Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2401,4,Mod(1,2401)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2401.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2401.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: | \(141.663585924\) |
Analytic rank: | \(0\) |
Dimension: | \(39\) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 2401.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.904464 | −0.319776 | −0.159888 | − | 0.987135i | \(-0.551113\pi\) | ||||
−0.159888 | + | 0.987135i | \(0.551113\pi\) | |||||||
\(3\) | 9.08614 | 1.74863 | 0.874314 | − | 0.485361i | \(-0.161312\pi\) | ||||
0.874314 | + | 0.485361i | \(0.161312\pi\) | |||||||
\(4\) | −7.18194 | −0.897743 | ||||||||
\(5\) | −3.14137 | −0.280972 | −0.140486 | − | 0.990083i | \(-0.544867\pi\) | ||||
−0.140486 | + | 0.990083i | \(0.544867\pi\) | |||||||
\(6\) | −8.21809 | −0.559170 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 13.7315 | 0.606853 | ||||||||
\(9\) | 55.5579 | 2.05770 | ||||||||
\(10\) | 2.84125 | 0.0898483 | ||||||||
\(11\) | 53.3996 | 1.46369 | 0.731845 | − | 0.681471i | \(-0.238659\pi\) | ||||
0.731845 | + | 0.681471i | \(0.238659\pi\) | |||||||
\(12\) | −65.2561 | −1.56982 | ||||||||
\(13\) | −57.9905 | −1.23721 | −0.618603 | − | 0.785704i | \(-0.712301\pi\) | ||||
−0.618603 | + | 0.785704i | \(0.712301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −28.5429 | −0.491316 | ||||||||
\(16\) | 45.0359 | 0.703686 | ||||||||
\(17\) | 76.7741 | 1.09532 | 0.547660 | − | 0.836701i | \(-0.315519\pi\) | ||||
0.547660 | + | 0.836701i | \(0.315519\pi\) | |||||||
\(18\) | −50.2501 | −0.658004 | ||||||||
\(19\) | 20.7785 | 0.250890 | 0.125445 | − | 0.992101i | \(-0.459964\pi\) | ||||
0.125445 | + | 0.992101i | \(0.459964\pi\) | |||||||
\(20\) | 22.5611 | 0.252241 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −48.2981 | −0.468054 | ||||||||
\(23\) | 66.2950 | 0.601020 | 0.300510 | − | 0.953779i | \(-0.402843\pi\) | ||||
0.300510 | + | 0.953779i | \(0.402843\pi\) | |||||||
\(24\) | 124.767 | 1.06116 | ||||||||
\(25\) | −115.132 | −0.921055 | ||||||||
\(26\) | 52.4504 | 0.395629 | ||||||||
\(27\) | 259.481 | 1.84952 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.2983 | 0.174799 | 0.0873996 | − | 0.996173i | \(-0.472144\pi\) | ||||
0.0873996 | + | 0.996173i | \(0.472144\pi\) | |||||||
\(30\) | 25.8160 | 0.157111 | ||||||||
\(31\) | 294.724 | 1.70755 | 0.853774 | − | 0.520643i | \(-0.174308\pi\) | ||||
0.853774 | + | 0.520643i | \(0.174308\pi\) | |||||||
\(32\) | −150.586 | −0.831875 | ||||||||
\(33\) | 485.196 | 2.55945 | ||||||||
\(34\) | −69.4394 | −0.350258 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −399.014 | −1.84729 | ||||||||
\(37\) | 33.3900 | 0.148359 | 0.0741795 | − | 0.997245i | \(-0.476366\pi\) | ||||
0.0741795 | + | 0.997245i | \(0.476366\pi\) | |||||||
\(38\) | −18.7934 | −0.0802288 | ||||||||
\(39\) | −526.910 | −2.16341 | ||||||||
\(40\) | −43.1357 | −0.170509 | ||||||||
\(41\) | −92.5468 | −0.352521 | −0.176261 | − | 0.984344i | \(-0.556400\pi\) | ||||
−0.176261 | + | 0.984344i | \(0.556400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −321.813 | −1.14130 | −0.570651 | − | 0.821193i | \(-0.693309\pi\) | ||||
−0.570651 | + | 0.821193i | \(0.693309\pi\) | |||||||
\(44\) | −383.513 | −1.31402 | ||||||||
\(45\) | −174.528 | −0.578157 | ||||||||
\(46\) | −59.9615 | −0.192192 | ||||||||
\(47\) | −393.190 | −1.22027 | −0.610134 | − | 0.792298i | \(-0.708884\pi\) | ||||
−0.610134 | + | 0.792298i | \(0.708884\pi\) | |||||||
\(48\) | 409.202 | 1.23048 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 104.133 | 0.294532 | ||||||||
\(51\) | 697.580 | 1.91531 | ||||||||
\(52\) | 416.485 | 1.11069 | ||||||||
\(53\) | 514.909 | 1.33449 | 0.667247 | − | 0.744836i | \(-0.267472\pi\) | ||||
0.667247 | + | 0.744836i | \(0.267472\pi\) | |||||||
\(54\) | −234.691 | −0.591434 | ||||||||
\(55\) | −167.748 | −0.411256 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 188.796 | 0.438714 | ||||||||
\(58\) | −24.6904 | −0.0558966 | ||||||||
\(59\) | 113.337 | 0.250088 | 0.125044 | − | 0.992151i | \(-0.460093\pi\) | ||||
0.125044 | + | 0.992151i | \(0.460093\pi\) | |||||||
\(60\) | 204.993 | 0.441076 | ||||||||
\(61\) | 258.048 | 0.541634 | 0.270817 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270817 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(62\) | −266.567 | −0.546034 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −224.088 | −0.437672 | ||||||||
\(65\) | 182.169 | 0.347621 | ||||||||
\(66\) | −438.843 | −0.818452 | ||||||||
\(67\) | 49.2473 | 0.0897988 | 0.0448994 | − | 0.998992i | \(-0.485703\pi\) | ||||
0.0448994 | + | 0.998992i | \(0.485703\pi\) | |||||||
\(68\) | −551.387 | −0.983316 | ||||||||
\(69\) | 602.366 | 1.05096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 461.374 | 0.771198 | 0.385599 | − | 0.922666i | \(-0.373995\pi\) | ||||
0.385599 | + | 0.922666i | \(0.373995\pi\) | |||||||
\(72\) | 762.894 | 1.24872 | ||||||||
\(73\) | −428.267 | −0.686642 | −0.343321 | − | 0.939218i | \(-0.611552\pi\) | ||||
−0.343321 | + | 0.939218i | \(0.611552\pi\) | |||||||
\(74\) | −30.2001 | −0.0474417 | ||||||||
\(75\) | −1046.10 | −1.61058 | ||||||||
\(76\) | −149.230 | −0.225235 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 476.571 | 0.691808 | ||||||||
\(79\) | 93.0732 | 0.132551 | 0.0662756 | − | 0.997801i | \(-0.478888\pi\) | ||||
0.0662756 | + | 0.997801i | \(0.478888\pi\) | |||||||
\(80\) | −141.474 | −0.197716 | ||||||||
\(81\) | 857.615 | 1.17643 | ||||||||
\(82\) | 83.7053 | 0.112728 | ||||||||
\(83\) | 1154.75 | 1.52711 | 0.763556 | − | 0.645741i | \(-0.223451\pi\) | ||||
0.763556 | + | 0.645741i | \(0.223451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −241.175 | −0.307755 | ||||||||
\(86\) | 291.068 | 0.364962 | ||||||||
\(87\) | 248.036 | 0.305659 | ||||||||
\(88\) | 733.258 | 0.888245 | ||||||||
\(89\) | −581.259 | −0.692285 | −0.346142 | − | 0.938182i | \(-0.612509\pi\) | ||||
−0.346142 | + | 0.938182i | \(0.612509\pi\) | |||||||
\(90\) | 157.854 | 0.184881 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −476.127 | −0.539562 | ||||||||
\(93\) | 2677.90 | 2.98587 | ||||||||
\(94\) | 355.626 | 0.390213 | ||||||||
\(95\) | −65.2729 | −0.0704932 | ||||||||
\(96\) | −1368.24 | −1.45464 | ||||||||
\(97\) | 348.070 | 0.364341 | 0.182171 | − | 0.983267i | \(-0.441688\pi\) | ||||
0.182171 | + | 0.983267i | \(0.441688\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2966.77 | 3.01183 | ||||||||
\(100\) | 826.870 | 0.826870 | ||||||||
\(101\) | −693.964 | −0.683683 | −0.341842 | − | 0.939758i | \(-0.611051\pi\) | ||||
−0.341842 | + | 0.939758i | \(0.611051\pi\) | |||||||
\(102\) | −630.936 | −0.612470 | ||||||||
\(103\) | 1967.75 | 1.88241 | 0.941206 | − | 0.337833i | \(-0.109694\pi\) | ||||
0.941206 | + | 0.337833i | \(0.109694\pi\) | |||||||
\(104\) | −796.298 | −0.750803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −465.717 | −0.426740 | ||||||||
\(107\) | −663.690 | −0.599638 | −0.299819 | − | 0.953996i | \(-0.596926\pi\) | ||||
