Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80114 | −1.98071 | −0.990353 | − | 0.138567i | \(-0.955750\pi\) | ||||
−0.990353 | + | 0.138567i | \(0.955750\pi\) | |||||||
\(3\) | −3.24231 | −1.87195 | −0.935975 | − | 0.352065i | \(-0.885480\pi\) | ||||
−0.935975 | + | 0.352065i | \(0.885480\pi\) | |||||||
\(4\) | 5.84639 | 2.92320 | ||||||||
\(5\) | −0.362239 | −0.161998 | −0.0809992 | − | 0.996714i | \(-0.525811\pi\) | ||||
−0.0809992 | + | 0.996714i | \(0.525811\pi\) | |||||||
\(6\) | 9.08218 | 3.70778 | ||||||||
\(7\) | 0.683027 | 0.258160 | 0.129080 | − | 0.991634i | \(-0.458798\pi\) | ||||
0.129080 | + | 0.991634i | \(0.458798\pi\) | |||||||
\(8\) | −10.7743 | −3.80929 | ||||||||
\(9\) | 7.51260 | 2.50420 | ||||||||
\(10\) | 1.01468 | 0.320871 | ||||||||
\(11\) | −2.13162 | −0.642708 | −0.321354 | − | 0.946959i | \(-0.604138\pi\) | ||||
−0.321354 | + | 0.946959i | \(0.604138\pi\) | |||||||
\(12\) | −18.9558 | −5.47208 | ||||||||
\(13\) | −1.68516 | −0.467379 | −0.233690 | − | 0.972311i | \(-0.575080\pi\) | ||||
−0.233690 | + | 0.972311i | \(0.575080\pi\) | |||||||
\(14\) | −1.91326 | −0.511339 | ||||||||
\(15\) | 1.17449 | 0.303253 | ||||||||
\(16\) | 18.4875 | 4.62188 | ||||||||
\(17\) | −5.09163 | −1.23490 | −0.617450 | − | 0.786610i | \(-0.711834\pi\) | ||||
−0.617450 | + | 0.786610i | \(0.711834\pi\) | |||||||
\(18\) | −21.0439 | −4.96009 | ||||||||
\(19\) | −0.801920 | −0.183973 | −0.0919865 | − | 0.995760i | \(-0.529322\pi\) | ||||
−0.0919865 | + | 0.995760i | \(0.529322\pi\) | |||||||
\(20\) | −2.11779 | −0.473553 | ||||||||
\(21\) | −2.21459 | −0.483263 | ||||||||
\(22\) | 5.97097 | 1.27302 | ||||||||
\(23\) | −8.57971 | −1.78899 | −0.894497 | − | 0.447075i | \(-0.852466\pi\) | ||||
−0.894497 | + | 0.447075i | \(0.852466\pi\) | |||||||
\(24\) | 34.9336 | 7.13080 | ||||||||
\(25\) | −4.86878 | −0.973757 | ||||||||
\(26\) | 4.72037 | 0.925741 | ||||||||
\(27\) | −14.6313 | −2.81579 | ||||||||
\(28\) | 3.99325 | 0.754653 | ||||||||
\(29\) | −3.50963 | −0.651721 | −0.325861 | − | 0.945418i | \(-0.605654\pi\) | ||||
−0.325861 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(30\) | −3.28992 | −0.600655 | ||||||||
\(31\) | 1.80809 | 0.324743 | 0.162372 | − | 0.986730i | \(-0.448086\pi\) | ||||
0.162372 | + | 0.986730i | \(0.448086\pi\) | |||||||
\(32\) | −30.2376 | −5.34531 | ||||||||
\(33\) | 6.91138 | 1.20312 | ||||||||
\(34\) | 14.2624 | 2.44598 | ||||||||
\(35\) | −0.247419 | −0.0418215 | ||||||||
\(36\) | 43.9216 | 7.32027 | ||||||||
\(37\) | −5.00800 | −0.823310 | −0.411655 | − | 0.911340i | \(-0.635049\pi\) | ||||
−0.411655 | + | 0.911340i | \(0.635049\pi\) | |||||||
\(38\) | 2.24629 | 0.364396 | ||||||||
\(39\) | 5.46382 | 0.874911 | ||||||||
\(40\) | 3.90287 | 0.617098 | ||||||||
\(41\) | −9.31222 | −1.45432 | −0.727162 | − | 0.686465i | \(-0.759161\pi\) | ||||
−0.727162 | + | 0.686465i | \(0.759161\pi\) | |||||||
\(42\) | 6.20338 | 0.957202 | ||||||||
\(43\) | −7.60034 | −1.15904 | −0.579520 | − | 0.814958i | \(-0.696760\pi\) | ||||
−0.579520 | + | 0.814958i | \(0.696760\pi\) | |||||||
\(44\) | −12.4623 | −1.87876 | ||||||||
\(45\) | −2.72136 | −0.405676 | ||||||||
\(46\) | 24.0330 | 3.54347 | ||||||||
\(47\) | 1.24331 | 0.181356 | 0.0906780 | − | 0.995880i | \(-0.471097\pi\) | ||||
0.0906780 | + | 0.995880i | \(0.471097\pi\) | |||||||
\(48\) | −59.9424 | −8.65194 | ||||||||
\(49\) | −6.53347 | −0.933353 | ||||||||
\(50\) | 13.6381 | 1.92873 | ||||||||
\(51\) | 16.5087 | 2.31167 | ||||||||
\(52\) | −9.85210 | −1.36624 | ||||||||
\(53\) | 7.78403 | 1.06922 | 0.534609 | − | 0.845099i | \(-0.320459\pi\) | ||||
0.534609 | + | 0.845099i | \(0.320459\pi\) | |||||||
\(54\) | 40.9843 | 5.57725 | ||||||||
\(55\) | 0.772157 | 0.104118 | ||||||||
\(56\) | −7.35914 | −0.983406 | ||||||||
\(57\) | 2.60008 | 0.344388 | ||||||||
\(58\) | 9.83096 | 1.29087 | ||||||||
\(59\) | −1.98291 | −0.258153 | −0.129076 | − | 0.991635i | \(-0.541201\pi\) | ||||
−0.129076 | + | 0.991635i | \(0.541201\pi\) | |||||||
\(60\) | 6.86655 | 0.886468 | ||||||||
\(61\) | −3.99389 | −0.511366 | −0.255683 | − | 0.966761i | \(-0.582300\pi\) | ||||
−0.255683 | + | 0.966761i | \(0.582300\pi\) | |||||||
\(62\) | −5.06473 | −0.643221 | ||||||||
\(63\) | 5.13131 | 0.646484 | ||||||||
\(64\) | 47.7248 | 5.96560 | ||||||||
\(65\) | 0.610431 | 0.0757146 | ||||||||
\(66\) | −19.3598 | −2.38302 | ||||||||
\(67\) | 5.71728 | 0.698476 | 0.349238 | − | 0.937034i | \(-0.386440\pi\) | ||||
0.349238 | + | 0.937034i | \(0.386440\pi\) | |||||||
\(68\) | −29.7677 | −3.60986 | ||||||||
\(69\) | 27.8181 | 3.34891 | ||||||||
\(70\) | 0.693057 | 0.0828361 | ||||||||
\(71\) | 8.29768 | 0.984753 | 0.492377 | − | 0.870382i | \(-0.336128\pi\) | ||||
0.492377 | + | 0.870382i | \(0.336128\pi\) | |||||||
\(72\) | −80.9430 | −9.53922 | ||||||||
\(73\) | −1.66674 | −0.195077 | −0.0975385 | − | 0.995232i | \(-0.531097\pi\) | ||||
−0.0975385 | + | 0.995232i | \(0.531097\pi\) | |||||||
\(74\) | 14.0281 | 1.63074 | ||||||||
\(75\) | 15.7861 | 1.82282 | ||||||||
\(76\) | −4.68834 | −0.537789 | ||||||||
\(77\) | −1.45595 | −0.165921 | ||||||||
\(78\) | −15.3049 | −1.73294 | ||||||||
\(79\) | 1.42417 | 0.160232 | 0.0801160 | − | 0.996786i | \(-0.474471\pi\) | ||||
0.0801160 | + | 0.996786i | \(0.474471\pi\) | |||||||
\(80\) | −6.69691 | −0.748738 | ||||||||
\(81\) | 24.9014 | 2.76682 | ||||||||
\(82\) | 26.0849 | 2.88059 | ||||||||
\(83\) | −1.86129 | −0.204303 | −0.102152 | − | 0.994769i | \(-0.532573\pi\) | ||||
−0.102152 | + | 0.994769i | \(0.532573\pi\) | |||||||
\(84\) | −12.9474 | −1.41267 | ||||||||
\(85\) | 1.84439 | 0.200052 | ||||||||
\(86\) | 21.2896 | 2.29572 | ||||||||
\(87\) | 11.3793 | 1.21999 | ||||||||
\(88\) | 22.9667 | 2.44826 | ||||||||
\(89\) | −6.35369 | −0.673490 | −0.336745 | − | 0.941596i | \(-0.609326\pi\) | ||||
−0.336745 | + | 0.941596i | \(0.609326\pi\) | |||||||
\(90\) | 7.62291 | 0.803526 | ||||||||
\(91\) | −1.15101 | −0.120659 | ||||||||
\(92\) | −50.1604 | −5.22958 | ||||||||
\(93\) | −5.86241 | −0.607904 | ||||||||
\(94\) | −3.48270 | −0.359213 | ||||||||
\(95\) | 0.290487 | 0.0298033 | ||||||||
\(96\) | 98.0399 | 10.0062 | ||||||||
\(97\) | 10.6003 | 1.07630 | 0.538150 | − | 0.842849i | \(-0.319123\pi\) | ||||
0.538150 | + | 0.842849i | \(0.319123\pi\) | |||||||
\(98\) | 18.3012 | 1.84870 | ||||||||
\(99\) | −16.0140 | −1.60947 | ||||||||
\(100\) | −28.4648 | −2.84648 | ||||||||
\(101\) | −13.7583 | −1.36900 | −0.684500 | − | 0.729013i | \(-0.739980\pi\) | ||||
−0.684500 | + | 0.729013i | \(0.739980\pi\) | |||||||
\(102\) | −46.2431 | −4.57875 | ||||||||
\(103\) | 2.15900 | 0.212732 | 0.106366 | − | 0.994327i | \(-0.466078\pi\) | ||||
0.106366 | + | 0.994327i | \(0.466078\pi\) | |||||||
\(104\) | 18.1564 | 1.78038 | ||||||||
\(105\) | 0.802211 | 0.0782878 | ||||||||
\(106\) | −21.8042 | −2.11781 | ||||||||
\(107\) | −8.78706 | −0.849477 | −0.424738 | − | 0.905316i | \(-0.639634\pi\) | ||||
−0.424738 | + | 0.905316i | \(0.639634\pi\) | |||||||
\(108\) | −85.5402 | −8.23111 | ||||||||
\(109\) | −15.6529 | −1.49928 | −0.749638 | − | 0.661848i | \(-0.769772\pi\) | ||||
−0.749638 | + | 0.661848i | \(0.769772\pi\) | |||||||
