Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42751 | −1.71651 | −0.858255 | − | 0.513224i | \(-0.828451\pi\) | ||||
−0.858255 | + | 0.513224i | \(0.828451\pi\) | |||||||
\(3\) | 0.768452 | 0.443666 | 0.221833 | − | 0.975085i | \(-0.428796\pi\) | ||||
0.221833 | + | 0.975085i | \(0.428796\pi\) | |||||||
\(4\) | 3.89281 | 1.94640 | ||||||||
\(5\) | −1.80408 | −0.806810 | −0.403405 | − | 0.915022i | \(-0.632173\pi\) | ||||
−0.403405 | + | 0.915022i | \(0.632173\pi\) | |||||||
\(6\) | −1.86543 | −0.761557 | ||||||||
\(7\) | −1.49541 | −0.565213 | −0.282607 | − | 0.959236i | \(-0.591199\pi\) | ||||
−0.282607 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(8\) | −4.59481 | −1.62451 | ||||||||
\(9\) | −2.40948 | −0.803160 | ||||||||
\(10\) | 4.37943 | 1.38490 | ||||||||
\(11\) | 2.97086 | 0.895747 | 0.447874 | − | 0.894097i | \(-0.352181\pi\) | ||||
0.447874 | + | 0.894097i | \(0.352181\pi\) | |||||||
\(12\) | 2.99144 | 0.863554 | ||||||||
\(13\) | −1.84647 | −0.512119 | −0.256060 | − | 0.966661i | \(-0.582424\pi\) | ||||
−0.256060 | + | 0.966661i | \(0.582424\pi\) | |||||||
\(14\) | 3.63013 | 0.970194 | ||||||||
\(15\) | −1.38635 | −0.357954 | ||||||||
\(16\) | 3.36833 | 0.842084 | ||||||||
\(17\) | −6.82756 | −1.65593 | −0.827963 | − | 0.560782i | \(-0.810501\pi\) | ||||
−0.827963 | + | 0.560782i | \(0.810501\pi\) | |||||||
\(18\) | 5.84904 | 1.37863 | ||||||||
\(19\) | −5.71406 | −1.31090 | −0.655448 | − | 0.755240i | \(-0.727520\pi\) | ||||
−0.655448 | + | 0.755240i | \(0.727520\pi\) | |||||||
\(20\) | −7.02294 | −1.57038 | ||||||||
\(21\) | −1.14915 | −0.250766 | ||||||||
\(22\) | −7.21179 | −1.53756 | ||||||||
\(23\) | −5.61717 | −1.17126 | −0.585630 | − | 0.810578i | \(-0.699153\pi\) | ||||
−0.585630 | + | 0.810578i | \(0.699153\pi\) | |||||||
\(24\) | −3.53089 | −0.720740 | ||||||||
\(25\) | −1.74529 | −0.349057 | ||||||||
\(26\) | 4.48233 | 0.879057 | ||||||||
\(27\) | −4.15693 | −0.800001 | ||||||||
\(28\) | −5.82136 | −1.10013 | ||||||||
\(29\) | −3.47630 | −0.645532 | −0.322766 | − | 0.946479i | \(-0.604613\pi\) | ||||
−0.322766 | + | 0.946479i | \(0.604613\pi\) | |||||||
\(30\) | 3.36538 | 0.614432 | ||||||||
\(31\) | −5.39445 | −0.968873 | −0.484436 | − | 0.874827i | \(-0.660975\pi\) | ||||
−0.484436 | + | 0.874827i | \(0.660975\pi\) | |||||||
\(32\) | 1.01295 | 0.179066 | ||||||||
\(33\) | 2.28296 | 0.397413 | ||||||||
\(34\) | 16.5740 | 2.84241 | ||||||||
\(35\) | 2.69785 | 0.456020 | ||||||||
\(36\) | −9.37964 | −1.56327 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 13.8709 | 2.25016 | ||||||||
\(39\) | −1.41893 | −0.227210 | ||||||||
\(40\) | 8.28942 | 1.31067 | ||||||||
\(41\) | 3.17793 | 0.496309 | 0.248154 | − | 0.968720i | \(-0.420176\pi\) | ||||
0.248154 | + | 0.968720i | \(0.420176\pi\) | |||||||
\(42\) | 2.78958 | 0.430442 | ||||||||
\(43\) | 7.12496 | 1.08655 | 0.543273 | − | 0.839556i | \(-0.317185\pi\) | ||||
0.543273 | + | 0.839556i | \(0.317185\pi\) | |||||||
\(44\) | 11.5650 | 1.74349 | ||||||||
\(45\) | 4.34690 | 0.647998 | ||||||||
\(46\) | 13.6357 | 2.01048 | ||||||||
\(47\) | 9.94586 | 1.45075 | 0.725376 | − | 0.688352i | \(-0.241666\pi\) | ||||
0.725376 | + | 0.688352i | \(0.241666\pi\) | |||||||
\(48\) | 2.58841 | 0.373604 | ||||||||
\(49\) | −4.76374 | −0.680534 | ||||||||
\(50\) | 4.23670 | 0.599160 | ||||||||
\(51\) | −5.24666 | −0.734679 | ||||||||
\(52\) | −7.18796 | −0.996791 | ||||||||
\(53\) | −2.03347 | −0.279319 | −0.139659 | − | 0.990200i | \(-0.544601\pi\) | ||||
−0.139659 | + | 0.990200i | \(0.544601\pi\) | |||||||
\(54\) | 10.0910 | 1.37321 | ||||||||
\(55\) | −5.35967 | −0.722698 | ||||||||
\(56\) | 6.87114 | 0.918195 | ||||||||
\(57\) | −4.39098 | −0.581600 | ||||||||
\(58\) | 8.43875 | 1.10806 | ||||||||
\(59\) | −0.552160 | −0.0718852 | −0.0359426 | − | 0.999354i | \(-0.511443\pi\) | ||||
−0.0359426 | + | 0.999354i | \(0.511443\pi\) | |||||||
\(60\) | −5.39680 | −0.696724 | ||||||||
\(61\) | −1.33903 | −0.171445 | −0.0857225 | − | 0.996319i | \(-0.527320\pi\) | ||||
−0.0857225 | + | 0.996319i | \(0.527320\pi\) | |||||||
\(62\) | 13.0951 | 1.66308 | ||||||||
\(63\) | 3.60317 | 0.453957 | ||||||||
\(64\) | −9.19562 | −1.14945 | ||||||||
\(65\) | 3.33119 | 0.413183 | ||||||||
\(66\) | −5.54192 | −0.682163 | ||||||||
\(67\) | −13.5490 | −1.65528 | −0.827639 | − | 0.561260i | \(-0.810317\pi\) | ||||
−0.827639 | + | 0.561260i | \(0.810317\pi\) | |||||||
\(68\) | −26.5784 | −3.22310 | ||||||||
\(69\) | −4.31652 | −0.519649 | ||||||||
\(70\) | −6.54906 | −0.782762 | ||||||||
\(71\) | 3.11420 | 0.369588 | 0.184794 | − | 0.982777i | \(-0.440838\pi\) | ||||
0.184794 | + | 0.982777i | \(0.440838\pi\) | |||||||
\(72\) | 11.0711 | 1.30474 | ||||||||
\(73\) | 5.87331 | 0.687419 | 0.343710 | − | 0.939076i | \(-0.388316\pi\) | ||||
0.343710 | + | 0.939076i | \(0.388316\pi\) | |||||||
\(74\) | −2.42751 | −0.282192 | ||||||||
\(75\) | −1.34117 | −0.154865 | ||||||||
\(76\) | −22.2437 | −2.55153 | ||||||||
\(77\) | −4.44266 | −0.506288 | ||||||||
\(78\) | 3.44446 | 0.390008 | ||||||||
\(79\) | −3.44403 | −0.387484 | −0.193742 | − | 0.981053i | \(-0.562062\pi\) | ||||
−0.193742 | + | 0.981053i | \(0.562062\pi\) | |||||||
\(80\) | −6.07675 | −0.679402 | ||||||||
\(81\) | 4.03404 | 0.448227 | ||||||||
\(82\) | −7.71445 | −0.851919 | ||||||||
\(83\) | 10.5073 | 1.15332 | 0.576662 | − | 0.816983i | \(-0.304355\pi\) | ||||
0.576662 | + | 0.816983i | \(0.304355\pi\) | |||||||
\(84\) | −4.47344 | −0.488092 | ||||||||
\(85\) | 12.3175 | 1.33602 | ||||||||
\(86\) | −17.2959 | −1.86507 | ||||||||
\(87\) | −2.67137 | −0.286401 | ||||||||
\(88\) | −13.6505 | −1.45515 | ||||||||
\(89\) | −7.22436 | −0.765781 | −0.382890 | − | 0.923794i | \(-0.625071\pi\) | ||||
−0.382890 | + | 0.923794i | \(0.625071\pi\) | |||||||
\(90\) | −10.5521 | −1.11229 | ||||||||
\(91\) | 2.76124 | 0.289456 | ||||||||
\(92\) | −21.8665 | −2.27974 | ||||||||
\(93\) | −4.14538 | −0.429856 | ||||||||
\(94\) | −24.1437 | −2.49023 | ||||||||
\(95\) | 10.3086 | 1.05764 | ||||||||
\(96\) | 0.778405 | 0.0794457 | ||||||||
\(97\) | 7.20542 | 0.731600 | 0.365800 | − | 0.930694i | \(-0.380795\pi\) | ||||
0.365800 | + | 0.930694i | \(0.380795\pi\) | |||||||
\(98\) | 11.5640 | 1.16814 | ||||||||
\(99\) | −7.15822 | −0.719429 | ||||||||
\(100\) | −6.79407 | −0.679407 | ||||||||
\(101\) | 8.44211 | 0.840021 | 0.420011 | − | 0.907519i | \(-0.362026\pi\) | ||||
0.420011 | + | 0.907519i | \(0.362026\pi\) | |||||||
\(102\) | 12.7363 | 1.26108 | ||||||||
\(103\) | −9.22361 | −0.908829 | −0.454414 | − | 0.890790i | \(-0.650151\pi\) | ||||
−0.454414 | + | 0.890790i | \(0.650151\pi\) | |||||||
\(104\) | 8.48419 | 0.831943 | ||||||||
\(105\) | 2.07317 | 0.202321 | ||||||||
\(106\) | 4.93627 | 0.479453 | ||||||||
\(107\) | 15.7803 | 1.52554 | 0.762770 | − | 0.646670i | \(-0.223839\pi\) | ||||
0.762770 | + | 0.646670i | \(0.223839\pi\) | |||||||
\(108\) | −16.1821 | −1.55713 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 13.0107 | 1.24052 | ||||||||
\(111\) | 0.768452 | 0.0729383 | ||||||||
\(112\) | −5.03705 | −0.475957 | ||||||||