−0.299819 | + | 0.953996i | \(0.596926\pi\) | |||||||
\(108\) | −1863.58 | −1.66040 | ||||||||
\(109\) | −1310.25 | −1.15136 | −0.575682 | − | 0.817673i | \(-0.695263\pi\) | ||||
−0.575682 | + | 0.817673i | \(0.695263\pi\) | |||||||
\(110\) | 151.722 | 0.131510 | ||||||||
\(111\) | 303.386 | 0.259425 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2163.06 | −1.80074 | −0.900369 | − | 0.435128i | \(-0.856703\pi\) | ||||
−0.900369 | + | 0.435128i | \(0.856703\pi\) | |||||||
\(114\) | −170.760 | −0.140290 | ||||||||
\(115\) | −208.257 | −0.168870 | ||||||||
\(116\) | −196.055 | −0.156925 | ||||||||
\(117\) | −3221.83 | −2.54580 | ||||||||
\(118\) | −102.509 | −0.0799724 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −391.937 | −0.298157 | ||||||||
\(121\) | 1520.52 | 1.14239 | ||||||||
\(122\) | −233.395 | −0.173202 | ||||||||
\(123\) | −840.893 | −0.616429 | ||||||||
\(124\) | −2116.69 | −1.53294 | ||||||||
\(125\) | 754.342 | 0.539763 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1606.07 | 1.12217 | 0.561084 | − | 0.827759i | \(-0.310384\pi\) | ||||
0.561084 | + | 0.827759i | \(0.310384\pi\) | |||||||
\(128\) | 1407.36 | 0.971833 | ||||||||
\(129\) | −2924.04 | −1.99571 | ||||||||
\(130\) | −164.766 | −0.111161 | ||||||||
\(131\) | 109.787 | 0.0732221 | 0.0366111 | − | 0.999330i | \(-0.488344\pi\) | ||||
0.0366111 | + | 0.999330i | \(0.488344\pi\) | |||||||
\(132\) | −3484.65 | −2.29773 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −44.5425 | −0.0287155 | ||||||||
\(135\) | −815.124 | −0.519665 | ||||||||
\(136\) | 1054.23 | 0.664699 | ||||||||
\(137\) | 2009.57 | 1.25321 | 0.626603 | − | 0.779339i | \(-0.284445\pi\) | ||||
0.626603 | + | 0.779339i | \(0.284445\pi\) | |||||||
\(138\) | −544.818 | −0.336073 | ||||||||
\(139\) | −313.953 | −0.191577 | −0.0957884 | − | 0.995402i | \(-0.530537\pi\) | ||||
−0.0957884 | + | 0.995402i | \(0.530537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3572.57 | −2.13379 | ||||||||
\(142\) | −417.297 | −0.246611 | ||||||||
\(143\) | −3096.67 | −1.81089 | ||||||||
\(144\) | 2502.10 | 1.44797 | ||||||||
\(145\) | −85.7541 | −0.0491137 | ||||||||
\(146\) | 387.352 | 0.219572 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −239.805 | −0.133188 | ||||||||
\(149\) | 703.586 | 0.386845 | 0.193423 | − | 0.981116i | \(-0.438041\pi\) | ||||
0.193423 | + | 0.981116i | \(0.438041\pi\) | |||||||
\(150\) | 946.163 | 0.515026 | ||||||||
\(151\) | −689.283 | −0.371477 | −0.185739 | − | 0.982599i | \(-0.559468\pi\) | ||||
−0.185739 | + | 0.982599i | \(0.559468\pi\) | |||||||
\(152\) | 285.321 | 0.152254 | ||||||||
\(153\) | 4265.40 | 2.25384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −925.836 | −0.479774 | ||||||||
\(156\) | 3784.24 | 1.94219 | ||||||||
\(157\) | 678.513 | 0.344912 | 0.172456 | − | 0.985017i | \(-0.444830\pi\) | ||||
0.172456 | + | 0.985017i | \(0.444830\pi\) | |||||||
\(158\) | −84.1814 | −0.0423868 | ||||||||
\(159\) | 4678.54 | 2.33353 | ||||||||
\(160\) | 473.044 | 0.233734 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −775.682 | −0.376194 | ||||||||
\(163\) | 3215.69 | 1.54523 | 0.772615 | − | 0.634875i | \(-0.218948\pi\) | ||||
0.772615 | + | 0.634875i | \(0.218948\pi\) | |||||||
\(164\) | 664.666 | 0.316474 | ||||||||
\(165\) | −1524.18 | −0.719134 | ||||||||
\(166\) | −1044.43 | −0.488335 | ||||||||
\(167\) | −279.523 | −0.129522 | −0.0647610 | − | 0.997901i | \(-0.520628\pi\) | ||||
−0.0647610 | + | 0.997901i | \(0.520628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1165.90 | 0.530679 | ||||||||
\(170\) | 218.135 | 0.0984127 | ||||||||
\(171\) | 1154.41 | 0.516257 | ||||||||
\(172\) | 2311.24 | 1.02460 | ||||||||
\(173\) | 2956.70 | 1.29939 | 0.649693 | − | 0.760197i | \(-0.274897\pi\) | ||||
0.649693 | + | 0.760197i | \(0.274897\pi\) | |||||||
\(174\) | −224.340 | −0.0977424 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2404.90 | 1.02998 | ||||||||
\(177\) | 1029.80 | 0.437312 | ||||||||
\(178\) | 525.728 | 0.221376 | ||||||||
\(179\) | −4007.68 | −1.67345 | −0.836726 | − | 0.547622i | \(-0.815533\pi\) | ||||
−0.836726 | + | 0.547622i | \(0.815533\pi\) | |||||||
\(180\) | 1253.45 | 0.519036 | ||||||||
\(181\) | 1861.15 | 0.764299 | 0.382150 | − | 0.924100i | \(-0.375184\pi\) | ||||
0.382150 | + | 0.924100i | \(0.375184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2344.66 | 0.947116 | ||||||||
\(184\) | 910.332 | 0.364731 | ||||||||
\(185\) | −104.890 | −0.0416848 | ||||||||
\(186\) | −2422.07 | −0.954810 | ||||||||
\(187\) | 4099.71 | 1.60321 | ||||||||
\(188\) | 2823.87 | 1.09549 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 59.0370 | 0.0225421 | ||||||||
\(191\) | −1099.71 | −0.416607 | −0.208304 | − | 0.978064i | \(-0.566794\pi\) | ||||
−0.208304 | + | 0.978064i | \(0.566794\pi\) | |||||||
\(192\) | −2036.09 | −0.765325 | ||||||||
\(193\) | −1888.51 | −0.704341 | −0.352171 | − | 0.935936i | \(-0.614556\pi\) | ||||
−0.352171 | + | 0.935936i | \(0.614556\pi\) | |||||||
\(194\) | −314.817 | −0.116508 | ||||||||
\(195\) | 1655.22 | 0.607859 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5265.05 | 1.90416 | 0.952080 | − | 0.305851i | \(-0.0989408\pi\) | ||||
0.952080 | + | 0.305851i | \(0.0989408\pi\) | |||||||
\(198\) | −2683.34 | −0.963113 | ||||||||
\(199\) | 114.838 | 0.0409077 | 0.0204538 | − | 0.999791i | \(-0.493489\pi\) | ||||
0.0204538 | + | 0.999791i | \(0.493489\pi\) | |||||||
\(200\) | −1580.94 | −0.558945 | ||||||||
\(201\) | 447.468 | 0.157025 | ||||||||
\(202\) | 627.665 | 0.218626 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5009.98 | −1.71945 | ||||||||
\(205\) | 290.723 | 0.0990488 | ||||||||
\(206\) | −1779.76 | −0.601951 | ||||||||
\(207\) | 3683.21 | 1.23672 | ||||||||
\(208\) | −2611.65 | −0.870604 | ||||||||
\(209\) | 1109.56 | 0.367226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3695.54 | 1.20574 | 0.602871 | − | 0.797839i | \(-0.294023\pi\) | ||||
0.602871 | + | 0.797839i | \(0.294023\pi\) | |||||||
\(212\) | −3698.05 | −1.19803 | ||||||||
\(213\) | 4192.11 | 1.34854 | ||||||||
\(214\) | 600.284 | 0.191750 | ||||||||
\(215\) | 1010.93 | 0.320674 | ||||||||
\(216\) | 3563.07 | 1.12239 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1185.07 | 0.368179 | ||||||||
\(219\) | −3891.29 | −1.20068 | ||||||||
\(220\) | 1204.76 | 0.369203 | ||||||||
\(221\) | −4452.17 | −1.35514 | ||||||||
\(222\) | −274.402 | −0.0829579 | ||||||||
\(223\) | 2487.77 | 0.747055 | 0.373527 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373527 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6396.48 | −1.89525 | ||||||||
\(226\) | 1956.41 | 0.575833 | ||||||||
\(227\) | −856.423 | −0.250409 | −0.125204 | − | 0.992131i | \(-0.539959\pi\) | ||||
−0.125204 | + | 0.992131i | \(0.539959\pi\) | |||||||
\(228\) | −1355.92 | −0.393852 | ||||||||
\(229\) | 3433.96 | 0.990928 | 0.495464 | − | 0.868628i | \(-0.334998\pi\) | ||||
0.495464 | + | 0.868628i | \(0.334998\pi\) | |||||||