\(110\) | −2.16292 | −0.206226 | ||||||||
\(111\) | 16.2375 | 1.54120 | ||||||||
\(112\) | 12.6275 | 1.19319 | ||||||||
\(113\) | −8.99890 | −0.846545 | −0.423273 | − | 0.906002i | \(-0.639119\pi\) | ||||
−0.423273 | + | 0.906002i | \(0.639119\pi\) | |||||||
\(114\) | −7.28318 | −0.682132 | ||||||||
\(115\) | 3.10791 | 0.289814 | ||||||||
\(116\) | −20.5187 | −1.90511 | ||||||||
\(117\) | −12.6599 | −1.17041 | ||||||||
\(118\) | 5.55441 | 0.511324 | ||||||||
\(119\) | −3.47772 | −0.318802 | ||||||||
\(120\) | −12.6543 | −1.15518 | ||||||||
\(121\) | −6.45619 | −0.586927 | ||||||||
\(122\) | 11.1875 | 1.01287 | ||||||||
\(123\) | 30.1931 | 2.72242 | ||||||||
\(124\) | 10.5708 | 0.949289 | ||||||||
\(125\) | 3.57486 | 0.319745 | ||||||||
\(126\) | −14.3735 | −1.28050 | ||||||||
\(127\) | 13.3030 | 1.18045 | 0.590227 | − | 0.807237i | \(-0.299038\pi\) | ||||
0.590227 | + | 0.807237i | \(0.299038\pi\) | |||||||
\(128\) | −73.2086 | −6.47079 | ||||||||
\(129\) | 24.6427 | 2.16967 | ||||||||
\(130\) | −1.70990 | −0.149968 | ||||||||
\(131\) | −2.62380 | −0.229242 | −0.114621 | − | 0.993409i | \(-0.536565\pi\) | ||||
−0.114621 | + | 0.993409i | \(0.536565\pi\) | |||||||
\(132\) | 40.4067 | 3.51695 | ||||||||
\(133\) | −0.547733 | −0.0474945 | ||||||||
\(134\) | −16.0149 | −1.38348 | ||||||||
\(135\) | 5.30002 | 0.456153 | ||||||||
\(136\) | 54.8587 | 4.70409 | ||||||||
\(137\) | 5.48350 | 0.468487 | 0.234244 | − | 0.972178i | \(-0.424739\pi\) | ||||
0.234244 | + | 0.972178i | \(0.424739\pi\) | |||||||
\(138\) | −77.9225 | −6.63320 | ||||||||
\(139\) | −20.8221 | −1.76611 | −0.883055 | − | 0.469269i | \(-0.844518\pi\) | ||||
−0.883055 | + | 0.469269i | \(0.844518\pi\) | |||||||
\(140\) | −1.44651 | −0.122252 | ||||||||
\(141\) | −4.03122 | −0.339490 | ||||||||
\(142\) | −23.2430 | −1.95051 | ||||||||
\(143\) | 3.59212 | 0.300388 | ||||||||
\(144\) | 138.889 | 11.5741 | ||||||||
\(145\) | 1.27132 | 0.105578 | ||||||||
\(146\) | 4.66877 | 0.386390 | ||||||||
\(147\) | 21.1836 | 1.74719 | ||||||||
\(148\) | −29.2788 | −2.40670 | ||||||||
\(149\) | −13.3985 | −1.09765 | −0.548826 | − | 0.835937i | \(-0.684925\pi\) | ||||
−0.548826 | + | 0.835937i | \(0.684925\pi\) | |||||||
\(150\) | −44.2192 | −3.61048 | ||||||||
\(151\) | −14.7845 | −1.20315 | −0.601573 | − | 0.798818i | \(-0.705459\pi\) | ||||
−0.601573 | + | 0.798818i | \(0.705459\pi\) | |||||||
\(152\) | 8.64012 | 0.700806 | ||||||||
\(153\) | −38.2514 | −3.09244 | ||||||||
\(154\) | 4.07834 | 0.328642 | ||||||||
\(155\) | −0.654963 | −0.0526079 | ||||||||
\(156\) | 31.9436 | 2.55754 | ||||||||
\(157\) | −13.8881 | −1.10839 | −0.554195 | − | 0.832387i | \(-0.686974\pi\) | ||||
−0.554195 | + | 0.832387i | \(0.686974\pi\) | |||||||
\(158\) | −3.98931 | −0.317373 | ||||||||
\(159\) | −25.2383 | −2.00152 | ||||||||
\(160\) | 10.9533 | 0.865931 | ||||||||
\(161\) | −5.86018 | −0.461847 | ||||||||
\(162\) | −69.7523 | −5.48026 | ||||||||
\(163\) | 7.74695 | 0.606788 | 0.303394 | − | 0.952865i | \(-0.401880\pi\) | ||||
0.303394 | + | 0.952865i | \(0.401880\pi\) | |||||||
\(164\) | −54.4429 | −4.25128 | ||||||||
\(165\) | −2.50357 | −0.194903 | ||||||||
\(166\) | 5.21373 | 0.404664 | ||||||||
\(167\) | 13.7092 | 1.06085 | 0.530424 | − | 0.847732i | \(-0.322033\pi\) | ||||
0.530424 | + | 0.847732i | \(0.322033\pi\) | |||||||
\(168\) | 23.8606 | 1.84089 | ||||||||
\(169\) | −10.1602 | −0.781557 | ||||||||
\(170\) | −5.16639 | −0.396244 | ||||||||
\(171\) | −6.02450 | −0.460705 | ||||||||
\(172\) | −44.4346 | −3.38810 | ||||||||
\(173\) | 19.1159 | 1.45335 | 0.726677 | − | 0.686979i | \(-0.241064\pi\) | ||||
0.726677 | + | 0.686979i | \(0.241064\pi\) | |||||||
\(174\) | −31.8751 | −2.41644 | ||||||||
\(175\) | −3.32551 | −0.251385 | ||||||||
\(176\) | −39.4084 | −2.97052 | ||||||||
\(177\) | 6.42921 | 0.483249 | ||||||||
\(178\) | 17.7976 | 1.33399 | ||||||||
\(179\) | 16.0029 | 1.19611 | 0.598055 | − | 0.801455i | \(-0.295940\pi\) | ||||
0.598055 | + | 0.801455i | \(0.295940\pi\) | |||||||
\(180\) | −15.9101 | −1.18587 | ||||||||
\(181\) | 6.21687 | 0.462096 | 0.231048 | − | 0.972942i | \(-0.425785\pi\) | ||||
0.231048 | + | 0.972942i | \(0.425785\pi\) | |||||||
\(182\) | 3.22414 | 0.238989 | ||||||||
\(183\) | 12.9495 | 0.957251 | ||||||||
\(184\) | 92.4403 | 6.81479 | ||||||||
\(185\) | 1.81410 | 0.133375 | ||||||||
\(186\) | 16.4214 | 1.20408 | ||||||||
\(187\) | 10.8534 | 0.793680 | ||||||||
\(188\) | 7.26891 | 0.530140 | ||||||||
\(189\) | −9.99356 | −0.726924 | ||||||||
\(190\) | −0.813695 | −0.0590316 | ||||||||
\(191\) | −16.3139 | −1.18043 | −0.590215 | − | 0.807246i | \(-0.700957\pi\) | ||||
−0.590215 | + | 0.807246i | \(0.700957\pi\) | |||||||
\(192\) | −154.739 | −11.1673 | ||||||||
\(193\) | −0.312001 | −0.0224583 | −0.0112291 | − | 0.999937i | \(-0.503574\pi\) | ||||
−0.0112291 | + | 0.999937i | \(0.503574\pi\) | |||||||
\(194\) | −29.6930 | −2.13183 | ||||||||
\(195\) | −1.97921 | −0.141734 | ||||||||
\(196\) | −38.1973 | −2.72838 | ||||||||
\(197\) | −19.5223 | −1.39091 | −0.695453 | − | 0.718571i | \(-0.744796\pi\) | ||||
−0.695453 | + | 0.718571i | \(0.744796\pi\) | |||||||
\(198\) | 44.8575 | 3.18789 | ||||||||
\(199\) | 16.3357 | 1.15801 | 0.579003 | − | 0.815326i | \(-0.303442\pi\) | ||||
0.579003 | + | 0.815326i | \(0.303442\pi\) | |||||||
\(200\) | 52.4577 | 3.70932 | ||||||||
\(201\) | −18.5372 | −1.30751 | ||||||||
\(202\) | 38.5389 | 2.71159 | ||||||||
\(203\) | −2.39717 | −0.168248 | ||||||||
\(204\) | 96.5161 | 6.75748 | ||||||||
\(205\) | 3.37325 | 0.235598 | ||||||||
\(206\) | −6.04766 | −0.421360 | ||||||||
\(207\) | −64.4559 | −4.48000 | ||||||||
\(208\) | −31.1544 | −2.16017 | ||||||||
\(209\) | 1.70939 | 0.118241 | ||||||||
\(210\) | −2.24711 | −0.155065 | ||||||||
\(211\) | −25.7810 | −1.77484 | −0.887418 | − | 0.460966i | \(-0.847503\pi\) | ||||
−0.887418 | + | 0.460966i | \(0.847503\pi\) | |||||||
\(212\) | 45.5085 | 3.12554 | ||||||||
\(213\) | −26.9037 | −1.84341 | ||||||||
\(214\) | 24.6138 | 1.68256 | ||||||||
\(215\) | 2.75314 | 0.187763 | ||||||||
\(216\) | 157.642 | 10.7262 | ||||||||
\(217\) | 1.23498 | 0.0838358 | ||||||||
\(218\) | 43.8460 | 2.96962 | ||||||||
\(219\) | 5.40409 | 0.365175 | ||||||||
\(220\) | 4.51433 | 0.304356 | ||||||||
\(221\) | 8.58020 | 0.577167 | ||||||||
\(222\) | −45.4836 | −3.05266 | ||||||||
\(223\) | −1.23190 | −0.0824938 | −0.0412469 | − | 0.999149i | \(-0.513133\pi\) | ||||
−0.0412469 | + | 0.999149i | \(0.513133\pi\) | |||||||
\(224\) | −20.6531 | −1.37994 | ||||||||
\(225\) | −36.5772 | −2.43848 | ||||||||
\(226\) | 25.2072 | 1.67676 | ||||||||
\(227\) | −4.81199 | −0.319383 | −0.159692 | − | 0.987167i | \(-0.551050\pi\) | ||||
−0.159692 | + | 0.987167i | \(0.551050\pi\) | |||||||
\(228\) | 15.2011 | 1.00672 | ||||||||
\(229\) | −22.2208 | −1.46839 | −0.734195 | − | 0.678938i | \(-0.762440\pi\) | ||||
−0.734195 | + | 0.678938i | \(0.762440\pi\) | |||||||
\(230\) | −8.70569 | −0.574036 | ||||||||
\(231\) | 4.72066 | 0.310597 | ||||||||
\(232\) | 37.8138 | 2.48259 | ||||||||
\(233\) | −12.3169 | −0.806910 | −0.403455 | − | 0.914999i | \(-0.632191\pi\) | ||||