\(113\) | 6.58148 | 0.619134 | 0.309567 | − | 0.950878i | \(-0.399816\pi\) | ||||
0.309567 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(114\) | 10.6592 | 0.998322 | ||||||||
\(115\) | 10.1338 | 0.944984 | ||||||||
\(116\) | −13.5326 | −1.25647 | ||||||||
\(117\) | 4.44904 | 0.411314 | ||||||||
\(118\) | 1.34038 | 0.123392 | ||||||||
\(119\) | 10.2100 | 0.935952 | ||||||||
\(120\) | 6.37002 | 0.581501 | ||||||||
\(121\) | −2.17401 | −0.197637 | ||||||||
\(122\) | 3.25051 | 0.294287 | ||||||||
\(123\) | 2.44209 | 0.220195 | ||||||||
\(124\) | −20.9996 | −1.88582 | ||||||||
\(125\) | 12.1691 | 1.08843 | ||||||||
\(126\) | −8.74673 | −0.779221 | ||||||||
\(127\) | 2.62821 | 0.233216 | 0.116608 | − | 0.993178i | \(-0.462798\pi\) | ||||
0.116608 | + | 0.993178i | \(0.462798\pi\) | |||||||
\(128\) | 20.2966 | 1.79398 | ||||||||
\(129\) | 5.47519 | 0.482064 | ||||||||
\(130\) | −8.08649 | −0.709232 | ||||||||
\(131\) | −16.6664 | −1.45615 | −0.728075 | − | 0.685497i | \(-0.759585\pi\) | ||||
−0.728075 | + | 0.685497i | \(0.759585\pi\) | |||||||
\(132\) | 8.88713 | 0.773526 | ||||||||
\(133\) | 8.54489 | 0.740936 | ||||||||
\(134\) | 32.8904 | 2.84130 | ||||||||
\(135\) | 7.49944 | 0.645449 | ||||||||
\(136\) | 31.3713 | 2.69007 | ||||||||
\(137\) | −10.3835 | −0.887120 | −0.443560 | − | 0.896245i | \(-0.646285\pi\) | ||||
−0.443560 | + | 0.896245i | \(0.646285\pi\) | |||||||
\(138\) | 10.4784 | 0.891981 | ||||||||
\(139\) | −15.7388 | −1.33495 | −0.667473 | − | 0.744634i | \(-0.732624\pi\) | ||||
−0.667473 | + | 0.744634i | \(0.732624\pi\) | |||||||
\(140\) | 10.5022 | 0.887598 | ||||||||
\(141\) | 7.64292 | 0.643650 | ||||||||
\(142\) | −7.55975 | −0.634400 | ||||||||
\(143\) | −5.48561 | −0.458729 | ||||||||
\(144\) | −8.11594 | −0.676328 | ||||||||
\(145\) | 6.27152 | 0.520822 | ||||||||
\(146\) | −14.2575 | −1.17996 | ||||||||
\(147\) | −3.66071 | −0.301930 | ||||||||
\(148\) | 3.89281 | 0.319987 | ||||||||
\(149\) | −13.3812 | −1.09623 | −0.548116 | − | 0.836402i | \(-0.684655\pi\) | ||||
−0.548116 | + | 0.836402i | \(0.684655\pi\) | |||||||
\(150\) | 3.25570 | 0.265827 | ||||||||
\(151\) | −5.21263 | −0.424198 | −0.212099 | − | 0.977248i | \(-0.568030\pi\) | ||||
−0.212099 | + | 0.977248i | \(0.568030\pi\) | |||||||
\(152\) | 26.2550 | 2.12956 | ||||||||
\(153\) | 16.4509 | 1.32997 | ||||||||
\(154\) | 10.7846 | 0.869048 | ||||||||
\(155\) | 9.73204 | 0.781696 | ||||||||
\(156\) | −5.52361 | −0.442242 | ||||||||
\(157\) | 21.6289 | 1.72617 | 0.863085 | − | 0.505058i | \(-0.168529\pi\) | ||||
0.863085 | + | 0.505058i | \(0.168529\pi\) | |||||||
\(158\) | 8.36042 | 0.665120 | ||||||||
\(159\) | −1.56262 | −0.123924 | ||||||||
\(160\) | −1.82745 | −0.144472 | ||||||||
\(161\) | 8.39999 | 0.662012 | ||||||||
\(162\) | −9.79268 | −0.769385 | ||||||||
\(163\) | 4.61421 | 0.361413 | 0.180706 | − | 0.983537i | \(-0.442162\pi\) | ||||
0.180706 | + | 0.983537i | \(0.442162\pi\) | |||||||
\(164\) | 12.3711 | 0.966017 | ||||||||
\(165\) | −4.11865 | −0.320637 | ||||||||
\(166\) | −25.5065 | −1.97969 | ||||||||
\(167\) | 7.92133 | 0.612971 | 0.306486 | − | 0.951875i | \(-0.400847\pi\) | ||||
0.306486 | + | 0.951875i | \(0.400847\pi\) | |||||||
\(168\) | 5.28014 | 0.407372 | ||||||||
\(169\) | −9.59054 | −0.737734 | ||||||||
\(170\) | −29.9008 | −2.29329 | ||||||||
\(171\) | 13.7679 | 1.05286 | ||||||||
\(172\) | 27.7361 | 2.11486 | ||||||||
\(173\) | 2.80971 | 0.213618 | 0.106809 | − | 0.994280i | \(-0.465937\pi\) | ||||
0.106809 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(174\) | 6.48477 | 0.491609 | ||||||||
\(175\) | 2.60993 | 0.197292 | ||||||||
\(176\) | 10.0068 | 0.754294 | ||||||||
\(177\) | −0.424309 | −0.0318930 | ||||||||
\(178\) | 17.5372 | 1.31447 | ||||||||
\(179\) | 23.4144 | 1.75008 | 0.875038 | − | 0.484055i | \(-0.160837\pi\) | ||||
0.875038 | + | 0.484055i | \(0.160837\pi\) | |||||||
\(180\) | 16.9217 | 1.26127 | ||||||||
\(181\) | −1.29466 | −0.0962316 | −0.0481158 | − | 0.998842i | \(-0.515322\pi\) | ||||
−0.0481158 | + | 0.998842i | \(0.515322\pi\) | |||||||
\(182\) | −6.70294 | −0.496855 | ||||||||
\(183\) | −1.02898 | −0.0760644 | ||||||||
\(184\) | 25.8098 | 1.90272 | ||||||||
\(185\) | −1.80408 | −0.132639 | ||||||||
\(186\) | 10.0630 | 0.737852 | ||||||||
\(187\) | −20.2837 | −1.48329 | ||||||||
\(188\) | 38.7173 | 2.82375 | ||||||||
\(189\) | 6.21633 | 0.452171 | ||||||||
\(190\) | −25.0243 | −1.81546 | ||||||||
\(191\) | −10.4978 | −0.759594 | −0.379797 | − | 0.925070i | \(-0.624006\pi\) | ||||
−0.379797 | + | 0.925070i | \(0.624006\pi\) | |||||||
\(192\) | −7.06640 | −0.509973 | ||||||||
\(193\) | −17.2135 | −1.23906 | −0.619528 | − | 0.784974i | \(-0.712676\pi\) | ||||
−0.619528 | + | 0.784974i | \(0.712676\pi\) | |||||||
\(194\) | −17.4912 | −1.25580 | ||||||||
\(195\) | 2.55986 | 0.183315 | ||||||||
\(196\) | −18.5443 | −1.32459 | ||||||||
\(197\) | −25.9580 | −1.84943 | −0.924715 | − | 0.380659i | \(-0.875697\pi\) | ||||
−0.924715 | + | 0.380659i | \(0.875697\pi\) | |||||||
\(198\) | 17.3767 | 1.23491 | ||||||||
\(199\) | −11.2636 | −0.798453 | −0.399227 | − | 0.916852i | \(-0.630721\pi\) | ||||
−0.399227 | + | 0.916852i | \(0.630721\pi\) | |||||||
\(200\) | 8.01926 | 0.567048 | ||||||||
\(201\) | −10.4118 | −0.734391 | ||||||||
\(202\) | −20.4933 | −1.44190 | ||||||||
\(203\) | 5.19850 | 0.364863 | ||||||||
\(204\) | −20.4242 | −1.42998 | ||||||||
\(205\) | −5.73324 | −0.400427 | ||||||||
\(206\) | 22.3904 | 1.56001 | ||||||||
\(207\) | 13.5345 | 0.940710 | ||||||||
\(208\) | −6.21954 | −0.431247 | ||||||||
\(209\) | −16.9757 | −1.17423 | ||||||||
\(210\) | −5.03264 | −0.347285 | ||||||||
\(211\) | 13.5970 | 0.936059 | 0.468029 | − | 0.883713i | \(-0.344964\pi\) | ||||
0.468029 | + | 0.883713i | \(0.344964\pi\) | |||||||
\(212\) | −7.91591 | −0.543667 | ||||||||
\(213\) | 2.39311 | 0.163974 | ||||||||
\(214\) | −38.3069 | −2.61860 | ||||||||
\(215\) | −12.8540 | −0.876636 | ||||||||
\(216\) | 19.1003 | 1.29961 | ||||||||
\(217\) | 8.06694 | 0.547619 | ||||||||
\(218\) | 2.42751 | 0.164412 | ||||||||
\(219\) | 4.51336 | 0.304985 | ||||||||
\(220\) | −20.8642 | −1.40666 | ||||||||
\(221\) | 12.6069 | 0.848032 | ||||||||
\(222\) | −1.86543 | −0.125199 | ||||||||
\(223\) | −4.64712 | −0.311194 | −0.155597 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155597 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(224\) | −1.51478 | −0.101211 | ||||||||
\(225\) | 4.20524 | 0.280349 | ||||||||
\(226\) | −15.9766 | −1.06275 | ||||||||
\(227\) | −1.34031 | −0.0889596 | −0.0444798 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444798 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(228\) | −17.0933 | −1.13203 | ||||||||
\(229\) | 16.5231 | 1.09187 | 0.545937 | − | 0.837826i | \(-0.316174\pi\) | ||||
0.545937 | + | 0.837826i | \(0.316174\pi\) | |||||||
\(230\) | −24.6000 | −1.62207 | ||||||||
\(231\) | −3.41397 | −0.224623 | ||||||||
\(232\) | 15.9729 | 1.04867 | ||||||||
\(233\) | 26.1575 | 1.71364 | 0.856818 | − | 0.515618i | \(-0.172438\pi\) | ||||
0.856818 | + | 0.515618i | \(0.172438\pi\) | |||||||
\(234\) | −10.8001 | −0.706024 | ||||||||