\(230\) | 188.361 | 0.0540007 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 374.848 | 0.106077 | ||||||||
\(233\) | 2244.94 | 0.631206 | 0.315603 | − | 0.948891i | \(-0.397793\pi\) | ||||
0.315603 | + | 0.948891i | \(0.397793\pi\) | |||||||
\(234\) | 2914.03 | 0.814086 | ||||||||
\(235\) | 1235.15 | 0.342862 | ||||||||
\(236\) | −813.980 | −0.224515 | ||||||||
\(237\) | 845.676 | 0.231783 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2047.64 | 0.554189 | 0.277094 | − | 0.960843i | \(-0.410629\pi\) | ||||
0.277094 | + | 0.960843i | \(0.410629\pi\) | |||||||
\(240\) | −1285.45 | −0.345732 | ||||||||
\(241\) | 719.345 | 0.192270 | 0.0961350 | − | 0.995368i | \(-0.469352\pi\) | ||||
0.0961350 | + | 0.995368i | \(0.469352\pi\) | |||||||
\(242\) | −1375.26 | −0.365309 | ||||||||
\(243\) | 786.427 | 0.207610 | ||||||||
\(244\) | −1853.29 | −0.486248 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 760.557 | 0.197119 | ||||||||
\(247\) | −1204.96 | −0.310403 | ||||||||
\(248\) | 4047.01 | 1.03623 | ||||||||
\(249\) | 10492.2 | 2.67035 | ||||||||
\(250\) | −682.275 | −0.172604 | ||||||||
\(251\) | −3348.08 | −0.841947 | −0.420973 | − | 0.907073i | \(-0.638311\pi\) | ||||
−0.420973 | + | 0.907073i | \(0.638311\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3540.13 | 0.879708 | ||||||||
\(254\) | −1452.63 | −0.358843 | ||||||||
\(255\) | −2191.35 | −0.538148 | ||||||||
\(256\) | 519.792 | 0.126902 | ||||||||
\(257\) | −4011.43 | −0.973643 | −0.486822 | − | 0.873501i | \(-0.661844\pi\) | ||||
−0.486822 | + | 0.873501i | \(0.661844\pi\) | |||||||
\(258\) | 2644.69 | 0.638182 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1308.33 | −0.312074 | ||||||||
\(261\) | 1516.64 | 0.359684 | ||||||||
\(262\) | −99.2981 | −0.0234147 | ||||||||
\(263\) | 6062.30 | 1.42136 | 0.710680 | − | 0.703516i | \(-0.248388\pi\) | ||||
0.710680 | + | 0.703516i | \(0.248388\pi\) | |||||||
\(264\) | 6662.49 | 1.55321 | ||||||||
\(265\) | −1617.52 | −0.374956 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5281.40 | −1.21055 | ||||||||
\(268\) | −353.692 | −0.0806163 | ||||||||
\(269\) | −1854.70 | −0.420384 | −0.210192 | − | 0.977660i | \(-0.567409\pi\) | ||||
−0.210192 | + | 0.977660i | \(0.567409\pi\) | |||||||
\(270\) | 737.251 | 0.166176 | ||||||||
\(271\) | 1616.24 | 0.362287 | 0.181143 | − | 0.983457i | \(-0.442020\pi\) | ||||
0.181143 | + | 0.983457i | \(0.442020\pi\) | |||||||
\(272\) | 3457.59 | 0.770761 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1817.58 | −0.400746 | ||||||||
\(275\) | −6148.00 | −1.34814 | ||||||||
\(276\) | −4326.16 | −0.943493 | ||||||||
\(277\) | 7395.03 | 1.60406 | 0.802029 | − | 0.597285i | \(-0.203754\pi\) | ||||
0.802029 | + | 0.597285i | \(0.203754\pi\) | |||||||
\(278\) | 283.959 | 0.0612617 | ||||||||
\(279\) | 16374.2 | 3.51362 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5488.05 | 1.16509 | 0.582544 | − | 0.812799i | \(-0.302057\pi\) | ||||
0.582544 | + | 0.812799i | \(0.302057\pi\) | |||||||
\(282\) | 3231.27 | 0.682337 | ||||||||
\(283\) | 7255.74 | 1.52406 | 0.762030 | − | 0.647542i | \(-0.224203\pi\) | ||||
0.762030 | + | 0.647542i | \(0.224203\pi\) | |||||||
\(284\) | −3313.57 | −0.692338 | ||||||||
\(285\) | −593.078 | −0.123266 | ||||||||
\(286\) | 2800.83 | 0.579079 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8366.21 | −1.71175 | ||||||||
\(289\) | 981.257 | 0.199727 | ||||||||
\(290\) | 77.5615 | 0.0157054 | ||||||||
\(291\) | 3162.61 | 0.637098 | ||||||||
\(292\) | 3075.79 | 0.616428 | ||||||||
\(293\) | 1168.80 | 0.233045 | 0.116523 | − | 0.993188i | \(-0.462825\pi\) | ||||
0.116523 | + | 0.993188i | \(0.462825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −356.033 | −0.0702679 | ||||||||
\(296\) | 458.496 | 0.0900322 | ||||||||
\(297\) | 13856.2 | 2.70713 | ||||||||
\(298\) | −636.368 | −0.123704 | ||||||||
\(299\) | −3844.48 | −0.743586 | ||||||||
\(300\) | 7513.06 | 1.44589 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 623.432 | 0.118790 | ||||||||
\(303\) | −6305.45 | −1.19551 | ||||||||
\(304\) | 935.778 | 0.176548 | ||||||||
\(305\) | −810.624 | −0.152184 | ||||||||
\(306\) | −3857.91 | −0.720725 | ||||||||
\(307\) | 6628.11 | 1.23220 | 0.616101 | − | 0.787667i | \(-0.288711\pi\) | ||||
0.616101 | + | 0.787667i | \(0.288711\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17879.3 | 3.29164 | ||||||||
\(310\) | 837.386 | 0.153420 | ||||||||
\(311\) | −6231.85 | −1.13626 | −0.568128 | − | 0.822940i | \(-0.692332\pi\) | ||||
−0.568128 | + | 0.822940i | \(0.692332\pi\) | |||||||
\(312\) | −7235.28 | −1.31287 | ||||||||
\(313\) | 1662.13 | 0.300158 | 0.150079 | − | 0.988674i | \(-0.452047\pi\) | ||||
0.150079 | + | 0.988674i | \(0.452047\pi\) | |||||||
\(314\) | −613.691 | −0.110295 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −668.446 | −0.118997 | ||||||||
\(317\) | −2588.65 | −0.458653 | −0.229326 | − | 0.973350i | \(-0.573652\pi\) | ||||
−0.229326 | + | 0.973350i | \(0.573652\pi\) | |||||||
\(318\) | −4231.57 | −0.746209 | ||||||||
\(319\) | 1457.72 | 0.255852 | ||||||||
\(320\) | 703.942 | 0.122974 | ||||||||
\(321\) | −6030.38 | −1.04854 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1595.25 | 0.274805 | ||||||||
\(324\) | −6159.34 | −1.05613 | ||||||||
\(325\) | 6676.55 | 1.13953 | ||||||||
\(326\) | −2908.48 | −0.494128 | ||||||||
\(327\) | −11905.1 | −2.01331 | ||||||||
\(328\) | −1270.81 | −0.213929 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1378.57 | 0.229962 | ||||||||
\(331\) | −1315.48 | −0.218445 | −0.109223 | − | 0.994017i | \(-0.534836\pi\) | ||||
−0.109223 | + | 0.994017i | \(0.534836\pi\) | |||||||
\(332\) | −8293.36 | −1.37095 | ||||||||
\(333\) | 1855.08 | 0.305278 | ||||||||
\(334\) | 252.819 | 0.0414181 | ||||||||
\(335\) | −154.704 | −0.0252310 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3019.13 | −0.488019 | −0.244010 | − | 0.969773i | \(-0.578463\pi\) | ||||
−0.244010 | + | 0.969773i | \(0.578463\pi\) | |||||||
\(338\) | −1054.52 | −0.169699 | ||||||||
\(339\) | −19653.8 | −3.14882 | ||||||||
\(340\) | 1732.11 | 0.276285 | ||||||||
\(341\) | 15738.2 | 2.49932 | ||||||||
\(342\) | −1044.12 | −0.165087 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4418.98 | −0.692603 | ||||||||
\(345\) | −1892.25 | −0.295291 | ||||||||
\(346\) | −2674.23 | −0.415513 | ||||||||
\(347\) | −409.784 | −0.0633958 | −0.0316979 | − | 0.999497i | \(-0.510091\pi\) | ||||
−0.0316979 | + | 0.999497i | \(0.510091\pi\) | |||||||
\(348\) | −1781.38 | −0.274403 | ||||||||
\(349\) | −4353.76 | −0.667769 | −0.333884 | − | 0.942614i | \(-0.608360\pi\) | ||||
−0.333884 | + | 0.942614i | \(0.608360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15047.4 | −2.28824 | ||||||||
\(352\) | −8041.21 | −1.21761 | ||||||||
\(353\) | −11101.6 | −1.67388 | −0.836940 | − | 0.547295i | \(-0.815658\pi\) | ||||
−0.836940 | + | 0.547295i | \(0.815658\pi\) | |||||||
\(354\) | −931.413 | −0.139842 | ||||||||
\(355\) | −1449.35 | −0.216685 | ||||||||