−0.403455 | + | 0.914999i | \(0.632191\pi\) | |||||||
\(234\) | 35.4623 | 2.31824 | ||||||||
\(235\) | −0.450378 | −0.0293794 | ||||||||
\(236\) | −11.5929 | −0.754631 | ||||||||
\(237\) | −4.61762 | −0.299946 | ||||||||
\(238\) | 9.74158 | 0.631453 | ||||||||
\(239\) | 6.39467 | 0.413637 | 0.206818 | − | 0.978379i | \(-0.433689\pi\) | ||||
0.206818 | + | 0.978379i | \(0.433689\pi\) | |||||||
\(240\) | 21.7135 | 1.40160 | ||||||||
\(241\) | 16.5963 | 1.06906 | 0.534531 | − | 0.845149i | \(-0.320488\pi\) | ||||
0.534531 | + | 0.845149i | \(0.320488\pi\) | |||||||
\(242\) | 18.0847 | 1.16253 | ||||||||
\(243\) | −36.8443 | −2.36356 | ||||||||
\(244\) | −23.3499 | −1.49482 | ||||||||
\(245\) | 2.36668 | 0.151202 | ||||||||
\(246\) | −84.5753 | −5.39232 | ||||||||
\(247\) | 1.35136 | 0.0859851 | ||||||||
\(248\) | −19.4809 | −1.23704 | ||||||||
\(249\) | 6.03488 | 0.382445 | ||||||||
\(250\) | −10.0137 | −0.633322 | ||||||||
\(251\) | 3.92502 | 0.247745 | 0.123873 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123873 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(252\) | 29.9997 | 1.88980 | ||||||||
\(253\) | 18.2887 | 1.14980 | ||||||||
\(254\) | −37.2637 | −2.33813 | ||||||||
\(255\) | −5.98008 | −0.374487 | ||||||||
\(256\) | 109.618 | 6.85113 | ||||||||
\(257\) | −29.1741 | −1.81983 | −0.909916 | − | 0.414792i | \(-0.863854\pi\) | ||||
−0.909916 | + | 0.414792i | \(0.863854\pi\) | |||||||
\(258\) | −69.0276 | −4.29747 | ||||||||
\(259\) | −3.42060 | −0.212546 | ||||||||
\(260\) | 3.56882 | 0.221329 | ||||||||
\(261\) | −26.3664 | −1.63204 | ||||||||
\(262\) | 7.34962 | 0.454061 | ||||||||
\(263\) | −15.1007 | −0.931152 | −0.465576 | − | 0.885008i | \(-0.654153\pi\) | ||||
−0.465576 | + | 0.885008i | \(0.654153\pi\) | |||||||
\(264\) | −74.4653 | −4.58302 | ||||||||
\(265\) | −2.81968 | −0.173212 | ||||||||
\(266\) | 1.53428 | 0.0940726 | ||||||||
\(267\) | 20.6007 | 1.26074 | ||||||||
\(268\) | 33.4254 | 2.04178 | ||||||||
\(269\) | 21.7530 | 1.32631 | 0.663153 | − | 0.748484i | \(-0.269218\pi\) | ||||
0.663153 | + | 0.748484i | \(0.269218\pi\) | |||||||
\(270\) | −14.8461 | −0.903506 | ||||||||
\(271\) | −22.4406 | −1.36317 | −0.681583 | − | 0.731741i | \(-0.738708\pi\) | ||||
−0.681583 | + | 0.731741i | \(0.738708\pi\) | |||||||
\(272\) | −94.1316 | −5.70757 | ||||||||
\(273\) | 3.73193 | 0.225867 | ||||||||
\(274\) | −15.3601 | −0.927936 | ||||||||
\(275\) | 10.3784 | 0.625841 | ||||||||
\(276\) | 162.636 | 9.78952 | ||||||||
\(277\) | −22.3480 | −1.34276 | −0.671382 | − | 0.741112i | \(-0.734299\pi\) | ||||
−0.671382 | + | 0.741112i | \(0.734299\pi\) | |||||||
\(278\) | 58.3258 | 3.49815 | ||||||||
\(279\) | 13.5835 | 0.813222 | ||||||||
\(280\) | 2.66577 | 0.159310 | ||||||||
\(281\) | 30.8208 | 1.83861 | 0.919307 | − | 0.393542i | \(-0.128750\pi\) | ||||
0.919307 | + | 0.393542i | \(0.128750\pi\) | |||||||
\(282\) | 11.2920 | 0.672429 | ||||||||
\(283\) | 17.7865 | 1.05730 | 0.528649 | − | 0.848841i | \(-0.322699\pi\) | ||||
0.528649 | + | 0.848841i | \(0.322699\pi\) | |||||||
\(284\) | 48.5115 | 2.87863 | ||||||||
\(285\) | −0.941849 | −0.0557903 | ||||||||
\(286\) | −10.0620 | −0.594981 | ||||||||
\(287\) | −6.36050 | −0.375449 | ||||||||
\(288\) | −227.163 | −13.3857 | ||||||||
\(289\) | 8.92466 | 0.524980 | ||||||||
\(290\) | −3.56116 | −0.209119 | ||||||||
\(291\) | −34.3696 | −2.01478 | ||||||||
\(292\) | −9.74441 | −0.570249 | ||||||||
\(293\) | −21.5171 | −1.25704 | −0.628522 | − | 0.777792i | \(-0.716340\pi\) | ||||
−0.628522 | + | 0.777792i | \(0.716340\pi\) | |||||||
\(294\) | −59.3382 | −3.46067 | ||||||||
\(295\) | 0.718287 | 0.0418203 | ||||||||
\(296\) | 53.9577 | 3.13623 | ||||||||
\(297\) | 31.1883 | 1.80973 | ||||||||
\(298\) | 37.5312 | 2.17413 | ||||||||
\(299\) | 14.4582 | 0.836138 | ||||||||
\(300\) | 92.2919 | 5.32848 | ||||||||
\(301\) | −5.19124 | −0.299218 | ||||||||
\(302\) | 41.4135 | 2.38308 | ||||||||
\(303\) | 44.6087 | 2.56270 | ||||||||
\(304\) | −14.8255 | −0.850302 | ||||||||
\(305\) | 1.44675 | 0.0828404 | ||||||||
\(306\) | 107.147 | 6.12521 | ||||||||
\(307\) | −20.6707 | −1.17974 | −0.589869 | − | 0.807499i | \(-0.700821\pi\) | ||||
−0.589869 | + | 0.807499i | \(0.700821\pi\) | |||||||
\(308\) | −8.51209 | −0.485021 | ||||||||
\(309\) | −7.00015 | −0.398225 | ||||||||
\(310\) | 1.83464 | 0.104201 | ||||||||
\(311\) | 4.80834 | 0.272656 | 0.136328 | − | 0.990664i | \(-0.456470\pi\) | ||||
0.136328 | + | 0.990664i | \(0.456470\pi\) | |||||||
\(312\) | −58.8688 | −3.33279 | ||||||||
\(313\) | 13.7358 | 0.776396 | 0.388198 | − | 0.921576i | \(-0.373098\pi\) | ||||
0.388198 | + | 0.921576i | \(0.373098\pi\) | |||||||
\(314\) | 38.9025 | 2.19539 | ||||||||
\(315\) | −1.85876 | −0.104729 | ||||||||
\(316\) | 8.32628 | 0.468390 | ||||||||
\(317\) | 2.59886 | 0.145966 | 0.0729832 | − | 0.997333i | \(-0.476748\pi\) | ||||
0.0729832 | + | 0.997333i | \(0.476748\pi\) | |||||||
\(318\) | 70.6959 | 3.96443 | ||||||||
\(319\) | 7.48119 | 0.418866 | ||||||||
\(320\) | −17.2878 | −0.966417 | ||||||||
\(321\) | 28.4904 | 1.59018 | ||||||||
\(322\) | 16.4152 | 0.914782 | ||||||||
\(323\) | 4.08307 | 0.227188 | ||||||||
\(324\) | 145.583 | 8.08796 | ||||||||
\(325\) | 8.20467 | 0.455113 | ||||||||
\(326\) | −21.7003 | −1.20187 | ||||||||
\(327\) | 50.7516 | 2.80657 | ||||||||
\(328\) | 100.333 | 5.53994 | ||||||||
\(329\) | 0.849218 | 0.0468189 | ||||||||
\(330\) | 7.01287 | 0.386046 | ||||||||
\(331\) | 16.5472 | 0.909516 | 0.454758 | − | 0.890615i | \(-0.349726\pi\) | ||||
0.454758 | + | 0.890615i | \(0.349726\pi\) | |||||||
\(332\) | −10.8818 | −0.597218 | ||||||||
\(333\) | −37.6231 | −2.06173 | ||||||||
\(334\) | −38.4014 | −2.10123 | ||||||||
\(335\) | −2.07102 | −0.113152 | ||||||||
\(336\) | −40.9423 | −2.23359 | ||||||||
\(337\) | 30.7087 | 1.67281 | 0.836405 | − | 0.548112i | \(-0.184653\pi\) | ||||
0.836405 | + | 0.548112i | \(0.184653\pi\) | |||||||
\(338\) | 28.4603 | 1.54803 | ||||||||
\(339\) | 29.1773 | 1.58469 | ||||||||
\(340\) | 10.7830 | 0.584791 | ||||||||
\(341\) | −3.85417 | −0.208715 | ||||||||
\(342\) | 16.8755 | 0.912522 | ||||||||
\(343\) | −9.24373 | −0.499115 | ||||||||
\(344\) | 81.8883 | 4.41512 | ||||||||
\(345\) | −10.0768 | −0.542518 | ||||||||
\(346\) | −53.5463 | −2.87867 | ||||||||
\(347\) | 30.0224 | 1.61169 | 0.805843 | − | 0.592129i | \(-0.201712\pi\) | ||||
0.805843 | + | 0.592129i | \(0.201712\pi\) | |||||||
\(348\) | 66.5279 | 3.56627 | ||||||||
\(349\) | 15.6654 | 0.838550 | 0.419275 | − | 0.907859i | \(-0.362284\pi\) | ||||
0.419275 | + | 0.907859i | \(0.362284\pi\) | |||||||
\(350\) | 9.31523 | 0.497920 | ||||||||
\(351\) | 24.6560 | 1.31604 | ||||||||
\(352\) | 64.4551 | 3.43547 | ||||||||
\(353\) | 5.19326 | 0.276409 | 0.138205 | − | 0.990404i | \(-0.455867\pi\) | ||||
0.138205 | + | 0.990404i | \(0.455867\pi\) | |||||||
\(354\) | −18.0091 | −0.957174 | ||||||||
\(355\) | −3.00574 | −0.159528 | ||||||||
\(356\) | −37.1462 | −1.96874 | ||||||||
\(357\) | 11.2759 | 0.596782 | ||||||||
\(358\) | −44.8263 | −2.36914 | ||||||||
\(359\) | 14.1782 | 0.748297 | 0.374148 | − | 0.927369i | \(-0.377935\pi\) | ||||