\(235\) | −17.9431 | −1.17048 | ||||||||
\(236\) | −2.14945 | −0.139918 | ||||||||
\(237\) | −2.64657 | −0.171913 | ||||||||
\(238\) | −24.7849 | −1.60657 | ||||||||
\(239\) | −3.63978 | −0.235438 | −0.117719 | − | 0.993047i | \(-0.537558\pi\) | ||||
−0.117719 | + | 0.993047i | \(0.537558\pi\) | |||||||
\(240\) | −4.66970 | −0.301428 | ||||||||
\(241\) | 28.8732 | 1.85989 | 0.929943 | − | 0.367704i | \(-0.119856\pi\) | ||||
0.929943 | + | 0.367704i | \(0.119856\pi\) | |||||||
\(242\) | 5.27742 | 0.339245 | ||||||||
\(243\) | 15.5708 | 0.998864 | ||||||||
\(244\) | −5.21258 | −0.333701 | ||||||||
\(245\) | 8.59418 | 0.549062 | ||||||||
\(246\) | −5.92819 | −0.377968 | ||||||||
\(247\) | 10.5509 | 0.671335 | ||||||||
\(248\) | 24.7865 | 1.57394 | ||||||||
\(249\) | 8.07435 | 0.511691 | ||||||||
\(250\) | −29.5405 | −1.86831 | ||||||||
\(251\) | −9.68954 | −0.611598 | −0.305799 | − | 0.952096i | \(-0.598924\pi\) | ||||
−0.305799 | + | 0.952096i | \(0.598924\pi\) | |||||||
\(252\) | 14.0264 | 0.883583 | ||||||||
\(253\) | −16.6878 | −1.04915 | ||||||||
\(254\) | −6.38001 | −0.400317 | ||||||||
\(255\) | 9.46540 | 0.592746 | ||||||||
\(256\) | −30.8789 | −1.92993 | ||||||||
\(257\) | −14.8035 | −0.923416 | −0.461708 | − | 0.887032i | \(-0.652763\pi\) | ||||
−0.461708 | + | 0.887032i | \(0.652763\pi\) | |||||||
\(258\) | −13.2911 | −0.827467 | ||||||||
\(259\) | −1.49541 | −0.0929205 | ||||||||
\(260\) | 12.9677 | 0.804221 | ||||||||
\(261\) | 8.37607 | 0.518466 | ||||||||
\(262\) | 40.4579 | 2.49950 | ||||||||
\(263\) | −6.50204 | −0.400933 | −0.200467 | − | 0.979701i | \(-0.564246\pi\) | ||||
−0.200467 | + | 0.979701i | \(0.564246\pi\) | |||||||
\(264\) | −10.4898 | −0.645601 | ||||||||
\(265\) | 3.66855 | 0.225357 | ||||||||
\(266\) | −20.7428 | −1.27182 | ||||||||
\(267\) | −5.55158 | −0.339751 | ||||||||
\(268\) | −52.7438 | −3.22184 | ||||||||
\(269\) | 3.12058 | 0.190265 | 0.0951326 | − | 0.995465i | \(-0.469672\pi\) | ||||
0.0951326 | + | 0.995465i | \(0.469672\pi\) | |||||||
\(270\) | −18.2050 | −1.10792 | ||||||||
\(271\) | −26.9663 | −1.63809 | −0.819043 | − | 0.573732i | \(-0.805495\pi\) | ||||
−0.819043 | + | 0.573732i | \(0.805495\pi\) | |||||||
\(272\) | −22.9975 | −1.39443 | ||||||||
\(273\) | 2.12188 | 0.128422 | ||||||||
\(274\) | 25.2060 | 1.52275 | ||||||||
\(275\) | −5.18500 | −0.312667 | ||||||||
\(276\) | −16.8034 | −1.01145 | ||||||||
\(277\) | 20.3106 | 1.22034 | 0.610172 | − | 0.792269i | \(-0.291100\pi\) | ||||
0.610172 | + | 0.792269i | \(0.291100\pi\) | |||||||
\(278\) | 38.2061 | 2.29145 | ||||||||
\(279\) | 12.9978 | 0.778160 | ||||||||
\(280\) | −12.3961 | −0.740809 | ||||||||
\(281\) | −26.7524 | −1.59591 | −0.797956 | − | 0.602716i | \(-0.794085\pi\) | ||||
−0.797956 | + | 0.602716i | \(0.794085\pi\) | |||||||
\(282\) | −18.5533 | −1.10483 | ||||||||
\(283\) | −13.2987 | −0.790524 | −0.395262 | − | 0.918568i | \(-0.629346\pi\) | ||||
−0.395262 | + | 0.918568i | \(0.629346\pi\) | |||||||
\(284\) | 12.1230 | 0.719367 | ||||||||
\(285\) | 7.92170 | 0.469241 | ||||||||
\(286\) | 13.3164 | 0.787413 | ||||||||
\(287\) | −4.75232 | −0.280520 | ||||||||
\(288\) | −2.44069 | −0.143819 | ||||||||
\(289\) | 29.6156 | 1.74209 | ||||||||
\(290\) | −15.2242 | −0.893995 | ||||||||
\(291\) | 5.53702 | 0.324586 | ||||||||
\(292\) | 22.8637 | 1.33800 | ||||||||
\(293\) | 9.15156 | 0.534640 | 0.267320 | − | 0.963608i | \(-0.413862\pi\) | ||||
0.267320 | + | 0.963608i | \(0.413862\pi\) | |||||||
\(294\) | 8.88640 | 0.518266 | ||||||||
\(295\) | 0.996143 | 0.0579977 | ||||||||
\(296\) | −4.59481 | −0.267068 | ||||||||
\(297\) | −12.3496 | −0.716599 | ||||||||
\(298\) | 32.4830 | 1.88169 | ||||||||
\(299\) | 10.3719 | 0.599825 | ||||||||
\(300\) | −5.22092 | −0.301430 | ||||||||
\(301\) | −10.6548 | −0.614130 | ||||||||
\(302\) | 12.6537 | 0.728139 | ||||||||
\(303\) | 6.48736 | 0.372689 | ||||||||
\(304\) | −19.2469 | −1.10388 | ||||||||
\(305\) | 2.41572 | 0.138324 | ||||||||
\(306\) | −39.9347 | −2.28291 | ||||||||
\(307\) | −26.3195 | −1.50214 | −0.751068 | − | 0.660225i | \(-0.770461\pi\) | ||||
−0.751068 | + | 0.660225i | \(0.770461\pi\) | |||||||
\(308\) | −17.2944 | −0.985441 | ||||||||
\(309\) | −7.08790 | −0.403217 | ||||||||
\(310\) | −23.6246 | −1.34179 | ||||||||
\(311\) | 31.0047 | 1.75812 | 0.879058 | − | 0.476715i | \(-0.158173\pi\) | ||||
0.879058 | + | 0.476715i | \(0.158173\pi\) | |||||||
\(312\) | 6.51969 | 0.369105 | ||||||||
\(313\) | −1.40460 | −0.0793925 | −0.0396963 | − | 0.999212i | \(-0.512639\pi\) | ||||
−0.0396963 | + | 0.999212i | \(0.512639\pi\) | |||||||
\(314\) | −52.5043 | −2.96299 | ||||||||
\(315\) | −6.50041 | −0.366257 | ||||||||
\(316\) | −13.4070 | −0.754200 | ||||||||
\(317\) | 29.3446 | 1.64816 | 0.824079 | − | 0.566475i | \(-0.191693\pi\) | ||||
0.824079 | + | 0.566475i | \(0.191693\pi\) | |||||||
\(318\) | 3.79329 | 0.212717 | ||||||||
\(319\) | −10.3276 | −0.578234 | ||||||||
\(320\) | 16.5897 | 0.927390 | ||||||||
\(321\) | 12.1264 | 0.676831 | ||||||||
\(322\) | −20.3911 | −1.13635 | ||||||||
\(323\) | 39.0131 | 2.17075 | ||||||||
\(324\) | 15.7037 | 0.872430 | ||||||||
\(325\) | 3.22262 | 0.178759 | ||||||||
\(326\) | −11.2010 | −0.620368 | ||||||||
\(327\) | −0.768452 | −0.0424955 | ||||||||
\(328\) | −14.6020 | −0.806259 | ||||||||
\(329\) | −14.8732 | −0.819984 | ||||||||
\(330\) | 9.99807 | 0.550376 | ||||||||
\(331\) | −7.92208 | −0.435437 | −0.217719 | − | 0.976012i | \(-0.569861\pi\) | ||||
−0.217719 | + | 0.976012i | \(0.569861\pi\) | |||||||
\(332\) | 40.9028 | 2.24483 | ||||||||
\(333\) | −2.40948 | −0.132039 | ||||||||
\(334\) | −19.2291 | −1.05217 | ||||||||
\(335\) | 24.4436 | 1.33550 | ||||||||
\(336\) | −3.87074 | −0.211166 | ||||||||
\(337\) | −30.1705 | −1.64349 | −0.821746 | − | 0.569853i | \(-0.807000\pi\) | ||||
−0.821746 | + | 0.569853i | \(0.807000\pi\) | |||||||
\(338\) | 23.2811 | 1.26633 | ||||||||
\(339\) | 5.05755 | 0.274689 | ||||||||
\(340\) | 47.9496 | 2.60043 | ||||||||
\(341\) | −16.0262 | −0.867865 | ||||||||
\(342\) | −33.4218 | −1.80724 | ||||||||
\(343\) | 17.5917 | 0.949860 | ||||||||
\(344\) | −32.7378 | −1.76511 | ||||||||
\(345\) | 7.78737 | 0.419258 | ||||||||
\(346\) | −6.82059 | −0.366677 | ||||||||
\(347\) | 11.0403 | 0.592677 | 0.296338 | − | 0.955083i | \(-0.404234\pi\) | ||||
0.296338 | + | 0.955083i | \(0.404234\pi\) | |||||||
\(348\) | −10.3991 | −0.557451 | ||||||||
\(349\) | −7.66309 | −0.410196 | −0.205098 | − | 0.978741i | \(-0.565751\pi\) | ||||
−0.205098 | + | 0.978741i | \(0.565751\pi\) | |||||||
\(350\) | −6.33562 | −0.338653 | ||||||||
\(351\) | 7.67565 | 0.409696 | ||||||||
\(352\) | 3.00934 | 0.160398 | ||||||||
\(353\) | 30.9741 | 1.64858 | 0.824291 | − | 0.566166i | \(-0.191574\pi\) | ||||
0.824291 | + | 0.566166i | \(0.191574\pi\) | |||||||
\(354\) | 1.03001 | 0.0547447 | ||||||||
\(355\) | −5.61827 | −0.298187 | ||||||||
\(356\) | −28.1230 | −1.49052 | ||||||||
\(357\) | 7.84592 | 0.415250 | ||||||||
\(358\) | −56.8387 | −3.00402 | ||||||||
\(359\) | −16.3775 | −0.864370 | −0.432185 | − | 0.901785i | \(-0.642257\pi\) | ||||
