||
\(753\) | −14828.0 | −0.717615 | ||||||||
\(754\) | 3741.74 | 0.180724 | ||||||||
\(755\) | 13801.0 | 0.665258 | ||||||||
\(756\) | −952.380 | −0.0458171 | ||||||||
\(757\) | 30213.7 | 1.45064 | 0.725320 | − | 0.688412i | \(-0.241692\pi\) | ||||
0.725320 | + | 0.688412i | \(0.241692\pi\) | |||||||
\(758\) | −15036.5 | −0.720517 | ||||||||
\(759\) | 922.111 | 0.0440982 | ||||||||
\(760\) | −2729.76 | −0.130288 | ||||||||
\(761\) | 7521.30 | 0.358274 | 0.179137 | − | 0.983824i | \(-0.442669\pi\) | ||||
0.179137 | + | 0.983824i | \(0.442669\pi\) | |||||||
\(762\) | 5493.67 | 0.261174 | ||||||||
\(763\) | −1958.00 | −0.0929020 | ||||||||
\(764\) | −4242.83 | −0.200916 | ||||||||
\(765\) | 5247.76 | 0.248017 | ||||||||
\(766\) | −15000.9 | −0.707578 | ||||||||
\(767\) | −28139.6 | −1.32472 | ||||||||
\(768\) | 5925.01 | 0.278386 | ||||||||
\(769\) | −31256.5 | −1.46572 | −0.732859 | − | 0.680380i | \(-0.761815\pi\) | ||||
−0.732859 | + | 0.680380i | \(0.761815\pi\) | |||||||
\(770\) | 2764.75 | 0.129396 | ||||||||
\(771\) | −10029.8 | −0.468499 | ||||||||
\(772\) | 94.0510 | 0.00438467 | ||||||||
\(773\) | 6657.91 | 0.309791 | 0.154895 | − | 0.987931i | \(-0.450496\pi\) | ||||
0.154895 | + | 0.987931i | \(0.450496\pi\) | |||||||
\(774\) | 6415.13 | 0.297916 | ||||||||
\(775\) | −220.632 | −0.0102262 | ||||||||
\(776\) | −20890.0 | −0.966376 | ||||||||
\(777\) | 24057.5 | 1.11076 | ||||||||
\(778\) | 19871.4 | 0.915711 | ||||||||
\(779\) | 6920.92 | 0.318315 | ||||||||
\(780\) | 991.805 | 0.0455286 | ||||||||
\(781\) | −5045.15 | −0.231152 | ||||||||
\(782\) | 11528.7 | 0.527193 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | −18940.6 | −0.862817 | ||||||||
\(785\) | 9609.98 | 0.436936 | ||||||||
\(786\) | 15764.6 | 0.715402 | ||||||||
\(787\) | 18918.1 | 0.856872 | 0.428436 | − | 0.903572i | \(-0.359065\pi\) | ||||
0.428436 | + | 0.903572i | \(0.359065\pi\) | |||||||
\(788\) | −1669.04 | −0.0754531 | ||||||||
\(789\) | −3160.82 | −0.142621 | ||||||||
\(790\) | 14976.3 | 0.674473 | ||||||||
\(791\) | 55109.4 | 2.47720 | ||||||||
\(792\) | 1741.82 | 0.0781475 | ||||||||
\(793\) | 24236.6 | 1.08533 | ||||||||
\(794\) | −4232.84 | −0.189191 | ||||||||
\(795\) | 7450.24 | 0.332368 | ||||||||
\(796\) | −3131.73 | −0.139449 | ||||||||
\(797\) | −16329.2 | −0.725734 | −0.362867 | − | 0.931841i | \(-0.618202\pi\) | ||||
−0.362867 | + | 0.931841i | \(0.618202\pi\) | |||||||
\(798\) | 4679.52 | 0.207585 | ||||||||
\(799\) | −55892.4 | −2.47476 | ||||||||
\(800\) | 1481.70 | 0.0654826 | ||||||||
\(801\) | 7184.70 | 0.316927 | ||||||||
\(802\) | 9768.99 | 0.430119 | ||||||||
\(803\) | 5482.80 | 0.240951 | ||||||||
\(804\) | 862.678 | 0.0378412 | ||||||||
\(805\) | −5096.42 | −0.223137 | ||||||||
\(806\) | −1138.69 | −0.0497624 | ||||||||