0.374148 | + | 0.927369i | \(0.377935\pi\) | |||||||
\(360\) | 29.3207 | 1.54534 | ||||||||
\(361\) | −18.3569 | −0.966154 | ||||||||
\(362\) | −17.4143 | −0.915276 | ||||||||
\(363\) | 20.9330 | 1.09870 | ||||||||
\(364\) | −6.72926 | −0.352709 | ||||||||
\(365\) | 0.603758 | 0.0316022 | ||||||||
\(366\) | −36.2733 | −1.89603 | ||||||||
\(367\) | 36.4637 | 1.90339 | 0.951696 | − | 0.307043i | \(-0.0993396\pi\) | ||||
0.951696 | + | 0.307043i | \(0.0993396\pi\) | |||||||
\(368\) | −158.618 | −8.26852 | ||||||||
\(369\) | −69.9590 | −3.64192 | ||||||||
\(370\) | −5.08154 | −0.264177 | ||||||||
\(371\) | 5.31670 | 0.276029 | ||||||||
\(372\) | −34.2740 | −1.77702 | ||||||||
\(373\) | 7.99296 | 0.413860 | 0.206930 | − | 0.978356i | \(-0.433653\pi\) | ||||
0.206930 | + | 0.978356i | \(0.433653\pi\) | |||||||
\(374\) | −30.4019 | −1.57205 | ||||||||
\(375\) | −11.5908 | −0.598548 | ||||||||
\(376\) | −13.3958 | −0.690838 | ||||||||
\(377\) | 5.91428 | 0.304601 | ||||||||
\(378\) | 27.9934 | 1.43982 | ||||||||
\(379\) | −24.3021 | −1.24832 | −0.624158 | − | 0.781298i | \(-0.714558\pi\) | ||||
−0.624158 | + | 0.781298i | \(0.714558\pi\) | |||||||
\(380\) | 1.69830 | 0.0871210 | ||||||||
\(381\) | −43.1326 | −2.20975 | ||||||||
\(382\) | 45.6975 | 2.33809 | ||||||||
\(383\) | −10.8819 | −0.556038 | −0.278019 | − | 0.960576i | \(-0.589678\pi\) | ||||
−0.278019 | + | 0.960576i | \(0.589678\pi\) | |||||||
\(384\) | 237.365 | 12.1130 | ||||||||
\(385\) | 0.527404 | 0.0268790 | ||||||||
\(386\) | 0.873958 | 0.0444833 | ||||||||
\(387\) | −57.0983 | −2.90247 | ||||||||
\(388\) | 61.9737 | 3.14624 | ||||||||
\(389\) | −38.8963 | −1.97212 | −0.986061 | − | 0.166387i | \(-0.946790\pi\) | ||||
−0.986061 | + | 0.166387i | \(0.946790\pi\) | |||||||
\(390\) | 5.54404 | 0.280734 | ||||||||
\(391\) | 43.6847 | 2.20923 | ||||||||
\(392\) | 70.3936 | 3.55541 | ||||||||
\(393\) | 8.50717 | 0.429130 | ||||||||
\(394\) | 54.6847 | 2.75498 | ||||||||
\(395\) | −0.515892 | −0.0259573 | ||||||||
\(396\) | −93.6242 | −4.70480 | ||||||||
\(397\) | −27.3289 | −1.37160 | −0.685800 | − | 0.727790i | \(-0.740547\pi\) | ||||
−0.685800 | + | 0.727790i | \(0.740547\pi\) | |||||||
\(398\) | −45.7585 | −2.29367 | ||||||||
\(399\) | 1.77592 | 0.0889073 | ||||||||
\(400\) | −90.0118 | −4.50059 | ||||||||
\(401\) | 18.3083 | 0.914272 | 0.457136 | − | 0.889397i | \(-0.348875\pi\) | ||||
0.457136 | + | 0.889397i | \(0.348875\pi\) | |||||||
\(402\) | 51.9253 | 2.58980 | ||||||||
\(403\) | −3.04693 | −0.151778 | ||||||||
\(404\) | −80.4364 | −4.00186 | ||||||||
\(405\) | −9.02026 | −0.448220 | ||||||||
\(406\) | 6.71481 | 0.333251 | ||||||||
\(407\) | 10.6752 | 0.529148 | ||||||||
\(408\) | −177.869 | −8.80583 | ||||||||
\(409\) | −2.75652 | −0.136301 | −0.0681505 | − | 0.997675i | \(-0.521710\pi\) | ||||
−0.0681505 | + | 0.997675i | \(0.521710\pi\) | |||||||
\(410\) | −9.44896 | −0.466651 | ||||||||
\(411\) | −17.7792 | −0.876985 | ||||||||
\(412\) | 12.6224 | 0.621859 | ||||||||
\(413\) | −1.35438 | −0.0666447 | ||||||||
\(414\) | 180.550 | 8.87356 | ||||||||
\(415\) | 0.674232 | 0.0330968 | ||||||||
\(416\) | 50.9552 | 2.49828 | ||||||||
\(417\) | 67.5119 | 3.30607 | ||||||||
\(418\) | −4.78824 | −0.234200 | ||||||||
\(419\) | 35.9064 | 1.75414 | 0.877071 | − | 0.480360i | \(-0.159494\pi\) | ||||
0.877071 | + | 0.480360i | \(0.159494\pi\) | |||||||
\(420\) | 4.69004 | 0.228851 | ||||||||
\(421\) | −30.0350 | −1.46382 | −0.731908 | − | 0.681403i | \(-0.761370\pi\) | ||||
−0.731908 | + | 0.681403i | \(0.761370\pi\) | |||||||
\(422\) | 72.2162 | 3.51543 | ||||||||
\(423\) | 9.34053 | 0.454152 | ||||||||
\(424\) | −83.8674 | −4.07296 | ||||||||
\(425\) | 24.7900 | 1.20249 | ||||||||
\(426\) | 75.3610 | 3.65125 | ||||||||
\(427\) | −2.72794 | −0.132014 | ||||||||
\(428\) | −51.3726 | −2.48319 | ||||||||
\(429\) | −11.6468 | −0.562312 | ||||||||
\(430\) | −7.71194 | −0.371903 | ||||||||
\(431\) | −25.4638 | −1.22655 | −0.613273 | − | 0.789871i | \(-0.710148\pi\) | ||||
−0.613273 | + | 0.789871i | \(0.710148\pi\) | |||||||
\(432\) | −270.496 | −13.0143 | ||||||||
\(433\) | −15.6738 | −0.753233 | −0.376616 | − | 0.926369i | \(-0.622913\pi\) | ||||
−0.376616 | + | 0.926369i | \(0.622913\pi\) | |||||||
\(434\) | −3.45935 | −0.166054 | ||||||||
\(435\) | −4.12203 | −0.197636 | ||||||||
\(436\) | −91.5130 | −4.38268 | ||||||||
\(437\) | 6.88024 | 0.329126 | ||||||||
\(438\) | −15.1376 | −0.723304 | ||||||||
\(439\) | 1.10537 | 0.0527567 | 0.0263783 | − | 0.999652i | \(-0.491603\pi\) | ||||
0.0263783 | + | 0.999652i | \(0.491603\pi\) | |||||||
\(440\) | −8.31944 | −0.396614 | ||||||||
\(441\) | −49.0834 | −2.33730 | ||||||||
\(442\) | −24.0344 | −1.14320 | ||||||||
\(443\) | −26.2214 | −1.24581 | −0.622907 | − | 0.782296i | \(-0.714049\pi\) | ||||
−0.622907 | + | 0.782296i | \(0.714049\pi\) | |||||||
\(444\) | 94.9309 | 4.50522 | ||||||||
\(445\) | 2.30156 | 0.109104 | ||||||||
\(446\) | 3.45071 | 0.163396 | ||||||||
\(447\) | 43.4423 | 2.05475 | ||||||||
\(448\) | 32.5973 | 1.54008 | ||||||||
\(449\) | 6.25150 | 0.295027 | 0.147513 | − | 0.989060i | \(-0.452873\pi\) | ||||
0.147513 | + | 0.989060i | \(0.452873\pi\) | |||||||
\(450\) | 102.458 | 4.82992 | ||||||||
\(451\) | 19.8501 | 0.934706 | ||||||||
\(452\) | −52.6111 | −2.47462 | ||||||||
\(453\) | 47.9360 | 2.25223 | ||||||||
\(454\) | 13.4791 | 0.632604 | ||||||||
\(455\) | 0.416941 | 0.0195465 | ||||||||
\(456\) | −28.0140 | −1.31187 | ||||||||
\(457\) | 26.6932 | 1.24866 | 0.624328 | − | 0.781163i | \(-0.285373\pi\) | ||||
0.624328 | + | 0.781163i | \(0.285373\pi\) | |||||||
\(458\) | 62.2436 | 2.90845 | ||||||||
\(459\) | 74.4970 | 3.47722 | ||||||||
\(460\) | 18.1701 | 0.847183 | ||||||||
\(461\) | 16.2849 | 0.758464 | 0.379232 | − | 0.925302i | \(-0.376188\pi\) | ||||
0.379232 | + | 0.925302i | \(0.376188\pi\) | |||||||
\(462\) | −13.2232 | −0.615201 | ||||||||
\(463\) | −0.447975 | −0.0208191 | −0.0104096 | − | 0.999946i | \(-0.503314\pi\) | ||||
−0.0104096 | + | 0.999946i | \(0.503314\pi\) | |||||||
\(464\) | −64.8844 | −3.01218 | ||||||||
\(465\) | 2.12360 | 0.0984794 | ||||||||
\(466\) | 34.5015 | 1.59825 | ||||||||
\(467\) | 27.7029 | 1.28194 | 0.640970 | − | 0.767566i | \(-0.278532\pi\) | ||||
0.640970 | + | 0.767566i | \(0.278532\pi\) | |||||||
\(468\) | −74.0149 | −3.42134 | ||||||||
\(469\) | 3.90505 | 0.180319 | ||||||||
\(470\) | 1.26157 | 0.0581919 | ||||||||
\(471\) | 45.0295 | 2.07485 | ||||||||
\(472\) | 21.3644 | 0.983378 | ||||||||
\(473\) | 16.2010 | 0.744924 | ||||||||
\(474\) | 12.9346 | 0.594106 | ||||||||
\(475\) | 3.90437 | 0.179145 | ||||||||
\(476\) | −20.3321 | −0.931921 | ||||||||
\(477\) | 58.4783 | 2.67754 | ||||||||
\(478\) | −17.9124 | −0.819293 | ||||||||
\(479\) | 25.3320 | 1.15745 | 0.578725 | − | 0.815523i | \(-0.303550\pi\) | ||||
0.578725 | + | 0.815523i | \(0.303550\pi\) | |||||||
\(480\) | −35.5139 | −1.62098 | ||||||||
\(481\) | 8.43928 | 0.384798 | ||||||||
\(482\) | −46.4886 | −2.11750 | ||||||||
\(483\) | 19.0005 | 0.864554 | ||||||||
\(484\) | −37.7455 | −1.71570 | ||||||||
\(485\) | −3.83986 | −0.174359 | ||||||||