−0.432185 | + | 0.901785i | \(0.642257\pi\) | |||||||
\(360\) | −19.9732 | −1.05268 | ||||||||
\(361\) | 13.6505 | 0.718448 | ||||||||
\(362\) | 3.14281 | 0.165182 | ||||||||
\(363\) | −1.67062 | −0.0876848 | ||||||||
\(364\) | 10.7490 | 0.563399 | ||||||||
\(365\) | −10.5959 | −0.554617 | ||||||||
\(366\) | 2.49786 | 0.130565 | ||||||||
\(367\) | 6.75363 | 0.352537 | 0.176268 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176268 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(368\) | −18.9205 | −0.986299 | ||||||||
\(369\) | −7.65716 | −0.398616 | ||||||||
\(370\) | 4.37943 | 0.227676 | ||||||||
\(371\) | 3.04088 | 0.157875 | ||||||||
\(372\) | −16.1372 | −0.836673 | ||||||||
\(373\) | 7.94066 | 0.411152 | 0.205576 | − | 0.978641i | \(-0.434093\pi\) | ||||
0.205576 | + | 0.978641i | \(0.434093\pi\) | |||||||
\(374\) | 49.2389 | 2.54608 | ||||||||
\(375\) | 9.35134 | 0.482901 | ||||||||
\(376\) | −45.6993 | −2.35676 | ||||||||
\(377\) | 6.41888 | 0.330589 | ||||||||
\(378\) | −15.0902 | −0.776156 | ||||||||
\(379\) | −7.92977 | −0.407325 | −0.203663 | − | 0.979041i | \(-0.565285\pi\) | ||||
−0.203663 | + | 0.979041i | \(0.565285\pi\) | |||||||
\(380\) | 40.1295 | 2.05860 | ||||||||
\(381\) | 2.01965 | 0.103470 | ||||||||
\(382\) | 25.4835 | 1.30385 | ||||||||
\(383\) | 4.61879 | 0.236009 | 0.118004 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118004 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(384\) | 15.5969 | 0.795928 | ||||||||
\(385\) | 8.01492 | 0.408478 | ||||||||
\(386\) | 41.7860 | 2.12685 | ||||||||
\(387\) | −17.1674 | −0.872670 | ||||||||
\(388\) | 28.0493 | 1.42399 | ||||||||
\(389\) | −14.7434 | −0.747521 | −0.373760 | − | 0.927525i | \(-0.621932\pi\) | ||||
−0.373760 | + | 0.927525i | \(0.621932\pi\) | |||||||
\(390\) | −6.21408 | −0.314662 | ||||||||
\(391\) | 38.3515 | 1.93952 | ||||||||
\(392\) | 21.8885 | 1.10553 | ||||||||
\(393\) | −12.8073 | −0.646045 | ||||||||
\(394\) | 63.0133 | 3.17457 | ||||||||
\(395\) | 6.21332 | 0.312626 | ||||||||
\(396\) | −27.8656 | −1.40030 | ||||||||
\(397\) | −10.5883 | −0.531412 | −0.265706 | − | 0.964054i | \(-0.585605\pi\) | ||||
−0.265706 | + | 0.964054i | \(0.585605\pi\) | |||||||
\(398\) | 27.3424 | 1.37055 | ||||||||
\(399\) | 6.56634 | 0.328728 | ||||||||
\(400\) | −5.87871 | −0.293936 | ||||||||
\(401\) | 32.2288 | 1.60943 | 0.804715 | − | 0.593662i | \(-0.202318\pi\) | ||||
0.804715 | + | 0.593662i | \(0.202318\pi\) | |||||||
\(402\) | 25.2747 | 1.26059 | ||||||||
\(403\) | 9.96071 | 0.496178 | ||||||||
\(404\) | 32.8635 | 1.63502 | ||||||||
\(405\) | −7.27774 | −0.361634 | ||||||||
\(406\) | −12.6194 | −0.626291 | ||||||||
\(407\) | 2.97086 | 0.147260 | ||||||||
\(408\) | 24.1074 | 1.19349 | ||||||||
\(409\) | −0.719509 | −0.0355775 | −0.0177887 | − | 0.999842i | \(-0.505663\pi\) | ||||
−0.0177887 | + | 0.999842i | \(0.505663\pi\) | |||||||
\(410\) | 13.9175 | 0.687337 | ||||||||
\(411\) | −7.97921 | −0.393585 | ||||||||
\(412\) | −35.9057 | −1.76895 | ||||||||
\(413\) | 0.825708 | 0.0406304 | ||||||||
\(414\) | −32.8550 | −1.61474 | ||||||||
\(415\) | −18.9560 | −0.930514 | ||||||||
\(416\) | −1.87039 | −0.0917033 | ||||||||
\(417\) | −12.0945 | −0.592271 | ||||||||
\(418\) | 41.2086 | 2.01558 | ||||||||
\(419\) | −24.0515 | −1.17499 | −0.587496 | − | 0.809227i | \(-0.699886\pi\) | ||||
−0.587496 | + | 0.809227i | \(0.699886\pi\) | |||||||
\(420\) | 8.07045 | 0.393797 | ||||||||
\(421\) | −1.84902 | −0.0901159 | −0.0450579 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450579 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(422\) | −33.0069 | −1.60675 | ||||||||
\(423\) | −23.9644 | −1.16519 | ||||||||
\(424\) | 9.34341 | 0.453756 | ||||||||
\(425\) | 11.9161 | 0.578014 | ||||||||
\(426\) | −5.80931 | −0.281462 | ||||||||
\(427\) | 2.00240 | 0.0969030 | ||||||||
\(428\) | 61.4297 | 2.96932 | ||||||||
\(429\) | −4.21543 | −0.203523 | ||||||||
\(430\) | 31.2032 | 1.50475 | ||||||||
\(431\) | −4.55937 | −0.219617 | −0.109809 | − | 0.993953i | \(-0.535024\pi\) | ||||
−0.109809 | + | 0.993953i | \(0.535024\pi\) | |||||||
\(432\) | −14.0019 | −0.673668 | ||||||||
\(433\) | −2.12948 | −0.102336 | −0.0511681 | − | 0.998690i | \(-0.516294\pi\) | ||||
−0.0511681 | + | 0.998690i | \(0.516294\pi\) | |||||||
\(434\) | −19.5826 | −0.939994 | ||||||||
\(435\) | 4.81937 | 0.231071 | ||||||||
\(436\) | −3.89281 | −0.186432 | ||||||||
\(437\) | 32.0968 | 1.53540 | ||||||||
\(438\) | −10.9562 | −0.523509 | ||||||||
\(439\) | −6.17343 | −0.294642 | −0.147321 | − | 0.989089i | \(-0.547065\pi\) | ||||
−0.147321 | + | 0.989089i | \(0.547065\pi\) | |||||||
\(440\) | 24.6267 | 1.17403 | ||||||||
\(441\) | 11.4781 | 0.546578 | ||||||||
\(442\) | −30.6034 | −1.45565 | ||||||||
\(443\) | −36.6404 | −1.74084 | −0.870419 | − | 0.492312i | \(-0.836152\pi\) | ||||
−0.870419 | + | 0.492312i | \(0.836152\pi\) | |||||||
\(444\) | 2.99144 | 0.141967 | ||||||||
\(445\) | 13.0333 | 0.617840 | ||||||||
\(446\) | 11.2809 | 0.534167 | ||||||||
\(447\) | −10.2828 | −0.486361 | ||||||||
\(448\) | 13.7513 | 0.649686 | ||||||||
\(449\) | −13.2742 | −0.626450 | −0.313225 | − | 0.949679i | \(-0.601409\pi\) | ||||
−0.313225 | + | 0.949679i | \(0.601409\pi\) | |||||||
\(450\) | −10.2083 | −0.481222 | ||||||||
\(451\) | 9.44117 | 0.444567 | ||||||||
\(452\) | 25.6204 | 1.20508 | ||||||||
\(453\) | −4.00566 | −0.188202 | ||||||||
\(454\) | 3.25362 | 0.152700 | ||||||||
\(455\) | −4.98150 | −0.233536 | ||||||||
\(456\) | 20.1757 | 0.944816 | ||||||||
\(457\) | 9.93558 | 0.464767 | 0.232383 | − | 0.972624i | \(-0.425348\pi\) | ||||
0.232383 | + | 0.972624i | \(0.425348\pi\) | |||||||
\(458\) | −40.1099 | −1.87421 | ||||||||
\(459\) | 28.3817 | 1.32474 | ||||||||
\(460\) | 39.4490 | 1.83932 | ||||||||
\(461\) | 18.0982 | 0.842917 | 0.421459 | − | 0.906848i | \(-0.361518\pi\) | ||||
0.421459 | + | 0.906848i | \(0.361518\pi\) | |||||||
\(462\) | 8.28746 | 0.385567 | ||||||||
\(463\) | 15.5171 | 0.721139 | 0.360569 | − | 0.932732i | \(-0.382582\pi\) | ||||
0.360569 | + | 0.932732i | \(0.382582\pi\) | |||||||
\(464\) | −11.7093 | −0.543592 | ||||||||
\(465\) | 7.47861 | 0.346812 | ||||||||
\(466\) | −63.4977 | −2.94147 | ||||||||
\(467\) | 28.8867 | 1.33672 | 0.668358 | − | 0.743840i | \(-0.266997\pi\) | ||||
0.668358 | + | 0.743840i | \(0.266997\pi\) | |||||||
\(468\) | 17.3193 | 0.800583 | ||||||||
\(469\) | 20.2614 | 0.935585 | ||||||||
\(470\) | 43.5572 | 2.00914 | ||||||||
\(471\) | 16.6207 | 0.765843 | ||||||||
\(472\) | 2.53707 | 0.116778 | ||||||||
\(473\) | 21.1672 | 0.973270 | ||||||||
\(474\) | 6.42459 | 0.295091 | ||||||||
\(475\) | 9.97268 | 0.457578 | ||||||||
\(476\) | 39.7457 | 1.82174 | ||||||||
\(477\) | 4.89961 | 0.224338 | ||||||||
\(478\) | 8.83560 | 0.404131 | ||||||||
\(479\) | −15.7258 | −0.718528 | −0.359264 | − | 0.933236i | \(-0.616972\pi\) | ||||
−0.359264 | + | 0.933236i | \(0.616972\pi\) | |||||||
\(480\) | −1.40431 | −0.0640976 | ||||||||
\(481\) | −1.84647 | −0.0841919 | ||||||||
\(482\) | −70.0900 | −3.19251 | ||||||||
\(483\) | 6.45499 | 0.293712 | ||||||||