\(356\) | 4174.57 | 0.621494 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3624.80 | 0.535130 | ||||||||
\(359\) | −9976.84 | −1.46673 | −0.733367 | − | 0.679833i | \(-0.762052\pi\) | ||||
−0.733367 | + | 0.679833i | \(0.762052\pi\) | |||||||
\(360\) | −2396.53 | −0.350856 | ||||||||
\(361\) | −6427.25 | −0.937054 | ||||||||
\(362\) | −1683.34 | −0.244405 | ||||||||
\(363\) | 13815.7 | 1.99761 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1345.34 | 0.192927 | ||||||||
\(366\) | −2120.66 | −0.302865 | ||||||||
\(367\) | 6008.60 | 0.854622 | 0.427311 | − | 0.904105i | \(-0.359461\pi\) | ||||
0.427311 | + | 0.904105i | \(0.359461\pi\) | |||||||
\(368\) | 2985.66 | 0.422929 | ||||||||
\(369\) | −5141.70 | −0.725383 | ||||||||
\(370\) | 94.8695 | 0.0133298 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19232.6 | −2.68054 | ||||||||
\(373\) | 22.3692 | 0.00310518 | 0.00155259 | − | 0.999999i | \(-0.499506\pi\) | ||||
0.00155259 | + | 0.999999i | \(0.499506\pi\) | |||||||
\(374\) | −3708.04 | −0.512669 | ||||||||
\(375\) | 6854.05 | 0.943845 | ||||||||
\(376\) | −5399.09 | −0.740524 | ||||||||
\(377\) | −1583.05 | −0.216263 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6700.80 | 0.908172 | 0.454086 | − | 0.890958i | \(-0.349966\pi\) | ||||
0.454086 | + | 0.890958i | \(0.349966\pi\) | |||||||
\(380\) | 468.786 | 0.0632848 | ||||||||
\(381\) | 14592.9 | 1.96225 | ||||||||
\(382\) | 994.645 | 0.133221 | ||||||||
\(383\) | −7418.11 | −0.989681 | −0.494841 | − | 0.868984i | \(-0.664774\pi\) | ||||
−0.494841 | + | 0.868984i | \(0.664774\pi\) | |||||||
\(384\) | 12787.5 | 1.69937 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1708.09 | 0.225232 | ||||||||
\(387\) | −17879.2 | −2.34846 | ||||||||
\(388\) | −2499.82 | −0.327085 | ||||||||
\(389\) | −4351.30 | −0.567146 | −0.283573 | − | 0.958951i | \(-0.591520\pi\) | ||||
−0.283573 | + | 0.958951i | \(0.591520\pi\) | |||||||
\(390\) | −1497.08 | −0.194379 | ||||||||
\(391\) | 5089.74 | 0.658310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 997.536 | 0.128038 | ||||||||
\(394\) | −4762.05 | −0.608905 | ||||||||
\(395\) | −292.377 | −0.0372432 | ||||||||
\(396\) | −21307.2 | −2.70385 | ||||||||
\(397\) | 7184.81 | 0.908300 | 0.454150 | − | 0.890925i | \(-0.349943\pi\) | ||||
0.454150 | + | 0.890925i | \(0.349943\pi\) | |||||||
\(398\) | −103.867 | −0.0130813 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5185.06 | −0.648133 | ||||||||
\(401\) | 11999.7 | 1.49436 | 0.747178 | − | 0.664624i | \(-0.231408\pi\) | ||||
0.747178 | + | 0.664624i | \(0.231408\pi\) | |||||||
\(402\) | −404.719 | −0.0502128 | ||||||||
\(403\) | −17091.2 | −2.11259 | ||||||||
\(404\) | 4984.01 | 0.613772 | ||||||||
\(405\) | −2694.08 | −0.330543 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1783.01 | 0.217152 | ||||||||
\(408\) | 9578.83 | 1.16231 | ||||||||
\(409\) | 12518.5 | 1.51345 | 0.756723 | − | 0.653735i | \(-0.226799\pi\) | ||||
0.756723 | + | 0.653735i | \(0.226799\pi\) | |||||||
\(410\) | −262.949 | −0.0316735 | ||||||||
\(411\) | 18259.2 | 2.19139 | ||||||||
\(412\) | −14132.3 | −1.68992 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3331.33 | −0.395474 | ||||||||
\(415\) | −3627.49 | −0.429076 | ||||||||
\(416\) | 8732.54 | 1.02920 | ||||||||
\(417\) | −2852.62 | −0.334996 | ||||||||
\(418\) | −1003.56 | −0.117430 | ||||||||
\(419\) | 9523.60 | 1.11040 | 0.555201 | − | 0.831716i | \(-0.312641\pi\) | ||||
0.555201 | + | 0.831716i | \(0.312641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11087.1 | −1.28350 | −0.641751 | − | 0.766913i | \(-0.721792\pi\) | ||||
−0.641751 | + | 0.766913i | \(0.721792\pi\) | |||||||
\(422\) | −3342.48 | −0.385568 | ||||||||
\(423\) | −21844.8 | −2.51094 | ||||||||
\(424\) | 7070.49 | 0.809843 | ||||||||
\(425\) | −8839.14 | −1.00885 | ||||||||
\(426\) | −3791.61 | −0.431231 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4766.58 | 0.538321 | ||||||||
\(429\) | −28136.8 | −3.16657 | ||||||||
\(430\) | −914.352 | −0.102544 | ||||||||
\(431\) | −1026.44 | −0.114715 | −0.0573573 | − | 0.998354i | \(-0.518267\pi\) | ||||
−0.0573573 | + | 0.998354i | \(0.518267\pi\) | |||||||
\(432\) | 11685.9 | 1.30148 | ||||||||
\(433\) | −13804.7 | −1.53212 | −0.766062 | − | 0.642767i | \(-0.777786\pi\) | ||||
−0.766062 | + | 0.642767i | \(0.777786\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −779.173 | −0.0858816 | ||||||||
\(436\) | 9410.11 | 1.03363 | ||||||||
\(437\) | 1377.51 | 0.150790 | ||||||||
\(438\) | 3519.53 | 0.383949 | ||||||||
\(439\) | 1587.56 | 0.172597 | 0.0862984 | − | 0.996269i | \(-0.472496\pi\) | ||||
0.0862984 | + | 0.996269i | \(0.472496\pi\) | |||||||
\(440\) | −2303.43 | −0.249572 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4026.83 | 0.433341 | ||||||||
\(443\) | −6213.84 | −0.666430 | −0.333215 | − | 0.942851i | \(-0.608134\pi\) | ||||
−0.333215 | + | 0.942851i | \(0.608134\pi\) | |||||||
\(444\) | −2178.90 | −0.232897 | ||||||||
\(445\) | 1825.95 | 0.194513 | ||||||||
\(446\) | −2250.10 | −0.238890 | ||||||||
\(447\) | 6392.87 | 0.676449 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5023.31 | −0.527984 | −0.263992 | − | 0.964525i | \(-0.585039\pi\) | ||||
−0.263992 | + | 0.964525i | \(0.585039\pi\) | |||||||
\(450\) | 5785.39 | 0.606057 | ||||||||
\(451\) | −4941.96 | −0.515982 | ||||||||
\(452\) | 15535.0 | 1.61660 | ||||||||
\(453\) | −6262.92 | −0.649575 | ||||||||
\(454\) | 774.604 | 0.0800748 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2592.46 | 0.266235 | ||||||||
\(457\) | −9345.09 | −0.956553 | −0.478277 | − | 0.878209i | \(-0.658738\pi\) | ||||
−0.478277 | + | 0.878209i | \(0.658738\pi\) | |||||||
\(458\) | −3105.89 | −0.316875 | ||||||||
\(459\) | 19921.4 | 2.02582 | ||||||||
\(460\) | 1495.69 | 0.151602 | ||||||||
\(461\) | 10592.5 | 1.07015 | 0.535077 | − | 0.844803i | \(-0.320283\pi\) | ||||
0.535077 | + | 0.844803i | \(0.320283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5186.28 | −0.520576 | −0.260288 | − | 0.965531i | \(-0.583818\pi\) | ||||
−0.260288 | + | 0.965531i | \(0.583818\pi\) | |||||||
\(464\) | 1229.40 | 0.123004 | ||||||||
\(465\) | −8412.28 | −0.838946 | ||||||||
\(466\) | −2030.47 | −0.201845 | ||||||||
\(467\) | 5292.77 | 0.524454 | 0.262227 | − | 0.965006i | \(-0.415543\pi\) | ||||
0.262227 | + | 0.965006i | \(0.415543\pi\) | |||||||
\(468\) | 23139.0 | 2.28547 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1117.15 | −0.109639 | ||||||||
\(471\) | 6165.06 | 0.603123 | ||||||||
\(472\) | 1556.29 | 0.151767 | ||||||||
\(473\) | −17184.7 | −1.67051 | ||||||||
\(474\) | −764.883 | −0.0741187 | ||||||||
\(475\) | −2392.27 | −0.231084 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28607.3 | 2.74599 | ||||||||
\(478\) | −1852.02 | −0.177216 | ||||||||
\(479\) | 3971.90 | 0.378874 | 0.189437 | − | 0.981893i | \(-0.439334\pi\) | ||||
0.189437 | + | 0.981893i | \(0.439334\pi\) | |||||||
\(480\) | 4298.15 | 0.408714 | ||||||||
\(481\) | −1936.30 | −0.183551 | ||||||||
\(482\) | −650.622 | −0.0614834 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10920.3 | −1.02557 | ||||||||