\(807\) | −7044.16 | −0.307269 | ||||||||
\(808\) | −30609.7 | −1.33273 | ||||||||
\(809\) | −2755.55 | −0.119753 | −0.0598764 | − | 0.998206i | \(-0.519071\pi\) | ||||
−0.0598764 | + | 0.998206i | \(0.519071\pi\) | |||||||
\(810\) | 1046.43 | 0.0453924 | ||||||||
\(811\) | −8552.83 | −0.370321 | −0.185161 | − | 0.982708i | \(-0.559281\pi\) | ||||
−0.185161 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(812\) | 1022.93 | 0.0442090 | ||||||||
\(813\) | −12692.0 | −0.547511 | ||||||||
\(814\) | −6248.15 | −0.269039 | ||||||||
\(815\) | −13920.2 | −0.598286 | ||||||||
\(816\) | 18071.2 | 0.775269 | ||||||||
\(817\) | 6251.73 | 0.267712 | ||||||||
\(818\) | −855.181 | −0.0365534 | ||||||||
\(819\) | −11972.8 | −0.510820 | ||||||||
\(820\) | −2021.88 | −0.0861063 | ||||||||
\(821\) | 20670.4 | 0.878686 | 0.439343 | − | 0.898319i | \(-0.355211\pi\) | ||||
0.439343 | + | 0.898319i | \(0.355211\pi\) | |||||||
\(822\) | −20432.2 | −0.866977 | ||||||||
\(823\) | 474.045 | 0.0200780 | 0.0100390 | − | 0.999950i | \(-0.496804\pi\) | ||||
0.0100390 | + | 0.999950i | \(0.496804\pi\) | |||||||
\(824\) | 21311.1 | 0.900981 | ||||||||
\(825\) | 602.504 | 0.0254260 | ||||||||
\(826\) | 38786.8 | 1.63386 | ||||||||
\(827\) | 25547.5 | 1.07421 | 0.537106 | − | 0.843515i | \(-0.319517\pi\) | ||||
0.537106 | + | 0.843515i | \(0.319517\pi\) | |||||||
\(828\) | −455.954 | −0.0191371 | ||||||||
\(829\) | −36219.9 | −1.51745 | −0.758726 | − | 0.651410i | \(-0.774178\pi\) | ||||
−0.758726 | + | 0.651410i | \(0.774178\pi\) | |||||||
\(830\) | 8637.50 | 0.361219 | ||||||||
\(831\) | −6440.17 | −0.268841 | ||||||||
\(832\) | 28282.6 | 1.17851 | ||||||||
\(833\) | 42761.1 | 1.77861 | ||||||||
\(834\) | 9953.13 | 0.413248 | ||||||||
\(835\) | −8347.89 | −0.345977 | ||||||||
\(836\) | 241.050 | 0.00997235 | ||||||||
\(837\) | 238.283 | 0.00984020 | ||||||||
\(838\) | 25614.1 | 1.05588 | ||||||||
\(839\) | −17875.0 | −0.735535 | −0.367767 | − | 0.929918i | \(-0.619878\pi\) | ||||
−0.367767 | + | 0.929918i | \(0.619878\pi\) | |||||||
\(840\) | −9626.85 | −0.395426 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 16243.1 | 0.664814 | ||||||||
\(843\) | 4337.41 | 0.177210 | ||||||||
\(844\) | 2124.37 | 0.0866394 | ||||||||
\(845\) | 1483.38 | 0.0603905 | ||||||||
\(846\) | −11145.2 | −0.452933 | ||||||||
\(847\) | 33738.4 | 1.36867 | ||||||||
\(848\) | 25655.7 | 1.03894 | ||||||||
\(849\) | −11327.6 | −0.457904 | ||||||||
\(850\) | 7532.80 | 0.303968 | ||||||||
\(851\) | 11517.6 | 0.463945 | ||||||||
\(852\) | 2494.66 | 0.100312 | ||||||||
\(853\) | −1402.84 | −0.0563097 | −0.0281549 | − | 0.999604i | \(-0.508963\pi\) | ||||
−0.0281549 | + | 0.999604i | \(0.508963\pi\) | |||||||
\(854\) | −33407.1 | −1.33860 | ||||||||
\(855\) | 1019.78 | 0.0407903 | ||||||||