\(484\) | −8.46298 | −0.384681 | ||||||||
\(485\) | −12.9992 | −0.590262 | ||||||||
\(486\) | −37.7982 | −1.71456 | ||||||||
\(487\) | 9.75574 | 0.442075 | 0.221037 | − | 0.975265i | \(-0.429056\pi\) | ||||
0.221037 | + | 0.975265i | \(0.429056\pi\) | |||||||
\(488\) | 6.15258 | 0.278514 | ||||||||
\(489\) | 3.54580 | 0.160347 | ||||||||
\(490\) | −20.8625 | −0.942470 | ||||||||
\(491\) | 26.7865 | 1.20886 | 0.604430 | − | 0.796658i | \(-0.293401\pi\) | ||||
0.604430 | + | 0.796658i | \(0.293401\pi\) | |||||||
\(492\) | 9.50657 | 0.428589 | ||||||||
\(493\) | 23.7346 | 1.06895 | ||||||||
\(494\) | −25.6123 | −1.15235 | ||||||||
\(495\) | 12.9140 | 0.580442 | ||||||||
\(496\) | −18.1703 | −0.815872 | ||||||||
\(497\) | −4.65702 | −0.208896 | ||||||||
\(498\) | −19.6006 | −0.878322 | ||||||||
\(499\) | 22.6275 | 1.01295 | 0.506473 | − | 0.862256i | \(-0.330949\pi\) | ||||
0.506473 | + | 0.862256i | \(0.330949\pi\) | |||||||
\(500\) | 47.3718 | 2.11853 | ||||||||
\(501\) | 6.08717 | 0.271955 | ||||||||
\(502\) | 23.5215 | 1.04981 | ||||||||
\(503\) | −26.0984 | −1.16367 | −0.581834 | − | 0.813307i | \(-0.697665\pi\) | ||||
−0.581834 | + | 0.813307i | \(0.697665\pi\) | |||||||
\(504\) | −16.5559 | −0.737458 | ||||||||
\(505\) | −15.2303 | −0.677738 | ||||||||
\(506\) | 40.5098 | 1.80088 | ||||||||
\(507\) | −7.36987 | −0.327308 | ||||||||
\(508\) | 10.2311 | 0.453932 | ||||||||
\(509\) | 24.6889 | 1.09431 | 0.547157 | − | 0.837030i | \(-0.315710\pi\) | ||||
0.547157 | + | 0.837030i | \(0.315710\pi\) | |||||||
\(510\) | −22.9774 | −1.01745 | ||||||||
\(511\) | −8.78303 | −0.388538 | ||||||||
\(512\) | 34.3657 | 1.51876 | ||||||||
\(513\) | 23.7529 | 1.04872 | ||||||||
\(514\) | 35.9356 | 1.58505 | ||||||||
\(515\) | 16.6401 | 0.733252 | ||||||||
\(516\) | 21.3139 | 0.938291 | ||||||||
\(517\) | 29.5477 | 1.29951 | ||||||||
\(518\) | 3.63013 | 0.159499 | ||||||||
\(519\) | 2.15913 | 0.0947751 | ||||||||
\(520\) | −15.3062 | −0.671220 | ||||||||
\(521\) | 38.3615 | 1.68065 | 0.840324 | − | 0.542084i | \(-0.182364\pi\) | ||||
0.840324 | + | 0.542084i | \(0.182364\pi\) | |||||||
\(522\) | −20.3330 | −0.889951 | ||||||||
\(523\) | −32.4665 | −1.41966 | −0.709830 | − | 0.704373i | \(-0.751228\pi\) | ||||
−0.709830 | + | 0.704373i | \(0.751228\pi\) | |||||||
\(524\) | −64.8791 | −2.83426 | ||||||||
\(525\) | 2.00560 | 0.0875317 | ||||||||
\(526\) | 15.7838 | 0.688206 | ||||||||
\(527\) | 36.8310 | 1.60438 | ||||||||
\(528\) | 7.68978 | 0.334655 | ||||||||
\(529\) | 8.55255 | 0.371850 | ||||||||
\(530\) | −8.90544 | −0.386827 | ||||||||
\(531\) | 1.33042 | 0.0577353 | ||||||||
\(532\) | 33.2636 | 1.44216 | ||||||||
\(533\) | −5.86795 | −0.254169 | ||||||||
\(534\) | 13.4765 | 0.583186 | ||||||||
\(535\) | −28.4690 | −1.23082 | ||||||||
\(536\) | 62.2553 | 2.68902 | ||||||||
\(537\) | 17.9929 | 0.776449 | ||||||||
\(538\) | −7.57524 | −0.326592 | ||||||||
\(539\) | −14.1524 | −0.609587 | ||||||||
\(540\) | 29.1939 | 1.25630 | ||||||||
\(541\) | 43.3814 | 1.86511 | 0.932555 | − | 0.361027i | \(-0.117574\pi\) | ||||
0.932555 | + | 0.361027i | \(0.117574\pi\) | |||||||
\(542\) | 65.4610 | 2.81179 | ||||||||
\(543\) | −0.994887 | −0.0426947 | ||||||||
\(544\) | −6.91599 | −0.296521 | ||||||||
\(545\) | 1.80408 | 0.0772784 | ||||||||
\(546\) | −5.15089 | −0.220438 | ||||||||
\(547\) | 9.07706 | 0.388107 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(548\) | −40.4209 | −1.72669 | ||||||||
\(549\) | 3.22636 | 0.137698 | ||||||||
\(550\) | 12.5866 | 0.536696 | ||||||||
\(551\) | 19.8638 | 0.846225 | ||||||||
\(552\) | 19.8336 | 0.844175 | ||||||||
\(553\) | 5.15025 | 0.219011 | ||||||||
\(554\) | −49.3041 | −2.09473 | ||||||||
\(555\) | −1.38635 | −0.0588473 | ||||||||
\(556\) | −61.2681 | −2.59834 | ||||||||
\(557\) | 13.2666 | 0.562122 | 0.281061 | − | 0.959690i | \(-0.409314\pi\) | ||||
0.281061 | + | 0.959690i | \(0.409314\pi\) | |||||||
\(558\) | −31.5524 | −1.33572 | ||||||||
\(559\) | −13.1560 | −0.556441 | ||||||||
\(560\) | 9.08726 | 0.384007 | ||||||||
\(561\) | −15.5871 | −0.658087 | ||||||||
\(562\) | 64.9416 | 2.73940 | ||||||||
\(563\) | 16.3421 | 0.688738 | 0.344369 | − | 0.938834i | \(-0.388093\pi\) | ||||
0.344369 | + | 0.938834i | \(0.388093\pi\) | |||||||
\(564\) | 29.7524 | 1.25280 | ||||||||
\(565\) | −11.8735 | −0.499523 | ||||||||
\(566\) | 32.2827 | 1.35694 | ||||||||
\(567\) | −6.03256 | −0.253344 | ||||||||
\(568\) | −14.3092 | −0.600399 | ||||||||
\(569\) | −19.1386 | −0.802332 | −0.401166 | − | 0.916005i | \(-0.631395\pi\) | ||||
−0.401166 | + | 0.916005i | \(0.631395\pi\) | |||||||
\(570\) | −19.2300 | −0.805456 | ||||||||
\(571\) | −29.1169 | −1.21850 | −0.609251 | − | 0.792977i | \(-0.708530\pi\) | ||||
−0.609251 | + | 0.792977i | \(0.708530\pi\) | |||||||
\(572\) | −21.3544 | −0.892873 | ||||||||
\(573\) | −8.06705 | −0.337006 | ||||||||
\(574\) | 11.5363 | 0.481516 | ||||||||
\(575\) | 9.80357 | 0.408837 | ||||||||
\(576\) | 22.1567 | 0.923195 | ||||||||
\(577\) | 16.9472 | 0.705521 | 0.352760 | − | 0.935714i | \(-0.385243\pi\) | ||||
0.352760 | + | 0.935714i | \(0.385243\pi\) | |||||||
\(578\) | −71.8922 | −2.99032 | ||||||||
\(579\) | −13.2278 | −0.549727 | ||||||||
\(580\) | 24.4138 | 1.01373 | ||||||||
\(581\) | −15.7127 | −0.651874 | ||||||||
\(582\) | −13.4412 | −0.557155 | ||||||||
\(583\) | −6.04115 | −0.250199 | ||||||||
\(584\) | −26.9867 | −1.11672 | ||||||||
\(585\) | −8.02643 | −0.331852 | ||||||||
\(586\) | −22.2155 | −0.917714 | ||||||||
\(587\) | 7.67418 | 0.316747 | 0.158374 | − | 0.987379i | \(-0.449375\pi\) | ||||
0.158374 | + | 0.987379i | \(0.449375\pi\) | |||||||
\(588\) | −14.2504 | −0.587678 | ||||||||
\(589\) | 30.8242 | 1.27009 | ||||||||
\(590\) | −2.41815 | −0.0995535 | ||||||||
\(591\) | −19.9475 | −0.820530 | ||||||||
\(592\) | 3.36833 | 0.138438 | ||||||||
\(593\) | −35.0815 | −1.44063 | −0.720313 | − | 0.693649i | \(-0.756002\pi\) | ||||
−0.720313 | + | 0.693649i | \(0.756002\pi\) | |||||||
\(594\) | 29.9789 | 1.23005 | ||||||||
\(595\) | −18.4197 | −0.755135 | ||||||||
\(596\) | −52.0905 | −2.13371 | ||||||||
\(597\) | −8.65552 | −0.354247 | ||||||||
\(598\) | −25.1780 | −1.02960 | ||||||||
\(599\) | 22.3188 | 0.911922 | 0.455961 | − | 0.890000i | \(-0.349296\pi\) | ||||
0.455961 | + | 0.890000i | \(0.349296\pi\) | |||||||
\(600\) | 6.16242 | 0.251580 | ||||||||
\(601\) | −32.0374 | −1.30683 | −0.653417 | − | 0.756998i | \(-0.726665\pi\) | ||||
−0.653417 | + | 0.756998i | \(0.726665\pi\) | |||||||
\(602\) | 25.8645 | 1.05416 | ||||||||
\(603\) | 32.6462 | 1.32945 | ||||||||
\(604\) | −20.2918 | −0.825660 | ||||||||
\(605\) | 3.92208 | 0.159455 | ||||||||
\(606\) | −15.7481 | −0.639724 | ||||||||
\(607\) | −25.8635 | −1.04977 | −0.524884 | − | 0.851174i | \(-0.675891\pi\) | ||||
−0.524884 | + | 0.851174i | \(0.675891\pi\) | |||||||
\(608\) | −5.78807 | −0.234737 | ||||||||
\(609\) | 3.99480 | 0.161877 | ||||||||
\(610\) | −5.86418 | −0.237434 | ||||||||
\(611\) | −18.3648 | −0.742958 | ||||||||
\(612\) | 64.0401 | 2.58867 | ||||||||
\(613\) | 22.5697 | 0.911580 | 0.455790 | − | 0.890087i | \(-0.349357\pi\) | ||||