\(485\) | −1093.41 | −0.102370 | ||||||||
\(486\) | −711.295 | −0.0663889 | ||||||||
\(487\) | −11943.5 | −1.11132 | −0.555659 | − | 0.831410i | \(-0.687534\pi\) | ||||
−0.555659 | + | 0.831410i | \(0.687534\pi\) | |||||||
\(488\) | 3543.39 | 0.328693 | ||||||||
\(489\) | 29218.2 | 2.70203 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9512.82 | 0.874353 | 0.437177 | − | 0.899376i | \(-0.355978\pi\) | ||||
0.437177 | + | 0.899376i | \(0.355978\pi\) | |||||||
\(492\) | 6039.24 | 0.553395 | ||||||||
\(493\) | 2095.80 | 0.191461 | ||||||||
\(494\) | 1089.84 | 0.0992596 | ||||||||
\(495\) | −9319.71 | −0.846242 | ||||||||
\(496\) | 13273.2 | 1.20158 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9489.84 | −0.853916 | ||||||||
\(499\) | −3780.91 | −0.339192 | −0.169596 | − | 0.985514i | \(-0.554246\pi\) | ||||
−0.169596 | + | 0.985514i | \(0.554246\pi\) | |||||||
\(500\) | −5417.64 | −0.484569 | ||||||||
\(501\) | −2539.79 | −0.226486 | ||||||||
\(502\) | 3028.21 | 0.269235 | ||||||||
\(503\) | −15560.0 | −1.37930 | −0.689648 | − | 0.724145i | \(-0.742235\pi\) | ||||
−0.689648 | + | 0.724145i | \(0.742235\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2179.99 | 0.192096 | ||||||||
\(506\) | −3201.92 | −0.281310 | ||||||||
\(507\) | 10593.5 | 0.927960 | ||||||||
\(508\) | −11534.7 | −1.00742 | ||||||||
\(509\) | −16928.5 | −1.47415 | −0.737073 | − | 0.675813i | \(-0.763793\pi\) | ||||
−0.737073 | + | 0.675813i | \(0.763793\pi\) | |||||||
\(510\) | 1982.00 | 0.172087 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11729.0 | −1.01241 | ||||||||
\(513\) | 5391.62 | 0.464027 | ||||||||
\(514\) | 3628.20 | 0.311348 | ||||||||
\(515\) | −6181.43 | −0.528906 | ||||||||
\(516\) | 21000.3 | 1.79164 | ||||||||
\(517\) | −20996.2 | −1.78609 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26865.0 | 2.27214 | ||||||||
\(520\) | 2501.46 | 0.210955 | ||||||||
\(521\) | 14567.1 | 1.22495 | 0.612474 | − | 0.790491i | \(-0.290175\pi\) | ||||
0.612474 | + | 0.790491i | \(0.290175\pi\) | |||||||
\(522\) | −1371.74 | −0.115018 | ||||||||
\(523\) | −1694.23 | −0.141651 | −0.0708254 | − | 0.997489i | \(-0.522563\pi\) | ||||
−0.0708254 | + | 0.997489i | \(0.522563\pi\) | |||||||
\(524\) | −788.481 | −0.0657347 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5483.13 | −0.454517 | ||||||||
\(527\) | 22627.2 | 1.87031 | ||||||||
\(528\) | 21851.2 | 1.80105 | ||||||||
\(529\) | −7771.97 | −0.638774 | ||||||||
\(530\) | 1462.99 | 0.119902 | ||||||||
\(531\) | 6296.76 | 0.514607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5366.84 | 0.436142 | ||||||||
\(534\) | 4776.84 | 0.387105 | ||||||||
\(535\) | 2084.89 | 0.168482 | ||||||||
\(536\) | 676.241 | 0.0544947 | ||||||||
\(537\) | −36414.3 | −2.92624 | ||||||||
\(538\) | 1677.51 | 0.134429 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5854.18 | 0.466525 | ||||||||
\(541\) | 10056.5 | 0.799191 | 0.399596 | − | 0.916691i | \(-0.369151\pi\) | ||||
0.399596 | + | 0.916691i | \(0.369151\pi\) | |||||||
\(542\) | −1461.83 | −0.115851 | ||||||||
\(543\) | 16910.7 | 1.33647 | ||||||||
\(544\) | −11561.1 | −0.911170 | ||||||||
\(545\) | 4115.96 | 0.323502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13385.9 | 1.04633 | 0.523163 | − | 0.852233i | \(-0.324752\pi\) | ||||
0.523163 | + | 0.852233i | \(0.324752\pi\) | |||||||
\(548\) | −14432.6 | −1.12506 | ||||||||
\(549\) | 14336.6 | 1.11452 | ||||||||
\(550\) | 5560.64 | 0.431103 | ||||||||
\(551\) | 567.219 | 0.0438554 | ||||||||
\(552\) | 8271.40 | 0.637779 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6688.54 | −0.512940 | ||||||||
\(555\) | −953.047 | −0.0728912 | ||||||||
\(556\) | 2254.79 | 0.171987 | ||||||||
\(557\) | 13511.5 | 1.02783 | 0.513914 | − | 0.857842i | \(-0.328195\pi\) | ||||
0.513914 | + | 0.857842i | \(0.328195\pi\) | |||||||
\(558\) | −14809.9 | −1.12357 | ||||||||
\(559\) | 18662.1 | 1.41203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 37250.5 | 2.80342 | ||||||||
\(562\) | −4963.74 | −0.372567 | ||||||||
\(563\) | 21009.0 | 1.57269 | 0.786344 | − | 0.617789i | \(-0.211971\pi\) | ||||
0.786344 | + | 0.617789i | \(0.211971\pi\) | |||||||
\(564\) | 25658.0 | 1.91560 | ||||||||
\(565\) | 6794.96 | 0.505957 | ||||||||
\(566\) | −6562.56 | −0.487358 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6335.37 | 0.468004 | ||||||||
\(569\) | 14913.0 | 1.09875 | 0.549373 | − | 0.835577i | \(-0.314866\pi\) | ||||
0.549373 | + | 0.835577i | \(0.314866\pi\) | |||||||
\(570\) | 536.418 | 0.0394177 | ||||||||
\(571\) | −17668.8 | −1.29495 | −0.647474 | − | 0.762087i | \(-0.724175\pi\) | ||||
−0.647474 | + | 0.762087i | \(0.724175\pi\) | |||||||
\(572\) | 22240.1 | 1.62571 | ||||||||
\(573\) | −9992.08 | −0.728491 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7632.67 | −0.553573 | ||||||||
\(576\) | −12449.8 | −0.900596 | ||||||||
\(577\) | 6857.88 | 0.494796 | 0.247398 | − | 0.968914i | \(-0.420424\pi\) | ||||
0.247398 | + | 0.968914i | \(0.420424\pi\) | |||||||
\(578\) | −887.512 | −0.0638679 | ||||||||
\(579\) | −17159.2 | −1.23163 | ||||||||
\(580\) | 615.881 | 0.0440915 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2860.47 | −0.203729 | ||||||||
\(583\) | 27496.0 | 1.95329 | ||||||||
\(584\) | −5880.76 | −0.416691 | ||||||||
\(585\) | 10120.9 | 0.715299 | ||||||||
\(586\) | −1057.14 | −0.0745224 | ||||||||
\(587\) | 5215.96 | 0.366756 | 0.183378 | − | 0.983042i | \(-0.441297\pi\) | ||||
0.183378 | + | 0.983042i | \(0.441297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6123.93 | 0.428407 | ||||||||
\(590\) | 322.019 | 0.0224700 | ||||||||
\(591\) | 47839.0 | 3.32967 | ||||||||
\(592\) | 1503.75 | 0.104398 | ||||||||
\(593\) | −11235.6 | −0.778065 | −0.389032 | − | 0.921224i | \(-0.627191\pi\) | ||||
−0.389032 | + | 0.921224i | \(0.627191\pi\) | |||||||
\(594\) | −12532.4 | −0.865676 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5053.11 | −0.347288 | ||||||||
\(597\) | 1043.43 | 0.0715323 | ||||||||
\(598\) | 3477.20 | 0.237781 | ||||||||
\(599\) | 2209.24 | 0.150696 | 0.0753482 | − | 0.997157i | \(-0.475993\pi\) | ||||
0.0753482 | + | 0.997157i | \(0.475993\pi\) | |||||||
\(600\) | −14364.6 | −0.977387 | ||||||||
\(601\) | 11191.5 | 0.759587 | 0.379793 | − | 0.925071i | \(-0.375995\pi\) | ||||
0.379793 | + | 0.925071i | \(0.375995\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2736.08 | 0.184779 | ||||||||
\(604\) | 4950.39 | 0.333491 | ||||||||
\(605\) | −4776.51 | −0.320980 | ||||||||
\(606\) | 5703.05 | 0.382295 | ||||||||
\(607\) | 37.2973 | 0.00249399 | 0.00124699 | − | 0.999999i | \(-0.499603\pi\) | ||||
0.00124699 | + | 0.999999i | \(0.499603\pi\) | |||||||
\(608\) | −3128.94 | −0.208710 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 733.180 | 0.0486649 | ||||||||
\(611\) | 22801.3 | 1.50972 | ||||||||
\(612\) | −30633.9 | −2.02337 | ||||||||
\(613\) | −8887.23 | −0.585566 | −0.292783 | − | 0.956179i | \(-0.594581\pi\) | ||||
−0.292783 | + | 0.956179i | \(0.594581\pi\) | |||||||