\(856\) | −22307.1 | −0.890702 | ||||||||
\(857\) | 32810.4 | 1.30780 | 0.653898 | − | 0.756582i | \(-0.273132\pi\) | ||||
0.653898 | + | 0.756582i | \(0.273132\pi\) | |||||||
\(858\) | 3109.53 | 0.123727 | ||||||||
\(859\) | −19007.6 | −0.754982 | −0.377491 | − | 0.926013i | \(-0.623213\pi\) | ||||
−0.377491 | + | 0.926013i | \(0.623213\pi\) | |||||||
\(860\) | −1826.39 | −0.0724177 | ||||||||
\(861\) | 24407.5 | 0.966092 | ||||||||
\(862\) | 14982.2 | 0.591991 | ||||||||
\(863\) | −6248.92 | −0.246484 | −0.123242 | − | 0.992377i | \(-0.539329\pi\) | ||||
−0.123242 | + | 0.992377i | \(0.539329\pi\) | |||||||
\(864\) | −1600.24 | −0.0630107 | ||||||||
\(865\) | −17443.1 | −0.685645 | ||||||||
\(866\) | 29652.3 | 1.16354 | ||||||||
\(867\) | −26059.4 | −1.02079 | ||||||||
\(868\) | −311.297 | −0.0121729 | ||||||||
\(869\) | −9312.75 | −0.363537 | ||||||||
\(870\) | −1123.94 | −0.0437992 | ||||||||
\(871\) | 10845.1 | 0.421896 | ||||||||
\(872\) | −1770.69 | −0.0687650 | ||||||||
\(873\) | 7804.05 | 0.302551 | ||||||||
\(874\) | 2240.33 | 0.0867051 | ||||||||
\(875\) | −3329.98 | −0.128656 | ||||||||
\(876\) | −2711.07 | −0.104564 | ||||||||
\(877\) | 18018.5 | 0.693777 | 0.346888 | − | 0.937906i | \(-0.387238\pi\) | ||||
0.346888 | + | 0.937906i | \(0.387238\pi\) | |||||||
\(878\) | 37282.7 | 1.43306 | ||||||||
\(879\) | −19354.2 | −0.742661 | ||||||||
\(880\) | 2074.79 | 0.0794785 | ||||||||
\(881\) | 28136.0 | 1.07597 | 0.537983 | − | 0.842956i | \(-0.319186\pi\) | ||||
0.537983 | + | 0.842956i | \(0.319186\pi\) | |||||||
\(882\) | 8526.79 | 0.325524 | ||||||||
\(883\) | −41964.1 | −1.59933 | −0.799663 | − | 0.600450i | \(-0.794988\pi\) | ||||
−0.799663 | + | 0.600450i | \(0.794988\pi\) | |||||||
\(884\) | −7710.74 | −0.293371 | ||||||||
\(885\) | 8452.57 | 0.321051 | ||||||||
\(886\) | −30726.2 | −1.16509 | ||||||||
\(887\) | 10526.5 | 0.398474 | 0.199237 | − | 0.979951i | \(-0.436154\pi\) | ||||
0.199237 | + | 0.979951i | \(0.436154\pi\) | |||||||
\(888\) | 21756.1 | 0.822169 | ||||||||
\(889\) | 18880.7 | 0.712302 | ||||||||
\(890\) | 10313.2 | 0.388424 | ||||||||
\(891\) | −650.704 | −0.0244662 | ||||||||
\(892\) | 3693.21 | 0.138630 | ||||||||
\(893\) | −10861.4 | −0.407012 | ||||||||
\(894\) | −2029.63 | −0.0759296 | ||||||||
\(895\) | 20082.4 | 0.750034 | ||||||||
\(896\) | −26352.8 | −0.982575 | ||||||||
\(897\) | −5731.98 | −0.213362 | ||||||||
\(898\) | −25531.7 | −0.948780 | ||||||||
\(899\) | −255.933 | −0.00949482 | ||||||||
\(900\) | −297.919 | −0.0110340 | ||||||||
\(901\) | −57921.6 | −2.14167 | ||||||||
\(902\) | −6339.06 | −0.233999 | ||||||||
\(903\) | 22047.5 | 0.812510 | ||||||||
\(904\) | 49837.5 | 1.83359 | ||||||||
\(905\) | −11379.0 | −0.417958 | ||||||||
\(906\) | −21395.2 | −0.784557 | ||||||||