0.455790 | + | 0.890087i | \(0.349357\pi\) | |||||||
\(614\) | 63.8909 | 2.57843 | ||||||||
\(615\) | −4.40572 | −0.177656 | ||||||||
\(616\) | 20.4132 | 0.822470 | ||||||||
\(617\) | 5.70917 | 0.229842 | 0.114921 | − | 0.993375i | \(-0.463338\pi\) | ||||
0.114921 | + | 0.993375i | \(0.463338\pi\) | |||||||
\(618\) | 17.2060 | 0.692125 | ||||||||
\(619\) | −14.4862 | −0.582248 | −0.291124 | − | 0.956685i | \(-0.594029\pi\) | ||||
−0.291124 | + | 0.956685i | \(0.594029\pi\) | |||||||
\(620\) | 37.8850 | 1.52150 | ||||||||
\(621\) | 23.3502 | 0.937010 | ||||||||
\(622\) | −75.2643 | −3.01782 | ||||||||
\(623\) | 10.8034 | 0.432829 | ||||||||
\(624\) | −4.77942 | −0.191330 | ||||||||
\(625\) | −13.2275 | −0.529101 | ||||||||
\(626\) | 3.40968 | 0.136278 | ||||||||
\(627\) | −13.0450 | −0.520967 | ||||||||
\(628\) | 84.1970 | 3.35982 | ||||||||
\(629\) | −6.82756 | −0.272233 | ||||||||
\(630\) | 15.7798 | 0.628683 | ||||||||
\(631\) | −11.3676 | −0.452536 | −0.226268 | − | 0.974065i | \(-0.572653\pi\) | ||||
−0.226268 | + | 0.974065i | \(0.572653\pi\) | |||||||
\(632\) | 15.8247 | 0.629472 | ||||||||
\(633\) | 10.4487 | 0.415298 | ||||||||
\(634\) | −71.2343 | −2.82908 | ||||||||
\(635\) | −4.74151 | −0.188161 | ||||||||
\(636\) | −6.08300 | −0.241207 | ||||||||
\(637\) | 8.79611 | 0.348515 | ||||||||
\(638\) | 25.0703 | 0.992543 | ||||||||
\(639\) | −7.50361 | −0.296838 | ||||||||
\(640\) | −36.6167 | −1.44740 | ||||||||
\(641\) | 43.9382 | 1.73546 | 0.867728 | − | 0.497040i | \(-0.165580\pi\) | ||||
0.867728 | + | 0.497040i | \(0.165580\pi\) | |||||||
\(642\) | −29.4370 | −1.16179 | ||||||||
\(643\) | 35.6279 | 1.40503 | 0.702513 | − | 0.711671i | \(-0.252061\pi\) | ||||
0.702513 | + | 0.711671i | \(0.252061\pi\) | |||||||
\(644\) | 32.6995 | 1.28854 | ||||||||
\(645\) | −9.87769 | −0.388934 | ||||||||
\(646\) | −94.7047 | −3.72611 | ||||||||
\(647\) | −28.8264 | −1.13328 | −0.566641 | − | 0.823965i | \(-0.691757\pi\) | ||||
−0.566641 | + | 0.823965i | \(0.691757\pi\) | |||||||
\(648\) | −18.5356 | −0.728149 | ||||||||
\(649\) | −1.64039 | −0.0643909 | ||||||||
\(650\) | −7.82295 | −0.306841 | ||||||||
\(651\) | 6.19906 | 0.242960 | ||||||||
\(652\) | 17.9622 | 0.703455 | ||||||||
\(653\) | −39.1269 | −1.53115 | −0.765576 | − | 0.643345i | \(-0.777546\pi\) | ||||
−0.765576 | + | 0.643345i | \(0.777546\pi\) | |||||||
\(654\) | 1.86543 | 0.0729439 | ||||||||
\(655\) | 30.0676 | 1.17484 | ||||||||
\(656\) | 10.7043 | 0.417934 | ||||||||
\(657\) | −14.1516 | −0.552108 | ||||||||
\(658\) | 36.1048 | 1.40751 | ||||||||
\(659\) | 46.7538 | 1.82127 | 0.910635 | − | 0.413212i | \(-0.135593\pi\) | ||||
0.910635 | + | 0.413212i | \(0.135593\pi\) | |||||||
\(660\) | −16.0331 | −0.624088 | ||||||||
\(661\) | −21.2214 | −0.825417 | −0.412709 | − | 0.910863i | \(-0.635417\pi\) | ||||
−0.412709 | + | 0.910863i | \(0.635417\pi\) | |||||||
\(662\) | 19.2309 | 0.747432 | ||||||||
\(663\) | 9.68780 | 0.376243 | ||||||||
\(664\) | −48.2790 | −1.87359 | ||||||||
\(665\) | −15.4157 | −0.597794 | ||||||||
\(666\) | 5.84904 | 0.226646 | ||||||||
\(667\) | 19.5269 | 0.756086 | ||||||||
\(668\) | 30.8362 | 1.19309 | ||||||||
\(669\) | −3.57109 | −0.138066 | ||||||||
\(670\) | −59.3371 | −2.29239 | ||||||||
\(671\) | −3.97806 | −0.153571 | ||||||||
\(672\) | −1.16404 | −0.0449037 | ||||||||
\(673\) | −42.5169 | −1.63891 | −0.819453 | − | 0.573146i | \(-0.805723\pi\) | ||||
−0.819453 | + | 0.573146i | \(0.805723\pi\) | |||||||
\(674\) | 73.2393 | 2.82107 | ||||||||
\(675\) | 7.25503 | 0.279246 | ||||||||
\(676\) | −37.3341 | −1.43593 | ||||||||
\(677\) | 25.9938 | 0.999023 | 0.499512 | − | 0.866307i | \(-0.333513\pi\) | ||||
0.499512 | + | 0.866307i | \(0.333513\pi\) | |||||||
\(678\) | −12.2773 | −0.471506 | ||||||||
\(679\) | −10.7751 | −0.413510 | ||||||||
\(680\) | −56.5965 | −2.17038 | ||||||||
\(681\) | −1.02997 | −0.0394684 | ||||||||
\(682\) | 38.9037 | 1.48970 | ||||||||
\(683\) | 8.52276 | 0.326114 | 0.163057 | − | 0.986617i | \(-0.447865\pi\) | ||||
0.163057 | + | 0.986617i | \(0.447865\pi\) | |||||||
\(684\) | 53.5959 | 2.04929 | ||||||||
\(685\) | 18.7326 | 0.715738 | ||||||||
\(686\) | −42.7039 | −1.63044 | ||||||||
\(687\) | 12.6972 | 0.484428 | ||||||||
\(688\) | 23.9992 | 0.914963 | ||||||||
\(689\) | 3.75475 | 0.143044 | ||||||||
\(690\) | −18.9039 | −0.719660 | ||||||||
\(691\) | −11.4557 | −0.435796 | −0.217898 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217898 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(692\) | 10.9376 | 0.415787 | ||||||||
\(693\) | 10.7045 | 0.406631 | ||||||||
\(694\) | −26.8006 | −1.01734 | ||||||||
\(695\) | 28.3941 | 1.07705 | ||||||||
\(696\) | 12.2744 | 0.465261 | ||||||||
\(697\) | −21.6975 | −0.821851 | ||||||||
\(698\) | 18.6022 | 0.704105 | ||||||||
\(699\) | 20.1008 | 0.760283 | ||||||||
\(700\) | 10.1599 | 0.384010 | ||||||||
\(701\) | 31.6903 | 1.19693 | 0.598464 | − | 0.801150i | \(-0.295778\pi\) | ||||
0.598464 | + | 0.801150i | \(0.295778\pi\) | |||||||
\(702\) | −18.6327 | −0.703247 | ||||||||
\(703\) | −5.71406 | −0.215510 | ||||||||
\(704\) | −27.3189 | −1.02962 | ||||||||
\(705\) | −13.7885 | −0.519303 | ||||||||
\(706\) | −75.1898 | −2.82981 | ||||||||
\(707\) | −12.6244 | −0.474791 | ||||||||
\(708\) | −1.65175 | −0.0620767 | ||||||||
\(709\) | −9.43588 | −0.354372 | −0.177186 | − | 0.984177i | \(-0.556699\pi\) | ||||
−0.177186 | + | 0.984177i | \(0.556699\pi\) | |||||||
\(710\) | 13.6384 | 0.511841 | ||||||||
\(711\) | 8.29833 | 0.311212 | ||||||||
\(712\) | 33.1946 | 1.24402 | ||||||||
\(713\) | 30.3015 | 1.13480 | ||||||||
\(714\) | −19.0461 | −0.712781 | ||||||||
\(715\) | 9.89648 | 0.370107 | ||||||||
\(716\) | 91.1478 | 3.40635 | ||||||||
\(717\) | −2.79700 | −0.104456 | ||||||||
\(718\) | 39.7565 | 1.48370 | ||||||||
\(719\) | 32.5271 | 1.21305 | 0.606527 | − | 0.795063i | \(-0.292562\pi\) | ||||
0.606527 | + | 0.795063i | \(0.292562\pi\) | |||||||
\(720\) | 14.6418 | 0.545668 | ||||||||
\(721\) | 13.7931 | 0.513682 | ||||||||
\(722\) | −33.1367 | −1.23322 | ||||||||
\(723\) | 22.1877 | 0.825169 | ||||||||
\(724\) | −5.03988 | −0.187306 | ||||||||
\(725\) | 6.06713 | 0.225328 | ||||||||
\(726\) | 4.05545 | 0.150512 | ||||||||
\(727\) | 19.4193 | 0.720222 | 0.360111 | − | 0.932909i | \(-0.382739\pi\) | ||||
0.360111 | + | 0.932909i | \(0.382739\pi\) | |||||||
\(728\) | −12.6874 | −0.470225 | ||||||||
\(729\) | −0.136737 | −0.00506435 | ||||||||
\(730\) | 25.7217 | 0.952005 | ||||||||
\(731\) | −48.6461 | −1.79924 | ||||||||
\(732\) | −4.00562 | −0.148052 | ||||||||
\(733\) | 37.7826 | 1.39553 | 0.697765 | − | 0.716326i | \(-0.254178\pi\) | ||||
0.697765 | + | 0.716326i | \(0.254178\pi\) | |||||||
\(734\) | −16.3945 | −0.605133 | ||||||||
\(735\) | 6.60422 | 0.243600 | ||||||||
\(736\) | −5.68992 | −0.209733 | ||||||||
\(737\) | −40.2523 | −1.48271 | ||||||||
\(738\) | 18.5878 | 0.684227 | ||||||||
\(739\) | 23.5061 | 0.864686 | 0.432343 | − | 0.901709i | \(-0.357687\pi\) | ||||
0.432343 | + | 0.901709i | \(0.357687\pi\) | |||||||
\(740\) | −7.02294 | −0.258169 | ||||||||
\(741\) | 8.10783 | 0.297849 | ||||||||