\(486\) | 103.206 | 4.68152 | ||||||||
\(487\) | −36.4431 | −1.65139 | −0.825697 | − | 0.564113i | \(-0.809218\pi\) | ||||
−0.825697 | + | 0.564113i | \(0.809218\pi\) | |||||||
\(488\) | 43.0314 | 1.94794 | ||||||||
\(489\) | −25.1181 | −1.13588 | ||||||||
\(490\) | −6.62941 | −0.299486 | ||||||||
\(491\) | −21.3805 | −0.964887 | −0.482443 | − | 0.875927i | \(-0.660251\pi\) | ||||
−0.482443 | + | 0.875927i | \(0.660251\pi\) | |||||||
\(492\) | 176.521 | 7.95818 | ||||||||
\(493\) | 17.8697 | 0.804811 | ||||||||
\(494\) | −3.78536 | −0.170311 | ||||||||
\(495\) | 5.80091 | 0.260731 | ||||||||
\(496\) | 33.4272 | 1.50093 | ||||||||
\(497\) | 5.66754 | 0.254224 | ||||||||
\(498\) | −16.9046 | −0.757512 | ||||||||
\(499\) | 7.43051 | 0.332635 | 0.166318 | − | 0.986072i | \(-0.446812\pi\) | ||||
0.166318 | + | 0.986072i | \(0.446812\pi\) | |||||||
\(500\) | 20.9000 | 0.934679 | ||||||||
\(501\) | −44.4495 | −1.98586 | ||||||||
\(502\) | −10.9945 | −0.490710 | ||||||||
\(503\) | 12.0516 | 0.537355 | 0.268677 | − | 0.963230i | \(-0.413413\pi\) | ||||
0.268677 | + | 0.963230i | \(0.413413\pi\) | |||||||
\(504\) | −55.2863 | −2.46265 | ||||||||
\(505\) | 4.98379 | 0.221776 | ||||||||
\(506\) | −51.2292 | −2.27742 | ||||||||
\(507\) | 32.9427 | 1.46304 | ||||||||
\(508\) | 77.7748 | 3.45070 | ||||||||
\(509\) | 18.4659 | 0.818488 | 0.409244 | − | 0.912425i | \(-0.365792\pi\) | ||||
0.409244 | + | 0.912425i | \(0.365792\pi\) | |||||||
\(510\) | 16.7511 | 0.741749 | ||||||||
\(511\) | −1.13843 | −0.0503611 | ||||||||
\(512\) | −160.639 | −7.09930 | ||||||||
\(513\) | 11.7331 | 0.518029 | ||||||||
\(514\) | 81.7209 | 3.60455 | ||||||||
\(515\) | −0.782074 | −0.0344623 | ||||||||
\(516\) | 144.071 | 6.34236 | ||||||||
\(517\) | −2.65028 | −0.116559 | ||||||||
\(518\) | 9.58159 | 0.420991 | ||||||||
\(519\) | −61.9797 | −2.72061 | ||||||||
\(520\) | −6.57696 | −0.288419 | ||||||||
\(521\) | −27.5513 | −1.20704 | −0.603522 | − | 0.797346i | \(-0.706237\pi\) | ||||
−0.603522 | + | 0.797346i | \(0.706237\pi\) | |||||||
\(522\) | 73.8561 | 3.23259 | ||||||||
\(523\) | 18.7489 | 0.819831 | 0.409916 | − | 0.912123i | \(-0.365558\pi\) | ||||
0.409916 | + | 0.912123i | \(0.365558\pi\) | |||||||
\(524\) | −15.3397 | −0.670120 | ||||||||
\(525\) | 10.7824 | 0.470580 | ||||||||
\(526\) | 42.2993 | 1.84434 | ||||||||
\(527\) | −9.20614 | −0.401026 | ||||||||
\(528\) | 127.774 | 5.56067 | ||||||||
\(529\) | 50.6114 | 2.20050 | ||||||||
\(530\) | 7.89833 | 0.343081 | ||||||||
\(531\) | −14.8968 | −0.646466 | ||||||||
\(532\) | −3.20226 | −0.138836 | ||||||||
\(533\) | 15.6926 | 0.679721 | ||||||||
\(534\) | −57.7054 | −2.49716 | ||||||||
\(535\) | 3.18302 | 0.137614 | ||||||||
\(536\) | −61.5996 | −2.66070 | ||||||||
\(537\) | −51.8863 | −2.23906 | ||||||||
\(538\) | −60.9334 | −2.62702 | ||||||||
\(539\) | 13.9269 | 0.599873 | ||||||||
\(540\) | 30.9860 | 1.33343 | ||||||||
\(541\) | −30.0662 | −1.29265 | −0.646323 | − | 0.763064i | \(-0.723694\pi\) | ||||
−0.646323 | + | 0.763064i | \(0.723694\pi\) | |||||||
\(542\) | 62.8592 | 2.70003 | ||||||||
\(543\) | −20.1570 | −0.865021 | ||||||||
\(544\) | 153.959 | 6.60092 | ||||||||
\(545\) | 5.67010 | 0.242880 | ||||||||
\(546\) | −10.4537 | −0.447376 | ||||||||
\(547\) | −39.9761 | −1.70925 | −0.854627 | − | 0.519242i | \(-0.826214\pi\) | ||||
−0.854627 | + | 0.519242i | \(0.826214\pi\) | |||||||
\(548\) | 32.0587 | 1.36948 | ||||||||
\(549\) | −30.0045 | −1.28056 | ||||||||
\(550\) | −29.0714 | −1.23961 | ||||||||
\(551\) | 2.81444 | 0.119899 | ||||||||
\(552\) | −299.721 | −12.7570 | ||||||||
\(553\) | 0.972749 | 0.0413655 | ||||||||
\(554\) | 62.6000 | 2.65962 | ||||||||
\(555\) | −5.88187 | −0.249671 | ||||||||
\(556\) | −121.734 | −5.16269 | ||||||||
\(557\) | −12.4425 | −0.527204 | −0.263602 | − | 0.964631i | \(-0.584911\pi\) | ||||
−0.263602 | + | 0.964631i | \(0.584911\pi\) | |||||||
\(558\) | −38.0493 | −1.61075 | ||||||||
\(559\) | 12.8078 | 0.541711 | ||||||||
\(560\) | −4.57417 | −0.193294 | ||||||||
\(561\) | −35.1902 | −1.48573 | ||||||||
\(562\) | −86.3334 | −3.64175 | ||||||||
\(563\) | −11.0166 | −0.464294 | −0.232147 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232147 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(564\) | −23.5681 | −0.992395 | ||||||||
\(565\) | 3.25976 | 0.137139 | ||||||||
\(566\) | −49.8225 | −2.09420 | ||||||||
\(567\) | 17.0083 | 0.714282 | ||||||||
\(568\) | −89.4016 | −3.75121 | ||||||||
\(569\) | 11.3267 | 0.474839 | 0.237420 | − | 0.971407i | \(-0.423698\pi\) | ||||
0.237420 | + | 0.971407i | \(0.423698\pi\) | |||||||
\(570\) | 2.63825 | 0.110504 | ||||||||
\(571\) | −14.5739 | −0.609899 | −0.304949 | − | 0.952369i | \(-0.598640\pi\) | ||||
−0.304949 | + | 0.952369i | \(0.598640\pi\) | |||||||
\(572\) | 21.0009 | 0.878094 | ||||||||
\(573\) | 52.8947 | 2.20971 | ||||||||
\(574\) | 17.8167 | 0.743653 | ||||||||
\(575\) | 41.7727 | 1.74204 | ||||||||
\(576\) | 358.537 | 14.9390 | ||||||||
\(577\) | −44.5889 | −1.85626 | −0.928131 | − | 0.372254i | \(-0.878585\pi\) | ||||
−0.928131 | + | 0.372254i | \(0.878585\pi\) | |||||||
\(578\) | −24.9992 | −1.03983 | ||||||||
\(579\) | 1.01160 | 0.0420408 | ||||||||
\(580\) | 7.43267 | 0.308625 | ||||||||
\(581\) | −1.27131 | −0.0527429 | ||||||||
\(582\) | 96.2741 | 3.99069 | ||||||||
\(583\) | −16.5926 | −0.687195 | ||||||||
\(584\) | 17.9579 | 0.743105 | ||||||||
\(585\) | 4.58592 | 0.189605 | ||||||||
\(586\) | 60.2726 | 2.48984 | ||||||||
\(587\) | −3.53774 | −0.146018 | −0.0730091 | − | 0.997331i | \(-0.523260\pi\) | ||||
−0.0730091 | + | 0.997331i | \(0.523260\pi\) | |||||||
\(588\) | 123.848 | 5.10739 | ||||||||
\(589\) | −1.44995 | −0.0597440 | ||||||||
\(590\) | −2.01202 | −0.0828337 | ||||||||
\(591\) | 63.2974 | 2.60371 | ||||||||
\(592\) | −92.5856 | −3.80525 | ||||||||
\(593\) | −33.6146 | −1.38038 | −0.690192 | − | 0.723626i | \(-0.742474\pi\) | ||||
−0.690192 | + | 0.723626i | \(0.742474\pi\) | |||||||
\(594\) | −87.3629 | −3.58454 | ||||||||
\(595\) | 1.25977 | 0.0516454 | ||||||||
\(596\) | −78.3332 | −3.20865 | ||||||||
\(597\) | −52.9654 | −2.16773 | ||||||||
\(598\) | −40.4994 | −1.65614 | ||||||||
\(599\) | −26.8304 | −1.09626 | −0.548130 | − | 0.836393i | \(-0.684660\pi\) | ||||
−0.548130 | + | 0.836393i | \(0.684660\pi\) | |||||||
\(600\) | −170.084 | −6.94366 | ||||||||
\(601\) | 31.0040 | 1.26468 | 0.632339 | − | 0.774692i | \(-0.282095\pi\) | ||||
0.632339 | + | 0.774692i | \(0.282095\pi\) | |||||||
\(602\) | 14.5414 | 0.592663 | ||||||||
\(603\) | 42.9516 | 1.74912 | ||||||||
\(604\) | −86.4361 | −3.51703 | ||||||||
\(605\) | 2.33869 | 0.0950812 | ||||||||
\(606\) | −124.955 | −5.07596 | ||||||||
\(607\) | 11.6366 | 0.472316 | 0.236158 | − | 0.971715i | \(-0.424112\pi\) | ||||
0.236158 | + | 0.971715i | \(0.424112\pi\) | |||||||
\(608\) | 24.2481 | 0.983392 | ||||||||
\(609\) | 7.77238 | 0.314953 | ||||||||
\(610\) | −4.05254 | −0.164082 | ||||||||
\(611\) | −2.09518 | −0.0847620 | ||||||||
\(612\) | −223.633 | −9.03981 | ||||||||
\(613\) | 23.0572 | 0.931270 | 0.465635 | − | 0.884977i | \(-0.345826\pi\) | ||||