\(907\) | −41574.7 | −1.52201 | −0.761006 | − | 0.648744i | \(-0.775294\pi\) | ||||
−0.761006 | + | 0.648744i | \(0.775294\pi\) | |||||||
\(908\) | −4093.63 | −0.149617 | ||||||||
\(909\) | 11435.1 | 0.417248 | ||||||||
\(910\) | −17186.1 | −0.626058 | ||||||||
\(911\) | −978.851 | −0.0355991 | −0.0177996 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177996 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(912\) | 3511.72 | 0.127505 | ||||||||
\(913\) | −5371.07 | −0.194695 | ||||||||
\(914\) | 30078.4 | 1.08852 | ||||||||
\(915\) | −7280.19 | −0.263034 | ||||||||
\(916\) | 8580.04 | 0.309490 | ||||||||
\(917\) | 54180.0 | 1.95112 | ||||||||
\(918\) | −8135.43 | −0.292494 | ||||||||
\(919\) | −2296.62 | −0.0824358 | −0.0412179 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412179 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(920\) | −4608.88 | −0.165163 | ||||||||
\(921\) | −12591.2 | −0.450482 | ||||||||
\(922\) | −20787.2 | −0.742507 | ||||||||
\(923\) | 31361.4 | 1.11839 | ||||||||
\(924\) | 850.093 | 0.0302662 | ||||||||
\(925\) | 7525.54 | 0.267501 | ||||||||
\(926\) | −11215.0 | −0.398000 | ||||||||
\(927\) | −7961.37 | −0.282077 | ||||||||
\(928\) | 1718.77 | 0.0607991 | ||||||||
\(929\) | 29033.8 | 1.02537 | 0.512684 | − | 0.858578i | \(-0.328651\pi\) | ||||
0.512684 | + | 0.858578i | \(0.328651\pi\) | |||||||
\(930\) | 342.039 | 0.0120601 | ||||||||
\(931\) | 8309.61 | 0.292520 | ||||||||
\(932\) | 4828.95 | 0.169718 | ||||||||
\(933\) | −20727.8 | −0.727330 | ||||||||
\(934\) | −8944.15 | −0.313342 | ||||||||
\(935\) | −4684.14 | −0.163837 | ||||||||
\(936\) | −10827.4 | −0.378103 | ||||||||
\(937\) | 22945.7 | 0.800005 | 0.400002 | − | 0.916514i | \(-0.369009\pi\) | ||||
0.400002 | + | 0.916514i | \(0.369009\pi\) | |||||||
\(938\) | −14948.5 | −0.520349 | ||||||||
\(939\) | −2505.93 | −0.0870906 | ||||||||
\(940\) | 3173.05 | 0.110099 | ||||||||
\(941\) | 31712.3 | 1.09861 | 0.549304 | − | 0.835622i | \(-0.314893\pi\) | ||||
0.549304 | + | 0.835622i | \(0.314893\pi\) | |||||||
\(942\) | −14898.0 | −0.515291 | ||||||||
\(943\) | 11685.1 | 0.403521 | ||||||||
\(944\) | 29107.3 | 1.00356 | ||||||||
\(945\) | 3596.38 | 0.123799 | ||||||||
\(946\) | −5726.13 | −0.196800 | ||||||||
\(947\) | −7050.99 | −0.241950 | −0.120975 | − | 0.992656i | \(-0.538602\pi\) | ||||
−0.120975 | + | 0.992656i | \(0.538602\pi\) | |||||||
\(948\) | 4604.85 | 0.157762 | ||||||||
\(949\) | −34081.9 | −1.16580 | ||||||||
\(950\) | 1463.82 | 0.0499923 | ||||||||
\(951\) | 1362.40 | 0.0464551 | ||||||||
\(952\) | 74843.5 | 2.54800 | ||||||||
\(953\) | −12178.0 | −0.413938 | −0.206969 | − | 0.978348i | \(-0.566360\pi\) | ||||
−0.206969 | + | 0.978348i | \(0.566360\pi\) | |||||||
\(954\) | −11549.9 | −0.391972 | ||||||||