\(614\) | −5994.89 | −0.394029 | ||||||||
\(615\) | 2641.55 | 0.173199 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2240.48 | 0.146189 | 0.0730944 | − | 0.997325i | \(-0.476713\pi\) | ||||
0.0730944 | + | 0.997325i | \(0.476713\pi\) | |||||||
\(618\) | −16171.2 | −1.05259 | ||||||||
\(619\) | −7839.71 | −0.509054 | −0.254527 | − | 0.967066i | \(-0.581920\pi\) | ||||
−0.254527 | + | 0.967066i | \(0.581920\pi\) | |||||||
\(620\) | 6649.31 | 0.430714 | ||||||||
\(621\) | 17202.3 | 1.11160 | ||||||||
\(622\) | 5636.48 | 0.363348 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23729.8 | −1.52236 | ||||||||
\(625\) | 12021.8 | 0.769396 | ||||||||
\(626\) | −1503.34 | −0.0959833 | ||||||||
\(627\) | 10081.7 | 0.642141 | ||||||||
\(628\) | −4873.04 | −0.309643 | ||||||||
\(629\) | 2563.49 | 0.162501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5772.45 | −0.364180 | −0.182090 | − | 0.983282i | \(-0.558286\pi\) | ||||
−0.182090 | + | 0.983282i | \(0.558286\pi\) | |||||||
\(632\) | 1278.04 | 0.0804392 | ||||||||
\(633\) | 33578.2 | 2.10839 | ||||||||
\(634\) | 2341.34 | 0.146666 | ||||||||
\(635\) | −5045.24 | −0.315298 | ||||||||
\(636\) | −33601.0 | −2.09491 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1318.46 | −0.0818154 | ||||||||
\(639\) | 25633.0 | 1.58689 | ||||||||
\(640\) | −4421.04 | −0.273058 | ||||||||
\(641\) | 2309.83 | 0.142329 | 0.0711645 | − | 0.997465i | \(-0.477328\pi\) | ||||
0.0711645 | + | 0.997465i | \(0.477328\pi\) | |||||||
\(642\) | 5454.26 | 0.335300 | ||||||||
\(643\) | 11706.6 | 0.717982 | 0.358991 | − | 0.933341i | \(-0.383121\pi\) | ||||
0.358991 | + | 0.933341i | \(0.383121\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9185.47 | 0.560740 | ||||||||
\(646\) | −1442.85 | −0.0878762 | ||||||||
\(647\) | −9280.94 | −0.563944 | −0.281972 | − | 0.959423i | \(-0.590988\pi\) | ||||
−0.281972 | + | 0.959423i | \(0.590988\pi\) | |||||||
\(648\) | 11776.4 | 0.713919 | ||||||||
\(649\) | 6052.15 | 0.366052 | ||||||||
\(650\) | −6038.70 | −0.364396 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23094.9 | −1.38722 | ||||||||
\(653\) | 7650.07 | 0.458454 | 0.229227 | − | 0.973373i | \(-0.426380\pi\) | ||||
0.229227 | + | 0.973373i | \(0.426380\pi\) | |||||||
\(654\) | 10767.7 | 0.643808 | ||||||||
\(655\) | −344.880 | −0.0205734 | ||||||||
\(656\) | −4167.93 | −0.248064 | ||||||||
\(657\) | −23793.6 | −1.41290 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27325.1 | −1.61523 | −0.807615 | − | 0.589710i | \(-0.799242\pi\) | ||||
−0.807615 | + | 0.589710i | \(0.799242\pi\) | |||||||
\(660\) | 10946.6 | 0.645598 | ||||||||
\(661\) | −1197.16 | −0.0704448 | −0.0352224 | − | 0.999379i | \(-0.511214\pi\) | ||||
−0.0352224 | + | 0.999379i | \(0.511214\pi\) | |||||||
\(662\) | 1189.81 | 0.0698536 | ||||||||
\(663\) | −40453.0 | −2.36963 | ||||||||
\(664\) | 15856.5 | 0.926734 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1677.85 | −0.0976208 | ||||||||
\(667\) | 1809.74 | 0.105058 | ||||||||
\(668\) | 2007.52 | 0.116277 | ||||||||
\(669\) | 22604.2 | 1.30632 | ||||||||
\(670\) | 139.924 | 0.00806827 | ||||||||
\(671\) | 13779.7 | 0.792785 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18550.7 | −1.06252 | −0.531262 | − | 0.847208i | \(-0.678282\pi\) | ||||
−0.531262 | + | 0.847208i | \(0.678282\pi\) | |||||||
\(674\) | 2730.69 | 0.156057 | ||||||||
\(675\) | −29874.5 | −1.70351 | ||||||||
\(676\) | −8373.44 | −0.476413 | ||||||||
\(677\) | 20273.3 | 1.15091 | 0.575456 | − | 0.817833i | \(-0.304825\pi\) | ||||
0.575456 | + | 0.817833i | \(0.304825\pi\) | |||||||
\(678\) | 17776.2 | 1.00692 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3311.71 | −0.186762 | ||||||||
\(681\) | −7781.57 | −0.437872 | ||||||||
\(682\) | −14234.6 | −0.799224 | ||||||||
\(683\) | −18260.7 | −1.02302 | −0.511511 | − | 0.859277i | \(-0.670914\pi\) | ||||
−0.511511 | + | 0.859277i | \(0.670914\pi\) | |||||||
\(684\) | −8290.91 | −0.463466 | ||||||||
\(685\) | −6312.80 | −0.352116 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31201.4 | 1.73276 | ||||||||
\(688\) | −14493.1 | −0.803118 | ||||||||
\(689\) | −29859.9 | −1.65105 | ||||||||
\(690\) | 1711.47 | 0.0944271 | ||||||||
\(691\) | 30343.2 | 1.67049 | 0.835247 | − | 0.549875i | \(-0.185325\pi\) | ||||
0.835247 | + | 0.549875i | \(0.185325\pi\) | |||||||
\(692\) | −21234.9 | −1.16652 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 370.635 | 0.0202725 | ||||||||
\(695\) | 986.242 | 0.0538278 | ||||||||
\(696\) | 3405.92 | 0.185490 | ||||||||
\(697\) | −7105.19 | −0.386124 | ||||||||
\(698\) | 3937.82 | 0.213537 | ||||||||
\(699\) | 20397.9 | 1.10375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9464.46 | −0.509940 | −0.254970 | − | 0.966949i | \(-0.582066\pi\) | ||||
−0.254970 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(702\) | 13609.9 | 0.731725 | ||||||||
\(703\) | 693.794 | 0.0372218 | ||||||||
\(704\) | −11966.2 | −0.640616 | ||||||||
\(705\) | 11222.8 | 0.599537 | ||||||||
\(706\) | 10041.0 | 0.535267 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7395.93 | −0.392593 | ||||||||
\(709\) | 10796.2 | 0.571878 | 0.285939 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285939 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(710\) | 1310.88 | 0.0692909 | ||||||||
\(711\) | 5170.95 | 0.272751 | ||||||||
\(712\) | −7981.58 | −0.420115 | ||||||||
\(713\) | 19538.7 | 1.02627 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9727.78 | 0.508809 | ||||||||
\(716\) | 28782.9 | 1.50233 | ||||||||
\(717\) | 18605.2 | 0.969070 | ||||||||
\(718\) | 9023.70 | 0.469027 | ||||||||
\(719\) | 20577.7 | 1.06734 | 0.533672 | − | 0.845692i | \(-0.320812\pi\) | ||||
0.533672 | + | 0.845692i | \(0.320812\pi\) | |||||||
\(720\) | −7860.01 | −0.406840 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5813.22 | 0.299648 | ||||||||
\(723\) | 6536.07 | 0.336209 | ||||||||
\(724\) | −13366.7 | −0.686144 | ||||||||
\(725\) | −3142.91 | −0.161000 | ||||||||
\(726\) | −12495.8 | −0.638790 | ||||||||
\(727\) | 877.412 | 0.0447612 | 0.0223806 | − | 0.999750i | \(-0.492875\pi\) | ||||
0.0223806 | + | 0.999750i | \(0.492875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16010.0 | −0.813394 | ||||||||
\(730\) | −1216.81 | −0.0616936 | ||||||||
\(731\) | −24706.9 | −1.25009 | ||||||||
\(732\) | −16839.2 | −0.850267 | ||||||||
\(733\) | −29385.1 | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(734\) | −5434.56 | −0.273288 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9983.07 | −0.499974 | ||||||||
\(737\) | 2629.79 | 0.131438 | ||||||||
\(738\) | 4650.49 | 0.231960 | ||||||||
\(739\) | −33547.4 | −1.66991 | −0.834954 | − | 0.550320i | \(-0.814506\pi\) | ||||
−0.834954 | + | 0.550320i | \(0.814506\pi\) | |||||||
\(740\) | 753.316 | 0.0374222 | ||||||||
\(741\) | −10948.4 | −0.542779 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6519.35 | 0.321900 | 0.160950 | − | 0.986963i | \(-0.448544\pi\) | ||||
0.160950 | + | 0.986963i | \(0.448544\pi\) | |||||||