0.465635 | + | 0.884977i | \(0.345826\pi\) | |||||||
\(614\) | 57.9015 | 2.33672 | ||||||||
\(615\) | −10.9371 | −0.441028 | ||||||||
\(616\) | 15.6869 | 0.632043 | ||||||||
\(617\) | 18.5259 | 0.745824 | 0.372912 | − | 0.927867i | \(-0.378359\pi\) | ||||
0.372912 | + | 0.927867i | \(0.378359\pi\) | |||||||
\(618\) | 19.6084 | 0.788766 | ||||||||
\(619\) | 10.3076 | 0.414297 | 0.207148 | − | 0.978310i | \(-0.433582\pi\) | ||||
0.207148 | + | 0.978310i | \(0.433582\pi\) | |||||||
\(620\) | −3.82917 | −0.153783 | ||||||||
\(621\) | 125.532 | 5.03743 | ||||||||
\(622\) | −13.4689 | −0.540052 | ||||||||
\(623\) | −4.33974 | −0.173868 | ||||||||
\(624\) | 101.012 | 4.04374 | ||||||||
\(625\) | 23.0490 | 0.921958 | ||||||||
\(626\) | −38.4761 | −1.53781 | ||||||||
\(627\) | −5.54237 | −0.221341 | ||||||||
\(628\) | −81.1952 | −3.24004 | ||||||||
\(629\) | 25.4989 | 1.01671 | ||||||||
\(630\) | 5.20666 | 0.207438 | ||||||||
\(631\) | 15.6901 | 0.624612 | 0.312306 | − | 0.949982i | \(-0.398899\pi\) | ||||
0.312306 | + | 0.949982i | \(0.398899\pi\) | |||||||
\(632\) | −15.3445 | −0.610370 | ||||||||
\(633\) | 83.5900 | 3.32241 | ||||||||
\(634\) | −7.27977 | −0.289116 | ||||||||
\(635\) | −4.81889 | −0.191232 | ||||||||
\(636\) | −147.553 | −5.85085 | ||||||||
\(637\) | 11.0099 | 0.436230 | ||||||||
\(638\) | −20.9559 | −0.829651 | ||||||||
\(639\) | 62.3371 | 2.46602 | ||||||||
\(640\) | 26.5190 | 1.04826 | ||||||||
\(641\) | −10.8883 | −0.430061 | −0.215030 | − | 0.976607i | \(-0.568985\pi\) | ||||
−0.215030 | + | 0.976607i | \(0.568985\pi\) | |||||||
\(642\) | −79.8056 | −3.14968 | ||||||||
\(643\) | 30.5679 | 1.20548 | 0.602740 | − | 0.797937i | \(-0.294075\pi\) | ||||
0.602740 | + | 0.797937i | \(0.294075\pi\) | |||||||
\(644\) | −34.2609 | −1.35007 | ||||||||
\(645\) | −8.92655 | −0.351482 | ||||||||
\(646\) | −11.4373 | −0.449993 | ||||||||
\(647\) | −40.1376 | −1.57797 | −0.788986 | − | 0.614411i | \(-0.789394\pi\) | ||||
−0.788986 | + | 0.614411i | \(0.789394\pi\) | |||||||
\(648\) | −268.295 | −10.5396 | ||||||||
\(649\) | 4.22681 | 0.165917 | ||||||||
\(650\) | −22.9825 | −0.901446 | ||||||||
\(651\) | −4.00419 | −0.156936 | ||||||||
\(652\) | 45.2917 | 1.77376 | ||||||||
\(653\) | −32.3278 | −1.26509 | −0.632543 | − | 0.774525i | \(-0.717989\pi\) | ||||
−0.632543 | + | 0.774525i | \(0.717989\pi\) | |||||||
\(654\) | −142.162 | −5.55899 | ||||||||
\(655\) | 0.950442 | 0.0371369 | ||||||||
\(656\) | −172.160 | −6.72172 | ||||||||
\(657\) | −12.5215 | −0.488512 | ||||||||
\(658\) | −2.37878 | −0.0927345 | ||||||||
\(659\) | 25.0061 | 0.974099 | 0.487049 | − | 0.873374i | \(-0.338073\pi\) | ||||
0.487049 | + | 0.873374i | \(0.338073\pi\) | |||||||
\(660\) | −14.6369 | −0.569740 | ||||||||
\(661\) | 12.0993 | 0.470607 | 0.235304 | − | 0.971922i | \(-0.424392\pi\) | ||||
0.235304 | + | 0.971922i | \(0.424392\pi\) | |||||||
\(662\) | −46.3510 | −1.80148 | ||||||||
\(663\) | −27.8197 | −1.08043 | ||||||||
\(664\) | 20.0541 | 0.778249 | ||||||||
\(665\) | 0.198410 | 0.00769402 | ||||||||
\(666\) | 105.388 | 4.08369 | ||||||||
\(667\) | 30.1116 | 1.16593 | ||||||||
\(668\) | 80.1493 | 3.10107 | ||||||||
\(669\) | 3.99419 | 0.154424 | ||||||||
\(670\) | 5.80123 | 0.224121 | ||||||||
\(671\) | 8.51347 | 0.328659 | ||||||||
\(672\) | 66.9639 | 2.58319 | ||||||||
\(673\) | 6.14022 | 0.236688 | 0.118344 | − | 0.992973i | \(-0.462241\pi\) | ||||
0.118344 | + | 0.992973i | \(0.462241\pi\) | |||||||
\(674\) | −86.0195 | −3.31335 | ||||||||
\(675\) | 71.2365 | 2.74189 | ||||||||
\(676\) | −59.4008 | −2.28464 | ||||||||
\(677\) | −7.12019 | −0.273651 | −0.136826 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136826 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(678\) | −81.7296 | −3.13881 | ||||||||
\(679\) | 7.24031 | 0.277858 | ||||||||
\(680\) | −19.8720 | −0.762055 | ||||||||
\(681\) | 15.6020 | 0.597870 | ||||||||
\(682\) | 10.7961 | 0.413403 | ||||||||
\(683\) | −38.5686 | −1.47579 | −0.737893 | − | 0.674917i | \(-0.764179\pi\) | ||||
−0.737893 | + | 0.674917i | \(0.764179\pi\) | |||||||
\(684\) | −35.2216 | −1.34673 | ||||||||
\(685\) | −1.98634 | −0.0758942 | ||||||||
\(686\) | 25.8930 | 0.988599 | ||||||||
\(687\) | 72.0468 | 2.74875 | ||||||||
\(688\) | −140.511 | −5.35695 | ||||||||
\(689\) | −13.1173 | −0.499730 | ||||||||
\(690\) | 28.2266 | 1.07457 | ||||||||
\(691\) | −46.1305 | −1.75489 | −0.877443 | − | 0.479681i | \(-0.840752\pi\) | ||||
−0.877443 | + | 0.479681i | \(0.840752\pi\) | |||||||
\(692\) | 111.759 | 4.24844 | ||||||||
\(693\) | −10.9380 | −0.415501 | ||||||||
\(694\) | −84.0970 | −3.19228 | ||||||||
\(695\) | 7.54260 | 0.286107 | ||||||||
\(696\) | −122.604 | −4.64730 | ||||||||
\(697\) | 47.4144 | 1.79595 | ||||||||
\(698\) | −43.8810 | −1.66092 | ||||||||
\(699\) | 39.9354 | 1.51050 | ||||||||
\(700\) | −19.4422 | −0.734848 | ||||||||
\(701\) | −9.24854 | −0.349312 | −0.174656 | − | 0.984629i | \(-0.555881\pi\) | ||||
−0.174656 | + | 0.984629i | \(0.555881\pi\) | |||||||
\(702\) | −69.0650 | −2.60669 | ||||||||
\(703\) | 4.01601 | 0.151467 | ||||||||
\(704\) | −101.731 | −3.83414 | ||||||||
\(705\) | 1.46027 | 0.0549968 | ||||||||
\(706\) | −14.5471 | −0.547485 | ||||||||
\(707\) | −9.39728 | −0.353421 | ||||||||
\(708\) | 37.5877 | 1.41263 | ||||||||
\(709\) | 11.6155 | 0.436231 | 0.218115 | − | 0.975923i | \(-0.430009\pi\) | ||||
0.218115 | + | 0.975923i | \(0.430009\pi\) | |||||||
\(710\) | 8.41952 | 0.315979 | ||||||||
\(711\) | 10.6992 | 0.401253 | ||||||||
\(712\) | 68.4565 | 2.56552 | ||||||||
\(713\) | −15.5129 | −0.580964 | ||||||||
\(714\) | −31.5853 | −1.18205 | ||||||||
\(715\) | −1.30121 | −0.0486624 | ||||||||
\(716\) | 93.5591 | 3.49647 | ||||||||
\(717\) | −20.7335 | −0.774308 | ||||||||
\(718\) | −39.7152 | −1.48216 | ||||||||
\(719\) | −11.1114 | −0.414387 | −0.207193 | − | 0.978300i | \(-0.566433\pi\) | ||||
−0.207193 | + | 0.978300i | \(0.566433\pi\) | |||||||
\(720\) | −50.3112 | −1.87499 | ||||||||
\(721\) | 1.47465 | 0.0549190 | ||||||||
\(722\) | 51.4203 | 1.91367 | ||||||||
\(723\) | −53.8104 | −2.00123 | ||||||||
\(724\) | 36.3462 | 1.35080 | ||||||||
\(725\) | 17.0876 | 0.634618 | ||||||||
\(726\) | −58.6363 | −2.17620 | ||||||||
\(727\) | 19.1828 | 0.711449 | 0.355725 | − | 0.934591i | \(-0.384234\pi\) | ||||
0.355725 | + | 0.934591i | \(0.384234\pi\) | |||||||
\(728\) | 12.4013 | 0.459623 | ||||||||
\(729\) | 44.7566 | 1.65765 | ||||||||
\(730\) | −1.69121 | −0.0625946 | ||||||||
\(731\) | 38.6981 | 1.43130 | ||||||||
\(732\) | 75.7076 | 2.79823 | ||||||||
\(733\) | 2.39648 | 0.0885161 | 0.0442580 | − | 0.999020i | \(-0.485908\pi\) | ||||
0.0442580 | + | 0.999020i | \(0.485908\pi\) | |||||||
\(734\) | −102.140 | −3.77006 | ||||||||
\(735\) | −7.67352 | −0.283042 | ||||||||
\(736\) | 259.430 | 9.56272 | ||||||||
\(737\) | −12.1871 | −0.448916 | ||||||||
\(738\) | 195.965 | 7.21357 | ||||||||
\(739\) | 44.8936 | 1.65144 | 0.825720 | − | 0.564081i | \(-0.190769\pi\) | ||||
0.825720 | + | 0.564081i | \(0.190769\pi\) | |||||||
\(740\) | 10.6059 | 0.389881 | ||||||||
\(741\) | −4.38154 | −0.160960 | ||||||||
\(742\) | −14.8928 | −0.546733 | ||||||||