\(742\) | −7.38176 | −0.270993 | ||||||||
\(743\) | −22.1057 | −0.810979 | −0.405489 | − | 0.914100i | \(-0.632899\pi\) | ||||
−0.405489 | + | 0.914100i | \(0.632899\pi\) | |||||||
\(744\) | 19.0472 | 0.698306 | ||||||||
\(745\) | 24.1408 | 0.884451 | ||||||||
\(746\) | −19.2760 | −0.705746 | ||||||||
\(747\) | −25.3171 | −0.926304 | ||||||||
\(748\) | −78.9606 | −2.88709 | ||||||||
\(749\) | −23.5981 | −0.862255 | ||||||||
\(750\) | −22.7005 | −0.828904 | ||||||||
\(751\) | 16.1621 | 0.589764 | 0.294882 | − | 0.955534i | \(-0.404720\pi\) | ||||
0.294882 | + | 0.955534i | \(0.404720\pi\) | |||||||
\(752\) | 33.5010 | 1.22166 | ||||||||
\(753\) | −7.44595 | −0.271346 | ||||||||
\(754\) | −15.5819 | −0.567460 | ||||||||
\(755\) | 9.40401 | 0.342247 | ||||||||
\(756\) | 24.1990 | 0.880108 | ||||||||
\(757\) | −9.69500 | −0.352371 | −0.176185 | − | 0.984357i | \(-0.556376\pi\) | ||||
−0.176185 | + | 0.984357i | \(0.556376\pi\) | |||||||
\(758\) | 19.2496 | 0.699177 | ||||||||
\(759\) | −12.8238 | −0.465474 | ||||||||
\(760\) | −47.3662 | −1.71815 | ||||||||
\(761\) | −42.1444 | −1.52773 | −0.763867 | − | 0.645374i | \(-0.776702\pi\) | ||||
−0.763867 | + | 0.645374i | \(0.776702\pi\) | |||||||
\(762\) | −4.90273 | −0.177607 | ||||||||
\(763\) | 1.49541 | 0.0541376 | ||||||||
\(764\) | −40.8659 | −1.47848 | ||||||||
\(765\) | −29.6787 | −1.07304 | ||||||||
\(766\) | −11.2122 | −0.405112 | ||||||||
\(767\) | 1.01955 | 0.0368138 | ||||||||
\(768\) | −23.7289 | −0.856245 | ||||||||
\(769\) | −41.3788 | −1.49216 | −0.746080 | − | 0.665857i | \(-0.768066\pi\) | ||||
−0.746080 | + | 0.665857i | \(0.768066\pi\) | |||||||
\(770\) | −19.4563 | −0.701157 | ||||||||
\(771\) | −11.3758 | −0.409688 | ||||||||
\(772\) | −67.0089 | −2.41170 | ||||||||
\(773\) | 3.21809 | 0.115747 | 0.0578733 | − | 0.998324i | \(-0.481568\pi\) | ||||
0.0578733 | + | 0.998324i | \(0.481568\pi\) | |||||||
\(774\) | 41.6742 | 1.49795 | ||||||||
\(775\) | 9.41487 | 0.338192 | ||||||||
\(776\) | −33.1075 | −1.18849 | ||||||||
\(777\) | −1.14915 | −0.0412257 | ||||||||
\(778\) | 35.7898 | 1.28313 | ||||||||
\(779\) | −18.1589 | −0.650609 | ||||||||
\(780\) | 9.96504 | 0.356806 | ||||||||
\(781\) | 9.25185 | 0.331057 | ||||||||
\(782\) | −93.0988 | −3.32921 | ||||||||
\(783\) | 14.4507 | 0.516426 | ||||||||
\(784\) | −16.0459 | −0.573067 | ||||||||
\(785\) | −39.0202 | −1.39269 | ||||||||
\(786\) | 31.0899 | 1.10894 | ||||||||
\(787\) | 17.2217 | 0.613886 | 0.306943 | − | 0.951728i | \(-0.400694\pi\) | ||||
0.306943 | + | 0.951728i | \(0.400694\pi\) | |||||||
\(788\) | −101.049 | −3.59974 | ||||||||
\(789\) | −4.99651 | −0.177881 | ||||||||
\(790\) | −15.0829 | −0.536625 | ||||||||
\(791\) | −9.84203 | −0.349942 | ||||||||
\(792\) | 32.8907 | 1.16872 | ||||||||
\(793\) | 2.47248 | 0.0878003 | ||||||||
\(794\) | 25.7032 | 0.912173 | ||||||||
\(795\) | 2.81910 | 0.0999833 | ||||||||
\(796\) | −43.8469 | −1.55411 | ||||||||
\(797\) | 11.8976 | 0.421435 | 0.210718 | − | 0.977547i | \(-0.432420\pi\) | ||||
0.210718 | + | 0.977547i | \(0.432420\pi\) | |||||||
\(798\) | −15.9399 | −0.564265 | ||||||||
\(799\) | −67.9060 | −2.40234 | ||||||||
\(800\) | −1.76789 | −0.0625044 | ||||||||
\(801\) | 17.4070 | 0.615045 | ||||||||
\(802\) | −78.2358 | −2.76260 | ||||||||
\(803\) | 17.4488 | 0.615754 | ||||||||
\(804\) | −40.5311 | −1.42942 | ||||||||
\(805\) | −15.1543 | −0.534118 | ||||||||
\(806\) | −24.1797 | −0.851694 | ||||||||
\(807\) | 2.39802 | 0.0844142 | ||||||||
\(808\) | −38.7899 | −1.36462 | ||||||||
\(809\) | −47.0706 | −1.65491 | −0.827457 | − | 0.561530i | \(-0.810213\pi\) | ||||
−0.827457 | + | 0.561530i | \(0.810213\pi\) | |||||||
\(810\) | 17.6668 | 0.620748 | ||||||||
\(811\) | 0.533781 | 0.0187436 | 0.00937179 | − | 0.999956i | \(-0.497017\pi\) | ||||
0.00937179 | + | 0.999956i | \(0.497017\pi\) | |||||||
\(812\) | 20.2368 | 0.710171 | ||||||||
\(813\) | −20.7223 | −0.726764 | ||||||||
\(814\) | −7.21179 | −0.252773 | ||||||||
\(815\) | −8.32441 | −0.291591 | ||||||||
\(816\) | −17.6725 | −0.618661 | ||||||||
\(817\) | −40.7124 | −1.42435 | ||||||||
\(818\) | 1.74662 | 0.0610690 | ||||||||
\(819\) | −6.65315 | −0.232480 | ||||||||
\(820\) | −22.3184 | −0.779393 | ||||||||
\(821\) | 22.7810 | 0.795062 | 0.397531 | − | 0.917589i | \(-0.369867\pi\) | ||||
0.397531 | + | 0.917589i | \(0.369867\pi\) | |||||||
\(822\) | 19.3696 | 0.675593 | ||||||||
\(823\) | 15.3633 | 0.535532 | 0.267766 | − | 0.963484i | \(-0.413715\pi\) | ||||
0.267766 | + | 0.963484i | \(0.413715\pi\) | |||||||
\(824\) | 42.3807 | 1.47640 | ||||||||
\(825\) | −3.98443 | −0.138720 | ||||||||
\(826\) | −2.00441 | −0.0697425 | ||||||||
\(827\) | −47.0424 | −1.63582 | −0.817912 | − | 0.575343i | \(-0.804869\pi\) | ||||
−0.817912 | + | 0.575343i | \(0.804869\pi\) | |||||||
\(828\) | 52.6870 | 1.83100 | ||||||||
\(829\) | −2.02486 | −0.0703262 | −0.0351631 | − | 0.999382i | \(-0.511195\pi\) | ||||
−0.0351631 | + | 0.999382i | \(0.511195\pi\) | |||||||
\(830\) | 46.0159 | 1.59724 | ||||||||
\(831\) | 15.6077 | 0.541425 | ||||||||
\(832\) | 16.9795 | 0.588657 | ||||||||
\(833\) | 32.5247 | 1.12691 | ||||||||
\(834\) | 29.3595 | 1.01664 | ||||||||
\(835\) | −14.2907 | −0.494551 | ||||||||
\(836\) | −66.0830 | −2.28553 | ||||||||
\(837\) | 22.4244 | 0.775099 | ||||||||
\(838\) | 58.3853 | 2.01689 | ||||||||
\(839\) | −27.3951 | −0.945784 | −0.472892 | − | 0.881120i | \(-0.656790\pi\) | ||||
−0.472892 | + | 0.881120i | \(0.656790\pi\) | |||||||
\(840\) | −9.52582 | −0.328672 | ||||||||
\(841\) | −16.9154 | −0.583288 | ||||||||
\(842\) | 4.48852 | 0.154685 | ||||||||
\(843\) | −20.5579 | −0.708052 | ||||||||
\(844\) | 52.9306 | 1.82195 | ||||||||
\(845\) | 17.3021 | 0.595211 | ||||||||
\(846\) | 58.1737 | 2.00005 | ||||||||
\(847\) | 3.25104 | 0.111707 | ||||||||
\(848\) | −6.84941 | −0.235210 | ||||||||
\(849\) | −10.2194 | −0.350729 | ||||||||
\(850\) | −28.9264 | −0.992166 | ||||||||
\(851\) | −5.61717 | −0.192554 | ||||||||
\(852\) | 9.31594 | 0.319159 | ||||||||
\(853\) | −18.8910 | −0.646815 | −0.323407 | − | 0.946260i | \(-0.604828\pi\) | ||||
−0.323407 | + | 0.946260i | \(0.604828\pi\) | |||||||
\(854\) | −4.86085 | −0.166335 | ||||||||
\(855\) | −24.8385 | −0.849458 | ||||||||
\(856\) | −72.5075 | −2.47826 | ||||||||
\(857\) | −18.3001 | −0.625119 | −0.312559 | − | 0.949898i | \(-0.601186\pi\) | ||||
−0.312559 | + | 0.949898i | \(0.601186\pi\) | |||||||
\(858\) | 10.2330 | 0.349349 | ||||||||
\(859\) | 13.9083 | 0.474546 | 0.237273 | − | 0.971443i | \(-0.423746\pi\) | ||||
0.237273 | + | 0.971443i | \(0.423746\pi\) | |||||||
\(860\) | −50.0382 | −1.70629 | ||||||||
\(861\) | −3.65193 | −0.124457 | ||||||||
\(862\) | 11.0679 | 0.376975 | ||||||||
\(863\) | −43.9533 | −1.49619 | −0.748093 | − | 0.663594i | \(-0.769030\pi\) | ||||
−0.748093 | + | 0.663594i | \(0.769030\pi\) | |||||||
\(864\) | −4.21077 | −0.143253 | ||||||||
\(865\) | −5.06894 | −0.172349 | ||||||||
\(866\) | 5.16933 | 0.175661 | ||||||||
\(867\) | 22.7582 | 0.772908 | ||||||||
\(868\) | 31.4030 | 1.06589 | ||||||||
\(869\) | −10.2317 | −0.347088 | ||||||||