\(744\) | 36771.7 | 1.81198 | ||||||||
\(745\) | −2210.22 | −0.108693 | ||||||||
\(746\) | −20.2321 | −0.000992965 0 | ||||||||
\(747\) | 64155.5 | 3.14234 | ||||||||
\(748\) | −29443.9 | −1.43927 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6199.25 | −0.301819 | ||||||||
\(751\) | −19844.3 | −0.964219 | −0.482109 | − | 0.876111i | \(-0.660129\pi\) | ||||
−0.482109 | + | 0.876111i | \(0.660129\pi\) | |||||||
\(752\) | −17707.6 | −0.858685 | ||||||||
\(753\) | −30421.1 | −1.47225 | ||||||||
\(754\) | 1431.81 | 0.0691557 | ||||||||
\(755\) | 2165.29 | 0.104375 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35038.1 | 1.68228 | 0.841138 | − | 0.540821i | \(-0.181886\pi\) | ||||
0.841138 | + | 0.540821i | \(0.181886\pi\) | |||||||
\(758\) | −6060.64 | −0.290412 | ||||||||
\(759\) | 32166.1 | 1.53828 | ||||||||
\(760\) | −896.296 | −0.0427791 | ||||||||
\(761\) | −14439.0 | −0.687798 | −0.343899 | − | 0.939007i | \(-0.611748\pi\) | ||||
−0.343899 | + | 0.939007i | \(0.611748\pi\) | |||||||
\(762\) | −13198.8 | −0.627482 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7898.03 | 0.374006 | ||||||||
\(765\) | −13399.2 | −0.633267 | ||||||||
\(766\) | 6709.42 | 0.316477 | ||||||||
\(767\) | −6572.47 | −0.309411 | ||||||||
\(768\) | 4722.90 | 0.221905 | ||||||||
\(769\) | 19397.3 | 0.909603 | 0.454802 | − | 0.890593i | \(-0.349710\pi\) | ||||
0.454802 | + | 0.890593i | \(0.349710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36448.4 | −1.70254 | ||||||||
\(772\) | 13563.2 | 0.632317 | ||||||||
\(773\) | −6769.59 | −0.314987 | −0.157494 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157494 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(774\) | 16171.1 | 0.750981 | ||||||||
\(775\) | −33932.1 | −1.57275 | ||||||||
\(776\) | 4779.53 | 0.221102 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3935.60 | 0.181360 | ||||||||
\(779\) | −1922.98 | −0.0884442 | ||||||||
\(780\) | −11887.7 | −0.545701 | ||||||||
\(781\) | 24637.2 | 1.12880 | ||||||||
\(782\) | −4603.49 | −0.210512 | ||||||||
\(783\) | 7083.40 | 0.323295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2131.46 | −0.0969108 | ||||||||
\(786\) | −902.236 | −0.0409436 | ||||||||
\(787\) | −33135.5 | −1.50083 | −0.750415 | − | 0.660967i | \(-0.770146\pi\) | ||||
−0.750415 | + | 0.660967i | \(0.770146\pi\) | |||||||
\(788\) | −37813.3 | −1.70945 | ||||||||
\(789\) | 55082.9 | 2.48543 | ||||||||
\(790\) | 264.444 | 0.0119095 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 40738.3 | 1.82774 | ||||||||
\(793\) | −14964.3 | −0.670113 | ||||||||
\(794\) | −6498.40 | −0.290453 | ||||||||
\(795\) | −14697.0 | −0.655659 | ||||||||
\(796\) | −824.758 | −0.0367246 | ||||||||
\(797\) | −25165.0 | −1.11843 | −0.559216 | − | 0.829022i | \(-0.688898\pi\) | ||||
−0.559216 | + | 0.829022i | \(0.688898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30186.8 | −1.33658 | ||||||||
\(800\) | 17337.2 | 0.766203 | ||||||||
\(801\) | −32293.5 | −1.42451 | ||||||||
\(802\) | −10853.3 | −0.477860 | ||||||||
\(803\) | −22869.3 | −1.00503 | ||||||||
\(804\) | −3213.69 | −0.140968 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15458.4 | 0.675556 | ||||||||
\(807\) | −16852.1 | −0.735094 | ||||||||
\(808\) | −9529.18 | −0.414895 | ||||||||
\(809\) | −2860.50 | −0.124314 | −0.0621570 | − | 0.998066i | \(-0.519798\pi\) | ||||
−0.0621570 | + | 0.998066i | \(0.519798\pi\) | |||||||
\(810\) | 2436.70 | 0.105700 | ||||||||
\(811\) | −24431.2 | −1.05782 | −0.528911 | − | 0.848677i | \(-0.677400\pi\) | ||||
−0.528911 | + | 0.848677i | \(0.677400\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14685.4 | 0.633505 | ||||||||
\(814\) | −1612.67 | −0.0694400 | ||||||||
\(815\) | −10101.7 | −0.434167 | ||||||||
\(816\) | 31416.1 | 1.34777 | ||||||||
\(817\) | −6686.79 | −0.286342 | ||||||||
\(818\) | −11322.5 | −0.483965 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2087.96 | −0.0889203 | ||||||||
\(821\) | 28644.4 | 1.21766 | 0.608830 | − | 0.793301i | \(-0.291639\pi\) | ||||
0.608830 | + | 0.793301i | \(0.291639\pi\) | |||||||
\(822\) | −16514.8 | −0.700755 | ||||||||
\(823\) | −22649.4 | −0.959307 | −0.479654 | − | 0.877458i | \(-0.659238\pi\) | ||||
−0.479654 | + | 0.877458i | \(0.659238\pi\) | |||||||
\(824\) | 27020.2 | 1.14235 | ||||||||
\(825\) | −55861.5 | −2.35739 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11914.8 | −0.500991 | −0.250495 | − | 0.968118i | \(-0.580594\pi\) | ||||
−0.250495 | + | 0.968118i | \(0.580594\pi\) | |||||||
\(828\) | −26452.6 | −1.11026 | ||||||||
\(829\) | 414.521 | 0.0173666 | 0.00868329 | − | 0.999962i | \(-0.497236\pi\) | ||||
0.00868329 | + | 0.999962i | \(0.497236\pi\) | |||||||
\(830\) | 3280.94 | 0.137209 | ||||||||
\(831\) | 67192.2 | 2.80490 | ||||||||
\(832\) | 12995.0 | 0.541490 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2580.09 | 0.107124 | ||||||||
\(835\) | 878.085 | 0.0363921 | ||||||||
\(836\) | −7968.83 | −0.329674 | ||||||||
\(837\) | 76475.2 | 3.15815 | ||||||||
\(838\) | −8613.76 | −0.355080 | ||||||||
\(839\) | 10486.6 | 0.431512 | 0.215756 | − | 0.976447i | \(-0.430778\pi\) | ||||
0.215756 | + | 0.976447i | \(0.430778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23643.8 | −0.969445 | ||||||||
\(842\) | 10027.9 | 0.410434 | ||||||||
\(843\) | 49865.2 | 2.03730 | ||||||||
\(844\) | −26541.2 | −1.08245 | ||||||||
\(845\) | −3662.52 | −0.149106 | ||||||||
\(846\) | 19757.8 | 0.802941 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23189.4 | 0.939065 | ||||||||
\(849\) | 65926.6 | 2.66501 | ||||||||
\(850\) | 7994.68 | 0.322606 | ||||||||
\(851\) | 2213.59 | 0.0891668 | ||||||||
\(852\) | −30107.5 | −1.21064 | ||||||||
\(853\) | −32314.7 | −1.29711 | −0.648554 | − | 0.761169i | \(-0.724626\pi\) | ||||
−0.648554 | + | 0.761169i | \(0.724626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3626.42 | −0.145054 | ||||||||
\(856\) | −9113.47 | −0.363893 | ||||||||
\(857\) | −33881.2 | −1.35048 | −0.675239 | − | 0.737599i | \(-0.735960\pi\) | ||||
−0.675239 | + | 0.737599i | \(0.735960\pi\) | |||||||
\(858\) | 25448.7 | 1.01259 | ||||||||
\(859\) | 34132.6 | 1.35575 | 0.677876 | − | 0.735176i | \(-0.262901\pi\) | ||||
0.677876 | + | 0.735176i | \(0.262901\pi\) | |||||||
\(860\) | −7260.46 | −0.287883 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 928.381 | 0.0366830 | ||||||||
\(863\) | −10222.3 | −0.403212 | −0.201606 | − | 0.979467i | \(-0.564616\pi\) | ||||
−0.201606 | + | 0.979467i | \(0.564616\pi\) | |||||||
\(864\) | −39074.1 | −1.53857 | ||||||||
\(865\) | −9288.08 | −0.365092 | ||||||||
\(866\) | 12485.8 | 0.489937 | ||||||||
\(867\) | 8915.83 | 0.349248 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4970.07 | 0.194014 | ||||||||
\(870\) | 704.734 | 0.0274629 | ||||||||
\(871\) | −2855.88 | −0.111100 | ||||||||
\(872\) | −17991.7 | −0.698710 | ||||||||
\(873\) | 19338.0 | 0.749705 | ||||||||
\(874\) | −1245.91 | −0.0482192 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27947.0 | 1.07790 | ||||||||