\(743\) | 13.0768 | 0.479741 | 0.239870 | − | 0.970805i | \(-0.422895\pi\) | ||||
0.239870 | + | 0.970805i | \(0.422895\pi\) | |||||||
\(744\) | 63.1633 | 2.31568 | ||||||||
\(745\) | 4.85348 | 0.177818 | ||||||||
\(746\) | −22.3894 | −0.819735 | ||||||||
\(747\) | −13.9831 | −0.511616 | ||||||||
\(748\) | 63.4533 | 2.32008 | ||||||||
\(749\) | −6.00180 | −0.219301 | ||||||||
\(750\) | 32.4675 | 1.18555 | ||||||||
\(751\) | 44.4244 | 1.62107 | 0.810535 | − | 0.585691i | \(-0.199177\pi\) | ||||
0.810535 | + | 0.585691i | \(0.199177\pi\) | |||||||
\(752\) | 22.9858 | 0.838207 | ||||||||
\(753\) | −12.7261 | −0.463767 | ||||||||
\(754\) | −16.5667 | −0.603325 | ||||||||
\(755\) | 5.35553 | 0.194908 | ||||||||
\(756\) | −58.4263 | −2.12494 | ||||||||
\(757\) | −26.8094 | −0.974404 | −0.487202 | − | 0.873289i | \(-0.661982\pi\) | ||||
−0.487202 | + | 0.873289i | \(0.661982\pi\) | |||||||
\(758\) | 68.0737 | 2.47255 | ||||||||
\(759\) | −59.2977 | −2.15237 | ||||||||
\(760\) | −3.12979 | −0.113529 | ||||||||
\(761\) | −43.1614 | −1.56460 | −0.782299 | − | 0.622903i | \(-0.785953\pi\) | ||||
−0.782299 | + | 0.622903i | \(0.785953\pi\) | |||||||
\(762\) | 120.821 | 4.37687 | ||||||||
\(763\) | −10.6914 | −0.387053 | ||||||||
\(764\) | −95.3773 | −3.45063 | ||||||||
\(765\) | 13.8561 | 0.500970 | ||||||||
\(766\) | 30.4817 | 1.10135 | ||||||||
\(767\) | 3.34152 | 0.120655 | ||||||||
\(768\) | −355.416 | −12.8250 | ||||||||
\(769\) | 39.3145 | 1.41772 | 0.708858 | − | 0.705351i | \(-0.249210\pi\) | ||||
0.708858 | + | 0.705351i | \(0.249210\pi\) | |||||||
\(770\) | −1.47733 | −0.0532394 | ||||||||
\(771\) | 94.5917 | 3.40664 | ||||||||
\(772\) | −1.82408 | −0.0656500 | ||||||||
\(773\) | −3.66142 | −0.131692 | −0.0658461 | − | 0.997830i | \(-0.520975\pi\) | ||||
−0.0658461 | + | 0.997830i | \(0.520975\pi\) | |||||||
\(774\) | 159.940 | 5.74894 | ||||||||
\(775\) | −8.80322 | −0.316221 | ||||||||
\(776\) | −114.211 | −4.09994 | ||||||||
\(777\) | 11.0907 | 0.397875 | ||||||||
\(778\) | 108.954 | 3.90619 | ||||||||
\(779\) | 7.46765 | 0.267556 | ||||||||
\(780\) | −11.5712 | −0.414317 | ||||||||
\(781\) | −17.6875 | −0.632908 | ||||||||
\(782\) | −122.367 | −4.37583 | ||||||||
\(783\) | 51.3503 | 1.83511 | ||||||||
\(784\) | −120.788 | −4.31385 | ||||||||
\(785\) | 5.03081 | 0.179557 | ||||||||
\(786\) | −23.8298 | −0.849981 | ||||||||
\(787\) | −11.0215 | −0.392875 | −0.196438 | − | 0.980516i | \(-0.562937\pi\) | ||||
−0.196438 | + | 0.980516i | \(0.562937\pi\) | |||||||
\(788\) | −114.135 | −4.06589 | ||||||||
\(789\) | 48.9614 | 1.74307 | ||||||||
\(790\) | 1.44509 | 0.0514138 | ||||||||
\(791\) | −6.14649 | −0.218544 | ||||||||
\(792\) | 172.540 | 6.13093 | ||||||||
\(793\) | 6.73035 | 0.239002 | ||||||||
\(794\) | 76.5522 | 2.71674 | ||||||||
\(795\) | 9.14229 | 0.324244 | ||||||||
\(796\) | 95.5048 | 3.38508 | ||||||||
\(797\) | −20.3549 | −0.721008 | −0.360504 | − | 0.932758i | \(-0.617395\pi\) | ||||
−0.360504 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(798\) | −4.97461 | −0.176099 | ||||||||
\(799\) | −6.33049 | −0.223957 | ||||||||
\(800\) | 147.220 | 5.20503 | ||||||||
\(801\) | −47.7327 | −1.68655 | ||||||||
\(802\) | −51.2841 | −1.81090 | ||||||||
\(803\) | 3.55285 | 0.125378 | ||||||||
\(804\) | −108.376 | −3.82212 | ||||||||
\(805\) | 2.12279 | 0.0748184 | ||||||||
\(806\) | 8.53487 | 0.300628 | ||||||||
\(807\) | −70.5302 | −2.48278 | ||||||||
\(808\) | 148.236 | 5.21492 | ||||||||
\(809\) | −13.7301 | −0.482723 | −0.241362 | − | 0.970435i | \(-0.577594\pi\) | ||||
−0.241362 | + | 0.970435i | \(0.577594\pi\) | |||||||
\(810\) | 25.2670 | 0.887793 | ||||||||
\(811\) | −24.5967 | −0.863705 | −0.431853 | − | 0.901944i | \(-0.642140\pi\) | ||||
−0.431853 | + | 0.901944i | \(0.642140\pi\) | |||||||
\(812\) | −14.0148 | −0.491823 | ||||||||
\(813\) | 72.7593 | 2.55178 | ||||||||
\(814\) | −29.9026 | −1.04809 | ||||||||
\(815\) | −2.80625 | −0.0982987 | ||||||||
\(816\) | 305.204 | 10.6843 | ||||||||
\(817\) | 6.09486 | 0.213232 | ||||||||
\(818\) | 7.72139 | 0.269972 | ||||||||
\(819\) | −8.64708 | −0.302153 | ||||||||
\(820\) | 19.7214 | 0.688700 | ||||||||
\(821\) | −15.9617 | −0.557067 | −0.278534 | − | 0.960427i | \(-0.589848\pi\) | ||||
−0.278534 | + | 0.960427i | \(0.589848\pi\) | |||||||
\(822\) | 49.8022 | 1.73705 | ||||||||
\(823\) | −53.1865 | −1.85396 | −0.926982 | − | 0.375106i | \(-0.877606\pi\) | ||||
−0.926982 | + | 0.375106i | \(0.877606\pi\) | |||||||
\(824\) | −23.2617 | −0.810359 | ||||||||
\(825\) | −33.6500 | −1.17154 | ||||||||
\(826\) | 3.79381 | 0.132004 | ||||||||
\(827\) | 33.9173 | 1.17942 | 0.589711 | − | 0.807615i | \(-0.299242\pi\) | ||||
0.589711 | + | 0.807615i | \(0.299242\pi\) | |||||||
\(828\) | −376.835 | −13.0959 | ||||||||
\(829\) | 14.4787 | 0.502866 | 0.251433 | − | 0.967875i | \(-0.419098\pi\) | ||||
0.251433 | + | 0.967875i | \(0.419098\pi\) | |||||||
\(830\) | −1.88862 | −0.0655549 | ||||||||
\(831\) | 72.4594 | 2.51359 | ||||||||
\(832\) | −80.4238 | −2.78819 | ||||||||
\(833\) | 33.2660 | 1.15260 | ||||||||
\(834\) | −189.110 | −6.54836 | ||||||||
\(835\) | −4.96601 | −0.171856 | ||||||||
\(836\) | 9.99376 | 0.345641 | ||||||||
\(837\) | −26.4547 | −0.914409 | ||||||||
\(838\) | −100.579 | −3.47444 | ||||||||
\(839\) | −26.1228 | −0.901859 | −0.450929 | − | 0.892560i | \(-0.648907\pi\) | ||||
−0.450929 | + | 0.892560i | \(0.648907\pi\) | |||||||
\(840\) | −8.64326 | −0.298221 | ||||||||
\(841\) | −16.6825 | −0.575259 | ||||||||
\(842\) | 84.1323 | 2.89939 | ||||||||
\(843\) | −99.9307 | −3.44179 | ||||||||
\(844\) | −150.726 | −5.18819 | ||||||||
\(845\) | 3.68044 | 0.126611 | ||||||||
\(846\) | −26.1641 | −0.899542 | ||||||||
\(847\) | −4.40976 | −0.151521 | ||||||||
\(848\) | 143.907 | 4.94180 | ||||||||
\(849\) | −57.6694 | −1.97921 | ||||||||
\(850\) | −69.4404 | −2.38178 | ||||||||
\(851\) | 42.9672 | 1.47290 | ||||||||
\(852\) | −157.289 | −5.38865 | ||||||||
\(853\) | 41.5148 | 1.42144 | 0.710719 | − | 0.703476i | \(-0.248370\pi\) | ||||
0.710719 | + | 0.703476i | \(0.248370\pi\) | |||||||
\(854\) | 7.64134 | 0.261481 | ||||||||
\(855\) | 2.18231 | 0.0746335 | ||||||||
\(856\) | 94.6743 | 3.23590 | ||||||||
\(857\) | −18.7795 | −0.641496 | −0.320748 | − | 0.947165i | \(-0.603934\pi\) | ||||
−0.320748 | + | 0.947165i | \(0.603934\pi\) | |||||||
\(858\) | 32.6243 | 1.11377 | ||||||||
\(859\) | 8.94616 | 0.305239 | 0.152619 | − | 0.988285i | \(-0.451229\pi\) | ||||
0.152619 | + | 0.988285i | \(0.451229\pi\) | |||||||
\(860\) | 16.0959 | 0.548867 | ||||||||
\(861\) | 20.6227 | 0.702821 | ||||||||
\(862\) | 71.3276 | 2.42943 | ||||||||
\(863\) | −4.20772 | −0.143232 | −0.0716161 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716161 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(864\) | 442.415 | 15.0513 | ||||||||
\(865\) | −6.92453 | −0.235441 | ||||||||
\(866\) | 43.9044 | 1.49193 | ||||||||
\(867\) | −28.9365 | −0.982736 | ||||||||
\(868\) | 7.22017 | 0.245068 | ||||||||
\(869\) | −3.03580 | −0.102982 | ||||||||
\(870\) | 11.5464 | 0.391460 | ||||||||
\(871\) | −9.63452 | −0.326453 | ||||||||