\(870\) | −11.6991 | −0.396636 | ||||||||
\(871\) | 25.0179 | 0.847700 | ||||||||
\(872\) | 4.59481 | 0.155600 | ||||||||
\(873\) | −17.3613 | −0.587592 | ||||||||
\(874\) | −77.9154 | −2.63553 | ||||||||
\(875\) | −18.1978 | −0.615197 | ||||||||
\(876\) | 17.5696 | 0.593623 | ||||||||
\(877\) | −27.7996 | −0.938727 | −0.469363 | − | 0.883005i | \(-0.655517\pi\) | ||||
−0.469363 | + | 0.883005i | \(0.655517\pi\) | |||||||
\(878\) | 14.9861 | 0.505756 | ||||||||
\(879\) | 7.03254 | 0.237202 | ||||||||
\(880\) | −18.0532 | −0.608572 | ||||||||
\(881\) | 12.5856 | 0.424020 | 0.212010 | − | 0.977268i | \(-0.431999\pi\) | ||||
0.212010 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(882\) | −27.8633 | −0.938206 | ||||||||
\(883\) | −1.66946 | −0.0561820 | −0.0280910 | − | 0.999605i | \(-0.508943\pi\) | ||||
−0.0280910 | + | 0.999605i | \(0.508943\pi\) | |||||||
\(884\) | 49.0762 | 1.65061 | ||||||||
\(885\) | 0.765488 | 0.0257316 | ||||||||
\(886\) | 88.9449 | 2.98816 | ||||||||
\(887\) | 35.6071 | 1.19557 | 0.597785 | − | 0.801656i | \(-0.296048\pi\) | ||||
0.597785 | + | 0.801656i | \(0.296048\pi\) | |||||||
\(888\) | −3.53089 | −0.118489 | ||||||||
\(889\) | −3.93026 | −0.131817 | ||||||||
\(890\) | −31.6386 | −1.06053 | ||||||||
\(891\) | 11.9846 | 0.401498 | ||||||||
\(892\) | −18.0903 | −0.605709 | ||||||||
\(893\) | −56.8313 | −1.90179 | ||||||||
\(894\) | 24.9617 | 0.834843 | ||||||||
\(895\) | −42.2415 | −1.41198 | ||||||||
\(896\) | −30.3518 | −1.01398 | ||||||||
\(897\) | 7.97034 | 0.266122 | ||||||||
\(898\) | 32.2234 | 1.07531 | ||||||||
\(899\) | 18.7527 | 0.625438 | ||||||||
\(900\) | 16.3702 | 0.545672 | ||||||||
\(901\) | 13.8836 | 0.462531 | ||||||||
\(902\) | −22.9185 | −0.763104 | ||||||||
\(903\) | −8.18767 | −0.272469 | ||||||||
\(904\) | −30.2406 | −1.00579 | ||||||||
\(905\) | 2.33568 | 0.0776406 | ||||||||
\(906\) | 9.72378 | 0.323051 | ||||||||
\(907\) | 18.0801 | 0.600339 | 0.300169 | − | 0.953886i | \(-0.402957\pi\) | ||||
0.300169 | + | 0.953886i | \(0.402957\pi\) | |||||||
\(908\) | −5.21758 | −0.173151 | ||||||||
\(909\) | −20.3411 | −0.674672 | ||||||||
\(910\) | 12.0926 | 0.400867 | ||||||||
\(911\) | −10.4180 | −0.345164 | −0.172582 | − | 0.984995i | \(-0.555211\pi\) | ||||
−0.172582 | + | 0.984995i | \(0.555211\pi\) | |||||||
\(912\) | −14.7903 | −0.489756 | ||||||||
\(913\) | 31.2156 | 1.03309 | ||||||||
\(914\) | −24.1187 | −0.797776 | ||||||||
\(915\) | 1.85636 | 0.0613695 | ||||||||
\(916\) | 64.3211 | 2.12523 | ||||||||
\(917\) | 24.9232 | 0.823035 | ||||||||
\(918\) | −68.8968 | −2.27393 | ||||||||
\(919\) | −47.8241 | −1.57757 | −0.788786 | − | 0.614667i | \(-0.789290\pi\) | ||||
−0.788786 | + | 0.614667i | \(0.789290\pi\) | |||||||
\(920\) | −46.5630 | −1.53514 | ||||||||
\(921\) | −20.2253 | −0.666447 | ||||||||
\(922\) | −43.9336 | −1.44688 | ||||||||
\(923\) | −5.75028 | −0.189273 | ||||||||
\(924\) | −13.2899 | −0.437207 | ||||||||
\(925\) | −1.74529 | −0.0573847 | ||||||||
\(926\) | −37.6678 | −1.23784 | ||||||||
\(927\) | 22.2241 | 0.729935 | ||||||||
\(928\) | −3.52132 | −0.115593 | ||||||||
\(929\) | 27.2410 | 0.893748 | 0.446874 | − | 0.894597i | \(-0.352537\pi\) | ||||
0.446874 | + | 0.894597i | \(0.352537\pi\) | |||||||
\(930\) | −18.1544 | −0.595306 | ||||||||
\(931\) | 27.2203 | 0.892109 | ||||||||
\(932\) | 101.826 | 3.33543 | ||||||||
\(933\) | 23.8256 | 0.780017 | ||||||||
\(934\) | −70.1227 | −2.29449 | ||||||||
\(935\) | 36.5935 | 1.19674 | ||||||||
\(936\) | −20.4425 | −0.668184 | ||||||||
\(937\) | 21.6530 | 0.707371 | 0.353686 | − | 0.935364i | \(-0.384928\pi\) | ||||
0.353686 | + | 0.935364i | \(0.384928\pi\) | |||||||
\(938\) | −49.1848 | −1.60594 | ||||||||
\(939\) | −1.07937 | −0.0352238 | ||||||||
\(940\) | −69.8492 | −2.27823 | ||||||||
\(941\) | −20.5011 | −0.668318 | −0.334159 | − | 0.942517i | \(-0.608452\pi\) | ||||
−0.334159 | + | 0.942517i | \(0.608452\pi\) | |||||||
\(942\) | −40.3470 | −1.31458 | ||||||||
\(943\) | −17.8509 | −0.581307 | ||||||||
\(944\) | −1.85986 | −0.0605333 | ||||||||
\(945\) | −11.2148 | −0.364816 | ||||||||
\(946\) | −51.3837 | −1.67063 | ||||||||
\(947\) | −0.779229 | −0.0253215 | −0.0126608 | − | 0.999920i | \(-0.504030\pi\) | ||||
−0.0126608 | + | 0.999920i | \(0.504030\pi\) | |||||||
\(948\) | −10.3026 | −0.334613 | ||||||||
\(949\) | −10.8449 | −0.352040 | ||||||||
\(950\) | −24.2088 | −0.785437 | ||||||||
\(951\) | 22.5499 | 0.731232 | ||||||||
\(952\) | −46.9131 | −1.52046 | ||||||||
\(953\) | 19.7057 | 0.638329 | 0.319164 | − | 0.947699i | \(-0.396598\pi\) | ||||
0.319164 | + | 0.947699i | \(0.396598\pi\) | |||||||
\(954\) | −11.8938 | −0.385078 | ||||||||
\(955\) | 18.9389 | 0.612848 | ||||||||
\(956\) | −14.1690 | −0.458257 | ||||||||
\(957\) | −7.93625 | −0.256543 | ||||||||
\(958\) | 38.1744 | 1.23336 | ||||||||
\(959\) | 15.5276 | 0.501412 | ||||||||
\(960\) | 12.7484 | 0.411452 | ||||||||
\(961\) | −1.89986 | −0.0612860 | ||||||||
\(962\) | 4.48233 | 0.144516 | ||||||||
\(963\) | −38.0224 | −1.22525 | ||||||||
\(964\) | 112.398 | 3.62009 | ||||||||
\(965\) | 31.0546 | 0.999683 | ||||||||
\(966\) | −15.6696 | −0.504160 | ||||||||
\(967\) | −10.7340 | −0.345181 | −0.172590 | − | 0.984994i | \(-0.555214\pi\) | ||||
−0.172590 | + | 0.984994i | \(0.555214\pi\) | |||||||
\(968\) | 9.98914 | 0.321063 | ||||||||
\(969\) | 29.9797 | 0.963087 | ||||||||
\(970\) | 31.5556 | 1.01319 | ||||||||
\(971\) | −41.1901 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(972\) | 60.6139 | 1.94419 | ||||||||
\(973\) | 23.5360 | 0.754529 | ||||||||
\(974\) | −23.6822 | −0.758825 | ||||||||
\(975\) | 2.47643 | 0.0793093 | ||||||||
\(976\) | −4.51030 | −0.144371 | ||||||||
\(977\) | −18.9453 | −0.606114 | −0.303057 | − | 0.952972i | \(-0.598007\pi\) | ||||
−0.303057 | + | 0.952972i | \(0.598007\pi\) | |||||||
\(978\) | −8.60747 | −0.275236 | ||||||||
\(979\) | −21.4625 | −0.685946 | ||||||||
\(980\) | 33.4555 | 1.06870 | ||||||||
\(981\) | 2.40948 | 0.0769288 | ||||||||
\(982\) | −65.0246 | −2.07502 | ||||||||
\(983\) | 42.5920 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(984\) | −11.2209 | −0.357710 | ||||||||
\(985\) | 46.8304 | 1.49214 | ||||||||
\(986\) | −57.6161 | −1.83487 | ||||||||
\(987\) | −11.4293 | −0.363799 | ||||||||
\(988\) | 41.0724 | 1.30669 | ||||||||
\(989\) | −40.0221 | −1.27263 | ||||||||
\(990\) | −31.3489 | −0.996335 | ||||||||
\(991\) | 23.2385 | 0.738196 | 0.369098 | − | 0.929391i | \(-0.379667\pi\) | ||||
0.369098 | + | 0.929391i | \(0.379667\pi\) | |||||||
\(992\) | −5.46432 | −0.173492 | ||||||||
\(993\) | −6.08774 | −0.193189 | ||||||||
\(994\) | 11.3050 | 0.358571 | ||||||||
\(995\) | 20.3204 | 0.644200 | ||||||||
\(996\) | 31.4319 | 0.995957 | ||||||||
\(997\) | 38.5164 | 1.21983 | 0.609914 | − | 0.792468i | \(-0.291204\pi\) | ||||
0.609914 | + | 0.792468i | \(0.291204\pi\) | |||||||
\(998\) | −54.9284 | −1.73873 | ||||||||
\(999\) | −4.15693 | −0.131519 |
(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 | 4033.2.a.f.1.6 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.6 | ✓ | 85 | 1.1 | even | 1 | trivial |