\(955\) | 16021.8 | 0.542882 | ||||||||
\(956\) | −5114.93 | −0.173043 | ||||||||
\(957\) | 698.904 | 0.0236075 | ||||||||
\(958\) | 16238.1 | 0.547628 | ||||||||
\(959\) | −70221.5 | −2.36452 | ||||||||
\(960\) | −8495.53 | −0.285617 | ||||||||
\(961\) | −29713.1 | −0.997386 | ||||||||
\(962\) | 38839.5 | 1.30170 | ||||||||
\(963\) | 8333.43 | 0.278859 | ||||||||
\(964\) | −8219.58 | −0.274621 | ||||||||
\(965\) | −355.155 | −0.0118475 | ||||||||
\(966\) | 7900.81 | 0.263151 | ||||||||
\(967\) | −13762.2 | −0.457665 | −0.228833 | − | 0.973466i | \(-0.573491\pi\) | ||||
−0.228833 | + | 0.973466i | \(0.573491\pi\) | |||||||
\(968\) | 30510.9 | 1.01308 | ||||||||
\(969\) | −7928.22 | −0.262839 | ||||||||
\(970\) | 11202.2 | 0.370805 | ||||||||
\(971\) | −33646.0 | −1.11200 | −0.555999 | − | 0.831183i | \(-0.687664\pi\) | ||||
−0.555999 | + | 0.831183i | \(0.687664\pi\) | |||||||
\(972\) | 321.752 | 0.0106175 | ||||||||
\(973\) | 34206.9 | 1.12705 | ||||||||
\(974\) | −4675.69 | −0.153818 | ||||||||
\(975\) | −3745.25 | −0.123020 | ||||||||
\(976\) | −25070.1 | −0.822208 | ||||||||
\(977\) | −42129.5 | −1.37957 | −0.689786 | − | 0.724013i | \(-0.742296\pi\) | ||||
−0.689786 | + | 0.724013i | \(0.742296\pi\) | |||||||
\(978\) | 21580.0 | 0.705576 | ||||||||
\(979\) | −6413.05 | −0.209358 | ||||||||
\(980\) | −2427.58 | −0.0791286 | ||||||||
\(981\) | 661.490 | 0.0215288 | ||||||||
\(982\) | 24675.8 | 0.801870 | ||||||||
\(983\) | −39740.6 | −1.28945 | −0.644724 | − | 0.764415i | \(-0.723028\pi\) | ||||
−0.644724 | + | 0.764415i | \(0.723028\pi\) | |||||||
\(984\) | 22072.6 | 0.715090 | ||||||||
\(985\) | 6302.62 | 0.203876 | ||||||||
\(986\) | 8738.05 | 0.282227 | ||||||||
\(987\) | −38304.0 | −1.23529 | ||||||||
\(988\) | −1498.40 | −0.0482495 | ||||||||
\(989\) | 10555.3 | 0.339372 | ||||||||
\(990\) | −934.042 | −0.0299857 | ||||||||
\(991\) | 34300.8 | 1.09950 | 0.549748 | − | 0.835330i | \(-0.314724\pi\) | ||||
0.549748 | + | 0.835330i | \(0.314724\pi\) | |||||||
\(992\) | −523.057 | −0.0167410 | ||||||||
\(993\) | 19104.8 | 0.610545 | ||||||||
\(994\) | −43227.7 | −1.37938 | ||||||||
\(995\) | 11826.1 | 0.376795 | ||||||||
\(996\) | 2655.82 | 0.0844909 | ||||||||
\(997\) | −36545.8 | −1.16090 | −0.580449 | − | 0.814296i | \(-0.697123\pi\) | ||||
−0.580449 | + | 0.814296i | \(0.697123\pi\) | |||||||
\(998\) | −35327.7 | −1.12052 | ||||||||
\(999\) | −8127.58 | −0.257403 |
(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 | 435.4.a.i.1.6 | ✓ | 7 | |
3.2 | odd | 2 | 1305.4.a.n.1.2 | 7 | |||
5.4 | even | 2 | 2175.4.a.n.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.i.1.6 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.4.a.n.1.2 | 7 | 3.2 | odd | 2 | |||
2175.4.a.n.1.2 | 7 | 5.4 | even | 2 |