\(872\) | 168.649 | 5.71117 | ||||||||
\(873\) | 79.6360 | 2.69527 | ||||||||
\(874\) | −19.2725 | −0.651903 | ||||||||
\(875\) | 2.44173 | 0.0825455 | ||||||||
\(876\) | 31.5944 | 1.06748 | ||||||||
\(877\) | 12.4072 | 0.418960 | 0.209480 | − | 0.977813i | \(-0.432823\pi\) | ||||
0.209480 | + | 0.977813i | \(0.432823\pi\) | |||||||
\(878\) | −3.09631 | −0.104495 | ||||||||
\(879\) | 69.7653 | 2.35313 | ||||||||
\(880\) | 14.2753 | 0.481219 | ||||||||
\(881\) | 43.0471 | 1.45029 | 0.725147 | − | 0.688594i | \(-0.241772\pi\) | ||||
0.725147 | + | 0.688594i | \(0.241772\pi\) | |||||||
\(882\) | 137.490 | 4.62951 | ||||||||
\(883\) | −12.9742 | −0.436618 | −0.218309 | − | 0.975880i | \(-0.570054\pi\) | ||||
−0.218309 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(884\) | 50.1632 | 1.68717 | ||||||||
\(885\) | −2.32891 | −0.0782855 | ||||||||
\(886\) | 73.4497 | 2.46759 | ||||||||
\(887\) | −34.3568 | −1.15359 | −0.576794 | − | 0.816890i | \(-0.695696\pi\) | ||||
−0.576794 | + | 0.816890i | \(0.695696\pi\) | |||||||
\(888\) | −174.948 | −5.87086 | ||||||||
\(889\) | 9.08634 | 0.304746 | ||||||||
\(890\) | −6.44698 | −0.216103 | ||||||||
\(891\) | −53.0803 | −1.77826 | ||||||||
\(892\) | −7.20214 | −0.241146 | ||||||||
\(893\) | −0.997038 | −0.0333646 | ||||||||
\(894\) | −121.688 | −4.06986 | ||||||||
\(895\) | −5.79687 | −0.193768 | ||||||||
\(896\) | −50.0035 | −1.67050 | ||||||||
\(897\) | −46.8780 | −1.56521 | ||||||||
\(898\) | −17.5113 | −0.584361 | ||||||||
\(899\) | −6.34574 | −0.211642 | ||||||||
\(900\) | −213.845 | −7.12816 | ||||||||
\(901\) | −39.6334 | −1.32038 | ||||||||
\(902\) | −55.6030 | −1.85138 | ||||||||
\(903\) | 16.8316 | 0.560121 | ||||||||
\(904\) | 96.9568 | 3.22474 | ||||||||
\(905\) | −2.25199 | −0.0748588 | ||||||||
\(906\) | −134.276 | −4.46101 | ||||||||
\(907\) | 12.9011 | 0.428374 | 0.214187 | − | 0.976793i | \(-0.431290\pi\) | ||||
0.214187 | + | 0.976793i | \(0.431290\pi\) | |||||||
\(908\) | −28.1328 | −0.933620 | ||||||||
\(909\) | −103.361 | −3.42825 | ||||||||
\(910\) | −1.16791 | −0.0387159 | ||||||||
\(911\) | 31.6977 | 1.05019 | 0.525096 | − | 0.851043i | \(-0.324030\pi\) | ||||
0.525096 | + | 0.851043i | \(0.324030\pi\) | |||||||
\(912\) | 48.0690 | 1.59172 | ||||||||
\(913\) | 3.96756 | 0.131307 | ||||||||
\(914\) | −74.7714 | −2.47322 | ||||||||
\(915\) | −4.69080 | −0.155073 | ||||||||
\(916\) | −129.911 | −4.29239 | ||||||||
\(917\) | −1.79212 | −0.0591812 | ||||||||
\(918\) | −208.677 | −6.88735 | ||||||||
\(919\) | −22.1725 | −0.731402 | −0.365701 | − | 0.930732i | \(-0.619171\pi\) | ||||
−0.365701 | + | 0.930732i | \(0.619171\pi\) | |||||||
\(920\) | −33.4855 | −1.10399 | ||||||||
\(921\) | 67.0209 | 2.20841 | ||||||||
\(922\) | −45.6164 | −1.50229 | ||||||||
\(923\) | −13.9829 | −0.460253 | ||||||||
\(924\) | 27.5989 | 0.907936 | ||||||||
\(925\) | 24.3829 | 0.801704 | ||||||||
\(926\) | 1.25484 | 0.0412366 | ||||||||
\(927\) | 16.2197 | 0.532725 | ||||||||
\(928\) | 106.123 | 3.48365 | ||||||||
\(929\) | 35.0901 | 1.15127 | 0.575635 | − | 0.817707i | \(-0.304755\pi\) | ||||
0.575635 | + | 0.817707i | \(0.304755\pi\) | |||||||
\(930\) | −5.94849 | −0.195059 | ||||||||
\(931\) | 5.23932 | 0.171712 | ||||||||
\(932\) | −72.0097 | −2.35876 | ||||||||
\(933\) | −15.5902 | −0.510399 | ||||||||
\(934\) | −77.5999 | −2.53914 | ||||||||
\(935\) | −3.93153 | −0.128575 | ||||||||
\(936\) | 136.402 | 4.45843 | ||||||||
\(937\) | −41.6743 | −1.36144 | −0.680720 | − | 0.732544i | \(-0.738333\pi\) | ||||
−0.680720 | + | 0.732544i | \(0.738333\pi\) | |||||||
\(938\) | −10.9386 | −0.357158 | ||||||||
\(939\) | −44.5359 | −1.45338 | ||||||||
\(940\) | −2.63308 | −0.0858817 | ||||||||
\(941\) | −30.5881 | −0.997142 | −0.498571 | − | 0.866849i | \(-0.666142\pi\) | ||||
−0.498571 | + | 0.866849i | \(0.666142\pi\) | |||||||
\(942\) | −126.134 | −4.10967 | ||||||||
\(943\) | 79.8962 | 2.60178 | ||||||||
\(944\) | −36.6591 | −1.19315 | ||||||||
\(945\) | 3.62006 | 0.117761 | ||||||||
\(946\) | −45.3814 | −1.47548 | ||||||||
\(947\) | 3.41766 | 0.111059 | 0.0555295 | − | 0.998457i | \(-0.482315\pi\) | ||||
0.0555295 | + | 0.998457i | \(0.482315\pi\) | |||||||
\(948\) | −26.9964 | −0.876803 | ||||||||
\(949\) | 2.80872 | 0.0911749 | ||||||||
\(950\) | −10.9367 | −0.354833 | ||||||||
\(951\) | −8.42631 | −0.273242 | ||||||||
\(952\) | 37.4700 | 1.21441 | ||||||||
\(953\) | −39.4300 | −1.27726 | −0.638631 | − | 0.769513i | \(-0.720499\pi\) | ||||
−0.638631 | + | 0.769513i | \(0.720499\pi\) | |||||||
\(954\) | −163.806 | −5.30341 | ||||||||
\(955\) | 5.90952 | 0.191228 | ||||||||
\(956\) | 37.3858 | 1.20914 | ||||||||
\(957\) | −24.2564 | −0.784097 | ||||||||
\(958\) | −70.9586 | −2.29257 | ||||||||
\(959\) | 3.74538 | 0.120945 | ||||||||
\(960\) | 56.0524 | 1.80908 | ||||||||
\(961\) | −27.7308 | −0.894542 | ||||||||
\(962\) | −23.6396 | −0.762172 | ||||||||
\(963\) | −66.0136 | −2.12726 | ||||||||
\(964\) | 97.0285 | 3.12508 | ||||||||
\(965\) | 0.113019 | 0.00363821 | ||||||||
\(966\) | −53.2232 | −1.71243 | ||||||||
\(967\) | −4.46965 | −0.143734 | −0.0718672 | − | 0.997414i | \(-0.522896\pi\) | ||||
−0.0718672 | + | 0.997414i | \(0.522896\pi\) | |||||||
\(968\) | 69.5609 | 2.23577 | ||||||||
\(969\) | −13.2386 | −0.425285 | ||||||||
\(970\) | 10.7560 | 0.345354 | ||||||||
\(971\) | 15.6251 | 0.501434 | 0.250717 | − | 0.968060i | \(-0.419334\pi\) | ||||
0.250717 | + | 0.968060i | \(0.419334\pi\) | |||||||
\(972\) | −215.406 | −6.90915 | ||||||||
\(973\) | −14.2221 | −0.455939 | ||||||||
\(974\) | 102.082 | 3.27093 | ||||||||
\(975\) | −26.6021 | −0.851950 | ||||||||
\(976\) | −73.8373 | −2.36347 | ||||||||
\(977\) | 42.7389 | 1.36734 | 0.683669 | − | 0.729792i | \(-0.260383\pi\) | ||||
0.683669 | + | 0.729792i | \(0.260383\pi\) | |||||||
\(978\) | 70.3592 | 2.24984 | ||||||||
\(979\) | 13.5437 | 0.432857 | ||||||||
\(980\) | 13.8366 | 0.441992 | ||||||||
\(981\) | −117.594 | −3.75449 | ||||||||
\(982\) | 59.8897 | 1.91116 | ||||||||
\(983\) | 30.1285 | 0.960948 | 0.480474 | − | 0.877009i | \(-0.340465\pi\) | ||||
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(984\) | −325.310 | −10.3705 | ||||||||
\(985\) | 7.07175 | 0.225325 | ||||||||
\(986\) | −50.0556 | −1.59409 | ||||||||
\(987\) | −2.75343 | −0.0876427 | ||||||||
\(988\) | 7.90060 | 0.251351 | ||||||||
\(989\) | 65.2087 | 2.07352 | ||||||||
\(990\) | −16.2492 | −0.516432 | ||||||||
\(991\) | −33.5491 | −1.06572 | −0.532861 | − | 0.846203i | \(-0.678883\pi\) | ||||
−0.532861 | + | 0.846203i | \(0.678883\pi\) | |||||||
\(992\) | −54.6725 | −1.73585 | ||||||||
\(993\) | −53.6512 | −1.70257 | ||||||||
\(994\) | −15.8756 | −0.503543 | ||||||||
\(995\) | −5.91743 | −0.187595 | ||||||||
\(996\) | 35.2823 | 1.11796 | ||||||||
\(997\) | −22.5615 | −0.714531 | −0.357266 | − | 0.934003i | \(-0.616291\pi\) | ||||
−0.357266 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(998\) | −20.8139 | −0.658853 | ||||||||
\(999\) | 73.2734 | 2.31827 |
(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 | 4001.2.a.b.1.1 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.1 | ✓ | 184 | 1.1 | even | 1 | trivial |