\(877\) | −12326.7 | −0.474623 | −0.237311 | − | 0.971434i | \(-0.576266\pi\) | ||||
−0.237311 | + | 0.971434i | \(0.576266\pi\) | |||||||
\(878\) | −1435.89 | −0.0551924 | ||||||||
\(879\) | 10619.9 | 0.407510 | ||||||||
\(880\) | −7554.67 | −0.289395 | ||||||||
\(881\) | −25636.2 | −0.980370 | −0.490185 | − | 0.871618i | \(-0.663071\pi\) | ||||
−0.490185 | + | 0.871618i | \(0.663071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8508.94 | −0.324291 | −0.162145 | − | 0.986767i | \(-0.551841\pi\) | ||||
−0.162145 | + | 0.986767i | \(0.551841\pi\) | |||||||
\(884\) | 31975.2 | 1.21656 | ||||||||
\(885\) | −3234.96 | −0.122872 | ||||||||
\(886\) | 5620.20 | 0.213109 | ||||||||
\(887\) | 12446.3 | 0.471144 | 0.235572 | − | 0.971857i | \(-0.424304\pi\) | ||||
0.235572 | + | 0.971857i | \(0.424304\pi\) | |||||||
\(888\) | 4165.96 | 0.157433 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1651.50 | −0.0622006 | ||||||||
\(891\) | 45796.3 | 1.72192 | ||||||||
\(892\) | −17867.0 | −0.670663 | ||||||||
\(893\) | −8169.89 | −0.306153 | ||||||||
\(894\) | −5782.13 | −0.216312 | ||||||||
\(895\) | 12589.6 | 0.470194 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34931.5 | −1.30026 | ||||||||
\(898\) | 4543.40 | 0.168837 | ||||||||
\(899\) | 8045.48 | 0.298478 | ||||||||
\(900\) | 45939.2 | 1.70145 | ||||||||
\(901\) | 39531.7 | 1.46170 | ||||||||
\(902\) | 4469.83 | 0.164999 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29702.1 | −1.09278 | ||||||||
\(905\) | −5846.55 | −0.214747 | ||||||||
\(906\) | 5664.59 | 0.207719 | ||||||||
\(907\) | −51327.1 | −1.87904 | −0.939519 | − | 0.342496i | \(-0.888728\pi\) | ||||
−0.939519 | + | 0.342496i | \(0.888728\pi\) | |||||||
\(908\) | 6150.78 | 0.224803 | ||||||||
\(909\) | −38555.2 | −1.40681 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5816.49 | −0.211536 | −0.105768 | − | 0.994391i | \(-0.533730\pi\) | ||||
−0.105768 | + | 0.994391i | \(0.533730\pi\) | |||||||
\(912\) | 8502.61 | 0.308717 | ||||||||
\(913\) | 61663.3 | 2.23522 | ||||||||
\(914\) | 8452.30 | 0.305883 | ||||||||
\(915\) | −7365.44 | −0.266114 | ||||||||
\(916\) | −24662.5 | −0.889599 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −18018.2 | −0.647809 | ||||||||
\(919\) | 15116.7 | 0.542605 | 0.271303 | − | 0.962494i | \(-0.412546\pi\) | ||||
0.271303 | + | 0.962494i | \(0.412546\pi\) | |||||||
\(920\) | −2859.69 | −0.102479 | ||||||||
\(921\) | 60223.9 | 2.15466 | ||||||||
\(922\) | −9580.52 | −0.342210 | ||||||||
\(923\) | −26755.3 | −0.954131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3844.25 | −0.136647 | ||||||||
\(926\) | 4690.80 | 0.166468 | ||||||||
\(927\) | 109324. | 3.87344 | ||||||||
\(928\) | −4110.74 | −0.145411 | ||||||||
\(929\) | 18602.8 | 0.656982 | 0.328491 | − | 0.944507i | \(-0.393460\pi\) | ||||
0.328491 | + | 0.944507i | \(0.393460\pi\) | |||||||
\(930\) | 7608.60 | 0.268275 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16123.1 | −0.566661 | ||||||||
\(933\) | −56623.4 | −1.98689 | ||||||||
\(934\) | −4787.12 | −0.167708 | ||||||||
\(935\) | −12878.7 | −0.450458 | ||||||||
\(936\) | −44240.6 | −1.54493 | ||||||||
\(937\) | −38612.0 | −1.34621 | −0.673106 | − | 0.739546i | \(-0.735040\pi\) | ||||
−0.673106 | + | 0.739546i | \(0.735040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15102.4 | 0.524864 | ||||||||
\(940\) | −8870.80 | −0.307802 | ||||||||
\(941\) | 13430.2 | 0.465263 | 0.232632 | − | 0.972565i | \(-0.425266\pi\) | ||||
0.232632 | + | 0.972565i | \(0.425266\pi\) | |||||||
\(942\) | −5576.08 | −0.192865 | ||||||||
\(943\) | −6135.39 | −0.211873 | ||||||||
\(944\) | 5104.23 | 0.175984 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15542.9 | 0.534191 | ||||||||
\(947\) | −55421.6 | −1.90175 | −0.950876 | − | 0.309573i | \(-0.899814\pi\) | ||||
−0.950876 | + | 0.309573i | \(0.899814\pi\) | |||||||
\(948\) | −6073.60 | −0.208081 | ||||||||
\(949\) | 24835.4 | 0.849517 | ||||||||
\(950\) | 2163.72 | 0.0738951 | ||||||||
\(951\) | −23520.8 | −0.802013 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4133.93 | −0.140515 | −0.0702577 | − | 0.997529i | \(-0.522382\pi\) | ||||
−0.0702577 | + | 0.997529i | \(0.522382\pi\) | |||||||
\(954\) | −25874.2 | −0.878102 | ||||||||
\(955\) | 3454.58 | 0.117055 | ||||||||
\(956\) | −14706.1 | −0.497519 | ||||||||
\(957\) | 13245.1 | 0.447390 | ||||||||
\(958\) | −3592.44 | −0.121155 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6396.11 | 0.215035 | ||||||||
\(961\) | 57071.3 | 1.91572 | ||||||||
\(962\) | 1751.32 | 0.0586952 | ||||||||
\(963\) | −36873.2 | −1.23388 | ||||||||
\(964\) | −5166.30 | −0.172609 | ||||||||
\(965\) | 5932.50 | 0.197900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34755.2 | 1.15579 | 0.577897 | − | 0.816110i | \(-0.303874\pi\) | ||||
0.577897 | + | 0.816110i | \(0.303874\pi\) | |||||||
\(968\) | 20879.1 | 0.693263 | ||||||||
\(969\) | 14494.7 | 0.480532 | ||||||||
\(970\) | 988.954 | 0.0327355 | ||||||||
\(971\) | 44827.8 | 1.48156 | 0.740780 | − | 0.671748i | \(-0.234456\pi\) | ||||
0.740780 | + | 0.671748i | \(0.234456\pi\) | |||||||
\(972\) | −5648.07 | −0.186381 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10802.5 | 0.355373 | ||||||||
\(975\) | 60664.1 | 1.99262 | ||||||||
\(976\) | 11621.4 | 0.381140 | ||||||||
\(977\) | 7189.43 | 0.235425 | 0.117712 | − | 0.993048i | \(-0.462444\pi\) | ||||
0.117712 | + | 0.993048i | \(0.462444\pi\) | |||||||
\(978\) | −26426.8 | −0.864046 | ||||||||
\(979\) | −31039.0 | −1.01329 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −72794.4 | −2.36916 | ||||||||
\(982\) | −8604.00 | −0.279597 | ||||||||
\(983\) | −4290.04 | −0.139197 | −0.0695987 | − | 0.997575i | \(-0.522172\pi\) | ||||
−0.0695987 | + | 0.997575i | \(0.522172\pi\) | |||||||
\(984\) | −11546.7 | −0.374082 | ||||||||
\(985\) | −16539.5 | −0.535016 | ||||||||
\(986\) | −1895.58 | −0.0612247 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8653.93 | 0.278662 | ||||||||
\(989\) | −21334.6 | −0.685946 | ||||||||
\(990\) | 8429.34 | 0.270608 | ||||||||
\(991\) | 55039.0 | 1.76425 | 0.882125 | − | 0.471015i | \(-0.156112\pi\) | ||||
0.882125 | + | 0.471015i | \(0.156112\pi\) | |||||||
\(992\) | −44381.2 | −1.42047 | ||||||||
\(993\) | −11952.6 | −0.381980 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −360.747 | −0.0114939 | ||||||||
\(996\) | −75354.6 | −2.39729 | ||||||||
\(997\) | 8768.33 | 0.278531 | 0.139266 | − | 0.990255i | \(-0.455526\pi\) | ||||
0.139266 | + | 0.990255i | \(0.455526\pi\) | |||||||
\(998\) | 3419.70 | 0.108466 | ||||||||
\(999\) | 8664.07 | 0.274393 |
(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 | 2401.4.a.d.1.18 | 39 | ||
7.6 | odd | 2 | 2401.4.a.c.1.18 | 39 | |||
49.8 | even | 7 | 49.4.e.a.15.8 | ✓ | 78 | ||
49.43 | even | 7 | 49.4.e.a.36.8 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.15.8 | ✓ | 78 | 49.8 | even | 7 | ||
49.4.e.a.36.8 | yes | 78 | 49.43 | even | 7 | ||
2401.4.a.c.1.18 | 39 | 7.6 | odd | 2 | |||
2401.4.a.d.1.18 | 39 | 1.1 | even | 1 | trivial |